62 Dr. Meyer Wilderman on the Velocity of 



that case the conditions become very complicated and tbe 

 necessary data cannot be experimentally determined with anv 

 degree of accuracy, since the velocity with which the tube 

 assumes the temperature of the bath and of the liquid which 

 it contains cannot be investigated. 



Under the conditions of my experiments the following re- 

 lations hold good (though only approximately): — The velocity 

 with which the liquid in the U-tube (and therefore also the 

 liquid at its surface of contact with the solid) is cooled by the 



bath is ( )=C(T B — T), where T is the temperature of the 



upper layer of the liquid in contact with the solid while the 

 reaction is going on. The velocity with which the tempera- 

 ture of the liquid is raised during the reaction by the latent 



dT ' 

 heat of melting is / —j =C / (T — T), i.e. is directly pro- 

 portional to the velocity of reaction (T is the melting-point 

 of the liquid). Therefore the total rate of variation of the 

 temperature of the liquid at the surface of contact with the 



solid is, during the reaction, j- =C(T B — T) + C / (T J -T). If 



we assume that the temperature of the liquid in contact with 



the solidified mass remains constant during the reaction (this 



dT 

 cannot, however, be strictly correct), we get — =0. and 



T-T B C L T -T C 



dr 



= rv = constant, or ~ — -„- = ~ — r( .=k,i.e. the 



re- 



T -T ~ ' T -T B ~ C + C' ^ 



moteness of the temperature of the liquid in contact with 

 the solidified mass T from the melting-point T is, for all 

 values of the undercoolings, the same fraction of T — T B (T 

 cannot be =T during the reaction, since at the point of 

 equilibrium T no more reaction, i. e. no solidification, is 

 possible). I found, however, that this does not strictly hold 

 true, if the maximum temperature indicated by the small 

 thermometer in the platinum tube be taken as the true tem- 

 perature of the liquid at the surface of contact with the solid. 

 I concluded from this that the maximum temperature indi- 

 cated by the small thermometer T is still removed by about 

 0°1 or 0°*2 from the real temperature of the liquid at 

 the surface of contact with the solid. At the end of the 

 curve a diminution in the proportion between velocity of 

 reaction and the value T — T' was found. This I attributed 

 partly to the incomplete indications of the temperature by 

 the small thermometer, partly to the variation of temperature 

 of liquid in contact with the solid as the reaction is proceed- 

 ing, partly to the expected variation of the velocity constant 



