These two butterflies sat, one afternoon, upon the piazza, smoking very large cigars, lost, apparently, in profoundest meditation. Burnham, with his graceful head resting upon one delicate hand, his clear blue eyes full of a pleasant light, and his face warmed by a calm, unconscious smile, might have been revolving some splendid scheme of universal philanthropy. The only utterance, however, forced from him by the sublime thoughts that permeated his soul, was the emission of a white rolling volume of fragrant smoke, accompanied by two words: "Dooced hot!"

Salsbury did not reply. He sat, leaning back, with his fingers interlaced behind his head, and his shadowy eyes downcast, as in sad remembrance of some long-lost love. So might a poet have looked, while steeped in mournfully rapturous daydreams of remembered passion and severance. So might Tennyson's hero have mused, while he sang:

"Oh, that 'twere possible, After long grief and pain, To find the arms of my true love Round me once again!"

But the poetic lips opened not to such numbers. Salsbury gazed long and earnestly, and finally gave vent to his emotion, indicating, with the amber tip of his cigar-tube, the setter that slept in the sunshine at his feet.

"Shocking place, this, for dogs!"—I regret to say he pronounced it "dawgs"—"Why, Carlo is as fat—as fat as—as a—"

His mind was unequal to a simile even, and he terminated the sentence in a murmur.

More silence; more smoke; more profound meditation. Directly Charley Burnham looked around with some show of vitality.

"There comes the stage," said he.

The driver's bugle rang merrily among the drifted sand-hills that lay warm and glowing in the orange light of the setting sun. The young men leaned forward over the piazza-rail and scrutinized the occupants of the vehicle as it appeared.

"Old gentleman and lady, aw, and two children," said Ned Salsbury; "I hoped there would be some nice girls."

This, in a voice of ineffable tenderness and poetry, but with that odd, tired little drawl, so epidemic in some of our universities.

"Look there, by Jove!" cried Charley, with a real interest at last; "now that's what I call a regular thing!"

The "regular thing" was a low, four-wheeled pony-chaise of basket-work, drawn by two jolly little fat ponies, black and shiny as vulcanite, which jogged rapidly in, just far enough behind the stage to avoid its dust.

This vehicle was driven by a young lady of decided beauty, with a spice of Amazonian spirit. She was rather slender and very straight, with a jaunty little hat and feather perched coquettishly above her dark brown hair, which was arranged in one heavy mass and confined in a silken net. Her complexion was clear, without brilliancy; her eyes blue as the ocean horizon, and spanned by sharp, characteristic brows; her mouth small and decisive; and her whole cast of features indicative of quick talent and independence.

Upon the seat beside her sat another damsel, leaning indolently back in the corner of the carriage. This one was a little fairer than the first, having one of those beautiful English complexions of mingled rose and snow, and a dash of gold-dust in her hair where the sun touched it. Her eyes, however, were dark hazel and full of fire, shaded and intensified by their long, sweeping lashes. Her mouth was a rosebud, and her chin and throat faultless in the delicious curve of their lines. In a word, she was somewhat of the Venus-di-Milo type; her companion was more of a Diana. Both were neatly habited in plain travelling-dresses and cloaks of black and white plaid, and both seemed utterly unconscious of the battery of eyes and eye-glasses that enfiladed them from the whole length of the piazza as they passed.

"Who are they?" asked Salsbury; "I don't know them."

"Nor I," said Burnham; "but they look like people to know. They must be somebody."

Half an hour later the hotel-office was besieged by a score of young men, all anxious for a peep at the last names upon the register. It is needless to say that our friends were not in the crowd. Ned Salsbury was no more the man to exhibit curiosity than Charley Burnham was the man to join in a scramble for anything under the sun. They had educated their emotions clear down, out of sight, and piled upon them a mountain of well-bred inertia.

But, somehow or other, these fellows who take no trouble are always the first to gain the end. A special Providence seems to aid the poor, helpless creatures. So, while the crowd still pressed at the office-desk, Jerry Swayne, the head clerk, happened to pass directly by the piazza where the inert ones sat, and, raising a comical eye, saluted them.

"Heavy arrivals to-night. See the turnout?"

"Y-e-s," murmured Ned.

"Old Chapman and family. His daughter drove the pony-phaeton, with her friend, a Miss Thurston. Regular nobby ones. Chapman's the steam-ship man, you know. Worth thousands of millions! I'd like to be connected with his family—by marriage, say!"—and Jerry went off, rubbing his cropped head and smiling all over, as was his wont.

"I know who they are now," said Charley. "Met a cousin of theirs, Joe Faulkner, abroad two years ago. Dooced fine fellow. Army."

The manly art of wagoning is not pursued vigorously at Brant Beach. The roads are too heavy back from the water, and the drive is confined to a narrow strip of wet sand along the shore; so carriages are few, and the pony-chaise became a distinguished element at once. Salsbury and Burnham whirled past it in their light trotting-wagons at a furious pace, and looked hard at the two young ladies in passing, but without eliciting even the smallest glance from them in return.

"Confounded distingue-looking girls, and all that," owned Ned, "but, aw, fearfully unconscious of a fellow!"

This condition of matters continued until the young men were actually driven to acknowledge to each other that they should not mind knowing the occupants of the pony carriage. It was a great concession, and was rewarded duly. A bright, handsome boy of seventeen, Miss Thurston's brother, came to pass a few days at the seaside, and fraternized with everybody, but was especially delighted with Ned Salsbury, who took him out sailing and shooting, and, I am afraid, gave him cigars stealthily, when out of range of Miss Thurston's fine eyes. The result was that the first time the lad walked on the beach with the two girls and met the young man, introductions of an enthusiastic nature were instantly sprung upon them. An attempt at conversation followed.

"How do you like Brant Beach?" asked Ned.

"Oh, it is a very pretty place," said Miss Chapman, "but not lively enough."

"Well, Burnham and I find it pleasant; aw, we have lots of fun."

"Indeed! Why, what do you do?"

"Oh, I don't know. Everything."

"Is the shooting good? I saw you with your guns yesterday."

"Well, there isn't a great deal of game. There is some fishing, but we haven't caught much."

"How do you kill time, then?"

Salsbury looked puzzled.

