194 PROGRESS OF SCIENCE. 



comet, all but demonstrated the planetary nature of comets ; 

 he solved the problem of the ISOPERIMETERS whence the 

 discovery of the Calculus of Variations by Lagrange ; devoted 

 part of his life to the investigation of combinations, as con- 

 nected with that of Probability. His "Ars Conjectandi " is 

 one of the deepest mathematical works in existence on the 

 THEORY OF PROBABILITY. Bernouilli's Numbers, which 

 show his ingenuity and inventiveness, are among the most 

 familiar natural Constants known. His brother, JOHN 

 BERNOUILLI (1667 1748), also a mathematician, discovered 

 the EXPONENTIAL CALCULUS, and made experiments on the 

 elasticity of gases. DANIEL BERNOUILLI (17001782 

 John's son), a distinguished physicist, composed a celebrated 

 work called Hydrodynamica 1738. (See Thomson.) 



16981746. Maclaurin resolved the problem of the form 

 of the earth by means of certain properties of conic sections 

 a feat comparable to any performed by Archimedes ; found 

 the THEOREM which bears his name, and which is the gene- 

 ralisation of that of Newton upon the Asymptotes. 



1707 83. Euler found the method and the general 

 formulas to determine curves or surfaces for which certain 

 indefinite functions are lesser or greater than all others ; 

 enlarged the limits of the Differential Calculus by his 

 researches on the series of the Infinites, whilst his INTEGRAL 

 CALCULUS, a powerful instrument of his creation, simplified 

 the methods in use before him. As a physicist, he also 

 enunciated, after Descartes, Huygens, and Hooke, the 

 UNDULATORY THEORY OF LIGHT. 



1728 77. Lambert demonstrated the INCOMMENSU- 

 RABILITY OF THE ratio of the CIRCUMFERENCE to the 

 diameter; introduced the hyperbolical sinus; and found 

 the series which became the object of Euler's and Lagrange's 

 labours. 



1736 1813. Lagrange, by his method, called CALCULUS 

 OF VARIATIONS, extended Descartes's discovery in Indeter- 

 minate Analysis. His theories of ANALYTICAL FUNCTIONS, 

 and his theory of (musical) vibrations, proved the efficacy of 

 MATHEMATICS IN PHYSICAL PROBLEMS, whilst his ANALY- 

 TICAL MECHANICS transformed mechanics into a question of 



