436 DK W. PEDDIE ON 



per oscillation is much greater at large angles, much less at small angles, than it is when 

 the temperature is normal, even after heating to redness. 



In the second of the two experiments, performed immediately after the first, the 

 only change made was that the current was sent in the same direction round the two 

 coils. Thus, in addition to the maintenance of the wire at a temperature of about 

 80° C, a steady stale of magnetisation ivas maintained. The results were 



« = 2, ?« = 2-312, h = 2210, ra& = 5110. 



The effects just described are, therefore, in all respects greatly intensified. The 

 molecular theory of magnetisation would lead one to expect decreased loss of energy at 

 small angles, and increased loss at high angles, when the magnetisation is great.] 



Theory of the Oscillations of an Imperfectly -Elastic Solid. 



The first attempt at a theoretical investigation of the properties of a ductile solid 

 was made by James Thomson (Camb. and Dub. Math. Journ., 1848) in a paper "On 

 the Strength of Materials, as influenced by the existence or non-existence of certain 

 Mutual Strains among the Particles composing them." In applying his investigation to 

 the case of torsion of a wire, he assumed that a certain definite tangential stress per 

 unit area could be sustained without the production of permanent distortion, while an 

 infinitesimal increase of the stress over this value caused continuous sliding until the 

 stress diminished to the given definite value. In this way he explained the existence 

 of elastic limits, and the greater strength of a wire as regards torsion in one direction or 

 the opposite. 



A mathematical development of Maxwell's views of the molecular constitution of a 

 material substance is given by J. G. Butcher (Proc. Lond. Math. Soc, vol. viii.) in a 

 paper "On Viscous Fluids in Motion." In it, molecular groups are considered as con- 

 sisting of two classes — those in which finite strain can be sustained without rupture, 

 and those in which no strain can be sustained ; and the properties of substances are 

 regarded as depending upon the relative proportions in which those groups are present. 

 The investigation deals only with those cases in which fluidity is manifest. The 

 question of "elastic after-action" is included. 



In the present investigation, the question of an imperfectly-elastic solid is alone 

 considered, and elastic after-action is neglected. The case of torsion of a wire is 

 explicitly developed. The fact that the period of oscillation had no effect on the 

 experimental results obtained in the preceding part of the paper justifies the omission 

 of the consideration of after-action in the application of the theory to these cases. 



The time which elapses between the breaking down of a group and its formation 

 into a new configuration is regarded as being zero in comparison with the time of 

 motion of the wire through any finite range. 



