war

oj

m
3-

O

HJ

o
m

o

MANUALS

FOR

STUDENTS OF MEDICINE.

THE ELEMENTS

OF

PHYSIOLOGICAL PHYSICS:

AN OUTLINE OF THE ELEMENTARY FACTS,

PRINCIPLES, AND METHODS OF PHYSICS; AND

THEIR APPLICATIONS IN PHYSIOLOGY,

BY

J. M'GREGOR-EOBEKTSON,

M.A., M.B., C.M.,

3IUIRHEAD DEMONSTRATOR OF PHYSIOLOGY, AND ASSISTANT TO THE
PROFESSOR OF PHYSIOLOGY IN THE UNIVERSITY OF GLASGOW.

ILLUSTRATED WITH 219 ENGRAVINGS ON WOOD.

PHILADELPHIA :
HENRY C. LEA'S SON & CO.

1884.

/ 0 + (o

HENRY MTJIRHEAD, M.D.,

President of the Philosophical Society of Glasgow, and .Ex-President
of the Faculty of Physicians and Surgeons,

THIS BOOK IS DEDICATED,
AS A TRIBUTE TO GENEROUS ENTHUSIASM FOR SCIENCE.

PEE FACE.

THE modern development of Physiology has been
largely due to the application to this branch of science
of physical and chemical principles and laws. Physics
and chemistry are now constantly appealed to for aid
in working out physiological problems ; and the
physiologist finds himself continually resorting to
physical methods and apparatus, both for purposes of
illustration and research. In some respects, therefore,
the study and the teaching of Physiology have become
increasingly difficult because of the broadening of its
relations with other sciences.

In the teaching of the subject at the University of
Glasgow the want has been felt of a small text-book
for students, in which the elementary facts and prin-
ciples of physics might be given together with their
physiological applications, and in which might be in-
cluded some detailed description of physical apparatus
and methods as adapted to physiological purposes.
To meet this want to some extent, a series of weekly
demonstrations was given by me to the students
attending the class during the winter months ; and
one of the results of that series is this text-book.

viii PHYSIOLOGICAL PHYSICS.

The method followed has been to take up one branch
of physics after another, to state as briefly as possible
the main elementary facts and principles of each branch,
to describe such apparatus as seemed desirable, and
then to note the physiological application of the facts
and adaptations cf the instruments. The subject of
electricity and magnetism lent itself most readily to
this method, and seemed of special importance in view
of the great development of electro-physiology and
therapeutics. This accordingly was the first to be
considered. The experiments described in this section
are all those which it has been customary to employ
here in illustration of the part of the course devoted
to the physiology of muscle and nerve. An effort has
been made so to describe them that the student might
take the book to the laboratory, and, with its aid, set
up and work out the experiments for himself. For this
purpose a considerable number of diagrams, showing
arrangements of apparatus, has been introduced. In
this respect the book differs considerably from Wundt's
Traite Elemeniaire de Physique Medicale or Grehant's
Manuel de Physique Medicale. to both of which, and
to the former especially, I have to acknowledge my
great indebtedness.

To many other works I have to express my obliga-
tions : among them, to Du Bois-Reymond's Abhand-
lungen, etc., Morgan's Electro-Physiology and Thera-
peutics, Rosen thal's Electricitdts-lehre fur Mediciner,

PREFACE. ix

Gscheidleii's Physiologisclie Metliodik, and Cyon's
Methodik der Physiologischen Experimente.

Most of the woodcuts have been prepared by
Mr. Stephen Miller, of Glasgow, whom I have to
thank for the carefulness and accuracy of their
execution.

I must also express my gratitude to Mr. Andrew
Gray, now Professor of Natural Philosophy in the
University College of North Wales, who very kindly
read the first part of the book, and suggested altera-
tions.

I am conscious that the book as finished does not
reach even the level of my own hopes. I trust that,
at least, no errors or inaccuracies have been over-
looked in the revision.

J. M'G. K

Physiological Laboratory,

University ) September, 1884.

CONTENTS.

PART I.-ELECTRICITY AND MAGNETISM, AND THEIR
APPLICATIONS IN PHYSIOLOGY AND MEDICINE.

CHAPTER PAGE

I.— FRICTIONAL ELECTRICITY 1

II.— CURRENT ELECTRICITY 13

III.— RESISTANCE— OHM'S LAW— MODES OF JOINING

CELLS 26

IV.— INDUCTION AND INDUCTION COILS . . 34
V.— EFFECTS OF THE ELECTRICAL CURRENT . . 50
VI.— KEYS, COMMUTATORS, AND ELECTRODES FOR PHY-
SIOLOGICAL PURPOSES .54

VII.— EXPERIMENTS ON MUSCLE AND NERVE STIMULA-
TION ,62

VIII.— ELECTROTONUS .77

IX.— MAGNETS, AND THE ACTION ON THEM OF ELECTRIC

CURRENTS ... . .90

X.— GALVANOMETERS . . . .96

XI.— THE USE OF THE GALVANOMETER IN PHYSIOLOGY 110
XII.— THE GALVANOMETER AS A MEASURER OF TIME . 128
XIII.— RESISTANCES AND THEIR MEASUREMENT. . . 134
XIV.— THERMO-ELECTRIC CURRENTS . . 112

XV.— PHYSIOLOGICAL INDICATIONS FOR THE THERAPEU-
TICAL APPLICATIONS OF ELECTRICITY . . .148

PART II.— THE GRAPHIC METHOD.

XVI.— THE MEASUREMENT OF SMALL INTERVALS OF

TIME 170

XVIL— THE MYOGRAPHION 175

XVIII.— THE TRANSMISSION OF MOVEMENT .... 184

CONTENTS. xi

PART III.-FLUIDS AT REST AND IN MOTION: THE
MECHANICS OF THE CIRCULATION.

CHAPTER PAGE

XIX.— HYDROSTATICS . . .188

XX.— HYDRODYNAMICS— FLUIDS IN MOTION . 207

XXI.— THE MECHANICS OF THE CIRCULATION . . 222
XXII.— CAPILLARITY, DIFFUSION OF LIQUIDS, AND
OSMOSIS ; THEIR APPLICATION TO THE PHY-
SIOLOGY OF ABSORPTION AND SECRETION . 239

PART IV.— PNEUMATICS.

XXIII.— THE PHYSICS OF GASES AND THEIR APPLICA-
TION IN RESPIRATION . . . .270

PART V.-OPT1CS.

XXFV.— LIGHT : REFLECTION AND REFRACTION . . 296

XXV.— THE ACTION OF PRISMS AND LENSES . . .311

XXVI.— ANALYSIS OF LIGHT : COLOUR . . . .319

XX VII.— ABERRATIONS OF LENSES 344

XXVIII.— OPTICAL INSTRUMENTS 349

XXIX.— THE EYE AS AN OPTICAL INSTRUMENT . . 374
XXX — DOUBLE REFRACTION, POLARISATION, AND IN-
TERFERENCE OF LIGHT 397

PART VI.— SOUND.

XXXI.— SOUND: ITS NATURE, REFLECTION, AND RE-
FRACTION . 417

XXXH.— MUSICAL SOUND ... . . .423

XXXIIL— SYMPATHETIC VIBRATION AND RESONANCE . 439

PART VII.-HEAT.

XXXIV. —THE NATURE AND SOURCES OF HEAT . . .451
XXXV.— CONDUCTION, CONVECTION, AND RADIATION OF

HEAT . . 456

xii PHYSIOLOGICAL PHYSICS.

CHAPTER PA«E

XXXVI.— THERMOMETRY .

XXXVII.— CHANGES OF STATE PRODUCED BY HEAT . . 470

XXXVIII.— SPECIFIC HEAT: CALORIMETRY . . 476

XXXIX.-ANiMAL HEAT 481

PART VIII.-DYNAMICS.

XL.— MATTER AND FORCE . .485

XLL— THE LEVER, PULLEY, AND BALANCE . . 494

XLH.-GRAVITY .... 500

XLIIL— ANIMAL MECHANICS 507

INDEX . , . « . 515

ELEMENTS

OP

PHYSIOLOGICAL PHYSICS.

tfart IF.

ELECTRICITY AND MAGNETISM AND THEIR APPLI-
CATIONS IN PHYSIOLOGY AND MEDICINE.

CHAPTER I.

FRICTIONAL ELECTRICITY.

THERE are three principal methods of developing
electricity. The first method is by friction, the
second by chemical action, and the third by the action
of magnets. The electricity obtained by the first of
these methods, which is the subject of this chapter, is
called therefore Fractional Electricity.

It was known to the ancients that amber, when
rubbed with silk, possessed the property of attracting
light bodies ; but it was not till near the close of the
sixteenth century that an English physician, Dr.
Gilbert, showed that other bodies possessed similar
properties.

Take a small ball of some very light material,
like pith, and suspend it, by means of a silk thread,
from a glass support (Fig. 1). If now a stick of
resin or sealing-wax be rubbed vigorously with cat-
skin or flannel, and then brought near to the pith
B-7

PHYSIOLOGICAL PHYSICS.

[Chap. I.

Fig. 1.— The Electric
Pendulum.

ball, the ball will be attracted towards the wax. If
the pith be allowed to touch the wax, it will remain
in contact for only an instant, and will then
be repelled. Similarly, if a rod of polished glass

^ be rubbed with silk, and then

brought near to a pith ball, the
ball will be attracted till contact
is made ; thereafter it will be re-
pelled.

By the friction the sealing-wax
and the glass rod became elec-
trified, and attracted the unelec-
trified pith ball. As soon as the
ball touched the electrified body it
received itself a charge of elec-
tricity, and was then immediately
repelled.

Now let the glass rod be brought near to the
pith ball, which has received a charge from the sealing-
wax, and been consequently repelled by it, and it will
be attracted by the glass. Or, let a pith ball receive
a charge from an electrified glass rod, it will be
immediately repelled by the glass, but will now be
attracted by an electrified rod of wax. Thus there
seem to be two kinds of electricity, one generated on
smooth glass by friction, and hence called vitreous
electricity, and another generated on wax or resin by
friction, and hence called resinous electricity. But,
further, the above experiments show that a pith ball
charged with the same electricity as a rod of wax is
repelled by the wax, but is attracted by electrified
glass ; and similarly, that a pith ball charged with
vitreous electricity is repelled by the glass rod, but
attracted by the wax. In other words, bodies charged
with like electricities repel one another, and bodies
charged with unlike electricities attract one another.
The two-fluid theory, or the theory which

Chap, i.] THEORIES OF ELECTRICITY. 3

supposes that there are two kinds of electricity, is due
to the French academician, Dufay, and was afterwards
worked out by Robert Symmer. It supposes that
all bodies have a certain amount of both, which
equalise one another, so that the body appears im-
electrified. The body may, however, gain an excess
of one of the fluids, and as the total amount is always
the same, it loses a corresponding quantity of the
other, and then appears electrified by the fluid which
is in excess.

Neutralisation of one electricity by the other may
be shown by touching a pith-ball, previously charged
from a glass rod, by an electrified stick of resin. The
ball at once ceases to be electrified.

The one-fluid tlieory supposes only one kind of
electricity, of which all unelectrified bodies have a
normal amount. Bodies may, however, be caused to
have more than the normal amount when they are
said to be positively electrified ; or they may have less
than the normal amount when they are negatively
electrified. This is the theory propounded by
Franklin in 1747.

On both theories the fluids, or fluid, are mobile and
imponderable, and permeate all ponderable matter.

Franklin's phraseology is generally adopted, though
not his theory, positive and negative being convenient
terms for designating the electrical state of bodies.

o o

Positive is equivalent to vitreous, and negative to
resinous, the one being often signified by the sign + ,
and the other by the sign — .

When the glass becomes positively electrified by
friction, the rubber is found to be negatively electrified ;
and while the resin is negatively electrified, the skin
with which it is rubbed is positively electrified. This
is often difficult to show, because the electricity of the
rubber may be conducted away through the body to
the ground.

4 PHYSIOLOGICAL PHYSICS. ichap. i.

The nature of the electricity developed by friction
depends on the rubber as well as on the nature of the
thing rubbed. Glass receives a positive charge when
rubbed with silk, but a negative charge when rubbed
with cat-skin. Thus the same body may be either
positively or negatively electrified.

Idioelectrics and anelectrics. — It was at
first supposed that only certain bodies, like resin,
shellac, wax, sulphur, guttapercha, leather, glass, silk,
etc., could be electrified, and they were called idio-
electrics. Metals, carbon or coal, water, watery saline
solutions, etc., could not, it was believed, be electrified,
and they were, therefore, called anelectrics.

Non-conductors and conductors are the
terms now used which correspond to idioelectrics and
anelectrics. They indicate the real facts. Idio-
electrics are really bodies which retain the electricity
with which they are charged at the place where it has
been received. Thus only the part of the glass or wax
that has been rubbed is electrified. In other words,
the electricity is not diffused over the surface of glass
or wax because they are non-conductors. Anelectrics
can be electrified ; but, as soon as the electricity has
been generated, it is conducted away over the whole
surface of the body, and thus becomes dissipated.
Even the term " non-conductor " is not strictly accu-
rate, because no body is an absolute non-conductor.
Some bodies, however, conduct very badly, and they
retain the electricity ; other bodies conduct very well,
and therefore electricity disappears as soon as it is
developed on the surface. Suppose, however, a bar of
metal is united to a bad conductor, say a rod of glass.
If then the metal, held by its glass support, be rubbed
vigorously, electricity will be produced, and will diffuse
itself over the whole metal surface; but the intervention
of the glass rod will prevent further escape, and the
usual signs of electrification will then be obtained.

Chap, i.] LAWS OF ELECTRICAL ATTRACTION. 5

A bad conductor, when united in this way to a good con-
ductor to prevent the escape of the electricity, is called
an INSULATOR. The best conductors are the metals,
and following them are carbon, plumbago, acids, saline
solutions, animal fluids, water, animal and vegetable
tissues, and moist stones and earth. The best insulators
(bad or non-conductors) are shellac, amber, resins, wax,
glass, ebonite, guttapercha, silk, wool, feathers, porce-
lain, paper, oils, dry air, and wood. The human body is
a good conductor, dry air a bad one. It is difficult to
perform electrical experiments in an atmosphere con-
taining aqueous vapour, because a film of moisture is
deposited on the insulating supports of the apparatus,
rendering the insulation imperfect : hence the benefit in
damp weather of heating the apparatus just before use.

It is also in virtue of the fluid which it contains
that the human body is a conductor, water being a
good conductor. A charged body in a current of air
slowly loses its electricity by convection. Particles of
the air coming in contact with the body receive a
charge, and pass on, to be succeeded by other particles,
each of which also carries off its portion, till the whole
charge is thus dissipated.

The laws of electrical attraction and re-
pulsion are as follows :

(1) Like electricities repel one another.

(2) Unlike electricities attract one another.

(3) The force of attraction or repulsion varies
inversely as the square of the distance between the
two electrified bodies, and directly as the amount of
charge of the two bodies.

Electricity accumulated solely on tlie sur-
face of conductors. — If the body have a spherical
surface, the electrical layer is equal at all points of
the surface ; that is, is of uniform DENSITY, density
being the thickness of the layer of electricity. If,
however, the conductor be an ellipsoid, the electricity

PHYSIOLOGICAL PHYSICS

[Chap. I.

accumulates in greater amount at the pointed ex-
tremities. Suppose one of these ends to be extremely
pointed, then the accumulation may be so great that
the electricity tends to pass off from the conductor '
into the atmosphere. In other words, the TENSION at
that point will be considerable.

Induction is the term applied to the influence
exerted by electrified upon uiielectrified bodies.
Suppose two conductors (Fig. 2) s and AB, both in-
sulated by being
mounted on glass
stands, to be
brought near to
one another, s
having received
a charge of posi-
tive electricity,
and AB being un-
charged. Suppose
AB to have attach-
ed to it three

ELECTROSCOPES

Fig. 2.— Induction.

a d b. They consist of a metallic stem fixed by
metallic contact to the conductor ; and from the upper
end of each stem there hangs a pith-ball suspended
by a linen thread. When AB is unelectrified, the
pith-balls are in contact with the stems from which
they hang. Should the conductor become charged,
the pith-balls will also become charged by contact, .and
since, then, the stem and the pith-ball are charged
with similar electricity, they will repel one another.
The divergence of the pith-ball, therefore, indicates that
the conductor has received a charge. The conductor,
being charged, is brought into the neighbourhood of
AB uncharged. At once the electroscopes indicate
the electrification of AB. Remove s, and the signs of
AB'S electrification disappear ; again bring s near,

chap. I.] GOLD-LEAF ELECTROSCOPE. 7

they reappear. That is to say, the charged conductor
s has by its influence decomposed the neutral elec-
tricity of AB. Since unlike electricities attract, s being
charged positively, negative electricity will be at-
tracted to the end A, while the negative electricity of
AB will be repelled to the end B. At a place near the
centre there will be a neutral zone. The neutral zone
will be on the A side of the centre, because, owing to
the difference of distance, negative electricity will be
more strongly attracted towards A than positive re-
pelled to B. As soon as the influence of B is removed,
the separated electricities re-combine. This pheno-
menon is called induction, or electrification by in-
fluence. If, while s is in the neighbourhood of AB,
connection between the earth and AB be made, say
by touching AB with the finger, the repelled electricity
( + ), being free, will escape. The negative electricity
will remain attracted, and the pith-balls will collapse,
indicating the absence of free electricity. If now,
AB being again insulated, s be removed, the bound
electricity will become free, and the pith-balls will
again diverge. AB will thus have received by in-
duction a charge of negative electricity.

It is by induction that an electrified body attracts
one unelectrified. It induces opposite electricity to
its own on the end near to it, and the two unlike elec-
tricities attract one another. The similar electricity is
repelled to the end farthest from the electrified body ;
and as the repellent force has thus to act through a
greater distance, the attractive power has the advantage.

The gold-leaf electroscope, for indicating the
presence and kind of electricity in any body, has been
constructed by taking advantage of the fact of induc-
tion. It consists of a metallic stem BB (Fig. 3), from
one end of which hang, parallel to one another, two
very fine gold leaves a b. The other end terminates
in a metallic knob. The rod is fixed in the tube of a

8

PHYSIOLOGICAL PHYSICS.

[Chap. I.

glass shade, which rests on a metallic support. It is
used in the following way : If a charged body be
brought near, by induction the neutral fluid of the rod
and leaves is decomposed, and the kind of electricity
opposite to that of the charged body is
driven into the leaves, which diverge.
This shows that the body brought near
is charged. In this condition touch
the knob B with a finger, contact is
made with the ground and the free
electricity (i.e. that of the leaves)
escapes, and the leaves collapse.

Now remove the finger from
the knob, and take away next
the charged body. The electricity

Fig. 3.— Gold-leaf. , i j i, AI * ^

Electroscope. kept bound by the presence of the
charged body, and of the opposite
kind to it, is now free, and diffuses itself over
the knob, rod, and leaves, which last again diverge.
To discover with what kind of electricity the inducing
body was charged, bring an electrified glass rod ( + )
near the knob. If the leaves diverge still more,
because like electricities repel, it is positive electricity
that is in the electroscope, and then it must have
been electricity of the opposite kind ( — ) with which
the body was charged. It is necessary to approach
the glass rod (or resin, if it be used) slowly, and to
accept the first movement made by the leaves as the
required indication.

Electrical machines. — The ELECTROPHORUS
(Fig. 4) is also an instrument acting by induction.
It consists of a cake of resin or ebonite, etc., B, fitted
into a metallic mould, and of a metal disc A smaller
than B, so as to rest upon it, and provided with an
insulating handle of glass. The resin, having been
warmed, is beaten with a cat-skin, which develops
electricity. The metal disc, called the cover, is then

Chap. I.]

FRICTIONAL MACHINES.

placed on the resin, which, owing to its non-con-
ductivity, is still able to retain its charge. It,
however, by induction, decomposes the neutral elec-
tricity of the cover, and attracts positive electricity to
the surface of the cover in contact with it, repelling
negative to the upper
surface. The elec-
tricity of the upper
surface can now be
withdrawn by touch-
ing it with the finger.
If, then, the cover be
lifted by its glass
handle, it is found
to have a charge of
-f- electricity which
will give a consider-
able spark. The
process can then be
repeated, because the
resin retains its
negative charge for a
long time.

Frictional machines are constructed usually
of discs of glass, which are caused to revolve by a
handle, and in their revolution are rubbed by cushions
pushed against them. The friction develops +
electricity on the glass and — electricity on the
rubber. A chain leads from the cushion to conduct
off the negative electricity into the earth. Metallic
points, brought near to the surface of the glass,
conduct off its positive charge to large metal cylinders,
called the prime conductors. The conductors are
insulated, and soon become highly charged with the
electricity developed by the friction. The rubbers are
usually coated with an amalgam.

In Holtz' machine (Fig. />) the electricity is

Fig. 4.— Electropliorus.

TO PHYSIOLOGICAL PHYSICS. [Chap. i.

developed by induction. A and B are two plates of
glass distant three millimetres from one another ;
A is fixed, and B is movable on an axis revolved by
pulleys with great speed. In A are two oval windows,
at the extremities of the same diameter, represented

Fig. 5. — Holtz' Electrical Machine.

unshaded in the figure. On the back of A, under the
window of one side, and above that of the other, is
pasted a piece of paper f f, called an armature,
from which a tongue of cardboard projects through the
window towards plate B. The glass plates, paper, and
tongues, are covered with a coating of shellac varnish.

O ' O

Opposite each armature, but separated from it by the
revolving plate B, is a row of brass points connected
with an insulated conductor. To work the machine
one armature is electrified by excited vulcanite or

chap, i.] CONDENSERS. 1 1

sealing wax, and the discharging rods n m connected
with the conductors, are brought into contact. This
armature induces positive electricity on the surface of
the glass plate next to it, and negative electricity on
the surface opposite the brass points. The — elec-
tricity of the glass causes the brass points to discharge
+ electricity on to the glass, and so to become nega-
tively charged. The glass plate is now turned, and,
when the part positively charged from the brass
points comes opposite the second armature, it charges
it positively, and induces the opposite brass points to
discharge — electricity and to remain positively
charged. The portion of the plate, now negatively
charged, still being revolved, returns to the first
armature, increases its - - charge, and so heightens its
inductive action. The knobs n in in connection with
the brass points, are thus charged, the one with -+-
the other with — electricity. On the knobs being
separated, and the plate rapidly turned, a series of
sparks dart across from one knob to the other.

Condensers are instruments for concentrating
a large quantity of electricity on a small surface, an
action also effected by induction. The Leyden jar is
the best example. It consists of a
glass jar or bottle, coated inside
and outside with tinfoil, up to a
few inches from the neck. The
mouth is stopped with a cork or
a plug of hard wood, in which is
fixed a metal rod, terminating out-
side in a knob, and having a
chain hanging from it inside Fig. 6.-Leyden Jar.
and touching the inner li.iing
of tinfoil. The jar is charged by connecting the
outer coat with the ground, as, also, by holding it so
that the hand touches that coating, and presenting the
knob to the conductor of a friction machine. If the

12 PHYSIOLOGICAL PHYSICS. [Chap. i.

knob receive positive electricity, the inner coating will
be positively charged. Acting inductively through
the glass, it will decompose the neutral electricity of the
outer coat, repel the positive through the hand to the
ground, and attract the negative. The presence of
this negative electricity on the outer coat will allow
more positive to be given to the inner coat, which in
its turn will attract more negative to the outer, and
so on. Thus, in virtue of the inductive action of
the two coats on one another through the glass jar,
a much greater charge can be accumulated than on
any one coating beyond the influence of the other.
To discharge the jar at once it is only necessary to
connect the two coatings by the discharger, as shown
in the figure. To discharge the jar slowly, insulate it
it by placing it 011 a stool with glass legs, then touch
with the finger first the outer coating and then the
knob. At each touch a slight spark is seen. This
may be continued for some time before the charge is
dissipated. The jar was first made in the town of
Leyclen, its discovery being due to Cuneus, a pupil of
Muschenbroeck. It is also called Kleist's jar. Kleist
was a prebendary of Cammin, in Pomerariia, and is
said to have invented the jar independently of
Cuneus, and a year before him, viz. in 1745. A
shock may be given from a charged jar to several
people if they join hands and if the last one touches
the outer coating while the first one seizes the knob.

An electric battery may be formed by placing
a number of Ley den jars in a box lined with tinfoil,
so that their outer coatings are in contact. The tin-
foil should be in metallic contact with fche metallic
handle of the box, from which a chain should pass to
the water-pipes of the house to give a good earth
connection. The knobs of the jars are all connected
by brass rods. The battery can then be charged from
the conductor of a frictional machine.

CHAPTER II.

CURRENT ELECTRICITY.

Potential. — When two metals are placed in con-
tact there ensues a disturbance of their electrical
equilibrium. This disturbance is called a " difference
of potential." Thus, when zinc is placed in contact
with copper, or silver, or platinum, etc. , this difference
results, the zinc being at the higher potential, and the
copper, silver, or platinum at the lower. " Potential "
may be compared to "level." Water at a high level
inevitably tends to seek the lowest level ; and, con-
sequently, if it can find a channel, there will ensue a
flow until the place of zero has been reached. While
the water is at the high level it has the power of per-
forming work, i.e. it has "potential." In passing
from the higher to the lower level the water may per-
form work, but when it reaches the lowest level it has
lost all power of doing work, and is at zero of potential.
Similarly when two bodies have different electric
potentials, or two parts of the same body are at
different potentials, there is a tendency for a move-
ment from, the place of high to that of lower potential.
This movement is the so-called electric current, and it
is for the purpose of bringing both bodies to the same
potential. In the passage from a higher to a lower
potential work can be done. In fact, the " difference
of potential" is estimated by the amount of work
done in carrying each unit of electricity from the one
position to the other. It is necessary to observe that
though the phrase " current of electricity" and the
simile of water at different levels, have been used, they
are not meant to imply an actual transference of

PHYSIOLOGICAL PHYSICS.

[Chap. II.

particles from one place to another. These are simply
ways of representing to the mind what is yet not
thoroughly understood, and what, in the present state
of our knowledge regarding electricity, would not
without them be readily understood.

Voltaic pile. — Up to the year 1800 there was no
method, apart from friction, for the
development of el ectricity . In 1 7 9 1
Galvani of Bologna had announced
his theory of animal electricity, based
on his discovery that when, by means
of a metallic arc made half of copper
and half of zinc, a circuit was esta-
blished between the lumbar nerves of
a newly killed frog and the crural
muscles, contraction of the muscles
resulted. Volta of Pa via rejected
Galvam's explanation, and asserted
the contractions to be caused by
stimulation, due to the development
of electricity by contact of dissimilar
metals, the moist tissues of the frog-
affording merely a means of com-
pleting the circuit. In proof of his
view Volta constructed the VOLTAIC
PILE (Fig. 7). It is formed of a
series of discs of copper and zinc,
supported on an insulating column
of glass. The lowest disc is of
copper, above it is a disc of zinc,
then a disc of cloth moistened with
acidulated water or salt solution.
Fig. 7,— Voltaic Pile. Following in the same order are

alternate discs of copper and zinc,
succeeded by the layer of moist cloth, to any number
that pleases, the topmost disc being of zinc in contact
with a disc of copper. The whole pillar is supported

chap, ii.] VOLTAIC PILE. 15

in a frame. The lower end of the pile Volta showed
to be charged with negative, the upper with positive
electricity.

A copper wire is attached to the lower copper and
another to the upper zinc. These form the two poles
of the pile. On connecting them there is a flow of elec-
tricity through the wires. Volta believed the difference
of potential causing the current to be due to the con-
tact between the zinc and the copper, the moist cloth
playing no essential part in the process, but simply
acting as a conductor. It soon became evident that
the disengagement of electricity in the pile was not
due only to the contact between the lower copper disc
and the zinc above it, but also to chemical action, due to
the presence of the moist cloth between the zinc on one
side and the copper on the other, the acid or saline solu-
tion of the cloth attacking the copper and zinc unequally.
Thus, in the pile as originally constructed by Volta (in
which, beginning from below, there is a disc of copper
and then of zinc followed by moist cloth and again
copper) there is no need for the lowermost copper,
which acts merely as a conductor, the actual begin-
ning of the pile being at the second disc, viz. the
zinc. Similarly at the top of the original pile (which,
beginning from above, is as follows : zinc, copper,
moist cloth, zinc) it is evident that the copper, cloth,
and zinc form the last of the series of which the
pile is made, and that, therefore, the topmost zinc, is
useless. Thus, beginning from the insulating column
of glass the pile would consist of zinc, moistened
cloth, copper, zinc, moistened cloth, copper, in regular'
order to the top, the lowest disc being zinc, the
uppermost copper. The lower part would then be
charged with - , the upper with + electricity, and a
wire from the last zinc would be the negative pole,
one from the top copper the positive.

Naturally enough the view that the development

i6

PHYSIOLOGICAL PHYSICS.

[Chap. II.

of electricity in the voltaic pile was due to the unequal
action of a chemical agent on two dissimilar metals
gave rise to the voltaic element.

Voltaic couple, element, or cell. — (Fig. 8.)
A plate of zinc z and one of copper c are plunged
into a vessel, three-fourths filled with diluted sul-
phuric acid L (1 acid to 7 water). The metals must
not touch one another. The sulphuric acid acts upon
the zinc, producing sulphate of zinc and liberating
hydrogen, as expressed in the formula

Zn + H.2iSo4 = ZnSo4 + H2.

The hydrogen collects in bubbles on the copper plate.
With such a combination it is found that the zinc

plate is at a higher potential than
the copper; but, so long as the
metals remain unconnected, no cur-
rent is present. On connecting the
parts of the plates projecting above
the liquid, which are called the POLES,
by means of a copper wire E a
current flows from the plate of
higher potential through the liquid
to that of lower potential. In the
liquid, therefore, the current passes
from zinc to copper, outside of the
liquid from copper to zinc. Thus,
though the copper is the plate least
acted on, its pole is called positive,
because the direction of the current is from it to the
zinc pole. Properly speaking, the difference of poten-
tial is not limited to that between zinc and copper.
There is a difference between the zinc plate and the
liquid in contact with it, a difference between the
liquid in contact with the copper plate and the copper
plate ; and, again, a difference between the copper
wire in connection with the copper plate and the zinc

Fig. 8.— Voltaic
Couple.

Chap, ii.] ELECTROMOTIVE FORCE. 17

plate which it joins. Tn one case the difference may
be a + quantity, in another a — quantity ; but the
sum of the differences gives what is called the electro-
motive force of the element.

In the element, the chemical changes going on
between the plates and the liquid are the source of
the energy which enables the element to do work ;
that is, the energy of the element may be measured
by the chemical decompositions going on in it.

Electromotive force is another phrase for
"difference of potential." For measuring electro-
motive force a standard is adopted, just as for
measuring the weight of a body a standard, viz. the
pound, is employed. The standard or unit of electro-
motive force is called the VOLT, after Yolta, It is said
to be '9268 of the electromotive force given by a
Daniell cell. (See page 19.) That is to say, a Daniell
gives 1'079 volts.

Poles, or electrodes.— It has been noted that
the part of the metallic plates projecting above the
fluid of the element is termed the pole, positive or
negative as the case may be. If wires be attached to
these parts for conducting the electricity to some
distance they are also called poles (+ or • -). They
are also termed ELECTRODES (??Ae/cTpoz/? and <55bs, a way)
because they are the pathways along which the
electricity travels. The wires used may be made
of any length so as to convey the electricity to a
distance from the place of generation. They must, of
course, be made of good conductors. Copper is a good
conductor, and is preferred for its cheapness. The
electrodes are usually protected by a coating of cotton,
thread, silk, or guttapercha, all of which are insulators,
and prevent the electricity being led off by contact
with other bodies.

Polarisation of plates. — It has been already
noted that in the voltaic element hydrogen is liberated.
c— 7

1 8 PHYSIOLOGICAL PHYSICS. [Chap. n.

The gas settles in minute bubbles upon the surface of
the copper plate, and at once interferes with the
action in the battery. It interferes both by the resis-
tance it offers to the passage of the current and also
by setting up a current in an opposite direction,
which tends to weaken the original current by
neutralisation. This action is called polarisation of
the plates. Besides this, in such an element some of
the sulphate of zinc produced in the element is
attacked by the hydrogen, and deposited on the copper
plate. So that the copper plate begins to approach
the condition of the zinc plate, and, of course, the
difference of potential becomes reduced. In all these
ways the current is diminished. Thus such an ele-
ment is not of constant strength, but rapidly gets
weakened. To meet these difficulties various elements
have been devised, which have been called, therefore,
constant elements. Some of these will be immediately
described.

Amalgamated zinc. — In most elements zinc is
one of the metals employed. Chemically pure zinc
is, however, very dear, and impure zinc is unequally
attacked by acid. The impure zinc gets quickly
eaten through with holes, and, by this, local currents
are produced in the zinc plate itself, which interfere
with the main current. To rectify this, ordinary
rolled zinc is employed, but before use it is amalga-
mated in the following way : It is first washed with the
dilute sulphuric acid (1 to 7) to get a bright surface,
and then rubbed all over with mercury. The mercury
forms a bright coating all over the surface. Thus
coated, the zinc is not attacked by the dilute acid,
unless connection is made between it and the other
metal of the element, or, in other words, unless the
circuit is closed. Local currents are thus prevented.
Where zinc is mentioned as part of an element, it is
understood to be amalgamated.

Chap. II.]

D AN i ELL1 s ELEMENT.

Daiiiell's element (Fig. 9) was the first constant
element, and was devised in 1836. It consists of an
outer vessel of glass or glazed earthenware, in which
is placed a cylinder of copper c, perforated with
holes, and open at both ends. A saturated solution
of sulphate of copper is placed in the outer vessel.
Within the copper cylinder is placed a vessel of
porous earthenware P, which contains dilute sul-
phuric acid, having im-
mersed in it a cylinder of
zinc z. The porous vessel
thus marks off an outer
and inner compartment,
while, being porous, it
permits communication be-
tween the two. When the
element is in action, the
acid attacks the zinc of
the inner compartment,
produces sulphate of zinc,
and liberates hydrogen.
The hydrogen passing into
the outer compartment re-
duces the copper sulphate,
and deposits metallic copper on the copper cylinder,
which is thereby kept always bright. By this decom-
position, the hydrogen forms sulphuric acid, which re-
places that used in the inner compartment. The sul-
phate of copper is thus the only thing used up. To
replace it, the copper cylinder is supplied with a small
shelf G, on which crystals of the copper salt rest.
The fluid reaches up to the shelf; the crystals are dis-
solved as required, and thus the strength of the solu-
tion is maintained. Let it be noted how polarisation,
the cause of the inconstancy of elements, is got
lid of in this case : (1) The copper is kept clean
and fresh by deposition from the sulphate of copper

Fig. 9.— Darnell's Element.

2o PHYSIOLOGICAL PHYSICS. [Chap, n.

solution ; and (2) the deposition of the hydrogen
film is prevented by the recomposition of the liberated
H to form sulphuric acid. The Daniell is, by these
means, one of the most constant of elements. When
in good condition, the element may be worked for
hours without producing any amount of variation
of current. It is, therefore, specially valuable for
physiological purposes, where comparative experiments
are being made, and a uniform strength of current is
necessary. Usually, instead of having an outer glass
vessel, a vessel of copper is taken, which contains
the copper solution, and is provided with a copper shelf.
All that is further necessary is the porous cell, as an
inner compartment, with its cylinder of zinc and aci4.

Copper is + pole, zinc - .

A new form of Daniell, called the "gravity
element," depends on the difference in the density of
the two fluids for keeping them separate. An earthen-
ware vessel is taken, and in the bottom is laid a disc
of copper, on which is poured a saturated solution
of copper sulphate. Suspended by catches from the
top of the vessel is a sort of grating of zinc, which is
covered bv a solution of zinc sulphate. In the jar
there are thus two layers of fluid, one the layer of
copper solution at the bottom, and above it the layer
of zinc solution, and the difference in the density
prevents them mixing. The zinc grating is at the
surface of the uppermost fluid, and it has in its centre
a small opening through which crystals of copper
sulphate can be dropped to maintain the strength
of the lower stratum. One pole ( — ) comes off from
the zinc ; the + pole is an insulated wire, which
passes through the liquid and is soldered to the copper
plate. All that is required to maintain the element
is occasionally to drop a few crystals of copper into
the solution, and to pour a little water on to the

chap, li.] SMEE'S ELEMENT. 21

grating to keep up the level of the fluid, and to main-
tain the dilution of the upper stratum.

In § Mice's element the metals are zinc and
platinum, or platinised silver. Two plates of zinc are
clamped on a wooden frame, and the platinum, which
is roughened by being covered with a deposit of finely
divided platinum, is fixed between them, being kept
from touching by the frame. Thus both sides of the

o «<

platinum are used. Dilute sulphuric acid is the liquid.
The action is the same as that described in the voltaic
element, only the platinum presents a surface from
which the hydrogen bubbles can be more readily dis-
engaged, and so polarisation is mechanically prevented.

The platinum is + pole, and zinc — .

Orove's element has two metals and two fluids.
The containing vessel may be of glass or earthenware
or ebonite. It contains dilute sulphuric acid, and
a cylinder of zinc. An inner compartment, formed
by a porous cell placed inside the zinc roll, contains
strong nitric acid and a platinum plate. (See Eig. 10,
Bunseii's element, the construction of which is similar.)
The sulphuric acid attacks the zinc, forms zinc sul-
phate, and liberates hydrogen, which passes to the
inner compartment, and forms water at the expense
of the nitric acid, which is reduced to nitrous acid.

Thus,

H2S04 + Zn == ZnS04 + H2 (1) .
H2 + HX03 = HXOo + H,6 (2).

Grove's element gives great power, but the strong
acids make it unpleasant to handle, and the nitrous
fumes given off are extremely disagreeable and irrita-
ting, and besides are very injurious to instruments.
The cells should, therefore, be kept in a room or shed
apart from where persons are working.

Platinum is -f- pole, zinc — .

22

PHYSIOLOGICAL PHYSICS.

[Chap. II.

Bmiseii's element (Fig. 10) is similar to Grove's,
the only difference being that a plate of carbon, of the
sort deposited in the necks of the retorts during
the manufacture of coal gas, is substituted for the
platinum in the inner compartment. This makes the
element much less expensive. The chemical action is
the same.

Carbon is + pole, zinc — .

Orenet's element is a single-fluid cell. It is
also called the bichromate of potash cell. The plates

and liquid are contained in a
wide-mouthed globe-shaped bottle
(Fig. 11). Two plates of com-
pressed carbon c c reach from
the cap to nearly the bottom
of the vessel. Between these
is a plate of zinc z, half their
size, fixed to a rod which slides
up and down through the vul-
canite stopper. One binding
screw in the stopper com-
municates with both carbons,
and another with the zinc. The
solution is made of dilute sulphuric acid, and a
saturated solution of bichromate of
potash (about 4 oz. of the bichromate to
20 oz. of water). The acid of the solu-
tion attacks the zinc, and the liberated
hydrogen reduces the bichromate to
sesquioxide, which is deposited on the
zinc. The intensity of the current is
thereby diminished. This is remedied
by agitation, which separates the de-
posit.

Grenet's element is not remarkably
constant, but it is very convenient to Grenet's Cell.

Fig. 10.— Buu&eii's Ele-
ment.

Chap. II.]

LECLANCHE'S ELEMENT.

work with, owing to absence of fumes. It can,
therefore, be allowed on the table at which one is at
work.

Carbon is -f pole, zinc — .

L,eclaiielif»'s cell (Fig. 12) consists of an outer
compartment, containing a zinc
cylinder z in a solution of sal-
ammoniac. The inner compart-
ment is a porous cell T, filled
with a mixture of powdered
carbon and black oxide of
manganese (pyrolusite) sur-
rounding a plate of carbon,
the mixture being moistened
with water, and the whole
usually being sealed up. The
cell has little force, but remains
in good order for a long time, Fig" ^^niT*''
and is specially useful for

electric bells and telegraphic purposes. Its chemical
action is as follows :

2NH3HC1

Zn

2Mn02 = ZnCL, + Mn203 -f NH3 + H20.

That is, the ammonium chloride attacks the zinc, and
the liberated ammonia passing through the porous
cell reduces the manganese dioxide to sesquioxide.
Small openings in the cover permit of the escape of
the unabsorbed ammonia.

Carbon is -f- pole, zinc — .

CJailFe's cell is a modification of a cell (with
the invention of which are associated the names of
Marie-Davy, Warren cle la Rue, and Pincus) called
the chloride of silver cell. It consists of a plate
of zinc z, and a plate of fused chloride of silver
Y. They are contained in an ebonite vessel, with a

PHYSIOLOGICAL PHYSICS.

[Chap. II.

hermetically-sealed cover, through which communica
tioh is made by binding screws v v'. Little rubber

pads keep the plates of zinc and
silver from contact, the silver
being also surrounded by a
tube of muslin, while a band
JK fixes them. The liquid is
a solution of chloride of sodium.
By the action of the cell zinc
chloride is formed, and silver is
reduced and deposited, in a
Fig. 13.— Gaifl'e's Element, pulverised state, in the muslin

bag. The element is made in

a portable form, the liquid not being able to escape.
For recharging, new plates of zinc and silver are neces-
sary. [For elements for medical purposes, see page 150.]

Silver is + pole.

Suppose the electromotive force of a Darnell's
element to be represented by 1, then that of Grove
and Bunsen would be nearly 1-8, while that of Smee
would be less than *4.

Battery. — Several cells may be united together,
as shown in Fig. 14, to form a battery. Here the
zinc of one element is
connected with the copper
of another. There is
thus left at one end of
the series an unoccupied
copper, and at the other
end an unoccupied zinc.
These are the terminals,

or poles, of the battery, copper being + and zinc
-, and wires are attached to these for conducting
the electricity to the desired place. At page 28 the
different methods of connecting cells to form a battery
are discussed.

Fig. 14.— Battery.

Chap, ii.] DENSITY, TENSION, AND INTENSITY. 25

Density, tension, and intensity of an

electric current. — The intensity of a current is the
quantity of electricity flowing through the circuit in
a given time (i.e. the strength of the current), and
this will depend upon the electromotive force. When
the circuit of an element is closed, the electricity will
flow through the conductors or electrodes with greater
speed the greater the electromotive force. In a gal-
vanic element, quantity or intensity is conditioned by
the extent of surface of the plates of the cell ; the
larger the plates the greater the quantity. Density
is dependent on the quantity of electricity that flows
through a cross-section of a conductor in a given time.
Suppose the thickness of a wire to be reduced to one-
half, the quantity (that is, the intensity) of the cur-
rent flowing through it will not be altered, but the
current will be twice as dense flowing through the
thin conductor as it was when flowing through the
thick one. Thus the density is inversely proportional
to the cross-section of the conductor ; i.e. the less the
cross-section the greater the density. Tension is
defined as an outward force on the surrounding
medium, and measures the tendency of the opposite
electricities of two dissimilarly charged conductors to
discharge across the space intervening between them.
If the positive and negative poles of an element are
separated from one another by a space, the greater
the tension of the electricity the greater will be the
ease with which it will pass across the space. The
greater the difference of potentials between the con-
ductors, the greater will be the charges, and there-
fore the greater the tension or tendency to discharge.
Great difference of potentials can easily be obtained by
means of a frictional machine. Hence, sparks can be
obtained between the terminals of such a machine,
though they are separated by a distance of several
inches.

CHAPTER III.

RESISTANCE — OHM'S LAW — MODES OF JOINING CELLS.

Resistance. — In its course a current meets with
obstacles to its flow.* This arises from the fact that
no bodies are perfect conductors ; the greater the
conductivity the less the resistance, as it is called.
Metals are among the best conductors, as already
noted, and therefore offer less resistance than non-
metals. Liquids, specially saline solutions, also con-
duct, but they always ofler more resistance than
metals. Thus, in a cell or in a battery from which
the electricity is conducted by wires to some apparatus,
there are manifestly two main sources of resistance.
There is, first, the resistance the current experiences
in passing through the liquid of the cell from one
plate to another. This is the internal resistance,
or the resistance of the element. But in passing
through the wires and through the apparatus that
may be in use, the current meets with further resis-
tance. This is the external resistance, or the resistance
of the external part of the circuit. Now, it is found
that the internal resistance is inversely proportional to
the size of the plates in the cell, and directly proportional
to their distance from one another; i.e. the larger
the plates the less the resistance, and the greater the
distance the greater the resistance, the conducting

* Though this language is used, it is not to be supposed that
the electric current is a material thing, or that resistance is offered
by material obstacles. Part of the energy of the current is \ised
up in heating the conductor, and the enfeeblement of the current
from this cause comes under the head of resistance.

Chap, in.] OHM'S LA iv. 27

power of the liquid in the element being, of course,
always the same. Taking now the external resistance,
it depends on the conductivity of the conductor,
which is a constant quantity for each conductor.
Apart, however, from that, the external resistance is
directly proportional to the length of the conductor^
and inversely proportional to the cross-section ; i.e.
the longer the conductor the greater the resistance, and
the thicker the conductor the less the resistance.

Ohm's law.— There is a relation between the
intensity of the current and the amount of resistance.
Experiment readily shows that a current due to a
definite difference of potentials between the extremi-
ties of the conductor is feebler after passing through a
platinum wire than after passing through the same
length of copper wire, because the conducting power
of platinum is less than that of copper. Again, a cur-
rent sent through a long copper wire is feebler than
when sent through a short one, and feebler when sent

O '

through a thin than when sent through a thick one.
That is to say, the intensity of the current is inversely
proportional to the resistance, and it has been already
stated to be directly proportional to the electromotive,
force. This is the law of Ohm (so called because the
character of these relations was first expounded by
Dr. G. S. Ohm in 1827), and is put thus :

Electromotive force
Current strength = -

'•&•

Resistance

Let C stand for current strength, E for electro-
motive force, and E, for resistance, and the formula
becomes

E

But it has been already noted that there are two

28 PHYSIOLOGICAL PHYSICS. [Chap. in.

resistances ; so, letting II stand for internal resistance,
and putting r for external resistance, the formula is,

E

C =

R+ r'

So that taking a given cell whose electromotive force
is always the same, the strength of current obtained
from it will depend on the resistance that it has to
overcome, will depend, that is, on the length and thick-
ness of the wire along which it is sent, and the nature
of the apparatus through which it is conducted. We
shall see immediately the bearing of this law of Ohm.
Modes of joining cells. — There are two ways
of joining cells. The positive pole of one cell may be
joined to the positive pole of the other, and similarly
the two negative poles joined. Where there are
several cells, connect all the positive poles to one

wire ; this wire will be the posi-
tive electrode of the battery :
then connect all the negative
•p- i* TVT% r • : poles to one wire ; it will be the

Fig. 15. — Mode of joining- r _

Cells in " Multiple Arc." negative electrode, I he method

is called joining in "multiple

arc." Fig. 15 shows six cells so joined. The effect is
just the same as would have been obtained if, instead
of taking six cells, a single cell had been taken six times
the size of one of them. Now, it has been pointed out
(page 26) that the internal resistance of a cell is in-
versely proportional to the size of the plates, so that,
by multiplying the size of the plates six times, the
internal resistance is practically diminished td one-
sixth. Increased quantity of current is therefore ob-
tained. Thus, neglecting for a moment the external
resistance, according to Ohm's law,

E 6E

ft'' IT

Chap, in.] OHM'S LAU\ 29

The second method is shown in Fig. 1 6. The positive
pole of one cell is joined to the negative pole of the
other, and so on through the set of cells. This leaves
vacant the negative pole of the first cell and the
positive pole of the last, and wires joined to these are
the electrodes of the battery.

In this case each cell has its i(«?X*X5KsH£X2)£-
own electromotive force and Fig. iG.-Mode of joining
resistance unaffected, so that the Cells in "Series."
total electromotive force of the

battery is the sum of the electromotive forces of the
several cells forming it, and the total resistance of the
battery is the sum of the resistances of the several
cells. Thus,

6E E

6R R'

Thus, apparently, no advantage as regards quantity
of current is obtained by joining in series. Let us
now include both internal and external resistances,
and see under what circumstances one or other
method is preferable.
Take Ohm's formula,

C- E
R+V

as a basis, and let us first consider the results of
joining cells in " multiple arc,"

1. Suppose six cells to be connected by a thick
wire to some apparatus that presents little resistance ;
that is to say, let the external resistance be so small
in comparison to the internal that it may be set aside.
r may be considered as equal to o ; then, the cells
being joined in multiple arc,

~ J£ , ~ 6E

C = - - ; but r = o, .-. C = - ,

is, the current is six times as great.

30 PHYSIOLOGICAL PHYSICS. [Chap. in.

2. Suppose that -the external resistance is now
very great in comparison with the internal, which
can be neglected ; that is, let E, = o, and connect
the six cells again in multiple arc, then

E E

C = , — ; but R =.- o, .-. C = ~ ;
rC r

6 +r

i.e. the current is unaffected, is no greater with six
cells than with one.

To put these . results in other words, supposing
cells joined in multiple arc, (1) where there is LITTLE
EXTERNAL RESISTANCE the strength of the current is in-
creased in direct proportion to the number of elements
so joined, or (what is the same thing), in direct pro-
portion to the size of the plates ; (2) where the

EXTERNAL RESISTANCE IS GREAT 710 advantage IS

derived from increasing the number of the cells so
joined, or from increasing the size of the plates.

3. Suppose, again, six cells connected by a thick
wire to an apparatus presenting little resistance, that
is, consider the external resistance r to be — o, and
now join the four cells " in series "/ then

6E 6E E

that means, no greater advantage is derived from six
cells than from one.

4. Again, let the external resistance be very
great, i.e. suppose the internal to be so small in com-
parison as to be regarded as o, and join again " in
series "; then

n , _ ~

C = .^ -- ; but B = 0, .-. 0 = - - ;

6K -f r r

which means that the effect is sixfold.

Chap, in.] ASSOCIATION OF CELLS. 31

Therefore, supposing cells to be joined in series,
(1) when there is LITTLE EXTERNAL RESISTANCE, no ad-
vantage is gained by a number of cells so joined ; (2)
where the' EXTERNAL RESISTANCE is GREAT, the strength
of the current increases in direct proportion to the
number of cells so joined.

To summarise the four cases that have been con-
sidered: to get increased intensity of current with
small external resistance, either use large cells, or join
a number of smaller cells in "multiple arc"; with great
external resistance join the cells in series, small ele-
ments being as good as large.

Association of cells in groups. — Ohm's law
shows further, that increased intensity of current
may often be obtained not by a regular arrangement
of cells, either in "multiple arc," or "in series," but
by forming a number of groups, each group being
formed by uniting several cells " in multiple arc,"
and then connecting the groups " in series." It is
unnecessary here to detail how this is proved, but the
rule is, that the best effect is obtained when the group-
ing is such that the total resistance of the elements is
equal to the external resistance. That rule is ex-

T>

pressed by the formula n '- = r, where R = the

internal resistance of a cell, m = the number of cells
united " in multiple arc " into a group, n — the number
of groups united "in series," and r = the total external
resistance. All that it is necessary to know is the
resistance of each cell, and the resistance of the
apparatus through which the electricity is to be con-
ducted. Thus, suppose it is known that the resistance
of each cell is represented by 5 (= R), and the resis-
tance in the circuit by 20 (= r), it is easy to calculate
how to arrange thirty-six cells in order to give the

strongest current.

-p

In the formula n — = r, substitute the values

m

32 PHYSIOLOGICAL PHYSICS. [Chap. in.

given, then n — — 20, that is, 5?^ = 20m ; there-

w

fore n — 4m. That is, the number of groups is equal
to four times the number of cells in each group. But
there are thirty-six cells in all, or the number of
groups multiplied by the number of cells in each
group = 36, i.e. n x m = 36. But, as shown, n =
4m, therefore 4m X m •• 36, or 4m2 = 36, therefore
m2 = 9, i.e. m = 3, and n = 4m, i.e. 12. Therefore,
to get the strongest current the number of groups (?i)
should be 12, and the number of cells (m) in each

group should be three. (Fig. 17
shows on one side six cells arranged
in two series, and on the other the
same number arranged in three
series.)

Divided eircinifs. — In Fi<r. 18

C*

there is shown a main circuit, from
which at the point A two secondary

circuits arise to join tne main I"16

in Groups. again at B. Now the electricity

flowing along from P will divide at
the point A, part will continue along the straight course
to B, and part will pass by r2 and rs. The currents flow-
ing in r2 rs are called the " derived " currents, A and
B being the " points of derivation." Supposing the
wires rl r2 and rs to be of the same material, length,
and cross-section, then they would offer precisely the
same amount of resistance to the passage of the cur-
rent. The result would be that the same amount of cur-
rent would flow along the three wires, but that the total
quantity of current flowing between A and B would be
greater than if there had been only a single wire rl be-
tween A and B. If, however, for r} a wire of the same
length, but treble its thickness, were substituted, then
the intensity would be the same as passes by the three
wires. In other words, the presence of the three wires

Chap, in.] THE OHM. 33

has increased the intensity by diminishing the resis-
tance. If, however, the wires r^ r2 and r3 present
different resistances, then the quantity of electricity
will be different along the three
wires, and will be less in the
wire of great resistance. In
fact, the intensity of the cur-
rent in each wire will be in-
versely proportional to the re-
sistance. The knowledge of this Fig. 18.— Divided Circuits.

fact shows a method by which a

main circuit may be tapped, as it were, and a portion
of the current diverted through some apparatus, a
portion regulated by the resistance of the conductor
employed. This method will be seen in use in
certain physiological experiments to be described.

The unit of resistance. — It is necessary to be
able to measure with accuracy the amount of resis-
tance that is interposed in the pathway of a voltaic
current, and for this purpose a standard of measure is
required, just as, to return to the example used in
regard to electromotive force (page 17), it is necessary
to have a standard of comparison for the purpose of
estimating the weight of a body, viz. the pound.
Various standards have at various times been used
for resistance. Thus one standard proposed was the
amount of resistance offered by a copper wire of a par-
ticular weight, length, and diameter, and this amount
gave the unit of resistance. Another proposal was that
of Siemens, in which the unit was the resistance of
a column of mercury one metre long, and one square
millimetre in section. It should be noted that the
resistance in both cases was altered by the tempera-
ture of the copper or mercury, therefore the measure-
ments were to be taken at 0° C. The unit now
employed is usually called the British Association
unit, because it was determined by a committee of
D— 7

34 PHYSIOLOGICAL PHYSICS, [Chap. iv.

that Association in 1860 ; shortly it is called the B. A.
•unit, or, after the discoverer of the laws of resistance,
the OHM. This resistance would be represented by
that offered by a column of pure mercury 104 -SI cen-
timetres long, 1 square millimetre in section, at a
temperature of 0° Centigrade. For practical use
coils are made of wire of such leno-th and thickness

o

that they offer precisely this amount of resistance.
Thus a coil is made of wire formed of an alloy of two
parts of silver and one of platinum. The wire is
from one to two metres long, and from '5 to '8
millimetres in diameter. The wires are soldered to
thick copper electrodes, and properly insulated by silk
and paraffin. At a given temperature, which requires
to be determined for the particular coil, it will offer the
standard resistance, and will be, therefore, equal to
one ohm. The exact temperature at which it gives
this resistance should be marked on the coil.* Simi-
larly boxes may be made containing different coils of
wire of varying lengths, so as to offer varying resis-
tances. The amount of resistance each coil offers is
marked on it in ohms ; and these can be made use
of to interpose any given resistance in the path of
a current. (See chap, xiii.)

CHAPTER IV.

INDUCTION AND INDUCTION COILS.

IN 1831 Faraday discovered that a current flowing
along a closed circuit was able to produce a current in
a neighbouring coil of wire simply through influence.

* Refer to Clerk-Maxwell on " Electricity and Magnetism,"
vol. i. p. 390.

Chap. iv. j INDUCTION. 35

Let E (Fig. 19) be an element from the positive pole
of which the wire A passes to a cup containing
mercury, into which it dips at B. Let c be the wire
from the negative pole also dipping into the mercury.
Let FD be another wire running parallel to AB, and in
its neighbourhood, and let the ends of FD be connected
with a galvanometer, an instrument for indicating the
presence of currents of electricity by the movement of
a magnetic needle. It is fully
described in chapter x. We
have thus two circuits, the one
in connection with the cell, which
may be called the cell or battery
circuit, or better, the PRIMARY
CIRCUIT ; the other, in connection
with the galvanometer, is the

T . , Fig. 19.-Scheme of lu-

galvanometer circuit, or SECON- duction.

DARY CIRCUIT. When one of
the wires coming from E is withdrawn from the
mercury cup the circuit of the cell is opened, and the
electricity ceases to flow. When the wire is re-immersed
in the mercury the circuit is closed, and the current is
re-established. 1. Now supposing the battery circuit
to be open, let it be closed by dipping the wire into
the mercury ; at the moment of re-establishing the
current a current appears in the galvanometer cir-
cuit. It lasts for a very short time and then disap-
pears, provided no change takes place in the primary
circuit. 2. Supposing, next, the primary current to
be flowing steadily, let it be interrupted by removing one
of the electrodes from the mercury ; at that moment
a current appears in the secondary circuit, as indi-
cated by the swing of the magnetic needle. It lasts
also a very short time and then disappears. This
phenomenon is called INDUCTION ; the primary current
is the inducing, and the secondary the induced,
current. 3. If the primary current be flowing,

36 PHYSIOLOGICAL PHYSICS. [Chap. iv.

there is no current in the secondary coil. If,
however, the secondary coil be removed to a little
distance, a current immediately appears in it, which
continues while the removal is taking place, and
ceases when it stops. 4. Or if the secondary coil be
approximated to the primary circuit, again a current
appears, to cease as soon as the movement is suspended.
The same effects will follow if it is the primary coil
that is moved in the neighbourhood of the secondary.
5. If, while the current is flowing round the battery
circuit, its strength be increased, there is again a
current induced in the secondary coil, to disappear as
soon as the battery current is constant. 6. If, on the
other hand, the primary current be diminished, a
secondary current is induced, which lasts only while
the change is being effected.

The direction of the induced currents
varies. — The current that appears on the establish-
ment of the primary circuit is in the opposite direc-
tion to that of the primary current, and is, therefore,
called inverse ; that which appears on interruption is in
the same direction as the primary, and is called direct.
The current induced by separating the two circuits is
direct, that by approximating them is inverse. The
current induced by increase of battery strength is in
the opposite direction (inverse), that by diminution is
in the same direction (direct), to that of the battery
current. The direction of the induced currents is
easily remembered by the law of Lenz, according
to which the direction of the induced current is
always in a direction tending -to oppose the change
in the primary current. Thus, on the establishment
of the primary circuit, there is an induced current in
the opposite direction in the secondary circuit, to
oppose the establishment ; and on interruption, a cur-
rent in the same direction as the primary, i e. to
oppose the interruption, to continue the primary.

Chap. IV.]

INDUCTION.

37

For Ampere showed tliat two currents that are parallel
but in opposite directions repel one another, and that
two in the same direction attract one another.

In order to increase the effect of induction a
greater amount of wire than a single turn is neces-
sary. The primary circuit is made of a considerable
length of wire wound on a bobbin (Fig. 20). The
wire is comparatively thick, to diminish resistance.

Fig. 20.— Induction.

and is covered with silk or cotton so as to insulate
one turn from the other, and, to increase the in-
sulation, the turns are varnished with shellac. The
two ends of the wire are connected with brass
screws, to which the wires from the element can
be attached, when the current will pass round the
coil. The secondary coil is of similar construction,
but for it thin wire must be used of very much greater
length than that of the primary coil, since it is found
that the intensity of the induced currents depends on
the number of turns in the coil and the fineness of the

38 PHYSIOLOGICAL PHYSICS. [Chap. iv.

wire. The ends of the wire are connected to binding
screws, to which wires can be connected for leading off
the induced currents, for instance to a galvanometer,
as shown in the figure, which indicates their existence.
The coils are so made that the primary can slip out of
or into the interior of the secondary, which is hollow.
By such an arrangement all the phenomena described
can be readily observed. Such a coil is called an

INDUCTION COIL.

Induction toy a magnet. — Not only a current
of electricity, but also a magnet, is capable of produc-
ing induced currents. Thus, suppose the element of
primary coil of Fig. 20 to be removed, and let a
magnet (AB, Fig. 21) be substituted
for them. If the magnet be held
stationary above the secondary coil
no current is induced. But as soon as
the magnet is thrust into the interior
of the coil, or removed from it, induced
currents are evident, in opposite direc-
tions, which also obey Lenz's law.
If the magnet be stationary and the
neto-ETectrfc co^ moved, induction currents will also
induction. be produced. Thus, if coils be rotated
before the poles of a strong magnet, a
large number of induced currents can be produced,
rapidly following one another. This is the principle
made use of in the construction of the magneto-electric
machine for medical purposes, and in machines for the
production of the electric light. It is found also that
if in the interior of the secondary coil a core of soft
iron be placed, and if one pole of a strong magnet be
then brought into contact with the core, it becomes
magnetised ; on removing the magnet the core loses its
magnetism, but this magnetisation and demagnetisa-
tion of the soft iron core produce induction currents in
tha.coil. It is further known (page 53) that a current

Chap. IV.]

INDUCTION COILS.

39

of electricity, circulating round a wire wound on a
piece of soft iron, converts the iron into a temporary
magnet, and that on removal of the current the iron
speedily loses its magnetism. Thus, if the two coils be
used as shown in Fig. 20, and if, in the centre of the
primary coil, there be placed a core formed of a piece
of soft iron or of a bundle of iron wires, as soon as the
current is established in the primary coil the core
becomes magnetised, and by this means the inductive
action of the primary on the secondary coil is intensi-
fied. It is also needful to note that the nearer the
inducing current is, the more considerable becomes
the induced current, and the farther removed the
inducing current the feebler is the induced. These
are the general principles adopted in the construction
of induction coils
made for the pur-
pose of generating
induced currents
capable of being
employed for prac-
tical purposes. The
first successfully to
construct such a
coil was Ruhmkorff;
and hence the appa-
ratus is called RUHMKORFF'S COIL. It consists of a
hollow cylinder, on which is coiled a copper wire about
two to three millimetres in diameter, and about 40 to
50 yards in length. As already noted, the wire must
be carefully insulated. Inside the cylinder is a core
of soft iron, either in one piece or consisting of a
bundle of iron wires. This primary coil is inclosed in
a cylinder of insulating material, glass, or caoutchouc.
On the outside of the insulating case is wound the
secondary coil, each turn being carefully insulated from
another. This coil is made of wire much thinner than the

Fig. 22.— Buhrnkorff's Coil.

40 PHYSIOLOGICAL PHYSICS. [Chap, iv

primary, from one-fifth to one-tenth millimetre thick,
and is very long. In some large coils the secondary
wire may be sixty to ninety miles long. Thus the
secondary coil is wound round the outside of the
primary coil, though carefully insulated from it. The
ends of the primary wires are connected with the
binding screws b and 6', and the ends of the
secondary wires to the screws A and B, which may be
supported on glass pillars, as shown in the figure.
In such an arrangement the coils are not movable.
An arrangement is now required for interrupting and
re-establishing the current in the primary coil with
rapidity, so as to produce the induced currents. One
method of doing this is by what is called Foucault's
contact-breaker. This consists of a small cup M con-
taining mercury, which is in metallic communication
with the binding screw b. Dipping into the mercury
is a metallic point connected with a lever L movable
on an axis at L. The other end of the lever has
attached to it a small piece of soft iron (armature, as
it is called), which just projects above the core of soft
iron jutting out of the centre of the primary coil.
Now, if this core becomes magnetic it attracts the soft
iron armature. This draws down one end of the
lever moving on the axis L, and raises the other
end, so that the metallic point is raised out of the
mercury, and therefore breaks contact with it. The
lever L is supported on a spring, by the elasticity
of which it is pulled back to its original position,
should the core lose its magnetism, and so contact
with the mercury would be again established. Now,
suppose the positive pole of a battery to be attached
to the binding screw b', by means of a wire laid in the
wooden support of the coil, the current goes to c,
which is an arrangement called a commutator, and is
for the purpose of reversing the direction of the cur-
rent, or preventing it from passing. In chapter vi. a

Chap, iv.] RUHMKORFF'S COIL. 41

commutator is described. From c the current passes
by the wire f to the primary coil, round which it
passes, and gets exit by the wire/"', which conveys it
to the pillar to which L is attached. The current
having gained L, proceeds along it to the mercury
cup M, and from M to the binding screw b, to which
the negative pole of the battery is attached, by which
it regains the battery. Consequently, when the
metallic point of L is in the mercury the current is
allowed to pass, when it is out of the mercury the
current is interrupted. Now, when the current passes
round the primary coil, the core of soft iron wires
becomes magnetised, and attracts the armature at the
end of L ; this raises the point of L out of the mercury,
and the current ceases to flow. The current having
ceased the soft iron core loses its magnetism, and so
fails longer to attract the armature. The lever, there-
fore, by the elasticity of the spring, is restored to
its former position ; the point dips again into the
mercury, and the current is re-established. The core
again becomes magnetic, again attracts the armature
of L, and so again interrupts the current The core is
again demagnetised, L springs back, and the current
is once more re-established. So the action goes on,

o

the current being automatically interrupted and re-
established with great rapidity, and induced currents
being therefore formed also with great rapidity. If
wires be attached to the binding screws A and B of the

O

secondary coil, and the ends brought near to one
another, but not touching, the induced electricity
will be seen to leap across from one wire to another
in a stream of blue light. This is the spark of
induced electricity, and in large coils a spark of many
inches (18 inches) may be obtained by separating the
ends of the wires. Thus by means of a coil having
a large number of turns of very fine wire, very great
differences of potential, and great tension, can be

42 PHYSIOLOGICAL PHYSICS. [Chap. iv.

obtained. So a current of a few Grove's cells, which
might be permitted to pass through the body without
the person being aware of any effect, would, if sent
through a large coil, be able to generate induced cur-
rents sufficient to kill an ox.

Du Bois-Itcymoiid's iBidiictorium, or in-
duction coil, is constructed on similar principles with
a view to physiological experiments. The primary
coil R1, consisting of about 130 turns of a moderately
thick insulated copper wire, is fixed, and has

Fig. 23. — Du Bois-Eeyinond's Sledge Inductoriuin.

a core of soft iron rods. The secondary coil R2,
having 6,000 turns of thin (0-15 mm. in section)
copper wire, is quite separate, and slides in a groove
B along the wooden ways BB. These ways are made
double, and hinged, so that they can be folded back,
or unfolded, when a grooved roadway is obtained
twice the length shown in the figure, along which R2
may slide. Thus R2 may be brought quite over R1, or
may be moved away to a considerable distance. As
already noted (page 39), on the distance between the
two coils depends the amount of the induced currents.
A centimetre-millimetre scale is pasted along the edge
of BB, so that the distance between the two coils can
be always measured, and consequently the same
strength of current at any time reproduced, provided
other things, such as element, etc., are equal.

At the end of the apparatus is the arrangement
known as Wagner's hammer, adapted by Neef for

chap, iv.] Du BOIS-REYMOND'S COIL. 43

automatically making and breaking the primary
circuit. Let the current be brought to the binding
screw K in the far-off pillar, and let the negative
electrode be bound to z. The current passes up the
pillar and along the spring s extended horizontally,
till it reaches the binding screw s', which makes
contact with its platinum point on a small piece
of platinum placed on the upper surface of the spring
at that spot. The current passes up from s' to sx/,
then round R1, and out from it by a wire to the
electro-magnetic pillars b'. These consist of cores
formed of tubes of soft iron wound round with copper
wire. The electricity flows along the wire round both
columns, and then gains the screw z, by which it
reaches the negative electrode. When the current
passes round the pillars b' they become magnetic, and
attract the wedge-shaped piece of soft iron s, which
is just above them, and is fixed to the end of the
spring. The magnetised pillars attract the soft iron ;
this withdraws the spring from contact with the screw
point s', and the current is interrupted. The pillars
lose their magnetism, and fail to retain the spring,
which flies back by its own elasticity, and re-establishes
the current. Thus, by alternate magnetisation and
demagnetisation of the pillars the current is established
and interrupted rapidly, and so a rapid series of induc-
tion currents is obtained. The hammer interrupter
may be put out of use by connecting one wire of the
battery directly to s", and carrying the other wire to
s'". From s" the current passes straight round the
primary coil, then to s'", and so back to the battery.
To interrupt the current, then, the circuit must be
broken by loosening a wire, or by the use of a key.
Because of the sliding arrangement of the secondary
coil this induction apparatus has also been called the
" sledge " inductorium.

Extra current. — From what has been said about

44 PHYSIOLOGICAL PHYSICS. [Chap. iv.

induction, it will be readily understood that the use
of a bobbin round which is wound the spirals of a
coil introduces an element that would not be found
did the circuit pursue a straight course. For as the
current flows round one turn of the coil, it induces a
current in the neighbouring turns of the same coil.
This second current is called the EXTRA CURRENT, and
is in a direction tending to oppose the establishment
of the ordinary current. The arrangement in Fig. 24

was devised by Fara-
day to show this extra
current. It consists of
a battery of elements E,
from which wires are led
to c, a single coil of long
Fig. 24.— Extra Current, fine wire. At the point

A in the positive elec-
trode a branch wire is led off to the galvanometer G,
and a wire from G joins the negative electrode at B.
Thus the current from the battery splits at A ; part
goes round c, and back to the battery, part goes off at
A, passes round the galvanometer, and joins the main
circuit at B. The arrows indicate these directions. By
the action of the current, the needle of G takes up a
position a. By a simple arrangement the needle is
brought back to zero, and then contact is broken, so
that the current ceases to flow round the coil c. At
that instant the needle becomes deflected in a direction
opposite to the former, i.e. in the direction a. This
indicates a current flowing across from B to A, that is,
a current in the coil in the direction A c B A, which
was the direction of the battery current. Similarly,
when the current is established in the coil C, there will
be an inductive action of each turn of the wire on
its neighbours, and another extra current will appear.
It will, in accordance with the rule already laid down,
be in a direction tending to oppose the establishment

Chap, iv.j EXTRA CURRENT. 45

of the current, that is, in the reverse direction to the
battery current.

Thus there are two extra currents, one appearing
on the closing of the circuit, tending to oppose the
establishment of the current, that is, in the opposite
direction to, and therefore weakening, the battery
current. This is the INVERSE EXTRA CURRENT, or
extra current of closure. The second appears on
interrupting or opening the circuit, tends to oppose
the interruption, and is, therefore, in the same direc-
tion as the battery current, and for the instant inten-
sifies it. This is the DIRECT EXTRA CURRENT, or extra
current of opening. It explains why the spark
obtained on opening is more intense than that on
closing.

Now, in an ordinary induction coil, the production
of these extra currents in the coil of the primary
circuit occasions corresponding differences in the
induced currents of the secondary coil. For by the
inverse extra current the primary current is at the
moment of closing weakened for an instant, and, on
this account, attains its maximum strength only
gradually. On the other hand, the direct extra
current is suppressed on opening, because no arrange-
ment is made to maintain the circuit of the primary
coil when that of the battery is opened, and it also is
broken. Thus, the" current of the primary coil is
suddenly, not gradually, interrupted. On closing,
therefore, the primary current gradually attains its
maximum ; on opening, it is suddenly interrupted
when at its full strength. This must affect the cur-
rents of the secondary coil, which are induced by the
opening and closing of the primary current. Fig. 25
graphically represents the differences. The part of the
figure enclosed by bracket I applies to the primary
current ; that enclosed by bracket II applied to the
induced currents of the secondary coil. AA is the

46

PHYSIOL OGICA L PHYSICS.

[Chap. IV.

basement line of the upper part ; bb is that of the
lower. Now when the primary circuit is closed, the
current from the battery should at once rise to its
maximum, which would be represented by the perpen-
dicular dotted line AB, but, owing to the extra current

CLOSING

OPENING

•--. 3'

Fig. 25. — Effects of the Extra Current on the Induction Currents*

in the inverse direction, it attains its maximum com-
paratively slowly, as represented by the continuous
curved line 1. Simultaneously with the establish-
ment of the primary circuit is a secondary induced
current, represented by the curve 2, on the under side
of bb, because it is in the opposite direction to 1.
Again, on opening the primary circuit its current
is suddenly arrested, which is shown in the figure
by the perpendicular continuous line 3 3, unaffected
by any extra current because of the interruption
to the circuit. Corresponding to the opening is
an induced current in the secondary coil, which
suddenly attains its maximum, as represented by the
perpendicular 4 4, and then falls off more gradually,
as represented by the curved continuation of 4 4.
By this graphic method the difference between the
induced current of opening 2, and that of closing 4,
is plainly seen ; and this accounts for as great a
difference in the physiological effects of the two
induced currents, the effect of opening being always

Chap. IV.]

EXTRA CURRENT.

47

the more marked. In order to diminish the difference
between the two, Professor Helmholtz, of Berlin, has
devised a modification of the arrangement of the
coil.

Modification of the Dn Bois iiidiictoriiuii.
— This is shown in Fig. 26. It consists of an additional
pillar «, at the foot of which is a binding screw k.
The top of the pillar has a screw with a fine platinum
point f'j which can be raised or lowered, so as to
touch or be removed from the spring, above it. An
additional binding - screw
g is put on the first pillar,
and a wire carried from
it to f. Let E be the
element, and let its posi-
tive electrode be carried to
screw d of the first pillar,
and its negative electrode
to the binding screw k on
pillar a. The course of

fi , . » ,, Fig. 26.— The Helmholtz Modifi-

bne Current IS as lOliOWS : cation of the Sledge Inductor.

From E to the first pillar,

up that pillar, out from g by the wire g', to binding
screw f, and so round the primary coil c, and then on
to the electro-magnetic pillars b. From b it passes, by
a wire laid in the wood of the instrument, to pillar a,
and from it through the binding screw k, to gain the
negative electrode, and so back to E. Now when the
current is passing through the electro-magnets 6, they
become magnetised, and attract the hammer-head h.
This pulls the spring down, and causes it to make
contact with the point of the screw f, which is
adjusted at the proper height for this purpose. As
soon as f is touched by the spring, a second pathway
is opened to the current, viz. from E to the first pillar,
up that pillar, and along the spring toy, by means of
/', down pillar a, and back to the battery E. By this

48 , PHYSIOLOGICAL PHYSICS. [Chap. iv.

second pathway the current does not go round the
primary coil c at all. The current is, therefore, said
to be short-circuited, because a " short cut " is offered
to it instead of the longer way round the primary coil.
Thus, as soon as the spring touches f', the current
has two circuits: the first, Eclgg'fcbkE, and the
second, E df k E. At the binding screw d, therefore,
the current will branch off; part will flow through the
primary coil, and part will pass by the short circuit
straight back to the battery. The current through
the coil c and the electro-magnet b is, therefore,
weakened. As a result, the electro-magnet b is no
longer able to attract the hammer-head h, which flies
back by the elasticity of the spring, and the short
circuit is broken by contact between the spring
and f being interrupted. The current, therefore,
again proceeds in full force round the coil c and the
electro-magnet b. The latter again becomes strongly
magnetic, attracts h, again closes the short circuit at
/', and again weakens the current round c. Again
does the magnet become too weak to attract h, which
again flies off, and breaks the short circuit, and
restores the full force of the current round c, and so
on the action is repeated. The effect of this short-
circuiting arrangement on the induction currents is
shown in the dotted curves of Fig. 25. The weaken-
ing of the current round the coil is represented by the
line A'A" in its diminished distance from B. When
the short circuit is interrupted by the recoil of the
hammer-head, the strength of the current round the
coil c rises. This is represented by the curved dotted
line 1'.

Corresponding to this increased strength of the
current in the primary coil is an induced current
in the secondary, represented by the dotted curve
2'. But no sooner is the short circuit interrupted
than it is again closed by the increased action of the

Chap, iv.] HELMHOLTZ^ MODIFICATION. 49

electro-magnet b. The weakening of the primary
current by the sudden closing of the short-circuit is,
however, effected gradually, because the circuit of the
primary coil is still complete, and the extra current
produced in the primary coil can make its effect felt.
The extra current is in the direction of the primary
current, and therefore tends to delay its weakening.
The consequent gradual weakening of the primary
current is represented by the dotted curve 3'. Pro-
duced by this is an induced current in the secondary
coil, indicated by the dotted curved line 4'. Thus
the original induction currents of the Du Bois coil
are represented by the continuous curves and lines 2
and 4 4, the disproportion between which is graphi-
cally shown ; while the induction currents produced
through Helmholtz' modification are represented by
the dotted curves 2'4', which are. as nearly as
possible, of the same intensity, and produce, therefore,
similar physiological effects. The sledge inductorium,
as now made, has the arrangement shown in Fig. 26,
and by proper adjustment of the screw f the modi-
fication is made available. By lowering the screwy
so that the spring cannot come into contact with it,
and by loosening the wire g', the modification can be
thrown out, and the original arrangement employed.

It is to be noted that in the Helmholtz arrange-
ment the primary current is never quite interrupted.
It is only the increase and diminution in the strength
of the current round the primary coil that produces
the induced currents.

E— 7

CHAPTER V.

EFFECTS OF THE ELECTRICAL CURRENT.

Thermal effects. — A sufficiently strong electric
current is capable of fusing all metals, not excepting
platinum. By properly graduating the strength of
the current, varying degrees of thermal effects may
be obtained, from mere warmth up to redness, and on
to fusion. Heating effects, whether easily apparent
or not, always attend "the conduction of a current.
The amount of heating depends on the resistance of
the conductor. Thus, a fine wire will be heated to
a greater extent than a thick wire, and a wire of
great resistance to a greater extent than one of small
resistance. Thus, platinum wire interposes ten times
greater resistance to the passage of a current than a
copper wire of the same length and thickness. Con-
sequently, with the same current a platinum wire
would be unbearably hot, while a copper wire would
be hardly affected. At the same time, it is found
that the total resistance for the whole of the circuit
must be as small as possible. Therefore, when it is
desired to heat, say a small piece of platinum wire, as,
for instance, in surgery, for the removal by cautery of
a tumour, copper electrodes of considerable thickness
are attached to the battery, and the necessary length
of platinum wire is interposed between their ends.
(See chap, xi.) The heating effects of the currents
are made use of for firing mines, and for similar
purposes.

Electrolysis. — A current of electricity passed
through water decomposes it into its elements. Oxygen

Chap. V-]

ELECTROLYSIS.

51

is liberated at the positive pole, and hydrogen at the
negative. The apparatus figured in Pig. 27, called a
voltameter, is employed for showing this decomposi-
tion. It consists of two tubes filled with water.
The tubes are inverted in a vessel, also containing
water, over strips of platinum. The strips are con-
nected by wires to binding screws, to which the
positive and negative wires of a battery are attached.

Fig. 27.— The Voltameter,

The liberated gases rise from the strips, and are
collected in the tubes. The tube connected with the
negative pole has twice as much gas (hydrogen) as
that connected with the positive. Thus one obtains
not only a qualitative but also a quantitative analysis.
Pure water is not employed, because it is a bad
conductor. The water must be acidulated, usually
with sulphuric acid, and, of course, it may be really
only the acid that is decomposed. Other solutions
subjected to the passage of a current show similar
results, different elements appearing at different
electrodes. Salts may be decomposed by the current,
the acid appearing at the positive, and the base at

52 PHYSIOLOGICAL PHYSICS. [Chap. v.

the negative pole. Similarly other compounds can
be decomposed, animal substances like blood, milk, or
muscle, being also acted on. Faraday investigated
the subject of such decomposition, and applied the
phraseology now used. Thus the body decomposed
is called the ELECTROLYTE, and the action ELECTRO-
LYSIS ; the positive pole is called the ANODE, the negative
the KATODE ; the substances that collect at the positive
pole are called ANIONS, those that collect at the negative
pole are called RATIONS. Those that collect at the
positive pole are supposed to be charged with negative
electricity, and are called ELECTRO-NEGATIVES, while
those collecting at the negative pole are supposed to
be charged with positive electricity, and are called
ELECTRO-POSITIVES. It is to be noted, however, that
the same body may at one time be electro-positive
and at another electro-negative. It depends on
the body with which it is associated. Thus sulphur
is electro-negative to hydrogen, but electro-positive to
oxygen. It is a curious fact that the separation of
the different elements occurs only at the electrodes,
and not throughout the mass of the electrolyte.

To account for this, a theory was propounded by
Grotthiiss. The diagram (Fig. 27) shows its application
to water. Grotthiiss supposes that there is a decom-
position effected throughout the entire fluid, but that
this is followed by a recombination, except at the
electrodes. Thus the molecule of water in the neigh-
bourhood of the positive pole being split into oxygen
and hydrogen, the oxygen, being electro-negative,
attaches itself to the positive pole. Its liberated
hydrogen, however, seizes on the liberated oxygen of
a neighbouring decomposed molecule, and recombines
to form a molecule of water. The free hydrogen of
the second molecule seizes on another atom of oxygen
of a neighbouring molecule, and so on throughout the
liquid, the recombination being complete throughout

Chap. V.]

THE ELECTRO-MAGNET.

53

the liquid. As a result, however, hydrogen is left,
having no oxygen with which to recombine, and as it is
electro-positive, it attaches itself to the negative pole.
Thus only at the two poles are the effects of the
decomposition visible. The quantity of an electrolyte
decomposed is proportional to the action in the battery ;
and the quantities of the different substances pro-
duced at the different poles are in proportion to their
chemical equivalent.

Production of magnets by currents. — Let
AB (Fig. 28) be a portion of a large link of soft iron,
and let a thick copper wire
be wound round each end,
each turn being insulated
from the other. The wire
must be wound in such a
way that, if the link were
straightened out, the wire
would be all in the same
direction. Connect the ends
of the wire with a battery
of two or three Grove's
cells, and an electro-magnet
is formed. Let T be a bar
of soft iron with a hook at-
tached. While the current flows round the wire, the
soft iron will become converted into a horse-shoe mag-
net, of such strength as to attract the bar T, and keep
it in contact though a weight of many pounds be
suspended from it. Interrupt the current, then in u
moment the link will lose its magnetism, and the
weights will drop. The soft iron is thus only tem-
porarily magnetised by the passage round it of a
current. All the magnetism is not, however, lost ;
some generally remains, and is called residual
magnetism. The less thorough the annealing of the
iron, the greater is the tendency for some degree of

Fig. 28.— Electro-magnet.

54 PHYSIOLOGICAL PHYSICS. [Chap. vi.

magnetism to remain permanently. The discovery of
the electro-magnet is due to Arago. How it is adapted
for the automatic interruption of a current has been,
explained in noticing the construction of the induction
coil (page 39). The electro-magnet is also very ex-
tensively employed in the making of electromotors,
telegraph instruments, etc.

The luminous effects of the electric current
it is not necessary to discuss here. A brief reference
will be found in the chapter on the application of
electricity to medicine and surgery (chap. xv.).

The effects of a current 011 a magnet are
discussed in the chapter on galvanometers (chap. x.).

The physiological effects of the electric current
form the subject of other chapters.

CHAPTER VI.

KEYS, COMMUTATORS, AND ELECTRODES FOR PHYSIO-
LOGICAL PURPOSES.

A GALVANIC key is for the purpose of rapidly and
easily making or breaking a galvanic circuit. This
could be done, of course, by simply loosening one of
the wires from its connections with the battery, or
with the apparatus to which the current is conveyed ;
but the use of a key affords a great convenience.
There are various forms in general use.

A mercury key is shown in Fig. 29. It con-
sists of a circular block of wood which can be clamped
to the table. In. the centre is sunk a small porcelain
cup which contains clean mercury. A thick copper
wire is fixed across the block, with its end curving
down into the mercury. The projecting end is much
thicker than the rest, and is hollowed out so that a

Chap, vi.] GALVANIC KEYS. 55

wire can be inserted into it and fixed with a screw.

A second wire with a similar projecting end is movable

round an axis by an insulated handle.

It can be caused to dip into the

mercury or can be taken out. Wires

from the battery being connected with

both the binding screws, the current is

fi(r 29 JVIer-

passed when both wires dip into the ecury key.
mercury and is interrupted when the
handle is pulled backwards so as to lift one wire out.
A contact or spring1 key is shown in Fig- 30,
On a vulcanite or other insulating block is fixed a
spring, in metallic connection with a binding screw at
the base of the pillar supporting it. The end of the
spring has a little ivory button, 3, by which the finger
may press the spring down so as to
make contact with the metal pillar 1,
which is in metallic connection with
the binding screw 2. Thus, the elec-

Fig. 30.— Spring , i • /> i j ji i • i •

Key. trodes being fixed to the binding screws,

the current can pass only when the
spring is pressed down by the finger to make contact
with the pillar 1.

The friction key of Du Bois-Reymoiid is repre-
sented in Fig. 31. It consists of a plate of vulcanite
G attached to a screw clamp for fixing it to the edge
of a table. On the plate are two rectangular pieces
of brass A and B, placed in the position shown in the
figure. Each piece of brass has two holes drilled
through it, and a screw passes down to each hole to fix
any wire that may be inserted. A bridge of brass is
pivoted to B in such a way that when lowered by the
insulating handle c it makes close contact with the
end section of A. There are two ways of interposing
this key in a circuit. The best way is that shown in
Fig. 31, viz. : Carry a wire from the positive pole of
the element to binding screw 1, and from 2 on the same

PHYSIOLOGICAL PHYSICS.

[Chap. VI.

APf

side of the key carry a wire to the apparatus to which
the current is being conveyed, represented by APP.

From the apparatus take a
wire to 4 011 the opposite side
of the key, and from 3 on
that side take a wire back to E
to the negative pole N. Lower
the bridge so as to " close the
key," and now follow the
direction of the current. It
passes from P to A ; but as
soon as A is reached two path-
ways are open, one by the wire
from 2 round the apparatus,

Fig. 31.— Friction Key in ,-, -, u i

Short Circuit. then on to B, and so on back

to E, the other from A, straight

across the bridge to B, so gaining 3, and passing to E.
The first is a long route presenting considerable resis-
tance ; the second is a short circuit, and, since the
bridge is of large section, presents no resistance to
speak of. When, therefore, the key is closed, all the
current will pass straight across the bridge back to
the battery, and none will go the long route, owing to
the great difference of resistances. The battery cur-
rent is then said to be short-circuited, arid the key is
interposed in SHORT CIRCUIT. * Another term for
short circuit is accessory circuit.

When, however, the bridge is raised, the key is
opened, and in that case the current has no option, but
must go the long route, the short circuit being inter-
rupted. With a key in short circuit, therefore, closing
the key means interrupting the current in the apparatus^
and opening the key means sending on the current to
the apparatus. The same key may be used in a simple

* For the sake of those who read German and who might have difficulty
in fiuding the meaning of the word, it maybe noted that nebenscldiessung
is used as we use short circuit.

chap, vi.] UNIPOLAR INDUCTION. 57

fashion (Fig. 32). Carry a wire from p to A, another

from B to the apparatus, and a third from APP to N.

When the key is opened, the current cannot pass across?.

from A to B, and is therefore interrupted in APP, and

when it is closed the current

passes across the bridge C, and

the circuit is closed. Thus,

using the key in this simple way,

closing means establishing the

current, while opening it means

interrupting -the current.

Unipolar md«etion.-In
the stimulation of nerve by
induction currents, the key interposed in the circuit
ought always to be short -circuited for the preven-
tion of what is called unipolar contraction. Sup-
pose the circuit of the secondary coil not to be closed,
then on the opening and closing of the primary circuit
no induction stream can be produced, because of the
interruption in the secondary circuit. But it has
been shown that in such a case the passing of the
current through the primary coil decomposes the
neutral electricity of the secondary spiral, and thus
free static electricity accumulates at the ends of the
secondary wires. This free electricity is of consider-
able tension, and will pass off into the earth ; and if
it meet a nerve in its course, the nerve will be irri-
tated. These conditions are practically fulfilled when
the key of the secondary spiral is a simple key, a
mercury key, for example. When the key is open,
so that no induction stream can be produced, and when
a nerve is laid on the electrodes, without proper insu-
lation being employed, the nerve is connected with
only one pole of the secondary spiral. On the passing
off of the free electricity accumulated on the ends of
the wires, contraction of the muscle might result.
When, however, the secondary coil is short-circuited,

58 PHYSIOLOGICAL PHYSICS. [Chap. vi.

this cannot happen, because then the secondary circuit
is closed. Not only will unipolar contraction occur
when the secondary spiral is open, but it happens also
when the spiral is imperfectly closed. Imperfect closure
is present when part of the circuit is formed of a bad
conductor. Now, the resistance offered by a nerve to
the current is great, and it is, therefore, an imperfect
conductor. When, therefore, the short-circuiting key
is opened, and part of the circuit of the secondary coil
is the piece of nerve between the two electrodes,
imperfect closure is present, and unipolar contraction
is apt to occur and to be mistaken for contraction of
the muscle by excitation from the nerve. To prevent
this it is recommended to connect the upper of the
two electrodes, by means of a good conductor, with the
earth. This is effected by leading a short thick wire
to the gas-pipe or water-pipe connected with the apart-
ment. The free electricity is thus led off and prevented
from passing through the nerve and muscle. In any case,
where it is desired to make certain that the contraction
obtained is due to nervous stimulation, and not to
unipolar induction, it is advised, after getting the
contraction, to snip through the nerve between the
electrodes and the muscle, then cause the cut surfaces
of the nerve to make contact with one another, and
repeat the experiment. The propagation of the
nervous influence is prevented by the section, but the
conduction for electricity is still preserved. If,
therefore, the first contraction were actually due to
nervous stimulus, it will not appear on repeating the
experiment ; but if it were due to unipolar action, it
will occur just as before. This is called a control
experiment, because it tests the accuracy of the result.
Instead of cutting the nerve, ligaturing it between the
electrodes and the muscle is as effective, since the
ligature destroys nervous propagation but preserves
electrical conduction. Or the nerve may be kept

Chap, vi.j THE COMMUTATOR. 59

intact for further experiments, and the control experi-
ment performed, by laying a thread moistened in salt
solution over the electrodes, and placing the nerve on
the part of the thread projecting beyond the electrode.
The thread will equally well conduct the electricity,
but of course will not occasion nervous stimulation.

A commutator is an instrument for reversing
the direction of a current. It is also called GYROTROPE
or RHEOTROPE. Fig. 33 shows the form constructed
by Pohl. In a thick disc of
wood or vulcanite there are six
little cups for holding mercury.
Each cup has a binding screw
in connection. Attached to the
cups 1 and 2 are the upright thick
wires a and b, which are con-
nected to one another by a bridge
of glass tube filled with wax, so Fig> 33> _ Pohrs Com.
that, though connected, they are in- mutator.

sulated from one another. Spring-
ing transversely from the upright wire on each side
are arcs of thick copper wire, of such a length that the
bridge may be so inclined that the free ends on one
side may dip into the cups 5 and 6, or, by reversing
the bridge, the ends of the other side may dip into the
cups 3 and 4, but the free ends cannot dip into both
sides at once. Copper wires are also supplied, one, c,
stretching between 3 and 6, the other, «, between 4 and
5, and not touching one another. These two copper
wires form what is called "the cross." The cross may
be removed ; and, according as it is in or out, does the
instrument serve one or another purpose. (1) Let the
cross be in, bring the positive electrode of the battery
to 1, and the negative to 2. Let the bridge incline as
shown in the figure, and suppose a wire to pass from 3
to the same instrument, and a wire to come back from
it to 4. The current enters at 1, passes up «, then

60 PHYSIOLOGICAL PHYSICS. [Chap. vi.

down the arc to the wire at 3, which is, therefore, + ,
through the instrument and back by the wire at 4,
which is, therefore, — . From 4 the current passes up
the arc to b, down to 2, and so back to the battery.
Suppose now the bridge be reversed. The current
enters at 1, passes up a, but can no longer pass down
to 3, because the arc is raised out of the mercury. It
goes down the other side, therefore, which dips into 5.
But at 5 there is no wire to lead it off, except the limb
d of the cross. Along d, then, it proceeds to 4, and by
the wire at 4 passes to the instrument, from which it
returns by the wire to 3. The wire at 4 is therefore
4- instead of — , as before ; and that at 3 is —
instead of + , as before ; that is to say, the direction
of the current has been reversed. From 3 the current
passes across c to 6, up the arc to b, and back from 2
to the battery. Consequently, with the cross in, re-
versing the commutator reverses the direction of the
current through one and the same apparatus. Suppose
it were a nerve to which the current must be con-
veyed, by means of the commutator the current could
be sent up or down the nerve at pleasure. (2) Let the
cross be taken out ; then, when the bridge is inclined as
in the figure, the current would pass off by wires
attached to 3 and 4 ; when the bridge is reversed it
would pass off by wires at 5 and 6. So that one
apparatus might be connected with 3 and 4, and
another and entirely different apparatus with 5 and 6.
Hence, the cross being out, the current can be sent now
to one and now to another apparatus at pleasure, the
commutator acting thus as a double key.

Electrodes. — For convenience in the application
of electricity various forms of electrodes have been
devised. One form frequently used is that of Du
Bois-Reymond's platinum electrodes (Fig. 34). They
are formed of a stand with a projecting arm, movable
by a universal joint at c. The arm carries a glass

Chap. VI.]

ELECTRODES.

61

Fig. 34.— Platinum Electrodes.

plate e, fixed into a block of vulcanite h. Through holes
in the vulcanite pass platinum wires, the ends of which
are beaten out flat and L-shaped. At the end d of
the platinum wires are
binding screws, by means
of which short wires from
the screws on b can be
attached, and these again
can be connected with
wires from an element or
induction coil. If then a
nerve be laid across the
L-shaped points, which
are not allowed to touch
one another, the current
will reach the nerve by
one platinum electrode, travel along the nerve till the
other electrode is gained, and so return. By the
screws in h the distance between one electrode and
another can be increased or diminished, and thus the
current can be made to travel through a greater or less
length of nerve. An easy way of making electrodes
suitable for physiological work is to pass two plati-
num wires through a piece of cork at the desired
distance from one another. The cork may then be
fixed to a support. The wires from battery or coil
can then be easily attached to two of the free ends.
Electrodes may also be made by fastening two wires
on either side of a slip of wood of the thickness suffi-
cient to keep them the desired distance apart. Coat
the whole with paraffin, and when it is cool the paraffin
can be scraped away and the requisite length of wires
exposed.

The moist stimulation tube is devised to
meet an objection brought against other electrodes ;
the objection, namely, that a nerve laid over the
ordinary electrodes rapidly dries, and is, therefore^

62 PHYSIOLOGICAL PHYSICS. [Chap. vii.

destroyed. A small glass tube drawn to a point at
one end is taken. The tube contains two ring-shaped
pieces of platinum, fixed a short distance from one
another. A fine copper wire from each ring passes
through the glass, and terminates in a free end. The
tube can be carried on a support attached by a swivel
joint to an upright stand. To use it for sending a
current to a nerve, tie a piece of thread round one end
of the nerve, and by means of the thread pull the
nerve gently through the small end of the tube, and
lay it over the ring-shaped electrodes. The thread is
carried out at the wide end and is held there, and the
tube is closed by a small cork. The space in the tube
being small, the air is easily saturated with moisture,
and the nerve is thus kept for some hours from drying.
The free ends of the ring-shaped electrodes are for
connecting with the wires from the battery or coil.

Other forms of electrodes will be noticed farther on
in connection with various experiments. In chapter
xv. electrodes for use in medicine and surgery are
shown.

CHAPTER VII.

EXPERIMENTS ON MUSCLE AND NERVE STIMULATION.

THE muscle telegraph (Fig. 35) of Du Bois
Reymond is devised for signalling when a muscle con-
tracts, and to some extent to indicate the amount of
its contraction. On a rectangular piece of wood gg
are two upright pillars. One pillar D supports the
forceps A, fixed in a handle B, in and out of the socket
of which they can slide and be secured by the screw s ;
the other pillar can be approximated to or removed
from D by sliding on z. The second pillar has a little

Chap. VII.]

THE MUSCLE TELEGRAPH.

Fig. 35.— The Muscle Telegraph.

pulley which carries an arm a, terminating in a disc c.
A thread passes over the pulley, and supports at one end
a small bucket b. To the other end of the thread is
fastened the hook x. When a frog's muscle has been
prepared in the man-
ner presently to be
described, it is held
in the forceps A,
by the end of the
femur, and the hook
x is passed through
the 'tendo Achilles.
The distance be-
tween the two pil-
lars being then re-
gulated, an d the
bucket being weighted by some small shot, the
muscle'is so stretched that the slightest movement of
it will act on the pulley and raise the disc in the
direction of the arrow. By means of a binding screw
&•' at the forceps, and a little screw at x, wires can be
connected for stimulating the muscle to contraction by
a current of electricity.

The nerve - muscle preparation is the one
generally adopted for experiments on muscle. Kill a
frog by severing with scissors the spinal cord at the
back of the head, and destroy reflex actions by passing
a needle up into the brain, and down the spinal canal.
Separate the lower limbs from the trunk by cutting
through with scissors at the middle of the back.
Seize the backbone with finger and thumb of left
hand, catch the loose skin with the right, and strip
the skin right down off the limbs. Turn the back of
one thigh up, and with finger and thumb on each side
separate the outer and inner divisions of muscles
along the line of a well-marked furrow which divides
them. The sciatic nerve will then be revealed as

64 PHYSIOLOGICAL PHYSICS. [Chap. vir.

a white cord passing down between the muscles.
Keeping he muscles separate, with the point of a
scalpel, by a slight stroke here and there, and without
touching the nerve, divide the fascia in which the nerve
is imbedded till it is completely shown from its
division just behind the knee-joint up to the place
where it disappears between ilium and coccyx. With
scissors cut through the ilium and the muscles of the
back above it, keeping well to the outer side, and, by
turning over the flap left connected with the vertebral
column, the nerves from which the sciatic is derived
will be seen. By clearing away the connective tissue
a long stretch of nerve from the lumbar region right
down to the knee is obtained. Reflect this stretch of
nerve over the gastrocnemius muscle ; then, holding
by the foot, with the scalpel scrape the femur clean of
muscle, and cut it through just below the head.
With the point of the scalpel pierce a small slit, to
admit the hook of the muscle telegraph, through the
tendo Achilles. Separate the tendon
from the foot below this, and by
pulling on the tendon separate the
gastrocnemius from the muscles below
it up to the knee. Snip through the
leg bones just below the knee, avoiding
all injury to the nerve. Thus there is
obtained the gastrocnemius M (Fig. 36),
with the long piece of nerve N at-
tached, the whole depending from the
Fig. 36. — Nerve- femur F, by means of which the

Muscle Pre- -, •. -, • ,-, ,.

paration. muscle can be clamped in the torceps

of the muscle telegraph, while the hook
of the telegraph can be passed through the opening
I in the tendon.

Difference between continuous, inter-
rupted, and induced currents. — This may be
studied with 'the aid of the muscle telegraph. Make

Chap. VII. INTERRUPTED CURRENTS- 65

the muscle preparation, and adjust it in the telegraph
as described. Take a Daniell's element, and cany
one wire from the positive pole to one side of the
friction key (Fig. 29) ; from the same side take
another wire directly to the screw s of the forceps of
the telegraph. Connect the negative pole of the
Daniell with the opposite side of the key, and from
that side take a wire to the hook in the ten do
Achilles. When the key is closed the current is
short-circuited ; when open, it passes through the
muscle. It will now be noticed that on opening and
closing the key, that is, on sending the current through
the muscle and on interrupting it, varying effects are
observed. Frequently there is only a feeble con-
traction of the muscle, shown by slight movement of
the telegraph signal ; the contraction is generally
more marked on interrupting the current ; but
while the current flows steadily through the muscle
no effect is apparent. Doubtless during the passage
of the current chemical changes are occasioned, and,
as will be seen in chap, viii., the excitability of the
nerve is altered; but 'no contraction occurs. In
other words, (1) a continuous current does not
stimulate to contraction, tohile (2) an interrupted
current does. Next, connect one pole of the
Daniell to the screw s" of the induction coil
(Fig. 23), and the other pole to one side of a simple
key, a wire from the other side of the key passing
to s'". By closing the key the current is sent round
the primary coil, and a single induction current or
shock is obtained, and the same on opening. Now
carry the wires from the secondary coil, one to the
forceps, and the other to the hook. On opening the
key a single vigorous contraction of the muscle occurs,
and the same on closing. Thus, (3) induced currents
of electricity are more stimulating than primary
currents. The arrangements for this experiment
P— 7

66 PHYSIOLOGICAL PHYSICS. [Chap. vn.

will be made still more complete if a key be inter
posed in short-circuit in the circuit of the secon-
dary wires ; that is to say, connect the secondary
wires one to each side of the friction key, and from
each side of the key carry wires to the muscle. In
order, then, to stimulate the muscle the secondary key
must be opened before the primary circuit is estab-
lished or interrupted. The advantage of this is that,
e.g. when the shock due to establishing the primary
circuit has been given to the muscle, the shock of
interruption may be spared it, if desired, by closing
the secondary key, and so short-circuiting the induced
current before the primary circuit is broken.

