NOTES TO BOOK X. :>!>! 



deals with fifth and sixth powers, as with arithmetical and 

 geometrical ratios. Dr. Dalton had supposed that tin 

 expansion of mercury being as the square of the true tem- 

 perature above its freezing-point, the expansive force of 

 steam increases in geometrical ratio for equal increments 

 of temperature. And the author of the article Steam in 

 the Seventh Edition of the Encyclopaedia Britannica (Mr. 

 J. S. Russell), has found that the experiments are best 

 satisfied by supposing mercury, as well as steam, to expand 

 in a geometrical ratio for equal increments of the true 

 temperature. 



It appears by such calculation, that while dry gas 

 increases in the ratio of 11 to 8, by an increase of tem- 

 perature from freezing to boiling water ; steam in contact 

 of water, by the same increase of temperature above boil- 

 ing water, has its expansive force increased in the propor- 

 tion of 12 to 1. By an equal increase of temperature, 

 mercury expands in about the ratio of 9 to 8. 



Recently, M. Magnus of Berlin, Holzmann and Reg- 

 nault, have made series of observations on the relation 

 between temperature and elasticity of steam. See Taylor's 

 Scientific Memoirs, Aug. 1845, vol. iv. part xiv., and Ann. 

 de CJiimie. 



Prof. Magnus measured his temperatures by an air- 

 thermometer; a process which, I stated in the first edition, 

 seemed to afford the best promise of simplifying the law of 

 expansion. His result is, that the elasticity proceeds in a 

 geometric series when the temperature proceeds in an 

 arithmetical series nearly; the differences of temperature 

 for equal agumentations of the ratio of elasticity briuir 

 somewhat greater for the higher temperatures. 



The forces of the vapours of other liquids in contact 



