ut prælium incipiant, circumspectant. Pudor deinde commovit Plain in thy neatness? Oh how oft shall he aciem, et clamore sublato indigne in unum hostem tela conji. On faith and changed gods complain, and seas ciunt. Qua quum in objecto cuncta scuto hæsissent, neque ille Rough with black winds and storms minus obstinatus ingenti pontem obtineret gradu, jam impetu Unwonted shall admire. conabantur detrudere virum, quum simul fragor rupti pontis, Who now enjoys thee credulous, all gold, simul clamor Romanorum alacritate perfecti operis sublatus, Who always vacant, always amiable pavore subito impetum sustinuit. Tum Cocles, “Tiberine Hopes thee, of flattering gales pater," inquit, "te sancte precor, hæc arma et hunc militem Unmindful. Hapless they propitio flumino accipias." Ita sic armatus in Tiberim desiluit, To whom thou untried seem'st fair. Me in my vowed multisque super incidentibus telis incolumis ad suos tranavit, Picture the sacred wall declares to have hung rem ausns plus famæll habituram ad posteros quam fidei. Grata My dank and dropping weeds erga tantam virtutem civitas fuit; statua in comitio posita, To the stern god of sea.-Milton. agri quantum uno die circumaravit datum. NOTES. 1. Cedentiam pugnæ, retreating ; lit., yielding to the battle. LESSONS IN ASTRONOMY.-IV. 2. Et quod, etc., the most tumultuous part of the fray. 3. Revocantibusc, etc., while they who were cutting down the bridge were RESULTS OF NEWTON'S LAWS-FOUNDATION OF THE ROYAL calling them to come back. OBSERVATORY-FLAMSTEED-HALLEY-CALCULATION OF 4. Etruscorum, Clusium, from whence Porsenna came, was a city ORBIT OF COMET-BRADLEY-BODE'S LAW-DISCOVERIES of Etraria. OF HERSCHEL. 5. Prorocare-increpare, historical infinitives. 6. Servitia, put for servos, the abstract for the concrete. So knowledge of the fundamental laws of motion of the worlds THE grand discovery of Newton seems to have completed our we find militia for milites ; juventus for juvenes. To agree with it Live around us, and has afforded to us another most convincing puts immemores, a constructio kata üveg (according to the sense). 7. Suæ libertatis, etc. The infin. venire depends upon the verb proof of the wisdom and power of Him who created all things. increpare ; taunting them for coming, slaves of a proud king as they To make and sustain these bodies requires the power of Omniwere, and careless of their own freedom, to attack the freedom of others. potence; but when we find that all their motions depend on the 8. Oppugnatum ; supine in um; after venire, a verb of motion. two simple laws of inertia and mutual attraction, and that all 9. In unum hostem, on their solitary foe. their variations and movements can be fully explained by these ; 10. Conabantur, etc., hostes, when the darts had stuck fast the enemy and further, when deeper investigation shows us that though (who had thrown them) endeavoured. 11, Plus famæ, etc., destined to gain among posterity more fame than all the stars are in ceaseless motion, yet these motions run credit. through fixed and certain cycles, so that their very fluctuations 12. Comitio. The comitium, the place of meeting of the comitia, or ensure the stability of the entire system, we are lost in admirapublic assemblage, was a part of the Forum. tion at the wisdom of the great and omnipotent Architect of the Universe. In the course of a war (B.C. 319) with the Samnites, a people who inhabited the country north of Campania, the Roman army his task. He discovered the mutual attractions of the heavenly Great as Newton's work was, he did not live to complete all were entrapped in a narrow defile called the Furcule Caudinæ, bodies for one another, but left it to sacceeding astronomers to or Caudine Forks, and were obliged to surrender. The following calculate the effects this attraction would produce on the moveextract is remarkable as being one of the few descriptions of ments of each. That this was a work involving no slight scenery found in the Latin authors : difficulty will easily be seen if we consider the case of only LIVY, IX. 2, 4. a single planet. For illustration, we will take Venus. Sappose Duæ ad Luceriam ferebant viæ altera præter oram superi now for an instant that only this planet and the Sun existed, maris' patens apertaque sed quanto tutior tanto fere longior, we could then easily mark out the exact position of the planet altera per Furculas Caudinas brevior. Sed ita natus' locus est: for every moment if we knew its mean distance and the ecoensaltus duo alti angusti silvosique sunt montibus circa perpetuis tricity of its orbit. Now add the Earth to the system, and we inter se juncti : jacet inter eos satis patens clausus in medio shall find that a disturbing influence is at once introduced by campus herbidus aquosusque, per quem medium iter est : sed its attraction. As Venus comes in the part of its course nearest ante quam venias ad eum, intrandæ primæ angustiæ sunt, et the Earth, it is attracted by it, and thus drawn out of its path; aut eadem, qua te insinuaveris, retro via repetenda, aut si ire its