702 

for the intensity and distribution of sky-radiation as 
far as the observations available at that time could be 
tested. As a final test, the Smithsonian results were 
reduced with a view to obtaining a value for the 
number of molecules per cm.* of a gas at standard 
temperature and pressure; the result obtained by the 
writer,’ n,=(2-78+0-01) x 101’, and a later independent 
determination by Fowle,* n,=(2-70+0-02) x 101", indi- 
cate that we may rely with confidence on Rayleigh’s 
law in dealing with molecular extinction for wave- 
lengths not too close to regions of selective absorption. 
In dealing with attenuation in a stellar distance 
x=A, the term «A is so small that we may write | 
to sufficient degree of approximation kA=(E,—E)/E,, 
i.e. «A is the proportional loss of intensity in travelling 
a distance A. Denoting by «,A and «,A the propor- 
tional losses of intensities corresponding to ‘‘ photo- 
graphic”’ and ‘‘visual”’ light of average wave-lengths 
A, and 4, respectively, we derive on reducing to inten- 
sities the result obtained by Jones,* {(photographic)— 
(visual)] losses=+0-00473 +0-:00035 magnitude, the rela- 
tion (k,—K,)A=0-00435 +0-00032, the distance A being 
Io parsecs (1 parsec=distance corresponding to a 
stellar parallax of 1/’ =3-26 light-years=3-08 x 10!* cm.). 
If it is assumed that the extinction is brought about 
solely by molecular scattering, we also have the addi- 
tional equation k,/K,=(A./A,)*. 
Unfortunately, it is somewhat difficult to assign 
with accuracy the average wave-lengths corresponding 
to ‘‘ photographic’? and ‘“‘ visual” light. A rough esti- 
mate by the writer from Parlkhurst’s curves of spectral 
intensities corresponding to the plates and filters em- 
ployed in the photographic and visual determinations 
yielded the values A,=0-446u and A,=0-533u, so that 
we obtain «,/xk,=2-08, giving «,A=o0-0083, and 
k.A=o0-0040,.1° In order to realise more vividly the 
extremely small attenuation which these numbers re- 
present, it is easily verified that in order to lose one- 
tenth of its original intensity radiation of these wave- 
lengths must travel for about 4-1 and 8-5 centuries 
respectively. 
For the purposes of the present discussion we assume 
hydrogen to be the constituent of interstellar space 
(until we know more about the physical properties of 
““coronium,”’ “‘nebulium,’’ or other primordial gases 
which might possibly occupy these regions). Taking 
Po —1=0-000140, 1,=2-78 x 101°, A=4-46 x Io-* cm., we 
easily derive for the coefficient of attenuation in 
hydrogen at standard temperature and pressure the 
value «,=5-89 x Io-§ em.-!. For this wave-length in 
interstellar space we have x=2-72 x 10-7? cm.—', so 
that n/n,=x/«x,=462x 10-15, giving finally for the 
molecular density in interstellar space the estimate 
n=1-28x10° hydrogen molecules per cm*.?° 
Associated with the problem of attenuation by scat- 
tering is that of calculating the amount of star- 
light scattered by the molecules of interstellar gas.” 
In this way might be explained the extremely faint 
luminosity which several observers believe to exist 
over the background of the sky. This scattered light 
might also account for discrepancies which have been 
7 King, I.. V., Nature, xciii. (July 30, 1914), Pp. 557-559: 
8 Fowle, F. E., Astrophysical Journal, x\.(Decembher, 1914), DP. 435-442. 
9 Jones’ determination is in fair acreement with Kapteyn’s final result, 
(Astrophysical Journal, xxx., p. 398): 
((photographic)—(visual)] losses= +0™*0031 + 0°0026. 
The corresponding determinations by King (E. S.) of the coefficients of 
attenuation for photographic and visual light give values about five times 
that of the text. 
10 The losses +0™*oo80 and +o™"co33 estimated by Jones for “‘vhoto- 
graphic” and ‘‘visual” light lead to the values KjA=o'0073 and KgA= 
00030 (wave-lenaths not stated). Kapteyn’s (corrected) estimate for wave- 
length Ay=07431m is K}A=o0'00507, leading to the value z=0'68 X10 hydro- 
gen molecules per cm.%, which is of the same order of magnitude as the 
determination already made. _E. S. King's results (footnote 1) increase the 
estimate of the text about five fold. 
11 Note a discussion on this point by H. C. Plummer in a paper by 
H. H. Turner, Zoc. cit. (footnote 1). 
NO. 2391, VOL. 95] 
NATURE 

