Others again consider that the whole cycle is a metamorphosis which, beginning in the Heterocotylea as a direct development, has become complicated in the Holostomidae by a larval history, and finally in the Malacocotylea has acquired additional complexity by the intercalation of two larval forms, and is thus spread over several generations.
The Egyptian intercalary year, however, does not correspond to the Julian leap year, but is the year immediately preceding; and the intercalation takes place at the end of the year, or on the 29th of August.
Before the end of that year the Julian intercalation takes place, and the beginning of the following Egyptian year is restored to the 29th of August.
Hence to reduce a date according to this era to our own reckoning, it is necessary, for common years, to add 283 years and 240 days; but if the date belongs to the first three months of the year following the intercalation, or, which is the same thing, if in the third year of the Julian cycle it falls between the 30th of August and the end of the year, we must add 283 years and 241 days.
Till the year 1079 the Persian year resembled that of the ancient Egyptians, consisting of 365 days without intercalation; but at that time the Persian calendar was reformed by Jelal ud-Din Malik Shah, sultan of Khorasan, and a method of intercalation adopted which, though less convenient, is considerably more accurate than the Julian.
The intercalary period is 33 years, - one day being added to the common year seven times successively at the end of four years, and the eighth intercalation being deferred till the end of the fifth year.
As it does not appear that the above-mentioned rule of intercalation was ever regularly followed, it is impossible to assign exactly the days on which the different years begin.
The order of the days in the cycle is never interrupted by any intercalation that may be necessary for adjusting the months or years.
These very thick seams are, however, rarely constant in character for any great distance, being found commonly to degenerate into carbonaceous shales, or to split up into thinner beds by the intercalation of shale bands or partings.
They made use of no intercalation, and by losing a fourth of a day every year, the commencement of the year went back one day in every period of four years, and consequently made a revolution of the seasons in 1461 years.
Although The Julian Method Of Intercalation Is Perhaps The Most Convenient That Could Be Adopted, Yet, As It Supposes The Year Too Long By Ii Minutes 14 Seconds, It Could Not Without Correction Very Long Answer The Purpose For Which It Was Devised, Namely, That Of Preserving Always The Same Interval Of Time Between The Commencement Of The Year And The Equinox.
Directed Ten Days To Be Suppressed In The Calendar; And As The Error Of The Julian Intercalation Was Now Found To Amount To Three Days In 400 Years, He Ordered The Intercalations To Be Omitted On All The Centenary Years Excepting Those Which Are Multiples Of 400.
According To The Gregorian Rule Of Intercalation, Therefore, Every Year Of Which The Number Is Divisible By Four Without A Remainder Is A Leap Year, Excepting The Centurial Years, Which Are Only Leap Years When Divisible By Four After Omitting The Two Ciphers.
As The Gregorian Method Of Intercalation Has Been Adopted In All Christian Countries, Russia Excepted, It Becomes Interesting To Examine With What Degrees Of Accuracy It Reconciles The Civil With The Solar Year.
With This Correction The Rule Of Intercalation Is As Follows: Every Year The Number Of Which Is Divisible By 4 Is A Leap Year, Excepting The Last Year Of Each Century, Which Is A Leap Year Only When The Number Of The Century Is Divisible By 4; But 4000, And Its Multiples, 8000, 12,000, 16,000, &C. Are Common Years.
Thus The Uniformity Of The Intercalation, By Continuing To Depend On The Number Four, Is Preserved, And By Adopting The Last Correction The Commencement Of The Year Would Not Vary More Than A Day From Its Present Place In Two Hundred Centuries.
In Order To Discover Whether The Coincidence Of The Civil And Solar Year Could Not Be Restored In Shorter Periods By A Different Method Of Intercalation, We May Proceed As Follows: The Fraction 0.2422, Which Expresses The Excess Of The Solar Year Above A Whole Number Of Days, Being Converted Into A Continued Fraction, Becomes 4 I 7 1 I I 3 1 4 I 1, &C.
4' 2 9 ' 33' 128' 545' 673', Gives The Julian Intercalation Of One Day In The First Of These, 4 G J Y Four Years, And Is Considerably Too Great.
P.81) That The Persian Intercalation Combines The Two Periods 29 And 3 3.
If The Commencement Of The Year, Instead Of Being Retained At The Same Place In The Seasons By A Uniform Method Of Intercalation, Were Made To Depend On Astronomical Phenomena, The Intercalations Would Succeed Each Other In An Irregular Manner, Sometimes After Four Years And Sometimes After Five; And It Would Occasionally, Though Rarely Indeed, Happen, That It Would Be Impossible To Determine The Day On Which The Year Ought To Begin.
