30 Mr HOPKINS, ON RESEARCHES IN PHYSICAL GEOLOGY. 



approximately. Consequently, if the normal make an angle „ — »? with 

 AB, we shall have for the conditions of equilibrium of ^s, 



0, 



Again, let us suppose another physical line exactly similar and equal 

 to the former, with its extremities fixed to two other points in lines 

 through A and li respectively, and perpendicular to AS, and so that 

 the two lines shall be in contact, when not acted on by any force. 

 ^Vhen the force <p acts in exactly the same manner on both, they will 

 assume exactly similar positions, and those elements of the two lines 

 respectively which were in contact when the lines were straight, will 

 remain so when they have assumed their cvirvilinear form, and will be 

 in exactly the same relative positions with respect to each other, as if 

 the lines had been united into one previously to their becoming curved. 

 Whence it follows, that there can be no more action between these 

 lines when united, as we have just supposed, than if they were per- 

 fectly independent, and therefore the tension of each must remain the 

 same as if this independence existed. If we conceive any number of 

 lines to be united in a similar manner, so as to form a lamina, the 

 same conclusion will apply to each. 



25. Let us now take then a rectangular lamina ABGH, which 

 we may conceive to be formed in this manner, and which we will sup- 

 pose to be brought into the position represented in the annexed figure, 

 by the force (p acting perpendicularly to AB, and in the plane of the 

 lamina. EF represents a physical line originally parallel to AB; and 

 P3I another originally straight and parallel to AH, and therefore, still 

 evidently remaining so, though in a different position, in the curved 

 form of the lamina. Let x be the original distance of PM from AH, 