"Aw—it is a first-rate air, you know. The table is good, and you can sleep like a top. And then, you see, I like to smoke around, and do nothing, on the sea-shore. It is real jolly to lie on the sand, aw, with all sorts of little bugs running over you, and listen to the water swashing about!"

"Let's try it!" cried vivacious Miss Chapman; and down she sat on the sand. The others followed her example, and in five minutes they were picking up pretty pebbles and chatting away as sociably as could be. The rumbling of the warning gong surprised them.

At dinner Burnham and Salsbury took seats opposite the ladies, and were honored with an introduction to papa and mamma, a very dignified, heavy, rosy, old-school couple, who ate a good deal and said very little. That evening, when flute and viol wooed the lotos-eaters to agitate the light fantastic toe, these young gentlemen found themselves in dancing humor, and revolved themselves into a grievous condition of glow and wilt in various mystic and intoxicating measures with their new-made friends.

On retiring, somewhat after midnight, Miss Thurston paused while "doing her hair," and addressed Miss Chapman.

"Did you observe, Hattie, how very handsome those gentlemen are? Mr. Burnham looks like a prince of the sang azur, and Mr. Salsbury like his poet-laureate."

"Yes, dear," responded Hattie; "I have been considering those flowers of the field and lilies of the valley."

"Ned," said Charlie, at about the same time, "we won't find anything nicer here this season, I think."

"They're pretty worth while," replied Ned, "and I'm rather pleased with them."

"Which do you like best?"

"Oh, bother! I haven't thought of that yet."

The next day the young men delayed their "constitutional" until the ladies were ready to walk, and the four strolled off together, mamma and the children following in the pony-chaise. At the rocks on the end of the point Ned got his feet very wet fishing up specimens of seaweed for the damsels; and Charley exerted himself super-humanly in assisting them to a ledge which they considered favorable for sketching purposes.

In the afternoon a sail was arranged, and they took dinner on board the boat, with any amount of hilarity and a good deal of discomfort. In the evening more dancing and vigorous attentions to both the young ladies, but without a shadow of partiality being shown by either of the four.

This was very nearly the history of many days. It does not take long to get acquainted with people who are willing, especially at watering-places; and in the course of a few weeks these young folks were, to all intents and purposes, old friends—calling each other by their given names, and conducting themselves with an easy familiarity quite charming to behold. Their amusements were mostly in common now. The light wagons were made to hold two each instead of one, and the matinal snipe escaped death, and was happy over his early worm.

One day, however, Laura Thurston had a headache, and Hattie Chapman stayed at home to take care of her; so Burnham and Salsbury had to amuse themselves alone. They took their boat and idled about the waters inside the point, dozing under an awning, smoking, gaping, and wishing that headaches were out of fashion, while the taciturn and tarry skipper instructed the dignified and urbane Thomas in the science of trolling for blue-fish.

At length Ned tossed his cigar-end overboard and braced himself for an effort.

"I say, Charlie," said he, "this sort of thing can't go on forever, you know. I've been thinking lately."

"Phenomenon!" replied Charlie; "and what have you been thinking about?"

"Those girls. We've got to choose."

"Why? Isn't it well enough as it is?"

"Yes—so far. But I think, aw, that we don't quite do them justice. They're grands partis, you see. I hate to see clever girls wasting themselves on society, waiting and waiting, and we fellows swimming about just like fish around a hook that isn't baited properly."

Charley raised himself upon his elbow.

"You don't mean to tell me, Ned, that you have matrimonial intentions?"

"Oh, no! Still, why not? We've all got to come to it some day, I suppose."

"Not yet, though. It is a sacrifice we can escape for some years yet."

"Yes—of course—some years; but we may begin to look about us a bit. I'm, aw, I'm six and twenty, you know."

"And I'm very near that. I suppose a fellow can't put off the yoke too long. After thirty chances aren't so good. I don't know, by Jove! but what we ought to begin thinking of it."

"But it is a sacrifice. Society must lose a fellow, though, one time or another. And I don't believe we will ever do better than we can now."

"Hardly, I suspect."

"And we're keeping other fellows away, maybe. It is a shame!"

Thomas ran his line in rapidly, with nothing on the hook.

"Cap'n Hull," he said, gravely, "I had the biggest kind of a fish then I'm sure; but d'rectly I went to pull him in, sir, he took and let go."

"Yaas," muttered the taciturn skipper, "the biggest fish allers falls back inter the warter."

"I've been thinking a little about this matter, too," said Charlie, after a pause, "and I had about concluded we ought to pair off. But I'll be confounded if I know which is the best! They're both nice girls."

"There isn't much choice," Ned replied. "If they were as different, now, as you and me, I'd take the blonde, of course, aw, and you'd take the brunette. But Hattie Chapman's eyes are blue, and her hair isn't black, you know, so you can't call her dark, exactly."

"No more than Laura is exactly light. Her hair is brown more than golden, and her eyes are hazel. Hasn't she a lovely complexion, though? By Jove!"

"Better than Hattie's. Yet I don't know but Hattie's features are a little the best."

"They are. Now, honest, Ned, which do you prefer? Say either; I'll take the one you don't want. I haven't any choice."

"Neither have I."

"How shall we settle?"

"Aw, throw for it?"

"Yes. Isn't there a backgammon board forward, in that locker, Thomas?"

The board was found and the dice produced.

"The highest takes which?"

"Say Laura Thurston."

"Very good; throw."

"You first."

"No. Go on."

Charlie threw with about the same amount of excitement he might have exhibited in a turkey raffle.

"Five-three," said he; "now for your luck."

"Six-four! Laura's mine. Satisfied?"

"Perfectly—if you are. If not, I don't mind exchanging."

"Oh, no. I'm satisfied."

Both reclined upon the deck once more with a sigh of relief, and a long silence followed.

"I say," began Charlie, after a time, "it is a comfort to have these little matters arranged without any trouble, eh?"

"Y-e-s."

"Do you know, I think I'll marry mine?"

"I will, if you will."

"Done! It is a bargain."

This "little matter" being arranged, a change gradually took place in the relations of the four. Ned Salsbury began to invite Laura Thurston out driving and bathing somewhat oftener than before, and Hattie Chapman somewhat less often; while Charlie Burnham followed suit with the last-named young lady. As the line of demarcation became fixed, the damsels recognized it, and accepted with gracious readiness the cavaliers that Fate, through the agency of a chance-falling pair of dice, had allotted to them.

