LIBRARY
w.MVr>ity of California
IRVfNE
EX L I B R
CASSIUS MILTON
I S
JAY
924
CONTRIBUTIONS FROM THE LICK OBSERVATORY NO. 3.
TERRESTRIAL
ATMOSPHERIC ABSORPTION
PHOTOGRAPHIC BAYS OF LIGHT.
BY
J. M. SCHAEBERLE,
Astronomer in the Lick Observatory.
Printed by authority of the Regents of the University of California.
SACRAMENTO:
STATE OFFICE, : : : A. J. JOHNSTON, SUPT. STATE PRINTING.
1893.
ORGANIZATION OF THE LICK OBSERVATORY
Hon. T. G. PHELPS, Hon. C. F. CROCKER, Hon. H. S. FOOTE,
Committee of the Regents on the Lick Observatory.
MARTIN KELLOGG,
EDWARD S. HOLDEN,
J. M. SCHAEBERLE,
E. E. BARNARD,
W. W. CAMPBELL,
ALLEN L. COLTON
0. D. PERRINE
President of the University.
Director and Astronomer.
Astronomer.
Astronomer.
Astronomer.
Assistant Astronomer.
. ....... Secrft>i,->/.
H
i
TABLE OF CONTENTS.
Page.
Determination of the Relation between the Aperture, the Diameter of the
Star Image, and the Exposure-Time 2
' Determination of the Instrumental Constants 4
jj Exposures on Polaris with the Great Telescope, and Comparison with
Theory. Table I 9
Tabular values of Q, m', d, and t. Table II - 10
Atmospheric Absorption of the Photographic Rays of Light 15
Method of Observing 16
Method of Derivation of the Fundamental Equation 17
First Series of Observations (Mt. Hamilton) 18
Second Series of Observations (Cayenne) , 28
Third Series of Observations (Mt. Hamilton) .38
Fourth Series of Observations (Mt. Hamilton) 72
Final results based on all the Observations 84
The Law of Photographic Atmospheric Absorption. Equation (181) 85
Table LIX, giving the absorption in magnitudes for each degree of Z.-D... 86
The Probable Error of a Photographic Magnitude - 87
New Units of Brightness and Magnitude 87
Conclusion ___ 88
Works Issued by the Lick Observatory . 90
TERRESTRIAL ATMOSPHERIC ABSORPTION OF THE
PHOTOGRAPHIC RAYS OF LIGHT.
By J. M. SCHABBEELK.
The remarkable revolution in the methods of charting
celestial configurations, brought about by substituting <|br) the
photographic plate, the human eye, has opened up a most
inviting field of investigation. To obtain results which here-
tofore demanded months and years of labor on the part of
the observer only a few hours are now required.
As a necessary consequence of this radical change in the
methods of work many new problems confront the astronomer,
some of which must be solved before the information given by
the photographs can be presented in its final form.
The human eye as normally constituted is most sensitive to
a particular set of light rays. If now we could construct a
photographic plate, on which the set of rays which are most
effective visually would also be most effective photographically,
it is probable that the relative brightness determined photo-
graphically would not differ from that deduced from direct
visual observation.
Up to the present time ; however, the plates which have been
universally employed in photographic work are so prepared
that the action of the light from near the red end of the
solar spectrum or where the light is most effective visually
is very much less effective than that coming from near the
violet end. For this reason it would seem to follow at once,
that whatever unit of brightness is chosen, the relation between
the visual brightness and that deduced from the action of the
same source of light on the photographic plate, can only be
considered constant so long as the spectral type remains the
same. In general we should expect that for stars of different
types of spectra, the relation between the visual magnitudes
will not be the same as the relation between the corresponding
photographic magnitudes.
Investigations relating to the photographic magnitudes of
the fixed stars have been made by PICKERING, PRITCHARD,
2 Terrestrial Atmospheric Absorption of
CHARLIER, SCHEINER, GOULD, and others; a consideration of
the various results seems to show that the different forms of
photographic telescopes and plates do not, as a rule, give, under
otherwise similar conditions, exactly the same data. As will
be shown farther on, the law deduced hy the present writer
holds good for the three different telescopes available; two
being of 6-inch aperture, and the third 33-inch. SEED plates,
Sensitometer No. 26, were used in all cases.
This line of work was taken up in 1889, at the suggestion of
Professor HOLDEN. An equatorially-mounted DALLMEYER lens,
primarily intended for eclipse work at Cayenne, and loaned to
the Lick Observatory by the United States Naval Observatory,
was first employed for obtaining the necessary data; later on a
WILLARD lens, belonging to the CROCKER telescope, was also
used.
DETERMINATION OF THE RELATION WHICH, FOR A GIVEN STAR,
EXISTS BETWEEN THE APERTURE (Q) OF THE TELESCOPE
AND THE DIAMETER (d) OF THE STAR'S IMAGE FOR A GIVEN
EXPOSURE TIME (t).
Some of the results of a preliminary investigation made on
Mount Hamilton are embodied in a paper entitled, " On the
Photographic Magnitudes of the Fixed Stars." (See Publica-
tions of the Astronomical Society of the Pacific, Vol. I, No. 4.)
To obtain a general expression for the brightness of a fixed
star, as determined by means of its image impressed upon the
photographic plate during an exposure time t, and with aper-
ture D, I arranged the following scheme for obtaining the
necessary data:
With a known aperture of the objective, a series of images
of the star were first obtained, the exposure times being
respectively 1 s , 2 s , 4 s , 8 s , 16 s , 32 s , 64 s , and 128 s , the telescope being
slightly shifted after each exposure to keep the images from
overlapping. Other series of similar exposures on the same
star and plate were then made with different known apertures.
This scheme was then applied to different stars.
Now, in the case of any one of these stars, the source of
light, during the time of one series of exposures, remains prac-
tically constant; hence, it is evident that the relation between
the exposure time t, the diameter of the aperture D, and the
The Photographic Rays of Light.
diameter of the star's image d, must always be such that the
expression for the brightness B is a constant quantity for any
given star, whatever its magnitude may be.
From a discussion of the data given by these plates, I found
that the law governing the size and rate of growth of the
image could be expressed by means of an equation of the form,*
d = a + ft log D + y D log *. (1)
In which d is the measured diameter of the image for the
aperture D and exposure time t, while or, /?, and y are constants
which depend upon the telescope, the atmospheric condition,
and the kind of photographic plate employed.
Using this theoretical relation between d, D, and t, I showed
that if Q represents the theoretical aperture which a standard
star (Polaris) would require to produce in the time J, an image
having the same diameter d as that produced by any star
with a constant aperture Q (6-inch) in the same time f, the
equation which serves to determine the magnitude of any star
whose image is impressed upon the photographic plate is of
the following form:
d = <x + /31 gQ + yQlogt. (2)
The corresponding photographic magnitude m' is then found
by means of the expression
, , log * Q 2
-~~
k being a constant which depends upon the photographic
magnitude of the standard star. If we take Polaris as the
standard star, and assume for the present (only) its apparent
photographic magnitude to be 2.00 at the zenith-distance
52 40', corresponding to the co-latitude of the Lick Observa-
tory, equation (3) becomes
,
(For illustrative examples, see Publications of the Astronom-
ical Society of the Pacific, Vol. I, No. 4.)
*As I afterwards learned, Professor PRITCHARD, Director of the Savilian
Observatory, had previously also found that d could be expressed as a func-
tion of log t.
4 Terrestrial Atmospheric Absorption of
DETERMINATION OF THE INSTRUMENTAL CONSTANTS.
I shall now attempt to show that equation (2), when properly
interpreted, is quite general in its character, and apparently
applicable to similar telescopes of any aperture actually em-
ployed in photographic work.
Let us first consider the case of two similar telescopes having
equal apertures. From a series of experiments made with two
such instruments (one of which was a DALLMEYER, the other a
WILLARD lens of 5.9 inches aperture) I found that while the
growth of the images during equal units of time was practi-
cally the same for both instruments, there was a small and
almost constant difference between the dimensions of the images
for the same value of t. This difference, taking the DALLMEYER
telescope as the standard, might be called the constant correc-
tion of the WILLARD lens.
In order, therefore, to render the measured quantities homo-
geneous, we must first determine the correction to be applied to
each d of one instrument, in order to reduce it to the normal
d of a particular instrument taken as a standard.
In the following notation let the symbols which are not
primed refer to the standard (6-inch DALLMEYER) telescope,
and let those with the primes refer to a companion telescope
of equal (6-inch) aperture.
Let d and d ' denote the diameters corresponding to the
exposure time t :
Let d and d' denote the diameters corresponding to the ex-
posure time f:
And for brevity let
a-f/JlogQ=c (5)
a' + /JlogQ = c' (6)
Then, since the value of Q is the same for both telescopes
when the same star is observed, we can write
d = c + r Qlogt (7)
d = c + rQlog (8)
and
d ' = c+y Qlog (9)
The Photographic Rays of Light.
from which the expressions for Q become
0= _ _ nn
y (log -
O H21
/(log logt.)
Hence, the difference between the diameters of any two
images of the same star divided by the difference between the
logarithms of the corresponding times of exposure is a constant
for the same telescope and plate.
We must evidently have also
Now, although the values of d and d' in the two telescopes
may differ considerably for the same value of t, still experi-
ment seems to prove that the difference between the growths
(d d and d' d ') of the images in two similar telescopes can
be treated as a quantity of the second order, so that we can
write
Y = Y (14)
If now we make < = l s , the expressions for the value of Q
become
d-d. (15)
the value of y for the DALLMEYER telescope and SEED 26 plates
being 0.0033.
It is evident that a difference in the development of the
plates may have a great effect upon the resulting values of d.
A strong development will, as a rule, give larger images than
a weak development, and as the image of a bright star grows
faster than that of a faint star the relative effect may be most
marked. Therefore, not only should the plates be of the same
degree of sensitiveness, but the development of these plates should
be uniformly the same.
6 Terrestrial Atmospheric Absorption of
Equations (15) and (16) can be considered as special differ-
entials of (8) and (10), in which the increments are finite.
For if we differentiate (8) and (10), regarding d and i as vari-
ables, and designating the differential by the symbol 7 we
obtain
6d = yQ- (17)
dd' = yQ (18)
from which we have
which are identical with (15) and (16) when finite incre-
ments are employed.
To determine the value of the constant correction to be ap-
plied to the data given by the companion telescope, we first
find the value of Q by means of (16). With this Q as an
argument we enter Table II, and take out the values of d corre-
sponding to the exposure time t; then since we also have,
according to equations (7), (8), or (9), (10), the equation
c c ' = d d' (21)
it follows that each exposure on a given star furnishes an inde-
pendent value of the correction (c c') to be applied to the
measured values of d' to obtain the normal or tabular values.
It also follows that if the empirical formula is correct, the
several independent values of these corrections should agree
within the limits of the errors of observation.
Thus far we have been considering the problem of determin-
ing, with the aid of data given by an assumed standard tele-
scope, the photographic magnitude of a star from the data given
by a second telescope having the same aperture as the standard
instrument. Let us now consider the general problem of find-
ing the photographic magnitude from data given by a telescope
having an aperture n Q referred as before to the system of
magnitudes given by the standard telescope.
The Photographic Rays of Light.
Now, for theoretically perfect telescopes, the magnitude M'
corresponding to a given d, t, and aperture n Q o can be expressed
by means of the equation
M o (22)
0.4
And for the same values of d and t , but with the aperture Q ,
the required magnitude (m) necessary to satisfy the conditions
would be expressed by equation (4). The difference between
equations (4) and (22) for the same t and d will evidently be a
constant quantity, whose value is given by the equation
M ' m = 5 log n (23)
or,
M' = m + 5 log n (24)
Hence, with the aid of Table II we should also be able to
determine the theoretical photographic magnitude of a star pho-
tographed with an aperture n Q by simply adding 5 log n to the
tabular m corresponding to the observed arguments d and t.
However, in deducing the law expressed by equation (1) all
the imperfections peculiar to the particular standard instru-
ments are involved; that is, the law is so determined that the
constant corrections are already applied. But the imperfections
of another telescope will not necessarily be the same as those
of the standard instrument, so that generally the measured
values of d will be in error when referred to the standard
instrument. It is therefore essential to use the corrected value
of d'; or to determine the value of Q by means of equation (12)
or (16) where the constant is eliminated.
As I very much desired to learn how closely these formulae
represented the observations for those cases in which Q and
n Qo were very different, the theory was tested by means of the
most extreme practical case which could be applied at the pres-
ent time. At my request Professor HOLDEN, aided by Professor
CAMPBELL, made a series of suitable exposures for me upon the
star Polaris with the great refractor, the clear aperture of which
for photographic purposes is 33 inches.
8 Terrestrial Atmospheric Absorption of
As our unit of aperture is 6.00 inches we have for substitu
tion in equation (22) the values
Q.=4=1.00
^ '
The true tabular magnitude m is therefore according to
equation (24),
M' = m -f- 5 log 5.5 = m' -f 3.70.
To compare this result with actual observation we employ
equation (16) in order to eliminate the constant errors of the
d (given in the table) in determining the value of Q.
From the observed data we have for values of t = 1* and t =
256', the corresponding values d' = 0.0250 and d' = 0.0700;
hence, according to actual observations we have
nQ=5.67 (26)
Agreeing fairly well with the theoretical value 5.50 found
above. The tabular magnitude corresponding to n Q = 5.67 is
1.77; hence, according to equation (24),
m = 3.70 1.77=1.93 (27)
When it is considered that this result for the magnitude of
Polaris (differing only O m .07 from the adopted magnitude) is
practically the same as that given by the 6-inch objective, it
would seem to indicate that the results obtained with different
instruments are less heterogeneous than might naturally be
expected, for in the present case not only are the apertures very
different, but for the 33-inch telescope the ratio of aperture to
focal length is only about one third as great as it is for the
DALLMEYER lens. Discrepancies in the results given by differ-
ent observers are probably largely due to the fact that the con-
stants peculiar to each instrument and plate have not been
sufficiently sharply determined, and still more largely due to
differences in the degree of development of the photographic
plates.
To show the practical agreement between theory, as defined
by equation (2), and observation, I give the data obtained with
the great telescope, using all the exposures made on Polaris.
The Photographic Rays of Light. 9
In the following table the first column gives the duration of
the exposures; the second column, the diameters of the corre-
sponding stellar images; the third column, the tabular diameters
corresponding to n Q = 5.67, as found by observation; the last
column contains the individual values of the constant correction
c c to be applied to all measured values of d' to make them
comparable with the values given in Table II.
EXPOSURES ON POLARIS WITH THE 33-iNCH PHOTOGRAPHIC TEL-
ESCOPE, AND COMPARISON WITH THEORY, FOR TESTING THE LAW
DEDUCED FROM EXPERIMENTS MADE WITH A 6-iNCH PHOTO-
GRAPHIC TELESCOPE.
TABLE I.
Exposure Time.
Measured
d'
Computed
Constant
C Co
1 s
0.0250
0.0079
0.0171
2
.0305
.0136
.0169
4
.0360
.0192
.0168
8
.0415
.0248
.0167
16
.0470
.0305
.0165
32
.0525
.0361
.0164
64
.0590
.0417
.0173
128
.0645
.0474
.0171
256
.0700
.0530
.0170
On the hypothesis that the standard and comparison tele-
scopes have, photographically, the same peculiarities, the theo-
retical value of the constant term for the 33-inch telescope is
given by the expression
+ ft log Q'o = 0.0055 + 0.0033 X 0.74 = 0.0079 (28)
Polaris being taken as the standard star. But according to
observation the mean constant is 0.0248; the difference between
this value and that deduced from equation (2) must be
attributed to the peculiarities of the 33-inch lens as compared
with the 6-inch standard telescope. The explanation of this
difference seems to be that the initial images do not start from
a point, but from a sensible area; the magnitude of this area
is not only dependent upon the diameter of the objective but
also upon the character of the color curve.
The photographic magnitude of any star can best be deter-
mined by making two or more exposures on the same plate, so
10 Terrestrial Atmospheric Absorption of
as to give suitable values of d' for determining the rate of growth
of the image.
The law expressed by equation (2) will then, it seems, hold
good; equations (16) and (24) being used to find the proper
magnitude.
