Page:Cyclopaedia, Chambers - Supplement, Volume 1.djvu/937

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may be drawn out, without disordering either the mufcles or the membranes ; but we are not for this reafon to conclude, that all the Intercojiah on one fide of the breaft make but one mufcle ; becaufe the fame reafoning might prove, that all the mufcles which immediately furround the os femoris are but one ; fince by a like experiment, they together with the periofteum may be entirely feparated from the bone, without breaking their fibres. Window's Anatomy, p. 231. For the ufe of thefe in refpiration, fee the article Respira- tion.

Intercostal Nerves. Dr. Waltherhas given a very minute defcription of the Intercojlal nerves, and eighth pair. See Nov. Aft. Erud. Lipf. 1734- Feb. & ibid. 1736 Sept.

INTERCUS, a word ufed by fome medical writers, to exprefs that fort of dropfy more ufually called an anafarca. See the articles Dropsy and Anasarca.

INTEREST (Cycl) — Interest, Interejfe, inlaw, is com- monly taken for a chattel real, as a leafe for years, &c. and more particularly for a future term ; in which cafe it is faid in pleading, that one is poffeffed de Inter ejfe termini: There- fore an eftate in lands, is better than a right or Interejl m them. But in legal undemanding, an Interejl extends to eftates, rights, and titles, that a man hath in or out of lands, &c. fo as by grant of his whole Interejl in fuch land, a rc- verfion therein, as well as pofleffion in fee-fimple fhall pafs. Co. Litt. 345. Blount.

INTERFERE, in the manege. A horfe interferes, when the fide of one of his fhoes ftrikes againlt, and hurts one of the fetlocks. See the article Fetlock.

INTERFEMINEUM, a word ufed by fome to exprefs the perinasum.

INTERLUNIUS Morbus, a name by which fome authors have called the epilepfy, a difeafe often affected remarkably by the changes of the moon.

INTERMITTENT, or Intermitting- Fever (Cycl.)— See the article Fever.

INTERNUS {Cycl.) — Internus mallei, in anatomy, a name given by fome authors to one of the mufcles of the: ear. It is the mufcuhts Internus auris of Cowpcr, and is very properly called by Albinus ten/or tympani from its ufe. Spigelius calls it fun ply the Internus.

INTEROSSEUS, in anatomy, a name given by Spigelius in his account of the mufcles of the foot, to a mufcle called by Albinus the fexor brevis pollicis pedis, and by Winflow the thenar and Jiexor brevis.

INTERRING, or Interment (Cycl.) — See the articles Burial and Burying.

INTERSEPTUM, a word ufed by fome writers to exprefs the uvula, and by others the feptum narium.

INTERS1TNALES (Cycl.)— Interspinals dorft, in ana- tomv, a name given by Albinus to certain mufeks of the back, not mentioned by the old writers in anatomy, but cal- led by Winflow and other of the modern French writers, ks tetits epineux du dos ; as the Interfpihales lumborurn of the fame author, are the epineux des lambes.

Interspinales lumhorum, in anatomy, a flame given by Albinus to fome mufcles not mentioned by the generality of writers, but called by Winflow the epineux des lopibes, or j'pinales lumborurn.

INTERTRANSVERSARII dor/:, in anatomy, a name given by Albinus and others of the late anatomiits, to certain (mall mufcles of the back, not obferved by the old writers! on thefe fubjects, but called by the French les petit s tranfverfaires du dos.

Intertransversarii lumborurn, in anatomy, a name given by Albiims to thofe mufcles of the loins, which Douglafs alfo calls the Intertranfverfales, and Winflow and the other French writers tranfverfaires des lombes.

INTERVAL, in mutic (Cycl.) — Intervals arc founded on cer- tain ratio's or proportions expreffible in numbers, which may alli>e analyfcd into the.prime numbers 2, 3, and 5. And all Intervals "may be found from the octave, fjfth and third major, which refpectively correfpond to thofe- numbers. Thefe are the muficians elements, from the various combinations of which, all the agreeable variety of. relations of founds remit. This is the modern fy Herri, and a late author a allures us, it may be looked on as the ftendard of truth ; and that every Interval that occurs in mufic is good or bad, as it approaches to, or deviates from what it ought to be, on thefe principles. He obferves, that the doctrine of fome of die ant'tents feems different. Ptolemy, for inftance, introduces not only the primes 2, 3, 4, 5, but alfo 7 and 11, &c. Nay, he feems to think all fourths good, provided their component Intervals may be-^expreJTed by fuper-particuJar ratio's. But thefe are juftly exploded conceits ; and it feems not improbable, that the contradi&ons of different numerical hypothefes[ even in the age'of Ariftoxenus, and their ' iiiconuftency with expe- rience, might lead him to reject numbers altogether b. — [■•Dr. PepUfib. ap. Phil. Tranf. N°. 481. p. 26J, 268. b Id. Ibid. j i ' '

Mr. Eulcr defines an Interval, the jneafure of the difference of an acute and grave found. Tentam. Nov. Theor. Mafic, p. 72- and p. 103. Suppofe three founds a, b, c, of which c is the .moft acute.

