462 W. P. White — Melting Point Determination. 



the end of the melting, the only disadvantage will be the loss 

 of time in taking the first part so slowly ; and this may some- 

 times be less objectionable than the remedy — which is, to make 

 separate observations on the furnace temperature and thus 

 keep the external temperature gradient constant. 



Heat Distribution Within the Charge. 



The next three causes of obliquity constitute the chief prac- 

 tical problem in melting point work. They depend upon dif- 

 ferences of temperature within the charge and could be avoided 

 if thorough and effective stirring were possible. They are less 

 detrimental in the determination of freezing than of melting' 

 points, and are less also in metals whose high thermal conduc- 

 tivity is in part a substitute for stirring. To them it is due 

 that, other things being equal, the melting point of a salt usually 

 cannot be determined quite as accurately as that of a pure 

 metal or as its own freezing point. They may, however, be 

 greatly diminished by proper experimental arrangements. 



IV. The regular and normal temperature gradient across 

 the charge. — The error and uncertainty resulting from the fail- 

 ure to stir has often been greatly overestimated. The charge 

 as a whole may present great temperature differences, but the 

 thermoelement does not record all these at once. It accounts 

 only for the portion immediately surrounding it, and when this 

 portion melts it will show a " break " in the temperature curve. 

 Toward this small system of element and surrounding material, 

 the outer portions of the charge act in many respects as so 

 much foreign matter — though foreign matter which is particu- 

 larly troublesome, on account of its own heat absorptions. 

 Their effect can be investigated with quite enough exactness 

 for the present purpose, by the device already used, of treating 

 the melting charge as a body of variable specific heat. 



1. Expression for the temperature distribution in an 

 ordinary charge. — As a heated charge is brought toward its 

 melting point, the supply of heat is usually constant, and then 



the rate of temperature rise, — , soon becomes the same at all 



at 



points. The resulting temperature distribution at any instant 

 may then be found to a sufficiently close approximation as 

 follows : Suppose, first, that the body is spherical with a radius 

 equal to R, and the heat flow is entirely along radial lines. 

 Consider a spherical surface, A, at a distance, r, from the center 



47Tf 3 



of the sphere. Its area is 4t7rr 2 ; the inclosed volume — — . The 



flow of heat across it may be expressed in two ways: (1) 

 Directly, as the product of area, conductivity and tempera- 