In order to apply the formulae to any particular case, the
equivalent value of d should not be much less than 0.0055, as
the formulae could not well be tested, on the standard star, for
values of t less than one second of time.
The number of examples could, of course, be multiplied, but
for the present purpose the foregoing illustrations are deemed
sufficient, so far as the investigation of the atmospheric absorp-
tion of the photographic rays of light is concerned. Later on,
in dealing with the data given by the WILLARD lens, this sub-
ject will be further illustrated.
The foregoing investigations were, of course, necessary before
the observations on absorption could be reduced. To enable
any one to follow the various steps, and also to make use of the
tabular values for other purposes, all the necessary data are
given in abbreviated form. In making the exposures the
observer was not always able to guard against those causes
which produce imperfect images, nor was it always possible to
know before the developments of the plates whether such imper-
fect images were present. In nearly every case such imperfec-
tions are in the nature of an elongated image, caused by a failure
of the telescope to conform to the diurnal motion. A series of
dashes ( ) indicate that the particular measure was
rejected on this account.
TABULAR VALUES OF Q, ra', d, AND t.
In practice, if a large number of values of an involved ex-
pression are required, the ease and rapidity with which such
values can be obtained will be increased, if the functions corre-
sponding to certain arguments are first computed and then
arranged in suitable tabular 'form.
I have accordingly computed the values d for certain values
of t and equicrescent values of Q. These quantities are arranged
in tabular form. (See Table II.)
The arguments for entering this table are the measured d
and the corresponding exposure time t. The corresponding
The Photographic Rays of Light. 11
provisional magnitude m' is there found, by interpolation, in
the first horizontal column of the table.
The resulting tabular magnitudes are those given by the par-
ticular DALLMEYEB telescope and SEED plates No. 26, used in
these investigations. For convenience and completeness, I have
retained and used the quantity Q throughout the whole discus-
sion in preference to m', as the value of Q will not be affected
by any subsequent change in the light ratio which it may be
found advisable to make at any future time. I have therefore
also added another horizontal argument giving the values of Q.
In using the table it should be remembered that the pro-
visional unit of brightness is that given by Polaris at the
zenith-distance, 52 40', and the provisional magnitude at that
zenith-distance is 2.00. These units were adopted simply as a
matter of convenience, since the photographic absorption was
not known until the present investigation was completed.
In order, however, to make the photographic and visual
results directly comparable, Polaris will, as heretofore, be taken
as the standard star, but the brightness (1.00) and the magni-
tude (2.00) finally assigned will be that which the star would
have if it could be observed in the zenith of the LICK Obser-
vatory.
For facilitating the use of Table II in the finally adopted
system of brightness and magnitude, I have placed the new
arguments, corresponding to the tabular d, at the bottom of the
page.
As will be shown farther on, the atmospheric absorption of
the photographic rays at 52 40' zenith-distance amounts to 0.51
magnitudes on the provisional scale, consequently, the magni-
tude of Polaris in the zenith is l m .49.
If, therefore, we adopt 2.00 as the photographic magnitude of
Polaris in the zenith, we have simply to add O m .51 to each of
the corresponding tabular arguments for magnitude to obtain
the new tabular arguments for magnitude.
To find the relation which exists between the provisional
tabular values of Q, and the corresponding values of Q' in the
new system, we can write the two equations:
Q2 = (0.4)- 2 (29)
2 + wa (30)
12 Terrestrial Atmospheric Absorption of
Passing to logarithms, and taking the difference between
equations (29) and (30), we readily deduce the relation
Q' = 0.79 Q (31)
Hence, having given the tabular value of Q corresponding to
a given d in the provisional sj^stem, we have only to multiply
it by 0.79 to obtain the tabular Q', corresponding to the same
value of d in the new system.
In the following table I have carried the tabular quantities
to extreme values of Q, cZ, and f, not with the expectation that
the relations will be found to be strictly accurate at these ex-
treme limits, but rather for the purpose of giving a general
numerical view, so to speak, of the whole theory, and also to
more easily enable others to compare their results with those
here given:
The Photographic Rays of Light.
18
g 8
d
,s fj^o Ji
So ooo
Opq
ill
5 q q q q q q
888
38 &^.
!2S i?ic
^888 8.88 888
o
*!! 111 in |||
J OO ^ I
(M C^ CO CO CO <*<
888 888
I
14
J^errestrial Atmospheric Absorption of
r-lOCO <MOOO
!5
Is
ll 1!
O O
1C l^ O5 iH (
COCD CiCO<
The Photographic Rays of Light. 15
ATMOSPHERIC ABSORPTION OF THE PHOTOGRAPHIC RAYS OP LIGHT.
Owing to the ever changing condition of our atmosphere,
and to the want of definite information as to its density at
different heights for variations in temperature and pressure,
the complete solution of the problem of determining the path
of a ray of star-light has not yet been accomplished.
Many different expressions have been deduced by as many
different investigators for the law of atmospheric refraction,
and in all of these, quantities of a more or less empirical char-
acter have been so introduced that the assumed law satisfied
the observed data.
The determination of the amount of star-light lost to us
during its transmission through our atmosphere seems to be a
still more complicated problem. In the case of refraction,
observation seems to show that the relative humidity, for in-
stance, can be almost wholly neglected so far as its effect upon
the refraction is concerned. The same may be said of other
causes which do not affect refraction but which do tend to
diminish the final amount of light which would otherwise be
received.
It is probable that a ray of light in passing through a
medium of varying density suffers not only internal refraction,
but also internal reflection. The exact amount of light lost
by this latter property has, so far as I am aware, never been
determined.
When, in addition to these difficulties, the subject is further
complicated by the introduction of that still mysterious agent,
the photographic plate, as a recorder of certain data, the
task of satisfactorily discussing such material from a purely
theoretical standpoint is a hopeless one at the present state of
our knowledge.
A consideration of these difficulties impelled me to resort to
the same method of deducing an empirical expression which
should represent the terrestrial atmospheric absorption of the
photographic rays of light that I had used in deriving the
preceding formula for finding the photographic magnitudes of
the fixed stars.
The expressions deduced by LA PLACE, SEIDEL, MULLER,
PICKERING, and others, for the atmospheric absorption of the
visual rays, are all of a more or less empirical character.
16 Terrestrial Atmospheric Absorption of
This investigation, like the preceding, was undertaken at
the suggestion of Professor HOLDEN. Four different series of
observations were made, as follows:
Second Series. .At Cayenne, S. A., in Dec., 1889 V. S. N. O. Telescope.
Third Series... At Mt. Hamilton, in July and Aug., 1890.U. S. X. O. Telescope.
Fourth Series.. At Mt. Hamilton, in Nov., 1891 Crocker Telescope.
The exposures for the third series were kindly made for me
by Professor CAMPBELL, who, at the time, was spending his
vacation at the LICK Observatory. The exposures of the
remaining series were made by myself.
METHOD OF OBSERVING.
As the problem under consideration is one which can be said
to be of a differential character, the observations and reductions
can be so arranged that only systematic errors, if any, need be
involved. Such errors, so far as the effect upon the final result
is concerned, can be practically eliminated in the reductions.
To accomplish this object, certain conditions must be ful-
filled. Among others, care must be taken that during the time
required to make a single, complete, and independent determi-
nation, there shall be no changes in
(1) The source of light.
(2) The sensitiveness of the photographic films.
(3) The atmospheric conditions.
(4) The focal length of the telescope, as defined by the dis-
tance from the objective to the sensitive film.
(5) The development of the plates.
(6) The illumination of the plates while they are being
measured.
All the above-mentioned conditions can be practically ful-
filled, as will appear farther on:
First To secure constancy in the original source of light.
A bright star should be selected having a declination some-
where in the neighborhood of the latitude of the point of
observation, and whose position with reference to the observer's
zenith is such that during the interval between the time of the
star's meridian passage and the time of its rising or setting, the
exposures on this star, at various zenith-distances, are free
from twilight and moonlight. No star of variable light should
be employed.
The Photographic Rays of Light. 17
Second As no two sensitive plates, taken at random from
the same box, can a priori be said to be of positively the same
degree of sensitiveness, it is evident that the only way to secure
uniformity in this respect is to make all the exposures for a
given determination on the same plate; and even here we
assume that the film is equally sensitive in all its parts, which
is not strictly true.
Third Observations made under abnormal atmospheric
conditions (clear at one altitude, and foggy, smoky, or cloudy
at other altitudes) should be rejected.
Fourth In order to be sure of the invariability of the posi-
tion of the sensitive plate, so far as its distance from the
objective is concerned, the same plate-holder should be used
for all the exposures of a single determination; and all the
images should be near the center of the field.
Both the second and fourth conditions are fulfilled, if the
same plate and plate-holder are used.
Fifth As all the images of any given series will now be
found on a single plate, the method of development will evi-
dently be the same for all. Different plates should all be
developed in precisely the same way.
Sixth It is very essential that all the measures of a given
series be made under the same illumination; too much stress
cannot be laid upon this condition. As all the exposures will
be found upon a single plate, this condition can be fulfilled by
making all the measures of this plate at a single sitting. To
avoid the effect of personal equation, all the measures of the
present paper have been made by myself.
METHOD OP DERIVATION OF THE FUNDAMENTAL EQUATION.
To determine the form of the function which best represents
the law of apparent decrease in brightness of a star with increas-
ing zenith-distance, the theoretical value of Q, corresponding to
each measured d for exposures of 2 s , 4 s , and 8", was first obtained
with the aid of Table II, and the mean of the separate results
adopted as the value of Q at the zenith-distance corresponding
~to the mean of the times of observation.
Empirical equations of conditions were then formed, each
value of Q furnishing the constant or absolute term of an inde-
pendent equation. The form of the function must evidently be
9
18 Terrestrial Atmospheric Absorption of
such that its value is at a maximum for the zenith-distance
zero, and at a minimum when the zenith-distance is at a maxi-
mum.
Several of the simpler formulae which I deduced repre-
sented the observed data quite satisfactorily for zenith-distance?
down to 70 or 75 ; but for great zenith-distances all these first
attempts were found to lack generality, the residuals near the
horizon being relatively large, and of a systematic character.
After several tedious trials of more complicated formula?, in
each of which nearly the whole mass of available observations
was worked over, and the residuals (obtained by subtracting
the empirical values from the observed) discussed by a com-
bination of graphical and analytical results, I interpolated the
formula given below, which now represents the observed data,
in such a way that the sum of the squares of the residuals is
less than it is for any of the other formulae discussed.
If B and B denote, respectively, the photographic magnitude
of a star at the zenith-distances <2 = o and <? = <?", and if /
denotes a constant depending chiefly upon the condition of the
atmosphere, the equation which best represents the observed
data is of the form
(32)
In this expression ^ is to be regarded as an abstract number.
the square of which represents the number of degrees of which
the trigonometrical tangent is required.
FIRST SERIES OF OBSERVATIONS FOR ABSORPTION.
All the observations of this series were made with the U. S.
N. 0. telescope already referred to. This instrument was set
up on Mount Hamilton, so as to have a clear eastern sky. As
there was no covering of any kind to protect it from the wind,
which is often quite strong here, much trouble was experienced
from this source. Besides causing a vibration of the whole
instrument, the wind very frequently stopped the driving clock,
which, for this instrument, is governed by a swinging pendulum
which unlocks the train of wheelwork at every half vibration;
sudden variations in the speed being checked by revolving fans.
This form of governor works satisfactorily so long as the resist-
The Photographic Rays of Light. 19
ance to be overcome by the clock is uniform. If, however, for
any cause, the train of wheelwork lags so that the pendulum
reaches the unlocking point after the escapement shaft is in
proper position, the clock at once comes to a standstill. Later
on the fans were inclosed in a box, which improved matters
somewhat. So far as my own experience goes the very simple
and wholly satisfactory contrivance now so largely used by
American instrument makers to regulate the velocity of the
centrifugal or rotary pendulum governor is much to be pre-
ferred.
The first series of observations for atmospheric absorption
of the photographic rays was made on a Arietis. I should
have preferred to use a much brighter star, but this one seemed
to be in the best position for observation at both great and
small zenith-distances, as in other directions the view was
much more limited, owing to the proximity of the Observatory
buildings. I also regret that in the original program it was
thought to be sufficient to carry the observations to a zenith-
distance of only 75. (Later on I secured several series of
observations on a Lyrae to a zenith-distance of 90.)
At each altitude exposures of 2 s , 4 s , and 8 s were made on the
same plate, the telescope being slightly shifted after each expos-
ure to avoid the overlapping of the different images. A finding
view telescope attached to the tube of the photographic tele-
scope was furnished with a suitable network of wires, so that
the exposures for the different sets could be properly located.
The interval of time between the exposures at different alti-
tudes was, on an average, less than one hour.
All the exposures were made by removing the cap covering
the object-glass as quickly as possible at a given beat of the
chronometer, and replacing it as quickly as possible at another
given beat. A little practice enables one to make the exposure
times of the proper duration with a very small percentage of
error for all exposures of not less than 1 s . I have, however,
deemed it best to use only the exposures which are greater
than 1 s .
In the following pages the comparison between theory, as
represented by equation (32), and observation, is given with
sufficient detail. In each equation of condition the unknown
20 Terrestrial Atmospheric Absorption of
quantities involved are Q (= i/js ) and /, each equation being
of the form
/??(3) = Q. (33)
which = Q ; =/, or /? = / Q ; and ? (5) = tan [(0"'].
Explanation of the Tabular Data in Tables III- VII.
The first column gives the sidereal time corresponding to the
mean of the times of exposure. The corresponding hour-angle
(T), zenith-distance (), measured diameters (d), and result-
ing values of Q are given in the succeeding columns under
those headings. The last column gives the residual, found by
subtracting the computed theoretical value at a given zenith-
distance, as given by equation (32), from the observed value at
the same zenith-distance.
The values of d and Q for the separate exposures of 2 s , 4 s , and
8 s are given individually, in order that, first, all the observed
data may be available for any future use, and second, to show
more plainly how closely the degree of accuracy is dependent
upon the measured d corresponding to a given exposure time t.
The values of d are given in units of the fourth decimal place
of inches.
As a test for determining the sensitiveness of the particular
plate, a series of exposures on Polaris were also made; the
results will be found in Table VIII, which also gives the
provisional relative values of Q and m for both Polaris and
of Arietis. The last column gives the individual results of the
difference between the magnitudes of these two stars. The
abnormal condition of the results for September 6th is shown
to be the same for both stars.
* These values of a and ft have no relation to those given in the preceding
pages.
The Photographic Rays of Light.
21
U. S. N. O. Telescope. a Arietis. Bar -> 25 in .87.
Att, Ther., 76.
L. O., Sept. 4, 1889. TABLE III. Ex ^ 73 <>
d
T
T
c
2*
43
8'
Q
Mean
Q
o c
42
0.30
ii8
18h 17m
73.l
54
0.50
0.45
+ 0.05
63
0.55
20 55
18 54
66 .0
52
62
0.45
0.55
0.50
+ 0.02
50
0.50
21 33
19 32
58 .4
59
0.60
0.57
+ 0.02
66
0.60
48
0.45
22 48
20 47
43.5
59
0.60
0.57
0.07
68
0.65
56
0.70
21 59
29 .7
63
0.70
0.70
+ 0.01
55
0.65
10
22 9
27 .8
65
0.70
0.72
+ 0.02
75
0.80
56
0.70
1 3
23 2
18 .9
63
0.70
0.70
0.02
72
0.70
Equations of Condition.
a 0.76 /? = 0.45
a 0.58/5 = 0.50
a 0.44/3=0.57
a 0.23 /? = 0.57
or 0.11 /3 = 0.70
a 0.09 /? = 0.72
0.04 /? = 0.70
Normal Equations.
7.00 a 2.25 /3 = 4.21
2.25 a 1.18 /?= 1.15
Solution of Normals.
<x = 0.743
y3 = 0.443
(34)
(35)
(36)
22 Terrestrial Atmospheric Absorption of
U. S. X. 0. Telescope. a Arietis. Bar -. %>"&
Att., 71.
