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Full text of "Observations of the transit of Venus, December 8-9, 1874, made and reduced under the direction of the Commission created by Congress"

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T EL E 



EXECUTIVE DOCUMENTS 



PRINTED BY ORDER OF THE 



SENATE OF THE UNITED STATES 



FIRST SESSION OF THE FORTY-SIXTH CONGRESS, 



18 7 9. 



IN THREE VOLUMES. 

Volume! coutaius Nos. 1 to 38, inclusive, except Nosi 31 and 37. 

Volume 2 contains No. 31. 

Volnme 3 contains No. 37 and parts. 



WASHINGTON: 

GOVERNMENT FEINTING OFFICE. 
1879. 



46th Congress, ) SENATE. ( Ex. Doc. 

Ist Session. I ( No. 31. 



OBSERVATIONS 



TRANSIT OF VENUS, 



December 8-9, 1874, 



MADE AND REDDCED UNDER THE DIRECTION OF THE 



COMMISSION CREATED BY CONGRESS. 



EDITED BY 



SIMON NEWCOMB, 

PROFESSOR, U. 8. NAVY, 
SKCBET-A.I1Y OF THE COMIMIISSION'. 



PUBLISHED BY AUTHORITY OF THE HONOEABLE SECRETARY OP THE NAVY. 



WASHINGTON: 

aOVEENMENT PBTNTING OFFICE. 
1880. 



(B 



UNIVERSITY) 
N^UBRARY ^^ 




/ 



:f JL i^ T I 



GENERAL DISCUSSION OF RESULTS. 



SECRETARY OF THE COMMISSION. 



United States Naval Obsekvatoey, 

Washington, January 17, 1880. 
Sir : I have the honor to transmit herewith Part I of the Observations of the 
Transit of Venus, of December 8-9, 1874, made and reduced under the direction of 
the Commission created by Congress to superintend the work. 
Parts II, III, and IV will follow. 

The printing of the work has been ordered by concurrent resolution of Con- 
gress. 

Very respectfully, your obedient servant, 

JOHN RODGERS, 
Bear-Admiral, Superintendent, 

President of the Commission. 

Hon. R. W. Thompson, 

Secretary of the Navy, Washington. 



CONTENTS OF PART I, 



Page. 

Editor's Preface 7 

CHAPTER I. 

HISTORY OF THE OPERATIONS. 

Organization of the Commission 9 

Plan of observations 10 

Choice of stations .' 12 

Instrumental equipment — 14 

Organization of the parties ^ 16 

Preliminary practice 16 

Voyage of the Swatara 17 

CHAPTER II. 

PARTICULARS RELATING TO EACH STATION. 

Positions of stations provisionally adopted ., 21 

Numbers and constants of instruments at each station 22 

Organization of the parties - 23 

CHAPTER III. 

DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Descriplion and'use of the photoheliograph 25 

Method of adjusting the photoheliograph 31 

Method of investigating the relation between the apparent positions of Venus and the Sun on the celestial sphere, and tlie 

positions of their images on the photographic plate 33 

Corrections of the observed position of Venus on account of refraction 44 

Table for differential refraction in position angle and distance 53 

Expression of the position of Venus on the Sun's disc in terms of tabular elements ...,. 54 

Recapitulation of the preceding formulae for the reduction of the transit of Venus photographs 57 

Problem I. From the measures on the photographic plate and the known constants pertaining to the photo- 
graphic telescope, to find the apparent position angle and distance of the center of Venus referred 

to the center of the Sun 57 

Problem II. Having found f and s", or the apparent position angle and distance of Venus from the Sun's 

apparent center, to free them from the effect of atmospheric refiraction 59 

Problem III. To express the position angle and distance of Venus from the Sun's center in terms of the geocen- 
tric elements, and their corrections 60 

Special investigation of the constants pertaining to each photoheliograph 61 

Curvature of the mirrors 61 

Concluding corrections for curvature .' 65 

Position of centers of divergence of the objectives _ 66 

Focal lengths for different rays 71 

Concluding relation between measures on the photographic plates and angulai: distances on the celestial sphere 76 

Constants for determining the position angle , 77 

Reductions of the photographs in tabular form 77 

Wladiwostok - 78 

Nagasaki.. 79 

Peking 80 

Kerguelen, Molloy Point 80 

vii 



VUl CONTENTS OF PAET L 

Page. 

Reductions of the photographs in tabular form — Continued. 

Hobart Town 8l 

Campbelltown 82 

Queenstown 83 

Chatham Island, Wliangaroa 84 

Tabular data for comparison with observations .,■. . .-,.-- 84 

Elements of ths transit by Hill, Airy, and Oppolzer 85 

Geocentric tabular distances and position angles of the center of Venus from that of the Sun; Table I. 86 

Parallactic elements; Table II 90 

The same continued; Table III , 98 

Comparison of observed and tabular positions of Venus on>the face of the Sun 102 

Comparison of observed and tabular distances 104 

Comparison of observed and tabular position angles Ill 

CHAPTER IV. 

OPTICAL OBSERVATIONS OF THE TRANSIT. 

Remarks on observations of the artificial transit of Venus 118 

Practice on the model transit 120 

Recapitulation of mean results for errors in estimation of contacts 132 

Tabular and observed times of contact '. ; „....- 134 

APPENDIX I. 

Correction of atmospheric dispersion in astronomical photography, by J. Homer Lane 141 

APPENDIX II. 

records of contact observations. 

Wladiwostok - 14S 

Nagasaki 146 

Peking 149 

MoUoy Point, Kerguelen Island -. 154 

Campbelltown -. 154 

Queenstown , 154 

Reductions of the contacts to Greenwich time 155 



EDITOR'S PREFACE. 



In the issue of the following observations of the Transit of Venus, with their 
preliminary discussion, the scheme presented by the Astronomer Royal of England to 
the Royal Astronomical Society, in March, 1875, has been adhered to so far as seemed 
necessary and practicable. This scheme was worded as follows : 

(I). It is desirable that the Observations made in each of the National Expeditions should be printed with the 
least possible delay, under the superintendence of the head of the Expedition ; and should be at once distributed to 
the principal scientific institutions and libraries, and to the persons officially interested in the Transit. 

(II). It is desirable that these Observations should be printed in Quarto, of such size that all could be conveniently 
bound together. There.is little difference in the sizes of the French Memoirs, the Berlin Memoirs, the Smithsonian 
Memoirs, the Eoyal Astronomical Society's Memoirs; the size of the Philosophical Transactions is somewhat larger. 

(III). A brief history of each Expedition should be given, with the names and offices of the persons employed ; 
and description of the localities, accompanied by maps if necessary, and by such statements as may lead to identifica- 
tion of the localities of observation. 

(IV). In the accounts of telegraphic operations, it may not be necessary to give details, if the instruments and 
methods are described, and a few observation.s are given sufficient for check of the fundamental conclusions ; in the 
accounts of Transits, it is sufficient to give description of instruments and methods, constants of adjustments, and 
tables of clock-errors, and analogous abstracts of comparisons of chronometers, &o. 

. (V). But it is necessary to give in the fullest detail everything that bears upon the actual observation of contacts, 
or upon the observer's impression at the time of making the observation, or upon the micrometer-measures, or upon the 
photographs and the measures of the photographs, &c.; with sufficient description of the instruments and their 
adjustments at the time. Clock-fime and Local Sidereal Time are to be given for every observation. 

(VI). Reference must be made to the place of deposit of the original documents, observations, calculations, and 
instruments of each National Expedition. 

(VII). A large .portion of the calculations sketched in the preceding Articles can be best made under the superin- 
tendence of the head of each National Expedition, and these should be printed and distributed as part of the Observa- 
tions mentioned above. 

(VIII). It is to be hoped that some astronomer of eminence may undertake to superintend, in some degree, the 
publications which I have suggested ; and to make the final combination of observations and decide on the ultimate 
result. I can without difficulty fix on the foreign astronomer in whose hands I should be glad to see this work placed. 

To these proposals the Astronomische GesellscJiaft, at its meeting in Leyden, Au- 
gust 16, 1875, added the following: 

(IX). Publikationen von Einzelresultaten ftir die Sonnenparallaxe aus den Beobachtungen des Venusdurchgangs 
von 1874 sind als die Interessen der Wissenschaft beeintrachtigend thunlich zu vermeiden. 

[Publications of separate results for the solar parallax from the observations of the Transit of Venus of 1874 are, 
so far as practicable, to be avoided as detrimental to the interests of science.] 

In reference to IV, it may be said that the time observations are printed more 
fully than is contemplated in Professor Aiey's plan, partly for the reason that the 
transit instrument was an essential part of the photo-heliograph used by the American 
parties. 

With reference to VI, it may be stated that the original observations are at present 
all deposited in a small fire-proof building, erected by the Commission for the purpose, 
in the grounds of the Naval Observatory. Should the Observatory be removed, as is 

7 



8 TRANSIT OF VENUS, 1874. 

contemplated, they will probably be kept in its fire-proof record-room. It may be 
expected that the reductions will be kept with the observations. The instruments are 
also stored at the Observatory, with the exception of a certain number temporarily 
loaned to government offices and to some of the chiefs of parties who took part in the 
observations. In the general arrangement of the work, the ultimate combination of 
the observations with those made by other nations has been constantly kept in mind. 
Therefore, in accordance with the recommendation of the Astronomische Gesellschaft, no 
attempt has been made to deduce an independent value of the solar parallax from 
these observations. What has been done is to present a comparison of each observa- 
tion and result with the tables, and to give with each comparison all the necessary 
data for variations of the various elements involved. The results are presented in such 
form as to make the effect of any changes in fundamental data as easy as possible. 
The final step has been to present each result in the form of two sides of an equation, 
one side of which contains the result of observation, the other the result of theory. 
The theoretical quantities have been computed from the data of Mr. Gr. W. Hill, pub- 
lished in Part II of Papers relating to the Transit of Venus in 1874. The necessary 
quantities are, however, given for any change from one set of elements to another. 

The numerical reductions have been made, under direction of the Commission, 
by Mr. D. P. Todd, Mr. W. W. Townsend, Mr. W. F. McK. Ritter, and some other 
gentlemen only temporarily employed. 

It is intended to issue the whole of the observations, with their reduction, in four 
parts, with the following arrangement of subjects : 

Part I. General account of the operations, and reduction and discussion of the 
observations of the Transit of Venus. This part is issued herewith 

Part II. Observations in detail made at each station, with their reduction. This 
part is intended to follow immediately. 

Part III. Discussion of the longitudes of the stations. 

Part IV. Measures of the photographs with their reduction and discussion. 

Nautical Almanac Office, 

Bureau of Navigation, 

Navy Department, 

Washington, March, 1880. 



CHAPTER I. 
HISTORY OF THE OPERATIONS. 



§ I. Organization of the Commission. 

The first action taken by any public body in the United States, having in view 
the observation of the Transit of Venus, to occur in December, 1874, is beheved to be 
embodied in a resolution adopted by the National Academy of Sciences, April 16, 

1870. This resolution provided for the appointment of a committee to report to the 
Academy at its next stated session what measures might be necessary to secure the 
successful observation of the Transit of Venus by American astronomers. The com- 
mittee appointed in pursuance of this action consisted of — 

Pi'ofessor Benjamin Peirce, LL. D., 

Rear-Admiral C. H. Davis, United States Navy, 

And, by invitation — 

Commodore B. F Sands, United States Navy, the Supei'intendent of the United 
States Naval Observatory. 

It does not appear that the committee, as thus organized, made any report. At 
the next session of the Academy the number of the committee was increased ; but the 
necessity for action on the part of the Academy was soon done away with by the 
action of Congress. A clause in the naval appropriation bill, approved March 3, 

1 87 1, appropriated $2,000 for experiments preliminary to the observations of the 
Transit, and provided — 

That this and all other appropriations by Congress for the observation of the Transit of Venus shall be ex- 
pended by a Commission, to consist of the Suiierinteudeut of the Naval Observatory, the President of the National 
Academy of Scionces, the Superintendent of the Coast Survey, and two professors of mathematics of the Navy, 
attaclied to the Naval Observatory. 

The commission, as thus organized, consisted of the following persons: 

Rear- Admiral B. F. Sands, U. S. N., Superintendent Naval Observatory, President. 

Professor Joseph Henry, President National Academy of Sciences. 

Professor Benjamin Pktrce, Superintendent Coast Survey. 

Professor Simon Newcomb, U. S. N., Secretary. 

Professor William Harkness, U. S. N. 

Changes in the personnel have since occurred as follows : 

In February, 1874, Rear- Admiral Charles H. Davis, U. S. N., became Superin- 
tendent of the Naval Observatory and President of the Commission in place of Rear- 
Admiral Sands, retired. 

In May, 1877, Rear- Admiral John Rodgers, U. S N., took the place of Rear- 

Admiral Davis, deceased the preceding February. 

9 
S. Ex. 31 2 



lO TRANSIT OF VENUS, 1874. 

In 1874 Dr. C. P. Patterson became Superintendent of the Coast Survey in place 
of Professor Peirce, resigned. 

In 1879 President William B. Rogers became President of the National Acad- 
emy of Sciences in place of Professor Henry, deceased in May, 1878. 

The law of 1871, already referred to, made no provision for anything but some 
preliminary experiments. During the year following the subject was actively taken 
up by those interested, and petitions were sent to Congress asking for assistance from 
the Government. In tbe legislative branches of the Grovernment the subject was placed 
in charge of Hon. F. A. Sawyer, of South Carolina, in the Senate, and Hon. James A. 
G-ARFiELD, Chairman of the Committee on Appropriations, in the House of Representa- 
tives. Through the active interest in the subject taken by these distinguished .gentle- 
men, an item was inserted in the "Sundry Civil Bill," approved June 10, 1872, 
appropriating the sum of $50,000 for the purchase of instruments with which to ob- 
serve the Transit. In the year following- a further appropriation of $100,000 was 
made for the expenses of the active operations. 

§ 2. Plan of Observations. 

The considerations which guided the Commission in the formation of a plan of 
observation and the genei'al features of the plan to which they were thus led were 
as follows : 

(i). In studying the subject of contact observations, it was found that all past 
experience showed this method to be less accurate than had commonly been sup- 
posed. It was well known that the latest Transit of Venus (that of 1 769) had given 
a value of the solar parallax decidedly too small, and the most careful research had 
failed to show satisfactorily any other cause for this error than the difficulty and un- 
certainty of the contact observations themselves and of the interpretations to be put 
upon the language of the observers. It was also found that the observations of the 
transits of Mercury, even those made by the best observers and under the most 
favorable circumstances, showed important discrepancies. On the other hand, there 
was reason to suppose that these uncertainties had arisen in part from the want of 
practice on the part of the observers in noting the phenomena of a transit. No 
matter how much experience an observer might have in other directions, it was 
scarcely possible that he could observe more than one or two transits of a planet in 
the course of his life-time. There was, therefore, reason to hope that, by previous 
practice on an artificial representation of the phenomenon, the accuracy and certainty 
of the observation might be considerably improved. It therefore seemed best to 
choose some method other than that of observations of contacts as the main dependence 
for the determination of the solar parallax, but at the same time to endeavor to in- 
sure, as far as possible, their accurate observation by practicing the observers in con- 
nection with an artificial representation of the Transit of Venus. 

(2). It was found that the observations of contact miglit be advantageously sup- 
plemented by measures of the distance apart of the sharp cusps of Venus, made with 
the double-image micrometer, when the planet Avas nearly on the sun. It was there- 
fore, determined to equip the principal telescope of each station with such a micro- 
meter — of Airy's pattern, as modified by Valz. 



HISTORY OF THE OPERATIONS. II 

(3). It appeared that any other method than that of contacts must rest upon a 
determination of the position of the center of Venus relative to that of the sun. Esti- 
mates of the sun's semidiameter made by different observers were well known to be 
so discordant that no reliance whatever could be placed on a determination of the 
position of the center of Venus relative to the sun's limb. Measures with a filar 
micrometer appeared to be out of the question, owing not only to the large arc to be 
measured, but to the personal error in setting a wire tangent to the limb of the sun or 
of Venus. The differences among observers in noting the time of transit of the two 
limbs of the sun seemed also to be in the way of obtaining any reliable result from transits 
across the wires of an instrument. These methods aside, but two ways of determining 
the position of Venus on the sun were left — heliometer measures and photography. 

Notwithstanding the great precision of measures with the heliometer, its applica- 
tion was impracticable, from the fact that the instrument did not exist in this country; 
and it was not possible to devise, construct, and put into operation a sufficient number 
of such instruments in the limited time at the disposal of the Commission. 

(4). The only resource remaining was to be found in photography; and the Com- 
mission were especially predisposed to try this method from the great success with 
which their distinguished countryman, Mr. L. M. Ruthekfurd, had applied it to 
astronomical measurements. The question of the form of apparatus to be used next 
arose, and a correspondence on this subject was opened with Mr. Ruthekfurd, 
which has been published in Part I of the "Papers" issued by the Commission. At the 
same time, attention was called by Professor Joseph Winlock to a method which he 
had himself invented and put in operation at the Astronomical Observatory of Harvard 
College. The essential feature of this method is that the photographic telescope is 
fixed in a horizontal position, while the rays of the sun are reflected into it by means 
of a heliostat. The telescope may then be made of any required length, and the ne- 
cessity for a secondary enlargement of the image entirely avoided.* 

It was soon seen that this method would offer several striking advantages. 

a. The position-angle of the planet on the sun could be determined with much 
greater precision than by any other method. 

13. The linear value of one second of arc on the photographic plate could be de- 
termined with great precision by measuring the distance between one "principal point" 
of the lens and the sensitive plate. 

7. The image to be photographed could be formed in the dark-room itself, in a 
fixed position above a pier, without any of the inconveniences attending the use of a 
movable telescope. 

A fuller statement of the advantages claimed for the method will be found in the 
paper referred to, while the details of its application will be given subsequently. 

(5). The methods of contact- observations and of photography were combined in 
an ingenious plan proposed by Janssen, whereby the phase of internal contact was 
itself to be photographed It was not, however, judged advisable to lay stress on 
this method, for the reason that the phase, as seen in the photograph, would depend 

* Although this method was original with Professor Wixlock, priority in its application has been claimed by 
Captain Laussedat, of France. It does not appear necessary at present to discuss the validity of this claim, which 
may be well founded without detracting from the merit of the second inventor. 



12 TRANSIT OF VENUS, 1874. 

upon the actinic power of the sun's rays and the development of the photograph, as well 
as upon the actual advance of the phase itself For instance, a photograph taken at 
one station thirty seconds after internal contact, with the sun at a low altitude or with 
a feeble development, might present the same aspect as one taken at the moment of 
contact at another station with the sun higher, the air clearer, or the photograph more 
fully developed. 

The spectroscopic method of external contact, whereby it had been proposed to 
observe the approach of Venus on the sun's chromosphere, was believed to be subject 
to such variations arising from the different degrees of irradiation as not to justify trial. 

§3. Choice of Stations. 

The principal methods of observation being thus reduced to photograjohy when 
Venus is wholly on the sun, and observations of contacts, it was necessary to choose 
stations where these methods could be most advantageously applied. The greater 
the interval of time during which photographs could be taken, the greater the possible 
number of photographs, and the less the chances of total failure from clouds. It was 
therefore advantageous to the photographic method to choose stations from which the 
entire transit would be visible. Such stations would be about equally favorable for 
the observations of contacts ; for although each individual observation of contact 
would be worth less than if made at the station most suitable for the purpose, this 
defect would be compensated by the fact that both ingress and egress would be ob- 
servable. 

In order to obtain the best results at the least expense, it was judged necessary 
that the instruments and methods of observation should, so far as possible, be uniform 
at all the stations, in order that all the observations might be strictly comparable with 
each other. It was estimated that the means likely to be placed at the disposal of the 
Commission would suffice to equip eight stations, and, for the reason just given, 
it was determined to establish stations only at points from which the whole transit 
would be observable. 

Besides the astronomical considerations which would affect the choice of a station 
the chances of fair weather had to be studied. Efforts were, therefore, made to de- 
termine in what parts of China and Japan the weather would probably be most 
favorable in December, and what the meteorological conditions of the region around 
Kerguelen Island were at the same season. Correspondence was, therefore, opened 
through the Department of State with the consuls of the United States at Yokohama 
Nagasaki, and other points in that part of Asia, with a view of obtainino- exact obser- 
vations of the degree of cloudiness during the months of November and December 
1872 and 1873. The conclusion from these observations was that Nagasaki was the 
most favorable point in Japan. 

In the southern hemisphere it was intended to establish one or two stations on 
Kerguelen Island or in its neighborhood. Early in 1872, throuo'h the courteous 
intervention of Professor H. A. Newton, the Commission was placed in communication 
with the Messrs. Williams, Haven & Co., of New London, Conn., a firm which occu- 
pies a station on Kerguelen Island for hunting the sea-elephant. This island havino- 
already been selected as a British station, it seemed preferable to occupy a station on 



HISTORY OF THE OPERATIONS. 



13 



Heard's Island, in the neighborhood, if the meteorological conditions were not de- 
cidedly more unfavorable. An arrangement was therefore made with the firm in 
question to have a record of the weather at Heard's Island made during the months of 
November and December, 1872. This record was received in the summer of 1873, 
and showed that at Whiskey Bay, the sealing station on Heard's Island, the weather 
was almost constantly so bad as to render observations nearly hopeless. Assurances 
were also received from the officers of this firm that the weather at their station on 
Kerguelen Island was decidedly more favorable than at tieard's Island. This station 
being at a considerable distance from Christmas Harbor (which was supposed to have 
been selected as the English station), it was determined to occupy it. 

It had, at first, been intended to occu]jy four stations in tlie northern and four in 
the southern hemisphere, but an examination of the meteorological conditions of the 
stations showed the weather to be so much more favorable in the northern tlian in the 
southern hemisphere that it was decided to make an unequal division, occupying three 
northern and five southern stations. The points finally chosen by the Commission 
were as follows : 

(i) Wladkuostok, Siberia. — This point was selected in consequence of the favor- 
ableness of the weather and an intimation from Director S truvf-, of tlie Pulkowa Ob- 
servatory, that an application for permission to occupy it might be favorably received 
by the Russian Government 

(2) NagasaJii, Japan, was selected as being favorable meteorologically. An 
additional reason for choosing it was found in the expi'essed intention of the French 
expedition to Japan to occupy Yokohama 

(3) Peking, China, was selected, notwithstanding that a French station was to be 
established there, because the records of the Russian Physical Observatory at that 
point showed that an entirely cloudy day had scarcely ever happened at the period 
of the year in which the transit was to take place. These records, as was subse- 
quently remarked, took no notice of the dust-clouds which so frequently obscure the 
air in this part of China. 

(4) Grozet Islands. — This station being favorable astronomically, and not selected 
by any other nation, it seemed desirable to occupy it, if only the instruments and 
stores for tlie party could be safely landed. Ship Harbor, on the eastern, and there- 
fore the leeward side of Possession Island, was selected as the most favorable landing 
point. 

(5) Molloy Point, Kerguelen Island. — The sealing station of the Messrs. Williams, 
Haven & Co., in Three Island Harbor, was selected. 

(6) Hobart Town, Tasmania. — Meteorological observations had been taken there, 
showing the climate to be quite favorable for observations during December. 

(7) Bluff Harbor, New Zealand. — This point was selected as being at some dis- 
tance from those stations which had been chosen by other nations, and as being readily 
accessible. Commimications received through the Department of State indicating 
that some point in the interior might be more favorable, the party was not confined 
to the selection of Bluif Harbor 

■ (8) Whangaro.a Bay, Chatham Island, was selected on account of its having a good 
harbor, though no certain information in regard to its meteorology could be obtained. 



14 TRANSIT OF VENUS, 1874. 

The long line over which the southern stations extended would enable the solar 
parallax to be determined from the difference of position-angle observed from the 
two ends, though the northern observations should fail entirely. The stations might, 
in fact, be roughly divided into three groups, the combination of observations made 
at any two of which would give a valuable result for the solar parallax. 

§ 4. Instrumental Equipment. 

A uniform plan of observation being adopted at all the stations, it was de sirable 
that the instrumental equipment should also be uniform. Referring to the description 
given hereafter for fuller details, it will be sufficient to state here that the outfit of 
instruments supplied to each station included the photographic apparatus complete ; 
a transit instrument, with a clock, two chronometers and a chron ograph, and a five- 
inch equatorial telescope for observing contacts and occupations of stars hj the moon. 
A fundamental part of the plan was to place the transit instrument in the same meri- 
dian as the photographic telescope, in order that the central vertical line of the photo- 
graphic plate-holder could be set very near the meridian and its small deviations be 
accurately determined. 

The transit instruments were of the broken-tube construction, a prism being 
placed in the center of the cube, by interior reflection from which the pencil of rays is 
thrown along the axis; and the image is thus formed at the end of the latter. The 
detailed plans of the instrument were all devised by Professor Wm. Harkness, U. S. 
N., and the construction was carried out under his personal direction. This form of 
instrument has the great advantages of convenience in observing and of rapid and easy 
manipulation, but is still subject to the disadvantage of a collimation varying with 
the zenith-distance of the object observed. In the Pulkowa method of using the 
instrument the inconvenience arising from this source is obviated by a reversal sys- 
tematically practiced between each pair of stars, a transit of the pole star being 
observed before and after each reversal. This plan of observation could not be intro- 
duced at the American stations owing to the necessity of keeping the instrument in the 
meridian. The difficulty in question was therefore not so completely avoided as it 
might have been liad the instrument been intended for use out of the meridian. 

One of the chronometers furnished to each station was a sidereal one, breakino- 
the galvanic circuit at every second except the sixtieth of each minute, while the other 
chronometer was regulated to keep mean time. Several of the parties, however, used 
other chronometers than these two in the course of their observations. 

The sidei-eal clocks were all made by the Howard Clock Company of Boston 
after a plan furnished by Professor Wji. Harkness. They have gravity-escapements, 
a construction chosen on tlie ground that, if the escapement and pendulum Avere well 
made, the good performance of the clock would be insured without respect to the 
■■A- heel-work. The latter niiglit tlierefore be of a very cheap kind. The principal 
peculiarity of these clocks is the A\'eight of the pendulum, tlie jar of which holds 
about forty-five pounds of mercury. In general, the performance of the clo cks at the 
stations was not satisfactory ; but it is believed that this imperfection arose from insta- 
bility of the supports on which they were mounted rather than from defects of con- 
struction. 



HISTORY OF THE OPERATIONS. 1 5 

The chronographs were made by Alvan Clark & Sonp, and were regulated by the 
Hipp spring. This construction is inconvenient on account of the great weight re- 
quired to run the instrument, and the noise caused by the spring. It was, however, 
preferred to the Bond spring-governor, on account of a supposed liabiHty of the latter 
to get out of order when used in the field. Were the instruments to be reconstructed, 
it is probable that some form of conical pendulum would be adopted as a regu- 
lator. 

The photographic objectives were each five inches in clear aperture, and most of 
them between thirty-eight and thirty-nine feet in focal length. They were connected 
for the photographic rays. The heliostat, by which the rays of the sun were thrown 
into them, turned by clock-work on a single fixed axis, whicli was so adjusted that the 
rays of the sun would be thrown in a nearly constant direction during the whole of 
the transit. This plan was adopted as a compromise between having no clock motion 
at all in the heliostat, the adjustment being made by an assistant for each photograph, 
and the expensive apparatus necessary to throw the solar rays in a direction mathe- 
matically constant. The latter construction was the more willingly given up from the 
fear that any motion by a complex system of wheel-work, accompanied by a slow 
sliding of parts, as in the Foucault constrviction, might be accompanied by minute 
jerks. Probably these fears were entirely unfounded, but there was no opportunity 
of proving them to be so in time to begin the construction. 

The mirrors are seven inches in diameter, of unsilvered glass, and slightly thicker 
on one side than on the other, in order that the reflection from the second surface may 
be thrown away from the photographic plate. They were left unsilvered in order to 
prevent any unequal absorption of heat by the two surfaces of the glass. So far as 
could be detected, no distortion of the unsilvered glass was produced by the direct 
action of the sun's rays.* 

The plate-holder in the focus of the photographic objective consists of a brass 
frame, about eight inches square, turning on an axis passing vertically through its cen- 
ter, mounted on a hollow iron pier, and having a spirit-level attached to the top of the 
frame. A vertical cylindrical hole passes through the axis from top to bottom, in the 
center of which passed a fine silver plumb-line, the bob of which hung in a basin of 
water below. A square disk of plate-glass, about three-tenths of an inch thick, was 
set in one side of the brass frame, so that the plumb-line passed very near its surface. 
The surface nearest the plumb-line was ruled with a system of horizontal and vertical 
lines one-half an inch apart, by Professor W. A. Rogers, of the Observatory of Har- 
vard College. 

In taking the photograph the ruled plate was on the side of the plate-holder 
nearest the photographic objective, the sensitized plate being inserted from the other 
side. Between the ruled surface of the one and the sensitized surface of the other was 
a space of about o.™i6, through the middle of which hung the plumb-line. The 
images of the plumb-line and of the ruled lines were thus impressed on the plate 
with each photograph. 

* In some of the ]5reliiiiiiiary experiments the mirror was found to become concave under tlie influence of tlie solar 
rays, but tMs was traced to tlie heat from the black iron plate on which the heliostat was mounted. On covering the 
portion of the plate under the mirror with white cloth or paper, the distortion was no longer perceptible. 



1 6 TRANSIT OF VENUS, 1874. 

Each equatoreal was of five inches aperture, was adjustable to any latitude, and 
was furnished with divided circles, clock-motion, and double-image micrometer. The 
clock-motion -was regulated by a Bond spring-governor, with an auxiHary "fly", in 
the event of the governor getting out of order. This precaution was suggested by 
the extreme liability of the governor to break down. 

§ 5. Organization of the Parties. 

The instrumental equipment and method of observation being nearly the same at 
'all the stations, the force necessary to conduct the scientific operations should also be 
similar. After due consideration of the conditions to be fulfilled, it was decided that 
this force at each station should consist of one chief of party, one assistant astronomer 
(to be second in rank), one chief photogi-apher, and two assistant photographers. In 
addition, some of the stations were supplied with a mechanician, and two with ad- 
ditional assistant astronomers. 

In selecting the chiefs of parties it was decided that two would be furnished by 
the Naval Observatory, two by the Coast Survey, one by the Army, one by the 
Navy, and that two should be taken from outside the government service. 

Of the assistant astronomers the Army, Navy, and Coast Survey each fur- 
nished those of their own parties, while three were taken from outside the govern- 
ment service. The remaining assistant astronomer was supplied by the Army. 

In selecting photographers it was deemed necessary that the chiefs should all be 
professional practitioners of their art; but the greater part of the assistant photographers 
were young gentlemen of education, recent graduates of different colleges, who had 
been practiced in chemical and photographic manipulation. 

§ 6. Preliminary Practice. 

As an essential part of the plan, all the members of the several parties met at 
Washington, in the spring of 1874, in order to practice all the operations necessary 
for the successful observation of the Transit, with the same instruments Avhich they 
were to use at their various stations. The need was now felt of some one skilled in both 
chemical and physical manipulation, whose duty it should be to i)ut all the apparatus 
which had been designed by the Commission in complete working order ; to com- 
plete such details as were still wanting ; to try such experiments as might be neces- 
sary for this purpose : and to train the several parties in the photographic operations. 
DesiroTis of obtaining the co-operation of one of tlie two citizens of the country most 
noted for their success in astronomical photography, the Commission, on February 9, 
1874, adopted the following resolutions: 

(i) That Dr. Heniiy Drapeh, nf New York, be invited to take ehar!j;(-, under the dirc-etion of the Commission, 
witliout pay, of the work of iiutting into siiccessl'iil execntiou the various operations neeessar.v for photot;rapliiu"- tlie 
Transit of Venus by tlie nictliods alrc;i,dy decided upon by the Cdunuissiou, and ol' instructing tlie parties in those 
operations. 

(2) That all the nialerial, applianees, and assislance neeessavy to this end be placed in his hands during the 
period of his acti\'e enganeraent in tliia work. 

(3) That he re(;.lve his instructions in such way, or ilirough such channel, as the Commission may from time to 
time determine. 

(4) That his personal expenses while euga.ged in this work away from his home be reimbursed during the period 
of such absence, including the cost of railway tickets for the necessary travel. 



HISTORY OF THE OPERATIONS. 



17 



The need of this action was rendered more pressing from the backward state of 
the preparations. The Commission had deferred a decision of the question of the 
length of the photographic telescopes and the construction and application of the 
heliostat with a view of obtaining light from experimental trials, which, however, had 
to be finally abandoned. In consequence, there was no time for such deliberate trial 
of the apparatus as the members of the Commission would have desired to make had 
a longer interval been at their disposal. Dr Draper not only accepted the invitation 
thus offered, and devoted several weeks to the service of the Commission, at a great 
sacrifice of his private interests, and under circumstances which rendered his absence 
from home extremely embarrassing, but also refused to receive any reimbursement of 
the expenses incurred in performing the duty.* 

Valuable service was also rendered by another department of the Government in 
the examination of the photographers. The number of applications for the position of 
photographer and assistant photographer being considerably in excess of the number 
of places to be filled, the Commission preferred a request to the Honorable Secretary 
of the Treasury that the photographic office of his department should assist in the 
selection of photographers. 'I'he most promising of the applicants were therefore 
selected and sent to Mr. L. E. Walker, the chief of the photographic department of 
the Treasury, for examination. To this gentleman the Commission is indebted for a 
large part of the labor of selecting the photographers. 

§ 7. Voyage of the Swatara. 

On May 30, 1874, the preparations for the embarkation of the southern parties 
were completed, and all their instruments and equipments were shipped on the U. S. S. 
Gettyshurg, Lieut. D. Gr. McRitchie, U. S. N., commanding, and transported to New 
York. The parties, with their equipments, were there embarked on the U. S. S. 
Swatara, Capt. Ralph Chandler, U. S. N., commanding, the ship fitted out by the 
Navy Department for distributing the five southern parties among their several sta- 
tions. 

The following is a brief chronological summary of the movements of the Swa- 
tara in the execution of this duty: 

1874. 

June 7. — Left anchorage in New York harbor, and put to sea on the following 
day. 

July 1 1 . — Arrived at Bahia. 

July 15. — Left Bahia for Capetown. 

August 5. — Anchored in Table Bay, Cape of Good Hope. Communicated with 
the local authorities and with the English parties transported by Her Majesty's Cor- 
vette Encounter. It was learned that the destination of the English Kerguelen party 
had been changed from Christmas Harbor to Three Island Harbor, the fact that the 

* Desirous of expressing to Dr. Draper their appreciation of his disiuterested services, the Commission presented 
him, with its vote of thanks, a gold medal which it had struck for the purpose. The face of the medal bore the 
inscriptions: Veneris in sole SPECTANDiE curatokes R. P. F. S. Hknrico Draper, M. D., Dec. viii, jidccclxxiv. 
Decoei decus adDIT avito. The obverse contained a relief of the photographic heliostat, sun-ounded by the in- 
scription: FAMAM EXTENDEEE EACTI8 — HOC VIETUTIS OPUS. 

S. Ex. 31 3 



1 8 TRANSIT OF VENUS, 1874. 

latter position had been selected by the American Commission not having been com- 
municated to their Government. 

August 1 7. — Left, Capetown for the Crozet Islands. 

August 30. — Sighted Hog Island and the Twelve Apostles, the westernmost islands 
of the group. 

On the afternoon of the same day a heavy southwest gale came on and the ship 
had to be hove to. Next morning the gale abated somewhat and Possession Island 
was sighted to the southward. At 6.30 anchored on the east side, intending to go to 
Ship Bay at daylight. 

At 4 a. m. on September i a gale came on from the northward, obliging the ship 
to stand off shore. She stood on and off the land between Possession Island and East 
Island during the entire day. In the afternoon an opportunity offered of examining 
Ship Bay, during a lull in the wind. It was found to be a dangerous place for so 
large a vessel, as there was no swinging room inside the bay, and the headlands were 
only two cables' lengths apart. The nearest anchorage that could be found within a 
mile from the headlands, was in 20 fathoms of water, and exposed to wind and sea. 
Entertaining the hope that another day might develop better anchorage. Captain 
Chandler stood off shore some ten miles, and hove to under canvas and banked fires. 
A heavy gale sprung up during the night, and next morning reckoning placed the 
ship ^7 miles from Possession Island, the wind still blowing heavy from the northeast 
and northward. The outlook was now so unfavorable that Captain Chandler felt 
obliged to give up the attempt to land the party on Possession Island, owing to the 
danger of delays in landing other parties, a contingency which had been provided for 
in his instructions. 

Septemher 7. — Anchored in Three Island Harbor, Kerguelen Island. A site for 
the establishment of an observing station was selected on the north side of Royal Sound, 
about fifteen miles from its mouth. The ship moved over there, and the landing of 
stores and materials for Commander Ryam's party commenced on the afternoon of the 
loth, at a point called Fresh Water Bay, near MoUoy Point. Heavy gales were 
encountered during this time, in one of which the steam-launch was lost. On Sep- 
tember 1 2 leave was taken of the officers of the party. Commander Ryan, Lieutenant- 
Commander Train, and Passed Assistant Surgeon Kidder, and the ship sailed for 
Hobart Town. 

October i. — Reached Hobart Town, Tasmania. The hospitalities of the city were 
extended to the ship by the Colonial Secretary in the absence of the Governor. The 
parties of Professor Hai{kness and Captain Raymond were landed here, the latter 
being the one originally destined for Possession Island. Captain Raymond selected 
Camjjbelltown, 80 miles north of Hobart Town. 

October 10. — Left Hobart Town for Bluff Harbor. 

October 16. — Arrived at Bluff Harbor. Tliere Lieutenant Bass, Corps of Engi- 
neers, U. S. A., assistant astronomer to Dr. Pei'ERS, came on board, having made the 
journey by way of San Francisco and spent two weeks traveling in the island. He 
recommended Queenstown, at the north extremity of Lake Wakatipu, as the most 
eligible site for the observation of the Transit. By direction of the Colonial Governor 



HISTORY OF THE OPERATIONS. 1 9 

transportation for the party and its outfit was supplied over the government lines of 
railway free of charge. 

October 17. — Left Bluff Harbor for the Chatham Islands. Stopped at Port 
Chalmers, hoping to find a pilot familiar with the harbors of Chatham Island, but 
failed. 

October 19. — Reached the western end of Petre Bay, and sailed for the small town 
of Waitangi, at the head of the bay ; afterward made the entrance of Whangaroa Bay 
and found a safe and smooth anchorage just above Point Borgen. Next day Mr. 
Edward Smith, of the Coast Survey, chief of the Chatham party, went on shore with 
Captain Chandler and selected a station on the rising ground to the westward of the 
bay. Observations for comparison of chronometers were made by Mr. Smith. 

October 26. — Left Whangaroa Bay for Port Chalmers, New Zealand. 

October 29. — Reached Port Chalmers and communicated by telegraph with Dr. 
Peters. 

November i. — Telegraphic comparison of chronometers was made by the parties 
with Dr. Peters. 

November 4. — Left Port Chalmers and next day stopped at Bluff Harbor to give 
Dr. Peters another comparison, but he considered it unnecessary. 

November 7. — Left Bluff Harbor for Hobart Town. 

November 13. — Arrived at Hobart Town, and remained there until after the 
Transit. 

December 18. — Sailed for Auckland Island, to communicate with the German 
party. 

December 23. — Reached Auckland Island, found the German party well, and 
made a comparison of chronometers. 

December 25. — Sailed for Port Chalmers. 

December 2 7. — Arrived at Port Chalmers, and exchanged signals with Dr. Peters 
at Queenstown. 

December 30. — Sailed for Whangaroa, Chatham Island. 

1875- 

January 4. — Reached Whangaroa and communicated with Mr. Edwin Smith, 
chief of party. Took the party on board, and afterward sailed for Port Chalmers. 

January 15. — Sailed from Port Chalmers for Bluff Harbor, arriving next day, 
when Dr. Peters with his instruments and a portion of his party were taken on 
board. 

January 20. — Sailed for Hobart Town, but put into Port William, Stewart's 
Island, over night. 

January 29. — Arrived at Hobart Town. 

February 1 7. — Sailed for Melbourne. At this point the operations of the ship in 
connection with the Transit of Venus, after having been conducted by Captain 
Chakdlek with zeal, ability, and success for a period of eight months, were substan- 
tially terminated. 



20 TRANSIT OF VENUS, 1874. 

It is proper to add that the reports of Captain Chandler speak in the warmest 
terms of the hospitaUties and attentions everywhere tendered, both by the 'British and 
Colonial authorities. 

The parties designed for the northern stations left two months later, and were 
transported from San Francisco to Nagasaki by the Pacific Mail steamships. Thence, 
Professor Hall's party was taken to Wladiwostok by the U. S. S. Kearsarge, Com- 
mander D. B. Ha.rmony,U. S. N., commanding. The ship reached her destination on 
September 7, and the party with their instruments and baggage were landed on Sep- 
tember 9. 

Professor Watson's party was transported from Nagasaki to Tientsin by the 
U. S. S. Ashuelot, Commander E. 0. Matthews, U. S. N., commanding, arriving Sep- 
tember 9. The journey from Tientsin to Peking was made by the regular commercial 
conveyances. 

The detailed reports of the movements and operations of each party will be given 
in Part II. 



CHAPTER II. 

PARTICULARS RELATING TO EACH STATION. 



§ I. POSITIONS OF STATIONS. 

[The longitudes here given are those provisionally adopted in the following reductions. The discussion of the correc- 
tions which they may require wiU be given in Part III. ] 



Station. 


Astronomical 
Latitude. 


Geocentric 
Latitude. 


Logp 


Provisional Longitude West from — 


Greenwich. 


Washington. 




O ' /' 

+43 6 35.6 
+32 43 21. I 

+39 54 IS 
— 49 21 22. 1 
—42 53 24. 6 
—41 55 42.9 
-45 2 7 
—43 49 3- 2 


/ // 
+42 55 6.6 

+32 32 53-8 
+39 42 55-7 
—49 9 '59- 1 
— 42 41 56. 
—41 44 16.5 
—44 50 36.4 
-43 37 33-2 


9- 999324 
9. 999578 
9. 999405 
9. 999166 
9-99933° 
9- 999354 
9.999276 

9-999307 


h m s 

— 8 47 30- 9 

— 8 39 30.6 

— 7 45 47- 9 

— 4 40 18. 1 

— 9 49 20. 5 

— 9 50 0. 1 
— 1 1 14 40. 4 
— 12 13 II. 8 


h m s 
-13 55 43-0 

—13 47 42.7 
— 12 54 0. 
— 9 48 30. 2 
—14 57 32.6 

■ — 14 58 12. 2 
— 16 22 52. 5 
— 17 21 23.9 




Peking 


Mollov Point - 


(Kerguelen Island ) 
Hobart Town 

Camnbelltown ........ .... 


Queensto wn 


Whangaroa : .. 


(Chatham Island.) 



* The Nagasaki Telegraph Station, from which longitude-signals were exchanged with Wladiwostok, ig i".63 
west and 5o".3 north of the Transit-of- Venus Station. 



22 



TRANSIT OF VENUS, 1874. 
§ 2. NUMBERS AND CONSTANTS OF INSTRUMENTS. 



Station. 



Number of 
Transit, 



One rev. 

of its 
Microm. 



Five- inch 
Equatoreal. 



Howard 
Clock 



Mean Time 
Chronometer. 



Sidereal 
Chronometer. 



Additional Chro- 
nometers. 



Wladiwostok . . . 

Nagasaki 

Peking 

MoUoy Point 

Hobart Town - . 
Campbelltown . 

Queenstown 

Whangaroa - 

Station. 

Wladiwostok 

Nagasaki 

Peking 

MoUoy Point 

Hobart Town - . . 
Campbelltown - . . 

Queenstown 

Whangaroa 



1508 
1507 
1505 
1497 
1502 

1503 
1504 
1506 



68. 700 

69-34 

68. 605 

69. 00 

68.395 
69. II 
69-45 
68.94 



856 
862 
857 
859 
863 
860 
858 
861 



629 
622 
628 
623 
625 
624 
626 
627 



De Silva 1081 
Penlington 1742 



Murray 827 

De Silva 694 

Porter 118 

Negus 994 

Bond 243 



Negus 1519 
Negus 1503 
Negus 1 5 18 
Negus 1539 
Negus 1520 
Negus 1536 
Negus 1470 
Negus 1527 



< Negus 1563 o. t. 
I Negus 1378 m. t. 



Bond 335 s t. 
Bond 387 s. t. 



Heliostat 
Mirror. 



Photographic 
Objective. 



Measuring 
Rod. 



Length of Rod, 
620(Fahr.) 



Plate-Holder. 



Engineer 
Level. 



VII 
IV 
III 
VIII 
V 
VI 

II 
I 



I 

VIII 
VI 
V 

II 
III 

IV 

VII 



IV 

II 

I 

III 

VII 

VI 

VIII 



450, 
450, 

461 
453 
453' 
451 
451 
449. 



•357 
•437 
•425 
.488 
.498 
.946 
.491 
•48i 



7 
3 
4 
I 

5 
6 



1490 
1487 
1491 
1494 
1510 
1499 
1489 
1493 



PARTICULARS RELATING TO EACH ^STATION. 23 



§ 3. ORGANIZATION OF THE PARTIES. 

WLADIWOSTOK. 

Professor Asaph Hall, U. S. N .............. ....'... Chief of Party. 

Mr. O. B. Whkeler Assistant Astronomer. 

Mr. D. R. Clakk 

Mr. T. S. Tappan 

Mr. George J. Rockwell iPhotograpMc Assistants. 

Mr. F. M. Lacey . ' ... 

NAGASAKI. 

Professor George DivrosoN, U. S. C. S - - Chief of Party. 

Mr. O. H. TiTTMANN, U. S: C. S Assistant Astronomer. 

Mr. W. S. Edwakds, U. S. C. S 2nd Assistant Astronomer. 

Mr. S. R. Seibert \ 

Mr. H. E. Lodge \ Photographic Assistants. 

Dr. Frank H. Williams ) 

PEKING. 

Professor J. C. Watson Chief of Party. 

Professor C. A. Young Assistant Astronomer. 

Mr. W. V. Ranger 

Mr. E. Watson , ' - - \ Photographic Assistants. 

Mr. B. J. Conrad 

MOLLOY POINT, KERGUELEN ISLAND. 

Commander G. P. Ryan, U. S. N Chief of Party. 

Lieutenant-Commander C- J. Trvin, U. S. N Assistant Astronomer. 

Mr. D. R. Holmes 

Mr. G. W. Dryer ^ Photographic Assistants. 

Mr. Irvin Stanley 

HOBART TOWN. 

Professor William Harkness, U. S. N Chief of Party. 

Mr. Leonard Waldo Assistant Astronomer. 

Mr. John Moran 

Mr. W. H. Churchill \ Photographic Assistants. 

Mr. W. B. Devereux 



24 TRANSIT OF VENUS, 1874. 

OAMPBELLTOT^N. 

Captain C. W. Raymond, Corps of Engineers, U. S. A Chief of Party. 

Lieutenant S. E. Tillman, Corps of Engineers, U. S. A Assistant Astronomer. 

Mr. W. R. Pywell \ 

Mr. J. Gr. Campbell > Photographic Assistants. 

Mr. Theodore Richet ) 

QUEENSTOWN, NEW ZEALAND. 

Dr. C. H. F. Peters .. ..■. Chief of Party. 

Lieutenant E. W. Bass, Corps of Engineers, U. S. A Assistant Astronomer. 

Mr. C. L. Phillippi ^ 

Mr. Israel Russell ! 

Mr. E. B. PiEESON > Photographic Assistants. 

Mr. L. H Ayme j 

WHANGAROA, CHATHAM ISLAND. 

Mr. Edwin Smith, U. S. C. S Chief of Party. , 

Mr. Albert H. Sooit, U. S. C. S . . - Assistant Astronomer. 

Mr. Louis Seebohm* ^ 

Mr. Otto Buehler > Photographic Assistants. 

Mr. W. H. Rau ) 

Mr. Sumner Tainter Instrument Maker. 

* Mr. Sbbbohm died at BaMa, Brazil, during the voyage out and bis place iras taken by Mr. Buehler. 



CHAPTER III. 

DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



§ I. Desceiption and Use of the Photo-heliogeaph. 

The following considerations will give an idea of the objects aimed at in the de- 
sign of the instrument for photographing the Transit of Venus. It is evident that if 
we could point a very long telescope at any close pair of objects in the heavens, and, 
at the moment of taking their photographic images in the focus, photograph a meridian 
line passing through or near either of them, we should at once be able to determine 
their angle of position by the relation of the meridian to the line passing through 
their centers. It is also evident that if we could measure the distance from the second 
principal point of the objective to the sensitized plate, we should, by comparing this 
distance with that of the images, be able to determine the angular distance of the 
latter from each other. 

In using a telescope pointed at the sun or other heavenly body, neither of these 
requirements can be fulfilled. But, by using a horizontal telescope fixed in the merid- 
ian, and throwing the rays of the sun into it with a heliostat, the first condition^that 
of photographing a meridian line — can be potentially fulfilled, since a vertical line 
can be photographed, and the relation of this line to the meridian can be accurately 
determined; and the last — that of measuring the length of the telescope — can be really 
fulfilled. Thus, position-angle and distance can be determined with equal ease and 
certainty. 

The essential parts of the photo-heliograph are shown in figures i to 5, inclusive, 
figures I, 2, 3 being the heliostat and the clock-work by which it is moved; and 4, 
5 the photographic apparatus. In explanation of its construction, it may be remarked 
that, under favorable . circumstances, no clock-motion of the heliostat is necessary. 
Experience shows that a photograph of the sun can be taken in a small fraction of the 
hundredth of a second, so .that the want of definition produced by the diurnal motion 
will be entirely lost in the necessary effects of irradiation. Without clock-work, it 
would be necessary for an assistant to adjust the position of the reflector by tangent 
screws for each photograph, and this would have been very easy. There are, how- 
ever, two contingent circumstances which might make it imprudent to trust entirely 
to the motion by hand. One is that, in the event of the photographs having to be 
taken in moments of sunshine during a cloudy day, the sun might, after a brief inter- 
val, be covered again by the clouds before the assistant had time to make an adjust- 
S. Ex. 31 4 25 



26 TRANSIT OF VENUS, 1874. 

ment. The other is that, owing to mist or low altitude, a much longer interval than 
the normal time might be required for the photograph. As the result afterward 
showed, the photographs at Kerguelen and Peking would probably have been entirely 
lost from this cause had no clock-motion been applied to the heliostat. 

On the other hand, the construction of the apparatus necessary to give the mirror 
the movement which would throw the reflected ray in an invariable direction was, 
during the limited time at the disposal of the Commission, entirely impracticable. 
A middle course was therefore adopted, and a construction of the apparatus decided 
upon which would be inexpensive, and at the same time throw the ray in a direction 
so nearly constant that the necessary adjustment would involve but little trouble. 
The general principle on which the apparatus should be constructed was prescribed 
by the Commission, and the details, including the entire clock-movement proper, were 
worked out by Messrs. Alvan Claek & Son, the makers. These details are shown in 
figures I, 2, and 3, A hollow iron pier. A, Fig. i, about 13 inches in diameter and 
10 feet long, is set firmly into the ground (and embedded in masonry when prac- 
ticable.) Surmounting this pier is a flange, B, on which is firmly screwed a bed-plate, 
C, I inch in thickness and 33 inches in length, from north to south. Its greatest width 
is about 16 inches, and it tapers towards each end, so as to have the shape of a coffin. 

Upon the northerly end of this coffin-shaped bed-plate rests a triangular-shaped 
base, D, which is supported upon three leveling-screws, by which it may be adjusted to 
the level. Firmly afiixed to it is a massive standard, E, through the upper end of 
which passes the movable horizontal axis, x, upon which the hollow cylindrical sheath, 
F, can revolve in a vertical plane. The sheath F may be clamped in any of its posi- 
tions by the nut a on the end of the axis x. 

Through the hollow cylinder F passes a second axis, ^, which at one end is 
grasped by the clamp, G, which may be clamped by the thumb-screw, ~h. These de- 
tails may be more clearly seen in Fig. 3. The lower end of the clamp G terminates 
in an arc of a circle, upon the edge of which is cut a female screw. An arm, M, clasps 
the cylinder F, which may be clamped and adjusted by the set screw h'. This arm 
supports the wheel W, by which the motion is communicated from the clock-work. On 
the axle of this wheel is a ball-joint working in a socket within the bearing s, on the 
lower end of arm M; the axle terminates in a screw, b, which works in the female 
screw on the edge of clamp G, being pressed upwards and retained in gear by the 
spring c. As the screw b merely rests against the clamp G, when the latter has moved 
to the end of the thread, it may be thrown out of gear by simply depressing the end 
of the screw, and the clamp G then moved back and reclamped. 

The left-hand end of the axis s terminates in a pair of jaws, R JS', about 9 inches 
apart in the clear (only one being shown in Fig. i); between which, hung on a short 
axis, y, is the circiilar frame J, within which is placed the reflector K. In Fig. i, 
the axis ,5' is inclined 30° to the horizon, and the frame J, shown edgewise, at the 
angle of 60°. In Fig. 3 the axis is level, and the frame inclined at au angle of 
45°, showing a portion of the reverse side of tlie reflector. One end of the arm d en- 
circles the axis, y, to which it may be clamped by the thumb-screw e, while the other 
end contains a ball-and-socket joint, d', through which passes the thumb-screw/, which 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



27 



also passes through another ball-and-socket joint, g, on the jaw H. By this arrange- 
ment the inclination of the reflector K to the axis z may be altered. 

It is thus seen that the reflector can be tm-ned upon three axes, one of ^vhich, 
however, does not pass centrally through it, viz : 

(i) The horizontal east and west axis x, by which the entire movable portion of 
the heliostat may be revolved in the plane of the meridian, and clamped at any angle. 

(2) The axis s in the plane of the meridian, but usually inclined to the horizon, 
and passing centrally through the reflector. This axis is intended to be adjusted by 
turning upon axis ( i ) at such an angle that the motion of the reflected ray shall be as 
small as possible during the observations. 

(3) The axis y in the plane of the reflector, at an arbitrary elevation, and at right 
angles to the axis s. 

As the elevation of the center of the reflector is altered by the revolution of the 
heliostat on the axis x, it may be readjusted to the proper level by the capstan-head 
screws supporting the plate D. The range of inclination required for the heliostat is so 
small that an adjustment may readily be made in this way. 

On the southerly end of the bed-plate C is attached by the screw I the standard 
L ; and to insure firmness, two projections from the standard enter the hollow cylin- 
ders C C", cast on the bed-plate C, the space between being filled with cement. To 
the face of this standard is screwed the cell 7, which holds the objective. These de- 
tails are omitted in Fig. 3 to avoid confusion, merely the outline of the standard L 
being partly shown in dotted lines. The centers of the reflector and objective should 
be adjusted to the same level. 

The clock-work, by which the heliostat is made to revolve on the axis z, is very 
simple. It is shown in Fig. 2, and consists of a box, iV, of thin sheet-iron screwed 
together ; from the top of which, suspended from a hook, is a conical pendulum, P, 
which can be adjusted or regulated by the usual screw on the lower end of the pendulum- 
bar. Under its point of suspension is a vertical shaft, 0, pivoted at its lower end and 
supported above by the column Q ; to its upper part is attached, by the two ends, a 
bent or doubled wire, 0, forming two guides, between which the lower end of the pen- 
dulum P may revolve in a horizontal circle. Upon the shaft are cut the threads of 
a screw, in which work the teeth of the gear-wheel B. The shaft of this wheel B 
passes outside of the box N, and bears on it a belt-wheel, W, from which motion is 
imparted to the wheel TF by a suitable cord or belt. On the same shaft is also a 
small gear-wheel, r, shown in dotted lines in the figure, working in the gear-wheel /, 
on the axis r". This axis r" also bears the ratchet s', engaging a pawl on the wheel 
r' and the barrel s", on which is wound, by a suitable wrench, the cord by which mo- 
tion is communicated from the weight T. 

The action of these various parts is readily seen by the figure ; the weight T im- 
parts motion to the wheel r', and thence to the wheel W of the heliostat, and also to 
the gear-wheel B within the box, causing the pendulum P to revolve, the centrifugal 
force generated throwing it out between the guides 0. When near the limit of its 
motion the end of the rod is caught in the curved arm q and canies it around a vertical 
axis with a slight friction, thus lessening the motion. 



28 TRANSIT OF VENUS, 1874. 

The wire g is centered on the shaft and can turn on it, but is not a part of the 
movable works. 

The box N is supported upon three levehng-screws, two under the corners of the 
side shown in the drawing and the third under the middle of the opposite side. A 
door in the back of the box gives access to the inside. 

The box iV^ rests upon a wooden tripod placed in the ground a few feet behind 
the heliostat. 

The photographic part of the heliograph is shown in Figs. 4 and 5. A hollow 
boiler-iron pillar, A', similar to that in Fig. i, but smaller, is planted in the ground, 
over which is built the photographic house. This pier is also provided with a flange, 
B', on which rests a circular plate, D', 16 inches in diameter, supported on three cap- 
stan-head leveling-screws. These screws pass through the flange, and are secured to 
the plate by three other screws passing through the latter and acting as pivots in the 
heads of the leveling-screws. The plate being of the same diameter as the flange, there 
are cast on the under side of the former four small lugs, which enter the interior of the 
flange when the leveling-screws are removed, and retain the two parts compactly 
together for convenience in transportation. Upon the plate D' rests another plate, S, 
cross-shaped, and secured to the former by four small screws, slotted so as to allow a 
slight east and west movement for adjustment. From the center of this latter plate S 
projects downward a hollow cylindrical axis or bearing, U, passing through a circular 
hole in the center of the plate D' and extending somewhat below the flange B'. Its 
use is to steady the photographic plate-holder V by means of an axis fitting closely 
within it, and in which the latter may revolve on a vertical axis. The weight of the 
plate-holder rests on the two long ends and middle of the cross-piece S; two small 
standards rise from the extreme ends of the latter, in each of which is a thumb-screw, 
i i', passing through a slot in the standard, and sci-^'ving into the base of the movable 
plate-holder, to clamp the latter in position. The slots permit the frame to have a 
slight motion around a vertical axis, so that the ruled plate can be adjusted normal to 
the line from the objective 

The plate-holder consists of a frame, v, the side towards the heliostat being shown 
in Fig. 4, in which is seen an opening, Jc, seven inches square, with a groove around it, 
in which is set a piece of plate-glass, m, accurately ruled with very fine horizontal 
and vertical lines one- half of an inch apart. The glass on which the negative of the 
sun's image is to be taken is placed in anothpr groove on the further side of the frame, 
and held there by the spring n. > «nirit >«vel, p, is screwed upon the top of the 
plate-holder frame, for adjusting thf* -ame t / i'ne level by means of the screws under 
plate -D'. The level is not shown in Fig. 5. 

The frame of the plate-holder, ihoiuding the axis on which it turns, lias a vertical 
opening bored centrally through it from top to bottom. Through this opening passes 
centrally a plumb-line of delicate silver or platinum wire, fastened at the top to a 
small plug fitted into the opening, and capable of being turned round in the openino- 
by the hand or pointer t. This wire passes between the ruled plate and the sensitized 
plate, and supports the bob w, immersed in a jar of water in the interior of the pier, 
accesible through an opening in the pier. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 29 

Thus, in every pliotogi'aph, an image of the vertical wire is formed on the plate. 
Lest there might be any curvature to the wire, the hand t is reversed from time to 
time to eliminate any constant error from this source. The mechanical operation of 
the plate-holder is very satisfactory. When adjusted to verticality, the screws i i' 
may be withdrawn and the whole plate-holder quickly turned round without any dis- 
turbance of the plumb-line. 

Regarding the permanent adjustments, it may be mentioned that the screws by 
which the bed-plate C is attached to the pier A pass through slots in the former, so 
that the distance between the heliostat and plate-holder may be regulated. The 
cross-piece 8, on which the plate-holder rests, may, as above noted, be moved later- 
ally by its slotted screws, and thus adjusted to the meridian of the heliostat ; while 
both may be raised or lowered on their leveling-screws. In this way both parts may 
be adjusted in a horizontal meridian line. 

In the use of the foregoing apparatus the transit instrument formed an essential 
part of it. The arrangement of the various parts was as follows : Supposing a station 
iti the northern hemisphere, the transit was the northernmost instrument. It was 
mounted in a small portable house upon a pier rising to a convenient height. 

Next toward the south was the stand containing the clock-work of the heliostat. 
The space between the clock-work and the transit-house was wide enough to admit 
of the convenient setting and use of an engineer's level, for the purpose of determining 
the level of the photo-heliograph in the manner subsequently described. 

Next was set the iron pier and plate carrying the heliostat and objective. These 
were not placed under a house, it being judged sufficient to inclose the apparatus in 
a water-proof covering whenever threatened by the weather. 

A space of nearly 40 feet then intervened between the photographic objective 
and the photographic house. The iron pier carrying the reticule and sensitive plate 
was set inside the latter, as near as practicable to its northern end, the pier extending 
some depth into the ground. A hole was made in the floor to admit of setting it. 
A space of about 1 2 inches was left between the pier and the northern end of the 
house to admit 6i convenience in manipulation. A round opening about 8 inches in 
diameter was made through the side of the hoase, at the proper level, to admit the 
image reflected through the objective. This was ordinarily closed by a wooden slide 
having in it a slit, the width of which could be adjusted to suit the intensity of the 
solar rays. It was movable back and forth by a pair of springs, so arranged that the 
motion necessary to admit the rays for an instant to the photographic plate could be 
made in either direction. 

As the apparatus was originally constructed, the photographic telescope was fur- 
nished with a tin tube in several sections, which could be extended from the photo- 
graphic house nearly to the objective. In its interior were set several blackened dia- 
phragms, having circular openings 5 or 6 inches in diameter to admit the rays. To 
protect this tube from the sun, a shed sloping both towards the east and the west was 
built over it. But it was finally decided that the entire tube was at least unnecessary 
and possibly prejudicial to the quality of the sun's image rather than beneficial. It 
was therefore dispensed with, except one or two sections next the photographic house, 



30 TRANSIT OF VENUS, 1874. 

which were retained as an obstacle against the admission of stray Hght when such 
light would have proved injurious. The shed, however, was retained for the double 
purpose of protecting the ground immediately under the axis from the sun's rays and 
of furnishing a support for the measuring-rod. 

The use of the apparatus required the accurate measurement of the distances be- 
tween the photographic plate, or the glass reticule, Fig. 4, and the photographic ob- 
jective. The design of an apparatus for this purpose, which should be in every respect 
staisfactory, was not free from difficulty. It shoiild be portable, and of such a character 
as to admit of being used under unfavorable circumstances and by persons not expert in 
measuring. The difficulties were increased by the necessity of measuring through 
the side of the photographic house and along the optical axis of the telescope. The 
following arrangement was at length decided upon : 

A straight rod, about 1 2 inches shorter than the distances to be measured, was 
made by screwing together pieces of i-inch gas-pipe, each about 5 feet in length. 
These pieces could be unscrewed and packed in a small box and put together at pleas- 
ure, so as to form a rod of definite length. The horizontal pieces of the frame-wort 
which covered the space between the heliostat and the side of the photographic house 
had notches cut in the upper part, in the same straight line in which the measuring- 
rod was to be laid. The latter, when in position, was horizontal and about 1 2 inches 
above the central axis of the photographic objective. The end nearest the photo- 
graphic plate passed through a hole in the photographic house only large enough to 
receive it. It was then completely out of the way and could remain permanently when 
once set. The inner end was about 6 inches outside the face of the reticule, and the 
outer end about the same distance from the vertical line above the photographic ob- 
jective. A fine brass plumb-line could then be suspended over each end of the rod, 
and the distance between these lines and the respective faces of the reticule and the 
objective were the only quantities remaining to be measured. 

These spaces were measured by a species of jaw-micrometer, designed by Professor 
Haekness. One end of this micrometer could be pressed against the face of the glass 
from which the measurement was to be made, and the other end, which cari'ied the 
jaw, brought into coincidence with the plumb-line. The jaw itself consisted of two 
projecting pieces about an inch apart, pierced horizontally, and in a direction at right 
angles to the line measured, with pin-holes. By looking through this pair of pin- 
holes, it could be seen when the plumb-line was in a straight line joining them, and 
between the two projecting pieces. The jaw could be moved through a space of 2 
inches by a rack movement, and the distance read off by a vernier. 

The distance between the two surfaces therefore consisted of three parts, namely, 
the length of the rod and the intervals between the plumb-line and the glass surface 
read off at each end of it. The entire space between the center of divergence of the 
objective and the sensitive plate is composed of the following parts : 

(i) From the center of divergence of the objective to its inner face. 

(2) From the inner face of the objective to the first face of the glass reticule, a 
distance measured in three parts, as just described. 

(3) The thickness of tlie glass reticula 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 31 

(4) 'The space between the second or ruled face of the reticule and the sensitive 
plate. 

