The "figuring" and polishing may be done by hand just like the grinding. There are machines, however, which can be made to execute the proper motions, and a polisher is set in such a machine, and the mechanical work done is by no means inconsiderable. In fact for surfaces above six inches in diameter few people are strong enough to work a polisher by hand owing to the intense adhesion between it and the exactly fitting glass surface.

Such is a general outline of the processes required to produce a lens or mirror. These processes will now be dealt with in much greater detail, and a certain amount of repetition of the above will unfortunately be necessary: the reader is asked to pardon this. It will also be advisable for the reader to begin by reading the whole account before he commences any particular operation. The reason for this is that it has been desirable to keep to the main account as far as possible without inserting special instructions for subsidiary operations, however important they may be; consequently it may not always be quite clear how the steps described are to be performed. It will be found, however, that all necessary information is really given, though perhaps not always exactly in the place the reader might at first expect.

Sec. 54. All the discs that I have seen, come from the makers already roughly ground on the edges to a circular figure—but occasionally the figure is very rough indeed—and in some cases, especially if small lenses have to be made, it is convenient to begin by cutting the glass discs out of glass sheet, which also may be purchased of suit-able glass. To do this, the simplest way is to begin by cutting squares and then cutting off the corners with the diamond, the approximate circular figure being obtained by grinding the edges on an ordinary grindstone.

If the pieces are larger, time and material may be saved by using a diamond compass, i.e. an ordinary drawing compass armed with a diamond to cut circles on the glass, and breaking the superfluous glass away by means of a pair of spectacle-maker's shanks (Fig. 44), or what does equally well, a pair of pliers with soft iron jaws. With these instruments glass can be chipped gradually up to any line, whether diamond-cut or not, the jaws of the pincers being worked against the edge of the glass, so as to gradually crush it away.

Fig. 44.

Assuming that the glass has been bought or made roughly circular, it must be finished on the lathe. For this purpose it is necessary to chuck it on an iron or hardwood chuck, as shown in Fig. 46. For a lens below say an inch in diameter, the centering cement may be used; but for a lens of a diameter greater than this, sufficient adhesion is easily obtained with Regnault's mastic, and its low melting point gives it a decided advantage over the shellac composition.

The glass may be heated gradually by placing it on the water bath, or actually in the water, and gradually bringing the water up to the boiling-point. The glass, being taken out, is rapidly wiped, and rubbed with a bit of waste moistened, not wet, with a little turpentine: its surface is then rubbed with a stick of mastic previously warmed so as to melt easily. The surface of the chuck being also warm, and covered with a layer of melted cement, it is applied to the glass. The lathe is turned slowly by hand, and the glass pushed gradually into the most central position; it is then pressed tight against the chuck by the back rest, a bit of wood being interposed for obvious reasons.

When all is cold the turning may be proceeded with. The quickest way is to use the method already described (i.e. actual turning by a file tool); but if the student prefers (time being no object), he may accomplish the reduction to a circular form very easily by grinding.

Fig. 45.

Fig. 46.

For this purpose he will require to make the following arrangements (Fig. 45). If the lathe has a slide rest, a piece of stout iron may be bent and cut so as to fit the tool rest, and project beneath the glass. The iron must be fairly rigid, for if it springs appreciably beneath the pressure of the glass, it will not grind the latter really round. The lathe may run rather faster than for turning cast iron of the same size. Coarse emery, passing through a sieve of 80 threads to the inch (run), may be fed in between the glass and iron, and the latter screwed up till the disc just grinds slightly as it goes round.

A beginner will generally (in this as in all cases of grinding processes) tend to feed too fast—no grinding process can be hurried. If a slide rest is not available, a hinged board, carrying a bit of iron, may (see Fig. 45) be arranged so as to turn about its hinge at the back of the lathe; and it may be screwed up readily enough by passing a long set-screw through the front edge, so that the point of the screw bears upon the lathe bed. I may add that emery behaves as if it were greasy, and it is difficult to wet it with clean water. This is easily got over by adding a little soap or alcohol to the water, or exercising a little patience.

A good supply of emery and water should be kept between the disc and the iron; a little putty may be arranged round the point of contact on the iron to form a temporary trough. In any case the resulting emery mud should on no account be thrown away, but should be carefully kept for further use. The process is complete when the glass is perfectly round and of the required diameter as tested by callipers.

Sec. 55. The next step is to rough out the lens, and this may easily be done by rotating it more slowly, i.e. with a surface speed of ten feet per minute, and turning the glass with a hard file, as explained in Sec. 42. If it is desired to employ the slide rest, it is quicker and better to use a diamond tool—an instrument quite readily made, and of great service for turning emery wheels and the like,—a thing, in fact, which no workshop should be without. A bit of diamond bort, or even a clear though off-colour stone, may be employed.

An ordinary lathe tool is prepared by drawing down the tool steel to a long cone, resembling the ordinary practice in preparing a boring tool. The apex of the cone must be cut off till it is only slightly larger than the greatest transverse diameter of the diamond splinter. The latter may have almost any shape—a triangular point, one side of a three-sided prism is very convenient. A hole is drilled in the steel (which must have been well softened), only just large enough to allow the diamond to enter—if the splinter is thicker in the middle than at either end, so much the better—the diamond is fastened in position by squeezing the soft steel walls tightly down upon it. Personally I prefer to use a tool holder, and in this case generally mount the diamond in a bit of brass rod of the proper diameter; and instead of pinching in the sides of the cavity, I tin them, and set the diamond in position with a drop of soft solder.

Fig. 47.

In purchasing diamond bort, a good plan is to buy fragments that have been employed in diamond drilling, and have become too small to reset; in this case some idea as to the hardness of the bits may be obtained. Full details as to diamond tool-making are given in books on watch-making, and in Holtzapffell's great work on Mechanical Manipulation; but the above notes are all that are really necessary—it is, in fact, a very simple matter. The only advantage of using a diamond tool for glass turning is that one does not need to be always taking it out of the rest to sharpen it, which generally happens with hard steel, especially if the work is turned a little too fast.

I recommend, therefore, that the student should boldly go to work "free hand" with a hard file; but if he prefer the more formal method, or distrust his skill (which he should not do), then let him use a diamond point, even if he has the trouble of making it. When using a diamond it is not necessary to employ a lubricant, but there is some advantage in doing so.

The surface of the lens can be roughly shaped by turning to a template or pattern made by cutting a circular arc (of the same radius as the required surface) out of a bit of sheet zinc. Another very handy way of making templates of great accuracy is to use a beam compass (constructed from a light wooden bar) with a glazier's diamond instead of a pencil. A bit of thin sheet glass is cut across with this compass to the proper curvature—which can be done with considerable accuracy and the two halves of the plate, after breaking along the cut, are ground together with a view to avoiding slight local irregularities, by means of a little fine emery and water laid between the edges. In this process the glass is conveniently supported on a clean board or slate, and the bits are rubbed backwards and forwards against each other.

Sec. 56. It is not very easy for a beginner to turn a bit of anything—iron, wood, or glass—with great accuracy to fit a template, and consequently time may be saved by the following procedure, applied as soon as the figure of the template is roughly obtained. A disc of lead or iron, of the same diameter as the glass, and of approximately the proper curvature, is prepared by turning, and is armed with a handle projecting coaxially from the back of the disc. The glass revolving with moderate speed on the lathe, the lead tool, supplied with coarse emery and water, is held against it, care being taken to rotate the tool by the handle, and also to move it backwards and forwards across the disc, through a distance, say, up to half an inch; if it is allowed to overhang too much the edges of the glass disc will be overground. By the use of such a tool the glass can readily be brought up to the template.

The only thing that remains, so far as the description of this part of the process goes, is to give a note or two as to the best way of making the lead tools, and for this purpose the main narrative of processes must be interrupted. The easiest way is to make a set of discs to begin with. For this purpose take the mandrel out of the lathe, and place it nose downwards in the centre of an iron ring of proper diameter on a flat and level iron plate.

The discs are made by pouring lead round the screw-nose of the mandrel. This method, of course, leaves them with a hole in the centre; but this can be stopped up by placing the hot disc (from which the mandrel has been unscrewed) on a hot plate, and pouring in a sufficiency of very hot lead; or, better still, the mandrel can be supported vertically at any desired distance above the plate while the casting is being poured. Lead discs prepared in this way are easily turned so as to form very convenient chucks for brass work, and for use in the case now being treated, they are easily turned to a template, using woodturners' tools, which work better if oiled, and must be set to cut, not scrape.

If the operator does not mind the trouble of cutting a screw, or if he has a jaw chuck, the lead may be replaced by iron with some advantage.

