J34 PHILOSOPHICAL TRANSACTIONS. [ANNO 1784, 



of Mars being south preceding; whereas they would be too small before, and 

 too large after, the meridian passage, the pole being south following. These 

 two observations arranged, and reduced to the time of the 25th of June, will 

 stand as follows. 



Hmeofobserv. ^ les An § lc First cor- Second Corrected 



taken. q. rection. Correc. Angle. 



June 25" 1 1" 36 m 74°32' — 10° 14' + { ^ ? f . ... - 0° 0' 73° 1 1' 



July 15 10 12 7118 — 8 20 — 1 1 + 1 54 75 11 



He remarks, that having here admitted both measures as equally good, there- 

 fore the result is a mean of them both, and shows the axis of Mars, June 25, 

 178], to have been 75° ll' south preceding. 



The next business will be to reduce two geocentric observations to a helio- 

 centric measure. This is to be done, as shown before, by a calculation of the 

 angle a, fig. 8. The result of it shows, that 10° 14' are to be subtracted from 

 the mean corrected angle of position, reduced to June 25, 1781, and 23° 18' 

 to be added to the angle which is the corrected mean of 13 measures, reduced 

 to Oct. 4, 1783. Hence we learn, that on those days and hours, when the 

 heliocentric places of Mars were 9 s 24° 35', and s 7° 15' (which would happen 

 about July 18, 1781, and Sept. 29, 1783) an observer placed in the sun would 

 have seen, on the former, the axis of Mars inclined to the ecliptic 64° 57' the 

 north pole being towards the left ; and on the latter, he would have seen the 

 same axis inclined to the ecliptic 78° 59', the north pole being then towards 

 the right. 



The first conclusion we may draw from these principles is, that the north 

 pole of Mars must be directed towards some point of the heavens between 

 9 s 24° 35' and s 7° 15'; because the change of the situation of the pole from 

 left to right, which happened in the time the planet passed from one place to the 

 other, is a plain indication of its having gone through the node of the axis. 

 Next, we may also conclude, that the node must be considerably nearer the 

 latter point of the ecliptic than the former; for whatever be the inclination of 

 the axis, it will be seen under equal angles at equal distances from the node. 

 But, by a trigonometrical process of solving a few triangles, we soon discover 

 both the inclination of the axis, and the place where it intersects the ecliptic at 

 rectangles (which, for want of a better term, Dr. H. calls its node). Accord- 

 ingly he finds, by calculation, that the node is in 17° 47' of Pisces, the north 

 pole of Mars being directed towards that part of the heavens; and that the 

 inclination of the axis to the ecliptic is 59 42'. 



Dr. H. now compares the observations of an earlier date with these principles, 

 to see how far they agree. Some of the particulars and calculations relating to 

 them are as follow. 



