BAR 



^oiifitics, mcafiirod by tlie inches of mercury wliich tlieir 

 rlailicity fupports in the barometer, art ju'.'t the ten thou- 

 fandth parts of the fathoms contained in the correfpondiiig 

 portions of the axis of the atmofphtrical logarithmic. 

 Therefore if we multiply our common logarithms by loooo, 

 they will exprefs the fathoms of the axis of the atmolphcri- 

 cal logarithmic. Our logarithms contain the index or cha- 

 rafteriftic, which is an uiteger, and a number of decimal 

 places. Let us then remove the integer place four figures 

 to the right hand ; thus, the logarithm of 60 is 1.7781J 13 ; 

 multiply this by 10000, and we obtain 17781 j'-sV^j. 



This reafoning may be eafily applied to praAice, thus ; 

 obferve the heights of' the mercury in the barometer and at 

 the upper and lower ftations in inches and decimals ; take 

 the logarithms of thefe, and fubtrad the one from the o-.her ; 

 and the difference between them, accounting the four fijl 

 decimal figures as integers in the manner now propoftd, is 

 tlie difference of elevation in fathoms. 

 E.G. 



Mercurial height at the lower ft-ation 29.8 - 1.4742 163 

 At the upper rtation 29.1 - 1.4638930 



Difference of logarithms X loooo - - 00103.233 

 ot- 103 fathoms and 444-ct of a fathom, which is 619.192 

 feet or 619 feet 4J inches, differing from the approximated 

 value before found about f an inch. We have thus availed 

 ourfelves of tlie familiar and very intelligible illullration of 

 the method of meafuring heights by means of the barometer 

 propofed and reduced to praftice by Dr. Hallcy, given by 

 an ingenious anonymous writer in the " Encyclopedia Bri- 

 tannica" art. " Pneumatics." By this method it was 

 found that when the temperature of air and mercury was 

 32° of Fahrenheit, the difference of the logarithms of the 

 mercurial heights was precifely equal to the number of fa- 

 thoms of elevation ; and it was verified upon the whole in 

 praftice, by geometrical furveys and meafurements. 



The utility of it, however, was of very hmited extent ; and 

 it was feldora adopted, till M. De Luc firft and after him fir 

 George Shuckburgh and general Roy, introduced in con- 

 fequence of numerous obfervations and well-conducled expe- 

 riments futh improvements and correftions as were found 

 to be neceflary for expediting the pradlice of it and render- 

 ing the refult of it accurate. 



M. De Luc's apparatus of portable barometers, and their 

 annexed thermometers, with which he made his obfervations, 

 hath been already defcribed. In the conltrutlion of his 

 barorneters he guarded a^ much as pofiible againft the im- 

 perfedionsand faults to which thofe of the common fort are 

 lubjedf. The error arifing from the repulfion of 'he mercury 

 by the glafe tubes he remedied by fubilituting a fiphon ba- 

 rometer inftead of the fimple upright tube, fo that the re- 

 pulfion of the two leg,s of the fiphon might eounteraft 

 itlelf. Another error refulting from air and mciilure in the 

 barometrical tubt he obviated by boiling the niercary in the 

 tube, and by other precautions. And he alio fii^.v.s !iow to 

 coiTcail miilai^'.s in the ellimation of heights that are owing 

 to variations of the deofity of the mercury, and alfo of the 

 air, occafioned by heat and cold, by means of allowances de- 

 pending on two thermometers, one attached to the frame of 

 the barometer itfelf and the other expofed to the open air 

 for fliewing its degree of heat ; and thefe thermometers are 

 to be noted botli at the top and bottom of the hill. From 

 the life of iLiii apparatus in a great variety of obier\ation3 

 he deduced a rule for calculating the heights of places, 

 which he verified by numerous experiments. Dr. Mafke- 

 lyne and bifliop Horfley have reduced his rule from the 



BAR 



French to the Englifh meafure, and adapted it to the ther- 

 niometers of Fahrenheit's Icale. M. De Lue ( fee Recherches, 



Sic. vol. i. p. 362 364) in the winter feafon, heated the air 



of his room to as great a degree as pofiible, and obferved 

 the rife of the barometer occafioned by the diminution of 

 its dcnfity or fpecific gravity by heat ; and he alfo noted 

 the height of the thermometer, both before and aft^r the 

 room was heated. Hence he deduced a rule that when the 

 barometer is at 27 French inches, which was the cafe in 

 this experiment, an increafe of heat from freezing to that of 

 boiling water will raife the barometer 6 lines, or -j^th part of 

 the whole. But when the barometer is higher than 27 

 inches, this variation muft increafe in the fame proportion ; 

 or it will be always ^i^th of the height of the barometer. 

 Confequently if the height be called B, the rife of the baro- 

 meter correfponding to an increafe of heat from freezing to 



B 



lefs 



boiling water, will be -^^ ; and as it will be lefs for a 



54 

 difference of heat, if tlie number of degrees marked on the 

 thermometer between freezing and boiling water be called 

 K, and the rife of the thermometer from any given point 

 be called If, the correfponding rife of the barometer will be 



X ... , by the increafe of heat from the given point 



54 ^ 



by the number of degrees H. With a decreafe of heat, J{ 



would fignify the degrees of decreafe, and the barometer 

 R Ff 



would fink by X — — . The fixed temperature of 



54 

 heat to which M. De Luc reduced his obfervations of the 

 barometer is jth of the interval from freezing to boihng wa- 

 ter above the former point ; and if the thermometer was 



B .. H 



higher than this degree, he fubtradled- 



if it 



54 K 



lower, he added this quantity to the obferved height of the 

 barometer; and he thus obtained its cxaft height, or fuch as it 

 would have been, if the denfity of its quickfilver had been 

 the fame as aniVers to the fixed degree of temperature. 

 He thus corrected the height of both his barometers, that 

 at the bottom and that at the top of the hill, for the parti- 

 cular degree of heat, indicated by a thermometer attached 

 to the barometer at each ftation. Thefe corrected heights 

 of the barometers were thofe which he ufed in his calcula- 

 tions. Then, calling thefe two altitudes of the barometer 

 at the lower andattheuppcrilations,/? and 3, and ufing log.i?, 

 and log. ^ for their logarithms, taken out of the common 

 tables, and alFuming the four firft places of figures after the 

 index as integers, and the three remaining figures as deci- 

 mals, and putting C for the m.ean height of a thermometer, 

 expofed to the air at the top and boiton-; of the hill, the 

 freezing point being o, and the point of boihng water at 80, 

 he found by his experiments t'aat the height of the hill 

 would be given in French toifes, when C was 16^, by mere- 

 ly taking tiie difference of the logarithms of the 

 heights of the barometer, or logr B — log. b ; and ia 

 any other degree of heat, would be greater or lefs in pro- 

 portion as the rarity of the air was greater or lefs than in 

 the fixed temperature ; or greater or lefs, by ^T-jtli part of 

 the whole, for every degree of the thermometer reckoned 

 from the fixed tempeiature 164 : and confequently the 

 height of the place would be expreffed generally in French 

 toifes by this formula, viz. log. B — hg. b -f- log. ^ — log. b 



= log. B — log. * X I + 



The re- 



2I5' 215 



duftion of this formula to Englifh nieafuie and to the fcale 



of 



