LIBRARY UNlvemlTY OF CALIFORNIA SANTA CRUZ Digitized by the Internet Archive in 2007 with funding from IVIicrosoft Corporation http://www.archive.org/details/determinationofsOOperrrich THE HARKNESS-STACKPOLE MEASURING ENGINE p- DETERMINATION OF THE SOLAR PARALLAX FROM PHOTOGRAPHS OF EROS MADE WITH THE CROSSLEY REFLECTOR OF THE LICK OBSERVATORY UNIVERSITY OF CALIFORNIA BY CHARLES D. PERRINE, Astronomer in the Lick Observatory WITH THE ASSISTANCE OF HAROLD K. PALMER, Fellow in the Lick Observatory FREDRICA C. MOORE, Assistant ADELAIDE M. HOBE, Assistant WASHINGTON, D. C. PUBLISHKD BY THE CarNEQIE INSTITUTION OF WASHINGTON 1910 1^ i^l CAENEGIE INSTITUTION OF WASHINGTON Publication No. 119 J. 8. Cushing Co. — Berwick ft Smith Co. Norwood, Mass., U.S.A. PREFACE A few days following the untimely death of Director Keeler, in August, 1900, it became my duty, as astronomer in charge, to make provision for carrying out the requests and recommendations of the Conference Astro- graphique Internationale as to securing cooperative observations of Eros, for the determination of the solar parallax. To Assistant Astronomer Perrine was assigned the securing of such observations as could be advantageously made with the Crossley reflector. Mr. H. K. Palmer, who had assisted Professor Keeler in the photography of nebulge and star clusters, and who was therefore familiar with the peculiarities of the original reflector mounting, was asked to assist Dr. Perrine. The observations were secured in great numbers on all favorable nights throughout the advantageous part of the opposition, as pub- lished in Lick Observatory Bulletin, No. 13. There remained the work of measuring, reducing, and discussing the photo- graphic observations. It was arranged that these duties should be undertaken by another observatory, of great experience in dealing with photographic star positions. Unfortunately, the long-continued illness and final death of the director of the observatory delayed the utilization of the Crossley reflector pho- tographs for several years. The plates were returned to Mount Hamilton in 1905, and the work of measurement and reduction began in December, 1905, on the basis of a grant generously made by the Carnegie Institution of Washington for this purpose. This aid is herewith gratefully acknowledged. The plates were measured and the more routine parts of the calculation carried through by Mrs. Moore and Miss Hobe, as explained in the text, under the supervision of Dr. Perrine. The critical parts of the reductions and the complete discussion of the results were made by Dr. Perrine personally. A de- tailed account of methods and formulae employed is given in the following pages. W. W. CAMPBELL. Lick a© P4 Ul TABLE OF CONTENTS PAQ« Pbeface iii Introdiiction 1 General plan of work 1 Star-places for reduction of the plates 1 Selection of plates 2 Measurement of the plates 2 Reduction ... 3 Refraction 4 Refraction terms of the second order 4 Spherical corrections and corrections for refraction 4 Aberration 4 Parallax corrections 5 Formulae used in the reductions 5 Reductions to true place 8 Corrections to the Ephemeris of Eros 8 Derivation of the solar parallax 10 Systematic errors ............. 10 Weights 13 The final value of the solar parallax 14 TABLES I. Meridian plate measures 16 II. Meridian plate constants 28 III. Meridian mean places, reductions to apparent place, and parallax corrections . 32 IV. Meridian true places and 0-E 35 V. Parallax plate measures 38 VI. Parallax plate constants 67 VII. Parallax mean places, reduction to apparent place, and parallax corrections . 74 VIII. Parallax true places and 0-E 80 IX. Star positions used in parallax work 86 X. Selections of stars used in reductions 88 XI. Derivations of corrections to assumed parallax 89 XII. Positions of faint stars derived from Crossley plates 92 Appendix 95 Description of the Stackpole Measuring Engine 95 Table of Scale A of the Staokpole Measuring Engine 97 Table of Scale B of the Stackpole Measuring Engine . .... 98 DETERMINATION OF THE SOLAR PARALLAX FROM PHOTOGRAPHS OF EROS MADE WITH THE CROSSLEY REFLECTOR OF THE LICK OBSERV- ATORY, UNIVERSITY OF CALIFORNIA. By Charles D. Perrine. INTRODUCTION. Shortly after the lamented death of Director Keeler, I was asked by Director Campbell to take charge of all duties in connection with the Crossley reflecting tele- scope. Before any great amount of experience had been gained with the instrument I was under the necessity of making out a program for observing Eros for parallax. Fortunately, we still had the services of Mr. H. K. Palmer, who had assisted Professor Keeler in nearly all of his work with the reflector. His experience, enthusiasm, and ability throughout the trying conditions under which we worked on the Eros campaign made it possible to secure the observational material which was obtained. The instability of the mounting of the telescope, which had given Keeler so muph trouble in his work and about which he has written somewhat fully in his paper on, the instrument, was the chief source of our difficulties. It was early recognized thatothe only feasible plan was to give exposures as short as would furnish sufficient comparison- stars within the region of good definition on the plates, make as many exposutes as possible, and measure only the perfect images. ,;(■ Observations were secured on every possible opportunity, even when the seeingwas poor and the wind high. Round images were more desired than small ones. Avcfcm- plete account of the plates and of the conditions under which they were taken was printed in Lick Observatory Bulletin No. 1 3, and it seems unnecessary to repeat that account here. All of the measurements and reductions of the Eros plates have been made by Mrs. Moore and Miss Hobe, Carnegie Institution of Washington assistants. It is a pleasure to testify to their ability and interest through the entire work. GENERAL PLAN OF WORK. Owing to the distance of Mount Hamilton from the other observatories taking part in the Eros solar parallax determination, it seemed advisable to plan so that the obser- vations obtained there would be suitable for a determination of the parallax by them- selves, rather than in combination with those of other stations. To this end the plan adopted embraced the taking of photographs at large hour-angles both east and west of the meridian. In addition to the plates for displacements of Eros, a series was secured on the meridian, for the determination of the errors of the ephemeris. STAR-PLACES FOR REDUCTION OF THE PLATES. Within the small fields of the Crossley plates there were not enough catalogue stars of any kind to furnish a basis for obtaining positions of Eros or of comparison-stars near Eros. It therefore became necessary to have recourse to star-places obtained from the B 1 2 DETERMINATION OF THE SOLAR PARALLAX plates taken with the astrographic telescopes, which had much larger fields and for the reduction of which an especially planned list of stars was observed with meridian circles. In the preliminary investigations upon some of the Crossley plates it was necessary to have the places of sufficient stars for their reduction. On making a request to Director Loewy, the Paris Observatory measured and furnished the places of a list of stars for the purpose. In his work of discussing star-places, Professor Hinks, of the Cambridge Observatory, kindly offered to include the stars required for the proper reduction of the Crossley plates. The Royal Observatory at Greenwich specially measured and reduced nearly lOO star-positions for use by Professor Hinks in his list for the Crossley plates. Need- less to say, these star-places were an essential feature of our work, and our indebtedness to these sources is proportionately great. In the reduction of the meridian plates, after the plate constants had been derived, the positions of all the comparison-stars were computed from the plate measures. These places were compared with the catalogue places and in a few cases where the discord- ances were large and the weights of the catalogue places small, the Crossley places were adopted for the parallax solution. '' SELECTION OF PLATES. For the determination of the absolute places of Eros, 3 of the best plates on each of 44;'nights, or 129 plates in all, taken close to the meridian, were selected. These th#ee plates contain, on the average, ten images, which should furnish a strong plice of the asteroid. Only those images were measured which appeared to be per- fectly round. Star-places for some of the dates at the beginning of the meridian series