200 The Planet Mars in 1873. [April, 



the actual boundary of the disc. It is clear, moreover, that 

 the upper or southern part of the disc is viewed more directly 

 than it is illuminated ; for, where the edge of t{ie terminator 

 is there seen, the solar rays are falling tangentially on the 

 globe of Mars, whereas the lines of sight from the earth do 

 not here fall tangentially. (Of course the same remark 



note, by an inadvertency, the denominator in the expression for tan p is written 

 sin (Q — 5). The following formulae can be used, if preferred : — 

 cos I . sin p= — sin I . cos (a — N) 

 cos / * cos/ = sin I . sin (a — N) sin S + cos I cos 8 

 sin 1= sin I . sin (a— N) cos d — cos I sin d. 

 Moreover, if V be the elevation of the sun above the plane of the ring, \ the 

 heliocentric longitude of Mars, then, with sufficient approximation, — 

 sin /'= sin (X — X') sin I'. 

 Strictly speaking, formulas corresponding to those given at p. 229 of my 

 " Treatise on Saturn " should be employed, viz., putting — 

 8 = Mars' heliocentric latitude, 



v = longitude of ascending node of Mars' orbit on ecliptic, 

 and S3'= arc from ascending node of Mars' orbit on ecliptic to ascending 

 node of Mars' equator on his orbit. 

 Then assuming — 



cos ^ = cos (X-v) cos /3, 



108 21 

 115 12 

 122 10 

 129 15 

 136 29 



143 53 

 151 27 



159 13 

 167 11 



It will be seen that the value of/ changes very little during the four months. 

 Usually/ changes largely. Thus in the opposition-period of 1866-7, p ranged 

 in value between 9 50' and 21 52'. The reason of the approach to constancy 

 in the value of p during the present opposition is readily seen on a considera- 

 tion of the figure given above. For we see that, viewed from the earth, Mars 

 first slightly advances, then retrogrades through opposition, and then slightly 

 advances. As this motion takes place along a part of the ecliptic where that 

 circle is descending from the first point of Libra to the tropic of Capricorn, it 

 follows that, so far as this motion is concerned, the apparent slope of the 

 polar axis of Mars to a declination circle (west) at first slightly diminishes, 

 then increases, and towards the end slightly diminishes again. This change 

 depends simply on the inclination of different parts of the ecliptic to declina- 

 tion circles. But the apparent slope of the axis of Mars is also changing 

 precisely as the opening out of his equator is changing (see column under /), 

 being least when the opening out of the equator is greatest, and vice versa. 

 So far as this cause of change is concerned, the slope of the axis first slightly 

 increases, then diminishes, and towards the end slightly increases again. 

 Comparing these with the changes due to the other cause, we see that the two 

 changes are compensatory. Hence/ remains very nearly constant. 



we have — 

















sin I' 



= sin (<&- 



Si') sin 



r. 



Date. 













Greenwich. 

 Noon. 



P- 





I. 





/'. 



1873- 



1 





1 





1 



Feb. 26 



41 4 



W. 



15 7 



N. 



25 47 N. 



Mar. 13 



41 3 





H 7 





24 29 



28 



41 4 





14 15 





22 49 



April 12 



41 10 





15 34 





20 47 



27 



" 41 





i/ 57 





18 23 



May 12 



40 3i 





20 30 





15 40 



27 



40 2 





22 18 





12 30 



June 11 



40 2 





22 5 g 





9 21 



26 



40 33 





22 36 





5 5o 



