114 HISTORY OF MECHANICS. 



We have already seen how the generality of 

 the principle, that fluids press equally in all direc- 

 tions, was established. In applying it to calcula- 

 tion, Newton took for his fundamental principle, 

 the equal weight of columns of the fluid reaching 

 to the center; Huyghens took, as his basis, the per- 

 pendicularity of the resulting force at each point to 

 the surface of the fluid ; Bouguer conceived that 

 both principles were necessary; and Clairaut showed 

 that the equilibrium of all canals is requisite. He 

 also was the first mathematician who deduced from 

 this principle the Equations of Partial Differentials 

 by which these laws are expressed ; a step which, 

 as Lagrange says 10 , 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 attempted 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 Figure of the Earth, by 

 Clairaut, in 1743, extended Newton's solution of 

 10 Mec. AnalyL ii. p. 180. 



