tt se 
: 
- 
MAGNUS ON THE EXPANSIVE FORCE OF STEAM. 933 
tion of the coefficients. But the form which has been employed 
by the French academicians, by T. H. Young, Creighton, 
Southern, Tredgold and Coriolis, and also quite recently by the 
author of the article ‘Steam’ in the Encyclopedia Britannica, 
and in which the expansive force is equal to a power multiplied 
by a constant number of increased temperature, corresponds 
less well with them, whatever power be assumed, than the form 
proposed by Roche, August* and Strehlke, which is at the same 
time that to which theoretical ‘considerations have led Von 
Wrede, and in which the expansive force is expressed by a con- 
stant number multiplied by another constant number raised to 
a power whose exponent contains the temperature in numerator 
and denominator, so that if e denote the expansive force of the 
vapour expressed in millimetres, and ¢ the temperature in de- 
grees of the centesimal scale, we have 
t 
eé= a. pert 
I have consequently chosen this form of the equation. 
For ¢ = 0 we have e = a = 4°525™™; 
ae 
for t = 100 we have e = 760™ = 4:595 . 7 T 1. 
This equation exhibits a relation between 4 and y, and it now 
only remains to determine one of these two quantities from the 
observations. I have for this purpose selected the ten observa- 
tions marked with a * in the table, p. 229, and from this y is 
determined according to the method of least squares, whence 
resulted y = 234°69 and log b = 7°4475. We therefore obtain 
punt Lh 
e = 4mm5 25. 1084692, 
For comparison, I have appended to the observations given in 
the table inserted at p. 229, the values of e calculated according 
to this formula. The following table contains the expansive 
forces for all integer degrees from — 20 to + 118°C. 
* Poggendorff’s Annalen, vol, xiii. p. 122, and vol. lviii. p, 334, 
