510 



But A = A 1 -T-^-7ir]' and Dk = -—~--, so that 



1+y 7Y- 1+y 



7*2 is therefore always the higher of the temperatures, between 

 which the experimentally determined expansibility holds. When we 

 now apply this to Sodium, where 278 . iO^*^ has been found for « 

 between 101° and 1H8 C. (Hagen), we calculate {T, = 168-f 273=44r 



0,573 0,573 



or « = 



1970 — 0,573X441 1717 

 0,563 0,563 



334. 10-6 



380. 10-6' 



1730-0,563X441 1482 



As the coefficient of expansion near the melting point will prob- 

 ably be still somewhat too small (we need only think of water, 

 mercury, etc.), the found value 278 is probably to be raised to 334. 

 If we have to make a choice, the higher of the two assumed critical 

 temperatures, viz. 1970°, seems in any case to be nearest the truth. 



If we assume that the determined coefficient of expansion really 

 holds for the mean temperature (101 + 168): 2 = 134°,5 C. = 

 =: 408° abs., we should have calculated the values from 330 to 

 375.10^6, which are only slightly lower. 



Also from Vanstone's density determinations we can determine 

 the value of 7', hence also of «. Vanstone found namely at 110°, 

 184° and 237° C. resp. the values = 0,9265,0,9058 and 0,8891, 

 yielding y' = 280 . 10-^ between the two first, and y = 315 . 10— ^ 

 between the two last. Or 295 . 10— "^ between the first and the 

 third. If we assume this last value to hold at the mean tempera- 

 ture 173°,5, at which D = about 0,909, then 



295 .10-6 



a = — --— = 325 . 10—6 follows from cc = y' : D (see above), 



0,91 ' ^ 



hence very near the above calculated value 330. 



If we now assume the newer value 325 . 10 -^^ {q 13e jy,Q|.g ^QP^u-a^g 

 than the much older value 278, determined at somewhat lower tem- 

 peratures, then the value calculated above from 7 with 7^^1970° 

 appears to be much nearer 325 than the too high value 380, cal- 

 culated with Tk= 1730°. Tjc lies therefore near 1970°, and (according 

 to the density determinations) sooner somewhat higher than somewhat 



