White — Melting Point Methods at High Temperatures. 485 



the square of the time after freezing begins, and claims very 

 high accuracy. This method also involves some approxima- 

 tions and restrictions which, while not incompatible with excel- 

 lent agreement of the results, seem rather unnecessary, since 

 they can readily be avoided simply by a direct measurement 

 of the furnace temperature. Such a measurement is very 

 easily made ; it gives at once and without any uncertainty the 

 temperature difference on which the heat supply to the charge 

 depends, and leaves the observer a wider choice of methods in 

 controlling his furnace. Its results are also of easier inter- 

 pretation than with the " neutral body," whose temperature, 

 though a function of that of the furnace, is related to it in a com- 

 plicated way. In fact, no one seems to have attempted to deter- 

 mine heat absorption quantitatively by aid of the neutral body.* 

 The use of a single control element, though an improvement, 

 gives little more than a first approximation. The heat supply 

 to the charge is equal to GKT where Gis the external tempera- 

 ture gradient, that is, the temperature difference of charge and 

 furnace, K is a heat-now factor (conventionally called a radia- 

 tion factor), and T is the time. K varies with the absolute 

 temperature and this variation can be determined if a body of 

 known specific heat at different temperatures is available, or it 

 may often be negligible. f K also varies greatly with G, but 

 this variation is hard to determine, since the large values of 

 G which may occur during a melting often can not be obtained 

 at any other time.J The remedy for this diificulty is to keep 

 G constant throughout ; this has the further great advantage 

 of eliminating the effect of systematic errors in G, which can 

 hardly be avoided. This procedure, however, since it changes 

 the furnace rate, tends to aggravate another source of error, 

 the variation in temperature distribution in the furnace, as a 

 result of which the control-element reading bears a different 

 relation to the mean effective furnace temperature at different 

 times. Attempts to avoid, by special apparatus and procedure, 

 this source of error have shown it to be very serious at high 

 temperatures, but have not as yet indicated clearly the most 

 effective means of diminishing it. Another source of error 

 lies in the differences of temperature within the charge, and 

 especially the difference between the thermoelement, in the 

 center, and the outside surface, from which the loss of heat 



* See footnote, p. 460, previous article. 



f All the sources of error here treated have been hitherto disregarded in 

 work at high temperatures, though the least of thern may at times cause an 

 error of 5 per cent of the heat quantity measured. 



% Plato, though he does not appear to recognize this difficulty, does in 

 fact avoid it by making wha.t corresponds to a determination of K during 

 the violent temperature drop which immediately follows the freezing. But 

 this method seems open to grave objections, in spite of its excellent results 

 in his case. 



