2go Blackman. — Optima and Limiting Factors. 
another tenfold, I interpret as probably a case in which the supply of carbon 
dioxide was the limiting factor : its limit of arrival by osmosis being once 
reached no further increase of assimilation was possible. 
The experiments of Kreusler 1 on the effect of temperature on the 
assimilation of a shoot of Rubas gave, as higher and higher temperatures 
were used, at first a steady rise of assimilation up to 15 0 C. } but after this 
the assimilation practically never rose further. This state of things has 
been shown by Miss Matthaei 2 to be a case in which inadequate illumina- 
tion limited the assimilation to that obtained at 15 0 C., and so further heating 
produced no increase. There are also contemporary examples of such 
misinterpretation which will be discussed elsewhere. 
When the rate of a function exhibits, in experiment, a sudden transition 
from rapid increase to a stationary value, it becomes at once probable that a 
‘ limiting factor ’ has come into play. The form of curve obtained is then 
like the curve ABC in diagram II, where the limiting factor has soon come 
into play. If the factor in question only becomes 4 limiting ’ when the 
function is near its high values, then the curve A BF G represents the result 
attained. If the factor only 4 limits 5 when the function is close to its 
highest values we may get a curve recalling the conventional optimum 
curve with the top cut off. 
The relation of assimilation to intensity of illumination is shortly to be 
treated elsewhere, but something may be said here with advantage about the 
relation of assimilation to the supply of carbon dioxide. The willingness to 
believe in an 4 optimum amount of C 0 2 for assimilation ’ is almost universal, 
and the belief is quite general that Godlewski 3 showed it to be about eight 
per cent. In my opinion there is no justification whatever for speaking 
of an optimum at all in this connexion. 
Suppose a leaf in a glass chamber to have enough light falling upon it 
to give energy equal to decomposing 5 c.c. of carbon dioxide per hour. 
Then, as one gradually increases the carbon dioxide in the air current 
through the chamber from the amount (or pressure) that causes 1 c.c. to 
diffuse into the leaf through its stomata up to five times that pressure, 
so steadily the assimilation will increase from 1 c.c. to fivefold. After 
that, further increase of the carbon dioxide will produce no augmentation 
of the assimilation, but will give continually an effect of 5 c.c. of carbon 
dioxide assimilated — the light being now the limiting factor. The curve 
obtained will be of the form ABC, Ultimately, if the supply of carbon 
dioxide in the air current be increased up to 30, 50, or 70 per cent., the 
carbon dioxide will have a general depressing effect on the whole vitality, 
and before suspension of all function a diminution of assimilation un- 
doubtedly occurs ; this is, however, quite a separate process. Now, secondly, 
1 1 . c. ; see also Pfeffer, Physiology, vol. i, sect. 58. 3 1 . c., p. 69. 
3 Arb. bot. Inst, zu Wurzburg, Bd. 1, 1873. 