The other guests of the house remarked the new position of affairs, and passed whispers about it to the effect that the girls had at last succeeded in getting their fish on hooks instead of in a net. No suitors could have been more devoted than our friends. It seemed as if each knight bestowed upon the chosen one all the attentions he had hitherto given to both; and whether they went boating, sketching, or strolling upon the sands, they were the very picture of a partie carree of lovers.

Naturally enough, as the young men became more in earnest, with the reticence common to my sex they spoke less frequently and freely on the subject. Once, however, after an unusually pleasant afternoon, Salsbury ventured a few words.

"I say, we're a couple of lucky dogs! Who'd have thought now, aw, that our summer was going to turn out so well? I'm sure I didn't. How do you get along, Charley, boy?"

"Deliciously. Smooth sailing enough. Wasn't it a good idea, though, to pair off? I'm just as happy as a bee in clover. You seem to prosper, too, heh?"

"Couldn't ask anything different. Nothing but devotion, and all that. I'm delighted. I say, when are you going to pop?"

"Oh, I don't know. It is only a matter of form. Sooner the better, I suppose, and have it over."

"I was thinking of next week. What do you say to a quiet picnic down on the rocks, and a walk afterwards? We can separate, you know, and do the thing up systematically."

"All right. I will, if you will."

"That's another bargain. I notice there isn't much doubt about the results."

"Hardly!"

A close observer might have seen that the gentlemen increased their attentions a little from time to time. The objects of their devotion perceived it, and smiled more and more graciously upon them.

The day set for the picnic arrived duly, and was radiant. It pains me to confess that my heroes were a trifle nervous. Their apparel was more gorgeous and wonderful than ever, and Thomas, who was anxious to be off courting Miss Chapman's lady's-maid, found his masters dreadfully exacting in the matter of hair-dressing. At length, however, the toilet was over, and "Solomon in all his glory" would have been vastly astonished at finding himself "arrayed as one of these."

The boat lay at the pier, receiving large quantities of supplies for the trip, stowed by Thomas, under the supervision of the grim and tarry skipper. When all was ready the young men gingerly escorted their fair companions aboard, the lines were cast off, and the boat glided gently down the bay, leaving Thomas free to fly to the smart presence of Susan Jane and to draw glowing pictures for her of a neat little porter-house in the city, wherein they should hold supreme sway, be happy with each other, and let rooms up-stairs for single gentlemen.

The brisk land breeze swelling the sail, the fluttering of the gay little flag at the gaff, the musical rippling of water under the counter, and the spirited motion of the boat combined, with the bland air and pleasant sunshine, to inspire the party with much vivacity. They had not been many minutes afloat before the guitar-case was opened, and the girls' voices—Laura's soprano and Hattie's contralto—rang melodiously over the waves, mingled with feeble attempt at bass accompaniment from their gorgeous guardians.

Before these vocal exercises wearied, the skipper hauled down his jib, let go his anchor, and brought the craft to just off the rocks; and bringing the yawl alongside, unceremoniously plucked the girls down into it, without giving their cavaliers a chance for the least display of agile courtliness. Rowing ashore, this same tarry person left them huddled upon the beach, with their hopes, their hampers, their emotions, and their baskets, and returned to the vessel to do a little private fishing on his own account till wanted.

The maidens gave vent to their high spirits by chasing each other among the rocks, gathering shells and seaweed for the construction of those ephemeral little ornaments—fair, but frail—in which the sex delights, singing, laughing, quoting poetry, attitudinizing upon the peaks and ledges of the fine old boulders—mossy and weedy and green with the wash of a thousand storms, worn into strange shapes, and stained with the multitudinous dyes of mineral oxidization—and, in brief, behaved themselves with all the charming abandon that so well becomes young girls set free, by the entourage of a holiday ramble, from the buckram and clear-starch of social etiquette.

Meanwhile Ned and Charley smoked the pensive cigar of preparation in a sheltered corner, and gazed out seaward, dreaming and seeing nothing.

Erelong the breeze and the romp gave the young ladies not only a splendid color and sparkling eyes, but excellent appetites also. The baskets and hampers were speedily unpacked, the table-cloth laid on a broad, flat stone, so used by generations of Brant House picnickers, and the party fell to. Laura's beautiful hair, a little disordered, swept her blooming cheek, and cast a pearly shadow upon her neck. Her bright eyes glanced archly out from under her half-raised veil, and there was something inexpressibly naive in the freedom with which she ate, taking a bird's wing in her fingers, and boldly attacking it with teeth as white and even as can be imagined. Notwithstanding all the mawkish nonsense that has been put forth by sentimentalists concerning feminine eating, I hold that it is one of the nicest things in the world to see a pretty woman enjoying the creature comforts; and Byron himself, had he been one of this picnic party, would have been unable to resist the admiration that filled the souls of Burnham and Salsbury. Hattie Chapman stormed the fortress of boned turkey with a gusto equal to that of Laura, and made highly successful raids upon certain outlying salads and jellies. The young men were not in a very ravenous condition; they were, as I have said, a little nervous, and bent their energies principally to admiring the ladies and coquetting with pickled oysters.

When the repast was over, with much accompanying chat and laughter, Ned glanced significantly at Charley, and proposed to Laura that they should walk up the beach to a place where, he said, there were "some pretty rocks and things, you know." She consented, and they marched off. Hattie also arose, and took her parasol, as if to follow, but Charley remained seated, tracing mysterious diagrams upon the table-cloth with his fork, and looked sublimely unconscious.

"Sha'n't we walk, too?" Hattie asked.

"Oh, why, the fact is," said he, hesitatingly, "I—I sprained my ankle getting out of that confounded boat, so I don't feel much like exercising just now."

The young girl's face expressed concern.

"That is too bad! Why didn't you tell us of it before? Is it painful? I'm so sorry!"

"N-no—it doesn't hurt much. I dare say it will be all right in a minute. And then—I'd just as soon stay here—with you—as to walk anywhere."

This very tenderly, with a little sigh.

