Dr. E. J. Mills on Cumulative Resolution. 497 



from two silicic hydrates, of which the second is the cumulate 

 of the first. 



n H 4 Si0 4 -(n-l) H 2 = H 2rt+2 Si n 3n+l . 



3=v[H 2 Si0 3 ], 



3=. 2 [Sio 3 ]. 



After the first cumulate, the second series is vH 2 Si n 2w+1 . 



For the mixed series, 



?>tH 4 Si0 4 + nH 2 Si0 3 — (m + n— 2)H 2 = H 2wi+4 Si /rt+ «0 3wi + 2 «+2 ; 

 whence 



3=v[H 2 Si0 3 .Si0 2 ]. 



Series 1. — Peridote*, phenakite, zircon, almandine, grossu- 

 laria, tetrethylic silicate (n = l). 



Analcime? (n=l*3). 

 Okenite (n = 2). 



Magnesite, Labradorite (n = 3). 



Diopside, enstatite, chlorophasite, amphigene, 



pyrophyllite, talc, emerald, diethylic silicate 



(n= ex). 



Series 2. — Anorthite (n = *5). 



Fremy's hydrate (n = l*5). 

 Diethylic disilicate (n=2). 

 Doveri's hydrate (?i = 3). 



Mixed Series. — Orthose (w=4, ra = 2)« 

 Analcime (n= — 1, m = 5). 

 Fuchs's hydrate (n= oc ; ?w = oc). 



Before proceeding to the consideration of carbon compounds, 

 it is necessary to consider the relation of homology to cumu- 

 lative resolution. 



7. Homology. — If we take any starting-point X, and pro- 

 ceed to form homologues X . CH 2 , X . 2 CH 2; X . 3 CH 2 , &c, 

 we have in general X . G n H 2n . When, therefore, n becomes 

 very large, the composition of a member of any homologous 

 series is undistinguishable from that of an olefine. Such com- 

 position is moreover attained by a perfectly continuous ap- 

 proach. Take, for example, the fatty alcohols, C n H 2w+2 0, 

 which are homologues of water: T) is evidently vCH 2 , as 

 must also be the case with the aromatic alcohols C n H 2w _6 



* I have taken "Wurtz's authority for the formulae (Logons de Phil. 

 Chim. p. 181. In this place will be found some of the earlier suggestions 

 of a theory). 



Phil. Mag. S. 5. No. 21. Suppl. Vol. 3. 2 K 



