Standard Sine- Galvanometer. 3 69 



the distance between the mean planes of the coils, is difficult 

 to make with sufficient accuracy. 



The arrangement here proposed, and illustrated in figures 1 

 and 2, consists of one layer of wire wound on a tube of com- 

 paratively small diameter, say 10 centimetres or less, and of 

 great length. The force at the centre of such a tube, produced 

 by unit current, is given by the equation 



» 4:7rnl 



where I is half the length of the coil, r its radius, and n the 

 number of turns per centimetre of its length. When I is 

 very great compared with r the force becomes inrn, that is 

 to say, it depends wholly upon the number of turns n per 

 unit-length of the coil. The correction for the length of the 



tube is shown clearly by expanding 47rn( 1 + ™ ) , which 

 gives ^ ' 



When I is ten times the radius, this series becomes 



/=4^i- | L+g g l 5 r-&c.), 



which shows that for this moderate length the correction is 

 very small, and is amply obtained by taking in the second 

 term of the series. Any small error in the measurement of 

 the diameter of the coil is thus of little importance, and hence 

 the chief question becomes the degree of accuracy which can 

 be attained in the estimation of n, the number of turns per 

 centimetre. The total number of turns, or nl, can of course 

 be obtained with absolute accuracy, and the length, £, can be 

 easily measured to the tenth of a millimetre, which, on the 

 assumption of uniformity of winding, gives n to one part in 

 10,000. Providing that there exists no want of uniformity 

 which will affect the average value of n, perfect uniformity is 

 only important near the central part. Now an irregularity to 

 the extent of one hundredth part of n, or one tenth of a milli- 

 metre, can be readily detected by simple measurement ; and 

 supposing that this was due to an opening between the wind- 

 ings in the same plane as the needle (or at the most advantageous 

 position), and that there was no compensation due to denser 

 winding near the middle position, the effect would only amount 

 to about one in 1200 of the total force. The determination of 

 the value of n does not, however, depend altogether on the 

 measurements here described ; the operation of winding a 