The effective focal length made by all these parts is to be slightly diminished on 
account of the index of refraction of the reticule. 

§ 2. Adjustments op the Photo-heliograph. 

Besides the purely optical adjustments of the photo-heliograph, designed to se- 
cure a good image of the sun upon the plate, certain geometrical adjustments and 
determinations of errors are necessary in order that the relative positions of the two 
bodies might be determined from the measures of the photographs : 

1. In order that the relation of the vertical line on the photographic plate to the 
meridian shall be accurately known, it is necessary that the line of coUimation of the 
photogi'aphic telescope shall be horizontal and. in the meridian of the place ; or, at 
least, that its deviation from this direction be accurately known. The photo-helio- 
graph was therefore placed at the same elevation and in the same meridian as the 
transit instrument, in order that the middle vertical ruled line in the focus might be 
used as a meridian mark for the transit instrument. The Instructions required the 
transit instrument to be set on this mark every evening before the commencement of 
observations for time, so that the azimuth of the photographic telescope would be equal 
to either the sum or the difference of errors of azimuth and coUimation of the transit 
instrument. 

2. Tiie error of level of the photographic telescope could be obtained approxi- 
mately by pointing the transit instrument upon it and measuring the apparent zenith- 
distance of the middle horizontal line on the reticule plate. But as the vertical circle 
of the transit instrument read only to minutes, and the position angle had to be known 
within a few seconds of arc, this inethod was not sufficiently accurate. Each photo- 
heliograph was therefore furnished with an engineer's level as a part of its subsidiary 
apparatus. When the error of level of the photographic telescope was to be deter- 
mined, the transit instrument was pointed upon it, and the horizontal wire of the latter 
was set so as to cover accurately the center of the middle horizontal line of the reticule 
plate. The level error of the line of coUhnation of the photographic telescope would 
then be equal and opposite to that of the transit instrument, the one objective being 
too high when the other was too low. The engineer's level was then placed between 
the object glasses of the two instruments, and was pointed upon the horizontal line of 
the photographic telescope, and the reading of the level recorded. The level was 
then reversed, set upon the horizontal wire of the transit instrument, and the reading 
of its level again recorded. It is evident that if the photographic telescope were 
truly horizontal, the reading of the level should remain unaltered. If the level ad- 
justment is not perfect, the motion of the bubble will indicate twice the error of level. 
Several settings were generally made for each determination and the mean taken. 
There was thus no difficulty in determining the error of level within two or three 
seconds of arc. 

If the error of level was greater than half the distance which the engineer's level 
was calculated to measure, it is evident that this method could not be applied without 



32 TRANSIT- OF VENUS, 1874. 

some modification. In this case, when the telescope of the engineer's level was set 
on the middle horizontal line of the reticule-plate, its spirit-level was so adjusted that 
its bubble should be near the middle of the tube. It was then reversed and its stand 
adjusted so that its bubble should be brought into nearly the same position as before. 
The inclination of its line of coUimation would then be the same as when it was j 
pointed into the photographic telescope. The observer then returned to the transit 
instrument and determined how far it was necessary to move its horizontal wire in 
order that it should cover the image of the wire of the engineer's level. This distance 
would evidently be twice the error of level of the photographic telescope. 

3. The optical axis of the photographic objective should be directed to the center 
of the ruled plate. This was effected in the usual way by the observer standing in 
the photographic room and, holding a candle in his hand, noting the positions of the 
three images reflected by the surfaces of the objective. If these images coincided 
when the candle was held in fi:'ont of the center of the ruled plate, the adjustment was 
perfect. 

4. The reticule-plate was adjusted at right angles to the line of coUimation in the 
same way — or, still better, the observer mounted the engineer's level in the farther 
end of the photographic house, in the line of coUimation of the telescope, and then 
the plate-holder was turned until the reflected image of the center of the objective 
of the level was seen through the telescope on the same line with the photographic 
objective. 

5. The distance between the nearer surface of the photographic objective and 
the unruled surface of the reticule-plate was to be accurately measured from time to 
time. The method of doing this has already been described in connection with the 
description of the photographic apparatus. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. ^^ 

§ 3. Method of Investigating the Relation between the Apparent Positions of 
Venus and the Sun on the Celestial Sphere, and the Positions of their 
Images on the Photographic Plate. 

I. Let us first refer the relative positions of the bodies to a system of co-ordi- 
nates in which the axis of x passes from the station in the apparent direction of the 
sun ; the axis of 2/ to a point on the same meridian, 90° to the north ; and the axis of 
to the west, making a right angle with the other two axes. We suppose the direc- 
tion of the rays to be corrected for refraction by known formulae, so that the actual 
direction of the refracted ray, and not the real direction of the sun, is taken. The 
equations of a ray coming from the center of the sun and striking the center of the 
mirror will then be 

2/ zz o ; ^; — o. 

The equations of a ray, coming from a point of which the angular distance from 
the center of the sun. is s, and the angle of position counted from the sun's north point 
toward the east is p, will be 

y =.x tan s cos p 



. f (i) 

s =z — X tan s sm j9 5 

In these equations s and p may represent either the co-ordinates of a point on the 
sun's limb, or the co-ordinates of the center of Venus. In the former case s will not 
be constant, owing to the effect of refraction. 

2. Let us next refer the ray to a system of co-ordinates in which the axis of X 

shall be perpendicular to the face of the reflecting mirror, the latter being taken as 

the plane of Y Z, the positive side of which is that from which the ray is reflected. 

As before, we shall take the axis of Y in the same meridian with that of X, and 90° to 

the north ; and hence the axis of Z toward the west. Let us represent by a and d the 

right ascension and declination of the center of the sun, as affected by refraction, and 

by a' and d' those of the normal to the mirror, or of the new axis of X. Then, if we 

represent the new axes by accents, the values of the direction cosines will be 

a zz cos (X X') =z sin S sin S' -\- cos S cos S' cos (a — ac') 

b zz cos (Y X') zz cos d sin S' — sin S cos S' cos {a — a') 

c = cos (Z X') — cos S' sin (a — a') 

a' zz cos (X Y') ::: sin d cos S' — cos 6 sin d' cos (a — a') 
h' =GOS (YY') zzGOsS cos 6' -}-sm d sin S' cos {a— a') )■ • • (2) 
c' zz cos (Z Y') — — sin S' sin (a — a') 
a" zz cos (X Z') zz — cos S sin (a — a') 
b" = cos (Y Z') = + sin (^ sin (a — a') 
c" = cos (Z Z') = + cos (a — a') 

If for the moment we distinguish the co-ordinates referred to the new system of 
axes by accents, the relations for passing from the first system to the second will be 

x' ^ax + b «/ -{- Gz X ^ a, x' -\- a' y' -\- a." ^ 

y' = a'x -\-h'y -\-g'0 yzzhx' + h'y' + 'b"^} • • (3) 

s' zza"x-\-h"y-\-c" g zzzcx' -{■ c' y' -\- c" / 

S. Ex. 31 5 



34 TRANSIT OF VENUS, .874. 

If we now put for brevity, 

P = tan s cos p t 

y^ — tan 5 sin ^ 5 

the equations (i) for the course of the ray, by substituting the last values of a;, y, and 
z will take the form 

(a /? - b) a;' + (a' /3 - b') y' + (a" y5 - b") / = 
(a J/ — c) a;' + (a' y — c') y" + (a" y — c") s' = 

3. The ray is now reflected from the surface of Y Z, and this reflection being 
supposed to take place at the origin, it is evident that its effect will be simply to 
change the algebraic sign of the value of the co-ordinate x', which corresponds to given 
values of y' and 2'. The equations of the reflected ray may therefore be put into the 
form 

(a' yff - c') «/' + (a" yS - b") ^' - (a A - b) a;' zz o ^ 

(a' y — c') y' + (a" y — c") / — (a y — c) a;' = o J ' ' 



(5) 



The equations for the particular ray which emanates from the sun's center are 
given by putting both /? and y equal to zero, an4 are, therefore, 

b' y' + b" z' -h^\ , . 

c' 2/' + c" y = c a;' i ^ • 

4. Now, let us take a third system of co-ordinates in which the course of this ray 
shall be the axis of X, that of Y being, as before, in 90° greater declination, and that 
of Z on the equator in 90° less right ascension. If we distinguish the co-ordinates 
referred to this system by two accents, we shall have for the course of the central 
reflected ray. 



z"-o) 



(7) 



If we represent by a, h, c, &c., the direction cosines for passing from the second 
to the third system of co-ordinates, we have 

x' = ax" -\-a'y" -\-a" z" x" = ax' -\-ly' +c/ ) 

y' = 1 x" + h' y" + h" z" y" = a' x' -{-V y' + d z' \ . . (8) 

/ -cx" + c' y" -\- c" z" z" = a" x' + h" y' + c" z' ) 

Comparing (6), (7), and the last two equations of (8), we see that every system 
of values of x', y', and /, which fulfills the two conditions 

-hx' + h'y' + h" z' = o 
— cx' + c'y'-i- g" z' — o 
must also make 

a' x' + b' y' +c' z' = o 

a"x' + b"y' + c"z'=o 

and vice versa. Hence each equation of one set must be derivable from the other set 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 35 

by a linear transformation. If we call h, h', k and k' the coefficients for transforming 
the first set into the second, we shall have 

a' ^ — lih — /^' c a" =. — kh — Jc' c ^ 

b'= hh'+h'c' y- A;b'+A;'c'S . . (9) 

c' - h h" + h' c" c" = kh" + kf c" ) 

If we take the sum of the squares of the first set of equations (9), we find 
a'^ + h'^ + c'^ - h' (b= + b'= + h'") + h'^ (c= + c'^ + c"=) + 2hh' (hc + h' g' + b" c") 
which, by the known properties of the direction cosines, reduces to 

}i'-\-h''= I. 
' Taking the second set of equations (9), we find by the same process, 

t + k''= I. 

If we take the sum of the three products formed by multiplying each equation 
of the first set by the corresponding one of the second, we find 

a' a''+h'b''+c' c''=hk(h'+h''+h''')+h'k' (G'+G''+G''')-\-{hkf+h'k){hG-]-h' c'+h" g''), 

which, by the known properties of the direction cosines, reduces to 

hk + Ji' k' = 0. 

We thus have three equations between the four quantities h, h', k, k' , showing 
that they may all be expressed as a function of a single quantity A, as follows : 

hzzi — cos A A' — sin A 

k-=z — sin A k' ^ — cos A 

These values being substituted in (9) give 

a' =. b cos A — c sin A a" = + b sin A + c cos A 

&' = — b' cos A + c' sin A &" = — b' sin A — c' cos A ^ • • (10) 

c' = — b" cos A + g" sin A c" = — h" sin A — c" cos A 

These equations give, at once, 

a'= + fl"^ = b^ +c= 
b'^ + b"' = b'= -r g'^ 
c'^ + c"' z= h"' + c"= 

from which, by subtracting from the equations 

a" + a" + a'" zz i = a' + b' + c^ etc., 
we find 

:.i .... 



a' = si' 


a = 


a 


¥ = a'^ 


b-- 


-a 


c^ z= a'" 


Czr - 


- a 



s 



(II) 



The reasons for thus choosing the .algebraic signs of a, a', and a" will appear 
presently. 



36 TRANSIT OF VENUS, 1874. 

5. Now let ixs return to equations (5). By substituting for «', 2/', and /, in the 
first of these equations, their values in (8), we shall have the equations of any reflected 
ray referred to the reflected course of the central ray as the axis of X. The first of 
(5) thus becomes 

K—aa + a'b + a"c )A + ba —h'h — b"c } x" ) 
+ |(_aa' +a'6' + a'V ) /? + b a' -b'&' - b'V \ 1/' > • • (^2) 
+ j (_ a a" + a'b" + a"c") /? + b «" - b' b" - h"c" }^" = o) 

and the second is formed from the first by changing /3 into y and b, b', b" into c, c', c". 

By (7) when yS — o and y =z o, we must have y" — o and s" r= o for all values of 

x". Hence the coefficient of x" must vanish in this case, which requires that we have 

ha-h'b-h"c = o (13) 

It is evident from the fact that the normal to the rnirror, or the axis of X', bisects 
the respective courses of the direct and reflected central ray, or the axes of x and x", 
that we have — 

cos (X, X') = cos (X', X") 
or, a rr a 

which is the first equation (11), and by substituting the remaining equations (11) in 
(13) we see that the latter can be satisfied only by the algebraic signs adopted in the 
former. With these signs (13) becomes 

a & + a'b' + a"b" = o 

which is true by the property of the direction cosines. 

If we now substitute in (12) the values of a, b, c, a', V, c', a", b", c", given in (10) 
and (11), we find 

cos A y" + sin A/' =/3 x" 
— sin A y" + cos As" =zy x" 

If we eliminate, first s", and then y", from those equations, we find the equations 
of the reflected ray in the usual form to be 

y" = (/3 cos A — y sin A) x" 
z" — {13 sin A + y cos A) «" 

If we substitute for /? and y their values in (4) the equations will become 

y" zz x" tan s cos (A — j;) ') 

s" =x" tanssin Ia—p)1 (^4) 

6. The next step is to determine the value of A, which depends on the relation 
of the second and third systems of co-ordinates, but which can be more conveniently 
made to depend on the position of the first and third systems, and, indeed, on the 
direction of the sun and that in which the reflected rays of the sun are thrown. In 
the preceding suction we have made no supposition respecting the direction in which 
the axes of Y" and Z" are taken, and A depends solely on this direction. We are 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



2,7 



then to find its value when we suppose the axis of Y" to be on the same meridian 
with that of X", and since this value is independent of j), we can most conveniently 
find it by supposing p =: o, and finding the values of y" and z" which correspond to 
that supposition. Let us consider the two spherical triangles S M P and S' M P', the 
angles of which are on the following points of the celestial sphere: 

S, the sun, in the direction, R. A. rz a, Dec. = S. 

P, a point nortli of the sun at the arbitrary distance s, for which pz=:o. 

M, the normal to the mirror. 

S', P', the reflected directions of the rays from S and P. 

By the laws of reflection, the angles B M and P M are equal, respectively, to 
M S' and M P', and the angle S M P is equal to S' M P' ; the two triangles are there- 
fore equal in all their parts, and the angle M S' P' is equal to M S P. 

Consider next the spherical triangle formed by the north pole O, and the points 
S and S'. The given parts of this triangle are — 

O8 = go°-S OB' = 90° -6" S O S' = a" - a 

where a." and d" are the R. A. and Dec. of the point toward which the reflected central 
ray is thrown. The co-ordinates y" and z" of any point on the line P' are given by 
the equations 

y" = x" tan s cos S' F 
/' - x" tan s sin S' F 

which, compared with (14) for the case of ^ rr:o, shows that we have 

A = S' P' 

By the properties of the triangles already shown we have 

S' F = S' S + M S' P' = S' S + S S' 

That is, S' P' is the sum of the angles which the great circle S S' makes with the 
meridians at the points S S'. This sum is given at once by one of Napier's Analogies, 
from which we have 

cos5(OS'-OS) 

tan ^ S' P' = "- cot ^ S S' 

cosj(OS' + OS) ' 

By substituting for the arcs their expression in terms of d, 6" a, and a", this 
expression becomes 

cos I (d - 6") 
tan^Am- „„ cot-K-flf) .... (15) 

sm - (5 + (5 ) 

from which we obtain A. 

7, If the axis of the photographic telescope were exactly in the meridian, and if the 
image of the reflected central ray coincided with this axis, the equations (14) would at 
once give us the means of finding the position of any required point on the photographic 
plate. But, as such coincidence should not be supposed, let us take a fourth system of 



38 TRANSIT OF VENUS, 1874. 

rectangular co-ordinates, the axis of X being- the central axis of the photographic tele- 
scope, which we shall suppose to intersect the photographic plate at its center. The 
plane of X Y will be assumed as vertical, while that of Y Z will be parallel to the 
photographic plate. We shall suppose the positive direction of the axis of X to be 
from the objective to the focus ; that of Y to be 90° north of that of X, and that of 
Z to be, as usual, such that an observer, looking from the positive direction of Z on 
the plane of X Y, would see a rotation of the axis of Y through 90° into the position 
of the axis of X to take place in the direction of the hands of a watch. 

In finding the directions of these axes relative to those of the preceding system, 
we shall take advantage of the circumstance that both the axis of X and that of X" 
are very nearly horizontal and in the meridian. Let us then suppose the axis of X, 
as just defined, that is, the central axis of the telescope, to deviate from the meridian 
towards the axis of Z by the small angle of azimuth a, and to deviate from the hori- 
zontal line in the direction of Y by the small quantity h. These deviations will make an 
elevation of the center of the plate correspond to a positive value of b in the Northern 
Hemisphere and to a negative value in the Southern Hemisphere, while a deviation 
of this center west of the meridian of the objective will be positive in both hemispheres. 
Moreover, let S^ be the declination of the true horizon on that meridian toward which 
the reflector throws the sun's rays (south in the Northern Hemisphere, north in the 
Southern one) so that we have 

For the Northern Hemisphere §„ =: N. Lat. — 90° 
For the Southern Hemisphere S^ ziz 90° — S. Lat. 

Also, let ^o he the E. A. of the meridian. Now, reasoning as for the Northern 
Hemisphere, and neglecting quantities of the second order with respect to a and h, the 
axis of Y will point north of the zenith by the quantity h, while that of Z will point 
north of the west horizon in the Northern Hemisphere (or north of east in the Southern 
Hemisphere) by the quantity a. It is easy to see that, if we suppose the quantities 
a and b so small that we may regard their cosines as unity, the right ascensions and 
declinations of the points toward which the respective axes of X, Y, Z are directed 
will be 

'Ka=: a^ — a sec d^ X (5 — ^o -|- & 

Ya-a, YS = 6„-\-go° -\-b 

Za = a„ — 90° — a cos S„ ZS = — a sin 6^ 

The same formulae really hold true for the case of the Southern Hemisphere. 
The formulae will indeed give for Y (J a value exceeding 90°, but this will simply 
throw the point beyond the north pole to the point 

R.A. rr a„+ 180° i 

Dec. =go°-(S^ {-b)\ ('^) 

The direction of the axis of X" relative to that of X is to be deduced from the 
position of the sun's center on the photographic plate. If we represent the azimuthal 
deviation of this center from the centre of the plate in the direction of the axis of Z, 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 39 

reduced to arc, by a', and its angular height above the plate [or below it in the 
Southern Hemisphere] by V, the azimuth and error of level of the axis of X" will be 



a" zzia + a' y ^ ^ 



The right ascensions and declinations of the three axes on the celestial sphere 
will be, from the definitions already given, taking a" and h" so small that we may 
suppose their cosines unity : 

X" a- a,- a" sec d, X" d = d^ + V' ) 

Y" « - «„ - a" sec (^o Y" 8 = d^ + go° + h" \ . .(18) 

Z" a = a, — go°- a" sec S„ Z"S = o ) 

Each of the direction cosines is now given by an expression of the form 

sin S sin S" -\- cos S cos d" cos (a — a") 

where, for a, S, a" and S" are to be substituted the right ascensions and declinations 
of the points toward which the several axes are directed, as given above. 

By substituting the respective values of S and S" just given, and regarding a, b, 
a", and b" as quantities so small that we may put 

sin azr a cos a rz i, &c. 

the values of the direction cosines are found as follows : 

cos(XX") = i 

cos (X Y") - sin {d^ + b) sin {d„ + b" + 90°) 

+ cos ((^o + b) cos {S^ + b" 4- 90°) cos [(a — a") sec d^ 

Owing to the minuteness of a and a" we put cos [(a — a") sec S^^i, which 
reduces the last expression to 

cos ((J„ + & - (J„ - b" - 90°) = cos (&' + 90°) - - sin &' = - V 

In the same way the remaining cosines are found to be as follows : 

cos (X Z") = -a' >j 

cos(YX") = 6' 
cos (Y Y") = I 

cos (Y Z") = a" tan (y„ j> (19) 

cos (Z X") = a' 

cos (Z Y") = — a" tan So 

cos (Z Z") = I 

These formulae are true for both hemispheres. The relations between the co- 
ordinates, as referred to these two systems, are therefore 

x" z^ X -\- b' 1/ -\- a' 2 ^ 

y" z=. — y x-\-y — a" tan S^s\ (20) 

/' — — a' a; + <«" tan S^y -\- zi 



40 TRANSIT OF VENUS, 1874. 



To find the equations of a reflected ray, these values are to be substituted in 
equations (14), in which we shall put for brevity 

/?o = tan s cos (A — J?) i 

Xo = tan s sin (A — j9) 5 ^ ' 

thus making the equations of the ray 

y"-^,x", or y" -/3,x" = o 
/' — Yo x", or z" — y„ x" — o 

Substituting these expressions for y", s", and xf' in equations (20), and then solv- 
ing the linear equations in y, z, and x thus formed, we find expressions for 2 and y in 
terms of x. In solving these equations we regard a, a' , b, h', a", y„, /?„, as small quan- 
tities of which we may neglect all terms of the second order when multiplied by y or 
z, and all terms of the third order when multiplied by x. To find the probable mag- 
nitude of the errors thus produced, we remark that the quantities y^ and /?„ are, at the 
most, equal to the sun's semi-diameter expressed in arc, or to .0047, while in the pho- 
tographs taken by the parties the center of the sun was so near the center of the plate 
that a', V , 8,nd a" were generally less than 6', or .0017. The maximum value of ^^ 
or of Yo would therefore be .000,0001. But the terms multiplied by x and actually 
neglected do not contain the third power of /?„ or y^ as a factor, the largest being of 
the form 

^ 2/ = «" Ao 2/ 
so that we have, in general, for the limit of error of y or 2, 

J y or J <C. .000,007 y- 

The value of «/ itself will generally be less than iioo", hence we shall have, in 
general, 

-dy < o".oo8 

a quantity considerably smaller than the extreme limit of accuracy which we can hope 
to obtain in the measurement of a photograph. The equations of the ray, which we 
thus obtain, referred to the axis of the telescope, are as follows : 

y={^, + b' + (7„ + a') a" tan S„] x ^ 
0={y^-\-a'-{^„+b')a"Und,}xl ■ ■ ■ ■ (22) 

8. By what precedes, we have found expressions for the equations of a ray ema- 
nating from any assumed point of the sun's disc, and reflected from the mirror, referred 
to the axis of the photographic telescope, and a vertical plane passing through that 
axis. But our equations give only the direction of reflection from the mirror, and do 
not follow the ray through the object-glass. Moreover, the equations strictly apply 
only to a ray reflected from the center of the mirror, or from the point which lies on 
the prolongation of the axis of the telescope. But, since all the rays which emanate from 
the same point are considered as parallel, both before and after reflection from the 
mirror, which is supposed to be plane, it follows that the general equation of the rays 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 41 

emanatitig from an assumed point of the sun's disk will be found by simply adding 
arbitrary quantities y^ and s^ to the equations (21). That is, if we put, for brevity, 

/?. zz /?„ + &' + (x„ + a') a" tan d, 
r, = y„ + a'- (/?„ + V) a" tan d, 

the general equations of the rays, after reflection from the mirror and befAre strik- 
ing the objective, wiU be. 

Now, Gauss, in his Dioptrische Untersuchungen, §§ 1-4, has shown that all such 
rays having common values of /?, and y^ will come to a common focus at a point whose 
co-ordinates depend on /?i and y^ and on the curvatures and refractive indices of the 
lenses. A clear idea of the essential features of Gauss's theory may be found in the 
following way : Let us consider all the parallel rays which, emanating from a com- 
mon direction. A, strike the objective or other combination of lenses. After passing 
through the combination there will be one ray, and one only, which will emerge par- 
allel to its original direction, A. Let us call it the central ray, and conceive of it as 
isolated from all the other rays. We shall then have a single ray corresponding to 
the direction A, which we may call the central ray A. Then, by the theory of Gauss, 
supposing A to vary, all the central rays which strike the combination from various 
directions converge toward a certain fixed point, and after leaving it they diverge from 
another fixed point. These two points Gauss calls " Haupt Punkte," and it is on them 
alone that the magnitude of the focal image depends. A clearer idea of thei^ proper- 
ties may be afforded if we call the first of these points the center of convergence and 
the second the center of divergence. In fact, it is evident that if all the rays from a 
point meet the central ray in another point, or focus, the image of the point will lie on 
the line of the central ray. The linear distance of the images of two points will then 
be proportional to the distance of the focal plane from the center of divergence. If 
the condition that all rays emanating from a distant point converge to the same focus 
is not rigorously fulfilled, yet, if the central ray occupies a mean position among them, 
the same thing will hold true, the distance of the mean images being proportional to 
the distance from the center of divergence to the plane on which they are formed. 

9. We have next to consider the positions of Venus relative to the outline of the 
solar limb, as they appear on the photographic plate. For the center of the sun, /?„ and 
7o both vanish; the co-ordinates of the point on the photographic plate which corre- 
sponds to the center of the sun are therefore found from (22) by putting y6'„ — o; 
7o =: o. Representing the Gaussian co-ordinates 7* 5*, which correspond to this point 

by 7o and ^0, we find, 

77„rz(&'-l-a'a"tan5„)/) 

/ being the focal length, while the general co-ordinates corresponding to the point 
whose angular distance from the sun's center is s and position-angle p are 

V-(^o+i' + {ro + «') a" tan d,)f} 



^ = (X„ -j- a' -(/?o + &')«" tan (5„)/S • • • (^4) 



S. Ex. 31- 



42 



TRANSIT OF VENUS, 1874. 



(25) 



If we represent the co-ordinates relative to the sun's center by 7, and <?„ we have 
from (23) and (24) 

7i = 7 — 7o = (/?o + Vo a" tan S„)f) 
^1 = «? - 5c, = (Xo - /?o «" tan do) / ^ 

Taking the sum of the squares of these quantities, substituting for /?„ and y^ 
their values (21), and neglecting the factors of the fourth order, y a"'', we have, for 
the distance of the general point from the sun's center, 

p r: V 7' + 5' = V /?o' + 7o'/=/tan s] .... (26) 

which shows that the projection of the image of the sun, the sun itself being supposed 
circular, may be regarded as a circle drawn round the projection of the sun's center as 
a center. Indeed, it is easy to see, by geometrical construction, that the variations in 
the radius of the projected image will be of' the order of magnitude of /3^^ of' f, which 
we have neglected throughout. 

If we denote by 00 the angle of position on the photographic plate, reckoned from 
the sun's center, putting 



we have for the position-angle co, 



?/l = p cos CO 

^1=. — p sin CO 



. <?! _ Vo — Ao a" tan d„ 

tan coz=i — — ;5 — I 77-7 s- 

Vi Ao + Xo « tan <Jo 

which, being compared with (21), shows that, neglecting quantities of the fourth or- 
der, we have 

co=zp — A-f-a" tan (^ol (27) 

It will be seen that the quantities a, h, a', and h' do not individually appear in the 
expression for the relative co-ordinates of Venus and the sun. 

10. We now reduce the formulae already found to a form for computing the angle 
of position and distance of Venus from the sun's center, from the measures on the 
photographic plate. It is assumed that the photographic 
telescope is so near the meridian, and so nearly horizon- 
tal, that the deviation of the reflected central ray from 
the sun's center, from a horizontal meridian line (the arc 
O S' in the figure), does not in general exceed 6' of arc. 

The figure is supposed to represent the photographic 
plate as seen from the objective, the line Y to repre- 
sent the true meridian and therefore to be vertical, and 
Z to be truly horizontal and on a level with the optical 
center of the objective. For the southern hemisphere, 
the figure must be turned upside down, so that the positive axis of Y shall point down- 
ward, and that of Z to the left. It is assumed that, by a suitable micrometer, the 
co-ordinates of the center of Venus or of V, relative to the center of the sun, or of S', 
are determined with all possible accuracy, so that we know the distance S' V, which 




DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS.' 43 

we call p, in millimeters or other linear measure, and the angle which the line S' V 
makes with the vertical line Y, which angle, counted in the direction of the hands 
of a watch, from Y toward Z, we represent by cd. If the actual ruled lines on 
the plate are not truly horizontal and vertical, the value of co must be corrected for 
their inclination, and if the plate has no fiducial lines exactly in the meridian, the azi- 
muth and elevation of the sun's center must be corrected for the azimuth and elevation 
of the fiducial lines, so that we shall know the azimuth a" and the elevation h" to the 
nearest tenth of a minute of arc for each picture. It is also assumed that the distance 
from the center of divergence of the objective, or, if the mirror has any curvature, 
the distance from the mean optical center of the combination of mirror and objective, 
to the center of the photographic plate, is known in the same linear measure with 
which S' V is determined. This distance is called / We also put 

^0, the declination of the horizon toward which the sun's rays are reflected ; 

H, d, the apparent hour angle (west) and declination of the sun's center, as seen from 
the station, affected by parallax and refraction, to the nearest tenth of a minute 
of arc. These quantities may be computed by correcting the local mean time 
by the equation of time and then applying parallax and refraction in R. A. and 
Dec. The quantities 

are thus assumed to be known. Now compute 

6" = (5o + h" 

, cos ^ ((J -5") 

tan - A - . cot ; (H - a" sec 6^) .... (28) 

sm - ((5 + (J ) 

^ r= A + GJ — a" tan d„ (29) 

p is the angle of position of Venus relative to the sun's center and the north point of 
his limb, as it appears from the station. It must be next corrected for the relative 
refraction of Venus and the sun. 

The apparent angular distance of the centers of Venus and the sun is given by 
the equation 

tans=i^ (30) 

It is also to be corrected for relative refraction. 

1 1. Instead of taking the right ascension and dechnation of the sun as our funda- 
mental quantities, we might equally well have used altitudes and azimuths. The 
actual formulse to be finally employed in the computation would have been substan- 
tially the same, except that in computing A we should have put the sun's altitude in 
place of S and its azimuth in place of H — a" sec S^. The value of p would then 
have been referred, not to the meridian passing through the sun, but to the vertical 
circle passing through it. 



44 TRANSIT OF VENUS, 1874. 

§ 4. Corrections of the observed Position of Venus on account of Refraction. 

In the preceding investigation we have supposed the position of the sun, as seen 
from the station, at the moment of taking the photo^aph, to be affected by refraction, 
and we have shown how, when this position is computed, we may deduce, from the 
measures on the photographic plate, the position-angle and distance of the center of 
Venus, reckoned from that of the sun, as they must have appeared at the station. These 
relative co-ordinates are now to be corrected for refraction in order that we may 
obtain their values free from refraction. It is first to be remarked that what we really 
obtain from the measures on the plate is not the position of Venus i-elative to the true 
center of the sun considered as a point, but relative to a number of points on the sun's 
limb, from which the position relative to the center is to be deduced. We have, there- 
fore, to inquire into the effects of refraction upon the relative position of the sun's 
center and any point upon its limb — a problem which is nearly identical with that 
of determining the effect of the same cause upon the relative positions of the centers 
of the sun and Venus. This problem will be treated after the manner of Bessel, 
except that, instead of the angle which the middle point of the line joining the two 
centres makes with the meridian or the vertical circle, we shall consider the angle at 
the center of the sun, and shall put the results into a form more convenient for our 
present purpose. 

I. The quantities on which the various effects of refraction depend, such as the 
zenith distance and semi-diameter of the sun, and the parallactic angle, are to be com- 
puted from the tables. They are, in general, only required to be accurate to tenths 
of minutes ; it is therefore indifferent what tables we *use in the computation. Let 
us put 

8,, the zenith distance of the sun's center ; 
p, the change of 8, due to refraction ; 

g', the parallactic angle corresponding to the sun's center ; or the angle of posi- 
tion of the sun's vertex counted from his north point toward the left ; 
s, the angular distance of Venus, or of any point on the sun's limb, from the 

sun's center. We may call this simply "the point" ; 
V, the angle of position of the point, referred to the sun's center, and counted 

from the vertex toward the left ; 
R, the angle between the vertical circles drawn through the sun's center, and 

through the point, respectively ; 
H, the west hour angle as seen from the station. 

The values of <?, p, &c., which refer to Venus or the second point, will be dis- 
tinguished by a subscript index, or. as 5„ p„ &c. V, is the angle which the great 
circle from the sun's center through the point makes with the vertical circle through 
the point. 

Where it is necessary to distinguish between the values of the above quantities, 
as affected by refraction and as freed from it, we shall use two accents to mark those 
quantities which are affected by refraction. The unaccented quantities will therefore 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



45 



be those computed from the tables without refraction, while ^", g*", &c., will be the 
apparent values of the corresponding quantities affected by refraction. 

We shall, when necessary, designate by a single accent mean values between 
those affected by and freed from refraction. 

2. The relations which connect the quantities S, V, and V^ with ^, <?i, and R, 
are 

cos s = COS <? cos <?, + sin 5 sin 5, cos R \ 
sin s sin V = sin R sin S^ j 

sin s cos V =: sin 5 cos 5, — cos 5 sin 5^ cos R> . . (31) 
sin s sin V, zz sin R sin 5 V 

sin s cos Vj zm cos 5 sin ^^ — sin § cos 5, cos R/ 

We may consider the same relations to hold tme when s, V, <?, and 5, are affected 
with accents. 

If we differentiate the first of these equations with respect to <? and <?„ and then 
substitute in the second member the values of ^ <?i, etc., from the other equations, we 
find 

dszr. cos Y d ^ — cos V, d 5, 

If we represent by the symbol S the corrections to be applied to the refracted 
values of the various quantities to obtain the true values, we shall have, with all neces- 
sary accuracy, 

(Js = cos V 5^ — cos V/ (5 5, (32) 

If we put ^ to represent the difference between the quantities referring to Venu.3 
and those referring to the sun's center, we shall have, 

and thus we shall have 

S s — p (cos V — cos V/) — ^ p cos V/ . . . , {2)2>) 

Th6 greatest zenith distance at which the sun was advantageously photographed 
during the late transit is probably less than 79°. We shall then have, in round num- 
bers, 

Max.,p =300" 

Max. J p = 6" 

Therefore, to obtain S s to the accuracy of o".oi, we shall require cos V — cos V, 
to o'.i and V, to 5'. From the equation 

cos V, z= cos R cos V — sin R sin V cos <? 
we obtain 

cos V — cos V. = 2 sin' - R cos V + sin R sin V cos 5. 

2 ' 

The maximum value of 2 sin^ - R cos V for zenith distances exceeding 60° is less 



46 TRANSIT OF VENUS, 1874. 

than .00001 ; its product by p may therefore be entirely neglected, unless the sun is 
in the immediate neighborhood of the zenith. We may therefore put 

cos V — cos Vj = sin R sin V cos <? 

sin s sin° V cos <? 

~ sin 5, 

since the spherical triangle of which the sides are s, 5, and 5. gives 

sin R _ sin V 

sin s ~ sin (?i 

cos Si 
The maximum value of p sin s being little more than i", the factor —. — ^ need 

be true only to its hundredth part. We may therefore put 

<?, = <? — sin s cos V 
From this we obtain, by developing tO' quantities of the first order in s, 

I _ I + sin 5 cos V cot ^ 
sin <?i sin ^ 

which, being substituted in the preceding value of cos V — cos V„ gives 

cos V — cos Vi ■=. sin s sin" V cot 5 (i + sin s cos V cot ^) 

an expression in which the last factor may be put equal to unity for all zenith dis- 
tances greater than 45°. 

These same equations will hold substantially true if we affect all the quantities 
which enter into them by one or two accents. We have therefore, for the first term 
of (J s in (33), 

p (cos V — cos V/) = p sin s' sin" V cot -S' (i + sin s' cos V cot 5') . (34) 

Passing now to the second term, we remark that the value of the expression 

J p (cos V — cos VJ 

is always less than o".oo2 at all zenith distances at which the sun was photographed 
during the transit of Venus. We may therefore put ^ p cos V, instead oi J p cos V„ 
in the second term of d s. We have now to find J p from the refraction, tables as a 
function of the zenith distance. This value can be readily expressed in the form 

^/> = p {«.(.?.-.?) +*^.(^.-<?)1 , (35) 

where n^ and n^ may, with all necessary accuracy, be regarded as a function of the 
zenith distance simply, and tabulated as such. Moreover, the values of n^ and n^ can 
be so chosen that § may represent either ^, 5' or 5". 
We have, to terms of the second order in s, 

^^ — ^ = — s cos V + - 5 sin s cot <? sin' V 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



47 



The second term may be omitted entirely since, at the zenith distance of 80°, it 
only amounts to about o".5. Substituting the first term in the expression for J p, we 
find 

— z//) cos V zz s p {w, cos° V — »^2 sins cos^ V} . . . {2)^) 

The sum of (34) and (36) will be the total correction for refraction in distance. 
We can reduce it to a more convenient form after we find the corresponding correction 
to the angle V. 

3. If we differentiate the second and third of the equations (31), we find 

sin s cos V c? V + cos s sin V (? s r= sin R cos 5^ d <?, 
— sin s sin Y dY -\- cos s cos Y dszz. cos a d ^ 

— (sin ^ sin ^^ + cos <? cos 5, cos R) d <?i. 

Multiplying the first of these equations by cos V, and the second by — sin V, 
and adding, noticing also that 

sin R cos V + cos R sin V cos ^ z=. sin V, cos ^, 
sin V sin ^ ■=. sin V, sin ^, 

we find 

sin s rf V zr — cos s sin V (? <? + sin V, d ^, 

Putting, as before, the refractions for the diffierentials of the zenith distances, we 
have, with all necessary accuracy, 

sin s' 6Yz=ip (sin V/ — cos s' sin V ) + ^ p sin V/ 

From the fundamental formulas of spherical trigonometry, we have 

cos s sin V, := cos R sin V + sin R cos V cos ^ 
and thence 

sin V/ — cos s' sin V z=z (cos R sec s' — cos s') sin V + sin R cos V sec s' cos <§' 

For considerable zenith distances, the first term of the second member of this equa- 
tion will never amount to .00002 ; its product by p may therefore be neglected. The 
second term may be reduced to 

tan s' sin V/ cos Y' cot 5' 

For zenith distances exceeding 60°, the value of sin V — sin V, will never exceed 
.001 ; we may therefore put V for V/ in the last expression, from which the first term 
in the above value of sin s' d Y will become 

p tan s' sin V cos V cot ^ 
For the same reason as in the case of S s we may put V for V/ in the second 



48 TRANSIT OF VENUS, 1874. 

term of sin s' d V, so that we shall have, by substituting the value of ^ p already- 
found, reducing and neglecting the difference between sin s and tan s 

sin s' SY := p \ sin s' sin V cos V cot ^' ^ 

— sin s' (»/ cos V sin V —n'^ cos^ Y' sin V) > . (37) 
(J V = /) sin V {cos V cot ^' — n,' cos V + nj s cos' V'} ) 

In the case of (J V it is a matter of indifference whether we express it as a func- 
tion of the unaccented quantities or of either of the accented ones, and the same 
remark will apply to ^ s when s represents the angular distance of the centers of the 
Sun and Venus. But in the case of the Sun's angular radius it will be more con- 
venient to have a constant s for the various measures than one varying with each 
measure ; we miist therefore express 6 s for this particular case as a function of « 
unaccented. Putting s for sin s, and supposing, also, that we take n^ and % as func- 
tions of the singly accented zenith distances, the value of d s, as we have found it from 
the sum of (32) and (33), in the preceding section, will be 

6s = ps' {n\ cos= y + cot 5' sin= V + s' cos V (cot= S' sin^ V — n', cos= V) | . (38) 

To express this in terms of s we have only to put s S s for s' in the second 

member of the equation, while for the latter value of (J s it will be sufficient to suppose 

-ds=z-psn\ cos'' V 
2 2 

This being substituted in the expression for s' outside the parenthesis, the terms 
added to d s will be 

— -SsXP'h'. cos' V = — -p''s n'; cos V 
2 2 

Owing to the minuteness of the terms multiplied by s'' it will be indifferent 
whether we use s or s' inside the parenthesis ; the total expressions for d s will there- 
fore be 

6s = psln\ cos' V + cot <?' sin^ V' — - p n\' cos* V ) 

> ■ (39) 
+ s cos V (cot' <? sin' V — n'^ cos' V) } ) 

4. In measuring the photographs, the measures are always made along two nearly 
opposite radii ; the position of the sun's center will depend solely upon the difference 
of the radii and the sun's diameter upon the sum. Since the former quantity is the 
important one in the determination of the position of Venus upon the sun's face, while 
the latter is entirely subordinate, it will be better to obtain the sum and difference of 
S s for two opposite, points. Let us then suppose 

Y' = a; V' = a+i8o° 

to be two opposite values of V to be substituted in the expression for S s, and let us 
represent by S s^ and S s^ the corresponding values of 6 s. We find 

- (d s, — d s^) = p s' COS a (cot' <§' sin' a — n'^ cos' a) 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 49 

The values of p and s° are, approximately, 

p rz 60" tan S\ 
s^ — .00002 

giving for the approximate value of the first term of the expression sought 

o".ooi2 cot <? cos a sin^ a, 

which may be entirely neglected. The value of the expression for the displacement 
of the sun's center reduces to 

- (5 Sj — d s^) := — p n'^ s° cos^ a 

For the correction of the semi-diameter, or of half the measured diameter, we 
have 

- (^ s^ -\- S s^) z= p s {n' r cos,'' a -^ cot S' siii' (X' p w','' cos-* a } . . (40) 

The gi-eatest effect of the last term at zenith distance, 79°, is only 0^.05, and it 
diminishes very rapidly with the zenith distance. It may therefore be' entirely neg- 
lected in obtaining the sun's semi-diameter from the photographs. 

The actual measures of the photographs have been made at twelve equidistant 
points around the limb of the sun. There will therefore be twelve equidistant values 
of V and six of a to be taken into consideration, the latter being all in one-half of 
the circle. The position of the sun's center in the direction of the vertical co-ordi- 
nate is given as a function of the readings around the sun's circumference in the form 

7 2 Si cos Vi 2 ^ T7- 

^ cos'' Vi n 

s being the reading in the direction of the sun's radius, n the number of readings, 
here 12, and i the index by which they are distinguished. If now we determine the 
position of the center without regard to refraction, the total correction on account of 
refraction will be 

- p n'^ s^ S cos* a^ 
3 

Taking for the six values of a^ the values of V^, which are on one side of a 
horizontal diameter, we shall have, very nearly, 

-.2' CDS'* «;; = 0.75 

so that the correctiop to be applied to the zenith distance of the sun's center for re- 
fraction is 

SS = o.75pn\s^ 

This is the quantity by which the zenith distance of the sun's true center exceeds 
that of the center of his apparent mean circumference in consequence of the differential 
refraction. It may be tabulated as a function of <?. 

The correction to the semi-diameter may be reduced to a similar form. 
S. Ex. 31 7 



50 TRANSIT OF VENUS, 1874. 

5. Since the error of the tabular place of Venus from Hill's tables cannot be more 
than 3" in arc of a great circle, and is probably less than 2", it seems better to ex- 
press the corrections for the effect of refraction upon the position of Venus in terms of 
the singly accented quantities, and to take as the values of these quantities with which 
to enter the tables the mean of the tabular values, and of those derived immediately 
from the photographic measures. The values of the corrections sought will then be 

Ss = ps' ln\ cos^ V + cot <?' sin= V + s cos V (cot' 5 sin'' V — n'^ cos= V) } 
^ V — p sin V cos V {cot 5' — n\ + n', s cos V'} 

The position-angle from the north point, which we have represented by p, is 
given by the equation 

p = Y + q. 

The parallactic angle q is affected by refraction as well as V. The hour angle 
and declination of the sun and the latitude of the place are supposed to be known, 
and from them the sun's parallactic angle, zenith distance, and azimuth may be deter- 
mined, the six quantities in question, or their complements or supplements, fonning 
the parts of a .spherical triangle, of which the angles are at the pole, the zenith, and 
the direction of the sun's center. The equations for determining the quantities q, 5, 
and azimuth, a may be expressed in the form 

sin <? sin q=. cos g) sin H 
sin ^ cos q zz sin g) cos <^ — cos q) sin S cos H 
cos I? z= sin 9> sin d -j- cos 9> cos d cos H 
sin ^ sin a — cos S sin H 
sin § cos a = — cos 9* sin (5 4- sin (p cos d cos H 

If all three quantities, a, ^, and q are required, they may also be obtained firom 
Gauss's equations, 

sin - (a-\- a) sin - <? — sin - H cos - (<b -4- (J) 
2 2 2 2 -^ 

I . . . I ^ I T-T- . I _ 

cos - (« + 2) sin - 5 — cos - H sm - (9> — 0) 



. I 

sm - 
2 



(a — q) cos - 5 =: sin - H sin - (9) -f 6) 



I . . I ^ 1 __ I . 

cos - {a — q) cos - < =: cos - H cos - (9) — o) 

Actually, however, the computation of a may be dispensed with, and then the 
first three equations will be the most convenient. They may be a little simplified 
by the following process : Find two auxiliaries, h and ip, from the equations 

k sin Jp =: sin q) 

k cos V = cos (p cos H 
we shall then have, 

sin ^ sin q=. cos 9> sin H 
sin 5 cos 2 = A sin (if> — 6) 
cos S z=.k cos (V* — ^) 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



51 



The two quantities sin 8, and cos <?, being formed independently, will serve as a 
check upon the computation. 

Considering the right ascension, declination, and parallactic angle as functions of 
the azimuth and zenith distance, the differential co-efficients of the quantities in 
question with respect to <? are 

-rr—r =. sm q sec o 

dS 
d^=-'''^ 

-=-± rz — sin « tan S 
dS ^ 

From the last of these equations we derive 

q" — qz=. — S qz=.p sin q tan d. 

For the correction to free the observed position-angle jp from the effects of refrac- 
tion, we have 

p-p" = \-Y" + q-f 

r:- p sin 2 V ^ cot 8' — n\ + ^^'2 s cos V }— p sin 2 tan 6 

6. ,It remains to tabulate the numerical data for applying the corrections for re- 
fraction, beginning with the quantities w, and n^. In doing this, we shall make use of 
the Pulkowa refraction tables.* The formula here used for the refraction, so far as 
it is necessary for our present purpose, is of the form 

log p zz m -f A (B + T) -1- A 7 

m, A and A being functions of the zenith distance, while B, T and y are the factors 
of corrections for the barometer and thermometers. Differentiating this expression 
twice, the results may be expressed in the form 

d' p -KT 

wnere M zr modulus of logarithms 0.4343 

■^J_ I jdm,.-D,rnsdA,dX\ 



N-N/. 



dS 



* Tabulse Eefractiomiin in ustrai Speculae Pulcovensis congestse. Petropoli, 1870. 



52 TRANSIT OF VENUS, 1874. 

Owing to the extreme minuteness of the factors -j- and ^—^ and the generally 

small values of the corrections B, T, and y, we may neglect the products of these 
quantities. "We shall then have 

^-r \ d m dm 

'~M de^ ~ '^ dS 

The expression for J p being 
we find, by comparing with (35) 



2 



so that the values of n, and n^ are 



dm 

1 . , d" m 

2 ' ^ ^ d ^'■ 

The values of m, etc., which are to be used in these expressions, are those corre- 
sponding to the case in which the argument is the mean of the true and apparent 
zenith distances of the sun, and in the table the formulae have been made to correspond 
to this case. As a matter of fact, the difference between the results obtained by taking 
the one zenith distance or the other as the independent variable may be regarded as 
unimportant. 

The various quantities needed for the corrections on account of refraction, so far 
as they are a function of the zenith distance, are given in the following table. There 
(/>) represents the mean refraction, tt the parallax in altitude, and ^ <? their sum, as 
already used in the formulae. The argument is supposed to be S', or the mean of the 
zenith distances as corrected and as uncorrected for refraction. 

The value of p to be used in computing d s and 6 V should be computed from the 
refraction tables, having regard to the readings of the thermometer and barometer. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



53 



TABLE FOR REFRACTION IN POSITION ANGLE AND DISTANCE. 



?' 


(P) 


TC 


//? 


cotC 


n\ 


«'i-cot?' 


C 


(P) 


It ■ 


At, 


cot?' 


«'i 


«'i — cot ?' 





// 


II 


„ 











II 


II 




,, 








20 


+ ■21.0 


— 3-1 


+-18 


2-75 


3- II 


+ 0.36 


40 


48.4 


-5-8 




43 


1. 19 


2.03 


0.83 


21 


22.2 


— 3-2 


19 


2.61 


3.00 


•38 


41 


50.2 


-5-9 




44 


1. 15 


2.02 


.86 


22 


23-3 


— 3-4 


20 


2.48 


2.88 


.40 


42 


51-9 


— 6.0 




46 


I. II 


2.02 


.90 


23 


24-5 


-3-6 


21 


2.36 


2.78 


-42. 


43 


53-8 


— 6.1 




48 


1.07 


2.01 


-93 


24 


25.7 


- 3-7 


22 


^.25 


2.69 


•45 


44 


55-7 


— 6.2 




49 


1.04 


2.00 


.96 


25 


26.9 


-3-8 


23 


2.14 


Z.61 


■47 


45 


57-7 


-6.4 




51 


I. 00 


2.00 


0.99 


26 


28.2 


— 3-9 


24 


2.05 


2.54 


•49 


46 


59-7 


-6.5 




53 


0.966 


2.00 


1.03 


27 


29.4 


— 4.1 


25 


1.96 


2.47 


-51 


47 


61.8 


— 6.6 




55 


"-933 


2.00 


1.07 


28 


30.7 


— 4.2 


26 


1.88 


2.41 


■53 


48 


64.0 


-6.7 




57 


0.900 


2.01 


I. II 


29 


32-0 


— 4.4 


28 


1.80 


2.36 


•55 


49 


66.3 


— 6.8 




60 


0.869 


2.02 


I- 15 


30 


33-3 


— 4-5 


29 


'•73 


2.31 


•58 


50 


68.7 


-6.9 




62 


0.839 


2.03 


1. 19 


31 


34-7 


-4.6 


30 


1.66 


2.27 


.60 


51 


71.2 


— 7.0 




64 


0. 8io 


2.03 


1. 22 


32 


36.1 


-4.8 


31 


1.60 


2.23 


.62 


52 


73-8 


— 7.1 




67 


0.781 


2.05 


1.27 


33 


37-5 


— 4.9 


33 


1.54 


2.20 


•65 


53 


76.5 


— 7.2 




69 


0.754 


2.07 


I-3I 


34 


38.9 


-5.0 


34 


1.48 


2.16 


.67 


54 


79-3 


— 7-3 




72 


0.727 


2.09 


1-36 


3S 


40.4 


— 5-2 


35 


1-43 


2.13 


• 70 


55 


82.3 


— 7-4 




75 


0. 700 


2. 12 


1.42 


36 


41.9 


— 5-3 


37 


1.38 


2. 10 


.72 


56 


85- 4 


— 7-5 




78 


0.67s 


2.14 


1-47 


37 


43-5 


-5-4 


38 


1-33 


2.08 


•75 


57 


88.7 


— 7-5 




81 


0.649 


E.17 


1-52 


38 


45-1 


- 5-5 


40 


1.28 


2.06 


.78 


58 


92.1 


-7.6 




85 


0.625 


2.21 


1.58 


39 


46.7 


- 5-7 


41 


1.23 


2.04 


.80 


59 


95-8 


— 7-7 




88 


0.601 


2.25 


1.64 


40 


+ 48.4 


-5.8 


+ 43 


1. 19 


2.03 


0.83 


60 


99-7 


-7-8 




92 


0-577 


2.29 


I. 71 


C 


(P) 


It 


A^ 


cot?' 


«'i 


«' 


-cot?' 


«'. 


d" 


S 


pn'^ 
100 


log p n'i 





1 II 


It 




/ // 
















// 








60 


I 39.7 


-7.8 




I 32 




0.587 


2.292 




I. 71 


4.0 





.01 




4 


2.60 


61 


I 43.8 


— 7-9 




X 36 




0-554 


2.338 




1.78 


4-2 




.01 




4 


2.63 


62 


I 48.2 


— 7-9 




I 40 




0.532 


2.390 




1.86 


4-5 




.01 




5 


2.68 


63 


I 52.8 


— 8.0 




' 45 




0.510 


2-443 




1-93 


4.8 




.01 




5 


2.73 


64 


I 57.8 


— 8.1 




[ 50 




0.488 


2.517 




2.03 


5-1 




.01 




6 


2.78 


65 


2 3.2 


— 8.2 




■ 55 




0.466 


2.581 




2. 12 


5-4 




.01 




7 


2.82 


66 


2 8.9 


— 8.2 


'■ 


I I 




0.445 


2.657 




2.21 


5-8 




.01 




7 


2.87 


67 


2 15.2 


-8.3 


■ 


! 7 




0.425 


2.738 




2.31 


6.2 




.01 




8 


2.92 


68 


2 21. 9 


-8.3 


- '. 


! 14 




0.404 


2.831 




2-43 


6.8 




.02 




10 


2.98 


69 


2 29.3 


-8.4 


' 


>. 21 




0.384 


2.940 




2.56 


7-6 




.02 




II 


3-05 


70 


2 37-3 


-8.5 


2 


! 29 




0.364 


3-052 




2.69 


8-3 




.02 




13 


3.12 


71 


2 46. 1 


-8.5 


2 


- 38 




0-344 


3-178 




2.83 


9-1 




.02 




15 


3.18 


72 


2 55.8 


— 8.6 


2 


47 




0.325 


3-320 




2.99 


10. 




•03 




18 


3-24 


73 


3 6.6 


— 8.6 


2 


58 




0.306 


3-478 




3-17 


II. 2 




-03 




21 


3-31 


'74 


3 18.6 


-8.7 


' 


10 




0.287 


3-661 




3-37 


12.3 




.04 




24 


3-39 


75 


3 32.1 


-8.7 


3 


23 




0.268 


3.865 




3.60 


13.6 




•05 




29 


3-46 


76 


3 47-4 


-8.7 


3 


39 




0.249 


4. 100 




3-85 


15-5 




.06 




35 


3-54 


77 


4 49 


— 8.8 


3 


56 




0.231 


4-355 




4.12 


17-5 




•07 




43 


3-63 


78 


4 25-0 


— 8.8 


4 


16 




0.213 


4-658 




4-44 


20. 1 




.09 




S3 


3-73 


79 


4 48-5 


— 8.8 


4 


40 




0-194 


5-014 




4.82 


23-5 




. II 




67 


3-83 


80 


5 16.2 


-8.9 


5 


7 




0. 176 


S-423 




5-25 


27-3 




.14 




86 


3-94 



54 TRANSIT OF VENUS, 1874. 

§ 5. Expression of the Position of Venus on the Sun's disc in terms of 

Tabular Elements. 

The object of what precedes is to determine, from the measures on the photo- 
graphic plate, the position angle and distance of the center of Venus from that of the 
Sun as they would have been seen from the station, were there no refraction. These 
quantities will form the right-hand members of equations of condition on Professor 
Aiey's system of reduction. The left-hand members will be the corresponding quan- 
tities computed from theory, and containing symbolic corrections to the doubtful ele- 
ments of the theory. The formation of the latter quantities will next claim our attention. 
The methods of doing this are so simple and well understood that it is not necessary 
to discuss them in detail, and, since only one result can be correctly arrived at, it is 
merely a question of convenience to the computer whether one or another method 
shall be adopted. 

Since the distances and position angles are found from observation by entirely 
different instrumentalities, each subject to its own sources of error, it is necessary to 
discuss them separately. We must therefore find, for the moment of each photograph, 
the theoretical position-angle and distance of Venus from the Sun's center, as affected 
by arbitrary corrections to the elements, and as seen from the station. The method 
of doing this which seems to offer most security against error is to prepare a table of 
the geocentric values of s and p, and to compute the effects of parallax upon these 
quantities for each observation and each station. The system on which this is done 
is substantially that of Oppolzee in the SitzungsbericJite der Wiener Akademie, vol. 
61, p. 515, Vienna, 1870. The following is a brief outline of the way in which the 
formulae have been derived : 

First, s and p are given with sufficient accuracy by the equations 

s sin ^ — cos d^ (a^ — «) = A cos d^ ' 

s cos J) rr <J, — (^ + - A sin A sin 2 <J > . . . . (43) 

:=6^ — 6 — [9.252] A sin A . 

A being the difference of right ascensions and a, and 6^ the R. A. and Dec. of Venus. 
In these formulse quantities of the third order with respect to s are neglected ; that 
is, the sines of a^ — a and (5, — S are taken the same as the arcs themselves 

In determining the effect of parallax, quantities of the second order with respect 
to the parallax may be entirely neglected except when they contain quantities of the 
order of magnitude of s as a divisor. We put 

TT, the equatorial horizontal parallax of the Sun for the time of observation ; 

TT^, that of Venus ; 

H, the west hour angle of the Sun ; 

h:=. p sin (p' ) p being here the earth's radius at the station and cp' the geocen- 

k=: p cos cp' ) trie latitude ; 

A =: a, — a iz: H — H, ; 

^, symbol for change produced by parallax. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 55 

By differentiating the expressions for s sin p and s cos p, and using sin A instead 
of A, we obtain 

^ (s sin p) zz cos 5, ..^ A — sin A sin 6^ J S^ 

J (s cos p) =. ^ S^ — J 6 -\- - sin A sin 2 SJ A 

We have, by well known formulae for the parallax in right ascension and decli- 
nation 

-d A =:k (tt sec 5 sin H — yr^ sec S^ sin HJ 
^ S =:k7r sin S cos H — hjr cos S 
J S^^JcTT^ sin S^ cos H, — Jitt^ cos S^ 

If we consider only terms of the first order in A and 5, — S, and therefore put 

sin H, z: sin H — sin A cos H 
cos Hj =r cos H + sin A sin H 

then, by suitable reductions, by putting, for brevity, 

m := TV cos S^ sec S — ;r, 
n z= TT^ sin A cos" (J, 
m' =: TT^ sin S^ — tc sin 6 
n' zz TT sin A sin S 

p n - ^Tj sin A sin 2 S, 
p' := ;r cos S — tt^ cos c^j 

and by neglecting quantities of the second order in A and d,— S, we find 

z/ (s sin p)z=.h(m sin H + w cos H) + ^ p ) 
^ (s cos p) zz:k (ni' cos H + «' sin H) -f fe p' 3 



(44) 



It will be seen that w, n, p, w', etc., are functions of the absolute time alone, 
which can be tabulated as such, while k and h are constants for each station, leaving 
H, the Sun's hour angle, as the only independent variable at any one station. 

If, now, we put, with Oppolzee, 



^i zz cos Pa J (s sin p) — sin p^ ^ {s cos j?) ^ 
^^ ■=! sin Pa J (s sin p) -{- cos p^ ^ is cos jp) \ 

a subscript zero designating geocentric quantities, so that we have 

J {s sin ^) = s sin ^ — 5^ sin p^ 
^ {s cos p) zzs cos p — Sa cos Pa 

we find 



(45) 



s sin (p — i>o) zz ^ 
s cos O — _p„) = 5o + 4 



'I • . . • (46) 



56 



TRANSIT OF VENUS, 1874. 



from which s andp — p^ can be obtained either by a rigorous computation or by the 
following approximation, 



Jp=p—p^ = -^^^ ( I ?) 

sms„ \^ s^J 



^sz=s — s^ — ^^-{-— {J p sin i") 



ii\^ 



We have now to consider the most convenient expressions for J^ and J^. By 
substituting (44) in (45), we have 

J^-zili \{m cos p^ — n' sin p^ sin H + (*^ cos p^ — m' sin p^) cos H] 

+ ^ (p cos p, — p' sin p^) 
■d^ =zk {(m sin p^ -\- n' cos p^) sin H + (w sin p^ + m' cos p^) cos H } 

+ ^ (p sin 2^0 + p' Gosp^) 

If we put 

E cos (9 — OT cos j)o — n' sin ^^o 
E sin — n cos^o — m' sin ^^ 
E' sin & ■= — in sinp^ — n' cosp^ 
E' cos <9' — n sin p^ + m' cosp^ 
P = P cos jPo — p' sin p^ 

P' = P sin_p„ + p' cos^o 

the quantities E, E', 9, 6', P, P' can be tabulated as a function of the absolute time, 
and the quantities J^ and J^ can be obtained in the form 



J,=Jc'Rsm(K-\-9)-i-hF 
A^ - Ic E'cos (H + 6') + /i P 



(47) 



The computation of the quantities E, E', etc., can be still farther simplified by 
computing the auxiliaries >«, /<', >u", 9), 9>', and cp" from the formulae 



yw cos cp^m 



fj. sm g) 
when we shall have 



■=.n 



fj. cos (p ■=^n 
pt' sin 9>' = m' 



yw cos 9 — p 
fi" sin 9>" :=p' 



E sin = fj.' cos (<p' +jPo) ' 
E cos 9 zr /^ cos (9 ^-i^o) 
E' sin 61'— — >u sin (<p +^^0) 
E' cos 0' = /i' sin (93' +J5„) 
P = /i"cos(^"+i)„) 

F = /i"sin(^"+|g 



(48) 



The numerical values of these quantities for the case of the Transit of Venus are 
given subsequently. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 57 

§ 6. Recapitulation of the preceding formula for the reduction of the 

Transit of Venus photographs 

For convenience in applying the preceding theory, we collect the formulse de- 
duced in the preceding pages, so far as they are necessary for the actual computation. 
The process of reduction and comparison is divided into three problems. 

Problem I. 

From the measures on the photographic plate and the known constants pertaining to the pho- 
tographic telescope, to find the apparent position angle and distance of the center of Venus 
referred to the center of the Sun. 

The data required for solution are : 

(i). The west hour angle and declination of that point of the celestial sphere 
toward which the rays emanating from the apparent center of the Sun were thrown by 
reflection from the heliostat, in order to be photographed (to 5"). 

(2). The apparent hour angle and declination of the center of the Sun, as afiected 
by parallax and refraction (to 5"). This is to be computed from the sidereal time. 

(3). The distance of the center of Venus from that of the mean center of the Sun's 
disk, as measured on the photograph. 

(4). The angle which the line joining the centers of Venus and the sun makes 
with the vertical at the Sun's center. This angle is to be counted from the line drawn 
from the center of the Sun's image, vertically upward in the northern hemisphere and 
downward in the southei'n hemisphere (toward the north in each case), in the direction 
E N, or the opposite of that in which the hands of a watch move. 

(5). The reduced distance between the image on the sensitive plate and the second 
principal point of the. photographic objective. 

I . To express the solution we put — 
a, the west azimuth of the central line of the photographic telescope as found 

from transit instrument; 
6, the error of level of the middle horizontal line of the photographic plate, 

counted from the true horizon toward the north, so that a positive h means 

photographic plate too high in the northern hemisphere and too low in the 

southern ; 
a' V, the corresponding azimuth and level of the center of the Sun's image 

relative to the cardinal lines on the plate, reduced to seconds of arc. Then 

a" = a + «' will be the west azimuth of the reflected image of the sun's center. 

Put, also, 

<Jo, the declination of that point of the horizon toward which the reflected rays 
are thrown, so that in the northern hemisphere d^-=iq} — 90°, and in the 
southern d^ = 90° — south latitude. Then 6^=zS^-\- b" will be the decli- 
nation required in (i), and H^ =z a" sec d^ will be its west hour angle. 
S. Ex. 31 8 



58 TRANSIT OF VENUS, 1874. 

2. Put 

r, the local sidereal time at which the photograph was taken. 

r„, the corresponding Greenwich sidereal time. 

A, the west longitude of the place from Grreenwich, expressed in arc. 

9), its geographical latitude. 

a, d, the geocentric right ascension and declination of the Sun's center, to be 

taken from Airy's tables, with the argument r^. 
5, the sun's zenith distance (to be computed). 
q, its parallactic angle. 

Express r in arc and compute 

H — r — or, the Sun's west hour angle. 

Then compute <? and q by the following process : First find a quantity log h and an 
angle ^ by the formulae 

h sin ^ — sin g) 

k cos tl> = cos (p cos H 

and then find sin (?, tan q, cos <?, q and <?, by the formulae 

sin 5 sin q = cos 9? sin H 
sin <? cos q=:k sin {ip — d) 
cos ^=zk cos (tf> — 6) 

using six place logarithms in the computation. 

Find the mean refraction and parallax corresponding to <? from the table on page 
53, and put 

the correction for parallax and refraction, tt being the Sun's parallax in altitude and 
p its refraction. This quantity, J «?, is given in the fourth column of the table. Com- 
pute next 

z/ H = — sin q sec <J z/ <5 > 

z/ ^ r= -f cos qJ^ > using four place logarithms. 

^ g — -f- sin 2 tan S ^ s) 

The quantities required will then be 

H"rzH+z/H 
6"z= S-j-JS 
q"=z q + Jq 

3. Put 

r, the distance of centers of images of Sun and Venus on the plate ; 
/, the reduced distance from the plate to the center of divergence of the photo- 
graphic objective. Then 

s = jX 206265" = [5.31443] J 

will be the apparent angular distance of centers. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



59 



4. Put CO for tlie value of the position-angle described in (4), whicli is derived 
immediately from measures on the photographic plate. Compute A from the formula 

tan \ A = ^<y-^'^ eot \ (H" - HJ 
sin-^(<5" + 5,) '^ "^ 

Then 

p" -^k + co — a" tan 6^ 

will be the apparent position angle of Venus relative to the Sun's center. 

