the Unit-Steve Theory. 



329 



The above table shows conclusively that the molecular 

 volumes of the above compounds are additive, and, the only 

 satisfactory additive relation is that of valency. 



Having established additive relations at the melting-point 

 it is now necessary to discover what are the conditions for 

 the existence of similar ones above the melting-point. This 

 is possible, for Krafffc has given the specific gravities of a 

 large number of compounds for several temperatures up to 

 about 99° (Ber. 1882, xv. p. 1687). 



Krafft's determinations are suitable for the purposes of this 

 investigation for the following reasons : — 



(1) Owing to the purity of the compounds, that is, because 

 of their freedom from admixtures of other normal members 

 of the series and of related isomers. 



(2) On account of the undoubted accuracy of the experi- 

 mental results. 



It will be found that interpolation formulae with two 

 constants are, under the Conditions, quite satisfactory. 

 The general formula is as follows : — 



d T = d T ,{l-at + f3t 2 }, 



in which d T and d T , represent the specific gravities at the 

 temperatures T and T', the latter signifying the nlelting- 

 point, t = T — T', and a and /3 are temperature coefficients. 



IIL_Table of Constants. 



No. 



Hydrocarbon. 



M.W. 



W. 



M.P. 



T' 



d T . 



a. 



0. 



1. 



Dodecane, C 12 H 2G ... 



170 



74 | 261 



•7730 



- -0008668 



-•00000058 



2. 



Tridecane, C 13 H 28 ... 



184 



80 



266-8 1 7755 



- -000902 



-•00000013 



3. 



Tetradecane, C U H 30 ... 



198 



86 



277-5 | -7753 



-•000897 



-•000000106 



4. 



Pentadecane, C 15 H 32 ... 



212 



92 



283 j-7758 



-•000889 



-•000000106 



5. 



Hexadecane, C 16 H 31 ... 



226 



98 



291 



•7754 



-•000864 



-•00000028 



6. 



Heptadeeane, C 17 H 3G ... 



240 



104 



295-5 



•7766 



-•000895 



+ •00000027 



7. 



Octadecane, C 18 H 38 ... 



256 



110 



301 



; 



•7768 ! 



- -|000896 



+ •0000005 



In column 4 (Table IV.) the ratio V/W has the sam$ signi- 

 fication as before. In column 5 the ratios — - are calculated 

 by means of the expression 1~ at + /3t 2 . A comparison 



