Review of O. Gregory^ s Treatise on Mechanics. 79 



al to the components." This proposition, though taken 

 from Francoeur, and repeated by other French writers, we 

 venture to oppugn, as mathematically and physically in- 

 correct. 



A force acting perpendicularly on a mere mathematical 

 line, it is evident, can communicate no force to it, either 

 longitudinally, or laterally, except at the very point where 

 it acts : for the action, in such case, in the direction of 

 the line is nothing by the principles of mechanics, and no 

 other part of the line, admitting it to be cohesive, can be 

 affected by a force at a distance from il, unless there be 

 some longitudinal action ; this can take place only when 

 the line is not perpendicular to the direction of the force 

 acting on it, or when it is oblique to that direction; but it 

 may be maintained that by a line is meant a material sub- 

 stance of an evanescent breadth, cohesive and inflexible. 

 The supposition of perpendicularity will be found, in this 

 case, to be equally inconsistent and erroneous, and by no 

 means according with the author's own deductions, which 

 are grounded not on premises of a perpendicular, but an 

 oblique action on the line perpendicular to the parallel 

 forces. To produce the oblique action, two equal com- 

 ponents acting perpendicularly to the parallel forces, have 

 been introduced ; we then have the proljlem reduced to 

 the case of two forces acting at a point in an oblique di- 

 rection. Without the consideration of an oblique force, it 

 appears to us impossible to solve this problem, as its con- 

 ditions are evidently impossible. 



But supposing the line to be a physical quantity, or in 

 the practical sense, to have length, breadth, and thick- 

 ness, each of which is of some definite quantity, in this 

 case, it is no longer a line, but a material body, possessing 

 the properties and dimensions of a solid. If this material 

 substance be of sufficient cohesive strength, parallel forces, 

 acting in the manner of the proposition on its surface, will 

 produce a lateral action, together with a longitudinal ac- 

 tion, which, though the forces be unequal, at different dis- 

 tances, may counterbalance each other. But it should be 

 distinctly observed, that this is not because the parallel 

 forces diCt perpendicularly on the body, but because they 

 act, in such case, obliquely, and may be resolved into two 

 actions, one of which is perpendicular to the direction of 