motion is likewise accelerated as it approaches the Earth, porro pergas, per alium saltum arctiorem impeditioremque and retarded as it recedes from it; and the calculation of the evadendum. In eum campum via alia per cavam rupem Romani amount of this disturbance is rendered more difficult by the remisso agmine, quoniam ad alias angustias protinus pergerent,7 fact that the Earth is itself moving at a rate different from septas dejectu arborum” saxorumque ingentium objacentem that of Venus. molem invenere. Quum fraus hostilis apparuisset, præsidium When we have made allowance for this distarbance, we etiam in summo saltu conspicitur :' citati inde retro, qua vene- have to consider the effects produced by each of the other rant, pergunt repetere viam: eam quoque clausam sua obice planets in turn, remembering that they too are all in motion. armisque inveniunt. We thus get some idea of the complication of the problem. NOTES. It has, however, been completely worked out by modern astrono 1. Soperi maris, the Adriatic, which lies to the north-east of Italy, mers, the due allowance being made for each of these disturbing and so above it, as opposed to tho mare inferum, or Tyrrhenum, which forces; and, as we shall learn by and by, this has been done lies to the south-west. 2. Quanto tutior, etc. In a comparison of two qualities which are with such astounding accuracy that when certain minute irregafound in the same thing in an unequal degree, the one varying with the larities were discovered in the motions of one of the planets other, the Latins use two comparatives; we use the positive. Lit., as which could not be accounted for by the influence of any of the long as it was secure, its longth being proportionate to its security. known ones, it was conjectured that another planet mast exist 3. Ita natus, the nature of the spot is as follows. beyond them. Two astronomers, accordingly, quite indepen4. Satis patens, of tolerably wide ertent. dently of each other, set about the calculation, and determined 5. Venias-i.e., you, the reader. the very spot in which such a planet ought to be, if it existed 6. Cavam rupem, through a rocky gorge. at all; and on turning a telescope to that spot, the planet 7. Protinus pergerent, had got right through to the defile at the other end. (Neptune) was found, though at no portion of its orbit could it 8. Dejectu arborum, put for dejectis arboribus. 9. Conspicitur, the change to the present adds vividness and force come within 130,000,000 miles of the planet whose course had to the description. been disturbed by its attraction. 10. Sua, with its barrier, just like the other. One fact we particularly notice as the result of these investi gations, and that is the absolute stability of the system, it being Poetical Translation of Horace, " Odes," I. v., in last Reading. so beautifully balanced that all these perturbations exactly What slender youth, bedewed with liquid odours, compensate one for another, and after an infinite cycle Courts thee on roses in some pleasant cave, return to their original places. Pyrrha ? For whom bind'st thou Flamsteed was another celebrated astronomer, almost con In wreaths thy golden hair, temporary with Newton, and was the first Astronomer Royal The origin of the Royal Observatory and of this post was in eccentricity, however, was so great that a period of about the year 1675. Great inconvenience had been experienced in 600 years must elapse before it could again return to the sun, long voyages from the want of some method of determining After this comet had passed away, Halley still devoted his the longitude in which a vessel was at any time, but at length a attention to the subject, carefully inquiring into the recorded plan was proposed which was substantially the same as one in appearances of different comets, with the view of ascertaining use at the present time. This consisted in noticing very accu- whether the intervals between the appearances of any of the most rately the position of the moon with respect to neighbouring noticeable ones appeared in any way uniform. Shortly after fixed stars. As the earth moves in its path, this position seems this, in the year 1682, a second large comet appeared, and now, to vary. If then we have an accurate list of these "lunar dis- with the information he had already acquired, Halley was in a tances," as they are termed, calculated for any given meridian of better position to inquire into its motion. He accordingly did longitude, we shall be able to tell by observation what the time this, and after a time announced that he had calculated its is at that meridian. We can then compare this with the local orbit, and found that it moved in an ellipse, its aphelion distime of the place where we are, and in this way ascertain the tance being nearly 3,500,000,000 miles; also, that its period longitude; for since 15° of longitude make a difference of one was about seventy-five years. He then looked back through hour in the time, we have only to allow 15° for every hour of his list of comets, and found