240 Mr. Hopkins oti the Mechanism of Glacial Motion. 



Now 1 entirely deny the validity of such reasoning, and con- 

 tend that the reason here assigned would much rather justify 

 an opposite conclusion. Take two physical lines terminating 

 in the same point, and contiguous to each other, and let a 

 motion be given to the particles of each by distending the 

 lines; the degree in which any one particle of one line will 

 slide by an originally contiguous particle of the other line, 

 will obviously not depend on the whole distension of the two 

 lines, but on their difference of distension. If there be no such 

 difference, there will be no tendency in these particles to sepa- 

 rate, and therefore there would be no tangential action be- 

 tween them if they cohered. Instead of only two physical 

 lines, conceive any number still terminating in the same point, 

 and lying in one plane, and suppose them to be differently 

 distended according to some continuous law in passing from 

 one string to a contiguous one, such that the distension in a 

 certain direction shall be a maximum. Then by the property 

 of quantities in their maximum state, the distension of two 

 contiguous strings in the maximum direction would be equal, 

 and there would be no relative displacement along the strings 

 in that direction. We should have the case of the two equally 

 distended strings first supposed. And that this supposed case 

 presents no vague analogy with the actual one before us, will 

 be seen by the following simple investigation. 



Fiff. 2. 



Let Mw and Mw' be the directions of maximum extension 

 and compression, as in fig. 1. of my second letter. Take any 

 line Mj», having one extremity in any proposed point M of 

 the mass, and meeting w' n produced in any point p. Con- 

 sider this line as the line of separation between two linear 

 contiguous elements terminating in M and p. Also, let M P 

 be the original position of these elements. Then, in moving 

 to M^*, both elements will be extended, but the one nearest 

 to M n will be extended more than the other, since the ex- 



* It should here be recollected that P/) is not necessarily small com- 

 pared with M L, but of any magnitude less than that through which the 

 relative motion with respect to M of a point in N'N, might carry that 

 point without producing fracture of some kind. 



