70 
ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
are under observation, and when the platform is clamped by means of w' and w", the 
lines on pings b and cl can he viewed, and so on for the remaining positions. 
The reference standard is a scale of half millimetres, engraved on invar. The scale 
was standardised by Mr. Attwell before making any absolute measurements of 
resistance, and again after their completion. The results on the divisions employed 
in our work agree within less than 1/j.. 
The general procedure in making the measurements was to observe the invar scale, 
then the eight plug distances, and finally the invar scale again. The first and last of 
the observations agreed in general within l,u or 2/j~ An absolute measurement of 
resistance immediately followed and then another set of observations was made on 
the invar scale and the plugs. The coils were not reversed in position until a large 
number of resistance measurements had been made. 
The distance between coils Nos. 1 and 4 and between Nos. 2 and 3 is required with a 
much less degree of accuracy, an error of 1 mm. in both of these distances producing a 
change in the mutual inductance of less than 1'5 parts in 100,000. As the distances 
between coils Nos. 1 and 2 and Nos. 3 and 4 are known from the previous measurements 
within a few thousandths of a millimetre, it was only necessary to measure the 
distance 1 to 4, or 2 to 3. In practice we measured the distance between a plug on 
cylinder 2 and a plug on cylinder 3, and employed for this purpose a brass bar with 
half-millimetre divisions engraved at the ends; this enabled the distance to be 
determined within about O'l mm. The distances of the plugs from the mean diametral 
planes of the coils were known and no further measurements were therefore necessary. 
Instead of measuring the distance between two coils such as Nos. 2 and 3, we may, as 
an alternative, measure the distance between the two sets of five brushes, and a number 
of such measurements were made as checks. 
Section 18.— Calculation of Mutual Inductance of the Coils and the 
Contact Circles of Segments and Brushes. 
The arrangement of the coils and discs in the instrument may be represented 
diagrammatical]y in section by fig. 16. The coils are numbered 1, 2, 3, and 4, and the 
discs are denoted by Di and D 2 . 
Fig. 16. 
The mutual inductance M of any one coil and the contact circles is calculated in two 
parts. The first part gives the mutual inductance M x of the coil and the circumference 
