Molecular Constitution of Water. 467 



Ap 2 being negative when denoting a diminution. The values 

 of AR marked " calculated " in the last table are derived 

 from the values of Ap 2 by this formula. Ketteler considers 

 his values of n reliable to within a few units in the fifth decimal 

 place, which implies that we should not have given the values 

 of 10 6 R to more than five figures, and should not expect our 

 values of 10 6 AR, as calculated, to agree closer than within a 

 few units in the tens place of digits with the found values, as 

 the table shows to be actually the case. Thus for the two 

 ingredients of water the temperature effect for 10° seems to 

 be an increase o£ about 2*5 parts in 10,000, and with this 

 taken into account the composition of water as determined 

 optically is in agreement with that found from its expansion. 

 For (?i 2 -l)/(n 2 + 2)p for 2 (trihydrol) and 1 (dihydrol) we 

 have by (13) the values 



•20968 and -20434. 



3. Compressibility of Water and Dissociation of Trihydrol 

 into Dihydrol by Pressure, 



One of the peculiarities of water is that its compressibility 

 at low pressures diminishes with temperature to a minimum 

 and then increases. Denoting volume of a gramme by v we 

 can write the mixture formula for volume 



v—p x v x +p 2 v 2 , ..... (14) 



and denoting pressure by / we have 



dv dvi dvo , \ dvo ,., cx 



df=Pw +P2 W + {v ' 2 ~ Vl) W' ' ' (15) 



In this equation we have dv/df from the experimental com- 

 pressibilities of water at different temperatures, we know p l 

 and p 2 from previous sections, and also v 2 —v x , but there 

 remain three unknowns dv-i/df, dv 2 /df, and dp 2 /df } and their 

 variations with temperature are also unknown. To get 

 farther it is necessary that we should estimate the compres- 

 sibilities of our two ingredients. I propose to do this for 1 

 (dihydrol) in the following manner. In " The Laws of Mole- 

 cular Force " (Phil. Mag. [5] xxxv.) I have shown that within 

 a limited range of temperature and pressure the characteristic 

 equation for liquids is such that 



^T^=|/-|5RrT, .... (16) 



approximately, where I is the virial constant or parameter_of 