The following is a neat way of making concave tools. It is an application of the principle of having the cutting tool as long as the radius of curvature, and allowing it to move about the centre of curvature. Place the disc of iron or lead on the lathe mandrel or in the chuck, and set the slide rest so that it is free to slide up or down the lathe bed. Take a bar of tool steel and cut it a little longer than the radius of curvature required. Forge and finish one end of the bar into a pointed turning tool of the ordinary kind. Measure the radius of curvature from the point of the tool along the bar, and bore a hole, whose centre is at this point, through the bar from the upper to the lower face. I regard the upper face as the one whose horizontal plane contains the cutting point when the tool is in use. Clamp a temporary back centre to the lathe bed, and let it carry a pin in the vertical plane through the lathe centres, and let this pin exactly fit the hole in the bar.

Fig. 48.

Place the "radius" tool in position for cutting, and let it be lightly held in the slide rest nearly at the cutting point, the centre of rotation of the pedestal (or its equivalent) passing through the central line of the bar. Then adjust the temporary back rest, so that the tool will take a cut. In the sketch the tool is shown swinging about the back centre instead of about a pin—there is little to choose between the methods unless economy of tool steel is an object. The tool must now be fed across the work. The pedestal must of course be free to rotate, and the slide rest to slip up and down the bed. In this way a better concave grinding tool can be made than would be made by a beginner by turning to a template—though an expert turner would probably carry out the latter operation so as to obtain an' accuracy of the same order, and would certainly do it in much less time than would be required in setting up the special arrangements here described.

On the other hand, if several surfaces have to be prepared, as in the making of an achromatic lens, the quickest way would be by the use of the radius tool, bored of course to work at the several radii required. I have tried both methods, and my choice would depend partly on the lathe at my disposal, and partly on the number of grinding tools that had to be prepared.

Having obtained a concave tool of any given radius, it is easily copied—negatively, so as to make a convex tool in the following manner. Adjust the concave tool already made on the back rest, so that if it rotated about the line of centres, it would rotate about its axis of figure.

Arrangements for this can easily be made, but of course they will depend on the detailed structure of the lathe. Use the slide rest as before, i.e. let it grasp an ordinary turning tool lightly, the pedestal being fixed, but the rest free to slide up or down the lathe bed. Push the back rest up till the butt of the turning tool (ground to a rounded point) rests against the concave grinding tool. If the diameter of the convex tool required be very small compared with the radius of curvature of the surface (the most usual case), it is only necessary to feed the cutting tool across to "copy" the concave surface sufficiently nearly.

Fig. 49.

There seems no reason, however, why these methods should not be applied at once to the glass disc by means of a diamond point, and the rough grinding thus entirely avoided. I am informed that this has been done by Sir Henry Bessemer, but that the method was found to present no great advantage in practice. A reader with a taste for mechanical experimenting might try radius bar tools with small carborundum wheels rapidly driven instead of a diamond.

Enough has now been said to enable any one to prepare rough convex or concave grinding tools of iron or lead, and of the same diameter as the glass to be ground.

The general effect of the process of roughing the rotating lens surface is to alter the radius of curvature of both tool and glass; hence it is necessary to have for each grinding tool another to fit it, and enable it to be kept (by working the two together) at a constant figure. After a little practice it will be found possible to bring the glass exactly up to the required curvature as tested by template or spherometer. The art of the process consists in altering the shape of the grinding tool so as to take off the glass where required, as described in Sec. 53, and from this point of view lead has some advantages; (opinions vary as to the relative advantages of lead and iron tools for this purpose, however). The subsidiary grinding tool is not actually needed for this preliminary operation, but it has to be made some time with a view to further procedure, and occasionally is of service here.

Sec. 57. 'The glass disc must be ground approximately to the proper curvature on each side before any fine grinding is commenced. It is precisely for this purpose that the previous turning of the disc is recommended, for it is easy to unmount and recentre a round object, but not so easy if the object have an indefinite shape. Using a cement which is plastic before it sets, the disc may be easily taken off the chuck and centred by a little handicraft, i.e. by rotating the lathe slowly and pushing the disc into such a position that it rotates about its axis. The grinding of the second surface is accomplished exactly as in the former case; of course on reversing the glass the chuck has to be slightly turned up to fit the convex or concave surface.

Sec. 58. There is, however, one point of interest and importance—attention to which will save a good deal of useless labour afterwards. The glass must be ground in such a manner that the thickness at the edge is the same all round. In other words, the axes of figure of the two surfaces must coincide. This will be the case if the recentering has been accurately performed, and therefore no pains should be spared to see that it is exactly carried out. Any simple form of vernier gauge (such as Brown and Sharpe's vernier callipers) will serve to allow of a sufficiently accurate measurement of the edge thickness of the lens. If any difference of thickness is observed as the gauge moves round the edge, one or other of the surfaces must be reground. Of course the latitude of error which may be permitted depends so much on the final arrangements for a special finishing process called the "centering of the lens"—which will be described—that it is difficult to fix a limit, but perhaps one-thousandth of an inch may be mentioned as a suitable amount for a 2-inch disc. For rough work, of course; more margin may be admitted.

Sec. 59. In a large shop I imagine that lenses of only two inches diameter would be ground in nests; or, in other words, a number would be worked at a time, and centering, even of a rough kind, would be left to the last; but this process will be treated hereafter. At present I shall assume that only one lens will be made at a time. Consequently we now enter on the stage of fine grinding by hand. A leaden pedestal, for the sake of stability, must be provided on which to mount the lens, so that the surface to be operated on may be nearly horizontal (Fig. 50). Before this can be done, however, fresh grinding tools (two for each surface) must be properly prepared. After trying several plans I unhesitatingly recommend that all fine-grinding surfaces should be made of glass. This is easily done by taking two discs of lead, or iron, or slate, cut to a one-tenth inch smaller radius of curvature (in the case of a convex tool, and the opposite in the other case) than the lens surface (Fig. 51, A). On these, square bits of sheet glass, one-tenth of an inch thick, are to be cemented, so as to leave channels of about one-eighth of an inch between each bit of glass (Fig. 52, B). The "mastic" cement formerly described may be employed for this purpose.

Fig. 50.

The bits of glass ought first to have their edges dressed smooth on the grind-stone. A convex and concave glass surface having been thus roughly prepared, they must be mounted in turn in the lathe, and brought to the proper curvature by grinding with the tools formerly employed and tested by the template or spherometer. It is well to control this process by means of a spherometer, so that the desired radius may be approximately reached. The two glass-grinding tools are then ground together by hand (see Sec. 53 and Sec. 61), the spherometer being employed from time to time to check the progress of the work. In general, if large circular sweeps are taken, greatly overhanging the side of the glass surface to be figured, both the upper and lower surfaces will be more ground at the edges, while in the opposite event the centre will be chiefly affected.

Fig. 51.

A spherometer capable of measuring a 2-inch surface may be procured, having a screw of, say, 50 threads to the inch, and a micrometer surface divided into 200 parts, each part easily capable of subdivision—into tenths or even twentieths. To get the full advantage of the spherometer it must screw exceedingly freely (i.e. must be well oiled with clock oil), and must not be fingered except at the milled head. If one of the legs is held by the fingers the expansion is sufficient to throw the instrument quite out of adjustment. The glass-grinding tools being brought to the proper figure, the next process is to transfer the same to the lens, and this is done by similar means, the fellow tool being used to correct the one employed in grinding the lens surface. Before the grade of emery is changed all three surfaces must agree, as nearly, at least, as the spherometer will show.

In order to prevent confusion the following summary of the steps already taken may be given. The discs of glass are first ground or turned so as to be truly circular. Four "tools" are made for each surface—a rough pair of iron or lead, and a finishing pair of iron, lead, or slate faced by glass squares. For a small lens the iron or lead backing may be used, for a large one the slate. The rough tools are used to give an approximate figure both to the lens and to the finishing tools.

The final adjustment is attained by grinding one of the glass-faced tools alternately upon the lens and upon the fellow glass-faced tool. The spherometer is accepted at all stages of the process as the final arbiter as to curvature. Some hints on the form of strokes used in grinding will be given later on (see Sec. 61). It suffices to state here that the object throughout is to secure uniformity by allowing both the work and the tool to rotate, and exercising no pressure by the fingers. The tool backing may weigh from one to two pounds for a 2-inch lens.

Sec. 60. The tools and lens being all of the same curvature, the state of the surface is gradually improved by grinding with finer and finer emery. The best way of grading the emery is by washing it with clean water, and allowing the emery (at first stirred up with the water) to settle out. The longer the time required for this part of the process the finer will be the emery deposited. An ordinary bedroom jug is a very good utensil to employ during this process; a large glass jug is even better. The following grades will be found sufficient, though I daresay every operative's practice differs a little on this point.

