ACOUSTICS. 



native produce, for Constantinople was an emporium rather 

 than a manufacturing city. Grecian velvets, other silk utii 



I'liithn, liiM-M, and wool; nut*, saffron, oil, timber, pitch, 

 honey; K<<\>\, M!V. r, morcory, copper, iron, tin, load, weapon*, 

 Liven are enumerated. Restrictive lawn led to an illicit 

 trade in some varieties of goods, of which pnrple state robes 

 were an example, their export being prohibited. The commercial 

 vigour of the ancient Greeks never distinguished their Byzantine 

 posterity. The land trade of Constantinople was carried on 

 with no great activity. A military people called the Avars, 

 inhabiting the provinces of the Danube lying between the Greek 

 empire and Germany, had, up to the ninth century, the manage- 

 ment of the Western land traffic. They were the carriers of 

 goods, some of which eventually reached the most northern 

 ins of Europe. The wealth accruing from this trade 

 Ltod these Avars. It made them "refined barbarians," 

 l>tit could not save them from the inroads of a hardier tribe, like 

 themselves of Slavonian origin, and known as Bulgarians. 



For two centuries the Bulgarians carried on the trade between 

 Constantinople and Germany, till disputes arose between them 

 and tho Greeks, who were at first defeated in the fierce encounters 

 that ensued ; but the Bulgarians were at length subdued by tho 

 Emperor Basil in 1018. The Bulgarians had probably been driven 

 to invade the Greek territory by the advance of the Ungrians 

 and Magyars, who in the tenth century took possession of the 

 plain of the Danube, and established there a kingdom, which 

 still preserves in its name (Hungary) and that of its people 

 (Magyars) the memory of its founders. The Ungrians made 

 Semlin in Hungary the depot of the international transport 

 trade. They took upon themselves the conduct of the traffic 

 throughout, built factories, and established agencies in the 

 capital, whore Stephen I., who died in 1038, erected for 

 their encouragement a splendid place of worship. Hungary 

 flourished in every town because of the rich profits of their exten- 

 sive business as carriers and brokers. The Western land traffic 

 waned, and in the end disappeared, before the rising maritime 

 commerce of Venice, Genoa, and other Italian republics. The 

 commodities which specially distinguished the Western trade 

 consisted of raw produce, manufactures, and works of art ; Greek 

 artistic work ; olives, saffron, and hazel nuts ; oil, liquorice, 

 raw silk, silk and mixed stuffs ; purple and priestly robes ; 

 gold dust and Eastern spices ; pepper, ginger, cloves, nut- 

 megs, galanga root, and anise-seed. Sword belts bound with 

 brass and copper were sent by sea to the West, and in tho 

 land traffic Constantinople received overland from Germany 

 Wendish slaves or serfs ; from Bohemia and Moravia, weapons 

 of ancient Gorman manufacture ; wooden tools and saddles from 

 tho Low Countries ; woollen and linen, principally of Friesland 

 make, and metals, from Transylvania and Hungary. 



During a part only of this period could Byzantine commerce 

 take tho old Chaldean road to India. Obstructed by Persia 

 and by continual contentions with the Arabs from employing it, 

 the route through Independent Tartary was made use of. By- 

 zantine commerce both by land and sea at length lost all its im- 

 portance, and fell almost entirely into the hands of the Italians. 



ACOUSTICS. II. 



SAVART'S TOOTHED WHEEL RANGE OF THE HUMAN EAR 

 THE SYREN NUMBER OF VIBRATIONS REQUIRED TO PRO- 

 DUCE ANT GIVEN NOTE. 



IN our last lesson we learnt that sound was produced when tho 

 air was set in vibration by a sonorous body. If in any way we 

 can cause a succession of gentle taps to succeed one another 

 with sufficient rapidity, we shall find that they lose their indi- 

 viduality, and merge into a continuous note. 



An easy way of obtaining experimental illustration of this 

 consists in holding a piece of card against the teeth of a rapidly 

 revolving wheel. The separate taps produced as each cog 

 strikes it will not be distinguishable, but will coalesce to form 

 a clear and distinct note, the pitch of which becomes higher and 

 higher as tho wheel rotates more rapidly. In this manner we 

 may measure the number of vibrations per second required to 

 produce any given note, a number which will always be found 

 uniform. 