that he could distinctly trace difference in the times, and we shall at once tell the longitude. it back for a considerable period. This so far confirmed his The method of solving this problem usually employed now is former calculations that he distinctly foretold its reappearance merely to compare a good chronometer, set to Greenwich time, about the close of the year 1758; and so convinced was he of with the local time; but it was not till a comparatively recent the truth of this prediction that he requested, since he could period that chronometers were made accurate enough for this not live to witness its return, that, when it was fulfilled, people purpose, and even now it is a great advantage to be able occa- might remember it was an Englishman who had first traced the sionally to check them by means of lunar observations. path and prophesied the return of a comet. When this plan of ascertaining longitudes was proposed, an Long before the date assigned for the return of this comet, objection was taken to it on the ground that the tables of which was known as Halley's, he himself had passed away. the positions of the moon and fixed stars which then existed Astronomers were, however, on the watch, and some French were not sufficiently accurate to be of any practical use for this astronomers in particular investigated most carefully and inpurpose. dustriously the retarding effect which would be produced on the It was decided, therefore, that an observatory should be comet by the attraction of the planets, and as a result of built and sustained with this especial end in view, and Flam. their inquiries, announced that it would be slightly delayed steed was appointed Astronomer Royal. An elevated position by the action of Saturn and Jupiter, so that its passago round in Greenwich Park was accordingly selected as a suitable site for the sun might be expected on the 13th of April, 1759. Just at this observatory, and here it was erected in 1675, and from that the close of the previous year a wanderer was detected by an time to the present some of the greatest astronomers have amateur, and as it came nearer it proved to be the very one resided in it, and an almost uninterrupted series of observations whose return had been for so long a time foretold; and has been maintained. These have constantly proved in many though its period of revolution was upwards of three-quarters different ways to be of the greatest practical utility. One main of a century, yet the observations and calculations were so duty connected with the Observatory is the preparation of the accurate that it actually passed the sun within less than: “Nautical Almanack.” This is an almanack published three or three weeks of the predicted day. four years in advance, and containing a large number of impor. On the occasion of the next return of this comet, which was tant astronomical tables. The position of the moon with respect in 1835, not only was the date, but the place of its appearance, to many of the fixed stars is shown for every third hour pointed out; and on turning a large telescope to that spot, the throughout the year. The position of the various planets is comet was seen as a faint cloudy object. We see thus that also shown, as well as the eclipses and occultations of Jupiter's Halley's comet may now be reckoned as one of the members of satellites, and many similar tables, which are useful to the our system whose motions are fully understood. Its next return mariner in ascertaining his position, as well as to the astronomer. may be expected in the year 1912. The reason of its early publication is in order that captains Bradley was the next Astronomer Royal. The great disabout to set sail on long voyages may take it with them. covery which has rendered his name memorable is that of the Though the Observatory was thus founded by Government, it aberration of light, a phenomenon the explanation of which was some time before it was provided with instruments worthy must be deferred for the present. He also took an active part of the place, Flamsteed having to use his own for a considerable in the reform of the calendar, which had by this time varied period. No very important discoveries are associated with the considerably from the true seasons, and in order to rectify the name of this astronomer, but he was a very careful observer; error, joined in recommending that eleven days should be and it appears that it was to his accurate observations that struck out of the month of September, 1752, so that the day Newton was greatly indebted in many of his inquiries. following the 3rd of that month was called the 14th. This Halley succeeded Flamsteed in his duties at the Observatory. measure was very unpopular at the time, and Bradley came in He was for some time an intimate friend of Newton, and made for a large share of the popular dislike on this account; and his several long journeys in the interests of science. An expedition death, which occurred a few years afterwards, was by many of was fitted out under his charge to observe