1st grade: Flour emery, with the grit washed out, i.e. allowed to stand for 2" (sec.) before being poured off.

2nd grade: Stand 5" (secs.), settle in 1' (min.)

3rd grade: Stand 1', settle in 10'.

4th grade: Stand 10', settle in 60'.

It is generally advisable to repeat the washing process with each grade. Thus, selecting grade 2 for illustration, the liquor for grade 3 must be poured off without allowing any of the sediment to pass over with it. If any sediment at all passes, one has no security against its containing perhaps the largest particle in the jug. As soon as the liquor for No. 3 has been decanted, jug No. 2 is filled up again with clean water (filtered if necessary), and after standing 5" is decanted into jug No. 2b, the sediment is returned to jug No. 1, and the liquor, after standing 1', is transferred to jug No. 3.

The greatest care is necessary at each step of the operation to prevent "sediment" passing over with liquor. There is a little danger from the tendency which even comparatively large particles of emery have to float, in consequence of their refusing to get wet, and the emery worked up on the side of the jug is also a source of danger, therefore wipe the jug round inside before decanting.

In order to get a uniform grade stop the currents of water in the jug, which may work up coarse particles, by holding a thin bit of wood in the rotating liquid for a moment, and then gently withdrawing it in its own plane. These precautions are particularly necessary in the case of grades Nos. 2, 3, and 4, especially No. 4, for if a single coarse particle gets on the tool when the work has progressed up to this point it will probably necessitate a return to grinding by means of No. 2, and involve many hours' work.

The surface of the lens will require to be ground continuously with each grade till it has the uniform state of roughness corresponding to the grade in question. Two hours for each grade is about the usual time required in working such a lens as is here contemplated.

The coarser grades of emery may be obtained by washing ordinary flour of emery, but the finer ones have to be got from emery which has been used in the previous processes. It is not a good plan to wash the finer grades of emery out of the proceeds of very rough grinding say with anything coarser than flour of emery—as there is a danger of thereby contaminating the finer grades with comparatively coarse glass particles (owing to their lightness) and this may lead to scratching. If the finer grades are very light in colour, it may be inferred that a considerable portion of the dust is composed of glass, and this does no good. Consequently time may be saved by stirring up the light-coloured mass with a little hydrofluoric acid in a platinum capsule; this dissolves the finely divided glass almost instantaneously. The emery and excess of hydrofluoric acid may then be thrown into a large beaker of clean water and washed several times. Fine emery thus treated has much the same dark chocolate colour as the coarser varieties.

The operator should not wear a coat, and should have his arms bare while working with fine emery, for a workshop coat is sure to have gathered a good deal of dust, and increases the chances of coarse particles getting between the surfaces.

Sec. 61. Details of the Process of Fine Grinding.

A lens of the size selected for description is mounted as before mentioned on a leaden pedestal, and the operator places the latter on a table of convenient height in a room as free from dust as possible. Everything should be as clean as a pin, and no splashes of emery mud should be allowed to lie about. I have found it convenient to spread clean newspapers on the table and floor, and to wear clean linen clothes, which do not pick up dust. I have an idea that in large workshops some simpler means of avoiding scratches must have been discovered, but I can only give the results of my own experience. I never successfully avoided scratches till I adopted the precautions mentioned.

Fig. 52.

The left hand should be employed in rotating the pedestal either continuously (though slowly) or at intervals of, say, one minute. This point is rather important. Some operators require two hands to work the grinding tool, and in any case this is the safer practice. Under these circumstances the pedestal may be rotated through one-eighth or tenth of a revolution every three minutes, or thereabouts. The general motion given to the grinding tool should be a series of circular sweeps of about one-fourth the diameter of the glass disc, and gradually carried round an imaginary circle drawn on the surface of the lens and concentric with it (Fig. 52).

The tool may overhang the lens by a quarter of the diameter of the latter as a maximum. The circuit may be completed in from twelve to thirty sweeps. The grinding tool should be lightly held by the fingers and the necessary force applied parallel to the surface. The tool itself must be slowly rotated about its axis of figure. If the tool be lightly held, it will be found that it tends to rotate by itself. I say "tends to rotate," for if the tool be touching evenly all over the surface it will rotate in a direction opposite to the direction of the circular sweep. For instance, if the tool be carried round its looped path clockwise, it will tend to rotate about its own axis of figure counter-clockwise. If it touch more in the middle, this rotation will be increased, while if it touches more along the edge, the rotation will be diminished, or even reversed in an extreme case.

Every fifty sweeps or so the tool should be simply ground backwards and forwards along a diameter of the lens surface. This grinding should consist of three or four journeys to and fro along, say, eight different diameters. About one-quarter of the whole grinding should be accomplished by short straight strokes, during which the tool should only overhang about one-quarter of an inch. The object of the straight strokes is to counteract the tendency to a gradual accumulation of the emery in the centre, which results from the circular grinding.

A great deal of the art of the process consists in knowing how to work the tool to produce any given effect. For instance, if the lens requires to be ground down near the centre, the epicycloidal strokes must be nearly central; the tool must never overhang very much. If, on the other hand, it is the edges which require attention, these must be dealt with by wider overhanging strokes. The tool must be frequently tested on its fellow, and, indeed, ground upon it if any marked unevenness of action (such as that just described) is required for the lens. A check by spherometer will be applied at intervals according to the judgment of the operator, but, in any case, the fellow tool and lens should be kept at very nearly the same figure.

The emery should never be allowed to become anything like dry between the tool and the lens, for in some way (probably by capillary action increasing the pressure of the tool) this seems to lead to scratching and "rolling" of the emery. The channels in the glass tool between the squares are of the greatest importance in enabling the emery to distribute itself. Perhaps the best guide in enabling one to judge as to when it is time to wash off the emery and apply fresh is the "feel" of the tool; also when the mud gets light in colour we know that it is full of glass dust, and proportionately inoperative.

New emery may be put on, say, every five minutes, but no absolute rule can be given, for much depends on the pressure of the tool upon the lens. In the case considered a brass or lead, or even slate tool, of an inch, or even less, in thickness, will press quite heavily enough. In washing the lens and tool before new emery is introduced, a large enamelled iron bucket is very handy; the whole of the tool should be immersed and scrubbed with a nail-brush. The lens surface may be wiped with a bit of clean sponge, free from grit, or even a clean damp cloth.

When the time comes to alter the grade of emery, a fresh lot of newspapers should be put down, and tools, lens, and pedestal well washed and brushed by the nail-brush. The surfaces should be wiped dry by a fresh piece of rag, and examined for scratches and also for uniformity of appearance; a good opinion can be formed as to the fit of the surfaces by noting whether—and if so, to what degree—they differ in appearance from point to point when held so that the light falls on them obliquely.

It is necessary to exercise the greatest care in the washing between the application of successive grades of emery, and this will be facilitated if the edges of the glass squares were dressed on a grindstone before they were mounted. An additional precaution which may be of immense advantage is to allow the tool to dry between the application of successive grades of emery (of course, after it has been scrubbed), and then to brush it vigorously with a hat-brush. It sometimes happens that particles of mud which have resisted the wet scrubbing with the nail-brush may be removed by this method.

As my friend Mr. Cook informs me that his present practice differs slightly from the above, I will depart from the rule I laid down, and add a note on an alternative method.

Consider a single lens surface. This is roughed out as before by an iron tool, a rough fellow tool being made at the same time. The squares of glass are cemented to the roughing tool, and this is ground to the spherometer by means of the counterpart tool. The glass-coated tool is then applied to the lens surface and grinding with the first grade of emery commenced. The curvature is checked by the spherometer. Two auxiliary tools of, say, half the diameter of the lens, are prepared from slate, or glass backed with iron, and applied to grind down either the central part of the lens surface or tool surface, according to the indications of the spherometer. Any changes that may occur during grinding are corrected by these tools. The spherometer is accepted as the sole guide in obtaining the proper curvature. A slate backing is preferred for tools of any diameter over, say, 2 inches.

Sec. 62. Polishing.

After the surface has been ground with the last grade of emery, and commences to become translucent even when dry, the grinding may be considered to be accomplished, and the next step is the polishing. There are many ways of carrying out this process, and the relative suitability of these methods depends on a good many, so to speak, accidental circumstances. For instance, if the intention is to finish the polishing at a sitting, the polishing tool may be faced with squares of archangel—not mineral or coal-tar—pitch and brought to shape simply by pressing while warm against the face of the lens. A tool thus made is very convenient, accurate, and good, but it is difficult to keep it in shape for any length of time; if left on the lens it is apt to stick, and if it overhangs ever so little will, of course, droop at the edges.

