104 
ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
error arising from the observation of the galvanometer deflections. The probable 
observational error of the mean value in absolute measure of the O'OOl ohm resistance 
standard is about 3 parts in 1,000,000. 
The probable error of the diametral dimensions of the coils has been estimated in 
Section 13 to be not greater than 1^ plus the errors of the gauges employed. 
Inspection of the results given in Table III. shows that the mean value taken as 
correct differs from the results obtained in February and March, 1912, by about 1’4/x, 
and from those obtained in April, 1913, by about 07 /j.. The gauges employed are 
believed to be accurate within 0‘5/x, so that the maximum probable error of the 
diametral dimensions is about +l'5yu which corresponds to a probable error in the 
mutual inductance of about 8 parts in 1,000,000. This assumes that the error is of 
the same sign for all the coils. 
The probable error of the mean axial lengths of the coils has been estimated in 
Section 13 to be about 3/z, and a change of this amount in all the coils and in the 
same direction produces a change in the mutual inductance of 2 parts in 1,000,000. 
Any error due to lack of knowledge of the position of the mean diametral planes of 
the coils is practically eliminated by the reversals. An analysis of the plug 
measurements shows that the error cannot be so great as 2 parts in 1,000,000, and 
we may therefore dismiss it from consideration. 
The growth in the dimensions of the coils due to the passage of the current is not 
really large. The mutual inductance of the coils and brush contact circles is nearly 
3 parts in 100,000 greater after the current has been left on for 20 minutes, but the 
mean mutual inductance is only about 1'5 parts in 100,000 greater than that at the 
start. The error of estimation of the increase must have an exceedingly small effect 
on our final results and need not be considered. 
The mean diametral distance between opposite segments on the discs diminished by 
0'08 mm. during our experiments. Such a change would be a serious one in the old 
form of Lorenz apparatus, but in our instrument the change in the mutual inductance 
due to such a reduction in the mean diameter is less than 4 parts in 1,000,000. 
Evidence in favour of a small probable error is afforded by the satisfactory 
agreement between the results obtained when coils Nos. 1 and 2, and 3 and 4, were 
used independently. The resistance of the O'OOl ohm standard was found to be 
100090 4 cm./sec. when coils Nos. 1 and 2 only were used, and 100091 8 cm./sec. when 
coils Nos. 3 and 4 were used. The difference is 14 parts in 1,000,000 and part of 
this is possibly due to the errors of observations, for only four observations were made 
in each case. 
The electrical method of setting the coils in position has been shown to be subject to 
errors less than 1 part in 1,000,000 ; the magnetic susceptibility of the parts of the 
apparatus, excluding the motor, is too small to be measured with the apparatus at 
our disposal; and the effect of the motor on the mutual inductance of the coils and 
discs has been proved to be negligibly small. The errors of speed cannot be all of one 
