61S 



HARLEIAN COLLECTION". 



HARMONIUM. 



611 



are likely to be quiet and asleep all day, and that the healing 

 processes are then very active, it has the great advantage of enabling 

 them to resort at once to their natural food by restoring the power of 

 sucking. 



HARLEIAN COLLECTION. [BRITISH MUSEUM.] 



HARMALINE (C rt H,,N,0,) and Harminc (O^HjAOJ are alka- 

 loida occurring in the seeds of Peganum Harmala. They are united 

 with phosphoric acid. Harmaline forms yellow salts with the acids, 

 and is transformed into a red matter by oxidising agents. The harmala 

 red of commerce is the powder of the seeds. It is used in dyeing red, 

 rose-colour, and pink. It is used in large quantities in Russia. 

 Harmaline yields a number of substitution products, such as nitro- 

 harntalint, cyano/tarmaline, Ac. Harmiue forms colourless neutral salts 

 which crystallise in long delicate prisms. Harmaline is converted into 

 harmine by oxidation. 



HARMINE. [HABMALINE.] 



HARMONIC PROPORTION. The reciprocals of numbers which 

 are in arithmetical proportion are themselves said to be in harmonic 

 proportion; thus 



11 1 . 



- > r i . > &c -i 



a a + b a + 2* 



is a series in harmonic progression. 



A line AB is said to be harmonically divided when two points, 



I 



J 



C and D, one within it and one on its continuation, are so placed that 

 A c is to c B as A D to D B. In this construction, c D is an harmonic 

 mean between A D and B D, or A D, c D, and B D, are aa the reciprocals 

 of terms in arithmetical proportion. 



HARMONICA, also written An MONICA (from the Greek word for 

 harmony), but more familiarly Musical tjlanaet. Franklin in a letter to 

 Beccaria, says that Mr. Puckeridge, an Irish gentleman, was the first 

 who thought of playing tunes by collecting " a number of glasses of 

 different sizes, fixing them near each other on a table, and tuning them by 

 putting into them water, more or less as each note required ; the tones 

 were brought out by pressing his finger round their brims." Mr. Delaval, 

 F.R.S., constructed a set according to the above plan, and showed them 

 to Franklin, who endeavoured to improve the arrangement by mounting 

 a number of glasses OB an iron rod by means of a perforation in the 

 bottom of each glass. The glasses partly fitted into each other without 

 touching, and were tuned by grinding, and in this way three complete 

 octaves were got into a small space. The rod was then fixed in a box, 

 and being set in motion the tones were brought out by applying a 

 moistened finger to the surfaces of the glasses. To distinguish the 

 notes the more readily, the glasses were painted inside ; each semitone 

 white, and the other notes of the octave with the seven prismatic 

 colours. Franklin describes the tones produced as being superior in 

 mellifluous sweetness to anything he had ever heard before. The 

 arrangement, however, was objectionable on account of its being liable 

 to get out of order, so that the subsequent contrivers of musical glasmt 

 have resorted to the original method, which we may here state is 

 nearly 200 years older than Franklin supposed, as may be seen in 

 Harsdorffern's ' Mathematische und Philosophische Erquickstunden,' 

 Zweiter Theil, Nuremberg, 1651. This work is a sort of elaborate 

 " Endless Amusements," and contains a good deal that is really curious 

 and useful, in some cases forestalling modern inventions, which have 

 made more noise than that of musical glasses. Directions are given to 

 take eight glasses of equal size, to tune them by means of wine, and 

 with the wet finger " auf dess Glases Rand herumb fahren, so wirst du 

 eine lustige Wein Musica haben." 



Various methods of forming musical glasses have been introduced 

 from time to time, all of them costly except that by Mr. Toruliiis. ,n, who 

 selects soda-water glasses, finger-glasses, and tumblers of various sines, 

 and arranges them in a wooden case, fixing them by rneann of wooden 

 screws, and bringing them to the tame height by means of blocks of 

 wood. The beat way to select these glasses U to visit a glass ware- 

 house, and arranging the glasses likely to suit, as to size, on a table, to 

 sound on a flute the note required, and should the note be represented 

 by any one of the glasses, it will speak by sympathy. The reader 

 curious in the subject may be referred to Mr. Tomlinsoii's ' Student'* 

 Manual of Natural Philosophy,' 1838 ; which contains an elaborate 

 article on musical glasses their modes of vibration and acoustic 

 properties. 



HARMONICS. (Acoustics.) By the harmonics of a musical note 

 are meant all those other notes in which the number of vibrations per 

 second are twice, three times, four times, or any multiple of, the 

 number of vibrations which produce the note in question. Thus the 

 harmonics of a note which is sounded by 200 vibrations per second are 

 those notes which require 400, 600,800, to., vibrations per wcond. 

 The following explanation will be assisted by reference to Ai< 

 and TEMPERAMENT. It presumes the reader to be acquainted with the 

 fundamental mathematical laws of the scale. The harmonics of a note 

 are infinite in number, theoretically speaking, and proceed by less and 

 less intervals. And since every note may be considered aa identical 

 with any of its octaves, every harmonic has a corresponding note in 



any given octave. Denoting any key-note by c, and the octave above 

 it by c', there is no possible sound between c and c' which is not 

 theoretically either an harmonic of c, or as near to one as we please 

 (which is equivalent to the mathematical proposition that a whole 

 number, divided by a whole power of 2, may be made as near as we 

 please to any given number or fraction). 



