Da. Arnott on the Measurements of Heights. 13 



the boiling points by Fahrenheit's thermometer, along with the simultaneous 

 heights of the barometer : these, aiTangecl according to their values, are : — 



Mr, Forbes also mentions that his thermometer actually indicated 

 2l2°-62 under the pressure of 30 inches, and on deriving a foi-mula from 

 the 2d and 7th of the above observations, it would appear that each had 

 been reduced to 212° at that pressure, by subtracting 0°-62 from the 

 observed boiling points : the last column then indicates the boiling points 

 after 0°62 has been added to each of the recorded ones, and converted 

 into centesimal degrees. In order to obtain the co-efficient in and con- 

 stant n, by an average of these, we may divide the difference of the sum 

 of the first four boiling points and that of the last four, by the difference 

 of the sum of the logarithms of the first four pressures, and that of the 

 last four: this gives the formula 60-189 Log. p -j- 11-452 = h, the ther- 

 mometer showing 100°-344 at a pressui-e of 30 inches, or (when multiplied 



|jy ,j 59-973 Log. ]j -f- 11-41 = 6 for a thermometer showing 



100° under the same pressure. This may be said, in round numbers, to 

 be equivalent to 60 Log. p ■\- 11-373 = &.* 



I have already deduced from Saussure's observations two formulas : the 

 one from Leslie's data, is 61-3056 Log. p + 10-594 : the other, from Mr. 

 Forbes' account of them, is 61-0935 Log. p + 10-862. The co-efficient 

 and constant of these being reduced so as to be adapted to a thermometer 

 graduated to 100° at a pressure of 80 inches, are respectively 60-61 Log. j? 

 -f 10°-47, and 60-43 Log. p + 10°-76. On the whole, I prefer 60-6 

 i-og. p + 10-486 = h for the Centigrade scale, or 109 Log. ]) + 18-994 

 for Fahrenheit's, reckoned from the freezing point, or 109 Log. p -f- 50-994 

 for the precise boiling point. Dr. Horsley's formula gives 61-18 Log. jp 

 -I- 9-63, or in round numbers, 61 2 Log. p -f- 9°"6, for the Centigrade 

 scale, and 110-1223 Log. p -f- 17''-32 for Fahrenheit's above 32°, or 



♦ It may be remarked that, as by the formula just obtained from Professor 

 Forbes' observations, 60 times the difference of the logarithms of the barometer 

 gives the difference of the boiling jjoints, and since 60,000 times the same gives the 

 approximate heiglit, therefore, 1000 times the difference of the boiling point gives 

 the approximate height ; the same rule as given by Leslie — with this distinction, 

 that the atmosphere is supposed to be at the temperature of freezing, by Forbes ; 

 by Leslie, at 5^° Cent, above it, and that is of great importance. 



