A T lAI 



ture, he determined the altitudes of hills both by the baro- 

 meter and alio by geometrical meafurement ; and (hewinn- 

 how to allow for the difference of temperature, he has 

 given a rule Ytir th« meafurement of heights by the baro- 

 meter, deduced from a prreater number of experiments, and 

 much more accurate than any before pubLfhcd. Sec his 

 •♦' Recherches furies Modifications del' Atmofphere," vol. ii. 

 Similar ru'es have alio been deduced from accurate experi- 

 ments by fir George Sliuckburg and general Roy, both 

 concurring to flicv/ that fuch a rule for the ahitudes and 

 denfities holds trur for all heights tbnt are acceffible to us, 

 when the clsfticity of the air is corrected on account of its 

 denfirv ; and the rcfalt of their expennicnts ihcwed, that 

 the dirference of the logarithn;s of the heights of the mer- 

 cury in the baiometcr at two ftations. multiphed by io,coo, 

 is equal to tl'.e altitude in Engliih fathoms of the one place 

 above the other ; that is, when the temperature of the air 

 is about 31 or 52 degrees of Fahrenheit's thermometer ; 

 and'?, certain qv.aiitity i/iore or lefs, according as the actual 

 temperature is different fiom that degree. See the princi 

 pies and application of thefe rules, detailed more at large, 

 under the article Barometer. But it may be here (hewn, 

 that the fame rule may be deduced iiidependentlv of a 

 train of cxperim.pnts, merely by means of the deinlty of 

 the air at the furface of the earth. Thus, let D denote 

 the denfity of the air at one place, and t/the denfity at the 

 other ; both mcafured by the column of mercury in the 

 barometer ; then the difference of altitude between the two 

 places will be proportional to the log. of D-— the log. of d, 



or to the log. of — . But as this formula exprefles'only the 



relation between different altitude;, w-ith refpeft to their 

 denfities. recourfe mufl be had to fomc experiment in order 

 to obtain the real altitude which correfponds to any given 

 denfity, or tlie denfity which correlponds to a given altitude. 

 The firil and moll natural is that which refults from the 

 known fpecific gravity of air, with refpeft to the whole 

 preffure of the atrnofphere on the furface of the earth. 



Now, as the altitude a is always as the log. of —, affume 



D 



Zr, fo that a may be = /j X log. — , where h will be of 



one conflant value for all altitudes : and to determine that 

 value, ftiopofe a cafe i 1 which we know the altitude a cor- 

 jrefpondip. J' to a known denfity d; as e. g. take a zz \ foot 

 or I inch, or fome fuch Imall altitude ; and becaufe the 

 denfity D may be meafured by the preiTure of the whole at- 

 rnofphere, or the uniform column of 27,600 feet, when the 

 temperature is 55^, 27,600 feet will therefore denote the 

 denfity D at the lower place, ar.d 27,599 the lefs dciifity d 

 at one foot above it ; confequently, we have this equation, 



viz. I = /j X loff. of — , which by the nature of loga- 



27599 



.a.^42044.8 h . , 



rithms is nearly = h Y. '^^/^ = 7 — — near')' 5 and 

 ' 27600 63551 



hence h = 6'?CCi feet, which gives this formula for any 



, 1> _ 



altitudein general; VIZ. a = 63551 X log. -^, or <j — 



6^551 X log.— feet, or dividing by 6, the number of 

 m 



M 

 feet in a fathom, 10,592 X log. — fathoms, where M de- 



notes the column of mercury which is equal to the pref- 

 fure of the atrnofphere at the bottom, and m that at the 



A T M 



top of the altitude a ; and where M and m may be taken ia 

 any meafure, eithu- feet or inches, &c. This formula is 

 adapted to the m>an trmper?t'jrc of the air 55' ; I ut it has 

 been found by the cxperim.ents of fir Geoigt Shuckburgh 

 and general Roy, that for ever)- degree of temperature, in- 

 dicated by the thermometer, difitrent from 5;'^, in the 

 medium between the ttmperati.res at the top and bottom 

 of the altitude a, that the' ahitude a will varj- by its 435th 

 part, which null be added v>hen the medium exceeds 55^, 

 and otherwife furtraaed. It jhould alfo be obfencd, that 

 a column of 30 inches of mercury varies its length I.y about 

 the 320th part of an inch for every degree of lict, or rather 

 the 9>':octh part of the whole volume. Tiiis formula may 

 be rendered much more conveniei.t for ufe by reducing the 

 faflor 10,592 to 10,00c by chanting the Icmpcratur- pro- 

 portionably from 55° : Thus, as the differenc-: 592 is the 

 lyth part of ti.e whole faftor io»592, ancl as 18 is the 24th 

 part of 435 ; therefore the char.ge of ter-.pcrature, corrc- 

 Iponding to the change of the factor /j, is 24^, which re- 

 duces the ;^° to 31^^. Confequcatlv, the formula becomes 



M 

 a = I GOOD X log. of — fathoms, when the temperature is 



31°, or nearly the freezing point ; and for ever)- degree abnve 

 that, the refjit mull be increafcd by fo many times its 435th 

 part, and proportionably diniinilhrd below it. 



This lornuila may be comp.iieu under the following 

 practical precepts : j. Obfervc t!-.: height of the barometer 

 at the bottom of any height or depth propoftd to be mea- 

 fured, together with the temperature of the mercury by 

 means of the thermometer attached to the baiometer, and 

 alfo the temperature of the air in the (hade by another 

 thermometer which is detached from the barometer. 2. Let 

 the lame thing be done alfo at the top of the faid height or 

 depth, and as nearly as polTible at the fame time ; reduce 

 th.le altitudes of the mercury to the fame temperature, if 

 it be thought neceffary, by correcting either the one or the 

 other, viz. augmenting the height of the mercury in the 

 colder temperature, or diminifhing that in the warmer, by 

 its 9600th part for every degree of difference between the 

 two ; and the altitudes of the mercury fo corrected are thcfc 

 denoted by M and m in the above formula. 3. Take out 

 the common logarithms of the two heights of mercur)- fo 

 correfted, and fubtraft the lefs from the greater, cutting ofT 

 from the right hand fide of the remainder three places for 

 decimals, and then thofe on the left hand will be fathoms 

 in whole numbers, the tables of logarithms being fuppoled 

 to comprehend feven places of decimals. 4. Correct the 

 number lait found for the difference of the temperature of 

 the air, in the following manner ; viz. take h.ilf the fum ef 

 tl'.e two temperatures of the air, (hewn by the detached 

 thermometers, for the mean one ; and for every degree by 

 which this differs from the ftandard tcm.perature of 3i'-, 

 take fo many times the 435th part of the fathoms above 

 found, and add them if the mean temperature be more than 

 31°, but fubtraCi them if it be below 31', and the fum or 

 difference will be the true altitude in fathoms, or being mul- 

 tiplied by 6, it will give the true altitude in Engliih te-et. 



Example I. To find the altitude, when the (late of the 

 barometers and thermometers is as follows, viz. 



A* 



