214 



THE POPULAR EDUCATOR. 



4 7 10 16 28 52 100 



Mercury. Venus. Earth. Mars. Jupiter. Saturn. 



Thus, if we take 10 to represent the distance of the Earth, we 

 shall find that 4 represents that of Mercury, 7 that of Venus, 

 and so on. No planet was, however, known to occupy the space 

 between Mars and Jupiter, corresponding to the figure 28. 

 There was thus a gap left in the system, and Bode stated his 

 conviction that, as the sky was more carefully watched, and 

 better telescopes were employed, such a body would be dis- 

 covered. Nor was his prediction long unfulfilled, for on the 1st of 

 January, 1801, a planet, afterwards named Ceres, was discovered 

 by Piazzi, moving at a distance corresponding very closely with 

 that assigned to it by the law. This planet is, however, very 

 small, and soon afterwards three more were discovered moving 

 almost at the same distance. These were named Pallas, 

 Juno, and Vesta. Up to the present time (July, 1869), 108 of 

 these minute bodies have been detected thus revolving around 

 the sun, their distances and periods closely resembling one 

 another ; and thus in the place of one planet, we have a 

 large group of small ones. The other planets, namely, Uranus 

 and Neptune, which have been discovered subsequently to the 

 announcement of this law, are found not to differ very greatly 

 from it, though the difference in the case of Neptune is much 

 greater than in any of the others. 



We must now just look at the services which have been 

 rendered to the science of astronomy by another of those 

 men whose names will ever stand foremost in its annals Sir 

 William Herschel. He was a man of somewhat humble origin, 

 and unable to procure a telescope sufficiently powerful to enable 

 him to understand some of the mysteries of the heavens. He 

 had, however, an intense desire to do so, and having acquired a 

 knowledge of the principles of the telescope, set himself to the task 

 of constructing one. In this he succeeded well ; and altogether 

 he is said to have ground upwards of 500 specula for reflecting 

 telescopes. In March, 1781, aided with one of these instru- 

 ments, he was examining the sky, when he came upon a small 

 star, which, as he examined it with higher powers, seemed to 

 exhibit a disc. He, accordingly, took an accurate note of its posi- 

 tion, so as to watch it again on another evening. When he 

 again examined it, it was at once clear that it had changed 

 its position. The idea, however, that it was a new planet did 

 not appear to enter at all into his mind, so accustomed had 

 every one been to regard Saturn as the extreme member of 

 our system. Accordingly, he set it down as a new and strange 

 comet which he had discovered, and announced it as such. Its 

 motions, however, soon showed that, unlike the comets, it moved 

 in an orbit of but small eccentricity, and it was then found to 

 be a planet revolving outside Saturn. This planet Herschel 

 named Georgium Sidus, in honour of the king who had been 

 his patron, but the name was afterwards altered to Herschel, 

 and finally to Uranus, by which name it is now known. 



Soon after this he constructed a much larger instrument, the 

 speculum of which was four feet in diameter, and the tube 

 forty feet long. The penetrating power of this instrument was 

 reckoned at 194 ; that is, it would penetrate into space to a 

 depth 194 times as great as could the unassisted eye. With this 

 he discovered two more satellites of the planet Saturn. Sis out 

 of the eight which revolve around Uranus were also detected by 

 him ; so that he made a very large addition to the number of 

 the heavenly bodies then known. But his most important dis- 

 coveries were made about the nebulas and stars. A large num- 

 ber of double and triple stars were first observed by him, and 

 carefully noted, with a view of determining, if possible, 

 whether any of them exhibited any sensible parallax. The 

 Milky Way was also resolved by the power of his magnificent 

 telescope, and thus some estimate was formed of the size of 

 the cluster of which our complete system forms but an insig- 

 nificant fraction. 



