age of six years lie was taken with a passion for figures, and began to combine numbers in his head while at watch over his flock. He did not try to give his calculations a material form by counting on his fingers, or with stones, but the whole operation was mental. He conceived numbers by the names which his elder brother had recited to him. Neither he nor his brother could read then. He learned by ear the numbers to hundreds, and exercised himself in calculating with what he knew. When he had done his best with these numbers he asked to be taught those above a hundred so that he might extend the sphere of his operations. He has no recollection of his brother teaching him the multiplication table. At seven years of age he was capable of performing in his head multiplications of five figures. In a little while he started with his brother to wander through Provence, the brother playing the organ and Jacques exhibiting a marmoset and holding out his hand. To increase his receipts he proposed to the people he met to perform mental calculations for them; at the markets he assisted the peasants in making up their accounts, and performed difficult arithmetical operations in the cafés. A manager engaged him to give representations in the cities. He came to Paris for the first time in 1880, and was presented to the Anthropological Society by Broca, who wrote a brief note on the case.
Since 1880, M. Inaudi has made great progress. First, he learned to read and write, and then the sphere of his operations widened. His education, which was slow, is still rudimentary on many points; but he has a receptive intelligence and an inquiring spirit, is pleasant and modest, converses agreeably, with good sense, and sometimes with irony; and is ready at cards and billiards. It would be wrong to regard him as a simple calculating machine.
The operations he performs are additions, subtractions, multiplications, divisions, and extractions of roots. He also resolves by arithmetic problems corresponding with equations of the first degree. These are to him exercises of mental calculation, by which we mean a calculation made in the head, without the employment of figures or writing, or any material means to assist the memory. His general process is as follows: first, when the problem is stated to him aloud, he listens attentively and repeats the data, articulating them clearly, to fix them well in his mind; if he does not comprehend the problem, he has it repeated. It may be communicated to him by writing, but he prefers to receive it by hearing; and if we insist upon his reading it, he pronounces it in a low tone. When he has fully grasped the question, he says, "I begin," and proceeds to whisper very fast, in an indistinct murmur, in which we can catch from time to time a few names of numbers. At such times nothing can
