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Full text of "Observations of the transit of Venus : December 5 and 6, 1882, made at the Harvard College Observatory"

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/ 'S i, 7^ (L 



7 



I 



OBSEIIVATIONS 



OF 



THE TRANSIT OF VENUS, 



DeCEMBKK f) AND 6, 1882, 



MADK AT THE 



HARVARD COLLECiE OBSERVATORY. 



EDWARD C^ PICKERING, 

DIUECTOK. 



('AMIUni)OK: 

JOHN' WILSON AM) SOX. 

SUnibcrsi'tu ]Pres8. 

1 HHli, 



OBSERYATIONS 



OP 



THE TRANSIT OP VENUS, 



December 5 and 6, 1882, 



MADE AT THB 



HARVARD COLLEGE OBSERVATORY. 



EDWARD C. PICKERING, 

DIRECTOR. 



CAMBRIDGE : 
JOHN WILSON AND SON. 

1883. 



OF AitTS AND SCIENCES. 



n. 



OBSERVATIONS QF THE TRAfTSIT OF TEXTS, DE- 
CEMBER 5 AND G, 1882, MADE AT THE HAECVARD 
COLLEGE OBSERVATORY. 

Bv Edward C. Pickering. 



The chances of cloudy weatljer at this Observatory early in Decem- 
ber are large, aud Cambridge was not selected by tlie United States 
Commission on the Transit of Venus as a station for observations of 
tbe phenomeoon. It therefore seemed injndicioua to make any exten- 
sive preparations for the occasion. The available telescopes at the 
Observatory, however, were employed in observioj; the coutacls. 
Photometric and spectroscopic obaervaliona were also obtaiued with the 
East Equalorial, and measurements of the diameter of Vcdus were 
made with the telescope of Mr, Chandler, mounted ia tha West 
Dome, and also with the East Equatorial. 

The morning of the traueit was so cloudy that there seemed litUe 
prospect of observing the contacts ; but the sun gradually became vis- 
ible, and the clouds were thin enough at the time of ingress tu allow 
observation of both the lirst and tlie second contacts. The lirst part 
of the afternoon was^early clear, and the third contact was well seeu. 
A few minutes later the sun entered a mass of thin clouds, bat was 
still sufficiently well seen for observation of the last contact. 

Arrangements hod been made before the day of the transit with the 

1 Western Union Telegraph Company for the distribution of the time 
iignals of this Observatory among those who might desire to obtain 
them on December 6. The clock at which these signals originate 
was carefully compared with the standard sidereal clock of the Obser- 
vatory at frequent intervals, and also with the signals furnished by the 
United States Naval Ohaervatory at Washington, which were received 
here by telegraph. To determine the error of the sidensal clock, ob- 
servations were made with the meridian circle by Professor W. A. 
Rogers, the results of which are given below. Since the transit, in 
prder to remove any doubts with regard to the error of tlie sidereal 
clock ns determined by a large fixed instrument, Professor Rogers hai 



Wi 



16 



PROCEEDINGS OP THE AMERICAN ACADEMY 



made a special series of observations, in which he used both the merid- 
ian circle and the portable transit instrument on each of eight even- 
ings, determining the clock error independently with each instrument. 
The result confirms the correctness of the form of level employed 
with the meridian circle^ and shows that the instrument furnishes 
trustworthy results for the absolute as well as the relative clock error. 
The mean correction to be applied to the error found by the meridian 
circle in order to reduce it to that found by the portable transit in- 
strument, according to these observations, is -[-0".08 ; the eight sep- 
arate results are -f0-.20, -f-0'.06, +0'.09, -f0'.07, +0'.06, +0M1, 
+0".09, +0".05, the first having a weight of one third. As the mag- 
nifying powers and the reticules used with the two instruments differ 
materially, the amount of the correction is not surprising. 

The results for the error of the sidereal clock obtained from the 
observations with the meridian circle near the time of the transit are 
exhibited in Table I. The first two columns contain the date of the 
observations in mean solar days and tenths, and the sidereal time, to 
hundredths of an hour, for which the error was determined. The 
third column gives the number of stars on which each result for clock 
error depends. The next two columns give the amount by which the 
clock was slow at the time of each set of observations, and the corre- 
sponding error for noon of December 6, corrected by means of the 
hourly rate -[-0'.023. The last two columns contain the values of 
the instrumental constants n and b (angle at pole, and inclination of 
axis). 

TABLE I. — Observed Clock Errors. 



Date. 
1882. 


Sid. 
Time. 


No. of 
Stars. 


Clock Slow. 


n 


& 


Obserred. 


Red. to Dec. 6.0 


Dec. 4.2 
Dec. 4.8 
Dec. 6.4 
Dec. 6.2 


2P.92 

12.63 

3.07 

22.05 


6 
4 
4 

7 


+2» 21-.25 
+2 21.69 
+2 22.05 
-1-2 22.86 


* 
+2° 22-.24 

+2 22.46 

+2 22.37 

+2 22.24 


— IMO 
— 1.03 

— 1.05 

— 1.06 


+0'.77 
+ 0.77 
+ 0.77 
+ 0.77 



The mean result for noon of December 6 is +2™ 22'.33. Re- 
ducing this to the result to be expected from the portable transit 
instrument, by adding -f"^*-^^ ^^ above, we have +2" 22*. 41, with an 
hourly increase of -|-0'.023. 



I 

II 



OP ARTS AND SaENCPS, 17 

On December 5, G, and 7, at noon, llift Washington signals were 
received at CBinhriilge, niid compared by t-Uronojjrapli with our lidereal 
ctrtck. The result, aiXar allowiog for Llie difference iu longitude, was 
that the Washington (ilotk wus fast 0*.G, 0'.4, and 0v3 on the three 
days respectiTely. Tlio signals were promised for December 4 also, 
but were not received, as tlie lines woro occupied in transmitting po- 
litical news. A good example is thns afforded of the importance of 
degiending on the local observatories for supplying the public with 
time. 

The clock distributing ths meao-time signals from the Harvard 
College Obsenra'tory is kept as nearly as may be 15'.5 fast. The 
time is therefore that of the meridian passing through the Slate House 
in Boston, and 4" 44" lo'.S west of Greenwich. On the day of the 
transit the deviation of the Washington signals was noted, and, to 
avoid the confusion arising from two systems, oar signals were brouglit 
to an approximate agreement with tliem, ratlier than with our own 
determinatjou of the local time. Frequent comparisons were made with 
idereol clock, and showed that at December 5.8 our signals were 
0'.6 fast; at December 6.0, O'.o fast; at December 6.3. 0*.5 fast; 
nnd at December 6.8, 0'.2 fast. Allowing for the difference of longi- 
tude, these signals thsrefoi'e did not differ more than a tenth of a 
tecond from the Washington signals, but to reduce them to the true 
time both should be reganled as about 0'.^ fast. In other wonis, in 
reducing to Greenwich mean time, the longitude (or the Washington 
and Boston signals should be taken as b'' 8" 11'.7 and 4'' 44'" 15'.0 
respectively. Since the observed times of contact are known to be 
liable to variations of several seconds, these c 
are small, and may bo neglected without serious er 
it is Dseless to give the resulting times of contact n 

BiDgle seconds. 

CONT.\CTS. 

