On Salt Solutions and Attached Water. 49 



which is readily transformed into 



( 



l + q + q d + q 6 + q 10 + &c. \ 2 ^ 1 + 2q + 2? 4 + 2q d + 2q 16 + &c 

 l-q-q 3 + q 6 + q 10 -&cj l-2q + 2q*-2q 9 + 2q 1Q -&c. 



an identity derivable at once from elliptic-function formulae. 

 The above arithmetical process thus affords a proof of this 

 identity. 



VII. On Salt Solutions and Attached Water. 

 By Frederick Guthrie *. 



[Continued from S. 4. vol. xlix. p. 276.] 



III. 



A few special Cryogens and Cryohydrates. 



IHAVE ; in the first place, to redeem the promise given in 

 § 89, and, by discussing the behaviour as cryogens and 

 cryohydrates of a few peculiar salts, to complete one part of 

 my undertaking. 



§ 105. Chloride of Calcium as a Cryogen. A. Crystallized 

 CaCl 2 + 3 H 2 0. — The heat liberated when anhydrous CaCl 2 is 

 brought into contact with water interferes with, by diminish- 

 ing, the manifestation of cold due to the proper liquefaction of 

 the salt and of the ice when the two are brought together. 

 Accordingly in experiments with chloride of calcium as a cryo- 

 gen which are to serve as a guide to the temperature at which 

 the formation of the cryohydrate may be predicted, we may 

 conveniently begin with the crystallized salt. A seasonable 

 fall of snow last winter enabled me to extend my experiments 

 with the chloride of calcium, not only in regard to the relative 

 quantity of the two constituents, but to the relative effects of 

 snow and pounded ice, and to establish conclusively that the 

 two are of quite equal power when used as one element of a 

 cryogen. The crystallized CaCl 2 + 3 H 2 was finely powdered 

 and placed in weighed quantities on the weighed snow or 

 crushed ice in a beaker, the two being stirred continuously 

 with the thermometer. Under these conditions the lowest 

 temperature is quickly reached. 



* Communicated to the Physical Society, June 12, 1875. 



Phil. Mag, S. 5. Vol 1. No. 1. Jan. 1676, E 



