Chapter XII: Part 12

BICHAT, MARIE FRANCOIS XAVIER (1771-1802), French anatomist and physiologist, was born at Thoirette (Jura) on the 14th of November 1771. His father, a physician, was his first instructor. He entered the college of Nantua, and afterwards studied at Lyons. In mathematics and the physical sciences he made rapid progress, but ultimately devoted himself to the study of anatomy and surgery, under the guidance of M.A. Petit (1766-1811), chief surgeon to the Hotel Dieu at Lyons. The revolutionary disturbances compelled him to fly from Lyons and take refuge in Paris in 1793. He there became a pupil of P.J. Desault, who was so strongly impressed with his genius that he took him into his house and treated him as his adopted son. For two years he actively participated in all the labours of Desault, prosecuting at the same time his own researches in anatomy and physiology. The sudden death of Desault in 1795 was a severe blow to Bichat. His first care was to acquit himself of the obligations he owed his benefactor, by contributing to the support of his widow and her son, and by conducting to a close the fourth volume of Desault's _Journal de Chirurgie_, to which he added a biographical memoir of its author. His next object was to reunite and digest in one body the surgical doctrines which Desault had published in various periodical works. Of these he composed _Oeuvres chirurgicales de Desault, ou tableau de sa doctrine, et de sa pratique dans le traitement des maladies externes_ (1798-1799), a work in which, although he professes only to set forth the ideas of another, he develops them with the clearness of one who is a master of the subject. In 1797 he began a course of anatomical demonstrations, and his success encouraged him to extend the plan of his lectures, and boldly to announce a course of operative surgery. In the following year, 1798, he gave in addition a separate course of physiology. A dangerous attack of haemoptysis interrupted his labours for a time; but the danger was no sooner past than he plunged into new engagements with the same ardour as before. He had now scope in his physiological lectures for a fuller exposition of his original views on the animal economy, which excited much attention in the medical schools at Paris. Sketches of these doctrines were given by him in three papers contained in the Memoirs of the Societe Medicale d'Emulation, which he founded in 1796, and they were afterwards more fully developed in his _Traite sur les membranes_ (1800). His next publication was the _Recherches physiologiques sur la vie et sur la mort_ (1800), and it was quickly followed by his _Anatomie generale_ (1801), the work which contains the fruits of his most profound and original researches. He began another work, under the title _Anatomie descriptive_ (1801-1803), in which the organs were arranged according to his peculiar classification of their functions, but lived to publish only the first two volumes. It was completed on the same plan by his pupils, M.F.R. Buisson (1776-1805) and P.J. Roux (1780-1854).

Before Bichat had attained the age of eight-and-twenty he was appointed physician to the Hotel Dieu, a situation which opened an immense field to his ardent spirit of inquiry. In the investigation of diseases he pursued the same method of observation and experiment which had characterized his researches in physiology. He learned their history by studying them at the bedside of his patients, and by accurate dissection of their bodies after death. He engaged in a series of examinations, with a view to ascertain the changes induced in the various organs by disease, and in less than six months he had opened above six hundred bodies. He was anxious also to determine with more precision than had been attempted before, the effects of remedial agents, and instituted with this view a series of direct experiments which yielded a vast store of valuable material. Towards the end of his life he was also engaged on a new classification of diseases. A fall from a staircase at the Hotel Dieu resulted in a fever, and, exhausted by his excessive labours and by constantly breathing the tainted air of the dissecting-room, he died on the 22nd of July 1802. His bust, together with that of Desault, was placed in the Hotel Dieu by order of Napoleon.

BICHROMATES AND CHROMATES. Chromium trioxide dissolves readily in water, and the solution is supposed to contain chromic acid, H2CrO4; the salts of this acid are known as the chromates. In addition to these normal salts, others exist, namely bichromates, trichromates, &c., which may be regarded as combinations of one molecular proportion of the normal salt with one or more molecular proportions of chromium trioxide. The series will thus possess the following general formulae:--

M2CrO4 M2Cr2O7 M2Cr3O10 &c. (M = one atom of a
normal chromate bichromate trichromate monovalent metal.)

_Chromates._--The alkaline chromates are usually obtained by fusion of
a chromium compound with an alkaline carbonate and an oxidizing agent,
such for example as potassium nitrate or chlorate. The native
chrome-ironstone (Cr2O3.FeO) may be used in this way as a source of
such compounds, being fused in a reverberatory furnace, along with
soda-ash and lime, the oxidizing agent in this case being atmospheric
oxygen. They may also be prepared by oxidizing chromium salts (in
alkaline solution) with hydrogen peroxide, chlorine, bleaching powder,
potassium permanganate and manganese dioxide. The majority of the
chromates are yellow in colour, and many of them are isomorphous with
the corresponding sulphates. The alkaline chromates are soluble in
water, those of most other metals being insoluble. By the addition of
mineral acids, they are converted rapidly into bichromates. They are
easily reduced in acid solution by sulphuretted hydrogen, and also by
sulphur dioxide to chromium salts. The chromates are stable towards
heat; they are poisonous, and may be recognized by the yellow
precipitates they give with soluble barium and lead salts.

