266 PETTERSSON, OK WATER AND ICE. 



by zero of tliis part [the reservoir and stem] is denoted by L. 

 Let Q be the volume of the mercury in the reservoir, the ca- 

 pillary and the stem unto A and B. The stånd of the mercury 

 €olumn in the scale-tube at zero is 0. When the temperature 

 of the mercury bath has risen t degrees above zero, the mercury 

 index is supposed to have moved f millimetres. If the tem- 

 perature rises to ti degrees, the mercury index will indicate 

 fl millimetres. The scale-tube is supposed to possess the -tem- 

 perature of the room, which was regulated so as never to vary 

 more than from 2 to 4 degrees from zero, and the mercury 

 columns measured in the experiments are reduced to zero. I 

 think this calculation, which is almost without any infiuence 

 upon the results, may be safely omitted in the following for- 

 ni ul se. 



q is the coefficient of absolute dilatation of mercury 

 g the coefficient of absolute dilatation of glass [see p. 261] 

 X the total dilatation of the water between O"" and t° 

 xi » total ;> » » » » 0° » ti° 



p » volume in cc. corresponding to / m.m, 

 pi » » » » » » fl » 



W is the volume in cub-centim. at 0"^ of the water in the in- 

 strument. Then suppose the temperature of the instrument 

 to rise from 0° to t°. In this case 



(1) x = [Lg-Qq] t + p + pqt 



and if the temperature rises from O"" to ti°, 



(2) xi = [Lg -- Qq] ti + pi + piqti. 



By subtraction of (1) from (2) we obtain : 



xi — x = [Lg — Qq] (ti — t) + pi — p + (piti — pt) q 



(3) -•• T— r = Lg-Qq + -t7^ + ^l t,-t • 



The coefficient of expansion »ws of water between t° and 

 ti° referred to the unit of volume at 0° will be 



T r\ , Pi — P j Piti — pt 



(4) w = Lg-Qq+TT^ + q-t— r 



w 



This formula also holds good below zero, whether the water 

 in the instrument isfrozen or liquid. The standard unit in 

 ■either case is the cub. centim. of liquid water at zero. Only 

 in the case of pure ice another unit of volume is also intro- 

 duced, viz. the cub. centim. of the ice at its melting point. In 

 the case of ice from salt or brackish water this calculus be- 



