268 | Mr. Herscue’s Objervations 
In the firft place, it will be neceflary to fee whether: any dork 
rection be required on account of the different heliocentric and 
geocentric fouth latitude of Mars; which would apparently — 
comprefs the polar: diameter a little, by the defeé&t of illumina- 
tion on the north. On computation we find, that a differenéée 
arifing from that caufe would give the longitudinal diameter'te 
the latitudinal as 20000 to 19987; which bemg much lefs 
than one thoufandth Cia of the whole, may therefore be 
neglected. HG 
But next, avery confiderable correction muft be admitted, 
when we take into account the pofition of the axis of Mars. 
‘The declination of the fun on that planet, at the time the 
meafures were taken, was not lefs than 27° fouth; fo that the 
poles were not in the circumference of the difk by all that 
quantity. On a fuppofition then, that the figure of Mars is 
an elliptical {pheroid, we are now to find the real quantity of 
the polar diameter from the apparent one. It has been proved, 
that, in the ellipfis, the excefles of any diameters above’ the 
polar one are as the fquares of the cofines of the latitudes * ; 
but the diameter at rectangles to the equator of Mars, which 
was expofed to our view in the late oppofition, was not the 
polar one, but fuch as muft take place in a latitude of 63°. 
Putting therefore m=cofine of 63°, 4= 1355, 6=1289, «= 
; b— mm. 
the polar axis, we have.1:m*::a@-x:6-—x%. And : — 

= 
which gives us 1272 nearly, for the polar diameter. The true 
proportion, therefore, of the equatorial to the polar diameter 
will be as 1355 to 12723; which, reduced to fmaller but lefs 
accurate numbers, is 16 to 15 nearly. 
* Afir, par M. pE 1A LanpeE, § 2680, ' 3 
. I thal] 
