Reaction before Complete Equilibrium. 79 



deflexion is brought to the desired place on the bridge, and 

 the spot of light to the beginning of the slit, while the 

 platinum-thermometer is in the meantime immersed in the 

 overcooled or supersaturated liquid, which is quietly stirred. 

 The contact on the thick wire of the bridge is then fixed, 

 the screen opened, and a line parallel to the edge of the paper 

 is obtained, indicating T oy . The process of separation of ice 

 or salt, &c.,is then begun by bringing into the liquid a crystal 

 of ice or salt, the regular stirring of the liquid being 

 continued. The contact-maker remaining fixed, while the 

 temperature of the liquid is changing, the galvanometer- 

 mirror is deflected, and describes a curve, which again passes 

 over into a straight line, parallel to the edge of the paper, 

 when the point of equilibrium T is reached. After the 

 point of equilibrium has been attained the curve is calibrated 

 by shifting the point of contact on the thick manganin wire, 

 opening and shutting the screen ; the results are thus made 

 independent of variation in the electromotive force of the 

 cells, being expressed in terms of the resistance of the bridge- 

 wire. 



B. The Arrangement of Equilibrium. 



In my paper u On Real and Apparent Freezing-Points and 

 the Freezing-Point Methods " (Proc. Roy. Soc. 1896, Zeit- 

 schrift fur 2>^sikaUsche Chemie, 1896, and especially Phil. 

 Mag. Dec. 1897 and Zeitschrift fur physihalische ( Itemie, 

 1899, p. 577), I gave the phvsico-inathcmatical theory of 

 freezing-points. 



The essence of the results arrived at by it was : "Assuming 

 that all investigators have an absolutely perfect instrument for 

 registration of temperature, and that sources of error uncon- 

 nected with the method do not exist, the results obtained In- 

 different freezing-point methods are still affected by error 

 according to the conditions of the established equilibrium/' 

 " When the convergence-temperature is above or below the 

 freezing-temperature the point of equilibrium is not the real 

 temperature T„, but only an apparent one T', which lies above 

 or below T . The apparent freezing-temperature 



-i.+ c'(T -T OT +K)' 



where T — T „ is the amount of over-cooling of the liquid 

 below the freezing-temperature before it was brought to 

 crystallization by an ice crystal, and is directly proportional 

 to the quantity of ice present at the equilibrium, T^ is the 

 convergence-temperature (/. e. the temperature which the 



