158 Statics. 



the weight being d, and the radius of the surface R. We wish 

 to know what this addition must be, when the weight is j/, the 

 diameter of the cord tf', and the radius of the surface R'. It will 

 be observed, after what has been said, that if there were no dif- 

 ference except with respect to the entire weight by which the 

 cord is stretched, we should arrive at a solution by the propor- 

 tion 



p : p' : : k : - = the addition required. 



But if, beside the difference in the weights, there is also a differ- 

 ence in the curvature of the surfaces ; then, by the second of the 

 above remarks ; namely, that the additions arising from this 

 cause are in the inverse ratio of the radii of the surfaces, we 

 should obtain the addition in question, together with that due to 

 a change of weight, by the following proportion^ 



Rl . R . . 



Zt .ft 



kR P 

 R' 



Regard being had to the third remark, we shall obtain the addi- 

 tion to be made on account of the three causes united, by the 

 proportion 



, ., kRp' d'kRp' 



o : o' :; - _ : x = - _. 

 R p dR'p 



The resistance in the first case, therefore, will be to the resist- 

 ance in the second 



that is, the resistances arising from the stiffness of the cords are 

 as the weights which stretch the cords, multiplied by the diame- 

 ters of these cords, and divided by the radii of the surfaces over 

 which they pass. 



These conclusions, it may be observed, are not perfectly rig- 

 orous ; but they may be regarded as sufficiently exact for prac- 

 tice, till experiment has thrown new light upon the subject. In- 

 deed, experiment shows that the resistance arising from the stiff- 