[AucusT 26, 1915 

found to exist between calculated and observed dis- 
tributions of total starlight from different regions of 
the night sky.’* The estimation of the amount of 
solar radiation scattered to the earth by a distribu- 
tion of interstellar gas constitutes a definite problem, 
the complete statement of which (including the effect 
of self-illumination) is expressed as a particular case 
by a general integral equation already given by the 
writer.‘* The theoretical discussion applicable to the 
problem under discussion the writer hopes to under- 
take elsewhere; from the observational point of view 
it would seem that the difficult, but perhaps not im- 
possible, task of estimating the luminosity of the sky 
in regions void of stars affords the only hope of bring- 
ing additional direct evidence to bear on some of the — 
questions raised below. 
In a gas of the extreme degree of tenuity which 
we have just estimated, molecular collisions will be 
extremely infrequent; an estimate of the free path, 
according to the usual ideas of the kinetic theory, is 
impossible without a knowledge of the average mole- 
cular velocity or temperature of the gas. As has 
already been pointed out by the writer, it is difficult 
to see how molecular velocities can be directly affected 
by radiation travelling through a gaseous medium. 
It is probable that gravitation and radiation-pressure 
are the controlling forces in determining molecular 
velocities by an extremely slow process of equi- 
partition of energy with that of molecules escaping 
from planetary and stellar atmospheres. 
As the above estimate of molecular density gives a 
total amount of matter of the order 1/38 xearth’s 
mass in a sphere having a radius equal to that of 
Neptune’s orbit, it is improbable that the residual 
gas we are considering could have a noticeable effect 
on planetary motions. It might, however, be identified 
with the slightly resisting medium the existence of 
which has been thought necessary by some astro- 
nomers to account for the secular acceleration of 
Encke’s comet,'® and which is considered by See™ to 
have played an important réle in planetary and stellar 
evolution. 
The molecular density estimated above is very much 
less than that conjectured to exist in some of the 
nebulz, 10° molecules per cm.* being about the order 
of magnitude in this case.17 While the degree of 
rarefaction which we have derived is very much 
greater than it is possible to produce by any known 
physical means,'® the total amount of matter con- 
tained in regions of space of astronomical dimensions 
is formidable; thus we find for the number of mole- 
cules in a cubic parsec the estimate N=3-75 x 10°° 
hydrogen molecules per parsec’. ‘Taking the density 
of hydrogen at standard temperature and pressure to 
be o-o899 gramme per litre (containing 2-78 x 10** 
molecules), we obtain for the density of matter in 
interstellar space the estimate 1-21 x 10°’ grammes per 
parsec*®; as the sun’s mass is approximately 1-96 x 10** 
grammes, we have finally for the density of inter- 
stellar residual gas the estimate 63x 10° sun’s mass 
per parsec*. According to Eddington,’® a reasonable 
12 Abbot, C. G., Astronomical Journal, xxvii. (19tt), p. 20; ‘‘ Annals of 
the Smithsonian Astrophysical Observatory,” vol. ili. (1913), pp. 203-210. 
13 King, L. V., footnote (6), p. 379, equation (14). 
14 King, L. V., footnote (7). 
15 On the recent history of this comet see a paper by Backlund, ‘‘ Encke’s 
Comet, 1805-1908," Monthly Notices, \xx. (1910), pp- 429-442. 
16 See, T. J. J., ‘* Researches on the Evolution of the Stellar System,” 
1010, vol, ii., pn. 134-158. 
17 Henkel, F. W., in an article ‘“‘ Nébuleuses et Essaims,” Scientia, 
vol. xv. (1914), Pp. 294-307- Q 
18 The total number of molecules per cm.3 corresponding to the vapour 
pressure of mercury at the temperature of liquid air is estimated at 3% 107 
(Dunoyer, M. L.. “Les Gaz ultra-raréfiés,” in the collection ‘‘ Les Idées 
Modernes sur Ja Constitution de la Matiére,” Paris, Gauthier-Villars, 1913, 
. 216). 
P 19 Eddington, A. S., ‘‘Stellar Movements and the Structure of the 
Universe.” Macmillan and Co., Ltd., 1914, p. 255- 

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