NOTE. 
THE LAWS OF PROBABILITY AND THEIR MEANING.— The point 
has more than once been raised, in conversation and in correspondence, that the con¬ 
stancy of form shown by the frequency distributions of sizes of genera—the charts 
showing numbers of genera of i, 2, 3, . . . species—has no bearing on vital pheno¬ 
mena, but is in some way or other a necessary outcome of ‘ the laws of probability 
But the laws or rules of probability are only rules for the combination of chances 
and can give us nothing by themselves, any more than the rules of multiplication and 
division. If the chance of a given event occurring is p 1 and the chance of an 
independent event occurring is / 2 , the chance of both events occurring is p-rf>% : if the 
two events are not independent but alternative, the chance of either the first or 
the second occurring is p x + /> 2 —such rules alone can only lead us to a form of fre¬ 
quency distribution by applying them to given assumptions concerning the facts. A 
few illustrations may make the matter clearer. 
If we have n dice, and we assume (a) that the chance of throwing sixes is the 
same for every die, (b) that the same dice are used throughout the experiment, so that 
the chance of throwing sixes is the same at every throw, (c) that the result of the 
throw of every die is independent of that of every other, then the laws or rules 
of probability show that the frequencies of o, 1, 2, 3, . . . sixes in N throws of the 
n dice are given by the successive terms of N(q-\-p) n . If we find the results of a long 
series of throws differ significantly from this theoretical expression, we may conclude 
that our assumptions are in error: the dice are not all the same, or two different sets 
of dice with different values of p have been used, or it may be that we have merely 
taken an incorrect value of/>. 
Again, if we assume ( a ) that an error of observation is compounded of 
a number of elementary errors, (b) that the number of these elementary errors 
is large, ( c) that positive and negative elementary errors are equally frequent, (d) that 
elementary errors are independent, the form of frequency distribution deduced is the 
normal curve of errors. If we make different assumptions as to the way in which an 
error of observation is built up, we will—or may—arrive at a different form of distribu¬ 
tion, and conversely, if the curve observed is not the normal curve of errors, we are 
justified in concluding that our assumptions as to the genesis of an error of observation 
are wrong. 
The following case, taken from some recent work, 1 is particularly illuminating as 
regards the light which the form of the frequency distribution may throw on the facts. 
Data are given as to the number of girls in a munition works who have met with o, 
1, 2, 3, . . . accidents (trivial accidents, sufficient to send the girl to the Welfare Room) 
during a certain period. The actual form of frequency distribution is not unlike that 
1 Greenwood and Yule, Journ. Roy. Stat. Soc., March, 1920. 
[Annals of Botany, Vol. XXXVII. No. CXLVII. July, 1923.] 
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