Boiling Point of Liquid Hydrogen under Reduced Pressure. 227 



The generating functions under view are real in the sense of Cayley 

 and Sylvester. Enumerating generating functions of various kinds 

 are obtained by assigning equalities between the suffixed capitals 



X.j, -X. 2 , ...... -A. s . 



Putting, e.g., X x = X 2 = ...... = X s = x, 



we obtain the function which enumerates by the coefficient of x n , in the 

 ascending expansion, the numbers of solutions for which 



It will be gathered that the note of the following investigation is 

 the importation of the idea that the solution of any system of equations 

 of the form 



Ajfltj + A 2 a 2 + A 3 a g + ...... + A s a s > 



(all the quantities involved being integers) is a problem of partition 

 analysis, and that the theory proceeds pan passu with that of the 

 linear Diophantine analysis. 



" On the Boiling Point of Liquid Hydrogen under Keduced Pres- 

 sure." By JAMES DEWAR, M.A., LL.D., F.RS. Eeceived 

 and Eead December 15, 1898. 



The June number of the * Proceedings of the Chemical Society ' 

 contains a paper by the author on " The Boiling Point and Density of 

 Liquid Hydrogen." A resistance thermometer made of fine platinum 

 wire, called No. 7 Thermometer, was used in the investigation. It 

 had been- -carefully calibrated, and gave the following resistances at 

 different temperatures : 



Resistance. 

 Temperature. Ohms. 



+ 99-lC. 7-337 



+ 75-3 6-859 



+ 51-4 6-388 



+ 25-7 5-857 



+ 0-7 5-338 



-78-2 . 3-687 



-182-6 1-398 



-193-9 1-136 



-214-0 0-690 



The zero of the thermometer in platinum degrees was -263*27. 

 Mr. J. D. Hamilton Dickson, M.A., Fellow of Peterhouse, who con- 

 tributed a paper to the ' Phil. Mag.' for June, 1898, on "The Eeduction 



