On the Expression for the roots of a complete Cubic. 19S 



Hereford, Newcastle and Saffron Walden, and the average 

 number at these places was 41. The places at which the 

 largest falls have taken place were Guernsey, Truro, Wake- 

 field, Whitehaven, Falmouth and Helston. The falls were 

 smallest in amount at Saffron Walden, Stone, Hartwell and 

 Liverpool. The average fall in the counties of Cornwall 

 and Devonshire was \2°'S ; and at all other places except 

 Southampton, Beckington, Hereford, Stonyhurst and York, 

 was 8°-5. 



The numbers in column 13 to 17 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 December 31, IMS, was 3*2 grains. 



The mean additional weight required to saturate a cubic 

 foot of air in the quarter ending December 31, ISIS, was 0*49 

 grain. 



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

 the quarter ending December 31, 184-8, was 0'884. 



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*7 inches. 



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

 sea, under the mean pressure, temperature and humidity, at 

 the mean height of 160 feet, was 541 grains. 



And these values for Cornwall and Devonshire were 3*5 

 grains; 0*6 grain ; 0'839 ; 4*1 inches, and 540 grains respect- 

 ively. 



XXIV. On the Expression for the remaining roots of a cotn- 

 plete Cuhicy Xfihen one root is found. By J. R. Young, Pro- 

 fessor of Mathematics, Belfast^. 



THE following expression for two roots of an incomplete 

 cubic equation, in terms of the third root, is given at 

 page 216 of the Analyse Algebrique of Gamier, namely, 



where q represents the coefficient of x, the term in x^ being 

 absent, and where x^ is a root already found. 



This formula I obtained independently, and gave it at 

 page 322 of the second edition of my book on Equations. 1 



* Communicated by the Author, 



Phil, Mag, S. 3. Vol. 34. No, 228. March 1849. O 



