May 7, 1874] 



NATURE 



13 



the one case this chord is farther from the sun's centre, 

 and consequently shorter than the other. The duration 

 of the transit, so far as this effect is concerned, is directly 

 proportional to the length of the chord traced out by 

 Venus. Thus from observation we obtain the lengths of 

 these chords ; and by geometry we can deduce the least 

 distance between the centres of the sun and Venus at 

 each of the two stations, and hence we can determine the 

 sun's parallax. Fig. 12 illustrates this point very clearly. 

 The duration is determined by two distinct observations 

 made at each station, the intenial contact at ingress and 

 the internal contact at egress. The time of an internal 

 contact is the time at which Venus appears to be just 

 wholly within the sun's disc. These two times must be 

 accurately determined ; they will be separated by an 

 interval of nearly four hours. Fig. 12 represents the illumi- 

 nated hemispheres of the globe at the time of ingress and 

 at the time of egress respectively in 1874. At either of 

 these epochs the sun will be visible from every place 

 marked on the corresponding map. The sun will be verti- 

 cal at the place occupying the centre of the map ; at all 

 stations near the edges of the map the sun will at th.it 

 time be near the horizon. The point from which the 



phenomenon will be first observed is there indicated, and 

 likewise the point at which it is last seen. Straight lines 

 are drawn across each map, and the hours marked upon 

 them indicate the time at which the phenomenon will be 

 seen. 



Fig. 13, taken from Lockyer's "Popular Astronomy," 

 shows the same facts for the transit of 1 882. 



Take now the case of two particular stations. At some 

 point on the east coast of China the ingress is accelerated 

 by 6 minutes, but at the same point the egress is retarded 

 7 minutes ; consequently the duration of the transit is 

 lengthened 13 minutes. Again, at Kerguelen's Island the 

 ingress is retarded 10 minutes, while the egress is accele- 

 rated 5 minutes. Here then the duration of the transit 

 is shortened 15 minutes. The difference in duration as 

 observed from these two stations will therefore be about 

 28 minutes. These maps have no pretension to great 

 accuracy. They are calculated upon a certain assump- 

 tion as to the value of the solar parallax which is pro- 

 bably not far from the truth. 



In 1761 considerable preparations were made for ob- 

 serving the transit of Venus in this manner. The Enghsh 

 were represented by Messrs. Mason and Dixon at the 





Cape of Good Hope, and the French by the celebrated 

 Pingri^ at the island of Rodriguez. A host of observers 

 watched the phenomenon from northern regions. Unfor- 

 tunately at scarcely a single station was the transit seen 

 completely. Hence the method of durations was inap- 

 plicable, and another, originally proposed by De I'lsle,* 

 came into use. This takes advantage of the fact that the 

 ingress will take place later when seen from some parts 

 of the earth than from other parts, as explained above ; 

 so with the egress of the planet from the sun's disc. 

 Hence, if the .absolute time of contact of Venus with the 

 sun's edge at ingress or at egress be observed at two 

 places suitably chosen, the difference in time will be a 

 measure of Venus's parallax. 



The method of De 1 Isle will perhaps be better under- 

 stood by looking upon the orbit of Venus as a vast pro- 

 tractor for measuring small angles. Venus passes rela- 

 tively to the earth round the sun, that is through 360° in 

 584 days. From this it follows that she passes over i'''5 

 m one minute of time. Now conceive two straight lines 

 to be drawn from the sun's edge, the one to the Sandwich 



* Histoire de I'Acad. des Sciences, p. 112. 



Islands, where the ingress is most accelerated, and the 

 other to Kerguelen's Island, where it is most retarded. 

 Venus passes across these two lines like the radial arm of 

 a protractor. The observed difference in the time of 

 observing the phenomenon at these two stations will be 

 about 21 minutes. Of this about 1 1 minutes is due to the 

 fact that the Sandwich Islands are north of Kerguelen's 

 Island, as before explained ; the remaining 10 minutes 

 or so will be a measure of the angle between the two lines 

 drawn from the sun's edge to the two stations. Since 

 Venus passes over i"'S in i minute, 10 minutes gives us 

 15" for the effect of parallax looked at in this hght. 



It is a comparatively easy matter to set one's clock ac- 

 curately to local time by astronomical observations. But 

 it is a matter of considerable difficulty for an observer in 

 Kerguelen's Island to set his clock accurately to the local 

 time of the Sandwich Islands, or vice versd. Conse- 

 quently there will be some difficulty in determining the 

 absolute difference of time of contact as observed at these 

 two stations. The difficulty simply consists in determin- 

 ing the longitude accurately. This is a matter involving 

 a long series of astronomical observations even now ; still 



