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This table explains itself. If we therefore take the mean of the sun's parallax arising from each of those 16 total durations, it will be found 8".48; and if we reject the observations of number 7, 8, 9, 10, 12, 13, 14, which differ the most from the rest, the mean of the 9 remaining ones gives the sun's parallax 8.55, agreeing to a surprizing exactness with that found by the observations of the internal contact at the egress.
The observations at Tobolsk and Cajaneburg I consider as very good ones, these differing in the total duration only 6 seconds: this error in observation, from what is gone before, may be very easily allowed. The observation of the internal contact at the ingress at Stockholm is I believe too soon, and the uncertainty of this observation may be easily granted, when it is considered that the sun was only 3 or 4 degrees above the horizon at that time, and we find a difference of 22s between the observers at Upsal, where the sun was about the same altitude. This I apprehend was owing to the undulation on the limb of the sun, occasioned by the vapours near the horizon: but the same reason cannot be given for the observation at Tornea, where the sun was about 10° high, at the time of the internal contact at the ingress, unless there was an undulation at that altitude also, which may have been the case, though not mentioned. I have
reason to believe that the error of observation at Tornea is at the egress, where indeed the two observers differ considerably.
The parallax of the sun being thus found, by the observations of the internal 8".52 on the day of the transit, the mean horizontal 8".65.
contact at the egress,
parallax of the sun is I cannot help taking notice on this occasion, of a method employed by some astronomers, of determining the diameter of Venus by the duration of the egress over the sun's limb: for I am fully satisfied that the best eye, assisted by the best telescope, and in the best and clearest air, could not see the very last contact of Venus with the sun's limb, but must have lost sight of it several seconds before she really had left the sun's limb; and this will the more plainly appear, when it is considered that every second of the diameter of Venus took up about 19 of time in passing over the sun's limb. And to show this further, and in a stronger light, I shall mention the following particulars. Mr. Canton measured the diameter of Venus, and found it = 58", but by his duration of the the diameter of Venus is 57".8: the same diameter was measured by myself at Savile-house, and found 59", but by the duration of the egress observed there, the diameter of Venus is 58".6. Mr. Mason also at the Cape measured the diameter of Venus, which he found = 59"., but by his duration of the egress her diameter is found = 57".0: and therefore I must conclude that the diameter of Venus, found by the duration of the egress, must be always less than the true diameter for the reason given above. And since I am on this subject, I shall likewise mention the times of duration of the egress from several diameters of Venus. If the diameter of Venus be supposed = 57", then the duration of the egress at London should have been 18m 9s; if the diameter be =58", then the duration at London will be found 18m 28°; and if the diameter be 59", then the duration of the egress at London will be found = 18m 47s. The diameter of Venus being 59", and the diameter of the sun = 31' 31", the duration of the egress at Stockolm is 18m 43s, at Paris 18m 45s, at the Cape of Good Hope = 18m 8s, and at Rome 18m 38s. The duration of the egress at this last place was observed = 18m 31s; and if we suppose the diameter of Venus = 58", and the diameter of the sun = 31′ 33", the duration of the egress at Rome will be found = 18m 18'; which duration being less than the observed duration, it therefore follows that the diameter of Venus was more than 58" on the day of the transit; and the duration of the egress at Paris, observed by M. de la Lande and P. Clouet, by Mr. Mallet and Mr. Bergman at Upsal, by M. Chappe at Tobolsk, and by myself at Savile-house, prove the same thing.
Jupiter's satellites. I shall there- Tornea..
Latitude. 51° 28′ 37′′N 51 39 22 N
59 20 30 N
0 3 47 w
50 26 55 N
48 50 14 N
44 29 36 N
49 38 E
41 53 54 N
4.4. 16 E
63 26 10 N
10 16 E
59 51 50 N
1 5 28 E
56 40 30 N
1 28 18 E
60 27 0 N
65 50 50 N
64 13 30 N
58 12 22 N
13 8 ON
19 40 40 s
33 55 42 s
22 30 ON
59 56 0 N
10 56 0 N
11 56 30 N
Kingston, Jamaica ..
Port Royal, Jamaica...
fore set down in the annexed Tobolsk, Siberia * table the longitudes from Green- Madrid.
wich observatory of the differ- St. John's, Newfoundland + 3
ent places, where the late transit of Venus was observed, drawn from the said observations.
If the observation at Savile-house be compared with the observation of M. de la Lande at Paris, the difference of longitude between the royal observatories at Greenwich and Paris is = 93 16m.
* The latitude of this place was sent to the Royal Society, but no longitude of it, and therefore the internal contact at Tobolsk could not be compared with that at the Cape of Good Hope for the purpose of the sun's parallax.
Mr. Professor Winthrop went, at the expence of the province of Massachuset's Bay, to St. John's in Newfoundland, to observe the transit of Venus, which he did with great care, and as much exactness as the low situation of the sun at that time would permit. The internal contact happened there at 4h 47m 17. He had no other way of determining his longitude from Greenwich at that time of the year, but by taking the distance of a star from the moon, which gave him 3h 20m 56' for his longitude from Greenwich, and therefore his observation of the internal contact could not be compared with the same observation at the Cape.
