The New York Herald Newspaper, November 30, 1874, Page 3

ve TRANGIT OF VENES “The Great Astronomical Event of the Century. THE ARMY OF SCIENCE., What the Observers Will Decide--- The Mode of Observation. THE MOVEMENTS OF THE SPHERES. The Problem of the Sun’s Dis- tance from the Earth. THE DIAGRAMS EXPLAINED. ‘Progress of Astronom- ical Science. WHAT THE ANCIENTS BELIEVED. During the bright evenings of the past summer, @ spectator, turning his face westward, might see littering over the norizon, a planet of singular brilliancy, sparkling with a silvery giow before any star had opened its eye, and following tho track of the setting sun. This glorious orb’ was Venus, the Phosphorus and the Hesperus of an- cient astronomers, the morning and evening star, named after the fairest of tne heavenly goddesses, because of the surpassing beauty o! its rays. In size it is nearly equal to our own earth, and, like a@ll the otner planets, borrows its light from the sun, Except Mercury, it Is the nearest of all the planets to the sun, being at a distance from the great luminary of about sixty- six millions of miles, Ever since the gloves of the @olar system were moulded by the Creator’s band this unwearying planet has been travelling round and round the sun in an elliptical path at the vast rate of 77,200 miles per hour, making a complete Circuit in a little less than 225 days. At the pres- ent moment she is sweeping toward a point in ber orbit, or path, which lies directly between the earth and the sun; and on the evening of the 8th | of December, li the.sky be clear, observers a few hundred miles beyond the Californian coast, pointing their telescopes westward, may be- hold her advancing toward the edge of the sun and commencing to travel across his disc, as he winks into the Pacific waves, This passage of the Dlanet between os and the sun is called the transit of Venus. No person now living has ever witnessed a transit, and after 1882 no transit will take place within the iifetime of any child of the nineteenth century. After that date, Venus will circle round in her orbit 200 times without once rushing between us and the sun, and | the twenty-first century will have dawned before astronomers can hope to witness ‘the recurrence of the same phenomenon. To an ordinary spectator, this transit of Venus will seem to be a very uninteresting and Insignificant event. A black speck, scarcely visible to the naked eye, Will push its way in at the left hand side of the bright disc of the sun and slowly creep across his surface, vanishing into @pace as it departs toward the right. This ts all the display tuat Venus will make during the few hours that she will take to drift across the sun. The illuminated nalf of her surface being turned toward the sun we can then see only the dark- ened hemisphere, and we should fail to recognize in that pitchy speck, the beauteous evening star of last September. No wonder that the astrono- mers of old never dreamed tat this minute spot ‘was the same crystal orb whicn during eight previous months had been the joyful star of evening, and was now shifting to the west of the sun, gradually to brighten and become the morning star for an equal period of time. Pythagoras, however, is said to have learned this from Egyptian priests, and taught the same in early Greece, it being geuerally bellevea that the star of the morning and that of evening were two Giferent bodies, But wnat person unfamiliar ‘with the revolutions of the celestial spheres would ream that ip order to view and map the track of this planet across the solar disc, miilions of dollars have already been spen: by governments, societies ana individuals? Who would imagine that, for the past fifty years, the great mathematicians, astronomers and opticians of the earth have spent vast amounts of time and labor and monoy in making PREPARATIONS FOR SUCCESSFUL OBSERVATIONS of the coming transit? Yet such are the facts. No event of the century hus excited tn the scientific world such a deep and widespread interest. For the past s1x months, the literary and scientific periodicals have teemed with articles on it, and the newspapers have been in constant receipt of letters and telegrams from the formidable army of @cientists scattered over the four quarters of the globe, giving details of the gigantic enterprise and extensive lavor in fitting out expeditions prepara- tory to a successiul observance of tt. The Russian government has sent out twenty-seven expedi- tions; France, Germany and Engiand ten or tweive each, and the United States government has appropriated $150,000 for the purpose and placea vessels of the navy at the disposal of eight separate expeditionary parties. What, then, is the NATURE AND OBJECT OF THE OBSERVATIONS, the result of which isso anxiously waited for by the learned ones of the earth? Tue first and im- Mediate object is an accurate determination of the distance between the earth and the sun. When this distance is ascertained we can easily calculate the distances and sizes of all the planets ofthe solar system, and also the amazing dis- tances of many of the fixed stars, Without know- | ang the one, itis impossible to determine any of the others, because the line stretching from the earth to the sun is the yardstick, as it were, with which we measure off the distances of the other heavenly bodies, Any error in this line—this yardstick—is multiplied In counting up larger distances, A mistake of 1,000 miles in it would Cause an error of more than 200,000,000 of miles in estimating our distance from the nearest of the stars. Besides its importance in this re- spect, a knowledge of its exact length will aid in perfecting the art and ecience of navigation, on which the Progress and weljare of humanity so inuch de- pend. Moreover, it will settle a vexed question which has puzzied tne minds of scientists from the earliest ages of astronomical history, throw new Ught on the science of optics, and forge more golden links for the mystic chain which binds the mind of man tothe giorious wonders of the uni verse of God, Such being the exalted results of this astronomical labor, what course is to be pur. gued and what calculations are to be made by the expeditionary corps in order to accomplish those objects? Before directly answering these ques- tions {t will be necessary to oer a preliminary explanation of the METHODS OF DETERMINING DISTANCES in general, and then to speak bdriefy of the ener- getic attempts of the ancients to employ some of these methods in eudeavoring to solve the prob- lem Of the sun’s distance, One of the most famt- Mar of terrestrial phenomena is tbe small appear- anee of objects that are at a great distance irom the eye, Everybody knows how an expresy train aweaning pv hun canidly diminishes yp sige pe if rushes toward distant hills, and finally becomes so smail as to be scarcely discernible. But every- body is not aware that tnis ‘apparent decrease in | size takes place according to a fixed law. Li we} imagine a straight line to be drawn from the eye | to the top of the traip pnd another straight line rom thé eyé tO" thé Bottom’ of the train, thesé> two lines will form at the eye an angle. which enlarges e@ the train approaches, and diminishes as the train recedes, Whatever size this angle possesses at one mile’s | Gistance irom the train or other object, it will | measure half that size at two miles?’ distance, one- third of that size at three miles’ distance, one- fourth at four miles’ distance, and so un indefi- ni'ely, This law does not hola good for short dis- tances; but itis sufficiently true of tne distances to which the heavenly bodies are removed trom us. We have instraments for measuring sald angle—the visual angle aa tt is cailed—to an extra- ordinary degree of accuracy, Knowing this angie and the size of an object, we can detérmine tue distance; or, given this angie and the distance, we can calculate the size of any object. Military engineers when about to bombard a citadel or sheli a postition, measure the visual angle preseited by a steeple, wall, spire or some such object, the height of which they already know, in order to estimate their distance therefrom, and fill their cannon | with the quantities of powder and tron requisite | to carry such @ distance. So aiso,in throwing forward masses of sharpshooters to resist the onset of cuirassiers, the distance of the cavaliers is calculated by Measuring tue visual angle pre- sented by a line drawn irom the heads of the | latter to their horses’ ieet (the height of a caval- | rylWan’s head from the ground is generally about eight feet); and the distance being determined, the resisting colur:ns elevate or depress their rifes accordingly. Skiulful riflemen invariably, though pernaps Uaconsciously, estimate distance by mentany Comparing the apparent size of the ovject aimed ab Wito 118 actual siz The heigat of @ balloon 18 like Wise estimated in @ simular Way. To tlustrate SOME OF THE PRINCIPLES which underlie ail such caiculations, let us sup- Ose AL Observer Staudine on the sun, and loo<- ing toward the earth, Tu him tue earta’s diame- ter wou.d appear to be an extremely shor: tine lt would be about the seventy. two-thousancth part of a circle, that 18, i 72,000 earius were ranged in coniact om @ level and at equal dis- tances from the sun, in the same manuer as vovs sometimes fix a Dumber of marbles, 80 as to form acircie, they would make a complete rug of eartos round the sun, The circumiereuce of this ring would consequently measure 72,000 times the diameter of the earch, The solar observer, tuere- lore, would only ueed to find out with an accurate angle measurer, What fraction of a whole circle the said visual angle would pe, and per- Jorm @ simple mulUpncation in order to de- termine toe lenytb of the circumference of the circle already described. This circumierence would be tae path or orbit in wuich the earth moves round the sun, supposing it muved ina circie, Ivis eviuent (nat bile radius of tuls circle ig the eartu’s distance iromthe sun, This radius or distunce, the observer could determine Ly divie | ding the circumierence by the number 6.2882, be- | cause the circumierence of any circie contains its radius 6.2832 times. Let ms periorm these arith- Metical operations in round numbers. Ihe angie | Woich the earth’s diameter, presents to the | observer at the sun 18 the 72-1,000 part ot @ circle, The diameter of the earth 18 nearly 8,000 miles; 8,000 miles multiplied by 72,000 gives 670,000,000 Of miles, Tnis divided by 6.2832 gives avout 92,000,000 miles—the sun's Gis tance frum the earth. But isit not idle to talk ol ooservations being Maue, abd the eartu’s Visual angie measured by an astronomer standing on the suuy Surey, we can never hope to realize such @ fairy-tale fancy, And yel, marvellous though It seem, we are euabied, without flying away irom this earth of Ours, tu calculate the exact buik Of that angle by & very simple Metnoa, based on one ol the most beauiiiul truths of geometry, which comes dowu to ugirum the shudowy cycles Of a& gray autiquity, like so many other gorgeous monuments o1 the Mathematical genius which flourished tn days gone by. About 3,000 years ago, 1t was discovered toat when tue three corners of any triangle are added together, their sum 1s exactly equal to two right angies, Hence il we know tio 0} the corners 01 & triangle, we can readily calculate the magnitude o1 tie other corner, by subtracting the sum o1 the two trom two rignt angles. In fig. 2,10r example, if we meusure the angles at gand B, we can find | the angie at S. Having ascertained this angie, | and the lengtn of the earth’s diameter (which can | be easily computed), she sun’s distance can be de- | rived’ according to toe principies aiready ex- plained. And now, exciaims the reader, why can- hot these angles at Aand B (fig. 2) be measured apy day, when the sun is visibie, and when: tuere are angle meagurers of marvellous accuracy with which to gauge them? METHODS OF THE ANCIENTS, Such attempts have been frequently made, but with very uncertain resulta. The ancient astrono- mers tried it, but, owing’ to the imperfection of their instruments, fell far short tg the mark, esti- mating the distance to only — 5,000,000 mies, Aristarchus of Samos, who flourished apout the year 270 B, O©., observed that when the moon is exactly half tull, the sun, moon and earth are at the corners Of a triangle, the cor- her at the moon beiwg @ right angie, He then measured the co.ner at the earth, and, by the 6,m- ple subtraction before named, deduced the mag- Ditude of the corner or angle at the sun. Thence be concluded that the sun should be at leust twenty times more remote than the moon. But how ‘did the old astronomers succeed in calculating tne . remoteness of the latter spherey To an observer stationed at the moon the earth’s aiameter woula seem our times as large as the moou’s diameter seems to us, Aris- tarcuus, Archimedes and others were enabied to determine this