442 
PROFESSOR W. WATSON ON A DETERMINATION OF THE VALUE OF 
this error. The circumferences over each layer were measured as the coils were 
unwound, and the readings of the scale on the steel tape are given in the following 
table :— 
Circumferences over the different Layers. 
Over layer. 
1 
Coil A. 
Difference. 
Coil B. 
Difference. 
0 
3-0 
5'9 
3-0 
6T 
1 1 
8-9 
9-1 
f 
.5-5 
5-7 
2 
14-4 
5-7 
14-8 
5‘5 
3 
20T 
5-3 
20-3 
5'5 
4 
25-4 
5-4 
25-8 
5-4 
5 
30-8 
5-2 
31-2 
5-8 
6 
36-0 
5-3 
37-0 
5-4 
7 
41-3 
5T 
42-4 
4-9 
8 
46-4 
47-3 
This table shows that ou the whole the lower layers of wire are further apart than 
the upper layers; that is, the mean radius of the coil is really greater than the mean 
of the external and internal radii. The differences between the circumference below 
and above the first layer give the change in circumference due to the diameter of the 
wire. This quantity is not given by the difference of the circumferences of any 
other layers, since the circumference over any layer cannot be taken as the true 
circumference below the next layer, for each layer sinks down a little into the hollows 
between the wires of the layer beneath. The mean of the values obtained from the 
two coils is 6'0 divisions. That this value is probably very near the truth, is shown 
by the fact that, if we divide the mean value of the width of the groove by the 
number of turns of wire winch fill it, namely 12, and express the quotient as a change 
in circumference and in terms of divisions of the steel tape, we get 6‘0 as the value. 
Hence, taking 3'0 as the amount which has to be deducted from the circumference 
over any layer to give the circumference of the circle coinciding with tlie axis of the 
wire, we get the following values ;— 