Potassium chromate, K2CrO4, may be prepared by neutralizing a solution
of potassium bichromate with potassium carbonate or with caustic
potash. It crystallizes in yellow rhombic prisms, and is readily
soluble in water, the solution having a bitter taste and an alkaline
reaction. When heated in a current of sulphuretted hydrogen, or carbon
bisulphide, it yields a mixture of chromium sesquioxide and sulphide.
When heated with sulphur it yields chromium sesquioxide. Sodium
chromate, Na2CrO4.10(H2O), forms pale yellow crystals isomorphous with
hydrated sodium sulphate, Na2SO4.10(H2O). It is deliquescent, and
melts at 23 deg. C. (M. Berthelot). By evaporation of its aqueous solution
at temperatures above 30 deg. C. it may be obtained in the anhydrous
condition. Lead chromate, PbCrO4, occurs native as the mineral
crocoisite, and may be obtained as an amorphous pale yellow solid by
precipitating a soluble lead salt by an alkaline chromate. It is used
as a pigment under the name "chrome yellow." When digested for some
time with a caustic alkali it is converted into a basic salt,
PbCrO4.PbO, a pigment known as "chrome red." It melts readily, and on
cooling resolidifies to a brown mass, which at moderately high
temperatures gives off oxygen and leaves a residue of a basic lead
salt; for this reason fused lead chromate is sometimes made use of in
the analysis of organic compounds. Silver chromate, Ag2CrO4 is a dark
red amorphous powder obtained when silver nitrate is precipitated by
an alkaline chromate. It is decomposed by the addition of caustic
alkalis, forming silver oxide and an alkaline chromate.

_Bichromates._--The bichromates are usually of a red or reddish-brown
colour, those of the alkali metals being readily soluble in water.
They are readily decomposed by heat, leaving a residue of the normal
chromate and chromium sesquioxide, and liberating oxygen; ammonium
bichromate, however, is completely decomposed into chromium
sesquioxide, water and nitrogen. Sulphuretted hydrogen and sulphur
dioxide reduce them in acid solution to the condition of chromium
salts.

Potassium bichromate, K2Cr2O7, is obtained by fusing chrome ironstone
with soda ash and lime (see above), the calcium chromate formed in the
process being decomposed by a hot solution of potassium sulphate.
After the calcium sulphate has settled, the potassium chromate
solution is converted into bichromate by the action of sulphuric acid,
and the salt is allowed to crystallize. It forms large triclinic
prisms of specific gravity 2.6-2.7, which are moderately soluble in
cold water and readily soluble in hot water. The solution is strongly
acid in reaction and is very poisonous. Potassium bichromate finds
extensive application in organic chemistry as an oxidizing agent,
being used for this purpose in dilute sulphuric acid solution, K2Cr2O7
+ 4H2SO4 = KaSO4 + Cr2(SO4)3 + 4H2O + 3O. On the addition of
concentrated sulphuric acid to a cold saturated solution of the salt,
red crystals of chromium trioxide, CrO3, separate (see CHROMIUM),
whilst when warmed with concentrated hydrochloric acid and a little
water, potassium chlorochromate is produced. When heated with
phosphorus trichloride in a sealed tube to 160 deg. C., potassium
chlorochromate, phosphorus oxychloride, potassium chloride, and a
complex chromium oxide (possibly Cr3O6) are produced (A. Michaelis,
_Jour. prak. Chem._, 1871, ii. 4, p. 452). Potassium bichromate finds
application in photography, in calico-printing and in the preparation
of bichromate cells. Sodium bichromate, Na2Cr2O7.2{H2O}, may be
obtained by the addition of the requisite quantity of chromium
trioxide to a solution of sodium chromate. It crystallizes in
hyacinth-red prisms, which are very hygroscopic and melt at 320 deg. C.

_Trichromates._--The trichromates are obtained by the addition of
nitric acid (of specific gravity about 1.2) to solutions of the
bichromates. They form rhombic crystals of a red or brown red or brown
red colour and are readily decomposed by warm water, with formation of
the bichromate.

_Perchromic Acid._--By the addition of hydrogen peroxide to a solution
of chromic acid, a fine blue coloration due to a perchromic acid is
produced which is readily absorbed by shaking out with ether. The
following formulae have been assigned to the compound:--H2O2.CrO3 (H.
Moissan, _Comptes rendus_, 1883, 97, p. 96); H2O2.2HCrO4 (M.
Berthelot, _Comptes rendus_, 1889, 108, p. 25); Cr2O7.xH2O (L.C.A.
Barreswil, _Ann. chim. et phys._, 1847 [3], 20, p. 364), and
CrO6.3{H2O} (T. Fairley, _Chem. News_, 1876, 33, p. 237). The more
recent investigations of H.G. Byers and E.E. Reed (_Amer. Chem.
Jour._, 1904, 32, p. 503) show that if metallic potassium be added to
an ethereal solution of the blue compound at -20 deg. C., hydrogen is
liberated and a purple black precipitate of the perchromate, of
composition KCrO4 or K2Cl2O8, is produced; this compound is very
unstable, and readily decomposes into oxygen and potassium bichromate.
Similar sodium, ammonium, lithium, magnesium, calcium, barium and zinc
salts have been obtained. It is shown that the blue solution most
probably contains the acid of composition, H2Cr2O8, whilst in the
presence of an excess of hydrogen peroxide more highly oxidized
products probably exist.

BICKER (connected by Skeat with _bike_, to thrust or strike), an Old English word (traced from the 13th century) implying conflict or disputation. A poetical use, from the noise, is seen in Tennyson's _Brook_, "to bicker down the valley."

BICKERSTAFFE, ISAAC (c. 1735-c. 1812), English dramatist, was born in Ireland about 1735. At the age of eleven he was appointed a page to Lord Chesterfield, then lord lieutenant of Ireland, and subsequently held a commission in the Marines, but was dismissed the service under discreditable circumstances. He was the author of a large number of plays and burlesque farces interspersed with songs, produced between 1760 and 1771. The best-known are _Maid of the Mill_ (founded on Richardson's _Pamela_), _The Padlock, He Would if he Could, Love in a Village, The Hypocrite_ and _The Captive_. In 1772 Bickerstaffe, suspected of a capital offence, fled to the continent. The exact date of his death is unknown, but he is stated to have been still living in abject misery in 1812.

A full account of his dramatic productions is given in _Biographia
Dramatica_, edited by Stephen Jones (1812).