visual angle presented by tue, earth's diameter vo the moun in tae manuer pre- viously described, which they did, thougn not With any approach to agcuracy. Herodotus in- forms us that previous to their time, the sun was supposed to be ten miles off, driltiug soutnward every winter, beiore the ktesian winds, Anax- agoras cOmputea toe distance to be 14,000 miles, | The fact 1s that in attempting to solve the probiem they Were conironted by tou many obstacles, It | is very difficult to tell whea the moou 1s precisely hau 10:1, and a very small error in guessing that moment would create @ mistake Of millions of miles as to the distance of the san, Witu the im- Dlements at their disposal they could gauge an | angle only, to about the 16-1,000 part of a circié, AN error Of this quantity in their Measurement of the visual angie at the sun would cause & mistake Of 50,000,000 or 6v,000,000 | mnes at the very east. With ‘tne instruments now in use, angles Can be toldof to within the 131,000,000 part of @ circle; yet, even with such prodigies of delicate machinery, it 18 exe tremely difficult to obtain the desired angle. Owing to the bending or reiraction of the sun's | Tays in passing through the aerial regions of mid. | day, tne great luminary olten seems to ve where | he i8 not really; mureover bis rim, even when viewed througn the telescope, uuring the neces gary OUservations, is seen to quiver in the same Munver as terrestrial objects tremble when viewed across the heated and waving atmos. phere near a strong fire. These, and numerous other diticulties, which it is needless to enumer- ate bere, constituted a tormidable barrier against the repeated and ingenious efforts of previous scientists to arrive at @ settlement of tne question, Still, as the centartes moved on, cloud alter cloud disappeared, anu in the sixteenth century the solar distance Was ascertained Lo ve cer- tainly NOt jess than 14,000,000 miles. ‘This estimate was adopted by Kepler, one of the Titans of asiro- Domical history, who spent his declining years as Astronomer Royal at Prague, and vo wuoui We are indebted for the discovery of the celebrated 1aws | of planetary revolutions, to which We Will have to | make reterence again. tie subsequently calcu. lated, however, that the solar distance was not less than 26,000,000 inlies. In the following century, Dr. Halley Measured the solar angie from two distant stations and found it to be uch smaller than had been previously imagined, but he believed the | limit Of the sun’s distance to be 66,000,000 miles, Even this estimute, as subsequent calculations have proved, was too smali. In fact it was as- serted by Cassini, in the seventeenth century, to be fully 85,000,000 miles, but nu heed was paid to his deductions until alter the memorable TRANSITS OF THE EIGHTEENTH CENTURY, It may be deemed weil to summarize the history | Of those two transits, as it wili form @ necessary prelude to an explanation of the observations and Methods ol solving the great prooiem, In the year 1677 Dr. Hatley, a Epgish astronomer of great note, who had sailed to the island of St. Helena in order to map the star clusters overhanging the Southern Hemisphere Of the earch, observed the tiny plauet Mercury creeping westward directly between the eaith and the sun, His scratinizing observance Of it and close calculation of its stages led him to the conclusion that a careful opsery+ ance oi tue transit of Venus, irom distant stations, } would furnish &@ metuod of calculating the Solar distance to & degree of accuracy that no other scientific specuiations could be hoped to attain. Before his death he put on paper all | the plans, which stilt bear his name, hen the transit year came round the astronomical world was astir, Halley's calculations were reviewed, their trifling errors rectified, positions were se- lected. and governments aided the enterprise with ® generous hand. Astronomers sey sail toward | the east and toward the west, islands that le scattered over the south. | ern sphere, There an army of! learned men, whose of operations | was the itd globe itself, and whose hearts throbbed high with bright expectations of @ victory not less glorious than Py wl ever | perched upon imperial standards beneath the Jeaming sun of an Al rlitz or Marengo. But he conquest was not so easily to de achieved, Many of the expeditions were reiused permission to land, owing to wars then fiercely waging; So nr ™ | comprehension, others failed to see every stage of the planet's track, on account of clouds that cruelly drifted | | acroas the sun, and even those whose View was totally unobstructed observed a phenomenon which batied their expectations and compromised the accuracy of the estimates * consequently made, Just as Venus emerged from the trackiess space of darkness toward the | edee of tye apn, And while ashy was yoy | ! circle, HALLEY’S METH OD SS within sbout two-thirds of her diameter from his Tim, a black, inyisible band seemed to craw! be- tween, flattening the edges ol both, For a whiie the rims of both bodies trembled and struggied, then there was a pause in the planet’s motion, when all at ouce it was found that Venus had con- vulsively rushed in to @ considerable distanee on the sun’s disc. This same appearance was wit nessed at all the stations, and the observers failed to signal the exact instant of time at wich the contact took place, a knowledge Of which instant, as we shali see, 18 Of paramount importance in calculating the ~un’s distance, An error ol twenty seconds of time in noting this moment would cause @ grave one in the svular distance, and yet the observers generally declared that it was impossible for them to avoid @ liabil- ity to such 4 deviation {from accuracy. There was no occasion for despair, however, {or another transit was to take piace in 1769. In the Meanitme the lenses of the telescopes were changed, the instruments renovated (or it was to their defects that the intervention o! the mysteri- ous band had been attributed) and the expedi- tionary forces made ready fora tresh attempt Wealthy patrons o! science subscribed freely aud the European governments interposed no obsta- cles, but extended to the enterprise a liberal aid. Tne year 1769 circled on and the long-wished day in June arrived. The stations were selected as be- fore. Venus glided torwara, and was nearing the sun’s edge, When the same contusing band inter- vened, the appearances oO! 1761 were repeated, and at no station could the moment of contact