Hattie sat down again, and began to talk to this factitious cripple in the pleasant, purring way some damsels have, about the joys of the sea-shore, the happy summer that was, alas! drawing to a close, her own enjoyment of life, and kindred topics, till Charley saw an excellent opportunity to interrupt with some aspirations of his own, which, he averred, must be realized before his life would be considered a satisfactory success.

If you had ever been placed in analogous circumstances, you know, of course, just about the sort of thing that was being said by the two gentlemen at nearly the same moment: Ned, loitering slowly along the sands with Laura on his arm, and Charley, stretched in indolent picturesqueness upon the rocks, with Hattie sitting beside him. If you do not know from experience, ask any candid friend who has been through the form and ceremony of an orthodox proposal.

When the pedestrians returned the two couples looked very hard at each other. All were smiling and complacent, but devoid of any strange or unusual expression. Indeed, the countenance is subject to such severe education, in good society, that one almost always looks smiling and complacent. Demonstration is not fashionable, and a man must preserve the same demeanor over the loss of a wife or a glove-button, over the gift of a heart's whole devotion or a bundle of cigars. Under all these visitations the complacent smile is in favor as the neatest, most serviceable, and convenient form of non-committalism.

The sun was approaching the blue range of misty hills that bounded the mainland swamps by this time; so the skipper was signalled, the dinner paraphernalia gathered up, and the party were soon en route for home once more. When the young ladies were safely in, Ned and Charley met in their room, and each caught the other looking at him stealthily. Both smiled.

"Did I give you time, Charley?" asked Ned; "we came back rather soon."

"Oh, yes; plenty of time."

"Did you—aw, did you pop?

"Y-yes. Did you?"

"Well—yes."

"And you were—"

"Rejected, by Jove!"

"So was I!"

The day following this disastrous picnic the baggage of Mr. Edwin Salsbury and Mr. Charles Burnham was sent to the depot at Wikhasset Station, and they presented themselves at the hotel-office with a request for their bill. As Jerry Swayne deposited their key upon its hook, he drew forth a small tri-cornered billet from the pigeon-hole beneath, and presented it.

"Left for you this morning, gentlemen."

It was directed to both, and Charley read it over Ned's shoulder. It ran thus:

"DEAR BOYS: The next time you divert yourselves by throwing dice for two young ladies, we pray you not to do so in the presence of a valet who is upon terms of intimacy with the maid of one of them.

"With many sincere thanks for the amusement you have given us—often when you least suspected it—we bid you a lasting adieu, and remain, with the best wishes,

"HATTIE CHAPMAN, "LAURA THURSTON.

"Brant House, "Wednesday."

"It is all the fault of that, aw—that confounded Thomas!" said Ned.

So Thomas was discharged.

[4] Atlantic Monthly, June, 1863.



THE TACHYPOMP.[5]

A MATHEMATICAL DEMONSTRATION.

BY E.P. MITCHELL.

There was nothing mysterious about Professor Surd's dislike for me. I was the only poor mathematician in an exceptionally mathematical class. The old gentleman sought the lecture-room every morning with eagerness, and left it reluctantly. For was it not a thing of joy to find seventy young men who, individually and collectively, preferred x to XX; who had rather differentiate than dissipate; and for whom the limbs of the heavenly bodies had more attractions than those of earthly stars upon the spectacular stage?

So affairs went on swimmingly between the Professor of Mathematics and the Junior Class at Polyp University. In every man of the seventy the sage saw the logarithm of a possible La Place, of a Sturm, or of a Newton. It was a delightful task for him to lead them through the pleasant valleys of conic sections, and beside the still waters of the integral calculus. Figuratively speaking, his problem was not a hard one. He had only to manipulate, and eliminate, and to raise to a higher power, and the triumphant result of examination day was assured.

But I was a disturbing element, a perplexing unknown quantity, which had somehow crept into the work, and which seriously threatened to impair the accuracy of his calculations. It was a touching sight to behold the venerable mathematician as he pleaded with me not so utterly to disregard precedent in the use of cotangents; or as he urged, with eyes almost tearful, that ordinates were dangerous things to trifle with. All in vain. More theorems went on to my cuff than into my head. Never did chalk do so much work to so little purpose. And, therefore, it came that Furnace Second was reduced to zero in Professor Surd's estimation. He looked upon me with all the horror which an unalgebraic nature could inspire. I have seen the Professor walk around an entire square rather than meet the man who had no mathematics in his soul.

For Furnace Second were no invitations to Professor Surd's house. Seventy of the class supped in delegations around the periphery of the Professor's tea-table. The seventy-first knew nothing of the charms of that perfect ellipse, with its twin bunches of fuchsias and geraniums in gorgeous precision at the two foci.

This, unfortunately enough, was no trifling deprivation. Not that I longed especially for segments of Mrs. Surd's justly celebrated lemon pies; not that the spheroidal damsons of her excellent preserving had any marked allurements; not even that I yearned to hear the Professor's jocose table-talk about binomials, and chatty illustrations of abstruse paradoxes. The explanation is far different. Professor Surd had a daughter. Twenty years before, he made a proposition of marriage to the present Mrs. S. He added a little Corollary to his proposition not long after. The Corollary was a girl.

Abscissa Surd was as perfectly symmetrical as Giotto's circle, and as pure, withal, as the mathematics her father taught. It was just when spring was coming to extract the roots of frozen-up vegetation that I fell in love with the Corollary. That she herself was not indifferent I soon had reason to regard as a self-evident truth.

The sagacious reader will already recognize nearly all the elements necessary to a well-ordered plot. We have introduced a heroine, inferred a hero, and constructed a hostile parent after the most approved model. A movement for the story, a Deus ex machina, is alone lacking. With considerable satisfaction I can promise a perfect novelty in this line, a Deus ex machina never before offered to the public.

It would be discounting ordinary intelligence to say that I sought with unwearying assiduity to figure my way into the stern father's good-will; that never did dullard apply himself to mathematics more patiently than I; that never did faithfulness achieve such meagre reward. Then I engaged a private tutor. His instructions met with no better success.