On the whole, the following will be found a good and sufficient plan. The glass-grinding tool is converted into a polishing tool by pasting a bit of thin paper over its surface; a bit of woven letter paper of medium thickness with a smooth but not glazed surface does very well. We have found that what is called Smith's "21 lbs. Vellum Wove" is excellent. This is steeped in water till quite pliable and almost free from size. The glass tool is brushed over with a little thin arrowroot or starch paste, and the paper is laid upon it and squeezed down on the glass squares as well as possible; if the paper is wet enough and of the proper quality it will expand sufficiently to envelop the tool without creases, unless the curvature is quite out of the common.

This being accomplished, and the excess of water and paste removed, the face of the paper is (for security) washed with a little clean water and a bit of sponge, and, finally, the tool is slightly pressed on the lens so as to get the paper to take up the proper figure as nearly as possible. After the polishing tool has been thus brought to the proper figure, it is lifted off and allowed to dry slowly. When the paper is dry it may be trimmed round the edges so as not to project sensibly beyond the glass squares. The next step is to brush the surface over very carefully with polishing rouge (prepared as is described at the end of this section) by means of a hat-brush. When the surface of the paper is filled with rouge all excess must be removed by vigorous brushing.

Fig. 53.

The tool being placed on the lens, two or three strokes similar to those used in grinding may be taken, and the tool is then lifted off and examined. It will be found to be dotted with a few bright points, produced by the adhesion of glass at the places of contact. These points are then to be removed in the following manner. An old three-cornered file is ground on each side till the file marks disappear, and sharp edges are produced (Fig. 53). This tool is used as an ink eraser, and it will be found to scrape the paper of the polishing tool very cleanly and well.

The bright spots are the objects of attention, and they must be erased by the old file, and the polisher reapplied to the glass. A few strokes will develop other points, more numerous than before, and these in turn must be erased. The process is continued till the whole surface of the polishing tool is evenly covered with bright specks, and then the polishing may be proceeded with. The specks should not be more than about one-eighth of an inch apart, or the polishing will be irregular.

The operation of polishing is similar to that of grinding. A reasonable time for polishing a glass surface is twenty hours; if more time is required it is a sign that the fine grinding has not been carried far enough. The progress of the operation may be best watched by looking at the surface—not through it. For this purpose a good light is requisite. When the lens is dismounted it may be examined by a beam of sunlight in a dark room, under which circumstances the faintest signs of grayness are easily discernible.

It may be mentioned here that if the surface is in any way scratched the rouge will lodge in the scratches with great persistence, and an expert can generally tell from the appearance of scratches what kind of polishing powder has been employed.

The persistence with which rouge clings to a rough surface of glass is rather remarkable. Some glass polishers prefer to use putty powder as a polishing material, and it is sometimes said to act more quickly than rouge; from my rather limited experience I have not found this to be the case, but it may have merits that I do not know of. Is it possible that its recommendation lies in the fact that it does not render scratches so obtrusively obvious as rouge does?

Rouge is generally made in two or more grades. The softer grade is used for polishing silver, and is called jewellers' rouge. The harder grade, suitable for glass polishing, is best obtained from practical opticians (not mere sellers of optical instruments). I mean people like Messrs. Cook of York. Many years ago I prepared my own hard rouge by precipitating ferrous sulphate solution by aqueous ammonia, washing the precipitate, and heating it to a red heat. The product was ground up with water, and washed to get rid of large particles. This answered every purpose, and I could not find that it was in any way inferior to hard rouge as purchased. The same precipitate heated to a lower temperature is said to furnish a softer variety of rouge; at all events, it gives one more suitable for polishing speculum metal. Lord Rosso used rouge heated to a dull redness for this purpose.

Rouge, whether made or bought, should always be washed to get rid of grit. I ought to add that not the least remarkable fact about the polishing is the extraordinarily small quantity of the polishing material requisite, which suggests that the process of polishing is not by any means the same as that of exceptionally fine grinding. Is it possible that the chief proximate cause of the utility of rouge is to be sought in its curious property of adhering to a rough glass surface, causing it, so to speak, to drag the glass off in minute quantities, and redeposit it after a certain thickness has been attained on another part of the surface?

Sec. 63. Centering.

When a lens is ground and polished it will almost always happen that the axis of revolution of its cylindrical edge is inclined to the axis of revolution of its curved surfaces. Since in practice lenses have to be adjusted by their edges, it is generally necessary to adjust the edge to a cylinder about the axis of figure of the active surfaces. This is best done on a lathe with a hollow mandrel.. The lens is chucked on a chuck with a central aperture—generally by means of pitch or Regnault's mastic, or "centering" cement for small lenses—and a cross wire is fixed in the axis of revolution of the lathe, and is illuminated by a lamp. This cross wire is observed by an eye-piece (with cross wires only in the case of a convex lens, or a telescope similarly furnished in the case of a concave lens), also placed in the axis of rotation of the lathe.

Both cross wires are thus in the axis of revolution of the mandrel, and the distant one (B in the figure) is viewed through the lens and referred to the fixed cross wires at A. In general, as the lathe is rotated by turning the mandrel the image of the illuminated cross wires will be observed to rotate also. The lens is adjusted until the image remains steady on rotating the mandrel and it is to give time for this operation that a slow-setting cement is recommended. When the image remains stationary we know that the optical centre of the lens is in the axis of revolution, and that this axis is normal to both lens surfaces, i.e. is the principal axis of the lens, or axis of figure.

Fig. 54.

A much readier method, and one, in general, good enough for most purposes, is to put a candle on the end of the lathe-bed where the back centre generally is, and observe the images of the flame by reflection from both the lens surfaces. This method is very handy with small lenses; the mandrel is turned, and the lens adjusted by hand till the images are immovable. In both cases, of course, the edge of the lens is turned or ground till it is truly circular, the position of the lens remaining undisturbed on the chuck. If the edge gauge has been properly used in the earlier stages of figuring, it will be found that very little turning or grinding is requisite to produce a true centering.

The particular defect due to want of centering in a lens may be observed by using it as the objective of a telescope, and observing a star slightly out of focus. The interference fringes will not be concentric circles unless the lens is properly centred. I ought to say that I have not looked into the theory of this, but have merely taken it as a generally admitted fact. The diseases of lenses and the modes of treating them are dealt with in a book by Messrs. Cook of York, entitled On the Adjustment and Testing of Telescopic Objectives.

The final process of figuring will be dealt with later on (Sec. Sec. 66 and 67), as it applies not only to lenses but to mirrors, prisms, etc. If the instructions given have been carefully carried out on a 2-inch lens, it should perform fairly well, and possibly perfectly, without any further adjustment of the glass.

Sec. 64. Preparation of Small Lenses, where great Accuracy is not of the first Importance.

Such lenses may generally be made out of bits of good plate or sheet glass, and are of constant use in the physical laboratory. They may be purchased so cheaply, however, that only those who have the misfortune to work in out-of-the-way places need be driven to make them.

Suitable glass having been obtained and the curves calculated from the index of refraction, as obtained by any of the ordinary methods applicable to plates (the microscope method, in general, is quite good enough), squares circumscribing the desired circles are cut out by the help of a diamond. [Footnote: Glazebrook and Shaw's Practical Physics, p. 383 (4th ed.).] The squares are roughly snipped by means of a pair of pliers or spectacle-maker's shanks. The rough circles are then mounted on the end of a brass or iron rod of rather greater diameter than the finished lenses are to possess. This mounting is best done by centering cement.

The discs are then dressed circular on a grindstone, the rod serving both as a gauge and handle. A sufficient number of these discs having been prepared, a pair of brass tools of the form shown in the sketch (Fig. 55), and of about the proper radius of curvature, are made. One of these tools is used as a support for the glass discs.

Fig. 55.

A compass being set to scribe circles of the same diameter as the glass discs, centre marks are made on the surface of the appropriate tool, circles are drawn on this, and facets are filed or milled (for which the spiral head of the milling machine is excellent). In the case of concave supporting surfaces, i.e. in making concave lenses, I apprehend filing would be difficult, and the facets would have to be made by a rose cutter or mill; but if the discs are fairly round, then, in fact, no facets are required.

The facets being ready, the glass discs are cemented to them by centering cement, which may be used quite generally for small lenses. When the cutting of facets has been omitted on a concave surface, the best cement is hard pitch. The grinding tool is generally rather larger than the nest of lenses. Coarse and fine grinding is accomplished wholly on the lathe—the tool being rotated at a fair speed (see infra), and the nest of lenses moved about by its handle so as to grind all parts equally. It must, of course, be held anywhere except "dead on," for then the part round the axis would not get ground; this inoperative portion of the rotating tool must therefore be allowed to distribute its incapable efforts evenly over the nest of lenses.