Pkoblem II. 

Having found p" and s", or the apparent position angle and distance of Venus from the 
Sun's apparent center, to free them from the effect of atmospheric refraction. 

The corrections to be applied for this purpose are two in number: 

1. A small correction to reduce the center of the Sun's image, as measured on the 
plate, to the image of his true center. 

2. Correction for the effect of refraction in changing the altitude of the center of 
the Sun and of the center of Venus. 

1. Compute 

V" =p" - i' 
«5".?-o.75P<s' 

as a function of 5, s being the Sun's semidiameter in arc, and ri ^ the quantity defined 
in the preceding section. The corrections in question will then be' 

8"N - — ^\" ^"„ 8" <? 
sin s 

d" s = cosY"d"^ 

The quantity S" Z is tabulated on page 53, and it is indifferent whether we use 
V, V, or V" in the computation. 

2. For the computation of the second and larger correction, it is necessary to have 
an approximate value of s and V as corrected. The theoretical values computed in 
Problem III will answer for this purpose. Then put 

V :=^ — 2 

V' = i(V + V") 
2 

s' rr i (. + s") 

and compute log p from the refraction tables, having regard to the thermometer 
and barometer, and entering the tables with the argument 

<§" = 5 - ^ e 



6o TRANSIT OF VENUS, 1874. 

The corrections of the second class for refraction will then be 

S' s = p sin s' {cot <§' + (n\ — cot S') cos" V'} 

— p n'^ sin^ s' cos' V 
6'Y = — (n\ - cot <?') p sin V cos V 
+ p n\ sin s' sin V cos' V 
(^i) = <5' V - ^ ^ + (J" V 

We shall then have, from the photographs, 

s= s" -i-ds 
p =:p" + dp 

Problem III. 

To express the position angle and distance of Venus from the Sun^s center in terms of the 

geocentric elements, and their corrections. 

1. Compute, for the station, the quantities 

hrz p sin (p 
k^ p cos g)' 

Here p is the radius vector of the station and gj' the geocentric latitude. 

2. Find z:/, and ^^ from the equations 

z/, = 7cR sin (H + 5) + AP 
J, = It R' cos (H + &) + h F 

where the quantities R, R', (9, & , P, and P' are to be taken from the table given subse- 
quently with the argument r„ rr Greenwich sidereal time. They are computed by 
means of the formulie given in § 5. 

3. Find s and J p from 

smi^pz=.^^ p-=.p^-\-Jp 

s cos dp — s„-\-J^ s=: s„-\- z/ s 

and the equation to be written will be 

s = 5o + ^ s + on o ^ ^ -\- sin p COB S^S A -\- COS p Sd 

o .05 

o .05 sm s sm s 

in which all the quantities except s, d tt, 6 A, and <Jd are to be reduced to numbers. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 6 1 

§ 7. Special Investigation of the Constants Pertaining to each Photohelio- 

GEAPH. 

The most important of these constants is that which expresses the ratio between 
the measures on the collodion film and the angular distances of the points photo- 
graphed. In order to determine this ratio, the reflecting surface should either be a 
perfect plane, or its curvature should be known with great accuracy. The strongest 
reason for this requirement is that a curved reflector will, in combination with the ob- 
jective, form a compound system, the center of divergence of which will be displaced 
from that of the objective alone by a distance proportioned to the power of the mirror, 
relative to that of the objective, and to the distance of the mirror from the objective. 
It was found that, in order that the measures might be correct within their ten thous- 
andth part, the radius of curvature of the reflector should not be less than four miles, 
and therefore its focal distance for parallel rays should not be less than two miles. 
More exactly, the differences among the curvatures of the reflectors should not exceed 
the limit here set. A common curvature of all the mirrors would, indeed, influence the 
measured distance of Venus from the Sun's center, but would affect the solar parallax 
deduced from the measures by only a small fraction of its entire amount. It was 
therefore important to compare the curvatures of the several mirrors. This was done 
in three ways : 

I. A pair of 5" achromatic telescopes, each of 71" focal length, were focused 
upon each other, a straight edge being inserted in the focus of the one, and the other 
pointed into it ; a similar edge was adjusted in the eye-piece of the second telescope 
in such a way as to correspond to the image of that in the first, and the two were 
accurately focussed on each other. The one telescope was then turned 90° around a 
point midway between the two objectives, and each of the mirrors was set up in suc- 
cession with its center in this rotation point, and at an angle of 45° with each tele- 
scope, so that by looking into one telescope the image of the edge in the focus of the 
other could be seen by reflection. The amount by which the eye-piece had to be 
pushed in or out, to bring the one edge into focus with the reflected image of the 
other, was then measured. This showed the change in the focal length of the telescope 
produced by the curvature of the mirror. The following is the amount by which the 
focus appeared to be lengthened by each mirror : 





in. 


Mirror No. i 


— 0.030 


2 


— 0.027 


3 


— 0.060 


4 


— 0.015 


5 


-\- O.OIO 


6 


— 0.020 


7 


— 0.025 


8 


— 0.025 



Mean — 0.024 



62 



TRANSIT OF VENUS, 1874. 



This mean corresponds to a radius of curvature of 35,000 feet, the mirrors being, on the 
whole, concave. This curvature, with the mirror a foot from the objective, woxild 
make the measures on the photographic plate erroneous by about j^— of their whole 
amount. 

2. The relative curvatures of the mirrors could be compared with rather more 
precision by using them in succession in front of the photographic objective, and de- 
termining the distances between the positions in which the best images wore formed. 
This plan was devised and put into execution by Dr. Draper. In order to get the 
best optical image with the photographic telescope, the rays were passed through a 
cell containing a solution of ammoniacal sulphate of copper just before reaching the 
focus. A frame, containing a piece of ground glass to receive the image, could be 
slid in and out near the focus, and its position on a ruled scale of inches measured 
at each setting. Care was taken that the observer who brought the frame into 
focus should be unconscious of its position, and that the scale should be read by 
another. The following table shows the readings taken by Dr. Draper and myself in 
this way. In column D are given Draper's readings for focus, as taken on May 7, 
1874, and in column N my own, each of which immediately preceded the correspond- 
ing one of his. In the following columns are given the separate results for the amount 
by which each focal length exceeded the mean; (i) and (2), from the measures just 
given ; (3), from a set taken on the preceding day, and probably less accurate than 
those given ; (4), from the measures with telescopes already given, and reduced to 
the photographic telescope by multiplying them by the square of the ratio of the focal 
lengths. 





Mirror. 


in. 


N. 
in. 


(I) 


(2) 


(3) 


(4) 


Mean. 


Radius 
in feet. 


I. 


Chatham Island 


• 14-7 


13.8 


+ 0.7 


— 0.1 


— 0.2 


-0.3 


0.0 


OC 


2. 


Queenstown . 


13.0 


13.0 


— I.O 


— 0.9 


— 0.1 


— 0.1 


-0-5 


-j- 72.000 


3- 


Peking . . . 


• 137 


13-9 


-0-3 


0.0 


-1-5 


-1-5 


-0.8 


-f 45.000 


4- 


Nagasaki . . 


14.6 


13-9 


+ 0.6 


0.0 


+ 0.4 


-f 0.4 


+ 0.4 


— 90.000 


5- 


Hobart Town 


14-5 


14.7 


+ 0.5 


-1-0.8 


+ 1-5 


+ 1.4 


-Ki.o 


— 36.000 


6. 


Campbelltown 


13.0 


14.7 


— 1.0 


-f 0.8 


-I-0.2 


-(-0.2 


0.0 


OC 


7- 


Wladiwostok . 


14.2 


12.8 


+ 0.2 


— I.I 


0.0 


0.0 


— 0.2 


-l- 180.000 


8. 


Kerguelen . . 
Mean . . . 


13.8 
14.0 


14.6 
13-9 


— 0.2 


+ 0.7 


0.0 


0.0 


+ 0.1 


— 360.000 



Accepting these mean results, it would seem that, neglecting the curvature, the 
plate measures of the distance of centers of Venus and the Sun would be in error by 
amounts varying from zero to o."o5. 

3. After the return of the instruments in 1875, the curvatures were compared by 
Mr. Todd with a very delicate spherometer from Grunow, of New York, loaned to 
the Observatory by the U. S. Military Academy. The radius of the circle on which 
lay the three legs was only about o™.i less than that of the mirror, and as it was 
hardly to be expected that the figure of the mirror would be perfect to its edge, con- 
siderable deviations were expected. The readings were made with the greatest care, 
the reflecting surfaces of the mirrors being made horizontal by a spirit-level before 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



63 



the application of the instrument, and the screw being turned with the utmost dehcacy 
until the three legs began to turn round the center. Mr. Todd gives the following 
statement of his trials : 

In order to get a near approximation to the effect of supposed curvature in the 
entire mirror, the spherometer was applied to several parts of the surface, first by 
dividing one-third of the circumference of the mirror into three, and afterward into five, 
nearly equal arcs. A zero point of each mirror was therefore marked by a cros« near 
the thinner side of the mirror. The instrumental zero adopted for the spherometer 
was the pivot to which the upright scale of divisions is attached. 

The value of one rotation of the screw of the spherometer is o'".oi966* llie 
head of the screw carries a disk of about seven inches diameter, the circumference of 
which is graduated into five hundred parts. The radius of the circle passing through 
the pivots of the feet of the spherometer (that is, the distance from the axis of the 
screw to any one of the three pivots) is 3".543- 

In making the first reading for each mirror, the zero of the spherometer was 
placed coincident with the zero of the mirror, care being taken that the three feet of 
the instrument were at nearly equal distances from the nearest points of the circum- 
ference of the mirror. In this position the reading on the line " 0° " was made. Tlien, 
having moved the feet of the instrument through an arc of forty degrees, the reading 
"0° + 40°" was made; and afterward, having moved forty degrees farther, the read- 
ing "0° -f 80°" was. taken. The second scheme of readings gave five observations for 



each mirror — recorded in the lines " o*^ 



"0° 



+ 24' 



"o°-f48°", etc. The first 



three decimals are in units of the divided head of the spherometer ; the fourth decimal 
is the number of estimated tenths of the separate divisions, so tfet each unit of the 
fourth place measures nearly 0^.000004. 

Some of the observations are here given. The letters in the headings of the 
several columns are the initial letters of the stations at which the mirrors were used. 
The Roman numeral's underneath are the numbers of the several mirrors(see page 22). 

The Kerguelen mirror (No. VIII) had not been returned from the station. 

1876, May I, 1.30^. m. Temperature, 59°. o. 



Position 

of Instr. on 

Mirror. 


w. 

VII. 


N. 
IV. 


P. 
III. 


K. 

VIII. 


H. 

v. 


c. 

VI. 


Q- 
II. 


Ch. 
I. 


0° 

004.400 
0° -1- SqO 


0. 1330 
0. 1333 
0. 1333 


0. 1334 
0. 1332 
0. 1333 


0. 1333 
0. 1333 
0. 1333 




0. 1336 
0. 1334 
0. 1336 


0. 1333 
0. 1334 
0. 1333 


0. 1334 
0. 1334 
0. 1332 


0. 1335 
0. 1333 
0. 1334 








Means . . 


0. 1332 


0. 1333 


0- 1333 




0. 1335 


0. 1333 


o- 1333 


0. 1334 





The Queenstown mirror (No. II) was removed after these measures. 

* See page 28 of Reports on Telescopic Observations of the Transit of Mercury, May 5-6, 1878, forming Appendix II 
of tlie Washington Observations for 1876. 



64 



TRANSIT OF VENUS, 1874. 
1876, May I, 2.45 j?. m. Temperature, 59°.o. 



Position 
of Instr. on 

Mirror. 


W. 

VII. 


N. 
IV. 


P. 
III. 


K. 
VIII. 


H. 
V. 


C. 
VI. 


Q- 
II. 


Ch. 
I. 


0° 

0° + 40° 

0° + 80° 


0- 1337 
0. 1336 
0. 1334 


0. 133s 
0. 1334 
0. 1332 


0. 1332 
0. 1332 
0. 1333 




0. 1337 
0. 1335 
0. 1334 


0. 1335 
0. 1335 
0. 1333 




0. 1336 
0. 1335 
0. 1336 














Means . . 


0. 1336 


0. 1334 


0. 1332 




0. 1335 


0. 1334 




0. 1336 







1876, May J, 3 p. in. Temperature, 59°.o. 



Position 

of Instr. on 

Mirror. 


W. 
VII. 


N. 
IV. 


P. 
III. 


K. 
VIII. 


H. 
V. 


C. 
VI. 


Q. 
II. 


Ch. 

I. 


0° 

0° + 40° 

o° + 8oO 


0. 1334 
0. 1335 
0. 1335 


0. 133s 
0. 1334 
0. 1333 


0. 1334 
0. 1333 
0. 1332 




0. 1334 
0. 1334 
0. 1334 


0. 1334 
0. 1334 
0. 1333 




0. 1335 
0- 1335 
0. 1334 














Means - . 


0. 133s 


0. 1334 


0. 1333 




0. 1334 


0. 1334 




0. 1335 







1876, May I, 3.20 J?, m. Temperature, 59°. 5. 



Position 

of Instr. on 

Mirror. 


W. 
VII. 


N. 
IV. 


P. 
III. 


K. 
VIII. 


H. 

V. 


C. 

VI. 


Q. 
II. 


Ch. 

I. 


0° 

0° + 24° 

o°H-48° 

0° + 72° 

0° + 96° 


0. 1334 
0. 133s 
0. 1335 
O.J 335 
0. 1334 


0. 1334 
0. 1335 
0. 1334 
0. 1334 
0. 1333 


0. 1333 
0. 1333 
0. 1333 
0. 1335 
0. 1333 




0. 1336 
o- 1335 
0. 1335 
0. 1334 
0. 1336 


0. 1334 
0. 1336 
0. 1334 
0. 1336 
0. 1335 




0. 1335 

0. 1336 
0. 1336 
0. 1336 
0. 1335 






















Means - - 


0. 1335 


0. 1334 


0. 1333 




0. 1335 


0. 1335 




0. 1336 







1876, May 2, i.io p. m. Temperature, 59°.5. 



Position 

of Instr. on 

Mirror. 


W. 
VII. 


N. 
IV. 


P. 
III. 


K. 

VIII. 


H. 

V. 


C. 

VI. 


Q. 
II. 


Ch. 

I. 


0° 

0° + 24° 

o°+48° 

0° + 72° 

00+96° 


0. 1333 
0. 1333 
0. 1333 
0. 1333 
0. 1333 


0. 1335 
0. 1334 
0. 1334 
0. 1332 
0. 1332 


0. 1332* 
0. 1332 
0. 1333 
0. 1333 
0. 1333 




0. 1334 
0. 1334 
0. 1333 
0. 1334 
0. 1335 


0. 1334 
0. 1333 

0. 1334 
0. 133s 
0. 1334 




0. 1333 
0. 1333 
0. 1332 

0. 1333 

o. 1333 






















Means . . 


0. 1333 


0. 1333 


0. 1333 




0. 1334 


0. 1334 




o- 1333 







1876, May 2, 2.15 jj. m. Temperature, 64°.o. 



Position 

of Instr. on 

Mirror. 


W. 
VII. 


N. 
IV. 


P. 
III. 


Iv. 
VIII. 


H. 

V. 


C. 
VI. 


Q. 

II. 


Ch. 
I. 


0° 

00+24° 
00+48° 
0° + 72° 
0° + 96° 


0. 1333 
0. 1333 
0. 1334 
0. 1334 
0. 1333 


0. 1334 
0. 1333 
0. 1333 
0. 1334 
0. 1333 


0. 1334 
0. 1333 
0. 1333 
0. 1334 
0. 1333 




0. 1336 
0. 1334 
0. t334 
0. 1334 
0. 1334 


0. 1335 
0. 1334 
0. r334 
0. 1335 
0. 133s 




0. 1334 
0. 1333 
0. 1333 
0. 1334 
0. 1334 




















- 


Means.. 


0. 1333 


0. 1333 


0. 1333 




0. 1334 


o. 1335 




0. 1334 







DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



65 



In making the observations on May 2, the legs of the spherometer were protected 
from change of temperature in handling by a covering of chamois skin. 

The spherometer measures would show that there is absolutely no diiference 
among the mirrors exceeding four millionths of an inch, a depression which, if arising 
from regular curvature, would correspond to a radius of curvature of 1 5 miles. We 
have therefore a slight discordance between the optical tests applied by Dx". Deaper 
and myself and these spherometer tests by Mr. Todd. The latter are certainly the 
more free from accidental errors, and I should accept their results without hesitation 
but for two reasons. One is the possibility of a slight sticking of the screw at the 
particular point corresponding to perfect flatness of the support, whereby it might 

tend to show the same reading through the space of 7^5553 of an inch change in the 
support ; the other, that the form of the mirrors when in actual use, exposed to the 
Sun's rays, may be a little different from that which they assume when laid flat. If 
we determine the curvatures entirely from the optical measures, we must correct the 
column " Mean " in the preceding table by — i.o for mean concavity of the eight mir- 
rors determined by the telescopic measures. We shall thus have the amounts in the 
next table by which the astronomical focus is shortened by the concavity of the mir- 
rors. By this concavity the image will be enlarged in the ratio 



1 + 



2D 



p being the radius of curvature, and D the distance of the mirror from the objective. 
If we put s for the amount by which the focus is shortened, we shall have with suffi- 
cient approximation 

p (in feet) = — ^ 



s (in inches) 
We may suppose the value of D to be one foot, and shall then have 



2D 



s 
18000 



The table shows the values of s, and of the resulting factors by which the distance 

from the center of divergence to the ruled plate must be corrected to reduce to what 
it would have been had the mirrors been perfectly flat. 

8 F=i+ logF 

Wladiwostok -f- i.o -f- .00006 -f .000024 

Nagasaki + i-5 + .00008 + .000036 

Peking -f 1.8 -|- .00010 -j- .000043 

Kerguelen -{- 0.6 + .00003 + .000014 

Hobart Town 0.0 .00000 .000000 

Campbelltown -f 1.0 -f .00006 -f .000024 

Queenstown + i-2 + .00007 -|- .000029 

Chatham Island +0.9 -f- .00005 -f- .000022 

S. Ex. 31 9 



66 TRANSIT OF VENUS, 1874. 

Centers of divergence of the objectives. 

In order to compute the positions of these centers, it is necessary to know the 
form, thickness, and index of refraction of each of the lenses composing the objectives. 
The thicknesses were measured near the edges with a caUiper reading to .001 of an 
inch. The entire objectives were thicker near the center by .0036 of an inch, a differ- 
ence of which it was not deemed necessary to take account, in view of the fact that 
rays near the edge have most influence in forming the image. 

The curvatures were first determined with a small spherometer, the feet of which 
were on a circle of i™.25 radius. It was found that, within so small a circle, the devi- 
ation was so small that the instrument did not certainly indicate any differences among 
the several glasses, though it was known that differences must exist, since all were 
not of absolutely the same focal length. Recourse was therefore had to optical methods. 
The concave surfaces were investigated by setting the flint lenses in a vertical position, 
and finding the position of the focus for reflected rays. The process is too simple 
to require a detailed description. 

To investigate the several convex surfaces, a 5" telescope, of six feet focal length, 
was set up horizontally and its stellar focus found by setting up one of the plane mir- 
rors immediately in front of the objective, and "taking the shade" on a lamp placed 
a little, inside the focus * The mirror was then removed and each convex surface of 
the eight crown glasses was, in succession, placed in front of the objective, and the 
focal point of the rays reflected from each was determined. As the great radius of 
curvature of the first face of the flint glasses made their direct determinations trouble- 
some, these faces were treated in the same manner, but, being slightly concave, were 
also determined by finding their center of curvature by reflection from a distance 
equal to the radius of each. 

If/ and/ be the respective distances of a pair of conjugate principal foci from 
their corresponding centers of convergence, the astronomical focal distance/ is well 
known to be given by the equation 

f / / 

■^~/+X 

The positions of the centers of convergence of the objective used in the determi- 
nations were not computed, as the error which would arise from supposing them both to 
be situated in the outer surface of the objective could not have any serious influence on 
the present determinations of the cu.rvatures of the photographic objectives. A rough 

* The process of miikiug the measures was as follows : A graduated bar was placed nearly parallel lyith the axis of 
the five-inch telescope, one end of the bar being in contact with the eye-piece end of the telescope tube. In "ttildug 
the shade ", a lamp shining through a slit was placed an inch or two inside the focus, so that the imago of the slit, 
formed by reflection from the glass surface outside the objective, fell a, little outside the lamp. A small try-square 
was set up vertically upon the graduated bar, near the conjugate focus, and by moving it backward and forward in a 
direction perpendicular to the axis of the telescope, the pencil of light emanating by reflection from the surface of the 
photographic lens could be intercepted before reaching the eye of the observer. If, in moving the try -square, the 
surface of the photographic lens appeared to lose its illumination in the same direction as the square was moved, 
the " shade", or try-square, was too near the reflector ; if in the ojiposite direction, the shade, was too far from the 
reflector, or beyond (that is, outside of) the conjugate focus, lly a tentative process, then, that point was readily 
found where, moving the square very minutely across the axis of the pencil, the illumination of the entire surface dis- 
appeard simultaneously. This point marked the eon,jugato focus. The operation was several times repeated for all 
the convex surfaces of the photographic lenses, and the mean readings from the graduated horizontal bar were 
considered as delining the position of the conjugate foci. 

In investigating the short radius concave surfaces of the flint lenses, the shade wa,s taken on the direct reflection 
m the same manner, but entir(ily without the intervention of the achromatic objective of the horizontal telescope. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



67 



approximation would be attained by supposing the first one to be .05 of an inch out- 
side the outer face of the objective, and the second one to be 0^.25 within it. 

By reflection from the plane mirror, the distances of conjugate foci, both on the 
flint side of the objective, were found to be 

ft. 
/i = 5-951 
/= = 6.i73 

The accents indicate that the distances are measured from the outer crown-face of the 
objective, and not from the center of convergence. We therefore have for the posi- 
tion of the astronomical focus 

/ = 6.060 

As a check upon this determination, the positions of three pairs of conjugate foci were 
found by placing the lamp about 16 feet in front of the objective, and finding the 
points of the corresponding focus beyond the eye-end. Thus was found 

Values of /„ 15.957, 16.23, ^5-7^ 
Corresponding values of/'^,, 9-744, 9-6 14, 9 789 

Supposing/ =f'j — .004, / =f'2 — -021, we have, from the formula, 

Corresponding values of/ 6.041, 6.030, 6.034 
Corresponding values of /', 6.062, 6.o5i, 6.055 

The mean result is .004 less than that found by reflection from the mirror. The 
former has been used for the slightly concave faces of the flint, but the latter, being 
determined by placing the lamp at a distance very nearly equal to the radius of the 
convex surfaces of the crowns, was used in determining the curvature of those sur- 
faces. The following table shows, for various focal distances behind the objective, the 
respective distances of the corresponding conjugate foci in front of the objective, and 
hence the distance of the center of curvature of the convex lens tried from the front 
face of the objective. The distance between this face of the objective and the reflect- 
ing face of the lens to be tried being .020 of a foot, the actual radius of curvature of 
the reflecting surface of the lens will be .020 foot less. 

Table of conjugate foci, etc. 



/'. 


/'. 


Eadius of reflecting surface. 


(feet.) 


(feet.) 


(feet.) 


9-63 


16.224 


16.204 


9.64 


16.195 


■16.175 


9-65 


16 167 


16.147 


9.66 


16.139 


1 6. 1 1 9 


9.67 


1 6. 1 1 1 


16.091 


9.68 


16.084 


16.064 


9.69 


16.057 


16.037 


970 


16.030 


16.010 


9.71 


16.003 


15-983 


9.72 


15-976 


15956 


9-73 


15-950 


15-930 



68 



TRANSIT OF VENUS, 1874. 



The convex surfaces were now investigated, as follows : 

The lamp was placed behind the objective, so that the slit through which it shone 
was 9.544 feet from the front (crown) surface. The sixteen surfaces of the eight lenses 
to be examined were then successively placed in front of the objective, at a distance of 
.020 of a foot, and the conjugate focus was found for the rays from the lamp, which, 
after passing through the objective and being reflected from the surface of the lens, 
were retui^ned through the objective and brought to a focus as near the lamp as prac- 
ticable. The data and results are given in the following table, which gives 

/'j, the distance of the slit of the lamp from the front face of the objective ; 

/'^, the observed distance of the corresponding focus, formed by reflection, as 
just described ; 

y^, the distance at which the lamp should have been placed in order that the 
slit and its image should coincide ; that is, in order that all the rays, after 
passing through the objective, should have been normal to the reflecting 
surface of the lens, and therefore should have met at the center of curva- 
ture of the surface ; 

r, the corresponding radius of curvature of the surface, r^ referring to the outer 
surface and r^ to the inner one. r is taken immediately from the above 
table. The value of f ^ is found by the formula 

f — J jJ >, 



Wladiwostok ... 

Nagasaki 

Peking 

Kerguelen , 

Hobart Town . . 
Campbelltown . , 

Queenstown 

Chatham Island 



f'z 



First face of Crown. 



fU 



Feet. 
9-544 



Feet. 



792 

854 
810 
902 
726 
808 
880 
836 



f'-. 



Feet. 

9.666 

9.696 

9.675 
9. 720 

9.634 
9.674 
9.709 
9.688 



Feet. 
16. 102 
16. 021 
16. 078 
15-956 
16. 192 
16. 080 
15. 986 
16.042 



Second face of Crown. 



fU 



Feet. 

9.837 
874 
856 
819 
,824 



800 



A 



Feet. 

9.688 

9. 706 

9.697 

9.679 

9.682 

9.691 

9.670 

9-693 



Feet. 
16.044 

15-994 
16.018 
16. 067 
i6. 059 
16. 034 
16. 091 
16.029 



Second face of Flint. 



f\ 



Feet. 
5- 844 



f\ 



Feet. 
6. 009 
5.970 
5-932 
•974 



980 
980 
008 



A 



Feet. 



925 
906 
887 
908 
920 
911 
9" 
925 



Feet. 
266 

234 
208 
236 
256 
240 
240 
266 



As already stated, the curvatures 
termined by reflection, without the 
given in the following table, together 
Here the measures are all reduced to 
the radii of curvature, to accord with 
positive curvature is one in which the 
and one of negative curvature on the 



of the first surfaces of the flint lenses were de- 
intervention of an objective. The results are 
with the thicknesses of the lenses tis measured. 
English inches, and algebraic signs are given to 
the theory of the subject; that is, a surface of 
center is on the side from which the ray comes, 
side toward which it goes. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



69 



Wladiwostok . . , 

Nagasaki 

Peking 

Kerguelen 

Hobart Town . 
Campbelltown . 

Queenstown 

Cliatham Island 



Thickness. 



Crown. 



Indies. 
0.410 

0.434 
0.426 
0.283 
0.440 
0.389 
0.466 
0.391 



FUnt. 



Inches. 
0.530 
0.488 
0.481 
0.425 

0.443 
0.499 
0.463 
0.454 



Radii of curvature. 



Inches. 

— 193-22 

— 192-25 

— 192-94 

— 191-47 

— 194.30 

— 192.96 

— 191-83 

— 192. 50 



Inches. 
+ 192-53 
191-93 
192. 22 

192. 80 
192. 71 
192.41 
193. 09 
+ 192.3s 



Inches. 
+ 189.88 
190. 30 

189. 82 

190. 51 

189-54 

191.27 

190.42 

+ 189. 70 



Inches. 

— 3192 

— 2808 

— 2496 

— 2832 

— 3072 

— 2880 

— 2880 

— 3192 



The specific gravities of the lenses were determined at the Coast Survey Office 
for the objectives of longest and shortest focus, and found to be sensibly the same. 
The mean result was as follows : 

Specific gravity of crown, 2.5622 
Specific gravity of flint, 3.2176 

The specific gravities do not directly enter into the determinations which we seek, but 
only the indexes of refraction. The accurate determination of these indexes, though 
not impracticable, would be troublesome, and it was judged that values near enough 
for the present purpose could be inferred from the specific gravities. From the equal- 
ities of the specific gravities in the case of the two extreme glasses weighed, it was 
concluded that all the lenses were made from the same pots ; this, however, is not 
certain. 

The region of greatest photographic intensity in the spectrum being situated be- 
tween Gr and H, it was deemed sufficient to seek the indexes of refraction for these 
rays. Dr. J. Hopkinson gives, in the Proceedings of the Royal Society for 1877, 
a list of indexes of refraction for glasses of various specific gravities, from which the 
following results are extracted : 



Hard crown, sp. 


gr. = 2.48575; (n 


a) := 1.52835; 


(nH)- 


= 1-53279 


it I 


' 2.48664 ' 


' 1.52886 




1-53332 


Soft crown, ' 


2.55035 


' 1.52660 




1-53142 


Extra light flint, ' 


' 2.86636 ' 


1-55638 




1.56276 


Light flint, ' 


' 3.20609 ' 


' 1.59282 




1.60072 


Dense flint, ' 


3-65865 ' 


' 1.64607 




1.65622 


Extra dense flint, ' 


3.88947 ' 


' 1.67702 




1.68857 


Double extra flint, ' 


' 4.42162 ' 


' I-7432I 




1-75778 



From the specific gravities of the -photographic objectives, it seems that they belong 
to the classes soft crown and light flint. The crowns are a little more dense than Dr. 
Hopkinson's specimen, but I cannot say whether this increase of density would result 
in an increase or diminution of the index of refraction. An increase would be es- 



70 TRANSIT OF VENUS, 1874. 

teemed the natural result, but it seems that the soft crown, though more dense than 
the hard, has less refractive power. The effect being doubtful, we may suppose the 
indexes the same as in Dr. Hopkinson's specimen. The indexes for the flint maj be 
readily interpolated from the table. "We thus have, for the most probable values of 
the indexes of the photographic objectives : 

Crowns: Density, 2.5622; (n G) = 1.5266; (n H)=:i.53i4; ^ = 48 
Flints: Density, 3.2176; (n' Gr) = 1.5941 ; (n' H) zr 1.602 1 ; J = So 

The corresponding dispersive powers for the region from G to H are in the ratio 
of 48 : 80 or 3 : 5, while the corresponding powers of the lenses, as dependent on their 
curvatures alone, are in the ratio of about 15:8. This would indicate a decided un- 
der-correction, even for the photographic rays, in this region of the spectrum. 

We have now to compute the focal length and the second center of divergence 
from the curvatures of the lenses and the indexes of refraction. This may be done by 
the following formulae. Put, 

r^, r^, r^, r^, the radii of curvature of the four refracting surfaces, in the order in 
which the light passes them; 

n, the index of refraction for the crown lenses ; 

n', the same, for the flint lens ; 

t^, 4, ^3, the thicknesses of the spaces between the refracting surfaces, divided 
by the respective indexes of refraction, the first and third referring to the 
crown and flint glasses, respectively; the second, to the air-space between 
them. As nearly as could be determined, the thickness of the air-space 
was about .004 of an inch in all the glasses. 

We then compute 



n-— I 


, I —n 
11 — 






^3 


U 



These four values of u may be considered as representing the powers of the four sur- 
faces. 

k = u^-{- u' -i- u" +u"' 

l=i+u' t^ + u" (t, + Q + u'" {K -h 4 + ^3)* 
g=i+u{K + t^ + t;)+u' (4 + ^3) + u" t. 
Then 

f — _9 
■' ~ h 

will be the distance of the focus from the fourth surface, or inner face of the flint lens, 
and 

g — I 

will be the distance of the center of divergence inside the same face. 

* The value of I is not wanted in the case of photographs taken in the astronomical focus. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



71 



It is not to be expected that the value of /' will agi'ee exactly with me measured 
focus, owing to the uncertainty of the values of the measured curvatures and assumed 
indexes of refraction. The value of h derived from the equation 

^- T 

f being the focal distance found by actual trial, will probably be more accurate than 
that found by computation. If we substitute this in the equation for s, we shall have 

9 
Practically, it is indifferent which value of h is used. 

From the curvatures already given, we find the following values of the quantities 
sought for the two assumed indexes : 

I. Ray Gr, w = 1.5266 ; w' z=. 1.5941 



Data 



II. Ray H, %= 1.5314; »i' r= 1.6021 



Station, 



h 



G and H. 



Ti 



Ray G. 



Ray H. 



9 



Ray G. 



Ray H. 



Ray G. 



Ray H. 



Wladiwostok . . 

Nagasaki 

Peking 

Kerguelen 

Hobart Town . 
Campbelltown . 

Queenstown 

Chatham Island 



0.603 

• 593 
■583 
■455 
.568 

• 570 
.59S 
■544 



— 0.002145 

.002150 
.002101 
. 002152 
.002114 
.002153 
.002146 

— 0.002156 



0.002150 
.002155 
.002105 
. 002158 
.002119 
. 002159 
.002151 

o. 002160 



99848 



99856 

99855 
99846 
99861 



o. 99847 

■ 99847 

■ 99851 
. 99884 

■ 99855 

• 99854 

• 99845 

o. 99861 



o. 709 

.707 
.707 

• 538 

.682 

.674 

.717 

0.643 



0.713 
.709 
.708 

•539 
.682 
.675 
.719 
.644 



The computed focal lengths are as follows. We give, for comparison with them, 
the actual distances from the inner face of the objective to the collodion film as the 
instruments were adjusted by the observers. The lengths are in English inches: 



/' 


computed. 


/', as adjusted at 


EayG. 


EayH. 


the station. 


465.5 


464.4 


462.5 


464.4 


463-3 


461.2 


475-3 


474 4 


472.8 


464.1 


462.9 


462.7 


472.4 


471.2 


465 I 


463.8 


462.5 


462.2 


465-3 


4642 


463.2 


463.2 


4623 


461. 1 



Wladiwostok 
Nagasaki 
Peking . . 
Kerguelen . 
Hobart Town 
Campbelltown 
Queenstown 
Chatham Island 

In the case of Hobart Town the discrepancy is so great as to suggest the proba- 
bility that the glass of one of the lenses was different from that iised in the corre- 
sponding lenses of the other objectives. In all the other objectives the agreement is 
as good as could be expected, considering the uncertainty of the indexes of refraction, 



72 TRANSIT OF VENUS, 1874. 

and the difficulty of finding the best focus within the range of an inch, by trial. The 
important quantities which are the object oi this investigation are the distances of the 
centers of divergence from the inner face of the objective, and these seem to be deter- 
mined with all the precision that can be desired. 

Distances hekveen the inner or last face of the objective, and the outer or first face of the 

ruled plate in the plate-holder. 

The method of measuring these distances has already been described, and it now 
remains to collect and discuss the results. The distance, as measured, is made up of 
three parts : 

1. The distance between the face of the objective and the silver plumb-line sus- 
pended from the end of the long rod, as measured with the jaw micrometer. 

2. The length of the rod itself 

3. The distance between the plumb-line at the other end of the rod and the outer 
face of the ruled plate. 

The lengths of the several rods were determined at the Coast Survey Office be- 
fore the departure of the expeditions, and at the Observatory after their return The 
last determinations were made by comparison with standard ten-foot and five-foot 
steel rods of the Coast Survey Office, loaned for the purpose. To make the measures, 
a level platform 40 feet long was constructed in the transit-circle room of the Obser- 
vatory. A steel straight-edge was firmly fastened across one end of this platform, at 
a height of about one-fourth of an inch, and the end of each rod to be measured was 
brought into contact with this edge. The measures were made by placing the steel 
rods alternately end to end along the iron rod to be measured, commencing at the 
straight edge. The excess of the rods over 35 feet was measured with Daklin'g, 
Brown & Sharp's standard scales, allowance being made for the fact that each of 
them was "'.006 longer than the Coast-Survey standard. As a check upon all the 
measurements, the several rods were also compared differentially, so that there were 
two results for each rod, one an absolute measure, and the other the result of a com- 
parison with the absolute measures of the others. As no doubt or difficulty was ex- 
perienced in making the determinations with all necessary certainty, it is deemed un- 
necessary to enter into details, or give more than the final results for length of the 
rods. The following table shows the lengths, first as given by Mr. John Clark, of 
the Coast Survey, before the departure of the expeditions, and then as finally deter- 
mined by the method just described : 

Length. Length. Length. 

Station. No. of rod. (xj. s. C. S.) (Observatory.) (To notch.) 

Inches. Inches. 

Wladiwostok IV 450.34 450-357 .... 

Nagasaki II 450.42 450.437 .... 

Peking I 461.42 461.425 .... 

Kerguelen Ill 453-50 453-488 45I-5H 

liobart Town VII 453-50 453.498 .... 

Campbelltown VI 451-96 451.946 449717 

Queenstown VIII 451.50 451.491 . . . . 

Chatham Island V 449.49 449.485 .... 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



li 



It may be assumed that these lengths correspond to a temperature of 62° Fahr. 

The Kerguelen and Campbelltown rods were a Httle too long for the measure- 
ment of the focal lengths of the objectives; a narrow groove in which to hang the 
plumb-line was therefore cut around each of them at the following distances from the 
end of the rod : 

Kerguelen, 1-974 

Campbelltown, 2.229 

These quantities are therefore to be subtracted from the lengths of the rods. 

The next step is to determine the virtual thickness of the reticule plate, as affect- 
ing the size of the image ; that is, its actual thickness divided by its index of refraction 
for the photographic rays. The measured thicknesses, as determined by Professor 
Haekness, the indexes of refraction, and the virtual thicknesses thence concluded, are 
shown in the following table : 



Station. 



Wladiwostok .- 

Nagasaki 

Peking 

Kerguelen 

Hobart Town . . 
Campbelltown . 

Queenstown 

Chatham Island 



Thickness of 
Plate. 



0.327 
0.312 
0.301 

°-339 
0.320 
0.329 

0.344 
0.322 



Index of 
Refraction. 



540 
540 
555 
548 
555 
555 
540 

540 



Virtual 
Thickness. 



0.212 
0.203 
0.194 
0.219 
0.206 
o. 211 
-o. 223 
0.209 



The remaining element required for the distance between the center of divergence 
of the objective and the sensitive collodion film is the distance between this film and the 
ruled surface of the reticule plate. A correction for the possible contraction or expansion 
of the collodion film arising from change of temperature or other causes will also be 
necessary. But it has been deemed best to avoid corrections of this sort ly referring all 
tine measures to the ruled surface of the reticule plate as the fiducial focus. The ruled hues 
on this plate being photographed with the sun on every image of the latter, it follows 
that, by comparing any distance on the photographic plate with the corresponding one 
on the ruled plate, we shall have the excess of the image on the collodion film over that 
on the reticule plate, as due to all causes whatever. The ratio of any pair of such 
distances will be the factor by which distances on the reticule are increased on the 
collodion film. Then dividing the measures on the collodion film by this factor, we 
shall reduce them to what they would have been had they been impressed upon the 
ruled surface of the reticule plate itself The actual measures for this purpose will be 
given subsequently. From them it is concluded that there is no evidence of any unequal 
expansion or contraction of the collodion film depending on any cause whatever, but 
that the measures on the collodion may be reduced to measures upon the ruled plate 
by being multiplied by a factor which is constant for each station. The values of 
S. Ex. 31 10 



74 



TRANSIT OF VENUS, 18/4. 



F = i — 
.00038 


D 

incli. 

O.I 71 


D 

/ 
.00037 


Diff. 
— .00001 


logP 
— .000165 


.00040 
.00038 


.178 
.149 


.00039 
.0003 I 


— .00001 

— .00007 


— .000174 

— .000165 


.00033 


.169 


.00036 


+ .00003 


— .000143 


.00032 
.00039 


•155 
.169 


.00033 
.00036 


+ .00001 
— .00003 


— .000139 

— ,000169 


.0003 1 


.145 


.0003 I 


— 00000 


— .000135 


.00037 


.140 


.00030 


— .00007 


— .000161 



this factor, which is a Httle less than unity, as found by actual measurement, are shown 
in the following' table in the column F : 

Wladiwostok 
Nagasaki 
Peking . . 
Kerguelen . 
Hobart Town 
Campbelltown 
Queenstown 
Chatham Island 

In order to compare these results with those which would have been attained had 
the measures been continued to the collodion film, and had no allowance been made 
for changes in the film, due to differences of temperature or other causes, we present in 
column D the measured distances between the reticule plate and the film. In the case 
of Peking, and a few others, this distance is doubtful by one or two hundredths of an 
inch, as the parties were not supplied with any special apparatus for determining it, 
and the reticules were, through inadvertence, removed from the plates after the return 
of the latter, before the measurements were made at Washington. Dividing these 
numbers by f, the focal distance, we have the ratio which the excess of the images on 
the collodion film over those on the reticule plate should bear to the entire distance 
measured. In the last column are given the difii'erences between these ratios and the 
measured values of i — F. These differences probably arise from changes in the col- 
lodion film, due partly to the different temperatures to which it was subjected in the 
process of exposure and development. There can, I conceive, be no reasonable doubt 
that the factors F are the proper ones to pass from measures on the collodion film to 
those on the ruled scale. 

Another reduction is that for diff'erence of temperature of the reticule plate at the 
time of taking the photograph, and at the time of measuring the photograph. The 
measures being all made with a glass scale, of which the co-efficient of expansion may 
be assumed to be the same as in the reticule plate itself, this reduction will be most 
simply effected by taking for the length of a scale-division the value which corresponds 
to the temperature at which the photograph was taken. These temperatures may be 
assumed constant for the whole transit at each station except Peking. The following 
are the average values of this element in the photographic rooms, which we take for 
the temperatures of the reticules : 



Wladiwostok, temp. 


= 67° F. 


Nagasaki, " 


64 


Peking, " 


57 to 77 


Kerguelen, " 


59 


Hobart Town, " 


80 


Campbelltown, " 


79 


Queenstown, " 


73 


Chatham Island, " 


73 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



75 



The value of the scale-division, as determined by Professor Haekness from a 
Coast Survey scale, is, in fractions of an inch, 

.019 886 9 -f .000000096 4 (r — 32°) 
or .019 889 8 + .000 000 096 4 (r — 62°) 

As some doubt must exist whether this scale was strictly comparable with the steel 
rod which was used in 'determining the lengths of the station rods, it was deemed advis- 
able to check it by such comparison as would involve no hypothesis respecting the 
comparability of different scales. This was effected by the intervention of a pair of 
Darling, Brown & Sharp two-foot steel scales. By using these as end measures for 
determining the lengths of the station rods, it was found that these lengths came out 
o"'.i2 shorter than by the Coast Survey steel rods. It was thence concluded that these 
scales, used in this way, exceed the Coast Survey standard two feet by o'°.oo6. Pro- 
fessor Hakkness then determined the combined length of the two scales, used as end 
measures, in terms of the glass scale of his measuring engine. This was done by 
starting from an arbitrary division on one scale and measuring consecutive steps of 5 
inches. When the end of the scale was reached, the end of the other scale was brought 
into contact with it, and the measurement continued along that other scale. When the 
end of this scale was reached, that of the first scale was brought into contact with it, 
and the measurement continued until the starting point was reached. The total 
length measured was then the combined lengths of the two rods, independent of all 
errors of the scales. Thus was found 

48.012 Coast Survey inches r= 2413.76 divisions of engine at 62° 

which gives 

I div. = o'°.oi989io. 

This is greater by .0000012, or j~^ of its entire amount, than the value at the same 
temperature given by the first investigation. Notwithstanding that the last is the re- 
sult of a direct comparison, I consider it entitled to no greater weight than the other, 
for the reason that the arrangements for measuring the station rod with the two-foot 
rules were not so perfect as to preclude the possibility of an error. I shall therefore 
take the mean of the two results, putting 

I div. — o'".oi9 890 4 -\- .000 000 096 4 (r — 62°) 

We may remark that the difference of the two results corresponds to a difference of 
o".05 in the least distance of centers of Venus and the Sun, but that the value of the 
solar parallax will be appreciably the same whichever length is used. 

We have now all the data necessary for determining the value of one division of 
the measuring engine in seconds of arc. Firstly, we have the following values for the 
reduced distance between the center of divergence of the objective and the reticule 
plate on which the fiducial images were formed. This distance is made up of three 
parts : 

(i) The distance from the center of divergence to the second face of the flint 
lens, which we have called a. 



76 TRANSIT OF VENUS, 1874. 

(2) From the second face of the flint to the first face of the reticule plate. 
The measures of this distance will be given in Part II. The result we call 2. 

(3) The reduced thickness of the reticule plate. 

The mean results for these lengths are collected as follows : 





(I) 


(2) 


(3) 


/ 


log/ Corr'n for 


log/ 




s (incliea.) 


S 


(Reticule.) 


(Inches.) 


concavity 


corrected. 


Wladiwostok, 


0.71 1 


462.214 


212 


463-137 


UL lUlLlVl., 

2.665709 + 24 


2.665733 


Nagasaki, 


0.708 


461.008 


0.203 


461.919 


2.664566 + s^ 


2.664602 


Peking, 


0.708 


472.624 


0.194 


473-526 


2-675344 + 43 


2.675387 


Kerguelen, 


0.538 


464.480 


0.219 


465-237 


2 667674 + 14 


2.667688 


Hobart Town, 


0.682 


464.782 


0.206 


465.670 


2 668078 


2.668078 


Campbelltown, 


0.674 


461.972 


0.2II 


462.857 


2665447 + 24 


2.665471 


Queenstown, 


0.718 


463-015 


0.223 


463-956 


2.666477 + 29 


2.666506 


Chatham Island, 


0.644 


460.903 


0.209 


461.756 


2.664413 -(- 22 


2.664435 



Next we require the value of one division of the measuring engine, reduced to 
the same scale, at the temperature of the reticule during the taking of the photographs. 
In the following table we give — 

(i) The length of the division, as already given, .reduced for temperature. 

(2) The logarithm of this length. 

(3) The logarithm of the factor for reducing measures on the collodion film to 
measures on the reticule. 

(4) The concluded logarithm of the value, in seconds of arc, of the unit of scale- 
measure on the photographic plate, found from the formulae S rr 206265" — ;, D being 
the leaffth of one division of the measuringc engine. 



Wladiwostok 
Nagasaki . . 
Peking . . 

Kerguelen . 
Plobart Town 
Campbelltown 
Queenstown . 
Chatham Island 





(I) 


(2) 


(3) 


(4) 


T 


D 


logD 




logs 


67 


0.0198909 


8.298654 


-165 


O.947181 


64 


.0198906 


8.298648 


-174 


.948296 


57 


.0198899 


8.298633 


-165 


-937506 


77 


.0198918 


8.298674 


-165 


-937549 


59 


.0198901 


8.298637 


-143 


•945231 


80 


.0198921 


8.298681 


- 139 


.944889 


79 


.0198920 


8.298678 


— 169 


•947463 


73 


.0198915 


8.298667 


-135 


.946451 


73 


.0198915 


8.298667 


— 161 


0.948496 



In the case of Peking the temperature in the photograph house varied so widely 
during the transit that it is deemed advisable to use two values of log S, one for the 
four photographs taken just after the beginning, the other for those near the end. The 
adopted values are 



Photographs 15-22 
Photographs 44-72 



log 8 = 0.937510 
0.937540 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



n 



CONSTANTS FOR DETERMINING THE POSITION ANGLE. 

From the theoretical discussion already given, it will be seen that the constants 
required for deducing the position angle relative to the true meridian from that rela- 
tive to the image of the plumb-line on the photographic plate are the latitude of the 
place and the errors of level and azimuth of the photographic telescope. The mean 
results for these errors, as given by the determinations at the different stations, are 
here set forth. The separate observations on which they are founded will be given in 
the reports of the chiefs of parties. 



Station. 


Azimuth of 

Telescope, 

Plate Holder 

west. 


Plate Holder 
High. 


Latitude of 
Station. 


Wladiwostok . 


II 

— i6 

-f- 14 
+ 6 
+ 13 
+ 2 
+ 5 

— 4 
-F 3 


/' 


-1- 4 

— 9 

— 17 

— 5 

— 4 

— 18 

— 3 


/ // 
+ 43 6 35, 6 
+ 32 43 21. 1 
+ 39 54 15 

— 49 21 .22. 1 

— 42 S3 24. 6 

— 41 55 42. 9 
-45 2 7 

— 43 49 3. 2 








Hobart Town 


Campbelltown 




Chathim Island 



The error of level of the photographic telescope at Wladiwostok has to be re- 
garded as zero, since it was not determined in the way prescribed. A description of 
the process actually employed is given by Professor Hall in his report. The method 
employed, though not satisfactory, does not appear likely to be affected with a proba- 
ble error greater than that of the plate measures. 

§ 8. Reductions of the Photographs in Tabular form. 

The principal steps in the reductions of the photographs by the preceding method 
are shown in the following tables. The data required are enumerated in § 6, pp. 
57-59, under the head of Problem I. Data (i) and (2) are computed astronomically 
by well known methods, and need no further elucidations. Data (3^ and (4) are 
derived from measures of the photographic plates, executed by Prof William 
Harkness, U. S. N., and reduced under his direction so as to give the required quan- 
tities s and w. Datum (5) is deduced in § 7 in the discussion of the photographic ob- 
jectives. The following is the explanation of such of the columns as seem to need it. 

Greenwich sidereal time. — The chronometer time at which each photograph was 
taken, and the correction of the chronometer on local sidereal time, will be given in 
their appropriate tables in connection with the observations at each station. To this 
local time the provisional west longitude given in Chapter II, p. 21, is applied, with 
the symbolic correction & Aj, the index * representing the several stations in order. 

Distance of centers. — Here is given, firstly, the distance as measured by Professor 
Harkness by the methods to be described in connection with the measures, and, 



78 



TRANSIT OF VENUS, 1874. 



secondly, this distance reduced to seconds of arc by the factors just given. Tlie actual 
measures and their discussion are reserved for a subsequent part. 

Correction for refraction^ — These corrections are computed by the formulae, and 
table on page 53. 

Angle 00. — This, like the distance, is derived from the plate measures, being the 
angle of position of the centers of the images of Venus and the Sun relative to the 
vertical line photographed on the plate. 

The position angle p" is that derived from the angle co, as measured on the photo- 
graphic plate, by the formulae of §§ 4 and 6. No theoretical quantities enter into it 
except those dependent on the Sun's hour angle, H. The places of the Sun required 
for this purpose, which need be accurate only to o'.i, were interpolated from the ex- 
tended tables circulated by Professor Airy, using the formulae already quoted in § 6. 
The position angle, p", is not corrected for refraction. 

Applying the corrections for refraction to s" and^", we shall have the values of 
these quantities to be compared with theory. 

The computations were all made on printed forms, and were all executed in du- 
plicate by two independent computers, Mr. William F. McK. Ritter and Dr. William 
W. TowNSEND, and both sets are preserved in connection with the records. 



WLADIWOSTOK. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


6) on 


Plate. 


Sun's 
Angl 


Hour 
eH. 


Parallactic 
Angle / 


Position 
Angle/" 


Corr. 

for 
Refr. 


Plate. 


s" 


6 


h 
8 


m s 

I 32.7 + (!Ai 


d 
98. 179 


869. 36 


+ 1.02 


_ 
+218 


1 

31.0 



— 3 


/ 

31.0 


c / 
— 2 48.6 


/ 
+ 36 27. 1 


/ 

— 2.4 


7 


8 


3 24.2 " 


97- 837 


866.33 


1.03 


217 


40. 2 


- 3 


3-2 


— 2 26. 4 


35 52.6 


— 2.4 


13 


8 


54 10.2 " 


91- 747 


812.41 


1. 41 


196 


II. 9 


+ 9 


35-9 


+ 7 37-6 


21 48. 4 


— I. I 


14 


8 


56 6.7 " 


91.678 


8ii.8o 


1. 41 


195 


27.3 


10 


S.o 


8 0.3 


21 21. 1 


— I.O 


IS 


8 


57 56.2 " 


91-552 


810. 68 


1-43 


194 


47.0 


10 


32-3 


8 21.7, 


+ 20 s6. 3 


— 1.0 


3' 


10 


40 59.7 " 


99.013 


876. 75 


2.24 


149 


51.6 


36 


13-4 


26 40. 8 


— 8 31. 1 


+ 5.8 


32 


lO 


42 53-1 " 


99- 364 


879.84 


2.26 


149 


7-5 


36 


41.7 


26 59. 


- 8 57.8 


■6.2 


33 


10 


44 37-6 " 


99. 492 


880. 99 


2.27 


148 


16.2 


37 


7-7 


27 15-2 


— 9 33-6 


6.2 


34 


10 


46 23.2 " 


100. 040 


885. 84 


2.29 


147 


39-5 


37 


34-1 


27 31-4 


- 9 53-7 


6.5 


35 


10 


48 S.6 " 


100. 226 


887.49 


2-33 


146 


52.1 


37 


59-6 


27 47.1 


— 10 25. i: 


6.6 


36 


10 


49 53-6 " 


100. 598 


890. 78 


2-35 


146 


14. 1 


38 


26.5 


28 3.6 


— 10 46.2 


6.9 


37 


10 


51 27.9 " 


100. 895 


893.41 


2.36 


145 


29.0 


38 


50.0 


28 17.8 


— II 16.2 


6.9 


38 


10 


S3 i8-9 " 


loi. 164 


895- 79 


-f- 2.39 


+ 144 


55.6 


+ 39 


17.7 


+ 28 34.6 


— 11 32.2 


-1- 7.2 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



79 



NAGASAKI, 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


(J on 


Plate. 


Sun's 
Ang 


Hour 
eH. 


Parallactic 
Angle q' 


Position 
Angle/' 


Corr. 

for 

Refr. 


Plate. 


s" 


25 


h m s 
7 25 9.4 + <5Xj 


d 
106. 242 


II 

943-17 


+ 0-43 



234 


/ 

57-8 


' 
— «4 35-3 


' 
— 14 35-4 


/ 
+ 45 7-4 


/ 
— 1. I 


26 


7 25 


40.6 " 


105. 674 


938- 13 


0.43 


234 


52-7 




27-5 




28.0 


45 


6.9 


— 1. 1 


28 


26 


35-2 " 


105. 589 


937-38 


0.41 


234 


31.2 


14 


13-9 


14 


14.8 


44 


54-6 


— 1. 1 


30 


27 


51-9 " 


I05- 373 


935-46 


0.43 


233 


58.0 


13 


54-8 


13 


56.4 


44 


34-' 


— 1. 1 


31 


28 


23.8 " 


105. 260 


934- 46 


0-43 


233 


44-9 




46.8 




48.7 


44 


27.0 


— 1. 1 


33 


30 


25.2 " 


104. 682 


929- 33 


0.44 


232 


46.2 




16.6 




19.4 


43 


48.6 


— I. r 


34 


31 


5-9 " 


104. 540 


928. 06 


0.44 


232 


30.0 


13 


6.4 


13 


9:5 




39-3 


— 1. 1 


35 


33 


12.7 " 


104. 077 


923. 96 


0.44 


231 


38-9 


12 


34-8 


12 


38-8 




9.9 


— 1. 1 


36 


33 


52.8 " 


103. 834 


921.80 


0.45 


231 


28.4 




24.8 


12 


29.0 


43 


6.1 


— 1. 1 


37 


34 


23.6 " 


103. 840 


921.85 


0-45 


231 


12.0 


12 


17.2 


12 


21.5 


42 


54-8 


— 1. 1 


38 


36 


16.6 " 


103. 392 


917.87 


0.46 


230 


32.2 


11 


49-0 


11 


53-9 


42 


34-6 


— 1. 1 


44 


42 


12.6 " 


102. 161 


906. 94 


0.46 


228 


7-1 


10 


20.2 


10 


26. 5 


41 


9-3 


— 1. 1 


45 


43 


44.1 " 


101.695 


902. 81 


0-47 


227 


31.2 


9 


57-4 


10 


3-9 


40 


48.8 


— 1.1 


46 


44 


22. 7 " 


101.475 


900. 86" 


0.47 


227 


7-8 




47-8 


9 


54-3 


40 


31-7 


— 1. 1 


48 


45 


52.4 " 


loi. 108 


897. 60 


0.48 


226 


36-5 




25-5 




32.1 


40 


15-8 


— 1. 1 


49 


47 


21.0 " 


100. 992 


896. 57 


0.48 


226 


4.0 


9 


3-4 




10. 1 


39 


56.9 


— 1. 1 


50 


48 


1. 1 " 


100. 833 


895. 16 


0.48 


225 


38-3 


8 


53-4 


9 


0.2 


39 


38-9 


— 1. 1 


51 


50 


45. 1 " 


100. 296 


890. 39 


0.49 


224 


32-9 


8 


12.5 


8 


19-3 


39 


1.6 


— 1. 1 


52 


52 


31-9 " 


99.921 


887. 06 


0.50 


223 


51-4 


7 


45-9 


7 


52.6 


38 


37.9 


— 1. 1 


S3 


54 


1.3 " 


99. 820 


886. 16 


0.50 


223 


18.3 




23.6 


7 


30-3 




19.7 


— 1. 1 


54 


55 


0. 1 " 


99.468 


883.04 


0.51 


222 


53-2 


7 


9.0 


7 


15.6 


38 


4-5 


— 1. 1 


55 


7 56 


10.6 " 


99. 223 


880. 86 


0.51 


222 


24.1 


6 


51-4 


6 


57.8 


37 


47-4 


— 1. 1 


57 


8 I 


12.8 " 


98. 267 


872:38 


0.52 


220 


17.8 


S 


36.1 


5 


41.8 


36 


31-7 


— 1. 1 


58 


2 


58.6 " 


97. 864 


868. 80 


0.52 


219 


23.1 


• S 


9-7 


5 


15.2 


35 


54-9 


— I.O 


59 


4 


28.9 " 


97. 848 


868. 66 


0.53 


218 


54-7 


4 


47-2 


4 


52-4 


35 


41-3 


— 1.0 


6i 


7 


25-3 " 


97- 574 


866. 22 


0.54 


217 


34-5 


4 


3-2 


4 


7-8 


34 


50.9 


— 1.0 


62 


8 


7.9 " 


96. 987 


861.01 


0.55 


217 


14-3 


3 


52.6 


3 


57- 


34 


37.8 


— 1.0 


63 


9 


1.6 " 


97. 090 


861.93 


0-55 


216 


52.0 




39-2 


3 


43-4 


34 


24.9 


— 1.0 


64 


9 


40.8 " 


96. 972 


860. 88 


0-55 


216 


38.0 


3 


29.4 


3 


33-4 


34 


"7-5 


— 1.0 


65 


13 


9.4 " 


96. 625 


857.80 


0.56 


215 


1.2 


2 


37-5 


2 


40.6 


33 


15.4 


— 1.0 


67 


20 


3.1 " 


95-339 


846. 38 


0-.58 


212 


4.6 


— 


54-4 


— 


55-4 


31 


28.8 


— 0.9 


72 


38 


46. 6 " 


92. 912 




. . . 


■ 




* 


■ ■ 


• 




• 


. . 


. . 


74 


44 


11.3 " 


92.587 


821.95 


0.66 


201 


20.6 


+ 5 


6.6 


+ 5 


12.0 


24 


47-3 


— 0.6 


75 


45 


38.5 " 


92. 703 


822. 98 


0.66 


200 


49.0 


5 


28.3 


5 


34-0 


24 


30.7 


— 0.6 


76 


52 


14. 1 " 


92.017 


816. 89 


0.68 


197 


38.3 


7 


6-9 


7 


13-5 


22 


25.8 


-0.4 


77 


54 


0.9 " 


91.952 


816.31 


0.68 


196 


38-5 




33-5 




40.2 


21 


44.0 


-0.4 


78 


54 


32.0 " 


91-993 


816. 68 


0.68 


196 


34-3 




41-3 




48.0 


21 


44-9 


— 0.4 


79 


55 


17.3 " 


91- 773 


814. 72 


0.69 


196 


9-6 


7 


52.6 


7 


59-3 


21 


28.0 


— 0.4 


80 


55 


52.0 " 


91. 866 


815-55 


0.69 


195 


58.8 


8 


1.2 


8 


8.0 


21 


23.1 


— 0.4 


8i 


8 56 


23. I " 


91. 720 


814-25 


0.69 


195 


46.2 


8 


9.0 


8 


15.8 


21 


15-6 


— U.4 


84 


9 6 


7.6 " 


91-457 


811.92 


0. 72 


191 


14.0 


10 


34-7 


10 


40.7 


18 


21.9 


— 0. I 


93 


51 


55-6 " 


92-439 


820. 64 


0.80 


169 


56.3 


21 


59- 6 


21 


28.4 


4 


50.9 


+ 1.0 


94 


52 


24. 9 " 


92- 338 


819. 74 


0.80 


169 


41. 6 


22 


6.9 


21 


35- 


4 


41.0 


1.0 


95 


53 


8.9 " 


92. 468 


820. 89 


0.80 


169 


19.2 


22 


17.8 


21 


44-8 


4 


26.2 


1.0 


96 


53 


35-8 " 


92. 602 


822. 08 


0.81 


169 


7-6 


22 


24.6 


21 


50.7 


4 


19-3 


1.0 


99 


59 


3-9 " 


93.061 


826. 16 


+ 0.82 


166 


42-3 


+ 23 


46.3 


+ 23 


3-0 


+ 2 


50.0 


+ 1.2 



8o 



TRANSIT OF VENUS, 1874. 



PEKING. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


6) on 


Plate. 


Sun's 
Angl 


Hour 
e H. 


Parallactic 
Angle q' 


Position 
Angle/" 


Corr. 

for 

Refr. 


Plate. 


.r" 


15 


h m 
7 24 


s 
54. i + (5Aa 


d 
108. 895 


943. 02 


+ 0.49 



242 


35-2 



— 28 


4.8 


— 22 


55-4 



+ 45 


II. 8 


/ 
— 2.3 


19 


31 


36.3 " 


107. 183 


928. 19 


0.51 


240 


5-2 


— 26 


24.6 


21 


41.4 


43 


45-8 


— 2.4 


21 


34 


33-6 " 


106. 432 


921.68 


0.52 


239 


4-1 


- 25 


40.4 


21 


8-4 


43 


12.3 


— 2.4 


22 


7 36 


8.3 " 


105. 975 


917.73 


0.53 


238 


20. 1 


- 25 


16.8 


— 20 


50-7 


+ 42 


43- 


— 2.4. 


44 


10 40 


21.3 " 


101.007 


874. 76 


1.20 


159 


14.0 


+ 20 


38.1 


+ 17, 


15.8 


— 8 


4-3 


+ 2.0 


45 


41 


26.4 " 


loi. 167 


876. 15 


1. 21 


158 


45-6 


20 


54-3 


17 


28.6 


— 8 


23.0 


2.0 


46 


42 


32.8 ■' 


101.550 


879-47 


1.20 


.58 


22.6 


21 


10.8 


17 


41.6 


— 8 


35-4 


2. 1 


49 


46 


38. 7 " 


102.061 


883. 89 


1.21 


156 


37-0 


22 


12. 1 


18 


29.4 


— 9 


43-2 


2.2 


50 


47 


53.8 " 


102. 570 


-888. 30 


I. 21 


156 


9-6 


22 


30.8 


18 


43-8 


— 9 


58.6 


2.2 


SI 


49 


5.7 " 


102. 838 


890. 62 


1.22 


155 


40.8 


22 


48.8 


18 


57-7 


— 10 


16.6 


2.3 


53 


51 


43-3 " 


103.381 


895- 33 


1.22 


154 


35-8 


23 


28. u 


19 


28.0 


— 10 


57-2 


2.4 


54 


52 


57.2 " 


103.329 


894.87 


1.22 


154 


4-0 


23 


46- s 


19 


42.0 


— II 


16.6 


2.4 


56 


55 


22.8 " 


103. 986 


900. 57 


I. 22 


153 


10. u 


24 


22.8 


20 


9-6 


— II 


48.0 


2.5 


57 


56 


40.0 " 


104. 308 


903- 35 


1.22 


152 


39-0 


24 


42.0 


20 


24.2 


— 12 


7-3 


2.6 


58 


57 


57-5 " 


104. 482 


904. 86 


1.23 


152 


5-9 


25 


1-3 


20 


38-9 


— 12 


27.7 


2.6 


59 


10 59 


2.2 " 


104. 726 


906. 97 


1.22 


151 


42.6 


25 


17-4 


20 


51.0 


— 12 


41. 1 


2.7 


60 


II 


11.6 " 


105-053 


909. 80 


1.23 


IS' 


16. 1 


25 


34-7 


21 


4.0 


— 12 


56.6 


2.8 


61 


I 


26.0 " 


105.451 


913-25 


1.23 


150 


43-1 


25 


53-3 


21 


17.9 


— 13 


18.0 


2.8 


63 


3 


SO. 6 " 


105. 994 


917.96 


1.23 


149 


49.8 


26 


29-3 


21 


44.8 


— 13 


48.7 


2.8 


65 


.■ 6 


1.6 " 


106. 356 


921.09 


1-23 


148 


58.7 


27 


2.0 


22 


9.0 


— 14 


19.0 


:i.9 


67 


8 


28.6 " 


107. 199 


928. 39 


1.23 


147 


55-7 


27 


38.6 


22 


35-9 


— 14 


58.6 


3-0 


68 


9 


28. 7 " 


107. 136 


927.85 


1-23 


147 


38,9 


27 


53-6 


22 


47.0 


- 15 


6.1 


3-0 


69 


10 


55-5 " 


107. 589 


931-77 


1.24 


147 


10. 


