150 Royal Society: — Mr. Ellis on the Corrections for 



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 abnormal*. The total method, from omitting all considera- 

 tions of the preceding 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 temperature, and conse- 

 quently 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°*1 for 

 a barometric depression of *79 inch, which is nearly double the nor- 

 mal amount as previously determined for the 14 th inch of depres- 

 sion. 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 s, 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 therefore 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 be correct, the total method makes 

 the interval vw greater than the gradual by no less than 610 feet, 

 owing to its distributing the warm temperatures over so large an in- 

 terval of extreme cold. If we then omit the interval vw, we find 

 359 feet for the sum of all the cases in which the total method was 

 in excess of the gradual, and 201 feet for the cases of defect, leaving 

 a total excess of 158 feet in 2G450 or 26292 feet, which is thus 

 shown to be a very inadequate measure of the degree of uncertainty 

 due to the total method. 



In Table IV. the results to c, or even d, substantially agree ; but at 

 e?the temperature decreases very slowly, and soon becomes absolutely 

 stationary. Great differences immediately appear. From I to r the 

 temperature increases, and the total method gains greatly on the 

 gradual till at r it is 541 feet in advance. At stations s,t the 

 total method indicates a descent with a falling barometer, whereas 

 the gradual method gives a very slow ascent. Mr. Glaisher's obser- 

 vations show that for the same barometric pressure of 14*637 inches, 

 as at r, the temperature varied successively through 36°-l, 38°*2, 



* It is readily seen that on the assumed law of temperature, W-\-k. X= con- 

 stant ; the sign of dx-^dt depends on that of k, and is therefore supposed to be 

 constant. "When therefore dx-^dt alters its sign during part of the height, the 

 law is vitiated, and the formula inapplicable. The only chance of a decent ap- 

 proximation consists in separately calculating the intervals with decreasing and 

 increasing temperatures. 



