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



on the diminution of temperature with increase of height, gives a series of 

 average decrements such that on assuming the temperature to decrease m 

 degrees Fahrenheit for an elevation of n thousand feet, and representing a 

 degree Fahrenheit and a thousand feet, hy a horizontal and a vertical unit 

 of length respectively, we shall find that the resulting curve approaches to 

 a rectangular hyperbola mn+am + bn=0, referred to axes parallel to its 

 asymptotes. We may then by the principle of least squares determine the 

 values of a and b from his Tables*. But on comparing such a curve with the 

 curves of alteration of temperature really observed f, the deviation from 

 the average appears so great in particular cases, that no advantage would 

 accrue from complicating the integration by the introduction 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 contemplated 

 in the passage cited, and calculate the height by sections. For it also ap- 

 pears from Mr. Glaisher's curve, that for small alterations 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 com- 

 paratively considerable distances. When the difference of level is many 

 thousand feet the difference of temperature is generally *arge, 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 obtain 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 llth 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 de- 

 pression 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 inch J. This 



* In an article in the Reader newspaper (31 Oct. 1863, p. 513), purporting to be 

 an extract from Mr. Glaisher's Keport to the British Association in 1863 (the passage 

 does not occur in the published Eeport of the B. A.), it appears, on correcting two 

 obvious misprints, that he has thus calculated m = 5'6295 . w-=-(l+0'048. ), giving 

 mn+20-8333 . m 117'281 . =0, for which mn+ 21w-117=0 is a sufficiently close 

 approximation, and represents the mean variation very fairly, after the first 5(JOO feet 

 of ascent. 



t Mr. Glaisher has laid down these in the Proceedings of the British Meteorological 

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

 hyperbola. 



| These comparisons have been obtained by calculating the height attained for each 

 inch of depression of the barometer, from the 1st to the IGth, taking for the bottom 



