Before accepting these decennial averages (1860–69) as data indicative of the distribution of rain over the country, we have to offer a few prefatory remarks. The difference between the amount collected by any two raingauges depends on at least four separate and distinct conditions, three of which must be ascertained and corrected for before the fourth can be accurately determined.

The conditions are:-(1) length of series of observations; (2) correction for secular change; (3) height of gauges above ground.

(1) Even if there were no other evidence in existence than the accompany

ing diagram (fig. 1) of the fluctuations of rainfall, we feel that it would sufficiently prove the impossibility of determining accurately the rainfall at any place except by observations continued over a long series of years at that place, or by differentiation from some proximate long-continued series.

(2) It does not follow that simultaneous observations, even for ten years, giving for example a mean difference between two stations of five inches, prove that the rainfall at the one station is greater than the other by that amount, although if they are not very distant the one from the other it would probably be a safe assumption.

(3) Before mean results can be given with any pretensions to accuracy and finality, they must be corrected for the elevation of the rain-gauge above the ground.

The above remarks sufficiently show that the mere average of the fall of rain measured during ten or more years does not necessarily give the true mean rainfall at that place.

Let us take as an example the highest amount recorded in the Table (Seathwaite), which had during the ten years (1860-69) an average of 154 inches; many persons would say at once that that was therefore the mean rainfall at that station. It is, however, nothing like it. From Table II. and fig. 2 we see that the rainfall over England, generally, during those ten years was 1.5 per cent. above the average, upon which evidence we are bound to reduce the observed mean in that proportion, and then the average becomes 152 inches instead of 154. Even this, however, is not correct; for we pointed out in condition (2) that the same years, or groups of years, are not similarly wet in all parts of the country. Referring, therefore, to Table IV. we find that at the nearest station to Seathwaite, Kendal, the decade in question was 7 per cent. above the thirtyyear mean; hence, on the supposition that the Kendal values are applicable to this station, we have to reduce 154 inches by 7 per cent. instead of by 1.5 per cent., and hence the probable mean comes out 141.8 inches.

Now most fortunately we can test the accuracy of this calculation in three

ways.

(1) The mean fall at Seathwaite in the previous decade was 126.98; from the Kendal observations the fall in that decade was 10 per cent. less than the mean; therefore

26.98 = 141.09) we find the probable mean comes

(126

0.90

out 141.1 from this decade, and 141.8 from that of 1860-69. They thus agree within less than an inch, or one half per cent.

(2) The fall at Seathwaite has now been continuously observed for twenty-six years, viz. from 1845 to 1870 inclusive; the mean of the whole twenty-six years' observations is 140.03.

(3) This value, corrected according to the Table in our 1866 Report, becomes 141-44, agreeing exactly with that indicated by the decades 1850-59 and

1860-69.

This example proves three points :-(1) the great degree of accuracy which is attainable by proper methods; (2) the care requisite to secure it; (3) the serious errors inseparable from the use of mere arithmetical averages without reference to secular changes.

These observations, however, must of course be taken as general results, and not be construed as having any bearing on the relative rainfall even of proximate stations, the rainfall of which will vary considerably according to local circumstances.

Hence it will be seen that the probable average at Seathwaite is 141 inches