VOL. LXXXVII1.] PHILOSOPHICAL TRANSACTIONS. 3QQ 



and each division is T » T of an inch, and therefore subtends an angle at the centre, 

 whose arch is -^^ ; therefore the force which must be applied to each ball, to draw 

 the arm aside by 1 division, is to the weight of the ball, as gg ^ ^Tl to l > or as 



ah tol - 



The next thing is, to find the proportion which the attraction of the weight on 

 the ball bears to that of the earth on it, supposing the ball to be placed in the 

 middle of the case, that is, to be not nearer to one side than the other. When 

 the weights are approached to the balls, their centres are 8.85 inches from the 

 middle line of the case; but, through inadvertence, the distance, from each other, 

 of the rods which support these weights, was made equal to the distance of the 

 centres of the balls from each other, whereas it ought to have been somewhat 

 greater. Tn consequence of this, the centres of the weights are not exactly oppo- 

 site to those of the balls, when they are approached together; and the effect of 

 the weights, in drawing the arm aside, is less than it would otherwise have been, 

 in the triplicate ratio of rg-g? to the chord of the angle whose sine is ^~r, or in 

 the triplicate ratio of the cosine of 4- this angle to the radius, or in the ratio of 

 .9779 to 1. 



Each of the weights weighs 243()000 grains, and therefore is equal in weight to 

 30.64 spherical feet of water; therefore its attraction on a particle placed at the 

 centre of the ball, is to the attraction of a spherical foot of water on an equal par- 

 ticle placed on its surface, as 10.64 X .9779 X (^~f 5 Y to 1. The mean diameter 

 of the earth is 41800000 feet*; and therefore, if the mean density of the earth 

 be to that of water as d to 1, the attraction of the leaden weight on the ball will 

 be to that of the earth on it, as 10.64 X -9779 X (g^) 2 to 41800000D :: l to 



8739000D. 



It is shown therefore, that the force which must be applied to each ball, in order 



to draw the arm 1 division out of its natural position, is ■ ; of the weight of the 



ball ; and if the mean density of the earth be to that of water as d to 1 , the attraction 



of the weight on the ball is rr^-r^-r^- of the weight of that ball ; therefore the at- 



8/oyOOOD ° 



010 -|u2 



traction will be able to draw the arm out of its natural position by -jf^^r- or 

 divisions; and therefore, if on moving the weights from the midway to a 



10683d 



near position the arm is found to move b divisions, or if it moves 2b divisions on 

 moving the weights from one near position to the other, it follows that the density 



of the earth, or d, is jog^- 



* In strictness, we ought, instead of the mean diameter of the earth, to take the diameter of that 

 Bphere whose attraction is equal to the force of gravity in this climate j but the difference is not worth 

 regarding.— Orig. 