Thus it is apparent that stimulation is caused
by sudden changes in the strength of a current.
Tlie change may be effected by interruption of a
continuous stream, but induced currents excel by the
abruptness of their attack. For the same reason, in
an ordinary induction apparatus the induced shock of
closure is less irritating, because, owing to the acti >n
of the extra current, its maximum is gradually
acquired, while the induced shock of opening is more
stimulating because there is nothing to diminish its
suddenness.

By a modification of the arrangements a fourth
mode of stimulating muscle is obtained. Attach the
positive pole of the element to the pillar K of the
inductorium (Fig. 23), and the negative pole to a
simple key, the second wire from the key going to t/ie
binding screw z. Let the other arrangements be as
before. This throws into action the Wagner hammer,
or interrupter, and as soon as the primary key has
been closed, the screw s' being properly adjusted, the
primary circuit is rapidly opened and closed by the
movements of the hammer. This produces a rapid
series of induced shocks, which, on opening the
secondary key, go to the muscle, and irritate it so

Chap, vii.] DIRECT STIMULATION. 67

strongly that it is thrown into TETANIC CONTRACTION.
In other words, it has not time to relax after one
contraction before another shock is received. The
contraction is therefore continuous, and the muscle is
rigid. In all these experiments the current has been
sent through the muscle itself. This is called DIRECT

o

STIMULATION OF MUSCLE. The same experiments
should be repeated, using INDIRECT STIMULATION, that
is, stimulating through the nerve. For this purpose
detach the wires going to the forceps and the hook of
the telegraph, and attach them to the binding screws
of the platinum electrodes (Fig. 34). By means of a
camel-hair pencil, moistened with saliva, lift the nerve
hanging from the muscle preparation, and adjust it
over the points of the electrodes, the muscle being
secured in the telegraph as before. Let the nerve be
kept from drying by being moistened with saliva by
the brush. See that the nerve touches each electrode.
The space between the two points of contact should
be small. The nerve may in this way be stimu-
lated as the muscle was.

Difference between direct and indirect
stimulation. — Make a muscle -nerve preparation,
fix it in the telegraph, and stretch the nerve over the
platinum electrodes, or use the moist stimulation
tube (page 61). Connect a Daniell's cell with the
screws of the inductorium, so as to give single induc-
tion shocks, and interpose a simple key, as described
on page 57. Take the wires from the secondary coil
to cups 1 and 2 of the commutator (Fig. 33). From
cups 3 and 4 take two wires, and, for the sake of dis-
tinction, let them be covered with, say, red-coloured in-
sulating material, and connect them with the forceps
and the hook of the telegraph, so that the currenb will
stimulate directly. From cups 5 and 6 connect green-
covered wires to the electrodes, so that the current
will stimulate indirectly. Take out the cross of the

68 PHYSIOLOGICAL PHYSICS. [Chap. vn.

commutator. When the commutator inclines down
towards 3 and 4, direct stimulation is employed ; when
it is reversed, indirect stimulation. When the bridge
is placed quite horizontal, the arcs touch on neither
side ; no current passes, and so the commutator also
acts as a key. Now remove the secondary coil of the
induction machine along its roadway to some distance
from the primary ; incline the commutator bridge so
as to stimulate directly, and slowly approximate the
secondary coil to the primary, opening and closing the
primary key meanwhile. For a considerable time no
effect will be produced, and it is not till the secondary
is near to the primary coil (probably at a distance of
about 16 centimetres on the scale) that contraction
of the muscle is noted on opening (interrupting the
current), while very likely the secondary will require
to be a half nearer the primary coil (8 cc.) before
contraction 011 dosing is noted. Now, the key being
open, reverse the commutator, so as to send the
current to the nerve ; remove the secondary coil, and
repeat the manoeuvre of approximating it to the
primary, opening and closing the key the while. It
will then be found that the secondary coil at a much
greater distance from the primary, perhaps 70 cc.,
gives a shock, on opening, sufficient to cause contrac-
tion, and a little nearer produces a closing contraction.
By a similar arrangement, the greater stimulating
effect of a tetanising current, when applied me-
diately by the nerve rather than immediately to the
muscle, can be shown.

Fflueger's trip-2iammer, or fall-hammer. —
An objection to the accuracy of this comparison be-
tween opening and closing shocks is, that one cannot
be sure that the opening and closing are effected by
the use of an ordinary key with equal suddenness ;
for slight differences in the quickness of movement of
the key would produce a varying abruptness in the

Chap, vii.] PTLUEGER'S TRIP-HAMMER.

69

production of the induced currents, to which the
different effects might be due. To meet and obviate
this o b j e c ti o n,
Pflueger devised
the trip-ham in e r
(Fig. 37).

ebonite

supports

Tig. 37.— Pflueger's Trip-Hammer.

Aii

stand E

two brass up-
right pillars dd,
which carry two
electro-magnets K
K. A hammer-
head of soft iron
j is fixed at the
end of a steel
arm k, movable on an axle e. When the hammer
is raised, it touches the under surface of the electro-
magnets, and is retained by them there, provided a
current be passing round them to magnetise them.
The axle e is in connection with the binding screw c.

O

The hammer has a platinum-pointed brass hook m
attached to it, and when the head falls, owing to the
demagnetisation of the electro-magnets, the hook dips
into a cup of mercury x, which also has a binding
screw connected with it. a'b is a little spring-catch for
securely retaining the hammer when it has fallen. In
the front of the apparatus is a brass lever p, poised,
about its middle, on the axis connected with the
binding screw t. One end of the lever projects for-
wards, and rests on the screw-point R ; the other end
q projects behind under the hammer-head. Now,
suppose a current coming by a wire to R, it will pass
along the lever to the axle, and off by a wire at t.
Let, however, the hammer-head be released by demag-
netisation of the electro-magnets, it will fall on the end
q of the lever, depress it, and raise the other end so

PHYSIOLOGICAL PHYSICS.

[Chap. VII.

as to break contact with R, and thus, by the fall of the
hammer, the current ivill be interrupted. Secondly,
let one electrode from an element be attached to c at
the other end of the instrument, and let the second
electrode be attached to the screw in connection with
the mercury cup. The current would pass from c up
the handle of the hammer to the hammer-head, and,
when the head fell, would pass by the hook m through
the mercury, and off by the wire in connection. So that
by the fall of the hammer this current would be es-
tablished. In other words, by the fall of the hammer
the circuit at R would be opened, and that at X closed.
Thus, suppose these currents to be sent round the
primary coil of an induction machine, the secondary
wires of which were connected with a muscle, by the
fall of the hammer an opening or a closing shock
would be given to the muscle, and the opening
or closing would be effected with the same sudden-
ness in each case. The magnetisation
magnetisation of the eleetro-magnets is

a

BA '

de-

and

effected
Daniell's

element El, con-
nected with the
coils of wire by
means of bind-
ing screws, a key
or commutator,
with cross, being
interposed. A
Daniell is used
because it is just
sufficient to hold
the hammer up,
and consequently there is no delay in the hammer
dropping on interrupting the current. The arrange-
ment of the apparatus is shown in Fig. 38. E2 is
the element supplying the electro-magnets EZ-m, the.

Fig. 38.— Arrangement of Apparatus
Pflueger's Trip- Hammer.

with

Chap. VII.]

THE METRONOME.

commutator c, with cross, being interposed. The only
advantage of c over a key is, that by simply inclining
the bridge from one side to the other, Ei-m are demag-.
netised for an instant, and so the hammer falls, anclE -m
are immediately reinagnetised ; so that, to repeat the
experiment, one requires only to raise the head again.
El is the element for the primary coil I, and is so
connected with s and s' through the medium of L, that,
as already explained, the fall of the hammer-head
breaks the circuit. II represents the secondary coil,
whose wires can be led to muscle telegraph or elec-
trodes, as in former experiments. The second circuit
at H« and ax is not represented, for the sake of
simplicity. It is simply a repetition of EI s s', so
arranged that the fall of H closes the primary circuit.

Pflueger's hammer
can thus be arranged so
as to yield only an
opening induction shock,
or only a closing one,
according to the two
binding screws used.

The metronome.—
By using the ordinary
interrupter of the in-
duction coil, it is not
possible to estimate the
number of shocks given
to a muscle in a given
time. This it is desir-
able to do, to determine
what rapidity is neces-
sary for the production
of tetanus. By an
adaptation of the instrument used in music for
beating time, the metronome, this can be done, and
the rate of speed at which the shocks follow one

Fig. 39.— The Metronome.

72 PHYSIOLOGICAL PHYSICS. [ChnP. vn.

another can also be regulated by it to a large ex-
tent. The metronome (Fig. 39) consists of a box
containing clockwork, which causes the oscillations
of a rod t. The rod carries a small weight c, which
may be moved down the rod, causing the rod to
oscillate faster, or up the rod, when it will beat more
slowly. A scale fixed behind has marked on it the
number of oscillations per minute, corresponding to
different heights of the weight. On a little shelf at
the side of the metronome is a cup of mercury into
which dips one of the wires b of the primary circuit
of the inductorium. The other wire a is connected
by a binding screw with the oscillating rod. The rod
carries a projecting wire g, which, with one oscilla-
tion, is dipped into the mercury, forming the circuit,
and with the next is carried out of it, breaking the
circuit. Thus a definite number of contacts per
minute can be easily arranged, and consequently a
definite number of single induction shocks.

Secondary contraction. — An arrangement for
showing a very interesting experiment is represented
in Fig. 40. Two muscle telegraphs FI and F2 are so
placed that the muscle preparations fixed in them are
brought close to one another. The muscle mi of the
first telegraph is prepared without the nerve, that of the
second mz with the nerve. The nerve of ma is so laid
over mi that part touches the tendon of mi and part
the muscular fibres, mi has attached to it wires from
a secondary coil n, the primary of which receives a
current arranged for single shocks from a Daniell, a key
x being interposed, as shown in the figure. Muscle
2 receives no current. Then, by slowly approximating
the secondary to the primary coil and opening and
closing the key, a place will be found where a single
shock produces not only contraction of mi, but of
m2 also. The explanation is, that certain electrical
variations in mi, discussed in chapter ix., produced by

Chap. VII.]

CONTRACTION.

73

contraction, create a diiference of potential between
the part of the nerve that touches the tendon and the
part touching the muscle fibre of mi, and this difference
of potential irritates the nerve of ra2, causing its
contraction. Further, if the nerve of m-2 be laid on

.--r

Fig. 40. — Arrangements for showing Secondary Contraction of Muscle.

mi without any precaution as to position, and
tetanised, mz will be thrown into tetanus also.

Mechanical stimulation of nerve may be

effected by pinching the nerve, pricking, or beating
it, a contraction of the muscle resulting. An electro-
magnetic arrangement for producing tetanus by a rapid
series of such mechanical irritations was devised by
Heidenhain, and is called the TETANOMETER. It is a
modification of the Wagner hammer described on page
43, and is shown in Fig. 41. It consists of a block
of ebonite, on which there stands erect an electro-
magnet, consisting, as usual, of two soft iron cores
wound round with insulated coils of moderately thick
copper wire, so wound that on the passage of a current
the two pillars become like a horse-shoe magnet, of
which one is north pole, the other south. The keeper
of this magnet is a piece of soft iron L, which has
attached to it the lever 7iL,s"i. The lever is supported

74

PHYSIO LOGIC A L PHYSICS.

[Chap. VII.

Fig. 41. — Heidenhain's Tetanometer.

on a brass column by the axle «. The electro-magnet
is connected with the brass support of the arm k.
which can be caused to make or break contact with
the screw z by moving it with the insulated handle A.
The lever hass on its upper surface a steel spring i,

bearing a small
platinum plate which
presses against the
platinum point of
the screw sy, of the
brass column s. The
screw s" regulates
the pressure of the
platinum plate
against the platinum
point. The other
end of the lever
carries a wedge-
shaped piece of
ivory /<-, with the thin edge downwards, suspended
above a little ivory support t, which has a deep
groove. This ivory support can be raised up to the
lever or lowered from it by the screw sc. To
use the apparatus, the limb of a frog is taken, the
sciatic nerve is dissected out as long as possible,
and laid over the gastrocnemius. The muscles of the
thigh are then cleared away, and the femur snipped
through below the head. The limb is fixed by the
femur in a pair of forceps ; a fine silk thread is tied to
the end of the nerve, and by its means the nerve is
laid through the notches h' across the groove of
the ivory support t, and attached to the ivory axle A.
By turning this axle the nerve can be pulled through
the notches so as to bring a fresh piece across the
groove. One pole of an element is connected to the
screw stl and the other to z. The current passes up s
to the screw point st along the lever down the column

Chap. VII.] WOORARA EXPERIMENT. / 5

K, then to the electro- magnets, and from there to
the brass support of A, and by the arm K to z, if the
bridge be lowered. When the electro-magnet acts and
attracts the keeper L, the contact between st and the
platinum plate is broken and the current is interrupted.
The lever then, aided by its spring sp, flies back and
renews contact with s/5 and so the current is re-formed,
and immediately afterwards again broken by the
electro-magnets. By this means the little ivory
hammer h, when the apparatus is properly adjusted, is
kept beating on the nerve in the groove. The
attached limb is in consequence thrown into tetanus.
When the piece of nerve in the groove is beaten
through, a fresh piece is brought in by turning the
axle A.

Bernard's woorara experiment is de-
signed to prove the Hallerian doctrine that irritability
is inherent in muscular tissue ; that is, that muscular
tissue can be made to contract by the direct application
of other than nervous stimuli. For this purpose a
drug obtained from South America, and called the
Indian arrow poison, woorara, curara, or urari, is used,
because it paralyses the terminations of the motor
nerves. Five grains of the crude drug are rubbed
up with a little weak spirit in a mortar, and five drops
of glycerine and three drachms of distilled water are
added. Of this solution, six minims (equal to about
g^-th of a grain) are injected by a hypodermic syringe
under the skin of a frog. In a short time the muscles,
first those of the limbs, then those of the trunk, become
paralysed, and the frog lies flat out. The frog is then
decapitated, and the usual nerve-muscle preparation
made, and fixed in a muscle telegraph. A nerve-
muscle preparation from an unpoisoned frog is next
made and fixed in another telegraph placed in line
with the first. The best arrangement is to have a
double telegraph, in which there is only one forceps for

7 6 PHYSIOLOGICAL PHYSICS. [Chap. vn.

the muscles, but a flag arrangement on each side of it.
The two muscles are thus clamped in the same forceps,
but are directed opposite ways, so that the tendo
Achilles of one is fixed to the thread passing over the
pulley of the signal at one side, and that of the other is
fixed to the pulley of the other side. The nerve from
each preparation is laid over the same platinum
electrodes. Wires from the secondary coil of an in-
ductorium are led to the middle cups of a commutator
without the cross. From one side of the commutator
wires proceed to the platinum electrodes ; from the
other side wires are carried directly to the muscles, one
wire being attached to the hook in the tendon of each
muscle. Thus, when the commutator is laid over to
the one side, the induction current is sent to the
nerves ; when it is reversed, the current passes straight
through both muscles. First, then, stimulate by the
nerves. It is found that only the muscle of the un-
poisoned frog contracts, then stimulate the muscles
directly and both contract. The muscle, therefore, whose
motor nerves have been destroyed is still capable of re-
sponding to a stimulus by contraction. Another way
of performing the experiment is to ligature the artery
of one limb of a frog, or simply tightly ligature one
limb at the upper part, and then inject the woorara
solution under the skin of the back. The ligatured
limb receives no poison. In about half-an-hour the
frog is paralysed with the exception of the ligatured
limb. Make two preparations with the two limbs, and
it is found, as before, that while both muscles respond
when directly stimulated, only one responds when the
stimulus is applied to the nerves.

77

CHAPTER VIII.

ELECTROTONUS.

THE qualities of a nerve are found to be altered by
the passage through it of a current of electricity. To
the altered state of the nerve Du Bois-Reymond ap-
plied the term ELECTROTONUS, first used by Faraday
to denote the molecular disturbance produced in a
wire subject to induction. One of the most important
changes is in the nerve's excitability. The subject is
one of extreme difficulty, and at the same time of

\> *

great interest ; and in this chapter some of the ex-
periments connected with the subject will be given in
detail, in the hope that they may enable the student
more easily to pursue in other works the theoretical
portion of the subject.

The rheocord (pe'os = a stream ; x°P^ = a cord).
-The effects produced by the electrotonic state of a
nerve depend to a considerable extent on the strength of
the constant current used to produce the condition ;
and, consequently, some apparatus is required by means
of which the current strength may be varied at pleasure
and with rapidity. Such an apparatus is the rheocord
of Da Bois-Reymond (Fig. 42). It is formed of a
block of wood, near one end of which there runs a
transverse plate of ebonite, the shaded portion of the
figure. On this plate of ebonite are seven brass
plates (white in the figure), separated from one
another by a space. Each of these plates has a semi-
circular piece cut out of each side. The semicircular
gap of two opposing plates forms a round hole, into
which a brass plug, with an ebonite top, can be in-
serted to form a metallic connection between the

PHYSIOLOGICAL PHYSICS. [Chap. vin.

plates. These holes exist between all the plates,
except between the first two, and when all the plugs
are inserted the separated brass plates become, so far
as the conduction of a current is concerned, one con-
tinuous brass plate. From the first plate of brass at
a there runs a platinum wire, over one metre long.
It goes nearly to the other end of the block of wood,
and terminates at a screw at b, after passing over an

10

Fig. 42.— Rheocord of Du Bois-Reymond.

ivory knife ed^e. From the second plate at c another
similar wire runs parallel to the first, ending at d.
Stretching along the side of the block of wood from ac
to the ivory knife edge is a raised rail of wood, which
supports a little brass platform s, the one being dove-
tailed on to the other, so that they cannot be separated,
but so that the platform can slide along the rail from one
end to the other. The platform, or slider, as we shall
now call it, carries two little hollow cylinders of steel
shaped like conical bullets, with the pointed ends
directed to the brass plates. The cylinders are filled
with mercury, and closed at the wide end by corks.
The platinum wires pass through them by means of a
little hole in the pointed end and a small opening in
the centre of the corks. When the slider is brought
close up to the brass plates, the pointed extremities of
the cylinders make contact with the first and second
plates, between which, as already noted, there is no
space cut out for a connection by a brass plug. The
slider, therefore, establishes the connection, forming
by its steel cylinders in contact with one another and

Chap, viii.j THE RHEOCORD. 79

with the plates a bridge, over which the electricity may
pass from the one plate to the other.

When, however, the slider is pushed along its rail,
the current can only get across from the first plate to
the second by passing down one wire to reach the
bridge, crossing it, and so gaming the second platinum
wire, by which it passes back to the second plate.
The farther the slider is pushed in the direction of
the ivory knife edge, the longer road has the current
to travel before it can pass from the first to the second
plate, and the greater resistance it encounters on the
way. A millimetre scale pasted along the side of the
rail indicates the distance between the slider and the
brass plates. Now, suppose a current, brought to the
binding screw a, has, by passing over the bridge,
reached the second plate, it may pass directly across to
the third plate, provided a brass plug be inserted
between the second and third. If this brass plug be
removed, the current is not stopped, for there is
attached to the under edge of the second plate a
German silver wire (indicated by the dotted line in
the figure) which is sunk in the wood, and passes
along a considerable way to reach a pulley 1, round
which it turns, and goes back to reach the under edge
of the third plate, opposite to the second. This wire
affords, therefore, a sort of underground pathway
connecting the second and third plates, along which
the current may travel, when the removal of the
plug prevents it passing straight across. But this
underground pathway offers much more resistance
than the brass plug. It is of the same length as one
of the side platinum wires. Similarly between the
third and fourth brass plates there is an underground
road round the pulley 1', of the same length as that
round 1. Between the fourth and fifth plates another
German silver wire passes round pulley 2 ; it is twice
the length of the first, and therefore offers double the

8o PHYSIOLOGICAL PHYSICS. [chap. vin.

resistance. Between the fifth and sixth plates is a
similar wire, but five times the length of the
first, while that between the sixth and seventh is ten
times that of the first. Suppose, therefore, a current
enters at #, if the slider is pushed close up to the
brass plates, and all the plugs are in, no resistance
will be offered to the passage of the current
straight across to the binding screw at/; but then,
by pushing the slider up towards the knife edge, and
afterwards by removing one plug after another so as
to cause the current to traverse the German silver
wires also, a gradually increasing amount of resistance
may be interposed in the pathway of the current.
The resistance may also be varied at pleasure by
altering the position of the slider, inserting some
plugs or removing others.

The rlieocord must always foe connected
in sBiort circuit. — Thus, in Fig. 42, let E be the
element ; bring two wires from it, one, nl to a, at one
side, the other, n2 to/, at the other side, of the rheo-
cord, interposing a simple key x on the way. From a
take a wire hl to the apparatus, App, to which the
current is to be sent (the nerve to be electrotonised),
and from App bring a wire h2 back to the rheocord
at / Now when the current from the battery reaches
a it has two pathways ; it may go straight through
the rheocord and back to the battery (be short- circuited,
in fact), or it may go off by hl round App, and back
by h~ to / thence by n2 back to the battery, or part
may go through the rheocord, and part round App.
The course it takes depends on the resistance of the
two circuits. "When the slider is home, and the
plugs in, the resistance of the rheocord is practically
nil as compared with that offered by even a small
fragment of a nerve, and consequently all the current
will be short-circuited.

By then moving up the slider, and; if necessary,

chap, viii.] SCHEME OF ELECTROTONUS.

81

removing the plugs, resistance will be interposed in
the short circuit, the result of which will be that the
current will branch at screw e of plate a, part going the
short way and part the long. The intensity of the
current going to the nerve will be proportional to the
resistance thus thrown into the short circuit, and it
can, therefore, always be regulated and measured.

This being understood, let us now see what further
is necessary for showing some- of the effects of
electrotonus upon a
nerve. A reference
to Fig. 43 will show
what is required. The
figure shows the ordi-
nary muscle-nerve pre-
paration. On the upper
side of the nerve is an
element connected by
its poles with the side
cups of a commutator,
provided ivith a cross.
From the end cups pass

two electrodes to the Fig. 43.— Scheme of Electrotonus.

nerve. When the

bridge of the commutator is inclined in the direction
of the continuous arrow, the current will traverse the
nerve between the two poles in a downward direction,
towards the muscle, as shown by the. arrow above the
nerve. When the bridge is reversed, as indicated by
the dotted arrow, the current will be up the nerve, in
the direction of the dotted arrow below the muscle.
In the former case, the pole next the muscle will be
negative, in the latter, positive. Now the positive
pole is called the anode, and the negative the katode,
and it is found that the electrotonic condition of the
nerve is not the same at the positive and negative
poles. The condition at the positive pole is therefore
G— 7

82 PHYSIOLOGICAL PHYSICS. [Chap. vm.

called ANELECTROTONUS, at the negative, KATELECTRO-
TONUS. Further, the condition is not limited to the
poles, but extends for some distance on either side of
them. There is, accordingly, an area in the neigh-
bourhood of the positive pole that is in the an-
electrotonic state, and, similarly, a katelectrotonic
area in the neighbourhood of the negative pole. On
the under side of Fig. 43 are represented electrodes
from a secondary coil, for stimulating at one time
next the muscle, at another time away from it.

When the nerve is stimulated between the electro-
tonising electrodes and the muscle, the stimulation
is said to be MYOPOLAR, near to the muscle. When
the stimulus is applied beyond the electrotonising
electrodes, it is said to be CENTRO-POLAR, near the
centre from which the nerve proceeds. The dotted
lines in Fig. 43 represent the stimulating electrodes
in the centro-polar region.

Thus, to show the effects of electrotonus on the
excitability of a nerve, the following things are neces-
sary : (1) a constant current for throwing the nerve
into an electrotonic state, (2) an apparatus for
varying the strength of the current at pleasure, the
rheocord, (3) a means of sending the constant
current at one moment up, at another down, the
nerve, i.e. a commutator, (4) a current for stimulating
the electrotonised nerve, an induction current, (5)
an arrangement for stimulating near or far from the
muscle at pleasure, another commutator.

Fig. 44 is a diagram of the arrangements and
exact connections.

At the upper right-hand corner of the figure is
the muscle telegraph, with the muscle preparation M
fixed in the forceps. The nerve of M is laid over the
electrodes El. These electrodes are shown in Fig. 45.
They are formed of platinum wires stretched across a
little box of ebonite. The wires are at least four

chap, viii.] ARRANGEMENTS FOR ELECTROTONUS. 83

in number, separated from one another, and each
having a binding screw outside. A current may
enter by a, reach the nerve, pass down to the next wire,
and off by the binding screw b. So the constant

Fig. 44. — Diagram of Arrangements for Showing Effects of Electro-

tonus on Excitability.

current may pass by the wires connected with a and
6, and the stimulating current by the wires connected
with c and d, or vice versa. The little box is covered
with a glass lid to prevent evaporation, and a piece of
wet blotting paper may be laid
in the box to keep the nerve
moist. At the lower left-hand
corner of Fig. 44 are four Grove
cells, of a small size, as used
by Du Bois-Reymond. From
the positive pole ( + ) a wire
goes to one side of the com-
mutator c, and from the

negative pole a wire to the other side. This com-
mutator is supplied with a cross. DC is a double
commutator, formed of twTo ordinary commutators, but
without the cross. They stand side by side, and are
connected together by an insulating handle, which
enables the bridge of both to be inclined to the same

Fig. 45.— Electrodes.

84 PHYSIOLOGICAL PHYSICS. [Chap. vm.

side at the same time and by the same movement.
K is a simple mercury key interposed in the circuit of
the four Groves. At the right side of the figure is E,
a Daniell's element, connected, for the production of
tetanus, with the primary coil of the induction
machine, a key x being interposed. The secondary
coil ii is arranged in short circuit with the key k'.
To return to the single commutator c. Wires from it
pass to the rheocord R, arranged in short circuit.
The long circuit from R goes by the mercury key K,
to the left side of the double commutator DC, the wire
from d of the rheocord going through K to d' of the
double commutator, and that from c of the rheocord
going to c' of the double commutator. If now the
bridge of the commutator c be inclined in the direc-
tion of the continuous arrow, the wire to c of the
rheocord is +» the wire c' is then -J-, and suppose DC
inclined in the same direction, the wire from cup 4
is -}-. So that a current going by that wire would
reach the nerve by number 4 wire of the electrodes,
would pass up to wire 3, by it back to cup 3 of DC,
and back to the battery by d', k, and d of the rheo-
cord ; that is, the current would travel up the nerve.
If, on the other hand, the commutator c be inclined in
the direction of the dotted arrow, then the wire to d of
the rheocord, as shown by ••• , is +3 the current goes
through k to d', out by 3 to the electrodes, and, in order
to gain wire 4 and get back to the battery, it must go
down the nerve. By the commutator c, with its cross
in, the electrotonising current is sent up or down the
nerve. Observe next that the wires from the key k' go
to the cups a 'b' of the right half of DC. As already
noted, if the bridge of DC be down towards 3 and 4
(that is, towards 1 and 2 also, since the two sides of
DC are connected together) the current from the Grove
cells (electrotonising current) will go by the cups 3 and
4 to the similarly numbered wires of the electrodes,

Chap, viii.] ELECTROTONIC EXPERIMENTS. 85

and the current from the induction coil will go by the
cups 1 and 2 to these wires of the electrodes. In
other words, the electrotonising wires are 3 and 4,
next to the muscle, and the stimulating electrodes are
1 and 2, away from the muscle. The stimulus, there-
fore, is in the centro-polar region. But let DC be
reversed, so as to dip towards 1' 2' and 3' 4', then the
electrotonising current by the wires d' c' can no
longer get to the cups 3 and 4, the contact being
broken, but must go down to the opposite cups 1 ' and
2 ', where it catches the wires that carry it over to the
other half of DC to the cups 1 and 2. The wires
1 and 2, therefore, become electrotonising. In the
same way, the induction currents are led down to
3 ' and 4 ', and from them to 3 and 4, and so the wires
3 and 4 become the stimulating electrodes. The wires
have, therefore, by reversing DC, been reversed, and
the stimulation would now be applied by wires 3 and
4, between the muscle and the electrotonising wires,
in the myopolar region therefore. Thus by reversing
the commutator c, the constant current is sent up or
down the nerve, and by reversing the double commu-
tator DC, the stimulation is made centro-polar or
myopolar. The strength of the constant current is
regulated by the rheocord, and thus the desired con-
ditions are obtained.

To perform tlie experiments it is necessary
to remember the rule that the excitability of a nerve
in the electrotonic state is increased in the neighbour-
hood of the negative, and diminished in the neighbour-
hood of the positive, pole. There are four cases, which
are represented in the diagram (Fig. 46). In the first
two cases the stimulation is in the myopolar region,
in the second two, in the centro-polar region ; and in
each set there is one case of downward and another
of upward current. In the first case, the stimulation
is next the muscle, that is, in the myopolar region,

86

PHYSIOLOGICAL PHYSICS. [Chap.vm.

and, the electrotonising current being downward, the
stimulus is applied in the neighbourhood of the - - pole,
in the region, that is, of MYOPOLAR KATELECTROTONUS.
In the second case the stimulus is also myopolar, but
in the neighbourhood of the + pole, therefore MYO-
POLAR ANELECTROTONUS. The other two cases are seen
by the diagram to be CENTRO-POLAR ANELECTROTONUS,
and CENTRO-POLAR KATELECTROTONUS. Therefore, both
circuits being open, incline the commutator c (Fig. 44)

Meet _ISt

IcfSftF

Cenlrn<

Fig. 46. — Results of Electrotonus.

so that the constant current may be down the nerve ;
incline the double commutator to stimulate near the
muscle, that is, by wires 3 and 4 ; then open the key
of the induction coil, so as to send shocks to the
nerve; slowly approximate the secondary coil to the
primary, till the strength of the induction shocks is
just sufficient to cause the muscle to twitch the tele-
graph signal. At this point close the mercury key K,
and send on the constant current ; electrotonus is
established in the nerve ; the region of the negative
pole, where the stimulus is being applied, is thrown
into a state of increased excitability, and consequently
the current, before just sufficient to twitch the muscle,
now throws it into tetanus ; tetanus appears. In-
terrupt both currents.

chap, viii.] THE LAW OF CONTRACTION. 87

Reverse c, so that the electrotonising current is
now up the nerve. Proceed again to stimulate the
nerve, and this time approximate the secondary coil
just till the muscle becomes tetanised. Then close
the constant circuit. The stimulus is now in the
region of anelectrotonus (i.e. of diminished excita-
bility), and consequently the stimulus, before just
sufficient to tetaiiise, is now no longer sufficient ; the
telegraph signal drops ; tetanus disappears.

Proceed in the same way with the other two cases.
Reverse the double commutator, to change the position
of stimulating electrodes, which must now be the wires
1 2, distant from the muscle, and arrange commu-
tator c to get a downward constant current. Stimu-
late till tetanus affects the muscle, then electrotonise;
anelectrotonus (diminished excitability) is established
in the region where the stimulus is applied, and so
the stimulus is no longer sufficient ; tetanus dis-
appears. Send, lastly, an upward current; you
stimulate now in the region of increased excitability,
and consequently tetanus appears. Electrotonus also
alters the electromotive force of a nerve. (Refer to
chapter xi.) In the way thus detailed the student
can satisfy himself that the excitability is increased in
the neighbourhood of the negative pole when a nerve is
made electrotonic.

L,aw of contraction. — Another use of the
rheocord is for aiding in the study of the effects of
the interruption of the constant current upon a nerve.
As already noted (page 65), the passage of a continuous
stream through a nerve has 110 apparent effect. On
opening (breaking) the circuit, however, or on closing
it, varying effects result, sometimes a contraction
occurring on opening and none on closing, and vice
versa, and other differences. These variations have
been studied by various observers, Pfaff, Ritter,
Nobili, Heidenhain, Pflueger, and others. As a result

88 PHYSIOLOGICAL PHYSICS. [Chap. vm.

of investigation, it is found that the occurrence
of a contraction, and the amount of the contraction,
whether feeble or strong, depend ( 1 ) on the strength of
the current, and (2) on the direction of the current.
The rheocord gives the simplest means of graduating
the strength of the current, and the commutator the
means of reversing it. The diagram (Fig. 47) shows
how the arrangement ought to be made. R repre-
sents the rheocord, c a commutator, with cross, and
E the galvanic elements, which may be 3, 4, or other
number, of the small Grove elements, all arranged
precisely as shown in the diagram. The muscle-nerve

Fig. 47. — Arrangements for Studying the Law of Contraction.

preparation M is arranged in the telegraph, and the
nerve is laid over the platinum electrodes, which
are connected with the wires coming from the
rheocord. Now by altering the number of Grove's
elements, and especially by altering the position of
the rheocord slider, and by means of the plugs, as
explained (page 81), no current may be sent to the
nerve, or a current may be sent whose strength may
be graduated to any desired extent. To open and
close the current, a simple mercury key is interposed ;
or, better still, in order to make or break the current
always with the same rapidity, Pflueger's fall hammer
(page 69) may be used as a key. Make the experi-
ments in the following way.

By means of the rheocord send only a very weak
current to the nerve ; arrange by means of the com-
mutator that the current shall pass down the nerve,
close the key, and note the result ; then open the key,

chap, viii.] THE LAW OF CONTRACTION.

89

and note the result. Now reverse the commutator,
to get an upward current, and watch effects on
closing and opening with the same current strength.
Next, by moving the slider and taking out some plugs
of the rheocord, give a stronger current (medium),
and note results on closing and opening, first with a
downward, and then with an upward, current. Lastly,
interpose great resistance in the short circuit, to get
a strong current for the nerve, and observe the effects
of closing and opening with the current in different
directions. The results thus obtained should be
tabulated in the following way :

i.

LAW OF CONTRACTION.
II.

III.

•t

•I

"Weak Stream.

Medium Stream.

Strong Stream.

CL— c.

Op.— r.

CL— c.

Op.— c.

Cl.— c.

Op.— r.

OL— c.

Op. — r.

Cl.— c.

Op.— c.

CL— r.

Op.— c.

where, at the head of each column, the strength of
the stream is indicated. Cl. means closing the circuit,
Op. means opening or breaking it, c. means contraction
of the muscle, and r. means rest, no contraction ; while
the direction of the current, J, , down the nerve,
or ^, up the nerve, is indicated at the side. Thus,
the first column would read : With a weak current, in
an upward direction, there was contraction on closing
the circuit, and rest on opening ; and with a downward
current of the same strength there was also con-
traction on closing and rest on opening. Experiments
should be made both with a quite fresh nerve and
with a nerve that has been allowed to lie for some
time after the death of the animal. This will show
that a weak current will give with a fresh nerve the

90 PHYSIOLOGICAL PHYSICS. [Chap. ix.

results shown in the first column, that when the
nerve has been exposed for a little time, the same
strength of current gives the results shown in the
second column, that is, produces the same effects as
a stream of medium strength would do in a fresh
nerve ; and, when the nerve has been exposed for
a still longer time, the results of the third column are
obtained, i.e. the results of passing a strong stream
to a fresh nerve. Thus is obtained an experimental
demonstration of the fact that the excitability of a
nerve increases as the nerve dies, and reaches a maxi-
mum just before it finally disappears.

CHAPTER IX.

MAGNETS, AND THE ACTION ON THEM OF ELECTRIC

CURRENTS.

A magnet is a body that has the property of
attracting iron. Natural magnets exist as an ore of
iron, whose formula is F"e2O3, and which was known
to the ancients, from whom the term magnet (^71/777775)
is derived, because the ore was found in the neigh-
bourhood of the town of Magnesia in Lydia. Mag-
netic properties can be communicated in various ways
to iron and steel, and these become artificial magnets.
The natural magnet was also called loadstone (Saxon
for leading stone), because when freely suspended it
always turned in such a direction, that its long axis
pointed north and south, the same extremity of the long
axis always being to the north, no matter how the
magnet was turned, so long as it was free to move.
The attractive power of a magnet is found to be
greatest at the ends, which are accordingly called the

chap, ix.] MAGNETS. 91

POLES, and to vanish at the middle, where there is a
NEUTKAL ZOXE, or indifference point.

Attraction and repulsion. — It has been said
that a freely suspended magnet always turns so as to
set one pole towards the north pole of the earth, and
the other towards the south pole. If now a second
magnet be brought near, it is found that on presenting
the pole of the second that points north to the similar
pole of the first, freely suspended, the latter is at once
repelled ; but if the south pole of the second be pre-
sented to the north pole of the other, they attract one
another. Thus, like poles repel, but unlike poles at-
tract. An explanation of the invariable tendency of
a magnet to point north and south is, therefore, forth-

coming.

It is supposed that the earth is a magnet which
acts on freely suspended magnets in the way men-
tioned, attracting by each pole the unlike pole of the
magnet, and repelling by each pole the like pole of
the magnet. Thus, the north pole of the earth will
attract the south pole of a magnet, and repel the north :
and the south pole of the earth will attract the north,
and repel the south, of a magnet. Thus, the pole of a
freely suspended magnet that points north is actually
the south pole of the magnet. Owing to this circum-
stance, confusion in the designation of the poles of a
magnet has arisen. Thus, the one pole is called the
north-pointing, or north-seeking pole, and with that
there is no difficulty. But because this is actually the
south pole of the magnet it has been called the austral
pole, and the south-seeking pole has been called boreal.
.French writers speak of aiistral and boreal. In Eng-
lish, usually, by north pole is meant the pole that
points north, and by south pole the one that points
south. For convenience sake the pole of a magnet
that points north is usually marked, and is, there-
fore, also called the marked pole.

92 PHYSIOLOGICAL PHYSICS. [Chap. ix.

Two fl Beads. — As in electricity there ha,ve been
supposed to be two subtle imponderable fluids, posi-
tive and negative, pervading all objects, so there have
been supposed to be two magnetic fluids, which attract
one another. In unmagnetised bodies these fluids
neutralise one another j in magnetised bodies they are
separated.

Magnetic induction. — Just as a conductor
charged with electricity, when brought near an un-
charged body, was supposed to decompose the neutral
fluid of the uncharged body, attracting one of the
electricities to the end near it, and repelling the other
electricity to the other end (page 6), so a magnet, when
brought into contact with a substance capable of being
attracted by it, was supposed by induction to separate
the magnetic fluids of the attracted body, attracting
the one to one end and repelling the other. Thus,
when a piece of soft iron is touched, say by the north
pole of a magnet, the iron adheres to the magnet, and
becomes for the time also a magnet, having a north and
south pole, the south being the one in contact with
the north of the original magnet. As soon, however,
as the piece of soft iron is removed from the magnet
it loses all its magnetism. Iron that has been rendered
brittle, or hard steel, are not so easily affected by a
magnet as soft iron ; but when at length they are
affected, the magnetism developed in them is more
permanent. Well-tempered steel, especially, suffers
little attraction by a magnet, and is magnetised with
difficulty, rubbing with the magnet requiring to be re-
sorted to, but it then becomes a PERMANENT MAGNET.
The force which makes tempered steel resist the in-
fluences, and, when it has been affected, causes the mag-
netism to be retained, is called COERCIVE FORCE.

Permanent magnetisation is effected in
various ways : (1) by single touch, i.e. by laying on a
table the bar to be magnetised and stroking it several

chap, ix.j MAGNETIC NEEDLE. 93

times with one pole of a strong magnet held in a
sloping direction, moving always in the same direction,
from one end to the other of the bar, the end touched
last forming the pole opposite to that of the influencing
magnet used • (2) by separate touch, i.e. by using two
magnets of equal strength, placing opposite poles in
contact with the bar at the middle and moving them,
both at the same time, away from one another to
opposite ends, repeating the manoeuvre several times ;
(3) by double touch, i.e. by placing the opposite poles of
two magnets, separated by a piece of wood in the
middle of the bar, and moving them together to one
end, then from this to the other end, and from it back
to the middle. The method most frequently used is
by drawing the bar over the opposite poles of a strong
electro-magnet in opposite directions.

Strong magnets are formed of several bars, shaped
like a horse-shoe, bound together, like poles being
placed together. Suppose two bars equally strongly
magnetised are placed together, so that unlike poles
are in contact, then the magnetism of the one neu-
tralises that of the other, and the result is loss of all
magnetism so long as they remain in contact. There-
fore, for forming a MAGNETIC MAGAZINE or BATTERY, as
it is called, like poles are placed in contact. The
strength of such a magnet is found to be preserved
by placing across from one pole to the other a piece
of soft iron, called a KEEPER, or ARMATURE. This
reacts inductively on the poles, and so preserves their
magnetism and even increases it.

Inclination or dip. — Tf a magnet be suspended
so that it is free to move both horizontally and ver-
tically, it not only points north and south, but one
end is found to dip down. This is the inclination of
the magnet. In the northern hemisphere it is down
towards the north, and vice versa.

A magnetic needle is usually in the form of

94 PHYSIOLOGICAL PHYSICS. [Chap. ix.

a rhomb made of fine steel, long in proportion to its
breadth. Its north pole is usually coloured blue ; near
its centre is a little depression by which it can be
balanced on a point of support.

Care of a magnet. — Magnets should never be
left without their keeper, or they will lose strength.
The keepers should not be knocked off, but slowly
moved off by a turning movement from north to
south. Magnets should not be let fall, nor suddenly
struck, nor rubbed with sand-paper, as the magnetism
may by these means be greatly diminished. They
should be kept from rust by the use of fine sperm oil.

Paramagnetic and diamagnetic. — Bodies
that are attracted by either pole of a magnet are
called paramagnetic. Among them are iron, nickel,
cobalt, and platinum. When placed between the poles
of a horse-shoe magnet, they turn their long axis so
as to be in line with the poles.

Bodies that are repelled by either pole of a magnet
are said to be diamagnetic. Among them are bismuth,
antimony, lead, tin, copper, gold, and silver. Water,
sugar, starch, alcohol, muscle, and blood, are also dia-
magnetic. When placed between the poles of a
magnet they tend to set their length across the poles.

Action of electric currents on magnets.
—In 1819 Oersted of Copenhagen showed that a needle
suspended in the magnetic meridian was influenced
by a current of electricity passed along a wire
parallel to it. The experiment is performed by
placing a wire above a magnetic needle, and parallel
to it; and another wire below the needle, and parallel
to it. The poles of an element may then be attached
to the extremities of either wire, and a simple key
interposed in the circuit thus formed. On closing
the key the current passes along the wire. When
a sufficiently strong current traverses either of
the wires, the needle is deflected nearly to a right

Chap. ix. j AMPERE'S LAW. 95

angle. The side to which the needle is deflected de-
pends on the direction of the current, and whether
passed above or below the needle. The laws of
direction were worked out by Ampere ; and he has
given an easily remembered rule for determining the
directions. Suppose an observer placed parallel to
and facing the wires, and let the current be directed
as if passing from his feet to his head, then the north

Figs. 48_aud 49.— Ampfcre's Law.

pole will be deflected to his left, and the south pole in
the opposite direction. This rule is illustrated in
Figs. 48 and 49.

It is seen that a current flowing above the needle,
which deflects the needle to the left, will, if it flow in
the same direction below the needle, deflect it in the
opposite direction. In the figures, AB is the magnetic
needle, A the north pole and B the south, and XY
is the wire along which the current passes, the
arrow indicating the direction of the current.
Arrows and dotted lines indicate the deflection
of the needle. Thus the north pole A is de-
flected in the direction of the arrow to A, and the
south pole B to B'. Again, a needle deflected to the
left by a current flowing in one direction above it,
will be deflected still farther to the same side by
a current below the needle in the opposite direction.
Thus a current carried right round the needle will
travel above the needle in one direction, and below

96 PHYSIOLOGICAL PHYSICS. [Chap. x.

the needle in the opposite direction, and by this
means its effect on the needle will be increased. This
application of the principles of Oersted arid Ampere
was made by Schweigger in Germany in 1820, who
coiled the wire on a rectangular frame (Fig. 50). By
coiling the wire on the frame oftener than once the
effect of the current is increased, provided that each

turn of the wire be carefully insulated
from the other. Thus an instrument
called a MULTIPLIER is constructed,
by means of which a weak current,
which might not have any effect
on a needle, has its action so in-
Fig. 50.— Multiplier, creased that deflection of the needle

occurs. This instrument can now
be used as a means of detecting the presence of a
current. By its means not only the presence, but
also the direction and the amount of a current can be
estimated. Hence the term GALVANOMETER applied
to the instrument. Its developments are described in
the next chapter.

CHAPTER X.

GALVANOMETERS.

THE tangent galvanometer is an applica-
tion of the principle laid down by Schweigger. It
is formed of a vertical circle standing in the plane of
the magnetic meridian. The circle may be formed of
a ribbon of copper, or may consist of a wooden frame
with several turns of copper wire (each turn being
insulated) wound upon it. The ends of the wire are
connected to whatever is producing the current. In
the centre of the circle is mounted horizontally a

chap. x. ] SINE GA L VA NOME TER. 9 7

magnetic needle, whose length is small in comparison
with the radius of the circle. The needle is surrounded
by a horizontal circle marked in degrees ; and it
points to zero when the galvanometer is in proper
position. When a current traverses the wire the
needle is deflected. In its new position it is acted
on by the force of the earth's magnetism tending
to bring it back to zero, and by the repulsive action
of the current, which tends to set it at right angles.
It accordingly takes up a position between the twTo,
and this position is such that the tangent of the angle
of deflection is proportional to the intensity of the
current. When the amount of deflection caused by
the current is great the proportion is not accurately
maintained. To meet this the sine galvanometer
is constructed, in which the vertical circle is movable
round a vertical axis ; in this form the sine of the
angle of deflection is proportional to the intensity of the
current.

Now the great objection to the use of either of
these forms of galvanometer is that they always
require a comparatively strong current to influence
the magnet. As already indicated, multiplication
of the number of turns of the wire in the circle
surrounding the magnet will increase the effect upon
the needle, and the greater the multiplication, there-
fore, the weaker may the current become without
losing influence on the needle. But this multiplication
has its limits, since every turn interposes resistance,
and consequently weakens the current. The great
cause of the non-sensitiveness of the needle is, how-
ever, the directive action of the earth, since as soon
as the needle moves out of the magnetic meridian this
force comes into play, tending to bring the needle back
again. It was, therefore, a great step in the production
of sensitive galvanometers when Nobili, in 1827, de-
vised a method for diminishing as much as possible

H— 7

PHYSIOLOGICAL PHYSICS.

[Chap. X.

the action of terrestrial magnetism upon the needle.
In Nobili's arrangement, two needles ab a'b are taken,
both as nearly as possible equally magnetised. They
are united by a light piece of tortoise-shell, and are
^^^ so placed that the north pole of one

J | is opposite to the south pole of the
other (Fig. 51).

If both needles have exactly the
same degree of magnetisation, then
the influence of the earth on the north
pole of one is neutralised by the pre-
cisely equal influence on the south
pole of the other. The result is that
with such a system of needles the

Fig. 51.— The As- v ,. £ r J.T xi >

tatic Needle-pair, directive torce or the earths mag-
netism is removed, and then the
needles set perpendicular to the magnetic meri-
dian. Such a system is called ASTATIC. If such
a system be surrounded by a coil of wire (Fig. 52)
so that the under needle ab is in the centre of the
coil, and the upper needle a'b'
just above the coil, then a
current passed round the coil
will deflect both needles in the
same direction, according to
Ampere's rule. Thus, such a
system, being rid of the earth's
action, is not only free to obey
any other force, but by the
double needle the effect of a cur-
rent round the coil is increased.
Such an arrangement is conse-
quently able to detect a very much feebler current
than a single needle can. Should both needles not be
equally magnetised, then the earth will influence the
needle of greater magnetisation, and the system will
be brought into the plane of the magnetic meridian.

Fig. 52.

chap, x.] ASTATIC NEEDLES. 99

But the influence of the earth will be very much
diminished, because it will only affect the system
according to the excess of magnetisation of the one
needle over the other. In point of fact it is difficult
to get a perfectly astatic system. Usually when the
system has been deflected by the action of a current,
on the removal of the current the needle will be found,
after a few oscillations, to come at last to rest in the
plane of the magnetic meridian. The more nearly
astatic the system, the slower will be these oscillations,
so that, by this means, one may test the condition of
the system. By the use of a feeble magnet, however,
a pair of needles not quite astatic may be made
absolutely so. It is only necessary to bring such a
magnet into the neighbourhood of the needle-pair,
and to keep it in the magnetic meridian, and with its
north pole pointing south. By bringing it gradually
nearer to the needle-pair a position is at length found
where it completely neutralises the earth's influence,
and perfects the degree of astaticism. By a similar
means a single needle may be made astatic.

Aided by this astatic system of needles ISTobili
constructed a very sensitive galvanometer, by means
of which very feeble currents of electricity were
detected. The general form the galvanometer then
took was briefly this : A great length of fine copper
wire was wound on an ivory frame, each turn being
carefully insulated from its neighbour, and the ends
of the wire were connected with binding screws. The
needles were suspended from a support by a fine silk
fibre, so that one needle was within the coil, the other
just above it. The whole was carried on a block of
ebonite, and covered in by a glass case for the exclu-
sion of air currents. The chief modern workers who
have added to the sensitiveness of the galvanometer
are Du Bois-Revmond, of Berlin, and Sir William

«/

Thomson. The former himself constructed a very

TOO

PHYSIOLOGICAL PHYSICS.

[Chap.X.

sensitive instrument, Laving as many as 30,000 coils
of fine wire. The form of instrument mainly used
now is the reflecting galvanometer, of which two
forms will be described, that of Sir William Thomson,
largely employed in this country, and one of a German
origin, called Wiedemann's galvanometer.

The feature of Sir William Thomson's instrument
(Fig. 53) is the small size of the needles, so that they
possess little weight, with a high degree of magnetisa-
tion. The magnets are very thin,
usually not more than one- eighth
of an inch long, and are arranged
in two sets, an upper and a lower,
connected together by an aluminium
rod. The needles of each set are
arranged astatically. Round each
set is a separate coil of wire, the
lower coil (6, Fig. 53) having
its course in opposite direction to
the upper. The coils are brought
very near to the needles, and con-
tain a very large number of turns
of fine wire. Fixed to the upper
set of needles is a slightly concave
Fig. 53.— Sir Wm. mirror, not more than one quarter

Thomson'sReflect- r> i v j_ rrn

ing Galvanometer, of an inch in diameter. Hie
system of needles and mirror is so
light as to weigh barely a grain.

The system is suspended by a single fibre of fine
silk from a brass pin fixed on the top of the vulcanite
frame of the coils. The coils are supported on brass
uprights. The whole apparatus stands on a vulcanite
disc, brass-bound, and levelled by three screws, and is
enclosed in a brass-bound glass shade. The cover of
this shade is of brass, and supports a brass rod c, on
which slides a large curved magnet d, feebly magnetised,
by which an artificial meridian can be created in any

Chap, x.] THOMSON'S GALVANOMETER. 101

desired direction. The magnet may be brought near to,
or moved from, the needles by sliding down and up
the rod. Four binding screws have attached to them
the four ends of the wire of the coils.

To use the instrument a lamp-and-scale arrange-
ment is employed (Fig. 54).

The lamp and scale are placed facing the galvano-
meter at a distance of from two to three feet. A slit
below the scale permits a narrow beam of light to pass,
which is thrown on the mirror
of the upper needles, and from
it reflected on to the scale. The-
large magnet, which may be
turned by hand or by the fine
adjustment screw attached to
the cover, aids in bringing the

7 O O

beam to the zero point. AcrOSS Fig. 54.— Lamp and Scale for
the Slit is Stretched a wire, Galvanometer.

and the image of this ought to be focussed on the
scale. The current may be sent round both coils by
connecting the two middle binding screws, and then
joining the electrodes with the outer screws ; or the
instrument may be used to compare two currents, in
which case the electrodes for one current are to be
connected with the screws of one side, those for the
second current with the screws of the outer side. The
currents must be sent round both coils in the same
direction, so that the current passing round the
upper coil tends to deflect the needle in one
direction, and the current passing round the lower
coil tends to deflect the needle in the opposite
direction. If both are equal the spot of light will be
stationary on the scale ; if one is stronger than the
other the spot of light will travel over the scale, and
indicate the excess. By a preliminary experiment the
direction of deflection by each current can be deter-
mined separately, and thus it is easy to learn which is

102 PHYSIOLOGICAL PHYSICS. [Chap. x.

the more intense current of the two. When used in

this way the galvanometer is said to be DIFFERENTIAL.

To obtain the acme of sensibility of the

instrument, the following procedure should be adopted.
Place the galvanometer so that the coils face due east
and west, the galvanometer looking west towards the
lamp and scale, which are about three feet distant.
Having carefully levelled the instrument by the level-
ing screws, remove the glass shade, and see that the
needle swings freely in its small cellular space within
the coils. By gently moving the milled head of the
brass pin from which the needles hang, the needles
may be raised or lowered. Free suspension being
obtained, put on the glass shade, the controlling
magnet being removed. In the position of the
galvanometer, the system not being absolutely astatic,
the needles will take up a position of rest in the plane
of the magnetic meridian. Now put the controlling
magnet on its support quite at the top, with its
north pole pointing north, and slowly slide it
down its support. The aim is to obtain a position in
which the controlling magnet quite neutralises the in-
fluence of the earth's magnetism. As the magnet is
moved down, the needles will at first dance backwards
and forwards, but as the magnet approaches the
proper position the oscillations of the needles become
fewer and much more slow. It should be noted
that the more sensitive the needle is, the greater is the
time occupied by one oscillation, or, in other ivords, the
longer is the period of oscillation. This gives an
important indication in adjusting the magnet. Now,
as the magnet nears the position in which it renders
the needles astatic, the slightest movement of it to right
or left will cause the beam of light to travel from one
side to the other of the scale and even beyond the scale,
consequently the fine adjustment must now be used if
it is wished to turn the controlling magnet. Just

Chap, x.] GALVANOMETER SHUNT. 103

when the magnetism of the earth and that of the con-
trolling magnet are on the border land of neutralisa-
tion, the needles will be found to be unstable ; i.e.
the slightest movement of the magnet to one side will
cause the spot of light to dash across to that side, the
slightest movement to the other side will send it over

o

to that other side, and it will be impossible to bring it
by the influence of the magnet to the zero point.
This is because the influence of the earth has been
more than neutralised, and the needles consequently
come under the influence of the magnet, and tend to
turn right round to set their opposite pole under that
of the magnet. The position of greatest sensibility
will now be found by very carefully moving the
magnet up its support, by scarcely more than a hair's
breadth at a time, after. each movement giving the
fine adjustment the smallest possible turn, till the
instability disappears, when, by a very slight turning of
the screw, the beam of light can be brought to zero.
In this position the passage of an extremely feeble
current round the coils will cause a deflection of the
needles, and that deflection will take place slowly, so
that the spot of light will come to rest at the point of
maximum deflection after only one or two oscillations
on each side of it.

A shunt is usually provided with each instrument,
with which one may regulate, within limits, the amount
of current sent through the galvanometer. This is seen
in Pig. 55. It has a series of brass plates separated
from one another, but, like those of the rheocord,
capable of being connected by brass plugs. When all
the plugs are out the plates are connected by varying
lengths of wire, so that a current forced to traverse
these wires encounters a certain amount of resistance.
The shunt has two binding screws. Two electrodes
are led from the apparatus producing the current, one
to each binding screw, and then from each binding

104 PHYSIOLOGICAL PHYSICS. [Chap. x.

screw a wire is led to each of the outer binding screws
of the galvanometer. Between the two binding
screws of the shunt is a hole, and if the plug be
inserted here as in the figure, the current is short-
circuited ; for the current merely travels across from
one screw to the other and back to
the place whence it came, none going
to the galvanometer, because of the
greater resistance. If this plug be
now removed, as well as the other shown
in the figure, the current reaching one
screw cannot get straight across to the

Fig 55^Gaiva- °^ner) but must traverse the galva-
nometer Shunt, nometer. Suppose, however, one of
the plugs be inserted in the hole
marked ^, then such resistance is interposed in the
short circuit that -j^th of the total current goes to
the galvanometer, and the remaining T%ths are short-
circuited. If the plug be put into the hole marked -g^-,
only T^roth Part g°es to the galvanometer, if into
-g-i-g- only TJ^th part goes to the galvanometer.

Each shunt is graduated for the instrument which
it accompanies. For the coils of the shunt must be
graduated according to the resistance of the particular
galvanometer, since it is the ratio between the resis-
tance of the galvanometer and that of the shunt that
determines what proportion of current will go to the
galvanometer, and what will be short-circuited.

Wiedemann's galvanometer, or boussoSe
is shown in Fig. 56. It consists of a thick cylinder
of copper, through which a tunnel is bored. This
tunnel can be closed at each side by a cover with glass
front, or by a solid plug of copper. Within this copper
chamber hangs a magnetised ring A, shown at the side,
of such a size that it has just room to swing clear on
all sides. Connected with the ring is an aluminium
rod which passes up through a copper tube and is

Chap. X.]

WlEDEMA NN 's Bo US SOLE.

connected above with a light frame which holds a
circular plane mirror B. To prevent currents of air
from moving the mirror, a circular brass cover c
encloses it. The cover has a circular window w in
front, through which the mirror can be viewed. Above
the mirror is screwed a long glass tube, which carries

Fig. 56. — Wiedemanu's Galvanometer (Boussole).

at the top, on a little ebonite support, a little windlass,
whose centering on the glass tube is regulated by three
little screws. On it is wound a single filament of silk,
which passes down the glass tube through an opening
in the ebonite. At the end of the silk fibre is a loop,
to which a small platinum hook is attached, which
suspends the mirror and magnet by an eye in the
mirror frame. By this arrangement the needle can be
raised or lowered, and centered in the copper chamber.
The copper chamber and its attachments are supported

106 PHYSIOLOGICAL PHYSICS. [Chap. x.

by brass columns on a plate of mahogany, levelled by
three screws. The coils are arranged on each side of
the copper chamber, and by means of a sledge arrange-
ment can be caused to meet right over the chamber,
so that the chamber is contained in the centre of the
two, or the coils can be removed from the chamber.
In Fig. 56 the coils are represented close to one
another, and therefore hide the copper chamber which
is within them. In the upper corner of the figure
the magnetised ring is shown attached by the alumi-
nium rod to the plane mirror. In very sensitive
instruments the number of turns on the coils is as
great as 30,000.

The features of this instrument are the arrange-
ments for DAMPING THE OSCILLATIONS of the needle.
The copper chamber is called the DAMPER. The move-
ment of the magnetised needle sets up induction
currents in the copper mass in the opposite direction
to the movement of the needle, and this diminishes
the oscillations of the needle, and causes it, after deflec-
tion, to come quickly to rest. The close fitting of the
ring to the chamber aids this action, as well as the
proximity of the coils to the needle. Another point
is that by the ring shape the inactive portion of the
magnet, its centre, is taken away, and the needle is
made stronger in proportion to its size. Now, this
needle is not astatic, but is made so by means of a bar
magnet of considerable strength, to be immediately
described.

The position of the botissole should be care-
fully chosen. It may be placed on a strong oaken
shelf, fastened to a solid dry wall in front of a window,
brass fixings being used, and none of iron. No iron
structure whatever should be in the neighbourhood,
either about or outside of the window. If the instru-
ment is to be used in a laboratory on a ground floor,
then a pillar of concrete, with a cap of oak, and built

Chap, x.] THE ACCESSORY MAGNET. 107

on a solid stone foundation, is best. On such a sup-
port the boussole is so placed that the axis of the coils
is perpendicular to the magnetic meridian. In this
position the ring, being non-astatic, will place itself
so that its sides will point north and south, and the
mirror will face the east.

To render the needle astatic the arrange-
ment shown in Fig. 56 is used. It is called Hauy's bar
(Der Hauy'sche Stab), and the arrangement in Fig. 56
is that of Du Bois. It consists of a magnet, the
ACCESSORY MAGNET m, placed in the magnetic meri-
dian, and therefore horizontal to the needle. Its
north pole should be pointing north, as is that of the
needle. It is supported on the bar B, which is
directed perpendicular to the coils, and in a line with
their axis. The magnet can slide in its support up and
down the bar, which is divided into centimetres for
measuring the extent of movement. Further, one end
of the magnet is caught between a spring and a
screw. The screw may be turned by P1, so that the
magnet can be moved from the spring end on the
other end, so as to form an angle with the plane of
the coils. By means of the pulley arrangement P2
this angular movement can be effected by the ex-
perimenter seated at a distance. The galvanometer
then being placed, the accessory magnet is fixed on its
bar, by a clamp to the shelf, almost under the end of
the mahogany stand of the galvanometer. The magnet
is first put on the end of its bar, and is then slowly
moved down it. As it approaches nearer the boussole
it gradually neutralises the earth's action. The
moment the position of neutralisation is crossed the
needle swings round so as to place its opposite poles
over against the poles of the magnet. It would make
in this movement a full half twist on its fibre. To
prevent this being accomplished one of the brass
plugs should be put in at the opening of the chamber

io8 PHYSIOLOGICAL PHYSICS. [ChaP, x.

behind. It is long enough, when pushed not quite home,
to allow of the needle coming against it when about
one-third of the half twist is completed, so that the
needle's farther movement is blocked. In front a glass
plug may be placed to permit the needle to be seen.
As soon, then, as this twisting tendency is observed, the
magnet should be slightly removed, till the tendency
just disappears and the needle is left just sufficiently
under the directing influence of the earth to keep it in
the meridian. The instrument will now be found to
be very sensitive. When BOTH COILS are to be used a
wire must be carried from a binding screw of one to
a binding screw of the other ; thus, the binding screw
marked 1 of the first coil to that marked 2 of the second,
or 3 to 4, one vacant screw of each coil receiving one
of the wires conveying the current. To diminish the
effect of the current on the needle, the coils may be
removed by the sledge arrangement a little way from
the copper chamber ; a centimetre scale pasted at the
side indicates the distance. When both coils are close
over the chamber the most intense effect is obtained.
One coil only may be used ; or, to get a differential
effect, one current may be caused to traverse one coil,
and the current to be compared with it, the other. •

For demonstration purposes, a beam from a
lime or electric light, placed at a considerable distance
from the boussole, is received on a small plane mirror,
and thrown on to the mirror attached to the magnet.
The reflected spot is caught on a white scale placed
at some distance, 6 to 15 feet, according to the
amount of magnification desired. The scale, of
course, must be horizontal to the coils. With such
an arrangement the author has assisted in showing
galvanometer experiments of extreme delicacy to as
many as 2,000 people at once.

For private work a reflected spot of light is
not used. At a distance of from 6 to 9 feet from

Chap. X.]

GALVANOMETER SCALE.

109

Fig. 57. — Telescope and Scale.

the boussole is placed a table, on which stands an
astronomical telescope. Above the telescope, sup-
ported on uprights, is a metre scale ss, which is divided
into centimetres and millimetres. Each centimetre
is marked with REVERSED numbers (Fig. 57). The
table is so placed
that the scale is
directly opposite
the mirror, and at
right angles to the
axis of the tele-
scope. With a
little trouble, the
position of table
and scale is so ar-
ranged that, on
looking through
the telescope, the
mirror of the boussole is seen, and the image of
the scale reflected in it, the numbers of the scale
being seen, of course, in the ordinary position. By
adjusting the scale with a rack and pinion its 0 mark
can be brought into the centre of the field, and made
to coincide with the vertical thread of the telescope.
The distant pulley (p2, Fig. 56) of the accessory magnet
should be clamped to the telescope table. The slightest
movement of it will cause a deflection of the needle,
and this will be observed through the telescope, when
it will appear as if the scale were drawn across the
mirror. When the needle comes to rest, the reading,
through the telescope, of the number now reflected in
the mirror will indicate the amount of deflection.

On the same table on which are placed the tele-
scope and stand may be fixed keys and other arrange-
ments, these being connected with the galvanometer
by long wires, carried out of the way, overhead, to the
instrument.

no PHYSIOLOGICAL PHYSICS. [Chap. xi.

The advantages of Wiedem aim's boussole
are, that by the copper damper, the arrangement of
the coils, and the accessory magnet, the needle is made
quite " aperiodic," or " dead beat." In other words,
when affected by a current, it swings round with com-
parative slowness till the maximum deflection is ob-
tained, which it reaches, and at which it rests, without
oscillation. When the current is withdrawn, it swings
back and stops, again without oscillation, at the zero
point ; if it should pass the zero point, a current in
the contrary direction would be indicated.

CHAPTER XI.

THE USE OF THE GALVANOMETER IN PHYSIOLOGY.

THE great purpose for which the galvanometer is
employed is the detection of electrical currents in
living tissues ; the object, indeed, of all the search for
means of obtaining sensitive instruments, and the
indirect cause of the discovery of galvanic electricity
and all its subsequent developments. For an account
of the history and theories of animal electricity, and
for a discussion of the electrical currents detected in
muscle, nerve, and other textures, reference must be
made to the ordinary physiological text-books. What
will be described in this chapter are the apparatus
employed and the arrangements made for detecting
the currents and estimating their amount, and for
other similar experiments.

At the outset, however, it is evident that the
extreme sensitiveness of the galvanometer throws
great difficulty in the way. For it is evident that
very slight changes in the arrangements by which

Chap. XL] POLARIS A TION OF ELECTRODES. 1 1 1

muscles, nerves, or other structures are brought
into the circuit of the galvanometer, might produce
feeble electrical currents, which would cause deflec-
tions of the needle and would be erroneously attri-
buted to the tissue being examined. Such a source of
error is found in what is termed polarisation of the
electrodes.

Polarisation of the electrodes. — If two
platinum electrodes have been immersed in acidulated
water, and have been conveying a current for decom-
position, the positive pole will, after some time, be
found covered with bubbles of oxygen, while hydrogen
will be collected at the negative pole. If, now, these
electrodes be suddenly disconnected with the battery,
and connected with a galvanometer, the needle will
be deflected in such a way as to show a current in an
opposite direction to the original battery current.
This is due to the fact that the negative pole coated
with hydrogen becomes positive to the positive pole
coated with oxygen, This current naturally will
weaken the original current. This occurrence is called
POLARISATION OF THE ELECTRODES. Similarly, if a
nerve be laid across two copper wires, and a current
passed to the nerve, the electrodes will speedily be-
come polarised, and so sources of error will be in-
troduced into an experiment. In much the same way,
if a fresh muscle were to be connected to a galvano-
meter by means of copper electrodes, a movement of
the needle would be apparent at once ; but this might
be due simply to changes in the condition of the
electrodes produced at the two points of contact, and
not to any current obtained from the muscle. Even
very clean platinum electrodes would, after the lapse
of a little time, cease to be in precisely the same
electrical condition, and would thus give rise to electro-
motive force. To meet such objections, Du Bois-
Reymond constructed what are called NON-POLARISABLE

ii2 PHYSIOLOGICAL PHYSICS. [Chap. xi.

ELECTRODES. He took advantage of a discovery of
Regnanld, that a strip of chemically pure zinc plunged
into a solution of neutral sulphate of zinc exhi-
bited no polarisation, a discovery to which Matteucci
added the fact that ordinary zinc, properly amal-
gamated, had the same property when plunged in a
saturated solution of the sulphate. Du Bois, there-
fore, constructed troughs, of the shape shown in Fig.
58, made of zinc, and insulated by having a base of
vulcanite. The inner surface of the trough is care-
fully amalgamated, and the outer surface coated with
a layer of black varnish, to prevent the sulphate getting
access to any unamalgamated zinc. By an insulated
handle g the trough can be lifted, while on the base is

a binding screw k, for the at-
tachment of wires. Cushions,
called DERIVING CUSHIONS,
are made of white Swedish
filtering paper. They must
be thick enough to fill up
the cavity of the troughs.
The sides should be perpen-
dicularly cut with a sharp
razor. The various layers of
the cushion should be secured

Fig. 58.-Non-Polarisable Elec- by stitching at one end. The

trodes. J .. . c , , . ,

cushion is placed m tne

trough, and folded over the lip, the projecting part
being terminated by a perpendicular section 6. The
cushion is soaked in the zinc solution before being
finally arranged in the trough, and, when placed, is
retained in position by a plate of ebonite s, and an
indiarubber band; the trough is then filled up
•with the saturated solution of zinc. Two such troughs
are prepared and put into connection with the wires
from the galvanometer. It is easily seen that if both
are "not supplied with the same strength of zinc

Chap, xi.] NON-POLARISABLE ELECTRODES. 113

solution, the two troughs will not be in the same con-
dition. If now a piece of tissue were placed upon the
DERIVING CUSHIONS of the non-polarisable electrodes,
the zinc solution would attack it, corrode it, and
vitiate any result. To prevent this, a piece of sculp-
tor's clay is made into a soft mass with a ^ to 1 per
cent, solution of common salt, which is a good con-
ductor. This is made into a thin sheet, and is folded
over the cushion, as shown in Fig. 58, P. It is called
THE CLAY GUARD. To limit the part of the clay guard
to be touched by the piece of tissue, a small piece of
thin mica may be placed on the guard.

The clay guard is not used merely to prevent
corrosion and destruction of the tissue. If the animal

Fig. 59.— Non-Polarisable Tube-Electrodes.

tissue were placed directly upon the deriving cushions
soaked in its zinc solution, a peculiar action would
take place between the liquid conductor and the
tissue, the result of which would be the develop-
ment of what is called SECONDARY RESISTANCE, which
would grievously diminish the intensity of any current
that might be present. Salt solution is found incap-
able of developing this secondary resistance when in
contact with animal tissues, while at the same time it
is a good conductor.

ii4 PHYSIOLOGICAL PHYSICS. [Chap. xi.

A second form of non-polarisable electrodes is seen
in Fig. 59. A flattened tube of glass r contains a
slip of amalgamated zinc. The end of the tube is
closed by the moistened sculptor's clay, and the tube
itself is filled with the zinc solution. The clay pro-
jects from the end of the tube, and the projecting part t
can be made of any shape, and can be sharply pointed
so as to touch just a point of the tissue to be examined.
The tube is mounted on a universal joint h, and sup-
ported on a brass upright s. These electrodes are not
only suitable for leading off 'a current to the galvan-
ometer, but also for leading currents to nerve or
muscle. They are free from polarisation, even after
being used for hours. A nerve to which they have
conducted a current is not, therefore, injured by
products of electrolytic action, which would have col-
lected at the poles of ordinary metallic electrodes.

To amalgamate the troughs or slips of zinc
the best fluid is Berjot's amalgamating fluid. The
directions for making it are as follows : " Dissolve
at a gentle heat 200 grammes of metallic mercury in
1,000 grammes of a mixture of one part, by weight, of
nitric acid, and three parts of hydrochloric acid, and
then add 1,000 grammes of the last-mentioned acid."
When not in use, the liquid should be kept in a well-
stoppered bottle, and placed in a cool dark place, to
prevent decomposition.

The resistance offered by such non-polarisable
electrodes is considerable. To reduce it to the mini-
mum, the cushions of both troughs should be soaked
for several hours in the zinc solution, then gently
squeezed to express excess of fluid and air bubbles.
They should fit the troughs as accurately as possible,
so that the layer of zinc solution required to fill up
the trough is not great. Further, the clay guards
should be so placed on the cushions that no bubbles of
air may be between them, for this would greatly add

Chap, xi.] TESTING THE ELECTRODES. 115

to the resistance. It is also to be noted that the con-
siderable resistance offered by the deriving vessels is
largely counterbalanced by the absence of polarisation
which, when properly prepared, they ensure.

To put the cushions in circuit, carry a fine
silk-covered copper wire from the binding screw of
one trough to one side of a friction key, and another
wire from the second trough to the other side of the
key, and then carry a wire from each side of the key
to the binding screws of the galvanometer. When
the key is closed, the troughs are connected in short
circuit ; when the key is opened, they .are placed in
communication with the galvanometer.

The troughs have a CLOSING CUSHION, which is made
out of the same blotting paper and saturated with the
same solution as the others. It is used for connecting
both troughs by being placed as a bridge between the
deriving cushions.

To test the electrodes, connect them with the
galvanometer by a friction key as already described ;
get the needle of the galvanometer at rest at the zero
point in the way already indicated (page 103), connect
the two troughs by the closing cushion, and open the
key. The needle should remain stationary, indicating
absence of all currents from the apparatus. Fre-
quently, however, there will be a slight deflection to
one side or another, indicating that the two troughs
are not quite homogeneous. Close the key, turn the
closing cushion so as to change the ends in contact
with the troughs, and open the key ; if the deflection
is this time to the opposite side, it is this cushion that
is at fault. This may be rectified by soaking it fo?
some time longer in saturated zinc solution so as to
make it homogeneous throughout, or by making a new
one. Suppose the changed position of the closing
cushion does not alter the deflection, the fault does not
rest with the cushion. In the same way, by changing

n6 PHYSIOLOGICAL PHYSICS. [Chap. XL

the deriving cushions from one trough to another, it
may be seen whether they are at fault. As a rule, the
error will be found to exist in the amalgamation of
the troughs, or in their outer varnishing, which may
have cracked somewhere so as to expose un amalga-
mated zinc, or in want of saturation of the zinc
solution. The sources of error being removed by the
evident remedy, the deflection will disappear. Often
a very slight deflection may be caused to vanish by
setting up the troughs for twenty-four hours before
they are required and letting them stand for that
time, connected by means of the closing cushion and a
short piece of thick copper wire passing between the two
binding screws. To prevent evaporation, the troughs
should be covered with a glass shade, the inside of
which has a few pieces of wet blotting paper adhering
to it. It is not necessary to make fresh cushions on
every occasion the troughs are used. If they have
been properly stitched they may be placed in a well-
stoppered bottle with sufficient zinc solution to cover
them. If they are regularly returned to the bottle
after being used, they may keep for years. If they
have been permitted to get encrusted with zinc salts
by evaporation, suspend them for twenty-four hours in
distilled water. At the end of that time gently
express the water, and then place them for a few
hours in a saturated solution of the zinc sulphate,
after which they will be again ready for use.

To determine the direction of the current
sent through the galvanometer a preliminary experi-
ment is necessary. Let the galvanometer be con-
nected with a key in short circuit ; to one wire from
this key attach a slip of zinc, and to the other a slip
of copper. Place the slips in a glass with dilute sulphuric
acid, so that they just dip into the fluid. From this
small element send a momentary current to the
galvanometer by quickly opening and closing the key.

Chap. XL] THE MUSCLE CURRENT. 117

The needle will be suddenly deflected to one side, and
then will return to zero. Now, since copper is the
positive pole, the wire connected with it is + , and so
iiris known that when this wire is positive, the needle
will be deflected in a particular direction. Suppose
the deflection be to the right.1 then disconnect the

O ' 3

slips of copper and zinc, and connect the wire that
was positive to the trough on the right hand. Thus
it will always be known that when the deflection is
to the right, the trough on the right hand is positive ;
when the deflection is to the left, the trough 011 the
left hand is positive.

To obtain the electrical current from living
muscle, take the adductor magnus muscle, or the
gastrocnemius, of the newly-killed frog. Make a
clean transverse section at one end, and lay the
muscle on the clay guards of the troughs, disposing
the plates of mica in such a way that only the middle
of the longitudinal surface is allowed to touch one
pad, and the centre of the transverse section the
other one. The troughs being arranged in short
circuit, open the key, and at once a great deflection
will occur, indicating a current from the muscle.
If the direction of the current be determined, it will
be found to pass out of the muscle by the longitudinal
surface. By making the surfaces touch opposite
cushions, the deflection will be reversed. By alter-
ing the position of the muscle, touching now two
surfaces and now two sections, the experiments may
be varied till the student has worked out for him-
self the various results given in the descriptions of the
phenomena in the text-books. The electrodes shown
in Fig. 59, and already referred to, afford the most
convenient means of studying the differences of
different points of the muscle. The muscle is laid
upon a perfectly clean glass plate supported on a
stand, and the finely-pointed ends of the clay talons

n8

PHYSIO L OGICA L PHYSICS.

[Chap. XL

of the electrodes laid on different points of the muscle
to be examined, so that the position of the most
positive and most negative points of the muscle, etc.,
can be discovered.

Negative variation of the muscle current. —
Fig. 60 represents diagramatically the arrangements
necessary for this experiment. On the right hand
and upper part of the figure are the troughs, with a
gastrocneinius muscle prepared with the sciatic nerve

Fig. 60. — Arrangements for Negative Variation

attached. The muscle is laid with a transverse section
on one electrode, and a longitudinal surface on the
other. (The centre of each should touch the pad.) The
troughs are placed, through the intermedium of a key,
in connection with the galvanometer. The nerve is
laid across the platinum electrodes, which are
connected through a short-circuiting key with the
secondary coil of an induction machine, the primary
of which is in circuit through Wagner's hammer with
a key and a DanielFs cell. The needle being at zero,
the circuit of the troughs is opened, and the needle is

Chap. XL] NEC A TI l''E VA RIA TION. I I 9

deflected by the muscle current ; the key of the
primary circuit is then closed, and that of the short
circuit opened, so that the muscle is tetanised, when
the needle will be found to swing back, sometimes
almost to zero. On closing the short circuit the
muscle ceases to be stimulated, tetanus disappears,
and the needle is again deflected, but not so much as
before. Care must be taken that the induction coil
is so far away from the galvanometer that the
opening and closing of its circuit have no effect on
the needle, and also that the position of the
muscle is not shifted during contraction. A good
way to obtain the latter with certainty is to use
the electrodes (Fig. 59), and to make the points
press accurately on the centre of cross-section and
longitudinal surface. To prove that the tetanising
current does not gain access to the galvanometer
circuit and cause an error, tie a piece of wet silk
thread round the nerve below the exciting electrodes,
and, everything else being unmoved, send on the
tetanising stream as before. The continuity of the
nerve for nervous stimulation has been
destroyed ; no tetanus occurs in the muscle,
and no negative variation arises. The
continuity of the nerve for electrical cur-
rents is, however, still unimpaired, so
that the negative variation is not due to
any diffusion of electrical currents from
the exciting electrodes. Fio. 61

The electric currents of nerves neWe ar-

may be demonstrated in a similar way. thege
Here also it will be found convenient to poiarisabie
use the tube electrodes. The nerve (a long trodes.
piece of the sciatic nerve) may be laid
over one clay point turned up into a hook, and the
two depending ends made to touch, by their transverse
section, the clay point of the second electrode, placed

120 PHYSIOLOGICAL PHYSICS. [ChaP.-xi.

below the first. (See Fig. 61.) Negative variation can
also be produced in the current from nerves, though
the nerve current causes a much smaller deflection
than the muscle current. For this purpose one end of
the nerve should be laid over the platinum electrodes
arranged in connection with an induction coil, as
described for the negative variation of muscle.

To measure the electromotive force of the
muscle or nerve current, Du Bois-Keymond made use
of a method devised by Poggendorff to measure the
electromotive force of inconstant cells. The principle
of the method may be compared to the principle of
weighing, which consists in placing the body to be
weighed on one side of a balance, and accurately
counterbalancing its effects by standard bodies, whose
amount can be varied at pleasure, placed on the
opposite side. Thus the muscle current is sent round
the galvanometer, and deflects the needle in a par-
ticular direction. A current, whose amount can be
varied at pleasure and always accurately estimated, is
sent round the galvanometer in the opposite direction,
of such a strength that it exactly neutralises the
muscle current. This is indicated by the return of
the needle to the zero point. The amount of the
COMPENSATING CURRENT, as it is called, is then read
off", and it is a measure of the muscle current. Fig.
62 is a representation of the scheme of compensation.

A reference to the description of the rheocord
(page 78, Fig. 42) will show that in this instrument a
means is afforded of graduating to any extent the
strength of the compensating or measuring current.
A simpler arrangement than the rheocord is, however,
found to suit the purpose. It consists practically of
a single wire of the rheocord (Fig. 62, AB), a uniform
wire of brass 2 metres long and 1'75 mm. in
diameter. It is stretched on a piece of wood be-
tween two brass plates, fitted with binding screws

Chap, xi.] COMPENSATION OF CURRENT.

121

£

Com-

A and B. On the wire is a slider s, which may be
moved from one end to the other, and makes contact
all the way. -It also carries a binding screw. This
simple rheocord is called the LOSTG COMPENSATOR.
From a constant element (E, Fig. 62) lead a wire to
A, and another to B. A key
may be interposed on the way.
From A and s wires are led to
the side cups of the commu-
tator which has the cross in,
and from end cups wires go to G,
the galvanometer. Now the
current from E will pass to
A, and may here branch into
two circuits, the long circuit A
by the commutator to G and back
through the commutator to s,
then on to B and back to E, and
the short circuit straight along "lg*
the wire AB and back to E.
Now, if the slider s is close up to A, it is easy to see
that all the current will be short>circuited, and none will
go through the galvanometer. If, however, the slider
is moved away from A, then a small amount of the
current will find its way through G, and this current
increases the farther s is removed from A. In fact,
the amount of current sent through G will be propor-
tional to the distance AS. Thus the strength of the
current sent through G can be varied at pleasure and
measured. Further, the current can be sent in either
direction through G by means of the commutator. If
the commutator be down towards 1, the current will
pass in the direction of the continuous arrow ; if the
commutator be down towards 2, the current will
traverse G in the direction of the dotted arrow.

To carry out the scheme, the troughs are arranged in
the circuit of the galvanometer, as represented in Fig.

122

PHYSIOLOGICAL PHYSICS.

[Chap. XI.

63. The element K is connected with the long com-
pensator at a and b. From a and c (c is the slider)
wires go to the commutator c, the cross being in, and
from the end cups of c wires proceed, one to the bous-
sole B, the other to the troughs T, and from them to B,
a key (not represented in the figure) being interposed.

a

Fig. 63.— Compensation of Muscle Current.

To perform the experiment? push c close up
to a, and be sure that it makes contact with it, so
that no current from K at present gets access to B.
The muscle current, however, can pass round B.
Note the direction of the needle's deflection when the
muscle is so placed as to touch, say, the right-hand
trough with the transverse section. Then remove the
muscle, and connect the troughs by the closing cushion.
The needle being again at zero, slowly remove the
slider from a ; a portion of the current from the
Daniell will get to B, and will deflect the needle. Note
how the position of the commutator is related to the
direction of deflection. Now push c again into con-
tact with a, replace the muscle ; open the key, and get
the deflection due to the muscle current. Lay the

Chap. xi.] COMPENSATION METHOD. 123

commutator over, so that a current from K would
deflect the needle in the opposite direction. Then
slowly push c away from a. Step by step, with the
pushing away of c, the needle will swing back towards
zero, till a point is reached when it is exactly at zero.
In this condition of affairs, a current from, the muscle
passes round B in one direction, a portion of a Daniell
current passes round B in an opposite direction, and,
since the needle is at zero, both these currents are
equal, that is, they neutralise one another. Thus
the amount of Daniell sent is the measure of the
amount of muscle current, and this is proportional to
the distance between a and c. To put it more accu-
rately, the difference of potential between a and c is
equal to the difference of potential between the two
points of the muscle in contact with the clay guards
of the electrodes. Putting it that the difference of
potential between a and c is directly proportional to
the electromotive force of the muscle current, it will
be understood that if the compensator wire were pre-
viously graduated, it would be possible to arrive at an
accurate estimate of the amount of that force without
any delay. This previous graduation is, however,
necessary. That is to say, ab being a uniform wire,
having a millimetre scale pasted beneath it, and the
current through ab being constant, it is possible to so
graduate the compensator that every millimetre of the
wire through which the slider c is moved is equal to
a determined amount of current. It is then only
necessary to read off the distance between a and c, in
order to learn the amount of the constant current
which has been required to compensate for the muscle
current.

To put it in another way, suppose the resistance of
the rheocord wire to be infinitely great in comparison
with the internal resistance of the Daniell, then the
resistance of ac will have the same ratio to the whole

124 PHYSIOLOGICAL PHYSICS. [Chap. xi.

resistance of the rheocord circuit as the fraction of the
Daniell current sent round the galvanometer has to
the whole current of the Daniell. But the fraction
sent round B is the measure of the muscle current, so
the resistance of ac will be to the resistance of the
circuit as the current of the muscle is to that of the
Daniell. Now the resistance of ab, the rheocord
wire, may be made very great in comparison to that
of the Daniell, by interposing a resistance box, offering
say 5,000 ohms resistance, between b and E, and this
box becomes part of the circuit K«6K, and is as it
were a prolongation of ab. For simplicity this has
not been shown in the diagram. Let us represent the
result by a formula. Let V be the electromotive force
of the muscle current, and E the electromotive force
of the Daniell ; let R equal the resistance of the
rheocord wire between a and c, the length that permits
of compensation of the muscle current, and let R + R'
be the resistance of the whole circuit K«&K ; then the
electromotive force of the muscle current is to the
electromotive force of the Daniell as the resistance be-
tween a and c is to the total resistance of the Daniell
and rheocord circuit. That is,

Now E is known (it is the electromotive force of
the Daniell), previous graduation of the rheocord wire
gives R, and we have supposed R' to equal 5,000 ohms,
therefore it is only necessary to substitute for E, R and
R', their values, and the electromotive force of the
muscle current V is obtained.

The round compensator of Du Bois-Reymond
is a much more convenient instrument with which to
make these compensation measurements than the
ordinary long compensator. The round compensator
is shown in Fig. 64. It consists of a platinum wire,

Chap. XL]

ROUND COMPENSATOR.

125

"Vrl n

Fig. 64. — Eound Compensator.

which rests in a groove on the circumference of a
circular disc of ebonite. The wire is one millimetre
thick, and is marked off by a scale round the circum-
ference into 1,000 millimetres. A little platinum
wheel r makes contact
with the -platinum wire,
against which it is kept
pressed by a spring pro-
jecting from the support
at the side. The disc
is movable on a vertical
axis, and is turned by
the small projections
on its under surface.
When it is turned the
wheel r revolves on
the wire. The beginning of the platinum wire is
connected with the screw I, the end with the screw
ii. The wheel r is in communication with the
screw in, and a very short distance from its ter-
mination the wire passes over a small sharp wedge
of platinum, which is connected with screw iv. The
connections are diagramatically represented in Fig.
65, which shows further how a Daniell is connected
with screws I and 11, and a galvanometer and muscle
are interposed in the circuit of in and iv. In the
circuit of the Daniell a commutator with cross should
be interposed to enable one to reverse the direction of
the current, and in the circuit of the galvanometer a
key should be intercalated.

The pillar which supports the platinum wheel
(Fig. 64 ) supports also a simple microscope and a
vernier, which projects on to the millimetre scale, by
means of which can be ascertained the precise extent
of the turning of the disc.

The round compensator is used precisely as the
long one. The element, galvanometer, and troughs

126

PHYSIOLOGICAL PHYSICS.

[Chap. XI.

sator.

being properly arranged in circuit, as shown (Fig. 65),
the disc of the instrument is turned so that the
platinum wheel rests on the zero point of the wire.
The current from the muscle is then allowed to go
through the galvanometer, and a
deflection results. The disc is then
slowly turned, so that the zero
point is carried away from the wheel.
This permits the Daniell current
access to the galvanometer, and the
needle slowly returns as the disc
moves. "When the needle is again
at zero of the scale, the disc is
allowed to remain where it is, and
then the new position of the platinum
wheel r is read off. The distance
now between zero of the wire and
r is proportional to the strength of
the branch current from the Daniell, sent through the
galvanometer to compensate for the muscle current.

Effect of electrotomis on electromotive
force. — With the aid of the galvanometer, then, it
has been found that muscles and nerves give rise to
an electric current, that is, develop electromotive
force. It has been mentioned towards the close of
chapter viii., that the passage of a constant current
of electricity through a nerve alters its electromotive
force, but, because it involves the use of the galvano-
meter, it was left to this chapter to show how this is
proved. The arrangement is precisely that already
described ; a long nerve is, however, required. Let the
zinc troughs be placed in connection with the galvano-
meter, a key being interposed, and let the nerve be
placed with the transverse section of one end on one
clay pad, and let a part of the longitudinal surface
near that end touch the clay of the other trough.
This leaves the other end of the nerve free to be laid

chap. xi.] THE MUSCLE CURRENT. 127

over electrodes for conveying the constant current of
electricity. These electrodes should be of the non-
polarisable type, of the tube form shown in Fig. 59.
They are connected with a single Daniell's element,
through the medium of a commutator arranged for

O

reversing the direction of the current. The object of
the nerve being long is to have the electrodes which
convey the constant current, called the exciting
electrodes, as far away as possible from the galvano-
meter electrodes, which are called the deriving elec-
trodes. The key in connection with the galvanometer
is opened, and the natural nerve current is obtained.
The constant current is then passed through the piece
of nerve laid over the exciting electrodes, and a
variation is at once produced in the deflection of the
galvanometer, indicating some change in the electro-
motive force of the nerve. On reversing, by means of
the commutator, the direction of the constant current,
it is found that, w/ien the constant current floios in the
same direction as the nerve current, the deflection of
the needle is increased, and when the constant current
flows in the opposite direction the needle deflection is
diminished. The increase is called the positive phase,
and the decrease the negative phase.

To prove that the change is not due to some of
the battery current passing downwards, and getting
into the galvanometer, a ligature is tightly applied
between the portion of the nerve on the exciting and
the portion on the deriving electrodes. This ligature
destroys the nervous conductivity, but does not destroy
the conductivity for the galvanic current. But it is
found that then electrotonus has no effect, so that it
was not the diffusion of the galvanic current that
produced the change. To succeed with this experiment
care must be taken that insulation is complete, and no
moisture must be allowed to be present to act as a
conductor.

128 PHYSIOLOGICAL PHYSICS. [Chap. xn.

A further development of the experiment may be
made by using two galvanometers connected each with
zinc troughs. Then arrange a long nerve so that it is
in contact with the two troughs of one galvanometer
at one end, and that its other end is laid in the usual
fashion on the troughs connected with the second
galvanometer. The galvanometers each indicate a
current. The middle of the nerve is laid on the
exciting electrodes, and a constant current passed
through it, when at once the two needles indicate a
current, the deflection of the one being increased, that of
the other diminished, the one end of the wire being in
the positive, the other in the negative, phase. This
shows that in electrotonus a new electromotive force
is produced which adds itself to the natural nerve
current at the end of the nerve where the direction of
both coincide, and subtracts from the natural nerve
current at the end where the direction of both
differs.

The employment of the galvanometer for measuring
time and resistances is described in chapters xii.
and xiii.

CHAPTER XII.

THE GALVANOMETER AS A MEASURER OF TIME.

IT has been seen (page 102) that by means of the
accessory magnet the period of oscillation of the
needle of the galvanometer can be made very large,
and then the deflection of the needle, under the
influence of a current, occurs very slowly. If a
current lasting a very short time in proportion to the
period of the needles be sent through the galvano-
meter, the current will have ceased before the needle

Chap. XII.]

THE FROG-INTERRUPTER.

120

has begun to move. The needle will then move just
as if it had received a single blow, as it were, and
will be deflected till the influence of the earth's
magnetism neutralises the shock, and brings the
needle back to zero. Under these circumstances the
amount of observed deflection of the needle will be pro-
portional to the intensity of the current, and the time
during which it acted. If, however, the intensity of
the current be always constant, but the duration of
the current varied, then the deflection will be pro-
portional to the length of time during which the
current has acted, that is, the extent of deflection will
measure the time. Thus -by means of the galvano-
meter small intervals of time may be measured.

This principle is made use of in estimating the latent
period of stimulation of
the muscle, that is, the
time that elapses between
the moment of the muscle
receiving a shock, and the
moment of its response by
contraction, and in esti-
mating the rapidity of
the nerve current. For
this purpose the instru-
ment shown in Fig. 66,
devised by Helmholtz, and
modified by Reymond, has
been employed. It is
called the frog-interrupter
(frosch unterbrecher). It
consists of a brass plate

supported by two pillars Fig< 66.-The Frog-Interrupter.

on a block of mahogany

w, levelled by screws. From the brass plate rises
a pillar, up and down which a forceps can slide,
and be fixed at any point by a screw. On the
J — 7

130

PHYSIOLOGICAL PHYSICS.

[Chap. XII.

brass plate, pivoted at a and a', is a lever which
rests at the other end on the plate by means of two
screw points, q and p. The screw point p is of
platinum, and rests on an insulated plate of platinum
fixed to the table ; the point of the screw q is of
amalgamated copper, and dips into a little insulated
cup containing mercury. Connected with p and q,
and insulated from the table, are the screws k and A';
the latter screw in communication with p, the former
with q. A muscle, supported in the forceps, is
directly suspended over the lever, and is attached to
it by an insulating piece of tortoise-shell. Opposite
to this attachment, on the under side of the lever, is
connected a rod, which passes through a hole in the
table, and supports a scale for weights. If the muscle

be stimulated it will lift
the lever against the
resistance of the weight,
but so long as the lever
rests on the table the
weight does not affect the
muscle.

Now, suppose the
two wires from a con-
stant battery led to h'
and k. Let the current
pass by A', it will pro-
ceed to the platinum plate
in connection, thence by
p along the lever to g,
down through q to the
mercury cup, thence to k,
and back to the element.

If the lever be raised by the contraction of the
muscle, the current will be interrupted by the
breaking of contact at p and q. In this circuit
h interposed a galvanometer G, a key K, and the

Fig. 67.— Arrangement of Frog-In- v "e>" /

teiTupter and Galvanometer.

chap, xii.] USE OF FROG-INTERRUPTER. 131

primary coil of an induction machine I (Fig. 67).
Now, the instant the key is closed the current passes
through the coil, producing, therefore, an induced
current in the secondary, through the interrupter, and
through the galvanometer, deflecting the needle. But,

o O O

as we see, the same current that deflects the needle
produces a single induced current, which may be led
to the muscle, and stimulates it to contraction. As
soon as it contracts, contact is broken at p and q, the
current is interrupted,- and the needle returns to zero.
Now, practically the production of the induced
current is simultaneous with the closing of the
primary current, so that the muscle is stimulated at
the same instant that the primary circuit is closed.
If, therefore, the muscle contracted precisely at the
moment of stimulation, it would by its contraction
break the primary circuit the same moment it was
closed, and no current would circulate in the
primary circuit ; therefore no deflection of the
needle of the galvanometer would occur. But as a

^j

matter of ' fact the muscle does not contract the
moment it is stimulated, consequently for a very
short time the primary current affects the galvano-
meter, and then the current is interrupted. The
needle, therefore, is deflected to a certain extent and
then returns to zero. The short time is the time that
elapses between the moment of the muscle receiving
its stimulus and the moment of its contraction, i.e.
the period of latent stimulation. Thus, the con-
ditions mentioned at the beginning of this chapter
are fulfilled ; a constant stream acts on the galvano-
meter for a very short time, so that the amount of
deflection is the measure of the time during which the
current acted, that is, the measure of the period of
latent stimulation.

One further point about the apparatus is to be
noted. The muscle gets only a single shock ; it

132 PHYSIOLOGICAL PHYSICS, [Ciiap. xn.

quickly contracts, and quickly relaxes, being helped
thereto- by the weight in the scale. By its relaxation
the points p and q will again make contact, and cause
the primary current again to be established. As the
oscillation period of the needle is great all this might
occur before the observation of the extent of the first
deflection, had been completed. It was to obviate this
that the arrangement of platinum plate and mercury
cup was devised by Helmholtz. The upper corner of
Fig. 66 shows what is meant. By the screw attached
to the forceps the muscle raises the lever so that the
platinum point just rests 011 the platinum plate.
Then, by means of the screw s, the mercury in the
cup is raised till q dips well into it. Then the
mercury is lowered by the screw till the point q and
the mercury in the cup are connected only by a thread
of mercury adhering to the amalgamated copper point
q, and sufficient to conduct the current. If by the
contraction of the muscle contact is broken, then, on
the return of the lever, the point q will no longer
make contact with the mercury, but will be separated
from it by a small space across which, before rupture,
the mercury thread stretched. A second shock to the
needle is therefore prevented.

The wires that conduct the current from the
secondary coil may lead it directly to the muscle, one
being attached to the forceps, and the other to the
end of the muscle, or to a screw in the table, as in-
dicated by dotted lines in Fig. 67. But instead of
stimulating directly in this way, the nerve may be
left in connection with the muscle, and stretched over
two platinum electrodes at two different places, a and
b. By means of a commutator c, wit/tout the cross,
it can be arranged to send the stimulating shock to a
or to b at pleasure. Let it be sent to b, and take
the reading of the deflection of the galvanometer
needle that gives the latent period. Then reverse the'

chap, xii.] MEASUREMENT OF TIME.

commutator so as to stimulate at a, and take
another reading. There will be a difference between
them, indicating a longer period between the moment
of stimulation and that of contraction. Obviously
this difference is due to the time which the nerve
energy liberated at a has taken to travel the distance
between a and b. This distance is measured, and thus
one has an estimate of the length of time taken by the
nervous energy to travel a certain distance, an.
estimate, that is, of the rapidity of the nerve current.
Thus by means of the frog-interrupter and the gal-
vanometer, measurements can be made of the period
of latent stimulation, and of the rapidity of the nerve
current.

It is proper to say that the arrangement has been
slightly simplified for purposes of explanation. It is
not desirable to use the same primary current to
establish the current through the galvanometer, and
produce at the same time by its closure an induced
cm-rent sent to the muscle. One element is used for
the galvanometer and interrupter : but the kev of this

O 1 ' ./

circuit is two-sided, and is so arranged that the same
instant that it closes the galvanometer-interrupter
circuit, it opens the circuit of another element and the
primary coil, and so gives an induced current of
opening to the muscle. The representation of this
would make the diagram seem a little complicated, so
the simpler arrangement has been drawn to show the
principle of the method. Other methods of measuring
the latent period and the rapidity of the nerve cur-
rent are considered under the Graphic Method in
chapter xvii,

'34

CHAPTER XIII.

RESISTANCES AND THEIR MEASUREMENT.

THE measurement of the conducting power, i.e. the
conductivity, or, what is practically the same thing, the
measurement of the resistance, of various bodies, and
especially of the various animal tissues, is a subject of
growing importance in physiology and in therapeutics.
It is of importance in therapeutics because the em-
ployment of electricity in the treatment of disease is
daily being extended, and its proper application
depends upon an appreciation of just such points as
the resistance that different tissues offer to the passage
of the current.

It has been seen also (page 27) that the strength
of a current is, to a large extent, dependent on the
resistance, and that by varying the resistance the
current strength may be varied, while by increasing the
resistance the current may be weakened^ and vice
versa. It has been also noticed how, on this principle,
the rheocord (chapter viii. ) is so constructed as to per-
mit a very great extent of graduation in the strength
of tjie current, and how, on the same principle, the
compensator (long or round) affoi'ds a similar means,
though to a much more limited extent. On page 33
it has been pointed out that there is a standard of
resistance as there is a standard of weight, that a coil
of fine wire may be prepared, which, at a given tempera-
ture, will offer the standard resistance of one ohm, and
that by means of this standard other resistances may
be compared. It will, further, be readily understood
that by means of the standard resistance various ap-
paratus may be constructed, other than that of the

chap, xin.] RHEOSTAT OF WHEATSTONE.

