1863.] 511 



of phosphorus in the residue after diffusion ; for the reduction of 

 corrosive sublimate to calomel cannot he otherwise explained. More- 

 over, the presence of free chlorine in the diffused gases was shown 

 by the reaction with iodide of potassium and starch. 



We are continuing this research, and hope to lay before the 

 Society the results of an examination of the most prominent cases 

 of so-called abnormal vapour-density. 



IV. " On a Simple Formula and Practical Rule for calculating 

 Heights barometrically without Logarithms." By ALEX- 

 ANDER J. ELLIS, B.A., F.C.P.S. Communicated by Dr. 

 NEIL ARNOTT, F.R.S. Received February 23, 1863. 



The following formula and table for calculating heights barome- 

 trically without logarithms will be found to give the same results 

 as Laplace's formula up to 30,000 feet, and the table can be readily 

 extended if required. Let 



L degrees be the mean latitude of the two stations, 



/ =2-6257 cos2L, G= I +0-0026257 cos 2L, 



R= 20888629, the number of feet in the earth's radius. 



At the lower station. 



H feet, its height above the sea, H"=H 2 -r-R, 

 B units of any kind, height of barometer, uncorrected, 

 B' , corrected, 



A deg. Fahr., A' deg. Cent., A" deg. Reaum., temperature of air, 

 M,, , M' , M" , of mercury. 



At the upper station. 



hy k n , b y b 1 , 0, a'y a", m, m\ m" in the same sense. 

 Then 



+ -001.(A-H)H-A"-H", ...... (a) 



where M w=0, when B, 6=B', b' t and 



2-35 (M-m)=4-23 . (M'-i') = 5'2 



900 500 400 



The numbers c, I, h" f H" are to be taken from the table on the 

 next page, as will appear by the following examples. 



2o2 



