Dec, 26, 1878] 



NATURE 



171 



OUR BOOK SHELF 

 Manuals of Elementary Science — Crystallography. By 



H. P. Gurney, M.A. (Society for Promoting Christian 



Knowledge, 1878.) 

 This excellent little manual satisfies a want long felt, for, 

 up to the present time, there was no book in which a 

 general knowledge of the system of crj'stallography, first 

 developed by Prof. MiUer in his "Treatise on Crystallo- 

 graphy," 1839, could be obtained. Prof, Miller's treatise 

 and Tract are mainly occupied with the methods of 

 calculation, and require a considerable knowledge of 

 trigonometry. The manual before us aims at doing for 

 these books what the crj-styllographic introduction to 

 Naumann's " Mineralogie " does for his " Lehrbuch der 

 KrystaUographie." It therefore avoids all the analysis 

 used in the calculation of crystals, and limits* itself to 

 explaining the elementary geometrical principles involved 

 in the representation of the faces by indices. 



The method of development of systems of symmetr}', 

 rendered so familiar to us by Prof. Maskelj-ne, has been 

 almost necessarily followed, and the author has conse- 

 quently inverted the usual order of discussion of the differ- 

 ent systems, beginning with the Anorthic, that of simplest 

 symmetry, and proceeding through the different types of 

 symmetry up to the cubic system, that of most complex 

 symmetry. In the different systems the characteristic 

 forms are shown to flow so simply from the conditions of 

 symmetry that a moderately bright student ought to be 

 able to deduce them himself after following Mr. Gurney' s 

 exposition in the first two or three systems. In his dis- 

 cussion of the rhombohedral system the author follows 

 Prof. Miller. The hexagonal system, of which the 

 rhombohedral is a hemisymmetrical development, is so 

 imperfectly manifested by crystals that its discussion is 

 only of theoretic interest and is unsuited to an elementary 

 manual. In his discussion of merohedrism the author 

 has not attended to the limiting condition, pointed out by 

 von Lang, that the merohedral form should not be iden- 

 tical with the characteristic form of a system of lower 

 symmetry, although here, likewise, he has the sanction of 

 Prof. Miller's authority. The condition, however, is 

 justified by the most recent observations, which have 

 placed most of the minerals displaying such merohedrism 

 in the systems of lower holohedral symmetry. We can 

 heartily recommend the book to students even if they be 

 able to study the more advanced text-books. 



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 munications containing interesting and novel /acts.} 



On the Ancient Pitch of Organs 

 As I am obliged to intermit my researches on organ pitch for 

 a few months, owing to pressui-e of other work, I wish to make a 

 note of the point to which I have advanced, after consulting many 

 old books, and actually measuring pitch and length of many old 

 organ-pipes, for which I am obliged to the kind politeness of 

 organ-builders, organists, and friends. When my researches are 

 complete, they will appear with details in a paper to be read 

 before the Society of Arts on the History of Musical Pitch, 

 about a year hence. The delay arises from the difficulty of 

 getting information from the Continent. 



In England we have no organs older than the Restoration, 

 1660, as the PuriUns smashed all church-organs in 1644-46. 



The principle used by organ-builders was to make a certain 

 pipe of the length of some multiple or easy sub-multiple of the 

 standard length of measurement in their own country, and deter- 

 mine the other notes from its tone, according to the mean-tone 



or unequal temperament in universal use for organs everywhere 

 till 1830, but beginning to be disused in France in 1834 and in 

 England in 1854. There is an apparent exception in JSt. Jacobi 

 Kirche at Hamburg, where equal temperament is claimed for 

 1720, when J. S. Bach played on that organ, and possibly in 

 other old German organs. In England I have found the old 

 unequal temperament still existing at St. George's Chapel, 

 Windsor Castle, Kew Parish Church, St. Katherine's, R^ent's 

 Park, All Hallows the Great, Upper Thames Street, Maidstone 

 Parish Church, St. Mary's, Shrewsbury, and several other organs 

 which have been very recently re-tuned. The first equally tem- 

 pered organ by Messrs. Gray and Davison was sent cut in 1854. 



