816 



cases of divergency, above referred to, the corresponding convergent 

 solutions are in series infinite in both the ascending and descending 

 directions. 



The author observes in conclusion, that the inverse calculus of 

 the process here developed may be employed for the discovery of 

 the generating functions of series whose laws of relation are given. 



The Society then adjourned over the Easter holidays to meet 

 again on the 19th of April. 



April 19, 1849. 



The EARL OF ROSSE, President, in the Chair. 



A paper was read, entitled " On the Meteorology of the Lake 

 District of Cumberland and Westmoreland." By John Fletcher 

 Miller, Esq. Communicated by Lt.-Colonel Sabine, R.A., For. Sec. 

 R.S., &c. 



This paper contains the results of meteorological observations 

 made during 1848, similar to those made in the same district in 

 preceding years, which were last year communicated to the Society. 

 On these results, the author remarks that the fall of rain in the lake 

 district, during the year 1848, greatly exceeds the amount in any 

 other year since the register was commenced in 1844; and that 

 there is a similar excess with reference to the number of wet da3^s. 

 The total depth of rain, in 1 848, at Seathwaite, the wettest station, 

 was 160'89 inches ; and of this quantity, 114*32 inches fell in the 

 six months, February, July, August, October, November and De- 

 cember. In February there fell the unprecedented quantity 30*55 

 inches. 



The mountains flanking the lake-district valleys increase in alti- 

 tude with great regularity towards the head or eastern extremity of 

 the vale, and it appears that it is there that the greatest depth of 

 rain is invariably found. The amount increases rapidly as the sta- 

 tions recede from the sea, and towards the head of the valley the 

 incremental ratio is exceedingly great. At Loweswater, Buttermere 

 and Gatesgarth, about two miles apart in the same line of valley, 

 the depths of rain were respectively 76 inches, 98 inches and 133*5 

 inches. 



From the observations of the thermometer, the author concludes 

 that the climate in the mountain valleys in this district is milder and 

 more equable, not only than in the open country in their immediate 

 vicinity, but also than in that considerably to the south. This he 

 attributes to the lakes giving out during the winter the heat absorbed 

 by them in the summer, and to the radiation from the rocky moun- 

 tain breasts in the valleys, but principally to the heat evolved in a 

 sensible form by the condensation of enormous volumes of vapour. 



Last summer a pair of Rutherford's self-registering thermometers 



