1884.] Neic Spring for Electric and other Instruments. 301 



• • • ■ (3) > 



Maximum Rotation, Positive and Negative Springs. — If we merely 

 require that shall be a maximum for a given axial force E, inde- 

 pendently of the stresses produced in the material, and independently 

 of the axial elongation, then it is evident that a. ought to be equal to 

 45°, and I and r as great as possible. If oar other condition is that 

 the area of cross section of the strip is to be a constant — 



Let ab — s, 



and a=Jcb, 



so that 6 2 =^. 



k 



rm, 1 /a 2 +6 2 _4\_ 1 /F + l_4\ 



_ 1 fh 1 _4ZA 

 w»\N M E / 



or since N is equal usually to about two-fifths E, we find that 



0* 5_3&. 



A; 



Now when Jc is very small this is very great. On the other hand, 

 when ~k is very great this is also very great, but of the opposite sign. 

 As h increases from the expression to which 0, or the amount of 

 turning, is proportional diminishes until when h reaches a value 

 nearly 1*3, becomes 0, or there is no rotation of the spring pro- 

 duced by an axial force. In fact, for small values of h there is a 

 rotation of the spring in the direction of the coiling, and the 

 amount of rotation becomes the greater the smaller h is, while for 

 values of h greater than 1'3 there is a rotation of the spring opposite 

 to the direction of the coiling, the rotation becoming greater the 

 larger h is. 



Fig. 3 shows a spring in which h is greater than 1*3, and it is found 

 that there is an uncoiling on the application of an axial force. 

 Eig. 4 shows a spring made of the same material, but the wire has 

 been passed through rolls so as to flatten it in the opposite way, and 

 now a rotation tending to coil it up is found to be produced by the 

 application of an axial force. 