135

68.— Bheostat of Wheatstone.

rheocord and compensator, which will permit of a

perfectly definite amount of resistance being readily

interposed in the way of a current without altering any

of the wires. Such an instrument is the rheostat,

invented by Wheat- _ (

stone. As shown in

Fig. 68, it consists of

two cylinders, one, CB,

made of brass, and there-

fore a good conductor,

the other, AD, of wood

(an insulator) with a
spiral groove cut in it.
On CB is wound a fine brass wire about 40 yards long,
though the instrument can be made of any size and
the wire of any length. The wire is partly wound
also on the wood, so that each turn, lying in its groove,
is insulated from its neighbour. The end of the wire
on the wood cylinder is connected with a binding
screw, and the metallic cylinder is also in connection
with a binding screw. Now let the -f- wire from a
battery be led to the screw of the metallic cylinder; it
and the wire coiled on it form a thick conductor, and
offer no resistance of any consequence. The — pole
being connected with the wire wound on the wooden
cylinder, the current must pass from the metal
cylinder and traverse each turn of the wire wound on
the wood before it can pass off' at the binding screw. In
traversing this fine wire it meets with considerable
resistance, and the greater number of turns of wire
that lie in the spiral of AD, the greater is the
resistance. By turning the handle m, the wire may
be wound on to the cylinder AD and the resistance in
the circuit increased, or wound off on to CB and the
resistance diminished. By the dial on c the length of
the wire in feet and inches on AD can at once be
counted, and the resistance estimated.

T3^> PHYSIOLOGICAL PHYSICS. [Chap. xin.

By a resistance foox (Fig. G9) a much greater
resistance may be interposed in a circuit, and as easily
graduated. It is made of a series of bobbins on which
are coiled various lengths of insulated wire. The coils
are placed in a box, and the two ends of the wire of
each bobbin are connected with two different plates of
brass fitted on to the ebonite lid of the box. ABC at
the side of the figure show how the coils are con-
nected with two separate brass plates. Each coil

Fig. 69. -Resistance Box.

offers a certain amount of resistance, which is marked
in ohms on the lid of the box between the two brass
plates to which it is attached. There are also binding
screws attached to the lid. Suppose the wires from a
battery to be attached to the screws, the current would
require to traverse all the coils in the box, and would
thus encounter a resistance equal to the total offered
by the coils. But the brass plates on the lid are so
arranged that thick brass plugs, may be made to fit in
between them, so as to connect them. "Where two
brass plates were so connected the current would
not traverse the coil attached to them, but would
pass straight across from one plate to another by
means of the plug, and the resistance of that coil
would therefore be put out of the circuit. Suppose
all the plugs were in, the current would traverse none
of the coils, but would pass straight from one binding
screw through plates and plugs to the other, and
owing to the thickness of plates and plugs would
encounter practically no resistance in the box.

chap, xiii.] RESISTANCE OF FLUIDS. 137

Resistance of fluids. — A very simple arrange-
ment is shown in Fig. 70 for interposing resistance
even to an enormous extent, which could be used for
physiological or therapeutical purposes. It consists of
a glass tube filled with distilled water and closed at
each end by an indiarubber cork. Through each cork
is passed a copper wire. If the wires from a battery
be connected with the wires from the tube a current
will pass in the tube from one wire to
the other through the water, and will

o

encounter resistance directly proportional
to the extent of the layer of water between
the two wires. Since the wires may be
pushed through the cork so as to ap-
proximate to one another, or can be removed
still farther in the tube from one another,
the resistance can be readily diminished or Fl-g.ro_Re_
increased. It is calculated that a column of Ffu?<Lc.e °f
distilled water, one metre long and one
millimetre in diameter, would oppose resistance to an
electric current equal to that of a copper wire of the
same thickness long enough to make 1G7 turns round
the earth. Alcohol added to the water would increase
its resistance. The resistance of water could be dimin-
ished by dissolving salt in it, or by adding sulphuric
acid to it. The objection to water, salt solution, or
dilute sulphuric acid, is that by the passage of the
current polarisation is set up. As mentioned in the
paragraphs on non-polarisable electrodes, solutions
of neutral sulphate of zinc are free from this ob-
jection. Therefore by taking a narrow tube, say one
metre long, graduating it in millimetres, and filling it
with solution of sulphate of zinc, of a certain strength,
one would have a very simple and, at the same time,
useful means of regulating the strength of a current
of electricity.

It should be observed that the amount of resistance

138 PHYSIOLOGICAL PHYSICS. [Chap. xin.

offered by a conductor is dependent on the tempera-
ture. Increased temperature diminishes resistance,
that is, increases conductivity.

To measure resistances the simple rheostat
may be used. A Daniell's element is placed in the
circuit of a galvanometer ; an extremely sensitive one
is not necessary. When the current is permitted to
pass through the galvanometer the needle is deflected.
If, now, the body whose resistance is to be measured
be placed in the same circuit, the current from the
Daniell, encountering the resistance of the body, will
not be able to deflect the needle to the same extent.
Note the amount of deflection. Remove the body, and
place, instead, the rheostat in circuit. Send the cur-
rent again through the galvanometer, and then wind
the rheostat wire on to the wooden cylinder ; this
adds resistance, and the needle will be brought slowly
back from its maximum deflection caused by the
Daniell. Wind on the wire till the resistance it offers
causes the needle to be brought back to the position
it occupied when the body to be measured was in
circuit. At that position the amount of wire wound
on to the wooden cylinder will be the measure of the
resistance offered by the body.

A method of greater value is the method by

WHEATSTONE'S BRIDGE. It
shown in diagram in
71.

At e is a Daniell's ele-
ment; and AB is the platinum
e wire of a long compensator,

Fig 71. — Wheatstoue's Bridge. * i • r • xi v J

of which s is the slider.

(See page 121.) From e the positive electrode goes to
A, the negative to B. From A a wire passes to r, the
body whose resistance is to measured, from which
again a wire is carried to one binding screw of Re, a
resistance box, from whose other binding screw a wire

chap, xiii.] WHEATSTON&S BRIDGE. 139

makes connection with the end B of the compensator
wire. To the same binding screw c of the resis-
tance box Re, by which r is connected with it, is con-
nected a wire leading to the galvanometer G, and the
other terminal of G is attached to the slider s of the long
compensator. Now when the current reaches A it will
split into two branches, of which one branch current
will pass along the long compensator to B, and the
other will pass up to r, c, and Re. But at s and c the
two branches will also split, part of the branch rcne
passing down to the galvanometer, part of the branch
ASB passing up to G. These two currents, being in
opposite directions, will deflect the needle in opposite
ways. If one is in excess it will deflect the needle in
one direction, if the other is in excess, it will deflect
in the opposite direction ; if both are equal they will
neutralise one another, and the needle will remain
at zero ; or, to put it more accurately, when the
potential at s is equal to the potential at c, no
current will pass through the galvanometer.

Now, as already explained (page 33), the strength
of the current in the two branches depends on the resis-
tances in the two branches, and this can be altered by
the position of the slider s. Consequently, all that is
necessary to secure equal potentials at c and s is to
move the slider one way or the other till the needle
returns to zero, this indicating the desired equality.
Now, it can be shown that when no current traverses
the galvanometer, the resistance of r is to the resis-
tance of Re as the resistance of As is to the resistance

of SB • thus,

r : ~R£ : : AS : SB

Put in another way, this is

r AS

SB '

and therefore

AS

r — R* X —

SB

140

PHYSIOLOGICAL PHYSICS. [Chap. XIIL

Now r is the resistance to be measured, Re is the
resistance in the resistance box, which is read off at
once according to the number of plugs out (see page
136), and AS and SB are the resistances of the lengths
of the compensator wire on each side of the slider,
which are also known. Thus r, the resistance to be
measured, is given in terms of ne AS and SB, resis-
tances that are known. The resistance box is used,
because by pulling out or inserting plugs its resis-
tance can be varied at pleasure. According to the
resistance thrown in by it will be the position of the
slider, and thus, by varying it, it becomes easier to
adjust the proper position of the slider.

Here again is the long compensator found a little
awkward on account of its length ; so a modification
of the round compensator (page 125) of Du Bois-
Reymond has been made by Prof. A. Christiani, of the
Berlin Physiological Institute. The modification con-
sists only in the addition of another connection.

By comparing Fig. 72 with Fig. 65 (page 126), it
will be observed that the addition con-
sists in prolonging the compensator
wire beyond the point to which the
wire I is connected to it, and bring-
ing a wire from o to an additional
binding screw o' placed on the stand
of the instrument, by the side of the

f

screws Nps. I, u, in, and iv. (See
Fig. 65.) In fact, the two ends of
the platinum wi^e have each a double
connection. The screws o and n thus

of DU afford means by which the unknown re-
pensator. ° sistance and the resistance box are put
into circuit, when the modified round
compensator is used for Wheatstone's bridge. The
mode of arranging it for this purpose is shown in
Fig. 73. The element E is connected by binding

chap. xiii.j CHRISTIANAS COMPENSATOR.

141

screws to I and iv, o is connected to the resistance

box, and the resistance box with wx, the unknown

resistance, which is attached on the other side to n.

The galvanometer G is connected with the platinum

wheel of the compensator through

the binding screw connected with

in, and on the other side to s,

the binding screw on the re-

sistance box, from which also

a wire proceeds to Vfx. Thus

Wheatstone's bridge is formed.

The needle of the galvanometer

G is brought to zero by equalising

the potentials at in and s,

effected by turning the disc of Fig. 73,-Aramgement of
the round compensator, just as the Modified Com-
the position of the slider of the
long compensator is altered for the same purpose.

Then, just as in the long compensator, wx : R/t : :

the distance between I and in : the distance between

in and iv. Call the distance between I and in w,,

and the distance between in and iv W2, then wx : nh

: : w : W or

•\v.r—

.

[The student will be able to follow the comparison,
with Wheatstone's bridge (Fig. 71) if he observes that
\vx of Fig. 73 = r of Fig. 71, nh = Re, the distance
between I and ill (w,) = the distance between A and s,
and the distance between in and iv (w^) = the dis-
tance between s and B.]

Now, wx, the unknown resistance, may be a coil
of wire, a galvanometer, a piece of muscle or nerve,
it does not matter what. The method described is
applicable to all, and equally applicable for the de-
termination of the resistance of different parts of the

142 PHYSIOLOGICAL PHYSICS. [Chap. xiv.

living body. For instance, the resistance offered by
the skin of the body to the passage of a current, and
the difference in resistance when the skin was dry or
moistened with different solutions might be deter-
mined in this way.

CHAPTER XIV.

THERMO-ELECTRIC CURRENTS.

To the methods of producing electricity by friction,
by chemical action, and by induction, there remains
another method to be added, that is, by heat.

When two dissimilar metals are placed in circuit,
a difference of temperature between the two places of
junction causes a difference of potential, and so a
current is produced in the circuit, travelling in a
direction from the hot to the cold junction. The
current is called a THERMO-ELECTRIC current, and was
discovered by Seebeck, a professor in Berlin, in 1821.
Fig. 74 is an arrangement for showing this pheno-
menon. It is a plate of cop-
per bent to form three sides of
a rectangle, the fourth side
of which is formed by a bar of
bismuth. In the enclosed space
is a freely suspended magnetic
needle, the apparatus being

Fig.74.-Tkermo-Electric , -i « ,1 x- -T

Current. placed in the magnetic meridian,

so that the axis of the metals

and the needle coincide. Suppose one of the
junctions of copper and bismuth be heated by
means of a spirit lamp, the needle is at Once deflected
in a way to indicate a current through the copper from
the hot to the cold junction. At the hot junction
the current is from bismuth to copper, at the cold

Chap. xiv. j THERMO-ELECTRIC CURRENTS. 143

junction from copper to bismuth. Now this current
may be obtained wherever a circuit is formed of two
dissimilar metals ; and it is to be noted that it is
the difference of temperature that is the cause of the
current. The difference may be caused by cooling
instead of heating one junction. If the same junction
be cooled, the needle is deflected in an opposite direc-
tion to that obtained by heating ; but again the
current is from the hot to the cold junction.

The thermo-electric series consists of the fol-
lowing metals so arranged that each metal is positive
to those before it in the list, and negative to those
after it : bismuth, German silver, nickel, cobalt,
mercury, platinum, gold, brass, copper, tin, alumi-
nium, lead, zinc, silver, iron, antimony.

While, however, any dissimilar metals will yield
a thermal current, all do not yield it of the same
strength. Bismuth and antimony, for instance, give
a stronger current than bismuth and copper, in a
direction across the junction from, bismuth to anti-
inoiiv.

V

The positive metal of a thermo-electric couple is
the metal from which the current proceeds across the
hot junction.

The electromotive force of a thermal cur-
rent is, within limits, proportional to the difference
of temperature between the two junctions. This rule
indicates a means for the determination of the amount
of differences of temperature ; for if one junction be
always kept at a standard temperature, the extent of
the deflections of a needle would depend entirely on
the temperature of the other junction. Therefore, by
the amount of deflection is given a means of ascertain-
ing the temperature of the other junction, and so of
any body in contact with it.

The therano-electric pile is a means of in-
creasing the effects and producing a stronger current.

144

Pn \ -SIOL OGICA L PHYSICS.

[Chap. XIV.

Nobili's arrangement is shown in Figs. 75 and 76.
It is formed of bars of antimony and bismuth, arranged
as in Fig. 76, so that there is a series of five couples,
the electromotive force of the series being the sum of
the electromotive forces of the five elements. There
are four such sets of five couples each, and they are
arranged in a frame, one above the other, but not

/T^j " |

Fig. 7t>.

Fig. 75.
Thermo-Electric Pile.

touching (Fig. 75), the bismuth of the upper one being
soldered to the antimony of the lower. There is thus
left unconnected the first antimony, which is attached
to a binding screw m on the frame, and forms the
positive pole, and the last bismuth, which forms the
negative pole, and is attached to n binding screw of
the frame. The antimony is the negative metal of
the two, but it forms the positive pole, because in the
pile the current goes from bismuth to antimony, and
so passes out by antimony. In the frame the various
elements are carefully insulated from one another.
By such an arrangement there is one set of junctions
at one end (Fig. 75), and another set at the other end.
By heating the junctions of one end and keeping the
other end normal, a current will flow through the pile,
if the binding screws be connected with one another.
Usually the pile is completely enclosed in a box of

Chap. XIV.] G A LI' A NO METER AND THERMO-PILE. 145

brass, which has a small lid at one end, the lifting of
which exposes one set of junctions. The other end is
prolonged into a funnel for collecting heat rays and
leading them into the other junctions.

By means of the binding screws r o the thermo-pile
p can be connected with a sensitive galvanometer H
(Fig. 77), and thus the
slightest difference of
temperature will
cause a deflection of
the needle. The elec-
tromotive force of
thermal currents is

very small ; and their

Capacity for overcom- Fig< 77.— Galvanometer and Thermo-pile.

ing resistance is, there-
fore, very little. If, consequently, a high -resistance
galvanometer, such as that which is used for the de-
tection of the muscle currents, be employed, its 32,000
turns of wire interpose such resistance that the
heat current is so weakened as to be unable to affect
the needle. With Wiedemami's apparatus, the sliding
arrangement of the coils of wire (page 105) permits
of the coils of fine wire being removed, and other
coils, usually made of from 5 to 10 metres of insulated
copper wire, one mm. thick, being put on instead.
Usually with the instrument two sets of coils are
supplied, one set of high resistance and another of
low, arid thus in a moment the change can be made
from a high to a low resistance galvanometer. The
sliding device also permits of any number of coils
being made of varying resistances for the same instru-
ment. If Sir Wm. Thomson's instrument be used,
one ought to be obtained which has an arrangement
of plugs by which many or few turns of the coils
may be interposed in the circuit of the galvanometer,
which is thus made of high or low resistance at pleasure.
K— 7

146 PHYSIOLOGICAL PHYSICS. ich.ip.xiv

Measurements of temperature can be effected
with the aid of such apparatus as has been described.
So sensitive can the thermopile and galvanometer be
made that an elevation of temperature of O'OOOT of a
degree can be accurately estimated. This is owing to
the law that the electromotive force of the thermal
current is proportional to the difference of temperature
between the two junctions of the pile. Suppose, there-
fore, it is required to estimate the difference of tem-
perature between two bodies. They are placed in
contact jwith the two sides of the pile, and a deflection
of the needle is obtained. This deflection is proportional
to the difference of temperature of the two junctions,
and if the galvanometer has been previously graduated,
the difference can be easily calculated. The previous
graduation can be effected by keeping one set of
junctions of a pile at a constant temperature, and
varying the temperature of the other set. A note
can then be made of the extent of deflection corre-
sponding to certain differences. If it is desired to
determine the absolute temperature of a body, it is
necessary to place one side of the pile in contact with
some standard (say, melting ice), some body whose tem-
perature is known and is constant, and then place the
other side in contact with the body whose temperature
is to be measured. The difference of temperature
gives the absolute temperature by relation to the
standard.

It is found, however, that with high temperatures
the deflection becomes so great that the proportion
between it and the difference of temperature is lost.
To maintain the proportion, a less sensitive instrument,
such as the tangent galvanometer (page 96), may be
used, or the current may be short-circuited by a rheo-
cord, and only a proportion of it made use of.

To determine differences of temperature of dif-
ferent parts of body (say, of two sides of the body in.

Chap. xiv.] MEASUREMENT OF TEMPERATURE. 147

a case of paralysis) a modification of the instrument
is made. The pile is made in two halves, as it were,
in a plate form, and is small, so as to be quickly
affected. Each half consists of two metals arranged as
described, with two binding screws, one connected
with antimony, the other with bismuth, and is sup-
ported on an insulating handle. The flat surface of
one half is laid on a place on one side of the body,
and the surface of the other half on the other side of
the body. The two halves are connected by a wire
through a binding screw of each half attached to the
same metal, and from the other screw of each half a
wire is taken to the galvanometer. If the absolute
temperature of the body is to be determined, one half
is immersed in a fluid (say, oil) kept at a constant
temperature, and the other half laid on the body.
The temperature of the oil can be made pretty near to
that of the body to be measured, and this gives
greater delicacy and accuracy. To determine the
temperature of a tissue of the body (for instance, a
muscle) the pile is made in the form of a needle,
which can be inserted into the muscle without damage.
Bismuth and antimony are too brittle for this, but
iron and copper may be used. The needle used by
Helmholtz is made of an iron wire, to each end of
which is soldered a wire of German silver, of half the
length, sharpened at one end to pierce the tissues. To
get a stronger effect, several such needles are connected

o O '

by their German- silver extremities. One end is
pushed into the tissue to the length of the first junc-
tion of silver with iron. Helmholtz used this needle
for estimating the difference of temperature produced
by muscular contraction. The needle being pushed into
the tissue, the deflection is noted, and then the muscle
is caused to contract, and any movement of the gal-
vanometer is observed. A more exact method is to use
two needles, connect them by a wire joining similar

148 y // 1 'S I O LOG 1C A L Pin 'SICS. [Chap. XV.

metals, and insert one needle in the muscle to be
examined. A deflection of the galvanometer needle is
observed. The deflection may be abolished by placing
the other needle in oil or other fluid, to which the
same temperature as that of the muscle is given, that
is, till the needle is brought back to zero. Then, on
contraction of the muscle, the slightest change in
temperature will cause a deflection, The first current
might also be abolished by a compensation current
from a Daniell. (See page 121.) Helmholtz' method
was to transfix the muscles of the thigh of a frog with
one of his needles, formed of six couples, as described,
so that the first set of junctions between silver and
iron were embedded in one thigh, and the other set in
the other thigh. He then waited till the absence of
deflection indicated the same temperature in both, and
then stimulated one thigh to tetanus.

CHAPTER XV.

PHYSIOLOGICAL INDICATIONS FOR THE THERAPEUTICAL
APPLICATIONS OF ELECTRICITY.

THE purpose of this chapter is to give the briefest
possible outline of the purposes for which electricity
is used in medicine and surgery, and the types of
apparatus employed in its production and application.
It is hoped that this outline will act as a guide for
students and perhaps practitioners, and will aid in
the reference to the larger text-books on the subject,
a list of the chief of which is given at the end of the
chapter.

Terms in common use. — Both the constant
current (the current direct from a battery) and the
induced current are employed in medicine. By use

Chap, xv.] MEDICAL ELECTRICITY. 149

and custom the employment of the constant current is
spoken of as GALVANISM, and that of the induced cur-
rent as FARADISATION, after Faradav, the discoverer of

\j *

induction. Thus when a writer speaks of galvanising
a patient, a muscle, or part of the body, he means that
he applied the constant current ; when he speaks of
faradising, the induced current is indicated.

What we have hitherto called ELECTRODES are
often called RHEOPHORES (pe'os= a stream, and <t>ep<a= I
carry; Lat. fero), that is, current carrier*. The term
is specially applied, not to the wires connected with
the batterv or coil, but to the termination of the wire

K

specially adapted for applying the electricity to various
parts.

Batteries and coils. — Before indicating the
sort of apparatus used in therapeutics, it may be
well to mention that static electricity has often
been medicinally employed. It might be applied by
placing the patient on an insulated stool, and giving
him in his hand a connection with the prime con-
ductor of a frictional machine (page 10), or with the
cushions, and so electrifying him positively or nega-
tively.

Sparks could then be drawn from any part of the pa-
tient's body that one wished to stimulate, by approach-
ing a conductor to it, the knuckle of the operator's
hand, for example. Again, a single shock could be
given from the frictional machine or from a Leyden
jar (page 11). This method is not now in use, though
records seem to show it to be of value.

For the applications of current electricity, it is
obvious that two kinds of apparatus are necessary,
one to supply the constant current, consisting of a
battery of cells of one kind or another, and of conducting
wires, and another consisting of one or more cells
connected with an induction coil, and arrangements
of wires for employing the induced currents.

PHYSIOLOGICA L PH \

[Chap. XV.

Fig. 78.— Stohrer's Battery.

For the constant current, types of batteries may
be taken in the STOHRER and the LECLA.NCHE.

Stohrer's battery is figured in Fig. 78. It consists
of a case containing twenty to thirty cells of vulcanite

containing a
plate of carbon
and a plate of
zinc, the cell
being half full
of dilute sul-
phuric acid with
a little bisul-
phate of mercury
for keeping the
zincs amalga-
mated. In one form a small quantity of strong
solution of chromic acid is added, and gives the fluid a
claret colour.

The plates are fixed at the upper part of the box
on a wooden support. The cells can be raised by a
handle projecting at each end, so that they can be
raised up to meet the plates, which are so caused to dip
into the solution, and the cells can also be lowered so
that the plates are out of the solution. When the
cells are raised they can be fixed by a half turn of the
handle. The plate carrier carries a sledge, which on
its under surface makes contact by means of two
metal rails with the plates. The plate carrier has
numbers marked on it which indicate the number of
cells in circuit when the sledge is over that place.
The sledge should be so placed as to cover three wires
of the cells, the central wire of which tells the number
in circuit. The metal rails are long enough to make

o O

contact with the next cell before they break contact
with the one before. So that if a current is being
passed through a patient's body it is not necessary to
break the circuit in order to throw in more cells, but

chap, xv.] MEDICAL BATTERIES. 151

the movement of the sledge increases the number of
cells in circuit without breaking the circuit. Opening
and closing shocks are, therefore, avoided. The

B

sledge has binding screws for the attachment of wires.
It also has an arrangement c which acts both as key
and commutator. When the handle is perpendicular
no current is passing; when it is turned back the right-
hand binding screw is positive ; when it is turned
fortvard the left-hand screw is positive. Thus the
circuit may be interrupted and tbe direction of the
current altered.

By this arrangement, therefore, any strength of
current may be used, and the current may be inter-
rupted or sent in any desired direction.

The Leclanche battery is the one now largely
in use for medical purposes. It is compactly put
up in boxes containing twenty, forty, or more
cells. Each cell is about the size of a two ounce
bottle, and is divided into two compartments by a
porous partition, on one side of which is zinc in sal-
ammoniac solution, and on the other gas carbon and
native pyrolusite moistened with water (page 23). Fig.
79 is a representation
of the cover of such a
battery, s h ow i 11 g a
dial plate a, with a
series of brass Studs, Fig. 79.— The Leclanclie Battery.

each stud having a

number marked 011 it. A hand can be turned over
the dial and caused to make contact with one stud
after another. When it makes contact with a stud
the number attached indicates the number of
elements in circuit, the binding screws for connecting
with wires being always the same. The contact-point
of the hand should be so made that when exactly over
one stud it does not touch the stud 011 either side, but
when being moved to a new position it ought to he

152 PHYSIOLOGICAL PHYSICS. |_Chap. xv.

broad enough to make contact with the next stud

O

before leaving the preceding one, to prevent breaking
the circuit every time a change in the strength of
current is made. The cover has also a commutator
b for reversing the direction of the current, and a
key for interrupting it c.

The description of these two forms of batteries
sufficiently indicates what is wanted to make a ser-
viceable battery. The following points should be
noted :

(1) Batteries containing large cells are not required,
because, as explained in chapter iii., the resistance of
the body to be overcome is so great in proportion to
the resistance of the elements that the latter can
afford to be neglected. Consequently large plates
are of no advantage. For the same reason, (2) the
number of cells arranged in series should be multi-
plied, for with large external resistance this increases
the electromotive force.

Therefore, in selecting a battery one should choose
a case containing forty or fifty small elements.

There are two exceptions to this rule. If the
current is to be used for electrolysis, or for heating
purposes (cautery, for example), cells with large plates
are desirable, because in this case the external resis-
tance is small.

(3) The battery should have an arrangement for
altering the strength of the current without breaking
the circuit.

(4) It should be provided with a key for inter-
rupting the current ; and many are provided with an
arrangement for interrupting more frequently than
can be done by hand with a simple key, so as to give
a rapid series of shocks.

(5) Besides the accessories mentioned, a galvano-
meter is often supplied together with a battery
for testing the strength of current. The best is a

chap, xv.] PULVERMACHER'S CHAIN PILE.

'53

small tangent galvanometer, since in it the strength
of current is proportional to the tangent of the
angle of deflection.

A "battery said to be the best for therapeutic
purposes is a modified Daniell called the BECKER-

MUIRHEAD.

Fig. 80 exhibits a part of Pulvermacher's

chain pile. It consists of cylindrical pieces of wood,

on which are coiled in a spiral manner, a copper

and a zinc wire. Each turn of

the wires lies in a groove in

the wood, and is insulated from

its neighbours. The ends of the

zinc wire of one cylinder are

coupled to the ends of the copper

wire of the cylinder below. Any

number of cylinders may be

used. The first has the two ends

of its copper spiral free, and they

are united to form the positive

pole, as seen at b in the figure.

Similarly the free ends of the last

zinc spiral form the negative

pole. To put the chain into

A ,. ., . -,. , . , ,, Fig. 80. — Pulvermaclier's

action it is dipped into a basin of chain Pile,

acidulated water. The poles are

connected to copper tubes, each containing a sponge
moistened with acidulated water. The chain, having
been removed from the basin, may then be applied to
the body by making contact with the sponges at the
desired places. It is not a constant pile.

Induction apparatus is usually set up so
as to have cell, coil, and accessory apparatus, all
within the same box, which is usually of comparatively
small size, since induction currents of sufficient
strength for the human body can be generated by a
small cell and a small coil. One form of apparatus

154

PH YSIOLOGICA L PH YSICS.

[Chap. XV.

only will be described. It is that of Dr. C. Spamer.
It is small and compact, and seems well fitted for all
purposes of faradisation. It is represented in Fig. 81,
the lid being removed.

This apparatus shows well the conditions to be
fulfilled in such an instrument. (1) The extent of
action of the cell can be regulated by the extent of
immersion of the plates. (2) The induced currents of
the coil can be regulated as to strength. This is done
for the secondary coil by altering its position in
reference to the primary, and for the primary coil by
the position of the soft iron core. The regulation of
the number of induced currents is managed by
adjusting the Wagner hammer, which is the inter-
rupter of the primary circuit. (3) There should be
binding screws connected both with the primary coil,
to permit the use of the extra current (page 44) if
desired, and with the secondary coil, to permit the
use of the induced currents of that coil.

The description of the
apparatus is as follows :

The interior of the
case is divided by a par-
tition into two halves, the
right of which contains
the drawer for the acces-
sory apparatus, and above
it the interrupter, the ter-
minals, marked -f- and —
(positive and negative
pole) for the leading wires,
and the plugging arrange-
ment which serves to put
in circuit the primary or

secondary current. The plug being inserted in p, as
shown in the figure, the primary or extra current is
obtained, in s the secondary current.

Fig.

81.— Electro-induction
paratus.

chap, xv.] SPAMER'S INDUCTION COIL. 155

In the left part of the case is the cell, and behind
this the bobbins are provided. A is the iron core,
shown in the figure partly drawn out, which is kept
at any height by a sliding spring and which allows
the current to be diminished with ease. The cell
consists of an ebonite or glass jar, in the cover of
which the carbon is fixed hermetically. To enable
the cell to be taken out, the clamp E is unscrewed,
and the brass piece forming the connection between
the carbon and the apparatus, thus made free, is
turned to the front.

Behind E a zinc rod z rises from the cell. It is
fixed bv a screw to a brass fork sc, which can be turned

v

to the back. This is done when the apparatus is not
in use, and in this case the cell is closed by an india-
rubber cork.

The zinc rod, after having been cleaned from the
adhering acid, is put into the black groove provided in
the left wall of the case. In order to put the apparatus
in action the carbon is fixed to the clamp E and the
zinc rod connected with the brass fork is slowly
lowered into the cell until it is immersed in the liquid,
which usually will be perceived by the hammer being
put in vibration. This may be facilitated by touching
the hammer with the finger. As a rule the zinc rod
ought not to be immersed any deeper than is wanted
for making the interrupter act. For the first hours of
use 10 to 15 nun. immersion are sufficient. When
the current is getting weaker the zinc rod must be
lowered, but then a new filling up of the cell will
soon be required. The liquid consists of :

Potas. bichromici .... 8 parts

Aq. dest. ...... 100 „

Acidi sulph. puri .... 15'0 ,,

Hydrarg. bisulph. . . . . I'O „

This quantity allows the cell to be twice filled up.
Before filling again, the cell jar ought to be rinsed

156

PHYSIOLOGICAL PHYSICS,

[Chap. XV.

several times with cold water. The zinc rod is kept
amalgamated while hanging in the liquid.

The accessory apparatus consists of two leading
wires, two handles, three covered electrodes, and one
wire brush.

The size of this case is only 7 inches in each
direction, and it weighs only a little over 2^ pounds.
A larger size of the same apparatus can be had, if
desired.

Some manufacturers make cases containing on one
side a constant battery and on the other an induction
apparatus.

Magneto-electric machines are also used for
producing induced currents. Bobbins of wire with
cores of soft iron are caused to rotate in the neighbour-
hood of the poles of a strong magnet. As each coil
approaches one pole an induction current is produced,
and another when the coil goes away from the pole,
so that each coil produces four induced currents in

one rotation. Wires are
arranged to lead off the
currents, which can be
applied in the same way
as ordinary induced cur-
rents. Fig. 82 shows an
apparatus for magneto-
electric induction.

Wires for making con-
nections should always be
insulated with silk or guttapercha.

The electrodes or rheophores are of various
forms according to the part to which they are in-
tended to be applied. They consist usually of an
insulating handle of wood supporting a brass cup
from one-half to three inches in diameter, a binding
screw for the attachment of wires being connected.
The metal cup is not applied to the body, but is filled

Fig. 82. — Magneto-electric Induc-
tion Machine.

Chap, xy.j ELECTRODES FOR MEDICAL PURPOSES. 157

Fig.

83. — Forms
trodes.

of Elec-

with a sponge which projects beyond the cup, and is
moistened with warm salt water or merely warm water
(Fig. 83). The projecting part of the sponge only
touches the body, and it may be cut to any shape.

The cups should be
screwed to the handle, so that
they may be removed and
other forms of rheophores
attached to the same handle.
Further, the binding screw
ought to be at the junction
between cup and handle, and
not at the end of the handle,
as it often is. When the
screw is afc the junction, there
is no risk of contact being
made with, for instance, the
hands of the operator.

Fig. 83 shows some different forms of electrodes ;
4 is one of the usual forms ; 1 and 2 are brass knobs
covered with wash leather ; 3 is a wire brush on an
insulating handle, used for acting on the skin with
induction currents ; 5 is for cautery (not used with
induction currents ; it is referred to on page 168).

Similarly, electrodes can be made in any form to
suit throat, uterus, rectum, nasal passage, ear, etc.

MODES OF APPLYING ELECTRICITY.

First of all it is to be noted that, whatever kind
of current is used, the electrodes may be used wet or
dry, and the part of the body to which they are
applied may be moistened or dried. If moisture is
used the resistance of the skin is diminished, and the
current may then pass through the skin and reach the
moist tissues beneath, which are good conductors.
On the other hand, dry skin offers very great re-
sistance. Consequently, when it is desired to send

158 PHYSIOLOGICAL PHYSICS. [Chap. xv.

the current to the deep parts and to affect the skin as
little as possible, the electrodes are moistened, and the
skin also, with warm salt water or acidulated water ;
and when it is desired to affect the skin only, dry
electrodes are used and the skin is dried and powdered.

Oalvaiiism may be applied in two chief ways.
(1) The one electrode may be placed on some indif-
ferent part of the body (the nape of the neck, the pit
of the stomach, or held in one hand), while the other
electrode is applied to the the part it is desired to
influence, one side of the head, over the pneumo-
gastric or sympathetic, or to a particular muscle,
the two places being distant from one another.

(2) The two poles may be near to one another,
e.g. one at one side of the head and the other at the
other side, to influence the brain.

In the former case the current, entering at the
place of the positive pole in a dense stream, spreads
itself out in various directions in streams of less
density, and is then collected into one to pass out by
the negative pole. In such a case the current, being
broken up in its passage through the body, will have
its principal effect at the two poles, where its density
is greatest. In the latter case, the two poles being
near one another, the current will pass in one stream,
as it were, and therefore with almost undiminished
density.

When a current passes in the opposite direction
to the ordinary nerve current it is said to be inverse
(up a limb, for instance), when in the same direction
it is direct.

In the next place the current may be sent con-
tinuously through the body or part of it, or it may be
interrupted by keeping one electrode fixed, and alter-
nately lifting and then reapplying the other, so as to
make and break the circuit. The interruption may
also be effected by a cogged wheel, or some other

Chap, xv.] -FARADISATION. 159

mechanical contrivance, and may, therefore, be made
fast or slow, as desired. By the former way the
utmost heating and chemical effects are obtained, and
nutrition is, therefore, powerfully affected : by the latter
method the stimulating properties of the current are
obtained.

Faradisation may be applied generally. One
good way of doing this is to seat the patient in a chair,
stripped to the waist, and his bare feet on a metal
plate to which one pole is attached. The operator
has the other pole connected to a sponge electrode,
which he applies to various parts of the patient's body
as desired. This is the method of Beard and Rock-
well of New York. Localised faradisation is the
phrase used by Duchenne when the two electrodes are
applied near one another, so as to confine their action
to groups of muscles, or single muscles, or nerves, or
limited regions of the body. Again, a muscle may be
faradised directly, when the moist electrodes are so
applied that the current is sent to the muscle sub-
stance itself, or indirectly when the stimulus is applied
to the nerve which supplies the muscle. As has been
seen (page 68), a feebler current will produce contrac-
tion of a muscle when applied to its motor nerve, than
when applied to its own substance. Certain places can
be marked 011 the skin, from which an induced current,
applied by a moist sponge electrode, can reach the
motor nerves of separate muscles or groups. These
are termed MOTOR POINTS.

APPLICATIONS OF ELECTRICITY.

The two chief purposes for which electricity is
therapeutically employed are (A) for DIAGNOSIS, and

(B) for TREATMENT.

Diagnosis. — The electrical current is employed :

(1) To detect alterations of irritability or sensibility,

(2) to aid in distinguishing between forms of paralysis,

PHYSIOLOGICAL PHYSICS. [Chap. xv.

(3) to detect the presence in the tissues of foreign me-
tallic bodies, (4) to unmask malingerers, (5) as a final
test of death.

(1) To test irritability of muscle or nerve, use an
induction current, and apply well-moistened electrodes
to the part, the skin over which is also moist. This
ensures the current traversing the skin without affect-
ing it. Then graduate the intensity of the current by
moving the secondary coil or altering the extent of
surface of plates in action in the cell. Begin with
the healthy side, and find the feeblest current that
will produce a response on the part of the muscle or
group being tested. Compare the result obtained
•with that of a similar experiment on the suspected
side, taking care that the experiment is repeated under
precisely similar conditions. If both sides are sus-
pected, then a healthy standard must be obtained else-
where, and the physician must compare his results with
an average obtained from healthy individuals.

For testing sensibility the skin must be acted on,
and not the tissues beneath. Therefore the electrodes
must be dry (a wire brush), and the skin should be
well dried and dusted. Then find what strength of
current just begins to be painful on the healthy side
of the patient, and compare this with the diseased side.

(2) For purposes of electrical diagnosis paralysis is
considered to be due either to a CENTRAL or to a PERI-
PHERAL lesion, and the value of electricity is in the
aid it gives in distinguishing between these two. A
CENTRAL lesion is, for this purpose, counted one which
separates the muscles from the higher centres, a peri-
pheral lesion is one which cuts off the muscles from
their lower centres. Thus the muscles of the legs are
in nervous communication with centres in the spinal
cord, their lower centres ; but these lower centres are
subservient to centres in the brain, their higher
centres. Now these muscles may be cut off from

chap, xv.] ELECTRICITY IN DIAGNOSIS. 161

their higher centres, their lower being left intact, by
a lesion in the brain itself, or by a lesion in the cord
above the seat of their lower centres ; and in each of
these cases the lesion would be called central. If,
however, the lesion were to be in the cord affecting

O

the centre from which the nerves supplying the
muscles come off, or if it were to be in the nerves,
cutting off' communication between the cord and the
muscles themselves, it wTould be called PERIPHERAL.
Thus central paralysis is dependent upon disease in
the brain, or in the cord, higher up than the place of
origin of the nerves for the affected muscles, while
peripheral paralysis is due to disease in the cord
affecting the centres connected with the paralysed
muscles, or to disease of the nerves ; and this would
include injury to the nerves, e.g. cutting, bruising so
as to deprive them of nervous continuity.

Now, this being explained, the main fact, stated
broadly, is that nerves and muscles paralysed by a
central lesion have their irritability unaffected, while
nerves and muscles paralysed by a peripheral lesion
have their irritability rapidly diminished and finally
abolished.

In the central lesion the nerves and muscles still
retain their connection with the centres in the spinal
cord. They are only removed from the influence of
the will, so that voluntary motion is in abeyance, but

i • "

the nourishment of nerves and muscles remains, and
no sign of any impaired function ought, therefore, to
be present. Of course, volition being suspended as
regards them, their functions are no longer performed.
They fall into disuse, and since, in course of time,
enfeeblement always attends disuse, after an interval,
diminished irritability will be perceived. This is,
however, directly the result of disuse, and only in-
directly the result of the lesion. The irritability can
be restored by the use of faradisation, which affords

1 62 PHYSIOLOGICAL PHYSICS. [Chap. xv.

an artificial stimulus and causes the paralysed muscles
to work. So that the rule remains that the irritability
is unaffected by the lesion. There is an exception,
however. It occasionally happens that the irritability
seems to be increased. This will occur when the
lesion in the brain or upper part of the spinal cord is
an irritative one, and irritates the ends of the fibres
which it has cut off from their centres. In the
absence of any ground for supposing an irritative
lesion, a physiological explanation would be that the
moderating influence of the higher centres had been
removed, and the response of the lower was, therefore,
more easily elicited.

In the peripheral lesion communication has been
cut off with the centres in the cord. These centres
are not only reflex, but trophic ; the nerves, therefore,
cut off from their centre, degenerate, and the retro-
grade changes will in time also affect the muscles.
The rapid loss of irritability, then, is due to degenera-
tion. Here a curious circumstance arises which it is
difficult to explain. What has been said refers to
electricity used as induced currents, applied by
moistened electrodes. It is found then that in some
peripheral lesions, where, as is to be expected, response
to the induced or faradic current is entirely absent,
the muscles will respond to the galvanic current if it
be slowly interrupted, and the muscles of the paralysed
side will often respond vigorously to a galvanic current
so weak that it has no effect on the sound side.
Further, in such cases the nature of the response is
altered. As was seen when considering the law of
contraction, nominally the excitability is greater in
the neighbourhood of the cathode on closing, and in
the neighbourhood of the anode on opening the
circuit ; but in these cases it is contraction at the
cathode on opening and at the anode on closing that
is marked. It has been found difficult to explain

chap, xv.} ELECTRICITY IN DIAGNOSIS. 163

these facts. The explanation offered by Erb and
corroborated by Ziemssen is that nerve and muscle
respond differently to the electric current, that,
while the nerve responds readily to currents of very
short duration, like the induced, muscle responds
more to currents of longer duration, such as are ob-
tained by interruptions of the constant current.
Consequently, when the irritability of nerve and
muscle to faradisation has disappeared, the response of
the latter to galvanism may still be elicited. In time,
however, if the degeneration proceeds, galvanism will
also fail to elicit contraction of muscle. The cases
which show these DEGENERATIVE REACTIONS, as they
are called, are rheumatic paralysis, facial palsy (due,
e.g., to cold, i.e. not hemiplegia), lead palsy, paralysis
due to injury of nerve trunks, and others. To sum up,
then, in central paralysis irritability is unaffected,
in peripheral paralysis irritability rapidly disappears,
but in some cases irritability of the muscle to gal-
vanism is increased, and thereafter disappears.

(3) To detect foreign metallic bodies, e.g. a bullet,
in the tissues, the constant current is employed.
What is required is a battery sufficiently powerful to
ring an alarm bell, and in the same circuit a probe of
particular construction. The probe should be of in-
sulating material, having imbedded in it, and insulated
from one another, two copper wires. The ends of the
two wires are exposed at the end of the probe. If
these wires are put in the circuit of the battery and
bell, the bell will not ring, because contact is broken
between the two wires. If, however, the probe be
pushed into a wound and come in contact with a
bullet, then, both wires touching the lead, the circuit
is completed, and the ringing of the bell gives the
indication. Instead of a bell, a galvanometer may be
used (not one of sensitive construction), its deflection
intimating metallic contact.

164 PHYSIOLOGICAL PHYSICS. [Chap. xv.

(4) As a means of detecting malingerers electricity
must, of course, be used with caution. If a strong
induced current fail to produce contraction, paralysis
is evident, for the contraction set up by electricity is
beyond voluntary control. Though contraction be
produced, however, it does not follow that nothing is
amiss. Faradisation of the dry skin with the wire
brush, if strong enough, is very painful, and may
without danger be employed.

(5) Within, at most, two or three hours after
death induced currents of electricity fail to provoke
a response from the muscles. Failure to elicit re-
sponse is, therefore, a sure sign of death. Moistened
electrodes should be employed in the test, and the
skin also should be well moistened with warm salt
water.

Electricity is employed in therapeutics
as (1) stimulant and counter-irritant, (2) sedative and
antispasmodic, (3) for electrolysis, (4) as cautery.

(1) Obviously the commonest use of the stimulat-
ing properties of electricity is in paralysis. Where the
paralysis is central, and disuse has caused wasting of
the nerves and muscles, electricity is employed to
restore their tone and improve their nutrition. The
induced current is used, and of a strength just
sufficient to produce contraction, and the faradisation
ought to be local. It is obvious that the only benefit
to be expected in such cases is the restoration of the
normal state of the muscles and nerves as to their
irritability ; it is equally obvious that electricity
cannot be expected to restore voluntary motion, whose
abeyance is due to the central lesion, and whose
restoration is dependent upon the nature of the lesion.

In peripheral paralysis, where the lesion affects
the centres in the cord or the nerves and produces
rapid degeneration of nerves and muscles, electricity
frequently yields marvellous results. Faradisation is

Chap, xv.] ELECTRICITY AS A STIMULANT. 165

again employed, but, as explained, in certain cases it
has no effect, and in such cases the slowly-interrupted
galvanic current should be applied. As already
noted, such cases occur in paralysis from injury to a
nerve, fi-om rheumatism, and from cold, as in cases
of facial palsy and in lead palsy.

Faradisation has been also successfully used for
aphonia and asthma. In the latter case each electrode
is placed below the angle of the jaw and in front of the
sterno-cleido-mastoid muscle.*

As a stimulant, induced currents are used in
amenorrhcea and post-mortem haemorrhage.

To restore respiration in asphyxia from chloroform,
or in the diminished respiration of opium poisoning,
faradisation of the phrenic nerves is resorted to. The
phrenic nerves are affected by placing one electrode
over the scalenus anticus, behind the sterno-mastoid
at the root of the neck, and the other in the sixth or
seventh intercostal space.

Faradisation of the skin (dry electrodes) is practised
for anaesthesia and skin diseases.

Electricity may be employed as a stimulant to the
nutritive processes. For instance, this proceeding has
been recommended in suspected cerebral lesion, to
promote absorption of a clot or contraction of a cyst.
A weak constant current is, therefore, employed,
and is applied by placing one electrode (anode) on
the forehead and the other on the nape of the neck ;
or the process called galvanisation of the sympathetic
may be made use of. This is accomplished by one
electrode (moist) on the inner side of the sterno-
mastoid muscle, on a level with the third cervical
vertebra, and the other at the nape of the neck.
This procedure must, however, be employed with great
caution, and never until some weeks after the occur-
rence of the lesion, lest inflammatory action be set up.

* Sec paper by Dr. Burney Yeo in the Lancet of Nov. 27, 1880.

1 66 PHYSIOLOGICAL PHYSICS. [Chap. xv.

For nutritive purposes also galvanisation is employed
in chronic rheumatism.

As a counter-irritant for rheumatic joints, faradisa-
tion by a wire brush over the affected joints has been
said to yield good results.

(2) As a sedative in various forms of neuralgia
and headache, electricity is invaluable. According to
physiological theory, a weak constant current should
be used, and anelectrotonus produced over the
painful spot. For headache, one electrode may be on
the forehead and the other at the back of the head,
or one on one temple, the other on the opposite;
Great caution and the use of weak currents are
necessary. For ringing in the ears (tinnitus aurium)^
the constant current is of use, one electrode (cathode)
at the nape of the neck, and the other in the meatus
externus, which should be filled with salt solution.

As an antispasmodic in wry-neck, writer's cramp,
and other forms of spasm, the constant current is
applicable. In wry-neck it is applied directly over
the affected muscle ; in the writer's cramp Dr. Althaus
believes the best results are obtained by applying one
pole to the upper vertebrae, and the other over the
superior cervical sympathetic ganglion, the seat of
disease, according to him, being "in the upper portion
of the spinal axis."

Antispasmodic effects have also been observed in
blepharo-spasm and choreaic movements.

For ovarian pain a constant current may be tried ;
the anode over the painful spot, the cathode over some
indifferent part.

(3) Electrolysis. — A constant current of electricity
decomposes animal tissues as it decomposes water or so-
lutions of salts. This property may be made use of for
the production of eschars, or for decomposing .tumours,
etc. The caustic action of the negative pole is greater
than that of the positive. The negative pole, of a size

Chap, xv.] ELECTRICITY AS A CAUSTIC. 167

to suit the desired purpose, is therefore applied; and the
positive may be in the form of a metal plate resting
on another part of the body, a moist sponge being
interposed. Thus electrolysis has been used for
decomposing iiaevi, bronchocele, sebaceous tumour,
hydatid cysts, etc. In these cases the negative pole
was connected with one or more needles thrust into
the tumour, and the positive with a large sponge on
another part of the body. One of the chief uses of
electricity for electrolysis is for what is called galvano-
puncture in the treatment of aneurism. The object is
to produce a clot in the aneurismal sac, which by
successive additions may finally fill it up. The
strength of current used is that obtained from four
to eight cells of Stohrer's battery. The electrodes
inserted into the sac are of sharp steel needles (being
coated to within a short distance of the point with a
mixture of shellac and guttapercha), the shafts of
which are insulated by gum elastic ; one or more
needles maybe connected with the same pole. As re-
gards the pole to be used for the sac, the positive seems
indicated, since the clot formed on it is small but firm,
while that formed round the negative pole is large
and soft. Dr. Althaus believes in attaching needles
to both poles and inserting both. Dr. McCall
Anderson inserts one needle attached to the positive
pole, and places a zinc plate and sponge connected
with the negative pole on the chest wall, near to the
aneurism, the skin being well moistened. The needles
having been inserted, the current is passed, first of
feeble strength, then slightly increased, and allowed
to pass for fifteen to thirty minutes at a sitting.
The operation is repeated as indications warrant.
Electrolysis has been employed for urinary calcuk,
and is extolled as a depilatory.

(4) For purposes of cautery the elements should
be large and the conductors thick. The electrodes

1 68 PHYSIOLOGICAL PHYSICS. [Chap. xv.

are of various forms, usually of platinum wire,
because, offering great resistance, it quickly becomes
red hot. Fig. 83, 5, shows a galvanic cautery. It
consists of a handle of ebonite, in which are imbedded
two thick copper wires, which have binding screws for
the attachment of the battery wires. Connected with
these wires, at the point of the instrument, is a piece
of platinum wire a, which is bent as shown in the
figure, and flattened at the bend. This piece of
platinum wire becomes white hot when a sufficiently
strong current is passed through it. Usually there is
a spring at the side of the handle for breaking or
completing the continuity of one of the wires,
so that the circuit may be interrupted or com-
pleted. Thus the cold point of the instrument
may be accurately applied to the part, then the
current sent on, and the cauterising action localised.
For making larger eschars the terminal piece of
platinum wire is finer and wound on a thin porcelain
capsule of any desired shape, or a loop of fine wire
may take the place of these. With the current inter-
rupted the loop is properly adjusted and tightened
round a polypus or other tumour to be removed, and,
the circuit being formed, the wire becomes red hot ;
it can then be made to cut its way through the
tumour. The pain of the galvanic cautery is severe
at the moment, but afterwards slight, the extremities
of the nerves being destroyed. When the proper
amount of heat has been employed, and the tumour
cut through not too quickly, haemorrhage is prevented,
and healing is rapid.

Electro-magnetism has been employed in ophthalmic
surgery for the extraction of pieces of iron or steel
from the tissues of the eye.

A recent use of electricity in medicine is for the
purpose of illuminating certain passages and cavities of
the body. Thus lamps of the incandescent type may

Chap, xv.] WORKS ON MEDICAL ELECTRICITY. 169

be made small enough to be passed even into the
bladder or into the stomach, an arrangement of
mirrors permitting a view of the interior.

It thus appears that if the physical effects of elec-
trical currents be kept in view, as well as the
physiological effects on muscle and nerve, or excita-
bility of nerves and such other facts, valuable indi-
cations will be obtained as to the use of electricity,
the kind to be employed, and the method of appli-
cation.*

* Consult : "A Treatise on Medical Electricity, " by Julius
Althaus, M.D.; "A Text-Book of Electricity in Medicine and
Surgery," by G. Y. Poore, M.D. ; also in " Quain's Dictionary,"
article, "Electricity, "by Dr. Poore; "Electro-diagnosis in Diseases
of the Nervous System," by A. Hughes Bennett, M.D. ; "The
Electro-magnet and its Employment in Ophthalmic Surgery," by
Simeon Snell ; "A Practical Introduction to Medical Electricity,"
by A. De Watteville, M.A., M.D., etc. ; "Faradization Localisee,"
by Duchenne.

170

THE GRAPHIC METHOD,

BY the graphic method is meant the process by
which curves or tracings are obtained, which represent
various phenomena. Thus, a chart on which is traced
out daily the course a vessel has taken in crossing
from Europe to America is a graphic representation
of its voyage, the lines drawn from day to day repre-
senting not only the course of the vessel, but the
distance accomplished since the day previous, and con-
sequently the speed of the ship. Similarly a fever
chart, on which is marked daily the temperature of a
patient, each degree or fraction of a degree gained or
lost above the normal being represented by a mark at
a definite distance above or below the normal line,
and each successive day being indicated by a given
space across the chart, a fever chart is a graphic
representation of the course and variation of the
fever. Now this method is applied in many ways in
physiology and medicine, to obtain a record of time
of movement of heart, pulse, muscle, or chest, to obtain
a record of blood pressure, and so on. The means of
recording time will first be considered.

CHAPTER XVI.

THE MEASUREMENT OF SMALL INTERVALS OP TIME.

THE idea which has rendered possible great
advances in graphic registration, and especially that
of time, was suggested by Thomas Young in 1807.

Chap, xvi.] THE GRAPHIC METHOD. 171

If a cylinder be caused to revolve at a constant speed,
and if a lever be brought up against it, and caused to
make a mark upon it, the time during which the lever
acted on the cylinder can be estimated by the speed of
the cylinder. Thus, if the cylinder revolved once in
the second, and the mark extended half way round
the cylinder, the lever must have acted during half
the time of revolution of the cylinder, i.e. a half
second. Or, if the cylinder revolve once per second,
and the space of the cylinder be divided by 100
vertical lines into 100 equal parts, then each part
represents graphically the y^th of a second, and
so on.

This idea was speedily taken up and developed by
some French experimenters, and specially by Professor
Marey of the College of France. To render the
movement uniform he added to the revolving cylinder
the regulator used by Foucault in his determination of
the velocitv of li^ht.

•/ o

The cylinders now used are generally made of
copper, and are turned by clockwork, regulated by a
Foucault's regulator. There are usually two or three
axes of different degrees of speed, on any of which the
cylinder may be pivoted, or there is an arrangement
for altering the speed without moving the cylinder.
A dial plate indicates the number of revolutions.
The cylinder is covered with paper smoked by a tur-
pentine lamp. Any marker brought against the
cylinder removes the soot and makes a white mark as
a record of its contact.

Even without such a regulator, however, accurate
measurements can be made by the use of electro-
magnets. Fig. 84 shows such an instrument, which
is constructed on the same principle as Wagner's
hammer. (See page 42.) The current from a battery
entering by one binding screw passes round the bobbins
of wire, converting their soft iron cores into temporary

172 PHYSIOLOGICAL PHYSICS. [Chap. xvi.

magnets, and leaves by the other binding screw. The
keeper K has attached to it a lever b, which is drawn
down by the magnets. When the current is in-
terrupted the keeper is withdrawn by the elasticity of

the spring c, and the lever flies
up. Now, if the current of this
electro-magnet be interrupted and
then established by the movement
of a seconds pendulum, the lever
brought against the surface of a
revolving cylinder will mark
seconds.

The clock may be arranged to

Fig. 84.— Electric Sig- • , i_ T_ ir j i j.i

nai. interrupt each hair second, and the

lever will then mark half seconds.
Further, the metronome figured on page 71 can be
adapted to the electro-magnet, and the number of its
movements per minute will be reproduced by the
electro-magnet. Still more minute intervals of time,
however, can be registered by the use of tuning forks.
If to one limb of a fork a fine stylet be attached, and
if the fork be caused to vibrate and the stylet be
brought against the surface of a revolving cylinder, the
moving limb will write a series of curves, each curve
corresponding to a to-and*fro movement of the limb of
the fork. Suppose the limb vibrates 100 times per
second, then each curve will equal y^^th of a second.
Another fork vibrating 200 times per second, will
write ^iro'kh of a second, and so on. Such rapid
vibrations cannot, however, be well recorded without
the use of the electro-magnet. The method of
adapting this to the tuning fork has been devised
by Marey. Fig. 85 shows one part of the apparatus.
It is an electro-magnet of two bobbins with soft iron
cores ; on each is a soft iron keeper bb ; between the
keepers a triangular interval is left, which is occupied
by a wedge-shaped piece of soft iron c, supported on

Chap. XVI.]

THE CHRONOGRAPH.

Fig. 85.— Marey's
Vibrating Style.

a steel spring which runs between the bobbins. The

current is brought to the binding screws d d. When

the keepers are magnetic both act

on the little wedge, and pull it

down into the space between them.

When they are in proper position

they should act equally so as not to

attract the wedge to one side or

other. When the keepers are de-
magnetised the wedge is pulled

upwards by the spring. A finely

pointed piece of quill projects from

the wedge as marker. The current

circulating round the bobbins is interrupted by a

tuning fork, as shown in Fig. 86.

The tuning fork is fixed horizontally to a wooden

support, and has between its limbs, or at the side, a

small electro-magnet, marked Elect, in the figure. On

the support are two binding screws, one connected

with the magnet,
the other with the
fork. The fork
carries at the end
of one limb a small
piece of fine plati-
num wire, which
can be made to
touch a small plate

Fig. 86.— Tuning Fork for Chronograph. of platinum Sup-
ported, by means

of a screw, on a brass upright Pt. This upright is
connected with one end of the wire round the electro-
magnet. The current from the element E enters by
the binding screw connected with the fork along wThich
it passes to the limb bearing the wire. From the
wire it escapes to the platinum plate on the upright,
and from this passes round the bobbins, magnetising

174 PHYSIOLOGICAL PHYSICS, [Chap. xvi.

them, and from them to the other binding screw. The
electro-magnet attracts the limbs of the fork, and
so contact is broken between the platinum wire and
the platinum plate, and the current is interrupted.
The fork is restored to its original position by its
elasticity, and re-establishes the contact, so that the
bobbins again become magnetic, attract the fork,
and again contact is broken. Thus the fork is made
to vibrate, the current is alternately interrupted and
established, and the number of these interruptions
corresponds to the number of vibrations of the fork.
To connect this apparatus with the stylet, a
wire from the battery is led to one of the binding
screws of the fork ; from the other screw a wire
goes to one screw of the stylet, and from its re-
maining binding screw a wire goes back to the
battery. Both are now in circuit. The current
traversing the stylet is interrupted a certain number
of times by the fork, and its fine quill point can thus
be caused to vibrate in unison with the fork. When
this stylet is fixed to a support and brought against
the smoked surface of a revolving cylinder, intervals of
time are marked according to the number of vibrations
per second of the tuning fork. The fork can usually
be removed from its support, and another one vibrating
a fewer or greater number of times can be substituted,
so that different rates of movement can be communi-
cated to the vibrating stylet. Thus the -g^th of a
second can be measured with ease, and the measure-
ment of even more than half this interval has been
accomplished. Such an instrument as has been
described is called a CHRONOGRAPH, or time writer.

CHAPTER XVII.

THE MYOGRAPHION.

THE registration of muscular movements has been
accomplished with the aid of an. instrument called the
myographion. An extremely complicated instrument
was devised by Helmholtz for the purpose of measuring
the rapidity of the nerve current. The simple
myogvaphion of Pflueger is shown in Fig. 87. It con-
sists of a mahogany base s, from which rise brass
pillars a, which carry
the double lever 6. From
the forward end of b
hangs a rod with a steel
point projecting against
the glass plate p. The
weight of this part of the
lever is counter-balanced
by m. From the base rises
a brass column z, hold-
ing the forceps, in which
the nerve-muscle prepara-
tion is caught. Through

the tendo Achilles of the Fig. 87.— Simple Myographion.

muscle is passed a hook,

attached to c of the lever. From the under side of the
lever hangs a scale-pan for weighting the muscle. The
brass pillar supports a glass chamber in which the muscle
may be kept moist. If the glass plate is smoked,
and the steel point projects on to it, then, a basement
line having been obtained by drawing the plate in
front of the point, on the muscle contracting a line is
drawn, and the extent of contraction can be measured

176 PHYSIOLOGICAL PHYSICS. [Chap. xvn.

by the height of the line. The plate may then be
moved, and another tracing obtained for comparison
with the first. With such an arrangement a record
can be obtained of the varying degrees of contraction
by varying the stimulus, or varying the weight, or
varying the interval between each stimulus, and so on.
Again, without stimulating the muscle, the elasticity
of the muscle may be measured by putting weights
into the pan, and finding how the muscle returns to its
original length on removal of the weight. One may
note also different degrees of stretching with different
weights.

To obtain a curve of muscular contraction a modi-
fication of the instrument was made by Du Bois-
Reymond. In the original form of the instrument
the glass plate was not so long as shown in the figure,
and was movable by turning a screw by hand. Instead
of the plate being movable in its frame by hand or
by screw, a spring arrangement is substituted. The
glass plate is long, and is movable along wires, as
shown in the figure. When pushed to one end, the
plate is held there by a catch against the force of a
spring wound spirally on the rod B. But as soon as
the catch is released, the spring causes the plate to drish
across from one side of the frame to the other. On the
support beneath the plate are two binding screws con-
nected by a lever. These binding screws are in the cir-
cuit of the primary coil of an induction machine, and
when the lever touches both the current passes ; when
the contact of the lever is broken the current is inter-
rupted. The muscle is connected with wires from the
secondary coil of the inductorium, and if the current
in the primary coil be interrupted, the muscle is stimu-
lated to contraction. Now when the liberated glass
plate dashes across, a piece of brass projecting from its
under edge knocks the lever aside, and at this instant
the muscle gets a shock ; the muscle being supported

Chap. xvii.] MAKERS MYOGRAPHION. 177

in the forceps and attached to the lever, the marker of
which is against the glass plate, a curve of muscular
contraction is obtained. A mark can be made in the
plate indicating the moment the contact is broken, and
it can be seen whether the moment of contraction
coincides with this. The latent period of stimulation
can thus be measured, and if the stimulation be made
by the nerve, and the experiment be repeated by
stimulation at two different points of the nerve at some
distance from one another, as described on page 1 82,
the rapidity of the nerve current can also be estimated.
The newest addition to the spring myographion con-
sists in the adaptation of a tuning fork whose stylet
projects on the lower part of the plate. An ingenious
contrivance liberates the plate and at the same time
causes the fork to vibrate, so that curves of the oij-oth
of a second or so, according to the fork, are obtained
simultaneouslv with the contraction, to facilitate the

V '

estimation of time.

An arrangement adopted by Marey and shown in
Fig. 88 is specially advantageous, because the muscle
and nerve experimented on are not removed from the
frog but left in situ, so that drying is prevented and
nutrition is carried on. A frog is pithed and pinned
down on a frog-plate of cork, which is supported on
a brass upright. A slit in the skin of one leg over
the tendo Achilles is made, and the tendon freed from
its insertion. At the end of the frog-plate is a stylet,
attached to a spring, which is made to project on to
the surface of a cylinder, as seen in the figure. A
piece of thread tied to the tendon is attached to a
small hook at the side of the lever. If the muscle
contracts, the lever is pulled to one side ; when the
muscle relaxes, the elasticity of the spring returns the
lever to its original position. If the point of the
lever is resting on the surface of the revolving
cylinder, a curve of muscular contraction will be

M— 7

i78

PHYSIOLOGICAL PHYSICS. [Chap. xvn.

produced by the movement. The muscle is stimulated
indirectly. The figure shows two platinum wires
supported in a piece of vulcanite, the wires being in
connection with two little mercury cups. The vul-
canite is connected by a piece of flexible lead tube to

Fig. 88. — Marey's Myographion.

a brass support springing from the frog-plate. The
extremity of each wire is bent into a fine hook. A
slit is made in the skin of the thigh of the frog, and
the muscles are separated just sufficiently to show the
sciatic nerve. The wires are then placed under the
nerve by means of their hook-like extremities. The
nerve is therefore very little disturbed. Into each
mercury cup is put a wire from the secondary coil of
an induction machine ; by this means, the small
piece of nerve between the two platinum electrodes is
stimulated. The primary coil of the inductorium
may be arranged to give a single shock (page 65), or
for the production of tetanus, and the lever will
accordingly give the curve of a single contraction or
of tetanus, revealing the characteristics of contraction
and relaxation in each case. As seen in the figure, the

Chap, xvii.] MAREY'S MYOGRAPHION. 179

frog-plate is supported on a brass upright, springing
from a metal base on three wheels. The wheels move
on rails. Through the base there passes a thick screw
with a very fine thread. The screw is turned by
clockwork supplied with a regulator, and works on
pivots. By the motion of the screw the frog-plate
is slowly carried along the rails from one end to the
other. By this means, if the recording cylinder be
kept revolving, the lines drawn by the stylet do not
clash with one another, but each succeeding one, by
the movement of the frog-plate, is drawn in front of
the other. Now, if at exactly the same point in
each revolution of the cylinder the primary circuit
were closed and then opened, two curves, one of
the closing and another of the opening contrac-
tion, would be obtained side by side, and with every
succeeding revolution two other curves would be ob-
tained, those of one revolution always in advance of the
other. This process might be permitted to go on for
a half or one hour, and at the end of that time one
would have on the cylinder a register of the variations
in the form, height, etc., of the muscle curve due to
the constant repetition of the stimulus ; a registration
of fatigue would be obtained. On the same cylinder
time could be marked by the chronograph, so that one
could gauge how fatigue affected the speed of con-
traction and relaxation. An apparatus has been
adapted to the cylinder for the purpose of stimulating
muscles and nerves at certain moments in the revolu-
tion of the cylinder, but a very simple arrangement
easily accomplishes this in the ordinary cylinder.
To the circumference of the end of the cylinder b,
or to the axis, a small piece of copper wire can
easily be fixed with solder. This projects down wards
from the outer end of the cylinder. A shallow,
dish containing mercury is then placed beneath the
cylinder, or a wooden trough can be adapted in

180 PHYSIOLOGICAL PHYSICS. [Chap. xvn.

the space between the end of the cylinder and
the upright which supports it. By the revolution
of the cylinder the copper wire is dipped into the
dish or trough containing mercury, carried through
it and out at the other side. To make the circuit,
therefore, dip one end of a wire into the trough,
the other end being connected with a screw of the
primary spiral of the inductorium, from the induc-
torium lead one wire to the battery, and carry another
wire direct from the battery to the screw connected
with the pivot on which the cylinder moves (a, Fig. 88).
Thus the current from the battery reaches the screw
supporting the axis of the cylinder, passes across to
ike cylinder, and from it, when the copper wire which
it carries dips into the mercury trough, the current
passes to the mercury, and so gains the wire that
takes it to the inductorium round the primary coil,
and back to the battery. Thus, when the copper wire
carried round by the cylinder dips into the mercury
trouafh the circuit is closed, when the wire leaves the

O '

trough the circuit is opened, and with each opening
and closing an induced current is produced in the
secondary coil which stimulates the muscle.

The pendulum myograpliion of Pick is
shown in Fig. 89, in the improved form given to it by
Helmholtz. The lower end of the pendulum carries
a smoked glass plate A, which can be moved up or
down in its frame by turning the wheel shown above
it. It can also be moved to either side. By the up or
down movement the period of oscillation of the pen-
dulum would be altered, and to prevent this a similar
plate is placed at the back which moves up when the
front one moves down, and vice versa. [The second
plate is not shown in the figure.] When the pen-
dulum is pulled to one side, it is caught and held there
by a piece of brass a projecting downward, being
fixed by the catch b. When this catch is pulled

Chap, xvi i.] THE PEND UL UM MYOGRA PHION. 1 8 1

down the liberated pendulum swings back ; but by the
momentum it acquires it passes the middle line, and
swings up on the other side, where it can be caught by

Fig. 89. — Pendulum Myographiou.

another catch precisely similar to 5. When the pen-
dulum swings the glass plate is drawn in front of a
steel point projecting from a heavy lever, which is sup-
ported by a frog's gastrocnemius held in the forceps.
The nerve of the muscle is laid across electrodes of
platinum wire, similar to those shown in Fig. 45, on
page 83, so as to permit the nerve being stimulated

182

PHYSIOLOGICAL PHYSICS, [Chap. xvn.

at either of two different points. If the muscle is
stimulated when the glass plate passes in front of the
lever, a curve of the muscular contraction is obtained.
Below the glass plate is placed a very ingenious
arrangement for insuring stimulation of the muscle at
a given time. It consists of two binding screws con-
nected by a movable arm c. Suppose the two wires
from a battery fixed to the screws; when the arm is
in contact the circuit will be closed, when the arm
is moved away the circuit will be broken. It is, in
fact, a key, and is placed in circuit with the battery

and primary coil, while the
wires from the secondary
coil pass to the nerve.
Now a piece of brass pro-
jecting from the under
end of the pendulum is so
arranged as to come against
the movable arm. as the
pendulum swings, and sepa-
rate it from its contact
with one of the binding
screws, so that the current
is interrupted, and conse-
quently at that instant the

Fig. 90.— Arrangement for Pen- , . , . , , r™

duiuni Myograph. muscle is stimulated. Ihe

detailed arrangements are

shown in diagram in Fig 90. p is the smoked plate
of the pendulum, carrying the projection 3 for inter-
rupting the circuit. From the battery E a wire is
taken to binding screw 1, from which the current
passes across the lever 2, in connection with the other
binding screw, and so to the primary coil I of the
induction machine, and back to E. When the plate
swings across, 3 knocks 2 away from contact with 1,
making it take up the position indicated by the dotted
line, so that the circuit is interrupted. The wires

Chap, xvii.] THE PENDULUM MYOGRAPHION: 183

from the secondary coil n go to the sides of the com-
mutator c, which has no cross; wires pass from c to
a and b, points in the course of the nerve n of the
muscle m caught in the forceps F. The muscle is
attached to the lever I, whose point touches the glass
plate. According to the position of the commutator
the nerve may be stimulated at a or b. Let it be
arranged to stimulate at a ; set the pendulum as shown
in Fig. 89, release it, and get the curve of its contrac-
tion. Bring the pendulum back to its original posi-
tion ; see that the lever which has been knocked away
from contact is restored, taking care to give no shock
in doing so. Then reverse the commutator so as to
stimulate at b, release the pendulum, and get a second
curve. The second curve will be a little in front of
the first. The difference between the two, which
should spring from the same base line, is evidently due
to the delay caused by the time taken by the nervous
stimulus to pass from b to a. To measure this time a
chronograph must be brought up against the plate,
and, on allowing the pendulum to swing again, a
tracing of time in lOOths or 200ths sec. is obtained.
The difference of time, then, between the first and
second curve, is the time taken by the nerve current
to pass from b to a, and if this distance be carefully
measured the rapidity of the nerve current is obtained.
If now the pendulum be brought with the hand just
to the place where it breaks the contact of the lever
with the binding screws, and the lever of the myograph
be caused to make a vertical line there, without any
movement of the glass plate being allowed, a mark will
be obtained indicating the moment of interruption of
the primary current, i.e. the moment of stimulation of
the muscle. It will be found that this mark does not
coincide with the commencement of the muscle curve,
which occurs a little later ; and the difference in time
between the two gives the period of latent stimulation,

184 PHYSIOLOGICAL PHYSICS. [Chap. xvm.

Given the revolving cylinder, very many simple
arrangements may be made for the registration of
various phenomena. Thus the speed of propagation
of the wave of muscular contraction may be very easily
measured with the aid of two simple levers. A frog's
muscle is laid on a support, one end being tightly
clamped by a small forceps, and the other end being
attached to a weight by a cord passing over a pulley.
One lever is laid across the muscle at one end, and
another across the other end. Both levers are caused
to project on to the surface of a revolving cylinder
placed vertically, the levers being so arranged that the
point of the second touches the cylinder directly below
the point of the first. The muscle is then stimulated
at one end. The wave of contraction, passing through
the muscle, lifts the first lever, which writes its curve
on the cylinder, and immediately afterwards lifts the
second lever, which also writes its curve. Thus two
curves are obtained, one a little in advance of the other,
and the difference between the two measures the time
it took the wave of contraction to pass from one end
of the muscle to the other. A chronographic tracing
on the same cylinder will indicate the absolute value
of this time.

CHAPTER XVIII.

THE TRANSMISSION OF MOVEMENT.

A DEVICE of Marey's, called the tambour or drum,
brings within the region of graphic registration many
phenomena which it might be impossible to register
without it.

The tambour consists (Fig. 91) of a shallow
metallic capsule a, provided with a side tube f. The
capsule is closed above by a delicate caoutchouc

Chap, xviii.] TAMBOUR OF MAREY. 185

membrane b ; and to the centre of the membrane is
cemented a disc of aluminium c, from which two light
supports rise for pivoting a lever d. The lever can
be made of any required
length, and terminates in
a fine point for writing
on the revolving cylinder.

The attached end of the Fig. 91.— Tambour of Marey.

lever is freely movable

round a horizontal axis. Now the membrane covering
the capsule moves with every change in the volume of
air which the capsule contains, and this movement is
communicated by the aluminium disc and its uprights
to the lever supported by them. The apparatus has
arrangements for increasing or diminishing the move-
ment communicated from the membrane to the lever.
Thus the attached end of the lever is split and the
supports springing from the membrane can slide back-
wards or forwards upon it. If the supports be pushed
towards the attached end the movement of the lever
is increased, and vice versa. When the supports are
moved one way or other they cease to be vertically on
the membrane. This is corrected by the screw s,
which moves the tambour, and by means of it the
tambour may be brought directly under the point of
support of the lever. By these arrangements the sen-
sibility of the lever can be altered.

Such a tambour as this is brought into commu-
nication, with another similar instrument by means
of an indiarubber tube, which is attached at
each end to the tube f of each tambour. When two
tambours are thus connected with tubing they form a
closed system, and we may consider them as simply a
tube terminating at each end in an air-bag. When
the air is compressed in one tambour, e.y. by its
membrane being pressed downwards, the compression
passes through the tube to the other tambour, and

1 86 PHYSIOLOGICAL PHYSICS. '[Chap. xvm.

acting on the yielding caoutchouc membrane raises it
upwards ; and the movement is indicated by an
upward stroke of the lever. Thus a movement almost
imperceptible in the membrane itself will be rendered
quite visible by the lever. Again, if the membrane of
one tambour be raised or pulled upwards the air
within it will be rarefied. The rarefaction, acting
through the indiarubber tubing, will cause the
membrane of the second tambour to be depressed,
and this movement the lever will indicate by a down-
ward stroke. Thus with a system of two tambours a
downward movement of the membrane of one causes
an upward movement of the lever of the other, and
vice versa. If, however, it is desired to give the same
direction to both, it is only necessary to turn one
tambour upside down. Thus, not only may move-
ments be transmitted from a distance, but the move-
ment may be recorded in any direction at will, for the
tambour which writes the movement may be placed
so as to write on a horizontal cylinder, or may be
turned so as to write on a vertical cylinder. Thus a
horizontal may be converted into a vertical movement,
or vice versa, and otherwise.

The tambour which receives the movement is
called the receiving or transmitting tambour, and that
which writes as the registering or recording tambour.
The registering tambour will retain in all cases the
form described, being supported on a horizontal or
vertical arm, as may be wished, and its lever point
brought against the blackened moving surface. The
tambour, however, which receives the impulses to be
transmitted, is modified to suit the circumstances of
each case. Thus, Marey has adapted the instrument
for the purpose of obtaining a note of the contacts of
each foot with the ground in running. A shoe has in
its sole one tambour in the form of an air-chamber,
the air of which is compressed by the pressure of the

Chap, xviii.] THE PANTOGRAPH. 187

foot on the ground. It communicates with a recording
tambour of the usual form projecting on to the surface
of a revolving cylinder which the man carries in his
hand. The contacts of each foot are recorded side
by side on the same cylinder from a tambour in the
sole of each shoe. The man has also on his head a
tambour which transmits the vertical oscillation of his
body. Similarly Marey has adapted the apparatus for
recording the movements of a bird's wing in flight.
Modified forms of the apparatus have also been made
for registering the movements of the heart, of the
pulse, of the breathing. It is easy to understand also
how, by means of a series of tambours, disposed at in-
tervals along the course of an elastic pipe, informa-
tion may be obtained of the propagation of a wave
through the fluid which fills the pipe, and of the
differences in the characters of the wave when the pipe
ends in a wide or in a constricted opening, or when
the opening is entirely blocked. The apparatus may
also be adapted to the frog-plate of Marey, and the
muscle of the frog attached by its tendon to the short
lever of a receiving tambour, the registering one being
some distance away. An ingenious combination of
two tambours has been made by Marey for the
purpose of combining two movements in one tracing.
The arrangement is called the PANTOGRAPH. The two
tambours are placed at right angles to one another,
and their levers, jointed in a way to permit it, join
one common lever whose point is in contact with the
blackened surface on which the tracing is made.
Two such groups with their communicating tubes
form the pantograph. The lever of one group may be
made to pass over a series of curves, or to describe
circles, and so on, and the movement will be faith-
fully reproduced by the lever of the other group. By
means of this arrangement any figure may be repro-
duced, in its natural size, enlarged or reduced.

1 88

HE.

FLUIDS AT EEST AND IN MOTION: THE
MECHANICS OF THE CIRCULATION.

CHAPTER XIX.

HYDROSTATICS.

THE department of physics which has regard to
the laws of force as applied to fluids is termed HYDRO-
DYNAMICS. This has two subdivisions, one of which
considers the laws applicable to fluids at rest and is
termed HYDROSTATICS, the other considers fluids in
motion and is termed HYDRO-KINETICS.

A liquid is a body whose molecules attract one
another so feebly that a slight force suffices to displace
them relatively, to one another. Their cohesion, that is
to say, is slight Gases are also fluid, but differ from
liquids in this, that however the molecules of a liquid
be displaced relatively to one another, the distance
between the various molecules is always the same,
consequently the liquid does not expand, and main-
tains, as a rule, a constant volume, while the mole-
cules of gas vary in their distance from one another.
Gas is, therefore, expansible, and alters its volume
with every alteration of pressure. A liquid, therefore,
owing to the easy displacement of its molecules, alters
its form to suit any vessel in which it may be con-
tained. Experiments have shown that liquids are
almost, but not quite, incompressible. On removing
the pressure, however, a liquid returns to its original
volume and is thus perfectly elastic. The instrument

Chap, xix.] PASCAL'S LAW. 189

by which the compressibility is measured is called a
piezometer.

Transmission of pressure by liquids. —

Pascal's law.

The law or principle, first enunciated by Pascal, is,
that in a liquid, pressure exerted upon any point of its
mass is transmitted equally in all directions ; and the
pressure is at all times perpendicular to the surface
on which it is exercised. Thus, suppose a mass of
liquid, pressed upon by a piston at A (Fig. 92). Suppose,
also, in the interior of the mass of liquid a
molecule M, one of the infinite number of
molecules of which, it may be conceived,
the liquid consists ; then if the molecule
M retains its equilibrium when pressure
is exerted at A, it must be because
the tendency of M to move is resisted in Fig. 92.—

T ,- -i .1 -i Transmission

every direction by the pressure exerted Of Pressure,
upon it by the surrounding molecules. The
piston presses upon the molecules of the mass of liquid
in immediate contact with it; these, in turn, press
upon the neighbouring molecules, and thus the pres-
sure is transmitted to the walls of the vessel, which
re-act upon the molecules with a force equal to their
own. Thus the pressure exerted at A is transmitted
equally in all directions throughout the fluid, and
each molecule of the fluid is equally pressed in all
directions.

An important application of this principle is illus-
trated in Fig. 93. A closed vessel of water ABCD has,
in its upper wall, an opening pq, in which is fitted a
piston P. A piston of the same size p' is fitted on one
side, and one of double the size p" on the other side. If
a force be exerted at p, by the law already announced
it is transmitted equally in all directions, and will,
consequently, act with undiminished strength upon p'
and P". If, therefore, P be pushed in with a given

190

PHYSIOLOGICAL PHYSICS. [Chap. xix.

in Relation to Ex-
tent of Surface.

force, the force will act upon p' and p" to push them
out. The area of P' (p'q) being the same as that of p,

the force exerted upon it will be
the same in amount as that acting
on P, but ab being twice the area
of P, the force acting on p" will
be doubled. Thus the amount of
the force exerted upon any surface
in a liquid under pressure is
proportional to its extent.

The hydraulic press, made
by Bramah in 1796, embodies these
principles. Two cylinders of different diameter com-
municate by means of a transverse tube. In each
cylinder is fitted a piston. Suppose the large cylin-
der to be twenty times the diameter of the small,
then a weight of 1 pound on the small piston will
require a weight of 20 pounds on the large piston
to maintain equilibrium ; and if less than twenty
pounds be placed on the large piston it will be moved
upwards. Thus a small weight at one side of the
arrangement is capable of lifting a large weight at the
other. It is easily seen, however, that what is gained
by this arrangement in amount of force is lost in
extent of movement, for if the small piston be moved
downward for a distance of one foot the large piston
will be moved upward only the —^ of a foot. The
Bramah press consists of a small pump which forces
water through a pipe into a large cylinder in which is
fitted a large piston. The water forces up the piston,
which carries a cast-iron plate. Goods may be laid
on this plate, and by the upward movement of the
piston they are pressed against a second plate fixed
above. If the large piston be fifty or a hundred
times the cross section of that of the pump, then the
force of the small piston is increased fifty or a hundred
times, and is further multiplied by the pump being

Chap. xix.] HYDROSTATIC PARADOX. 191

worked by a lever. Of course the upward movement
of the press is correspondingly slow.

It arises further from the principle of Pascal
that the pressure exerted on the bottom of a vessel
depends upon the extent of surface of the bottom of
the vessel, and the height of the liquid column which
it supports. Thus, let AB'C' (Fig. 94) be a glass
vessel with the tube-shaped portion
AA', and let it be filled with some
liquid. Consider the area be of the
bottom of the vessel. It is manifest
that it sustains not only the pressure
of the column of liquid A'6c, but of
the column AA' as well, so that its
pressure is conditioned by its area Fig. 94. —

7 ,i i • 1 , r? ,1 i drostatic Para-

6c, and the height ot the column

of liquid it supports, viz. Ac. But
by Pascal's law, the column AA' transmits its
pressure equally in all directions, and not only,
therefore, on the small section of the bottom
be, but on the whole bottom B'C'. So that every
portion of the surface B'C' of area equal to be bears
not only the pressure of the liquid column up to the
level of A', but also the pressure of the column
AA'. Thus the pressure on the bottom B'C' is equal
to the pressure of a column of liquid whose base is
equal to B'C', and whose height is equal to AC ; and so
the pressure on B'C' is as great as it would be if the
vessel had had the shape BB'C'C, the shape indicated
by the dotted lines. Thus the pressure on the bottom
of a vessel is independent of the shape of the vessel,
but is determined by the area of the bottom, and the
height of the column of liquid it supports.

This must not be misunderstood. If two vessels,
one represented by BB'C'C (Fig. 94), and the other repre-
sented by AB'C', were filled with water, the pressure
on the bottom of each would be the same ; but if they

1 92 PHYSIOLOGICAL PHYSICS. [Chap. xix.

were compared in the scales of a balance, the weights,
that is, the pressure communicated to the scale, would
be different, the former being heavier than the other
by the amount of fluid enclosed by the walls of the
vessel represented by the dotted lines. This is called
the HYDROSTATIC PARADOX. It is to be noted that
the pressure communicated to the pan of the balance
is not merely the pressure on the bottom of the
vessel, but is the resultant pressure, for the whole
vessel. Thus in the vessel AB'C' there is exerted
on the upper surface of the wide portion of the
vessel, outside of AD, an upward pressure every-
where equal to the height of the column AA'.
This iipward pressure is equal to the downward
pressure that would be exerted by the additional
quantity of liquid contained if the vessel were of the
shape BB'CC'. Therefore the pressure transmitted
to the scale by a vessel of the latter shape would
exceed that of a vessel shaped like AB'C' by the amount
of this downward pressure, which a vesssl shaped like
AB'C' transmits upwards.

In estimating the pressure on a given surface on
the side of a vessel, the centre of gravity of the given
portion of the surface is obtained, and the height of
the column of liquid is taken from this point.

The upward pressure spoken of is also in ac-
cordance with, and, indeed, offers another proof of,
Pascal's law. It is illustrated by a very simple
experiment. A glass vessel is nearly filled with
water. A glass cylinder, open at both ends, is taken,
and a disc of cardboard is cut of sufficient size just
to close one end. A thread is attached to the middle
of the cardboard, by means of which the disc is held
in position against one end of the tube. This end is
now immersed in the vessel of water, and the up-
ward pressure of the water retains the disc in position
without further use of the thread. Push the cylinder

Chap, xix.] EQUILIBRIUM OF LIQUIDS.

193

well down into the water, and, holding it vertically,
proceed to pour water into it. The disc will continue
to close the end of the cylinder against the downward
pressure of the water being poured into it, until the
water inside the cylinder reaches the same level as
the water outside, and then the disc sinks away. This
shows that the disc wTas retained in position by an
upward pressure yielded by a column of water whose
base Avas the area of the disc, and whose height was
the distance between the disc and the level of the
fluid outside of the cylinder.

i/

Equilibrium of liquids in communica-
ting' vessels. — A further deduction from Pascal's
principle declares that where a series of vessels, com-
municating with one another, are filled with the same
liquid, equilibrium can only exist if the liquid stands
at the same height in each vessel, that is, if the free
surface of the liquid in each vessel is in the same hori-
zontal plane. This is readily understood from what
has been already said. Let c and
B (Fig. 95) be two vessels com-
municating with one another by the
tube A. ISTow, in order that the mole-
cules of the fluid in the tube A may
be at rest, they must be submitted
to the same force from the directions
B and c. If the force from the end
C, for example, predominates, the
fluid in A would move towards B.
In order that the pressure may be
the same at each end, the height of the
column of liquid at each end must be the same. In
the same way any number of vessels might be com-
municated with B and c, of any diameter and shape,
equilibrium is only established when the level of the
fluid is the same in each. If the equilibrium be
overthrown, for instance, by the addition of more
N— 7

u.

£

— _

|

—

—

=

j:

•

Fig. 95. — Equili
brium of Liquids
in communicating
Vessels.

194 PHYSIOLOGICAL PHYSICS. [Chap. xix.

fluid to one vessel, then a movement will take place
through the communicating tube for the re-establish-
ment of equilibrium.

The rule that the free surfaces must be in the same
horizontal line only applies when it is the same
liquid that fills all the communicating vessels. If
liquids of different densities are poured into the
vessels, then, provided they do not mix, the heights
of the different fluids above the surface of contact
will be in the reverse ratio of their densities. Increased
density means increased pressure, and consequently a
column of the denser liquid of less size will exert the
same pressure as a higher column of the less dense
liquid. This gives a means of calculating the density
of a liquid. The height of one liquid multiplied into
its density will be equal to the height of the other
liquid multiplied into its density. Let h stand for
the height in inches of the column of one liquid, and
h' the height in inches of the other, and let d and d'
represent the two densities ; then

v -t i I T/ ^ fv J\ €v

h x d = h x d or d = — •

h

In the circulation of the blood the sig-
nificance of the principle of the last paragraph has
been pointed out. The system of blood-vessels in an
animal is a system of communicating vessels con-
taining a single fluid. The tendency is, therefore,
for that fluid so to distribute itself throughout the
vessels as to bring about a condition of equilibrium.
But opposed to this equalising tendency is the inter-
mittent action of the heart, which disturbs the equi-
librium at one end of the series of vessels, as it were.
To meet this disturbance, a flow takes place again in
the direction of restoration, and so on. As a result
of this constant effort after equilibrium, and periodic

chap, xix.] PRINCIPLE OF ARCHIMEDES. 195

disturbance of it, a continuous flow takes place from
one end to the other of the series of vessels.

-The principle of Archimedes. - - When a
solid body is immersed in a liquid, in accordance with
Pascal's law the liquid exerts pressure upon it in all
directions, and the pressure at each point of its sur-
face will be equal to the column of liquid above the
point. Thus, the body ABCD (Fig. 96) plunged in
the liquid is pressed on every side. Sup-
pose it to be a cube, then it is evident
that the pressures on the four sides of
the cube being directed perpendicularly

to the surfaces, equalise one another, Fig. 96. — The
and all that is left for consideration 23BSL?
is the pressure on the upper surface
AB, which is directed downwards, and the pressure
on the under surface CD, which is directed upwards.
The downward pressure is equal to a column of the
liquid whose base is AB and whose height is AN, the
upward pressure is a column whose base is CD and
whose height is ex. These two partly destroy one
another. The column ABXN is common to both, and
its downward pressure is, therefore, counterbalanced
by its upward pressure. There remains, then, only
the difference between the two, an upward pressure
equal to a column of water whose base is CD and
whose height is CA ; in other words, a column of
water represented by the cube. The body is therefore
pressed upward by a force exerted by a column of the
liquid equal to the bulk of fluid which it displaces.
The weight of the body tends to make it sink, and
to this downward tendency is opposed an upward
one represented by the quantity of fluid displaced.
Thus every body plunged into a liquid loses weight
equal to that of the displaced liquid. Suppose the
weight of the displaced liquid is just equal to
the weight of the body, then the body will float in

196 PHYSIOLOGICAL PHYSICS. [Chap. xix.

a position of equilibrium ; if the weight of the dis-
placed liquid is less than that of the body, the latter
will sink, the downward exceeding the upward pres-
sure; if the displaced liquid exceed the body in weight,
then the body will be forced upwards partly out of
the water, till the quantity of displaced water is
reduced to equal the weight of the body.

Centre of gravity and inetaceiitre — A
floating body is thus under the action of two forces ;
one, the force of gravity acting through the centre of
gravity urging the body downwards ; the other, the
force of the displaced water acting through what
would be its centre of gravity, called the centre of
buoyancy, urging the body upwards; and these two
forces are equal. When the body floats in stable
equilibrium the two forces are opposed, that is, the two
centres are in the same vertical line. If the floating
body, being of irregular form, move to one side, the
amount of the liquid displaced by it will be different,
and consequently the centre of buoyancy will be
different. If, now, a vertical line be drawn through this
new centre 6f buoyancy and be continued to meet what
was, before the new position, the vertical through the
centre of gravity, the point of intersection marks what
is called the METACENTRE. The position of this is of
great moment, for when the rnetacentre is above the
centre of gravity, the upward force of buoyancy and
the downward force of gravity act in a way to restore
the equilibrium of the body. When the metacentre
is below the centre of gravity, the tendency is to in-
crease the displacement. The former is a condition of
stable and the latter of unstable equilibrium.

Fishes are capable of moving towards the surface
or the deep parts of water by their means of regulating
the quantity of water they displace, that is, the force
that urges them upwards. By a distension of their
air-bags the volume of their bodies is increased, the

Chap, xix.] METACENTRE. 197

weight remaining the same. The upward force is,

O O *

therefore, augmented, the downward being unaffected.
So they rise. By muscular compression of the air-sac
the volume of the body is diminished, and they sink.
Thus, if a fish in a jnr of water be placed under the
bell of an air pump, and the air exhausted, the fish
will come to the surface ; rupture of the air-sac will
occur, and on removing the jar the animal will sink to
the bottom, and be unable to float. It will also be
unable to keep itself in a proper position, the tendency
being for it .to turn on its back. This, it is said, is
due to the fact that the equilibrium of fishes is un-
stable, the centre of gravity being above the centre of
buoyancy, the condition of instability for completely
immersed bodies. In animals that swim on the
surface of the water the conditions of instability are
also present, the stable condition being maintained by
muscular effort. Swimming on the back for them is,
however, a condition of stable equilibrium, for then
the centre of gravity is below the centre of buoyancy.
Specific gravity. — The density, or relative mass,
of a body is obtained by comparing the weight of that
body with the weight of the same volume of a given
body used as a standard. The standard adopted is
that of water at its maximum density, viz. at a
temperature of 4° C. If, then, the weight of a
body is obtained, and is compared with the weight of
the same volume of water at a temperature of 4° C.,
the specific gravity of the body is obtained. A method
for determining this, accordingly, is to take the body
and weigh it. Let its weight be represented by 10.
Place the body in the pan of a balance, and in the same
pan place a flask with a wide neck, to which is care-
fully fitted a ground-glass stopper. The stopper has a
fine tube in connection with it, the bore of the tube
being continued through the axis of the stopper. Let
the flask be accurately filled with water up to a mark

198 PHYSIOLOGICAL PHYSICS. [Chap. xix.

on the tube. In the other pan of the balance counter-
poise with weights the flask with water a,nd the body.
Then remove the flask and place the body inside of it.
It will displace from the flask a quantity of water
equal to its own volume. Carefully dry the flask, see
that the water is at the same level as before, and
weigh it again. This time the weights in the opposite
pan . will be too much, because a certain amount of
water has been displaced. The diminution in weight,
consequently, will indicate the weight of water dis-
placed by the body, that is, the weight of a mass of
water whose volume is equal to the volume of the
body. Let this diminution be represented by 2-5. The
original weight of the body was 10, the weight of a

quantity of water of equal volume is 2-5, then 9> =

4 — the specific gravity of the body.

Similarly the specific gravity of a liquid could be
obtained. This requires a flask, the upper part of
which is drawn out into a fine tube. The flask is
placed in a balance and counterpoised. It is then
filled with water up to a mark on the fine tube. The
additional weights required give the weight of the
water. The water is then removed and the liquid
placed in the flask up to the same mark, and the weights
it requires determined. Thus, the weights of equal
volumes of water and of the liquid are obtained, and the
latter divided by the former gives the specific gravity.

The principle of Archimedes indicates other methods
for readily determining the specific gravity.

The hydrostatic Imlawce is one of these
methods. Any ordinary balance will suit the
purpose. Let it be raised on a stand, and suspend
by a thread, or fine wire, from 0118 of the pans the
body whose sp. gr. is to be measured. Counter-
poise with weights in the other pan, and so find
the weight of the body in air. Then, under the pan

chap, xix.j SPECIFIC GRAVITY. 199

to which the body is suspended, place a vessel with
water, and allow the body to hang in the water. The
body will displace its own volume of water, and will
be pressed upwards by the weight of that amount of
water. The body will, therefore, lose weight to this
extent. By the balance the weight of the body in
water is now estimated, and it will be equal to the
weight of the body in air, less the weight of a quantity
of water equal to its own volume. Thus, we have the
weight of the body in air, and we have the weight of
an equal volume of water, the loss of weight, namely,
experienced by the body, and the relation of these two
gives the specific gravity. Thus :

Weight in air

. , , . — . , . . = specific gravity :

weight in air — weight in water

{— weight of equal volume
of water)

or, to put it in symbols,

^ = sp- gr*

This method, it is observed, is applicable only to solid
bodies not soluble in water.

It is worthy of remark that if French weights
are employed (grammes) the process that has been
performed indicates not only the specific gravity of the
body, but also its volume. Since one cubic centi-
metre of water, at standard temperature, weighs one
gramme, if the solid body weighed in water is found
to displace ten grammes of water, that means its
volume is equal to ten cubic centimetres.

Precisely the same method is applicable to liquids.
From the pan of a balance is suspended a solid body,
not attacked by water or the liquid to be examined,
and its weight is accurately counterbalanced. The
body is now allowed to hang in water, and it being
pressed upward by the volume of water it displaces,

200 PHYSIOLOGICAL PHYSICS. [Chap. xix.

the balance is disturbed. Restore it accurately by
weights placed in the pan to which the body is sus-
pended ; these weights represent the weight of the
displaced volume of water. Let the weight be repre-
sented by 2. Plunge, next, the same solid body in the
liquid to be examined ; find, as before, what weights
are required to restore the balance ; this gives the
weight of the same volume of the displaced liquid as of
the water, and let it be represented by 3. Thus the

weights of the two equal volumes of water and of the

g

other liquid can be immediately compared : - = 1 '5.

£

It is to be observed that the general principle of
these methods is the comparison of the weight of the
body with the weight of an equal volume of water.
Special adaptations must be made when the body
is soluble in water. A very simple method, for which
only one weighing is required, has been recently
devised by Dr. J. J. Dobbie and Mr. Hutcheson,
of the Chemical Laboratory, Glasgow University. A
tube is taken of a bore similar to that of an ordinary
burette. At its lower end is united a tube of fine
bore, the two forming a U tube. In the middle of
the wide tube a zero mark is placed, and the fine
tube is marked off into cubic centimetres. Let water
be placed in the tubes up to the level of the zero line.
Then drop in the solid body whose sp. gr. is to
be determined, its weight in air in grammes having
previously been determined. It will displace some
water, which will rise above the zero line. The top
of the wide tube is now closed with an accurately
fitting indiarubber cork, connected with a stop-cock.
The cock is opened, and by blowing through it the
level of the liquid in the wide tube is depressed below
the zero line. The level is now permitted to rise
till it is exactly at the zero line, and the stop-cock
is closed. In the narrow tube there is now read off

Chap. XIX.]

HYDROMETERS.

201

the volume of water in c.c. displaced by the solid
body. But each c.c. =1 gramme, and, therefore, one
obtains at once the weight of water displaced equal
to the volume of the solid body, and the sp. gr.
of the body is at once ascertained by dividing its
weight in air by the weight of the displaced volume
of liquid. If the body is soluble in water, take some
liquid in which it is not soluble, and put this liquid
into the tube. Then proceed as before. The volume
of the displaced liquid is the same as that of water
would be. Therefore, the number of c.c. displaced
gives at once the weight in grammes of a volume of
water equal to the volume of the solid body, and the
calculation may be completed at once. The method
is applicable to any solid, if only
the tubes be filled with a liquid
in which the body is insoluble.

Hydrometers, or areo-
meters, are instruments designed
for readily indicating the specific
gravity of a body. Nicholson's
hydrometer is shown in Fig. 97.

It consists of a hollow metallic
cylinder AB, which is made to float

•/

by the weight of an attached cone

EF. The cylinder carries at its

upper end a thin stem which bears

a metallic disc CD. The instrument

is immersed in water, and weights

are placed on the disc sufficient to

bring the hydrometer down in the

water to the level of a mark o on

the stem. The body whose specific

gravity is to be determined is now placed on the disc.

Its weight brings the hydrometer lower in the water ;

weights are, therefore, taken off till the instrument is

at its former level. The weights removed give the

Fig, 97. — Nicholson's
Hydrometer.

202 PHYSIOLOGICAL PHYSICS. [Chap. xix.

weight of the body in air. The solid body is then
transferred to the lower cone of the instrument, whose
upper surface is flat for this purpose. The water is
no longer at the mark on the stem, since the instru-
ment is lighter by an amount represented by the
water displaced by the body. The weights put
on to bring the hydrometer to the level of the mark
give the weight of the displaced water whose
volume is equal to that of the solid body. The
weight of the body in air divided by the weight
of the displaced water is the specific gravity of
the body. For measuring the specific gravity of
liquids Nicholson's hydrometer may be used in a way
similar to the hydrostatic balance. Thus the hydro-
meter is immersed in water and loaded till brought
down to the mark on the stem. The weight of the
instrument and the weights which it carries in the
pan are equal to the weight of the volume of water
it displaces. Immerse it now in the liquid to be
examined, and load it again till it is down in the
liquid to the proper level. Again the weight of the
instrument and the weights in the pan a,re equal to the
weight of the volume of liquid it displaced. In both
cases the volumes are the same ; therefore, the latter
result divided by the former gives the specific gravity.
In other words, the weight of the instrument being in
both cases the same, the amount of weight in the pan
011 the second trial, divided by the amount on the
first, is the required specific gravity. The estimation
of the specific gravity of liquids in this way is
better performed by the HYDROMETER OF FAHRENHEIT,
which is made of glass so as not to be attacked by
the liquids in which it is immersed. It is of similar
shape to Nicholson's, the hollow cylinder being formed
of glass blown out to the proper shape and size, and
being continuous below with a small bulb containing
mercury, for maintaining the vertical position. No

Chap, xix.] SALJMETER. 203

lower surface for carrying bodies is needed here.
The stem, rising from the blown-out part, carries a
plate for weights, as in Nicholson's hydrometer.

