Order of succession to the throne
An order of succession is a device that determines the new sovereign at the time the old sovereign dies. It most often specifies a path to follow in the genealogical tree from the deceased sovereign, and frequently additional criteria is to be met by the potential successor. The first person to be found by the algorithm is the new sovereign.

At any point in time, there is a sovereign, and the rule of succession can be applied, as long as the sovereign is alive in the following way: "if the sovereign were to die this minute, who would succeed?" The answer is the heir.

You can, of course, extend this a step further, and ask who the heir’s heir is. Basically, the question becomes "if the sovereign and the heir were to die this minute, who would succeed?" By extending the question in this way, you create a "line of succession", where the heir is number 1 (or next in line), the heir's heir is number 2, and so forth. The line of succession is constructed repeatedly, by asking at each step N: "if the sovereign and the first N-1 people in the order were to die this minute, who would succeed?" The answer is person number N on the list.

Because British statutes (such as the Act of Settlement) impose additional criteria, this process is not purely genealogical. For each candidate found along the path in the genealogical tree, criteria must be evaluated. If an individual may be ineligible, in which case the individual is treated as if he or she "were naturally dead", and the search moves on to the next individual.

The procedure goes something like this. If individual A is dead or ineligible: 1. look for A's eldest-born male B (if none born, go to 3). 2. If B is dead or ineligible, go to 1 with "B" instead of "A". 3. If no candidate meeting the criteria is found, return to A, to find the next eldest-born male C; use steps 1-3 with "C" instead of "A", until a candidate is found or all of A's male children are worn out. 4. Repeat steps 1-3 with "female" instead of "male". 5. If no candidate has been found thus far, go to A's royal parent D and look for D's subsequent eldest-born male, repeating steps 1-4 with "D" in place of "A". 6.

If no candidate has been found, go to D's royal parent E and repeat steps 1-5. 7. Persevere climbing up the royal genealogy. If you reach step 6 with D = Electress Sophia, there are no candidates left (Which make take time, because there are about 4360 individuals descended from her.

The criteria essential for a candidate are that he or she be born in matrimony, of a marriage contracted conforming with the Royal Marriages Act of 1772, that he or she is not be a Roman Catholic or have married one (according to the Act of Settlement of 1701). More specifically, the Act recalls that the Bill of Rights of 1689 enacted "That all and every Person and Persons that then [in 1689] were or afterwards should be reconciled to or shall hold Communion with the See or Church of Rome or should profess the Popish religion or to marry a Papist should be excluded and are by that Act [the Bill of Rights] made forever incapable to inherit possess or enjoy the Crown"; and the Act enacts

"That all and every Person and Persons who shall be or may take or inherit the said Crown by vertue of the Limitation of this present Act [to Electress Sophia and the Heirs of Her Body being Protestants] and is are or shall be reconciled to or shall hold Communion with the See or Church of Rome or shall profess the Popish religion or shall marry a Papist shall be subject to such Incapacities as in such Case or Cases are by the said recited Act [the Bill of Rights]provided enacted and established".

As a result of this clause there is a debate of the meaning. One interpretation is, being a Roman Catholic at the time of succession forever results in incapacity to succeed at that time. The other, being a Roman Catholic at any time after 1689 ("then or afterwards") immediately creates a perpetual incapacity to succeed whenever the succession becomes open. Under the first interpretation, a Roman Catholic, if he or she converts before the crown comes to him or her, can succeed (even if he does so the minute before). Under the second, no matter brief that he or she is a is a Roman Catholic they are forever excluded.

Another source for disagreement is the phrase "marry a Papist". Its meaning maybe straightforward, but some think that it should be read as "being married to a Papist". If that be the case, a man whose deceased wife was Roman Catholic, could still succeed. Taking it in the exact reading of the phrase, anyone who ever marries a Roman Catholic is forever excluded. This seems to be the reading of 8(2) Halsbury's Laws of England par 39, which states: "a person who is a Roman Catholic or marries a Roman Catholic, is excluded from inheriting, possessing or enjoying the Crown [...]".

Because of the differences of interpretation, many individuals have been assigned a "bis" number in the line of succession that follows. It should be stated, however, that such an expert in British constitutional law as Vernon Bogdanor has written (The Monarchy and the Constitution, p. 55): "Any member of the Royal Family who marries a Catholic becomes ineligible to succeed. Thus when Prince Michael of Kent [...] married a Catholic [...] and when the Earl of St. Andrews [...] married a Catholic [...], they lost their rights of succession, for themselves, though not necessarily for their children."

These people are in line of succession to the Throne. It is limited to the first thirty-five or so in line of succession to keep the list in a practical length.

