739 



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 + 225 log A 

 ~ 5— log A 



t being the temp. Cent., and A the elasticity in atmospheres of 0™'76 

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

 the formula becomes 



lo<^A=5— -. 



225 +t 



The author compares with the experim^ents 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 Pe|it ; 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 — 1°*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 — l°-r2 and +0°*43. 



From zero to 100° the differences between the nev/ formula and 

 that of Magnus are all of one kind ; and v/hen 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. 



He then gives a table of temperature corresponding to elasticity 

 of vapour in atmospheres. Also modifying his formula, 



log/6-47712125- --J^, 

 873 -\-t 



