12 Dr. Schumann's Formulie for Diatom-lines, By W.J. Hiclcie. 
Si^ecial Case. 
Not unfrequently the width apart of the vertical series, or lines, 
is ahont equal to that of the horizontal lines, d.h.h - a. 
In this case (for which see Fig. 3), 
c = / = a /v/2, about ^ a. 
d = e — a a/ 5, ,, fa. 
Fig . 5 
6 
Q 
6a 
9 
E 
The two most distinct of the oblique systems of lines U C and 
UF form with the axis angles of 45°, and consequently stand 
perpendicular to each other. 
Of the secondary systems, U D and U E', as also U E and 
U D', stand perpendicular to each other, as they form with the 
axis angles of about 26|^ and 63^ degrees. 
To this class belong JEjjjithemia prohoscidea, Wester manni, 
granulata ; Himantidium jpectinale, Fragilaria virescens, Denti- 
cuJa elegans, AmpMpleura pellucida, Stauroneis Eichhornii and 
amphicephala, Pleurostaurum acutum, Pleurosigma lacustre, 
Melosira distans and salina. 
Yet this special case is seldom sharply marked. 
I found, for example, in one specimen of Fragilaria virescens, 
a = 38, 6 = 36, c 54. 
In both cases the relative error of the third not easy estimate, 
if we assume a and h to be exactly correct, or a = h = 37, is, 
suppose, 
© / — ©- 
Q Q 
B D' 