Polishing is accomplished by means of the grinding tool, coated with paper and rouge as before; or the tool may be coated with very thin cloth and used with rouge as before—in this case the polishing goes on fastest when the surface of the cloth is distinctly damp. In working by this method, each grade of emery need only be applied from five to ten minutes. The glass does not appear to get scratched when the emery is changed, provided everything is well washed. A good polish may be got in an hour. The lathe is run as for turning brass of the same diameter as the tool.

One side of the lenses being thus prepared, they are reversed, and the process gone through for the other side in a precisely similar manner. [Footnote: Unless the radius of curvature is very short and the lenses also convex, there is no necessity to recess the facets, provided hard pitch is used as the cement. See note on hard pitch.] To save trouble, it is usual, to make such lenses of equal curvature on both faces; but of course this is a matter of taste.

Fig. 56.

For very common work, bits of good plate glass are employed, and the manufacturer's surface treated as flat (Fig. 56). In this way plano-convex lenses are easily and cheaply made. Finally the lenses have to be centred, an essential operation in this case. This is easily done by the reflection method—the edge being turned off by the file and kerosene and the centering cement being used in making the preliminary adjustment on the chuck. I presume a lens made in this way is worth about a shilling, so that laboratory manufacture is not very remunerative. Fig. 56 shows the method of mounting small lenses for lathe grinding, when only one lens is required. The tool is generally rotated in the lathe and the lens held against it.

Sec. 65. Preparing Small Mirrors for Galvanometers.

To get good mirrors for galvanometers, I have found the best plan is to grind and polish a large number together, on a disc perhaps 8 or 10 inches in diameter. I was led to this after inspecting and rejecting four ounces of microscope cover slips, a most wearisome process. That regular cover slips should be few and far between is not unlikely, seeing that they are made (by one eminent firm at least) simply by "pot" blowing a huge thin bulb, and then smashing it on the floor and selecting the fragments. As in the case of large mirrors, it is of course only necessary to grind one side of the glass, theoretically at all events. The objections to this course are:

(1) A silver surface cannot, in my experience, be polished externally (on a minute object like a cover slip) to be anything like so bright as the silver surface next the glass; and,

(2) if one side only is ground, it will be found that the little mirror hopelessly loses its figure directly it is detached from the support on which it has been worked. Consequently, I recommend that these small mirrors should be ground and polished on both sides—enough may be made at one operation to last for a very long time.

A slate back is prepared of the same radius of curvature as it is desired to impart to the mirrors. Bits of thin sheet glass are then ground circular as described in the last section and cemented to this surface by the smallest quantity of clean archangel pitch, allowed to cool slowly and even to rest for a day before the work is proceeded with. The whole surface is then ground and polished as before.

The mirrors are now reversed, when they ought to nearly fit the tool (assuming that flats are being made, and the fellow tool in all other cases), and are recemented by pitch to the appropriate backing ground, and polished. If very excellent results are required, these processes may be preceded by a preliminary rough grinding of one surface, so that the little discs will "sit" exactly on the tool surface, and not run the risk of being strained by capillary forces in the pitch. We have always found this necessary for really good results.

On removing such mirrors from the backing, they generally, more or less lose their figure, becoming (in general fairly uniformly) more concave or convex. About 5 per cent of the mirrors thus prepared will be found almost perfect if the work has been well done, and the rest will probably be very fair, unless the diameter is very large as compared with the thickness. The best way of grinding and polishing such large surfaces (nests 10 inches in diameter) is on a grinding machine, such as will be described below. The polishing is best done by means of paper, as before described.

Having occasion to require hitherto unapproached lightness and optical accuracy in such mirrors, I got my assistant to try making them of fused quartz, slices being cut by a diamond wheel from a rod of that material. Chips of natural quartz were also obtained from broken "pebble" spectacles, and these were worked at the same time. The resulting mirrors were certainly superior to the best we could make from glass, but the labour of grinding was greater, and the labour of polishing less, than in the latter case. The pebble fragments gave practically as good mirrors as the fused slices. For the future it will be better always to make galvanometer mirrors from quartz crystals. These may be easily sliced, as will be described in Sec. 74. The slices are dressed on a grindstone according to instructions already given for small lenses.

The silvering of these mirrors is a point of great importance. After trying nearly every formula published, we have settled down to the following.

A solution of pure crystallised nitrate of silver in distilled water is made up to a strength of 125 grams of the salt per litre. This forms the stock solution and is kept in a dark bottle.

Let the volume of silvering liquor required in any operation be denoted by 4 v. The liquor is prepared as follows:

I. Measure out a volume v of the stock solution of silver nitrate, and calculate the weight of salt which it contains; let this be w. In another vessel dissolve pure Rochelle salt to the amount of 2.6 w, and make up the solution to the volume v. These two solutions are to be mixed together at a temperature of 55 deg. C, the vessels with their contents being heated to this temperature on the water bath. After mixing the liquids the temperature is to be kept approximately constant for five minutes, after which the liquor may be cooled. The white precipitate which first forms will become gray or black and very dense as the liquid cools. If it does not, the liquor must be reheated to 55 deg. C, and kept at that temperature for a few minutes and then again allowed to cool. The solution is in good order when all the precipitate is dense and gray or black and the liquor clear. The blacker and denser the precipitate the better is the solution. The liquor is decanted and filtered from the precipitate and brought up to the volume 2 v by addition of some of the wash water.

II. Measure out a volume 0.118 v of the stock solution into a separate vessel, and add to it a 5 per cent solution of ammonium hydrate, with proper precautions, so that the precipitate at first formed is all but redissolved after vigorous shaking. It is very important that this condition should be exactly attained. Therefore add the latter part of the ammonia very carefully. Make up the volume to 2 v.

Mix the solutions I. and II. in a separate vessel and pour the mixture into the depositing vessel. The surface to be silvered should face downwards, and lie just beneath the free surface of the liquid. Bubbles must of course be removed.

The silver deposit obtained in this manner is exceedingly white and, bright on the surface next to the glass, but the back is mat and requires polishing.

The detail of the process described above was worked out in my laboratory by Mr. A. Pollock, to whom my thanks are due.

This process gives good deposits when the solutions are freshly prepared, but the ammonia solution will not keep; The surfaces to be silvered require to be absolutely clean. The process is assisted by a summer temperature, say 70 deg. Fahr, and possibly by the action of light. Six or seven hours at least are required for a good deposit; a good plan is to leave the mirrors in the bath all night. On removal from the bath the mirrors require to be well washed, and allowed to dry thoroughly in sun heat for several hours before they are touched.

Care should be taken not to pull the mirrors out of shape when they are mounted for the bath. A single drop of varnish or paint (a mere speck) on the centre will suffice to hold them. The back of the deposit requires to be varnished or painted as a rule to preserve the silver. All paints and varnishes thus applied tend to spoil the figure by expanding or contracting. On the whole, I think boiled linseed oil and white or red lead—white or red paint in fact—is less deleterious than other things I have tried. Shellac varnish is the worst.

Of course, the best mirror can be easily spoiled by bad mounting. I have tried a great number of methods and can recommend as fairly successful the following:- A little pure white lead, i.e. bought as pure as a chemical—not as a paint—is mixed with an equal quantity of red lead and made into a paste with a little linseed oil. I say a paste, not putty. A trace of this is then worked on to the back of the mirror at the centre as nearly as may be, and to this is attached the support. The only objection to this is that nearly a week is required for the paste to set. If people must use shellac let it be remembered that it will go on changing its shape for months after it has cooled (whether it has been dissolved in alcohol or not).

Sec. 66. Preparation of Large Mirrors or Lenses for Telescopes.

So much has been written on this subject by astronomers, generally in the English Mechanic and in the Philosophical Transactions for 1840, that it might be thought nothing could be added. I will only say here that the processes already described apply perfectly to this case; but of course I only refer to silver on glass mirrors. For any size over 6 inches in diameter, the process of grinding and polishing by hand, particularly the latter, will probably be found to involve too much labour, and a machine will be required. A description of a modification of Mr. Nasmyth's machine—as made by my assistant, Mr. Cook—will be found below.

There is no difficulty in constructing or working such a machine, and considered as an all round appliance, it possesses solid advantages over the simple double pulley and crank arrangement, which, however, from its simplicity deserves a note. Two pulleys, A and B, of about 18 inches diameter by 4 inches on the face, are arranged to rotate about vertical axes, and belted together. The shaft of one of these pulleys is driven by a belt in any convenient manner. Each pulley is provided on its upper surface with a crank of adjustable length carrying a vertical crank-pin.

