38 THE COMPRESSIBILITY OF CARBON, SILICON, 



0.0000003, or only a tenth of that in graphite. A result of the same order 

 would be reached by comparing the linear coefficients of expansion of dia- 

 mond with that of graphite, Fizeau's values for these data being respec- 

 tively 0.0000012 and 0.0000079. If Dupre's equation, connecting com- 

 pressibility and coefficient of expansion 



P = f* 



p a'A' 2 T 



be assumed to hold for a single element, the compressibility of diamond 

 computed from that of graphite would be found to be about 0.0000007. 

 The mean between these guesses, namely, 0.5 X 10~ 6 , may be taken as the 

 most probable value for the present, until an experimental determination 

 is possible, of the compressibility of diamond. 



The difference between actually determined compressibilities of the dif- 

 ferent allotropic states of a given element is exhibited for the first time 

 by the comparison of the result recorded above concerning red phos- 

 phorus, with that found some years ago by Richards and Stull concerning 

 white phosphorus.* The former of these values, as found by the present 

 research, is 8.8 X 10~ 6 , while the latter of these values, as found in the 

 earlier investigation (between 100 and 150 pressure units), is 19.9 X 10~ 6 . 

 Thus the compressibility of the more compact modification of phosphorus 

 is less than one-half the compressibility of the less compact variety. This 

 is a highly interesting fact not only in itself as the first instance on record 

 of such relationship, but also in relation to the theory of compressible 

 atoms with which it is entirely consistent, as well as in connection with the 

 preceding discussion concerning the allotropic forms of carbon. Red phos- 

 phorus, having less than half the compressibility, is only about 20 per cent 

 denser than white phosphorus, whereas diamond is 36 per cent denser than 

 graphite. Accordingly, one would expect diamond to be not much more 

 than one-quarter as compressible as graphite, if as much as this. It will 

 be seen at once that the comparison, although of course it is capable 

 of giving nothing more than the order of result to be expected, substan- 

 tiates the approximations given above concerning carbon, and adds its 

 share toward giving the result more weight than would be adjudged to 

 a mere guess. 



The comparison of sulphur with selenium is interesting, because, 

 although the two elements have decidedly different atomic volumes, 15.7 

 and 18.5, respectively, their compressibilities are almost alike, 12.3 and 

 11.6 respectively; moveover, such difference as they exhibit is in the oppo- 

 site direction from that in the atomic volume. Among the causes likely 

 to bring about this greater compressibility of sulphur, its weaker cohesion, 

 as indicated both by its volatility and its slight tensile strength, may be 



*Carnegie Institution of Washington Publication No. 7, p. 37. 



