492 
David H. DoUey 
axis, as found, however, in a single section. This certainly affords con- 
sistent and harmonious results and appears permissible for several reasons. 
In the first place, the cells are for the niost part regularly disposed as 
well as so numerous that it is a simple matter to find the quantity desired 
properly in plane of section. In the second place, the course of activity 
in the Purkinje ceU is a succession of distinctly marked stages and all 
cells belonging within any given stage are sufficiently ahke in size to 
permit of averages of diameters being made. Hence the unknown third 
dimension could vary no more than the limits of its known counterpart 
in a fair average. Fifty cells to a stage were first uscd, then twenty five was 
fixed upon as giving exactly the same relation, thongh, so closely do the 
sizes run, that ten cells to a stage seldom resnlt in more than minor in'egu- 
larities of the curves of size. 
In the case of the crayfish ceUs, they are, to begin with, iiTcgularly 
disposed. A longitudinal section does, however, show the majority of 
cells in longitudinal rather than transverse section. Again, there are no 
distinct stages of chromatin formation as in the highly specialized cell, 
and if there were, the ceUs of certain types at least are too scanty to 
permit a satisfactory average of their diameters. Third, the transverse 
diameters (minor axes) themselves, when followed in serial section, were 
found rather frequently to differ from one another widely, the cells 
evidently being flattened rather than elliptical or pear-shaped. FinaUy, 
if this were not enough, the ränge of size and shape is so great outside 
of the point regarding scanty number in some stages that getting any 
averages of corresponding diameters was out of the question. Conse- 
quently, the volume had to be calculated for each individual ceU — the 
computation of mass being the ultimate and sole ahn. But doing this, 
whüe the majority of cells feil consistently and consecutively, it is 
apparent that, lacking the actual longest diameter, or from a false esti- 
m.ation of the unknown shorter diameter, there would be numerous dis- 
crepancies. Though fairly clear indications of the course of events were 
afforded, these were sufficient to invalidate the method. 
The difficulty was obviated by esthnation of the unknown diameter 
from the number of sections involved. The types of ceUs are so distinct 
and they are sufficiently few in number in any section and so placed 
that it is easy to foUow both ceU and nucleus throughout their extent. 
The number of sections in which they appear multiplied by the thick- 
ness of each section, namely, five micra, gives at least an approximation 
of the third dimension. With the other figures as obtained in mUlimetres 
reduced also in terms of micra, a uniformity and definiteness is reached. 
