( 609 ) 
According to a well known property of the parabola the point B 
da 
lies halfway between MZ and C, (fig. 6), and a being equal to zero 
av 
in 4,” and: increasing ae with a: 
da (B db 
ee ee = a MRT —- 
B de) dx 
db 
la 
So for the asymptote of oe — Oto be found in B, so (=) = MRT — 
oF, de ) 7 
B dx 
ae Carole : 
we must raise the temperature to te FT. A fortiori the thesis holds, 
of course, if, instead of «,,* = a,a,, as was put here, Ay? > a,a,. For 
instead of the combination of the curve with the right line HBC we 
get then the combination of the first-mentioned with the right line 
through B’, and B’ lying to the right of B, the temperature will 
have to be raised still higher than just now, for ad to, bees MRT 
in the point A’. f 
Also in the general case for 5 we can demonstrate the property 
mentioned, and it will appear afterwards that for these general considera- 
tions it is desirable not to replace the quadratic form of 5 unnecessarily 
by the linear one. We treat the case a,,? > a,a, at once, so that 
a==0 has two real roots. We choose the point 5’ as origin; we 
db da 
call the abseissae of the points where re 0, aa ==) anda = Om 
absolute value resp. 2, #,, #,, then we can write the equations for 
a and b (see fig. 7): 
a= a, (z Da ze) an (w, AD és)” a 1 (2° “tr 2a ®, “i ded, te #,”) | 
b=), (@ 4-4) — b, #,? = 6, a + 26, &, 2 
dp 
The temperature at which the asymptote of a =O reaches the 
Hi 
point B’ is determined by: 
41 
Proceedings Royal Acad. Amsterdam. Vol, XI. 
