VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS- 227 



cepted between them, in toises and 1000th parts, reckoning the 3 figures to the 

 right hand decimals, and the others integers, the index being neglected. This 

 temperature of 69°.32, when the logarithmic differences give the real height 

 without any equation, is reduced to 39°.74, the new zero of Mr. De Luc's 

 scale, when his formula is adapted to English fathoms and 1000th parts, instead 

 of French toises. And lastly, when the mean temperature of the air is above 

 or below 39°.74, an equation, amounting to -nh'-w-o P^rts of the logarithmic 

 heiglit for each degree of difference, is, in the first case to be added to, and in 

 the last subtracted from, that result, in order to obtain the real altitude. 



In Mr. De Luc's book, the experiments for ascertaining the expansion of the 

 quicksilver, are not given in detail ; neither are the particular temperatures of 

 the barometers specified. Tiie winter season was however chosen for the pur- 

 pose ; one being left in a cold room, and the other in a closet, heated as high as 

 could conveniently be sufiercd. The operation having been repeated several 

 times without any essential difference in the results, this general conclusion is 

 drawn, that between the temperatures of melting ice and boiling water, the ex- 

 pansion of the quicksilver is exactly 6 French lines, or .532875 decimal parts of 

 an English inch. But it is to be observed, that the barometer stood then at 

 28.77525 ; whereas, if it had stood at 30 inches, it would have been .555556, 

 because the expansion is in proportion to the length of the column. Further, 

 the interval between tiie freezing and boiling points, in all thermometers, varies 

 with the height of the barometer, or weight of the atmosphere ; and it is the 

 custom in England to make thermometers when the barometer stands at 30 

 inches; that is 1.225 or 13.8 French lines, higher than when Mr. De Luc's 

 boiling point was fixed : and since from his experiments it appears, that each line 

 of additional height in the barometer, raises the boiling point T-rVr P^''t of 

 the interval between that and freezing, it follows that VWt = 0.158 X 13.8 := 

 2°.2, will denote the number of degrees, that Mr. De Luc's boiling point is 

 lower than that of English thermometers ; which reduces it to 200.8 of Fahren- 

 heit, and makes the interval between freezing and boiling only 177-8 degrees. 

 Hence the expansion .555556, above found, must be increased in the proportion 

 of 177-8 to ISO, which gives for the total .5024297 or .56243, on a difference 

 of temperature of 180°. Thus the expansion for each degree, supposing it to 

 be arithmetic;)], or uniformly the same in all parts of the scale, will be 

 .0031246]. Having now shewn the expansion of quicksilver in the tubes of 

 barometers resulting from the Geneva observations, I shall next proceed to give 

 some account of those I made for that purpose. 



Sect. 1. Experiments on the expansion of quicksilver. — The experiments made 

 for this purpose were numerous as well as various, and were therefore subdivided 

 into several classes. To give a minute detail of them all, would be extremely 



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