of mountains in the north of England. 403 
at the two stations ; multiply this difference by and add 
or subtract this product, according as the thermometer was 
highest at the upper or lower station, which will give an 
approximate height. 
3dly. Take the mean of the two altitudes of the thermo- 
meter, and find the difference between this mean and 32^. 
Multiply the approximate height by this difference, and the 
product by the decimal fraction .00244. This last correction 
being added to, or subtracted from the approximate height, 
according as the mean of the two altitudes of Fahrenheit’s 
thermometer was greater or less than 32 0 , will give the true 
height of the upper station in English fathoms. 
Dr. Hutton’s rules. 
1st. Let the heights of the barometer at the top and 
bottom of any elevation intended to be measured, be observed 
as near the same time as may be, as also the temperatures 
of the attached thermometers, and also the temperature of 
the air in the shade at both stations, by means of detached 
thermometers. 
2dly. Reduce these altitudes of the barometer to the same 
temperature by augmenting the height of the mercury in the 
colder temperature, or diminishing that in the warmer by its 
- 9 - foo part for every degree of difference of the two. 
3dly. Take the difference of the common logarithms of 
the two heights of the barometer (so corrected), considering 
the four first figures (exclusive of the index) as whole 
numbers, and the rest to the right as decimals, which will 
give an approximate height. 
mdcccxviii. 3 G 
