1884.] New Spring for Electric and other Instruments. 315 



readings of the pointer is avoided by the horizontal scale being on 

 looking glass in the well-known way. 



By making the iron tube AA very thin, so that it is magnetically 

 saturated for a comparatively weak current, by fixing it so that it 

 projects into the solenoid a fixed distance which has been carefully 

 determined by experiment, and by constructing the spring in 

 conformity with the conditions worked out in this paper, so as to 

 obtain a large rotation with minimum stress, and with not too 

 much axial motion of the free end of the spring, we have succeeded 

 in obtaining deflections up to 270° directly proportional to the 

 current, and without any permanent set being given to the spring. 



To prevent a spring taking a permanent set for a large deflection, it 

 is of great importance that the spring after being delivered by the 

 maker should receive a large degree of permanent set in the direction 

 in which we wish it to be afterwards strained in ordinary working. 



In spite of the fact that Professor J. Thomson in the " Cambridge 

 and Dublin Math. Journ.," November, 1848, explained the importance 

 of initial strains in materials, the reason is not yet sufficiently well 

 understood why when a round bar has been well twisted beyond the 

 limit of permanent set in a certain direction it has twice as much 

 elastic strength to resist torsion in this direction as in the opposite 

 direction. Now in the very act of manufacturing our springs, that 

 is in the bending of the strip, the material acquires strains which are 

 just opposite in character to the initial strains which we wish it to 

 possess, for, as already explained, if the spring be constructed as in 

 fig. 3, an extension of the spring produces a rotation tending to 

 uncoil it. Hence a spring must not be regarded as ready for use until 

 it receives a good set by means of a weight hung from its end. 



Theory of the Solenoid Spring Ammeter or Voltmeter. — If C is the 

 current in amperes flowing through the coil, the attractive force on 

 the iron core is 



l + sc' 



where S is a constant, which is the greater as the current is smaller 

 for which the iron tube AA, fig. 7, becomes saturated with magnetism. 

 The position of this iron core in the solenoid is so selected that K 

 remains practically constant throughout the small range of downward 

 motion of the core. 



Since the rotation has been produced by an axial force, we know 

 from the theory of the spring already given, that this axial force is 

 p0, where jp is some constant. Hence 



