_ Professor Dean’s method of illustrating the equation of time. 33% 
is nearest its apogee, and advance when it is nearest its perigee. The 
distance of any two of these mean days must always be between 40 
and 120 days. In summer and winter there will always be periods 
of at least 40 days in which the sun will be too slow ; and in spring 
and autumn similar periods, in which it will be too fast. When the 
apsides coincide with the equinoxes, the summer and autumn equa- 
tions are equal but contrary, and also the spring and winter, and two 
of the mean days, are on the equinoxes, and the solstitial mean days 
each about 67 days from that equinox in which is the sun’s perigee. 
When the sun’s apsides coincide with the solstices, the spring and 
summer equations are ‘equal, and the autumnal and winter ; two of the 
mean days are on the solstice, while the equinoctial mean days are 
about 67 days from that solstice in which is the sun’s apogee. The 
mean day belonging to the vernal equinox is now advancing in the 
calendar at the rate of one day in about 347 years, that belonging to 
the summer solstice is retreating at the rate of a day in 92 years, that 
belonging to the autumnal equinox is advancing at the rate of a day 
in 242 years, that belonging to the winter solstice is advancing a day 
in 201 years. If the equation by the eccentricity of the earth’s orbit 
were just equal to that from the obliquity of its equator, the motion of 
the mean days in the calendar would be equal to one fourth of the 
year, advancing during three fourths of the revolutions of the apo. 
gee, and receding the other fourth ; and when the apsides were in the 
octants, two of them would coincide, and there would be only three 
mean days in the year. If the equation from the eccentricity were the 
greatest, the mean day formed by the coincidence of the other two 
would vanish, and there would be a number of years “about this ‘posi- 
tion of the apsides with only two mean days ineach. ’'The numt ml r of 
these years would increase with this ‘equation, till with an ‘equation 
from the eccentricity more than double that from the obliquity there 
