I/ONDOW

WALTON AND MABERLY,

UPPER GOWER STREET & IVY LANE.

Price Eighteenpence.

•IIIIIIV

LIBRARY

UNIVfRSITY Of
CALIFORNIA

EDITED BT

DIONYSIUS LAEDNEE, D.C.L.,

Formerly Professor of Natural Philosophy and Astronomy in University College, London.

ILLUSTRATED BY ENGRAVINGS ON WOOD.
VOL. Y.

LONDON :
WALTON AND MABERLY,

UPPER GOWER STREET AND IVY LANE, PATERNOSTER ROW.
1855.

LOAN STACK

I.ONDOK
BRADBI7BT AND EVANS, PFINTERS, WHITKF?MAR«.

(pill

L'37

+5

CONTENTS.

THE STEAM ENGINE.

PAQK

CHAP. I. — 1. The steam engine. — 2. Consists of two essential parts.
— 3. The boiler.— 4. Material employed in its formation. — 5.
Feeding apparatus. — 6. Importance of keeping the water in the
boiler at a proper level. — 7. Wet and dry steam. — 8. Priming. —
9. Means of ascertaining the level of the water in the boiler. — 10.
Self-acting feeders. — 11. Safety valve. — 12. Steam gauge. — 13.
The furnace. — 14. Proper mode of feeding the furnace. — 15.
Rarely observed. — 16. Contrivance for supplying fuel . . 1

CHAP. II. — 17. Method of regulating the activity of the furnace. —
18. How steam is made to produce a mechanical effect. — 19. The
cylinder and piston. — 20. Metallic pistons. — 21. Estimate of the
force with which the piston is moved. — 22. Transmission of this
force. — 23. Piston rod. — 24. Cocks, valves, and slides. — 25.
How employed. — 26. Stroke of the engine. — 27. Effective pres-
sure.— 28. Supply of steam to the cylinder. — 29. By valves. —
30. By slides.— 31. Seaward's slides.— 32. Single cock.— 33.
Four-way cock. — 34. Low and high pressure, more properly
called condensing and non-condensing, engines. — 35. Objections
to the latter and countervailing advantages. — 36. Condensing
engines. — 37. Condensing apparatus. — 38. Air-pump. — 39. Cold
water pump. — 40. Hot water pump . . . . .17

CHAP. III. — 41. Comparative merits of the two kinds of engines. —
42. Various modes of transmitting force. — 43. Description of a
factory engine. — 44. The governor. — 45. The eccentric. — 46. The
fly-wheel. — 47. Parallel motion. — 48. Barometer gauge. — 49.
How to compute the effective moving force of the piston. — 50.
Method not considered sufficiently accurate. — 51. Indicator. —
52. Mode of recording its positions. — 53. Its application in
finding effective force. — 54. Watt's counter. — 55. Conclusion . 33

THE EYE.

CHAP. I. — 1. Pleasures and advantages of the power of vision. — 2.
Reasons why a knowledge of the structure and functions of the
eye is desirable. — 3. Description of the eye. — 4. Sclerotica and

370

CONTENTS.

cornea. — 5. Aqueous humour, pupil, and Iris. — 6. Crystalline
humour and ciliary processes. — 7. Choroid. — 8. Ketina and
vitreous humour. — 9. Axis of the eye and optic nerve. — 10.
Numerical data. — 11. Limits of the play of the eye. — 12.
Achromatism of the eye. — 13-16. How vision is caused. — 17.
Conditions of perfect vision. — 18. Distinctness of the image. —
19. Parallel rays. — 20, 21. Defects of vision and their remedies.
— 22-24. Power of adaptation. — 25-29. Limits of this power. —
30, 31. — Causes of defective vision. — 32. Magnitude of the image
on the retina. — 33. Apparent magnitude defined. — 34-37. Nature
of its variation. — 38-40. Diminutiveness of the pictures on the
retina. — 41. Sufficiency of illumination .....

49

CHAP. II. — 42. Power of accommodation of the eye. — 43, 44. Apparent
brightness of luminous objects. — 45-47. Intensity of brightness.
— 48-57. The image must continue a sufficient time upon the
retina to enable that membrane to produce a perception of ifc —
Various illustrations of this. — 58. Conditions which determine
apparent motion. — 59. How affected by distance. — 60. Example.
— 61. When imperceptible. — 62. Motion of the firmament. — 63.
Objects in rapid motion invisible. — 64-66. Duration of the im-
pression on the retina. — 67. Optical toys. — 68, 69. Coincidence
of the optical and geometrical centres of the eye. — 70. Ocular
spectra and accidental colours. — 71. Why visible objects do not
appear inverted. — 72. The seat of vision.' — 73-75. The optic
nerve insensible to light .65

CHAP. III. — 76. Why objects-are not seen double. — 77. Exceptional
cases. — 78. The eye has no direct perception of distance or mag-
nitude.— 79. How distances are estimated. — 80. Appearance of
the sun and moon when rising or setting. — 81. How magnitudes
are estimated. — 82. Illusion produced in St. Peter's at Rome. —
83. Magnitude inferred from distance. — 84. Perception of angular
motion. — 85. How real direction of motion may be inferred. — 86.
Examples of the sun and moon. — 87-90. Effect of the motion of
the observer — Examples. — 91. Angular distance defined. — 92.
The eye has no direct perception of form — How inferred. — 93.
Visible area defined. — 94. Figure inferred from lights and
shadows. — 95. Power of distinguishing colours. — 96,97. Absence
of this power in particular cases 81

THE ATMOSPHERE.

Experimental proofs of the weight of the atmosphere. — 2.
bladder glass. — 3. Pressure equal in all directions. — 4. Pressure
of air in a room explained. — 5. Magdeburg hemispheres. — 6.
Suction with tube. — 7. Pascal's experiment at Rouen. — 8. Horror
of a vacuum. — 9. Galileo and the pump-makers. — 10. Torricelli's
celebrated experiment. — 11. Pascal's experiment on the Puy-de-
ddme. — 12. Actual pressure of atmosphere ascertained. — 13.
Height of an atmosphere of uniform density. — 14. Vastly greater

The

CONTENTS. T

PAGE

height of an elastic atmosphere. — 15. Air less and less dense in
ascending. — 16. Effects of atmospheric pressure. — 17. Boy's
plaything of a sucker. — 18. Flies walking on ceiling. — 19. Res-
piration.— 20. Action of bellows. — 21. Ventpeg — lid of tea-pot.
— 22. Pneumatic ink-bottle. — 23. Syringes. — 24. Exhausting
syringe. — 25. Eate of rarefaction. — 26. Absolute vacuum cannot
be obtained. — 27. But may be indefinitely approached. — 28. Air-
pump. — 29. Condensing syringe. — 30. Condenser . . .97

COMMON THINGS.— TIME.

CHAP. I. — 1. Simple notions difiicult to define. — 2. Conception of
Time, how obtained. — 3. By succession of sensible impressions. —
4. Proof that such succession is necessary. — 5. Time passes faster
with some than with others. — 6. Is measured only by a regular
and uniform succession. — 7. Periodic phenomena which may
measure time. — 8. Natural appearances intended for that purpose.
— 9. Significations of the word "day." — 10. Hours. — 11. Their
length in certain cases variable. — 12. Vulgar and equinoctial
hours. — 13. Commencement of the day with different nations.
— 14. Italian time. — 15. Inconvenience of such a mode of
reckoning. — 16. Modern method. — 17. Civil and astronomical
time. — 18. The day the standard unit. — 19. Necessary to deter-
mine it rigorously. — 20. What is a day ? — 21. Diurnal rotation
of the heavens. — 22. Its constancy and uniformity. — 23. Never-
theless not fitted to be the unit of civil time. — 24. The meridian.
—25. Diurnal motion of the sun — means of observing it. — 26.
Transit instrument. — 27. Method of observing with it. — 28.
Sidereal day — its subdivisions. — 29. Its permanency and uni-
formity— unfit, nevertheless, for a measure of time. — 30. Why
the sun is not fit 113

CHAP. II. — 81. How to observe the sun's transits. — 32. Interval
between them variable. — 33. Mean and apparent time. — 34.
Relative changes of mean and apparent time. — 35. The daysron
which they coincide. — 36. The Equation of time. — 37. Further
explained. — 38. Its extreme error. — 39. Mean time adopted in
France. — 40. Unfitness of apparent time. — 41. Local time varies
with longitude. — 42. Equalisation of local time proposed. — 43.
How time-pieces are regulated. — 44. Mean solar hours, minutes,
and seconds. — 45. Length of sidereal day. — 46. The week. — 47.
Opinions as to its origin.- — 48. Both opinions erroneous. — 49.
Origin of the names of the days. — 50. First day of the week. —
51. The month 129

CHAP. III. — The month (continued). — 52. Not conformable with lunar
periods. — 53. Difficulty of subdividing the year. — 54. Division
unequal. — 55. Egyptian months. — 56. Greek. — 57. Solon's
months. — 58. Roman months. — Romulus. — 59. Origin of names
of months. — 60. Additional months of Numa. — 61. Origin of
their names. — 62. Their lengths. — 63. Superstition in favour of

vi CONTENTS.

PACK

odd numbers — methods of remembering the lengths of the
months.— 64. Calends.— 65. Greek Calends.— 66. Nones.— 67.
Ides. — 68. Practice of counting backwards. — 69. Discordance of
the Roman year with the seasons. — 70. Month Mercedonius. —
71. Legal meaning of "month." — 72. The year. — 73. What is
a year ? — 74. Egyptian. — 75. Only a rude approximation to the
course of the seasons. — 76. The vague year and Sothic period. —
77. Advantage of Egyptian year. — 78. Greek year.— 79. Meton
and his cycle. — 80. Origin of Golden Number. — 81. Meton
ridiculed by Aristophanes. — 82. Near accordance of the lunar
phases with the Metonic cycle. — 83. Roman year. — 84. Pontifical
abuses. — 85. Julian Calendar. — 86. Bissextile years . . . 145

CHAP. IV. — 87. Year of confusion. — 88. New arrangement of the
months.— 89. Mistake of the Pontiffs.— 90. Leap-years.— 91.
Historical dates.— 92. Day of the equinox. — 93. What is the
equinox? — 94. The two equinoctial points. — 95. Sidereal year.
— 96. Precession of the equinoxes. — 97. Equinoctial year. — 98.
Civil year. — 99. Difference between it and the Julian year. — 100.
Effect of this difference. — 101. Cause of the reformation of the
Calendar. — 102. Discordance between the real and ecclesiastical
equinox. — 103. Gregorian reform. — 104. Gregorian Calendar. —
105. Its compensating effect. — 106. Resistance to its adoption.
— 107. Dates of its adoption in different countries. — 108. In
England. — 109. Its reception there. — 110. Occasional agreement
of the new and old styles. — 111. Anecdotes relating to the
change. — 112. Russia adheres to the old style. — 1 13. Commence-
ment of the year. — 114. Various in different countries. — 115. In
England. — 116. Old and new style in England. — 117. Temporary
inconvenience attending it 161

COMMON THINGS.— PUMPS.

1. Earliest methods of raising water. — 2. Bucket in a well. — 3. By
windlass and rope. — 4. By two buckets balanced over a pulley. —
5. Method of working these by animal power. — 6. The rope in
this case balances itself. — 7. The lifting pump. — 8. Double
lifting pump worked by animal power. — 9. Various forms of
valves. — 10. Clack valves. — 11. Conical spindle valves. — 12.
Ball valves. — 13. The suction pump. — 14. Analysis of its action.
— 15. Forcing pump. — 16. Same with air vessel. — 17. Same with
solid plunger. — 18. Double action forcing pump. — 19. Garden
watering pumps. — 20. Fire-engine. — 21. Chain pump. — 22.
Drainage of mines 177

COMMON THINGS.— SPECTACLES.

1. Their general utility. — 2. Should therefore be generally understood.
— 3. Vision. — 4. Blindness. — 5. Defective sight.— 6. Long and
short sight. — 7. Remedy. — 8. Spectacles. — 9. Effect of convex
lenses. — 10. Of concave lenses. — 11. Focal length of a lens. — 12.

CONTENTS. Tii

PAG*

Varies with distance of object. — 13. Peculiarities of vision in short
sight explained, — 14. In long sight. — 15. The mounting of spec-
tacles.— 16. Periscopic spectacles. — 17. Both eyes have not
always the same power of vision. — 18. Ophthalmometer. — 19.
Application in selecting glasses. — 20. Curious defects of vision . 193

THE KALEIDOSCOPE.

1. Origin of the name. — 2. Structure of the instrument. — 3. Its optical
effect. — 4. Varieties of its form. — 5. Its occasional use in the
arts. — 6. Another optical toy depending on two reflections . 205

DOUBLE ACTING ENGINE, ZINC WOKKS, CITY ROAD, LONDON.

THE STEAM ENGINE.

CHAPTER I.

1. The steam engine. — 2. Consists of two essential parts. — 3. The boiler.
— 4. Material employed in its formation. — 5. Feeding apparatus. —

6. Importance of keeping the water in the boiler at a proper level. —

7. Wet and dry steam. — 8. Priming. — 9. Meansof ascertaining the level
of the water in the boiler. — 10. Self-acting feeders. — 11. Safety valve.
— 12. Steam gauge. — 13. The furnace. — 14. Proper mode of feeding
the furnace. — 15 . Rarely'observed. — 16. Contrivance for supplying fuel.

LARLNER'S MUSEUM OP SCIENCE. B 1

No. 53.

THE STEAM ENGINE.

