1873-1 The Planet Mars in 1873. 199 



slightly forwards, for E 2 M 2 is slightly inclined (and in that 

 sense) to E, X M Z ; hence, precisely as happens from the for- 

 ward motion of Mars round the sun (in this part of his 

 orbit), the elevation of the earth south of his equator-plane 

 slightly diminishes. But from this position right onwards, 

 until the position M 8 (or thereabouts), Mars is swaying back- 

 wards (around the earth) ; hence all this time the elevation 

 of the earth south of the planet's equator-plane is increasing. 

 And lastly, as Mars moves forwards round the earth, after 

 passing M 8 , the elevation of the earth south of the equator- 

 plane slightly diminishes. These results are indicated in 

 the table which is given in the foot-note. 



Now it is easy to perceive how these results accord with 

 the presentation of Mars in the nine projections of the 

 illustrative plate. In projection 1 we see how the terminator, 

 continued beyond its northern extremity (at the bottom of 

 the projection), must pass farther from the -pole than does 



Longitude of pole of Mars .... .. 349 1 1 for ecliptic . 



Latitude 61 9 J r 



Assuming these numbers to apply to 1834*0, we find — 



Longitude of ascending node of equator of Mars upon 



his orbit (\ r ) 80 50*4 



Obliquity of martial ecliptic (1') 27 16*5 



And hence- 

 Ascending node of equator of Mars on the earth's 



equator (N) 47 33*9 



Inclination (I) 4 . 3955*6 



For 1873*0 -f£ these values give — 



N = 47 53 + "5°* 

 1=39 43-0'25*. 



I have adopted these values in the computation of p and I in the accom- 

 panying table ; p being the apparent inclination of the axis of Mars to the 

 circle of declination, and I the elevation of the earth above the equator of the 

 planet ; using the following formulae : — 



Let a be the geocentric right ascension of Mars 

 d „ declination „ 



and Q an auxiliary angle such that — 



tan Q =s tan i . sin (o-N), 

 then — 



and — 



tan I = tan (Q — 5) cos p. 



These formula? are given by Mr. Hind in the note referred to above, and are 

 the same as are used in the " Nautical Almanac " for determining the position 

 and phase of Saturn's ring. (They are given in full, with others, among the 

 explanations of the tables in my " Treatise on Saturn "). But in Mr. Hind's 



