474 Dr. M. Wildermann on Real and Apparent 



the temperature of the room (through this, the necessity of 

 using a colder bath at a higher temperature of the room) . 



The convergence-temperature is, in the first instance, to be 

 investigated at the temperature of the room at which we carry- 

 out our experiments. By determining the convergence- 

 temperature under successive changes of the temperature of 

 the ice-bath, we can get to the temperature of the bath at 

 which the convergence-temperature is at the given temperature 

 of the room very near to the freezing-temperature, i. e. to the 

 condition when t g — 1 is small. The accurate determination 

 of the convergence-temperature from measurements of the 

 velocity of overcooling is by no means so easy as might at 

 first glance be thought. Even if the greatest care be taken, 

 we cannot determine it with much greater accuracy than 

 to '1°. We are obliged to make a series of readings : the 

 falling of temperature must be so slow that the reading-error 

 does not exceed - 001° or '002°; we are therefore obliged to 

 keep the ice-bath constant during a very long time. From 

 Table I A. it will be seen that C = '003°, the velocity of cooling 

 of my beaker is therefore only '0003° per minute when 

 t q — t = '1°. Thus we come into regions where correct 

 measurements of temperature even at considerable intervals 

 of time are no longer possible and where observations are 

 of no use, since no air-chamber can be arranged with greater 

 accuracy than to '01°, and a change of temperature of the 

 air-chamber is followed by a still greater change of the con- 

 vergence-temperature, i. e. this has no constant value. But 

 the chief difficulty lies in getting the convergence-temperature 

 from calculation of the observed results. This is the reason 

 why we are unable to get t ff —t' = 0. Happily, as will be 

 seen, we do not need to heap difficulties and expenses on 

 the experimenter, and we are perfectly satisfied with knowing 

 the convergence-temperature to 'l or even '3° as long as we 

 do not require a greater accuracy than •0001°. 

 The convergence-temperature we calculate thus : 



^ = C(U-t). 

 dz 



C(0 2 -^ l ) = 1 °gfe-^)-log(^-^ 1 ). 

 A S* in > C(z z -z{)=hg(t g -t 2 ) -log it-h), 



. tg~h _ ( tg—ti Y 2 ~ Zl 

 " h-t x \t-h) 



This equation is of a higher order, but we can bring it to a 



