71 
moulds for such a production.” In the specimen found at 
Hanging Bridge, the letters are not prefaced with a cross, 
hut the cross appears on the hack. However, the supposi- 
tion that some of the earlier of these Criss Cross Rows were 
in ancient times cast in lead has received a remarkable 
confirmation by the finding of his specimen, and he hoped 
some time to be able to compare his cast with the mould in 
the late Sir George Musgrave’s possession. The characters 
of the letters appear to be about the beginning of the 
fifteenth century. 
“ On the Addition and Multiplication of Logical Relatives,” 
by Joseph John Murphy, F.G.S. ; communicated by the 
Rev. Robert Harley, F.R.S. 
In this paper the Logic of Relatives means any logical 
system wherein each relation is expressed by a special literal 
term. The common logic is co-extensive with so much of 
the Logic of Relatives as deals with the relations of inclusion 
and exclusion. These relations are expressed in the present 
system by Z and N respectively, so that " A is B,” or “ A 
is included in B,” is expressed by 
A = ZB or B = Z~ 1 A, 
and “ A is not B,” or “ A and B exclude each other,” is 
expressed by 
A = AB or B = AA. 
The problem of the multiplication of relatives is : — Given 
the relations of any two terms to a third term, to find the 
resultant relation of the first two to each other. This is 
identical with the problem of syllogism ; thus, if 
A = ZB and B = JfC, 
where L and M are any relative terms whatever, it follows 
that 
A = (Z x M)C. 
Prof. Pierce ( Logic of Relatives , Memoirs of the American 
Academy, vol ix.) speaks of the multiplication of relatives 
in this sense. But the corresponding problem of their 