Each crank-pin passes through a 3"X 2" wooden rod, say 3' 6" long, and these rods are pinned together at their farther extremities, and this pin carries the grinding or polishing tool, or rather engages loosely with the back of this tool which lies below the rod. It is clear that if the pulleys are of commensurable diameters, and are rigidly connected—say by belting which neither stretches nor slips—the polishing tool will describe a closed curve. If, however, the belt is arranged to slip slightly, or if the pulleys are of incommensurable diameters, the curve traced out by the grinding tool will be very complex, and in the case of the ratio of the diameters being incommensurable, will always remain open; for polishing purposes the consummation to be wished.

Mirror surfaces are ground spherical, the reduction to parabolic form being attained in the process of polishing. A very interesting account of the practice of dealing with very large lenses will be found in Nature, May 1886, or the Journal of the Society of Arts, same date (I presume), by Sir Howard Grubb. The author considers that the final adjustment of surfaces by "figuring"—of which more anon—is an art which cannot be learned by inspection, any more than a man could learn to paint by watching an artist. This is, no doubt, the case to some extent; still, a person wishing to learn how to figure a lens could not do better than take Sir Howard at his word, and spend a month at his works. Meanwhile the following remarks must suffice; it is not likely that anybody to whom these notes will be of service would embark on such large work as is contemplated by Sir Howard Grubb.

Fig. 57.

Description of Polishing Machine. Power is applied through belting to the speed cone A. By means of a bevel pinion rotation is communicated to the wheel D, which is of solid metal and carries a T-slot, C. A pedestal forming a crank-pin can be clamped so as to have any desired radius of motion by the screw E. A train of wheels E F G H K (ordinary cast lathe change wheels) communicate any desired ratio of motion to the tool-holder, which simply consists of two pins projecting vertically downwards from the spokes of wheel K.

These pins form a fork, and each prong engages in a corresponding hole in the back of the slate-grinding tool (not shown in figure). The connection with the tool is purposely loose. The wheel E, of course, cannot rotate about the crank-pin D. Provision for changing the ratio of tool rotation is achieved by mounting the wheels composing the train on pins capable of sliding along a long slot in the bar supporting them. The farther end of this bar is caused to oscillate to and fro very slowly by means of an additional crank-pin S and crank-shaft, the projecting face of the bed-plate W being placed so as to allow V to slide about easily and smoothly. Motion is communicated to this part of the system by means of gears at 0 and P, and a belt working from P to Q. Thus the vertical shaft R is set in motion and communicates by gears with S. A pulley placed on the axle of the wheel carrying the crank-pin S gives a slow rotation to the work which is mounted on the table M. A small but important feature is the tray L below the gear K. This prevents dirt falling from the teeth of the wheel on to the work. The motion of S is of course very much less than of B—say 100 times less. The work can be conveniently adjusted as to height by means of the screw N.

The machine must be on a steady foundation, and in a place as free from dust as possible. Though it looks complicated it is quite straight-forward to build and to operate.

It is explained in Lord Rayleigh's article on Optics in the Encyclopaedia Britannica that a very minute change in the form of the curvature of the surface of a lens will make a large difference in the spherical aberration. This is to be expected, seeing that spherical aberration is a phenomenon of a differential sort, i.e. a measure of the difference between the curvature actually attained, and the theoretical curvature at each point of the lens, for given positions of point and image. Sir H. Grubb gives an illustration of the minuteness of the abrasion required in passing from a curve of one sort to a curve of another, say from a spherical to a parabolic curve, consequently the process of figuring by the slow action of a polishing tool becomes quite intelligible. In making a large mirror or lens all the processes hitherto described under grinding and polishing, etc, have to be gone through and in the manner described, and when all this is accomplished the final process of correcting to test commences. This process is called figuring.

Sec. 67. Of the actual operation of this process I have no personal knowledge, and the following brief notes are drawn from the article by Sir H. Grubb, from my assistant's (Mr. Cook) experience, and from a small work On the Adjustment and Testing of Telescopic Objectives, by T. Cook and Sons, Buckingham Works, York (printed by Ben Johnson and Co, Micklegate, York). This work has excellent photographs of the interference rings of star images corresponding to various defects. It must be understood that the following is a mere sketch. The art will probably hardly ever be required in laboratory practice, and those who wish to construct large telescopes should not be above looking up the references.

The process is naturally divided for treatment into two parts.

(1) The detection of errors, and the cause of these errors.

(2) The application of a remedy.

(1) A lens, being mounted with its final adjustments, is turned on to a star, which must not be too bright, and should be fairly overhead. The following appearances may be noted:-

A. In focus, the star appears as a small disc with one or two rings round it; inside and outside of the focus the rings increase in number, are round, concentric with the disc, and the bright and dark rings are apparently equally wide. The appearance inside the focus exactly resembles that outside when allowance is made for chromatic effects. Conclusion: objective good, and correctly mounted.

B. The rings round the star in focus are not circular, nor is the star at the centre of the system. In bad cases the fringes are seen at one side only. Effects exaggerated outside and inside the focus. Conclusion: the lens is astigmatic, or the objective is not adjusted to be co-axial with the eyepiece.

C. When in focus the central disc is surrounded by an intermittent diffraction pattern, i.e. for instance the system of rings may appear along, and near, three or more radii. If these shift when the points of support of the lens are shifted, flexure may be suspected.

D. On observing inside and outside the focus, the rings are not equally bright and dark. This may be due to uncorrected spherical aberration, particularly to a fault known as "zonal aberration," where different zones of the lens have different foci, but each zone has a definite focus.

E. Irregular diffraction fringes point to bad annealing of the glass. This may be checked by an examination of the lens in polarised light.

F. If the disc appear blurred and coloured, however the focus be adjusted, incomplete correction for chromatic aberration is inferred. If in addition the colouring is unsymmetrical (in an extreme case the star disc is drawn out to a coloured band), want of centering is to be inferred. This will also show itself by the interference fringes having the characteristics described in C.

(2) The following steps may be taken in applying a remedy:

A. The adjusting screws of the cell mounting the object glass may be worked until the best result is attained; this requires great care and patience. Any errors left over are to be attributed to other causes than the want of collinearity of the axes of object glass and eyepiece.

B. Astigmatism is detected by rotating the object glass or object glass cell. If the oval fringes still persist and the longer axis follows the lens, astigmatism may be inferred. Similarly, by rotating one lens on the other, astigmatism, or want of centering (quite a different thing) may be localised to the lens.

C. The presence of flexure may be confirmed by altering the position of the points of support with respect to the eyepiece, the lens maintaining its original position. The addition of more points of support will in general reduce the ill effects. How to get rid of them I do not know; they are only serious with large lenses.

D. Spherical aberration may be located by using stops and zonal screens, and observing the effect on the image. Sir H. Grubb determines whether any point on the lens requires to be raised or lowered, by touching the glass at that point with a warm hand or cooling it by ether. The effects so produced are the differential results of the change of figure and of refractive index. By observing the effect of the heating or cooling of any part, the operator will know whether to raise or lower that part, provided that by a suitable preliminary experiment he has determined the relation between the effect produced by the change of figure, and that due to the temperature variation of the refractive index. In general it is sufficient to consider the change of shape only and neglect the change in refractive power.

E. Marked astigmatism has never been noticed by me, but I should think that the whole lens surface would require to be repolished or perhaps reground in this case.

F. To decide in which surface faults exist is not easy. By placing a film of oil between the two surfaces nearly in contact these may be easily examined. Thus a mixture of nut and almond oil of the right proportion, to be found by trial, for the temperature, will have the same refractive index as the crown glass, and will consequently reduce any errors of figure in the interior crown surface, if properly applied between the surfaces. Similarly the interior of the flint surface may have its imperfections greatly reduced in effect by using almond oil alone, or mixed with bisulphide of carbon. The outer surfaces, I presume, must be examined by warming or cooling over suitable areas or zones.

The defects being detected, a matter requiring a great deal of skill and experience according to Sir H. Grubb, the next step is to remedy them; and the remedial measures as applied to the glass constitute the process of figuring. There are two ways of correcting local defects, one by means of small paper or pitch covered tools, which according to Sir H. Grubb is dangerous, and according to the experience of Mr. Cook, and I think of many French opticians, safe and advantageous.

