;s ) 



CHAPTER XIII. 



ATTRACTIONS. 



203. IT aj. pears from considerations which are detailed in 

 works on Physical Astronomy, that two particles of matter 

 placed at any sensible distance apart attract each other with 

 a force directly proportional to the product of their masses, 

 and inversely proportional to the square of their distance. 



Suppose then a particle to be attracted by all the par 

 of a body; if we resolve the attraction of each particle of tin-, 

 body into components parallel to fixed rectangular axes, and 

 take the sum of the components which act in a given direc- 

 tion, we obtain the resolved attraction of the whole body on 

 the particle in that direction, and can thus ascertain the re- 

 sultant attraction of the body in magnitude and direction. 

 We shall give some particular examples, and then proceed to 

 general formula 1 . 



204. To find tJie attraction of a uniform straight line on 

 an external point. 



By a straight line we understand a cylinder such that the 

 section perpendicular to its axis is a curve, every chord of 

 which is indefinitely small. 



Let AB be the line, P the attracted particle; take A for 



"Hirm, and Alt for 

 the direction of the axis 

 of x. Draw PL perj>en- 

 dicular to Ax; let AB = I, 

 AL = a, PL = l. Let 

 M and N be adjacent 

 points in the line, AMx^ 

 . If p be the 

 density of the line, and K the area of a section perpendicular 



