ON PRACTICAL ASTRONOMY. 427 



it is usual, in calculating the place of a planet, to find from the tables of 

 its motion, the mean place, in which it would be found if its orbit were 

 circular, and thence to derive the true place, by means of various correc- 

 tions called equations. In France the solar time is considered as the true 

 time, and is used for all civil purposes, so that the clocks are some- 

 times embarrassed with a complicated apparatus, calculated for imitating 

 the inequalities of the actual apparent motion of the sun. (Plate XXXV. 

 Fig. 503.) 



The art of dialling consists principally in projecting, on a given surface, 

 such lines as will coincide with the shadow of an index or gnomon parallel 

 to the earth's axis, at intervals corresponding to the different hours of the 

 day : so that nothing more is necessary for the construction of a dial, than 

 to determine the intersections of the surface on which the dial is to be 

 constructed, w r ith planes passing through the edge of the gnomon, and 

 situated at equal angular distances from each other : thus, supposing the 

 plane of the dial perpendicular to the gnomon, and parallel to the equinoc- 

 tial, the hour lines of the dial will be at equal distances from each other ; 

 but in other cases their distances will be unequal, and must be determined 

 either by calculation or by construction. A point may also be used as a 

 gnomon, as well as a line ; but in this case the hour lines must cover a 

 larger portion of the surface, in order that the shadow of the point may 

 always fall among them. (Plate XXXV. Fig. 504... 506.) 



The changes of the seasons depend on the return of the sun to the same 

 position with respect to the equator, or on the length of the tropical year, 

 so called from the tropics, which are circles supposed to be parallel to the 

 equator, and between which the sun travels continually backwards and 

 forwards, appearing to remain for some time, when he is near them, with 

 very little change of declination ; whence the time when the sun touches 

 either tropic is called the solstice. The vicissitudes of light and darkness 

 depending also on the solar day, it is necessary, for the regulation of the 

 civil calendar, to establish the proportion between the periods of the solar 

 day and the tropical year ; and since the tropical year exceeds the time of 

 365 days, by 5 hours, 48 minutes, and 48 seconds, it is usual to add to the 

 common year an intercalary day once in about four years. The ancient 

 Egyptians reckoned only 365 days in a year, and their nominal new year 

 arrived continually earlier and earlier, so that after 1507 of their years, it 

 would have happened successively on each of the 365 days, and returned 

 to the original place : the same mode of computation was also adopted by 

 the Greek astronomers. The Romans inserted intercalary days, at first 

 without much regularity, according to the direction of their augurs, until 

 the time of Julius Caesar ; who, observing that the year was almost 6 hours 

 longer than 365 days, added a day every fourth year to the calendar, by 

 reckoning twice the day in February called sexto calendas Martias, whence 

 this year of 366 days was denominated a bissextile year. The new moon 

 immediately following the winter solstice, in the 707th year of Rome, was 

 .made the first of January of the first year of Caesar ; the 25th of December 

 in his 45th year is considered as the date of the Nativity of Christ, and 

 Caesar's 46th year is reckoned the first of our era. The preceding year is 