2S 


15-2 


23 


2.8 


- IS 


21.6 


3-2 


70 


II 


58.0 " 


107. 722 


932. 92 


1.24 


146 


40.8 


28 


30.8 


23 


14. z 


— 15 


39-8 


3-2 


71 


12 


58.2 " 


108. 259 


937-57 


1.24 


146 


17-3 


28 


45-8 


23 


25-1 


- 15 


55-2 


3-2 


72 


II 13 


59-4 " 


108. 570 


940. 26 


+ 1-24 


146 


3-1 


+ 29 


I.O 


+ 23 


36.2 


— 15 


59.0 


+ 3-3 



KERGUELEN. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


u on 


Plate. 


Sun's Hour 
Angle H. 


Parallactic 
Angle q' 


Position 
Angle/" 


Corr. 

for 

Refr. 


Plate. 


s" 


7 


h 

7 


m s 
56 12. 8 + (5X4 


d 
103. 827 


II 
915-25 


II 

+ 0.87 



-156 


34-6 



— 66 


38-6 


/ 
224 56.4 


• ' 
+ 37 3-8 


— 0. 1 


17 


10 


5 28.3 " 


97. 824 


863-75 


+ "-34 


184 


22.5 


— 34 


25-6 


216 52.4 


2 4. u 


+ 0.1 


• 18 


10 


9 12. 5 " 


98. 684 


869. 92 


+ 0.33 


185 


1.6 


- 33 


29.8 


216 20.4 


I 13-4 


0. I 


19 


10 


10 23.6 " 


98. 694 


870. 01 


+ 0.33 


185 


22.5 


- 33 


12. I 


2i6 9.9 


48. s 


0. I 


20 


10 


12 4. 7 " 


98.637 


869. 50 


+ 0.33 


185 


52-8 


- 32 


46.9 


215 54.8 


+ 13.9 


0. 1 


25 


10 


38 13-7 " 


102. 574 


904. 2 1 


+ 0.32 


191 


10. I 


- 26 


15-8 


2n 22.2 


- 6 17.4 


0. 1 


32 


10 


56 2.0 " 


IOS-5S9 


930. 52 


+ 0-32 


194 


36-3 


— 21 


49-6 


207 31.3 


— 10 34.4 


0. 1 


33 


II 


25 28. " 


III. 971 


987.04 


+ 0-31 


—199 


39-2 


- 14 


29-4 


199 43.2 


— 17 0.8 


+ 0.1 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



8l 



HOBART TOWN. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


a on Plate. 


Sun's 
Angl 


Hour 
i H. 


Parallactic 
Angle q' 


Position 
Angle/' 


Corr. 

for 

Refr, 


Plate. 


s" 


9, 


h m 
9 59 


s 
2.6 + 5X5 


d 
97- 257 


n 

856.66 


II 
+ 0.28 



—166 


26.7 



+ 41 


/ 
13-4 



130 


/ 

34.8 



+ 2 


34-5 


/ 
— 0. 1 


10 


9 59 


37.3 " 


97- 326 


857- 27 


0.28 


166 


43.8 


41 


22.1 


130 


31.9 


2 


15-3 


— 0. 1 


II 


10 


i6. 7 " 


97. 246 


856. 56 


0.28 


166 


53- 


41 


31.9 


130 


28.6 


2 


3-8 


— 0. I 


12 





45-° " 


97.212 


856. 26 


U.28 


166 


48.7 


41 


39- 


130 


26.3 


2 


6.6 


— 0. I 


'3 


2 


7.1 " 


97-465 


858. 50 


0. 29 


167 


13-6 


41 


59-4 


130 


19.6 


I 


36.8 


— 0. I 


'4 


3 


51-3 " 


97. 790 


861.36 


0.29 


167 


33.5 


42 


25-4 


130 


"•3 


I 


5.8 


— 0. 1 


15 


4 


38.7 " 


97- 635 


860. 00 


0.29 


167 


37.8 


42 


37-2 


130 


7.6 





58.6 


— 0. I 


i6 


6 


14. 7 " 


98. 026 


863.44 


0.29 


167 


57.3 


43 


1. 1 


130 


0.4 





31-3 


— 0. I 


17 


6 


32.3 " 


97-937 


862. 6s 


0.29 


167 


59-0 


43 


5-5 


129 


59. 





28.4 


— 0. I 


i8 


7 


57- 1 " 


98. 291 


865. 77 


0.29 


168 


15. 1 


43 


26.6 


129 


52.8 





6.8 


— 0. 1 


19 


8 


27. 1 " 


98. 227 


865. 21 


0.29 


168 


15-7 


43 


34-1 


129 


50.6 


+ 


4.2 


— 0. I 


22 


>4 


9.7 " 


98.943 


871.51 


0.31 


169 


24.0 


44 


59-5 


129 


27.2 


— I 


31.9 


— 0. 1 


23 


14 


54. " 


98.897 


•871. u 


0.31 


169 


34-7 


45 


10.6 


129 


24.4 


— I 


45-3 


— 0. I 


24 


«5 


33-3 " 


99- 125 


873. 12 


0.31 


169 


46.0 


45 


20.4 


129 


21.9 


— I 


59.3 


0. I 


25 


16 


18. 7 " 


99.321 


874.84 


0.31 


169 


56.6 


45 


31-7 


129 


19.0 


— 2 


12.6 


— 0. I 


' 26 


'7 


6.1 " 


99. 486 


876. 30 


0. 32 


169 


55- 6 


45 


43. 5 


129 


16. 1 


— 2 


14.9 


— 0. I 


27 


18 


48.2 " 


99- 366 


875. 24 


0.32 


^170 


8.4 


46 


8-9 


129 


10. 


— 2 


37- 


— 0. 1 


28 


19 


40. 8 ■' 


99. 562 


8.76.97 


0. 32 


"170 


31- 1 


46 


22.0 


129 


6.9 


— 3 


3-0 


— 0. I 


29 


20 


38. 5 " 


99- 834 


879.36 


0.32 


170 


40.2 


46 


36.4 


129 


3-6 


i- 3 


15-9 


— 0. I 


3° 


21 


12. 5 " 


99. 998 


880. 81 


0.32 


170 


50. z 


46 


44-9 


129 


1.6 


— 3 


27.8 


— 0. 1 


32 


22 


53-6 " 


100. 398 


884-33 


0.33 


171 


14.4 


47 


10. 1 


128 


56.0 


— 3 


58-7 


— 0. I 


33 


23 


12.2 " 


100. lOI 


881. 71 


0-33 


171 


5-8 


47 


14-7 


128 


55.0 


— 3 


51.2 


— 0. 1 


34 


23 


53-5 " 


100.251 


883.03 


0.33 


171 


16.4 


47 


25.0 


128 


52.8 


— 4 


4.4 


— 0. I 


35 


24 


31.2 " 


100. 472 


884. 98 


0.33 


171 


21.2 


47 


34-4 


128 


50.8 


— 4 


11.7 


— 0. I 


36 


25 


23.6 " 


100. 537 


885. 56 


0.34 


171 


43-3 


47 


47-5 


128 


48.0 


— 4 


37-1 


— 0. I 


37 


25 


46.4 " 


100. 627 


886.35 


0.34 


171 


31-9 


47 


53-^ 


128 


46.9 


— 4 


27.2 


— 0.2 


38 


26 


49. 6 " 


100. 849 


888. 30 


"•34 


171 


52.6 


48 


8-9 


128 


43.7 


- 4 


52. 1 


— 0.2 


39 


27 


47- 7 " 


101.079 


890.33 


0.34 


171 


58.6 


48 


23-4 


128 


40.8 


- 5 


2.2 


— 0.2 


40 


28 


30. 4 " 


100. 877 


888. S5 


0-34 


172 


15-0 


48 


34-0 


128 


38.7 


— 5 


21.4 


— 0.2 


41 


29 


55-3 " 


101.065 


890. 20 


0-35 


172 


15.6 


48 


55-2 


128 


34.6 


— 5 


36.7 


— 0.2 


42 


30 


40. 6 " 


101.516 


894. 19 


0.35 


172 


19.7 


49 


6.5 


128 


32-5 


- 5 


43-7 


— 0. 2 


43 


31 


21.2 " 


101.370 


892. 89 


0-35 


172 


35-2 


49 


16.6 


128 


30-7 


— 6 


1-7 


— 0. 2 


44 


32 


9.8 " 


101.845 


897. 08 


0-35 


172 


43-2 


49 


28.7 


128 


28.5 


— 6 


12.8 


— 0.2 


45 


32 


49. 2 " 


101.616 


895.06 


0.3s 


172 


47.6 


49 


38.5 


128 


26.7 


— 6 


19.8 


— 0. 2 


46 


33 


47. 1 " 


101.99s 


898. 40 


0.36 


173 


1-9 


49 


53-0 


128 


24.2 


— 6 


37.8 


— 0.2 


47 


34 


44.4 " 


102. 142 


899. 69 


0.36 


173 


4.0 


SO 


7.2 


128 


21.8 


- 6 


43-6 


— 0.2 


48 


10 35 


44-3 " ' 


102. 220 


900. 38 


+ 0.36 


-173 


15.2 


+ 50 


22.2 


128 


19-3 


- 6 


58-5 


0.2 



S. Ex. 31- 



-11 



82 



TRANSIT OF VENUS, 1874. 



CAMPBELLTOWN. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


6) on 


Plate. 


Sun's Hour 
Angle H. 


Parallactic 
Angle q', 


Position 
Angles" 


Corr. 

for 

Refr. 


Plate. 


s" 


10 


h m 
9 29 


s 
3-o + (5X6 


d 
95. 087 


842.53 


+ 0-25 



—159 


/ 
SO. 5 



+ 33 


/ 

54-8 



132 


/ 
12.2 



+ 10 


/ 
47-1 


/ 
0.0 


II 


32 


30- 3 " 


95. 008 


841. 83 


0.25 


160 


32.4 


34 


46.5 


131 


45-6 


9 


49-0 


0.0 


12 


33 


4.2 " 


95- los 


842. 69 


0.25 


160 


35-6 


34 


55-9 


131 


41.0 


9 


40-7 


0.0 


17 


42 


8.7 " 


95.46s 


845.88 


0.26 


162 


31-7 


37 


10.6 


130 


38-8- 


7 


10.4 


0.0 


18 


43 


6.4 " 


95-244 


843. 92 


0.26 


162 


50.0 


37 


25.0 


130 


32-7 


6 


47- S 


0.0 


19 


43 


58.8 " 


95- 323 


844.62 


0.26 


162 


48.1 


37 


38.0 


130 


27.2 


6 


45-4 


0.0 


23 


30 


35- 4 " 


95.898 


849. 71 


0.27 


164 


15.8 


39 


16.9 


129 


48.3 


4 


46.6 


0.0 


24 


9 SI 


27.3 " 


95.892 


849. 66 


0.27 


164 


12.9 


39 


29.8 


129 


43-5 


4 


45-5 


0.0 


28 


10 7 


44-9 " 


97-843 


866.95 


0.29 


167 


35-5 


43 


33-5 


128 


25.7 


+ 


9-5 


— 0. 1 


29 


II 


37.6 " 


98.151 


869. 68 


0.30 


168 


14. 6 


44 


31-5 


128 


10.3 


— 


47.9 


— 0. 1 


31 


16 


4S-9 " 


99.011 


877.30 


0.32 


169 


17-4 


■ 45 


48.4 


127 


51-7 


— 2 


IS- 1 


— 0. 1 


32 


18 


2.0 " 


99. 047 


877.61 


0.32 


169 


22.4 


46 


7-3 


127 


47-4 


— 2 


26.3 


— 0. 1 


33 


19 


55- " 


99-355 


880.3s 


0.32 


170 


6.0 


46 


35-5 


127 


41.2 


— 3 


17-5 


— 0. 1 


34 


22 


1.4 " 


99. 598 


882. 50 


0.32 


170 


15.0 


47 


7-0 


127 


34-6 


- 3 


36.8 


— 0. 1 


SS 


24 


44.^ " 


100. 076 


886. 73 


0.33 


170 


40.0 


47 


47-6 


127 


26.6 


— 4 


12. 6 


— 0. I 


36 


26 


46. 4 " 


100. 079 


886. 76 


0.34 


171 


2.6 


48 


18.0 


127 


20.8 


— 4 


45-0 


— 0. 2 


37 


27 


54-3 " 


100. 536 


890. 81 


0.34, 


171 


24.3 


48 


34-9 


127 


17.7 


— 5 


12.2 


— 0.2 


38 


28 


44.1 " 


100. 594 


891.32 


0-34 


171 


26.8 


48 


47-4 


127 


15-5 


— 5 


18.6 


— 0.2 


39 


30 


29.2 " 


100. 730 


892. 53 


0-34 


171 


44.2 


49 


13-5 


127 


II. 


— 5 


44-4 


— 0. 2 


40 


31 


49. " 


101.325 


897. 80 


0.35 


172 


3-3 


49 


33-4 


127 


7-6 


— 6 


10. I 


— 0.2 


41 


32 


48. 6 " 


101.271 


897. 32 


0.3s 


172 


16.0 


49 


48.3 


127 


5-2 


— 6 


27. 6 


— 0.2 


42 


34 


0.4 " 


101.509 


899. 43 


0.36 


172 


13-7 


SO 


6.2 


127 


2.4 


— 6 


30.8 


— 0.2 


44 


36 


18.8 " 


101.998 


903. 76 


0.36 


172 


46.0 


50 


40.7 


126 


57-2 


— 7 


14.6 


— 0.2 


45 


37 


47-4 " 


102. 169 


905.28 


0.37 


172 


54-8 


SI 


2.8 


126 


54- 


— 7 


30- 5 


— 0. 2 


46 


39 


4.4 " 


102. 483 


908. 05 


0.37 


173 


9-9 


SI 


22.0 


126 


Si-4 


— 7 


SI- 8 


— 0.2 


47 


40 


44-9 " 


102. 627 


909- 33 


0.38 


173 


23.6 


51 


47-0 


126 


48.1 


— 8 


14.2 


— 0.2 


48 


10 59 


S3-S " 


106. 884 


947. 06 


0.46 


176 


26.6 


56 


33-3 


126 


20.7 


— 12 


49-9 


— 0.3 


49 


II 2 


2.7 " 


107. 254 


950- 34 


0.47 


176 


54-3 


57 


5-5 


126 


18.7 


— 13 


28.0 


— 0.3 


50 


II 3 


5.0 " 


107. 407 


951.69 


0.47 


176 


56.1 


57 


21.0 


126 


17-9 


— 13 


35-0 


— 0.3 


SI 


II 4 


II. 6 " 


107.516 


952. 66 


0.48 


176 


56.9 


57 


37-6 


126 


17.0 


— 13 


41. 1 


— 0.3 


52 


II S 


2. 2 " 


107.675 


954.06 


0.48 


177 


6.9 


57 


50.2 


126 


16.4 


- 13 


55-4 


— 0.3 


S3 


II 6 


6.2 " 


107. 934 


956.36 


+ 0.49 


-177 


21.4 


+ 58 


6.2 


126 


IS- 6 


— 14 


IS- 2 


— 0.4 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



83 



QUEENSTOWN. 



No. of 


Greenwich Sid. Time. 


Distance of Centers. 


Corr. for 
Refr. 


a on 


Plate. 


Sun's 
Angl 


Hour 
eH. 


Parallactic 
Angle g' 


Position 
Angle/' 


Corr. 

for 

Refr. 


Photo. 


Plate. 


s" 




h m s 


d 


II 


II 





/ 





/ 





/ 





1 


/ 


IIS 


7 35 4i-4 + ''^7 


105.465 


932- 31 


+ 0.25 


-132 


53-5 


+ 26 


49-6 


141 


57.9 


+ 40 


47-1 


+ 0.1 


114 


37 34- " 


105. 174 


929- 74 


0.25 


133 


7-4 


27 


17.7 


141 


35-3 


40 


26. 3 


0. I 


116 


39 17-3 " 


104. 733 


925. 84 


0.25 


133 


25-4 


27 


43-4 


141 


15- 1 


40 


2.8 


0. 1 


"7 


40 23.7 " 


104. 679 


925- 36 


0.25 


133 


38.1 


28 


0.0 


141 


2.4 


39 


45-7 


u. 1 


Ii8 


42 26.0 " 


104. 582 


924. 50 


0.25 


'133 


56.2 


28 


30.5 


140 


39-3 


39 


16.8 


0. I 


1 19 


43 52-° " 


103. 930 


918. 74 


. 0.25 


134 


12.3 


28 


SJ-9 


140 


23-4 


38 


58.7 


0. 1 


120 


46 32.5 " 


103.418 


914.21 


0.25 


134 


51.9 


29 


31-9 


139 


54-6 


38 


8.8 


0. 1 


122 


51 23.2 " 


102. 409 


905. 29 


0.24 


135 


36.6' 


30 


44-4 


139 


4-7 


37 


7.2 


0. 1 


123 


53 26.0 " 


102. 382 


90s- OS 


0.24 


13s 


57- 1 


31 


15.0 


138 


44.6 


36 


38.5 


0. 1 


124 


SS 44-3 " . 


101.644 


■898.53 


0.24 


136 


20.9 


31 


49-4 


138 


22.6 


36 


5-4 


0. 1 


125 


7 57 50-7 " 


101.446 


896. 78 


0.24 


136 


49.8 


32 


20.9 


138 


3-" 


35 


28.2 


0. 1 


126 


8 38.4. " 


100. 861 


891.61 


0.24 


137 


17.4 


33 


2.8 


137 


37-9 


34 


49-4 


0. 1 


127 


3 1.8 " 


100. 367 


887. 24 


0. 24 


137 


45-2 


33 


38-5 


137 


17. 1 


34 


14-5 


0. 1 


128 


5 4-3 " 


100. 389 


887.44 


0.24 


138 


10.3 


34 


9.0 


137 


0.0 


33 


41.4 


0. 1 


129 


7 15- 1 " 


100.019 


884.17 


0.24 


138 


31.0 


34 


41.6 


136 


42.2 


33 


12.0 


0. 1 


130 


10 30.5 " 


99. 322 


878. 00 


0.24 


139 


II. 5 


35 


30-3 


136 


16.5 


32 


20.7 


0. 1 


131 


12 0.4 " 


98. 922 


874-47 


0.24 


139 


26.6 


35 


52-7 


136 


5-1 


31 


59-4 


0. 1 


132 


13 49-9 " 


99. 090 


875- 95 


0.24 


139 


S3- 7 


36 


20. 


13s 


Si-5 


31 


25.1 


0. 1 


133 


15 21.0 " 


98. 850 


873-83 


0.24 


140 


13- 5 


36 


42-7 


135 


40-4 


30 


59-2 


0. 1 


134 


17 6.4 " 


98. 482 


870. 58 


0.24 


140 


27-5 


37 


9-" 


13s 


27.9 


30 


38.0 


0. 1 


13s 


18 49. 6 " 


98. 164 


867. 77 


0.24 


140 


45-5 


37 


34-7 


135 


16.0 


30 


13. u 


+ 0.1 


142 


45 21.2 " 


95. 712 


846. 09 


0.24 


146 


21.0 


44 


11.4 


132 


46.2 


22 


55-4 


0.0 


139 


46 36.8 " 


95.892 


847. 68 


0.24 


146 


44.6 


44 


30.3 


132 


40.5 


22 


27-4 


0.0 


144 


47 38-' " 


95-633 


845-39 


0.24 


146 


48.0 


44 


45-5 


132 


36.0 


22 


18.9 


0.0 


143 


48 41.0 " 


95-665 


845. 68 


0.24 


147 


7-9 


45 


1.2 


132 


31-5 


21 


54-6 


0.0 


145 


8 50 28.9 " 


95-446 


843- 74 


0.25 


147 


24.2 


45 


28.1 


132 


23-9 


21 


30-7 


0.0 


151 


9 43 19-4 " 


95- 766 


846. 57 


0-33 


158 


39-4 


58 


38-3 


130 


10.4 


6 


32.2 


— 0.3 


153 


43 38.7 " 


95- 934 


848. 05 


0-34 


158 


55-4 


58 


43-1 


130 


10. 1 


6 


14.8 


- 0.3 


154 


44 31- 1 " 


95. 860 


847. 40 


0.34 


158 


46.5 


58 


56.2 


130 


9-1 


6 


19.8 


— 0.3 


15s 


46 6.6 " 


95-996 


848. 60 


0.34 


159 


U.4 


59 


20.0 


130 


7-5 


5 


47-7 


— 0.4 


156 


49 32-0 " 


96.172^ 


850. 16 


0. 36 


159 


57-1 


60 


II. 2 


130 


4-4 


4 


46.6 


— 0.4 


158 


52 6. 1 " 


96. 661' 


854.48 


0.36 


160 


29.9 


60 


49-6 


130 


1.9 


4 


2-3 


— 0.4 


159 


53 35-0 " 


96. 605 


853-99 


0.36 


160 


29.8 


61 


II. 8 


130 


1.4 


3 


55-6 


— 0.4 


160 


55 35-1 " 


96. 526 


853-29 


0.38 


161 


1.8 


6i 


41-7 


130 


0.2 


3 


14- 5 


— 0.4 


161 


9 56 15.8 " 


96. 674 


854. 60 


0.38 


161 


10.8 


61 


51-8 


129 


59-8 


3 


2.6 


— 0.5 


163 


10 6 2. 5 " 


98- 309 


869. 06 


0.44 


163 


19-4 


64 


18.0 


129 


56-5 


+ 


10.9 


— 0.6 


164 


7 41-4 " 


97.966 


866. 02 


0.44 


163 


43-8 


64 


42.7 


129 


56.4 


— 


22.0 


— 0.6 


16S 


8 30-9 " 


98. 151 


867. 65 


0.44 


163 


37-1 


64 


55-0 


129 


56-3 


— 


19.2 


— 0.6 


166 


9 52-3 " 


98. 308 


869. 04 


0.45 


163 


46.2 


65 


15-3 


129 


56-3 


— ■ 


34-4 


— 0.6 


167 


II 7.0 " 


98. 822 


873-58 


0.46 


164 


8-3 


65 


34-0 


129 


56.4 


— I 


2.2 


— 0.6 


171 


18 18. 7 " 


99-475 


879. 36 


0.51 


165 


18.0 


67 


21-5 


129 


57.8 


— z 


47-3 


— 0.7 


172 


21 26. 7 " 


100. 096 


884. 85 


0-53 


165 


■57-3 


68 


8.4 


129 


59-0 


— 3 


41. 1 


— 0.8 


173 


23 II. I " 


100. 142 


885. 25 


0-53 


166 


20.6 


68 


34-4 


129 


59-8 


— 4 


12.5 


— 0.8 


176 


41 26.0 " 


103. 606 


915.87 


0. 72 


169 


14.0 


73 


7-3 


130 


15.0 


— 8 


38-5 


— 1. 1 


177 


10 41 56.2 " 


103. 529 


915. 19 


+ 0.73 


—169 


12.2 


+ 73 


14.8 


130 


15.6 


— 8 


39-1 


— 1. 1 



84 



TRANSIT. OF VENUS, 1874. 



CHATHAM ISLAND. 



No. of 
Photo. 


Greenwich Sid. Time. 


Distance of Centers. 


Cprr. for 
Refr. 


(J on 


Plate. 


Sun's Hour 
Angle H. 


Parallactic 
Angle q' 


Position 
Angle/' 


Corr. 

for 

Refr. 


Plate. 


.r" 




h m 


s 


d 


II 


„ 





/ 


' 


/ 


' 


/ 


15 


8 20 


16. i + (!A8 


97. 265 


863. 88 


+ 0-25 


-136 


43-3 


+ 52 36.4 


129 14. 5 


+ 29 26. 5 


+ 0.1 


16 


21 


7.4 " 


97- 359 


864. 71 


0.25 


136 


46. 2 


52 49-1 


129 12. 7 


29 19.6 


0. 1 


17 


8 22 


10. 7 " 


97- 358 


864. 71 


0.25 


137 


5-7 


S3 4-9 


129 10.6 


28 55- 3 


+ 0.1 


24 


9 8 


32. 7 " 


94-372 


838. 18 


0. 30 


146 


9-7 


64 38.3 


128 28.8 


16 9. 1 


— 0-3 


25 


9 


41.6 " 


94- 430 


838. 70 


0.31 


146 


30.0 


64 55-5 


128 28.9 


15 43-2 


— 0-3 


27 


18 


29. 1 " 


94- 463 


838.99 


0.33 


148 


2.4 


67 7.0 


128 31.6 


13 28.4 


— o.s 


29 


9 32 


43.2 " 


94. 807 


842.05 


+ 0.41 


—ISO 


51-4 


+ 70 39-8 


128 41.9 


+ 9 23.0 


— 0.8 



§ 9. Tabulae Data foe Compaeison with Obseevations. 

All the observations of the Transit with which we have to deal in the present 
work may, in eflPect, be considered as determinations of the apparent angular distance 
between the center of Venus and that of the Sun, or of the angle of position of the 
line joining these centers. Observations of. contacts may be regarded as fixing the 
moments at which the angular distance of centers was equal to the sum or the differ- 
ence of the angular semi-diameters of the two bodies. For the purpose of comparing 
with observations, and deducing the final values of the required elements, it is neces- 
sary to express the distance of centers in terms of the tabular elements and of the 
corrections to them. The formulae for doing this having already been discussed, it 
only remains to present the numerical data. 

The tabular quantities required are the , geocentric right ascensions, declinations, 
and semi-diameters of the Sun and Venus, and their equatorial horizontal parallaxes. 
At least four sets of such quantities have been computed and published. 

The first of these in chronological order was by Dr. Theodoee von Oppolz^, 
and appeared in the Sitzungsbericlite of the ViennPo Academy of Sciences for 1870 
(Vol. 61, p. 515). Here the tabular quantities are computed with great care from Le 
Veeeiee's tables of the Sun and Venus, and very complete tables and formulae are 
given for computing the apparent distance of centers and position-angle as seen from 
any part of the Earth. But for the considerable magnitude of the errors of Le Vee- 
eiee's tables of Venus at the time of the transit, no further determination of the tabular 
elements would have been necessary. 

Secondly, in 1872 Mr. Geoege "W. Hill prepared tabular data from Hansen's 
tables of the Sun and his own tables of Venus, in a work published by the American 
Commission on the Transit of Venus, Part II of its papers. This paper refers mainly 
to times of contacts, for which very elaborate tables and formulae are given. On page 
44 are given formulae for position-angle and distance which, however, cannot be em- 
ployed in comparing with observations, because the angles refer not to the Sun's 
center, but to the point in which the line joining the centers of the Sun and Venus 
intersects the celestial sphere. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. ' 85 

Thirdly, in 1875 Professor Airy issued very complete tables of data, in which 
the tabular places of the Sun and Venus were interpolated from the Nautical Almanac. 
It is with these tables that the British observations have been compared. 

Fourthly, in the Additions to the Connaissance des Temps for 1878 (Paris, 1876), 
M. PcjiSEUX gives a set of tabular data in which the places of the Sun and Venus are 
derived from Le Veeeier's tables. Of course his geocentric elements are substan- 
tially identical with those of Oppolzee, as the same tables were used. 

In the present discussion the comparison is made with Hill's elements, because 
they are those of which the errors are the smallest. The differential co-efficients of 
the corrections to the elements are themselves functions of the elements, and any 
errors of the latter will necessarily affect the former. As, however, it may be deemed 
necessary to compare with Aiey's or some other elements, the following comparisons 
of the several elements referred to are given. In changing Washington to Greenwich 
time, the difference of longitude is assumed to be 5^ 8" I2^I. 









Hill's Elements. 






Washington 
Mean Time. 


Greenwich 
Sidereal Time. 


Right Ascensions. 


Declinations. 


Venus. 


The Sun. 


Venus. 


The Sun. 


d h 
Dec. 8 8 


h m s 
6 18 39. I 



255 


1 II 

58 56.03 


/ // 
255 42 16. 80 


/ // 
— 22 38 9. 96 


/ // 
— 22 48 24. 39 


9 


7 18 49. 


25s 


57 21.96 


255 45 1-47 


— 22 37 22. 29 


— 22 48 39. 36 


10 


8 18 58. 9 . 


255 


55 47-9° 


255 47 46.15 


— 22 36 34.60 


— 22 48 54. 28 


II 


9 19 8. 8 


25s 


54 13-86 


255 50 30.84 


— 22 35 46. 90 


— 22 49 9. 15 


12 


10 19 18.6 


255 


52 39-84 


255 53 15-54 


— 22 34 59. 18 


— 22 49 23. 98 


13 


II 19 28.5 


25s 


51 5- 83 


25s 56 0.25 


— 22 34 11.44 


— 22 49 38. 77 


14 


12 19 38.4 


255 


49 31-85 


255 58 44.98 


— 22 33 23.67 


— 22 49 53- 51 



Comparing these with the corresponding elements published by Professors Airy 
and Oppolzer, we find the following differences for the positions of Venus relative to 
those of the Sun : 



W.M.T. 
h 


AlKY-HlLL. 

A(o— a') A((5— d') 


Aiky-Oppolzer. 

A (a— a') A((i— d') 
// n 


Oppolzek-Hill. 

A (a— a') A ((5— (J') 
// v/ 


9 


— 3.62 


-0-95 


0.61 


— 0.14 


-3-04 


— 0.80 


10 


-3.61 


— 0.95 


-0-59 


— 0.14 


— 3.02 


— 0.81 


II 


-3-57 


-0.95 


-0.57 


-0.13 


— 3.02 


— 0.81 


12 


-3-56 


— 0.96 


-0.56 


— 0.13 


— 3.02 


— 0.82 


13 


-3-54 


— 0.98 


-0.55 


-0.13 


-3.01 


— 0.84 



Each of these three sets of comparisons was made directly and independently, 
which accounts for their failure to agree rigorously. The comparison of Airy with 
Oppolzer was not actually made for the Washington hours given, but for 14'^, 15'^, 
etc., Paris mean time. 

The constant of parallax is assumed to be 8". 848 in the papers of Hill and of 



86 



TRANSIT OF VENUS, 1874. 



Oppolzee, and 8". 95 in that of Airy. To reduce our comparisons to those with Airy's 
tables, we have to put 

<J A — between — 3".62 and — 3". 54 
5 D = between — o".94 and — o".98 
S TV :=z -\-o".i02 

the proper values of 5 A and 6 D being interpolated to the time of observation. 

The tabular quantities required by the theory are derived from the preceding 
positions of Venus and the Sun, supposing the mean solar parallax to be 8". 848. The 
formulae required for their construction and use have been given on pages 54 to 56. 



Table I. 

Geocentric Tabular Distances and Position-Angles of the Center of Venus from that of 
the Sun {derived from Hill's positions in ^^ Papers relating to the Transit of Venus, 
etc.," p. 9). 



Gr. Sid. 












Gr. Sid. 












Time. 


S 


Diff. 


p 


Diff. 


Time. 


S 


Diff. 


P 


Diff. 


h m 


H 


// 





1 


/ 


h m 


„ 


,1 





1 


/ 


6 20 


1104.051 


— 2. 707 


+ 56 


9.02 


— 9.63 


6 50 


1026. 871 


— 2.419 


+ 50 


59-17 


— II. 12 


21 


I 101.344 


2.698 


55 


59- 37 


9.67 


51 


1024. 452 


i!. 408 


50 


48.05 


II. 17 


22 


1098. 646 


2.689 


55 


49.72 


9.72 


52 


1022. 044 


2.397 


50 


36.88 


11.22 


23 


1095- 957 


2.680 


55 


40.00 


9.76 


53 


loig. 647 


2.386 


50 


25.66 


11.27 


24 


1093. 277 


2.672 


55 


30.24 


9.80 


54 


1017. 261 


^.375 


50 


'4.39 


11.32 


25 


1090. 605 


2.663 


+ 55 


20.44 


9.86 


55 


1014. 886 


2.364 


+ 50 


3.07 


11.38 


26 


1087.942 


2.655 


55 


10.58 


9.91 


56 


1012. 522 


2.353 


49 


51.69 


11.43 


27 


1085. 287 


2.645 


55 


0.67 


9-95 


57 


loio. 169 


2.342 


49 


40.26 


11.48 


28 


1082. 642 


2.637 


54 


50.72 


10.00 


. 58 


1007. 827 


2.330 


49 


28.78 


11.54 


29 


1080. 005 


— 2.627 


54 


40.72 


— 10.05 


59 


1005. 497 


— 2. 320 


49 


17.24 


— 11.58 


6 30 


1077. 378 


2.617 


+ 54 


30.67 


10. 10 


7 


1003.177 


^.308 


+ 49 


5.66 


11.64 


31 


1074. 761 


2.608 


54 


20.57 


10. 15 


I 


1000,869 


2. 296 


48 


54.02 


II. 70 


32 


1072. 153 


2.599 


• 54 


10.42 


10. 20 


2 


998.573 


2.285 


48 


42.32 


11.75 


33 


1069. 554 


2.590 


54 


0.22 


10.24 


3 


996. 288 


2.273 


48 


30.57 


II. 81 


34 


1066. 964 


2.581 


53 


49.98 


10. 29 


4 


994. 015 


2.261 


48 


18.76 


11.86 


35 


1064. 383 


2.571 


+ 53 


39.69 


10.34 


5 


991. 754 


2.249 


+ 48 


6.90 


11.91 


36 


1061.812 


2. 561 


53 


29.35 


10. 39 


6 


989. 505 


2.237 


47 


54.99 


11.97 


37 


1059. 251 


2.551 


53 


18.96 


10.45 


7 


987. 268 


2. 225 


47 


43.02 


12.02 


38 


1056. 700 


2.542 


53 


8.51 


10. 50 


8 


985.043 


2. 213 


47 


31.00 


12.08 


39 


1054. 158 


— 2.531 


52 


58.01 


— 10.55 


9 


982. 830 


— 2. 202 


47 


18.92 


— 12. 13 


6 40 


1051.627 


2. 521 


+ 52 


47.46 


10.60 


7 10 


980. 628 


2.189 


+ 47 


6.79 


12.18 


41 


1049. 106 


2.510 


52 


36.86 


10.65 


II 


978.439 


2.177 


46 


54.61 


12.24 


42 


1046. 596 


2. 501 


52 


26.21 


10. 70 


12 


976. 262 


2. 164 


46 


42.37 


12.29 


43 


1044. 09s 


2.490 


52 


15-5' 


10.75 


13 


974. 098 


2. 152 


46 


30.08 


"2.35 


44 


1041. 605 


2.481 


52 


4.76 


10. 80 


14 


971.946 


2. 140 


46 


17.73 


12.40 


45 


1039. 124 


2.471 


+ 51 


53.96 


10.86 


15 


969. 806 


2. 127 


+ 46 


S-33 


12,46 


46 


1036. 653 


2.461 


SI 


43.10 


10.91 


16 


967. 679 


2. 114 


45 


52.87 


12. 51 


47 


1034 192 


2.451 


51 


32.19 


10.96 


17 


965. 565 


2. 102 


45 


40.36 


12.57 


48 


1031. 741 


2.440 


51 


21.23 


11.00 


18 


963.463 


2.089 


45 


27.79 


12.62 


49 


1029. 301 


— 2.430 


51 


10.23 


— 11.06 


19 


961. 374 


— 2. 076 


45 


15.17 


— 12.67 


6 50 


1026. 871 




+ 50 


59.17 




7 20 


959. 298 




+ 45 


^.50 





DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 
^ABLE I — Continued. 



87 



Gr. Sid. 












Gr. Sid. 












Time. 


5 


Diff. 


P 


Diff. 


Time. 


S 


Diff. 


P 


Diff. 


h m 


II 


// 


. ° 


1 


/ 


Ii m 


II 


II 


c 


/ 


/ 


7 20 


959. 298 


— 2.062 


+ 45 


2.50 


— 12. 73 


8 7 


877.968 


— 1-353 


+ 34 


6.29 


— 15. 18 


21 


957. 236 


2.048 


44 


49-77 


12.78 


8 


876.615 


1-336 


33 


51.11 


15-23 


22 


955- 188 


2.036 


44 


36-99 


12.84 


9 


875- 279 


1-319 


33 


35-88 


15-28 


23 


953- 152 


2.023 


44 


24.15 


12.90 


8 10 


873. 960 


1.301 


+ 33 


20.60 


15-32 


24 


951. 129 


2. 009 


44 


11.25 


12.95 


II 


872. 659 


1.284 


33 


5-28 


«5-37 


25 


949. 120 


1.996 


+ 43 


58.30 


13. 00 


12 


871-375 


1.266 


32 


49.91 


15-41 


26 


947. 124 


1-983 


43 


45-3° 


13.06 


13 


870. 109 


1.248 


32 


34-50 


15.46 


27 


945. 141 


1.969 


43 


32.24 


13.11 


14 


868. 861 


1. 231 


32 


19.04 


15-51 


28 


943-172 


1-955 


43 


19-13 


13. 16 


15 


867. 630 


1.213 


+ 32 


3-53 


15-55 


29 


941.217 


— I- 941 


43 


5-97 


— 13-22 


16 


866.417 


1. 195 


31 


47-98 


15-59 


7 30 


939. 276 


1.927 


+ 42 


52-75 


13.28 


17 


865. 222 


1.177 


31 


32.39 


15-63 


3' 


937- 349 


I- 913 


42 


39-47 


13-33 


18 


864. 045 


1.159 


31 


16.76 


15.68 


32 


935-436 


J. 899 


42 


26. 14 


13-39 


19 


862. 886 


— 1. 142 


31 


1.08 


— 15-72 


33 


933- 537 


1.885 


42 


12.75 


13-44 


8 20 


861. 744 


1. 124 


+ 30 


45-36 


15-76 


34 


931.652 


1.870 


41 


59-31 


13-49 


21 


860. 620 


1. 106 


30 


29.60 


15.80 


35 


929. 782 


1.856 


+ 41 


45.82 


13-55 


22 


859. 514 


1.088 


30 


13.80 


15.84 


36 


927. 926 


1. 841 


41 


32.27 


13.60 


23 


858. 426 


1. 069 


29 


57.96 


15-87 


37 


926. 085 


1.827 


41 


18.67 


13.66 


24 


857- 357 


1.051 


29 


42.09 


15-92 


38 


924. 058 


1.812 


41 


5.01 


— 13- 71 


25 


856.306 


1.032 


+ 29 


26. 17 


15.96 


39 


922. 446 


- ^-798 


40 


51.30 


13-76 


26 


855- 274 


1. 014 


29 


10.21 


15-99 


7 40 


920. 648 


• I. 783 


+ 40 


37-54 


13.81 


27 


854. 260 


0.995 


28 


54.22 


16.03 


41 


918. 865 


1.768 


40 


23.73 


13-87 


28 


853. 265 


0.977 


28 


38. 19 


16.07 


42 


917.097 


1-754 


40 


09.86 


13-92 


29 


852. 288 


— 0. 958 


28 


22. 12 


— 16. 11 


43 


915- 343 


1. 739 


39 


55-94 


13-98 


8 30 


851-330 


0.940 


+ 28 


6.01 


16. 14 


44 


913. 604 


1.724 


39 


41.96 


14.04 


31 


850. 390 


0.922 


27 


49.87 


16.18 


45 


911.880 


1.708 


+ 39 


27.92 


14.08 


■32 


849. 468 


0.903 


27 


33-69 


16.21 


46 


910. 172 


1.693 


39 


13.84 


14-13 


33 


848. 565 


0.884 


27 


17.48 


16.24 


47 


908. 479 


1.677 


38 


59-71 


14.19 


34 


, 847. 681 


0.865 


27 


1.24 


16.28 


48 


- 906. 802 


1.662 


38 


45-52 


14.24 


35 


846.816 


0.84s 


+ 26 


44.96 


16.31 


49 


905. 140 


— 1.646 


38 


31. 28 


— 14.29 


36 


845- 971 


. 826 


26 


28.65 


16.34 


7 50 


903- 494 


1.631 


+ 38 


16.99 


14.35 


37 


845- 145 


0.807 


26 


12.31 


16.38 


SI 


901. 863 


I. 615 


38 


2.64 


14.40 


38 


844. 338 


0.788 


25 


55-93 


16.41 


52 


900. 248 


1-599 


37 


48.24 


14-45 


39 


843- 550 


— 0. 768 


25 


39-52 


— 16.44 


53 


898. 649 


1-583 


37 


33-79 


14.49 


8 40 


842. 782 


0. 749 


+ 25 


23-08 


16.47 


54 


897. 066 


i.568 


37 


19.30 


14-55 


41 


842. 033 


0.730 


25 


6.61 


16.50 


55 


895.498 


1. 551 


+ 37 


4-75 


14.60 


42 


841. 303 


0. 711 


24 


50. 11 


16.52 


56 


893- 947 


1-535 


36 


50.15 


14.65 


43 


840. 592 


0.692 


24 


33-59 


16.55 


57 


892. 412 


1-519 


36 


35-50 


14.70 


44 


839. 900 


0.672 


24 


17.04 


16.57 


58 


890. 893 


1.503 


36 


20.80 


14. 74 


45 


839. 228 


0. 652 


+ 24 


0.47 


16. 60 


59 


889.390 


— 1.486 


36 


6.06 


— 14.80 


46 


838.576 


0. 633 


23 


43-87 


16.63 


8 


887. 904 


1.469 


+ 35 


51.26 


14-85 


47 


837-943 


0.613 


23 


27.24 


16.66 


I 


886.435 


1-453 


35 


36. 4L 


14.90 


48 


837- 330 


0.594 


23 


10.58 


16.68 


2 


884. 982 


1.436 


35 


21.51 


14-95 


49 


, 836. 736 


— 0. 574 


22 


53-90 


— 16. 70 


3 


883.546 


1. 419 


35 


6.56 


15. 00 


8 50 


836. 162 


0-555 


+ 22 


37.20 


16.73 


4 


882. 127 


1.403 


34 


51-56 


15-04 


51 


835-607 


0.536 


22 


20.47 


16.75 


S 


880. 724 


1.386 


+ 34 


36-52 


15.09 


52 


835-071 


0. 516 


22 


3-72 


16. 77 


6 


879.338 


— 1.370 


34 


21.43 


— 15-14 


53 


834- 555 


— 0.496 


21 


46.95 


— 16. 78 


7 


877.968 




34 


6.29 




54 


834. 059 




+ 21 


30.17 





88 



TRANSIT OF VENUS, 1874. 
Table I — Continued. 



Gr. Sid. 










Gr. Sid. 












Time. 


S 


Diff. 


P 


Diff. 


Time. 


S 


Diff. 


P 


Diff. 


h m 


„ 


II 


' 


/ 


h m 


II 


• " 





/ 


/ 


8 54 


834. 059 


— 0-475 


+ 21 30. 17 


— 16.81 


9 41 


833- 518 


+ 0.473 


+ 8 


13-07 


— 16.81 


55 


833- 584 


0-455 


21 13-36 


16.83 


42 


833-991 


0.492 


7 


56.26 


16. 79 


56 


833. 129 


0-435 


20 56.53 


16.84 


43 


834-483 


0.512 


7 


39-47 


16.77 


57 


832. 694 


0.415 


20 39. 69 


16.86 


44 


834- 995 


0.531 


7 


22. 70 


16.75 


58 


832. 279 


0.396 


20 22. 83 


16.87 


45 


835. 526 


0-551 


+ 7 


5-95 


16.73 


59 


831. 883 


- 0. 375 


20 5. 96 


— 16.90 


46 


836. 077 


• 0. 572 


6 


49.22 


16. 70 


9 


831.508 


0.356 


+ 19 49-06 


16.91 


47 


836. 649 


0.591 


6 


32.52 


16.68 


I 


831. 152 


0-335 


19 32.15 


16.93 


48 


837. 240 


0.610 


6 


15.84 


16.66 


2 


830.817 


0. 316 


19 15.22 


16.93 


49 


837.850 


+ 0.630 


5 


59.18 


— 16.64 


3 


830. 501 


0.295 


18 58.29 


16.94 


9 50 


838. 480 


0.649 


+ 5 


42.54 


16.61 


4 


830. 206 


0.276 


18 41-35 


16.96 


SI 


839. 129 


0. 669 


5 


25-93 


16.58 


5 


829. 930 


0.255 


+ 18 24.39 


16.97 


52 


839- 798 


0.688 


5 


9-35 


16.55 


6 


829. 675 


0.235 


18 7.42 


16.98 


53 


840. 486 


0. 708 


4 


52.80 


16-53 


7 


829. 440 


0.214 


17 50.44 


16.99 


54 


841. 194 


0.728 


4 


36.27 


16.50 


8 


829. 226 


0.194 


17 33-45 


17.00 


55 


841.922 


0.748 


+ 4 


19.77 


16.47 


9 


829. 032 


0.174 


17 16.45 


— 17.01 


56 


842. 670 


0.767 


4 


3-30 


16.44 


9 10 


828. 858 


— 0. 154 


+ 16 59-44 


17.01 


57 


843- 437 


0.786 


3 


46.86 


16.41 


II 


828. 704 


"•133 


16 42.43 


17.02 


58 


844. 223 


0.805 


3 


30.45 


16.39 


12 


828. 571 


0. 112 


16 25.41 


17.02 


59 


845.028 


-1- 0.824 


3 


14.06 


— 16.35 


13 


.828. 459 


0.092 


16 8.39 


17.03 


10 


845. 852 


0.843 


+ - 


57-71 


16.32 


14 


828. 367 


0.071 


IS ,51-36 


17-03 


1 


846. 695 


U.862 


2 


41-39 


16. 29 


15 


828. 296 


0.052 


+ 15 34-33 


17.03 


2 


847-557 


0.881 


2 


25. 10 


16.25 


16 


828. 244 


0.032 


15 17.30 


17-03 


3 


848.438 


0. 900 


2 


8.85 


16. 22 


17 


828.212 


— 0.012 


15 0.27 


17-03 


4 


849- 338 


0.920 


1 


52-63 


16. 19 


18 


828. 200 


-|- 0.008 


14 43.24 


17.04 


S 


850. 258 


0.938 


+ I 


36-44 


16. 15 


19 


828. 208 


+ 0. 028 


14 26. 20 


— 17-04 


6 


851. 196 


0.957 


I 


20.29 


16. 11 


9 20 


828. 236 


0.049 


+ 14 9. 16 


17-03 


7 


852. 153 


0.975 


I 


4.18 


16.07 


21 


828. 285 


0.069 


13 52-13 


17.03 


8 


853. 128 


0.993 





48.11 


16.02 


22 


828.354 


0.090 


13 35- 10 


17-03 


9 


854. 121 


+ I. on 





32.09 


— 15-99 


23 


828. 444 


0. no 


13 18.07 


17.02 


10 10 


855- 132 


1.030 


+ 


16. 10 


15.96 


24 


828. 554 


0.130 


1*3 I- 05 


17.02 


II 


856. 162 


1.048 


+ 


0. 14 


15.92 


25 
26 


828. 684 


0. 151 


+ 12 44.03 


17.01 


12 


857.210 


1.067 


— 


15-78 


15.88 


828.835 


0. 171 


12 27. 02 


17.00 


13 


858.277 


1.086 





31.66 


15-85 


27 


829. 006 


0. 192 


12 10.02 


17.00 


14 


859- 363 


1. 103 





47-51 


15.81 


28 


829. 198 


0. 212 


II 53.02 


16.99 


'5 


860. 466 


1. 121 


— I 


3-32 


15.76 


29 


829.410 


+ 0. 232 


11 36.03 


— 16.99 


16 


861.587 


I- 139 


I 


19.08 


15.72 


9 30 


829. 642 


0.252 


+ 11 19.04 


1C.97 


17 


862. 726 


I- 157 


I 


34.80 


15.68 


31 


829. 894 


0.272 


11 2.07 


16.96 


18 


863. 883 


1.176 


I 


50.48 


15.64 


32 


830. 166 


0. 292 


10 45. II 


.16. 95 


19 


865. 059 


+ I- 193 


2 


6. 12 


— 15-60 


33. 


830.458 


0. 311 


' 10 28. 16 


16.94 


10 20 


866. 252 


I. 211 


— 2 


21. 72 


15-55 


34 


830. 769 


0.332 


10 11.22 


16.93 


21 


867.463 


1.228 


2 


37.27 


15-51 


35 


831. lOI 


0.352 


+ 9 54-29 


16.91 


22 


868. 691 


1.246 


2 


52-78 


15-47 


36 


831-453 


0.373 


9 37-38 


16.89 


23 


869. 937 


1.264 


3 


8.25 


15-42 


37 


831.826 


0-393 


9 20. 49 


16.88 


24 


871.201 


I. 281 


3 


23.67 


15-38 

15-33 

15-28 

— 15.24 


38 


832. 219 


0.414 


9 3-61 


16.86 


25 


872. 482 


1.299 


- 3 


39-05 


39 


832. 633 


0-433 


8 46-75 


16.85 


26 


873. 781 


1.316 


3 


54-38 


9 40 


833. 066 


+ 0.452 


8 29. 90 


- 16.83 


27 


875.097 


+ 1-333 


4 


9.66 


41 


833-518 




+ 8 13.07 




28 


876. 430 




— 4 


24.90 


I 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Table I — Continued. 



89 



Gr. Sid. 












Gr. Sid. 












Time. 


S 


Diff. 


P 


Diff. 


Time. 


S 


Diff. 


P 


Diff. 


h m 


// 


*/ 





/ 


/ 


h m 


II 


II 





/ 


/ 


10 28 


876. 430 


+ 1-35° 


—' 4 


24.90 


— >5-i9 


II IS 


956.965 


+ 2.061 


— 15 


23-90 


— 12. 74 


29 


877. 780 


1.368 


4 


40.09 


15-14 


16 


959. 026 


2.074 


15 


36-64 


12.68 


10 30 


879. 148 


1-385 


4 


55-23 


15- 10 


17 


961. 100 


2.087 


IS 


49-32 


12.63 


31 


880. 533 


1. 401 


5 


10-33 


15-05 


18 


963. 187 


2. 100 


16 


1-95 


12-57 


32 


881.934 


1. 418 


5 


25-38 


15.00 


19 


965.287 


+ 2. 113 


16 


14-52 


— 12.52 


33 


883.352 


1-434 


5 


40.38 


14.96 


II 20 


967. 400 


2. 125 


— 16 


27.04 


12.46 


34 


884. 786 


1.450 


5 


55-34 


14.90 


21 


969. 525 


2.138 


16 


39-50 


12.41 


35 


886. 236 


1.467 


- 6 


10.24 


14.85 


22 


971. 663 


2. 151 


16 


51-91 


12.36 


36 


887. 703 


1-483 


5 


25.09 


14.80 


23 


973- 814 


2.163 


17 


4-27 


12.30 


37 


889. 1 86 


1.500 


6 


39-89 


14.76 


24 


975-977 


2.175 


17 


16.57 


12.25 


38 


890. 686 


1-517 


6 


54-65 


14.71 


25 


978. 152 


2.188 


— 17 


28.82 


12.19 


39 


892. 203 


+ 1-533 


7 


9-36 


— 14.66 


26 


980. 340 


2.200 


17 


41.01 


12.14 


10 40 


893- 736 


1.549 


— 7 


24.02 


14.60 


27 


982. 540 


2.212 


17 


53-15 


12.08 


41 


895.285 


1-565 


7 


38.62 


14-55 


28 


984- 752 


2.224 


18 


5-23 


12. 02 


42 


896. 850 


1. 581 


7 


53-17 


14.51 


29 


986. 976 


+ 2.236 


18 


17-25 


— 11-97 


43 


898.431 


1.598 


8 


7.68 


14.46 


II 30 


989. 212 


2.248 


— 18 


29.22 


11.92 


44 


900. 029 


1. 613 


8 


22. 14 


14.41 


3' 


991.460 


2.260 


18 


41-14 


1..87 


45 


goi. 642 


1.629 


— 8 


36-55 


14-35 


32 


993- 720 


2.273 


18 


53-01 


11.81 


46 


903. 271 


1.644 


8 


50.90 


14.29 


33 


995- 993 


2.285 


19 


4.82 


11.76 


47 


904.915 


1.660 


9 


5-19 


14-25 


34 


998. 278 


2.296 


19 


16.58 


11.71 


48 


906. 575 


1.676 


9 


19.44 


14.20 


35 


1000. 574 


2.307 


— 19 


28.29 


11.65 


49 


908.251 


+ 1. 691 


9 


33-64 


— 14- 14 


36 


1002. 881 


2.318 


19 


39-94 


11-59 


10 50 


909.942 


1.707 


— 9 


47-78 


14.09 


37 


1005. 199 


2.329 


19 


51-53 


11-54 


SI 


911.649 


I. 722 


10 


1.87 


14.04 


38 


1007. 528 


2-341 


20 


3-07 


11.49 


52 


913-371 


1.736 


10 


15.91 


13.98 


39 


1009. 869 


+ 2.352 


20 


14.56 


— 11-44 


53 


915. 107 


I. 751 


10 


29.89 


13-93 


II 40 


1012.221 


2.363 


— 20 


26.00 


11-38 


54 


916.858 


1.766 


10 


43.82 


13.88 


41 


1014. 584 


2.374 


20 


37-38 


11-33 


55 


918. 624 


I. 781 


— 10 


57-70 


13-83 


42 


1016. 958 


--385 


20 


48.71 


11.28 


56 


920. 405 


1.796 


II 


"-53 


13-77 


43 


1019. 343 


2-395 


20 


59-99 


11.23 


57 


922. 201 


1. 811 


II 


25-30 


13-72 


44 


102 1. 738 


2.406 


21 


11.22 


II. 18 


58 


924. 012 


1.526 


II 


39.02 


13.66 


45 


1024. 144 


2.417 


— 21 


22.40 


11.12 


59 


925.838 


+ 1.840 


II 


52.68 


— 13-60 


46 


1026. 561 


2.428 


21 


33-52 


11.07 


II 


927. 678 


1.854 


— 12 


6.28 


13-55 


47 


1028. 989 


2.439 


21 


44-59 


11.02 


I 


929- 532 


1.869 


12 


19.83 


13-50 


48 


1031.428 


2.450 


21 


55-61 


10.96 


2 


931.401 


1.884 


12 


33-33 


13-45 


49 


1033-878 


+ 2.460 


22 


6-57 


— 10.91 


3 


933- 285 


1.898 


12 


46.78 


13-39 


II 50 


1036. 338 


2.470 


— 22 


17.48 


10.86 


4 


935- 183 


I- 913 


13 


0.17 


13-32 


51 


1038. 808 


2.480 


22 


28.34 


10.80 


5 


937.096 


1.926 


— 13 


13-52 


13.27 


52 


1041.288 


2.490 


22 


39-14 


10. 76 


6 


939. 022 


1.940 


»3 


26.79 


13-23 


53 


1043. 778 


2.500 


22 


49-90 


10. 70 


7 


940. 962 


1-953 


13 


40.02 


13.18 


54 


1046. 278 


2.510 


23 


0.60 


10.66 


8 


942. 915 


1.967 


13 


53-20 


13.12 


55 


1048. 788 


2.521 


— 23 


11.26 


10. 6i 


9 


944. 882 


+ 1.980 


14 


6.32 


— 13.07 


56 


1051.309 


2.531 


23 


21.87 


10.56 


II 10 


946. 862 


1.994 


— 14 


19-39 


13.01 


57 


1053. 840 


2.541 


23 


32.43 


10.50 


II 


948. 856 


2.007 


14 


32.40 


12.96 


58 


1056. 381 


2.551 


23 


42.93 


10.45 


12 


950. 863 


2.021 


14 


45-36 


12.90 


59 


1058. 932 


+ 2. 561 


23 


53-38 


— 10.40 


13 


952.884 


2.034 


14 


58.26 


12.85 


12 


1061.493 


2.570 


— 24 


3-78 


10.35 


14 


954.918 


+ 2-047 


15 


II. II 


— 12. 79 


I 


1064. 063 


+ 2-579 


24 


14-13 


— 10.30 


15 


956.965 




- 15 


23.90 




2 


1066. 642 




24 


24-43 





8. Ex. 31- 



-12 



90 



TRANSIT OF VENUS, 1874. 
Table I — Continued. 



Gr. Sid. 












Gr. Sid. 












Time. 


S 


Diff. 


^ 


Diff. 


Time. 


s 


Diff. 


P 


Diff. 


h m 


n 


II 





/ 


/ 


h m 


II 


II 





1 


/ 


12 2 


1066. 642 


+ 2. 588 


— 24 


2443 


— 10.26 


i-a II 


1090. 274 


+ 2.671 


— 25 


54-95 


— 9.81 


3 


1069. 230 


2.598 


24 


34-69 


10.21 


12 


1092. 945 


2.680 


26 


4.76 


g. 77 


4 


I071. 828 


2.607 


24 


44.90 


10. 16 


13 


1095. 625 


2.689 


26 


14-53 


9.72 


5 


1074-435 


2.617 


— 24 


55-06 


10. II 


14 


1098.314 


2.698 


26 


24.25 


9.67 


6 


1077. 052 


2.626 


25 


5-17 


10.05 


IS 


1101.012 


2. 706 


— 26 


33-92 


9.62 


7 


1079. 678 


2.636 


25 


15.22 


10.01 


16 


1 103. 718 


2-715 


26 


43-54 


9-57 


8 


1082. 314 


2.644 


25 


25-23 


9-95 


17 


1106.433 


2.724 


26 


53-" 


9-53 


9 


1084. 958 


+ 2.654 


25 


35- 1« 


— 9-91 


18 


nog. 157 


2-733 


27 


2.64 


9-49 


12 10 


1087. 612 


2.662 


-25 


45-09 


9.86 


19 


nil. 890 


+ 2. 741 


27 


12.13 


— 9.44 


II 


logo. 274 




25 


54 95 




12 20 


1 1 14. 631 

« 




— 27 


21-57 





Table II. 
Parallactic Elements, 0, 6' , R, R'. 



Gr. Sid. 






















Time. 


e 




Diff. 


6' 




Diff 


logR 


Diff 


logR' 


Diff. 


h m 





/ 


/ 





/ 


/ 










6 20 


149 


56.4 




104 


7-8 




1. 19691 




1. 32162 




21 


150 


5-4 


+ 9 
9 


u 



104 


13.0 


+ 5 
5 


2 
2 


1. 19807 


-|- 0.00116 
.00116 


1. 32og7 


— 0.00065 
. 00066 


22 


150 


14.4 




104 


18.2 




I- 19923 




1. 32031 




23 


150 


23-4 


9 





104 


23-5 


5 


3 


1.20039 


.00116 


1.31964 


. 00067 


24 


150 


32-4 


9 


u 


104 


28.8 


5 


3 


I. 20155 


.00116 


1-31897 


. 00067 


25 


150 


41.4 


9 





104 


34-1 


5 


3 


1. 20271 


.00116 


1.31829 


. 00068 


26 


ISO 


50.4 


9 





104 


39-4 


5 


3 


1.20388 


.00117 


1.31761 


. 00068 


27 


ISO 


59-4 


9 





104 


44.8 


5 


4 


1.20505 


.00117 


1. 31692 


. 00069 


28 


151 


8.4 


9 


u 


104 


50-2 


5 


4 


I. 20622 


.00117 


1.31622 


. 00070 


29 


151 


17-4 


9 





104 


55-6 


5 


4 


1. 20739 


.00117 


1-31551 


. 00071 


6 30 


151 


26.4 


9 





105 


I.O 


5 


4 


1.20856 


.00117 


1-31479 


. 00072 


31 


151 


35-4 


+ 9 





105 


6-5 


+ 5 


5 


1.20974 


+ 0. 001 18 


1. 31406 


— 0. 00073 


32 


151 


44-3 


8 


9 


105 


12.0 


5 


5 


I. 21092 


.00118 


I- 31333 


• 00073 


33 


151 


53-2 


8 


9 


105 


17.6 


5 


6 


1.21210 


. 00118 


1. 31259 


. 00074 


34 


152 


2. 1 


8 


9 


105 


23-3 


5 


7 


1. 21328 


.00118 


1.31184 


. 00075 


35 


152 


II. 


8 


9 


105 


29.0 


5 


7 


I. 21446 


.00118 


1.31108 


. 00076 


36 


152 


19-9 


8 


9 


105 


34-8 


S 


8 


I. 21564 


.00118 


1.31032 


. 00076 


37 


152 


28.8 


8 


9 


105 


40.6 


5 


8 


1.21682 


.00118 


I- 30955 


. 00077 


38 


152 


37-7 


8 


9 


105 


46- 5 


5 


9 


I. 21800 


.00118 


1. 30877 


. 00078 


39 


152 


46.6 


8 


9 


lOS 


52-5 


6 





1.21918 


.00118 


1.30799 


. 00078 


6 40 


152 


55-5 


8 


9 


105 


58-5 


6 





I. 22037 


.00119 


1.30720 


. 000 7g 


41 


153 


4-4 


+ 8 


9 


io5 


46 


+ 6 


I 


1. 22156 


+ 0.00119 


1.30639 


■ — 0. 00081 


42 


153 


13-3 


8 


9 


106 


10.7 


6 


I 


1.22275 


.00119 


1-30558 


.00081 


43 


153 


22.2 


8 


9 


106 


16.8 


6 


1 


I- 22394 


. 00119 


1-30476 


. 00082 


44 


153 


31- 1 


8 


9 


106 


23.0 


6 


2 


1.22513 


. 001 ig 


1-30393 


. 00083 


45 


153 


39-9 


8 


8 


io5 


29.2 


6 


2 


1.22632 


.00119 


1.30310 


. 00083 


46 


153 


48.7 


8 


8 


106 


35-5 


6 


3 


I. 22751 


.00119 


1. 30226 


. 00084 


47 


IS3 


57-5 


+ 8.« 


106 


41.8 


+ 6.3 


I. 22870 


+ 0. ooiig 


1.30141 


— 0. 00085 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

■t 

Table II — Continued. 



91 



Gr. Sid. 
Time. 





Diff. 


6' 


Diff. 


logR 


Diff. 


logR' 


Diff. 


h m 





/ 


/ 





/ 


1 










6 47 


153 


57-5 




106 


41.8 




1.22870 




1.30141 




48 


154 


6.3 


+ 8.8 


106 


48.1 


+ 6.3 


1. 22989 


+ 0.00119 


I. 30056 


— 0.00085 


49 


154 


15-1 


8.8 


106 


54-5 


6.4 


I. 23108 


.00119 


1. 29969 


.00087 


6 50 


154 


23-9 


8.8 


107 


0.9 


6.4 


I. 23228 


.00120 


1. 29881 


.00088 


51 


•54 


32.8 


+ 8.9 


107 


7-4 


+ 6.S 


I. 23348 


+ 0.00120 


1.29792 


— 0. 00089 


52 


154 


41.6 


8.8 


107 


13-9 


6-5 


1.23468 


. 00120 


1.29702 


.00090 


53 


154 


50-5 


8.9 


107 


20.5 


6.6 


1.23588 


.00120 


I. 29612 


. 00090 


54 


154 


59-3 


8.8 


107 


27.2 


6.7 


I. 23708 


. 00120 


1. 29521 


.00091 


55 


155 


8.1 


8.8 


107 


34- 


6.8 


1.23828 


. 00120 


1.29429 


.00092 


56 


155 


17.0 


8.9 


107 


40.9 


6.9 


1.23948 


. 00120 


1.29336 


. 00093 


57 


155 


25.8 


8.8 


107 


47-9 


7.0 


1.24068 


. 00120 


1. 29242 


. 00094 


58 


155 


34-6 


8.8 


107 


55-0 


7-1 


1. 24188 


. 00120 


1. 29147 


. 00095 


59 


155 


43-4 


8.8 


108 


2. 1 


7-1 


I. 24308 


. 00120 


I. 29051 


. 00096 


7 


155 


52.2 


8.8 


108 


9.2 


7-1 


1.24429 


.00121 


1.28953 


. 00098 


I 


156 


I.O 


+ 8.8 


108 


16.4 


+ 7.2 


1.24550 


+ 0. 00121 


1.28854 


— 0.00099 


2 


156 


9.8 


8.8 


108 


23-7 


7-3 


1. 24670 


.00120, 


1.28754 


.00100 


3 


156 


18.6 


8.8 


108 


31- 1 


7-4 


I. 24790 


. 00120 


1.28654 


. OOIOO 


4 


156 


27.4 


8.8 


108 


38.5 


7-4 


1.24910 


.00120 


1-28553 


.00101 


5 


156 


36.1 


8.7 


108 


45-9 


7-4 


1.25030 


. 00120 


I. 28452 


.00101 


6 


156 


44.8 


8.7 


108 


53-4 


7-5 


1. 25150 


.00120 


1. 28349 


. 00103 


7 


156 


53-5 


8.7 


109 


0.9 


7-5 


1.25270 


.00120 


I. 28245 


. 00104 


8 


157 


2.2 


8.7 


109 


8.4 


7-5 


I. 25390 


.00120 


1. 28139 


.00106 


9 


157 


10.9 


8.7 


109 


16.0 


7.6 


1. 25510 


. 00120 


I. 28032 


.00107 


7 10 


157 


19.6 


8.7 


10*9 


23.6 


7.6 


1.25630 


. 00120 


1.27924 


. 00108 


II 


157 


28.3 


+ 8.7 


109 


3'-3 


+ 7-7 


1-25750 


+ 0.00120 


1.278T5 


— 0.00109 


12 


157 


37-0 


8.7 
8.6 


109 


39-1 


7.8 
7-9 


1.25870 


. 00120 
. 00120 


1.27705 


.00110 
.00111 


13 


157 


45.6 




109 


47.0 


1.25990 




1.27594 




14 


157 


54-2 


8.6 


109 


55-1 


8.1 


1.26110 


.00120 


1.27482 


.00112 


IS 


158 


2.8 


8.6 


no 


3-2 


8.1 


1.26229 


.00119 


1.27369 


.00113 


16 


158 


II. 4 


8.6 


no 


II. 4 


8.2 


1.26348 


.00119 


1.27255 


.00114 


>7 


158 


20.0 


8.6 


no 


19.7 


8.3 


1.26467 


.00119 


1. 27140 


.00115 


18 


158 


28.6 


8.6 


no 


28.1 


8.4 


I. 26586 


.00119 


1.27024 


.00116 


19 


158 


37-2 


8.6 


no 


36.6 


8.5 


1.26705 


.00119 


1.26907 


.00117 


7 20 


158 


45.8 


+ 8.6 


no 


45-2 


+ 8.6 


I. 26824 


+ 0. 001 19 


I. 26789 


— 0. 00118 


21 


158 


54-4 


8.6 


no 


53-8 


8.6 


1.26943 


.00119 


1.26670 


.00119 


22 


159 


3-0 


8.6 


III 


2.5 


8.7 


I. 27062 


.00119 


1.26550 


. 00120 


23 


159 


II. s 


8.5 


III 


"■3 


8.8 


I. 27180 


.00118 


1.26429 


.00121 


24 


159 


20.0 


8.5 


in 


20.2 


8.9 


1.27298 


.00118 


1.26306 


. 00123 


25 


159 


28. s 


8.5 


III 


29.2 


9.U 


I. 27416 


.00118 


1. 26182 


. 00124 


26 


159 


37- 


8.5 


III 


38.2 


9.0 


1. 27534 


.00118 


1.26057 


.00125 


27 


159 


45-5 


8.5 


III 


47-3 


9.1 


1.27652 


.00118 


I. 25930 


.00127 


28 


159 


54.0 


8.5 


III 


56.5 


9.2 


1. 27769 


.00117 


I. 25802 


.00128 


• 29 


160 


2-5 


8.5 


112 


5-7 


9.2 


1.27886 


.00117 


1.25673 


.00129 


7 30 


160 


II. 


