5 
viction of man’s past existence on earth for several millions 
of years. 
5. Here, in the fundamental maxim assumed, there is a serious 
ambiguity. What is meant by “ causes now in operation ” ? 
Does it mean simply the central forces, the attractions and 
repulsions, varying by certain laws of distance, of all the 
bodies or their component atoms that now exist ? If so, the 
doctrine becomes only a sort of truism. The sudden bursting 
of a reservoir, the explosion of a magazine, the firing of a 
broadside, or a volcanic eruption, are as much from causes 
now in operation, as the quiet state, with no sudden or 
sensible change, which may have gone before, and lasted 
months or years. But if we mean by causes now in operation, 
all acting forces, with merely the same conditions as now 
exist, which vary with every hour, day, and year of their 
own action, the maxim is unphilosophical and untrue. Wo 
should explain the changes of the earth by causes acting under 
the conditions of the time when they occurred, and not under 
new conditions which may have come into being, through the 
action of those very causes, after many thousands or myriads of 
years. 
6. Averages give a fair approximation, or are wholly 
fallacious, according to the nature of the facts to which they 
are applied. They are safe, chiefly when they are taken 
between two observed limits, since a small part of any curve 
does not vary widely from the line which joins its extreme 
poiuts. In many cases the error may not be great for parts 
which lie beyond this limit, on one side at least. But let a 
chord of a hyperbola, near the vertex, be prolonged towards 
the vertex a hundred times beyond its own length, the distance 
from the answering point of the curve will be very great, and 
the two will be tending in wholly opposite directions. 
Now most of the cases to which the law of averages has 
been applied by uniformitarian geologists are of this very kind. 
Each step of past change tends to lessen the motive power 
on which the future changes depend. Thus every river trans- 
ports a certain amount of soil in suspension from the high 
ground near its sources or from the bed through which it travels 
to the sea. But every year the high ground is wasted, the 
mouth is silted up, and the soil probably hardens and becomes 
less easy to remove. The quantity annually carried down will 
thus diminish for three different reasons. It will also come 
to be spread over a wider area. Hence the present depth of 
the annual deposit is no pi’oper test by which to give the 
average for many thousand years. 
7. Let us take one case often referred to, — the Delta of the 
