metical processes curious evidence was afforded by the feats of a Chinese who visited America in 1875. He was simply a trained computer, asserting that hundreds in China were trained to equal readiness in arithmetical processes, and that among those thus trained those of exceptional abilities far surpassed himself in dexterity. Among the various tests applied during a platform exhibition of his powers was one of the following nature. About thirty numbers of four digits each were named to him, as fast as a quick writer could take them down. When all had been given he was told to add them, mentally, while a practised arithmetician was to add them on paper. "It is unnecessary for me to add them," he said, "I have done that as you gave them to me; the total is-so-and-so." It presently appeared that the total thus given was quite correct. At first sight such a feat seems astounding. Yet in reality it is but a slight modification of what many bankers' clerks can readily accomplish. They will take an array of numbers, each of four or five figures, and cast them up in one operation. Grant them only the power of as readily adding a number named as a number seen to a total already obtained, and their feat would be precisely that of the Chinese arithmetician. There can be no doubt that, with a very little practice, ninetenths, if not all, of the clerks who can achieve one feat would be able to achieve the other feat also. I do not know how clerks who add at once a column of four-figured numbers together accomplish the task. That is to say, I do not know the mental process they go through in obtaining their final result. It may be that they keep the units, tens, hundreds, and thousands apart in their mind, counting them properly at the end of the summation; or, on the other hand, they may treat each successive number as a whole, and keep the gradually growing total as a whole. Or some may follow one plan, and some the other. When I heard of the Chinese arithmetician's feats, my explanation was that he adopted the former plan. I should myself, if I wanted to acquire readiness in such processes, adopt that plan, applying it after a fashion suggested by my method of comput ing when I was a boy. I should picture the units, tens, hundreds, and thousands as objects of different sorts. Say the units as dots, the tens as lines, the hundreds as discs, the thousands as squares. When a number of four digits was named to me, I should see so many squares, discs, lines, and dots. When the next number of four digits was named, I should see my sets of squares, discs, lines, and dots correspondingly increased. When a new number was named these sets would be again correspondingly increased. And so on, until there were several hundreds of squares, of discs, of lines, and of dots. These (when the last number had been named) could be at once transmuted into a number, which would be the total required. Take for instance the numbers, 7234, 9815, 9127, 4183. When the first was named the mind's eye would picture 7 squares, 2 discs, 3 lines, and 4 dots. When the second (9815) was named there would be seen 16 squares, 10 discs, 4 lines, and 9 dots. After the third (9127), there would be 25 squares, 11 discs, 6 lines, and 16 dots ; after the fourth (4183), there would be 29 squares, 12 discs, 14 lines, and 19 dots. This being all, the total is at once run off from the units' place; the 19 dots give 9 for the units, one 10 to add to the 14 lines (each representing ten), making 15, so that 5 is the digit in the tens' place, while 100 is added to the 12 discs or hundreds, giving 13 or 3 in the hundreds' place, and 1000 to add to the 29 squares or thousands, making 30, or for the total 30,359. The process has taken many words in describing, but each part of it is perfectly simple, the mental picturing of the constantly increasing numbers of squares, discs, lines, and dots being almost instantaneous (in the case, of course, of those only who possess the power of forming these mental pictures). The final process is equally simple, and would be so even if the number of squares, discs, lines, and dots were great. Thus, suppose there were 324 squares, 411 discs, 391 lines, and 433 dots. We take 3 for units, carrying 43 lines or 434 in all, whence 4 for the tens, carrying 43 discs or 444 in all, whence 4 for the hundreds, carrying 44 squares or 468 in all, whence finally 468,443 is the total required. We can understand then how easy to Bidder must have been the summation of the fifteen products of crossmultiplication to the carried remainderthey would be added consecutively in far less time than the qickest penman could write them down. Probably they would be obtained as well as added in less time than they could be written down. Thus digit after digit of the result of what appears a tremendous sum in multiplication would be obtained with that rapidity which to many seemed almost miraculous. We must further take into account a circumstance pointed out by Mr. G. Bidder. "The faculty of rapid operation," he says, speaking of his father's wonderful feats in this respect," was no doubt congenital, but it was developed by incessant practice and by the confidence thereby acquired. I am certain," he proceeds, "that unhesitating confidence is half the battle. In mental arithmetic, it is most true that 'he who hesitates is lost.' When I speak of incessant practice, I do not mean deliberate drilling of set purpose; but with my father, as with myself, the mental handling of numbers or playing with figures afforded a positive pleasure and constant occupation of leisure moments. Even up to the last year of his life (his age was seventy-two) my father took delight in working out long and difficult arithmetical problems." * We must always remember, in