and also at the end were difficult to obtain. As they were not necessary in the parallax work, these dates were dropped. "!l©3r the parallax work, only those dates were selected which contained both east- andswest observations on the same night. It was necessary to discard five of these because of poor images. These restrictions necessarily reduced the amount of material, but in such cases only the good observations really justify measurement and reduction, and I believed that the result from carefully selected data would be stronger than if a considerable number of poor plates were included. Observations for which the parallax factors would be small were excluded for the same reason. The results obtained in the following discussion are based upon 281 plates on 18 nights; 823 selected images of Eros were measured. MEASUREMENT OF THE PLATES. All of the plates have been measured on the Harkness-Stackpole Engine belonging to the Lick Observatory. A very brief description of this engine is given in PubUca- tions of the Lick Observatory, vol. i, p. ^6. A more detailed account is desirable and is appended. A considerable amount of preliminary investigation of the engine was carried out before any of the final measurements were made. The slides were tested and found to be sensibly straight. Micrometers were attached to the microscopes for reading the glass scales more accurately. A number of plates were measured in this way. It was soon found, however, that there were errors in the positions of the star- images themselves larger than the errors of the scale divisions and of reading the scales by the glass-reticle microscopes. When several settings were taken and plates measured in direct and reversed positions, it was found that such errors were sufficiently reduced INTRODUCTION 3 to bring them well below the errors of the images themselves. The scale-micrometers, were, therefore, discontinued. All measures were referred directly to the glass scales, without the intervention of a reseau. The sky had previously been used as a source of illumination for the negative and the scales. Considerable difficulty was experienced from changes of intensity on cloudy days and late in the afternoons of clear days. Experimental plates were measured, using Rochester kerosene lamps, the sky light being screened off. The resulting meas- ures showed no indication of any systematic effect and the method was adopted for the Eros plates. All of them have been measured under these conditions. The general stability of the engine had been found to be good. The error of runs of the scale microscopes was very carefully adjusted to zero before beginning the work. This adjustment was tested frequently throughout the measuring, but required no change. The measurements of all plates were completed the same day on which they were begun. The plates were measured in each of two positions, i8o° apart. Three settings were made on Eros, then two settings on each of the comparison-stars in turn, then three more on Eros. This was the program for each of the sets of exposures selected. A complete measure rests upon 12 settings on Eros and 4 settings on each star. Set- tings were recorded to o.oooi inch and the means taken to o.ooooi inch. Before the measured plate was removed from the engine, the differences were taken, the direct and reversed coordinates compared, and any discrepancies looked up. The inclination of the slides was carefully determined on a number of days. The value of the angle between the \e^ end of the ^-slide and the farther end of the F- slide was found to be 89° 48' 30". The form of the correction for inclination to be applied to the vV-coordinates is, therefore, -f Y sin /, where / is the deviation of the F-slide from the true F-axis. The F-co6rdinates theoretically require the small corrections introduced by the term cos/. The coordinates are all less than 1000", for which the correction is neg- ligible. No plates or images have been rejected since the completion of the measures. During the work of measurement, a number of rejections of stars, images, and plates were made, when it was found that they were so bad as to weaken the result. REDUCTION. As the method of using photography for determinations of the highest precision is still in its infancy and can not be said to be on the same well-defined footing as the visual methods, and because there is a distrust of photographic results by some astrono- mers, it seemed desirable to take unusual precautions against peculiar errors in this work. To this end a plan of reduction was adopted which promised detection of errors peculiar to photographic methods, should they exist. As the apparent motion of the asteroid between evening and the following morning observations was only about 8' to 10', it was possible to select the comparison-stars so that they would fulfill two conditions : (i) The same stars would be used for both evening and morning reductions, thus eliminating to a great extent any errors of the star-places themselves. Such a selection of stars also permitted an investigation of the refractions and any possible distortion of the mirrors. This procedure had the objection that if there were any optical distortion it would remain in part because the asteroid was eccentrically placed among the stars, in opposite 4 DETERMINATION OF THE SOLAR PARALLAX directions at the two elongations. To test this point, a different selection was adopted, so that — (2) The stars would be as symmetrically placed about the asteroid as possible. This selection also had the advantage of reducing any effect on the scale value and orienta- tion due to errors in the places of the comparison-stars. The two different methods furnished in addition a valuable check on the numerical work. The measures of the images selected on each plate were combined and reduced as a whole. By using the center of gravity of the comparison-stars, as origin, it became possible to simplify the reduction of the individual plates. Instead of reducing each plate directly to the system of stars, a system of standard rectangular coordinates was first derived from all of the plates of a group (evening or morning) by taking their means after having corrected for refraction. The scale value and orientation correc- tions necessary to reduce each plate to the standard were then easily obtained, in rec- tangular coordinates. The constants necessary to reduce the standard coordinates to the star system were then obtained and the data necessary for the complete reduction of the group of plates were available. This plan was followed in all except a very few cases where it was necessary to reduce one or two plates directly to the star system on account of a change in the position of the optical axis. The same plan of reduction was used for the meridian observations. REFRACTION. The ranges of temperature and air-pressure were both small during the observations, and it was found, upon investigation, that a constant value of each could be used in com- puting the refraction corrections, without introducing any appreciable error into the final result. The refractions were therefore computed for a temperature of -1-55° F. and an air-pressure of 26.00 inches. REFRACTION TERMS OF THE SECOND ORDER. According to the criterion developed by Rambaut,* the refraction terms of the sec- ond order for a zenith distance of 60° do not amount to o'.'oi until the Aa or AS exceeds 950". As the greatest distances measured on the Eros plates are under this, and as the reductions are made to two decimal places, it is not necessary to consider refraction terms beyond the first order. SPHERICAL CORRECTIONS AND CORRECTIONS FOR REFRACTION. As it was desired to compare the east-and-west plate-measures as early as possible in the process of reduction, with the view of detecting optical distortions, etc., the refrac- tion corrections were applied in the rectangular form as given by Turner. The spher- ical corrections were computed by Jacoby's expansions, but on account of the above method of correcting for refraction, it was necessary to use the apparent center of the plate, as origin, instead of the true center, in applying the spherical corrections. ABERRATION. An investigation has shown that the maximum effect of differential diurnal aberra- tion which can occur under the conditions of the Eros parallax work, in the limited field of the Crossley reflector, is so small, when a number of stars are used, as to be insen- sible. Furthermore, any residuals of this kind become of an accidental order and are entirely eliminated in a series of sufficient length. * Astr. Nach., 3125, c. 65. INTRODUCTION 5 PARALLAX CORRECTIONS. The parallax corrections were computed with the value 8'.'8o; the value of log p used was 9.99954SS, which is the value for the Crossley reflector including the altitude of the instrument above sea level. FORMULAE USED IN THE REDUCTIONS. For convenience of reference the various formulae used in the investigation are here collected. The formulae for parallax take the well-known form : , 8.800 cos ' sin i" $ j, 8.800/ . j j.i ^, s • j/\ a — a' = '-- ^- = TT d — 6 = — -J-( — sm o cos

