122 Prof. Liveing, On the rocks of the Channel Islands. [Nov. 14, 



dco's give (y 1 — ax l — 6 t ) dai 1 + . . . + (y 4 — ax 4 — b) c£a> 4 = 0, that is, is 

 a single relation = 0; or the 3 equations thus reduce themselves 

 to 2 independent equations. 



Again, if the fixed curve be a quintic, m = 5, there are here 

 between the displacements the 6 equations 



Xx 2 dco — 0, %xyd(£> = 0, 2;y 2 c7a> = 0, 



Xxdco = 0, %yda) = 0, Sdo) — ; 



the two cases in which the number of independent equations 

 is less than 6 are 1° when the variable curve is a line, and 2° when 

 the variable curve is a conic. For the line n = 1, and the number 

 should be = 3. We have the above 6 equations ; but the equation 

 of the line is ax + by + c = 0, that is, we have ax x + by 1 + c — 0, 

 &c. ; we deduce the 3 identical equations 



1x (ax + by + c) = 0, Xy (ax + by + c) = 0, 2 (ax + by + c) = 0, 



and the number of independent equations is thus 6 — 3, =3 

 as it should be. 



So when the variable curve is a conic, n = 2 ; the number of 

 independent equations should be = 5. The points of intersection 

 lie on a conic (a, b, c, f g, h^x, y, I) 2 — ; we have therefore 

 the several equations (a, b, c, f g, li^x x , y x , 1) 2 = 0, &c. : we have 

 therefore the single identical equation 



t (a, b, c, f g, hjx, y, If dco = 0, 



and the number of independent equations is 6 — 1, = 5 as it 

 should be. 



Obviously the like considerations apply to the case where the 

 fixed curve is a curve of any given order whatever. 



November 14, 1881. 

 Mr F. M. Balfour, President, in the Chair. 



The following communication was made to the Society: 



On the rocks of the Channel Islands, No II. By Professor 

 Liveing. 



In a former communication on this subject I drew from my 

 observations of the rocks of the Channel Islands, principally those 

 of Guernsey, the conclusion that the granitic structure is a nieta- 

 morphic character which may be imparted either to stratified or to 

 igneous rocks, which is not due to igneous fusion, but is rather the 

 result of continued variations of temperature always far short 



