690 
LORD RAYLEIGH OK THE VALUE OF THE BRITISH 
In like manner two other very small corrections have to be introduced to make the 
results correspond exactly to a normal speed of rotation. The standard number of 
heats is taken at 59, and the standard temperature of the fork at 17°. In the 
specimen set the number of beats is 2 -J per minute too small, which means that the 
octave of the electrically maintained fork made (relatively to the other fork) 2 ^ 
complete vibrations per minute too many. The whole number of vibrations per 
minute being 60X 127, the speed was too great by parts in 60X127, by which 
fraction the observed deflection must be reduced. The correction is thus —TO. But 
besides this the standard fork at 13 ”05° vibrated faster than its normal rate at 17°, 
by about one part in 10,000 for each degree of difference. The correction for this is 
— T 2 . 
In addition to the corrections already mentioned the observations of November 5 
and after were subjected to another small correction for the observed change in D. 
The accompanying Table (II.) exhibits the results of the second series in a manner 
which after what has been said will not require much explanation. Column VIII. 
gives in each case what the deflection would have been if the revolving circuit and 
the copper connecting bars had exactly balanced the platinum-silver standard at 16°, 
the electric fork vibrating at such a speed as to give 59 beats per minute with the 
standard fork at 17°, and thus allows us to test the agreement or otherwise of the 
results obtained on various occasions at the same speed. From this point onwards 
the means only need be considered; but as there is reason (as already explained) to 
distrust the observations of August 29, I have added a second mean from which the 
distrusted elements are excluded. The deflection ( d ) thus arrived at is equal to 
D tan 2(j) } whereas what we require is 2 D tan </>. The connexion between the two 
quantities is obtained in a moment from the formula 
2 tan (j>= tan 2 <£ (l — tan 2 <f>) 
by successive approximation. Thus 
2 tan cj)= tan 2 </> {1 — J tan 2 2 <£-|-^ tan 4 2 </>}, 
or 
t-\ , , 7 , d 3 , d 5 
2 D tan —-f £—• 
Column X. gives the value of 2 D tan </>, XI. that of 2 D (tan <£ — tan <f> 0 ) in the 
notation of p. 675, and XIII. that of log (tan <j>— tan <£ 0 ). 
For the further calculation we require the value of o>. If f be the frequency of 
vibration of the electrically maintained fork, F that of the standard at 17°, N the 
number of teeth, 
and when the number of beats is 59 per minute, 