These hydrometers are of constant volume, but of
variable it-eight, because they are always immersed to
the same depth, and displace always the same volume
of liquid, the weights being altered to accomplish this.
Another type of hydrometer is the reverse of these, of
constant weight, but variable volume, where the instru-
ment is always loaded to the same extent, and the
specific gravity of different fluids is indicated by the
depth to which the instrument sinks. If a hydrometer
of this kind is put into water it sinks to a mark
on the stem. It must sink to the indicated extent
before it displaces sufficient water to give an upward
pressure equal to the weight of the instrument.
If it is now put into a fluid of less specific gravity
it will sink farther, because the same volume of this
fluid does not create sufficient upward pressure, and a
greater volume is required. If put, on the other
hand, into a fluid of greater density, the same volume
of this fluid gives rise to a greater upward pressure
than the weight of the hydrometer ; consequently
the instrument rises for some distance
higher out of the water than the mark,
because a diminished volume gives the
required upward force. Such an instru-
ment is shown in Fig. 98. It is made
of a glass tube, one part being blown
out, and terminated by a small bulb
containing mercury. On immersing it
in a liquid it floats upright, having sunk
to a distance that can be read off by FigiJf-t7rSali"
means of the marks on the stem, the
distance varying -with the density of the liquid.
The graduation of the instrument must be performed
empirically, however. Thus, let such an instrument

204 PHYSIOLOGICAL PHYSICS. [Chap. xix.

be so loaded that when immersed in distilled water
it sinks to the level of a mark placed near the
extremity of the stem. Call this zero. Then let
a solution be made of 15 parts of salt in 85 parts
of water, both by weight, and immerse the instru-
ment in the solution. Mark 15 at the level to which
it sinks. Provided now that the stem is quite
regular, the space between zero and 15 may bo
divided into equal parts, and this regular marking
may be continued down the stem, say to 100. Each
subdivision ought to represent an equal volume. To
the instrument so made the name SALIMETER is
applied, because it will give the density of any saline
fluid in relation to that of distilled water. For fluids
lighter than water the hydrometer is so loaded that in
distilled water the surface of the water is only up to
a level with the bottom of the stem, which is marked
0. Thus in GAY-LUSSAC'S CENTESIMAL ALCOHOLI-
METER, zero is at the bottom of the stem, the level of
distilled water. In pure alcohol the alcoholimeter
sinks to the top of the stem, which is marked 100.
Other marks down the stem indicate the level of
liquid containing different percentages of alcohol and
water, the levels having been determined by experi-
ment with each instrument.

The densimeter of Rousseau is of great value
in scientific work, affording as it does a means of
estimating the density of a fluid of which only a small
quantity may be available. It is shown in Fig. 99.
The stem A is divided off bv marks into intervals,

v f

which correspond to equal volumes ; e.g. i^th of a
cubic centimetre. The stem carries a little tube c,
into which is placed one cubic centimetre of the fluid
to be measured. The method is as follows :

The densimeter is placed in distilled water at four
degrees centigrade, and into the tube c is placed one
cubic centimetre of distilled water. This makes it

Chap. XIX,]

DENSIMETER OF ROUSSEAU.

20;

FlsfmeterDeof

float at zero on the scale. The water is now removed
from the tube, and in its place is poured one cubic
centimetre of the liquid whose density is to be
determined. The one cubic centimetre is
measured in both cases by means of a ps

little pipette P, the markings (1 — 0) on
whose stem indicate the volume of one cubic
centimetre. The fluid, being denser than
water, will sink the densimeter. Let the
reading be taken. Suppose it be fifteen ;
that is, it displaces J^^-ths of a cubic
centimetre of water more than the distilled
water, which is taken as unity. As each
cubic centimetre equals one gramme, this
means that the liquid is T^jths heavier
than the water, which equals 1 ; that is, its
density is 1'15.

In practical medicine densimeters are in
constant employment. Thus one densimeter is con-
structed for urine, and is called a URINOMETER, and
another for milk, which is termed a LACTOMETER. The
urinometer sinks in distilled water to the top of the
stem, which is marked 1,000, and at corresponding in-
tervals down the stem are marked 1,005, 1,010, 1,015,
1,020, and so on. The specific gravity of urine is on
an average 1 '025, and, therefore, in urine the urinometer
should stand at the level 1,025. ISTow the value of the
determination of the specific gravity is not so much
in obtaining the absolute amount, as in being able to
observe variations in it, and relating these variations to
the causes which produce them. Thus, suppose an
average specimen of urine indicated a specific gravity
of 1'036, this indicates a less proportion of water,
which might be due to concentration of the urine or
to increased secretion of solid matters. In diabetes
the sugar secreted at once raises the specific gravity.
Consequently with a high specific gravity one would

206 PHYSIOLOGICAL PHYSICS. [Chap. xix.

at once test to find whether this was the cause of the
variation. Again, albuminous urine is usually of ab-
normally low specific gravity, and in consequence a
urine of specific gravity of, e.g., 1*014, indicates the
necessity of testing for this abnormal constituent.
The variations, then, of the density of such a fluid
as the urine give important indications to the medical
practitioner. It may be noted that a solitary specimen
of urine ought not to be examined for its specific
gravity, as the density will vary according to the con-
ditions of the individual who passes it. The urine
passed during twenty-four hours ought to be collected,
mixed, and the specific gravity of this taken.

The lactometer, or lactodensimeter, is gra-
duated for specific gravities varying from 1'04"2 to
1-014.

Tho specific gravity of Imman milk is 1-0203

cow's ,, 1-0324
ass's 1-0355

„ „ cow's ,, 1-0324

The subjoined tables afford a means of approxi-
mately estimating the quality of cow's milk. The
specimen of milk taken should be well shaken so as
mix the cream thoroughly, and air bubbles should be
removed. Then

A specific gravity of 1-033 to

T029 indicates pure milk.

»>

1-029 „

1-026

10

per cent, of

5)

1-026 „.

1-023

20

added water

It

1-023 „

1-020

30

» >»

5>

1-020 „

1-017

» 40

)> >>

)>

1-017 ,

1-014

50

?» >5

If the cream has been previously removed the specific
gravity of pure milk ought to be 1*037 to 1-033.

A specific gravity of 1'033 to 1'029 indicates 10
per cent, added water, and every -003 below this an
additional 10 per cent, water.

chap, xx.] HYDRODYNAMICS. 207

The specific gravity of human blood is 1-055

,, ,, blood serum ,, 1-027

„ „ saliva „ T006

bile „ 1-026

„ „ the aqueous

humour of the

eye ,, 1'005

„ „ gastric juice „ 1-005

,, ,, muscle „ 1-060

„ „ tendon f, I1 125

nerve „ 1-040

brain „ 1-030

bone „ 1-975

brain „ 1-030

CHAPTER XX.

HYDRODYNAMICS — FLUIDS IX MOTION.

Principle 'of Torricelli. — Suppose a liquid
flowing freely through an opening in the thin wall of
a reservoir, by the principle announced by Torricelli,
the rate at which the fluid discharges itself is equal to
the velocity which would be acquired by a body falling
freely through a height equal to the distance between
the orifice and the surface of tJie liquid. The law for
falling bodies is, that a body falling freely from a
position of rest through a certain distance acquires a
velocity, determined by the distance it has travelled,
the accelerating action of gravity being taken into

account. The precise formula is v = \/2gh, where v
the velocity is equal to the square root of the accelera-
tion due to gravity x 2 X the distance fallen. Liquid
in a reservoir may be considered then as consisting of
a large number of molecules, and the speed with which
the molecules pass through an opening in the bottom
is the same as they would acquire if they fell from the
surface of the liquid straight down through the opening.

208 PHYSIOLOGICAL PHYSK.S. [Chap. xx.

The same law applies to an opening made in the
side of the vessel, but in this case the distance through
which the molecules fall is to be counted as the heighi
of the column of liquid from the centre of the
opening to the surface of the liquid. The fact that
the opening is in the side does not affect the result,
seeing that the pressure is transmitted equally in all
directions. Thus from an opening in the side of a
vessel the liquid molecules are projected with a velocity
determined by the height of the liquid column above
the level of the opening. The liquid so projected does
not pass horizontally outwards, but describes a para-
bolic curve, due to the downward force exerted upon
it by the action of gravity.

It is to be observed that, according to this principle,
the velocity of efflux is independent of the nature of
the fluid.

Experiment proves the law regarding the velocity
of efflux, but not immediately. For were the rule
rigidly true, the quantity of liquid that escapes in a
unit of time ought to be equal to the velocity of efflux
X the area of the orifice. * But experiment shows the
quantity of efflux to be only about '6 of this amount.
The reason of this, however, is speedily apparent. On
observing a now of water from a small orifice in the
bottom of a reservoir, the stream of water is found to
have the shape represented in the diagram (Fig. 100).
Immediately on leaving the orifice the stream begins to
contract, and at last reaches a maximum of contraction
at a distance from the orifice nearly equal to its dia-
meter. After that the liquid begins to divide into
diverging streams, and the streams into drops, owing to
the feeble cohesion between the molecules which form
the liquid permitting easy separation from one another.

* The velocity, we have seen, is J%gh ; the area of the orifice is
the square of its radius x 3 '14159 ; expressed thus, -nr2 (* =
3 14159).

chap, xx.) VENA CONTRACTA. 209

The phenomenon of contraction is called the VENA
CONTRACTA, and its cause is represented in the diagram.
The molecules vertically above the centre of the
orifice stream straight clown and pass
out by the orifice, but the molecules

at the side follow a curved course in — — v;i;-v-

the endeavour to get into the stream.
The direction of their motion can be
decomposed into the two elements,
one horizontal and the other vertical.
The horizontal components of op-
posite sides oppose one another. It
is thus evident that the molecules Fig. 100. — Vena
not in line with the vertical of the
orifice oppose one another, and that they do this the
more, the farther they are removed from the vertical.
In consequence, the escape of fluid is opposed, and the
vena contracta formed. Owing to this delay, then,
the quantity of efflux does not reach the theoretical
amount. If, however, the diameter of the contracted
portion be taken as the diameter of the orifice, the
results are in harmony with the theory. The diameter
of the vena contracta ab is usually about two-thirds
that of the orifice.

The normal quantity of efflux may be restored,
and the influence of the vena contracta counteracted,
by fitting a small tube to the orifice. If the tube
have a diameter equal to the orifice, and a length
two: or three times its diameter, the quantity dis-
charged in a limit of time is considerably increased.
The vena contracta is still formed, but the fluid,
expanding beyond it, reaches a greater diameter than
that of the jet, owing to the attraction exerted on the
fluid by the inner surface of the tube.

Marriotte's bottle. --It is apparent, in the
case of a reservoir, that if the velocity of out-
flow is to remain uniform, the original level of the
o — 7

210 PHYSIOLOGICAL PHYSICS. [Chap. xx.

fluid must be maintained, for instance, by a quantity
of water flowing in above constantly equal to the
quantity flowing out below. If, on the other hand,
the supply be not maintained, and the level be allowed
to fall, the outflow will at once diminish pari passu.
By the arrangement known as Marriotte's bottle,
however, a uniform outflow is maintained without
the need of maintaining the lowel of the fluid in the
bottle. Fig. 101 represents such a bottle. In
one side at the lower part is an exit
tube. The mouth is closed with a cork
pierced by a tube, both tightly fitted.
The tube dips down a considerable
way into the fluid. If the bottle and
the tube be full of water, the surface
of the water in the bottle will bear a
pressure equal to the atmospheric pres-
sure and the weight of the column of

Fig. 101. —Mar- ,, , , ,,

riotte's Bottle, water standing m the tube above the
surface of the water in the bottle. If,
now, b be opened, and the water be allowed to flow
out till it stands at the same level in bottle and tube,
then the water in the bottle will be at atmospheric
pressure. At 5, accordingly, the water is pressed out-
wards by a force equal to that of the atmosphere +
the weight of the liquid column, whose height
is from b to the surface, and whose base is re-
presented by the dotted line at b ; the water is
also being pressed inwards by atmospheric pressure ;
the pressure outwards being the greater, the water
flows out. But, if the water be allowed to flow out
till all of it has passed down out of the tube a, and air
bubbles have begun to rise up from the tube a through
the water to the upper part of the bottle, then, a pressure
equal to that of a column of water whose height is
the distance from the lower part of the tube a to
the surface of the liquid has been removed from

chap. xx. j FLOW OF LIQUIDS THROUGH TUBES. 211

the surface of the water in the bottle. The pressure
outwards at b is, accordingly, the atmospheric pres-
sure — the pressure of a liquid column from a to the
surface -f the pressure of a liquid column from b to
the surface. The liquid column from b to the
surface is made up of the column from a to the sur-
face, and the column from b to a. The — and -j- of
the column from a to the surface, therefore, eliminate
this factor, and the result is that the pressure at
b is the atmospheric pressure + that of the liquid
column between 6 and a. This is constant so long
as the level of the fluid is above a, and, therefore,
for a considerable time the outflow is of constant
quantity. This arrangement of Marriotte's will be
found adapted to the frog-heart apparatus described
on page 236.

Flow of liquids through imiform tubes.
— The law of Torricelli is not applicable to the flow of
fluids through tubes. Into this, elements of friction
and resistance enter 1 2 ,

which alter the results.

Let A (Fig. 102) be
a reservoir filled with
water, and let the hori-
zontal tube ab be in
communication with it
an opening o

the lower part of
one side, the velocity

of efflux at the end b does not obey Torricelli's
law. The reason is apparent. The water in its
course through the horizontal tube experiences re-
sistance by its friction against the walls. The fluid
tends to adhere to the walls of the tube, the mole-
cules of the fluid, that is, that are in immediate con-
tact with the walls. Their rate of flow is thereby re-
tarded, and the molecules streaming along the centre

through
at

11^

3^>H?t

*-*.

.

%*^

"»^

^A~-9

PC

y

*^

„

b^=§

r

Pa

f

^^

.,

:-Sg

^

\

P's

7

^Jj

Fig

-. 102

a

— ~" Jt.

JL

k

>w o

.u

f

F

Liq

a
ii

^

ids tliri

2i2 PHYSIOLOGICAL PHYSICS. [Chap. xx.

of the current encounter resistance by reason of the
adhesion of the outer molecules. Naturally, the re-

*/ '

sistance due to the friction along the sides of the tube
will depend on the length of the tube. It will be
greater the longer the tube, and vice versa. Thus
at the point a (Fig. 102) the resistance will be the
amount due to the friction encountered along the
whole tube «6, at i it will only be the friction
to be encountered between I and 6, at n only that
between n and. the outlet, and it is therefore a con-
stantly diminishing amount to the outflow point
where the water issues freely, and where the resistance
is consequently 0. Now the friction exerted on the
sides of the tube means pressure, and the deter-
mination of this pressure will give the amount
of resistance. In Fig. 102 vertical tubes are seen
communicating at intervals with the horizontal tube.
These being in free communication with a6, the
water will rise in them to a height which, accord-
ing to what has been previously seen, will be an
expression of the pressure exerted by the fluid upon
the walls of the tube through which it is flowing.
These vertical tubes are thus measures of pressure, of
pressure only at the point where they communicate
writh the horizontal tube. They are called PIEZOMETERS.
On filling up the apparatus shown in Fig. 102 it is
found that the height of the column of liquid regularly
diminishes in each tube, and is reduced to zero at b,
if the outlet there is free. So that a line joining the
surfaces of the fluid in each tube takes up a position
shown by the dotted line P P: P2, etc., experimentally
proving what has been said as to the diminution of
pressure onwards to the outlet. Now had the opening
at o been a free outlet, the water would have issued
from it with a velocity determined by the height of
the column of liquid above it, that is, by the pressure
HO, which is called the hydrostatic pressure. The

Chap. XX.] FLOW OF LIQUIDS THROUGH TUBES. 21 3

velocity of efflux at b, however, is less than this, be-
cause much of that pressure has been lost in over-
coming the resistance due to friction. The total re-
sistance to be encountered would be measured by the
height of the column of liquid that would be sup-
ported at the point 0 by the pressure along the hori-
zontal tube, and this height is OP, the level at which
the dotted line joining the surfaces of the liquid in
the piezometers strikes the reservoir. Thus, of the
total effective force HO of the head of water in the
reservoir, the total charge of the reservoir, as it is
called, the portion PO is required to overcome the
resistance encountered in the horizontal tube. There
remains only the portion HP to determine the velocity
of efflux at the outlet b. Suppose the end 6 of the
tube to be blocked, and an opening directed upwards
made instead, the water would issue from the tube ab
in an upward jet, and the height of that upward jet
would be a measure of the velocity of efflux ; that is,
the velocity which a body would acquire in falling
from rest through that distance is the velocity of dis-
charge. The height of the upward jet is the same
as the height HP. The velocitv of flow is uniform

^j t/

(constant) throughout the whole length of the tube.
To sum up :

(1) The rate of discharge is equal to the total
charge of the reservoir less the force required to over-
come the resistance.

(2) The resistance is directly proportional to the
length of the tube.

(3) Further, the resistance increases with the speed
of the stream. Since the resistance is due to the
friction of the molecules of the liquid at the centre of
the stream with the molecules outside of thern> which
are retarded more and more as they are nearer to
contact with the sides of the tube, it is evident when
there is no movement there is no friction, and as the

214 PHYSIOLOGICAL PHYSICS. [Chap. xx.

movement increases so does the friction, i.e. the
resistance. The smaller the diameter of the tube, the
greater is the speed of the current, so that

(4) The resistance is in inverse proportion to the
diameter of the tube.

In short, the resistance is directly proportional to
the length of the tube, is inversely proportional to its
cross section, and increases ivith the speed of the
stream. It may be added that the resistance will also
increase with the force of cohesion exercised by the
molecules of the liquid. So that a liquid like blood,
with greater cohesive power, would offer greater resis-
tance than water.

Heat diminishes the cohesion of a liquid, and so
lessens the resistance.

What has been said applies to tubes of uniform
diameter, but it explains also the influence of TUBES
OF VARYING DIAMETER. When a sma1! tube passes
suddenly into a tube of larger diameter there is
sudden increase of pressure at the surface of junction,
accompanied by a diminution in the speed of move-
ment through the wider tube. The molecules of
which the fluid consists cannot suddenly change the
swift movement into a slower one, and on account of
their inertia the pressure exerted by them on one
another develops the increased force. On the other
hand, the abrupt transition from a slow to a quick
movement, at the place where a wide tube passes into
a narrow one, diminishes the pressure. The effect
however, in a system of tubes of a series of widei
parts is to diminish the total resistance.

lending of the tube causes serious retardation
at the place of bend, and, if great, may produce some-
thing of the nature of a whirl still further to arrest
the movement by the pressure of the molecules on
the inner side of the bend. The result is, that behind
the bend the resistance is increased. This means,

Chap, xx.] RAMIFIED TUBES. 215

however, diminished resistance in front, diminished
amount of current, but a proportionately speedier
advance. The result of the counterbalancing is, that
in the end the pressure and speed of movement are
unaffected.

In a ramified system of tufees a similar
compensating arrangement is found to exist. Here
certain conditions exist tending to increase friction,
viz. increased surface of tubes, multiplying opportu-
nities for cohesion, as well as angles and bends ob-
structing the current. These exist at the places where
the main trunks branch out into others. Opposing
this tendency is the increased calibre permitting easier
flow. Similarly on the reunion of the branches to form
a common trunk, elements of increased resistance are
present in the retarding influence of the current of one
branch upon another as they meet, and on the in-
fluence of the angles at the junctions. This does cause
a backward pressure, which is yet to some extent
counterbalanced by the increased speed of a dimin-
ished current in front, and which is finally lost in
the increased calibre of the branches behind. Thus
it appears that, over all, a ramified system of tubes
does not offer more resistance than a single tube, and
may even effect a greater discharge than the single
tube.

The flow of liquids \\\ capiSlary tubes was
investigated by Poiseuille with great care, for it is
found that below a certain diameter the flow does not
follow the laws already laid down. The diameters of
the tubes used by Poiseuille were all under one milli-
metre. He found that with capillary tubes of equal
length, and with other things equal, the discharge
increases in proportion with the fourth power of the
diameter, while in other tubes it is directly as the
sections. For different lengths, other things being
equal, capillary tubes obey the same laws as others,

216 PHYSIOLOGICAL PHYSICS, [Chap.xx.

tlie resistance being directly as the length. The flow
of different liquids through tubes of the same length
and diameter, and under the same pressure, varied
greatly. For example, it took water 535-2 seconds
to pass through the same tube that ether passed
through in 160'5 seconds; alcohol took 1184-5
seconds; serum of blood, 1029; serum with alcohol
took longer time, 1223' 4; and with ammonia less,
9^1 '6. Salts like iodide of potassium and nitrate of
potassium increased the speed, chloride of sodium and
sulphate of soda diminished it.

The movement of liquids through elastic
tubes is not always the same as that described for
rigid tubes, because a new force, elasticity, is intro-
duced into the question. It is proper to observe,
however, that this new force need not always come
into play. Thus, suppose a constant flow of fluid
through an elastic tube, under the influence of a
constant pressure. The pressure may not be sufficient
to distend the tube beyond the normal, and in
that case the fluid will obey the same laws as if it
flowed through a rigid tube. The pressure may even
be sufficient to distend the tube, and even to distend it
to the uttermost, without any variation being produced
in the flow of the fluid. For the pressure, however
great it may be, is at the same time constant, and the
only influence it exerts through the elasticity is to
make the tube wider or narrower according as the
pressure is greater or less. The elasticity comes into
play only when the constancy (the equilibrium) is
disturbed. Thus, suppose an elastic tube, distended
already to some extent by a certain pressure, to come
under the influence of increased pressure, acting only
for a short time, by the introduction of an added
quantity of fluid, it dilates further in response to
the demand, but as soon as the additional pressure
passes away it is restored to its former calibre by the

Chap. XX.] FLOW OF LIQUIDS T PI ROUGH Ti^ES. 2IJ

action of its own elastic force. This elastic reaction
acts upon the fluid within the tube, pressing upon it,
and the increased pressure is thus passed on to a
succeeding part of the tube, which dilates, and then
recovers itself, by its recovery transferring the in-
creased pressure still farther, and so it is propelled
onwards. A wave is in this way propagated along the
tube. Now this propagation of a wave is to be dis-
tinguished from the passage of the fluid. The onward
movement of the molecules of the fluid, which forms
the current, is in the direction of the axis of the tube, in
a straight line, and is a movement of translation ; but

O ' '

the wave movement is one across this path, and is a
movement of oscillation, due to the molecules deserting
the straight line. In a rigid tube, as has been seen,
only the movement of progression exists. In an
elastic tube, with no current, the wave movement may
exist alone. In an elastic tube open at the end, not
only can both co-exist, but they may co-exist in
different directions. Thus the wave may pass in the
same direction as the current, in which case it is called
positive ; but it may travel in the opposite direction to
the movement of progression, and is then called a
negative wave. The characters of wave movements
have been very elaborately studied, by means of the
graphic method, by Professor Marey. He has adapted
the tambour, described on page 185, to obtain a register
of the movements. The tambour is contained in a
rectangular frame, the membranous side, which is
turned downwards, having attached to it the one half
of a piece of split tube. The other half rests on the
bottom of the frame. The elastic tube is made to pass
over the lower half, and then the tambour is lowered
by a screw, so that the tube is grasped by the upper
half, so as to be surrounded by the piece of tube. Any
movement, even the slightest, will affect the upper
portion, which, being attached to the membrane of the

218 PHYSIOLOGICAL PHYSICS. [Chap. xx.

tambour, causes oscillations of the air inside. These
oscillations are communicated through a tube to a
registering tambour, whose style presses on the surface
of a revolving cylinder. The box tambours are placed
at intervals along the elastic tube, each communicating
with a registering one. The styles of all the registering
tambours are arranged on the same recording surface,
one after the other in their proper order. Thus the
progression of the wave and other occurrences in the
fluid are registered on the same surface, and may be
studied at leisure.

It has been seen that it is intermittence of action
that produces the wave movement. Marey has shown
that the EXTENT OF THE WAVE depends on the sudden-
ness of the disturbance of equilibrium, and, when it is
due to the propulsion into the tube of an additional
quantity of fluid, it is proportional to the quantity.
Greatest at the moment of its production, it gradually
diminishes up to the end of the tube, if it be not
closed. A brief energetic impulse is capable of pro-
ducing, not only the primary wave, but a series of
SECONDARY WAVES. This is due to the fact that the
molecules of the liquid have been displaced above the
level of their normal position, as they took part in the
formation of the crest of the wave, and have then fallen
below their normal level in forming the hollow of the
wave. So that when, with the completion of the wave
movement, so far as each molecule is concerned, the
molecules are restored to their former position or level,
the force they have acquired compels them to pass
again beyond the normal, first in one direction and
then in the other. So they oscillate backwards and
forwards, producing secondary waves, until the ac-
quired energy is dissipated and they come to rest in
the usual position.

The speed of propagation of the wave is pro-
portional to the elastic force of the tube. Thus, the

chap, xx.] PRODUCTION OF WAVES. 219

less extensible the tube the faster will the wave travel,
while a slow rate, a retarded wave, means great exten-
sibility. The wave increases also with rapidity of the
impulses, and diminishes with increased density of fluid.
The Iiesgiit of the wave depends upon the ex-
tensibility of the walls of the tube. The more easily
distended the tubes are the higher will be the wave, but
the less will be its length. For if an additional quan-
tity of fluid be projected into a tube which readily
distends, a small portion of the tube will increase
its diameter sufficiently to contain the added quantity.
If, on the other hand, the tube is distended with
difficulty it will yield little to the increased pres-
sure, and, in consequence, a greater extent of wall
must yield in order to accommodate the added quan-
tity of fluid. Thus, the height of the wave will be
little, but its length will be considerable. Now it
is easily understood how one and the same tube may
present, at one moment, the features of a readily dis-
tensible tube with high short waves, and, at another
moment, the features of a tube distended with
difficulty showing low but long waves. Suppose a
moderately distensible tube which has a fluid flowing
through it under so little pressure that the tube is
hardly distended at all, the projection into the tube of
additional quantities of fluid will distend it consider-
ably at every projection, and the characters of a high
short wave will be produced. Let the same tube be
traversed by a fluid at great pressure, which, acting
on the elastic walls, distends them to their utmost
capacity. Under these circumstances the tubes are
nearly in the condition of a rigid tube, the projec-
tion of new quantities of fluid into it are capable of
dilating it further only to a very small amount, and
the characters of a low long wave are produced. The
application of these phenomena to the production of
the pulse will appear immediately.

22o PHYSIOLOGICAL PHYSICS. [Chap, xx,

Now what effect on the velocity and rate of dis-
charge of the fluid does the elastic force produce 1

Comparison between rigid and elastic
tubes. — Suppose both tubes to be under precisely the
same conditions, except that the one tube is distensible
and the other not. Let both be filled with fluid, and
be under the influence of the same intermittent force,
projecting additional quantities of fluid into them. In
the case of the rigid tube there is no means of increasing
the accommodation of the tube for the new quantity
of fluid, because it is already full, is inextensible, and
the fluid is not compressible. It follows, then, that a
quantity of fluid must pass out of the tube precisely
equal to the quantity that enters, and at the same
moment. In short, the intermittent action of the
pressure is accompanied by an intermittent efflux, the
interval between the cessation of the pressure and its
recurrence being marked by no flow. The shock, that
is to say, which has been received is communicated at
the same instant to the fluid in every part of the tube;
it has its maximum in every part at the same time,
and it disappears at the same time. In an elastic
tube, the molecules in the immediate neighbourhood
of the point of afflux experience almost the same
effect of intermitten.ee. Their equilibrium is suddenly
disturbed by a shock, which passes off, leaving them,
after a few oscillations, to come to rest until they are
disturbed by another shock. But this effect is not
communicated to the parts of the tube at some dis-
tance from the point of afflux. The impulse is not
transmitted in full force throughout the whole tube.
Part only is so transmitted, and a large portion is
expended in distending the elastic walls of the tube
in the immediate neighbourhood of the point of entry
of the projected fluid. As soon as the pressure begins
to diminish, the elastic reaction of the walls of the
tube comes into play, the recoil of the walls of the

Chap. XX.] RIGID AND ELASTIC TUBES. 221

tube presses forward the fluid which distended them,
and a succeeding portion of the tube then experiences
the pressure and proceeds to undergo the same pro-
cess. So that, while the fluid in the neighbourhood of
the point of atflux experiences discontinuous pressure
owing to the intermittent action of the force, fluid at
some distance . from the point experiences a less and
less degree of intermittence, owing to the elastic
reaction of the walls following up the intermittent
force. For this elastic reaction acts in the intervals
between the action of the intermittent force. The
farther one passes from the point of afflux the more
nearly does the fluid exhibit a continuousness of move-
ment, though showing still periodic variations in the
speed of progression, till at length, when the full
effect of the elastic reaction has developed, the fluid
has acquired a uniform continuous flow.

Thus elastic tubes have the power of transforming
an intermittent into a continuous flow.

Thus the fluid may be said to experience two
forces, one the intermittent force, the pressure com-
municated to the fluid, and the other the force ex-
erted by the elastic walls, due to their distension ; in
other words, the tension of the walls. It is well to
distinguish now between these two, so that there may
be no difficulty in understanding the difference between
the phrases BLOOD PRESSURE, the force exerted by the
blood upon the walls of the vessels, and due to the
heart's action, and ARTERIAL TENSION, the force exerted
by the walls of the arteries upon the blood, and due to
the elastic recoil of these vessels.

The effect of the action of elastic tubes on the
rate of movement of fluid through them is obviously
to slow it, for at the same instant that there enters the
tube a quantity of fluid, an equal quantity does not
issue from it, as in rigid tubes, owing to the distension
of the tubes. At the same time, experiment has

222 PHYSIOLOGICAL PHYSICS. [Chap. xxi.

shown that, all other things being equal, an elastic
tube is capable of discharging a greater quantity of
fluid than a rigid one in the same time. This Marey
proved experimentally by means of a Marriotte's
bottle (page 210), filled with water, whose outflow pipe
was furnished with a cock. From the outflow pipe
branched two tubes, one of brass and the other of
caoutchouc, both of the same length, both terminating

* o / o

in points of the same diameter. To prevent the
elastic recoil of the caoutchouc tube causing a back-
ward flow of water from it, a valve was placed at its
beginning. When the cock was opened, and a con-
tinuous flow permitted through both tubes, the quan-
tity discharged by both was the same. The continuous
action failed, in this case, to develop the elastic re-
action of the caoutchouc tube. When, however, the
cock was opened and closed intermittently, the quan-
tity discharged through the elastic tube exceeded that
from the glass tube. The explanation offered for this
is, that the slowing of the velocity of the current pro-
duced by the elastic distension diminishes the resistance
due to friction, and the force that would have been
expended in overcoming the resistance is now devoted
to furthering the advance of the fluid.

Thus, the elastic reaction of the walls of tubes
diminishes the velocity of the current, but increases
the quantity of Jluid discharged.

CHAPTER XXI.

THE MECHANICS OP THE CIRCULATION.

IT is now necessary to apply the laws that have
n indicated to
the blood-vessels.

been indicated to the circulation of the blood through

chap. XXL] MECHANICS OF THE CIRCULATION. 223

The blood-vessels form a system of branching
tubes of varying diameter. Beginning at one ex-
tremity in a large artery, the aorta, which gives off
branches at various angles, and these again other
branches, and so on, of constantly diminishing calibre,
the system passes into a series of remarkably small
vessels (the capillaries), which, in their turn, pass into
vessels now increasing in size, and uniting at various
angles to form the larger veins, which ultimately
end in two large vessels. Thus, to speak generally,
you have two series of wide vessels in communi-
cation through the medium of very small vessels.
The total calibre of the vessels increases from the
aorta to the capillaries, and again diminishes from
the capillaries to the great veins which open on the
right side of the heart. The force that circulates the
blood through this complex system of tubes is that
of the heart. To apply what has been noted of the
flow of fluid through such an arrangement of tubes,
the force exerted by the heart will be expended in
two directions, (1) to overcome resistance due to the
friction of the blood against the walls of the tubes (see
page 212), and (2) to produce a certain rate of flow.
Experiment proves that the laws applicable to fluid
flowing in tubes are equally applicable to the blood
flowing in the vessels. One of these laws is that the
pressure diminishes regularly from the source of force
onwards, and, in accordance with this law, it is found
that the pressure of the blood against the walls of the
vessels diminishes with the distance from the heart.
Since, however, we have here not tubes of uniform
diameter, but tubes of varying diameter, the pressure
will not diminish uniformly but irregularly. Thus,
owing to the resistance offered by the capillaries, the
pressure in the arteries diminishes slowly, but in the
capillaries themselves very fast, and again slowly in
the veins, which offer little resistance to the passage

224 PHYSIOLOGICAL PHYSICS. [Chap. xxi.

of the blood. While the rate of decrease varies, the
general fact remains that the pressure diminishes from
the aorta through the capillaries to the veins, in which
it is least of all.

It has also been seen that the velocity of the flow is
inversely as the diameter of the tubes. Now, owing
to the multiplication of branches, the total diameter
at the capillaries is much greater than at the aorta, or
than at the veins opening into the heart. It is,
accordingly, observed that the speed of the blood
diminishes from the aorta to the capillaries, and then
increases from the capillaries to the right side of the
heart, though the speed at the right side does not
come up to the rate in the aorta, the diameter at the
former level being greater than at the latter.

In considering next the part played by the
elasticity of the vessels, aid is also obtained from the
consideration of the purely physical conditions. For,
first of all, it is evident that the phenomenon of the
pulse is due to this factor, and that the characteristics
of the pulse are capable of affording valuable informa-
tion to the physiologist and physician, as to the
condition of the vessels and as to the character of the
force propelling the blood through them. From what
has been said (page 217) it will be understood that
the pulse is due to the dilatation of the artery under
the influence of the increased pressure transmitted
to the blood by the heart, and the subsequent recoil
of the elastic walls upon the blood within them, and
that this movement is not to be confounded with the
onward movement of the blood itself. Further, it has
been explained that the pressure exerted upon the
blood by the elastic recoil is called the tension of the
arterial walls.

The characters of the wave can be made visible
by a graphic tracing, obtained in a way to be men-
tioned immediately. What it is desired to note

chap. XXL] PULSE TRACINGS. 225

here is, that the characters are to be interpreted
according to the rules that have been already men-
tioned (page 219) as applicable to waves produced in
fluids by elastic tubes. For example, three tracings of
pulse waves are shown in Fig. 103. The tracing
011 the right is said to
be of low, that on the
left of high tension.
If we apply wThat

, , l l J . -, Fig. 103.— Pulse Tracings.

has been said on

page 219, the interpretation of these two tracings
will be that in the latter case the elastic wall is
exerting great force (tension) upon the blood within
it, so that at each increase of pressure, with each shock
of the heart, little additional effect is produced upon
the arterial wall to distend it ; while, in the former
case, little force is exerted by the wall, and every in-
crease of pressure affects it much more considerably.
In other words, in the case of high tension the
vessel is already so distended that any additional
pressure only feebly affects it; or, though not dis-
tended, it is extensible with such difficulty that it is
little affected by the force of the heart. These con-
ditions would be produced were the blood pressure
very high, or, specially, if the vessel had lost its elas-
ticity and had become more or less inextensible, that
is, more nearly approaching to the condition of a rigid
tube. On the other hand, the condition shown in the
right-hand tracing is the opposite, a vessel not very full,
so that each increase of pressure readily affects it, and
specially a vessel readily distended and very elastic,
so that it quickly returns to its normal state of dis-
tension. The middle tracing shows secondary waves,
the condition called DICROTISM showing consider-
able elasticity of the arterial wall, but little force
of tension, a condition which could not occur in rigid
vessels.

p— 7

226 PHYSIOLOGICAL PHYSICS. [Chap, x XL

The height of the pulse wave, then, reveals the
tension.

The law which has been stated, that the speed of
propagation of the wave is proportional to the elastic
force of the vessel explains how, the more rigid a
vessel becomes (for instance, by calcification and such
senile changes), the faster is the transmission of the
pulse ; it explains, too, the length of the wave in the
pulse tracing to the left of the figure, and in the
tracing obtained, for instance, from a person suffering
from hypertrophied vessels, due to chronic Bright's
disease of the kidney.

Again, the dependence of the extent of the wave
on the suddenness of the disturbance of equilibrium
(page 218), and on the quantity of fluid forced into the
vessel, by each shock, offers an explanation of the
abruptness that gives the "shotty" character to the
pulse of aortic insufficiency.

Thus the physical conditions explain the phe-
nomena of the pulse. The application of what has
been observed as to the effects of the elasticity of
vessels also shows that it is to the operation of this
force following up the shock of the heart, that the
continuous flow of blood through the capillaries is
due. It explains why loss of this elasticity, by calci-
fication of the arterial walls, should be followed by
pulsation continued into the capillaries, and even into
the veins. It also explains how the work of the heart
is economised by the quantity of discharge being in-
creased through elastic tubes.

It is now necessary to explain the methods by
which observations on blood pressure, arterial tension,
and velocity of the blood, have been made.

Blood pressure. — The figure on page 211 shows
how the pressure of the blood on the walls of the
vessels may be measured. The piezometers, described
on the same page are actually measurers of the force

chap, xxi.] BLOOD PRESSURE. 227

exerted on the tube, and the height of the column
of liquid that ascends in them is the measure of
the pressure exerted by the fluid. The first to
employ this method to measure the pressure of the
blood was Stephen Hales, rector of Faringdon. He
first (as early as the beginning of the eighteenth cen-
tury) experimented on dogs, and, later, on horses and
various other animals. His method was to open the
crural artery of the animal, and to fix into it a glass
tube, and then note the height to which the column of
blood rose in the tube. In experiments, however, to
determine the force of the sap in vines Hales used
tubes bent into a U-shape, in: the bend of which he
placed mercury. He noted the height to which the
column of mercury rose, and calculated how high a
column of water it represented. In his experiments
on blood pressure Hales noted not only
the height to which the column of blood
rose, but the time it took to attain its ^1
maximum, the stages by which it rose, Jlj
and the oscillations which it experienced
with the movements of the heart, and
other circumstances. In 1828 the bent
tube with mercury (Fig. 104), was em-
ployed by Poiseuille one end ab being in-
serted into the vessel of the animal, and
a reading then taken (by means of a scale Fi 104
rs, ii attached to each limb of the tube) Poiseuiiie's
of the difference of level of the surfaces mometei^
of mercury in the two limbs hd, gc. This
instrument Poiseuille called a hasmadynamometer,
or measurer of the force of the blood. Manometer is
another name given to the same arrangement.

The short limb of the bent tube was connected to
the artery of the animal to be experimented on
through the medium of a stiff elastic or a lead tube
with a fine extremity. A stop-cock permitted the

~

i

228

PHYSIOL OGICA L PHYSICS.

[Chap. XXI

tube and the manometer to be placed in communi-
cation at pleasure. The short limb of the mano-
meter, as well as the intermediary tubing, was
filled with a concentrated solution of bicarbonate
of soda before the connection with the artery was
established. This was for the purpose of preventing
coagulation of the blood by contact with the tube, a
circumstance which would prevent a correct result.
In 1848 Ludwig adapted to the mercury a float which
passed up the tube, and, after issuing from the top,

carried a horizontal arm with
a fine point, which, brought up
against the blackened surface of
a revolving cylinder, registered
in curve form the oscillation
of the mercury. To this form
the name of KYMOGRAPHION was
given by Volkmanii. Another
improvement consisted in so ar-
ranging the connection with the
vessel that the circulation should
not be arrested in it. This is
effected, not by simply tying

.—Scheme of Lud- ,, , , ' . .i/ i v 1 v

wig's Kymographion. tne tulje mto tne VCSSel, but by

One limb of the tube is repre- making a SlllD ill the side of the
sented tied in the vessel i L i • , « mi i

c, and the mercury in that Vessel, aild UlSertlllg a 1-Sliapecl
limb is depressed to the i • , ., mi i • . i

extent ««'. the mercury tube lllto it. llie horizontal pOl'-

in the other limb being -.- n , i rr\ • i • i • j i i

raised a corresponding tlOll OI tlie 1 IS tied 111 tlie VCSSel,
amount db. /is the point i ji •• i ,•

of the float s writing on aild the Vertical portion IS COll-
there volving cylinder c. •, -,i ,\~ ,

nected with the manometer.

Thus the horizontal part of the tube becomes part
of the vessel, from a part of the wall of which the
vertical portion springs, just as in the case of the
piezometers described on page 211.

One great objection to the mercury manometer
yet remains, viz. that owing to the inertia of the
mercury it does not record the absolute movements of

Chap, xxi.] THE KYMOGRAPHION. 229

the blood. The oscillations of the mercury tend to

«/

maintain themselves, and small variations thus escape
record. An arrangement for obtaining tracings with

O o o

more minute variations is that of Bourdon, adapted
by Fick. It consists of a hollow spring thrown into
the form of a curve (GB, Fig. 106). The interior is
filled with alcohol. One extremity
is sealed, and has passing from
it an arrangement of levers GD
for amplifying the movement. The
extremity of the lever projects, by
means of a writing point, against
a revolving cylinder. The lower
end of the spring communicates
with a lead tubing A ; which
is filled with bicarbonate of soda Fig. 106. — Tick's
solution, and is connected with a pblcnf
T-shaped tube in the blood-
vessel. To damp the oscillations, and prevent
them being continued by the mere elasticity of
the spring, a prolongation of the writing lever dips
below the writing point into a tube of glycerine.
Pressure causes the spring to expand, and a movement
is communicated to the lever. As soon as the
pressure is removed the spring returns to its former
position.

Marey's tambours (page 1 85) have been adapted to
register blood pressure. In 1861 Marey and Chauveau
obtained tracings of pressure by introducing into the
heart itself a sort of catheter carrying a small caout-
chouc bag at the heart end. The other end of the
sound communicated by means of an indiarubber
tube with a registering tambour writing on a revolving
cylinder. For the right side of the heart the sound
was introduced through the jugular vein, for the root
of the aorta and left side of the heart through the
carotid.

230

PHYSIOLOGICAL PHYSICS. [Chap. xxi.

By the cardiograph (Fig. 107) Marey has ap-
plied the same method to obtain tracings of the

movement of the heart from the
outside. The tambour is fitted in
a vulcanite box c. On the disc
in the centre of the membrane a
is fixed a vulcanite knob 6, which
is applied to the spot on the chest
where the shock of the heart is
felt. By means of the spiral

Fig. 107.— Cardiograph J , 7 ,

of Marey (in section), spring and screw a the sensi-
bility of the instrument can be
increased or diminished. The variations of pressure
produced by the movements of the heart are conveyed
by an iiidiarubber tube efto a registering instrument
in the usual manner.

The speed of the Moocl stream has been deter-
mined by various forms of ap-
paratus. First in point of time is
that of Yolkmann (1850), which is
called the haeinodromoiiBeter.
It consists of a bent U-tube with
limbs of equal length 2, 3 (Fig. 108),
between which a scale is fixed.
These are fixed in a basement piece
5, 6, fitted with cocks 1, 4, and sup-
plied at each end with a caiiule
7 8. The cocks of the basement
piece communicate with one
another, and have a passage bored
straight through and a passage at
right angles to it opposite each limb
of the U-tube. By a simple
mechanical contrivance the cocks can be turned so
that the through passage only is open, or the cross
passages only. By this means, in the first case, fluid
would pass straight through without entering the

108.— Volkmann's
Hamiodromometer.

Chap. XXI.]

Lunwids STROMUHR.

231

U-tube ; in the second case, the fluid would require to
pass the long route through the bent tube. In
Fig. 108, A illustrates the complete instrument; B
shows how, by turning the cocks, the fluid would pass
straight through, and c shows how it would be diverted

O O '

into the bent tube. The bent tube is filled with
water, or, better, serum, and the cocks turned so as
to shut it ofi from the through passage. The cut ends
of a severed artery are then ligatured to the two
canules. In this position the blood passes straight
through the basement piece, just as if it were part of
the length of the artery. At a given moment the
cocks are turned, the blood passes up one limb of the
bent tube and down the other, driving the serum
before it. The time it takes to travel the whole
length of the tube can be counted, and the length is
known, so that the rapidity is easily estimated. An
objection to this instrument is that the time occupied
by the blood in traversing the tube is very short,
and no account can be taken of vari-
ations produced by respiration and
the shock of the heart.

The stromuhr of Ludwig (Fig.
109) permits of a much longer obser-
vation, while constructed on a similar
principle. It consists of two glass
flasks, 1 and 2, of equal capacity, com-
municating with one another above by
an arch, surmounted by a metal cap AB.

The flasks are supported on
a metal disc 5 5', which is capable
of revolving on the metal support
6 6', below. Through 5 5' and
66' is a tube on each side, continuous with 1 and
2, and terminating in the canules 8 and 9. In
the position shown in the figure, 1 communicates
with 8, and 2 with 9, but, by a half turn of the flasks,

Fig. 109.— Ludwig's

Stromuhr.

Tlie left-band side is

shown in section.

232 PHYSIOLOGICAL PHYSICS. [Chap. xxi.

permitted by the disc 5 5', 1 may be put in communi-
cation with 9, and 2 with 8. Suppose the stromuhr
be applied to an artery, so that the proximal end is
bound to the canule 8 in communication with 1, and
the distal end bound to 9. 1 is filled with pure olive
oil, 2 with defibrinated blood. On communication
being made with the artery, the blood rushes through
8 into 1, and forces the oil into 2, and the defibrinated
blood from 2 into the artery ; as soon as the blood
reaches to the mark 3, the stromuhr is quickly turned,
so as to bring 2, now filled with oil, over 8, and 1,
filled with blood, over 9. The blood is thus permitted
to pass 011 wholly into the artery, and the operation is
repeated, 2 becoming in turn filled with blood, and 1
with oil, when the instrument is again turned. The
number of turns are noted, the time taken, and the
capacity of the flasks is known, so that the quantity
of blood passing in a given time is ascertained. To
tubes projecting from the wall of the tubes 8 and 9
manometers can be connected to give the pressure at
the entrance and exit of the blood.

The lisemotacliometer of Yierordt, devised later
than Yolkmann's instrument, but earlier than Lud-
wig's, affords another means of estima-
ting the velocity of the current. It is
formed of a metal chamber (Fig. 110),
with plain glass sides. Projecting from
each end is a canule, a and b. In the
chamber hangs a small pendulum. At-
no.— Vier- tached to one side is a scale, in the form
tachometer!" of an arc, for reading off the deviations
of the pendulum. The instrument is gra-
duated by forcing water through the chamber, and noting
the deviation of the pendulum with different veloci-
ties. It is then inserted in the course of a vessel, and the
rapidity of the current estimated by the deviation of the
pendulum interpreted by the prepared table of values.

chap, xxi.] THE SPHYGMOGRAPH. 233

The ctromograpli of Lortet and Chauveau em-
bodies the same idea as that of a recording instru-
ment. It consists of a tube, represented in the figure
(Fig. Ill) in cross section, T, which is interposed in
the course of the blood-vessel. A
square opening on one side of the
tube is closed by a plate of caout-
chouc. Projecting into the tube
and piercing the caoutchouc is the
flattened end s' of a light lever, the Fig. ill.— Dromo-

i . -i . T f 1 ' i • • 1 graph of Lortec and

long thin end s 01 which is outside chauveau.
the tube, and records movements
on a blackened surface. The lever is deflected by the
current of blood, and a curve obtained on the moving
blackened surface. The extent of the deviation can
also be measured by a scale attached to the instrument
in the direction of the axis of the tube. . From the
upper wall of the tube rises another tube provided
with a stop-cock, which can be placed in connection
with a sphygmoscope of Marey (page 234), and by it a
record of pulse movements is obtained on the same
blackened surface as that of the velocity. One great
advantage of this instrument is that it records varia-
tions of velocity, and these variations can be com-
pared with the movements of the heart, etc.

The spliygiwograpli is an instrument for obtain-
ing tracings of the movements in arteries which consti-
tute the pulse. While the kymographion records varia-
tions of blood pressure, the sphygmograph may be said
to record variations of arterial tension. It was originally
devised by Yierordt, but in the form given to it by him
it was extremely cumbersome. It has been modified
and improved by Marey, and is shown applied in Fig.
112. An ivory knob on the end of a steel spring is
placed over the artery for receiving its movements.
The tension of the spring is regulated by a screw. A
fine screw b rises from the knob, and has pressed

234

PHYSIOLOGICAL PHYSICS. [Chap. xxi.

against it a toothed wheel, to which is attached the lever
c. Every movement of the knob is communicated by
the screw to the wheel, and consequently to the lever.

The movements of
A

}ever are writ-
ten, by its point, on
a piece of smoked
glass or card d,
carried towards c by

Fig. 112.— Marey's Sphygmograph applied, the clockwork below

d. The instrument

is secured to the arm by side pieces and straps.
Sphygmographs have also been constructed on the
tambour principle, arrangements being also made to
determine by weights the pressure exerted on the
artery, and to vary it at pleasure.

The spliygmoscope of Marey (Fig. 113) con-
sists of a small glass cylinder 2, which
has two openings, one of which is closed
by an indiarubber tube, leading to a
registering tambour, whose lever is in

o O *

contact with a recording surface. Into
the other opening is tightly fitted a
tube, carrying at its end a little india-
rubber bag. The bag and tube are con-

o o

nected with a receiving tambour, whose

°.

membrane has attached to it a knob
which is placed over an artery. The
variations of pressure in the receiving tambour are
communicated to the indiarubber bag. The expansion
of the indiarubber bag compresses the air outside of
it, i.e. in the glass cylinder, and consequently affects
the recording lever. Similarly, the diminution of the
air in the bag rarefies the air in the cylinder. For
use with Lortet's dromograph, the indiarubber from
the bag is connected directly with the tube projecting
upwards from the instrument tied in the blood-vessel.

Chap, xxi.] THE SPHYGMOPHONE. 235

The gas spliygino scope is a little metal cham-
ber, having a tube projecting from the top and one
projecting at one side, and having the bottom,
formed of a delicate membrane. Gas is led by the
side tube into the chamber, and out by the top tube.
From its exit pipe the gas is led to a glass tube, bent
upwards, and drawn to a fine point, so that when the
gas is lit, a fine pointed flame is produced. The little
chamber is then placed with its membrane over an
artery. The movements of the pulse cause variations
of pressure in the gas, and these are signified by regu-
lar up and down movements of the flame.

The spliyganoplione is an adaptation of the
gas sphygmoscope, after the method used for obtaining
a sound from the hydrogen flame. A long glass
tube of sufficient diameter is brought down over the
gas jet, which is permitted to burn inside the wider
tube. The long tube is brought down till a pecu-
liar note is produced by the vibrations of the flame.
If, now, the gas chamber be placed over the pulse,
something like beats will be produced in the tone, due
to the variation of the pulse.

In a similar way A PULSE ALARUM might be con-
structed by means of a very small chamber, with
movable bottom, and glass tube projecting upwards.
The chamber is filled with mercury, which is also
allowed to rise some way in the tube. Plunged in
the mercury in the tube is a copper wire, forming
part of the circuit of an electric bell. A second wire,
completing the circuit, is passed down the tube, just
so far that when the mercury rises with the pulse
wave contact is made, and when the mercury falls
with the vessel's recoil, contact is broken. The bell
will ring each time contact is made, and will thus
indicate the rapidity of the pulse waves.

Before leaving this subject of the mechanics of the
circulation it may not be out of place to describe a

236

PHYSIOLOGICAL PHYSICS. [Chap. xxi.

method of studying and registering movements of the
heart under varying conditions.

The frog-heart apparatus of Ludwig and
pupils affords a most valuable and interesting means
of studying the heart, a means not very widely known
in this country. The apparatus is shown in Fig. 114.

It consists of two tubes (1 and 2)
similar to the burettes used for
quantitative chemical analysis, and
marked off into tenths of a cubic
centimetre. They communicate
with one outlet, guarded by a two-
way stop- cock. The tubes are
supported on a stand, and in the
same frame is held a small
mercury manometer m, one limb
of which is turned and pro-
longed downwards, so that it opens
at the same level as the burette
outlet. A branch of the same
limb is also prolonged upwards
and backwards and is guarded with a stop-cock. The
limb m contains a fine stem of glass floating in the
mercury by a bulbous extremity, the projecting end
being bent at right angles and terminating in a point
s for writing on a blackened revolving cylinder. For
fixing the frog heart to the apparatus, the Kronecker
heart canule, shown in the upper part of the figure,
is used. It is divided into two compartments, one
communicating with the branch A, and the other with
the branch B. To each of the branches is attached a
short piece of caoutchouc tubing. A frog having been
pithed and its spinal cord destroyed, the thorax is
opened and the heart exposed. The pericardium is
opened in front, the heart turned over, and a very fine
vessel passing from the pericardium to the back of the
heart ligatured. The sinus venosus is now opened by

Fig. 114.— Frog-heart
Apparatus.

Chap, xxi.] THE FROG-HEART APPARATUS, 237

a snip, and the caiiule passed through it, and through
the auricle into the ventricle, where it is bound. This
is an operation of some difficulty. The binding should
be above the auric ulo- ventricular furrow. The heart,
attached to the caiiule, is then separated from the
body, and the canule connected on the one hand with
the outlet tube of the burettes, on the other with the
manometer tube. Into one burette is placed a solution
consisting of one part of defibrinated rabbit's blood, and
two parts salt solution (-6 per cent.). The burette is
closed with a cork, through which passes a tube which
dips into the fluid, and so maintains a constant pressure,
on the principle of Marriotte's bottle (page 210). On
now opening the stop-cock connected with the burettes
and that of the manometer, the blood will flow into
and flll the heart, pass through it into the limb of the
manometer, and if allowed to flow will issue by the
upward branch, below which a vessel g should be
placed to receive it. If, however, the manometer cock
be closed, the blood will dilate the heart, and if, when it
is fully dilated, the burette cock be closed, then, on the
heart contracting, the blood, finding no other way of
escape, will be forced into the short limb of the mano-
meter, and will depress the column of mercury there.
The column in the long limb will consequently be
raised, and the glass float with it, the recording point
of the float marking the ascent on the blackened sur-
face. When the heart relaxes the blood will return,
the mercury will fall to its original level, and the
descent will be recorded. By this arrangement a
heart may be kept alive, rhythmically beating for
hours, and curves of its movements obtained on a
revolving cylinder. Every now and again the stop-
cocks require to be opened to give a fresh supply of
blood to the heart. The little vessel h is filled with
•6 per cent, salt solution, and brought up so that the
heart on the end of the canule dips into it and is kept

238 PHYSIOLOGICAL PHYSICS. [Chap. xxi.

moist. The effect of heat or cold can be stupied by
surrounding the vessel h by an outer vessel con-
taining hot or cold water, and a thermometer in
the salt solution will give the temperature. The
little projecting wire c on the canule is for at
taching a copper wire to be carried to one of the
binding screws of a key. Another wire from the
other binding screw dips into the salt solution sur-
rounding the heart by passing down the tube of h.
A little mercury in the botuom of this vessel will make
the connection better. By this means shocks may be
sent to the heart, and tracings of the -effect of electric
currents obtained. Into the second burette may be
placed a blood solution, similar to that in the first, but
having in addition a small quantity of ether, chloroform,
or other substance. By turning the cock the proper
way any required quantity of the drugged blood may
be sent to the heart and its effects recorded.

The projection c of the canule (Fig. 114) is for the
attachment of a wire from an induction coil. The
second wire from the coil is passed into the bottom of
the vessel h in which the heart is placed. A little
mercury is poured into the vessel, and into it the wire
dips. The heart is thus in the circuit of the coil, and
effects of shocks of electricity may be studied.

Lauder Brimton has shown a simple way of
demonstrating the effect of heat and poisons on the frog
heart. He cuts out the heart, places it on a copper
plate, and lays o\ar it a light lever of straw or some
such material. The lever indicates the heart's pulsa-
tions. On heating the plate, by means of a spirit
lamp, the heart's pulsations are quickened, on cooling
with ice they are slowed.

Marey has devised a pair of light forceps for
grasping the heart in situ, the thorax being opened.
Only one limb of the forceps can move ; and a lever
in connection writes on a blackened surface.

239

CHAPTER XXIL

CAPILLARITY, DIFFUSION OF LIQUIDS, AND OSMOSIS,
THEIR APPLICATION TO THE PHYSIOLOGY OF AB-
SORPTION AND SECRETION.

WE have had under consideration certain elementary
laws applicable to masses of liquids. There are, how-
ever, phenomena exhibited by liquids which are
capable of explanation only by supposing that the
ultimate molecules of all liquids exert forces on one
another, and on solid bodies with which they may be
in contact ; in the one case the force is that of cohesion,
in the other that of adhesion. Or, to put the terms in
a more general way, for they are equally applied to
solid and liquid bodies, attraction between the mole-
cules of the same body is cohesion, and between
different bodies in contact, adhesion.

Cohesion. — The molecules of a body mutually
attract one another with a certain intensity in all
directions. In liquids the intensity of the cohesion
is not great, the molecules are readily displaced,
and hence the ease with which a mass of liquid
suits itself to the vessel which contains it. Still,
the cohesion of liquids is manifested in various
common phenomena. Thus, a drop of water falling
freely assumes the spherical form, and this is due to
the mutual attraction of all its molecules. Again, a
globule of mercury on a plate of glass or wood main-
tains a more or less spherical form ; and it does this
against the force of gravity, which tends to flatten out
the globule, to destroy the sphere. If, however, the
drop becomes very large, then the form is generally
altered ; it becomes flattened. This is because the

240 PHYSIOLOGICAL PHYSICS. [Chap.xxn.

mass of the mercury in its spherical shape has become
too great for the force of cohesion to support against
gravity. Consider, now, the free surface of any
liquid, it is easy to see that the molecules on the sur-
face are attracted by the molecules deeper in the fluid,
but have no molecular attraction beyond them. The
attraction is, therefore, towards the deep part of the
liquid. At the surface of liquids, in consequence, a
force is directed inwards, which is called the SURFACE
TENSION of the liquid. It is this phenomenon of co-
hesion in particular which determines the spherical
form of drops already noted. Some very interesting
experiments on surface tension may be made with
camphor. Drop a minute piece on the surface of
perfectly clean water ; it is driven about in various
directions, owing to the fact that the surface tension of
pure water is much greater than that of camphor
water. The solution of the camphor, therefore,
diminishes the surface tension in its neighbourhood,
and currents are produced in all directions. The
solution being quicker in some places than in others,
the strength of the currents varies, and so the frag-
ment is driven about in a distracted manner. If a
small block of charcoal be taken, and coated with
paraffin, and if at each end, on opposite sides, a piece
of the paraffin be removed, and a drop of some
essential oil put on the charcoal, and then the char-
coal be dropped on the surface of water, it will not
be driven to and fro, but will be turned round and
round, This is due to the difference of surface
tension between the water and essential oil at the
two ends on opposite sides acting as a couple.

Adhesion of a liquid to a solid body is shown
when a perfectly clean piece of glass is dipped into
water. On removing it water is found adhering to
its surface. Or if a drop of water be placed on a per-
fectly clean glass plate, the drop of water does not

chap, xxii.] CAPILLARITY. 241

retain its spherical form, but spreads itself over the
smooth glass surface. That is to say, the force of
adhesion between the molecules of the glass and those
of the liquid has overcome the force of cohesion
between the molecules of the liquid. A drop of mer-
cury, however, will not lose its spherical form on
being placed on a perfectly clean glass surface.
That is to say, the cohesive force exerted between
the molecules of the mercury is able to overcome
the attractive action exerted by the molecules of the
glass on those of the mercury. Other liquids exhibit
similar phenomena, some adhering, others not adhering,
so that the degree of adhesive force varies with the
liquid. This is put in simpler language when it is
said that the water wets the glass, but the mercury
does not. But, while wTater wets glass, it will not wet
some other substances. Thus, if the glass were greasy,

O O •/ 7

the drop of water would retain its spherical form, and
would readily roll off the plate. And, again, while
mercury does not wet glass, it will adhere to copper ;
so that the degree of adhesive force depends both on
the nature of the liquid and of the solid body with
which the liquid is in contact.

Capillarity.— These facts are held as affording
the explanation of capillary action. If a glass tube
of narrow bore be plunged vertically into a vessel of
water, the water will rise in the capillary tube above
the level of the surface of the water in the vessel. The
surface of the water in the tube will not be horizontal,
but will present what is called the CONCAVE MENISCUS
(yUTjz/t'o-Kos, a crescent). The surface, that is, will be
curved, a depression existing in the centre, and the
water rising where it is in contact with the walls of
the tube. This fact of the ascension of water in a very
narrow tube was noted at the commencement of the
seventeenth century by an Italian physicist. It Avas
supposed for a time to be due to the action of the
Q— 7

242 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

atmosphere, till, in 1705, experiments made by
Hawksbee, at Gresham College, showed the action
to occur in vacuo as well as in air. The explanation
is that the force of attraction exerted by the walls of
the tube on the liquid molecules in contact with them
overcomes the force of cohesion of the liquid mole-
cules for one another, and raises the water where it is
in contact, causing thus the depression towards the
centre. As a result of this attractive force of adhesion,
the pressure on that part of the surface of the water
in contact with the tube is less than the pressure on
the rest of the liquid, by the amount of the force of
adhesion. In consequence of the diminution of pres-
sure the water rises in the tube, and will rise till
the column of water reaches a height above the rest of
the surface that will exert a weight equal to the force
of adhesion. This force of gravity, being equal and
opposite in direction to the force of adhesion, counter-
balances it, and thus the liquid comes to rest at a cer-
tain distance up the tube.

It has been found that wherever the liquid wets the
tube the height of the capillary ascent depends on the
liquid, and 011 the temperature (diminishing with in-
creasing temperature), but not on the material of the
tube. With the same liquid, the extent of elevation
varies inversely as the diameter of the tube. That is, the
narrower the tube, the higher the ascent, and vice versa.

On the other hand, if the force of cohesion is suffi-
cient to overcome the force of adhesion, then the liquid
in the tube assumes the CONVEX MENISCUS, the liquid
in the immediate neighbourhood of the walls of the
tube is depressed, and elevated towards the centre. The
liquid does not wet the tube. As already mentioned,
this is the case with mercury in a glass tube. Instead of
a capillary ascent of the liquid, there is a depression
below the level of the surface of the fluid outside of the
tube. This depression is explained on similar grounds to

Chap, xxii.] CAPILLARITY. 243

the ascent. The surface tension of the liquid is in this
case increased ; but, by the law of equal transmission
of pressure, the increased pressure within the tube
cannot be permitted to remain. Consequently, the
liquid falls in the tube till it is depressed so far below
the level of the outer liquid, that the column of liquid
representing the difference would exert a pressure equal
to the increased pressure produced within; and so
equilibrium is restored.

In the case of the convex meniscus the depression
of the liquid is in the inverse ratio to the diameter of
the tube. The result is, however, in this case affected
by the nature of the material forming the tube. Thus,
the depression of mercury in a tube of iron is greater
than the depression of mercury in a tube of platinum
of the same bore. It also varies with the nature of
the liquid and the temperature, diminishing with an
increasing temperature.

Suppose, then, that a vertical glass tube, wide
enough to permit the neglect of capillary phenomena,
communicates with a vertical capillary tube, and that
water is poured into the wide tube. The water will
rise in the capillary tube considerably above the level
of the water in the wide tube, because of the diminution
of hydrostatic pressure by the force of adhesion. If a
similar tube contain mercury, then the mercury wTill
be depressed in the capillary tube considerably below
the level of that in the wide tube, because of the in-
creased hydrostatic pressure.

Capillary phenomena of a similar character are
observed if two plane surfaces be brought near
enough to one another, whether parallel or inclined
to one another. If they are inclined to one
another, then a small quantity of a liquid that wets
the surface placed between them will move from the
wide to the narrow end ; and if the liquid does not
wet them it will move in the opposite direction.

244 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

Indeed, the phenomena are exhibited when any
solid body is plunged into a liquid. At the surfaces in
contact the liquid is either raised or depressed, accord-
ing as the force of adhesion or cohesion sufficiently
predominates.

The capillary electrometer. — It was known
for some time that if a globule of mercury in dilute

sulphuric acid was

-"-v <•' placed in contact with

V c a/ the positive pole of an

element, while the

Fig. 115.— Capillary Electrometer.

negative pole was in

the sulphuric acid, on the passage of a current of
electricity the globule would move towards the nega-
tive pole. By interrupting and re-establishing the
current oscillations of the globule are produced, due to
changes in the surface tension of the mercury in contact
with the acid. The phenomena are more marked if
the mercury be contained in a capillary tube. A tube
suitable for the production of the phenomena was first
constructed by Lippmann. It " consists of a tube of
ordinary glass, one metre long and seven millimetres
in diameter, open at both ends, and kept in a vertical
position by a stout support. The lower end is drawn
into a capillary point, until the diameter of the
capillary is '005 of a millimetre. The tube is filled
with mercury, and the capillary point is immersed in
dilute sulphuric acid (1 to 6 of water in volume), and
in the bottom of the vessel containing the acid there
is a little more mercury." A platinum wire is con-
nected with the mercury in the tube, and another with
the mercury in the outer vessel containing the acid.
The capillary tube can be brought to the side of the
outer vessel, and viewed through a microscope, and an
oscillation perceived due to an extremely feeble cur-
rent. A modification of the instrument has recently
been devised by Professor McKendrick of Glasgow,

Chap, xxn.] THE CAPILLARY ELECTROMETER. 245

which renders it easy for any one to make a capillary
electrometer for himself of sufficient delicacy to in-
dicate the muscle current, negative variation, the
current from the isolated beating heart of the frog,
etc. It is represented in Fig. 115. A small piece of
narrow glass tubing is taken, and drawn into a fine
capillary in the middle. Each end is bent up. Some
clean mercury is placed in a glass and covered by
dilute sulphuric acid (1 to 20 of water by volume).
One end of the tube is dipped under the surface of
the mercury, and suction applied by the mouth at the
other end till the mercury appears at the wide end
next the mouth. By raising the lower end, a little
acid is permitted to enter the tube, and then a little
more mercury is sucked in. After a little practice
one is able so to fill the tube that mercury occupies
each end, and a fine thread of mercury passes from
each end into the capillary, the centre of which is
occupied by acid. In the figure the dark portion in-
dicates the mercury, the clear part c in the middle
of the capillary is the dilute acid. No air-bubble must
be permitted in the tube. The tube should be sup-
ported in a frame, which can be laid on the stage of a
microscope. A platinum wire dips into the mercury
at each end a b of the tube ; and the other end of
the wires should be attached to binding screws on the
frame. The capillary is easily made fine enough to
be viewed by a lens magnifying 300 to 500 diameters.
To put the electrometer in circuit with the non-
polarisable troughs, all that is necessary is to connect
the binding screws of the frame to the troughs by
wires, one screw to one trough, a key being interposed
in the circuit. After placing a muscle on the troughs

J. O C1

in the usual way (see page 117), on looking down the
microscope, and then closing the key, the movement
of the mercury will be seen. To obtain a very sensi-
tive instrument, clean mercury, clean glass tubing, and

246 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

clean acid, with a little practice in making the instru-
ment, are all that is necessary.

Capillary action in porous bodies. Imbi-
bition.— Porous bodies may be considered as bodies
traversed in certain directions by capillary tubes.
Into the interstices of such porous bodies liquids are
capable of entering by capillary attraction. Thus,
a porous body plunged into water is permeated by
the liquid, which remains after the body has been
withdrawn from the mass of liquid. This is called IMBI-
BITION. The fluid may be expelled by pressure. It is
thus that a sponge takes up a large quantity of water,
expelled on squeezing. All animal and vegetable
tissues are porous, even though the microscope may
not be able to reveal the presence of the interstitial
spaces. All the tissues of the animal body are, ac-
cordingly, permeated by the fluids of the body. The
flexibility and silky lustre of tendons are due to the
fluid mechanically retained in the tissue. Let the
tissue be exposed till it becomes dry, it will then have
lost its lustre and a great degree of its flexibility ; and
will have become transparent. It will also be lighter
than before by the amount of water it has lost. But
let it be immersed in water for a time, much of its lost
properties will be restored, and its weight will also
have been restored by the amount of water imbibed.

Yellow elastic tissue, cartilage, the cornea of the
eye, give results of a like sort. The organic tissues,
such as wood, exhibit similar phenomena. But such
tissues placed in water will imbibe, not only their
normal quantity of water, but a quantity greatly in ex-
cess of it. The increased quantity of fluid will distend
the narrow passages in which it is lodged, and will
thus increase the bulk of the tissue. But with this
distension there is .brought into play elastic reaction,
and resistance to the distension arises. The water
will continue to be imbibed so long as the capillary

chap, xxi i.] IMBIBITION. 247

forces are able to overcome the forces of recoil, but as
soon as sufficient resistance has developed, the two
forces corne to be in equilibrium, and further imbibi-
tion ceases. The forces which determine imbibition
are sometimes enormous. As an example, take the
splitting asunder of rock by means of wedges of dry
wood placed in clefts and then allowed to imbibe water.
Various observers have made a large number of ex-
periments on the differences of imbibition dependent
on the nature of the liquid into which the solid body
is plunged. Some of those made by Liebig, and pub-
lished in 1848, in his Recherches sur quelques-unes des
causes du mouvement des liquides dans I'organisme
animal, may be quoted here. 100 parts by weight of
dry ox-bladder took up, in 24 hours, 268 volumes of
pure water ; the same quantity in a saturated solution
of sea salt took up only 133 volumes ; a third quantity
took up 38 of alcohol (84 per cent.), and a fourth 17
of oil of marrow. " Of all liquids, pure water is taken
up in the largest quantity ; and the absorptive power
for solution of salt diminishes in a certain ratio as the
proportion of salt increases. A similar relation holds
between the membranes and alcohol ; for the mixture
of alcohol and water is taken up more abundantly
the less alcohol it contains." The same has been found
to hold good for other animal tissues. The extent of
imbibition 'depends, therefore, both on the tissue and
on the liquid which moistens it. Membrane has less
affinity for brine than for pure water. If salt be
sprinkled on a membrane whose pores are occupied
with pure water, the water dissolves some of the salt,
forming a solution, and this brine solution diffuses
itself through the bladder. The pores of the mem-
brane come to be occupied by salt solution instead
of pure water ; but the membranes can contain less
of salt solution than of pure water, and, consequently,
it has to expel a quantity of the water, which collects

248 PHYSIOLOGICAL PHYSICS. ichap. xxn.

on its surface in drops. Similarly, a membrane
which contains water in its pores, on being placed in
alcohol, expels a considerable quantity of water,
because it can contain of alcohol only about one-
seventh of what it can contain of water. As a result
of this expulsion of water, the texture shrinks.

Diffusion of liquids. — Different liquids exercise
attractive forces between their molecules, just as the
molecules of a solid body and those of a liquid
coming into contact develop attractive forces.
When one liquid is in contact with another, if the
force of attraction exercised between the mole-
cules of the one liquid and those of the other are
greater than the forces of cohesion exercised between
the molecules of each liquid separately, then the two
liquids will be capable of advancing into one another's
substance, that is, will be miscible. If, however, the
forces of cohesion between the molecules of one liquid
are sufficient, they are superior to the force of attrac-
tion exerted by the other liquid ; and the liquids
remain separate and independent. They are not
miscible. Of this nature are water and oil, and water
and mercury. When the different liquids, then, whose
molecules mutually attract one another, are placed in
contact with one another, they proceed to mix, and
in time the mixture will become uniform. This is
called DIFFUSION.

A similar thing occurs when a liquid dissolves a
solid body with which it is in contact. The liquid over-
comes the force of cohesion between the molecules of
the solid body, separates them, and the two then form
a homogeneous liquid. A point is reached when the
liquid is unable to overcome any more the cohesion,
between the molecules of further quantities of the
foreign body. In this case the point of saturation of
the liquid is reached. This point of saturation varies
with the solid body, and the liquid which dissolves it.

Chap, xxii.] DIFFUSION OF LIQUIDS. 249

The phenomena and laws of diffusion were studied
at great length and with much care by Graham.
Graham employed in his experiments what he terms
a diffusion cell. It consisted of a 4-ounce phial, the
mouth and bottom of which were ground flat. This
phial was filled up to the base of the neck with the
solution for diffusion. The bottle was then placed in
a cylindrical jar with a flat bottom ; and when in the
jar it was filled up to the mouth with distilled water
in such a way as to prevent mixing of the water and
the solution by movement. Distilled water was then
placed in the jar till it stood one inch above the
mouth of the phial. By this means the saline solution
communicated freely with the distilled water. After
the phial had been allowed to stand undisturbed in
the jar for a varying time, its mouth was closed with
a plate of glass ; it was then lifted out of the jar, and
tests were employed to find how much of the salt had
found its way out of the phial into the surrounding
distilled water.

As the result of many experiments, Graham found
that the rate of diffusion, the speed, that is, with
which the different fluids mixed, varied with the
degree of concentration of the solution. If the solu-
tion were very concentrated it proceeded fast, if less,
more slowly ; and the rate was in direct proportion
to the concentration. At first, therefore, the diffusion
from the cell would proceed with a certain degree of
rapidity. But as the salt diffused, the concentration
would be diminished, and would be, besides, no longer
into distilled water but into water plus the quantity
of salt already diffused. As a result the rate would
constantly decrease, and when the liquid outside of
the diffusion cell had gained so much salt as to be
nearly of the same density as the liquid in the cell,
the rate would be very slow indeed, though the

«/

diffusion would not cease till both solutions were of

250 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

the same density. In. Graham's own words, " the
diffusion must necessarily follow a diminishing
progression." Secondly, Graham found that tem-
perature affected the result, the rate increasing
apparently in direct proportion with the rise of
temperature. Thirdly, the rate of diffusion for
different salts was different. Each salt had its own
rate of diffusion. Thus, under the same conditions,
69 '32 grains of sulphuric acid diffused in the same
time occupied by 58 '68 of chloride of sodium, 51 '56
of nitrate of soda, 27 '42 of sulphate of magnesia,
26-74 of crystallised cane-sugar, 13 '24 of gum arabic,
and 3*08 of albumen. In another series of experi-
ments the following ratios were obtained : Chloride
of sodium, 100; hydrate of potash, 151 '9 3; ammonia
(10 per cent, solution), 70 ; alcohol, 75*74. " The most
remarkable result is the diffusion of albumen, which is
low, out of all proportion when compared with saline
bodies." A result of great interest is that " albumen
does not impair the diffusion of salts dissolved together
with it in the same solution, although the liquid
retains its viscosity." Thus, chloride of sodium, urea,
and sugar in solution were found to diffuse as freely
out of a solution of egg albumen as out of pure
water.

A series of experiments was also made with
solutions of two salts, which could be mixed without
combining. They were found to diffuse separately,
but usually the salt of lower diffusibility had its rate
of diffusion somewhat lowered, so that the difference
in the rates of diffusion of the two different salts was
rather increased by mixture. This seemed to Graham
to afford a method by which different salts might be
separated from one another. Thus potash salts are
more diffusive than soda salts, and if a mixture of
both be put into a diffusion cell the potash salts will
diffuse more rapidly into the surrounding water,

Chap. XXII.] OSMOSIS. 251

leaving soda salts in a more concentrated form in the
cell.

Salts can be even decomposed by diffusion. Thus
from a solution of bisulphate of potash placed in a
cell the sulphuric acid was found to diffuse to about
double the extent, in equivalents, of the sulphate of
potash, so that in the outer jar were found bisulphate
of potash and sulphuric acid, and a few crystals of the
neutral sulphate were seen to deposit in the cell.
Again, a solution of common potash-alum was de-
composed by diffusion into alum and sulphate of
potash. A simple way of effecting this diffusion
separation is to place in a cylindrical glass jar a
quantity of distilled water to make a liquid column
five or six inches high. Under this column, by means
of a fine pipette, introduce the mixed solution.
After several days the water may be siphoned off
in several layers, as it were. Less and less of the
least diffusive substance will be obtained, the higher
one goes in the liquid, the most diffusive substance
being able more completely to free itself from the
other as it ascends in the column of water above it.
Finally, it was observed that the diffusion of one salt
was not very sensibly affected if it was allowed to
diffuse into a solution of another salt instead of into
pure water, even though the two salts were isomor-
phous. That is to say, a solution of one salt will
diffuse almost as readily into a solution of another salt
as into water. The experiments were not made,
however, with any but dilute solutions of the other
salt in the outer jar.

Osmosis. — The laws of capillarity and of diffusion
have been applied to explain some very remarkable
phenomena first observed by Dutrochet, and described
by him in 1837. The elementary phenomena are
these : if a tube is closed at one end with bladder or
other animal membrane, and is, after being filled with

252 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

a saline solution, its lower end is plunged into dis-
tilled water, in a very short time the liquid rises
in the tube, and some of the salt may be detected in
the surrounding water. It appears as if a current
had been set up from water through the membrane to
the saline solution, and a second current from saline
solution to water through the membrane, the former
being greater, and consequently raising the level of
the fluid in the tube. To the first current Dutrochet
applied the term ENDOSMOSIS, to the second, EXOSMOSIS.

The question of two contrary currents will be
considered immediately ; first of all, however, the
facts of the interchange must be stated with a little
more detail. Dutrochet's early experiment is thus
described : "I took the cseca of young chickens : I
filled them with liquids more dense than water, such
as milk, a solution of gum, of the albumen of egg, etc.,
and after having closed them by a ligature I plunged
them into water. The intestines speedily became
swollen up and turgid by the introduction of water
into their interior ; their weight increased consider-
ably."* The general fact is, that if two dissimilar
liquids are separated by an animal membrane, mixture
can go on through the membrane. A porous diaphragm
may take the place of the membrane without inter-
fering with the process.

The instrument employed by Dutrochet for his
later experiments, and that usually employed, consists
of a glass tube R?/, having at one end a bell-jar-shaped
expansion J. The mouth of the jar is tightly closed,
usually with thin animal membrane m. Down the tube
is poured the saline or other solution, and the instru-
ment, termed an OSMOMETER (Fig. 116), is immersed
in a jar F containing distilled water, the water out-
side standing to a level x with the solution inside.

* Dutrochet, "Memoires pour servir a 1'histoire anatomique et
physiologique des vegetaux et desanimaux," p. 8. Paris, 1837.

Chap. XXII.]

THE ENDOSMOMETER.

253

1

f

I

^
j

*

:

Til-

First, it is to be noticed that the two liquids on
opposite sides of the membrane must be miscible.
Liquids that cannot mix when in direct contact with
one another can mix still less through
a septum. They, or at least one of them,
must be capable also of permeating the
membrane. Secondly, there are two ele-
ments in the process, that of the mixture
of the dissimilar liquids and that of the
increased volume of one of them.

The increase of volume does not always
take place on the side of the fluid of
greater density. If salt solution be on one
side and water on the other, the increased
volume will be on the side of greater
density, that of the salt solution ; but osuiometer.
when alcohol is on one side of the animal
membrane, and water on the other, the increased
volume is on the side of the alcohol, the side of
less density. The character of the membrane has
to do with the change of volume; for while, as just
noted, when water and alcohol are separated by an
animal membrane more water passes to the alcohol
through the membrane than alcohol to the water,
when water and alcohol are separated by a septum of
caoutchouc the alcohol passes in greater abundance
through the membrane, and the volume on the side of
the water is increased. Further, the mixture of the dis-
similar liquids can still be carried on when the change
of volume is forcibly prevented. This is proved
by an experiment described by Liebig. A short
wide tube is connected to a long narrow tube, the
narrow tube being vertical and the wide tube standing
out from it. The wide tube is filled with brine, and
closed with a piece of bladder. Down the vertical
narrow tube mercury is now poured, whose pressure
is exerted against the brine in the wide tube, and

254 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

causes it to pass through the membrane in fine drops.
When this is seen some of the mercury is removed,
till no more drops are seen to ooze through the mem-
brane. The wide tube is then immersed in a vessel
of water, the water being tinged blue. After the
lapse of some hours a blue stratum will be found
inside the wide tube, though no change has taken
place in the level of the mercury. After a long enough
time the brine and water will mix so that the quantity
of salt is uniform, and still the level of mercury will
indicate no change of volume. The pressure of the
mercury has prevented [change of volume, though it
has been unable to prevent mixture of the liquids.

A large share in the production of osmosis is
ascribed to capillarity. The septum being a porous
body may be considered as containing a large number
of capillary tubes. Some liquids are capable of wetting
certain capillary tubes, others are not. Those that
wet the tube can ascend in it, the others cannot. Of
those liquids that wet the same kind of tubes, one can
ascend the tube higher than others. The tube, that
is, has . a greater attractive force for one liquid than
another ; or one liquid is able to resist the attractive
force better than another. Thus, of two liquids on
opposite sides of a porous partition, one is capable of
permeating the membrane to a greater extent than the
other. The liquid that has the greater affinity for the
tube meets, in its course through it, the other liquid
advancing in the opposite direction, but advancing
with less force because of its less degree of affinity.
The greater force overcomes the less, and the one
liquid, consequently, occupies the pores of the mem-
brane, having ejected, so to speak, the other. But
now the element of diffusion enters into the question.
The force of capillarity can cause one liquid to enter
and occupy the pores from one side, but it cannot
cause that same liquid to flow out of the membrane

chap, xxii.] THE OSMOTIC CURRENT. 255

at the other side. But this liquid, having advanced
into the pores, comes into contact with the liquid at
the opposite side, and diffusion at once proceeds to
take place. The pores thus become occupied by a
mixture of two liquids, for one of which it has less
affinity than for the other. In consequence of this
mixture, then, a new supply of the liquid of greater
affinity will advance and displace the mixture, which
will flow out on the side of less affinity. As this pro-
cess will be constantly repeated, the volume of liquid
on the side of less affinity will continually increase.

This explains the endosmotic current to be due to
the unequal affinity of two different liquids for the
same membrane. It is, however, unnecessary to sup-
pose a similar current in the opposite direction pro-
ducing the exosmose. This can be explained, to a
great extent, by simple diffusion. For the two
liquids are in contact with one another through the
pores of the membrane, and consequently diffuse into
one another, independently of any aqueous current.
Thus the molecules of the salt solution gain access to
the water on the other side of the membrane. The
diffusion will be aided by the saline solution being in
the osmometer, and being, by means of the membrane,
kept high in the water, in which it would sink, if
free, because of its greater density. The water which
has gained the saline side of the membrane, because
of its less specific gravity, rises upwards in the
saline solution, and this prevents the accumulation of
a layer of water next the membrane on the saline side,
which, in spite of diffusion, would rapidly interfere
with the process ; while whatever of the saline solu-
tion has diffused down to the water side of the mem-
brane is, by its specific gravity, speedily caused to
sink ; and thus is prevented, on the water side, the
accumulation of a saline layer, which would interfere
seriously with farther progress,

256 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

This is one explanation offered to account for the
phenomena, an explanation, however, which is rejected
by Graham. It is supported by Liebig with many
ingenious experiments.

Graham shows, by a series of experiments with
sulphate of magnesia, that when the strength of the
saline solution is increased in the osmometer, the
quantity of water and salt that exchange places is not
uniform. He concludes that the exosmose, to use
Dutrochet's term, of the salt is not due to pure diffu-
sion, for then the ratio between the exchanging water
and salt should remain constant.

Etidosmotic equivalent is the term applied
to the weight of water that passes into the osmometer,
in exchange for unit weight of the salt that escapes
from it. It expresses the relation that exists be-
tween the increased bulk of fluid in the osmometer
and the diminished bulk of salt. Where the quantity
of water exceeds in bulk the quantity of salt the
osmosis is said to be positive ; where it is inferior, the
osmosis is said to be negative. End osmotic equivalent
was a term first applied by Jolly (1849), to whom the
idea of there being a relation between the bulk of
water and salt exchanged first occurred. His results
showed for 1 gramme caustic potash as much as
215-75 grs. of water, for 1 of sulphate of potash,
12-28 water, sulphate of magnesia, 11 '65, gum, 7'16,
chloride of sodium, 4-22, alcohol, 4'16. Since then
numerous observations have been made by German
observers, Harzer, Ludwig, Cloetta, Eckard, and
others, which show Jolly to have been mistaken in
supposing the equivalent to be constant. It varies
with the degree of concentration, with the tempera-
ture, and with other circumstances.

As the degree of concentration increases, an in-
creased quantity of water enters the osmometer; but
it is soon observed, that if the concentration passes

Chap. xxn. ] ENDOSMOTIC EQUIVALENT. 257

beyond a certain limit, the increase in the quantity of
water does not nearly keep pace with the increase of
the salt in solution. Thus Graham found that "the
osmose absolutely greatest is obtained with small pro-
portions of salts in solution." He adds, "osmose
appeared, indeed, to be peculiarly the phenomenon of
dilute solutions."

It may also be remarked that the nature of the
solutions employed will affect the osmosis by affecting
the membrane. Thus, a membrane capable of im-
bibing a certain quantity of water can imbibe a much
less quantity of alcohol, because of the contracting
effect the alcohol has upon the membrane. A con-
centrated saline solution has a similar effect. This
has been referred to already in discussing imbibition
(page 246). This is supposed to be due to the size of
the pores being affected. Thus, any substances which
would increase the density of the membranes would
also increase the endosniotic equivalent. The thick-
ness of the membrane, that is, the length of the pores,
similarly affects the result.

If, instead of having pure water on one side of a
membrane and a saline solution on the other, a saline
solution be on each side, osmotic action will go 011
under certain circumstances. If a solution of the
same salt be on each side, osmosis will occur if there be
a difference of concentration between the two. The
increase of volume is on the side of the concentrated
solution, and salt passes from it to the more dilute.
The action will diminish as the difference between the
two becomes less ; but if the difference be maintained,
the action will remain constant. Thus, by maintaining
the concentration of the one solution, and by constantly
renewing the dilution of the other, the greatest effect
would be obtained. The concentration of the one
being maintained, a stream of the dilute solution

O '

i lowing past the membrane would admirably fulfil the

R— 7

258 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

conditions. The stream of the dilute solution would
carry off with it any salt that had passed out of the
osmometer, and would renew the contact of the mem-
brane with dilute fluid. It is of importance to note
this in the physiology of absorption.

Where the solutions on different sides of the
membrane are of different chemical constitution, the
osmotic action depends on the chemical affinity of one
for the other. Thus the amount of action would be
greater between an acid and a base than between two
acids or two bases.

If a galvanic current be passed through water,
provided with a porous diaphragm, in such a way that
the positive pole is on one side and the negative on
the other, the quantity of fluid will decrease 011 the
former and increase on the latter side. When the
current is passed through different liquids separated
by a membrane, it is capable of altering the results
according to its direction. Thus, when the current is
from water to a saline solution, it results in an in-
creased quantity of water passing into the salt ; when
it is reversed, an increased quantity of salt passes to
the water, and the volume of liquid will be increased
on the water side ; the endosmotic current, that is,
will be inverted. Sometimes, also, under the influence
of an electric current, there will pass through the
membranes substances which would be incapable of
passing through under ordinary circumstances.

Crystalloids and colloids. — Graham divided
bodies into these two classes, according to their
diffusive power. Thus, he found a class of substances
possessing this power, though in very different de-
grees, and capable of assuming the crystalline form,
and to this class he applied the term CRYSTALLOID.
On the other hand, there is another class of bodies, of
extremely low diffusive power, distinguished by their
absence of power to crystallise, by the gelatinous

chap, xxii.j CRYSTALLOIDS AND COLLOIDS. 259

character of their hydrates, their inertness in ordinary
chemical relations, and their mutability. To these he
applied the term COLLOID.

One remarkable peculiarity of colloidal substances
is, that while themselves of extremely low diffusive
power, they afford a medium of diffusion. They
permit the highly diffusive substances to permeate
them readily, resist less diffusive substances, and en-
tirely cut off substances like themselves. Thus, a sheet
of very thin letter-paper, sized with starch (a colloid)
was formed into a tray and laid on the surface of
water. Into it a solution of cane sugar and gum
arabic was placed. In twenty-four hours three-fourths
of the whole sugar had passed through, while barely a
trace of the gum could be detected in the water. Of
colloidal substances, gum, albumin, gela-tin, and starch
are the chief examples.

A very interesting experiment, described by
Graham, shows how colloidal substances in mass are
nearly as good media for diffusion as water. " Ten
grammes of chloride of sodium, and two grammes of
Japanese gelatine, or gelose of Pageii, were dissolved
together in so much hot water as to form 100 cubic
centimetres of fluid. Introduced into an empty
diffusion jar, and allowed to cool, this fluid set
into a firm jelly, occupying the lower part of the jar,
and containing of course 10 per cent, of chloride of
sodium. Instead of placing pure water over this jelly,
it was covered by 700 cubic centimetres of a solution
containing 2 per cent, of the same gelose, cooled so far
as to be on the point of gelatinising, the jar at the
same time being placed in a cooling mixture in order
to expedite that change. The jar, with its contents,
was now left undisturbed for eight clays at a tempera-
ture of 10°. After the lapse of this time, the jelly
was removed from the jar in successive portions of
50 cubic centimetres each from the top, and the

260 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

proportion of chloride of sodium in the various strata
ascertained. The results were very similar to those
obtained in diffusing the same salt in a jar of pure
water." *

11 Diffusion of a crystalloid thus appears to proceed
through a firm jelly with little or no abatement of
velocity. With a coloured crystalloid, such as bi-
chromate of potash, the gradual elevation of the salt
to the top of the jar is beautifully illustrated. On
the other hand, the diffusion of a coloured colloid,
such as caramel, through the jelly appeared scarcely
to have begun after eight days had elapsed."

IMaSysis. — Graham thus perceived a method for
effecting separation by means of colloidal matter. To
this method he applied the term dialysis, and the ap-
paratus used he called a dialyser. This is made by
using vegetable parchment paper, which is unsized
paper altered by a short immersion in sulphuric acid
or in chloride of zinc. When wetted, the parchment
expands and becomes translucent. A piece of such
paper, wetted., is applied to a light hoop of gutta-
percha, two inches in depth and eight to ten inches in
diameter, so as to form a sieve. The paper ought to
rise up round the hoop, to which it is then firmly
secured by tying. Better still, a second hoop of
slightly greater diameter may be slipped up from
below, over the turned-up edge of parchment paper,
which it binds like a ring to the inner hoop. The
dialyser so prepared is seen to be sound by sponging
its inner side with water and finding that no wet
spots appear on the other side. If it be defective,
the defects are remedied by painting over with liquid
albumen, which is coagulated by holding over steam.

The solution to be dialysed is poured into the hoop
to a depth of not more than half an inch, and the

* Graham : "Liquid Diffusion Applied to Analysis;" Philos.
Trans. 1861, p. 199.

chap, xxii.] DIALYSIS. 261

dialyser (a, Fig. 117) is then floated in a vessel con-
taining a considerable quantity of distilled water. The
crystalloids will readily pass through,
but colloids will be perfectly retained.

Liebig described, years before, an
arrangement not dissimilar to this. " If

O

we tie moist paper over the open end
of a cylindrical tube, and, after pour-
ing in above the paper white of egg to
the height of a few lines, place that end of the tube
in boiling water, the albumen is- coagulated ; and
when the paper is removed, we have a tube closed
with an accurately-fitting plug of coagulated al-
bumen, which allows neither water nor brine to run
through. If the tube be now filled to one-half with

O

brine and immersed in pure water, the brine is seen
gradually to rise, and in three or four days it in-
creases by from a quarter to one-half of its volume,
exactly as if the tube had been closed with a very
thick membrane." *

The dialyser affords a means of purifying colloidal
matter from crystalloids. The mixture requires only
to be placed in the dialyser on water, and the crystal-
loids are separated out. Albumen may be purified in
the same way. It was urged by Graham that the
method of dialysis could with advantage be applied in
medico-legal cases to- the separation of such crystal-
loids as arsenious acid from organic solutions, such
as the contents of the stomach, blood, etc. Strychnine
and tartar emetic were separated in the same way.

While the dialyser shows albumen to be very
feebly diffusible, peptones are largely so.

Mechanism of absorption. — There can be no
doubt that osmosis plays an important part in ab-
sorption, even though it may not explain the whole
of the process. Let the conditions be observed. In
* Liebig " On the Motion of the Juices in the Animal Body," 1848.

262 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

the stomach and intestines there are two different
liquids, the chyme or chyle on the one hand, the
blood circulating through the intestinal capillaries on
the other. These two are separated by a thin
organic membrane consisting of the epithelium of the
inner surface of the intestinal canal, the thin walls of
the capillaries, and the small amount of adenoid
tissue between the two. These are the conditions of
osmosis. Observe, again, that the blood is an al-
buminous fluid, and that albumen is one of the most
sparingly diffusible of substances, requiring a very
large quantity of water to pass through the membrane
to its side before even a small portion of it passes
through to the other side. On the other hand, the
substances in solution in the chyme or chyle are
diffusible. Herein, also, lies the rationale of the
action of the various digestive fluids. Their action
is on starch, albumen, and fat, non-diffusible and
non-dialysable substances. Starch is converted into
sugar, and albumen into peptone, both capable of
diffusion and dialysis. It is hardly within the province
of this work to discuss the other elements in connection
with the absorption of fat. By the action of the diges-
tive fluids, therefore, the obstacles to osmosis, so far as
the fluid food stuffs are concerned, are got rid of. Not
only, therefore, are the conditions of osmosis present so
far as the animal membrane separating two different
liquids is concerned, but, owing to the character of
the liquids, the direction of the osmosis is readily
determined.

A remarkably interesting fact bearing upon the
absorption from the stomach is to be noted. Graham
showed by experiments that a small quantity of
dilute hydrochloric acid present in an osmometer
interfered greatly with the passage of the endosmotic
current. Thus the feeble acidity of the contents of
the stomach, acting in this way, will greatly interfere

chap, xxii.] PHYSICS OF ABSORPTION. 263

with any current from the blood outwards into the
cavity of the stomach, and so will act in the same
direction as the serum of the blood, in determining
the current from the stomach inwards to the
capillaries. Besides all this, in the case of the
stomach and intestinal canal are to be found all the
other conditions favouring the passage of fluid con-
taining substances in solution from the cavity of the
alimentary canal to the current of the circulation.
Thus it has been pointed out that, if the fluid on each
side of the membrane were stationary, the inter-
changes would speedily become feeble, because of the
approach of both fluids to the same condition. It
has been noted that a continual dilution of the liquid
towards which the endosmotic current was directed,
would tend to maintain the activity of the process ; or,
what is equal to the same thing, if a current of this
liquid flowed over the membrane this result would be
attained. Now the blood towards which the current
from the intestine sets is in continual circulation. It
no sooner receives by endosmosis solutions of sub-
stances from the stomach and intestines, than it whirls
them off in the current of the circulation, and a new
quantity of blood takes its place, maintaining the
degree of dilution that wrill aid the process. But,
again, the process will go on with greater vigour, the
greater the extent of the animal membrane, or, more
properly speaking, the greater the surface of liquid
towards which the current is directed.

Now this condition is fulfilled by the richness of the
vascular supply of the alimentary tract and by the
folds permitting o? increased extent of surface.

The greater the difference that exists between the
liquids, the greater will be the speed and amount of
absorption by endosmosis. Thus, if a saline sub-
stance in the liquid food is very deficient in the blood,
its absorption, other things being equal, will be effected

264 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

more rapidly than that of another existing already to
some extent in the circulating fluid. Thus variations
in the composition of the blood, variations which will
be determined by many circumstances, but very
specially by the matters that have been removed from
the blood to meet the demands of the tissues for
nourishment, will largely determine the rapidity of
the absorption. Among other things, if the blood
has been deprived of a considerable quantity of its
watery elements, its power of determining an osmotic
current towards itself will be largely increased.

Special instances may now be given which illus-
trate these facts, and the great bearing of the
general laws of osmotic action. They are common
illustrations, but have been so clearly put by Baron
Liebig, in a work already referred to, that a few
paragraphs will be incorporated here.

" If we take, while fasting, every ten minutes, a
glass of ordinary spring water, the saline contents of
which are much less than those of the blood, there
occurs, after the second glass (each glass containing
four ounces), an evacuation of coloured urine, the
weight of which is very nearly equal to that of the
first glass ; and after taking in this way twenty such
glasses of water, we have had nineteen evacuations of
urine, the last of which is colourless, and contains
hardly more saline matter than the spring water.

" If we make the same experiment with a water
containing as much saline matter as the blood (three-
quarters to one per cent, of sea salt), there is no
unusual discharge of urine ; and it is difficult to drink
more than three glasses of such water. A sense of
repletion, pressure, and weight of the stomach point
out that water, as strongly charged with saline
matter as the blood, requires a longer time for its
absorption into the blood-vessels.

" Finally, if we drink a solution containing rather

chap, xxn.] DIURESIS AND CATHARSIS. 265

more salt than the blood, a more or less decided
catharsis ensues."

That is to say, that in the first case there was
rapid passage of a large quantity of water into the
blood, and a consequent activity of the excretory
action of the kidney to throw it out. In the second
case, the proportion of salt being the same on both
sides of the animal membrane, though mixture took
place by diffusion, or otherwise, there was no marked
change in the volume of fluid on either side of the mem-

^ • •

brane. In the last case the proportion of saline matter in
the draught was proportionately so much greater than
that in the blood, that a current, the reverse of that
in the first case, was set up, determining a flow of
serum from the blood-vessels into the cavity of the
intestines. Simultaneous with that flow, there was of
course the passage of certain of the saline constituents
of the draught into the blood, but the prominent
occurrence was the outward flow of serum.

What has been said of the physics of absorption
from the intestinal canal, is equally applicable to
absorption from serous cavities, or from areolse of the
tissues, where practically the same conditions are
present. Variations in the rapidity of absorption by
different tissues can to a large extent be explained by
the facts that are known as to the differences in ab-
sorptive power of various membranes, depending on
their thickness, their density, and other similar cir-
cumstances.

Circumstances also may be present which seriously
impede the progress of the process of eiidosinosis. Even
as hydrochloric acid has been seen to have the power
to determine the direction of the current, to impede it
in one direction and to aid it in another, so there are
other substances which act inversely to hydrochloric
acid, and retard the process from the cavity, intestinal
canal, or other part, inwards to the blood. There are

266 PHYSIOLOGICAL PHYSICS. tchap. xxn.

substances which, by their action on the animal
membranes, alter or interfere with their affinity for
certain substances. Fat, for instance, would so modify
the attractive power of a tissue. Thus it may be that
certain substances taken with food, even though not

o

interfering with the digestion, would seriously retard
the process of absorption, and set up all the trouble-
some sensations of bad digestion.

Absorption by lymphatics may be considered as
presenting, so far as the physics are concerned, similar
features to that by blood-vessels.

The mechanism of secretion is much more obscure
than that of absorption. The laws of diffusion, and
of osmosis, are to a certain extent applicable, but
other elements enter into the consideration of the
question which physics are unable to account for.
That, however, to some extent conditions similar to
those of absorption are present, seems without doubt,
a thin animal membrane separating on one side the
current of the circulation, and on the other the fluid
of the gland.

TraiiKiidatioii or filtration must be carefully
distinguished from osmotic action. Experiments on
animal membranes show that under varying degrees
of pressure various solutions can be forced through
them. Thus a pressure of mercury will cause water
to pass out of a tube through a membrane closing its
mouth, the water gathering in minute drops on the
outer surface, and coalescing into larger ones. Brine
requires a greater pressure, and fat can be forced
through with a greater pressure still, while alcohol
requires even a larger amount. The readiness of
the passage of the fluid is thus dependent upon
the nature of the fluid ; and it depends also
upon the character of the membrane, being easier
when the membrane is thin, and not very dense.
Transu elation or filtration, therefore, is a passage

chap, xxii.] FILTRATION. 267

of fluids through membranes under pressure, the
membrane requiring to be permeable. This is entirely
different from the passage of fluids through a mem-
brane when the membrane is bathed by two different
fluids on opposite sides.

Elaborate researches on filtration have been made
by various experimenters. A large number of great
interest and importance are published by Dr. Wilibald
Schmidt of Voigtland, in Po^gendorfFs " Anna! en des
Physic uncl Chemie," for 1856 (p. 337), and 1861
(p. 337): Schmidt used animal membranes, specially
the pericardium of the ox. Briefly put, Schmidt's
more important results are, that each substance has
its own rate of filtration, that crystalloids filter more
quickly than colloids, that the amount of a colloid which
will filter through a membrane from a liquid containing
colloid in solution increases with the concentration of
the liquid in the filter, and with the pressure that it
diminishes with the weakness of the solution in the
filter, with diminished pressure, and with increased
temperature ; if the liquid containing colloid in
solution contains also crystalloids, the quantity of
colloid filtered through is less than it would have
been had the crystalloids been absent, and the filtrate
is richer in crystalloids than the liquid in the filter
(i.e. the presence of crystalloids diminishes the speed
of filtration of colloids). In regard to the filtration
of mixed solutions of crystalloids and colloids, Schmidt
corroborates previous results of von Wittich, that the
change in a liquid by filtration is a quantitative, not a
qualitative, one ; the filtrate, that is, contains the
same substances as the liquid on the filter, though in.
different proportions.

