1. Co. Litt. 18.
2. See Vol. I. pag. 74, 75.Vol. II. Pag. 83, 85.
3. See pag. 112, etc.
4. A fuller explanation of the doctrine of consanguinity, and the consequences resulting from a right apprehension of its nature, fee an essay on collateral consanguinity, in the first volume of law tracts. Oxon. 1762. 80.
5. Ff. 38. 10. 10.
6. Decretal. l. 4. tit. 14.
7. Co. Litt. 23.
8. Ibid. 12.
9. This will seem surprising to those who are unacquainted with the increasing power of progressive numbers; but is palpably evident from the following table of a geometrical progression, in which the first term is 2, and the denominator also 2: or, to speak more intelligibly, it is evident, for that each of us has two ancestors in the first degree; the number of whom is doubled at every remove, because each of our ancestors has also two immediate ancestors of his own.
Lineal Degrees.
Number of Ancestors.
Lineal Degrees.
Number of Ancestors.
1
2
2
4
3
8
4
16
5
32
6
64
7
128
8
256
9
512
10
1,024
11
2,048
12
4,096
13
8,192
14
16,384
15
32,768
16
65,536
17
131,072
18
262,144
19
524,288
20
1,048,576
A shorter method of finding the number of ancestors at any even degree is by squaring the number of ancestors at half that number of degree. Thus 16 (the number so ancestors at four degrees) is the square of 4,the number of ancestors at two; 256 is the square of 16; 65536 of 256; and the number of ancestors at 40 degrees would be the square of 1048576, or upwards of a million millions.
10. This will swell more considerably than the former calculation: or here, though the first term is but 1,the denominator is 4; that is, there is one kinsman (a brother) in the first degree, who makes, together with the propostus the two descendants from the first couple of ancestors; and in every other degree the number of kindred must
be the quadruple of those in the degree which immediately precedes it. For, since each couple of ancestors has two descendants, who increase in a duplicate ratio, it will follow that the ratio, in which all the descendants increase downwards, must be double to that in which the ancestors increase upwards: but we have seen that the ancestors increase in a duplicate ratio: therefore the descend. Ants must increase in a double duplicate, that is, in a quadruple, ratio.
Lineal Degrees.
Number of Ancestors.
Lineal Degrees.
Number of Ancestors.
1
1
2
4
3
16
4
64
5
256
6
1,024
7
4,096
8
16,384
9
65,536
10
262,144
11
1,048,576
12
4,194,304
13
16,777,216
14
67,108,864
15
268,435,456
16
1,073,741,824
17
4,294,967,296
18
17,179,869,184
19
68,719,476,736
20
274,877,906,944
This calculation may also be formed by a more compendious process, viz. by squaring the couples, or half the number, of ancestors at any given degree; which will furnish us with the number of kindred we have in the same degree, at equal distance with ourselves from the common stock, besides those at unequal distances. Thus, in the tenth lineal degree, the number of ancestors is 1024; its half, or the couples, amount to 512; the number of kindred in the tenth collateral degree amounts therefore to 262144, or the square of 512. And if we will be at the trouble to recollect the state of the several families within our own knowledge, and observe how far they agree with this account; that is, whether, on an average, every man has not one brother or sister, four first cousins, sixteen second confines, and so on; we shall find that the present calculation is very far from being over-charged.
11. Decretal. 4. 14. 3 & 9.
