558 Further Measurements of Wave-lenjths. 
variations, 
dP = | (-15) akdoL = | (-15) 1 P*#«, 
dV/da being somewhat dependent upon the total pressure P. 
For the purposes of experiment a spring-balance was 
mounted upon the frame of the apparatus (carrying the 
distance-pieces) so as to diminish the pressure exerted over 
one of the distance-pieces, that is to diminish the pressure 
by which one of the plates was held up to one of the distance- 
pieces. Starting from perfect parallelism of the plates and 
keeping the eye carefully fixed so as to receive the light from 
the centre of the plates, it was observed that to cause a shift 
of one band (helium yellow) the spring-balance needed to 
exert a pull of 'IS kilo. At this stage the plates were of 
course no longer parallel and a moderate shift of the eye 
would cause a displacement independently of any change in 
the spring-balance. At the same time the rings lost their 
sharpness. On this account it is hardly practicable to use a 
shift of more than one band, and indeed a smaller shift of 
half a band was usually preferred. The total force required 
to compensate the spring of the apparatus, and so to relieve 
the compression of the distance-piece on this side, was 2*4 
kilos. This is what is represented by P in the above formula, 
while dF = -'IS. 
In order now to compare theory and observation we must 
remember that the one band (corresponding to half a wave- 
length) observed at the centre implies three times as great a 
shift at the particular distance-piece where alone the force 
was varied. Thus the observed dY corresponds to da—— 3. 
For this da, the calculated dF is 
d? = -§ (-15)1 (2-4)* = --85 kilo. 
The agreement with the observed —'78 is certainly as good 
as could have been expected. 
In considering what differences of distance are to be 
expected when the plates are adjusted to parallelism under 
different pressures, we must remember that the above calcu- 
lation and observation relates to the compression which may 
occur at the contact of a single distance-piece with a single 
plate. There are in all six contacts of this kind, and we 
may conclude that when no special pains are taken to regulate 
the absolute pressures employed, a shift of 6 bands or more 
on remounting need not cause surprise. 