Sir John Herschel, the son of this great man, displayed a 

 similar love for astronomy ; but so many names now occur, 

 and so many fresh discoveries have been made, that we must 

 leave them to be noticed in their special places. There is, how- 

 ever, one instrument which we must refer to before closing this 

 historical sketch of the science, as having been of the utmost 

 service in the determination of many difficult points. This is a 

 reflecting telescope, erected by the late Earl of Rosse at Pai-sons- 

 town, the speculum of which is six feet in diameter, and its focal 

 length fifty-four feet. The whole of the work of this was 



carried out under the personal superintendence of Lord Rosse, 

 and the instrument may fairly be ranked as one of the wonders 

 of the age. 



LESSONS IN ALGEBRA. XIX. 



EXERCISE 30. MISCELLANEOUS PROBLEMS IN SIMPLE 

 EQUATIONS (continued.) 



45. Divide the number 68 into two such parts, that the differ, 

 ence between the greater and 84 shall be equal to three times 

 the difference between the less and 40. 



46. Four places are situated in the order of the letters A, B, 



C, D. The distance from A to D is 34 miles. The distance 

 from A to B is to the distance from C to D as 2 to 3 ; and j of 

 the distance from A to B, added to half the distance from C to 



D, is three times the distance from B to C. What are the 

 respective distances ? 



47. Divide the number 36 into three such parts, that i of the 

 first, | of the second, and | of the third, shall be equal to each 

 other. 



48. A merchant supported himself 3 years for <50 a year, and 

 at the end of each year added to that part of his stock which 

 was not thus expended a sum equal to ^ of this part. At the 

 end of the third year his original stock was doubled. What waa 

 that stock ? 



49. A general having lost a battle, found that he had only 

 half of his army + 3,600 men left fit for action ; | of the army 

 + 600 men being wounded ; and the rest, who were of the 

 whole, either slain, taken prisoners, or missing. Of how many 

 men did his army consist ? 



50. To find a number to the sum of whose digits if 7 be 

 added, the result will be 3 times the left-hand digit ; and if from 

 the number itself 18 be taken, the digits will be inverted. 



51. To find a number consisting of two digits, the sum of 

 which is 5 ; and if 9 be added to the number itself, the digits 

 will be inverted. 



52. There is a certain fraction such, that if you add 1 to its 

 numerator it becomes ; but if you add 3 to its denominator, 

 it becomes ^. Required the fraction. 



53. It is required to find two numbers whose difference is 7, 

 and their sum 33. 



54. At a town meeting, 375 votes were cast, and the person 

 elected to office had a majority of 91. How many votes had 

 each candidate ? 



55. A post stands 1 in the ground, 1 in the water, and 10 feet 

 above the water. What is the whole length of it ? 



56. A young man, the first day after his arrival in London, 

 spent | of his money, the second day |, the third day , and 

 he then had only 26 pence left. How much did he have at 

 first? 



57. A person being asked his age, answered that 2 of his age 

 multiplied by T 1 5 of his age, would give a product equal to hia 

 age. How many years old was he ? 



58. A man leased a house for 99 years ; and being asked how 

 much of the time had expired, replied that | of the time past 

 was equal to | of the time to come. How many years had 

 expired ? 



59. On commencing the study of his profession, a man found 

 that } of his life had been spent before he learned his letters, ^ 

 at a public school, at an academy, and 4 years at college. How 

 old was he ? 



60. It is required to find a number such, that whether it be 

 divided into two equal parts, or three equal parts, the product 

 of its parts will be equal. 



61. Two persons, 154 miles apart, set out at the same time 

 to meet each other, one travelling at the rate of 3 miles in 2 

 hours, the other 5 miles in 4 hours. How long will it be before 

 they meet ? 



62. A man and his wife usually drank a cask of beer in 12 

 days, but when the man was absent it lasted the wife 30 days. 

 How long would it last the man if his wife were absent ? 



63. A shepherd being asked how many sheep he had, replied, 

 if he had as many more, half as many more, and 7^ sheep, he 

 would then have 500. How many had he ? 



64. A farmer hired two men to do a job of work for him ; one 

 could do the work in 10 days, the other in 15. How long would 

 it take both together to do the same job? 