Transudation under pressure is seen in the living
body. Pressure on a vein, obstructing the course
of the blood, will cause in time filtration, owing to
the accumulating pressure behind the obstruction.

268 PHYSIOLOGICAL PHYSICS. [Chap. xxn.

Dropsies are of this nature. The backward pressure
communicated through the veins on lungs, liver, and
other organs, owing to obstruction to the onward
current of blood from the heart, are very good
examples of the amount of filtration that can occur
through the walls of the blood-vessels by great
increase of the pressure within them. This, again,
has nothing to do with exosmosis. As soon as the
obstacle to the current of blood is removed, and the
normal flow re-established, absorption comes in,
endosmosis from the infiltrated tissues arises, and the
poured-out fluid (serum) is taken up again into the
circulating stream. Whether or not transudation
under pressure has anything to do with secretion,
with such a secretion as that of the kidney, is another
question. It is generally supposed that into the
capsule of the glomerulus of the kidney such a filtra-
tion takes place. At least the physical conditions are
present, and the current of blood is separated from
the cavity of the glomerulus by the fine walls of the
vessels, and the epithelium of the capsule ; the
afferent vessel is large in proportion to the efferent
vessel. Owing to the difference between the two, and
the difference in favour of the incoming blood, the
pressure must be considerably increased in the tuft,
and thus filtration under pressure is a natural result.
How such filtration should permit the escape of saline
matters and retain albumen, it is not easy to explain.
If the agent were osmosis, the retention of albuminous
substance by the colloidal septum (the walls of the
vessels) is easily enough understood. But the con-
ditions in the kidney are not such as to favour
osmosis, at least so far as the glomerules are con-
cerned.

If we accept the process as one of filtration, and
take the results of Schmidt referred to, there seems
no rational ground for holding that in the kidney

chap. KX\\.\ FILTRATION ANDURINARV SECRETION. 269

water and salts in solution pass from the blood-vessels
into the dilated extremities of the uriniferous tubules,
but that albumen does not pass. This would imply a
qualitative change in the fluid by filtration, which is
contrary to all the results of accurate observation of
the physical process. If we accept the filtration
process, then, we must admit the passage of albumen
through the glomeruli into the tubules. It is to be
observed, however, that the conditions in the kidney
(only a moderate pressure in the blood-vessels, and the
blood being a saline solution) are just the conditions
fitted to make the quantity of filtered albumen small.
Yet the facts seem to confine us to the conclusion"
that the process in the glomerules of the kidney is
one by which all the constituents of the blood plasma
transude, though in largely different proportions from
that in which they exist in the blood. This view is
not at present popular among physiologists, though
it has been suggested by von Wittich, Kiiss, and
others, and that mainly because of the difficulty of
accounting for the absence of the albumen in normal
urine. It does not belong to this work to discuss
that difficulty, though it may be mentioned that the
difficulty is, to some extent, met by the view that the
active cells of the renal tubules absorb the albumen,
and pass it back into the surrounding lymphatics,
a view in favour of which, the author believes, much
can be said.

270

rt W3.

PNEUMATICS.

CHAPTER XXIII.

TIIK PHYSICS OF GASES AND THEIR APPLICATION IN

RESPIRATION.

THE gaseous state,— Gas is a fluid, and possesses
those properties that have been seen to belong to
other fluids and to liquids. Chief among these is the
mobility of the particles of which gas is composed.
It is, of course, this extreme mobility of the gaseous
particles that permits movement in air to be so
readily effected. Like liquids (Pascal's law), gases
transmit pressure equally in all directions, and so a
body surrounded by gas is pressed upon equally on all
sides. Gases, however, differ from liquids, in their
greater elasticity and compressibility.

The elastic force or expansibility of gas is
due to a repulsive action exercised between the
molecules of the fluid. In virtue of this property,
gases always tend to expand and fill the space in
which they are placed ; and they exert, in con-
sequence, pressure on anything which contains them,
and offers itself as an obstacle to their continued
expansion. This is easily proved by partly tilling a
bladder with air, and placing it under the receiver of
an air-pump. As soon as one begins to exhaust the
air from the receiver the air within the bladder finds
itself unopposed by air outside, and its pressure is
thus sufficient to distend the bladder. As the
exhaustion goes on the bladder will become more
and more inflated, till the resistance, developed in the

chap. xxin. j COMPRESSIBILITY OF GASES. 271

walls of the bladder by the stretching, comes to be
equal to the elastic force of the gas, when further
dilatation will cease. As soon as air is permitted to
enter the receiver the bladder becomes restored to its
former size. Owing to their constant tendency to
expand, gases have no definite volume.

Compressibility of gas. — A liquid has been
seen to be very little compressible. The slight com-
pression, however, to which liquid is subject develops
in it a very great force of reaction. Gas, on the other
hand, is readily compressible, and may be reduced to
one half its volume without developing a force greater
than that of the atmosphere. The compressibility of
gases is easily shown by means of a syringe closed at
one end and fitted at the other with an air-tight
piston. By pressing sufficiently on the piston, the
volume of air in the syringe may be reduced very con-
siderably. On removing the pressure, the reaction of
the gas will force out the piston.

As gas is reduced in volume by pressure in this
way, it exerts pressure on the vessel or tube contain-
ing it, which increases as the volume diminishes.

^7 7

This is expressed by a law discovered independently
by Boyle and Marriotte, and called by their name.

BoyJe's or Marriotte' s laiv. — According to it,
the pressure of a given quantity of gas increases as its
volume is diminished, and vice, versa. Its pressure,
that is, is inversely proportional to its volume. Since
diminished volume means increased density, the law
may also be expressed by saying that the pressure of
a given quantity of gas is directly proportional to its
density. The experiments by means of which this
law was proved were made with an apparatus repre-
sented in Fig. 118. It consists of a bent tube, with a
short limb closed at its extremity A, and a long limb
open ate. Attached to both limbs is a scale, the divisions
of which mark equal capacities of the parts of the tube

272

PHYSIOLOGICAL PHYSICS. [Chap. xxui.

they divide off. Into the long tube a small quantity
of mercury is poured, the tube being inclined. The

mercury tills the bend B, and is
poured in till it stands at zero in
both limbs. The mercury thus
cuts off the air enclosed in the short
limb from communication with the
outside, and the equal level of the
mercury in both limbs shows that
the pressure exerted on the enclosed
air is equal to the external pres-
sure, i.e. the pressure of the atmo-
sphere. Mercury is then poured
in till, by its pressure, the enclosed
air is reduced to half its volume AD.
The added mercury gives the in-
crease of pressure. The air is
found to be reduced to half its
volume when the original pressure
is doubled, to one- third its volume
when the original pressure is
trebled, and so on ; that is, pressure
is inversely proportional to volume.
Other experimenters, Dulong and
Arago, increased the pressure 27
times, and found the law to hold

Sn

p«~

•jo-

r

00 -

5o-_

io —

JO -

-

A

10 —

ftp

~

Dn:

tl ' —

*

! "
-O

H ,?

Is

w^

B

m

good.

But Regnault showed that

it was not rigorously true, and that

air, nitrogen, carbonic acid, and
ittj oxygen diminish in volume with

increasing pressure more quickly
Fig' nSu-Marriotte's than Marriotte's law allowed, while

hydrogen is less compressible with
increasing pressures.

Unequal compressibility.— - Different gases
are unequally compressible. This was shown first of
all by Despretz in 1825, who took several cylindrical

Chap, xxni.] DENSITY OF GASES. 273

tubes of the same length and capacity, closed at one
end. Each tube contained the same volume of gas,
and they were all plunged into a vessel filled with
mercury. This was then placed in a stout glass
cylinder filled with water and fitted with a screw piston.
The pressure exerted by the piston was communicated
through the water to the mercury, which was thus
forced up the tubes, and compressed the gas. The
different heights of the columns of mercury in the
different tubes showed the different compressibility of
the various gases. Though the difference between
any two gases is very slight, yet each has its own
degree of compressibility.

Weight of gases. — That gases have weight is
easily proved by suspending a globe, exhausted of air,
from the scale of a balance and counterpoising it. On
permitting air or other gas to enter, the beam will go
down to the globe side, indicating increased weight.
A litre of dry air at 0° C. is 1*293 grammes. A litre
is 1,000 cubic centimetres, and 1,000 cubic centi-
metres of water weigh 1,000 grammes. So that the
weight of air is to the weight of water as 1-293 is to

1,000 ; that is, the ratio is = ~. Water is thus

773 times heavier than air. Hydrogen weighs only
0-089 gramme per litre, oxygen, 143, carbonic
acid, 1-97.

The density of a gas can be measured in a
similar way to that of liquids. Its ratio to that of
water has been shown to be 0 -00 1 2 9 3. A given volume
of gas may then be considered as a volume of a
liquid of very much less density than water. It is,
then, understood how laws, applicable to liquids, are
similarly applicable to gases. Suppose we have a
mass of gas, and a body somewhere within the mass.
Just as in the case of liquids (page 180), the body will
be pressed upon on all sides. If we consider the mass
s— 7

274 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

of gas as made up of layers, then the topmost layer of
gas will exert a pressure equal to its own weight ; the
second layer will exert a pressure equal to its own
weight plus the pressure of the layer above it. Thus
the body will come to support a pressure equal to that
exerted by the layers above it over an extent of
surface equal to its area. In other words, the weight
on the body will be equal to a column of gas whose
base is the surface of the body and whose height is the
distance between the body and the surface of the
gaseous mass. Just as in liquids, also, the body will
be pressed upwards by a force equal to the weight of
gas which it displaces. The weight of a body in air,
therefore, is not its true weight, but only the differ-
ence between the true weight and the weight of the
displaced volume of air.

Atmospheric pressure. — A mass of air (the
atmosphere) completely surrounds the earth. In
accordance with what has been already stated, it will
exert" pressure in all directions, and the pressure will
vary according to the thickness of the mass. The
pressure exerted by the atmosphere on any body will,
therefore, dimmish as the body rises in the air. The
pressure on the top of a hill is less than in the valley.
Gas is compressible, and since the lowest layers of the
atmospheres will sustain the pressure of all the layers
above them, they will be very much compressed arid
consequently more dense. The density will thus be
greatest on the surface of the earth, and will diminish
with the distance from the surface. Suppose the
density had been uniform, then a layer of air about
five miles in thickness encircling the earth would give
a pressure equal to the ordinary atmospheric pressure.
This height (five miles) is called the height of the
homogeneous atmosphere. The constantly diminishing
density as one ascends necessitates a much greater
thickness of layer to give the pressure. The real

Chap, xxiii.] ATMOSPHERIC PRESSURE. 275

extent of the atmospheric layer is supposed to be
between 50 and 100 miles. The pressure, then, on a
square inch of the earth's surface, let us say, will be
equal to the weight of the column of air which it
supports ; it is about 14 '7 pounds.

The effects of the atmospheric pressure are easily
made manifest. Let a glass cylinder be covered over
at one end with a piece of bladder. Place the open
end with greased edges on the plate of an air pump ;
let it be pressed close on the plate to prevent the
passage of air. After working the pump a little, the
air will be exhausted from within the cylinder, and
the bladder will be bearing the full weight of the
atmosphere on the outside without any counterbalan-
cing force within. It will yield, become concave, and
finally burst with a loud report. Let the same
cylinder be put on the plate of the air pump, but not
over the pipe by which the exhaustion is made, and
let it be covered by a globe. On exhausting the
globe of air, the cylinder containing air will be in a
space devoid of it, and the air by its elastic force will
cause the bladder to bulge outwards.

The pressure of the atmosphere might be estimated
by the height of the column of water which it would
support. If a long glass tube closed at one end were
exhausted of air, and the open end plunged into a
vessel of water, which was open to the air, the sur-
face of the water would bear the atmospheric pressure,
while the surface within the glass tube would be under
no pressure, the tube being free of air. Consequently
the water would rise in the tube until the height of
the column of water above the level of the water in
the vessel produced a pressure equal to the atmo-
spheric pressure, when equilibrium would be restored.
The height of such a column would be thirty-four
feet. Suppose mercury were used instead of water,
then since the density of mercury is to the density of

276 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

water as 13-59 to 1, the height of the mercury column,
which would balance the atmospheric pressure, is
]3'59 times less than 34 feet, that is nearly 30 inches
of mercury, in French measure exactly 760 milli-
metres. This method of measuring the weight of the
atmosphere is due to Torricelli, a pupil of Galileo.

The Torricellian experiment is performed by
taking a glass tube about 3 feet long, and a quarter of
an inch internal diameter, closed at one end. The
tube is completely filled with mercury ; the open end
is then closed by the thumb, the tube inverted in a
vessel of mercury, and secured in the
vertical position. On withdrawing the
thumb, the mercury sinks a short distance
in the tube, leaving a vacuous space above,
and after a few oscillations remains at
a certain height, which is determined by
the atmospheric pressure at the place.
The tube, therefore, becomes a measurer
of the pressure at the place, a BAROMETER.
Should the pressure increase, the mercury
rise in the tube, there being no ail-
above to hinder its ascent ; if the pressure
Fig. 119.— Tor- diminishes, the mercury column will di-
periiaent. minish in height. At the sea level the
height will be 760 millimetres of mercury,
and in proportion as we ascend in the atmosphere
the mercury column becomes lower.

It has to be noted, however, that besides the
height of the mercury column the temperature at the
time of observation must be taken into account. For
the density of the mercury will vary with the tem-
perature, diminishing with increased temperature and
increasing with diminished temperature. At the
same place, therefore, the column will stand higher
with a high than with a low temperature, though the
pressure does not vary. Accordingly the standard

chap, xxiii.] BAROMETERS. 277

temperature is fixed at 0° C.5 and at this temperature
at the sea level the barometric height is 760 mm.
For higher temperatures corrections must be made.
Through the action of capillarity, a convex meniscus
(page 242) terminates the mercury column, and this,
modified with the height of ascent of the mercury,
requires also correction in very rigorous measure-
ments.

At 0°C., then, the pressure of a column of mer-
cury 760 mm. high is called the pressure of one atmo-
sphere. A pressure that would be equal to that exerted
by a column of mercury twice this height is called the
pressure of two atmospheres ; a pressure equal to
thrice the height is known as the pressure of three
atmospheres, and so on. There is thus a standard
afforded for the determination of pressures.

Barometers. — The simplest barometer is the
Torricellian tube fixed vertically in its vessel of
mercury. The mercury requires to be rid of air and
moisture by boiling, otherwise the Torricellian vacuum
would become occupied with vapour, which would
interfere with the rise of the mercury column. The
cistern barometer is a modification in which the vessel
containing the mercury is closed, and is supplied with
a bottom, movable by a screw for adjusting the level
of the surface. In the syphon barometer the glass
tube is bent, so as to have a short and a long limb.
The upper part of the long limb is sealed, and encloses
the vacuous space, the short limb takes the place of
the cistern, and it is open at the upper part. The
difference of levels in the two limbs gives the height
of the mercury column. The wheel barometer is just
the syphon barometer having a float on the surface
of the mercury in the short limb. A thread attached
to the float passes over a little wheel, and carries at
the other end a weight to counterpoise the float.
The rising and falling of the mercury column by

278 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

means of the float and thread move the wheel, which
has attached to it a hand travelling over a dial, and
indicating the variations. In the aneroid barometers
mercury columns are discarded, and a metallic box,
partly exhausted of air, is employed. Variations of
pressure cause movements of the top of the box, which
are transmitted to levers, and move an indicator.
The position of the indicator is determined for
different pressures by means of the mercury column,
and these positions are then marked on a dial over
which the indicator moves.

Effects of atmospheric pressure. — It has
been seen that into a tube from which the air is ex-
hausted, and in which the atmospheric pressure, there-
fore, is reduced to zero, a column of mercury will rise
to 30 inches, and a column of water to 34 feet. Other
fluids will also rise to a height in the inverse ratio of
their density. It is obvious that there is thus afforded
a means of raising water or other liquid from a low
level to a higher one. It is equally obvious that there
is a limit to the height to which the liquid
can be raised by exhaustion of the air ;
that, in fact, it will rise only to the height
sufficient to produce a downward pressure
equal to the upward pressure of the
atmosphere, a height which, as already
said, varies with the density of the liquid.

The suction pump is an application
of these facts. It consists essentially of a
barrel or cylinder fitted with a piston

(Fig. 120). The lower part of the barrel is

Fi<* 120.— continued into a tube which dips into the

fraction water to be pumped. When the piston is

pulled from the lower end of the barrel to

the upper, the space it leaves below is devoid of air, and

the water rises in the tube, filling the barrel, and closely

following the piston upwards. When the piston

chap, xxin.] THE PIPETTE AND SYPHON. 279

descends again the water is prevented passing back-
wards by a valve c, while by the opening of other
valves A and B it is permitted to pass through the
piston, and is lodged in the upper part of the barrel.
The re-ascent of the piston causes the piston valves
to close, and the water is therefore driven out through
the outlet tube.

The pipette also illustrates the same principles
(Fig. 121). It is a glass tube blown out in the centre
into a bulbous portion. One end is pro-
longed into a fine point, the other is the
full diameter of the tube, and is evenly
ground. By applying the mouth to the
wide end and sucking, the air is rarefied,
and if the lower end be dipping in liquid,
the liquid rises in the tube, and into the
bulb. As soon as the desired quantity is
drawn into the bulb, the upper end is
quickly covered with the wet finger or
thumb. The air is thus prevented from
entering, and the pipette can be lifted out

O' a1

of the fluid without any of its contents The Pipette,
escaping. Any desired quantity can be per-
mitted to escape by slightly moving the finger to permit
the entrance of a little air. By this means part
of the liquid in a vessel may be removed without
disturbing the remainder.

The syphon consists of a tube open at both ends
but curved on itself, so as to have two limbs. It is so
placed that one limb dips into the liquid to be removed,
and the other discharges at a lower level (Fig. 122).

By suction at the lower end the tube is first of all
filled with the liquid, and then under the influence of
atmospheric pressure, and the difference of levels, the
flow will continue unless air be permitted to enter, or
the levels become equal.

Where the liquid to be withdrawn would be

280

PHYSIOLOGICAL PHYSICS. [Chap. xxm.

injurious if it got into the mouth, the suction may
be applied by means of a side tube to the syphon,
the lower opening being kept closed
till the tube is filled, or the tube may
be filled before immersion in the
liquid.

It is to be noted that for water the
suction tube of a pump, or the ascend-
ing limb of a syphon, should not be 34
feet above the water level, for beyond

Fig. 122.—
byphou.

that height the water cannot be

pumped. For other liquids the varia-
tion in the height depends on the density.

The air pump is an instrument for diminishing
the atmospheric pressure by removing the air enclosed
in a space; it is shown in Fig. 123. It was in-
vented by Otto von Guericke, in 1650. It consists
of a cylinder fitted
with a piston. From
the cylinder passes a
tube, which opens on
a brass plate. The
plate supports a bell
jar (the receiver), the
lower edge of which is
carefully ground and
smeared with grease, so
as to be closely united
with the plate. When
the piston is raised,
air is drawn out of the
receiver to occupy the
space left void by the piston. A valve opens so
as to permit air to pass from the bell-jar. In the
piston is an opening guarded by a valve, but its
direction of opening is such that the atmospheric
pressure keeps it closed during the ascent of the

Fig. 123.— Tlie Air Pump.

Chap, xxiii.] THE AIR PUMP. 281

piston, When the piston descends the pressure closes
the receiver valve, and prevents the air being driven
back, and it, at the same time, opens the piston valve
and permits the. escape of the air outwards ; when the
piston again ascends its valve closes, and a further
quantity of air is withdrawn from the receiver. With
each movement of the pump only a fraction of the air is
removed, the gas becoming more and more rarefied,
because, owing to its elastic property, it expands to
occupy the space. Writh each stroke the quantity
removed, therefore, diminishes, and a perfect vacuum
can never be produced in this way, because it is
always just a fraction of the rarefied air that is with-
drawn. There is a limit, then, which cannot be passed.
It will be readily understood, that, as the rarefaction
proceeds, the two sides of the piston will be under
different pressures ; the outer side under atmospheric
pressure, and the inner side under the pressure of the
rarefied air, the former greatly preponderating. Every
upward movement of the piston will be made with in-
creasing difficulty against the atmospheric pressure.
This is overcome by using a two-barrelled pump, (as
in the figure) the pistons being worked by a horizontal
lever, so that one is up when the other is down. The
hindrance by pressure to the upward movement of
one is balanced by the aid to the downward movement
of the other. To indicate the degree of rarefaction one
limb of a bent tube containing mercury, opens into
the tube connecting barrel and receiver, the other
limb bein£ closed. The difference in the level of

O

the mercury in the two limbs indicates the pressure ;
the more nearly the two columns of mercury are of
the same level, the more nearly perfect is the vacuum,
for the elastic force of the gas acting from the receiver
would force the mercury down in the open limb
and up to the top of the closed limb. Consequently, as
this elastic force is reduced by the rarefaction of

282 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

the gas the mercury falls in the closed limb and rises
in the other.

Spreiijfel's air pump procures a better vacuum
than the barrel pumps, though it takes a considerably
longer time. It consists of a funnel A, projecting, and
sealed into, a glass tube cd, not exceeding one-tenth of
an inch in diameter, and longer than
the barometer tube. The lower end
of the tube dips into an open glass
vessel B. A branch from the upper
part of the tube leads off to a receiver n,
which is to be exhausted. Mercury is
poured into the funnel, and falls from
it down the tube. In doing so it
carries air with it, drawn from the
receiver ; a series of short columns of
mercury, separated by air spaces, thus
move down the tube. The mercury being
Fig. 124.— Spreu- caught in the open vessel below, soon
gel s Pump. covers the lower opening of the tube and
prevents air entering from below. As the exhaustion
becomes more and more complete the columns of mer-
cury become longer, and the air spaces less. At
length a regular column of mercury stands in the tube
to nearly the barometer height, and if mercury be now
allowed to fall from the funnel 011 to the mercury
column, no air is enclosed, and a hard metallic sound
is produced by the fall.

The effects on the human body of atmo-
spheric pressure are various. On every square inch of
surface the pressure is 14*7 pounds. This pressure is
not felt because it is exercised in all directions, and
over all is, therefore, in equilibrium. It plays, never-
theless, a very important part in certain necessary
processes. The entrance of air into the lungs, and
exit from the lungs, are dependent on variations of
pressure. The cavity of the chest is air-tight, having

Chap, xxiii.] ATMOSPHERIC PRESSURE. 283

no communication with the outside air. Suspended in it
are the two lungs, which may be considered as two sacs
communicating by means of the bronchial tubes and
trachea with the external air, there being no connec-
tion between the cavities of the sacs and that of the
thorax. In what may be called the normal position,
the cavity of the chest is completely filled with the
lungs, heart, and other thoracic organs ; and there is
equilibrium. The walls of the lungs are thus sub-
jected to two forces ; one, that of the atmosphere, from
without ; the other from the cavity of the thorax, from
within ; two equal and opposite forces, that is. By
the descent of the muscular floor of the chest (the
diaphragm), and by the raising and rotation of the ribs,
the extent of the cavity is increased, the thoracic
organs are no longer sufficient to fill the enlarged
thoracic chamber, and there is thus a tendency to
create a void space. The walls of the lungs will no
longer be in equilibrium by two equal and opposite
forces, for the force acting from the cavity outwards is
diminished. Consequently the atmospheric pressure
gains the mastery and distends the lungs, till their in-
crease in size corresponds to the increase of thoracic
space, when equilibrium is again restored. Thus, in-
spiration is effected. But the increased size of the
chamber has been produced by muscular effort, and as
soon as that effort is over the elastic reaction of the
thoracic walls, etc., comes into play ; the diaphragm
ascends, the ribs proceed to assume their former posi-
tion. The play of these forces, all tending to reduce
the size of the chest cavity, is too much for the
atmospheric pressure. The state of affairs is thus
reversed, for the greater force is now acting on the
wall of the lungs from within outwards. The
diminishing size of the chest cavity, aided by the
elasticity of the lung tissue itself, reduces the volume
of the lung, air is thus expelled, and the act of

284

PHYSIOLOGICAL PHYSICS. [Chap. xxm.

respiration accomplished, when again equilibrium is
restored, only, however, to be again disturbed, after a
short pause, by a re-enlargement of the chest cavity,
and a repetition of the old process.

Though the phrase chest cavity is used, it must be
noted that there is no actual space between the chest
walls and their contained organs. The lungs distend
pari passu with the enlargement of the chest, and
consequently a space is not actually produced.

The distension of the lungs, then, producing inspi-
ration is simply due to diminution of pressure in the
chamber in which they are suspended. Reference to
page 270 will show that rarefaction of the air in a
receiver will cause a bladder contained in it, and
partially filled with air, to become expanded by the
elastic force of the air it contains. Much more will
such distension occur when the bladder is not shut
off from the outer air. Fig. 125 shows how the pro-
cess of inspiration and
expiration may be me-
chanically simulated.

It represents a
glass flask with a
bottom of leather 4
movable by a knob
5. The wide mouth
of the flask is closed

Fig. 125.— The Mechanism of luspira- by ail air-tight-fitting

Expirat cork, through which

passes a glass tube. The tube divides into two
branches, the extremity of each having attached to it
an indiarubber ba^. The ba«}s have 110 communication

O O

with the air in the flask, but communicate with the
air outside by means of the tube. At one side of the
flask is a mercury manometer 3 open to the air in
the flask. At the other side a small portion of the
wall 6 is formed of indiarubber. In the position

Chap, xxni.] MECHANISM OF RESPIRATION. 285

indicated by the left-hand figure the walls of the
indiarubber bags are pressed 011 from without by the
atmospheric pressure, and from within by the pressure
in the cavity of the flask. Those two forces are in
equilibrium, as indicated by the level of mercury in
the two limbs of the manometer, and the bags are
collapsed. Now let the leather bottom be pulled
down by the knob 5, the air in the flask is at once
rarefied to fill the increased space ; pressure is, there-
fore, lowered, as indicated by the rise of mercury in
the limb of the manometer next to the flask, and by
the forcing inwards of- the indiarubber part of the
opposite wall. But this diminution of pressure does
not continue, for the atmospheric pressure being
constant, and opposed by a diminished resistance,
distends the indiarubber bags. As they distend the
increased space gets occupied by their increased
volume, and the diminution of pressure gets less and
less, as indicated by the fall of the mercury towards
its former level. When the bags are sufficiently dis-
tended equilibrium is re-established, the mercury is
again equal in both limbs, and the indiarubber part of
the wall is no longer pressed inwards. If now the
leather bottom be forced upwards, a rapid rise of
mercury in the off-limb of the manometer, and a
bulging outwards of the indiarubber wall, indicate
increase of pressure in the cavity of the flask. But
at once the indiarubber bags, pressed upon, become
diminished in size, and expel the air they contain.
Thus the increase of pressure is no more constant
than was the decrease. As the bags diminish in
volume the mercury falls in the ofi-limb, till, when they
have been restored to their former size, the level is
again what it was at first. Thus alternate distension
and collapse of the indiarubber bags can be produced
by variations of the pressure in the cavity of the
flask, just as the alternate distension and diminution

286 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

in size of the lungs are produced by variations of
pressure in the cavity of the chest.

The variations may be shortly expressed as diminu-
tion of pressure on inspiration, and increase of pressure
on expiration. They will produce effects on other
thoracic organs. Notably will they affect the circula
tion of the blood. For the diminution will aid the
flow from the large veins into the heart, while it will
interfere with the outward now from the heart into
the arteries, the result being favourable to the venous
circulation.

What the constant effects of atmospheric pressure
are, becomes very apparent when one ascends a consider-
able distance from the sea-level, either by means of a
balloon or by climbing a high mountain. The pressure
gradually diminishes as one ascends, and the air
becomes rarefied. The first effects are quickening of
the respirations, because, the air being rarefied, less
oxygen is taken in with every inspiration, and to get
the ordinary amount more frequent inspiration is
necessary. The heart's action is also increased. If
the ascent be continued a sense of fatigue is experienced,
dyspnoea and venous congestions occur ; and, owing
to the pressure from within remaining constant, while
the external pressure is greatly reduced, the thin walls
of the capillaries may give way, and haemorrhage take
place, especially in situations where, owing to the
looseness of the texture, external support to the
vessels is least, as in the walls of the lungs, the
mucous lining of nose and air-passages, lips, etc.

Still further, the close apposition of bones connected
at the joints is largely effected and maintained by the
atmospheric pressure, without the need of muscular
effort. The brothers Weber showed this by cutting
all the muscles and ligaments surrounding the coxo-
femoral articulation and the capsule of the joint, but
the head of the femur still remained closely applied to

Chap, xxiii.] LIQUEFACTION OF GASES. 287

the walls of the cotyloid cavity. As soon as a hole
was drilled through the pelvic wall into the depth of
the cavity the femur fell away.

Cupping- instruments exhibit very well locally
the effects of diminished pressure. A small glass cup,
exhausted of air, is closely applied to the skin, and at
once the part bulges out into the cup, becomes red
and congested by the afflux of blood. If the part
have been previously scarified a copious flow of blood
is produced. Dry cupping is the phrase applied to the
use of the instruments without scarification. It pro-
duces merely a local determination of blood. The
exhaustion is accomplished by moistening the inner
surface of the cup with spirit, setting fire to it, and
immediately applying it ; or a cup may be used, con-
nected with an aspirator, for withdrawing the air after
it is applied.

Liquefaction of gas. — It has been observed
that gases resemble liquids in many respects, but differ
from them in the mutual repulsion of their molecules,
in virtue of which they tend to expand and fill what-
ever space may enclose them. Diminution of pressure
permits the expansion to take place, and increased
temperature encourages it. On the other hand,
increased pressure and diminished temperature would
both alike hinder the rarefaction and produce a con-
densation. It might be expected that if the pressure
could be sufficiently increased and the temperature
sufficiently lowered the condensation might be so
great as to reduce the gas to the liquid state. Both
increased pressure and diminished temperature can
liquefy certain gases, a combination of both being
often used. Thus sulphuric acid gas, carbonic acid
gas, and nitrous oxide gas were early liquefied by
pressures varying from 2| to 45 atmospheres ; but till
recent years air, oxygen, hydrogen, nitrogen, nitric
oxide, and marsh gas had resisted. Lately, however,

288 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

oxygen has been liquefied by a pressure of 300
atmospheres, aided by a very low temperature,
obtained by the evaporation of liquid sulphurous
acid and solid carbonic acid, and other means.
Nitrogen required a pressure of 200, and hydrogen
of 280 atmospheres.

DIFFUSION AND ABSORPTION OF GASES.

Diffusion of gases. — When two gases are
placed in contact with one another at the same tem-
perature and pressure, they mix rapidly until the one
gas is uniformly diffused throughout the other. The
diffusion is quite independent of gravity, for it will
occur between a mass of carbonic acid gas below and

O

a mass of hydrogen above, the heavy gas rising up
into the light one, and the light one diffusing through-
out the heavy one below. All gases possess this
property in virtue of their tendency always to expand
and fill any space open to them. One gas will not
expand into a space occupied by the same gas, if the
temperatures and pressures are the same. But when
the gases are different diffusion goes on just as if the
gases were expanding into a vacuum, only with
diminished speed. In a mixture, according to D ALTON'S
LAW, each gas exerts its own pressure as if it were the
only gas present, a pressure dependent upon its
volume ; and thus the total pressure exerted by the
mixed gases will be the sum of the pressures due to
each gas separately. The pressure exerted by each
gas is called the PARTIAL PRESSURE of each gas in the
mixture, and its amount is calculated by multiplying
the total pressure by the number representing the
amount of gas in 100 volumes of the mixture. Thus,
oxygen being present in the atmosphere to the extent,
roughly, of 21 volumes in 100, and the atmosphere
being at 760mm. pressure, the partial pressure of
O is 760 x AV

chap, xxiii.] DIFFUSION OF GASES. 289

Gases are found to differ from one another in the
rate with which they diffuse. Experiments made by
Graham showed the diffusive power to vary with the
density, the less dense gas diffusing more rapidly than
the denser gas, the gases diffusing in the inverse
proportion to the square roots of their densities.
Thus, the ratio of the density of hydrogen to that of
oxygen being as 1 : 4, their diffusive rates will be as
4:1. Two gases being placed in contact with one
another, experiment has shown that the mixture will
be more rapid as the difference of density between
the two is greater. This is to be expected from what
has been already seen to apply between two liquids of
different densities in contact. The greater the differ-
ence of densities the more rapid is the rate of
exchange, and as the two liquids come to approximate
more nearly to the same condition the rate of exchange
is lowered.

The physiological application of these laws
is apparent in respiration. About thirty cubic
inches, of a gas containing O, N, and C02 in certain
proportions in mechanical mixture are drawn into the
trachea and upper air-passage with each inspiration.
These air passages, as well as those more deeply
situated in the lungs, and the air cells into which they
ultimately open, are already occupied by a gaseous
mixture containing the same gases in different pro-
portions. Owing to the expiration immediately suc-
ceeding the inspiration, a certain quantity of the
inspired air, calculated at a third, is at once expelled,
but the remaining two-thirds have already begun to
mix by diffusion with the air already in the lungs.
Now, the air already in the lungs contains an amount
of O that gradually diminishes towards the air cells,
where it is least ;• and similarly the quantity of CO2
gradually increases towards the air cells, where it is
greatest. Thus, though the two-thirds of the inspired

T— 7

290 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

air, as it penetrates more and more deeply into the
bronchial tubes, loses its O and receives more and
more CO2, its rate of diffusion is not impaired, since
with its advance it is meeting a continually increasing
density of mixed gases. Thus, from the upper air-
passages down to the air cells, a gaseous exchange
is constantly going on between the less dense mixture
of inspired air and the denser mixture of the air
occupying the lungs, fresh inspirations maintaining
the lower density of the air in the upper parts ; and
the exchange going on between the blood circulating
in the walls of the air cells, and the air occupying
the cells themselves constantly maintaining the density
in the deeper parts. The application of physical laws
to this exchange between blood and air will be dis-
cussed later.

Diffusion of gases through porous septa.
— Gases have been found able to pass through porous
septa. Elaborate experiments have been made both
by Bunsen and Graham as to the laws regulating the
diffusion. A glass tube, filled with the gas to be
experimented with, closed at one end with a plug of
gypsum, the other end being immersed in mercury,
was employed. It is called a DIFFUSIOMETER. The
diffusion took place through the septum, but not at
the same rate as it would have taken place without it.
The septum was not found to affect the exchange by
any absorption of the separated gases. But it was
necessary to take into account the nature of the gas
and of the porous diaphragm, determining the co-
efficient of friction, as it is called, between the gas and
the diaphragm. Where the tube was filled with
hydrogen and air was on the other side of the septum,
both being at the same pressure, the hydrogen passed
out faster than the air entered, and so the mercury
rose in the tube. On the other hand, if the tube
were filled with C02 the air entered faster than the

'Chap, xxni] ABSORPTION OF GASES. 291

C02 could escape, and so the mercury fell in the tube.
Where the septum separated gas at different pressures,
the effect of the diffusion was to restore equilibrium ;
that is, the diffusion went on until the pressure on
each side of the septum was the same, and the rate of
diffusion was greater the greater the difference of
pressure on the two sides. Suppose, then, a septum
to separate two masses of mixed gases, each mixture
containing O and CO2, the partial pressure of O being
great and of CO2 small on one side, and that of O
small and CO2 great on the other, the result would
be an exchange between the two mixtures through
the septum, 0 passing in one direction and CO2 in the
other, till the partial pressure of each gas was the
same on each side of the septum.

Absorption of gases toy liquids. — Gases may
be absorbed by liquids and retained in solution by
them. Graham concludes "that gases may owe their
absorption by liquids to their capability of being
liquefied and to the affinities of liquids (apparent in
their miscibility), to which they become in this way
exposed," and that " solutions of gases in liquids are
mixtures of a more volatile with a less volatile liquid ;
and to them may be extended the laws which hold in
such liquids." It is found that the gases most readily
liquefied are those which are absorbed in greatest
amount. Thus carbonic acid gas, ammonia, sulphur-
ous acid gas, hydrochloric acid gas are at once easily
liquefied and absorbed, while oxygen, nitrogen, and
hydrogen, liquefied with difficulty, are feebly absorbed.
Different liquids absorb different quantities of the
same gas. The coefficient of absorption or solubility
of a gas is the volume of the gas absorbed by unit
volume of the liquid at 0° C. and 760 mm. pressure.
The amount of gas absorbed by the same liquid varies
with the temperature and pressure. Increased
temperature diminishes the amount the liquid is

2 92 PHYSIOLOGICAL PHYSICS. [Chap. xxm.

capable of holding in solution, while diminished
pressure has the same effect. Diminished tempera-
ture or increased pressure have the reverse effect.
Thus, when a liquid has absorbed its quantity of a
particular gas at a certain temperature and pressure,
a diminution of the former and increase of the latter
will cause an added amount of gas to be absorbed,
but not in direct proportion. On the other hand,
raising the temperature or diminishing the pressure
will cause the liquid to give off some of its absorbed
gas.

The absorptive power of a liquid for a particular
gas is independent of other gases which it may already
hold in solution. Thus a liquid in contact with a
mixture of gases absorbs a quantity of each gas, just
as if it were the only one present, the amount being
determined by the coefficient of absorption and the
pressure of the gas in the mixture. The coefficient of
absorption between water and oxygen is 0 '02989,
between water and nitrogen is 0-01748 ; the pressure
of O in the atmosphere is 0-21 of the total, that of
N, 0-79. Thus the ratio of the absorption by water
of O and N is as 34 and 66.

If a liquid containing already in solution a certain
amount of CO2 be exposed to an atmosphere of CO2,
the absorption of additional gas or the giving off of
some already in solution, will be determined by the
relation between the pressure of CO2 in the liquid
and in the atmosphere. If the pressure of CO2 be the
same in both, no exchange will be effected ; if,
however, the pressure of CO2 in the atmosphere be
greater than in the liquid, absorption will go on till
the pressures are equalised ; while, if the excess be
on the side of the gas in the liquid, gas will be
evolved. Suppose, then, a liquid containing already
in solution both O and CO2 be exposed to an atmo-
sphere of mixed gas containing also O and C02, any

Chap, xxiii.] EXCHANGE OF GASES IN LUNGS. 293

exchange that may be effected will depend on the
partial pressures of each gas in the liquid and in the
atmosphere. Suppose the liquid to contain O at a
less and C02 at a greater pressure than the atmo-
sphere, then O will pass from the atmosphere into the
liquid, and C02 from the liquid into the atmosphere.

The exchanges in the lung's between the blood
and the air cells, is, to a large extent, a physical problem
to be solved by the application of the laws that have
been stated. The delicate walls of the air cells and of
the pulmonary capillaries form a septum, separating, on
the one side, blood containing oxygen and carbonic acid
gas and nitrogen, from air on the other side, containing
the same gases. Disregarding the nitrogen, the pres-
sures of O and C02 in the two cases are found to be
very different, as the following tables show :

PRESSURE or OXYGEN.

In the Pulmonary In the Air of Differ-

Capillaries. the Air Cells. ence

Inspiration (calm) . . 44 129 85

Inspiration (deep) . . 44 140 96

Expiration (calm) . . 44 121 77

Expiration (deep) . . 44 110 66

PRESSURE OF CARBONIC ACID GAS.

In the Pulmonary In the Air of Differ-

Capillaries. the Air Cells. ence.

Inspiration (calm) . . 82 30 52

Inspiration (deep) . . 82 7 75

Expiration (calm) . . 82 38 44

Expiration (deep) . . 82 67 15

(Beaunis.)

Supposing for the moment the blood to be in direct
contact with the air in the air cells, the differences of
pressure show that oxygen would be passing from the
air cells into the blood during expiration as well as
during inspiration, though less freely in the former case,

294 PHYSIOLOGICAL PHYSICS. [chap. xxui.

the differences of pressure during both acts being so
considerable. A transference of carbonic acid gas
from the blood into the air cells would also be ac-
complished specially during inspiration, since during
expiration the pressures approach one another.
The problem, however, is not the simple one thus
represented, for between the blood and the air is
the organic septum, moistened on one side by the
blood, and on the side of the air also moist, like
the rest of the mucous lining of the lungs. The mem-
brane, therefore, separates two solutions containing
different quantities of the same gases, and the process
of osmosis, already discussed in chap, xxii., enters as
an agent in the transference. A second and more im-
portant modifying agent, however, must also be
considered. Blood, deprived of its red blood-cor-
puscles, is found to absorb about the same quantity of
oxygen as water, and in accordance with the law of
pressures, but a much less quantity than the usual
oxygen of the blood. Further, blood not deprived of
its corpuscles is found not to absorb oxygen in ac-
cordance with Dalton's law of pressures. If placed in
a receiver, which is gradually exhausted, the blood does
not yield up its gases in proportion as the rarefaction
proceeds, but when a certain degree of exhaustion has
been reached a large quantity rapidly comes off. The
haemoglobin of the red blood-corpuscles explains these
variations from the physical law. It is found to have
a strong affinity for oxygen. If, itself free of
oxygen, except what forms part of its chemical consti-
tution, it be exposed to an atmosphere of oxygen, it
at first rapidly absorbs a considerable quantity, and
afterwards does not absorb amounts increasing with
increasing pressures according to Dalton's law. What
it does absorb can be dissociated from it by exposing
it to a sufficiently low pressure. Oxygen seems thus
to form a loose chemical combination with the hsemo-

Chap xxin.] THE GASES OF THE BLOOD. 295

globin of the blood. The great difference of pressure,
then, between the O in the blood and that in the air
cells, while a very important factor in the absorption
of that gas by the blood, is not the only one.
Similarly, the carbonic acid gas is not in the blood
in a simple state of solution. A diminution of
pressure will not cause all the C02 to be evolved,
nor does the evolution follow the law of pressures.
It seems to be in loose chemical combination with cer-
tain salts of the serum. Here, also, therefore, in
addition to the physical explanation offered by the
difference in tension between the CO2 of the blood and
that of the air cells, the chemical explanation must
be taken into account.

A sufficiently low pressure, however, will cause to
be evolved from the blood the gas it contains in solu-
tion as well as the gas held in unstable combination,
with the exception of a small percentage (2 to 5) of
carbonic acid gas, which requires the addition of some
acid to drive it off. The method of obtaining the gases
of the blood for analysis proceeds on this principle. A
vacuum is created in a receiver, usually by means of a
mass of mercury, producing the Torricellian vacuum.
The receiver is connected, by means of a short tube and
canule, with an artery of the animal whose blood is to
be analysed. As soon as a sufficient exhaustion has
been obtained, the communication between the artery
and receiver is opened and the blood rushes in, the gas
being immediately evolved. If the receiver be placed
.in an outer vessel containing warm water, the libera-
tion of the gas is aided. If, then, a small quantity of
carbonic acid solution be permitted to enter the
receiver, the " fixed " C02 is liberated, and thereafter
all the gases may be collected into a graduated tube
over mercury, and analysed.

296

OPTICS.
CHAPTER XXIY.

LIGHT : REFLECTION AND REFRACTION.

THE nature of light. — The generally accepted
explanation of the nature of light is that offered by
what is called the UNDULATORY THEORY, a theory
proposed by Huyghens, in opposition to the EMISSION
OR CORPUSCULAR theory, supported by Newton.
The latter theory supposed that luminous bodies gave
out in all directions very subtle particles, which,
reaching the eye, affected it and gave rise to the
sensation that we call light, the intensity of the light
being determined by the number of emanations. The
former theory, advocated also by Young, views light
as a mode of motion, as heat and sound are viewed as
modes of motion. A luminous body is thus held to
be a body whose particles are in a state of vibration.
The vibrations require to be transmitted to our eyes
if they are to give rise to a luminous impression.
The ordinary atmosphere is the medium by which the
vibrations of a sounding body are communicated to1
our ears ; but a luminous body does not become in-
visible in a vacuum, as a sounding body becomes
inaudible. Hence it became necessary to suppose
the existence of a highly elastic medium pervading
all space and all bodies, to which luminous bodies
communicated their vibrations, and which transmitted
them with enormous velocity. The medium is called

chap, xxiv.] THE NATURE OF LIGHT. 297

the LUMINIFEROUS ETHER. The undulations of light
are in a particular direction, namely, transverse to
the direction of propagation of the wave. If one
watches the movement of two or three pieces of cork
on the surface of water thrown into Avaves, the trans-
verse vibration will be understood. As the wave
reaches one piece of cork, the cork rises, occupying
different levels with the progress of the wave, till it
has reached its highest level, corresponding to the
crest of the wave. As the wave progresses still
farther the cork begins to descend on its backward
side, and is at its lowest level in the trough of the
wave. If several pieces of cork happen to have been
properly disposed, one piece may be just beginning
the forward ascent of the slope when another is half
way up, another at the crest, another descending the
backward slope, and another in the trough of the
wave. If one wave succeeds another, then each piece
of cork will be seen bobbing up and down as the
wave advances and passes, each piece being at a
different level according to the part of the wave that
has reached it. When the wave has passed, however,
all the pieces of cork will be found to occupy the
position they occupied before ; they have only bobbed
up and then down in the same place, while the wave
has passed onwards. Now if one could conceive of
the material of the wave being formed of a large
number of particles, then one could see how the wave
form is produced by the transverse movements of the
particles, in a way similar to that of the piece of cork.
Thus the wave form progresses, but the vibrating par-
ticles simply move to and fro across the direction of
the propagation.

What is called the period of vibration is
the time occupied by one of the particles from the
moment it leaves one position to the moment when it
returns to the same position in the same direction.

298 PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

Thus, to return to our illustration, the period of vibra-
tion of one of the pieces of cork may be counted from
the moment the advancing wave reaches it in its
position of rest, to the moment when, the wave having
advanced and passed, it has returned to the same
position in readiness for the next wave. Or, again,
its period may be counted from the moment it has
reached the crest of one wave to the moment when it
reaches the crest of the next, supposing it to be
vibrating through a regular series of waves. By the
same illustration the PHASE OP VIBRATION will be
represented by the position occupied by a piece of
cork in the wave. Thus the phase of each particle in
the wave will be different.

The amplitude of a vibration is the distance
from the middle position of the particle to one of its
extreme positions. Thus, for one of the pieces of
cork it is the distance between its point of rest and
one extreme (the crest of the wave), or the other
extreme (the trough of the wave).

The frequency of vibration is determined by the
number of vibrations per second of time. The fre-
quency is related to the period. Thus if the number
of vibrations be 150 per second, the length of each
period is T^th of a second.

The wave length is the distance through which
the change of form has been propagated during the
complete period of vibration of a particle. The
longer this period, the greater will be the wave length;
the shorter the period, the shorter will be the wave
length. Thus, with our illustration, the wave length
is measured by the distance to which the wave has
advanced between the moment when one piece of
cork began the ascent of one wave of a series to the
moment when it begins the ascent of the succeeding
wave of the series. The faster the vibrations are the
shorter will be the wave length.

Chap, xxiv.] THE VELOCITY OF LIGHT. 299

Specially as regards light, the intensity depends
on the amplitude of the vibrations of the luminous
body. The frequency of vibrations will be found to
determine the difference in colours, red being pro-
duced by vibrations of less frequency, or, what is the
same thing, by longer wave lengths, than the vibra-
tions producing yellow or violet. This is referred to
again in speaking of colour. (See chap, xxvi.)

Self-luminous bodies, then, are bodies in the
state 01 vibration to produce light. TRANSPARENT
bodies are those which transmit the vibrations so that
on reaching the *eye they produce images of the
object ; while TRANSLUCENT bodies permit the passage
of the vibrations, but so that the body from which
they proceed cannot be distinguished. OPAQUE bodies
do not transmit the vibrations, but reflect them.

Light is propagated in straight lines. It is thus
that an opaque body casts a shadow, since it intercepts
the light and causes the space immediately behind it
to be devoid of light. ?

The velocity of light has been calculated by
various experimenters. Fizeau's method consists in
placing a plane mirror directly in front of a source of
light, but] at a great distance from it. An observer,

o ' e O '

stationed behind the light, perceives the beam reflected
from the mirror, that is, after it has travelled from
the light to the mirror and back again. In front of
the source of light is a toothed wheel capable of
being revolved with a varying degree of rapidity.
The wheel may be turned at such a rate that a beam
of light travelling from the source may pass in the
space between two teeth and be reflected in time to
be intercepted by a tooth, so that the light will be
invisible. Thus, from the rapidity of the wheel's
revolution, and the number of teeth, the time occupied
by the light in travelling to the mirror and back again
can be estimated, and, the distance being known, the

3°o PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

velocity of light can be calculated. The velocity is
said to be 186,000 miles per second, or seven and
a half times round the earth per second. This is
the velocity in air ; the velocity in other substances,
e.g. water, can be estimated by interposing a layer of
water in the pathway of the beam and finding the
result. The velocity in water is only three-fourths
of that in air ; and, in general, the denser the medium
the slower the rate.

Due entirely to the rectilinear propagation of
light is the phenomenon that rays transmitted from a
luminous object through a small opening in the wall
of a dark chamber will form an inverted image of
the object on the opposite wall. Thus, in Fig. 126,

the candle trans-
mitting rays
through the open-
ing o in the cham-
ber will form an
inverted image.
A ray a from the

±ig. 12b.— Inverted linage formed by Rays flQTrio ~ f + V, 0
passing through a small Opening into a nam€

dark Chamber. candle passing in

a straight line

will reach a on the wall of the dark chamber,
and will have a brightness corresponding to a. Rays
from a, owing to the smallness of the aperture, will
not illuminate any part other than a. Similarly
rays from other parts of the candle passing through
the opening will illuminate, each to its own extent,
a definite piece of the wall, and thus an image
will be formed, inverted, as seen in the figure. The
size of the image will depend on the distance of the
opposite wall from the wall containing the opening.
Thus the inverted image of a landscape may be pro-
duced in a darkened room through an opening in the
shutter. The smaller the opening the more distinct

*

Chap, xxiv.] THE REFLECTION OF LIGHT. 301

the image ; because the more limited the extent of
surface illuminated by the separate rays, the less ten-
dency there is to overlapping.

The intensity of light varies inversely as the
square of the distance from the source of light.

Fig. 127.— Reflection of Light.

REFLECTION OF LIGHT.

"When a ray of light falls upon a polished surface,
it is reflected in a definite direction. Let CD (Fig. 127)
be a polished surface on which a ray of light AB
falls, the ray will be re-
flected from the surface
in the direction BE. AB
is called the incident, and
BE the reflected ray. Let
a line FB be dropped per-
pendicular to the surface ;
this line is called the
normal to the surface. The point B where the ray
falls is the point of incidence, and the angle ABF
(the angle a), made by the incident ray and the
normal, is the angle of incidence, while the angle
EBF (angle b), made by the reflected ray and the
normal, is the angle of reflection. Now it is found
that these two angles are equal to one another and
are in the same plane. Thus the two laws of re-
flection of light are : (1) the angle of incidence is equal
to the angle of re/lection ; and (2) the incident and re-
flected rays are in the same plane. The application of
these rules explains the formation of images of ob-
jects by mirrors.

Mirrors may be plane or curved.

Plane mirror*. — Let PP' be a plane mirror
(Fig. 128) ; and suppose AB to be an arrow placed in
front of it. Consider rays of light falling from the
point A of the arrow, and meeting the mirror ;

302

PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

B

they are reflected and received by an eye placed
as shown in the figure. Similarly reflected rays
from B enter the eye. and from each part of the arrow
reflected rays will meet the eye. Thus the eye will
perceive an image of AB. But the eye always refers

the object from which rays
reach it straight outwards
in the direction of the rays.
Thus the eye will not seem
to see the arrow in its proper
position. Suppose the re-
flected rays from A to be pro-
longed in a straight line back-
Fig. 128.-Image formed by a Wards> the7 wil1 meet at tlie
Plane Mirror. point a behind the mirror, and

in the line of the perpen-
dicular let fall from A on the mirror. The prolonga-
tion backwards of the reflected rays from B will meet at
b, and similarly the prolongation backwards of reflected
rays from intermediate points between A and B will
meet as shown in the figure. The eye will then see
the arrow AB as if it were behind the mirror. It
can be shown that this image of the arrow will be of
the same size as the real arrow, and will seem to be as
far behind the mirror as AB is in front of it. Thus in
plane mirrors images are produced of the same form
and size as the objects, and seem to be situated the same
distance behind as the object is in front. As shown in
Fig. 128, the image is not inverted, but it is reversed,
that is, right appears left and left right.

Spherical mirrors are those which form part of
the surface of a hollow sphere. Polishing the inner
surface forms a concave mirror, and the outer surface
a convex mirror. A point in the polished surface at
an equal distance from all parts of the circumference
is the centre of the figure, and a line joining this
point and the centre of the sphere of which the

chap. xxiv. CONCAVE MIRRORS. 303

mirror is a part is the principal axis of the mirror.
The centre of the sphere is called the centre of curva-
ture. The distance between the centre of curvature and
the surface of the mirror is the radius of curvature.
A secondary axis is any line passing through the
centre of curvature to the mirror, but not through the
centre of the figure. The aperture of the mirror is
the angle formed by
lines drawn from the
circumference of the M ~

mirror to the centre of G~

r r^-'- — "F

curvature.

These points are M ^_

shown in Fig. 129,

where AB is the mirror, _. . „ . p

Fig. 129. — Principal Focus of a Con-
O its centre, C the cave Mirror.

centre of curvature,

LCO the principal axis, CO the radius of curvature,
and the angle ACB the aperture. CA and CB are
secondary axes.

Concave mirrors. — 1. Let rays of light par-
allel to the principal axis fall upon a concave mirror
(for practical purposes rays from the sun are considered
parallel), they will be reflected according to the laws
of reflection, and will meet in a point F on the prin-
cipal axis of the mirror (Fig. 129). By drawing the
normals CH, CD, etc., it can be shown, that because
the angle of incidence GDC is equal to the angle of
reflection FDC, CF and FD are equal. FD is equal to
FO, and so CF and FO are equal to one another. That
is, the reflected rays meet in a point which bisects
the radius of curvature. F is called the principal
focus of the mirror, and the distance FO is the prin-
cipal focal distance. Thus, rays parallel to the prin-
cipal axis, falling on a concave mirror, are reflected to
meet in the principal focal point, ^uhich is at a distance
from the mirror equal to half the radius of curvature.

304 PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

It is not strictly true for spherical mirrors that
all the reflected rays meet at one point. It becomes
more and more true, however, the smaller the aper-
ture of the mirror. It is strictly true for parabolic
mirrors.

If the rays proceed from F, then, when reflected,
they will be parallel.

To find the principal focus of a concave mirror,
expose it to the sun's rays and catch the reflection on
a screen. Move the screen nearer to, or farther away
from, the mirror, till the position is found where the
image is best. That is the principal focal distance
and half the radius of curvature.

2. Suppose the rays are not parallel, but diverge
from a point /(Fig. 130) the angle of incidence is less

than in the first case,
so also will be the
angle of reflection, and
the reflected rays will
consequently meet in
a point F' outside of
the principal focus

Fig. 130. — Coujug-ate Foci of Concave / i • u • . j

Mirror. (which is represented

by a dot) and between

it and the centre of curvature. Should the source
of light be at F', then F'AC becomes the angle of in-
cidence, and CA/ the angle of reflection. Since they
remain equal to one another, then the reflected rays
will meet at f. f and F' are thus related to one
another, and this relation is expressed by saying they
are CONJUGATE FOCI.

3. By reference to Fig. 130 it is readily seen that
the farther y is removed the larger grows the angle of
incidence, and the larger, consequently, the angle of re-
flection. As a result, the nearer will F' approach to the
principle focus. When f has reached an infinite dis-
tance, its rays become parallel, and when reflected

Chap, xxiv.] REAL AND VIRTUAL Foci. 305

meet in the principal focus. Similarly, the more f
approaches the mirror the smaller angle do its rays
make with the normal, the smaller, therefore, grows
the angle of reflection, and the more does F' approach
to c. When f is at c, its rays are normal to the sur-
face ; they are reflected in the same line, and the
source of light and the focus coincide.

Real and virtual . foci. — In all the cases that
have been considered the source of light is not nearer
the mirror than the principal focus, and the principal
and conjugate foci liave all been on the same side of the
mirror as the source of light. They are, therefore,
called real foci. When, however, the source of light
is nearer the mirror than the principal focus, the
angle of incidence is so great that the reflected rays
become divergent from the axis. Thus, in Fig. 181,
AB is again the mirror, and the other letters are also
the same as before, f is the
source of light, /A /B are the in-
cident, and AM BN the reflected
rays. Being divergent, the re-
flected rays cannot meet on the
same side of the mirror as this
source of light, but if prolonged
backwards they meet in a point Fig.131._VirtualFocus

F , which IS a Virtual foCUS, because of Concave Mirror.

it is not on the same side of the
mirror as the source of light.

In convex mirrors the foci are always virtual.
The principal focus (virtual) is formed by letting
parallel rays fall upon the mirror. The reflected rays
diverge, but if prolonged backwards meet in a point
on the prolongation of the principal axis. That point
is the principal virtual focus, and gives the principal
focal distance, equal to half the radius of curvature.
As in concave mirrors, if the rays falling on the
mirror be divergent, they form a conjugate focus,
u— 7

306 PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

also virtual, whose position varies as in concave
mirrors, with that of the source.

Formation of images in spherical mirrors.

— 1. Concave mirrors. — Let MN (Fig. 132) be a concave
mirror, p its principal focus, and in front of it, beyond
its centre of curvature c, let an object (the arrow
AB) be placed ; how may the position of the reflected
image of the arrow be found ? First draw the principal
axis 00, and secondary axis from A and B, namely,
AK and BP. From A let fall on the mirror the incident
rays AE and AG, and from B incident rays BN and BL.
These rays are reflected. The reflected rays of A will
meet at a point a on the secondary axis AK, and those
of B at a point b on the secondary axis BP. The point
a is thus the conjugate focus of A, and an image
of the point A is formed there, while b is the conju-
gate focus of B, and an image of B is formed there.
Similarly, conjugate foci of all points between A and B
will l)e formed between a and b, and thus between
a and b an image of AB will be formed. The image
is in front of the mirror, it is upside down, and is
smaller than AB. Thus in concave mirrors, where the
object is beyond the centre of curvature, an image will
be formed between the centre of curvature and the
principal focus, and the image is real, inverted, and
smaller than the object. Suppose the object were at
an infinite distance, the image would be at the prin-
cipal focus. As the object approaches the centre of
curvature, the image moves outwards from the prin-
cipal focus towards the centre. If the object were at
the centre, the image would coincide with it. This
will be understood from what has been said about
conjugate foci (page 304). For the same reasons it will
be understood that should the object be within the
centre of curvature, the image will be formed beyond
it. Thus, should ab (Fig. 132) be the object, the rays
aE are now incident, and GA EA are the reflected

chap, xxiv.] FORMATION OF IMAGES BY MIRRORS. 307

rays ; the image of a is therefore formed at A, and b at
B. AB would thus become the image. If, then, the
object be between the centre of curvature and the
principal focus, the
image is real, and in-
verted, but larger than
the object; and the
nearer the object ap-
proaches to the princi-
pal focus, the larger will Fig. 132.— Formation of a real Image
be the image. Should, b>T a Concave Mirror.

however, the object be

at the principal focus, the incident rays are reflected
in a direction parallel to one another (page 303). No
conjugate focus is formed, and hence no image.

Finally, suppose the object to be nearer to the
mirror than the principal focus, then, as already noted

(page 305), the reflected
rays are divergent. They
do not meet in front of the
mirror, and no real image
is formed. If the reflected

Fig. 183.— Virtual Image of Concave raVS be prolonged back-

wards, however, they will

meet behind the mirror and so form a virtual image.
Thus, let MN (Fig. 133) be a concave mirror, xQx' its
principal axis, c its centre of curvature, and F its
principal focus. Within F place an arrow AB. Let AG
AE be incident rays from A. They are reflected in the
directions p and R. Rays BH BL from B are reflected
in the directions s and T. Prolonged backwards, the
former met at a and the latter at b. Thus ab becomes
the image of AB. It is behind the mirror, virtual;
is ERECT, and larger than the object. The nearer the
object is to the principal focus, without coinciding with
it, the larger is the virtual image, the nearer the object
is to the surface of the mirror, the smaller is the image.

3o8

PHYSIOLOGICAL PHYSICS. [Chap. xxiv.

To summarise, a concave mirror will give a mag-
nified view of an object, so long as the object is nearer
to the mirror than the centre of curvature ; when the
object is outside of the principal focus, the image is
inverted, when within the principal focus it is erect.

2. Convex mirrors. — We have seen that in con-
vex mirrors the foci are virtual ; hence, images will

also be virtual.

Let MN be a convex
mirror (Fig. 134),a%e'its
principal axis, and ab
an arrow in front of it.
Incident rays from ab

rr.

Fig. 134. — Virtual Image of Convex

Mirror.

are reflected in diver-
gent directions, i' G H
and i, their backward

prolongations meet at A and B. Here a virtual image
is formed, erect, but smaller than the object. Convex
mirrors, then, diminish the apparent size of objects.

The size of the image may be calculated from
various data. Thus, the size of the image may be
calculated from the size of the object, if, besides, the
distance of each from the centre of curvature be
known. The formula stands thus :

length of image
length of object

distance of image from centre
distance of object from centre

distance of image
length of image = length of object X distance of object'

In a similar way the size of the object may be calcu-
lated, provided the size of the image be known, and
their respective distances from the centre of cur-
vature.

REFRACTION OF LIGHT.

A ray of light in passing obliquely out of one

chap, xxiv.] REFRACTION. 309

medium into another of different density, is bent out
of its path at the surface of separation of the two
media. The deflection is called REFRACTION. Fig. 135
represents a ray of light passing from air into water.
If the ray passed perpendicularly into
the water, i.e. in the direction of the
normal NN', its course would be un-
affected by the water ; but when it
strikes the water obliquely as in-
dicated by the arrow, then it does not

r Fig. 135.— Refrac-

contmue a straight course as HB, but tiou of Light.
is bent towards the normal as HC. Or
suppose c to be a bright object in the water, and CH
to be a ray of light reflected by it, when the ray
emerged from the water it would not continue a
straight course, but owing to the different density of the
air it would be bent away from the normal, and would
assume the direction of the line above H. An eye
placed at the end of that line would, therefore, receive
the rays proceeding from c ; since the eye always
refers the luminous object in the direction of the
rays which reach it, the eye would seem to see the
object c at B, displaced from its true position.

Thus, a ray of light passing from one, medium into
another of greater density, is refracted towards the
normal ; and passing from one medium into another
of less density, is refracted away from the normal.

It is refraction that causes a stick plunged
obliquely into water to appear bent, the immersed
part being raised nearer to the surface. It is re-
fraction also that causes the sun to appear still above
the horizon when it has actually sunk below it, the
rays from the sun being bent by the atmosphere sur-
rounding the earth, the sun is caused to appear
higher than it actually is. The mirage seen most
commonly in hot climates is also an effect of refrac-
tion. Fig. 136 shows how rays, say from a tree A, are

310 PHYSIOLOGICAL PHYSICS. ichap. xxiv.

bent upwards, owing to the diminished density of the
air by contact with the heated ground, so as to reach
the eye of .an observer at a. The observer refers the
object from which the rays proceed
to the direction in which the rays
reach him, and thus an inverted

ff' t

J&-" image of A would be seen at A', and,

Fig. 136.— Eefrac- in the same way, an inverted image
of a landscape would be seen.

In the case of a ray of light passing from one
medium into another less dense, the angle of refrac-
tion must not be greater than a right angle, else the
refracted ray will not emerge from the dense medium,
but will be reflected at its surface. If the angle of
refraction be a right angle, the ray is refracted
parallel to the surface of the dense medium. The
value of the angle of incidence giving rise to the right
angle of refraction, is called the critical angle, because
any greater angle will prevent the emergence of the
ray. When, owing to the greatness of the angle of
refraction, the ray does not emerge, the occurrence is
called TOTAL REFLECTION.

The laws of refraction are that the incident
and refracted rays are in the same plane, and that
there is a definite relationship between the angle of
incidence and the angle of refraction. The angle of
incidence is that made by the incident ray and the
normal ; that of refraction is made by the refracted
ray and the normal. In Fig. 135, NN' is the normal,
the angle i is the angle of incidence, and the angle r
is the angle of refraction. The relation between
these two angles is such that their sines are in a
constant ratio. This is .expressed by saying that

O i y» Q n

= a constant quantity designated by /t. This
sine r J J

constant ratio is called the INDEX OF BEFRACTIOH,
From air to water the index is four- thirds, or 1 '33.

Chap, xxv.] PRISMS. 311

The refractive index of the diamond is very high,
2755; that of flint glass is 1-576, of water 1'336, of
the aqueous humour of the eye, 1'337, of vitreous
humour, 1'339, of crystalline lens, 1*337 to 14.

CHAPTER XXV.

THE ACTION OF PRISMS AND LENSES.

Refraction by a plate with parallel faces.

—If a ray of light pass through a transparent body
and out at the other side, it is evident that it will
be twice refracted, first when it enters the body,
secondly when it leaves, and that the two refractions
will be in different directions. This is shown in Fig.
137, where the ray AB falls on a plate whose faces
are parallel. On entering the plate
it is bent towards the normal, and
becomes EC ; on emerging it is bent
awav from the normal, and becomes ,

V ..- s v - r , v ^7

CD. Since the plate is parallel and fc~-.- ..- ^ . '...-..-' 41
the divergence in both cases of
similar amount, the ray will issue,
pursuing the same direction as

wlip-n it pnfprprl TVmt i<s to <?nv FiZ- 137. — Refraction
ea< Sa7> lay a Plate with Paral-

the entering and the emergent rays lei Faces,
will be parallel, but, owing to the
refraction on entering, the beam will be displaced. The
result is, that, supposing D to be a luminous object,
and an eye to be at A, the object would appear dis-
placed to D' in the direction indicated by the dotted
line.

Refraction by a prism. — Rays of light which
have passed through a transparent body, whose

3i2 PHYSIOLOGICAL PHYSICS. [Chap. xxv.

faces are not parallel but form an angle with one
another, do not emerge parallel to one another.
A figure whose surfaces are inclined to one another
at an angle is called a PRISM. A principal section of
a prism is represented in Fig. 138, a section, that is,

made by a plane perpendicular
to both surfaces. The appear-
ance is that of a wedge. The
line R, in which the faces PR
and SR meet, is called the edge
of the prism ; the line PS is the
base of the prism.
Fig. 138.— Prism. Now let a ray AB be

incident on the face PR of

the prism making an angle of incidence with the
normal nn'. On entering the prism the ray is re-
fracted towards the normal, and takes the course BB'.
On emerging from the prism the ray is again refracted,
but this time, because passing into a rarer medium,
the refraction is away from the normal n"n", and
takes a course B". An eye placed at B" will see the
ray as if it proceeded from b. The ray of light is
thus refracted towards the base of the prism by the
action at both surfaces. The angle B"OA' formed by
the direction of the incident ray with the direction of
the emergent ray expresses the amount of deviation
the light has undergone in passing through the prism,
and is called the angle of deviation. Other things
being equal, it depends on the refractive index of the
material forming the prism. There is a value of this
angle in which the refracted ray BB' would not
emerge from the side of the prism, but would so fall
on the internal surface of RS as to be totally reflected,
in which case the ray would be directed by the reflec-
tion towards the base within the prism.

Lenses are transparent media, which refract rays
of light passing through them. They have curved

Chap, xxv.] LENSES. 313

surfaces, and the direction which the rays take on
emerging from the lens depends on the nature of the
curvature. The CHIEF FORMS OF LENSES are shown
in Fig. 139. They are convex or concave. In the
figure, A is doubly convex, B plano-
convex, c concavo-convex, while D
is doubly concave, E plano-concave,
and F convexo-concave.

Convex lenses, owing to the
nature of their curvature, cause Fig. lou.— Lenses.
the rays of light issuing from them
to converge to one another. They are, therefore,
called converging lenses. Supposing the surfaces of
the lens to be parts of spheres, the centres from which
the sphere would be described in each case are called
the centres of curvature of the lens, and the straight line
joining the two centres is the principal axis of the lens.

Each lens has also what is called its OPTICAL
CENTRE or simply its CENTRE, which lies on the prin-
cipal axis, and is such that every ray passing through
it emerges from the lens in a direction parallel to that
in which it entered the lens. In a doubly convex or
concave lens the centre is in the interior of the lens ;
in plano-convex or plano-concave lenses it is on the
convex or concave surface ; in a concavo-convex lens
it is outside the lens. Any straight line passing
through the centre is a SECONDARY AXIS.

1. Let parallel rays of light fall on a convex lens,
they are so refracted as to meet in a point on the
other side, and this point is called the principal focus,
the distance from it and the lens being the focal dis-
tance of the lens. In Fig. 140 LL' is a convex lens.
The ray 5 which falls perpendicularly on the surfaces
passes straight through unaffected. The other rays
123 and 4, fall obliquely, and are, therefore,
refracted. In each case the refraction occurs twice,
first on entering the lens, and secondly on issuing from

314 PHI 'SIOL OG1 CA L PH YSICS. [Chap. XXV.

it. Thus, in the case of ray 1, the refraction on
entering the lens is towards the normal n, on leaving,

because the ray passes from
a rarer to a denser medium,
the bending is away from the
normal n', the result of both
refractions being to direct the
ray towards F, the principal

Tig. 140.-Principal Focus of J °CUS- Jhe a^le . LFL/ f°rUied

a Convex Lens. by rays irom the circumference

of the lens and the principal
focus is the aperture of the lens.

On the other hand, if the luminous body be at F,
the rays after emergence from the lens will be parallel
to one another.

2. Let the rays diverge from a luminous point,
and fall on a convex lens, they are no longer focussed
at the principal focus. Suppose, as in Fig. 141, the
rays proceed from a
pointy* which is farther
from the lens than the
focal distance. After
refraction they w.ll
meet in a point f
outside of the principal Fig. 141._Coujugate Foci of a Convex
focus F. Or if the Lens,

luminous point be at/'',

the refracted rays will meet &tf. Because of the re-
lation thus existing between f and f, they are called
CONJUGATE FOCI. That is, f is the conjugate focus of
/"', and/' of/'. Just as in the case of mirrors, as/"
comes more and more nearly to be at the focal dis-
tance from the lens its conjugate focus f moves
farther and farther off, till if f coincide with the focal
distance, the emergent rays will be parallel, and there
will be no conjugate focus. Again, as y moves farther
and farther from the focal distance its conjugate focus

Chap. XXV.]

CONCAVE LENSES.

approaches nearer to F, till, if f be at an infinite dis-
tance, when rays from it may be considered to be
parallel, f will approach to F till it coincides with it,
In all these cases the foci are real. Suppose now
that the luminous point is nearer to the lens than the
focal distance, the emergent
rays will be divergent. They
will not meet, and no real
focus will be formed. This
is shown in Fio;. 142, where

.LI £ i IT j. i Fig. 142.— Virtual Focus of a

F is at the local distance, and Convex Lens.

the luminous point is f.

These divergent rays, however, if prolonged back-
wards, as represented by the dotted lines, will meet in
a point at /' on the same side of the lens as the luminous
point. This point is a virtual focus; convex lenses,
then, have both real and virtual foci.

Concave lenses. — In Fig. 143, LL' represents a
concave lens, with parallel rays falling upon it, n and

Fig. 143. — Principal Focus
(Virtual) of a Concave
Lens.

Fig. 144.— Conjugate Foci
of a Concave Lens.

n being the normals. After refraction the rays
diverge, but their prolongations backwards meet in F ;
F is called the principal focus, but it is virtual.

Should the rays diverge towards the concave lens,
their conjugate foci will be obtained, as in the convex
lens ; but both will be on the same side of the lens.
The conjugate foci are also virtual. Thus, in Fig. 144,
if the luminous point be at F, outside of the principal

316 PHYSIOLOGICAL PHYSICS. [Chap. xxv.

focus, the rays after refraction will diverge : but
their backward prolongations will meet in the point F'
inside of the principal focus. The point F' is the conju-
gate focus (virtual) of F. If F' be the luminous point
its conjugate focus is F.

The focal distance of lenses may be deter-
mined experimentally, and may be calculated. Thus,
if a convex lens be caused to intercept rays of light
from the sun, a well-defined luminous point may be
thrown on a screen placed at a proper distance on
the other side of the lens from the source of light.
The distance of the screen from the curved surface
when the luminous point is quite distinct, is the focal
distance. The focal distance may also be calculated,
if the conjugate foci be known, from the formula

1 l 1
P pf ~ f*

where p and p are the conjugate foci, and f is the
principal focal distance ; the formula, as given, applies
to convex lenses, provided the source of light p be
farther from the lens than the focal distance. When

the source of light is nearer than the focal distance, -/

P

is negative. For concave lenses the formula becomes

1 1 1

P' ~ P ~ f '

Formation of images by lenses. — The for-
mation of images by lenses exhibits similar rules to
those observed in the formation of images by reflection
from mirrors.

CONVEX LENSES. — Let LL' (Fig. 145) be a convex
lens, c its centre, and F its principal focus, and
let AB be an arrow outside of the principal focus.
From A and B let rays parallel to the principal axis

Chap, xxv.] FORMATION OF IMAGES BY LENSES. 317

xx fall on the lens ; they will be refracted to meet at
F', at a distance from the lens equal to the focal dis-
tance. At that point the rays will cross, and if con-
tinued, diverge. From A draw a secondary axis AC.
If prolonged it will
meet the refracted
ray at a. Thus, a
pencil or cone of rays
passing from the ^'

point A will have its Fig. 145.— Formation of a Eeal linage by a

conjugate focus at a, Couvex Lens-

and thus a will be the

image of A. Similarly, draw a secondary axis from B ; it
will intersect the refracted ray from B at 6. A cone of
rays from B will find its conjugate focus at b, and b will
be the image of B. Each point of AB will have pro-
ceeding from it as a focus a pencil of rays, which will
find its conjugate focus between a and b. Thus an
image ab of the arrow AB is formed. It is a real
image, that is, on the opposite side from the object,
and is inverted and smaller than the object. Should ab
be the object, then AB would be the image. This
follows from the relation between conjugate foci.
From what has been seen about conjugate foci, it also
follows that the nearer AB approaches to the focal
distance from the lens, the farther ab recedes from
the lens and the larger it becomes ; while the farther
AB is from the lens the nearer is the image to the
focal distance, and the smaller it is. To put it in
another way, the image of an object placed at a much
greater distance from the lens than the focal length is a
real image, very small and inverted, and in the neigh-
bourhood of the focal distance, while the image of an
object placed very near to the focal distance of the lens,
yet outside of it, is still a real image and inverted, but
much larger than the object, and far beyond the focal
distance.

3i 8 PHYSIOLOGICAL PHYSICS. tchap. xxv.

Now consider what occurs when the object is nearer
to the lens than the focal distance. Let AB (Fig. 1 46) be
such an object. The cone of rays from A, namely, a', no
longer converge after passing through the lens, but

are still divergent. They
have, therefore, no conju-
gate focus on the opposite
side of the lens from A.
If prolonged backwards,
however, they will meet in
a, which is, therefore, the

Fig. 146.— Formation of a Vir- Conjugate foCUS of A, and

tuaJ image by a Convex Lens. on the same side, a virtual

focus, therefore. Similarly,

the pencil of rays from B after refraction is still a
divergent pencil b', and has no real conjugate focus,
but a virtual one in b. Each point between A and B
has also its virtual conjugate focus, and thus there is
formed a virtual image of AB, namely, ab, and this
virtual image is erect and larger than the object. The
nearer the object is to the focal distance, if still inside
of it, the larger will be the virtual image produced.

CONCAVE LENSES have only virtual images, which
are erect and smaller than the object. This is evident
from the fact that the conjugate focus of a concave
lens is virtual.

Size of image formed by convex lens.—
The proportion between the sizes of image and object
is directly as the proportion between the distances of
the t\\ o from the lens. Thus,

size of object distance of object from lens
size of image distance of image from lens

If AB be the image, ab the object, p the distance of
the former from the lens, and p the latter distance,

AB p

„' '

p
AB = ab X ~/«

CHAPTER XXVI.

ANALYSIS OF LIGHT : COLOUR.

A PRISM has a remarkable effect on white light as
the result of its refractive properties.

The spectrum. — If a ray of sunlight s entering
a room through a narrow slit in a shutter, be caused

O

to pass through a prism A interposed in its path, as
shown in the figure, a band of colour will be thrown

O

on to a screen placed beyond the shutter. Seven

Fig- 147— The Spectrum.

colours will be made out in regular order from below
upwards, as follows : red, orange, yellow, green,
blue, indigo, violet. No sharp line of demarcation is
visible between different colours, but one merges
gradually into the succeeding colour. The band of
colours is called the spectrum. Suppose ail the
colours except the violet v at the high end of the spec-
trum, to be caught on the screen E, but the violet to
be permitted to pass the screen, and be intercepted
by a second prism B, it is found that the violet rays
are again refracted, but no further decomposition

320 PHYSIOLOGICAL PHYSICS. [Chap. XXVL

ensues, and it is violet rays that are received on the
second screen H.

Recomposition of white light. — If a spec-
trum, produced by passing a ray of white light s

through one prism, be
immediately passed
through a second
prism, in every way
the same as the first,
but inverted, the re-
fraction of the two

Fig. 148. — Kecomposition of White

Light. prisms is opposite in

direction, the coloured

rays are reunited, and a white ray E emerges from
the second prism.

Theory of the spectrum. — White light is
not, then, simple, but is a compound of various
colours. Each colour of the spectrum has its own
degree of refrangibility. All the colours are refracted
when passed through a prism, though unequally.
Thus, red light is refracted to a certain extent, yellow
light to a greater extent, violet light most of all. . In
a word, the refrangibility increases from red, where
it is least, up to violet, where it is greatest. Thus
the red end of the spectrum is called the low end, or
end of least refrangibility ; while the violet end is
the high end, or that of greatest refrangibility, When
white light, which is thus a compound of rays of
different refrangibilities, is passed through a prism,
each ray is refracted according to its own degree, and
thus the different colours are separated out and pro-
jected on to a screen in the order of their refrangi-
bility, the two extremes being red and violet, with
the rays of intermediate refrangibilities between them.

As we have seen, the coloured band produced is
called the spectrum, the separation of the different
rays being called DISPERSION.

Chap XXVI.]

THE SPECTRUM.

321

According to the undulatory theory, the different
colours are due to vibrations of different rates of
rapidity, vibrations whose periods and wave lengths
are different. The wave length of red light is greater
than that of violet, and the time of vibration of red
is also greater than that of violet. Thus the extreme
red rays vibrate at the rate of 395 billion times per
second, and their period of vibration is, therefore, one
395 billionth of a second ; the violet rays vibrate 763
billion times per second. But the wave length of the
ray changes in passing through different media, the
velocity of propagation changes. Some rays are re-
tarded, the violet more than the red. The rays are,
therefore, differently refracted, and dispersion is the
result.

B>aa'k lines of the solar spectrum. — If the
beam of light, which has been split up into its con-
stituents, be obtained from the oxy hydrogen lamp, or

ACBCD E I F H

1 '

~T

!

~J — d

1

— ~ ^T-T-

j

1
i

!

•

_

Fig. 149.— The Dark Lines of the Solar Spectrum.

The brackets below indu-ate the regions occupied by the different colours, in
the order, red, orange, yellow, etc,

a gas flame, the band of colours is continuous, one
colour gradually merging into another. If, however,
sunlight has been used, tli3 spectrum is seen to be
interrupted by a series of dark bands crossing it
vertically. They are called Fraunhofer's lines,
because Fraunhofer first described them in 1814.
Fraunhofer counted a large number of these lines, and
marked their positions. The more prominent he
signified by letters of the alphabet ; thus, A, B, and c
lines are all in the red part of the spectrum, the D
line is in the border-land between orange and yellow,
v— 7

322 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

E in the yellow end of the green, F in the blue end of
the green, G in the indigo, and H in the violet. The
explanation of these dark lines is the result of the
thought and labour of various scientific men, notably
Stokes, Bunsen, and Kirchhoff, but was not fully
offered till 1859 by Kirchhoff.

One of the most prominent of the dark lines of the
solar spectrum is the D line, which, properly speaking,
consists of two lines, and is in the brightest part
of the spectrum. Frauiihofer observed that if the
source of light, instead of being the sun, were the
vapour of sodium, such as might be obtained by burn-
ing in the hot part of a bunsen flame some common
salt, and if the light from this vapour were passed
through a prism, a band of colours like the solar
spectrum was not obtained, but instead two narrow
bands of yellow light. If an arrangement is made for
obtaining the solar spectrum and the spectrum of
sodium side by side, one above the other, the two
bright yellow lines of the sodium flame are found to
correspond in position with the two dark lines, called
D, of the solar spectrum. A very minute trace of
sodium, even the 18 millionth part of a grain, it is
asserted, will give the yellow band. Similarly,
potassium, burnt in a bunsen flame, gives two bright
red lines and one violet line. Strontium gives various
bright red lines, and an orange line at the red side of
the D line. A large number of substances have been
examined by being volatilised before a prism, and have
yielded various coloured lines, the coloured lines of
many substances, such as sodium, hydrogen, calcium,
barium, iron, etc., being found identical in position with
dark lines of the solar spectrum. The dark lines,
then, of the solar spectrum indicate the absence of
certain rays, which, in the case of the D lines, for ex-
ample, the glowing vapour of sodium emits. Now, to
take the case of the D line, it is found that if some

chap, xxvi.i SPECTRUM ANALYSIS. 323

sodium be rendered incandescent in the name of a
bunsen gas lamp, and the rays be transmitted through
a prism, the bright yellow lines constituting the
spectrum of sodium will be obtained, but if between
the bunsen lamp and the prism an ordinary spirit
lamp, burning with a salted wick, be interposed, the
bright yellow disappears. That is to say, the vapour
of sodium produced by the spirit lamp has absorbed
the light proceeding from the vapour of higher tem-
perature and of the same quality behind it. The
vapour of sodium will absorb and retain light whose
period of vibration is identical with its own. If light
proceeding from a source pass through an atmosphere,
the atmosphere will prevent the passage of such rays
as correspond to those which it would itself produce.
In the case of the solar spectrum, therefore, the dark
lines are due to the absorption of certain rays in
passing through the atmosphere surrounding the sun.
To take again the D lines, this implies that there is
incandescent sodium vapour in the sun's atmosphere,
and that it separates out and retains the vibrations of
its own period. It is evident that this affords a means
of information as to the chemical constitution of the
sun and other luminaries.

Spectrum analysis. — Since it has been found
that certain substances give definite coloured lines
when the rays from their incandescent vapour are
passed through a prism, and since the same bands will
not be produced by two different substances, it is
evident that there is afforded a method for analysing
compound bodies, and detecting the presence of cer-
tain constituents. The spectra of gases can be
obtained by the use of tubes exhausted of air and
containing a small quantity of the particular gas. An
electric spark is passed through the tube from an
induction coil, and the spectrum of this obtained.

The spectroscope (Fig. 150) is an arrangement of

PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

prisms and lenses for the purpose of readily obtaining
spectra. The chief parts of it are a slit s, a prism p,
and a telescope L. Through the slit a narrow beam of
light is permitted to fall on the prism, which produces
the dispersion. A person looking through the tele-
scope sees an image of the spectrum. More than this

Fig. 150. — The Spectroscope.

simple arrangement is used, however, in the construc-
tion of spectroscopes. In order that the rays coming
from the slit may be parallel a collimator is interposed
between the slit and the prism. This is a convex lens I.
It is fitted in a tube, at the outer end of which is the
slit (narrow, and cleanly cut, and placed vertically),
and it is distant its focal length from the slit, so that
the rays of light from the slit pass through the lens
and emerge parallel. The prism is placed with its
edge parallel to the slit, and receives the rays from
the collimator. Further, a convex lens may be placed
between the source of light and the slit to concentrate
the light on the slit, and thus obtain greater brilliancy.
The dispersed rays fall 011 the telescope, placed to

Chap, xxvi.] THE SPECTROSCOPE. 325

receive them, and form a vertical image. Now a gas
lamp placed in front of the slit will give a continuous
spectrum, or a sodium flame may be brought in front
of the slit, and so on.

A single prism cannot give very great dispersion.
If, therefore, great dispersion is wanted a train of
prisms is made use of. The second prism is so placed
that it receives the rays refracted by the first, and
increases the divergence : the third is so placed that
it receives the refracted rays from the second and still
further disperses them, and so on. A considerable
number of prisms may be used. They require, of
course, to be arranged in a curve in order that one
prism may catch the rays from the preceding one, and
the telescope is placed so as to catch the rays from the
last. With such an arrangement a spectrum of great
length may be obtained. Many spectroscopes have a
third tube, which carries at the outer end a small
transparent scale. A candle illuminates the scale.
At the other end of the tube is a lens. This tube is
so placed that the light from the scale falls on the
surface of the prism next the telescope and is reflected
into the telescope. On focussing, an image of the
scale may be seen in the telescope. Thus in the same
field of view one may have both a scale and a spec-
trum, and may determine the position of any band in
a spectrum by means of the scale, so aiding in the
comparison of different spectra.

It is often of great advantage to have in the same
field both the solar spectrum and the spectrum of the
particular substance under examination. For this
purpose a small rectangular prism of glass is placed
directly in front of the lower part of the slit. Rays
of light from a source at the side penetrate this prism,
and undergo reflection at one of the internal faces, so
that the light is directed through the slit on to the
upper part of the prism, and produces a spectrum. The

326 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

upper portion of the slit receives light from another
source ; and it passes to the lower part of the prism.
Two spectra are thus produced, one below the other,
and comparison can easily be made.

The spectroscope in physiology. — Hoppe
Seyler and Stokes were the first to show that blood
had a distinguishing spectrum of its own. If a layer
of blood be interposed between the source of light and
the slit of a spectroscope, the only rays that are per-
mitted to pass through the layer of blood are the red,
and only the red end of the spectrum is visible. As
the blood is diluted, more and more light is able to
pass through it, orange first, then yellow, and so on
till the whole spectrum is almost restored. But there
remain towards the red end two dark bands ; they
are situated between D and E of the solar spectrum.
One of them is on the violet side of D, is the thinner
of the two, but the more intense ; the other is much
broader, and lies to the red side of E, its edge coming
close up to E. These are the ABSORPTION BANDS OF
HAEMOGLOBIN, the red colouring matter of the red
blood corpuscles. More particularly this is the
spectrum of haemoglobin as it exists in normal blood
in loose chemical combination with oxygen. When
oxygen has been removed from the blood by increased
temperature and sufficiently low pressure, or by the
passage through the blood of some indifferent gas such
as hydrogen, or, still more rapidly and easily, by the
addition to the blood of reducing agents, such as
sulphide of ammonium, the spectrum gives a new
absorption band. The two bands disappear, and in
their place is one band, situated midway between the
positions of the bands of oxy haemoglobin. It is much
broader than either of the two, though not so dark,
and in its case less of the blue end of the solar
spectrum is absorbed. This band is distinguished
from the other as the ABSORPTION BAND OF REDUCED

chap. xxvi. i SPECTROSCOPE IN PHYSIOLOGY. 327

H.EMOGLOBIN. In solutions of a strength sufficient
with oxylipernoglobin to absorb all but the red and
orange rays of the spectrum, reduced haemoglobin will
permit the passage of the red and of some rays from
the green side of the absorption band. This fact ex-
plains the difference of colour between oxygenated
blood and blood from which the oxygen has been
removed, the former being of a bright red, the latter
of a purple claret colour owing to the passage of the
greenish rays and the absorption of the orange. If
the vessel retaining the reduced blood under examina-
tion be shaken with air for an instant, and immediately
re-examined, the double band will be seen, due to the
haemoglobin seizing on oxygen from the air. In a
short time, if the reducing agent be still acting on the
solution, the double band will give place to the single
band of reduced haemoglobin. This manoeuvre may
often be repeated with a like result. It is not to be
supposed that it is only arterial blood that gives the
band of oxyhaemoglobin. ; the double band is found
also in venous blood ; because all the oxviren. is not

«/ o

removed in venous blood, much reduced hemoglobin
exists, but sufficient oxyhaemoglobin also to give the
two lines, which are more conspicuous than the single
band of reduced haemoglobin.

If carbonic acid be substituted in the blood solu-
tion for oxygen, the spectrum still gives two bands
similar to those of oxy haemoglobin, but not occupying
precisely similar positions, though this is not ascer-
tained without careful measurement. The BANDS OF
CARBONIC OXIDE HAEMOGLOBIN are slightly displaced
towards the violet end of the spectrum ; and they do
not disappear on the addition of reducing agents.

Haemoglobin when acted on by acids or alkalies
yields two substances, a proteid called globulin, and a
colouring matter, haematin. The haematin may be in
one of two conditions, according as acid or alkali has

PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

been used. Each condition has a spectrum of its
own. Tlie ACID H^MATIN (Stokes) gives one absorp-
tion band in the red in close proximity to the dark
band c of the solar spectrum. The spectrum of
ALKALI H^EMATIN consists of one dark band to the red
side of the D line.

REDUCED H^MATHST gives two faint bands, one
broad, and immediately to the violet side of D, the
other narrower, and a little to the red side of the E
line, the violet end of the spectrum being less ab-
sorbed than with unreduced hsematin.

Fig. 151.— Blood Spectra.

Fig. 151 shows several of these characters, i being
the spectrum of oxyhsemoglobin, n of reduced hsema-
globin, v of reduced hsematin, vi and vn of hsematin
in alkaline and acid solutions, in and iv of methse-
moglobin in alkaline and acid solutions respectively.
Methsemoglobin is obtained by exposure of a solu-
tion of hsemaglobin for a long time to the air, or by
the use of oxydising agents. The letters mark the

Chap, xxvi.] THE SPECTRA OF HEMOGLOBIN. 329

positions of the dark lines of the solar spectrum ; and
the numbers indicate the wave lengths in millionth s
of a millimetre.

The importance of these absorption bands of blood
is apparent. Even as the spectroscope supplies an
unrivalled means for detecting the presence of various
substances, so can it be made available for detecting
the presence of blood. In medico-legal inquiries,
therefore, it is of great value. A small quantity of
blood in an ordinary spectroscope will give the two
bands. They persist even after great dilution. If
the dilution be continued they begin to disappear,
first the band near the E line, and later that near the
D line. The adaptation of a spectral apparatus to the
ordinary microscope renders it easy to detect even a
very small trace of blood in a solution.

The micro-spectroscope is the term applied to
the combined apparatus. A detailed description of
its const ru ction and method
of employment may be valu-
able. Browning, Hartnach,
and Zeiss all make the in-
strument. A sketch plan of
Browning's form is shown in
Fig. 152. It is made for
fitting into the draw-tube of
any ordinary microscope by
means of the tube M, the
eye-piece of the microscope
being removed. The con-
tinuation upwards of M is a

wider tube, towards the upper Fig. i52.-The Micro-si
end of which there is a troscope.

diaphragm E, with a slit,

the diameter of the slit being variable by means
of a screw H. The light which has passed up the
tube of the microscope is thrown on the slit by

Li^^^-vJJ

ec-

33° PHYSIOLOGICAL PHYSICS. ichap. xxvi.

means of the convex lens N. Beyond the slit the
tube narrows to the size of the ordinary microscope
tube. The rays which have passed through the
slit fall first on the lens L, by means of which they are
rendered parallel, and in this condition fall on a set of
five prisms B. The set of prisms consists of three of
crown glass and two of flint glass, those of crown glass
being all set with their edges in the same direction, and
the two of flint fflass fitting in between the crown-

O O

glass prisms, their edges being in the opposite direc-
tion. This is shown in the figure, where the shaded
prisms are those of crown glass. The effect of this

combination of prisms is
to produce dispersion
without deviation ; that
is, the light is split up
into its elements without

Fig. 153. — Direct Vision I'rism. i • i • i u

being bent aside out or

its straight path. This is shown in Fig. 153. The
ray of light falling on the first prism is dispersed
and bent to the side. The dispersed rays enter the
prism of flint glass, their dispersion is increased, but
they are bent in the opposite direction. In the third
prism the dispersion is again increased, but the deviation
is again reversed, and so on through the five prisms,
till the rays leave the last prism with a considerable
amount of dispersion, but with their direction similar
to that of entrance into the first prism. A spectro-
scope with this arrangement of prisms is called a
" direct vision spectroscope." This system of prisms
is contained in the micro-spectroscope in an inner
tube of its own, and can be removed from the tube A
or inserted into it at pleasure. In use, the prisms are
removed from tube A, and the object on the stage of
the microscope focussed, the prisms are then replaced.
A screw D permits the collimating lens L to be placed
at its focal distance from the slit E, the screw H, as

chap, xxvi.] THE MICRO-SPECTROSCOPE. 331

already mentioned, being moved so that the slit is nar-
rowed till a sharply defined spectrum is obtained. For
the spectrum of blood a dilute solution of blood is
placed in a small cell on the stage of the microscope,
and the light from a mirror transmitted through it.
The cell recommended by Sorby is made by taking a
piece of barometer tubing half an inch long and one-
eighth of an inch in internal diameter. It is cemented
vertically on a piece of plate-glass by purified gutta-
percha. Either a low or a high power lens may be
used, though with high powers the illumination is too
weak for colours beyond the green, unless a condenser
be used underneath the stage. With such an arrange-
ment as has been described, only the spectrum, as
modified by the substance on the stage, is observed.
There remains to be noted a device for obtaining an ordi-
nary spectrum for comparison. In the wall of the wide
part of the tube (Fig. 152) is a small opening K, pro-
vided with a slit. In front of this opening, suspended
from a projecting arm and movable in all directions,
is a small mirror I, which reflects light into the tube
through K. K is just below the level of the slit E.
A small part of the slit E is covered by a small rect-
angular prism c, so placed that the reflected light
from the mirror passes straight through the near face
of the prism, but undergoes total reflection at the
internal surface of the diagonal face. The result of
the total reflection is to direct the rays from the
mirror straight up the tube of the micro-spectroscope,
by the prisms of which they are dispersed and a
spectrum produced. Thus, through one part of the
slit E rays pass from the microscope mirror up through
the fluid on the stage producing the clear characteristic
spectrum of the substance, while through the other
part of the prism rays proceed from the side mirror,
which pass through no absorbing substance, and yield
an ordinary spectrum. As seen by the eye the two

332 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

spectra are placed one above the other, and the posi-
tion of the absorption bands of one can be determined
by the other. By means of the spring s, a thin tube
containing a solution can be held over the opening K,
so that the spectrum of a substance on the stage of the
microscope can be compared with the spectrum of the
substance at the side. In some forms of micro-spectro-
scopes a contrivance is added for measuring the exact
position of the absorption bands. It is inserted into
the tube A just at the level of the upper end of the
series of prisms. It consists of an arrangement for
throwing an image of a fine line on the upper sur-
face of the last prism in such a direction that the
prism reflects it into the eye of the person looking
down the tube. This fine line is seen, therefore,
crossing the spectrum. By means of a screw the line
can be moved along the spectrum from one end to the
other, and made to coincide with anv of its dark

•>

lines. A micrometer attached to the screw measures
the extent of movement of the line. Thus, suppose
the screw had to be moved through a distance,
measured by 30 on the micrometer, in order to
make the line coincide with a dark line of the solar
spectrum, and suppose then some substance laid on
the stage gave an absorption band, and that the fine
line of the micrometer had again to be moved through
30 to make it coincide with the absorption band, it
would be known that the absorption band coincided
with a dark line of the spectrum.

A micro-spectroscope would readily indicate
whether a stain on clothing had been caused by blood
or not. The stain simply requires to be cut out of
the cloth, and placed in a watch-glass in a few drops
of water. The coloured solution obtained, placed in a
cell on the stage of a micro-spectroscope, would give
the two bands of oxy haemoglobin, even though the
drop of blood had been very small. There are various

Chap, xxvi.] THE MICRO-SPECTROSCOPE. 333

ways of corroborating the conclusion that blood is
present, by the addition of various reagents, and the
consequent alteration on the bands, reactions which
can be produced by even the one-hundredth of a
grain of blood.

Among other applications the rnicro-spectroscope
can be used for the detection of blood in urine.

Bile gives no spectrum if fresh ; but various com-
pounds produced in bile by decompositions and oxyda-
tion processes, e.g. by nitric acid, give spectra, by
which, therefore, indirect but conclusive evidence of
the presence of bile in a fluid can be obtained.

For demonstrating to a large number of persons
at one time the bands of haemoglobin., an oxyhydrogen
light, or, preferably, an electric light, is required. The
tube of the condensing lens of the lantern is fitted with
a cap having a vertical slit with a screw arrangement
for making the slit broad or narrow at pleasure. In
front of the lantern is placed a convex lens, by means
of which an image of the slit is focussed on to a
screen several feet in front. A sharp image being
secured, a prism is interposed in the path of the beam
of light between the lantern and lens, and the
prism turned till the best position for disper-
sion is secured, indicated by a good spectrum
being obtained. The prism frequently employed is
a hollow wedge-shaped cell of glass filled with bi-
sulphide of carbon, whose refractive index is 1'678,
and has, therefore, greater dispersive power than any
kind of glass. The rays are, of course, bent out of a
straight course and do not fall 011 the screen, but on
the walls or objects to the side. To save moving the
screen to the side to catch the spectrum, and so losing
the proper focus, the lantern, lens, and prism should
all be supported on one long board, which rotates on
a vertical axis. As soon as a proper position of the
prism is secured the board is turned, and the whole

334 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

apparatus carried round together, till the spectrum
is brought on to the screen. Now take a vessel, the
front and back of which are formed by two plates of
plane glass fixed parallel to one another, and only a
few millimetres apart. Into this pour a dilute solu-
tion of blood, and hold it in front of the slit. The
layer of blood will absorb certain rays, and the
spectrum of haemoglobin will be thrown on the screen.
The solution can easily be diluted to the strength
that gives the two bands sharply defined. Reducing
agents can be added to the blood in the vessel, and
after sufficient time has elapsed the band of reduced
haemoglobin will be obtained.

EFFECTS OF THE SPECTRUM.

Various observations have shown that the spec-
trum possesses (besides illuminating) heating and
chemical properties. These different properties are
not limited to definite regions of the spectrum. No
matter how great the dispersion, the illuminating
part of the spectrum cannot be separated entirely
from the heating portion, nor either of these two
absolutely from the chemically active part. But one
property is more intense in one part, and another
property in another part.

The illuminating effects of the spectrum were
shown to attain their maximum in the yellow portion,
and to shade off at each side, but to be least in the
violet end. This is sufficiently indicated to the eye
by the sombre hue of the violet end of the spectrum,
and the brilliancy of the orange and yellow part, a
brilliancy even beyond that of the red, and specially
of the extreme red.

The heating effects of the spectrum were first
shown by Herschell, in 1800, to be specially marked
in the red end. There are various ways of proving
this fact. A galvanometer attached to a thermopile

chap. xxvi.] PROPERTIES OF THE SPECTRUM. 33$

gives a greater deflection when the pile is in the red
end than when it is in either the yellow or violet part.
As the result of various elaborate researches made
since Herschell's time, by Seebeck, Milloni, and Tyn-
dall, a large number of facts regarding the calorific
effects of the spectrum has been obtained. It is now
known that the greatest heating effect is not obtained
even in the red, but beyond it. There are rays, that
is to say, of less refrangibility than the red, outside
of the red and invisible to our eyes, whose heating
effects are greater than those of the red. The maxi-
mum heating effects are obtained by these ultra-red
rays as they are called. It was found that certain
substances had the property of absorbing some of the
heat rays, while others, and notably rock salt, per-
mitted the heat rays to pass, absorbing very little.
The property of transmitting heat rays is called
DIATHERMANCY, that of absorbing them ATHERMANCY.
Tynclall found that solutions of iodine refused to
transmit light rays, but were quite pervious to heat
rays. He therefore interposed in the path of an
electric beam, a globe containing a solution of iodine
in bisulphide of carbon. The light rays were all
retained, and no visible rays issued from the lamp.
Yet he was able to focus the invisible heat rays on
to a piece of carbon,, and render it red hot, and to
treat a piece of platinum in a similar way. The heat
rays were detected as far beyond the extreme red as
the whole length of the visible spectrum.

