VOL. LXXIV.] PHILOSOPHICAL TRANSACTIONS. 535 



Times of Observ. Estim. Geoc. Long. Angle q. 2d correc. 



1779, May 9" 12" ro 42° . . . . 7 s 22° 20' + 14° 45' + 



May 11 12 52 7 21 40 +15 11 +26' 



1777, Apr. 17 7 50 63 6' 3 34 + 23 26' 



May the 9th, 1779, the angle of position was roughly estimated at 42°, and 

 May 11, at 62°. The great disagreement of these coarse estimations is un- 

 doubtedly owing to the very different situation of the dark spot from which they 

 were taken; however, since he did not mean to use these observations in the 

 calculations, they may suffice in a general way to show, that the axis of Mars 

 was actually about that time in such a situation as the principles give it : for, 

 reducing the two positions to the 9th of May, that of the 1 1 th, from an 

 allowance of 26' for the situation of the planets, will become 62 26' ; and a 

 mean of the two, 50° 13' south preceding; which, reduced to a heliocentric 

 observation gives 66° 30', the north pole lying towards the left. Now, on cal- 

 culating from the position of the node and inclination of the axis before deter- 

 mined, we find, that the heliocentric angle was 62° 49', the north pole pointing 

 towards the left ; and a nearer agreement with these principles could hardly be 

 expected from estimations so coarse. If we go to the year 1777, and take the 

 position of the two bright spots observed the 17th of April, we have 63° 

 south preceding; this, reduced to a heliocentric quantity, gives 86° 26' of incli- 

 nation, the north pole being to the left. By calculating we find, that the pole 

 was then actually 81° 27' inclined to the ecliptic, and pointed towards the left as 

 seen from the sun. 



The inclination and situation of the node of the axis of Mars with respect to 

 the ecliptic being found, may thus be reduced to that planet's own orbit. Let 

 ec, fig. 9, be a part of the ecliptic ; om part of the orbit of Mars ; peo a line 

 drawn from p, the celestial pole of Mars, through e, that point which has been 

 determined to be the place of the node of the axis of Mars in the ecliptic, and 

 continued to o where it intersects the orbit of Mars. Now if, according to 

 Mr. De Lalande, we put the node of the orbit of Mars for 1783, in I s 17° 58', 

 we have from the place of the node of the axis (that is, 1 I s 17° 47') to the place 

 of the node of the orbit, an arch en of 60° 1 1' ; in the triangle neo, right- 

 angle at e, there is also given the angle eno, according to the same author, 

 1° 51', which is the inclination of the orbit of Mars to the ecliptic. Hence we 

 find the angle eon 89 5', and side on 6o° 12'. Again, when Mars is in the 

 node of its orbit, we have, by calculation from our principles, the angle pne 

 = 63° 7', to which adding the angle eno = 1° 5l', we have pno = 64° 58'; 

 from which two pon and pno, with the distance on, we obtain the inclination 

 of the axis of Mars, and the place of its node with respect to that planet's own 

 orbit; the inclination being 6l° 18', and the place of the node of the axis 