considering such feats as Bidder and other * Mr. G. Bidder's powers as a mental arithmetician would be considered astonishing if the achievements of his father and others were not known." I myself," he says, can perform pretty extensive arithmetical operations mentally, but I cannot pretend to approach even distantly to the rapidity and accuracy with which my father worked. I have occasionally multiplied 15 figures by 15 in my head, but it takes me a long time, and I am liable to occasional errors. Last week, after speaking to Prof. Elliot, I tried the following sum to see if I could still do it: 378,201,969,513,825 199,631,057,265,413 and I got, in my head, the answer, 75.576,299.427.512,145,197,597,834,725; in which I think, if you take the trouble to work it out, you will find 4 figures out of the 29 are wrong." I have only run through the crossmultiplication far enough to detect the first error, which is in the digit representing thousands of millions. This should be 4 not 7. 66 calculating boys" accomplished, that the power of mentally picturing numbers is in their case far greater than we are apt to imagine such a power can possibly be. Precisely as the feats of a Morphy seem beyond belief till actually witnessed, and even then (especially to those who know what his chess-play meant) almost miraculous so the mnemonic powers of some arithmetician would seem incredible if they had not been tested, and even as witnessed seem altogether marvellous. Colburn tells us that a notorious free-thinker who had seen his arithmetical achievements at the age of six, "went home much disturbed, passed a sleepless night, and ever afterwards renounced infidel opinions." "And this," says the writer in the "Spectator," from whom I have already quoted, was only one illustration of the vague feeling of awe and open-mouthed wonder, which his performances excited. People came to consult him about stolen spoons; and he himself evidently thought that there was something decidedly uncanny, something supernatural, about his gift." 66 But so far as actual mnemonic arithmetical power is concerned, the feats of Colburn, and even of Bidder, have been surpassed. Consider, for instance, the following instances of the strong power of abstraction possessed by Dr. Wallis - December 22, 1669.-In a dark night in bed," he says in a letter to his friend, Mr. Thomas Smith, B.D., Fellow of Magdalen College," without pen ink or paper, or anything equivalent, I did by memory extract the square root of 30000,00000,00000,00000,00000,00000,00000,00000, which I found to be 1,77205,08075,68077,29353, ferè, and did the next day commit it to writing.' And again: February 18, 1670.Johannes Georgius Pelshower (Regiomontanus Borussus) giving me a visit, and desiring an example of the like, I did that night propose to myself in the dark, without help to my memory, a number in 53 places: 24681357910121411131516182017192122242628302325272931, of which I extracted the square root in 27 places: 157103016871482805817152171 proximè; which numbers I did not commit to paper till he gave me another visit, March following, when I did from memory dictate them to him.'" 66 Mr. E. W. Craigie, commenting on power was based. Hereafter I may take these feats, says that they are not per- occasion to discuss this evidence more haps as difficult as multiplying 15 figures at length, and with particular reference by 15, for while of course it is easy to to its bearing on the question of herediremember such a number as three thou- tary genius. Let it suffice to mention sand billion trillions, being nothing but here that, although Mr. G. Bidder and noughts, so also it may be noticed that other members of the family have posthere is a certain order in the row of 53 sessed in large degree the power of dealfigures; the numbers follow each other ing mentally with large numbers, yet in in little sets of arithmetical progression other cases, though the same special (2, 4, 6, 8), (1, 3, 5, 7, 9), (10, 12, 14), mental quality involved has been pre11, 13, 15), (16, 18, 20), and so on; sent, the way in which that quality has not regularly, but still enough to render shown itself has been altogether differit an immense assistance to a man enent. Thus Mr. G. Bidder states that his gaged in a mental calculation. A row father's eldest brother, "who was a of 53 figures set down at hazard would Unitarian minister, was not remarkable have been much more difficult to re- as an arithmetician; but he had an exmember, like Foote's famous sentence traordinary memory for Biblical texts, with which he puzzled the quack mne- and could quote almost any text in the monician; but still we must give the Bible, and give chapter and verse." A doctor the credit for remembering the granddaughter of G. P. Bidder's once answer." Mr. Craigie seems to over- said to Prof. Elliot, "Isn't it strange, look the circumstance that remembering when I hear anything remarkable said or the original number, and remembering read to me, I think I see it in print ?'' the answer, in cases of this kind, are Mr. G. Bidder, " can play two games of utterly unimportant feats compared with chess simultaneously," Prof. Elliot menthe work of obtaining the answer. If tions, "without seeing the board." any one will be at the pains to work out "Several of Mr. G. P. Bidder's the problem of extracting the square root nephews and grandchildren," he adds, of any number in 53 places, he will see that it would be a very small help indeed to have the original number written down before him, if the solution was to be worked out mnemonically. Probably in both cases, Wallis took easily remembered numbers, not to help him at the time, but so that if occasion required he might be able to recall the problem months or years after