258 The Philippine Journal of Science ms 
center of cells at the ends of the diameters. We take 618 as an 
approximate mean diameter. Then we sketch, as in fig. 5, the 
selected area of the surface of the coenobium showing the cells 
and the micrometer lines. The cells counted are 119. We now 
place our constant mark on the slide rule under the 1.19 place on 
the scale A, bring the hair line of the runner over the 6.18 place 
on the scale C, and read under the hair line on scale A the number 
sought, which is about 17.7. A glance at our prepared table 
shows that for a count of 120 cells and diameters between 463 
and 1,035 p, the range of cell numbers is from 10,000 to 50,000. 
Consequently our number must be 17,700. 
A modification of the above procedure was devised for the 
purpose of more closely approximating the number sought, and 
for simplifying the operation of the slide rule. The former 
purpose was attained by using a circular area instead of a square 
for the count, thereby eliminating the cells at the corners, these 
being more crowded in the microscope field because projected 
into the image plane from more sloping parts of the spherical 
surface. The area selected was, necessarily, smaller than the 
square, and for simplification of the slide-rule operation the 
area taken was 3141 square microns, for which area the constant, 
c,= a divided by tt = 1,000. The circle was drawn by taking the 
radius 31.6 microns as measured on the drawing paper under the 
camera lucida from the image of a stage micrometer. For use 
with semitransparent drawing paper the circle was drawn with 
India ink on a white card, and for use with opaque paper the 
circle was carefuly cut out of a card. This was done to avoid 
errors which might arise from disadjustment of a pair of com- 
passes. The circles were drawn on paper and within them the 
cells were sketched for counting. The counting was made easier 
in all cases by subdividing the area sketched, with red ink, into 
areolae containing ten cells each. 
This method was first applied to checking over sketches and 
notes previously made by use of the square areas, and it served 
to disclose several clerical errors as well as errors which arose 
from projection. 
An error which increases with decrease in the diameter of 
the coenobia is that which occurs if the diameter of the coenobia 
be measured from surface to surface of the spheroids. On this 
account, especially when working with small coenobia, the diam- 
eters were measured from center to center of cells on opposite 
sides of the coenobium, thus basing the reckoning on the 
spheroid in which the centers of the cells lie. 
