April (), 1874J 



I^ATUR^ 



449 



phenomena, are in part regulated by the positions of 

 Venus and Jupiter with respect to the sun.* 



Mr. Horrox's observations have been of great value 

 in perfecting the tables of Venus. He was further led 

 by a kind of analogy, much in vogue at the time, to 

 deduce from his observations a value of the sun's dis- 

 tance from the earth. It will readily be understood that 

 if we could find out what size, in angular measure, the 

 earth would seem to have if viewed from the sun, we 

 should have a means of determining how much greater 

 the distance from the earth to the sun is than the diameter 

 of the earth. For, suppose S (Fig. 6) to be the position 

 of an observer placed upon the sun, S L, S M the direc- 

 tions in which he must look to see the opposite sides of 

 the earth, so that the inclination of these lines is known. 

 All we have to do now is to draw a circle of any size 

 and move it about between the lines S L, S M, until it 

 just fills the interval, as at E E'. If now we measure 

 with a ruler how much greater S E is than E E' we shall 

 know the distance from the earth to the sun, the earth's 

 diameter being taken as the unit of measurement ; and 

 if we multiply this by the diameter of the earth measured 

 in miles we shall know the distance from the earth 

 to the sun, in miles. All that we require to know 

 is the size of the angle E S E'. Horrox esti- 

 mated the probable value of this angle in the follow- 

 ing manner. From the observations of Tycho Brahd 

 it appeared that during the transit of Venus the apparent 

 diameter of the planet would be 12' 18" ; while Lansberg 

 found 12' 21"; and Kepler 6' 51". Horrox found from 

 his measurements that it was only i' 16". The error of 

 ordinary observations arises from the apparent enlarge- 

 ment of the planet's disc through irradiation. Gassendi 

 had in the same manner, during the transit of Mercury in 

 1631, reduced the apparent diameter of Mercury to 

 scarcely 20". From these data it can be found that the 

 apparent diameters of Venus and Mercury as seen from 

 the sun would be 21" and 34" respectively. Proceednig 

 to the other planets he arrived at the general conclusion 

 that each of them would, if viewed from the sun, have an 

 apparent diameter of aboutzS". Applying this to the case of 

 the earth, he showed that the distance of the earth from 

 the sun must be 7,500 diameters of the earth (it may be 

 well here to state that the latest measurements show the 

 apparent diameter of the earth as viewed from the sun to 

 be about 18", and the distance = 11,400 diameters). 



This analogy by Horrox gave a much closer approach to 

 the truth than any previous cotijectures. 



Before taking leave of Horrox, we must say a few words 

 to his memory. He died at the early age of 23. During 

 his short career he showed a remarkable aptitude for the 

 acquisition of knowledge, and for the striking out of new 

 ideas. He lived at a time when the scientific spirit of 

 the age was leading up to the theory of gravitation, and 

 many passages in his writings show that he had even then 

 grasped the grand idea of the theory, and that he was 

 well fitted to become its constructor and its expounder. 

 His researches on the lunar and planetary theories indicate 

 the magnitude of his talents. 



We have already mentioned some of the uses to which 

 careful observations of a transit of Venus may be applied ; 

 viz. the correction of the elements of the planet's orbit. 

 But the observation also leads us to a knowledge of the 

 distance of the sun from the earth, and in a manner much 

 more direct and logical than that employed by Horrox. 

 There is an opinion very pre\-alent that a transit of Venus 

 affords the best means of determining this distance. So 



far as our present knowledge goes we are hardly justified 

 in such a statement until after the observations that shall 

 be made in the present year. 



Before entering upon the method by which we measure 

 the sun's distance, let us devote a few lines to explaining 

 what is meant by the wor A paral /ax, which is continually 

 employed in such discussions. Let a man stand in a 

 street exactly north of a lamp-post. The lamp-post will 

 seem to be south of him. Now let him cross over to the 

 other side of the street. The lamp-post will now be in 

 some other direction, such as south-west. This move- 

 ment of the direction of the lamp-post is the effect of 

 parallax. Now let us suppose, by a stretch of imagina- 

 tion, that a man observes the moon from the centre of 

 the earth. He will see it in the direction C M (Fig. 7). If 

 now he goes to A he will see it in the direction AM. The 

 angle AMC through which the moon appears to have been 

 moved is the parallax of the moon as observed from A. 



It will be noticed that the parallax is an error introduced 

 ! into the observed position of the moon, and which must 

 , be allowed for if we wish to get the position as seen from 

 I C. Moreover, the parallax at B is different from what it 

 I is at A. But at no point on the surface of the earth can 

 I the parallax be greater than at A. And if we know the 

 I parallax of the moon at A, we can deduce that at B from 

 I a knowledge of the relative positions of A, B, and C. 



Hence it is useful to have a distinct name for the parallax 

 I at A. Now it will be noticed that a line drawn from C 

 , to A is the vertical line at A ; hence the moon M will ap- 

 !i pear to be on the horizon to an observer at A ; and hence 



searches of Messrs, De la Rue. Stewarl, and Loewy 

 vviuiti.iiv.. ^. ^un-spot frequency with planetary positions, " Phil. "^ 

 ^1 also the writings of iMr. Meldrum, Mr. E. J. Stone, Pro/.^B^alf 

 M. Poey, and others, ' ' - *- - - -'"" 



sun-spot frequency. 



. - , Stewart, 



tiic connection between terrestrial phenomena and 



the moon has its greatest parallax when on the horizon. 

 For this reason the parallax at A is called the moon's 

 horizontal parallax. Further, since the equatorial dia- 

 meter of the earth is greater than the polar, the parallax 

 will be greater, when the moon is on the horizon, to an 

 observer at the equator than to an observer at one of the 

 poles. Hence the greatest parallax we can have occurs 

 when the moon is on the horizon and the observer is at 

 the equator ; this value of the parallax is the equatorial 

 horizontal parallax. In the same way the sun has an 

 equatorial horizontal parallax, and if we knew its value we 

 could find out the sun's distance from the earth as ex- 

 plained above (Fig. 6). 



George Forbes 



{To be continued.) 



