in the military school. At the age of twenty-one he went to Paris to read before the Academy of Sciences a memoir on the resolution of numerical equations, which
was an improvement on Newton's method of approximation. This investigation of his early youth he never lost sight of. He lectured upon it in the Polytechnic School; he developed it on the banks of the Nile; it constituted a part of a work entitled Analyse des equationes determines (1831), which was in press when death overtook him. This work contained "Fourier's theorem" on the number of real roots between
two chosen limits. Budan had published this result as early
as 1807, but there is evidence to show that Fourier had established it before Budan's publication. These brilliant results were eclipsed by the theorem of Sturm, published in 1835.
Fourier took a prominent part at his home in promoting the Revolution. Under the French Revolution the arts and sciences seemed for a time to flourish. The reformation of the weights and measures was planned with grandeur of conception. The Normal School was created in 1795, of which Fourier became at first pupil, then lecturer. His brilliant success secured him a chair in the Polytechnic School, the duties of which he afterwards quitted, along with Monge and
Berthollet, to accompany Napoleon on his campaign to Egypt. Napoleon founded the Institute of Egypt, of which Fourier became secretary. In Egypt he engaged not only in scientific work, but discharged important political functions. After his return to France he held for fourteen years the prefecture of Grenoble. During this period he carried on his elaborate investigations on the propagation of heat in solid bodies, published in 1822 in his work entitled La Theorie Analytique de la Chaleur. This work marks an epoch in the history of