438 Mr. T. Mather on the Shape of Movable Coils 



the smallest size of the latter is usually determined by con- 

 siderations of heating, and their length is limited by questions 

 of portability, compactness, and resistance. This means that 

 the control cannot be diminished below a certain minimum, 

 and hence, by reasoning as in the last paragraph, the moment 

 of inertia of the coil must not exceed a certain value. 



The third case, where the leading-in wires are independent 

 of the control, the conditions are somewhat similar to those 

 in the first case ; for the size of these wires is determined by 

 considerations of heating by the current to be measured, and 

 they necessarily possess some viscosity or internal friction, 

 which requires a certain control to give definiteness of zero. 



In addition to the assumption of constant Moment of 

 Inertia, the field in which the coil swings is taken to be uni- 

 form and parallel ; and consequently the reasoning will not 

 apply to radial fields which exist in instruments such as the 

 new d'Arsonval milliamperemeter, having a range c-f 180°. 

 In such case it would be advantageous to make the coil of 

 a section similar to that in No. 4 (see table), keeping the 

 radius b as small as possible. 



The shape given in No. 1 of table cannot be imitated 

 exactly in practice, for insulation-space is required between 

 the two halves, and unless the coil is used in a zero-instrument, 

 parts near the axis might oppose the rest when a considerable 

 deflexion exists. Shapes (3), (5), and (6) are also open to 

 the same objection, but this is easily surmounted by allowing 

 a small space to exist about the axis ; in fact some such space 

 is almost necessary to enable the coil to be wound conveniently. 



Again, in Siemens dynamometers for fairly large currents 

 it would be difficult to make the coil of the best shape, owing 

 to the space required for the mercury-cups being considerable ; 

 but a much closer approximation to this shape than the one 

 often employed could be used. 



In ordinary d'Arsonvals, which deflect through a consider- 

 able angle, the shape should be modified so that no part of it 

 crosses the line A B (fig. 2) even at the maximum deflexion, 

 for any such part would oppose the rest of the coil. The 

 resulting figure would be lemniscate-shaped. There are some 

 cases, however, such as deflexional dynamometers, where it is 

 advisable to make the coil of such a shape as to cross the fine 

 A B when deflected ; for then the deflexion would increase 

 less rapidly than the square of the current, and hence the 

 instrument would have a greater useful range for a given 

 length of scale. 



