202 



NOTES AND QUERIES. 



[No. 99. 



added to the Tegular of any month to indicate, in 

 a similar niaunei", the commencing day of that 

 month. 



It follows, therefore, that tlie only burthen the 

 memory need be charged with is the distribution 

 of the regulars among the several months ; because 

 the other element, the solar epact (which also 

 ranges from 1 to 7), may either be obtained from a 

 short mental calculation, or, should the system 

 come into general use, it would soon become a 

 matter of public notoriety during the continuance 

 of each current year. 



Now, these solar epacts hxve several practical 

 advantages over the Dominical letters. 1. They 

 are numerical in themselves, and therefore they 

 are found at once, and used directly, without the 

 com])lication of converting figures into letters and 

 letters into figures. 2. They increase progressively 

 in every year; whereas the Dominical letters have 

 a crab-like retrogressive progress, which impedes 

 facility of practice. 3. The rationale of the solar 

 epacts is more easily explained and more readily im- 

 derstood : they are the accumulated odd days short 

 of a complete week ; consequently the accumula- 

 tion must increase by 1 in every year, except in 

 leap yeai's, when it increases by 2 ; because in leap 

 years there are 2 odd days over 52 complete weeks. 

 But this irregularity in the epact of leap year does 

 not come into operation until the additional day has 

 actually been added to the year; that is, not until 

 after the 29th of February. Or, as Bede describes 

 it, " in leap yeais one of the covcvrrent days is 

 ivtermitted, hitt the mimlicr so irderniitied must he 

 used for January and Fcbj'uary; after ivhich, the 

 epact obtained from cyclical tables (or from calcula- 

 tion) must be used for the remaining moidhs." By 

 ■which he means, that the epacts increase in arith- 

 metical succession, except in le:ip years, when the 

 series is interrupted by one number being passed 

 over ; the number so jjassed over being used for 

 January and February only. Thus, 2 being the 

 epact of 1851, 3 would be its natural successor for 

 1852; but, in consequence of this latter being leap 

 year, 3 is intermitted (except for January and 

 February), and 4 becomes the real epact, as ob- 

 tained from calculation. 



To calculate the solar epact for any year, Bede 

 in another place gives the Ibllowing rule : 



" Si vis scire fcncurreiitcs septinianre dies, sume 

 annos Domini et eorum (juaitum partem adjice ; his 

 quoque qiiatuor adde. (quia) quinque concurrcntes 

 fucrunt aiuio Nativitatis Domini : hos pai tire per sept jni 

 et remanent Epacta; Sol is." 



That is : l:\ke the given year, add to it its 

 fourth part, and also the constant ninnbcr 4 (which 

 was the epact preceding the first year of the Chris- 

 tian era), divide the sum by 7, and what remains 

 is the solar epact. (If there be no remainder, the 

 epact may be calle<l either or 7.) 



This is an excellent rule; the same, I believe. 



that is to this day prescribed for arriving nt the 

 Dominical letter of the Old Style. Let it be 

 applied, for example, to find upon what day of the 

 week the battle of Agincouit was fought (Oct. 25, 

 1415). Here we have 1415, and its fourth 353, 

 and the constant 4, which together make 1772, 

 divided by 7 leaves 1 as the solar epact; and this, 

 added to 2, the regular for the month of October, 

 informs us that 3, or Tuesday, was the first day of 

 that month ; consequently it was the 22nd, and 

 Friday, the 25th, was Saint Crispin's day. 



But this lule of Bede's, in consequence of the 

 addition, since his time, of a thousand years to the 

 number to be operated upon, is no longer so con- 

 venient as a meidal resource. 



It may be greatly simplified by separating the 

 centuries from the odd years, by which the opera- 

 tion is reduced to two places of figures instead of 

 four. Such a method, moreover, has the very 

 great advantage of assimilating the operation of 

 finding the solar epact, in both styles, the Old and 

 the New ; the only remaining dillerence between 

 them being in the rules for finding the constant 

 7iumber to be added in each centuiy. These rules 

 ai e as follow : — 



For the Old Style. — In any date, divide the 

 number of centuries by 7, and deduct the remain- 

 der from 4 (or 11) ; the result is the constant for 

 that century. 



For the Neic Style. — In any date, divide the 

 number of centuries by 4, double the remainder, 

 and deduct it from 6 : the result is the constant for 

 that century. 



For the Solar Epact, in either Style. — To the 

 odd years of any date (rejecting the centuries) 

 add their fourth part, and also the constant num- 

 ber found by the preceding rules ; divide the turn 

 by 7, and what remains is the solar epact. 



As an example of these rules in Old Style, let 

 the former example be repeated, viz. a.d. 1415 : 



First, since the centuries (14), divided by 7, 

 leave no remainder, 4 is the constant number. 

 Therefore 15, and 3 (the fourth), and 4 (the con- 

 stant), amount to 22, from which eliminating the 

 sevens, remains 1 as the solar epact. 



For an example in Netc Style, let the present 

 year be taken. In the first place, 18 divided by 

 4 leaves 2, which doitbled is 4, deducted from 6 

 results 2, the constant number tor the present 

 century. Therefore 51, and 12 (the fourth), and 

 2 (the constant), together make G5, from which 

 the sevens being eliminated, remains 2, the solar 

 epact for this year. 



But in appreciating the practical facility of this 

 method, we mu^t bear in mind that the constant, 

 when once ascertained for any century, remains 

 unchanged thioughout the whole of that century; 

 and that the solar epact, when once ascertained tor 

 any year, can scarcely require recalculation during 

 the remainder of that year: furthermore,^,that 



