700 Mr. W. Bennett on 
The objection urged by Mr. Cook against accepting the 
inductive proof of the actual rate of escape of gases from 
atmospheres, is analogous to the objection urged by some 
scientific men when in 1867 I brought forward a proof * that in 
an atmosphere of mixed gases the atmosphere of each gas must 
have a different limit, the lighter constituents overlapping 
and extending beyond those which are denser. “Oh!” it 
was then said, “That can’t be the case. It is inconsistent 
with Dalton’s Law of the equal diffusion of gases.” Yet I 
have lived tosee my conclusion generally, I believe univer- 
sally, accepted by physical astronomers; and I look forward 
with some hope to an ultimate acquiescence in what is now 
being objected to, in reference to the escape of gases from 
atmospheres. In both cases the objection rests on the same 
error—the mistake of hypothesis for theory, and the con- 
sequent mistake of a law which is approximate for a law of 
nature. 
I am, dear Sirs, faithfully yours, 
30 Ledbury Road, W., G. JGHNSTONE STONEY. 
May 12, 1904. 

LXXVII. Notes on Non-homocentric Pencils, and the Shadows 
produced by them—I. An Elementary Treatment of the 
Standard Astigmatic Pencil. By WitL1AM BENNETTT. 
STANDARD astigmatic pencil is one of which all the 
rays pass through two focal lines, at right angles to 
_one another and to the axis of the pencil. Let the axis 
of the pencil be taken as the axis of Z, and let the focal 
lines be parallel to the axes of X and Y respectively, and at 
distances a and b from the origin. Then the projections of the 
pencil on the planes of XZ and YZ are as shown in fig. 1. 
It is evident from this figure that the change in the 
transverse sections of the pencil consists in a uniform 
stretching or compression in a direction perpendicular to 
each of the focal lines, the stretchings or compressions 
proceeding at unequal rates. Thus, if the section is any- 
where a conic with axes parallel to the focal lines, it is 
everywhere so. The pencil is also of rectangular section 
with sides parallel to the focal lines at all points if at any ; 
and this is the section obtained if the extent of the pencil is 
defined by limiting the lengths of the focal lines. 

* «On the Physical Constitution of the Sun and Stars.” By G. 
Johnstone Stoney, F.R.S. See Proceedings of the Royal Society, 
No. 105, p. 1 (1898). See especially paragraphs 23, 24, 25. 
+ Communicated by the Physical Society: read January 22, 1904. 
