VOL. LXIV.] PHILOSOPHICAL TRANSACTIONS. , 525 



if the difference of height of this thermometer, at the two stations, be called d, 

 we shall have d — 0.452 X d; for rf: d :: 81.4 : 180 :: 0.452 : 1 ; and the num- 

 ber of degrees expressed by d, will show immediately the correction for the dif- 

 ference of heat of the two barometers. If the thermometer, designed to show 

 the temperature of the air, be divided with the interval between freezing and 

 boiling water = 200, and the freezing point be marked — 9, and the boiling 

 point -j- 191, and the heights of this thermometer, at the two stations, be 

 called G and i, we shall have ^ ~^ ' = ° /■ = — tt- For f — 40 = f — 



449 2 X 500 1000 



32 — 8, is the height of Fahrenlieit's thermometer, reckoned from 8 degrees 



above freezing, and 449 : 500 :: 180 : 200 :: 8 : 9, and the fraction -— , 



if both the numerator and denominator be increased in the ratio of 449 to 500, 

 will become = i) 



500 - 500 -2x500-1000'^^^^"^^ 2~+9-{^— 



32) X ^TT. Therefore, if the thermometer of the barometer has the freezing 

 point marked O, and the point of boiling water 8 1 .4, and the difference of its 

 height, at the two stations, be called d; and the thermometer for measuring the 

 temperature of the air, be divided with the interval of 200 between the freezing 

 point and that of boiling water, and the first be marked — 9, and the latter -|- 

 191, and the degrees shown by this, at the two stations, be called g and i; the 

 formula, that will give the height of the upper station above the lower one, in 

 English fathoms, will be (log. b — log. b :f d) x (l -|- \^ ;) which conse- 

 quently multiplied by 6, will give the height in English feet. It is to be observed, 

 as before, that — d or -f- f/ is to be used, according as the thermometer, attached 

 to the barometer, is highest at the lower or upper station ; and if g and 1 should 

 happen to fall below O of the scale, or to be subtractive, they must be applied 

 accordingly in the calculation. 



I shall now add nothing more, but to give the rule for finding heights by the 

 barometer, according to the formulas delivered above, in common language; 

 first, as adapted to Fahrenheit's thermometer, and next, as adapted to the 2 

 thermometers of particular scales. Take the difference of the tabular logarithms 

 of the observed heights of the barometer, at the two stations, considering the 

 first 4 figures, exclusive of the index, as whole numbers, and the 3 remaining 

 figures to the right as decimals, and subtract or add -jVirV o( the difference of 

 the altitude of the Fahrenheit's thermometer, attached to the barometer at the 

 two stations, according as it was highest at the lower or upper station; thus you 

 will have the height of the upper station above the lower, in English fathoms 

 nearly : to be corrected, as follows : make this proportion ; as 449 is to the dif- 

 ference of the mean altitude of Fahrenheit's thermometer, exposed to the air at 