be fixed within less than twenty seconds of the ac- tual time. With such data as they could collect they made the necessary calculations and, hope- Jess Of better results, hung down their weapons of science, leaving the battle to be fought again by their enlightened successors of 1874. The estimates then made were mingled with so many elements of uncertainty that they ranged from 88,000,000 to 108,000,000 of miles. Sudsequent mathematicians reviewed the various entries and accounts of the observers, and finally tae astronomer Encke scrutinized all the estimates, and alter much lavor concluded that the sun’s distance was 95,274,000 miles. This was accepted by the entire scientilic world until a few years past, When two strong argu- mente were urged against its correctness, Arrago, Foucault and Fizeau, alter a series of Ingenious experiments Made at Paris and Versailles, found that lignt travels with @ velocity of about 184,000 miles per second. Now we know from observances of the echpses of Jupiter’s sateliives that light takes 498 seconds to cross irom the sun to the earth, and consequently the solar distance must Measure 498 times 184,000 miles, which gives about ninety-one and @ half millions. The second cogent objection to Encke’s estimate arises irom OBSERVATIONS OF THE PLANET MARS made in 1862, These observations were made in order to ascertain the visual. angle presented to an imaginary ovserver at Mars looking down upon a pair of distant stations on the earth, and to deduce the distance of Mars from the earth on the same plans of determining distances in gen- eral as those already explained. it must be borne tn mind that Mars 1s about one and A half times as far as the earth from the sun, and that he travels round that luminary as we do, coming sometimes on the same side of the sua with ourselves. Such was his location in 1862, Observers acting in concert were stationed at Washington, Greenwich, Uape of Good Hope, Pulkova, santiago and Williamstown in Australia. The results were found to agree, and Mars’ dis- tance estimated. What Mars’ distance had to do With vhe sun's will be unfolded a litue further on, At all events the sun’s distance was then esti- mated to be about ninety-one and a batt millions, Thus most living astronomers agree within a iew hundred thousand miles as to the solution of the vexed question, Still, the long sought accuracy haa not been arrived at, all the observations and estimates of the past hunared years cannot equal 1D approach to perfection the methods about to be employeu during THE COMING TRANSIT OBSERVATIONS, an elucidation of which will now be less diMcult of We have already learned how Di. Halley was the first to propose such observ- ances, His method we will proceed to de Scribe, reminding the reader that while no part of our own Continent, except the western strip of Alaska peninsuia, wul be turned toward the luminary of the day during the event. ful period, the transit will be visivle to all places between Siveria and the South Pole and between the middie of the Pacific Ocean and the eastern Portion sof Africa, in the nortuern region Of wis tract of territory a favorable position ig9 taken up by a company of observers, fully equipped with clocks, that keep exact time; tele. Scopes, photographic apparatus and a hundred otaer appliances necdiess to be mentioued here. Directly south of this position—and distant, say 4 miles therefrom—anotner station Is selected by @ separate company of acientists, destined to act tn concert with the former. As seen trom the horwbern station, the central point of Venus will appear to move across the sun's disc io a straignt line. Let us imayine tnis straight line to be pro- jected on the brilliant disc, resembliug a black thread stretched across @ dazzling silver plate. To the spectator at the southern station the planet will appear higher up oa the sun’s disc and will move across in @ diferent imaginary line hike another black thread stretcbed parallel to the first across the plate o1 silver. The diagram (fig. 1) Mlustrates this. The northern station on the earth is at the letter 0, and to an observer there, a8 Venus advances Westward in her path, she seems to stroll over the line NN1. The southern station Is at D, and from that point Venus seems to steal across the sun’s disc, ia the line MMI. The black spots on the sun resembie the specks of the sun's suriace which the pianey will conceal jrom the respective observers during its passage. They seem to be a trife smaller than tue planet itsel!, and such ac- tually wiil be the case, owing to a delusion of tne eye, The planet itself is made to look smaller than the earth, and the lines NN1 and MMI are stretched lurther apart than they wil really seem to be; butall this is done tur the sake of clea: ness in the explanation, which becomes more intelugibie by reason of those exaggerations in the scaie, ‘The North Pole of the earth, on the 8th of Decem- ber, will be tnrned from the gun to an extent that can taf glia dha by inspecting the representation thereof given in the dtagram. vw the imaginary passage lines across the sun, the observers cannot see them, but by photograph- ing the Recte Position at several stages of its track, the observers Can precisely map them on an image of the sun, The observers at the south wil map the line MM1; those at the north, the line NN1. Neither band o/ observers can tell what track the planet has presented to the other until they com- are notes. ‘Then, however, they can map the two ines on one photograph. The angular distance between these lines is tne key to the solution. It will be found to be the 1-80 of the sun's breadta, or the 64-1000 part of a whole The calculations herein made are based on the probable distance of the sun, and are given inround numbers. Li, now, we picture to ourselves @ celestial astronomer stationed at Venus, and looking at the two tmaginary lines MM1 and NN1; then, according to the principles of visual angles, shese ues would appear Largper Anat tQ Alm | ot than they would tous, Their distance asunder would present to his eye an angie equal to the 1-89000 part Of a circié, the measure of the anzie Al, Butitis maniest irom the diagram thai the angie A 1s the same size as Al. it is plain also that the angle A 18 the visual angie presented to the observer aforesaid by the line U D, and as tnis line 13 4,000 miles, we can determine the distance UV; the distance trom the earth to Venus in the same way as it wus shown that an