V * ...' **& t .: .. < ^. : *iS LIBRARY OF THE UNIVERSITY OF CALIFORNIA GIFT OF" Class UNIVERSITY OF CALIFORNIA PUBLICATIONS Determination of The Constant of Refraction from Observations made with The Repsold Meridian Circle of The Lick Observatory DISSERTATION IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN THE UNIVERSITY OF CALIFORNIA PRESENTED IN IQOI BY RUSSELL TRACY CRAWFORD [Reprinted from the Proceedings of the California Academy of Sciences, Third Series; Math.-Physics; Vol. I, No. 8.] DETERMINATION OF THE CONSTANT OF REFRACTION FROM OBSERVATIONS MADE WITH THE REPSOLD MERIDIAN CIRCLE OF THE LICK OBSERVATORY. BY RUSSEI.L TRACY CRAWFORD. OF THE UNIVERSITY CONTENTS. PAGE. INTRODUCTION . . - . 105 1. The Meridian Circle 105 2. The Room 107 j. Meteorology 108 4. Plan for Observing 114 OBSERVATIONS 1 18 /. List 118 2. Details of Observations 119 j. Reduction of Observations 122 4. The Cons/ant of Refraction 190 j. Latitude 191 CONCLUSION 192 ADDENDUM 193 INTRODUCTION. i. The Meridian Circle. The instrument with which these observations for refraction were made has been fully described by Astronomer Tucker in Volume IV of the " Publications of the Lick Observatory, 1900." For the sake of completeness, however, it will be described again in this paper. The instrument was made by Messrs. Repsold and Sons, and was described by Professors Auwers and Krueger to be " in its construction in every way suited to be the chief instrument in an observatory of the first class/' (cf. Vol. I, " Publications of the Lick Observatory.") The aperture of the object glass, which was made by Clark and Sons, is 6.4 inches. Its focal length is 6 feet IO6 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. 4 inches. The tube of the telescope is in two parts, each of which is attached to a central cube. Their diameters decrease from 8.1 inches at the cube to 6.5 inches near their outer ends. An eyepiece giving a power of 90 and a field of 12' was used for these observations. The star images formed are not exactly round, but are slightly elon- gated in a direction parallel to the horizontal (declination) thread. There being no component of this elongation parallel to the vertical threads, it can have no effect upon observations for zenith distance. The axis is 3 feet 2^4 inches long, the distance between the counterpoises being 2 feet 2 inches. The pivots are 3.6 inches in diameter and are protected by brass covers. The telescope is furnished with clamps which, however, were never used during these observations. After the telescope was once set for a star it was not moved again to make the bisection, this being done by means of the declination micrometer. The value of one revolution oi the screw of this micrometer is 48". 10. This value has been adopted as the result of many determinations made in past years. The micrometer thread is single. The instrument has two circles, one of which can be rotated about the axis of the instrument while the other is rigidly fixed to it. They are both graduated to 2'. The degrees, as numbered, increase counter-clockwise. The diameter of the silver circle, upon which the graduations are marked, is 26 inches. There are 130 graduations to the inch. The fixed circle was used throughout these observations. , The four reading microscopes on each side are alike in all respects. They are 26.5 inches long and have clear aperturqs of 0.55 of an inch. Their powers are 40 and their fields are nearly one degree. The objectives are 5 inches from the circle and their eye ends project 8 inches from the frame holding them. The micrometer heads are divided into 60 parts. One revolution of a micrometer head carries the threads over:ne minute of arc of the circle. There M.-P. VOL. L] CRAWFORD CONSTANT OF REFRACTION. 107 are two pairs of threads in every micrometer, but one of which is generally used. There is a separate broken telescope for setting. This is supported on wyes attached to either pier and is at the level of the lower rim of the circle. By means of this the circle can be seen either from the north or from the south, so that the settings can be made very conveniently. The illumination for both the field of view and for the circles under the microscopes is furnished by a Rochester lamp placed in a cylindrical case 9 feet from the axis of the instrument. This light also illuminates the heads of the microscope micrometers. Most of the heat from this lamp is carried out of the room by a pipe which extends from directly over the lamp through the roof to the outside air. A simple mechanism enables the observer to change the system of illumination from a bright field with dark wires to a dark field with bright wires and vice versa; he can also reduce the amount of illumination at will. The brick piers supporting the instrument are 34 inches by 44 inches at the floor of the room and 22 inches square at the top. The sides next to the telescope are vertical. They are cased in wood with a layer of felt between the surfaces. The platforms for the microscope reader are entirely disconnected from the casing of the piers. The microscope bearers are 23 inches in diameter and 17 inches long. The wyes for the pivots of the instrument are attached to the inner faces of these frames. The weights of the counterpoises hang from levers 26 inches long. The fulcra are in the centers of the levers and are 6 inches from the inner faces of the microscope bearers. Two collimators, of same aperture and focal length as the Meridian Circle, are suitably mounted. The collimator micrometers are 35 feet 6 inches apart. 2. The Room. The Meridian Circle house on Mount Hamilton has been most admirably designed. Its efficiency will become apparent from the meteorological data to be given later. (2) May 5, 1903- 108 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. The observing room is 43 feet long (north and south) and 38 feet wide. All of the walls are double. The outer of the two is a louvre-work of galvanized iron which prevents the sunlight from touching any part of the building proper. The inner wall is of California redwood, and is separated from the outer by a two foot air space. The ceiling is also of redwood. It is about 16 feet above the floor. Above the ceiling is an air space 8 feet high at the observing slit and sloping to meet the east and the west walls. The observing slit is slightly over three feet in width. The covering for the slit is in four parts which open out- ward. The ends are closed by shutters, each of which is in two parts opening inwards. Each end is also provided with a single shutter which slides up and down. For stars at zenith distances greater than, 72 degrees these shutters have to be lifted. When down they are very efficient wind breaks. There is a large canopy which can be rolled over the instrument to serve as an additional protection in stormy weather or when the instrument is not in use. For a more detailed account of the instrument and room see Astronomer Tucker's account of them in Volume IV of the " Publications of the Lick Observatory, 1900." j. Meteorology. To make quite sure of the condition of the atmosphere at any time during the observations, the thermometers were read, on the average, three times an hour (at nearly equal intervals); and the barometer was observed every hour. The reading of the wet bulb ther- mometer was also taken when the dry was read. The relative humidity has not been introduced into the reduc- tions, but it was thought desirable to have it for possible future reductions. The barometer, Green 2839, nan g s on the north wall of the observing room. It reads to one two-hundredth of an inch. The dry and the wet bulb thermometers (F) hang in the air space between the north walls. . The dry bulb ther- mometer, used to indicate the external temperatures, is Green 494. This thermometer has been calibrated at the M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACWON. 109 Yale Observatory. The corrections which have been applied to all the readings have been taken from the following table sent from Yale Observatory: /(Fj Cor. +o.i 32 Q w 2 52:! ! .1 , N j 112 j . 1 The table which follows contains the unconnected temper- atures (t), the readings of the attached thermometer (T), of the barometer (B), and the times at which they were taken. The readings of the wet bulb thermometer are not given here. no CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. vO M IT) Tl- vo M if) vO M tO 00 io o ON 00 00 o io ovo t^co co oc co co OO CO t^ \O t^ t*. - t^ f M t * M M to io 10 10 10 ON CO vO vO O CO CM rf r^CO t~ M O to to to O t-^ t^-co vO vO VO vO vO vO OOvor^iOC*OOMO iT' 1 > vo VO VO vO vo O r^ t^ ONCO coco M o OVOOOCQCO vO vO vO VO ^O vO ^D vO vD vO ^O VO vO ^ * 0_ IO t^ vO to M vO vO vO vO M M M M IO to to to M co VO CO CO t^ VO vO vO vO vO J2> 0 N ON t^ io co I s * r-. r^ to io io io ON s t^ vO vO vO O to to io > t^CO ^t fO rO ON io ^OO M O W O -rf- o |^^ i^.vrt to to to VO vo to to to tovO vO vo t^vO toiO'OtoiOioiotO'O'OtO 00 ^ ? ON ON ON ON to >o to 10 s h 3 i > ^ VO^ M vOOO O O O ON t^ t^ t> vo rj- ON ON ON ONVO to (S ON lOCO RRR O O O O O O ON ONCO ONCO S3 t^ O fO O ON rOvO O ^ t>. M rj- t^ O & 4 jo VO t^- 00 ON MM M M M.-P. VOL. I.] C^^ WFORD CONST A NT OF REFRA CTION, III 3 t^ t^* t*> vo cO M M M M M vo vo vo vo vo ~ O ON t^ CO t- t^. vO VO vO M O O O O ONOO t^OO cO O 00 M ^t ** M o t^ ON ON 00 CO t^ *t~>i t^ t^. r^-CO CO tx, c^vO vo vO vO vo vO vO vO vO vO vO vO :liJii|l| "&ii&* * Tf VO M CO vO vO vO VO vo lO O vo vo vo vo (*'' O t> t^OO OlNvOcOdOOvOOOcO 2= 8 S S S t r '*!? 11 15 *l s Wl 8 -1 S 1 j -s| S.rigs U 7g.s|g t^txt^t^t^t^t^t^t^t^t^l^t^t^ llrllitp *'S) S -SSS ttj^iWi SQ o c CO vo -rf N ON iO vo vo vo vo o co t>t t^ r^ t>, vo vo vO . *O vOvNOOOOCO COCOW cOvorJ- T^CO vO VO t^vO vo vovO vOvOvOvOvOvOvOvO vOvOvOvOvOvOvOvOvOvOvOvOvOvO ^^'"o-S^S^ sffriiil? g^l !!& s < [ "s * 1 1 5 j > . c: w n8~wS S '2 ftgfirtug-ng^ .*5i1liiall . "(s G p M to _ M O CO C? I? ^O vO ^O ^O ^O O O vN CO COVO CO VOCQ O ^ (N M t^ vO 3 o o oo co t^ l^ t^ vo vo vo vo vo vo O iO d ON ON ON CO vo vo vo O *O O ^VO MWOOOOMOJCHcOcOWO ON O^CO CO ON ON ON O O O ON ON ONOO vOvOvOvOvOvOvO t^C-^ i^vO vO vO vO t* CO 00 t- t^ t^. r^ t^CO CO CO CO 00 CO CO vovovovovovovovovovovovovovo CO 1** CO ON vO t^ t^ CO OO CO CO CO vo vo vo vo vo t^ \yO vO vO vO VO 3 lO vo vo iO *O CO 00 C< CO O O O O O ON vo vo t*^ ^^ co co r- t^ t^vo vo t^-oo co co i>. t^ t^ vO vO vO vO vO vO vO vO VO vO vO VO vO vO *^3 t t^O covo ON covo Tf^M^.^0 T3 c. t^i O cOvO ON cOvO O ^ t^^ ^ ^ t^ O en ^ -rf vo vo t^ CO ON MM MM M M .;; CN C^ ^ ^- vo vO t->> CO ON 112 CA LIFORNIA A CA DEMY OF SCIENCES. [PROC. 30 SER. In this table the unit of B is one two-hundredth of an inch. From this table the following data have been taken: Maximum temperature = 74. o, July 3 Minimum temperature = 55. i, June 12 , Maximum range = 18. 