January 7, 1892] 



NATURE 



223 



by applying that abstract universal and necessary law to such 

 things as "terms," we see that a term applicable to anything 

 cannot at the same time be the very opposite. ^ 



Mr. Dixon says : " If anyone chooses to say a thing both ' is 

 and ' is not,' there is no law against his doing so, only if he does 

 so he is not talking the Queen's English." But by so doing he 

 breaks the law of reason, if not the law of the land ; and, 

 indeed, to act on such a principle when on oath in a court of 

 law might, after ail, have inconvenient consequences. 



My critic is obliging enough to say in plain and simple terms : 

 "Dr. Mivart is wrong in speaking of the objective absolute validity 

 of the law of contradiction." To this 1 might content myself by 

 replying : " Quod gratis asseritur gratis negatur" ! But let us 

 avoid the use of the terms " is" and "is not" : they are not 

 necessary for my purpose. Does Mr. Dixon really doubt 

 whether, if he had lost one eye, he would still remain, after 

 that loss, in the very same condition he was in before ? If any- 

 one does not see the objective impossibility of such a thing 

 every-wfure and cverynvhen—i e. if he does not apprehend the 

 application of the law of contradiction — then he either does not 

 understand the question, or his mental condition is pathological. 

 The implications of science are implied. Men may pretend to 

 doubt them, their own existence, or the objectivity of mathe- 

 matical truths. But their practice shows their unfailing con- 

 fidence in them on each occasion as it arises— as when cheated 

 by false accounts, personally injured, or engaged in scientific 

 research. When we enter the laboratory, we leave these follies 

 outside. St. George Mivart. 



Hurstcote, December 22, 1891. 



Will you allow me to say a few words in reference to four 

 points in Mr. E. T. Dixon's indictment (Nature, December 10, 

 p. 125) of Mr. St. George Mivart? 



(1) Mr. Dixon asserts that the law of contradiction "is not a 

 necessary truth at all, it only expresses a verbal convention " — 

 it "never tells us whether anything 'is' or 'is not.' It only 

 informs us that the terms ' is ' and ' is not ' are not applicable 

 to the same thing." But though it may be only a " verbal con- 

 vention " that in "the Queen's English" not is the sign of 

 negation, it is not a mere verbal convention that if a signifies 

 the negation of A (whatever A may stand for), then A and a 

 "are not applicable to the same thing" — as the law of contra- 

 diction asserts, and as Mr. Dixon himself allows. A highly 

 abstract law that is concerned with the relations of propositions 

 cannot, of course, tell us whether any particular thing exists or 

 not — but then no one has ever expected that it should ; and 

 moreover, assertions (or denials) of the "existence" of particular 

 objects are not the only "real" propositions (Mr. Dixon 

 appears to be misled here partly by the ambiguity of is). 



(2) Mr. Dixon says that the law of gravitation — like other 

 laws suggested by particular experiences — depends ultimately 

 upon induction per emimerationen simplicem ; that is, upon an 

 inference of the form This A is X, that A is X, <s:'c. ( = Some 

 A's are X), . ■. All A's are X (for we can make nothing better 

 out of an induction by simple enumeration). But this inference 

 is merely an immediate inference, and moreover an illegitimate 

 one ; hence, according to Mr. Dixon's view, inductions have no 

 logical justification whatever. 



(3) Further, Mr. Dixon asserts that " the supposed peculiar 

 certainty of mathematical conclusions is solely due to the fact 

 that they are truisms," or " purely verbal assertions," — by which 

 I understand him to mean definitions. In answer to this I 

 should maintain that the peculiar certainty of mathematical 

 propositions, and the fact that here, by help of a single instance, 

 we unhesitatingly conclude to the universal, are (as I have 

 observed elsewhere) explicable by "the consideration that we 

 here see at once the connection, which in other cases we believe 

 on grounds very different from a perception of self-evident inter- 

 dependence of attributes. When the equality of the interior 

 angles of any one triangle to two right angles has been demon- 

 strated to us, we infer without a moment's doubt that the same 

 relation of equality may be asserted of the interior angles of 

 every triangle ; and this because we have seen that with the 

 attributes signified by ' the interior angles of a triangle ' there 

 is bound up the attribute of ' being equal to two right angles.' 

