160 Wisconsin Academy of /Sciences, Arts, and Letters. 



co-ordinates are x, j, z, then J* may be resolved into 

 three component forces acting along axes at right angles 

 to each other, the values of which components will be 

 P cos a, P cos /3, P cos y — alpha, beta, gamma, denoting 

 the angles made by the direction of the force P, with the 

 three co-ordinate axes. 



Let the straight line joining p and o be called P. Then 

 ^ — V{i— x)' -f (g — y)* + (h — z)S ^■iid the expressions 

 for the component forces will then become 



X = P 



cos a 



Y = P cos /3 = P 



_ p (f-x)' 

 ~ D 



_-p (g-.y) 



D 



Z = P cos y = P 



_-p (b-z) 



D 



which are to be made 

 negative when the force 

 (A) P is attractive towards 

 O, as it then tends io'dl- 

 minisli the distance D. 



(A reference to Fig. 1 will show the applicability of 

 these formulae.) 



If the force P be one which depends on the mass of a 

 solid, like gravity ; or, like Electricity or Magnetism, one 

 whose accumulation or density., as we may say, is greater at 

 some points than others ; and if it also depend in any man- 