9 Maximum barometer 5194, June 14 Minimum barometer = 5145, June 12" Maximum range = 49. During this period of observing, the maximum differ- ence .between the dry and the wet bulb thermometers was 75. 5. 48. o = 22. 5. This was on June 29. The minimum was 65. o 56. o = 9.o, which occurred June 27. Concerning the maximum temperature noted above, 74. o, it should be remarked that this was the first reading of the period, and was taken several minutes before the sun had set. Besides the regular thermometers in the air space be- tween the north walls, three other thermometers were sus- pended from the ceiling of the observing room. All three were swung under the observing slit, near the plane of the meridian. One was directly over the instrument, and three or four feet from the ceiling. The other two were hung, one north and one south, about half way between the instrument and the north and south walls respectively, and at such a distance above the floor that the plane of the axis of the instrument and the line of sight of the telescope, pointed at about 83 zenith distance (north and south respectively), would intersect the thermometers near their bulbs. Before being thus placed, these thermometers were compared with Green 494, so that their readings could be reduced for comparison with those of the external ther- mometer (Green 494). During the course of an evening's observations these three thermometers were read just after reading the regular thermometer. The average difference between the inside and the outside thermometers was found to be the same M.-P. VOL. I.} CKAWFORD CONS7*ANT OF REFRACTION. 113 for all three, and is o.3 (F). It is nearly always the case (in this hemisphere) that the southern part of a room is a trifle warmer than the northern. But this is not the case on Mount Hamilton. The temperature of the air inside is, on the average, very uniform and but very little (o.3) warmer than the air outside. In his " Untersuchung liber die Astronomische Refraction u. s. w.," Dr. Bauschinger notes that the southern part of his observing room in Munich was warmer than the northern, and that at night the average difference between the inside and the outside temperatures is i-3 (C). From his investigation, he con- cludes that the temperature of the air within the observing room should be taken into account. Because of these difficulties, many observers have seri- ously considered the idea of mounting their instruments under a movable house, so that when at work the instru- ment will be entirely out of doors, and thus completely obviate this difficulty. But this would needlessly endanger the instrument. To accomplish the same purpose, the Meridian Circle house being built at Kiel is to be con- structed in the shape of a cylinder whose axis coincides with the axis of the instrument. This is undoubtedly the best form of construction. For the efficiency of the Meridian Circle house on Mount Hamilton, the difference between the inside and the outside thermometers can speak. As has been said, the average difference (in the sense Inside-Outside) is -\- o.3 (F). The maximum difference noted was one evening, a few minutes before the sun had set, when the difference was.+ i.i (F). The maximum difference noted here is less than half the average at Munich. After this Meridian Circle house has been completely opened for an hour and a half, the temperature inside is practically the same as it is outside. During the months October to December, inclusive, a similar set of observations was secured. For these months the average difference between the inside and the outside temperatures is even less than for the summer months. But the range of the difference is much greater for the 114 CALIFORNIA ACADEMY OF SCIENCES. [PROC, 30 SER. fall and the winter months. The maximum differences observed were 2.o ( F) and -f- 2.i (F). There was one still larger difference, viz. 3. 7 (F), which can hardly be counted in the series, for it occurred on a poor night, immediately after observing had been suspended because of clouds and poor "seeing." The hot wave, which caused the outside temperature to rise suddenly, undoubtedly destroyed the "seeing." Although the winter months present conditions not so favorable as those of the summer months, nevertheless they also speak well for the efficiency of the Lick Observatory Meridian Circle house. ^. Plan for Observing. The method of determining the refractions here may be stated as being a quasi con- verse to Talcott's method of determining the latitude. Instead of eliminating the refractions to get the latitude, the method is to determine the refractions by eliminating the latitude, as follows: Let z 8 = the zenith distance of a southern star, z n = the zenith distance of a northern star, z' g = the apparent zenith distance of the southern star, z' n = the apparent zenith distance of the northern star, S 8 = the declination of the southern star, 8 n = the declination of the northern star, r s = the refraction of the southern star, r n == the refraction of the northern star,

- (II) r B =#(A B) + tf(r,, r.)) In case the northern star is at lower culmination we shall have: S n =i8o z n v (9) S 8 =z s (10) S n +S.=i8o_z u z. (ii) ^180 [ Z ' n + r n +z' 8 -fr 8 ]. (12) Hence r n -+r 8 =i8o [z' n +z' B ] -[ + .] (13) and 2 r 8 = i8o-[ Z ' n + Z ' 8 ]-[A+ 8J+ [r. rj. ( 14) Calling A'=S n +S 8 (15) and since B=z'.+z' B (5) we have r 8=9 o-^ [A'+B] + y 2 [r -r D ] ) and > (III) r=90 ^[A' + B] + ^[r n rj ) In order to obtain the refractions from (II) and (III) it is necessary to know the declinations of the stars, their apparent zenith distances (or rather the sums of the zenith distances of the pairs of north and south stars), and the differences between the refractions of the pairs. The stars chosen for this work are all fundamental, and in a first approximation their declinations are to be considered 1 1 6 CA LIFOKNIA A CA DEMY OF SCIENCES. [ PROG. 3 D SER. absolute. The list of stars, given later, has been taken from Professor Newcomb's "Catalogue of Fundamental Stars for 1875 and 1900, reduced to an absolute System." The apparent zenith distances, or the sums of the zenith distances of the several pairs, are obtained from the Meridian Circle observations; and the differences in the refractions are found by computing the refractions from some standard table. In this work the Pulkowa tables have been used. The term ^(r s r n ) being of the nature of a differential refraction, any error in the constant of refraction of the table used will have practically no effect upon this difference. The more nearly ideal conditions (/. ., when r s =r n ) are approached, of course, the better the determination of the refractions will be. This method has both its advantages and its disadvantages. Among the former, the most important are: first, the total elimination of the latitude and hence also of its variation ; second, the elimination of the nadir, since (z' s +z' n ) is nothing more nor less than the difference between the circle readings, and is therefore independent of the zenith point; third, there is no wait of twelve hours or of six months in order to observe a star at both culminations, as is usually done; and fourth, the simplicity of the reductions. The greatest disadvantage in this method lies in the fact that the declinations of the stars have to be considered known. But by taking fundamental stars, such as those whose places are given by Professor Newcomb's new Fundamental Catalogue, and by taking a large number of these stars, this difficulty will be nearly completely eliminated. Having now the new refractions, the correction to the constant of the table used (Pulkowa) is found from the following equation [eq. (701) pg. 672, Vol. I, Chauvenet, " Spherical and Practical Astronomy''] : dr=Ada + Bd, where A=I a and ,,- ~ r> -a 2 /^dQ Q B = sm^z + - ( - - \/3 W 2/3 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 117 For this observatory, whose altitude is 4,209 feet and where the mean annual pressure is less than 26 inches, an investigation into the effect of the higher powers of A /3 involved in the factor fi== i -) - = i -| r> B B (in Bessel's notation for r) was necessary. In his memoir, " Untersuchungen iiber die Constitution der Atmosphare und die Strahlenbrechung in Derselben," St. Petersburg, 1866, (jylden has neglected the squares and higher powers of %-, since for places at low altitudes An is a very small D ' . D quantity. This investigation was made by Professor Corn- stock (Vol. I, " Publications of the Lick Observatory"). From his investigation the conclusion is drawn that " the Pulkowa Refraction Tables may be used for atmospheric pressures as low as 25 inches without taking into account the squares and higher powers of ^b, and the quantities so neglected will not be sensible at zenith distances less than 80. " The minimum reading of the barometer during these observations was 25.72 inches, so that in these reductions no modification of the factor of the refraction depending upon the barometer need be made. This question having been disposed of, the assumption is here made that all of the error in the refractions is due to an error in the constant of refraction. This amounts to assuming the constant j3 to be correct or that d/3=o. The equation above then reduces to the very simple expression dr Ada = da ; hence da dr a r or dloga = dlogr. Having dlogr from the reductions, we thus have dloga, and hence da. This assumption would perhaps seem somewhat risky f6r stars whose zenith distances are greater than 80. But at the conclusion of the reductions, the value of dloga deduced Il8 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. from such stars was found to fit in very well with those deduced from the other stars. Furthermore, down to 85 zenith distance the observing was very good. In con- sequence of these facts it was decided to take into account all the stars observed. The zenith distances of the stars in this list range from 21 21' to 89 12' (apparent). From 85 zenith distance down, the quality of the " seeing" decreases quite rapidly. This can be seen from the following table of average weights. These weights were derived from the probable errors of the individual determinations of dloga. Z. D. Av. Wt. 20 tO 30 2.0 50 to 60 7-5 60 to 70 7-5 70 to 80 ii. 8 80 to 85 14.8 85 to 90 3-6 The small weight for the small zenith distances is due to the fact that in the expression for da the refraction occurs in the denominator. The small weight for the stars at zenith distances greater than 85 is, of course, due to uncertainties in observing at such low altitudes. OBSERVATIONS. /. List. The following list of 31 stars was observed on seventeen nights, from 1899 June 7 to 1899 July 6, inclusive, and have been reduced according to the plan outlined in the preceding section. Eleven other stars were on the same observing list, but they have not been used here. They were put on to obtain data for determining bisection error, and for other purposes. The numbers of the stars are those of Newcomb's " Catalogue of Fundamental Stars for 1875 and 1900, reduced to an Absolute System." M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. No. a (1900) B i 1900) 948 14* Sim 59* 42 43' 52". 