1807.] 
not be unacceptable, therefore, to your 
readers, should I offer a few reasons for 
this apparent irregularity in the celestial 
phenomena, and endeavour to account 
for it by arguments which are commen- 
surate to the capacities of the unlearned 
in astronomical science. 
That it has been usual to call the in- 
terval of time of the sun’s rising or set-~ 
ting before or after six o’clock, by the 
hame of ascensional difference, is well 
known; and that the ditference of good 
clocks and watches, from the time shewn 
by the sun on the most accurate sun- 
dials, sometimes sooner, and sometimes 
later, is called the Equation of Time, is 
not less notorious. Though the meaning 
of these terms is fully understood by 
astronomers, it is necessary to premise 
thus much by way of information to the 
unscientific. 
From the table of Equation of Time 
given in many almanacs for every day, it 
is obvious that there are but four days in 
the year on which good clocks and 
watches shew the same precise time with 
the sun, On all others they are some- 
times before the sun’s apparent time, and 
sometimes after it. Without any design 
of demonstrating the cause of this vari- 
ance, I shall only observe that it pro- 
ceeds from certain eccentric inequalities 
in the earth’s orbit round the sun, which 
give this irregularity to the sun’s appa- 
rent daily motion, so as at some times to 
fall short of the mean daily motion, and 
at other times to exceed it. How these 
atfect the phenomena of the sun, to pro- 
duce the fact above stated, is what I 
shall now endeavour to show, by applying 
these principles to the effects which will 
be produced in the present year. With 
the difference of the fraction of a day 
only, they will equally apply to any other 
year. 
As these phenomena are most conspi- 
cuous in the winter half year, and more 
particularly from about the third of No- 
vember to the 10th or 11th of February, 
I shall specially note the circumstances 
immediately applicable to the subject 
during that interval. And it is manifest 
to any attentive observer, that from 
about the former of these days in each 
year to the 13th of December, the days 
shorten in the evenings much less than 
they do in the mormngs; and farther, 
that on the latter day the evening begins 
to lengthen, though the mornings will 
continue to shorten for eighteen days 
louger, or until the 31st of that month. 
Zn this interval of eighteen days the 
the Lengthening and Shortening of Days, 341 
daily variance of ascensional difference 
being smaller than the daily variance of 
the equation of time, gives all the excess 
of the latter in favour of the evening; 
and hence the shortest evening will hap- 
pen about the 13th of December, though 
the shortest morning will not happen 
until eighteen days later. 
For let us consider that on the 13th of 
December, 1807, for instance, the equa- 
tion will be about five minutes forty- 
eight seconds, to be taken from the sun’s 
apparent time, in order to shewthe equal 
time pointed out by good clocks and 
watches ; for at this time the almanacs 
represent good clocks and watches be- 
hind the sun. This is done away in about 
twelve days, and in six days more the 
equation is three minutes five seconds 
nearly on the other side, when good clocks 
and watches are so much before the sun. 
At the two extremities of this interval of 
eighteen days, therefore, though the sun 
rises and sets precisely at the same time, 
the apparent time is nearly nine minutes 
later in the morming, and as much later 
in the evening, so that whilst the former 
is so much shortened, the other is so 
much lengthened. It should always be 
remembered, however, that this is stated 
according to the true representation of 
good clocks and watches. The ascen- 
sional difference having less daily vari- 
ation in the latitude of London (which is 
the place I am considering) during these 
eighteen days, than the daily variation of 
the equation exhibits, evidently produces 
an appearance of lengthened evenings 
from the moment that such daily variance 
of the equation exceeds the daily vari- 
ation of the ascensional difference. 
We may farther add, that from the 
1st of January in each year, the morn- 
ings will apparentky begin to lengthen a. 
little; but the evenings will still continue 
to have the advantage by as many se- 
conds of time daily, as is the daily vari- 
ation of the equation of time, and the 
improvement of longer mornings is still 
retarded by as much as that daily vari- 
ation of equation amounts to. The ad- 
vantage which the daily variation of as- 
censional difference has now gained, will 
still operace but slowly in the morning, as 
the daily variation of the equation of 
time must first be subtracted; but it will 
Operate fully in the evening, as it will 
then receive all the advantage of the va- 
riation of such ascensional difference, with 
the addition of the variation of the equa- 
tion of time. And this advantage will 
continue, though gradually and daily es 
an 
