538 PHILOSOPHICAL TRANSACTIONS. [_ANNO 1784. 



measured twice; and as no reason appears against either of" the observations, he 

 takes the mean of both, which is 2l" 29'", or 1289'"; so that by these measures 

 the equatorial diameter of Mars is to the polar as 1355 to 1289. A less perfect 

 agreement between the proportions of the diameters arising from the measures of 

 the 20-feet reflector and those now deduced from the 7-feet, would have been 

 sufficient for our purpose, as we might easily have excused 1 or 2000ths of the 

 whole quantity; however, we have no cause to be displeased with this coinci- 

 dence, though it should in part be owing to accident, and therefore shall admit 

 the above proportion, and proceed to a further examination of it. 



In the first place, it will be necessary to see whether any correction be required 

 on account of the different heliocentric and geocentric south latitude of Mars; 

 which would apparently compress the polar diameter a little, by the defect of 

 illumination on the north. . On computation we find, that a difference arising 

 from that cause would give the longitudinal diameter to the latitudinal as 20000 

 to 1QQ87; which being much less than a 1000th part of the whole, may there- 

 fore be neglected. But next, a very considerable correction must be admitted, 

 when we take into account the position of the axis of Mars. The declination of 

 the sun on that planet, at the time the measures were taken, was not less than 

 27° south; so that the poles were not in the circumference of the disc by all that 

 quantity. On a supposition then, that the figure of Mars is an elliptical sphe- 

 roid, we are now to find the real quantity of the polar diameter from the apparent 

 one. It has been proved, that, in the ellipsis, the excesses of any diameters 

 above the polar one are as the squares of the cosines of the latitudes; but the 

 diameter at rectangles to the equator of Mars, which was exposed to view in the 

 late opposition, was not the polar one, but such as must take place in a latitude 

 of 63°. Putting therefore m = cosine of 63°, a = 1355, b = 128Q, * = the 

 polar axis, we have 1 : m~ :: a — x : b — x, which gives x = 1272 nearly, for the 

 polar diameter. The true proportion therefore, of the equatorial to the polar 

 diameter, will be as 1355 to 1272; which, reduced to smaller but less accurate 

 numbers, is as 1 6 to 15 nearly. 



On the subject of the figure of Mars, says Dr. H., I ought to remark also, 

 that perhaps the measures which were taken of its diameters during the last op- 

 position will enable us to ascertain its real size with greater accuracy than has 

 been done before. The micrometer which can distinguish with precision be- 

 tween the equatorial and polar diameters of this small planet, will certainly be 

 admitted as an evidence of considerable consequence; and since the result of 

 these measures is pretty different from what former observations give us, I should 

 not omit mentioning it. We have seen that the equatorial diameter, on the day 

 of the opposition, measured 22" 35"'. The distance of Mars from the earth at 

 that time was .40457, the mean distance of the earth from the sun being l; 

 therefore, 22" 35'" reduced to the same distance will be no more than 9" 8'". 



