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Table 90. Excess of revolution for the Sun in expanded years

Nu, f. 96r: Tabula revolucionum annorum Rc, f. 79r: Tabula de revolutionibus annorum

Ed. 1526, f. 386r: Tabella annuarum conversionum post bisextum anni

Tables 90-93 are used to determine the time, t, at which the Sun has the same position as it had at a given epoch, t0, before the time sought, that is, after very nearly an integer number of tropical years has elapsed. Chapter 40 gives two worked examples for the use of these tables: for times close to the epoch, that is, when the solar apogee does not change significantly, and for times well after the epoch. Different tables apply in these two cases.

The argument of this table is the number of years from 1y to 40y at intervals of 1y: see Table 90. In addition to the column for the argument, there are 4 columns, one for each year in a 4 year-cycle, beginning with a leap year. One enters the table in the row which has the number of years since the epoch and then looks in the column for the character of the year of the epoch, i.e., if it is a leap year, one looks in the column so labeled, and if it is not a leap year one looks at the entry in the appropriate column. The entries, in hours, minutes, and seconds, are the excesses over 365 days after a number of years have elapsed. Thus, in the first row we are told to add (A) 5;49,16h to the time of the epoch when one year has elapsed or to subtract (M) 18;10,44h (= 24h

- 5;49,16h) from it when the year of the epoch is the third year after a leap year. We note that 5;49,15,36h derives from the standard Alfonsine tropical year-length of 365d 5;49,15,36h = 365;14,33,6d. In the second row we are told to add (A) 11;38,32h (= 2 ■ 5;49,16h) to the time of the epoch when two years have elapsed, in the case of an epoch that was in a leap year or 1 year after a leap year, or to subtract 12;21,18h (= 24h

- 11;38,32h) from it when the year of the epoch is 2 or 3 years after a leap year. In row 4 (and multiples of 4) the increment in time is the same in all four columns (4 ■ 5;49,16h = 23;17,4h = 24h - 0;42,56h), and each entry in row 40 is then 10 times the entry in row 4.

Table 90: Excess of revolution for the Sun in expanded years (excerpt)

Years

Leap year

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