62 
ME. F. E. SMITH ON THE ABSOLUTE MEASUREMENTS OF A 
been perfectly uniform in pitch, the differences would, when plotted, have lain on a 
perfectly straight line, but, instead, wavy lines result (fig. 13). As an example of the 
difference readings those for the coils on cylinder No. 1 are given in Table VI. 
Table VI. — Giving the Difference Readings in Microns for the Coils on 
Cylinder No. 1. 
A 
A 
A 
A 
16 
21 
36 
32 
11 
20 
31 
38 
7 
24 
36 
37 
12 
39 
47 
38 
28 
43 
51 
31 
31 
25 
42 
35 
23 
25 
36 
33 
17 
19 
25 
. 37 
5 
15 
27 
37 
8 
17 
35 
44 
3 
30 
45 
39 
23 
45 
53 
43 
27 
38 
40 
42 
37 
31 
35 
32 
27 
25 
29 
38 
22 
23 
23 
33 
10 
26 
28 
36 
12 
31 
33 
41 
15 
43 
45 
47 
28 
50 
44 
39 
46 
52 
41 
36 
42 
42 
34 
44 
35 
40 
30 
43 
28 
31 
27 
37 
From the products resulting when the numbers 1, 4, 7, 10, &c., up to 94 were 
multiplied by 0‘065635, the half centimetre readings for the invar metre were 
subtracted and the differences when plotted were found to lie on a straight line as 
they should do if all the corrections have been properly applied. The graphs for the 
invar metre are shown in fig. 13 and are distinguished as Invar^ Invar 2 , &c., the 
numbers corresponding to the numbering of the four cylinders. A phosphor-bronze 
ring is screwed into one end of each cylinder, and these ends are called the “ ring ends.” 
It is clear from fig. 13 that there is a periodic variation in the pitch of all the coils. 
The distance corresponding to a complete cycle is half an inch, which is equal to the 
pitch of the leading screw of the lathe on which the cylinders were turned. The 
cause of the periodicity may be in the leading screw itself, or it may be due to want 
of parallelism of the surfaces at which the thrust was taken, or it may be due to both 
of these. Such periodic variations in pitch are present in nearly all screws. In 
addition to these periodic irregularities, the gi'aphs show others which are taken into 
consideration when the mutual inductance is calculated of a coil and disc 
circumference. 
The graphs for the coils enable one to place the cylinders in pairs. The lengths at 
