740 A Relation between lension and Torsion. 



the aim must be to separate feeble constant effects from 

 chance disturbances. 



It may be that, besides that of the corona, there are other 

 astronomical problems to which one or other of the methods 

 above described, or a combination of both, might be applied 

 with a prospect of attaining a further advance. 



Am?. 1911. 





QLXXII. A Relation between Tension and Torsion. By R. A. 

 Houstoun, ALA., D.Sc, Ph.D., Lecturer on Physical 

 Optics in the University of Glasgow *. 



TN this Journal (" On Magnetostriction," Phil. Mag. xxi. 

 JL p. 78, 1911) I recently! gave a simple relation connecting 

 magnetostriction with the change of magnetization produced 

 in a wire by stretching. I desire here to call attention to a 

 similar relation connecting the torsion of a wire with its 

 tension. This relation appears to me to be wholly new. 



Suppose that a ware is hanging vertically, its upper end 

 being fixed, and that its lower end is acted on by a stretching 

 force F vertically downwards and by a couple L. Let x 

 be the increase of length and Q the angle of twist at the 

 lower end. 



If U denote the intrinsic energy of the wire, 



dTJ = Fdx + Ld0 





Since this is a perfect differential, 



(*B +L !-w=^( F !i+4D 



d (■& d;c _, T B0 \ _ 9 (v ~bx , T 30 

 3L 



30 3x 



BF-BL- 



This is the new relation referred to. 



It also comes very simply from consideration of a cycle. 



* Communicated by the Author. 



t In the Beibllitter (1911, xxxv. p. 717) Prof. R. Gans states that the 

 former paper is inaccurate inasmuch as the volume is taken independent 

 of stretching force and Held strength. Bat the terms thus introduced 

 can be neglected. 



