1896.] A new Method of determining Freezing Points. 



253 



tions, and in more concentrated solutions the rule : the bath must be 

 arranged successively cooler, so that the convergence temperature of 

 the solutions falls beloAV the convergence temperature of water by 

 the amount of the freezing point depression. Careful measurements 

 of c, K, t g — tg have shown that in the method I use, the apparent 

 freezing point depression cannot differ from the real even by 



Trtfg—tg') = 00001° to 0-0002°, as far as the equilibrium in the 



heterogeneous system is concerned. If the convergence temperature be 

 below the freezing temperature, we have dtjdz = c"(t —tjt), sep. ice 

 + c(tg—t fl ), exp. arr. Equilibrium takes place when dtjdz == 



c"(t — t')+c(t g — t') = and t' is = t + %(tg — t'), i.e., the point of 



c 



rest of the mercury thread is not at the real freezing temperature t , but 

 at the apparent freezing temperature t' , which is more or less different 

 from t Q , and t' will be between t and tg. In order that the apparent 

 and real freezing points, as well as the apparent and real freezing 

 point depressions, may be as equal as possible, the same conditions 

 and rules of the freezing point method must be fulfilled as in the 

 case when the convergence temperature is above the freezing tempei- 

 atare. Careful measurements of c, c", t g — t', tg — tg have shown that 

 in the method I use t' cannot differ from t even by —0*00006° to 



—0-00018°, and t' — t" from t —t ' even by %{t g -tg) = 0-00006° to 



0*00012°. These rules, which we now explain theoretically, were 

 found at first empirically, after a very detailed investigation, by my 

 late friend, P. B. Lewis, and then by myself, and form to a great 

 extent the subject of this paper. 



Under these arrangements of the equilibrium we get the result 

 that the freezing temperature can be kept within the very narrow 

 limits of one, two, three ten-thousandths of a degree (including other 

 experimental errors) during a time of 15 — 20 minutes, and longer, 

 as well when the convergence temperature is above as when it is 

 below the freezing temperature. 



B. The Proper Treatment of the Instrument used for Measuring the 

 Temperature. — I used the 1/100° and the 1/1000° thermometers 

 simultaneously. On the 1/100° thermometer the reading error is, 

 even under the most favourable conditions, one to two thousandths 

 of a degree, often less, seldom more. Through this the upper limit 

 to which we can get quantitative results is, in the method I use, with 

 the 1/100° thermometer c.a. 04 mol. normal, in the case of non- 

 electrolytes. The 1/1000° thermometer allows much more accurate 

 readings, gives us the possibility of investigating more dilute solu- 

 tions, but requires a great series of precautions if a good result be 

 obtained. (1.) The thermometer must always be kept at 0°. (2.) It is 



