558 
NATURE 
[JULY 30, 1914 
cular scattering was first pointed out by Schuster’; |*terms of the zenith transmission a, for the most part 
the question was examined in further detail by Natan- 
son ® and independently by the writer.° 
If S refer to the intensity of wave-length 2 outside 
the earth’s atmosphere, and E(x) to the intensity 
normal to the sun’s rays reaching a level x above the 
sea from a zenith distance ¢, we have E(x) =Se-€z see. ¢ 
where C, is the coefficient of attenuation at the station 
in question. If allowance be made for the conversion 
of radiant energy into heat, it is shown by the writer 
that C, may be expressed in the form C,=y+ fA-‘; 
f is proportional to the pressure of the atmosphere, 
so that if 8, refer to standard conditions of pressure 
and temperature we have 8,=£p,/p, where p is the 
barometric pressure at the station at the time of 
observation. Finally, in terms ot the refractive index 
of air under standard conditions, it is shown that 
By = §7°(v?,—1)?H,/n,, where H, is the height of the 
“homogeneous atmosphere”’ calculated at o° C., and 
n, the number of molecules of air per cm.*? under 
standard conditions. It may be remarked that these 
relations may be obtained in a.very general manner 
independently of any assumptions regarding the atmo- 
spheric gradients of temperature and pressure, pro- 
vided that the planes of equal density be parallel to 
the earth’s surface. 
The accuracy of the experimental measure of the 
zenith transmission, a=e-©2, rests ultimately on the 
ratio-of two galvanometer deflections, or the measure- 
ments of two ordinates of a bolograph record, quan- 
tities measurable to well within 1 per cent. Owing 
to the occurrence of the ratio only, corrections due to 
the imperfect reflecting powers of mirrors, absorption 
by prisms, slight reflection from the bolometer-strip, 
etc., do not appear. The determination of the re- 
maining observed quantities, zenith distances of the 
sun, wave-lengths, and barometric pressures are all 
over a range of ten wave-lengths, avoiding regions of 
selective transmission. The average zenith trans- 
mission, a, is determined for a large number of days 
each year; unfortunately it is not quite exact to derive 
the mean coefficient of attentuation as log, a; the 
error committed is difficult to estimate beforehand, 
but will be negligible only when the attentuation 
coefficients are small or when they deviate very little 
from their mean value; actual trial shows that the 
error committed may amount to as much as 2 or 3 
per cent. In addition, there is the probability that the 
constants 6 and y are independent variables; for these 
reasons it seemed advisable to the writer to determine 
B and y independently from each day’s observations 
from the constants of the line of closest fit (calculated 
by least squares) corresponding to the formula 
C,=y+fA-*, taking as variables C, and A~* measured 
in units chosen according to a suitable scale. The 
computations were very ably carried out by Mr. A. A. 
Scott and Mr. Etienne S. Bieler, both of McGill Uni- 
versity, working under a grant from the Rumford ~ 
Fund of the National Academy of Sciences. The daily 
determinations of 8 and y have now been extended to 
all the transmission observations as yet published by 
the Smithsonian Astrophysical Observatory. | Com- 
parison with theory is most conveniently made by cal- 
culating n, according to the preceding formula. For 
each selection of wave-lengths a value of (u?,—1)? 
weighted according to A~* was employed, while the 
barometric pressures at the times of observation were 
obtained through the courtesy of Dr. Abbot. 
Pending full publication and a more detailed dis- 
cussion of the results obtained, a summary of the 
mean values of 6 and y, together with the correspond- 
ing determinations of ,, and the probable deviation 
from the mean is given in the following table :— 
Constants of Atmospheric Absorption. 
Mount Whitney, California. 
Annals, vol. Table No. 
lil. 46 4 
Days 
(1909-10) 
Mean y 
0°014+0'003 
Bassour, Algeria. 
ill. 46 9 (1911-12) 
ill. 46 2 (1912) 
o'080+0'012 
0°27 +0°'OI 
Elevation, 4420 Metres. 
Mean B 
0°0049 +O0‘OOOI 
Average Barometer, 446-7 mm. 
Wave-lengths 
10 wave-lengths, 
0°3274 to 0°574u 
Mean zo 
(2°84 +0°06) x 1o!9 { 
Elevation, 1160 Metres. Mean Barometer, 664-6 mm, 
0°00723 +0°0002 
0700696 £0'0001 
(2°85-£0°:07) x10! ff 
{ Io wave-lengths, 
(2°96+0°03) it 
0°340m to 0°5324 
The marked increase of y in the second series at Bassour is due to the presence of volcanic haze from 
the Mount Katmai eruption, June 6-7, 1912. 
Mount Wilson, California. 
Elevation, 1780 Metres. 
Mean Barometer, 623-5 mm. 
ii. 14 59 (1905) © 052+0'002 0'00673 +0'0001 (2°82+0°'04) x 10!9 4 wave-lengths, 
ll. 4 Oe (1906) 0°058+0'002 0 006134000006 (3°10+0°03) O°40u O'45u O'SOp 
ill 33 114 (1908) 0°076+0'002 000691 +0°00006 (2°75 £0'02) | and 0°60" 
iil : : pee ka : 4 ; ; ( 9 wave-lengths, 
1, 34 96 (1909) 0°031+0'001 0°00687 +0'00008 (2°80+0'03) | us Cane 
iil. 35 15 (1910) 0°023+0'00I 0°00696 £0°00908 (2°76+0°02) J 35é@ O°4Ou O°45u 
a 2 az = ie O'50u 0°70" O'8ou 
iil. 30 113 (1911) 0'022+0°001 0°00606 +0°00005 (2'76+0'02) | (oop t'20p uF6OE 
The mean value of n, obtained by combining the results of Tables 34, 35, 
Hence we obtain for Avogadro’s number the value N=(6+23+0-03) x 102°, 
gives n,=(2-°78,+0°01,) x 162°. 
and 36 (324 days, 1909-11) 
and for the charge on the electron e=(4+64+0:02) x 10-?° e.s. units. 
measurable to a high degree of accuracy, so that it | 
does not seem too much to say that the zenith trans- 
mission can be determined over a considerable range 
of wave-lengths to an accuracy well within 1 per cent. 
Data on atmospheric extinction recently made avail- 
able by the publication of vol. iii. of the Annals of the 
Smithsonian Astrophysical Observatory are given in 
f Schuster, NaTure, July 22, 1909: ‘‘ Optics,” 2nd ed., 1909, Pp. 370. 
Natanson, Bu/l. Inter. de l' Académie des Sciences de Cracovie, 
December 13, T9QCQ. 
*: King, Phil. Trans. Roy. Soc., 212 A, P. 392, 1912. 
NO. 2335, VOL. 93] 
The above determination of n, compares favourably 
with Rutherford’s '° 2-78, Planck’s™ 2-77, and Milli- 
kan’s ?* (2-705+0-005), while the value recently ob- 
tained by Fowle'* from a somewhat different treat- 
ment of the Mount Wilson data gave 2-56. 
10 E, Rutherford and H. Geiger, Roy. Soc. Proc., A, vol. Ixxxi., Igo 
p. 171. 
ll Planck, Zoc. céz., p. 172. 
12 Millikan, Phys. Rev., ii., ser. 2, pp. 109-143, August, 1913: Prys. 
Zeitschrift, xiv., pp. 796-812, September 1, 1913. 
13 Fowle, Astrothysical Journal, xxxviii., No. 4, p- 398, November, 
1Q13. 