30 190 2 57 33 +53 6 959 15 5 6 5 1 43 6 .62 968 977 15 J5 13 21 29 9 +67 +15 43 46 35 -08 46 -45 984 15 28 28 40 49 50 .61 225 3 33 28 +62 53 33 -74 997 15 39 21 + 6 44 24 -53 1005 15 47 32 19 52 5 -65 1009 15 50 +15 59 1 6 .46 1019 16 I +58 49 56 .19 264 4 5 6 +85 17 29 .06 1032 16 12 21 49 54 36 -79 282 4 24 6 +53 37 -37 1084 1094 16 17 52 8 56 30 + 9 +65 50 49 -32 15 -88 1105 17 15 52 24 53 59 -07 IIIO 17 20 58 29 46 35 -61 349 5 26 21 +74 58 39 -95 356 5 2 9 54 +85 8 49 .60 U35 17 40 35 40 5 17 -65 377 5 46 28 +55 i .68 1156 17 58 51 50 5 53 -20 1162 18 3 48 -45 58 18 .07 406 6 10 48 +59 2 50 .18 1179 18 19 34 -46 I 24 -50 1182 18 21 48 25 28 37 -40 424 6 29 10 +79 40 22 .10 438 6 45 29 +77 6 17 -47 444 6 48 37 +58 33 14 .18 1225 19 42 27 48 59 -80 2. Details of Observations. A night's program consisted in observing the above list, together with three nadirs, one before, one during, and one after the observing of the stars. As has been pointed out, the nadirs are not necessary for the refraction determinations, but, were taken for the reduction of the latitude, which is a problem practically inseparable from the main one undertaken here. No transits were observed during these observations, the whole attention being devoted to the observations for zenith distance. The telescope was set to the nearest 2' and not disturbed until the observation had been completed. The bisection was made (with but a very few exceptions) at the central transit wire, by means of the declination micrometer. For the sake of uniformity every star was bisected but once during its transit. Because of unavoidable circumstances a few of the stars had passed the meridian before the bisection 120 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. could have been made. In these cases the readings have been reduced to the meridian. For the position of the circle four microscopes were read. Settings were made upon two scratches under every micro- scope. The circle microscopes were usually read after the star had been bisected. In a few cases, because of a following star culminating very soon, the microscopes were read before the bisection. In such cases the position of the circle was quickly checked after the bisection. The correction for funs for a night was obtained from all of the microscope readings of the night. This correction has been applied to all of the observations. Its values for the several nights of observing are given in the following table: Date R Date R Date R June 7 +o".o6 June 19 -J-0".02 June 30 -f o" . 06 8 -j-o .08 21 +o .03 July 3 H-o .07 9 +o .08 22 +0 -03 4 +o .08 12 +o .05 27 +o .04 5 +o .05 13 +o .03 23 +o .07 6 -fo .08 14 +o .07 2 9 + .06 These corrections were applied to the circle readings to reduce them to the mean position of the two scratches; so that for a reading of o" the correction is -J-R, for 6o v it is o, and for 120" it is R. In the few cases where the bisections were made a little late the reductions to the meridian were computed from the formula, , sin 2 \ (r m) , S = 8 : sin 20 sin i The horizontal flexure in this instrument is very small. In his work published in Vol. IV, " Publications of the Lick Observatory," Astronomer Tucker adopts the correction o".isin Z.- D., which was determined from a series of observations extending over two and a half years. In this work but two observations for flexure were made, one on 1899 June 3, and the other, 1899 July 8. The mean of M.-P. VOL. I.] CRA WFORD CONSTANT OF REFRA CTION. 121 the two gives the correction o".oisin Z. D.; so that for these observations the flexure correction has been considered zero. The mean of the values of one revolution of the declination micrometer, determined at the same time, is 48". 05. The value adopted, as noted before, is 48". 10. For the computation of the preliminary refractions (called r' in the reductions) the Pulkowa tables have been used. The reductions for the barometer, for the attached, and for the external thermometers were taken from Vol. I, " Publications of the Lick Observatory." The graduation errors of the i divisions of the fixed circle have been determined by Aetronomer Tucker. His results are given in Vol. IV, " Publications of the Lick Observatory." He says there, in part: "The probable error of a reading upon four divisions of the fixed circle due to graduation may be adopted as o".i5. * * " * There is some evidence of periodic character in the errors, and it may be assumed, in absence of further data, that the probable error due to errors of graduation is not diminished by reading upon two adjoining divisions under each microscope. * * * The largest error measured is o".7 for the mean of four divisions." The errors are not sufficiently systematic to warrant interpolating for undetermined divisions, so that no correc- tion for division error has been applied. Three nadirs were observed every night. The changes during a night were usually very small. The following table gives the means of the three determinations on the several nights: Date Nadir 134 57'. t Date Nadir 134 57' t June 7 22". 87 62 June 27 20". 95 66 8 22 .18 66 28 21 .32 67 9 22 .14 6 9 29 21 .40 6 9 12 24 .41 ' 57 3o 21 .70 66 13 22 .70 62 July 3 21 .43 72 14 21 .6l 70 4 21 .46 69 19 23 .81 57 5 22 .91 61 21 22 .36 66 6 22 .10 58 22 21 -59 67 122 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. All of the observations were taken with the fixed circle west. Had more time been available the instrument would have been reversed. Weights, ranging from 5, the highest, to I (occasionally j^), the lowest, were arbitrarily assigned to all the obser- vations. Judgment on a weight was formed from the steadiness of the image during the observation. These weights have been applied all through the reductions. j. Reduction of Observations. The first thing done on the reductions was to take the means of the microscope readings and to apply the micrometer corrections, giving the circle readings (called C' in the tables following). The means of the microscopes were checked by taking the difference of every microscope reading from the mean of .the four. If the sums of these differences for the two opposite pairs of microscopes was the same, the mean was correct. The corrections for the micrometers were checked by duplicating this part of the work. From the readings C 7 the quantity B [equations (II) and (III)] is obtained. The terms A and A' of these equations are obtained from the declinations. The declinations have been reduced to 1899.0 by means of the data furnished in Newcomb's Catalogue. The reductions to apparent places were computed by using the Besselian Star Numbers from the American Ephemeris. The factors a', b', c' and d' were computed from the American Ephemeris data. The reductions to apparent places for the first night (June 7) were computed by means of the Independent Star Numbers also. The places for the remaining nights were checked by differences. The apparent declinations are placed in the columns S of the tables given later. The following table exhibits the stars' approximate zenith distances and the stars with which they are grouped in the reductions for the refractions : M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. I2 3 STAR No. Z. D. SOUTH Z. D. NORTH GROUPED WITH STAR No. 948 79 59-9 . / 225 /. c. 190 /. c. 89 12.0 959 959 88 45-5 { 282/1^. 968 30 22.9 997 977 21 33-2 1019 984 78 6.6 225 /. c. 948 225 /. c. 79 41-9 984 1135 997 30 35-5 968 1005 57 "3 f 264 /. c. 1009 21 20.7 1019 1019 21 29.3 f 977 \ 1009 264 /. c. 57 21.0 1005 1032 87 3-1 377 / c. 282 /. c. 88 40.0 959 1084 27 48.1 1094 1094 28 29.4 1084 1105 62 12.9 424 /. c. IIIO 67 349 /. c. 349 / c. 67 39.0 IIIO 356 /. c. 57 29.5 1005 H35 77 22.1 225 /. c. 377 /. c. 86 47-2 f 1032 11156 1156 87 13-9 377 /. c. 1162 83 12.4 [ 406 /. c. \ 444 /. c. 406 /. c. 83 30-2 f 1162 \ii79 1179 83 15-5 / 406 /. c. \ 444 I.e. 1182 62 47-5 424 /. c. 424 /. c. 62 57-5 {1105 \Il82 438 /. c. 65 31-4 1225 444 /. c. 83 59-3 / Il62 1 1179 1225 65 7-7 438 /. c. It will be noticed from this table that some of the stars are grouped with two others and that one is grouped with three others. ( 3 > May 6, 1903. 124 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. The following tables show the reductions for the new refractions. The column ^ contains the means of the weights of the pairs of stars. The other columns have already been explained. In the grouping of the pairs on the several dates the northern star is written first and the southern star below it. The numbers of the stars given at the tops are arranged in this same order. The pairs which have their northern stars at upper culmination are placed first. It will be noticed that the headings of the columns for these pairs are slightly different from the later ones containing the lower culmination stars. Because of very bad "seeing" or of occasional accidents, some of the stars were not observed on some nights. In such cases blanks appear after the dates. No observations have been rejected. M . -P. VOL. I . ] CRA WFORD CONS TA NT OF REFRA CTION. 125 r* ^^. ^^. ^co M M MM COCO OCO VOVO IO O CS CS CO CO vO vO M co O CS r^ ON ON M CO CS co ON ON C^ v ON M CS ^~ VO GO cO ^^ ON CS VO ON ^"VO O CS CS CO M cO OO CS ON M vo CO CO M k COON ONON CO GO ONON COON COCO O^ ON ONON CSCS CSCS CSCS CSCS CSCS CS CS CSCS CS CN <8 33 3^ v o o g vO CS M co O O vO CO ^ ?l 8 3 ON ON CO ON ON CO ON ON cscscscscscscscs ON CO ON CS CS M M o v 2 s a ^8 = 2 s> 8- CO M CS s oooooooo 000 + + 4- 5 vScg 3 3 Jo co 5 ^ ^cS c^S 8c? g,^ o t^ co o 10 o cO >O *sf t">. TJ- t>. X k CO CO CO CO CO CO CO 00 CO OO CO CO ON ON CO CO CSCS CSCS CSCS CSCS CSCS CSCS CSCS CSCS CO CO OO CO 00 00 cs cs cs cs cs o ^00 IOVO M Tj-fOlOONCS ON vO vO ^ iO O CS CS cOCS cOrfcO^ cscscscscscscscs rj- IO 10 cs cs cs 05 CO IO vO v 10 OVO t^fO r T ON ON r^ O ON O ^ cscscscscscscscs cs cs cs vg M cO CO I s *" CS CO O ON T}~ M M 10 t^vO CO "^~ v vOt~^ COCO MON COCS O "ft" cOiO VOcO M\O IOVO CS ON t~> ON t^ O CO M oo ^cs TJ-CS ^cs ^cs ^j-cs ^~cs iocs iocs M CO cs ON CS ON IO CS IO CS IO CS v CO Tj- , t^CO ON CS.cO * ON M CS t^ CO cs cs cs q a 126 CALIFORNIA ACADEMY OF SCIENCES. LPROC. 3D SER. *, cO cO ^^ ^ k : H NM CNCS CNCM M(N v 1 CO O 10 cO iO CO 00 ON ON CN CM CN CN * v a L * O cO rt M M . M M 6 d d 6 ir + + 4- + H- O CN ONCN CN-3-voco CO M \ CO 00 CN CN l^CO CO CO 00 CO CO ON CNCN CNCN MCN CSCJ v ; O ^* c^ CN N CN CN CN CN 3 00 rf 3% % S V M 00 cs 1 ^- *% cT^P c?