1. WHET* the prodigious impetus given to civilisation all over
the world, during the last hundred years, by the invention and
improvement of the steam-engine is considered, and when it is
observed that this, so far from being a temporary influence, is one
that has constantly gone on, and still goes on with augmented and
vastly accelerated energy,

Mobilitate viget viresque acquirit eundo,

it cannot be matter of surprise, that every one endowed with the
most moderate gifts of sense and intelligence, whatever may be
his position on the social scale, is animated with a strong desire to
obtain some knowledge of the extraordinary machine by which
results of such vast, enduring, and wide-spread importance have
been attained.

Though comparatively few have the time, the inclination, or
the peculiar intellectual aptitude to follow out the details of the
mechanism of this great invention, as developed in its numerous
applications to the various arts of life, all who are by circum-
stances and education raised above the condition of the rudest
and most unskilled labourer have both the time and the mental
qualifications to acquire a general acquaintance with the machine,
and with the physical principles from which it derives its power.
To this large class we now address ourselves, and propose to
present them in a very brief compass with a general view of the
principle and mechanism of the steam-engine, confining ourselves
chiefly to those broad and general features which are common to
all varieties of the machine, and discarding for the present
such minute details of the mechanism as are applied only
in particular forms of steam-engine, and which, though often
admirable for ingenuity of design and contrivance, are neverthe-
less subordinate in interest when brought beside the larger
and more general views we now refer to.

2. The steam-engine, whatever be its form or purpose,
consists of two essentially different parts ; the first, that in which
the steam is generated, and the second, that in which the steam is
worked. Although these taken together are essential to the per-
formance of the machine, thename steam-engine in its strictest sense
would signify only the latter, the former being called theboiler.

3. Boilers vary much in magnitude, form, structure, and even
in material, according to the purpose to which they are applied,
and the circumstances under which they are used. There are,
however, certain characters common to all.

Every boiler consists of a reservoir for the water and steam, and
a furnace with its appendages for the combustion of the fuel, the
heat evolved from which is the physical agency by which th

iicn the

THE BOILEE,

evaporation is produced and maintained. The boiler is formed of
plates of metal, of suitable thickness, rivetted together, so as to
be steam-tight, that is to say, so that steam cannot be forced be-
tween them.

The manner in which the plates are rivetted together is shown
in fig. 1, the edges of the plates being laid one upon the other
and their surfaces forced Fig. 1.

into steam-tight contact by y <j<*

rivets r r' passing through ^.^.....^.^nn,,,^^:^^^
holes punched in them, the y T'

heads of the rivets being formed by the hammer while the iron is
still soft by heat.

The appearance of the rows of rivets along the edges of the
plates composing the boiler is shown in the general view of a
waggon-boiler in fig. 7.

4. The material of the boiler is most commonly wrought iron.
Copper is sometimes though very rarely used. It has an advan-
tage over iron, inasmuch as it is a better conductor of heat, and
is less liable to become incrusted by lime and other earthy matter,
which is always held in solution by the water, and precipitated
in the process of evaporation. It is also more durable than iron,
but is excluded, save in, rare and exceptional cases, because of its
greater cost.

Cast iron, though cheaper than wrought iron, would be inadmis-
sible for several reasons, one of which is its brittleness. If
explosion happened it would fly in pieces, the fragments becoming
destructive missiles. In case of explosion wrought iron would be
ripped and torn. The one is tough, the other brittle.

5. The boiler is a reservoir not only for water but for steam.
The steam, being much lighter, bulk for bulk, than water will always
ascend in bubbles through the water, and will collect in the upper
parts of the boiler. The space within the boiler, therefore, may be
conceived to be divided at a certain level between the water and
the steam. All the space below that level is appropriated to the
water, all above it to the steam.

But according as the water is converted into steam, the quantity
contained in the boiler being proportionally diminished, this level
would fall continually lower and lower. That, however, is pre-
vented by a FEEDING APPARATUS, which generally consists of
forcing pumps, of adequate power, by which as much water is
driven into the boiler as is converted into steam by the furnaces.
This feeding apparatus is, in some cases, worked only from time
to time to replenish the boiler, in other cases the supply is con-
tinual. In the former case, the level which separates the steam
from the water alternately rises and falls within certain limits.

B 2 3

While the action of the feeding apparatus is suspended it falls
gradually as the evaporation proceeds. When it has descended to
a certain point the feeding apparatus is put in action and the level
rises again to its former limit, after which it is again suspended,
and so on. This rise and fall of the level of the water in the
boiler is, or ought to be, restrained between such limits, that tho
level is never either injuriously high or injuriously low.

When the feeding apparatus works incessantly, the water in tho
boiler is kept always at the same level, the arrangements being
such that by a self-adjusting mechanism, the quantity of water
supplied to the boiler, from minute to minute, is exactly equal to
the quantity evaporated.

6. The importance of keeping the boiler duly supplied with
water will be easily understood. So long as those parts of tho
boiler which are exposed to the action of the furnace are filled
with water the metal can never become unduly heated, because all
the heat imparted by the furnace is absorbed by the water in
evaporation. But if the level of the water were allowed to sub-
side below any part which is exposed to the action of the furnace,
the heat acting upon such parts not being taken up by the water,
and the steam which in that case would alone be in contact with
them, being a slow recipient of heat, the plates of the boiler would
soon become red hot, and would consequently be softened, so as
no longer to possess the strength necessary to resist the pressure
within them, and the boiler would burst. For this reason, it is
always of the utmost importance to provide means to ensure such
a supply of water as shall prevent the level from ever falling
below the highest parts upon which the furnace acts.

Inconvenience of a different kind would be produced by over-
feeding, and consequently by raising the level of the water above
a certain limit. When the water in a boiler is in a state of strong
ebullition, which it always is in the boilers of engines in full
operation, bubbles of steam are produced in great quantities in
the lowest parts, these being the parts upon which the action of
the furnace is most energetic. These bubbles, rising with violenca
to the surface, throw up the water in spray, so that the part of
the boiler above the level of the water is filled with a mixture of
pure steam and of particles of water in minute subdivision. The
latter, however, fall back into the water by their gravity, provided
that the space left for the steam have sufficient height. The
upper part of that space will then be supplied with pure steam
without intermixture with spray. But if the boiler be over-filled
with water, so that the space left for the steam have so little
height that more or less spray is mixed even with the highest
parts of it, this spray will be drawn into the working part of the

PJRIMING — GAUGE-COCKS.

machine, and will be attended with the two-fold evil of injuring
the performance of the engine and wasting a quantity of heat
which would otherwise be employed in producing steam, and
therefore producing mechanical power.

7. Nevertheless with all practicable precautions spray some-
times issues with the steam from the boiler to the engine. Steam,
in this condition, is like the air when a fine misty rain floats
in it, and is called WET STEAM by the engineers ; the steam
when free from this defect being called DRY STEAM. A handker-
chief held in dry steam issuing from the valve of a boiler will be
no more damped than it would be by a blast of wind ; but if the
steam be charged more or less with spray, its presence will be
shown at once by the moisture it would deposit.

8. The spray with which wet steam is charged is called by the
engineers PRIMING.

9. It appears, therefore, that whatever be the form of the
machine, or the purpose to which it is applied, it is of great
importance so to regulate the feed of the boiler, that the level of
the water in it shall neither fall too low nor rise too high.

Considering then the great importance of keeping the level of
the water in the boiler within the limits here defined, it will be
evident that some expedient ought to be provided by means of
which the engineman can at all times ascertain what the level of
the water actually is.

Different methods, all more or less efficient and ingenious, have
been invented for accomplishing this object.

One of the most simple consists in two common cocks, called
gauge cocks, like those used in a beer barrel, which are inserted
in the side or end of the boiler, one of which is placed at the
lowest, and the other at the highest limit of the water level. If
the engineman, on opening the latter, finds that water issues
from it, he knows that the level has risen to its highest limit, and
he suspends the feed. If, on opening the former, he finds the
steam issue from it, he knows that the water level has fallen too
low, and he lays on the feed. But so long as water issues from
the one and steam from the other, he knows that the water level
is within the required limits.

This method, though generally adopted, is not exclusively
depended on, and others are used.

A weight F (fig. 2), half immersed in the water, is supported by
a wire, which, passing steam-tight through a small hole in the
top, is connected by a flexible string or chain, passing over a
wheel w, with a counterpoise A, just sufficient to balance F when
half immersed. If F be raised above the water, A being lighter
will no longer balance it, and F will descend pulling up A, and

5

THE STEAM ENGINE.

turning the wheel w. If F be plunged deeper in the water, A
more than balance it, and will pull it up, so that the only position
in which F and A will balance each
other is, when F is half immersed.
The wheel w is so adjusted, that
when two pins placed on its rim.
are in the horizontal position, the
water is at its proper level. Con-
sequently it follows, that if the water
rise above this level, the weight E
is lifted and A falls, so that the pins
come into another position, and if
it fall lower, F falls and A rises, so
that the pins assume a differ en';
position. Thus, in general, tho
position of the pins becomes

indication of the quantity of water in the boiler.

Another method is to place a glass tube (fig. 3), with one end
entering the boiler above the proper level, and the other end T'
entering it below the proper level. It must be evident that the
water in the tube will always stand at the same level as the water
in the boiler, since the lower part has a free communication with
that water, while the surface is submitted to the pressure of

the same steam as the water in the boiler.

This and the last-mentioned gauge have
r the advantage of addressing the eye of the

engineer at once, without any adjustment ;

whereas the gauge- cocks must be both

opened, whenever the depth is to be

ascertained.

These gauges, however, require the

constant attention of the engine-man;

and it becomes desirable either to find some more effectual
means of awakening that attention, or to render the supply
of the boiler independent of any attention. In order to enforce
the attention of the engineman to replenish the boiler when
partially exhausted by evaporation, a tube was sometimes
inserted at the lowest level to which it was intended that the
water should be permitted to fall. This tube was conducted from
the boiler into the engine-house, where it terminated in a mouth-
piece or whistle, so that whenever the water fell below the level
at which this tube was inserted in the boiler, the steam would
rush through it, and issuing with great velocity at the mouth-
piece, would summon the engineer to his duty with a call that
would rouse him even from sleep.
C

;:

SELF-ACTING FEEDEE.

Fig. 4.

In the most effectual of these methods, the task of replenishing
the boiler must still be executed by the engineer ; and the utmost
that the boiler itself was made to do, was to give due notice of
the necessity for the supply of water. The consequence was,
among other inconveniences, that the level of the water was
subject to constant variation.

10. To remedy this a method has been invented, by which the
engine is made to feed its own boiler. The pipe G (fig. 4), which
leads from the hot water pump, terminates in a small cistern c in
which the water is received. In the bottom of this cistern, a
valve v is placed, which opens upwards and communicates with a
feed pipe, which descends into
the boiler below the level of the
water in it. The stem of the
valve v is connected with a lever
turning on the centre D, and
loaded with a weight F dipped
in the water in the boiler in a
manner similar to that described
in fig. 2, and balanced by a
counterpoise A in exactly the
same way. When the level of
the water in the boiler falls,
the float F falls with it, and
pulling down the arm of the
lever raises the valve v, and
lets the water descend into the
boiler from the cistern c. When

the boiler has thus been replenished, and the level raised to its
former place, F will again be raised, and the valve v closed by
the weight A. In practice, however, the valve v adjusts itself by
means of the effect of the water on the weight F, so as to permit
the water from the feeding cistern c to flow in a continued stream,
just sufficient in quantity to supply the consumption from evapo-
ration, and to maintain the level of the water in thejboiler
constantly the same.

By this arrangement the boiler is made to replenish itself ; or,
more properly speaking, it is made to receive such a supply, as
that it never wants replenishing — an effect which no effort of
attention on the part of an engineman could produce. But
this is not the only good effect produced by this contrivance.
A part of the steam which originally left the boiler, having
discharged its duty in moving the engine, is lodged in the hot
well c (fig. 4), and is again restored to the source from which it
came, bringing back to the boiler all the unconsumed portion

7

THE STEAM ENGINE.

of its heat preparatory to being- once more put in circulation
through the machine.

Another method of arranging a self-regulating feeder is shown
in fig. 5. A is a hollow ball of metal attached to the end of a
lever, whese fulcrum is at B. The other arm of the lever c is
connected with the stem of a spindle valve, communicating with a

tube which receives water from the feeding cistern. Thus, when
the level of the water in the boiler subsides, the ball A prepon-
derating over the weight of the opposite arm, the lever falls, the
arm c rises and opens the valve, and admits the feeding water.

SAFETY VALVE.

This apparatus will evidently act in the same manner and on the
same principles as that already described.

11. In different applications of the engine, steam of different
pressure is required. The pressure of steam is usually expressed
by stating the number of pounds weight upon each square inch of
surface which would exactly resist or balance it. All boilers are
provided with a valve which opens outwards, and which is loaded
with a certain limited and regulated weight. When the bursting
pressure with which the steam urges this valve exceeds the weight
with which it is loaded, the valve yields, is opened, and the steam
escapes through it, and thus continues to escape until the quantity
pent up in the boiler is so diminished, that its pressure upon the
valve no longer exceeds the weight with which the valve is
loaded. When this happens, the valve will remain closed, but
will be ready to yield and to open upon the least increase of the
pressure of the steam.

Such a valve is called a " safety valve" for the obvious
reason that it prevents the pressure of the steam in the boiler
from ever attaining such a force as Avould endanger the boiler.

It sometimes happens that it is necessary to vary from time to
time the pressure of the steam according to the work to which the
engine is applied, and consequently to vary the weight upon the
safety valve. In such cases it is usual to provide two safety
valves, one of which shall be regulated by the engineer, and the
other placed out of his power. The latter in that case is loaded
with the greatest pressure which the boiler can bear without
danger ; so that even though the engineer should indiscreetly load
the valve left at his disposition beyond the limit of safety, the
other valve would yield the moment the steam attained a dangerous
pressure.

