of Natural Philosophy. 1 35 



lion is lost In passing from one plane to another. The dem- 

 onstration of the 38th is also inconclusive, because it has 

 not been previously shown that the toial loss of motion in 

 passing through a set of planes becomes evanescent, when 

 the planes become indefinitely numerous, and their suc- 

 cessive inclinations indefinitely small. 



Prop. 47. The demonstration shews that we may form a 

 body by assembling particles round Hi given point, such that 

 the body shall balance itself about this point ; but it by no 

 means shews that when the body is given, a point about 

 which it will balance itself can be found ; — much less that 

 this point, as the proposition implies, is the same for all posi- 

 tions of the same body. 



Prop. 49. The diagram employed in the proof of this 

 proposition is drawn so inaccurately as to render it scarce- 

 ly intelligible. There was the less reason for this inaccura- 

 cy, as in Rutherforth, from whom the diagram is copied, it 

 is drawn correctly. 



Prop. 51. The demonstration of this important theorem 

 is less general than the enunciation requires, by being con- 

 fined to the case in which the bodies move in tlie same 

 plane. The statement with which the first corollary begins 

 is true only under such limitations as the student can scarce- 

 ly be supposed -able to apply. 



Prop. 56. In the great majority of instances in which the 

 screw is employed, the resisting force is not moved up 

 through an inclined plane, as the demonstration supposes. 

 It would be far more simple and satisfactory to infer the law- 

 of equilibrium directly from the relative velocities of the 

 points of application of the power and resistance. 



Prop. 57. Schol. 1. "In all compound machines there 

 will be an equilibrium, when the sum of the powers are to 

 the weight, as the velocity of the weight is to the sum of 

 the velocities of the powers." No interpretation can be put 

 upon this statement which will render it true. The error 

 arose, we presume, in some such manner as she following. 

 It was apparent that in compound machines, (or rather in 

 machines where sever-al powers put several resistances in 

 cquilibrio.) the sura of the products of the powers each inta 

 its velocity, u^as equal to the sum of the products of the 

 weights each into its velocity. This equation had the ap- 

 pearance of being capable of resolution into an analogy : 



