1902.] Expansion of Ice, etc., at Low Temperatures. 241 



All that is possible in the present instance is to adopt a linear formula. 

 The usual formula is v T = v (1 + aT), where the value v at 0° C. 

 hecomes % at T° C. when a is the coefficient of expansion. If we use 

 densities (d) instead of volumes (v) this formula becomes 



d = d T (l+ocT), or a = fe^; a = 0' 000538. 



Another formula, when T and T' are the temperatures dealt with, is 



rf T = tf T <{l + a(T-T)}, or « = J?'^ ; « = 0-000595. 

 Again 



*y = ^ T {l- a (T'-T)}; or a = a = 0*000558. 



Also we may choose a mean formula 



dr-d 



^—^i a = 0-000576. 



(T' - T) 



+ 



The differences in the results of applying these formulse are shown 

 in the numerical values attached to each, which are calculated from 

 the first experiment on solid carbonic acid in Table III, coupled with 

 the specific gravity 1*53 of the solid at - 78° C. 



Perhaps as a matter of general convenience, the first of these 

 formulse is the best; however, the second was chosen to conform with 

 the old work of Playfair and Joule, and it is the results of this 

 formula which appear in the table. 



The temperature range is taken from about -186°C. to 17° 0., 

 unless otherwise stated. 



Ice. — In determining the density at the temperature of liquid air 

 of pieces of clear ice cut from large blocks, both the silver and copper 

 balls already referred to were used as indicated. The true weight in 

 vacuo of the silver ball was 132*2855 grammes, and that of the copper 

 ball was 38*0802 grammes. The observations and results are given in 

 Table II. The mean of the three densities at - 188°*7 C. is 0*92999. 



Recently Vincent* has redetermined the density of artificial ice at 

 the freezing-point, and also its coefficient of expansion. He finds the 

 density to be 0*916, or from his tabulated results 0*91599. Playfair 

 and Joule find the mean of the densities given by eight observers 

 previous to them, to be 0*919, and they themselves get 0*9184 ; Bunsen 

 found it to be 0*9167. If we take this most recent determination, 

 namely, 0*91599 at 0°, and 0*92999 at - 188°*7, and use the formula 



d = d T (l + aT) 



we get a = 0*00008099. 



* < Eoy. Soc. Proc.,' 1901. 

 VOL. LXX. S 