BICKERSTETH, EDWARD (1786-1850), English evangelical divine, brother of Henry, Baron Langdale, master of the rolls (1836-1851), and uncle of Robert Bickersteth, bishop of Ripon (1857-1884), was born at Kirkby Lonsdale, and practised as a solicitor at Norwich from 1812 to 1815. In 1816 he took orders, and was made one of the secretaries of the Church Missionary Society. On receiving the living of Watton, Hertfordshire, in 1830, he resigned his secretaryship, but continued to lecture and preach, both for the Church Missionary Society and the Society for the Conversion of the Jews. His works include _A Scripture Help_ (London, 1816), which has been translated into many European languages, and _Christian Psalmody_ (London, 1833), a collection of over 700 hymns, which forms the basis of the _Hymnal Companion_ (London, 1870), compiled by his son, E.H. Bickersteth, bishop of Exeter (1885-1890). He was active in promoting the Evangelical Alliance of 1845, strongly opposed the Tractarian Movement, and was one of the founders of the Irish Church Missions, and Parker, Societies.

EDWARD BICKERSTETH (1814-1892), dean of Lichfield, was his nephew, and EDWARD BICKERSTETH (1850-1897), bishop of South Tokyo, his grandson.

BICYCLE (from prefix _bi_ = twice, and [Greek: kyklos] a circle, wheel). The modern bicycle, as developed from the old velocipede (see CYCLING), consists essentially of two wheels placed one behind the other and mounted on a frame which carries a saddle for the rider. Between the wheels is a crank-axle which the rider drives by means of the cranks and pedals, and its motion is transmitted to the rear or driving wheel either by a chain which passes over two chain wheels, one fixed on the crank-axle and the other on the hub of the rear wheel, or, in the chainless bicycle, by a tubular shaft and two pairs of bevel-wheels. The rear wheel is usually so arranged that it can turn, when the bicycle is running by its own momentum, independently of the chain and pedals ("free-wheel"), and a variable speed gear is often provided so that the rider may at will alter the ratio between the rate of revolution of the crank-axle and the driving wheel. The front, or steering wheel, is mounted in a fork having its two upper ends brazed into the "crown," to which also the lower end of the steering tube is brazed. The steering tube is mounted by ball bearings in the socket tube, which forms the forward portion of the rear-frame.

The highest quality of materials and the most accurate workmanship are required to produce a first-class bicycle. Steel of 75 to 100 tons per sq. in. tensile strength is used in chains, spokes, &c. In balls and ball-races, hardness without brittleness, and homogeneity are of primary importance. Broken balls, or even traces of wear in bearings, are now seldom heard of in a first-class bicycle. The process of case-hardening, whereby an extremely hard outer skin is combined with a tough interior, has been brought to a high degree of perfection, and is applied to many parts of the bicycle, particularly chains, free-wheels and toothed-wheel variable speed gears. Interchangeability of parts is secured by working to the smallest possible limits of error of workmanship.

_Frames._--Fig. 1 represents a road-racer. A full roadster would have
the handles a little higher relatively to the saddle, and would be
provided with mud-guards, free-wheel and sometimes a gear-case and
variable speed gear. Fig. 2 shows a lady's bicycle with gear-case and
dress-guard. The rear frame of the "diamond" type (fig. 1) is
subjected to very small stresses due to vertical load. The front fork
and steering post are subject to bending moment due to the reaction
from the ground in the direction _dcb_. A slight amount of elasticity
in the front fork adds considerably to the comfort in riding over
rough roads. When the brake is applied lightly to the front wheel, the
reaction from the ground falls more closely along the axis of the
front fork, and the bending moment at the crown is diminished. If the
front brake is applied harder the reaction from the ground at d may
pass through the crown, in which case the bending moment at the crown
is zero. Still harder application of the brake causes a bending moment
in the opposite direction. In fig. 1 the axes of the top and bottom
tubes of the rear frame are produced to meet at _a_. If the reaction
from the ground is in the direction _da_, the top and bottom tubes are
subjected to pure compressive and tensile stresses respectively. When
no brake pressure is applied a bending moment due to the overhang _ab_
is superimposed on these tubes. Thus a short socket head with top tube
sloping downwards towards the head gives a stronger frame than a
horizontal top tube. The steering axis _ef_ is arranged so as to cut
the ground at _f_, a little in front of the point of contact _d_ of
the wheel with the ground, giving a slight castor action, and making
steering possible without use of the handle-bar. The rake of the
steering head (that is the angle between _ef_ and _bd_) and the set of
the fork (that is the displacement of the wheel centre _c_ from the
axis _ef_) may be varied within tolerably large limits without much
affecting the easy steering properties of the bicycle. The transverse
stresses on the rear frame due to the action of pedalling are more
severe than those due to the vertical load. The pedal pressure is
applied at a considerable distance from the central plane of the
bicycle, and the pedal pin, cranks and crank-axle are subjected to a
bending moment which is transmitted by the ball bearings to the frame.
The down-tube from the seat lug to the crank-bracket and the bottom
tube from the foot of the steering socket tube to the crank-bracket
are made fairly stout to resist this bending moment. Further, the pull
of the chain causes a transverse bending moment in the plane of the
chain-stays, which must be stiff enough under heavy pedal pressure.

The tubular portions of the frame are made of weldless cold-drawn
steel tube. The junctions or lugs are usually of malleable cast iron,
bored to fit the outside of the tube, the final union being effected
by brazing. In very light bicycles the tubes are kept thin, 22 or 24
W.G. (.028 in. or .022 in. thickness) at the middle, and are
strengthened at the ends by internal liners. Or butt-ended tubes are
employed, the tubes being drawn thicker at the ends than in the
middle. The steering post and fork sides especially should be thus
strengthened at their junction with the crown. Some of the best makers
use sheet steel stampings instead of cast lugs, greater lightness and
strength being secured, and in some cases the sheet steel lugs are
inside the tubes, so that the joints are all flush on the outside. The
front fork blades are best made of sheet steel stamped to shape and
with the edges brazed together to form a hollow tube. The sheet steel
that can be thus employed has a much higher elastic limit than a
weldless steel tube.

