374; On Sines and Cosines of Multiples of a variable angle, 



latitudes 52° and 53° was 4 inches; and south of 53°, omitting 

 Stonyhurst, was 4*3 inches. 



The smallness of the fall at Durham is remarkable ; between 

 January 31 and March 28 only 0*14 inch fell. 



The numbers in column 14 to 18 show the mean values of 

 the hygrometrical results at every station ; from which we find 

 that— 



The mean weight of vapour in a cubic foot of air for all 

 places (excepting Cornwall and Devonshire) in the quarter 

 ending March 31, 1849, was 2-8 grains. 



The mean additional weight required to saturate a cubic 

 foot of air in the quarter ending March 31,1 849, was 0*4 grain. 



The mean degree of humidity (complete saturation = 1) in 

 the quarter ending March 31, 1849, was 0'860. 



The mean amount of vapour mixed with the air would have 

 produced water, if all had been precipitated at one time on 

 the surface of the earth, to the depth of 3*3 inches. 



The mean weight of a cubic foot of air at the mean height 

 of 160 feet under the mean pressure, temperature and humi- 

 dity, was 547 grains. 



And these values for Cornwall and Devonshire were 3*2 

 grains; 0'5 grain ; 0*878 ; 3*8 inches ; 547 grains, at the mean 

 height of 120 feet. 



Errata. — In the formula for calculating the pressure of dry air, in the 

 last Number of the Magazine,/or + read — ; and/or 83 inches read 820 feet. 



For the formula for calculating the weight of a cubic foot of air, substi- 

 tute the following : 



541 trains /^^^^ght of place in feet above the level of the sea ,q\ 



^ \ 820 feet /* 



LIV. On the Determination of the Coefficients in any series of 

 Sines and CosiJies of Multiples of a variable angle from par- 

 ticular values of that series. By the Rcv.Brice Bronwin*. 



MY last paper in this Journal having been terminated 

 rather in haste, I did not observe that the step con- 

 tained in (16.) might be repeated. Thus 



/ 1 N ^'''' , ^''^ / r.\ ^T 3/7r . 



COS in— 1) — = 4- cos — , cos (n — S)— — + cos , &c. : 



' n ~ n ^ ' n — n 



•I ,s.i'n _ . iit i% _ , Siir „ 



sm (w— 1)— = + sm— , sm {71— S)— = + sm — , &c. 

 n n ^ ' n n 



Therefore if we make 



Wj + Un = w„ 2^2 ± "«._ = '^a* &c. ; 

 2 2 ' 



V{^Vn — a?!, Vcp^Vn = X^t &c. ; 



2 2 ^ 



* ConuQunicated by the Author. 



