No. V. ADDITIONAL.

RULES for converting French Weights and Measures into correspondent English Denominations[62].

Sec. 1. Weights.

The Paris pound, poids de mark of Charlemagne, contains 9216 Paris grains; it is divided into 16 ounces, each ounce into 8 gros, and each gros into 72 grains. It is equal to 7561 English Troy grains.

The English Troy pound of 12 ounces contains 5760 English Troy grains, and is equal to 7021 Paris grains.

The English averdupois pound of 16 ounces contains 7000 English Troy grains, and is equal to 8538 Paris grains.

To reduce Paris grs. to English Troy } grs. divide by } 1.2189 To reduce English Troy grs. to Paris } grs. multiply by }

To reduce Paris ounces to English } Troy, divide by } To reduce English Troy ounces to } 1.015734 Paris, multiply by }

Or the conversion may be made by means of the following Tables.

I. To reduce French to English Troy Weight.

The Paris pound = 7561 } The ounce = 472.5625 } English. The gros = 59.0703 } Troy. The grain = .8194 } Grains.

II. To Reduce English Troy to Paris Weight.

The English Troy pound } = 7021. } of 12 ounces } } The Troy ounce = 585.0830 } The dram of 60 grs. = 73.1353 } Paris The penny weight, or } = 29.2540 } grains. denier, of 24 grs. } } The scruple, of 20 grs. = 24.3784 }

III. To Reduce English Averdupois to Paris Weight.

The averdupois pound of } } 16 ounces, or 7000 } = 8538. } Paris Troy grains. } } grains. The ounce = 533.6250 }

Sec. 2. Long and Cubical Measures.

To reduce Paris feet or inches into } English, multiply by } 1.065977 English feet or inches into Paris, } divide by }

To reduce Paris cubic feet or inches } to English, multiply by } English cubic feet or inches to Paris, } 1.211278 divide by }

Or by means of the following tables:

IV. To Reduce Paris Long Measure to English.

The Paris royal foot of } } 12 inches } = 12.7977 } English The inch = 1.0659 } The line, or 1/12 of an inch = .0888 } inches. The 1/12 of a line = .0074 }

V. To Reduce English Long Measure to French.

The English foot = 11.2596 } The inch = .9383 } The 1/8 of an inch = .1173 } Paris inches. The 1/10 = .0938 } The line, or 1/12 = .0782 }

VI. To Reduce French Cube Measure to English.

The Paris } English { } cube foot = 1.211278 } cubical { 2093.088384 } The cubic } feet, { } inches. inch = .000700 } or { 1.211278 }

VII. To Reduce English Cube Measure to French.

The English cube foot, } or 1728 cubical inches } = 1427.4864 } French The cubical inch = .8260 } cubical The cube tenth = .0008 } inches.

Sec. 3. Measure of Capacity.

The Paris pint contains 58.145[63] English cubical inches, and the English wine pint contains 28.85 cubical inches; or, the Paris pint contains 2.01508 English pints, and the English pint contains .49617 Paris pints; hence,

To reduce the Paris pint to the English, } multiply by } 2.01508. To reduce the English pint to the } Paris, divide by }

No. VI.

TABLE of the Weights of the different Gasses, at 28 French inches, or 29.84 English inches barometrical pressure, and at 10 deg. (54.5 deg.) of temperature, expressed in English measure and English Troy weight.

Names of the Gasses. Weight of a Weight of a cubical inch. cubical foot. (A) qrs. oz. dr. qrs. Atmospheric air .32112 1 1 15 Azotic gas .30064 1 0 39.5 Oxygen gas .34211 1 1 51 Hydrogen gas .02394 0 0 41.26 Carbonic acid gas .44108 1 4 41 (B) Nitrous gas .37000 1 2 39 Ammoniacal gas .18515 0 5 19.73 Sulphurous acid gas .71580 2 4 38

[Note A: These five were ascertained by Mr Lavoisier himself.—E.]

[Note B: The last three are inserted by Mr Lavoisier upon the authority of Mr Kirwan.—E.]

No. VII.

Tables of the Specific Gravities of different bodies.

Sec. 1. Metallic Substances.

GOLD.

Pure gold of 24 carats melted but not hammered 19.2581 The same hammered 19.3617 Gold of the Parisian standard, 22 carats fine, not hammered(A) 17.4863 The same hammered 17.5894 Gold of the standard of French coin, 21-22/32 carats fine, not hammered 17.4022 The same coined 17.6474 Gold of the French trinket standard, 20 carats fine, not hammered 15.7090 The same hammered 15.7746

[Note A: The same with Sterling.]

