234 



NATURE 



\yuly 14, 188] 



In connection with tliese complex logical diagrams 

 arises a curious and almost amusing illustration of the 

 impossibility of knowing all that has been ^yritten on a 

 subject. IVIr. Venn in the Historic Notes has carefully 

 CTone over all logical writings known to him, and concludes 

 (p. 426) that "hardly any attempts have been made to 

 represent diagrammatically the combinations of four terms 

 and upwards. The only serious attempt that I have seen 

 in this way is by Bolzano." This statement is qualified 

 in the Introduction or Preface (p. xxx.) by reference to 

 H. Scheffler's "Naturgesetze," published in 1880. But 

 if Mr. Venn had happened to look much nearer home, 

 into the able " Outline of Logic for the Use of Teachers 

 and Students," by the Rev. Francis Garden, M.A., Trinity 

 College, Cambridge (1867), he would have found at p. 39 a 

 diagram of five interlacing circles representing the rela- 

 tions of five terms. The diagram is thus described at the 

 foot, " Genus A partly overlapped by genera B, C, D, and 

 E, giving for species A B, ABC, AC, A CD, AD, 

 A D E, A E, A C D E." The circles are broken in their 

 unessential parts for the purpose of saving space. Mr. 

 Venn's ellipses are in this respect much more convenient 

 than circles, and the method of shading segments so as 

 to show their propositional treatment to the eye is an 

 important improvement ; but the principle on which 

 complex logical relations may be graphically represented 

 is clearly seized by Mr. Garden. 



Mr. Venn, although an ardent admirer of Boole, as 

 indeed all advanced logicians must be, remarks (p. xxviii.) 

 that his actual originality (priority ?) was by no means 

 so complete as is commonly supposed and asserted. But 

 I am a little surprised to notice that Mr. Venn, although 

 mentioning (p. 9) Thomas Solly's " Syllabus of Logic" ^ in 

 relation to another matter, does not draw attention to 

 the remarkable symbolical expression for the laws of the 

 syllogism given therein. This brief work is throughout 

 highly acute and philosophical. 



The really important question which underlies the 

 wdiole discussion of symbolic logic regards a technical 

 and apparently minor poinf, namely the exclusive or un- 

 exclusive character of logical alternatives. When we 

 say, for instance, that " capital is either fixed or circu- 

 lating," is it implied in the mere form of the statemenf 

 that capital cannot be at the same time fixed and circu- 

 lating? Boole held so; or, at any rate, he held that any 

 logical equation of his o^Yn system, not conforming to this 

 condition was imperfect and uninterpretable. But since 

 Boole's time several logicians have contended that this 

 condition was arbitrary, and in fact an error of Boole's. 

 It is one chief purpose of Mr. Venn's book to uphold 

 Boole's system in its integrity, and he writes in an attitude 

 more or less of protest against subsequent innovators. 

 This question has been noticed by Mr. MacColI in his 

 letter (Nature, voL xxiv. pp. 124-126). It is however a 

 question which requires chapters, if not books, for its 

 adequate treatment ; it is in fact to be judged by the 

 success of a system, rather than by any simple direct 

 arguments. 



In regard to this letter of Mr. MacColl, I may point to 

 the fact that I have already disputed the philosophical 

 correctness of MacCoU's symbolic innovations (Nature, 



' "A SylK^bus of Logic, in which the vieW!^ of Kant are generally adopted 

 nnd the Laws of the Syllogism symboUcally expressed," by Thomas Solly, 

 Ls.i., late of Caius College, Cambridge. (Cambridge, 1839.) 



vol. xxiii. p. 485), while as regards the main principles of 

 his calculus, it is out of the question that he should claim 

 novelty. But we may nevertheless regret that Mr. Venn 

 has referred in a slighting tone to investigations which 

 have been carried out with great earnestness and acute- 

 ness. Mr. Venn does not speak in the same slighting 

 manner of Prof. Schroder's essay, though I presume it is 

 clear that the latter was as completely forestalled by 

 previous writers unknown to him as was Mr. MacColl. 

 In fact the way in which independent investigators are 

 converging and meeting in a modified Boolian system is 

 strong evidence that the questions so clearly set forth by 

 Mr. Venn are becoming ripe for decision. 



W. Stanley Jevons 



ASTRONOMY FOR AMATEURS 

 A Cycle of Celestial Objects. Observed, Reduced, and 

 Discussed by Admiral William Henry Smyth, R.N., 

 K.S.F., D.C.L. Revised, Condensed, and greatly 

 Enlarged by George F. Chambers, F.R.A.S., of the 

 Inner Temple, Barrister-at-Law. (Oxford: The Cla- 

 rendon Press, 1881.) 

 '"pHERE can be, we think, little doubt that the publica- 

 - tion of Admiral Smyth's " Cycle of Celestial Objects" 

 powerfully stimulated a taste for astronomy amongst 

 amateurs in this country. It was popular in style, and 

 the contents generally were such as possessed interest for 

 the numerous class of readers who neither require nor 

 would appreciate more technical treatises. The gossiping 

 notes interspersed throughout the work had their special 

 attraction for many readers. 



Mr. Chambers says he would not have undertaken the 

 task of preparing a new edition of Smyth's work for the 

 press had he not been convinced that there was a wide- 

 spread desire for it. The copyright of the work, with the 

 Admiral's notes, unpublished drawings, &c., had come 

 into his hands, but there remained the digesting of these 

 materials and interweaving them with the contents of the 

 first edition. His programme he states to have been " so 

 to revise, prune, and amplify Admiral Smyth's Bedford 

 Catalogue, as to provide a Telescopist's Manual for Re- 

 fractors up to, say, 8 inches of aperture, and to embody 

 the progress of the science up to 1880, just as the original 

 edition might have been considered fairly complete for 

 5 inches of aperture up to 1S45." In carrying out this 

 programme he has deemed it essential to include objects 

 in the southern heavens, which we do not command in 

 these latitudes. 



It is to be understood that the new edition is confined 

 to the Cycle proper, or to the second volume of the 

 original work, the Prolegomena being, as Mr. Chambers 

 remarks, for the most part written up to date in the last 

 edition of his " Handbook of Astronomy." The number 

 of objects included by Smyth was 850, the number in the 

 present volume is 1604. Viewing the work as one in- 

 tended for the guidance of the amateur as to the objects 

 which it may be worth his while to observe, the additions, 

 upon the selection of which considerable pains appear to 

 have been bestowed, nevertheless include many stars that 

 can hardly claim to be so regarded : we allude to such 

 objects as Nos. 252, 334, 335, 346, 37i> 396, 737, 974, 

 1025, 1 149, &c. Perhaps a less e.xtended list with fuller 