1. HRH The Prince of Wales (b. 1948)
2. HRH Prince William of Wales (b. 1982)
3. HRH Prince Henry of Wales (b. 1984)
4. HRH The Duke of York (b. 1960)
5. HRH Princess Beatrice of York (b. 1988)
6. HRH Princess Eugenie of York (b. 1990)
7. HRH The Earl of Wessex (b. 1964)
8. HRH The Princess Royal (b. 1950)
9. Peter Phillips (b. 1977)
10. Zara Phillips (b. 1981)
11. David Armstrong-Jones, Viscount Linley (b. 1961)
12. Hon. Charles Patrick Inigo Armstrong-Jones (b. 1999)
13. Hon. Margarita Elizabeth Alleyne Armstrong-Jones (b. 2002)
14. Lady Sarah Chatto (b. 1964)
15. Samuel Chatto (b. 1996)
16. Arthur David Nathaniel Chatto (b. 1999)
17. HRH Prince Richard, Duke of Gloucester (b. 1944)
18. Alexander Windsor, Earl of Ulster (b. 1974)
19. Lady Davina Windsor (b. 1977)
20. Lady Rose Windsor (b. 1980)
21. HRH Prince Edward, Duke of Kent (b. 1935)
Lady Marina-Charlotte Windsor (b. 1992)
22. Lady Amelia Windsor (b. 1995)
Lady Helen Taylor (b. 1964)
23. Columbus Taylor (b. 1994)
24. Cassius Taylor (b. 1996)
25. Eloise Taylor (b. 2003)
bis. HRH Prince Michael of Kent
26. Lord Frederick Windsor (b. 1979)
27. Lady Gabriella Windsor (b. 1981)
28. HRH Princess Alexandra, the Honorable Lady Ogilvy (1936)
29. James Ogilvy (b. 1964)
30. Alexander Ogilvy (b. 1996)
31. Flora Ogilvy (b. 1994)
32. Marina Mowatt (b. 1966)
33. Christian Mowatt (b. 1993)
34. Zenouska Mowatt (b. 1990)

Notes:
1. The Duke of Kent's elder son, George Windsor, Earl of St. Andrews (the father of three next persons in the line), could not presently succeed because of his marriage to Sylvana Tomaselli, a Roman Catholic. George's children, however, could succeed as long as they are not Roman Catholics themselves.
The duchess of Kent converted to the Roman Catholic faith on Jan 14, 1994. This does not affect the rights of the duke of Kent.

2. The Earl of St. Andrews's son, Lord Downpatrick, converted to the Roman Catholic faith on May 4, 2003.

3. Lord Nicholas Windsor converted to the Roman Catholic faith around Easter 2001.

4. The father of Lord Frederick and Lady Gabriella Windsor, Prince Michael of Kent, could not presently succeed because of his marriage to Baroness Marie-Christine von Reibnitz, a Roman Catholic. Prince Michael's children, however, could succeed as long as they are not Roman Catholics themselves.

The line of succession has a legal meaning. It is referred to (but not defined) in the Regency Act 1937, by which an eventual Regent is chosen to be the next in line of succession, subject to the exclusions of section 2 of the Act of Settlement as recalled above, and other conditions (being a British citizen of full age, residing in the UK, holding Communion with the Church of England); and by which the sovereign can temporarily delegate his or her powers to a group of people consisting of his or her spouse, and the next four persons in the line of succession who satisfy the conditions to be regent.

In general terms, the modern rules for eligibility as an heir or heiress are (adapted from "The Royal Line of Succession: From William the Conqueror to Prince William of Wales", compiled by John Butcher, edited by Sir Iain Moncreiffe of that Ilk, Harmondsworth, Middlesex: Penguin Books Ltd., 1983):

1. the reigning sovereign's sons (and their sons then daughters), then daughters (and their sons then daughters), in order of their birth; if a child dies or is already dead, it passes to that child's sons then daughters, in order of their birth

2. if the reigning sovereign has no descendants, the line passes to either his younger brothers (if he's a king), then sisters, in order of their birth; if the sibling dies or is already dead, it passes to that sibling's sons, then daughters, in order of their birth; or, to her younger sisters (if she is a queen), in order of their birth; if the sister dies or is already dead, then it passes to that sister's sons, then daughters, in order of their birth

3. if there are no descendants of the sovereign's lineal parent, the line passes to that parent's brothers or sisters; so on and so forth

4. no one born out of wedlock or born to an eligible parent whose marriage contravenes the Royal Marriages Act of 1772 can be in line of succession

5. no one who is, or becomes, or marries a Roman Catholic (according to the Act of Settlement 1701) can be in line of succession