of Edinburgh, Session 1878 - 79 . 229 
This is, of course, an important point. Leslie Ellis expresses 
Shem was a son of Noah 
S = sN; 
hut, so far as I have yet studied the matter, I am inclined to hold 
that s must he considered as in general a plural symbol, and that 
S = sN 
asserts implicitly that Shem was the only son of Noah. The truth 
Shem was a son of Noah 
is properly expressed by 
S < sN ; 
hut the truth 
Shem was the eldest son of Noah, 
fcy 
s = kjT. 
20. Let /denote father of and m denote mother of. Then 
f= — — and m = 
s + d 
(T + 8 
21. To find expressions for one's ancestors of the nth generation, 
back. 
f + m 
f + m. 
Multiply together 
then ff + mf + fm + mm . 
These are the expressions for one’s grandparents. 
Multiply again by / + m , 
then fff + mff + fmf + mmf + ffm + mfm + fmm + mmm . 
These are the expressions for one’s great-grandparents. 
And so on. 
The maximum number of ancestors of the nih. generation back 
which a person can have is 2 n , and the minimum number according 
to the Laws of Consanguinity is 4. 
22. According to the above, the relation of great-grandmother 
may denote any one of the four different relations — 
mff , mmf , mfm , mmm ; 
and, taking into account the gender of the great-grandchild, there 
will be eight different relationships. 
