Minot. 194 [March 5, 
as to continually counterbalance the multiplication of the cells. Let 
a= number of cells lost, then the n” generation = 2b” — az. 
8. The intervals between the births of two successive generations 
continually increases, or, in other words the frequency of the divisions 
continually diminishes. From our point of view this change is the 
most important alteration produced by senescence; that it really oc- 
curs is not only a deduction, but is also shown by actual observation; 
for no one can question that the division of the cells during segmen- 
tation of the yolk proceeds at shorter intervals than during adult 
life; thus in an egg say 8 or 10, perhaps more, generations of cells 
may be born in the course of a single day, all the cells dividing; but 
we cannot for an instant imagine that all the cells of the human 
adult, for example, divide upon an average even once a day, — more 
probably a new generation of cells does not appear in an adult 
animal as often even as once a year. Possibly the rate at which 
segmentation occurs may offer an opportunity of discovering the 
rate at which the intervals between the divisions increases, but at 
present at least it is impossible to determine the frequency of the 
divisions either in the adult or the embryo; all that we know is that 
the frequency diminishes. 
We have next to consider growth as a function of the time; we 
will construct a formula in which the abscissae x shall equal the time 
and z the ordinates, the number of cells. Let 2=the interval be- 
tween impregnation and the first division and let it be the unit of 
time. Let c” be the coefficient of senescence, which determines 
the increase in the intervals between the generations of cells. I have 
given it the exponent ”" merely to suggest to the eye by the 
formula that the senescence rises with each generation. c is not 
necessarily a constant even for a given individual, but may be the 
product of variable factors —these factors, which determine the 
course of the development of senescence, are unknown. The n* 
generation then will exist at the following time after impregnation : - 
n 
facial eB cla ceie  ee 
The time of the existence and the number of cells of the n® gen- 
eration are given by the following formula: — 
hy ae ae 
