VOL. LXXIV.] PHILOSOPHICAL TRANSACTIONS. 533 



opposition, but at some other place m, a second correction is to be applied in the 

 following manner. Let the angle q, of the triangle p 25 q, be found as before, 

 and properly applied to the position of the axis of Mars now at m ; then make 

 the single ms^, at the sun s, equal to the angle smT, and ^ will be the helio- 

 centric place, where the angle of position, when seen from s, will appear to be 

 as it was found at m, after the application of the first correction: for s^ being 

 parallel to Tin, and supposing the axis of Mars to preserve its parallelism while it 

 moves from m to p, appearances of Mars at p to an eye at s, must be the same 

 as they are at m to an eye at t. Dr. H. then sets down in a table the results of 

 the calculations of the foregoing observations. And then adds, as we have no 

 particular reason to select one measure rather than another, a mean of all the 13, 

 (the number of them) will probably be nearest the truth; so that, by these obser- 

 vations, which are reduced to the 4th of Oct. 1783, we find the position of the 

 axis of Mars that day to have been 55° 4l' south following. 



From the appearances of the south polar spot in 1781, he concludes, that its 

 centre was nearly polar. It continued visible all the time Mars revolved on his 

 axis; and, to present us generally with a pretty equal share of the luminous 

 appearance, a spot which covered from 45° to 60° of a great circle on the globe 

 of Mars could not have any considerable polar distance: however, a small cor- 

 rection in the angle of position seems to be necessary which should be taken from 

 the measure of the loth of July, -because that branch of the spot which pro- 

 bably extended farthest towards the equator was then in the following quadrant. 

 The measure of both the spots on June the 25th, 1781, is still more to be 

 depended on, as giving very nearly the position of the true pole ; for it appears 

 evident from the phenomena of the bright north polar spot, that the spot was in 

 the meridian when the measure was taken, while the southern spot was in the 

 preceding quadrant near its greatest limit. Now, since an angle at the circum- 

 ference of a circle is but half the angle at the centre, when the arches which 

 subtend these angles are equal, the correction necessary to be applied to the 

 measure taken through the two spots will be but one half of the correction which 

 would have been requisite had it been through the centre; therefore, in order to 

 reduce this to the condition of the former, we may suppose it to have been taken 

 through the centre of Mars when the spot was only 30, or 1 50 degrees from the 

 meridian. It is also necessary to add 1° 54' to the angle of July 15, which it 

 would have measured more had the planets remained where they were June 25. 

 This done, we may have the polar distance of the centre of the spot as before. 

 Half the sum of the sines (of 231° 38' and 150°) to radius, as 50' (half the 

 difference between 74° 32' and 76 12') to a 4th number, which is 1° 18'. 



Dr. H. observes here, that the measures of the angle of position would be 

 too large before the spot came to the meridian, and too small afterwards, the axis 