SILVER.

Pure or virgin silver, 24 deniers, not hammered 10.4743 The same hammered 10.5107 Silver of the Paris standard, 11 deniers 10 grains fine, not hammered(B) 10.1752 The same hammered 10.3765 Silver, standard of French coin, 10 deniers 21 grains fine, not hammered 10.0476 The same coined 10.4077

[Note B: This is 10 grs. finer than Sterling.]

PLATINA.

Crude platina in grains 15.6017 The same, after being treated with muriatic acid 16.7521 Purified platina, not hammered 19.5000 The same hammered 20.3366 The same drawn into wire 21.0417 The same passed through rollers 22.0690

COPPER AND BRASS.

Copper, not hammered 7.7880 The same wire drawn 8.8785 Brass, not hammered 8.3958 The same wire drawn 8.5441

IRON AND STEEL.

Cast iron 7.2070 Bar iron, either screwed or not 7.7880 Steel neither tempered nor screwed 7.8331 Steel screwed but not tempered 7.8404 Steel tempered and screwed 7.8180 Steel tempered and not screwed 7.8163

TIN.

Pure tin from Cornwall melted and not screwed 7.2914 The same screwed 7.2994 Malacca tin, not screwed 7.2963 The same screwed 7.3065 Molten lead 11.3523 Molten zinc 7.1908 Molten bismuth 9.8227 Molten cobalt 7.8119 Molten arsenic 5.7633 Molten nickel 7.8070 Molten antimony 6.7021 Crude antimony 4.0643 Glass of antimony 4.9464 Molybdena 4.7385 Tungstein 6.0665 Mercury 13.5681

Sec. 2. Precious Stones.

White Oriental diamond 3.5212 Rose-coloured Oriental ditto 3.5310 Oriental ruby 4.2833 Spinell ditto 3.7600 Ballas ditto 3.6458 Brasillian ditto 3.5311 Oriental topas 4.0106 Ditto Pistachio ditto 4.0615 Brasillian ditto 3.5365 Saxon topas 3.5640 Ditto white ditto 3.5535 Oriental saphir 3.9941 Ditto white ditto 3.9911 Saphir of Puy 4.0769 Ditto of Brasil 3.1307 Girasol 4.0000 Ceylon jargon 4.4161 Hyacinth 3.6873 Vermillion 4.2299 Bohemian garnet 4.1888 Dodecahedral ditto 4.0627 Syrian ditto 4.0000 Volcanic ditto, with 24 sides 2.4684 Peruvian emerald 2.7755 Crysolite of the jewellers 2.7821 Ditto of Brasil 2.6923 Beryl, or Oriental aqua marine 3.5489 Occidental aqua marine 2.7227

Sec. 3. Silicious Stones.

Pure rock cristal of Madagascar 2.6530 Ditto of Brasil 2.6526 Ditto of Europe, or gelatinous 2.6548 Cristallized quartz 2.6546 Amorphous ditto 2.6471 Oriental agate 2.5901 Agate onyx 2.6375 Transparent calcedony 2.6640 Carnelian 2.6137 Sardonyx 2.6025 Prase 2.5805 Onyx pebble 2.6644 Pebble of Rennes 2.6538 White jade 2.9502 Green jade 2.9660 Red jasper 2.6612 Brown ditto 2.6911 Yellow ditto 2.7101 Violet ditto 2.7111 Gray ditto 2.7640 Jasponyx 2.8160 Black prismatic hexahedral schorl 3.3852 Black spary ditto 3.3852 Black amorphous schorl, called antique basaltes 2.9225 Paving stone 2.4158 Grind stone 2.1429 Cutler's stone 2.1113 Fountainbleau stone 2.5616 Scyth stone of Auvergne 2.5638 Ditto of Lorrain 2.5298 Mill stone 2.4835 White flint 2.5941 Blackish ditto 2.5817

Sec. 4. Various Stones, &c.