The longitude of Kingston in Jamaica is determined by the observation of the transit of Mercury over the sun on the 25th of October 1743 o. s. mentioned in the Phil. Trans.: the effect of the parallaxes is considered, and here included.
The longitudes of Tornea and Madras are determined from the contact at the
egress, because I have good reason to believe that the observation at the egress at these two places was not correct, and the observation of the contact at the ingress is more certain than that of the egress, and the observers at the ingress at these two places agree to 2".
The elements I made use of in the preceding calculations are The sun's diameter
=8 30 10
Distance of the centres of the sun and Venus as seen from the
centre of the earth...
Difference of the parallaxes of the sun and Venus
9 35 0 O 21.35
I shall now give the method I followed in these calculations. In pl. 15, fig. 2, let FG represent the horizon, zvн a vertical circle passing through the centre of Venus, PVR a circle of declination, BV a circle of latitude, Ec the ecliptic, ovn the orbit of Venus, vL the parallax of altitude, VN the parallax of longitude, LN the parallax of latitude, zvp the angle of the vertical with the circle of declination, BVP the angle of the equator with the ecliptic, zvв the angle of the vertical with the circle of latitude, EVO the angle of the orbit of Venus with the ecliptic, zvo the angle of the orbit of Venus with the vertical, ZP the complement of the latitude of the place, vp the complement of the declination of the planet, zpv the horary angle or distance of the planet from the meridian, zv the complement of the altitude of the planet.
In the triangle zpv, the sides zp and PV and the angle zev are given, therefore the angle zve may be found, and also the side zv; and as the parallax of altitude is to the horizontal parallax as the cosine of the apparent altitude is to the radius, therefore LV is found. BVP added to or subtracted from zvp, as the nature of the case requires, leaves the angle zvB; the angle zvв subtracted from BVO leaves zvo= to the angle of the orbit of Venus with the vertical, zvo= LVN. Therefore in the right-angled triangle LNV, the angle LNV, the angle LVN being given, and the side LV, the side VN, the parallax of longitude, and the side LN, to the parallax of latitude, may be found. The parallax of longitude is reduced to time by knowing the horary motion of Venus in her orbit or path. Thus the value of one second of longitude is known in time. But to reduce the parallax of latitude to time, in fig. 3, let ECP represent the ecliptic, or the path of Venus over the sun as seen from the centre of the earth, LRD the path of Venus as affected by parallax at any one place, cr the nearest distance of the centres of the sun and Venus as seen from the centre of the earth, CR the nearest distance of the same centres as seen from the place of observation, ar or Nv the parallax of latitude, cs the sun's semidiameter, vs the semidiameter of Venus,
NV the difference of the semichords rv and RV, cv and cv = the difference of the semidiameters of the sun and Venus.
In the right-angled triangles crv and CRV, two sides are given, therefore the other sides rv and RV may be found; the difference of these two sides NV being reduced to time, by the horary motion of Venus in her path, will give the time answering to the parallax of latitude. The parallax of longitude being added to or subtracted from the parallax of latitude, as the case requires, will give the retardation or acceleration of the contact of the place of observation, after or before the contact as seen from the centre of the earth.
In all the above calculations, I have considered the place of Venus, with respect to the centre of the sun, both in right ascension and declination; and I have neglected the fractions of seconds in the results of the parallaxes of longitude and latitude, having always taken the second that was nearest to the fractional part.
I take this opportunity of acquainting the Royal Society, that I have, by means of an achromic object-glass micrometer of 40 feet focus, adapted to a reflecting telescope of two feet focal length, measured the least and greatest diameters of the sun, and I find the apogeal diameter = 31′ 28′′, and the perigeal diameter 32′ 33′′.
CI. Some Suggestions concerning the Preventing the Mischiefs which happen to Ships and their Masts by Lightning. By Wm. Watson, M.D., F.R.S. p. 629. These observations were drawn up in consequence of what had happened to the Harriot packet, in her passage to New York. This vessel was struck with lightning, which split the mainmast, main top mast, and main top gallant mast in pieces, ripped up the partners of the main mast, broke down the bulk head between the steerage and the hold, tore off the locks from the cabin doors, burnt the tarpaulin off the main hatches, made several holes between the coomings of the hatches and the deck, rendered all the compasses useless, broke one of the beams between decks, stove the boat, wounded one of the men very much, and the rest were stunned for some time. Most of the rigging was burnt off the mast head. The whole caused such a smoke in the ship, that taking her to be on fire below, they threw water a considerable time into the cabin; but providentially no other damage was done.'
A few years since a ship belonging to Capt. John Waddel, was almost beaten to pieces by thunder and lightning, of which a particular account is published in the Phil. Trans.* And very lately the main mast of the Bellona, a 74 gun ship,. was split in pieces by the lightning, which happened in Jan. 1762. What hap
* Vol. xlvi. p. 111.-Orig,