On Salt Solutions and Attached Water. 



211 



nate one starting from the end an a, in every alternate one of 

 those that are vacant beginning with the second a b, in every 

 alternate one of those that are still vacant, beginning with the 

 fourth, a c, and so on, we obtain the order in question, which is 



pabacabadabacabaeabacabadabacabaf abaca .... 

 This is of course the binary law ; viz., if we write down in order 

 the numbers in the binary scale 1, 10, 11, 100, 101, 110, 111, 

 1000, 1001, 1010, 1011, 1100,- &c, then every alternate one 

 ends with 1 ; every fourth one, starting with the second, ends 

 with 10 ; every eighth one, beginning with the fourth, ends 

 with 100, and so on ; and the reason is the same in the two 

 cases. 



A little thought shows that if in the differentiations this suc- 

 cession be followed, each letter must disappear when its turn 

 comes, and that, after all the operations are performed, each 

 letter except p will be left in the denominator with exponent J. 

 This and the way in which it happens render the result an 

 interesting one. 



As for the numerical coefficient, it is clearly equal to the 

 reciprocal of 



T . (2 n ) 1 (2 w_1 J 2 . . . 4 2 "~ 2 . 2 2 " -1 , 



viz. of 



2 2(2U - 1} . 



XXVIII. On Salt Solutions and Attached Water. 

 By Frederick Guthrie*. 



[Continued from vol. i. p. 455.] 



V. 



(1) Separation of Ice, Salt, Hydrate or Cry ohydr ate from Salt 

 Solutions (continued). 

 § 148. Separation of Ice §c. from Solutions of Chloride of 

 Barium. 



Table XXIX. 



BaCl 2 per cent, 

 by weight. 



H 2 O per cent, 

 by weight. 



Temperature 

 at which solidi- 

 fication begins. 



Nature of solid. 



5 



95 



o 



- 0-9 



Ice. 



10 



90 



- 22 





15 



85 



- 40 





20 



80 



- 60 





21-83 



78-17 



- 7 5 



Cryohydrate. 



23-98 



7602 



00 



BaCl 2 +H 2 0. 



30 



70 



+ 25 



>» 



* Communicated to the Physical Society, .Tune 24, 187B. 



P 2 