My tutor's name was Jean Marie Rivarol. He was a unique Alsatian—though Gallic in name, thoroughly Teuton in nature; by birth a Frenchman, by education a German. His age was thirty; his profession, omniscience; the wolf at his door, poverty; the skeleton in his closet, a consuming but unrequited passion. The most recondite principles of practical science were his toys; the deepest intricacies of abstract science his diversions. Problems which were foreordained mysteries to me were to him as clear as Tahoe water. Perhaps this very fact will explain our lack of success in the relation of tutor and pupil; perhaps the failure is alone due to my own unmitigated stupidity. Rivarol had hung about the skirts of the University for several years; supplying his few wants by writing for scientific journals, or by giving assistance to students who, like myself, were characterized by a plethora of purse and a paucity of ideas; cooking, studying and sleeping in his attic lodgings; and prosecuting queer experiments all by himself.

We were not long discovering that even this eccentric genius could not transplant brains into my deficient skull. I gave over the struggle in despair. An unhappy year dragged its slow length around. A gloomy year it was, brightened only by occasional interviews with Abscissa, the Abbie of my thoughts and dreams.

Commencement day was coming on apace. I was soon to go forth, with the rest of my class, to astonish and delight a waiting world. The Professor seemed to avoid me more than ever. Nothing but the conventionalities, I think kept him from shaping his treatment of me on the basis of unconcealed disgust.

At last, in the very recklessness of despair, I resolved to see him, plead with him, threaten him if need be, and risk all my fortunes on one desperate chance. I wrote him a somewhat defiant letter, stating my aspirations, and, as I flattered myself, shrewdly giving him a week to get over the first shock of horrified surprise. Then I was to call and learn my fate.

During the week of suspense I nearly worried myself into a fever. It was first crazy hope, and then saner despair. On Friday evening, when I presented myself at the Professor's door, I was such a haggard, sleepy, dragged-out spectre, that even Miss Jocasta, the harsh-favored maiden sister of the Surd's, admitted me with commiserate regard, and suggested pennyroyal tea.

Professor Surd was at a faculty meeting. Would I wait?

Yes, till all was blue, if need be. Miss Abbie?

Abscissa had gone to Wheelborough to visit a school-friend. The aged maiden hoped I would make myself comfortable, and departed to the unknown haunts which knew Jocasta's daily walk.

Comfortable! But I settled myself in a great uneasy chair and waited, with the contradictory spirit common to such junctures, dreading every step lest it should herald the man whom, of all men, I wished to see.

I had been there at least an hour, and was growing right drowsy.

At length Professor Surd came in. He sat down in the dusk opposite me, and I thought his eyes glinted with malignant pleasure as he said, abruptly:

"So, young man, you think you are a fit husband for my girl?"

I stammered some inanity about making up in affection what I lacked in merit; about my expectations, family and the like. He quickly interrupted me.

"You misapprehend me, sir. Your nature is destitute of those mathematical perceptions and acquirements which are the only sure foundations of character. You have no mathematics in you. You are fit for treason, stratagems, and spoils.—Shakespeare. Your narrow intellect cannot understand and appreciate a generous mind. There is all the difference between you and a Surd, if I may say it, which intervenes between an infinitesimal and an infinite. Why, I will even venture to say that you do not comprehend the Problem of the Couriers!"

I admitted that the Problem of the Couriers should be classed rather without my list of accomplishments than within it. I regretted this fault very deeply, and suggested amendment. I faintly hoped that my fortune would be such—

"Money!" he impatiently exclaimed. "Do you seek to bribe a Roman Senator with a penny whistle? Why, boy, do you parade your paltry wealth, which, expressed in mills, will not cover ten decimal places, before the eyes of a man who measures the planets in their orbits, and close crowds infinity itself?"

I hastily disclaimed any intention of obtruding my foolish dollars, and he went on:

"Your letter surprised me not a little. I thought you would be the last person in the world to presume to an alliance here. But having a regard for you personally"—and again I saw malice twinkle in his small eyes—"and still more regard for Abscissa's happiness, I have decided that you shall have her—upon conditions. Upon conditions," he repeated, with a half-smothered sneer.

"What are they?" cried I, eagerly enough. "Only name them."

"Well, sir," he continued, and the deliberation of his speech seemed the very refinement of cruelty, "you have only to prove yourself worthy an alliance with a mathematical family. You have only to accomplish a task which I shall presently give you. Your eyes ask me what it is. I will tell you. Distinguish yourself in that noble branch of abstract science in which, you cannot but acknowledge, you are at present sadly deficient. I will place Abscissa's hand in yours whenever you shall come before me and square the circle to my satisfaction. No! That is too easy a condition. I should cheat myself. Say perpetual motion. How do you like that? Do you think it lies within the range of your mental capabilities? You don't smile. Perhaps your talents don't run in the way of perpetual motion. Several people have found that theirs didn't. I'll give you another chance. We were speaking of the Problem of the Couriers, and I think you expressed a desire to know more of that ingenious question. You shall have the opportunity. Sit down some day, when you have nothing else to do, and discover the principle of infinite speed. I mean the law of motion which shall accomplish an infinitely great distance in an infinitely short time. You may mix in a little practical mechanics, if you choose. Invent some method of taking the tardy Courier over his road at the rate of sixty miles a minute. Demonstrate me this discovery (when you have made it!) mathematically, and approximate it practically, and Abscissa is yours. Until you can, I will thank you to trouble neither myself nor her."

I could stand his mocking no longer. I stumbled mechanically out of the room, and out of the house. I even forgot my hat and gloves. For an hour I walked in the moonlight. Gradually I succeeded to a more hopeful frame of mind. This was due to my ignorance of mathematics. Had I understood the real meaning of what he asked, I should have been utterly despondent.

Perhaps this problem of sixty miles a minute was not so impossible after all. At any rate I could attempt, though I might not succeed. And Rivarol came to my mind. I would ask him. I would enlist his knowledge to accompany my own devoted perseverance. I sought his lodgings at once.

The man of science lived in the fourth story, back. I had never been in his room before. When I entered, he was in the act of filling a beer mug from a carboy labelled Aqua fortis.

"Seat you," he said. "No, not in that chair. That is my Petty Cash Adjuster." But he was a second too late. I had carelessly thrown myself into a chair of seductive appearance. To my utter amazement it reached out two skeleton arms and clutched me with a grasp against which I struggled in vain. Then a skull stretched itself over my shoulder and grinned with ghastly familiarity close to my face.