[Z>"]a, etc., are taken from tables computed in accordance with the formulae given in the Lick Observatory Bulletin 4, 78 (1906); these are applied to the individual stars giving places freed from curvature. [^"]a, [Z?"]o, etc., are the sums of all of the sensible terms of the curvature correc- tions, computed by the following formulae : For X sec S Ai" = ^1 (X sec 8) y Ai" = A^ (X sec 8) K= A," = Ai (X sec 8)» Ai" = At (X sec 8)8 y A," = A, {X sec 8) K» A^" = A^ (X sec 8)» y Aj" = A^ {X sec 8)' ^g" = A^ {X sec 8) K < For Y Di" = Di {X sec 8)'' A" = A(^ sec hy K A" = D3 K» Dt" = Di{Xscchyy D," = D, (X sec Sy D^" = D^ (X sec 8)* y D." = Dj (X stc sy yo D^'^D^y- The auxiliary quantities A^, etc., Z^i, etc., are computed by the following formulae: ^x = sin I" ten 8 [4-68557-10] i?i =- Ki5)''sini" sinz 8 [„6.4357o - lo] ^j = sin''i"ten«8 [9.37115-20] /?, = - i(l5)=sm2 1" [„i.4223o - 10] As = - J(i5)'^sin2 i" [„i.2462i - 10] A = - ^sin^ i" [„8.89403 - 20] ^^=-(15)3 sin' I" tan 8 [„6.4o890 - 20] A = - i(i5)2sin» i" sin2 8tan 8 [06.10787-20] /<5 = sin' I" tan' 8 [4.05672-20] A = j(i5)*sin' i" (3sin 8 cos'S y4, = - 2(is)2sin*i"tan2 8 [n 1-3955 '- 20] +sin'Scos8) [7.85799-20] Aj = \{l^ysvB*'l" [2.74769-20] A= \{i^ys\n*i" [3.02069-20] /«g = sin*i"tan*8 [8.74230-30] A= KiS)^sin* '" (' - tan^S) [0.79345-20] Z?,= isin^i" [8.04333-30] The logarithms of the constant quantities are given in brackets. The corrected star-places are now reduced to the center of gravity separately for " east " and " west " by _ «„ + «;,+ • • • «„ s _ K + h+ • • • K Ct-. — ^k V V and, for each star, «o - «c = -*" sec S 8„-Si = ^ The rectangular coordinates of the " standard " plates are next converted into polar coordinates by means of the adopted values for scale A and scale B; then a com- parison is made of these plate coordinates with the star coordinates : «^ = ^a,— sec S, — j: sec S w^ = F„, • jj — / Using the values «^ = (Xa^ - ^ sec S - 4r sec S j 1 5 cos S riy = Y,„ - s^ -y tr = Xa, -^ sec S - 15 cos S p = K, ■ -f* INTRODUCTION 7 the equations irp + pr+n'^ = o pp-7rr+n„=o are formed, where p and r are the corrections to be found to the adopted values of the scale and the orientation. Letting ^=[,r7r] £=[K] C=[7r«;] C = lpn,] i? = [p/a] ^' = - [tt^J the corrections to scale value and orientation are derived for the " standard " plate, C-C E + E' A = -T-r77 ^ = A+n ' A+D Next are derived the values /' and r' of the individual plates reduced to the " stand- ard "; this is done precisely as above, except that there is no reduction to polar coor- dinates, giving fix ^ -Opiate — -^Btandard ''v ^^ M)l»te •''•tendard """Pp T pfp + nj.= O, CtC. and for any plate P=A+/>p r=r, + rp Applying these corrections to the center of gravity coordinates (transformed to polar) in the following form C+pC+^ rKsQC B = A«Ero. K + 1$ rCcosB\+/>K= AS^„, gives the desired right ascension and declination of Eros : A a -1- «center of gravity ^ *EroB ^" T ^center of gravity ^ °Ero« This is done independently for " east " and " west " plates. These coordinates must be reduced to apparent place to compare with the computed value. To make the a com- parable the equations «Ero8 -I- Aa' -t- TT are formed for each plate, where A«' is composed of A« from Circulaire 9, p. 191, and ^ k' = r^ sec 8 sm{I/+ a)h (that part of the regular apparent place reduction omitted from Aa). For each plate a value of a is interpolated from Millosevich's ephemeris. This is corrected by terms due to the obliquity of the ecliptic and perturbations. For the " west " plates an additional correction is applied, due to the fact that the meridian plates afford a correction to Millosevich's ephemeris, and is obtained by multiplying the intervals between "east" and "west" plates by the correction to the ephemeris over those periods. Thus we derive for the a ephemeris «epiiemeri. = «Miiio8evich + (interval X correction to ephemeris) + (obliquity correction) -f- (perturbation correction) A comparison of these values with the observations gives a series of values of Obs.- Eph. for "east" and "west" plates on each date. The "east" and "west" values are now combined and multiplied by the parallax factor, giving {E- Pr)"i5cosa _^^^ where E and W= differences Obs.-Eph. in seconds of arc. 297/= sum of parallax factors for the plates combined. Attq = the correction to the value 8.80". 8 DETERMINATION OF THE SOLAR PARALLAX From the extensive literature relating to formulae and methods used in reducing photographic plates, the following titles, in addition to those quoted in the text, are given as bearing most closely upon the present research : H. H. Turner. Preliminary note on the reduction of measures of photographic plates. Monthly Notices, 54, II. H. Jacoby. Comparison of methods for the reduction of star-photographs. Astronomical Journal, 22, 8l. On the reduction of stellar photographs, with special reference to the astro-photographic chart plates. Columbia Observatory Contributions, No. lo. Tables for the reduction of astronomical photographs. Columbia Observatory Contributions, No. 23. C. D. Perrine. How to obtain the position of a star from a photograph. Popular Astronomy, 15, 259. Preliminary note on some simplifications in the reduction of stellar photographs. Lick Observatory Bulletin, 4, 77 and 99. REDUCTIONS TO TRUE PLACE. In the reductions to true place the aberrations were computed with data derived from the American Ephemeris for 1900, the precessions and nutations being taken from Circular No. 9 of the " Conference Astrophotographique Internationale de Juillet, 1900." To render the observations and ephemeris homogeneous, the reductions to Newcomb's value of the obliquity, as published by Witt in Circular 12 of the "Conference Astro- photographique Internationale de Juillet, 1900," have been applied. CORRECTIONS TO THE EPHEMERIS OF EROS. The deviations of Eros from the ephemeris in Circular No. 9 of the " Conference Astrophotographique Internationale de Juillet, 1900," were derived from the observa- tions made near the meridian. Each final position used is the mean of from ten to twelve images. An inspection of the charted residuals in right ascension showed some evidence of a periodic inequality. The residuals of the intervals Oct. 5 to 10, inclusive Nov. 9 to 13, inclusive Nov. 23 to Dec. 12, inclusive can be represented much better by a curve whose double amplitude is o".o5 and period about 9 days than by a straight line. The accompanying reproduction of the chart will make this clear. It should be noticed, however, that the interval from Oct. 12 to Nov. 5 inclusive, over which observations are fairly well distributed, does not show any periodicity of this kind. In fact, these residuals are satisfactorily represented by a straight line. The first possibility examined in search for an explanation was that of a connection with the light period of 2" 38°" found by Oppolzer. 