^ ^ CO J O ^J" ON C^ TJ- rt -rf IO ^ c? CO CO cO cO N CN CN CN s d CO COCO vOCN con- M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 127 * ^" ^J" Tt" ^3" *O ^O MM MM COCO COCO COCO COCO 10 0404 a\ t^ ON in 10 M - 0404 VOO4 CO^ ONIO cOON O. ' ^ iO lOvO cOcO MM coco 0404 ^ O^ ^^ O^ Q\ O > * s * ONON ONON ONON ONON ONON ONON ONON ONON v o o q cO 04 CO ^04 "3- O iO vO 'O vo cO M cO C^ 1 ON ON ON ON ON- ON ON ON ON ON ON 5 v O v a V odd iO co cO cO cO M cO co OOOOOOOO d d d d o" o d d v ^oT 8^ 8?8 MM CQIO QvO Mt^ COO ^tt^ 04ON O4OO O> O^ O^ O^ OO O^ ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON ON v 10 ON o M 00 t^ V -4 1 CO rj- T^ co ^~ ^* iO vo vO vO o ^ - vO >-> t^vO cO cO cO co cO ^ OO O 04 CO ON cO O4 CO ONON rj-cO O4O OOvO MCO CO'* 1 lOiO vOvO cO CO cO cO ^O cO iO cO *O CO vo cO 00 t^ 04 04 vO t>* CO 04 04 04 04 cO ^O M CO ^^ O ^ cOcOco^-'rJ-'rJ-iOio ^ 3 00 vO r-^ co TtCO v 04 VO lOCO 00 ON v3 o>^ SR ^vS- ^8 vS? JC2?. 8c^ cO O co O co O IO IO IO v O VO 10 Tf CO IO IO M 1 t^ 00 ON 1 > 1 04 CO^ONM O4 t^CO MMMMO404O404 ON t^ M 1^ O ON 128 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. ON t>- M r^ O ON *. CO CO ^ CO CO >0 CO CO CMC, v ^ COCO CO co M ON VO 00 MM CO CO f>- t^ 0.3 ^ ON ON ON ON ON ON ON ON ON ON ON ON ^00 ^ cO cO CO M CO t^ (S 1 2 ON ) 1 ON ON ON ON ON * y , 8 3- o M O v 'w O O 000 o ^ + + -H + + + IO iO W Tf M M iO rh t-^vO VO CO OO 00 ON O CN C4 5$ v ON ON ON ON 00 00 00 ON ON ON ON ON v O O o vo" co O fN 8 ") vO ^ CO CO CO CO 5 **^ iO IO IO M ^^ VO M w VO M CO t^ M VO vO O CM .00 x vO cO iO co vO co O CO O cO iO CM CO ^ iO co >O CO iO cO to o iO cO ^ - s-s. c?3 CO CN CO cO M "3- M VO t^ CO ON 10 10 iO iO *O iO X v cO rO , v VO C^ ON *O M i*->. c^ CO ^O M MM CNM COM COM COM lOrJ- MQ ONl~. ^CJ fNM ^ ON CO ONON ONON ONON ONON ON ON ONON ONON COOO ONON ONON ^ ^ ON ONONcOvO Tj-ONM T^-lOCO MMfNCSCN'^'MOOCOM 00 ON ON ON ON ON ON ON OO ON ON Ca o" o'o'o'o'o'o'o'o'o'o* v ' o oooooooooo "ST 1 1 1 1 1 1 1 1 1 1 1 , V3 O ON ONOO co M M O O CO to co M ON O ON M ON M ON V ON ON ONCO OO 00 ON ON ON ON ONOO ON ON ONCO ONOO ONCO ONCO ^00 * o ^lOMVO ^"OCO M ONM t>> 00 M M co^cOO ^ON , : : rj- ^- >O iO O *O vO l~vOvO vO IO l^, t-H cOOO ON O cO O CN vO CO CO *^ ON CO ON to *3~ vO l^ O 00 t"^ ^O t^ ON M rO lOCO ON co t >> O d C4 r** d *^ O COCO cO t^* CS t^ ^" ON cOGO M sO M t^. ONVO CO to VO cO t^* ^1" IO *O to to ^ v 00 00 d M 00 f^ cOvO o ON cO , 8 (N cOOO ONCNCO cOONONt^ M CS lOVOCO COVOVO M CN cOcOcOcocO'^f'^'^'toiO " ^ CO CO v d d r^. to ^ M Tj-^o Md Ooo ONM ton csco tovo O co iO "^" CO vO vO O ON d d co t^ *^" cO t^* vO ON t^ to O t~** 8 co O co O ^ M ^" M 10 M vO d t^ d t s > d OO cO ON co (Mddddddddd o CO IO vr> M 4 + t- COONdcO^-ONMdr>.00 13 0) c 1 , 130 CALIFORNIA ACADEMY OF SCIENCES. [P^oc. 3D SER. ^ ** ^* -? " k ON ON VO d ON to >* t^* O vO ^" O cocs cor>- WON TJ- o< vo>o ON ON CO CO ONCO ON 6\ ON ON v O O I ON M CS CO O cO O ON CO ON ON ON M I-" M M M 5 O V , q 6 i o* o" o" o* o* 60606 1 i 1 I 1 V, IO M v O Ov 0\CO CS t^ IO O ^^ CM VO w cOCO M ON CO t^. ONCO CM 1-1 rj- CS o\co coco coco oVoN oVoN v O O 00 ON VO t^ t^^ cN O ON 00 O t^ M.-P. Voi>. I.] CRAWFORD CONSTANT OF REFRACTION. *, 10 10 ^^ toto MM cscs toto co to rtTt r^-^- IO>O CSCS O vO *O ' ^"00 vO O tO ON CO ^t" to M v VO CO ON CS to iO iOCO iO t^ O to CO M ^vg" ffp; 5S ^3 k cscs cscs cscs cscs cscs cscs cscs cscs cscs cscs cscs -00 ^ to co ; vo co vo M co ^ cs 10 ON M M t^ T^- vO to to O O t^* O O 3 s^O 10 to vO vo to vO cs cs cs cs cs cs cs cs cs cs cs * v o 1 t^ t^ CO CO f^ f^ t^ vtO fO fO tO to CO tO 6606066 ! II 1 1 1 1 tO tO to to 6666 1 1 1 1 5S 3& cTto S< $. 3 & tOO ONfO <-> **") OCO V v vO to vO to VO to VO to vO to VO to VO vO cscs cscs cscs cscs cscs cscs cscs cscs cscs cscs cscs v O O cs r^ co to cs co to ON fO t^ CO O O to to to M 10 * S *, X 3 * ft * . c^ \Q CS VO CS I> tO VO CS fO O ^^ O to to >o to to to toto to to to to >o to cs o O ON ON r*>. ONCO toco iocs rtcs TJ-CS t^ to " CS Tj- VO CS o -*f CS fO CO to O ON to O ON vfOiOt~>-M tOtOCS ^ ^ fc ^g r^ t^ t^ co co co ON cs cs cs cs cs cs cs CS CS fO to X CO % O \Q ^OCO vO O^ vO r ^~ O^ *O w l"^ O t^ co o to r-^. ^ to ^co VOM OCS rJ-ON t^O !> O^ t> O^ l>* ON 00 O 00 O O 11 ^ O MM MCS cscs toes toco CStO CSlO CSIO CSlO * V O M to to ;+ * ^ > S Z ? 2- M CS t^ CO cs cs cs cs 15 c 3 132 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. CO CO CO CO IO IO CO M IO vO *O vO CH CH CM O O cs cs I I <% <& <& odd I I I IO vO *O 04 CS CN t^CN M CO CN CO M 3- -* M COCO ONCO ONCO !> f^- ON (N 10 co M.-P.-VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 133 *, ^ ^ fOtO WM 0404 tOtO H\M\ M\-t\ fOtO -J- ^t fOtO IOIO 0404 t^ ON tO iO tOON lOt^ IOM O 041O '^'^ t-HQ MDO vO '^ tO ** 04 04 OO tO O ON ^ OO vO iO fO Tti-i COt^ COvO Tt04 MOO VO^I- vOfO vO^t t^fO * *<* + CO ^ v IO 00 -" VO CO -3- ON ON O to s> a- s 5- a 1 04 ON 04 M t^ 04 04 CO M P4 04 M tO O ON O O O4 04 M O4 O4 v a V v O4 ON Tf tO 4- 4- 00 M CO M tO rfr fO fO O4 M ^f- fO 04 rj- Q\ IT) CO ^f tO tO tO tO to 2ft & ^^ Rtt ^r^ ^^ vO ^" M ON CO ON M CO O ON s ' ON l^ t^ IO ^0 fO O ON ONt^ vO Tj- tOO COto vOfO OOtO OO^d- IO tO v IO fO ^ ^ 8 g *& % s- ^ , ft % VQ IO tO VO CO OO O^ ON ON <^- 10 to to vo ON o to 00 fO vg w 832^^^ c^cg tO^f fOON VD^ I>-^i" OCO 04 i-l O4 04 c s 134 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. M .r ^OcO ^OcO ood oo 6 006 060 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 135 < CO CO MM MM COCO Tt -^- coco VO VO CO CO t^ iO cO M O O ONOO M vO cO vo CN vO vo ON ^ M io r- o t^oo CN *xt' Tj" CN cOVO OCN MvOOOcO COVO Tt Tj- Tt M covo v O r^ o co M oo CN M' 8^ S^ g^ CN M 3 * VO CN VO Tf VO CO cO vO t** CO rj- cO CN CO -^ ON ON 4- M co 6 M CN . CN ^ ^ ^ CN CN -xf *f> VO ^ cO ON " CO t^ VO iO VO VO vo % t^ VO VO CN CN MQ ^vS 5 ctg^ % S'c? CN CO CO Tf cO M Tf >O CO CO CO Tf TJ- IO VO CN VO Tf v ^ cO VO cO VO CN rj-fN VOCN VOCN voco *S CO vO CN ON M O O OO ON O 00 cO M Tf -8 - CS CN CN M VO Tf Tt co CN CN CN CN cO CN vo s* VO l^ O ^" ^3" CN vO vO CO O vovo vo vo vO GO O t^ O CO O vO CN vO t^ O s ON iO M ON ^2 $? co^? ON co ON ^t" ON ^" O^ vo COM COM COM COM ON VO cO M 6 V * it- VO VO \ + 1 in .oco MMC^M MM MM + ^ if) ON M J M CO MM M M cO i V M V fl & ? Z J t^ t* iO ON V X II II 2 ^ o 5 $ 2 # V M \,O ** vO 00 00 vO t^ v O 00 O CO O CO ""! CO (N CA hH VO CO" S5 M % CO t^ CO t^ \ to >o 10 10 s ON t^-* t >> O O ^O ^~ IO O ^ CO OO MM cOSO Tt M M U-> M M Tt VJ v Tf fO "O M OCO IO M M 3 C? M O !O ^~ \ v CO CO MM MM MM M GOtO'Tj-cO MCOMCO ONOO ON ON CO M CO cO - W ^ R ^ '+1 1. ON O *O ^" *O vO M to * 1 3 i > ' > M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 137 ^ Tj- Tj- fO CO COtO MM CO fO coco Tt Tt CO CO IO tO CN CN cO ON O O ^tvO CS 00 v CS Tj- t^VO ^t t^ CO CO O vO vO CS fO 10 00 O IO IO M to CO ON to to vO vO to to fO CO 00 M *< t^OO CO CO 00 CS O ". t^ OO OO t^OO CO CO t^ao r^co t^co t^ t^ 5 s OO vO vO vO CO s IO tO vO O tO O X cs co o t->. CO rj- IO to iO vo' 5 to cs to to to i ^- 1 oo r^> t^ oo ^ 00 ^ ^ ^ ^ a M M M v tO to vo 00 R a O cs co O 8 M 5 i v to ^J- cs vo fO ^ Tj- CS T^- M ^> M M l-l M M M M M M M * + + 4- + + + + 4- + + v &g . .0 O t^ CS 00 ^c^ t^- t^ to O O vo ON &\ O^ O^ CS \ i^oo 66 vo' M cd cs IO CS IO CS ^ M Tj- ^ s^- cO *^ vO M IO CS Tl- M Z> ^M^ v r^oo t^oo t^oo co co t^co 0000 t^co t^co t^oo r-^oo to M iO -3- % M cO CO Tf ON <^- ON CS ON ON vO 'O M CO CO Tj- CS ^ VO Tj- IO iO to VO to 10 M cq IO iO vO O to ^ to to to vO cs cs cs cs cs es cs cs cs cs 3 GO t^. t^ CS ONVO to CS iio iOt>- cOON ON^I" CO to CS VO vO t^ cs to ^g M^vS to to to cs r^ co 0*0 t-^co !O ^i- M to cs TJ- cs co to ON to ^t cocs "% M ^ cO O OO ^i- V s r^cs t^co voco t-.N vo cs t^ cs t^ CS f>. CN t^ cO VO cO MTt M^3- M^J- M^t M rj- M Tf M f M rl- M rt vO *"O r^ t> V O to ,-J- CO to cs cs' -, M M M M M M M M M ^ 00 IO M ^ T}*VO co C~> CS ON OO to vS^ ^.5 OO O vO vO r^- IO -^"VO CS ON CO to ^)M 5)M $> $2 M co 2" 00 rt 00 Tj- CS M CS M CS M CS M CS ON ^ T ' ^ M CO O J^^j tfl tt + 1 H in t^ OO ON CS to ^ ON M CS r^ oo ta M M ^ ^_f CS CN cs cs 1 % & i3. CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. (S ON CO >O d ON vO to 8% 58 M (S M lO lO CO cO O ON CN \Q M ON t^CO 00 CO co o 10 TT M CO M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 139 * \N\N \NNN MM CN CN COCO cOcO cOcO COCO IO IO CN CN && S^ ?& S 38 s 8 2& k s T^CO TJ- cO "3-cO "^-cO Ttco ^tcO rtcO rfco 3 1 v t~>.CN lOO t^iOcO'^f M MOOVD O oVo' M 1 \\l\\\\\ V ^rj-co -^ CO TfcO Tf rO Tt CO rfcO ^tco TJ-CO , TtCN cOCNOO M ONl^ ^~ ^O cO IO ^J" CN IO ^" s 00 M M IO 00 ^" 00 CN IO O VD M OO O *O M \^5 O < CO CNOCN CO>OCNIOCN CNIOCNIO IO ^f IO cO iO ^t O CO O CO >O rj- IO CO iO cO v f < 1 M M M M M M o CO ON CN CO - VO lOlO^'TfcOOl CN CNCNCNCNCSCNCNCN - Tj-t">- OO IO May 7, 1903. 140 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. VO <0 h- i ^" v^r? S3 83 #. ^ CO CM vO O Tf ON M CO M CO M CM 2 s ?, ^^ JC 5 ?; $j$ ^^ ^ PJ & v Tf CO Tf CO Tf CO TfCO TfcO TfCO TfCO TfCO TfCO TfCO TfCO i CM VO CM Tf 10 O O O co O Tf M co t"* 3 IO co CM iO O iO VO TfCMCO TfcOTfTf lOlOlOlOiOlOiOlO i v co Y cO cO CM CM CM CM COCMCO t-MCOCO Tf COCOCM cOcOCM CM cO CMCMCMCMCMCMCMCM * 1 I" 1 1 1 1 1 I 1 1 1 CO M rO CS vQ ^OCO cO ON vO t^^* t^^ t** O CM M^f COO COO *OM VOO COCO OcO VOlO ON CM IO cO CO Tf CM CO CM CO CM cO Oco r^.io cMTf MCM Tfco CMCO CMCO Tfio cOcO CMcO CMCO cOcO CMCO CMcO CMCO CMcO x "0 ON o CO ON CM CO cO CO cO 10 CM O ^S 5 ^^^^^^: 10 .0 10 ^-TttO M VO Mt^ Mt^ Mt^ Ot>* Ot^. ONt^ ONCO ONOO v. cO IO o 0. + 1 b * t^ CO ON CM cOTfONM CM t^OO MMMMCMCMCMCM | IO iO (M co CM M I 4 2 *, CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3 D SKR. cot^ 1000 CO CO IO to cO "-0 rj- co ^co Ttco ^-co ON cO O \o ^o 06 oV M.-P.-VoL. I.] CRAWFORD CONSTANT OF REFRACTION. 143 *, ** * coco MM CMCM coco COCO 'vf ^t ^ Tf lOlO CMCM CO CN CO >O ^ ^3" O ON "^t* CMCM tOcO MIO COM OO ONCO tot>. cOt~>- COON M^O COco CMt^ cOON VOM ONIO OO rfON COM ^ to iO *sf rh T^" cO to to to "*sj" to ^st" VO VO ^3" ^^ ^J" ^" to ^" ^}" T^~ - ~ M 5 10 O^ GO to ON M CO t^- CO CN to ^ 10 ^t cOtO-^tiOMD ^t^lOTt 1 X M v a k, V CO Tfr v CM CN \ \ IO vO cO M to cO ^t" cO t^- CNCMCNCMCMCNCMCMCN ooooooooo \l\\\\\\\ , ^ 2^ foe? c^co $$ 5$ .&$ ^ 2 ^2 v to to to rj- 10^- vo^o ^o^o uo^- t^.vo 10*0 10*^ iovo 1010 v M M CN CM CS r^ ^c}" *~* 1 O O *O C4 ON , M Q\ vO CO CO vO O ^ < CS MM'MMWWWJNCS t-. ON O CM CM cO CO cO Q- O^ *O vO Is* ^D ^O I>-C^ OO GOO vOO C4CO IS-CO ^GO iO GN rO C7N v O vO O MO O^^sO O^ Is* 00 Is- CO Is* is-^O ^O ^O \O 'O ^O^O 1 O'O , , iO ON CO M - + 1 C 1 "** GO QNCM CO^ONM CM r-^oo M M M CM (N CM CM 1 a D 144 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER t^ to ON to O 10 O vO VO to VO 10 10 n- 10 to TJ- co to to M (N tOOO OO ON vO cs O 00 00 vO t^. IOVO 1-1 M.