Reviexo of O. Gregory^- Treatise on Mechanics. 81 



This principle of oblique action, and the equilibrium of 

 its components, is in our opinion the only one, on which the 

 theory of the lever, and the other mechanical powers de- 

 pends. If it be asked, why a less weight on the longer arm 

 of a lever, will counterbalance a greater weight on the 

 shorter arm, if their distances from the prop be in the in- 

 verse ratio of the weights attached to them, the answer is 

 very ready, viz. that the action which supports the weights 

 is oblique, and the less oblique it is, the greater is the 

 force, which by the resolution of forces is necessary to 

 support any weight; and that, as has been shown, will 

 be in proportion to the distance of the weight from the 

 fulcrum, or prop. If this force be made constant, so as to 

 balance any given opposite force, the weight must be di- 

 minished in proportion to the length of the arm on which 

 it acts. 



The case of a cord fastened at its ends, and acted on by 

 a weight between them, is precisely identical with that of 

 the lever which we have been considering, the tension of 

 the cord, when perpendicular to the direction in which the 

 weight acts will have no tendency to support it, or the least 

 weight will produce an infinite tension in the cord ; it is only 

 when the cord and weight act obliquely, that a finite weight 

 can be supported by a finite tension, and when this is given, 

 the weight sustained by it, will be inversely proportional to 

 the length of the cord. 



We conclude therefore, that a bar, or some material solid 

 substance, is the only right line which can be acted on in the 

 manner propounded by our author, and this in fact, because 

 such a physical body includes in it not a line perpendicular to 

 the forces, but one which is oblique to them. 



Th6 next chapter on Statics, is that which treats of the 

 center of gravity and the manner of finding it in bodies of 

 different forms. Considering the triteness, and tediousness 

 of this subject as handled by most writers on mechanics, 

 and that the author's sole object must have been to select 

 from all of them, we think he has done this with judgment 

 if we except the solutions in articles 118, 121 ; the first is 

 circuitous, formal, and prolix, and in the author's usualstyle 

 of elaborating every thing ; the latter is erroneous either in 

 the premises, or conclusion ; it is rather a jumble of two 

 different solutions. 



Vol. VII.— No. 1. II 



