354 Mr. T. S. Hunt's Examinations of some Felspathic Rocks. 

 then 



:»*( 



M + N £C08j f e-/3); 

 pa 



D = N— crsin( a -y3) 

 u 



1 



tan<9= — 



tana' 



and 



M = -i-/Ap 9 + 2B^cos(a-/3) + (m + l)^) 

 2mJ\ r u u l ) 



N = t^/Bd 2 + 2m p — cos (« - /3) Y 

 <imj\ u J 



The practical object will of course be to find those forms of 

 lenses which by their combination reduce At; and A£ to nothing, 

 if possible, for all values of y, z, b, c. This involves the solution 

 of five equations, upon the discussion of which I do not propose 

 to enter at present. It may be desirable at some future time to 

 extend the solution so as to introduce the 4th powers of b and c, 

 but not of y and z. I would suggest also the want of some fixed 

 principle of selection among imperfect foci. I have found the 

 results of assuming a law which answers the obvious require- 

 ments of the case, as follows : — If that be called the best section 

 (focus) of a pencil which gives the sum of the squares of the 

 distances from their centre of intensity of the points where the 

 several rays meet the plane of the section, we find that the circle 

 of least confusion conforms accurately to this condition, and that 

 for a large direct pencil the distance of the best focus from the 

 least circle of aberration is ^th of the whole longitudinal aberra- 

 tion. I think some satisfactory conclusion on this point might 

 be attained by careful experiment. 



L. Examinations of some Felspathic Rocks. 

 By T. S. Hunt, of the Geological Commission of Canada*. 



THE oldest known group of rocks in North America is that 

 to which the name of the Laurentian System has been 

 given in the Reports of the Geological Survey of Canada, and is 

 made up of very much disturbed and highly crystalline strata, 

 which are in great part gneissoid and quartzose. Interstratified 

 with these, however, are beds of crystalline limestone, often of 

 great thickness, and holding scapolite, pyroxene, phlogopite, ser- 

 pentine, fluor, apatite, spinel, corundum, condrodite, sphene, 



* Communicated by the Author. 