and catalogue those the ignorant regarded as a mark of Divine displeasure at his stars in the southern hemisphere which are invisible in this presumption in thus daring to interfere with the regular order country, and a list of nearly 400 was compiled. This, however, of the calendar. was by no means a complete one, as the station chosen for This alteration has since been made in nearly all countries. observation (St. Helena) was in many respects unfavourable. except Russia, where dates are still reckoned according to the After the discovery which Newton had made, that bodies old style, and are now thirteen days behind those used in the under the joint influence of an original impulse, and the attrac. rest of Europe. tion of a central body, might revolve in an hyperbola or para In the year 1778 Professor Bode, of Berlin, published a very bola as well as in an ellipse, the appearance of a comet was remarkable law relating to the distances of the planets from. anxiously awaited, in order that if possible it might be ascer. the sun, which, though it is said to have been discovered by tained whether these bodies moved in fixed orbits of either of Titius, is always known as "Bode's Law.” It was at first these forms, or whether they were merely stray wanderers merely a bold conjecture, but has since attracted much attendashing swiftly past our system, and then for ever lost in the tion, as it partly led to the discovery of the first of the minor deep abysses of space. planets or asteroids. In the year 1680 this desire was gratified by the appearance He observed that if we take the numbers of a very large and remarkable comet, which attracted great 0 3 12 24 48 attention both by its brilliancy and the rapidity with which it 96 travelled. Halley devoted his earnest attention to the study each of which (after the second) is double that which precedes of this body; its motion was accurately noticed and recorded it, and add the number 4 to each of them, we obtain the follow by him, and he discovered that a parabolic orbit could be con ing list, which represents approximately the distances of the structed which would account for all its movements. Ite planets named ander them : 6 23 16 Mars. 10 52 100 carried out under the personal superintendence of Lord Rosse, Mercury. Venus. Earth. Jupiter, Saturn. and the instrument may fairly be ranked as one of the wonders Thus, if we take 10 to represent the distance of the Earth, we of the age. 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. LESSONS IN ALGEBRA.--XIX. There was thus a gap left in the system, and Bode stated his EXERCISE 30.-MISCELLANEOUS PROBLEMS IN SIMPLE conviction that, as the sky was more carefully watched, and EQUATIONS (continued.) better telescopes were employed, such a body would be discovered. Nor was his prediction long unfulfilled, for on the 1st of 45. Divide the number 68 into two such parts, that the differJanuary, 1801, a planet, afterwards named Ceres, was discovered ence between the greater and 84 shall be equal to three times by Piazzi, moving at a distance corresponding very closely with the difference between the less and 40. that assigned to it by the law. This planet is, however, very 46. Four places are situated in the order of the letters A, B, small, and soon afterwards three more were discovered moving C, D. The distance from A to D is 34 miles. The distance almost at the same distance. These were named Pallas, from A to B is to the distance from C to D as 2 to 3; and of Juno, and Vesta. Up to the present time (July, 1869), 108 of the distance from A to B, added to half the distance from C to these minute bodies have been detected thus revolving around D, is three times the distance from B to C. What are the the sun, their distances and periods closely resembling one respective distances ? another; and thus in the place of one planet, we have a 47. Divide the number 36 into three such parts, that I of the large group of small ones. The other planets, namely, Uranus first, 1 of the second, and of the third, shall be equal to each and Neptune, which have been discovered subsequently to the other. announcement of this law, are found not to differ very greatly 48. A merchant supported himself 3 years for £50 a year, and from it, though the difference in the case of Neptune is much at the end of each year added to that part of his stock which greater than in any of the others. was not thus expended a sum equal to of this part. At the Wo must now just look at the services which have been end of the third year his original stock was doubled. What was rendered to the science of astronomy by another of those that stock ? men whose names will ever stand foremost in its annals-Sir 49. A general having lost a battle, found that he had only William Herschel. He was a man of somewhat humble origin, half of his army +3,600 men left fit for action; of the army and unable to procure a telescope sufficiently powerful to enable + 600 men being wounded ; and the rest, who were of the him to understand some of the mysteries