The chemical effects of the spectrum were
proved by Scheele in 1777 to be specially intense at
the violet end, since chloride of silver blackened more
speedily in the violet than in any other part of the
spectrum. Hitter proved that in the invisible part of
the spectrum, beyond the violet, there existed chemi-
cally active rays. Beyond the violet there are rays
of greater refrangibility than the violet, vibrations of

336 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

greater rapidity than those of the violet, which do
not affect the eye, but can effect chemical changes.
These are called ultra-violet rays. If a beam
of intense white light be focussed on to a fine
glass bulb containing a mixture of hydrogen and
chlorine gases, the gases will violently unite to form
hydrochloric acid, and the globe will be burst with
a loud report. But if the beam be split up into a
spectrum, and the red part focussed on the globe, no
explosion occurs, nor yet with the yellow rays ; but
as soon as the violet rays fall upon the globe the
explosion takes place. It is the chemical activity of
the spectrum that permits of photography ; and photo-
graphy has been carried on by the agency of the
invisible rays beyond the violet. The spectrum, then,
has heating, illuminating, and chemical properties.
These properties are distributed throughout the whole
spectrum, but in different proportions, the most in-
tense heating effect being beyond the red end, the
most intense illuminating effect being in the yellow,
and the most intense chemical activity being beyond
the violet.

These effects are all due to vibrations, 'but vibra-
tions of varying rates of rapidity, the rapidity in-
creasing from the ultra-red region, where it is least,
through the red to the yellow, and still increasing
through the violet into the ultra-violet region. The
vibrations of the ultra red are not rapid enough to
excite the retina of the eye so as to produce the sensa-
tion of light, while the vibrations of the ultra violet
are too rapid for vision.

Fluorescence and pkosphorescence. — If a
glass cell containing a solution of sulphate of quinine
be placed beyond the violet rays of the spectrum, the
solution becomes self-luminous, and emits a pale blue
light. If the spectrum be thrown on to a screen
which has been washed with a solution of quinine,

chip, xxvi.] FLUORESCENCE. 337

the length of the visible spectrum is increased, the
increase taking place beyond the violet, and the light
being of the colour stated. Rays in the ultra-violet
part become by this means visible.

Canary glass, that is, glass coloured with uranium,
emits a faint nebulous light under similarcircumstances.
Many substances become self-luminous when light
falls upon them, the kind of light emitted being
dependent on the substance. Certain forms of fluor-
spar have this property, which, on this account, is
called FLUORESCENCE. A solution of chlorophyll emits
red light, a decoction of madder in alum emits
yellow and violet light. An aqueous solution of
asculiiie (extracted from horse-chestnut), and alco-
holic solutions of stramonium are also fluorescent.
All these substances exhibit the property when ordi-
nary white light falls upon them ; but they do not
necessarily exhibit it with all the separate colours of
the spectrum. Thus, as we have seen, sulphate of
quinine gives a blue colour when placed in the ultra-
violet rays ; but if placed in the green or yellow
region of the spectrum, no fluorescence is visible ;
while chlorophyll will emit the red in whatever part
of the visible sp3ctrum it may be placed. It thus
appears that the rays which are emitted by the
fluorescent body are never of a greater refrangibility
than those which fall upon them, and are generally of
a less refrangibility. The phenomena are explained
by supposing that the molecules of a particular body
tend to vibrate at a particular rate. Vibrations of
a longer period cannot excite the molecules of the
body, but vibrations of the same period will excite
vibrations in the body, just as one tuning-fork, tuned
to vibrate with a certain rapidity, will throw a neigh-
bouring tuning-fork, tuned to the same rapidity, into
activity. While, however, vibrations of a slower rate
cannot excite the molecules of the body, vibrations of
w— 7

338 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

a higher rate may, though the molecules of the body
thrown into vibration by more rapid movements
than their own, will still vibrate in their own period.
Thus a fluorescent body will permit vibrations of a
longer period than that to which its molecules tend to
oscillate to pass through it unaffected. Vibrations of
its own period it will, however, absorb, and its own
molecules being thrown into activity, it will itself
produce the vibrations. That is to say, light of the
same colour as the body itself emits, it will absorb
and emit, but light of a less refrangibility, of a less
speed of vibrations, it will permit to pass unaffected.
The molecules of the fluorescent body will, however,
be thrown into vibration by vibrations faster than
their own, but thus excited, thev will vibrate with

' \>

their own rapidity. In other words, light of a dif-
ferent colour than that which the fluorescent body
emits, but due to vibrations whose period is less than
that of the molecules, will excite the fluorescent body,
and it will emit a light of its own period of vibration.
Thus the sulphate of quinine solution is excited by
vibrations of the ultra-violet region, and emits a blue
light ; light, that is, whose period of vibration is less
than that of the ultra-violet rays. By this means
vibrations whose rapidity is too great to produce the
sensation of vision are transformed into vibrations
whose rapidity is less, and can excite the retina, and
they are thus rendered visible. Sulphate of quinine,
therefore, increases the length of the visible spectrum
by diminishing the rate, by diminishing the refrangi-
bility, of the ultra-violet rays. But sulphate of
quinine is not fluorescent in the yellow because the
period of vibration of the yellow rays is less than that
in which the molecules of sulphate of quinine os-
cillate.

PHOSPHORESCENCE is the property which some
bodies possess of being luminous in the dark after

chap, x xvi. ] PHOSPHORESCENCE. 339

they have been exposed to the light. The sulphides
of calcium and strontium remain luminous in the
dark for several hours after exposure to a strong
light, diamonds, chloride of calcium, some barium
compounds, magnesium and other substances also. E.
Becquerel has shown that there are few substances
not phosphorescent, though in many the luminosity
lasts for so short a time that it is made apparent only
by special contrivances, such as Becquerel's PHOS-
PHOROSCOPE. Phosphorescence is explained in a way
similar to fluorescence. The phosphorescent body
absorbs certain rays, transforms them, and emits
them changed. Becquerel holds the two phenomena
to be of a similar character, the fluorescent body occu-
pying much less time than the phosphorescent in the
process, the former effecting the transformation while
the light is upon it.

Some animals are luminous in the dark ; the
glowworm, the lampyre, and certain marine animals
whose light produces the phosphorescence of the sea.
That this property in animals is due to the same
causes as the phosphorescence of sulphide of calcium,
for instance, is not certain. The phosphorescent
material of the animals is probably a secretion.
Both fluorescence and phosphorescence can be produced
by passing an electric discharge from an induction coil
through a Geissler's tube containing the body to be
observed.

Colour. — If in front of the slit of a lantern,
whose beams afford a spectrum, a sheet of red glass be
placed, nearly all the spectrum will be cut off but the
red ; .the red will pass through and appear on the
screen ; the yellow will pass with difficulty, and the
colours beyond the yellow with increasing difficulty.
Similarly, yellow glass will permit yellow rays to pass;
all others will be enfeebled , notably the blue and violet.
If in the red part of the spectrum some red ribbon be

340 PHYSIOLOGICAL PHYSICS. [Chap. xxvi.

placed, it will appear of a brilliant red; but as the red
ribbon is moved through the spectrum it loses its
brilliancy, till, when quite beyond the red, it appears
black. Yellow ribbons, in the same way, are yellow
only in that part of the spectrum, in other parts colour
is absent. It thus appears that bodies are coloured in
one way or another according as they behave towards
white light. If they transmit the red rays they appear
red, if they transmit yellow rays they appear yellow, and
so on. If they transmit more than one colour of rays
their apparent colour will be a blend. In fact, coloured
bodies may be regarded as splitting white light up
into its elements, as absorbing some of these ele-
ments and as transmitting or reflecting others. Ac-
cording to the rays they transmit or reflect is the
colour they appear to have. If they transmit the
rays they are transparent and of the colour of the rays
transmitted, if they reflect the rays they are opaque
bodies of the particular colour. If a body reflects all
the rays it is white ; if it absorbs all it is black.

Mixture of colours.— A body might transmit
or reflect not only rays of one simple colour, but rays
of several kinds, and in such a case it would appear
to have a colour which is a compound of the different
rays. The results produced by the admixture of two
or more simple colours of a pure kind were carefully
worked out by Helmholtz, who used a spectroscope
with a V-shaped slit, by means of which he obtained
two spectra, which he was able to manipulate so as to
superimpose one on the other. The one limb of the
slit was placed at right angles to the other limb, so
that the violet of one spectrum was superposed on
the red of another. Helmholtz' results are given in
the following table, where the top line and the side
column indicate the superposed colours of the two
spectra, and the other columns give the results of the
blending of the two.

Chap. XXVI.]

MIXTURE OF COLOURS.

Violet.

Indigo.

Blue.

Green-
Blue.

Green.

Yellow-
Green.

Yellow.

Red

Purple

f Deep
( Rose

(L-ght
(. Rose

White

( Light
( Yellow

Golden \
Yellow )

Orau;/ e

Orange .

j Deep
( Rose

(Light
(. Rose

White

f Light
I Yellow

Yellow

Yellow

Yellow .

j Light
( Rose

White

f Light
( Green

j L-ght
( Green

f Green-
( Yellow

Yellow-
Green

j- White

f Light
I Green

Light )
Green f

Green

Green .

( Light
I Blue

Blue

(Greeu-
}Blue

Green-
Blue

j-Blue

Blue

Blue

Indigo

The mixture of colours can be shown by taking a
rotating disc and placing sectors of different colours
on it. On rotating the disc rapidly the eye cannot
distinguish each colour separately, but the different
impressions are blended, and an impression of a com-
pound colour produced. If sectors of all the seven
colours of the spectrum are placed on a disc in this
way, in a definite proportion, and the disc rapidly
rotated, the impression is of white light, or, rather,
grey, because colours cannot be got of such purity as
those of the spectrum. The colour top of Clerk-
Maxwell is an application of this method.

Fundamental and complementary
colours. — Reference to the table shows that red
mixed with greenish-blue produced white, that orange
and blue produced white, yellow and indigo also, and
greenish-yellow and violet. To put it in another way :
given red, all that is necessary to produce white is
greenish-blue; given violet, all that is necessary for
white is yellowish-green. These colours, then, are

342 PHYSIOLOGICAL PHYSICS, tchap. xxvi.

said to be COMPLEMENTARY to one another, white light
being the result of their union. It is evident, also,
that, suppose red and violet were taken, to produce
white, greenish-blue and yellowish green are all that
are necessary ; but, as the table shows, green is the
result of a mixture of greenish-blue and yellowish-
green, so that a mixture of red, green, and violet
would produce white. This the colour top or rotating
disc shows to be the case. If the three colours are
arranged on the disc, in proper proportions, and
rapidly rotated, the eye has an impression of white.
Further, by varying the proportions of the three colours
on the disc all the shades of the spectrum may be
produced, not with the brilliancy of the spectrum,
because of the admixture of white or the less degree
of saturation, as it is phrased. These three colours,
red, green, and violet, are for these reasons called

FUNDAMENTAL Colours.

Primary colours they are also called ; and, as we
have seen, if mixed in various proportions they pro-
duce various other colours. Thus the spectral red
and green produce yellow, the resultant colour being
called a secondary colour. The following table shows
similar combinations, the arrows indicating the two
colours combined and pointing to the result :

Primary. Secondary.

Red-".™;-.;— — -;.::;:.-"->Yellow.
G reen-c.-:-.."""' """"""^P urple.

It is not to be supposed, however, that the three
colours exist as such in the spectrum, and that the
blending of them in different proportions produces the
gradations of colour. Colour is only a subjective
thing. The colours of the spectrum are due to vibra-
tions of varying rates of rapidity, of different wave
lengths, and when these vibrations affect the eye they

Chap, xxvi.] THE YOUNG-HELMHOLTZ THEORY. 343

produce the sensation of colour, which is, therefore,
not an objective fact. It is the mixture, in varying
intensities, of three fundamental sensations, that of
red, that of green, and that of violet, that gives the
sensation of varying colours.

Another error must be guarded against. The
mixture of red, green, and violet pigments will not
give white, but this is not a mixture of colours. If a
beam of white light be passed through a plate of red
glass, and then through one of blue, the result will be
almost darkness, because we have absorption of rays.
The red glass keeps back almost all rays, and transmits
only red to any extent ; but then these rays passing
through the green glass are retained, because it trans-
mits only green. Similarly with a mixture of powders,
the reflected light which gives the powder its colour
is that which comes from the deeper layers of the
powder after it has travelled through the upper layers,
and has, therefore, undergone absorption.

Thus, in a mixture of two simple coloured pigments,
the apparent colour will be that due to the light which
has escaped the united absorption of the two, rather
than the colour due to a mixture of the two corre-
sponding colours of the spectrum.

Young-If elmholtz theory.— The view of three
fundamental colours is specially that of Thomas
Young, and has been advocated by Helmholtz. It
gave a means of explaining the facts of colour sen-
sations. Young supposed that in the retina there
were nerve-fibres readily affected by vibrations of the
rapidity of the red rays of the spectrum, another set
sensitive to the vibrations of the green, and a third set
sensitive to the vibrations of the violet. If the first
set was chiefly affected, the sensation was of red, if
the second set chiefly, the sensation was of green, and
so on. The vibrations corresponding to the yellow
of the spectrum, according to this theory, excite

344 PHYSIOLOGICAL PHYSICS. [Chap. xxvn.

moderately the fibres sensitive to red and to green,
and feebly the fibres sensitive to violet, the resultant
sensation being yellow. So the vibrations corre-
sponding to the blue of the spectrum excite moderately
the fibres sensitive to green and violet, and feebly
those sensitive to red, the resultant sensation being
blue. Thus the sensations of various kinds of colour
are all due to excitations in different degrees of three
sets of nerve-fibres in the retina, each set being
specially affected by vibrations of definite rapidity.

Qualities of compound colour. — Tone of
colour is determined by the simple colour which pre-
dominates in the mixture. Intensity is dependent on
the amplitude or extent of the vibratory movements
of the ether by which the sensation of light is produced.
The degree of saturation of colour signifies the extent
to which the colour is or is not mixed with white
light. The colours of the spectrum are fully
saturated.

CHAPTER XXVII.

ABERRATIONS OF LENSES.

Chromatic aberration.— A lens is practically
an arrangement of prisms. Thus, a doubly convex
lens may be considered as two prisms set with their
bases together, the angles being rounded off, as shown
in Fig. 154, and a doubly concave lens may be con-
sidered as two prisms with their edges together.
Now we have seen, in the last chapter, that when a
ray of white light passes through a prism it is dis-
persed into its seven constituent colours, red, orange,
yellow, green, blue, indigo, and violet, because of the

chap, xxvii.] CHROMATIC ABERRATION.

345

different degrees to which these colours are refracted
by the prism. It is to be expected that the same
thing will happen in a lens,
and that the most refracted
rays will be brought to a
focus sooner than those least
refracted, the violet rays,
that is to say, will be
focussed nearer to the lens
than the red. This actually
happens, and is represented F'g. 154.

155, where two

n Fig.

rays at extremities of the lens are shown to be dis-
persed, the violet rays forming a focus at b, the red at
r, and the rays of the spectrum between the red and
violet being disposed regularly between r and 6. If
the light has proceeded from an object, no proper white
image will be formed, but, instead, circles of colour will

Fig. 153. — Chromatic Aberration.

surround the object, which, if placed at b, will have a
central circle of violet changing gradually till the
outer ring of the circle is red ; and, if placed at r, will
have a central circle of red, changing gradually through
the colours of the spectrum to violet. This is called
chromatic aberration. This property of lenses seemed
at first to offer an insuperable obstacle to the employ-
ment of lenses for magnifying purposes, since, owing to
it, no clear definition of an object could be obtained ;
and it seemed impossible to obtain, a lens which would

346 PHYSIOLOGICAL PHYSICS. [Chap. xxvn.

refract rays of light without, at the same time, dis-
persing them. In 1733 Hall, of Worcestershire, was
able to construct a lens which refracted rays of light
without dispersing them. He did not make known
his discovery. In 1757 a London optician, named
Dollond, rediscovered the method of getting rid of the
chromatic aberration. Lenses constructed with this
object are called ACHROMATIC.

Suppose two prisms of the same material and pre-
cisely the same in other ways, and suppose a ray of
light to fall on one, it will be bent out of its course
and split up into a spectrum, in other words, dispersed.
The second prism will refract and disperse the ray to
the same extent. If, then, the second prism be placed
so as to receive the rays emerging from the first, but
placed with its refracting edge in the opposite direc-
tion, it will refract and disperse the rays to the same
extent as the first, but in an opposite direction. It
will, that is to say, exactly neutralise the action of the
first one, and the rays will be recombined and will
emerge from it in a direction parallel to that in which
they entered the first one. It was found, however,
that the extent to which a prism refracted a ray of
light was not necessarily a measure of the extent to
which it dispersed the ray. In other words, one might
have two prisms of different materials, so constructed
that while both dispersed a ray to the same extent,
one refracted less than the other. So that if these
two prisms were placed in opposite directions, the
second one would disperse equally with the first, but
in an opposite direction, and so reunite the dispersed
rays ; but it would refract less than the first, so that
the ray would emerge from the second prism unclis-
persed but not parallel to the entering ray, since all
the refraction produced by the first prism was not re-
versed by the second. It would still be refracted to an
extent equal to the difference between the refractions

Chap, xxvii.] ACHROMATIC LENS. 347

of the two prisms. Thus it became possible to make
a convex lens of two different substances, so that
the dispersion produced by the first part of the lens
would be destroyed by the second, while the refrac-
tion, though diminished, still persisted. Rays of
light passing through such a lens are brought to a
focus without the accompaniment of rings of colour,
except to a very slight extent, the lens being prac-
tically achromatic. Such a combination is obtained
when crown glass and flint glass are used. A doubly
convex lens of crown glass is used, fitted to a concave
lens of flint glass.
The action of such
a lens is repre-
sented in Fig. 156,
where the ray P

passing through Fig. 156. -A chroma tic Lens.

the convex lens

would be refracted, and at the same time dispersed,
so that the violet rays would be focussed at q,
and the red rays at q ; but the concave lens overcomes
the dispersion, diminishing at the same time the re-
fraction, and the ray P is focussed at Q'.

Different substances do not disperse different
colours in the same ratio, so that while the total
dispersion by two substances may be made the same,
the dispersion of the colours between the extremes
may be in different proportions. A combination of
lenses, such as has been noted, will recombine two
given colours, but will not absolutely recombine the
others. The rays usually sought to be recombined
are the more luminous, such as orange and blue, and
this degree of achromatism is generally found sufficient,
though absolute achromatism can be obtained by
further combinations on the same principles.

Spherical aberration. — In speaking of mirrors
it was remarked (page 304) that it is not absolutely

PHYSIOLOGICAL PHYSICS. [Chap. xxvn.

true for spherical mirrors that all the reflected rays
meet in one point. Similarly, it is not absolutely true
for lenses that the refracted rays meet in one point,
though it becomes more nearly true the smaller the
aperture (page 314) of the lens. The rays from the
circumference of the lens are focussed nearer to the
lens than rays from more central parts of the lens.
The result is, that when the centre of the image is well
defined the circumference is blurred, and vice versa,
because the focal points for the outer and inner rays

do not correspond. This is
shown in Fig. 157, where A is
the focus for the outer rays a
c, and JB is the focus for the
central rays b. At the position
B the centre is in focus, but not

Fig. 157.— S herical AVer- ,u . ,, mi . ,

ration. the circumterence. Ihis aber-

ration is easily rectified by cut-
ting off the external rays. In front of the lens, there-
fore, a diaphragm or stop is usually placed with an
opening in the centre. In photography the diaphragm
is of the utmost consequence. Every photographer
prefers to have such illumination as will permit him
to use a diaphragm with a very small opening, since
this adds to the definition and sharpness of his image.
It, of course, at the same time diminishes the
amount of light. In the chapter on the eye it is
noted how the iris acts as diaphragm, and varies in the
size of its pupil with the amount of light.

Spherical aberration can also be corrected by a
combination of lenses of suitable curvature.

349

CHAPTER XXVIII.

OPTICAL INSTRUMENTS.

THE application of the facts and la\vs relating to
mirrors and lenses that have been considered in pre-
ceding chapters has resulted in the construction of
various instruments of the utmost value in various
departments of science. The nature of some of these
instruments it is the business of this chapter to con-
sider. There will first be described in some detail
two instruments of which mirrors form the chief
part, and which are of great importance in practical
medicine,, the laryngoscope and the ophthalmoscope.

The laryngoscope is for the purpose of illumi-
nating the fauces and pharynx and rendering their
inspection more complete, and for making visible the
larynx, or, at least, an image of it. The idea of the
instrument is due to Listen, the credit of its practical
application belongs to Czermak.

The illumination of the fauces is accomplished in
various ways. The usual method is to place the
patient opposite to the observer ; at one side of the
former, slightly behind him, and on a level with his
ear, is a lamp furnishing a steady bright light.
Strapped to the forehead of the observer, or supported
in a spectacle frame, is a concave mirror. The mirror
is pierced in the centre by a small opening, so that
when it is brought in front of the observer's eye he
can look through the opening. The rays from the
lamp are caught on the mirror, and reflected by it
into the patient's mouth, which is widely opened, his
tongue being held down by a tongue depressor, or by
its point being grasped between finger and thumb of

35°

PHYSIOLOGICAL PHYSICS, [Chap, xxvin.

the observer, and pulled slightly forwards and down-
wards. The rays from the concave mirror are thus
brought to a focus in the fauces, the proper position
Tbeing secured by adjusting the position of the lamp,
and by movements of the head of the examiner, who
sees the brightly illuminated fauces, one
eye looking through the opening in the
mirror.

The other and essential part of the
apparatus (Fig. 158) consists of a small
plane mirror, which may be round, oval,
or square. Passing off directly from the
edge of the mirror is a long stem, which
makes an angle with the mirror of about
125°, and terminates in a handle. The
mirror is to be placed in the fauces of the
person whose larynx is being examined.
Before introduction it is heated to the
temperature of the body to prevent the
breath of the patient depositing moisture
upon it, and so obstructing the view.

The plane mirror being placed in
the patient's fauces, the light from the
concave mirror is focussed upon it, and
its position is then so adjusted that its reflected
rays pass down into the larynx, which may thus
be brightly illuminated. This position is usually
secured when the plane of the mirror forms an angle
of 45° with the horizon. Now the larynx being
illuminated just acts as any luminous body, and from
its various points rays pass upwards and fall on the
plane mirror. From that mirror they are reflected,
and, if it be in a proper position, they pass straight
outwards to the observer's eye, who thus sees an image
of the larynx as if behind the plane mirror, as de-
scribed on page 302. Usually the first parts to come
into view are the back of the tongue and tip of the

Fig. 158.-
Laryngoscopic

Mirrors.

Chap, xxviii.] THE OPHTHALMOSCOPE. 351

epiglottis, and then, as the plane mirror is adjusted,
the cartilages of the larynx and the vocal cords. The
image is reversed to this extent, that what appears
posterior in the mirror is anterior in the patient, and
vice versa. But the right side of the image is also the
right side of the patient, only, because of the relative
positions of patient and observer, the right hand of
the observer is opposite the left of the patient, and
consequently the vocal cord seen in the mirror to the
observer's right is the patient's left vocal cord, and
the patient's right cord is to the observer's left.

An ingenious arrangement devised by the late
Dr. Foulis, of Glasgow, permits a person to examine
his own larynx. A glass globe, such as is used by
jewellers to focus the light on their work, is filled with
water and mounted on a candlestick. Above it is
placed vertically a piece of plane looking-glass. The
person sits down with this on a table in front of him.
On the other side of the globe is a lamp. The globe
concentrates the light on the person's face. He opens
his mouth and allows the light to be focussed on the
faucvQ,s, which he sees illuminated by looking in the
mirror. Guided by the image in the mirror, he intro-
duces the small laryngoscopic mirror in the usual way,
and thus sees in the mirror in front of him an image
of the image in the laryngoscope.

The ophthalmoscope is a small concave mirror
by means of which rays of light are directed through
the pupil of the eye so that the deep parts are illumi-
nated and rendered visible. It was invented by
Helmholtz in 1851. The deep structures of the eye
cannot usually be seen, because rays reflected from
them diverge as from any luminous point at a finite
distance. The divergent rays, as they pass through
the media of the eye, are converged, and meet in a
conjugate focus outside of the eye. The observer,
to perceive the image thus formed, must have his eye

352 PHYSIOLOGICAL PHYSICS, rchap. xxvin.

placed at a distance from it equal to that of distinct
vision, that is, still farther from the observed eye.
But at this distance the field of vision is so extremely
small that nothing can be distinguished. Moreover,
the person in endeavouring to see this image interposes
himself between the source of light and the eye to be
observed, and so cuts off the verj- rays whose reflection
he wishes to intercept. In all circumstances, con-
sequently, the eye appears dark. If, however, an
observer throws light into the eye from a mirror, and
if he places his eye behind the mirror, through an
opening in which he can look, he does not intercept
the rays, and he can find the conjugate focus of the
rays reflected from the ocular chamber, and thus per-
ceive an image of the structures reflecting the light.
This was the method at first employed by Helmholtz.
He sat in front of a patient, at whose side was a
lamp. By means of a plate of glass held in front of
one of his eyes, and placed at an angle to the light, he
directed rays from the lamp into the person's eye
through the pupil. Some of the light is absorbed by
the eye, but some is reflected outwards, along the
same paths by which it reaches the eye, to the plate
of glass. Here again some of the rays are reflected ;
but some pass through the plate into the observer's
eye, and so there is perceived an image of the retina
and other deep parts.

Instead of the plate of glass a slightly concave
mirror was afterwards substituted, which permits a
greater concentration of light through the pupil of
the observed eye. The concave mirror is pierced in
the centre by a small opening, through which the
observer looks.

Now the ophthalmoscope may be used with or
without lenses. If the ophthalmoscope be used
without lenses, on illuminating the back of the eye to
be observed, and on the observer bringing his eye

chap, xxviii.] THE OPHTHALMOSCOPE. 353

near enough, an image is seen of the retina, optic
nerve entrance, etc. The image is virtual, erect, and
magnified, as represented in Fig. 159, ed. This
image can be obtained only if the observing and the
observed eyes are both focussed for an infinite
distance. This is practically secured by making the
person look to a distant point, say at the other end of
the room, and by the observer looking as if to a
distance. This condition, however, it is often not
possible to obtain. The result is that the reflected
rays from the eye are not accurately focussed on the

Fig. 159.— The Ophthalmoscope with Erect Image.

retina of the observing eye, and circles of diffusion
are formed.

Under such circumstances the use of a diverging
lens will render the image distinct. The action of
such a lens is shown in Fig. 159.

The observed eye is A, and the small arrow a
represents a part of the retina 011 which light is
thrown by the concave mirror. Rays from a passing
outwards would be converged by the media of the eye,
and would come to a focus at 6. An image would
thus be formed, 6c, magnified, and inverted, a real
image moreover. But by the action of the concave
lens B (whose focal distance is pB) the rays are made
to diverge, and thus a virtual image is formed behind
the eye, an image larger than the object, but erect.
That is, the rays from a, which reach the observer's
eye, appear by the action of the lens to proceed from
the point d. .
x— 8

354 PHYSIOLOGICAL PHYSICS. [Chap, xxvin.

A converging lens is also frequently employed.
The effect on the reflected rays is shown in Fig. 160.
The observed eye is represented by A, and a is a point
on the retina. The reflected rays passing through the
media of the eye would, if permitted, meet at 6, and an
image of part of the retina represented by the arrow
a would be produced, represented by the arrow eb.
1 But the convex lens B refracts the rays still more,
and the result is that the rays are focussed at d,
nearer to the observed eye than eb. Consequently the

n-

Fig. 160.— The Ophthalmoscope, with Inverted Image.

observer's eye c, placed at the distance for distinct
vision, sees an image f, smaller than eb, inverted, and
real.

Thus the ophthalmoscopic mirror, alone or in con-
junction with a concave lens, gives a virtual erect
image, considerably magnified. The convex lens gives
a real inverted image, and considerably less magnified.
The focal length of the convex lens usually employed
is about 6 centimetres. With such a lens the extent
of magnification is about four times, but with a lens
of longer focus it would be increased.

There are many forms of ophthalmoscope which it
is not necessary to consider here. In general the
concave mirror ought to have a focal length of about

*— ' O

18 centimetres, and the convex lens one of 6 cc.
Usually there are also supplied two discs, each of
which has, round its circumference, a series of circular j
openings, about 8 millimetres in diameter. In one
disc, each of these openings is occupied by small con-
vex lenses of varying focal length, in the other by

chap, xxviii.] ENDOSCOPE. 355

small concave lenses. Each disc can be fitted on an
axis at the back of the ophthalmoscopic mirror, and
can be so revolved that any one of the small lenses
can be brought directly over the small opening
through which the observer looks. If the observer be
short-sighted, he can thus bring in front of his eye a
small concave lens of sufficient focal length to correct
his short sight ; if long-sighted, he puts on the
ophthalmoscope the disc of convex lenses, and corrects
with one of them. Similarly, if the observed eye be
short or long-sighted, the retinal image could not be
brought into focus with the mirror only, but the
observer can adjust his concave or convex disc, as the
case may be, and find a lens that will correct the
short sight or long sight of the eye he is observing.
In this way the ophthalmoscope may be made a test of
the normal degree of refraction of an observed eye, and
a measurer of the degree of variation from the normal.
Endoscope is the term applied to an instrument,
devised in 1853 by Desormeaux, specially for illu-
minating the canal of the urethra. It consists of a
straight, hollow, metallic sound wrhich is passed into
the urethral canal. The outer end is terminated in a
wider tube, at the end of which is an eye-piece,
through which an eye may look into the sound. Near
to the outer end of the tube is a plane mirror, set at an
angle, and perforated by a small opening in the centre.
Opposite to the mirror a tube comes off at right
angles, in which is a plano-convex lens. The rays
from a lamp, placed to the outside of the lens, are
caught by the lens and concentrated on the mirror,
whose angle is so adjusted that the light is reflected
into the sound. The canal is thus illuminated, and
rendered visible to an eye at the eye-piece, owing to
the opening in the centre of the mirror. In the in-
strument of Desormeaux, the lamp is in one with the
sound and other parts, and the light is placed in the

356 PHYSIOLOGICAL PHYSICS. [Chap, xxvin.

focus of a concave mirror, so that a greater amount of
light is thereby thrown 011 the lens for concentrating
on the plane mirror. By similar dispositions of
mirrors and lenses, other canals and cavities of the
body have been explored.

MICROSCOPES.

The simple microscope. — It has been seen
(page 318) that when an object is placed between a
double convex lens and its principal focus, the cones
of light proceeding from various points of the object
do not meet after passing through the lens, but are
still divergent. No conjugate focus on the opposite
side of the lens is formed, but, instead, the pro-
longations backwards of the divergent pencils meet in
points on the same side of the lens as the object, but
outside of the principal focus. A virtual image is
thus formed, which, on account of its position, is
erect and highly magnified. (See Fig. 146.) It is thus
evident that a simple biconvex lens affords an easy
means of magnifying small objects, and rendering
them more clearly visible. The eye looks through
the biconvex lens, which has a small object on its
other side, nearer than its principal focus, receives
the divergent rays, focusses them on to the retina by
its own refractive media, and the image so produced
is referred outwards in the direction of the rays
falling on the retina, and the eye thus perceives the
highly magnified virtual image. It will be seen also,,
from reference to page 318, that the nearer the object-
is to the principal focus, while within it, the more
highly magnified is the object, and the nearer the
object is to the lens than it is to the principal
focus, the less highly magnified will be the image.
It is equally evident that the more convex the lens,
the more will the rays passing through it be refracted,
and when they do not converge, the more wide will

chap, xxviii.] SIMPLE MICROSCOPE 357

be the divergence between their backward pro-
longations, and consequently the more magnified the
image. The single biconvex lens, then, forms a simple
microscope for viewing very small objects. The
property of a biconvex lens was evidently known to
the ancients, at least to the Greeks and Romans.
" There is in the French cabinet of medals a seal,
said to have belonged to Michael Angelo, the fabri-
cation of which, it is believed, belongs to a very
remote epoch, and upon which fifteen figures have
been engraven in a circular space of fourteen milli-
metres in diameter. These figures are not all visible
to the naked eye" At the Belfast meeting of the
British Association in 1852, Sir David Brewster
showed a lens, made out of rock crystal, which had
been found among the ruins of Nineveh, and which
he believed to have been used for optical purposes.
The magnifying power of globes filled with water was
also known at an early period. Nevertheless, the
valuable properties of lenses were not to any extent
known till the middle of the seventeenth century.

The application of these properties to form an in-
strument for magnifying small objects, is ascribed to
Zacharias Jansen and his son, of Middleborough, in
the low countries, who made microscopes in 1590.
A Neapolitan, named Francis Fontana, claims to have
invented the instrument independently in 1618. A
Dutch alchemist, Cornelius Drebbel, brought one of
Jansen's instruments to London in 1619, which was
seen by William Borrelli and others. Drebbel him-
self made microscopes in London in 1621. With the
simple microscope much remarkable work was done.
It was with such an instrument that Lieberkiihn,
Leuwenhoech, and Swammerdam worked. Leuwen-
hoech had a separate lens for nearly every object he
examined.

The difficulties, however, in the use of highly

353

PHYSIOLOGICAL PHYSICS. [Chap. xxvm.

magnifying lenses were very great, difficulties arising
from the aberrations of sphericity, which rendered the
object difficult to focus with good definition, and from
the error of chromatism due to the dispersive power
of the lens. These prevented much progress being
made in the improvement of the instrument. One
improvement consisted in the employment of two
plano-convex lenses instead of one, the convex sides
being directed towards the eye, the focal length of the
one next to the eye being three times that of the
lens next the object. This was called Wollaston's
doublet. It diminished the amount of the aberra-
tions, and specially so when, later, a diaphragm was
interposed between the two lenses.

The compound microscope consists, in its
simplest form, of two lenses, one next the object,

called the object-glass^ and one
next the eye called the eye-glass.
The action of the two is shown in
Fig. 161, where LL' is the object-
glass, and MM' the eye-glass. AB is
a small object placed beyond/, the
focal distance of LL'. By the action
of LL' a real inverted image of
AB is formed on the other side of
LL', viz. ab. Rays from ab diverge
towards the eye-glass MM', which
is so placed that its focal distance
ist/i Thus, ab is within the prin-
cipal focus of MM'. Rays from ab
will, therefore, still diverge after
Passing through the lens MM', but
will, by the action of the media of
the eye of the observer placed beyond MM', be brought
to a focus on the retina. The image on the retina will
be referred in the direction of the divergent rays enter-
ing the eye, in the direction, that is, of the dotted lines,

Chap, xxvi ii.] CORRECTION FOR ABERRATION. 359

and will see a virtual image A'B'. Now it is to be
observed that while ab is a real image of AB, A'B' is
only a virtual image of ab. In other words, it is an
image of an image. If the lens LL' is an ordinary
one. the image ab will exhibit spherical and chro-
matic errors, and consequently the image A'B' will
exhibit these still more, since it is a magnified image
of ab. Errors, that is, made by the object-glass, are
all exaggerated by the action of the eye-glass, and the
more refracting the lenses the more striking are the
aberrations. Hence it is easily seen how difficulties
grow in the effort to get higher magnifying powers,
and how specially great are the difficulties in the way
of the development of compound microscopes.

Between the lens LL' and the position in which
its image would be formed, there may be interposed
another convex lens, the effect of which will be to
refract to a greater extent the rays going to form the
image «6, and thus to produce a smaller image, the
whole of which will more easily come within the
range of the eye-glass. The eye-glass and this addi-
tional glass are placed in one tube at a proper distance
from one another, and their combination is called the
eye-piece, the lens next the eye being still called the
eye-glass, and the distant one being the field-glass.

Correction for aberration in microscopes.
— The compound microscope was rendered practically
useless by reason of aberrations, till the discovery of
Hall and Dollond rendered it possible to correct a
lens so as to destroy its dispersive power without
abolishing its refractive power. It has been pointed
out (page 347) that a double convex lens of crown
glass properly adjusted to a plano-concave lens of flint
glass makes an achromatic combination for two colours,
but for only two. This is not, however, sufficient for
microscopic objects. By the labours of MM. Selligues
and Chevalier of Paris (1823), and those of Professor

36°

PHYSIOLOGICAL PHYSICS. [Chap, xxvin.

Amici, of Modena (1827), there was shown a method
for rendering the object-glass of a highly magnifying
microscope completely achromatic. The combination
consists of three pairs of lenses, each pair being made
of a doubly convex lens of crown glass, cemented by
means of Canada balsam (whose refractive index is
the same as that of crown glass) to a plano-concave
lens. These lenses are placed close to one another,
the plane surface being towards the object, and are so
arranged that one lens corrects the errors of the other.
Fig. 162 shows this combination, in position in the

supporting tuoe. With corrected
lenses also the angular aperture is
increased. The angular aperture
is represented by the side part of
Fig. 162 by the angle bfb'. This is
the angle formed by the extreme rays
which are able to pass through the
system of lenses. Thus in the figure,

Fig. 162. - Achro- tne ravs fa /«' are too oblique to
matic combina- pass through the three pairs of

tion and Angle J i ?i 7 /., / *

of Aperture. lenses, but the rays jb fb pass, and
it is between them the angle of
aperture is contained. It is evident, of course, that
the more rays that pass through the system of lenses
the better illuminated will the object appear to be,
and the fewer the rays the dimmer the object. So
that, from this point of view, any method which in-
creases the angular aperture, and thus increases the
illumination, is an improvement. Yet it is to be
noted that the more that oblique rays are caused to
pass through the system, the greater is the difficulty of
correcting for spherical aberration; and, even when
the correction is complete, the narrower is the
border-land between clear definition and blurring of
the object.

Another point remains to be noted about the

Chap. XXVI II.] ACHR OMA TIC OBJECTIVE. 361

objective. The object on the stage of the microscope
is often covered with fluid, and a cover-glass. Rays
from the object are dispersed to some extent in pass-
ing through the film of liquid or the cover, and if the
magnifying power employed be very high, chroma-
tism results. This may be corrected by altering
the position of the lenses in the object-glass. Hoss,
of London, therefore, constructed an objective as
shown in Fig. 162, such that the lens next the object
was placed in the tube «, while the other two were
fixed in the tube b. A screw at the side permits
the lowermost lens to be moved nearer to, or farther
away from, the other two, and so the lens can be
adjusted for viewing an uncovered or a covered
object.

The general principles that have been explained
are those applied in the construction of the best
modern microscopes. Lenses made of crown and flint
glass are used and combined into sets. The method
of combination varies, however. Thus, instead of
three lenses, each of which is a doublet (i.e. made of
two lenses cemented together), in one arrangement
the middle lens is a triplet, consisting of a doubly
concave lens of flint between two convex lenses of
crown glass, the other two being plano-convex lenses
of crown glass. In another combination the back lens
is a triplet, the middle one a doublet, and the front
one a single plano-convex lens.

Now supposing an object-glass is obtained cor-
rected for spherical and chromatic aberration, it is
evident that, if the eye-piece is chromatic, blurred
and coloured images will still be obtained, though

O o

to a less extent. The eye-piece must be achromatic
as well as the object-glass. An eye-piece devised
by Huyghens for getting rid of spherical aber-
ration in the eye-piece of telescopes is found to
answer the purpose, and to be not only free from

362 -PHYSIOLOGICAL PHYSICS. tchap- xxvm.

spherical, but also from chromatic aberration,
Huyghens himself, it appears, was unaware that his
eye-piece served both purposes. It was applied to
the microscope by Campani.

Hiiygliens' eye-piece consists of two plano-
convex lenses fitted into one tube at some distance
from one another. The plane surface of each lens is
towards the observer's eye. The distance between
the two should be equal to half the sum of their focal
length. The disposition of the two lenses is such that
the aberration of one corrects that of the other. The
first lens disperses the rays from the object, but the
dispersed rays by passing through the eye lens are
rendered parallel. They appear to the eye on that
account to come from the same point ; the different
colours, therefore, coincide, and a white, instead of a
coloured image, is the result. Between the two
lenses there is a stop, which cuts off outside rays, and
so the aberration' of sphericity, as well as that of
chromatism. is got rid of.

Immersion lenses. — The more one increases
the magnifying power of a lens the shorter becomes
the focal distance. The more nearly the object ap-
proaches to the objective, the more obliquely do the
rays proceeding from it fall upon the object-glass, the
fewer rays are able to pass through the system of
lenses, and the weaker is the illumination. Besides,
the shorter the focal length becomes the greater is the
difficulty of obtaining cover-glasses of sufficient thin-
ness to interpose between the object and the object-
glass. Amici conceived the idea of placing on the
cover-glass a drop of water or other liquid into which
the first lens of the object-glass dips. The rays of
light passing from the object through the cover-glass
into the water are less refracted than if they passed
through the cover-glass into air. In the former case
the rays fall less obliquely on the object-glass, and are

Chap, xxvi ii.] IMMERSION LENSES. 363

thus able to pass through it ; while, in the latter case,
the difference between the refractive index of glass
and air is so much greater that the rays would fall 011
the objective more obliquely, more would be unable
to pass through, and loss of light would result.
Instead of water, glycerine may be used. Oil of cedar
wood has been found specially useful by Prof. Abbe
of Jena, because its refractive and dispersive powers
are nearly that of glass. Lenses made for use in this
way are called immersion lenses, but it is usually
only for very high powers that they are employed.

Mechanical parts of a compound micro-
scope.— Pig. 163 represents a compound microscope
of Zeiss's model. It consists of a firm foot which sup-
ports an upright stand. The stand is jointed so as to
permit of the microscope being inclined or placed
horizontally. From the stand projects a horizontal
arm p, terminating in a ring r, in which is screwed a
tube T. This tube is split so as to permit the lens
tube ti, to slide up and down easily. The lens tube
consists of an outer tube t, movable up and down in
the split tube T,, by means of the milled edge m'.
Fitting into the tube t, and also movable in it, is a
second tube D, which is called the draw-tube, and is
pushed home into t, or drawn out, by the milled edge
m. E points to the outer end of the eye-piece which
fits into D. At the other end L of the microscope
tube is a screw adjustment which permits of the lenses
being screwed on or off the tube, s is the stage on
which the object to be examined is laid, and on it are
two little spring slips for holding down the slide on
which the object lies. In the centre of the stage is
pierced an opening through which light can be directed
by the mirror M, placed a little distance under the
stage and movable in all directions. Under the stage
is a disc pierced with openings of various sizes, the
smallest no larger than a pin-head, any one of which

364

PHYSIOLOGICAL PHYSICS. [Chap, xxvin.

can be brought under the opening in the stage. It
thus acts as a stop, and regulates the quantity of light,
aiding in definition with high powers by cutting off

the outside rays.
Under the stage is
fitted A66, a con-
denser, an arrange-
ment of convex
lenses for concen-
trating the light
from the mirror on
the object and so
increasing the il-
lumination. The
form used in Zeiss's
microscopes is
Abbe's, and can be
removed or replaced
at pleasure. It is
specially serviceable
for high powers.
There are two

All

focussing

arrange-

Fig.

ments in such an
instrument. The
coarse adjustment is
made by grasping

ejge ^

leS.-Compom^Microscope (Zeiss's

with finger and

thumb of one hand , the other hand steadying the foot of
the instrument, and, by means of a slightly turning
movement, slowly moving t down or up the split tube
as may be desired, thus bringing the lenses nearer to or
taking them farther away from the object. The object
having been brought into view, accuracy of definition
is obtained by a slight turning, in one direction or
in another, of the fine screw F, the fine adjustment.

chap, xxviii.] COMPOUND MICROSCOPE. 365

By this screw the whole body of the instrument above
/ is moved up or down on a pillar, and so focussing
is effected.

The magnifying power of such a microscope can
be affected in three ways : (1) by different lenses, (2)
by different eye-pieces, and (3) by the extent to which
the draw-tube D is pulled out of the tube t. In-
creased magnification by different lenses is already
understood. The eye-piece, it has been seen (page
359), magnifies the real image formed by the objective,
and this image may be magnified more or less accord-
ing to the power of the eye-piece. The shorter the
eye-piece the more does it magnify. A short eye-piece
is often called " deep." Great magnification by the
eye-piece is objectionable, since any faults caused by
the object-glass are also magnified. By increasing the
length of the tube the magnifying power is increased.
The increased length is effected by pulling out the
draw-tube D. Many instruments have a scale marked
on the draw tube, so that the distance it is pulled out
may be accurately known. Loss of light follows
increased length of the tube, since the light is thus
distributed over a greater length, and fewer rays will
be focussed by the field-glass of the eye-piece. With
each microscope two eye-pieces at least are supplied,
a long one, one of small magnifying power, and a
short one, of higher magnifying power. The objectives
are usually numbered or lettered. Thus, in Zeiss's
list, A objective magnifies 38 diameters with No. 1 eye-
piece, 52 with No. 2 eye-piece, and 71 with No. 3 ;
B magnifies by 70 diameters with No. 1 eye-piece, 95
with No. 2, and 130 with No. 3 ; D objective magni-
fies by 175 diameters with No. 1 eye-piece, 230 with
No. 2, and 320 with No. 3. With Zeiss's instru-
ment, the student would have an admirable microscope,
using lenses A and D and eye-pieces Nos. 1, 2, and 3.
Such an instrument (without Abbe's condenser)

PHYSIOLOGICAL PHYSICS. [Chap. xxvm.

would cost him about £9 5s., with the condenser
£11.

Some makers designate their objectives by the
length of their focal distance. Thus the 1-in. objective
magnifies on an average by 80 diameters, J-in.
magnifies by 130 diameters, and the ^-in. objective
350 diameters.

To measure magnifying power. — The
magnifying power is the ratio of the magnitude
of the image to the magnitude of the object. Ther«
are various experimental methods of determining
it. For these a MICROMETER is necessary. This is a
glass slide on which a series of lines is ruled by means
of a diamond, the lines being at stated distances from
one another, several being distant y-^th of an inch,
several y^Voth of an inch, or it may be y^th and
y-Q^th of a millimetre. The micrometer is placed on
the stage and focussed. Suppose two lines y^-^th of
an inch apart, the question is how far do they seem to
be apart when viewed under the microscope. Take a
pair of compasses, separate their points and hold them
close up to and on a level with the slide on the stage.
Both eyes are kept open, the one opposite to the hand
holding the compasses looking down the tube of the
microscope. With a little practice, one eye will see the
image of the lines of the micrometer scale, and the
other the points of the compasses. Open or close the
limbs of the compass till the images of the two lines
coincide with the points of the compass. The distance
between the two points is now the apparent distance
between the two micrometer lines. The actual dis-
tance between the two lines is the yg-^th of an inch.
Measure on an inch scale the distance between the
two points of the compasses. Let it be \ inch. The
apparent distance is ^ inch, the actual distance is
yjyo-th of an inch, and the apparent distance divided
by the real distance gives the magnifying power.

chap, xxviii.i MAGNIFYING POWER. 367

i

-|- = magnifying power.

Tcfo

= 50 diameters.

If the distances marked on the micrometer be in
millimetres, then a millimetre scale must be used to
measure the distance between the two points.

A second method consists in fitting to the eye-
piece of the microscope a neutral tint reflector (page
373). The microscope is bent so as to be placed hori-
zontally : on the table straight under the reflector and
at the nearest distance for distinct vision (10 inches)
is placed an inch scale or a millimetre scale, according
as the micrometer is ruled to give to British or French
measurement. The reflector is placed at an angle of
45° to the line of the microscope tube, and the
observer's eye is placed immediately above the reflector
and looking straight down upon it. The rays from the
micrometer scale, after passing out by the eye-piece,
fall on the reflector and are partly reflected upwards
into the observer's eye, who accordingly sees an image
of the micrometer lines. At the same time rays from
the scale on the table pass upwards, pass through the
tinted glass unaffected, and reach the eye. The image
of the micrometer scale and the rays from the scale on
the table thus coincide, and the observer can read off
how many divisions of the scale on the table are in-
cluded between two lines of the micrometer scale. He
thus obtains the apparent size, and can make the
calculation as before.

The inch or millimetre scale might also be held at
the side of the microscope stage, as the compasses
were held, and a direct reading taken in this way of
the apparent size of the object.

It need scarcely be observed that the magnifying
power determined by any such method is true only
for the particular objective and eye-piece that are in

368 PHYSIOLOGICAL PHYSICS. [Chap, xxvin.

use, and for the position of the draw-tiibe, at the time
when the determination is made.

To measure the actual size of the object.

— If one had determined the magnifying power of the
microscope and then focussed the object, the actual
size would be known by measuring with compasses or
scale the apparent size. The apparent size divided by
the magnifying power gives the actual size. Thus, if
the apparent size were 1 inch and the magnifying
power 300 diameters, the real size would be -anoth
inch. This method, however, is not quite exact. A
more correct method requires a micrometer scale for
both stage and eye-piece. The stage micrometer has
been already described. The eye-piece micrometer
consists of a piece of glass having fine lines, equi-
distant from one another, drawn upon it, and it is of
great advantage that every fifth line should be longer
than the other four. This micrometer may be in
the form of a circular piece of glass fitted into a
piece of tube of proper length, arranged for dropping
into the eye-piece by unscrewing the eye lens, which
is then replaced. The micrometer tube rests on the
diaphragm of the eye-piece, and ought to be of a
length to permit of the lines being in proper focus.
Or the eye-piece micrometer may be on a slide which
is slipped into the eye-piece by a slit in the side.
It being adjusted, the lines on the stage micrometer
are brought into focus, the lines of the eye-piece
micrometer then appear superimposed on those of the
stage micrometer, and it is found how many divisions
of the former are equal to one of the latter, which is
equal, let us say, to the T^oo^n °f an inch. Suppose
five of the eye-piece divisions were equal to one of the
stage divisions, then each line of the eye-piece micro-
meter is distant from the other the -g^Qth of an inch.
Now remove the stage micrometer, and place on the
stage the object to be measured. On focussing it will be

Chap, xxviii.] BINOCULAR MICROSCOPE. • 369

seen through how many divisions of the micrometer eye-
piece the object extends. Suppose it is accurately
enclosed by t\vo divisions, then, since each equals the
Woo^h of an inch, the diameter of the object is the
smooth of an inch.

The binocular microscope is an arrangement
for permitting both eyes to view the image. The
benefit of such an instrument is due to the fact that
both images will not be precisely alike. One eye
will receive rays which the other does not receive,
and the result will be the same as the effect of a
stereoscope, the object will be perceived in relief,
and elevations and depressions of the surface more
easily recognised. One method consists in inter-
cepting the rays from the objective by means of
two prisms, one prism deviating the rays from one
half of the lens, and the other prism from the other
half. There are thus two different tubes for such a
microscope, one for each set of rays. The objection to
this method is that the prism must be achromatic, and
so adds to the difficulty, while the fusion
of the two images gives rise to a pseu-
doscopic instead of a stereoscopic effect,
the elevations being made depressions
and the depressions elevations; the
relief is in the opposite direction to
what it is in reality, owing to the revers-
ing of the image. A method free from pr;Sms4'~ar-
these objections is shown in Fis. 164. ranged for

mi • n , , , c Bin ocular

inree prisms are used, but they are Microscope,
placed not for dispersion but for
total reflection, dd' is the object, and rr the objec-
tive by which rays from dd are converged, so that
rays from d' entering the first prism, are totally re-
flected from the internal surface at u, and are
thrown into the second prism s' on the opposite side,
by whose internal surface at o' they are reflected up
Y— 7

37°

PHYSIOLOGICAL PHYSICS. [Chap.

the tube, in the direction P', to the eye of the observer.
Rays from the opposite side of the object are reflected
from u' into the prism s, and from its face 0 are thrown
in the direction p to the other eye of the observer.

An arrangement of Nachet's, capable of being
adapted to any microscope, is represented in Fig.
165. Above the objective a is a totally reflecting prism
D, so placed as to receive half of the rays
from the object c passing through a.
The rays are reflected by D into a second
prism E, by which they are again re-
flected, and pass up the microscope tube
to the eye-piece A'B'. The other half of
the rays pursue their straight course
unmolested to the eye-piece AB. The
prisms can be arranged so as to permit
the rays from the right half of the
objective to reach the right eye, and
the rays from the left half the left
eye, and so produce a pseudoscopic
effect ; or they may be arranged to
cross the rays
scopic picture.

of Nachet's the additional tube can be removed with
its prisms, and the microscope used as an ordinary
monocular instrument.

In Wenham's arrangement a single prism of pe-
culiar shape, placed above the objective, effects the
same purpose as the two of Nachet's. Hartnack has
contrived a binocular eye-piece in which there are
four rectangular prisms (Fig. 166) placed as shown.
Rays proceeding up the tube of the microscope
towards E are intercepted by the prisms A and B,
and totally reflected. Half proceed towards D,
where they are again reflected up into the ob-
server's eye at F, while the other half proceed
towards c, and are reflected up to the other eye at E.

Ar-

rangeruent for
converting a

Monocular into

,

arranged

and §'ive the true stereo-
With this arrangement

Chap. XXVIII.]

CAMERA Luc IDA.

Here the change of eye-piece is all that is necessary

to convert a monocular into a binocular, or to reverse

the process. In all forms of

the stereoscopic microscope,

however, the loss of light,

owing to so many reflecting

surfaces, is so considerable,

that for ordinary practical use

the monocular microscope is

the most serviceable.

THE DRAWING OF MICRO-
SCOPIC OBJECTS.

Various forms of optical Fig> lee.-Hartnack's Bino
apparatus have been devised for cuiar Eye-piece,

fitting to a microscope, in order

to permit of a faithful drawing being taken of the
magnified image.

Wollaston's camera liirida, devised in
1807, is one form very generally employed. It con-
sists of a prism of glass set in a
brass case fixed to a short tube
which is slipped on the eye-piece
instead of its eye-glass. The body
of the microscope must be placed
horizontally. Fig. 167 represents
the path of the rays.
Rays of light oo, passing
up the microscope tube,
fall upon the perpendicular
face of the prism which
is next to the tube. They
meet this face at right
Fig. 167.— Camera Lucida. angles, and pass unaffected

into the prism, to fall

on the lower internal face, where, owing to the
angle, they are totally reflected in an upward direction.

372

PHYSIOLOGICAL PHYSICS. [Chap. XXVIIT.

By their striking on another internal face, as shown
in the figure, a second total reflection occurs, the rays
passing up into the eye of an observer at E looking
straight down. On the table, at a distance of about
ten inches from the eye-piece is a sheet of white paper
pp, the reflected rays from which pass straight upwards,
and reach the eye in lines parallel with the rays from
the object. The eye on looking straight down through
the small square corner of the prism that is uncovered
by the brass case, will see the image of the object on
the sheet of white paper. If a pencil be then taken in
the hand and held with its point on the paper in the
position to draw, after a little practice the image and
the point of the pencil can be made to coincide, and
thus one is able with the pencil to follow on the
paper the image of the object, and so produce an
accurate sketch of it. To facilitate the coincidence of
pencil and image, a slightly convex lens is placed
below the prism to concentrate the light.

Chevalier's camera liicida is adapted for
a microscops in a vertical position. It is represented

in Fig. 168. The eye-
piece of the micro-
scope is removed and
the camera put on
instead, the screen s
serving to fix the
camera tube to the
microscope tube M. At

Fig. 168.-Chevalier's Camera Lucida. P is a rectangular prism

by which the rays from

the object are totally reflected into the tube at right
angles. At the end of the tube is a second prism p',
which reflects the rays into the observer's eye above.
At the same time, rays from a sheet of paper and the
point of a pencil, placed on the table ten inches below,
reach the eye from the direction p", and thus with the

Chap. XXVIII.] ^flCRO-PHOTOGRAPHY. 373

point of the pencil we can follow the lines of the
image on the paper.

The raetitral tint reflector of Dr. Beale is one
of the simplest and least expensive of all aids to draw-
ing. It consists simply of a circle of tinted glass set on
a ring at an angle of 45°. By means of the ring it is
slipped on the eye-piece. The microscope is hori-
zontal, and the eye placed above the eye-piece looks
straight down through the reflector. The rays from
the microscope falling on the glass are reflected upwards
into the eye, and at the same time light from a paper
below can pass through the glass and fall on the eye,
so that the coincidence of the image and the point of
the pencil on the paper can be obtained. The glass
is of neutral tint, to diminish the glare from the paper,
which would interfere with the distinctness of the

image.

MICRO-PHOTOGRAPHY.

Photographs of objects, as magnified by a micro-
scope, may be taken in various ways, which ought to
receive mention in this place. The ordinary com-
pound microscope may be used, the mirror having a
condensing arrangement bevoiid it for concentrating

*/ C3

the light on the object. Instead of the eye-piece a
dark slide is fitted to the tube of the microscope, so
that the image is focussed on the plate which it con-
tains. The plate is one of the usual sensitive plates,
and after exposure and development a photograph of
the object will be obtained. In this case the image
is not very large.

A very simple arrangement permits the ordinary
photographic camera to be used with the microscope.
The lens of the camera is unscrewed, and, the eye-
piece of the microscope being removed, the microscope
tube, placed horizontally, is closely fitted into the
opening in front of the camera. The camera should

374 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

be capable of considerable extension, and on extending
it an image of the object will be cast on the ground-
glass plate. One initial obstacle in the way of micro-
photography is the great loss of light that is involved
in the arrangement, and the consequent difficulty in
the way of using high powers. To some extent this
is overcome by the extreme degree of sensitive-
ness which can now be given to photographic plates.
Any one can now attempt micro-photography without
going through a long apprenticeship in the preparing
of plates fit for working with. Plates of extreme
sensibility can be readily procured, and all one has
to acquire is the art of taking and developing the
picture, since material to work with of the best pos-
sible description is to be had at comparatively small
cost.

CHAPTER XXIX.

THE EYE AS AN OPTICAL INSTRUMENT.

Camera obscura. — We saw (page 300) that if
a small opening exists in the wall of a dark chamber,
the rays of light from the outside passing through the
opening will form an inverted image of the external
object on the opposite wall of the chamber. Unless
the opening be very small, the image will be blurred
and indistinct from the overlapping of rays from
various points of the object. If the opening be small
enough the overlapping rays are cut off, and a distinct
image formed, but a very dim one, owing to the loss of
light. If, however, a conyex lens be interposed in the
path of the rays, the opening may be enlarged, and the
various rays are brought to a focus so that the images of
diffusion are prevented. Now the dark chamber or

Chap. xxix. j THE CAMERA OBSCURA. 375

camera obscura is well known in its form of photo-
graphic camera. It consists of a box (Fig. 169), black-
ened in the interior to prevent reflection from the walls.
In front is a short tube hi containing a system of
achromatic lenses. For the back wall of the box is sub-
stituted a ground-glass plate g,
on which the image formed by
the lens is focussed. In photo-
graphy, for the ground-glass
plate a plate sensitive to light is
substituted, on which the imaoje

,-1 mi £ v i i Fig. 169. —Camera Obscura

is thrown. I he action or light

on the sensitive surface of the plate produces
chemical changes, varying in degree according to the
varying intensity of the light in different parts of the
image. So that on developing the image by various
solutions, the salts of the sensitive coating, that have
been acted on by the light, are deposited on the plate.
At a point of the image corresponding to a point of
the object from which no light was reflected to the
camera, no change will have occurred, and that part of
the sensitive plate will be removed from the plate.
Thus grades of thickness in the plate's coating will be
produced, according to the varying lights and shades of
the object, and these will constitute the developed
image. Besides dark chamber, lens, and sensitive
plate, other arrangements are necessary. If the
camera be so adapted that parallel rays falling on the
lens are brought to a focus on the sensitive plate, it is
obvious that divergent rays will not be focussed on. the
plate, but behind the plate, so that a blurred instead
of a sharp image would result. If, however, the
sensitive plate could be moved backwards, it could be
made to coincide with the conjugate focus of the rays
diverging from the object. This is effected by making
the chamber in two halves (b and a), one telescoping into
ths other, so that the chamber can be lengthened ov

37 6 PHYSIOLOGICAL PHYSICS. ichap. xxix.

shortened at pleasure. The focussing for different
distances is also effected by altering the position of the
lens, in reference to its distance from the plate, and
this is clone by the screw r. Finally we have
noted (page 348) that spherical aberration interferes
with the distinctness of images, and that this is got rid
of by cutting off outside rays proceeding from the
object. In the camera this is accomplished by insert-
ing a diaphragm, through a slit in the lens tube,
between the glasses of the lens. In the diaphragm a
central hole is pierced, a diaphragm with a large or
small hole being used according as the light is feeble
or strong.

Now the EYE is to be regarded as a camera obscura
with a small hole in front, through which rays of light
pass, and with refractive media. The sclerotic and
choroid coats form the walls ; the cornea, aqueous
humour, crystalline lens, and vitreous body are
different refractive media, but they all tend to effect
the same purpose, to bring parallel rays of light to a
focus on the sensitive coat, the retina, and so to form
there a sharp, real, and inverted image of the object.
There is also a focussing arrangement for always
bringing the clear image on to the retina, in spite of
varying distances of the object. Lastly, the iris with
its pupil acts as a diaphragm, contracting with strong
light so as to limit the rays, and dilating with little
light so that more rays pass through.

In the eye the converging apparatus does not
consist of a single refracting medium. There is the
aqueous humour, separated from air by the convex
cornea, and the aqueous and vitreous humours, separ-
ated from one another by the more dense crystalline
lens. The refraction effected by the cornea alone
would bring rays, falling on the eye from a distance,
to a focus about 10 millimetres behind the retina, and
it is the additional convergence produced by the

Chap. XXIX.]

OPTICAL CONSTANTS.

377

lens that brings the focal point forwards so as to fall
on the retina. The crystalline lens refracts the rajs
more than once, first by its anterior surface, when the
rays enter it from the aqueous humour, and last by its
posterior surface, when the rays issue from it to pass
into the vitreous body. But it has been shown
to be composed of various layers with different
densities and, consequently, different indices of
refraction, so that even while passing through the
substance of the lens rays of light will undergo a series
of successive refractions, all tending to converge the
rays to a focus. Thus rays of light in passing through
the eye encounter various media, with different
refractive indices, and the determination of the path
of the rays is to some extent complicated. We shall
therefore consider first the method of determining the
course of the rays in any system of refractive media,
and then apply the method to the particular case of
the human eye.

In a system of several different refractive
media the path of a ray of light may be found by a

Fig. 170. — Construction of an Image by means of the Cardinal Points.

geometrical construction. In Fig. 170 let ab CD and
El be spherical surfaces separating four different
refractive media, 1,2,3,4, and let the centres of curva-
ture of the media be in the same straight line, the line
passing through FF', which is called the principal
axis, the admission of six cardinal points or optical

378 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

constants of Gauss enables one to find the path of
rays passing through the system, and to construct an
image of the object from which the rays have passed.

The cardinal points or optical constants are as
follows : (1) two focal points ; (2) two principal points;
(3) two nodal points.

The focal points are represented in the figure by F
and F'. P is the anterior and F' the posterior focal
point. Planes passing through these focal points
perpendicular to the axis are focal planes, oo the
anterior focal plane, and o'o' the posterior focal plane.
Now the feature of these points is, that all rays which
diverge from the anterior focal point F, and pass
through the refractive media, issue from the media in
a direction parallel to the axis ; and all rays, which
before entering the media are parallel to the axis,
issue from the media so as to converge to the posterior
focal point F' ; that is, F and F' are to the system
wrhat the principal focus is to a single refractive
medium.

The principal points are represented in the figure
by P and P', and the relation between the two is such
that, both being in a transparent medium, a luminous
point in the medium, which, to an observer situated on
the left, seemed, owing to the refraction, to be at P,
would, to an observer situated on the right, seem to
be at P'. The two points, that is to say, are conjugate
foci, and therefore rays passing through one point will
pass through the other also. Through P and P' let vv
and vV be planes perpendicular to the axis ; they are
principal planes. Any point in the plane vv will
have a conjugate focus in vV, and thus any ray passing
through a point in one plane will pass through a
corresponding point in the other plane, situated at the
same distance from the axis, and on the same side.
The planes represent the two ideal surfaces of separa-
tion of the transparent media. The distance FP is

Chap. XXIX.] OP TIC A L CONS TA NTS. 379

called the anterior focal length, and the distance F'P'
the posterior focal length.

The nodal points are N and N', and are such that
an incident ray, which passes through N, the first nodal
point, will correspond to an emergent ray, which will
pass through N', the second nodal point, and both rays
will be parallel to one another. In a simple lens the
only point through which a ray may pass and issue
parallel to its original direction is the optical centre,
and straight lines other than the principal axis, pass-
ing through the optical centre of a lens, are secondary
axes. In a system of media, then, lines which pass
through both nodal points may be counted as secondary
axes. N and N' thus represent the optical centres for
the surfaces to which p and p' belong.

The optical constants being known, the path of
rays through the different media may be traced, and
the image of an object constructed.

Thus in the figure let AB represent an object from
which rays pass through the system of media. From
A draw a line parallel to the axis. It cuts the first
principal plane in c, and the second principal plane
in c', equally distant from the axis. From c' it passes
through the point F', since incident rays parallel to the
axis emerge so as to converge to the posterior focal
point. ISText draw a line to the first nodal point, it
must pass through the second nodal point N', and
emerge parallel to its incident direction, that is, in the
line N'A'. It cuts the line through F' in A'. Draw a
third line from A, and let it pass through the anterior
focal point F. After cutting w in H and vV in the
corresponding point Kf, it issues from the media
parallel to the axis, and thus cuts the other two
lines in A'. All these lines meet in A', and therefore
A' is the image of A. By the same construction the
image of B would be found in B'. Thus A'B' is the
image of AB.

380 PHYSIOLOGICAL PHYSICS, [Chap. xxix.

The position of the optical constants can be deter-
mined by a mathematical formula, provided the
indices of refraction, the radii of curvature, and the
thicknesses of the different media be given.

In the case of the eye, these values, according to
Listing, are as follows :

Index of refraction for air ... ... 1

Index of ref rac ;ion for aqueous humour. . . i ^ — 1 '3379*

Index of refraction for crystalline lens ... \\ = 1'4545*

Index of refraction for vitreous body ... V^ = 1-3379*

Radius of curvature of cornea ... ... 8 mm.

Radius of curvature of anterior surface of

crystalline lens ... ... ... 10 mm.

Radius of curvature of posterior surface

of crystalline lens ... ... ... 6mm.

Distance of the anterior face of the cornea

from the anterior surface of the

crystalline lens ... ... ... 4 mm.

Thickness of the crystalline lens ... 4 mm.

* Helrnholtz gives 1'3365 for aqueous humour ;
1 '3382 for vitreous body ;
1/4415 for crystalline lens.

The centres of curvature of the different media,
are in the same straight line, THE OPTICAL AXIS OF
THE EYE, which passes through the centre of the
globe and the summit of the cornea.

Using the above values, the positions of the car-
dinal points of the human eye on the optical axis,
calculated from the summit of the cornea, are as
follows :

Anterior principal focus ... 12-8326 mm.

Posterior principal focus ... 22-6470 mm.

Anterior principal point ... 2-1746 mm. ] Difference,

Posterior principal point ... 2*5724 mm. / 0-3978.

First nodal point ... ... 7 '2420 mm. 1 Difference,

Second nodal point 7'6398 mm. j 0-3978.

Of these, the anterior principal focus is in front of
the cornea, the others are behind.

Chap. XXIX.] SlZE OF RETINAL IMAGES, 381

The distance between the anterior principal focus
and the anterior principal point ( = the anterior focal
length) is 15-0072 mm. ; and the distance between the
posterior principal focus and the posterior principal
point (= the posterior focal length) is 20 '0746 mm.

From these data may be shown the course of rays
through the eye and the position and size of images.

The size of the retinal image. — In consider-
ing simple lenses, we saw that the size of the image
was obtained by the formula,

size of image distance of image from lens

size of object distance of object from lens

The same rule applies to the eye when we calculate
the distances of image and object as from the nodal
points. The two nodal points may be taken as coin-
ciding ; therefore

size of image distance of image from nodal point

size of object distance of object from nodal point

The distance of the image from the nodal point is
the posterior focal distance ; this distance in distinct
vision may be counted as the distance between retina
and cornea, less the distance between cornea and
nodal point ; while the distance of the object from the
nodal point is the distance of the object from the
cornea + the distance between cornea and nodal
point.

Let I = size of image, 0 = size of object, P = dis-
tance between object and cornea, P' =• distance between
retina and cornea, and B, distance between cornea
and nodal point ; then

I ZjzJ?

o — P + R'

NY>w the distance P' — 22 '6470 mm., and the

382 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

distance of the nodal point R= 7 '4; therefore P' —

R= 22-6470 - 7-4 = 15-2470.

Therefore

J_ 15-247

O P+7-4'

and

15-247

I = O

P+7'4-

Suppose an object 1,000 mm. (1 metre) high, seen
at a distance of 15-2396 metres (15239-6 mm.), what
is the size of the retinal image ?

15-247
1>0' "15239-6 + 7-4

= 1*0 mm.

That is, at a distance of rather more than 15
metres, the image is a thousand times smaller than
the object.

The visual angle is usually defined as the
angle included by the lines from the extreme points
of the object where they cross at the nodal point,
the angle x enclosed by the lines A and B of
Fig. 171. Helmholtz, however, has shown that the

visual angle is properly the
angle enclosed by the visual
\ lines, which are lines from a
point in space which pass through
the centre of the image of the
Fig. 171.— Visual Angle. pupil formed by the cornea, and

pass to the centre of the yellow

spot. The apparent size of objects depends upon
the visual angle. Thus the objects c d e all form
the same angle x, and thus appear to the eye to be
of the same size. The size of the angle depends
on (1) the size of the object, and (2) its distance from

Chap, xxix.] THE VISUAL ANGLE. 383

the eye. Thus one body larger than another, but at
a greater distance from the eye, will be seen under
the same angle x. The smallest visual angle per-
mitting distinct vision is 60 sec., and it corresponds
to a retinal image about 0'004 mm. in size, a size
just sufficient to cover one of the cones of the retina.
Two points seen under an angle of 60 sec. would
appear as one.

The smaller the visual angle under which distinct
vision is possible, the more acute is the vision, so
that acuteiiess of vision is inversely as the size of the
visual angle. Test types now in use for estimating
acuteness of vision are constructed on this principle.
Thus, Snellen's types are all arranged to be seen under
an angle of o minutes. Let D be the distance at which
the types ought to be seen under the angle of 5
minutes, and d the shortest distance at which the
person whose sight is being tested sees the object,
then the acuteness of vision is given by the formula

When d = D, acuteness of vision is normal.

Accommodation of the eye for distance. — The
refractive media of the eye are such that parallel rays
are brought to a focus on the retina ; the posterior
principal focus, that is to say, is on the retina. Such
an eye is called emmetropic. It is evident that if
divergent rays fall upon the eye, that is, rays from a
finite distance, they will not be brought to a focus
on the retina, but behind the retina, if the eye
remains in the same condition so far as its refraction
is concerned. The result of this would be circles of
diffusion, and a blurred and indistinct image. The
experiment of Schemer illustrates the diffusion
images. A card is taken, in which two small holes

Pff 1 -'SIOL OGICA L PH I 'S/CS. [Chap. XXI X .

are pierced close to one another. The card is
held close to the eye, and in front of it is held
a needle. On moving the needle nearer to the card
and then farther from it, a position is found where it
is distinctly seen. If it be brought slightly nearer,
the needle appears double, and the same thing happens
if it be moved away a little from its first position.
The explanation is evident from Fig. 172, where A

and B represent the
holes in the card, a the
point of the needle ; c
represents a lens, and D,
E, and F, a screen at
Pig. 172.— Schemer's Experiment varying distances from

it. With the screen

at E, a distinct single image of the needle is perceived,
because the rays from A and B coincide, and are
focussed at o ; at the position F, the image is blurred
and double, because the rays from A do not coincide
with those from B, while at D the image is also double
and blurred, because the rays are intercepted after
they have diverged from their focus. With the
screen in a fixed position, the same effects are pro-
duced by varying the distance of a from the screen.
Let C and the screen represent the refractive media
of the eye and the retina, the explanation applies, and
the phenomena of diffusion images are understood.

It is evident, then, that the eye in its condition
for focussing parallel rays will produce on the retina
images of diffusion with divergent rays, because the
focal point is thrown behind the retina. It is equally
evident that if an increase of refractive power were
given to the media, the focal point would be brought
forward and made to coincide with the retina. Every
different distance of the object looked at would
require a new adjustment. The increased refractive
power would be conferred by the addition of another

Chap. XXIX.]

THE PHAROSCOPE.

385

convex lens in front of the crystalline. This is
practically accomplished by the lens itself being
capable of adjustment for varying distances, a
capacity termed the power of accommodation. It
consists of an ability to alter the convexity of the
lens. This is effected by the contraction of the
ciliary muscle, which relaxes the anterior ligament

Fig. 173. — Accommodation of the Eye.

of the lens, permits the lens to bulge forwards
by its own elasticity, and thus increases its con-
vexitv. The figure shows on the side marked I

«/ o

the position of the lens when the mechanism of
accommodation is in repose, and on the side marked
p the new position in accommodation. It is mainly
the anterior surface of the lens that takes part in
the process. Its curvature augments, and its radius
of curvature for the greatest amount of accommodation
is diminished from 10 to 6 mm. The posterior sur-
face of the lens practically does not alter.

The phakoscope is an instrument devised by
Helmholtz for rendering visible the alteration in
curvature of the anterior surface of the lens. It is
shown in Fig. 174. It consists of a black box made
of pasteboard, of the triangular shape shown in the
•figure, and mounted on a stand. In. the centre of

386

PHYSIOLOGICAL PHYSICS. [Chap. xxix.

the base of the triangle is a little window, just above
a in the figure, projecting vertically upwards, in

which is a needle point. Di-
rectly opposite, in the truncated
apex of the triangle, is an opening
through which the eye to be
observed looks. The person at
this opening is directed to look
across through the window a, as
if to a far-off object. At one of
the angles of the triangular box
are placed two prisms b and 6',
in front of which a candle is
Fig. 174.— The Pimko- placed, the lisjlit from which is

scope of Helmholtz. 7, 1 , i "" ' • • j i i

thrown by the prisms in the ob-
served eye. The observer looks through the opening
at o towards the eye to be observed, on which he
sees three images, being images of the candle flame.
They are reflected images ; the first is large, bright and
upright (a, Fig. 1 75), a virtual image, the reflection from
the surface of the cornea acting as a
convex mirror ; the second image b is
larger and erect, but dim. It is the
reflection from the anterior surface
of the lens, a virtual image also. The
third image c is small, inverted, and
still dimmer, a real inverted image from
the posterior surface of the lens,
actino- as a concave mirror. Now

Fig. 175.— Pur-
kinje's Images.

when the person whose eye is being
observed looks, not through the window to a distant
object, but to the needle point in the window, he
brings his accommodation into play, and the second
image is seen to become smaller and to approach the
first, that is to say, the anterior surface of the lens
moves forwards. The discovery of the three images
is due to Purkinje.

Chap. XXIX.] RA NGE OF AcCOMMODA TION. 387

The range of accommodation.— For parallel
rays, then, the normal eye requires no adjustment.
Practically, rays falling on the eye for any distance
not less than sixty-five metres do not necessitate
accommodation. For any object within this distance,
however, increased convexity is necessary. At this
distance, and up to infinity, we have, therefore, the
puncium remotum of distinct vision. The nearer
within the limit the object coires, the more is the
accommodating power caJ'.eJ. '.rite play, the lens
becomes more and more convex. Bat ib is apparent
that there must be another Hmit. A point must be
reached beyond which any approach of the object to
the eye cannot be compensaved for by the lens. The
accommodation is strained to its uttermost ; and, if the
object comes nearer, its raps cannot be focussed on
the retina. This is the punctum proximum, and
normally is distant 1 2 centimetres from the eye.

Between the two limits is the range of accommo-
dation of the eye for distance.

The power of accommodation of an eye would be
measured by the converging power of a lens which
produced distinct vision of an object placed at the
punctuin proximum, without calling in the accom-
modation of the eye, a lens, that is, which would so
act on the rays diverging from the near point as to
give them the direction of rays coming from the far
point, a parallel direction, namely, for which accom-
modation is not required in the normal eye. The
focal length of such a lens is given by the formula

_
P - I = /'

where / = the focal length of the lens, P - the
distance of the pimctum proximum (normally 12
centimetres), and R = that of the punctum remotum.

388 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

which, in the normal eye, = infinity. Therefore, nor-
mally p = -j ; 12 cm. is the focal distance of the con-

vex lens, which represents the power of accommodation.
Presbyopia is the term applied when the range
of accommodation becomes diminished, usually as the
result of age. The punctual proximum is farther and
farther removed, probably because both a flattening
of the lens and a diminished elasticity prevent it
assuming the same degree of convexity as formerly,
The deficiency in accommodation may be rectified by
a convex lens, which, placed before the eye, would
give the rays the direction they would have if they
proceeded from the near point in a normal eye. Let
p = the normal near point, and let the near point of
the presbyopic eye be 30 cm., then

10 30 " ~ /

where / = the focal length of the desired lens.
For very fine work Donders makes P— 8 Paris inches
(21 '66 cm.). Presbyopia, then, it is to be noted, is an
anomaly of accommodation, thus differing from short-
sightedness and long-sightedness, which are anomalies
of refraction ; these must now be considered.

Anomalies of refraction. - - Hypermetropla
and myopia. We have seen that in the normal or
emmetropic eye, parallel rays of light are brought to a
focus on the retina. The eye may not be normal,
however, and the focus for parallel rays may be behind
the retina, or in front of the retina, in both cases
circles of diffusion being formed. The former condition
is termed hypermetropia or long sight, the latter
myopia or short sight. The reason of the terms long
or short sight is apparent. The hypermetropic eye
does not form images of objects at a long distance on
the retina with the accommodation in repose, else, in

Chap, xxix.] ANOMALIES OF REFRACTION. 389

that case, indistinct vision would result. The accom-
modation is called into play even for parallel rays, and
the image is thus focussed. But as the object is
brought nearer and nearer, the accommodation is more
and more called into play. As a result, the power of
accommodation fails before the object reaches the near
point of distinct vision for the normal eye. The
punctum proximum is, therefore, farther from the
eye than usual, and an object is held farther from the
eye than usual, hence the phrase long sight. It may
be that the focus for parallel rays falls so far behind
the retina that the utmost convexity of the lens, the
utmost effort of accommodation, will not bring it suffi-
ciently forwards to coincide with the retina. It will
be therefore impossible to get a distinct image with
parallel rays at all; and, thus, distant objects cannot
be properly seen. On the other hand, if the hypermr-
tropia be slight, a small amount of accommodation will
correct it, and the person may consequently be unaware
of the defect. But the accommodation is never at
rest, and hence a feeling of strain and fatigue of the
eyes may in time arise. The myopic eye, with its
shorter focal distance is able to see objects distinctly
when held nearer to the eye than usual, the punctum
proximum is nearer, and hence the phrase short sight.
In myopia, because the focus for parallel rays is in
front of the retina, they cannot be focussed on the
retina, and it is only as the object comes nearer that
the focal point passes backwards, and at last coincides
with the retina. The punctum remotum for a short-
sighted eye is, therefore, not infinity, but at a finite
distance.

The cause of both conditions appears to be not a
difference in the refractive power of the media, but,
according to Bonders, a difference in the position of the
retina. In other words, the optic axis is in the one
case shorter, and in the other case longer than usual.

390 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

The knowledge of the physics of these conditions
indicates at once the means of correcting them. It is
evident that parallel rays ought to focus on the
retina. In the former condition (hypermetropia) they
come to a focus too late, i.e. behind the retina, in the
latter case (myopia) too soon. i.e. in front of the retina.
Obviously the interposition in front of the eye of a
converging lens just sufficient to bring forward the
focus to the retina, or of a diverging lens just sufficient
to displace the focus backwards to the retina, will
cure the conditions. This is what is done : the long-
sighted person gets a convex lens that adds to the
refraction of his eyes, and focusses parallel rays on his
retina; and the short-sighted person gets a concave
lens that diminishes the refraction of his eyes, and so
focusses the image on the retina.

The focal distances of the lenses to be used can be
calculated by a formula.

For hypermetropia the formula is

111

7 " ' i> " " d,

where / = the focal distance of the convex glass
desired, D is the distance at which the object would be
held for distinct vision for a normal eve, and d the

«, /

distance at which it is held for the long-sighted eye.
The normal distance D is usually taken as 10 inches.
Then

1 1 1

/" io " " d'

Suppose the person requires to hold small type
printing he is desired to read, at 30 inches, d = 30.
Then

1 _ 1 _l _ 2_ _ 1
/ " ' 10 " " fcO " 30 ' -15 '

15 inches is the focal length of the desired con vex lens.

Chap XXTX.]

ASTIGMATISM.

For the myopic eye the formula becomes

1

d

10'

Suppose the person reads at 8 inches distance. Then

I
f

1
8

1
10"

1
40'

40 is the focal distance of the desired concave lens.

AstigsiaaJisiii is an anomaly of refraction due to
an asymmetrical condition of the refracting media.
The condition is such that the focal length of the
different meridians of the refracting media are different.
The result of this is that rays of light passing
through the lens or system of lenses are not brought

J o

to a focus at the same
point. They are not
/tomocentric. Consider,
for example, the hori-
zontal and the vertical
meridians, and sup-
pose that the former
has a less curvature,

i.e. a greater focal
length, than the latter,
then rays which pass

Fig. 176. — Astigmatism.

through the vertical meri-
dian will reach their focus before rays which pass
through the horizontal meridian. Hence the name
astigmatism, a not, and 0-rLy/j.a a point. The effect of
such differences in the curvature is to produce diffusion
images of a particular sort, which will be understood
by referring to Fig. 176.

Let ACD be a curved medium on which parallel
rays of light fall. They should all come to one focus
after passing through the medium. But let the verti-
cal meridian CAD have a greater curvature than the

392 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

horizontal meridian FAE. These meridians are
represented by the straight lines CD and FE inter-
secting one another. Now the rays of light through
the vertical meridian will come to a focus at i, and
those through the horizontal meridian will come to a
focus at 5. I is called the anterior focal point, and
5 the posterior focal point, and the interval
between them is the focal interval of Sturm. The
result of the two foci is that between I and 5 a
series of circles of diffusion is formed, each circle
having a shape dependent upon its position. To
understand the formation of these images let con-
sideration be limited to one set of rays passing
horizontally, represented by the line FE, and another
set passing perpendicularly to them, represented by
the line CD, and that they thus intersect one another
as represented by the figure CFDE. Now at I
the vertical rays come to focus at a point while there
is still an interval F'E' between the horizontal rays.
To one looking from the front straight on this position
the intersection of the rays would produce a figure
represented in the diagram, to which the dotted line
from i points, where F and E show the interval between
the still converging rays, and c and D show the
vertical rays having reached their focal point. Ex-
amine a new position of the intersecting rays nearer
5. Here the vertical rays, having met in their focus,
now diverge, still in their vertical plane; but they have
diverged only a little as yet, while the horizontal rays
have approached nearer to one another as they move
to their focus. That is represented in 2, where c and
D are the now diverging vertical rays, and F and E the
still converging horizontal rays, and the diffusion
image is oval. At 3 the vertical rays have diverged •
still more, the horizontal have converged, and a circle
is the diffusion image. At 4 is represented a point
still nearer to the focus of F and E, and where the

chap, xxix.] CORRECTION FOR ASTIGMATISM. 393

divergence of c and D is now considerable \ at 5 F and
E have reached their focus, c and D have diverged to
the extent LM, the diffusion- image being a line.

Thomas Young was the discoverer of astigmatism,
having observed it in his own eye. It appears that
the cornea has a different radius of curvature in
its several meridians. Generally the maximum cur-
vature is towards the vertical, and the minimum
towards the horizontal meridian. Indeed, it is
asserted that few eyes are absolutely without this
defect. This, one can test for himself in his own eyes,
by testing the farthest point of distinct vision for fine
vertical lines, and the farthest point for distinct vision
for fine horizontal lines. If both meridians were the
same in curvature, the distances ought to be equal,
but generally the distances are unequal. If two
threads intersecting one another, the one vertical, the
other horizontal, are not seen with equal distinctness
at the same time, the defect is present.

The correction for astigmatism is secured,
if a lens be interposed in front of the eye which shall
either add to the curvature of the meridian with
the less curvature, or diminish the curvature of the
meridian of greater curvature, so that both meridians
have practically the same curvature. The former
procedure is that usually employed. It is effected by
cylindrical glasses. If one makes a section of a
cylinder in a plane parallel to the long axis of the
cylinder, it is seen that, if placed vertically, in the
vertical meridian the anterior and posterior surfaces
of the section are parallel to one another, so that rays
will pass through that meridian and issue in a direc-
tion parallel to that of entrance, i.e. they are not
converged, just like rays passing through a plate with
parallel faces (page 311). On the other hand, in the
horizontal meridian the surface is curved. If the
section be placed with long axis horizontal, then the

394 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

condition is reversed, and it is in the horizontal meri-
dian that there is no convergence.

The meridian of less curvature, then, is found,
and the difference between its curvature and that of
the greater determined. The difference indicates
the focal length of the lens required. A cylindrical
lens is then used and so placed that its convergence
added to that of the smaller curvature will make
the focal length of that meridian coincide with the
other.

The astigmatism that has been described is regular
astigmatism. Irregular astigmatism consists of irregu-
larities of curvature in the same meridian.

Aberrations of the eye, chromatic and
spherical. — These aberrations, the causes of which
have been already described (chap, xxvii.), are not ab-
sent altogether from the eye, but their correction is pro-
vided for in very remarkable ways. Spherical aberra-
tion is met by the power of the iris to contract and
shut off outside rays, acting precisely as the diaphragm
in the camera obscura ; the refractive power of the
lens is less at the circumference than at the centre;
and the cornea is, owing to its form, less refractive at
the circumference than nearer to the optic axis ;
by such means, therefore, there is less refraction of the
outer rays. The aberration of colour is slight. Yet
it has been determined that the foci for red and violet
rays do not absolutely coincide in the eye, but that
there is an interval of about \ mm. The focus for
red rays is farther back than that for violet. The
power of accommodation is, therefore, more called into
play for red than for violet rays, and thus red objects
appear nearer to the eye than violet, though both be in
the same plane. Yet the amount of aberration is so
small that it is usually ignored. Its smallness is, doubt-
less, due to the different densities of the lens, already re-
ferred to, and to the different curvatures of the lens,

Chap. XXIX.]

THE OPHTHALMOMETER,

395

the one compensating for the other. The iris also aids
in diminishing the aberration.

The ophthalmometer.— It may be well before
concluding this chapter to describe briefly the principle
on which this instrument is constructed. It was
devised by Helmholtz for the purpose of measuring
the size of the images reflected from the surface of the
cornea or lens. Knowing the size of the images and
the distance of the object from the reflecting surface,
the radius of curvature of the surface can be calcu-
lated.

The ophthalmometer consists of a tube in which are
placed one above another two similar plates of glass
with parallel faces. The glass plates revolve on a
vertical axis common to both, but, on turning the

7 O

screw, the plates revolve in opposite directions. Now
we have seen that rays of light falling perpendicularly
on a plate with parallel faces will
pass straight through without
deviation. If the rays fall ob-
liquely they will undergo deviation,
but will issue from the plate in a
direction parallel to that in which
they fell upon the glass. One end of
the tube T is directed towards the
object to be observed, and in the
other end is an eye-piece formed of
two achromatic lenses, through

* o

which the observer looks. The
principle of the instrument is illus-
trated in Fig. 177. In the figure
to the left hand, A represents
an object from which rays are
reflected to the ophthalmometer.
Suppose the plates not to have been revolved and
that the reflected rays fall perpendicularly upon
the plates, they will pass straight through in the

Fig. 177.— The Oph-
thalmometer.

396 PHYSIOLOGICAL PHYSICS. [Chap. xxix.

direction of the dotted line AO. But let the plates
be rotated, the rays strike the plates obliquely and are
refracted. Thus, to consider only one plate, the ray
AO assumes the direction AO', and is displaced to the
right by the plate n. Similarly the plate n' will dis-
place the rays, and thus another image would be seen on
the left side of o, and at the same distance from it as o'.
A double image would be produced. The main part
of the figure shows an object AB viewed through the
ophthalmometer. By rotating the plates MN QP, AB is
seen as if double, and if the two images just touch one
another then the distance between the outer edges of
the double images is equal to twice the size of AB.
The size of the double image can be calculated from
the angle through which the plates have been turned
to make the images stand edge to edge. Connected
with the plates there is a circle on which is measured
in degrees the inclination of the plates.
The formula is

— sn a\

a = 2<? sin a (1 -- -. ) ;

— sin 2a

where d is the distance between the outer edges of
the double image, e is the thickness of the plates, n
their index of refraction, and o the angle through
which the plates were turned.

A simpler method of using the ophthalmometer is
to place it at a given distance from a scale on which
are marked fractions of a millimetre. Turn the plates
and note the angle corresponding to certain distances
on the scale. In this way a table may be constructed
for the ophthalmometer, giving the size of the object
for a definite movement of the plates with the instru-
ment at the fixed distance from the object.

To determine the size of the images reflected from
the cornea, a person is seated in a darkened room, at

Chap, xxx.] DOUBLE REFRACTION. 397

a distance of 10 feet from the ophthalmometer, with,
his eye on a level with it. In front of the ophthal-
mometer is a rod carrying three small rectangular
mirrors by means of which three images are thrown >
on the cornea from a candle flame placed on one
side of the person being observed, whose eye is
screened from all light except that reflected from the
mirrors. On looking through the ophthalmometer
three images (small specks of light) are seen. The
plates are then turned till the images are doubled,
when, from the angle through which the plates have
been turned, the distance between the three images
is ascertained. If the size of object and image be
known, and the distance of the object from the reflect-
ing surface be also known, the radius of curvature of

o '

the surface may be calculated.

For the radius of curvature is equal to twice the
focal distance of the reflecting surface, and f (the

focal distance) = p • '— where p is the distance from
the object, o the size of the object, and i that of the

image.

CHAPTER XXX.

DOUBLE REFRACTION, POLARISATION, AND INTER-
FERENCE OF LIGHT.

Double refraction. — If a crystal of Iceland

t/

spar, whose ordinary form is rhombohedral, be placed
on a piece of paper, in the centre of which a black
spot has been marked, on looking down on the crystal
two black dots will be seen ; the image of the black
dot will be double. If now the crystal be rotated
on the piece of paper, one dark spot will be seen to

39S

PHYSIOLOGICAL PHYSICS. ichap. xxx.

move round the other which is stationary. This
phenomenon is due to double refraction, and was dis-
covered in 1669 by the Professor of Geometry in
Copenhagen, Erasmus Bartholinus. The explana-
tion is that when a ray of light enters such a crystal
it is split up into two, and the two rays travel through
the crystal, with different velocities. One ray is
retarded more than another, that ray is, consequently,
refracted more than the other, and when the rays
issue from the crystal they do not unite, but are dis-
placed from one another, so that a double image is pro-
duced (Fig. 178). One ray travels through the crystal

just as it would
do through a

o

plate of glass,
being refract e d
in the ordinary
way. This is the
ordinary ray,
and is the ray
which gives the
stationary image.

* o

The other ray,
which suffers

the smaller degree of retardation, is called the extra-
ordinary ray, and is the ray which gives the movable
image when the crystal is rotated. To this ray the or-
dinary laws of refraction do not apply. Both rays are
of equal brilliancy. An explanation of the different
course of the two rays is offered by supposing
that doubly refractive crystals are not equally
elastic in all directions, and consequently vibrations
in different directions are subject to differences in
retardation. There is, however, always one direction
in which a ray of light will be transmitted without
double refraction. This direction is that of the optic-
axis of the crystal. Crystals that have more than

Fig. 178.— Iceland Spar.

Chap, xxx ] NICOL'S PRISM. 399

one optic axis have a corresponding number of direc-
tions in which a ray may be transmitted singly. The
ordinary form of Iceland spar consists of six surfaces.
Three of the surfaces meet one another at an obtuse
angle, and at the lower opposite angle three surfaces
also meet at an obtuse angle. The other angles of the
crystal are acute. This is shown in diagram in Fig.
179. A line drawn diagonally through
the crystal to join the obtuse angles
is the axis of the crystal cd in the
figure. The plane of the axis is
called a principal plane, and any
plane parallel to it is also a prin-
cipal plane. In Fig. 179 cadb is
the plane of the axis, and 1 and 2 Fig i79._principai
are other principal planes. It is seen planes and Optic

,, 7, T f> n, ,1 Axis of Iceland

that 111 the ordinary torm oi the spar,
crystal incident rays all form an angle
with the axis in whatever position the crystal lies. If
now the obtuse angles be cut off by a plane at right
angles to the optic axis, the new surface obtained will
be at right angles to the axis. Rays which fall per-
pendicularly 011 this surface will be parallel to the
axis, and they will be transmitted through the crystal
without double refraction, subject only, therefore, to
the laws of simple refraction. Therefore ivhen the
plane of incidence is at, rig lit angles to the optic axis
there is no double refraction.

If the rays are made to fall obliquely, double
refraction appears, and is the more pronounced the
greater the obliquity of the rays.

T¥icol's prism consists of a rhombohedroii of
Iceland spar, which is divided into two by a section
through its obtuse angles. The cut surfaces are care-
fully polished and then cemented in their former
position with Canada balsam, which has an index of
refraction intermediate between that of the ordinary

400

PHYSIOLOGICAL PHYSICS. [Chap. xxx.

and extraordinary rays. The effect of this prism is
shown in Fig. 180, where the line IIC/H is the line in
which the cut was made. A ray of light ab falling
on the prism undergoes double refraction into the
extraordinary ray bd, and the ordinary
be. The extraordinary ray passes on
through the Canada balsam junction, and
emerges at c in a direction parallel to the
entering ray ab. The ordinary ray meets
the balsam at c and is totally reflected.
Only one of the two rays, therefore, tra-
verses the prism. This ray is, however,
found to be of a character different from
an ordinary beam of light. If two
^ic°l's prisms be taken and the one
placed in a line with the other so that
the extraordinary ray which passes through the
first is able to enter the second, it would be expected
that the ray from the first prism would undergo
double refraction oil entering the second, that the
ordinary ray would be totally reflected as in the first,
but that the extraordinary ray would pass 011 and a
circle of light would appear on looking through the
second Nicol. In one position of the prisms, namely,
when they are in such a position that their principal
planes are parallel, the circle of light is seen, and at
its greatest intensity. If, however, one of the prisms
be rotated on the other, the circle of light becomes
less brilliant, and as the rotation is continued it
becomes more and more dim, till, when the prism has
passed through a right angle, the light is extinguished.
If the rotation be carried on the light returns slowly,
till, after going through another right angle the light
is a second time at its greatest intensity \ and, if one
continues turning, the light will again disappear, and
again be restored. In two positions opposite to one
another the light is most intense, and in other two

Chap, xxx.] POLARISATION OF LIGHT. 401

at right angles to the former it is extinguished. The
ray, therefore, which exhibits these phenomena, when
examined by a Nicol's prism, has peculiar characters.
It is said to be plane polarised.

Polarisation of light. — Ordinary light, ac-
cording to the wave theory, is due to vibrations
occurring transversely to the direction of propaga-
tion of the wave, but the vibrations take place in all
planes across the direction of the wave. Light is said
to be plane polarised when the vibrations take place
all in one plane. To put it in another way. The par-
ticles of ether, whose vibrations produce light, all
move in directions transverse to the direction of
propagation, but in their vibrations they may de-
scribe figures of various forms, straight lines, circles,
etc. When light is polarised, however, the particles
of ether are all made to vibrate in the
same direction, e.g. in straight lines in
the same plane. In. Fig. 181 let BA
represent a ray of ordinary light. The ^
velocity of a body along the line BA
may be decomposed into two velocities
at right angles, one, namely, in the
direction BY, the velocity in that

, . , . -, V i j Fig.181.— Decoin-

direction being represented by BA , and position of a
the other in the direction BX, the ^o^^ht
velocity being represented by BB'. Angles to one
Similarly the velocity of a body along
BC may be considered as compounded of a velocity
BC' and BD, BC being, in short, the resultant of the
two velocities. So, letting BA represent a ray of
ordinary light, it may be considered as compounded
of vibrations occurring in the direction By and B.T,
with different velocities represented by BA' and BB'.
BA' and BB' will represent polarised rays. An
ordinary ray of light may then be decomposed into
two rays polarised in planes at right angles to one
A A — 7

B D 13' 3G

402 PHYSIOLOGICAL PHYSICS. [Chap. xxx.

another. Thus the phenomena witnessed in Iceland
spar are due to the light being polarised, both the
extraordinary and the ordinary ray being polarised,
the one at right angles to the other.

Simply refractive bodies do not possess the pro-
perties of splitting up natural light in this way, at
least to the same extent. They are called isotropous,
while doubly refractive bodies are called anisotropous.

It is to be noticed that in the polarised ray which
emerges from a Nicol's prism there is nothing to render
its peculiar condition appreciable by the unaided eye ;
but as soon as the eye is aided by a second Nicol's
prism, the condition is recognised by the fact that on
rotating the prism the beam of light from the first
prism is extinguished, and reappears on continuing
the rotation. The condition produced by the first
prism is only recognisable by the aid of a second or a
similar doubly refractive body. The second is, there-
fore, called the analyser, while the first is called the
polariser. The explanation of the alternate darkness
and light produced by rotation of one prism on
another is, that the ray which emerges from the first
prism will be transmitted by the other so long as the
principal planes of the two prisms are parallel, and
will not be transmitted at all when the planes are at
right angles to one another. In two positions the
planes are parallel, and in two at right angles. Sup-
pose they are parallel at first, the light is bright ; on
rotating one through an angle of 90° they are at right
angles and the ray is extinguished. If the rotation
be carried on to 180° the. planes are again parallel
and again the light is bright ; but on passing through
another 90° they are again at right angles and the
light is again extinguished. A further quarter turn
brings the prisms back to their original parallel con-
pition. With many other crystals similar phenomena
may be exhibited.

Chap. XXX.]

TOURMALIN PLATES.

4°3

With the plates of the crystal TOURMALIN, cut
parallel to the optic axis, polarisation may be shown.
When the plates are laid on one another, so that the
axes are parallel, the light is transmitted. When one
is rotated the light becomes more and more dim, till
when they are crossed it is extinguished. If the
rotation be continued till they are again parallel, the

Fig. 182.— Tourmalin Pjates.

light is again transmitted (Fig. 182). The tourmalin,
plates, if sufficiently thick, completely extinguish the
ordinary ray.

Polarisation by reflection of light was dis-
covered by Malus in 1810. An apparatus for pro-
ducing it is shown in Fig. 183. When a ray of light
falls on an unsilvered polished surface of glass, placed
at a particular angle to the incident ray, the reflected
ray is polarised. This may be shown by permitting
the ray to fall on a prism of Iceland spar, when the
phenomena already described will be produced. It is
also shown by receiving the reflected ray on a second
reflecting surface placed at the same angle as the
former. If the surfaces are parallel the light from
the second surface will be perceived by an eye
placed in the direction of the reflected ray. If the
second surface be now turned the intensity of the
light diminishes, till when the two surfaces are at
right angles it is extinguished, but is again reflected
on turning till the surfaces are again parallel. The
Fig. 183 shows the two reflecting surfaces A and B,

404

PHYSIOLOGICAL PHYSICS. [Chap. xxx.

the ray reflected from A being received by B. B is
capable of rotation on cc. In the position shown on
the right-hand side of the figure the ray will be re-
flected by B ; in the position of the left-hand figure it
will be extinguished.