-P. VOL. I.] CRAWFORD-CONSTANT OF REFRACTION. *. \N\N cOcO MM M N coco cOcO Tf'rt Tf T^- IO IO M N IO cO t~>. M ONt->. GO ^ Tf *3" O *t~ v vo to TJ-LO ONQ vor^ vo i>- t-^co M ON O M M VO vO IO IO Tt lOCO ^ iO rj- VO to iO iO iO * t^vO iO Tf O rf VO to iO Tj- v M M 1 ON ON co M ON I> v O ON iO N M CN O CO ON M ON M 3 >O iO iO O l^ iO M M M M MM M M M ] v M 1 666666 \l\\\\ M t^ CO iO IO CO 666 \ \ \ CS ON O "^t" ON t^ 1 ^ O ^O ^-O vO ON ^O v r^^o cooo CNCO vovo iovo ON HH o co t^ co t^ o V 10^- vo^o vo^o *o^f t^vo 10 to tO Tf VO >O iO to v MM tO tO O4 00 IO CO IO O CN cO O 00 Tfr Tt Tf Tf ^f IO M M CN to to to i- ON ?NI ON d O C^ t 1 ^- to ^f ON t^^* *O v O"O ^ M M cO t^ Tj- <* ONOO IO tO ^O ^" ^O ^" ^st" tO IO to ^" tO t^OO VO t^ lOOO VJ s ^^ t^ (S ft % s v a ^ ^ IO to M ^ CO - cs M M o ON CO M CO t^ vC tO to to tf) ff) MM vOTf t^O lOt^ cO^f CNON -^tO -" O COO WOO vOCO g g; t^^D . v ONVD co t co t~* t t^ vo vo ^ovo Tt Tf * Tf Tt Tt tovO ^"VO cO^O t^OO ONCS cOrj-ON-i * M M M Cl (N t^ CO M (N| co CN r^ M co ON CO ^D k CN M -rf CN M IO rj- CN oo -rf ON * r^ * cO CO M 8^ ^ ^-cT c7co CN to CO ON *O co M" cl C^ M" N ^% CO co CN co ON M tO cO cO tO TT oo oo oo oo W M HH M ON O O O ON O M 00 CN o CN O CN rj- (N ON co v) CO cO Tf V O O CO CO t^. vO to o 10 COM VOt~~ CNON MIO O CN to CN O ^ Tf Tf Tt- IO 'sj- ON M OO CN CO CN IO Tt- to rj- to "3- * v ^ T}- M O Tj- IO Tj- Tt + 1 * t^ CO ONCN CO^fONM CN t^ CO CN CN CN q 148 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 31) SER. * cOcO *3" ^t COCO ^ ^ ^ ^f CNCNJ k M cO ON cO vO CO co ON co ^ w w v CN O >-H CN h-i CO VO t~^ t^ ON CN CN VO ^O t^ t^>- CN M T^J- Q Q Q^ Q * Tj- ^- rj-MlOCNlOCN + CN M t-. vO M M VO t^ M (N O 6 CN CN CJ CO Tf Tj- I '+ + + + + + \ v o co r>-co o CN voco vo co ^ ^j- MlO MlO ^ MlO CN COl-l co co o r^ vo CN v TJ- ON Ol O VO VO IO CO VO Tt 01 CN - ^ ONO OO ONQ OO OO OO CO . O VO ^O ^ oo oV CM IO ON vO s 10 ON N O CN ON CN IO 150 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. *, tO tO ^* ^~ to to ^O ^O ^* ^ j- OCM VOCO coco coco coco cOcO coco fO CO IO HH ^t* t ( VO CO t^ t~^ VO M CM CO v M M *3- CO M O CO CO cO cO CO cO * o o (M IOO O M COCM COON IO t^* ^O t^* ^J" vO cO ^t* 1 O O w vO ON CO M Tt r o " cOiO cOiO MVO CMiO -^t- 10 -^h r ^~ , S52 o >o r^ CS CO iO iO cO 1-1 t->. -^ IO O) ON O ^ CM CM M M . M (J\ to <^00 *^fOJ CSO OCC !>. IO rfCS MQ O MO CN CN O VO rf CN ON t>. k r^* *^t" t^ ^~ vO to CO ^t" I> "^J* t^>. ^t 1 0^*0 t^* ro vO fO r^. ^f vo co IO 10 IO IO + O^ ^" l>* ^O M CS GO ^^ M v *O CO *O ^J* M GO *O ^J" ^O CN CO CO co I *o *o ^t* ^o vo ^o r^ LO TJ- IO to ^O *O *O iO iO to IO to 10 g V M Y CO CO GO O O s \ s * GO CO CO v to tO >O VO to iO to iO iO vO to V 1 1 1 1 1 I 1 1 1 1 tOvO ^tOO iO ON rf tO t^ ON lOvO ^t t^ M -rt r^OO v ^-O ^d" M O^* GO vO to rO t 1 ^ to VD "^" t>* to rO ^^ O GO rj- cO vO CN t^ iO ONCO v I>* *^t" t^- . to 10^0 10^0 1010 ioio toto 10*0 ioio to^o to^o v MM l^ Tf- vO cO IO IO to IO oco coONON^r-^co t- CN , cOTfl^rftovO Tj-ONM 6 M M M IOO COvO ONCN CNM COf^- IOCN COlO cOt~>. CNlO IO CN O CN to ON ^r ON co O vO O co ON CN CO "^ ON O O CO ON CNCN CNCN CNCO CNCO CNCN CNCN CNCN CNCO MCN M CN M CN ^ CO CN t^ CN ON vO co ^r M t^ CN vo cO ON CN 00 vo COCOCOCN CN M O ONON 10 10 IO to V " v CN CN M IO vO ON t^* cO M cO ON ON vO vO ^ CN vO ON M CN co r^ TJ-Tf MlO ONIO Mt^ ONCO r>-ON CNON t-^O "*f O CN co ON t^ co Tfr O "=J- v ONtO ONto COiO COtO r^-iO t^.to vOtO tOvO tOvO cOcO coco coco cOcO cOcO coco cOcO cOcO coco "^t* vO ^~vO cO co cO CO * v CO vO 10 Tf ^ c? 4- 1 %J t^co ONCN COTJ-ONM CN t^. CO CN CN 13 V B ON O COM I$2 CALIFORNIA ACADEMY OF SCIENCES. [!>ROC. 30 SER. to to " 10 tO + M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 153 *, iO iO ^- ^- co co N^\N rOcO fO fO ^"^f ^^" ^u^ ^O^O 00 ON IO ^ !>. CN CO ^ 8(S} l/^ M T^- C 1 ^ O ^O ^"GO r4 ^O CO cO <*O CO ^" ^O O*^ <*O^O vO *O K MCN M CN MM CN CN O t^* to <^) vO ^" ^O O l**^ ^" O 00 ^M CSrO MCS MCS MM MM MM MM MM MM $ 5 CN CN r^ co IO ^ Tf IO M cO ^O CO M C^ ON rO ^O CS O ^O TJ- iO iO ^f iO 5 8. ^ M v a V 10 vo co r>. M ^o o^ CO !> v*O rO ^" ^O <"O rO tO * 4-4-4- 4- 4-H-4- + + 4- M CN IOCO 00 iO COCO v CN rO ^1- co t^ CN COCO iO t^. rO O ONCO iO CN iO O cO iO CO *O M M GO ^ CN VO ^sO O ^O ^O v k M o OO ^O ^O ^* CN O CN CO M CN MCN CNcO iO rO ^O iO 00 vO t^ T^ M ON VO T ^' MCN cO'Tf MCN MCN CNCN MCN 00 O co cO 10 !>. M M CN CN Tf M * t^ VO ON i> r^ CO ON M v rO co CO O CN IO M CO CN v> CN IO M M M CS 5 M ^" CS r^ t^ 00 M Q rO CNCO rOO CNrj- ONO rOCN TtM CNO CNO ^-Tf'CN'^- M T^- r^-cO O 00 Tt- iO O rO ^ O IO t > * 00 t^ CN T^ ON ^O ri MM M IOM M IOCN V SN 55^ S5% <$>% %% , v M IO M O + 1 1 HH HH c s Tt- ON M CN t^ 00 M M CN CN CN CN 154 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. . "3-rh -rl-^t coco 10 10 coco CN CN v VO O ON iO ON t^ O CN MM 10 ON v ^ >H -^ CN iO ON ON ON COCO ON *O lOcO COM CNCO M ON ONCO cO CN M MCN MM MCN CNCO MM MM MM MM MM MM ^ t 5 co t^ co M M r^ v CM CO IX ON CO CN ON t^ iO iO Tt* CO Y V CN CO ON M O CN CO CO M O iO CO CO CO cO -3- -3- -3- co CO CO CO cO CO V MlO IOCN COCN COO CNCN cOt^ iO CN t^ ^O CO ^^ ^ cO ^O ^J" O ON MCN MCS M MO) CNCO COCO MCN MCN MCN MCN MCN MCS , ' t">. CN vO M cO cO O CN cO ^r ON cO CO CN ^- CN IOCN cOiO CO^ cO^ ONCN cO^O ^T CN CN ^T CN CN M v ON M o ON O ^ N - Tf ^T CO CN CN CN ^ , cOO COON MCN MTt COIX IOCN T^~ O CN M >sO ^O ^t~^O CN r^ O ON "^co^ co^ r^^- t^Tj- ixTf t^^ IOIO IOIO IOIO OlO IOIO *OIO v o 10 + \ 1 CN CO ^ 3 3 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 155 *, cOcO cO cO cO cO rf Tf- rj- rj- 10 >O cO cO v iOiO cO CS iO TJ- i-iON l~. t-*. 85 .(S S-S k CSM COM CSM COCS COM a at ^? + x v O CO ON to cs t^. ON ON O cs cs 3 CS VO M ON CO CS CS CS CS CS co 10 cs cs cs cs 1 * vo N a ; s a s or ^ vO t> cO TJ- rh vo V \ 1 1 1 1 1 1 1 iOt^>. Mt^ ONCO CSrJ- lOiO Tf M t^ CS COVO CO ^ * O 00 O V COM COCS COM Tj-CS COM ^^ %? ^ v vO vo ON Os ^. ON cO ' T^ vO , M r^vo ONCO oo 10 cs cs cs M V CSCS CSON l>.rfvOCO COCS cOvO OO CS IO M V o ON r^ r t^co oo >o oo ON MTt MTt rJ-MTt Tj- ^ ^: ^^ ^gj MOO CS CO ^ $ p. 8 K S ^ -, rO cO cO cO cO CO cO co && 2& SvO $Z %$> ^S? ^8 2cS $>~ JO^M Jo^ 5^ & O t^* ONOO ONOO v CS 00 + I y l> 00 ON. t^ CM CO M CO M CM M t^ O ON CM cO ON cO ^3" t^vo co CM CM CM f^ ON t^ ON VO M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 157 *, COCO W OJ cO cO rf rf - v t^ d 8* S? 8^?: 5-^ <$ 5^ v k % dO ONt^ OOvO OOO d 10 M d M ^^ M 2 s ^ v vO vO t^vO vO vO t^vO r^vo vO vO t^vO t^vO ON M d rf 00 ON GO t^* ON d d d vO , X M ON d d IO CO rfr CO Tj- IQ Tf Q , s-* MON t^Tf GOOD ONd rfvO O d IO M ^t M 10 O vO d ON Tf OO tx IOOO d IO cO ON Tf ^t IO V v 00 ON v IO ' &% * N ^ d ON tx ON 00 t- V ^ , CO d M 6 O 00 00 ^ v O a a 5^ t^. 10 lOvO ^ IH ON cO d cO CO O M rf ^ Q if) ONVO ONVO 00 t- Ix t^ t^ t^ vO 00 vO 00 , o QOj ^ + 1 * I s * 00 O*^ Cl M cO -^f ON M M M M d d t> OO d d d I iS8 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER.. ^ *>*> ^ *>*> ^"> M\\ tO tO CS CN , 3 # M-& oo o to t^ CO IO IO 10 k IO M IO M IOM IO M CS CN v vO vO vO vO vO vO vO vO ^^3 ^^0 5 O M ON O C4 CS ? X 3 IO IO M IO to to to . 5 M CN ^- rl- i vo v a v O GO >O ON ON 00 V M O O ON CS M CS l-i N W ^T 1 i 1 1 1 1 C4^ IOM Mt-N. VOM v ONt^ OON OOO vOOO ^- iO O to k 00 VO ON t~> ^i" C^ t >s t^^ IOM IOM IOM IOM M CM v ^^ ^vo VOVO vovo t-vo t-vo vO tO OO tO rt CO t^>, f/^ , v O C^ O to IO IO VO ^O 3- t^* ^" OO C4 O ON M ^J" VO O Tj- N CO VO CO N OM QtO lOiO COM iO iO iO 10 iO IO ^ ^ ^ ^ CO ON t> !> v IO IO IO CO CO iO to o tO ON w to fO Q >O to ON fO 00 10 ; IO tO iO ' I M.-P.-VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 159 , v* i <* ^ ^ #> <++ <++ -0.0 $15 GO "<3- M w VO M 00 ^f x CO O O >O O vO 04t>. ONON ^t" ^ COM ^O vO O O O It CO04 COM MM COM CM COM MM MM MO ON t^ co M MM v VO VO ? ON 04 00 O ON ON O t**- M vO t^. TJ- ^ a 3 04 O4 04 04 CO M CO CO M CO M M * 0? { vO V O ^ v ON t^. 04 04 IO IO VO VO ill 1 M Tj- 04 M vO vO vO vO 1 1 1 1 3 -2 vO vO 1 I Tf ON IO O O Q Mt^ v VOt^M^O O400 04VO ONOO MM 10 ON TJ- O ^co c^vo \ c^o? %Z co^ XX M ON M ON cO O M ON COM Tj-04 COM COM cO M CO M VO vO 04 ON M O % 8 3 P. % v 04 t^ CO O4 cO co ^ cO CO CO IO VO ^" 04 T^- ^* 5" ^ aq 5? co^ ?,o? oT^ $& COVO MM 04M CO 1 * t^t^ VOM OOO COCO ^o? %3 v 2"^ M 2j 2 Jo " IO M Tt IO IO 00 ON 10 cO u v O4 M MCO o co ON 00 IO 04 ON $ % 0. VO Tf M - cO CO CO . O4 M M M M ID IO M M cooo o t^ g co a 04 co ^ M 10 ONVO M 04 04 !> vO cO ON ON vO O OO COCO COON MM M CO M ON , ^rOM COM 04M O4O4 IO04 IO04 >O04 IO04 v O4 M + 1 04M OM OM OcO IOM IOOJ IOM lOM ON co ON co Tf M Tf M 1 r^ co ON co rj- ON M M M M M M M M 3 c ^ l6o CALIFORNIA ACADEMY OF SCIENCES. IPROC. 3 D SER. -0 VOV.O to to IO W M CS vO vO I I 00 TJ- M (j\ as M.-P.-VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 161 (N O N O vO ^O vO vO vO vO v^O vO O\ Ok M M I I ON ON ON ON ON ON ON ON GO vO vO O O ON CO O ON t~^ cO 00 !>. M M Tj- v^^ "% k vO t^ vO t*> CM cO tO M IO M IO M ^n7 CM CM ^ CO CM CM v vO vO vO vO vO vO vO vO r-vo t^vo + CM CO vO R HH IO t- CO I t~^* vO co VO CO CM CO 1 CM M -<3- ON M IO M ON CN s s * 1 1 1 I 1 1 CM r^ to CM M CM v ON Tt IO CO O M vo g vO ON 33 2$ V % 8 H? t^CO IO M CM CM v vO vO vO vO vO vO vovo r^vo t^vo vO O vO CM IO !> % < v CO rj- CM tO tO vO Tt CM 3- n- ON tO cO cO t^ cO v t^ O CO cO O CO 2^; vO ON rj- ^ - CO M OO CM s % %% CO co VO VO vO HH vo ON u CO CM t^ v IO M IO VO CO 00 VO tO C? CO ft 8 ON vO O CM ON v V CM HH O IO VO VO O O ON M O O t CM M CO 4^ M CM rh^t t^OO M IO ONVO t^*CO * - <8& g ON O cO CM CO <* 10 vO 3 >> ^ ^ M.-P. VOL. I.]. CRAWFORD CONSTANT OF REFRACTION. I6 3 * tO tO ^tt" ^t" r ^" ^" %* ^^ ^^ ^ ^^ ^^ ^^ ^J" O CO CM O VO v CM IO ^00 CO W Oio ^OCM toON COO CM>O tOiO OO M Tt Tj-CO t^ O t>- M lOCO 00 M t^. O k IO rf ^f to fO tO to to fO to fO to !O Ti" IO T}~ VO ^O ^t" Tt" ^^ tO ^" ^" ^" *^J" tO. ON M IO iO VO ON ON CO oj to *^ ^d" IO IO O n 3 Th 10 10 $ *d- O 'O M (N ^ g:^: 33 *% ?, fLZ $& CM O M O O 1-1 IO to >O "0 iO O O ON O O^ c^ O t^** ON 10 ON cOOO ^~ ON ^O^j" iO^* lO^O ^"^f ^"^" ^J"'^f '^T'^J' ' ^5 iO t^ CM tO vD O O^ rt CM 00 R * S * ? % v Jo a to a a $ * * * * rj- 10 t^^o ^rT "2 cT M rO CO cO C^ CM vO *^ tO HH ON cO vO rO v CO VO CO vO 00 VO W fO CM tO CM O t^vO *O vO ^O^O ^*vO "^"^^ CM vO CM v^ CMcO dro CMcO CMrO (NrO CNtO MrO * x O CO t^c? a M to ^1" ON M CM r^ CO M M M CM CM CM CN * e ^ * i 164 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. v> (N s 33 co 10 i Q M ON C^ O *O Tt Tf Tf IO S3 O 00 OMO l> CM M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. s CO cO ^ ^f ^ Tf H $$ coco ^^ ^ M ^^> v CO ON Tj* to cO ^" OOvO vOO COON ONIO cotO totO Tt~vO t*> O t^GO cO ^^ t^OO M d 3-^ k vO ^^" to cO to cO v MM vO Ti~ vO to t^ to VO ^* ' to cO vO ^" w p M 00 M v ON - $& OM 8^ # c7^ 0$ v ^3 *3 33 vO ^" to cO OO VO vO ^" to cO vO ^" ** vo r^ M vO ^" vO t s> to vO 00 to O cO ON 10 CO O cO Tf- d d d vO t^. ^ * * $ g. cO to GO d to t^ v ON to O CO O M cOON MIO cOON cOO d't^ vOd lOOO O M CO M CO d COM COM ONM Tj-Q COO MON 10 to to to to to to d ON to to ^ vO to tO lO Tt * ON C TtOO d CO tO CO O M M cO ON t~^ T 4" vO - d d d \O tO ^t cO cO d d d d d d d M & 8 R ^vo cO d vO to vO cO ' r ^~ to M Tt" ON to t^ t^ -^- t^ O^vO cO to O to vO vO 528 d lO d >O d lO dtO dtO dtO dtO dto MIO M" <* v vo 00 t^ d + ! M h? M M d d d % ^ D 3 1 ) GO tO ^ d 1 66 CALIFORNIA ACADEMY OF SCIENCES. [PROC. jn SKR. TJ-V> IO ON M rf IO O O M COO iO iO OM fO ^ ON ON d 6 \ \ CTN IO -^ O^ O^ O*\ 6 6 6 \ I \ , ON ^O Os CT\ MlO MIO MlO MlO M.-P.-VOL. I.] CRAW FORD- CONSTANT OF REFRACTION. 