ATMOSPHERE. 



gioas very high in the atmosphere, which 

 it is likely may more copiously abound 

 with the electrical fluid. Be this how- 

 ever as it may, it lias been discovered that 

 the law above given holds very well, for 

 all such altitudes as are within our reach, 

 or as far as to the tops of the highest 

 mountains on the earth, when a correction 

 is made for the difference of the heat or 

 temperature of the air only, as was fully 

 evinced by M. De Luc, in a long series of 

 observations, in which he determined the 

 altitudes of hills, both by the barometer, 

 and by geometrical measurement, from 

 which he deduced a practical rule to al- 

 low for the difference of temperature. 

 Similar rules have also been deduced, 

 from accurate experiments, by Sir George 

 Shuckburgh and General Roy, both con- 

 curring to shew, that such a rule for the 

 altitudes and densities holds true for all 

 heights that are accessible to us, when 

 the elasticity of the air is corrected on 

 account of its density : and the result of 

 their experiments shewed, that the dif- 

 ference of the logarithms of the heights 

 of the mercury in the barometer, at two 

 stations, when multiplied by 10000, is 

 equal to the altitude, in English fathoms, 

 of the one place above the other ; that is, 

 when the temperature of the air is about 

 31 or 32 degrees of Fahrenheit's ther- 

 mometer, and a certain quantity more or 

 less, according as the actual temperature 

 is different from that degree. 



But it may be shewn, that the same 

 rule may be deduced, independent of such 

 a train of experiments as those referred 

 to, merely by the density of the air at the 

 surface of the earth. Thus, let D denote 

 the density of the air at one place, and d 

 the density at the other ; both measured 

 by the column of mercury in the barome- 

 trical tube ; then the difference of alti- 

 tude between the two places will be pro- 

 portional to the log. of D the log. of d, 



or to the log. of. But as this formula 



expresses only the relation between dif- 

 ferent altitudes, and not the absolute 

 quantity of them, assume some indeter- 

 minate, but constant, quantity h, which 



multiplying the expression log. , may 

 be equal to the real difference of altitude 

 a, that is, a h X lg- ^~T- Then, to 



determine the value of the general quan- 

 tity h, let us take a case, in which we 

 know the altitude a that corresponds to a 

 known density d; as for instance, taking 

 a = 1 foot, or 1 inch, or some such small 



altitude : then, because the density D may 

 be measured by the pressure of the whole 

 atmosphere, or the uniform column oi" 

 27600 feet, when the temperature is 55 ; 

 therefore 27600 feet will denote the den- 

 sity D at the lower place, and 27599 the 

 less density d at 1 foot above it ; conse- 



quently 1 = h x log. of. which, by 



the nature of logarithms, is nearly = A x 



.43429448 1 



and henCC 



27600 63551 



we find h = 63551 feet ; which gives us 

 this formula for any altitude a in general, 



viz. a = 63551 X log. of , or a = 63551 



X log. of^ feet, or 10592 X log. of- 



fathoms; where M denotes the column 

 of mercury in the tube at (he lower place 

 and m that at the upper. This formula 

 is adapted to the mean temperature of 

 the air 55 : but it has been found, by the 

 experiments of Sir George Shuckburgh 

 and general Roy, that for every degree 

 of the thermometer, different from 55, 

 the altitude a will vary by its 435th part ; 

 hence, if we would change the factor h 

 from 10592 to 10000, because the differ- 

 ence 592 is the 18th part of the whole 

 factor 10592, and because 18 is the 24th 

 part of 435 ; therefore the change of 

 temperature, answering to the change of 

 the factor /, is 24, which reduces the 55 



to 31. So that, a = 10000 X log. of- 

 fathoms, is the easiest expression for the 

 altitude, and answers to the temperature 

 of 31, or very nearly the freezing point : 

 and for every degree above that, the re- 

 sult must be increased by so many times 

 its 435ih part, and diminished when be- 

 low it. 



From this theorem it follows, that, at 

 the height of 3^ miles, the density of the 

 atmosphere is nearly 2 times rarer than 

 it is at the surface of the earth ; at the 

 height of 7 miles, 4 times rarer; and so 

 on, according to the following table : 



Height in miles. 



14 

 21 

 28 

 35 

 42 

 49 

 56 

 63 

 70 



Number of times rarer, 

 o 



<j 



4 



16 



64 



256 



1024 



4096 



16384 



65536 



262144 



1048576 





