402 PHILOSOPHICAL TRANSACTIONS. [ANNO 17Q8. 



The attraction of the weight on the farther ball, in the direction bw, is to its at- 

 traction on the nearer ball :: ud 3 : wd 3 :: .0017 : 1; and therefore the effect of 

 the attraction of the weight on both balls, is to that of its attraction on the nearer 

 ball :: .9983 : 1 . 



To find the attraction of the copper rod on the nearer ball, let b and w, fig. 6, 

 be the centres of the ball and weight, and ea the perpendicular part of the copper 

 rod, which consists of 2 parts, ad and de: ad weighs 22000 grains, and is 16 

 inches long, and is nearly bisected by w\ de weighs 41000, and is 46 inches lone-; 

 wb is 8.85 inches, and is perpendicular to ew. Now the attraction of a line ew, of 

 uniform thickness, on b, in the direction bw 9 is to that of the same quantity of 

 matter placed at w :: bw : eb\ therefore the attraction of the part da equals that of 

 ~~°~L* — • or 1 ^ 300 j placed at w; and the attraction of de equals that of 41000 



X ^ x T "" 41000 x Td X M» ° r 2500 > P laced at the same point; so that the 

 attraction of the perpendicular part of the copper rod on b, is to that of the weight 

 on it, as 18800 : 2439000, or as .00771 to 1. As for the attraction of the in- 

 clined part of the rod and wooden bar, marked vr and rr in fig. 1, it may safely 

 be neglected, and so may the attraction of the whole rod on the arm and farthest 

 ball; therefore the attraction of the weight and copper rod, on the arm and both 

 balls together, exceeds the attraction of the weight on the nearest ball, in the pro- 

 portion of .9983 -f- .0139 -f- .0077 to 1, or of I.OI99 to ]. 



The next thing to be considered, is the attraction of the mahogany case. Now 

 it is evident, that when the arm stands at the middle division, the attractions of 

 the opposite sides of the case balance each other, and have no power to draw the 

 arm either way. When the arm is removed from this division, it is attracted a 

 little towards the nearest side, so that the force required to draw the arm aside is 

 rather less than it would otherwise be ; but yet, if this force is proportional to the 

 distance of the arm from the middle division, it makes no error in the result; for 

 though the attraction will draw the arm aside more than it would otherwise do, yet, 

 as the accelerating force by which the arm is made to vibrate is diminished in the 

 same proportion, the square of the time of a vibration will be increased in the 

 same proportion as the space by which the arm is drawn aside, and therefore the 

 result will be the same as if the case exerted no attraction; but if the attraction of 

 the case is not proportional to the distance of the arm from the middle point, the 

 ratio in which the accelerating force is diminished is different in different parts of 

 the vibration, and the square of the time of a vibration will not be increased in 

 the same proportion as the quantity by which the arm is drawn aside, and therefore 

 the result will be altered by it. 



On computation, I find that the force by which the attraction draws the arm 

 from the centre is far from being proportional to the distance, but the whole force 

 is so small as not to be worth regarding; for, in no position of the arm does the 



