Freezing-Points and the Freezing-Point Methods. 485 



have, are : that during 5 minutes of the experiment *05 to 

 '15 per cent, ice separates, and that the quantity of the ice 

 present in the liquid at equilibrium is ='3°. From the 



equation t , =t + r?; t~ — 7\> ^ follows that when t g — t'=0, 



^ \Zo too; 



t'=t , and C(t g —t') = 0, i.e., no cooling by experimental 

 arrangements, no further separation of ice, takes place. 

 Therefore the separation of ice first of all shows that t g —t' is 

 not equal 0, and that the convergence-temperature is in the 

 given method below the freezing-temperature. After tins we 

 can easily calculate the comparative error in the methods. In 

 my method C = 0°-003, keeping t g -l' = 0°% G{t g -t') = 0°-006, 

 in 5 minutes, 0°*003. To one degree overcooling, a quantity 

 of separated ice = l'25 per cent, corresponds. This gives 

 about 0°"004 per cent, separated ice in my method during 

 5 minutes. In the given method the experiment lasts 

 5 minutes, the value of 05 per cent, to 0*15 per cent, shows 

 that the total value of C(t g —t f ) in the given method is about 

 12 to 36 times greater than in mine. Now t —t 0v is three 



times smaller than in mine, therefore ™, M — -^, i.e., the 



Lv {t — t ov ) 



difference between the real and apparent freezing-points, is 

 from 36 to 110 times greater than mine, if my t g — 1' = 0°'2. 

 Again, the fact that the quantities of separated ice in two 

 different experiments were 0*05 per cent., and 0'15 per 

 cent. = 0"l per cent, difference, shows that the value of 



Tjr, , 9 j-t, i.e., the apparent freezing-point of one and the 



same liquid obtained by repeating the experiment, and also 

 the apparent freezing-point depressions, are affected by errors 

 150 times greater than iu my method, if my t g — t g ' = o, l, &c. 



Conclusion. 



The quintessence of this paper is to show that, assuming 

 all the investigators hud an absolutely perfect instrument 

 for registration of temperature, and that other sources of 

 error, which have nothing to do with the method, do not exist, 

 tJie residts obtained by the different methods are still affected 

 by errors according to the conditions of the established etpiili- 

 brium. Neither does a constant apparent freezing -temperature 

 give us any evidence as to the absolute value of the obtained 

 freezing-temperature, nor does a depression obtained from 

 two observed constant apparent freezing-points as to the correct 

 value of the depression we ought to get. A repetition of an 

 experiment under the same conditions must lead to nearly 