_Bearings._--Ball bearings are universally used. Each row of balls
runs between two ball-races of hardened steel, one on the stationary
member, the other on the rotating member. The outer is called the
"cup," and the inner the "cone." One of the four ball-races is
adjustable axially so that the bearing may run without any shake. The
ball-races are often made of separate pieces of steel, but the
crank-axle usually has the cones formed integral with it, the
necessary hardness being obtained by case-hardening. According as the
two cups face outwards or inwards the bearing is said to have outward
or inward cups, and according as the adjustable ball race is the cone
or cup, the bearing is said to be cone-adjusting or cup-adjusting.
Fig. 3 shows a ball-bearing hub with outward cups. The hub-shell H is
turned out of mild steel, and the cups C are forced into the ends of
the hub-shell and soldered thereto. A thin washer W is then spun into
the end, for the purpose of retaining oil, and a thin internal tube T
unites the two cups, and guides the oil fed in at the middle of the
hub to the balls. The projecting flanges S are for the attachment of
the tangent spokes used to build the hub into the wheel. The spindle A
has the two cones screwed on it, one C1 against a shoulder, the other
C2 adjustable. The spindle ends are passed through the back-fork ends
and are there adjusted in position by the chain-tension adjusters.
After adjustment the nuts N clamp the spindle securely between the
fork-ends. The chain-wheel or free-wheel clutch is screwed on the end
of the hub-shell, with a right-hand thread. The chain being at the
right-hand side of the bicycle (as the rider is seated) the driving
pull of the chain tends to screw the chain-wheel tight against the
shoulder. A locking-ring R with a left-hand thread, screwed tight
against the chain-wheel, prevents the latter from being unscrewed by
back-pedalling. With a free-wheel clutch screwed on the hub, the
locking-ring may be omitted.

Fig. 4 shows one end of the cup-adjusting hub, with inward bearings.
The cones are formed of one piece with the spindles, and the adjusting
cup C is screwed in the end of the hub shell, and locked in position
by the screwed locking-ring R. The figure also illustrates a divided
spindle for facilitating the removal of the tire for repair when
required without disturbing the wheel, bearings, chain or gear-case.
The chain side of the hub-spindle, not shown in the figure, is secured
to the frame in the usual way; on the left side the spindle S projects
very little beyond the adjusting cup. A distance washer W is placed
between the end of the spindle S and the fork-end F. A detachable
screw-pin, or the footstep, P, passes through the chain-adjusting
draw-bolt B, the fork-end F, and the distance washer W, and is screwed
into the end of the spindle S, the hexagon head of the detachable pin
drawing all the parts securely together. On unscrewing the detachable
pin, the distance washer W drops out of place, leaving a clear space
for removing the tire without disturbing any other part.

The inward-cups bearing retains more oil than the other form. The
pressure on a ball being normal to the surface of contact with the
ball race, and each ball touching two ball races, the two points of
contact must be in line with the centre of the ball. All the lines of
pressure on the balls of a row meet at a point _f_ on the axis of the
spindle. The distance between the two points _f_ (fig. 5) may be
called the virtual length of the bearing. Other things being equal,
the outward-cups bearing has a greater virtual length than the
inward-cups bearing. In hubs and pedals where the actual distance
between the two rows of balls is sufficient, this point is of little
importance. At the crank-axle bearing, however, where the pedal
pressure which produces pressure on the axle bearings is applied at a
considerable overhang beyond the ball-races, the greater virtual
length of the outward-cups is an advantage.

Fig. 5 shows diagrammatically the usual form of crank-axle bearing
which has inward-cups and is cup-adjusting. The end of the bracket is
split and the cup after adjustment is clamped in position by the
clamping screw S. The usual mode of fastening the cranks to the axle
is by round cotters C with a flat surface at a slight angle to the
axis, thus forming a wedge, which is driven in tight. The small end of
the cotter projects through the crank, and is screwed and held in
place by a nut. The chain-wheel at the crank-axle is usually
detachably fastened to the right-hand crank.

The Rudge-Whitworth crank-bracket has outward cups and is
cup-adjusting. The cranks are cotterless. Fig. 6 is a sectional view.
The left crank and axle are forged in one piece. The fastening of the
right crank and chain-wheel is by multiple grooves and teeth, this
fastening being better mechanically than the cotter type.

_Pedals._--The pedal consists of a pedal body, on which the foot of
the rider rests, mounted by ball-bearings on a pedal-pin, which is
secured to the end of the crank and turns with it. The pedal body is
made in many forms, but usually the bearing-cups are contained in a
tube from the ends of which project plates, carrying rubber blocks, or
serrated plates (rat-trap pedals), on which the foot of the rider
rests. Cone adjustment is most used. The fastening of the pedal pin to
the crank is best effected by screwing it up against a shoulder, the
right and left crank eyes being tapped with right and left hand screws
respectively. With this arrangement, if the pedal pin screw is a slack
fit in the crank eye, the pressure on the pedal tends to screw it up
against the shoulder.