Opake green Italian serpentine, or gabro of the Florentines 2.4295 Coarse Briancon chalk 2.7274 Spanish chalk 2.7902 Foliated lapis ollaris of Dauphiny 2.7687 Ditto ditto from Sweden 2.8531 Muscovy talc 2.7917 Black mica 2.9004 Common schistus or slate 2.6718 New slate 2.8535 White rasor hone 2.8763 Black and white hone 3.1311 Rhombic or Iceland cristal 2.7151 Pyramidal calcareous spar 2.7141 Oriental or white antique alabaster 2.7302 Green Campan marble 2.7417 Red Campan marble 2.7242 White Carara marble 2.7168 White Parian marble 2.8376 Various kinds of calcareous stones } from 1.3864 used in France for building. } to 2.3902 Heavy spar 4.4300 White fluor 3.1555 Red ditto 3.1911 Green ditto 3.1817 Blue ditto 3.1688 Violet ditto 3.1757 Red scintilant zeolite from Edelfors 2.4868 White scintilant zeolite 2.0739 Cristallized zeolite 2.0833 Black pitch stone 2.0499 Yellow pitch stone 2.0860 Red ditto 2.6695 Blackish ditto 2.3191 Red porphyry 2.7651 Ditto of Dauphiny 2.7033 Green serpentine 2.8960 Black ditto of Dauphiny, called variolite 2.9339 Green ditto from Dauphiny 2.9883 Ophites 2.9722 Granitello 3.0626 Red Egyptian granite 2.6541 Beautiful red granite 2.7609 Granite of Girardmas 2.7163 Pumice stone .9145 Lapis obsidianus 2.3480 Pierre de Volvic 2.3205 Touch stone 2.4153 Basaltes from Giants Causeway 2.8642 Ditto prismatic from Auvergne 2.4153 Glass gall 2.8548 Bottle glass 2.7325 Green glass 2.6423 White glass 2.8922 St Gobin cristal 2.4882 Flint glass 3.3293 Borax glass 2.6070 Seves porcelain 2.1457 Limoges ditto 2.3410 China ditto 2.3847 Native sulphur 2.0332 Melted sulphur 1.9907 Hard peat 1.3290 Ambergrease .9263 Yellow transparent amber 1.0780

Sec. 5. Liquids.

Distilled water 1.0000 Rain water 1.0000 Filtered water of the Seine 1.00015 Arcueil water 1.00046 Avray water 1.00043 Sea water 1.0263 Water of the Dead Sea 1.2403 Burgundy wine .9915 Bourdeaux ditto .9939 Malmsey Madeira 1.0382 Red beer 1.0338 White ditto 1.0231 Cyder 1.0181 Highly rectified alkohol .8293 Common spirits of wine .8371

Alkohol 15 pts. water 1 part. .8527 14 2 .8674 13 3 .8815 12 4 .8947 11 5 .9075 10 6 .9199 9 7 .9317 8 8 .9427 7 9 .9519 6 10 .9594 5 11 .9674 4 12 .9733 3 13 .9791 2 14 .9852 1 15 .9919

Sulphuric ether .7394 Nitric ether .9088 Muriatic ether .7298 Acetic ether .8664 Sulphuric acid 1.8409 Nitric ditto 1.2715 Muriatic ditto 1.1940 Red acetous ditto 1.0251 White acetous ditto 1.0135 Distilled ditto ditto 1.0095 Acetic ditto 1.0626 Formic ditto .9942 Solution of caustic ammoniac, or volatil alkali fluor .8970 Essential or volatile oil of turpentine .8697 Liquid turpentine .9910 Volatile oil of lavender .8938 Volatile oil of cloves 1.0363 Volatile oil of cinnamon 1.0439 Oil of olives .9153 Oil of sweet almonds .9170 Lintseed oil .9403 Oil of poppy seed .9288 Oil of beech mast .9176 Whale oil .9233 Womans milk 1.0203 Mares milk 1.0346 Ass milk 1.0355 Goats milk 1.0341 Ewe milk 1.0409 Cows milk 1.0324 Cow whey 1.0193 Human urine 1.0106

Sec. 6. Resins and Gums

Common yellow or white rosin 1.0727 Arcanson 1.0857 Galipot(A) 1.0819 Baras(A) 1.0441 Sandarac 1.0920 Mastic 1.0742 Storax 1.1098 Opake copal 1.1398 Transparent ditto 1.0452 Madagascar ditto 1.0600 Chinese ditto 1.0628 Elemi 1.0182 Oriental anime 1.0284 Occidental ditto 1.0426 Labdanum 1.1862 Ditto in tortis 2.4933 Resin of guaiac 1.2289 Ditto of jallap 1.2185 Dragons blood 1.2045 Gum lac 1.1390 Tacamahaca 1.0463 Benzoin 1.0924 Alouchi(B) 1.0604 Caragna(C) 1.1244 Elastic gum .9335 Camphor .9887 Gum ammoniac 1.2071 Sagapenum 1.2008 Ivy gum(D) 1.2948 Gamboge 1.2216 Euphorbium 1.1244 Olibanum 1.1732 Myrrh 1.3600 Bdellium 1.3717 Aleppo Scamony 1.2354 Smyrna ditto 1.2743 Galbanum 1.2120 Assafoetida 1.3275 Sarcocolla 1.2684 Opoponax 1.6226 Cherry tree gum 1.4817 Gum Arabic 1.4523 Tragacanth 1.3161 Basora gum 1.4346 Acajou gum(E) 1.4456 Monbain gum(F) 1.4206 Inspissated juice of liquorice 1.7228 —— Acacia 1.5153 —— Areca 1.4573 Terra Japonica 1.3980 Hepatic aloes 1.3586 Socotrine aloes 1.3795 Inspissated juice of St John's wort 1.5263 Opium 1.3366 Indigo .7690 Arnotto .5956 Yellow wax .9648 White ditto .9686 Ouarouchi ditto(G) .8970 Cacao butter .8916 Spermaceti .9433 Beef fat .9232 Veal fat .9342 Mutton fat .9235 Tallow .9419 Hoggs fat .9368 Lard .9478 Butter .9423

