84 tteview of O. Gregory^s Treatise on Mechanics, 



Chapter 3d, on centripetal forces Is taken almost, word 

 for word, from Simpson's Fluxions, with the exception of a 

 proposition, or two, introduced by Mr. Gregory, perhaps 

 from some other writer; that in Art. 280, to prove the equal 

 velocities at equal distances from the center of bodies de- 

 scending in curves, or right lines, is an awkward attempt by 

 a blind, and circuitous route to supersede what had been 

 done better by Simpson, and infinitely better by Newton. 

 Few learners can be made to understand the jumbled solu- 

 tion given by our author. 



Chapter 4th, treats of rotatory motion, and of the centers 

 of Gyration, Oscillation, Percussion and spontaneous Rota- 

 tion, together with other subjects connected with them. We 

 find not much to censure, or much to applaud in this, ex- 

 cept a more glaring instance of that pedantry, and ostenta- 

 tion of learning, of which there are so many in this book. 

 After having proved, what is very easily, and evidently 

 shown by elementary principles, that the force of bodies or 

 the particles of bodies, in rotatory motion, is as the squares 

 of their distances from the axis of motion ; such a plain Eu- 

 clidean 'demonstration does not appear to have satisfied the 

 magnificent ideas of the author, who every where prefers 

 demonstrations even of the simplest theorems, if derived 

 from the most exalted and obscure source of Analytics. 

 Accordingly, we have in Art. 302 a long demonstration de- 

 pending on the differential calculus, and the principles of 

 D'Alembert, to show that the force of bodies in rotary mo- 

 tion is truly as had been before estimated by the princi- 

 ples of geometry and mechanics. As the diiferential 

 calculus, and D'Alembert's principles, are founded on these, 

 if they have any foundation, it is evident that this proof is a 

 mere argumentum in Circulo and therefore ostentatious, 

 and delu'ive. 



Chapter 5th, is a treatise on Percussion founded on the 

 principle of its effects arising from a continued, and succes- 

 sive action of the particles of the bodies, which undergo 

 percussion, and therefore, that it is in itself a kind of press- 

 ure produced in a very small moment of time. On this 

 hypothesis, the deductions are made a priori, and are con- 

 sentaneous to those derived from other principles. The 

 conservatio virinm, of Huygenius and Bernouilli, follows easi- 

 ly from this doctrine, but all this had been shown with much 