_Wheels._--Bicycle and tricycle wheels are made on the "suspension"
principle, the spokes being of high-tenacity steel wire, screwed up to
a certain initial tension, thus putting a circumferential compression
on the rim. In the "artillery" wheel, the wooden spokes are in
compression, and the rim is under tension. The rims, which are made to
a section suitable for pneumatic tires (see TIRE), may be of sheet
steel or aluminium alloy rolled to the required section, either
without joint or jointed by brazing or riveting. Wood rims are used on
racing bicycles, but in England are not popular for roadster bicycles.
Holes are drilled at or near the central plane of the rim for the
spoke nipples, which have shoulders resting on the outer surface of
the rim and shanks projecting through the rim towards the hub. The
spoke ends are screwed to fit the nipples. The shank of the nipple has
a square cut on its outside surface by which it can be screwed up. The
spoke flanges on the hub are placed far apart and the spread of the
spokes gives the wheel lateral stability. Tangential rigidity under
driving and braking is obtained by fastening the spokes to the hub
tangentially (figs. 1 and 2). The hub fastening of the spoke is simply
obtained by forming a hook and head on the spoke end, and passing it
through a hole in the hub flange. The best spokes are butted at the
ends, i.e. made of larger diameter than at the middle, to allow for
screwing at one end and the hook bend at the other.

_Chains._--There are two widely used types of chains. The "block"
chain (fig. 7) consists of a series of central blocks connected by
side plates. The "roller" chain (fig. 8) consists of a series of
outside and inside links. The outside link A is made up of two steel
side plates P united by two shouldered rivets R. The inside link B
consists of two side plates P united by two tubular pieces T, which
form bushes for the rivets R and pivots for the rollers L. The rivets,
bushes and rollers are case-hardened.

Roller chains for cycles are made in two pitches, 1/2 in. and 5/8 in.,
and in widths from 1/8 in. to 1/4 in. between the side plates of the
inside links. The weight of 4 ft. length (96 links) of a 1/2 in. pitch
1/8 in. wide roller chain is about 121/4 oz., and its breaking load is
about 2000 lb. In a block chain the ends of the blocks engage with the
teeth of the chain-wheels, and the same surfaces continually coming
into contact, the wear may become excessive, especially when exposed
to mud and grit. In the roller chain the outer surfaces of the rollers
engage with the teeth of the chain-wheels, and during the engagement
and disengagement may roll slightly on the tubular rivets. The surface
of contact of the roller and tubular rivet is not directly exposed to
the dust and grit from the road. The rollers therefore serve the
double purpose of (1) transferring the relative motion of the parts to
a pair of surfaces under better conditions as regards lubrication, and
(2) presenting a new part of the outside surface of the roller for the
next engagement with the chain-wheel. The durability of roller chains
is thus much greater than that of block chains, under the usual
conditions of cycling.

_Chain-wheels._--The pitch line of the chain-wheel is polygonal (fig.
9), _a, b, c, d_ being centres of adjacent joints of the chain when
lying in contact with the wheel. The path of the joint _a_ of the
chain, relative to the chain-wheel as it enters on to and leaves the
chain-wheel, is evidently the curve _a3 a2 a a'1 a'2_ made up of a
series of circular arcs having centres _d, c, b, b', c'_,
respectively. Similarly for the path of the adjacent joint _b_. The
fullest possible form of the tooth is that between the two parallel
curves, of radii less by an amount equal to the radius of the roller,
as indicated in fig. 9. But since it is neither necessary nor
desirable that the roller should roll along the whole length of the
tooth, the radii of curvature of the tooth outline may be less than
shown in fig. 9. A good arrangement of tooth form is shown in fig. 10.

Owing to the polygonal pitch surfaces of the chain-wheels a chain does
not transmit motion with constant speed-ratio of the shafts. The
variation of speed-ratio in a chain with links of equal pitch is
approximately inversely proportional to the square of the number of
teeth in the smaller chain-wheel, as shown in the table annexed, in
which the percentage variation is--

maximum speed-ratio - minimum speed-ratio
----------------------------------------- x 100.
average speed-ratio

+----------------------------+-----+-----+-----+-----+-----+-----+-----+-----+
| Number of teeth on hub | | | | | | | | |
| chain-wheel | 10 | 12 | 14 | 16 | 18 | 20 | 24 | 28 |
+----------------------------+-----+-----+-----+-----+-----+-----+-----+-----+
| Percentage Variation | 5.1 | 3.5 | 2.7 | 2.1 | 1.6 | 1.3 | 0.9 | 0.7 |
+----------------------------+-----+-----+-----+-----+-----+-----+-----+-----+

The rollers as they come in contact with the chain-wheel strike it
with a speed proportional to the angular speed of the chain-wheel and
to the pitch of the chain, causing a certain amount of noise.

_Chain Adjustment._--To keep the chain running at correct tension, it
is necessary to have some adjustment of the distance between the
crank-axle and hub. This is obtained either by an eccentric adjustment
at the crank-bracket, an eccentric adjustment at the hub-spindle or by
draw-bolts at the fork-ends, the last method being most common.

_Gear-case._--The modern roller chain by makers of repute is so
durable that the necessity for a gear-case is not so great as when
chains were of inferior quality. But if the bicycle is to require the
minimum amount of care and attention a gear-case should be fitted. The
Sunbeam gear-case is built into the frame and is oil-retaining, and
the chain, chain-wheels, free-wheel and two-speed gear are continually
lubricated by an oil-bath. A detachable gear-case is not usually
oil-retaining, but serves to exclude grit and mud from the chain.

_Gear and Crank-length._--The "gear" of a bicycle is given by the
formula Dn1/n2 where D is the diameter of the driving wheel in inches,
n1 and n2 the numbers of teeth on the crank-axle and hub chain-wheels
respectively. At each revolution of the crank-axle, the bicycle is
moved forward a distance equal to the circumference of the circle of
diameter equal to the gear. Thus with a 28 in. diameter driving-wheel,
18 teeth on the hub chain-wheel, 45 teeth on the crank-axle
chain-wheel, the bicycle is geared to 70 in. The usual crank-length is
61/2 to 7 in. Cranks of 71/2, 8 and 9 in. length can be had, but require a
bicycle frame of special design. The gear should be roughly
proportional to the crank-length. The gear 10 times the crank-length
is a good proportion for an average rider.