Savart's toothed wheel (Fig. 6) is an apparatus devised for 

 this purpose. It consists of two wheels, A and B, mounted in a 



strong wooden frame-work. The larger of thaw. A, is fitted 

 with a handle by which to torn it, and a strap passing ore* its 

 own circumference and also over a pulley on tb axle of the 

 toothed wheel, B, Cannes the Utter to rotate with oonsidenble 

 Telocity. A piece of card u fixed to the plate B in och a way 

 that the teeth of the wheel may catch against it and art it in 

 i>ration, the rapidity of the pulsations being determined 

 by the rate at which the teeth strike against it To the axis of 

 this wheel there is fixed an indicator, H, which nbowt the num- 

 ber of revolutions it makes, and, multiplying thin by the number 

 of teeth, we learn the number of vibrations. The bet way of 

 using the instrument is, when a steady not* is being produced, 

 to allow it to continue for several seconds, and then divide the 

 number of vibrations made by the card by the number of 

 seconds. We thus ascertain the number of vibrations per 

 second required to produce the sound. To produce the note 

 an octave higher, we must just double this number. 



It is important for us to remember that when we speak here 

 of a vibration, we mean the oscillation of the vibrating particle* 

 to and fro, that is, its complete donble motion. In France, 

 each single oscillation to or fro is counted, and hence twice 

 tho number of vibrations are said to be required to produce any 

 note. If this distinction be clearly borne in mind, little incon- 

 venience will be caused by the different modes of speaking of 

 the same thing. 



The question now suggests itself, how many vibrations per 

 second are requisite in order to produce a distinct musical 

 sound. To this wo cannot givo a decided answer, since different 

 ears are found to vary considerably in their power of appre- 

 ciating sounds. To ascertain the limit, Savart slightly modified 

 his apparatus, removing the toothed wheel, and substituting for 

 it an iron bar, which passed between two thin wooden plates, so 

 placed as almost to touch it. When the bar passed between them, 

 a grave sound was produced by the displacement of the air, and 

 he imagined that a distinct but very deep sound could be per- 

 ceived when the number of these pulsations was about 12 or 14 

 per second. Other observers have placed the number as high 

 as 32, while some place it as low as 8. 



The upper limit to the number of vibrations that can be 

 heard also varies very considerably. It depends partly upon 

 the intensity of the vibrations and their amplitude. Some place 

 the limit at from 20,000 to 24,000 vibrations per second ; there 

 seems, however, little doubt that a sound corresponding to 

 38,000 vibrations is audible in most ears. By experimenting 

 with very acute sounds, Dr. Wollaston found that the limits of 

 hearing in different people varied greatly. He sounded a series 

 of small pipes in succession, before a number of people, and 

 found that frequently the ascent of a single note produced to 

 some the change from sound to complete silence ; and while 

 some experienced a sound of penetrating shrillness, others were 

 quite unconscious of any sound whatever. 



There are in Nature sounds so shrill that they are beyond 

 the hearing of many people ; thus, for instance, the needle-like 

 cries of the bat are unheard by many ; some, too, fail to hear 

 the chirp of the cricket. 



We may say, then, that sounds which the oar can distinguish 

 range between 14 and 40,000 vibrations per second. The 

 practical range of musical sounds is, however, much more 

 imited. The deepest sound produced by any musical instru- 

 ment appears to require about 28 vibrations, and the highest 

 note, which is probably the upper D of the piccolo flute, requires 

 4,752 vibrations. For ordinary purposes, however, the range is 

 rom 40 to 4,000 vibrations, that is, a compass of about seven 

 octaves. 



There are several other ways in which we may cause a regular 

 series of pulsations to produce a musical note. If we can 

 nterrupt a stream of air sufficiently often, we shall produce 

 a series of puffs, which will combine into a tone. This can be 

 easily effected by taking a circular sheet of tin, or millboard, 

 and puncturing a series of holes in a circle round its centre 

 Fig. 7). Fix the disc to a whirling table, or cause it, by 

 means of a multiplying wheel, to revolve rapidly. Then take a 

 )lowpipe or a piece of india-rubber tubing with a jet at the end. 

 and holding the jet opposite to the line of the openings blow 

 ihrough it ; the current will be interrupted when the card is 

 against the jet, but will pass whenever an aperture comes 

 opposite it. In this way the current will be frequently inter- 

 rupted, and a musical note will be produced, the pitch of which 



