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hours 29 minutes 15 seconds, for the time of total ingress, as seen from the banks of the Ganges, and Il hours 11 minutes 49 seconds from the beginning of egress, as affected by these parallaxes.

Draw Gf perpendicular to Venus's orbit VOC, and by measurement on the scale AB (Fig. 3.) it will be found to contain 10": take 10" from the scale in Fig. 1. and find, by trials, a point c, in the arch N, where, if one foot of the compasses be placed, the other will just touch the central transit-line kl. Take the nearest distance from this point c to CL, the axis of Venus's orbit, and applying it from t toward k, you will find it fall a minute short of k; which shows, that Venus's parallax in this direction shortens the beginning of the line of her visible transit at the Ganges by one minute of time. Therefore, as this makes the visible ingress a minute later, add one minute to the above VIII hours 29 minutes 15 scconds, and it will give VIII hours 30 minutes 15 seconds for the time of total ingress in the morning, as seen from the eastern mouth of the Ganges. At the beginning of egress, the parallax gp in the same direction is 21" (by measurement on the scale AB), which will protract the beginning of egress by about 30 seconds of time, and must therefore be added to the above II hours 11 minutes 49 seconds, which will make the visible beginning of egress to be at II hours 12 minutes 19 seconds in the afternoon.

58. Bencoolen is 102 degrees east from the meridian of London; and therefore, when the time is 28 minutes past II in the morning at London, it is 16 minutes past IX in the morning at Bencoolen ; and when it is 20 minutes past VIII in the morning at London, it is 8 minutes past III in the afternoon at Bencoolen. Therefore, in Fig. 4. Bencoolen will be at B at the time of Venus's total ingress, as seen from the Earth's centre; and at 6 when her egress begins.

Draw Bi and bk parallel to Venus's orbit VCO, and measure them on the scale : the former will be found to be 22" for Venus's eastern parallax in the direction of her path at the time of her total ingress; and the latter to be 191" for her western parallax in the same direction when her egress begins, as seen from the Earth's centre. The first of these parallaxes gives 5 minutes 30 seconds (by the analogy in g 54.) to be added to IX hours 16 minutes, and the latter parallax gives 4 minutes 52 seconds to be subtracted from III hours 8 minutes; whence we have IX hours 21 minutes 30 seconds for the time of total ingress at Bencoolen: and III hours 3 minutes and 8 seconds for the time when the egress begins there, as affected by these two parallaxes.

59. Draw bv and bm perpendicular to Venus's orbit VCO, and measure them on the scale AB : the former will be 5" for Venus's northern parallax in a direction perpendicular to her path, as seen from Bencoolen, at the time of her total ingress; and the latter will be 15}" for her northern parallax in that direction when her egress begins. Take these pa. rallaxes from the scale, Fig. 1. in your compasses, and find, by trials, two points in the arcs N and T (Fig. 2.) where if one foot of the compasses be placed, the other will touch the central transit-line kl: draw a line from a to b, for the line of Venus's transit as seen from Bencoolen; the centre of Venus being at a, as seen from Bencoolen, at the moment of her total ingress; and at b at the moment when her egress begins.

But as seen from the Earth's centre, the centre of Venus is at k in the former case, and at l in the latter : so that we find the line of the transit is longer as seen from Bencoolen than as seen from the Earth's centre, which is the effect of Venus's northeru parallax.—Take Ba in your compasses, and setting that extent backward from t toward g, on the central transit-line, you will find it will reach two minutes beyond ki and taking the extent Bb

in your compasses, and setting it forward from t toward w, on the central transit-line, it will be found to reach 3 minutes beyond l. Consequently, if we subtract 2 minutes from IX hours 21 minutes 30 seconds (above found), we have IX hours 19 minutes 30 seconds in the morning, for the time of total ingress, as seen from Bencoolen: and if we add 3 minutes to the above-found III hours 3 minutes 8 seconds, we shall have III hours 6 minutes 8 seconds afternoon, for the time when the egress begins, as seen from Bencoolen.

60. The whole duration of the transit, from the total ingress to the beginning of egress, as seen from the Earth's centre, is 5 hours 52 minutes (by 40.); but the whole duration from the total ingress to the beginning of egress, as seen from Bencoolen, is only 5 hours 46 minutes 38 seconds : which is 5 minutes 22 seconds less than as seen from the Earth's centre: and this 5 minutes 22 seconds is the whole effect of the parallaxes (both in longitude and latitude) on the duration of the transit at Bencoolen.