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a the molt grave, and b the intermediate found. From the preceding definition, it appears that the Interval between the founds a and c, is the aggregate of the Intervals between a and b, and between b and c. Therefore if the Interval be- ' tween a and b, be equal to that between b and c, which hap- pens when a : b ;: c : d, the Interval between a to c, will be double the Interval a to b, or b to c This being confidered, it will appear that Intervals ought to be exprefled by the meafures of the ratio's, conftituting the founds forming thofe Intervals : But ratio's are meafured by the logarithms of fractions, the numerators of which denote the acute founds, and the denominators the grave. Hence the Interval be- tween the founds a and b, will be exprefled by the logarithm

of the fraction -, which is ufually denoted by /-, or, which

comes to the fame, lb — la. The Interval therefore of equal founds, a to a, will be null, as la — la = 0. The Interval called an octave or diapafon, will be expreffed by the lo- garithm of 2 ; and the Interval of the fifth or diapente, will be l\ = /g — li. From whence it appears, that thefe Inter- vals are incommenfurable ; fo that no Interval, however fmall, can be an aliquot part, both of the octave and fifth. The like-may be faid of the Intervals l\ and l\, and others whofe logarithms are difhmilar. But Intervals expounded by lo- garithms of numbers, which are powers of the fame root, may be compared — ■Thus, the Interval of the founds 27 : 8, will be to the Interval of the founds 9:4, as 3 is to 2 : For 1 V=3'« and 1% = 7.11. Evlei; ibid. p. 74. But thu' the logarithms of numbers, which are not powers of the fame root, be incommenfurable, yet an approximating ratio of fuch may be found. Thus the meafure of the oc- tave is li = 0.3010300, and the meafure of the fifth is ^3 — 1% — 0.1760913. Hence the Interval of the octave will be to that of the fifth, nearly as 3010300 to 1760913; which ratio being reduced -to fmaller terms, in the method explained under the head Ratio, will give us thefe fimpler exprellions for the ratio of the octave and fifth, 2:1, 3:2, 5: 3, 7: 4, 12: 7, 17: 10, 29: 17, 41 : 24, 53: 31, which laft is very near the truth, huler, ibid. p. 75. In like manner Intervals may be divided into any number of equal parts : for this purpofe we need only divide the lo- garithm of the propofed Interval into the fame number of parts, and then find its correfpondent number by the tables. The ratio of the number fo found, to unity, will give th« required ratio of the divided Interval to its propofed part. Thus let the third part of an octave be required ; its logarithm will be — 0.1003433 = -3-/2: The ratio correfponding nearly to this will be, 63 : 50, or lefs accurately, 29 : 23, or 5 : 4, which laft cxprefies the third major ; and this is by the lefs knowing taken for the third part of an octave, and feems to be fuch on our harplichords and organs, where from C to E is a third, from E to G$ another, and from G^ or A b to c an- other third. But the more intelligent know, that Gty. and A b ought not to be reputed the fame found, fince they differ by a dielis enharmonica, which is nearly equal to two commas. Eu'.er, ibid.

Mr. Euler has inferted a table of Intervals in his Tentamen Nova Theories Mufias : He fuppofes the logarithm or meafure of the octave to be 1. 000000, whence the logarithm of the fifth will be 0.584962, and the logarithm of the third major will be 0.321928 ; from thefe the meafures of all other Intervals may be found. But as it has been cuftomary for muficians to' meafure their Intervals by commas, we fhall here infert a table of Intervals with their meafures in commas; where we fuppofe the logarithm or meafure of the comma •§■£- 'to be 1. 00000 : hence the logarithm of the octave 3 will be 55-79763, that of the fifth 32.63952, and lafily that of the third major 17.96282. From thefe all the other In- tervals may be found in the manner exprefled in the table ; wb,ere the fhft column fhews the names of the feveral Inter- vals 5 the fecond the proportions of founds forming thefts Intervals ; the third the compofition of thefe proportions from the primes 2, 3, and 5. The fmaller figures marked above, and fpmewhat to the right of the larger, indicate the power to which the number exprefled by the larger figures is

raifed. Thus ^~ mews that the feventeenth power of %

5 multiplied by 3, and divided by the eighth power of 5, will

produce ||^|t| in the fecond column, and that this is the

proportion exprefling the Interval called efchaton in the firft

column. The fourth column of the table contains fome

fimple figns of fome of the Intervals, as /; for hyperoche,

d for diejis, &c. and the fifth column fhews how the Intervals

arife from others : Thus, over-againfl femitone major, I find

in the fourth column S, which is here only an arbitrary mark

for this femitone; and in the fifth column I find s-\-d=x

IV— in, which fignifies that the femitone major is equal to

the fum of the femitone minor and diefis, or to the difference

between the fourth and third major. Obferve, that the

comma is marked by a dot (.) ; when this is placed over the

letter or other fymbol, it fignifies that the Interval is fup-

pofed to be heightened by a comma ; and on the contrary,

when the point is placed below, it fignifies ,that the Interval

nvuft be diminifhed by a comma : Thus t = T' fignifies that

14 H th*