_Free-wheels._--A free-wheel clutch transmits the drive in one
direction only, allowing the pedals to remain at rest at the will of
the rider, while the bicycle runs on. With a free-wheel, chain
breakages are reduced or nearly eliminated, as should the chain get
accidentally caught the free-wheel comes into play. There are three
principal types of free-wheel clutches--roller, ratchet and friction
cone. The roller type was the earliest in use, but has fallen into
disfavour. A sectional view of a ball-bearing ratchet free-wheel, with
outer cover removed, is shown in fig. 11. The ring on which the three
pawls and springs are carried is screwed on the end of the hub; the
chain-wheel is combined with an inner ratchet wheel and is mounted by
two rows of ball bearings on the pawl ring. The friction cone type of
free-wheel clutch is usually combined with a brake inside the hub,
the whole combination being termed a coaster hub. Fig. 12 shows a
sectional view of the Eadie two-speed coaster, in which the free-wheel
clutch and brake are combined with a two-speed gear. The free-wheel
clutch action is as follows: A forward pressure of the pedals turns
the externally threaded driving cone H in the internally threaded cone
F, the latter being thus forced to the right into engagement with the
cup J which is screwed to the hub-shell, thus forming a friction
driving clutch. The pedals being held stationary the driving cone H is
stationary, and the hub running on the ball bearings G, the cone F
travels towards the left until released from the cup J, when it also
remains at rest. In this type of free-wheel clutch it is essential
that there be little or no friction between the screwed surfaces of H
and F, else on beginning to pedal, the cone F may remain stationary
relative to the driving cone H, and no engagement between F and J may
take place. If F be prevented from turning faster than the hub-shell,
as is sometimes done by a light spring between the two, the engagement
of the friction clutch must take place as soon as the pedals tend to
move faster than the speed corresponding to that of the hub-shell.

_Brakes_ of many types are used, differing in the place and mode of
application. The tire brake has fallen into disuse, rim brakes and
internal hub brakes being usual. The retarding force that can be
applied by a brake is limited by the possibility of skidding the
wheel. In riding at uniform speed, without acceleration, the greater
part of the load is on the rear-wheel; but as soon as the brake is
applied to cause retardation the wheel load distribution is altered,
more load being thrown on the front wheel. Thus the most powerful
brake is one applied to the front wheel. On the other hand, a
front-wheel brake often sets up an unpleasant vibration of the front
fork. On a greasy road too powerful pressure on the front-wheel brake
may cause a side-slip with no chance of recovery; while with the
back-wheel brake recovery is possible. The Bowden system of
transmission, which is largely used for cycle brake work, consists of
a steel stranded cable inside a flexible tube formed by a closely
wound spiral of steel wire, the cable being practically inextensible
and the spiral tube practically incompressible; if the ends of the
latter be fastened it forms a guide tube for the cable, any movement
given to one end of the cable being transmitted to the other end. The
spiral tube may be led round any corners, but the frictional
resistance of the cable inside the spiral tube increases with the
total angle of curvature of the guide tube; the laws of friction of a
rope passing over a drum apply. In fitting the Bowden system the total
curvature should therefore be kept as small as possible. With a
back-pedalling rim brake the cycle cannot be wheeled backwards unless
a special device is used to throw the operating clutch out of action.
A back-pedalling brake is most conveniently applied inside the hub, as
in the coaster hub. In the Eadie two-speed coaster (fig. 12) the
braking action is obtained by the expansion of the steel band I
against a phosphor bronze ring L carried by the rotating hub-shell.
The steel band I is mounted on a disk with a projecting arm, the end
of which is clipped to the frame tube. The expansion of the steel band
is effected by the movement of the lever K fixed to the cone E. On
moving the pedals backward the screw drive-ring H forces the cone nut
F with which it engages to the left into contact with the cone E. The
backward movement of the pedals being continued sets up the required
movement of the lever K, and applies the brake.

_Variable Speed Gears._--The effort required to propel a bicycle
varies greatly, according to the conditions of road surface, gradient
up or down hill, wind against or behind. To meet these variable
conditions, a variable speed-gear is an advantage. The action of the
human motor is, however, so entirely different from that of a
mechanical motor that it is easy, without practical experience, to
over-estimate the value of a variable speed gear. Probably from 50 in.
to 80 in. represents the greatest useful range of gear for an average
rider. With a gear lower than 50 in., the speed of climbing a steep
gradient is so slow that balancing difficulties begin, and it is
better to walk up. With 80 in. gear and 7 in. cranks, the speed of
pedalling, even at 25 miles an hour, is not irksome, provided the
conditions are favourable. For those who have not cultivated the art
of quick pedalling the useful range of gear under favourable
conditions may be extended to say 90 in. or 100 in. The gear-ratio of
a two-speed gear is the ratio of the high to the low gear. The most
suitable gear-ratio for any rider will depend upon his personal
physique and the nature of the country in which he rides. For a
middle-aged rider of average physique a gear-ratio of 125:100 is
suitable, for those of weaker physique the gear-ratio may with
advantage be greater, say 137.5:100; while for road racing it may be
smaller, say 117:100. With a three-speed gear the low and high gears
should be chosen respectively below and above the single gear which
suits the rider, the middle gear being about the same as the rider's
usual single gear.