Safety valves are of numerous forms. They consist usually of
a circular aperture cut in the boiler, with conical edges inclining
from within outwards. In this is placed a circular plate or
stopper of corresponding size, with corresponding conical edges, so
that it shall exactly fit the aperture ; and when pressed upon it, the
conical edges shall be in steam-tight contact. This circular plate
is attached at its centre to an iron rod, which rises perpendicular
to it. Upon this rod sliding weights are placed so as to press
down the valve with a greater or less force, according as their
number is increased or diminished.

In the general view of a boiler of the form called waggon boiler,
shown in fig. 7, the safety valve is shown at IT. It is provided
with a handle, by means of which the engineman can raise it
when necessary.

12. It is necessary to provide a ready method of indicating at all

9

THE STEAM ENGINE.

Fig. 6.

imes the actual pressure of the steam in 'the boiler. Various
methods are used for this purpose. In boilers where steam of
great pressure is used, the pressure is indicated by a spring gauge,
similar in its principle to those used for steel yards to weigh bodies
in commerce. The pressure of the steam acts against a valve
which is connected with the arm of the lever of the steel-yard,
the other arm being connected with the spring. In this way the
varying tension of the spring is made to measure the pressure on
the valve.

When steam of low pressure is used, an expedient called a mer-
curial steam gauge is used. A bent tube containing mercury is
inserted into some part of the apparatus, which has free commu-
nication with the steam. Lot
ABC (fig. 6), be such a tube. The
pressure of the steam forces the
mercury down in the leg A B, and
up in the leg B c. If the mercury
in both legs be at exactly the
same level, the pressure of the
steam must be exactly equal to
that of the atmosphere ; because
the steam pressure on the mer-
cury in A B balances the atmo-
spheric pressure on the mercury
in B c. If, however, the level of
the mercury in B c be above the
level of the mercury in B A, the
pressure of the steam will exceed
that of the atmosphere. The ex-
cess of its pressure above that of
the atmosphere may be found by
observing the difference of the
level of the mercury in the tubes
B c and B A, allowing a pressure
of one pound on each square
inch for every two inches in the difference of the levels.

If, on the contrary, the level of the mercury in B c should fall
below its level in A B, the atmospheric pressure will exceed that
of the steam, and the quantity of the excess may be ascertained
exactly in the same way.

If the tube be glass, the difference of levels of the mercury would
be visible ; but it is most commonly made of iron ; and, in order to
ascertain the level, a thin wooden rod with a float is inserted in the
open end of B c, so that the portion of the stick within the tube
indicates the depth of the level of the mercury below its mouth.

10

STEAM GAUGE — FUEIsTACE.

13. The most important appendage of the boiler is the furnace,
which consists of a grate, upon which the fuel is maintained in
combustion, — a system of flues, by which the flame and heated
gases proceeding from the fuel in combustion are conducted in
contact with the boiler, so as to impart more or less of their
heat to the boiler, and, in fine, a chimney by which these gases
escape into the atmosphere, and which maintains the draft neces-
sary to give effect to the combustion.

The explanation of the furnace and its appendages, as well as
that of the boiler already given, will be rendered much more easily
intelligible by the aid of the figures 7, 8, 9, and 10, which, though
they represent a particular form of boiler, indicate those provisions
and arrangements which are most generally used in boilers of all
forms.

The form here represented is called the waggon-boiler, and con-
sists of a semi- cylindrical top, flat perpendicular sides, flat ends,
and a slightly concave bottom. The steam intended to be used in
boilers of this description does not exceed the pressure of the
external atmosphere by more than from 3 to, 5lbs. per square
inch ; and the flat sides and ends, though unfavourable to strength,
can be constructed sufficiently strong for this purpose. In a
boiler of this sort, the air and smoke passing through the flues
that are carried round it, are in contact at one side only with the
boiler. The brickwork, or other materials forming*athe flue, must
therefore be non-conductors of heat, that they may not absorb
any considerable portion of heat from the air passing in contact
with them.

A perspective view of the boiler and furnace is presented in
fig. 7. The grate and a part of the flues are rendered visible by
the removal of a portion of the surrounding masonry in which the
boiler is set. The interior of the boiler is also shown by cutting
off one half of the semi-cylindrical roof. A longitudinal vertical
section is shown in fig. 8, and a cross section in fig. 9. A
horizontal section taken above the level of the grate, and below
the level of the water in the boiler, shewing the course of the
flues, is given in fig. 10. The corresponding parts in all the figures
are marked by the same letters.

14. The door by which fuel is introduced upon the grate is repre-
sented at A, and the door leading to the ash-pit at B. The fire
bars at c slope downwards from the front at an angle of about 25°,
giving a tendency to the fuel to move from the front towards the
back of the grate. The ash-pit D is constructed of such a magni-
tude, form, and depth, as to admit a current of atmospheric air to
the grate-bars, sufficient to sustain the combustion. The form
of the ash-pit is usually wide below, contracting towards the top.

11

le fuel, when introduced at the fire-door A, should be laid on
that part of the grate nearest to the fire-door, called the dead
plates : there it is submitted to the process of coking, by which
the gases and volatile matter which it contains are expelled, and

Fig. 7.

being carried by a current of air admitted through small apertures
in the fire-door over the burning fuel in the hinder part of the
grate, they are burnt. When the fuel in front of the grate has
been thus coked, it is pushed back, and a fresh feed introduced in
front. The coal thus pushed back soon becomes vividly ignited,
and by continuing this process, the fuel spread over the grate is
maintained in the most active state of combustion at the hinder
part of the grate. By such an arrangement, the smoke produced
by the combustion of the fuel may be burnt before it enters the

12

FURNACE AND ITS APPENDAGES.

flues. The flame and heated air proceeding from the burning fuel
arising from the grate, and rushing towards the back of the fur-
nace, passes over the fire-bridge E, and is carried through the
flue P which passes under the boiler. This flue (the cross section
of which is shown in fig. 9, by the dark shade put under the
boiler), is very nearly equal in width to the bottom of the boiler,
the space at the bottom of the boiler, near the corners, being only
what is sufficient to give the weight of the boiler support on the

Fig. 8.

masonry forming the sides of the flue. The bottom of the boiler
being concave, the flame and heated air as they pass along the
flue rise to the upper part by the effects of their high temperature,
and lick the bottom of the boiler from the fire-bridge at E to the
further end G.

At G the flue rises to H, and turning to the side of the boiler at
1 1, conducts the flame in contact with the side from the back to
the front ; it then passes through the flue K across the front, and
returns to the back by the other side flue L. The side flue is
represented, stripped of the masonry, in fig. 7, and also appears in

13

THE STEAM ENGINE.

plan in fig. 10, and in the cross section in fig. 9. The
of the air is represented in fig. 10 by the arrows. From the flue L
the air is conducted into the chimney at M.

By such an arrangement, the flame and heated air proceeding
from the grate are made to circulate round the boiler, and the
length and magnitude of the flues through which they are con-
ducted should be such, that when they arrive at the chimney their
temperature shall be reduced, as nearly as is consistent with the
maintenance of draught in the chimney, to the temperature of
the water.

15. The method of feeding the furnace, which has been described
above, is one which, if conducted with skill and care, would pro-

Fig. 9.

duce a much more perfect combustion of the fuel than would
attend the common method of filling the grate from the back to
the front with fresh fuel, whenever the furnace is fed. This
method, however, is rarely observed in the management of the
furnace. It requires the constant attention of the stokers (such is
the name given to those who feed the furnaces). The fuel must
14

FURNACE AND ITS APPENDAGES.

be supplied, not in large quantities, and at distant intervals, but
in small quantities and more frequently. On the other hand, the
more common practice is to allow the fuel on the grate to be in a
great degree burned away, and then to heap on a large quantity
of fresh fuel, covering over with it the burning fuel from the

Fig. 10.

back to the front of the grate. "When this is done, the heat of the
ignited coal acting upon the fresh fuel introduced, expels the gases
combined with it, and, mixed with these, a quantity of carbon, in
a state of minute division, forming an opaque black smoke. This
is carried through the flues and drawn up the chimney. The
consequence is, that not only a quantity of solid fuel is sent out
of the chimney unconsumed, but the hydrogen and other gases
also escape unburned, and a proportional waste of the combustible
is produced ; besides which, the nuisance of an atmosphere filled
with smoke ensues. Such effects are visible to all who observe
the chimneys of steam vessels, while the engine is in operation.
When the furnaces are thus filled with fresh fuel, a large volume
of dense black smoke is observed to issue from the chimney. This
gradually subsides as the fuel on the grate is ignited, and does
not reappear until a fresh feed is introduced.

16. The former method of feeding, by which the furnace would
be made to consume its own smoke, and the combustion of the fuel
be rendered complete, is not however free from counteracting
effects. In ordinary furnaces the feed can only be introduced by
opening the fire-doors, and during the time the fire-doors are
opened a volume of cold air rushes in, which passing through the
furnace is carried through the flues to the chimney. Such is the
effect of this in lowering the temperature of the flues, that in
many cases the loss of heat occasioned is greater than any economy

15

:HE STEAM ENGINE.

of fuel obtained by the complete consumption of smoke. Various
methods, however, may be adopted by which fuel may be supplied
to the grate without opening the fire-doors, and without disturbing
the supply of air to the fire. A hopper built into the front of the
furnace, with a moveable bottom or valve, by which coals may be
allowed to drop in from time to time upon the front of the grate,
would accomplish this.

In order to secure the combustion of the gases evolved from the
coals placed in the front of the grate, it is necessary that a supply
of atmospheric air should be admitted with them over the burning
fuel. This is effected by small apertures or regulators, provided
in the fire-doors, governed by sliding plates, by which they may
be opened or closed to any required extent.

S~T- -.fe

DOUBLE-ACTING ENGINE— CITV SAW-MILLS.

THE STEAM ENGINE.

CHAPTER II.

17. Method of regulating the activity of the furnace. — 18. How steam is
made to produce a mechanical effect. — 19. The cylinder and piston. —
20. Metallic pistons. — 21. Estimate of the force with which the piston
is moved. — 22. Transmission of this force. — 23. Piston rod. — 24.
Cocks, valves, and slides. — 25. How employed. — 26. Stroke of the
engine. — 27. Effective pressure. — 28. Supply of steam to the cylinder.
—29. By valves.— 30. By slides.— 31. Seaward' s slides.— 32. Single
cock. — 33. Four-way cock. — 34. Low and high pressure, more pro-
perly called condensing and non-condensing, engines. — 35. Objections

LARDNER'S MUSEUM OP SCIENCE. c 17

No. 57.

THE STEAM EXGI]

-. . — latter and countervailing advantages. — 36. Condensing
engines. — 37. Condensing apparatus. — 38. Air-pump. — 39. Cold water
pump. — 40. Hot water pump.

17. WHATEVER be the form of boiler used, its magnitude and
proportions, as well as those of the furnaces and their appendages,
must be determined by the rate at which the steam is required to
be produced, and in some degree also by the quality of the fuel.

The principle upon which a chimney more or less lofty produces
a draft through the fuel in a fire-place in connection with it, has
been already explained in our Tract on " Fire." The chimney
connected with the furnace of a steam-boiler acts on the same
principle, and its dimensions and height must necessarily be pro-
portionate to those of the furnace, and to the quantity of fuel 1 o
be consumed in a given time.

But since the evaporation produced in the boiler requires to be
varied with the varying work exacted from the engine ; and since
this evaporation will necessarily be proportionate to the rate at
which the fuel is consumed in the furnace, it follows that the rate
of combustion in the furnace should be varied with the varying
power to be exacted from the engine. In order, therefore, to
maintain this proportion between the force of the furnace and the
demands upon the engine, it is necessary to stimulate or mitigate
the furnace, as the evaporation is to be augmented or diminished.

The activity of the furnace must depend on the current of air
which is drawn through the grate bars, and this will depend on
the magnitude of the space aflbrded for the passage of that current
through the flues. A plate called a damper is accordingly placed
with its plane at right angles to the flue, so that by raising and
lowering it in the same manner as the sash of a window is raised
or lowered, the space allowed for the passage of air through the
flue may be regulated. This plate might be regulated by the
hand, so that by raising or lowering it the draught might be
increased or diminished, and a corresponding effect produced on
the evaporation in the boiler : but the force of the fire is rendered
uniformly proportional to the rate of evaporation by the following
arrangement, without the intervention of the engineer. The
column of water sustained in the feed pipe (figs. 7, 8), represents
by its weight the difference between the pressure of steam within
the boiler and that of the atmosphere. If the engine consumes
steam faster than the boiler produces it, the steam contained in
.the boiler acquires a diminished pressure, and consequently the
column of water in the feed pipe will fall. If, on the other hand,
the boiler produce steam faster than the engine consumes it, the
accumulation of steam in the boiler will cause an increased
pressure on the water it contains, and thereby increase the height
18

SELF-REGULATING DAMPER.

of the column of water sustained in the feed pipe. This column,
therefore, necessarily rises and falls with every variation in the
rate of evaporation in the boiler. A hollow float P is placed upon
the surface of the water of this column ; a chain connected with
this float is carried upwards, and passed over two pulleys, after
which it is carried downwards through an aperture leading to the
flue which passes beside the boiler : to this chain is attached the
damper. By such an arrangement it is evident that the damper will
rise when the float P falls, and will fall when the float P rises, since
the weight of the damper is so adjusted, that it will only balance
the float P when the latter rests on the surface of the water.

"Whenever the evaporation of the boiler is insuflicient, it is
evident from what has been stated, that the float P will fall and
the damper will rise, and will afford a greater passage for air
through the flue. This will stimulate the furnace, will augment
its heating power, and will therefore increase the rate of evapo-
ration in the boiler. If, on the other hand, the production of
steam in the boiler be more than is requisite for the supply of the
engine, the float will be raised and the damper let down, so as to
contract the flue, N to diminish the draught, to mitigate the fire,
and therefore to check the evaporation. In this way the excess,
or defect, of evaporation in the boiler is made to act upon the fire,
so as to render the heat proceeding from the combustion as nearly
as possible proportional to the wants of the engine.

