46 M. G. Van dcr Mensbruophe on the Variations 



oto' 



whicli soliilificiition commences ; there it maintains itself, and 

 then rises again a fraction of a degree, ending by decreasing 

 very rapidly until the alloy passes through its maximum den- 

 sity ; at this point the temperature reascends about 7°, and 

 this in spite of the cooling, and then descends, following a 

 regular course. Darcet's alloy exhibits similar phenomena. 



M. vSpring concludes from these singular facts that it is im- 

 possible to determine the specific heat even at the temperature 

 of the maximum density, since, notwithstanding the cooling, 

 the temperature rises a considerable quantity. Now this is 

 how, in my theory, I succeed in explaining in a very simple 

 fashion these anomalies, so contrary to all receiA^ed ideas, jn^e- 

 sented by the alloys of Rose and Darcet, as well as by 

 others : — 



Let us resume our equation (3), and apply it successively 

 to the three temperatures t' ^ t" ^ t'" — of which the first desig- 

 nates a temperature a little above that of the maximum density, 

 the second that of the maximum density itself, and the third a 

 temperature a little below t" \ we can then, accentuating in 

 the same way the corresponding values of K, k^ S, and T, and 

 supposing a negative change of temperature (that is, a cool- 

 ing) as in M. Spring's experiments, write: — 



-KW =-^W ■\-Kt'cl (S'^'); 

 -Wdt" =--k"dt" -^M'd \^"^)\ 



-W"dt"'= -k"'dt'"-\-kt"'d {^"'^^^Pj' 



Now, as I have said above, the variation of the term which 

 depends on the surface may, at least starting from pretty large 

 values of S, be regarded as notably higher than that of h 

 Under these conditions the sign of the observed specific heat 

 K would be precisely the same as that of the term containing 



S and — . But at the maximum of density each of the two 



terras of the second member cancels itself; in fact, since the 

 volume passes to the minimum, the quantity ^kl'dt" of heat 

 to be supplied to cause the body to pass from the point which 

 immediately precedes or follo"SAS the volume at the minimum 

 itself must be nil. As for the term which is a function of S, 

 on the one hand the surface S passes through a minimum to 

 the point we are considering ; on the other, the potential 

 energy ^" passes through a maximum (neglecting its sign) ; 

 for the molecules of the alloy innnersed in the oil are then 