All the variable speed gears at present made consist of toothed wheel
mechanism either at the hub or crank-bracket, and nearly all are based
on the same epicyclic train of toothed wheels. At one speed there is
no relative motion of the toothed wheels, the whole mechanism
revolving as one solid piece; this is called the "normal" speed. At
the other speed one part of the mechanism is held stationary and the
driven part revolves faster or slower than the driver, according as
the gearing is up or down. In some two-speed gears the normal is the
high speed, in others the low. In expressing the gear-ratio, the
normal speed will be denoted by 100. At the normal gear there is of
course no additional friction. The type of two-speed gear used
practically settles whether the normal gear is at high or low speed;
but it seems best, other things being equal, to have the low speed the
normal gear, as then the conditions are worst. If the high speed is at
normal gear, then at low speed the chain gears up and the two-speed
gear gears down; which is, to say the least, a roundabout
transmission.

Fig. 13 is a sectional view of the Sunbeam two-speed gear which is
arranged at the crank-axle, and clearly shows the relative disposition
of the toothed wheel mechanism common to nearly all cycle speed gears.
The chain-wheel is fixed to the annular wheel A; the planet carrier C
is fixed to the crank; and when the sun-wheel D is held stationary,
the chain-wheel is driven faster than the cranks. When the sun-wheel D
is released, the planet carrier C drives the annular wheel A by the
ratchet free-wheel clutch; the part thus revolves as a solid piece,
and gives the normal or low speed. The gear-ratio is 133.3:100.

Fig. 14 is a sectional view of the "Hub" two-speed gear, the
chain-wheel or free-wheel clutch being omitted. In this the annular
wheel is the driver, and the planet carrier is part of the hub-shell.
When the central pinion is held stationary the hub is driven at a less
speed than the chain-wheel; the gear-ratio is 100:76.2.

In the Fagan two-speed gear, shown combined with the Eadie coaster hub
in fig. 12, the sun-wheel B can be moved laterally by the striking
gear, so as to engage with the chain-wheel centre C, giving normal
gear, or with an internally toothed wheel A fixed to the spindle. The
chain-wheel centre C carries the annular wheel, and the four planet
pinions D are mounted on the driving cone H. Thus the gear gives a
reduction of speed, the gear-ratio being 100:75. The Sturmey-Archer
three-speed hub (fig. 15) has gear-ratios 125:100:80. In the high gear
position the epicyclic toothed wheels are to the extreme left
position. The chain-wheel is mounted by a free-wheel on a drive-ring,
with which the ends of the spindles of the planet wheels engage at
high gear. The sun-wheel, not shown in the figure, is held stationary,
and the annular wheel engages with a ring screwed to the hub-shell, by
means of keys engaging in notches. The hub is thus driven at a higher
speed than the chain-wheel. For normal gear, the striking gear draws
the internal mechanism of the hub towards a central position,
compressing a spring, disengaging the sun-wheel and locking the
drive-ring hub and annular wheel together. At low gear, the internal
mechanism is drawn to the right-hand side, where the planet carrier
engages with the end plate of the hub by means of claw-clutches. The
annular wheel is still engaged with the drive-ring, and the sun-wheel
is again locked to the spindle. The hub is thus driven at a lower
speed.

_Tandem Bicycles._--The weight of a roadster tandem is about the same
as, or a trifle less than, that of two single roadster bicycles, but
the frictional resistance of the mechanism, the rolling resistance of
the tires, and the air resistance at a given speed are much less than
twice the values for a single bicycle. Consequently, much higher
speeds are attained on the level, and free-wheeling down hill is much
faster. On the other hand for riding up hill on a moderate gradient,
the effort required is about the same as on a single, while on very
steep gradients the tandem is at a slight disadvantage. For the full
enjoyment of tandem riding, therefore, a two-speed gear is a
necessity, while a three-speed gear is better. In the Raleigh tandem
(fig. 16) the frame design is such that it can be ridden by two
ladies, and the strength and rigidity is sufficient for two
heavyweight riders. The steering and control of the brakes is done by
the front rider. Connected steering is employed in some tandems,
allowing the rear rider to steer if necessary. For two expert tandem
riders, connected steering is slightly more pleasurable than fixed
handle grips for the rear rider, but on the other hand, divided
control may lead to disaster at a critical moment. Most passengers on
a tandem with connected steering unconsciously give the steering a
bias in one direction or the other, putting a nervous strain on the
steersman which becomes almost intolerable towards the end of a long
ride.

_Motor Bicycles._--Fig. 17 shows a touring motor bicycle, fitted with
luggage carrier and stand, the latter for supporting the bicycle while
at rest. The average speed of a motor bicycle being much greater than
that of a pedal bicycle the stresses on the frame due to moving over
rough roads are greater. This necessitates greater strength and weight
in all parts--frame, wheels and tires. To take this increased weight
up steep gradients requires increased engine power. The weight of a
touring motor bicycle may be from 150 to 200 lb. The drive is usually
by a V belt of leather, or of canvas and rubber, the angle of the V
being 28 deg.. The engine speed at maximum power is from 1500 to 2000
revolutions a minute, and the belt gears down in a ratio varying
between 1/3 and 1/6 according to the cylinder capacity of the engine.
The possibility of the belt slipping slightly is conducive to
smoothness of drive; chain-driving, except in combination with a
slipping clutch, is too harsh. The principal defect of the belt drive
is that the belt stretches, and on coming to a steep hill may have to
be tightened before the bicycle can be driven up. The control of the
speed and power of the engine is effected by the throttle, extra air
valve and spark advance, the levers for which are all placed within
convenient reach of the driver. As the engine is almost invariably
air-cooled, the skilful manipulation of these three levers is
essential for satisfactory results. On a good level road when the
engine may be working at a small fraction of its maximum power, the
proportion of air mixed with the petrol vapour from the carburettor
may be great, giving a "weak" mixture, yet one rich enough to be
ignited in the cylinder. The throttle valve may be fully open and the
spark advanced for high speed; the throttle partially closed and spark
retarded for slow speed. Under these conditions the engine will run
for an indefinite period without overheating. Up a steep gradient, the
mixture may have to be made "richer" by partial closing of the extra
air opening, and as more heat is evolved, the cylinder walls may
become overheated, unless the engine power is sufficient to keep the
bicycle moving through the air at a good speed. As the engine cannot
run steadily at low speed, pedalling is resorted to for starting and
for riding slowly through traffic. For this purpose, an "exhaust valve
lifter" is usually fitted, by means of which the exhaust can be kept
permanently open, in order to relieve the resistance to pedalling
which the compression stroke would otherwise offer.