L. O., Sept. 5, 1889. TABLE IV. Ex-) 710>
d
T
r
C
2 s
4 s
Q ^
oc
8'
40
0.30
19 45 m
jyh 4401
79.4
45
0.30
0.33
-0.12
55
0.40
55
0.65
21 1
19
64 .8
60
0.60
0.65
0.06
70
0.70
60
0.80
21 47
19 46
55.0
67
0.80
0.87
+ 0.05
85
1.00
65
1.00
23 28
21 27
35.1
77
1.05
1.03
+ 0.06
87
1.05
67
1.05
43
22 42
22 .3
77
90
1.05
1.10
1.07
+ 0.05
Equations of Condition.
^ 0.96 ,5 = 0.33
a 0.56,5 = 0.65
a 0.38,5 = 0.87
a 0.15,5=1.03
a- 0.06,5=1.07
Normal Equations.
5.00 a 2.11 ,5 = 3.95
2.11 or 1.59 ,5=1.22
Solution of Normals.
a= 1.057
P = 0.633
(37)
(38)
(39)
T/te Photographic Rays of Light.
23
r. s. X. O. Telescope.
L. 0., Sept, 6, 1889.
a Arietis.
TABLE V.
Bar., 25">.90.
Att., 71.
Ex., 71.
T
T
I
2 s
4*
8'
Q
Mean
Q
o c
30
0.15
IQh 40m lyh 39m
80.3
40
0.25 ! 0.23
+0.04
45
0.30
35
0.20
21 3
19 2
64.6
45
0.30
0.28
0.03
50
0.35
40
0.30
21 53 19 52
54 .4
45
0.30
0.33
-0.02
55
0.40
40
0.30
23 4 21 3
40 .3 50
0.40
0.37
0.03
55
040
45
0.40
00 ! 21 59
29.7
55
0.50
0.47
+ 0.05
1
60
0.50
Equations of Condition.
a 0.99,5 = 0.23
a 0.55 ,3 = 0.28
a 0.37/5 = 0.33
a 0.20,5 = 0.37
or 0.11 ,5 = 0.47
Normal Equations.
5.00 a 2.22/5= 1.68
2.22 a 1.47/5=0.62
Solution of Normals.
a = 0.452
,* = 0.261
(40)
(41)
(42)
24 Terrestrial Atmospheric Absorption of
U. S. N. 0. Telescope.
L. O., Sept. 7, 1889.
a Arietis.
TABLE VI.
Bar., 25.87.
Att., 72.
Ex., 72.
r
r
c
d
Q
Mean
Q
C
20" 21"
18" 20"
72 .6
50
60
0.50
0.60
0.55
0.00
21 29
19 28
59.2
60
70
70
0.80
0.85
0.70
0.78
+ 0.01
22 17
20 16
49.7
60
70
85
0.80
0.85
1.00
0.88
0.00
23 15
21 14
38 .1
65
75
85
1.00
1.00
1.00
1.00
+ 0.04
31
22 30
24.2
65
75
90
1.00
1.00
1.10
1.03
0.03
Equations of Condition.
a 0.74,3 = 0.55
a 0.45 ,5 = 0.78
a 0.31 ,3 = 0.88
a 0.18,5 = 1.00
a 0.07,3 = 1.03
Normal Equations.
5.00 a 1.75,5 = 4.24
1.75 a 0.88,3 = 1.28
Solution of Normals.
a =1.113
,3 = 0.758
(43)
(44)
(45)
The Photographic Rays of Light.
25
V. S. X. O. Telescope.
L. 0., Sept. 14, 1889.
a Arietis.
TABLE VII.
Bar., 25i.83.
Att., 67.
Ex., 67.
T
*
r
d
2'
4*
8 s
Q
Mean
Q
C
49 0.50
20" 18-"
18" 17 m 73.l
53 0.45
0.50
+ 0.02
62 0.55
51 0.55
20 55
18 54
66 .0
57 0.55
0.58
+ 0.02
67
0.65
52
0.55
21 33
19 32
58 .4
62
0.65
0.63
0.01
1
72
0.70
55
0.65
22 48
20 47 43 .5
65 I 0.70
0.72
0.02
75 ! 0.80
57 i 0.70
3
22 2 29 .1
67 0.80
0.80
0.01
80
0.90
60
0.80
10
22 9
27 .9
67
0.80
0.83
+ 0.02
80
0.90
60
0.80
1
22 59 19 .3
67 0.80
0.83
0.01
80 0.90
Equations of Condition.
a 0.75,5 = 0.50
a 0.58 ,3 = 0.58
a 0.44,5 = 0.63
a 0.23,5-0.72
a 0.10/5 = 0.80
a 0.09 ,5 = 0.83
a 0.04/5 = 0.83
Normal Equations.
7.00^ 2.23,5 = 4.89
2.23 a 1.14,5=1.34
Solution of Normals.
a = 0.862
= 0.510
(46)
(47)
(48)
NOTE. In the following table it should be remembered that for Polaris the
Q refers to a zenith-distance 52 40*, while for a Arietis, it corresponds to the
zenith-distance 0. The same remark is to be applied to the comparisons
with other stars.
26 Terrestrial Atmospheric Absorption of
TABLE VIII.
Polaris.
<?
m'
A m'
Date.
d
c
Polaris.
a
Arietis.
Polaris.
a
Ariel in.
1889.
Sept. 4
60
65
75
65
75
85
55
60
65
65
75
90
60
75
90
0.80
0.85
0.90
1.00
1.00
1.00
0.50
0.60
0.60
1.00
1.00
1.10
0.53
0.66
1.10
0.85
1.00
0.57
1.03
076
0.74
1.06
0.45
1.11
0.86
2.54
2.00
3.L2
1.93
2.59
2.65
1.88
3.74
1.78
2.33
0.11
+ 0.12
0.52
+ 0.15
+ 0.26
Sept. 5
Sept. 6
Sept. 7
Sept. 14
The mean zenith-distance of a Arietis, the atmospheric press-
ure and temperature, and the resulting values of /, are given
in Table IX.
a Arietis.
TABLE IX.
Date.
Mean
Zenith-
Distance.
Pressure.
Temper-
ature.
/=!
HEM ARKS.
1889.
Sept. 4.
45.3
25 in .76
73
0.60
Sept 5
51 3
25 79
71
060
Sept. 6
53 .9
25 .80
71
058
Moon.
Sept. 7
48 .8
25 .77
72
0.68
Moon and smoke.
Sept. 14
45 .3
25 .74
67
0.59
The Photographic Rays of Light. 27
That the plates exposed on a Arietis were not all of the same
degree of sensitiveness seems to be quite plainly shown by the
results given in Table VIII, where the magnitude of Polaris,
as deduced from its uncorrected measured images, varies all
the way from l m .93 on September 7th to 3 m .22 on September
6th. That this variation is not due to errors of observation
follows from the fact that the range in magnitude of a Arietis,
using the uncorrected measures, is also greatest for these same
dates.
The plate exposed September 6th was the least sensitive, and
that exposed September 7th the most sensitive of the whole set.
A part of this difference in magnitude for different dates
may of course be due to different atmospheric conditions, the
air being more free from foreign matter at one time than
another.
So far as the meteorological conditions of pressure and tem-
perature are concerned, the range, as shown in Table IX, is
entirely too small to account for any considerable portion of
variation in the computed results; for this same reason no
reliable inferences can be drawn from this series as to the effect
of pressure and temperature on the absorption of the photo-
graphic rays.
A difference in the development of the plates would also
cause a variation of precisely this kind, and this particular
phase of the investigation will be treated more fully farther
on. In this place I only wish to call attention to the fact that
those plates which give results indicating greater sensitiveness
(whether such is the actual case or not) give as a rule larger
values of / than those plates which appear to be less sensitive.
Compare, for instance, m and the corresponding value of / for
the same plate in the above tables.
If we take the mean of all the results for a Arietis, giving
the observations of each night the same weight, we obtain the
following expression for atmospheric absorption of the photo-
graphic rays expressed in brightness:
= l 0.61 tp (<?) (49)
28 Terrestrial Atmospheric Absorption of
DISCUSSION OF THE SECOND SERIES OF OBSERVATIONS FOR
ABSORPTION.
The second series of observations for absorption was made in
Cayenne, South America, to which place the LICK Observa-
tory was enabled to send an eclipse expedition through the
liberality of Hon. CHARLES F. CROCKER, a Regent of our State
University. The eclipse observers from this Observatory were
S. \V. BURNHAM and the writer. C. H. ROCKWELL, of Tarry-
town, New York, also joined our party as a volunteer observer.
In addition to the regular work of the eclipse expedition it
was my intention to make an extended series of observations
on a large number of bright stars, for the purpose of determin-
ing their photographic magnitudes, and also to make a very
complete series of observations on atmospheric absorption of
the photographic rays. That this plan of work was not as
completely carried out as originally intended must be attributed
wholly to the extremely unfavorable condition of the weather.
During our entire stay of one month clouds were never wholly
absent from the sky during an entire night, and ordinarily the
difference between the dry and wet bulb thermometers was only
a degree or two.
I believe it rained on nearly every day of our stay in Cay-
enne. Clouds would at times suddenly form in the clearest
sky, so that in making exposures it was very necessary for the
observer to keep the closest watch for perfectly clear spaces.
Another, and even greater, source of annoyance was the con-
stant tendency of the objective to become covered with dew.
If reliable results were to be obtained it was evidently useless
to make exposures with a lens (only incompletely wiped off
with a dry cloth) which might fog over before the 2 s , 4 s , and 8 s
exposures could be completed.
After my first night's experience I kept a large tin can, which
was open at one end, near the instrument. This can was kept
in a heated state during the whole time the observations were
going on, by placing it in an inverted position over a burning
lamp. Just before making the exposures this can was placed
over the objective end of the tube, and allowed to remain there
until the heated air within the can dispelled the dew. Often it
was necessary to reheat the can several times before the desired
effect could be produced.
The Photographic Rays of Light. 29
As all the exposures were made east of the meridian the
early observations would correspond to those made at great
zenith-distances. The instrument at these times would, ordi-
narily, be still somewhat warm from the day temperature, and,
consequently, the objective would be more apt to be wholly free
from dew than would be the case later in the evening when the
stars used would be at a greater altitude. The effect of dew on
the objective would, for a moderately faint star, of course tend
to diminish the size of the images on the photographic plate,
while for very bright stars, like ft Orionis and Sirius, there
would also be a blurring of the image over a considerable larger
area than that occupied by the normal image. On the whole,
therefore, it is quite probable that the later exposures, in spite
of the precautions taken, gave images which were of less diam-
eter than would have been obtained earlier in the evening for
an equal altitude.
A very striking case, illustrating this phase of the problem,
is shown on a plate exposed on December 13th. From O h 37 m
to 2 h 18, sidereal time, the images of ft Orionis increased accord-
ing to the usual experience, but after 2 h 30 m the images of this
star actually began to decrease in size, although the star had
not yet reached the meridian. The peculiar appearance of the
images and the blurred outline of the trail, shown after devel-
opment, at once indicated that something was wrong. On
referring to my note-book the words, " objective covered with
deAV at close of observations," cleared up the mystery. After
this night's work, which was the first made use of in Cayenne,
the above mentioned precautions were taken to keep the object-
ive as free from dew as possible. The 2 s , 4 s , and 8 s exposures
were always made at times when the star appeared to be at least
several degrees from the nearest clouds, and, so far as the
observer could judge, of normal brightness. It was often neces-
sary to wait half an hour or more before a suitable exposure
could be made. After each set of exposures the star was allowed
to trail for one minute. These trails, in many instances, show
the effects of passing clouds. From the foregoing statements it
is evident that the results obtained for Cayenne are not as trust-
worthy as is desirable.
As the data given in the following tables are arranged in the
same way as for the first series, no separate explanation need be
given here.
Terrestrial Atmospheric Absorption of
U. s. X. O. Telescope.
Cayenne, Dec. 13, 1889.
a Orionis.
TABLE X.
Aneroid, 30"' .0.
Dry Ex., 76 .0.
Wet, 75 .5.
T
T
c
2 s
4-
8*
Q
Mean
Q
o c
50
0.50
Qh 28 m
18" 39 79.7
60
0.60
0.60
0.02
70
0.70
60
0.80
51 ! 19 2
74 .0
70
0.85
0.85
+ 0.07
80
0.90
60
0.85
1 8
19 19
69 .8
70
0.85
0.88
0.00
85
1.00
65
1.00
1 22
19 33
66 .3
75
1.00
1.03
+ 0.08
90
1.10
65
1.00
1 46
19 57
60.4
75
1.00
1.00
0.06
S5
1.00
65
1.00
2 9*
20 20
54 .7
80
1.15
1.08
-0.06
90
1.10
* Object-glass covered with dew; images from here on begin to decrease
in diameter (on the plate) with diminishing zenith-distance.
Equations of Condition.
a 0.97 fi = 0.60
a 0.78/5=0.85
a 0.67/5 = 0.88
a 0.59/5=1.03
a 0.47/5=1.00
^0.38^=1.08
(50)
Normal Equations.
6.00 a 3.86/5=5.44
3.86 or 2.71 /?=3.30
Solution of Normals.
(51)
= 0.8S
(52)
The Photographic Rays of Light.
U. S. X. 0. Telescope.
Cayenne, Dec. 13, 1889.
Rigel.
TABLE XI.
T
r
S
d
4 s
8-'
Q
Mean
Q
o c
REMARKS.
90 2.30
That the object-
0" 37"'
19 28"' 69 .5
110 2.20
135 j 2.30
2.27
0.04
glass gradually
became covered
095 2.60
with dew is plain-
ly shown on the
57
19 48
64 .2
115 2.40
2.47
0.03
glass negative;
140 2.40
the images after
2 h 41 m are all
1 14
20 5
60 .1
95
125
145
2.60
2.80
2.60
2.67
+ 0.08
blurred and very
indistinct; they
have, therefore,
been wholly re-
90
2.30
jected.
1 30
20 21
56 .2
120
2.60
(2.43)
140
2.40
100
3.00
1 52
20 43 50 .9
130
3.00
2.90
0.05
150
2.70
105
2.30
2 18
21 9
44 .6
125
2.80
2.93
0.05
150
2.70
105
3.30
2 41
21 32
39 .2
130
3.00
3.10
+ 0.05
160
3.00
Equations of Condition.
a 0.66/5 = 2.27
a 0.54/5 = 2.47
a 0.47 /? = 2.67
a 0.40/3 =(2.43)
a 0.32 yS = 2.90
a 0.24 /?= 2.93
a 0.19 p = 3.10
Normal Equations.
6.00 a 2.42 /? = 16.34
2.42 a 1.15/3= 6.31
Solution of Normals.
a = 3.37
(53)
(54)
(55)
32 Terrestrial Atmospheric Absorption of
4
r. s. N.O. Telescope. a Orionis. Aneroid, 29*92.
Thor Drv, 80-.0.
Cayenne, Dec. 15, 1889. TABLE XII. her ' ( Wet,76.0.
r
T
c
d
2
4 s
8
Q M ^f n
56
1 31
2 4
2 30
3 3
4 4
5 14
5 49
1840>
19 7
19 42
20 15
20 41
21 14
22 15
23 25
77.2
72 .8
64 .1
55 .9
49 .5
41 .3
26 .2
9 .0
2 .3
1
70 006
70
60
70
80
65
0.70
0.80
0.85
0.90
1.00
0.85 +0.01
1.05 +0.09
1.00 0.04
1.15 0.05
1.17 0.01
1.22 0.01
1.22 0.05
1.33 +0.05
i
90
65
75
85
70
1.10
1.00
1.00
1.00
1.20
90
70
80
90
70
1.10
1.20
1.20
1.10
1.20
95
70
80
95
75
85
95
1.25
1.20
1.20
1.25
1.45
1.30
1.25
Equations of Condition.
0.88 /? = 0.70
oc 0.75 ft = 0.85
oc 0.54/2=1.05
a 0.40/3=1.00
0.31 /?=1.15
<* 0.21 /?=1.17
0.08 /?= 1.22
0.01 /?=1.22
a 0.00 ft= 1.33
Normal Equations.
9.00 a 3.18/3 = 9.60
3.18 1.93/3 = 2.95
Solution of Normals.
a=U28
ft = 0.59
(56)
(57)
(58)
The Photographic Rays of Light.
