1884.] Prof. Maletfs Invariants and Sir J. Cockles Criticoids. 45 



testing, repeated heating and cooling, combined with oscillations for 

 a great number of hours and long rest, having had the effect of 

 rendering the iron much less susceptible to alteration of torsional 

 rigidity from change of temperature. 



At the present stage of the inquiry it is impossible to arrive at 

 any definite conclusion as to any relationship between the viscosity of 

 metals and their specific electrical resistance. It would seem indeed 

 that in the case of the pure metals, those which have the greatest 

 viscosity, such as lead and tin, are those whose specific electrical 

 resistance is comparatively great, but even with the pure metals so 

 many circumstances influence the loss of energy that a much more 

 extended investigation must be made ere one can write with sufficient 

 certainty on the point. In the case of the alloys, German silver, 

 platinum- silver, and brass, the values of the logarithmic decrements 

 do not seem to be greater than those pertaining to their components, 

 whereas as regards specific electrical resistance we know that this 

 is not so. Again we encounter the curious fact that whereas with iron 

 the electrical resistance is more increased by rise of temperature than is 

 the case with any other metal, the logarithmic decrement is on the con- 

 trary decreased by the same cause. 



A review of the whole experiments shows that the loss of energy 

 due to internal friction of a torsionally vibrating wire does not 

 accord with laws of fluid friction, but with those of external friction, 

 inasmuch as the loss of energy from internal friction, like that from 

 external friction, is to a great extent independent of the velocity. 

 Whether with external as with internal friction the loss of energy 

 would be independent of the pressure provided the molecules of the two 

 surfaces were brought into very close proximity, remains yet to be 

 decided. 



V. " Professor Malet's Classes of Invariants identified with Sir 

 James Cockle's Criticoids." By the Rev. Robert Harley, 

 F.R.S. Received December 10, 1884. Read December 18. 



1. Professor Malet, in a paper entitled " On a Class of Invariants," 

 printed in the "Philosophical Transactions" for 1882, Part III, pp. 

 751-776, says he has not seen it noticed by any mathematician that 

 " in the theory of Linear Differential Equations there are two important 

 classes of functions of the coefficients which have remarkable analogies 

 to the invariants of Algebraic Binary Quantics." He then proceeds 

 to determine the forms of such functions, and to give examples of 

 their application. Soon after the publication of the abstract of 

 Professor Malet's paper in the Proceedings of the Society (vol, 3&, 



