336 G. K Becker— Proof of the Earth's Rigidity. 



illustration of the fact that in the case of two electrified spheres 

 the potential function is a measure of work, is new to me and 

 I feel sure that it will prove helpful to persons who already 

 familiar with indicator diagrams, are struggling to get an idea 

 of the use of the potential function." This opinion of Pro- 

 fessor Peirce determined me to publish this paper. 



It should be stated that Maxwell also used the indicator dia- 

 gram in illustration of an electrical problem, though different 

 from the one here considered. Section 27 of his work, "An 

 elementary treatise on electricity," is thus headed " Indicator 

 diagram of electric work. The indicator diagram, employed 

 by Watt for measuring the work done by a steam engine, may 

 be made use of in in vestigating the work done during the 

 charging of a conductor with electricity. . . ." 



Stevens Institute of Technology, Hoboken, N. J. 



Akt. XLIII. — An elementary proof of the Earth's Rigidity ; 



by Geo. F. Beckeb. 



Definition of rigidity. — The term rigidity, as used in the 

 theory of elastic bodies and in the theory of the earth, denotes 

 any degree of resistance to change of shape. It must be con- 

 fessed that the selection of this word to express this quality is 

 not a fortunate one. In ordinary mechanics, as in ordinary 

 life, a rigid body means one which is incapable of change of 

 shape. Such a body would be called by elasticians infinitely 

 rigid, and they attribute to every substance which shows elas- 

 ticity of shape, however small, or in other words to every solid 

 substance, the property of rigidity. Thus both india-rubber 

 and steel are in their language rigid bodies, the difference in 

 this respect being that the " modulus of rigidity" of steel is 

 much greater than that of rubber. From the ambiguity of the 

 term rigid, some geologists who were unfamiliar with his 

 writings have been led to suppose that Sir William Thomson 

 maintained that the earth is incapable of deformation. So far 

 is this from the truth that Thomson was the first physicist 

 who investigated the tidal problem on the hypothesis that the 

 earth undergoes deformation by the attraction of the moon or 

 sun. It is to be understood, then, that the title of this paper 

 may be stated less concisely, but without change of meaning, 

 as " an elementary proof of the earth's resistance to change of 

 shape." It will not be found that the term rigidity, once 

 understood in its special sense, leads to confusion. 



Difficulty of Thomson's Problem. — No geologist would 

 think of denying that the question of the earth's solidity is the 