U. S. X. O. Telescope.
Cayenne, Dec. 15, 1889.
Procyon.
TABLE XIII.
Aneroid, 29 iQ .92.
Tho. 'Dry, 80.
Ther. '
T
T
c
d
&
4 s
8 s
Q
Mean
Q
o c
!h54m
18" 21 m
84 .4
47
57
0.35
0.45
0.40
0.19
2 12
18 39
79 .9
65
72
1.00
0.90
0.95
+ 0.08
2 52
19 19
69 .9
90
105
1.50
1.50
1.50
+ 0.17
3 27
19 54
61 .2
82
97
110
1.90
1.70
1.60
1.73
+ 0.14
4 10
20 37
50 .5
85
97
115
2.00
1.75
1.75
1.83
+ 0.01
5 40
22 7
28.1
87
102
122
2.15
1.95
1.90
2.00
0.16
Equations of Condition.
a 1.17/5 = 0.40
a 0.98 /3 = 0.95
a- 0.67 /3= 1.50
a 0.49/3=1.73
a 0.32 /3=1.83
a 0.10/5=2.00
Normal Equations.
6.000- 3.73 /? = 8.41
3.73 a 3.13 /? = 4.04
Solution of Normals.
a = 2.31
/?=1.47
(59)
(60)
(61)
34 Terrestrial Atmospheric Absorption of
U. 8. N. 0. Telescope.
Cayenne, Dec. 16, 1889.
a Orionis.
TABLE XIV.
Aneroid, 29 in .90.
T
r
c
d
2*
43
8 s
Q
Mean
Q
o c
60
0.80
Oh4 7 m
18" 58""
75.0
70
0.85
0.85
0.02
80
0.90
65
1.00
1 23
19 34
66 .1
1.00
0.01
67
1.10
1 51
20 2
59 .2
1.12
_|_0.02
90
1.15
70
L20
2 20
20 31
52 .0
80
1.15
1.17
0.01
90
1.15
75
1.45
3 25
21 36
35 .9
85
1.30
1.33
+ 0.04
95
1.25
75
1.45
5 45
23 56
2 .8
85
1.30
1.37
0.03
Equations of Condition.
0.81 /5 = 0.85
a 0.59 0= 1.00
a 0.45 /3= 1.12
a 0.34/5=1.17
a 0.16/5=1.33
a 0.00/5=1.37
Normal Equations.
6.00 or 2.35/5=6.84
2.35 1.36)3=2.39
Solution of Normals.
a = 1.40
(62)
(63)
(64)
The Photographic Rays of Light.
35
U. S. X. O. Telescope.
Cayenne, Dec. 16, 1889.
Sirius.
TABLE XV
T
T
c
d
2*
4*
8'
Q
Mean
Q
o c
lh I 7 m
1 57
3 28
4 59
Igh 37m
19 17
2048
22 19
82 .6
73 .1
52 .1
32 .9
87
100
100
125
140
115
140
190
120
1.40
1.35
2.95
2.80
2.60
4.00
3.40
3.90
4.40
1.37
2.78
3.77
4.30
0.14
+ 0.23
0.06
0.19
5 51
23 11
24 .7
200
125
175
220
4.20
4.80
4.90
4.80
4.83
+ 0.15
Equations of Condition.
a 1.08/5=1.37
a 0.75 /3= 2.78
a 0.34 ft = 3.77
a 0.13/3 = 4.30
a 0.07 /3 = 4.83
Normal Equations.
5.00 a 2.73/3=17.05
2.73 or 1.87/3= 5.74
Solution of Normals.
a = 4.90
(65)
(66)
(67)
36 Terrestrial Atmospheric Absorption of
In Table XVI are given the mean values of <2, pressure r
temperature, Q , and /for each date and star.
TABLE XVI.
Date.
Star.
Mean
Z.-D.
Pressure.
Temper-
ature.
Qo
/=!
1889.
December 13. }
December 15. V
December 16 J
a Orionis.
( 67.5
{ 44 .3
[ 48 .5
SO'a.OO
29 .92
29 .90
76
80
1.47
1.28
1.40
0.59
0.46
0.47
December 13-..
Rigel.
55 .0
30 .00
76
3.37
0.4&
December 15. ..
December 16
Procyon.
Sinus.
62 .3
53 .1
29 .92
29 .90
80
2.31
4.90
0.64
0.64
The separate results for the value of /=- as found for
Cayenne at sea-level are given in Table XVII.
TABLE XVII.
Star.
/-I
Weight.
a Orionis ..
0.51
1
Rigel
Procyon
Sinus
0.46
0.64
0.64
1
2
4
In the column headed " weight," a Orionis has been given
such small weight, firstly, because it is a variable star, and
secondly, because its spectral type is different from the other
stars, and consequently the coefficient of absorption may be
different. To Rigel has been assigned the same weight, because
it was only used on the first night, for which the conditions
were rather uncertain. In the case of Procyon the zenith-
distance was greater than for any of the other stars, while for
giving good measurable images of a star near the horizon
Sirius is by far the best source of stellar light. Polaris was
photographed on two occasions; the data and results are given
in Table XVIII.
The Photographic Rays of Light.
Cayenne, Dec., 1889.
Polaris.
TABLE XVIII.
d
8 s
Q
ra'
32"
64*
Obs.
Comp.
Obs.
Comp.
50
0.35
Dec. 15..
2 30
1 12
83.7
1.14
55
60
0.35
0.40
0.37
0.40
4.17
3.99
65
0.40
55
0.40
Dec. 17..
3 18
2
83.8
1.14
60
65
0.40
0.45
0.42
0.40
3.89
3.99
70
0.45
To obtain the computed values of Q, it must be remembered
that Polaris has been given the brightness 1.00, and the pho-
tographic magnitude 2.00 for a zenith-distance equal to the
latitude of Mount Hamilton.
As found from both the preceding Mount Hamilton series
and the Cayenne observations, the value of the factor/ is very
nearly 0.60. In the equation
Q=Q (l- 0.60 <?(<?))
(68)
We must place Q = l and <2 = 52 40', and solve for Q .
this value of < we have <p (<2) = 0.35; hence,
For
= 1.26
(69)
Substituting this value of Q in equation (70), and placing
<p () = 1.14, we obtain the tabulated value 0.40 for Q; the
corresponding magnitude is 3.99. The mean of the two
observed photographic magnitudes is 4.03; the practical agree-
ment between theory and observation is therefore all that could
be desired.
Taking the weighted mean of all the determinations made
at Cayenne, we have the expression
B = B (i 0.59 g>
(70)
One would naturally expect that at sea-level the value of
the factor / should come out greater than for a considerable
altitude, but the figures do not show such a condition of things.
38 Terrestrial Atmospheric Absorption of
Perhaps, however, the effect of dew on the object-glass has not
been completely eliminated. If a simultaneous series of obser-
vations had been carried on for decreasing star-altitudes, the
effect of a gradual dewing of the object-glass would have been
to cause an increase in resulting value of /.
In a clear sky the stars, at considerable altitudes, appeared
fully as bright at Cayenne as they do on Mount Hamilton, so
far as the observer could judge by estimation.
DISCUSSION OF THE THIRD SERIES OF OBSERVATIONS FOR
ABSORPTION.
After our return from Cayenne the U. S. N. 0. telescope was
again set up on Mount Hamilton, and a third series of observa-
tions undertaken. At the time I was busily engaged on "A
Mechanical Theory of the Corona," so Professor CAMPBELL
kindly consented to make the exposures of this series for me
while the DALLMEYER telescope was still available.
As in the first series, there chanced to be no suitable very
bright star on which the exposures could be made. It was
finally decided to use ex Andromedae.
To utilize the whole time available for making suitable
exposures, five different plate-holders were used. Each plate-
holder was carefully fitted to the tube, so that the sensitive
film in every case was at the same distance from the objective.
Variations of an abnormal character in the diameters of the
stellar images on the different plates could now be attributed
to varying sensitiveness of these plates, as the atmospheric
conditions were practically the same for all the plates exposed
on any given day. The tabular data and results are arranged
as in the previous observations, and therefore require no
further explanation.
The Photographic Rays of Light.
U. S. N. 0. Telescope. a Andromedae. Bar., 25">.95.
July 1, 1890. Att., 64.5.
Plate No. 1. TABLE XIX. Ex., 63.0.
d
T
r
c
2 s
4 s
8"
Q
Mean
Q
o c
171l34 m
_ 6h29m
78.4
55
60
0.65
0.60
0.65
0.06
70
0.70
60
0.80
17 49 6 14
76 .1
65
0.70
0.77
+ 0.01
75
0.80
60
0.80
17 57
6 1
74 .0
70
0.85
0.85
+ 0.05
80
0.90
65
1.00
18 39
5 24
66 .5
70
0.85
0.92
+ 0.01
80
0.90
65
1.00
19 5
4 58
61 .6
75
1.00
1.00
+ 0.03
85
1.00
65
1.00
19 45
4 18
54 .0
75
1.00
0.97
0.08
80
0.90
70
1.20
20 11
3 52
48 .7
80
1.20
1.13
+ 0.04
85
1.10
70
1.20
20 36
3 27
43 .8
75
1.00
1.10
0.02
90
1.10
70
1.20
20 49
3 14
41 .3
80
1.20
1.17
+ 0.03
90
1.10
Equations of Condition.
a 0.92 /? = 0.65 a 0.50 (3 = 1.00
a 0.84 ft = 0.77 a 0.37 ft = 0.97
a 0.78 fi = 0.85 a 0.30 /? = 1.13 (71)
a 0.59 ft = 0.92 a 0.24 /3 = 1.10
a 0.21 /5 = 1.22
Normal Equations.
9.00^ 4.75/3 = 8.56
4.75 or 3.10/3 = 4.16
Solution of Normals.
<x= 1.273
? = 0.608
(72)
(73)
40
Terrestrial Atmospheric Absorption of
U. S. N. 0. Telescope. a Andromedae. Bar -. 25 in -95.
July 1, 1890. Att., 64.
Plate No. 2. TABLE XX. Ex., 63.
T
r
C
d
Q
Mean
Q
oc
55
0.65
17" 24"
6" 39"
80.2
60
0.60
0.62
0.10
65
0.60
60
0.80
17 39
6 24
77.5
65
0.70
0.77
0.00
70
0.70
60
0.80
17 44
6 19
76.6
70
0.85
0.82
+ 0.04
75
0.80
60
0.80
18 1
6 2
73 .6
70
0.85
0.85
0.02
80
0.90
65
1.00
18 34
5 29
67 .4
75
1.00
1.00
+ 0.10
85
LOO
65
1.00
19 11
4 52
60.5
75
1.00
1.00
+ 0.03
85
1.00
65
1.00
19 41
4 22
54 .6
75
1.00
1.00
0.02
85
1.00
65
1.00
20 20
3 43
46 .9
75
1.00
1.03
0.04
90
1.10
70
1.20
20 54
3 9
40.3
75
1.00
1.07
0.03
85
1.00
21 21
2 42
34 .9
65
80
1.00
1.20
1.10
0.03
90
L10
Equations of Condition.
a 0.99/3 = 0.62 a 0.47 /3 = 1 .00
a 0.89/5=0.77 a 0.38 /3= 1.00
a 0.86/3 = 0.82 a- 0.27 /3 = 1.03 (74)
a 0.77^ = 0.85 a 0.20 /3 = 1.07
a 0.62 /?= 1.00 a 0.15/5=1.10
Normal Equations.
10.00 a 5.60/5 = 9.26 (75)
5.60 a 3.97 /? = 4.78
Solution of Normals.
a = 1.196 (76)
ft = 0.483
The Photographic Rays of Light.
41
U. S. N. O. Telescope.
July 2, 1890.
Plate No. 1.
a Andromedae.
TABLE XXI.
Bar., 25'.90.
Att., 64.
Ex., 63.
T
T
C
d
Q
Mean
Q
o c
60
0.80
17h 8 m
6 h 65 m
83.2
0.85
0.03
80
0.90
65
LOO
17 29
6 34
79.4
75
1.00
1.00
+ 0.04
70
1.20
18 10
5 53
71 .9
75
1.00
1.10
+ 0.01
90
1.10
19 9
4 54
60 .9
70
1.20
1.20
0.02
75
1.45
20 20
3 43
46 .9
85
1.30
1.33
0.00
95
1.25
Equations of Condition.
a 1.18/5 = 0.85
of 0.96 /? = 1.00
a 0.72/5=1.10
a 0.48 /3 = 1.20
a 0.27 ft = 1.33
Normal Equations.
5.00 a 3.54 /?= 5.48
3.54 2.97/5 = 3.63
Solution of Normals.
or =1.480
/5 = 0.542
(77)
(78)
(79)
42 Terrestrial Atmospheric Absorption of
r.s. X. 0. Telescope.
July 2, 1890.
a Andromedae.
TABLE XXII.
Plate Xo. 2.
T
r
r
d
Q
Mean
Q
o c
55
0.65
lyh 12 111
6" 51>
82.4
0.65
0.04
60
0.80
17 32
6 31
78 .8
65
0.70
0.77
+ 0.01
75
0.80
65
1.00
18 14
5 49
71 .1
0.95
+ 0.07
80
0.90
65
1.00
19 13
4 50
60.1
75
85
1.00
1.00
1.00
+ 0.01
65
1.00
20 23
3 40
46.3
75
1.00
1.03
0.06
90
1.10
Equations of Condition.
a 1.08 /3 = 0.65
a 0.94/5 = 0.77
0.70 /5 = 0.95
a 0.47/5=1.00
r 0.27 /S = 1.03
Normal Equations.
5.00 a 3.46 /? = 4.40
3.46 a 2.83/5 = 2.83
Solution of Normals.
a= 1.220
/?= 0.492
(80)
(81)
(82)
The Photographic Rays of Light.
43
I". S. X. O. Telescope.
July 2, 1890.
a Andromedae.
TABLE XXIII.
Plate No. 3.
T
r
'
d
Q
Mean
Q
o c
55
0.65
17" 16"
6M7 m
81.6
65
0.70
0.72
0.12
75
0.80
65
LOO
17 36
6 27
78.1
75
1.00
1.00
+ 0.08
85
1.00
70
1.20
18 9
5 54
72 .1
80
1.20
1.13
+ 0.11
85
1.00
70
1.20
19 16
4 47
59 .5
80
1.20
1.18
+ 0.01
90
1.15
70
1.20
20 34
3 29
44 .2
80
1.20
1.22
0.07
95
1.25
Equations of Condition,
a 1.04 p = 0.72
a 0.91 /? = 1.00
a 0.73/3 = 1.13
a 0.46^ = 1.18
a 0.24 ft = 1.22
Normal Equations.
5.00 a 3.38/5 = 5.25
3.38 or 2.71 ft = 3.31
Solution of Normals.
a = 1.431
/? = 0.564
(83)
(84)
(85)
44
Terrestrial Atmospheric Absorption of
U. S. N. O. Telescope.
July 2, 1890.
a Andromedae.
TABLE XXIV.
Plate No. 4.
T
r
e
d
Q
Mean
Q
o c
60
0.80
17 h 20"
6"43
81.0
70
0.85
0.82
0.03
65
1.00
17 39
6 24
77 .5
75
80
1.00
0.90
0.97
+ 0.04
65
1.00
18 19
5 44
70.2
80
90
L15
1.10
1.08
+ 0.02
70
1.20
19 19
4 44
58 .9
80
1.20
1.17
0.04
90
1.10
75
1.45
20 39
3 24
43 .2
85
100
1.30
1.35
1.37
+ 0.02
Equations of Condition.
a 1.02 p = 0.82
a 0.89 ft = 0.97
a 0.68 fi = 1.08
a 0.45 p = 1.17
a 0.23/3 = 1.37
Normal Equations.
5.00 a 3.27 /?= 5.41
3.27 2.54/5 = 3.28
Solution of Normals.
a =1.502
/? = 0.642
(86)
(87)
(88)
The Photographic Rays of Light.
45
r. S. X. 0. Telescope.
July 2, 1890.
a Andromedae.
TABLE XXV.