observer at the sun could estimate his distance trom the earth. Thus far, one thing has been asserted without proof and that is that fo au observer at Venus the angular distance between the lines MM1 and NN1 would be 1-s9000 part of @ circie, thac 1s, they would appear avout land 7 times as far asunder, the earth being land 37 times as far from the sun as Venus is, This latter assertion is based on one ot Kepler’s celebrated laws, which demonstrates that the longer a planet takes to go round the sun tue iurther itis from the sun. Hence we only need ascertain by telescopic observation the re- Spective periods of the plinets’ revolutions in order to Calculate their relative distances from toe sun. The law may be thus applied:—The earth goes round the sun in 62 weeks nearly; Venus moves round in avout 82 weeks. If we multiply 62 by itself, then 32 by itself, and divide tue former product (2,604) by the latter (964) vhe quotient is about 2 and 7-10, The cube Toot of this oumber will give the number of times that the distance of Venus is con- tained in that of the earth—viz., about Land 3-10 times, This is the rule which holds good tor all the planets, nO matter what their distances, the discovery of which cost Kepler twenty years of NEW YORK HERALD, MONDAY, NOVEMBER 30, 1874.—TRIPLE - SHEET. Will arrive at the stage represented at V 3! io she a apanring diakeaae dane 4) htcoy 4 tm | addition, snows the planet's course as viewed from | @ Dorthern station :— NS Ly FANS My | iw bse The moment when fhe lef edge of the planet barely toucnes the sun’s eastern rim (V 2) is cailed the instant of the firat internal contact. Upwards of tour hours will then elapse before the plavet ches that portion of its journey which is pictured at V 8 in fig. 4, where the planet 1s represented as just touching the western por- ticn of the sun’s rim, ‘This 8 called the secend Internal contact, Finally the planet reaches @ position portrayed at fig. 8, where it mukes the second external contact, and then vabisnes into space, soon again t giow with solar light on the morning sky of early spring. Thus, the planet makes two coutacts at each side of the luminary, Half way between the first ex- ternal and the first internal contact the central point of Venus entered the solar disc; half way be- tween the second internal and the second exter- nal contact the centre of Venus made its exit irom the dise, The time thus required ior the centre of the planet to travel from the eastern to the west- ern edge is the true length of the passage or tran: ait live a3 expressed iv time, It will be perceived, from ap inspecuon of figs, 3 and 4, that the pas- Sige lines are nearer to the upper portion of the Sun than they are to the lower. Such will really be the Case, although the distance between the transit lines will nut be so great a8 appears in the diagrams, being, as has been stated, only about 1-80 of the sun’s breadth. The whole problem, then, resolves itself into an exact Calculation of the distance between the obser- vatories, and fauitiess determination of the in- stants of time when the four contacts take place, These data once known to @ certatoty, the solution of the grand probiem becomes a mere matter of arithmetical and geometrical calcula. tion, based on the fundamental priuciples hitherto explained, The eflorts now being put forth to estimate the time of te first contact, in view of the possibility of the reappearance o! the shadowy band, are very numerous, and it will indeed be disheartening if they do not succeed, A simple pa was proposed in @ letter which first appeared u the HERALD of the 8th of June, as the American expeditions were about to take their departure, but itt will not be “sed during the coming transic, ag ihere Was not sumctent time jor & preparation of the apparatus necessary to an application of it, fy i tiustrated in the accompanying diagram, iB. ese The letter V represents Venus approaching the first stage of her transit, and apparently distant from the sun bya space equal to Ler own breadth belore the embarrassing band appears. The inter- vening lines are exceedingly fine threads so fitted in the telescope as to run along the rim of the sun in such a way that the parallel line to the right always touches it. The distance between the lines is previously fixed with perfect accuracy. As Venus advances, the observer oscillates the lines up and down until the planet attains the position indicated in the diagram, just touching fimultaneously the left hand line LS and the cross line, ‘This instant is the stage at Which she touches the dottea circle drawn round the sun. Sim‘tarly it is ascertained when she touches the same circle at her egress. In tts way her contact with the dotted circle might be found before the obstacie alluded Pinner sat labor and study, Kepler demonstrated that the law actually did apply to the planetary worlds, and Sir Isago Newton, not long alterwaras, snowed beyond all cavil that tt should apply, proving it Mathematically after his discovery ‘of the law Of the aniversal mutual attraction of material bodies, ‘The reader will now understand how the solar distance was dedaved from the Knowl- edge of Mars’ distance that was arrived atin 1862, The only problem remaining, then, accoraing to Halley’s method, is the extremely delicate task of measuring to @ nicety the distance be- tween the two passage limes MMI and NNL Tue smaliest error in so doing would lead to an embarrassing one in the con- clusion, The measuremeot on a photograpnic image would involve much uncertainty. Tis plan cannot succeed, ‘The digiance might be approxi- mated by gauging the planet’s distance from the top or bottumm o: the san’s rim during the transit. But no scheme can equal the one to ve used by the observers Of 1874, weather permitting. It is this:—Tne length of each passage line depends upon the time occupied by the planet in tracing tt. ‘the more time Venus takes up in moving across, the longer the transit line; aud the less the time, the less the passage line. Knowing the respective umes consumed in moving over the lines, we can determine the lengths of them, It is a geometri- cal truth that when we know the lengtus of two such lines We can calculate their distance srom each other, The more accurate we are in esti- mating the former the greater will be our cer- tainty of the latter. Hence the importance of noting the time spent by Venus in making her transit. Now, this time can be easily iound by fixing the Moment at which