DIEULAFOY. 2U DIFFERENCE OF LONGITUDE. sistod him materially. Her works include La Pcrsf, la Chaldte el la Susiiiiic (188G). She was made a member of the Legion of Honor. DIEZ, dets. Krikdrich l'iiRisTi..N ( I7!>4- 1876). A German philologist and founder of the scientific study of Komance philology. He was horn and educated at (.iiessen. served in the War of Liberation, and later took a suiipleuientary course in philologj- at Oilttingcn. In ls:t0 he was called to the chair of Komance |)lulologj' at IVinn. The works respectively entitled Die I'uesic der Troubadours (1826: id ed. 1883) and J.ebcn und Werke dcr Trottbadotirs (2d ed. 1882) soon made him widely known. These and the standard publication entitled Orammalik dcr rcniniiischcn Si)rucluii (5th ed., 1882; Kngl. trans. by Cayley, 1SG3) and Etymologischcs M'orlrrbuch dcr ruiiniiiixrhvii Sitriichcii (oth cd. by von Scheler, 1887; Eng. trans, by Donkyn) <iblained recognition even among the Komance nal ions as works of l)asic importance. They are written in a clear and concise style, and in them the author has given to the world a classic ex- ample of the historical and comparative method of invc-^tigal ii>ii, DIFFERENCE. See Identity, DIFFERENCE, .Mkthod of. See Indi-ction, DIFFERENCE ((jr.. Fr. diffrreiwr. Lat. diY- ferentia, from diffcrrc, to difTer, from dis-, apart -f fcrre, to bear). In heraldry, an addition to or alteration in an escutcheon to mark a distinction between the eoat-of-arms of two closely related persons whose shields would citherwisc be the same. Though generally confounded with marks of cadency (q.v.). dilTcrences liavc. in strict us- age, a totally diirerent function — the former be- ing employed to distinguish brothers and their descendants after the death of the father, the latter while he is still alive. Differences in this limited sense may consist either of a chief added to or a bordure placed round the plain shiel4 borne hy the head of the house; or should the shield exhibit any of the ordinaries, as the bend, fcss, or pale, the dilference maybe indiiated l>y an alteration in the lines of the ordinary. The prox- imity of the bearer to the head of the lunise is iiidicateil l>y the character of the line by which the differencing chief, or bordure, or ordinary is marked off from the field, the following being the order usually observed: the first or eldest brother on the death of his father inherits the pure arms of the house; the second brother, if the difference is to consist of a bordure, carries it plain: the third, ingrailed: the fourth, invect- ed: the fifth, embattled; etc. Other modes of differencing have been invented by heralds, and are not unknown to practice, such, for example, as changing the tinctures either of the field or of the principal figures, of which Xisbet gives many famous examples; altering the position or num- ber of the figures on the shield: adding different figures from the mother's coat or from lands, and the like. Where the cadet is far removed from the principal family, if the field be of one tinc- ture, it is sometimes divided into two, the charge or charges being counlerchanged, so that metal may not lie on metal, nor color on color. The confusion betwi-en differences and marks of cadency, above referred to, occurs in the heraldic usage of Kngland, Scotland, and the countries of the Pontinent. In Kranec the cadets of the House of Bourbon have been in the habit of continuing these marks, and at the present day the label or lambel is to he seen on the arms of all the mem- bers of the Orleans family. That no distinction between what we call marks of cadency and dif- ferences was there observed is further apparent from the fact that, while such was the practice of the House of Orleans, the House of Anjou car- ried :i liordiire gules, ami that of Alem,on a bor- dure gules charged with eight bezants. In tier- many, according to Sir George Maclvenzie, sev- eral branches of great families are distinguished only by different crests; and he gives as the rea- son that all (he sons succeed ecpially to the hon- ors of the family. In Great Uritain and in l' ranee, some change is always made on the shield as cairied by the head of the house; but the practice even of good heralds has been so irregu- lar as to bring the rule very nearly to what Mac Kenzie holds to be the correct one — that every private person should be allowed, with the sanc- tion of the proper authorities, "to make what marks of distinction can suit best with the coat which Ills cliicf liear-i." See Heraldry, DIFFERENCE, In mathematics, difference usually means the excess of one quantity over another of the same kind, and this is its mean- ing in arithmetic. In higher mathematics, how- ever, it is used in connection with series and functions in a special sense. Consider the follow- ing systems : Given series 4, 7. U, 18, :!1, ;-)4, 02. 151, 238, , , . First differences 3,4, 7, 13, 23, 38, .5!), 87,,., Sec(md " 1,3, C, 10, 15, 21, 28 Third " 2, 3, 4, .5, 6, 7,... Fourth " 1, 1, I, 1, 1,... The law of formation is not obvious in the first series, but by subtracting its successive terms and forming the (irst dilferences, repeating the process and furming the second differences, and repeating it again for the third differences, a series is found whose law of formation is obvious, beginning with 7, the sixth term of the third dif- ferences, me ninth term of the given series is evi- dently 238. The general formula for the nth term of such a series is (n — l)(n —2) tn = a + {n — 1)6 -f (n— l)(n — 2)(n- 1-2 ■0 + •3) d + I-2-3 in which a, b, c . , , represent respectively the first term of the several series. The sum of h terms is expressed thus: «((! — 1) So = no + p^j • b + Certain calculating machines (q.v.), particularly (he ililference engine, are constructed on thi» lirinciple. Out of the method of differences arose the calculus for finite differences. (See Calcu- MS.) Pierre Kavniond de Montmort (1678- 1710). Francois N'icole ( 1683- 17,58 ) . and Brook Taylor (1685-1731) were pioneers in this subject, DIFFERENCE, Spkcific, or DIFFEREN- TIA. See riiKliICMU.KS. DIFFERENCE OF LATITUDE. See I>ati- Ti'oi: AMI l.oM.iTi 111;. DIFFERENCE OF LONGITUDE. See Lati Ti UK AM) l.iiM.i I nil;.
