1858.] On Hypsometrical Measurements. 851 



6. The same value of k as found from equation (12) may also be 

 derived, in a different form, from equation (10), by multiplying 

 log 30 — log B by L, thus :— 



k = 521.684 (212 — T) + 0.8655 (212 — T) 8 



+ 0.0019 (212 — T) 3 (14) 



or, as a good approximation in two terms, — 



h = 520.476 (212 — T) + 0.967 (212 — T) 2 . . (15) 



7. For the height in metres in terms of T on the Centigrade scale, 

 we may, instead of equation (9), use, — 



£ m =286.2(100— T) + .8546(100— T) 8 + 0.00341 (100— T) 3 , 



(16)* 

 or approximately, 7i m = 285.54 (100 — T) + 0.955 (100 — T) 8 . 



8. The equations now deduced for expressing the height in terms 

 of the boiling-point of water require to be corrected in the same 

 manner for the temperature of the air, &c. as those derived from 

 barometrical observations. Hence substituting equation (11) in the 

 formula already given for the barometer, and omitting the terms 

 depending upon the hy groin etrical state of the atmosphere, and the 

 diminution of gravity with the height, we have for the correct height — ■ 



5.10827 (T — T') 



H' — H=: 



1 



167.319 + T + T' + D D' 



600 



398.37 (1 + at) 1 



X L. * (17) 



397.37 — at (g) 



or, adopting the notation already employed — 



* Professor Forbes has arrived at almost exactly the same results. For 

 equation (15), he gives — 



517 (212° — T) -f (212° — T) 2 j 

 and for equation (16) — 



h m = 284 (100 — T) + (100 — T)* j 

 the equation — 



£=519.66 (212° — T)-|- (212° — T) 2 

 will give almost exactly the same results as equation (15). 



2 z 2 