A statement of the results of the contact observations is given below. 
In Table II. The upper part of the Table contains in successive 
columns the names of the observers and recorders, the apertures and 
focal 'lengths of the telescopes in centimeters, their magnifying powers 
in diameters, and the corrections required at ingress and at egress to 
reduce the observed times to Cambrid«e mean or sidereal time 
according to the timepiece employed. These corrections are given 
in accordance with the assumption that the signals furnished by the 
mean-lime clock give the time of a meridian 4'' 44" 15'.5 west of 
.) 2 



:, especially as 
■e closely than 




PROCEEDINOB OP THE AMERICAN ACADEM7 



Greenwich. The second part of the Table girea the observed times 
of the four contacts, without an; corrections. The third part contains 
the concluded Greenwich mean timea of the contacts noted by each 



TABLE n. — CosTACTS. 



0.™. 


BeeoBkr. 


^nr 


LeV^h 


IM.tr 


Tlmf^pUM. 


E. C. Pickering 


A. W. Cutler 


14.5 


082.6 


200 


+lj=.0, +10>.3 


Arthur Searla 


W. A. Hogera 


13.2 


230 


220 


— 76».2 


0. C. Wendell 


A. W. Cutler 


10.2 


141.4 


40,90 


+iH.O, +10.8 


J. R. Ellin aoda 


R. G. Saunder 


10,2 


110 


150 


+82>.3. +82>,S 


S.C. Chandler, Jr. 


W. V. Brown 


162 


244 


180 


-2G».8. -24».7 


W. H, Piclioring 


R. Q. BaundiT 


B.4. 10.2 


71,64 


20,110 


+82>.3, +82..3 


»— ■ 


ObBonrf Tlnum nf ContKiM. 1 


I. 


11. 


in. 


IV. 


E. C. P. 


21'' Id-^ 43M 


21'' 39" 61a,3 


3" > S'.B 


3" 23" 10>.0 


A. S. 






20 6 23.4 


30 28 28 


0. C. W. 






3 3 8.2 


3 23 14.2 


J. R. E. 




14 40 1 


20 3 40 


20 23 40 


S. C. C. 


21 20 32 


21 40 30 


S 3 30 


3 24 10 


W. H. P. 




14 10 9 


20 3 S3 


20 24 


»™'- 




DUrmncD Tmni Wcaa. 1 


I. 


n. 


III. 


IV. 


1. 


11. 


III. 


IV. 


E. C. P. 


2h i:^ 23' 


21^ 24" Bl> 


7- 47"' 46= 


8" 7- Gl= 


—0= 


-12» 


+5. 


— 1 


A. S. 






7 47 41 


8 7 42 






+1 


—10 


0. c. w. 


2 4 48 




T 47 49 


8 7 66 


+10 




+9 


+8 


J. H. E. 




2 24 60 


7 47 Sfl 


8 T 33 




+^ 


—4 


-19 


B. C. C. 


2 4 2a 


2 21 84 


7 47 B6 


8 8 16 


-6 


—9 


—i 


+24 


W. H. P. 




2 24 B8 


7 47 30 


8 7 54 




+15 


—10 


+2 


Mean 


2 4 B2 


2 24 43 


7 47 40 


8 7 53 





op AHT3 AND SCIENCES. 



19 






oTreerver, obtained by adding 4'' 44° 31' to each of the Cambridge 
toe^u times. The mean result for each contact is given in the last line 
of the Table, At the right are given the liiflereaces of each obaerver's 
result from the mean of all. 

The following notes coDtain, oncler the oaroe of each observer, the 
details of his work. 

E. C. Pickering. 

The inatrament employed was the East Equatorial, Its fall aper- 
l^re is 15 inches, which on this oeeaaioo was reduced to about C inches 
iGT the object-glass. An audible signal was given to the 
lorder at the time of each phenomenon noted. The recorder took 
the time of each signal from the chronometer, and recorded it, with 
any subseqaent remarks by ihe observer. The wedge of shade glass 
placed between the eyepiece and the eye was of a greenish tint. In 
observing the first contact, the last time recorded before the appear- 
ance of the notch was 9" 19" 29'.6 by the chronometer, Venus was 
first seen at 9'' 19" 44',2 by the cbroaometer. The edge of the sun 
was wavy, rendering it difficult to decide whether an indentation was 
real. At 9'" 19" 49". the interval between the cusps was estimated 
at 9"; two parallel lines 6" apart served aa the unit of measure. 
From a redaction of this observation the time of first contact appears 
to be ^'°- 19" 42'.6 ; the moan of this and of the time directly observed 
is here assumed to be the time of the first contact, which ts therefore 
9^ 1 S" 4.S".4 by the chronometer. A scale in the eyepiece would allow 
the observer of phenomena like these to make estimates of ihe inter- 
val of the cusps without removing his eye from the telescope, and 
would accordingly afford him many of the advantages of a double-image 
micrometer without its disadvantages. 

The images at the second contact were unusually well defined, and 
the contact was recorded aa occurring at 9'' 39° 51',3, Eight seconds 
later it was clearly past. 

The third contact was recorded aa occurring at 3" 3™ 3'.8. At 
3** 3" 21'.4 the interval between the cusps was estimated as double 
that between ihe lines in the field, and consequently as 1^", A 
reduction of this observation would make the IJme of contact 
8'' 3" O'.O. 

The fourth contact was recorded as occurring at 3'" 23" lO'.O. 
gh 23m g.^ jj jj^ ^^j occurred, at S"" 23" I9".4 it was certdnly 
t. 
fTbe chronometer used hy the recorder, who also recorded for Mr. 



20 PROCEEDINGS OF THE AMEBICAN ACADEMT 

Wendell, was Bliss & Creighton 1182 ; it b regulated to mean time, 
and has been in frequent use at the Obsenratorj. 

Arthur Searle, 

The instrument was the five-inch telescope formerly mounted in the 
West Dome. As it was not provided with any stand, and as economy 
was ai> object kept strictly in view during the preparations for the 
transit, the best plan for using this telescope seemed to be to lay it 
horizontally upon a rough frame, at a height of three feet from the 
ground, before the south entrance of the Observatory. A plane mir« 
ror of unsilvered glass, formerly used in photographing the sun, was 
placed upon the block of stone at the east side of the steps of the 
entrance. This mirror was attached to the frame originally prepared 
for it, which is provided with screws for moving it approximately in 
altitude and in azimuth. The dimensions of the mirror are 7^ by 6 
inches, so that the sunlight reflected from it at moderate hour angles 
was thrown upon the whole surface of the object-glass before it The 
two surfaces of the mirror are inclined to each other, so that only one 
image of the sun is seen. In order to keep this image of the sun in 
the field, the services of an assistant were necessary. Unfortunately, 
the assistant who had accustomed himself before the transit to the 
management of the mirror, considering the morning too cloudy for 
any observation, did not arrive at the Observatory in season to take 
part in the observations at ingress. No other assistant having the 
necessary skill was available, and an attempt made to use the tele^ 
scope at ingress was therefore unsuccessful. 

At egress, the mirror was very successfully managed so as to keep 
the required part of the sun's limb in view, and Professor W. A. 
Rogers kindly undertook to record the times at which the observer 
gave his signals. The observation of the third contact was accordingly 
a satisfactory one. Nine seconds before the time recorded as that of 
the contact, the sun's limb became noticeably darkened at the place 
of egress, but the shade was lighter than the tint of the planet itself. 
The shade gradually darkened as the planet advanced, and at the time 
recorded as that of contact a darkness equal to that of the planet's 
disk had reached the limb of the sun. This phenomenon could not 
be distinguished from that of geometrical contact. If the limb of the 
sun had been steadier, it is possible that such a distinction might have 
been made. The image, in fact, was by no means bad, but there was 
sufficient undulation to make a very exact observation of geometrical 
contact impossible. Thirteen seconds after the recorded time it had 




OP ARTS AND SCIENCES, 

become evident that the cusps were separated by a part of the planet's 
limb, and that geometrical contact was past. 

