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<W he commanded the former to be retain'd on the great Seal. The fame is to be underftood of the late Queen Anne, who ufed the Motto, Semper Eadem ; which had been before ufed by Queen Elizabeth.

DIFFAMATORY, a Term chiefly ufed in the Phrafe Diffamatory Libel, fignifying a Writing intended to fcan- dalize, or difcredit a Perfon, Be. See Libel.

By the Roman Law, and the ancient Ordonnanccs of Trance, the Makers of diffamatory Libels were punifh'd with Death. See Salduin. Commentarius ad Leges de Libellis famofis. .

The Hiftorian tells us, that Cardinal Xtmenes was mfen- fible to all Diffamatory Libels. He found it but rcafon- abie to leave Inferiours the Liberty of venting their Grief by Writings, which only laft while the Perfon is offended at them, and lofc all their Spirit and Malignity when defpis'd, or disregarded.

DIFFAREATION, among the Romans, a Ceremony Whereby the Divorce of their Priefts was folemnized. See Divorce.

Diffareation was properly the diflolving of Marriages contracted by Confarreation 5 which were thofe of the Pontifices. F eftus fays, it was perform'd with a wheaten Cake; and that it was call'd Diffarreation from Far, Wheat. Vigenere will have Confarreation and Diffarea- tion to be the fame Thing. Sec Confarreation.

The Word comes from the Prepofition Dis, which is ufed in Compofition for Diviflon, or Separation ; and Farea- tion, a Ceremony with Wheat, of Far, Wheat.

DIFFERENCE, in Logic, an Effential Attribute belong- ing to fome Species, and not found in the Genus ; being the uiiiverfal Idea that defines the Species. Sec Genus, and Species.

Thus, Body and Spirit are the two Species of Subftance, which in their Ideas include fomething more than is inclu- ded in the Idea of Subftance. In Body, for Inftance, is found Impenetrability, and Extention ; In Spirit, a Power of Thinking, and Rcafoning. So that the Difference of Body is impenetrable Extenfion ; and the Difference of a Spirit is Cogitation. See Definition.

Difference, in Mathematicks, the Excefs of one Quantity above another.

This Angle is 60 Degrees, and that 90 5 Their Differ- ence is 30. See Angle,

When a lefs Quantity is fubftracfed from a greater, what remains is call'd the Difference. See Substraction.

Difference of Longitude of two Places, is an Arch of the Equator intercepted between the Meridians of the Places. See Longitude.

Afcenfwnal Difference, in Aflronomy, is an Arch of the Equator comprehended between the Circle of fix a- Clock, and the Horary Circle of the Sun. See Ascen- sional.

Differences in Heraldry, are certain Additaments to Coat Armour, whereby fomething is alter'd, or added to diftinguifh the younger Families from the elder, or /hew how far they are removed from the principal Houfc. They are call'd in Latin Diminutiones, and Difcernicula Armo- ¥tim, and by the French Srifitres. See Diminution.

Of thefe Differences Sylii. Morgan gives us nine, which obtain principally among us : viz. the Label, which de- notes the firft, or eldeft Son : The Crefcent, the fecond : The Mullet, the Third : The Martlet, the fourth : The Annulet, the fifth : The Flower de Lis, the fixth : The Rofe, the feventh : The Eight foil, the eighth : And the Crop Moline, the ninth. See each under its proper Article, Label, $Sc.

Again, as the firft Differences are fingle for the Sons of the firft Houfe, or Defcent ; the Sons of the younger Houfes are differ'd by combining or putting the faid Dif- ferences upon each other. As the firtt Differences are the Label, Crefcent, &c. for the firft Houfe ; the Difference for the fecond Houfe is the Label on a Crefcent, for the firft of that Houfe : For the third Brother of the fecond Houfe a Mullet on a Crefcent, &c.

The Original of Differences is controverted. Cambden will have them to have begun about the Time of King Richard. Paradin afligns Differences wore as early as the Year 870. The President Fanchet obferves Differences ■to have been hereditary in the French Families before the Time of Louis le Gros, who came to the Crown in the lear mo. Moreau refers them to the Time of St.Louis 5 and Lallonette, Selleforejl, &c. to that of Philip Au- gvftus. The Occafion of their Rife is well accounted for by Colombiere.

All Nations, fays he, prefer the elder Brothers to the younger 5 whence thofe, in a direct Line, fucceeding their Fathers, and becoming Matters of their Lands, took on them their Coat Armour, without any Change, or Alteration ; and tranfmitted the fame again to their eldeft Sons ; the younger Brothers, orBaftards not being allowed to bear the fame' Arms, without fome additional Mark, to diftinguift)

them from the elder. Flence fome Heralds, he goes on, have endeavour 'd to confine them to certain fix'd, and de- terminate Figures, for diftinguifhing the fecond from the firft, the third from the fecond ; and fo on to the fixth : Afligning the fecond a Label, the third a Sordiire, the fourth an Orle, the fifth a Battoou, and the fixth a Send, or Cottice.

