196 MR. IVORY ON THE THEORY OP ASTRONOMICAL REFRACTIONS. 



Now it is obvious that D is the density of the air at the earth's surface, reduced to 

 zero of the thermometer; and hence we learn that -^ is independent on the magni- 

 tude of jo', and has the same value in all atmospheres of dry air ; for, D being the 

 density of the air produced by the pressure y at the fixed temperature zero of the 

 thermometer, it will vary proportionally to j»'. 



The value of the constant quantity ^ is next to be found. It has been ascertained, 



by very careful experiments, that the density of mercury is to the density of dry air as 

 10462 to 1, the temperature being 0° centigrade, or 32° of Fahrenheit's scale, and the 

 barometric pressure 0™'76, or 29*9218 English inches. The temperature remaining 

 at 32° Fahrhenheit, if the barometric pressure be changed to /?', the density of mer- 

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



29*92 18 

 the pressure JO, as 10462 X — :d — 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 : 



10462 ^ 29-9218* 

 hence 



^=10462X29-9218; 

 and, by reducing the inches to fathoms, 



^ = L = 4347*8 fath. 



This quantity being found, we deduce from the foregoing formula for z, 



' 1 +/ 1 z 



— ^ X 



A single experiment in which z and i^ — r were ascertained, should be su-^cient for 



determining r andy-. but it is well known that great irregularity prevails in the 



rate at which the heat decreases in the atmosphere, more especially when the eleva- 

 tions 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 thermometer, even the errors 

 unavoidable in the use of that instrument 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 atmosphere, which have 

 been inferred from their own researches by philosophers on whose judgement and 

 accuracy dependence can be had, becomes very valuable. Professor Playfair, in his 



