Rit (Vísindafélag Íslendinga) - 01.06.1931, Page 13

13
1 d y
y d x
(21)
which shows that by the determination of the constants in
this class of frequency curves it is necessary to know the
first five semi invariants although only four constants are to
be determined.
It may be readily shown that in this case the higher semi-
invariants must satisfy the condition:
2á2 /.;s X4-f-2X2
3X3 /4 X5-!- 3X2X3-)- 3X3 A2
4X4 X3 Xfi -(-4X2X4 -f'6X32“!_ 4/4X2
0
(22)
The integration of (21) may be easily carried out, but to
save space its general form will not be set down here, it
being of little interest.
E. In this case we assume a4=^i=/?2=/J3=^4 = 0 and
the relations (I6a—d) give:
n0 ~ — k (6X24X345X22X3X4-i-3X2X3®+XgXsXf-XgX^Xr.-X.j^Xrj+XsX^2),
<h - - k(12X35 + 30X28X4- 36Xa*Xs*+2X2*X«-15X2^X5
+ 12X2X42+9X3*X4+X4X6-Xb2),
«2= k (6X28X3+3X2X3X4+9X3s+XBX0-X4X5), (23)
Further it is required that the higher semi-invariants satisfy
certain conditions which may readily be found from (16e)
and the subsequent relations derived from (13).
The practical value of the frequency curves of this and
the foregoing class is considerably reduced by the fact that,
for the determination of the constants, X5 and even X6, in the
class E, are required, but as a matter of fact these semi-