10 Dn. Aknott on the Measurements of Heights. 



some lofty mountain. We shall prefer at present the observation made 

 by Saussure on the summit of Mont Blanc. This diligent philosopher 

 found, by means of a very delicate thermometer constructed on purpose, 

 that water which boiled at 101°'62 in the plain below when the barometer 

 stood at 30'534 English inches, boiled at 86°'24 on the top of that moun- 

 tain, while the barometer had sunk to 17'136. Wherefore, the distance 

 between the points of ebullition, or 15""38 centesimal degrees, must cor- 

 respond to an approximate elevation of 1 5,050 feet; which gives 978J feet 

 of ascent for each degree, supposing the mean temperature of the atmos- 

 pheric column to be that of congellation. But it will be more convenient 

 to assume 1000 feet for the constant multiplier, which corresponds to the 

 temperature of 5J°." 



In order to understand this last clause, we must bear in mind that Leslie 

 directs us in barometrical measurements to multiply the approximate 

 height by twice the sum of the centesimal degrees shown by the ther- 

 mometer indicating the temperature of the external air ; the product, with 

 the decimal point shifted three places to the left, gives the correction to 

 be added to the approximate height. So, after establishing that 978'5 

 feet corresponds to a diiference of 1° Cent, in the boiling point, the atmos- 

 phere being supposed to be at freezing or 0" at both stations, he changes 

 the multiplier to 1000, and finds the new medium temperature correspond- 

 ing ; this, from what I have said, wiU be — = 22 nearly; and 



one-fourth of this, or 5J, is the result, as stated by Leslie. 



It is remarkable that Professor Forbes als» refers to one of the same 

 observations made by Saussure, in order to prove his constant multiplier 

 obtained empirically. This is 549J for Fahrenheit's thermometer at 

 the temperature of freezing, which gives 989*1 as the multiplier for each 

 centesimal degree at the mean temperature of 0° Cent., or 1000 at a 

 medium temperature of 2J° Cent. There is thus a difference on the 

 approximate heights of eleven feet in a thousand from this source alone — 

 IVIr. Forbes' multiplier making it so much more than Leslie's : and although 

 this is of no great consequence, it becomes important to have the means 

 of reducing it, or ascertaining the cause of the difference. 



Mr. Forbes states, that Saussure's thermometer boiled at 212° Fahr., or 

 100° Cent., when the barometer stood at 28'777 English inches. There 

 must be either some slight error in this, or in the other observations made 

 by Saussui-c, and depended on by Leslie. And here let us take Deluc's 

 formula, where m Log. 2^ + n = h the temperature of the boiling point, 

 p being the barometric pressure : now if we make two observations by the 

 same instruments, and call the pressures P, p, and the boiling points B, b, 



the difference is m (Log. P — w) = B — b: hence m = .= ^ ^ , 



Log. P — Log.jp. 



and « = B — v= =r = x Log. P. Thus, we readily find the 



liOg. P — Log. 1^- J J 



co-eflScient m, and the constant n, by means of two observations made by 



