D I E 



740 



D I E 



J>\eze. has been in a great degree removed to Loheia and 

 — -*{—* Hodeida. The town is well supplied with water, 

 fruits, and excellent fish. It is particularly subject to 

 fevers Its distance from Abu Arisch is about one 

 day's journey. East Long. 42° 6', and North Lat. 16° 

 53', according to Lord Valentia's chart of the Red Sea. 

 See Bruce's Travels, and Niebuhr's Travels, (j) 



DIEZE, in Music, an interval, so called by Mr Ed- 

 mund Stone, whose ratio is i£, = 36 2 + 1*^ 3 m, or the 

 Semitone Minor, which see. 



_ „ , . 387,428,489 



DIEZE, Double Minime, has a ratio -~ iooOOOO' 



or — 3 ' „,, , =28.149661 2 + f + 2m, or 28 2 -f-2f 



4. 2m ; its log.= 9861225,9363. ltis=f+x, =S+r, 

 =3/-8, =/+x + 2S + f+22, =/+ t>32, =/+ 

 R_r, =/+--<*, =/+P-5c, = /+rf_3c, =/ 

 -fr— 2, =§+£— 2, =J+L— 4c, = 3 + S — 5c, =S 

 +S — 6 c, &c. 



DIEZE Major of Rameau, has a ratio \\\, =212 

 ^-2m, or the Enharmonic Diesis, which see. 



DIEZE Maxime of Rameau, has a ratio ^fl; aa 

 25 2 + f + 2 m,or the Semitone Submiuimis, which see. 



DIEZE Minime (D), an interval so named by M. 



Rameau, it being the remainder when the semitone 



minimum is taken from the limma. Its ratio is i-§f|i> 



S 9 

 the component primes of which are t^-t; : its com- 



mon log. is .9930612,9682, and its reciprocal log. 

 .0069387,0318 : in the Binary logarithms of Euler, or 

 decimals of the octave, it is = .023054, in major com- 

 ma logarithms 1.286130, and in schisma logs. = 

 14.157524. In Farey's notation, (see our article Afo- 

 tome, and Plate XXX. in Vol. II.), it is =14 2-f-f-f 

 m, or when reduced to his regular increasing series, 

 ■wherein negative signs are wholly avoided, either in 

 the terms or the intervals between them, = 14.14966096 

 2-f-m. 



In tuneable intervals, it is = 4-4ths — III — 5-3rds ; 

 and thus it may be tuned on an instrument like Mr 

 Liston's, by ascending four perfect fourths, and from 

 the upper note descending a major third and five mi- 

 nor thirds : none of the 59 notes on the euharmonic 

 organ stand in this relation to each other, although four 

 adjacent intervals thereon differ only a schisma in ex- 

 cess, being each C+fe instead of -C-j-Je. See the 

 Phil. Mag. vol. xxxix. p. 419. 



The equations which follow, expresssd in the sym- 

 bols of Plate XXX. above referred to, will shew the ex- 

 act relation of this interval to all the others in that 

 Table, viz. 



D= & + r 

 = c-fj€ 



D=L— / D= /— c 



= 3— ct = J— 2c 



=* — S = S— 3c 



= P— 4c 



D=R+2J€ 



= ?-j- 4 ' 3 



D=2/— S 



~2d— P 

 =4S_3P 

 =3rf— 28 



D= 2+c +r 



= 22 + <i + f 



z=3x+ c-f- f 

 =32 + R+B. 



»=14d +43 f •— 13m 

 = ?+ j€— f 



=152 -f 2m — F 

 = « 4. K — r 



D=4 2+€+ f 

 =112 + % + m 

 = 142 + f -fm 



D= 



92 + 



s 4- 



r — 



m — 

 S— 



% 

 5e 



ct 



D=2€+2 S— P 



Dfeze 





=28+2 *■ — P 

 =6ct+2 f— P 



n 



Dijon. 



i 



= T+ *- t 





3 



= T+ X -T 





p 



= t+ /-T 





p 



= 2t+ d — 2T 





p 



=3* + §— 3T 





p 



= 4t+ P— 41 





p 



= T+ /— T 





p 



— t + d — T 



D= t— £— P 



= 2t — 2S— P 

 = 2t_ T— S 

 = 3t — 2T— S 

 = T— J— P 

 = 2T— S— P 

 = T— S— 3c 





D= /+ 2- 



= v -f- c — 



= £+ #- 



= d + x - 



= /+ «•- 



- S+ *- — 



= s+ /- 



-s L+ S — 



= S+ Jfc- 



= 2c +2 / — 



= 6 c +2 % — 



D=2ct— R— 4 2 

 =4£— 2R— P 



= /- €_ 2 

 =3/— x— P 

 = 2L— 2€— P 

 =2S— 2 c— P 

 =2 3—2/"— P 

 = t— S— C 



DIEZE Minor of Rameau, has a ratio ]f if =15 2 

 -f-f-f-m, or the Hype roche, which see (*) 



DIFFERENTIAL Calculus. See Fluxions. 



DIFFERENTIAL Thermometer. See Chemis- 

 try, vol. vi. p. 152. 



DIFFRACTION of light. See Inflection in the 

 Index of Optics* 



DIGESTION. See Anatomy, Medicine, and Phy- 

 siology. 



DIGITALIS, a genus of plants of the class Didyna- 

 mia, and order Angiospermia. See Botany, p. 250. 



DIGNE, Dfnia, or Di&na, is an ancient town of 

 France, and principal place of the department of the 

 Lower Alps. It is situated in a fertile valley at the 

 foot of mountains, upon the left bank of the river 

 Bleonne, which is still called Mardoric. The principal 

 buildings in the town are the cathedral, five convents, 

 a seminary, a college, and an hospital. This town, 

 however, is chiefly celebrated for its mineral waters 

 and warm baths which are at the distance of about a 

 league. The temperature of the water varies from 30° 

 to 40° of Reaumur. In cases of anchylosis, or stiffness 

 of the joints, produced by gun-shot wounds, it has 

 produced wonderful cures. The mountains in the 

 neighbourhood abound in petrifactions, and the crater 

 of an extinct volcano appears on one of the highest sum- 

 mits. There is here a manufacture of paper, of caps 

 and stockings, and of drabs called kalmoucks; and 

 great quantities of excellent fruits are collected in the 

 adjacent valleys, and are exported to other parts of 

 France, Italy, and Germany. Population of the town 

 2872. East Long. 6° 14' 19", and North Lat. 44° 5' 



* 8 "- CD 



DIGYNIA. See Botany, p. 73. 



DIJON, a town of France, formerly the capital of 

 Burgundy, but now the chief place in the department 

 of the Cote d"Or > and of the 6th cohort of, the legion 

 of honour. It is situated in an agreeable and fertile 

 plain, between the rivers Ouche and Suzon, the first of 

 which rises to the south of the town, while the last,, 

 which is frequently dry, flows past it on the north. The 

 town is entered by five gates, viz. the Gate of Bour- 

 bon, the Gate of St Nicholas, the Gate of William, the 

 Gate of Ouche, and the Gate of St Peter. It has three 

 feuxbourgs, viz. those of St Peter's, of Ouche, and 

 of St Nicholas, which eomrminkated with the Char- 

 treuse, before its destruction, by a long and fine ave- 

 nue of large trees. Tile town is of an oval form, itsr 

 length being 1500 paces, its br-eadth 1000, and its cir- 



