3Q2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1 7Q8. 



in contrary directions; but if the point of rest move uniformly, the time of moving 

 from one extreme to the middle point of the vibration, will be equal to that of 

 moving from the middle point to the other extreme, and also, the time of 1 suc- 

 cessive vibrations will be very little altered ; and therefore the time of moving from 

 the middle point of one vibration to the middle point of the next, will also be very 

 little altered. It appears therefore, that on account of the resistance of the air, 

 the time at which the arm comes to the middle point of the vibration, is not ex- 

 actly the mean between the times of its coming to the extreme points, which causes 

 some inaccuracy in my method of finding the time of a vibration. It must be ob- 

 served however, that as the time of coming to the middle point is before the middle 

 of the vibration, both in the first and last vibration, and in general is nearly equally 

 so, the error produced from this cause must be inconsiderable; and, on the whole, 

 I see no method of finding the time of a vibration which is liable to less objection. 



The time of a vibration may be determined, either by previous trials, or it may 

 be done at each experiment, by ascertaining the time of the vibrations which the 

 arm is actually put into by the motion of the weights; but there is one advantage 

 in the latter method, namely, that if there should be any accidental attraction, such 

 as electricity, in the glass plates through which the motion of the arm is seen, 

 which should increase the force necessary to draw the arm aside, it would also dimi- 

 nish the time of vibration ; and consequently the error in the result would be much 

 less, when the force required to draw the arm aside was deduced from experiments 

 made at the time, than when it was taken from previous experiments. 



Account of the Experiments. — In the first experiments, the wire by which the 

 arm was suspended was 394- inches long, and was of copper silvered, one foot of 

 which weighed 2 T v grains: its stiffness was such, as to make the arm perform a 

 vibration in about 15 minutes. I immediately found indeed that it was not stiff 

 enough, as the attraction of the weights drew the balls so much aside, as to make 

 them touch the sides of the case; I chose however to make some experiments with 

 it before I changed it. In this trial, the rods by which the leaden weights were sus- 

 pended were of iron; for, as I had taken care that there should be nothing mag- 

 netical in the arm, it seemed of no signification whether the rods were magnetical 

 or not; but, for greater security, I took off the leaden weights, and tried what 

 effect the rods would have by themselves. Now I find, by computation, that the 

 attraction of gravity of these rods on the balls, is to that of the weights, nearly 

 as 17 to 2500; so that, as the attraction of the weights appeared, by the foregoing 

 trial, to be sufficient to draw the arm aside by about 1 5 divisions, the attraction of 

 the rods alone should draw it aside about -^ of a division; and therefore the motion 

 of the rods from one near position to the other, should move it about | of a 

 division. 



The result of the experiment was, that for the first 15 minutes after the rods 

 were removed from one near position to the other, very little motion was produced 

 in the arm, and hardly more than ought to be produced by the action of gravity; 