These observalions were made through a dark red shade-glass be- 
tneea tJie eyepiece and the eyestop. The limb of the sun was dis- 
tinctly seen, and was free from glare. As the sun entered the thin 
clouds mentioned in the introductory vemarks above, the red glass 
was replaced by a blue one, which admitted much mare light. The 
part of the planet exterior to the limb of the Bun was then certainly. 
though indistinctly, seen. Its outlioe seemed to be part of a smaller 
drcle than that bounding the portion of the disk interior to the Bun'a 
I limb. The increasing cloudiness soon put an end to this appear- 
I ance, the Greenwich mean time of which, derived from the record, 
a 1^ aT^ 31'. 

The fourth contact was observed with some difficulty, owing to the 

clouds and to the necessity of an occasional movement of the mirror 

to keep the image in the field. The time given is that of a signal 

\ accompanied by the remark " Notch doubtful " ; the notch was 

\ alter wards seen. 

'uring the transit, the disk of the planet was uniformly dark, ex- 

I cept that at times it seemed to be crossed by faint streaks of Itghl 

I yery likely due to slight defects in tbe ehade-glass or other parts 

the optical apparatus employed. 

The eyepiece used was positive, Ko. 5 of the set of eyepieces I 
longing to the large filar micrometer of the East Bquatorial, and, 
with that instrument, having a nominal magnifying power o 
Its power, with the telescope used during the transit, has been deter- 
mined by two methods, and the approximate mean result 220 is ^ven 
in the Table. 

Tbe chronometer employed was Bond 236, regulated to sidereal 
time ; it has been in constant use at the Observatory for many 
years. 

0. 0. WendeU. 
Tbe instrument employed was the finder of the East Equatorial. 
The object-glass was silvered to reduce the light, and an additional 
reduction was effected by a shade-glass. Between the first and second 
contacts the silverirg was partially removed, owing to an apprehension 
that the clouds would grow thicker ; but as the sky actually became 
clearer, the second contact could not he observed. Before the third con- 
tact, the film of silver was entirely removed, and the object-glass was 
smoked by Mr. Clacey's method, which sufficed, with the aid of one 
shade-glass, to reduce the light. 



22 PROCEEDINGS OP THE JLMERICAN ACADEMY 

The Ant contact was well observed, but the recorder did not notice 
the signal, and the time is derived by estimate. According to the 
observer, the signal was given half-way between the last two signals 
of Professor Pickering, whose own estimate, however, placed it six 
seconds later. The mean of these estimates was adopted. 

The third and fourth contacts were well seen and recorded. The 
dme given for the third contact is that when the diminishing thread of 
light at the place of egress definitely broke. Eighteen seconds earlier 
contact had certainly not yet occurred. 

Eight seconds previous to the time of fourth contact it was evident 
that the egress had not been completed. 

•71 J?. JSdmands, 

The telescope was one borrowed from Dr. E. T. Caswell, of Provi- 
dence, R. I., and originally owned by Dr. Alexis Caswell, of Brown 
University. It was attached to a portable equatorial mounting (with- 
out clock) belonging to the Observatory. The observations at ingress 
were made on the east balcony of the dome, and at egress on the west 
balcony. The eyepiece was negative, and the light was reduced by 
one shade-glass placed near the focus of this eyepiece at second con- 
tact, and by three shade-glasses, one on each side of the focus and one 
next the eye, at the third and fourth contacts. 

Hie chronometer used in recording these observations, as well as 
for those of Mr. W. H. Pickering, was Frodsham 8451, regulated to 
sidereal time. This is an excellent instrument, of much value in the 
work of the Observatory Time Service. 

At first contact the rapid changes in the opacity of the clouds pre- 
vented observation of the phenomenon, as the observer had no wedge 
of shade-glass, and could not readily control the brightness of the 
field. At second contact, the recorder found it impracticable to note 
the times from the signals of the two observers, aud the assumed times 
are derived by estimate. The original estimate of the time of the 
signal " Past " was derived from an inspection of the chronometer 
made immediately after the observer learned that no record had been 
secured. But he was satisfied, on consideration, that this first estimate 
allowed too little for the interval between the signal and his inspection 
of the chronometer ; besides which, his signal '* Past " must have been 
given an appreciable time after the contact itself. His last signal, 
"Not yet," preceded the signal "Past" by about ten seconds. On 
these accounts, he estimated the observed time of contact, which has 
been entered in the Table, as Rve seconds earlier than the original 



op ARTS AND 8CIENCE8, 



atimate of the time of tbe Bigoal " Fast." Tbis decision was made 

before correcting the result for error of chronometer, and before com- 
paring il with any other observation. 

At the third and fourth contacts, the recorder counted the seconda 
from the chronometer, and the observers recorded the times of ihelr 
observations. At the third contact, the seeing was good, and the fo!- 
■JiDwiug note waa made : " No black drop seen. Purposely used faint 
Te." The clouds impeded any similar observation at the second 
bDntact. The telescope was somewhat disturbed by wind duriug the 
B at egress, which prevented tho observation of additional 
ihenomena. 

S. C. Chandler, Jr. 
The first contact was looked for at a part of the limb estimated to 
5° to the right of the apparent vertex. Tlie notch was sud- 
denly noticed still nearer the apparent vertex at the time given as 
that of contact. Nineteen seconds later the notch had increased, 
confirming the first observation with regard to the pla£e of ingress. 

The time given as that of second contact is that of geometrical 
contact in the opinion of the observer. Seven seconda before the 
recorded time the contact had not occurred. Four seconds after the 
recorded lime it was still uncertain whether tDo contact was past. 
Beconds after the recorded time the contact was certainly past. 
black drop " was seen. 
Thirty-five seconds before tho recorded time of third oontapt a shade 
appeared on the sun's limb, very much fainter tlian the disk of Venus. 
This shade increased in darkness, but did not seem to confuse the de- 
termination of the time of geometrical contact, which is that recorded 
for this phase of the transit. The Jeoorded time roust be as early as 
that of geometrical contact, which might possibly, however, have been 
thought to occur ten seconds later than tlie recorded time. Twenty- 
two seconds after tho recorded time, contact was certainly past by sev- 
eral seconds. 

The fourth contact was very satisfactorily observed. Eight seconds 
ifore the recorded time the notch waa still certainly visible ; at the 

trded time it was certainly gone. 

The telescope was one belonging to the observer, and lately placed 

on the equatorial mounting in the West Dome. No shade-glasses 

were used. The necessary reduction of the light was effected by pre- 

smoking the front surfaoe of the crown and the back eurfa.ce of 



rec( 

^^^rec( 

mp 

' * app 

Thi 
ten 
for 
thai 
tho: 

eral 

r Ti 

^HVfoi 

^^V Tl 
^^^^on t 



r^ie flint lens of the object-glas 



This 



,s done by Mr. John Clacey, 



24 PBOCEEDINOS OP THE AMERICAN ACADEMY 

the maker of the telescope, and the result proved verj satisfactory. A 
negative eyepiece was used in observing the contacts. 

The timepiece used was the pocket-chronometer Patek, Phillipe, Sd 
Cie. 34,807. 

