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



curves of alteration of temperature really observed*, the deviation 

 from the average appears so great in particular cases, that no advan- 

 tage would accrue from complicating the integration by the intro- 

 duction of such a law. 



The only course that appears open to pursue is to confine the 

 limits of the integration to those small amounts which Laplace con- 

 templated in the passage cited, and calculate the height by sections. 

 For it also appears from Mr. Glaisher's curve, that for small altera- 

 tions of height the alteration of temperature varies approximately 

 as the alteration of height, that is, that the curve does not deviate 

 materially from its tangent for comparatively considerable distances. 

 When the difference of level is many thousand feet the difference 

 of temperature is generally large, and the curve consequently differs 

 materially from a straight line. No dependence can then be placed 

 on the result. It would appear that we should be more likely to ob- 

 tain correct results by dividing the whole height into a number of 

 partial heights, not exceeding 1000 metres or 3000 feet, and taking 

 fresh observations whenever the temperature altered abnormally. To 

 have a rough notion of when this occurs, an aneroid barometer 

 and common thermometer should be watched on the ascent. Mr. 

 Glaisher's observations tend to show that we may expect on an 

 average a fall of very nearly 4° Fahr. for each inch of depression of 

 the barometer under a cloudy sky, the first inch, and the 1 lth to the 

 16th inch of depression being accompanied by a slightly more rapid 

 fall of temperature. Under a clear or nearly clear sky, there is a fall 

 of about 5° Fahr. for each of the first 4 inches of depression of the 

 barometer; then about 4°-2 per inch from the 5th to the 13th inch, 

 and about 4 0, 5 per inch from the 14th to the 16th inchf . This may 

 therefore be considered as the normal alteration of temperature. In 

 order to secure simultaneous observations at both stations for each 

 section, it would be necessary to have two ascending parties, one for 

 each variable station, each of which should be able to signal to the 

 other. A stationary observer at the lowest station would serve as 

 a check on the other two. This method introduces many practical 

 difficulties, but the reduction of the observations is rendered very 

 easy by Tables I. and II. The great importance of thus calculating 

 heights by sections will be rendered evident by the following exam- 

 ples. 



Taking the data in the Ann. Meteor, de F. for 1852, p. 70, we 

 have for Geneva as the lower and St. Bernard as the upper station, 

 L46, 



B' 072643 A' 8-97 H x 408, 



V 0-56364 a' -1*89 h x 2463. 



* Mr. Glaisher has laid down these in the Proceedings of the British Meteo- 

 rological Society, vol. i. (19 Nov. 1862) plate 13, with which I have compared 

 the theoretical hyperbola. 



t These comparisons have been obtained by calculating the height attained 

 for each inch of depression of the barometer, from the 1st to the 16th, taking 

 for the bottom station B'SO, AGO, H 0, L45, and supposing the temperature to 

 decrease according to Mr. Glaisher's Tables. The increase of height for each 

 inch of depression was then divided by the number of feet of ascent in which, 

 according to Mr. Glaisher, the temperature falls one degree at the height reached. 



