An accurate method of obtaining the parallax of the sun, by the transit of Venus, may be by two observers 90° from each other, observing the ingress of the planet upon the sun's disk, or egress from the same.* (Plate VIII, Fig. 4.) Suppose the ingress. Let S be the sun in his apparent magnitude; VAB a part of Venus's orbit; C D E an arch of the equator or parallel of latitude on the earth; G, its centre. Let an observer at C, be on that meridian, which will pass the sun at or near the beginning of the transit; let another observer be at E, on a meridian 90° from C. It is manifest, that if there were no diurnal motion to the earth, Venus must pass from V to B, after her ingress at I, on the disk of the sun as seen from C, before she would seem to touch the sun as seen from E, and the difference of the observed time, allowance being made for longitude, turned into the heliocentrick motion of Venus over that of the earth, would measure the angle VIB or GIE, viz. the angle which a semidiameter of the earth would subtend at the sun.

sun.

But during the interval between the ingress observed at C and that at E, the observer at E must be carried eastward by the diurnal rotation of the earth. Suppose him arrived at D, when he first observes Venus indenting the disk of the Venus will then appear to touch the sun at I, when she has passed to A. In the difference of absolute time between the beginning of the transit, as observed at C and that of the observer arrived at D, Venus by the excess of her heliocentrick motion will pass from V to A, measuring the angle VI A. The number of degrees in the arch ED may be easily known by computation, a degree being allowed for each four minutes of time. The co-sine of the arch E D is the line DF = GH. The length of the line D F or G H is found by comparing it with the semi-diameter of the earth, as the co-sine of the angle measured by the arch ED is to radius. Then as D F, or its equal G H, is to the time Venus is pass

* For a suggestion of this method, the author is indebted to a very ingenious Friend.

ing from to A by the excess of her motion; so would G E be to the time Venus is passing by that excess from V to B The arch VB measures the angle V I B, subtended by G E equal to the semi diameter of the earth. Allowance must here be made for obliquity of motion in the planet and observer; unless the observer should be so situated, that his motion and that of Venus must be directly opposite.

The angle, which a semi-diameter of the earth subtends at the sun being known, the distance of the earth from the su may be easily found by rectangular trigonometry; for the angle at E is a right angle, the line E I being a tangent to the earth's surface, and the semi-diameter of the earth is known. Making the distance radius, say, as the tangent of the angle GI E, is to the line GE; so is radius to the line GI, the distance of the earth from the sun.

In case of two observers, great care must be taken that the time keepers be accurate and regulated on the same principle.

This principle of finding the parallax may be applied to other distances in the places of observation beside 90°; and equally, if both observers be not on the same parallel.

Mr. Short, of London, took great pains in deducing the quantity of the sun's parallax from the best observations made both in Britain and abroad, and found it to have been 8.52′′, on the day of the transit, when the sun was near its greatest distance from the earth; and consequently 8 65", when the sun is at its mean distance from the earth. From this Mr. Ferguson makes 23,882.84 the number of semi-diameters of the earth, which it is distant from the sun. As he reckoned the semi-diameter of the earth 3985 miles, multiplying these together he made the mean distance of the earth from the sun 95,173,127 miles. If we take the semi-diameter of the earth 3982 miles, which it would be, according to Dr. Bowditch, and multiply it by the same number 23,882.84, the result is 95,101,469, for the earth's mean distance from the It is amusing and gratifying, to know what vast interest

sun.

was felt m the transit of 1761, and what great pains were taken to observe it with accuracy.

Early in the morning," June 6th, "when every astronomer was prepared for observing the transit, it unluckily happened, that both at London and the royal observatory at Greenwich, the sky was so overcast with clouds, as to render it doubtful whether any part of the transit should be seen; and it was 38 minutes 21 seconds past 7 o'clock, apparent time, at Greenwich, when the Rev. Mr. Bliss, astronomer royal, first saw Venus on the sun

Mr. Short made his observations at Saville house, London, in the presence of several of the royal family. The transit was observed at several other places in England; at Paris by M. De la Lande. At Stockholm observatory, latitude 59°. 20 N. longitude 18' east from Greenwich, the whole transit being visible, was observed by Wargentin. It was observed also at Hernosand in Sweden, at Torneo in Lapland, at Tobolsk in Siberia, at Madrass, at Calcutta, and at the Cape of Good Hope. Dr. Maskelyne's observations at St. Helena "were not completely successful on account of the cloudy state of the weather."

The parallax deduced from observations on the transit of 1761, was confirmed by the transit of 1769 without material alteration.

Professor Vince has given the following convenient method of ascertaining when the transits of Mercury and Venus will happen. "The mean time from conjunction to conjunction of Venus or Mercury being known, and the time of one mean conjunction, we shall know the time of all the future mean conjunctions Observe, therefore, those which happen near to the node, and compute the geocentrick latitude of the planet at the time of conjunction, and, if it be less thau the apparent semi-diameter of the sun, there will be a transit of the planet over the sun's disk; and we may determine the periods when such conjunctions happen in the following manner. Let P the periodic time of the earth, p that of Venus or Mercury. Now that a transit may happen again at

the same node, the earth must perform a certain number of complete revolutions, in the same time that the planet performs a certain number, for then they must come into conjunction again at the same point of the earth's orbit,or nearly in the same position in respect to the node. Let the earth perform x revolutions whilst the planet performs y revolutions; then will P x = p y, therefore, Ρ Now P$65.256,

x

=

Уу P

and for Mercury, p= 87.968; therefore

x

p 87.968 29

=

y P 365,256

From this he ascertained, "that 1, 6, 7, 13, 33, 46, &c. revolutions of the earth are nearly equal to 4, 25, 29, 54, 137, &c. revolutions of Mercury, approaching nearer to a state of equality the further you go. The first period or that of one year is not sufficiently exact; the period of six years will sometimes bring on a return of a transit at the same node; that of seven years more frequently; that of 13 years still more frequently, and so on." For Venus p=224.7; From this he makes the periods

hence

p

224,7

y P 365,256*

8, 235, 713, &c. years. "The transits at the same node will, therefore, sometimes return in 8 years, but oftener in 235, and still oftener in 713."

Those, who wish to be more particular, and calculate or project the transits of these planets, can have recourse to those larger works in astronomy, where the motions of the planets, their aphelia and nodes with secular variations, may be found at length in tables. Their insertion here would exceed the limits designed for this work.

The following table, showing the times of transits, was formed by abridging Dr. Brewster's account of them in his supplement to Ferguson.

1769 November 9:868 November 42117 December 10 2984 June

14

CHAPTER XI.

COMETS.

Comets are large opaque bodies, moving round the sun in various directions, and in very eccentric orbits. It is not wonderful, if, as we are told, comets were considered portentous in the days of barbarism and superstition; if they were regarded as the harbingers of war, famine, and pestilence; if they presented to the frighted imaginations of men the convulsions of states, the dethronement of kings, and the fall of nations. Astronomers of the present day view them in a light entirely different. By the allwise Creator they are without doubt designed for benevolent and important purposes; though most of those purposes must be to us unknown, or deduced only by reasoning from analogy. A comet, when viewed through a good telescope, resembles a mass of aqueous vapour surrounding a dark nucleus, of different shades in different comets; though sometimes no nucleus is observed. Of the last kind were some seen by Dr. Herschel, and some by his sister. As the comet approaches the sun, its nebulous light becomes more brilliant, its luminous train increas