W. If, Pickering, 

The instrument selected for the observations was the Bowditch 
Comet-seeker ; but as dew upon its reflecting prism prevented obser- 
vations with it at ingress, the Quincy Comet-seeker, a smaller instru- 
ment, was employed in observing the second contact. No complete 
record of these observations was secured, owing to the circumstances 
explained in the notes relating to Mr. Edmands's observations. The 
estimate of the time of contact ib based upon the circumstance that 
the observer's signal '* Past *' was given one second later than the cor- 
responding signal by Mr. Edmands, according to the judgment of both 
observers. But on consideration, previous to any comparison with 
other observations, it appeared likely that this signal *'Past" was 
given a little too early. The observer, therefore, assigned for his 
observation of contact a time three seconds later than the original 
estimate of Mr. Edmands for the time of his own signal. 

The Bowditch Comet-seeker was used at egress. 

I 

Observers at other Stations, 

The following observations of the transit have been conmiunicated 
to me for publication, and are here inserted. 

1. Station, the establishment of Messrs. Alvan Clark & Sons in 
Cambridgeport, Massachusetts. Approximate latitude, -|-42^ 21' 16" ; 
approximate longitude, west of Greenwich, 4** 44™ 26'.7. The times 
are given according to the clock signals of this Observatory. 

Observer, Alvan G. Clark. Second contact, 21»» 40"* 3»; third, 
8^ 2™ 30' (the observer has no doubt that the minute should be 3 
instead of 2) ; fourth, S^ 23°» 54V5. 

Observer, C. A. R. Lundin. Third contact, 3^ 3°» 13'; fourth, 
3*» 23"» 34'. 

Reducing these observations to Greenwich mean time by the ad- 
dition of 4?" 44°» 15-.5, we have, for Mr. Clark, 2^ 24"* 18% 7^ 47"* 46% 
8^ 8"* 10" ; and for Mr. Lundin, 7»* 47°* 28', 8*^ 7°* 50'. 

2. Station, near St. Paul's Church, New York. Approximate 
latitude, -}-40® 46'.0 ; approximate longitude, west of Greenwich, 
4*" 56"* 0'. Observer, Rev. G. M. Searle. Telescope by Dollond ; 
aperture, 2.65 inches ; focal length, 44 inches ; magnifying power, 60. 



' AllTS AND SCTESCES. 



25 



^nepieoe, a good watch, tlie errors of which were determined by 
sextmit observatioDs fit 2i'' 16", 22'' 34 , and l' 11", which gave the 
respective correctiooB -|-9't +8', -j-3*. Ko "black drop" was Been 
at eiiber internal contact. The first contact was lost; the real were 
observed as follows: 21" 28" 2', 2' SI" 49'. 3" U" 50'. The 
correciM moan limes are 21" 28"' 10", 2" SI" 52", 3" II" 53*; and 
tbe corresponding Greeuwicb mean times are S* 24" 10", 7" 47" 52", 
S** 7*° 53*. The sun's limb was remarkably steady at egress, but some- 
what disturbed at ingress. 

3. Station, terrace at No. 55 Habana Street, Havana, Cuba. 
Approximate latitude, -}-23° 9' 21"; approximate longitude, west of 
Greenwich, 5'' 29™ 2C'. Observer, Profeasor Charles Hasselbrink 
(U. 8, Signal Service observer in Havana). Telescope by Negretti 
and Zamhra; aperture, 2.0 inches ; focal length, 30 inches; magnify- 
ing power, 80. Chronometer Negus 582, slow 3', by comparisonB 
furnished by the observatory of Don -Tos^ Maria Garcia de Haro, 
Bcmi-official observer for the Spauisb Navy and tlie mercantile marine. 
The observer recorded for himself; the telescope was shaken by wind 
in the afternoon. The external contacts are considered doubtful, bnt 
the internal contacts were well observed. Observed times of contacts, 
SO" 38''57'. 20" 54" 30', 2" 19" 0*, 2" 36"" 47' j corrected mean times, 
20^ 84" 0', 20" 54" 33", 2" lO"- 3", 2" 8G" 50**, resulting Greenwich 
mean tunes, 2" S" 2G', 2" 23" 5!)', 7" 48" 29*, 8" 6" 16'. 

Just before internal contact at mgress, the observer saw a fine line 
of light round the disk of V(^nu9, beyond tlie limb of the sun. During 
the transit, a delicate aureola of very white light was noticed around 
the planet, suggesting the illumination of its atmosphere. Patches of 
a dark grayish tint were noticed at times upon the deep black disk of 
Venus. 



Photometric Observations. 
was constructed for comparing the brightness of the 
ring transit with that of the sky in immediate prox- 

limb. In the accompanying figure, A and £ are two 

Srst having parallel sides, tlie other with sides inclined 

O is a double-image prism, D a positive eyepiece, E 

n eyeslop. A graduated circle, G, and an index, ff, 

the angle through which the eyepiece and Nicol are 
lie is inst^rted, like an eyepiece, in the tailpiece of the 

of the Observatory. The light from the object-glass, 

prism A, is not deviated, but is divided by the prism 



A photometer 
disk of Venus du 
iroity to the sun's 
glass prisms, the f 
at a small angle. 
a Nicol. and /"ai 
serve to measure 
turned. The whr 
l.Vinch lulescnpe 
striking upon the 



I 



26 



PBOCEEDINOa OF THE AMERICAN ACADEMT 




O iDto two peDcils, one of which 
passes without deviation through the 
eyepiece and the hole in the cyestop 
to the eye. The other pencil is 
thrown to one side by C7, and is cut 
J off by the eyestop. The light passing 
through B is deviated about 6^ by 
the difierence in inclination of its 
two inclined sides. This light is 
also divided into two pencils by Cy 
one retaining the deviation imparted 
by By and being cut off by the eye- 
stop. Tlie other is deviated by (7, 
but in such a manner as to counteract the inclination imparted to 
it by ^. It therefore passes centrally through the hole in the eye*- 
stop to the eye of the observer. The latter accordingly receives two 
pencils of light formed by the same object-glass, one receiving the 
light from Ay the other that from B. These two pencils are polarized 
by C in planes at right angles, and their relative brightness may 
accordingly be varied at will by turning the Nicol E, The instrument 
in principle closely resembles the meridian photometer for some years 
in use at this Observatory. The same device is employed to secure 
t.wo equal pencils polarized in perpendicular planes, but in that instru- 
ment two equal object-glasses are employed, instead of two images of 
the same objective. 

The eyepiece is focused on the front surface of the prisms Ay By 
so that their adjacent edges appear as a line dividing the field into two 
equal parts. By turning the Nicol the brightness of either part of the 
field may be reduced indefinitely, so that the brighter may always be 
brought to equality with the fainter. Placing the whole instrument 
at the principal focus of the telescope, we see side by side in the two 
halves of the field images of objects really about 1 G' apart. 

The observations were made by placing the edge of the prism par- 
allel to the sun's limb at the point nearest Venus, and bringing Venus 
into one half of the field. A portion of the sun's disk near its centre will 
be seen in the other half of this field, and may be compared directly 
with Venus by turning the Nicol. Settings were made in the four posi- 
tions of the Nicol in which the images appeared equal, and the posi- 
tions read to tenths of a degree. The observation was then repeated, 
moving the telescope so that the portion of the sky close to the sun's 
limb should be measured in the same manner. Eight settings taken 



OP ABT3 AND SCIENCES. 



