266 Dr. A. Marquand on Logical 



concerned, have been overlooked. It is therefore perhaps not 

 astonishing that the result is not, on this very point, in ac- 

 cordance with experimental fact. While molecules are in 

 close proximity, forces must act which depend on their vibra- 

 tions; and the relative phase of vibrations will be an important 

 factor in the determination of the strength and sign of these 

 forces. As the molecules approach each other they try to 

 place themselves in unison ; that is to say, the vibrations of 

 those already in unison will be strengthened, while the vibra- 

 tions of those the phases of which are in disagreement will 

 be weakened. At the moment of the shock a sudden altera- 

 tion in phase may take place ; and observations on natural 

 light seem to show that it does take place. If this alteration 

 takes place according to fixed laws, the forces acting between 

 the molecules during the second part of the shock will be 

 altogether different from those acting while the molecules are 

 approaching. Boltzmann assumes that all the phenomena of 

 an encounter take place as often in a reverse order ; but if 

 forces such as those suggested act, this need not be true. 



XXXIII. On Logical Diagrams for n terms. By Allan 

 Marquand, Ph.D., late Fellow of the Johns Hopkins Uni- 

 versity*. t 



IN the Philosophical Magazine for July 1880 Mr. Venn has 

 offered diagrams for the solution of logical problems in- 

 volving three, four, and five terms. From the fact that he 

 makes use of circles, ellipses, and other curvilinear figures, 

 the construction of diagrams becomes more and more difficult 

 as new terms are added. Mr. Venn stops with the five-term 

 diagram, and suggests that for six terms " the best plan would 

 be to take two five-term figures." 



It is the object of this paper to suggest a mode of construct- 

 ing logical diagrams, by which they may be indefinitely ex- 

 tended to any number of terms, without losing so rapidly "their 

 special function, viz. that of affording visual aid in the solu- 

 tion of problems. 



Conceiving the logical universe as always more or less 

 limited, it may be represented by any closed figure. For con- 

 venience we take a square. If then we drop a perpendicular 

 from the middle point of the upper to the lower side of the 

 square, the universe is prepared for a classification of its con- 

 tents by means of a single logical term. 



* Communicated by the Author. 



