400 THE SCIENTIFIC MONTHLY 



Laplace, and many others of whom a brief mention only can be made, 

 was characterised also by social ferment which has profoundly changed 

 the basis of society. The French revolution with all its far reaching 

 consequences took place in the middle of the time of greatest mathe- 

 matical activity, and the Napoleonic wars, carried into almost every 

 country of Europe, served to stir up intercourse between the nations 

 to a degree which must have had much effect on all forms of scientific 

 activity. At the same time, the American revolution produced a new 

 body of political thought which has had its development in the forma- 

 tion of a great and powerful nation. In England, comparatively free 

 from invasion or social disturbance, little was produced of permanent 

 value, the influence of Maclaurin being directed to the retention of 

 published Newtonian methods. With the single exception of the 

 Italian Lagrange, the great names of the period belong to France and 

 Switzerland. 



Those who have had the most far reaching influence, judged by 

 modern standards, besides Euler, Lagrange, and Laplace, are Legendre, 

 Fourier, Poisson, Monge, and Poncelet. I omit those whose chief 

 labors were more closely associated with experimental work. The 

 means for publication in this period were becoming more extensive and 

 it is less easy to discover what each man owed to personal meetings 

 with his contemporaries. The principal academies of Europe were 

 starting or had started their volumes of transactions, extended treatises 

 could be published and circulated, and the scientific men had new op- 

 portunities to meet and discuss, even to some extent with those of other 

 countries, especially on the continent. The more enlightened courts 

 sought the services of the ablest scientific men and, when the latter did 

 not mingle too much in politics, on the whole treated them well. 

 Fortunately, at least for the leaders, their teaching was usually con- 

 fined to small bodies of earnest students and they appear to have been 

 little hampered by demands on their time and energy for administrative 

 duties. It is interesting to note that in a time of political disturbance 

 which was perhaps comparable to that produced by the great war, the 

 main foundations of modern mathematics, both pure and applied 

 mathematics, were firmly laid. 



Leonard Euler, born in 1707 at Basle in Switzerland and educated 

 in mathematics by Bernouilli, was perhaps the most industrious of all 

 his contemporaries and it is difficult to say whether his services to 

 mathematics are to be judged best by his excellent treatises on analysis, 

 including the calculus, or by his original memoirs on applied mathe- 

 matics. In the former, he followed up all that was known at the time, 

 recasting proofs and setting the whole in logical order. In the latter, 

 he is best known for his formulation of the equations of motion of a 

 rigid body, for a similar service in the equations of motion of a fluid 



