7W MOON. 



with the sun. 3. The average anomalistic month, or revolution from 

 perigee to perigee. 4. The average tropical month, or from the vernal 

 equinox to the vernal equinox again (the equinox being in retrograde 

 motion [PKECESSIOH]). 5. The average nodical month, or from a 

 node to a node of the same kind. The quantities of these months 

 are as follows (Baily, ' Astron, Tables and Formula) ') in mean solar 

 days : 



Ohms d 



Sidereal month . . 27 7 43 11-5 or 27-32166145 



MOON. 



760 



Lunation . . 

 Anomalistic month 

 Tropical month . 

 Nodical month 



29 12 44 2-9 



27 13 18 37-4 



S7 7 43 4-7 



27 5 5 3G-0 



29-53058872 

 27-55459950 

 27-32158242 

 27-21222223 



If we compare the lunation with the common year, we shall find 

 that 235 lunations make 6939'69 days, while 19 years make 6939 or 

 6940 days, according as there are four or five leap-years in the number. 

 Neither is wrong by a day ; consequently in 19 years the new and full 

 moons are restored to the same days of the year. This does not abso- 

 lutely follow, either from the preceding or from the method which 

 gave it, since neither is the coincidence exact, nor are the mouths 

 exactly equal. But it will generally so happen ; and this is the founda- 

 tion of the Metonic Cycle. [CALIPPUS and METON, in BIOG. Div.] 

 Again, 223 lunations make 6585-322 days, and 242 nodical revolutions 

 make 6585'357 days, so that there is only -035 of a day, or 50 minutes, 

 difference between the two. This period of 223 lunations is the SAROS, 

 a celebrated Chaldean period, and contains in round numbers of days 

 18 years and 10 days, or 18 years and 11 days, according as there are 

 five or four leap-years. It may be worth while to express these num- 

 bers of lunations in terms of the other months. 



Mtlonic Cycle. 235 lunations make 253'999 sidereal mouths, 251'852 

 anomalistic months, and 256'021 nodical months. 



Saras. 223 lunations make 241-029 sidereal months, 238'992 anoma- 

 listic months, and 241 999 nodical months. 



The rate at which the moon moves is different in different parts of 

 the orbit. We may speak either of the rate at which she changes 

 longitude, latitude, or distance from the earth ; t ind owing to the 

 siuallness of the inclination of her path to the ecliptic, her motion in 

 longitude is nearly the same thing as her motion in her own orbit. 

 The quickest motion U at or near the perigee, and the slowest at or 

 near the apogee. The moon's rate of motion follows no easily obtain- 

 able law in its changes, which are different in different months. The 

 rate of change of latitude is greatest near the nodes, and the rate of 

 change of distance from the earth is least at the apogee and perigee, 

 and greatest at and about the intermediate points. We have hitherto 

 considered the apparent path of the moon among the stars : we 

 now pass to the real orbit in space. Her average distance from the 

 earth is 29-982175 times the equatorial diameter of the earth, which 

 makes about 60 radii of the earth, or 237,000 miles. But the radius 

 of the BUD'S body is 1 11 i times the radius of the earth : so that a 

 large sphere, which, having its centre in the earth, should contain 

 every part of the moon'* orbit, would not be a quarter of the size of 

 the sun. 



Again, the sun's distance is 23,984 radii of the earth, or nearly 400 

 times the moon's average distance. A good idea of the relative magni- 

 tudes of the distances may be obtained as follows : Take a ball one 

 inch in diameter to be the sun, and another of half an inch in diameter 

 to be the sphere which envelopes the moon's real orbit ; place these 

 nine feet apart, and a proper idea of the distance of the sun, compared 

 with its size and that of the moon's orbit, will be obtained. 



To form a sufficient notion of the real orbit, imagine another body, 

 directly under the moon on the plane of the ecliptic, to accompany 

 her in her motion. Let e s 8 8 represent the plane of the ecliptic, iu 

 which the sun must be, and A L B a part of the real orbit, from an 

 to a descending node ; L being a position of the moon, P is 



the projected body on the plane of the ecliptic ; and the motion of p 

 will be very nearly that of L, owing to the smallness of the rise of A L B 

 above the plane of the ecliptic. The motion of the projected body will 

 then be of the kind of which the following diagram is an exaggeration. 

