34 Mr. J. Burgess on the Measurement of Altitudes 



dd' 

 but the term '00lQ9dd f , or ^r^ nearly, may be omitted, except 



when both stations are at great elevations. We may also use the 

 constants 308837 ft. and 168° from equation (12) instead of 

 309971 ft. and 170°-174. 



7. It only remains to introduce the corrections for the tempe- 

 rature of the air, &c. Putting t and t' for the temperature of 

 the air at the lower and upper stations, and t=J(£-K'), also 

 a= the coefficient of the dilatation of the air for 1° F. as deter- 

 mined by Regnault, we have, by substitution in BessePs formula 

 for barometrical measurements, the corrected difference of level 



H' '- H-W h) X 3 98'37[1 +<t-32°)] 1 



g being the ratio of the force of gravity in the latitude X of the 

 stations to that in latitude 45°. Hence from equations (12) 

 and. (13) 



„, „ 289358(T-T') n , „ nrvm , , 1 1 



H'— H=- * 5t, x (1 +0'00205t) x = — T^ni — oZ 



168+T+T'+^ l-0026cos2X 



and 



log (H'- H) = 5-461436 + log (T-T') + log (1 + 0«00205t) 



-log(l68 + T + T' + ~)-log(l-'0026cos2\), 



in which the term ^-r need rarely be employed, and the correc- 

 tion for latitude never, except for great altitudes in low lati- 

 tudes. Now for the sake of brevity let us write 



i qhqqq*a 212-T , . 398-37[1+5(t-32 )] t 

 £=308837 ft. x 3^^, and A= g^.^ x L; 



then we have 



H , H __ fA , » 398-37[l + fl (T-32°)] , ( » 



and 



log (H-H') = log (log B - log B') + log A nearly, . (16) 



of which the termslog A and the multiplier qq 7 .q* } — qo^ 



may be tabulated in terms of t, and h and log B in terms of T, 

 as in the Tables appended. 



8. Lastly, when the observations are taken at the upper sta- 

 tion only, and consequently t' is known, and it is necessary to 

 estimate r, the mean temperature between the sea-level and the 

 station, if we suppose the diminution of temperature, in terms of 



