Csmhttjlion of PhafphQi'us.—Correfpmuhnce. 283 



Xn. When the atmofpheric air or oxygene gas enters the receiver by a cock from above, 

 a little before or the inftant after the light of the combuftion has difappcarei!, and when 

 care is taken to admit no more air or gas than fiiall be fufficient to raife the gauge one or 

 two lines, the phofphorus ufually takes fire a fecond time. In this manner the phenomenon 

 maybe made to appear repeatedly; and accordingly as a greater or lefs quantity of air is 

 fuffered to enter, the circumllances are found to vary in a very remarkable manner. This 

 communication would be too long if I were to attempt to defcribe the variety of appear- 

 ances which I have obferved in thefe experiments. They are not entirely the fame, in cir- 

 cumftances which appear perfe£lly fimilar. I have obferved that pieces of phofphorus 

 obtained by different operations have exhibited different phenomena. The fiery globules 

 emitted by the burning phofphorus are in fome cafes larger and more numerous than ia 

 others. 



MATHEMATICAL and PHILOSOPHICAL CORRESPONDENCE. 



Question V. Atifwered iy the Proposer. 



J_iET X denote the weight of the fait, and s its fpecific gravity ; iu the weight of the 

 bottle of diftilled water, and W that of the folutlon ; the magnitude, or content, of the 

 bottle, and the fpecific gravity of the water, being each confidered as i. 



Then, fince the magnitudes of bodies of the fame kind are as their weights, w : W— *• : : 

 W— .V 



1 : = magnitude of the aqueous part of the folution : and, becaufe the magnitudes 



of bodies of different kinds are as their weights divided by their fpecific gravities, — : — 



: : I : = magnitude of the falc. Whence ■ H = I ; from which equation 



.V is found = -^^ (W — w) =: weight of the fait. And fince .r = 2.8, W = 2810 gr. 

 and TO = 2506 gr. by the queftion, we (hall have x = -^-^ — (2810— 2506) = -^x 304. 

 — 47 2 J g*"' ^^^ quantity of fait required. 



And if the cafe be reverfed, by fuppofing x to be known, the value of / will be readily 

 found from the general formula ; by which means we fliall be enabled to make a proper 

 allowance for the difference in the fpecific gravity of the fait, arifing from chemical con- 

 dcnfation, as was done in the propofing of the queftion, where it is taken as 2.8 ijiftead 

 of 2f, which it is fuppofcd to be in its feparate (late. 



QunsTloN VI. Anfiuercd by C. TV. 



LET m be put for the mean temperature at the equator, « for the difference between 

 this temperature and that of the north pole, and / for the latitude of any place, radius 

 being I ; tlicn the mean temperature of that latitude will be m — n X fine V. For the heat 



P o 2 produced 