18. Having thus explained generally the principal expedients
by which the efficiency of the boiler and furnace of a steam-engine
is maintained, it will be only necessary to add, that although
these expedients, in the forms in which they are represented in
the diagrams, will not be found in every steam boiler, yet equi-
valents to them in other forms or positions are almost universal.
In certain cases the self-regulating apparatus of the boiler and
furnace are excluded by want of the necessary height, and then
the proper regulation of the machine must depend on the skill and
vigilance of those who are in charge of it.

Supposing, then, that by these or other similar or equivalent
provisions a supply of steam in the necessary quantity and of the
requisite pressure is obtained, it remains to show how the steam is
made to produce the desired mechanical effect.

The method universally adopted to render the power of steam
available for mechanical purposes is that of a solid piston moving
freely in a hollow cylinder in steam-tight contact with its sides.
The steam is admitted alternately at one end and at the other, of
the cylinder. When it is let in at either end, it is permitted to
escape by the other, so that the piston is blown by the steam
alternately from end to end of the cylinder. The ends of the

o 2 19

THE STEAM ENGINE.

cylinder are closed by steam-tight covers, but proper openings
are provided for the alternate admission and escape of the steam.

19. The cylinder is made of cast iron of adequate thickness and
strength. It is bored with the nicest precision, so that its inner
surface is truly cylindrical and of uniform diameter from end to end.
The piston is also made of iron, and its contact with the cylinder is
rendered steam-tight, either by a packing of hemp and soft rope,
called gasket, which fills a circular groove or channel surrounding
the piston, or by constructing the external rim of the piston of several
metallic segments, which are urged against the side of the cylinder
by springs which act upon them from the centre of the piston.

A section of a packed piston is given in fig. 1 1 . The hollow

groove containing tho
Pac^ing is represented
at the sides next the
cylinder, and the top
is attached to the piston
by screws, by turning
which the packing is
compressed so as to be
I forced outwards against
the sides of the cylinder
until it is in steam-tight contact with them.

20. Pistons which maintain steam-tight contact with the
cylinder without packing, and which are called metallic pistons,

are of very various
construction, though
all of essentially the
same principle. One of
these is represented in
section in fig. 12, and
in plan in fig. 13, p.
21. A deep groove,
^ square in its section, is
m formed around the pis-
ton, so that while the top and bottom form circles equal in
magnitude to that of the cylinder, the intermediate part of the
body forms a circle less than the former by the depth of the
groove. Let a ring of brass, cast iron, or cast steel, be made to
correspond in magnitude and form with this groove, and let it be
divided, as represented in fig. 13, into four segments c c c c, and
four corresponding angular pieces, D D D D. Let the groove which
surrounds the piston be filled by the four segments with the four
wedge-like angular pieces within them, and let the latter be
urged against the former by eight spiral springs, as represented

Fig. 12,

20

PISTONS.

Fig. 13.

in fig. 12 and fig. 13. These springs will abut against the solid
centre of the piston, and will urge the segments c against the
cylinder. The spiral springs which urge the wedges are confined
in their action by steel pins which pass through their centre, and
by being confined in cylindrical cavities worked into the wedges
and into corresponding parts of the solid centre of the piston, as
the segments c wear, the springs urge the wedges outwards, and
the points of the latter protruding, are gradually worn down so as
to fill up the spaces left between the segments, and thus to com-
plete the outer surface of the piston.

21. The force with
which the piston is
moved from end to end
of the cylinder is esti-
mated by the pressure
of the steam which acts
upon it, diminished by
the reaction of the steam
escaping from the side
towards which it moves,
and the resistance pro-
duced by its friction
against the sides of the
cylinder.

22. The mechanical
force with which the
piston is thus moved

would be practically useless unless an expedient were provided by
which it could be transmitted to some convenient point outside
the cylinder, and since it is essential that the steam which impels
the piston shall be confined within the cylinder, and that no air
be allowed to enter, so as to react on the other side of the piston
by its pressure, it is also essential that whatever be the means of
transmitting the force of the piston to the outside of the cylinder,
it shall be accomplished without leaving any interstitial space
through which steam can escape or air enter.

23. This object is perfectly attained by. a very simple con-
trivance. A hole is made through the centre of the piston,
in which a truly formed cylindrical iron rod, called the piston-
rod, is inserted and firmly fixed by a key or linch-pin. This
piston-rod passes through a hole made in the iron cover of the
cylinder, as shown in fig. 14. The piston-rod is kept in steam-
tight contact with the edges of the hole by a contrivance called
a stuffing box, B, represented in fig. 14. The hole made in the

cover of the cylinder is very little

greater in magnitude than
21

THE STEAM ENGINE.

Fig. 14.

the diameter of the piston rod. Above this hole is a cup, in
which, around the piston, is placed a stuffing of hemp or tow,
which is saturated with oil or melted tallow. This collar of

hemp is pressed down by another
piece, also perforated with a hole
through which the piston rod
plays, and which is screwed down
on the said collar of hemp.

The piston-rod, by this con-
trivance, being moved with the
same alternate motion, and tho
same force as the piston itself,
can be made to impart that fore 3
to any suitable piece of mecha-
nism outside the cylinder, wit'i
which it may be put in connection.

24. Since the ends of the cylinder are closed by metallic covers,
in the manner explained above, the openings for the exit and
entrance of the steam at the ends, are placed, not in the covers,
but in the sides, at points in immediate contiguity with the
covers. These openings are governed by contrivances of various
forms, and variously denominated COCKS, VALVES, and SLIDES.

25. Let two openings be imagined to be provided at each end
of the cylinder, one leading from the boiler, and the other for the
escape of the steam. Let stop-cocks, or valves, or sliding
shutters, be adapted to these openings, so that they can be closed
or opened by acting upon the handles of the cock valve or slide,
and let these handles be supposed to be put in such connection
with the piston-rod that when the piston arrives at either end of
the cylinder the handles are driven by the rod, so as to open the
passage which admits steam to the end of the cylinder at which
the piston has arrived, and to close the passage which is provided
for its escape, and, on the contrary, to open the passage for the
escape of the steam from the other end of the cylinder, and to
close the passage for its admission from the boiler. By this
means the piston, being acted upon by the steam at the end at
which it has arrived, and, being relieved from the action of the
steam on the other side of it, will be driven to the other end of the
cylinder where the piston-rod will again act upon the handles of
the cocks, valves, or slides, so as to reverse the flow of the steam,
allowing that which has just impelled the piston to escape, and
introducing steam from the boiler to the end of the cylinder
at which the piston has just arrived. In this way the piston will
be driven back to the other end of the cylinder, and so on alter-
nately from end to end.

22

VALVES AND SLIDES.

26. "We are accustomed to consider the cylinder in a vertical
position, to call the covers of its ends the top and bottom, and to
speak of the up stroke and the down stroke of the piston. Such is
very often the position of the apparatus, but it is not necessarily nor
always so. The cylinder is often horizontal. It is almost always
so, for example, in locomotive engines, and often so in steamboat
engines. It is sometimes placed in an inclined position, and is some-
times moveable, changing its position with the motion of the piston.

The motion of the piston from end to end of the cylinder is
called its STROKE, and the dimensions are usually expressed by
stating the diameter of the piston and the length of the stroke.

27. The EFFECTIVE PRESSURE of steam per square inch on the
piston is found by deducting from the actual pressure the reaction
of the steam escaping, and the friction. This effective pressure
being multiplied by the number of square inches in the piston,
which is known by its diameter, gives the total effective force of
the piston, and this force, multiplied by the number of feet
through which the piston moves per minute, which is known by
the length of the stroke, and observing the number of strokes per
minute, will give the actual mechanical force produced per minute
by the steam acting on the piston.

28. From what has been explained it will be apparent that
much of the efficiency of the machine must depend upon the pre-
cision and regularity with which the steam is alternately admitted
to and withdrawn from either end of the cylinder. If it be
admitted or withdrawn too soon or too late, it will either obstruct
the force of the piston, or delay its return to the other end of the
cylinder. For these reasons, and also because there is much
beauty and ingenuity in the contrivances

by which the steam is admitted and with-
drawn, we shall here explain a few of the
expedients by which that object is attained.

29. In the arrangement represented in
fig. 15, the object is attained by four conical
valves, two placed at each end of the cylin-
der. Let B and B' be two steam boxes, B the
upper, and B' the lower, communicating
respectively with the top and bottom of the
cylinder by proper passages D V. Let two
valves be placed in B, one, s, above the s/
passage D, and the other, c, below it ; and
in like manner two other valves in the
lower valve box B', one, s', above the passage
D, and the other c', below it. Above the

valve s in the upper steam box is an opening at which the steam

23

THE STEAM ENGINE.

pipe from the boiler enters, and below the valve c is another opening,
at which enters the exhausting pipe. In like manner, above the
valve s' in the lower steam box enters a steam pipe leading from
the boiler, and below the valve c' enters an exhausting pipe. It
is evident, therefore, that steam can always be admitted above the
piston by opening the valve s, and below it by opening the valve
s' ; and, in like manner, steam can be withdrawn from the cylinder
above the piston, by opening the valve c, and from below it by
opening the valve c'.

Supposing the piston p to be at the top of the cylinder, and the
cylinder below the piston to be filled with pure steam, let the
valves s and c' be opened, the valves c and s' being closed, as
represented in fig. 15. Steam from the boiler will, therefore, flow
in through the open valve s, and will press the piston downwards,
while the steam that has filled the cylinder below the piston will
pass through the open valve c' into the exhausting pipe. The
piston will, therefore, be pressed downwards by the action of the
steam above it. Having arrived at the bottom of the cylinder,
let the valves s and c' be both closed, and
the valves s' and c be opened, as represented
in fig. 16. Steam will now be admitted
through the open valve s' and through the
passage B' below the piston, while the steam
which has just driven the piston down-
wards, filling the cylinder above the piston,
will be drawn off through the open valve c,
and the exhausting pipe, leaving in the
cylinder above the piston a vacuum. The
piston will, therefore, be pressed upwards
by the action of the steam below it, and will
ascend with the same force as that with
which it had descended.

The alternate action of the piston up-
wards and downwards may evidently be
continued by opening and closing the valves alternately in
pairs. Whenever the piston is at the top of the cylinder, as
represented in fig. 15, the valves s and c', that is, the upper
steam valve and the lower exhausting valve are opened ; and the
valves c and s', that is, the upper exhausting valve and the lower
steam valve, are closed ; and when the piston has arrived at the
bottom of the cylinder, as represented in fig. 16, the valves c and s',
that is, the upper exhausting valve and the lower steam valve,
are opened, and the valves s and c', that is, the upper steam valve
and the lower exhausting valve, are closed.
If these valves, as has been here supposed, be opened and closed
24

VALVES AND SLIDES.

at the moments at which the piston reaches the top and bottom
of the cylinder, it is evident that they may be all worked by a
single lever connected with them by proper mechanism. When
the piston arrives at the top of the cylinder, this lever would be
made to open the valves s and c', and at the same time to close
the valves s' and c ; and when it arrives at the bottom of the
cylinder, it would be made to close the valves s and c', and to
open the valves s' and c.

30. The methods of opening and closing the passages by means
of lids slipping over them called slides, are those most generally
used, and have infinitely various forms, although they differ one
from another but little in the principle of their action. One of
these expedients shown in fig. 17 — 18, will render the mode o£

their action easily under-
stood. A B is a steam-tight

case attached to the side of

the cylinder ; E r is a rod,

which receives an'alternate

motion, upwards and down-
wards, from the eccentric,

or from whatever other part

of the engine is intended

to move the slide. This

rod, passing through a

stuffing box, moves the

slide G upwards and down-
wards, s is the mouth of

the steam pipe coming from

the boiler ; T is the mouth

of a tube or pipe leading

to the condenser; H is a

passage leading to the top,

and I to the bottom, of the

cylinder. In the position

of the slide represented in fig. 17, the steam coming from the boiler
through s passes through the space H to the top of the cylinder,
while the steam from the bottom of the cylinder passes through the
space i into the tube T, and goes to the condenser. When the rod
E F is raised to the position represented in fig. 18, then the passage
H is thrown into communication with the tube T, while the passage I
is made to communicate with the tube s. Steam, therefore, passes
from the boiler through i below the piston, while the steam which
was above the piston, passing through H into T, goes to the con-
denser. Thus the single slide G performs the office of the four
valves described in § 29.

25

31. Another form of slides is shown in fig. 19. The steam
pipe proceeding from the boiler to the cylinder is represented at

Fig. ID.

A A, and it com-
municates with
passages s and s'
leading to the
top and bottom
of the cylinder.
These passages
are formed in
nozzles of iron or
other hard metal
cast upon the side
of the cylinder.
These nozzles
present a smooth
face outwards,
upon which the
slides B B', also
formed with
smooth faces,
play. The slides B B' are attached by knuckle-joints to rods
E E', which move through stuffing-boxes, and the connection of
these rods with the slides is such that the slides have play so as to
detach their surfaces easily from the smooth surfaces of the nozzles
when not pressed against these surfaces. The steam in the steam
pipe A A will press against the backs of the slides B B', and keep their
faces in steam-tight contact with the smooth surfaces of the nozzles.
These slides may be opened or closed by proper mechanism, at any
point of the stroke. When steam is to be admitted to the top of
the cylinder, the upper slide is raised and the passage s opened ;
and when it is to be admitted to the bottom of the cylinder, the
lower slide is raised and the passage s' opened : and its communi-
cation with the top or bottom of the cylinder is stopped by the
lowering of these slides respectively. On the other side of the
cylinder are provided two passages c c' leading to a pipe G, which
is continued to the condenser. On this pipe are cast nozzles of
iron or other metal presenting smooth faces towards the cylinder,
and having passages D D' communicating between the top and
bottom of the cylinder respectively and the pipe G G leading to
the condenser. Two slides b 6', having smooth faces turned from
the cylinder, and pressing upon the faces of the nozzles D D', are
governed by rods playing through stuffing-boxes, in the same
manner as already described. The faces of these slides being
turned from the cylinder, the steam in the cylinder having free

26

STEAM COCKS.

communication with them, has a tendency to keep them by its
pressure in steam-tight contact with the surfaces in which the
apertures leading to the condenser are formed. These two slides
may be opened or closed whenever it is necessary.

