**Aléxis Petit** was a child prodigy. He attended the École Centrale in Besançon where he amazed everyone with the quality of his work. He then went to a private school in Paris where he was taught by teachers who also taught at the École Polytechnique. By the age of ten and a half Petit had achieved the entry standard to become a student at the École Polytechnique but the entrance requirements insisted that students could not enter until they were sixteen years old. He therefore had to wait for around five years before he could enter, which of course he did at the earliest possible date ranked first among all the entering students. Entering the École in 1807 he was in the same class as Poncelet who was nearly three years older than Petit. In 1809 Petit graduated from the École and immediately joined the teaching staff. He was awarded a doctorate in 1811 for an outstanding thesis on capillary action. However, by this time he was already teaching physics at the Lycée Bonaparte where he had been appointed in 1810 [1]:-

As a teacher he was both popular and successful, and when he succeeded to J-H Hassenfratz's chair of physics at the École Polytechnique in1815, after a year as assistant professor, he extended and improved the courses in his subject.

Petit married the sister of François Arago and the Petit and Arago collaborated on experiments on the refraction of light in gases. In particular, they examined the effect of temperature on the refractive index of gases. Petit had been taught physics at the École Polytechnique of a conventional nature. In particular he had been taught that light was composed of corpuscles, so it is not surprising that in 1814-15, when he himself was teaching physics at the École, he was presenting the same views to his students as those he had been taught. His work with Arago in 1815, however, made him take a different view on the nature of light and in December of that year he stated his position as a believer in the wave theory of light.

Petit worked with Pierre Louis Dulong from 1815 with the aim of submitting an entry for the 1818 Grand Prix of the Academy of Sciences which had been set on the topic of thermometry and the laws of cooling. In 1818 Petit and Dulong won the Academy Prize for their work on the law of cooling but at this stage they had now yet discovered the Dulong-Petit law for which they are best known. Their prize essay reported on their [1]:-

... classic experimental investigation, which established the gas thermometer as the only reliable standard and put the approximate nature of Newton's law of cooling beyond all doubt.

The following year he published the Dulong-Petit law on the theory of heat. The two scientists formulated an empirical law concerning the specific heat of elements which states that the specific heat of all elements is the same on a per atom basis. The law has exceptions and was not fully understood until quantum theory was used. However, it gave chemists, who at that time were having difficulty determining atomic weights and distinguishing them from equivalent weights, a means of estimating the approximate weight of an element merely by measuring its specific heat.

In 1818 Petit also published on the general principles of machine theory. This work, in addition to his exceptional doctoral thesis, showed that he was at least as great a mathematician as he was experimental physicist. Sadly, however, Petit did not live to make further scientific discoveries [1]:-

His last years ... were clouded by grief and illness; shortly after the death of his young wife, in1817, he contracted tuberculosis, the disease from which he died.

Despite his short life (he was only 28 years old when he died) he had already been honoured with election to the Societé Philomatique. He died too young to have made it to the Academy of Sciences but there is little doubt that his election would have come soon given the exceptional quality of his work.

**Article by:** *J J O'Connor* and *E F Robertson*

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