424 On the Freezing of Water at Temperatures lower than 32° F. 



question proposed. Let W denote the weight in pounds of the 

 given quantity of water inclusive of the containing vessel reduced, 

 32° — 1° its temperature, and Q the weight of the ice formed; 

 let q Y denote the weight of any particle of ice, t x the temperature 

 at which it was formed, X, X p c x being as above ; let q 2 , t 2 , X 2 , c 2 

 be similarly related to a second particle, q B , t 3 , \ 3 , c s to a third, 

 and so on ; then, as q ]} q q , &c. are respectively heated as water 

 through f — tf, t° — t 2 , &c, and as ice through t°, t 2 °, &c, 

 while W — (<?! + q% + q 3 + &c.) is heated as water through t°, by 

 equating the quantity of latent heat rendered sensible to the quan- 

 tity of heat spent in raising the temperature of the whole we 

 obtain the following equation : — 



\Qi+\Qi + \%+ &c - =^( w -fl r i-S , 2-fe- &c + ?i (' - *j) 

 + qc Z (t-Q+q 3 (t—Q + &c. +c l q l t l + c 2 qJt + c fi q<fa+ &c. 



Or substituting for \ v \—(l—c 1 )t v for X 2 , X— (1 — c 2 )/ 2 , and 

 similarly for X 3 , &c, we obtain 



M?i + ? 2 + ? 3 +&c.)=*W, 

 or 



XQ=*W. 



If we denote by x the ratio of Q to W, we nave 



t 



The quantity which is here denoted by X is the number of units 

 of heat requisite to convert a pound of ice at the temperature of 

 32° F. into a pound of water at the same temperature, the unit 

 of heat being that quantity which is sufficient to raise the tem- 

 perature of a pound of water through 1° F. The value of X, 

 according to the experiments of Provostaye, Desains, and Reg- 



nault, is 142*65; so that x= r-^- . If instead of measuring 



change of temperature by the Fahrenheit scale we employ the 

 Centigrade, and define the unit of heat to be the quantity of heat 

 requisite to raise a pound of water through 1° of that scale, 



f) ■ 

 we have os = p. , where — 6° denotes the temperature of the 



water in its initial state, as determined by the Centigrade ther- 

 mometer. If we adopt the measure of the latent heat of ice at 

 32° F., or zero Cent., deduced from the experiments of Person, 



the above expressions will become =-jt and ~= respectively. 



Queen's College, Galway/ 

 November 10, 1866.'* 



