80 
MR. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
individual corrections are alternately plus and minus, and the total effect of these 
half-period elements depends on the difference of phase at the beginning and end 
as in the case of diffraction effects in light. 
To obtain the corrections we have calculated the mutual inductance of small 
portions of the coils and the corresponding circles. The mutual inductances calculated 
are (l) those of the circle and of coils each of which is 0‘635 cm. in length, the 
distance between the circle and the end of the coil nearer to it increasing from 
7*3885 cm. to 23'2635 cm. in steps of 0'635 cm.; (2) those of the circle and of coils, 
each 25/x long, the distance between the coil and circle increasing from 8*0235 cm. to 
23'2635 cm. in steps of 1‘27 cm. In all cases the number of windings on a coil is at 
the rate of 12 turns per cm. The results of these calculations were plotted and by 
means of the curves we have corrected for the variation in pitch. 
As an illustration, let us examine the second section of coil No. 3 when the ring 
end of the cylinder is nearer to the disc. For clearness, this section is reproduced in 
fig. 17 and is denoted by CB. The end of the section nearer to the disc is 5/x nearer 
than the end of the corresponding perfect section, and the other end of the section is 
20 iul farther from the disc than the other end of the corresponding perfect section. 
The ratio of the lengths of the two sections is therefore 6375/6350 and the ratio of 
the current densities in the equivalent current sheets is 6350/6375. The M of the 
perfect section and the disc is 1723'692 ; if its length is increased by 5/x at the end 
nearer the disc and by 20// at its other end, M is increased by the amounts 1'382 and 
5*340. (These corrections are obtained from the curve.) The total M is now 
1730'414. If next we reduce the number of turns to its original value the M becomes 
1730'414 (6350/6375) = 1723*628, and since the section is now identical with the 
actual section, the correction for variation of pitch and displacement of section is 
1723*628 —1723'692 = —0'064 or — 3*7 parts in 100,000. 
In this way we have calculated the corrections for all the sections of the coils both 
when the ring end is nearer to the disc and when farther from it. 
The values of the corrections are as follows :—- 
Table XYIII. 
Correction to M. 
Coils on cylinder 
No. 
Ring end of cylinder 
near disc. 
Ring end of cylinder 
away from disc. 
1 
+ 0-502 
V 
-0-369 
2 
+ 0-987 
-0-874 
3 
-0-734 
+ 0-536 
4 
- 1-535 
+ 0-486 