27 



8U 

I thi 



in this way constitute a Bet, and give the relative light of the sky and 
VeQUB. To eliminate any ditTerence in the prisma the photometer 
was rotated 180^ alter each eet, but no perceptible difference is indi- 
cated in thia way. To reduce the obserrations, the first reading waa 
subtracted from the second, and the third frooi the fourth. Calling 
the sum of these differences A, the relative light, £;= tan^ J A. It 
mil also be convenient to use a method of expressing the light in 
magnitudes, according to the method already used in this Ob- 
irvatory for comparing nebulas and portions of the moon. When 
Burfaces ai'e thus compared, portions of equal area are selected and 
reduced to stellnr magnitudes by the formula of Fogson. We shall 
then have the difference in magnitude, M^2.5 log L. lu Table III. 
the successive columns give a current number, the Cambridge mean 
time, the diHerence in light of equal areas of Venus and the sun 
expressed in stellar magnitudes, the corresponding quantities for the 
sky near the edge of the sun, and these s^mc ratios expressed in per- 
centages, that is, assuming the light of the centre of the sun equal to 
one hundred. The last column gives the mitial of the observer. 



TABLE III, — PnoTosiBTttic Obsbbvatioi 



Bo. 




nim^o.^,. 


Magnitudo. 


PtKB 


a«EO», 


Ob.cr«t. 














T.nn.. 


Skj-. 


V»m«. 


Skf. 




1 


1' 7" a 


430 


2.54 


i,n 


9.6 


W 


2 


X 18.4 


4,65 


2,94 


1,6 


6-7 


w. 


3 


1 24.8 


4.05 


2,79 


2.4 


T.7 


w. 


i 


1 29,4 


4.46 


2.40 


1.6 


11.0 




6 


•2 48.3 


5.68 


3,32 


o.a 


4.7 


F. 


6 


2 61,6 


4.44 


2,74 


1.7 


8.0 


r. 


7 


2 54.4 


4.37 


80(1 


1.8 


6.0 


1'. 


8 


Mean W. 


4,.34 


2.fi7 


1.8 


8,8 


w. 


9 


Mean P. 


4.B0 


3,04 


1.4 


6,2 


p. 


10 


Mean W.. P. 


4,57 


2.S5 


1,6 


7.5 


Both. 



The result for the light of the sky in the first line of tlie table 
depends upon eight settings. 

These observations show a well-defined increase in light of the sky 
near the edge of the sun as compared with that received from Venus. 

tThis effect also seemed to me to he very perceptible without the pho- 
tometer. To confirm it. I asked KTi*. Wendell which looked to him 
the brighter. Ho Batisfled himself that Venus certainly appeared 
darker than the sky. A slight difference was to be expecteil, since 
there are insULUces on record of the visibility of Venus before first 



28 PROCEEDINGS OF THE AMERICAN ACADEMT 

contact. In the interval between the exterior and interior contacts, 
the edge of the planet has sometimes been traced beyond the limb of 
the sun. The effect was noticed by Mr. Searle shortly after the third 
contact, as above stated. According to his recollection of the appear- 
ance of the field, the difference in darkness beween the planet's disk 
and the sky was obvious, and might have been expected to make the 
planet more distinctly vbible outside of the sun's limb than was 
actually the case. 

No appreciable light could be received from Venus itself, unless that 
planet is incandescent or phosphorescent, an extremely improbable 
hypothesis. Doubtless the greater portion of the light, like that of 
the sky near the sun, is due to reflection of the light of the sun from 
the particles of the earth's atmosphere. During a total solar eclipse 
the interposition of the moon suffices to cut off nearly all the light 
near the sun, except -the small portion due to the solar corona. It is 
therefore obvious that the light of the sky near the sun originates at 
no great distance from the earth, and is doubtless caused by reflection 
in the terrestrial atmosphere. In a communication to this Academy nine 
years ago {Proceedings^ IX. 1), I showed that many of the phenomena 
of atmospheric illumination and polarization could be explained by 
specular reflection from the particles of the air, whose index of refrac- 
tion differs very slightly from unity. In this case, if the sun was 
reduced to a point, the light of the sky at small distances would vary 
inversely as the fourth power of the distance. In any case, a glance 
towards the sun is sufficient to show that the light increases very rap- 
idly as we approach the sun's limb. We should expect that the light 
of the portion of the atmosphere between us and the sun would be 
much greater than that outside of the sun's disk. Most of the light 
would be received from the portion of* the sun at a very small angular 
distance. A point between us and the sun would be illuminated in all 
directions, that is. through the entire 360°. A point outside the sun's 
disk could at most receive light only from 180°. Moreover, the edge 
of the sun is much fainter than its centre, which would still farther 
reduce the light. We should then expect that the light received from 
Venus would be greater than that of the sky near the sun's limb, the 
opposite result from that indicated by the observations. This effect 
would be modified by the solar atmosphere, which would increase the 
light outside of the sun. The observations of Professor Langley, 
however, during the eclipse of 1878, seem to prove that the light of 
the corona is entirely insufficient to produce this effect. The difficulty 
of photographing the corona confirms this view, but its spectrum in- 



OP ARTS AND SCIENCES. 29 

diOBtea that it is composed of light of a wave-length to which the 
pholographio plate is not very eenaitire. 

An important source of i.'rror arises in almost all these measures 
from the diffuse reflectioa from dust or scratches on the object-glass. 
The effect of diis would lie simttor to an increased bazinesa of tbe 
sky, and would tend to increase the apparent light received both 
from Venus and tbe sky. In our measures this effect was reduced 
to a minimum, as the object-glass had been cleaned shortly before the 
transit, and tbe diffuse reflection was therefore very slight. A remedy 
for this diOiculty would be found by removing the object-gluss and 
substituting for it a minute bole. When tbe sky ia hazy we should 
expect an increased relative brightness near the edge of the sun. 
This may account for the larger readings obtained by Mr. Wendell, 
as the sky was somewhat clearer during my observations than during 
his. Aa tbe portion of the sky observed was only about 1' distant 
from Venus, irregular clouds could not produce the observed differeuce 
light. In fact, the persistence of the phenomena under varying 
conditions seems to leave little doubt that the disk of Venus was 
ly much darker than the sky near it. 

The solution of tliis problem would be greatly aided by researches 

the kind described below, a portion of which will probably be under- 

this Observatory. Measurement of the relative light of different 

portions of the sun's disk and of the sky at various distances fi'om it. 

Measures of the sky at various distances from the moon, thus eliminat- 

l^^ing any effect corresponding to that of a solar atmosphere. Measures 

^^^^Bf the light of the disk of the moon during the progress of a partial 

^^^^Blipse of the sun. 

jj^f T1 



condit 
^^^ nnrtioi 



Spectroscopic Obsebtations. 



The spectrum of the light received from Venus was observed with 
ft star spectroscope constructed by Ililger. The dispersion was such 
that about one third of the spectrum was visible in the field of view 
at a time. Two prisms of dense flint gliiss were employed. This 
spectroscope was attached to tlie large Equatorial, and was foeuseii 
on the limb of tbe sun. When Venus was brought upon the slit it 

|~ppeai-ed as a broad band traversing tbe spectrum lengthwise, which 
Quid be compared directly with the solar spectrum on each side of 
L The slit was then brought tangential to the limb of Venus, f 
) receive the light grazing its surface. 
raati 



The breadth ot the dark band 
s thus reduced and flickered owiiig to the slight unsteadiness of the 



80 PBOCEEDINOS OP THE AMEBICAN ACADEMT 

atmosphere. No difierence in the spectrum was detected either bj 
myself or by Mr. W. II. Pickering after careful examinaUon. 

This negative result should not be regarded as throwing doubt on 
the positive results attained by so skilful an observer as Professor 
Young, who is said to have detected the presence of aqueous vapor in 
Venus. I have not yet seen the details of his observation, but his facili- 
ties for making this observation were much greater than mine, and he 
probably used a much higher dispersion. I satisfied myself that there 
were no very marked absorption bands, and doubtless the phenomenon 
is one which requires more careful preparation than we were permitted 
to make without interfering with the other portions of our programme 
to which, in preparing our plans, we had attached more importance. 