Rivarol came to my aid with many apologies. He touched a spring somewhere and the Petty Cash Adjuster relaxed its horrid hold. I placed myself gingerly in a plain cane-bottomed rocking-chair, which Rivarol assured me was a safe location.

"That seat," he said, "is an arrangement upon which I much felicitate myself. I made it at Heidelberg. It has saved me a vast deal of small annoyance. I consign to its embraces the friends who bore, and the visitors who exasperate, me. But it is never so useful as when terrifying some tradesman with an insignificant account. Hence the pet name which I have facetiously given it. They are invariably too glad to purchase release at the price of a bill receipted. Do you well apprehend the idea?"

While the Alsatian diluted his glass of Aqua fortis, shook into it an infusion of bitters, and tossed off the bumper with apparent relish, I had time to look around the strange apartment.

The four corners of the room were occupied respectively by a turning-lathe, a Rhumkorff Coil, a small steam-engine and an orrery in stately motion. Tables, shelves, chairs and floor supported an odd aggregation of tools, retorts, chemicals, gas-receivers, philosophical instruments, boots, flasks, paper-collar boxes, books diminutive and books of preposterous size. There were plaster busts of Aristotle, Archimedes, and Comte, while a great drowsy owl was blinking away, perched on the benign brow of Martin Farquhar Tupper. "He always roosts there when he proposes to slumber," explained my tutor. "You are a bird of no ordinary mind. Schlafen Sie wohl."

Through a closet door, half open, I could see a human-like form covered with a sheet. Rivarol caught my glance.

"That," said he, "will be my masterpiece. It is a Microcosm, an Android, as yet only partially complete. And why not? Albertus Magnus constructed an image perfect to talk metaphysics and confute the schools. So did Sylvester II.; so did Robertus Greathead. Roger Bacon made a brazen head that held discourses. But the first named of these came to destruction. Thomas Aquinas got wrathful at some of its syllogisms and smashed its head. The idea is reasonable enough. Mental action will yet be reduced to laws as definite as those which govern the physical. Why should not I accomplish a manikin which shall preach as original discourses as the Rev. Dr. Allchin, or talk poetry as mechanically as Paul Anapest? My Android can already work problems in vulgar fractions and compose sonnets. I hope to teach it the Positive Philosophy."

Out of the bewildering confusion of his effects Rivarol produced two pipes and filled them. He handed one to me.

"And here," he said, "I live and am tolerably comfortable. When my coat wears out at the elbows I seek the tailor and am measured for another. When I am hungry I promenade myself to the butcher's and bring home a pound or so of steak, which I cook very nicely in three seconds by this oxy-hydrogen flame. Thirsty, perhaps, I send for a carboy of Aqua fortis. But I have it charged, all charged. My spirit is above any small pecuniary transaction. I loathe your dirty greenbacks, and never handle what they call scrip."

"But are you never pestered with bills?" I asked. "Don't the creditors worry your life out?"

"Creditors!" gasped Rivarol. "I have learned no such word in your very admirable language. He who will allow his soul to be vexed by creditors is a relic of an imperfect civilization. Of what use is science if it cannot avail a man who has accounts current? Listen. The moment you or any one else enters the outside door this little electric bell sounds me warning. Every successive step on Mrs. Grimier's staircase is a spy and informer vigilant for my benefit. The first step is trod upon. That trusty first step immediately telegraphs your weight. Nothing could be simpler. It is exactly like any platform scale. The weight is registered up here upon this dial. The second step records the size of my visitor's feet. The third his height, the fourth his complexion, and so on. By the time he reaches the top of the first flight I have a pretty accurate description of him right here at my elbow, and quite a margin of time for deliberation and action. Do you follow me? It is plain enough. Only the A B C of my science."

"I see all that," I said, "but I don't see how it helps you any. The knowledge that a creditor is coming won't pay his bill. You can't escape unless you jump out of the window."

Rivarol laughed softly. "I will tell you. You shall see what becomes of any poor devil who goes to demand money of me—of a man of science. Ha! ha! It pleases me. I was seven weeks perfecting my Dun Suppressor. Did you know"—he whispered exultingly—"did you know that there is a hole through the earth's centre? Physicists have long suspected it; I was the first to find it. You have read how Rhuyghens, the Dutch navigator, discovered in Kerguellen's Land an abysmal pit which fourteen hundred fathoms of plumb-line failed to sound. Herr Tom, that hole has no bottom! It runs from one surface of the earth to the antipodal surface. It is diametric. But where is the antipodal spot? You stand upon it. I learned this by the merest chance. I was deep-digging in Mrs. Grimler's cellar, to bury a poor cat I had sacrificed in a galvanic experiment, when the earth under my spade crumbled, caved in, and wonder-stricken I stood upon the brink of a yawning shaft. I dropped a coal-hod in. It went down, down down, bounding and rebounding. In two hours and a quarter that coal-hod came up again. I caught it and restored it to the angry Grimler. Just think a minute. The coal-hod went down, faster and faster, till it reached the centre of the earth. There it would stop, were it not for acquired momentum. Beyond the centre its journey was relatively upward, toward the opposite surface of the globe. So, losing velocity, it went slower and slower till it reached that surface. Here it came to rest for a second and then fell back again, eight thousand odd miles, into my hands. Had I not interfered with it, it would have repeated its journey, time after time, each trip of shorter extent, like the diminishing oscillations of a pendulum, till it finally came to eternal rest at the centre of the sphere. I am not slow to give a practical application to any such grand discovery. My Dun Suppressor was born of it. A trap, just outside my chamber door: a spring in here: a creditor on the trap:—need I say more?"

"But isn't it a trifle inhuman?" I mildly suggested. "Plunging an unhappy being into a perpetual journey to and from Kerguellen's Land, without a moment's warning."

"I give them a chance. When they come up the first time I wait at the mouth of the shaft with a rope in hand. If they are reasonable and will come to terms, I fling them the line. If they perish, 'tis their own fault. Only," he added, with a melancholy smile, "the centre is getting so plugged up with creditors that I am afraid there soon will be no choice whatever for 'em."

By this time I had conceived a high opinion of my tutor's ability. If anybody could send me waltzing through space at an infinite speed, Rivarol could do it. I filled my pipe and told him the story. He heard with grave and patient attention. Then, for full half an hour, he whiffed away in silence. Finally he spoke.

