EULOGY ON AMPERE. loo 



npturiiiug the priuciples of science. I must acknowledge I was not a 

 little astonished not to ilud him struggling with the quadrature of the 

 circle. This inexplicable hiatus, in the youth of our associate, has just 

 been filled. A manuscript note from the secretary of the Academy of 

 Lyons apprises me that, on the 8th of July, 1788, Ampere, then thir- 

 teen years of age, addressed to that learned body a paper relating to 

 the celebrated problem just mentioned. Later duriug the same year 

 he submitted to the examination of his compatriots an analogous memoir, 

 entitled " The rectification of any arc of a circle less than the semi-circum- 

 ferencc:'' These memoirs have not reached us. If the manuscript note 

 sent to me can be relied upon, young Ampere, not only did not think 

 the problem insoluble, but flattered himself he had almost solved it. 

 Scruples, respected by me without being shared, demanded the sacri- 

 fice of this anecdote. It certainly would have been a very small sacri- 

 fice, but I did not consider it consistent with my duty to make it. The 

 scientific weaknesses of men of a very high order of intellect are lessons 

 quite as useful and i^rofitable as their successes, and the biographer has 

 no right to cover them with a vail. Is it quite certain, too, that there is 

 anything here to excuse or conceal 5 that a geometer need blush for 

 efforts made in his childhood, or even at a riper age, to square the cir- 

 cle geometrically ? To sustain, however, such a proposition, we have 

 only to recall the fact that antiquity presents to us, as deeply engaged 

 in this problem, Anaxagoras, Meton, Hippocrates, Archimedes, and 

 ApoUonius; and to these we may add the modern names of Snellius, 

 Huygens, Gregory, Wallis and Kewton ; and, finally, that amongst those 

 whose sagacity the quadrature of the circle has set at defiance — I mean 

 who have been involved by it in palpable errors there are many who 

 have, in other respects, rendered genuine service to science ; for example 

 J. B. Porta, the inventor of the camera-obscura; then Gregon^e de 

 Saint Vincent, the Jesuit, to whom we owe the discovery of the won- 

 derful properties of hyperbolic spaces terminated by asymptotes; Lon- 

 gomontanus, the astronomer, &c., &c. 



If your mind is engrossed with the idea that, in order to justify their 

 efibrts to square the circle, others will cite hereafter, to their advan- 

 tage, the attempts of a child of thirteen, I reply unhesitatiugly — for my 

 academic duties bring me frequently in and personal relations with the 

 squarers of the circle — that authorities have absolutely.no weight in their 

 eyes; that they have long since entirely separated themselves from every- 

 thing that bears or has borne the name of geometer; that Euclid himself, 

 in his principal theorems — for example, that of the square of the hypothe- 

 neuse — seems to them scarcely worthy of trust. If a mania — I was on 

 the point of saying a furor which manifests itself especially in spring, 

 as proved by experience — couk^ ever be amenable to logic, it would be 

 necessary, in order to battle it successfully, to distinguish more carefully 

 than has ever yet been done the various aspects under which the prob- 

 lem of the quadrature of the circle ought to be considered. An example 



