1841.] 



Notes on Capt. Shortrede's Scheme . 



601 



1, or rather the succession which it shews, may be represented by 

 the following progression : — 



Series, 12 3 4 5... 25 ...50, &c. 



Years ending these series, . 4 8 12 16 20... 100 ... 



Days beginning these years, 4 9 14 19 24... 



The common difference of the years is 4, of the days 5 : the 25th 

 term will therefore be year 100 and day 124: 124 days equal 17 

 weeks and 5 days ; therefore the lOOdth year will begin with the day e. 



9. According to Old Style this progression may be extended to series 

 50. The fiftieth term of the progression will be, year 200 and day 

 249 ; 249 days equal 35 weeks and 4 days ; therefore the 200dth year 

 begins with the 4th day d. In the same manner it may be found that 

 the year 300 begins with the third day c ; the 400dth with the 2d 

 day h ; the 500dth on the first day a ; the 600dth on the 7th day g ; 

 and the 700dth on the 6th day/ 



10. Hence every lOOdth year commences on a week-day, one day 

 earlier than the preceding lOOdth year : consequently if the year 1 of 

 any century begins on any week-day a, the year 1 of the next century 

 will begin on the week-day g^ — i. e. a day earlier. 



11. In Old Style all the days of the week in their turn commence a 

 century and a lOOdth year. 



12. The following Tables are formed according to Articles 8 — 10. 

 The Table marked (2) shews how each hundredth year begins. Table 

 (3) shews how each century or first year of each 100 begins : — 



Days of the week 



begin Hundredth 

 years, i. e. years 

 100,200, 300, &c. 



1 



8 

 15 



22 

 29 

 36 



d 



c 



b 



a 



g 



f 



2 



3 



4 



5 



6 



7 



9 



10 



11 



12 



13 



14 



16 



17 



18 



19 



20 



21 



23 



24 



25 



26 



27 



28 



30 



31 



32 



33 



34 



35 



37 



38 



39 



40 



41 



42 



(Table 2.) 



Days of the week 



begin centuries or 

 years 1 of 100; 1 

 of 200, &c. 



1 



8 



15 



22 



16 

 231 



3 

 10 



17 

 24 



e 



d 



4 



5 



11 



12 



18 



19 



25 



261 



6 7 



13 14 



20 21 



26| 27 28! 



(Table 3.) 