It Is Therefore Infinitely More Commodious To Determine The Commencement Of The Year By A Fixed Rule Of Intercalation; And Of The Various Methods Which Might Be Employed, No One, Perhaps Is On The Whole More Easy Of Application, Or Better Adapted For The Purpose Of Computation, Than The Gregorian Now In Use.
It Is Therefore So Obviously Ill Adapted To The Computation Of Time, That, Excepting The Modern Jews And Mahommedans, Almost All Nations Who Have Regulated Their Months By The Moon Have Employed Some Method Of Intercalation By Means Of Which The Beginning Of The Year Is Retained At Nearly The Same Fixed Place In The Seasons.
Two Lunar Years Would Thus Contain 25 Months, Or 738 Days, While Two Solar Years, Of 3654 Days Each, Contain 7302 Days.V The `, Difference Of 72 Days Was Still Too Great To Escape Observation; It Was Accordingly Proposed By Cleostratus Of Tenedos, Who Flourished Shortly After The Time Of Thales, To Omit The Biennary Intercalation Every Eighth Year.
On The Other Hand, As The Golden Numbers Were Only Adapted To The Julian Calendar, Every Omission Of The Centenary Intercalation Would Require Them To Be Placed One Line Lower, Opposite The 6Th, For Example, Instead Of The 5Th Of The Month; So That, Generally Speaking, The Places Of The Golden Numbers Would Have To Be Changed Every Century.
This Method Of Forming The Epacts Might Have Been Continued Indefinitely If The Julian Intercalation Had Been Followed Without Correction, And The Cycle Been Perfectly Exact; But As Neither Of These Suppositions Is True, Two Equations Or Corrections Must Be Applied, One Depending On The Error Of The Julian Year, Which Is Called The Solar Equation; The Other On The Error Of The Lunar Cycle, Which Is Called The Lunar Equation.
The Solar Equation Occurs Three Times In 400 Years, Namely, In Every Secular Year Which Is Not A Leap Year; For In This Case The Omission Of The Intercalary Day Causes The New Moons To Arrive One Day Later In All The Following Months, So That The Moon'S Age At The End Of The Month Is One Day Less Than It Would Have Been If The Intercalation Had Been Made, And The Epacts Must Accordingly Be All Diminished By Unity.
The Year 1600 Was A Leap Year; The Intercalation Accordingly Took Place As Usual, And There Was No Interruption In The Order Of The Epacts; The Line D Was Employed Till 1700.
But Every Fourth Year Is A Leap Year, And The Effect Of The Intercalation Is To Throw The Dominical Letter One Place Farther Back.
In This Case, As The Formula Supposes The Intercalation Already Made, The Resulting Letter Is That Which Applies After The 29Th Of February.
Before The Intercalation The Dominical Letter Had Retrograded One Place Less.
As 1600 Was A Leap Year, The First Correction Of The Julian Intercalation Took Place In 1700; Hence, Taking C To Denote The Number Of The Century As Before, The Correction Becomes (C 16) (C 416) W, Which.
Now, From The Manner In Which The Intercalation Is Directed To Be Made (Namely, Seven Times Successively At The End Of 300 Years, And Once At The End Of 400), It Is Evident That The Fraction 2 Must Amount To Unity When The 5 Number Of Centuries Amounts To Twenty Four.
In The Protestant States Of Germany The Julian Calendar Was Adhered To Till The Year 1700, When It Was Decreed By The Diet Of Regensburg That The New Style And The Gregorian Correction Of The Intercalation Should Be Adopted.
The Difference Of The Two Styles, Which Then Amounted To Eleven Days, Was Removed By Ordering The Day Following The 2Nd Of September Of The Year 1752 To Be Accounted The 14Th Of That Month; And In Order To Preserve Uniformity In Future, The Gregorian Rule Of Intercalation Respecting The Secular Years Was Adopted.
The Years Of The Hegira Are Purely Lunar, And Always Consist Of Twelve Lunar Months, Commencing With The Approximate New Moon, Without Any Intercalation To Keep Them To The Same Season With Respect To The Sun, So That They Retrograde Through All The Seasons In About 321 Years.
It should be observed, however, that the repeated intercalation of marine deposits within the continental series and the frequent occurrence of thin coaly layers in the marine series makes any hard and fast distinction of this kind impossible.
It is by no means certain that even the higher rate is greater than that exhibited by a tropical bamboo which will grow over a foot a day, or even common grasses, or asparagus, during the active period of cell-division, though the phenomenon is here complicated by the phase of extension due to intercalation of water.
The system of intercalation in the lunar calendar of the heathen Arabs was designed to secure that the feast should always fall at the time when the hides, fruits and other merchandise were ready for market, 4 and the Meccans, who knew how to attract the Bedouins by hospitality, bought up these wares in exchange for imported goods, and so became the leaders of the international trade of Arabia.