the transit begins, and the instant at which it ends. All the efforts of the astronomers are directed toward this object, The observers of the last century were about to signal the decisive moment of the com- mencement of the transit when the mysterious blur appeared and irustrated their attempts, ‘The question now being universally discussed is Will this strange phenomenon occur agaiu? Many are Ol Opivion that it will not, in view of the mar- vellous improvements of our telescopic lenses, Many others expect the recurrence of the same delusive appearance. The chances are that the obstacle will again present Itsell, though, perhaps in a diminishea form. There is an atmospnere of great density enveloping the planet Venus, through which the sun’s rays, in racing toward the earth will undergo refraction, or bending, similar to that which takes place in our own terrestrial air and which sometimes is made manifest In the beavtiiul mirage, or the enchapting views of the fata Morgana Besides this bending of the solar beams In traversing the airy fields of Venus, there is the parallel phenomenon of an intervening blur be- tween two gloves at different distances rom the eye daring the passage of one between the ob- server and the other. The young students who were in training lor several months at ureenwich were lurnished with an artiucial planet with which to practise, the better to judge the moment of contact on the eventiul day. Even with the artificial Venus @ slight biur was perceptible whenever it was brought near the image of the sun's rim. The grand secret, theretore, of the labors of the 8tn of December will be a successful determination of the moment of contact, all the ob- | stacies notwithstanding. The true moment of first contact will be when the centre of Venus passes the eastern edge of the sun, But as we cannot see or determine by visual judgment where the centre of Venus 18, We Must Calculate this moment ‘rom other observations, Accordingly, the tirst entry made on the records of the obse: vers will be the moment when the planet's circumierence grazes the sun’sedge, This is shown in the ac- companying diagram (fig. 8), which represents the first contact between the two bodies and the srack ol the planet as seen from the southern station :— {t may be well to remind the reader that, inas- Much as the observers in the southern Hemi sphere of the earth will be inverted, having their feet toward ours, they Will see the planet moving in the manner which he can perceive by turn- ing fig. 8 upside down, The arrow indi- the direction of the planet’s motion, The spot marked V 1 denotes the first position of the planet in commencing the trausit. This Bs A ee a ear Cif contact. Myke Will Shen posh. slow MY westward and seem to cut wae a Au. Jo a sew minuses ane | ROWS OF th moves so as to meet the shadow, and It ma, be Inierred that the shadow would trave) to B in Jess than the ten minutes previously esti. mated. This difficulty does not oalfe the mathe. matician, who knows well bow to estimate the rate at which tus station is carried forward to meet the shadow. This he does on the principie involved in the assertion that the velocity of the station diminishes in proportion to its pro; tmity to eitner pole oF the earth. Tha nearer the observer is to the Equator. the nearer does his velocity approach 1,036 milea an hour. It is scarcely necessary to that the shadow of Venus will not be perceptible on the! earth, Inasmuch as ine light emanating from the. Uoconcealed portion of the sun’s disc 1s Lyn | 0 blostt Otte The time, however, at which imperceptible shadow strikes the station at A, is the same instant at which the observer she. pense pass between him and the sun’s centre Ut the middle of the sun cannot be seen, nor cal its position be well judged by the astronomer,, Whose telescope magnifies 80 powertully that can only see a very small portion of itatatime. H must have resource to the plan of observing th first and last contacts of the planet with the sun's, edge in the same manner as the observers ust , Halley's method. Half way between the first pals, of contacts and the second pair, the planet Will have amet between the station and the central point of we sun, In ltke manner, the observers at B, by noting the contacts at the left and rignt edges of tne sun’s rim can calculate the moment at which Venus crosses between B and the middle of the solar sphere. Many other difficulties artse,in the process of the work, which invoive probléms in toe higher fields of mathematical science. Venus. does nob always move with the same velocity; neither does the earth, because they revolve in patus what ar elliptical, as shown in fig. 6, and move fast when they are nearest to the sun and slowest when they are at the most remote points of their respective orbits, The earth 18 3,000,000 of miles nearer to the sun in our winter than in summer and Venus, at some times i8 1,000,000 of mules nearer to the sun than she {8 at other periods, I¢ will be necessary, then, after the observations of the 8th of December to ascertain the average dis- tance and the greatest and leass distance of each planet irom the sun, ag well ag the particular distance at which each will stand trom the grand central Inminary on thas day. Even these obstacles {ail to daunt the keen Mathematicians, By measuring the apparent size. of the sun and of Veuus, from time to time, they are enabled to transfer to paper an exact map of those orbits. I the sun looks one-thirtieth larger in January than in June then we are assured ¢ he is one-thirtieth nearer in the former than im the latter month. In the same way we can esti mate our relative distance irom the sun at any part of the year. It remains to determine the particular velocity of the planets on any aay. This can be deduced irum another law discovered by Kepler, whereby tue precise velocity of the earth or of Venus at any time may accurately be tound, The law ts that @ liné drawn from the sun to any planetary orb passes over equal spaces in equal times. A fure ther discussion of this topic ana the numerous other tasks tnvolved in the calculations would lead us pntak regiments of figures, through wile derneases of lagramns and trigonometrical calcus lations that would tend to prejudice very strongly the popular mind against the beauties of abatrace science, Thus far We have steered clear of sines, tangents, differential and integral caicu)us, bore zoutal parallaxes and other mathematical nobs goblins