When the piston commences its descent, the upper steam slide
is raised, so as to open the passage s, and admit steam above the
piston ; and the lower exhausting slide b' is also raised, so as to
allow the steam below the piston to escape through G, the other
two passages s' and c being closed by their respective slides. The
slide which governs s is lowered at that part of the stroke at which
the steam is intended to be cut off, the other slides remaining
unchanged ; and when the piston has reached the bottom of the
cylinder, the lower steam slide opens the passage s', and the upper
exhausting slide opens the passage c, and at the same time the
lower exhausting slide closes the passage c'. Steam being admitted
below the piston through s', and at the same time the steam above
it being drawn away through the open passage c and the tube G,
the piston ascends. "When it has reached that point at which the
steam is intended to be cut off, the slide which governs s'(is
lowered, the other slides remaining unaltered, and the upward
stroke is completed in the same manner as the downward.

These four slides may be governed by a single lever, or they

may be moved by separate means. From the small spaces between

the several slides and the body of the cylinder, it will be evident

that the waste of steam by this contrivance will be very small.

32. The admission and escape of the steam is sometimes

governed by cocks, more espe-
cially in engines constructed on a
small scale. The most common
form for cocks is that of a cylin-
drical or slightly conical plug
(fig. 20), inserted in an aperture
of corresponding magnitude pass-
ing across the pipe or passage
which the cock is intended to open
or close. One or more holes are
pierced transversely in the cock, and when the cock is turned, so
that these holes run in the direction of the tube, the passage
through the tube is opened ; but when the passage through the
cock is placed at right angles to the tube, then the sides of the
tube stop the ends of the passage in the cock, and the passage
through the tube is obstructed. The simple cock is designed to
open or close the passage through a single tube. When the cock
is turned, as in fig. 21, so that the passage through the cock shall
be at right angles to the length of the tube, then the passage

27

THE STEAM ENGINE.

through the tube is stopped ; but when the cock is turned from
that position through a quarter of a revolution, as in fig. 22, then
the passage through the cock takes the direction of the passage

Fig. 21.

Fig. 22.

Fig. £

through the tube, and the cock is opened, and the passage through
the tube unobstructed. In such a cock the passage may be mo:-e
or less throttled by adjusting the position of the cock, so that a
part of the opening in it shall be covered by the side of the tube..

33. It is sometimes required to put one tube or passage alter-
nately in communication with two others. This is accomplished
by a two-way cock. In this cock the passage is curved, opening
usually at points on the surface of the cock, at right angles to each
other. "When it is required to put four passages alternately in com-
munication by pairs, a four-way cock is used. Such a cock has
two curved passages (fig. 23), each similar to the curved passage
in the two-way cock. Let s c B T be
the four tube? which it is required to
throw alternately into communication
by pairs. When the cock is in the
position (fig. 23), the tube s communi-
cates with T, and the tube c with B.
By turning the cock through a quarter
of a revolution, as in fig. 24, the tube s
is made to communicate with B, and
the tube c with T ; and if the cock
continue to be turned at intervals
through a quarter of a revolution, these changes of communication
will continue to be alternately made. It is evident that this may be
accomplished by turning the cock continually in the same direction.
The four- way cock is sometimes used as a substitute for the
valves or slides to conduct the steam to and from the cylinder.
If s represent a pipe conducting steam from the boiler, c the
exhausting pipe, T the tube which leads to the top of the
cylinder, and B that which leads to the bottom, then when the
cock is in the position (fig. 23), steam would flow from the boiler
to the top of the piston, while the steam below it would be drawn
off: and in the position (fig. 24), steam would flow from the boiler
to the bottom of the piston, while the steam above it would be
28

FOUR-WAY COCK.

drawn off. Thus by turning the cock through a quarter of a
revolution towards the termination of each stroke, the operation
of the machine would be continued.

34. It will be understood from all that has been stated that the
mechanical effect of the steam engine

depends, other things being given,
upon the excess of the pressure of the
steam which impels the piston above
the reaction of the steam which escapes
at the end of the cylinder towards
which the piston is moving. To what-
ever extent, therefore, this reaction is
diminished, the efficacy of the engine
will be increased.

Steam engines are resolved into two
distinct classes, according to the way in which the steam escaping
from the cylinder is disposed of, called non-condensing and con-
densing engines, or, more commonly, though less properly, high
pressure and low pressure engines. The objection to the latter
denomination being that, although non-condensing engines must
necessarily be worked with high pressure steam, condensing en-
gines need not be worked with low pressure steam, as will presently
appear.

In the class of non-condensing or high pressure engines, the
exhaustion pipes of the cylinder open into the atmosphere ; in the
condensing or low pressure engines, they lead to an apparatus in
which the steam is condensed, the name given to the process of
reconverting it into water by exposure to cold.

35. In non-condensing engines the exhausting pipe communicat-
ing with the external air, this air will, when the exhausting valve
is open, have a tendency to rush into the cylinder, while the steam
has, on the contrary, a tendency to rush out. ' If, in this case, the
pressure of the steam were not greater than that of the atmosphere,
its escape would be prevented by the counter pressure of the air,
and as the pressure of the steam is the measure of its reaction
against the piston, it follows that in this class of steam engine,
the reaction on the piston must always be somewhat greater than
the atmospheric pressure, which, as has been shown in vol. ii., p. 4,
amounts on an average to 15lbs. per square inch.

Since, then, the piston of a non-condensing engine is subject,
necessarily and constantly, to a reaction exceeding 15lbs. per
square inch, the pressure of the steam by which it is impelled
must greatly exceed 151bs. per square inch. Thus a pressure of
SOlbs. per square inch would give an effective pressure much less
than 151bs. per square inch, because, besides the reaction of the

29

THE STEAM ENGINE.

steam, tlie impelling power is resisted by friction. A pressure of
45lbs. per square inch would give an effective force amounting to
less than 301bs. per square inch, and so on.

Notwithstanding the disadvantage of this reaction on the piston,
and the consequent necessity of providing a boiler suitable to the
production of steam of this high pressure, non- condensing engines
are attended with several countervailing advantages which render
them not only preferable in certain cases to condensing engines,
but which render them efficient where the adoption of condensing
engines would be altogether impracticable.

36. In condensing engines, the exhausting pipes which proceed
from the ends of the cylinder lead to a reservoir or vessel called a
condenser, in which the steam, being exposed to cold, is reduced
to water. Now, since a cubic foot of steam will, when re-converted
into liquid, form only about a cubic inch of water, it is plain that
by this process of condensation, efficiently conducted, the steam
escaping from the cylinder may be considered as passing into a
vacuum, and therefore not only is it not subject to the resistance
of the atmosphere, but to no resistance whatever, except what may
arise from the contracted dimensions of the exhausting pipe. The
conversion of the steam into water being, moreover, almost instan-
taneous, the reaction attending its escape, small as it is, is only
momentary, and affects the piston only at the commencement of
the stroke, throughout the remainder of which it will be subject
to no reaction whatever.

Thus it appears, that, in condensing engines the pressure of the
steam which impels the piston instead of being subject, as in non-
condensing engines, to a reaction exceeding 15 Ibs. per square
inch, is subject to scarcely any reaction at all ; and consequently
its pressure, to be effective, need not exceed a few pounds, say
from 4 Ibs. to 0 Ibs. per square inch. It is for this reason that
condensing engines have been commonly called low-pressure
engines.

But although low-pressure steam may be used in this class of
engines, and in most cases is used, it is not thus used exclusively
or necessarily. Steam of any pressure, however high, may be
worked in them, and the condensing apparatus will still render
equal service. In certain applications of the engine, steam having
a pressure several times greater than that of the atmosphere is
worked with great advantage in engines constructed on this
principle.

37. Since the condensing apparatus discharges such important
functions, it will be useful to show its structure and arrangement,
in connection with the piston and cylinder.

A section of such an apparatus is shown in fig. 2o. A cistern,
30

CONDENSEK.

c c, is filled with cold water. Immersed in it is a metal vessel,
B, called the condenser. A pipe, s s, connects this condenser
with the exhausting pipe of the cylinder, of which s s may be

s

considered as the continuation. A jet-pipe, E, enters the con-
denser, and is bent upwards. It is terminated with a piece pierced
with holes like the rose of a watering-pot, and the cold water of the
cistern, c c, being pressed in through the pipe, E, is thrown up in
the condenser, as shown in the figure. The steam, escaping from
the cylinder along the pipe, s s, encounters this cold jet and is
instantly condensed. Mixing with the cold water of the jet, it
forms warm water, which collects in the bottom of the condenser.

If means were not provided for the removal of this water, the
vessel B would soon become choked with it, so as to arrest the
action of the apparatus.

38. But there is also another effect, which it is important to
explain. Water as it commonly exists always contains more or
less air fixed in or mingled with it. The air thus fixed in the
water of the cistern, c c, is disengaged in greater or less quantity
by the heat to which it is exposed when the steam is mixed with
it in the vessel B. This air, rising through the tube, s s, offers
more or less resistance to the escape of the steam, and reacts upon
the piston to the detriment of the moving power. Its accumula-

31

HNE.

tion, if not removed, would soon obstruct and altogether arrest
the action of the machine.

This air, as well as the warm water deposited in the bottom of
the condenser, is withdrawn by a pump, A, called the AIII-PFMP,
because of its use in the removal of the air just mentioned. In
the piston of this pump are valves which open upwards, so that
when the piston descends the water and air force themselves
through the valves, and when it ascends it lifts the water and air
which have thus passed through the valves, and throws them into
a small reservoir, D, through a valve, K. This reservoir, D, is
called the hot cistern, the water deposited in it having a tempera-
ture more or less elevated, owing to the steam which has been
condensed by it.

The ascent of the piston of the air-pump has also the effect of
drawing by suction, as it is commonly called, the water and air
from the condenser, B, through the valve M into the bottom of the
barrel of the air-pump, from which they cannot get back into the
condenser, inasmuch as the valve, M, opens towards the air-pump,
and their returning pressure only closes it more firmly.

39. The continual affluence of the steam to the vessel B, and the
water constantly passing through it, the air-pump, and the
cistern, D, would at length raise the temperature of the water in
the cistern, c c, in which the condensing apparatus is immersed,
to such a point that the jet projected into the condenser would be
no longer cold enough to condense the steam.

To prevent this a pump, called the cold-water pump, is pro-
vided, which throws into the cistern a sufficient quantity of cold
water. This water is introduced near the bottom of the cistern, a
waste-pipe being provided at the top by which the warm water,
which always collects near the upper surface, flows off. In this
way the temperature of the water in the cistern, c c, is kept
sufficiently low, notwithstanding the heat proceeding from the
condensing vessels.

40. To prevent the accumulation of warm water in the cistern,
D, a pump called the hot- water pump is connected with it, by
which the water is drawn off from it and transferred to the feeding
apparatus of the boiler. Thus a part of the heat given out by the
condensed steam, and which has already done duty in working
the piston, is returned to the boiler to take another round of duty.

Thus it appears that the condensing apparatus consists of the
cold cistern, c c, the cold-water pump which supplies it, the con-
denser, B, the air-pump, A, the hot cistern, D, and the hot-water
pump, which draws the water from it.

32

FURNACE AT THE CITY SAW MILLS.

THE STEAM ENGINE.

CHAPTER III.

41. Comparative merits of the two kinds of engines. — 42. Various modes
of transmitting force. — 43. Description of a factory engine. — 44. The
governor. — 45. The eccentric.— 46. The fly-wheel. — 47. Parallel
motion. — 48. Barometer gauge. — 49. How to compute the effective
moving force of the piston. — 50. Method not considered sufficiently
accurate. — 51. Indicator. — 52. Mode of recording its positions. — 53.
Its application in finding effective force. — 54. Watt's counter. — 55.
Conclusion.

41. THAT the advantages arising from the diminished reaction
on the piston, produced hy the condensation of the steam, are not
altogether to he placed to the account of increased moving power,
will he apparent when it is observed that no inconsiderable part
of the power thus gained is absorbed by the cold-water pump, the
air pump, and the hot-water pump, all of which are worked by
the engine. Neither is the vacuum into which the piston moves,
LARDNER'S MUSEUM OF SCIENCE. D 33

No. 61.

THE STEAM ENGINE.

so absolute as it might at first appear to be. It
practicable to keep the water in the condenser 'at a temperature
lower than 100°, and at that temperature steam is evolved which
has a pressure of about one pound per square inch, which, after
all, will still react upon the piston.

In comparing, then, the non-condensing and condensing engine,
it is apparent, that while the latter gives a much greater amount of
moving power with the same rate of evaporation, and consequently
with the same consumption of fuel, the former is vastly more
simple in its mechanism, lighter in its weight, more inexpensive
in its construction and maintenance, and much more portable.

42. From what has been explained, it will be understood how
the piston-rod is made to move with any desired force alternately
in one direction or other, through a space equal to the stroke of th3
piston, or, what is the same, to the length of the cylinder.