of the heavens. He whole, either slain, taken prisoners, or missing. Of how many had, however, an intense desire to do so, and having acquired a men did his army consist ? knowledge of the principles of the telescope, set himself to the task 50. To find a number to the sum of whose digits if 7 be of constructing one. In this he succeeded well; and altogether added, the result will be 3 times the left-hand digit; and if from he is said to have ground upwards of 500 specula for reflecting the number itself 18 be taken, the digits will be inverted. telescopes. In March, 1781, aided with one of these instru- 51. To find a number consisting of two digits, the sum of ments, he was examining the sky, when he came upon a small which is 5; and if 9 be added to the number itself, the digits star, which, as he examined it with higher powers, seemed to will be inverted. exhibit a disc. He, accordingly, took an accurate note of its posi- 52. There is a certain fraction such, that if you add 1 to its tion, so as to watch it again on another evening. When he numerator it becomes ; but if you add 3 to its denominator, again examined it, it was at once clear that it had changed it becomes Required the fraction. its position. The idea, however, that it was a new planet did 53. It is required to find two numbers whose difference is 7, not appear to enter at all into his mind, so accustomed had and their sum 33. overy one been to regard Saturn as the extreme member of 54. At a town meeting, 375 votes were cast, and the person our system. Accordingly, he set it down as a new and strange elected to office had a majority of 91. How many votes had comet which he had discovered, and announced it as such. Its each candidate ? motions, however, soon showed that, unlike the comets, it moved 55. A post stands in the ground, I in the water, and 10 feet in an orbit of but small eccentricity, and it was then found to above the water. What is the whole length of it ? be a planet revolving outside Satarn. This planet Herschel 56. A young man, the first day after his arrival in London, named Georgium Sidus, in honour of the king who had been spent of his money, the second day , the third day and his patron, but the name was afterwards altered to Herschel, he then had only 26 pence left. How much did he hare at and finally to Uranus, by which name it is now known. first? Soon after this he constructed a much larger instrument, the 57. A person being asked his age, answered that of his aga speculum of which was four feet in diameter, and the tube multiplied by s of his age, would give a product equal to his forty feet long. The ponetrating power of this instrument was age. How many years old was he ? reckoned at 194; that is, it would penetrate into space to a 58. A man leased a house for 99 years; and being asked how depth 194 times as great as could the unassisted eye. With this much of the time had expired, replied that of the time past ha discovered two more satellites of the planet Saturn. Six out was equal to of the time to come. How many years had of the eight which revolve around Uranus were also detected by expired ? him ; so that he made a very large addition to the number of 59. On commencing the study of his profession, a man found the heavonly bodies then known. But his most important dis- that of his life had been spent before he learned his letters, coveries were made about the nebulæ and stars. A large num. at a public school, s at an academy, and 4 years at college. How ber of double and triple stars were first observed by him, and old was he? carefully noted, with a view of determining, if possible, 60. It is required to find a number such, that whether it ba whether any of them exhibited any sensible parallax. The divided into two equal parts, or three equal parts, the prodnet Milky Way was also resolved by the power of his magnificent of its parts will be equal. telescope, and thus some estimate was formed of the size of 61. Two persons, 154 miles apart, set out at the same tim the cluster of which our complete system forms but an insig- to meet each other, one travelling at the rate of 3 niles in nificant fraction. hours, the other 5 miles in 4 hours. How long will it be befor Sir John Herschel, the son of this great man, displayed a they meet ? similar love for astronomy; but so many names now ocour, 62. A man and his wife usually drank a cask of beer in I and so many fresh discoveries have been made, that we must days, but when the man was absent it lasted the wife 30 days leave them to be notiood in their special places. There is, how How long would it last the man if his wife were absent? ever, one instrument which we must refer to before closing this 63. A shepherd being asked how many sheep he had, replied historical sketch of the science, as having been of the atmost if he had as many more, half as many more, and 71 sheep, service in the determination of many difficult points. This is a would then have 500. How many had he ? reflecting telescope, created by the late Earl of Rosse at Parsong. 