356 



• KNOWLEDGE ♦ 



[Oct. 27, 1882. 



and that after two revolutions she is only behind by tl»e 

 amount which the Earth traverses in 84 1448 days. Thus 

 she has gaiuetl in 449-4016 days by the amount which the 

 Earth traverses in 281 1 1 IG days ; and what we require is 

 to know in what time slie will gain a complete circuit, or 

 the amount traversed by tlie earth in 36r>'25t34 days. This 

 is in effect a were ruleofthree sum, which would in the 

 ordinary way Ih' stated as follows :^ 

 As l'8rillG : 3G5 2504 :: 449-401G : period we require. 



It will Im? found, if this sum bo worked out, that the 

 required period is one of 583 9204 days, and this is the 

 p«'rio«l which is given in tables of elements of the planets as 

 the mean synodical period of the Earth and ^'enus, that is 

 tlie mean interval between the successive conjunctions of 

 theso planets on the same side of tlie sun.* 



Now let this be noticed : The Earth in 5839204 days 

 will l>e at E, where the arc E Ei is one traversed in 

 2 1 ^ 6640 days, and the remaining are Ej E, therefore, is 

 oil'- traversed in 1465924 days. But we know that the 

 tifth part of an ordinary year contains 73 days, or about 

 the half of the period required for traversing the arc E, E. 

 Tliis arc, then, is about two-fifths of the orbit ; and tlie 

 arc E E, is therefore about threelifths of the orbit. Let 

 us inquire more particularly into this relation, because it 

 is an important one in many respects. 



The true tifth part of a year is a period of 73 05 13 days, 

 and tliree times this period amounts to 219'1539. Kow, 

 wf have seen that the arc EE, is traversed in 218-GClO 

 days. Tlie dill'erence amounts to 0-489i) of a day, or less 

 than half a day. Thus, if we drew lines (EV one), 

 dividing the orbits e.xactly into tive equal parts, then the 

 conjanction-line E,ViS lies less than half a degree from tin- 

 nearest of these lines (for the earth's mean daily motion is 

 sliglitly less than one degree), and behind, ns respects the 

 direction of the planet's motions. Manifestly, the next 

 conjunction-line will be as E.V.S, rather less than a degree 

 short of the nearest of the equidistant lines. The ne.xtwill 

 \je as EjVaS ; the next as EiV,S. And, lastly, the next 

 will be as E^V^S, rather less than 3i degrees from EVS. 

 Five synodical revolutions have now passed, giving, there- 

 fore, a period amounting to 2019-6020 days. Venus has 

 made nearly thirteen revolutions, and the earth has made 

 nearly eight Since eight sidereal years amount to 

 2927-05 12 days, the actual difference, or in other words 

 the period in which the Earth traverses the arc E^E, 



• Of coaree, the mctbod given above is not intended to indicito 

 the inost concise process for obtaining the synodicnl period of two 

 pUnctt. It ia only intended to preHcnt the matter bo reasoned out 

 as to involve uo t«cbnicalitica. The proper process is as follows : 

 Vcnun's mean daily motion in her orbit 



— r of tho complete circuit. 



224-7008 "^ 



Thn Karth'n daily motion in her orbit 



•■— — of her complete circuit. 



Therefore Vcnoa's mean daily gain on tho Eartli 



\2Z*-" 



7008 3H52651 



lof the complete circuit. 



And Tcona'i synodical period, in dayx, 



224 7008 X 3C5-2.''.G !■ 

 3<»-250l-2Z-l-70t« 



1__ 1_ 



Z»4-;00fJ - 3<i5266t 

 Or thus— 



Venos's main daily motion iu 

 The Karth's 



VenTin'ri mean daily |^tn in her orbit « 2219-475 

 And Vcnai'a rvnodical period — 



300 X 60 K OO . r^n.r.,n, i 



-2219-476 doy-S^S-O' ■'")'- 



amounts to 24492 days. Now the Earth's meai» daily 

 motion in her orbit is 3548-193". Multiplying this by 

 2-4492, we obtain for the mean value of the arc E,-,E, 

 8690-23G', or 2^ 24' 50-23G". Thus we see that in five 

 synodical periods there is a return to the immediate 

 neighbourhood of the conjunction-line at the beginning. 

 These live periods last \ery nearly eight years. We 

 may say, in fact, that in eight years, wanting 2-4492 

 days, the conjunction-line EVS is shifted to the position 

 E/V,,S, 2° 24' 50-23G" behind its former position. Thus 

 we see that this conjunction-line will travel completely 

 round iu as many times eight years as 2° 24' 50 236" is 

 contained in 360°, less one year, this one year resulting 

 from tho slight defect of five synodical periods from eight 

 years. This period, which may bo called a grand cycle of 

 Venus .-xnd the Earth, has a mean value of 1 192 0632 years. 

 But it is manifest from Fig. 1 that in ii lifth part of this 

 time tho conjunction-line EiV,S, will have passed to the 

 position E^V^S^* ; while every other conjunction-line of the 

 live equidistant ones in Fig. 1 will have passed round 

 (backwards) to the position of the ne.\t. In other words, 

 in the course of 238-412 years (on the average) there will 

 have been conjunctions of Venus and the Earth all round 

 their orbits at intervals as close as those which separate 

 each of the live conjunction lines of Fig. 1 from its nearest 

 neighbour. (It will presently bo seen that this period, 

 238-4126, has to bo somewhat enlarged to represent the 

 mean interval between transits occurring at either the 

 ascending or descending node of \'enus's orbit.) 

 (To be continued.) 



Pehpetual Motion. — After describing the electric 

 launch recently run on the Thames, the Spectator of 

 Sept. 30 says: "Nothing is said about expense, but ;i 

 boat which can travel at this speed without coal and with 

 no funnel must for many purposes be of almost immediate 

 us('. As the charging machines can be put up anywhere, 

 the practical problem of electricians must be to reduce the 

 size and weight of the accumulators. Once small enough 

 to be carried, they might drive a steamer across the 

 Atlantic, being perpetually recharged by a dynamo driven 

 by the motion itself." 



Lady Compaxions fou the Insane. — Dr. Rees Philipps, 

 in his reports on the Wonford Lunatic Hospital for the 

 Insane, at Exeter, strongly advocates the appointment of 

 educated ladies as companions to the inmates of the femalo 

 departments of asylums for lunatics of tho upper and 

 middle classes. Every hour that he .spends in tho femaU; 

 wards of the hospital under his charge strengthens his con- 

 viction of the beneficial iiilluencc on lady patients of kindly 

 companionship and the nursing of gentlewomen. A 

 certain proportion of lady nurses has been introduced into 

 that admirably-conducted registered hospital — Bamwooil 

 House — at Gloucester, and the medical superintendent, 

 iJr. Needham, is satisfied that he obtains more work from 

 these lady-nurses, and at no increased cost, than from 

 nurses drawn from the domestic servant class. If this 

 opening for u.s(!ful and meritorious work were more widely 

 known than it is at present, many gentlewomen of suitable 

 position and temperauK^it would doubtless avail them- 

 selves of it. The emoluments oflered are not large ; but 

 an honourable livelihood and interesting occupation are not 

 without their attractions. — JMical J'vh^. 



• Tho correct way of stating thin, that tho mean period in which 

 any conjunction-lino rcachcH the place of the next liehiml in a fifth 

 part of the grand cycle. Thc^ro is not an actual conjunction along 

 tho line E,VjS at tho end of this time, because the grand cycle does 

 not contain an exact number of years. 



