120 THE PRINCIPLES OF SCIENCE. 



examined ; not only may the requisite labour become 

 formidable, but a considerable chance of mistake may 

 arise. 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 abecedarium, for any number of letters, instead 

 of being printed in fixed order on a piece of paper or 

 slate, were marked upon light moveable pieces of wood, 

 mechanical arrangements could readily be devised for 

 selecting the combinations in any required order. The 

 labour of comparison and rejection might thus be im- 

 mensely 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 TJie Substitution of 

 SimilarsS, and I will here give only a general description. 

 The 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 abece- 

 darium (see p. 109), are printed in somewhat large type, 

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



o 



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

 instead of being in horizontal lines as in p. 109. Each 

 combination of letters is separately fixed to the surface 

 of a thin slip of wood one inch broad and about one- 

 eighth inch thick. Short steel pins are then driven in an 

 inclined position into the wood. When a letter is a large 

 capital representing a positive term, the pin is fixed in 

 the upper part of its space ; when the letter is a small 



g P P- 55-59. 81-86. 



