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



Mr. Glaisher's balloon ascents offer a very convenient series of examples 

 on account of the comparative closeness of his observations. I have there- 

 fore calculated two, Tables III. and IV., p. 286, which are important from 

 their height or remarkable changes of temperature, first, by determining 

 the height of each station from the lowest (which I call the total method) ; 

 and secondly, by calculating the height of each station from the height of 

 the next lower station (which I call the gradual method). I have added 

 the differences of level between the stations as determined from both 

 methods and the differences between them, which are important for 

 discovering how the discrepancies between the two results are produced by 

 temperature. Each station is lettered. Two letters against a number, as 

 ah 5720, show that the height of the station A above the sea is found as 

 5720 feet, when station a is taken as the lower station with the height 

 assigned to it in the same column. The distance a A is termed an interval. 

 A careful examination of these results will show that the gradual method 

 is probably the most trustworthy. 



In Table III. up to station i, both results substantially agree, but in the 

 interval ij there is a sudden increase of temperature, which is quite ab- 

 normal*. The total method, from omitting all considerations of the pre- 

 ceding lower temperatures, makes the height of the interval ij exceed its 

 value as determined by the gradual method by 59 feet, an enormous amount 

 in a total height of 7518 or 7579 feet. The temperature again decreasing 

 from.;' to k, the difference is not so great, but the total method is 8 feet in 

 defect for this interval. Again, for m n there is only a slight fall of tem- 

 perature, and consequently the total method, ignoring the low absolute 

 temperature of the interval, makes the difference of level greater than the 

 gradual method by 27 feet. In pq there is absolutely a rise of tempera- 

 ture, and for the reason last stated, the total method makes the interval 

 73 feet greater than the gradual. The interval q r is a great contrast to 

 this. The temperature falls very rapidly, 7'l for a barometric depression 

 of '79 inch, which is nearly double the normal amount as previously de- 

 termined for the 14th inch of depression. Hence the total method, by 

 distributing the cold over the warm parts, makes the interval q r 73 feet 

 less than the gradual method. Again, r s shows an excess of 103 feet in 

 the total method for a steady temperature, and s t a defect of 100 feet for a 

 sudden fall of temperature. Mr. Glaisher's observations show that there 

 was a rise and fall of temperature between r and *, but as there were no 

 simultaneous observations of barometer and thermometer, I have not been 

 able to introduce them into the calculation. The results after r are there- 

 fore very doubtful. The interval v w is liable to grave suspicion, not only 

 from the great length of the interval, but the imperfect manner in which 

 the observations were unavoidably made. Supposing the observations to 

 * It is readily seen that on the assumed law of temperature, E 2 + . X= constant j the 

 sign of dx-i-dt depends on that of k, and is therefore supposed to be constant. Whdn 

 therefore dx~d( alters its sign during part of the height, the Ittw is vitiated, and the 

 formula inapplicable. The only chance of a decent approximation consists in separately 

 calculating the intervals with decreasing and increasing temperatures. 



