MEAN CIRCUMFERENCE OF A COIL. 73 



or, if the thread is very small compared with the diameter of the coil, 

 very nearly 



As the factor within the bracket differs from unity by a 

 quantity which may be neglected, the winding may be confounded 

 with the projection of its circumference. 



The mean circumference of the windings of a coil, is that whose 

 length is the mean of the circumferences of all the windings ; the 

 mean radius is the mean of all the radii. This radius is evidently 

 equal to the distance a of the centre of gravity of the section of the 

 channel to the axis of the coil, and therefore is independent of the 

 diameter of the wire. We get from this, for the total length of the 

 wire 



(i) l 



or, allowing for the correction due to the obliquity of the windings, 



We have, moreover, 

 If the coiling is uniform, 



the expression (i) for the length of the wire becomes thus 

 (2) /= 2Traa>n\ = n'JJ = 2-rrn\b (a"' a'*) = < 



725. VOLUME AND WEIGHT OF THE WIRE. Most frequently 

 we assume the coiling uniform ; we may then consider each section 

 of the wire as occupying, in the mean section of the channel, the 



centre of a square, the side of which is equal to . 



7l-\ 



2 



If we represent by 8 the ratio - of the thickness of the envelope 

 to the radius of the wire, we see that the section of the bare wire 