64. A farmer hired two men to do a job of work for him ; or town, the speculum of which is six feet in diameter, and its focal could do the work in 10 days, the other in 15. How long won length fifty-four feet. The whole of the work of this was it take both together to do the same job? 65. A and B together can build a boat in 20 days; with the day, and proceed in the same direction, the one travelling 30 assistance of C they can do it in 12 days. How long would it miles the first day, and going each day a mile less than he did take C to build the boat ? on the preceding; while the other travels at the constant rate of 66. There is a cistern with two aqueducts; one will fill it in 20 miles a day. When will they next be together? 30 minutes, the other will empty it in 40. How long will it take 87. How many lines are contained in a page of a book, and to fill it if both run together ? how many letters at an average in each line of that page, if it be 67. Required to divide 1 shilling into pence and farthings in found that by adding one line to each page, and making each such a proportion that there may be 39 pieces. line contain an additional letter, the page will be increased by 68. A man divided a small sum of money among his children 96 letters; while, by adding two lines to the original page, and in the following manner: viz., to the first he gave of the whole making each line contain four additional letters, the number of + 4 penco, to the second of the remainder + 8 pence, to the letters will be increased by 286 ? third of the remainder + 12 pence, and so on, giving to all an 88. Two persons get each a legacy of £300, and one of them equal sum till he had distributed the whole. Required the num- is then found to be worth three times as much as the other; but ber of shares and the sum distributed. had the legacy to each been £800, the one would have been 69. A hare has 50 leaps the start of a hound, and takes 4 worth only twice as much as the other. How much had teach leaps while the hound takes 3; but 2 leaps of the hound are originally ? equal to 3 of the hare. How many leaps will the hound take in 89. A cistern can be filled by three pipes ; by the first in 80 catching the hare ? minutes, by the second in 200 minutes, and by the third in 300 70. A and B start at the same time and place to go round an minutes. In what time will the cistern be filled when all three island 600 miles in circumference. A goes 30 miles a day, and pipes are open at once ? B 20. How long before they will both be at the starting point 90. Two gentlemen play at billiards ; A, before he began to together, and how far will each have travelled ? play, had £42, and B £24. Each lost and won in turn, when 71. A has £100, B £48. A robber takes twice as much from A found he had five times as much as B had remaining. How A as from B. A now has 3 times as much as B. What was much did A win? taken from each ? 91. What capital is that which, with five years' interest at 4 72. It is required to divide £1,200 between A, B, and C; B per cent., will amount to £8,208 ? has £256 + $ of A's share ; C has £270 + 1 of B's. What was 92. A capital was put out for one year at 4} per cent. per the share of each? annum; at the expiration of the year there was received back, 73. There are three pieces of cloth of different value. The as capital and interest, £13,167. What was the amount of the average price of the first and second is 79. per yard, that of the capital ? second and third is 9s., and the average price of all is of the 93. A fortress has a garrison of 2,600 men, among whom are third. What are the several prices ? 9 times as many foot soldiers and 3 times as many artillery 74. A pipe will fill a cistern in 11 hours. After running 5 as cavalry. How many are there in each corps ? hours another is opened, and then the two fill it in 2 hours. 94. Divide the number 46 into two parts, so that when the In what time would the last fill it ? one is divided by 7, and the other by 3, the quotients together 75. A man bought a cask of wine, and of it leaking out, he may amount to 10. What are the parts ? sold the rest at 25s. per gallon, and neither gained nor lost by 95. From the first of two mortars in a battery 36 shells are his bargain. What did he give per gallon for his wine ? thrown before the second is ready for firing. Shells are then 76. A and B start at the same time and in the same direction, thrown from both in the proportion of 8 from the first to 7 of but directly opposite each other, to go round a circular pond the second; the second mortar requiring as much powder for 3 536 yards in circumference; A goes 11 yards a minute, and B charges as the first does for 4. It is required to determine after 34 in 3 minutes. In what time will B overtake A ? how many discharges of the second mortar the quantity of powder 77. A cask contains a certain number of gallons of rum, and consumed by it is equal to the quantity consumed by the first. an mth part of that quantity of water: but if a gallons of rum 96. Suppose the crown of Hiero