DiAMETEB OF YeNUS. 

The measurements of the diameter of Venus, mentioned in the first 
paragraph of this communication, were made by Professor William A. 
Rogers and by Mr. S. C. Chandler, Jr. The subjoined reports from 
these gentlemen furnish the account of the work undertaken. In these 
reports, Mr. Chandler's telescope, mounted in the West Dome, has 
been called the West Equatorial. 

Report hy WiUiam A. Rogers. 

The following method for the determination of the diameter of a 
planet was first employed by the writer in 1877, having been used in 
the determination of the diameter of Mars. 

Let: — 

oTq = a line ruled upon glass and set in the direction of diurnal motion. 
OTj = a line ruled at a given angle, t, with respect to ar^, and reckoned 

from east to west, 
arg = a line ruled at the angle (180° — t) with respect to x^. 
y = 2L line ruled at right angles to x^ and bisecting the angle formed 

between ar, and x^ 
Ti = the observed time of transit of the preceding limb of the 

planet over x^. 
' Tj = the time of transit of the following limb over x^. 
Tj, T4 = the corresponding times over x^. 
D = the diameter of the planet. 

Then : 

i> = 15 cos 8 (tj — Ti) sin % = 15 cos S (t^ — r J sin t 



OF ABT3 AND SCIENCES. 81 

For any Tariation whatever of the angle t we have : 

Ai = ^ 

15 cos d (r, — Tj) cos t 

and hence, from transits over the line x^^ 
D=lo coa S (tj — Ti) sin (t -j- At) 

= 15 cos 8 (to — Tj) sin \i + ^ —. r :! 

^^ ^^ L ' locos 5 (Ta — Tj) cos t J 

and from the transits over the line x^ 

D=Z 15 cos 8 (t. Tg) sin \t :r^ r-7 r ; | 

^ * ^^ L 15 cos 5 (r^ — Tg) cos tj 

If therefore the times of transit of each limb are taken over the 
lines Xj^ and x^, any error in D due to an erroneously assumed position 
angle will be eliminated. 

It must be noted, however, that any error in At arising from an un- 
known error in the angles between x^^ a?^, and ar^ will be only partially 
eliminated. Designating by i and i' the angles which x^ and x^ make 
with Xq, and their variations on account of errors of graduation by Ai 
and At' respectively, we have, from transits over x^, 

2> = 15 cos 8 (tj — Ti) [sin t + cos t At] 
and from the transits over x^^ 

2> = 15 cos 8 (t4 — Tj) [sin »'-|- cos t' At'] 

or, since t' = 180° — t nearly, 

Z> = 15 cos 8 (T4 — Tg) [sin t — cos t At'] 
whence 

D = V cos 8 [[(tj — Ti) -f (t^ — Tg)] sin t 

+ cos t [(tj — Ti) At — (t^ — T^ At']] 

The only case, therefore, in which the elimination will take place is 
that in which 

(Tj — Ti) At = (t^ — Tg) At' 

But since, on Dec. 6, the time required for Venus to make a complete 
transit over a line having t = 20** was only 24', the effect of any 
small error in the graduation will be practically insensible. 
For the equatorial diameter we have : 

i) = 15 cos 8 (tj — Tj) sin (90° -f At*) 
Unless At, therefore, is very large, we shall have : 

i) = 15 cos 5 (Tj Tj) 

Assuming the same constant of differential refraction for Venus 
north and for Venus south, any error in the observed value of D 



82 



PROCEEDINGS OF THE AMERICAN ACADEMY 



due to the differential refraction B^ will be eliminated if we combine 
the observations over x^ and x^ with corresponding observations over 
these lines extended below the line x^ Designating the times of 
transit for Venus north of x^, by t'i, t'^ t^^ and 1^4, we shall have : 



For Venus South. 

i> = V cos 8 r (r, — tO sin f t + ^^ 5— ^ r . ) + 

* L\ 2 1/ V^ I 15co8d(r,— Ti)cost/ ' 

D 



iu — T.) sin (i — 



1)] + ^' 



15 cos d (t^ — T3) cos 
For Venus North. 

i) = -yi cos 5 Ut- — Ti) sin (i + =-= r-rj , v _ . ) + 

a [\ i u \ I 15 cos « (7^2 — t'i) cos t/ ' 

15"cos d (7^4 — i'^ coTt/J ~ "^ 



iu — '^d sin (» 



Combining these equations, we shall still have, for any case except 

where At is due to an error in the assumed value of i, an equation of 

the form : 

X) = 15 cos 5 (tj — Tj) sin t 

Two ruled plates were prepared for the observation of Dec. 6, 
one for the East Equatorial and one for the West Equatorial. They 
consist of one horizontal line, two vertical lines, and a series of lines 
having the inclinations 10°, 20°, 30°, 40°, 45°, and the inclinations 
135°, 140°, 150°, 160°, and 170°, respectively, to the horizontal line. 
These lines were all extended below the line x^, giving the angles 
225°, 230°, 240°, 250°, 260°, and the angles 315°, 320°, 330°, 340°, 
and 350^ 

In general, a complete series of observations consists of 10 transits 
over each of the inclined lines, and 20 transits over the vertical lines, 
both for Venus souih and for Venus north of the horizontal line. 

The results for Dec. 6, arranged in the order of the times of obser- 
vation are as follows. 

TABLE IV. — East Equatobial. 



Position of 

Venus with 

respect to 

horizontal 

line. 


t = 80o 


» = 46o 


i = 90o 


Bamariu. 


D. 


No. 
Obs. 

18 
20 
22 
22 


D. 


No. 
Obs. 


D. 


No. 
Obs. 

82 
40 
42 
44 


South. 
South. 
North. 
South. 


// 
62.51 

62.27 

69.73 

59.21 


n 
62.46 

60.85 

60.26 

58.98 


18 
20 
22 

22 


II 
60.45 

69.62 

60.18 

68.37 


Seeing &ir. 

Seeing Mr. New aero of position. 

Seeing very bad. 

Image of Venus boiling. Reject. 



OF ARTS iSD BCIBNCBS. 
TABLE y. — Wan Eouatoual. 



■oiitioB 


, = !(. 


,=». 


.-.ao^ 


■="• 


. = ^ 


Itonulu. 


D. 


a' 

22 


i. 


Z 


ft 

IM).D4 


24 

20 

22 


8l!w 
61.43 


22 
20 
2i 


ft 


Ko. 

Olw. 


Sot.<h. 

North. 
SotilA. 
NarlA. 




6l"l8 
01,37 
50.62 


24 


6o!l8 
G0.69 
6M.S& 
(11,70 
6U,e2 


44 S»lDB nvf (wiO. 
40 iMloglkto. N..w«!fo, 
44 ScBlag UDitaulj. 
44 SwlDKhlr 



























Collecting the results for each instrument, bat rejecting the last 
series with the E&st Equ&torial, we have : 



InltnuHDt 


i = 10» 


i = 3y 


i = «fi 


i = lE' 


i = 90= 


Eut Bqiutorial ! 
Mean* 


. .". . 


.'.'.. 


02!61 

02.27 
69. 7S 


62.46 
60.86 
60,26 


6o!i6 

69.62 
60.18 






61.50 


61,19 


60.08 


We*t Equatorial 
Ueani 


60.50 

5e.&i 


Ol.lB 

01 ..17 
69.Q2 


60.78 
60.M 
60.68 


61,04 
61,48 

09,28 


60.1B 

60.5U 

6a.8(> 

01.70 

69.62 


58.M 


flO.69 


00,78 


60.58 


60,20 



Combining the results of the obserrntions over the inclined lines, 
and assigning the same weight for each value of t, we have: 



TABLE Vn. 





