Dr. Aenott on the Measurements of Heights. 11 



the same barometer and thermometer. If we assume as correct, the 

 observations quoted by Leslie, then m ==61-30563, n = 10'5944, whence 

 Gl"306 Log. 2^ + 10'>'594 = temperature of the boiling point on the 

 Centigrade thermometer. But by this formula the barometric pressure 

 28-777 gives the boiling point equal to lOO^-OS Cent., or 212°-056 Fahr., 

 in place of 100'' and 212° Fahr. On the other hand, if we assume that 

 the thermometer showed 100° under the pressure of 28-777, and 86-241 

 under the pressure 17-133, as stated by Mr. Forbes, the formula becomes 

 61-0935 Log. j) + 10-862 = b, which gives, at the pressure of 30-534, 

 b — 101*57, instead of 101-62, mentioned by Leslie, as having been 

 observed. The diflerence is 0°*05 Cent., or 0''-09 Fahr. Hence there is 

 some error of observation, which, although trivial, must affect considerably 

 any co-efficients obtained. 



TVTien a thermometer does not exhibit the boiling point of 100", under 

 the pressure of thirty inches, it is customary to reduce it to that standard 

 by adding or subtracting the same difference from aU the observations 

 made by it. This is obviously incorrect ; for the difference at the boiling 

 point of 100° can only be got by multiplying the difference at some other 

 point by 100, and dividing by what the thermometer does indicate at that 

 pressui-e. It appears to me, therefore, preferable to derive all the co-effi- 

 cients by means of the same instruments, and afterwards reduce them 

 in the way just mentioned. Not only does every thermometer require 

 a co-efficient and constant multiplier for itself, so as to make the actual 

 boDing points coiTcspond with those calculated from the barometer, but 

 the co-efficient or constant multiplier of the difference of the boiling points 

 by the same instrument requires to be adapted to the mode of calcination 

 followed for ascertaining the approximate heights by a barometer. Thus, 

 let the barometer stand at 30, and 17-133 inches respectively, according 

 to Professor Forbes ; "by Galbraith's tables, 



For 30 inches, 29228 



— 17-133 do 14593 



Difference, 14635," 



whereas, by the more usual method, and that adopted by Leslie, 60,000 

 X (Log. 30 — Log. 17-133,) = 14597, exhibiting a difference of 38 feet, 

 or about 2f feet in every thousand. 



It thus appears that every one must discover that co-efficient for him- 

 self which is most suited to his barometer and thermometer, as well as to 

 the method of calculation he adopts for measurements by the barometer, 

 otherwise the heights ascertained by the barometer and the boiling points, 

 cannot be expected to correspond. The following is the simple practical 

 rule: — 



" Observe the hoilmg points tender two as mdely different barometric 

 jrresHures as j)ossiblc, and calculate the a/pijroximcde difference of height by 

 the mdltod nmicUly oxlopted; the difference befvicen the boiliiif/ points 