82 periods of 2" 38" very nearly equal 9 days, hence the relation might be to the shorter period, where daily observations only are used. Comparison over the entire period of 79 days covered by the observations showed a lack of synchronism. Comparison was then made with the period of 2" 38'", using a separate epoch for each group. This comparison showed strong evidence of some relation to a period of about that length. The accompanying diagrams will make plain the apparent connection. It seemed very desirable, if not absolutely essential, that the light variations of Eros during the period covered by these observations should be utilized in this connection. INTRODUCTION 9 before making further attempt to locate the cause of an apparent connection with a period approximating closely to that of the brightness variation. Efforts have been made to secure the unpublished photometric observations of Eros made in 1900 at other observatories, but they are not yet available. A careful examination was made to see if there was any relation to the Moon. While the three maxima observed fall pretty close to maxima of the nutation term, the length of the Eros period appears to be 9 days instead of 14, as in the nutation. This length of period seems pretty well established from the interval Nov. 23 to Dec. 12, where two complete periods are well outlined. There does not appear to be any indication in these observations of an error in the assumed mass of the Moon. It seems very unlikely that there should be any relation to the very small term in which 3 c appears. On the whole, it appears more probable that the inequality is connected with the variation of light in some way. This explanation has grave difficulties also, for the asteroid presented no sensible disk and the most ready explanation would be one of varying surface brightness. Failing to find a satisfactory explanation, the reality of the periodic inequality may be questioned, although appearances certainly favor its genuineness, particularly in the first and last intervals. It is difficult to see how so many observations can be so well represented by a curve, simply on the doctrine of chance, to say nothing of the probable accuracy being greater than would be shown by the residuals on the assumption of a straight line. The declination residuals were then plotted to see if they would throw any light on the matter. The residuals in the first interval from Oct. 5 to 10 require a curve similar to that found for the right ascensions of the same interval, to represent them. There are also some evidences of a similar periodicity throughout the other two intervals, although not nearly so well marked as in the right ascensions. Comparison was also made with all of the available residuals pubHshed by other photographic observers of Eros, which showed that the Crossley residuals all fall inside the belt formed by such observations. The total of the observations fails to disclose any such periodicity. Various other possible sources were considered, such as the plate- constants, refraction, displacements in a secondary orbit, etc., but no reasonable expla- nation has been found. A similar systematic error in the star-places would be carried through the work, but that seems impossible. In view of these facts, the deviations have been treated as accidental, for the present, in deriving the corrections to the ephemeris. The daily variations found in the ephemeris right ascensions during three intervals, covering our parallax dates, are : Oct. 6 to 29 inclusive —.0071 Nov. 3, 10 0000 Nov. 28 to Dec. 24 inclusive + .0041 These values were used in our parallax derivations. An examination of the parallax dates, with respect to the possible effect of any such periodic inequality in the motion of Eros if of 9-day period, shows that the observations are so numerous and so distributed that but little effect can enter, even if such a periodic inequality is real. If the con- nection should be with the short light period, it is also probable that the observations are numerous enough to eliminate any serious effect in the final result. lO DETERMINATION OF THE SOLAK PARALLAX DERIVATION OF THE SOLAR PARALLAX. The change in the ephemeris correction during the interval between evening and morning observations was applied before deriving the correction to the solar parallax. The parallax corrections were derived, as nearly as possible, from pairs of plates, one evening with one morning plate, with the view of showing the agreement between small groups of observations, and for check purposes. The details of the derivation will be evident from the table containing the data. In accordance with preliminary investigations made by us and other astronomers, it did not seem justifiable to include in the solution any other unknowns than that of the parallax. 1900 Octolwr 3 8 U 18 23 29 November 2 5 12 17 Righl Ascension 22 December 27 2 7 12 17 22 27 ?000 oo'^oo Ooooo o ©ooo o oOooo o" °» oo ooo oo oooo oo. Oo" ■•■MO Declination 'tJOO oooOoo „„oOo • o""" O ooooo „„ „^ •o Ooo oo o**Oo OOo .•• • 3 51.6209 ft ft 1325 1330 W. 264 2 32 22.1950 2 32 22.2008 2 32 22.3915 9-5 -.0028 -.0256 -.0321 -.1360 --1302 26s 22.0483 22.0459 22.2373 it " (( ti 1285 1309 266 21.8844 21.8888 22.0731 tt (( ft (( 1282 1238 267 21.4045 21.4024 21.6029 it tt tt " 1379 1400 268 21.2631 21.2629 21-4799 It ft tt it 1563 1565 269 20.7875 20.7833 20.9933 (t tt tt it 1453 1495 270 20.6479 20.6451 20.8407 fi tt (( 322 1322 1350 271 20.2650 20.2602 20.4635 it tt tf « 1379 1427 Oct. 24 E. 27s 2 28 42-3843 2 28 42.3892 2 28 42.6110 —.0270 -•0373 — .1624 -.1575 276 42.2296 42.2344 42.4465 tt tt 1526 1478 277 42.0561 42.0579 42.2593 tt tt 1389 1371 278 41-5113 41.5162 41.7322 tt tt 1566 1517 8a DETERMINATION OF THE SOLAR PARALLAX Table VIII. — Parallax True Places and Corrections to Ephemeris — Continued. Observed 0. Init:rval Obuqutty Pertue- O-E Date. Plate No. Efheueris a. Inter- VAL. Correc- tions TO Epheme- ECLIPTIC NATION First De- Second De- Correc- tions TO Epheme- Correc- tions TO Ephesce- First Determi- Second DETERMi- termination. termination. ris. ris. BiS. nation. nation. 1900 h m s h m 8 h m s h 8 S s s > Oct. 24 W. 291 2 28 7.0027 2 28 6.9893 2 28 7.2247 9.6 -.0028 — .0270 -.0381 -■1541 -•1675 292 6.8038 6.7922 7-0415 (( it it 1698 1814 293 6.6190 6.6074 6.8436 (( ft tt 1567 1683 294 6.0386 6.0281 6.2624 l( tt tl 1559 1664 29s 5-8813 5-8705 6.0908 (( tt it 1416 1524 296 5-3196 5-3064 5-SS53 tl tl tt 1678 1810 297 5-1472 5-1380 5-3645 ft It It 1494 1586 298 4.6820 4.6746 4.9117 it n tt 382 1617 1691 Oct. 26 E. 319 2 25 35.4858 2 25 35.4891 2 25 35-7341 — .0280 — .0412 -.1791 -.1758 320 35-3145 35-3228 35-5642 It ({ 1805 ;I722 321 35-1492 35-1502 35-3979 tt (( 1795 1785 322 34-7094 34-7113 34-9495 It tt 1709 1690 in 34.4968 34-S017 34-7331 n tt 1671 1622 324 34-0903 34-0958 34-3300 tt It 1705 1650 32s 33-8813 33.8884 34-1341 11 11 1836 1765 326 33-4055 33-4090 336583 tt tl 1836 I80I 327 33-1534 33.1607 33-4046 (1 tl 1820 1747 W. 336 2 24 55-3274 2 24 55-3314 2 24 55-5779 9.8 —.0029 — .0280 — .0416 -.1780 -.1740 337 55-1066 55.1092 55-3594 (( <( tt tl 1803 1777 338 54-9069 54-9053 55-1444 (( it tt It 1650 1666 339 54-3813 54-3895 54.6248 it It 11 tl 1710 1628 340 54.1821 54.1880 54.4190 li tt tt 11 1644 1585 341 53-6505 53.6671 53.9026 n n tl It 1796 1630 342 53-4407 53-4504 53-7035 it tl It tt 1903 1806 343 52-8685 52.8770 53-1329 ti it tl tt 1919 1834 344 52.6607 52.6733 52-9131 (f It tt tt 1799 1673 Oct. 29 E. 345 2 20 26.2468 2 20 26.2472 2 20 26.5088 — .0292 — .0462 -.1866 -.1862 346 26.0578 26.0563 26.3184 tl (( 1852 1867 347 25-8137 25-8087 26.0767 tt tl 1876 1926 348 25-3085 25-3026 25.5686 tt tt 1847 1906 349 250764 25.0667 25-3154 tt It 1636 1733 35° 24-5560 24-5527 24.8208 tt It 1894 1927 3SI 24-3526 24-3443 24.6040 tt tt 1760 1843 W. 3S7 2 19 40.6074 2 19 40.6230 2 19 40.8983 9.9 —.0029 — .0296 — .0466 -.2118 — .1962 358 40.4219 40.4327 40.6931 (( (( tt tt 1921 I8I3 3S9 40.1261 40.1370 40.4029 " tt it tt 1977 1868 Nov. 3E. 396 2 lo 54-1975 2 10 54-2035 2 10 54-4987 -.0320 -•0531 —.2161 —.2101 397 53-9594 53-9620 54-2583 (( {( 2138 2II2 398 53-7094 53-7054 54-0125 (1 tt 2180 2220 399 53-1782 53-1912 53-4747 tt u 2114 1984 400 52.8961 52.8991 53-2105 tt (( 2293 2263 401 52.4014 52.4007 52.6921 tt 532 2055 2062 402 52.1047 52.1139 52.4280 tt (( 2381 2289 404 51.2642 51.2670 51-5744 It (( 2250 2222 W. 417 2 10 1. 6701 2 10 1.6829 2 10 2.0147 lo.s .0000 -.0320 --0536 -.2590 — .2462 419 1. 1224 1.1410 1-4779 (( tt tt 2699 2513 420 0.7388 0-7543 1.0837 It tt tt 2593 2438 421 0.4271 0.4246 0.7734 tl it tt 2607 2632 422 0.0026 0.0149 0.3219 tl tt tt 2337 2214 423 9 59-7574 9 59-7708 0.0856 tt tt tt 2426 2292 424 59-2955 59.2922 9 59-6371 tl It tt 2560 2593 42s 59-0566 59.0690 59-3998 n tt tt 2576 2452 426 58.8172 58.8266 59.1480 i( tt it It 2452 2358 PARALLAX TRXJE PLACES AND CORRECTIONS TO EPHEMERIS 83 Table VIII. — Parallax True Places and Corrections to Ephemeris — Continued. Date. Plate No. Observed 0. Ephemeris a. Inter- val. Interval Correc- tions TO Epheme- ris. Obliquity Ecliptic Correc- tions TO Epheme- ris. Pertur- bation Correc- tions TO Epheme- ris. O-E First De- termination. Second De- TERMINA-nON. First Determi- nation. Second Determi- nation. 