Dr. Schumann s Formula for Diatom-lines. By W. J. Hiehie. 7 
he had to let. Light reading we certainly cannot promise them ; 
but, such as it is, we commend it to the perusal of those " qui volunt 
et possunt." 
The learned author begins by observing that, though several 
microscopists have published valuable remarks on the diatom - 
frustule and its striae, yet one essential property has been left 
uninvestigated, namely, the dependence of the different striae- 
systems on one another — in other words, the relation in which the 
diatom-lines stand to one another. 
He proposes therefore at the outset to investigate certain 
principles which regulate the ^position and closeness of the diatom- 
lines, w^ithout dwelling on the form of the material puncta or the 
dots. He then adds, "I shall first discuss two simple cases of 
frequent occurrence, and then subjoin some data, which apply to 
every position of rectilinear diatom-lines. 
If we examine a Navicula, we observe on each side of the 
median line striae running to the marginal edge in a direction 
perpendicular to the median line ; these transverse lines, in some 
species, it would seem, consist of canals, in others of material 
puncta, more or less distinct, whose centres are mostly equidistant 
from one another. 
But the canals also constantly form equidistant spaces ; perhaps 
in consequence of constrictions or intrusive ridges. Frequently 
they look like strings of pearls communicating with one another by 
wide openings. If we examine one of the two adjacent series, we 
find in most species of Navicula that this series is a repetition of 
the fundamental series ; that therefore the connecting line of 
adjacent puncta of both series runs parallel to the longitudinal axis 
of the Navicula. Thus the transverse and longitudinal lines 
present the appearance of a chess-board. 
Yet the longitudinal lines generally have a width apart different 
Fig. 11. — Nitzschia thermalls. "One specimen exliibitecl 16 eye-like puncta 
and 80 transverse lines in t^o'", and another 18 such puncta in i^-j^'". " 
Fig. 12. — Nitzschia inedia. "Three frustules from the Mengsdorfthal showed 
26 puncta and 74 transverse lines in -i^,'". " 
Fig. 13. — JSitzschia communis Synedra notata Klz.). " Sevi n specimens 
gave 28 puncta and 80 transverse lines in ^^o'". " 
Fig. U.—Nitzschiella closterioides (Grunow, Wien, 1862, p. 582, Xll. 1 9). " Two 
fiustules exhibited 31 puncta and 90 transveise lines in -j^,^'", whilst another 
from the Ko/ilbuchthcd, though only half the length, showtd 29 puncta and about 
100 transverse lines in lio'"-^' 
Fig. 15. — Achnanthes eiliptica m. " The number of the coarse lines in the lower, 
middle, and upper stations of the Tatra amounts to 35, 38, and 41 respectively 
ill Tiyo'"- " 
Fig. 16. — Gomphonema montanum. "The transverse markings of the shell are 
canal-formed. In two specimens with 25 canals the shell exhibited G2 fine trans- 
verse lines in -y^o'". " 
The author adds that the entire number of species foui.d on the Tatra amounts 
to 235 at least. 
