14 Br. Schumann's Formulas for Diatom-lines. By W. J. Hichie. 
where A denotes the angle BAG, which one may easily get from 
A. a 
the estimated line-numbers, since sin. "2 ~ 2 & ' 
Whilst diatoms of an extended form mostly exhibit corresponding 
series of pnncta, those whose obverse sides are developed about a 
point not unfrequently exhibit alternating series. 
First Special Case. 
When A = 60°, then the triangle A B C is equilateral (see 
Fig. 5).* 
In this case, 
a = 6 = c, e=f = g = aAj2>, about ^ a, 
= 90° <p^=i<p^ = 30°, 
<l>4 = 0°, 0g = </), = 60° 
The three primary systems cut one another at an angle of 60° ; 
the secondary likewise. The latter stand perpendicular to the 
former, and may be easily found in consequence. 
To this class belong most of those species of Pleurosigma which 
Smith and Kabenhorst treat of as Section 1. 
Further: 
Biddulphia turgida and radiata (Syn. LXII. 384, 885). 
Triceratium favus (Syn. XXX. 44). 
Podosira Montagnei (Syn. XLIX. 326). 
Melosira suhflexilis, orichalcea. 
Yet even here some notable deviations from the uniformity 
of the numbers of the lines occur. I found, for instance, in a 
specimen of 
Pleurosigma angulatum, a — 44, h = 46, c = 46, 
and in 
Pleurosigma strigosum, a = 46, 6 = 46, c = 39. 
In the latter case, according to my estimate, the angles of 
inclination also of the two oblique systems were sensibly different. 
Second Sjpecial Case. 
When A = 90° (for which case see Fig. 6),* then 
b = c = ^ a/2, about. a, d — a, 
e =f =^ a/ 5, about fa, = 90°, 
<p2 = ^3 = 45°, • ct>, = 0° 
tan. = tan. <p^ = 3, 0, = <|)g, about 71^°. 
See footnote on preceding page. 
