328 A SHORT HISTORY OF SCIENCE 



duced Dolland to construct his achromatic lenses. . . . Euler was 

 thus the only physicist of the eighteenth century who advanced the 

 undulatory theory." Bull. Amer. Math. Soc., Dec., 1907. 



Euler gained a share of the prize of 20,000 offered by the 

 British parliament for a method of determining longitude at 

 sea, half of the same prize falling to Harrison the maker of a ship's 

 chronometer sufficiently accurate for the same purpose. 



He was probably the most versatile as well as the most prolific 

 of mathematicians of all time. There is scarcely any branch of 

 modern analysis to which he was not a large contributor, and his 

 extraordinary powers of devising and applying methods of calculation 

 were employed by him with great success in each of the existing 

 branches of applied mathematics; problems of abstract dynamics, 

 of optics, of the motion of fluids, and of astronomy were all in turn 

 subjected to his analysis and solved. Berry. 



It is the invaluable merit of the great Basle mathematician 

 Leonhard Euler, to have freed the analytical calculus from all geo- 

 metrical bonds, and thus to have established analysis as an inde- 

 pendent science, which from his time on has maintained an unchal- 

 lenged leadership in the field of mathematics. Hankel. 



PROGRESS IN THEORETICAL MECHANICS. The rapid develop- 

 ment of mechanics in the eighteenth century culminated in the 

 great classical treatises of d'Alembert (1717-1783) Traite de 

 dynamique and Lagrange (1736-1813) Mecanique analytique, 

 systematizing and coordinating the theories and results thus far 

 obtained. D'Alembert, working out ideas based on Huy gens' 

 theory of the centre of oscillation, formulated a very general dy- 

 namical principle since known under his name : 



On a system of points M, M', M" ... connected with one 

 another in any way, the forces P, P', P" ... are impressed. These 

 forces would impart to the free points of the system certain deter- 

 minate motions. To the connected points, however, different motions 

 are usually imparted motions which could be produced by the forces 

 W t W, W" ... These last are the motions which we shall study. 



Conceive the force P resolved into W and V, the force P' into W 

 and V, and the force P" into W" and V", and so on. Since, owing 



