168 Mr. M'Coll on the Diagrammatic and Mechanical 



retrograde (or opposite to that of the translation of fluid in the 

 undisturbed vortex) ; and, as was to be expected, the values of 

 — n are approximately equal in the two cases when ma is small 

 enough ; but it is smaller by a relatively small difference in 

 (60) than in (43), as was also to be expected. 



The case of ma small and i > 1 has a particularly simple ap- 

 proximate solution for the smallest g-root of the transcendental 

 (50). With any value of i instead of unity we still have (58), 

 as a first approximation for q small. Eliminating g 2 /m 2 d 2 be- 

 tween this and (52), we still find X = ^ ; but instead of n=0 

 by (51), we now have n = (i — 1)oj. Thus is proved the solu- 

 tion for waves of deformation of sectional figure travelling 

 round a cylindrical vortex, announced thirteen years ago with- 

 out proof in my first article respecting Vortex Motion*. 



XXV. On the Diagrammatic and Mechanical Pepresenta- 

 tion of Propositions and Reasoning s. 



To the Editors of the Philosophiccd Magazine and Journal. 



Gentlemek, 



MR. VENN has kindly sent me a copy of his very inter- 

 esting paper in the Philosophical Magazine for July, 

 in which he explains a method which he has invented for sol- 

 ving logical problems by means of diagrams. The method is 

 certainly ingenious, and for verifying analytical solutions of 

 easy and elementary problems it would, I think, be useful in 

 the hands of a teacher ; but I cannot agree with its inventor's 

 estimate of its practical utility in other respects, much less 

 with his opinion as to its superiority over rival methods. 

 Speaking of his diagram for five-letter problems, Mr. Venn 

 says :— 



" It must be admitted that such a diagram is not quite so simple 

 to draw as one might wish it to be ; but then we must remember 

 what are the alternatives before any one who wishes to grapple 

 effectively with five terms and all the thirty-two possibilities which 

 they yield. He must either write down, or in some way or other have 

 set before him, all those thirty-two compounds of ivliich XTZ "W V is 

 a sample^ that is, he must contemplate the array produced by 160 

 letters" 



Fom the words in italics it is evident that Mr. Venn does 

 not yet appreciate the advantages of my own method, which 

 assuredly lays one under no such onerous obligation as he 

 mentions. It grapples effectively, not merely with problems 



* "Vortex Atoms," Proc. Eoy. Soc. Edinb. Feb. 18, 1867- 



