of JVatural Philosophy. 131 



tiatc an assertion which may perhaps be deemed harsh, 

 xve will just glance at the contents of the Second Book, — 

 a part which certainly affords a not unfavourable specimen 

 of the execution of the whole. As all the improvements 

 which we propose are predicated on the supposition that the 

 size remains unaltered, (a supposition rendered necessary 

 by the limited time which can be properly devoted to this 

 subject in our colleges,) we begin with the general remark 

 that room might be gained for several important topics now 

 omitted, by abridgements in the demonstrations, particular- 

 ly those in which variations are introduced, and various oth^ 

 ers in which prolixity contributes not at all to clearness.— 

 The chapter on percussion might have been easily made 

 to include, within its present limits, a general theory of imr 

 pact in bodies imperfectly elastic, and a statement and recon- 

 ciliation of the apparently jarring theories of Newton and 

 Leibnitz concerning the measure of force in moving bodies. 

 To that on the composition of forces, might have been ad- 

 vantageously subjoined the results of impact in spherical 

 bodies, whether non-elastic or elastic, which meet each oth- 

 er from directions not in the same right line. If the theory of 

 the cycloidal pendulum, detailed at length inch. v. sec. 3. de- 

 serves to be retained, it is only for the sake of a theorem which 

 Enfield has by a strange oversight omitted ; we mean that which 

 determines the time of vibration. This theorem is valuable 

 principally as it also determines the limit of the time of vi- 

 bration of the common pendulum, when the arc is made in- 

 definitely small. But as the subject is now left, not only 

 is no true information given to the student concerning the 

 time of vibration in a circular arc, but the unaccountable 

 blunder of Keill, Parent, Musschenbroek and others, in 

 making it equal to that in the chord,* is imposed upon him. 



*■ This is not indeed in so many words afSrmed ; but several of the demon- 

 ■itralions imply it, and become nngalory unless it is admitted. Thus in prov- 

 ing that vibrations in small unequal arcs are performed in nearly equal times, 

 fhe inference is made from Ihe chords to the arcs on the ground that "very 

 small arcs dift'er very little from their respective ciiords in length or decliv- 

 ity." The same language had been used before by Flelsham and Rutber- 

 forth. But it must be obvious to ail who are in the least familiarized to the 

 subject of ultimate ratios, that although the arc and its corresponding chord 

 ultimately agree in " length,'' tliey differ totally in " declivity." In all 

 states of the arc and chord, (and therefore when both are indefinitely small,) 

 ihe declivity of the former, at the highest point, is twice that of fhe latter. 

 The acceieratitig force do'.vnthe oiierd isuaiform ; lathe arc it is as the sine 



