NEWTONIAN CONSTANT OF GRAVITATION. 5 
of deflection and period were concerned an advantage could_so be obtained, it did not 
at all follow that I should be able to determine the geometry of small apparatus with 
sufficient accuracy. Of course, as the apparatus is made smaller, this difficulty 
necessarily increases. 
Tf in the apparatus upon which I have finally decided the angular deflections and 
squares of the periods can be determined with greater proportionate accuracy than 
the masses or lengths, or lengths squared, as the case may be, then I have gone too far, 
and the apparatus is too small, but if, as I expect to satisfactorily prove in this paper, 
my geometry and weighings (of course, the latter) are well in excess of the 
deflections and squares of the periods in point of accuracy, then I maintain that I am 
justified in having acted up to my principles, even though I did so in opposition to 
the views which I heard expressed. 
There is one point referred to (p. 258), but not sufficiently in detail, in my paper 
already quoted which I should like to develope, more especially as Professor Poyntinc* 
has noticed it, and has, I think, agreed with my conclusion. At the same time I owe 
to him the discovery of a mistake which I made which led me to attribute too high an 
importance to the advantage of smallness from this point of view. What follows is 
the result of a discussion, which I took the opportunity of entering upon while 
travelling recently with Professor Poyntinc. The point is, that the disturbances 
due to convection are likely to be relatively of less importance in small than in large 
apparatus, even though the period is maintained the same. As convection disturb- 
ances are those which are the last and the most difficult to avoid, and as I feel sure 
that they set the limit to the accuracy that is obtainable in this experiment, and that 
discrepancies attributed to silk, or even to quartz fibres, and to other causes, are in 
many physical investigations simply due to convection, I think that too much 
attention cannot be given to this part of the subject. 
Let there be two pieces of apparatus, precisely similar in all respects, but with the 
linear dimensions in one 7 times those in the other, then when the pieces of 
apparatus are set up, they are subject under the best conditions to infinitesimal 
variations of temperature from the outside of two kinds; in the first, the surrounding 
space may not be uniform in temperature, it may be hotter on one side than on the 
other; in the other, the temperature, whether uniform or not, may slowly change 
from day to day. 
In the first case the instruments may be considered as being placed in a region 
which would, but for their existence, possess a constant but very small temperature 
gradient. If an instrument be placed in such a region, the temperature gradient in 
the instrument will be also constant in certain cases, and will depend simply on the 
conductivity for heat of the material of which it is made and of the medium in which 
it is placed, but it will be independent of the linear dimensions. Further, whatever 
form a pair of similar instruments may have, the gradients at corresponding points in 
* ©Phil. Trans.,’ 1892, vol. 182, p. 601, and “‘The Mean Density of the Earth,” p. 107, 