1900 h m s h m s h m s b 3 8 a a 8 Nov. 10 E. 472 I 56 35.2403 I 56 35-2324 I 56 35-5503 -.0360 —.0610 -.2130 — .2209 473 34-9566 34-9592 35-2962 il (( 2426 2400 474 34-7386 34-7301 35-0380 tt (( 2024 2109 475 34-1045 34.0870 34.4180 ** it 2165 2340 476 33-9085 33.9010 34-2035 it it 1980 2055 477 33-3702 33-3632 33-6778 it it 2106 2176 478 33.1066 33-0946 33-4243 It It 2207 2327 W. 495 I 55 46.0422 I 55 46-0340 I 55 46-3127 9.6 .0000 -.0360 — .0610 -•1735 -.1817 496 4S-7450 45-7355 46.0216 11 " it tt 1796 189I 498 44.9916 44.9881 45.2910 ti tt it tt 2024 2059 sot 43.9649 43-9585 44.2409 tt (( tl it 1790 1854 Nov. 28 R. 61S I 28 57-7363 I 28 57.7403 I 28 58.0156 -.0430 -.1112 -.1251 — .1211 616 57-6554 57-6543 57-9230 ti it "34 "45 617 57-5689 57-5677 57-8399 ti ft 1168 1 180 618 57-4723 57-4748 57.7420 tt tl "55 1 130 619 57-3717 57-3776 57-6553 it it 1294 1235 620 57-2721 57-2739 57-5467 tt It 1204 1 186 621 57.1768 57-1787 57-4549 tl It 1239 1220 622 57.1112 57.1121 57-3730 tl 1113 107s 1066 623 57-0135 57.0140 57-2832 11 (( "54 "49 624 56-9149 56.9139 57-1832 ft (( 1140 1150 62s 56-8341 56.8304 57.0967 tt tl 1083 1 1 20 W. 63s 637 I 28 43-1239 42-9330 I 28 43.1239 I 28 43-3897 43.2146 8-3 +.0014 --0430 tt — .1119 -.1123 1281 -.1123 637 42-9496 43.2231 tl ** It (( 1200 639 42.7127 42-7314 43-0151 It (( tt tt 1489 1302 640 42.6737 42.6840 42-9553 tl it it " 1281 1178 643 42-0253 42-0357 42.3101 H it tt u 1313 1209 644 41.9466 42.2224 tt tl tl tt 1223 644 41.9240 42.2056 " ti tt tl .... 1281 647 41.6599 41.6645 41-9593 (( tt tt tt 1459 1413 Nov. 29 E. 648 I 28 16.9249 I 28 16.9263 I 28 17-2175 -.0430 -.1132 -.1364 --1350 649 16.8744 16.8704 17-1485 It (( "79 1219 650 16.7743 16.7707 17-0576 It (( 1271 1307 651 16.7170 16.7197 16.9916 tt tt 1 184 "57 652 16.6278 16.6301 16.9035 It tt "95 1172 6S3 16.5363 16.5338 16.8220 tt tt 1 29s 1320 654 16.4453 16.4494 16.7405 tt ft 1390 1349 655 16.3815 16.3817 16.6682 tl ft 1305 1303 656 16.3104 16.3114 16.5836 tt tt 1170 1 160 6S7 16.2314 16.2329 16.5108 tl It 1232 1217 658 16.1577 16.1585 16.4374 It 1133 1234 1226 W. 668 I 28 4.4723 I 28 4.4751 I 28 4.7618 8.2 -I-.0014 -.0430 -•"39 -.1340 -.1312 669 4.3922 4-3986 4.6920 (( tt " tt 1443 1379 670 4-3286 4-3301 4.6092 (( 11 (1 tt 1251 1236 671 4.2668 4.2702 4-5403 " i( (( tl 1 180 1 146 672 4.1678 4-I7S5 4.4602 (( it (( tl 1369 1292 673 4.0998 4.0999 4-3834 (( tt (( tt 1281 1280 674 4.0166 4.0197 4.2987 it it tl ft 1266 1235 675 3-9271 3.9302 4.2176 11 '* It ft 1350 1319 676 3-8565 3.8580 4-1437 it it tt ft 1317 1302 677 3-7735 3-7789 4.0642 tl it it tt 1352 1298 678 3-7047 3-7078 3-9934 tt It tt tt 1332 1301 84 DETERMINATION OF THE SOLAR PARALLAX Table VIII. — Parallax True Places and Corrections to Ephemeris — Continued. Date. Plate No. Observed 0. Ephemeris 0. Interval Correc- tions TO Epheme- ris. Obuquity Ecliptic Correc- tions TO Epheme- ris. Pertur- bation Correc- tions TO Epheme- ris. 0- E First De- termination. Second De- termination. Inter- val. FmsT Determi- nation. Second Determi- nation. I goo b m s h m s h m s h 9 s s s • Dec. s E. 713 I 26 31.6945 I 26 31.6954 I 26 32.0194 -.0430 -.1231 -.1588 -•1579 714 31.7277 31.7292 32.0242 it (( 1304 1289 715 31.7282 31-7382 320300 tt tt 1357 1257 716 31.7321 31.7411 32-0358 ti tt 1376 1286 717 31-7591 31-7656 32.0408 tt tt 1156 1091 718 31-7457 31.7614 32.0462 tf it 1344 H87 719 31-75" 31.7627 32.0515 tt tt 1343 1227 720 31.7623 31-7725 32.0582 ti tt 1298 1 196 721 31.7702 31.7826 32.0646 tt it 1283 1159 722 31.7696 31-7775 32.0700 tt it 1343 1264 733 31-7955 31-8053 32.0763 tt tt 1147 1049 W. 733 1 26 32-8953 I 26 32.8939 I 26 33.1924 8. 6 +.0015 -.0430 --1234 --1322 -.1336 734 32-8953 32.9025 33.2020 H It tt 1418 1346 73S 32.9104 32.9100 33.2121 tt il tt 1368 1372 736 32.9038 32.9177 33.2221 it * tt it 1534 1395 737 32.9468 32.9456 33-2309 " tt tt 1192 1204 738 32-9335 32.9373 33-2409 it tt tt 1425 1387 739 32.9454 32.9556 33-2525 n tt tt 1422 1320 740 32.9508 32.9563 33-2622 il tt it 1465 1410 741 32.9647 32.9718 33-2731 it tt tt 1435 1364 742 32.9890 32-9932 33.2824 t( It tt 1285 1243 743 32.9839 32-9851 33.2928 <( tt tt 1440 1428 Dec. 6 E. 744 I 26 37.6811 I 26 37.6838 I 26 37-9703 -.0430 — .1241 —.1221 -•"94 745 37.7306 37.7204 37.9889 tt tt 0912 1014 746 37-7134 37.7201 38.0084 tt it 1279 1212 747 37-7414 37-7356 38.0260 ti it "75 1233 748 37.7624 37-7644 38-0452 tt it "57 "37 749 37-7553 37.7612 38.0652 tt tt 1428 1369 75° 37-7919 37.7976 38.087s tt tt 1285 1228 7SI 37.8141 37-8175 38.1062 tt tt 1250 1216 752 37-8314 37-8308 38.1263 tt 11 1278 1284 753 37.8602 37.8672 38-1455 tt tt 1182 H12 754 37-8654 37-8708 38.1651 n ft 1326 1272 W. 764 I 26 40.923s I 26 40.9280 I 26 41.2225 8.6 +•0015 -.0430 -.1244 -•1^31 -.1286 765 40.9531 40-9523 41.2490 ti (( 1300 1308 766 40.9764 40.9768 41.2748 tt (( 1325 1321 767 40.9956 41.0008 41.2980 It (( 1365 1313 768 41.0216 41.0215 41-321S it n 1340 1341 769 41.0469 41.0486 41-3441 tt It 1313 1296 770 41.0712 41-0753 41.3649 it It 1278 1237 771 41.0960 41.1004 41-3935 ft II 1316 1272 772 41-1155 41.1162 41.4148 tt ti 1334 1327 773 41.1458 41.1504 41.4410 tt tt 1293 1247 774 41.1689 41.1712 41.4650 tt It 1302 1279 Dec. 7 E. 775 I 26 50.2897 I 26 50.2886 I 26 50.5778 -.0430 -.1251 — .1200 —.1211 776 50.3351 50.3345 50.6143 41 tl iiii 1117 777 50.3546 50.3614 50.6454 (1 It 1227 "59 778 50.4052 50.4061 50.6766 tt tt 1033 1024 779 50.4542 50.4507 50.7098 tt It 087s 0910 780 50.4857 50.4916 50.7597 tt It 1059 1000 781 50.5277 50-5315 SO. 7903 tt 11 094s 0907 782 50-5596 50.5569 50.8224 tt tt 0947 0974 783 50.5859 50.5854 50.8572 tt tt 1032 1037 784 50.6210 50.6227 50.8932 tt 11 1041 1024 785 50.6565 50.6538 50.9251 tt It IOCS 1032 PARALLAX TRLTE PLACES AND CORRECTIONS TO EPHEMERIS 85 Table VIII. — Parallax Thue Places and Corrections to Ephemeris — Continued. Date. Plate No. Observed a. Ephemeris a. Inter- val. Interval Correc- tions to Epheme- ris. Obuquity Ecliptic Correc- tions to Epheme- ris. Pertur- bation 0- -E First De- termination. Second De- termination. Correc- tions TO Epheme- ris. FlRST Determi- nation. Second Determi- nation. 1900 h m 8 h m s h m s b a s 1 s s Dec. 7 W. 796 I 26 55-4888 I 26 55-4857 I 26 55.7611 7-4 +.0013 -.0430 -.1254 -.1052 -.1083 797 53-5139 55-5097 55-7977 H 1167 1209 798 5S-SSS9 55-5572 55-8355 It 1125 1112 799 55-5962 SS-5938 55.8680 (t 1047 1071 800 55.6220 55.6206 55-9092 n 1 201 121S 801 55-6763 55-6746 55-9468 n 1034 1051 802 55-7128 55-7050 55-9810 (< lOII 1089 803 55-7402 55-7379 56.0218 " <( "45 1168 804 55-7713 55-7707 56.0582 tt 1 198 1204 80s 55.8169 55-7966 56.0968 tt 1128 1331 806 55-8679 55-8633 56.1354 tt 1004 1050 Dec. 24 E. 89s I 46 11.3770 I 46 11-3755 I 46 II. 6016 - .0360 — .1219 — .0667 -.0682 896 11.6784 11-6775 11.9066 tt it 703 712 897 11.8622 11.8638 12.0854 tt tt 653 637 898 12.1443 12.1417 12.3557 tt tt 535 561 899 12.3932 12.3940 12.6085 tt tt 574 566 900 12.6590 12.6562 12.8787 tt tt 618 646 901 12.8718 12.8684 13-0992 tt tt 69s 729 W. 908 I 46 44.4562 I 46 44.46x4 I 46 44.6684 6.8 -f-.0012 —.0360 — .1216 -•0558 —.0506 909 44.7063 44.7110 44.9131 (( 1< tt 504 457 910 44.9078 44.9161 45-1254 tt « tt 612 529 911 45-2485 45-2554 45-4668 ti tt tt 619 S50 912 45-5325 45-5383 45-7447 (( tt tt 558 500 913 45-7664 45-7723 45-9857 tt tt tt 629 570 914 46.0248 46.0292 46.2346 tt tt tt 534 490 86 DETERMINATION OF THE SOLAR PARALLAX Table IX. — Star Positions used in Parallax Work. Date. Stak. o igoo. O. 5 igoo. 0. Authority. Date. Star. a 1900. 0. 5 1900. 0. AtrrHORTTY. h m s t It h m s . , „ Oct. 6 a 2 43 18.309 46 50 22.46 A. R. Hinks Oct. 15 a 2 38 16.158 49 54 S-66 A. R. H. b 43 17.367 47 I 15-55 Crossley b 38 30.805 57 9-06 11 c 43 20.313 46 57 54-98 " f 39 14-377 51 57-83 C( d 43 34.583 59 53-10 A. R. H. g 34-881 53 7-32 ti e 43 42.884 52 3-37 *' h 39-059 58 56.52 II f 43 48.042 47 10.04 (( i 48.887 SO 33.83 (1 E 43 54.418 47 331-10 " n 39 59-657 49 53 16.32 <1 h 44 II. 017 46 51 32-13 11 38 27.981 50 7 30.26 It i 44 28.897 57 24-77 (( 1 43 57.585 42 12.97 (( m 43 8.890 45 22.37 " n 43 38.445 47 10 59.10 (1 43 4.018 10 4-25 ii Oct. 12 a 2 40 25.259 49 6 4.83 A. R. H. Oct. 16 a 2 37 18.440 50 24 35.32 A. R. H. b 40 46.648 6 17.80 il b 40-523 12 16.20 11 c 40 55.416 I 57-98 t( c 42-353 16 1.70 H d 40 58.831 48 53 55-59 (t d 37 53-126 17 27.92 tt e 41 20.447 49 2 11.39 tl e 38 4.868 18 13.28 11 f 41 26.331 48 51 22.98 (1 f 7.661 25 43-50 11 S 42 15.629 49 4 0.13 (1 g 12.844 17 43.40 11 m 41 25.409 4848 6.34 " h 25-133 1933.28 (( n 41 58.921 46 7.19 l( i 50.890 1459.57 Crossley .to 8.385 49 8 23.94 11 1 49-781 II 8.68 A. R. H. P 41 57.534 12 53-17 H m n 38 27.981 37 21.625 37 56-528 7 30.26 27 1. 