Freezing -Points and the Freezing-Point Methods. 475 

 very simple expression by making — — — — 2. We get 



{t 9 -h) {tg-hY^tg-ti) (tg~t 2 y OV 



_ t\t3 t 2 



In 



t\ i £3 ^*2 



Therefore we require to make readings at equal intervals of 

 time: z 2 — Z\=z% — z 2 — z± — z 3 and so on. But the reading- 

 error is here of great importance if the temperature-intervals 

 are not very great. Because of this we have to use the 

 greater temperature-intervals and to make many readings. 

 Table I. gives the convergence-temperature as obtained from 

 the first column of Table I A. 



One is helped in obtaining the value of t g ' by plotting out 



dt 

 the results. In —=C(t g — t) } t becomes = ^, when dt = 0. 



Taking the dt as ordinates, the t as abscissas, we get an almost 

 straight line which cuts the axis of abscissas at the conver- 

 gence-temperature. The observations must be made not very 

 far from the convergence-temperature, otherwise it may be 

 determined very erroneously. In this way I obtained for a 

 convergence-temperature the results given in Table I A. : — 



Table I. 



By calculation. 



By plotting. 



+ 1-17 



+ 1'1 



+ 0-54 



-1-0-6 



+ 0-45 



+ 0-25? 



-0-07 



-0-1 



-0-21 



-0-1 



-0-05 



-0-03 



Having the value of t g , we calculate the value of C (see 

 Table I A.). As almost all my experiments for over two years 

 were carried out at a temperature of about 18-22°, I investi- 

 gated the convergence-temperature at these temperatures of 

 the room. 



As we see, the lowering of the temperature of the ice-bath 

 by '1° is therefore accompanied by a lowering of the con- 

 vergence-temperature by about *15 . Passing from 40 to 45 

 stirring movements to 35 per minute and from temperature 

 of room 21°-5 to. 17°, we find, at same temperature of the 

 bath of — '2°, that the convergence-temperature has fallen by 

 about -28 -'35°. 



