264 HENRY S. WASHINGTON 
This use of ratios which may vary from zero to infinity, however, 
leads to hyperbolic curves, complicating the relationships and intro- 
ducing very serious and misleading distortion through the extension 
of the diagram to infinity in one direction, and is therefore disad- 
vantageous.t Consequently, and at the suggestion of Dr. Cross and 
Professor Iddings, this basis of plotting has been abandoned, and the 
percentage of silica used for the abscissas and the percentage of potash 
for the ordinates, both being expressed molecularly. While the rela- 
tion of silica to potash, an important factor in the question of the 
formation of leucite, is thus rendered not quite so evident, yet the 
diagrams gain in simplicity and intelligibility, and there is also the 
ereat advantage of dealing only with straight lines, thus immensely 
simplifying the calculations and the construction, as well as the com- 
parison of the actual rocks with the theoretical data. 
The calculation of any given magma is readily carried out by — 
means of the equations already employed for the calculation of the 
center-points.?, The results will be given in Table I at the end of 
this paper. Plotting these data for our assumed peralkalic and per- 
salic magmas, with variable amounts of soda and potash, we obtain 
the results shown in Plate I. In this the solid lines are those passing 
through magmatic center-points, and the broken ones those passing 
through the border-points of the magmatic divisions. The purely 
sodic magmas lie along the bottom of the diagram, while the purely 
potassic ones are at the top. One hundred per cent of silica is at the 
left and zero at the right, as this is in accordance with the diagrams 
of Iddings and facilitates. comparison with them. Furthermore, 
this corresponds with the order in which the various divisions are 
arranged in the Quantitative Classification. 
It will be observed that these lines resemble those of Iddings? in 
some respects. The latter, however, employs for the ordinates the 
ratio EO mNa2 
S10, 
1 Cf. Michel Lévy, Builetin de ta Carte géologique de la France, No. 92 (1903), 
p- 25. 
2H. S. Washington, Professional Paper, U. S. Geological Survey, No. 14 (1903), 
pp- 84-87. 
3 J. P. Iddings, Journal of Geology, Vol. VI (1808), Plates IX and X; and Pro- 
fessional Paper, U. S. Geological Survey, No. 18 (1903), Plate II. 
, instead of the percentage of potash, and conse- 
