32 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



— . Sx.Sy - S(T'. Sx) cos v = 0, 

 P 



S(T.Sy) + HT'.Sx)smv = 0, 

 or since S{T'.Sx) = ^ Si/.Sx, and HT.Si/) = ^ SxJi/, 



and ti is by hypothesis very small, 



T dT „ 



(IT (IT _ ^ 



(Ix (ItJ 



neglecting terms involving rf. 



T 



In the case we are considering, — is a function of x alone, and there- 



P 

 fore the first of the above equations gives 



T 



T = -.y JrC 



P 

 T 



= -y 0) 



p 



since T" = 0, when y = 0. This is subject to the condition T'.Sx = 

 force at M = (p. PM. ^x, or T = <p . P3L 



The second equation gives 



T = const, nearly (2). 



26. If instead of supposing the lamina inextensible in the direction 

 P3I, we suppose it capable of small extension in that direction as well 

 as in that parallel to AB, and still assume it to be acted on by forces 

 applied at each point of HMG, so as to keep that extreme boundary 

 in the same position as before, the physical line EF will assume a position 

 differing in a small degree from its former one. Since the angle »? will 

 still be very small, we shall still have T = const, nearly. The curva- 

 ture at Q will no longer be the same as that at M, and p will therefore 

 be a function of y, as well as of x. Consequently equation (1) of the 



