10 Dr. Schumann s For mul-ee for Diatom- lines. By \\ . J. Htckie. 
The two latter we get from the triangle B C (t. Moreover the 
number of the secondary series is not limited to these ; for we may 
divide the structure in many other directions by straight lines drawn 
through fixed points. Their common line-number is f p 1 a 2 -f <f L 2 , 
where p and <j are any whole numbers. 
'/ 
But it is of no practical utility to concern oneself with these, 
since it is difficulty enough to find out the lines U D, U E, and 
those corresponding to them, even in coarsely marked shells. 
The form also of the dots in this case plays an important part. 
Lastly, if the inquiry is after the smallest angles which the 
lines U C, U I), UE make with the longitudinal axis, the question 
is one of easy answer. The trigonometrical tangents of these 
angles are, respectively, 
a a 2 a 
V 2 V T ' 
The following genera and species, so far as my observation goes, 
exhibit corresponding series: 
Epithemici, Eunotia , Himaniidium, Meridion. Podosphenia, 
Bhipidopliora, Odontidium, Diatoma vidgare, Fragilaria virescens 
and elliptic a, Synedra , Tabellaria. G omphogr amnia, all species of 
Surirella known to me, in their fine systems of puncta, Amplii- 
