1903-4.] Thermal Expansion of Solutions of Hydroxides. 289 
Here also solutions of strontium hydrate exhibit this negative 
expansion, and this negative expansion becomes less numerically 
with rise of temperature, and in the case of the last solution 
examined it changes from being a negative to a positive expansion 
with rise of temperature. Strontium hydrate is thus analogous to 
sodium hydrate (see fig. 2). 
The following are curves exhibiting expansion on solution plotted 
Fig. 2. 
against temperature for the hydroxides of sodium, barium, and 
strontium. 
Thermal Expansion. 
Adopting tbe formula Y f = V 15 [l + a(t - \5) + b(t - 15) 2 + c(t— 15) 3 ] 
where V t is the specific' volume at t° C., and a, b and e are con- 
stants, I have determined by a modified method of least squares 
the constants a, b, c ; the formula gives the volume at any 
temperature between 15° C. and 20° C. correct to within 5 in the 
fifth decimal place. By the aid of the above formula the expan- 
sion coefficients, oq= — where a t is the expansion coefficient 
v t dt 
at t° C., were calculated. 
PROC. ROY. SOC. EDIN. — VOL. XXV. 
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