Plate Xo. 5.
r
r
c
d
Q
Mean
Q
o c
17*24*
6" 39-
80.2
60
70
0.80
0.85
0.82
0.03
17 42
6 21
77 .0
65
1.00
0.95
+ 0.04
18 22
5 41
69 .7
80
65
0.90
1.00
1.00
0.00
19 22
20 46
4 41
3 17
58 .3
41 .1
85
70
80
90
70
85
90
1.00
1.20
1.15
1.10
1.20
1.30
1.10
1.15
1.20
+ 0.04
0.02
Equations of Condition.
a 0.99/5 = 0.82
a 0.87/5 = 0.95
a 0.67/3= 1.00
a 0.44/3=1.15
a 0.21 =1.20
Normal Equations.
5.00 a 3.18/5=5.12
3.1 8 a 2.42/5 = 3.07
Solution of Normals.
a =1.323
/5 = 0.472
(89)
(90)
(91)
46
Terrestrial Atmospheric Absorption of
U. S. N. 0. Telescope.
July 30, 1890.
Plate No. 1.
a Andromedae.
TABLE XXVI.
Bar., 25K86.
Att., 67.
Ex., 65.
r
T
c
d
Q
Mean
Q
o c
55
0.65
17 31>
632'
79.0
65
0.70
0.72
0.08
75
0.80
60
0.80
17 47
6 23
77 .3
0.85
0.01
80
0.90
65
1.00
18 5
5 58
72 .8
75
1.00
1.00
+ 0.07
70
1.20
19 21
4 42
58 .5
80
1.20
1.18
+ 0.07
90
1.15
(
70
1.20
20 52
3 11
40 .7
1.22
0.04
95
1.25
70
1.20
21 48
2 15
29 .5
90
1.45
1.30
0.03
95
1.25
Equations of Condition.
a 0.94/5 = 0.72
a 0.84 ft = 0.85
a 0.74/5=1.00
a 0.44 /3 = 1.18
a 0.21 ytf = 1.22
a 0.10/5=1.30
Normal Equations.
6.00 3.27/5 = 6.27
3.27 a 2.38 /5 = 3.04
Solution of Normals.
a= 1.387
/5 = 0.628
(92)
(93)
(94)
The Photographic Rays of Light.
47
U. S. N. 0. Telescope.
July 30, 1890.
a Andromedae.
TABLE XXVII.
Plate No. 2.
T
r
c
-
Q
Mean
Q
o c
60
0.80
17 h 34 m
6 h 29 m
78.4
70
0.85
0.82
0.05
75
0.80
65
1.00
17 50
6 13
75 .5
75
1.00
0.97
+ 0.05
80
0.90
60
0.80
18 7
5 56
72 .4
75
1.00
0.93
0.03
85
1.00
70
1.20
19 23
4 40
58 .1
80
90
1.20
1.10
1.17
+ 0.06
70
1.20
20 56
3 7
39.9
80
1.20
1.22
0.01
95
1.25
70
1.20
21 54
2 9
28 .3
85
1.30
1.25
0.02
95
1.25
70
1.20
22 24
1 39
22 .5
1.27
0.02
1.00
1.35
Equations of Condition.
a 0.92 /5 = 0.82
a 0.83 /5 = 0.97
a 0.74/5 = 0.93
a 0.43 /5 = 1.17
0.19 y3 = 1.22
or 0.10/5=1.25
0.06/5=1.27
Normal Equations.
7.00 or 3.27/5=7.63
3.27 a 2.32/5=3.18
Solution of Normals.
a= 1.317
/? = 0.486
(95)
(96)
(97)
48 Terrestrial Atmospheric Absorption of
U. S. N. O. Telescope.
July 30, 1890.
a. Andromedae.
TABLE XXVIII.
Plate No. 3.
T
r
c
d
Q
Mean
Q
o c
17" 38>
17 52
18 10
19 26
_ 6 n 25"
6 11
5 53
4 37
77.7
75 .2
71 .9
57 .5
65
75
85
70
80
90
75
85
95
80
1.00
1.00
1.00
1.20
1.20
L10
1.40
1.30
L25
1.70
1.00
1.17
1.32
1.52
0.07
0.01
+ 0.08-
+ 0.10
20 59
3 4
39 .3
100
80
90
1.35
1.70
1.50
1.60
+ 0.04
21 57
2 6
27 .7
80
90
1.70
1.50
1.60
0.02
22 27
1 36
21 .9
95
110
1.65
1.60
1.62
0.08
Equations of Condition,
a 0.90 /3 = 1.00
a 0.82/3 = 1.17
a 0.72/5=1.32
a 0.42 /3 = 1.52
a 0.19 /3 = 1.60
a 0.09 ft = 1.60
a 0.06/5 = 1.62
Normal Equations.
7.00 or 3.20/5 = 9.83
3.20 a 2.23 /5 = 3.99
Solution of Normals,
a = 1.703
/?= 0.654
(98)
(99)
(100)
The Photographic Rays of Light.
U. S. N. 0. Telescope.
July 30, 1890.
a Andromedae.
TABLE XXIX.
49
Plate No. 4.
T
r
c
d
Q
Mean
Q
o c
17 h 41
6 h 22
77.2
60
70
80
0.80
0.85
0.90
0.85
0.07
17 54
18 12
19 29
6 9
5 51
4 34
74.8
71 .5
56 .9
70
85
65
75
90
70
80
95
0.85
1.00
1.00
1.00
1.10
1.20
1.20
1.25
0.92
L03
1.22
0.04
+ 0.03
+ 0.07
21 1
3 2
38 .9
80
1.20
1.20
0.06
22
2 3
27 .1
85
1.30
1.30
0.01
Equations of Condition.
0.88/3 = 0.85
a 0.80 ft = 0.92
a 0.71 /3 = 1.03
a 0.41 = 1.22
a 0.19/3=1.20
a 0.09/5=1.30
Normal Equations.
6.00 a 3.08/3 = 6.52
3.08 a 2.13/3 = 3.07
Solution of Normals.
a =1.359
/3 = 0.503
(101)
(102)
(103)
50 Terrestrial Atmospheric Absorption of
V . s. N. O. Telescope.
July 30, 1890.
x Andromedae.
TABLE XXX.
Plate No. 5.
r
r
c
d
Q
Mean
Q
o c
17" 44"'
6 h 19 m
76.6
60
70
80
0.80
0.85
0.90
0.85
0.11
17 56
6 7
74 .4
65
1.00
1.00
-f-001
18 14
5 49
71 .1
70
80
90
1.20
1.20
1.10
1.17
-fO.13
19 32
4 31
56 .4
70
80
95
1.20
1.20
1.25
1.22
+0.04
21 4
2 59
38 .3
70
85
95
1.20
1.30
1.25
1.25
0.05
22 3
2
26.5
75
85
1.40
1.30
1.35
0.00
Equations of Condition.
a 0.86 ft = 0.85
0.79/3 = 1.00
a 0.70/5 = 1.17
a 0.41/5=1.22
a 0.18/5 = 1.25
a 0.08 /? = 1.35
Normal Equations.
6.00 a- 3.02/5=6.84
3.02 a 2.06/5=3.17
Solution of Normals.
a =1.393
/5 = 0.503
(104)
(105)
(106)
The Photographic Rays of Light.
51
U. S. X. (). Telescope. a Andromedae. Bar., 26i".04.
August 6, 1890. Att.. 69.
Plate No. 1. TABLE XXXI. Ex-) 6g o
T
T
c
d
Q
Mean
Q
o c
I 7 h 44m
_ 6 h 19 m
76.6
60
75
85
0.80
1.00
1.00
0.93
0.02
18 32
5 31
(37 .8
70
80
90
1.20
1.20
1.10
1.17
+ 0.04
19 29
4 34
57 .0
70
85
95
1.20
1.30
1.35
1.25
0.03
Equations of Condition.
^_0.86yS = 0.93
or 0.62 0=1.17
a 0.42 /?= 1.25
Normal Equations.
3.00 a 1.90 j3= 3.35
1.90 a 1.30/J = 2.05
Solution of Normals.
a= 1.589
ft = 0.745
(107)
(108)
(109)
Terrestrial Atmospheric Absorption of
1". s. X. O. Telescope.
August 6, 1890.
of Andromedae .
TABLE XXX II.
Plate No. 2.
T
r
r
'
Q
Mean
Q
o c
65
1.00
17* 1 47 m
6" 16 m 76.0 70
0.85
0.92 ! 0.02
80
0.90
70
1.20
18 34
5 29
67 .4
80
90
1.20
1.10
L17
4-0.07
70
1.20
19 32
4 31 56 .4 85
1.30 i 1.20
0.05
90
1.10
Equations of Condition.
a 0.84 /? = 0.92
a 0.61/5 = 1.17
a 0.41 /? = 1.20
Normal Equations.
3.00 a 1.86 yff = 3.29
1.86 a 1.25 /? = 1.97
Solution of Normals.
a= 1.550
/? = 0.731
(110)
(111)
(112)
The Photographic Rays of Light.
u. s. N. 0. Telescope. Andromedae. Poor focus.
August 6, 1890. TABLE XXXIII. Plate No. 3.
T
T
C
d
Q
Mean
Q
o c
17" 50'
6" 13-"
75.5
65
70
80
1.00
0.85
0.90
0.92
+ 0.01
18 37
5 26
66 .8
70
80
90
1.20
1.20
1.10
1.17
+ 0.02
19 34
4 29
56 .0
70
80
95
1.20
1.20
1.25
1.22
-0.03
Equations of Condition.
a 0.83 /3 = 0.92
a 0.60/5 1.17
,r_ 0.40/? = 1.22
Normal Equations.
3.00 or 1.83 /? = 3.31
1.83 or 1.21 /? = 1.95
Solution of Normals.
a =1.545
ft = 0.725
(113)
(114)
(115)
54
Terrestrial Atmospheric Absorption of
V . S. N. O. Telescope.
August 6, 1890.
a Andromedae.
TABLE XXXIV.
Plate No. 4.
T
r
c
d
Q
Mean
Q
oc
65
1.00
17h 52"'
6 h ll m
75.2
1.00
+ 001
85
1.00
70
1.20
18 40
5 23
66 .3
80
90
1.20
1.10
1.17
+ 0.02
70
1.20
19 37
4 26
55 .0
85
1.30
1.25
0.04
95
1.25
Equations of Condition.
a 0.82 ft= 1.00
a 0.59 yS =1.17
cc 0.38 /3= 1.25
Normal Equations.
3.00 a 1.79/5 = 3.42
1.79 a 1.16/5 = 1.98
Solution of Normals.
a =1.538
/9 = 0.667
(116)
(117)
(118)
The Photographic Rays of Light.
55
U. S. N. 0. Telescope.
August 6, 1890.
of Andromedae.
TABLE XXXV.
Plate No. 5.
T
r
c
d
Q
Mean
Q
o c
60
0.80
ITU 54m
6" 9'
74.8
70
0.85
0.85
+ 0.01
80
0.90
65
1.00
18 42
5 21
66.0
75
1.00
1.00
0.00
85
1.00
70
1.20
19 39
4 24
55.0
80
1.20
1.13
0.02
85
1.00
Equations of Condition.
a 0.80 /3 = 0.85
a 0.58 /3 = 1.00
a 0.38 /3= 1.03
Normal Equations.
3.00 a 1.76/? = 2.88
1.76 a 1.12 /?=1.65
Solution of Normals.
a= 1.235
/? = 0.469
(119)
(120)
(121)
56 Terrestrial Atmospheric Absorption of
U. s. X. 0. Telescope. a Andromedae. Bar., 25>.85.
August 12, 1890. Att., 69.
Plate Xo. 1. TABLE XXXVI. Ex, 67.
T
T
: d q
Mean
Q
17 h 56
18 32
21 50
22 60
6" 7 m
5 31
2 13
1 13
74.3
67 .8
29 .1
17 .8
0.75 0.07
1.00 +0.08
1.25 +0.03
1.22 0.04
65
75
65
75
0.70
0.80
1.00
1.00
95
1.25
70
80
95
1.20
1.20
1.25
Equations of Condition.
a 0.79/6 = 0.75
a 0.62 = 1.00
a 0.10 /3 = 1.25
a 0.04/5 = 1.22
Normal Equations.
4.00 a 1.55 ft = 4.22
1.55 a 1.04/5 = 1.38
Solution of Normals.
a= 1.280
= 0.581
(122)
(123)
(124)
The Photographic Rays of Light.
57
U. S. N. 0. Telescope.
August 12, 1890.
a Andromedae.
TABLE XXXVII.
Plate No. 2.
r
r
c
d
Q
Mean
Q
o c
17" 59"
_ 6 h 4 m
73 .6
60
70
80
0.80
0.85
0.90
0.85
0.04
18 34
5 29
67 .4
75
1.00
1.00
+ 0.04
19 29
4 34
57 .0
90
1.10
1.10
0.03
20 45
3 18
41 .6
80
1.20
1.20
+ 0.02
21 53
2 10
28 .5
80
1.20
1.20
0.04
22 52
1 11
17 .5
1.25
0.02
95
1.25
Equations of Condition.
a 0.77/5 = 0.85
a 0.62/3 = 1.00
a 0.42/5=1.10
a 0.21/3 = 1.20
_ 0.10/5 =1.20
Normal Equations.
6.00 a 2.15/5=6.60
2.15 a 1.20/5 = 2.14
Solution of Normals.
a- =1.288
A = 0.525
(125)
(126)
(127)
58 Terrestrial Atmospheric Absorption of
\ . - N . o. Telescope.
August 12, 1890.
a Andromedae.
TABLE XXXVIII.
Plate No. 3.
r
T
r
;
d
Q
Mean
Q
oc
18" 1">
_ 6 h 2">
73.4
60
70
80
0.80
0.85
0.90
0.85
-0.03
18 36
5 27
67 .0
1.00
0.00
19 32
4 31
56 4
85
70
1.00
1.20
120
+006
20 48
3 15
41 .5
85
1.30
1.30
+ 0.01
21 55
2 8
28 .1
75
85
95
1,45
1.30
1.25
1.33
0.04
Equations of Condition.
a 0.76/5 = 0.85
a 0.60 /? = 1.00
or 0.41 /? = 1.20
a 0.21 /3=1.30
a 0.09/5 = 1.33
Normal Equations.
5.00 a 2.07/5=5.68
2.07a 1.16 /? = 2.
Solution of Normals.
= 1.439
/? = 0.733
(128)
(129)
(130)
The Photographic Rays of Light.
59
U. S. N. O. Telescope.
August 12, 1890.
(x Andromedae.
TABLE XXXIX.
Plate No. 4.
r
r
-
d
Q
Mean
Q
o c
65
1.00
18" 4 m
5" 59>
73 .0
75
1.00
1.00
0.04
85
1.00
70
1.20
18 39
5 24
66 .5
80
1.20
1.17
+ 0.04
90
1.10
70
1.20
19 35
4 28
55 .8
85
1.30
1.25
+ 0.02
95
1.25
75
1.45
20 51
3 12
40 .9
85
1.30
1.37
+ 0.03
95
1.35
21 58
2 5
27 .5
1.35
.05
100
1.35
Equations of Condition.
a 0.75 /3 =1.00
a 0.59/5=1.17
a 0.40 /3= 1.25
a 0.20 /3= 1.37
a 0.09 ft= 1.35
Normal Equations.
5.00 a 2.03 fi = 6.14
2.03 1.12 yS =
(131)
(132)
Solution of Normals.
= 0.548
(133)
60 Terrestrial Atmospheric Absorption of
r. s. N.O. Telescope.
August 12, 1890.
of Andromedae.
TABLE XL.
Plate No. 5.
r
T
c
d
Q
Mean
Q
o c
I 8 h 7 m
5^56"
72.5
60
65
75
0.80
0.70
0.80
0.77
0.01
18 41
5 22
66 .2
70
0.85
0.85
+ 0.01
20 54
3 9
40 .3
L10
+ 001
22 1
2 2
26 .9
90
70
L10
1.20
L20
+ 003
23 2
1 1
15 .8
80
95
L15
1.25
1.20
0.01
Equations of Condition.
a 0.59/5 = 0.77
a 0.51 /3 = 0.85
0.19 /S = 1.10
a 0.09/5 = 1.20
a 0.03/5 = 1.20
Normal Equations.