8.5 


112 


15.0 


9-3 


1.28003 


.00117 


1.25543 


.00130 


31 


160 


19.5 


+ 8.5 


112 


24.4 


+ 9-4 


I. 28120 


+ 0.00117 


I. 2541 I 


— 0.00132 


32 


160 


28.0 


8.5 


112 


33-9 


9.5 


1. 28237 


.00117 


1.25277 


.00134 


33 


160 


36.4 


8.4 


112 


43-5 


9.6 


1. 28354 


.00117 


1. 25142 


.00135 


34 


160 


44.8 


8.4 


112 


53-3 


9.8 


1. 28471 


0. 00117 


I. 25005 


0.00137 



92 



TRANSIT OF VENUS, 1874. 

Table II— Continued. 



Gr. Sid. 
Time. 


e 


Diff. 


e' 


DiiT. 


logR 


Diff. 


logR' 


Diff. 


h m 





/ 


/ 





/ 


/ 










7 34 


160 


44.8 




112 


53-3 




1. 28471 




1.25005 




35 


160 


53-^ 


+ 8.4 


"3 


3-2 


+ 9-9 


1. 28588 


+ 0. 00117 


1.24867 


— 0.00138 


36 


161 


1.6 


8.4 


"3 


13-2 


10. 


1. 28704 


.00116 


1.24728 


.00139 


37 


i6i 


10. 


8.4 


"3 


23.4 


10.2 


I. 28820 


.00116 


1.24587 


.00141 


38 


161 


18.4 


8.4 


"3 


33-7 


10.3 


1.28936 


.00116 


1.24445 


. 00142 


39 


161 


26.8 


8.4 


"3 


44.1 


10.4 


I. 29051 


.00115 


1. 24302 


• 00143 


7 40 


i6i 


35-2 


8.4 


"3 


54-7 


10.6 


I. 29166 


.00115 


1.24158 


.00144 


41 


161 


43-5 


+ 8.3 


,14 


5-4 


+ 10.7 


1.29280 


+ 0. 001 14 


1. 24012 


— 0. 00146 


42 


161 


51.8 


8.3 


114 


16.2 


10.8 


1.29394 


.00114 


1. 23865 


. 00147 


43 


162 


0. 1 


8.3 


114 


27.0 


10.8 


1.29507 


.00113 


1. 23717 


. 00148 


44 


162 


8.4 


8.3 


114 


37-9 


10.9 


1.29620 


.00113 


1. 23568 


.00149 


45 


162 


16.7 


8.3 


114 


48.9 


II. 


1.29732 


.00112 


1. 23418 


.00150 


46 


162 


25.0 


8.3 


"5 


0.0 


II. I 


1.29844 


.00112 


1. 23267 


.00151 


47 


162 


33-3 


8.3 


"5 


II. 2 


II. 2 


1. 29956 


.00112 


I. 231 14 


.00153 


48 


162 


41.6 


8.3 


"5 


22. s 


".3 


1. 30067 


.00111 


1. 22959 


.00155 


49 


162 


49-9 


8-3 


"5 


33.8 


"•3 


1. 30178 


•OOIII 


1.22803 


.00156 


7 So 


162 


58.1 


8.2 


"5 


45-2 


II. 4 


I. 30289 


.00111 


1.22645 


.00158 


51 


163 


6.3 


+ 8.2 


"5 


56.8 


+ II. 6 


1. 30400 


+ 0. OOIII 


1.22485 


— 0. 00160 


52 


163 


14.5 


8.2 


116 


8.6 


II. 8 


I. 30510 


.00110 


1.22325 


.00160 


S3 


163 


22. 7 


-8.2 


116 


20.6 


12.0 


1.30620 


y .00110 


1. 22164 


.00161 


54 


.63 


30-9 


8.2 


116 


32.7 


12. 1 


1. 30730 


.00110 


1.22000 


. 00164 


55 


163 


39-' 


8.2 


116 


44-9 


12.2 


1.30839 


.00109 


1.2183s 


. 00165 


56 


163 


47-3 


8.2 


116 


57.2 


12.3 


1.30948 


. 00109 


1.21669 


. 00166 


57 


163 


55-5 


8.2 


117 


9.6 


12.4 


1. 31056 


. 00108 


I.2I50I 


. 00168 


58 


164 


3-7 


8.2 


117 


22.2 


12.6 


1.31164 


. 00108 


I. 21332 


.00169 


59 


164 


II. 9 


8.2 


117 


35- 


12.8 


1. 31271 


. 00107 


I.2II6I 


.00171 


8 


164 


20.0 


8.1 


117 


48.0 


13.0 


1.31378 


.00107 


I. 20989 


.00172 


I 


164 


28.1 


+ 8.1 


118 


1. 1 


+ 13-1 


1. 31484 


4- 0.00106 


1. 20815 


— 0.00174 


2 


164 


36.2 


8.1 


118 


14.4 


13-3 


••31590 


. 00106 


1. 20640 


.00175 


3 


164 


44-3 


8.1 


118 


27.8 


13-4 


I- 31695 


. 00105 


1.20464 


.00176 


4 


164 


52.4 


8.1 


118 


41.4 


13.6 


1. 31799 


. 00104 


1.20287 


.00177 


S 


165 


0.5 


8.1 


118 


55- 1 


13-7 


1-31903 


. 00104 


1. 20108 


.00179 


6 


165 


8.S 


8.0 


119 


8.9 


13-8 


1. 32007 


. 00104 


1. 19928 


. 00180 


7 


16S 


16. 5 


8.0 


119 


22.9 


14.0 


1.32111 


. 00104 


1. 19746 


. 00182 


8 


- 165 


24-5 


8.0 


119 


37.0 


14. 1 


I. 32214 


. 00103 


1. 19562 


. 00184 


9 


16s 


32.5 


8.0 


119 


51-3 


14-3 


1. 32317 


. 00103 


I- 19377 


. 00185 


8 10 


165 


40.5 


8.0 


120 


5.8 


14.5 


1. 32419 


. 00102 


I. I9I90 


.00187 


II 


165 


48.4 


+ 7-9 


120 


20.4 


+ 14-6 


1.32520 


+ 0. OOIOI 


1. 19002 


— 0.00188 


12 


165 


56.3 


7.9 


120 


35-2 


14.8 


1. 32621 


. OOIOI 


1. I88I2 


. 00190 


13 


166 


4.2 


7-9 


120 


50.2 


15.0 


1. 32721 


.00100 


1.18621 


.00191 


14 


166 


12. 1 


7.9 


121 


5-4 


15-2 


1. 32821 


. OOIOO 


1. 18429 


. 00192 


15 


166 


20.0 


7.9 


121 


20. 7 


15-3 


1.32920 


. 00099 


1. 18236 


.00193 


16 


166 


27.9 


7.9 


121 


36.2 


15-5 


I- 33019 


. 00099 


1. 1 8041 


.. 00195 


17 


166 


35-8 


7.9 


121 


51-9 


15-7 


1-33117 


.00098 


1. 17844 


.00197 


18 


166 


43-7 


7-9 


122 


7.9 


16.0 


I-332H 


. 00097 


1. 17646 


.00198 


19 


166 


51.6 


7-9 


122 


24.1 


16.2 


'•333" 


. 00097 


1. 17446 


. 00200 


8 20 


166 


59.5 


7-9 


122 


40.5 


16.4 


1-33407 


. 00096 


I- 17245 


. 00201 


21 


167 


7-3 


+ 7-8 


122 


57.0 


+ 16.5 


1.33502 


+ 0.00095 


1. 17043 


— 0.00202 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Table II — Continued. 



93 



Gr. Sid. 




















Time. 


fl 




Diff. 


ff 


Diff. 


logR 


Diff. 


log R', 


Diff. 


h m 





/ 


t 


' 


/ 










8 21 


167 


7-3 




122 57- 




1.33502 




1. 17043 




22 


167 


15-1 


+ 7.8 


123 13-7 


+ 16.7 


1-33597 


+ 0.00095 


1. 16840 


— 0. 00203 


23 


167 


22.9 


7.8 


123 30.6 


16.9 


1.33691 


. 00094 


1. 16636 


.00204 


24 


167 


30-7 


7.8 


123 47.7 


17. 1 


I- 33783 


. 00092 


1. 16430 


. 00206 


2S 


167 


38-5 


7.8 


124 5. 1 


17.4 


1-33874 


. 00091 


1. 16223 


. 00207 


26 


167 


46.3 


7.8 


124 22. 6 


17-5 


1-33965 


.00091 


1. 16015 


. 00208 


27 


167 


54.1 


7.8 


124 40.3 


17.7 


I- 34056 


. 0U091 


1. 15806 


. 00209 


28 


168 


1.9 


7.8 


124 58. 2 


17.9 


I- 34147 


.00091 


I- 1S59S 


.00211 


29 


168 


9-7 


7.8 


125 16. 3 


18. 1 


I- 34237 


.00090 


1. 15382 


.00213 


8 30 


168 


17.5 


7.8 


125 34. 6 


18.3 


1-34327 


.00090 


1. 15168 


. 00214 


31 


168 


25.2 


+ 7-7 


125 53-2 


+ 18.6 


1. 34416 


-|- 0. 00089 


1. 14952 


— 0.00216 


32 


168 


32.9 


7-7 


126 12.0 


18.8 


1. 34504 


. 00088 


I- 14735 


.00217 


33 


168 


40.6 


7-7 


126 31.0 


19.0 


I- 34S9I 


. 00087 


1.14517 


.00218 


34 


168 


48.3 


7-7 


126 50. 2 


19.2 


1.34677 


. 00086 


1. 14298 


.00219 


35 


168 


56.0 


7-7 


127 9.6 


19.4 


1.34762 


.00085 


1. 14078 


.00220 


36 


169 


3-6 


7.6 


127 29.3 


19.7 


I- 34847 


. 00085 


1-13857 


.00221 


37 


169 


II. z 


7,6 


127 49.3 


20.0 


1-34931 


. 00084 


I- 13635 


. 00222 


38 


169 


18.8 


7.6 


128 9. s 


20.2 


1.35014 


.00083 


1.13411 


.00224 


39 


169 


26.4 


7.6 


128 29. 9 


20.4 


1. 35096 


. 00082 


1. 13 186 


. 00225 


8 40 


169 


34- 


7.6 


128 50. 6 


20. 7 


1-35178 


.00082 


1. 12961 


. 00225 


41 


169 


41-5 


+ 7.5 


129 II. 6 


+ 21.0 


I- 35259 


-f 0.00081 


1. 12735 


— 0. 00226 


42 


169 


49.0 


7.5 


129 32. 8 


21.2 


1.35339 


.00080 


1. 12508 


.00227 


43 


169 


56.5 


7-5 


129 54,2 


21.4 


1.35419 


. 00080 


I. 12280 


.00228 


44 


170 


4.0 


7-5 


130 16.0 


21.8 


1. 35498 


.00079 


1. 12050 


. 00230 


45 


170 


ii.S 


7-5 


130 38.0 


22.0 


I- 35575 


.00077 


1. 11820 


. 00230 


46 


170 


19.0 


7-5 


131 0.2 


22.2 


1- 35651 


.00076 


1. 1 1589 


.00231 


47 


170 


26.5 


7-5 


131 22. 7 


22.5 


1-35726 


.00075 


1-11358 


.00231 


48 


170 


34-0 


7-5 


131 45-6 


22.9 


I- 35801 


.00075 


1. 1 1 126 


. 00232 


49 


170 


41-5 


7-5 


132 8. 7 


23-1 


1-35875 


. 00074 


1. 10892 


. 00234 


8 so 


170 


49.0 


7-5 


132 32.1 


23-4 


1- 35949 


. 00074 


1. 10658 


.00234 


51 


170 


56.4 


+ 7.4 


•32 55-8 


+ 23.7 


I . 36022 


H- 0. 00073 


1. 10423 


— 0. 00235 


52 


171 


3.8 


7-4 


133 19-8 


24.0 


1.36094 


. 00072 


1. 10188 


.00235 


S3 


171 


II. 2 


7-4 


133 44-0 


24.2 


1. 36164 


.00070 


1.09952 


. 00236 


54 


171 


18. s 


7-3 


134 8. s 


24.5 


1.36233 


.00069 


1. 09716 


. 00236 


55 


171 


25.8 


7-3 


'34 33-3 


24.8 


1. 36301 


. 00068 


* 1.09480 


. 00236 


56 


171 


33-1 


7-3 


134 58.4 


25-1 


1.36368 


.00067 


1.09244 


. 00236 


57 


171 


40.4 


7-3 


135 23.9 


25-5 


1. 36434 


. 00066 


1. 09008 


. 00236 


58 


171 


47-7 


7.3 


135 49-7 


25.8 


1. 36500 


.00066 


1.08771 


. 00237 


59 


171 


55-0 


7.3 


136 15-8 


26.1 


1. 36566 


.00066 


1.08534 


.00237 


9 


172 


2.3 


7-3 


136 42.1 


26.3 


1. 36631 


.00065 


1. 08297 


.00237 


I 


172 


9-5 


+ 7.2 


137 8.8 


+ 26.7 


1-36695 


-|- 0.00064 


1.08059 


— 0.00238 


2 


172 


16.7 


7.2 


137 35-8 


27.0 


1-36759 


. 00064 


1. 07821 


. 00238 


3 


172 


23.9 


7.2 


138 3- 


27.2 


I. 36821 


.00062 


1-07583 


. 00238 


4 


172 


31- 1 


7.2 


138 30-5 


27-5 


I. 36882 


.00061 


1-07345 


.00238 


5- 


172 


38.3 


7.2 


138 58.3 


27.8 


1.36942 


. 00060 


1. 07108 


. 00237 


6 


172 


45-5 


7.2 


139 26.5 


28.2 


1. 37001 


.00059 


1. 06872 


. 00236 


7 


172 


52.7 


7.2 


139 55- I 


28.6 


1- 37059 


.00058 


1.06637 


.00235 


8 


172 


59-9 


7.2 


140 24. 


28.9 


i-37"7 


-f- 0.00058 


1. 06403 


— 0. 00234 



94 



TRANSIT OF VENUS, 1874. 
Table II — Continued. 



Gr. Sid. 
Time. 



9 
10 
II 
12 
13 
H 
IS 
16 

17 
18 

19 
20 
21 
22 

23 

24 

25 

26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 



Diff. 



o / 
172 59- 
173 
173 
173 
173 
173 
173 
173 
173 
174 
174 
174 
174 
174 
174 



7-1 
14-3 
21.4 
28.5 
35-6 
42.6 
49.6 
56.6 

3-6 
10.6 
17. 6 
24.6 
31-5 
38-4 



174 


45-3 


174 


52.2 


174 


59-1 


175 


6.0 


'75 


12.9 


175 


19.8 


175 


26.7 


175 


33-5 


175 


40.3 


175 


47.1 


175 


53-9 


176 


0.6 


176 


7-3 


176 


14.0 


176 


20.7 


176 


27.4 


176 


34-1 


176 


40.8 


176 


47-4 


176 


54- 


177 


0.6 


177 


7.2 


177 


13-8 


177 


20.4 


177 


27.0 


177 


33-6 


177 


40. 1 


177 


46.6 


177 


53-1 


177 


59-6 


178 


6.1 


178 


12. 5 


.78 


18.9 



+ 7.2 

7.2 

+ 7-1 
7-1 
7-1 
7.0 
7.0 
7.U 
7.0 
7.0 
7.0 

4- 7.U 
6.9 
6.9 
6.9 
6.9 
6.9 
6.9 
6.9 
6.9 
6.9 
6.8 

+ 6.8 
6.8 
6.8 
6.7 
6.7 
6.7 

6.7 
6.7 
6.7 
6.7 

+ 6.6 
6.6 
6.6 
6.6 
6.6 
6.6 
6.6 
6.6 
6.5 
6.5 

+ 6.5 
6.5 

6.5 
6.4 

6.4 



140 


24.0 


140 


53-3 


141 


22.9 


141 


52.8 


142 


23.1 


142 


53-6 


143 


24.4 


143 


55-6 


144 


27.1 


144 


59.0 


145 


31-3 


146 


3-9 


146 


36.7 


147 


9.9 


147 


43-5 


148 


17.4 


148 


51-5 


149 


26.0 


150 


0.9 


150 


36.2 


151 


II. 7 


151 


47-5 


152 


23-7 


153 


0. 1 


153 


36.8 


154 


13-8 


154 


51.0 


155 


28.5 


156 


6.3 


156 


44-4 


157 


22.8 


158 


1.4 


158 


40.2 


159 


19-3 


159 


58.6 


160 


38.2 


161 


18.0 


161 


58.1 


162 


38.4 


163 


19.0 


163 


59-7 


164 


40.5 


165 


21.5 


166 


2.7 


166 


44.0 


167 


25-4 


168 


6.9 


168 


48.5 



Diff. 



+ 29.3 
29.6 

+ 29.9 
30-3 
30-5 
30.8 
31.2 
3I.5 
31-9 
32.3 
32.6 

+ 32.8 
33-2 
33-6 
33-9 
34-1 
34-5 
34-9 
35-3 
35-5 
35-8 
36.2 

+ 36-4 
36.7 
37- o 
37-2 
37-5 
37-8 
38.1 
38.4 
38.6 
38.8 

+ 39-1 
39-3 
39-6 
39.8 
40. 1 

40-3 
40.6 
40.7 
40.8 
41.0 
+ 41.2 

41.3 
41.4 

41.5 
41.6 



logR 



37117 
37174 
37230 
37285 
37338 
37390 
37441 
37492 
37543 
37593 
37641 
37687 

37732 
37776 
37820 
37864 
37907 
37950 
37992 
38032 
38071 
38108 

38143 
38178 
38212 
38246 
38279 
383" 
38342 
38373 
38403 
38432 
38460 

38487 
38513 
38538 
,38562 

.38584 
,38605 
, 38626 
, 38646 
.38665 



Diff. 



• 38700 
•38717 

• 38733 
.38748 
.38762 



+ 0.00057 

. 00056 

+ o. 0005s 

• 00053 
. 00052 
.00051 
.00051 
.00051 
. 00050 
. 00048 
. 00046 

+ o. 00045 
.00044 
.00044 
.00044 

. 00043 
. 00043 

.00042 
. 00040 

. 00039 

.00037 

. 00035 

+ 0.00035 

. 00034 

. 00034 

• 00033 

. 00032 
.00031 
.00031 
. 00030 
. 00029 
. 00028 
+ o. 00027 
. 00026 
. 00025 
. 00024 

. 00022 
.00021 
. 00021 
. 00020 
.00019 
.00018 

+ o. 00017 

.00017 

. 00016 

.00015 

+ 0.00014 



logR' 



I. 06403 
1. 06169 

1-05935 

1. 05702 

1.05470 

1.05240 
I.050II 

1.04783 
1.04556 
1. 04330 

1. 04106 

1.03883 

I. 03661 

1. 03441 

1.03224 
I. 03010 
1.02799 
1.02590 

1. 02383 

1. 02177 

1. 01974 
1. 01773 
I- 01575 

1. 01380 
i.ou88 
1 . 00999 
1. 00813 
1.00630 
1. 00451 

1.00276 
1. 00106 
o. 99940 
0. 99777 

u. 99618 

o. 99464 
o. 99315 
o. 99171 
0.99031 

o. 98895 
o. 98764 
o. 98637 
0.98514 
o. 98396 
o. 98284 

0.98178 

o. 98077 
0.97981 
o. 97889 



Diff. 



o. 00J34 
• 00234 

o. 00233 
. 00232 
. 00230 
. 00229 
. 00228 
. 00227 
. 00226 
. 00224 
. 00223 

O. 00222 
. 00220 
.00217 
. 00214 
.00211 
. 00209 
. 00207 
. 00206 
. 00203 
. 00201 
. 00198 

o. 00195 

. 00192 
. 00189 
. 00186 
. 00183 
.00179 
.00175 
.00170 
. 00166 
. 00163 

■ o. 00159 

.00154 

. 00149 
. 00144 
.00140 
. 00136 
.00131 
. 00127 
.00123 
.00118 

- u. 00112 

. 00106 
.00101 
. 00096 

- o. 00092 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Table II — Continued. 



95 



Gr. Sid. 






















Time. 


e 




Diff. 


6' 




Diff. 


logR 


Diff. 


logR' 


Diff. 


h m 
9 55 


178 


18.9 


/ 


c 
168 


/ 

48. 5 


/ 


1.38762 




0. 97889 




56 


178 


25-3 


+ 6.4 


169 


30-3 


+ 41.8 


1.38775 


-|- 0.00013 


0. 97803 


— 0. 00086 


57 


178 


31-7 


6.4 


170 


12.2 


41.9 


1.38787 


.00012 


0. 97723 


. 00080 


S8 


178 


38.1 


6.4 


170 


54.1 


41.9 


1.38798 


.00011 


0. 97649 


. 00074 


59 


178 


44-5 


6.4 


171 


36.1 


42.0 


1.38808 


.00010 


0.97580 


. 00069 


10 


178 


50.9 


6.4 


172 


18. 1 


42.0 


1. 38817 


. 00009 


0.97516 


. 00064 


I 


178 


57.2 


+ 6.3 


173 


0.1 


-J- 42.0 


1.38825 


-f. 0.00008 


0. 97457 


— 0. 00059 


2 


179 


3-5 


6.3 


173 


42.2 


42.1 


■ .38832 


. 00007 


0. 97403 


. 00054 


3 


179 


9.8 


6.3 


174 


24.2 


42.0 


1.38839 


. 00007 


0.97355 


. 00048 


4 


179 


16. 1 


6.3 


175 


6.2 


42.0 


1.38845 


. 00006 


0. 97313 


.00042 


S 


179 


22.4 


6.3 


175 


48.2 


42.0 


1.38850 


. 00005 


0. 97276 


.00037 


6 


179 


28.7 


6.3 


176 


20.2 


42.0 


1.38854 


. 00004 


0. 97245 


.00031 


7 


179 


35-0 


6.3 


177 


2.2 


42.0 


1.38857 


. 00003 


0. 97220 


. 00025 


8 


179 


41.3 


6-3 


177 


44.2 


42.0 


1. 38860 


. 00003 


0. 97201 


.00019 


9 


179 


47.6 


6-3 


178 


26.2 


42.0 


1.38863 


. 00003 


0.97188 


. 00013 


10 10 


179 


53.9 


6.3 


179 


18. 1 


41.9 


1.38865 


. 00002 


0.97180 


. 00008 


II 


180 


0. 1 


-f- 6.2 


179 


59-9 


+ 41.8 


1.38866 


-f- 0. 0000 1 


0.97177 


— 0. 00003 


12 


180 


6.3 


6.2 


180 


41. 6 


41.7 


1.3886s 


— 0. 0000 1 


0.97180 


-|- 0.00003 


13 


180 


12. 5 


6.2 


i8i 


23.1 


41. s 


1.38864 


. 0000 1 


0. 97188 


. 00008 


14 


180 


18.6 


6.1 


182 


4.4 


41.3 


1.38862 


. 00002 


0. 97202 


. 00014 


IS 


180 


24.7 


6.1 


182 


45-5 


41. 1 


1.38859 


.00003 


0. 97221 


. 00019 


16 


180 


30.8 


6.1 


183 


26. s 


41.0 


1.38856 


. 00003 


0. 97245 


. 00024 


17 


180 


36.9 


6.1 


184 


7.4 


40.9 


1.38852 


. 00004 


0. 97274 


.00029 


18 


180 


43.0 


6.1 


184 


48.1 


40.7 


1.38847 


. 00005 


0. 97307 


. 00033 


19 


180 


49.1 


6.1 


185 


28.7 


40.6 


1. 38841 


. 00006 


0. 97344 


. 00037 


10 20 


180 


55-2 


6.1 


186 


9-1 


40.4 


1.38834 


. 00007 


0. 97386 


. 00042 


21 


181 


1.2 


-1-6.0 


186 


49-3 


+ 40.2 


1.38827 


— 0. 00007 


0. 97433 


-f- 0.00047 


22 


181 


7.2 


6.0 


187 


29.4 


40. 1 


1. 38819 


. 00008 


0. 97886 


. 00053 


23 


181 


13.2 


6.0 


188 


9.2 


39.8 


1. 38810 


. 00009 


0. 97544 


. 00058 


24 


181 


19.2 


6.0 


188 


48.7 


39-5 


1.38800 


. OOOIO 


0. 97606 


. 00062 


25 


181 


25.2 


6.0 


189 


28.1 


39.4 


1.38789 


.00011 


0. 97673 


. 00067 


26 


181 


31.2 


6.0 


190 


7.3 


39.2 


1.38778 


.00011 


0. 97744 


. 00071 


27 


181 


37-1 


5-9 


190 


46. 1 


38.8 


1.38766 


. 00012 


u. 97819 


. 00075 


28 


181 


43-0 


5-9 


191 


24.7 


38.6 


1.38754 


. 00012 


0. 97899 


. 00080 


29 


181 


48.9 


5-9 


192 


3.0 


38.3 


1.3S742 


. 00012 


0. 97984 


. 00085 


10 30 


181 


54-8 


5-9 


192 


40.9 


37-9 


1.38729 


. 00013 


0. 98073 


. 00089 


31 


182 


0.7 


+ 5-9 


193 


18.6 


+ 37.7 


1. 38715 


— 0.00014 


0.98166 


-(- 0. 00093 


32 


182 


6.6 


5.9 


193 


56. 1 


37.5 


1. 38700 


.00015 


0. 98263 


. 00097 


33 


182 


12.5 


5-9 


194 


33-3 


37.2 


1. 38684 


. 00016 


0. 98363 


.00100 


34 


182 


18.4 


5.9 


195 


10.3 


37.0 


1.38667 


.00017 


0. 98466 


. 00103 


35 


182 


24.3 


5-9 


'95 


47.0 


36.7 


1.38650 


.00017 


0.98572 


. 00106 


36 


182 


30.1 


5.8 


196 


23.4 


36.4 


1.38633 


.00017 


0. 98682 


.00110 


37 


182 


35-9 


5-8 


196 


59.4 


36.0 


1. 38615 


.00018 


0. 98795 


.00113 


38 


182 


41.7 


5-8 


197 


35.1 


35-7 


1.38596 


. 00019 


0.989 1 1 


.00116 


39 


182 


47-5 


5-8 


198 


10. s 


35-4 


1.38576 


. 00020 


0.99031 


. 00120 


10 40 


182 


53-3 


5-8 


198 


45.6 


35-1 


1.38556 


. 00020 


0.99155 


.00124 


41 


182 


59.0 


5-7 


199 


20.4 


34-8 


1.38536 


. 00020 


0. 99282 


.00127 


42 


183 


4.7 


+ 5.7 


199 


54.9 


+ 34-5 


1.38515 


— 0.00021 


0. 99411 


-f- 0.00129 



96 



TRANSIT OF VENUS, 1874. 
Table II — Continued. 



Gr. Sid. 






















Time. 


s 




Diflf. 


6' 




Diff. 


logR 


Diff. 


logR' 


Diff. 


h m 





/ 


/ 





/ 


/ 










10 42 


183 


4-7 




199 


54-9 




1-38515 




0.9941 1 




43 


183 


10.4 


+ 5-7 


200 


29.0 


+ 34-1 


1.38493 


— 0.00022 


0. 99542 


+ 0.00131 


44 


183 


16. 1 


5-7 


201 


2.8 


33-8 


1. 38471 


. 00022 


0. 99676 


. 00134 


45 


183 


21.8 


5-7 


201 


36.2 


33-4 


1.38448 


.00023 


0.99813 


.00137 


46 


183 


27. S 


■ 5-7 


202 


9-3 


33-1 


1.38425 


.00023 


0.99952 


- 00139 


47 


183 


33-2 


S-7 


202 


42.1 


' 32-8 


1. 38401 


. 00024 


1.00093 


. 00141 


48 


183 


38.9 


5-7 


203 


14.6 


32-5 


1.38376 


. 00025 


1. 00236 


. 00143 


49 


183 


44.6 


5-7 


203 


46.7 


32.1 


1-38350 


.00026 


1.00381 


-00145 


10 So 


183 


50.2 


S-6 


204 


18.5 


31.8 


1.38324 


. 00026 


1 . 00528 


. 00147 


SI 


183 


55-8 


+ 5.6 


204 


50.0 


+ 31-5 


1.38297 


— 0.00027 


1.00678 


+ 0.00150 


52 


184 


1.4 


S-6 


20s 


21.2 


31.2 


1.38270 


. 00027 


1. 00830 


.00152 


53 


184 


7.0 


5-6 


20s 


52.0 


30.8 


1-38243 


. 00027 


1.00983 


. 00153 


54 


184 


12.6 


S-6 


206 


22. s 


3°-S 


I- 3821s 


.00028 


1.01137 


. 00154 


55 


184 


18.1 


5.5 


206 


52.7 


30.2 


1. 38187 


.00028 


1. 01292 


.00155 


56 


184 


23.6 


5-5 


207 


22.5 


29.8 


I. 38158 


. 00029 


I. 01448 


.00156 


57 


184 


29.1 


5-5 


207 


51-9 


29.4 


1. 38129 


.00029 


1. 01606 


.00158 


58 


184 


34-6 


5-5 


208 


21.0 


29. 1 


1.38099 


. 00030 


1.01765 


.00159 


59 


184 


40. 1 


5-5 


208 


49.8 


28.8 


1.38068 


.00031 


1. 01925 


. 00160 


II 


184 


45.6 


5-5 


209 


18.2 


28.4 


1.38037 


.00031 


1.02086 


.00161 


I 


184 


SI. I 


+ 5-5 


209 


46.4 


+ 28.2 


1. 3800s 


— 0.00032 


1.02249 


+ 0.00163 


2 


184 


56.6 


5-5 


210 


14-3 


27-9 


1.37972 


.00033 


1. 02414 


.00165 


3 


185 


2.0 


S-4 


210 


42.0 


27.7 


1-37939 


.00033 


1. 02580 


. 00166 


4 


185 


7.4 


5-4 


211 


9.2 


27.2 


1.37906 


. 00033 


1. 02746 


.00166 


5 


185 


12.8 


5-4 


211 


35-9 


26.7 


I- 37873 


- 00033 


1. 02912 


.00166 


6 


185 


18.2 


5-4 


212 


2-4 


26. s 


1. 37840 


- 00033 


1-03079 


. 00167 


7 


185 


23.6 


5-4 


212 


28.7 


26.3 


1.37806 


. 00034 


1.03246 


.00167 


8 


185 


29.0 


5-4 


212 


S4-6 


25-9 


1. 37771 


.00035 


1-03413 


.00167 


9 


185 


34-4 


5-* 


213 


20.2 


25.6 


1-37736 


. 00035 


1-03581 


. 00168 


11 10 


185 


39.8 


5-4 


213 


45.6 


25-4 


I. 37701 


. 00035 


1-03749 


. 00168 


II 


185 


45-1 


+ 5-3 


214 


10.6 


+ 25.0 


1.37666 


— 0. 0003s 


1. 03917 


+ 0.00168 


12 


185 


50.4 


S-3 


214 


35-3 


24-7 


1.37630 


. 00036 


1. 04086 


.00169 


13 


185 


55-7 


5-3 


214 


59-8 


24.5 


1-37594 


. 00036 


1.04255 


. 00169 


14 


186 


I.O 


5-3 


215 


23-9 


24. 1 


1-37558 


.00036 


1.04424 


. 00169 


IS 


186 


6.3 


5-3 


215 


47.7 


23.8 


I- 37521 


.00037 


1-04593 


. 00169 


16 


186 


11.6 


5-3 


216 


II. 2 


23- 5 


I- 37484 


.00037 


1.04763 


.00170 


17 


186 


16.9 


5-3 


216 


34-5 


23-3 


I. 37446 


. 00038 


1-04933 


.00170 


18 


186 


22. 1 


5-2 


216 


57-5 


23.0 


I. 37408 


. 00038 


1. 05103 


.00170 


19 


186 


27-3 


S-2 


217 


20.4 


22.9 


I- 37369 


. 00039 


1.05274 


.00171 


II 20 


186 


32. 5 


5-2 


217 


43-0 


22.6 


I- 37330 


. 00039 


1-05445 


.00171 


21 


186 


37.7 


+ 5-2 


218 


5-2 


+ 22.2 


1. 37291 


— 0. 00039 


1. 05615 


+ 0.00170 


22 


186 


42.9 


5-2 


218 


27.0 


21.8 


I- 37251 


. 00040 


1.05785 


.00170 


23 


186 


48.1 


s-2 


218 


48.6 


21.6 


I. 37211 


. 00040 


1.05954 


. 00169 


24 


186 


53-3 


s-2 


219 


10. 


21.4 


1.37171 


. 00040 


1. 06122 


.00168 


25 


186 


58.4 


5-1 


219 


31-2 


21.2 


1.37130 


. 00041 


1 . 06290 


. 00168 


26 


187 


3-5 


5-1 


219 


52.2 


21. 


1.37089 


. 00041 


1.06458 


.00168 


27 


187 


8.6 


5-1 


220 


12.9 


20. 7 


I. 37048 


. 00041 


1.06625 


.00167 


28 


187 


13-7 


5- 1 


220 


33-2 


20.3 


I. 37006 


. 00042 


1.06792 


, 00167 


29 


187 


18.8 


+ S-I 


220 


53-3 


+ 20. 1 


1.36964 


— 0. 00042 


1. 06959 


+ 0.00167 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Table II — Continued. 



97 



Gr. Sid. 




















Time. 


fl 


Diff. 


& 




Diff. lo 


gR 


Diff. 


logR' 


Diff 


h m 
II 29 


/ 
187 18.8 


/ 



220 


53-3 


/ 


36964 




1.06959 




II 30 


187 23.9 


+ 5-1 


221 


13-2 


+ 19-9 I 


36922 


— 0. 00042 


1. 07125 


+ 0.00166 


31 


187 28.9 


+ 5.0 


221 


32.9 


+ 19.7 I 


36879 


— 0. 00043 


1.07291 


+ 0.00166 


32 


187 33-9 


S.o 


221 


52.3 


19.4 I 


36836 


.00043 


1.07456 


. 00165 


33 


187 38.9 


5.0 


222 


11.4 


19. 1 J 


36793 


. 00043 


1. 07621 


. 00165 


34 


187 43.9 


5-0 


222 


30.3 


18.9 J 


36750 


. 00043 


1. 07785 


. 00164 


35 


187 48.9 


5.0 


222 


49.1 


18.8 , 


36707 


.00043 


1.07949 


. 00164 


36 


187 53-9 


S-o 


223 


7.8 


18.7 J 


36664 


.000813 


1. 081 13 


. 00164 


37 


187 58.9 


5-0 


223 


26.2 


18.4 J 


36620 


.00044 


1.08276 


. 00163 


38 


188 3.9 


5.0 


223 


44-3 


18. 1 J 


36576 


.00044 


1.08438 


. 00162 


39 


188 8. 9 


5.0 


224 


2. 1 


17.8 1 , 


36532 


.00044 


1.08599 


.00161 


II 40 


188 13.9 


5.0 


224 


19.8 


17-7 I 


36488 


.00044 


1.08759 


. 00160 


41 


188 18.8 


+ 4-9 


224 


37-2 


+ 17.4 I 


36443 


— 0. 00045 


1. 08918 


+ 0. 00159 


42 


188 23.7 


4.9 


224 


54.3 


17. 1 , 


36398 


.00045 


1.09077 


. 00159 


43 


188 28.6 


4.9 


225 


"■3 


17.0 J 


36353 


.00045 


1. 09235 


. 00158 


44 


188 33. 5 


4.9 


225 


28.2 


16.9 J 


36307 


.00046 


I- 09393 


.00158 


45 


188 38.4 


4.9 


225 


44.8 


16.6 , 


36261 


. 00046 


1. 09551 


.00158 


46 


188 43-3 


4-9 


226 


1.3 


16.5 , 


36215 


. 00046 


1. 09708 


.00157 


47 


188 48.2 


4.9 


226 


17.7 


16.4 J 


36169 


.00046 


1.09864 


. 00156 


48 


188 53.1 


4.9 


226 


33-8 


16. 1 J 


36123 


,00046 


1. 10019 


.00155 


49 


188 58.0 


4.9 


226 


49-7 


15-9 I 


36077 


.00046 


1. 10172 


.00153 


II 50 


189 2. 8 


4.8 


227 


5-3 


15-6 , 


36030 


. 00047 


1. 10324 


. 00152 


51 


189 7. 6 


+ 4.8 


227 


20. 7 


+ 15-4 , 


35983 


— 0. 00047 


1. 10476 


+ 0.00152 


52 


189 12. 4 


4.8 


227 


35-9 


15-2 , 


35935 


. 00048 


1. 10627 


. 00151 


53 


189 17.2 


4.8 


227 


Si-o 


15- 1 , 


35887 


. 00048 


1. 10777 


. 00150 


54 


189 22. 


4.8 


228 


6.0 


'5-0 , 


35839 


. 00048 


1. 10926 


. 00149 


55 


189 26.8 


4.8 


228 


20.8 


14.8 J 


35791 


. 00048 


1. 1)074 


. 00148 


56 


189 31- S 


4-7 


228 


35-5 


14.7 , 


35743 


,. 00048 


1. 11222 


. 00148 


57 


189 36.2 


4-7 


228 


so. I 


14.6 J 


35695 


. 00048 


1.11369 


.00147 


58 


189 40. 9 


4-7 


229 


4-4 


14-3 I 


35647 


. 00048 


1-11515 


. 00146 


59 


189 45.6 


4.7 


229 


18.4 


14.0 J 


35599 


. 00048 


1. 11660 


.00145 


12 


189 50.3 


4-7 


229 


32.3 


13-9 I 


35551 


. 00048 


1. 11804 


.00144 


I 


189 55-0 


+ 4-7 


229 


46. I 


+ 13.8 , 


35503 


— 0. 00048 


1. 11947 


+ 0.00143 


2 


189 59.7 


4-7 


229 


59-7 


13.6 , 


35455 


. 00048 


I. X2089 


.00142 


3 


190 4.4 


4-7 


230 


13.2 


13-5 I 


35406 


. 00049 


I. 12230 


. 00141 


4 


190 9. 1 


4-7 


230 


26.6 


13-4 , 


35357 


. 00049 


1. 12370 


. 00140 


5 


190 13.7 


4.6 


230 


39-9 


'3-3 , 


35308 


.00049. 


1. 12510 


. 00140 


6 


190 18. 3 


4.6 


230 


53-9 


«3-i I 


35259 


. 00049 


1. 12650 


. 00140 


7 


190 22. 9 


4.6 


231 


6 


13-0 , 


35210 


. 00049 


1. 12789 


• 00139 


8 


190 27.5 


4.6 


231 


18.8 


12.8 J 


35161 


. 00049 


1. 12927 


. 0Q138 


9 


190 32.1 


4.6 


231 


31-3 


12.5 I 


35112 


. 00049 


1. 13063 


. 00136 


12 10 


190 36.7 


4.6 


231 


43-7 


12.4 J 


35063 


. 00049 


1. 13198 


■ 00135 


II 


190 41.3 


+ 4.6 


231 


56.0 


+ 12.3 I 


35013 


— 0.00050 


1. 13332 


-(- 0. 00134 


12 


190 45.9 


4.6 


232 


8.1 


12. 1 J 


34963 


.00050 


I- 13465 


■00133 


13 


190 50.4 


4-5 


232 


20.0 


11.9 J 


34913 


. 00050 


I- 13598 


.00133 


14 


190 54.9 


4.5 


232 


31.9 


11.9 , 


34863 


. 00050 


I- 13730 


. 00132 


15 


190 59.4 


4-5 


232 


43-7 


11.8 J 


34813 


. 00050 


1. 13861 


. 00131 


16 


191 3-9 


4-5 


232 


55-5 


II. 8 J 


34763 


. 00050 


1. 13991 


.00130 



S. Ex. 31- 



-13 



98 



TRANSIT OF VENUS, 1874. 

Table II — Continued. 



Gr. Sid. 




















Time. 


e 




Diff. 


6' 


Diff. 


logR 


Diff. 


logR' 


Diff. 


h m 





/ 


/ 


' 


/ 










12 16 


191 


3-9 




232 55-5 




1.34763 




I. 13991 




17 


191 


8.4 


+ 4-5 


233 7-2 


+ 11-7 


1-34713 


— 0.00050 


1. 14120 


+ 0.00129 


18 


191 


12.9 


4-S 


233 18. 7 


"•5 


1. 34662 


. 00051 


1. 14249 


. 00129 


19 


191 


17.4 


4 5 


233 30.0 


"•3 


1.34611 


.00051 


I- 14377 


. 00128 


12 20 


191 


21.9 


+ 45 


233 41-3 


+ "-3 


1.34560 


— 0.00051 


1. 14504 


+ 0.00127 



Table III. 
Parallactic Elements P, P'. 



Gr. Sid. 










Gr. Sid. 












Time. 


logP 


Diff. 


logP' 


Diff. 


Time. 




logP 


Diff. 


log?' 


Diff 


h m 










h m 












6 20 


+ 1.27294 




— 1. 10183 




6 52 


+ 


1. 24171 




— I- 1579s 




21 


1. 27213 


— 0. 00081 


1. 10363 


— 0.00180 


S3 




1-24055 


— 0.00116 


1. 15966 


— 0.00171 


22 


1.27131 


. 00082 


1. 10542 


.00179 


54 




I- 23937 


0. oon8 


1. 16136 


.00170 


23 


1.27048 


. 00083 


1. 10721 


.00179 


55 




1. 23817 


. oor^o 


1. 16306 


. 00170 


24 


1.26963 


. 00085 


1. 10900 


.00179 


56 




1.23696 


.00121 


1. 16476 


.00170 


25 


1.26877 


. 00086 


1. 11078 


.00178 


57 




I- 23574 


. 00122 


1. 16646 


.00170 


26 


1.26790 


. 00087 


1. 11256 


. 001 78 


58 




1. 23450 


.00124 


1. 16816 


.00170 


27 


1. 26702 


. 00088 


I- 1 1434 


.00178 


59 




1. 23325 


.00125 


1. 16985 


. 00169 


28 


1. 26613 


. 00089 


1. 11612 


.00178 


7 


+ 


1.23199 


. 00126 


— 1.17154 


. 00169 


29 


1.26523 


. 00090 


1. 11789 


.00177 


1 




1. 23072 


— 0.00127 


1. 17323 


— 0.00169 


6 30 


+ 1-26433 


. 00090 


— 1. 1 1966 


.00177 


2 




I. 22943 


.00129 


I. 17491 


.00168 


31 


1.26342 


— 0. 00091 


1. 12143 


— 0.00177 


3 




I. 22812 


.00131 


1. 17658 


. 00167 


32 


1. 26250 


. 00092 


1. 12320 


.00177 


4 




I. 22679 


- 00133 


I. 17825 


.00167 


33 


1. 26157 


. 00093 


1. 12496 


.00176 


5 




1. 22544 


. 0013s 


1. 17991 


.00166 


34 


1.26062 


. 00095 


1. 12672 


.00176 


6 




1. 22408 


. 00136 


1.18157 


.00166 


35 


1. 25966 


. 00096 


1. 12848 


.00176 


7 




1. 22271 


.00137 


1. 18323 


.00166 


36 


1.25869 


. 00097 


1. 13023 


.00175 


8 




1.22132 


. 00139 


1. J8489 


. ooi65 


37 


1.25771 


. 00098 


1. 13198 


.00175 


9 




I. 21992 


. 00140 


1. .8654 


.00165 


38 


1.25672 


. 00099 


1- 13373 


.00175 


7 10 


+ 


1.21850 


. 00142 


— 1. 18819 


. 00165 


39 


'-25573 


. 00099 


1. 13548 


.00175 


11 




1.21707 


— 0. 00143 


1. 18984 


— u. 00165 


6 40 


+ 1-25473 


. OOIOO 


— 1. 13722 


.00174 


12 




1.21563 


. 00144 


1. 19148 


. 00164 


41 


I- 25373 


— 0. OOIOO 


1. 13896 


— 0. 00174 


13 




1.21417 


.00146 


1.19312 


.00164 


42 


1. 25271 


. 00102 


1. 14070 


.00174 


14 




1.21269 


. 00148 


I- 19475 


.00163 


43 


I. 25167 


. 00104 


1. 14244 


.00174 


15 




1.21118 


.00151 


1. 19637 


.00162 


44 


I . 25062 


. 00105 


1. 14418 


. 001 74 


16 




I. 20965 


-00153 


1. 19798 


.00161 


45 


1.24955 


. 00107 


1. 14591 


.00173 


17 




I. 20810 


.00155 


I. 19959 


.00161 


46 


1.24846 


. 00109 


1. 14764 


.00173 


18 




1.20654 


.00156 


1. 20119 


. 00160 


47 


1.24736 


. 001 10 


I- 14937 


. 00173 


19 




1. 20496 


.00158 


1.20279 


.00160 


48 


1 . 24625 


.00111 


1. 15109 


.00172 


7 20 


• 

+ 


1.20337 


— 0. 00159 


— 1-20439 


. 00160 


49 


J. 24513 


. 00112 


1. 15281 


.00172 


21 




1.20177 


.00160 


1.20599 


— 0. 00160 


6 50 


4- 1.24400 


.00113 


- 1- 15453 


.00172 


22 




1.20015 


. 00162 


1.20758 


.00159 


51 


1.24286 


— 0, 00114 


I. 15624 


— 0.00171 


23 




1. 19850 


. 00165 


1.20917 


.00159 


52 


+ 1.24171 


— 0.00115 


- I- 15795 


— 0.00171 


24 


+ 


1. 19683 


— 0. 00167 


— 1.21076 


— 0.00159 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 
Table III — Continued. 



99 



Gr. Sid. 
Time. 


logP 


Diir. 


logP' 


Diff. 


Gr. Sid. 
Time. 


logP 


Diff. 


logP' 


Diff. 


h m 










h m 










7 24 


+ 1. 19683 




— 1. 21076 




8 11 


+ 1-09073 




— 1.27796 




25 


1-19513 


— 0.00170 


1. 21234 


— 0. 00158 


12 


1. 08776 


— 0. 00297 


1. 27921 


— 0. 00125 


■ 26 


'• 19341 


.00172 


1.21391 


.00157 


13 


1.08474 


. 00302 


1.28045 


.00124 


27 


I. 19168 


.00173 


1.21547 


.00156 


14 


1.08166 


. 00308 


1.28169 


. 00124 


28 


I. 18993 


-00175 


1. 21703 


.00156 


15 


1.07853 


-00313 


1.28292 


. 00123 


29 


I. 18817 


.00176 


1.21858 


.00155 


16 


1.07536 


.00317 


1.28414 


. 00122 


7 30 


+ 1. 18638 


.00179 


— I. 22013 


-00155 


17 


1.07216 


. 00320 


1-28535 


.00121 


31 


1. 18456 


— 0.00182 


1.22167 


— 0. 00154 


18 


1.06892 


. 00324 


1. 28655 


.00120 


32 


1. 18272 


. 00184 


1.22320 


-00153 


19 


1.06565 


- 00327 


1. 28775 


. 00120 


33 


1. 18087 


. 00185 


1.22473 


.00153 


8 20 


+ 1.06234 


■ 00331 


— 1.28894 


.00119 


34 


1. 17899 


.00188 


1.22625 


. 00152 


21 


1.05898 


— 0. 00336 


I. 29012 


— 0. 001 18 


35 


1. 1770S 


.00191 


1. 22776 


.00151 


22 


1-05557 


- 00341 


1. 29129 


.00117 


36 


1-17515 


. 00193 


1. 22927 


.00151 


23 


1.05212 


• 00345 


1.29245 


.00116 


37 


1-17319 


. 00196 


1.23078 


.00151 


24 


1.04862 


- 00350 


I. 29360 


.00115 


38 


1. 17122 


.00197 


1.23228 


.00150 


25 


1.04507 


-00355 


I. 29474 


.00114 


39 


1. 16923 


. 00199 


1-23378 


.00150 


26 


1. 04147 


. 00360 


1.29587 


.00113 


7 40 


+ 1. 16722 


. 00201 


— 1.23527 


. 00149 


27 


1-03783 


. 00364 


I. 29699 


.00112 


41 


1.16519 


— 0. 00203 


1.23675 


— 0.00148 


28 


1.03414 


. 00369 


1.29810 


.00111 


42 


I. 16314 


. 00205 


1.23823 


. 00148 


29- 


1 . 03040 


■00374 


1.29920 


.00110 


43 


I. 16106 


. 00208 


1. 23971 


. 00148 


8 30 


+ 1.02661 


- 00379 


— I. 30028 


. 00108 


44 


1. 15894 


.00212 


1.24118 


. 00147 


31 


1.02276 


— 0.00385 


■■30135 


— 0.00107 


45 


I- 15678 


.00216 


1.24264 


. 00146 


32 


1.01886 


. 00390 


I. 30241 


.00106 


46 


I- 15459 


. 00219 


1.24409 


. 00145 


33 


1. 01492 


.00394 


1. 30346 


. 00105 


47 


I- 15238 


.00221 


1-24553 


.00144 


34 


1.01092 


. 00400 


I. 30450 


. 00104 


48 


1. 15016 


. 00222 


I. 24696 


- 00143 


35 


1.00687 


. 00405 


1.30553 


. 00103 


49 


1. 14792 


. 00224 


I. 24839 


. 00143 


36 


1. 00276 


. 0041 1 


1.30655 


. 00102 


7 50 


+ I- 14565 


. 00227 


- 1.24981 


.00142 


37 


0. 99859 


.00417 


I. 30757 


. 00102 


51 


I- 14335 


— 0. 00230 


1.25123 


— 0. 00142 


38 


0- 99436 


. 00423 


1.30859 


. 00102 


52 


I. 14102 


- 00233 


1.25265 


. 00142 


39 


0. 99007 


. 00429 


1.30960 


.00101 


53 


I. 13865 


. 00237 


1. 25406 


. 00141 


8 40 


+ 0. 98572 


• 00435 


— 1. 31060 


.00100 


54 


I- 13625 


. 00240 


I- 25545 


- 00139 


41 


0. 98130 


— 0.00442 


1.31159 


— 0. 00099 


55 


I- 13381 


.00244 


I. 25683 


.00138 


42 


0. 97682 


.00448 


1.31256 


.00097 


56 


•■13135 


. 00246 


1.25820 


■ 00137 


43 


0. 97228 


. 00454 


'.31352 


.00096 


57 


1. 12887 


. 00248 


1.25956 


. 00136 


44 


0. 96767 


. 00461 


1.31447 


. 00095 


58 


1. 12636 


.00251 


1. 26092 


. 00136 


45 


0. 96299 


. 00468 


1.31541 


.00094 


59 


1. 12382 


. 00254 


1.26227 


-00135 


46 


0. 95825 


. 00474 


I. 31633 


. 00092 


8 


+ 1. 12126 


. 00256 


— 1.26362 


.00135 


47 


0- 95344 


. 00481 


1. 31723 


. 00090 


I 


1. 1 1868 


— 0.00258 


I. 26497 


— 0. 00135 


48 


0. 94856 


. 00488 


1.31812 


. 00089 


2 


1. 11607 


. 00261 


1.26631 


. 00134 


49 


0. 94361 


- 00495 


1.31901 


. 00089 


3 


1.11341 


. 00266 


I. 26764 


■ 00133 


8 50 


+ 0-93858 


. 00503 


— 1. 31989 


. 00088 


4 


1. 11071 


. 00270 


1. 26896 


.00132 


51 


0- 93347 


— 0.00511 


1.32077 


— 0.00088 


5 


I. 10795 


. 002 76 


1.27027 


.00131 


52 


0. 92829 


.00518 


1.32164 


.00087 


6 


1.10515 


. 00280 


1.27157 


. 00130 


53 


0. 92303 


. 00526 


1. 32249 


. 00085 


7 


1. 10232 


. 00283 


1.27286 


. 00129 


54 


0.91768 


.00535 


1-32332 


. 00083 


8 


1.09947 


. 00285 


1.27415 


.00129 


55 


0. 91226 


. 00542 


1.32414 


. 00082 


9 


1.09659 


. 00288 


I- 27543 


. 00128 


56 


0. 90677 


. 00549 


I- 32495 


.00081 


8 10 


+ 1-09367 


. 00292 


— 1. 27670 


. 00127 


57 


0.90118 


. 00559 


1-32575 


.00080 


II 


+ 1-09073 


— 0. 00294 


— 1.27796 


— 0. 00126 


58 


+ 0. 89549 


— 0.00569 


— 1-32654 


— 0. 00079 



lOO 



TRANSIT OF VENUS, 1874. 

Table III — Continued 



Gr. Sid. 










Gr. Sid. 










Time. 


logP 


Difif. 


logP' 


Diff. 


Time. 


logP 


Diff. 


logP' 


Diff. 


h m 










h m 








• 


8 58 


+ 0.89549 




— !• 32654 




9 45 


+ 0. 44552 




— 1.35122 




59 


0. 88970 


— 0.00579 


1.32733 


— 0. 00079 


46 


0.42817 


— 0.01735 


1.35147 


— 0.00025 


9 


+ 0. 88381 


— 0. 00589 


- 1.32811 


— 0. 00078 


47 


0.41019 


.01798 


1.35171 


. 00024 


I 


0. 87781 


. 00600 


1.32888 


. 00077 


48 


0. 39'4i 


.01878 


1.35195 


. 00024 


2 


0.87172 


. 00609 


1.32964 


. 00076 


49 


0.37179 


. 01962 


1.35218 


.00023 


3 


0. 86554 


.00618 


1.33038 


. 00074 


9 50 


+ 0.35126 


— 0.02053 


— 1.35240 


— 0. 00022 


4 


0. 85926 


. 00628 


1.33110 


. 00072 


SI 


0. 32972 


.02154 


1.35261 


.00021 


5 


0. 85287 


. 00639 


1.33180 


. 00070 


52 


0. 30708 


. 02264 


1.35281 


. 00020 


6 


0. 84638 


. 00649 


1.33249 


. 00069 


53 


0.28331 


.02377 


1.35300 


. 00019 


7 


0.83978 


. 00660 


I. 33318 


. 00069 


54 


0. 25813 


.02518 


1.35317 


.00017 


8 


0. 83306 


. 00672 


1.33386 


. 00068 


55 


0.23143 


. 02670 


1.35333 


. 00016 


9 


0. 82622 


. 00684 


1.33454 


. 00068 


56 


0. 20306 


.02837 


1.35348 


. 00015 


9 10 


+ 0.81925 


. 00697 


— 1.33521 


. 00067 


57 


0. 17270 


• 03036 


1.35362 


. 00014 


n 


0. 81216 


— 0. 00709 


••33586 


— 0. 00065 


58 


0. 14015 


•03255 


I.3S375 


. 00013 


12 


0. 80493 


.00723 


!• 33650 


. 00064 


59 


0. 10496 


•03519 


1. 35387 


. 00012 


13 


0. 79754 


•00739 


'•33713 


. 00663 


10 


+ 0. 06678 


. 03818 


— 1.35398 


.00011 


H 


0. 79002 


.00752 


"•33774 


. 00061 


I 


0. 02497 


— 0.04181 


1.35409 


— 0. 0001 1 


15 


0. 78235 


. 00767 


!• 33834 


. 00060 


2 


9. 97881 


.04616 


1. 35419 


. OOOIO 


16 


0. 77456 


.00779 


1-33893 


.00059 


3 


9. 92723 


.05158 


1.35428 


.00009 


17 


0. 76662 


. 00794 


I. 33951 


. 00058 


4 


9. 86884 


.05839 


1. 35435 


.00007 


18 


0. 75852 


.00810 


1.34008 


• 00057 


5 


9. 80145 


.06739 


1. 35441 


. 00006 


»9 


0. 75026 


. 00826 


1.34065 


. 000S7 


6 


9. 72187 


.07958 


1.354^5 


.00004 


9 20 


+ 0. 74182 


— 0. 00844 


— 1.34121 


— 0.00056 


7 


9. 62462 


• 09725 


1. 35449 


. 00004 


21 


0. 73318 


. 00864 


1. 34175 


• 00054 


8 


9. 49950 


. 12512 


1.35452 


. 00003 


22 


0. 72435 


. 00883 


1.34227 


. 00052 


9 


9. 32366 


•17584 


1. 35453 


. 0000 1 


23 


0- 71533 


. 00902 


1.34278 


. 0005 1 


10 10 


+ 9. 02407 


— 0. 29959 


- 1.35454 


— 0.00001 


24 


0. 70612 


. 00921 


1.34328 


. 00050 


11 


+ 6.96368 


— 2. 06039 


1.35454 


. 00000 


25 


0. 69672 


. 00940 


1.34377 


. 00049 


12 


— 9. 01539 




1-35453 


+ 0. 0000 1 


26 


0. 68710 


. 00962 


1.34424 


. 00047 


13 


9.31774 


— 0. 30235 


1.35452 


. OOOOI 


27 


0. 67726 


. 00984 


1. 34470 


. 00046 


14 


9. 49405 


• 17631 


1. 35450 


. 00002 


28 


0.66719 


.01007 


1. 34516 


. 00046 


15 


9. 61875 


. 12470 


1. 35448 


. 00002 


29 


0. 65687 


. 01032 


1. 34561 


. 00045 


16 


9. 71526 


.09651 


!• 35445 


. 00003 


9 3° 


+ 0.64629 


.01058 


— 1.34605 


.00044 


>7 


9. 79401 


•0787s 


!• 35441 


. 00004 


31 


0. 6354s 


— 0. 01084 


1.34648 


— 0.00043 


18 


9. 86046 


. 06645 


1. 35435 


.00006 


32 


0. 62433 


.01112 


1.34689 


. 00041 


19 


9.91792 


.05746 


1.35428 


.00007 


33 


0. 61289 


.01144 


1. 34729 


. 00040 


10 20 


— 9. 96856 


— 0. 05064 


— 1.35420 


+ 0.00008 


34 


0.601 13 


.01176 


1. 34768 


. 00039 


21 


0.01376 


. 04520 


1.35412 


. 00008 


35 


0. 58906 


. 01207 


1. 34806 


. 00038 


22 


0.05455 


. 04079 


1.35403 


. 00009 


36 


0.57663 


. 01243 


1.34842 


. 00036 


23 


0.09177 


.03722 


1.35393 


.00010 


37 


0. 56382 


.01281 


1.34877 


• 00035 


24 


0. 12592 


•03415 


I • 35382 


.00011 


38 


0. 55063 


.01319 


1.349" 


. 00034 


25 


0. 15751 


.03159 


1^35370 


.00012 


39 


0. 53706 


•01357 


— 1.34945 


. 00034 


26 


0. 18684 


•02933 


1.35357 


. 00013 


9 40 


+ 0. 52308 


• 01398 


1.34978 


•00033 


27 


0.21422 


.02738 


1.35343 


. 00014 


41 


0. 50875 


— 0.01443 


1.35010 


— 0. 00032 


28 


0.23991 


. 02569 


1.35329 


. 00014 


42 


0.49373 


.01502 


1.35040 


. 00030 


29 


0. 26408 


.02417 


1.35314 


. 00015 


43 


0. 47822 


•01551 


1. 35069 


. 00029 


10 30 


— 0. 28687 


.02279 


— 1.35298 


.00016 


44 


0.46216 


.01606 


1. 35096 


. 00027 


31 


0. 30848 


— 0.02161 


I. 352S1 


+ u. 00017 


45 


+ 0.44552 


— 0.01664 


— 1.35122 


— 0. 00026 


32 


— 0. 32899 


— 0.02051 


— 1.35263 


+ 0. 00018 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

Table III — Continued. 



lOI 



Gr. Sid. 
Time. 


logP 


Diff. 


logP' 


Diff. 


Gr. Sid. 
Time. 


logP 


Diff. 


logP' 


Diff. 


h m 










h m 










10 32 


— 0. 32899 




— 1.35263 




II 19 


— 0.80022 




— !• 33707 




33 


0. 34850 


— 0.01951 


1-35245 


+ 0.00018 


11 20 


— 0.80559 


— 0.00537 


— 1.33662 


+ 0.0004s 


34 


0. 36712 


.01862 


1.35226 


. 00019 


21 


0. 81089 


— 0. 00530 


!• 33615 


+ 0.00047 


35 


0. 38489 


.01777 


1. 35207 


. 00019 


22 


0.81607 


.00518 


1-33567 


. 00048 


36 


0. 40192 


.01703 


1.35188 


. 00019 


23 


0.821 18 


.00511 


1-33519 


. 00048 


37 


0.41821 


. 01629 


1. 35168 


.00020 


24 


0. 82624 


. 00506 


I. 33471 


.00048 


38 


0. 43389 


.01568 


1-35146 


.00022 


25 


0.831 1 7 


. 00493 


1-33423 


.00048 


39. 