The nominal rating of the horse-power of a motor cycle engine is
rather vague and indefinite. A 3-H.P. engine may have a cylinder of
76-80 mm. diameter and 76-80 mm. stroke. Twin-cylinder engines, with
one crank, are largely used, and some excellent 4-cylinder motor
bicycles are made with bevel gear transmission. The chief advantage of
the multicylinder engine is the smoother drive obtained.

A "trailer" with two wheels for carrying a passenger can be attached
to a motor bicycle, but the element of risk is increased. A side-car,
with one additional wheel, forms a safer passenger carrier.
(A. Sp.)

BIDA, a town and administrative district in the British protectorate of Northern Nigeria. Bida town, situated in 9 deg. 5' N., 6 deg. E., 25 m. N. by E. of Muraji on the Niger, is the capital of the province of Nupe. It was founded in 1859 when Fula rule was established in Nupe, is walled and of considerable size. In 1909 it was connected by railway with Baro, 40 m. S.S.E., the river terminus of the Northern Nigeria railway. The inhabitants, mostly Hausa, carry on an extensive trade and are especially noted for their embossed brass and copper work. The Bida goblets, in which brass and copper are beautifully blended, are of extremely elegant design. The town also boasts a glass factory. The preparation of indigo and the dyeing of cloths are other flourishing industries. The streets are planted with huge shade-trees, so that as Bida is approached it looks like a forest.

In 1897 there was a two-days' fight outside the walls of Bida between the forces of the emir of Nupe and those of the Royal Niger Company, ending in the defeat of the Fula army (mostly cavalry). The victory was not followed at the time by a British occupation, and the defeated king returned after the withdrawal of the company's troops and re-established himself upon the throne. In 1900 he allied himself with other hostile chiefs and adopted an openly antagonistic attitude to the British government. In 1901 it became necessary for British troops to march on Bida. The emir fled, without fighting, to Kano. Another emir was appointed in his place, and the province of Nupe was placed under British administrative control. Since that date the town has been peaceful and very prosperous. A mission school has been established, and is attended by the sons of the emir and of the principal chiefs, who are desirous of learning to read and write English. The administrative district of Bida includes the town and is the western division of the province of Nupe (q.v.). (See also NIGERIA: _History_.)

BIDDEFORD, a city of York county, Maine, U.S.A., on the Saco river, opposite Saco, and on the Atlantic Ocean, 15 m. S.W. of Portland. Pop. (1890) 14,443; (1900) 16,145, of whom 7,149 were foreign-born (mostly French Canadians); (census, 1910) 17,079. Biddeford is served by the Boston & Maine railway, and is connected by electric lines with Portland and with Old Orchard Beach, a popular summer resort north of the Saco river. The climate and the scenery in and about Biddeford attract summer visitors and there are two resorts, Biddeford Pool and Fortune Rocks within the municipal limits; but the city is chiefly a manufacturing centre (third in rank among the cities of the state in 1905)--good water-power being furnished by the river--and cotton goods, foundry and machine shop products and lumber are the principal products, the first being by far the most important. The value of the factory products increased from $5,472,254 in 1900 to $6,948,722 in 1905, or 27%. There are large quarries of granite of excellent quality. A permanent settlement was established on both sides of the river about 1630 under the leadership of Richard Vines (1585-1651) and was named Saco. In 1718 the present name was adopted. In 1762 that portion of Biddeford which lay east of the river was incorporated as the town of Pepperellborough, for which name Saco was substituted in 1805. Biddeford was incorporated as a city in 1855.

BIDDER, GEORGE PARKER (1806-1878), English engineer, was born at Moreton Hampstead, in Devonshire, on the 14th of June 1806. From a very early age he manifested an extraordinary natural aptitude for calculation, which induced his father, who was a stone-mason, to exhibit him as a "calculating boy." In this way his talent was turned to profitable account, but his general education was in danger of being completely neglected. Interest, however, was taken in him by some of those who happened to witness his performances, among them being Sir John Herschel, and it was arranged that he should be sent to school in Camberwell. There he did not remain long, being removed by his father, who wished to exhibit him again, but he was saved from this misfortune and enabled to attend classes at Edinburgh University, largely through the kindness of Sir Henry Jardine, to whom he subsequently showed his gratitude by founding a "Jardine Bursary" at the university. On leaving college in 1824 he received a post in the ordnance survey, but gradually drifted into engineering work. In 1834 Robert Stephenson, whose acquaintance he had made in Edinburgh, offered him an appointment on the London & Birmingham railway, and in the succeeding year or two he began to assist George Stephenson in his parliamentary work, which at that time included schemes for railways between London and Brighton and between Manchester and Rugby via the Potteries. In this way he was introduced to engineering and parliamentary practice at a period of great activity which saw the establishment of the main features and principles that have since governed English railway construction. He is said to have been the best witness that ever entered a committee-room. He was quick to discover and take advantage of the weak points in an opponent's case, and his powers of mental calculation frequently stood him in good stead, as when, for example, an apparently casual glance at the plans of a railway enabled him to point out errors in the engineering data that were sufficient to secure rejection of the scheme to which he was opposed. In consequence there was scarcely an engineering proposal of any importance brought before parliament in connexion with which his services were not secured by one party or the other.