U N D 



U N D 



Prop. I. 

 All impulfes are propagated in a homogeneous elaftic 

 medium with an equable velocity. In different mediums, 

 the velocity will vary in the fubduplicate ratio of the force 

 diredlly, and of the denfity inverfely. From the phenomena 

 of elaftic bodies and of founds it appears, that the undula- 

 tions may crofs each other without interruption. 



Prop. II. 



An undulation, conceived to originate from the vibration 

 of a Tingle particle, muft expand through a homogeneous 

 medium in a fpherical form, but with different quantities of 

 motion in different parts. 



Prop. III. 



A portion of a fpherical undulation, admitted through an 

 aperture into a quiefcent medium, will proceed to be further 

 propagated reftilinearly in concentric fuperficies, terminated 

 laterally by weak and irregular portions of nearly diverging 

 undulations. This propofition, though the principle of it 

 is objefted to by Newton, is, according to our author, per- 

 feftly confiftent with analogy and experiment. 



Prop. IV. 



When an undulation arrives at a furface which is the 

 limit of mediums of different deniities, a partial reflection 

 takes place, proportionate in force to the difference of the 

 denfities. 



Prop. V. 



When an undulation is tranfmitted through a furface ter- 

 minating different mediums, it proceeds in fuch a direftion, 

 that the fines of the angles of incidence and refradlion are 

 in the conftant ratio of the velocity of propagation in the 

 two mediums. The demonftration of this propofition will 

 prove the equality of the angles of reflexion and incidence. 



Prop. VI. 



When an undulation falls on the furface of a rarer 

 medium, fo obliquely that it cannot be regularly refrafted, 

 it is totally reflefted, at an angle equal to that of its 

 incidence. 



Prop. VII. 



If equidiftant undulations be fiippofed to pafs through a 

 medium, of which the parts are fufceptible of permanent 

 vibrations, fomewhat (lower than the undulations, their ve- 

 locity will be fomewhat leflened by their vibratory tendency ; 

 and in the fame medium, the more, as the undulations are 

 more frequent. 



Prop. VIII. 



When two undulations, from different origins, coincide 

 either perfedlly or very nearly in direfiion, their joint effeft 

 is a combination of the motions belonging to each. 



Prop. IX. 



Radiant light confitls in undulations of theluminiferous 

 ether. For the illuflration and proof of thefe propofitions, 

 the corollaries deducible from them, as particularly appli- 

 cable to the colours of ilriated furfaces, thin and thick 

 plates, and thofe by infleftion, and a reply to the objec- 

 tions that may be urged againft the author's theory, we 

 refer to Young's Philofophy, vol. ii. See alfo Phil. Tranf. 

 for 1800. 



UrfDULATIOK, in Phyfics, a kind of tremulous motion 

 or vibration, obfervable in a hquid ; by which it alternately 

 rifes and falls, like the waves of the fea ; and hence it is 

 that the term takes its rife, from xinda, luave. See Wave. 



This undulatory motion, if the hquid be fmooth, and at 

 reft, is propagated in concentric circles, as moft people 

 have obferved upon throwing a ftone, or other matter, upon 

 the furface of a ftagnant water, or even upon touching the 

 furface of the water lightly with the finger, or the like. 



The caufe of thefe circular undulations is, that, by 

 touching the furface with the finger, there is produced a 

 deprefiion of the water in the place of contaft. By this de- 

 preffion, the fubjacent parts are moved fuccefllvely out of 

 their place, and the other adjacent parts thruft upwards, 

 which, lying fucceffively on the defcending liquid, follow 

 it ; and thus the parts of the liquid are alternately raifed 

 and depreffed, and that circularly. 



When a ftone is thrown into the liquid, the reciprocal 

 vibrations are more confpicuous : here the water in the place 

 of immerfion rifing higher, by means of the impulfe or re- 

 bound, till it comes to fall again, gives an impulfe to the 

 adjoining liquid, by which means that is likewife raifed 

 about the place of the ftone, as about a centre, and forms 

 the firft undulous circle ; this falling again, gives another 

 impulfe to the fluid next to it farther from the centre, which 

 rifes hkewife in a circle ; and thus, fucceffively, greater and 

 greater circles are produced. 



Undulation, in Medicine, the term ufed by fome to 

 exprefs an uneafy fenfation in the heart, of an undulatory 

 motion, which may fometimes be perceived externally. 



Undulation, or Beat, in Miific, is ufed for that rat- 

 tling or jarring of founds, which is obferved, chiefly, when 

 difcordant notes are founded together. See Beats. 



The phenomenon is more fully defcribed thus, by Dr. 

 Smith. In tuning mufical inftruments, cfpecially organs, 

 it is a known thing, that while a confonance is imperfcdl, it 

 is not fmooth and uniform, as when perfcft, but interrupted 

 with very fenfiblc undulations or beats ; which, while the 

 two founds continue at the fame pitch, fucceed one another 

 in equal times, and in longer and longer times, while either 

 of the founds approach gradually to a perfeft confonance 

 with the other, till at laft the undulations vanifli, and leave 

 fmooth, uniform confonance. Smith's Harmonics, p. 107. 

 See Harmonics. 



This learned author obferves farther, that quicker undu- 

 lations are beats, and are remarkably difagreeable in a con- 

 cert of ftrong, treble voices, when fome of them are out of 

 tune ; or in a ring of bells ill tuned, the hearer being near 

 the fteeple ; or in a full organ badly tuned. Nor can the 

 beft tuning wholly prevent that difagreeable battering of the 

 ears with a conftant rattling noife of beats, quite different 

 from all mufical founds, and deftruftive of them, and chiefly 

 caufed by the compound ftops called the cornet and fefqui- 

 alter, and by all other loud ftops of a high pitch, when 

 mixed with the reft. But if we be content with compofi- 

 tions of unifons and oftaves to the diapafon, whatever be the 

 quahty of their founds, the beft manner of tuning will render 

 the noife of their beats inoffenfive, if not imperceptible. 



The dodor has with great ingenuity deduced the theory 

 of thefe undulations from his principles, and has applied his 

 doftrine to the tuning of inftruments ; by which he has 

 ftiewn, that a perfon of no ear at all for mufic may foon 

 learn to tune an organ, according to any propofed tempera- 

 ment of the fcale, and to any defired degree of exaftnefs, 

 far beyond what the niceft ear, unaffifted by theory, can 

 poffibly attain to. This may be done by counting the 

 number of undulations in a certain time, fuch as fifteen 



feconds. 



