242 PROFESSOR J. D. FORBES ON THE MEASUREMENT OF HEIGHTS 



but I imagine that the difference will almost disappear, if he adopt the slightly- 

 altered value of the coefficient given in this paper, from which we have seen that 

 the coefficient deduced from his observations alone does not sensibly differ. 



To complete the subject, I have discussed, in the same manner with Dr 

 Hooker's and my own, the observations made in the Alps and Pyrenees by 

 MM. Martins and Bravais, by M. Marie', and M. Izarn, which M. Regxault 

 has quoted very justly in confirmation of his formula, which represents them ex- 

 cellently well. These I find also extremely closely represented as far as 90° Cent., 

 or 194° Fahr., by a linear formula, of which the coefficient for l c Fahr. is 531 Eng. 

 feet ; but the greater part are made at comparatively small elevations. The ob- 

 servation for Mont Blanc alone gives 543*4 feet for 1°.* 



These results, it will be seen, give a coefficient somewhat less than Dr 

 Hooker's or my own. The greater part, however, were made at small eleva- 

 tion, and, consequently, give a less accurate mean coefficient. 



It has been shown, in the previous part of this paper, that the Table of M. 

 Regnault (which had not been published when I last wrote) represents my obser- 

 vations as satisfactorily as the simpler formula which I used, whilst it expresses 

 probably better the results at very great and at very small elevations. Dr 

 Hooker's observations, though hardly decisive as to the preference of one or 

 the other formula, are also well represented by M. Regnault's numbers ; whilst 

 those made under M. Regnault's immediate superintendence, with instruments 

 expressly constructed and graduated by his direction, coincide, as might be ex- 

 pected, very nearly with his Table. I claim, therefore, no preference for my for- 

 mula, except as a convenient approximation to the truth, sufficiently accurate for 

 heights under 12,000 or 13,000 feet. But I find that the results of M. Regnault's 

 empirical table may be expressed with an accuracy almost perfect, within the 

 extreme limits of observation, by a formula so remarkably simple as to dispense 

 with the use of any tables whatsoever, and which, therefore, may be used in- 

 stead of the still simpler approximation, and with little more trouble. If we as- 

 sume the boiling point at the lower station to be 212 D , then the elevation in feet 

 of a station where water boils T degrees of Fahrenheit lower will be exactly 



k = 517 T + T 2 (A) 



or in metres and centigrade degrees, h — 284 T + T 2 .f 



* In the calculation of De Saussure's observation on Mont Blanc, in my former paper (Ed. 

 Trans., vol. xv., p. 414), a slight mistake occurs. The depression of the boiling point should be 

 26°*81, instead of 26°-71, giving 545-9 feet for 1°, agreeing strikingly with the other results. 



■f It happens by a double fortunate coincidence, that the coefficient of T 2 , is equivalent to unity in 

 both cases, when the proper reductions are made. 