of Syracuse weighed 100 and b of water be added to the mixture, the water in the whole ounces; suppose the two crowns, one gold and the other silver, compound will be an nth part of the ram. Required the quantity weighed the same, 100 ounces each; and supposing, what would of each contained in the cask at first. Examine also and explain be very nearly the case, that the gold crown, weighed in water, the case, in which m being equal to n, a is equal to nb, and the lost 5 ounces, the silver one lost 9 ounces; and supposing the one in which it is not equal to it; and also the case in which compound or mixed crown lost 6 ounces, it is required to find and y come out negative, « denoting the original number of the proportion of gold and silver in the crown of Hiero. gallons of the rum, and y those of the water. 97. A footman agreed to serve his master for £8 a year and 78. Find a fraction, such that if its denominator be increased a livery, but was turned away at the end of 7 months, and by 1, the value becomes }; while if the numerator be increased received only £2 13s. 4d. and his livery. What was its value ? by 1, the value is : 98. A fish was caught whose tail weighed 9lbs. ; his head 79. Required a fraction, such that if the numerator and weighed as much as his tail and half his body; and his body denominator be each increased by 1, the value is changed into weighed as much as his head and tail. What is the weight of }; but if they be each diminished by 1, the value becomes . the whole fish ? 80. One person says to another: “If you give me half your 99. If A and B together can perform a piece of work in 8 money, I shall have a hundred pounds." The other replies : days, A and C together in 9 days, and B and C together in "I shall have a hundred pounds if you give me a third of your 10 days, how long will each person take to perform it alone ? money." How much had each? 100. The fore-wheel of a carriage makes 6 revolutions more 81. At what time between 10 and 11 o'clock are the hour than the hind-wheel in going 120 yards; but if the circumference and minute hands of a common clock exactly together ? of each wheel be increased by 3 feot, the fore-wheel makes only 4 82. Find two numbers , such that of the first exceeds of the revolutions more than the hind-wheel. What is the circumference second by 3, and that of the first and of the second are of each wheel? together equal to 10. 83. Required two numbers, such that the sum of } of the first and 1 of the second may be 29, and that of the first and of RECREATIVE SCIENCE.-III. the second may amount to 21. THE NATURE AND MEASUREMENT OF LIGHT84. A number expressed by three digits, whose sum is 22, is PHOTOMETRY. less by 297 than the number expressed by the same digits in a The sources of light and the principles which regulate the proreversed order, and its first digit is less by 1 than its second. duction of artificial light having been discussed in the previous What is the number? papers, it seems quite in the natural order of things to go 85. A bill of £100 may be paid by 50 bank notes of one value further and attempt to solve the nature of light-in fact, to each, and by 38 of another; or it may be paid by means of 75 try to understand its relation to non-luminous bodies, and the of the former kind, and 17 of the latter. What are the values uses of various optical instruments. In determining the nature of light, it may be asked why it can travel so fast from the 86. Two persons set out from a certain place on the same sun, and although the distance of that luminary from the earth of the notes? is about 91,000,000 miles, how it is that light can achieve this ness, may be caused. If the waves move softly, as in diffused enormous interspace in eight and a half minutes, when a rail. daylight, the gentle ripple of the ether dies away harmlessly on way train, going at a speed of thirty miles per hour and starting the nerve of vision. on the 1st of July, 1869, would not reach the sun until the end The ether is not only the incarnation of levity, but of elas. of the year 2207. ticity, and just as sound travels more quickly through an elastic The velocity of light is, according to Mons. Foucault, 185,177 | substance, so the waves of light are propagated from the sun miles per second ; but his experi. at the enormous velocity already ments were tried through distances stated. on the earth. Römer, by astrono A rod of wood is infinitely less mical observations, gives a greater dense and lighter than a bar of castrate of speed, viz., 192,500 miles per iron, but in consequence of its elas. second ; and this is very nearly the ticity being greater than that of the same as that determined subsequently metal, the vibrations of sound travel by Bradley, who calculated the velocity more quickly through its particles to be 191,515 miles per second. than they do through the cast-iron. The immortal Newton explained The luminiferous ether is supposed the manner in which light travelled to possess a spring or elasticity through space by supposing, firstly, greater