494 
David H. DoUey 
to the experience gained from measuring and so very probably there 
are confusions left uncorrected. The final results have run appreciably 
more smoothly. 
The Calculations of Volume and of Nucleus-plasma Coef- 
ficients. — The relative volumes of the cell and nucleus were calculated 
from the three diameters of each reduced in terms of micra by multiplying 
them together. This expresses the volume relations in terms of the parallel- 
opiped corresponding to each cell and is the procedure which was used 
by PoPOFF (1908) in his work on Frontonia leucas, etc. The relative 
sizes thus obtained give just as accurate a conception of the relations. 
The formula for computing the volume of sohd bodies varying from 
pear shape taken as an ellipsoid to the sphere (in which it becomes 
is ^/3{2a‘7t-b^), or with unequal minor radii, Vs (2 a • jv • fcc). 
If the ratio to be determined between two bodies whose radii are a, b 
and c and a', b' and c' respectively be expressed as a fraction, cancelling 
out the common factors, it becomes or the diameters themselves 
a b c 
may be used. 
To accord with Richard Hertwig’s conception of the nucleus- 
plasma relation, the computation of the coefficient of this relation in- 
volves the Separation of the plasma mass from the total cell mass. This 
was derived by subtracting the nuclear volume from the cell volume. 
The resulting figure for the plasma mass when dmded by the nuclear mass 
gives the size ratio between the two. 
By way of checking the results, certain tests have been applied to 
determine the extent and possibihties of Variation. These as well as 
the Problem itself have been of the simplest character beyond which 
the writer would disclaini the ability to carry them. When it is considered 
that a difference of only five micra in one diameter of the ceU body vdth 
the Same size of nucleus makes a difference of two units or even more 
in the nucleus-plasma coefficient, the importance of the smaller variations 
from the mean is considerably lessened. Again, for certain groups of 
cells in Tables IV and VI, the Standard deviation and the coefficient of 
Variation (Yule, 1911) have been calculated for the nucleus-plasma 
coefficient. This would seem to be the only application of these proce- 
dures, as this coefficient is the only definite point of resemblance. In 
Table IV, the Standard deviation for the second group of cells is =b 1.3, 
and for the fourth group, ± 3.59, and their coefficients of vaiiation are 
.114 and .192 respectively. Taking the coefficients of the thhty-eight 
cells from 200,000 to 450,000 cubic micra, their Standard deviation is 
