Til.] INDUCTION. 143 



condition exists, make up the total of 65,536 possible 

 selections. 



The inconsistent cases are distributed in the manner 

 shown in the following table ; — 



When more than eight combinations of the Logical 

 Alphabet (p. 94, column V.) remain unexckuled, there cannot 

 be inconsistency. The whole numbers of ways of selecting 

 o, I, 2, &c., combinations out of 16 are given in the 17th 

 line of tlie Arithmetical Triangle given further on in the 

 Chapter on Combinations and Permutations, the sum of 

 the numbers in that line being 65,536. 



Professor Clifford on the Types of Co7npound Statement 

 involving Four Classes. 



In the first edition (vol. i, p. 163), I asserted that some 

 •years of labour would be required to ascertain even the 

 precise number of types of law governing the combinations 

 of four chisses of things. Though I still believe that some 

 years' hxbour would be required to work out the types 

 themselves, it is clearly a mistake to suppose that the 

 numbers of such types cannot be calculated with a reason- 

 able amount of labour, Professor W. K. Clitford having 

 actually accomplished the task. His solution of tlie 

 numerical problem involves the use of a complete new 

 system of nomenclature and is far too intricate to be fully 

 described here. I can only give a brief abstract of the 

 results, and refer readers, who wish to follow out the 

 reasoning, to the Proceedings of the Literary and Philo- 

 sophical Society of Manchester, for the 9th January, 1877, 

 vol. xvi., p. 88, where I'rofessor Clifford's paper is })iinted 

 m full. 



By a simple statement Professor Clifford means the denial 

 ol" the existence of any single combination or cross- 



