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