516 PKOFESSOK W.-E. AYRTON, MR T. MATHER AND MR. F. E. SMITH: 



thus secure greater accuracy. The values of 2wH obtained on these occasions are as 

 follows : 0'5 5 and 0'4 8 milligramme ; 0'4 and 0'3 8 milligramme ; 0'5 and 0'5 milli- 

 gramme ; 0'3 6 and 0'4 milligramme ; and 0'4 and 0'3 milligramme, the sign being 

 such as to indicate that M L was the greater. The mean value of mj is 0'21 milligramme, 

 and the probable error of this value is about 10 per cent. A current of 1'02 amperes 

 was used, so that 2/ = 0-102x14-1724 and y h = 0'102. Hence the experimental 

 value of M L M R is 0-00021^/0-147 = +1*40 centims., and is subject to a probable 

 error of about 10 per cent. The agreement with those independently calculated by 

 T. M. and F. E. S. from the dimensions of the coils (1'56 centims. and 1'61 centims.) 

 is remarkably good. 



Estimation of the Difference in the Diameters of the Coils on the Fixed Cylinders. 

 Suppose the current in Ul is in opposite direction to that in U2, those in Ll and L2 

 to be in opposite directions to each other, and that the currents in the suspended 

 coils a and 6 are co-directional. Let the system on the right be inoperative. Then 

 the force is 



y'r* [M ula +M 016 -(M u2a +M TO ) {M tla +M L16 -(M L2a +M L26 )}] 5 



where / and y h have the same meanings as before. Here M uio M U2a and M m6 M CK 

 are very small and practically equal; similarly M Lla M L2a is equal to M U6 M^ very 

 nearly. Hence the force may be written 2y'y A {(M cla M U2a ) (M^-MLa,)}. By trial 

 this may be made a maximum. If we assume M ula to be greater than M UJa , and MUO 

 to be greater than M L3a , the maximum force is 



2/y A {(M ma +M L10 ) - (M^+M^)}. 



The difference of the mean diameters of the separate helices on the upper and lower 

 portions of the fixed cylinders was measured as 3/x for the coils on the left and as 2/u, 

 for those on the right (p. 488). For a mean difference in radius of 1 '2/t, the value of the 

 force for one system, as calculated by the last equation, is 0*02 dyne, and on reversal 

 of the current through the fixed coils the necessary change in the balancing mass to 

 maintain equilibrium should be 0'04 milligramme. If the left and right systems be 

 made co-operative in their effect, the change in the balancing mass will be twice this, 

 i.e., very nearly O'l milligramme. In experiments made to check this value, all the 

 possible combinations of the coils on the fixed cylinders were made, subject only to 

 the condition that the currents were in opposite directions in adjacent helices. Some 

 smadl displacement of the resting point of the balance was invariably recorded on 

 reversing the current in the fixed coils, but the change was exceedingly small and 

 not always in the same direction. The mean of the first five observations is O'O milli- 

 gramme as the balancing mass, and the mean of the first ten observations is O'l milli- 

 gramme, results which are of little value except to show that the difference in 

 diameter of the helices on the fixed cylinders is very small 