167 The following tables contain the reductions for dlogr or its equivalent dloga. The second column contains the logarithms of the computed refractions; the next column contains the logarithms of the observed refractions; the fourth the difference between the two preceding, in the sense of Observed Computed; the column^ contains the weights and the last column the weighted differences. The residuals and their weighted squares are not given. Log \_-pw~\ is given in every case, as is also the resulting probable error of the weighted mean of every set. All of the results in the following tables have been checked. STAR No. 948. Date log. r ' log. r A / /A June 7 2.42742 2.42617 0.00125 4 0.00500 8 2.42399 2.42119 280 4 1 120 9 2.42126 2.41762 3 6 4 3 1092 12 2.43095 2.42727 368 i 3 68 13 2.42658 2.42490 1 68 2 336 14 2.42169 2.41838 33i 3 993 19 2.43214 2.42889 325 3 975 21 2.42478 2.42185 293 4 1172 22 2.42149 2 . 42042 107 3^ 375 27 2.42459 2.42243 216 5 1080 28 2.42313 2.42147 166 2^ 4i5 29 2.42262 2.42014 248 3^ 868 3 J"iy 3 2.41600 2.41678 + 78 2^ + 195 4 2.41916 2.4l8l6 IOO 5 500 5 2 . 42644 2 . 42605 39 3 117 6 2.43042 2.42602 440 l# 660 I 0.00205 [p] = 50^ ; logpw\ = 5-8653 p. e. = 0.00015 1 68 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. STAR No. 190 /. c. Date log. r ' log. r A P /A June 7 9 3.09609 3.08699 0.00910 3 0.02730 12 3.10852 3-09598 1254 i 1254 13 3.10231 3 . 10302 + 71 % + 35 H 3.09619 3.09129 490 3 1470 19 21 3.10009 3-09349 660 4 2640 22 3-09543 3-09387 156 ^ 546 27 3-09851 3.09629 222 5 mo 28 3-09793 3.09046 747 3 2241 29 3.09748 3.08610 - 1138 3 34M 30 3.09728 3-09563 165 4 660 July 3 4 3.09289 3.08925 364 5 1820 I 3.10261 3-097I3 548 3 1644 ::= 38; = 6.6II2 A 0.00513 p. e. = 0.00047 STAR No. 959. (With 190 /. c.) Date />. r ' log. r A P /A June 7 O 9 3-03783 3.02741 0.01042 3 0.03126 12 3.05008 3-0357I H37 i 1437 13 3-04374 3-04454 + 80 /^ + 40 14 3-037I4 3-03I75 539 3 1617 21 3.04205 3-0345I 754 4 3016 22 3.03782 3-03605 177 619 27 3.04138 3-03886 252 5 1260 28 3.04032 3-03I77 855 3 2565 29 3-03986 3.02685 1301 3 3903 3 3-03983 3-03795 188 4 752 July 3 4 3 . 03667 3-03252 415 5 2075 5 3.04442 3-03815 627 3 1881 6 A I o . 00584 [p ] = 38 ; log = 6. 7298 P-e.= 0.00053 M.-P. VOL. I. ] CRA WFORD CONST A NT OF REFRA CTION. 1 69 STAR No. 959. -(With 282 /. c.) Date , log. r A P /A June 7 3.04492 3 . 04068 0.00424 M 0.01908 8 3.04160 3.03886 274 3^2 959 9 3-03783 3-03050 733 3 - 2199 12 3 . 05008 3-04703 35 i 305 13 3-037I4 3-03633 81 3 243 19 3-05165 3.04787 378- 3 21 3.04205 3-03741 464 4 1856 22 3.03782 3-03645 137 3/^ 479 27 3.04138 3-037I7 421 5 2105 28 3.04032 3.03228 804 2 /^ 2OIO 29 3.03986 3-03043 943 3 t 2829 3 3-03983 3.03611 372 1674 July 3 4 3.03667 3.03112 555 5 2775 5 3.04442 3.03910 532 3/^ 1862 6 3.04920 3-04347 573 2 /^ 1432 | 0.00462 = 5i# J log[pvv] = 6.3662 p. e. = 0.00027 STAR No. 968. Date /qg\ r ' log.r A P /A June 7 1.45651 .46180 + 0.00529 4 -f- 0.02116 8 .45383 46553 + 1170 4 4680 9 I.45H9 45637 488 3 1464 12 .45985 .46790 805 i 805 13 456i4 46225 611 I# 916 M .45172 .45758 586 3 1758 19 . 46276 46879 603 3 1809 21 -45485 .46374 889 3K 3111 22 .45181 .46120 939 3^ 3286 27 45453 45652 199 5 995 28 .45407 .46060 653 2^ + 1632 29 45340 45984 644 3^ 2254 3 July 2 44653 45347 + 694 3 -f 2082 4 .45114 .45408 294 5 1470 5 45656 1.46835 1179 3 3537 6 .46066 1.46850 + 784 ig + 1176 0.00662 [P } = 5 ; = 6. 6307 p. e. = 0.00036 1 70 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 977. Date **;< log. r A * /A June 7 i . 28488 . 28488 ^ o.ooooo 4 ^ o.ooooo 8 1.28218 . 28892 -f- 674 4 + 2696 9 .28019 .28126 107 3 321 12 .28796 . 29270 474 i 474 13 . 28439 .29491 + 1052 1^2 1578 . 28022 .29092 1070 3 3210 19 .29163 173 3 519 21 .28336 .28758 422 H77 22 . 28043 .28149 106 3/^ 37i 27 . 28302 .28758 456 5 2280 28 . 28288 28533 245 612 29 . 28206 .28691 485 3^2 1697 30 . 28204 . 28648 444 4 + 1776 July 3 .27518 .28171 653 3 1959 4 i .28003 .28758 755 5 3775 5 1.28512 29623 mi 3 + 3333 6 i . 28948 . 28870 - 78 2 156 I + 0.00476 = 54 1 A ; log [pvv} = 6.7951 STAR No. 984. p. e. = 0.00040 Date /0g\ r ' log.r A / /A June 7 9 - 12 2 . 35626 2 -35 I 99 0.00427 I 0.00427 J 3 2.35336 2.35114 222 2^ 555 14 2.34902 2.34616 286 3 858 19 2.36071 2.35971 IOO 3 300 21 2.35175 2.35042 133 3 399 22 2-34937 2.34805 132 3^ 462 27 2.35175 2.34951 224 5 1 1 20 28 2.35162 2.35176 + 14 2 + 28 29 2 . 35060 2.34874 i 86 4 744 3 July 3 2.34417 2.34616 f 199 3 + 597 4 2 34844 2.34713 131 5 655 5 2.35414 2.35319 95 3 - 285 6 1 2.35871 2.35581 290 i# 435 A 0.00142 [pvv] = 5.8091 p. e. = ^E 0.00017 M.-P. VOL. I.] -7 CRA WFORD CONSTANT OF REFRA CTION. 171 STAR No. 225 /. ^r. (With 948.) Date %" f ' log. r A / /A June 7 2-41352 2.41224 0.00128 4 0.00512 8 2.41100 2.40812 288 4 1152 9 2.40895 2.40523 372 3 1116 12 2.41618 2.41237 381 i 38i 13 2.41359 2.41187 172 2 344 H 2.40930 2 . 4059 1 339 3 1017 19 2.42102 2.41769 333 3 999 21 2.41181 2 . 40880 301 4 1204 22 2.40967 2.40858 109 3^ 38i 27 2.41188 2 . 40966 222 5 IIIO 28 2.4H75 2.41007 168 2^ 420 29 2.41072 2.40815 257 3^ 899 3 July 3 2.40463 2.40542 + 79 2^ + 197 4 2.40845 2.40741 104 5 520 5 2.41441 2.41400 4i 3 123 6 2.41907 2.41457 45o I# - 675 0.002II [/ 1 = 50^ ; log [pvv ] = 5.8809 STAR No. 225 /. c. (With 984.) p. e. = 0.00015 Date r.r- log.r A > /A June 7 8 9 12 2.41618 2.41246 0.00372 i 0.00372 13 2.41359 2.41165 194 2 % 485 2.40930 2 . 40678 252 3 756 19 2.42102 2.42014 88 3 264 21 2.41181 2.4IO66 115 3 345 22 2.40967 2 . 40849 . 118 413 27 2.41188 2.40983 205 5 1025 28 2.41175 2.41186 + ii 2 + 22 29 2.41072 2.40914 158 4 6 3 2 3 July 3 4 2 . 40463 2.40845 2.40637 2.40729 4- i74 116 3 5 + 522 580 5 2.4I44I 2.41357 84 3 252 6 2.41907 2.41652 255 382 | 0.00126 [p ] = 39^ ; log [pvv 1 = 5-6934 p. e. = 0.00015 (6) May 9, 1903. 172 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. STAR No. 225 /. c. (With 1135.) Date log. r ' log. r A P /A June 7 2.41352 2.41299 0.00053 4^ 0.00238 8 2.41100 2 . 40928 172 4 688 9 2.40895 2.40601 294 3 882 12 2.41618 2.41416 202 i 202 J 3 2.41359 2.4II05 254 2 508 14 2.40930 2.40724 2O6 3 618 19 2.42102 2.41858 244 3 732 21 2.41181 2.4IIOO 81 4 324 22 2.40967 2 . 40882 85 4 340 27 2.41188 2.40981 207 5 1035 28 2.41175 2.4IIOO 2^ 187 2 9 2.41072 2.40744 328 4 1312 3 July 3 2.40463 2.40488 + 25 3 + 75 4 2.40845 2.40691 154 5 770 5 2.41441 2.41437 4 3^ 14 6 2.41907 2.41547 360 2 720 = 5.7856 A I 0.00159 P> e > 0.00013 STAR No. 997. Date /cjg-. r ' log.r A / /A June 7 1.45932 1.46479 + 0.00547 4 -f- 0.02188 8 I.45705 1.46879 1174 4 4696 9 1.45504 1.45969 465 3 + 1395 12 1.46180 1.46967 787 i 787 13 1-45953 I-46553 600 i# 900 14 1-45544 i .46120 576 3 1728 19 i . 46676 1.47261 585 3 1755 21 45774 i . 46642 868 3^ 3038 22 45588 1.46509 921 3^ 3223 27 45791 1.45984 193 5 965 28 45782 1.46419 637 2^ + 1592 29 45671 1-46315 644 3^ + 2254 3 July 3 1.45099 1-45773 -f 674 3 -|- 2O22 4 I.45436 1.45712 + '276 5 I 3 80 5 i . 46049 1.47217 1168 3 3504 6 i . 46492 1.47261 + 769 i# + U53 [p ] = 50 ; log \_pvv] = 6.6325 A I + 0.00652 p. e. = Jz 0.00036 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 173 STAR No. 1005. (With 264 /. c.) Date /<. r ' log.r A P /A June 7 .87711 1.87518 0.00193 4 0.00772 8 .87496 1.87186 310 4 1240 9 .87269 .86700 569 3 1707 12 .87989 .87697 292 i 292 13 .87719 .87361 358 2 716 H .87307 87454 + H7 3 + 44i 19 88455 .88138 3!7 3 95i 21 22 .87581 .87378 : 86964 348 414 4 4 - 1392 1656 27 -87582 .87489 93 5 465 28 87565 .87093 472 2 944 2 9 .87436 .87256 180 4 720 30 .87545 .87489 56 4 224 July 3 .86915 .86847 68 3 204 4 .87220 .87157 63 5 3*5 5 1.87863 .87823 40 3 1 20 6 1.88269 .87881 - 388 2 - 776 = 56 ; log = 6.2452 A I 0.00215 P. e. = STAR No. 1005. (With 356 /. c.) Date log. r ' log. r A P /A June 7 9 .87269 87233 0.00036 3 0.00108 12 .87989 .87800 189 i 189 13 .87719 87547 172 2^ 43 14 .87307 87355 + 48 3 144 19 -88455 .88502 + 47 3 + HI 21 .87581 87413 168 4 672 22 .87378 .87268 no 4 44o 27 -87582 .87743 -f 161 5 + 805 28 87565 87425 140 2 280 29 30 .87436 87545 .87512 .87714 + 76 + 169 4 4 + 304 + 676 July 3 86915 .86788 127 3 381 4 .87220 .87326 + 106 5 + 53 5 .87863 .87547 3i6 3^ 1106 6 .88269 .88064 205 2^ 512 A I 0.00031 [P ] = 49 % ; log [pvv] = 6.0442 p, e. = 0.00019 174 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. STAR No. 1009. Date &#. r ' log.r A P /A June 7 .27967 .27600 0.00367 4 0.01468 9 27759 27515 . 28149 .28149 390 + 634 4 3 + 1560 4- 1902 12 . 28250 . 28240 10 IO 13 .27963 28307 + 344 2 + 688 14 27547 . 28262 7i5 3 2H5 J 9 . 28706 .28825 119 3 357 21 27843 27989 + 146 4 22 . 27648 27346 302 4 1208 27 27834 .28511 + 677 5 + 3385 28 .27819 1.28126 307 2 614 29 . 27674 1.28149 475 4 1900 30 .27815 1-28375 560 4 2240 July 3 4 .27187 27473 1.27300 1.27807 U3 334 3 5 339 1670 5 1.28132 i . 28466 334 3 1 002 6 1.28519 1.29003 + 484 2 + 968 = 56 ; log [pvv] = 6.7629 I + 0.00298 p. e. = zt 0.00038 Star No. 1019 (With~977.) Date log. r ' log.r A P /A June 7 .28286 . 28307 + 0.00021 4 -(- 0.00084 8 28075 .28758 68 3 4 2732 9 .27851 . 27987 136 3 408 12 .28578 . 29048 470 i 470 13 .28283 29358 1075 I* 1612 H .27867 28959 1092 3 3276 19 - 29036 . 29203 I6 7 3 501 21 .28165 . 28623 458 3^ 1603 22 . 27970 .28103 133 3^ 465 27 .28158 . 28623 465 5 2325 28 .28158 .28398 240 2^ 600 29 . 27989 . 28466 477 3^ 1669 30 .28139 . 28601 462 4 1848 July 3 27536 .28171 635 3 1905 4 27798 28578 780 5 3900 5 . 28468 29579 -j- mi 3 + 3333 6 .28837 . 28780 57 2 114 =. 54 /^ i log[pw] = 6.7903 A I + 0.00488 . e. = 0.00040 M.-P. VOL. I.] CRA WFORD- CONSTA NT OF REFRA CTION. 175 STAR No. 1019 -(With 1009.) Date /0-. r ' log. r A P /A June 7 . 28286 .27921 0.00365 4 0.01460 8 . 28075 . 28466 391 4 + 1564 9 .27851 . 28466 + 615 3 + 1845 12 .28578 .28556 22 i 22 13 .28283 .28623 340 2 -f 680 H .27867 .28578 711 3 2133 19 . 29036 .29137 101 3 303 21 .28165 .28307 142 4 + 568 22 . 27970 .27669 301 4 1204 27 .28158 .28825 + 66 7 5 + 3335 28 .28158 .28443 285 2 57o 29 27989 .28466 477 4 1908 3 .28139 .28691 552 4 -j- 2208 July 3 27536 27623 87 3 261 4 . 27798 .28126 328 5 1640 5 . 28468 . 28780 312 3 936 6 28837 .293H + 477 2 + 954 A -f- 0.00290 \.p} = 56 ; log [pvv ] = 6.7654 STAR No. 264 /. c. P- = it 0.00038 Date log. r ' log. r A P /A June 7 .87981 87783 '0.00198 4 0.00792 8 .87779 .87466 313 4 1252 9 .87564 .86994 570 3 1710 12 .88285 .87996 289 i 289 J 3 .87988 .87628 360 2 720 H .87560 .87697 + 137 3 + 411 19 .88743 .88423 320 3 960 21 .87852 .87500 352 4 1408 22 87657 87245 412 4 1648 27 87853 .87754 99 5 495 28 .87878 . 87408 470 2 940 2 9 87673 .87489 184 4 736 30 .87825 1.87766 59 4 236 July 3 .87237 87163 74 3 222 4 87492 .87425 67 5 335 5 .88164 1.88121 43 3 129 6 .88517 1.88133 - 384 2 - 768 A 0.00218 [p ] = 56 ; log [pw} = 6. 2338 p. e. = -r 0.00020 176 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 1032. Date log. r ' log. r A P /A June 7 8 9 12 13 2 . 85820 2.86091 -f 0.00271 i -j- 0.00271 14 2 . 85280 2.85044 236 3^ 826 *9 2.86657 2.86178 479 3 1437 21 2-85637 2.85442 195 4 780 22 2.854II 2.85258 153 4 612 2 2 . 