104 THE PRINCIPLES OF SCIENCE. [CHAP. 



that is, " a fixed star is not a planet, but is either subject 

 or not, as the case may be, to gravity." Here we have no 

 conclusion concerning the connection of fixed stars and 

 gravity. 



The Logical Abacus. 



The Indirect Method of Inference has now been suffi- 

 ciently described, and a careful examination of its powers 

 will show that it is capable of giving a full analysis and 

 solution of every question involving only logical relations. 

 The chief difficulty of the method consists in the great 

 number of combinations which may have to be examined ; 

 not only may the requisite labour become formidable, but 

 a considerable chance of mistake arises. I have therefore 

 given much attention to modes of facilitating the work, 

 and have succeeded in reducing the method to an almost 

 mechanical form. It soon appeared obvious that if the 

 conceivable combinations of the Logical Alphabet, for any 

 number of letters, instead of being printed in fixed order 

 on a piece of paper or slate, were marked upon light 

 movable pieces of wood, mechanical arrangements could 

 readily be devised for selecting any required class of the 

 combinations. The labour of comparison and rejection 

 might thus be immensely reduced. This idea was first 

 carried out in the Logical Abacus, which I have found 

 useful in the lecture-room for exhibiting the complete 

 solution of logical problems. A minute description of the 

 construction and use of the Abacus, together with figures 

 of the parts, has already been given in my essay called 

 The Substitution of Similars* and I will here give only 

 a general description. 



The Logical Abacus consists of a common school black- 

 board placed in a sloping position and furnished with four 

 horizontal and equi-distant ledges. The combinations 

 of the letters shown in the first four columns of the 

 Logical Alphabet are printed in somewhat large type, 

 so that each letter is about an inch from the neighbour- 

 ing one, but the letters are placed one above the other 

 instead of being in horizontal lines as in p. 94. Each 

 combination of letters is separately fixed to the surface of 



1 Pp- 55-59, 8186. 



