B I N 



Binclie 



II 

 Binocular. 



Charac- 

 ters. 



c 



a 



D 

 



i 



'* 



L 



8 



s 

 p 

 s 



4 



t 



T 



T 



3 rd 



III. 



4th 



V. 

 6 th 



VI. 



VIII. 



Names of Intervals. 



Reciprocals 

 of the Bina- 

 ry Logar- 

 ithms. 



Major Comma 0.017920 



Diaschisma, and least sum of 4 th 1 oi QUi 

 and V th Temperaments ... J 



Diaze minime . . . . 0.023054 



Hyperoche 002*679 



Enharmonic Diesis 0.0U4215 j 



Semitone subminimis 0.040974 



Chromatic Diesis 0.042599 



Semitone minimum . 0.052135 j 



Semitone minor 0.058S94 



Limma . . 0.075189 ; 



Semitone medius 0.076814! 



Semitone major 0.093109 



Apotome 0.094734 



Semitone maxime 0,111029 



SumofIII d and6 th Temperaments 0.136861 



Tone minor 0.1520O1. 



Sumof 3 d and VI th Temperaments 0.1 56406 



Tone major 0.169924 



Tone maximum 0.187844 



Minor Third 10.263034 



Major Third 0.321928 



Minor Fourth ,0.415038 



Fifth 0.584962 



Minor Sixth 0.678072 



Major Sixth 0.7:36906 



Octave 1.000000 



By help of the above, and the tables of equations 

 among the musical intervals, given under the several 

 articles Ai-otome, Comma, Sec. the binary logar- 

 ithms of any other interval of the diatonic scale may 

 be found. (5) 



BINCHE, a town of France, in the new depart- 

 ment of Temmapes, situated on the banks of the river 

 Hairre. It was burned in the year 1554 by Hen- 

 ry II. of France, but was soon afterwards rebuilt. 

 Population 3798. (_;') 



BINGEN, a town of France, in the new depart- 

 ment of Mont-Tonerre, situated near the confluence 

 of the Rhine and the Nah, the latter of which is 

 crossed by a fine stone bridge. The curn which sup- 

 plies the neighbouring country passes through this 

 town, which also furnishes it with drugs, and articles 

 of foreign commerce. Near Bingen is the famous 

 Bingen loch, or gulf of Bingen, formed by the con- 

 flux of the Nah and the Rhine, by a chain of narrow 

 rocks, where the water precipitates itself in cataracts. 

 The navigation of this part of the Rhine is very dan- 

 gerous. Not far from Bingen is a small island in the 

 Rhine, called Maustbum, or the Tower of Rats, in 

 con sequence of a tradition, that the Archbishop of 

 Mentz was devoured by these animals, for having 

 compared the poor to rats that preyed upon the sub- 

 stance of the rich. The fortifications of Bingen 

 were destroyed in 1689 by Louis XIV., but it was 

 again fortified by the desire of Bonaparte, when he 

 was first consul. Population 2663. E. Long. 7 

 33', N. Lat. 49 54'. ( 



BINOCULAR Telescope, the name of an in- 



506 BIO 



itrument invented by Father Rheita, in which the Binoculm 

 object was observed by both eyes. Binocular tele- II . 



scopes have been long completely exploded, (ic) " " ' p . 



BINOCULUS, a genus of crustaceous animals 

 that inhabit fresh water. See Crustacea, (f) 



BINOMIAL Theorem. See Algebra Index. 



BIOGRAPHY, (from /3 ? , life, and v*P". to 

 write,) is a species of history which describes the lives 

 of persons of eminence. In tracing the history of History, 

 biography, we find it at first, in all countries, in the 

 hands of the minstrels. The exploits of the chiefs 

 were the subject of their song ; and, as their heroes 

 were raised into demigods, actions were ascribed to 

 them surpassing human ability. This was the fabu- 

 lous age of biography, when nothing was too mar- 

 vellous for credulity. In Iceland and in Arabia the 

 harper was the first historian ; and both in ancient 

 and modern Europe, the period of youthful romance 

 preceded the sober day of truth. Legitimate bio- 

 graphy was scarcely known in Greece till that coun- 

 try had passed the age of manhood ; for what was 

 done by Xenophon, in the institution of Cyrus, when 

 Athens was in its glory, is of too equivocal authori- 

 ty to be classed under that head. It was not till 

 the commencement of the 2d century, that Plutarch 

 gave to biography the place which it now occupies 

 among the departments of literature ; and to him we 

 are indebted for a more intimate acquaintance with 

 the principal characters of antiquity, than we have 

 with many persons of the first distinction in modern 

 times. Writers of greater elegance, and of more phi- 

 losophical views, may have followed in his track, 

 but none have succeeded better in accomplishing the 

 great ends of this species of writing, in combining 



entertainment and instruction, in stamping upon his 

 productions the indubitable character of truth, in 

 presenting a near and familiar view of the subjects 

 of his records, and in filling up the sketches which 

 the historian is obliged, by the nature and extent of 

 his design, to leave to the biographer. During the 

 long night of ignorance which preceded the revival 

 of learning in Europe, biography, degraded from 

 the rank it once held, was enlisted in the service 

 of superstition. The only men of letters in those 

 time? were the ecclesiastics, who were disqualified, 

 both by credulity and artifice, for the office of 

 the historian. In their hands biography exhibited a 

 strange mixture of truth and falsehood, gravity and 

 puerility, simplicity and fraud. Fabulous without 

 being romantic, wanting both the authority of truth 

 and the grace of fiction, their tales of wonder could 

 neither instruct the judgment, nor delight the imagi- 

 nation. The subjects of their pen were supplied by 

 the calendar of saints, some of whom were adorned 

 with great virtues, and displayed a heroism in the de- 

 fence of their opinions which entitle them to the ve- 

 neration of posterity; whilst others had no better 

 title than is conferred by successful hypocrisy spread- 

 ing the cloak of 6anctity over pride, avarice, and am- 

 bition. The narrative of their lives, instead of deve- 

 loping the nature of man, and marking the progress 

 of passion or of intellect, was for the most part a re- 

 cord of nothing but miracles pretended to have been 

 performed by themselves, or entailed upon their 

 ashes. Since the restoration of letters, biography 



