Latitude and Temperature in Barometric Hypsometry. 147 



The coefficient 36*764 in (a) results from Ramond's comparison 

 of trigonometrical with barometrical measurements (Mec. Cel. iv. 

 290). Bessel's theory, with the numbers corrected by Plantamour 

 (Ann. Meteor, de F. 1852), makes it 36-809. If this coefficient 

 were adopted the values of log G in Table II. would have to be 

 increased by -00053, This would increase the results in the fore- 

 going examples by 4 feet, 2'8 metres, and 1*3 toise respectively. 

 Verification of these numbers by actual levelling is much needed, 

 but it is rendered difficult by the uncertainty attending the cor- 

 rection for temperature*. Thus if E= 1 + '003665 . r, where r 

 degrees Centigrade is the temperature of the air at the height of # 

 metres, and X— R I # + (R 1 + #), it becomes necessary in the deter- 

 mination of the formula to integrarte d X + E (see especially Bessel 

 in Schumacher's Astron. Nachr. vol. xv. no. 356. art. 2. eq. 5), 

 and consequently to know the relation between E and X. Laplace 

 then says (I. c), "comrne les inte'grales ne s'etendent jamais qu'a 

 un intervalle peu conside'rable, relativement a la hauteur entiere de 

 I'atmosphere ; t out e fori ction qui represente a-la-fois les temperatures 

 des deux stations inferieure et superieure, et suivant laquelle la 

 temperature diminue a-peu-pres en progression arithmetique de rune 

 a 1' autre, est admissible, et Ton peut chosir celle qui simplifie le plus 

 le calcul." Bessel (7. c.) says " we are entirely ignorant of this 

 relation, and have therefore no reason to assume the alteration of 

 temperature as otherwise than proportional to the alteration of 

 height." Laplace and Bessel then make an assumption which ap- 

 proximatively fulfils this condition and is equivalent to taking 

 E 2 + £ . X = a constant, k being determined by the observed tempe- 

 ratures at the two stations. This makes the integration easy, but it 

 is evident that the result should not be applied in cases where the 

 difference of level is not small in relation to the extent of the appreci- 

 able atmosphere, or where the temperature does not diminish approxi- 

 mately as the height increases. Now Mr. Glaisher, as the result of 

 his observations 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, by a horizontal and a vertical unit of length respectively, we 

 shall find that the resulting curve approaches to a rectangular hyper- 

 bola 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 



* The errors in determining the actual temperatures of the air in mountain 

 ascents, arising from the radiation of the ground, are not considered, because 

 they are rather errors of observation than of theory. 



t In an article in the Beader newspaper (31 Oct. 1863, p. 513), purporting 

 to be an extract from Mr. Grlaisher's Keport to the British Association in 1863 

 (the passage does not occur in the published Report of tne E. A.), it appears, 

 on correcting two obvious misprints, that he has thus calculated m = 5*6295 . n 

 + (l+0-0±8 • n), giving mra +20*8333 . m- 117-281 . n=0, for which mw+21w 

 — 117w=0 is a sufficiently close approximation, and represents the mean vari- 

 ation very fairly, after the first 5000 feet of ascent. 



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