he had solved it. Anyone who could work out in his mind such a problem as the second of those given above, would have no difficulty in remembering an array of two or three hundred figures set down entirely at random. I have left small space in which to consider the singular evidence given by Prof. Elliot and Mr. G. Bidder respecting the transmission in the Bidder family of that special mental quality on which the elder Bidder's arithmetical 66 possess also very remarkable powers. One of his nephews at an early age showed a degree of mechanical ingenuity beyond anything I had ever seen in a boy. The summer before last, to test the calculating powers of some of his grandchildren (daughters of Mr. G. Bidder, the barrister), I gave them a question which I scarcely expected any of them to answer. I asked them, 'At what point in the scale do Fahrenheit's thermometer and the Centigrade show the same number at the same temperature?' The nature of the two scales had to be explained, but after that they were left to their own resources. next morning one of the younger ones (about ten years old) came to tell me it was at 40 degrees below zero. This was the correct answer; she had worked it out in bed."-Belgravia Magazine. The AN INVITATION TO THE SLEDGE. BY J. A. SYMONDS. COME forth, for dawn is breaking; All day o'er snow-drifts gliding Above black swirling death-waves We'll talk of love and friendship And hero-hearted men, Mid the stems of spangled larches With flight as swift as swallows We'll thread the sombre forest, Where giant pines are crowned With snow caps on their branches Strong wine of exultation, Free thoughts that laugh at death, Shall warm our wingèd spirits, Though the shrill air freeze our breath. With many a waif of music. And memory-wafted song, With the melody of faces Loved when the world was young. With dear Hellenic stories And names of old romance, We'll wake our souls' deep echoes Dance to the arrowy motion Of our sledge so firm and free, Like love, like all that's joyous, O friend, 'tis ours to clasp it! Hath heaven or earth than this! -Cornhill Magazine. RUSSIAN COURT LIFE UNDER PETER THE THIRD AND CATHERINE THE SECOND. WHILE the Empress Elizabeth was slowly dying of disease and inebriation, the Grand Duchess Catherine was seeking popularity with both priesthood and people by much display of extreme grief and piety. She attended the public masses, and prayed with affected fervor for hours together, before the pictures and images of saints, for the restoration of the Empress's health. The Grand Duke in the meantime, "halting between two opinions,' was hesitating whether to receive the imperial crown at the hands of the senate, as advised by Count Panin, or to be proclaimed by the army, in accordance with Russian usage, as urged by the veteran Prince Trubetskoi. The pretended reconciliation of the Grand Duke and Duchess had but intensified their mutual aversion; but Peter still regarded the mental endowments of his wife as so greatly superior to his own that he now sought her opinion as to which course it would be preferable to pursue. Very disdainfully she replied" qu'il falloit se conformer à l'usage," for she saw in his question a confession of inability to rule without her aid, and, as its natural consequences, his speedy downfall and her own elevation. It had been the object of eighteen years' plotting and caballing to frustrate the accession of the Grand Duke to the throne; yet it took place without the slightest disturbance or show of opposition. The officers of the imperial guard readily swore allegiance to him. A crowd of anxious courtiers, some trembling for their liberty and their possessions, others full of avaricious hope of succeeding to the spoil, speedily surrounded him. The new Czar received them with dignity. He was then thirtyfour, and, being freed from the servile restraint in which the late empress had held him, seemed to have cast aside with t the indecision of character for which he had hitherto been remarkable. Adverse as the ministers of the former reign had been to him, he confirmed most of them in their posts; while those whom he dismissed he neither banished to Siberia nor despoiled of their estates. His first reception ended, he mounted his horse and, attended by a numerous staff, rode through all the streets of St. Petersburg, distributing money amongst the people. The troops thronged about him, calling out, "Behave well to us and we will serve you as faithfully as we did our great mother the Czarina Elizabeth." With the acclamations of the soldiers were mingled the joyous huzzas of the populace, and although Peter's enemies had so long done their best to make even his name hated, and his accession dreaded as a calamity to the country, no sign of discontent was perceptible, no word of ill-will towards him heard. One of his first acts, after concluding with Frederick II. an armistice which led to a peace that released the Prussian king from difficulties and embarrassments to which, at that stage of the Seven Years' War, he well-nigh succumbed, was to recall the vast multitude of state prisoners with whom the fears and suspicions of Elizabeth and the vindictive jealousy of her favorites had peopled the Siberian deserts. Their number was estimated at not less than 17,000. Amongst them came Biren, the haughty favorite and inhuman minister of the Empress Anne; also L'Estorq, to whom Elizabeth was chiefly indebted for her throne. Field-Marshal de Munich, too, at eighty-two years of age, and after twenty-one years of exile, revisited St. Petersburg. Dressed in the sheepskin he had worn in Siberia, and surrounded by a numerous family of grandchildren and great-grandchildren, the old soldier appeared before the Emperor. Peter redecorated him with |