1865.] and Temperature in Barometric Hypsometry, fyc. 277 



W -08808 



The coefficient 36- 764 in (a) results from Ramond's comparison of tri- 

 gonometrical with barometrical measurements (Mec. Cel. iv. 290). Bessel's 

 theory, with the numbers corrected by Plantamour (Ann. Met6or. 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 foregoing 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 correction for temperature*. Thus if E = 1 + -003665 . r, where r 

 degrees Centigrade is the temperature of the air at a height of x metres, 

 and X=R 1 #-;-(R 1 +a?), it becomes necessary in the determination of the 

 formula to integrate rfX-r-E (see especially Bessel in Schumacher's Astr on. 

 Nachr. vol. xv. no. 356. art. 2. eq. 5), and consequently to know the 

 relation between E and X. Laplace then says (1. c.), " comme les inte- 

 grales ne s'etendent jamais qu'a un intervalle peu considerable, relativement 

 a la hauteur entiere de 1' atmosphere ; toute fonction 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 

 1'une a 1'autre, est admissible., et Ton peut choisir celle qui simplifie le plus 

 le calcul." Bessel (I. 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 approximatively fulfils this condition 

 and is equivalent to taking E 2 + . X=a constant, k being determined by 

 the observed temperatures 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 appreciable 

 atmosphere, or where the temperature does not diminish approximately as 

 the height increases. Now Mr. Glaisher, as the result of his observations 



* 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 theorv. 



