24 



SYSTEMS OF CONSANGUINITY AND AFFINITY 



If we should follow the chain of relationship beyond the diagrams, and compute 

 the number of the kindred of Ego, it would produce remarkable results. In strict- 

 ness two lines commence at Ego, one ascending to his father and one to his mother ; 

 from these last the number is increased to four, one of which ascends to the father 

 and one to the mother of his father, another to the father and another to the 

 mother of his mother ; and again from these four common ancestors the lines are 

 increased to eight ; and so upwards in geometrical progression. As a matter of 

 computation it will be seen that at the fifth degree each person has thirty-two 

 ancestors, at the tenth a thousand and twenty-four, and at the twentieth upwards 

 of a million.^ Carried to the thirty-first degree, or generation, it would give to 

 each person a greater number of ancestors than the entire population of the earth. 

 Such a .marvellous result, although correct as a matter of computation, is prevented 

 by the intermarriage of these common ancestors, by which a multitude of them are 

 reduced ta one. In the collateral lines the relatives are quadrupled at each gene- 

 ration. " If Ave only suppose each couple of our ancestors to have left, one with 

 anotlier, two children ; and each of those on an average to have left two more (and 

 without such a supposition the human species must be daily diminishing!, we shall 

 find that all of us have now subsisting near two hundred and seventy millions of 

 kindred at the fifteenth degree, at the same distance from the several common 

 ancestors as ourselves are ; besides those that are one or two descents nearer to or 

 farther from the common stock, who may amoimt to as many more."^ But, as in 

 the former case, the intermarriage of these collateral relatives would consolidate 

 many thousands of these relationships into one, while others would, from the same 

 cause, be related to Ego in many thousand diff"erent ways. The rapidity Avith 

 Avhich the blood of a people is interfused, or, in other words, tends to intermingle 

 througliout the entire mass of the population, with the progress of the generations. 



' lu Black. Cora. II. 204, note, is the following 



Lineal Number of Lineal 



Degrees. Ancestors. Degrees. 



1 2 8 . . , 



... 4 



16 



32 



04 



128 



9 

 10 

 11 

 12 

 13 

 14 



° Black. Com. II. 20*7, note, vide as follows :- 



Collateral 

 Degrees. 



1 . . 



Number of 

 Kindred. 

 1 

 4 

 IG 

 . 64 

 . 256 

 . 1026 

 . 4096 



Collateral 

 Degrees. 



9 



10 

 11 

 12 

 13 

 14 



Number of 

 Ancestors. 

 256 



515 

 1024 

 2048 

 4096 

 8192 

 . 16384 



Nuralier of 



Kindred. 



16384 



65536 



262146 



1048576 



4194304 



16777216 



G71088G4 



Lineal 

 Degrees. 



15 



16 



17 



18 



19 



20 



Collateral 

 Degrees. 



15 



10 



17 



18 



19 



20 



Number of 

 Ancestors. 



32768 



65536 



131072 



262144 



524288 



1048576 



Number of 



Kindred. 



. 268435456 



. 1073741824 



. 4294967296 



17179809184 



68719476736 



274877906944 