0. 44893 


.01504 


I- 35123 


. 00023 


26 


0. 83605 


. 00488 


1- 33375 


.00048 


10 40 


— 0. 46347 


• 01454 


— 1-35099 


.00024 


27 


0. 84082 


-00477 


1-33327 


. 00048 


41 


0.47749 


— 0.01402 


1-35074 


+ 0.00025 


28 


0.84552 


. 00470 


I- 33278 


. 00049 


42 


0.49094 


•01345 


1.35049 


. 00025 


29 


0. 85018 


. 00466 


1.33229 


. 00049 


43 


0. 50394 


. 01300 


1.35024 


. 00025 


u 30 


— 0. 85470 


.00452 


— 1-33179 


. 00050 


44 


0. 51649 


.01255 


1.34998 


. 00026 


31 


0. 85922 


— 0.00452 


1.33128 


+ 0.00051 


45 


0. 52866 


.01217 


I- 34971 


. 00027 


32 


0. 86362 


.00440 


1-33077 


.00051 


46 


0. 54053 


.01187 


I -.34943 


. 00028 


33 


0. 86798 


. 00436 


1. 33026 


. 0005 1 


47 


0. 55196 


.01143 


I- 34915 


. 00028 


34 


0. 87223 


. 00425 


1. 32975 


.00051 


48 


0. 56309 


.01113 


1. 34886 


. 00029 


35 


0. 87643 


.00420 


1.32923 


. 00052 


49 


0. 57383 


. 01074 


1-34856 


. 00030 


36 


0. 8805s 


. 00412 


1.32871 


. 00052 


lo 50 


— 0. 58430 


. 01047 


— 1-34825 


.00031 


37 


0. 88463 


. 00408 


1.32818 


.00053 


51 


0- 59455 


— 0. 01025 


1-34794 


+ 0.00031 


38 


' 0.88866 


. 00403 


1.32765 


. 00053 


52 


0.60444 


. 00989 


1.34762 


. 00032 


39 


0. 89261 


.00395 


1.32712 


.00053 


S3 


0. 61410 


. 00966 


1.34728 


. 00034 


II 40 


— 0.89651 


. 00390 


— 1-32659 


• 00053 


54 


0. 62346 


. 00936 


1.34694 


. 00034 


41 


0. 90039 


— 0. 00388 


1. 32606 


+ 0.00053 


55 


0. 6326s 


.00919 


1-34659 


.00035 


42 


0.90417 


.00378 


1- 32552 


. 00054 


56 


0.64159 


. 00894 


1.34624 


.00035 


43 


0. 90793 


. 00376 


1-32497 


• 00055 


57 


0. 65028 


. 00869 


1-34599 


. 0003s 


44 


0.91160 


■ 00367 


1. 32442 


. 00055 


58 


0. 65880 


. 00852 


1-34564 


. 00035 


45 


0.91517 


-00357 


1-32387 


. 00055 


59 


0.6671 1 


.00831 


1.34528 


. 00036 


46 


0.91873 


-00356 


1. 32332 


. 0005s 


II 


— 0. 67523 


. 00812 


— I- 34491 


. 00037 


47 


0. 92226 


•00353 


1.32277 


• 00055 


I 


0. 68322 


— 0.00799 


I- 34454 


+ 0.00037 


48 


0.92571 


■ 00345 


1. 32222 


. 0005s 


2 


0. 69095 


.00773 


1. 34417 


.00037 


49 


0. 92913 


.00342 


1.32167 


• 0005s 


3 


0. 69854 


• 00759 


1- 34380 


. 00037 


11 50 


— 0. 93252 


-00339 


— 1.32112 


.00055 


4 


0. 70592- 


.00738 


1-34342 


. 00038 


5' 


0-93583 


— 0. 00331 


1.32056 


+ 0.00056 


5 


0. 71309 


.00717 


I- 34303 


.00039 


52 


0. 93912 


. 00329 


1.32000 


.00056 


6 


0. 72013 


. 00704 


I. 34263 


.00040 


53 


0. 94239 


. 00327 


I- 31943 


.00057 


7 


0. 72708 


. 00695 


I- 34223 


. 00040 


54 


0. 94558 


• 00319 


1.31886 


.00057 


8 


0. 73382 


. 00674 


1.34182 


. 00041 


55 


0. 94875 


•00317 


1.31829 


• 00057 


9 


0. 74047 


. 00665 


1.34141 


. 00041 


56 


0.95185 


. 00310 


1.31772 


.00057 


II 10 


— 0. 74692 


. 00645 


— I. 34100 


. 00041 


57 


0. 95492 


. 00307 


I- 31715 


.00057 


II 


0. 75330 


— 0.00638 


1. 34058 


-\- 0.00042 


58 


0-95798 


. 00306 


1.31658 


.00057 


12 


0. 75959 


. 00629 


I- 34015 


. 00043 


59 


0. 96097 


. 00299 


1. 31601 


• 00057 


13 


0. 76571 


. 00612 


1-33972 


. 00043 


12 


— 0.96391 


. 00294 


— 1-31543 


. 00058 


14 


0.77173 


. 00602 


1-33929 


. 00043 


1 


0. 96687 


— 0.00296 


I- 31485 


-\- 0.00058 


15 


0. 77761 


. 00588 


1-33885 


.00044 


2 


0. 96975 


. 00288 


I- 31427 


. 00058 


16 


0. 78341 


. 00580 


I. 33841 


.00044 


3 


0. 97262 


. 00287 


1.31369 


. 00058 


17 


0. 78913 


.00572 


1-33797 


.00044 


4 


0. 97540 


. 00278 


1. 31310 


. 00059 


18 


0. 79471 


.00558 


1-33752 


. 00045 


S 


0.97818 


.00278 


1.31251 


.00059 


19 


— 0,80022 


— 0.00551 


— 1-33707 


+ 0.00045 


6 


— 0.98090 


— 0.00272 


— 1. 31192 


+ 0,00059 



I02 



TRANSIT OF VENUS, 1874. 

Table Ill^Continued. 



Gr. Sid. 










Gr. Sid. 










Time. 


logP 


Diff. 


logP' 


Diff. 


Time. 


logP 


Diff. 


logP' 


Diff. 


h m 










h m 










12 6 


— 0. 98090 




— 1.31192 




12 13 


— 0.99912 




— 1.30772 




7 


0. 98359 


— . 00269 


1.31132 


+ 0.00060 


1. 00163 


— 0.00251 


1. 30712 


+ 0. 00060 


8 


0. 98627 


. 00268 


1. 31072 


. 00060 J e 


I. 00408 


. 00245 


1.30652 


. 00060 


9 


0. 98890 


. 00263 


1.31012 


. 00060 jg 


1. 00651 


. 00243 


I. 30592 


. 00060 


12 10 


— 0.99148 


. 00258 


— 1.30952 


.00060 


1. 00887 


. 00236 


1-30531 


. 00061 


II 


0. 99408 


— 0. 00260 


1.30892 


-)- 0.00060 Q 


1. 01 124 


■ 00237 


I. 30470 


. 00061 


12 


0. 99662 


.00254 


1.30832 


. 00060 


I. 01359 


.00235 


1.30408 


. 00062 


13 


— 0.99912 


— 0. 00250 


— 1.30772 


+ 0.00060 j2 2„ 


— I. 01585 


— 0.00226 


— 1.30346 


+ 0. 00062 



§ 10. COMPAEISON OF OBSERVED AND TABULAR POSITIONS OF VeNUS ON THE FaCE OF 

THE Sun. 

The comparison of the observed positions, as deduced from the measures of the 
photographic plates, with those computed from the theory, are presented in the fol- 
lowing tables in a form which admits of their ready translation into equations of 
condition. There are two sets of results, the one giving position-angles, the other 
distances. 

The second column of each set of tables gives the distances or position-angles 
derived from observation in the first eight sections of the preceding discussion. 

The third column gives the corresponding distances or position-angles derived 
from the tables in the last two sections. This is followed by the corrections which 
would result from changes in the longitude of the station, in the relative right ascen- 
sion and declination of the two bodies, and in the adopted mean solar parallax (8". 848). 
The quantity SA. is the correction to the provisional west longitude of the station, 
expressed in seconds of time. The provisional longitudes to be corrected are found 
on p. 21. The co-efficient of SX shows the correction to be applied to the tabular 
element for each second of time that the station is removed toward the west. 

The last column shows the excess of the observed distance or position-angle above 
that computed, and is the constant term in the equation of condition to be derived 
from each comparison. 

If the observed distances or position-angles needed no further correction, and if 
6 X were satisfactorily known, nothing would remain but the easy task of solving the 
equations thus formed. But the photographic positions of Venus on the Sun's limb 
may still need several classes of corrections, all arising from the absorption of the 
solar and terrestrial atmosphere. These corrections are as follows : 

First, Mr. J. Homer Lane, of Washington, called attention to the fact that a 
vertical displacement of Venus, relative to the center of the Sun, would be caused by 
the absorption of the solar atmosphere, combined with the chromatic dispersion of the 
terrestrial atmosphere. His communication is intended to appear in the appendix to 
this phapter, and may be referred to for a discussion of the action of this cause. At 
present it will suffice to say that the light emanating from the limb of the Sun has 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 103 

more red rays than that emanating from the interior of the disc on which Venus is 
projected. Consequently the rays emanating from the circumference of the disc of 
Venus will be more refracted by the atmosphere of the earth than those emanating 
from the Sun's limb. The position of Venus being measured from the limb, the planet 
will appear more elevated above the horizon than it should appear. The effect of 
relative parallax being to depress the planet, this cause will operate to apparently 
diminish the parallax. Thus the parallax will be too small if the effect is not allowed 
for. 

Secondly, the nearer the Sun approaches the horizon, the greater the absorption 
of the photographic rays by the Earth's atmosphere. Hence, in each photograph, the 
intensity of the rays from the upper limb of the Sun must be greater than that of the 
rays from the lower limb. The upper limb will therefore be more enlarged by pho- 
tographic irradiation than will the lower one, so that the Sun will appear too high on 
the plate. Venus will therefore be too low relative to the center of the Sun's apparent 
disc, and the parallax will come out too great from this cause. This last effect, it will 
be seen, is the opposite of the first. 

Thirdly, the photographic intensity of the Sun's rays diminishes from the center 
toward the circumference of the disc. The planet will, when near the Sun's limb, be 
less intensely photographed on its outer limb than on its inner limb. It will therefore 
be apparently drawn toward the Sun's limb by photographic irradiation. The ob- 
served distances must therefore be too great from this cause. 

The determination of the numerical value of each of these corrections requires a 
special investigation, which has not yet been undertaken. Without such investigation, 
it is not possible to say whether the causes just described will appreciably affect the 
solar parallax. The determination of the numerical value of the first eff'ect is not diffi- 
cult. It is only necessary to form separate curves of the photographic intensity of 
different parts of the spectrum for the limb of the Sun and for its center, and to com- 
bine this with atmospheric dispersion. The second pause may be determined by find- 
ing the increased amount of photographic irradiation due to increased intensity of the 
impression on the plate. As a general rule, the exposure was so considerable that 
there is no striking difference of intensity between the limb and the center of the Sun 
on the photographic plates. For this reason I incline to the opinion that the effect in 
question will not be considerable. The third effect can be deduced from the equations 
of condition and also from the same data which gave the second effect. 

It is to be remarked that all the effects thus described will also be found in any 
optical determination of the position of Venus on the disc of the Sim, the eye taking 
the place of the photographic plate and being affected in the same way. It is proba- 
ble, however, that the occular effect is smaller than the photographic one. 

Some interest would, no doubt, attach to the solution of these equations disre- 
garding the small corrections in question. In accordance, however, with the recom- 
mendation of the Astronomische Gesellschaft, such a solution has been postponed until 
other data are ready to be combined with them. As now presented, they are open to 
investigation and criticism by all astronomers. 



I04 



TRANSIT OF VENUS, 1874. 



The discussion of the errors and discrepancies among the photographic results 
properly belongs to their final discussion, and is therefore postponed for the present. 
It will, however, be remarked that the probable error, as indicated by a comparison 
of different photographs, far exceeds what was originally estimated. 

The errors of the position-angles will be found roughly by dividing the residuals 
by 4, which will give nearly seconds of arc on a great circle. Such an inspection 
shows that the probable en-or of each individual photograph is fully one second of arc 
in each co-ordinate, but that it differs at the different stations. I am of opinion that 
the principal source of the error is to be found in the undulations of the Sun's limb 
produced by the atmosphere. These undulations will produce a greater effect in pho- 
tographs than in visual observations, because in the latter the observer can generally 
select moments of good seeing to make his observations, whereas the photograph pic- 
tures the Sun as it appears at the moment. 

It does not, however, seem probable that the method is attended with any con- 
siderable systematic error. It will, therefore, be well adapted to give the error of the 
tabular position of Venus on the face of the Sun. It does not seem likely that the 
final probable error of this position, as deduced from these photographs, will much 
exceed o". 10, a degree of accuracy which can hardly be exceeded by other methods 
of observation. 

COMPARISON OF OBSERVED AND TABULAR DISTANCES. 

WLADIWOSTOK. 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


0. — C. 




II 


*/ 


II 








II 


6 


870. 38 


868.31 


— 0. 026 6 Xx 


-1- 0.5s rfA 


-f o.8o(5D 


— 1.961) 7r 


-1-2.07 


7 


867. 36 


865.44 


— 0. 026 


+ 0.54 


-1- 0.81 


— 1.98 


-1- 1-92 


13 


813. 82 


812.31 


— * 0. 009 


-f 0.34 


-)- 0-93 


— 2.45 


-1- 1-5' 


14 


813.21 


811.33 


— 0.008 


-1- 0-33 


-1- 0-93 


— 2.46 


-1- 1.88 


15 


812. II 


810.46 


— 0.007 


-f- 0-33 


-f- 0.94 


— 2-47 


+ 1.65 


31 


878.99 


876. 08 


4- 0.028 


— 0. 14 


-t- 0.99 


— 2.17 


+ 2.91 


32 


882. 10 


879. 20 


-[-■ 0. 028 


^0.14 


-J- 0.99 


— 2.13 


+ 2-90 


33 


. 883.26 


882. IS 


-f- 0.028 


-0.15 


-t- 0.99 


— 2.14 


+ l.II 


34 


888. 13 


885. 16 


+ 0.028 


— 0. 16 


-1- 0.98 


— 2. 11 


-H 2.97 


35 


§89. 82 


888. 14 


-1- 0.029 


— 0. i6 


+ 0.98 


— 3.09 


-1- 1.68 


36 


893- 13 


891-33 


-I- 0.029 


— 0.17 


-1-0.98 


— 2.08 


-f- 1.80 


37 


895- 77 


894. 16 


-t- 0.030 


— 0.18 


4- 0.98 


— 2. o5 


+ 1. 61 


38 


898. 17 


897- 54 


■\- 0.030 


— 0.18 


-f-0.98 


— 2.04 


+ 0.63 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

NAGASAKI. 



105 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


O.-C. 


25 


943. 60 


938- 35 


— 0. 036 d A2 


+ 0. 65 6 A 


+ 0. 71 (!D 


— 1. 18 (iff 


+ 5-25 


26 


938. 56 


937- 24 


— 0.035 


+ 0.65 


+ 0.71 


— 1. 19 


+ 1.32 


28 


937- 79 


935- 31 


- 0. 035 


+ 0.65 


+ U-7I 


— 1. 21 


+ 2.48 


30 


935- 89 


932. 63 


- 0.035 


+ 0.64 


+ 0.71 


1.22 


+ 3-26 


31 


934- 89 


931-51 


— 0.035 


+ 0.64 


+ 0.72 


— 1-23 


+ 3-38 


33 


929. 77 


927. 30 


— 0. 034 


+ 0.64 


+ 0.72 


— 1.26 


+ 2.47 


34 


928. 50 


925.92 


— 0. 034 


+ 0.64 


+ 0.72 


- i.27 


+ 2.58 


35 


924. 40 


921.61 


— 0- 033 


+ 0.63 


+ 0.73 


— I- 31 


+ 2.79 


36 


922. 25 


920. 27 


— 0.033 


+ 0.63 


+ 0.73 


— I- 31 


+ 1.98 


37 


922. 30 


919-25 


— 0. 033 


+ 0.63 


+ 0.73 


— 1-32 


+ 3-05 


38 


918. 33 


915-50 


— 0. 033 


+ 0.62 


+ 0.74 


- 1-35 


+ 2.83 


44 


907.41 


904- 05 


— 0.032 


+ 0.61 


+ 0.75 


— 1-43 


+ 3-36 


45 


903. 28 


901. )8 


— 0.031 


+ 0.60 


+ 0.76 


— 1.46 


+ 2. 10 


46 


901.33 


899. 99 


— 0.031 


+ 0.60 


+ 0.76 


— 1-47 


+ 1-34 


48 


898. 08 


897. 15 


— 0. 030 


+ 0.59 


+ 0.76 


— 1-49 


+ 0.93 


49 


897-05 


894- 57 


— 0. 030 


+ 0.59 


+ 0.77 


— 1-5' 


+ 2.48 


50 


895-65 


893-35 


— 0.029 


+ 0.59 


+ 0.77 


— i.52 


+ 2.30 


SI 


890. 88 


888.51 


— 0. 029 


+ 0.58 


+ 0.78 


-1-56 


+ 2.37 


52 


887.56 


885-44 


— 0.029 


+ 0.57 


+ 0.78 


-1.58 


+ 2. 12 


53 


886. 66 


882. 88 


— 0. 028 


+ 0.57 


+ 0.78 


— 1.60 


+ 3-78 


54 


883.55 


881.24 


— 0.028 


+ "-S7 


+ 0-79 


— 1. 61 


+ 2.31 


55 


881.37 


879. 28 


— 0. 027 


+ 0.56 


+ 0.79 


-1.63 


+ 2.09 


57 


872. 90 


871. 14 


— 0. 026 


+ 0.55 


•^- 0.80 


— 1.68 


+ 1-76 


58 


869.33 


868. 40 


— 0. 026 


+ 0.54 


+ 0.81 


— 1.72 


+ 0.93 


59 


S69. 19 


866. 09 


— 0. 025 


+ 0.54 


+ 0.81 


— 1-74 


+ 3-10 


61 


866. 76 


861. 71 


— 0. 024 


+ 0.53 


+ U.82 


— 1-77 


+ 5-05 


62 


861.56 


860. 68 


— 0. 024 


+ 0.52 


+ 0.82 


-1.78 


+ 0.88 


63 


862.48 


859- 39 


— 0. 024 


+ 0.52 


+ 0.82 


— 1-79 


+ 3-09 


64 


861.43 


858.44 


— 0. 023 


+ 0.52 


■ + 0. 83 


— 1.80 


+ 2.99 


65 


858. 36 


853-62 


— 0.022 


+ 0.50 


+ 0.84 


— 1.84 


+ 4-74 


67 


846. 96 


844.70 


— 0.021 


+ 0.48 


+ 0.85 


— 1.92 


+ 2.26 


72 


. 


825. 14 


— 0.013 


+ 0-41 


+ 0.90 


— 2. II 




74 


822. 61 


820. 79 


— 0.012 


+ 0.38 


+ 0.91 


— 2.14 


+ 1.82 


75 


823. 64 


819- 73 


— 0. 010 


+ 0.38 


+ 0-91 


— 2. 16 


+ 3-91 


76 


817-57 


815-47 


— 0. 009 


+ 0.35 


+ 0.92 


— 2.21 


+ 2. 10 


77 


816.99 


814.48 


— 0.009 


+ 0-34 


+ 0.93 


— 2.21 


+ 2.51 


78 


817-36 


814.21 


— 0. 009 


+ 0.34 


+ 0.93 


— 2.22 


+ 3-15 


79 


815.41 


813.81 


— 0.008 


+ ^-34 


+ 0.93 


— 2.22 


+ 1.60 


80 


816. 24 


813-53 


— 0. 008 


+ 0.33 


+ 0-93 


— 2.23 


+ 2.71 


81 


814. 94 


813-27 


— 0. 008 


+ 0-33 


+ 0-93 


— 2.23 


+ 1-67 


84 


812.65 


• 809.54 


— 0.006 


+ 0.29 


+ 0.95 


— 2.27 


+ 3-" 


93 


821.46 


819. 69 


+ 0.012 


+ 0.08 


+ 1. 00 


— 2.27 


+ 1-77 


94 


820. 56 


820. 05 


+ 0.012 


+ 0.07 


4- 1. 00 


— 2.26 


+ 0.51 


95 


821. 71 


820. 56 


+ 0.013 


+ 0.07 


+ 1. 00 


— 2.26 


+ 1-15 


96 


820. go 


820. 90 


+ 0. 013 


+ 0.07 


-j- 1. 00 


— 2.26 


0.00 


99 


826. 99 


825. 30 


+ 0.014 


■Jr 0.04 


+ 1.00 


— 2.24 


+ 1-69 


S 


. Ex. 31- 


14 













io6 



TRANSIT OF VENUS, 1874. 
PEKING. 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


0. — C. 




// 


// 


n 








// 


IS 


943-51 


940. 77 


— 0.035(5^3 + 0.6s (5 A 


-f o.7odD 


— 0. 96 (5 vr 


+ 2.74 


19 


928. 70 


926. 68 


— 0. 034 


+ 0.64 


+ 0.72 


— 1.07 


+ 2.02 


21 


922. 20 


920. 69 


— 0. 033 


+ 0.63 


+ 0.73 


— I. H 


+ i-Si 


22 


918.26 


917-54 


— 0.033 


+ 0.63 


+ 0.73 


— I. 14 


+ 0.72 


44 


875-96 


874. 21 


+ 0.027 


— 0. 13 


+ 0.99 


— 2.27 


+ 1-75 


45 


877-36 


875-96 


+ 0. 028 


— 0. 13' 


+ 0.99 


— 2.26 


+ 1-40 


46 


880. 67 


877. 78 


H- 0.028 


— 0. 14 


+ 0.99 


— 2.25 


+ 2.89 


49 


885. 10 


884. 67 


+ 0.029 


— o.is 


+ 0.99 


— 2.22 


+ 0.43 


50 


889.51 


886.82 


+ 0.029 


— 0. i6 


+ 0.98 


— 2.22 


+ 2.69 


51 


891.84 


888. 92 


+ 0.030 


— 0. 16 


+ 0.98 


— 2.20 


+ 2.92 


53 


896.55 


893- 59 


+ 0.030 


-0.17 


4- 0.98 


- 2.18 


+ 2.96 


54 


896. 08 


89s. 81 


+ 0.030 


— 0.18 


+ 0.98 


— 2.17 


+ 0.27 


56 


901. 79 


900. 26 


+ 0,031 


— 0. 19 


+ 0.98 


-2. IS 


+ 1-53 


57 


904- 57 


902. 67 


+ 0. 031 


— 0. 19 


+ 0.98 


— 2.14 


+ 1-90 


58 


906. 09 


90s. 10 


+ 0. 032 


— 0.20 


+ 0.98 


— 2.13 


+ 0.99 


59 


908. 19 


907- 15 


+ 0.032 


— 0.20 


+ 0.98 


— 2.12 


+ 1.04 


60 


911.03 


909. 38 


+ 0.032 


— 0.21 


+ 0.97 


— 2. II 


+ 1-65 


6i 


914.48 


911.77 


+ 0. 033 


— 0.21 


+ 0.97 


— 2.09 


+ 2.71 


63 


919. 18 


916. S2 


+ 0. 033 


— 0.22 


+ 0.97 


— 2.07 


+ 2.66 


65 


922. 32 


920. 88 


+ "-034 


-0.23 


+ 0.97 


- 2.0s 


+ 1.44 


67 


929. 62 


925. 87 


+ 0.034 


— 0.24 


+ 0.97 


— 2.03 


+ 3-75 


68 


929. 07 


927. 95 


+ 0.034 


— 0.24 


+ 0.97 


— 2.02 


+ 1. 12 


69 


933- 01 


930- 93 


+ 0. 035 


— 0. 24 


+ 0.96 


— 2.01 


-H- 2.08 


70 


934- 16 


933- 12 


+ 0.03s 


- 0.25 


+ "-96 


— 1-99 


+ 1-04 


71 


938. 82 


935-23 


+ 0.03s 


— 0.2s 


+ 0.96 


— 1,98 


+ 3-59 


72 


941- 50 


937-4° 


+ 0. 03s 


— 0.25 


+ 0.96 


— 1-97 


4- 4-10 



KERGUELEN. 



No. of 
Photo. 


Observed 
Distance. 




Tabular Distance. 






0. — c. 


7 


916. II 


// 
914.17 


— 0.02'jd'Ki +0. SS(!A 


+ o.8o(5D 


+ 2.31(5 - 


II 

+ 1-94 


17 


864. 08 


863. 02 


+ 0. 015 + 0. 03 


+ 1. 00 


•1- 1-40 


+ 1.06 


18 


870. 24 


866. 43 


+ 0.016 + 0.02 


+ 1. 00 


+ 1-37 


+ 3-81 


19 


870. 33 


867. 57 


+ 0.016 -f 0. 01 


+ 1. 00 


+ 1-36 


+ 2.76 


20 


869. 82 


869.23 


+ 0.016 0.00 


+ 1. 00 


+ 1-35 


+ 0.59 


25 


904. S4 


901- 73 


+ 0. 02s — 0. 10 


+ 0.99 


+ ;-2i 


+ 2.81 


32 


930- 83 


930- 53 


+ 0. 029 — 0. 1 7 


+ 0.98 


+ J- 14 


+ 0.30 


33 


987.36 


988. 6s 


+ 0.036 — 0.27 


+ 0.95 


+ 1.07 


- 1.29 



Note. — The Kerguelen distances have been reduced on the supposition that the measures with the rod were from 
the end and not from the notch. Had the notch length given on pages 72-73 been used, the distances would b.ave been 
about 4" greater. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 
HOBART TOWN. 



107 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


0. — C. 




II 


// 


II 










// 


9 


856. 94 


854.64 


+ o.oisSli 


+ o.o4(!A 


+ l.oodD 


+ 1 


.ogrf TT 


+ 2.30 


ID 


857- ss 


855- 15 


+ 0.01S 


+ 0.04 


+ I. 00 


+ 1 


.09 


+ 2.40 


II 


856. 84 


855- 74 


+ o.ois 


+ 0.03 


+ I. 00 


+ I 


. 10 


-\- 1. 10 


12 


856. 54 


856. 17 


+ 0.016 


+ 0.03 


4- 1. 00 


+ I 


. 10 


+ 0.37 


13 


858. 79 


857.46 


+ 0.016 


+ 0.02 


+ I. 00 


+ 1 


. II 


+ 1-33 


14 


861.65 


859- 15 


+ 0.016 


+ 0.02 


-f- 1. 00 


+ 1 


■ 13 


+ 2.50 


"S 


860. 29 


859.92 


+ 0.017 


+ O.OI 


H- I. 00 


+ 1 


-13 


+ 0.37 


16 


863. 73 


861.54 


+ 0.017 


+ 0.01 


+ I. 00 


+ I 


-15 


+ ^-19 


17 


862. 94 


861.84 


+ 0.017 


+ O.OI 


-\- I. 00 


+ 1 


•IS 


+ 1. 10 


18 


866. 06 


863.32 


+ 0.018 


0.00 


+ I. 00 


+ 1 


.16 


+ 2.74 


19 


865.50 


863.86 


+ 0.018 


0.00 


+ 1. 00 


+ I 


• 17 


+ 1.64 


22 


871.82 


870. 28 


+ 0.019 


— 0.03 


+ I. 00 


+ 1 


.22 


+ 1-54 


23 


871.42 


871.14 


+ 0.020 


— 0.03 


+ I. 00 


+ 1 


.22 


+ 0.28 


24 


873-43 


871.94 


+ 0.020 


— 0.03 


+ I. 00 


+ 1 


• 23 


+ 1-49 


25 


875- 15 


872.83 


+ 0.020 


— 0.04 


+ 1. 00 


+ 1 


.24 


+ 2.32 


26 


876. 62 


873-80 


-\- 0.021 


— 0.04 


+ I. 00 


+ 1 


-24 


+ 2.82 


27 


875- 56 


875.92 


+ 0.021 


— 0.05 


+ 1. 00 


+ 1 


.26 


— 0.36 


28 


877.29 


877-05 


+ o.oti 


— 0.05 


+ I. 00 


+ I 


-27 


+ 0.24 


29 


879. 68 


878. 29 


4- 0.021 


— 0.05 


+ I. 00 


+ I 


.28 


+ 1-39 


30 


881. 13 


879. 02 


+ 0.022 


— 0.06 


+ I. 00 


+ 1 


.28 


+ 2. II 


32 


884. 66 


881.24 


+ 0.022 


— 0.06 


+ I. 00 


+ 1 


-30 


+ 3-42 


33 


882. 04 


881.65 


+ 0.023 


— 0.06 


-l- 1. 00 


+ 1 


• 31 


+ 0.39 


34 


883.36 


882. 58 


+ 0. 023 


— 0.07 


+ I. 00 


+ 1 


-31 


+ 0.78 


35 


885.31 


883.44 


+ 0.023 


— 0.07 


+ I. 00 


+ 1 


-31 


+ 1-87 


36 


885. 89 


884. 63. 


+ 0.023 


— 0.07 


+ I. 00 


+ 1 


•32 


+ 1.26 


37 


886. 69 


885. 16 


+ 0.023 


— 0.07 


+ I. 00 


+ 1 


• 32 


+ 1-53 


38 


888. 64 


. 886. 6^ 


+ 0.023 


— 0.08 


+ I. 00 


+ 1 


•33 


+ 2.01 


39 


890. 67 


888. 00 


+ 0.023 


— 0.08 


+ I. 00 


+ 1 


•34 


+ 2.67 


40 


888. 89 


889. 00 


+ 0.023 


— 0.09 


+ I. 00 


+ 1 


-35 


— O.II 


41 


890. 55 


891.04 


+ 0.024 


— 0.09 


+ 0.99 


+ 1 


•36 


— 0.49 


42 


894- 54 


892. 15 


+ 0.024 


— 0.09 


+ 0.99 


+ 1 


-37 


+ 2.39 


43 


893. 24 


893- IS 


+ 0.025 


— 0. 10 


+ 0.99 


+ 1 


•37 


+ 0.09 


44 


897-43 


894. 36 


+ 0.025 


— 0. 10 


+ 0.99 


+ 1 


•38 


+ 3-07 


45 


895-41 


895-34 


+ 0.025 


— 0. 10 


+ 0.99 


+ 1 


•39 


+ 0.07 


46 


898. 76 


896. 8i 


+ 0.025 


— 0. 10 


+ 0.99 


+ 1 


.40 


+ I-9S 


47 


900. 05 


898.26 


+ 0.025 


— 0. II 


+ 0.99 


+ 1 


•41 


+ 1-79 


48 


900. 74 


899. 81 


+ 0.026 


— O.II 


+ 0.99 


+ 1 


.42 


+ ©•93 



io8 



TRANSIT OF VENUS, 1874. 
CAMPBELLTOWN. 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


0. — C. 




II 


// 


II 








// 


ID 


842. 78 


836.51 


+ 0. 006 5^6 


4- 0.17 (5 A 


4- 0. 98 d D 


4- 0. 81 (5 TT 


4-6.27 


II 


842. 08 


837-61 


+ 0.006 


4- 0.16 


4-0.98 


4-0.83 


+ 4-47 


12 


842. 94 


837.81 


+ 0.006 


+ o.iS 


+ 0.99 


4- 0.83 


+ S-13 


17 


846. 14 


842. 01 


+ 0.009 


4- 0. II 


+ 0.99 


+ 0.91 


+ 4-13 


18 


844.18 


842.56 


4- 0.009 


4- 0. II 


4- 0.99 


4- 0.91 


+ 1.62 


19 


844.88 


843-05 


+ O.OIO 


4- 0. ID 


4- 0.99 


4- 0.92 


+ 1-83 


23 


849. 98 


847- 40 


+ 0.013 


4- 0.08 


4- 1. 00 


4-0.97 


4-2.58 


24 


849- 93 


848. 06 


+ 0. 013 


4- 0.07 


4- 1. 00 


4- 0.98 


-h 1.87 


28 


867. 24 


862. 75 


+ 0.017 


0.00 


4- 1. 00 


4- 1. 12 


+ 4-49 


29 


869. 98 


867. 00 


+ 0.019 


— 0.02 


4- 1. 00 


4- I. 16 


4- 2.98 


31 


877.62 


873.06 


+ 0.021 


— 0.04 


4- 1. 00 


4- 1. 21 


+ 4.56 


32 


877- 93 


874.65 


+ 0.021 


— 0.04 


4- 1. 00 


4- 1.22 


+ 3-28 


33 


880. 67 


877.03 


+ 0.021 


— 0.05 


4- 1. 00 


4- 1.24 


+ 3-64 


34 


882. 82 


879- 77 


+ 0.022 


— 0.06 


4- 1. 00 


H- 1. 25 


+ 3-05 


35 


887. 06 


883. 40 


+ 0.022 


— 0.07 


4- 1. 00 


4- 1.28 


4-3-66 


36 


887. 10 


886. 22 


4- 0.024 


— 0.08 


4- 1. 00 


+ 1.30 


4- 0.88 


37 


891. 15 


887.83 


+ 0.024 


— 0.08 


4- 1. 00 


+ 1.31 


-1- 3-32 


38 


891. 66 


889. 01 


+ 0.024 


— 0.09 


4- 1. 00 


+ 1-31 


4- 2.65 


39 


892. 87 


891.57 


4- 0.024 


— 0.09 


4- 0.99 


+ 1-33 


-f- 1-30 


40 


898. IS 


893- 52 


+ 0.025 


— 0. 10 


4- 0.99 


4- '-34 


4- 4.63 


41 


897.67 


895. 02 


+ 0.02s 


— 0. 10 


4- 0.99 


+ 1-35 


4- 2.65 


42 


899. 78 


896. 84 


+ 0. 025 


— 0. 11 


4- 0.99 


+ 1-37 


4- 2.94 


44 


904. 12 


900. 40 


+ 0.026 


— 0. 12 


4- 0.99 


-t- 1-39 


-1- 3.72 


45 


905.65 


902. 73 


4- 0.026 


— 0. 12 


-1- 0.99 


4- '-40 


4- 2.92 


46 


908.42 


904. 77 


4- 0.027 


— U.13 


4- 0.99 


4- I- 41 


-t- 3-65 


47 


909. 71 


907. 50 


4- 0.027 


— 0.13 


4- 0.99 


4- 1-43 


4- 2.21 


48 


947- 52 


941. 70 


4- 0. 032 


— 0.20 


4- 0.97 


4- r6i 


4- 5. 82 


49 


950. 80 


945. 88 


+ 0.033 


— 0.21 


4- 0.97 


+ 1-63 


4- 4.92 


50 


952. 16 


947- 93 


+ 0.033 


— 0.22 


4- 0.97 


4- 1-64 


+ 4-23 


SI 


953- 14 


950. 13 


+ 0.033 


— 0.22 


4- 0.97 


+ 1-65 


+ 3.01 


52 


954- 54 


951.80 


+ 0.033 


— 0.22 


+ 0.97 


4- 1.66 


4- 2.74 


S3 


« 956^5 


9S3-9S 


+ 0. 033 


— 0.23 


4- 0.97 


4- 1.67 


4- 2.90 



DISCUSSION OF THE PHOTOGRAPHIC OPEEATIONS. 
QUEENSTOWN. 



109 





No. of 
Photo. 


Observed 
Distance. 




Tabular Distance 






0.— C. 






// 


II 


// 








// 




114 


932.56 


930. 90 


— 0. 030 <! A7 


+ o.6o(iA 


-f- 0. 76 (! D 


4- 0.27(5 TT 


4- 1.66 




"5 


929.99 


927. 47 


— 0.030 


-)- 0.60 


+ 0.76 


4- 0.27 


+ 2.52 




116 


926. 09 


924. 39 


— 0.030 


+ 0.59 


+ 0.77 


4- 0.27 


4- 1.70 




117 


925.61 


922.42 


— 0.029 


+ 0-59 


+ 0.77 • 


4- 0.28 


+ 3-19 




118 


924- 75 


918.86 


— 0. 029 


+ 0.58 


+ 0.77 


4- 0.28 


+ 5.89 




119 


918.99 


916. 39 


— 0.029 


+ 0.58 


+ 0.78 


4- 0.28 


4- 2.60 




120 


914. 46 


911.87 


— 0.028 


+ 0.57 


+ 0.78 


4- 0.29 


+ 2.59 




122 


905. S3 


.903. 99 


— 0.027 


+ 0.56 


+ 0.80 


+ 0.31 


+ 1-54 




123 


905.29 


900. 76 


— 0.026 


+ 0.55 


+ 0.80 


+ 0.31 


+ 4-53 




124 


898. 77 


897. 23 


— 0. 026 


+ 0.54 


+ 0.81 


4- 0.32 


4- 1. 54 




"S 


897. 02 


894. 07 


— 0. 025 


+ 0.53 


+ 0.81 


+ 0.33 


+ 2.95 




126 


891.85 


890700 


— 0. 024 


+ 0.53 


+ 0.82 


+ 0.34 


4- 1.85 




127 


887. 48 


886. 63 


— 0.024 


+ 0.52 


+ 0.83 


+ 0.35 


4-0.85 




128 


887. 68 


883.82 


— 0. 023 


+ 0.51 


+ 0.83 


4- 0.36 


4-3.86 




129 


884. 41 


880. 92 


— 0.022 


+ 0.50 


+ 0.84 


+ 0.37 


+ 3-49 




130 


878. 24 


876. 76 


— 0. 021 


+ 0.49 


+ 0.84 


+ 0.39 


4- 1.48 




131 


874. 71 


874.87 


— 0.021 


+ 0.49 


+ 0.85 


4- 0.40 


— 0. 16 




132 


876. 19 


872. 66 


— 0.020 


+ 0.48 


+ 0.85 


4- 0.41 


+ 3-53 




133 


874. 07 


870. 86 


— 0.020 


+ 0.47 


+ 0.86 


4- 0.41 


4-3.21 




134 


870. 82 


868. 84 


— 0.019 


+ 0.47 


+ 0.86 


4- 0.42 


+ 1.98 




13s 


868. 01 


866.92 


— 0. 019 


+ 0.46 


+ 0.86 


+ 0.43 


4- 1.09 




139 (») 


847.92 


843. 75 


— 0. 009 


+ 0.35 


+ 0.92 


4- 0.63 


+ 4.17 




142 


846.33 


844.47 


— 0. 009 


+ 0.36 


+ 0.92 


4- 0.62 


4- 1.86 




143 


845.92 


842.63 


— 0. 009 


+ 0.34 


+ 0.93 


4-0.65 


-f 3.29 




144 


845-63 


843. 18 


— 0.009 


+ 0.35 


+ 0.93 


4- 0.64 


+ 2-45 




145 


843. 99 


841. 74 


— 0.008 


+ 0.34 


+ 0.93 


4- 0.67 


4- 2.25 




151 


846. 90 


845.25 


H- 0. 010 


+ 0. 10 


+ 0.99 


4- 1.20 


4- 1.65 




153 


848. 39 


845.44 


+ 0. on 


+ 0. 10 


+ 0.99 


4- 1.21 


+ 2.95 




154 


847. 74 


845.99 


+ 0. on 


+ 0. lO 


+ 0.99 


4- 1.22 


4- 1-75 




'55 


848. 94 


847. 01 


+ 0.012 


+ 0.09 


+ 0.99 


4- 1.24 


+ 1.93 




156 


850. 52 


849- 37 


+ 0.013 


4- 0.08 


+ 1.00 


4- 1.27 


+ 1. 15 




158 


854.84 


851.32 


+ 0.013 


+ 0.06 


4- 1.00 


4- 1.30 


-t- 3.52 




159 


854.35 


852. 50 


+ 0.014 


+ 0.06 


+ 1. 00 


4- 1.32 


4- 1. 85 




160 


853.67 


854. 16 


+ 0.014 


+ 0.05 


+ 1.00 


+ 1.34 


— 0.49 




161 


854.98 


854. 74 


+ 0.014 


+ 0.05 


+ 1.00 


+ 1-35 


4- 0.24 




163 


869. 50 


864. 06 


+ 0.018 


-|- 0.00 


+ 1. 00 


+ 1.46 


+ 5-44 




164 


866. 46 


865.81 


+ 0.018 


— 0. 00 


4- 1. 00 


+ 1-47 


4- 0.65 




165 (!) 


868. 09 


866. 72 


+ 0.018 


— 0. 01 


4- 1. 00 


4- 1.48 


-f 1-37 




166 


869. 49 


868. 19 


+ 0.018 


— 0.01 


4- 1.00 


+ 1-50 


+ 1.30 




167 


874. 04 


869. 63 


+ 0.019 


— 0.02 


4- 1. 00 


4- 1.51 


4- 4.41 




171 


879.87 


878. 29 


4- 0.022 


— 0.05 


4- 1. 00 


+ 1.59 


-1- 1.58 




172 


885.38 


882. 36 


+ 0.022 


— 0.06 


4- 1.00 


+ 1.63 


4- 3.02 




173 


885. 78 


884. 68 


+ 0.022 


— 0.07 


4- 1.00 


4- 1.65 


4- 1. 10 




176 


916.59 


912. 18 


+ 0.028 


— 0. 14 


4- 1. 00 


4- 1.84 


4- 4.41 




177 


915.92 


913- 03 


+ 0.028 


— 0. 14 


4- 1. 00 


+ 1.8s 


4- 2.89 



no 



TRANSIT OF VENUS, 1874. 
CHATHAM ISLAND. 



No. of 
Photo. 


Observed 
Distance. 


Tabular Distance. 


O.-C. 




// 


// 


;/ 








II 


IS 


864. 13 


864.34 


— 0.018 6 Tls 


+ 0. 4S (5 A 


+ o.87(5D 


+ o.33(Jff 


— 0.21 


16 


864.96 


863.44 


— 0.017 


+ 0.4S 


+ 0.87 


+ 0.34 


+ 1.52 


17 


864. 96 


862. 36 


— 0.017 


+ 0.4s 


+ 0.87 


+ 0.3S 


-f 2. 60 


24 


838.48 


836. 66 


— 0. 001 


+ 0.26 


+ 0.96 


+ 0.86 


+ 1.82 


2S 


839. 01 


836.57 


— O.OOI 


+ 0.2S 


+ 0.96 


+ 0.88 


+ 2.44 


27 


839.32 


836.84 


+ 0.002 


+ 0.21 


+ 0.97 


+ 0-99 


+ 4-48.. 


29 


843.46 ~ 

Me. 


840. 64 


+ 0.006 


+ 0.IS 


+ 0.99 


+ 1. 17 


+ 1.82. 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 



Ill 



COMPARISON OF OBSERVED AND TABULAR POSITION-ANGLES. 

WLADIWOSTOK. 



No. of 
Photo. 


Observed 
Position- Angle. 


Tabular Position-Angle. 


0. — c. 


6 


' 
+ 36 24. 7 


' 
+ 36 23.0 


/ 

— 0. 2S7d;i, 


+ 177 <S A 


_ 


141 SB 


/ 

+ 6. 15 d TT 


+ 1-7 


7 


35 50.2 


35 54-4 


— 0.257 


+ 178 


— 


140 


+ 6.07 


— 4.2 


8 


. . . . 


.35- 25.6 


— 0.257 


+ 180 


— 


139 


+ 5-97 


. . . 


13 


21 47.3 


21 49-9 


— 0. 294 


-f 218 


— 


94 


+ 2.53 


- 2.6 


14 


21 20. 1 


21 15-7 


— 0. 294 


-f 218 


— 


92 


+ 2-37 


+ 4-4 


IS 


+ 20 55-4 


+ 20 43.6 


— 0.293 


4- 220 


— 


90 


-|- 2.22 


+ II. 8 


31 


- 8 25.4 


- 8 30.5 


— 0.251 


+ 215 


+ 


35 


— 5-88 


+ S-i 


32 


- 8 SI. 7 


- 8 58.9 


— 0.249 


+ 213 


+ 


36 


- S-97 


+ 7-2 


33 


— 9 27.3 


- 9 24.8 


— 0. 247 


+ 213 


+ 


38 


— 6.05 


- 2.5 


34 


— 9 47.3 


— 9 50.9 


— 0.244 


+ 211 


+ 


40 


-6. IS 


+ 3-6 


35 


— 10 18.3 


— ID 15.8 


— 0.243 


H- 211 


+ 


41 


— 6.22 


— 2.S 


36 


— 10 39-3 


— 10 42. 1 


— 0. 241 


+ 209 


+ 


43 


— 6.32 


+ 2.8 


37 


— II 9.2 


— II 4.8 


— 0. 241 


+ 209 


+ 


44 


-6.38 


— 4-4 


38 


— n 25.0 


— " 31s 


— 0.241 


+ 207 


+ 


46 


— 6.47 


+ 6.5 



112 



TRANSIT OF VENUS, 1874. 
NAGASAKI. 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position-Angle. 


0. — C. 


25 


/ 
+ 45 6.3 



+ 45 


0-5 


/ 

— 0. 220 (5 1, 


+ 143 (JA 


— i56(!D 


/ 

-f- 7. 22 (S TT 


+ S-8 


26 


45 5-8 


44 


53-6 


— 0.220 


+ 144 


— 155 


+ 7-22 


+ 12.2 


28 


44 53-4 


44 


41.6 


— 0. 222 


+ 145 


- "55 


+ 7-20 


-f II. 8 


30 


44 33-0 


44 


24. 5 


— 0.223 


+ 146 


- «55 


+ 7- IS 


+ 8.5 


31 


44 25.9 


44 


17.4 


— 0.223 


+ 146 


— 155 


+. 7- 13 


+ 8.5 


33 


43 47-5 


43 


50.2 


— 0.225 


+ 148 


— 154 


+ 7- 08 


— 2.7 


34 


43 38.1 


43 


41.0 


— 0.226 


+ 149 


— 154 


+ 7-07 


— 2-9 


35 


43 8.7 


43 


12.2 


— 0.227 


+ 150 


- 153 


+ 7-02 


- 3-5 


36 


43 4-9 


43 


3-1 


— 0.229 


+ 151 


- "53 


+ 7-00 


+ 1.8 


37 


42 53-6 


42 


56.0 


— 0.230 


+ 151 


— 153 


+ 6.97 


— 2.4 


38 


42 33-4 


42 


30.0 


— 0.231 


+ 153 


— 152 


+ 6.92 


+ 3-4 


44 


41 8.2 


41 


6.7 


— 0. 238 


+ 158 


— 150 


+ 6-72 


+ i-S 


45 


40 47.7 


40 


44.8 


— 0. 238 


+ 160 


— 149 


+ 6.67 


+ 2.9 


46 


40 30. 6 


40 


35-7 


— 0. 239 


+ 160 


— 149 


+ 6.63 


- 5-1 


48 


40 14. 7 


40 


14.2 


— 0. 240 


-)- 162 


— 149 


+ 6.58 


+ 0.5 


49 


39 55-9 


39 


52.8 


— 0. 241 


+ 163 


— 148 


+ 6.52 


+ 3-' 


5° 


39 37.9 


39 


43-1 


— 0.243 


+ 164 


— 148 


+ 6.50 


- 5-2 


SI 


39 o-S 


39 


3-0 


— 0. 24s 


+ 166 


— 146 


•h 6.38 


— 2.5 


52 


38 36.8 


38 


36.7 


— 0-247 


4- 168 


— 145 


+ 6.32 


+ O.I 


53 


38 18.6 


38 


14.6 


— 0.249 


+ 169 


— 145 


+ 6.25 


+ 4-0 


54 


38 3.4 


37 


59-9 


— 0. 250 


+ 170 


— 144 


+ 6.20 


+ 3-5 


55 


37 46.3 


37 


42.3 


— 0. 25 1 


+ 171 


— 143 


+ 6.15 


+ 4-0 


57 


36 30.6 


36 


25.8 


— 0-255 


+ 176 


— 141 


+ 5-90 


+ 4-8 


58 


35 53.9 


35 


58.7 


- 0. 257 


+ 177 


— 140 


+ 5-82 


- 4-8 


59 


35 40.3 


35 


35-4 


— 0.258 


+ 179 


— 139 


+ 5-73 


+ 4-9 


61 


34 49-9 


34 


49.6 


— 0. 260 


+ 181 


— 137 


+ 5-58 


+ 0.3 


62 


34 36.8 


34 


38.5 


— 0. 261 


+ 182 


-136 


+ 5-55 


— 1-7 


63 


34 23.9 


34 


24.4 


— 0. 262 


+ 183 


-136 


+ 5-50 


— 0.5 


64 


34 '6.5 


34 


14. 1 


— 0. 263 


+ 184 


— 135 


+ 5-45 


+ 2.4 


65 


33 14.5 


33 


18.8 


— 0. 265 


+ i86 


— 132 


+ 5-25 


— 4-3 


67 


31 27.9 


31 


27.6 


— 0.272 


+ 192 


- 127 


+ 4-83 


+ 0.3 


72 




26 


14-5 


— 0. 284 


+ 207 


— Ill 


+ 3-52 


. 


74 


24 46.7 


24 


41.4 


— 0. 288 


-|- 210 


— 105 


+ 3- 08 


+ 5-3 


75 


24 30.1 


24 


16.3 


— 0.290 


+ 211 


— 103 


+ 2.97 


+ 13-8 


76 


22 25. 4 


22 


21.4 


— 0. 291 


+ 216 


- 96 


+ 2-42 


+ 4-0 


77 


21 43-5 


21 


50-3 


— 0. 292 


+ 217 


— 94 


+ 2.28 


- 6.8 


78 


21 44. 5 


21 


41.2 


— 0. 293 


+ 217 


— 94 


+ 2.23 


+ 3-3 


79 


21 27. 7 


21 


27.8 


— 0. 293 


+ 217 


— 93 


+ 2.17 


— 0. 1 


80 


21 22. 7 


21 


17.8 


— 0. 293 


+ 2l8 


— 92 


+ 2.13 


+ 4-9 


81 


21 15-3 


21 


8.6 


— 0. 293 


-f 218 


— 92 


+ 2.08 


+ 6-7 


84 


18 21.7 


18 


16.3 


— 0. 294 


+ 223 


— 80 


+ 1.23 


+ 5-4 


93 


4 51-9 


4 


45-9 


— 0. 290 


+ 231 


— 21 


— 2.82 


+ 6.0 


94 


4 42-0 


4 


37-2 


— 0. 290 


+ 231 


— 20 


— 2.85 


+ 4-8 


95 


4 27.2 


4 


24. 6 


— 0. 289 


+ 231 


— 20 


— 2.90 


+ 2.6 


96 


4 20.3 


4 


16.8 


— 0. 288 


+ 231 


— 19 


- 2-95 


+ 3-5 


99 


-f 2 51.2 


+ 2 


43-° 


— 0. 285 


+ 230 


— 12 


— 3-40 


+ 8.2 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 

PEKING. 



113 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position-Angle. 


0.— C. 




/ 





/ 


./ 








/ 


/ 


'5 


+ 45 9-5 


+ 45 


15.7 


— 0.217 dPIg 


+ 142 (5A 


— 


156 dD 


+ 8. 58 (3 IT 


— 6.2 


19 


43 43-5 


43 


46.7 


— 0. 224 


+ 148 


— 


154 


+ 8.48 


— 3.2 


21 


43 9-9 


43 


6.7 


— 0. 228 


+ 151 


— 


153 


+ 8.45 


+ 3-2 


23 


+ 42 40- 7 


+ 42 


45.0 


— 0. 230 


+ 153 


— 


153 


-f 8.42 


— 4-3 


44 


— 8 2.2 


— 8 


5-9 


— 0. 254 


+ 215 


+ 


33 


— 4.13 


+ 3-7 


45 


— 8 20. 9 


— 8 


22.4 


— 0.253 


+ 214 


+ 


34 


— 4.20 


+ 1.5 


46 


- 8 33.2 


— 8 


39-1 


— 0. 252 


+ 214 


+ 


35 


— 4.28 


+ 5.9 


49 


— 9 40-9 


— 9 


40.2 


— 0. 249 


+ 212 


+ 


39 


— 4.54 


-0.7 


5° 


- 9 56.3 


— 9 


58.8 


- 0.247 


+ 211 


+ 


40 


— 4.60 


+ 2.5 


SI 


— 10 14.3 


— 10 


16. s 


— 0. 24s 


+ 210 


+ 


41 


— 4.68 


+ 2.2 


S3 


— 10 54.8 


— 10 


54.7 


— 0. 243 


+ 209 


+ 


44 


— 4.82 


— 0. 1 


54 


— II 14.2 


— II 


12.6 


— 0. 242 


+ 208 


+ 


45 


— 4.88 


— 1.6 


56 


— II 45-5 


— II 


47-5 


— 0. 239 


+ 207 


+ 


47 


— 5.02 


+ 2.0 


57 


— 12 4. 7 


— 12 


5.8 


— 0.23S 


-f- 206 


+ 


48 


— 5.08 


+ I.I 


58 


— 12 25.0 


— 12 


24.1 


— 0.237 


+ 205 


+ 


49 


-5.15 


— 0.9 


59 


— 12 38.4 


— 12 


39-4 


— 0. 23s 


+ 204 


+ 


50 


- 5-20 


+ I.O 


60 


— 12 53-9 


— 12 


55.6 


— 0.233 


+ 204 


+ 


51 


- S.27 


+ 1.7 


61 


— 13 IS- 2 


— 13 


12.9 


— 0. 232 


+ 203 


+ 


52 


-S.32 


— 2.3 


63 


— 13 45-8 


— 13 


46.3 


— 0. 230 


+ 201 


+ 


54 


-5-45 


+ O.S 


65 


— 14 16.0 


— 14 


16.3 


— 0. 228 


+ 200 


+ 


55 


— 5.55 


+ 0.3 


67 


- 14 55-5 


— 14 


49.6 


— 0.226 


+ 198 


+ 


57 


-5-65 


— 5.9 


68 


— 15 3-0 


- IS 


3.1 


— 0.225 


+ 198 


+ 


58 


— 5.70 


+ 0.1 


. 69 


— 15 18.4 


- 15 


22.5 


— 0.223 


+ 197 


+ 


59 


-5. 77 


+ 4.1 


70 


— IS 36.4 


— 15 


36.4 


— 0. 222 


+ 196 


+ 


59 


-5.82 


0.0 


71 


- 15 51-9 


- IS 


49.7 


— 0. 221 


+ 196 


+ 


60 


- 5. 85 


— 2.2 


72 


- IS 55-8 


— 16 


3-2 


— 0. 220 


+ 195 


+ 


61 


— 5.90 


+ 7.4 



KERGUELEN. 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position- Angle. 


0. — C. 


7 


' 
+ 37 3. 7 



+ 36 


58.4 


— 0. 244 6 ^4 


+ 166 <5A — 


136(5 D 


+ 1.25 (5 jr 


+ 5-3 


17 


+ 2 4.1 


+ 2 


3.5 


— 0. 269 


+ 220 — 


9 


+ 3.90 


4- 0.6 


18 


+ I 13.5 


+ I 


3.4 


— 0. 267 


+ 219 — 


5 


+ 3.90 


-f 10. 1 


19 


-f 48.6 


+ 


44.3 


— 0. 266 


+ 219 


3 


+ 3.88 


+ 4-3 


20 


+ 14. 


+ 


17.4 


— 0.265 


+ 219 — 


• I 


+ 3.90 


— 3.4 


25 


— 6 17.3 


— 6 


26.0 


— 0. 248 


+ 210 + 


26 


+ 3.63 


+ 8.7 


32 


— 10 34.3 


— 10 


42.3 


— 0. 232 


+ 201 -f 


41 


+ 3.37 


-(- 8.0 


33 


— 17 0.7 


— 17 


9.7 


— 0.207 


+ 184 + 


62 


+ 2.85 


+ 9.0 



S. Ex. 31 15 



114 



TRANSIT OF VENUS, 1874. 
HOBART TOWN. 



No. of 
Photo. 


Observed 
Position-Angle. 






Tabular Position-AngU 




♦ 


0. — C. 


9 


' 
4- 2 34. 4 



+ 2 


/ 

23-5 


— 0. 275 <5 ^6 


+ 222 dA 


— lodD 


/ 
— S. 63d n 


/ 

[+ 10.9] 


10 


+ 2 15.2 


+ 2 


14. u 


— 0.273 


+ 222 


— 10 


-S-(>2, 


+ 1.2 


II 


+ 2 3-7 


+ 2 


3-3 


— 0.272 


+ 222 


- 9 


-5.63 


+ 0.4 


12 


+ 2 6.5 


+ I 


55-6 


— 0. 272 


+ 222 


— 8 


-5.63 


+ 10.9 


13 


+ I 36.8 


+ I 


33-3 


— 0.271 


+ 222 


— 7 


-5-63 


+ 3-5 


14 


+ I 5-7 


+ I 


5-1 


— 0.271 


+ 221 


— 4 


-5-63 


+ 0.6 


IS 


+ 58.S 


+ 


52-3 


— 0. 268 


+ 221 


— 4 


-5-63 


+ 6.2 


16 


+ 31.2 


+ 


26.5 


— 0.267 


+ 221 


— 2 


-5-63 


+ 4-7 


17 


+ 28.3 


+ 


21.8 


— 0.267 


+ 221 


— 2 


-5- 63 


+ 6.5 


i8 


+ 6.7 


— *o 


Q.9 


— 0.267 


+ 220 





-5-63 


+ 7-6 


19 


+ 4.1 


— 


8.9 


— 0. 266 


+ 220 


+ I 


— 5.62 


+ 13-0 


22 


— I 32.0 


— I 


39-6 


— 0. 264 


+ 219 


+ 7 


-S.60 


+ 7-6 


23 


— I 45-4 


— I 


SI- 2 


— 0.262 


+ 218 


+ 8 


-5.58 


+ 5-8 


24 


— I 59-4 


— 2 


1-5 


— 0. 262 


+ 218 


+ 9 


-5-57 


+ 2.1 


25 


— 2 12. 7 


— 2 


13-4 


— 0. 262 


+ 218 


+ 9 


-5.58 


+ 0.7 


26 


— 2 15.0 


— 2 


25.8 


— 0.260 


+ 217 


+ 10 


-5.58 


+ 10.8 


27 


— 2 37. 1 


— 2 


52.3 


— 0. 260 


+ 217 


+ 12 


- 5-57 


+ 15-2 


28 


— 3 3-2 


— 3 


6.0 


— 0. 259 


+ 216 


+ 13 


— 5- 57 


+ 2.8 


29 


— 3 16.0 


— 3 


20.9 


— 0. 258 


+ 216 


+ 14 


— 5-57 


+ 4-9 


30 


— 3 28.0 


— 3 


29.6 


— 0. 258 


+ 216 


+ 14 


— 5-55 


+ 1.6 


32 


-3 58.8 


— 3 


55-8 


— 0. 257 


+ 215 


+ 16 


- 5-53 


— 3-0 


33 


— 3 51-4 


— 4 


0.4 


— 0-257 


+ 215 


+ 16 


- 5-55 


+ 9-0 


34 


— 4 4-6 


— 4 


II. I 


— 0.256 


+ 215 


+ 17 


— 5-53 


+ 6.5 


35 


— 4 11-9 


— 4 


20.5 


— 0. 256 


+ 215 


+ 18 


-S-52 


+ 8.6* 


36 


— 4 37-2 


— 4 


33-9 


- 0.25s 


+ 214 


+ 19 


— 5-52 


— 3-3 


37 


— 4 27. 3 


— 4 


39-7 


— 0. 255 


+ 214 


+ 19 


-S-52 


+ 12.4 


38 


— 4 52. 2 


— 4 


55-7 


— 0.254 


+ 214 


4- 20 


-5-52 


+ 3-5 


39 


— 5 2.4 


-s 


10.4 


— 0.253 


+ 213 


+ 21 


— 5-50 


+ 8.0 


40 


— 5 21.6 


-5 


21.4 


— 0.251 


+ 213 


+ 22 


-5- 48 


— 0.2 


41 


-5 36.8 


- 5 


42.6 


— 0. 251 


+ 212 


-f 23 


- S-48 


+ 5-8 


42 


— 5 43-9 


— 5 


54.0 


— 0. 249 


+ 212 


+ 24 


— 5-47 


+ 10. 1 


43 


— 6 1.9 


— 6 


4.0 


— 0. 248 


+ 212 


+ 24 


- 5-47 


+ 2.1 


44 


— 6 12.9 


— 6 


16.2 


— 0. 247 


+ 211 


+ 25 


— 5-45 


+ 3-3 


45 


— 6 20. 


— 6 


25-9 


— 0. 246 


+ 211 


+ 26 


-S-43 


+ 5.9 


46 


— 6 38.0 


.— 6 


40.3 


— Q. 246 


+ 211 


+ 27 


- 5-43 


+ 2.3 


47 


— 6 43-7 


— 6 


54-5 


— 0. 246 


+ 210 


+ 28 


— S-43 


+ 10.8 


48 


-6 58.7 


- 7 


9.2 


— 0.246 


+ 210 


+ 29 


- 5-42 


+ VI.0.5 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 
CAMPBELL TOWN. 



"5 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position-Angle. 


O.-C. 


10 


( 
+ 10 47-1 


+ 


c 
10 


/ 

46.7 


— 0.286(5^6 


+ 224(5 A 


— 46(!D 


— 5. 5o(Jff 


+ 0.4 


11 


+ 9 49- 


+ 


9 


47-7 


— 0. 285 


+ 224 


— 42 


- 5-55 


+ 1-3 


12 


+ 9 43-1 


+ 


9 


38.0 


— 0. 285 


+ 224 


— 41 


-5-55 


+ 5-1* 


17 


+ 7 10.4 


+ 


7 


4-1 


— 0.282 


+ 225 


— 30 


-5-65 


+ 6.3 


i8 


+ 6 47. s 


+ 


6 


47-9 


— 0. 282 


+ 224 


— 29 


-5.65 


— 0.4 


19 


+ 6 45-4 


+ 


6 


33-0 


— 0.282 


+ 224 


— 28 


-5-65 


+ 12.4 


23 


+ 4 46. 5 


+ 


4 


42.4 


— 0. 279 


+ 224 


— 20 


- 5-7° 


+ 4-1 


24 


+ 4 45-4 


+ 


4 


28.0 


— 0.277 


+ 223 


— 19 


— 5-70 


+ 17-4 


28 


+ 9.4 


+ 





1-5 


— 0. 269 


H- 220 





- 5-73 


+ 7.9 


29 


— 48. 


— 


I 


0-5 


— 0.265 


+ 219 


+ 4 


— 5-72 


+ 12.5 


31 


— 2 15.2 


— 


2 


21. S 


— 0. 262 


+ 218 


+ 10 


— 5.70 


+ 6.3 


32 


— 2 26. 4 


— 


2 


41-3 


— 0.260 


+ 217 


+ 11 


— 5.68 


+ 14-9 


33 


- 3 17-7 


— 


3 


10.7 


— 0. 258 


-f 216 


+ 13 


— 5.68 


- 7-0 


34 


— 3 37." 


— 


3 


43-2 


— 0. 256 


+ 216 


+ IS 


-5-67 


+ 6.2 


35 


— 4 12.8 


— 


4 


24.9 


— 0.2SS 


+ 215 


+ 18 


-5-63 


+ 12.1 


36 


- 4 45-2 


— 


4 


56.0 


— 0-253 


+ 214 


4- 20 


— 5- 62 


+ 10.8 


37 


— 5 12.3 


— 


5 


13- 1 


— 0- 253 


+ 213 


+ 21 


-5- 62 


-f 0.8 


38 


- 5 18.7 


— 


5 


25.7 


— 0. 252 


+ 213 


+ 22 


-5-60 


+ 7-0 


39 


— 5 44-5 


— 


5 


52.0 


— 0.251 


+ 212 


+ 24 


-5-58 


+ 7-5 


40 


— 6 10. 2 


— 


6 


12.0 


— 0. 249 


+ 212 


+ 25 


- 5-57 


+ 1.8 


41 


- 6 27.7 


— 


6 


26.8 


— 0.248 


+ 211 


-f 26 


- 5-57 


- 0.9 


42 


— 6 31.0 


— 


6 


44-5 


— 0. 247 


+ 211 


+ 27 


- 5- 55 


+ 13-5 


. 44 


— 7 14-7 


— 


7 


18.6 


— 0.246 


4- 210 


+ 29 


- 5- 52 


+ 3-9 


45 


- 7 30.7 


— 


■7 


40-3 


— 0.244 


+ 209 


+ 31 


-5-50 


+ 9-6 


46 


— 7 52.0 


— 


7 


59.0 


— 0.242 


-f 208 


+ 32 


- 5-48 


+ 7-0 


47 


— 8 14.4 


— 


8 


23-3 


— 0.240 


+ 207 


+ 33 


-5-47 


+ 8.9 


48 


— 12 50.2 


— 


12 


50.4 


— 0.225 


+ 197 


+ 49 


— 5-17 


+ 0.2 


49 


— 13 28.4 


— 


13 


19-3 


— 0.222 


+ 196 


+ 50 


-5-12 


— 9.1 


SO 


— 13 35-3 


— 


13 


33-1 


— 0.221 


+ 195 


+ 51 


-5-10 


— 2.2 


SI 


— 13 41.4 


— 


13 


47.8 


— 0.220 


+ 195 


+ 52 


-5-08 


+ 6.4 


52 


- 13 55- 8 


— 


13 


58.9 


— 0.219 


+ 194 


+ 52 


— 5-07 


+ 3-1 


S3 


— 14 IS- 5 


~— 


14 


12.9 


— 0. 218 


+ 193 


+ 53 


-5-05 


— 2.6 



* Time unceitata. 



ii6 



TRANSIT OF VENUS, 1874. 
QUEENSTOWN. 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position-Angle. 


0.- 


-C. 


