XIII, C, 4 
Shaw: Microtechnical Methods 
255 
This measurement of the periphery was reduced to terms of 
average intercellular distance by multiplying it by the number of 
intercellular distances in the selected row. From this measure- 
ment of the periphery=:27rr he calculated r and then 4t rr 2 . He 
thus obtained the area of the spheroidal surface in terms of the 
average area occupied by a single cell assuming the latter area 
to be equal to the square of the intercellular distance. 
Janet 6 has recently applied to the above method the assump- 
tion, more in accord with fact, that each cell occupies a hexagonal 
area. Taking e the average intercellular distance, and d the 
mean diameter of the sphere, he gives the formula 7 for the 
total number, N, of cells as : 
3.627 O 
He also gives the formula for the calculation of the number of 
cells, N, from the number, n, of cells counted in the great circle 
which forms the visible contour of the median optica] section. 
Based on the assumption that each cell occupies a hexagonal area 
of the spherical surface, the formula 8 is : 
N = 0.367 n\ 
“Janet, C., Le Volvox. Ducourtieux et Gout, Limoges (1912), 28. 
1 This formula may be derived from those for the area of the surface 
of a sphere in which A is the area, r the radius, and d the diameter: 
A — 4vr 2 — itd*. 
Since the area of a hexagon having a diameter of unity is equal to 
the sine of 60°, which is 0.86603, the number, N, of hexagons of unity 
diameter in the spherical surface is: 
N-- 
A 
0.86603 
wd 2 
0.86603 
0.86603 
d 2 = 3.627 d 2 . 
The coefficient in this formula is, then, v divided by the sine of 60°; and 
d over e is the diameter of the sphere in terms of the average diameter of 
the area occupied by a single cell. 
s This formula may be derived from that for obtaining the area of the 
surface of a sphere from the circumference of a great circle. A being that 
area, and c the circumference: 
A = TT 
IT 2 W TT 
Taking account of the fact that the area of a hexagon having a diameter 
of unity is 0.86603, the formula for the number, N, is: 
I c 2 
N = 
0.86603 0.86603 0.86603 
C 2 = 0.367 c 2 . 
The coefficient in this formula is, then, the reciprocal of ir divided by 
the sine of 60°; and n is the circumference of a great circle in terms of 
the average diameter of the area occupied by a single cell. 
