1884.] New Spring for Electric and other Instruments. 313 



a d , 



= — =tan /3, 



c — b r0 



so that — =2— L-l i. 



N a—(c—b) 



We have used three springs made from round wire respectively of 

 brass, iron, and steel for the sake of illustration. In all of them we 

 find that c — b is small in comparison with a, so that roughly we may 



say that the excess of — over 2 is — — , that is, is proportional to 

 N a 



(c— b). The cylindric scale has only been introduced for the sake of 



E 



illustration. For an accurate determination of — , a telescope would 



N 



be employed having a motion about the axis of the spring, and also a 

 motion parallel to the axis, and by means of which the motion of a 

 point on centre line of the wire when an axial force is employed, 

 would be accurately observed. It is sufficient to say that the brass 



E 



spring of round wire exhibited- to the Society gives a value of — which 



is 8 per cent, less than the value given by the similar spring of round 

 iron wire exhibited. 



Instead of using a round wire, we may use for the experimental 

 E 



determination of — a strip of rectangular section, whose breadth is 



very great in comparison with its thickness. If the angle of the 

 spiral is 45°, then from equations (16) and (17) it follows that 



1 _1 



'0r_4N__E_ 

 ~d~ 1 1_' 

 4N E 



E_,cZ + 0r 



N d-0r 



therefore measuring 0r as c — b, and d as a, by the method just 

 described, we have 



E_ 4 a + (c-5 ) 

 JN" a-(c-b)' 



Some Practical Uses of the Springs. — By the employment of springs 

 such as we have described, we have succeeded in making ammeters 

 and voltmeters, or instruments for measuring respectively electric 

 currents and differences of potential, in which the pointer moves over 

 in some cases as much as 270° of the scale instead of only 50°, which 

 is all that can be obtained with ordinary galvanometers. One form 

 of the instrument is shown in fig. 7, where AA is a thin hollow tube 