114 



+ 40 


/ 
47.2 



+ 40 


50.7 


— 0.232tf;i7 


+ 155-5 A 




14s (5 D 


— 5. 23 (Jtt 


_ 


/ 

3-5 


"5 


+ 40 


26.4 


+ 40 


24.6 


— 0.233 


+ 156 


— 


144 


-5-30 


+ 


1.8 


116 


+ 40 


2.9 


+ 40 


0-5 


— 0.233 


+ 158 


— 


H3 


- 5-35 


+ 


2.4 


117 


+ 39 


45. 8 


+ 39 


45.0 


— 0. 235 


+ 158 


— 


143 


-5.38 


+ 


0.8 


118 


+ 39 


16.9 


+ 39 


16. 1 


— 0. 236 


+ 160 


— 


142 


- 5-45 


+ 


0.8 


119 


+ 38 


58.9 


+ 38 


55-7 


— 0. 238 


+ i6i 


— 


142 


-5-48 


+ 


3-2 


120 


+ 38 


8.9 


+ 38 


17-3 


— 0. 240 


+ 164 


— 


140 


-5-58 


— 


8.4 


122 


+ 37 


7.2 


+ 37 


6.9 


— 0.244 


+ 168 


— 


138 


— 5-73 


+ 


0.3 


123 


+ 36 


38.6 


+ 36 


36.7 


— 0. 246 


+ 169 


— 


137 


— 5.80 


+ 


1.9 


124 


+ 36 


5-4 


+ 36 


2.6 


— 0.248 


+ 171 


— 


135 


-5. 87 


+ 


2.8 


125 


+ 35 


28.3 


+ 35 


31.2 


— 0. 250 


+ 173 


— 


134 


— 5-92 


— 


2.9 


126 


+ 34 


49-5 


+ 34 


49.1 


— 0.252 


+ 175 


— 


132 


— 6.02 


+ 


0.4 


127 


+ 34 


14.6 


+ 34 


12.7 


— 0. 254 


+ 177 


— 


131 


— 6.08 


+ 


1-9 


128 


+ 33 


41.4 


+ 33 


41.6 


— 0.255 


+ 179 


— 


129 


-6.15 


— 


0.2 


129 


+ 33 


12. 1 


+ 33 


8.0 


— 0.257 


+ 181 


— 


128 


— 6.22 


+ 


4-1 


130 


+ 32 


20.8 


+ 32 


17- S 


— 0. 259 


+ 183 


— 


126 


— 6.30 


+ 


3-3 


131 


+ 31 


59-5 


+ 31 


54- 


— 0.261 


+ 185 


— 


125 


-6.35 


+ 


5- 5 


132 


+ 31 


25.2 


+ 31 


25-4 


— 0. 262 


+ 186 


— 


123 


— 6.40 


— 


0.2 


133 


+ 30 


59-2 


+ 31 


1.4 


— 0.264 


+ 187 


— 


122 


— 6.45 


— 


2.2 


134 


+ 30 


38.1 


+ 30 


33-6 


— 0.265 


+ 188 • 


— 


121 


— 6.50 


+ 


4-5 


13s 


+ 30 


13- 1 


+ 30 


6.3 


— 0. 266 


+ 190 


— 


119 


-6.5s 


+ 


6.8 


i39(?) 


+ 22 


27.4 


+ 22 


30-3 


— 0.280 


-f 208 


— 


94 


— 7.20 


— 


2.9 


142 


+ 22 


55- 5 


+ 22 


51-5 


— 0. 280 


+ 208 


— 


95 


-7- 18 


+ 


4.0 


143 


+ 21 


54-6 


+ 21 


55-4 


— 0. 281 


+ 209 


— 


91 


— 7-23 


— 


0.8 


144 


H-22 


18.9 


-)- 22 


13- 1 


— 0. 281 


+ 209 


— 


93 


— 7.22 


+ 


5.8 


145 


+ 21 


30-7 


+ 21 


'25.1 


— 0. 281 


+ 210 


— 


89 


- 7-27 


+ 


5.6 


151 


+ 6 


31.8 


+ 6 


27.7 


— 0.280 


+ 224 


— 


28 


- 7-50 


+ 


4-1 


153 


+ 6 


14.4 


+ 6 


22.3 


— 0. 278 


+ 224 


— 


27 


— 7.50 


— 


7.9 


IS4 


+ 6 


19-5 


+ 6 


7.8 


— 0.277 


+ 223 


— 


26 


- 7.48 


+ 


11.7 


IS5 


+ ■5 


47-4 


+ 5 


41.3 


— 0. 276 


+ 223 


— 


24 


— 7-47 


+ 


6.1 


156 


+ 4 


46.2 


+ 4 


44.6 


— 0.275 


+ 223 


— 


20 


— 7-43 


+ 


1.6 


158 


+ 4 


1-9 


+ 4 


2.2 


— 0. 274 


+ 223 


- T- 


17 


— 7- 40 


— 


0.3 


159 


+ 3 


55-1 


+ 3 


37-9 


— 0. 273 


+ 223 


— 


IS 


— 7.37 


+ 


17.2 


160 


+ 3 


141 


+ 3 


5- 1 


— 0. 273 


4- 222 


— 


13 


- 7-35 


+ 


9.0 


161 


+ 3 


2.2 


+ 2 


54-" 


— 0. 272 


-J- 222 


— 


12 


— 7-33 


+ 


8.2 


163 


+ 


10.4 


+ 


16.3 


— 0. 266 


-f 220 


— 


I 


- 7-15 


— 


S-9 


164 


— 


22.5 


— 


9.9 


— 0.264 


-f 220 


+ 


I 


— 7.12 


— 


12.6 


165 


— 


19. 8m 


— 


22.9 


— 0. 264 


+ 219 


+ 


2 


— 7. 10 


+ 


3-im 


166 


— 


35-0 


— 


44.4 


— 9. 263 


+ 219 


+ 


3 


— 7.07 


+ 


9-4 


167 


— I 


2.8 


— I 


4.0 


— 0. 262 


+ 219 


+ 


4 


— 7-03 


+ 


1.2 


171 


— 2 


48.0 


. — 2 


56.1 


— 0- 259 


+ 216 


+ 


12 


— 6.87 


+ 


8.1 


172 


— 3 


41.9 


— 3 


44.2 


— 0. 256 


+ 215 


+ 


15 


— 6.78 


+ 


2-3 


173 


— 4 


13 2 


— 4 


10.7 


— 0. 254 


+ 214 


+ 


17 


— 6. 73 


— 


2.5 


176 


— 8 


39-5 


— 8 


39.8 


— 0.235 


+ 206 


+ 


34 


— 6.18 


+ 


0-3 


177 


— 8 


40. 1 


- 8 


46.9 


- 0-235 


-f 206 


+ 


35 


— 6.17 


+ 


6.8 



DISCUSSION OF THE PHOTOGRAPHIC OPERATIONS. 
CHATHAM ISLAND. 



117 



No. of 
Photo. 


Observed 
Position-Angle. 


Tabular Position-Angle. 


0. — c. 




' 


' 


/ 






/ 


/ 


IS 


+ 29 26. 6 


+ 29 29. 7 


— o.267(!A8 


+ 191 (5 A — 


118 dD 


— 8.08 Stt 


— 3-1 


16 


+ 29 19. 7 


+ 29 16.0 


— 0.267 


+ 192 — 


117 


— 8.10 


+ 3-7 


17 


+ 28 55.4 


+ 28 59. 1 


— 0. 267 


+ 193 — 


116 


-8.13 


— 3-7 


24 


+ 16 8.7 


-f 16 6.0 


— 0. 284 


-f 218 — 


68 


— 8.8s 


+ 2.7 


25 


+ IS 42.9 


+ IS 46.4 


— 0. 283 


+ 219 — 


67 


— 8.8s 


- 3-5 


27 


+ 13 28.0 


+ 13 i6-9 


— 0. 282 


-f 221 — 


S7 


-8.83 


+ II. I 


29 


4- 9 22.3 


+ 9 iS-9 


— 0. 281 


+ 223 — 


39 


-8.72 


+ 6.4 



CHAPTER IV. 



OPTICAL OBSERVATIONS OF THE TRANSIT. 

The optical observations relating to the Transit of Venus, included in the pro- 
gramme of the Commission, were as follows : 

I. Observations of the moment at which the indentation made by Venus in enter- 
ing upon the limb of the Sun first became visible. 

2 Observations of the distance apart of the cusps, during the ten minutes pre- 
ceding first internal contact, made with the Aiey-Valz double-image micrometer. 

3. Observations of the time of internal contact. 

4. Measures of the thickness of the strip of light between the limbs of Venus and 
of the Sun during a few minutes following internal contact. 

5. At the egress of the planet, a series of observations and measures in reverse 
order made in the same manner. 

6. Observations of an artificial Transit of Venus, made for the double purpose of 
practicing the observers and of determining their personal equations in observations 
of this class. 

§ I. Remaeks on Observations of the Aetificial Teansit of Venus. 

In describing and discussing the observations, we shall begin with those made 
on the artificial transit, because they are expected to be used in discussing the subse- 
quent observations. They may be divided into two classes, of which the objects are 
slightly dissimilar, those made before the parties went out and those made after their 
return. 

The principal object of the first class was the practice of the observers and the 
ascertainment of the errors to which the observations were liable. As a general rule, 
the observed times were compared with the actual times noted by an observer imme- 
diately behind the model transit, but the observers frequently practiced themselves 
without having any such record. 

After the return of the parties, the object aimed at was to secure an observation 
as much as possible like that actvially made at the station, and to ascertain its ewor. 
This was a very desirable object to attain, and one which must be considered worth 
attempting in all such observations. Many practical difficulties were, however, en- 
countered in carrying it out, one being that several of the observers did not return to 
Washington for a long period after their observations. The results are, however, 
presented in full in the following section. 
118 



OPTICAL OBSERVATIONS OF THE TRANSIT. ng 

Among the general results concluded from the observations of the model transit 
were the following: 

That external contacts admit of fully as accurate observation and comparison as 
internal ones, if allowance be made for the fact that the contact must become sensible 
before being seen ; that the accuracy of the observations is gradually increased by 
practice on the part of the observer ; that there is only one definite phase at internal 
contact which can be clearly differentiated, namely, one which, with slight accidental 
and personal differences, corresponds to the moment of true contact. The formation 
of the black drop and the succession' of phenomena described by various observers 
all run into each other by insensible gradations, and therefore do not admit of dis- 
tinctive observations. The following more special statement of conclusions to be 
drawn from the observations is principally extracted from a paper in the Monthly 
Notices of the Royal Astronomical Society for March, 1877 (volume ^y, page 237): 

(i) A defect of much of the reasoning on this subject is this: It has too generally been assumed that the 
geometric outlines of Venus and the Sun, considered as mathematical Hues, can be noted in observation with the 
same sort of definiteness and precision as that with which the mind conceives them, and sufficient attention has not 
been paid to the practical difficulties which the eye meets with in representing this geometric conception. I conceive 
that the question whether a certain phase can or cannot be definitely distinguished and observed by the eye is to be 
settled by actual trial and by a consideration of the imperfections of vision rather than by a consideration of its 
purely geometric definiteness of form. 

(2) One result of the trials with the artificial transit is that there is a certain phase near that of external con- 
tact which can be observed with the same order of precision as the internal contact, provided that the proper condi- 
tions are fulfilled. Among these conditions are that the observer shall previously have practiced on the artificial 
transit ; that he shall Imow at exactly what point of the Sun's Umb to look for the first contact ; that he shall know 
when to look for the contact with an uncertainty of not much less than half a minute nor much more than a minute ; 
and that he shall have a telescope of fixed size and power. Of course the phase thus observed wiU not be geometric 
contact, but that occurring at the time when the notch in the Sun's limb first became visible. This phase varies 
much less with variations in the atmospheric condition and in the size and power of the telescopes than might have 
been supposed. 

(3) The phase of external contact at egress is more uncertain than at ingress, owing to the doubt of the observer 
as to whether the notch has or has not disappeared from his view, that doubt extending over a longer period than the 
doubt as to when he first sees the notch at ingress. 

(4) In describing the phenomena near the time of internal contact, I shall consider the. planet to be approaching 
egress. For reasons which I shall soon mention, the artificial transit was placed at a distance of about eleven hun- 
dred yards from the place of observation, so that a greater or less amount of atmospheric undulation was always 
present. Supposing, then, that the planet was approaching the Sun's Umb, and, the thread of light growing thin 
owing to the approach of contact, the first thing which an observer would remark was that, in consequence of the 
constant changes of outline, caused by atmospheric disturbance of the images, no set of phenomena could be described 
as invariable. It would be necessary to combine judgment with sight by considering what might be called a mean 
phenomenon. Different observers might form different judgments as to what this mean phenomenon was. It would, 
however, always be seen that, as the thread of light became quite thin, it looked darker than the rest of the Sun, and 
unless the atmospbere was more steady than is usual in the day-time the line of light would occasionally "be broken 
up into two or more very irregular threads or twists of Ught, which would gradually grow fainter until they would 
Occasionally almost disappear from view. Repeated trials showed that the time of true internal contact wa« marked 
by the moment at which light entirely ceased to glimmer across the dark space formed by the approach of the limb 
of the planet to that of the Sun. 

(5) Every attempt to estimate an apparent contact, or moment at which the limbs of Venus and the Sun were 
tangent to each other, without reference to the appearance of the thread of light, was a total failure. It was, in fact, 
impossible to make any such estimate without an uncertainty of half a minute or more. This will not appear sur- 
prising if we reflect that the outlines of Venus and the Sun cannot present themselves to the vision as geometric 
lines, but only as more or less indefinite edges of a visible surface of sunlight, which visible surface disappears most 
gradually near the region of contact, and, in fact, at the moment of ideal "apparent contact" cannot be seen at all at 
the point of contact. Any one who wishes to satisfy himself on this point has only to examine a series of figures in 
which the black drop is represented, and try to decide which of them represents apparent contact. If he wishes to 
come as near nature as possible, he must shade off the outlines both of Venus and the Sun so that they shall terminate 
in a soft border, and view the picture through a rising current of hot air. 

(6) Any artificial representation of these phenomena in which the bright surface of the Sun is surrounded by 
a dark background, must fail to be correct in a very important particular. As a matter of fact, we know that the 



I20 TRANSIT OF VENUS, 1874. 

atmosphere immediately around the Smi's limb is of dazzling briUiancy. In meridian observations of tbe Sun, when 
the light is so cut down by a dark glass as no longer to dazzle the eye, the fine spider lines are visible on the back- 
ground of the atmosphere, else it would be impossible to observe the transit of the Sun's first limb. This brilliancy 
of the atmosphere mast greatly diminish irradiation, and if the Sun is observed through haze (as must often be the 
case in obsorvationa of contact when the Sun is near the horizon) irradiation may be entirely destroyed. It will there- 
fore be impossible to observe an actual internal contact of Venus or Mercury with a precision corresponding to that 
of an artificial contact on a black background. 

(7) The atmosphere affects the phenomena of contact in three ways : 
a. By illuminating the background, as just described; 

0. By producing undulations in the outlines of the images, thereby preventing the phenomena from being 
invariable; 

y. By softening the outline of the Sun's limb and thus rendering it'more or less indefinite. 

The artificial transit to which I have alluded was placed at a distance, in order that all these effects might be 
produced and studied, otherwise the optical phenomena of contact may be entirely different. For instance, because the 
black drop is sharply seen in the -artificial transit when the background is quite black, it does not follow that it will 
be noticed in the actual transit. 

(8) I have said little of the black drop, partly because I do not think there can be much room for a real differ- 
ence of opinion respecting its nature and causes, and partly because the question whether it is seen is of entirely 
secondary importance except as affording some indication of the sharpness of definition. In looking at the artificial 
ti'ansit it was very easy, about the moment of internal contact, by taking a general mean outline of the undulating 
imago of the planet, and imagining that outline continued across the undulating line of light and darkness mixed, 
into which the ideal thread was reduced by the imperfections of vision, to see something like a black drop. On the 
other hand another observer, with his attention fixed solely on the thread of light, would see nothing of the sort. 
The final disappearance of the thread of sunlight being the only phase which can be actually observed, an observer, 
fixing his attention exclusively on this, would not see any black drop at all, unless the amount of irradiation was 
cxcexjtionally great. 

(9) The general conclusion to which I am led is that there is but one phase of each contact which can be 
observed with any approach to accuracy, namely : 

u. The time when the notch made by Venus advancing on the Sun becomes visible ; 

13. The time at which true sunlight is first seen all the way around the following limb of the planet ; 

7. The planet approaching egress, the time when it first completely cuts off the true limb of the Sun, and the 
space connecting the limb of the planet with the sky becomes as dark as the planet itself; 

(S. The time when the last limb of the planet, leaving the limb of the Sun, disappears from view. 

If an observer, at the time of internal contact, does not note, or try to note, the phases /3 and 7, there is no defi- 
nite phase to which his observation can be referred. The old belief that at second internal contact there is a sudden 
formation of the black drop, which marks the moment of true contact, seems to be entirely disproved. The more 
clear and dark the atmosphere around the Sun the more rapidly will contact appear to form, whether a black drop is 
seen or not, but under no circumstances under which an actiial transit is likely to be observed for parallax will it be 
really sudden. When it appears so it is only because the observer fails to notice the gradual darkening and breaking 
up of the thread of light. From the commencement of this darkening and diffusion, until the "apparent contact," 
which comes last of all, tliere are a series of progressive changes, which may extend over a period ranging anywhere 
from twenty or thirty to ninety seconds, at any point of which a random observation of internal contact may fall. 
The worse the definition and the lower the planet the greater the range, but the time of true contact is always near 
the mean of the period. 

§ 2. Peactice on the Model Transit. 

From what has just been said, it will be seen that an arrangement of the model 
transit in which vision on the bright cusps should be perfectly sharp, with a perfectly- 
dark background to represent the sky around the Sun and over Venus, would fail to 
present to the eye phenomena like those of the actual transit in at least three points : 

1. When observed with a sufficiently high power, 200 or upward, the limb of the 
Sun is always subject to more or less atmospheric undulation, especially when the 
Sun is not near the zenith. 

2. The outline of the limb is never perfectly hard, but must always be more or 
less softened, owing to action of our atmosphere and, perhaps, to that of the solar at- 
mosphere also. 

3. The background around the Sun is not black, but is so highly illuminated by 
the Sun's rays as to be clearly visible even through a dark glass which reduces the 
Sun's light to such an extent as to make it entirely pleasant to the eye. 



OPTICAL OBSERVATIONS OF THE TRANSIT. 121 

To attain the conditions of undulating images, a softened outline and a slightly- 
illuminated background, the artificial transit was placed on Winder's Building, an ele- 
vated structure about 3,300 feet from the Observatory. The line of sight from the 
dome of the Observatory is from 60 to 80 feet above the ground, over a part of the 
city where there are but few buildings. The amount of disturbance of images from 
atmospheric undulations is very varied, being greatest when the Sun is shining during 
a summer's day. An average amount of undulation, equal to that o£.the Sun as ordi- 
narily viewed at modei'ate altitudes, is easily attained by selecting an appropriate time 
of day and condition of the atmosphere for the experiments. 

The essential features of the apparatus are a triangular opening through a black- 
ened disk of metal, through which a white screen is viewed. The contrast between 
the screen and the metal appears about the same as between the Sun and the sur- 
rounding sky under ordinary atmospheric conditions. The inclined sides of the 
triangle are at an inclination about equal to that of the path of Venus to the limb of 
the Sun as seen from a southern station during the transit of 1874. The diameter of 
the disk which represents Venus is twelve inches, and the angle subtended is nearly 
that subtended by the planet during the transit. It is made of sheet-metal, painted 
black, and moves immediately behind the triangle, the sides of which represent the 
limb of the Sun. To keep it in place, a second triangle is built immediately behind 
the first, the space between the two being just sufficient to allow the disc to slide along. 
This second triangle is slightly larger than the first, so as to be invisible fi.-om the dome 
of the Observatory. The Venus is therefore entirely invisible until it emerges from 
behind the internal edge of the triangle, when it is seen by projection against the white 
screen beyond. 

The time occupied in passing from external to internal contact is 32 minutes. If 
the disk be allowed to run on, it will reach second internal contact in less than 5 min- 
utes after the first, and 32 minutes more will bring it to second external contact. 

T^e actual times of the geometric contacts were observed by an assistant alongside 
the instrument. At first he noted .the times by holding his eye in the plane of the 
Observatory and the edge of the metal from which the disc emerged, but in the later 
observations he was stationed behind the screen, and observed the contact through a 
minute hole on a line from the Observatory to the point of contact. 

Observations on this apparatus from the dome of the Observatory were com- 
menced in May, 1873, before the telescopes with which the actual transit was observed 
were obtained. The instruments used in the early observations were : 

(i.) Observatory equatoreal of 9.6 inches aperture, sometimes reduced to 5 
inches, with magnifying power of 130. This is designated as E. 

(2.) Telescope of 5 inches aperture, belonging to Miss Mitchell ; powers 80 to 
200. This is designated as M. 

(3.) Comet-seeker of 4 inches aperture ; power 40 This is designated as C. 

The results of these observations are given in the form of errors of observation, 
or excesses of the times noted by the observers over the true moments of geometric 
contact. The chronometer comparisons, and other original data on which these results 
depend, are considered too simple to render their reproduction necessary. 
S. Ex. 31 16 



122 



TRANSIT OF VENUS, 1874. 



The contacts are designated in their order as I, II, III, IV, the first and last 
being the external ones; the other two the internal ones. 

The first observations were made June 12, 1873, on internal contacts only, there 
being three observers. Professors Newcomb, Hall, and Haekness, who alternated at 
each of the three instruments. The resulting errors of observation, in seconds of time, 
are as follows ; the letters following the times indicate the instruments used : 



Second contact. 


Third contact. 


Newcomb. 


Harkness. 


Hall. 


Newcomb. 


Harkness. 


Hall. 


+ s'm 


s. 
+ SC 


s. 


— gM 


s. 
— 8 C 




s. 


— 17 M 


-I9C 


. 


— 3 M 


- 7C 


. 


, , 


— 2 C 


— 10 M 


— 12 E 


- 9C 


+ S M 


+ 


S E 


- 7C 


— 18 M 


— 16 E 


— 18 C 


M 


+ 


4E 


-13E 


— 16 C 


. . 


- 3E 


- 3C 






- 3E 


— 12 C 


. 


- SE 


- 4C 






- IS M 


+ 2E 


+ 32C 


- 3 M 


+ I E 






— 19 M 


- 4E 


-27C 


M 


- 3E 






- sc 


— 2 E 


— 14 M 


-13C 


- 3E 






+ SC 


E 


— 2 M 


- 9C 


- 4E 







June 13. 



First contact. 


Second contact. 


Third contact. 


Newcomb. 


Hall. 


Newcomb. 


Hall. 


Newcomb. 


Hall. 


+ 45 M 
+ 44:M 

+ 34 
+ 22 

+ II 

+ 14 


s. 

+ 71: E 
+ 2SE* 
+ 20 
+ 26 

+ 22 


s. 

- 9 M 

- 7 

- 7 

- 6 


s. 

— 29 E 

— 28 

— 26 

— 8 


s. 

— 2 M 

— 5 

— 2 

— 3 


+ 7E 
+ I 
+ 2 
+ 3 



















The entire minutes of Hall's observations are sometimes doubtful, as he did not 
record the times himself. 

June 14. 



First contact. 


Second contact. 


Third contact. 


Fourth contact. 


Newcomb. 


HaU. 


Harkness. 


Newcomb. 


Hall. 


Harkness. 


Newcomb. 


Hall. 


Harkness. 


Newcomb. 


Hall. 


+ 14M 
+ 15 M 


s. 

+ 22 E 
+ 23E 
+ 26 E 


s. 

+ 17C 
+ 26 C 

+ 36C 


+ 4M 

— 8 M 

M 

SM 


s. 
E 

— I E 

- I E 

-3E 


s. 

— 10 C 

+ I c 

+ 2C 

— 2 C 


s. 
+ 12 

+ 2 

+ 3 

+ 6 

+ 6 


s. 
+ 4 
+ 8 
+ 4 
+ 2 
+ 8 


s. 

+ 4 

+ 8 
+ 3 
+ 7 
+ 3 


Tf- 2 M 

-5 M 
— 4 


— 30' E 

— 21 E 

-24E 

— 22 E 



























* Time increased by 1 minute. 



OPTICAL OBSERVATIONS OF THE TRANSIT. 123 

The foregoing observations are given to illustrate the large errors to which 
contact observations are liable when undertaken without pi-evious practice. It must, 
however, be added that the images were generally very bad, owing to the atmospheric 
undulations of a summer's day. 

In the spring of 1874, previous to the departure of the expeditions, as many of 
the observers as practicable were engaged in practice with the instrument from day 
to day ; the results showing a gradual improvement in the accuracy with which the 
contacts could be observed. The exhibition of the results of these observations is 
not deemed necessary here, as it is believed that any coiTections for personal error 
should rather depend on trials made after the return of the parties. 

The Pekin party erected a somewhat similar instrument for their own practice 
while at the station, and the Japan party painted artificial representations of the 
planet at and near the times of interval contact, which they studied through their 
telescopes. 

After the return of the parties home, the probable corrections to be applied to 
the observations of contacts were investigated. Most of the observers who had 
observed a contact afterward came to Washington and made observations of the 
artificial transit with the same telescope and eye-piece which they had employed in 
the actual observation. Efforts were made to have the state of the images, the degree 
of illumination, and the aspects of the phenomenon in general as nearly as possible 
like they were in the actual transit. As a general rule, it was found by the observers 
that on an average sunny day the images of the artificial object were more disturbed 
than they had been in the actual transit; so that it was sometimes necessary to observe 
the artificial transit during a partially cloudy day, or to wait till near the time of 
sunset in order to have sufficiently good images. 

"We present the observations in regular chronological order. There is, however, 
one important remark to be made respecting the first four series of the following 
observations, including those made during the last week of August, 1875. It was 
found that the observers reported the image of the artificial Venus as seen near 
midday to be decidedly worse than was that of the actual Venus. To have suffi- 
ciently good images it was necessary to wait until nearly 5 o'clock in the afternoon, 
and the phenomenon was then interfered with by the shadow of the apparatus being 
thrown upon the white screen. To remedy this at a moment's notice, a shefet of 
white paper was inserted immediately behind the artificial Venus, so that the latter 
touched it as it passed along. The result of this was that if the Sun was not shining, 
which was sometimes the case, those portions of the white paper bordering immedi- 
ately on the limbs of the Sun and Venus were appreciably darker than the rest of the 
solar disc, and the apparent occurrence of second contact might therefore be delayed 
and that of third contact accelerated. If the Sun was shining, it was found that in 
case the position of the actual Sun was such that the shadow of the straight edge 
representing the border of the solar disc was visible to the observer, it was the 
contact with the shadow that was seen, and the observer at the instrument therefore 
recorded these contacts for comparison. 

The general probable result of this defective arrangement on the contacts may 
be mentioned. The observation of first contact could hardly be affected, as the 



124 TRANSIT OF. VENUS, 1874. 

position occupied by the real Sun during the observations was nearly in the plane of 
the straight edge and the observer. Still, when the Sun was not shining, there was 
a possibility that the slight darkening which surrounded the artificial Venus might 
result in accelerating this contact. The second and third contacts would probably be 
correctly observed in sunlight, but might have been noted too soon when the Sun was 
not shining. The fourth contacts would be entirely uncertain in sunlight, but would 
probably be nearly correct in the shade. 

These suspicious observations are presented in full, with a view of facilitating 
any judgment upon the reliability of their results. 

Series i. 1875, August 25. 

Observer, Commander Gr. P. Ryan, U. S. Navy, who observed first .external 
contact of Venus at Kerguelen very sharply. Errors of his observations of the 
corresponding contact with the artificial transit were: 



No. in 




No. in 




order. 


At 


order. 


At 

8. 


I 


+ 12.8 


8 


+ 6.0 


2 


+ 25-0 


9 


+ 6.0 


3 


+ 7.5 


10 


+ 7.0 


4 


+ 6.6 


1 1 


+ 3-9 


5 


+ 1.9 


12 


+ 5-5 


6 


+ 8.5 


13 


+ 3-9 


7 


+ 5-5 


14 


+ 5-5 



The first observations were not good from inferior images and want of prepara- 
tion. "The last two are very good, as nearly as possible like the Kerguelen obser- 
vations, though I think two or three seconds later, perhaps." 

Taking this opinion of the observer, and rejecting his opinion of the observation 
being late, as clearly impossible, the correction to reduce his observation to geomet- 
rical contact would be — 417. Taking the mean of all except the first two, the correc- 
tion would be — 5^7. But, for a cause we shall presently mention, these observations 
are not entirely reliable. 

Series 2. August 25. 

Capt. C. W. Raymond, Corps of Engineers, U. S. Army, who observed the 
third contact at Campbelltown, Tasmania, observed the corresponding contact with 
the artificial transit, as follows : 



No. in 
order. 


At 

8. 


No. in 
order. 


At 
s. 


I 


-3.5 


6 


-3-0 


2 


-2.5 


7 


— 1.0 


3 


+ 0.5 


8 


-0-5 


4 


- i-S 


9 


+ 0.5 


5 


— I.O 


10 


0.0 




,n - - 


II 


-4.0 


Mea 


— i.e; 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



125 



The mean of these results indicate that Captain Eaymond's observed time of 
third contact requires the correction 

+ 1^5• 

Series 3. August 30. 

Observers, Prof. A. Hall, U. S. Navy, who observed the transit at Wladiwostok, 
Siberia, and Prof C. A. Young, of Dartmouth College, who observed at Pekin. 





First Contacts 


i. 


No. in 


At 


At 


order. 


Hall. 

s. 


Young. 

8. 


I 


+ 2.7 


+ 4.2 


2 


+ 1.2 


— 3-3 


3 


+ 5-2 


+ 4-2 


4 


+ 3-3 




5 


+ 3-8 


+ 5-8 


6 


+ 6.3 


-1.7 


7 


+ 3-4 


— 2.6 


8 


+ 2.9 


+ 4-4 


9 


+ 2.9 


+ 1.4 



Mean + 3.5 • + 1.6 





Second Contabts. 


No. in 




At 


At 


order. 


Hall. 

B. 


Young. 

s. 


I 




0.2 


+ 10.3 


2 


+ 


7-3 


+ 8.8 


3 


+ 


10.4 


+ lO.I 


4 


+ 


6.9 


+ 7-4 


5 


+ 


9-5 


+ 8.5 


6 


+ 


6.6 


+ 5-1 


7 


+ 


5-6 


+ 9.6 


8 


+ 


6.2 


+ 6.7 


9 


+ 


0.2 


- 2.3 


iO 


+ 


2.7 


+ 1.2 



Mean +5.5 + 6.5 



Thjrd Contact. 
No. in At 
order. Young. 
s. 


I 


- 4.2 


2 


- 7,2 


3 

4 


- 7-6 

— 6.1 


5 
6 


- 10.5 

- 6.5 


7 
8 


-16.5 
— 16.0 


9 


- 19.9 


10 


- 1 1.9 


Mean 


— 10.6 



Fourth Contact. 


No. in 
order. 


At 

Young. 




s. 


I 


- 4-3 


2 


- 4-3 


3 


- 4.2 


4 


— II. I 


5 


— 2.1 


6 


— I.I 


7 


- 4.0 


8 


- 7-5 


9 


- 5-0 


10 


- 9-5 


Mean 


— ^-3 



Ohservers' notes on these contacts. 

Contact I. — A fair representation of actual case at Wladiwostok. — Hall. 

Contact II. — At second contact images were better in artificial transit than in actual one. — Hall. Image 
quite steady. None of the hesitation which was noted in the actual transit. — ^Young. 

Contact III. — The phenomena do not at all resemble those seen by me with this telescope at the transit. 
There seems to be very little hesitation, and the observed moment seems doubtful not more than one second. — ^YouNG. 



126 



TRANSIT OF VENUS, 1874. 



It will be seen that in three cases out of ten Professor Youxg noted the first 
external contact before it really occurred. The explanation of this seeming paradox 
will be given hereafter in connection with Professor Watson's observations. 

Series 4. August 31. 

Observer, H. C. Russell, Esq., who observed the transit in Australia under the 
auspices of the Colonial Government, and Professor Newcomb. 



First Contacts. 




Second Contacts. 


Third Contacts. 


Fourth Contacts. 


No. in 


Ai 


No. in 


Ai 


A« 


No. in At 


No. in 


At 


order. 


Russell. 


order. 


Russell. 


Newcomb. 


order. Russell. 


order. 


Russell. 


I 


a. 
+ 10.5 


I 


8. 

+ 3-7 


+ 6.2 


I — 16.6 


I 


s. 
— 2.9 


2 


+ "•5 


2 


+ 4.2 


+ 3-2 


2 + 7.4 


2 


— 0.4 


3 


+ 13-0 


3 


+ 1.8 


+ 4-3 


3 +17-5 


3 


+ 1.2 


4 


+ 2.5 


4 


+ 3-8 


+ 1-3 


4 + 0.5 


4 


— 2.3 


5 


+ 20.6 


5 


-1-7 


+ 3.8 


5 - 8.5 


5 


- 2.8 


6 


+ 10. 1 


6 


— 0.2 


+ 4.8 


6 lost 


6 


— 2.6 


7 


+ 6.1 


7 


+ 2.8 


+ 6.8 


7 - 6.4 


7 


— 4.2 


8 


+ 9-6 


8 


+ 2.4 


+ 4-4 


8 - 3.4 


8 


- 3-2 


9 


+ 3-2 


9 


+ 0.4 


+ 5-9 


•9 +3-6 


9 


- 5-5 


10 


+ 1-2 


10 


+ 0.4 


+ 29 


10 + 3.6 

• 


10 
II 


— 20.2 

- 5-2 


Mean 


+ 8.8 


Mean +1.8 


+ 4.4 


Mean — 0.3 
















Mean 


- 4-4 










observer's notes. 









Contact I. — Sun behind a cloud. — H. C. R. 
Contact II. — Sun clouded all the time. — H. C. R. 

Contact III. — (i) A mean of 39».5 and 50= [or of — 22».i and — ii».6]; (3) and (4) not good, owing to conversa- 
tion; (9) contact space smaller than usual. — H. C. R. 

Contact IV. — Light not strong enough, otherwise observations appeared to be good. 

The possible uncertainty arising from the screen being held immediately behind 
the disc was remarked for the first time during Mr. Russell's observations. A white 
sheet placed at a distance of several yards behind the transit was therefore used as a 
screen in all the following observations, an arrangement which precludes all possibility 
of errors arising from the shadows of the disc. 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



Series 5. 1875, September 22. 



127 



Observers, Prof. Asaph Hall, and Mr. 0. B. Wheeler, his assistant, who 
observed the Transit of Venus at Wladiwostok, Siberia. 





First Contacts 


1. 




Second Contacts. 






Third Contacts. 


No. in 


At 


At 


No. in 


At 


At 


No. In 


At 


At 


order. 


Hall. 


Wheeler. 


order. 


Hall. 


WHEBLEK. 


order. 


Hall. 


Wheeler. 




8. 


8. 




8. 


1 


B. 




8. 


n. 


I 


+ II.O 


+ 28.0 


I 


— 


— 




I 


— 2.2 


-5-7 


2 


+ 10.5 


+ 20.0 


2 


— 


+ 


1-5 


2 


-0.8 


+ 3-2 


3 


+ II.5 


+ 13-0 


3 


— 


+ 


3-0 


3 


-3-8 


-4-3 


4 


+ 17-0 


+ 25.0 


4 


— 


+ 


10.5 


4 


-0-5 


-4-5 


5 


+ 12.0 


+ 15-0 


5 


— 


+ 


4.0 


5 


— 1.8 


-0.8 


6 


+ 12.0 


+ 12.5 


6 


— 


. 


• • ■ 


6 


— 4.0 


-3-5 


7 


+ 15-7 


.... 


7 


+ 2.5 


+ 


6.0 


7 


-2.5 


-5-5 


8 


+ 7-2 


+ 26.7 


8 


+ 4.0 


+ 


4.0 


8 


-0-5 


-4-5 


9 


+ 15-8 


+ 27.8 


9 


+ 2.7 


+ 


7-70) 


9 


-2.5 


-4-5 


10 


+ I5-0 


+ 22.0 


10 
Mean 


+ 3-5 


+ 


5-3 


10 
Mean 


— 2.0 


-30 


Mean 


+ 12.8 


+ 21. 1 


+ 3-2 


+ 


4.9 


— 2.1 


— 3-3 








Observer!? remarka. 











Contact I. — ^Very bad images. — Hall. By no means as fair an object for observation as that seen at Wladi- 
wostok. — ^Wheeler. 

Contact II. — Images fair. — Hall. Much better conditions of atmosphere than daring first contacts. — 
Wheelek. 

Contact III. — Fair images. 



Series 6. 1875, September 22. 



Second Contacts repeated. 



No. in 


At 


At 


order. 


Hall. 


Wheblee. 


I 


6. 

+ 4-5 


+ 5:5 


2 


+ 2.5 


+ 12.5 


3 


+ 2.2 


+ 3-2 


4 


*+i-7 


+ 5-? 


5 


+ 0.7 


- 5.8 


6 


+ 2.0 


+ 5:5 


7 


+ 1.0 


+ 515 


8 


+ 2.0 


+ 6f5 


9 


+ 2.7 


+ 2,7 


10 


+ 2.5 


+ iS 


Mean 


+ 2.2 

Observeri? remark. 


+^ %12 



Fair images; (3) best. — Wheeler. 



128 



TRANSIT OF VENUS, 1874. 



Seeies 7. 1875, September 23 and 24. 



Same observers; first contacts. 



No. in 
order. 


September 

At 
Hall. 


23. 

A t 

"Wheblee. 


No. in 
order. 


September 24, 

At 
Hall. 


At 
Whbelbk. 


I 


s. 
+ 12.0 


8. 
+ 21.0 


I 


+ "6.2 


s. 

+ 13-8 


2 


+ 13-0 


+ 25.5 


2 


+ 7-5 


+ 12.2 


3 


+ II.O 


+ 18.5 


3 


+ 14-5 


+ 7-5 


4 


+ 6.5 


+ 17-0 


4 


+ 5.0 


+ 14-5 


5 


+ 8.0 


+ 16.0 


5 


+ 5-5 


+ 6.5 


6 


+ 70 


+ 10.5 


6 


+ 5-7 


+ 5-5 


7 


+ 9-0 


+ 13-5 


7 


+ 8.0 


+ 0.7 


8 


+ 7-5 


+ 12.0 


8 


+ 8.5 


+ 1 0.0 


9 


+ 8.2 


+ 16.7 


9 


+ 5-5 


+ 5-0 


10 


+ 12.0 


+ 26.5 


10 


.... 


+ 5-0 



Mean + 9.4 + 17.6 



Mean + 7.6 + 8.1 



Observers' remarks, 

September 23. — Images fair, but some boiling, and not so sharp as the real contact at Wladiwostok. — Hall. 
Fair images, but not as well defined as the actual observation at Wladiwostok. — ^Wheeler. 

September 24. — ^No. 7 doubtful, eye not being at the telescope soon enough. Images very good, but not quite 
so sharp as in real contact as observed at Wladiwostok. — Hall. Conditions of atmosphere very favorable. Image 
very distinct, but not as well defined as the actual observation at Wladiwostok. — Wheeler. 

Series 8. 1875, October 29. 

Observers, Commander Gteoege P. Ryan, who repeats observations of August 25, 
and Professor Newoomb. 





First Contacts. 




No. in 


A t 


At 


order. 


Ryan. 


Newcomb. 


I 


s. 
0.0 


s. 

+ 3-0 


2 


+ II.O 


+ 9.0 


3 


+ 1 0.0 


+ 8.5 


4 


+ 8.0 


+ 7.0 


5 


+ 7-5 


+ 7-5 


6 


+ 7-3 


+ 6.3 


7 


+ 5-0 


+ 4.0 


8 


+ 4-0 


.... 


9 


+ 9-0 


.... 


10 


+ II-5 


.... 



Mean + 7-3 



+ 6.5 



OPTICAL OBSERVATIONS OF THE TRANSIT. 

Series 9. 1876, January 14. 



129 



Observer, Prof. J. C. Watson, of Ann Arbor, Michigan, who observed the 
Transit of Venus at Pekin. 



First Contact. 


Second Contact. 


No. in 
order. 


A* 

Watson. 


No. in 
order. 


At 
Watson. 


I 


s. 
+ 9.2 


I 


»* 
-0.5 


2 


-0.8 


2 


-0.8 


3 


— 0.2 


3 


0.0 


4 


+ 2.0 






5 


+ 6.5 






6 


+ 9.0 






7 


+ 3-0 






8 


-2.5 






9 


-4.0 






10 


— 0.2 






II 


+ 1-5 






12 


— i.o 






Mean 


+ 2.2 






observer's 


remarlcs. 





Telescope disturbed greatly by wind; seeing otherwise good. First contact not qnite like real transit as 
observed at Pekin. Second contact not like what I saw in case of transit. Only one phase of the real contact 
exhibited. 



Before commencing another series, the attention of Professor Watson was called 
to the fact that one-half his observations of first contact were recorded before they 
had occurred, and therefore at a time when the disk representing Venus was absolutely 
invisible from his station. He explained this by the fact that the image was frequently 
disturbed in a way which led him to suspect the occurrence of contact, and if, on 
watching this disturbance, it grew into a well-ascertained contact, the time when it 
was first noticed was recorded as that of contact. The disturbing influence of the 
wind added to the difficulty of deciding when the contact should be considered as 
having been first actually seen. 

The fact that these doubtful contacts were incompatible with the description of 
the actual contact made at Pekin escaped the attention both of Professor Watson and 
myself at the time. This will be seen by examining his records of contact observa- 
tions to be given hereafter. 
S. Ex. 31 17 



ISO 



TKANSIT OF VENUS, 1874. 

Series 10. 1876, January 15. 



Observer, Professor Watson. 



Second Contacts. 


Third Contacts. 


No. in 


A< 


No. in 


At 


order. 


Watson. 


order. 


Watson. 


I 


8. 

- 5-5 


I 


+ 97 


2 


- 8.0 


2 


+ 11. 1 


3 


— 21.6 


3 


+ 8.8 


4 


— 10.4 


4 


+ 8.1 


5 


-1 1.4 


5 


+ 8.0 


6 


- 97 


6 


+ lO.I 


7 


-13-5 


7 


+ 9-0 


8 


-15-3 


8 


(+ 5.4) 


9 


-14.4 


9 


+ 6.8 


10 
II 


— 13-0 


10 


+ 9-0 










Mean 


+ 9-0 






Mean 


-12.3 








Observer's remarks. 





Images very nnsteady. Seeing very bad. Althougli the images were dancing, the appearance was not like the 
real transit. Only a single phase of it shown. In the case of II or III contact, I observed the formation or ending 
of a penumbra which surrounded dark image caused by rapid vibration of images. 

Series ii. 1876, January 20. 

Observers, Professor Watson, Professor Newcomb, who used 5" telescope (power 
about 120) ; and, for second contacts. Professor C H. F. Peters, who observed this 
contact during the Transit of Venus, at Queenstown, New Zealand. 



No. in 
order. 



I 
2 

3 

4 
5 
6 

7 
8 

9 
10 
1 1 
12 

13 
14 



First Contacts. 

A t 
Watson. 

s. 
+ 2.6 

2.0 



Second Contacts. 



Third Contacts. 



+ 



+ 
+ 



17 

0.5 
2.4 

— 1.2 

+ 4-1 
+ 10.5 
+ 4-5 



+ 
+ 



3-5 
2.1 



At 

Newcomb. 

s. 

+ II.6 
+ 14-5 
+ 9-3 
+ ii-o 

+ 134 
+ 1 1-3 
+ I5-I 
+ 155 
+ 9-0 

+ 155 
+ 9-1 



At 

Watson. 



-3-2 
-8.8 

-3-6 

— 2.6 
-0.4 
-4.0 
-2,4 

— 19 
-2.9 
-5-3 

— 2.2 

-1-5 
-54 



At 
Pbteks. 



— 1.2 

+ 0.7 

+ 3-4 

+ 2.9 

+ I.I 

0.0 

+ 0.6 

+ 1.6 

+ I.I 



At 

Newcomb. 



-47 
-3-8 

— 06 

— 1.6 

-3-9 
-0.5 
-3-4 
-1.9 
-0.4 



At 

Watson. 

s. 

+ 1.0 

-1-5 
+ 0.4 

-3-0 
+ 2.8 

— 2.1 

— 4.0 
+ 0.1 

+ 47 
+ 2.6 

+ 1-4 



Fourth Contacts. 

At 

Watson. 

s. 

- 8.4 

- 6.5 

- 7-0 

- 8.8 

- 10.3 

- 93 

- 8.0 

- 10.8 

- 8.4 



Means + 2.7 +12.3 —3.4 + i.i —2.3 



+ 0.2 



8.6 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



Observers^ remarJcs. 



131 



First contacts. — Images quite steady. Sometimes, however, wind shook telescope considerably; (8) doubtful 
from this cause. — Watson. 

Second contacts. — ^Not so distinct as in case of transit December 9, 1874. — Watson. (1) and (2) blurred; (3) (6) 
(8) good ; (4) fair. — Nbwcomb. 

Third contacts. — The images were sometimes quite unsteady, and besides the wind shook the observing tele- 
scope. The vision was very much worse than in the case of Pekin observation of transit. The uncertainty of these 
observations greater than in case of transit [of Venus] observations. — Watson. 

Fourth contacts. — Wind shaking telescope. The shadow on the screen . began to fall where the contact took 
place, and interfered with the observations. — Watson. 

Series 12. 1876, Febeuary 12. 

Observer, Prof. Gteorge Davidson, of the United States Coast Survey, and chief 
of the party stationed at Nagasaki, Japan. 

The Sun was, for a few seconds, nearly obscured by clouds at Japan, during 
which time the first contact took place; and when the fair outline of the solar disk 
was seen " the edge of the planet was just on the Sun's limb." Professor Davidson, 
from his study of the painted representations of Venus when ten and twenty seconds 
on the Sun, was enabled to estimate with some degree of certainty how many seconds 
Venus had advanced beyond actual contact at the time when he first saw the Sun 
after the clouds had passed. This estimation he recorded as ten seconds. In 
observing the artificial transit. Professor Davidson noted the time when Venus 
appeared to him as he first saw it projected on the solar disk at Nagasaki. Ten 
seconds were then added to the time of each geometric contact observed by the 
assistant at the artificial transit, and the resulting instants were then compared with 
the times noted by Professor Davidson. These comparisons are given in column one, 
J t. In the second column, z/ 1, are given the values from similar estimates of the 
time when Venus was thought by the observer to be twenty seconds on the Sun. In 
the second and third columns are given the values of ^ ^ for actual II and III con- 
tacts, respectively. 



First Contacts + 
ten seconds. 
No. in A < 
order. s. 

I + 10.2 


First Contacts -|- 
twenty seconds. 
No. in A < 
order. s. 

I + 16.3 


Second Contacts. 
No. in At 
order. b. 

I +6.5 


Third Contacts. 
No. in A t 
order. s. 

I - 0.5 


2 


+ 8.7 


2 


+ 10.6 


2 


+ 4.8 


2 


- 7-5 


3 


+ 12.4 


3 


+ 17.6 


3 - 


+ 1-7 


3 


— II.O 


4 


+ 18.0 


4 


+ 9-0 


4 


-0.7 


4 


- 3-4 


5 


+ 8.5 


5 
Mea 


+ 13-3 


5 
6 

7 


-1.8 
— 09 

-7-5 


5 
6 

7 


— 10.8 

+ 3-2 
+ 1.8 


Mean + 11.6 


n + 13-4 










8 


-2.3 


8 


- 7-3 










9 

10 
II 


-2.3 
— I.I 
+ 2.0 


9 


- 5-0 










Mean 


- 4-5 










12 
Mean 


+ 2.2 








00 





132 



TRANSIT OF VENUS, 1874. 



Ohsett'er's remarlcs. 

First contacts. — Those noted 20' after were taken because, sooner than that, the ohjects were too unsteady to form 
any judgment. All the conditions to-day are more unfavorable, as regards steadiness, than at Nagasaki, — Davidson. 

Second contacts. — Atmosphere very unsteady, and wind shaking telescope badly ; much more unfavorable than 
at actual transit. — Davidson. 

Third contacts. — Atmosphere very unsteady and images with very diffused edge, whereas it was very steady 
when I was observing the III contact [at Nagasaki]. — Davidson. 

Series 13 1876, Febeuaey 12. 

The foregoing series of observations was repeated by Professor Davidson, under 
more favorable atmospheric conditions. The values oi ^ t in column one are the 
errors of estimation of Venus ten seconds on the Sun's limb. 



First Contacts + 
ten seconds. 


Second Contacts. 


Third Contacts. 


No. in 
order. 


i 


it 

s. 


No. in 
order. 


At 

s. 


No. in 
order. 


At 

8. 


I 


+ 


7.0 


I 


+ 0.4 


I 


+ 


1.6 


2 


+ 


10.4 


2 


+ 0.7 


2 


— 


2.1 


3 


+ 


13.0 


3 


+ 0.9 


3 


+ 


0.7 


4 


+ 


12.7 


4 


0.0 


4 


— 


0.7 


5 


+ 


15-5 


5 


+ 0.5 


5 


+ 


1.2 


6 


+ 


12.2 


6 


+ 1-3 


6 


+ 


2.4 


7 


+ 


12.5 


7 


+ 1.2 


7 


— 


2.7 


8 


+ 


14.7 


8 


+ 1.4 


8 


+ 


1.9 








9 


+ 0.7 


9 


+ 


1-7 








Mean + 


12.2 


10 


+ 1.0 


10 


+ 


1.6 












II 


+ 


I.I 












Mean 


+ 0.7 


12 
Mean 


+ 


1-5 




+ 


0.7 








Observer'a remarlcs. 









Mrst contacts. — Objects far better than [in series 12], and very much better than at Nagasaki. — Davidson. 
. Second contacts. — ^Atmosphere moderately steady. I think the images steadier and sliarper than at NagasakL- 
Davidson. 

Third contacts. — ^Weather clear. Images almost as quiet as at Nagasaki. — Davidson. 



Becapitulation of mean results for errors in estimation of contacts. 

First Contact. 

B. 

Uncertain from arrangement of screen. 

Very bad images. 

Images fair, but not so sharp as the real contact at 

Wladiwostok. 
Same remark. 

Not so good as at "Wladiwostok. 

Fair images, but not so well defined as at Wladiwostok. 

Same remark. 



Hall . . 


+ 


3-5 




+ 


12.8 




+ 


9.4 




+ 


7.6 


Wheeler 


+ : 


21. 1 




+ 


17.6 




+- 


8.1 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



133 



Observer, Davidson 



Watson 



Ryan 



First Contact. 

8. 

+ 21.6 Estimated 10' after first contact as observed at Naga- 
saki, but bad seeing. 

+ 22.2 The same, but images good. 

+ 2.2 Does not correspond to actual transit. 

+ 1.9 Does not correspond to actual transit. 

+ 9.7 Mean of 7 bad observations. Uncertain. 

+ 7.3 Correspond well to actual observation. 



A circumstance to be allowed for in dealing with these results is that the observers 
improve with practice, and so see the contact sooner. For this reason I am inclined 
to take for the correction the first one which was derived under conditions corre- 
sponding to those of the actual trajisit. We therefore conclude for the corrections to 
reduce the actual observations to geometric contact. 

8. 

Observer, Hall . — 9.4 

Wheeler — 17.6 

Davidson — 21.6 

Ryan . — '].-^ 

Nothing can be deduced for the correction to Watson and Young, which must be 
inferred from the remarks of the observers and the attendant circumstances. 



Second Contact. 



Observer, Hall 



Wheeler 



Davidson 



Watson . 



Young 

Peters 



s. 

5-5 

3-2 
2.2 
4.9 
4.2 
0.0 
0.7 

— 0.4 

— 12.3 

— 3-4 
+ 6.5 

+ i-i 



+ 
+ 
+ 
+ 
+ 

+ 



Images fair. 



Images better than in actual transit. 



Not like actual transit. 

"Penumbra." See observer's remarks. 

Less disturbed than in actual transit. 

None of the hesitation noted in actual transit. 

No remarks. 



The following seem to be the most probable corrections to reduce the observa- 
tions to geometrical contact: 

Personal corrections for second contact. 



Observer, Hall 


-3-6 


Wheeler 


-4-5 


Davidson 


-0.4 


Watson 


+ 5-3 


YOUKG 


-6.5 


Peters 


— I.I 



134 TRANSIT OF VENUS, 1874. 

Third Contact. 



Observer, 


Hall . 


— 2.1 




Wheeler 


— 3-3 




Davidson 


- 4-5 
+ 0.7 




Watson 


+ 9-0 
+ 0.2 




Young 


— 10.6 




Raymond 


- 1-5 



Atmosphere much worse than in actual ti'ansit. 
Images almost as quiet as at Nagasaki. 
See observer's note. 

Not like actual transit. 



Concluded personal corrections for geometric third contact. 

B. 

Observer, Hall . +2.1 

Wheeler + 3.3 

Davidson 0.0 

Watson — 6.0 

Young +10.6 

Raymond + 1.5 

Fourth Contact. 

8. 

Observer, Watson — 8.6 Observations interfered with. 
Young — 5-3 

The only data for corrections to fourth contact given by the artiiicial transit are 
found by changing the signs of these quantities. 

§ 3. Tabular and Observed Times of Contact. 

There are two ways in which the comparison with observations of contact uiay 
be made; the one by comparing the observed and tabular times; the other by com- 
paring the observed and tabular distances; the observed distance being equal to the 
sum or difference of the semidiameters of the two bodies, according to whether the 
contact observed is an external or an internal one. I prefer the latter, but there may 
sometimes be a difference of opinion what instant of time should be taken as that of 
the observed contact, and the tabular distance being a function of the time observed 
cannot be definitively given in this case. The results will therefore be presented in 
such a form that either mode of comparison may be used. 

In the preceding discussion of the photographic observations, formulas and 
tables are given whereby the tabular distance and position angle of the centers of the 
two bodies, as seen from any station, and the coefficients of these quantities for 
changes in the relative right ascension and declination of the two bodies, and in the 
horizontal parallax of the Sun, ma)' be readily computed. These have been computed 
for several times near those of the contacts observed at the several stations, as follows: 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



135 



Station and Contact. 


Greenwich Side, 
real Time. 


Distanceof 
Centers. 




dS 


dS 


Position 
Angle. 


dp 
dA 


dp 
dT> 


dp 
di, 


Kerguelen I 


h 


m s 
8 


1007.35 


+ 0.679 


+ 0. 676 


+ 2.51 


' 
47 27.1 


+ 128 


— 151 


— 27 






9 


1005. II 


+ 0. 678 


0.679 


2.51 


47 15-3 


129 


— 151 


— 2S 






10 


1002. 89 


+ 0.676 


0.681 


2.51 


47 3-5 


129 


— 151 


- 23 






27 20. 2 


966. IS 


+ 0- 634 


0-725 


2-45 


43 29.7 


143 


— 147 


+ 13 






29 20. 6 


962. 15 


+ 0. 629 


0.730 


2.44 


43 .4-0 


144 


— 146 


+ 17 






31 20.9 


958.21 


+ 0.624 


0.736 


2.44 


42 38.0 


146 


— 146 


+ 22 






33 21-2 


954- 33 


+ 0.619 


0.741 


.2.43 


42 II. 8 


148 


— 145 


+ 26 






35 21.5 


950. 51 


+ 0.614 


0.746 


2.42 


41 45-3 


149 


— 144 


+ 30 






37 21.9 


946. 72 


+ 0.608 


0.751 


2.41 


41 18. 7 


151 


— 144 


+ 35 


II 




40 


941.92 


+ 0. 603 


+ 0. 758 


+ 2.40 


40 43-4 


+ 153 


— 143 


+ 40 






41 


940. 09 


+ 0.600 


0.760 


2.39 


40 29.9 


154 


— 143 


+ 42 






42 


938.29 


+ 0. 597 


0.763 


2-39 


40 16. 3 


155 


— 142 


+ 44 


Campbelltown III.. 




59 


939-97 


— 0. 202 


+ 0.976 


+ 1.60 


--12 38-5 


+ 197 


+ 48 


- 311 









941.89 


— 0.205 


0-975 


1. 61 


— 12 S1.9 


197 


+ 49 


-3(0 






I 


943- 83 


— 0.209 


0.974 


1.62 


-13 5-3 


196 


+ 49 


— 309 






2 


945- 78 


— 0.212 


0-973 


1.63 


-13 18-7 


196 


+ 50 


— 308 






2 52.4 


947- 52 


— 0.215 


0.972 


1.64 


— 13 30-3 


■195 


+ 51 


- 307 






3 45-6 

4 54-8 

5 36.9 

6 55-1 


949. 26 
951-55 
952. 96 
955- 58 








— 13 42-0 
-13 57-2 

— 14 6. 4 

— 14 29.4 












































— 0.231 


+ 0. 968 


1.68 


193 


+ 54 


— 302 


Queenstown I 




58 


1010.24 


+ 0.69s 


+ 0. 658 


— 0.26 


48 52-3 


+ 124 


— 154 


— 248 






59 


1007. 89 


+ 0.693 


0.660 


— 0.26 


48 40.5 


125 


— 154 


— 249 









1005. 56 


+ 0.690 


0.663 


— 0.26 


48 28.7 


125 


— 153 


- 251 






I 


1003. 24 


+ 0.689 


0.666 


-0.25 


48 16.8 


126 


— 153 


— 253 






3 


998. 49 


+ 0.684 


0.671 


— 0.25 


47 52-9 


128 


— 153 


-256 






7 

II 


989.44 
980. 60 
971.96 








47 4-3 
46 14. 8 
45 25.7 
























15 


+ 0.657 


0. 702 


— 0.25 


137 


- 151 


- 277 






19 
23 
27 


963-51 
955- 32 
947- 34 








44 33-3 
43 41-2 
42 48.3 
























+ 0.626 


0.734 


— 0.25 


147 


— 148 


— 298 


II 




28 


945- 50 


-\- 0. 624 


+ 0. 736 


— 0.25 


42 34-9 


+ 148 


— 148 


— 300 






29 • 


943- 56 


-)- 0.622 


0.739 


— 0.26 


42 21.5 


149 


— 147 


— 302 






30 


941. 62 


+ 0. 619 


0.742 


— 0.26 


42 8.0 


150 


— 147 


— 304 


Chatham Island 




16 
18 


967. 21 
963- 03 
958-93 
954.88 


+ 0. 652 


+ 0. 707 


— 0.05 


45 0.7 
44 35-0 
44 9-1 
43 42.9 


+ 139 


— 151 


— 353 




20 






.... 










22 


+ 0.637 


0.723 


— 0.03 


144 


— 149 


— 366 






35 


929. 90 


-1- 0. 602 


0-757 


+ 0.02 


40 47.6 


155 


— 145 


— 395 






36 
37 


928. 09 
926. 29 








40 33-7 
40 19. 8 










+ 0. 597 


0. 762 


+ 0.03 


156 


— 144 


— 399 


Wladiwostok I 


6 


54 


1008. 35 


+ 0. 721 


-|- 0.624 


— 0.98 


51 25.6 


+ 118 


— 160 


+ 483 




6 


55 


1005. 85 


+ 0. 720 


0.626 


— 1. 00 


51 14.2 


+ 119 


— 160 


+ 482 




6 


56 


1003. 34 


+ 0. 718 


0.629 


— 1-03 


51 2.8 


+ 119 


— 160 


+ 482 


II.... 


7 


21 


944-78 


+ 0.664 


+ 0. 695 


— 1.40 


45 57-1 


+ 140 


- 157 


+ 457 




7 


22 


942.59 


+ 0.661 


0.698 


— 1.42 


45 44-2 


4- 141 


- 157 


+ 455 




7 


23 


940- 43 


+ 0.658 


0. 701 


— 1-43 


45 31- 1 


+ 142 


-156 


+ 454 




7 


24 


938. 28 


+ 0.656 


0.703 


— 1.45 


45 18. 


+ 143 


- 156 


+ 453 



136 



TRANSIT OF VENUS, 1874. 



Station and Contact. 


Greenwich Side- 
real Time. 


Distance of 
Centers. 


dS 
dA 


dS 
dT> 


dS 

d-K 


Position 
Angle. 


dK 


dp 
dV) 


dp 
dn 


Wladiwostok III 


h m s 
II 14 


938. 80 


— 0. 258 


+ 0. 960 


— I. 81 


' 
-16 13.8 


+ 195 


+ 61 


— 432 




II 15 


940. 93 


— 0. 261 


0-959 


— 1.80 


— 16 27. 8 


194 


6z 


— 434 




II 16 


943- 12 


— 0. 265 


0.958 


— 1-79 


— 16 40. 8 


193 


63 


— 435 


Nagasaki I 


6 55 


1008. 57 


+ 0. 719 


+ 0. 627 


— 0.71 


+ 50 10. 8 


-f 118 


— 159 


+ 460 


• 


6 56 


1006. 05 


-|- 0. 716 


0.629 


— 0.73 


50 59-4 


119 


- 159 


+ 459 




6 57 


1003.57 


+ 0. 714 


0.632 


-0.75 


50 47.9 


120 


— 159 


+ 459 




6 58 


looi. 10 


+ 0-713 


0.635 


— 0.76 


50 36- 4 


121 


— 159 


+ 458 




7 14 


962. 99 


■f 0. 678 


0.677 


— 1. 01 


47 23.6 


134 


-158 


+ 447 




7 16 


958.44 


+ 0-674 


0.682 


— 1.05 


46 58.5 


13s 


- 157 


+ 445 




7 18 


953- 95 


-f 0.669 


0.688 


— 1.08 


46 33-0 


137 


— 157 


+ 443 




7 20 


949. 52 


+ 0.664 


0.693 


— 1. 10 


46 7.4 


139 


- 157 


+ 440 


II 


7 22 


945- 15 


+ 0. 661 


+ 0.698 


— I- 13 


— 45 41-5 


+ 141 


-156 


+ 438 




7 23 


942.97 


+ 0. 658 


0. 701 


-1-15 


45 28. 5 


142 


-156 


+ 436 




7 24 


940. 82 


+ 0- 655 


0.704 


— 1. 16 


45 15-4 


143 


-156 


+ 435 




7 25 


938. 68 


+ 0. 653 


0.707 


-i.iS 


45 2.2 


143 


- 156 


+ 434 




7 26 


936- 54 


-f 0.650 


0.709 


— 1.20 


44 49-0 


144 


- 155 


+ 432 


Ill 


II 13 


939- 25 


- 0.255 


+ 0. 961 


-1-53 


— 16 3.2 


+ 195 


+ 61 


— 447 




11 14 


941.40 


— u- 258 


0. 960 


— 1-52 


— 16 16.3 


194 


+ 61 


-448 




II 15 


943- 55 


— 0. 262 


0-959 


-I- 51 


-16 30.3 


194 


+ 62 


— 450 


Peking I 


6 55 
6 56 


loio. 51 
1007. 99 


+ 0. 721 


+ 0.625 
0. 627 


— 0.49 

— 0.50 


+ 51 19-8 
51 8.5 


+ 118 
■ 119 


— 159 

- 159 


+ 520 
+ 521 




+ 0. 718 




6 57 


1005.51 


+ 0. 716 


0.630 


— 0. 52 


50 57- 1 


119 


— 159 


+ 521 




6 58 


1003. 04 


+ 0. 714 


0.633 


— 0-54 


50 45-6 


120 


— 159 


+ 521 




7 22 54.51 


945- 07 


+ u. 660 


0.698 


— 0.93 


45 41-5 


141 


-156 


+ 517 


II 


7 23 
7 24 


944.87 
942. 71 


+ 0.661 
+ 0. 658 


+ 0. 699 
0. 702 


— 0.93 

— 0.95 


+ 45 40- 3 
45 27.3 


+ 141 
142 


-156 
-156 


+ S16 

+ 516 






7 25 


940. 55 


+ 0.655 


0.704 


— 0.96 


45 14- 3 


143 


-156 


+ 515 




7 26 


938. 41 


+ U.653 


0.707 


— 0.98 


45 1-2 


143 


- 156 


+ 514 


HI 


II i5 


939- 53 
941. 70 


— 0.258 

— 0.262 


+ 0. 960 
0-9S9 


— 1.96 
-1-95 


— 16 16.4 
— 16 29.5 


+ 195 
194 


+ 62 
+ 62 


-356 
-358 






II 17 


943- 85 


— 0. 265 


0.958 


— 1-94 


— 16 42.5 


193 


+ 63 


-361 




II 19 11.52 


948. 64 


— 0. 272 


0-955 


— 1.92 


— 17 10.9 


191 


+ 64 


-366 




1 1 22 19. 03 


955-57 


— 0. 282 


0.952 


-1.89 


— 17. 50.8 


189 


+ 66 


- 373 




II 33 53-53 


982.36 


— 0-319 


0.938 


— 1-77 


— 20 13. 5 


182 


+ 73 


— 395 


IV 


II 42 
II 43 


1002. 10 


— 0. 343 

— 0. 346 


+ 0.928 
0.927 


-1.67 
— 1.66 


— 21 48.9 

— 22 0. 3 


+ 177 
175 


+ 76 
+ 77 


— 408 

— 409 




1004. 58 




II 44 


1007. 08 


-- 0. 348 


0.926 


-1-65 


— 22 II. 7 


175 


+ 77 


— 410 



OPTICAL OBSERVATIONS OF THE TRANSIT. 