85620 2.85690 2.85429 2.85286 191 404 \x 955 IOIO 29 2.85421 2.84821 600 3^ 2IOO 3 2.85600 2.84956 644 4 2576 July 3 2.84957 2.84596 36i 3 I08 3 4 2.85239 2.85174 65 4^ 2 9 2 5 2.86022 2.85728 294 4 1176 6 2.86417 2.85807 610 2j^ 1525 | 0.00317 [p] = 44% ; log [pvv] = 6.2854 STAR No. 282 /. c. p. e. = 0.00029 Date %.r' log.r A P PA June 7 3-03250 3.02825 0.00425 4^ O.OI9I2 8 3.02963 3.02682 281 3# 983 9 3 . 02804 3-02054 750 3 2250 12 3.03690 3.03376 314 i 3H 13 14 3.02661 3-02556 105 3 315 19 3.04241 3-03855 386 3 H58 21 3-03063 3.02586 477 4 1908 22 3.02814 3.02674 140 3/^ 490 27 3.03018 3.02586 432 5 2l6o 28 3.03140 3.02319 821 2 /^ 2052 29 3.02815 3.01847 968 3 x 2904 30 3.02989 3 . 02608 381 1714 July 3 4 3.02636 3 . 02069 567 5 - 2835 5 3-035II 3.02968 543 3/^ I9OO 6 3.03907 3.03320 587 2^ 1467 A | 0.00473 log [pvv] = 6.3770 p. e. 0.00027 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACJ^ION. 177 STAR No. 1084. Date log. r ' log. r A p /A June 7 I-40959. 1.41263 -\- 0.00304 5 -f- 0.01520 8 .40788 1.40157 63i 4 2524 9 .40678 .40790 + H2 3 + 336 12 41235 .41162 73 i 13 .41026 .41145 + 119 2 + 238 14 40551 .40381 170 3 510 19 .41774 .41681 93 3 279 21 .40831 .40976 -f J 45 4 + 1256 22 .40704 .40432 ^272 4 1088 27 .40883 . 40926 + : 43 5 + 215 28 .40783 . 40892 ' 109 2 218 29 .40587 .40500 - I '87 3 261 3 . 40780 .41010 ' 230 4 + 9 20 July 3 .40181 39863 318 3 954 4 40565 40552 13 5 65 5 4II59 .40449 710 4 2840 6 .41433 40993 440 3 1320 A I o.ooioi [/] = 58; log[pw] =6.7152 STAR No. 1094. p. e. = 0.00035 Date log. r ' log. r A P /A June 7 i . 42207 i . 42488 + 0.00281 5 -f 0.01405 8 . 42036 1.41414 622 4 2488 9 41943 . 42062 + 119 3 + 357 12 . 42492 .42423 69 i 69 13 .42275 42374 + 99 2 + 198 14 .41809 .41631 178 3 534 19 .43008 .42894 114 3 342 21 . 42082 .42210 + 128 4 , + 5i2 22 .41979 .41714 265 4 1060 27 42185 .42226 + 4i 5 205 28 41995 .42095 + 100 2 + 200 29 .41807 .41714 93 3 279 30 42033 42243 210 4 + 8 4 0. July 3 .41401 41095 306 3 9l8 4 .41844 .41830 14 5 70 5 .42416 4i73i 68 5 4 2740 6 1.42679 42259 420 3 I26O A I 0.00104 p. e. 0.00034 178 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. STAR No. 1105. Date /<#-. r ' log. r A P PL June 7 o 9 1.96122 1.95861 - 0.00261 3/2 0.00913 12 T 3 .96464 .96209 255 2 510 14 .96010 .96468 + 458 3^ + 1603 !9 .97190 97257 + 67 3 4- 201 21 -96285 96i37 148 4 592 22 96i73 .96114 59 4 236 27 .96404 .96161 243 5 1215 28 .96169 .96223 + 54 3 + 162 29 9599 .95985 5 3 15 3 .96218 .96142 76 4^ 342 July 3 95599 1-95650 + 5i 3 153 4 .96028 .96099 + 7i 5 + 355 5 .96610 1.96577 33 4 132 6 .96874 .96876 + 2 3 + 6 =6.1881 A 0.00029 p. e. 0.00023 STAR No. mo. Date / 1116 July 3 2.06268 2.06104 164 2^ 410 4 2.06687 2.06685 2 5 10 5 2.07272 2.07159 H3 4 452 6 2-07535 2.07316 219 3 - 657 A I 0.00084 [p] = 58; log [pvv] = 6.1255 STAR No. 356 /. c. p. e. = 0.00018 Date /0\ r ' log. r A / /A June 7 o 9 .87922 1.87881 0.00041 3 0.00123 12 .88536 .88349 187 i 187 13 .88248 .88076 172 2^ 430 H .87854 .87898 44 3 + 132 19 .88965 .89009 44 3 + 132 21 .88077 .87910 167 4 668 22 .87968 .87858 no 4 440 27 .88234 88395 -|- 161 5 + 805 28 .87948 .87806 142 2 284 29 .87811 .87881 + 70 4 4- 280 30 .88005 .88173 + 168 4 + 672 July 3 .87414 .87280 134 3 402 4 .87840 87938 + 98 5 + 49 5 .88413 .88098 315 3^ IIO2 6 .88677 .88474 203 2^ 507 I 0-00033 \.P ] = log [pvv ] = 6.0359 p. e. = 0.00019 l8o CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 1135. Date /eg-, r ' log. r A P /A June* 7 2.32700 2.32638 0.00062 4K 0.00279 8 2.3 2 535 2.32327 208 4 832 9 2.32443 2.32087 356 3 1068 12 2 . 33060 2.32816 244 i 244 13 2.32766 2.32457 309 2 618 14 2 . 32400 2.32149 251 3 753 19 2.33465 2.33169 296 3 888 21 2.32578 2.32479 99 4 396 22 2.32463 2.32362 101 4 404 27 2.32747 2.32496 251 5 1255 28 2.32461 2.32368 93 2^ 232 2 9 2.32347 2.31946 401 4 1604 30 July 3 2.31931 2.31962 + 3i 3 + 93 4 2.32378 2.32193 185 5 925 5 2.32932 2-32927 5 3 1 A 17 6 | 2 . 33200 2.32760 44 2 880 ~\ = 5-9589 A 0.00193 . e. = 0.00016 STAR No. 377 /. c. (With 1032.) Date &JT- * ' log.r A P /A June 7 8 9 12 13 2 . 83400 2.83705 + 0.00305 i -f 0.00305 14 2.82985 2.82736 249 3^ 871 19 2 . 84207 2.83701 506 3 1518 21 2.83180 2.82974 206 4 824 22 2.83075 2.82914 161 4 644 27 2.83356 2.83148 208 5 1040 28 2-83035 2 . 82600 435 2^ 1087 29 2.82931 2.82296 635 3^ 2222 30 2.83107 2.82425 682 4 2728 July 3 2 . 82480 2.82096 384 3 H52 4 2 . 82968 2 . 82900 68 4^ 3 06 5 2 . 83608 2.83298 310 4 I24O 6 2.83912 2.83265 647 2^ l6l7 A I 0.00336 [p] = 6.2716 p. e. = 0.00028 M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. l8l STAR No. 377 /. c. (With 1156.) Date /qf. *" ' log. r A / /A June 7 2.83328 2.83115 0.00213 5 0.01065 8 2.83152 2.82838 314 4 1256 9 2.83045 2.82720 325 3 975 12 13 2 . 83400 2.83306 94 % 47 14 2.82985 2 . 82607 378 3^ !3 2 3 19 2 . 84207 2.83464 743 3 2229 21 2.83180 2 . 83048 132 4 528 22 2.83075 2 . 82840 235 4 940 27 2.83356 2.83081 275 5 1375 \j i \j 28 2.83035 2 . 82647 388 3 1164 29 2.82931 2.82312 619 4 2476 30 2.83107 2.82833 274 4 1096 July 3 2 . 82480 2.82124 356 3 1068 4 2.82968 2 . 82730 238 5 1190 5 2.83608 2.83239 369 3^ 1291 6 2.83912 2 83502 410 2^ 1025 A I O.OQ334 = 57 ; log [pvv] = 6.0815 STAR No. 1156. p. e. = 0.00018 Date #. r ' log.r A P /A June 7 2.87524 2.87330 0.00194 5 0.00970 8 2.87296 2.87010 286 4 1144 9 2.87172 2.86876 296 3 888 12 13 2-87557 2.87471 86 tf 43 H 2.87138 2.86795 343 3^ 1 200 19 2 . 88372 2.87698 674 3 2022 21 2.87302 2.87182 120 4 480 22 2.87193 2 ..86980 213 4 852 27 2 . 87448 2.87197 251 5 1255 28 2.87189 2.86837 352 3 1056 29 2 . 87078 2.86516 562 4 2248 3 2 . 87246 2.86996 250 4 IOOO July 3 2.86594 2.86271 323 3 969 4 2.87134 2.86918 216 5 1080 5 2-87773 2.87437 336 3^ 1176 6 2 . 88028 2.87655 373 2^ .933 = 57 ; log [pw} = 6.0105 I 0.00304 p. e. = it 0.00016 182 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 1162. (With 406 /. c.) Date /#-. r ' log. r A P /A June 7 Q O 9 2.57666 2-57349 0.00317 3/2 0.01109 12 13 2.57998 2.57897 IOI % 50 14 2.57649 2-57339 310 3 1 A 1085 19 2.58742 2.58196 546 3 - 1638 21 2.57789 2.57491 298 4 1192 22 2.57681 2-57474 207 4 828 27 2.57924 2.57728 196 5 980 28 2.57699 2-57364 335 3^ ! 1173 29 2.57604 2.57302 302 4 1208 3 2-57739 2.57226 513 4 2052 July 3 2-57156 2.56791 365 3^ 1277 4 2.57727 2.57417 310 5 1550 5 2.58212 2.58006 206 3^ 72i 6 2.58448 2.57905 543 3 l6 29 0.00330 = 50 ; log [pvv] = 5.8169 STAR No. 1162 (With 444 /. c.) P> e. = 0.00015 Date &. r ' log.r A P /A June 7 8 9 2 . 57666 2.57219 0.00447 3 1 A 0.01564 12 13 2.57998 2 . 57648 350 X 175 14 2.57649 2.57545 104 2^ 260 19 2.58742 2.58178 564 3 1692 21 2.57789 2.57518 271 4 1084 22 2.57681 2.57583 98 4 392 27 2.57924 2.57694 230 5 1150 28 2.57699 2.57306 393 4 - 1572 2 9 2.57604 2.57358 246 3/ 2 86 1 30 2-57739 2.57309 430 4 1720 Jly 3 2.57156 2 - 56904 252 3 756 4 2.57727 2.57438 289 5 H45 5 2.58212 2.58035 177 3^ 619 6 2.58448 2 . 58043 405 2 810 v] = 5-8851 A I 0.00297 p. e. db 0.00017 M.-P. VOL. I.] CRAWFORD-CONSTANT OF REFRACTION. 183 STAR No. 406 /. c. (With 1162.) Date /cg-. r ' log.r A P /A June 7 Q O 9 2-59357 2.59052 0.00305 3$ 0.01067 12 13 2.59683 2.59586 97 l /2 49 14 2.59350 2.59052 298 3^ 1043 19 2 . 60425 2.59900 525 3 1575 2r 2-59477 2.59191 286 4 H44 22 2.59366 2.59i 6 5 2OI 4 804 27 2 . 59602 2.59413 I8 9 5 945 28 2.59420 2.59097 323 3^ 1130 2 9 2.59315 2.59022 293 4 1172 30 2.59432 2-58939 493 4 1972 July 3 2.58842 2.58491 35i 3^ 1229 4 2.59297 2.58997 300 5 1500 5 2.59909 2.59711 198 3^ 693 6 2.60148 2.59625 523 3 1569 I 0.00318 = 50 ; log [pvv} = 5-7810 STAR No. 406 /. c. (With 1179.; P> e- = db 0.00015 Date /< r ' log. r A P /A June 7 2-59730 2-59537 0.00193 4 0.00772 8 2.59456 2.59219 237 4 948 9 2-59357 2.59002 355 4 1420 12 13 2.59683 2.59691 + 8 % + 4 14 2.59350 2.59039 3ii 4 1244 19 2 . 60425 2.60003 4 22 3 1266 21 2-59477 2 . 59104 373 4 1492 22 2.59366 2.59077 289 4 1156 11 2.59602 2.59420 2.59413 2.59084 I8 9 336 5 3^ 945 1176 29 2.593 r 5 2.59041 274 3 l /2 959 30 2.59432 2 . 59002 43 3*/2 1505 July 3 2.58842 2.58574 268 3/2 938 4 2.59297 2.59II2 185 4^ 832 5 2.59909 2 . 59686 223 4 892 6 2 . 60148 2 59683 465 3 1395 A 0.00292 = 5-6978 p. e. = o. oooi i 184 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 1179. (With 406 /. c.) Date log. r ' log. r A P *>A June 7 2.58409 2.58211 0.00198 4 0.00792 8 2.58167 2.57922 245 4 980 9 2-57955 2.57590 365 4 1460 12 13 2.58282 2 . 58290 + 8 % + 4 14 2 - 57953 2.57633 320 4 1280 19 2.59007 2.58573 434 3 1302 21 2.58069 2.57682 387 4 - 1548 22 2-57955 2.5/657 298 4 1192 27 2.58185 2.57990 !95 5 975 28 2.58049 2.57703 346 3# I2II 29 2.57918 2.57635 283 3^ 991 30 2.58015 2.57569 446 3^ 1561 July 3 2.57417 2.57142 275 3^ 962 4 2.57852 2.57661 191 4^ 860 5 2.58493 2.58263 230 4 920 6 2.58735 2.58255 480 3 1440 0.00301 [p. 1 = 58 ; log [pvv} = 5-7112 STAR No. 1179 (With 444 /. . Date log. r ' log.r A P /A June 7 2.58409 2-58351 0.00058 3 0.00174 8 2.58167 2.57807 360 4 1440 9 2 - 57955 2.57462 493 4 1972 12 13 14 2.58282 2-57953 2.58043 2-57837 239 116 # 3 348 19 2.59007 2 58554 453 3 1359 21 2.58069 2.57709 360 4 1440 22 2 57955 2 . 57766 189 4 756 27 2.58185 2.57956 229 5 U45 28 2-58049 2.57646 403 4 1612 29 2.57918 2 - 57692 - 226 3 678 3 2.58015 2.57654 361 3/2 1264 July 3 2.57417 2.57254 163 3 489 4 2-57852 2.57681 171 *y* 769 5 2-58493 2.58293 200 4 800 6 2-58735 2 - 58392 343 2 686 = 54 T A ; log[pvv] = 5-9 I2 5 0.00276 p. e. = 0.00015 M.-P. VOL, I.] CRAWFORD CONSTANT OF REFRACTION. 185 STAR No. 1182. Date />. r ' log.r A P /A June 7 .97645 1-97543 0.00102 3 0.00306 8 .97288 1.97230 58 4 232 9 .97180 .96923 257 4 1028 12 J 3 .97496 .97520 + 2 4 2>^ + 60 H .97208 .97690 482 4 1928 19 .98178 .98268 90 3 270 21 .97296 97359 63 4 252 22 .97167 .97248 4- 81 4 + 324 27 .97413 .97382 31 5 155 28 .97291 .97313 + 22 4 + 88 2 9 97153 .97179 + 26 3 + 78 30 .97242 .97128 114 3/2 399 July 3 1.96655 .96918 + 263 3 + 789 4 .97073 97058 15 5 75 5 1.97694 97520 174 4 696 6 1.97923 .97855 68 3 204 OJ = 59; log [pvv] = 6.2272 {- O.OOOI2 p. e. = 0.00020 STAR No. 424 /. c. (With 1105.) Date log.r' log. r A P /A June 7 9 1.97474 1.97216 0.00258 3 1 /* 0.00903 12 13 .97816 97571 245 2 490 14 .97502 .97941 439 3/2 + 1536 19 .98471 .98534 + 63 3 1 80 21 .97609 .97465 144 4 576 22 97473 .97414 59 4 236 27 .97727 .97488 239 5 1195 28 .97613 .97658 + 45 3 + 135 29 .97468 .97465 3 3 , 9 3 97549 .97470 79 4/2 356 July 3 .96971 .97021 + 5o 3 150 4 97371 97437 + 66 5 + 33 5 .98000 .97964 36 4 144 6 98238 .98236 2 3 6 I 0.00031 = 6.1588 p. e. = 0.00022 1 86 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3 D SER. STAR No. 424 /. c. (With 1182.) Date /-. r ' log. r A P /A June 7 1.97982 .97882 o.ooioo 3 0.00300 8 97599 97534 65 4 260 9 97474 .97220 254 4 1016 12 13 .97816 .97841 + 25 2^ + 62 14 .97502 .97982 + 480 4 -f- 1920 19 .98471 .98556 85 3 255 21 .97609 .97672 63 4 + 252 22 97473 97552 + 79 4 4- 316 27 .97727 97695 3 2 5 160 28 .97613 97635 + 22 4 + t-88 29 .97468 97493 + 2 5 3 + 75 30 97549 97433 116 3 1 A T4o6 July 3 .96971 .97225 + 254 3 + [762 4 97371 97354 17 5 85 5 1.98000 .97823 177 4 708 6 1.98238 .98164 74 3 222 I + o.oooio = 59 ; log [pvv ] = 6. 