than that of any other created that it consisted of material particles matter, and thus the first question, or corpuscles, so rare and subtile “Why does light travel so fast?" that no balance, however exquisitely Fig. 1. is answered by the ware theory, devised, could be made to appreciate Some acoustic experiments may assist them; and, secondly, that these cor. the learner to appreciate the idea of puscles were shot out from the sun an undulating medium. and all luminous bodies with amaz If the wetted finger is drawn around ing velocity, and in consequence of the edge of an ordinary finger-glass their rarity passed bodily through B a loud sound is emitted, and the visolids, liquids, or gases, and caused bration of the glass is easily shown the sensation of vision by ultimately by suspending a bit of cork with a finding their way to and impinging on thread, and allowing it to touch the the expanded nerve or retina of the Fig. 2. trembling glass. As long as the eye. This theory is called the cor sound lasts, the cork will be driven puscular or emissive theory of light, away by the constant succession of and when applied even to explain the reflection or refraction blows or impulses it receives. (Fig. 1.) Substitute ideally the of light it fails to do so, and with the more complicated sun or any other self-luminous body for the trembling glasa, phenomena—such as the colours of thin plates, and especially and the analogy between the two is at once established, only with polarised light—the difficulty of reconciling the theory instead of air being set in motion it is the hypothetical ether with the facts increases. Thus it has come to pass that the which is affected by the vibrating molecules of the luminous hypothesis of Newton is now rejected and that another one body. is deservedly substituted for it. Ether conveys the vibrations like a solid substance ; such a It was probably in consequence of conveyance or travelling of vibrations the great musical knowledge of may be shown by placing the ear at Huygens that this celebrated astro one end of a long piece of timber, nomer was led to oppose the New. and scratching with a nail at the tonian theory, and to insist that the other, or by placing a watch at the mechanism of sound and light was extremity of a light wooden rod and identical, and that it was in both listening at the other. The vibrations cases an undulating or wave motion. set up in a finger-glass may soon be Euler, like Huygens, was perfectly communicated to another, by connectacquainted with the philosophy of ing the two together with a wooden sound, and he also, being a great rod, which may be of any convenient mathematician, opposed the emissive length. In this experiment the lumi. theory. The arguments of these nous body is represented by the glass great men, however weighty, would A, the ether by the rod B, and the body have had but little effect if they had upon which the luminiferous ether not been succeeded by the practical impinges by the glass c. (Fig. 2.) experiments and mathematical powers A musical note is produced when of Dr. Thomas Young, who reasserted the impulses in the air are suffiand revived the theory of undulations ciently frequent, and its pitch deabout the beginning of the present pends upon the number of aērial century. The wave theory of light waves which recur in a second. If starts with the assumption that there the undulations follow each other very is an infinitely rare medium filling rapidly, an acute sound is heard; or space, and contained in all solid, fluid, the reverse, a grave one, when the and gaseous bodies, which is called recurrences of the waves are less ether. The latter is not light, air is Fig. 3. rapid. Tyndall says, “Colour is to not sound, water is not necessarily light what pitch is to sound; the a wave; but light is produced in the colour of light depends on the number ether by the setting up of an undulating or wave motion by of ethereal waves which strike the eye in a second. Thus the the vibration or trembling of the particles of the luminous sensation of red is produced by imparting to the opäo nerve body. The sun, or rather the molecules of which its photo four hundred and seventy-four millions of millions of impulses sphere or source of light is composed, is supposed to be in a per second, while the sensation of violet is produced by impartvibratory condition ; these vibrations are communicated to the ing to the nerve six hundred and ninety-nine millions of millions ether, and transmitted in the form of waves, which may of impulses per second. In the emissive theory' numbers not ultimately dash or gently impinge against the retina. If they less immense occur.” "Now,” remarks Herschel, "is there strike violently-as, for instance, when the astronomer forgets any mode of conceiving the subject which does not call upon us to use the coloured glass or tank oí diated ink whilst viewing to admit the exertion of mechanical forces which may well be the sun through his telescope-then great damage, even blind called infinite ?” |