similar way parallel to the first: one of the strings should be provided with a moveable bridge, which can be planted at any arbitrary point under it. For producing sound, a common violin-bow is to be used. Confining ourselves for the present to the single string, we may point out as the experiments most worthy of attention that, by damping the motion of the string by a touch of the finger at the middle, at length, at length, &c., still exciting the movements by the bow, pure notes will be produced which the musical ear will recognize as the harmonics of the fundamental note; and that, by putting small pieces of paper on the string, when the damping is at length or length, those which are (in the former) at length, or those which are (in the latter) at length and length will remain, showing that those points of the string are quiescent, while all others are thrown off by the vibrations. Also, by weighing the string, and ascertaining the weight in the pan, the number of vibrations per second can be found (see Article 73). 85. Number of vibrations of air in a second for a fundamental musical note. This may be a convenient place for alluding to the number of vibrations corresponding to a known musical note called C of the counter-tenor scale (see Article 71). The oldest accurate information that we possess is that given by Dr Smith, Master of Trinity College, in his Harmonics. He determined the number by the vibra tions of a string to which a weight was suspended; the vibrating part of the string being measured from its suspension-point to its point of attachment to the weight. And he says (in 1755 we believe), "The Trinity organ was now depressed a tone lower, and thereby reduced to the Roman pitch, as I judge by its agreement with that of the pitch-pipes made about 1720." His experiments, duly interpreted, give for C, second. about the year 1720, 4658 vibrations per The history since that time is given in a Report of the Society of Arts. It contains the following abstract. Handel's value for c, 1740 ..... A pitch recommended on grounds of of continued halving The Philharmonic Society, 1812-1842... A German Congress (Stuttgard), 1834... 4991. 512. 5183. 528. The Society of Arts recommended 528 for permanent adoption, and tuning-forks made under their authority are sold at a trifling price by Messrs Cramer, guaranteed to give that number of vibrations. Theoretically, the number is convenient, as it can be halved down to 33, and can also be divided by 3. (On these advantages, see a subsequent section.) It seems nearly impossible to prevent the continued rise of pitch. Among other causes, the desire of an ambitious singer to exhibit a voice higher in tone than can be imitated by any other, leads to the occasional raising of the pitch of all instruments: then in a short time music is written for the use of ordinary singers with reference to that raised pitch, and then the rise is established for ever. 86. Apparatus for experiments on musical pipes, and results of some experiments. For experiments on pipes, we would recommend the student, having furnished himself with a tuning-fork as above mentioned, to procure some pipes which admit of alteration of length, and which can also be stopped at pleasure. A light wooden pipe 1 inch square and 18 inches long, open at both ends; with a tin pipe 12 inches long that will just slide in it; and with plugs for the two parts of the pipe, each plug managed by a long wire-stalk; will be found convenient. The student will be struck with the effect of a stopped pipe 6 inches or 18 inches long, or an open pipe 12 inches or 24 inches long, in resounding to a tuning-fork whose note without the pipe could scarcely be heard at all (see Articles 79 and 80). Various openings in the side of the pipe will suggest themselves. This combination also facilitates the observation of the different intensities of sound produced by the tuning-fork as it is turned into different positions, and of the vanishing of the sound in some positions (Article 49). Among the special experiments on the vibrations of air in musical pipes, we know none so important as those by the late Mr Hopkins, published in the Transactions of the Cambridge Philosophical Society, Vol. v. The vibrations of air at the mouth of the pipe were produced by the vibrations of a plate of glass, vibrating (apparently) in a known time: it was found that a small distance of the glass-plate from the pipe made the phænomena the same as if the pipe had been quite open to the external air (as the experimenter who uses a tuning-fork will also find), but with particular cautions in some instances the phænomena were made identical with those which belong to a closed pipe. The examination, however, in which Mr Hopkins was most successful was the determination of nodal points; which was effected by gradually lowering into the tube a stretched membrane carrying a very small quantity of sand, and noting its place when the sand was not shaken by the air. It was thus found that the node next to the open mouth of the pipe was somewhat less distant from it than that given by theory (Article 79); or, which amounts to the same thing, that the place where the air has always the same density as the external air is not exactly at the pipe's mouth but somewhat exterior to it (as is suggested in Article 79). The experiments, generally, were experiments on resonance; and in one of these, Mr Hopkins appears to have fallen precisely on the case described in Article 81, where a very loud sound is produced. The whole of this paper, theory and experiment, is well worthy of the reader's attention. Professor Tyndall has succeeded in exhibiting (though not with the same accuracy) the tremulous variations of density within a pipe, by placing thin membranes upon holes in the side of the pipe, and using these membranes as the bases of small gaschambers for gas-lights; at those places where the variations of density are considerable, the agitation of the membranes extinguishes the gas-lights. |