SEQUEL TO THE GENERALIZATION. 113 



to the satisfaction of the mathematical world, that 

 the functions introduced in such cases are not 

 necessarily continuous, but are arbitrary to the 

 same degree that the motion is so practically; 

 though capable of expression by a series of circular 

 functions. This controversy, concerning the degree 

 of lawlessness with which the conditions of the 

 solution may be assumed, is of consequence, not 

 only with respect to vibrating strings, but also with 

 respect to many problems, belonging to a branch of 

 Mechanics which we now have to mention, the 

 Doctrine of Fluids. 



11. Equilibrium of Fluids. Figure of the 

 Earth. Tides. The application of the general 

 doctrines of Mechanics to fluids was a natural and 

 inevitable step, when the principles of the science 

 had been generalized. It was easily seen that a 

 fluid is, for this purpose, nothing more than a body 

 of which the parts are moveable amongst each 

 other with entire facility; and that the mathema- 

 tician must trace the consequences of this condition 

 upon his equations. This accordingly was done, by 

 the founders of mechanics, both for the cases of the 

 equilibrium and of motion. Newton's attempt to 

 solve the problem of the figure of the earth, sup- 

 posing it fluid, is the first example of such an inves*- 

 tigation: and this solution rested upon principles 

 which we have already explained, applied with the 

 skill and sagacity which distinguished all that New- 

 ton did. 



VOL. II. I 



