ON THE KAINFALL OF THE BRITISH ISLES. 115 



ing diagram (fig. 1) of the fluctuations of rainfall, we feel that it would suffi- 

 ciently 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 difterentiation 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 sufaciently 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 tliat 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 yeaz's 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, how- 

 ever, is not correct ; for we pointed out in condition (2) that the same 

 years, or groups of years, are not similarly wet in aU parts of the country. 

 Referring, therefore, to Table lY. we find that at the nearest station to 

 Seathwaite, Kendal, the decade in question was 7 per cent, above the thirty- 

 year 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 



(126-98 \ 



— ^—=141-09 \ we find the probable 



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 ourl866Eeport, 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 thepi-obable average at Seathwaite is 141 inches 



i2 



mean comes 