"The ancient cipher has overreached himself. He has given you a choice of two problems, both of which he deems insoluble. Neither of them is insoluble. The only gleam of intelligence Old Cotangent showed was when he said that squaring the circle was too easy. He was right. It would have given you your Liebchen in five minutes. I squared the circle before I discarded pantalets. I will show you the work—but it would be a digression, and you are in no mood for digressions. Our first chance, therefore, lies in perpetual motion. Now, my good friend, I will frankly tell you that, although I have compassed this interesting problem, I do not choose to use it in your behalf. I too, Herr Tom, have a heart. The loveliest of her sex frowns upon me. Her somewhat mature charms are not for Jean Marie Rivarol. She has cruelly said that her years demand of me filial rather than connubial regard. Is love a matter of years or of eternity? This question did I put to the cold, yet lovely Jocasta."

"Jocasta Surd!" I remarked in surprise, "Abscissa's aunt!"

"The same," he said, sadly. "I will not attempt to conceal that upon the maiden Jocasta my maiden heart has been bestowed. Give me your hand, my nephew in affliction as in affection!"

Rivarol dashed away a not discreditable tear, and resumed:

"My only hope lies in this discovery of perpetual motion. It will give me the fame, the wealth. Can Jocasta refuse these? If she can, there is only the trap-door and—Kerguellen's Land!"

I bashfully asked to see the perpetual-motion machine. My uncle in affliction shook his head.

"At another time," he said. "Suffice it at present to say, that it is something upon the principle of a woman's tongue. But you see now why we must turn in your case to the alternative condition—infinite speed. There are several ways in which this may be accomplished, theoretically. By the lever, for instance. Imagine a lever with a very long and a very short arm. Apply power to the shorter arm which will move it with great velocity. The end of the long arm will move much faster. Now keep shortening the short arm and lengthening the long one, and as you approach infinity in their difference of length, you approach infinity in the speed of the long arm. It would be difficult to demonstrate this practically to the Professor. We must seek another solution. Jean Marie will meditate. Come to me in a fortnight. Good-night. But stop! Have you the money—das Geld?"

"Much more than I need."

"Good! Let us strike hands. Gold and Knowledge; Science and Love. What may not such a partnership achieve? We go to conquer thee, Abscissa. Vorwaerts!"

When, at the end of a fortnight, I sought Rivarol's chamber, I passed with some little trepidation over the terminus of the Air Line to Kerguellen's Land, and evaded the extended arms of the Petty Cash Adjuster. Rivarol drew a mug of ale for me, and filled himself a retort of his own peculiar beverage.

"Come," he said at length. "Let us drink success to the TACHYPOMP."

"The TACHYPOMP?"

"Yes. Why not? Tachu, quickly, and pempo, pepompa to send. May it send you quickly to your wedding-day. Abscissa is yours. It is done. When shall we start for the prairies?"

"Where is it?" I asked, looking in vain around the room for any contrivance which might seem calculated to advance matrimonial prospects.

"It is here," and he gave his forehead a significant tap. Then he held forth didactically.

"There is force enough in existence to yield us a speed of sixty miles a minute, or even more. All we need is the knowledge how to combine and apply it. The wise man will not attempt to make some great force yield some great speed. He will keep adding the little force to the little force, making each little force yield its little speed, until an aggregate of little forces shall be a great force, yielding an aggregate of little speeds, a great speed. The difficulty is not in aggregating the forces; it lies in the corresponding aggregation of the speeds. One musket-ball will go, say a mile. It is not hard to increase the force of muskets to a thousand, yet the thousand musket-balls will go no farther, and no faster, than the one. You see, then, where our trouble lies. We cannot readily add speed to speed, as we add force to force. My discovery is simply the utilization of a principle which extorts an increment of speed from each increment of power. But this is the metaphysics of physics. Let us be practical or nothing.

"When you have walked forward, on a moving train, from the rear car, toward the engine, did you ever think what you were really doing?"

"Why, yes, I have generally been going to the smoking-car to have a cigar."

"Tut, tut—not that! I mean, did it ever occur to you on such an occasion, that absolutely you were moving faster than the train? The train passes the telegraph poles at the rate of thirty miles an hour, say. You walk toward the smoking-car at the rate of four miles an hour. Then you pass the telegraph poles at the rate of thirty-four miles. Your absolute speed is the speed of the engine, plus the speed of your own locomotion. Do you follow me?"

I began to get an inkling of his meaning, and told him so.

"Very well. Let us advance a step. Your addition to the speed of the engine is trivial, and the space in which you can exercise it, limited. Now suppose two stations, A and B, two miles distant by the track. Imagine a train of platform cars, the last car resting at station A. The train is a mile long, say. The engine is therefore within a mile of station B. Say the train can move a mile in ten minutes. The last car, having two miles to go, would reach B in twenty minutes, but the engine, a mile ahead, would get there in ten. You jump on the last car, at A, in a prodigious hurry to reach Abscissa, who is at B. If you stay on the last car it will be twenty long minutes before you see her. But the engine reaches B and the fair lady in ten. You will be a stupid reasoner, and an indifferent lover, if you don't put for the engine over those platform cars, as fast as your legs will carry you. You can run a mile, the length of the train, in ten minutes. Therefore, you reach Abscissa when the engine does, or in ten minutes—ten minutes sooner than if you had lazily sat down upon the rear car and talked politics with the brakeman. You have diminished the time by one half. You have added your speed to that of the locomotive to some purpose. Nicht wahr?"

I saw it perfectly; much plainer, perhaps, for his putting in the clause about Abscissa.

He continued:

"This illustration, though a slow one, leads up to a principle which may be carried to any extent. Our first anxiety will be to spare your legs and wind. Let us suppose that the two miles of track are perfectly straight, and make our train one platform car, a mile long, with parallel rails laid upon its top. Put a little dummy engine on these rails, and let it run to and fro along the platform car, while the platform car is pulled along the ground track. Catch the idea? The dummy takes your place. But it can run its mile much faster. Fancy that our locomotive is strong enough to pull the platform car over the two miles in two minutes. The dummy can attain the same speed. When the engine reaches B in one minute, the dummy, having gone a mile a-top the platform car, reaches B also. We have so combined the speeds of those two engines as to accomplish two miles in one minute. Is this all we can do? Prepare to exercise your imagination."

