502 PROFESSOR W. E. AYRTON, MR. T. MATHER AND MR. F. E. SMITH: 



This mechanical method of setting the coils is subject to errors which may be 

 serious in an instrument intended for observations of high precision. So far as we 

 know, no attempt has hitherto been made to set two coaxial coils in a position 

 of maximum force by an electrical method. The ampere balance lends itself to such 

 a setting, and the accuracy thereby attained is considerable. 



ELECTRICAL METHOD OF SETTING THE Cons. 



(1) Setting to Coincidence of the Mean Diametral Plane of the Suspended Coils 

 with the Corresponding Plane of all the Coils on the Concentric Fixed Cylinder. If 

 M B is the difference of the mutual induction of the upper fixed coils and the 

 circular ends of the suspended coils, and M, that of the lower fixed coils and the 

 same, and if the currents flow in opposite directions in the upper and lower fixed 

 coils, the force between them and the suspended system is y h y (M B 4-M(), where y h is 

 the current through the fixed coils and y is the current per unit axial length in the 

 current sheet equivalent to the current in the suspended coils. This is the maximum 

 force possible for the coaxial system, and variations in the force for small axial 

 displacements are also small. The rate of change was determined by passing a 

 current of 1 '02 amperes through all the balance coils, the direction of the current in the 

 various helices being such that the two suspended systems were subject to the maximum 

 axial forces, but opposed to each other so that the total turning moment on the beam 

 was small and almost nil. One set of fixed coils was now displaced through known 

 axial distances and the change in the resting point of the balance observed ; that 

 position of these fixed coils when the force due to them is a maximum is the correct 

 axial position for minimum mutual induction. The results obtained with one of the 

 systems are plotted in fig. 18 ; for such displacements as those made the force is 

 approximately given by the expression : maximum force multiplied by (1 1 1 x 10~ 8 cP), 

 where d is the displacement in mils and is measured from the plane of minimum 

 mutual induction. The force may also be written : maximum force multiplied by 

 (1 O'OlTx 3 ), where x is the displacement in centimetres. For a displacement of 

 10 mils (254/n) the change in force is 11 in 1,000,000, which for a current of 1 ampere 

 is equal to 0*04 dyne approximately. 



There is, however, another method of setting the cylinders which is even more 

 sensitive. If, instead of the currents flowing in opposite directions in the upper and 

 lower fixed coils, they flow in the same direction, the force between them and the 

 suspended system is y A y(M u M,). When the coils are set in their correct position, 

 this is nearly the minimum force possible for the arrangement, and the rate of change 

 of force with axial displacement is large. Observations were made with the current 

 circulating in this manner in one set of fixed coils, the current in the system on the 

 opposite side of the balance being so directed that no measurable force was produced 

 by it. The correct position of the fixed coils in one of the systems is when the 