[Note A: Resinous juices extracted in France from the Pine. Vide Bomare's Dict.]

[Note B: Odoriferous gum from the tree which produces the Cortex Winteranus. Bomare.]

[Note C: Resin of the tree called in Mexico Caragna, or Tree of Madness. Ibid.]

[Note D: Extracted in Persia and the warm countries from Hedera terrestris.—Bomare.]

[Note E: From a Brasilian tree of this name.—Ibid.]

[Note F: From a tree of this name.—Ibid.]

[Note G: The produce of the Tallow Tree of Guayana. Vide Bomare's Dict.]

Sec. 7. Woods.

Heart of oak 60 years old 1.1700 Cork .2400 Elm trunk .6710 Ash ditto .8450 Beech .8520 Alder .8000 Maple .7550 Walnut .6710 Willow .5850 Linden .6040 Male fir .5500 Female ditto .4980 Poplar .3830 White Spanish ditto .5294 Apple tree .7930 Pear tree .6610 Quince tree .7050 Medlar .9440 Plumb tree .7850 Olive wood .9270 Cherry tree .7150 Filbert tree .6000 French box .9120 Dutch ditto 1.3280 Dutch yew .7880 Spanish ditto .8070 Spanish cypress .6440 American cedar .5608 Pomgranate tree 1.3540 Spanish mulberry tree .8970 Lignum vitae 1.3330 Orange tree .7050

Note—The numbers in the above Table, if the Decimal point be carried three figures farther to the right hand, nearly express the absolute weight of an English cube foot of each substance in averdupois ounces. See No. VIII. of the Appendix.—E.

No. VIII. ADDITIONAL.

RULES for Calculating the Absolute Gravity in English Troy Weight of a Cubic Foot and Inch, English Measure, of any Substance whose Specific Gravity is known[64].

In 1696, Mr Everard, balance-maker to the Exchequer, weighed before the Commissioners of the House of Commons 2145.6 cubical inches, by the Exchequer standard foot, of distilled water, at the temperature of 55 deg. of Fahrenheit, and found it to weigh 1131 oz. 14 dts. Troy, of the Exchequer standard. The beam turned with 6 grs. when loaded with 30 pounds in each scale. Hence, supposing the pound averdupois to weigh 7000 grs. Troy, a cubic foot of water weighs 62-1/2 pounds averdupois, or 1000 ounces averdupois, wanting 106 grains Troy. And hence, if the specific gravity of water be called 1000, the proportional specific gravities of all other bodies will nearly express the number of averdupois ounces in a cubic foot. Or more accurately, supposing the specific gravity of water expressed by 1. and of all other bodies in proportional numbers, as the cubic foot of water weighs, at the above temperature, exactly 437489.4 grains Troy, and the cubic inch of water 253.175 grains, the absolute weight of a cubical foot or inch of any body in Troy grains may be found by multiplying their specific gravity by either of the above numbers respectively.

By Everard's experiment, and the proportions of the English and French foot, as established by the Royal Society and French Academy of Sciences, the following numbers are ascertained.

Paris grains in a Paris cube foot of water = 645511

English grains in a Paris cube foot of water = 529922

Paris grains in an English cube foot of water = 533247

English grains in an English cube foot of water = 437489.4

English grains in an English cube inch of water = 253.175

By an experiment of Picard with the measure and weight of the Chatelet, the Paris cube foot of water contains of Paris grains = 641326

By one of Du Hamel, made with great care = 641376

By Homberg = 641666

These show some uncertainty in measures or in weights; but the above computation from Everard's experiment may be relied on, because the comparison of the foot of England with that of France was made by the joint labours of the Royal Society of London and the French Academy of Sciences: It agrees likewise very nearly with the weight assigned by Mr Lavoisier, 70 Paris pounds to the cubical foot of water.

