526 Smith.— The Temperahtr e-coefficient of 
Now Expts. 13 and 14 of Brown and Heise’s Table V (Matthaei’s 
Fig. 2) differ by 0-00088. It is therefore not true to say that o-ooioo, the 
difference between the experiments at 9*2° and 11*4° with four units of light, 
is within the previous extreme limits of error. It is outside those limits. 
Moreover, that error in itself was an extreme error and one which by the 
laws of chance would occur extremely rarely. This is made perfectly clear 
when one sets out precisely the probable error of the long series of fourteen 
experiments with light of unit intensity, ranging from —6° to +33-1°. 
The set of fourteen experiments gives a mean value of 0-0029 and 
a standard deviation of 0*000235, so that the probable error of a single 
experiment works out at +0*000158. 
That the small deviations throughout the series are devoid of any 
significance is shown by considering them in three groups: ( a ) the five 
coldest observations, (b) the four medium observations, and (c) the five 
hottest observations. The probable error between the mean of a group of 
four and the mean of a group of five is, according to the formula kindly 
given me by Mr. G. Udny Yule, +0-000158 x + £ = +o-ooon. As the 
actual means of the three groups respectively are (a) 0-00286, (b) 0-00292, 
(c) 0-00288, the differences between these means are found to be actually 
only about half the probable error. 
Brown and Heise go against all the probabilities in saying that such 
a large difference between two values as o*ooio is not significant and is to 
be attributed to experimental error, for the unlikely deviation of +0-00044 
only occurred once. 
Having claimed q-ooioo, i. e. +0-00050, as within the limits of experi- 
mental error, Brown and Heise immediately go on to claim a much smaller 
difference, i. e. + 0-00020 (the difference between the results for light 
intensities of four and six units at 11*4°), as a real light effect, not due to 
experimental error, indicating that further increase of light would increase 
still further the assimilation. This is surely merely juggling with figures in 
the interests of a theory. As a matter of fact, Matthaei is interpreting the 
results according to the probabilities, considering the general form of all 
her previous curves and considering how little wider this variation is than 
the probable error of her previous experiments, in claiming that these two 
results are the same within the limits of experimental error. 
Brown and Heise next turn their attention to the results embodied in 
Matthaei’s Fig. 4. These are the results of eleven experiments with eight units 
of light at temperatures of n° (one expt.), 25*4° (2 expts.), 32-1° (2 expts.), 
38-3° (2 expts.), 40-9° (2 expts.), and 42-9° (2 expts.). With the exception 
of the two highest temperatures, over 40°, these results, like those of previous 
sets with less light, present an initial rising curve, followed by a flat top. 
The difference between the results at n° and 25-4° here is too great to be 
attributed by Brown and Heise to experimental error, y<st, as it is necessary 
