110 



A perpetual Moon Table. 



[No. 134. 



other Table the corresponding week day • the first Sunday after Easter. 

 If full Moon in March falls before the 21st, set the Table to April, and 

 proceed as before. 



Professor Gauss has given a formula for finding Easter without 

 using the Epact, as may be seen in Delambre's Astronomy. It is as 

 follows : — 



Divide the given number of the year by 19, 

 and let a be the remainder. 



Divide the given number by 4, and let b 

 be the remainder. 



Divide the number by 7> and let c be the 

 remainder. 



Divide (19 a + M) by 30, and let dbe the 

 remainder. 



Divide (2 b + 4 c + 6 d + N) by 7, and 

 let e be the remainder. 



Then Easter-day will be the (22 + d + e) 

 of March or the (d + e — 9) of April- For 

 the Julian Calendar, this rule is general, where 

 M an 15 and N = 6 alwaysg it requires 

 a correction for the Gregorian Calendar. If 

 the calculation gives the 25th or 26th of 

 April, take away seven days. 



The following Table 

 gives M and N in the 

 Gregorian Calendar as 

 far as 2,500. 



MN 



From 1582 to 1699 22 3 



1700 1799 23 3 



1800 



1899 23 4 



1900 



1999 24 5 



2000 



2099 24 5 



2100 



2199 24 6 



2200 



2299 25 



2300 



2399 26 1 



2400 



2499 25 1 



On the Treatment of Geometry as a branch of Analysis. By S. G. 



ToLLEMACHE HEATLY, ESQ. 



1. The clothing of purely geometric principles in analytical language 

 — in other words — the conduct of elementary geometric inquiries by 

 functional equations is historically connected with the subject of my 

 former papers. Legendre's endeavour to prove on functional princi- 

 ples, that the three angles of a triangle are equal to two right angles, 

 and thence to deduce the theory of parallels will readily occur to the 

 memory of those familiar with mathematical records. But the first 

 step in developing the idea may be traced higher, and I think success- 

 fully, to a yet more illustrious origin. 



