106 Mr. Ivory on the TJieory of the Astronomical Refractions. 



the barometric pressure be changed to /»', the density of mer- 

 cury will be to the density of dry air, at the temperature 32° 



Fahrenheit and under the pressure p', as 10462 x -, 



to 1 ; wherefore, as D stands for the density of dry air in the 

 circumstances mentioned, its value estimated in parts of the 

 density of mercury, will be thus expressed : 



hence 



104<62 ^29-9218 



^ = 104-62 X 29-9218; 



and, by reducing the inches to fathoms, 

 -^ = L = 4.347-8 fath. 



This quantity being found, we deduce from the foregoing 

 formula for z^ 



i±/_ J_ _^ 



A single experiment in which z and t'— t were ascertained, 



should be sufficient for determining — j^ and f: but it is 



well known that great irregularity prevails in the rate at 

 which the heat decreases in the atmosphere, more especially 

 when the elevations are small. This is owing chiefly to the 

 thermometer, which is often affected by local and temporary 

 causes. When we reflect that a considerable variation in the 

 height is required to produce a small change of the thermo- 

 meter, even the errors unavoidable in the use of that instru- 

 ment must produce notable discrepancies in the rate, when 

 the whole observed difference of temperature is only a few 

 degrees. It thus appears that the quantity sought cannot be 

 determined with tolerable exactness, except by taking a mean 

 of the results obtained from many experiments. In this view, 

 the average estimations of the decrease of heat in the atmo- 

 sphere, which have been inferred from their own researches 

 by philosophers on whose judgement and accuracy depend- 

 ence can be had, becomes very valuable. Professor Playfair, 

 in his Outlines, states that the decrease of heat is nearly uni- 

 form for the greatest heights we can reach ; and that it may 

 betaken on an average as equal to 1° of Fahrenheit's thermo- 

 meter for 270 feet, or 45 fathoms, of perpendicular ascent. 



