46 Sir W. R. Hamilton on some 



at which the elastic force of its vapour is capable of overcoming 

 the pressure, not only of the air, but also that of the liquid 

 above. This temperature is therefore a little higher than that 

 which it would be if the liquid boiled under the pressure of the 

 air alone. Further, as the bubbles of vapour from the lower 

 liquid pass through the upper one, the temperature of the latter 

 is nearly the same. But while the bubbles from below pass 

 through the upper liquid, they carry vapour from the latter 

 along with them, so that the escaping bubbles are formed of a 

 mixture of the vapour of both liquids. Without doubt these 

 bubbles at the momeDt of their escape from the liquid have the 

 same temperature as the latter. But as the elastic force of the 

 vapour of the more volatile liquid would alone be able to over- 

 come the atmospheric pressure, the elastic force of the vapours 

 of both liquids together is greater than the pressure of the 

 atmosphere ; hence these vapours expand until the sum of their 

 tensions is just sufficient to overcome the pressure of the atmo- 

 sphere, and by expansion are brought to the lower temperature 

 observed. 



With the exception of this latter phenomenon, namely, that 

 the temperature of the vapour escaping from a mixture of two 

 liquids which do not mutually act upon each other, is less than 

 that of the liquid mixture, which phamomenon is not mentioned 

 by M. Regnault, my results are corroborated by him. They 

 were, however, made public by me eighteen years ago, and since 

 that time it has been known to what extent the law of Dalton is 

 applicable, and the deportment of the vapours of mixtures of two 

 liquids has been understood. 



VIII. On some Extensions of Quaternions. By Sir William 

 Rowan Hamilton, LL.D., M.R.I. A., F.R.A.S., Correspond- 

 ing Member of the French Institute, Hon. or Corr. Member of 

 several other Scientific Societies in British and Foreign Coun- 

 tries, Andrews' Professor of Astronomy in the University of 

 Dublin, and Royal Astronomer of Ireland. 



[Continued from vol. viii. p. 269.] 

 Section IV. 



[26.] TT^OR quines, the equations of condition between the 

 -i- 24 symbols /, . . u 3 amount (as haB been already 

 remarked) to 80 in all; namely to 8, 24, 12, 24, and 12 equa- 

 tions, included respectively in the five types last mentioned, and 

 sufficiently developed above, by the formula? (117) (118) (143) 

 (145) (148) (152) (153) (155) : which also enable us, with the 

 help of (141) (144), to determine the values of the four symbols 