that make a dictionary go terrible; and we shall leave them undisturbed for the present, Suffice it to say that the stupendous difficulties to be met with in the solution of the greas problem @re not more numerous or formidable than the preparations by which it 19 fondly hoped to sure mount them. But by this time we can understand the tmpa- tence of the reader to know why it is that Venue goes round the sun in the manuer heretofore de- scribed, overtaking the earth every 584 days, and Yet lets 120 years pass by without once coming between the earth and the sun. WHY TRANSITS SO RARELY OCCUR, If Venus and the earth travelled in the same plane, on the same level, round the sun, then, as surely as Venug Overtook the earth, so surely would she pass betvreen it and (he sun, and there would be a transit of Venus every nineteen months. Butitis notso, Tee elhpse in which Venus travels is tilted so that one hall of it ties above the plane of the earth’s path and the other half below it. To obtain @ familiar representation of this, let & circular vessel, five feet wide, ve fillea with water, On the suriace of the liquid and directly tn the centre 8cta circular sheet of timber three and a half feet in diameter. ‘Then tit the sheet of wood 80 that one-lall of it May remain somewnat avove the water, the other hal! being correspondingly de- pressed beneath tt, The circumference of the lumber now resembles the track in which Venus travels and the circumference of the pond repre- seuts the path of the earth’s movement, the sun’s position being the central point of the board, A conception of tnis Jaciitates the Ulustrauon given in fig. One-halt of Venus’ orvit 18 sup-; posed to be lifted ubove the plave of the earth’s path, while the other portion ts depressed below it, The amount of Iuciimation between whe orbits is equivalent to the hundredth part of a circle. The only place where the two planes cut each other 1s at the line NL. The earth passes the point L on the 7th ol every Decemove nd, the position N on the oth of June. At to could intervene, because the binr does not make its appearance until the planet is within two-thirds of its own diameter from the sun, Tnis method would not interfere with the existing arrangement of the paraliel threads of the micro- meter used by the astronomers, but would diver irom the present method, inasmuch a8 the pas- Sage line of the planet would be measured: across the imaginary circle drawn round tne sun, and | not across the sun merely. The diagram shows only the external contact with tho dotted circie, but from whas has been satd it can be understoo how, with additional parallel threads, internal contact with such an imaginary circle could be signalied. DELISLE’S METHOD. Long after Halley had propounded his plans for the observation of the transit and unfolded the method whereby the problem could be solved, ano her mode, tar simpler and more beautiful than his, was proposed betore the transits of 1761 ana 1769 by Detisie, a celebrated astronomer. For the sake of clearness in the description thereo!, we will conceive the sun to be condensed into an intensely luminous star, shooting nts beams toward the earth like a blinding calctum light. When Venus begins ber transit she will cast @ shadow, which of course Wiil sweep along toe earth as Venus roils westward between us and the sun. To persons standing on this track the planet's transit would occur under pre- cisely the same conditions, viz.:—Venus would appear to carve out the same passage line | on the disc of the sun, The same holda trae of two observers stationed on any line paiallel to this track, These lines would run nearly east. and west. Two distant stations, say 6.830 miles apart, are chosen on such a line. As the planet travels trom east to west her shadow will first pass over the eastern station, then fy westward along the ground with extraor- dinary rapidity, reaching the western station in a | very few minates, The number of minutes and sec- onds consumed during the westward journey o! the shadow from one station to the other ts the key to | the solution of the problem, according to the | method of Delisle. In fig. 2 the outline of this plan is sketched, The reader is supposed to be luted toward heaven, casting bis eves downward upon the north pole and the northern hemisphere ol the earth, Venus and the sun being also in view. The eastern stution is at A, the western at B, The observer at <A_ signals the instant at which he sees the planet passing be- tween him and the sun’s centre. Venus moves onward until she reaches the position W, passing directly between the sun aud the obse! B This moment is similarly recorded by the astrono- | mer at the latter position, At whatever time the pianet’s shadow passes A it will be found to arrive at B in about ten minutes afterward. Hence tt would travel 6,830 miles tn ten minutes. Now the velocity of & shadow depends upon the velocity of the object that casts 1t; moreover, if the shadow be twice as far as the object trom the luminous centre the swiftness of tho shadow is double that of the object, and soon. We know by Kepler’s law that the earth's distance from the sun 1g ten-sevenths of that of Venus, and, consequently, Venus’ shadow on the eartn travels with ten-sevenths ag much velocity as Venus herseif. Consequently, the miles passed over by Venus’ shadow | in ten minutes, is ten-sevenths of the distance traversed by Venus herself inthe same time, Venus must, thereiore, in ten minutes have roshed over a distance of 4,040 miles, The reader may now ask how itis possible that Venus only goes thus far In ten minutes, whereas, a8 was stated at the commencement 0! this article, she traverses space at the rate of 77,200 miles per hour. Whence this apparent discrepancy? It must b> borne in mind that while it is quite true that she courses round in her oroit with wis latter velocity, the earth 1s performing a similar ouward movement in ite own orbit at the rate of 1,100 miles a minute, Both bodies are consequently rushing around like two chargers on a circular race track, the inner | horse oOutrunning the other, as does Venus with the earth, The distance of 4,940 miles is hence only the amount of space by whicn Venus outstrips the earth in ten minutes. And so will the planet continue to gain upon the earth, untilat length (after the expiration of 584 days) it will have beaten us out by a distance equal to the length of its own track, for at the end of that time it will bave circled around