578 



NATURE 



{_April 2 1 



The Tide-Predicter 



Mr. Edward Roberts' letter in Nature for April 14 

 contains statements giving an erroneous view of the origin of 

 the tide-predicter. Any one who feels sufficient interest in the sub- 

 ject to derive full information will find it in my paiJer on " The 

 Tide-Gauge, Tidal Harmonic Analyser, and Tide-Predicter," 

 read before the Institution of Civil Engineers on March i and in 

 the abstra'it of the discus4on which followed it, to be published 

 in the Minutes of the ProeeeJiiigs of the Institution (vol. Ixv. 

 sess. 1S80 Si, part iii.), and he will see that my letter in Nature 

 of March 31 is correct. William Thomson 



The University, Glasgow, April 16 



Geological Relations of Gold in Nova Scotia 



In the notice of the report of Mr. Murray on the gold of 

 Newfoundlanl (Nature, vol. xxiii. p. 472) I observe a reference 

 to my own opinion of the age of the gold of Nova Scotia wliich 

 needs sojie correction. In the second edition of "Acadian 

 Geology" (186S) the gold-bearing series is included in the Lower 

 Silurian, but this referred to the larger sense of that term in 

 which it was used to include the Cambrian as well. In the 

 third edition (1878, Supplement, pp. 81, 85, 92) I have referred 

 this formation, on the evidence of fos41s and stratigraphical 

 position, to the age of the Lower Cambrian or Longmynd series, 

 thus placing it on a lower horizon than the fossiliferous Primor- 

 dial of Eastern Newfoundland, which I suppose to be of the 

 age of the Acadian or Menevian group. There is therefore 

 little difference between Mr. Murray's estimate of the age of the 

 gold-bearing rocks of Neivfoundlind and my own of that of 

 the similar rocks in Nova Scotii, except that I presume he 

 would classify the Newfoundland series as Upper Huronian 

 rather than Lower Cambrian. With reference to this I liave 

 been disposed to regard Mr. Murray's Aspidella slates and the 

 associated rocks as equivalents of the Keweniin or " Upper 

 copper-bearing group " of the West, and probably Upper Huro- 

 nian, in which case they might be a little below my Nova Scotia 

 Lower Cambrian ; but the precise age of both series is deter- 

 milled merely by the fact that they appear to belong to the 

 period between the Huronian proper, or Lower Huronian, and 

 the Acalian group, or Menevian (Etage C. of Barrande). 



It is proper to add that in the third edition of "Acadian 

 Geology " I have shown that the filling of the Nova Scotia 

 gold veins is much mjre recent than the containing rocks, and 

 belongs to the time intervening between the Upper Silurian and 

 the Lower CarbDniferous, the richer deposits als n appearing to be 

 related to the occurrence of intrusive granites of Devonian age. 

 There is no reason, therefore, other than the mineral character 

 of the containing beds, why such veins might not occur in any 

 rocks older thin the Devonian, and gold discoveries have been 

 rep Dried in localities where the rocks are supposed to be 

 Huronian and Silurian ; but I have had no opportunity of 

 personally verifying these statements. Thus far the important 

 gold veins are known only in that great series of slates and 

 quartzites of the Atlantic coast which I have referred to tlie 

 Lower Cambrian. J. W. Dawson 



McGill College, Montreal, April 4 



Symbolical Logic 



Prof. Jevons, in his criticism of my method in Nature, 

 vol. xxiii. p. 485, has stated the main points at issue between us 

 so fully and clearly, and on the whole so fairly, that I need only 

 say a very few words in reply. 



As to the charge that my method is ante-Boolian or anti- 

 Boolian, I do not seek to repel it ; on the contrary, I maintain 

 that my method is different from Boole's in principle, and very 

 different indeed in its practical working. The really important 

 questions to be settled are these : 



1. Are the definitions which I give of my symbols clear and 

 unambiguous ? 



2. Are the rules and formula; which I derive from these 

 definitions correct ? 



3. Are the iunovations which I propose of any practical 

 utUity? 



Now, 1 do not think that any one who has read my papers in 

 the Proceedings of the London Mathematical Society and my 

 articles in Mind and in the Philosophical Magazine will refuse to 

 answer Yes to questions I and 2 ; and with regard to question 



3 I can ouly say that any one who answers No is bound in fair- 

 ness to prove the inutility of my innovations by solving one or 

 two of my hardest problems without their aid, and in an equally 

 clear and concise manner. My proposal of an amicable contest 

 in the Educational Times meant nothing more serious than this. 