The manner in which this force is transmitted to the object to
which the engine is applied, is extremely various. In some cases
the end of the piston-rod is connected with that of a vibrating
beam, to which a motion of oscillation is imparted like that of the
handle of a pump. In other cases it is put in connection with a
winch or crank, by which a motion of revolution is imparted to an
axle or shaft, in the same manner as a man working at a windlass
causes a rope to wind upon its axle. In other cases it is connected
with a wheel, to which it imparts rotation, as in some forms of
the locomotive engine. In short, the expedients by which the
alternate force of the piston is applied to the particular work to
be performed by the engine are so numerous, and differ so much
one from another, that it would be quite impossible to give any
general account which would include them.

43. To convey, however, some idea of one of the most common
methods of transmitting the force of the piston, we shall take the
case of the steam engine generally used to propel the machinery
of the larger class of factories, a view of which is given in fig. 26.
The several parts will be easily understood, after what has been
stated, without further explanation.

c is the steam cylinder.

p, the steam piston.

v v', the valves for admitting and withdrawing the steam, at
each end of the cylinder.

E, the piston-rod of the air pump.

L, the piston-rod of the hot-water pump.

K", the piston-rod of the cold-water pump.

i, the handle of the cock by which the jet in the condc
made to play with more or less force.

&, d,y, c, a system of jointed rods called the parallel motion, by
34

lenser is

FACTOKY ENGINE.

means of which the motion of the beam in the arc of a circle is
rendered compatible with that of the piston-rod in a straight line.

Fig. 26.

h, the pin on the end of the beam connected with the end of the
piston-rod by the joint h g.

b, the pin on the beam connected with the piston-rod of the air
pump by the joint b d.

H, the pin on the working end of the beam.

o, a rod called the connecting rod, by which the end H of the
beam is connected with a crank or winch upon the main shaft, to
which it is required to impart rotation.

D 2 35

THE STEAM ENGINE.

m, a lever jointed to a system of rods by which the valves
v v' admitting and withdrawing the steam at the top and bottom
of the cylinder are opened and closed. This lever m is acted upon
by pins which project from the piston-rod of the air pump, and
which appear in the figure. When the piston descends, the
upper pin strikes the arm m, which closes the upper steam valve
and lower exhausting valve, and opens the lower steam valve and
upper exhausting valve, so that the steam is admitted below and
withdrawn from above the piston, which is accordingly driven up.
"When the up-stroke is nearly terminated, the lower pin on the
rod R strikes the arm m, driving it upwards, and closes the upper
exhausting valve and the lower steam valve, while it opens the
upper steam valve and lower exhausting valve, by which means the
piston is driven down.

This method of working the valves is however at present rarely
used, being replaced by another expedient which we shall pre-
sently describe.

s, the pipe leading from the boiler by which steam is supplied
to the cylinder to impel the piston. This pipe communicates with
both ends of the cylinder by means of a passage s', which is
parallel to the cylinder.

T, the handle of a valve called the throttle valve, which is within
the steam pipe s, and which is turned by the handle, so as to contract
or widen more or less the passage for the steam. By this means
the supply of steam to the cylinder is increased or diminished.

Q, a system of revolving balls called the governor, witli which
the handle T of the throttle valve is connected by a series of levers
and joints, which are so constructed, that when the balls recede
from the axis of the governor, the valve is more or less closed,
and when they fall near the axis, the valve is fully open. These
balls receive a motion of revolution from the main shaft upon
which the crank is constracted by means of a band or by toothed
wheels. In either case their velocity of rotation will be always
proportionate to that of the shaft. In all applications of the
engine to the purposes of manufacture and the arts, there is some
determinate velocity which is required to be given to the shaft.
If steam be supplied in too great quantity to the cylinder, the
motion given to the shaft will be too rapid ; and if it be supplied
in too small quantity, the motion will be too slow.

Such irregularities of motion are prevented by the governor.
The moment the motion begins to be too rapid, the centrifugal
force produced by the revolution causes the balls to fly out, to
recede from the axis, and to close more or less the throttle valve.
If, on the contrary, the motion begins to be two slow, the balls
fall in, approach the axis, and open the throttle valve. Thus

GOVERNOR.

every undue increase of speed diminishes the supply of steam, and
moderates the velocity; and every undue decrease of speed
increases the supply of steam, and augments the velocity. In
this manner the action of the governor keeps the engine constantly
moving at a regulated rate.

44. The manner in which the governor opens the throttle valve
will be still more easily understood by the aid of fig. 27.

A small grooved wheel A B is attached to a vertical spindle
supported in pivots or sockets c and D, in which it is capable of
revolving. An endless cord works in the groove A B, and is
carried over proper pulleys to the axle of the fly-wheel, where it
likewise works in a groove. When this cord is properly tightened,

Fig. 27.

the motion of the fly-wheel will give motion to the wheel A B, so
that the velocity of the one will be subject to all the changes inci-
dental to the velocity of the other. By this means the speed of
the grooved wheel A B may be considered as representing the
speed of the fly-wheel, and of the machinery which the axle of
the fly-wheel drives.

It is evident that the same end might be obtained by substi-
tuting for the grooved wheel A B a toothed wheel, which might be
connected by other toothed wheels, and proper shafts and axles
with the axle of the fly-wheel.

37

THE STEAM ENGINE.

A ring or collar E is placed on the upright spindle, so as to be
capable of moving freely upwards and downwards. To this ring-
are attached by pivots two short levers, E F, the pivots or joints
at E allowing these levers to play upon them. At F these levers
are joined by pivots to other levers F G, which cross each other
at H, where an axle or pin passes through them, and attaches
them to the upright spindle c D. These intersecting levers are
capable, however, of playing on this axle or pin H. To the ends
G of these levers are attached tAVO heavy balls of metal. The
levers F G pass through slits in a metallic arc attached to the
upright spindle, so as to be capable of revolving upon it. If the
balls are drawn outwards from the vertical axis, it is evident
that the ends F of the levers will be drawn down, and therefore
the pivots E likewise drawn down. In fact, the angles E F H will
become more acute, and the angles F E F more obtuse. By these
means the sliding ring E will be drawn down. To this sliding
ring E, and immediately above it, is attached a grooved collar.,
which slides on the vertical spindle upwards and downwards with
the ring E. In the grooved collar are inserted the prongs of a
fork K, formed at the end of the lever K L, the fulcrum or pivot of
the lever being at L. By this arrangement, when the divergence
of the balls causes the collar E to be drawn down, the fork K,
whose prongs are inserted in the groove of that collar, is likewise
drawn down ; and, on the other hand, when by reason of the
balls falling towards the vertical spindle, the collar E is raised,
the fork K is likewise raised.

The ascent and descent of the fork K necessarily produce a
contrary motion in the other end sr of the lever. This end is
connected by a rod, or system of rods, with the end M of the short
lever which works the throttle valve T. By such means the
motion of the balls, towards or from the vertical spindle, pro-
duces in the throttle valve a corresponding motion ; and they are
so connected that the divergence of the balls will cause the throttle
valve to close, while their descent towards the vertical spindle
will cause it to open.

These arrangements being comprehended, let us suppose that
either by reason of a diminished load upon the engine or an
increased activity of the boiler, the speed has a tendency to
increase. This would impart increased velocity to the grooved
wheel A B, which would cause the balls to revolve with an
accelerated speed. The centrifugal force which attends their
motion would therefore give them a tendency to move from the
axle, or to diverge. This would cause, by the means already
explained, the throttle valve T to be partially closed, by which
the supply of steam from the boiler to the cylinder would be
38

ECCENTRIC.

diminished, and the energy of the moving power, therefore,
mitigated. The undue increase of speed would thereby he
prevented.

If, on the other hand, either hy an increase of the load, or a
diminished activity in the hoiler, the speed of the machine was
lessened, a corresponding diminution of velocity would take place
in the grooved wheel A B. This would cause the. balls to revolve
with less speed, and the centrifugal force produced by their
circular motion would be diminished. This force being thus no
longer able fully to counteract their gravity, they would fall
towards the spindle, which would cause, as already explained, the
throttle valve to be more fully opened. This would produce a
more ample supply of steam to the cylinder, by which the velocity
of the machine would be restored to its proper amount.

45. The method of working the valves by means of pins pro-
jecting from the rod of the air pump has been in most cases super-
seded by an apparatus called an eccentric, by which the motion of
the axle of the fly-wheel is made to open and close the valves at
the proper times.

An eccentric is a metallic circle attached to a revolving axle, so
that the centre of the circle shall not coincide with the centre
round which the axle revolves. Let us suppose that G (fig. 28) is
a square revolving" shaft. Let a circular plate of metal, B D,

having its centre at c, have a square hole cut in it corresponding
to the shaft, G, and let the shaft, G, pass through this square
aperture, so that the circular plate, B D, shall be fastened upon
the shaft, and capable of revolving with it as the shaft revolves.
The centre, c, of the circular plate will be carried round the
centre, G, of the revolving shaft, and will describe round it a

THE STEAM ENGINE.

circle, the radius oi which will be the distance of the centre, c, of
the circular plate from the centre ol the shaft. Such circular
plate, so placed upon a shaft, and revolving with it, is an
eccentric.

Let E F be a metallic ring, formed of two semicircles of metal
screwed together at H, so as to be capable, by the adjustment of
the screws, of having the circular aperture formed by the ring
enlarged and diminished within certain small limits. Let this
circular aperture be supposed to be equal to the magnitude of
the eccentric, B D. To the circular ring, E F, let an arm, L M,
be attached. If the ring, E r, be placed around the eccentric,
and the screws, H, be so adjusted as to allow the eccentric io
revolve within the ring, E F, then, while the eccentric revolves,
the ring not partaking of its revolution, the arm, L M, will be
alternately driven to the right and to the left, by the motion of the
centre, c, of the eccentric as it revolves round the centre, G, of the
axle. When the centre, c, of the eccentric is in the same horizontal
line with the centre, G, and. to the left of it, then the position of L :\r
will be that which is represented in fig. 28 ; but when, after half
a revolution of the main axle, the centre, c, of the eccentric is
thrown on the other side of the centre, G, then the point, M, will
be transferred to the right, to a distance equal to twice the
distance c G. Thus, as the eccentric revolves within the ring,
E F, that ring, together with the arm, L ar, will be alternately
driven right and left, through a space equal to twice the distance
between the centre of the eccentric and the centre of the revolving
shaft.

If we suppose a notch formed at the extremity of the arm, L M,
which is capable of embracing a lever, x M, moveable on a pivot
at N, the motion of the eccentric would give to such a lever an
alternate motion from right to left, and vice versa. If we suppose
another lever, N o, connected with N" M, and at right angles to it,
forming what is called a bell-crank, then the alternate motion
received by M, from right to left, would give a corresponding
motion to the extremity, o, of the lever, N o, upwards and down-
wards. If this last point, o, were attached to a vertical arm or
shaft, it would impart to such arm or shaft an alternate motion
upwards and downwards, the extent of which would be regulated
by the length of the levers respectively.

By such a contrivance the revolution of the shaft is made to
give an alternate vertical motion of any required extent to a
vertical shaft placed near the cylinder, which may be so connected
with the valves as to open and close them. Since the upward and
downward motion of this vertical shaft is governed by the alternate
motion of the centre, c, to the right and to the left of the cejitre,
40

FLY-WHEEL.

G, it is evident that, by the adjustment of the eccentric upon the
shaft, the valves may be opened and closed at any required position
of the crank, and therefore at any required position of the piston
in the cylinder.

Such is the contrivance by which the valves, whatever form may
be given to them, are now almost universal!^ worked in double-
acting steam engines.

46. Notwithstanding the regulating influence of the governor,
the motion of the engine would still be subject to a certain
inequality, owing to the varying action of the connecting rod, o
(fig. 26), on the crank. It will be quite evident that this action
is most efficient when o is placed at right angles to the crank,
which it is twice in every revolution, but that the more oblique it
is to the crank the less efficient will be its action upon it.

Now this inequality is effaced very nearly, if not altogether, by
means of a large and massive wheel of cast iron, called the FLY-
WHEEL, which is keyed upon the axle of the crank so as to revolve
with it, as shown in fig. 26. This wheel being well constructed,
and nicely balanced on its axle, is subject to very little resistance
from friction; any moving force which it receives it therefore
retains, and is ready to impart such moving force to the main
axle whenever that axle ceases to be driven by the power. "When
the crank, therefore, is in those positions in which the action of
the power upon it is most efficient, a portion of the energy of the
power is expended in increasing the velocity of the mass of matter
composing the fly-wheel. As the crank approaches the dead
points, that is the points where it is in the same straight line with
the connecting rod, the effect of the moving power upon the axle
and upon the crank is gradually enfeebled, and at these points
vanishes altogether. The momentum which has been imparted to
the fly-wheel then comes into play, and carries forward the axle
and crank out of the dead points with a velocity very little less
than that which it had when the crank was in the most favourable
position for receiving the action of the moving power.

By this expedient, the motion of revolution received by the
axle from the steam piston is subject to no other variation than
just the amount of change of momentum in the great mass of the
fly-wheel which is sufficient to extricate the crank twice in every
revolution from the mechanical dilemma to which its peculiar form
exposes it ; and this change of velocity may be reduced to as small
an amount as can be requisite by giving the necessary weight and
magnitude to the fly-wheel.

47. The- combination of jointed rods represented at cdgb, in
fig. 26, called the parallel motion, constitutes one of the many
inventions of Watt, which has always excited the greatest admi-

41

THE STEAM ENGINE.

ration, by reason of the remarkable geometrical intuition which it
manifested in one who was uninstructed in the advanced prin-
ciples of geometrical analysis upon which the perfection of its
action depends. Although this beautiful arrangement has been
very generally superseded by others of greater simplicity, and of
sufficient, though less, precision of action, it will not be unin-
teresting here to attempt a brief and popular explanation of the
principles upon which its performance depends.

