Draft proposals for calendar reform

Author: Isaac Newton

Source: Yahuda Ms. 24d, National Library of Israel, Jerusalem, Israel

Published online: October 2009

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  - 1 January 2001
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Related Texts
- This document is part of Yahuda Ms. 24
  The previous part of this document is Draft proposals for rectifying the Julian calendar [Yahuda Ms. 24c]
  The next part of this document is 'Regulæ pro determinatione Paschæ' (draft and fair copy) [Yahuda Ms. 24e]

<1r>

Annis
365 $\frac{1}{4}$ ^d.	− 11′. 13″. 92
365 $\frac{1}{4}$	− 11′. 31″. 2
365 $\frac{1}{4}$	− 10′. 56. 64
365 $\frac{1}{4}$	− 10′. 48″	Ann. Greg

10′. 48″ // 10′. 56″. 64 // 11′. {illeg}″ {illeg} 13′. 92 // 11′. 31″. 2 facit in annis 5000 facit 37 $\frac{1}{2}$ , 38, 39, 40 dies respective.

Observationes Hipparchi

Anno
Periodi 3 Calippi	Ante Christū	Alexandriæ	Temp. appar Grenovici	Temp. med Grenovici	Locus ☉ ex calculo si annus 365 $\frac{1}{4}$ dies − 11′
17	162	Sept 27 sub occas. ☉	27.^d 3.^h 44′
20	159	Sept 27 sub ort ☉	26. 15. 44
21	158	Sept 27 in ips. merid.	26. 21. 44
2\|3\|2	147	Sept 26 media nocte	26. 9. 44
32\|3\|	146	Sept 27 mane	26. 15. 44
3{illeg}\|2\|	146	Mar 24 mane et iterū hora diei 5^ta	23. 15. 44 & 23. 20. 44
36	143	Sept. 26 vesp.	26. 3. 44
43	135	Mart 23 circa med. noct	23. 9. 44
49	128	Mart 23 sub occas. ☉	23. 3. 44
	162	Sept 26\|7\|. 13{illeg} $\frac{1}{4}$		26. 22. 59
	158	Sept 27. 12 $\frac{1}{2}$	26. 22. 14
	146	Sept 27. 10 $\frac{1}{4}$	26. 20\|19\|. 59
	159	Sept. 27. 1 $\frac{3}{4}$	26. 11. 29
	147	Sept. 27\|6\|. 23 $\frac{1}{2}$	26. 9. 14
	143	Sept. 26 22 $\frac{3}{4}$	26 8. 29
17	162.	Sept. 27. 00.44	27. 06. 0	− 5. 16
20	159	Sept. 27\|6\|. 17\|8\|.11	26. 18. 0	+ 0. 11
21	158	Sept. 27. 00.00	27. 00. 0	+ 0. 00
32	147	Sept. 26. 15.59	26. 12. 0	+ 3. 59
33	146	Sept. 26. 21.48	26. 18. 0	+ 3. 48
36	143	Sept. 26. 15.15	26. 06. 0	+ 9. 15
32	146	Mar 23. 20. 1	23. 20. 30.	(6) + 12. 29 (2. 5 − 0. 29
43	135	Mar 23. 12. 0	23. 12. 0	− 0. 0
49	128	Mar 23. 4.43	23. 06. 0	− 1. 17
50.				3) − 1. 46 (35 $\frac{1}{3}$

− 7.′ 14″ æq. t.

	Diff merid 2^h 15′	Diff merid 2^h 15′
Temp appar mediocre cor Alexand	Temp appar Grenovici Alexand	Temp. appar. Grenovici
27. 8. 5	26. 22. 39	26. 20. 24
26. 20. 5	26. 16. 6	26. 13. 51
27. 2. 5	26. 21. 55	26. 19.40
26. 14. 5	26. 13. 54	26. 11. 39
26. 20. 5	26. 19. 43	26. 17. 28
26. 8. 5	26. 13. 10	26. 9. 55

	23. 20. 36	23 18. 21
	23. 12. 35	23. 10. 20
	23. 5. 18	23. 3. 3

And at y^e end of every 500 years the larger period of \lunar/ months w^ch shall or should be then running shall contein only 45 m lunar months & consist of \the/ three lesser periods each of w^ch shall \of w^ch that larger period consists shall each of them/ contein only 15 \lunar/ months, the two last months of the \two/ periods {illeg} \co conteining/ 17 months being \then/ omitted.

The advantage of this Calendar above y^e Gregorian \in respect of the solar y/ is that in y^e Gregorian the Solar year errs a day in 5000 years in this it errs a day & by that error recedes from y^e state it had in y^e age of Christ, in this it errs a day in 10000 years & by that error approaches the state it had in y^e age of Christ so that in 30000 years it will a the equinox will fall on y^e 24^th of March as it did in y^e age of {illeg}|C|hrist & in 110000 years the beginning of Ianuary will fall on y^e winter solstice as it ought to do. Also y^e recconing by 500, 1000, 1500 &c runs in rounder \& fewer/ numbers then that by 400, 800, 1200, 1600. And tho y^e Kalendars differ yet y^e stiles \they/ will agree \in stile/ for 700 years to come.

<1v>

The advantage in respect of y^e Lunar year is that much greater. For \in/ the Gregorian Kalendar the full Moon on w^ch Easter depends requires is not to be found w^th out y^e help of \three or four/ Tables, & when you have that full moon there is no rule in that Kalendar for finding y^e other full moons & y^e new moons throughout y^e year. But in this Kalendar \all/ the new & full Moons are found perpetually without any Tables at all or any other recconing then y^e continuall addition of y^e 2|3|0 & 29 days w^ch is so \very/ easy a work that any Novice may perform it. And besides this rule is exacter then y^e Gregorian for that errs thre hours & t in 2|3|9 years this errs but 3 hours in five hundred years.

^{[Editorial Note 1]} <3r>

The advantage of this Kalendar above y^e Gregorian in respect of y^e solar year is that y^e solar year in y^e Gregorian errs a day in 5000 years & by that error recedes from y^e state it had in y^e age of Christ, in this it errs a day in 10000 years & by that error approaches the state it had in y^e age of Christ so that in 30000 years the equinox will fall on y^e 24^th of March as it did in y^e age of Christ & in 110000 years the beginning of Ianuary will fall on y^e winter solstice as it ought to do. Also the recconing by 500, 1000, 1500 &c runs in rounder & fewer numbers then that by 400, 800, 1200, 1600 &c. And tho y^e Kalendars differ yet they will agree in stile for 700 years to come.

The advantage in respect of y^e Lunar year is much greater. For in y^e Gregorian Kalendar y^e full Moon on w^ch Easter depends is not to be found w^thout the help of three or four Tables, and when you have that full moon there is no rule in that Kalendar for finding the other full moons & y^e new moons throughout y^e year. But in this Kalendar all y^e new & full moons are found perpetually w^thout any Tables or any other recconing then y^e continual addition of 30 & 29 days alternately w^ch is so very easy a work that any Novice may perform it. And besides this rule is much exacter then the Gregorian for that errs three hours in 39 years this errs but 3 hours in 500 years, & may be corrected evey {sic} 500 years to keep it exact.

^{[Editorial Note 1]} Folio 2r is blank. A series of calculations on f. 2v is here omitted from the transcription.