Some of my critics (not including Prof. Jevons however) seem 

 anxious to magnify the points of resemblance between my 

 method and it- predecessors, esjiecially Boole's, and to minimise 

 the points of difference. It may be as well therefore to state 

 briefly what characteristics distinguish my method, so far as I 

 know, from all the methods which hive preceded it, and what 

 advantages, in my opinion, accompany the-e characteristics. 



In the first place, then, every single letter in my notation, as 

 well as every combination of letters, denotes a statement. By 

 this simble device I gain the important advantages of generality 

 of expression and uniformity of interpretation and treatment. It 

 enables me to express many important logical laws in simple 

 and symmetrical formulae, as, for instance, 



[A:a)(B:b)[C:c-):I^A ^ B ^ C:a + h -^^ c), 

 which otherwise could not be so expressed. To secure these 

 advantages I sacrifice ab.olutely nothing. The relations of 

 classes, including the ordinary syllogisms, I express by speaking 

 throughout of one individual, just as mathematicians express the 

 properties of curves, surfaces, and volumes, by speaking through- 

 out of the varying distances of one representative point. 



My claim to priority on this head has been called in question 

 on the ground that Boole too, in his equations about "secondary 

 proposition;," denotes stateuents by single letters. The plain 

 truth however is that Boole takes sojie pains to prevent his 

 readers from imagining that he does anything of the kind. He 

 says distinctly, and in perfect consistency with the whole tenor 

 of his book, in which he describes his algebra of logic as a mere 

 offshoot and part of the ordinary algebra of quantity, that in his 

 equitions any single letter, such as x, denotes the portion of time 

 during which some proposition x is true, the whole universe of 

 time to which the discourse refers being the unit (see " Laws of 

 Thought," from p. 164 to p. 170). Neither will one find any- 

 where in Boole's work the idea (suggested to me by analytical 

 geometry) of investigating the relations of different classes, while 

 speaking only of one individual, and thus dispensing entirely 

 with the quantitative words all, some, and none, which are so 

 characteristic of the old logic. 



Another peculiarity of my method is that my symbol of denial 

 (an accent) is made repeatedly to apply to expressions of varying 

 complexity, as, for instance, (xy)', \x + y z)' . (x : y')', leading to 

 rules and formulce of operations, to which I find no parallel in 

 any prior symbolic sy-tem with which I am acquainted. 



Boole uses x as an abbreviation for i - x. Let those who 

 insist that Boole's horizontal stroke is exactly equivalent to my 

 accent express in his notation the complex equation 



[x -yY= {x:y)' + (y.x)', 



and explain its meaning clearly without departing from Boole's 

 quantitative interpretation of his symbols. 



Lastly, my symbol ; expresses implication or inference, and does 

 not, therefore, exact'y coincide in meaning with Prof. Peirce's 

 symbol of inclu-ion — <, as defined by him in his "Logic of 

 Relatives," published in 1870. This symbol of inclusion, as I 

 understand Prof. Peirce's definition of it, is simply equivalent to 

 the words "is not greater than," and is therefore restricted to 

 number and quantity. It is true that Prof. Peirce in his recent 

 memoir on the "Algebra of Logic " extends the meaning of 

 this symbol of inclusion, so as to make it also convey the same 

 meaning as my symbol of implication ; but as this memoir was 

 published subsequently to my second and third papers in the 

 Proceedings of the Mathematical Society, to which Prof. Peirce 

 explicitly refers in his memoir and accompanying circular note, 

 this later definition does not bear upon the point in discussion. 



Prof. Jevons objects to my a ; S as an abbreviation for 

 o = o;3, because he thinks it obscures the real mture of the 

 reasoning operation. But one might with equal justice object 

 on the same grounds to a' as an abbreviation for a a a, or to the 

 left side of the equation in the binomial theorem as an abbre- 

 viation for the right side. The symbol a : ;8 is the exact equiva- 

 lent of a = ayS, just as a = S is the exact equivalent of (a ; $) 

 (6 : a), and I do not see that I create any obscurity by adopting 

 in any investigation, and at any stage of the investigation, what- 

 ever form seems most suitable for the immediate purpose in 

 view. But whether I am right or wrong in this opinion can only 



