THE LATEST ARITHMETICAL PRODIGY. 69 



if the sound of the vowel kept pure in tone, it was certain he did 

 not articulate the figures. The experiment caused M. Inaudi 

 great embarrassment. He was still able to calculate in his head, 

 but it took him four or five times as long as under the usual con- 

 ditions, and he succeeded in doing it only by cheating a little — 

 that is, he made some articulations of figures in a low voice, the 

 production of which was at once detected on listening attentively 

 to the sound of the sung vowel. 



These experiments showed that articulation constitutes an 

 integral part of M. Inaudi's mental calculations, as well as that 

 every experimental artifice that interferes with articulation 

 makes the calculation longer or modifies its accuracy. In other 

 words, M. Inaudi uses auditive and motor images of articulation 

 concurrently. "We have no experimental means of determining 

 which is the predominant factor. M. Inaudi thinks that the 

 sound guides him, and that the motion of articulation intervenes 

 only to re-enforce the auditive image. We might be liable to sup- 

 pose, in view of the part that is played by the memory in mental 

 calculation, that it is the only faculty developed in arithmetical 

 prodigies ; and some authors have fallen into this error. But it 

 will be well -to guard against such a supposition, which is con- 

 trary to the most certain and best established psychological facts. 

 If we take any elementary act of the mind and analyze it, we shall 

 find that it involves the concurrence of a large number of co-ordi- 

 nated operations ; with much stronger reason must such a con- 

 currence be supposed necessary for acts as complex as mental 

 calculations. We have found in our studies of M. Inaudi that a 

 considerable number of his faculties have attained an extreme 

 development, and they are precisely the ones that concur in 

 operations of mental calculations. Perception, attention, and 

 judgment, to the extent and in the shape in which they are 

 needed in his work, have acquired the same perfection as his 

 memory for figures. 



It remains to inquire how these aptitudes for calculation have 

 been formed. When we examine the history of these arithmetical 

 prodigies, we are struck by the three facts of their precocity ; the 

 impulsive, in a certain sense all-possessing, character of their 

 passion for calculation ; and the generally illiterate, often miser- 

 able, medium in which they have grown up. Their stories have 

 many traits in common. They are most frequently children of 

 poor and ignorant parents. They are seized with the passion for 

 calculating in their earliest years — at from five to ten years of age 

 on the average — the age when most children are living in the illu- 

 sions of plays and stories ; they begin to combine numbers in their 

 heads, apparently without any exterior provocation, and without 

 the influence of parents or schoolmasters. As they grow up 