and come up with us again, as has been determined from ov- servations of hes movements among the stars. If, then, in ten minutes Venus outstrips the earth 4.940 miles, in an hour she would distance it 29,640 miles, in a day twenty-four times this amount and in 584 days about, 416,000,000 miles, which 1s con- sequently the pes of her orbit Venus, like the inner and swilter steed on tne race course, passes us by on the 8th of December, and steadily gains at a rapid pace, 80 that eventually she performs two and three-fi{ths jour. heys ronnd the sun, while the et makes only one and three-fifths circuits in the same time—584 days, In this pertod she makes one revolution more than the earth; ane distances it by one lengtn of her orbit, ‘The probiem then resolves itsell into this suape:—If Venus outstrips the earth 29,400 miles in one hour What must be the length of her orvit or the distance by woich she outrans it in 684 days? In order to avoid somniferous com- Piications we have omitted one important fact in. ‘he above calculation, While tne shadow of Venus is dashing from to (fig. 2) the station at B is being carried eastward by the revoiution of the earth on its own axis, ith @ velocity Which ts tusignificant near the Norm and South Poles, but which #xceeds 1,000 miles per uator, The Atasan af B. therafora, these giations only are transits possible, When the earth isin any other part of its orbi¢ Venus capnot pass between {t and the sun, be- cause she Will appear to be either above or below the solar giobe. In order that a transit occur Venus must overtake the earth at or very near the pointNorL. On the 8th of December the earth, Venus and the sun will be in the positions Mapped on this diagram. The arrows show the direction of the planetary movements. While the earth makes a circuit round the sun Venus per- forms one aod five-eighths nearly, and conse- quently when the earth returns t@ this same Position a year hence Venus will pot be in the @ame piace, vut will appear im th spot marked ‘75, In December, 1876, Venu: will have made one and five-elghiis saddi- tional rounds, apd 80 on, until at length in December of tue yéar 1852 she will occupy nearly the same position that she will pass during the coming transit, and the phenomenon will again be ubserved. The phases which Venus would present to an observer at the earth are portrayea in the diagram, and her position in December of each year until 1882. It is plain, then, tuat the earta will make eight complete revolutions with- out @ transit taking place, During the same. period Venus will perform thirteen. If thirteen revolutions of Venus were exactly equal to eight ol the earth’s we should have a transit every eight years. But this not being the case, alter eight hee more, the earth will arrive at tne position only to find thet Venus has just departed irom the position '82 Aijter eight years more this amount of departure will be doubled Bad 80 it will increase every eight years ull 1b becomes 80 grcat as to equal & whole length of Venus’ orbit, This takes place after 235 years; Transits, therefore, take place at the position L at intervals of eight and 235 years. it 13 now 235 years ago since a trausit took place while the earth, was at the position L—viz., in December, 1039, Eight years previously (1631) a similar one had taken place. Butsince transits can also occur at N in the month of June, it will not ve 235 years from 1882 before @ transit takes place. In the Meantine a transit will occur at N and another eight years thereafter, None can take place at that point afterwards for 235 years, DATES OF THE TRANSITS. Transits have been known to take place follows:—December 6, 1631; December 4, 1639}, June 6, iol; June 38, 176% ‘Transits are calculated to occur ferealter on December 8-9, 1874; December 6, 1882; June 7, 2004; June 5, 2012; December 10, 2117; December 8, 2125; June 11, 3247; June 8, 2253; December 12, 2360; December 10, 2368. It may hence be ob- served that thev take place in pairs eight years apart, and that the intervals of years between them are respectively 8, 12154,'8, 1044¢, 8, 121% and 80 On, this being the order of succession for a jong duration of time, ‘The photograph instrument will be employed for determiniug the contacts, and the electric battery: for ascertaining the longitudes of the stations, THE SPECTROSCOPE. This wonderful appliance, unknown to former observers, t8 likewise to be employed in ascer- taining the moments of contact, It is Known that the gaseous envelope of the sun prints. upon the spectrum, ines digerent from those presented by the sun itself, Wheo Venus 18 about to the manner anaiogous to the photographing process. But the momeut Venus touches the rim of the sup proper she shuts of a portion of tne light from this envelope. The spectroscope 1s so arranged that no light from the enveloping gas, except thas from the small patch thereof! now concealed by Venus, can enter it The moment, then, thas the said light ceases to be visivie in the spectro- Scope 13 the moment when Venus must have shut. it of and made her first contact with the sua. Similar adjustments are made for the devermi- nation of the o.her contacts. The employment of two ‘methods 80 essentially distinct will serve wonderfully in detecting any errors that may possibly arise in the procesa, The numerous sets 01 stations Will enable the astrono- mers to check one another’s estimates and arrive ata compromise. With our poweriul eerie delicate angle measures and ciocks beating pet fect ume we can tell within a iew eet vhe precige lo- cation of every station upon tne earth, their la Jongitudes and distances apart, In- stances Of this are given when vessels sail out upon the trackless ocean and bp ae grappling apparatus to the lowest depth of the sea in recover. ing the lost or broken telegraphic cat En skill, perseverance and the indispensable mon have been geverousiy fort ones and the ruling po! carrying the enterpr: tion, t wa All the means that devise wilt be made use of mk an on the great day so rat ds over- the hopes of tuany yearst fad indeed If @ brilliant victory. joes not efforts and sacrifices of that noble have penetrated the imm universe, who have explored ‘and worlas that ghtter throughout th Of space and time, aud who, by opening to the mind of man the dazzling glories of the mentai worids, have filled the human overflow ith gratitude and ami works, of the. Great Architect who bas (aid the foundations af them all and disposed all well,