5.00 or 1.41/3=5.12
1.41 a 0.66/3=1. 24
Solution of Normals.
a =1.244
/? = 0.780
(134)
(135)
(136)
The Photographic Rays of Light.
61
U. S. X. O. Telescope.
August 13, 1890.
Plate No. 1.
a. Andromedae.
TABLE XLI.
Bar., 25'
Att., 65.
Ex., 64.
T
T
^
d
Q
Mean
Q
o c
17 h 28'
6i 35"
79.5
60
70
0.80
0.85
0.82
0.02
65
1.00
18 22
5 41
69 .7
1.00
+ 0.01
85
1.00
70
1.20
19 45
4 18
53 .8
80
1.20
1.17
+ 0.04
90
1.10
70
1.20
21
3 3
39 .1
85
1.30
1.25
+ 0.03
95
1.25
70
1.20
22 29
1 34
21 .6
85
1.30
1.25
0.03
95
1.25
Equations of Condition.
a 0.96/5 = 0.82
a Q.67/5 = 1.00
'a 0.37,3 = 1.17
a 0.19/5 = 1.25
<* 0.06/5 = 1.25
Normal Equations.
5.00 a 2.25 /? = 5.49
2.25 a 1.55/5 = 2.21
Solution of Normals.
a = 1.314
/5 = 0.485
(137)
(138)
(139)
62 Terrestrial Atmospheric Absorption of
U.S. \ . O. Telescope.
August 13, 1890.
a Andromedae.
TABLE XLTI.
Plate Xo. 2
T
r
C
d
2>
4*
8 s
Q
Mean
Q
o c
.
0.80
17 h 31 m
6 h 32"
79
080
- 001
65
1.00
18 35
5 28
67 .2
75
1.00
1.00
+ 0.01
70
1.20
19 47
4 16
53 .4
80
90
1.20
1.15
1.17
+ 0.04
70
1.20
21 5
2 58
38 .1
80
1.20
1.22
0.00
95
1.25
70
1.20
22 32
1 31
21 .0
85
1.30
1.25
-0.04
95
1.25
Equations of Condition.
a 0.94/5 = 0.80
a 0.61 ,5 = 1.00
a 0.36/5=1.17
ex 0.18/5=1.22
a 0.05/5=1.25
Normal Equations.
5.00^ 2.14/5 = 5.44
2.1 4 a 1.41 /5 = 2.06
Solution of Normals.
or = 1.320
= 0.541
(140)
(141)
(142)
The Photographic Rays of Light.
63
U. S. N. 0. Telescope.
August 13, 1890.
a Andromedae.
TABLE XLIII.
Plate No. 3.
T
r
c
d
Q
Mean
Q
o c
17 h 33 m
6 h 30"
78 .6
65
1.00
1.00
+ 0.05
18 37
5 26
66 .9
75
85
95
1.45
1.30
1.25
1.33
0.03
19 50
4 13
52 .8
80
90
1.70
1.50
1.60
0.08
21 10
2 53
37 .1
90
100
120
2.30
1.80
1.85
1.98
+ 0.07
22 35
1 28
20 .4
90
105
120
2.30
2.00
1.85
2.05
0.01
Equations of Condition.
a 0.93 /?= 1.00
0.60 /?= 1.33
a 0.35 ft= 1.60
a 0.17/5=1.98
a 0.05/3 = 2.05
Normal Equations.
5.00 a 2.10 /? = 7.96
2.100' 1.37/5=2.73
Solution of Normals.
a= 2.121
/?== 1.259
(143)
(144)
(145)
64
Terrestrial Atmospheric Absorption of
V . s. X. O. Telescope.
August 13, 1890.
a Andromedae.
TABLE XLIV.
Plate No. 4.
r
r
c
d
Q
Mean
Q
o c
0.65
1.00
17" 36"
6" 28-
78.2
0.60
0.60
0.80
0.09
0.70
1.20
18 39
5 24
66 .5
0.80
1.20
1.17
+ 0.08
0.90
1.10
0.75
1.40
19 52
4 11
52.6
0.80
1.20
1.28
+ 0.06
0.95
L25
0.75
1.40
21 15
2 48
36 .1
0.85
1.30
1.32
0.02
0.95
1.25
0.75
1.40
22 37
1 26
20.0
0.85
1.30
1.35
0.05
1.00
1.35
Equations of Condition.
a 0.92 /3 = 0.80
a 0.59 /?= 1.17
a 0.35/5=1.28
a 0.16/3=1.32
a 0.05 /S=1.35
Normal Equations.
5.00 2.07 ytf=5.92
2.07 a 1.35/3 = 2.16
Solution of Normals.
a = 1.429
yff = 0.592
(146)
(147)
(148)
TJie Photographic Rays of Light,
65
U. S. N. O. Telescope.
August 13, 1890.
a. Andromedae.
TABLE XLY.
Plate No. 5.
r
T
c
d
2
4
8
Q
Mean
Q
o c
60
0.80
17" 38"
625 m
77 .7
65
0.70
0.75
0.00
65
1.00
18 41
5 22
66.2
70
0.85
0.92
+ 0.01
80
0.90
65
1.00
19 55
4 8
51.8
75
1.00
1.03
-0.02
90
L10
21 20
2 43
35 .1
70
80
1.20
1.20
1.17
+ 0.02
90
1.10
70
1.20
22 39
1 24
19.7
80
1.20
1.17
0.03
90
1.10
Equations of Condition.
a 0.90/5 = 0.75
a 0.59/5 = 0.92
a 0.34,5 = 1.03
a 0.15/5=1.17
tf 0.05/5=1.17
Normal Equations.
5.00 a 2.03/5=5.04
2.03 a 1.30/5=1.79
Solution of Normals.
a= 1.226
p = 0.536
(149)
(150)
(151)
66
Terrestrial Atmospheric Absorption of
Exposures on Polaris.
In addition to the observations on a Andromedae each plate
was exposed on Polaris; ordinarily one set of 2", 4 s , and 8 s ex-
posures was made on each plate at the beginning of the night's
work, and a similar set at the close. The observations and
results are given in Table XL VI. The last column gives the
quantity (expressed in magnitudes), found by subtracting the
provisional magnitude of a Andromedae from that of Polaris.
(See note to Table VIII.)
TABLE XLVI.
Polaris.
Q
1
mf
i f
Date.
Plate.
d
Q
Polaris.
a
Andro.
Polaris.
a
Andro. \
1890.
65
II
1.00 ;1
July 1..
1
70
0.85
0.88
1.25
2.28
1.52 +0.76
75
0.80
65 65
1.00
July I.-
2
70 70
0.85
0.88
1.20
2.28
1.61 + 0.67
75 75
0.80
65 65
1.00
July 2..
1
70 70
0.85
0.88
1.48
2.28
1.15 + 1.13
75 75
0.80
60 60
0.80
July 2__
2
70 70
0.85
0.82
1.22
2.43
1.57 + 0.86
75 75
0.80
70 65
1.05
July 2..
3
75 70
0.90
0.95
1.43
2.12
1.22 +0.90
85 75
0.90
65 65
1.00
July 2..
4
75 70
0.90
0.93
1.50
2.15
1.12 + 1.03
85 80
0.90
60 60
0.80
July 2._
5
70 70
0.85
0.85
1.32
2.35
1.40 + 0.95
80 80
0.90
65 60
0.85
July 30..
1
75 70
0.80
0.87
1.39
2.30
1.29 ! + 1.01
80 80
0.90
60 60
0.80
July 30..
2
65 65
75 75
0.70
0.80
0.77
1.32
2.56
1.38 + 1.18
The Photographic Rays of Light.
67
TABLE XLVI Continued.
Polaris.
Q
m'
J m'
Date.
Plate.
d
Q
Polaris.
a
Andro.
Polaris.
a
Andro.
1890.
75 65
1.10
.
July 30-
3
80 75
85 80
1.05
0.90
1.02
1.70
1.96
0.85 +1.11
65 65
1.00
July 30-
4
70 70
0.85
0.88
1.36
2.28
1.33
+ 0.95
75 75
0.80
60 60
0.80
July 30-
5
65 65
0.70
0.78
1.35
2.54
1.35
+ 1.19
75 75
0.80
65 70
1.05
Aug. 6-
1
75 75
1.00
1.02
1.59
1.96
1.00
+0.96
85 85
1.00
65 65
1.00
Aug. 6-
2
75 70
0.90 0.97
1.55
2.06
1.05
+ 1.01
85 85
1.00
\ f
65 70
1.05
Aug. 6-
3
70 70
0.85
0.93
1.55
2.15
1.05 1 + 1.10
80 80
0.90
65 65
1.00
Aug. 6-
4
70 70
0.85
0.92
1.54
2.18
1.07
+ 1.11
80 -
0.90
65 65
1.00
Aug. 6-
5
70 70
0.85
0.88
1.43
2.28
1.22
+ 1.06
75 75
0.80
60 60
0.80
Aug. 12-
1
65 65
0.70
0.77
1.28
2.57
1.47
+ 1.10
75 75
0.80
!
.
68 Terrestrial Atmospheric Absorption of
TABLE XLVI Continued.
Polaris.
Q
TO'
A m'
Date.
1890.
Aug. 12..
Plate.
d
Q
Polaris.
a
Andro.
Polaris.
a;
Andro.
2
60 65
65 65
80 80
0.80
0.70
I 0.80
0.77
1.29
2.57
1.45
+ 1.12
Aug. 12..
3
65 65
75 75
90 85
1.00
1.00
1.05
1.02
1.44
1.96
1.21
+ r 75
Aug. 12-
4
65 70
70 75
80 85
1.05
1.05
0.90
1.00
1.52
2.00
1.09
+ 0.91
Aug. 12-
5
60 60
65 70
75 80
0.80
0.80
0.80
0.80
1.24
2.48
1.54
+ 0.94
Aug. 13..
1
65 70
75 75
85 85
1.05
1.00
1.00
1.02
1.31
1.96
1.41
+ 0.55
Aug. 13-
2
65 65
75 75
85 85
1.00
1.00
1.00
1.00
1.32
2.00
1.39
+ 0.61
Aug. 13-
3
75 75
85 85
90 90
1.45
1.30
L15
1.30
2.12
1.43
0.37
+ 1.06
Aug. 13-
4
65 65
75 75
85 80
1.00 .
1.00 0.97
0.90
1.43
2.06
1.22
+ 0.84
Aug. 13..
5
60 60
65 70
75 80
0.80
0.80
0.80
0.80
1.23
2.48
1.55
+ 0.93
In Table XLVII the factor / is given for each plate. As
the several values are consistently smaller than for the other
series, I was for a time at a loss to account for this difference.
A comparison of the negatives developed by W. W. C. with those
developed by J. M. S. at once showed that the latter films are
considerably darker than the former.
As some of the negatives of this third series are darker than
others, the following test, as to whether the value of the factor
/ is a function of the degree of development of the plate, was
made: All the plates of the third series were fastened side by
side to a large, white, semi-transparent background (a frosted
Avindow pane); thus arranged, slight differences of shade could
at once be detected. Only two grades of density will be used
The Photographic Rays of Light.
69
to designate the degree of opacity, light (L) and dark (D);
the corresponding value of / is found in the horizontal line.
It should also be remarked that on three of the six nights
of observation the moon was nearly full, so that a light
development under such conditions would correspond to a
considerably lighter development on a moonless night, as the
diffused light resulting from the presence of the moon in the
sky would, to a certain extent, fog the whole plate.
TABLE XLVII.
Date.
Plate.
Develop-
ment.
Mean
Zenith-
Distance.
/=!
REMARKS.
1890.
July 1-
1
D
60.5
1.25
0.44
Moon nearly full
July 1-
2
D
61.2
1.20
0.40
very windy.
July 2-
1
L
68.5
1.48
0.37
Full moon
July 2-
2
L
67.7
1.22
0.40
very windy.
Julv 2..
3
L
67.1
1.43
0.40
July 2..
4
L
66.2
1.50
0.43
July 2..
5
L
65.3
1.32
0.36
July 30..
July 30-
1
2
L
L
59.3
53.6
1.39
1.32
0.45
0.36
Moon nearly full.
July 30..
3
L
53.0
1.70
0.38
July 30-
4
L
57.8
1.36
0.37
July 30-
5
L
57.2
1.35
0.36
Aug. 6..
1
D
67.1
1.59
0.47
Moon rise near close
Aug. 6-
2
D
66.6
1.55
0.41
of observations.
Aug. 6..
3
D
66.1
1.55
0.47
Aug. 6..
4
D
65.5
1.54
0.43
Aug. 6_.
5
D
65.3
1.43
0.52
Aug. 12..
1
D
47.2
1.28
0.46
Aug. 12..
2
D
47.6
1.29
0.41
Aug. 12-
3
D
53.3
1.44
0.51
Windy.
Aug. 12-
4
D
52.7
1.52
0.44
Aug. 12-
5
D
44.3
1.24
0.63
Aug. 13..
1
L
52.7
1.31
0.37
Aug. 13..
2
L
51.8
1.32
0.41
Aug. 13-
3
L
51.2
[2.121
(0.59)
Aug. 13..
4
L
50.7
1 43
0.41
Aug. 13-
5
D
50.1
L23
0.44
In Table XL VIII the mean results for each day, together
with the meteorological factors, pressure and temperature,
will be found tabulated. The variations in pressure and tem-
perature are altogether too small to enable one to decide just
what effect the purely meteorological factors have upon the ab-
Terrestrial Atmospheric Absorption of
sorption. Such an effect can, however, probably be considered
as evanescent compared with the unknown errors arising from
other sources, as, for instance, impurities in the atmosphere.
TABLE XLVIII.
hsr
Mean
Zenith-
Distance.
Pressure.
Temper-
ature.
<?o
f
July 1 D
60. 8
2o in .ll
63
1.22
0.42
July 2 ! L
70 .0
25 .07
63
1.39
0.39
July 30 L
56 .2
24 .96
65
1.42
0.38
Aug 6 D
66 .1
25 .09
68
1.53
046
Aug. 12 I D
49 .0
24 .90
67
1.34
0.49
Aug. 13 1 L
51 .3
25 .03
64
1.32
0.41
It will be noticed that values of /, corresponding to a D
development, are all greater than those for an L development.
The D developments again are all very much less dense than
my own, for which the value of / is about 0.60. I therefore
conclude that the small value of /, in the case of a Andromedae,
is to some extent at least due to the difference found in the
developments of the plates. An idea of the relative blackness
of the films, as well as an approximation to the absolute densi-
ties, can be obtained from the following experiment: Any three
negatives developed by J. M. S., when superposed, form a good
dark glass for viewing the sun without telescopic aid, while it
takes five of the D negatives, developed by W. W. C., to cut off
the same amount of light. The LICK Observatory has tem-
porarily in its possession some HARVARD College Observatory
plates, of which it takes seven to make a dark glass of the
same degree of opacity as described above. (BACHE telescope
plates of D. M. stars.)
That the value of the factor / is to a certain degree dependent
upon the degree of development seems to be evident from the
following considerations:
The image of a bright star grows more rapidly than does the
image of a faint star. In developing, the faint star will, after
its first appearance, increase but very little in size; but such is
not the case for a bright star the longer the development,
the larger, as a rule, will be the size of the disk. So that for
a long development the ratio of the diameters of the images of
the same star for the two extremes of altitude will differ more
The Photographic Rays of Light. 71
from unity than will be the case for a short development. It
consequently seems to follow that the factor / should theoretic-
ally be greater for long developments than for light develop-
ments, agreeing apparently with actual observation.
Another cause which has a tendency to diminish the value
of the factor / is improper focal adjustment of the sensitive
plate. It is evident that if the images are slightly out of focus,
the ratio of the diameters of the images for the extreme values
will differ less from unity for the faulty focus than it will for
the good focus; since the ratio of the increase in diameter to
the whole diameter will be much greater for the smaller images
than it will be for the larger, provided the density or blackness
of the badly focused image is sufficiently great to admit of
proper measurement.
In the present series, however, the focus seems to have been
right, so that this explanation cannot be applied to account for
the discrepancy.
