
British Rainfall 1896 page 18
Tarn (1472ft.), four gauges  A, B, C, D  on The Stye
(1077ft.), and one at Seathwaite (422ft.)
So much for the history. Before giving the results we must
ask attention to Tables I. and II., and to the accompanying
maps. Table I. contains the early observations, 18471857;
at its foot will be seen two lines of means, marked
respectively "Arithmetical" and "Reduced." Reduced, in this
case, does not mean made less. Very often the "Reduced" is
more than the "Arithmetical," and as this may puzzle some
readers, it had better be explained. Everybody knows that an
"Arithmetical" mean is the sum of the entries divided by
their number; the total for 5 years at Sca Fell (Table I.),
372.08 divided by 5 gives 74.42 in. That is clear enough.
But the years 184953 might have been wet ones, like
185052, and if so that "Arithmetical" average, although
correct as a matter of calculation, would not correctly
represent the average rainfall  and that is why "Reduction"
comes in. In British Rainfall, 1895, we gave the
rainfall in every one of the 50 years at Seathwaite, and we
gave the ratio which the fall in each individual year bore
to the average of the 50 years. A wet year  for instance,
1872  had 182.05 in., whereas the average for 50 years was
137.31 in., so that in 1872 the rainfall was 44.74 in. above
the average, or an excess of about 1/3, therefore the ratio
of that year was given as 133, and the ratios were similarly
given for every year. The "Reduction," then, is merely
correcting of the "Arithmetical" mean for the effect of the
group of years being wet or dry. As it happens, in the case
we have quoted, the "Arithmetical" and the "Reduced" mean
are nearly identical; we had better explain why. The last
column in Table I. gives the Seathwaite ratios (from p.25 of
Brit. Rain., 1895), and it will be found that for the
years above mentioned (184953) the average ratio was 99,
therefore the "Arithmetical" mean has to be increased by
only one per cent., and so the "Reduced" becomes 75 inches.
This process has been adopted, because it is without doubt
the right one; but, as already implied, there is probably no
area of the same size in the British Isles in which the
application of this method is, owing to the deflection of
the air currents by the mountains, equally unsatisfactory.
The construction of Table II. is precisely similar to that
of No.1.
It is necessary to say a few words respecting the maps,
also, before we proceed to consider the results. The area
is, as already stated,
