448 NEW OBSERVATIONS OP THE PLANET MERCURY. 
■ 
As tlie markings showed that the planet's polar axis was substantially perpendicular 
the plane of its orbit, these phase polar and phase equatorial diameters practically 
conicided with the 
/ 
29. Conection for Threads. — The correction for the threads, owing 
^y 
the diameters were taken, is a very small quantity and is massed with that for the 
spurious disk. The correction for the micrometer thread and the spurious disk is 
taken at 0".20 for the old micrometer; at 0".10 for the new micrometer in January; 
and at 0''.07 for the new micrometer in February and March. 
30. Correction for Irradiation. — A word upon the correction for irradiation is 
necessary. In all planetary measures the correction for irradiation is of fundamental 
importance, in spite of which it is usually either not applied at all, or applied en hloc 
to the final result. Determinations are obtained ignoring it, which in consequence 
are quite worthless. To show the magnitude of the error thus committed, I may 
take the expression for the polar compression say of Mars ^^—^, with a and b 
nearly equal. If the correction for irradiation, as frequently happens in conse- 
quence of phase, be a third as great again on b as on a, while on either it is two 
or three times as great as the difference between them, it is evident that by 
ignoring it the value obtained for the ellipticity is vitiated nearly one hundred 
per cent. 
The correction for irradiation I got from intercomparison of measures made upon 
a painted disk, upon Mars, Yenus, and Mercury, and from estimates made upon the 
old moon in the new moon's arms, taking in all these cases relative albedos, 
eyepieces, object-glass, and sky illumination into account. That the resulting 
correction is not far from the truth seems to be indicated by the fact that the 
diameters thus got for Yenus and Mars agree closely with the best previous deter- 
mmations; the polar diameter of Yenus, at distance unity, coming out 16".96, and 
that of Mars 9''.32. 
For the polar diameter, the correction for the irradiation is taken at 0".07 at 
the beginning of the time, and thence graded to 0".20 at the end, because of the 
constantly increasing illumination at the cusps. 