Fig. 183. — Apparatus for Polarisation by Reflection.

The angle which the incident ray must make with
the normal to the reflecting surface in order to be
completely polarised, is the ANGLE OF POLARISATION.
For glass the angle is 54° 35', for water, 52° 45', for
quartz 57° 32', and for diamonds 68°. The PLANE
OF POLARISATION is the plane in which the light be-
comes polarised.

Doubly refractive substances may be
detected by means of a polarising apparatus. Let
two Nicol prisms be placed in line with their
principal planes at right angles to one another, the
extraordinary ray, transmitted by the first prism, will
not be transmitted by the second, because it is at
right angles ; no light will, therefore, be visible on
looking through the second prism. In this condition

chap, xxx.] DOUBLE REFRACTION. 405

of affairs interpose a plate of a doubly refractive
substance, for example, a plate of Iceland spar, and
let its principal plane be parallel to the first prism.
The ray from the first prism will be transmitted
unaffected by the plate, since their principal planes are
parallel, but will be extinguished by the second Nicol
since their planes are at right angles. Suppose next
that the plate is parallel to the second Nicol, that is,
is at right angles to the first Nicol. The plate, being
in its ordinary crystalline form, will transmit an
ordinary and an extraordinary ray, i.e. two rays
polarised at right angles to one another. The ray,
then, emerging from the first Nicol will not be ex-
tinguished by the plate because it can transmit rays
at right angles, but the second Nicol will extinguish
the ray because it can transmit rays only if vibrating
in its one plane, and not at right angles. But now
suppose the two Nicols still crossed, but the plate
interposed between them no longer parallel to either,
but with its principal plane forming an angle with
both, the lio'ht will now be transmitted through both

o o

Nicols. In short, if a plate of doubly refractive
material be interposed between the two crossed Nicols
in any position other than one in which its principal
plane coincides with that of either of the Nicols, light
will be enabled to pass through both Nicols. In other
words, if between two crossed Nicols, which con-
sequently appear dark, a substance be interposed
which makes the darkness give place to illumination,
however feeble, that substance is doubly refractive.
Hence there is supplied by a polarising apparatus a
test for discovering doubly refractive substances.

How the doubly refractive plate can illuminate the
crossed Nicols, if forming an angle with both, may
be briefly indicated. Let NN1 (Fig. 184) represent
the principal plane of the first Nicol, and N'-'N2 the
principal plane of the second. They are at right

406

PHYSIOLOGICAL PHYSICS. [Chap. xxx.

x*'

angles to one another because the Nicols are crossed,
and, consequently, the ray transmitted by the first
will be extinguished by the second. Let Pt Pt
represent the principal plane of the doubly refractive

plate. The extraordinary
/ ray transmitted by the first
Nicol vibrates parallel
to the plane NN1, and, since
it falls obliquely on the
~N2 plate, it is split into two
rays, an extraordinary and
an ordinary at right angles
to one another, i.e. one
vibrating in the plane Pt,
Fig. 184.— Polarisation of Light, arid another in the plane Ptr.

These two rays meet the

second Nicol, but it can only transmit vibrations
in the plane N2. The vibrations in Pt can, however,
be resolved into a vibration in N1 and a vibration in
N2 (see page 40 1 ) ; the former is extinguished, the latter
transmitted. Similarly the vibration in pf can be
resolved into a vibration in N1 and a vibration in N2,
the former being extinguished, and the latter
transmitted. Thus by the position of the doubly
refractive plate the crossed Nicols become illumi-
nated, the illumination being due to two sub-rays, one
a sub-ray of the vibration in pt, and the other a sub-ray
of the vibration in Ptr, which have been made to
vibrate in N2.

Interference. — Another phenomenon makes its
appearance when the arrangement of two Nicols and
an interposed refractive plate is used, as just described,
a phenomenon not visible with a thick plate of
Iceland spar, but seen when a very thin plate is used
or a thin lamina of selenite (crystallised gypsum). It
consists in the appearance of colours varying accord-
ing to the position of the Nicols. They are brightest

chap, xxx.] INTERFERENCE OF LIGHT. 407

when the first Nicol and the plate have their
principal planes at an angle of 45° to one another.
If with this position of the plate the second Nicol be
rotated till the two Nicols stand at an angle of 45° to
one another, the colour disappears and the light
becomes white. When the Nicols are parallel,
another colour is produced complementary to the
former. Thus, with the plate of selenite in the first
position described, the Nicols being crossed the colour
is red, and with the Nicols parallel the colour is
green. The colours are due to what is called
interference. Suppose two waves on the surface of
water, if the crest of one coincides with the crest of
the other, the height of the united wave will be
doubled. In such a case both vibrations would be in
the same phase, the vibrations of each wave would be
proceeding in the same direction, and would be in the
same position at the same time. Suppose, however,
the crest of one wave coincided with the hollow of
another wave, then a particle which would be at its
extreme displacement above the line of rest for the
crest of one wave would be at its extreme displace-
ment below its line of rest for the hollow of the other
wave. That is to say, the waves being similar, the
particle would be at the same moment under the
influence of two equal and opposite forces, and would,
therefore, remain at rest. This is the phenomenon of
interference. If, however, the crest of one wave did
not absolutely coincide with the hollow of another,
then the particle having received an impulse to
vibrate in one direction, would have already started
in that direction before it received the impulse in the
opposite direction. Its motion would still be inter-
fered with but not completely arrested. The distance
between the crest and the hollow of a wave is a half
wave length. Thus, we see that when two waves
differ by half a wave length, they extinguish one

408 PHYSIOLOGICAL PHYSICS, [Chap. xxx.

another. Now, with the plate of selenite as
described, we have seen that the light passes through
the crossed Nicols because it is decomposed into two
vibrations at right angles to one another, the ordinary
and extraordinary ray. We have seen, also, that the
illumination is due to two sub-rays, one of P£ (Fig.
184), and another of p£r, which have been made to
vibrate in the same plane, one being a sub-ray of the
ordinary and the other of the extraordinary ray. But
though the sub-rays vibrate in the same plane they are
of different velocities, because of the difference between
the retardation experienced by the ordinary and extra-
ordinary ray in passing through the doubly refractive
plate. Hence the phases of the two vibrations do not
coincide, and thus they exhibit the phenomena of
interference. This implies the extinction of certain
rays of the white light, and the light that is seen
through the second Nicol will be white light less the
extinguished rays. The interference affects different
rays of white light according to the position of the
Nicol's prisms, but the rays that are extinguished and
the rays that are transmitted will together form white
light, and are thus complementary to one another.

Coloured rings, due to interference, are observed
when a thin film, of transparent material separates
two media with refractive index different from its
own. Thus the colours of a soap bubble are due to
interference by the reflections from the surfaces of the
film in contact with air on each side. These rings of
colours are called Newton's rings, because Newton
first studied them carefully.

The polariscope in physiology. — " When
muscular fibres are examined with a microscope, to
which a polarising apparatus is attached, remarkable
and instructive phenomena are observed. If the field
be darkened by crossing the planes of polarisation of
the Nicol's prisms, those fibres only disappear which

Chap. XXX.] POLARISCOPE IN PHYSIOLOGY. 409

lie parallel to the plane of polarisation of one or other
of the prisms ; the rest, which cut those planes at
various angles between 0° and 90°, appear of a grey
colour upon a black ground, the most distinct being
those which cut them at an angle of 458. In those
parts where the muscular fibres running parallel with
one another are arranged in several layers, the colour
assumes a whitish tint, passing into yellow. The tint
varies with the thickness of the layers, precisely as
the succession of colours in Newton's rings, from the
centre towards the circumference. If one of the
Nicol's prisms be turned to the extent of 90°, so that
the field becomes clear and attains its maximum
brightness, the complementary tints make their ap-
pearance. These phenomena, with others . . . ., are
equally apparent when the muscular fibres are
thoroughly impregnated with, and surrounded by,
strongly refracting fluids, as glycerine, turpentine,
and Canada balsam. This is essentially owing to the
circumstance that the muscle substance is doubly
refractile, two systems of undulations propagating
themselves according to different laws, and interfering

<J J !^

with one another.

"This explanation had already been given in 1839
by Professor C. Boeck, of Christiania, who was the
first that applied the polarising microscope to the
investigation of animal and vegetable tissues ; and no
other intelligible explanation of the phenomena ob-
served has, since that period, been advanced.

" The next question to determine is, whether the
entire substance of the muscular fibres possesses an
equal power of double refraction, or whether it is
possible to distinguish doubly refracting from isotropal
parts. If sufficiently high magnifying powers are
employed, and the observations be made on animals
which have large sarcous elements, amongst which
our large water beetle, the Hydrophilus piceus, is the

410 PHYSIOLOGICAL PHYSICS. [Chap. xxx.

best, it will be immediately seen that only the sarcous
elements are doubly refracting, and that the inter-
vening material which separates them from one
another is isotropal ; for it remains dark in the dark
field of the crossed Nicol's prisms, in whatever
azimuth the muscular fibre to which it forms a part
may be placed. It is just as dark in those muscular
fibres which form an angle of 45° with the polarising
planes of the prisms, as in those which make an angle
of 0° or of 90° with those planes."*

Professor Briicke's explanation of the behaviour of
muscular fibres in polarised light has been quoted,
because he is the greatest living authority on the
subject. With the aid of what has been said on
polarisation and double refraction, it will be quite
easily understood. Polarising apparatus is made to
fit the ordinary microscope. It consists of two
Nicol's prisms, each mounted in a short tube. One
(the polariser) is fitted under the stage so that the
light from the mirror passes through it before reach-
ing the object on the stage. The other prism (the
analyser) is fitted in a tube similar to that of the
ordinary eye-piece, and is put in place of the ordinary
eye-piece when the polarising apparatus is in use.
This form of analyser, however, diminishes the field,
which is an objection. Other forms of analysers are
made, e.g. Abbe's, consisting of an ordinary Huyghens'
eye-piece with a doubly refractive prism between,
arranged in such a way that one of the two refracted
rays is so strongly refracted as to be intercepted by a
diaphragm placed above the eye-glass.

Rotation of plane of polarisation. — We
have seen that a plate of Iceland spar interposed
between two crossed Nicol's prisms will cause illumi-
nation of the field, provided the principal plane of the

* E. Briicke in Strieker's "Human and Comparative Histology."

Chap, xxx.] ROTATION OF PLANE. 411

doubly refractive plate is not parallel to either of the
prisms. If a plate of quartz (rock-crystal) be substi-
tuted for Iceland spar, the light will not be extin-
guished in any position of the prisms, but will pass
through various colours from red to orange, yellow,
etc., to violet as the rotation is continued. It appears
that the colours are due to the extinction of some
particular rays of white light. Thus, in one position
of the rotating prism red is extinguished ; as the prism
is farther rotated it is the orange rays that are not
transmitted, and so on, the colour visible in the field
being due to the remaining rays of white light trans-
mitted. For the extinction of the red rays the
Nicol's prism must be turned 60° out of the crossed
position, in which position the red rays must be
vibrating at right angles to the principal plane of the
prism (for this is necessary for their extinction).
That is to say, before the quartz plate was introduced
the second prism required to be placed at right angles
to the first in order to extinguish the rays from the
first, but after the quartz plate is interposed it re-
quires to be turned through 60° to meet the polarised
ray at right angles, and thus to extinguish it. Conse-
quently the quartz has rotated the plane of polarisa-
tion to this extent. It also appears that the rotation
is different for the different colours of the spectrum, so
that the white light is dispersed, and thus on rotating
the prism farther one colour after another is extin-
guished. There are two kinds of quartz, one of which
rotates the plane to the right, another to the left.
The rotation of the plane of polarisation by the quartz
plate is due to CIRCULAR POLARISATION. The ray
on entering the quartz plate is broken up into two
rays, not polarised at right angles, as in the case of
Iceland spar, but polarised circularly, that is, the
vibrations are not rectilinear, do not describe straight
lines, as in plane polarised light, but describe circles,

4i2 PHYSIOLOGICAL PHYSICS. [Chap. xxx.

the vibrations of each ray being all in the same direc-
tions. The two rays into which the quartz plate
splits the ray which enters it are polarised circularly,
but in opposite directions, one right-handed, the other
left-handed. These rays travel through the quartz
plate with unequal velocities. They unite on issuing
from the quartz plate. That is to say, the ether at
the surface of the quartz plate receives an impulse to
vibrate in the direction of the first circularly polarised
ray which reaches it, the ray which travels through
the plate with greatest velocity ; and it has just
begun to vibrate in that direction when the retarded
ray reaches it and gives it an impulse to vibrate in
the opposite direction. The result of the impulse to
vibrate in the direction of two opposite circularly-
polarised rays is a plane polarised ray, but with the
plane rotated to right or left, according as the right
circularly-polarised ray, or the left, proceeded through
the quartz with the greater velocity.

Besides quartz various other substances rotate
the plane of polarisation, some to the right, others to
the left. Thus, crystals of chlorate, bromate, and
iodate of sodium, of sulphate of strychnine, crystallised
with thirteen equivalents of water, and of other sub-
stances, rotate the plane of polarisation. Essences of
turpentine, lemon, lavender, peppermint, rosemary,
aniseed, fennel, caraway, etc., also possess a similar
property. Of these, essence of turpentine, aniseed,
and peppermint rotate to the left, the others to the
right.

Solution of cane sugar rotates the plane to the
right, through an angle of 33° 64' if the solution
contain 50 per cent, sugar.

The following table gives a number of substances
which in solution exercise a rotatory power, the
amount of which is stated in degrees, right or left
being indicated by the + or — sign :

chap, xxx.] THE SACCHARIMETER. 413

DEXTRO-ROTATORY.

Sucrose -f 73-84°

Glucose -f 56-00°

Lactose + 59 -30°

Galactose + 82-20°

Dextrine -j- 118-00°

Glycocholic acid + 29-00°

Cholic acid + 35.00°

Taurocholate of sodiurn (dissolved in alcohol) -j- 24-50°

L^EVO-ROTATORY.

Levulose 106-00°

Albumen (egg, in watery solution) . . — o5'50°

Albumen (serum) . . . . — 56-00°

Gelatine - 130-00°

r,, , . ( alkaline solution . . . - 213-50°

1 ( with great excess of alkali . - 552-00°

The measurements are all for rotatory power with
yellow light.

Inosite (muscle sugar) is inactive, does not affect
polarised light.

A six per cent, solution of quinine in alcohol gives
a rotation of 30° to the left.

This rotatory action has been taken advantage of
to determine the strength of solutions of sugar, and
an instrument, the saccharimeter, has been constructed
for the purpose.

The saccharimeter is shown in Fig. 185. It
consists of two Nicol's prisms a and b, between which
is placed a tube cc, filled with the sugar solution.
Suppose the tube to be removed, and the Nicols to
be crossed, the field will be dark. If the tube con-
taining the susrar solution be now inserted, the field

o o j

will be illuminated. If the Nicol's prism that acts
as analyser be now rotated, the field will be again
darkened, and the angle through which the prism
must be turned for this purpose gives the rotatory
power of the liquid. The rotation is effected by the
screw d, and its amount read oil on the scale e.

414

PHYSIOLOGICAL PHYSICS. [Chap. xxx.

The amount of rotation is dependent upon the
length of the column of liquid, and the amount of the
substance in solution. In a tube, 20 centimetres
long, the rotation is 1'333° for every gramme of

Fig. 185. — The Saccharuneter.

sugar in 100 cubic centimetres. Thus, by the amount
of the rotation can be determined the strength of the
solution. To make the determination more exact,
between c and b there is interposed the double
quartz plate of Soleil. It consists of a plate of quartz
rotating to the right, cemented to a plate rotating to
the left, each cut perpendicular to the axis, and of the
same thickness (3 '15 mm.). The effect of this plate
is, that with the Nicol's prisms in a particular position
(parallel), a circle of light will be seen, all of one
colour (a violet tint), teinte sensible. If now the
plane of polarisation be turned the field will change
in colour, one half changing to the red end, and
the other towards the violet end of the spectrum,
because the two halves of the quartz are opposite.

Chap. XXX.] USE OF SACCHARIMETER. 415

The feeblest rotation will thus be exhibited, and the
extent to which the analyser must be turned to
restore the former tint, indicates the extent of the
rotation. If, then, the original tint has been obtained,
the tube containing the solution to be examined is put
in its place, when the slightest change in the colour
indicates a rotation of the plane. In Soleil's
saccharimeter the amount of rotation is estimated
not by turning the analyser, but by a compensating
arrangement placed between the solution tube and the
analyser. The compensator consists of a single quartz
plate rotating to the right, and then of a quartz plate
rotating to the left. The latter is, however, made of
two wedges, sliding on one another, the sharp end of
one being over the blunt end of the other. By a
screw the wedges may be moved from one another,
the practical effect of which is to diminish the
thickness of the quartz plate which they compose, or
they may be moved towards one another, which
increases the thickness of the plate. Thus, if the
solution of sugar has rotated the plane of polarisation
to the right, by turning the screw a sufficient thick-
ness of the quartz plate rotating to the left is
interposed to compensate for the rotation to the right
of the sugar. The thickness of the quartz plate
interposed is read off on a scale, and the rotation of a
quartz plate of a definite thickness being known, the
measure of the rotation effected by the sugar solution
is determined.

Use of the saceharinieter in medicine. —
The instrument may be used for estimating the
amount of sugar present in diabetic urine. The
urine is first clarified by heating with acetate of lead,
and then filtered. The field of the saccharimeter
being all of the same colour, the tube filled with the
diabetic urine is put in its place, when the two sides of
the field will at once appear of a different colour by

416 PHYSIOLOGICAL PHYSICS. [Chap. xxx.

the rotation clue to the sugar. The screw of the
compensator is now turned till the uniform hue is
restored, and the extent to which the compensator has
been moved is read off on the scale. It has been
found that with Soleil's instrument a displacement of
100 divisions of the scale is effected by a solution of
sugar containing 225'6 grains of sugar in a litre. Each
division of the scale, therefore, represents 2-256
grains of sugar. Suppose 10 divisions are indicated on
the scale when the original tint of the field is restored,
then 10 X 2 -256 = the quantity in grains of sugar
present in 1 litre of the urine.

To put it generally, to determine x, the amount in
grammes of the substance in 1 cc. of the solution
employed, one requires to know r the rotatory power
of the substance, I the length in decimetres of the
column of solution in the tube, and a the angle
of rotation. Then

a

* - 7S7 '

4^7

part ©

SOUND

CHAPTER XXXI.

SOUND : ITS NATURE, REFLECTION, AND REFRACTION.

THE nature of sound. — Like light, sound is
also considered a mode of motion, as due to vibrations.
But, whereas the vibrations of the luminiferous ether
are regarded as transverse, the vibrations of the sound-
conducting medium are regarded as longitudinal to
the direction of propagation of the sound. The
movements are still to and fro movements, no longer
across, buc in the line of the advancing sound.
Suppose a series of particles in line with one another,
and at rest, and let a shock be communicated to the
tirst of the series. Under the influence of the
impulse it moves along the line, and pushes against
the second particle, to which it communicates the
pulse. After its impact with the second particle, it
recoils and returns to its original position, completing
its to and fro movement. It has, moreover, handed
on its motion to the second particle, and the second,
owing to the shock, moves towards the third particle,
from the impact with which it also recoils and returns
to its own position., having, in its turn, communicated
the motion to a succeeding particle. So the process
goes on, each particle performing only a to and fro
movement, the impulse nevertheless being carried
from one end to the other of the series. It must not,
however, be supposed that the medium in which
B B — 7

4i 8 PHYSIOLOGICAL PHYSICS. [Chap. xx?<r.

sound is propagated can be represented as composed
of particles so separated from one another that one
may move without affecting another. Between all
the particles of the air there is a certain elastic
force, owing to which one particle cannot move
without affecting the others, because of the changes
produced in the elastic force. Thus, as soon as the
first particle has begun to move, owing to the
elasticity between it and the second, the second is
moved also ; and similarly, as soon as the movement of
the second has begun, the third is also set in motion.
So that, by the time the first particle has reached its
greatest excursion from its place of rest, the forward
movement has been propagated for a considerable
distance along the line, and the general effect of the
movement will be to squeeze the particles, as it were,
nearer to one another, the first approaching the
second, the second the third, and so on. In fact a
condensation is produced. Then, when the first
particle recoils and starts on its backward movement,
the elastic force between it and the second particle
will be less than the force between the second and the
third ; the second will, therefore, follow the first, and
for the same reason the third will follow the second.
There will be a backward movement for some distance
along the line, the wave of condensation being passed
farther onwards. Then the first particle will not
have exhausted its force of recoil when it reaches its
position of rest, and it will pass this position for some
distance, and then return to rest. Consequently,
by this excursion in the direction opposite to
the condensation there will be increased distance
between the particles, a rarefaction will be pro-
duced. Like the condensation, the rarefaction will
travel in a wave ; it will affect a considerable
number of the particles at once, but in different
degrees, each particle having its maximum, one after

chap, xxxr.i SOUXD. 419

the other, the maximum declining to a minimum, till
it finally disappears when the particle comes to rest.
The whole history, then, of a particle sharing in the
propagation of a wave of sound is, that under the
influence of a shock it moves forward from its
position of rest for a certain distance, then moves
backward past its position of rest, but in the same
line, and finally returns to its middle position. Each
particle thus oscillates to and fro on each side of its
middle position. While this is the history for each
particle, the combined movements of the series of
particles produce an alternate condensation and rare-
faction, the two forming a sound wave.

The movement of a particle from its position of
rest to one extreme, then to the opposite extreme,
and finally back to its original position, is one com-
plete oscillation or vibration, the time occupied in
completing the movement being the period of oscilla-
tion, while the distance between the period of rest
and either of the extremes gives the amplitude of the
vibration. Two particles which are moving in the
same direction and are at the moment occupying the
same position, are said to be in the same phase ; and
the distance between one particle and the succeeding
particle in the same phase is the wave length, the
distance between one condensation and the succeeding

o

one, or between one rarefaction and its successor.

There is another difference between the propaga-
tion of sound waves and light waves. For the propa-
gation of light it was found necessary to assume the
existence of a subtle ether pervading all space and all
bodies, an ether which was present even where no
atmosphere existed. A simple experiment shows
how different is the case with sound. Let an alarum
bell be placed within the jar of an air pump. It
must be suspended in the jar by threads, and not
simply placed in the jar of the air pump. Suppose

420 PHYSIOLOGICAL PHYSICS. [Chap. xxxi.

the spring be released before the bell is placed inside
the jar, the ringing of the bell will be heard quite
distinctly through the walls of the jar. As one pro-
ceeds to exhaust the jar the sound is heard more and
more faintly, till, when the exhaustion is as complete
as possible, only one near to the bell hears it. If
hydrogen gas be now permitted to fill the jar the
sound of the ringing bell is not much intensified.
But on again exhausting, as completely as possible, the
sound is 110 longer heard, even if one's ear be pressed
closely against the jar's sides, and while it is evident
to the eyes that the hammer is still hitting the bell ;
as soon as even a small quantity of air is permitted to
enter the exhausted receiver, the sound of the bell is
restored.

In ordinary circumstances, then, sound is propa-
gated by air. It may, however, be propagated by
many different media, gases, liquids, solids. In. water
sound is readily propagated, and everyone knows how
it is conducted by solid bodies like wood, how, for
example, the merest scrape with a pin at one end of
a long log of wood will easily be heard by an ear at
the other end. While sounds may be propagated in
gaseou's, liquid, and solid bodies, it is not with the
same velocity in each, the velocity of propagation
being dependent upon the elasticity of the medium in
relation to its density. Generally speaking, the
greater the elasticity the greater the velocity, and the
greater the density the less the velocity. The velo-
city of sound in air at 0° G. is 1,090 feet, and it
increases 2 feet for every degree centigrade of increased
temperature. In oxygen the velocity is 1'040 feet,
in carbonic acid gas 858 feet, in hydrogen 4-164 feet,
in water nearly 5,000 feet, in copper (at 20UG) 11,666
feet, in iron (at 20°G) 16,822 feet, in pine wood,
along the fibre, 10,900 feet. In these solid substances
the increased velocity is not due to the increased

Chap, xxxi.] REFLECTION OF SOUND. 421

density, but to the high elasticity in relation to the
density.

MeHectioii of soimd. — Sound may be reflected
just as light. Tims, suppose one takes a concave
mirror, and from a lamp at a distance throws upon it
a beam of light, and finds the position in front of the
mirror to which the light is reflected (the conjugate
focus), then removes the lamp, in its place puts a
watch, and holds the ear in the position of the conju-
gate focus, the ticking of the watch will be heard
with great distinctness, though in any other position
the person might not hear it at all. Or let the watch
be placed in the focus near the mirror, a person with
his ear at the place of distant focus will hear it dis-
tinctly. The laws for the reflection of sound are the
same as those for light. An echo is a reflected sound.

Refraction of soimd may also be shown expe-
rimentally. For a converging lens thin indiarubber
balloons filled with a denser gas than air, e.g. car-
bonic acid gas, may be used. They will converge the
sound waves of a sounding body, placed behind, to a
focus in front, just as a lens would do with light.

Transmission of sound toy tubes, etc,—
In free air the intensitv of a sound diminishes as the

V

distance through which it is transmitted increases ;
it varies inversely as the square of the distance.
From the centre of disturbance the waves of sound
expand in all directions, and the more they travel the
more widely are they diffused, so that their intensity
diminishes as they advance. By the use of tubes
(a speaking trumpet, for example) the expansion on
all sides is prevented and the waves are concentrated
in one direction, so that the intensity is maintained.
This is one reason why a sound of no great loudness
may be transmitted with little enfeeblement through
narrow tubes of considerable length, if the inner
walls be smooth. Biot, in Paris, was able to hold a

422 PHYSIOLOGICAL PHYSICS. [Chap. xxxi.

conversation in a low voice through an iron tube
3,120 feet long. The intensity of a sound increases
also with the density of the medium in which it is
produced. Such principles explain to some extent the
action of the otoscope and stethoscope. The former
consists of a narrow iiidiarubber tube with ivory
ends. One end is placed in the canal of the ob-
server's ear, and the other in relation to the sounding
body, and thus the sound is conveyed to the observer's
ear without enfeeblement. The stethoscope acts not
only by its own particles conducting the sound, but
because the tube prevents the dissipation of the vibra-
tions.

A stethoscope, bearing some resemblance to a
Marey's tambour, was devised by Koenig in 1864.
It consists of a metallic ring, oil each side of
which is attached a thin indiarubber membrane, so
disposed that when the enclosed space is inflated
through an opening in the ring the chamber assumes
the form of a bi-convex lens. A stopcock shuts the
chamber oft' from the outside. Connected with the
edge of the metallic ring is a hemisphere of metal
which covers in one of the indiarubber membranes, a
space intervening between the two. In the middle of
the hemisphere is a tube from which an indiarubber
tube, terminating in an ivory end, is carried to the
ear. The exposed indiarubber wall is applied to the
body to be examined. Vibrations are communicated
to the air in the indiarubber chamber, and from it to
the air in the space between the metal hemisphere and
the indiarubber chamber, and so along the tube to the
ear. Several tubes may be led from the hemisphere,
and several persons may hear at the same time.

A reflection of sound is effected by the auricular
appendages of the ears. It has been shown that their
form is peculiarly adapted for concentrating the
sound waves into the external canal by which they

chap, xxxn.] MUSICAL SOUND. 423

are conducted to the tympanum. The concavities of
the concha and of the inner surface of the tragus are
adapted specially for directing the sonorous waves
into the external canal. The two surfaces are so
arranged with regard to one another that sound waves
coming from before will be reflected by the concha on
to the inner face of the tragus, where they undergo a
second reflection, which concentrates them in the
direction of the external canal.

CHAPTER XXXII.

MUSICAL SOUND.

ALL sounds are due to vibrations, but the differ-
ence between ordinary sounds (between noises, for in-
stance) and musical sounds is in the rhythmic or
periodic character of the latter. Musical sounds are
also distinguished by their continuous character, the
vibrations following one another with such rapidity
that each one is not perceived separately, the per-
ception being only of the fused whole. Various
characters of musical sounds must be noted, namely,
their loudness or intensity, their pitch, and their
quality.

The intensity of any sound is due to the
amplitude of the vibration, the extent of the excursion,
as one might say, the height of the wave.

The pitch of a musical sound is determined by
the rapidity of the vibrations, the number of
vibrations affecting the auditory apparatus in a second
of time. This has been shown in various ways.
Savart, for instance, used a toothed wheel which could
be revolved with varying degrees of rapidity. As the

424 PHYSIOLOGICAL PHYSICS. [Chap. xxxn.

wheel revolved each tooth struck against the edge of
a card, each stroke producing a vibration. "With a
certain rapidity a musical note was produced, rising
in pitch as the rapidity was increased, and falling as it
was diminished.

The siren shows the dependence of pitch upon
rapidity still more accurately. The simple siren
consists of a zinc disc, which is perforated with holes
arranged in rings, one ring having the holes verv near

O O ' v

to one another, and others having them at greater
distances. By multiplying wheels the disc can be
made to revolve with great rapidity. A tube with
a fine opening at one end is brought up near the
surface of the disc, and air may be driven through the
tube by a bellows, or by the mouth. Now when air
is blown through the tube it will pass through a hole
in the zinc plate, and communicate an impulse to the
air on the opposite side, should the open end of the
tube happen to be opposite a hole in the disc. If the
disc be slowly revolved, at one moment a hole in the
plate will be opposite the tube and air will pass
through, at the next moment an unperforated part of
the plate will be opposite the tube, and the air will
not puss through. With a slight further turn another
hole will be opposite the tube, and the air will receive
a second impulse. As the plate is revolved with
greater rapidity, an increasing number of impulses
will be given to the air. At first, then, on revolving the
plate nothing is heard but the separate pufts as one
hole after another comes opposite the tube through
which the air is being blown. Gradually, however,
with increased speed, the putt's follow one another with
greater rapidity, till they become fused, and a low
musical note is heard, which rises higher and higher
as the plate revolves faster and faster, till the pitch
becomes very high with the utmost speed that can be
communicated to the plate.

Chap. XXXTI.]

THE SIREN.

425

The siren of Cagniard de la Tour (Fig. 186) permits
the number of vibrations producing sounds of different
pitch to be accurately estimated. It consists of a
brass air-chamber B, the top of which is perforated
with fifteen holes, disposed at regular intervals from
one another. Above the perforated lid is a circular
plate D, finely pivoted, capable of rotation on the
centre of the lid, and
pierced with an. equal
number of holes at dis-
tances from one another
corresponding to those
of the lid of B. In
particular positions the
holes of the two plates
will exactly coincide. B
has an inlet tube through
which air may be driven
into the chamber by a
bellows. Now the holes
of the lid and rotating
plate are not pierced in
a straight direction, but
obliquely, and those of
the plate are in an op-
posite direction to those
of the lid. Fig. 186
shows the section carried
through one hole, by
which the nature of the obliquity is seen. There-
fore, when air is blown into B, it escapes through
the openings in the lid, and then through those of the
disc D. But in pnssiiig from lid to disc, the air
strikes obliquely on the holes of the latter, and since
it is easily movable, causes it to rotate. By a
slight turn of D the holes of B are blocked ; but the
disc rotating farther, the holes again coincide, the

Fig. 186.— The Siren.

426 PHYSIOLOGICAL PHYSICS. [Chap. xxxn.

air again escapes, and the disc gets an increased
rotatory impulse. In a single revolution of the disc,
fifteen separate shocks will have been given to the air.
Now if the bellows be worked slowly, the plate D will
revolve slowly, and only the sounds of the separate
puffs of air will be heard. But if the bellows be
driven vigorously the disc will revolve faster and
faster, and an increasing number of shocks will be
given. With a certain velocity a low musical note
will begin to be heard, and as the speed increases, the
pitch will increase till the limit of velocity, when the
pitch will be very high. At the upper part of the
instrument are two wheels c and c, which register on
dial plates in front the number of revolutions of the
disc. At the side is a button, by which the wheels
may be put into or out of action. Suppose it is
desired to learn the number of vibrations producing
a sound of a given pitch, the siren is worked till
the proper pitch is obtained, then by pressing the
button the wheels are thrown into action, the time
being carefully noted. At the end of one minute,
during which, by proper working of the bellows, the
same pitch has been maintained, the wheels are
stopped by pulling out the button, and the number of
revolutions made by the disc in one minute are read
off. With each revolution fifteen shocks are given
to the air, therefore the number of vibrations pro-
ducing the given pitch is obtained by multiplying
15 by the number of revolutions per minute.
This gives the number of vibrations per minute, and
dividing by 60, one obtains the number per second.
Suppose the vibrations to be 100 per second,
then the period of each vibration will be T^tli °f a
second. The length of the wave can also be obtained
if the number of vibrations be given. At freezing
temperature sound travels 1090 feet per second, and
in that time we have one hundred wave movements

Chap. XXXI I. ] MUSIC A L INTER VALS. 427

to produce the given sound. Then -y^ = the wave
length in feet=il0'9 feet. "With a higher temper-
ature the wave length would increase.

With such an instrument it is easily shown that
there are vibrations occurring too slowly, i.e. too few
of them in a second of time, to be perceived by the
ear as a continuous sound. Helmholtz fixed this
lower limit at sixteen vibrations per second. W7ith
fewer than sixteen vibrations per second, the ear has
no power to fuse them together to produce the
sensation of a musical tone. If the disc could be
rotated swiftly enough, the same instrument might
also show that there are vibrations occurring too
swiftly to be perceived by the ear. The upper limit
has been fixed by Helmholtz at 38,000 vibrations per
second. The highest musical sound capable of being
perceived by the human ear is produced by 38,000
vibrations per second. There are, of course, many
people who cannot hear at all sounds of this pitch.
The resemblance to the case of light is here interesting.
Just as there are vibrations, fewer than those pro-
ducing the red of the spectrum, which are not visible
to our eyes, and which have yet been shown to
possess very great heating properties, and as there are
vibrations faster than those producing the spectral
violet, which are invisible to our eyes, and are yet of
great chemical activity, so there are vibrations of

O V '

another kind fewer than 16 per second, and more
than 38,000 per second, of which, however, the ear
has no cognisance, so far as the perception of musical
sound is concerned.

Intervals. — Pitch of sound the siren proves to
be due to number of vibrations per second of time.
But the siren, as modified by Helmholtz, can render
still other service. Helmholtz devised what is called
the DOUBLE SIREN. The lid of the air chamber is
perforated by four series of holes arranged in four

428 PHYSIOLOGICAL PHYSICS. [Chap, xxxii.

concentric circles, the outer circle containing eighteen
holes, the next twelve, the next ten, and the inner-
most eight. By means of four stops any one of these
circles of holes may be opened or closed at pleasure.
Thus only the set of eighteen may be open, or the set
of twelve, and of ten, or all of them, may be opened,
which would mean forty-eight shocks to the air with
each revolution. The rotating disc has, of course,
a hole for each one of the lid. This improvement in
the siren is due to Dove. Helmholtz takes two such
boxes, and fixes one a little way above the other,
a.nd upside clown so that they face one another.
Both may have the same number of holes in the lids,
arranged with stops in the same way ; but in Helm-
holtz's siren the upper box has four concentric series
of sixteen, fifteen, twelve, and nine holes respectively.
The rotating disc of both is on one axis, so that if one
rotates, the other does also. The inlet tube of the
upper box is bent down, that of the lower one bent
up ; thus they meet one another in a common pipe to
which the tube from the bellows is attached, and so
both can be worked simultaneously and with the
same blast. Of course, by stopping all the holes of
one box only one may be worked at a time. Now with
such a siren it is possible to make one box produce
in the same time double the number of vibrations of
the other. In such a case the sound produced by one
box is found to be the octave of that produced by
the other. An octave is, therefore, a note produced
by double the number of vibrations of the note of
which it is the octave. Double the number of the
vibrations of the octave will produce its octave, or the
second octave of the original note, and so on. Again,
twelve holes of one box may be opened, and eight of the
other, when the two musical notes produced will be
perceived by trained ears to be a fifth. The musical
interval of a fifth is shown, thus, to be due to two

(.'imp. xxxn.] INTERFERENCE OF SOUND. 429

sounds, one of which is produced by twelve vibrations
for every eight of the other, i.e. three for every two,
and is expressed thus, -|. In the same way the various
relations may be worked out, as shown in the accom-
panying list.

octave,
fifth,
fourth,
major third.

£ = minor third,
f = major sixth.
£• = minor sixth.

With the same instrument the lowest C of the ordi-
nary pianoforte is determined by Helmholtz as due to
thirty-three vibrations per second, the middle C as due
to 264 vibrations per second. Taking the ordinary
scale, the relations are approximately given as
follows :

CDEFGABC'

(ut) Do Ee Mi Fa Sol La Si Do' (ut)

2G4 297 330 352 396 440 495 528

1 I f f ! f ¥ 2

The upper two lines give the names of the notes,
as designated by letters, or the French or Italian
names, the tirst line of figures gives approximated
the number of vibrations per second, and the last
line gives the fraction which expresses the relation of
each note to the fundamental note.

Interference of sound: Beats. — By means
of the double siren of Helmholtz, another phenomenon
may be illustrated. The upper of the two boxes is
movable on an axis, and may be turned, by means of
a toothed wheel with a handle, either in the direction
of the rotating disc, or in the opposite direction.
Suppose the disc to be revolving, and the box to be
turned in the opposite direction, the holes in the lid
of the box will come opposite to the holes in the disc
more quickly than if the box were stationary, a
slightly greater number of pulses will be given to the

4^0 PHYSIOLOGICAL PHYSICS. [Chap. xxxn.

air in a second of time, and the note produced by the
box will be sharpened. If, however, the box be
turned in the same direction as the disc, the two sets
of holes will coincide less speedily, and a flattening of
the note will result. Now suppose both boxes to be
producing the same number of vibrations in a second
of time, i.e. sounding the same note, let the upper
box be turned in either direction, a slight difference
will be produced between the number of vibrations of
each box ; and this difference will announce itself by
the appearance of what are called BEATS, alternate rising
and falling of the sound, or intensification and diminu-
tion of the sound. This occurrence may be explained
in the following way. Suppose two men walking
side by side, and keeping step. Consider only the
right foot of each. The right foot of each will ad-
vance and touch the ground in front at the same
instant of time. With the forward movement of the
body and the advance of the left feet, the right feet
will come to be behind, and as the advance continues
will leave the ground at the same instant. The foot
may be considered as oscillating with each step
between two extremes from its middle position, and
the movement from the place where the foot touches
the ground in front to the place where it leaves the
ground behind, and forwards again to the position in
front as a complete wave movement, one complete
vibration or oscillation. The distance, then, between
the extreme position in front and the extreme position
behind will be half a wave length ; and, in the lan-
guage of wave motion, the foot in its extreme position
in front and its extreme position behind may be said to
be in opposite phases. Suppose now that the two men
start by each touching the ground in front with the
right foot at the same instant, but suppose that one
walks very slightly faster than the other. If he is
not to go ahead of his neighbour his steps must be

chap, xxxn.] THE PRODUCTION OF BEATS. 431

slightly shorter to counterbalance their increased
rapidity. The oscillation, so to speak, of his foot will
be faster, but the wave lengths will be shorter. The
result will be that at the second step his foot will be
slightly in advance of his friend's ; his friend's foot,
that is, will be slightly behind. With each step this
difference will be slightly increased, till after several
steps his right foot will touch the ground in front,
when his friend's is just being lifted from the ground
behind. The two feet, that is to say, will be in oppo-
site phases. The foot of each will be on opposite
sides of the middle line, the position of rest ; one
will be nearly as far forward as the other is behind,
and the mean position would be very nearly in the
position of rest. Suppose the walking to be pro-
ceeded with, with each step the difference will be
added to ; but now the foot that is behind will with
each step come farther and farther forward, till
after a few more steps the right foot of each man will
again touch the ground in front at the same instant,
and the two feet will be in the same phase. If the same
relative pace be maintained, after a few more steps
the feet will again be in opposite phases, and after a
few more again in the same phase ; they will alter-
nately coincide and be opposite to one another. The
more nearly the speed of the two is similar, the more
seldom will they coincide and be opposed ; and the
greater the difference in speed the oftener will the
coincidence and opposition happen. Now, for the
feet of the two men substitute two wave movements,
whose periods are very nearly the same, one being,
however, shorter than the other, that is, with slightly
quicker vibrations, and suppose them to start together
through the air. Because of the slight difference
they will alternately coincide and be opposite. When
they coincide the vibrating particles will be in the
same phase, will be moved by both in the same

43 2 PHYSIOLOGICAL PHYSICS. [Chap. xxxn.

direction, and the extent of movement will be greatly
increased ; when they are in opposite phases, the par-
ticles will be urged in one direction by one and in the
opposite by the other, and will, therefore, assume the
mean position, very nearly the position of rest ; the
movement will be arrested. To apply this to sonorous
waves, when the two waves coincide the condensation
of one is added to that of the other, with the result of
increased condensation, the rarefaction of one to the
rarefaction of another, with the result of increased
rarefaction. Then, owing to the difference of period,
they do not coincide ; gradually the difference increases
till the rarefaction of one coincides with the conden-
sation of another (they are in opposite phases), and
the result is abolition of the sound (interference],
After a few more vibrations the condensations again
coincide, and there is intensification of the sound.
Thus, when two notes are produced by nearly the
same number of vibrations, they alternately add to
one another and subtract from one another, the sound
alternately grows louder and then fades away, to grow
loud again, and again fade ; beats are produced. The
more nearly alike they are the fewer will be the beats,
and the more they differ, within limits, the more fre-
quent the beats. The beats, in short, represent the
difference between the number of vibrations of the
two notes ; so that the number of vibrations of the
lower note + the number of beats per second will
give the number of vibrations per second of the higher
note.

IMssoiiaiice.— This physical phenomenon of
interference is found to have a physiological side.
When the two notes are very near one another we
see the beats are few, and the ear readily distinguishes
each separately, when there are no more, for instance,
than four to six in a second. When the two notes are
farther apart the beats become partly fused by the

Chap, xxxn.] DISSONANCE. 433

ear, because of their increased number, and give a
harsh grating character to the sound, and with a still
greater number a cutting character. The rising and
falling of the sound, within very narrow limits and
under special circumstances, may produce a pleasing
or effective impression, but beyond these limits and
circumstances they are disagreeable to the ear, giving
rise, as they do, to the same sort of nervous impression
that a flickering light has upon the eye. The
sensation produced by the beats is that of dissonance.
When beats reach the number of thirty-three per
second, according to Helmholtz, the dissonance is
intolerable ; as the number increases the roughness
lessens, though it is still present when they occur at
the rate of one hundred per second, but when they
reach 132 per second the roughness disappears.
When two notes are sounded together as for the
production of beats, a new note may be heard,
different from either, whose pitch is due to a number
of vibrations equal to the difference between the two
primary notes. The rate of vibration of this resultant
tone, or difference tone as it has been called by Helm-
holtz, corresponds to the number of beats produced by
the two primaries, and was supposed by Young to be
a tone produced by the fusion of beats. Helmholtz,
however, explains them to be due not to beats, but to
secondary waves caused by the disturbance of the
beats.

As showing how the physical theory of beats and
the physiological sensation of dissonance harmonise, a
comparison may be made. Given a note to start
with, the most perfect combinations are of the funda-
mental note with its octave, with its fifth, and with
its fourth ; the consonance with its third is less com-
plete. Now a note due to 264 vibrations per second
has as its octave one due to 528 per second ; the
difference, 264, is so great that beats cannot be
c c— 7

434 PHYSIOLOGICAL PHYSICS, tchap. xxxn.

produced. Again, the fifth, f , would be produced by
one note of 264 vibrations, and another of 396, the
difference being 132, the number at which roughness
disappears. The fourth, -|, gives the following :

352 — 264 = 88;

and here the roughness will be perceptible. This will
be more marked with the major third, |-, viz. :

330 — 264=66.

With the interval of" a second, |^ the roughness is very
great, namely,

297 --264 = 33;

for here, according to Helmholtz, the number of beats
is the most discordant.

Thus, it is seen that in their results, the physical
theory and the physiological sensation agree remark-
ably. It is to be noted that where the difference
between the fundamental tones is too great to occasion
beats, their overtones may beat, and so produce dis-
sonance. (See page 438.)

Quality of musical sounds.— The third feature
of musical sounds is their quality. Every one knows
that there is a marked difference between the note of
a pianoforte and a note of the same pitch produced 011
a violin, and between these two and a note of the
same pitch produced by the human voice, a marked
difference also between a note of the same pitch pro-
duced by two voices. This distinction between notes
of the same pitch as produced by different instruments
is signified by saying that they differ in quality, that,
for instance, one produces rich tones and another thin,
one produces mellow tones and another harsh, and so
on. It is apparent that neither the amplitude of the
vibrations nor their frequency can account for this
feature. The difference in character is said to depend
on the quality of the note. The Germans use the

chap,

.} QUALITY OF MUSICAL SOUNDS.

435

phrase klang farbe, meaning sound tint, or sound
colour, while the French term is timbre, meaning
stamp. On what, then, does quality depend ]
Consider waves ; they differ in size, in rapidity or
frequence, but they also differ in form. Size is
equivalent to amplitude of vibration, i.e. loudness of
sound, and rapidity to the number of vibrations per
second, i.e. pitch of sound, while the form of the
wave is found to correspond to the quality of sound.

Waves may be simple or compound ; if simple,
their form will be exhibited by rounded crest and
hollow, the crest being as much above the middle line
as the hollow is below. Apart
from such simple forms, waves
may be of many shapes, high
and sharp, flat and broad, and
so on. Now it has been shown
that every compound wave is
capable of being resolved into
simple waves. Fig. 187 shows
three waves, whose vibrations
are as 1 : 2 : 3. The

blending of these three simple
waves produces the compound
form marked 4. The form of
the complex wave is obtained
by drawing a series of vertical Fig. 187.— Compound
lines. The position of the com- ^aves.

pound wave at any one of these lines is marked
by taking the algebraic sum of the distances of
the three simple waves above or below the line of
rest, and in that vertical line. Thus, take the ver-
tical line a'b', the position of a point of the com-
pound wave in this line is obtained by taking the
distance in the same line between a' and a2, the
distance between a3 and a4, and between a5 and a6, and
taking their algebraical sum. They are all above the

436 PHYSIOLOGICAL PHYSICS. [Chap. xxxn.

line of rest, are all + , that is to say, and consequently
the three distances added together give the distance
A6' above the line of rest. Take the vertical line cc',
the position of a point of the compound wave in that
line is obtained by taking the algebraical sum of the
distances c'c2, c3c4, and c5c6. c c2 and c5 c6 are
negative, c3 c4 is positive ; the result is a negative
quantity, the distance AC below the line of rest. So
the position of any other point in the compound
wave may be determined. It is, consequently,
apparent that the compound wave could be resolved
into the simple waves 1, 2, 3. It can, moreover, be
shown that any complex wave can be analysed into
simple waves, whose corresponding number of
vibrations are in the proportion of 1, 2, 3, 4, etc.
That is to say, a compound wave may be resolved
into one simple wave, representing a number of
vibrations that may be taken as 1, and into a series of
other simple waves, representing each a number of
vibrations that is a multiple of the first, 2, 3, 4, 5,
and so on. Vibrations whose numbers are in this
proportion, 1, 2, 3, etc., are said to form a HARMONIC
series.

Of course, sounds do not produce transverse waves,
such as are depicted in the figure. These are simply
graphic representations of waves. The varying dis-
tances of the curves above or below the middle line
represent varying degrees of condensation and rare-
faction of the atmosphere in which the sound is propa-
gated.

Now if a string be fixed at both ends, pulled by
the centre to one side and let go, the string will
vibrate in its whole length, first to one side then to
the other, and if riders of paper be placed at different
points on the string, they will be all thrown off
(Fig. 188). The string while it vibrates will utter a
note of a definite pitch and particular quality, the

Chap, xxxii.] VIBRATIONS OF A STRING. 437

fundamental or primary note of the string. Now let
the string be damped at the centre by one finger, and
let it be plucked at the centre of one half, the string
will divide

itself into two ^J^Z <Z ^-gjgff

equal parts,

each of which Fig. 188.-The Vibration of a Steng sounding

its Fundamental Note.

will vibrate,

the centre being motionless even when the finger
is removed, as shown by a rider remaining on the
string at that point while others are thrown off. The
string will now utter the octave of the first note,
a note, that is, produced by double the number of
vibrations of the first, and, therefore, also the first
harmonic of the primary. In the same way, if the
string be damped at a third of its length, on plucking
it in the middle of this third it will divide into three
equal segments, each vibrating in a similar way
(Fig. 189). There will be two points at which the

A, A

C D B

Fig. 189. — Vibration of a String damped at a Third of its Length.

paper rider will not be tossed off. The note produced
will be the second harmonic. The points where the
string remains at rest are called nodes, and the parts
between the nodes which are in movement are called
ventral segments. By damping the string at one-
fourth of its length, it will be caused to vibrate in
four segments, and the fourth harmonic will be pro-
duced, and so on.

Now the string, when it vibrates in its whole
length, produces its fundamental note of a particular
quality, but that note is not a simple one. If a graphic

438 PHYSIOLOGICAL PHYSICS. [ChaP. xxxn.

tracing of it is obtained it does not exhibit smoothly
rounded crests and hollows of equal size, but a curve
of considerable irregularity, in fact a compound wave
would be represented. This compound wave, in
accordance with the principle already noted, would be
capable of analysis into several simple waves of a
harmonic series. In fact, the note of the vibrating
string is a compound of a simple note, due to the
vibrations of the string as a whole, and of other notes
whose vibrations correspond to the movements of the
string when divided into two or more segments. It
is this mixture of harmonics, partial notes or overtones
as they are also called, with the simple fundamental
tone that gives the quality to the tone emitted by the
string. Indeed, with some attention a trained ear
can always detect in the sound of a vibrating string
one or more tones higher than the fundamental, i.e.
one or more overtones. Each musical instrument
produces different harmonics with its fundamental
notes. Thus the violin string produces specially the
lower harmonics of the series^ hence its mellow sound ;
brazen instruments produce specially the higher har-
monics, hence their shrill piercing sounds. The tone
of a pianoforte, the string of a harp, etc., each pro-
duces its own particular mixture of overtones with
its fundamental, its own special blend, so to speak,
and hence has its own particular quality of sound.
The difference in the qualities of human voices singing
notes of the same pitch are due to the same causes,
namely, the differences in the harmonics that specially
predominate in each voice. Dissonance may be
produced by overtones even when the fundamental
notes are too far removed to produce audible
beats. One overtone of one note may be near
enough in the number of its vibrations to an overtone
of another note to produce beats, and give roughness
to the sound.

439

CHAPTER XXXIII.

SYMPATHETIC VIBRATION AND RESONANCE.

§ympat!ietic vibration. - - If we take two
tuning forks (see Fig. 191), tuned to precisely the
same pitch, and sound one in the immediate neigh-
bourhood of the other, the untouched fork will pick
up the sound and vibrate in harmony with it. This
is what is called sympathetic vibration. Each fork
makes the same number of vibrations per second.
When the waves (of condensation and rarefaction)
produced by the motion of the first fork batter upon
the second, they tend to set it in motion also. Each
separate impulse is too feeble to move the fork, but
one after another at regular intervals finally sets the
second fork in vibration.

Suppose a child upon a swing and a boy setting
the swing in motion. He gives a slight impulse at
first, and the swing sways feebly. He waits till it
has come back towards him and is just about to sway
forwards slightly again. At that instant he gives
another push, and waits a similar interval till the
swing has again come backwards and is about to
move forwards, when he gives another impulse. So
in a short time he gets up a good movement of the
swing, and can maintain it with slight effort if only he
gives the impulse at the proper moment. Suppose,
when the swing was half way on its backward course,
he gave it a push forwards, he might bring it to a
dead stop, and would at least entirely destroy the
regular movement. So the tuning-fork, tending to

o o O

sway to and fro by condensation and rarefaction
reaching it from the sounding fork, is finally set into

440 PHYSIOLOGICAL PHYSICS. [Chap, xxxni.

vibration by the regular rhythmic alternation. If it is
caused to move it will only be by a vibration of its
own period, for if, when it is moving in the direction of
condensation, it is met by a rarefaction due to the other
fork, its motion will be disordered and will cease, just as
the swing is stopped by its backward movement
being met by the forward impulse from the boy.
But when the oscillations of the two forks agree,
then the activity of the one will excite that of
the other. If a small coin be attached by wax to a
limb of the second fork, then the vibrations of the
first will no longer maintain those of the second,
because the vibrations of the two are no longer pre-
cisely alike, and the one will interfere with the other.
Sympathetic vibration may be produced with a piano-
forte. If the dampers be raised, and loud musical
sounds be uttered in the neighbourhood, a number of
strings may be heard humming. Each string has
picked out of the mass of sound the particular vibra-
tions to which it is tuned, and is sounding in harmony
with it. The strings have analysed the complex
sound, and the separate strings set into vibration
indicate its different elements.

This phenomenon is of the utmost significance in
physiology, since it affords the basis of the theory of
the perception of musical sounds. The complex mass
of sound is conveyed to the inner ear, in which there
are supposed to be delicate structures which will
vibrate in harmony with particular vibrations, and
with none other. The ear, in this view, becomes an
analytical organ, and separates the complex sound
into its elements. An impression is thus made on the
nerve fibril in connection with each delicate vibrating
body, and the separate impulses, carried to the centre
in the brain, are fused again into a complex sensation.
The trained musician can, to some extent, become con-
scious of the analysis, and thus can distinguish in the

Chap. XXXIII.]

RESONANCE.

441

body of the sound many of its elements; while the
untrained person becomes conscious only of the fused
whole, is aware only of the synthesis and not of
the analysis. The details of this theory must, how-
ever, be sought in the systematic text-books. It is
referred to here only to show how a knowledge of
the physical aspect of the problem is necessary to a
good comprehension of the physiological process.

Resonance. — Sympathetic vibration offers an
explanation of another remarkable occurrence. Take
a tuning fork (B, Fig. 190) and cause it to vibrate by
drawing a bow across it, or by
striking it (the former pre-
ferably), the sound emitted
will be very feeble, and will
be heard only when the ear is
close to it. Hold it now close
to the mouth of the tall jar A,
still the sound is feeble.
Then from a jug pour water
slowly and as noiselessly as
possible into the jar. The
sound will be slightly in-
tensified, till, when a certain
quantity of water has been
added, the amount being de-
pendent upon the pitch of
the fork, the sound will
become greatly intensified so
as to be heard over a con-
siderable distance. Go on pouring in more water,
the loudness of the note will slowly diminish, till
it again becomes almost inaudible. It is evident
that when the column of air in the jar is of a par-
ticular length it intensifies the sound of the fork. If
one could blow across the mouth of the jar so
as to throw the air into vibration, the jaT itself

Fig. 190.— Eesonance.

The fork is represented as if
touching the edge of the
jar. This should not be so.
It would also be better turned
with the front of the limb
facing the jar.

442 PHYSIOLOGICAL PHYSICS. [Chap. xxxm.

would give out a musical note, and if this were done
when the column of air was just the length to inten-
sify the sound of the fork it would be found that the
two sounds were precisely of the same pitch. The
column of air is of such a length as to vibrate in har-
mony with the fork. Consequently when the fork is
sounded in its neighbourhood it sets the air of the jar
in synchronous oscillation, and thus the intensity of
the sound is increased. The term applied to the
reinforcement of the sound is resonance, and the body
which reinforces it is called a resonator. If the
column of air be shortened or lengthened, its period
of vibration is no longer the same as that of the fork,
and the intensification is not produced. The column
of air in the jar will not vibrate in harmony with
any fork but that with which its vibrations agree.
If a fork of another pitch is brought near to its mouth
it is dumb. Now each limb of the fork moves to and
fro on each side of its position of rest. When the
limb moves outwards it produces a condensation of
the air in contact with it; when it moves inwards
a rarefaction is the result. The condensation travels
through the air in the jar till it reaches the surface of
the water, by which it is reflected. If the condensa-
tion reaches the mouth of the jar, on its return
journey, just when the outward excursion of the limb
of the fork is completed and its recoil is about to
begin, it is in time with it, and the succeeding rare-
faction will be propagated through the jar and will be
completed when the outward excursion of the fork
is about to be renewed, and a second condensation to
begin. The movements in the jar are thus in time
with the movements of the fork. The condensation
is half a wave length, and it travels through the
column of air in the jar twice, once downwards and
once upwards, so that the length of the column of
air in the jar is half that of a condensation, i.e. a

Chap, xxxin.] RESONATORS. 443

quarter wave length. If the column of air were
longer the condensation would not have travelled
through the jar till after the recoil of the fork (the
rarefaction) had begun, and thus the two would not
harmonise. Such a jar, then, open at only one end
must be equal to a quarter the wave length of the
vibration of the fork if it is to vibrate in harmony
with it. If a fork vibrating more rapidly be used,
its wave length is shorter and a shorter column of
air is required to be in harmony with it. This may
be obtained by pouring more water into the tall jar
till the proper length is secured, or by using a shorter
jar. The column of air in a tube open at both ends
will also vibrate in harmony with a given sound. A
tube open at both ends must be twice the length of a
tube closed at one end, in order to vibrate synchro-
nously with the same note. A tube open at both ends
is called briefly an open tube or pipe, and one closed at
one end is called a stopped tube or pipe. We have seen
that a stopped pipe must be a quarter the wave length
of a given vibration if it is to vibrate in harmony with
it, so an open pipe must be half the wave length to be
in harmony. If an open pipe is the same length as
a stopped pipe, it will vibrate in harmony with the
octave of the note of the stopped pipe, for it can only
be half the wave length of a vibration which is half as
short as that to which the stopped pipe responds ;
that is, the vibration to which the open pipe responds
must have twice the rapidity of the vibration of the
note to which the stopped pipe responds ; it must be
its octave.

Forms of resonators. — The fact of resonance
is made use of for practical purposes. Thus, tuning
forks are usually mounted upon boxes, of such a
length that the column of air in the box will vibrate in
harmony with the note of a particular fork, and with
none other. The sound is thus rendered audible to a

444

PHYSIOLOGICAL PHYSICS. [Chap. XXXIIL

large number of people, while otherwise it would be
heard only by those close to the fork. Fig. 191 shows

such a tuning-fork mounted on its
resonator. The box may be open
at both ends, or closed at one.
As we have seen, if one end be
closed, the box must be equal to
a quarter the wave length of the
sound it is to reinforce, and a half
the wave length if both ends be
Fig. 191— Tuning Fork O])eil< ^ resonator may take the

mounted ou Kesou- A .,..*'

auceBox. torm ot a pyramidal pipe open at

both ends. One of Helmholtz's
resonators is shown in Fig. 192. It consists of a
brass box of globular form, with two openings op-
posite one another, one of them much narrower
than the other. They are made of various sizes ; the
smaller ones, generally speaking, will harmonise with
notes of higher pitch than the larger,
but each one will respond to a note
of one definite pitch only. Now
suppose an orchestra to be playing,
let a person take one of these re-
sonators and place it at the side
of his head, so that the small end Fig. 192.— Resonator
enters the external canal of the ear. of Helmholtz.
If the note to which the resonator
is tuned be sounded in the orchestra, the resonator
will immediately pick it out, and vibrate in harmony
with it, and the person will hear this note suddenly
burst out with great force. Let him take another, it
also will select its own note, and intimate its produc-
tion by its resonance. No matter how complex the
body of sound, the resonator cannot be deceived.
With inevitable precision it selects the note to which
it corresponds, and vibrates in harmony with it.
How resonators can be made use of to analyse

chap, xxxiii.] THE ORGAN PIPE. 445

sounds will thus be evident. This will be referred to
immediately.

The sounds produced by an organ-pipe are due to
resonance. Such a pipe is shown in Fig. 193. It
consists of a tube, open or closed at the upper end, as
the case may be. The lower end terminates in a
part of a construction similar to what may be seen,
in an ordinary whistle, and called the embouchure.
Air is blown in by a narrow pipe, and enters a small
chamber separated from the body of the pipe by a
wedge of wood except for a narrow slit i through which
the compressed air passes. The air, issuing in a thin
stream, strikes against a sharp edge projecting from the
wall of the pipe inside of a rectangular window bo in
the lower part of the pipe, through which the broken
air passes to the outside. The air is thus broken up
into pulses, and the pipe is tuned to take up some
one pulse and vibrate in harmony with it. Thus by
altering the length of the tube, everything else
remaining the same, the pitch of the note of the pipe
will be altered ; it resounds now to a shorter or longer
pulse than before.

That the air in the organ-pipe is thrown into
vibration may be shown in various ways. If a light
ring, covered with membrane on which sand is strewn,
be lowered into an open sounding organ pipe, the
pattering sound of the sand on the membrane will
indicate the agitation of the air in the pipe. If the
pipe be sounding its fundamental note a node will be
found at the centre and ventral segments at each end.
"When the membrane is lowered to the middle the
noise of the agitated sand ceases, to be again resumed
if the membrane be raised or lowered. The same
thing may be shown in a still more remarkable way.
A small circular opening is made 'in the side of the
organ-pipe ; over this is fixed a small wooden box M
(Fig. 193), with an indiarubber floor, the indiarubber

446

PHYSIOLOGICAL PHYSICS, ichap. xxxm.

covering the aperture in the pipe. To the front of the
box are connected two narrow tubes, to one of which
an indiarubber tube, conveying gas, is
attached, to the other a small _J -shaped
tube terminating at the upper extremity
in a fine point m. Gas enters the little
chamber by one tube and leaves by the
other, at which it is lighted, and a fine
tongue of flame is produced. Now at
the centre of the pipe, sounding its
fundamental note, the greatest changes
in density will occur. When the density

Fig. 193.— Organ . , J, ., . -,. ,, n £ ,-,J

Pipe. is greatest the mdiarubber wall or the

gas chamber will be forced outwards
from the organ-pipe, and when, the density is least it
will be forced inwards by the pressure of the outer
air. Agitations of the gas in the chamber will be pro-
duced, and agitations of the flame. Experiment con-
firms this, for the flame may be extinguished when
the note of the pipe is sounded. If other gas
chambers be connected with the pipe towards either
extremity, the flames will be affected, but not nearly
to the same extent.

The analysis of sound. — By means of such
gas jets as have been described, and with the aid of
resonators of Hehnholtz, an analysis of a complex
sound may be made. Fig. 194 shows Koenig's appa-
ratus for the analysis of a compound tone, by means
of manometric flames. It consists of eight resonators,
the largest vibrating with 256 vibrations per second,
ut2 (do2) ; and of the first seven of its harmonics,
numbers 1 (ut3), 2, 3, 4, etc. From the narrow
aperture of each resonator a narrow indiarubber tube
leads to a small chamber divided into two by an
indiarubber partition. The air on one side of this
partition is in communication with the air in the
resonator. On the other side of the partition is gas,

chap, xxxiii.] ANALYSIS OF SOUND,

447

led thither from an ordinary gas-pipe, and from this
side of the chamber is a little burner similar to that
already described (Fig. 193). Each resonator is con-
nected in this way with its own gas chamber and
burner, and the bur-
ners are all placed in
a row one above
another, as shown in
Fig. 194. Now if the
air in any one resona-
tor be agitated, the
indiarubber partiti o 11
of the chamber,
separating gas on one
side from air continu-
ous with the resonator
on the other, will be

thrown into vibration, Fig 194._Analysis of Sound by
the gas and the flame Koenig's Apparatus.

will both be agitated.

The agitation of the flame will be perceptible to the
naked eye by its becoming thinner and bluer. By a de-
vice due to Wheatstone, this may be rendered more
striking. Opposite the eight gas burners is a long mirror
with four reflecting sides, at right angles to one another.
This may be revolved on an almost perpendicular axis,
by a toothed wheel arrangement. If the gas issuing
from the burners be lighted, and the mirror revolved,
the light reflected from the four surfaces of the mirror
gives the impression of a continuous band. If the
flame be agitated the revolutions of the mirror separate
out each movement, and the band of flame is now
segmented (Fig. 194, a b). There are, then, eight
flames, one corresponding to each resonator ; in the
revolving mirror are seen eight bands of flame. If
any one flame be agitated it is at once detected by
the segmentation, as seen in the mirror ; so that if

448 PHYSIOLOGICAL PHYSICS. [Chap. xxxm.

the air in any one of the eight resonators be thrown
into vibration, the fact will be revealed in the mirror
by the segmentation of the corresponding flame band.
Now if a tuning-fork, vibrating 256 times per second,
be sounded in the neighbourhood of the apparatus,
the flame belonging to the largest resonator will be
seen, on rotation of the mirror, to be segmented ; but
none of the other flames will be affected if the
tuning-fork has been properly bowed, for forks give
pure sounds. Similarly the octave of ' the first fork
will affect the second resonator, and none other. If,
however, the note of the middle C of the pianoforte
be sounded in the neighbourhood, the lowest resonator
will be affected and also some of the higher, indicating
the mixture of harmonics with the fundamental tone.
A note of the same pitch produced by a violin will
aft'ect others of the higher resonators along with the
lowermost one. Thus an optical demonstration is
given of the fact that quality is dependent upon a
mixture of harmonics with the primary tone, and thus
also the harmonics which determine the quality of the
notes of a particular instrument may be determined.
The same apparatus can be made to single out the
harmonics of the human voice if a note of the pitch
C be sung near it.

The production of the voice is readily under-
stood by such facts as have been considered. The
continuous current of air issuing from the lungs is
broken up into separate puffs by the vibrations of the
vocal cords. The cords in this respect act the part
of reeds. The rapidity of the vibrations are deter-
mined by the length and tension of the cords. How
the pitch of the voice is affected by the varying
lengths of the vocal cords in children, and in adult
males and females is, therefore, apparent. It is also
evident how the action of the crico-thyroid muscles
in depressing the thyroid cartilage will increase the

Chap, xxxiii.] THE PRODUCTION OF VOICE. 449

tension of the cords, and so elevate the pitch, while
the action of the thyro-arytenoid muscles will have
a reverse effect by pulling up the thyroid cartilage,
and lessening the tension of the cords. In the pro-
duction of tones of very high pitch, doubtless the
overlapping of the posterior parts of the cords by the
action of the lateral crico-arytenoid muscles, aided by
the arytenoid muscles, will have some effect by limit-
ing the vibrations to a smaller part of the cords.
While pitch is regulated in such ways, loudness is
affected by the greater or less degree of force of the
outgoing current producing movements of greater
or less amplitude. All this, however, as it appears,
is bat a small and elementary part of the production
of voice. The larynx above the cords, the pharynx,
and the cavities of the nose and mouth play a very
important part in the process. They act the part of
resonators, and reinforce the sound of one or other of
-the overtones produced by the vibrations of the cords.
Now these resonating passages and cavities are not
of a fixed shape or size, but can be altered in various
ways, so as to be capable of resounding now to one
note, now to another. Helmholtz remarks that they
admit " of much variety of form, so that many more
qualities of tone can be thus produced than in any
instrument of artificial construction." Thus the form
of the air passages above the cords will determine the
quality of sound, not only for separate individuals,
but also for the same individual at different times.
The important part played by these resonating pas-
sages is shown by Helmholtz's elaborate investigations
on the production of vowel sounds. The different
vowels may be produced when the vocal cords are
vibrating the same number of times per second, that
is, when they are sounding the same fundamental
note, and with the same intensity. The only differ-
ence necessary is in the form of the mouth, so that for

D D— 7

450 PHYSIOLOGICAL PHYSICS. [Chap. xxxm.

the production of one vowel the mouth will act as
resonator for a particular harmonic, and for the pro-
duction of another vowel a new form will be given to
it for the reinforcement of a different overtone of the
vibrating cord. This may be shown with the aid of
Koenig's manometric flames already described. An
analysis so conducted has revealed differences in
the vowel sounds, which may be briefly stated as
follows :

" The vowel A contains, besides the fundamental
note, the second harmonic feeble, the third strong,
and the fourth feeble ;

" E has the fundamental note feeble, the second
harmonic rather strong, the third feeble ; on the other
hand, the fourth is very strong and the fifth feeble ;

" i has very high harmonics, especially the fifth,
strongly marked ;

" o contains the fundamental note, the second
harmonic very strong, and the third and fourth har-
monics slightly ;

"u is composed of the fundamental note very
strong, and the third harmonic sufficiently pro-
nounced."

Thus it is evident that a knowledge of the
physics of sound is necessary for a proper appreciation
of the action of the ear in perceiving sounds, and of
the action of the vocal apparatus in producing
sounds.

$art

HEAT.
CHAPTER XXXIY.

THE NATURE AND SOURCES OF HEAT.

Nature of heat. — Just as, according to the
theory espoused by Newton, light was supposed to be
due to material particles emitted by a luminous body,
which, travelling through space, reached the eye, and
by their impact gave rise to a sensation of light, so
heat was by many supposed also to be an actual
substance. By these heat was held to consist of
atoms which had the power of forcing their way into
the substance of bodies, and so attacking them as to
dissociate their particles from one another, and pro-
duce, in consequence, the liquid or gaseous state.
The entrance of the heat atoms into a person's body
produced the sensation of heat, and their exit that of
cold. Caloric was the name given to the material of
heat. Yet the material view of heat was not univer-
sally accepted, and many philosophers entertained the
notion that heat was not a thing but a motion, espe-
cially Bacon, Boyle, Hooke, Rumford, Davy, and
Thomas Young. The modern view regards heat,
like light and sound, as a mode of motion. The
dynamical theory of heat, as it is called, is the elabo-
ration of recent years, and of such men as Professors
R. Clausius of Ziirich, Rankine, and Sir William
Thomson of Glasgow ; but it was suggested by

452 PHYSIOLOGICAL PHYSICS. [Chap, xxxiv.

Mayer, a physician of Heilbronn, in 1842, and
experimentally demonstrated by Joule, of Manchester,
in 1843.

According to the theory, mechanical energy is
capable of being converted into heat, and heat into
mechanical energy, the amount of one being directly
determined by the amount of the other. The conver-
sion of mechanical energy into heat is exhibited in
many well-known occurrences. The production of
heat by friction is one of the commonest illustrations.
Thus, the rapid twirling of a pointed stick on a piece
of hard wood is the method pursued by savages for
obtaining fire, while everyone knows that the heat
developed by the friction of the various parts of a
machine is one great cause of loss of power. The
hammering of a mass of metal on an anvil involves
the expenditure of a large amount of energy, but the
hammered metal is found to be much warmer at the
end of the process than it was at the beginning. When
a falling stone is suddenly stopped by concussion with
something which destroys its motion, the energy of
the falling body is not destroyed, for a large amount
of heat is developed by the shock, and an amount
proportional to the mass of the body and the distance
through which it has fallen. Similarly, the energy of
a rifle bullet which hits a target is not lost, but may
produce sufficient heat to fuse the ball. The produc-
tion of heat by various other forms of mechanical
work is easily shown experimentally. If air be com-
pressed in a metallic box heat is generated. This
can be shown by using the thermopile, whose con-
struction and mode of use are explained in chapter
xiv. If a thermopile be connected with a galvano-
meter in the way represented in Fig. 77, and if, by
means of a pair of bellows, a current of air be driven
against one set of junctions of the pile the needle of
the galvanometer will be deflected in a direction that

Chap, xxxiv.] MECHANICAL EQUIVALENT OF HE A T. 453

indicates heating of the junction against which the
current was directed. The energy required to com-
press the air and drive it out of the bellows has
partly heated the air. The converse experiment,
the transformation of heat into mechanical energy,
has teen, beautifully shown by an experiment of
Tyndall's. Air was compressed in a small metallic
box by means of a pump, and the stopcock then closed.
Heat was developed in the process. By letting the
box stand for a time the heat disappeared. The
stopcock was then opened, and the current, expelled by
the force of the compressed air, was directed against
a face of the thermopile, which indicated cooling by
a deflection of the needle ; the expansion of the air
had used up heat.

But there is a definite relationship between the
mechanical energy and the amount of heat. This
relationship Joule worked out, and called " the
mechanical equivalent of heat." He used a weight
which was permitted to fall a certain distance.
During its fall it turned a brass paddle-wheel, rotating
about a vertical axis in a copper vessel tilled with
water. The agitation of the water by the wheel
raised the temperature, the increase of temperature
being measured at the conclusion of the experiment.
He found that by permitting a weight of 1 pound
to fall through a distance of 772 feet sufficient heat
was generated to raise the temperature of 1 pound
of water 1° Fahr. The work done is that of a weight
of 1 pound falling through a distance of 772 feet, or,
what is the same thing, 772 pounds falling through a
distance of 1 foot. This is expressed shortly by the
phrase 772 foot-pounds. The same amount of work
would be required to raise 1 pound 772 feet high, or
772 pounds 1 foot high. This amount of work, then,
is equivalent to an amount of heat sufficient to raise
the temperature of 1 pound of water 1° Fahr. But

454 PHYSIOLOGICAL PHYSICS. [Chap, xxxiv.

the amount of heat necessary to raise the temperature
of 1 pound of cold water 1° Fahr. is called the unit of
heat, so that the unit of heat is equal to mechanical
work measured by 772 foot-pounds. If, instead of
the Fahrenheit, the Centigrade scale be used, then the
amount of heat necessary to raise the temperature of
1 pound of water 1° 0. is equivalent to 1,392 foot-
pounds mechanical work. The unit of heat, or
thermal unit, may also be measured on other
scales. Thus by French measure it would be the
amount of heat required to raise the temperature of
1 gramme, or 1 kilogramme, of water 1° C., and
could be estimated by its equivalent of mechanical
work necessary to raise so many grammes or kilo-
grammes so many metres high.

In French measure the unit of heat, or calorie,
as it is called, is the quantity of heat necessary to
raise the temperature of 1 kilogramme of water from
0° to 1° C. Joule's equivalent becomes then in
French measure the work performed by raising 424
kilogrammes 1 metre high, which is expressed shortly
by saying that 1 calorie is equal to 424 kilogram-
metres.

Heat is, then, a mode of motion, a form of energy.
When a falling body reaches the ground its energy is
not destroyed, it is only transformed ; the movement
of the body as a mass becomes transformed into
movements of the atoms of the body, one manifesta-
tion of which is the development of heat.

Sources of heat. — As has been seen, mecha-
nical work of all kinds may be sources of heat.
There are also chemical sources of heat ; wherever
chemical combination occurs, heat is produced. The
combination is due to affinity of two substances for
one another. So Tyndall represents the mutually
attracting atoms as "rushing together, and acquiring,
while crossing the insensible interval which separates

Chap. XXXIV.] SOUXCES OF HEAT. 455

them, the velocity with which they strike each other.
That this velocity is enormous is proved by the
amount of heat which it generates/5 " When the
atoms clash they recoil, and the subsequent tremulous
motion is one form of heat." When the heat pro-
duced by the combination is sufficiently great, light
is also produced, and combustion occurs. In most
cases of combustion the chemical combination is of
some substance with the oxygen of the air, and as
the affinity for oxygen is great so is the heat pro-
duced intense.

If heat is evolved when two bodies enter into
combination, heat ought to disappear when the bodies
are severed from their combination, when decom-
position [ is effected. This is the case : the heat lost
in chemical decomposition is exactly equal to that
generated by combination.

The amount of heat produced by the combination
of a substance with oxygen is always constant. No
matter whether the body be oxydised immediately, or
in various stages, the total amount of heat disengaged,
till the process is complete, is always the same. Thus
a given amount of carbon will always unite with a
definite amount of oxygen to produce carbonic acid gas,
and will evolve the same amount of heat whether the
process be sudden or slow. So it is possible to deter-
mine once for all the amount of heat produced by the
oxydation of certain quantities of given substances.
Thus, the heat generated by the combustion of 1
pound of hydrogen would raise the temperature of
34-, 46 2 pounds of water 1° C. ; 1 pound of wood
charcoal would raise the temperature of 8,080 pounds
of water 1° C., and oxide of carbon, 2,403 pounds.
The following table of Favre, Silbermann, and
Frankland shows the amount of heat (in heat units)
disengaged by the oxydation of 1 pound of various
food stuffs, etc. The substance was first dried and

456

PHYSIOLOGICAL PHYSICS. [Chap, xxxv.

then completely burnt. The table is of great interest
from a physiological point of view.

Potatoes .
Albumen .
Cabbage .
Carrot
Bread
Sugar
Rice
Starch
Ham (lean)
Veal (lean)
Milk
Beef (lean)

3-752
4-998
3-776

Cheese (Chester]
Yolk of egg-
Alcohol

3-967

Stearin

3-984

Palmatin .

3-277

Olein

3-813
5-000

Glycerine .
Leucin

4-343

Kreatin .

4-514

Urea

5-093

Uric acid .

5-313

Hippuric acid

6-114
6-460
8-958
9-036
8-883
8-958
4-175
6-141
4-118
2-206
2-615
5-383

The greatest source of heat is, of course, the sun,
which not only gives us heat directly by its rays, but
indirectly, since the organic substances, by burning
which we obtain what heat we desire, could not have
been formed but for the influence of the sun's heat.

Heat is also produced in capillary actions.

CHAPTER XXXV.

CONDUCTION, CONVECTION, AND RADIATION OF HEAT.

Conduction of heat* — If the end of a rod of

copper be thrust into a fire, very soon not only the end
in the fire will become warm, but the other end also.
The heat will be propagated from one end of the bar
to the other, the tendency being to make the whole
bar of the same temperature. If a second bar be
placed in contact with the outer end of the first, the
heat will be passed on to it also. By the dynamical
theory, as we have seen, this propagation of heat by
conduction is not a transference of matter, but a

Chap, xxxv.] CONDUCTION OF HEAT. 457

transference of movement. The particles of the part
of the rod that is in the fire are thrown into vibra-
tion more or less vigorous, according to the heat of
the fire, and the vibration of these particles is com-
municated to others in their neighbourhood, till all
the particles of the bar are thrown into oscillation.
All substances do not conduct heat with the same
facility. Copper is a specially good conductor of
heat ; iron is not such a good conductor ; while stone,
glass, and organic substances, wood, hair, feathers,
etc., are bad conductors. Liquids and gases have
feeble conducting power. The difference in the con-
ducting power of different substances is measured by
the quantity of heat that will pass in a unit of time
through a unit area of the substance of unit thickness
with 1° difference of temperature between the sur-
faces. The number obtained is the " coefficient of
conductivity."

Wood and brick have a less conducting power
than stone ; they are, therefore, best for house build-
ing, where it is desired to conduct heat either out-
w^ards or inwards as little as possible. According to
Rumford, the fur of the hare conducts least of all
substances used for clothing. Following it conies
eider-down, silk, wool, cotton, and hemp. The prac-
tical application of these facts is apparent. What is
called warm clothing is so because it prevents the
outward passage of the heat of the body, at least by
conduction, and the warmth is thus retained. Thus the
reason of the preference for woollen clothing in cold
weather is apparent. But woollen clothing will not
only prevent the passage of warmth outward from
the body, it will also prevent the passage of heat
inwards to the body. An example of this is seen
when a block of ice is surrounded by woollen material
to prevent it thawing. It may be packed in sawdust
for the same purpose. The heat is not conducted

458 PHYSIOLOGICAL PHYSICS. [Chap. xxxv.

inwards to the ice, and its melting is delayed. Wool-
len clothing is not, however, used in hot weather to
keep the external heat from the body, for a reason
that is very apparent. The body is kept cool in a hot
atmosphere by the large amount of heat that is given
off from its surface by evaporating the sweat and in
other similar ways. It is not by keeping the heat from
gaining access to the body that it is kept cool, but
by a large amount of heat being given off. But if
the body be enveloped in woollen clothing this heat
is prevented from passing off, is retained, and the
cooling does not occur. In hot climates, therefore,
clothing made of good conductors of heat is sought.
This is the reason why linen, materials, which conduct
heat better than woollen substances, are used. The
varying conductivity of different substances also
explains why two bodies at the same temperature
may seem to the touch to be very different. A piece
of iron at the same temperature as a piece of wood,
will seem colder, because it conducts the heat from
the hand more readily. Again, if a piece of metal
and a piece of wood be both at the same temperature,
and that a high one, the nietal will seem to be much
hotter, and may burn the hand, while the wood may
be held without pain. The metal, being a good con-
ductor, readily communicates its heat, while the wood
does not.

Convection of leeat is to be distinguished'
from conduction. Convection is the propagation of heat
by the transference of heated particles from one place
to another. Liquids have little conductivity for heat,
but a mass of liquid will speedily become heated
through its whole substance, if exposed to a source of
heat. This is due to convection currents. Thus, if
water in a flask be held over a spirit lamp, the layer
of water in contact with the bottom of the vessel
becomes heated and then rises to the surface, its

Chap, xxxv.] RADIATION OF HEAT. 459

place being taken by a cold layer, which in turn
becomes heated, and rises, to be replaced by another
cold layer. This distribution of heat through the
liquid by convection will go on till the whole mass is
of one temperature. Gases also have little conducting
power, but can also distribute heat by convection.
If, in a mass of air, one stratum be heated, a current
is produced, the heated air giving place to colder.
The trade winds are examples of convection currents
in air. The air heated at the equator flows to both
sides and high in the atmosphere, while colder cur-
rents flow towards the equator and lower in the
atmosphere to take its place.

Radiation of heat. — On a winter's day we
may feel warmed by the rays of the sun, even although
the air by which we are surrounded is below the
freezing temperature. As soon as the smallest obstacle
intervenes to cut the sun's rays off from us, we feel
the sudden withdrawal of heat, although the sun's
rays may be cast all about us. We do not feel the
warmth, that is to say, unless the rays are directly
falling upon us. These facts show that the warmth
is not communicated to us by the air, but that the
rays from the sun travel through the air without
heating it. In the same way, if we stand before a
fire we feel the heat emitted by it ; and it can be
shown that the t.lr surrounding is not warm enough
to communicate the heat experienced, that the heat
passes from the fire without warming the air through
which it passes. A red-hot ball suspended in a room
will be felt by the hand held at some distance from
it, to be very warm ; but if a thermometer be screened
from the ball it will not indicate any high tempera-
ture. A lens of ice can be made to focus the rays of
the sun upon a substance to set it on fire, just as a
burning glass would do, and yet the heat is not im-
parted to the ice which conveys it.

460 PHYSIOLOGICAL PHYSICS. [Chap. xxxv.

Rumford showed that a thermometer suspended
in a globe exhausted of air was affected by heat out-
side of the globe, just as it would be if the globe were
filled with air. Heat can pass, then, through a
vacuum. It can be propagated in a way that is
neither conduction nor convection, by what is called
radiation. Now we have seen that air is not-
necessary for the propagation of light, which is held
to be due to vibrations of a subtle elastic ether per-
vading all space. By the vibrations of the same
ether, heat also is held to be propagated. So that
heat reaching us from the sun or from any other
source of heat is independent of the atmosphere,
and travels through it by wave-like movements of
ether without necessarily affecting it. The motion is
communicated from the heated body, whose particles
are in a state of vibration, to the ether by which it is
surrounded. So that when we hold our hands before
a fire, and experience its warmth, we are to imagine
we see countless waves of ether breaking against
our hands, and throwing their sensory nerves into
a state of agitation, which we become aware of as
a sensation of heat. When the agitation is of mode-
rate amount it is pleasurable ; when it becomes
too intense it is painful, and we have the sensa-
tion of burning. Radiant heat is subject to the same
laws as light. It undergoes refraction and reflection,
as light does. In fact, the difference between light
and heat, as we have seen (page 335), is that the vibra-
tions of light are much more rapid, and the wave-
lengths shorter. Thus the red end of the spectrum,
and the part beyond it, are rich in heat rays, which have
a rapidity too slow to be perceived as light, but which
can be shown to be present by the heating effects.
The notable experiment of heating platinum to incan-
descence by the dark rays of the spectrum has been
mentioned (page 335). Even as the dark rays of heat

Chap. xxxv.] ABSORPTION OF HEAT. 461

can be foeussed, so they can be reflected. A source
of heat placed at a distance from a concave mirror
has a conjugate focus in front of a mirror, and if an
explosive substance be placed in the conjugate focus,
the concentration of heat at that point is speedily
evident.

Heat rays are also subject to interference like
light rays.

Absorption and emission of heat. — In
other ways heat rays present remarkable analogies to
light rays. It has been observed how certain substances
transmit the undulations of light, and how others
intercept them, the former being called transparent,
the latter opaque bodies. The explanation of their
action is that certain bodies permit the vibrations to
pass through them unaffected, while others pick out
the vibrations and thus absorb them. We have seen
also how this explains the production of colour.
Various substances act selectively on light rays,
which consist of vibrations of various lengths, one
substance selecting vibrations of particular lengths,
which it intercepts, while it permits others to pass.
Thus, a piece of red glass permits the vibrations of
red to pass, but absorbs the others. In the same
way different bodies act differently on heat rays.
One body will permit them to pass unchallenged,
another body will intercept them wholly or partially.
Thus glass refuses to pass on heat vibrations, while
it permits light rays to pass. It is transparent to
light, but not transparent (that is, opaque) to heat.
Rock salt, on the other hand, permits heat rays to
traverse its substance very readily. Water inter-
cepts heat to a large extent, so also does a solution
of alum, while bisulphide of carbon gives them a free
way. So that if the beam from an electric lamp be
passed through a cell of alum solution, its heat rays
will, to a very large extent, be sifted out, while the

462 PHYSIOLOGICAL PHYSICS. [Chap xxxv.

light rays will be permitted to pass ; a cell of bisul-
phide of carbon will intercept neither.

The words "transparent" and "opaque" might,
then, be applied to bodies according to their conduct
towards heat rays, as well as according to their con-
duct towards light rays. To avoid confusion, how-
ever, two other words are used, diathermanous and
athermanous, the former being applied to substances
like rock-salt, which permit the passage of radiant
heat, the latter being applied to those which inter-
cept the heat. To put it in another way, one body
transmits heat, the other absorbs it. Now the body
which transmits heat will not become elevated in
temperature. The particles of the body have no sym-
pathy, so to speak, with the particular vibrations
which are the cause of heat ; they are not in tune
with them, and offer no response to their movements.
On the other hand, the particles of the athermanous
body vibrate in harmony with the heat vibrations ;
they thus intercept the vibrations, and they them-
selves are set into harmonious oscillation. Bodies,
then, that absorb heat, are elevated in temperature by
the heat they absorb. Their own particles being
thrown into oscillation, they will themselves become
a source of heat and will radiate it outwards, just in
proportion to the degree with which they absorb it.
This offers an explanation of the fact noticed at the
beginning of these paragraphs on radiation, that heat
rays pass through air without raising its tempera-
ture ; air is found to have no absorptive power towards
heat rays. Tyndall has shown, by some remarkable
experiments, that while air is diathermanous, olefiant
gas is peculiarly opaque to heat rays, even a small
amount of it effectually intercepting them.

The close connection between absorption and emis-
sion of heat has received experimental demonstration.
Glass absorbs heat ; rock-salt, generally speaking, does

Chap. xxxv.] EMISSION OF HEAT. 463

not. A piece of glass and a piece of rock-salt, heated
to the same temperature, affect a thermopile in their
neighbourhood very differently. The needle of the
thermopile is deflected to a large extent when the
face of the pile is opposite the glass, and to a much
smaller extent when opposite the rock-salt, because
the latter, which feebly absorbs, also feebly radiates
heat. A metallic surface absorbs feebly, a surface
coated with varnish or lamp-black absorbs readily.
Accordingly a metallic surface will radiate less than
a black-coated surface. Thus, a black kettle will
radiate more freely than a bright metallic kettle, and
will consequently cool faster. Tyndall has corrobo-
rated experiments by Leslie and Melloni, which prove
that colour has not the effect on absorption and radia-
tion that is generally supposed. The blackened sur-
face of a warm cube radiated as much heat to a
thermopile as another surface of the same cube coated
with whitening, and the bulb of a thermometer coated
with alum absorbed more radiant heat than the
bulb of another thermometer coated with iodine
powder, which was almost black. The white layer of
alum was more absorbent than the black layer of
iodine. The influence of colour, therefore, is less
than is supposed. A white surface, certainly, re-
flects the light, while a black surface absorbs it ;
but it is not to be supposed that the white similarly
reflects the heat rays, since, as has been seen, the
most intensely heating rays are invisible rays, and
not necessarily thrown off with the visible light rays.

464

CHAPTER XXXVL

THERMOMETRY.

.Expansion toy heat. — The action of heat causes
gaseous, liquid, and solid bodies to expand. Gases
expand most, solid bodies least. Yet the expansion of
solid bodies by heat is readily shown. A brass ball is
taken of such a size that it just passes through a ring of
the same metal. The ball is heated, and it is then not
possible for it to pass through the ring ; but if the ring
also be heated, it may be made to expand sufficiently
to permit the heated ball to pass. On cooling, both
regain their former size. The expansion of liquids is
seen by immersing a flask filled with cold water in an
outer vessel of hot water. The neck of the flask is
continued into a long capillary tube ; and as the
water expands it rises in the tube. Alcohol, or other
more volatile liquids, would show the expansion more
readily. Similarly, if a flask filled with air, and having
a capillary prolongation, be heated, the expansion of
air may be shown. All that is necessary is to have
a small quantity, an inch or so, of coloured liquid
in the capillary tube as an index ; when the air is
expanded by heating, the index is pushed up, and
when by cooling the air contracts, the index passes
down the tube. Water affords a remarkable excep-
tion to the general rule of expansion by heat and
contraction by cold. If water be cooled it gradually
contracts till at a temperature of 4° C. (39° Fahr.)
it reaches its condition of maximum density. If the
cooling be continued the liquid begins to expand
until it becomes frozen, when a sudden considerable

Chap, xxxvi.] TEMPERATURE. 465

expansion occurs. It is this that causes bursting of
water-pipes in times of frost. The pipe is burst by
the enormous force capable of being exerted by the
freezing water, but the burst is not then observed
because the water is frozen. It is when the period of
thaw arrives and the ice becomes liquefied that the
burst is declared.

All the permanent gases expand almost to the
same extent for every degree of elevation of tempera-
ture. This amount is called their coefficient of expan-
sion. It amounts to -^r^rd °f the volume (whatever
be the volume) for every degree centigrade, or xf^th
of the volume for every degree Fahrenheit.

Thus, given the same pressure, a volume of gas at
0° C. will be increased by 10 x -^-g °f its volume at
10° C. This is expressed by formula in the following
way : Suppose Yo to be the volume of a gas at 0° C.,
and it is required to find its volume (V) at t° C.,
then V = Yo (1 + at), a is the coefficient of expan-
sion, which, as we have seen, is -^~, or, expressed in
decimals, '00366. So the equation becomes

V = Vo (1 + -00366 t}.

Suppose the volume to be 1 litre (1000 cc.) at 0°,
what is the volume at 100° C. 1

V = 1000 (1 + -00366 x 100).

The temperature of a body is a " quantity which
indicates how hot or how cold the body is." The
fact of expansion indicates a method by means of
which differences of temperature may be measured,
Thus, if we take a flask of air with a coloured index,
as described on page 469, and if we find that with a
constant pressure the index now rises and now falls,
this will indicate that the air is now expanding, now
contracting, that, in fact, it is being subjected to differ-
ences of temperature ; and the extent of the variations
E E — 7

466 • PHYSIOLOGICAL PHYSICS. [Chap, xxxvi,

of the position of the index will be a measure of the
differences of temperature experienced. In the same
way with a flask of alcohol, provided, again, the pressure
be constant, variations in the height of the column of
alcohol in the capillary continuation of the neck of the
flask will indicate the fact and the amount of varia-
tions in temperature.

Thermometer is the name applied to an instru-
ment devised on the principle just laid down for
measuring variations and amounts of temperature. If
a thermometer be placed in contact with a body
warmer than itself, heat will pass from the warmer
body till the temperature of both is alike ; the liquid
will rise in the thermometer, owing to its expansion,
till equilibrium is attained, and the difference between
the former and the present level will indicate the
difference between the temperatures of the thermo-
meter and the body. If the thermometer be placed
in contact with a colder body heat will pass from the
thermometer till it becomes of the same temperature
as the body with which it is in contact ; the liquid
will contract in the thermometer, and the diminution
of volume will indicate -the decrease of temperature.

The mercio'ial thermometer is the one in
common use. It is made of a capillary tube blown
out into a bulb at the lower end. A small funnel
is blown at the upper end to permit of filling the
tube with mercury. Into the funnel at the upper
end a little dry mercury is poured, and the empty
bulb is gently heated. Some air is expelled by the
heat, and on cooling the remaining air contracts, so
that mercury rushes in to fill up the space. The
mercury which has thus gained access to the bulb is
now heated, and then allowed to cool, when more
mercury enter-s. This process is repeated till the
bulb is full, and the mercury extends for some
distance up the tube. The mercury is then heated to

Chap, xxxvi.] MERCURIAL THERMOMETER. 467

boiling, so that air and moisture are expelled from
the tube, which is filled with mercurial vapour. At
this moment the upper end below the funnel is sealed
by a hot flame. This instrument will measure varia-
tions of temperature, but in this form will not
indicate corresponding values. The stem must, there-
fore, be graduated. For this purpose two standard
temperatures are taken, viz. the temperature of the
freezing point, and that of the boiling point. The
former is found by immersing the thermometer in a
mixture of ice and water till the mercury reaches
a level at which it remains. At this point a mark is
made on the stem. The boiling point is obtained not
by immersing the thermometer in boiling water, but
by surrounding it with steam from boiling water.
Water boils at different temperatures in different
vessels, but the temperature of steam is constant.
The thermometer is, therefore, suspended in a vessel
at the bottom of which water is kept boiling. It is
surrounded by a steam jacket, and when the level of
the mercury has become stationary a mark is made on
the stem. Both marks ought to be obtained at
standard pressure, for water will boil at a lower tem-
perature if the pressure be diminished. The space
between the two marks is now divided off by marks
into lengths of equal volumes, and the graduation
continued above the mark for the boiling point, and
below that for the freezing point. The instrument
will now indicate degrees of temperature which can
be used for comparison. If the thermometer is
brought into contact with two bodies successively,
and the reading of the level of the mercury is the
same in both cases, both bodies are at the same
temperature ; if there is a difference in the reading,
the number of degrees of difference on the scale
indicates the difference of temperature.

To the thermometer thus constructed different

468 PHYSIOLOGICAL PHYSICS. [Chap, xxxvi.

scales may be applied. Fahrenheit, of Dantzic,
introduced, in 1714, a scale in which the freezing
point is marked 32°, and the boiling point 212° ; 32°
below the freezing point is zero, or 0°. Between
32° and 212° the stem is divided into 180 degrees.
In the Centigrade scale, introduced by Celsius, a pro-
fessor of Upsala, the freezing point is marked 0°, and
the boiling point 100°, and between the two 100 spaces
are marked off. In Reaumur's scale the boiling
point is 80°, and the freezing point 0°. The different
scales introduce an element of confusion. The
Fahrenheit is used in England ; Centigrade is becoming
the scale for scientific use. The reading of any one
scale can easily be expressed in terms of the other.
Nine degrees of Fahrenheit's scale = 5 of Centigrade ;
therefore, to express a temperature Fahrenheit in
terms of Centigrade subtract 32, and then multiply

tyf

0 = (F - 32) \.

To express a temperature Centigrade in terms of
Fahrenheit, multiply by •§-, and then add 32.

F — (C x §) + 32.

Four degrees of Reaumur's scale are equal to 5°
Centigrade, therefore

C == R| and E = Of.

Nine degrees Fahrenheit = 4° Reaumur, therefore
F = fR-f 32, andR=(F- 32) |.

By means of the following table approximately the
same temperature on the different scales may be easily
read.

Alcohol is also used for thermometers, being
coloured to be more easily observed. Air thermo-
meters are also employed, and give larger indications

chap, xxxvi.] THERMOMETRIC SCALES.

469

than mercury or alcohol. Thermometers may be
made to register their elevations by means of an
index, a short thread of mercury which is pushed
up by the expanding mercury, and when the mercury

I
S.

212

E

3
«

K

9O-
80-
70-

200

190

70

. -9O
. -50
- 4O

ISO

170

ISO

ISO

60-

140

60-
AO
80-
20-

130

120

110

100

90

- -20

- .IO

- -0 Freezing point.

80

7O

60

50

40

Freeilnf point, o-
-10-
-20-

32

20

IO

ZERO

20

-10

contracts the index is left registering the highest
point to which it rose in the tube. In other ways
also thermometers may be made self-registering.

More delicate thermometers than those described
are made, which register differences of temperature of
a much smaller range than between 0° and 100°.
Thus mercury thermometers made of tubing with
a very fine bore, and with a bulb of very thin
walls, are capable of measuring with rapidity very

470 PHYSIOLOGICAL PHYSICS. [Chap, xxxvn.

small differences of temperature. For the same
amount of expansion the mercury will extend a
much longer distance in a very fine tube than
it would in a tube of wider calibre, so by the
fine tube a small difference will be readily regis-
tered, which would be scarcely observed in a ther-
mometer of wide bore. If, however, the
fine instrument were required to register
from the freezing to the boiling temperature,
it would require to be of a length very
inconvenient for practical purposes. Such

94

90
38
3G

thermometers are, accordingly, made to regis-

30

ter only a part of the scale. Thus the
ordinary clinical thermometers register tem-
peratures between 95° and 114° Fahr., and
each degree is divided into fifths. An ex-
ample of such a thermometer is shown in
Fig. 195 : one which is constructed for ascer-
taining the internal temperature of the body.

CHAPTER XXXVII.

CHANGES OF STATE PRODUCED BY HEAT.

Fusion and ebullition.— Heat coii-
^^^H verts solid bodies into liquids, and liquids
Fig. 195. into gas. Fusion is the term applied in the
moineter f°rmerj vaporisation in the latter case. The
temperature at which a solid body passes
into the liquid state is called the point of fusion, or
melting point ; and it is a definite temperature for
each substance. The temperature at which a liquid
passes into vapour, which rises through its substance
in bubbles, and disengages itself from the surface,

Chap, xxxvii.j FUSION. 471

is its point of ebullition, or boiling point. It also is
a fixed temperature for each substance.

Water illustrates very well what takes place in
these occurrences. If a mass of ice at 0° C. be placed
in a vessel, and heat applied, in a short time part
of the ice will become converted into water, part
will still remain undissolvecl. If the ice and water
be well stirred, the temperature throughout will be
found uniform, and still 0° C. If the heat be again
applied just till the ice is all converted into water,
the temperature will still be 0° C. In spite of the
application of heat, and the solution of the ice, there
is no increase of temperature. If the heat continue to
be applied, it is only after all the ice has been converted
into water that the continued application of the heat
becomes manifest in an increased temperature of the
water. A considerable amount of heat, that is to say,
has become absorbed, has apparently disappeared in
the conversion of the solid into the liquid state.
Work has been done in the conversion ; and the
equivalent of the work done is given by the amount
of heat spent in the process. In order that the water
may pass back into the solid state a similar amount of
heat must be given off. So the heat consumed in the
process of melting was said to become latent in the
water ; and the amount of heat necessary to convert a
unit mass of ice into water without raising the tem-
perature is called the latent lieat of water. Since the
same phenomenon is seen in the liquefaction of any
solid, though the amount of heat spent varies with
the substance, the phrase latent heat of fusion is
employed.

The latent heat of water may be estimated by
determining the temperature which a pound of water
must have to convert a pound of ice at 0° C. into
water, so that the mixture has a temperature of 0° C.
That temperature, it is found, must be 79° to 80° C.t

47 2 PHYSIOLOGICAL PHYSICS. [Chap, xxxvn.

or about 174° F. The same amount of heat is required
to convert 1 pound of ice into water at 0° C., as
would raise the temperature of 1 pound of water
from 0°C. to 79°C.? or from 32° F. to 174° F. The
latent heat of water is expressed by the figure 79, or
142 (174 - 32), according to the scale employed.