The end of the beam with which the top of the piston-rod is
connected vibrating upon its centre, necessarily plays in a circular
arc, the convexity of which is presented to the right in fig. 26.
Now it is clear, that if the end y of the piston-rod were imme-
diately jointed to this end of the beam, it would be bent towards
the right through the convexity of the arc, while the beam moves
from its highest or lowest position to the middle of its play, and
that while it moves from the latter to the former position it will
be deflected back towards the left. Now, the efficient performance
of the engine absolutely requires that the piston-rod should not be
exposed to any such alternate strain, but that it should be guided
in a perfectly straight line in the direction of the axis of the cylinder ;
and this is precisely what the parallel motion accomplishes.

As we have just explained, the point h plays in an arc whose
convexity is presented to the right. Now, the joint c d, or link, as
it is called, moves upon a fixed centre, c. and consequently plays
in an arc whose convexity is presented to the left, that is, contrary
to the former. "While the point h throws the upper end of the
link g h to the right, by reason of the convexity of its play being
on that side, the point d throws the lower end g to the left, by
reason of its convexity being on the contrary side.

Now, the proportion of the lengths of the rods is so nicely
adjusted, that the effect of the rod c d in throwing the point g to
the left is exactly equal to the effect of the beam in throwing it
to the right ; and the consequence of this mutual compensation is,
that the point g, to which the end of the piston-rod is jointed, is
thrown neither to the right nor to the left, but is moved upwards
and downwards in a straight line.

48. To be enabled to verify the efficiency of the engine and
enforce a due economy of fuel, it is necessary to be provided with
indicators, by which at all times the effective force of the piston can
be ascertained. Now this effective force depends conjointly upon
the pressure of the steam which moves the piston and the reaction
of the tmcondensed steam, and of the gases which the air pump
may fail to withdraw from the condenser. Two mercurial gauges
are accordingly provided for this purpose in all large stationary
engines which are constructed on the condensing principle.

42

•

PARALLEL MOTION — BAROMETER GAUGE.

The force of steam which moves the piston is indicated by the
steam gauge already described, and which is shown attached to
the exposed end, K, of the boiler in fig. 7. The reaction of the
uncondensed steam and gases is indicated by a gauge called the
barometer gauge, inasmuch as it would be in fact a barometer if
an absolute vacuum were produced before the piston. This gauge
consists of a glass tube, A B (fig. 29), more than thirty inches long,
and open at both ends, placed in an upright or vertical
position, having the lower end B immersed in a
cistern of mercury, c. To the upper end is attached
a metal tube, which communicates with the condenser,
in which a constant vacuum, or rather high degree of
rarefaction, is sustained. The same vacuum must
therefore exist in the tube A B, above the level of the
mercury, and the atmospheric pressure on the surface
of the mercury in the cistern c will force the mercury
up in the tube A B, until the column which is sus-
pended in it is equal to the difference between the
atmospheric pressure and the pressure of the uncon-
densed/ steam. The difference between the column of
mercury sustained in this instrument and in the
common barometer, will determine the strength of the uncondensed
steam, allowing a force proportional to one pound per square inch
for every two inches of mercury in the difference of the two
columns. In a well-constructed engine which is in good order,
there is very little difference between the altitude in the barometer
gauge and the common barometer.

49. To compute the force with which the piston descends, thus
becomes a very simple arithmetical process. First, ascertain the
difference of the levels of the mercury in the steam gauge ; this
gives the excess of. the steam pressure above the atmospheric
pressure. Then find the height of the mercury in the barometer
gauge ; this gives the excess of the atmospheric pressure above
the uncondensed steam. Hence, if these two heights be added
together, we shall obtain the excess of the impelling force of the
steam from the boiler, on the one side of the piston, above the
resistance of the uncondensed steam on the other side ; this will
give the effective impelling force. Now, if one pound be allowed
for every two inches of mercury in the two columns just mentioned,
we shall have the number of pounds of impelling pressure on every
square inch of the piston. Then, if the number of square inches
in the section of the piston be found, and multiplied by the
number of pounds on each square inch, the force with which it
moves will be obtained.

From what we have stated it appears that, in order to estimate

43

the force with which the piston is urged, it is necessary to refer to
both the barometer and the steam gauge. This double computa-
tion may be obviated by making one gauge serve both purposes.
If the end c of the steam gauge (fig. 7), instead of communi-
cating with the atmosphere, were continued to the condenser, we
should have the pressure of the steam acting upon the mercury in
the tube B A, and the pressure of the uncondensed vapour which
resists the piston acting on the mercury in the tube B c. Hence
the difference of the levels of the mercury in the tubes would at
once indicate the difference between the force of the steam and
that of the uncondensed vapour, which is the effective force with
which the piston is urged.

50. Perfect as these expedients must appear, they have been
deemed insufficient as indicators of an element so important as the
economy of steam power. If, during the motion of the piston
from end to end of the cylinder, the steam really acted upon it
with an uniform force, and if the reaction against it were also
uniform, then the steam and barometer gauges would give an exact
measure of the effective power. But many causes co-operate in
preventing such uniformity of action and reaction.

In the first place, the end of the cylinder from which the piston
moves is never left in free communication with the boiler through
the entire stroke. In all cases the steam is shut off by closing
the steam valve before the stroke is completed, and if the engine
works by expansion, which most engines do,, the steam is shut off
after a certain part of the stroke — such as three-fourths, two-
thirds, a half, and sometimes even a third, or a fourth — has been
made. In all such cases, the pressure on the piston after the
steam has been shut off becomes less and less, as the steam in the
cylinder expands by the advance of the piston.

Neither is the reaction uniform; for the condensation of the
steam in the condenser is not absolutely instantaneous, though
very rapid, but still less is the removal of the air and gases, which
are fixed in the water injected to produce the condensation,
instantaneous. The action of the air pump is gradual, and con-
sequently the reaction on the piston, considerable at first, becomes
gradually less and less towards the end of the stroke.

Now it is clear that, under these circumstances, the effective
power of the piston, being always measured by the excess of the
impelling force over the reaction, must vary continually from the
beginning to the end of the stroke ; and as the total effective force
must consist of the aggregate of this varying action, it would seem
to be a problem of the greatest practical difficulty to ascertain it.

51. Nevertheless, the inexhaustible resources of the genius of
Watt, which surmounted so many other difficulties, did not shrink

44

INDICATOR.

before this ; and produced an instrument of most felicitous per-
fection, called an Indicator, by which the object was perfectly and
simply attained.

This contrivance consists of a cylinder of about 1| inch in diameter,
and 8 inches in length. It is bored with great accuracy, and fitted
with a solid piston moving steam-tight in it with very little friction.
The rod of this piston is guided in the direction of the axis of the
cylinder through a collar in the top, so as not to be subject to fric-
tion in any part of its play. At the bottom of the cylinder is a pipe
governed by a stop-cock and terminated in a screw, by which the
instrument may be screwed on the top of the steam cylinder of the%
engine. In this position, if the stop-cock of the indicator be
opened, a free communication will be made between the cylinder
of the indicator and that of the engine. The piston-rod of the
indicator is attached to a spiral spring, which is capable of exten-
sion and compression, and which by its elasticity is capable of
measuring the force which extends or compresses it in the same
manner as a spring steel-yard or balance. If a scale be attached
to the instrument at any point on the piston-rod to which an index
might be attached, then the position of that index upon the
scale would be governed by the position of the indicator piston in
its cylinder. If any force pressed the indicator piston upwards,
so as to compress the spring, the index would rise upon the scale ;
and if, on the other hand, a force pressed the indicator piston
downwards, then the spiral spring would be extended, and the
index on the piston-rod descend upon the scale. In each case
the force of the spring, whether compressed or extended, would
be equal to the force urging the indicator piston, and the scale
might be so divided as to show the amount of this force.

Now let the instrument be supposed to be screwed upon the top
of the cylinder of a steam engine, and the stop-cock opened so as to
leave a free communication between the cylinder of the indicator
below its piston and the cylinder of the steam engine above the
steam piston. At the moment the upper steam valve is opened,
the steam rushing in upon the steam piston will also pass into the
indicator, and press the indicator piston upwards : the index upon
its piston-rod will point upon the scale to the amount of pressure
thus exerted. As the steam piston descends, the indicator piston
will vary its position with the varying pressure of the steam in the
cylinder, and the index on the piston-rod will play upon the
scale, so as to show the pressure of the steam at each point during
the descent of the piston.

52. If it were possible to observe and record the varying positions
of the index on the piston-rod of the indicator, and to refer each
of these varying positions to the corresponding point of the

45

THE STEAM ENGINE.

descending stroke, we should then be able to declare the actual
pressure of the steam at every point of the stroke. But it is
evident that such an observation would not be practicable. A
method, however, was contrived by Mr. Southern, an assistant of
Messrs, Boulton and Watt, by which this is perfectly effected. A
square piece of paper, or card, is stretched upon a board, which
slides in grooves formed in a frame. This frame is placed in a
vertical position near the indicator, so that the paper may be
moved in a horizontal direction backwards and forwards, through
a space of fourteen or fifteen inches. Instead of an index, a
pencil is attached to the indicator of the piston-rod : this pencil is
lightly pressed by a spring against the paper above mentioned,
and as the paper is moved in a horizontal direction, the pencil
would trace upon it a line. If the pencil were stationary, this
line would be straight and horizontal, but if the pencil were
subject to a vertical motion, the line traced on the paper moved
under the pencil horizontally would be a curve, the form of which
would depend on the vertical motion of the pencil. The board
thus supporting the paper is put into connection by a light cord
carried over pulleys with some part of the parallel motion, by
which it is alternately moved to the right and to the left, As the
piston ascends or descends, the whole play of the board in the
horizontal direction will therefore represent the length of the
stroke, and every fractional part of that play will correspond to a
proportional part of the stroke of the steam piston.

53. The apparatus being thus arranged, let us suppose the steam
piston at the top of the cylinder commencing its descent. As it
descends, the pencil attached to the indicator piston-rod, varies its
height according to the varying pressure of the steam in the
cylinder. At the same time the paper is moved uniformly under
the pencil, and a curved line is traced upon it from right to left.
"When the piston has reached the bottom of the cylinder, the
upper exhausting valve is opened, and the steam drawn off to the
condenser. The indicator piston being immediately relieved from
a part of the pressure acting upon it, descends, and with it the
pencil also descends ; but at the same time the steam piston has
begun to ascend, and the paper to return from left to right under
the pencil. While the steam piston continues to ascend, the con-
densation becomes more and more perfect, and the vacuum in the
cylinder, and therefore also in the indicator, being gradually
increased in power, the atmospheric pressure above the indicator
piston presses it downwards and stretches the spring. The pencil
meanwhile, with the paper moving under it from right to left,
traces a second curve. As the former curve showed the actual
pressure of the steam impelling the piston in its descent, this latter
46

INDICATOR.

will show the pressure of the uncondensed steam resisting the
piston in its ascent, and a comparison of the two will exhibit the
effective force on the piston. Fig 30 represents such a diagram
as would be produced by this instrument. A B c is the curve
traced by the pencil during the descent of the piston, and c i> E

Fig. 30.

that during its ascent. A is the position of the pencil at the
moment the piston commences its descent, B is its position at the
middle of the stroke, and c at the termination of the stroke.
On closing the upper steam valve and closing the exhausting
valve, the indicator piston being gradually relieved from the
pressure of the steam, the pencil descends, and at the same time
the paper moving from left to right, the pencil traces the curve
c D E, the gradual descent of this curve showing the progressive
increase of the vacuum. As the atmospheric pressure constantly
acts above the piston of the indicator, its position will be deter-
mined by the difference between the atmospheric pressure and the
pressure of the steam below it ; and therefore the difference be-
tween the heights of the pencil at corresponding points in the
ascending and descending stroke will express the difference
between the pressure of the steam impelling the piston in the
ascent and resisting it in the descent at these points. Thus, at
the middle of the stroke, the line B D will express the extent to
which the spring governing the indicator piston would be stretched
by the difference between the force of steam impelling the piston
at the middle of the descending stroke, and the force of steam
resisting it at the middle of the ascending stroke. The force,
therefore, measured by the line B D will be the effective force on
the piston at that point, and the same may be said of every part of
the diagram produced by the indicator.

The whole mechanical effect produced by the stroke of the
piston being composed of the aggregate of all its varying effects
throughout the stroke, the determination of its amount is a matter
of easy calculation by the measurement of the diagram supplied

47

THE STEAM ENGINE.

by the indicator. Let the horizontal play of the pencil from A.to
c be divided into any proposed number of equal parts, say ten : at
the middle of the stroke, B n expresses the effective force on the
piston ; and if this be considered to be uniform through the tenth
part of the stroke, as from / to g, then the number of pounds
expressed by B D multiplied by the tenth part of the stroke ex-
pressed in parts of a foot, will be the mechanical effect through
that part of the stroke expressed in pounds' weight raised one
foot. In like manner m n will express the effective force on the
piston after three-fourths of the stroke have been performed, and
if this be multiplied by a tenth part of the stroke as before, the
mechanical effect similarly expressed will be obtained ; and the
same process being applied to every successive tenth part of the
stroke, and the numerical results thus obtained being added
together, the whole effect of the stroke will be obtained, expressed
in pounds' weight raised one foot.

54. By means of the indicator, the actual mechanical effect pro-
duced by each stroke of the engine can be obtained, and if the actual
number of strokes made in any given time be known, the whole
effect of the moving power would be determined. An instrument
called a counter was also contrived by Watt, to be attached either
to the working beam, or to any other reciprocating part of the
engine. This instrument consisted of a train of wheel-work with
governing hands, or indices moved upon divided dials, like the
hands of a clock. A record of the strokes was preserved by means
precisely similar to those by which the hands of a clock or time-
piece indicate and record the number of vibrations of the pendulum
or balance-wheel.

