404 NEW INVESTIGATION OF 



riched science with valuable artifices, modes of 

 investigation, and results which they have obtained 

 by means of successfully developing the artifices 

 and new views which they have created. 



To investigate the resultant of the forces Pj ; 

 P2 &c. &c. which act upon the point P, it will be 

 necessary in the first place, to refer all the points 

 in the system to three planes Ji7 O _y ; x O z; 

 1/ O z a.t right angles to each other and arbitrarily 

 fixed. We then resolve each force in the di- 

 rection of these three fixed co-ordinate planes 

 and sum the efi'ects of the attractions in these 

 directions, then these sums will enable us to cal- 

 culate the resultant in magnitude and direction by 

 the well known formula R zi \/ A^ + B^ + C^ and 



A R C 



— = Cos.«; ^ 1= Cos./? ; ^^ iz Cos.y ; where R := 



The resultant and A, B, C the sum of the forces 

 in the direction of the co-ordinate axes .r, j/, z re- 

 spectively ; and a, /3, y the angles which R makes 

 with the co-ordinate planes. (See Poisson's 

 Traite Mecanique, page 55.) 



This mode of investigation was first laid down 

 and pursued by the celebrated Maclaurin in his 

 Treatise on Fluxions. See Mecanique Ana- 



