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Cape, and to make their observations there, and it was extremely fortunate they did so, for, by reason of cloudy weather, Mr. Maskelyne was hindered from making the proper observations, and in that case, the observation of the internal contact at the egress at Bencoolen, when compared with the same observation at Greenwich, could have determined nothing with regard to the parallax of the sun.
To determine the parallax of the sun, by means of the observations of the internal contact of Venus with the sun's limb, made at two different places, it is absolutely necessary that the difference of longitude between these two places be exactly determined. For this purpose Mr. Mason applied himself assiduously to observe the eclipses of Jupiter's satellites, and Mr. Green, the assistant observer at Greenwich, observed as many of the same eclipses, as the unfavourable season would allow. Dr. Bevis and myself likewise observed the same eclipses in Surry-street, London. The insufficiency of these sort of observations in determining the longitude of places where accuracy is required, is well known to those who have the practice of them.
By comparing the observations of the first and second satellites made at the Cape with those made in Surry-street, the difference of longitude between Greenwich and the Cape comes out, on a mean, = 1h 13m 30°, and rejecting those of the 2d satellite, which are always more uncertain than those of the first, I fix the difference of longitude between Greenwich and the Cape of Good Hope = 1h 13m 35s, which I have made use of in the following computations.
In order to ascertain the sun's parallax with more certainty, I have compared the observation of the internal contact at the egress at the Cape, with the observations of the same contact made at 15 different places in Europe. But before proceeding any farther I shall mention the times of such observations whence I had them; and the longitudes of those places, and whence I likewise had those.
13 35 w. Phil. Trans.
Internal contact at h. m. s.
8 15 14..
Saville house......at.. 8 18 22.. ditto
from Greenwich = 0
1 w. ditto.
9 5 0
0 40 37 E. ditto
0 43 58 E. a private letter
9 30 11
.at.. 9 28 52.. Swedish acts.. from Paris .... = 1 2 12 E. Phil. Trans.
.at.. 9 30 8..ditto
1 10 E. Phil. Trans.
3 10 E. Con. des Tems.
Internal contact at Abo .....
h. m. s.
h. m. s.
= 1 19 17 E. Phil. Trans.
...at 9 45 59.. Phil. Trans.... from Paris .at.. 9 54 8.. ditto ... .. from Paris = 1 27 28 E. ditto .at.. 10 8 59. Swedish acts .. from Stockholm = 0 39 20 E. Swedish acts. Cape of Good Hope at.. 9 39 48.. Phil. Trans.... from Greenwich = 1 13 35 E. Phil. Trans.
9 39 52.
Diff. in obs. 3..... = O sec. 4..
= 16 4
As there were several observers at some places, I have therefore set down the two extreme observations, that I may afterwards take the mean of them. One reason I apprehend why the observers, even at the same place, differ some seconds in the time of the contact, may arise from this, that some of them judged of the contact when there was no light between the limb of Venus and that of the sun, others did not imagine the contact to happen till they lost a part of the circumference of Venus; I shall therefore set down the difference between the observers at the same place, that an estimate may be formed of the limit of this error.
The mean therefore of all these comes out to be = 6$.6, an error that may be committed in judging of the contact, even at the same place.
After having computed the parallaxes of longitude and latitude, on the supposition that the sun's parallax was 81", for each of the above places, I compared the observation at each place with the observation at the Cape of Good Hope, and deduced the sun's parallax from each, as may be seen more fully in the following table.
In the Phil. Trans. it is at 9h 46′ 59′′, but that this is a mistake, in writing down the minutes, may be easily proved.-Orig.
+ M. de la Lande, in a letter to Mr. Maskelyne, says that M. de la Caille observed with a tele-
I shall explain this table by the example of the observation at Greenwich compared with the observation at the Cape, which is the first in the table. Thus, 9h 39m 50s is the mean of the times of the internal contact observed at the Cape, 1h 13m 35s is the difference of longitude between Greenwich and the Cape, this being subtracted from the time of the observed contact at the Cape, leaves 8h 26m 15s for the time the observers at Greenwich should have seen the contact, if there had been no parallax of Venus; subtracting therefore the time of the observed contact at Greenwich from this time, the remainder 7m 15s is the effect of the parallaxes of longitude and latitude at the two places of observation. But the effect of these two parallaxes at the Cape, on the supposition of the sun's parallax being = 81′′, is = 6m 8s, by which quantity of time the observers at the Cape should have seen the internal contact later than at the centre of the earth; and the effect of the same parallaxes at Greenwich is = 1m 118, by which quantity of time the observers at Greenwich should have seen the internal con
scope of Mr. Dolland's construction, which was not well fitted up; it may therefore be presumed that there is some mistake in the observation of M. Maraldi, because his observation is later than that of M. de la Caille, and differs so considerably from the rest.—Orig.