Dtai = W 


DKai = Vf'....W 


From the Efiit Equatorial . . . 


6o!o6 


8i!m 


From the WMt Equatorial . . , 
Meant .... 


60,20 
6018 


60.28 

ooii 


Valuei pi D at the dUtance unity 


\hxa 


. loloa 



It will be seen, by an examination of Tables IV. and V. that the 
magnitude of D apparently dependa to a certain extent upon the 



84 



PBOCEEDINGS OP THE AMERICAN ACADEMT 



character of the atmospheric conditions under which the observa- 
tions were made. Arranging the results according to the character of 
the seeing, we have : 

TABLE VIII. — SsBiiro Fair to Good. 



Initroment 


»=zlOO 


» = 20o 


t=aoo 


t=46o, 


« = 90o 


East Equatorial < 
West Equatorial ) 

Means 


• • • • 

• • • • 

• • a • 

00.56 
60.56 


• • • • 

• • • • 

61.18 
61.87 

• • • • 

61.27 


// 
62.51 

62.27 

60.78 

60.94 

• • • • 

61.61 


II 
62.46 

60.85 

61.04 

61.43 

• • • • 

61.45 


60.45 
59.62 
60.18 
60.50 
61.70 

60.51 




Seeing B 


AD TO Vert Bad. 






East Equatorial j 
West Equatorial | 

Means 


• • • • 

• • • • 

• • • • 

56.51 
56.51 


• • • • 

• • • • 

59.52 

• • • • 

59.52 


59.73 
59.21 
60.58 

• • • • 

59.82 


60.26 
59.98 
50.28 

• 
• • • • 

59.84 


60.18 
58.87 
59.85 
59.62 

59.88 



Combining by weights proportional to the number of observations, 
we have : 

TABLE IX. 





Dfort = 90o 


Dfor« = l(K>...46o 


For seeing fair to good . . 
For seeing bad to very bad 


// 
60.61 

59.88 


6l!39 
59.38 



From the observations made under favorable conditions, we have 
for the distance unity : 



Dfori = 90«> 
16''.01 



Dfort = 10«>. .. .460 

16".24 



There is a general tendency of the observations to indicate a lesser 
value for the equatorial diameter, but the method of obtaining this 
quantity by direct transits over a vertical line is not a very reliable one. 
The apparent difference, therefore, between the diameter determined 
at different angles of inclination, is probably fictitious rather than real. 

In order to determine the difference in the amount of the irradiation 





^^m OF ABTS AND SCIEKCES. S5 

}^5)uk disk upon a brigll^ ground and of a brightdiak upon a darker 

succeeding the transit. Since it was oaly poBsible to observe boti 
points of tangency of the inclined lines with the disk of the planet on 
one side of the vertical lines, the elimination of the effect of an error 
a the position angle of the line x^ does not here take place. Care 
was token, however, to make the setting for the zero of position as 
exact as possible. 

The following reanlts were obtained. 

TABLE X. 






..u. 


,«„.„„ 


.-.lo- 


i = K- 


( = 80- 


i = 4(C 


. = «■ 


Ubdi; 


1 


1882. 
Dec. 13-14 
Dec. 14-15 
Dae. 24-25 
Dec. 2U-27 

188-3. 
Jan. 1-2 


> E. Equutorial < 
Weet Eqoalorial 


17.73 


17.96 


10.76 
16.66 
16,90 
17.66 


16'45 
10.68 
17.83 
17.47 


16.49 
16.14 

17".'2'9 


16,50 
16.46 
17.12 
17.47 

17.73 


1 


If these observations can be trusted we may conclude: — 

(a.) That the difference in the value of the diameter at the dis 

tauce unity, due to irradiation on Dec. G,and on the days immediately 

bllowing, is not far from 0".4 
(b.) That up to a certain point this difference increases with the 

crease, however, is probably not quite aa great as the observations 

were not favorable to good obserrations. 

Heporl by S. 0. Cliandler, Jr. 

The following determinations of the diameter of Venus during the 
transit on Doc. 6, 1882, were made by Professor Rogers's plan of 
ransils over inclined tines, wilh the West Equatorial. The telescope 
lad been prepared for solar observation by the maker, Mr. John 
jlaoey, by smoking the front of the crown and the back of the flint 
ens of the object-glass ; a process which he £nds affords a better effect 
than a silver film, the image being sharper and the effect of contrast 
with the sky more agreeable. The result in the present instance wna 
completely satisfactory. The obscuration produced by the double 
smoke film was sufficient to render a shade glass unnecessary with the 
jower used, which was about 180 diameters. 


1 



86 



PROCEEDINGS OP THE AMERICAN ACADEMT 



The scheme of observation, and the plate, were the same as used 
by Professor Rogers. The transits were taken in sets consisting of 
an equal number of contacts of both limbs with lines ruled at equal 
and contrary angles with the middle transit lines, thus eliminating the 
error of the zero of position. The formula of reduction follows simply 
from equation (2) hereafter given. Thus, if we call Afj, A^^ the dif- 
ferences of the observed times of transit of opposite limbs, for the 
angles p and — -p, respectively, we get 

i> = J^ cos S cos /I (A<i -}- A^j). 

Hie corrections for proper motion and differential refraction are so 
far within the uncertainty of observation, in their effect on the con- 
cluded diameter, that they have been neglected. Table XI. gives the 
value of the observed diameter and the number of observations in each 
pair of sets arranged according to the position angle of the lines em- 
ployed. Table XIL gives the means, taken with reference to the 
number of observations, of the results of Table XI. 

TABLE XL 



p = B(P 


p = 7(P 


p = eoo 


p-b(P 


P = 46o 


pz=.{p 


n 




II 




// 




II 




II 




II 




69.66 


6 


61.61 


17 


62.07 





68.73 


6 


62.47 


6 


61.60 


6 


62.36 


6 


59.17 


4 


61.08 


6 






61.28 


6 


61.13 


6 






60.87 


6. 


:BL30 


6 






63.11 


6 


61.08 


6 








•■ 


62.76 
W.06 


6 






62.76 


6 


61.03 


17 








. 'v 


17 






62.18 


17 


^1.03 


4 










<60.«7 


4 






62.61 

« 


4 


59.91 
61.28 
61.64 


6 
6. 

8 



TABLE Xn. 



Position Angle 


Observed 


No of 


Diameter reduced 


of Lines. 


Diameter. 


ObeerrationB. 


to Mean IMstanoe. 




// 




II 


80«> 


61.01 


12 


16.14 


70° 


61.09 


27 


16.16 


60<> 


61.41 


45 


16.24 


60° 


63.73 


6 


16.86 


46° 


62.88 


46 


16.49 


0° 
Mean 

• 


62.09 


69 
194 


16.42 


61.83 


16.36 



The mean value of the diameter from the 194 observations is, 

i)=16".85. 



OF ARTS AND SCIENCES. 87 

It is noteworthy tliat the results over the different lines, with the 
exception of that at 50^, which is based on ooly G observations, 
all give values less than that of 16'^Gl, adopted in the Berlin Jahrbuch, 
Nautical Almanac, and Connaissance des Temps, and that the lines of 
greatest position angle, which by this method would be expected to 
afibrd the most accurate results, give the smallest values of the series. 

