Balls . — Temperature and Growth . 587 
We also know that ‘ x' is excreted with greater rapidity at high 
temperatures, so we will further assume that both these chemical reactions 
follow Van ’t Hoff’s law. 
Let us now apply this mass of assumptions to the modification of the 
theoretical growth-curve which is represented above the base line (upper 
curve ). 1 The practical curve is also shown above the base line (lower 
curve). The difference between these curves represents the antagonistic 
force exerted by the action of ' x' upon G\ this difference is drawn 
below the base line. 
Our object is to find what force, or combination of forces, will simulate 
this antagonistic curve. 
Take first the accumulation of 6 x* with rise of temperature. This will 
give us a curve below the base line, of less altitude than the theoretical 
growth-curve, but otherwise similar. Consequently, it can never neutralize 
the latter, but can only depress it, without even altering its form. 
The same applies to a curve which shall represent the action of 6 x* 
upon G. 
As yet we have only taken into account the rise in temperature, and 
have disregarded the fact that time is also increasing. Now, the production 
of ‘ x ’ from the protoplasm is obviously a slow reaction ; consequently, its 
rate of accumulation in the cell will be represented by a curve showing 
an arithmetical progression at constant temperature, and by the com- 
bination of this with the previous curve when the temperature is rising. 
It is possible that other time-curves may be involved, such as one 
representing the mass-reaction between { x* and G. 
The results of three such antagonistic curves acting on the theoretical 
growth-curve are, however, not unlike the results obtained in practice. 
Another curve is appended , 2 based on the same assumptions, in order 
to analyse the effects of a constant high temperature. The rates of 
acceleration have, of course, been deliberately adjusted. 
With regard to the manner in which these antagonistic forces might be 
determined : — 
It is clear that the first data will be given by the stopping-point 
depressions effected by solutions of known concentration of 1 x\ and the 
remainder by comparison of different rates of heating. Lastly, if ‘ x ’ can 
be isolated (and this should in any case be the next step in the work) we 
might be able to determine something as to the chemical nature of G. 
There are three apparent objections to this scheme of attack : — - 
It may not be possible to isolate ‘x’, which seems to be a somewhat 
unstable substance ; possibly a substitute might be found. The heating 
apparatus will have to be under much better control than it has been in 
my experiments. Lastly, we are confronted with a doubt as to whether 
1 Curve 6. 2 Curve 7. 
