Rev. H. Moseley on the Theory of Resistances in Statics. 438 



A 



tan a = -=y- 



Jd 



1 B 



whence cos a — 



A 



sin a = 



Let the perpendicular upon this line from the point xy be 

 represented by j. 



t = — = -f x sin a-\-y cos a 



* a/AVB 3 



•"• (X) •V+V = 1+A.r + By 

 and P = Vv^+iW 



From the above it appears that the resistance varies in- 

 versely as a perpendicular from the point in which its direc- 

 tion meets the plane of xy, upon a certain line or axis in that 

 plane; and therefore, that the moments of all the resistances 

 of the system about that axis are the same. Where the re- 

 sistances are all in the same right line, this axis resolves itself 

 into a point. 



It is clear that whatever be the magnitudes of the other 

 forces which compose the system, the resistances which enter 

 into it will all be parallel to their resultant; provided only 

 that each resisting point be capable of supplying a resistance 

 parallel to that direction. This follows from the conside- 

 ration that the swn of the resistances is a minimum ; for it 

 is clear that their sum will be the least possible when, by 

 reason of their parallelism, they do not tend to counteract 

 one another. 



The values of A, B and C are determined by the following 

 equations, which result from substituting the values of P„ P 2 , 

 &c„ in equations (I). 



-C— -X + M = o 

 A.r + By J 



-{\ + Ax + By} + Nl = 

 ~\l+A,r+B/yJ 



N, = 

 Third Series. Vol. 3. No. 18. Dec. \H33, 3 K 



