304- RoTjal Soa'efj/. 



experiments, he adopts the indications of the smaller thermometer in 

 the steam in preference to those of the larger thermometer in the 

 water. Of Dr. Young's sort of formulse, he notices that of the Aca- 

 demy'- and several others with exponents varying from 5 to 7. From 

 the elasticity at freezing, as given by Magnus, compared with four 

 of the Academy's experiments, he shows that for the range of obser- 

 vation the number 6 is preferable to 5 as an exponent ; but, as he 

 states, no formula of this sort with a constant index can be found to 

 agree with the observations throughout. 



The formula of Magnus he finds to agree with these observations 

 better than any of the others ; but being adapted to the air-thermo- 

 meter, and therefore not convenient for ordinary use, he gives his 

 own formula adapted to the mercurial thermometer, 

 500 + 22.5 log A 

 ~ 5 -log A ■ 

 t being the temp. Cent., and A the elasticity in atmospheres of 0"''7G 

 at zero, or 30 inches at 58° Fahr, ; /. the temperature being given, 

 the formula becomes 



logA=5 



" 225 -f^ 



The author compares with the experiments the formula of the 

 Academy and those of Southern, Coriolis, Tredgold, and one deduced 

 as above ; also that given by August, and the same modified so as 

 to give at freezing the elasticity found by Magnus ; also that of 

 Magnus, and the same reduced to the mercurial thermometer by the 

 data of Dulong and Petit ; and lastly, his own formula. Then as- 

 suming that the experiments of Magnus are represented by his for- 

 mula, he compares the other formula with it at every 10° from — 10° 

 to 100° Cent. He shows that for the range of their experiments the 

 Academy's formula is better than the others of Dr. Young's sort ; 

 but at low temperatures it is very erroneous. Southern's formula 

 at low temperatures is better than that of Coriolis, but at high tem- 

 peratures not so good. Tredgold and the other like it are better at 

 low temperatures than that of Coriolis, but worse at high tempera- 

 tures. August's formula is very erroneous ; and in its modified form 

 it is still worse, the errors increasing to about 10° or more, showing 

 that the theoretic considerations by which it is deduced are not 

 founded in truth. With the Academy's experiments, the errors of 

 Magnus's formula are — , but when reduced to the mercurial ther- 

 mometer they are all +, the mean of the whole being 0°'33. With 

 the new formula the errors are nearly balanced, the sums on the 

 thirty experiments being — l°-78 and +3°-55, in only two cases 

 amounting to half a degree. On the twelve experiments, at or near 

 the maximum, the errors are — 1°'12 and +0°'43. 



From zero to 100° the diflferences between the new formula and 

 that of Magnus are all of one kind ; and when reduced to tempera- 

 ture are less than 0°'4, which the author thinks to be within the 

 probable difference between the air and mercurial thermometers, and 

 within the errors of observation. 