Pitch polishing tools are generally used for figuring. They are made by covering a slate backing with squares of pitch. The backing is floated with pitch say one-eighth of an inch thick. This is then scored into squares by a hot iron rod. The tool, while slightly warm, is laid upon the lens surface, previously slightly smeared with dilute glycerine, until the pitch takes the figure of the glass. The polishing material is rouge and water. Small tools are applied locally, and probably can only be so applied with advantage for grave defects.

The other method is longer and probably safer. It consists in furnishing the polishing tool with squares of pitch as before. These being slightly warm, the lens is placed upon them so that they will flow to the exact figure also as before. I presume that the lens is to be slightly smeared with glycerine, or some equivalent, to keep the pitch from sticking. The squares are most thickly distributed where the abrasion is most required, i.e. less pitch is melted out by the iron rod. This may be supplemented by taking advantage of differences of hardness of pitch, making some squares out of harder, others out of softer pitch. The aim is to produce a polishing tool which will polish unequally so as to remove the glass chiefly from predetermined parts of the lens surface. The tool is worked over the surface of the lens by the polishing machine, and part of the art consists in adjusting the strokes to assist in the production of the local variations required.

A source of difficulty and danger lies in the fact that the pitch squares are rarely of the same hardness, so that some abrade the glass more rapidly than others. This is particularly likely to occur if the pitch has been overheated. [Footnote: When pitch is heated till it evolves bubbles of gas its hardness increases with the duration of the process.] The reader must be good enough to regard these remarks as of the barest possible kind, and not intended to convey more than a general idea of the nature of the process of figuring.

Sec. 68. A few remarks on cleaning lenses will fittingly close this part of the subject. There is no need to go beyond the following instructions given by Mr. Brashear in Popular Astronomy, 1894, which are reproduced here verbatim.

"The writer does not advise the use of either fine chamois skin, tissue paper, or an old soft silk handkerchief, nor any other such material to wipe the lenses, as is usually advised. It is not, however, these wiping materials that do the mischief, but the dust particles on the lenses, many of them perhaps of a silicious nature, which are always harder than optical glass, and as these particles attach themselves to the wiping material they cut microscopic or greater scratches on the surfaces of the objective in the process of wiping.

"I write this article with the hope of helping to solve this apparently difficult problem, but which in reality is a very simple one.

"Let us commence by taking the object glass out of its cell. Take out the screws that hold the ring in place, and lift out the ring. Placing the fingers of both hands so as to grasp the objective on opposite sides, reverse the cell, and with the thumbs gently press the objective squarely out of the cell on to a book, block of wood, or anything a little less in diameter than the objective, which has had a cushion of muslin or any soft substance laid upon it. One person can thus handle any objective up to 12 inches in diameter.

"Before separating the lenses it should be carefully noted how they were put together with relation to the cell, and to one another, and if they art not marked they should be marked on the edges conspicuously with a hard lead pencil, so that when separated they may be put together in the same way, and placed in the same relation to the cell. With only ordinary precaution this should be an easy matter.

"Setting the objective on edge the two lenses may be readily separated.

"And now as to the cleaning of the lenses. I have, on rare occasions, found the inner surfaces of an object glass covered with a curious film, not caused directly by moisture but by the apparent oxidation of the tin-foil used to keep the lenses apart. "A year or more ago a 7-inch objective made by Mr. Clark was brought to me to clean. It had evidently been sadly neglected. The inside of the lenses were covered with such a film as I have mentioned, and I feared the glass was ruined. When taken apart it was found that the tin-foil had oxidised totally and had distributed itself all over the inner surfaces. I feared the result, but was delighted to find that nitric acid and a tuft of absorbent cotton cut all the deposit off, leaving no stains after having passed through a subsequent washing with soap and water.

"I mention this as others may have a similar case to deal with.

"For the ordinary cleaning of an objective let a suitable sized vessel, always a wooden one, be thoroughly cleaned with soap and water, then half filled with clean water about the same temperature as the glass. Slight differences of temperature are of no moment. Great differences are dangerous in large objectives.

"I usually put a teaspoonful of ammonia in half a pail of water, and it is well to let a piece of washed 'cheese cloth' lie in the pail, as then there is no danger if the lens slips away from the hand, and, by the way, every observatory, indeed every amateur owning a telescope, should have plenty of 'cheese cloth' handy. It is cheap (about 3 cts. per yard) and is superior for wiping purposes to any 'old soft silk handkerchief,' chamois skin, etc. Before using it have it thoroughly washed with soap and water, then rinsed in clean water, dried and laid away in a box or other place where it can be kept clean. When you use a piece to clean an objective throw it away, it is so cheap you can afford to do so.

"If the lenses are very dirty or 'dusty,' a tuft of cotton or a camel's-hair brush may be used to brush off the loose material before placing the lenses in the water, but no pressure other than the weight of the cotton or brush should be used. The writer prefers to use the palms of the hand with plenty of good soap on them to rub the surfaces, although the cheese cloth and the soap answers nicely, and there seems to be absolutely no danger of scratching when using the hands or the cheese cloth when plenty of water is used; indeed when I wish to wipe off the front surface of an objective in use, and the lens cannot well be taken out, I first dust off the gross particles and then use the cheese cloth with soap and water, and having gone over the surface gently with one piece of cloth, throw it away and take another, perhaps a third one, and then when the dirt is, as it were, all lifted up from the surface, a piece of dry cheese cloth will finish the work, leaving a clean brilliant surface, and no scratches of any kind.

"In washing large objectives in water I generally use a 'tub' and stand the lenses on their edge. When thoroughly washed they are taken out and laid on a bundle of cheese cloth and several pieces of the same used to dry them.

"I think it best not to leave them to drain dry; better take up all moisture with the cloth, and vigorous rubbing will do no harm if the surfaces have no abrading material on them. I have yet to injure a glass cleaned in this way.

"This process may seem a rather long and tedious one, but it is not so in practice, and it pays.

"In some places objectives must be frequently cleaned, not only because they become covered with an adherent dust, but because that dust produces so much diffused light in the field as to ruin some kinds of telescope work. Mr. Hale of the Kenwood Observatory tells me he cannot do any good prominence photography unless his objective has a clean surface; indeed every observer of faint objects or delicate planetary markings knows full well the value of a dark field free from diffused light. The object-glass maker uses his best efforts to produce the most perfect polish on his lenses, aside from the accuracy of the curves, both for high light value and freedom from diffused light in the field, and if the surfaces are allowed to become covered with dust, his good work counts for little.

"If only the front surface needs cleaning, the method of cleaning with cheese cloth, soap and water, as described above, answers very well, but always throw away the first and, if necessary, the second cloth, then wipe dry with a third or fourth cloth; but if the surfaces all need cleaning I know of no better method than that of taking the objective out of its cell, always using abundance of soap and water, and keep in a good humor."

Sec. 69. The Preparation of Flat Surfaces of Rock Salt.

The preliminary grinding is accomplished as in the case of glass, except that it goes on vastly faster. The polishing process is the only part of the operation which presents any difficulty. The following is an extract from a paper on the subject, by Mr. J. A. Brashear, Pittsburg, Pa, U.S.A, from the Proceedings of the American Association for the Advancement of Science, 1885. Practically the same method was shown me by Mr. Cook some years earlier, so that I can endorse all that Mr. Brashear says, with the following exceptions. We consider that for small salt surfaces the pitch is better scored into squares than provided with the holes recommended by Mr. Brashear.

Mr. Brashear's instructions are as follows. After alluding to the difficulty of drying the polished salt surface—which is of course wet—Mr. Brashear says:-

"Happily I have no trouble in this respect now, and as my method is easily carried out by any physicist who desires to work with rock salt surfaces, it gives me pleasure to explain it. For polishing a prism I make an ordinary pitch bed of about two and one-half or three times the area of the surface of the prism to be polished. While the pitch is still warm I press upon it any approximately flat surface, such as a piece of ordinary plate glass. The pitch bed is then cooled by a stream of water, and conical holes are then drilled in the pitch with an ordinary counter sink bit, say one-quarter of an inch in diameter, and at intervals of half an inch over the entire surface. This is done to relieve the atmospheric pressure in the final work. The upper surface of the pitch is now very slightly warmed and a true plane surface (usually a glass one, prepared by grinding and polishing three surfaces in the ordinary way, previously wetted) is pressed upon it until the pitch surface becomes an approximately true plane itself. Fortunately, moderately hard pitch retains its figure quite persistently through short periods and small changes of temperature, and it always pays to spend a little time in the preparation of the pitch bed.