The same rule applies to every solid body. Its
liquefaction involves the disappearance of heat ; and
the liquefaction may be accomplished without eleva-
tion of temperature. Ice, however, requires more
heat for its liquefaction than other bodies. While
the latent heat of water is about 79, that of tin is
about 14, of lead over 5, of sulphur over 9.

Freezing- mixtures exemplify very well the
facts that have been stated. When ice is mixed with
salt in the proportion of two parts of the former
to one of the latter, the ice is rapidly melted, the
rapid thaw involving a rapid disappearance of heat.
If the mixture surrounds a liquid at the ordinary
temperature, and if care is taken to prevent the ice
obtaining the necessary heat from other sources, the
heat will be abstracted from the liquid, and in a short
time its temperature will be so reduced that it will
become frozen. The temperature obtained by the
mixture of ice and salt, or snow and salt, is about
zero Fahrenheit. Other freezing mixtures are snow
and crystallised chloride of calcium (3 to 4), nitrate of
ammonia and water (equal parts), sulphate of soda
and hydrochloric acid (8 to 5).

EbuISitiosa is the condition in which, by heating,
bubbles of vapour are formed in the interior of a
liquid which pass to the surface, and there become
disengaged. In water, being heated in a flask over a
lamp, bubbles may be seen to become disengaged
from the bottom of the flask, on the outside of which
the flame is playing ; but they do not become disen-
gaged at the surface. They disappear as they pass

Chap, xxxvn.] EBULLITION. 473

upwards in the liquid, probably because, coming in
contact with colder layers of water, they become con-
densed. It is thought that it is the collapsing of
such bubbles that causes the singing sound heard
before the liquid is at the boiling point. When the
boiling point is reached, the vapour escapes from the
liquid and gives rise to the commotion called ebulli-
tion. In order that the vapour may escape into the
atmosphere, its tension must be equal to that of the
atmosphere. Different liquids have different boiling
points. Distilled water is 100° C., ether 37°, alcohol
79°, mercury 353°, sulphur, 440°.

Although the application of heat be continued
after the boiling point has been reached, the tempera-
ture of the liquid does not rise. The additional heat
is consumed in the conversion of the liquid into the
gaseous state. Thus heat disappears in the passage
from the liquid to the gaseous state, as well as in the
passage from the solid to the liquid state. To express
this disappearance, the phrase latent heat of vapour
is employed. For this reason a kettle will not be-
come red hot so long as it contains water, the tem-
perature not being able to exceed 100° C. Similarly,
water may be boiled in a capsule of paper, because
the temperature of 100° C. is not sufficient to ignite
the paper. For the conversion of unit mass of water
at 100° C. into vapour, 536 units of heat measured on
the centigrade scale, are required, or about 965 units
Fahrenheit.

The boiling point is affected by various circum-
stances. The presence of saline bodies in solution
raises it. Thus, 7*7 per cent, of common salt raises
the boiling point 1° C. ; 39*7 per cent, raises it 8°.
This is supposed to be due to the force of cohesion
exerted by the salt molecules on the particles of
water. The fact that the boiling point is affected by
the nature of the vessel in which the water is placed

474 PHYSIOLOGICAL PHYSICS. [Chap, xxxvn.

is supposed to be due to the force of adhesion exer-
cised by the particles of the vessel on the water. In
a glass vessel the boiling point is usually 101° C., in
one of iron 100° C. The introduction, however, of
fragments of platinum into a glass vessel will lower
the boiling point to 100°.

Pressure influences the melting and boiling points,
an increase of pressure raising both temperatures.
The effect on the boiling point is very marked. A
fall of pressure from the normal 760 rnin. of mercury to
730 lowers the temperature of the boiling point by 1°.

Evaporation. — Yapour is given off' by liquids
and solids through a wide range of temperature ; and
the evaporation is accompanied by the disappearance
of heat ; but, as in the case of ebullition, evaporation
occurs only from the surface of the body. It is by
evaporation that the volume of a liquid exposed to
the air gradually diminishes. Some liquids pass into
vapour more quickly than others, alcohol more
quickly than water, and ether than alcohol, the
abstraction of heat being more marked as the rapidity
of evaporation is greater. The vapour of ether is
thus used to produce a freezing temperature. This
fact is applied in surgery for producing local anaes-
thesia. By means of a spray producer a fine spray of
ether is directed on the part of the body to be rendered
insensible. Its rapid evaporation abstracts the heat
from the part to such an extent, that intense local
cold is produced, accompanied by loss of sensibility in
the part, so that an incision may be made without
causing pain. A similar method is employed in his-
tology, for cutting sections of tissues. The tissue is
placed on a metal plate on the under surface of which
a current of ether spray is directed. The plate and
the tissue it supports are thus reduced to the freezing
temperature, and sections of the tissue may then be
readily cut in the frozen condition.

Chap, xxxvii.j THE SPHEROIDAL STATE. 475

Particles of a solid body, camphor for example,
may also pass into vapour without a previous tran-
sition to the liquid state.

By a very simple apparatus, Wollaston showed
that water could be frozen by its own evaporation.
Two bulbs are connected by means of a tube. Water
is contained in one bulb, the other has an opening
communicating with the air. The water is boiled till
its steam fills the tube and the other bulb, and then
the communication of that bulb with the air is sealed.
The bulb which contains no water is then surrounded
by a freezing mixture which condenses the steam,
and thus tends to produce a vacuum. Vapour rises
from the water in the other bulb to fill the empty
bulb, and the rapid evaporation soon causes the water
to freeze.

Increase of temperature favours evaporation. At
a given temperature the process will go on till the
atmosphere surrounding the liquid is saturated with
the vapour, in which condition the vapour is at maxi-
mum density, and exerts its maximum tension. If
the temperature be raised, the atmosphere is not
saturated for that temperature, and more vapour
will pass off till saturation is again produced. If
the temperature fall, the atmosphere is unable to
retain the former quantity of vapour, and some is
deposited in the liquid state. This explains the for-
mation of dew.

The spheroidal state. — If water be dropped on
a red-hot metal the water does not immediately hiss
and boil, as might be expected. It assumes a spherical
form, and rolls and tumbles on the hot metal. It can
be shown that the water is not in direct contact with
the metal, but is separated from it by an appreciable
interval. The reason is that by the intense heat of
the metal, steam is produced of sufficient tension to
support the liquid above the metallic surface. The

47 6 PHYSIOLOGICAL PHYSICS. [Chap, xxxvin.

layer of steam between the drop of liquid and the hot
metal does not permit sufficient heat to radiate to the
drop to boil it. As soon as the metal cools so that it
is no longer able to produce steam of sufficient ten-
sion, the drop comes into contact with the metal, and
at once hisses and boils away.

All volatile liquids show this property. It is in
virtue of it that the hand, moistened with water, can
be momentarily plunged into a mass of red-hot metal
without being burnt. A layer of vapour is formed
between the moist tissue and the hot metal, which
acts as a protective. This experiment must be per-
formed with rapidity.

CHAPTER XXXVIII.

SPECIFIC HEAT : CALORIMETRY.

Specific heat. — It takes a much larger quan-
tity of heat to raise the temperature of 1 pound of
water by 1° than to raise the temperature of the
same weight of lead by 1°. This is expressed by
saying that water has a greater capacity for heat than
lead, or that the thermal capacity of water is greater
than that of lead. The thermal capacity of a body is
denned as " the number of units of heat required to
raise that body 1° of temperature." If water be
taken as a standard, then the thermal capacity of one
body may be estimated in reference to it. If the
quantity of heat necessary to raise 1 pound of water
1° of temperature be called 1, the quantity necessary
to raise 1 pound of lead 1° of temperature will be a
fraction of 1. The number that expresses this ratio
between the quantity of heat necessary to increase

Chap. XXX VII I.]

SPECIFIC HEAT.

477

the temperature of a body 1°, and the quantity neces-
sary to raise the temperature of the same weight of
water, is called the specific heat of the body.

For example, the specific heat of water being 1,
that of iron is -11379, lead -0314, brass -09391, mer-
cury -03332, ether -5157.

Water has the greatest thermal capacity, hence
its value for heating purposes.

The differences in the specific heat of different
substances explains how two bodies at the same tem-
perature will give out different amounts of heat.

The average specific heat of the animal
body is given as about 0'83 (water being 1).

The following table gives the specific heat of
various animal substances :

Blood (human)
Arterial blood
Venous blood
Defibrinated blood
Muscle (striated)
Compact bone
Spongy bone
Adipose tissue

Muscle of oxen
Cow's milk

1-020
1-031
0-892
0-927
0-825
0300
0-710
0-712

0-787
0-992

Calorimetry. — The determination of latent and
specific heat implies the measurement of quantities of
heat. This is called calorimetry ', and the instrument
by means of which the measurement is made is called
a calorimeter. It is obvious that a standard unit of
heat is required. This we have already seen (page
454) to be the quantity of heat necessary to raise
the temperature of unit mass of water from 0° to
1° C. , and is called the caloric. The quantity of
heat given out by a body may, therefore, be measured
by the quantity of water whose temperature it will raise

47 8 PHYSIOLOGICAL PHYSICS. [Chap, xxxvm.

1°. One pound of water requiring 1 unit of heat, 50
pounds will require 50 units to raise their temperature
1 degree. The quantity may also be measured by
the number of degrees of temperature through which
the body has raised the unit mass of water. Thus, if
a hot iron ball be plunged into 1 pound of water
at an ordinary temperature, and if, when the ball and
the water have become of equal temperature, it is
found that the water is 10° warmer than before, then
the ball has given out 10 units of heat. The trouble
in such an experiment is to ensure that the pound of
water gets all the heat that is given out from the ball,
and that none of it is given off in other ways, which
would make the calculation erroneous. It is ne-
cessary, therefore, to plunge the ball into water
contained in a vessel surrounded by non-conducting
material, and arranged also to prevent radiation of
heat. The vessel would also be heated, and the heat
imparted to it would require to be taken into account.
Thus, suppose the water to weigh 10 pounds, and its
temperature to be raised 1°, it has obviously gained
10 heat units. If the vessel weighed 5 pounds and it
is heated 1°, it has not gained 5 heat units, since its
capacity for heat is not so great as water. Suppose
it to be made of iron, the capacity for heat of iron as
compared with that of water (its specific heat) is
about '114 for each unit of mass, and we take the
unit as 1 pound, so that for the 5 pounds the amount
is '570. So that if its temperature is raised 1°, the
units of heat gained amount to '570. The total lost by
the ball is, therefore, 5*570 units. One form of
calorimeter consists, then, of a vessel filled with
water and surrounded by non-conducting material.
Into the water the hot body is plunged, and the dif-
ference in temperature of the water before and after
gives, by a simple calculation, the units of heat
gained by the water, that is, given off by the body.

chap, xxxviii.] CALORIMETRY. 479

This form is called the WATER CALORIMETER. In the
ICE CALORIMETER the body whose specific heat is to
be measured is placed in a receiver made of thin
sheet copper. It is placed in an outer vessel con-
taining broken ice at the melting point, the space
between the two vessels being entirely filled with the
broken ice. The heat from the body melts the ice,
and is measured by the quantity of water produced.
As we have seen, it takes always a definite quantity
of heat to convert 1 pound of ice at the freezing
point into 1 pound of water at the same temperature.
The water produced trickles down through the ice,
and escapes through a tube at the bottom of the
vessel into a vessel placed to receive it. To ensure
that all the ice is melted by the heat of the body,
and none by the heat of the surrounding air, a third
vessel also containing broken ice surrounds the other
two. The heat of the surrounding air is intercepted
bv this outer ice jacket, and the water produced is
caused to flow into a different vessel from that which
catches the water produced in the calorimeter. This
form of calorimeter was constructed by Laplace and
Lavoisier.

The construction of the calorimeter will be
understood by reference to Fig. 196. It shows the
water calorimeter employed by Favre and Silbermann
to measure the quantity of heat produced by the com-
bustion of different substances. (See page 460.) It
consists of a vessel K in which the substance to be
burnt is placed. K is enclosed in a chamber L, in
which it is completely surrounded with water. The
chamber L is supported on feet in a larger chamber M,
the space betw-een the two being packed with a non-
conducting material An outermost vessel N tilled with
water encloses the whole. The heat given off by the
burning substance in K is communicated to the water
in LJ raising its temperature the non-conducting

480

PHYSIOLOGICAL PHYSICS. [Chap, xxxvm.

substance in M preventing heat passing outwards,
while the layer of water in N intercepts heat passing
inwards, and ensures the elevation of the tem-
perature of the water in
L being due to the com-
bustion in K. A tube o
passes from outside to con-
duct oxygenated air to the
bottom of the chamber for
combustion purposes. The
tube eeg permits the es-
cape of the gases that are
produced by the combus-
tion. It takes a winding
course through the water
of L so that all the avail-

able heat of the gases is
given off to the water before
they escape to the outside.
The tube b, usually closed
by a cock, is for the pur-
pose of passing inflammable gases into K if desired.
The prolongation a of the chamber is closed by a
thick glass plate, and provided outside with a mirror
s, set at an angle, to permit an observer to watch the
process of combustion. Modifications can be made in
such an arrangement as this to suit particular pur-
poses. To measure the specific heat of a substance,
one may substitute for K a receiver into which the
substance, which has been previously heated to a
known temperature, is dropped. Or one may sub-
stitute a chamber (c in Fig. 197) in which some small
animal may be lodged, respirable air reaching it by
one tube, and the products of respiration being con-
veyed outwards through the water, so that the heat
given off by the animal in a given time may be esti-
mated. In all cases the temperature of the water in

Fig. 196.— Water Calorimeter.

Chap, xxxix.] ANIMAL HEAT. 481

L is taken by a delicate thermometer before the ex-
periment is begun. Again, at the close of the ex-
periment, the temperature of the water is taken.
The increase affords the basis for estimating the
quantity of heat given off.

The calorimetric method, as applied to animal
heat, will be referred to in the next chapter.

CHAPTER XXXIX.

ANIMAL HEAT.

Sources of animal heat. — The energy of the
human body is derived from the food consumed and
the air breathed by means of oxidation processes.
Part of that energy is converted into mechanical
work, and part is transformed into heat. Chemical
actions going on in the body are thus the main
sources of heat. Oxidation processes being the chief
sources of heat in the body, and oxygen being neces-
sary for them, it is evident that the quantity of O
consumed, and of C02 produced, would give an esti-
mate of the amount of heat produced. For example,
the oxidation of 1 grm. of carbon to C02 gives 8,088
units of heat, and the oxidation of 1 grm. of hydro-
gen to H2O yields 34,460 heat units. The amount of
heat capable of being produced may also be estimated
by noting the amount of albumen, fats, sugars, etc.,
taken as food, and calculating how much heat units
they are capable of producing by complete oxidation
(page 456). They do not, however, undergo com-
plete oxidation in the body. Thus, albumen is
oxidised to urea, and urea is capable of further
combustion.

F F — 7

482

PHYSIOLOGICAL PHYSICS. [Chap, xxxix.

For example, while 1 grin, of egg albumen fully
oxidised yields 4,998 heat units, the same quantity
oxidised to urea yields 4,263 heat units, that is, 735
units less ; and 1 grm. ox flesh completely oxidised
yields 5,103, l>ut only 4,368 if oxidised to urea.

The quantity of heat capable of being yielded up
by the food on complete oxidation must, therefore, be
reduced by the amount which the excreta will pro-
duce.

During bodily repose, the energy due to chemical
combination all' appears as heat. If work be done,
heat disappears to the extent of the equivalent of the
work done. About one-fifth of the total energy of
the human body appears as mechanical work, and
four-fifths are expended as heat.

Apart from chemical actions, there are physical
causes at work in the production of heat, the friction
of parts, for example, of which, however, it is impos-
sible to render an account.

The amount of heat liberated by the animal

body in a given time has
been estimated by various
experiments by means of
the calorimeter. The
apparatus of Dulong is
shown in Fig. 197. It
consists of a chamber c
into which the animal to
be experimented on is

Placed" chamber is

Fig. 197.-Calorimeter of Dulong.

immersed in the calori-

meter w, made of metal with a bright outer surface
and japanned inside, which is itself contained in a
much larger wooden case, so that a space M exists be-
tween the calorimeter and outer case. The space is
stuffed with tow or some such non-conducting material.
The case is also higher than the calorimeter, and is

chap, xxxix.] REGULATION OF ANIMAL HEAT. 483

furnished with a lid, stuffing being between the latter
and the calorimeter top. Loss of heat is thus pre-
vented. Through the outer case and calorimeter a
tube 1 passes to convey air to the animal. The tube
2 for conducting away the foul air is bent several
times through the water of the calorimeter, so that
the air parts with all the heat it has gained before
escaping from the apparatus. A thermometer dips
into the water. The temperature of the water in
the calorimeter is taken, next the temperature of
the animal is ascertained by means of a thermometer
in the rectum. The animal is then placed in its box,
which is quickly made air-tight, its tubes for the
entrance and exit of air being attached, and is
without delay lowered into the calorimeter, the whole
being closed, and left for some time. At the end of a
definite time the water in the calorimeter is mixed
by means of an agitator, whose handle projects
through the lid of the box, and the temperature of the
water read off. The animal is then removed and its
temperature tested. The weight of water in the
calorimeter, multiplied by its gain in degrees -of tem-
perature, added to the sum of the weight of the
metal case x its' specific heat x its gain in tempera-
ture, gives the units of heat gained by the calori-
meter. If the animal has gained or lost in heat, the
difference in heat units gained or lost is obtained by
multiplying the weight of the animal into its specific
heat (083) into the difference of temperature, and
this must be added to or subtracted from the calori-
meter total, as the case may be.

According to Helmholtz, the quantity of heat
produced daily by man is about 2,700 calories.

Regulation of animal heat. — The tempera-
ture of the animal body is regulated largely by the
loss of heat. Heat is lost to a large extent in warm-
ing the ingest-a, to a much larger extent, however by

484 PHYSIOLOGICAL PHYSICS. [Chap, xxxix.

perspiration, by conduction, and by radiation. How
great the loss by perspiration may be is readily under-
stood when one takes into account that the perspiration
passes off from the body in vapour, and that the trans-
formation into vapour means the abstraction from the
body of a large amount of heat which becomes latent in
the vapour. The tendency to increased temperature
of the body by increased external heat is counter-
balanced by increased afflux of blood to the skin, in-
volving increased perspiration, and therefore increased
abstraction of heat ; while external cold by its action
on the skin diminishes the supply of blood, and, in
consequence, the amount of perspiration, and so
diminishes the abstraction. In such ways a more or
less uniform temperature of 98'4 Fahr. (37 '6° C.) is
maintained by the human body.

Loss of heat by the skin may be increased or
diminished, according as the clothing is a good or
bad conductor of heat. Reference to page 457 shows
how variously different substances used for clothing con-
duct heat, and how the hair and feathers of animals
are fitted to affect the loss of heat by conduction.
Besides the conductivity of clothes for heat, their
absorbing and emissive power determine their value
as warm or cold clothing. Rough clothing radiates
more readily than smooth. Colour does not seem to
affect the radiating power, contrary to the popular
opinion, as we have seen. Dark clothing, however,
absorbs heat most readily. The hygroscopic qualities
of clothing also determine its value, since if it
readily absorbs moisture from the skin, a great loss of
heat will be experienced. Finally, the compactness
of the ^cloth should be noted. The less compact the
material the more easily will the air penetrate it and
carry off heat by convection.

$art Vtt*.

DYNAMICS.
CHAPTER XL.

MATTER AND FORCE.

DYNAMICS is defined as the science which investi-
gates the action of force. The common term mechanics
is often applied to this science, erroneously, according
to the highest modern authorities, who restrict that
term to the " science of machines and the art of
making them." The ideas of force and matter are
inseparably associated together, force being recog-
nisable by its effects on material bodies. Dynamics
considers the action of forces on solid, liquid, and
gaseous bodies. Liquid and gaseous bodies have already
been considered, so far as seemed necessary for our
purpose. In this part of the work some of the
elementary dynamical facts and principles applied
to solid bodies will be noted.

The measurement of foodies is accomplished
by means of standard bodies with which the body to
be measured is compared.

The STANDARD OF LENGTH, by means of which
the linear extension of a body is estimated, is called
the yard in English measure (one yard = 3 feet
= 36 inches). It is an arbitrary measure enacted
by Parliament, and is the distance between the
centres of the transverse lines in the two gold
plugs in the bronze bar deposited at the office of
the Exchequer. The French standard of length is the

486 PHYSIOLOGICAL PHYSICS. [Chap. XL.

metre. It is intended to be about a ten millionth
part of the distance along the surface of the earth
between the pole and the equator. But it also is
measured by a standard metre of platinum. The
metre standard was intended to be a universal stan-
dard ; and it is rapidly becoming the standard of
length for scientific use. The system of measurement
by means of the metre is called the metric system.
It is also applied, as we shall see, to the estimation
of weight. The metre is divided into tenths and
multiples of ten, and this method of division and sub-
division makes the system extremely convenient to
work with.

One metre (1 m.) = 10 decimetres (10 dcm.) =
100 centimetres (100 cm.) = 1,000 millimetres
(1,000 mm.). 1,000 metres is 1 kilometre.

One English inch * = 25-399 millimetres (i.e. 1 ram. = about
„ „ foot =304-792 „ [^thinch.)

„ yard =914-376

One metre contains 39*370432 inches
One kilometre „ 39370-43200 „

(nearly 1093-6 yards).

There are 1-60932 kilometres to the mile.

Of the following scales (Fig. 198) the first shows
T^th of a metre (1 dcm.), divided into centimetres (10),
and millimetres (100) ; the second shows English
inches and tenths.

The STANDARD OF WEIGHT or mass is in Britain
the pound (avoirdupois), which is the weight of a
piece of platinum kept in the office of the Exchequer.
It contains 7,000 grains. One pound troy contains
5.760 grains.

The French unit of mass is the weight of a cubic
decimetre of distilled water at 4° C. of temperature.
It is called a kilogramme. It contains 1,000 grammes,

* One Paris inch — 27 '069 mm.

Chap. XL.]

STANDARDS OF LENGTH.

487

a gramme

being the mass of a cubic
centimetre of distilled water at 4° C.
A cubic millimetre is a milligramme.

One gramme (1 g.) = 10 decigram-
mes (10 dcg.), - 100 centigrammes
(100 eg.) = 1,000 milligrammes (1,000
mg.).

One pound avoirdupois = -453593 kgme.
„ ounce ,, = 28-3496 grammes.

,, drachm ,, = 1*771 ,,

„ grain „ = 0-064799 gramme.

In Troy weight :

One ounce = 31-103 grammes
,, drachm ^= 3-881 ,,
„ grain = 0-065 gramme.

One kilogramme = 15432-349 grains (2-204

pounds avoir.)
„ gramme = 15-43249 „

By the metric system capacity is
also measured. Thus, the measure of
capacity is the litre, equal to 1,000 cubic
centimetres (1,000 cc.). It equals
1-76172 imperial joints.

Force is defined as " whatever
changes or tends to change the motion of
a body by altering either its direction
or its magnitude." If a force act
upon a body at rest, it will cause it to
move in a particular direction with a
particular velocity. If two equal forces
act upon two bodies for the same time,
and impart to them equal velocities,
then the two bodies are of equal mass.
So that the velocity of a body is depen-
dent not only upon the force which acted

< u

Fig. 198.— A.
Decimetre di-
vided into Cen-
timetres and
MilKin etres.
B. Inches and
Tenths of an
Inch.

488 PHYSIOLOGICAL PHYSICS. [Chap. XL.

on it, and the time during which it acted, but also on
the mass of the body. The velocity of a body multi-
plied by its mass gives what is called the momentum of
the body, A body at rest tends to remain at rest, and
a body in motion tends to remain in motion. To
change its state of rest or motion, the application of
a force is necessary. This is due to the inertia of the
body.

The measurement of force. — Suppose two
forces of unknown amount to act upon two bodies of
equal mass and free to move under the same condi-
tions. It is evident that the forces could be esti-
mated by the velocities imparted to the bodies. If
the velocities were equal the forces would be equal.
If the velocity of one body were half that of the
other, the force acting on the body must have been
the half of that acting on the other. So that a force
can be measured by the velocity imparted to a body
of unit mass after acting upon it for a second (unit of
time). This is called the absolute measurement of
force. Forces are also estimated by the gravitation
method. A standard pound weight is attracted
towards the earth with a definite force. A weight of
2 pounds is attracted with twice the force, a weight
of 3 pounds with thrice the force, and so on. If the
weight is to be prevented from falling, the force of
the earth's attraction must be counterbalanced by an
equal force in an opposite direction. The force with
which a pound weight is attracted towards the earth
can, therefore, be used as a measurer of force ; and
we can speak of a force of 10 pounds, of a pressure of
50 pounds, and so on.

Now in London, a weight of 1 pound, if allowed
to fall freely, would fall a distance of 32-1889 feet
in a second of time. That is to say, the force of
gravity at that place acting on the pound weight
(the unit of mass) for one second would produce a

Chap. XL.] DYNAMOMETERS. 489

velocity of 32 '1889 feet ; and we have seen that
force, can be measured by the velocity produced in
unit mass in unit time. So that the gravitation
measurement can become absolute measure. At
London, the pound weight produces 32-1889 units of
force. It is to be noted that the action of gravity
differs in amount in different places (page 504), so
that for the same body the force differs at different
parts of the earth's surface.

Dynamometers are instruments for measuring
forces in pounds or kilogrs. Fig. 199 shows one form.
It consists of two steel arcs
AB and CD, connected together
at the extremities. The in-
strument is suspended by the
ring R, and a weight is at-
tached to the opposite hook.
The curves of the arcs are
increased by the weight, the
action being resisted by the Fig-. 199.— Dynamometer,
elasticity of the steel. The

«/

amount by which the arcs are separated in the
middle is measured by the graduated bars, one
being attached to the middle of each arc. The bars
slide on one another, and are graduated by hanging
on various known weights, which mark the extent
of separation effected. An unknown force can
then be estimated in terms of the previous graduation.
Another form of the same instrument is made for
estimating force exerted not by traction, but by pres-
sure.

For instance, such a form is made for estimating
the pressure that can be exerted by the hand in
squeezing. The instrument is grasped in the hand and
the arcs pressed together. Between the arcp is a dial
plate and an indicator, which travels a greater or less
distance over the dial plate according to the pressure

49°

PHYSIOLOGICAL PHYSICS.

[Chap. XL.

exerted. The dial plate also requires previous gradua-
tion. Thus the zero mark is placed where the hand
points when no pressure is exerted. A pressure of
1 pound, or 1 kilogramme, is then applied, and a
mark placed where the indicator points, and so on.
The pressure in pounds or kilogrammes exerted by
the hand can then be speedily ascertained.

In both forms of the instrument the elasticity of
the steel restores the arcs to their former position,
when the force no longer acts.

Quetelet states that the pressure of both hands
of a man equals, on the average, 70 kilogrs., and that
the pressure of a woman's hands is a third less.

Representation of forces. - - Forces are
graphically represented by straight lines. A force of
1 pound, or 1 kilogr., is represented by a line of a defi-
nite length, and a force of 2, 3, 4, etc., pounds or
kilogrs., by a line 2, 3, or 4, etc., times that length. The
direction in which the force is acting is indicated by
a barb on the line.

Resultant force. — Let o (Fig. 200) be a particle

under the influence of
two forces, one, OB,
urging it in the direc-
tion of B, and the
other, OA, urging it in
the direction A. It is
evident that the par-
ticle cannot proceed
along either path, but
will choose a path
which is a compromise
between the two. It
will move upwards.
Let a third force, re-
presented by the weight, be applied to o, and let this
third force be adjusted so that o remains in its original

Fig. 200.— Resultant Force.

Chap. XL.] PARALLELOGRAM OF FORCE.

491

position, and suppose the weight to represent a force of
1 pound. Then o is under the influence of three forces ;
but it is at rest, so that the forces are in equilibrium.
The forces OA and OB are both tending to draw o
upwards, and they are completely counterbalanced by
the 1 pound weight. To put it in another way,
the weight is tending to pull o downwards, but
is counterbalanced by OA and OB. But the weight

Fig. 201.— Parallelogram of Force,

would be counterbalanced exactly by a force of 1
pound acting in the direction directly opposed to it,
that is, in the direction of the straight line drawn up
from o. If, therefore, OA and OB be withdrawn,
and one force substituted equal to the weight oppo-
sing them, equilibrium will still be maintained. So
the two forces OA and OB can be replaced by a
single force, which is called the EESULTANT FORCE.
If a parallelogram be constructed on OB- OA, as indi-
cated in the figure, it will be seen that the resultant
force is the diagonal of the parallelogram. This is
represented also in Fig. 201, where two forces OA OB are
represented acting on a particle. To find the direc-
tion in which the particle will move, a parallelogram
is constructed of which OA and OB form two sides, and
then the diagonal OR of the parallelogram is drawn.
It gives the direction which the particle takes ; it is

492 PHYSIOLOGICAL PHYSICS. rchap. XL.

the resultant of the two forces OA, OB ; and if the lines
OA and OB represent by their lengths the magnitude
of the forces, then the diagonal will represent by its
length the magnitude of the resultant force. This is the
parallelogram of force.

In a similar way one force may be made to take
the place of several forces. Let a parallelogram be
constructed on the lines representing two of the
forces. Take the diagonal, and with it and the line
representing the third force construct another paral-
lelogram. Its diagonal is the resultant of the three
forces ; with it and the line representing the fourth
force, the resultant of the four forces may be found,
and so on.

The process of finding a single force which can be
substituted for more than one, is called the composi-
tion of forces. It is apparent also that the converse
of the composition of forces is true, namely, that a
single force can be resolved into two forces. Thus,
the force OR, if it be the resultant of OA and OB, can
be replaced by them. If it be given as a single force,
then, by constructing the parallelogram of which it
is a diagonal, it can be resolved into' two forces
acting at an. angle. This is called the resolution of
forces.

Resultant of parallel forces. — Suppose two
parallel forces acting on a rigid bar in the same direc-
tion, the resultant will be equal in magnitude to
their sum, and if they are equal forces they may be
replaced by the resultant force midway between
them. If they are unequal, then the point of ap-
plication of the resultant force will be at a distance
from the points of application of the two forces which
is inversely proportional to the magnitude of the forces ;
that is to say, the point of application of the resultant
will be nearer to the greater force. Thus, in Fig. 202,
the diagram to the right represents a bar AB under the

Chap. XL.]

PARALLEL FORCES.

493

acting on a
Their

8

a

v
c

V
c

Fig. 202.— Resultant of Parallel Forces.

influence of a force Aa at one end, and of a second
Bb at the other end, both being equal to one another.
Their resultant is cc, applied midway between A and B,
and equal in magnitude to both forces added together.
In the left-hand
diagram we have
represented two
unequal forces
and :

rigid bar.
resultant is cc,
equal to their sum,
acting from the
point c, c being so
placed that the
distance CB is in-
versely propor-
tional to Bb, re-
presenting the mag-
nitude of the force acting at B, and the distance CA is
inversely proportional to Aa. Suppose AB to be 12
inches, the force Aa to equal 6 pounds, and Bb to
equal 12 pounds, then the distances CB CA being in-
versely proportional to 12 and 6, CB will equal 4,
and CA will equal 8. The distance CB is called the arm
of the force Bb, and CA is the arm of the force Aa.
Suppose c to be a fixed point, it is evident that the
force Bb acting on the bar will tend to pull that end
of the bar down. It will tend, that is to say, to turn
the bar on the point c. Similarly, the force Aa will
tend to turn the bar on the point c. The measure of
the power with which the force tends to turn the bar
on the point c is called the MOMENT OF THE FORCE,
and is obtained by multiplying the force into the
distance of the arm, that is, multiply Aa by the
distance CA. Let Aa — 6, and Bb = 12. The
moment of Aa will = 6 x 8 = 48, and that of Bb

494 PHYSIOLOGICAL PHYSICS. [Chap. XLI.

will = 12 x 4 — 48. If the force cc be applied in
the opposite direction, as indicated by the line cc',
then the forces Act, B&, and cc', will be in equilibrium.
The two forces tending downwards will be counter-
balanced by a single force in the opposite direction,
applied at the point c. This shows that cc is the
resultant of Act and B&.

A couple. — Two unequal parallel .forces in op-
posite directions can also be reduced to a single force
acting in the direction of the greater force and equal
in amount to the difference between the two forces.
When two equal and parallel forces are opposite they
have no resultant, and there is no single force which
can balance them. This is called a COUPLE, and it
tends to produce a movement of rotation.

CHAPTER XLI.

THE LEVER, PULLEY, AND BALANCE.

THE principles that have been explained are exem-
plified in certain simple machines, the lever, etc.

The lever is simply an application of the facts
of parallel forces. This is evident from Fig. 203, which

represents a rigid bar
under the influence
of two forces, p and
w. F is the fixed

Fig. 203.-Lever of the First Order.

Now the tendency of the force w to pull the bar
down towards it is measured by its moment, i.e. its
amount multiplied by the distance between its point
of application and the point of application of F.
Suppose w to be the force of a 10-pound weight, and

Chap. XLI.] LEVERS. 495

its distance from F to be 2 feet, its moment = 20.
Now let the distance between F and p = 5 feet, a
force of 4 pounds will give a moment of 20. Thus
with these distances a force of 4 pounds at P will
balance a force of 10 pounds at w. If p be made
5 pounds its moment will exceed that of w, and
will pull the bar
down towards it ; w
will be raised. The
smaller weight acting
through the longer
distance will raise

the heavier weight. FiS- 204.-Lever of the First Order.

The power and weight

are in the inverse ratio to their arms. There are
three classes of levers, according to the relative posi-
tions of P, w, and F, the power, weight, and fulcrum.
That which has been already described is a lever of
the first order, where the fulcrum is between the
power and the weight. Its advantage is that a small

power may be made
to raise a very heavy
weight if the arms of
the lever are properly
adjusted. But it is
apparent that the

1 12. 205. —Lever of Second Older.

power must travel

through a very considerable distance to raise a heavy
weight even, a small amount. This is well shown in

O

Fig. 204, where the weight w is raised only a short
distance, while the power performs a considerable
excursion from P to P'. One great advantage evident
from Fig. 203 is that by this lever two forces may
readily be balanced by adjusting the position of F.

Fig. 205 represents a lever of the second order,
where the weight is between the power and the fulcrum.
In it the power always acts through a longer arm

496

PH YSIOL OGJCA L PH YSICS.

[Chap. XLI.

the
the
longer

than the resistance, and has consequently always the
advantage. It is the lever of power, though, as in
the first order, the power must always move through a
greater distance than the weight.

The third order of levers is shown in Fig. 206.

The power is between
the weight and
fulcrum. Here
weight has a
arm than the power.
Let w be distant 4 feet

Fig. 206.— Lever of Third Order. » n ,,

irom F, and p 2 feet,
and let w = 10. The moment of w is 40. Acting

o

through 2 feet a power of 20 is necessary to yield the
same moment. Therefore, with these distances the
power must be more than double the weight to raise
it. Here, therefore, the weight has the advantage.
But it is evident from Fig. 207 that the weight
moves through a much greater
distance (from w to w') than the
power (from p to P'). A small
movement of the power will,
therefore, give a good sweep of
the weight. This lever is,
therefore, a lever of velocity ;
the weight passes over a con-
siderable distance in a short time.

We shall see, in the chapter on Animal Mechanics,
(chap, xliii.) how the muscles, bones, and joints of the
body can be classified under such a system of levers.

The balance is another illustration of the prin-
ciples applicable to parallel forces. This is particu-
larly well shown in the Danish balance (Fig. 208).
It consists of a steel arm with a fixed weight P at
one end. At the other end is a hook carrying a scale
pan. The arm is supported fr.m a beam resting on
the edge of the ring-shaped oody F, which is the

Fig. 207.— Lever of Third
Order.

Chap. XLI.] THE BALANCE. 497

fulcrum. The weight R in the scales, and P, are counter-
poised by moving the position of the arm in F, the
distances of R and P from
F being inversely as their
weights. Previous gradua-
tion enables one to say
what positions correspond
to various weights in the
scale pan.

The ordinary balance Fis- 208.-Dauisli Balance,
consists of two scales

hanging from the ends of a horizontal bar, which
is suspended by a fine edge. The point of sus-
pension is so arranged that the scales are equi-
poised. This balance should exemplify two equal
and parallel forces acting on a rigid bar suspended
by its middle. The accuracy and sensibility of the
instrument depend on the diminution of friction at
the point of suspension of the bar and the points of
suspension of the scales from its ends. This is
effected by making these points of very hard material
(steel or agate), in the form of knife edges. S'riisi-
bility also depends on the length and lightness of the
beam, and on the centre of gravity of the beam being
in the same vertical line as the axis of suspension,
and very little below it.

Pulleys also exemplify the elementary dynamical
principles that have been referred to.

The SINGLE PULLEY (Fig. 209) does not effect any
advantage in the way of diminishing the power to be
employed. Suppose c to be a fixed pulley acted on
by two parallel forces represented by the weights X
and Y. The moment of x is its amount multiplied by
the distance from its point of application to the axis
on which the pulley turns (i.e. AC), and the moment of Y
is its amount into its distance. Now the distance is
in each case the same. It is, therefore, evident that
G G — 7

Fig. 209.— The Single
Pulley.

PHYSIOLOGICAL PHYSICS. [Chap. XLI.

if the two forces are to be in equilibrium, so that the
pulley is not turned, the two forces must be equal. A
small power will not, therefore, raise a larger weight.

The advantage of the single
fixed pulley is that it alters the
direction of the force. Thus, a
man wishing to raise a load from
the ground may do so by placing
himself above the load and pul-
ling it upwards ; by using a
pulley, however, he pulls down-
wards, and thus is able to add
the weight of his body to the
power. Similarly in Fig. 209
the load P (of moment PX BC)
requires an equal weight R on
the other side of the large pulley to counterpoise it.

The single fixed pulley is used in the body for
altering the direction of a force. Thus the digastric
muscle and the oblique muscles of the eye have the
direction of their action changed by bands of fibrous
tissue, etc.., acting the part of pulleys.

It is, however, otherwise with the movable pulley
represented in Fig. 210. Here
we have a rope, fixed by a
hook to a beam, passing down-
wards round a movable pulley,
and then upwards. It next
passes over a fixed pulley, and
its free end has a weight at-
tached. The fixed pulley is
placed merely for changing the
direction of pull, it being incon-
venient to pull on the free end of
the rope after it has passed
round the movable pulley. But

the fixed pulley does not affect

Fig. 210.— The Movable
Pulley.

Chap. XLL]

PULLEYS,

499

xS\'.\y ••'. \

in the least the result of the movable one. The
latter has a hook attached from which a weight
is suspended. Now when the rope is pulled with a
force of 1 pound, let us say, that force is communi-
cated to the hook in the beam. It is a law of
dynamics that action and reaction are equal. If the
hook is pulled on with a force of 1 pound, it reacts
with a force of 1 pound. Now the force of 1 pound
acts in a direction to raise the movable pulley, and
the force of reaction acts for the same end. The
pulley with its attached weight is thus pulled up-
wards with a force of 2 pounds. But
the movable pulley does not rise in the
same degree that the free end of the
rope descends ; owing to the doubling
of the rope, it is raised by only half the
distance. It is also plain that if several
movable pulleys were used, connected
together, the rope passing from one to
the other, and the weight hanging to
the sj^stem, the power necessary to
raise the weight would be diminished
in proportion to the number of pulleys.
Such a system of pulleys is shown in
Fig. 211. It is to be noted that the
height to which the weight is raised
with a certain length of rope pulled,
smaller and smaller as the
of pulleys is increased. A
force is capable of raising

becomes

number

smaller

w

through

the weight, but it must act
distance. In short, the work done is
whether the pulleys be many or few.
done is estimated bv the weight raised

distance through which it is
of 10 pounds raised 1 foot is
of 1 pound raised 10 feet.

Fig. 211.— A
Sys t e m of
Movable Pul-
leys.

a longer
the same
The work
into the

weight

same as a weight
weight

raised. Thus a
the
So that if

500 PHYSIOLOGICAL PHYSICS. tchap. XLII.

of 10 pounds were raised by a pulley arrangement
by means of a weight of 1 pound, the weight would
only rise 1 foot for every 10 feet of rope pulled in.

CHAPTER XLII.

GRAVITY.

Gravity. — The tendency which all bodies have
to fall to the earth is due to the action of gravity,
i.e. the mutual attraction exerted between the earth
and the body. This tendency is a particular exem-
plification of the universal law that all material particles
attract one another. The direction in which gravity
acts is always the vertical at the place ; hence, to
determine the vertical, a weight is permitted to hang
freely from the end of a string, the plumb line. The
line of the string gives the vertical.

Centre of gravity. — It is the force of gravity
attracting bodies towards the centre of the earth that
gives them weight. If a body could be entirely re-
moved from the influence of gravity it would have no
weight. The force of gravity acts on each particle
forming the mass of the body, attracting it with a
certain degree of force. A solid body may, therefore^
be considered as under the influence of a vast number
of forces, each particle being separately solicited by
gravity; that is to say, the body may be considered as
operated on by a number of parallel forces, all acting
in the same direction. Now we have seen that
parallel forces are capable of being compounded into
one force equal in amount to the sum of the different
parallel forces, and acting through one point in the
bodv. The action of gravity on all the separate

Chap. XLII.]

EQUILIBRIUM.

501

particles of a solid body can therefore be compounded
into one resultant acting through one point in the
body. That point is the CENTRE OF GRAVITY. We
see also from this that the attractive force of gravity
depends upon the number of particles of the body,
and that it is directly proportional to the mass of the
body. Weight, then, depends upon mass. The centre of
gravity may be experimentally determined for a body by
suspending it from one point by a string which is pro-
longed, and has a small weight attached. The vertical
line is thus obtained. The body is next suspended
from another point. The point of intersection of the
vertical lines is the centre of gravity. The centre of
gravity of a line is its middle, of a circle its centre,
of a parallelogram the place of intersection of its
diagonals.

Stable and unstable equilibrium. — When
a body is in equilibrium, the force of gravity acting
through the centre of gravity is
opposed by another force equal in
amount and opposite to it in di-
rection, acting through the same
point ; or when it is not opposed
by a single force, but by several
forces, the resultant of these forces
must act from the centre of
gravity. Suppose a plate of wood
BCD Fior 212) whose centre of

., . Hi. Fig. 212.-Stable and

gravity, as experimentally deter- unstable Equilibrium.
mined in the way mentioned, is G.
It is evident that if the plate be supported by a pin
passed through G, on which, however, the plate is free
to turn, it will remain in equilibrium in whatever posi-
tion it is placed. Let the plate be supported by a pin
at A, directly above the centre of gravity, it will remain
in equilibrium, and, if moved to one side or another,
will return again to its former position. For the

502 PHYSIOLOGICAL PHYSICS. [Chap. XLII.

force of gravity and the force of resistance through
the pin are both acting through the same vertical
line, and if the plate be displaced, both forces act so
as to bring themselves again into the same vertical.
This position is called the position of stable equili-
brium, because the body, if displaced, will not de-
part farther from equilibrium, but will return to it.
Now let the plate be suspended from a pin at A' ; it
is plain the body is not in equilibrium at all. It is
under the influence of the force of gravity acting
downwards through G, and of the force of resistance
acting upwards through A' ; the plate will, conse-
quently, turn so as to place the centre of gravity
directly under the point of support A', and will then
rest in stable equilibrium. In the same way, if the
pin be at A" the body is under the influence of an up-
ward force at A", and a downward force at G, and
again it will turn till A" comes to be over G, where it
will rest. Let the pin be placed at A'", directly under G.
If G and A'" be accurately in the same vertical line,
the body will be in a position of equilibrium, for the
downward force of gravity and the upward force of
resistance are opposing one another along the same
vertical line. But let the body be displaced to either
side, and suppose it to be displaced, as shown in Fig.
212 B'C'D', it is evident that the forces no longer
act in the same vertical, gravity is acting through G',
and resistance through A"'. The result will be that
the plate will rapidly turn round A'", till the centre of
gravity is below the point of suspension, when the
body will be again in stable equilibrium. The body
is, then, in equilibrium when its point of suspension is
below its centre of gravity ; but it is unstable equi-
librium, and the body falls away from it on the
slightest movement. The same facts apply to a body
resting on a table. It is in equilibrium when the
vertical through the centre of gravity also passes

Chap. XLII.] FALLING BODIES. 503

through the point of support. But there are two
positions in which this may occur : one in which the
centre of gravity is at its highest point, as, for instance,
when an egg is balanced on its long axis ; and the
other when the centre of gravity is at its lowest point,
as when the egg is lying on its side. In the former
case, the egg is in the position of unstable, and, in the
latter case, of stable, equilibrium.

If a body be supported on a base, the vertical
from the centre of gravity must fall within the base
if the body is to be in equilibrium.

The laws of falling bodies. — It is owing to
the action of gravity that bodies fall to the earth.
We have already seen (page 488) that a force can be
estimated by the velocity it confers on a body of unit
mass in a unit of time. The intensity of the action of
gravity may then be calculated by the velocity which
a body, falling freely, will acquire at the end of one
second. The laws that prevail in falling bodies were
first investigated by Galileo, who experimented by
letting bodies fall from the leaning tower of Pisa.
He found that the action of gravity was independent
of the nature of the body. Balls of different sub-
stances fell with equal rapidity. This has been
proved since Galileo's time by observing that in a
vacuum a piece of clown will fall as fast as a piece of
metal. Bodies fall with different rapidities in air,
because of the resistance which air offers, and which,
of course, affects a large surface more than a small one.
The laws of falling bodies have been very accurately
determined by the well-known Attwood's machine,
and other instruments. When a body falls freely
in air its motion is not uniform, that is, it does not
pass through equal spaces in equal times. If a force
acted on a body for a certain time, and then suddenly
ceased acting, it would confer a certain velocity on
the body proportional to the time during which it

504 PHYSIOLOGICAL PHYSICS. [Chap. XLII.

acted. Suppose the body were not acted on by any
other force, such as friction, resistance of the air, etc.,
it would go on moving with the velocity it had ac-
quired, and this would be uniform motion. It would
never cease moving. But various forces, resistance, etc.,
oppose its uniform motion, so that in the end it comes
to rest. If, however, the force acts for a longer time,
the motion is uniformly accelerated, and the velocity
will be in proportion to the length of time during
which the force acts. Gravity is a constantly acting
force, so a falling body will have a uniformly accele-
rated motion. A body falling from rest is found at
the end of one second to have in London a velocity
equal to 32-1889 feet, 32-2 approximately. The in-
tensity of gravity in London is then 32 -2, expressed
by saying g = 32 -2. But the intensity of gravity
varies in different places, being least at the equator,
so that the amount must be experimentally found for
each place. The acceleration being uniform, the
velocity at the end of a given number of seconds will
be 3 2 -2 x by the number of seconds. Let v = the
velocity, and t = the number of seconds, then

The velocity at the end of 10 seconds will be 32 -2
X 10, expressed in feet per second.

It was found that the actual space traversed by
a body falling from rest was 16'1 feet at the end of
the first second. (Distinguish between the space
traversed during the second, and the velocity at the
end of the second.) At the end of two seconds the
space traversed is 64-4 feet ; at the end of three
seconds it is 144-9. During 1 second IG'l feet, 2
seconds 64*4, 3 seconds 144'9, these figures give the
proportions for time 1, 2, 3, and for the space tra-
versed 1, 4, 9 ; that is to say, the space traversed the
first second (which = 1 6' 1 feet, i.e. ^ of 32, i.e. ^ g)

Chap. XLII.]

SIM PL E PEND UL UM.

505

multiplied by the square of the time, gives the
distance at the end of the time. Let s = the space,
the formula becomes

s = $ g t2 — 16-1 x t*.

Thus, at the end of 2 seconds, s = 16-1 x 4 = 64 -4.
The rule, put in words, is, the spaces described are
proportional to the squares of the time employed in the
description.

A third formula, v = \/2 gs, gives the velocity v
a body acquires by falling through a certain space s ;
thus the velocity acquired by a body falling 30 feet=

v = \/64-4Tx~367

The simple pendulum is formed by a weight
attached to the end of a fine inextensible thread, the
other end of the thread being fixed. The centre of
gravity is below the point of
suspension. If the weight be
pulled to one side of its posi-
tion of rest, and then be let go,
it will move towards its former
position by the force of gravity ;
but in moving it acquires
energy, and thus it does not
come to rest, but passes its
middle position to the other
side, moving upwards along a
small arc. It will move up
till it has expended all the
energy it acquired by its previous
downward movement. But it has now gained energy
of position which causes it to move backwards over
its former path. If it did not encounter resistance,
friction, etc., it would move back to its former posi-
tion. But energy is expended in overcoming resistance,
etc., and thus it gradually loses its energy, describing
movements, on each side of its position of rest, of ever

Fig. 213. — The Simple
Pendulum.

506 PHYSIOLOGICAL PHYSICS. [Chap. XLII.

diminishing extent till it finally comes to rest. If the
pendulum be at B' (Fig. 213), the force urging it towards
B is that of gravity acting in the direction B'G, and
equal to the energy gained in falling through the dis-
tance CB. But this force can be resolved into two
others, namely, fi'e, in the line of the thread which is
counterbalanced by the thread, and By, which acts
along a tangent to the arc, and is that part of the
force which is effective in moving B' to B.

The movement of the weight from B' to B" a.nd
back to B' is a complete vibration, and the time occu-
pied is called the periodic time. The distance from
the position of rest B to either extreme B' or B" is the
amplitude of vibration, and is usually measured by
the angle BAB'.

The time of oscillation of a pendulum is usually
estimated, not by the time of a complete vibration,
but the time occupied in travelling from the middle
position to the extreme, and then back to the middle
position ; or, what is the same thing, the time of
travelling from one extreme, to another B' to B", the
time of an oscillation. When the oscillations of the
pendulum do not exceed a certain extent the time
of vibration is independent of the amplitude. The time
t is obtained by the formula

where I = the length of the pendulum, g = the
acceleration due to gravity, and -* = the ratio of the
circumference of a circle to the diameter = 3-14159.
From this formula the length of the pendulum can be
estimated if t be given ; thus,

7T2

Where the length is known, the intensity of gravity

Chap. XLIII.] ANIMAL MECHANICS. 507

at a place can be estimated from the same formula.
Thus, in a seconds pendulum, where t = 1,

" '

7T2

CHAPTER XLIIL

ANIMAL MECHANICS.

IN the animal body the system of bones connected
together by means of joints, and movable on one
another by the contraction of muscles, is found to form
an arrangement of levers. All the three orders of
levers described in chapter xli. are found exemplified
in the human body. The fulcrum is offered by the
joint, the power is given by the muscular contraction,
and the weight is the resistance to be overcome in the
movement of the part, the lifting of some weight, etc.
Of the first order of levers a good example is afforded
in the means by which the head is maintained in the
erect position. The fulcrum is the articulation between
the condyles of the occipital bone and the atlas, the
weight is the weight of the fore part of the head and
face, and the power is supplied by the muscles passing
upwards to the skull behind, the fulcrum being be-
tween the power and weight. The feature of this
lever, as one conducing to stability, is seen in the ease
with which the head is held up. That it is so held by
voluntary muscular effort is evident from the fact
that it tends to fall forward, so that the chin rests on
the breast, when unconsciousness comes on. When
the fore-arm is flexed, and extension is performed
by the triceps muscle, we have another example of a
lever of the first order, the joint being between

5oS

PHYSIOLOGICAL PHYSICS. [Chap. XLIII.

Fig. 214.— The Foot
as a Lever of the
First Order.

power (triceps), and weight (that of the fore-arm).
Here, however, the power arm (page 495) is short,
and the resistance arm is long, so that the power is at
a disadvantage. At the same time a small movement
of the triceps effects a considerable movement of the

hand, and thus rapidity of move-
ment is obtained. Again, a lever
of the first order is seen when the
raised foot is extended on the ankle
joint. The joint is fulcrum F, while
by the tendo Achilles power p is ap-
plied, and the weight w of the fore
part of the foot offers the resistance
(Fig. 214).

An example of a lever of the second order is
found in the support of the body on the ball of the
toes, where the fulcrum is at the ball of the toes. The
power is applied by the muscles of the calf to the
heel, and the weight is that of the
body communicated through the
tibia, the weight being between the
power and fulcrum (Fig. 215). This,
we have seen, is the lever of power,
because the power arm is longer than
the weight arm. It is not so com-
mon in the body as the lever of the
third order. The latter is the lever
of quickness at the cost of power, for the power is
between fulcrum and weight, and has a shorter arm
than the weight. As a compensation, however, a
small movement of it will effect a considerable move-
ment of the weight. Rapidity of movement is thus
the object attained by the third kind of lever. Thus,
a good example is afforded in flexion of the fore-arm
on the upper arm, with a weight in the hand. The
power is at the attachment of the biceps between the
elbow-joint and the centre of gravity of the fore-arm,

Fig. 215.— The Foot
as a Lever of the
Second Order.

Chap. XLIII.]

LEVERS IN THE BODY.

509

through which the weight acts. The great length of
the weight arm is here very apparent. If the heel
rests on the ground and the toes are raised, we have a
lever of the third order. The
fulcrum is the ankle joint, the
power is in front communicated p
by flexor muscles, and the weight
is farther in front (Fig. 216).

We have seen how to esti- „. „, „

„ „ . Fjg. 216.— The Foot as a

mate the moment OI forces, I.e. Lever of the Third Order.

the amount of the force multi-
plied by the perpendicular distance between the line
of direction of the force and the fulcrum. Thus, in
Fig. 217, let AB represent the arm, and BC the fore-arm,
and BC' the position of the fore-arm when more ex-
tended. At a the biceps is act-
ing in the direction ad, and at
c the weight is acting downwards.
The moment of the biceps, which
we shall call x, is the amount
of force produced by its con-
traction, which we shall call P,
multiplied by the perpendicular
distance from its point of ap-
plication to the elbow joint B.

Fig. 217. -Moment of x = p. x «B- .The moment of

Biceps in Different the weight (call it ?/) is the pro-

Fore^m3 ' duct of its amount (let the amount

= w) multiplied by its distance
CB, y = w x CB. Let them be in equilibrium,
then x = i.e. P x «B=:W x CB.

•"B

Therefore

P =

X CB

a B

When the fore-arm is more extended, the perpen-
dicular from the line of direction of the power to the
fulcrum is less than before ; it is now &B, the power

510 PHYSIOLOGICAL PHYSICS. [ChsP. XLIIT.

acting in the line b"b' ; therefore, X=P X &B. The
distance of the weight becomes CB. The moment of
the forces is consequently, affected by the positions.

We thus see that when the arm is straightened
the moment of the biceps is at its smallest, and that
its greatest moment is when the fore-arm is at right
angles to the upper arm, when the muscle acts more
perpendicularly upon the radius. It is to be noted,
however, that the loss of power due to the great
obliquity of the muscle with the fore-arm at an open
angle is counterbalanced to some extent by the fact
that the biceps is stretched more fully, and has the
whole of its contraction to perform.

Standing-, walking, etc. - The dynamical
principles that have been briefly referred to in pre-
vious chapters are capable of explaining the mechanics
of standing, sitting, etc. ; as also of walking, and other
movements of locomotion.

In standing erect the first condition of equilibrium
is fulfilled, viz. the vertical from the centre of gravity
falls within the base of support. According to E.
Weber, the position of the centre of gravity of the
body as a whole is in the vertebral canal, near the
level of the upper border of the second lumbar ver-
tebra. In the erect posture, therefore, the vertical
through it falls between the two feet. But when the
feet are close together, the base of support is com-
paratively small, and a slight movement to one side
or other will throw the vertical outside of the
line, when the tendency will be to fall. The body is
not, accordingly, in stable equilibrium. The erect
posture, especially the military posture, is not one
which is maintained without a considerable amount
of muscular effort, the tendency being for the body to
fall forward, a tendency which is met by the resis-
tance of the muscles of the calf. For this reason,
maintaining the erect position is more tiring than

Chap. XLIII.] SITTING. 511

walking. If, however, the feet be separated from
one another, the base of support is enlarged, and stand-
ing becomes more easy.

As regards different parts of the body, the vertical
from the centre of gravity of the head passes in front
of the atlas articulation ; hence the head tends to
fall forward. The centre of gravity of head and
trunk, including the arms, is in front of the tenth
dorsal vertebra, at the level of the xiphoid process of
the breast bone. It is nearer the front the shorter the
individual happens to be. The vertical passes behind
a line joining the hip joints, and the tendency of head
and trunk is to fall backwards. This is overcome by
muscular effort aided by the ligaments, ileo-femoral,
fascia lata, etc. The perpendicular through the centre
of gravity of head, trunk, and thighs falls slightly
behind the knee joints, so that the tendency is still to
fall backwards. But the vertical from the centre of
gravity of the body as a whole passes in front of the
ankle joint ; hence the tendency to fall forward.

In sitting* the body is supported on the tuberosities
of the ischia, and the legs are thrown out of action.
The vertical through the centre of gravity may pass
between the tubera, in front of them, or behind them.
In the two last cases, muscular effort or some support
prevents the body falling forwards or backwards.
The arm leaning on a table, for instance, gives sup-
port to the forward inclination, and the back of a chair
prevents the backward displacement. In the first
case, slight muscular effort maintains the balance.

WaSking. — The feature of walking is that the
body never entirely leaves the ground, but its weight
passes alternately from one foot to the other. The
dynamics of walking are shown in Fig. 218, where
the body is represented with one leg j perpendi-
cularly under the centre of gravity G, while the
other is behind, resting on the ground by the ball

5*2

PHYSIOLOGICAL PHYSICS. [Chap. XLIII.

of the toes. At this instant the leg behind begins
the advance by giving the body an impulse forwards

from its point of sup-
port. The force acts
in the direction J'F.
Let GF represent the
intensity of the force.
If a parallelogram be
constructed, of which
GF is the diagonal, the
force GF is evidently
resolvable into GV, an
upward force acting
against gravity, and
neutralised by it and
a force GH, which is
the part of the impulse-
that d eter mines the
forward movement. If
the upward movement
GV is quite neutralised
by the downward force
of gravity, the body
will simply be ad-
vanced in a horizontal
line, and it is found,
as a fact, that up and

}' L >

Fig. 218.— The Dynamics of Walking.

down oscillations of the

body are of very small
amount. To give the forward impulse, the leg that is
behind is extended, and in continuation of that action
the heel is raised from the ground by the extension of
the ankle joint, till the leg rests on the ground by the
tip of the toes only (Fig. 219, 1, hkfm). By this exten-
sion the leg finally leaves the ground, as represented by
the thin line of 3. Meanwhile, to permit the exten-
sion referred to, the forward leg is slightly bent at the

Chap. XLIII.]

WALKING.

knee, but when the leg behind it leaves the ground,
it gradually becomes straightened (3, 4, 5 of Fig.
219, thick line), so that the body is kept from
being lowered. The leg behind is thus hanging,
so to speak, and performs a pendular movement
(indicated by the arrow between 4 and 5), swinging
forwards past the leg which is now supporting the
body, till it
reaches a posi-
tion as far in
front of the
supporting leg
as it was for-
merly behind
it, when it
toil c h e s the

ground. It has Fig> 219.-Different Positions of the Legs

now become Walking,

the forward leg

(had beg of 1, 2, and 3), while the leg formerly in front
lias come to occupy the posterior position (4, 5, dark
lines; and 1, thin line). In slow walking there is a
time when both feet are on the ground, the forward
foot acting as a fulcrum, on which the foot behind
pushes the body. But as the pace increases, the
period during which both feet touch the ground grows

O O O

less and less, till one foot has no sooner touched the
ground than the other leaves it. This is shown spe-
cially well by Marey's graphic method of registering
the movements of the two feet by a tambour in each
shoe, connected with a revolving cylinder. The same
method shows that in running there is an appreciable
period when both feet are off the ground.

The forward impelling force urges the body on
wards against the resistance of the air, the friction
between the feet and the ground, etc. It is evident
from Fig. 218 that the horizontal component of the

H H— 7

514 PHYSIOLOGICAL PHYSICS. [chap. XLIII.

force will be the greater, the greater the inclination
of the leg behind with the ground. Again, the
faster the movement the greater will be the resistance
of the air. A forward inclination of the body will act
against the resistance, and so aid the progression.
Besides, the impulse from behind acting through the
centre of gravity will tend to throw the trunk back-
wards. The forward inclination neutralises this, and
prevents the necessity of muscular action being called
in to preserve the equilibrium.

Besides the forward movement, there is a slight
movement of rotation on the head of the femurs,
owing to one leg moving forward and the other back-
wards. This is to some extent compensated for by
the arms, the arm of one side moving in the same
direction as the leg of the opposite side.

The motion of the leg as it leaves the ground

O

behind is akin to that of a pendulum. The swing
of a pendulum is directly as its length, and the time
occupied directly as its swing. In natural walk-
ing, therefore, the length of the step will be deter-
mined by the length of the leg, and the rapidity of
the movement also. There is, therefore, a certain
length of step which is least fatiguing to the individual,
since it permits the full development of the rhythmic
movement suitable to the limb.

INDEX

Abbe's condenser,

Aberration, Chromatic, 344

, Correction for, in micro-
scopes, 359

of the eye, 394

, Spherical, 347

Absorption bands, Mode of de-
monstrating, 333

of carbonic oxide haemo-
globin, 327

of hsematin, 328

of niethaemoglobin, 328

of oxy haemoglobin, 326

• of reduced haemoglobin,

326

of sunlight, 321

by endosmosis, 261

by lymphatics, 266

of gases by liquid, 291

of heat, 461

Acceleration due to gravity, 504

Accessory circuit, 56

magnet, 107

Accommodation of the eye, 383

, Kange of, 3S7

Achromatic lens, 347

lenses, Combination of, 360

Achromatism, 347

Acuteness of vision, 383

Adhesion, 239

Air pump, 280

, Sprengel's, 2C2

Albumen, Diffusion of, 259

, Filtration of, 269

in iirine, 205

, Units of heat yielded on oxy-

dation of, 456, 482

Alcoholimeter, Gay-Lussac's, 204

Althaus on electricity for aneu-
rism, 167

Amalgamated zinc, 18

Amalgamating fluid (Berjot's),
114

Amber, 1

Amici's object-glass, 360

Ampere's laws, 94

Amplitude of vibration, 298

- of pendulum, 5i)6

Anaesthesia, Production of, by
evaporation of ether, 474

Analyser of polariscope, 402

Analysis of light, 319

of sound by Koenig's appa-
ratus, 440

, Spectral, 323

Anderson, McCall, on electricity
in aneurism, 167

Anelectric, 4

Anelectrotonus, 82

Aneroid barometer, 278

Angle, Critical, 310

of aperture, 360

of deviation, 312

of incidence, 301

of polarisation, 404

of reflection, 301

— -r-, Visual, 382

Animal heat, 481
, Kegulat-'on of, 483

-T— mechanics, £07

Anions, 53

Anisotropous, 402

Anode, 52

Anomalies of accommodation, 388

of refraction, 388

Aperiodic needle of galvanometer,
110

Aperture, Angle of, 360

of mirror, 303

Arago and electro-magnet, 54

, experiments on pressure of

gas, 272

Archimedes' principle, 195

Areometer, 2ol

Armature of Holtz' machine, 10

of magnet, 93

Arterial tension, 221

Arytenoid muscles, 449

Asculine, Fluorescence of, 327

Association of cells in groups, 31

Astaticism, 98

Astigmatism, 391

PH\ 'SIOL OGICA L PHYSICS.

Astigmatism, Covrectiou for, 393

— , irregular, 394
Athermancy, 335
Athermauous, 462
Atmosphere, Homogeneous,

L eight of, 274

, Pressure of, 275

Atmospheric pressure, Effects of,

278

- on body, 282
Attraction, Electric, 5

, Magnetic, 91

Attwood's machine, 503
Auricular appendages of ears, their

action on sound waves, 422
Austral, 91
Axis of lens, 313

of mirror, 303

, Optic, of Iceland spar, 399

, , of the eye, 310

, Secondary, 303, 313

B. A. unit of resistance, 34
Bacon, 451
Balance, Danish, 497
Bands, Absorption, 321, 327
Barium and phosphorescence,

339
Barometer, Aneroid, 278

, Cistern, 277

, Syphon, 277

, Wheel, 277

Bartholinus, 398

Battery, Becker Muirhead's, 153

, Group'ng of cells in, 31

, Leclauche"s medical, 151

, Mole of joining cells in, 28

- of galvanic cells, 24

- of Lev den jars, 12

, Requirements of, for medic: 1

purposes, 152
-, Stohrer's, 1EO

Beale's neutral tint reflector, 373
Beard and Rockwell's method of

faradisation, 159

Peats, Production of, in music, 429
Becker M airhead battery, 153
Becqiierel's phosphoscope, 339
Berjot's amalgamating fluid, 114
Bernard's woorara experiment, 75
Binocular eye-piece of Hartnack,
370

microscopes, 369

Biot, 421

Blood current, Methods of esti-
mating velocity of, 230

pressure, 221

• , Instruments for mea-
suring, 227

Boeck on double refraction by

muscle, 409
Boiling point, 471
Boreal, 91

Bourdon, spring kymograph, 229
Boussole, Wiedemann's, 104
Boyle's or Marriotte's law, 271
Brain ah press, 190
Brewster, 357
BrowniDg's microspectroscope,

329
Bru eke, behaviour of muscle to

polarised light, 410
Brunton (Lauder), apparatus for

frog heart, 238
Bunsen and dark lines of spec-

trum, 322

- cell, 22

- on diffusion of gases, 290

Caorniard de la Tour's siren, 4?5
Calcium salts, Phosphorescence

of, 339
Caloric, 454;
Calorie, 451
Calorimeters, 479, 480
Calorimetry, 477
Camera lucida, Chevalier's, 372
-- , Wollaston's, 371
Camera obscura, 374
Canipani's eye-piece, 362
Camphor, Experiments on surface

tension of, 240
Canada balsam, 360, 399, 409
Canary glass, 337
Canule, Kronecker's, for frog-

heart, 236

Capacity, Thermal, 476
Capillarity. 241
Capillary action in porous

bodies, 246

- electrometer, Lippmann, 244
-- , McKeudrick, 245

- tubes, Flow of fluids in, 215
Cardinal points, Construction of

image by, 377
-- of system of refractive

media, 377
Cardiograph, 230
Cedar-wood oil for immersion lens,

363
Cell, Galvanic (See Element)

— , Diffusion (Graham's), 249
Modes of joining, 28, 31

Celsius' thermometer scale,
Central lesion (nervous), Diagno-

sis of by electricity, 160
Centre of figure of mirror, 302
- of gravity, 196

INDEX.

Centres of curvature of lens, 313

of miiTor, 303

Chain-pile ( Pulvermacher), 153

Chauveau, 229

Chevalier's camera lucida, 372

Chlorophyll, Fluorescence of, 337

Christiaiii's compensator, 140

Chromatic aberration, 34 1

Chronograph (Marey's), 174

Circuit, Accessory, 56

, Divided, 32

, Primary, 35

, Secondary, 35

— , Short, 56

Circular polarisation, 411

Circulation of the blood, 194

, Mechanics of, 222

Clausius, 451

Clay guard, 113

Cloetta, 256

Closing cushion, 115

Coefficient of absorption or solu-
bility of a gas, 291*

of conductivity, 457

of expansion, 465

of friction in gaseous diffu-
sion, 290

Coercive force, 9"2

Cohesion, 188, 239

Coils, Induction, 34

, , Du Bois-Reymond's, 42

, , for medical purposes,-

141

Ruhmkorffs, 39

Collimator, 524
Colloids, 258
Colour, 339

sensation, Youug-Helmholtz'

theory, 343

-top, Maxwell's, 341

342

Colours, Complementary,

, Compound, 341

, Fundamental, 312

— , Intensity of, 344
— , Mixture of, 340
- of spectrum, 319

, Primary, 342

, Saturation of, 344

, Secondary, 342

, Toue of, 344

Coloured rings of Newton, 408

Communicating vessels, Equili-
brium of liquids in, 193

Commutator, 59

Compensation of muscle current,
120

Compensator, Long, 121

, Round (Du Bois-Reymoud),

124

Compensator, Round, Modified

by Christiani, 140
Compound microscope, 358, 363

waves, 435

Compressibility of gas, 271, 272

- of liquids, 188
Concave lenses, 318

meniscus, 241

— mirrors, 303 et seq.
Condensation,' Wave of, in sound,

418
Condenser, Abbe's, 8o4

, Electric, 11

Conduction of heat, 456
Conductors of electricity, 4

of heat, 457

Conjugate foci, 304, 314, 315
Constant current, 64

elements, 18

Contact breaker, Foucault's, 40

key,- 55

Contraction, Muscular, 65

— , , Curve of, 136

, , Law of, 87 et seq.

— -, , Secondary, 72

— , , Tetanic, 67

Convection of heat, 458
Converging lens, 313
Convex lenses, 313, 316

meniscus, 242

mirrors, 305 et seq.

Corpuscular theory of light, 296
Couple, Dynamical, 494

, Voltaic, 16

Crico-thyroid muscles, 448

Critical angle, 310

Crystalloids, 258

Cuneus, 12

Cupping instruments, 287

Curare.P'reparation of solution of,

for experiment, 75
Current electricity, 13 et seq.

-, Action of on magnets,

94

by, 53

Extra, 43

Effects of, 50 et seq.
Production of magnets

from muscle, 117

from nerve, 119

Rapidity of; 129

Induced, 34—36
Interrupted, 64

142

— , Thermo-electric,
Curve of fatigue, 179
of muscular contraction,

176

Cylinder, Revolving, 171
Czermak, 349

5*8

PHYSIOLOGICAL PHYSICS.

Dalton's law, 288

Damping chamber for galvano-
meter, 106

Daniell's element, 19

Danish balance, 497

Dark lines of solar spectrum, 321

Decoction of madder,- Fluores-
cence of, 337

Decomposition by diffusion, 251

of a vibration into' two at

right angles, 401

of light, 319

Degenerative reactions of Erb,
163

Densimeter of Rousseau, 20$

Density, Electrical, 5, 25

of gas, 273

— — of liquids, 197

, , Methods of estimating,

198 et seq.

• , , Relation of to pressures

194

Derived currents, 32

Deriving cushions, 112

Desormeaux, Endoscope of, 355

Despretz' experiments on com-
pressibility of gas, 272

Dextro-rotatory, 413

Diabetes, Specific gravity of urine
in, 204

, Use of saccharimeter in, 145

Diagnosis, Electricity for, 159

Dialyser, 261

Dialysis, 260

Diamagnetic, 94

Diathermancy, 335

Diathermanous, 462

Dicrotism, 225

Difference of potential, 13

- of tones, 433

Differential galvanometer, 108
Diffusiometer, 280

Diffusion affected by galvanic

current, 258

, Decomposition by, 251

images, 383

of albumen, 259

of gases, 288

through porous septa,

290

- of liquids, 248

Dip of magnetic needle, 93
Direct vision prism, 330

spectroscope, 330

Discharger, Electric, 12
Dispersion of light, 320
Dissonance, 432

Diverging lens (see Concave), 315
Divided circuits, 32

Dobbie and Hutchison's method

for estimating sp. gr., 200
Dollond, 346, 359

Donders on anomalies of refrac-
tion, 389

Double refraction, 397
Doublet, Wollaston's, 358

for achromatic lenses, 361

Doubly refractive substances, De-
tection of, 404
Drawing of micro'scopic objects,

371
Droinograph of Lortet and Chau-

veau, 233

Dropsies, Mechanism of, 267
Du Bois-Reymond :

electrodes, n6n-polarisable,
111, 119

- (platirium), 61
friction-key; 55
galvanometer, 99
iuductorium, 42

modified by Helmholtz,47

modification of Poggendortt's

compensation method, 120
modified frog-interrupter, 129
modified spring myograph, 176
muscle telegraph, 63
rheocord, 77
round compensator, 125
Duchenne, 159
Dufay, 3

Dulong, Calorimeter of, 482
, experiments on gaseous pres-
sure, 272
Dut rochet, 251
Dynamics, General, 485 et seq.

of sitting, 511

of walking, etc., 511

Dynamometer, 4S9

Ebullition, 473

, Point of, 471

Eckard, 256

Efflux, Velocity of, 208

Elastic force of gas, 270

tubes and flow of liquids, 220

Electric attraction and repulsion, 5

battery of galvanic cells, 24

— of Leyden jars, 12

condensers, 11

density, 5

discharger, 12

induction, 34

potential, 13

signal, 172

tension, 6

Electrical machines, 8
Electricity, Conductors of, 4

INDEX.

Electricity, Current, 13

Density of, 5, 25

Effects of, 50

on magnets, 94

Frictional, 1

Induced, 6, 3i

Intensity of, 25
- of muscle, 117

of nerve, 119

, Resinous and vitreous, 2

, Resistance to, 26

, Tension of, 6, 25

, Theories of, 3

— — , Therapeutical applications

of, 148

Electrification by influence, 7
Electrodes, 17

for medical purposes, 157

• , ISTon-polarisable, 112

— — , Platinum, 60

, Polarisation of, 111

Electrolysis, 50
Electrolyte, 52
Electro-magnet, 53
Electro-magnetism, 168
Electromotive force, 17

of a thermal current,

143

of various elements, 24

to measure by compen-
sation, 120

Electromotor, Capillary, 244
Electro-negative, 52
Electrophorus, 9
Electro-positive, 52
Electroscope, Gold-leaf, 7
•, Pith-ball, 6

Electrotonus, 77
, Effects of, on

electromotive

force of a nerve, 126

— , , on excitability

nerve, 83, 87
— , Experiments on, 85

Results of, 86

Scheme of, 81

Varieties of, 86

of a

Element, Galvanic, Bunsen's, 22

— Chloride of silver, 23

— Constant, 18

— D ameH's, 19

— Gaiffe's, 23

— Gravity, 20

— Grenet's, 22

— Leclanche's, 23

— Marie-Davy's, 23

— Pincus', 23

— Srnee's, 21
- Volta's, 16

— Warren de la Eue's, 23

Elements, Modes of joining, to
form battery, 28, 31

Emission of heat, 461
- theory of light, 296

Emmetropic, 383

Eudoscope, 355

Eudosmosis, 252

, Absorption by, 261

affected by hydrochloric acid,

262

Eiidpsmotic equivalent, 256

Equilibrium of liquids in com-
municating vessels, 193

, Stable and unstable, 501

Equivalent of heat, 453

Erb, 163

Ether, Cold produced by evapo-
ration of, 474

Evaporation, 474

Exchanges of gases in lungs, 293

Excitability of nerve affected by
electrotonus, 77

Ex osmosis, 252

Expansibility of gas, 270

Expansion by heat, 464
— , Coefficient of, 465

Extra current, 43

Extraordinary ray, 308

Eye, Aberrations of, 394

, Accommodation of, 383, 3^7 .

as an optical instrument, 374

, Emmetropic, 383

• , Hypermetropic, 388

, Myopic, 389

, Optic axis of, 380

, Optical constants of, 380

, Refraction of, 388

, Visual angle of, 332

Eye-glass, 358

Eye-piece, 359

, Micrometer, 368

of Hartnack (binocular),

370

of Huyghens, 362

Fahrenheit's therniometric scale,

468

Fall hammer, Pflueger's, 68
Falliug bodies, Laws of, 503
Faraday, discovery of induction

currents, 34
Faradisation, 149
, Local and general, of body,

159

Favre, 455. 479

Fick's sprinsr kymographion, 229
Field-glass, 359

Fifth, Interval of, in music, 423
Filtration, 266

520

PHYSIOLOGICAL PHYSICS.

Fizeau's method of calculating

the velocity of light, 299
Fluorescence, 336
Focal distance of lens, 313
of mirror, 303

interval of Sturm, 392
points, 392

Focus of lens, Conjugate, 314
Principal, 315
Real, 315
Virtual, 315

of mirrors, Conjugate, 304
Principal, 303
Real and virtual, 305

Force, 487

, Composition of, 492

— , Electromotive, 17, 27, 120

, Measurement of, 488

, Parallelogram of, 491

, Eepresentation of, 490

, Resultant, 490

Formation of images by lenses,

316

by mirrors, 306

Formula for focal distance of

lenses, 30t»

for ophthalmometer, 396

for size of image formed by

lenses, 318
3J8

formed by mirrors,

of retinal image, 381

for pendulum, 506
for spectacles, 3fe8, 390

Foucault's regulator, 111
Foulis' auto-laryngoscope, 351
Frankland, 455
Franklin, 3

Fraunhofer's lines, 321
Freezing mixtures, 472

point, 467

temperature, 474

Freqiiency of a vibration, 298
Friction, Coefficient of, in diffusion

of gases, 290

key, Galvanic, 55

Frictional electricity, 1

machines, 9

— , Holtz', 9
Frog-heart apparatus of Ludwig,

236

Frog-interrupter, 129
Fundamental colours, 341
Fusion, 470
, Latent heat of, 471

Gaiffe's cell, 23

Galvani, theory cf animal electri-
city, 14

Galvanic battery, 24

current, Effect of in osmosis,

258

elements, 19 et seq.
keys, 54

Galvanism, 149

, Application of, in medicine,

158
Galvanometer, Aperiodic, 110

Astatic, of Nobili, 98

Differential, 103

its use in the measurement

of

resistances, 138

• of temperatui'e, 145
of time, 128

in physiology, HO

— , Reflecting, of Sir W. Thom-
son, ILO

-, of Wiedemann, 105

shunt, 103
-, Tangent, 96

Gas, Absorption of, by liquids,

291
, Coefficient of absorption of,

291

, Compressibility of, 271

, Density of, 273

, Diffusion of. 283

- through porous septa,

290

-, Elastic force or expansibility
of, 270

— , Liquefaction of, 273
— , Olefiant, 462

-, Partial pressure of, in a mix-

ture, 288
— sphygmoscope, 235
— , Unequal compressibility of,

272
-, Weight of, 273

Gaseous state, 270

Gauss' optical constants, 378

Geissler's tubes, 339

Gilbert, 1

Glass, Canary, 337

, Uranium, 337

Glowworm, 339

Graham on absorption of gases

by liquids, 291
on gaseous diffusion, 290

— on liquid diffusion, 249
Graphic method, 170

registration, 170

Gravity, Centre of, 196, etc.

element, 20

, Specific, 197

— , , of pure milk, etc., 206

Grenet's element, 22
Grotthiis, 52

INDEX.

521

of,

Grove's element, 21
Gyrotrope, 59

Hsemadynamometer, 227
Hsematin, Absorption band

327
Hseniosrlobin, Absorption bands

of, 327
, Methods of demonstrating

bands of, 333
Hsernodromometer, 230
Hsetnotachometer, Vierordt's, 232
Hales, 227
Hall, 346, 359
Harmonic series, 436
Hartnack's micro-spectroscope,

329

Harzer, 256
Hauy's bar, 107
Heat, Absorption of, 461
, Amount of, liberated by

body, 482

• , Capacity for, 476

, CondiTCtion of, 456

, Convection of, 458

, Emission of, 461

, Expansion by, 464

, Latent, 471

. , of fusion, 471

-, of vapour, 473

, Mechanical energy converted

into, 452

Equivalent of, 453

, Nature and sources of, 451

, Radiation of, 459

— , Regulation of, of body, 483

, Specific, 476

, , of the animal body,

477

, Unit of, 455

Heidenhain's tetanometer, 74

Height of homogeneous atmo-
sphere, 274

Helmholtz, Colour sensation^
theory of, 343

, Modification of Du Bois'

incluctorium, 47

, Myographion of, 175

on difference tones, 433

- on mixture of colours, 340
— — on visual angle, 382

• on vowel sounds, 449

, Ophthalmometer of, 395

, Ophthalmoscope of, 351

— , Phakoscope of, 385

, Resonators of, 444

, Siren of, 427

Thermo-electric needle of,

Herschell, 334

Homocentric, 391

Hooke, 451

Hoppe Seyler on spectrum of

blood, 328
Hujghen's eye-piece, 362

undulatory theory, 296

Hydraulic press, 190
Hydrodynamics, 188, 207
Hydrometer, Fahrenheit's, 202

, Nicholson's, 202

of constant volume, 203

weight, 203

Hydrokinetics, 188
Hydrostatic balance, 198

— paradox, 191

pressure, 212

Hydrostatics, 188
Hypermetropia, 388

Iceland spar, 397, 402
Idioelectrics, 4
Images, Diffusion, 383

, Formation of, by lenses, 316

, , by mirrors, 306

- — , Real, 307

, retinal, Size of, 381

Size of, formed by lenses,

, formed by mirrors, 308

318

-, Virtual, 307

Imbibition, 246
Inclination of magnet, 93
Indifference point, 91
Induced currents, 35

, Direction of, 36

, Effects of, on muscle,

64
Induction coils, Reymond's, 42

, Ruhmkorfi's, 39

Electric, 34

-, apparatus, 154

Electrostatic, 6
Magnetic, 92
Magneto-electric, 38
-, Apparatus for, 156

Unipolar, 57

147

Insulators, 5
Intensity of colour, 344

of electric current, 25

of light, 301

of sound, 423

Interference of light, 397

of sound, 429

Interrupted currents, Effects of,

on muscle, 65
Intervals in music, 427
Irregular astigmatism, 394
Isotropous, 402

522

PHYSIOLOGICAL PHYSICS.

Jolly, 256

Joule's equivalent, 452

Katelectrotonus, 82, 86

Kations, 52

Katode, 52

Keys, Galvanic, 54

, , Contact or spring, 55

, , Friction, of Du Bois-

Reyuiond, 56

-, Mercury, 54

Kirchhoff, 322

Klangfarbe, 435

Kleist's jar, 12

Koenig's appai-atus for analysing

sound, 447

stethoscope, 422

Kronecker's cauule for frog-heart,

236

Kiiss, 267

KyrnographioH, Fick's, 229'
, Lud wig's, 228

Lactodensimeter, 206.

L-ictometer, 206

Lanipyre, 339

Laplace, 479

Laryngoscope, 349
- of Foulis, 351

Latent heat of fusion, 471
- of vapour, 473

period of stimulation, 129,

177

Lauder Brunton's meth'od of ex-
perimenting on frog-heart, 238

Lavoisier, 479

Law of contraction, 87 et seq.

of falling bodies, 503

of Leuz, 36

Leclauch^'s element, 23, 150

Length, Standard of, 485

Lenses, Aberrations of, 34i

- — -, Achromatic, 347

Collimating, 330

Focal distance of, 316

Foci of, 313 et seq.

— — Formation of images by, 316

Forms of, 312

Immersion, 362

Size of image formed by, 318

Lena' law for induction currents.

36, 38
Leslie, 463
Leuwenhoech, 357
Levers, 494

in human body, 507

Leyden jar, 11

L ebig on dialysis, 261

on imbibition, 247

action in

of

Liebig on osmotic

absorption, 264
Li^bt, Analysis of, 319

Double refraction of, 397
Intensity of, 301
Interference of, 406
Nature of, 296
Polai-isation of, 401
Recomposition of spectrum
320

Reflection of, 301
Refraction of, 308 et seq.
Spectrum of, 319
Theories of, 296
Velocity of, 299
Vibrations of, 297
Lippmann's capillary electro-
meter, 244
Liquids, Absorption of, 261

, of gases by, 291

, Adhesion of, 240

and capillary action, 241

, Cohesion of, 188, 239

, Diffusion of, 248

, Equilibrium of, in communi-
cating vessels, 193

. Filtration of, 266

, Flow of, in uniform tubes,

211

, , in bent tubes, 214

, — — , in capillary tubes, 215

, , in elastic tubes, 216, 220

, , in ramified tubes, 215

, , in tubes of varying

diameter, 214

— , Point of saturation of, 248
— , Specific gravity of, 197
— , Surface tension of, 240

, Transmission of pressure by,

189

, Transudation of, 266

, Upward pressure of, 192

, Velocity of efflux of, 208

Liquefaction of gas, 287
Listing's values for cardinal points

of the human eye, 380
Listen, 349
Loadstone, 90
Local aneesthesia, 474
Localised faradisation, 159
Ludwig's frog-heart apparatus,
236

kymographion, 228

observations on endosmotic

equivalent, 256
Luminiferous ether, 296
Luminous bodies, 299
Lungs, Exchange of gases in,
293

INDEX.

523

M ichines, Electrical, 8
, Frictional, 9

— , , Holtz', 9

Magnesium, Phosphorescence of,

339
Magnetic attraction, 91

- inclination, 93

induction, 92

keeper, 93

• magazine or battery, 93

needle, 93

-, Astatic, 98

repiilsiou, 91

Magnetisation, Methods of, 92

— , Permanent, 92
Magnetism, Residual, 53

— , Theories of, 92
Magneto-electric induction, 38?

156
Magnets, 90

, Accessory, 107

, Action of electric currents

on, 94

, Artificial, 90

- — , Care of, 94
— , Electro-, 53

, Induction by, 38

, Natural, 90

, Permanent, 92

, Production of, by currents,

53

Manometers, 227
Manometric flames, 446
Marey's cardiograph, 230

chronograph, 173

• heart forceps, 238

method of registration, 185

et seq.

myograph, 178

pantograph, 187

sphygmograph, 233

sphygmosc^pe, 234

tambour, 185

• vibrating stylet for chrono-
graph, 173

Marked pole, 91

Marriotte's bottle, 238

law, 271

• tube, 272

Matteucci, 112

Mayer, 452

McKendrick's capillary electro-
meter, 244

Measurement of bodies (length
and weight), 485

of electromotive force, 120

of force, 4S8

• of quantity of heat, 479

of resistance, 134

Measurement of temperature, 146,

465
of time by chronograph, 173

by galvanometer, 128

Mechanics of circulation, 222
Mechanism of absorption, 261

of circulation , 222

of filtration, 266

of inspiration, 284

of expiration, 284

of secretion, 266

• of transudation, 266

Melloni's experiments on heat,

463

Melting point, 470
Mercurial manometer, 227

— thermometer, 466
Mercury key, 54
Methgeinoglobin, Absorption band

of, 328

Metronome, 71
Micrometer for eye-piece of micro-

scope, 368

— for stage of microscope, 363
Microscopes, Aberrations in, 359

— , Binocular, 369 etseq.
, Compound, 358

— , Drawing apparatus for, 371
, Measurement of magnifying

power of, 366

of actual size of object

under, 368

, Mechanical parts of, 363

, Simple, 356

Microphotography, 373
Microspectroscope, 329
Microspectroscopic examination

of blood, 331

•— of urine, 333

Mirage, 309

Mirrors, Aperture of, 303

— , Axis of, 303

— , Centre of curvature of, 303

, Concave, 303

, Convex, 305

, Foci of, 305

— , Formation of images in, 306

, Laryngoscopic, 350

, Radius of curvature of, 303

— , Size of image of, 308
Mixture of colours, 340
Moist stimulation tube, 61
Multiple arc, 28
Multiplier, Schweigger's, 96
Muscle current, 117

, Measurement of, 120

— , Negative variation of, 118

, Curve of contraction of, 179

. of fatigue of, 179

524

Pit YSIOL OGICA L PHYSICS.

Muscle, Experiments on stimula-
tion of, 62 et seq.

, Inherent irritability of, 75

, Latent period of stimulation

of, 129, 177

, Law of contraction of, 89

preparation, 63

, Secondary contraction of, 72

telegraph, 62

Myogrnph, Pick's, 180

Helmholtz's, 175

Marey's, 178

Pendulum, 180

Pflueger's, 175

Simple, 175

Myopia, 388

Myopolar, 82

auelectrotonus, 86

katelectrotonus, 86

Nebenschliessung, 56
Needle, Magnetic, 93
, Thermo-electric of Helm-

holtz, 147
Neef's hammer, 42
Negative electricity, 3
phase of electromotive force

of muscle current, 127
variation of muscle current,

118
Neutral tint reflector, Beale's, 367

— - zone, 91
Newton's rings, 408

theory of light, 296

Nicol's prism, 399
Nicholson's hydrometer, 201
Nobili's galvanometer, 97

law of contraction, 87

thermo-electric pile, 144

Nodal points, 378
Nodes, 437
Non-conductors, 4
Nou-polarisable electrodes, 119

Octave, 428
Oersted, 94
Ohm, The 34

, Law of, 27

Olefiant gas, Atherrnancy of, 462
One-fluid theory of electricity, 3
Opaque, 461
Open organ pipe, 443
Ophthalniorneter, 395
Ophthalmoscope, 351

, used without lenses, 352

, with erect image, 353

, with inverted image, 354

Optical axis of the eye, 380
centre, 313

Optical constants of Gauss, 378

instruments, 349 et seq.

instrument, The eye as an,

374

Ordinary ray, 398
Organ pipe, 445
Osmometer, 252
Osmosis, 251
Otoscopes, 422
Overtones, 438
Oxyhsemoglobin, Absorption

bands of, 326

Pantograph," 187
Paradox, Hydrostatic, 191
Parallel forces, 493
Parallelogram of force, 491
Paramagnetic, 94
Partial notes, 438

pressure of a gas, 288

Pascal's law, 189

Pendulum, Myographion, 180

, Simple, 505

Period of vibration, 296

Periodic time of'pendulum, 50o

Peripheral lesion, 162

Pfaff, 87

Pflueger's law of contraction, 87

myograph, 175

trip or fall hammer, 68

Phakoscope of Hemboltz, 3S5
Phase of vibration, 298
Phosphorescence, 336—338

of sea, 339

Photography, 336, 348
Physiological optics, 296
Piezometers, 189, 212, 226
Pile, Voltaic, 14

, Forms of (See Element)

Pipette, 279
Pincus' cell, 23
Pitch of sound, 423
Pith-ball, 3
Plane mirrors, 301, 350

polarised light, 401

Poggendorff's compensation

method, 120
Point, Boiling, 467, 471

, Freezing, 467

of fusion, 470

— of saturation of liquids, 248
Points of derivation, 32
Poiseuille's experiments on flow

of fluids in capillary tubes, 215

— baemadynamometer, 227
Polarisation of electrodes, 111
of light, 397

— , Angle of, 404
by reflection, 403

INDEX.

525

Polarisation of light, Circular, 411

, Plane, 401

, Plane of, 404

, , Rotation of, 410

of plates in galvanic element,

17

Polariscope in physiology, 408
Polarised light, Behaviour of

muscle in, 408
Polariser, 402
Poles or electrodes, 17

for xise in therapeutics, 157

of magnets, 91

Porous septa, Diffusion of gases

through, 290
Positive electricity, 3
— phase of muscle current, 127

wave in liquids, 217

Potential, 13

, Difference of, 13

Presbyopia, 388

•, Spectacles for, 388

Press, Hydraulic, 190
Pressure, Atmospheric, 274

, Blood, 2.J1

, .Estimation of, 226 et feq.

by liquids, Transmission of,

189

, Hydrostatic, 212

of carbonic acid gas in lungs,

293

of oxygen in lungs, 2°3

, Partial,flof a gas, 288

, Resultant, 192

Upward, 192

» — J. 7

Primary circuit, 35

coil, 35

colours, 342

- tone, 437

Principal axis of lens, 313
• of mirror, 303

planes of Iceland spar, 399
points, 378

Principle of Archimedes, 195

of TorriceDi, 207

Prisms, 312

for binocular microscopes, 370

Production of the voice, 448
Propagation of waves, 217

, Speed of, 218

Pulleys, Movable, 498

— , Single, 497
Pulse alarm, 235

, Suotty character of, 226

tracings, 225

Pulvermacher's chain pile, 153

Pump, Air, 230

, , Sprengel's, 282

— , Suction, 278*

Punctum proximum, 387

remotum, 387

Purkinje's images, 386

Quality of compound colonr, 344

of musical sounds, 434

Quartz, Effect of, on polarised

light, 411
plate of Soleil, 414

Radiation of heat, 459

Radius of curvature of cornea, 380

of crystalline lens, 380

of mirror, 303

Range of accommodation, 387
Rankin, 451

Rapidity of nerve current, 129, 177
Ray, Extraordinary, 398

— , Ordinary, 398
Real foci of lens, 315

of mirror, 305

image formed by lens, 3f7
formed by mirror,,'306

Reaumur's thermometric scale,

468

Receiving tambour, 186
Recomposition of rays of white

light, 320
Reflection of light, 301

, Angle of, 301

by mirrors, 301 et seq.

, Laws of, 301

Reflector, neutral tint, Beale's,

373
Refraction, Double, 397

of eye, 380

, Anomalies of, 388

of light, 308

, Angle of, 310

by plate with parallel

faces, 311

by a prism, 311

, Index of, 310

, Laws of, 310

Refrangibility of different rays of

spectrum, 320
Registering tambour, 186
Registration, Graphic methods of,

170 et seq.
Regnault, 272

Regulation of animal heat, 483
Repulsion, Electiic, 5

, Magnetic, 91

, Mutual, of electric currents,

37

Reservoir, Charge of, 213
Residual magnetism, 53
Resinous electricity, 2
Resistance, 26

PHYSIOLOGICAL PHYSICS.

Resistance box, 136

External, 26

Internal, 26

Measurement of, 138

of fluids, 136

Secondary, 113

Unit of, 33

Resolution of forces, 492
Resonance, 441
Resonator, 442

, Forms of, 443

, Helmholtz', 444

Re&ultant force, 490

pressure, 192

tone, 433 .

Betinnl image, Size of, 381

Rheocord, 77

Rheophores, 149

Rheostat of Wheatstone, 135

Rheotrope, 59

Ritter, 87, 335

Rock salt, 462

Rotation of plane of polarisation,

410

Round compensator, 124
Ruhmkorff's coil, 39
Rumford, 451, 460

Saccharimeter, 413

, Soleil'e, 415

, Use of in medicine, 415

Salimeter, 203—4
Saturation of colour, 344

point of liquid, 248

Scheiner's experiment, 384
Schmidt's experiments on nitra-
tion, 267
Scheele, 335

Schweigger's multiplier, 96
Secondary axis, 303, 313

circxiit, 35

colours, 342

contraction, 72

- resistance, 113
Seebeck, 142, 335
Selligues, 359
Seyler, Hoppe, 326
Short circuit, 48, 56
Shunt for galvanometer, 103
Siemens' unit of resistance, 33
Signal, Electric, 172
Silbermann, 455, 479

Siren of Cagniard de la Tour, 42 I

- of Dove, 428

— , Double, of Helmholtz, 427
Sitting, Dynamics of, 511
Sledge inductor, 43
Smee's element, 21
Suelleu's types, 383

Soleil's quartz plate, 414

saccbarimeter, 415

Solubility, Coefficient of, for gas,

291

Sorby's cell for spectroscope, 331
Sound, Analysis of, 446

, Intensity of, 423

, Interference of, 429

, Musical, 423

, Nature of, 417

, Pitch of musical, 423

, Quality of musical,

, Rarefaction of, 418

, Reflection of, 421

— , Refraction of, 421
, Transmission of by tubes,

421

, Vowel, 450

, Wave of condensation of, 418

, of rarefaction of, 418

Spamer's medical induction appa-
ratus, 154
Specific gravity, 197

of auiinal fluids, 208

heat, 476

Spectroscope, 323

for direct vision, 330

- in physiology, 326
Spectrum, 319
- — analysis, 323

, Dark lines of, 321

, Effects of, 334

— , Theory of, 320
Speed of blood stream, 320
Spherical aberration of the eye,

394

of lenses, 347

mirrors, 302

, Foci of, 303 et set],

, Formation of images in,

306

, Reflection by, 303 et seq.

Spheroidal state, 475
Sphygmograph, 233
Sphygmophone, 235
Spbygmoscope, 2:34
Spreug 1's air pump, 2S2
Stable equilibrium, 501
Stage micrometer, 366. 3(58
Standard of length, 485

of weight, 486

Standing, Dynamics of, 570
Stethoscopes, 422

, Konig's, 422

Stimulation of muscle, 67

, Latent period of, 177

of nerve, 62

, Mechanical, 73

tube, 61

INDEX.

527

Stuhrer's battery, 150

Stokes, 322, 326

Stopped tube or pipe, 443

Stromuhr, Ludwig's, 231

Sturm, Focal interval of, 392

Suction pump, 278

Sulphate" of quinine, Phosphor-
escence of, 336

Sulphide of calcium, Phosphor-
escence of, 339

of strontium, Phosphores-
cence of, 339

Surface tension, 240

Symmer, 3

Sympathetic vibration, 439

Syphon, 279

barometer, 277

System of refractive media, 377

Tambour of Marey, 185
Tangent galvanometer, 96
Temperature, 465
, Measurement of by galvano-
meter, 146

by thermometers, 468

Tension, Arterial, 221, 224

, Electric, 6, 25

Tetanic contraction, 67

Tetanometer, 73

Thermal capacity, 476

effects of electric current,

50
unit, 454

Thermo-electric currents, 142

needle, 147

pile, 144

series, 143

Thermometers, 466

Thermometric scales, 468

Thermometry, 464

Thomson's, Sir Wm., galvano-
meter, 99

Thyro-arytenoid muscles, 449

Thyroid cartilage, 448

Timbre of musical sounds, 435

Torricellian experiment, 276

Tourmalin, Polarisation by, 4 3

Trade winds, 459

Train of prisms, 325

Translucent, 299

Transparent, 299, 461

Transmission of movement 184

of pressure, 189

Transudation, 266

Triplet, 361

Troughs for galvanometer, 114

Tubes, Capillary, 215

, Elastic, 216

, Flow of liquids in, 211

Tubed, Rigid and elastic com-
pared, 220
Tuning fork, 44 1

for chronograph, 173

Two-fluid theory of electricity- 2
Tj ndall, 335, 453, 463

Ultra-red rays, 335
Ultra-violet rays, 336
Undulatory theory of light, 29S
Unipolar induction, 57
Unit of electromotive force, 17

of resistance, 33

, Thermal, 454

Unpolarisable electrodes, 111
Unstable equilibrium, 501
Upward pressure, 192
Urari, 75
TJrinometer, 205

Vaporisation, 470
Vapour, Latent heat of, 473
Variation of muscle-current, 118
Velocity of efflux, 208

of light, 299

Vena contracts, 209
Ventral segments, 437
Vibrating style of Marey, 173
Vibration, Amplitude of, 298

, Frequence of, 298

of a pendulum, 506

-, Time of, 508 .

of a string, 437

, Period of, 297

, I'hase of, 298

, Sympathetic, 439

Vierordt's haemotachometer, 2'>2

sphygmograph, 233

Virtual foci of lens, 315
of mirror, 305

image r f lens, 318
of mirror, 307

Visual angle, 382

Voice, Production of, 448

Volkmann's haemodromometer,

230

Volt, 17
Volta, 14
Voltaic couple, 16

pile, 14

Voltameter, 51
Vowel sounds, 450

Wagner's hammer, 42
Walking, Dynamics of, 511
Warren de la Rue's element, C3
Water calorimeter, 479
Waves, character of, 217
, Compound, 435

PH 1 7siOL OGICA L PHYSICS.

Waves, Extent of, 218

, Height of, 219

, Length of, 298

of muscular contraction, Re-
gistration of, 184

of pulse, 225

of sound, 418

, Positive and negative, 217

, Propagation of, 217

-, Registration of, by graphic

method, 217
Weight of g.is, 273

, Standard of, 486

Wenham's binocular prism, 370
Wheatstone's bridge, 138
rheostat, 135

Wheatstone's revolving mirror,

447

Wheel barometer, 277
Wiedemann's boussole, 104
Wittich, Von, 267
Wollaston's camera lucida, 371

doublet, 358

experiment on freezing by

evaporation, 475

Young, 170, 296, 393, 433, 451
Young-Helmholtz' theory of colour
sensation, 343

Ziemssen, 163

Zeiss' microscope, 329

CASSELL & COMPANY', LIMITED, BELLF SAUVAUE WORKS, LONDON, E.G.