588

OUTLINES OF ASTRONOMY.

(art. 383). The tropical year is actually about 4-21 s shorter thanit was in the time of Hipparchus . This absence of the mostessential requisite for a standard, viz. invariability, renders itnecessary, since we cannot help employing the tropical year in ourreckoning of time, to adopt an arbitrary or artificial value for it, sonear the truth, as not to admit of the accumulation of its error forseveral centuries producing any practical mischief, and thus satisfy-ing the ordinary wants of civil life; while, for scientific purposes,the tropical year, so adopted, is considered only as the representa-tive of a certain number of integer days and a fraction—the day-being, in effect, the only standard employed. The case is nearlyanalogous to the reckoning of value by guineas and shillings, anartificial relation of the two coins being fixed by law, near to, butscarcely ever exactly coincident with, the natural one, determinedby the relative market price of gold and silver, of which either theone or the other—whichever is really the most invariable, or themost in use with other nations,—may be assumed as the true theo-retical standard of value.

(913.) The other inconvenience of the tropical year as a greaterunit is its incommensurability with the lesser. In our measure ofspace all our subdivisions are into aliquot parts: a yard is threefeet, a mile eight furlongs, &c. But a year is no exact number ofdays, nor an integer number with any exact fraction, as one thirdor one fourth, over and above ; but the surplus is an incommensu-rable fraction, composed of hours, minutes, seconds, &c., whichproduces the same kind of inconvenience in the reckoning of timethat it would do in that of money, if we had gold coins of thevalue of twenty-one shillings, with odd pence and farthings, anda fraction of a farthing over. For this, however, there is noremedy but to keep a strict register of the surplus fractions ; and,when they amount to a whole day, cast them over into the integeraccount.

(914.) To do this in the simplest and most convenient manneris the object of a well-adjusted calendar. In the Gregoriancalendar, which we follow, it is accomplished with as much sim-plicity and neatness as the case admits, by carrying a little fartherthan is done above, the principle of an assumed or artificial year,and adopting two such years, both consisting of an exact integernumber of days, viz. one of 365 and the other of 366, and laying