not only had barbicane announced that he would attain his object—and now the capital at his command enabled him to reach it without hindrance—but he would certainly not have appealed for funds if he was not certain of success.

the north pole was at last to be conquered by the audacious genius of man!

barbicane and his co-directors had the means of succeeding where so many others had failed. they would do what had not been done by franklin, kane, nares, or greely. they would advance beyond the eighty-fourth parallel. they would take possession of the vast portion 48of the globe that had fallen to them under the hammer. they would add to the american flag the forty-third star for the forty-third state annexed to the american confederation.

“rubbish!” said the european delegates.

and the means of conquering the pole—means that were practical, logical, indisputable, and of a simplicity quite infantine—were the suggestion of j. t. maston. it was in his brain, where ideas were cooked in cerebral matter in a state of constant ebullition, that there had been conceived this great geographical work, and the means devised of bringing it to a successful issue.

the secretary of the gun club was a remarkable calculator. the solution of the most complicated problems of mathematical science was but sport to him. he laughed at difficulties, whether in the science of magnitudes, that is algebra, or in the science of numbers, that is arithmetic; and it was a treat to see him handle the symbols, the conventional signs which form the algebraic notation, whether letters of the alphabet, representing quantities or magnitudes, or lines coupled or crossed, which indicate the relation between the quantities and the operations to which they are submitted.

ah! the co-efficients, the exponents, the radicals, the indices, and the other arrangements adopted in that language! how the signs leapt from his pen, or rather from the piece of chalk which wriggled at the end of his metal hook, for he preferred to work on a blackboard. there, on a surface of ten square yards—for nothing less would do for j. t. maston—he revelled in all the ardour of his algebraical temperament. they were no miserable little figures that he employed in his calculations. no; the 49figures were fantastic, gigantic, traced with a furious hand. his 2’s and 3’s waltzed like shavings in a whirlwind; his 7’s were like gibbets, and only wanted a corpse to complete them; his 8’s were like spectacles; and his 6’s and 9’s had flourishes interminable!

and the letters with which he built up his formulæ! the a’s and b’s and c’s he used for his quantities given or known; and the x’s, y’s, and z’s he used for the quantities sought or unknown, and especially his z’s, which twisted in zigzags like lightning flashes! and what turns and twiggles there were in his π’s, his λ’s, his ω’s! even a euclid or an archimedes would have been proud of them!

and as to his signs, in pure unblurred chalk, they were simply marvellous. his + showed the addition was unmistakable. his -, though humbler, was quite a work of art. his × was as clear as a st. andrew’s cross. and as to his =, so rigorously equal were they, as to indicate without a chance of mistake, that j. t. maston lived in a country where equality was no vain formula. his <, his >, and his ≷ were really grand! and as to his √, the root of a quantity or of a number, it was really a triumph, and when he completed the horizontal bar in this style

√‾‾‾‾‾‾

it seemed as if the indicatory vinculum would shoot clean off the blackboard and menace the world with inclusion within the maniacal equation.

but do not suppose that the mathematical intelligence of j. t. maston was bounded by the horizon of elementary algebra. no! the differential calculus, the integral calculus, the calculus of variations were no strangers to him, and with unshaking hand he dashed down the famous 50sign of integration, the shape so terrible in its simplicity, the

f

that speaks of an infinity of elements of the infinitely little.

and like it was his σ which represents the sum of a finite number of finite elements; like it was his ∝ with which mathematicians indicate the variant; like it were all the mysterious symbols employed in this language so unintelligible to ordinary mortals. in short, this astonishing man was capable of mounting the mathematical ladder to the very topmost rung.

such was j. t. maston. no wonder his colleagues had every confidence in him when he undertook to solve the wildest abracadabrant calculations that occurred to their audacious brains! no wonder that the gun club had confided to him the problem regarding the hurling of the projectile from the earth to the moon! no wonder that evangelina scorbitt was intoxicated with his glory, and had conceived for him an admiration which perilously bordered on love!

but in the case under consideration, the solution of the problem regarding the conquest of the north pole, j. t. maston had no flight to take in the sublime regions of analysis. to allow the concessionaries of the arctic regions to make use of their new possessions, the secretary of the gun club had but a simple problem in mechanics to occupy his mind. it was a complicated problem, no doubt, requiring ingenious and possibly novel formulæ, but it could be done.

yes! they could trust j. t. maston, although the slightest slip might entail the loss of millions! but never 51since his baby head had toyed with the first notions of arithmetic had he made a mistake, never had he been the millionth of an inch out in a matter of measurement, and if he had made an error in the last of twenty places of decimals his gutta-percha cranium would have burst its fixings.

it was important to insist on the remarkable mathematical powers of j. t. maston. we have done so! now we have to show him at work, and to do that we must go back a few weeks.

about a month before the famous advertisement, j. t. maston had been requested to work out the elements of the project of which he had suggested to his colleagues the marvellous consequences.

for many years he had lived at no. 179, franklin street, one of the quietest streets in baltimore, far from the business quarter, for in commerce he took no interest; far from the noise of the crowd, for the mob he abhorred.

