VOL. LXXIV.] PHILOSOPHICAL TRANSACTIONS. 537 



tion of such doctrines. So far from creating difficulties or doubts, it will rather 

 appear singular, that the spheroidical form of this planet, which the following 

 observations will establish, has not already been noticed by former astronomers ; 

 and yet, reflecting on the general appearances of Mars, we soon find that oppor- 

 tunities for making observations on its real form cannot be very frequent : for, 

 when it is near enough to be viewed to advantage, we see it generally gibbous, 

 and its oppositions are so scarce, and of so short a duration, that in more than 2 

 years time we have not above 3 or 4 weeks for such observations. Besides, 

 astronomers being already used to see this planet generally distorted, the sphe- 

 roidical form might easily be overlooked. Dr. H. then gives a number of obser- 

 vations relating to the polar flattening of Mars, showing that there is always a 

 difference between the observed polar and equatorial diameters of that planet, the 

 former being the less in proper positions. 



We find that the quick alterations in the visible disc of Mars, during the time 

 it is in the best situation for us to observe it, are such, that if we were to use 

 many measures which have been taken of its diameters, we should be obliged to 

 have recourse to a computation of its phases, in order to make proper allowance 

 for them. Now, since these changes are in a longitudinal direction, and the 

 poles of Mars are not perpendicular to the ecliptic, it would bring on a calcula- 

 tion of small quantities, which it is always best not to run into where it can be 

 avoided. For this reason, Dr. H. at once settles the proportion of the equatorial 

 to the polar diameter of this planet, from the measures which were taken on the 

 very day of the opposition. He prefers them also on another account, which is, 

 that they were made in a very fine, clear air, and were repeated with a very high 

 power, and with two different instruments, of whose faithful representation of 

 celestial objects, the many observations on very close double stars he had made 

 with them gave him very evident proofs. 



Being only in quest of the proportion of one diameter to the other, the mea- 

 sures of the 20-feet reflector, though not given in angular quantities, will equally 

 suffice for the purpose. By them we have the equatorial diameter to the 

 polar as J03 to 98, or as 1355 to 1289. He turned the proportion into the 

 latter numbers by v/ay of comparing them the better with the measures of the 

 7 -feet reflector. By that instrument the equator of Mars, Oct. 1, was measured 

 3 times ; but from the remarks annexed to the different results, he thinks the 3d 

 measure should be used. Indeed, on taking the difference of the first two, which is 

 34'", and dividing by 3, we have the quotient 11^-'"; then, allowing -| to the 

 first, because the remark says positively " narrow measure," it becomes 

 22" 34-§"', and taking J- from the 2d, which is expressed doubtfully, " rather too 

 full," it becomes 22" 35'" : this reflection on the first two measures gives addi- 

 tional validity to the 3d, which is 22" 35'", or 1355"'. The polar diameter was 



vol. xv. 3 Z 



