298 Profs. W. E. Ayrton and J. Perry. [Feb. 14, 



In order to ascertain this fact, it is necessary to consider what are 

 the general laws governing the behavionr of spiral springs. Let the 

 centres of all cross sections of the wire, or strip, forming the spring 

 lie on a right circular cylinder of radins r, let the spiral have every- 

 where an inclination cc to the plane perpendicular to the axis of the 

 cylinder, and let a force F act at one end of the spring along the axis, 

 the other end of the spring being fixed. 



In the cross section of the wire at any point P (fig. 2), we have, 

 due to the axial force F, tensile stress whose effect in deforming the 

 spring may be neglected in comparison with the other effects to be 

 described, and we have the stresses produced by a couple Fr acting 

 about the axis PM. PS, PM, and PU are all in a plane tangential to 

 the cylinder at the point P, PM being drawn in this plane perpen- 

 dicular to the axis of the cylinder, PU tangential to the spiral line, 

 and PS perpendicular to PU. 



This couple is equivalent to the couple Fr cos «, which is a twisting 

 couple about the axis PU, and to Fr sin «, a bending couple about the 

 axis PS. If now B is the flexural rigidity of the wire in the oscu- 

 lating plane, and if A is the torsional rigidity about the spiral line at 

 P we have — 



Fr cos a 

 A 



