546 Royal Society : — 



Excluding the last, which depends upon the weighings in 1824, 

 U=Sp + 0-0079 grain. 



Excluding all except the results of the comparisons of U with 

 the two platinum troy pounds, U=Sp + 0*0083 grain. 



The temperatures were determined by means of three thermo- 

 meters by Bunten, having centesimal scales etched upon the tube, 

 and two thermometers having arbitrary scales traced upon the tubes 

 with a diamond point. The zero-pouits of these were determined 

 at distant intervals. They were often compared with each other, 

 and, lastly, with an excellent standard thermometer constructed at 

 Kew under the directions of Mr. Welsh, in order to form tables of 

 the errors at any point of their scales, and to determine the position 

 of their zeros at any given time. The barometer employed was a 

 portable cistern barometer by Ernst of Paris, the scale of which was 

 divided into milHmetres. It was compared first with the standard 

 barometer of the Paris Observatory, and afterwards with a standard 

 barometer, having a tube of very large bore, belonging to the Taylor 

 Library of Sidney Sussex College, Cambridge. 



According to Ritter (Memoires de la Societe de Physique de Ge- 

 neve, t. iii. p. 361), the observations of Regnault show that in Paris, 

 lat. 48° 50' 14", GO metres above the mean level of the sea, a litre of 

 dry atmospheric air, containing the average amount, 0*0004 of its 

 volume, of carbonic acid, the density of which is 1*529 of that of 

 atmospheric air at 0° Cent., under the pressure of 760 mm. of mer- 

 cury at 0° Cent., weighs 1*2934963 gramme. If G be taken to 

 denote the force of gravity at the mean level of the sea in lat. 

 46°, the force of gravity in lat. X, at the mean level of the sea, 

 = G(1 -0*0025659 cos 2\) (Baily, Mem. Ast. Soc. vol. vii. p. 94). 

 The force of gravity in a given latitude at a place on the surface 

 of the earth at the height g above the mean level of the sea 



= 'j 1— f2— - -j-r X force of gravity at the level of the sea in the 



same latitude, where r is the radius of the earth, p its mean density, 

 and p' the density of that part of the earth which is above the mean 

 level of the sea (Poisson, Traite de Mecanique, t. ii. p. 629). 



According to Regnault, the expansion of air und* constant pressure 

 from 0° to 100 Cent., is 036706 of its volume at 0° Cent.; also at 

 50° Cent., the mercurial thermometer is about 0°*2 in advance of 

 the air thermometer (Memoires de I'lnstitut, t. xxi. p. 91. p. 238, 

 Annales de Chimie, 3 serie, t. v. p. 99). HencCi density air at 

 0° : density air at t= 1 +0*003656^. The density of the vapour of 

 water is 0*622 of that of air. Hence, if t be the temperature of the 

 air in centesimal degrees, 6 its barometric pressure, v the pressure 

 of vapour, both in millimetres of mercury at 0° Cent., the weight in 

 grammes of a litre of air at a place on the surface of the earth at a 

 height z above the mean level of the sea in lat. X, will be 



1*2930693 6-0*378t;/, , oo-^Vi a nno^^^^n o^^ 

 , 1 + 0*003656^ _^^^^^l-.1.32-j(l-0*0025659cos2X). 



Regnault finds that in rooms dot heated artificially^ the pressure of 

 vapour is two-thirds of the maximum pressure corresponding to the 