It appears to me that the method of Professor Rogers is not limited, 
in its application to the interior planets, to their transits over the sun's 
disk, or to times when the conditions permit the whole disk to be seen ; 
but that it may, by an appropriate construction of the plate and 
arrangement of the observations, be employed at any time when they 
are near inferior conjunction, and that determinations both before and 
after conjunction will eliminate any errors peculiar to each elongation. 

Jjetpbethe position angle, counted from an assumed zero, of a 
line on the plate drawn from some point taken as a centre ; the true 
position angle being p -{- ^p. Let D and 8 be the diameter and 
declination of the planet ; A8 the difference of declination from tlie 
centre of the plate when it passes nortli, and A'8 when it passes south 
of that centre ; and t and ^, the corresponding observed times when 
the planet's limb in its diurnal motion is tangent to the line. Tlien 
in the triangle formed by the planet's centre, the intersection of its 
path with the line, and the observed point of tangency, the distance be- 
tween the first two points is, 

l^D sec (p -f- ^P) = i^ sec p + ^D tan.p sec/? A/? 

where, Ap being small, the terms involving its squares are neglected. 

If we imagine a line drawn from the centre of the plate at the angle 
p from the true position zero, we have, from the triangle formed by 
the actual and imaginary lines and the portion of the path of the 
planet's centre between them, the length of the intercepted path : 

Ad Ap seep sec (p -|- A/?) = A8 Ap sec^ p 

If now we call T the time when the centre of the planet is on this 
imaginary line when the planet passes north, and T^ the time for a 
corresponding position when the planet passes south of the centre, we 
have the general equations : 

T = e-{-— I ± ^Dsecp ± ^D tan /) sec p Ap -|- AS sec*/? A/? I 

(1) """^ 

r' = ^-{-p r:f ^Dsecp if jZ^tanpsec/i Ap'{-A'6 sec^p Apl 



88 PROCEEDINGS OP THE AMERICAN ACADEMY 

j9 being reckoned as usual from 0° to 8G()^ in the direction n. f. a. p. ; 
the upper sign being used for the prect;diiig« and the lower sign for the 
following limb. 

Let t^ and t^ be the observed times when the planet, passing north 
of the centre, has either limb tangent to lines at the angles p and — p 
from the assumed zero. Then the Ist equation of (1) gives: 

(2) ^ 

^« = ^« + 15co8 5 [^ i^^^P ^ i^ tan ;; sec ;> A/> + A8 secV ApJ 

If t^ be the corresponding time for a third line drawn through the 
intersection of the other two and bisecting the angle between them, we 
shall have p = 0, and 

But we have T^— T^= T^— Ty Hence, putting t = /, + ^^ — 2 <;, 
and noting that (1 — cos p) sec p = tan /> tan ^p, 

(4) q= ^D tan /) tan J /> — AS tan* /? A/) = ^ t cos 8 

In a similar way, when the planet passes south of centre, we get 

(5) If iZ) tan ;? tan i p — A'8 tan*;? Ap = ^ ^ cos 8 
The addition of (4) and (5) gives, 

(6) I>=z T cot ip [-ij^cos 8 (t + t') cot jD + (A84- A'8) <»n/i Ap]; 
and their difference, 

(7) A;, = Vco8 8(T'-r)^|^ 

But we have also, puttmg r = ^j — t^, and r^ = t'^ — t\^ 

. . AS = -^ r cos 8 cot p — JZ> Ap sec p 

^ ^ A'8 = — -^ r' cos 8 cotp — ^I) Ap seep 

whence 

A8 + A'8 = ^ (r — r') cos 8 cotp (nearly) 

A8 — A'8 = J^ (r + r') cos 8 cotp 
which substituted in (6) and (7) give finally, 

(9) 2> = :f V cos 8 cot p cot ^ jt? [t + t' — (t — t') f^'\ 

(10) A;i = J^cot;? 



OP ARTS AND SCIENCES. 89 

The last term in equation (9) disappears when the planet passes 
at equal distances north and south, and in general is inappreciable ex- 
cept when the error of position zero is large, or when the planet 
l^isses at very uuet^ual distances north or south of the centre, which 
iu practice need never occur. 

^Equation (9) consequently permits the determination of the 
diameter by observations on one limb only. As has been remarked, 
observations on the preceding limb before inferior conjunction, and on 
the following limb after it, may be expected to eliminate errors pe- 
culiar to the elongation. 

It should be remarked that the quantity cot p cot ^ p becomes 
unity for p = 60°, and for larger angles rapidly increases. In general 
the advantageous application of the method requires the use of lines 
at greats position angles than 60°. 

In what precedes it has been assumed that the line corresponding to 
the time t^ bisects the angle formed by the others, and also passes 
throngh their intersection. In ruling the plates for the observations 
tt the diameter during the transit of Yenus, these conditions may 
pdesibly not have been exactly fulfilled ; sinoe, as they did not affect 
the observations then contemplated, Prpfessor Roger.-* did not especially 
attend to those points in the preparation of the plates. Any such 
errors may, however, be eliminated. Thus, if we put a = the dis- 
tance between the transit line on the plate from an imaginary line 
|>arall^ to it passing through the point of intersection of the inclined 
lines, and ^i the inclination to a line bisecting the angle of the in- 
clined lines, equation (3) becomes, 

and equation (9), 

B— ^ ^ cos Scot p cot ip [t -f t' — 2 a — 2 (AS — A'8) A» 



Since At changes sign by turning the plate 180*^ in position angle, 
and a changes sign by turning the other side of the plate toward the 
eye these sources of error may be determined or eliminated by arran- 
ging the observations with appropriate reversals. 

To exemplify partially the use of this method, I avail myself of 
some observations of the following limb of Venus, on various days 
succeeding the recent transit, by Professor Rogers and myself. As 



40 



PROCEEDINGS OF THE AMERICAN ACADEMY 



these were not arraoged with a view to eliminate the possible errors 
involved in a and At, as it is the intention to do in the fatnre, the 
results cannot be considered as having other than an illustrative Talae. 
The angle, 60°, Was less than should properly be used for adTan* 
tageous results, and the record gives no means of knowing in whidi 
series the plate was in the direct, and in which it was in the reversed 
position. The results are as follows. 



TABLE XIII. 



Date. 

• 


Number of 
Observatioua 

25 
20 
22 
21 
17 


Diameter. 


Obaerrer. 


1882 
Dec. 13-14 
•' 14-16 
" 24-25 

" 26-27 


16.39 
17.00 
17.58 
18.^:0 
17.80 


W. A. R. 

II 

ii 

O* v/. 0* 

II 



These results are of interest for comparison with those obtained on 
the same days by Professor Rogers from different observations. The 
series is not sufficient to determine the '^ irradiation constant" 



t 



In conclusion, the results may be summarized as follows: — 

1. Observations of the four contacts by six observers. 

2. The determination, by a photometer especially devised for the 
purpose, of the relative amounts of light received from the disk of 
Venus, from the sky near the sun's edge, and from the sun's centre. 
Denoting the last amount by 100.0, that received from Venus was 1.6, 
and that received from the sky 7.5. Contrary to expectation, Venus 
was thus shown to be distinctly darker than the adjacent sky, and this 
result was confirmed by direct observation. 

3. The spectroscopic observations. These gave negative results* 
and showed that no marked absorption was caused by the atmosphere 
of Venus. 

4. A careful determination of the diameter of Venus by a method 
not previously attempted, and the suggestion of an application of this 
method to planets when both limbs cannot be observed. The result 
obtained by Professor Rogers was 16"flO from transits over inclined 
lines, and that obtained by Mr. Chandler was 16".35, which woulQ be 
reduced 0".02 by using only the transits over inclined lines. 



#! 



n