I lit my pipe.

"Still two miles of straight track, between A and B. On the track a long platform car, reaching from A to within a quarter of a mile of B. We will now discard ordinary locomotives and adopt as our motive power a series of compact magnetic engines, distributed underneath the platform car, all along its length."

"I don't understand those magnetic engines."

"Well, each of them consists of a great iron horseshoe, rendered alternately a magnet and not a magnet by an intermittent current of electricity from a battery, this current in its turn regulated by clock-work. When the horseshoe is in the circuit, it is a magnet, and it pulls its clapper toward it with enormous power. When it is out of the circuit, the next second, it is not a magnet, and it lets the clapper go. The clapper, oscillating to and fro, imparts a rotatory motion to a fly-wheel, which transmits it to the drivers on the rails. Such are our motors. They are no novelty, for trial has proved them practicable.

"With a magnetic engine for every truck of wheels, we can reasonably expect to move our immense car, and to drive it along at a speed, say, of a mile a minute.

"The forward end, having but a quarter of a mile to go, will reach B in fifteen seconds. We will call this platform car number 1. On top of number 1 are laid rails on which another platform car, number 2, a quarter of a mile shorter than number 1, is moved in precisely the same way. Number 2, in its turn, is surmounted by number 3, moving independently of the tiers beneath, and a quarter of a mile shorter than number 2. Number 2 is a mile and a half long; number 3 a mile and a quarter. Above, on successive levels, are number 4, a mile long; number 5, three quarters of a mile; number 6, half a mile; number 7, a quarter of a mile, and number 8, a short passenger car, on top of all.

"Each car moves upon the car beneath it, independently of all the others, at the rate of a mile a minute. Each car has its own magnetic engines. Well, the train being drawn up with the latter end of each car resting against a lofty bumping-post at A, Tom Furnace, the gentlemanly conductor, and Jean Marie Rivarol, engineer, mount by a long ladder to the exalted number 8. The complicated mechanism is set in motion. What happens?

"Number 8 runs a quarter of a mile in fifteen seconds and reaches the end of number 7. Meanwhile number 7 has run a quarter of a mile in the same time and reached the end of number 6; number 6, a quarter of a mile in fifteen seconds, and reached the end of number 5; number 5, the end of number 4; number 4, of number 3; number 3, of number 2; number 2, of number 1. And number 1, in fifteen seconds, has gone its quarter of a mile along the ground track, and has reached station B. All this has been done in fifteen seconds. Wherefore, numbers 1, 2, 3, 4, 5, 6, 7, and 8 come to rest against the bumping-post at B, at precisely the same second. We, in number 8, reach B just when number 1 reaches it. In other words, we accomplish two miles in fifteen seconds. Each of the eight cars, moving at the rate of a mile a minute, has contributed a quarter of a mile to our journey, and has done its work in fifteen seconds. All the eight did their work at once, during the same fifteen seconds. Consequently we have been whizzed through the air at the somewhat startling speed of seven and a half seconds to the mile. This is the Tachypomp. Does it justify the name?"

Although a little bewildered by the complexity of cars, I apprehended the general principle of the machine. I made a diagram, and understood it much better. "You have merely improved on the idea of my moving faster than the train when I was going to the smoking car?"

"Precisely. So far we have kept within the bounds of the practicable. To satisfy the Professor, you can theorize in something after this fashion: If we double the number of cars, thus decreasing by one half the distance which each has to go, we shall attain twice the speed. Each of the sixteen cars will have but one eighth of a mile to go. At the uniform rate we have adopted, the two miles can be done in seven and a half instead of fifteen seconds. With thirty-two cars, and a sixteenth of a mile, or twenty rods difference in their length, we arrive at the speed of a mile in less than two seconds; with sixty-four cars, each travelling but ten rods, a mile under the second. More than sixty miles a minute! If this isn't rapid enough for the Professor, tell him to go on, increasing the number of his cars and diminishing the distance each one has to run. If sixty-four cars yield a speed of a mile inside the second, let him fancy a Tachypomp of six hundred and forty cars, and amuse himself calculating the rate of car number 640. Just whisper to him that when he has an infinite number of cars with an infinitesimal difference in their lengths, he will have obtained that infinite speed for which he seems to yearn. Then demand Abscissa."

I wrung my friend's hand in silent and grateful admiration. I could say nothing.

"You have listened to the man of theory," he said proudly. "You shall now behold the practical engineer. We will go to the west of the Mississippi and find some suitably level locality. We will erect thereon a model Tachypomp. We will summon thereunto the professor, his daughter, and why not his fair sister Jocasta, as well? We will take them a journey which shall much astonish the venerable Surd. He shall place Abscissa's digits in yours and bless you both with an algebraic formula. Jocasta shall contemplate with wonder the genius of Rivarol. But we have much to do. We must ship to St. Joseph the vast amount of material to be employed in the construction of the Tachypomp. We must engage a small army of workmen to effect that construction, for we are to annihilate time and space. Perhaps you had better see your bankers."

I rushed impetuously to the door. There should be no delay.

"Stop! stop! Um Gottes Willen, stop!" shrieked Rivarol. "I launched my butcher this morning and I haven't bolted the——"

But it was too late. I was upon the trap. It swung open with a crash, and I was plunged down, down, down! I felt as if I were falling through illimitable space. I remember wondering, as I rushed through the darkness, whether I should reach Kerguellen's Land or stop at the centre. It seemed an eternity. Then my course was suddenly and painfully arrested.

I opened my eyes. Around me were the walls of Professor Surd's study. Under me was a hard, unyielding plane which I knew too well was Professor Surd's study floor. Behind me was the black, slippery, hair-cloth chair which had belched me forth, much as the whale served Jonah. In front of me stood Professor Surd himself, looking down with a not unpleasant smile.

"Good-evening, Mr. Furnace. Let me help you up. You look tired, sir. No wonder you fell asleep when I kept you so long waiting. Shall I get you a glass of wine? No? By the way, since receiving your letter I find that you are a son of my old friend, Judge Furnace. I have made inquiries, and see no reason why you should not make Abscissa a good husband."

Still I can see no reason why the Tachypomp should not have succeeded. Can you?

[5] Scribner's Monthly, March, 1874.

THE END