120 B. A. Gould—Algebraic Expression of the 
knowledge, be at first advantageously assumed as 2 P. M.; and 
also show how a rough approximate knowledge of the epochs 
may be made to contribute essentially to that of the formula. 
Tq aid the attainment of this let us consider the facts at our 
disposal regarding the values of these epochs in general. 
ery extensive materials are available for this purpose, but 
it is safer to restrict ourselves to a limited number of points 
for which the observations have been scrutinized, and the in- 
ferences deduced, with special care, than to base our researches 
upon a larger number of less trustworthy results. For these 
reasons the values adopted by Dr. Wild in the work already 
cited, have generally been preferred to others; and those for a 
number of places, such as Upsala, Berne, Leipzig, Greenwich, 
St. Helena, Lisbon, have been specially determined here. ll 
depend upon hourly observations, with the single exception 
of Schwerin; but at Santiago de Chile, and Valparaiso, the 
observations were made during only a few days in each month, 
in different years. At Santiago the total number of days’ of 
observation was 130, at Valparaiso, 60. To facilitate the ex- 
amination of the results here given, and the deduction of 
analogous ones for other places, it may be convenient for those 
who are not astronomers, to have ready access to general 
tables of the equation of time, the sun’s declination, and the 
times of sunrise and sunset in different latitudes. Those which 
follow* represent the mean values; and although not strictly 
accurate in every year, they may be used without hesitation for 
meteorological purposes. The equation of time as here given 
is to be applied to the mean time, to obtain the apparent; or 
with reversed sign to the apparent if the mean is desired. 
The first of these tables gives the mean values for each 
decade during the year, corresponding to our arrangement, 
according to which all the days subsequent to the 20th of each 
month are made to form the third decade. The second table 
gives the apparent time of sunrise if the latitude be North, 
and of sunset if it be South, for the middle of each month. 
Our data relative to the mean epochs of the diurnal ex- 
tremes are deduced from the observations in each month 
arrival of the sun’s center at the horizon is used, without any 
correction for refraction. 
* The tables mentioned are giveu in the original article, but are necessarily 
omitted here.— Eps. 
