309. I subjoin a table, compiled by the help of Dr. Scripture's collection, which will broadly illustrate the main points above mentioned. Some more detailed remarks may then follow.

Table Of Principal Arithmetical Prodigies

Now among these thirteen names we have two men of transcendent, and three of high ability. What accounts have they given us of their methods ?

310. Of the gift of Gauss and Ampere we know nothing except a few striking anecdotes. After manifesting itself at an age when there is usually no continuous supraliminal mental effort worth speaking of, it appears to have been soon merged in the general blaze of their genius. With Bidder the gift persisted through life, but grew weaker as he grew older. His paper in Vol. XV. of the Proceedings of the Institute of Civil Engineers, while furnishing a number of practical hints to the calculator, indicates also a singular readiness of communication between different mental strata. "Whenever," he says (p. 255), "I feel called upon to make use of the stores of my mind, they seem to rise with the rapidity of lightning." And in Vol. CIII. of the same Proceedings, Mr. W. Pole, F.R.S., in describing how Mr. Bidder could determine mentally the logarithm of any number to 7 or 8 places, says (p. 252): "He had an almost miraculous power of seeing, as it were, intuitively what factors would divide any large number, not a prime.

Thus, if he were given the number 17,861, he would instantly remark it was 337 X 53.... He could not, he said, explain how he did this; it seemed a natural instinct to him".

Mr. Bidder's case is well known; but it may be of interest to quote here some passages from an autobiographical statement kindly furnished to me by Mr. Blyth, of Edinburgh, the well-known civil engineer, whose own gift, like that of the younger Mr. Bidder, though not such as to entitle him to rank as a " prodigy," yet marks him out distinctly from ordinary mankind.

(From Proceedings S.P.R., vol. viii. p. 352).

12 Belgrave Crescent, Edinburgh, February 28th, 1892.

I shall now endeavour, in response to your request, to give some account of my late brother's and my own faculty of arithmetical calculation mentally, and it may be interesting if I allude to influences even before birth which I have always felt may have had something to do with my brother's great power.

Benjamin Hall Blyth was born on July 6th, 1819. Our mother had a natural arithmetical gift - not to any very marked degree, but decidedly above the average, and especially so among females. Some months before Benjamin's birth the wonderful calculating boy, Bidder (then, I think, about 12 or 14 years of age), was exhibiting in Edinburgh, and made a private exhibition in my father's house. My mother was greatly astonished and interested, put various questions to Bidder, and some weeks later requested my father to invite him to another séance, which was done. Her interest increased on this second occa-iion, and the wonderful boy continued to occupy her mind frequently.

It is, I believe, admitted by physiologists, that anything greatly occupying a nother's mind certainly may, and frequently does, influence the character of her inborn child. At all events, my brother, whether from this or heredity, or both, rery early manifested a marvellous power of mental calculation. When almost exactly six years of age Benjamin was walking with his father before breakfast, when he said, "Papa, at what hour was I born?" He was told four a.m.

Ben

•' What o'clock is it at present ? "

Ans

" Seven fifty a.m." [My father always took exercise before breakfast in summer].

The child walked on a few hundred yards, then turned to his father and stated the number of seconds he had lived. My father noted down the figures, made the calculation when he got home, and told Ben he was 172,800 seconds wrong, to which he got a ready reply: "Oh, papa, you have left out two days or the leap-years - 1820 and 1824," which was the case.

This latter fact of the extra day in leap-year is not known to many children of six, and if any one will try to teach an ordinary child of these years the mul-iplication table up to 12 x 12 he will be better able to realise how extraordinary was this calculation for such an infant.

I am conscious of an intuitive recognition of the relation of figures. For instance, in reading statements of figures in newspapers, which are very often egregiously wrong, it seems to come to me intuitively that something is wrong, and when that occurs I am usually right.

I have always felt that there were times when my power was much weaker than others, not only when tired, but, like a musician, when not in the mood. I have not the same confidence now at 66 years of age as when younger. That is to say, I like to check a calculation before stating it, though I can do nearly as difficult ones as at any time of my life, though not so rapidly.

As to there being any degree of connection between this arithmetical power and ambidexterity, there is none, I think, in my case. I do not possess the latter gift consciously, though I may perhaps be able to use the left hand better than the average of people, but I should not for a moment claim to be ambidextrous.... Left-handedness runs in our family on both sides, and so I say I may have some little ambidexterity without knowing it.

Edward L. I. Blyth.

Mr. Blyth's interesting record contains other illustrations of several points above mentioned; - the early and instinctive appearance of the faculty; its gradual subjection to supraliminal guidance; yet the persistence of occasional "subliminal uprushes," which give the problem's answer without its intermediate steps.

Passing on to the two other men of high ability known to have possessed this gift, Professor Safford and Archbishop Whately, we are struck with the evanescence of the power after early youth, - or even before the end of childhood. I quote from Dr. Scripture Archbishop Whately's account of his powers: -