And the Defcendents of thefe to bear double Differ- ences, or Differences charg'd on one another, viz. the eldeft Son of the fecond Son to retain his paternal Coat, with the Difference of the Label of ; Points ; the fecond the Label of 4 Points ; the third fuch a Label on a Chief 5 the fourth a Ztffo/charged with certain Figures, ssEaglets, Lioncels, Martlets, Crefcents, Rofes, Sic. And for the fame reafon, the fecond Son of the third Son ifiall bear a Sordiire engrailed, the third a Sordure charged with Be- zants, or Tourtcaux, £SV.

But the fame Author judges the fixing any certain in- variable Differences at all an Abufe ; by reafon they may- happen not to be agreeable to the paternal Coat, but very much deface, and blemifh it. He adds, that many other Figures befide thofe abovementioned, may be ufed as Dif- ferences ; As Shells, Bezants, Cinque-foils, and a thoufantl more. Some younger Families have made the Difference in their Arms by only dimini/hing the Ordinaries, or changing the Pofturc ; And ethers by only changing the Metal, or Colour.

It Mil be added, that the Differences may be of Metal on Metal, or Colour on Colour ; which in other Cafes is falfe Heraldry.

DIFFERENTIAL, Differential in the higher Geo- metry, an infinitely fmall Quantity, or a Particle ot aQuan- tity fo fmall as to be incommenfurable thereto, or lefs than a ny aflignable one. See Quantity.

It is call'd a Differential, or Differential Quan- tity, becaufe frequently confider'd as the Difference of two Quantities; and as fuch is the Foundation of the Dif- ferential Calculus : Sir Jfaac Newton, and the Englfjll, call it a Fluxion, as being confider'd as the momentary In- creafe of a Quantity. See Fluxion.

Mr. Leibnitz, and others, call it an Infmitejimal. See Infinitesimal.

Differential of the firfl, fecond, &c. Degree. See Differentio-Differential.

Differential Calculus, or Methoius, is a Method of differencing Quantities ; that is, of finding a differentia!, or infinitely fmall Quantity, which taken an infinite Num- ber of Times, is equal to a given Quantity.

This Method is one of the fineft, and fubtileft in all Ma- thematicks, Mr. Leibnitz, who claims the Invention there- of to himfelf, calls it Differentialis Calculus, as confidering the infinitely fmall Quantities found hereby as the Z)/#er- ences of the Quantities ; and accordingly exprefling them by the Letter d prefix'd : as the differential of x, by dx j that ofy by dy, &c.

Sir Jfaac Newton, who has a better Title to the Difcovery, calk it the Method of Fluxions, as con- fidering the infinitely little Quantities rather as Flu- xions, or momentary Increments, e. gr. of a Line, ge- nerated by the Fluxion of a Point ; of a Surface, bv the Flux of a Line ; or a Solid, by the Flux of a Surface \ and inftead of d notes 'em by a dot ; e. gr. the Fluxion of x, inftead of dx he writes 'x ; that of y, y, &c. which is the only Difference between the Differential Calculus, and the Method of Fluxions.

For the Hijlory, DcSrine, Ufe, &c. thereof, fee Fluxions.

Differentio-Differential Calculus, is a Method of differencing Differential Quantities.

As the Sign of a Differential is the Letter d ; that of a Differential of dx, is ddx ; and the Differential of ddx, dddx, or d*x, d l x, &c ; or x, x, Ike.

Thus, we have 'Powers, or Degrees of Differentials.

The Differential of an ordinary Quantity is call'd a Differential of the firfl l 'Power, or Degree ; as dx.

A Differential of the fecond Power, orDcgree, is an Infinitefimal of a Differential Quantity of the firft Degree j as ddx, or dxdx, or dx 1, dxdy, ike,

A Differential of the third Degree, is an Infinite- fimal of a Differential Quantity of the fecond Degree 5 as dddx, dx', dxdydz, and fo on.

The Po-wers of Differentials, as dx', are differenced after the fame Manner, as the Powers of ordinary Quan- tities. And again, as Compound Differentials either mul- tiply, or divide each other, or are Powers ot Differentials of the firft Degree ; Differentials are differenced afte* the fame manner as ordinary Quantities. And, therefore, the Differentio-Differential Calculus, is the fame, in Effect, with the Differential. -

Differential, in the Doctrine ofLogarithms. Kep- ler calls the Logarithms of Tangents, Differentiates ; which we ufually call Artificial 'Tangents. See Loga- rithm and Tangent.

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