16 29 42.10 (I ti tt Oct. 13 b 2 39 33.241 49 21 32-44 Crossley Oct. 21 a 2 31 44-838 51 49 24.71 Crossley c 40 15.60 25 18.6 A. R. H. b 32 2.918 45 47.04 A. R. H. e 40 39.87 2331-5 (( c 14-579 41 48.94 11 f 40 48.788 15 56.47 It d 25-609 54 29.59 11 g 40 53454 21 21.82 Crossley e 30-685 36 59.21 11 h 40 54.71 27 15-8 A. R. H. f 32 58.211 37 33.41 If m 40 8.366 8 23.49 Crossley g 33 11-541 43 54.78 11 39 30.284 30 30-85 A. R. H. h 1 m n 21.596 30.965 33 33-4" 31 33-302 32 39-465 42 33.83 37 3.48 34 27.55 57 12.78 56 36-85 tt tt it tt it Oct. 14 a 2 38 51.599 49 34 54-85 A. R. H. Oct. 24 a 2 27 16.861 52 23 26.00 A. R. H. b 39 16.70S 38 24.00 Crossley b 36-495 33 17.66 (( c 30.284 30 30.85 A. R. H. c 44-893 24 21.73 Crossley d 31.890 4045-31 (( d 27 52-139 19 30.16 A. R. H. e 37-704 47 29.68 (( e 28 18.59s 30 38-02 tl f 42.818 43 41-21 " £ 20.788 27 54-33 Ii g 39 58.380 37 8.87 " g 24.692 ii 51-33 tt h 40 1.623 47 58-01 tl h 40.461 30 47-99 tt i 23.334 40 4.66 tt i 28 54-428 22 16.70 It m 40 53-14 37 33-1 " J 29 3.641 27 47.12 II 39 59-43' 51 17-06 tt 1 m n 24.847 29 19.304 27 7-387 27 40.966 16 20.87 21 18.78 35 33-15 38 51.82 It tt tt tt STAR POSITIONS USED IN PARALLAX WORK 87 Table IX. — Star Positions used in Parallax Work — Continued. Date. Star. 0. 1900. 0. S IQOO. 0. Authority. Date. Star. a igoo. 0. S 1900. 0. Authority. h m 8 f /r h m s f II Oct. 26 a 2 24 24.576 52 55 11-43 A. R. H. Nov. 29 a I 26 48.651 5058 5.12 A. R. H. b 55-838 57 9-21 tt b 27 14.732 S3 1.02 ft c 58-712 54 53-96 it c 27 16.032 52 13-88 t( d 24 58.963 47 4791 Crossley d 28 23.488 SI I 26.91 (( f 25 29-245 56 55-78 A. R. H. e 29.882 SO 59 23.74 tt g 32.083 51 50-15 Crossley fi 32.652 48 54-39 Crossley h 31-215 45 43-48 it h 32.660 48 54.70 A. R. H. 1 25 59-857 46 26.08 A. R. H. g 42.774 55 19-67 Crossley m 26 7.886 49 30-40 it h 48.374 56 44.66 A. R. H. n 24 30-170 53 3 22.93 a 1 28 18.361 51 5 42.97 " 23 57-327 46.23 ti m n 27 36.907 30.022 27 10.929 9 21.30 SO 42 0.70 43 20.01 tt it Oct. 29 a 2 19 3.966 53 26 53.95 A. R. H. Dec. 5 a I 25 51.471 48 51 2.88 A. R. H. b 14.044 23 31.32 tt b 26 12.465 47 54.65 (1 c 17.214 30 18.25 tt c 24.964 57 53.26 (( d 19 41.747 28 41. II It d 30.780 54 14.85 (( e 20 4.053 31 43-54 tt e 40.665 59 53.03 tt f 18.659 2837-59 ti f 26 49.138 49 4 59.76 tt g 17.698 27 19.21 tt g 27 3-377 48 51 11.90 Crossley h 36.315 28 13.95 tt h 27 30.167 58 56.58 A. R. H. i 39-714 23 34-51 it 1 26 50.532 49 10 55.87 ti 1 2031.617 17 3-80 a 26 44.949 48 44 41.31 it m 21 21.501 24 58.65 It P 27 8.327 44 12.21 it 18 34.133 37 27-52 a P 1845-287 27 7-74 tt Nov. 3 a 2 941-252 54 1 3-7S A. R. H. Dec. 6 a I 25 52.056 48 29 8.4s A. R. H. b 9 4S-6oi 7 50-31 (( b 53-842 32 53.38 tt d 10 4-731 8 14.72 (( c 26 22.548 30 28.64 it e 10 42.388 7 36.29 (( d 27-341 33 35.32 it f II 2.288 6 21.36 tt e 58.064 26 27.72 ii - h II 6.889 3.10 tt f 27 4-931 39 47.14 ti I II 54-635 2 11.30 tt g 8.541 26 36.90 a m 12 6.458 5 44-66 tt h 16.197 30 18.69 a 9 16.540 10 38.08 tt 1 26 44.949 4441.31 ti P 8 33-545 II 47.76 H m 27 8.327 27 19.261 44 12.21 26 21.16 tt it Nov. 10 a I 55 16.378 54 21 59.01 Crossley Dec. 7 a I 26 25.959 48 4 36.11 A. R. H. b 16.978 18 36.86 A. R. H. b 30.209 9 25.01 " c 25.248 14 33-59 (( c 34-284 7 6.50 tt d 47-394 18 12.56 (1 d 43-127 9 25.10 ii e 55 51-131 23 40.71 (( e 26 44.108 10 5.97 it f 56 34-218 28 59.22 Crossley f 27 7.068 II 46.14 tt g 35-581 25 31.23 A. R. H. g 26 57.140 16 4.51 it h 56 42-921 22 33.93 it h 27 45-245 10 28.54 tt 1 57 12.806 20 10.09 a 1 26 58.064 26 27.72 tt m 57 42-971 22 39.69 *' m 27 8.541 26 36.90 tt P 55 0.636 21 3.05 ti P 27 24-625 2 5.53 (•) Nov. 28 a I 27 42.885 51 1647.67 Crossley Dec. 24 a I 45 31.946 41 1837-87 A. R. H. c 28 34.347 12 10.95 A. R. H. b 48.725 6 24.92 it e 29 3-560 7 46.25 ** c 47-579 13 46.44 it f 29 16.310 6 55.65 tt d 50.488 21 46.48 it g 29 25.865 10 54.25 It e 46 18.675 9 38.34 ii h 29 41.498 16 52.75 It f 25.027 8 20.77 (*) m 28 39.500 28 49.68 It g 26.888 7 29.69 Crossley n 28 18.361 5 42.97 (t i 52.327 15 29.08 (t 27 36.907 9 2130 i< J 1 m P 8.058 45 54028 45 35.559 46 58.670 13 44.52 26 0.27 23 55.83 3 59.68 A. R. H. 1( ' Conference Astrophotographique Internationale Circulaire 11, 12. 88 DETERMINATION OF THE SOLAK PARALLAX Table X. — Selections of Stars used in Reductions. Daii. First Solution. Second Solution. Oct. 6 abcdefghi East West abcdefghilm abcdefghino 12 a b cdef g E. W. abcdefgmn abcdegop 13 b c ef g h E. W. b c ef ghm b c ef gh 14 abcdefghi E. W. b cd gim bd ef ho 15 a bfg h i E. W. a bf ghin ab hi 16 abcdefghi E. W. b d e gilm ab c efg hn 21 ab c d ef g h E. W. bcefghlm ab c d ef hn 24 a b cd ef g h ij E. W. bdeghijlm bcefghno 26 abed ef g h E. W. b c dfg him a b cfg n 29 abcdefghi E. W. cdefghilm abcdefgiop Nov. 3 abed ef h E. W. ab d ef hi m ab d e p 10 ab c d ef gh E. W. ad e g hi m abcefgp 28 a c ef g h E. W. a c ef ghm a c efg n 29 ab c def gh E. W. abed efg h I m ab c d ef gh n Dec. s ab c d ef gh E. W. abed efl abcdegop 6 abed ef g h E. W. a b c d fl m ab c d e gh 7 abed ef g h E. W. abcdefglm abed efg p 24 ab cd ef g ij E. W. acdehijlm efgijp DERIVATIONS OF CORRECTIONS TO ASSUMED PARALLAX 89 Table XI. — Derivations of Corrections to Assumed Parallax. Date. Nos. Plates Combined. (E-W)'- IS cos J (E-W)". Sirf. Att. Weight. East. West. First Detekw- Second Determi- First Determi- Second Determi- First Deter- Second Deter- mina- mina- NATION. nation. nation. nation. tion. tion. • > // // // It Oct. 6 92 104 -.0036 -.0077 10.24 -.0369 -.0788 2.49 -.ois -.032 12.S 93 los — 222 - 197 -.2273 — .2017 2SI - 91 - 80 17.6 94 106 - 64 - 97 - 6S5 - 993 2.S3 - 26 - 39 12.7 9S 107 + 49 - 14 + S°2 - 143 2.S5 -f 20 - 6 iS-3 96 108 - 278 - 340 --.2847 -.3482 2S7 — Ill -.045 - 13s -.058 12.8 Oct.I2 134 MS +.0078 + -02SS 9.84 + .0768 +.2509 2.81 +.027 -(-.090 22.S 13s. 6 146 - 91 + 73 - 89s + 718 2.83 - 32 + 25 22.6 137.8 147 - 30 + 112 - 29s -t-.II02 2.86 — 10 + 39 28.6 139, 40 148 + S9 + 1S4 + S8i +-ISIS 2.88 + 20 +.001 + S3 +.052 31-7 Oct. 13 ISO 163 -•0653 — .0408 9.76 -•6373 -.3982 2.90 — 220 -•137 11.6 IS! 164, S, 6, 7 + 17 + 152 + 166 +.1484 2-9S + 6 + SO 20.7 »Sa x68 — 126 4 - 1230 - 39 2.99 - 41 — I 17.9 153 169 - 30s — Ill - 2977 -.1083 3.01 - 99 -.088 - 36 -.031 iS-i Oct. 14 170,1,2 187 +.0092 +.0098 9.71 +.0893 +.0952 2.90 +•031 +•033 26.1 173 188 + 367 + 146 +■3564 -f.1418 2.90 +.123 + 49 I4S 174 189 - 108 - 89 -.1049 - 864 2-93 - 36 - 30 234 I7S 190 — 120 - 163 -.1165 -•1583 2-9S - 39 - S4 14.8 176 191 + 96 + 28 + 932 + 272 2.96 + 31 + 9 11.8 177 193 + 177 + 148 +■1719 +•1437 2.97 + S8 + 48 II.9 178 »93 - 23s - 143 -.2282 -.1389 2.98 - 77 +.013 - 47 +.001 17.9 Oct. IS 19s 213 -.0108 -.0093 9-6s —.1042 -.0897 2.9s -•03s -•030 11.8 196 214 - 119 — 160 -.1148 -•IS44 2.97 - 39 - S2 17.8 197 aiS + 30 - 13 + 290 - I2S 2.97 + lO - 4 17.8 198 216 - 62 - 24 - 598 - 232 301 — 20 - 08 18.1 199 217 - I7S - 164 -.1689 -•IS83 301 - 56 - S3 iS-i 30I 218, 19, 20 - 63 7 - 608 - 68 303 — 20 — 2 21.2 303 331 - 76 - 214 - 733 -.2065 30s - 24 -.026 - 68 -.031 12.2 Oct. 16 222,3 239 +.02S4 +.0124 9-S8 +•2433 +.1188 3-07 +.079 +■039 iS-4 224, s 240 + 97 + 28 + 929 + 268 309 + 30 + 9 27.8 226 241 + 123 - 60 +.1178 - S7S 3.10 + 38 - 19 18.6 227 242 + 114 + 16 -I-.1092 + IS3 3" + 35 + S iS-6 338 243 + 9S - 72 + 910 — 690 3" + 29 — 22 iS-6 230 344 + 227 + 41 +-2I7S + 393 3.12 + 70 +.047 + 13 -t-.0O4 21.8 Oct. 21 247 264 +.0113 +.0052 9.29 +.1050 +.0483 3-29 +.032 +.01S 23.0 248 26s - S4 - 47 - 502 - 437 330 - IS - 13 16.S 3SO 366 — 106 - I2S - 98s —.1161 3-29 - 30 - 3% 16.4 as I 267 + 97 + 141 + 901 +.1310 332 + 27 + 39 23.2 253 268,9 + 280 + 3^S -t-.26oi -f.2926 3-34 + 78 + 88 23-4 2S3 270 - iSS - 49 -.1440 - 4SS 3-3S - 43 - 14 16.7 2S4 371 + S4 + 97 + S02 + 901 336 + IS +.009 + 27 +.015 16.8 Oct. 24 27s 291,2 — .0004 +.0169 914 -.0037 + -IS4S 3-40 — .001 +-04S 20.4 276 293.4 + 37 + 196 + 338 +•1791 3-43 + lO + 52 27.4 277 29s. 6 + is8 + 296 +.1444 +.270S 346 + 42 + 78 27.7 278 297,8 - 10 + 121 - 91 +.1106 348 - 3 +.0X2 + 32 +.052 27.8 90 DETERMINATION OF THE SOLAR PARALLAX Table XI. — Derivations of Corrections to Assumed Parallax — Continued. Date. Nos. Plates Combined. (E-W)'- IS cos J (E-W)". 