132 MR. JOSEPH JOHN MURPHY ON THE * 



end without further information*. The whole of the 

 Withington district will require also careful revision, as 

 there is a large area of Permian measures not shown at all 

 on the maps. 



XII. On the Transformations of a Logical Proposition 

 containing a single Relative Term. By Joseph John 

 Murphy. Communicated by the Rev. Robert Har- 



LEY, F.R.S. 



Read November 28th, 1882. 



The present paper has been suggested by De Morgan's 

 " On the Syllogism, No. IV., and on the Logic of Rela- 

 tions," from the ' Transactions of the Cambridge Philoso- 

 phical Society/ vol. x. part ii. 



I indicate absolute terms, that is to say the terms between 

 which the relations subsist, by Roman letters, and the rela- 

 tive terms by Italic ones. 



So long as the relation is not transitive, R shall be taken 

 to indicate any relation, and R~* the converse relation. 

 The relation of teacher, and the converse relation of pupil, 

 are not transitive ; that is to say, if X is a teacher of Y 



* Mr. Binney (Lit. & Phil. Trans, vol. ii. pp. 31, 32) says that the existence 

 of this fault was first pointed out to him by Mr. Hull ; and he adds, " On 

 taking the direction of the fault at Heaton Norris, it appears to run more in 

 a line through Chorlton-on-Medlock, into the great Pendleton fault in the 

 valley of the Irwell^j^han that of Bradford and Clayton." It will be thus 

 seen that Mr. Binney^s observations point in the direction of the Slade Lane 

 ^discovery ; but I do not think he is correct in his further surmise. There is 

 another fault at Heaton Mersey which appears to be a continuation of the 

 great Pendleton fault. 



