of Edinburgh, Session 1880-81. 
19 
proportional to the times, while the moon’s geocentric semidiameter, 
as well as the horizontal parallax, is supposed to be constant during 
the eclipse. In this way some exceedingly small errors are intro- 
duced into the calculation. 
In order to take full advantage of the admirably minute and exact 
ephemerides given in the body of the “ Almanac,” I thence, using 
second differences wherever they had any influence, computed the 
geocentric positions of the sun and moon, and the moon’s parallax 
and semidiameter, for intervals of 10 m. during the eclipse. 
From these again I deduced strictly the declinations, hour 
angles, semidiameters, and separations, as seen from the Royal 
Observatory of Edinburgh, using 300 : 299 as the ratio of the earth’s 
oblateness. Lastly, from these results, and with the same precau- 
tions, I calculated the instants of the first and last contacts, and that 
of the closest approach. My table of the values of circular seg- 
ments enables me also, with great ease, to determine the part of 
the sun’s disc hid by the moon. 
The following are the results : — 
n. m. s. 
First contact at 1 30 10 Green. M. S. Time 
Greatest phase, 2 29 26 ,, 
Last contact, 3 26 15 ,, 
Portion of sun’s diameter uncovered 17' 03". Ratio of uncovered 
to covered portions of sun’s disc 631 : 369, the whole surface being 
1 , 000 . 
I may remark that the moon’s parallax and semidiameter, as 
given among the elements, have been obtained by simple inter- 
polation from those for 0 h. and 12 h. ; whereas the moon is in 
perigee during the eclipse, and the parallax instead of decreasing 
uniformly from 0 h. till 12 h., actually increases to a maximum 
and then decreases; so that in place of 61' 27" ’3 we should have 
had 61' 27". 6. 
The comparison of these predictions with the times observed at 
the Calton Hill will be interesting, should the weather permit. 
