NEWTONIAN CONSTANT OF GRAVITATION. 35 
owing to their centrifugal force when this acceleration has given rise to an angular 
velocity, and must be pulled by the gravitation of the lead balls so as to be further 
apart than supposed. Moreover, since each ball can rotate separately on its own fibre 
with a period of its own of as much as 6°720 and 9°055 seconds in Experiments 4 to 8 
and 10 to 12, they must, in their rotation about their own axes, lag behind the 
rotation of the mirror when it is being accelerated. The magnitude of these several 
errors is infinitesimal, or greatly below the limiting accuracy aimed at, and, in all 
cases, may be calculated and allowed for if necessary. Thus, in Experiment 8, the 
lower ball in the extreme case of an amplitude of 10,000 divisions, or 100,000 units 
(I make +5 division the unit, to avoid decimals), is at the middle of the swing thrown 
out by centrifugal force sso inch, and the upper one about half as much. The 
linear acceleration on the balls, due to the action of the torsion fibre, is the same as 
that due to a pendulum nearly six miles long, or, more exactly, 364,335 inches, so 
that the actual acceleration produced by the fibre in the case of the lower ball is 
about 1 in 33,000 more than is supposed, and, on. the upper ball, about 1 in 70,000. 
The amount by which the lower ball is pulled outwards by the gravitation of the lead 
ball next to it, even when that is in its neutral position, where its actual attraction is 
a maximum, is less than a ten-millionth of an inch. The rotational mobility of the 
gold balls, however, in Experiments 4 to 8 and 10 to 12, was more than I had 
intended, and, as I felt that it was important to know precisely what effect this 
would have upon the result, I referred the problem to Professor GREENHILL, who very 
kindly explained to me exactly how to evaluate it, and, with Professor Mincuin, went 
through the great labour of obtaining and solving the resulting cubic equation. The 
rigidity of the fibre, in this the worst case, should “be diminished by less than 
1 im 7850. An increase in the thickness of the two suspending fibres of a few 
ten-thousandths of an inch, such as I made use of in Experiment 9, would reduce 
this to the order of 1 in 100,000, or even less, and the complex calculation of this 
correction would no longer be necessary. 
Finally, it is assumed that the counterweight, when it has replaced the gold ball, 
is also rigidly connected with the mirror and acts axially. With respect to the 
rigidity of the attachment, it is unnecessary to do more than state that the friction on 
the suspending hook must be many thousand times greater than the greatest couple 
ever developed by the torsion fibre, and that, with regard to its axiality, the same 
remarks that were made with respect to the beam mirror apply with even greater 
force. There is only one point about which, in consequence of the microscopic 
examination after Experiment 12, I am not altogether satisfied. It seemed as if the 
hook suspension was not quite pendularly free so that the counterweight could rest 
hanging from the beam mirror at a very small angle to its natural position of verti- 
cality. This was not observable on the counterweight itself, but only by microscopic 
examination of the beam. Though the beam hook rarely varied in position by so 
much as ‘001 inch, I was able, by using great care in trying to make it rest in 
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