 We believe that, if a certain amount of arsenic has on some occa- 

 sions produced death, it will always produce death, on the 

 ground that the apparent likenesses are connected with un- 

 apparent likenesses ; but we have not seen in this case (as we 

 have in the case of the triangle) that there is a self-evident 



NO. II 58. VOL. 45] 



interdependence. And here we see why it is that, in the case 

 of mathematical inductions, we do not need to use Mill's 

 'Inductive Methods.'" 



(4) When Mr. Dixon goes on to say that, "j/the inhabitants 

 of the Dog Star defined 'twice,' ' two,' and 'four' as we do, 

 then ' twice two ' would be to them ' four ' ; but to say that it 

 was so could only give verbal information," he may be refuted 

 out of his own mouth. For he goes on to remark that, " if the 

 people in the Dog Star chose to define four as i -f i -H, the so- 

 called ' necessary truth' would not even be true ! " ; thus showing 

 clearly that it is the facts signified, and not the words which 

 signify them, that we are concerned with. According to Mr. 

 Dixon, it would be (for me) a necessary truth that I have a head- 

 ache, or am writing with a lead-pencil ; while mathematical 

 truths, in as far as " real," are obtained by induction, and are 

 therefore not necessary. I hold, on the contrary, that mathe- 

 matical truths, though obtained by induction, are "necessary " 

 — that is, true under all circumstances — and that it is only by a 

 confusion between " necessary " and " certain " that a statement 

 of the apprehension of present fact can be called a " necessary 

 truth." E. E. C. Jones. 



Cambridge, December 14, 1891. 



Supernumerary Rainbows observed in the Orkneys. 

 I INCLOSE a letter just received. The writer has charge of 

 the anemometer formerly kept by the late Dr. Clouston. Dr. 

 Clouston first drew my attention to the extraordinary bow seen 

 at Kirkwall in 1871. My note is in the Quarterly Journal of 

 the Meteorological Society, vol. i. p. 237. 



Robert H. Scott. 

 Meteorological Office, 63 Victoria Street, S.W., 

 December 31, 1891. 



Deerness Public School, Kirkwall, December 2%, 1891. 



Sir, — On reading your very interesting workjon " Elementary 

 Meteorology," I find, on p. 201, reference made to "an extra- 

 ordinary bow" which appeared at Kirkwall, November 13, 

 1871, which you explain by the reflection of the sun's rays from 

 a water surface. 



On Saturday, the 26th inst., at 3.20, when the sun was on the 

 horizon, I saw a very distinct rainbow ; there was no trace what- 

 ever of the secondary bow, but between where it ought to have 

 been and the primary one there were several patches of vyhat are 

 called "supernumerary " bows. The only colour I saw distinctly 

 was the red. 



This lasted for about four minutes, when, finally, a second 

 bow appeared just inside the primary, with the colours arranged 

 as in the primary — not reversed, as the secondary. The space 

 between the violet of the primary and this one was almost nil. 

 The red next the violet of the primary was about as distinct as 

 that of the primary. The orange and yellow were distinct also, 

 but the others could hardly be seen. This was, no doubt, owing 

 to the fading light of day, and to the dark colour of the clouds 

 in the north-east, where the bows appeared. These lasted dis- 

 tinctly and complete for about one minute. The bows formed, 

 as is well known, half a circle. The sun was setting behind land 

 at the time, and the wind was blowing at the rate of forty-five 

 miles, so that there could be no water reflection. 



If I am not troubling you too much, would you kindly say if 

 this is unusual, and if caused by the "interference " of rays? 

 Yours respectfully, 



(Signed) M. Spence. 



Aurora Borealis. 



A FINE display of aurora was observed here on the even- 

 ing of January 4. A faint northern glow was seen at 8.30, 

 which quickly grew in brightness, and at 8.45, streamers in 

 great quantity were visible. At 9 these became tinted with 

 glowing red on their upper [portions. After exhibiting lively 

 motions for a quarter of an hour or so, the phenomenon settled 

 down into a brilliant and steady arch of light, red on the outside 

 and white within, resting on what appeared to be a bank of 

 dark cloud. By eye estimate this arch would extend about 90 

 along the horizon, its apex over the north-north-west from 

 25° to 30° in height. The glow was still visible at 10 p.m., 

 though considerably diminished in intensity. During the whole 

 of the day a dry and frosty north-west wind prevailed, and the 

 temperature at 10 p.m. was 28 . J. LovEL. 



Driffield, East Yorkshire, January 5. 



