SEQUEL TO THE GENERALIZATION. 371 



weight of columns of the fluid reaching to the centre ; 



O <J 



took, as his basis, the prepeudicularity of the resulting force at each 

 point to the surface of the fluid ; Bouguer conceived that both prin- 

 ciples were necessary ; and Clairaut showed that the equilibrium ol 

 all canals is requisite. He also was the first mathematician who de- 

 duced from this principle the Equations of Partial Differentials by 

 which these laws are expressed ; a step which, as Lagrange says, 12 

 changed the face of Hydrostatics, and made it a new science. Euler 

 simplified the mode of obtaining the Equations of Equilibrium for any 

 forces whatever ; and put them in the form which is now generally 

 adopted in our treatises. 



The explanation of the Tides, in the way in which Newton at- 

 tempted it in the third book of the Principia, is another example of 

 a hydrostatical investigation : for he considered only the form that 

 the ocean would have if it were at rest. The memoirs of Maclaurin, 

 Daniel Bernoulli, and Euler, on the question of the Tides, which 

 shared among them the prize of the Academy of Sciences in 1740, 

 went upon the same views. 



The Treatise of the Firjure of the Earth, by Clairaut, in 1743, ex- 

 tended Newton's solution of the same problem, by supposing a solid 

 nucleus covered with a fluid of different density. No peculiar novelty 

 has been introduced into this subject, except a method employed by 

 Laplace for determining the attractions of spheroids of small eccen- 

 tricity, which is, as Professor Airy has said, 13 " a calculus the most 

 singular in its nature, and the most powerful in its effects, of any 

 which has yet appeared." 



12. Capillary Action. There is only one other problem of the 

 statics of fluids on which it is necessary to say a word, the doctrine 

 of Capillary Attraction. Daniel Bernoulli, u in 1738, states that he 

 passes over the subject, because he could not reduce the facts to gen- 

 eral laws : but Clairaut was more successful, and Laplace and Poisson 

 have since given great analytical completeness to his theory. At pres- 

 ent our business is, not so much with the sufficiency of the theory tc 

 explain phenomena, as with the mechanical problem of which this is 

 an example, which is one of a very remarkable and important char- 

 acter; namely, to determine the effect of attractions which are exer- 

 cised by all the particles of bodies, on the hypothesis that the attrac- 



12 Mic. Anal'jt. ii. p. ISO. 1S Enc. lid. Fig. of Earth, p. 192. 



14 Hydrodyn. Tref. p. 5. 



