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Transactions of the Society . 
approaching those of the adjacent ones at certain definite and regularly 
disposed points, at -which they become connected together by short 
transverse costae. There are thus formed quadrangular interspaces, 
somewhat resembling in shape the areolae of the mature valve, but, as 
yet, with only the slightest vestige of bars across, and with no eye- 
spots beneath. 
In the last, or mature stage (fig. 5), the cros3-bars and eye-spots 
have developed. So far as my observation goes, they appear almost 
simultaneously. At first they are very delicate, and visible only with 
great difficulty ; but they gradually increase in strength until they 
reach the condition of the perfectly formed valve. 
In one variety of the species the original costae become connected 
by the transverse ones, so as to form short areolae, only towards the 
axis of the valve ; and remain parallel, and without union, near 
the margins (fig. 6). In this marginal portion, therefore, the ulti- 
mate areolae are linear, and very elongated. The cross-bars on them 
are numerous; but, however elongated the areolae may be, I have 
never seen more than one eye-spot beneath each. 
In another variety (fig. 7) similar elongated areolae are found 
near the median line. 
The question whether in any other genera of diatoms the course 
of the development of the valve resembles, in its main features, that 
which we have seen to take place in Trachyneis , requires further 
investigation before it can be answered; but a few circumstances 
may be mentioned, as perhaps having some bearing upon this point, 
although, as yet, only suggestive. The only instance I can adduce 
of direct observation of a similar condition is of a frustule of Caloneis 
probabilis Cleve, in which the young inner valves are in a flexible 
costate condition, with the puncta between much less conspicuous 
than in the mature valves. [Shown on screen.] 
In a pap'er on the structure of the valve in Pleurosigma, read 
before the New York Microscopical Society, and published in their 
Journal for April 1891, Mr. T. F. Smith describes the ultimate 
structure of the outer layer of the valve of P. formosum as con- 
sisting of long fibrils, placed side by side, lengthwise on the valve, 
and undulating so as to form oblique rows of interspaces ; and he 
figures (his fig. 9) two of these fibrils isolated. Never having met 
with anything of the kind myself, I cannot express any opinion as to 
whether these “ fibrils ” are at all analogous to the primitive costae 
of Trachyneis when they have passed into the slightly undulated 
condition ; and that it is by the subsequent coalescence of the fibrils, 
at adjacent undulations, that the well-known areolae of the mature 
Pleurosigma are formed. One obvious difference is that, while Mr. 
Smith describes the fibrils of the Pleurosigma as longitudinal to the 
valve, the costae of the Trachyneis are transverse. 
Among those species of Navicula , which Prof. Cleve has recently 
included in Diploneis, there are some forms, which puzzled the older 