But the duration, as seen at the mouth of the Ganges, from ingress to egress, is still less; for it is only 5 hours 42 minutes 4 seconds; which is 9 minutes 56 seconds less than as seen from the Earth's centre, and 4 minutes 34 seconds less than as seen at Bencoolen.

61. The island of St. Helena (to which only a small part of the transit is visible at the end) will be at H (as in Fig. 4.) when the egress begins as seen from the Earth's centre. And since the mid. dle of that island is 6° west from the meridian of London, and the said egress begins when the time at London is 20 minutes past VIII in the morning, it will then be only 56 minutes past VII in the morning at St. Helena.

Draw Hn parallel to Venus's orbit VCO, and Ho perpendicular to it; and by measuring them on the scale AB (Fig. 3.) the former will be found to amount to 29' for Venus's eastern parallax in the

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direction of her path, as seen from St. Helena, when her egress begins, as seen from the Earth's centre; and the latter to be 6'' for her northern parallax in a direction at right angles to her path.

By the analogy in 54, the parallax in the direction of the path of Venus gives 10 minutes 2 seconds of time; which being added (on account of its being eastward) to VII hours 56 minutes, gives VIII hours 6 ininutes 2 seconds for the beginning of egress at St. Helena, as affected by this parallax. -But 6" of parallax in a perpendicular direction to þer path (applied as in the case of Bencoolen) length. ens out the end of the transit-line by one minute ; which being added to VIII hours 6 minutes 2 seconds, gives VIII hours 7 minutes 2 seconds for the beginning of egress, as seen from St. Helena.

62. We shall now collect the above-mentioned times into a small table, that they may be seen at once, as follows: M signifies morning, A afternoon.

Total ingress. Beg. of egress. Duration.

H. M. S. H. M. S. H. M. S.
The Earth's centre II 28 OM VIII 20 OM 5 52 0*
London - . Invisible MI VIII 17 41M
The Ganges mouth VIII 30 15 M II 12 19 A5 42 4
Bencoolen

IX 19 30M III 6 8 A 5 46 38
St. Helena Invisible M| VIII 7 2M

63. The times at the three last-mentioned places are reduced to the meridian of London, by subtracting 5 hours 56 minutes from the times of ingress and egress at the Ganges; 6 hours 48 miuutes from the times at Bencoolen; and adding 24

* This duration as seen from the Earth's centre, is on supposition that the semidiameter of Venus would be found equal to 371" on the Sun's disc as stated by Dr. Halley (see Art. V. $ 31.), to which all the other durations are accommodated. But, from later observations, it is highly probable, that the semidiameter of Venus will be found not to exceed 30' on the Sun; and if so, the duration between the two internal contacts, as seen from the Earth's centre, will be 5 hours 58 minutes; and the duration as seen from the above-mentioned places, will be lengthened very nearly in the same proportion.

minutes to the time of beginning of egress at St. Helena: and being thus reduced, they are as follows:

Total Ingress. Beg. of egress.

H.M.S. H. M. S. Times at S Ganges mouth 11 34 15M VIII 16 19M2. DuraLondon Bencoolen

for St. Helena - Invisible M VIII 31 2MS above.

64 All this is on supposition, that we have the true longitudes of the three last-mentioned places, that the Sun's horizontal parallax is 12" that the true latitude of Venus is given, and that her semidiameter will subtend an angle of 37" on the Sun's disc.

As for the longitudes, we must suppose them true, until the observers ascertain them, which is a very important part of their business; and without which they can by no means find the interval of absolute time that elapses between either the ingress or egress, as seen from any two given places: and there is much greater dependence to be had on this elapse, than upon the whole contraction of duration at any given place, as it will undoubtedly afford a surer basis for determining the Sun's parallax.

65. I have good reason to believe that the latitude of Venus, as given in $ 31, will be found by observation to be very near the truth; but that the time of conjunction there mentioned will be found later than the true time by almost 5 minutes; that Venus's semidiameter will subtend an angle of no more than 30" on the Sun's disc; and that the middle of her transit as seen from the Earth's centre, will be at 24 minutes after V in the morning, as reckoned by the equal time at London.

66. Subtract VIII hours 17 minutes 41 seconds, the time when the egress begins at London, from VIII hours 31 minutes 2 seconds, the time reckoned at London when the egress begins at St. Helena, and

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