Latitude and Temperature in Barometric Hypsometry. 151 



38°i, 42°*2 Fahr., which on the. total method indicate different 

 heights, whereas the gradual methods cannot admit any variation of 

 height without a variation of pressure. The rapid fall of the ther- 

 mometer from u to w causes the total method to give very much 

 smaller intervals than the gradual, but the nearly stationary tempe- 

 ratures of x, y, z turn the balance the other way. On the whole, 

 the total method gives 686 feet in excess, and 335 feet in defect of 

 the gradual method, remaining 351 feet in excess. The temperature 

 varied so abnormally in this ascent that little confidence can be re- 

 posed in either result after station h, when the total method is only 

 32 feet out of 941 1 or 9379 in advance of the gradual, which is still 

 a large amount. 



It may be objected to the gradual method that, by multiplying 

 stations, it multiplies errors of observation. But even when the sta- 

 tions are so unnecessarily multiplied as in Tables III. and IV. (in 

 which nearly every recorded case of a simultaneous observation of 

 barometer and thermometer has been admitted), the error is not likely 

 to approach that arising from the total method. We may, however, 

 calculate the ascent of Table III. as far as r, beyond which, as already 

 remarked, the variation of temperatures renders the results uncer- 

 tain, in six instead of sixteen stations, as follows. 



Abridged Gradual Method. 





Gradual Method. 



Difference of Level. 



Abridged 



abridged. 



Abridged. 



Table III. 



Abridged. 



Table III. 



less 

 Table III. 



a 



490 



490 



490 



490 







ad 



3655 



3655 



3165 



3165 







df 



5017 



5019 



1362 



1364 



r, 2 



fk 



9875 



9885 



4858 



4866 



- 8 



kn 



13633 



13640 



3758 



3755 



+ 3 



np 



17552 



17559 



3919 



3919 







pr 



20339 



20357 



2787 



2798 



-11 



The final result is 18 feet less than that obtained in Table III. 

 This difference may be easily accounted for. Up to /both results 

 substantially agree. Between /and k there was first a rise and then 

 a fall of temperature, which are overlooked in the abridged calcula- 

 tion, and it consequently loses 8 feet. In the interval^ r there was 

 a steady temperature during 1400 feet, which disappears in the 

 abridgement, and consequently it again loses 1 1 feet. It is evident, 

 therefore, that the sections in this abridgement have been badly 

 selected, and the importance of determining them rather by change 

 of temperature than by height ascended becomes apparent. A 

 better result is obtained by means of the seven sections ai 6327, 

 ij 7520, jk 9887, kn 13649, np 17568, pq 18963, qr 20366, 

 determined with reference to the change of temperature. The result, 

 r 20366, is only 9 feet more than that of the gradual method in 

 Table III., but is 104 feet less than that of the total method. 



If /3, /3', /3" be the barometric readings reduced to 32° F., and a, 