No. IX.

TABLES for Converting Ounces, Drams, and Grains, Troy, into Decimals of the Troy Pound of 12 Ounces, and for Converting Decimals of the Pound Troy into Ounces, &c.

I. For Grains.

Grains = Pound.

1 .0001736 2 .0003472 3 .0005208 4 .0006944 5 .0008681 6 .0010417 7 .0012153 8 .0013889 9 .0015625 10 .0017361

20 .0034722 30 .0052083 40 .0069444 50 .0086806 60 .0104167 70 .0121528 80 .0138889 90 .0156250

100 .0173611 200 .0374222 300 .0520833 400 .0694444 500 .0868055 600 .1041666 700 .1215277 800 .1388888 900 .1562499 1000 .1736110

2000 .3472220 3000 .5208330 4000 .6944440 5000 .8680550 6000 1.0418660 7000 1.2152770 8000 1.3888880 9000 1.5624990

II. For Drams.

Drams = Pound.

1 .0104167 2 .0208333 3 .0312500 4 .0416667 5 .0520833 6 .0625000 7 .0729167 8 .0833333

III. For Ounces.

Ounces = Pounds.

1 .0833333 2 .1666667 3 .2500000 4 .3333333 5 .4166667 6 .5000000 7 .5833333 8 .6666667 9 .7500000 10 .8333333 11 .9166667 12 1.0000000

IV. Decimals of the Pound into Ounces, &c.

Tenth parts.

lib. = oz. dr. gr.

0.1 1 1 36 0.2 2 3 12 0.3 3 4 48 0.4 4 6 24 0.5 6 0 0 0.6 7 1 36 0.7 8 3 12 0.8 9 4 48 0.9 10 6 24

Hundredth parts.

0.01 0 0 57.6 0.02 0 1 55.2 0.03 0 2 52.8 0.04 0 3 50.4 0.05 0 4 48.0 0.06 0 5 45.6 0.07 0 6 43.2 0.08 0 7 40.8 0.09 0 3 38.4

Thousandths.

0.001 0 0 5.76 0.002 0 0 11.52 0.003 0 0 17.28 0.004 0 0 23.04 0.005 0 0 28.80

lib. = grs.

0.006 34.56 0.007 40.32 0.008 46.08 0.009 51.84

Ten thousandth parts.

0.0001 0.576 0.0002 1.152 0.0003 1.728 0.0004 2.304 0.0005 2.880 0.0006 3.456 0.0007 4.032 0.0008 4.608 0.0009 5.184

Hundred thousandth parts.

0.00001 0.052 0.00002 0.115 0.00003 0.173 0.00004 0.230 0.00005 0.288 0.00006 0.346 0.00007 0.403 0.00008 0.461 0.00009 0.518

No. X.

TABLE of the English Cubical Inches and Decimals corresponding to a determinate Troy Weight of Distilled Water at the Temperature of 55 deg., calculated from Everard's experiment.

For Grains.

Grs. Cubical inches.

1 = .0039 2 .0078 3 .0118 4 .0157 5 .0197 6 .0236 7 .0275 8 .0315 9 .0354 10 .0394 20 .0788 30 .1182 40 .1577 50 .1971

For Drams.

Drams. Cubical inches.

1 = .2365 2 .4731 3 .7094 4 .9463 5 1.1829 6 1.4195 7 1.6561

For Ounces.

Oz. Cubical inches.

1 = 1.8927 2 3.7855 3 5.6782 4 7.5710 5 9.4631 6 11.3565 7 13.2493 8 15.1420 9 17.0748 10 18.9276 11 20.8204

For Pounds.

Libs. Cubical inches.

1 = 22.7131 2 45.4263 3 68.1394 4 90.8525 5 113.5657 6 136.2788 7 158.9919 8 181.7051 9 204.4183 10 227.1314 50 1135.6574 100 2271.3148 1000 22713.1488

FOOTNOTES:

[62] For the materials of this Article the Translator is indebted to Professor Robertson.

[63] It is said, Belidor Archit. Hydrog. to contain 31 oz. 64 grs. of water, which makes it 58.075 English inches; but, as there is considerable uncertainty in the determinations of the weight of the French cubical measure of water, owing to the uncertainty of the standards made use of, it is better to abide by Mr Everard's measure, which was with the Exchequer standards, and by the proportions of the English and French foot, as established by the French Academy and Royal Society.

[64] The whole of this and the following article was communicated to the Translator by Professor Robinson.—E.



THE PLATES



THE END.