Dr. Macfarlane's Analysis of Relationships. 445 



(5) Deduce all the logical consequences of the law which 

 prohibits a man marrying a sister of his deceased wife. 

 The primary equation is 



where A may be any inhabitant of the British Islands. It 

 expresses that a man cannot (lawfully) be the husband of a 

 sister of his wife. The Rule for transforming an equation 

 which is true for any A is as follows : — 



To transform a universal equation which has a compound 

 term of the second degree equated to 0, suppose all the symbols 

 brought to one factor in accordance with the rule of transposition 

 given above (p. 444) ; then removing a symbol from the front 

 gives one derived equation, and removing a symbol from the 

 end gives another derived equation. Transform each of these 

 two in a similar manner, then each of their four residtants, and 

 so on until cdl the terms have been brought to the other factor. The 

 total of these derived equations is the total number of transfor- 

 mations of the given universal equation. 



Applied to the above equation, transposition of the first 

 symbol gives 



Xc m .c / cc- 1 f c- 1 c m A=0', 



that is, a child of a man cannot be the child of a sister of a 

 wife of the man. Transposition of the last symbol gives 



%mc~ l • m c~ ] ] c f ccr x f G~ l A=0. 



that is, the father of a person cannot be the husband of a sister 

 of the mother of that person. By continuing the process other 

 19 forms (different from one another) are obtained, which 

 respectively express that — 



A -wife of a man cannot be the sister of a wife of the man. 



A child of the father of a person cannot be the child of a sister of the 



mother of the person. 

 A husband of a woman cannot be the husband of a sister of the woman. 

 A parent of a wife of a man cannot be the parent of another wife of the 



man. 

 A step-mother of a person cannot be the sister of the mother of the 



person. 

 A step-child of a woman cannot be the child of a sister of the woman. 

 A son-in-law of a person cannot be the husband of another daughter of 



the person. 

 A parent of a step-mother of a person cannot be the parent of the 



mother of the person. 

 A wife of a husband of a woman cannot be the sister of the woman. 

 A child of a husband of a daughter of a person cannot be the child of 



another daughter of the person. 

 A sister of a step-mother of a person cannot be the mother of the person. 

 A parent of another wife of a husband of a woman cannot be the parent 



of the woman. 

 Phil. Mag. S. 5. Vol. 11. No. 70. June 1881. 2K 



