213 



CORD. 



CORIANDRUM SATIVUM. 



211 



a direct and retrograde disturbance of such a kind, there will be at the 

 first moment no velocity at any point of A c B, since those of the direct 

 and retrograde disturbance compensate each other throughout. But 



let a time elapse during which the direct and retrograde disturbances 

 travel to M and L. Then the form of the string at that moment will 

 be A c m n c B, where the part in n arises from the composition of the 

 two parts of the disturbances which yet remain acting on the same 

 points. 



We may thus trace the effect of disturbance upon an indefinitely 

 extended string ; but such a string would produce no musical sound, 

 for which it is necessary that there should be a continued reiteration 

 of the game action upon the air repeated at equal intervals. Now 

 supposing a finite string, stretched at the ends, we must ask what 

 takes place when the disturbance comes to the end of the string. 

 Aud from mathematical analysis again, the following is the answer : 

 Let P be the fixed end of the string, and choose the instant at which, 



ha 1 the string continued, the disturbance would have been B v A. 

 Make a disturbance B A' equal and opposite to o A, and let it be com- 

 pounded with G v n, on the supposition that it is part of a disturbance 

 proceeding from p, such as would by itself bend the string in the 



t e direction. Then p v B or p v A' is the state of the string at 

 that instant. In fact, the disturbance is converted into an equal and 

 opposite disturbance proceeding in the contrary direction. 



Now let us suppose a string like that of a pianoforte, sharply 



struck near one end. It is altogether a gratuitous assumption, 



knowing what we do of the imperfect elasticity of matter, to suppose 



that the disturbing effect of the blow immediately affects the whole 



A certain disturbance is produced upon a part (it may be a 



.mil irt) of the string. Then what is that perceptible pheno- 

 menon, the reiteration of which produces a musical tone ? Let us 



o the string struck at one-fourth of the length from its end, 

 and suppose that the tension is such that disturbance is propagated at 

 the rate of 2000 feat a second, the length being four feet. A disturb- 

 ance is produced at w, from which two simple disturbances begin to 



travel towards P and Q, at which they aro reflected with the same 



Velocities. They will be at N together producing a disturbance (now 



recompounded) of the same amount as before, but on the opposite 



the string. This takes place while four feet are described at 



r second, or is repeated 250 times per second. From 



M to N there is then a succession of effects upon the air, which are 



most powerful at M and N, owing to the coincidence of the disturbances. 



This is repeated 250 times in a second, and yields the musical note 



ontlin;,' to that number of aerial pulsations per second. This is 



:!)rations. If we define as a double vibration the time in 



'he ilisturbance comes to M again, we should say that there are 



uble vibrations in a second. There is much confusion among 



writers on this point ; some use simple vibrations, or reversal* ; others 



ue double vibrations, or reiterations. 



l!y mipposing the whole string put in vibration, or any simultaneous 



communicated to it, the effect may similarly be shown to 



t at the eii'l n{ the time during which disturbance would be 



itcd along the whole string the effects are all reversed, but are 



same magnitude ; while in a second of such time they are all 



-ily arrive at what is called the fundamental 



With regard to the harmonics of a string 



{!, they are not so easily shown to be necessary. We shall 

 .vthat such effects are always possible ; that is to 

 string begin to vibrate O v that its two halves, or its three- 



thirds, &c., are disturbed together, such an effect will be produced. 

 Suppose, for instance, the initial state of the string to be p M N Q t 



U 



whare P M, M N, and N Q are the thirds. During the time in which the 

 direct disturbance of p M would be communicated to M N, that of M N 

 would be communicated to N Q, the direct disturbance in N Q would be 

 made retrograde, and so on. Hence though the whole string may 

 vibrate, each of the parts has a vibration by itself in one-third of the 

 time. If we were to modify the vibration of the whole string by 

 compounding with the preceding such a disturbance as would always 

 destroy the velocities at M and N, there would then be three strings, 

 each vibrating in one-third of the time of the whole string. The ear 

 can appreciate such contemporaneous sets of vibrations, and accordingly 

 in this case perceives both the fundamental note of the string and the 

 twelfth above it. If a large and miscellaneous set of disturbances be 

 communicated at once, those only will exhibit cycles of effects which 

 make the halves, the thirds, &c., vibrate together, and we can say little 

 more without entering into mathematics. But in a string it may 

 always be observed that we seldom hear the octave of the fundamental 

 note, and generally the twelfth and seventeenth. No reason can be 

 given for this which is perfectly unobjectionable ; we do not know 

 whether it is the aptitude of the ear to distinguish these, or of the 

 string to take the corresponding divisions, which is the cause of the 

 phenomenon. 



