232 



KNOWLEDGE. 



[October 1, 1895. 



distance of Mercury will be represented by 387, Venus 723, 

 Mars 1523, the minor planets 208G to 4262, Jupiter 5203, 

 Saturn 9538, Uranus 19,183, and Neptune 30,055. These 

 are the mean or average distances, the orbits not being 

 exact circles but ellipses of various eccentricities, that of 

 Mercury — among the large planets — being the most 

 eccentric, and that of Venus the least so. Among the 

 minor planets, the eccentricities vary from 0, or a perfect 

 circle, to 0'44, the value found for a small planet discovered 

 by M. Wolf in November, 1891. 



The first scientific attempt to determine the sun's 

 distance from the earth seems to have been made by 

 Aristarchus, of Samos. His method was to note the 

 exact time when the moon is exactly half full, and then 

 to measure the apparent angle between the centres of the 

 sun and moon. It is evident that when the moon is half 

 full the earth and sun, as seen from the moon, must form 

 a right angle with each other, and if we could then 

 measure the angle between the sun and moon, as seen 

 from the earth, all the angles of the right-angled triangle 

 formed by the sun, moon and earth would be known, and 

 we could deduce at once the relative distances of the sim 

 and moon from the earth. This method is, of course, 

 perfectly correct in theory, but in practice it would be 

 impossible, even with a telescope, to determine the moment 

 when the moon is exactly half fuU, owing to the irregu- 

 larities of its surface. Aristarchus had no accurate 

 instruments, and no knowledge of modern trigonometry, 

 but by means of a tedious geometrical method he concluded 

 that the sun is nineteen times further from the earth than 

 the moon. This result we now know to be far too small, 

 the sun's distance from the earth being in reality about 

 three hundred and eighty-eight times the moon's distance. 



In modem times the sun's distance has been determined 

 by various methods. The most recent results tend to 

 show that the sun's parallax, as it is termed, cannot differ 

 much from 8-81 seconds of are. The solar parallax is 

 the angle subtended at the sun by the earth's semi- 

 diameter. A parallax of 8'81 seconds implies that the earth's 

 mean distance from the sun is about 92,790,000 miles. 

 Multiplying this number by the figures given above, we 

 find that the mean distances of the planets from the sun 

 are as follows, in round numbers : — Mercury 35,909,000 

 miles, Venus 67,087,000, Mars 111,381,000, the minor 

 planets 193,000,000 to 395,170,000 miles, Jupiter 

 482,780,000, Saturn 885,105,000, Uranus 1,779,990,000, 

 and Neptune 2,788,800,000. This makes the diameter of 

 the solar system, so far as at present known, about 5578 

 millions of miles. Across this vast space hght, travelling 

 at the rate of 186,300 miles per second, would take eight 

 hours nineteen minutes to pass. 



But vast as this diameter really is, compared with the 

 size of our earth, or even with the distance of the moon, 

 it is very small indeed when compared with the distance 

 of even the nearest fixed star, from which light takes over 

 four years to reach us. The most reliable measures of the 

 distance of Alpha Centauri, the nearest of the fixed stars, 

 j)laces it at 275,000 times the sun's distance from the earth, 

 or about 9150 times the distance of Neptune from the sun. 

 If we represent the diameter of Neptune's orbit by a circle 

 of two inches in diameter. Alpha Centauri would he at a 

 distance of 762 feet, or 254 yards, from the centre of the 

 small circle. If we make the circle representing Neptime's 

 orbit two feet in diameter, then Alpha Centauri would be 

 distant from the centre of this circle 9150 feet, or about If 

 mile. As the volumes of spheres vary as the cubes of their 

 diameters, we have the volume of the sphere which extends 

 to Alpha Centauri 766,000 milhon times the volume of the 

 sphere containing the whole solar system to the orbit of 



Neptune. If we represent the sphere containing the solar 

 system by a grain of shot one-twentieth of an inch in 

 diameter, the sphere which extends to Alpha Centauri 

 would be represented by a globe 38 feet in diameter. 



It wOl thus be seen what a relatively small portion of 

 space the solar system occupies compared with the sphere 

 which extends to even the nearest fixed star. But this 

 latter sphere, vast as this is, is again relatively small com- 

 pared with the size of the sphere which contains the great 

 majority of the visible stars. Alpha Centauri is an 

 exceptionally near star. Most of the stars are at least ten 

 times as far away, and probably many a hundred times 

 further off. A sphere with a radius lOU times greater 

 than the distance of Alpha Centauri would have a million 

 times the volume, and therefore 766,000 billion times the 

 volume of the sphere which contains the whole solar 

 system ! 



From these facts it will be seen that enormously large 

 as the solar system absolutely is, compared with the size of 

 our own earth, it is, compared with the size of the visible 

 universe, merely as a drop in the ocean. 



PHOTOGRAPHS OF THE CLUSTER MESSIER 

 13 HERCULIS. 



By IsAic EoBERTs, D.Sc, F.R.S. 



R.A. 16h. 38m. 6s., Decl. N. 36° 39-0'. 



THE photographs were taken with the 20-inch 

 reflector ; that with an exposure of five minutes, 

 at sidereal time 16h. 42m., on June 15th, 1895, 

 and the other with an exposure of sixty minutes, 

 between sidereal time 14h. 51m. and 15h. 51m., 

 on May 28th, 1895. 



Scale, 1 milhmetre to 6-18 seconds of arc. 



References. 



N. G. C. No. 6205, G. C. No. 4230, h 1968. Sb J. 

 Herschel, Phil. Trans. 1833, p. 458, PI. XVI., Fig. 86. 

 Lord Eosse, Phil. Trans. 1861, p. 732, PI. XXVIII., Fig. 

 33, and Ohs. of Neb. and CI. of Stars, p. 150. A. C. 

 Ranyard, Knowledge, 1st May, 1893, pp. 90-93. 



The photograph with an exposure of five minutes shows 

 the stars with only a faint trace of nebulosity at the 

 central part of the cluster, and that with sixty minutes' 

 exposure shows the central part involved in nebulosity so 

 dense that, on the print, the stars cannot be seen in the 

 midst of it, though on the negative they are clearly visible. 

 The two prints, when correlated, therefore, convey to us 

 nearly the same amount of information as can be gathered 

 from the negative exposed for sixty minutes. 



Nine photographs of the cluster have been taken by me 

 during the past eight years. The first, on May 22nd, 1887, 

 is published in Phutoi/raplis of Stars, Star-Clusters, and 

 Nebula, PI. 34, p. 93. An interval of fully eight years has, 

 therefore, elapsed since these and the first photograph 

 were taken, and now, by the publication of these photo- 

 graphs in a form available like the first, and enlarged to 

 the same scale, there is evidently work ready to hand for 

 those who take a practical interest in astronomy to con-elate 

 these new photographs with the earlier one, in order to find 

 out what, if any , change or changes have taken place amongst 

 the stars during the interval of eight years. These 

 operations can readily be performed by placing the dual 

 photographs of 1887 and 1895, that have been exposed 

 during sixty minutes each, side by side, and judging by 

 eye-alignments of the stars if changes have taken place 

 amongst them. Another method is to use a reseau ruled 

 on glass, about ten centimetres square, with the inter- 



