35 



means of an excellent Aneroid barometer (previously compared with 

 a standard), and a standard barometer read simultaneously, or nearly 

 so, at the sea-level; and he gives the heights of the several stations 

 as thus estimated. 



The most important fact connected with these observations is 

 stated to be the discovery of a mountain station which promises to 

 yield nearly one- third more rain than the hamlet of Seath waits in 

 Borrowdale, hitherto, with good reason, considered to be the wettest 

 spot in the three kingdoms. This, the new station, "the Stye," on 

 Sprinkling Fell, is about a mile and a half distant from Seathwaite, 

 in a south-westerly direction, and 5S0 feet above it, at the extreme 

 southern termination of the valley. The actual quantity of water 

 measured in eleven months of 1850 was ]74-'33 inches; but as the 

 receiver was found running over on four different occasions, the loss 

 is calculated at 5 or 6 inches at least ; and 5'67 is added, making 

 the Cjuantity in eleven months 180*00 inches. Adding to this 9'49 

 inches, the depth for January computed from that for January at 

 Seathwaite, it appears that the whole depth of rain fallen at " the 

 Stye" in 1850 was 1 89*49 inches. The author further remarks, 

 that the wettest year since the commencement of the observations 

 was 184^8, when 160-89 inches fell at Seathwaite; and computing 

 the fall at the new station for that year, we have 211*62 inches for 

 the depth of rain at the Stye" in 1£48. 



2. "On the Rolling Motion of a Cylinder." Bv the Rev. H. 

 Moseley, M.A., F.R.S. &c. Received March 6, 1851. 



The time occupied by a heterogeneous cylinder in oscillating 

 upon a horizontal plane through a small arc has been investigated 

 by Euler; and he has determined the pressure of the cylinder upon 

 the plane when oscillating through an^ arc, applying the formula he 

 has arrived at to find the pressure upon the plane at the highest and 

 lowest points of oscillation. It is the object of the present paper to 

 endeavour to extend this investigation to the contimwus rolling of 

 the cylinder, under which more general form its oscillation is ob- 

 viously included as a particular case. In the first part of the paper, 

 the time of rolling through any angle, and therefore of completing 

 any given number of revolutions, is investigated ; and in the second, 

 the conditions of the pressure upon the plane at any period of a 

 revolution. The complete determination of the time of rolling in- 

 volves the integration of a function of the form [*( ^ — ^ 1 "t/d, 



J — COS07 



which is shown to be reducible to an elliptic function of the third 

 order, capable of being expressed (by a theorem of Legendre) in 

 terms of elliptic funetions of the first and second orders, and there- 

 fore of having its numerical value calculated from the tables of Le- 

 gendre. The theorem resulting from this reduction, when applied 

 to the particular case of the oscillation of the cylinder, gives an ex- 

 pression for the time of oscillation, through any arc, of a pendulum 

 having a cylindrical axis. If the diameter of this axis be assumed 

 infinitely small, the case becomes that of a pendulum oscillatinj? on 



3* 



