1 2 Dr. Schumann’s Formulas for Diatom-lines. By W. J. Hicltie. 
Special Case. 
Not unfrequently the width apart of the vertical series, or lines, 
is about equal to that of the horizontal lines, d.h.b = a. 
In this case (for which see Fig. 3), 
c=/=«V 2, about a. 
d — e = a ,, 
Fig . 5 
B D C E 
G -Q © — — — 0 
The two most distinct of the oblique systems of lines U C and 
U I form with the axis angles of 45°, and consequently stand 
perpendicular to each other. 
Of the secondary systems, UD and U E', as also U E and 
h D , stand perpendicular to each other, as they form with the 
axis angles of about 2G4 and 634 degrees. 
To this class belong Epitkemia probosciclea, Westermanni, 
granulata ; Himantidium pectinate, Fragilaria virescens, Denti- 
cula elegans, Ampkipleura pellucida, Stauroneis Eichhornii and 
amphicephala, Fleur ostaurum. acutum, Pleurosigma lacustre, 
Melusira distans and salina. 
Yet this special case is seldom sharply marked. 
I found, for example, in one specimen of Fragilaria virescens . 
a ~ 38, b — 36, c — 54. 
In both cases the relative error of the third not easy estimate, 
il we assume a and b to he exactly correct, or a = b = 37 is 
suppose, E. 
