374 Mr. C. Vernon Boys [June 8, 



side, definitely bends to a small extent, becoming slightly convex on 

 the glass side when in hydrogen, and instantly recovers its form when 

 surrounded by air again. This happened many times, producing a 

 change of focus in the telescope of about f inch. I do not offer any 

 explanation of the fact. 



There is an observation which should be of interest to elasticians. 

 In experiments 4 to 8 the torsion fibre carried the beam mirror and 

 the '25-inch gold balls, weighing, with their hooks and fibres, 5*312 

 grammes. In experiment 9, gold cylinders were substituted, weigh- 

 ing, with their hooks and fibres, 7 ■ 976 grammes. The weight of the 

 mirror was '844 gramme. In consequence of the small increase of 

 load the torsional rigidity of the fibre fell more than 4 per cent., an 

 amount far too great to be accounted for by the change of dimensions, 

 even if Poisson's ratio were as great as J. There is no doubt about 

 the great reduction in stiffness, for this figure is one of the factors in 

 the final expression for G, which does not show a change of more than 

 1 part in 1570. 



It will not be possible at this late hour to explain how the ob- 

 servations are treated so as to obtain the value of G. It is sufficient 

 to state that in one of these clips all the observed deflections and 

 corrected periods are collected. In the second all the geometrical 

 observations are collected and reduced, so as to obtain what I call the 

 geometrical factor, i.e. a number which, when multiplied by^the un- 

 known G, gives the torsion on the fibre. In the third, the moments 

 of inertia and periods are made use of to find the actual stiffness of 

 the fibre in the several experiments, and in the fourth these are com- 

 bined so as to find G. From G the density of the earth A immediately 

 follows. 



The annexed table contains the important particulars of each ex- 

 periment. From this it will be seen that the lead balls were twisted 

 and interchanged in every way, so as to show any want of gravita- 

 tional symmetry if it should exist. For instance, after experiment 7 

 the ball that was high was made low, the side that was outwards was 

 turned inwards, and their distance apart was reduced by 1/50 inch, 

 but the change in the result was less than 1 part in 2400. The experi- 

 ments 7, 8, 9, 10 were made under widely different circumstances. 

 After experiment 8 the gold balls were changed for heavier gold 

 cylinders, which, as has already been stated, reduced the torsion of 

 the fibre nearly 5 per cent., but the result differs from that of experi- 

 ment 7 by 1 part in 3700. I then broke the end of the torsion fibre. 

 After keeping it in London three months I broke the other end. I 

 then resoldered each end and put the fibre back in its place, and 

 after making every observation afresh, found with the new shorter and 

 stiffer fibre a result differing from that of experiment 8 by only 1 part 

 in 60,000. These four experiments were all made under favourable 

 circumstances, and on this account I feel more able to rely upon them 

 than on the earlier ones, which were subject to greater uncertainty. 

 The last experiment was made under most unfavourable conditions. 



