HEIGHTS, ETC., OF ATMOSPHERE. ] MECHANICAL PHILOSOPHY. PNEUMATICS. 



771 



K = 1 -Mog. ?- or K = 1 -T- log. ?. 

 H p 



Now when the barometer stands at 30, and the tem- 

 perature of the air is 55 Fah., the weight of a volume of 

 air is to that of an equal volume of mercury as 1'22 is to 

 13568 : hence the pressure of the 30 inches of mercury 



13568x30 . 

 is equal to the pressure of a column of p^ inches 



of air of the same uniform density as that in which the 

 barometer is placed that is, of the air at the level of the 

 sea. The height of this equiponderant column of homo- 

 geneous air is therefore 



13568x30, 



-7S feet i 



27803 feet 



1-22x12 



and, therefore, the height of the column measured from 

 a foot above the level of the sea, is 27802 feet. 



, 27803 , , . 1 

 1 -T- log. 



K 



27802 



But log. 



.:^> - '43429448 



(MATHEMATICAL SCIENCES, page 519), therefore, neglect- 

 ing the powers of so small a fraction, 



43429448 27802 

 -27808- = -43429448 



K " 



or dividing by 6, K = 10670 fathoms. Consequently 

 the formula for the computation of any altitude A above 

 the level of the sea, is 



height of bar. at alt. A 



A = 10070 log. , r-r T fathoms. 



B height of bar. at the sea-level. 



The constant factor 10670 has been determined on the 

 supposition that the temperature of the air ia 55 Fah. 

 The more convenient multiplier 10000 may be employed 

 instead, by a suitable alteration of the temperature ; 

 that is, by assuming the air to be in a different state. 

 Experiment has shown that the altitude of a place, as 

 deduced from the foregoing formula, will vary by j^th 

 of its whole value, for every degree by which the mean 

 of the temperatures at the two stations differs from 65 ; 

 the variation to be added when the mean exceeds 55, 

 and subtracted when the contrary is the case. 



Now, the difference between 10670 and 10000 is 670, 

 and the difference between 10070 and the value it would 



hive for one degree less of temperature is ~7qx~ " 24 '5 : 



hence, to find for how many degrees less of temperature 

 the difference is 670, we have the proportion 



24-5 : 670 : : 1 : 27. 



Consequently 55 27 = 28 is the temperature of 

 the air for which the altitude A in fathoms is 



.,...- height of bar. at alt. A 



log ' height of bar. at the sea-level 



And this value must be increased or diminished by the 

 jjjth part of itself for every degree shown by the mean 

 temperature of the two stations above or below 28. 



In taking the logarithms, we may employ only five 

 figures for each, including the index 1. Regarding these 

 as whole numbers, we take their difference ; then if E be 

 the excess of the mean temperature of the two stations 



p 



above 28", we must multiply this difference by -rs=i 



ww 



and add the result to the said difference to obtain the 

 altitude in fathoms. This fraction of the difference 

 must be subtracted if E be negative. The following is 

 an example : 



Required the height of a mountain when the barome- 

 ter at the bottom stands at 29 '68 inches, and at the top 

 at 25-28 inches, the mean temperature, that is, half the 

 sum of the temperatures at the two stations, being 47. 



The excess of the mean temperature above 28 is 47" 

 28 = 19 



10000 



.... 14725 

 .... 14028 



E 19^ 



435 " 435 



~> 



C97 

 30 



,'. the height is 727 fathoms = 43G2 



feet. 



Where minute accuracy is required, certain particulars, 

 here disregarded, must be taken into consideration ; as, 

 for instance, the latitude of the place of observation, 

 and the dilatation of the mercurial column, which 

 lengthens to the extent of rotao 7 ** 1 f the whole for every 

 additional degree of temperature : but the determination 

 of altitudes by the foregoing formula will, in general, 

 differ from the truth only by a fathom or two, and will 

 therefore be sufficiently accurate for most practical pur- 

 poses. (See Chapter V. Section, Meteorology.) 



The higher we ascend into the regions of the atmo- 

 sphere, the colder does it become. There are two reasons 

 for this : in the first place, the direct rays of the sun 

 pass through the air without being arrested, as it were, 

 as in the case of a solid body, which absorbs a great por- 

 tion of the heat poured upon it ; and, in the next place, 

 experiment proves that air by rarefaction loses part of 

 its original heat, so that when air of a certain tempera- 

 ture is relieved of part of the pressure upon it, and 

 allowed to expand (as the air in the receiver of an air- 

 pump), it is found that the temperature becomes less and 

 less as the pressure diminishes ; so that if the original 

 temperature is to be maintained, fresh heat must be com- 

 municated. As there is no external source for the supply 

 of such heat in the more elevated regions of the atmo- 

 sphere, the superior coldness of those regions becomes 

 sufficiently accounted for. 



WEIGHT OF THE WHOLE ATMOSPHERE. 

 We have already seen that the weight of the atmosphere 

 surrounding the earth is equal to the weight of a sur- 

 rounding coating of mercury, on the average 30 inches 

 thick : the amount of this weight may be found by mul- 

 tiplying the volume of the mercurial shell by the specific 

 gravity of the mercury, and the product by g = 1000 

 ounces (HYDROSTATICS, page 752). Let E, = radius of 

 the earth in feet, r height of the mercury in feet, and 

 s its specific gravity : then subtracting the volume of a 

 sphere of radius R from that of a sphere of radius 

 R + r, in order to get the volume of the spherical shell 

 of mercury, we shall have for the weight W of that 

 shell 



W< 



8 



[ 3RV 4 3Rr 2 4 r 3 j sg 

 R 2 4 Rr 4 \r"- 1 s + 1000 oz. 



4*- 

 3 



This weight the celebrated Cotes calculated to be equal 

 to that of a globe of lead of 60 miles in diameter, or 

 upwards of 77,670,000,000,000,000 tons. 



The weight of the atmosphere can be much more ' 

 accurately estimated than its height, since the former 

 can be submitted to experimental examination, while ; 

 the latter is beyond our reach. But there are many 

 cogent reasons which preclude the notion that the atmo- 

 sphere is illimitable. Thus, we have seen that it has 

 weight ; that is, that it is a material substance, like all 

 other material substances, operated upon by the attrac- 

 tion of gravitation. There must be an elevation, there- 

 fore, at which its elasticity, or its tendency to expand 

 further upwards, is just balanced by its gravitating ten- 

 dency downwards, and which must therefore mark the 

 limit of its altitude. Again, if its extent were bound- 

 less, the moon and all the other planets would each, by 

 its attraction, appropriate a share of it ; and, as in tlie 

 case of our earth, the density of it would increase towards 



