442 Dr. Macfarlane's Analysis of Relationships. 



of the laws of marriage of a given nation. For example, 



te m . c f c^ A=0, 



A being any British subject. This means that the children of 

 any man A who are also children of any niece or daughter of 

 the man A are none. 



The principles of the English Law of Marriage are expressed 

 as follows : — 



I. For the direct line, 



tc m .c f (<f + c-») m A=0, 



where p may be any number. This means that the children 

 of any man A must not be the children of any female descend- 

 ant or ancestress of A. 



II. For the collateral line, 



2c OT .c / (c 2 - 1 + c 1 - 1 +c 1 -%A=0. 



This expresses that the children of any man A must not be 

 the children of any niece, sister, or aunt of A. 



III. For the direct line with one affinity, 



This means that the children of any man A must not be the 

 children of any female descendant or ancestress of any wife 

 of A, nor the children of any wife of any descendant "or an- 

 cestor of A. 



IY. For the collateral line with one affinity, 



Sc Jw .c / {(c 2 - 1 + c 1 - 1 + c l - 2 )c- 1+1 + c- 1+1 (c 2 - 1 + c 1 - 1 + c 1 - 2 )} m A==0. 



This means that the children of any man A must not be the 

 children of any niece, sister, or aunt of any wife of A, nor the 

 children of any wife of any nephew, brother, or uncle of A. 



As the result of my investigations, I am led to consider 

 the Analysis of Kelationships a special branch of the Algebra 

 of Logic, that the processes of that method as described in my 

 work ' Algebra of Logic ' apply to this subject, and that we 

 have special laws in addition, such as those mentioned above. 

 In 1879 Dr. Halsted expressed his opinion* that little 

 cosmos had not yet been brought out of the chaos of Eola- 

 tions ; whether I have been successful in reducing a small 

 part more approximately to order must be left to the reader 

 of this article and of the original papers to judge. 



I append some illustrations. 



(1) To express the relationship of Queen Victoria to William 



* Journ. of. Spec. Philos. vol. xiii. p. 107. 



