Lower Palceozoic Rocks of the South-East of Ireland. 603 



Another equation may be found from the consideration that all the iron in 

 the analyses of Table VI. belongs to the black and white micas. White mica 

 contains of iron, Table III., estimated as peroxide, 457 per cent., and black 

 mica contains of peroxide of iron, estimating with it the protoxides of iron and 

 manganese, Table V., 29*81 per cent. ; while from Table VI., the granite 

 contains 2'22 per cent. If we assume all the iron to belong to the two micas, 

 which is nearly certain, we obtain an additional equation, viz., counting FeO 

 and MnO with peroxides, 



29-8U + 4-57m = 222. (C) 



Bringing together all the equations A, B, and C, we have nine equations, 

 and nine unknown quantities to determine, viz., Q, F, M, £, 9,/, n«, I, (p. 



For convenience of solution, it is desirable to set down all the equations 

 together: 



l-G0l = Q + iF+3M+9L, (a) 



0-313= F+23f+7L, (b) 



0-273= F+ M+GL, (c) 



q= 45Q, {d) 



m= 402.M, {e) (11) 



1= 1115Z, if) 



^ + ?« + ;+/= 100-05, {h) 



298H+ 457??? = 22200, (J) 



Subtracting (c) from (6), we find 



0-040 = ilf+i:; 



which, by {e) and (/), becomes 



0-040 = ^+ ^ 



402 1115' 



which, after reduction, gives in combination with (i) the following system for 



the determination of w and ^, theper-centagesofmargarodite and lepidomelane 



in the granite : 



402^+ 1115m = 17929, 



298H+ 457wi = 22200. ^ ' 



