April 22,, 1 8 74 J 



l^ATVl^n 



to the possibility of determining the sun's parallax by 

 means of the transit of an inferior planet. He has been 

 showing methods of finding the parallax of a planet by 

 comparison of observations made at different parts of the 

 earth upon the position of the planet compared with that 

 of a star. He then takes, in place of a fixed star, another 

 planet, the two being in one line, as seen from the earth. 

 The application of ttiis to the case of Mercury or Venus 

 and the sun, was obvious. 



But Halley was the first to see clearly what a powerful 

 means of determining the sun's parallax an obser- 

 vation of contact really is. So far as I can discover, 

 he first mentions the method in a letter to Sir 

 Jonas Moore, written at St. Helena in 1677,* just 

 after having seen a transit of Mercury. The exact- 

 ness with which he believed the time of contact to be 

 determinable, led him frequently afterwards to urge his 

 countrymen to make every effort to utilise the method on 

 the occasion of the transits of 1761 and 1769, when he 

 should be dead.f And thus, in addition to his celebrated 

 prediction of a comet, he left a second legacy to his suc- 

 cessors, who, as Enghshmen, might be entitled to be 

 proud of his foresight though he could not live to reap 

 the glory of it. 



It is a matter of some difficulty to show, in an elemen- 

 tary manner, the way in which the value of the sun's 

 parallax can be found from observations of contact. We 

 will try, however, to put it in a light which anyone, with 

 a little attention, will understand. 



1. It must be thoroughly understood, from what has 

 already been said, that if we know the amount of the 

 sun's parallax we know its distance. In other words, if 

 we know the angle subtended by any known distance on 

 the earth's surface at the distance of the sun. 



2. We know that the relative positions of the earth, 

 Venus, and the sun, are given by supposing the earth to 

 go round the sun in 365 days, and Venus in 224 days. 

 Or, if we please, we may take no account of the earth's 

 revolution, but suppose it fixed, in which case the revo- 

 lution of Venus rclalivcly to the earth (i c. the synodical 

 revolution) is 584 days. 



3. If, then, Venus moves round the sun through 360° 

 relatively to the earth in 584 days, she moves through 



— ?- of that in one day, and through -^~ — of a degree 

 584 5H X 24 



in one hour ; which is at the rate of about I5- seconds of 

 arc in a minute of time. 



Now wc are ready to understand H alley's reasoning. 



Let A (Fig. 10) be the position of an observer on the 

 • earth at the time of ist internal contact. S is the sun, and 

 V, is now the position of Venus. This observer sees the con- 

 tact earlier than a hypothetical observer at the earth's centre 

 would see it, by the time Venus takes to move over V,V.,. 

 If we knew by calculation the instant when an observer 

 at E would see it, and the observer at A saw it 8 minutes 

 sooner, then, since Venus moves over iV''" a minute, 

 she has moved over Sx i^ orgf' of arc in this time, and 

 hence we learn that the angle A S E = gf". 



Suppose that by the time of the last contact the pomt 

 A on the earth's surface has been carried by her rotation 

 to B : the time of the last contact will now be too 

 late by 8' ; since the whole duration of the transit as 

 seen by this observer is 16' too long, and the angle 

 moved over by Venus in 16' is the sum of the sun's 

 parallax as seen from A and from B. 



But we cannot calculate with absolute accuracy the 

 duration a transit would have when seen from E, 

 because we should require to know more accurately than 

 we do the values of Venus' and the sun's diameters. 



Halley got rid of this by taking another station which 

 should be in the position A at the beginning of the transit. 

 In the case we have been considering the time of the 



• Hooke's " Lectures and Collections," 1673. 



* "Catalogus SfUaruin Australium ; " also "Phil. Trans., 1694 and 



first contact would here be too late by 8 minutes ; and 

 if this place had reached B' by the end of the transit, the 

 time of contact would be too soon by 8 minutes. Hence in 

 this case the whole duration would be shortened by 16 

 minutes ; but in the former case it was lengthened by 

 16 minutes. Hence 32 minutes is the time taken by 

 Venus to pass over an angle equal to the sum of the 

 parallaxes in the four cases considered. This difference 

 of duration, whether it be 32 minutes or anything else, 

 is a quantity which can be observed. Now Venus moves 

 over about ij" of arc in a minute, or 38?" in these 32 

 minutes. Hence one-fourth of 38I" or 9'^" would appear, 

 from the above hypothetical observation, to be the value 

 of Venus's parallax. 



It must be noticed that we have here supposed that the 

 transit takes exactly twelve hours, whereas the longest 

 transit cannot exceed 8 hours. We have also supposed 

 that two stations had been selected which were exactly 

 situated so as to bring out the full eft'ect of parallax at 

 the time of each observation. These suppositions have 

 been introduced only to simplify the understanding of the 

 method. Anyone who has followed the above explana- 

 tion will see how the method may be applied to actual 

 cases that may occur. 



Halley saw (what many people fail to see even now) that 

 the great accuracy of the method consists in this, that in 

 one second of time Venus moves over about o"'o2 ; and if 

 we can determine the time of contact, with an error of no 

 more than a second, we are measuring the sun's parallax 

 with an error of no more than '02 of a second of arc. 



Halley even pointed out the best stations for observa- 

 tion. We may consider the earth to be at rest if we 

 suppose \'enus to move with the velocity she has relative 

 to the earth. He supposed that the planet would cross 

 near the sun's centre, and that the transit would occupy 

 about eight hours. An observer in India would see the 

 commencement of the transit four hours before mid-day, 

 and the end of the transit four hours after mid-day. But, 

 in the meantime, the part of the earth where he is has 

 been moving from west to east, and Venus has moved 

 from east to west, hence the duration of transit will have 

 been shortened. But at Hudson's Bay the transit begins 

 just before sunset and ends just after sunrise, that part 

 of the earth having moved in mean time from east to 

 west so as to lengthen the transit ; and thus at one place 

 the duration of transit is lengthened, and at the other 

 shortened, and the difference of time depends upon the 

 parallaxes of Venus and the sun * at the two stations, and 

 after finding these parallaxes we can calculate the equa- 

 torial horizontal parallax. 



George Forbes 

 [To be continued^ 



THE LECTURES AT THE ZOOLOGICAL 



SOCIETY'S GARDENS 



I. 



ON Tuesday, April 14, Mr. P. L. Sclater, F.R.S., gave 

 the Introductory of the twelve lectures which are to 

 be continued during the spring. His remarks on that 

 occasion were chiefly confin d to the subject of Zoological 

 Gardens in general. After an interesting account of the 

 most important continental gardens, including those of 

 Paris, Amsterdam, Antwerp, Beriin, and Hamburg, he 



• This lengthening or shortening of the time of transit will be rendered 

 more evident by an analogy. K person standiug still sees a carriage pass 

 between him and a distant house The carrmge will take a certain time to 

 pass the house. But if he be also moving, and in the sime direction with 

 the carriage, the transit of th- carri.age will take longer : but if he move in 

 the opposite direction to the carriage, the transit will take a shurter time. 

 If then, two persons be seated at opposite sides of a merry-gn-i ound, so that 

 at' the time the carriage seems to be passing the distant house, one observer 

 is moving with the carriage and the other in the opposite direction ; then 

 one observer will see the time lengthened, and the other shortened Now. 

 the world is such a merry-go-round, and the positions of these two people 

 correspond to the positions of India and Hudson s Bay. as pointed out by 

 Halley. 



