4 
The relation of exclusion is expressed by iV : — A is not 
B ” is expressed by A=JSfB. Co-exclusion is expressed by 
Exclusion is not a transitive relation, and it is in- 
vertible ; in other words, iV is not equal to its own second 
power, and is equal to its own reciprocal. The only 
numerical coefhcient which unites these two properties is 
negative unity. In logic the following equations are true : 
A^.Az=JSr 
N.N^=zN 
That is to say 
The exclndent of an excludent 
is a co-excludent. 
N\^^=N 
The co-exchident of an exclu- 
dent is an exclndent. 
The excludent of a co-exclndent The co-excludent of a co-excln- 
is an excludent. dent is a co-excludent. 
And the interpretations are similar if N means not in 
relation with’’ or ^^not related to, as either cause or effect.” 
These four equations are also true in arithmetic, if N is 
taken to mean negative unity and unity. 
The President described a simple means for checking 
the oscillations of a telescope. It consisted of a leaden ring 
placed centrally about the axis of the tube of the telescope 
and attached thereto by three or more elastic caoutchouc 
bands. He had employed two of these rings for his tele- 
scope, one placed near the object glass, the other near the 
eyepiece. Their united weights were only one quarter of 
that of the telescope tube, but nevertheless they diminished 
the time required for the cessation of vibration to one sixth 
of what is was before their application. 
Dr. E. ScHUNCK, F.KS., exhibited some specimens of the 
colouring matters, &c., referred to in his paper “ On the 
Purple of the Ancients,” lately published. 