2irf. At. Weight. East. West. First Determi- nation. Second Determi- nation. First Determi- nation. Second Determi- nation. First Deter- mina- tion. Second Deter- mina- tion. Oct. 26 319 336 5 — .oon a -.0018 9-os — .0100 -.0163 3^55 -.003 -.005 21.3 320 337 — 2 + 55 - 18 + 498 3-55 — I + 14 17.8 321 338 - 145 - 119 -.1312 -.1077 3^56 - 37 - 30 14.2 322 339 -f- I - 62 + 9 - 561 357 - 16 25.0 323 340 - 27 - 37 - 244 - 335 3^57 - 7 - 9 14-3 324 341 + 91 — 20 + 824 - 181 3-58 + 23 - 5 21^5 32s 342 + 67 + 41 + 606 + 371 3^57 + 17 + 10 21.4 326 343 + 83 + 33 + 751 + 299 3^58 + 21 + 8 17.9 327 344 — 21 - 74 - 190 — 670 358 - 5 -l-.OOI - 19 -.006 143 Oct. 29 34S>6 357 +.0259 -I-.0098 8.93 + •2313 +•0875 3^72 -f-.o62 +■024 40.9 347,8 358 + 59 - 103 + 527 — 920 3^70 + 14 - 25 33-3 349.50.51 359 + 214 + 34 -f.i9ii + 304 3-68 + 52 +.043 + 8 -I-.002 40.5 Nov. 3 396 417 +.0429 -I-.036I 8.80 + ■3775 +•3177 3^93 -f.096 -I-.081 27-S 397 419 + 561 + 401 +•4937 +•3529 3^94 +•125 + 90 27.6 398 420 + 413 + 218 +•3634 -I-.1918 3-93 + 92 + 49 19.6 399 421,2 + 358 + 439 +•315° +.3863 393 -1- 80 + 98 27-5 400 423 + 133 + 29 +.1170 + 255 390 + 30 + 7 19s 401 424 + 505 + 531 +•4444 +•4673 3^88 +•115 -1- 120 19.4 402 42s + 19s + 163 + •1716 +•1434 3.88 + 44 + 37 19.4 404 426 + 202 + 136 + •1778 +•1197 384 + 46 +.078 + 31 -f-.o64 19.2 Nov. 10 472,3 495 -•0543 -.0487 8.75 -■4751 — .4261 4-os -.117 -.IDS 243 474 496 - 228 - 218 -•1995 -.1908 4.04 - 49 - 47 20.2 47S 498 - 141 - 281 -•1234 -•2459 4.02 - 31 - 61 24.1 476,7,8 SOI - 308 - 332 -.269s -.2905 4.00 - 67 -.066 - 73 -.071 28.0 Nov. 28 61S 635 -.0128 -.0088 9-39 — .1202 -.0826 4^05 -.030 — .020 28.4 616 637 + 147 + 55 +.1380 + S16 4.04 + 34 + 13 32.3 617 639 + 321 + 122 +•3014 -f.1146 4.04 + 75 + 28 16.2 618 640 -t- 126 + 48 +•1183 + 451 4.02 + 29 + II 28.1 619, 20 643 + 64 — I + 601 9 4.02 + IS 44.2 621, 2 644 + 66 + 138 -t- 620 -I-.1296 398 + 16 + 33 47.8 623,4.5 647 + 333 + 273 +•3127 +.2563 3-92 -1- 80 +.031 + 65 +.019 549 Nov. 29 648 668 —.0024 -.0038 9-45 — .0227 -•0359 4.10 —.006 -.009 24.6 649 669 -1- 264 -t- 160 +•2495 +.1512 4.09 + 61 + 37 20.4 650 670 — 20 - 71 - 189 - 671 4.07 - 5 - 16 16.3 651 671 4 — II - 38 — 104 4^05 — I - 3 16.2 652 672 + 174 + 120 + .1644 +•1134 4.04 + 41 + 28 20.2 653 673 - 14 - 40 - 132 - 378 4^03 - 3 - 9 24.2 654 674 - 124 - 114 — .1172 -.1077 4.00 - 29 - 27 28.0 6SS 67s + 45 + 16 + 425 + 151 399 + II + 4 27.9 656 676 + 147 + 142 +•1389 + 1342 3-98 + 35 + 34 35-8 657 677 -1- 120 + 81 +•1134 + 765 3^96 + 29 + 19 27.7 658 678 + 98 + 75 + 926 + 709 3^93 + 24 +.014 + 18 + •007 19.7 DERIVATIONS OF CORRECTIONS TO ASSUMED PARALLAX 9I Table XI. — Derivations of Corrections to Assumed Parallax — Continued. Date. ^os. Plates Combined. (E-W)'- 15 cos S (E-W)". Sirf. Air. Weight. East. West. First Determi- nation. Second Determi- nation. First Determi- nation. Second Determi- nation. First Deter- mina- tion. Second Deter- mina- tion. s s « // // ft Dec. s 713 733 -.0266 -.0243 9.86 -.2623 -.2396 3-98 -.066 —.060 27.0 714 734 + it4 + 57 +.1124 + 562 3-97 + 28 + 14 27.8 71S 735 + II + 115 -1- 108 +■1134 396 + 3 + 29 27.7 716 736 + 158 + 109 +.1558 +•1075 3-96 + 39 + 27 31-7 717 737 + 36 + 113 + 355 -t-.ni4 3-93 + 9 + 28 23.6 718 738 + 81 -1- 200 + 799 +•1972 392 + 20 + 5° 19.6 719 739 + 79 + 93 + 779 + 917 3-9° + 20 + 24 19-5 720 740 + 167 + 214 -f.1647 -f .2110 3.88 + 42 + 54 31.0 721 741 + 152 + 20s +•1499 -I-.2021 3-86 + 39 + 52 23.2 722 742 - 58 — 21 - 572 - 207 3-84 - IS - 5 30.7 723 743 + 293 + 379 -t- 2889 +■3737 3-83 + 75 +.018 + 98 +.028 30-6 Dec. 6 744 764 + .0110 +.0092 9-93 +.1092 +.0914 398 +.027 +.023 27.9 74S 765 + 388 + 294 +.3853 +.2919 3-97 + 97 + 74 31.8 746 766 + 46 + 109 + 457 +.1082 3-97 + 12 + 27 27.8 747 767 + 190 + 80 +.1887 + 794 3-95 + 48 + 20 27.7 748 768 + 183 + 204 +.1817 +.2026 3-93 + 46 + 52 27-5 749 769 - 115 - 73 -.1142 - 72s 391 - 29 - 19 313 7SO 770 7 + 9 - 70 + 89 3-90 — 2 + 2 234 751 771 -t- 66 + 56 + 655 + 556 3-88 + 17 + 14 27.2 752 772 + 56 + 43 + 556 + 427 3-86 + 14 + II 27.0 753 773 + III + 135 -)-.II02 + 1341 384 + 29 + 35 30-7 754 774 - 24 + 7 - 238 + 70 3.82 - 6 +.023 + 2 +.022 30.6 Dec. 7 775 796 —.0148 -.0128 10.00 -.1480 -.1280 3-94 -.038 -.032 27.6 776 797 + 56 + 92 + 560 + 920 3-92 + 14 + 23 31-4 777 798 — 102 - 47 — .1020 - 470 391 - 26 — 12 27.4 778 799 + 14 + 47 + 140 + 470 3-88 + 4 + 12 19.4 779 800 + 326 + 30s +.3260 +.3050 3.87 + 84 + 79 27.1 780 801 - 2S + SI - 250 + 510 3-84 - 7 + 13 26.9 781 802 + 66 + 182 + 660 +.1820 3-83 + 17 + 48 23-0 782 803 + 198 + 194 + .1980 +.1940 3-82 + 52 + SI 22.9 783 804 + 166 + 167 -f.i66o +.1670 3-79 + 44 + 44 26.5 784 80s + 87 + 307 + 870 +.3070 3-77 + 23 + 81 26.4 78s 806 — I + 18 — 10 + 180 3-76 +.015 + 5 +.028 30.1 Dec. 24 895 go8 — .oiog — .0176 11.28 -.1230 -.1985 363 -•034 -•055 25-4 896 909 - 199 - 255 -.2245 -.2876 3.60 - 62 - 80 25.2 897 ■ 910 - 41 - io8 — 462 -.1218 3-S8 - 13 - 34 14-3 898 911 + 84 — II + 948 - 124 3-S6 + 27 - 3 21.4 899 912 - 16 - 66 - 180 - 744 3-53 - S — 21 28.2 900 913 + IX - 76 + 124 - 8S7 351 + 4 - 24 21. 1 901 914 - 161 - 239 -.1816 —.2696 3-49 - 52 -.019 - 77 -.042 17.4 92 DETERMINATION OF THE SOLAK PARALLAX Table XII. — Positions of Faint Stars Derived from Crossley Plates. Date. Plate No. SlAK. 1900. 0. S iQoo. . No. OF Images. Remarks. 1900 Oct. 9 123 123 125 U h m s 2 42 S4-470 .482 .488 / // +47 53 39-89 ■85 •75 5 4 4 122 123 125 Xl 2 42 48.637 .628 -653 47 55 516 •13 .10 5 4 4 Faint. 122 X2 2 42 50.090 47 55 35-92 5 • 122 123 y 2 43 I-IS7 .169 47 56 7-79 •94 5 4 123 123 1 25 z 2 43 2.621 .604 .617 47 54 49-92 .82 •71 5 4 4 Faint. Oct. 10 129 130 X 2 42 14.987 •999 iS-oos 48 21 47.79 -79 -53 3 5 3 Oct. IS 204 205 207 X 2 39 3-154 .136 •133 49 52 32-85 .62 -70 4 5 5 Very faint. Oct. 16 232 235 236 X 2 38 4.007 3-998 4.002 SO 17 13.90 .89 .69 4 4 3 Very faint. Very faint. Oct. 21 258 266 267 268 X 2 31 35-526 -534 -513 •537 SI 52 23.19 22.83 23-19 22.86 2 2 4 I Faint. Very faint. Very faint. 258 348 250 y 2 33 36-723 .739 .718 51 28 48.20 •IS .33 3 3 3 Faint. Oct. 26 329 331 X 2 2S 4-230 .249 52 57 21.05 30.71 4 3 Image I very faint. Oct. 39 353 354 355 X 3 20 15-254 .214 .307 53 23 21.51 .46 .70 3 3 3 Faint. Faint. 353 354 355 y 3 30 16.376 .378 .365 S3 23 44-27 .68 •76 3 3 3 Faint. Faint. 354 355 z 2 18 43-359 •370 S3 34 S-OS •43 3 3 Nov. I 360 361 362 X 2 13 43-196 .319 .308 53 53 36-14 •13 .16 5 3 3 Images of plate generally distorted. 360 361 y 3 14 46.894 .874 S3 54 16.04 .14 5 3 Very faint and distorted. Faint. 360 361 362 z 2 14 54-137 .179 .189 53 49 3470 -50 -58 5 3 3 Faint and distorted. POSITIONS OF FAINT STARS DERI\rED FROM CROSSLEY PLATES 93 Table XII. — Positions of Faint Stars Derived from Crossley Plates — Continued. Date. Plate No. Star. 1900. 0. S 1900. 0. No. OF Images. Rehabjcs. Nov. 2 384 385 386 z b m s 2 13 5.086 •125 .178 + 53 58 7-90 .61 -87 4 4 4 Very poor images — faint and distorted. « » (( tt t( tt <4 « It « « U Nov. 3 408 411 414 X 2 10 47.656 .685 .684 54 3 42.91 -92 43.00 S 4 3 Nov. 5 445 447 450 y 2 6 8.760 .691 •705 54 13 59-79 14 0.01 0.21 5 5 4 Image I poor. Nov. 10 486 487 t I 56 30.481 •475 54 19 35.79 .76 5 5 486 487 492 w I 56 57-193 .182 .181 54 22 36.14 35-58 •55 5 5 5 486 487 492 X I 55 48-955 .941 .985 54 20 17.09 .08 .13 S S S 486 487 492 y I SS 50-385 .356 ■444 54 20 10.29 •30 .66 5 S 5 Faint and distorted. 486 487 492 z I SS 53-842 .883 -877 S4 20 10.92 .70 .88 5 5 5 Nov. 12 518 519 520 X 1 SI 43.617 •593 -583 54 12 11.29 11.00 It. 26 3 3 4 S18 519 520 z I 52 49-954 •930 .920 54 14 40.58 .66 •74 3 3 4 Nov. 13 538 t I 48 46.131 54 7 32.96 3 538 539 540 u I 50 57556 •S70 .581 54 12 o.ss .86 •83 3 S 5 538 539 540 V I 49 10.162 • 151 .164 54 8 21.19 .2094 •92 3 5 5 538 539 540 w I so 45-256 -239 .276 54 7 33^95 3421 33-88 3 5 S Dec. 2 679 681 z I 26 48.030 -051 50 8 7.94 8.33 3 3 Dec. II 848 X I 28 54.83s 46 48 35-43 5 APPENDIX. DESCRIPTION OF THE MEASURING-ENGINE. This engine was constructed by the firm of Stackpole & Brother, New York, from designs by Professor William Harkness, of the U. S. Naval Observatory. As no account other than the paragraph on page 76, vol. i, Lick Observatory Publications, has been published, it seems desirable to include a short description here. The engine is intended for the measurement of plates 6x6 inches or smaller, at one setting, either by rectangular or by polar coordinates, with the plates in a horizontal position only. The accompanying illustration will make plain its general features as used in the Eros work. It is of brass throughout (excepting the screws) and is very solidly built. A micrometer-microscope and a small transit telescope are provided with the engine. The transit telescope is used to test the straightness of the slides. A spirit-level, extra microscope-objectives, and eye-pieces are also provided. The machine is provided with a circle 12 inches in diameter, divided on silver to 5' and read by verniers to s". On this circle is fastened a glass stage to carry the negative to be measured. Two slides and scales, approximately parallel to the X and Y axes, respectively, permit of the determination of both rectangular coordinates simultaneously. The setting-telescope containing a fixed glass reticle is attached rigidly to the car- riage moving along the X-axis. This carriage and its ways are in turn attached to a larger one which moves along the Y-axis. Clamps and slow-motions are provided in both cases. The scales are of glass and read by microscopes rigidly fixed to the telescope car- riages. The divisions of the