there he occupied a modest habitation known as ballistic cottage, living on the pension he drew as an old artillery officer, and on the salary paid him as the gun club secretary. he lived alone with one servant, fire-fire, a name worthy of an artilleryman’s valet. this negro was a servant of the first-water, and he served his master as faithfully as he would have served a gun.

j. t. maston was a confirmed bachelor, being of opinion that bachelorhood is the only state worth caring about in this sublunary sphere. he knew the sclav proverb, that a woman draws more with one hair than four oxen in a plough; and he was on his guard.

if he was alone at ballistic cottage, it was because he wished to be alone. he had only to nod to change his solitude of one into a solitude of two, and help himself 52to half the fortune of a millionaire. there was no doubt of it. mrs. scorbitt would only have been too happy; but j. t. maston was not going to be too happy; and it seemed that these two people so admirably adapted for each other—in the widow’s opinion—would never understand each other.

the cottage was a very quiet one. there was a groundfloor and a first-floor. the ground floor had its verandah, its reception-room and dining-room, and the kitchen in a small annexe in the garden. above them was a bedroom in front, and a workroom facing the garden away from the noise, a buen retiro of the savant and the sage within whose walls were solved calculations that would have raised the envy of a newton or a laplace.

different, indeed, was the home of mrs. scorbitt, in the fashionable quarter of new park, with the balconies on its front covered with the fantastic sculpture of american architecture, gothic and renascence jumbled together; its enormous hall, its picture galleries, its double twisted staircase, its numerous domestics, its stables, its coach-houses, its gardens, its lawns, its trees, its fountains, and the tower which dominated its battlements from the summit of which fluttered in the breeze the blue and gold banner of the scorbitts.

three miles divided new park from ballistic cottage. but a telephone-wire united the two habitations, and at the ringing of the call between the mansion and the cottage conversation could be instantly established. if the talkers could not see each other, they could hear each other; and no one will be surprised to learn that evangelina scorbitt called j. t. maston much oftener before his telephonic plate than j. t. maston called evangelina 53scorbitt before hers. the mathematician would leave his work, not without some disgust, to receive a friendly “good morning,” and he would reply by a growl along the wire, which he hoped would soften as it went, and then he would return to his problems.

it was on the 3rd of october, after a last and long conference, that j. t. maston took leave of his colleagues to devote himself to his task. it was the most important investigation he had undertaken. he had to calculate the mechanical formulæ required for the advance on the pole, and the economical working of the coal-beds thereof. he estimated that it would take him rather more than a week to accomplish this mysterious task. it was a complicated and delicate inquiry, necessitating the resolution of a large number of equations dealing with mechanics, analytical geometry of the three dimensions, and spherical trigonometry.

to be free from trouble, it had been arranged that the secretary of the gun club should retire to his cottage, and be visited and disturbed by no one. this was a great trial for mrs. scorbitt, but she had to resign herself to it. she and president barbicane, captain nicholl, the brisk bilsby, colonel bloomsberry, and tom hunter with his wooden legs, had called on maston in the afternoon to bid him farewell for a time.

“you will succeed, dear maston,” she said, as she rose to go.

“but be sure you don’t make a mistake,” said barbicane, with a smile.

“a mistake! he!” exclaimed mrs. scorbitt, with horror at the thought.

with a grip of the hand from some, a sigh from one, 54wishes for success, and recommendations not to overwork himself from others, the mathematician saw his friends depart. the door of ballistic cottage was shut, and fire-fire received orders to open it to no one—not even to the president of the united states of america.

for the first two days of his seclusion j. t. maston thought over the problem without touching the chalk. he read over certain works relative to the elements, the earth, its mass, its density, its volume, its form, its rotation on its axis, and translation round its orbit—elements which were to form the bases of his calculations.

these are the principal, which it is as well the reader should have before him:—

form of the earth: an ellipsoid of revolution, with a major diameter of 7926·6 miles, and a minor diameter of 7899·6 miles. the difference between the two, owing to the flattening of the spheroid at the poles being 27 miles, or one two-hundred-and-ninety-third of its mean diameter.

circumference of the earth at the equator: 24,899 miles, the meridional circumference being 24,856 miles.

surface of the earth: 197,000,000 square miles.

volume of the earth: 260,000,000,000 cubic miles.

density of the earth: five and a half times that of water, the mass being approximately 6,000,000,000,000,000,000,000 tons.

duration of the earth’s journey round the sun: 365 days and a quarter, constituting the solar year, or more exactly 365 days, 6 hours, 9 minutes, thus giving the spheroid an average velocity of 66,000 miles an hour.

rate of the earth’s rotation at the equator: 1037·4583 miles per hour.

the following were the units of length, force, time, and 55inclination which j. t. maston required for his calculations; the mile, the ton, the second, and the angle at the centre which cuts off in any circle an arc equal to the radius.

