164 



KNOWLEDGE 



[Sept. 14, 1883. 



THE HARVEST MOOX. 



By Richard A. Proctor. 



{Concluded from page 157.) 



OXOE ill each sidereal month the moon completes the 

 circuit of her orlnt, sliown in its mean position in 

 Fig. :.', the lunar day varying in length as the sidereal 

 month proceeds as the solar day varies each year, only in 

 greater degree because a lunar day is a larger proportion 

 of a lunar sidereal month than a solar day is of a year. 

 For, there are only ahout 20.', lunar days in a sidei-eal 

 month, as compared with Si]~'\ solar days in a sidereal 

 year. 



Suppose the moon at O on the half of the path M O m 

 remotest from the eye outside the disc. Then at the end 

 of a lunar day she is at ;(. Whereas then her path above 

 the horizon would have been represented by E O E' had 

 she remained at O on her path among the stars, her path 

 above the horizon would now be represented by a n a', if 

 she stayed for a lunar day at the point ii. Her point of 

 rising will be at k, nearly enough for such an inquiry as 

 the present, in which we may suppose EO E' her diurnal 

 path in one day, and a n a! her diurnal path on the next 

 day. >She rises then at the point k on the nearer half of 



the farther hemisphere were her setting point,* Thus 

 suppose the circle a c a of Fig. 2 ( foreshortened there) 

 opened out as in Fig. 3, the nearer half taking the position 

 a da' while the farther half takes the position ad' a'. 

 Then /(/ay represents the arc above the horizon, while 

 /' n./' represents the arc below tht! horizon. The equal arcs df 

 and (/'/■' indicate the amount Viy which the time of rising 

 precedes and the time of setting follows the mid times 

 between a' and a and between a and a'. This arc will be 

 found, if the projection is carefully made according to the 

 known position of the orbit 31 )n Fig. 2, and the moon's 

 motion therein, to correspond to about half an hour's 

 diurnal motion when M m has its mean position as in 

 Fig. 2, to about twenty minutes diurnal motion when the 

 moon's orbit has its least inclination (m m' Fig. 1, p. 156,) 

 and to about forty minutes diurnal motion when the moon's 

 orljit has its greatest inclination (M O M', Fig. 1). Thus the 

 day after passing the point O of her orbit, the moon rises 

 half an hour or so (on the average) earlier than she would 

 if she remained all the time on the equator. In this last- 

 named case of course she would rise day after day 50| 

 minutes later, a mean lunar day being 1 mean solar day 

 and .50 J. minutes. But when at this particular part of her 

 path around the star sphere, she rises not .50^ minutes later 

 on successive nights, but only about 20:'; minutes later 



the sphere S Z N Z', is carried to a her highest point above 

 the horizon, and pas?es down to the western lioiizon at k 

 again ; then bel iw the horizon to a' and so ba';k to k 

 again, — though in reality by this time she has reached (in 

 her path round the stellar heavens) the mark on M next 

 beyond ». 



Manifestly th^n the mion rises sooner an 1 sets later in 

 traversing the dinrnal ptth a fi' than in traversing the 

 diurnal path EOE' The straight line A- c, is in reality 

 the foreshortening of ' the arc by which the time of rising 

 precedes what it would be if the middle point c (on the 

 nearer hemi-phere) of her half circuit a c a' were her 

 rising poin*^ : k c is also the foreshortening of the arc by 

 which her time of setting follows what it would be if c on 



because her movement northwards from the equator makes 

 her rise about 30 minutes earlier than she otherwise would.f 



* I take tliis opportunity to correct what I find to be a prevalent 

 error, — the supposition that the sua is due east at six o'clock in the 

 morning, and due east at sis o'clock in the evenin.sr, all the year 

 round. A moment's study of Fig. 2 which gives the sun's path 

 -U m among the stars (as well as the moon's), shows tliat the points 

 occupied by the sun at six morning and evening, which of course 

 lie along the circle POP' (since thiscii-ole divides every transverse 

 semicircle as a c a', M C m' into equal arcs) are to the north of east 

 and west from the vernal equinox to the autumnal, and to the south, 

 of east and west from the autumnal equinox to the vernal. 



t The sun when at the corresponding part of his orbit, namely at 

 the vernal equinox, rises earlier by about 2} minutes on successive 

 days and sets about 24 minutes later, so that the interval between 

 succe.osive sunrises is less at this time than a mean solar day and at 



