1879.] 193 [Minot. 
- From the impregnated egg are born successive generations of cells; 
now the process of division necessitates the disappearance of the 
parent generation, so that two generations of cells cannot exist at 
once, except when they are of different lineage. If all the members 
of each cell generation were born after the same interval then growth 
would proceed by jumps; that it does not do so is due to the fact 
that some cells are formed later, others earlier than the rest of their 
generation, hence it comes that alongside of cells of the n® gener- 
ation there may exist others belonging to the n +1”, or to the 
n+a” generation. Thus it comes that we can say merely, that ata 
given moment the cells of the body belong to the n®” generation, 
upon the average. Upon this basis it becomes perfectly accurate to say 
that the phenomena of growth depend upon the succession of cell 
generations. Starting from this conception I think the following fac- 
tors may be established. 
1. The number of cells increase in geometrical ratio. Although 
there may exist in the body at the same time cells belonging to gen- 
erations which, counted in the order of their numerical sequence, are 
some previous, some subsequent, to the ninth generation, or that gener- 
ation to which the average of the cells belong, nevertheless there is 
no inaccuracy in saying that at a given time the number of cells de- 
pends upon the number of the generation. This unequal rate of 
division is very important in determining the course of embryo- 
logical development, being indeed as I have elsewhere shown (1. c.) 
the most marked characteristic distinguishing the ectoderm from the 
entoderm. To return: we may assume that the number of cells is 
doubled at every division, the least possible increase (to the slight 
inaccuracy of this assumption I shall recur) ; according to it, the gen- 
erations would run 1, (egg cell) 2, 4, 8, 16 andsoon. Ata given 
time or after n divisions there would be one cell, put =z, the basis 
of the progression, multiplied by 0, the ratio (in this case 6 = 2) 
raised to the n — 1” power: — 
n veneration of cells =z (6"~"). 
2. The rate of multiplication increases. ‘This is a corollary of the 
proposition that the multiplication of the cells is a geometrical pro- 
gression; since however growth is not indefinite, this increase must be 
counteracted by some means. The cessation of growth is doubtless 
partly to be accounted for by the death and loss of a portion of the 
cells, such as we know to occur in the epidermis and some other 
parts, but we have no reasons for supposing that this loss increases so 
ROCEEDINGS B.S. N. H.— VOL. XX. 13 OCTOBER, 1879. 
epee ———— 
RR ng 4 
