o9b A. C. LAXE PORPHYKITIC APPEAEAXXE OF ROCKS 



(10) C = K! ch' (2 u ! Uo — ly = Ki ch' (2/-' — 1) ^ . 



(11) A = KIch (i//?/„)^ ]/T = KIchr ;/2". 



(12) B = Ky':ch (uiii,)i\/2~ = Ky',chf V'Y . 



(13) E= Kl'V^^o=KI-f. 



From 11 and 12 we can determine y\ the effective contact zone, which 

 is 5 A. 



(1^) y' = 4- 



If y is less than 1, 12 c, we may be sure that so far as the contact zone 

 is concerned our approximate solutions are pretty close. From (11) and 

 (13) we can find c in terms of A, E, and K — that is, we can sometimes 

 by observation of the grain determine the thickness of the dike when it 

 was not known. Moreover, we can find / in terms of A, E, and c, and if 

 f- does not come out too near to unity we ma}" feel that our approximate 

 formulae and results from them are not likel}^ to be far out. We can 

 also find Kin terms of J., E, and c, or if we have formulae (10) we can 

 either check on our observations or get along without c or some other 

 factor. From formula? (10) and (11) we can find /in terms of C and A, 

 although the equation is a cubic best solved by approximation. We can 

 then find Ki c. 



Suppose we find a certain rate of increase of grain, the slope of a cer- 

 tain straight line tangent to the curve of the grain. We may not know 

 surel}^ whether it represents C or A. Take, for instance, Queneau's 

 equations. They give a small value for the grain of the augite at the 

 margin. Now, theoretically, if the slope represents C, there should be 

 no grain at the margin, but practically there is liable to be grain at the 

 margin according to the equation derived from our observations owing 

 to the imperfection of the same or to some minor irregularities. We 

 will therefore call this slope s. Now, from equations (11) and (loj we 

 have equation 



(1-5) r = uluo = EjAo hAc = E!Ab hsc. 



From (10) and (13) we have equation 



(16) 2/-^ = 1 + (E:Ad UCcf (2/-')* = l-\-{E .45 h'scf (2/0^ 



Thus it will be comparatively easy to obtain the alternative values of 

 ulu^ on the two hypotheses. Since 2u/Wo is always between 1 and 2 and 



