282 Mr. Ellis on the Corrections for Latitude [May 18, 



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

 difference may be easily accounted for. Up toy both results substantially 

 agree. Between / and k there was first a rise and then a fall of tempera- 

 ture, which are overlooked in the abridged calculation, and it consequently 

 loses 8 feet. In the interval p 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 abridge- 

 ment have been badly selected, and the importance of determining them 

 rather by change of temperature than by height ascended becomes appa- 

 rent. A better result is obtained by means of the seven sections a i 6327, 

 ij7520,jk 9887, fen 13649, np 17568, pq 18963, qr 20366, deter- 

 mined 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, ft', ft" be the barometric readings reduced to 32 F., and a, a', a" 

 the corresponding temperatures of the air for any three stations, then the 

 formula (a) shows that, rejecting the small corrections v v V lf the height, 

 as determined by the total method, will be the same as that determined 

 by the gradual method when 



(a + a").(lo g /3-log/3") = 



(a + a') . (bg/3-log /3') + (' + ") . (log ft'-log ft"), 



that is, when a a' _log/3 log/3' 



a'-a" log ft 1 -log ft"' 



When the difference in barometric pressure is not great, and hence ft f/3' 

 is nearly =ft'+ft", by applying the reductions in 'Proceedings,' vol. xii. 

 p. 516, the above condition becomes very nearly, that the decrement of 

 temperature should vary as the decrement of pressure, and this is the case 

 for the normal decrements. Thus in Table III. the intervals a i,j k, lm,np 

 give for the quotients of the decrements of temperature divided by the 

 decrements of pressure 4'635, 4-07, 3*26, 3'92 respectively, and the dif- 

 ferences of the lengths of these intervals, as determined by the total and 

 gradual methods, are only 2, 8, 13, 13 respectively. But for the intervals 

 ij,mn these quotients are 3'55, 1*27, and the differences 59, 37. 

 Similarly in Table IV., for the intervals a d, ae, ah the quotients are 4 '78, 

 3-91, 3-97, and the differences 9, 31, 32. These results confirm the 

 above conclusion, and also tend to show that the normal quotient is 4, and 

 to explain why the gradual method is the most generally trustworthy. 



Since, then, it is advisable to calculate bv such short sections, the prac- 

 tical rules which I gave in a former paper (' Proceedings,' March 26, 1863, 

 vol. xii. pp. 513, 514) may be condensed into one, which will enable any 

 traveller to calculate heights without the assistance of any tables whatever. 

 I conclude this paper, therefore, by annexing it in its improved form, 

 together with a rule calculated on the same principles for foreign data, and 

 an example of each to show the method of working. 



