THERMOMETEil. 



pentnciils on the heat of boihng water, at different heights 

 above the level of the fea, he hath found, that the height of 

 I'.is thermometer, plunged in boiling water, may be exprefTed, 

 i:-. all flates of the barometer, by the following formula, -vix. 



— — — log:. V — a =; T : in which y denotes the height of 

 200000 ^ -^ -^ " 



th? barometer in fixteenths of a Parifian line, T the height 

 of a thermometer, plunged in boiling water, above melting 

 ice, in hundredths of a degree of his fcale ; and a the con- 

 ilant number 10387. 



By logarithms he always means the tabular or Briggian 

 logarithms, and confiders the feven figures given by the 

 tables, befides the index, as integral figures, ;'. e. he con- 

 f.ders tlie eighth figure of the logarithm as Handing in the 

 place of units. But as it is more ufual with mathemati- 

 cians, aud, in general, more convenient, to coiifider all the 

 figures after tiie index as decimals, the number which M. do 



Luc exprefles by — ~ — log. y, would in that cafe be 



200000 



99 X loo 



log- Ji ; Of 99 X 50 log. y. However, in the 



fequel, M. de Luc's notation is retained. 



Now if care were taken by the above formula, or in any 

 other way, to adjuft the boiling point to the main height of 

 the barometer in every country, the inftruments of the fame 

 country would always be confiftent ; but thofe of different 

 countries would ftill difagree ; that is, they would exprefs the 

 fame temperature differently, though tlieir fimilar intervals 

 ftould be fimilai-ly divided ; for in every fcale, the number 

 of degrees above or below melting ice, by which any given 

 temperature is expreffed, will be as the value of each degjree 

 inverfely ; that is, if each be a given part of the fundamen- 

 tal interval, as the value of the fundamental interval in- 

 Terlely ; but if the degrees of different fcales be different 

 parts of the fundamental intervals, as the value of the fun- 

 damental interval inverfely, and the number of degrees con- 

 tained in it diredtly. 



In order, therefore, to compare the thermometers of dif- 

 ferent countries, the proportions of their fundamental inter- 

 vals to each other mull be afcertained, or we rauft have fome 

 means of finding, upon one fcale, the place of the boiling 

 point of another. For this piirpofe, a general folution is re- 

 <juslke of the following problem, viz. the fundamental in- 

 ttrval being given for a given height of the barometer, 

 to find the fundamental interval for any other given height 

 of the barometer. The folution is fumifhed by M> de 

 Luc's relearches ; and his formula, above given, is re- 

 duced to Englifli meafurcs, and adapted to Engliili in- 

 ftruments, by Dr. Horfley. As the fubjeft is curious 

 and important, we Ihall fubjoin the proeefs he has pur- 

 fued for tliis purpofe. It is but feldom that the baro- 

 meter in this country flar.ds fo low as 27 Paris inches. 

 Its main height upon the plain country about London is 

 near 30 EngUfli inches. It may, tlicretore, be proper for 

 the London workmen to fix their boiling point when the 

 barometer is at 30 inches. Fahrenheit's divifion of the fcale, 

 which makes 180 degrees between melting ice and boiling 

 water, and places the point o at the 3 2d degree below melting 

 ice, may be retained : and the thermometer thus ccnftrufted 

 is called by Dr. Horfley, Bird's P'ahrenheit, bccaufe Mr. 

 Bird, he apprehends, is the firfl; workman who took the pains 

 to attend to the ftate of the barometer in making thermo- 

 meters, and has always fixed the boiling point when his ba- 

 rometer has ilood at 30 inches. 



T, then, being pv.t f^^r the height of a thermometer 



7 



plunged in boihng water, above nicltuig ict, in lo&dllio ol 

 a degree of De Luc's fcale, in any given ftate of the baro- 

 meter ; let fe> denote the fame height in loodths of a dcgrte 

 oi Bird's Fahrenheit ; put y for the height of the barome- 

 ter, in i6ths of a Paris line ; -u, for its height in Paris 

 fines ; .r, in loths of a Paris inch ; 2, in loths of an Eng- 

 hlh inch ; and for 10387 put a ; for 16, 6 ; for 10, c ; for 

 12, d; and let E :md F reprefcnt numbers expreifing the 

 proportion of the Englilli foot to the French foot. 



M. dc Luc hath found that, whatever be the value ot y. 



99 



■log. 



a ■■ 



T. But log. y = log. V + log. i ; 



200000 



and log. V = log. x + log. d — log. c ; and log. w = log. 

 « + log. E — log. F ; therefore log. y = log. z + log. 



99 



E + Jog. J + log. 1/ 



■ log-. F — log. c ; and — — — log. 

 ^ ^ 200000 ^ 



99 



+ i^ooSS ^°S- ^ + ^°S- '^ + ^°^- ^ - ^°^' ^ 



log. 



But 



F — log. c — a = 



to the Engliflt as 2. 13 15 to 2 



- 4171-55 = T; and 



99 : 



z'SS^ ^°S- E + log. J + log. 6 - log. 

 = — 4171.55; the French foot being 



Therefore - — — — log. c 

 200000 



99 



20000000 



log. 



41.7155 = 



= the height of the thermometer, plunged in boiling 



water, above melting ice, in degrees of De Luc's fcale, 

 when the height of the barometer in tenths of an EagliOi 



T 



inch, is z. For a write 300 : then = 80.002 ; which 



-^ 100 ' 



is therefore the height of the thermometer, in boiling water, 

 above melting ice, in degrees of De Luc's fcale, when the 

 barometer is at 30 inches Enghfli. And in the fame ftate of 

 tlie barometer, the height of the thermometer plunged in 

 boiling W3ter, above melting ice, in degrees of Bird's Fah- 

 renheit, or , is 1 80. Hence the numbers T and © 



too 



are in the conftant proportion of 809 and 1 800, whatever 

 be the value of z. For the change produced in the heat 

 of boiling water, by any change of z, being always the 

 fame for both thermometers, the temperature expreffed by 

 T in parts of one fcale is always the fame, as ex. 



preffes in parts of the other ; and therefore putting - - 



and — for the values of the loodthpart of a degree of tlie 



T 



icales of De Luc and Bird refpeftively, the fraftions — , 



^ are always equal, and T, Q are m the conftant propor- 

 tion of the invariable numbers L, B : confequently, when 

 the proportion of T and is determined for any particular 

 value of », it is found generally for all : confequently T : 



:: 8co : 1800. And T = -„-'- = — ^- e very nearly 



IBCO 2000 



in air values 01 -.; : and fubftituting this val jc for T in the 



equation 



