Rev. H. Moseley on the Theory of Resistances in Statics. 431 



a moment backward in the same course, from Greece to Italy, 

 whither it was twice sent from the same quarter, and from 

 Italy to both sides of the Rhine and to Britain, — is in that 

 westerly or north-westerly direction which conforms to, and so 

 far confirms the dependence of all these phenomena on, one 

 general law — the cause I have assigned. 



Alexander Walker. 



LXIX. On the Theory of Resistances in Statics. By the Rev. 

 H. Moseley, B.A., Professor of Natural Philosophy in 

 Kitig's College, London*. 



TN a paper inserted in the Philosophical Magazine for Oc- 

 -*- tober, I have given a demonstration of the following 

 theorem : If there be a system of forces in equilibrium among 

 which there enter the resistances of any number qf fixed points, 

 then are these resistances such that their sum is a minimum ; 

 each being considered a function of the coordinates of its point 

 of application, taken with a positive sign, and subjected to the 

 conditions imposed by the equilibrium of the whole. I have 

 also pointed out the steps by which- this principle may be ap- 

 plied to the actual determination of the amount and direction 

 of the resistance upon each point of the system in terms of 

 the other forces which compose it. 



It is my object at present to give the actual solution of that 

 particidar but very important case, of the more general pro- 

 position, in which the forces and resistances of the system are 

 all parallel to one another. The solution of this case is en- 

 tirely free" from that elaboration of analysis which besets the 

 more general proposition. 



Let the plane of xy be taken perpendicular to the given 

 parallel directions of the forces of the system. 



Let the resistances of the system be P,, P 2 , P 3 , &c, and 

 let the coordinates of the points where these directions inter- 

 sect the plane of xy, be x x y x , oc^y^, x 3 y 3 , &c. Also let the 

 sum of those forces of the system which are not resistances be 

 M, and the sums of their moments about the axes of y and x 

 respectively N 2 and N 2 . 



By the known conditions of equilibrium, therefore, we have 



SPtf+N, = Ol (1) 



2Pj,+ N 2 = oj 

 * Communicated by the Author, 



