| 
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 of4,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 but1,the denominator is4; 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.
| Collateral Degrees. | Number of Kindred. | Collateral Degrees. | Number of Kindred. | |
| 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.
12. Co. Litt. 23.
13. See the table of consanguinity annexed; wherein all the degrees of collateral kindred to the propositus are computed, so far as the tenth of the civilians and the seventh of the canonists inclusive; the former being distinguished by the numeral letters, the latter by the common ciphers.
14. Bro. tit. descent. 58.
15. Co. Litt. 15.
16. Ibid. 11.
17. Flet. l. 6. c. 2. § 2.
18. Litt. § 3.
19. Selden. De successe. Ebracor. C. 12.
20. Ff. 38. 15. 1. Nov. 118. 127.
21. Inst. 3. 3. 1.
22. Craig. De jur. Feud. l. 2. t. 13. § 15. Locke on gov. part. 1. § 90.
23. 2 Feud. 50.
24. Domat. P. 2. l. 2. t. 2. Montesqu. Esp.
25. LL. Hen. I. C 70.
26. l.7. c. 1.
27. 1 Feud. 20.
28. Descendit itaque jus, quasi ponderosum quid cadens deorsum recta linea, et nunquam reascendit. [Therefore the right descends, like a heavy weight falling downwards in a straight line, and never reascends.] l. 2. c. 29.
29. 1 Inst. 11.
30. Hal. H. C. L. 235.
31. Numb. C. 27.
32. Petit. LL. Attic. L.6. r. 6.
33. Inst. 3. 1. 6.
34. Stat. Wall. 12 Edw. I.
35. LL. Canut. c. 68.
36. tit. 7. § 1 & 4.
37. c. 70.
38. 1 Feud. 8.
39. Litt. § 5. Hale. H. C. L. 238.
40. Selden. De succ. Ebr. c. 5.
41. c. 70.
42. Glanvil. l. 7. c. 3.
43. Feud. 55.
44. Hale. H. C. I. 221.
45. l. 7. c. 3.
46. l. 1. § 3.
47. l. 2. co. 30, 31.
48. Somner. Gavelk. 7.
49. c. Litt. 165.
50. Ibid.
51. 1 Feud. i.
52. Hale. H. C. L. 236, 237.
53. Selden de succ. Ebr. c. 1.
54. Nov. 118. c.3.Inst. 3. 1. 6.
55. Mod. Un. Hist. xliii. 334.
56. l. 7. c. 3.
57. Hale. H. C. L. 217, 229.
58. Bracton. L. 2. c. 30. § 2.
59. Co. Litt. 12.
60. Gr. Coustum. 6. 25.
61. 1 Feud. 1. § 2.
62. Crag. L. 1. t. 9. § 36.
63. Domat. Part. 2. pr.
64. M. 12. Edw. IV. 14.
65. Abr. T. discent. 2.
66. Ibid. 38.
67. H. C. L. 243.
68. Tacitus de mor. Germ. 21.
69. Numb. C. 27.
70. Selden. de succ. Ebr. c. 12.
71. 1 Sid. 193. 1 Lev. 60. 12 Mod. 619.
72. Hale. H. C. L. 238.
73. Tenures. 186.
74. l. 2. t. 15. § 14.
75. Gr. Coustum. c. 25.
76. l. 2. c. 30. § 3.
77. l. 6. c. i. § 14.
78. de laud. LL. Angl. 5.
79. Plowd. 245. Co. Litt. 15.
80. 12 Will. III. C. 2.
81. Litt. § 14, 15.
82. See pag. 204.
83. Litt. § 4.
84. de succ. Ebracor. c. 12.
85. LL. Attic. l. 1. t. 6.
86. (Symbol). 606.
87. Nov. 118.
88. Gr. Coustum. c. 25.
89. See the table of descents annexed.
90. Plowd. 450.
91. Elem. c. 1.
92. H. C. L. 240, 244.
93. Dyer. 314.
94. Law of inheritances. 2d. edit. Pag. 30, 38, 61, 62, 66.
95. Hist. C. L. 247.
96. Co. Litt. 12. Hawk. Abr. In loc.
97. Fitzh. Abr. Tit. Discent. 2. Bro. Abr. T. discent. 3.
98. Hist. C. L. 243.