( 379 ) 
The conic @ lying in the plane ® of C; belongs six times to 
the section of = and @, 
Moreover as each bisecant of PR; lying in ® determines a conic 
Qs of =, this surface is of order 4 X 2+ 6X 2+ 10= 30. 
Through the point Sz of R; lying in ® ten conics @ of so, 
pass, viz. the four conics determined by the chords S;S; and the 
conic Qs to be counted six times containing all the points S;. So 
Rk; is a tenfold curve. 
If C, breaks up into two right lines / and m intersecting each 
other in ZP the locus consists of the cubic surface 4/3 belonging 
to P and the surface Po; formed by the conics Qs resting on / and 
m, And now according to 12. the curve ZR; is a ninefold curve of Po, 
and according to 7. a single curve on 413; so in accordance with 
what was mentioned above it is a tenfold curve of 23, = Wo, + 413. 
As Cz and &; have @ points in common, we find in a similar 
way that the conics Q, which meet C3 in two points not situated 
on £; form a surface of order °/.(4—a@)(5—«a), where LR; isa curve 
of multiplicity 1/.(4—)(5—@), C being a (4—qa)-fold line. 
14. We shall still determine the number of conics Qs resting 
on the @-conic Cy, the -conic D, and the y-conic Za. 
The surface J’; of the conics Qs, cutting R; in P and P',and Cs 
have (6—ea) points in common. So R; is a (6—e)-fold curve of the 
locus of the conic Qe, passing through P and meeting C2; so this 
surface is of order 3 (6—a), 
Of its sections with D, a number of (6—«)(6—/) are not situated 
on Bs, which proves that R; is a (6—«a)(6—/)-fold curve of the 
surface of the conics Q, resting on Cz and D2; so this latter surface 
is of order 3 (6—a@) (6—/). < 
Consequently there are (6—«a)(6—/?)(6—y) conics Q:, having a 
point in common with each of the conics Cy, Do, Ey. 
In particular any three conics Q, are cut by one conic Qs only. 
Physics. — “The cooling of a current of gas by sudden change 
of pressure.” By Prof. J. D. vAN DER WAALS. 
If a gas stream under a constant high pressure is conducted 
through a tube, so wide that we may neglect the internal friction, 
and this stream is suddenly brought under a smaller pressure, either 
by means of a tap with a fine aperture, or, as in the experiments 
of Lord Kertvin and JOULE by means of a porous plug, the 
