SIZE CHANGES IN NERVE CELL BODIES 319 
heading of his table 2, ‘‘Volume expressed as square inches,” 
a very plane conception of volume. 
The area method necessitates the same resource to averaging. 
Where relative sizes are all-important, the smaller variations in- 
herent in the two dimensional measurements as compared with 
the corresponding augmentation of these differences in greater and 
ereater degree in three dimensional calculations is quantitatively 
misleading and may cause important points to be minimized. 
Take 2 x 2, and 3 x 3; one is 4, the other 9; but 2x 2x 2 is 8, and 
3x 3x3 is 27. Here is another fault in all size comparisons in 
the literature which makes them less productive—the diameters 
alone were used (compare tables 2 and 3). Mathematically 
stated, in a series of increasing squares the first differences are in 
arithmetical progression, in one of cubes the second differences 
are in arithmetical progression. 
Along with the confirmation of previous technical methods 
certain important conclusions are corroborated by the added 
data. 
In the first place, the nucleus-plasma coefficients of the resting 
cell (stage 1) are 12.4 for the control, and 11.2 for the exercised 
animal by the diameter method, and 4.3 and 4.1 respectively by 
the area method. The average resting cell coefficient so far is 
11.7 by the diameter method, and the range of deviation is 11 to 
12.4. The two figures above, 12.4 and 11.2, fall therefore within 
this range. Two additional individuals conform to the law, of 
species identity of the nucleus-plasma norm (Dolley, ‘14). 
In the second place, it may be noted that the coefficient figures 
of stage 2 do not vary more than those of stage 1 just discussed 
—12.4 to 11.2 and 11.2 to 11.4. In short, as has always occurred 
in stage 2, though the size undergoes a 50 per cent or greater 
increase, the nucleus-plasma relation remains constant. This 
is most important for the deduction of an exact proportionate 
increase of nuclear and plasmic materials in the beginning of 
activity, a purely quantitative increase of the same materials in 
each element. 
The third point is the close identity of area and volume for 
the resting cells in the two cases—16.33 and 80.71 with 16.45 
and 81.77. What does it probably mean? The deduction has 
