HARKER : PRESIDENTIAL ADDRESS 
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a large number of factors. Some of these are taken into account, but 
others are left out, or are simplified in an arbitrary manner ; and this 
is done with reference, not to the relative importance of these various 
factors, but to the exigencies of mathematical treatment. Indeed it 
is no reproach to the mathematician or the physicist to say that he 
is not always a good judge of what is essential in the statement of a 
complicated geological problem. This is a necessary consequence 
of that division of labour in the field of science which we call special- 
isation. We may recognize it with the less scruple, inasmuch as the 
same kind of criticism is applicable, mutatis mutandis, to ourselves ; 
for there is no doubt that geological speculation is often vitiated by 
disregard of mathematical considerations, and those of no very 
recondite order. 
It is often said that figures can be made to prove anything ; and 
certain it is that a series of arithmetical operations does sometimes 
serve as introduction to very strange, conclusions. The fault, of 
course, is not in the tool, but in the hand that uses it. In the larger 
issues of geology especially, where the gulf to be bridged between 
data and conclusions is so often a wide one, ingenuity of reasoning 
ought surely to be accompanied by a due sense of responsibility in the 
handling of figures. Calculation, in such applications, is by no means 
so simple an art as it may appear. In wrestling with problems of the 
kind indicated, and, I must add, in reading some very fascinating 
speculations by geologists of high standing, I have often wished 
that some obliging mathematician would put forth a small manual of 
applied arithmetic for the guidance of workers in the descriptive 
sciences. There are absolutely necessary precautions to be observed 
when calculation is based upon data always partial and at best roughly 
approximate, and these precautions are too often neglected. To be 
safe, we must have some conception of the probable error attaching 
to our observations, and we must note how the initial errors may be 
multiplied in the process of calculation. Especially there is the 
cumulation of error which must ensue when results obtained in this 
fashion are used as links in a chain of deduction. Here it is quite 
inadequate to say that the chain is no stronger than its weakest link ; 
it is of necessity far weaker than its weakest link. 
Without entering into these matters, some of which, as I have 
suggested, call for expert aid, I will take for illustration a single point, 
the frequent abuse of the average. Say that we wish to determine 
the amount of mud annually carried down by the Nile. Since there 