If we use only those values of / which correspond to the D
developments of the a Andromedae plates, we have the ex-
pression
B = B l 0.46 <p (<2) 2 (152)
If for determining the relative photographic magnitudes of
tx Andromedae in the zenith, and Polaris at the pole, we assign
equal weights to all the observations, we have the relative
numbers
Uncorrected magnitude of Polaris at the pole,
= 2".21 .... =56 40'. ,
Uncorrected magnitude of a Androm. in the zenith, '
= l m .25 .... < = 00'.
Photographically, therefore, a Andromedae can become nearly
a whole magnitude brighter than Polaris, as seen from the LICK
Observatory, if atmospheric absorption is not allowed for.
The fact that the Uncorrected magnitude of Polaris comes out
2.21 instead of 2.00, would also seem to indicate that the plates
were under-developed, using my developments as a standard
of reference. If a brighter star than a Andromedae had been
used, more satisfactory results would doubtless have been
obtained, since for a comparatively faint star the images for
72 Terrestrial Atmospheric Absorption of
short exposures are small, and at great zenith-distances more
or less ill-defined, so that a very slight error in the measures
produces a very large error in the deduced brightness. If the
observations are to be carried to the horizon, a first magnitude
star must be selected, as no impression suitable for measure-
ment can ordinarily be obtained from fainter stars.
As has already been stated, the photographic magnitude 2.00
has been given to Polaris at the zenith-distance 52 40'. At the
close of this paper a new unit of brightness will be adopted, in
which the correction for the atmospheric absorption of the
photographic rays will be allowed for in such a way that the
brightness 1.00 and the magnitude 2.00 will be assigned to
Polaris, as it would appear in the zenith of the LICK Obser-
vatory.
DISCUSSION OF THE FOURTH SERIES OF OBSERVATIONS FOR
ABSORPTION.
After I had made a preliminary discussion of the several
series of observations already recorded in the preceding pages,
I was very anxious to supplement these observations by an-
other series, to see whether the law which I had found to rep-
resent the observations to 80-85 zenith-distance would also
represent observed data corresponding to 90 zenith-distance.
I was all the more impelled to make these additional ob-
servations, as there seemed to be some doubt as to whether the
proper explanation had been given to account for the small
value of the factor / in the case of the a Andromedae results.
As the DALLMEYER telescope had in the meantime been re-
turned to Washington, it was determined to use the newly
mounted CROCKER telescope, containing the WILLABD lens (re-
figured by BRASHEAR) already spoken of.
This instrument is in a building with a revolving dome.
The pointings are made with a small telescope about two feet
long, which, with the photographic telescope, is fastened to an
equatorial mounting by BRASHEAR. In all the previous ex-
posures 4x5 SEED plates (No. 26) were used. As the plate-
holders for the CROCKER telescope were all of the 8 x 10 size,
SEED plates of the same size were consequently used on all the
exposures of this series.
The Photographic Rays of Light.
As the primary object of this series was to test the law for
very great zenith-distances, a star of the first magnitude (pho-
tographic) was required to give the most reliable results. For
various reasons, which need not be considered here, a Lyrae
seemed to be the most suitable star available, although its
zenith-distance at the close of evening twilight was already
about "45; this, however, was not considered to be a serious
objection, as the law from the zenith down to about 80 z.-d.
was already known.
To determine the correction to be applied to the measured
values of d' in the case of a Lyrae, I made a series of exposures
on this star with the CROCKER telescope. The measured
diameters of the images are given in the column headed d' of
the following table.
According to equation (12), taken in connection with that
of (14), the required correction (c c) can now be obtained
from any two values of d' corresponding to given values of t.
For obvious reasons, the errors in the individual measures
will have the least effect upon the resulting values of (c c')
when the difference between the two values of d' is the greatest.
If, therefore, we let t =l" and t = 512 s , the corresponding
values of d' and d' being respectively 0.0099 and 0.0395. the
equation (16) at once gives for Q the value
0.0296
0.0033 X 2.709
(154)
With this value of Q as an argument, we now take from
Table II the tabular values given in the column headed d'.
The fourth column contains the individual values of d d' =
cc'.
TABLE XLIX.
t
d'
d
cc'
1
0.0099
0.0071 0.0028
2
0.0132
0.0104 0.0028
4
0.0165
0.0137 0.0028
8
0.0195
0.0170 0.0025
16
0.0225
0.0203 0.0022
32
0.0260
0.0236 0.0024
64
0.0297
0.0268 U."<>2*..
128
0.0327 0.0301 0.0028
256
0.0360 0.0334
0.0026
512
0.0395
0.0367
0.0028
74 Terrestrial Atmospheric Absorption of
From the above comparisons, it will be seen tbat tbe agree-
ment between theory and observation is as close as could be
expected. The quantity c c' is large, and indicates that the
WILLARD lens is much more effective than the DALLMEYER. I
have, however, assumed this quantity to be a constant for
a Lyrae, as all the other plates of this series were exposed,
developed, and measured in the same way.
The photographic magnitude (provisional) corresponding to
Q= 3.3 is, according to Table II, TO= 0.597, agreeing fairly
well with the magnitude given by the standard telescope.
. Explanation of the Tables L-LV.
The first three columns need no explanation, as the arrange-
ment is the same as for the preceding tables. In the fourth
column, two independent measures of the diameters of each
stellar image are given. As the images are slightly elongated,
these measures were made along two diameters, at right angles
to each other. The fifth column gives the corrected mean
diameter, found by subtracting 0.0027 from the mean of the
measured diameters. These two columns correspond to the
2 s exposures. The same explanation applies to the columns
for the 4 s , 8 s , and 16 s exposures.
In forming the equations .of condition in the previous
investigations, I have used the mean of the results correspond-
ing to the 2 s , 4 s , and 8 s exposures.
In the present case I have treated each set of exposures
corresponding to the same value of t separately, and for two
reasons: First, the short exposures near the horizon will give
more uncertain results than the longer exposures, and there-
fore the least weight should be given to the 2 s exposures, and
the greatest weight to the 16 s exposures; second, the relation
between d, Q, and t may not be exactly the same for this tele-
scope as that found for the standard instrument.
Any marked deviation from the assumed law, for this instru-
ment, would then become apparent through the relations, which
would show that the final results are in each case functions of
the time of exposure.
77ie Photographic Rays of Light.
75
Crocker Telescope. a Lyrae. Bar-. 25>.92.
Att.. 57.
Nov. 4, 1891. TABLE L. Ex 5r
-
2* 4* 8*
16'
T
r
T
d
do
d
</.,
* \ *
d
do
0.0
0.0 0.0
0.0
0.0
0.0
0.0
0.0
2lh42-
3" 9
37.2
125
98 1 160
125
195
168
230
198
125
145
195
220
22 13
3 40
42 .9
125
95 155
123
195
165
235
203
120
145
190
225
23 13
4 40
'>'- .8
125
.93
150
118
190
158
225
190
115
140
180
210
13
5 40
64.5
120
85
140
108
185
145
210
178
105
130
180
200
1 5
6 32
7 .0
110
75
130
95
170
133 i 185
155
95
115
150
180
1 34
7 1
77.5
95
60
100
68
145
110
170
138
80
90
130
160
1 48 7 15
79.5
90
60
100
68
145
108 160
128
35
90
125
150
Equations of Condition.
Values of Q corresponding to do.
a tan 1 ( T^ ) 1 ft
2"
4 s
,
16 s
a 0.17/3= 2.80
a 0.22 f^ 2.60
2.80
2.70
|
3.15 i
3.20
3.30
(155)
a 0.37/7= 2.50
2.50
2.90
3.00
a 0.55/7= 2.00
2.10
2.55 i
2.75
a 0.75 /?= 1.45
1.60
2.20 !
2.25
a 0.89/3 =
0.80
0.80
1.60 '
1.90
a 0.96/5 =
0.80
0.80
1.55 1
1.65
76 Terrestrial Atmospheric Absorption of
Normal Equations.
First Members.
Second Members.
(156)
2 s
4 s
8*
16 s
7.00 a 3.91 ft =
3.91 a ~ 2.79/3 =
12.95
5.64
13.30
5.82
17.10
8.26
18.00
8.85
Nov. 4, 1891.
Solution of Normals.
Weight.
1
Time.
OS
$ = 3.32
4 s
' t/3 = 2.Q3
U = 3.38
8 s
- ^ = 2.65
j a = 3.64
16 s
-- (/3 = 2.14
(a = 3.68
" 1/3=1.99
(157)
(158)
(159)
(160)
Observation Computation.
TABLE LI.
2'
4 s
8*
16'
37.2
0.07 0.13 0.08
0.13
42 .9
53 .8
64 .5
73 .0
77 .5
0.14 0.10
+ 0.15 +0.10
+ 0.13 +0.18
+ 0.10 +0.21
0.22 0.22
0.02 +0.06
+ 0.05 +0.05
+ 0.08 + 0.16
+ 0.16 +0.06
0.14 0.01
79 .5
0.00
0.04
0.04 0.12
The Photographic Rays of Light.
77
Crocker Telescope.
Nov. 6, 189L
a Lyrae.
TABLE LII.
Bar., 25 i ".84.
Att., 46.
Ex., 47.
5
4 s
8s
16'
' T T
f
d
do
d
do
d
do
d | do
\ II
1! o.o
0.0
0.0
0.0 |! 0.0
0.0
0.0
0.0
2244
4" 11 48.5 145
115
180
148 200
170
235
208
i 140
170
195
23 46 5 13
59 .6 i 140
108
165
135
190
155
220
193
135
160
175
46
6 13
70.5 135
100
150
120
175
140
210
175
I 120
145
160
195
1 49
7 16
79 .7 i; 115
83
125 95 150
118
175
140
! 105
120
rvrr
140
f**v it -trte
160
2 27
2 34
2 42
7 54
8 1
8 9
85 .2 100
85
2 47 8 14
86 .1
87 .2
87.5
125
110
110
90
100
80
90
75
63
125
120
115
100
100
90
Equations of Condition.
Values of Q corresponding to do.
" ""LOwl'
4 s
8*
16 s
a -0.29/3=
4.00
3.70
3.30
3.40
or 0.46/5 =
3.60
3.20
2.85
3.10
(161)
a 0.69/5 =
3.00
2.60
2.40
2.70
a 0.97 /?=f
1.90
L60
L80
1.90
a 1.21 /5 =
1.00
0.80
L10
LOO
a 1.26/3 =
0.70
0.50
0.75
0.75
a 1.32/5= 0.40
0.35
0.60
0.60
or 1.33/5= 0.30
0.30
0.40
0.50
1
78 Terrestrial Atmospheric Absorption of
Normal Equations.
First Membe
Second Members.
j
4'
8* 16*
(162)
8.00 a 7.53/5= 14.
7.53 a 8.27/3= 9.8
) 13.05
L 8.34
13.20 13.95
957 9.72
Solutio
Time.
n of Normals.
Weight.
= 3^56 1
= 4.76 2
= 2'.89 8
m Computation.
LBLE LIU. _
(163)
(164)
(165)
(166)
16
Nov. 6, 1891.
<p =
Observati
T.
c
C
2 s
4 s 8*
16*
48.5
59.6
70.5
79 .7
85.2
86 .1
87 .2
>7 6
0.18
0.02
+ 0.20
+ 0.14
+ 0.10
+ 0.03
0.06
0.18
0.09
0.03
+ 0.14
+ 0.07
+ 0.07
0.06
0.01
0.03
0.09
- 0.08
+ 0.08
+ 053
+ 0.17
-0.05
0.04
0.21
053
+ 0.04
+ 052
+ 0.23
+ 0.02
0.09
0.06
0.13
The Photographic Rays of Light.
Crocker Telescope.
Nov. 8, 1891.
a Lyrae. '
TABLE LIV.
Bar., 26">.03.
Alt., 57.
Ex., 58.
T
r
s
*
4
g
' 'l
3
d
do
d
do
d
do
d
do
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
23 h 7 m
4h 3401
52 6
125
93
145
113
115
135
1
6' 27
72 2
105
70
90
1 40
7 7
78 .3
100
70
105
73
120
88
145
110
95
95
110
130
2 10
7 37
82.7
85
53
90
60
100
70
120
90
75
85
95
115
2 24
7 51
84 .7
75
43
80
50
90
60
65
75
85
2 33
8
85.9
70
38
75
43
80
48
95
63
60
65
70
85
2 45
8 12
87 .5
55
25
60
33
70
40
75
48
50
60
65
75
2 52
8 19
88 .3
45
18
55
28
65
33
65
38
45
55
55
65
2 57
8 24
88 .9
50
23
55
23
60
30
50
45
55
3 05
8 27^
89 3
50
18
40
80
Terrestrial Atmospheric Absorption of
Equations
o/ Condition.
Values of Q corresponding to dc
" J^i-GOr
2"
8- 16
8
a 0.35/3 =
a 0.73^ =
a 0.92/3 =
a L09/3 =
a L19 /3
2.50
1.20
L20
0.60
0.35
0.25
0.10
0.07
2.35
0.95 1.10
0.60 0.70
040 050
1.30
D.90
/ -1 e* f '\
a 1.25/3 =
a 1.33/3 =
nr 1.39/3 =
a 1.42/3 =
a: 1 45 /3
0.30 0.30
0.20 0.20
0.15 0.15
0.10 0.09
006
iCw' (16
D.30
D.20
).10
"" """
2 s
4 s . ._
Normal
( 8.00 a
j 8.25 a
$ 8.00 a
( 8.94 a
$ 8.00 a
1 10.04 a
1 6.00 a
i 7.40 a
/SoZwfion
Equations.
8.25/5 = 6.27
9.37/5 = 4.46
8.94 y5 = 5.05
10.86 ft = 3.78
10.04 ft = 3.10
12.84/5 = 3.44
7.40/5 = 3.35
9.32/5 = 3.69
o/ Normals.
Weight.
J
3.00
2.12
2.68 4
3.36
(168)
(169)
(170)
(171)
(172)
(173)
(174)
(175^
8 s
16 s
Time.
2 s
4 s
( =
8 s . .
\ft =
( a =
16 s ..
The Photographic Rays of Light.
81
Xov. 8, 1891.
Observation Computation.
TABLE LY.
o c
c
4 s
*
16-
52 6
+ 014
+ 009
028
78 .3
82 .7
84 7
+ 0.16
0.05
007
-0.10
0.09
008
+ 0.10
+ 0.03
0.00
+ 0.03
+ 0.01
85 .9
87 .5
88 .3
88 9
0.03
0.00
+ 0.11
0.05
+ 0.02
+ 0.10
+ 0.11
0.08
0.03
+ 0.03
+ 0.02
0.02
0.04
0.00
0.04
89 .3
+ 0.05
To see whether any definite relation exists between the
values of a and /?, and t (or / and t) for this particular tele-
scope, we find, by taking simple means, the following figures:
TABLE LVI.
Exposure.
a
ft
/
Weight.
2"
3.90
2.83 0.70
t
4
3.71
2.70 0.73 2
8
3.49
2.21 0.63 4
16
3.83
2.38 0.62
8
The values of / resulting from the shorter exposures are, for
the reason already given, less reliable than those which cor-
respond to the longer exposures; there is, however, an evident
tendency for / to increase as the exposure time diminishes. I
account for this, at least partly, as follows: The correction
0.0027 has only been deduced from observations on a Lyrae,
which correspond to exposures of one second and more. The
smallest image to which this correction has been applied and
found to hold good, has the diameter 0.0099 (see Table
XLIX), while the smallest image measured in the series of
observations for absorption has a diameter of 0.0045, which,
however, was used but once to form a single equation of con-
dition, the other values all being greater than 0.0065. It is
evident that if the constant grows sensibly smaller as the
image decreases from 0.0099 to the above values, the corrected
6
82 Terrestrial. Atmospheric Absorption of
diameters for the short exposures at great zenith-distances will
be too small, and consequently will have the effect of making
the factor/ (and, therefore, also the absorption) greater than it
actually is. It is quite probable that the constant does grow
smaller within the above range, but as I had no accurate
method of testing the law for extremely short exposures, and
as there are no evidences pointing to such a conclusion in
Table XLIX, I deemed it best to use a constant correction for
all the measures. It is of course certain that there is a limit
near which this constant becomes a variable, which decreases
in magnitude as the exposure time diminishes. A series of
exposures on Polaris with this same telescope, in February,
1892, made on a new series of plates, gave the correction
0.0010 for all exposures from 1 s to 256 s duration, but the
value of the photographic magnitude was not affected.
