Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/347

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709.]

MEASUREMENT OF THE COIL.

to enter, and one end of the covered wire is pushed out through this hole to form the inner connexion of the coil. The channel is placed on a lathe, and a wooden axis is fastened to it; see Fig. 50. The end of a long string is nailed to the wooden axis at the same part of the circumference as the entrance of the wire. The whole is then turned round, and the wire is smoothly and regularly laid on the bottom of the channel till it is completely covered by $n$ windings. During this process the string has been wound $n$ times round the wooden axis, and a nail is driven into the string at the $n$ th turn. The windings of the string should be kept exposed so that they can easily be counted. The external circumference of the first layer of windings is then measured and a new layer is begun, and so on till the proper number of layers has been wound on. The use of the string is to count the number of windings. If for any reason we have to unwind part of the coil, the string is also unwound, so that we do not lose our reckoning of the actual number of windings of the coil. The nails serve to distinguish the number of windings in each layer.

The measure of the circumference of each layer furnishes a test of the regularity of the winding, and enables us to calculate the electrical constants of the coil. For if we take the arithmetic mean of the circumferences of the channel and of the outer layer, and then add to this the circumferences of all the intermediate layers, and divide the sum by the number of layers, we shall obtain the mean circumference, and from this we can deduce the mean radius of the coil. The circumference of each layer may be measured by means of a steel tape, or better by means of a graduated wheel which rolls on the coil as the coil revolves in the process of winding. The value of the divisions of the tape or wheel must be ascertained by comparison with a straight scale.

709.] The moment of the force with which a unit current in the coil acts upon the suspended apparatus may be expressed in the series

G_{1}g_{1}\sin \theta +G_{2}g_{2}\sin \theta Q_{2}^{\prime }(\theta )+\mathrm {\&c.}

,

where the coefficients $G$ refer to the coil, and the coefficients $g$ to the suspended apparatus, $\theta$ being the angle between the axis of the coil and that of the suspended apparatus; see Art. 700. When the suspended apparatus is a thin uniformly and longitudinally magnetized bar magnet of length $2l$ and strength unity, suspended by its middle,

g_{1}=2l

,⁠

g_{2}=0

, ⁠

g_{3}=2l^{3}

, &c.