132' Bemarks on Dr. Enfield's Institutes 



The theory of equihbrium in the mechanical powers (chap, 

 vi.) might have been stated in a more concise and popular 

 form, grounded on the principle of virtual velocities, to make 

 room for a brief account of prime movers, and the motion 

 and maximum effect of machines. The subjects of friction, 

 and the construction of wheel carriages, are now dispatched 

 in half a page, — less than half the room occupied by the 

 difficult and almost useless proposition on the wedge. These 

 important and practical subjects ought to be discussed much 

 more in detail ; nor ought the former to be grounded on the 

 experiments of Vince, to the exclusion of the much more 

 important and diversified ones of Coulomb. In chapter vii. 

 the mathematical theory of projectiles is pursued to the 

 length of ten or twelve propositions ; and we are left to an 

 incidental remark of a single sentence inserted by the editor 

 of the second edition, for all our information concerning- the 

 total discrepancy between theory and practice. Several 

 parts of this chapter possess very little interest, even in a 

 mathematical point of view ; and had they been much more 

 important than they are, they ought to have given way to 

 such a statement of the principal results of experiment on 

 the motion of projectiles as the writings of Robins, Rum- 

 ford, and Hutton mighthave easily furnished. Several lem-^ 

 mas introduced from the Principia, into the concluding sec- 

 tion on central forces, although needed for the objects which 

 the original author had in view, are here entirely out of 

 place. Such of them as were wanted should have been di- 

 vested of their latinized idiom, and translated into a more 

 modern and intelligible dialect. Several of the more im- 

 portant theorems relating to motion by a central force vary- 

 ing inversely as the square of the distance, might have been 

 subjoined with the utmost advantage to the single one with 

 which the Book now closes. — The subjects of rotatory mo- 

 tion, the funicular polygon and equilibrium of arches, the 



of the distance from ihe lowest point, or ultimately as the distance itself. This 

 last ciiTuniPtaiice establishes the equality of the times of vibration in vavy 

 small circular arcs and in Ihe cycloid, on grounds independent of the high- 

 er Calculus ; for it is evident tiiat the radius of curvature at thelowest point 

 is the same for both curves. Instead, therefore, of its being true that the 

 times of vibration in tlic arc and chord approacli to an ultimate ratio of 

 equality, they approac!) !o a ratio of finite inequality. INo one but the stu- 

 dent can need to Lc infoirned tliat the former is the least, in the ralio of 

 0,7S54 to 1 . 



