258 The Philippine Journal of Science wis 



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 /* 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 ■* = 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. 



