' t 101 ] 
Quell. What year of our Lord in the 19th cen- 
tury will have the folar cycle either 1, 7, 18, or 24, 
when the lunar cycle is 14? Or, which is the fame 
thing 5 
Quell. What number is there between 1800 and 
1900, which divided by 28 leaves 1, 7, 1 8, or 24; 
and being divided by 19 leaves 14? 
SOLUTION. 
Here then in the general theorem ~ xd — e 4. d t 
is <7—28, 1 9, D— 1 , 7, 18, or 24 ; E=i4,/=i. 
To find r, the quotients are * i, 2, 9; * ip)28( 1 
drop the firfl and laid, becaufe their 9)19(2 
number is odd: then the feries re- 09(9 
quired will be o, 1 2 ; therefore r ~ 2. 
N. B. If to any year of Chrifl be added 9, and 
the fum divided by 28 ; the remainder, or 
28, if o remains, will be the cycle of the fun 
for that year ; and if 1 be added to any 
year of Chrifl, and the fum divided by 19; 
the remainder, or 19, if o remains, is the 
cycle of the moon . Hence, if any year of 
Chrifl be federally divided by 28 and 19, and 
the remainders be d and e refpedtively ; then 
d 4- 9, or d - 1 - 9 — 28 — : D ; and e -j- 1, 
or e -] -1 — 19 — E. In the prefent cafe, 
taking D — 1, d 9 ±= 1 cannot be; be- 
caufe d would be negative : but d muft not 
only be affirmative , but alfo greater than e \ 
wherefore make d -|- 9 — 28 = D — 1 ; 
therefore 
