VOL. LXVII.] PHILOSOPHICAL TRANSACTIONS. 243 



By Mr. De Luc's equation for the air and obsserved temperature. By the manometrical equation 



and reduced temperature. 

 Coldest of the morning observations, from 25°.2 to 30 .oat33°.7 from 25°.2to30°.5at 33°.l'2 



Coldest of tlie ordinary obsei-vations 27 .1. . 4.1 .9. . 38 .7 26 . . . 35 . ..3> .97 



Hottest of the ordinary observations "6 . . . 8+ .5. . 36 .2 73 .5. 77 ... 36" .32 



On the Dole 59 .?. • 7 1 .5. . 27 .6 58 . . . 70 . . . 32 . 



Light house of Genoa 75 . ..79- • • 26 . 75 . ..79- . . 33 .40 



DeLaCaiUes 58... 30. 58 . . . 33 .35 



Zero at 32 .03 Zero at. . . . 33 .52 



From the mean of these observations, though the results are irregular among 

 themselves, it appears sufficiently evident, that if the morning observations on 

 Saleve had been retained, instead of being made exceptions from the rule, the 

 zero of the scale would have descended about 8*^; viz. from 69°.3 to 6l°.4 of 

 Fahrenheit, supposing always the equation 2.1 for each degree of temperature, 

 and the French toise, as the standard measure, to have been adhered to; for the 

 French toise bears to the English fathom, the proportion of 106575 to 100000; 

 therefore -rlffH = H:t' = '29''-4 + 32° = Sg".-!, denotes the relative posi- 

 tions of the 2 zeros, the intermediate equation fi^,? being to be subtracted 

 when the toise is used. But it has been shown, that the mean expansion of air 

 is really greater, for such temperatuies at least as the barometer can be applied 

 in, than what Mr. De Luc supposed it, in the proportion of 245 to 210; hence 

 it follows, that V.W = 25°. 18 -j- 32° = 57°. 18. will denote the relative posi- 

 tions of the two zeros; which, instead of almost 30°, are only distant from each 

 other a little more than 25°. 



From what has been said it is easy to see, that in calculating heights according 

 to Mr. De Luc's rule, when the temperature of the air is below his zero, which 

 we may take at 40°, the English measure being used, the common error in the 

 result will be equal to the sum of the two equations 2.1 + 2.45 = 4.55 for each 

 degree; which amounts to .YwP^fts for the 8° that the zero is too high. Above 

 40°, the former error -fA_i^ will be augmented by the difference of the equations 

 for each degree that the temperature is above his zero, viz. 2.45 — 2.1 = -fi^^-. 

 It may be proper now to compare these observations, with others that have been 

 made towards the pole and at the equator: from which it will appear probable, 

 that the rule which answers in middle latitudes, will not in the frigid and torrid 

 zones. In 1773, Captain Phipps, now Lord Mulgrave, commanding two of 

 his Majesty's ships then sent on discoveries towards the North Pole, measured 

 geometrically, with great care, the height of a mountain in Hakluyt's island 

 near Spitzbergen, and found it to be 1503 feet above the level of the sea. On 

 the morning of the 1 8th of August, the barometrical observations, at the sea- 

 shore and top of the mountain, when reduced and calculated, gave 1577 for the 

 same height, being -j-^^-j- to much. Hence it appears that, instead of the usual 



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