2248 STAR No. 438 /. c. p. e. = 0.00020 Date /<#. r ' log. r A / /A June 7 2 . 02896 2.02882 0.00014 3 0.00042 8 2.02529 2.02288 241 4 964 9 2 . 02369 2.02263 106 4 424 12 13 2.02753 2.02727 26 i# 39 M 2.02398 2.02841 + 443 2^ + 1107 19 2.03351 2.03234 117 3 35i 21 2 . 02530 2 . 02690 + 160 4 640 22 2.02385 2.O242O + 35 4 + HO 27 2 . 02640 2.02592 48 5 240 28 2.02535 2.02702 + 167 4 668 29 2 . 02403 2.02415 12 3^ 42 30 2 . 02436 2.02547 III 4 444 July 3 2.OI9OO 2 . 02057 157 3 471 4 2.O2276 2.02333 57 5 285 5 2.029T5 2.02958 43 4 172 6 2.03160 2.03338 + 178 2 + 356 A -f 0.00040 [p ] = 56^ ; log [fiw] = 6.0647 P. e. = i 0.00017 .: I.] CRAWFORD CONSTANT OF REFRACTION. 187 STAR No. 444 /. c (With 1162.) Date log. r ' log. r A P /A June 7 o 9 2.62193 2.61791 0.00402 3 1 A 0.01407 12 T 3 2.62622 2 . 62306 316 % 158 H 2.62223 2.62129 94 *X 235 !9 , 2.63245 2.62736 509 3 1527 21 2,62367 2.62123 244 4 976 22 2.62220 2.62132 88 4 372 27 2.62478 2.62271 207 5 1035 28 2 . 62369 2.62016 353 4 1412 29 2.62213 2.61992 221 ZY* 774 3 2.62278 2.61891 387 4 1548 July 3 2.61701 2.61475 226 3 678 4 2.62082 2.61819 263 5 1315 5 2.62782 2.62622 160 3^ 560 6 2.63053 2.62688 - 365 2 730 =47% I log[pvv] 5-7941 I 0.00268 P. e. = 0.00015 STAR No. 444 /. c. (With 1179.) Date log. r ' log. r A P /A July 7 2.62762 2 . 62709 - 0.00053 3 0.00159 8 2.62363 2.62036 327 4 1308 9 2.62193 2.61745 448 4 1792 12 13 2.62622 2.62405 217 % 108 14 2.62223 2.62118 105 3 315 19 2.63245 2.62834 411 3 1233 21 2.62367 2 . 62042 325 4 22 2.62220 2.62048 172 4 688 27 2.6-478 2.62270 208 5 1040 28 2.62369 2 . 62003 366 4 1464 29 2.62213 2 . 62OO7 206 3 618 3 2.62278 2.61950 328 2.Y* 1148 July 3 2.61701 2.61553 148 3 444 4 2 . 62082 2.61927 155 4^ 698 5 2 . 62784 2.62599 185 4 740 6 2-63053 2.62743 3'Q 2 620 A | 0.00251 ; log = 5-8266 p. e. = 0.00013 1 88 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. STAR No. 1225. Date ^ log. r A P /A June 7 2.02116 2.02103 0.00013 3 0.00039 8 2.01757 2.01515 242 4 968 9 2.01589 2.01481 108 4 432 12 13 2 . O2OO4 2.01978 26 i l 4 39 *4 2.01668 2.02119 -f 45i 2/4 -f 1127 J 9 2 . 02602 2 . 02486 116 3 348 21 2.01728 2.01891 + 163 4 -f 952 22 2.01609 2.0I64I + 32 4 -f 128 27 2.01853 2.01804 - 46 5 230 28 2.01726 2.01895 + 169 4 + 676 29 2.01634 2.01645 + ii 3% 39 30 2.01658 2.01770 -}- 112 4 448 July 3 2.0II55 2.01322 4- 167 3 SOT 4 2.01453 2.0I5II 58 5 290 2.02135 2.O2l8l + 46 4 184 6 2.02390 j 2.02576 + 186 2 + 372 I + 0.00042 = 6.0780 p. e. = 0.00018 The next table contains the results collected from those preceding. The weights given in the column^ have been derived from the probable errors as given in column r. The remaining columns are self-explanatory. M.-P. VOL. I.] CRA WFORD- CONSTANT OF REFRA CT1ON. 189 Star A r log. r 2 log. p p PA 948 - 205 15 2.3522 1.0964 12.5 0.02562 190 /. c. 513 47 3 3442 0.1044 !-3 667 959(D - 584 53 3.4486 o.oooo 1.0 584 9592) 462 27 2.8627 0.5859 3-9 1802 968 -f 662 36 3 . i i 26 0.3360 2.2 + 1456 977 + 476 40 3.2041 0.2445 1.8 + 857 984 142 17 2.4609 0.9877 9-7 1377 225(1)7.*. 211 15 2.3522 1.0964 12.5 2637 225,2) /. c. 126 15 2.3522 1.0964 !2-5 1675 225*3) I- C. 997 10051) - 159 + 6 5 2 215 i 21 2.2279 3.1126 2.6444 I . 2207 0.3360 0.8042 16.6 2.2 6.4 2639 + 1434 1376 1005(2, 3 1 19 2-5575 0.8911 7-8 242 1009 1019(1) + 298 f 488 38 40 3^596 3 2041 o . 2890 0.2445 i.-9 1.8 + 566 878 1019:2) + 290 38 3-1596 o . 2890 1-9 + 55 1 264 /. c. 218 20 2.6021 0.8465 7-o 1526 1032 3*7 29 2 . 9248 0.5238 3-3 1046 282 /. c. 473 27 2.8627 0.5859 39 1845 1084 101 35 3.0881 0.3605 2-3 232 1094 - 104 34 3.0630 0.3856 2.4 250 1105 29 23 2.7235 0.7251 5-3 154 I IIO - 84 18 2.5105 0.9381 8.7 73i 349 l - c - - 84 18 2.5105 0.9381 8-7 73i 356 /- c. 33 19 2-5575 o . 89 1 1 7-8 257 H35 193 16 2.4065 I .0421 n .0 2123 377d) I. c. -336 28 2-8943 0.5543 3-6 1210 377(2 I.e. 334 18 2-5'o5 0.9381 8.7 2906 1156 34 16 2.4065 .0421 II. 3344 Il62;i) - 33 15 2.3522 .0964 12.5 4125 Il62 (2) 297 17 2 . 4609 0.9877 9-7 2881 406,, /. c. -318 15 2.3522 .0964 12.5 3975 406,2, /. c. 292 n 2 . 0828 .3658 23.2 6774 ii79(D 301 n 2.0828 -3658 23.2 6983 1 179 2) -276 15 2.3522 .0964 12.5 3450 1182 + 12 20 2. 6O2I 0.8465 7-o + 84 424(1) /. c. 31 22 2.6848 0.7638 5-8 180 42412) LJC. + 10 20 2. 6021 0.8465 7-o + 70 438 /. c. + 40 17 2.4609 0.9877 9-7 + 388 444D /. c. 268 15 2.3522 1.0964 12.5 3350 444(2) /. c 251 13 2.2279 I . 2207 16.6 4167 1225 + 42 18 2.5105 0.9381 8-7 + 365 A I 0.00180 = 340.6 [pVV ] = O.OO A = 0.00180 0.00019 190 CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. 4. The Constant of Refraction. The value of a deduced by Gylden for the Pulkowa Tables, as given in his "Unter- suchungen iiber die Constitution der Atmosphare u.s.w.," is a =0.00027985 = 57". 723. This is for B = 29.5966 inches at o and / = 7. 44 R. The Pulkowa Tables used here, however, are Gylden's with JJL systematically reduced by 0.00124. Combining this with the value found for A, the correction to Gylden's constant becomes and a = 57". 548. This reduced to the condition of 760 mm. pressure at o and o C temperature gives a= 60". 159. To this value of a correspond the following: c = 0.00029182 and ^=1.00029178. For the sake of comparison, the most important deter- minations of the constant of refraction are given below. These values are for the conditions B = 760 mm. at o C and external thermometer = o C. (These values are taken from Professor Bauschinger's * 'Untersuchungen iiber die Astronomische Refraction u.s.w."). a /A 1. Fund. Astr 60". 320 1.00029257 2. Tab Reg 440 29315 3. Tab. Pulk 268 29232 4. FuSS .122 29161 5. Greenw. 1857-1865 .. .120 29160 6. Pulk. 1865 .209 29203 7. -Greenw. 1877-1886. . .192 2 9 I 95 8. Pulk. 1885 058 29130 9. Miinchen .104 29152 M.-P.-VOL. I.] CRA WFORD- CONSTANT OF REFRA CTION. The first and second of these are determinations by Bessel; the third by Gylden; the fifth by Stone; the sixth by Nyren; the seventh by Newcomb; the eighth by Nyren; and the last by Bauschinger. Bauschinger gives weight zero to each of Bessel's determinations; to the first, because there was considerable uncertainty in Bradley's meteorological instruments; to the second, because of the uncertainty in reading the Meridian Circle (read by vernier to one second). He gives equal weight to the last seven, and gets for a mean a = 60". 1 53 and i*> = 1.00029176. 5. Latitude. The following table gives the value of viz., from 0.00584 to -f- 0.00662. This discordance is due partly to the values of the declinations adopted, but is also very clearly a function of the zenith distance. By introducing a term depending upon the zenith distance, and re-solving by Least Squares, this discordance can be greatly diminished. From this investigation the following conclusions can be drawn: 1 . That this preliminary reduction gives for the Constant of Refraction a = 60". 159 for B = 760 mm. at o (C) and / = o (C). 2. That for the epoch 1899 June 22, the latitude of the Lick Observatory Meridian Circle was v = + 37 20' 25". 3 7. 3. That the final reduction will show that the Constant of Refraction of the Pulkowa Tables is too large. 4. That the observing room of the Lick Observatory Meridian Circle is of a very good design, and that there is no need of mounting Meridian Circles in the open air. M.-P. VOL. I.] CRAWFORD CONSTANT OF REFRACTION. 193 ADDENDUM. The table on page 189 shows a large range in the values of A, viz., from -{-0.00662 to 0.00584. Upon plotting these values, using the zenith distance z for abscissa, and A for ordinate, it is easily seen that A varies quite uniform- ally with the zenith distance. A straight line, inclined about 145 to the zenith distance axis, and cutting'it at z = about 55, appears to represent A very well. Therefore, assuming Z to be the zenith distance for A = o, we can set up an observation equation of the following type for every star : loga=loga -[- [Z z]x, or loga Ioga = A = Zx zx= D zx , where and where a is the a of the tables used (Pulkowa). Equations of this kind were, accordingly, formed and solved for Z and x by the method of Least Squares. CALIFORNIA ACADEMY OF SCIENCES. [PROC. 30 SER. Equations of Condition. = zx. No. Star D zx A P i 948 D 80.00 x = o . 00205 12.5 2 190 1. e. 89.20 513 3 959 88.76 = - 487 4-9 4 968 30-38 = 4- 662 2.2 5 977 21-55 = 4- 476 1.8 6 984 78.11 = 142 9-7 7 225 1. c. 79.70 = 167 41.6 8 997 30-59 = + 652 2.2 9 1005 57- J 9 = 114 14.2 10 1009 21.34 = + 298 ii 1019 21-49 = + 386 3-7 12 264 I.e. 57-35 = 218 7.0 13 IO}2 87.05 = 317 3-3 14 282 1. c. 88.67 = 473 3-9 15 1084 27.80 = 101 2-3 16 1094 28.49 = 104 2.4 17 1105 62.21 = 29 5 3 18 IIIO 67.08 84 8.7 19 349 I- c. 67.65 = - 84 8.7 20 356 1. c. 57-49 33 7-3 21 H35 77-37 = 193 II. 22 377 Lc. 86.79 = 335 12/3 23 1156 87.23 = 304 II 24 1162 83.21 22.2 25 406 1. c. 83-50 = 301 35-7 26 1179 83.26 292 35-7 2 7 1182 62.79 12 7.0 28 424 1. c. 62.96 9 12.8 29 438 1. c. 65-52 = 4- 40 9-7 30 444 1. c. 83 99 = - 258 29. i 31 1225 65-13 = 4- 42 8-7 To reduce the number of equations, those nearly alike were combined, as follows: Equations No. i, 6, 7 and 21; 2, 3 and 14; 4 and 8; 5, 10 and n ; 9, 12 and 20; 13, 22 and 23; 15 and 16; 17, 27 and 28; 18 and 19; 24, 25, 26 and 30; and 29 and 31, giving the n equations: No. i 2 3 9 10 ii 79.20 8S.78 30.48 21.47 57-31 87.03 27-I5 62 75 67.36 83 49 65.34 x = I i P .00174 74.8 485 IO. I 657 4-4 385 7-4 117 29.0 320 26.6 I0 3 4-7 7 25.1 84 17.4 291 122.7 18.4 8.6 3 2 2. I 2.7 5-4 5-2 2.2 50 4.2 II. I 4-3 M.-P.-VoL. I.] CRAWFORD-CONSTANT OF REFRACTION. 195 Weighted Observation Equations. fo. a b n I 8.6 D 681.1 x = 0.01496 2 3-2 284.1 =: 1552 3 2.1 57 9 = + 1248 4 2-7 58.0 = -j- 1040 5 5-4 309-5 = - 632 6 5-2 452-4 S= 1664 7 2.2 59-7 = 227 8 50 3I3-7 = 35 9 4-2 282.9 = 353 10 II . I 926.7 t= - 3230 ii 4-3 281.0 == + 176 ; . ; - ' . , ' 'V i - ' To render these more nearly homogeneous, let D=D; loox y and multiply the absolute term by 100. Then we have the following Weighted Homogeneous Observation Equations. Vo. a b n i 8.6 D 6.811 y = ' 1.496 2 3-2 2.841 1-552 3 2. [ o 579 i 1.248 4 2-7 0.580 _|_ i .040 5 54 3 095 = O.6}2 6 5-2 4-524 1.664 7 2.2 . 0-597 = 0.227 8 5-o 3-137 = 0.035 9 4.2 2.829 = o-353 10 II. I 9.267 = ; 3-230 ii 4 3 2 8lO - + 0.176 Combining these by the method of Least Squares we obtain the following Normal Equations. + 341.28 D 254.512 y= 61.7188 254-5 1 -fipV-JS 1 -f53-4383 Solving these, remembering that the absolute terms had been multiplied by 100, we have log 7.75694; log y=8. 00376 or log x=6. 00376. Now since D=Zx, we have log Z = 1.75318, Whence x= -{-0.0001009 and Z=56 Substituting the values of D and x, thus found, in the Weighted Observation Equations, we find \_pw~\ = 196 i CALIFORNIA ACADEMY OF SCIENCES. [PROC. 3D SER. 0.00024690, from v^hjch the following probable errors have been deduced: ^