146 METHODS OF ABBREVIATION. [CHAP. IX. 



In none of the above examples has it been my object to ex- 

 hibit in any special manner the power of the method. That, 

 i conceive, can only be fully displayed in connexion with the 

 mathematical theory of probabilities. I would, however, suggest 

 to any who may be desirous of forming a correct opinion upon 

 this point, that they examine by the rules of ordinary logic the 

 following problem, before inspecting its solution ; remembering 

 at the same time, that whatever complexity it possesses might 

 be multiplied indefinitely, with no other effect than to render its 

 solution by the method of this work more operose, but not less 

 certainly attainable. 



Ex. 5. Let the observation of a class of natural productions 

 be supposed to have led to the following general results. 



1st, That in whichsoever of these productions the properties 

 A and C are missing, the property E is found, together with one 

 of the properties B and D, but not with both. 



2nd, That wherever the properties A and D are found while 

 E is missing, the properties B and C will either both be found, 

 or both be missing. 



3rd, That wherever the property A is found in conjunction 

 with either B or E, or both of them, there either the property 

 C or the property D will be found, but not both of them. And 

 conversely, wherever the property C or D is found singly, there 

 the property A will be found in conjunction with either B or E, 

 or both of them. 



Let it then be required to ascertain, first, what in any parti- 

 cular instance may be concluded from the ascertained presence of 

 the property A 9 with reference to the properties B, C, and D ; 

 also whether any relations exist independently among the pro- 

 perties By C, and D. Secondly, what may be concluded in like 

 manner respecting the property B, and the properties A 9 C, 

 andD. 



It will be observed, that in each of the three data, the informa- 

 tion conveyed respecting the properties A , 5, C, and D, is com- 

 plicated with another element, E, about which we desire to say 

 nothing in our conclusion. It will hence be requisite to eliminate 

 the symbol representing the property E from the system of equa- 

 tions, by which the given propositions will be expressed. 