^37 



The assumed semidiameters for mean distance unity are: 

The Sun, <r„ = 96o".oo 
Venus, 0'^= 8". 50 

These values give for the geocentric semidiameters during the time of the transit: 

The Sun, Ingress, 974".974 -{- d <f 

Egress, 974".972 -\-d G 

Venus 32."i56 + 5<r' 

The corrections to reduce these last values to those of Airy and Hill, respectively, 
are: 

The Sun, d 6 (Aiey) zr + i".85o S a (Hill) = — o."2 1 2 
Venus, 8 a' (Aiey) — — o." 736 do' (Hill) = + o." 1 74 

The corrections to reduce the relative right ascension and declination of Venus 
to Aiey's values are : 

Ingress, 5 A — — 3".62 ; 5 D — — o".gs 
Egress, 6k = — 2,".SA; <JD = — o".98 

The quantity by whjch the assumed constant of solar parallax, 8".848, must be 
corrected to reduce it to that assumed by Aiey, 8".95, is 

<J;r — + o".i02 

We now have from the preceding data the following summary of the tabular and 
observed times of contact, which must be examined in connection with the observa- 
tions to appear in Part II. The first column, which needs explanation, is that giving 
the Greenwich sidereal times of observation. Here, S A^, d A^, etc., indicate the correc- 
tions to the assumed west longitudes of the stations, which have been already given. 
The reductions to geometric contacts have been already given, in part, as deductions 
from the observations with the artificial transit. In some cases, however, the observer 
either made no observations with this instrument, or those he did make are of doubtful 
applicability. In these cases, the most probable reduction is judged . of from other 
circumstances, or, when there are no data for forming a judgment, the column is filled 
with a mark of interrogation. The following are the cases in which the reduction 
does not depend solely on observations with the artificial transit. 

Nagasaki, III. Davidson — The Sun being obscured for a few seconds at the 
moment of contact, the observer judged contact to have passed 5 seconds when it 
reappeared. Hence, reduction rr — 5^ 

PeJcing, I. Watson and Young. — The reductions are inferred from the remarks of 
the observers respecting the visibility of the planet at intervals of a few seconds after 
the recorded times, compared with the general character of the results with the artifi- 
cial transit. It will be noted that Young was not fully certain that he saw the planet 
until 10 seconds after the recorded time; the correction is therefore smaller than it 
would otherwise have been. 
S. Ex. 31 18 



138 



TRANSIT OF VENUS, 1874. 



Queenstown, I. Peters. — For the correction the usual time after geometric contact 
at which the indentation becomes plainly perceptible is taken. 



Summary of times of contact noted at the several stations, with the concluded reductions to 
geometric contact, as derived from observations of the artificial transit. 



Station. 



Wladiwostok 



Nagasaki 



Peking 



Kerguelen 

Campbelltown . 
Queenstown . . . 



a 
o 
U 



II 

III 
I 

II 

III 



II 



III 



IV 



I 

III 

I 

II 



Observer. 



Hall , 

Wheeler ., 

Hall , 

Wheeler ., 

Wheeler ., 
Davidson .. 

TiTTMANN . 

Davidson . 

TiTTMANN - 

Davidson . 

TiTTMANN - 

Watson 

Young 

Watson . . . 
Young 

Watson . . . 

Young 

Woodward 

Watson 

Young 

Woodward 

Ryan 

Raymond.. 

Peters 

Peters 



Greenwich Sid. Time 
of Observation. 



7 

7 

II 

6 
6 

7 

7 

II 

II 



SS 
55 

23 
23 

15 

57 
57 

25 
23 

14 

14 



6 57 
6 57 



7 

7 

II 

II 

II 



25 
25 

IS 
15 
15 



II 42 
II 42 
II 42 



7 
II 

7 
7 



5i.2-f(5;ii 

56.5 " 

12.6 " 
19.0 " 

42.9 : : 

9- 7 + -S ^ 
24. 3 " 

4.2 " 

31.6 " 

9.7 " 
29. 5 " 

28.s + (5;i3 
23- S " 
28. 3 " 
i.o " 

32.2 " 

13-3 " 

31-3 " 

SO. 3 " 

33- 7 " 

24. 7 " 

35. i + (5;i.4 

22.0 + <5A6 

3- 5 + ''^7 
SI- 5 " 



p4 S 



— 9-4 

— 17.6 

— 3-6 

— 4-5 

+ 3-3 

— 21.6 

(?) 

— 0.4 
(?) 

— 5 (?) 
(?) 

— 7.0 

— S-o 

+ S-3(?) 

— 6.5 

— 6.0 
+ 10.6 

(?) 
+ 8.6 
+ 10.: 
+ 20.2 

— 7-3 
+ i-S 
-IS. (?) 

— I.I 



Green. Sid. Time of 
Geometric Phase. 



m s 

SS 4i.8 + .5;ii 

55 38.9 " 
23 9. o " 
23 14- 5 " 
IS 46. 2 : : 

56 48. 1 + (5 A2 



25 
23 



I 14 

6 57 
6 57 



7 

7 

II 

II 

II 



II 42 
II 42 
II 42 



7 

II 

6 

7 



3-^ + SX, 
31.6 « 

4.7 " 
29. s " 

2I.S+<!X3 

18. s 

33-6 (?) 

54-5 

26.2 

23-9 

31-3 

58.9 
43-7 
44-7 : 
27. 8 + (5 X, 
23. 5 + <! ^ 
48.S + <5;i7 
SO. 4 " 



Remarks. 



Very doubtful. 



"Too late." 



No. for 
Ref. 


h 


m 


I. 


6 


54 


2. 


7 


21 


3- 


II 


15 


4- 


6 


55 


5- 


7 


23 


6. 


II 


H 


7- 


6 


56 


8. 


7 


23 


9- 


II 


16 


lO. 


II 


44 


II. 


7 


8 


12. 


II 





13- 


6 


59 


H- 


7 


29 



OPTICAL OBSERVATIONS OF THE TRANSIT. 139 

Greenwich sidereal times of tabular contact for comparison with the above observations. 



29.5 + 17.3 S A-\- 15.0^0 — 24.0 ((5 (T+ d g') — 2^ d TT 

54.5 + 18.2 SA-i- 19.2 SB — 27.5 (d G — 6 g') — 29 S ^ 

52.1 + 7.2 ^A — 26.2 <JD + 27.4(50-— 5 (j') + 49 (J;r 
34.5 + 17.2 (5 A + 15.1 (5 D — 24.0 ((S 0- + 5 <7') — 17 d;r 

4.8 + 18 I 5 A + 19.3 (J D — 27.5 (<J (T — (5 (?') — 32 (J ;r 
39.5 + y.2 S A — 26.4 5 D + 27.5 (S G — d g') -j- 426 tt 

21.2 + 17.2 SA + 15. 1 SD — 24.0 {6 G -}- d g') — 12 d tt 
57.5 + 18.2 5A + 19.4 <yD — 27.7(50-— 5 ff') — 26S TV 
3^-3 + 7-3 ^ A — 26.5 5D + 27.7 (5 (5- — <5 o') + 54 5 ;r 

1.2 + 8.4 5 A — 22.2 5 D + 24.0 (5 O- + 5 (>') + 40 5 TT 

6.2 + 18.1 5A+ 18.0 5 D — 26.y {d G -\- 6 g') ^ 67 d tt 

28.8 + 6.2 5A — 30.1 5D + 31. 1 (5(? — do') — 51 5;r 

19.3 + 1 7.8 5 A + 1 7.0 5 D — 25.7 (dG-\-SG') — y dTT 

22.9 + 19.2 5 A + 22.8 SB — 30.9 (S G—S g') — SS TT 

After reading Professor Watson's report of his observations, the writer was led 
to doubt the strict applicability of the corrections for internal contact derived from 
the artificial transit, partly from the want of correspondence between the actual obser- 
vations and those made on the model, and partly because many observers did not 
determine their errors, and it is desirable that all the observations should be discussed 
on a uniform plan. This is a question to be considered by such persons as discuss all 
the observations.* 

We next give a similar comparison with respect to distance of centers instead of 
times. The first column of the following table gives the name of the observer, the 
contact observed, and the time actually noted, reduced to Greenwich sidereal time, as 
before. The sum of all the corrections to each of these times, including correction 
of longitude, reduction to geometric phase, and errors of observation, is represented 
by the general symbol r. This quantity has a separate and independent value for 
each observation. The determination of its most probable value and probable error 
is left for the final discussion of the observations. 

* Tho present discussion was prepared during the years 1876 and 1877, and is printed witlaout alteration. 
Since that time several puhlications Qf contact observations have been made, the study of which leads me to doubt 
the advisability of applying the above corrections derived from the artificial transit to the observed times of internal 
contact. 

1. It is necessary that all the observations shall be reduced on a uniform plan, and the personal corrections 
derived by the artificial transit are not known to be satisfactorily attainable for any but the American parties, 
and only for a small part of them. 

2. There are various nonconformities between the observations of the real and those of the artificial transit, 
which have beea pointed out in the preceding discussion. 

It therefore appears likely that the best way of treating the observations will be to infer the most probable 
times of contact from the descriptions and drawings of the observers. 

These conclusions do not detract from the value of the artificial transit as a method of previous practice on 
the part of the observers. Moreover, if most of the observers could be practiced on a uniform system, and with an 
instrument showing phenomena as much as possible like those of the real transit, I think the corrections might be 
regarded as real. — The Editok. 



I40 



TRANSIT OF VENUS, 1874. 



Next, the observed distance of centers is given, being supposed equal to the sum 
or difference of the semidiameters. The symboHc corrections of the semidiameters 
are here included. 

Thirdly, the tabular distance of centers as affected with parallax is given. It is 
interpolated from the values near the times of contact given on pages 135 and 136. 



Observer, Contact, and Greenwich 
Sidereal Times. 


Observed Distance of 
Centers. 


Tabular Distance of Centers. 


Hall 


I 


h m s 

6 55 Sl.2 + r 


// 
1007. 12 + d (T + (i (t' 


// 
1003. 71 — 


.0427 


+ 0.72 


5A + 0.63 dl 


— 1.02 6 IT 


Wheeler .. 


I 


6 55 56. S H- i- 


1007. 12 " 


1003.48 — 


.042 


+ 0-72 


+ 0-63 


— 1.03 


Hall 


II 


7 23 12. 6 + T 


942. 80 + (! (7 — d ff' 


939-99 — 


.036 


+ 0.66 


+ 0-70 


— 1.44 


Wheeler .. 


II 


7 23 19.04-T 


942. 80 " 


939- 76 — 


.036 


+ 0.66 


+ <J-7o 


— 1-44 


Wheeler .. 


III 


II 15 42.9 + '- 


942. 80 " 


942.49 + 


• 037'- 


— 0.26 


+ 0.96 


- 1-79 


Davidson .. 


I 


6 57 9-1 +r 


1007. 12 + () a + d ij' 


1003. 18 — 


.042 


+ 0.71 


+ 0.63 


- 0.75 


TiTTMANN .. 


• I 


6 57 24.3 +r 


1007. 12 " 


1002.57 — 


.042 


+ 0.71 


+ 0.63 


- 0.75 


Davidson .. 


II 


7 25 4-2 + 7- 


- 942. 80 + 6 a — S a' 


938- 53 - 


.036 


+ 0.6S 


+ 0.71 


- 1. 18 


TiTTMANN .. 


II 


7 23 31.6 + r 


942'. 80 " 


941.83 — 


.036 


+ 0.66 


+ "-70 


— 1. 16 


Davidson .. 


III 


II 14 9-7 + 1- 


942. 82 " 


941- 75 + 


.036 


— 0. 26 


+ 0.96 


- 1-52 


TiTTMANN .. 


III 


II 14 29.5 +T 


942. 82 


942. 46 + 


.036 


— 26 


+ 0-96 


- 1.52 


Watson 


I 


6 57 28. 5 + r 


1007. 12 + i a + d a' 


1004. 34 — 


■041 


+ 0.72 


+ 0.63 


— 0.52 


Young 


I 


6 57 23.5 + r 


1007. 12 " 


1004. 54 — 


.041 


+ 0.72 


+ 0.63 


- 0.52 


Watson 


II 


7 25 28. 3 + T 


942. 80 + 6 a — 6 a' 


939. 55 — 


.036 


+ 0.65 


+ 0-70 


— 0.97 


Young 


II 


7 25 1.0 + r 


942.80 " 


940.51 — 


.036 


+ 0.65 


+ 0.70 


— 0.96 


Watson 


III 


II 15 32, 2 +T 


942. 82 " 


940. 71 + 


.036 


— 0.26 


+ 0.96 


- 1.96 


Young 


III 


II 15 13.3 +r 


942. 82 " 


940.01 + 


.036 


— 0.26 


+ 0-96 


— 1.96 


Woodward. 


III 


II IS 31-3 + '- 


942. 82 " 


940. 67 + 


.036 


— 0.26 


+ 0.96 


- 1.96 


Watson 


IV 


II 42 50-3 +r 


1007. n -\- 6 a + 6 a' 


1004. 18 + 


.041 


— 0-35 


+ 0.93 


- 1.67 


Young 


IV 


II 42 33-7 + '- 


1007.14 '• 


1003.50 + 


.041 


— 0.34 


4- 0. 93 


- 1.67 


Woodward - 


IV 


II 42 24.7 + r 


1007. 14 " 


1003. 13 + 


.041 


— 0-34 


+ 0.93 


— 1.66 


Ryan 


I 


7 9 35- 1 + 1- 


1007. 12 " 


1003. 80 — 


• 037 


+ 0.68 


+ 0.68 


+ 2.51 


Raymond... 


III 


II 22. +T 


942. 84 + 1! (T — 6 a' 


942.60 + 


.032 


— 0. 71 


+ 0-97 


+ 1. 61 


Peters 


I 


7 3-5+'- 


1007. 14 + 6 a + 6 a' 


1005.42 — 


-039 


+ 0.69 


+ 0.66 


— 0.26 


Peters 


II 


7 29 51- 5+ 1- 


942.82 + 6 a — 6 a' 


941.89 — 


•039 


+ 0.62 


+ 0.74 


— 0.26 



APPENDIX I.* 



Coast Survey Office, 

Washington, D. C, January 2, 1874. 
Dear Sib: Upon the subject of Atmospheric Dispersion, as connected with 
photographs of the Transit of Venus, I take the liberty to send you the inclosed 
notes as giving my own view of some of the questions involved. 
Yours, 'truly, 

J. HOMER LANE. 

Professor Newcomb. 



CORRECTION OF ATMOSPHERIC DISPERSION IN ASTRONOMICAL 

PHOTOGRAPHY. 

The design of this paper is to make some suggestions in regard to the correction 
of atmospheric dispersion in taking photographs of the approaching Transit of Venus. 
So far as I have heard, no attention has been drawn to the possible influence of 
atmospheric dispersion upon a parallax deduced from photographs. 

There are two ways in which the atmospheric dispersion may cause a displace- 
ment of the assigned position of the photographic print of the limb of Venus 
relatively to the photographic print of the Sun's limb, and any such displacement 
enters, of course, with its full amount directly into the deduced parallax of Venus 
from the Sun. 

In the first place, since the radiation which reaches us from the Sun's limb is less 
intense than that of the disc within, the atmospheric spectrum of a radiant point 
must be expected to leave in the photograph a longer print for the limb of Venus 
than for that of the Sun, and the excess may fall more towards one end of the 
spectrum than towards the other. 

In the second place, the absorption of the Sun's atmosphere, to which the inferior 
brightness of the Sun's limb is due, may, for the photographic rays, be greater towards 
one end of the spectrum than towards the other. 

Although the amount of this displacement will doubtless be small, being, of 
course, less than the length of the air spectrum of photographic rays, yet it must be 
remembered that at a zenith distance of 45° the whole refraction will be something 
like 4 times greater than the corresponding parallax of Venus from the Sun; and if 
the metliod be applied at a greater zenith distance, the ratio will be still greater. On 
my mentioning this subject to Prof. C. S. Peiece, he referred me to some investiga- 
tions of Ketteler on the chromatic dispersion of air and several gases. Ketteler's 

* The very able author of this note died while it was in the printer's hands, and therefore Lad no opportunity 
to revise the proof. — S. N. 

141 



142 



APPENDIX. 



experiments were made with tlie monochromatic lights of the Hthium flame, the 
sodium flame, and the thallium flame ; and his results are confined to the three corre- 
sponding points of the spectrum. At a zenith distance of 45°, his numbers give, for 
the lithium a-nd thallium lines — wave lengths o""'.ooo67o6i and o""".ooo5345i — an 
atmospheric dispersion of about o".g. I take this space for comparison, supposing it 
to be, as I find it in a curve given by Roscoe, equal to the space which includes the 
denser parts of the chemical spectrum. 

I have been informed by Professor Lyman that Professor Airy has introduced a 
correction of atmospheric dispersion into the eye-piece. For photographing the 
transit it would of course be imperative to introduce the correction at the object-glass; 
and the way of all others to do it will be by means of an eccentricity of the crown 
and flint lenses of the object-glass, made to vary with the tangent of the zenith 
distance. 

Now, as the zero from which to measure this eccentric motion of the one lens 
over the other depends on the perfect centering of the two lenses, the suggestion 
becomes an obvious one that the whole ^object-glass may be rotated 180° for alternate 
photographs taken near together in order to extinguish any error of the centering or 
zero; and this half rotation of the object-glass would be equally useful even if any 
other method were chosen for extinguishing the atmospheric spectrum. 
Let 

/, and X represent the stellar focal lengths of the one lens that is moved 
eccentrically over the aperture for two assumed points of the 
photographic spectrum. 
«j and n^, the corresponding indices of refraction of the glass composing it. 
v^ and Vr,, the corresponding indices of refraction of the air. 
s, the zenith distance; 
and e, the eccentricity of the lens in linear measure of the same units as 
/ and/^. 
Then the proper value of this eccentricity is 

e=/x/.^4-^^ tan. ^, 

or 

c z=f, in, — I) — ' tan. s. 

n^ — n^ 

It seems highly imjirobable that the irrationality of the air spectrum with the 
glass spectrum — in the photographic rays, where, I believe, it has not yet been deter- 
mined — should prove to be so great as to defeat the complete extinction, practically, 
of the atmospheric spectrum in this way. 

Supposing the inner surface of the flint lens of the objective to be flat, an 
eccentric displacement of this lens, sliding on its concave surface, is equivalent to the 
introduction of a refracting prism in the manner of the compound prism of Boscovich ; 
and the fact that this prism is introduced into the converging rays at the back of the 
objective, instead of being introduced, as an extra prism would be, into the parallel 
rays in front, gives the measure of the effect which the eccenti'icity produces upon 



APPENDIX. 143 

spherical aberration. Evidently, this effect is altogether insignificant in comparison 
with the dispersion produced or corrected, the dispersion for the lines D and G being, 
in flint glass, say ^^th the refraction. 

The question arises whether the two glasses of the objective might have individual 
mutually-compensated irregularities of form, of which the compensation would be 
disturbed by the eccentric displacement. I do not suppose this likely, and trial would 
probably show the dispersional effect to stand sensibly alone. 

Besides, an effect depending on the supposed irregularities of the lenses can 
hardly be supposed to have any common law of connection, in different instruments, 
with the direction of the displacement and the parallax. The atmospheric spectrum 
has not, so far as I know, been successfully examined in the more refrangible part, 
and I do not know as we could do better at present than to assume the whole air 
spectrum to be similar to the glass spectrum. 

On this assumption, applying the above formula to a crown-glass lens with 
indices of refraction given by Feaunhofer for a specimen of crown glass, we have 

-? ? = , and e — — — /, tan g — 0.000169 f^ tan 2. 

n^ — n^ 3100 3100 

I need not repeat that /, here means the focal distance of the lens alone, not of 
the objective. 



APPENDIX II. 



RECORDS OF CONTACT OBSERVATIONS. 

When the present publication was sent to press it was intended that Part II, con- 
taining the observations made at each station, should follow it immediately. But some 
of the reductions are still unfinished, and it is deemed advisable to await their com- 
pletion rather than to issue the observations in an imperfect form. As it is desirable 
that the observations of contact should be available to investigators without further 
delay, they are here presented in full, as copied from original notes of the observers. 
No discussion has been attempted, for the reason that this can be most profitably, 
undertaken in some work including all the available observations of the transit. The 
time reductions are, however, applied to the chronometer observations, and may be 
regarded as definitive, with the exception of the longitudes, some of which require 

further investigation. 

WLADIWOSTOK. 

Professor RalVs notes of observations of contact. 

h. m. 8. 
E'BGTJS 772. i I 44 43.5 - 8«.S* 

First contact of Yenus. ( i 44 35.0 

Kegus 772 { ^ ^° 20.5— Black drop begins. 

Second contact.)^ '° S?-o-Contact? 

'-2 II 29.5 — Planet wholly on. 

At second contact planet faint on account of liaze, and observation difiicult. 

Times of the above contacts were noted by Mr. Gakdnee on chronometer Negus 772 ; also 
the second contact by Lieutenant Mokong. 

Third contact lost by clouds. Strained my eye very much, but could not be sure of the third 
contact. 

The preceding observations were made with the Alvan Olark telescope 856, and with the plain 
eye-piece and power of 140. I tried to use the double-image micrometer, but the haze was too 
dense. At first contact the sun's limb very steady and well defined, and I was looking near the 
right point. At second contact the haze was much more dense, but think I saw the real contact. 
At first the contact between the planet and Sun's limb seemed to lengthen, and this is the time 
first noted. Then flashes of light passed between the planet and Sun's limb, and this is the time 
noted as the contact. There is some doubt about the minute of second contact, which may be 11, 
as the hour and minute hands were near each other. 

When the haze gave us a view of the Sun, Venus was seen beautifully defined ; she was much 

sharper in outline than I expected. I think that without the haze the contacts could have been 

very exactly observed. 

A. HALL. 

P. S. — I had been looking at the planet very steadily for three or four minutes, and my eye was 
tired and strained a little, I think, at second contact. 

Have never seen the Sun's limb steadier or better defined than at first contact, and five or six 
minutes before second contact. 

*This8=.5 is the time counted after seeing contact before noting chronometer, which was done at lii 44" 43».5. 
The second time is therefore that at which the contact was ohserved. 

145 



146 



APPENDIX. 



At third contact a good prospect of getting a good observation five minutes beforehand, but 
haze rapidly grew dense and the Sun quite low. Think I should have got this contact but for the 
colored shade, which I did not dare to take off. The same power used in all the contact observa- 
tions. It was the plain eye- piece of power 140. 

Mr. 0. B. Wheeler's notes. 

Alvan Clark 3-inch objective equatorially-mounted telescope. Power, 30.62. 

h. m. B. 
Contacts. — First: 10 30 47.0, good. 

Second: lo 58 5.0, poor; too cloudy. 

Third: 2 49 50.5, very poor!! not at all reliable ; too cloudy. 

Remarlcs. — Very good image through haze at first contact, but could not use the higher powers 
of eye-pieces. 

Clouds getting thicker, and second contact observed with great difficulty. .' 
"Black drop" not definitely seen. 
Very favorable about ten minutes before third contact. 
Disk of Sun not visible at time of fourth contact. 

Spots on the Sun seen very finely once, and only once, during the day, at about 2^ 20™ p. m. 

O. B. W. 

NAGASAKI. 

Prof. George Davidson's notes of his observations. 

Decbmbee, 9 a. m., civil, 1874. 

Meridian instrument U. S. C. S. 2 leveled and yet on the meridian mark. Chronograph in 
working order. At 9 a. m. lower stratum of clouds partially broke away. Sky covered with cirrus. 
Took reversed pictures in photograph work. 

Bank of heavy clouds forming to southward ; cirrus and cirro-stratus above. Equatorial clock 
running well. At ro a. m. clouds are thicker; at 10'' 13"^, mean time, slight break in clouds. 
Commenced watching at English computed time; clouds oft' and on. 

I. Contact by chronometer 1563 (sidereal break circuit), le,'^ 36™ 52^. 

Sun nearly obscured. Observation doubtful ; Venus on. I judge time within ten seconds. 
Passing clouds nearly obscured the Sun after coming on of planet. The Sun just before the time 
unsteady. — [Mrs. G. D., Eecorder.] 

At 1 5^' 42™ the Sun was obscured by clouds and continued so. The lightest colored shade was 
used during the first contact ; image white. 

II. Contact, lei" 4™ 468.5.— [Observer, G. D.; Eecorder, G. D.] 

Sun partially obscured and image faint, but have no doubt about it within two seconds. 

[There was no ligament or black drop, but there was a slight atmospheric disturbance by which 
the exact instant of the joining of the cusps could not be determined with the precision which I 
noted in the total eclipse of 1869. But the disturbance was exactly wh?it I have been accustomed 
to for the last twenty-nine years in the geodetic and astronomical work of the Coast Survey. I 
noted the time when the dark disturbed overlapping of the limb of Venus over the limb of the Sun 
was discontinued.] 

This note added December n. I was down with neuralgia all the loth. 

III. Contact, chronometer 1563, ig^ 53™ 52". This is a few seconds past contact; no colored 
glass ; flying thick clouds. Ten or fifteen seconds before, I saw the clear separation ; no ligament or 
band ; clouds covered it at exact instant and opened just after, but I feel that it was not past- 5 
seconds. With sharp outline ; then clouds. 

December 9, 1874. — Compared 1503 and 1563 on the chronograph sheet and by coincidence : 

h. m. 8. h. m. s. 

1742 = lO.o I 1742 = 3 39 52.0 



CONTACT OBSERVATIONS. 1 47 

December 9, 1874. — Comparison chronometers: 

h. m. 8. h. m. s. 

1742 = 6 43 32.0 1742 = 6 44 52.0 
1563 = 23 55 43-5 1503 = 23 56 48.5 
Eain during- night and heavj^ gnsts of wind. 

Mem. from Tittmann's boolc. — Time of second contact, 10'' 52™ 20=.. He was using chronometer 
1742: Hassler 3-inch equatorial of the Coast Survey. On December 1 2 he informed me that when he 
had taken his eye from the telescope to note the " tens," he heard Captain Yanagi call out "time" 
to his assistant, thus indicating that he had observed it 4 seconds later than Tittmann. Tanagi 
was using U. S. C. S. Eecou. telescope No. 35, i^-inch objective.— C D., December 16, 1874. 

DECEMBEE II, 1874. 

I was too ill yesterday to give a remmi of what was done on the 9th. Everything was in good 
working order. The equatorial was running well; the chronograph ditto. Photographic arrange- 
ments complete and satisfactory; heliostat doing well. In the photograph-room were Messrs. 
Seibert, Lodge, Williams, and Ayens, photographers, and Professor Murray recording. In 
adjacent room were photographers assisting in 

One hour before the transit I had made the measurements for focal distance of the photo- 
graphic objective, and with Mr. Tittmann had examined all the adjustments and found them as per 
record. And here it is proper to state that from the beginning no change has been necessary in 
said adjustments. 

Eeversed ijictures had been taken, and all were waiting. Transit observations had been taken 
about 4.30 a. m., when clouds suddenly covered the sky. The clouds began to thicken at 9.30 a. 
m. There were two strata, the upper of cirrus and cirro-stratus forming a complete covering over 
the whole sky ; the lower was a stratum of heavy cumulo-stratus, forming nearly as low as 2,000 
feet (it nearly capped the mountain 1,900 feet high and 4 miles south of us). This lower stratum 
came from the southward. There was little wind at the station, but the clouds flying across the 
sky were from the SW. 

At 10 a. m. the prospect looked very bad; Sun not seen through the clouds. At 10.13 
whilst at the equatorial the clouds of lower stratum began to break in the vicinity of the sun, but 
thick below it. At is'' 33>^'", by chronometer 1563, began to watch steadily for the first contact; 
clouds flying over sun ; upper stratum still existing as an upper curtain. 

Changed colored glass to lightest shade before commencement of watching. Sometimes Sun 
nearly clear, then almost instantly obscured, again partially out. 

The Sun was nearly obscured at time of contact, and when light permitted fair outline to be 
seen the edge of planet was just on the Sun's limb at the exact point at which I had all along been 
looking. 

From my practice on the artificial Venus, I judge the planet was ten seconds on at the time I 
noted. 

About 7 or 8 seconds thereafter I called out to the photographers to commence, and I prepared 
to obtain measures of the planet on the Sun as I had in the artificial Venus, but it was too much 
obscured by clouds to admit such measures, and no sharpness of outline, [{a) I should have stated 
that here as well as at I. contact I tried to observe without any shade, but when the Sun would 
suddenly burst through, it was too much for my eyes, and this record, therefore, refers to the con- 
ditions when I had the shade on. — G. D., December 16, 1874.] 

I had then to wait for better light, and when the planet was half on the limb of the Sun I began 
measures of cusps. The Sun's limb was quite unsteady just before first contact, and I could not see 
any approach of Venus nor any different indications at point of contact from other parts of the limb 
to which I occasionally looked. 

The measures of cusps were made with varying conditions of the Sun's brightness, but from 
my pi-actice on the artificial Venus I was prepared for the work. The cusps were not, so bright as 
I could desire. They were made with lightest shade. Without shade I could not make them. A 
shade between them would have been of great help. 



148 APPENDIX. 

After cusps I turned micrometer to zero for the second contact. This I got as well as such an 
observation can be made, and I am satisfied that it has not an error of 2'. 

There was no black drop, no ligament, and only a slight disturbance of the limbs that prevented 
a sharp separation such as I had in the total solar eclipse of 1869 in Alaska. 

But this disturbance was what I have been accustomed to meet with in twenty-nine years' 
experience on the Coast Survey at all moderate elevations. 

After the second contact I turned micrometer and commenced measures for the separation of 
the limbs, and continued them until Yenus was about one diameter from the Sun's limb. The posi- 
tion of the micrometer was not changed during these measures. 

It then clouded up and prevented further observations. Before noon it broke away slightly, 
and then I observed the transit of the limbs of the Sun and of Venus over the nine threads of the 
United States Coast Survey meridian transit No. 2 ; recording same on fillet of Coast Survey chrono- 
graph, my son watching the running of the fillet, &c. 

Mr. TiTTMANN observed the difference of declination of the upper limb of the Sun with the upper 
and lower limbs of Venus in the Stackpole transit instrument 1507, at and near the meridian 
passage. 

In my meridian transit observations I used two glasses from my sextant, giving a light orange 
image of the Sun. The planet was moderately sharply defined after the first three threads, and 
until the last one. The Sun's limbs were moderately sharply defined. The transits are not as good 
as star transits. The Sun continuing slightly unobscured, I returned to the equatorial and observed 
the horizontal diameter of Venus with the double-image micrometer, discontinuing observations 
when clouds overshadowed us. 

In subsequent openings Mr. Tittmann and Professor Murray made some measures, the latter 
as showing what the instrument would do in the hands of an inexperienced observer. Clouds 
covered the Sun densely, and Mr. Edwards had no opportunity for making measures. 

The Sun was wholly obscured until Venus was about one diameter from the western limb, when 
the clouds broke for two or three minutes and I was commencing diameter measures, but clouds 
again hindered. I then watched without colored glass until near third contact, the Sun showing 
occasionally, but changing from bright to obscure rapidly, quicker Ihan I could change shades. 
Near third contact the seeing was good without shade until 10 or 15 seconds of the contact, during 
which time the line of separation was well defined and moderately sharp. No sign of ligament, 
black drop, or distortion. If anything, it promised to be better than second contact, but just as 
the line of separation was closing, a dense cloud drifted over the Sun for a few seconds, and when 
it had passed the line of separation was just past: I should judge about five seconds; not more, 
and probably less. 

Then clouds drifted over in a dense bank, and we saw no more Sun. At 4 p. m. the rain began 
to fall and the night was threatening ; but at dark a slight break was noticed in the clouds, and 
I immediately went to transit No. 2 and managed to observe the stars, as per record. 

As the photographic arrangement was complete,- and Mrs. Davidson was in the equatorial 
observatory as recorder, and my son to hold the chronometer quite near my ear (to prevent inter- 
ference by the beat of the equatorial pendulum), I gave Mr. Tittmann the use of the Coast Survey 
equatorial of 3 inches, using astronomical eye-piece and power of . 

Hereto he adds his record of what he saw therewith : 

My account is contained in the transit book used on the occasion to note the times of contact in. The notes were 
made immediately after each contact, and I have nothing to add save that the expression there used viz "the dis- 
turbance of the Sun's limb * * * not nearly so much disturbance as during the Washington artificial transits at 
their worst," is not meant to imply a great disturbance. — 0. H. T., December 14. 

There was no part of the time during the transit when the Sun was seen from a clear, blue sky. 
During the whole time of transit there was that upper stratum of moderately thin clouds that 
would have been a decided benefit, as they prevented the heat rays coining through to the lower 
atmosphere and creating irregular undulations of the atmosphere. As far as Volcano Wunxen, 30 
miles -eastward, the outline of objects was sharp and steady; the same to the north; to the south- 
ward were heavy clouds of cumulo-stratus and threatening weather. The atmosphere was mod- 



CONTACT OBSERVATIONS. 14c) 

erately steady throughout, at least so we would designate it in Coast Survey work. Had there 
been no upper stratum of clouds and only the lower stratum, I am satisfied from experience else- 
where and here that the atmospheric disturbances would have been much greater. 

I have other suggestions to malie upon the questions which arise as to size of telescope, details 
in instruments, and the necessity for high elevations for such work ; but I reserve them for my report 
to the President of the Commission. — D. 

31r. TittmawrCs notes of his observations. 

Decembee 9. 

Transit of Venus, 10'' 26™ 17= mean time of first contact noted by mean time chronometer 1742. 
It was not seen until after Professor Davidson called time to the photographers. It was then seen 
further on the Sun than twice the amount of the artificial Venus on the hill through the same tele- 
scope. 10'' 52™ 20^ time of second internal contact. The Sun seen through haze and not much 
apparent disturbance of the Sun's limb. Not nearly so much disturbance as during the Washington 
artificial transits at their worst. The line of light broke clearly and in an apparent true continua- 
tion of Venus's limb, and when exj)ected. 

Third internal contact, mean time chronometer 1742, 2'^ 42"" 40^. Sun seen through break in 
the clouds and viewed without a shade; clouds passing interfered with the exactness of the deter- 
mination, but apparently the clouds caused the only uncertainty. 

Observer cannot form estimate of the error of his notation. 

Instrument used TJ. S. C. S. equatorial No. 12; aperture, 3 inches; focal length, 46".5; made 
by TJtsohneidee & Frauenhoper, Munich. 

PBKIN. 

Professor Watson^s notes. 

Wednesbat, December 9, 1874 
Transit of Venus. Micrometer set- at le'^. 2 04. 

First contact i'' 55" Io^o; uncertain; Sun shining through clouds, and could scarcely see weU 
with shade on, and too bright to observe without it. 

Internal contact 2^ 22" s'.o. This time uncertain; could not see the planet well steadily; 
sometimes only glimpses of it; it is probably 5 seconds and possibly 10 seconds late; no black 
ligament; faiut gleams of light across 30^ earlier. 

At first contact the planet just clearly indented the Sun's limb, as I could faintly see it. Time 
uncertain, 3 or 4 seconds. At internal contact had sometimes only glimpses of Venus. • When time 
recorded a momentary good glimpse showed the planet just fairly free from Sun's limb; could not 
see any black ligament; definition good; observed line of white light completed. I am not sure 
that the minute is correct for first contact. The seconds of contact were instantly recorded and 
the minute afterwards. I do not think the time seconds are more than 3 or 4 seconds out, and of 
course late. 

Third contact at 6^ ii"" 30^5. 

At 6'^ II™ 6^.0 band of light momentarily disappeared, and I supposed at first it was the con- 
tact, but the line was immediately re-established and remaiued so until the time recorded as contact. 

The time of third contact is good ; not uncertain half a second. Just as chronometer ticked 
30^.5 the planet and sky were instantly united. The instant appeared as sharply defined as the 
immersion of a star at the moon's limb in an occultation. For about 15^ after the contact the space 
between the cusps was faintly illuminated with an even tint of light. Before the contact the line 
of light was disturbed by irregular shadows. 

Last contact at 6'^ 38™ 44^0; time by Bond 290. All the times of the contacts and measures 
are from Bond 290. 

The limb of the Sun was very unsteady, and after the last measures the cusps became so blunt 
and ill defined that I ceased measuring to be ready for last contact. I think the time observed is 
not more than a second out. I could see the planet certainly to the very edge of the Sun, although 
edge undulating very much. At 43^.0 I was sure I could see it, and at 45^.0 I could not see it. I 
therefore estimated the time at 44^.0, at which time I feel sure the planet was clear of the Sun's limb. 



I JO APPENDIX. 

Wednesday, December 9, 1874. 

The notes accompanying the foregoing observations were made at the time of the observations 
as soon as an opportunity afforded after they were taken. In order to make the record intelligible, 
I record here, a few hours later, while the phenomena witnessed are fresh in my mind, a circum- 
stantial statement of my observations with the equatorial. At 9"^ a. m., local time, I put the 
equatorial on the Sun, which could be just discerned through the clouds. The preceding night 
had been clear and the Sun rose in clear sky, but at 8 o'clock a. m. it began to cloud up. As the 
time of first contact approached I was distressed to find that the only shade which I could use 
with the double-image micrometer eye-piece was too dense to enable me to see well unless the clouds 
became thinner. In order to be ready I put the position-circle so that the wire (already put par- 
allel to the line of separation of images) would cut off a small segment at the point of computed 
contact, and I placed the micrometer at the reading 16^.204, which I had found to be that of the 
coincidence of images. Whenever I could see the Sun well through the shade the definition was 
excellent, and the clock kept the point of contact steadily in its proper position relatively to the 
wire. The thin clouds which were passing sometimes almost totally obscured the Sun, but I.found 
that I could not attempt to observe without the shade, and with the shade I feared I might lose 
the first contact. The seconds were called every ten seconds of the chronometer by my wife, who 
acted as recorder, aud I had the chronometer on a high stand so near me that I could keep the 
count without any interference by the beats of the equatorial driving-clock. My recollection is 
very distinct that the time lo^.o corresponds very nearly to actual first contact. At 12^.0 I could 
see the indentation very plainly, and at 14^.0 it was about what I had a few days previously noticed 
to be the indentation after 4 or 5 seconds in the case of an artificial transit in which relative sizes 
and motion were accurately represented. I am quite sure that the time recorded, i"^ 55™ lo^.o, by 
Bond 290 is, although uncertain, not to exceed 5^ out, and I doubt whether it is really more than 
1° or 2= out, although I felt at the time that it was uncertain, and made the first record of it as 
" verjk uncertain." The power was high, and when I could see the definition was excellent, and I 
tried to catch sharply the instant of contact. What I saw at lo^o, and supposed to be the planet, 
proved by following to be such, and I noticed the comparative indentation as above stated. I 
therefore finally marked out " very," and let the record stand as " uncertain." These explanations 
are necessary, because my practice with the artificial transit, less than a week ago, led me to expect 
to be able to catch the instant of first contact almost to the nearest second. 

As soon as the first contact had been recorded, I proceeded to measure the cusps — which were 
excessively faint. 1 took the time from the chronometer right before me, and whenever I thought 
I had a contact of points, I noted the instant and called to the recorder the time to be recorded 
and then the readings of the micrometer. In order to be sure that the records were correctly made, 
I had her call them back to me as soon as they were written down. 

I went on this way making measures of what I saw faintly and supposed to be the cusps, until 
all at once a break in the cloud showed me the cusps plainly, and that I had for the last preceding 
few measures perhaps been measuring probably the diameter of the planet, as the limb of the 
Sun had not in some of the measures been visible to the border, as the bright glimpse showed me. 
I succeeded in getting one more good measure, the last one recorded of the actual cusps. I think 
that the first four measures belong to the actual cusps. I am sure that the first two do, and 1 have 
as yet no means of knowing whether the next two do or not. Just when I lost the actual cusps 
and commenced measuring points further in, I know not. I did not have time to look at the 
record, and the break in the clouds at about 2'' 17"" first showed me that I was then attempting to 
measure almost, if not exactly, the diameter of Venus. 

After the last measure recorded, 1 immediately placed the micrometer at 16^^.204 for coinci- 
dence of images, as I saw that second contact was near. The light was feeble, and at the instant 
recorded I saw an unbroken line of light clear across and exceedingly thin. I did not see anv 
black ligament preceding its formation, the space between the cusps simply becoming brighter and 
when I first noticed it, clear across and unbroken, I supposed it to be a momentary flash and I 
did not fix upon the instant for a few seconds, not until I was sure the planet was fairly upon the 
Sun. The time was recorded as very uncertain, as I expected to see the final formation "of this line 



CONTACT OBSERVATIONS. 151 

very sharply. I afterwards marked out " very uncertain" and let it stand as "uncertain," by which 
I wish to be understood that I think it is correct within 5 seconds. It may possibly be 10' late, 
but I feel confident that 5' is a liberal estimate of its uncertainty. At 2^ 21"" 35^ light appeared 
between the cusps, and during the period of 30^ the line of light across was broken and hazy, and 
hence on this account also I felt uncertain in regard to the instant of contact. 

Although the band of light was faint, I think the measures of its width are pretty good. It 
was difficult for me to fix upon the exact position in the measures, and 1 have given the readin.y- of 
the position circle when the measures of distance were taken. The readings of the circle are given 
first for all the measures before the revolutions of the screw. The second set of measures were 
stopped at last by dense clouds. The sky was completely overcast, and there was no hope from the 
immediate prospect of our being able to see anything more of the transit. About an hour before the 
last contact, the wind shifted to the northwest, and the clouds began to disperse so that it was 
again possible to observe the Sun, although through thin clouds and haze. The change of wind 
brought thin dust haze, and the definition was not good, although the brilliancy was suflQcieiit to 
enable me to see well and to make measures. The measures of the width of the band of liyht 
between the limbs of the Sun and of Venus preceding the third contact are pretty good. I kept 
the count of time carefully from the chronometer directly in front of me, and at the instant when I 
succeeded in getting a proper contact, I called the time and read the micrometer. The times and 
readings given were recorded by my wife, and by her called back to me after she had written 
them down. I ceased measuring about five minutes before the third contact, so as to be fully pre- 
pared to observe this contact with great care, the brightness being now pretty good, what I suppose 
to be meant by the designation " average" referred to in the instructions to observers. I placed the 
micrometer at the coincidence of images, and the driving-clock held the limb steadily in the middle 
of the field. I took the count from the chronometer directly in front of me, and the recorder called 
every ten seconds. As the planet approached the limb of the sun very closely the narrow band of 
light appeared disturbed. At 6"^ 1 1"' 6^.0 a narrow dark band shot across, connecting Venus with sky. 
But immediately, perhaps as soon as one second after its formation, it ceased, and the line of light 
between Venus and the edge of the Sun was until contact distinct, although at times broken by 
dark shadows flitting across it. At the exact instant recorded the line of light was suddenly 
broken, and Venus was connected with the sky. The cusps were quite sharp, and nothing more 
than a very slight apparent dark ligament was formed. 

In fact, so far as I could judge, the amount of the blunting of the cusps was not more than 
could be attributed to the want of perfect definition in the telescope. 

The time of the third contact as finally taken, and the phase as described, which I supposed 
to be the amount of actual contact, viz, 6"^ 11° 3o'.5, 1 am confident is not in error half a second, 
since the apparent congelation of the fine line of light was almost instantaneous. The space be- 
tween the cusps did not at once become black, but was illuminated by a sort of twilight for a period 
of 15 or 20 seconds. 

I next proceeded to measure the distance between the cusps, and although there was consider- 
able motion I was careful in making the contacts and keeping the time count (the tens being called 
by the recorder). At the time when the measures ceased, the cusps had become so blunt that 
accurate distances could not be measured, and I then placed the micrometer at the reading for 
coincidence of images so as to be ready to observe the last contact. The limb of the Sun was quite 
unsteady and undulating, but the indentation of the planet was easily seen and kept in view when 
very small. I kept my eye fixed upon it until the outline of the sun was perfect, and estimated 
the contact from the instant when it had ceased to be discernible. I consider the time to be accurate 
to a second. The recorder made note of the seconds and fractions called at the contacts, and I 
myself wrote down an independent note of the seconds and fractions. The minutes were imme- 
diately identified and recorded, except in the case of the first contact. When I came to identify 
the minute the chronometer had passed $6", and I wrote down 56, but immediately noticed that it 
had just passed 56"" 10^, and hence I changed the record to 55™. I did not think that more than a 
minute had elapsed between the observation and the identification of the minute, but it is possible' 
that such was the case and that the minute should have been 54. The seconds I am sure of, and 
it can be known hereafter whether the recorded minute is correct. I do not now recall any cir- 



152 APPENDIX. 

cumstance not mentioned wMch might be necessary to explain any of these observations. I have 

written out this more extended memorandum, this Wednesday evening, December 9, 1874, so that 

not yet knowing Avhat may have been found by others, I can give an unbiased statement in regard 

to these observations. 

JAMES 0. WATSOlsT, Observer. 

P. S. — I forgot to mention that several times I noticed that the sun appeared brighter at the 
limb of Venus than at a little distance from it. 

Thuesdat, December 10. 

Clouds prevented observations for value of one revolution of micrometer screw of double-image 
micrometer. 

Sattjedat, December 12, 1874. 

On reflection, it occurs to me that I did not observe as contacts corresponding actual phases at 
second and thu'd contacts on the 9th. At second contact I recorded (as the contact) the time when 
the line of white solar light was complete clear across and remained so. This line of light was 
very thin, but it certainly continued distinct and unbroken. The passing haze made the brilliancy 
irregular, but still there was sufi&cient light to enable me to see it without interruption. If the 
actual contact was when the line of light was occasionally broken in places and not steadily com- 
plete, this contact was earlier than that which I recorded; just how much I cannot say, because 1 
recorded the instant when I considered it to be complete, and I was in a state of uncertainty about 
it for several seconds. The first gleam of light between the cusps was 30 seconds before the time 
recorded, and the whole period during which the space connecting the planet with the sky was 
filled with hazy light was, I think, fully this interval. At the third contact I was familiar with 
the phenomena to be expected, and I then recorded two instants sharply. As already stated in 
the note of the observation, I first saw, as the planet approached the limb of the Sun, the line of 
light momentarily broken 24^.5 before the formation of the distinct cusps and the joining of the 
planet and the sky. During this interval there were flitting shadows along the line of light. I 
suppose the actual contact to be that when I saw the cusps suddenly formed. At this contact the 
brilliancy was good, but the definition was not so sharp as in the forenoon. 

The first interruption of the line of light was by a single very narrow band, and after its dis- 
appearance the shadows which flitted back and forth were radial to Venus. After the sudden 
formation of the cusps there was between them a very distinct gleam of uniform grayish light, 
which I called at the time a sort of twilight. I did not see any such light at second contact, but 
this may be owing to the interruption of the light by the clouds and the shade glass which I was 
obliged to use. The whole transformation was so gradual that to fix sharply distinct phases re- 
quired a brighter image than I could obtain at this (second) contact, but what I did see convinces 
me that the phenomena were repeated in reverse order. And I ought to record here, while the 
recollection is fresh, that although the observer by practice upon the artificial transit may Icnow 
pretty well what to expect, there is a lack of definiteness that makes him feel that the moment 
fixed upon is quite uncertain, and the time during the observation in which he feels this uncer- 
tainty seems to be much longer than it really is. Hence, I record here my conviction that prac- 
ticed observers will assign probable errors to their observed times within which the actual time is 
sure to be. I think further that the last two contacts will be observed much more sharply than 
the first two, even when the seeing is equally good in both cases. In my own case, I have not a 
doubt as to the sharpness of my determinations of the times of the third and fourth contacts, and 
I think that the forenoon observations, although under more disadvantageous circumstances, are 
to be relied upon within the limits of error assigned. The first contact had certainly taken place 
at the instant recorded, and the 'time given, if in error, is too late. At the second contact the 
line of white light was certainly completely established at the time recorded, and it might have 
been so completed a few seconds earlier, perliaps 5 seconds earlier. 

The diflerence between the phenomena of the actual transit and the artificial transit, I feel 
confident, are to be explained by the action of the atmosphere of Venus, and I think it cannot be 
determined which of the dift'erent phases observed is the actual contact of limbs until the effect of 
this atmosphere is carefully investigated by means of the observations of the actual transit. The 
effect of the chromosphere and solar corona must also be considered in this connection. 



CONTACT OBSERVATIONS. 153 

Notes of Prof. 0. A. Young and Mr. T. P. Woodward. 

Decembee 9. 
First contact observed with Dillon ; sure at 2^ 9" 30^ ; true time, 10= earlier (?) Instrument 
small Claek telescope ; power, 25, lowest belonging to the instrument; seeing bad; limb undulat- 
ing ; lightest shade glass. 

Second contact, 2^ 37°" 3= ± 05 ; magnifying power next higher than preceding = 80 ; seeing 
steady, but very faint through haze ; no black drop seen ; planet fairly clear of Sun's limb at 
recorded time. 

The comet seeter not having a sufficiently light shade glass, impossible to observe the contacts 
with it. — T. P. W., (not) observer, 
h. m. 8. 

Third contact. — 6 26 38 ± 5 C. A. Y. — Small Clakk. 
6 26 56 T. P. W. — Comet seeter. 

C. A. Y. : Eecorded the lirst formation of any black band between Venus and the limb of the 
Sun. Perhaps somewhat early; limb of Sun very tremulous ; power same as at second contact (80) ; 
no distinct connection between Venus and Sun's limbs for 15^ more; appearance not like the arti- 
ficial transit on account of the extreme tremulousness of limb. 
]i. m. s. 

Fourth contact. — 6 53 54 ± 2 C. A. Y. — Claek glass. 
6 53 45 T. P. W. — Comet seeker. 

C. A. Y.: Limb tremulous, but egress unexpectedly distinct ; magnifying power same as at 
second and third contacts, i. e., 80. 

T. P. W. : Third contact. — Observed Venus apparently touching the Sun at 6^ 26" 30=, and after 
verifying the time from the chronometer looked again through the comet seeker, when I saw she 
was still separated by a slight line. After several apparent connections and separations I took 
the time at 6'' 26"° 56=, when she was certainly in contact and perhai^s had been for 5 seconds. 

Both disks were well defined and steady. The secoildary spectrum and the size of the image 
are all that was disadvantageous. No drop was seen ; magnifying power, 40. 

Fourth contact. — Followed Venus as long as possible, and recorded the time when she disap- 
peared. I can assign no probable error; seeing was good and steady; secondary spectrum not so 
apparent ; observation good ; power, 40. 

Fuller remarks on observations of contacts recorded above. 

C. A. Y.: First contact. — At the time noted, 2'' 9"° 30^, I perceived, or thought I perceived, a 
modification of the Sun's limb at the precise point I was watching. I continued my count, how- 
ever. By 2^' 9"" 40' the mark was unmistakable, and by 2^' 9"" 45^ was plainly a notch, which in- 
creased in depth until 2^ 10" o^, when I ceased counting and recorded my observation as above. 
The Sun was seen through clouds, and there was a good deal of disturbance of the limb, but with 
my very light shade glass the image was quite bright. I now hardly think the contact was visible 
in my telescope 10^ before the recorded time. The word "probably" was erased in my notes and 
the "?" added at the time of the second contact, my conclusion being modified by the rapidity of 
the motion then observed. 

Second contact. — The time recorded, 2'^ 37"" 3", is that at which light first broke through between 
the planet and the Sun's limb. There were one or two suspected glimmerings about two seconds 
earlier. The separation did not become permanent, i. e., unbroken by occasional momentary dark 
fringes, until 10^ or 15= later. The clouds were somewhat thicker than at the time of first contact, 
but the image of the Sun was very steady, and the seeing and definition good. The image was 
white, somewhat fogged by the clouds, but bright enough for accurate observation. 

Third contact. — The time recorded undoubtedly belongs to a phase of the phenomenon earlier 
than that described in tbe "instructions," which, unfortunately, circumstances prevented me from 
looking at until after the observation. 

The time recorded, &^ 26"" 38^, is that at which several patches or lines of darkness first appeared 
to connect the limbs of Venus and the Sun. A single such connection was formed for an instant 



124 APPENDIX. 

at 6'^ 26"" 30^, but instantly disappeared. Light did not cease to glimmer through the interval untU 
gh 26"" 53% at which time the last streak of light I saw flashed across ; so that after that time the 
dark band between the limbs of Venus and the Sun became distinct and permanent. I saw no 
" sudden congelation" and no black drop. 

There were no clouds at the time, but there was a thick haze of yellow dust, and the air was 
very unquiet, so that the seeing was decidedly bad. I think, however, my ± 5= is an exceedingly 
liberal estimate of the probable error of the phase observed, and that 6^^ 26"" 53= corresponds pretty 
closely to the phase contemplated in the instructions — within 5 seconds certainly. 

Fourth contact. — I am sure I saw the planet at 6^ 53'" 50% and that it was not visible at 6^ 53" 
58^ I am pretty confident I still perceived it at €^ 53" 53% and that I could not perceive it at 
(>^ SS"" 56^ Hence I recorded the time as stated in the notes, 6'^ 53" S4^ The light was abundant, 
the air tremulous, and the seeing bad, causing the image of the Sun to look like a circular saw; 
but, as noted, the egress was unexpectedly definite, for until the planet left the Sun the serrations 
at the point of contact were plainly blunted. — 0. A. T. 

The magnifying powers were determined December 1 1 by measuring the diameter of the image 
of the object glass formed at the eye-piece. Lowest power of Clark telescope, 25 ; second power, 
80 ; comet seeker, 40. — 0. A. Y. 

December 10. — Chronometer comparisons. Chronograph started at 17'' 25" o'. Marked ly'' 

27" o=. 

h. m. 

KeGTJS 3 S4 00 10 20 30. 

Bond 4 35 30 40 5° 6°- 

Dillon 4 52 00 10 20 30. 

MOLLOT POINT, KERGUELEN ISLAND. 

Commander ByarCs record of Ms contact observations. 
Chronometer 827 Murray L. M. T. First contact 6^ 41"" 3s=.5 excellent. 

Took off colored eyepiece. 

yh i3'» 41% time when first seen after second contact, cloud having passed. Bright strip too 
wide to be called contact. 

CAMPBELLTOWN", TASMANIA. 

Captain Baymond's record of Ms observation of tUrd contact. 

Third contact.— Time, 3'' 40™ 50=; dim and cloudy; planet pear-shaped at the time of contact; 
limb of Sun unsteady ; not a satisfactory observation on account of clouds. I took the time when 
the thin, shadow-like link connecting limbs of planet and Sun seemed to congeal, as near as possi- 
ble.— C. W.E. 

[A pencil sketch of the third contact was given by the observer, but it is not possible to repro- 
duce it in such a way as to assist in judging the observation. Contact seems in it to be complete.]— 
Editor. 

QUEENSTOWN, NEW ZEALAND. 

Professor Peters' notes. 

December 9, 1874.— Adjusted focus and position-micrometer upon solar spot. The imao'es 
seem to coincide at 14^.02 ; position-micrometer, 245°. 

Turned the position-micrometer upon 196°, which should make the wire tangent to the Sun's 
limb where first contact occurs. 

Bond 335 chronometer was used [contact I should come at iS'' 13'" 16" chronometer]- 18^ o"" 
clouds are racing with blue patches between them ; 18" 8'°, Sun near edge of a big cloud, but still 
behind it; 1?,'^ 14™ o^ first indentation perceptible, but very uncertain. 



CONTACT OBSEEVATIONS. 



155 



18'' 43"" 48", first internal contact, well observed; no indications whatever of irradiation or 
other physical phenomena. 

Additional remarks for observation of first internal contact: The slit of the double-image 
micrometer was placed, a little before, at right angles to the Sun's limb, the two images apart. The 
bright rim of Venus that had been seen outside the sun for several minutes before already, increased 
in brightness. But this increase in brightness was at once more sudden, and almost instantaneous, 
that is to say within a second or two. This moment was taken as the true contact. Soon after, 
the Sun's light was distinctly seen entirely surrounding the disk of Venus, or Venus was seen 
entirely upon the Sun. [Note written at 2o'> o"" chronometer.] 

All the observations are made with lowest of the two powers of double-image micrometer 
[— 90 diameters]. 

2jii 5m_ — After little rain showers and clouds, cleared up again ; wind pretty strong from SW. 
Sun's and Venus' limbs very much undulating. Try to measure distance of Venus' and Sun's limbs. 

2 2h 12m i58__A moment through clouds; Venus already on the limb of Sun; third contact 
passed. 

22'' 43" 30=.— The Sun comes out suddenly from behind a dense cloud ; the limb is strongly un- 
dulating, so that last external contact, even if it had not happened one minute before, could not 
have been remarked. 

The time reductions of the preceding observations of contact are shown in the 
following tables. But the times given are not at all to be regarded as the definitive 
moments of contact to be deduced from the remarks of the observers, but only as 
times so near those of contacts that the necessary reductions can be applied differen- 
tially without serious trouble. Where only one time is noted by the observer tliat 
time is quoted in the column chronometer time. Where several are noted by the 
observer one is selected for reduction. 

The determination of the times which should be finally concluded as those of 
contact necessarily form a separate branch of the work. All that is here attempted 
is to present the material in such a shape that the necessary discussions can be under- 
taken with the greatest facility. 

The Greenwich times still require a symbolic correction for the provisional longi- 
tude : ' 

WLADIWOSTOK. 



§ 


Observer. 


II 


1 

P4 


Chronome- 
ter time. 


Correction of 
chronometer. 


Wladiwos- 

tok mean 

time. 


Wladiwostok 

west of 
Greenwich. 


Greenwich 
mean time. 


Greenwich 

sidereal 

time. 


I. 
II. 
I. 

\ II. 
; HI. 


Hall 

Hall 

Wheeler.. 
Wheeler.. 
Wheeler.. 


Inches. 

5 
5 
3 
3 
3 


140 

140 

30 

30 

30 


h m s 

1 44 35-0 

2 10:52.0 
10 30 47.0 
10 58 5.0 

2 49 50-5 


h m s 

— 3 " 45-9 

— 3 " 45.9 
+ 2 7.4 
-1- 2 7.4 
+ 2 7.8 


h m s 

22 32 49.1 

23 6.1 

22 32 54-4 

23 I2'4 
2 51 58.3 


h m s 

— 8 47 30.9 

— 8 47 30-9 

— 8 47 3°-9 

— 8 47 30-9 

— 8 47 30-9 


h m s 

13 45 18.2 

14 12 35.2 

13 45 23.5 

14 12 41.5 
18 4 27.4 


h m s 

6 55 51-4 

7 23 12.9 

6 55 56.7 

7 23 19.2 
11 15 43-1 



JiEMARK. — The difference of 0^.2 between these times and those given in the body of the work 
arises from the application of a different chronometer correction. 

It is assumed that Hall's chronometer time of second contact requires to be increased by one 
minute, as suggested in his notes. 



156 



APPENDIX. 
NAGASAKI. 



1 


Observer. 




biO 

a . 

la 


Recorded 
time. 


Correction 
of cliro- 
nometer. 


Nagasaki 
mean time. 


Nagasaki 

west of 

Greenwicli. 


Greenwicli 
mean time. 


Greenwich 
sidereal time. 










h m s 


s 


h m s 


h m s 


h m s 


h m s 


I. 


Davidson 


s 


... 


IS 36 52 


- 11-5 


22 26 7.1 


IS 20 29.4 


13 46 36.5 


657 9-9 


II. 


Davidson 


5 


... 


16 4 46.5 


— "-5 


22 53 57.0 


15 20 29.4 


14 14 26.4 


725 4.4 


III. 


Davidson 


S 


... 


19 53 52 


— "-5 


2 42 2S.-0 


15 20 29.4 


18 2 54.4 


II 14 9.9 


I. 


TlTTMANN 


3 


6o 


10 26 17 


+ 4-7 


22 26 21.7 


15 20 29.4 


13 46 SI. I 


6 57 24.S 


II. 


TiTTMANN 


3 


6o 


10 52 20 


+ 4-7 


22 52 24.7 


15 20 29.4 


14 12 54. 1 


7 23 31-8 


III. 


TlTTMANN 


3 


6o 


2 42 40 


+ 4.S 


2 42 44.8 


IS 20 29.4 


18 3 14.2 


II 14 29.7 



Note. — Careful inquiry has failed to throw any light upon the cause of the discordance of a minute and a half 
between the times of secono contact recorded hy Professor Davidson and Mr. Tittmann. There is little doubt that an 
error was made by one or both observers in recording the chronometer time. 



PEKING. 



1 


Observer. 


" i 
3 a 


bo- 

B) 


Recorded time. 


Correction of 
chronometer. 


Peking 
mean time. 


Peking west 
of Greenwich. 


Greenwich 
mean time. 


Greenwich 
sidereal time. 


6 




^.g 


S ^' 


















Inch's. 




h m s 


h m s 


h m s 


h m s 


h m s 


h m s 


I. 


Watson 


5 


165: 


I 55: lo.o 


+ 7 38 33-0 


21 32 43.0 


16 14 I2.I 


13 46 55-1 


6 S7 28.S 


,11. 


Watson 


5 


16s : 


2 22 S-° 


+ 7 38 33-2 


22 38.2 


16 14 12. 1 


14 14 50-3 


7 25 28.3 


III. 


Watson 


5 


165: 


6 n 30.S 


+ 7 38 33-9 


I SO 4-4 


16 14 12.1 


18 4 16.5 


11 IS 32.2 


IV. 


Watson 


5 


165: 


6 38 44.0 


+ 7 38 34.0 


2 17 i8.o 


16 14 12. 1 


18 31 30.1 


II 42 50.3 


I. 


Yot;NG 


2.5 


25 


2 9 30 


+ 7 23 8.0 


21 32 38.0 


16 14 12. 1 


13 46 SO. I 


6 57 23.5 


II. 


Young 


2-5 


80 


2 37 3± 5 


+ 7 23 8.0 


22 II. 


16 14 12.1 


14 14 23.1 


7 2S i.o 


III. 


Young 


2.5 


80 


6 26 38 J- s 


+ 7 23 7-5 


I 49 45-5 


16 14 12.1 


18 3 57-6 


II 15 13-3 


IV. 


Young 


^•5 


80 


6 53 54± 2 


+ 7 23 7.5 


2 17 i.s 


16 14 12.1 


18 31 13.6 


II 42 33-7 


III. 


Woodward . 


3 


40 


6 26 56 


+ 7 23 7-5 


I 50 3-5 


16 14 12. 1 


18 41 S-6 


II 15 31-3 


IV. 


Woodward . 


3 


40 


6 53 45 


+ 7 23 7-5 


2 16 S2.S 


16 14 12. I 


18 31 4.6 


II 42 24.7 



Note, — From Professor Watson's notes, p. 151, it is supposed that his minute of first contact should have been 54. 



MOLLOY POINT, KERGUELEN. 



a 



Observer. 




li 

W) 


Recorded time, 

Murray 827 

mean time. 


Correction of 
MURRAY827 
mean time. 


Kerguelen 
mean time. 


Kerguelen 

west of 

Greenwich. 


Greenwich 
mean time. 


Greenwich 
sidereal time. 


I. 

II. 


Ryan 

Ryan 


Inches. 
5 
5 


-- 


h m s 

18 41 35-5 

19 13 41 


m s 

— 2 16.2 

— 2 16. 1 


h m s 

18 39 19.3 

19 II 24.9 


h m s 

19 19 40.4 
19 19 40.4 


h m s 

13 58 59-7 

14 31 5-3 


h m s 

7 9 35.1 
7 41 46.0 



CONTACT OBSERVATIONS. 
CAMPBELLTOWN. 



157 



1 

■3 

6 


Observer. 


Aperture of 
instrument. 


is 

M fX. 


Recorded 

time, Porter 

llSmeari 

time. 


Correction of 
Porter 118 
mean time. 


Campbell- 
town mean 
time. 


Campbell- 
town west of 
Greenwich. 


Greenwich 
mean time. 


Green-vi ich 
sidereal time. 


III. 


Raymond. 


Inches. 
5 


90 


h m s 
3 40 5° 


m s 
— I 41.1 


h m s 
3 39 8-9 


h m s 
14 9 59-9 


h m s 
17 49 8.8 


h m s 
no 22.0 



QUEENSTOWN. 



1 



3 


Observer. 


p s 

B 1 


00 

a 

'■£• si 


Recorded 

time. Bond 

335 sidereal 

time. 


Correction of 

Bond 335 

sidereal time. 


Queenstown 
mean time. 


Queenstown 

west of 
Greenwich. 


Greenwich 
mean time. 


Greenwich 
sidereal time. 






Inches. 




h m s 


s 


h m s 


h m s 


h m s 


h m s 


I. 


Peters.. 


S 


90 


18 14 


+ 43-9 


I 4 lO.O 


12 45 19.6 


13 49 29.6 


7 3.5 


II. 


Peters. - 


5 


90 


18 43 48 


4-43-9 


I 33 S3-2 


12 45 19.6 


14 19 12.8 


7 29 51.5 


III. 


Peters.. 


S 


90 


22 12 IS 


+ 43-8 


5 I 45-9 


12 45 19.6 


17 47 5-5 


10 58 18.4 


IV. 


Peters.. 


S 


90 


22 43 30 


+ 43-8 


S 32 55-8 


12 45 19.6 


18 '18 15.4 


11 29 33.4 



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