&Q8 PHILOSOPHICAL TRANSACTIONS. [ANNO 1798. 



Exper. 13. Motion of the arm on moving weights from — to -f- = 6.12 



+ to - = 5.97 

 Time of vibration at , 4. = 7m g« 



- = 7 7 

 Exper. 14. Motion of arm by moving the weights from — to + = 6.27 



-f- to — = 6.13 



Time of vibration at -J- = 7 m 6 9 



- = 7 6 



In the next experiment 15, on May 27, the balls, before the motion of the 

 weights, were made to rest as near as possible to the sides of the case, but on the 

 contrary side from what they did in the 9th, 10th, and 1 1 th experiments. The 

 result as follows : 



Exper. 15. Motion of the arm from -f- 6.34 



Time of vibration 7 m 7 s 



The following 2 experiments, 16, 17, on May 28 and 30, were made by Mr. 

 Gilpin, who was so good as to assist me on the occasion. The results thus : 



Exper. 16. Motion of the arm =6.1 



Time of vibration = 7 m 16 s 



Exper. 17. Motion of the arm on moving weights from — to -f- = 5.78 



-f to — s= 5.64 

 Time of vibration at -\- = y m 2 9 



- =7 3 



On computing the density of the earth from these experiments. — I shall first 

 compute this, on the supposition that the arm and copper rods have no weight, 

 and that the weights exert no sensible attraction, except on the nearest ball ; and 

 shall then examine what corrections are necessary, on account of the arm and rods, 

 and some other small causes. The first thing is, to find the force required to 

 draw the arm aside, which, as before said, is to be determined by the time of a 

 vibration. 



The distance of the centres of the 2 balls from each other is 73.3 inches, and 

 therefore the distance of each from the centre of motion is 36.65, and the length 

 of a pendulum vibrating seconds, in this climate, is 39.14 ; therefore, if the stiff- 

 ness of the wire by which the arm is suspended is such, that the force which must 

 be applied to each ball, in order to draw the arm aside by the angle a, is to the 

 weight of that ball, as the arch of a to the radius, the arm will vibrate in the same 

 time as a pendulum whose length is 36.65 inches, that is, in \/%r-r. seconds; 

 and therefore, if the stiffness of the wire is such as to make it vibrate in n seconds, 

 the force which must be applied to each ball, in order to draw it aside by the angle 



A, is to the weight of the ball, as the arch of A X -, X %^n: to tne ra ^ ms * But 

 the ivory scale at the end of the arm is 38.3 inches from the centre of motion, 



