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It is stated by Montucla that Bovillus makes $\pi ={\sqrt {10}}$. But Montucla cites a work of 1507, Introductorium Geometricum, which I have never seen. He finds in it an account which Bovillus gives of the quadrature of the peasant labourer, and describes it as agreeing with his own. But the description makes $\textstyle \pi =3{\frac {1}{8}}$, which it thus appears Bovillus could not distinguish from ${\sqrt {10}}$. It seems also that this 3 1/8, about which we shall see so much in the sequel, takes its rise in the thoughtful head of a poor labourer. It does him great honour, being so near the truth, and he having no means of instruction. In our day, when an ignorant person chooses to bring his fancy forward in opposition to demonstration which he will not study, he is deservedly laughed at.

Mr. James Smith, of Liverpool—hereinafter notorified—attributes the first announcement of 3 1/8 to M. Joseph Lacomme, a French well-sinker, of whom he gives the following account:—

In the year 1836, at which time Lacomme could neither read nor write, he had constructed a circular reservoir and wished to know the quantity of stone that would be required to pave the bottom, and for this purpose called on a professor of mathematics. On putting his question and giving the diameter, he was surprised at getting the following answer from the Professor—'Qu'il lui était impossible de le lui dire au juste, attendu que personne n'avait encore pu trouver d'une manière exacte le rapport de la circonférence an diamètre.'

From this he was led to attempt the solution of the problem. His first process was purely mechanical, and he was so far convinced he had made the discovery that he took to educating himself, and became an expert arithmetician, and then found that arithmetical results agreed with his mechanical experiments. He appears to have eked out a bare existence for many years by teaching arithmetic, all the time struggling to get a hearing from some of the learned societies, but without success. In the year 1855 he found his way to Paris, where, as if by accident, he made the acquaintance of a young gentleman, son of M. Winter, a commissioner of police, and taught him his peculiar methods of calculation. The young man was so enchanted that he strongly recommended Lacomme to his father, and subsequently through M. Winter he obtained an introduction to the President of the Society of Arts and Sciences of Paris. A committee of the society was appointed to examine and report upon his discovery, and the society at its séance of March 17, 1856, awarded a silver medal of the first class to M. Joseph Lacomme for his discovery of the true ratio of diameter to circumference in a circle. He subsequently received three other medals from other societies. While writiug this I have his likeness before me, with his medals on his breast, which stands as a frontispiece