404 PHILOSOPHICAL TKANSACTIONS. 



[ANNO 1798. 



BW 



by the attraction, =ab X — « ? so that the actual force by which it is drawn to- 

 wards A is = AX — 5 = AB + B07 — AB X (H — ) 3± BX— 2BX X AB 



wr v ' wb ' WB ? 



very nearly. So that the actual force with which the ball is drawn towards the mid- 

 dle point of the vibration, is less than it would be if the weights were removed, in 

 the ratio of J to 1, and the square of the time of a vibration is increased in 



the ratio of J to 1 — — — ; which differs very little from that of 1 4- b6 to 1 



which is the ratio in which the motion of the arm, by moving the weights from one 

 near position to the other, is increased. 



The motion of the ball answering; to 1 division of the arm, is = '■ ; and 



b ' 20x38.3 ' 



if wb be the motion of the ball answering to d divisions on the arm, 



l£r = 20 x f*Tx 8.85 P W5 ; therefore the time of vibration, and motion of the 

 arm, must be corrected as follows : If the time of vibration is determined by an ex- 

 periment in which the weights are in the near position, and the motion of the arm, 

 by moving the weights from the near to the midway position, is d divisions, the ob- 

 served time must be diminished in the subduplicate ratio of 1 to 1, that is, 



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in the ratio of 1 — to 1 ; but when it is determined by an experiment in 



which the weights are in the midway position, no correction must be applied. 



To correct the motion of the arm caused by moving the weights from a near to 

 the midway position, or the reverse, observe how much the position of the arm 

 diners from 20 divisions, when the weights are in the near position : let this be n 

 divisions, then if the arm at that time be on the same side of the division of 20 as 

 the weight, the observed motion must be diminished by the — — part of the whole; 

 but otherwise it must be as much increased. If the weights are moved from one near 

 position to the other, and the motion of the arm be 2d -divisions, the observed motion 



must be diminished by the — — - part of the whole. If the weights are moved from 



one near position to the other, and the time of vibration be determined while the 

 weights are in one of those positions, there is no need of correcting either the mo- 

 tion of the arm, or the time of vibration. 