If we give weights to these results, which are proportional to
the exposure times, the value of the factor / becomes
/ = 0.64 (176)
If we take the weighted mean of the separate results of each
night, as found for the 2 s , 4 s , 8 s , and 16' exposures, we have
the following expressions for Q; the corresponding values
of /== ^, and the mean zenith-distances <? are also tabulated:
TABLE LVII.
Date.
r
Q=a fiq>(t)
f
1891.
November 4
61
3.60 2.16 <?()
0.60
November 6
75
4 4(j 2 93 <p (C)
0.66
November 8
81
3 19 9 13 (p l\
069
The nights on which these observations were made were not of
the first class, either as to clearness or steadiness of the atmos-
phere. It is evident that for observations at great zenith-
distances a small change in the general transparency of the
air will have a great effect upon the resulting brightness in the
zenith, found by means of the formula applied to data derived
from observations made near the horizon. It will be noticed
that the individual values of a and $ are unusually large on
November 6th, compared with those of the other two nights.
The Photographic Rays of Light. 83
I am inclined to attribute this difference rather to greater
sensitiveness of the particular plate used than to greater trans-
parency of the atmosphere. The practical constancy of the
factor /, even for decided variations of a and ft, gives evidence
that the empirical law here deduced represents the true physical
law with a very fair degree of accuracy.
If we take the mean of the whole series of observations the
equation for a Lyrae takes the form
Q = 3.73 2.53 <?(<?) (177)
The photographic magnitude (provisional) of ex Lyrae, de-
duced from exposures made at a mean zenith-distance of more
than 70, and reduced to the zenith by means of the formula,
is, therefore,
m'= 0.85 (178)
If, for determining the magnitude, we reject the abnormal
result of November 6th, and take the mean of the values for
November 4th and November 8th, we have the expression
Q =3.28 2.24 tp (<?) (179)
This equation gives for a Lyrae the provisional magnitude
m'= 0.58
agreeing closely with the provisional magnitude found by
means of the standard instrument, and also with the special
determination made with the WILLARD lens.
The equation which expresses the law of atmospheric ab-
sorption, as derived from all the observations on a Lyrae, is,
therefore,
= [l 0.64 ?> (<?)]' (180)
It is a rather curious fact that the resulting mean value of
/ comes out such that for ? = 90 we have Q = 0.04, cor-
responding to a loss of seven magnitudes. If this result could
be regarded as freed from all sources of error, it would at once
follow that the difference -between the apparent visual and
the apparent photographic magnitudes of the same star at
different altitudes is not a constant quantity; the decrease in
the photographic brightness being much more rapid than that
of the visual brightness for increasing zenith-distances. For,
84 Terrestrial Atmospheric Absorption of
in the horizon of the LICK Observatory, the star a Lyrae is still
plainly visible to the naked eye; it is, therefore, among other
things, highly probable that much the greater portion of the
light which reaches the observer from stars near the horizon
comes from the visual or non-actinic part of the spectrum,
agreeing, I believe, with results obtained by other methods.
Other causes which unite to bring about the peculiar result
for <? = 90, in the case of a. Lyrae, I believe to be the following:
First For the shorter exposures the images impressed upon
the photographic plates are too small and indefinite to afford
accurate data for measurement when the zenith-distance is
nearly 90.
Second The smaller images can be considered as equivalent
to images of bright stars having exposure times less than one
second; the constant correction ( 0.0027) used may not be
strictly accurate for the extreme measures here considered.
Third Near the horizon the images are almost always very
unsteady; so that even those actinic rays which strike the
photographic plate do not produce* the effect which would be
caused by a similar set of rays in a perfectly steady atmos-
phere. For short exposures, therefore, the observed photo-
graphic magnitude, at great zenith-distances, will, as a rule,
always come out less than the true photographic magnitude;
for the same reason just the opposite result might be obtained
from long exposures on a bright star.
FINAL RESULTS BASED UPON ALL THE OBSERVATIONS.
In combining all the observations discussed in the preceding
pages, the question, just what weight should be assigned to each
series, depends mainly for its answer upon three other questions,
that refer to causes which exercise a preponderating influence
upon the observed results.
First To what zenith-distance have the exposures been
carried?
Second What were the atmospheric conditions at the times
the exposures were made?
Third How were the plates developed?
The variations of d, for moderate zenith-distances, are so
small, that no matter how accurate the observed data may be,
the law for great zenith-distances could not be deduced from
The Photographic Rays of Light. 85
such observations, as a great number of different functions
could be found which would represent such data for moderate
zenith-distances quite accurately. Hence, other things being
equal, the very greatest weight should be given to those deter-
minations which depend upon observations made at the greatest
zenith-distances.
The question as to how to treat observations made under
unfavorable atmospheric conditions will depend almost entirely
upon the judgment of the observer. In any case such observa-
tions should be given the smallest weight.
Had the development of the plates of the third series been
carried as far as for the other plates the observations on
a Andromedae would have been given considerable weight; but
the fact of the persistently small value of / points so strongly
to a difference due either to excessive development in one case,
or under-development in the other case, that using the first,
second, and fourth series as standards, the third series must be
given smaller weight. The fact that on three of the six observ-
ing nights the moon was nearly full would also require us to
diminish the weight of the third series of observations.
The following are the values of / for each series, together
with corresponding weights assigned:
TABLE LVIII.
Series.
f
Weight.
First Mt. Hamilton
061
2
Second Cayenne
059
1
Third Mt. Hamilton
0.46
1
Fourth Mt. Hamilton
064
3
Taking the weighted mean of these four values of /, we have
finally the following expression for the adopted value of the
"Atmospheric Absorption of the Photographic Rays of Light:"
B = B [l 0.60 ?>(<2)J (181)
Explanation of Table.
With the aid of equations (181) and (4) the final tabular
quantities given in Table LIX have been computed directly
for each whole degree of zenith-distance from to 90.
Terrestrial Atmospheric Absorption of
The first column gives the observed zenith-distance, the
second column the corresponding brightness, and the third
column the amount of absorption, expressed in magnitudes,
for the same zenith-distance. The brightness in the zenith is
placed equal to unity.
TABLE LIX.
TERRESTRIAL ATMOSPHERIC ABSORPTION.
Ob-
served
Zenith-
Dis-
tance.
Photographic
Ob-
served
Zenith-
Dis-
tance.
Photographic
Ob-
served
Zenith-
Dis-
tance.
Photographic
Bright-
ness.
Absorp-
tion.
Bright-
ness.
Absorp-
tion.
Bright-
ness.
Absorp-
tion.
B
M
B
M
B m
1.00 ,
0.00
30
0.87
0.15
60
0.52 0.71
1
1.00
0.00
31
0.86
0.16
61
0.50
0.74
2
1.00
0.00
32
0.86
0.17
62
0.49
0.78
3
1.00
0.00
33
0.85
0.18
63
0.47
0.81
4
1.00
0.00
34
0.84
0.19
64
0.46
0.85
5
1.00
0.00
35
0.83
0.20
65
0.44
0.89
6
0.99
0.01
36
0.82
0.21
66 0.42
0.93
7
0.99
0.01
37 ; 0.81
* 0.23
67 i 0.41
0.98
8
0.99
0.01
38
0.80
0.24
68
0.39
1.03
9
0.99
0.01
39
0.79
0.26
69
0.37
1.07
10
0.99
0.01
40
0.78
0.27
70
0.36
1.12
11
0.99
0.02
41
0.77
0.29
71
0.34
1.18
12
0.98
0.02
42
0.76
0.30
72
0.32 1.24
13
0.98
0.02
43
0.74
0.32
73
0.30 1.31
14
0.97
0.03
44
0.73
0.34
74
0.28 1.39
15
0.97
0.03
45
0.72
0.35
75
0.26
1.45
16 0.96 0.04
46
0.71
0.37
76
0.25
1.52
17 0.96
0.04
47
0.70
0.39
77
0.23
1.62
18 0.95
0.05
48
0.69
0.41
78
0.21
1.71
19
0.95 0.05
49
0.67
0.43
79
0.19
1.81
20
0.94 0.06
50
0.66
0.45
80
0.17
1.93
21
0.94 0.07
51
0.65
0.47
81
0.15
2.05
22
0.93 0.07
52
0.64
0.49
82
0.13
2.19
23
0.93 0.08
53
0.62
0.52
83
0.11
2.36
24
0.92
0.09
54
0.61
0.54
84
0.10
2.54
25
0.91 0.10
55
0.59
0.57
85
0.08
2.75
26
0.90 0.11
56
0.58
0.59
86
0.06
3.00
27
0.90 0.12
57
0.56
0.62
87
0.05
3.30
28
0.88 0.13
58
0.55
0.65
88
0.03
3.70
29
0.88
0.14
59
0.53
0.68
89
0.02
4.18
30
0.87
0.15
60
0.52
0.71
90
0.01
4.96
The Photographic Rays of Light. 87
ON THE PROBABLE ERROR OF A PHOTOGRAPHIC MAGNITUDE.
If we differentiate equation (4), regarding m' and Q as vari-
ables, we have
dm' = 2^- (182)
The expression shows that slightly erroneous values of Q,
due to constant or accidental errors of observation, will produce
large errors in the resulting values of m' when Q is very small.
For a given value of t, the error of m' varies nearly inversely
as Q.
In general the smaller the value of the measured d, the
greater will be the error of the resulting value of m'.
However, when t is very great, other sources of error (due to
(1) imperfect pointing of the telescope, (2) change in the dif-
ferential refraction, (3) change in atmospheric absorption, (4)
internal reflections in the photographic plate, etc.) tend to
diminish the accuracy of the measured results.
The value of the probable error, corresponding to a brightness
in the neighborhood of that assigned to the standard star, can be
obtained from the data given in Table XL VI. Using all the
observations of this table. I find that the probable error of
an observed magnitude, deduced from the mean of any three
exposures of 2 s , 4 s , and 8 s duration, comes out somewhat less
than one tenth of a magnitude.
NEW UNITS OF BRIGHTNESS AND MAGNITUDE.
In the preceding discussion, Polaris has been given the
photographic brightness 1.00, and magnitude 2.00, at the
zenith-distance 52 40'. From Table LIX we learn that the
corresponding brightness and magnitude of the same star, if
it were situated in the zenith, would be B = 1.59, and m =1.49.
Consequently^ if we change this unit of brightness, so as to
make it 1.00 in the zenith, we have only to proceed in the way
already outlined on page 11, and in equations (29), (30), and
(31) to obtain the new arguments given for Table II, found at
the bottom of the page.
There seems to be no marked change in the law for increas-
ing altitudes of the observer, if the Cayenne results can be
88 Terrestrial Atmospheric Absorption of
taken as a test. Just what the absolute atmospheric absorp-
tion is in the zenith is not known, nor is this a necessary
datum for the purposes of this paper, as the law has been so
determined that only the observed brightness enters into the
discussion.
In Table LX will be found the final photographic magnitudes
of the stars mentioned in this memoir, as determined from the
observations.
TABLE LX.
Star.
Place of
Observation.
Provisional Final
Photographic Photographic
Magnitude Magnitude
(Observed), j (Observed).
i
aArietis [ Mt. Hamilton... +2.10 +2.61
a Andromedae I Mt. Hamilton... I +1.04 +1.55
aOrionis j Cayenne ... | (+1.30) (+1.81)
ft Orionis | Cayenne j (0.64) (0.13)
c c Canis Majoris ..'... - - - : Cayenne i (1.45) ( 0.94)
a Canis Minoris ! Cayenne j (+0.10) (+ 0.51)
a Lyrae Mt. Hamilton...! 0.59 0.08
Polaris ...: Cayenne j (+1.52) (+2.03)
The bracketed figures in the above table indicate that the
values may be considerably in error, as no impressions of the
standard star that were worthy of being used could be obtained
at Cayenne; the zenith-distance of Polaris, even at upper cul-
mination, being greater than 83.
CONCLUSION.
In the practical application of the finally adopted values of
the absorption at different zenith-distances, the character of
the particular kind of plate used and the spectral type of the
star observed must be taken into consideration.
A plate exposed to the action of two different sources of
light of equal intensity (visually), but coming from different
parts of the spectrum, Avill not, as a rule, be affected in the
same way, for equal exposure times, by these two lights. Con-
sequently, the law of absorption of the photographic rays, as
determined with a particular kind of plate, may be different for
stars having different types of spectrum.
Photographic Rays of Light. 89
As some kinds of plates are more sensitive to a particular
part of the spectrum than others, it follows that the character
of the plate may largely influence the final result obtained for
absorption.
When we take into consideration the fact that the rays from
the blue end of the spectrum appear to be more absorbed near
the horizon than the rays from the red end, the force of the
above remarks becomes still more apparent.
The results given in this paper are derived from exposures
made on SEED plates, Sensitometer No. 26, of their scale, and
should represent the actual conditions for a normal state of
the atmosphere. For an unusually thick sky, suitable for
observations of a certain class, it is probable that the value of
the factor / is greater than 0.60; while for an unusually clear
sky, its value may be somewhat less than the normal value
given. It is, of course, evident that within a few degrees of
the horizon considerable uncertainty will always exist in all
measured data, and consequently also in the computed theo-
retical results.
MOUNT HAMILTON, October, 1892.
7
WORKS ISSUED BY THE LICK OBSERVATORY.
*** I* i s intended to issue, at irregular intervals, two series of works, the first,
in quarto, to be known as Publications of the Lick Observatory; the second, in
octavo, to be known as Contributions from the Lick Observatory. Occasional
pamphlets, such as No. 2 below, may not be included in either series. At the
end of every book a list of all the works issued will be given, for the con-
venience of librarians and others.
For the sake of uniformity, Nos. 3 and 4 below will be counted as Contribu-
tions Nos. 1 and 2.
1. Publications of the Lick Observatory of the University of California, pre-
pared under the direction of the Lick Trustees by EDWARD S. HOLDER.
Volume 1, 1887. Sacramento, 1887. 4to. [Containing a brief history of the
Observatory, with descriptions of the buildings and instruments; observa-
tions of double stars by S. "NV. BUBNHAM, 1879, of the transit of Mercury,
1881, by Messrs. FLOYD, HOLDEX, and BURNHAM, of the transit of Venus,
1882, by D. P. TODD; meteorological observations, by T. E. FRASBH, 1880-85;
and Reduction Tables for Mt. Hamilton, by G. C. COMSTOCK.]
2. Suggestions for Observing the Total Eclipse of the Sun on January 1, 1889,
by EDWARD S. HOLDEN. Printed by authority of the Regents of the Uni-
versity of California. Sacramento, 1888. 8vo. [Out of print.]
3. Contributions from the Lick Observatory, No. 1. Reports on the Observa-
tions of the Total Eclipse of the Sun of January 1, 1889, published by the
Lick Observatory. Printed by authority of the Regents of the University
of California. Sacramento, 1889. 8vo. [Out of print.]
4. Contributions from the Lick Observatory, No. 2. Reports on the Observa-
tions of the Total Eclipse of the Sun, December 21-22, 1889, and of the
Total Eclipse of the Moon, July 22, 1888, to which is added a Catalogue of
the Library, published by the Lick Observatory. Printed by authority of
the Regents of the University ^California. Sacramento, 1891. 8vo. [Out
of print.]
5. Contributions from the Lick Observatory, No. 3. Terrestrial Atmospheric
Absorption of the Photographic Rays of Light, by J. M. SCHAEBERLE,
Astronomer in the Lick Observatory. Printed by authority of the Re-
gents of the University of California. Sacramento, 1893. 8vo.
6. Publications of the Lick Observatory of the University of California.
Printed by authority of the Regents of the University. Volume II, 1893.
Sacramento, 1893. 4to. [Containing double star observations made with
the thirty-six-inch and twelve-inch refractors of the Lick Observatory
from August, 1888, to June, 1892, by S. W. BURNHAM.]
(90)
Date Due
CAT. NO. 24 161 (**f
970 00178 3270