GRAVITATION AS AFFECTED BY TEMPERATURE. 
385 
errors in the work. The results are, of course, as the tables show, outside the 
range of observational error; but the delicate torsion system would be very 
susceptible to spurious effects, due directly or indirectly to the heat in the large 
masses, M, M. The steps taken and the tests made to weed out spurious effects 
will now be indicated. 
In §IV. above some likely sources of error have been mentioned, and special 
precautions were taken against them in designing the apparatus. There are some 
other troubles possible, mostly mechanical. 
(1) The vacuum tube containing the torsion system and spheres, m , rn, hangs from 
steel springs, and is steadied in every direction by a set of rubber corks separating it 
from the wooden frame carrying the large masses, M, M. The bottom of the vacuum 
tube is steadied and can be adjusted by four horizontal set-screws; these screws 
being set in a metal frame supported from the cement floor of the room. The large 
masses are separately supported by a stout scaffold. Suppose the position of M, M. 
relative to the small spheres, m, m, is ideal, i.e., central and symmetrical. If rn, rn 
were now to move in the plane containing M, M, the sensitiveness of the system 
would increase—the telescope readings would change ; whereas, if they moved in a 
perpendicular sense the sensitiveness would decrease and telescope readings would 
change in the contrary sense. It is important, therefore, that during an experiment 
no movement of either mass system, e.g., due to warping of the framework, should occur. 
Thus the supports should be rigid and screened from heat. 
(2) The rubber corks, mentioned above, must be maintained firmly in place. 
(3) It is possible that the masses, M, M, might be hung under strains by the 
copper wires, and when heating occurs this strain might vary. This possibility was 
tested (and found non-existent) by turning both masses, M, M, by 180° C. on a 
vertical axis, as in the last experiment in Table IV. 
(f) The centre of mass of the spheres, M, M, might be displaced vertically by 
expansion as temperature rises. This movement would decrease the couple, due to 
M, M, on the torsion system, supposing the centres of M and m lie exactly in a horizontal 
line. The masses, M, M, are carried by copper discs (see fig. 9) attached to copper rods 
which pass through holes in the masses. The radius of each mass is 10 cm. Thus, 
when temperature rises 200 C. we have the centre of mass rising 2'8 x 200m = 560m, 
due to expansion of the lead; and falling 3’2 x 200m = 640,u, due to expansion 
of copper (the coefficients of the two materials being 28xl0 -6 and 16xl0~ ri 
respectively). The net fall in the centre of mass would then be 80m- Now the large 
masses, M, M, are 150 mm. from, the small ones, rn, m, and the small cosine error 
resulting from the vertical movement 80m, will be found negligible. If, however, due 
to error in setting, M and rn are not on a horizontal level, but that the former be 
5 mm. above its ideal position (an error of setting which is most unlikely) we should 
then find that the fall in the lead would give an effect of order 10~ 5 , which is 
negligible compared with our effect of 2 x 10~ 3 . 