glass scales are 0.02 inch apart and are identified by means of auxiUary silver scales. The microscopes for reading the glass scales have glass reticles which enable readings to be made directly to 0.00 1 inch and by estimation to o.oooi inch. Scale A is used to measure X-coordinates ; scale B, to measure Y-co6rdinates. The errors of scale A were investigated in the Department of Weights and Measures, U. S. Coast and Geodetic Survey. The results of the investigation are printed in vol. Ill, part III, of the Lick Observatory Publications. Using scale A as a standard, the errors of divisions 100 to 260, inclusive, of scale B were determined by Dr. H. K. Palmer. These results have not been printed heretofore. They are given at the end of this paper. For the sake of convenience, the numerical results for scale A are also given. The errors of both scales have been found to be so small, in the portions used in the Eros work, as to be neghgible. This measuring-engine had been in use for a number of years prior to the com- mencement of the Eros measurements. During this time several difficulties had become apparent. The one which gave most trouble was the illumination. This defect could not be remedied without reconstructing the entire stage for carrying the negatives. As the stage provided with the engine was of weak design, an entirely new one, with more convenient illumination, was made in the Lick Observatory shops and attached. 95 96 DETERMINATION OF THE SOLAR PARALLAX lW/ The clamps and slow-motions for the circle and its vernier were badly placed. The slow-motion screw for the vernier was in front where it was occasionally displaced accidentally by the observer. This was remedied. The clamp and slow-motion for the circle (and attached negative) were changed to a more convenient position. The slides of this engine are not exactly at right angles. The deviation amounts to ii' 30". If we face the A scale of the engine, looking along the longer slides (Y-axis) and across the shorter slides (X-axis) the inclination is such as to cause the upper left- hand and lower right-hand angles to be l«ss than 90°, by 11' 30". A negative made in the ordinary way, where proper orientation in the sky is secured by looking through the negative with the Jilm side away, when placed on the engine film side up and measured, requires corrections as follows : The X-measures are to be corrected by + Y sin I. The Y-measures are to be multiplied by cos I, where I is the defect of inclination (II' 30"). The division-errors of the circle have not been determined, so far as I know, but are doubtless small. In determining the inclination of the sHdes, different parts of the circle were used to eliminate any such errors. No noticeable errors were found, however. / \ A S^oJU APPENDIX 97 Table of Scale A of the L. 0. Measuring-Engine (Stackpole). The table gives the distance from o division to any division-mark on the scale at i6°.67 C. Let Sn be any such distance at i6°.8 C. and St be the same distance at / degrees. 5«=5o (i + o.ooooo8(<-i6"'.8)) Scale. Inch. Scale. Inch. Scale. Inch. Scale. Inch. Scale, Inch. Scale. Inch. o 0.00000 SI 1.01941 101 2.01847 151 3-01741 201 4.01636 251 5^01545 I .01995 52 •03938 102 .03846 152 ■03741 202 •03638 252 ■03543 3 •03994 53 •05934 103 .05844 153 ■05741 203 ■05641 253 ■05542 3 •OS997 54 .07928 104 •07845 1 54 ■07737 204 .07641 254 ■07541 4 •07997 55 .09926 105 .09845 155 .09732 205 ■09643 255 ■09540 S .09998 56 .11924 106 .11843 156 .11728 206 .11640 256 ■IIS37 6 .11994 57 .13918 107 •13839 157 •13724 207 ■13639 257 •13534 7 .13992 58 •15919 108 .15838 158 •15725 208 .15641 258 •15531 8 •15991 59 •1791S 109 •17835 159 .17724 209 ■17637 259 •17532 9 .17989 60 1.19916 110 2.19836 160 3^i9723 210 4.19639 260 5-19532 lO 0.19988 II 0.21991 61 1.21918 III 2.21831 161 3^21715 211 4.21632 261 5-21531 12 •2399s 62 .23918 112 •23825 162 ■23713 212 .23628 262 •23530 13 •2S999 63 •25917 "3 • 25827 163 .25711 213 .25623 263 • 25528 14 .27996 64 .27912 114 .27823 164 ■27713 214 .27619 264 .27526 IS .29990 65 .29912 "S .29818 i6s ■29713 215 .29619 26s •29523 i6 •31988 66 .31911 116 •31813 166 .31712 216 .31617 266 •31519 17 •33987 67 •33910 117 •33812 167 ■33705 217 ■33615 267 •33516 i8 •35984 68 •35908 118 •35813 168 ■35705 218 •35617 268 •35515 19 •37981 69 •37904 119 .37810 169 ■37704 219 .37610 269 •37512 20 0.39978 70 '•39905 120 2.39805 170 3-39704 220 4.39606 270 5-39513 21 0.41980 71 1.41903 121 2.41801 171 3.41699 221 441603 271 5-41512 32 •43978 72 •43898 122 .43800 172 •43702 222 .43600 272 •43514 23 •45977 73 .45899 123 ■45790 173 ■45701 223 •45596 273 •45510 24 •47979 74 •4789s 124 ■47791 174 .47701 224 •47596 274 .47506 as .49976 75 .49888 125 .49788 175 ■49695 225 •49593 27s .49506 26 •S1974 76 .51888 126 ■51784 176 .51694 226 •51593 276 •51507 27 •53973 77 •53887 127 ■53782 177 -53692 227 •53587 277 •53504 28 •SS97S 78 •55888 128 •55780 178 ■55691 228 •SSS9I 278 •55509 29 •57973 79 • 57887 129 ■57778 179 ■57693 229 ■57585 279 •57SIO 3° 0.59969 80 1.59882 130 2^59777 180 359689 230 4-59581 280 5^59512 31 0.61968 81 1.61881 131 2.61775 181 3.61690 231 4-61583 281 5-61515 32 .63964 82 .63878 132 ■63774 182 .63688 232 ■63580 282 •63517 33 .65962 83 .65878 133 ■65774 183 .65690 233 ■65576 283 •65515 34 •67959 84 .67877 134 .67772 184 .67689 234 .67570 284 •67514 3S •6995s 85 .69879 135 .69767 i8s .69683 23s ■69571 285 .69521 36 •71958 86 •71875 136 ■71763 186 .71682 236 .71568 286 •71519 37 •73956 87 •73876 137 ■73758 187 ■73677 237 ■73568 287 •73520 38 •75955 88 •75872 138 ■7S7S7 188 ■75673 238 ■75568 288 •75519 39 •77956 89 ■77867 139 ■77757 189 .77669 239 ■77568 289 •77514 40 0.79951 90 1.79867 140 2.79756 190 3.79668 240 4-79570 290 579514 41 0.81952 91 1.81867 141 2.81756 191 3.81665 241 4.81564 291 5.81516 42 •83948 92 .83862 142 •83754 192 .83664 242 -83564 292 ■83517 43 .85946 93 .85863 143 •85752 193 .85658 243 -85558 293 •85517 44 .87947 94 •87859 144 ■87750 194 .87656 244 •87562 294 •87523 4S •89947 95 .89861 145 ■89745 19s .89654 24s ■89558 295 .89524 46 .91947 96 .91858 146 ■91745 1 96 .91652 246 ■91553 296 .91520 47 .93948 97 •93854 147 •93741 197 •93647 247 •93551 297 •93517 48 •95946 98 •95854 148 ■95739 198 ■95644 248 •95549 298 •95518 49 .97944 99 •97851 149 ■97739 199 ■97645 249 •97552 299 •97516 SO 0.99943 100 1.99848 ISO 2.99741 200 3.99641 250 499S47 300 $•99515 ± I ± 3 ± 3 ± 4 ± 5 ± 5 qS determination of the solar parallax Table of Scale B of the L. O. Measuring-Engine (Stackpole) — Continued. SCAIE. Inch. Scale. Inch. Scale. Inch. Scale. Inch. lOO 2.00000 141 2.82053 181 3.62124 221 4.42187 lOI .02007 142 .84063 182 .64124 222 ■44193 I02 .04006 143 .86064 183 .66127 223 .46196 103 .06006 144 .88064 184 .68130 224 .48202 104 .08007 14s .90070 185 .70129 225 ■5020s loS .10009 146 .92069 i86 .72127 226 ■52205 106 .12014 147 •9407 s 187 ■74133 227 ■54202 107 .14016 148 .96074 188 •76133 228 .56203 108 .16019 149 .98071 189 •78137 229 .58208 109 .18021 ISO 3.00078 190 3.80136 230 4.60208 no 2.20022 III 2.22022 iSi 3.02071 191 3.82140 231 4.62209 112 .24020 IS2 .04081 192 .84141 232 .64212 "3 .26024 ^53 .06082 193 .86146 233 .66215 114 .28031 IS4 .08080 194 .88150 234 .68214 "S .30028 ^SS .10085 19s .90145 23s .70212 116 •32036 156 .12085 196 .92146 236 .72217 117 ■34036 IS7 .14095 197 .94146 237 .74222 118 •3603s 158 •16093 198 .96149 238 .76221 119 •38039 IS9 .18091 "99 .98158 239 .78228 120 2.40037 160 3.20097 200 4.00155 240 4.80232 121 2.42036 161 3.22095 201 4^02157 241 4-82235 122 ■44041 162 .24102 202 .04165 242 .84236 123 ..;■ 042 163 .26099 203 .06170 243 ■86237 124 •48043 164 .28099 204 .08172 244 .88239 125 .50042 i6s .30100 205 .10174 24s .90238 126 •52037 166 .32101 206 .12169 246 ■92237 127 .54046 167 •34105 207 .14174 247 ■94239 128 .56048 168 .36107 208 .16174 248 .96234 129 .58048 169 .38105 209 .18176 249 .98239 130 2.60049 170 3^40ii3 3IO 4.20176 250 5.00238 131 2.62051 171 3^42ii6 211 4.22177 251 5.02242 132 .64056 172 .44123 212 •2417s 252 ■04251 133 .66050 173 .46120 213 .26172 253 .06256 134 .68050 174 .48120 214 .28179 254 ■08254 13s •700SS 17s .50122 215 .30180 25s .10256 136 •72056 176 .52120 216 •32179 256 .12258 137 •74059 177 ■54127 217 .34180 257 .14263 138 .76061 178 .56120 218 •36185 258 .16264 139 .78063 179 •58123 219 .38190 259 .18265 140 2.80060 180 3.601 18 220 4.40191 260 5.20261 THE UNIVERSITY LIBRARY UNIVERSITY OF CALIFORNIA, SANTA CRUZ SCIENCE LIBRARY This book is due on the last DATE stamped below. To renew by phone, call 459-2050. Books not returned or renewed within 14 days after due date are subject to billing. ^^ii^ll m