it was on the 5th of october, at five o’clock in the afternoon—it is important to know the precise time in a work of such celebrity—that j. t. maston, after much reflecting, began to write. and, to begin with, he attacked the problem at its base—that is, by the number representing the circumference of the earth, and one of its great circles, viz. the equator.

the blackboard was placed in an angle of the room on an easel of polished oak, well in the light of one of the windows which opened on to the garden. little sticks of chalk were placed on the shelf at the bottom of the board. a sponge to wipe out with was in the calculator’s left hand. his right hand, or rather his hook, was reserved for writing down the figures of his working.

he began by describing the circumference of the terrestrial spheroid. at the equator the curve of the globe was marked by a plain line representing the front part of the curve, and by a dotted line representing the back half of the curve. the axis was a perpendicular line cutting the equator, and marked n.s.

on the left-hand top corner of the board he wrote the number that used to represent the earth’s circumference in metrical measurement—

40,000,000.

he knew that this was an assumption admitted to be erroneous, but it afforded a good round integer to begin with, and the subsequent rectification of his calculations by the inclusion of the missing meters was but child’s-play to so transcendental a mathematician as j. t. maston.

he was so pre-occupied that he had not noticed the state of the sky—which had changed considerably during the afternoon. for the last hour one of those great storms had been gathering which affect the organizations of all living things. livid clouds like whitish wool flocks had accumulated on the grey expanse and hung heavily over the city. the roll of distant thunder was heard. one or two flashes had already rent the atmosphere where the electric tension was at its highest.

j. t. maston, more and more absorbed, saw nothing, heard nothing.

suddenly an electric bell troubled the silence of the room with its hurried tinkling.

“good!” exclaimed the mathematician. “if interrupters can’t get in by the door, they come through the wire! a fine invention for people who wish to be left alone! i’ll see if i can’t turn that current off while i am at work!”

and stepping up to the telephone, he asked,—

“who wants me?”

“i want a moment’s talk with you,” said a feminine voice.

“and who is speaking?”

“have you not recognized my voice, dear mr. maston? it is mrs. scorbitt.”

“mrs. scorbitt! she will not leave me a moment’s peace.”

but the last words were prudently muttered above the instrument, so that the widow heard them not. and j. t. maston, seeing that he must say something civil, replied,—

“ah! it is you, mrs. scorbitt?”

“i, dear mr. maston!”

“and what does mrs. scorbitt want with me?”

“to tell you that there is a storm coming your way.”

“well, i cannot stop it—”

“no, but i wanted to ask if you had taken care to shut your window—”

mrs. scorbitt had hardly ended before a tremendous clap of thunder filled the air. it seemed as though a vast sheet of silk had been torn apart for an infinity of length. the lightning had flashed down over ballistic cottage, and, conducted by the telephone-wire, had invaded the mathematician’s room with a brutality quite electric.

j. t. maston, bending over the mouthpiece of the instrument, received the hardest voltaic knock that had ever found the mouth of a philosopher. the flash had run along his metal hook, and spun him round like a teetotum. the blackboard he struck with his back was hurled down in the corner. and the lightning disappeared out of window.

stunned for a moment—and it was a wonder it was no worse—j. t. maston slowly rose, and rubbed the different parts of his body to make sure he was not hurt.

then, having lost none of his coolness, as beseemed the ancient pointer of the columbiad, he put his room in order, picked up his easel, hoisted up his blackboard, gathered up the fragments of chalk scattered on the carpet, and resumed his work, which had been so rudely interrupted.

but he noticed that by the fall of the blackboard the figures he had written on the right-hand top corner, which represented in meters the approximate equatorial circumference of the earth, had been partially erased. he stretched his hook up to re-write them when the bell sounded with a feverish tinkle.

“again!” exclaimed j. t. maston. and he went to the telephone.

“who is there?” he asked.

“mrs. scorbitt.”

“and what does mrs. scorbitt want?”

“did that horrible flash of lightning strike ballistic cottage?”

“i have every reason to believe so.”

“good heavens! the lightning—”

“do not be uneasy, mrs. scorbitt.”

“you are not hurt, dear mr. maston?”

“not at all.”

“you are sure you have not been touched?”

“i am only touched by your thoughtfulness for me,” said the philosopher gallantly.

“good evening, dear mr. maston.”

“good evening, dear mrs. scorbitt.”

and he returned to his blackboard.

“confound that excellent woman,” he said; “if she hadn’t called me to the telephone i should not have run the chance of being struck by lightning.”

and to insure being left in quiet, he judiciously put the telephone out of action.

then he resumed his work. from the number on the board he gradually built up a definitive formula, and then noting it on the left, he cleared away the working by which he had arrived at it, and launched forth into an appalling series of figures and signs.

eight days later the wonderful calculation was finished, and the secretary of the gun club triumphantly bore off to his colleagues the solution of the problem which they had awaited with a very natural impatience.

the practical means of arriving at the north pole to work its coal-mines were mathematically established. then the company was formed under the title of the north polar practical association. then the arctic regions were purchased under the auctioneer’s hammer. and then the shares were offered to the world.