196 



NATURE 



{Jan. 4, 1877 



students such as attend the Royal College of Chemistry 

 and other science schools, but rather for those who take 

 up chemistry either as a branch of general education or 

 as an evening study, and for this purpose it seems to be 

 well fitted ; at the same time there is the danger of cram 

 to be guarded against. The author evidently feels this 

 and has endeavoured to provide against it in a somewhat 

 original manner. Pages 102-12 1 are divided into double 

 columns, the left hand one on each page containing the 

 preparation or reaction formulce of one of the non-metallic 

 elements and their more simple compounds ; the right 

 hand column is left blank, and the student is requested 

 to note the conditions under which each substance is 

 prepared either from the lecture or from a text-book. 

 This device would if conscientiously carried out by the 

 teacher, probably prevent cram of a certain sort, and 

 compel the student to know a little more than the mere 

 formula of a reaction or preparation. At the same time 

 we must confess that we must still regard this knowledge 

 as only another form of cram which is infinite in its 

 varieties and made to suit the idiosyncrasies of each indi- 

 vidual examiner, and which will exist as long as any form 

 of knowledge continues to be looked on as something to 

 "pass" an examination in; and as long as examiners 

 continue to look only to a set of answers given on a cer- 

 tain day in a certain time to a particular set of questions, 

 and not to the general character and capacity of the 

 student. We therefore think that Mr. Eltoft will meet 

 with failure in his well-meant effort ; we trust, however, 

 that he will continue to persevere. 



The rest of the book is divided into double pages, 

 meant for notes on particular elements, the pages being 

 divided according to a scheme in which specific gravity, 

 in the state of solid, liquid, or gas, colour, melting-point, 

 and boiling-point, are successively considered. Another 

 space is reserved for the description of the experiment, a 

 third for sketches of apparatus, and a fourth for tests for 

 the identification of the body. These pages will no doubt 

 teach the student to systematise his notes to a very con- 

 siderable extent and indicate to him a detailed method of 

 observation. 



In conclusion, we note that Mr. Eltoft, in his short pre- 

 face, expressly states that his "note-book" is "not in any 

 way supposed to take the place of a text-book, but to act 

 as an adjunct to it." We regard it in this light as an honest 

 effort to assist the large class of students for whom it is 

 intended, and we hope that the author will watch the 

 effect of the book on the classes he is teaching, look on 

 his present effort as experimental, and come forward again 

 with the aid of his increased experience to still further 

 improve his work. 



R. J. Friswell 



LETTERS TO THE EDITOR 



[The Editor does not hold hi?nself responsible for opinions expressed 

 by his correspondents. Neither can he unde7'take to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications i\ 



Solar Physics at the Present Time 



In reference to Trof. C. P. Smyth's letter in Nature, 

 vol. XV. p. 157, I think it my duty to state that Prof. Smyth's 

 remark on the priority of his exhibited results of observations 

 of deep-sunk thermometers (as bearing on the question of trans- 

 mis- ion of waves of temperature into or from^the interior of the 

 earth) is perfectly correct. 



It was only in the last summer that, having occasion to 

 inspect some parts of Prof. Smyth's printed "Observations," 

 I became acquainted with the extensive series of diagrams illus- 

 trating this matter. I have not yet been able to refer to his cited 

 paper in the *' Philosophical Transactions." G. B. Airy 



Royal Observatory, Greenwich, S.E., 

 J877> January \ 



Just Intonation, &c. 



Under this heading your correspondent "A. R. C," while 

 explaining Mr. Colin Brown's "natural finger-board," writes 

 thus: — "The vibration numbers of the diatonic scale being 

 represented by — 



I 9 5 4 3 S 15 2 

 043 238 



If we build upon the dominant 5, the vibration numbers will be — 

 2 

 9 5 45 3 27 IS 

 ' 8' 4' ^' 2' I6' 8' ' 



and if we build upon the subdominant - the vibration luunbt-ij 



3 

 will be — 



J 10 5 4 3 5 16 „ 

 94323 9 



Unless "A. R. C." proposes some new system of tuning, I 

 submit that he is in error in the first steps of his two examples. 