But, in practice, not only is it impossible to produce any number of 

 harmonics we please, that is, to maintain in vibration any aliquot part 

 we please of a string or column of air, but even among the harmonics 

 which we can produce we find a limit to the number of those distinct 

 harmonics which deserve the name, etymologically considered. Some 

 few of the first harmonics are melodious sounds, considered in relation 

 to the key-note, but others are discordant, and find no place in the 

 scale according to any system of temperament. We shall therefore, 

 taking a given note, say c, simply mention the most important 

 harmonics, and reduce them to their proper places between c and c'. 



Let a be the number of vibrations per second which produce c ; 

 then 2o is well known to produce c', so that the first harmonic of a 

 note is its octave. The next has 3a vibrations, answering to G' ; so 

 that the twelfth, or octave of the fifth, is the second harmonic. The 

 third has 4a vibrations, and answers to c'', the octave of the octave. 

 The fourth harmonic has 5a vibrations, and gives E", the double octave 

 above the third, in the untempered diatonic scale. The fifth harmonic, 

 with 6a vibrations, gives a", the octave of G' the second harmonic. In 

 general, every harmonic whose vibrations are an even multiple of those 

 in the key-note, is an octave to a preceding harmonic, and presents no 

 new character. The sixth harmonic, having 7a vibrations, is an 

 imperfect (being too flat) double octave to the flat seventh above the 

 key-note, or B flat. This last note, in the common mode of tempering, 

 makes 177a vibrations per second; whereas the same note derived 

 from the harmonic makes l'75a vibrations. The eighth harmonic, 

 with 9a vibrations, is correctly D'", or three octaves above the 

 untempered major second. The tenth, with lire vibrations, is a little 

 too sharp for '", being llo instead of 10|a. The twelfth, with 13a 

 vibrations, is a little too flat for A"', being 13rt instead of 13 Jo. 



The preceding summation is useful, as giving an account of the 

 scale of all those musical instruments which consist of one unaltered 

 pipe. These are the bugle, the French horn, the trumpet, and (but 

 for its slide) the trombone ; in all of which (except the last) no note 

 can be produced except a harmonic of the fundamental note of the 

 whole tube. Calling the fundamental note c (which however is not 

 very easily sounded), the ordinary scale of these instruments is 



c c' G' c" B" o" (B" flat) c"' D'" E"' i'" c'" A'", in which B" fiat is 

 too flat, i"' is too sharp, and A'" too flat. A short pipe however will 

 not produce many harmonics ; the bugle- goes no further than a", at 

 least with common lips. Various contrivances have been introduced 

 to extend and correct this scale ; the keyed bugle, the use of the hand 

 in the French horn, the pistons sometimes applied to the same instru- 

 ment, and the short slide of the trumpet, to say nothing of the slide 

 which is the principal distinction of the trombone, will suggest them- 

 selves to all who are acquainted with musical instruments. It will 

 be seen under HORN that Mr. Sax has added other contrivances for 

 the extension of the scale. In other instruments harmonics are much 

 used, particularly in those of the violin class, and in the flute. The 

 performance of Paganini upon a single string, which many yearn ago 

 created great sensation among violin players, arose from an extraordinary 

 power in producing harmonics. In the flute c'" may be attained with- 

 out much practice, aa an harmonic of the fundamental note of the 

 instrument ; and we have heard of players who could produce D"' and 

 even E" in the same way. On the long strings of a piano-forte, as the 

 fundamental note subsides, o', c", and E" may be perceived ; and we 

 have heard, among the vaulted roofs of a cathedral, several of the 

 harmonics of the notes sounded in chanting. For further information 

 see the references hi ACOUSTICS. 



HARMONIUM. This is one of a numerous family of instruments 

 which owe their origin to the invention, or rather the revival, of the 

 free reed. There are many claimants to this invention ; but, as stated 

 under ACCORDION, the Chinese were acquainted with it before its intro- 

 duction into Europe, and the Chinese organ and the musical trumpet 

 depended for their effects upon vibrating tongues of metal. The 

 French, who are often as happy in re-inventing the inventions of other 

 nations as they are undoubtedly clever in their own, claim the free 

 reed ; and so respectable an authority as M. Biot (' Pr<5cis e'le'mentaire 

 de Physique experimentale,' Paris, 1817, tome i., p. 386, fig. 50) assigns 

 the invention to M. Greni<!, " habile amateur de imisique." Biot says, 

 in his usual perspicuous manner, " La languette est une lame de laiton 

 parfaitement plane, et coupe'e en forme de rectangle, de maniere ?i 

 remplis exactemcnt, ou plutdt presque exactement la face eVidde de la 

 rigole." This was in the year 1810; and two instruments were con- 

 structed, one of which was sent to the Conservatoire des Arts. In 

 lb'J7 three free reed stops were introduced into the organ nt Beauvais 

 Cathedral, and in 182!) M. Sebastian Erard introduced a free reed stop 

 into an organ built by him for the Tuileries. After this, the free reed 

 gave rise to a number of new inKtruments, such as the accordion, 

 Wheatstone's reolina, the predecessor of that exquisite little instrument 

 the CONCERTINA. Many attempts were made to improve the accordion 

 by enlarging and completing its scale, so that it naturally assumed the 

 form of an organ in which a free reed stop took the place of pipes 