tact sooner than at the centre of the earth. The sum therefore of these two quantities is 7m 195, by which quantity of time the observers at Greenwich should have seen the internal contact sooner than the observers at the Cape in absolute time, had the sun's parallax been = 81". But the difference in absolute time as found by observation as above, is only =7m 15, therefore the sun's parallax by supposition, viz. 8".5, is to the parallax of the sun found by observation, as 7m 19s is to 7m 15s, which gives 8".42 for the sun's parallax, on the day of the transit, by this observation, which numbers and result are set down in number 1st, and so of all the rest in the table. By taking a mean of the results of these 15 observations, the parallax of the sun, on the day of the transit, comes out = 8′′.47, and by rejecting the 2d, the 8th, the 12th, and 14th results, which differ the most from the rest, the sun's parallax, on the day of the transit, by the mean of the 11 remaining ones, is = 8".52.
We have received from Sweden several obser
= 10 75
= 6 70
vations of the total duration of the transit from Cajaneburg. the internal contact at the ingress, to the inter- Calcutta nal contact at the egress, and also the observation of the same duration by M. Chappe at Tobolsk in Siberia, and by several persons in the East Indies; but the differences between these durations are too small to determine with any accuracy, the sun's parallax from them, by comparing the duration at one place with the duration at another. The greatest difference between them, and the duration at Tobolsk, which is the least, amounting only to 2m 50s, and the least difference amounting only to 1m 4s: in which small quantities the unavoidable errors of observations must bear a considerable proportion, and yet by comparing 15 total durations observed at different places with the total duration observed at Tobolsk, I find the annexed results of the sun's parallax from each of them.
=.9 70 = 8 50 = 8 75 The mean of these 15 results gives the sun's parallax = 9.56; and if we reject 4 of them, which differ the most from the rest, the mean, of the remaining 11, gives the sun's parallax =8".69.
However, on calculation by another method, I find so great an agreement between them, on the supposition that the sun's parallax is = 84′′, that I have determined the sun's parallax from them also, as a corroboration of the sun's parallax being very nearly the same as found by the observations of the internal contact; and this is done in such a manner that each observation of the total duration at any one place, determines the sun's parallax independent of any observation of the same duration made at any other place, and in which an exact knowledge of the longitude, of the latitude, and of the time at the place of ob
servation, is not required; all that is necessary to be known, is the time of duration from the internal contact at the ingress, to the internal contact at the egress, and that the clock moved equably during the interval of the contacts, and that the least distance of the centres of the sun and Venus, as seen from the centre of the earth, is also known.
The method I have followed in this inquiry, was by finding the total duration. at the centre of the earth: in order to find this, it was necessary to know the least distance of the centres of the sun and Venus as seen from the earth's centre. By the measurements of the distance of the limb of Venus from the sun's limb taken at Savile-house, and also by the like measurements taken by Mr. Haydon at Leskeard, I found, on the above supposition of the sun's parallax, that the least distance of the centres, as seen from the centre of the earth, was = 9′32′′. The total duration therefore at the centre of the earth was 5h 58m 13. I have compared the several observations of the total duration with this central duration, and from each I have determined the sun's parallax, as may be seen more fully in the following table. I have inserted in this table the alteration of duration by one second of the sun's parallax at each place, by which may be seen the quantity of error in the determination of the sun's parallax arising from any quantity of error in the observation.
The times of the total duration at those different places I have taken from the Phil. Trans.; only those of Calmar and Cajaneburg I have taken from the Swedish acts; the internal contact at the ingress at Cajaneburg, in those acts, is at 4h 18m 5s, whereas it should be at 4h 19m 55, as may be easily proved, this being an error in writing down the minutes, which has happened more than oncein these observations, occasioned by the hurry of writing down the times. of the observations. The observations in the East Indies I have taken from
letters sent by the East India Company to the R.S. I have also been obliged to make a correction of the minutes in the observation at Tranquebar and at the Grand Mount, a place about 8 miles to the s. w. of Madras.