 The dominant of C is G, and from G to A is a minor, and not a 

 major, tone. Also the subdominant to C is F, and from F to G 

 is a major, and not a minor, tone. I do not pursue the analysis, 

 not desiring to criticise oversights, but to draw attention" to a not 

 uncommon misconception of the figures in the above scale, and to 

 the general adoption of a miscalculation as to the so-called 

 " Comma of Pythagoras." 



An eminent mathematician, not long deceased, derived our 

 diatonic scale from the one note F, by the following process : — 

 "FAC — CEG — GBD,"thus taking the common chords of 

 three different keys. Had he followed out his system of adding 

 on a new scale from the Fifth of the preceding, he would have 

 gone the round of the keys, and have derived them all from F, 

 which would have been the redastio ad absurdum. 



Nothing can be clearer than the history of the scale, and it 

 carries with it conviction of its truth. The octave was formed 

 out of two Greek conjoined tetrachords, such as B C D E and 

 E F G A, the E being common to both. Then the lower A was 

 added at the bottom, to complete the octave, and it was called 

 "the added note" {proslambanomenos) because it did not form 

 part of any tetrachord. The reduction from the eight notes of 

 the two tetracliords to seven is attributed to a superstition in 

 favour of the number seven. Thus came our A B C D E F G A — 

 a minor scale with a minor Seventh— -and from it came our truer 

 major scale, by commencing on the third note, C, but carrying 

 with it all the imperfections of the double root of the' original. 

 No improvement has been made in the scale since the days when 

 Archytas, the friend of Plato, introduced the consonant major 

 Third, and Eratosthenes the minor Third. Our present scale 

 is therefore absolutely anterior to the Christian era ; the ratios of 

 its intervals given by Greek authors prove the identity irresistibly. 

 Let us then look to the figures which represent our scale as 

 "A. R. C." has justly given them. The large i and 2 refer to C 

 as the fundamental note and its octave. The 3 to 2, the 5 to 4, 

 the 9 to 8, and the 15 to 8 represent octaves of the key-note 

 (2, 4, or 8) ; but the 4 to 3 (the interval of a Fourth) and the 

 5 to 3 (the interval of a major Sixth) refer to C only as the so- 

 called " Twelfth" above F, and not to C as the octave. If we 

 play either of these two notes, F or A, with C, we cannot use C 

 as a consonant bass. We must take F, and thus we have the 

 old tetrachord system, with its double root, running in our pre- 

 sent scale. In all keys the tonic and the subdominant are both 

 necessary basses. F and A belong exclusively to F ; but B and 

 D have no relation to F, not being aliquot parts of the F string. 

 They belong to the scale of C, but more intimately to that of G. 

 The F string exceeds the length of the C string by 3 to 2, be- 

 cause its sound is that of a Fifth below C ; therefore any 

 attempts to bring the sounds of our scale to a common denomi- 

 nator are fallacious, the first law of Proportion being that 

 " Ratio can subsist only between quantities of the same kind." 

 Thus the " 24, 27, 30, 32, 36, 40, 45, 48," cannot be accepted, , 

 because the 32 intended for the 4 to 3 of the scale, and the 40 \ 

 for 5 to 3, represent other intervals. The 4 to 3 of C is the ; 

 Fourth from C down to G, and the 5 to 3 of C is the major j 

 Sixth from E down to G. The 32 and 40 are not applicable to . 

 the interval of a Fourth from F down to C, nor to the major ] 

 Sixth from A down to C. 



And now as to the so-called "comma of Pythagoras," a 

 strange name for the interval of 531441 to 524288! Can the 

 modest inventor, who has concealed his own name, have sup- 

 posed that the Greeks had musical instruments so very far 



