760 WHITMAN CROSS 
rated symbols may also be readily determined. Referring to the 
original paper, already cited, for details of the new proposition, it 
may be briefly explained in this place. 
It is recognized that it is desirable to express in the quantitative 
system two frequently observed relations of rocks which cannot 
be shown by the simple magmatic name or the symbol hitherto 
used. Two rocks often fall in opposite extreme portions of a 
division, while two others may be found occurring in two adjacent 
divisions but very near the boundary line. It has been proposed 
to establish intermediate and transition zones, the former extending 
TABLE OF NORMATIVE RATIOS 
Class Order 
Rang Subrang 
Sal Q K.0’+Na.0’ K.0’ 
Fem F CaO’ Na.0’ 
ya se ter aae URN te eee er 3.50 0.19 1.88 Ona] 
1 Bets Rear ante ee aur A Eee Lake 3.87 0.23 Tig ills 0.57 
Cee a eet ey tees Bn 25 O.11 1.661 0.53 
1 Drei eel ete R ane ek Aa tes ky 3.64 0.21 I .43 0.59 
IBC ele he ma bent cash re im See eee ee DBO Omrss 1.36 0.54 
Gees ilee ha eerie amy anys 4.36 0.176 an) (te) 0.55 
Ae oR ag es gens, Weare aa 6.50 0.17 2.04 0.67 
| De eee tum reTnIe en Nae) neuen Bel) 0.26 0.95 0.36 
A cera rece ime SOs cere Me RUA Ree ed Buoy 0.19 1.47 0.57 
TEE See estes auc er iS rarhiearagi hoped eae 5.01 0.09 2.64 ©.49 
Ie eranee aren career nN EN e eiet 3.06 O.1I1 1.58 0.56 
IN eee THiS SA Eee arene 3.67 0.137 1.74 0.83 
(OES irsceielic deta CoA AE erie ig 3.68 0.15 1.51 0.58 
Meare me ee nen MUNA Batra cos An2t 0.21 1.22 0.35 
REN ig enka STOR TED cee 3.70 0.178 1.44 0.56 
on each side of a given division line one-half the distance to the 
center points of adjacent divisions and the latter one-fourth of 
this distance. The boundaries of both intermediate and transi- 
tion zones are determined accurately by the ratios of the two 
quantities concerned in the formation of classes, orders, etc. These 
determining ratios are given in the cited publication. 
The transitional position of a rock may be expressed by a com- 
pound name, but where it is transitional in more than one respect, 
as frequently happens, it is desirable to use only the two subrang 
names expressing the lowest systematic stage in which such transi- 
tional relation exists. This usage is illustrated in the following 
table. In the symbols the transitional relation is indicated by 
giving in parentheses, beside the number of the division in which 