The time of simple vibration of a string, that is, of complete reversal 

 of all the initial effects, is I -f- </'2 g c, where I is the length, and c is 

 as before. It is therefore directly as the length and inversely as the 

 square root of the tension; results which are amply confirmed by 

 experiment. 



In all that has preceded we have supposed the string perfectly 

 elastic, and without friction. Neither of these suppositions is true, 

 but since the velocity of propagation of every disturbance is inde- 

 pendent of its extent, the gradual diminution of the latter will not 

 affect the phenomenon on which the musical qualities of the string 

 depend. 



The method of observing the curves in which each point of a string 

 vibrates, recommended by Dr. Young, was to use a string round which 

 small wire is coiled, like the larger string of a violoncello, and to 

 observe with a microscope the reflection of a candle or other bright 

 spot on one of the coils. Sir J. Herschel suggests that a thin slit 

 should be made in a window-shutter, and that the string should be 

 placed with the point to be examined cutting the vertical plane of 

 light. This point would therefore appear bright while the rest is dark. 

 In either case the rapidity of the vibrations would make the curve 

 described by the bright point permanent. 



A single string fitted up for experiments is called a MONOCHORD. 



CORDELIERS, so named from wearing a knotted cord for a girdle, 

 were the strictest branch of the Franciscan, or Gray, or Barefooted 

 Friars, established towards the end of the 14th century. Chaucer 

 mentions them in the ' Romaunt of the Rose,' 1. 7461. There were 

 ultimately in France, according to Moreri (' Diet. Historique '), no 

 fewer than 284 male and 123 female convents of Cordeliers. A 

 political society, who were opposed to the Jacobins during the French 

 revolution, also assumed this title, from having held its meetings in an 

 old Franciscan convent. 



CORDIALS. The beverages known by this name are made of 

 ardent spirits, flavoured with sweetening and aromatic substances. A 

 distiller who produces raw spirits from corn or malt, is not allowed by 

 the excise laws of this country to give any additional or artificial 

 flavour to his spirit ; he must sell it in the crude ardent state in which 

 it leaves the still. This is not done out of any consideration in which 

 the consumers are concerned, but simply as a matter of revenue. The 

 distillers rarely if ever sell spirit to the public generally. It is sold to 

 the rectijiers, who re-distil it, and impart flavour to it by various means. 

 Cordials are among the liquors which are so treated. Some are made 

 simply by adding essential oils and syrup to diluted spirit; while 

 others are made by adding aromatics to the spirit, boiling and re- 

 distilling it, and sweetening the re-distilled liquor. Some cordials are 

 made from raw spirit, but the best from rectified spirit of wine. 



The various cordials are known by the names of the vegetable sub- 

 stance to which they chiefly owe their distinguishing flavours. Hence 

 we hear of aniseed, caraway, cedrat, cinnamon, citron, clove, coriander, 

 lemon, lovage, orange, peppermint, and other cordials. 



CORDON, a military term to denote a line of posts and sentries 

 placed around a district or town to prevent any communication between 

 it and the rest of the country. It is chiefly resorted to in cases of auy 

 contagious disease having broken out in a place, when it is called a 

 cordon sanitaire; and in order to be effectual, each sentry ought to U 1 

 able to see his two next comrades right and left. 



Cordon in French means also the insignia of an order of knigbt.li"".!. 

 answering to the English word riband when taken in a similar 

 " cordon bleu," " blue riband," &c. 



CORIANDRUM SATTVUM, Medical Properties of. This unit .[- 

 liferous annual plant is a native oi the south of Europe, Tartary, &c., 