 Suppose the moon to set out from 1 on the left, being then in 

 apogee, and also at a node : the projected body will then describe 111, 

 Ac., until it cornea to its perigee at the first '2, which is in advance of 

 the point opposite to the apogee. But the real moon will have come 

 to the plane of the ecliptic before it is opposite to the first 1, so that at 

 the first 2 the moon will be below the projected orbit. The projected 

 body then describes 2 2 2 ... up to the next apogee 3, and so on ; the 



real moon having come above the ecliptic before the last 2 but one. 

 In the present figure the number of folds is limited, and the last joins 



the first ; in the moon's orbit the number of folds is unlimited. The 

 real relation between the greatest and least distances is slightly variable 

 in the different folds ; one with another it may be thus stated : 5i per 

 cent, being added to the mean distance will give the greatest or 

 apogean distance, and subtracted, the least or perigean distance. 

 Taking the fiction of the moving ellipse for- the moon's orbit, its eccen- 

 tricity is -0548442. 



In the article GRAVITATION will be found a sketch of the producing 

 causes of the inequality of the lunar motions, showing that they arise 

 from the effect of the sun's unequal attraction of the earth and moon ; 

 were it not for which, the latter would describe an ellipse round the 

 former. In the present article we intend only to describe the motions 

 themselves. We have pointed out both the apparent orbit iu the 

 heavens, and the real orbit : It remains to ask, In which manner is the 

 real orbit described ? At a given time, how is the moon's place in the 

 heavens to be ascertained 1 



Returning again to the apparent orbit, we first consider motion in 

 longitude only ; that is we ask how to find the moon's longitude at the 

 end of a given time. Let us suppose then that, Q being the apparent 

 place of the moon in the heavens, we draw Q M on the sphere perpen- 

 dicular to the ecliptic, so that M has the same longitude as Q. To con- 

 nect this figure with the last, suppose that the moon was at L when it 

 was projected in the heavens to Q, and let p be the projection of L on 

 the ecliptic : then p will be thrown upon M in the heavens. The 

 average motion of M will be that of the moon, or a circuit in 27'32166 

 days. If then we were to suppose a fictitious moon setting out from 

 M, and moving with this average motion, it would never be far from 

 the point M ; which last, from the irregularity of the real moon's 

 motion, would be sometimes before and sometimes behind the fictitious 

 moon. 



If we could observe the fictitious moon, thus regularly moving in 

 the ecliptic (say every day at midnight), and also the real moon, we 

 might take a long series of years' observations, and sum all the excesses 

 of M'S longitude over that of the fictitious body, when there are 

 excesses, and all the defects when there are defects. We might expect 

 to find the one sum equal to the other ; but we are taught by the 

 theory (which, as before seen, is exact enough to find the moon's 

 place within a second) that the equality of these sums will not be 

 absolutely attained in any series of years, however great, if we take 

 the commencing point, at which M is to coincide with the fictitious 

 body, at our own caprice. Wherever Q may be, there is a proper 

 place for this fictitious moon, before or behind M, from which if we 

 allow the former to start, the longer we go on with the series of sup- 

 posed observations, the more nearly will the excesses balance the 

 defects ; supposing always that our series of observations stops at the 

 end of a complete number of circuits, and not in the middle of one. 

 This position is called the mean place of the moon, as distinguished 

 from <J, its real place. Let us suppose it to be at v ; then if the 

 average moon start from v, with the moon's average motion, it will at 

 every instant of time point out what is called the mean place of the 

 moon corresponding to the then real place. At the commencement of 

 the present century, that is, when it was 12 o'clock at Greenwich on 

 the night of December 31, 1800, the longitude of theaverage moon, or 

 the moon's mean longitude, was (according to BurckLardt) 118 17' 3'' ; 



