63'2 PHILOSOPHICAL TRANSACTIONS. [ANNO 1784. 



bv overlooking these circumstances. The following observations will assist us 

 in the investigation of the preliminary points. Dr. H. here details the numerous 

 observations he made of the spots on the planet, and exhibits the several views 

 of its disc in the numerous figures. Hence he concludes in general, that none 

 of the bright spots on Mars were exactly at the poles, though they could cer- 

 tainly not be far from them. But, more particularly, from the appearance 

 and disappearance of the bright north polar spot in 1781, he collects that the 

 circle of its motion was at some considerable distance from the pole. By a cal- 

 culation, made according to the principles hereafter explained, its latitude must 

 have been about 7 6° or 77° north; for, to the inhabitants of Mars, the declina- 

 tion of the sun, June 25, 12 h 15 m of our time, was about 9° 56' south; and 

 the spot must have been at least so far removed from the north pole as to fall a 

 few degrees within the enlightened part of the disc, to become visible to us. The 

 south pole of Mars could not be many degrees from the centre of the large 

 bright southern spot of the year 1781; though the spot was of such a magni- 

 tude as to cover all the polar regions farther than the 70th or 65th degree, and 

 in that part which was on the meridian July 3, at 10 h 54 m , perhaps a little 

 farther. 



The bright polar spots therefore on Mars being the most convenient objects 

 for determining the situation of the axis of this planet; Dr. H. collects, in one 

 view, all the measures he had taken of these spots for that purpose. He then 

 applies the observations to determine the situation of the axis of Mars. To this 

 end, we see that, in the first place, the measures must be corrected for the lati- 

 tude of the spot; next, they must be reduced to a heliocentric observation, 

 which will also correct them from the difference occasioned by the different 

 situation of the planet when they were taken. This being done, we may select 

 two observations at a proper distance; from which, by trigonometry, we shall 

 have the node and inclination of the axis. When these elements are obtained, 

 it will be easy to see how other observations agree with them ; which will afford 

 the means of correcting or verifying the former calculations. 



Let t, fig. 8, pi. 7, be the earth; 25 aq V? the ecliptic as seen from t; 

 p the point of the heavens towards which the north pole of the earth is directed; 

 m the place of the orbit of Mars jumivi, where an observation of the poles of 

 that planet has been made, which is to be reduced to its heliocentric measure. 

 And first suppose it to have been made at the time of the opposition of that 

 planet. Then, the place m or q in the ecliptic being given, we have the sides 

 Q 25, 25 p; whence the angle q, of the right angled triangle p 25 a, is found. 

 This being added to, or taken from, the observed angle of position of the axis 

 of Mars, according to circumstances easily to be determined, reduces it to its 

 heliocentric position. But if this observation was not made at the time of an 



