Cousins, Removes and Other Such Stuff
Among genealogists and wannabe genealogists there appears to be great confusion over relationships between relatives. Published authors frequently get this wrong in their texts.
We are speaking here of "cousins" and "removes" as in "4th cousin twice removed."
Everyone seems to know, even instinctively, that parents of a parent are their grandparents and the sibling of a parent is an uncle or aunt.
(Henceforth, and without loss of generality, we will stick to male terms as God and the English Language ordained before the PC people mucked with it).
Also recognized is that an uncle's child is your cousin, or first cousin (more formally, cousin-german).
But that's as far as many are able to go without error. The child of your cousin is NOT your second cousin, an error some people compound even farther by declaring that the grandchild of one's cousin is therefore a third cousin. No, no and no! The child of your cousin is your child's second cousin. So who exactly are all these folks? We'll now begin to delve into cousins and removes, saving the more esoteric for later.
The children of first cousins are, to each other, second cousins. Their children are third cousins, etc. Working backwards it would be logical to call brothers "zero cousins." Every society has special names for certain close relationships and resorts to numbers only for the rarer or less important relationships. For some reason our society abhors the term "zero cousin" and, accordingly, goes to great lengths to avoid it; hence "great aunts", "great grand uncles," etc. Let us now draw a chart of several generations and label some of the "special" relationships.
Some "special" relationships:Now we might ask, "What is my (first) cousin's child to me?" Many people mistakenly say "second cousin" but that is an error. He is your first cousin once removed. To find relationships between two people in different generations, we need to count the "extra" number of generations of one path vs. the other. Each of these "excess generations" is a "removed." Using the same chart, we now insert a few additional nomenclatures as examples.
- 0c0r brothers and sisters
- 0c1r aunts/uncles nieces/nephews
- 0c2r great aunts/uncles; great nieces/nephews
- 0c3r great grand aunts/uncles; great grand nieces/nephews
- 1c0r cousins (common usage of term)
Brothers have the same parents. If they have but one parent in common then they are Half Brothers -- but still 0c0r from the common ancestor (parent).
"In-Law" and "step" simply refer to a relationship created via (someone's) marriage. Your spouse's brother is your brother-in-law but (in this context) not a blood relative. Your spouse's father is your father-in-law, but again not blood related. Your grandfather's second wife is your step-grandmother. 
If two people with previous children marry, their collective children are not biologically brothers (think Brady Bunch here, as in TV show). However, within the family they may certainly be thought of, loved as, and referred to in those terms. Each set of children is the other spouse's step-children. And the kids are, properly speaking, step-brothers. 
If siblings marry siblings and each pair has children then those children share all four grandparents in common and not just two as do most first cousins. In this case they are referred to as "double first cousins." 
There are other types of "double" relationships which can get complicated very rapidly. These fall into two basic types: The first occurs when two people share the same common ancestor in more than one way. This, in itself can become more complex because it usually happens when the common ancestor is four, five or more generations ago. If one path, for example, follows the eldest child of the eldest child of that ancestor and another path the youngest of the youngest, It is easy to come up with a case of two people being 4th cousins one way and 3rd cousins once removed the other. And, of course there is nothing which limits reaching the common ancestor only two ways. Your author descends from Johannes Hottle at least three ways. 
Secondly, two people may share multiple ancestors; as in "we are third cousins on my father's side and fifth cousins on my mother's." Again, there is nothing restricting this to only two common ancestors, it may be many.
Blends of the first (multiple ways to a common ancestor) and the second (multiple ancestors involved) types also occur making each case almost unique. These are best handled by graphing the family tree. There is no system I am aware of that can produce a simplified relationship. (One would never say, for example, that because two individuals are third cousins in two ways, that is equivalent to being second cousins.) Of course one can calculate the closeness of relationships and come up with, say, "3/16 of my blood is the same as 9/32 of yours." But the only practical way I can think of to handle it is simply to list each of the multiple relationships individually.
What about the case of a husband and wife whose fathers are half-brothers (yes, there is such a case in COS)? This would be a marriage between two half first cousins and their children would have only seven unique great grandparents unlike "normal" kids with eight, or six for children of first cousins, or four for children of double first cousins. Don't know whether there is a term for it. I suspect not.
There is an interesting dichotomy in play regarding how we address the spouses of those "zero cousins" and most others which has been hinted at in the previous graphics but not explicitly stated. One introduces his uncle's wife as his "aunt;" similarly, the husband of his aunt as his "uncle." This deliberately confuses the situation.
For if you introduce me to your "Aunt Emma and Uncle Gene," I have no way of knowing which is the blood relative. On the other hand, "numbered" cousins are rarely, if ever, subjected to such confusion. We say, "This is my second cousin, Patricia, and her husband, Daniel," not, "These are my second cousins, Patricia and Daniel."
One is tempted to assume the first named is the blood relative, but can never be sure unless the explicit query is made. There are a multitude of reasons to reverse the blood first order, such as gender (ladies first), favoritism (he always brings me presents), age (he's much older than his trophy wife and is named first in deference to his longevity [or my jealousy]), ignorance or "I don't care" attitude of the younger generation, etc.
In any case, ain't English the most wonderfulness of languages? No matter how badly you massacre it, it's still generally possible to get your point across.
There are, of course, many other relationships which could be cited, but I'm getting exhausted. I would be interested in hearing should you encounter a really interesing relationship in your research.
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