The pitch note used from 1500 to 1650, at least in Germany, 

 seems to have been F, for which a 13-foot pipe was employed 

 for our F in the 16-foot octave. But the foot varied so much in 

 Germany, being 3 per cent, longer than the English on the 

 Rhine, and in Austria, and much shorter than the English in 

 Central Germany, that the pitch thus determined varies by one 

 to two equal semitones. The Brunswick foot, in 1620, where 

 we have Prxtorius's reference, possibly gave a tone of 35 vib. for 

 the 13 foot pipe, an octave below the ordinary violoncello C. 



In England Tomkyns (before the Commonwealth) fixes the F 

 as 5 feet, which gives the A as 4 feet, and the double octave of 

 this as I foot, and hence comes under the next cat^ory. The 

 13-foot F gives a 13-inch treble C, which, for Rhenish feet, 

 would have a pitch of 425, whereas Handel's A was 423, having 

 a pitch a minor thu-d higher. This minor third constantly 

 recurs. In Hamburg the St Jacobi organ is a minor third 

 sharper than the St. Michaelis organ, the first being a tone 

 sharper and the latter a semitone flatter than French pitch. And 

 strangest of all, the St. Jacobi organ had formerly one of its 

 stops tuned to the low St. MichaeUs pitch. 



The old reason for fixing the pitch seems to have been to pat 

 the ecclesiastical tones within easy fingering for the organist, 

 without using the chromatic notes (which Arnold Hchlick, 1512, 

 naively says is not convenient for most players), at the same time 

 that they were within easy reach of a baritone voice. This is a 

 point I have not yet worked out completely. 



In England the foot-r\ile seems to have been generally adopted 

 in early organs as the means of giving a standard, and it is not 

 till about Green's time — a century ago — that I find it varied from 

 this by a small fraction of an inch — not exceeding t^vo-fifths. 



The pitch of an open metal cylindrical flue-pipe used for 

 the open diapason stop (but not " a show-pipe '), measuring 12 

 inches from the lower lip to the open end, varies from 472 to 

 475 vibrations in a second at 60° F. The variations are due to 

 the size of the diameter, the force of wind, the opening at the 

 foot, and the method of voicing, I have known such a pipe 

 raised two vibrations in a moment iby a slight alteration in 

 voicing. This is the old standard pitch in England, Varieties 

 depend upon the name of the note which it represents, and the 

 classes of organs which I have met with in books or in realitj-, 

 have hence been called by me the A foot, B flat foot, B foot 

 and C foot organs. 



I, The A fo:t organ has A 472 to 475. This was Tomky m's 

 pitch, as shown by Sir F, Gore Ouseley in his edition of 

 " Orlando Gibbons,"' and seems to have been the pitch for which 

 that composer wrote his Church music. It gives the mean tone 

 C 565 to 570, As the French diapason normal is really A 435'875 

 (as determined originally by M. Cavaille-Colt, and verified this 

 year by Mr, Hipkins in Paris, by means of a Scheibler 440), this 

 makes Tomkyns's pitch about three-quarters of a tone sharper 

 than French pitch. This is the present existing pitch of St. 

 Katherinen Kirche at Hamburg, The St. Jacobi organ, and 

 also that in the Cathedral of St. Marie, at Liibeck, is a whole 

 tone higher than French pitch. The great Franciscan organ at 

 Vienna, 240 years old and untouched, gives A 460, which is only 

 a semitone sharper than French pitch. These are the sharpest 

 existing organs I have met with. The Franciscan organ is only 

 used for the old ecclesiastical tone singing of the monks. This 

 was also possibly the pitch recommended by Prcvtoritts for church 

 organs, the drawing in his book (1618) giving the B pipe one 

 Saxon foot in length, with strong pressure of wind, and the 

 Saxon foot being 7 per cent, shorter than the English. 



It is as well to mention in passing that the tones and semitones 

 here spoken of for measuring purposes, if not otherwise quali- 

 fied, are equal semitones, and that, near enough for such pur- 

 poses, an equal semitone and tone higher have 6 and \7.\ per 

 cent, more vibrations, and thus a quarter and three-quarters of a 

 tone higher have 3 and 9 vibrations more per cent. For unequal 