"The polisher being now ready, a very small quantity of rouge and water is taken upon a fine sponge and equally distributed over its surface. The previously ground and fined salt surface (this work is done the same as in glass working) is now placed upon the polisher and motion instantly set up in diametral strokes. I usually walk around the polisher while working a surface. It is well to note that motion must be constant, for a moment's rest is fatal to good results, for the reason that the surface is quickly eaten away, and irregularly so, owing to the holes that are in the pitch bed. Now comes the most important part of this method. After a few minutes' work the moisture will begin to evaporate quite rapidly. No new application of water is to be made, but a careful watch must be kept upon the pitch bed, and as the last vestige of moisture disappears the prism is to be slipped off the polisher in a perfectly horizontal direction, and if the work has been well done, a clean, bright, and dry surface is the result. The surface is now tested by the well-known method of interference from a perfect glass test plate (see Fig. 178).

"If an error of concavity presents itself the process of polishing is gone over again, using short diametral strokes. If the error is one of convexity, the polishing strokes are to be made along the chords, extending over the edge of the polisher. The one essential feature of this method is the fact that the surface is wiped dry in the final strokes, thus getting rid of the one great difficulty of pitch polishing, a method undoubtedly far superior to that of polishing on broadcloth. If in the final strokes the surface is not quite cleaned I usually breathe upon the pitch bed, and thus by condensation place enough moisture upon it to give a few more strokes, finishing just the same as before. In ten minutes I have polished prisms of rock salt in this manner that have not only shown the D line double, but Professor Langley has informed me that his assistant, Mr. Keeler (J. E.), has seen the nickel line clearly between the D lines. This speaks for the superiority of the surfaces over those polished on broadcloth.

"In polishing prisms I prefer to work them on top of the polisher, as they can be easily held, but as it is difficult to hold lenses or planes in this way without injuring the surfaces, I usually support them in a block of soft wood, turned so as to touch only at their edges, and work the polisher over them. Though it takes considerable practice to succeed at first, the results are so good that it well repays the few hours' work it requires to master the few difficulties it presents."

Fig. 58.

Sec. 70. Casting Specula for Mirrors.

According to Sir H. Grubb (loc. cit.) the best alloy is made of four atoms of copper and one of tin; this gives by weight, copper 252, tin 117.8.

The copper is melted first in a plumbago crucible; the tin is added gradually. Of course, in the process of melting, even though a little fine charcoal be sprinkled over the copper, some loss of that metal will occur from oxidation. It is convenient in practice, therefore to reserve a portion of the tin and test the contents of the crucible by lifting a little of the alloy out and examining it.

The following indications may be noted: When the copper is in excess the tint of the alloy is slightly red, and the structure, as shown at a fractured surface, is coarsely crystalline. As the proper proportions are more nearly attained, the crystalline structure becomes finer, the colour whiter, and the crystals brighter. The alloy is ready for use when the maximum brightness is attained and the grain is fine.

If too much tin be added, the lustre diminishes. The correct proportion is, therefore, attained when a further small addition of tin produces no apparent increase of brightness or fineness of grain. About three-quarters of the tin may be added at first, and the other quarter added with testing as described. The alloy is allowed to cool until on skimming the surface the metal appears bright and remains so without losing its lustre by oxidation for a sensible time; it will still be quite red-hot.

Fig. 59. Fig. 60.

As the speculum alloy is too difficult to work with ordinary tools, it is best to cast the speculum of exactly the required shape and size. This is done by means of a ring of iron turned inside (and out) and on one edge. This ring is laid on a plate of figured iron, and before the metal is poured the plate (G) (Figs 59 and 61) is heated to, say, 300 deg. C. In order to avoid the presence of oxide as far as possible, the following arrangements for pouring are made. A portion of the lower surface of the ring is removed by radial filing until a notch equal to, say, one-twentieth of the whole circumference is produced. This is cut to an axial depth of, say, half an inch.

A bar of iron is then dovetailed loosely into the notch (Fig. 60, B), so that it will rest on the iron plate, and half fill the notch. The aperture thus left forms the port of ingress for the hot metal (see Fig. 61, M). A bit of sheet iron is attached to the upper surface of the ring, and lies as a sort of flap, shaped like a deep shovel, against the outside of the ring overhanging the port (Figs. 59 and 61 at F). This flap does not quite reach the iron plate, and its sides are bent so as to be in contact with the ring. A portion of a smaller ring is then applied in such a manner as to form a pouring lip or pool on the outside of the main ring at E, and the metal can only get into the main ring by passing under the edge of the flap and up through the port. This forms an efficient skimming arrangement. The process of casting is carried out by pouring steadily into the lip.

To avoid air bubbles it is convenient to cause the metal to spread slowly over the chill, and Mr. Nasmyth's method of accomplishing this is shown in the figure (61). The chill rests on three pins, A B C (Figs. 59 and 61). Before pouring begins the chill is tilted up off C by means of the counterpoise D, which is insufficient to tilt it after the speculum is poured. It is important that the chill should be horizontal at the close of the operation, in order that the speculum may be of even thickness throughout. This is noted by means of levels placed on the ring (at K for instance).

Fig. 61.

This apparatus may appear unnecessarily complex, but it is worth while to set it up, for it makes the operation of casting a speculum fairly certain. If the metal is at the right temperature it will form a uniformly liquid disc inside the ring. The mass sets almost directly, and as soon as this occurs it is pushed to the edge of the plate and the metal in the lip broken off by a smart upward tap with a hammer. The dovetailed bit of iron is knocked downwards and falls off, and the ring may then be lifted clear of the casting. The object of the dovetail will now be understood, for without it there is great risk of breaking into the speculum in knocking the "tail" off.

A box of quite dry sawdust is prepared in readiness for the process of annealing before the speculum is cast. The box must be a sound wooden or metal box, and must be approximately air-tight. For a speculum a foot in diameter the box must measure at least 3 feet both ways in plan, and be 2 feet 6 inches deep. Half the sawdust is in the box and is well pressed down so as to half fill it. The other half must be conveniently ready to hand. As soon as possible after casting, the speculum is thrown into the box, covered over with the sawdust, and the lid is put on.

The object in having the box nearly air-tight is to avoid air-currents, which would increase the rate of cooling. A speculum a foot in diameter may conveniently take about three days to anneal, and should be sensibly warm when the box is opened on the fourth day. For larger sizes longer times will be required. We will say that the sawdust thickness on each side must be proportional to the dimensions of the speculum, or may even increase faster with advantage if time is of no moment.

The process of annealing may be considered successful if the disc does not fly to pieces in working; it is to be worked on the chilled side. The object of giving the chill the approximate counterpart form will now appear; it saves some rough grinding, and causes the finished surface to be more homogeneous than it would be if the centre were sunk by grinding through the chilled surface.

In 1889 I learned from Mr. Schneider, Professor Row-land's assistant at Baltimore, that in casting specula for concave gratings a good deal of trouble had been saved by carrying out the operation in an atmosphere consisting mostly of coal gas. It was claimed that in this way the presence of specks of oxide was avoided. I did not see the process in operation, but the results attained are known and admired by all experimenters.

Sec. 71. Grinding and polishing Specula.

The rough grinding is accomplished by means of a lead tool and coarse emery; the size of grain may be such as will pass a sieve of 60 threads to the inch. The process of grinding is quite similar to that previously described, but it goes on comparatively quickly. The rough grinding is checked by the spherometer, and is interrupted when that instrument gives accordant and correct measurements all over the surface.

The fine grinding may be proceeded with by means of a glass-faced tool as before described, or the labour may be reduced in the following manner. A slate tool, which must be free from green spots (a source of uneven hardness), is prepared, and this is brought nearly to the curvature of the roughly ground speculum, by turning or otherwise. It is finished on the speculum itself with a little flour of emery. The fine grinding is then carried on by means of slate dust and water, the slate tool being the grinder. The tool is, of course, scored into squares on the surface.

If the casting process has been carried out successfully, the rough grinding may take, say six hours, and the fine grinding say thirty hours for a disc a foot in diameter. The greatest source of trouble is want of homogeneity in the casting, as evidenced by blowholes, etc. In general, the shortest way is to discard the disc and start afresh if there is any serious want of perfection in the continuity or homogeneity of the metal.

Fig. 62.

The finely ground surface must, of course, be apparently correct in so far as a spherometer (with 3 inches between the legs for a disc 1 foot in diameter) will show. Polishing and figuring are carried out simultaneously. Half an hour's polishing with a slate-backed pitch tool and rouge and water will enable an optical test to be made. The most convenient test is that of Foucault, a simple appliance for the purpose being shown in the figure (62). It essentially consists of a small lamp surrounded by an opaque chimney (A) through which a minute aperture (pin-hole) is made. A small lens may be used, of very great curvature, or even a transparent marble to throw an image of the flame on the pin-hole.