Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



31 



which will be approximately = AP, or EQ ; then will ^x be the original 

 width of the element P3I-, and if AE, or PQ = y, S// will be the 

 width of EQF. Also, if T denote the tension of the lamina at Q, 

 (estimated as in Art. 2.), in the direction of a tangent to EQF at 



that point, it is evident that T.Sp will equal the tension above denoted 

 by T. Therefore the force produced by this tension in the direction of 



T 



the normal to EQF at Q, wiU = — .^x .^y, acting on the element 



P 

 common to the two physical lines PM and EQF at Q. 



Now it is manifest, that the tension T, and — , will remain unaltered 



P 

 so long as the position of every element of the lamina remains so, what- 

 ever be the forces by which it is kept in that position. The action 

 of will be the same at any point Q in P3I as at P, since Q and 

 P are similarly situated points in EQF and APS, and by hypothesis 

 this force acts in the same manner upon each physical line, similar to 

 APB. Consequently, the whole force on P3I = (p . PM . Sx. Let us 

 suppose this force instead of acting on each element of PJ\f, to be ap- 

 plied entirely at its extremity M. If this be done to every such line 

 as PM, and the lamina be sensibly inextensible in the direction of these 



T 



lines, the position will remain undisturbed, and the normal force — Sx . Sy, 



at Q will not be altered. Hence, if T' denote the tension of the lamina 

 at Q in the direction PM, and therefore T'Sx the tension of P3I at 

 that point, and v the angle which the normal there to EQF makes 

 with P3I, we shall have for the conditions of equilibrium of the ele- 

 ment common to PM and EQF, 



