694 
LORD RAYLEIGH ON THE VALHE OE THE BRITISH 
Table Y.—Third series. 
Humber of teeth. 
60 
45 
35 
30 
R by formula. 
Resistance of standard at 13° . 
23-616 
23 619 
23-618 
23-621 
23-627 
23-630 
23-635 
23-638 
If we compare the results of the second and third series at the same speed, we find 
the agreement satisfactory (with a partial exception at the speed corresponding to 
45 teeth), especially if we take the means from which the observations of August 29 
in the second series are excluded. Adding together all the results of each series we 
should obtain from the second series, 23*638, or with exclusion of August 29, 23*633, 
and from the third series 23*627, between which the extreme difference is less than 
one part in 2000. When, however, we compare the values obtained from observations 
at different speeds, we see from both series, but more especially from the third, evident 
signs of a tendency to rise with the speed, as if the self-induction of the revolving 
circuit had been underestimated. In view of the remarkable concordance of the 
results obtained at the same speed on different nights, it is impossible to attribute 
these discrepancies to errors of observation, and it is important to consider what cause 
of systematic disturbance can have remained unallowed for. The first question which 
presents itself is whether it is possible to admit an error in the adopted value of L 
sufficient to explain the progression. The proportional correction for self-induction 
is approximately —U tan 3 <f>, or for the speed of 30 teeth *0457. For the speed of 
60 teeth the correction will be only one-fourth of this. To bring the results for the 
two speeds into agreement it would be necessary to increase the value of U by nearly 
3 per cent., which would correspond to an increase of about one per cent, in L. It is 
difficult to believe that the value of L adopted for the wire circuit can be in error to 
this extent. 
Another direction in which an explanation might be looked for would be the 
influence of air disturbance, or from tremor. The accompanying table, however, shows 
such an extraordinary agreement of the open contact deflections, both among them¬ 
selves and with numbers proportional to the speeds of rotation, as to prevent us from 
supposing that this cause of disturbance can have operated. 
