January 19, 1900.] 



SCIENCE. 



87 



the concept with regard to the distortions 

 of the particle which result from the stresses. 

 If the particle be a rectangular parallele- 

 piped, for example, these stresses may be 

 represented by three pressures or tensions 

 acting perpendicularly to its facea together 

 with three tensions acting along, or tan- 

 gentially to, those faces. Thus the adjacent 

 parts of the medium alone contribute six 

 independent force components to the equa- 

 tions of equilibrium or motion ; and the 

 stresses, or the amounts of force per unit 

 area, which produce these components are 

 technically known as tractions or shears 

 according as they act perpendicularly to 

 or tangentially along the sides of the 

 particle.* Corresponding to these six com- 

 ponents there are six different ways in 

 which the particle may undergo distortion. 

 That is, it may be stretched or squeezed in 

 the three direction^ parallel to its edges ; 

 or, its parallel faces may slide in three 

 ways relatively to one another. These six 

 different distortions, which 'lead in general 

 to a change in the relative positions of the 

 ends of a diagonal of the parallelepiped, 

 are measured by their rates of change, 

 technically called strains, and distinguished 

 as stretches or slides according as they 

 refer to linear or angular distortion. f 



It is from such elementary dynamical 

 and kinematical considerations as these 



* The terminology here used is that of Todhunter 

 and Pearson, History of the Theory of Elasticity and 

 Strength of Materials, Vol. I., Note B. 



tThe terminology and symbology of the theory of 

 elasticity appear to be more highly developed than 

 those of any other mathematical science. A compar- 

 ison of the terms and symbols of elasticity with those 

 of the older subject of hydromeclianics, as shown, in 

 part, below, is instructive : 



In Elasticity. 



Strains. 



Stretches 



Tractions -J pyy 

 Shears i jizx 



that this theory has grown to be not only 

 an indispensable aid to the engineer and 

 physicist, but one of the most attractive 

 fields for the pui-e mathematician. As Pear- 

 son has remarked, "There is scarcely a 

 branch of physical investigation, from the 

 planning of a gigantic bridge to the most 

 delicate fringes of color exhibited by a 

 crystal, wherein it does not play its part."* 

 It is, indeed, fundamental in its relations 



i c_\_ /_?^ __?^ \ 



I '~2 \d^ 'di ) 



Component spins, or -, , ^ ., , 



, , , I 1 / 3m dw\ 



components of molec- ■{ V = ^ { -^ ^ — ) 



l 2^ 



du \ 

 dy J 



Velooity potential in irrotational motion. 

 * History of Elasticity, etc., Vol. I., p. 872. 



