by the same
author, _Tr. Linn. Soc. London_, Zool. ser. ii. vol. iv., 1886-1888,
must on no account be omitted. (A. E. S.)

FOOTNOTE:

[1] Subgenera are indicated by round, synonyms by square brackets.

BRACHISTOCHRONE (from the Gr. [Greek: brachistos], shortest, and
[Greek: chronos], time), a term invented by John Bernoulli in 1694 to
denote the curve along which a body passes from one fixed point to
another in the shortest time. When the directive force is constant, the
curve is a cycloid (q.v.); under other conditions, spirals and other
curves are described (see MECHANICS).

BRACHYCEPHALIC (Gr. for short-headed), a term invented by Andreas
Retzius to denote those skulls of which the width from side to side was
little less than the length from front to back, their ratio being as 80
to 100, as in those of the Mongolian type. Thus taking the length as
100, if the width exceeds 80, the skull is to be classed as
brachycephalic. The prevailing form of the head of civilized races is
brachycephalic. It is supposed that a brachycephalic race inhabited
Europe before the Celts. Among those peoples whose heads show marked
brachycephaly are the Indo-Chinese, the Savoyards, Croatians,
Bavarians, Lapps, Burmese, Armenians and Peruvians. (See CRANIOMETRY.)

BRACKYLOGUS (from Gr. [Greek: brachys], short, and [Greek: logos],
word), title applied in the middle of the 16th century to a work
containing a systematic exposition of the Roman law, which some writers
have assigned to the reign of the emperor Justinian, and others have
treated as an apocryphal work of the 16th century. The earliest extant
edition of this work was published at Lyons in 1549, under the title of
_Corpus Legum per modum Institutionum_; and the title _Brachylogus
totius Juris Civilis_ appears for the first time in an edition published
at Lyons in 1553. The origin of the work may be referred with great
probability to the 12th century. There is internal evidence that it was
composed subsequently to the reign of Louis le Debonnaire (778-840), as
it contains a Lombard law of that king's, which forbids the testimony of
a clerk to be received against a layman. On the other hand its style and
reasoning is far superior to that of the law writers of the 10th and
11th centuries; while the circumstance that the method of its author has
not been in the slightest degree influenced by the school of the
Gloss-writers (Glossatores) leads fairly