55. Such, then, is the machine, and such the principal expedients
by which it has been adapted as a moving power of unparalleled
importance and efficiency in all the industrial arts. In certain
applications of the engine some of these provisions are unnecessary
or inapplicable. In others supplementary expedients are required
and supplied. Our present purpose, however, will be attained, if
we have succeeded in rendering clearly intelligible the general
principle upon which the machine as described above acts,
and the special uses of the accessories that have been described.
These being well understood, no great difficulty will be encountered
in comprehending the mechanism and the action of any special
form of engine.

A ..".

p W

Fig. 1.

THE EYE.

CHAPTER I.

1. Pleasures and advantages of the power of vision. — 2. Reasons why a
knowledge of the structure and functions of the eye is desirable. —
3. Description of the eye. — 4. Sclerotica and cornea. — 5. Aqueous
humour, pupil, and iris. — 6. Crystalline humour and ciliary processes.
— 7. 'Choroid. — 8. Retina and vitreous humour. — 9. Axis of the eye
and optic nerve. — 10. Numerical data. — 11. Limits of the play of
the eye. — 12. Achromatism of the eye. — 13-16. How vision is
caused. — 17. Conditions of perfect vision. — 18. Distinctness of the
image. — 19. Parallel rays. — 20, 21. Defects of vision and their
remedies. — 22-24. Power of adaptation. — 25-29. Limits of this
power. — 30, 31. — Causes of defective vision. — 32. Magnitude of the
image on the retina. — 33. Apparent magnitude denned. — 34-37.
Nature of its variation. — 38-40. Diminutiveness of the pictures on
the retina. — 41. Sufficiency of illumination.

1. Or all the organs of sense, that to which we are most
largely indebted is un questionably THE EYE. It opens to us the
widest and most varied range of observation. The pleasures and
advantages we derive from it directly and indirectly have neither
cessation nor bounds. It guides our steps through the world we

LARDHER'S MUSEUM OF SCIENCE. E 49

No. 54.

THE EYE.

inhabit. It invests us with a space-penetrating power to which
there seems to be no practical limit. By the exercise of this
power, we enjoy the unspeakable pleasure of surveying the phy-
sical universe, consisting of countless myriads of worlds dispersed
through the measureless abysses of space, worlds compared with
most of which this of ours is of most diminutive dimensions.
These stupendous globes roll in silent majesty round remote suns
which warm and illuminate distant spheres, and collected in vast
groups, are often presented to our eye as mere nebulous specks,
but when viewed with high telescopic aid, blaze into stellar masses
of the most dazzling splendour. System after system of worlds
like our own are thus displayed before us, which, according to all
analogy, are similarly peopled, and destined to fulfil like destiniss
in the moral economy of creations, — theatres of life and intelligence
teeming with evidence of the incessant play of boundless power,
wisdom, and goodness.

Although the eye, strictly speaking, is cognisant only of light
and colours, yet from an habitual comparison of combinations and
tints of colour with the forms of bodies, as ascertained by the
sense of touch, we are enabled, with the greatest facility, promp-
titude, and precision, to recognise by the sight, the forms, mag-
nitudes, motions, distances, and positions, not only of the objects
which surround us, and which we can approach, but also of
those constituting the material universe, which are inaccessible.

This vast range of observation, however, great as it is, forms
but a small part of the sources of pleasure and advantage supplied
by this organ. We have, besides, the inestimable advantages and
the great moral powers which arise from the ability it bestows
upon us to acquire knowledge through the study of books. It
enables us to converse with and derive instruction from the most
learned, the most wise, and the most virtuous of our own and all
former ages ; and although those who have the misfortune to be
deprived of this important organ, can, to some small extent,
replace it by the car, aided by the eye of another ; yet this, and all
other expedients contrived for their relief, supply results infinitely
small and insignificant compared with those which are obtained jy
the organ itself.

2. The eye, considered in itself apart from its uses, is a most in-
teresting and instructive object. It affords beyond comparison the
most beautiful example of design, structure, and contrivance, that
is to be found in the animal economy. Nowhere do we find so
remarkable an adaptation of means to an end, of means consisting
of the most profound combination of scientific principles, and an
end manifesting the operation of a will directed by the most
boundless beneficence.
50

STRUCTURE OF THE EYE.

Tliis organ is, for these reasons, a subject of inquiry and expo-
sition, which must be regarded with, the most lively interest by
every one, whatever be his station, who is endowed with the least
understanding or reflection. But besides the general considera-
tions here developed, it is also to be remembered that, without a
previous knowledge of the structure and functions of the eye, it is
impossible to comprehend the use and application of the innumer-
able optical instruments which have been invented to aid its
defects, whether natural or accidental ; to repair the ravages of
time, and to supply to age a renovated and re-invigorated organ of
vision ; to replace the diseased optical membrane removed by the
knife of the surgeon, and thus restore sight where absolute blind-
ness had ensued ; to bring within the range of accurate vision
objects rendered indistinctly visible, or altogether invisible, either
by reason of their remoteness or minuteness. These admirable
instruments can be easily rendered intelligible, provided a general
knowledge of the structure and functions of the eye be first
obtained, but not otherwise.

"We purpose, therefore, to devote the present tract to a popular
and simple exposition of the eye, and more particularly, the
human eye.

3. The eyes, as they exist in the human species, have the form,
as is well known, of two spheres, each about an inch in diameter,
which are surrounded and protected by strong bony sockets
placed on each side of the upper part of the nose. The external
coating of these spheres is lubricated by a fluid secreted in adjacent
glands, and spread upon them from time to time by the action of
the eye-lids in winking.

The eye-balls are moved by muscles connected with them within
the socket upon the principle known in mechanics as the ball and
socket joint.

A front view of the eyes and surrounding parts is shown in
fig. 1, a section of them made by a horizontal plane through the
line A B, which passes through the centre of the front of the eye-
balls, being shown in fig. 2 (see p. 49).

4. The external coating c D F E consists of a strong and tough
membrane, called the sclerotica, or sclerotic coat. A part of this
membrane is visible when the eye-lids are open at w, and is called
the white of the eye. In this part of the eye-ball there is a
circular opening, covered by a thin and perfectly transparent shell
D G F, called the cornea. This cornea is more convex than the
general surface of the eye-ball, and may be compared to a watch-
glass. It is connected round its edge with the sclerotica, which
•differs from it, however, both in colour and opacity, the sclerotica
being white and opaque, while the cornea is perfectly colourless

E 2 51

itioB

ated

THE EYE.

and transparent. The thickness of the cornea is everywhere the
same.

The cornea covers that part of the front of the eye which is
coloured, and is terminated round the coloured part at the com-
mencement of the white of the eye.

5. Within the cornea is a small chamber filled with a trans-
parent liquid, called the aqueous humour, partially divided by a
thin annular partition I, called the iris, in the centre of which
is a circular aperture P, called fas pupil. The iris is a membra-
neous substance varying in colour in different individuals, which
gives the peculiar colour to the eye. The pupil presents the
appearance of a black spot in the centre of the coloured part. A
front view of the iris and pupil is given at I and r, and a sec

is indicated by the same letters in fig. 2.

6. The membrane containing the aqueous humour is terminate
at its posterior part by a substance in the form of a double convex
lens, which contains another transparent liquid, called the crys-
talline humour. This lens K is somewhat greater in diameter than
the pupil, and is supported by a ring of muscles, called the ciliary
processes (represented at L), in such a position that its axis passes
through the centre of the pupil.

Thus the crystalline and the ciliary processes, with the c
include the membrane containing the aqueous humour.

7. Within the sclerotica is a second coat IST, called the ch
This is a vascular membrane which lines the internal surface of
the sclerotic coat, and which terminates in front in the ciliary
processes, by which the crystalline lens is set in it in the same
manner as the cornea is set in the sclerotic coat.

Some anatomists maintain that the iris is only a continuation
of the choroid, and that the cornea is a continuation of the
sclerotic coat, which there becomes transparent. The inner surface
of this choroid coat is covered with a slimy pigment of an intensely
black colour, by which the reflection of the light which enters the
eye is prevented.

8. A third coat, represented at o, called the retina, from the
resemblance of its structure to network, lines this black coating,

The internal chamber Q of the eye-ball is filled with a trans-
parent liquor, called the vitreous humour, which is included in
a membraneous capsule, called the hyaloid.

Thus between the cornea and the posterior surface of the eye
there are three successive humours ; the aqueous, contained by
the cornea ; the crystalline, contained by the crystalline lens ;
and the vitreous, which fills the inner and larger chamber of the
eve -ball.

9. A straight line ir T passing through the centre of the cornea,

STRUCTURE OF THE EYE.

coinciding with, the axis of the crystalline lens, and through
the centre of the eye-ball, is called the optical axis, or the axis
of the eye.

At a point of the posterior surface of the eye-ball between
the optical axis M T and the nose, the sclerotic coat is formed
into a tube, which leads backwards and upwards to the brain.
This tube contains within it the optic nerve, which at the point
c E, where it enters the eye-ball, spreads out over the inner
surface of the choroid and forms the retina, and includes the
hyaloid capsule containing the vitreous humour.

The retina must therefore be regarded as nothing more than the
continuation and diffusion of the optic nerve.

The retina, which in dissection admits of being easily separated
from the choroid, is absolutely transparent, so that the light or
colours which enter the inner chamber of the eye are not inter-
cepted by it, but penetrate it as they would any other thin and
perfectly transparent substance, and are only arrested by the black
coating spread upon the choroid.

10. The following are the average numerical data connected
with the eye : —

lOOths ofaninch^

Radius of sclerotic coating . . . . 39 to 43

Radius of cornea . 28 — 32

External diameter of iris

Diameter of pupil ....

Thickness of cornea ....

Distance of pupil from centre of cornea

Distance of pupil from centre of crystalline

Radius of anterior surface of crystalline

Radius of posterior surface of crystalline .

Diameter of crystalline

Thickness of crystalline

Length of optic axis ....

43 — 47
12 — 28

4

8

4

28 — 39
20 — 24
39
30
87 — 95

11. The limits of the play of the eye-baU are as follows :— The
optic axis can turn in the horizontal plane through an angle of
60° towards the nose, and 90° outwards, giving an entire hori-
zontal play of 150°. In the vertical direction it is capable of
turning through an angle of 50° upwards and 70° downwards,
giving a total vertical play of 120°.

12. When an image of any object is formed by a lens composed of
a single piece of glass or other transparent substance, it is always
tinged more or less at its edges with the prismatic colours, giving
it a sort of iridescence. This constituted a defect of the telescope,
which seemed so irremediable that many astronomers had recourse
by preference to reflectors, in which no such effect is produced. At
length it was discovered that this defect could be completely

53

THE EYE.

removed by lenses, composed of two species of glass, having diffe-
rent refracting powers, and whose curvatures are mutually adapted
according to principles established in optics.

Now, it is a curious and highly interesting fact, that the eye,
which, as we know, is entirely free from this defect, owes its
perfection in this respect to the application of precisely the same
optical principle in its structure, so that if the first inventors of
the telescope had only thought of copying more closely the struc-
ture of the eye, they would have discovered sooner the principle
of ACHROMATISM, the name given to this precious quality of lenses,
from two Greek words, signifying the absence of colour.

13. The structure of the eye being thus understood, it will bo
easy to explain the effect produced within it by luminous or illu-
minated objects placed before it.

Let us suppose rays of light proceeding from any luminous
object, such as the sun, incident upon that part of the eye-ball
which is left uncovered by the open eye-lids.

Those rays which fall upon the white of the eye, w, fig. 1 ,
render visible that part of the eye-ball. Those rays which fall
upon the cornea pass through it. The exterior rays fall upon the
iris, by which they are reflected, and render it visible. The
internal rays pass through the pupil, are incident upon the crys-
talline, which, being transparent, is also penetrated by them,
from which they pass through the vitreous humour, and finally
reach the posterior surface of the inner part of the eye, where
they penetrate the transparent retina, and are received by the
black surface of the choroid, upon which they produce an illu-
minated spot.

The aqueous humour being more dense than the external air,
and the surface of the cornea, which includes it, being convex, rays
passing from the air into it will be rendered by a general law of
optics more convergent, or less divergent.

In like manner, the anterior surface of the crystalline lens
being convex, and that humour being more dense than tho
aqueous, a further convergent effect will be produced.

Again, the posterior surface of the crystalline being convex
towards the vitreous humour, and this latter humour being lest1,
dense than the crystalline, another convergent effect will take
place. These rays passing successively through these three
humours, are rendered at each surface more and more convergent.

14. If an object be placed before the eye, pencils of rays will
proceed from it, and penetrate the successive humours ; and if
these pencils be brought to a focus at the posterior surface, an
inverted image of the object will be formed there, exactly as it
would be formed by lenses composed of any transparent media

54

IMAGES ON THE RETINA.

whose refracting powers would correspond with each, of the
humours.

15. That this phenomenon is actually produced, may he ren-
dered experimentally manifest hy taking the eye-ball of an ox
recently killed, and dissecting the posterior part, so as to lay hare
the choroid. If the eye thus prepared he fixed in an aperture in a
screen, and a candle he placed before it at a distance of eighteen
or twenty inches, an inverted image of the candle will be seen
through the retina, as if it were produced upon ground glass or
oiled paper.

16. It appears, then, that the immediate cause of vision, and
the immediate object of perception, is the image thus pro-
duced by means of the refracting powers of the humours of
the eye.

17. In order, therefore, to perfect vision, the following conditions
must be fulfilled :—

1°. The image must be perfectly distinct.

2°. It must have sufficient magnitude,

3°. It must be sufficiently illuminated.

4°. It must continue on the retina for a sufficient length of
time.

Let us examine the. circumstances which affect these conditions.

18. — 1°. DISTINCTNESS OP THE IMAGE.

The image formed on the retina will be distinct or not, according
as the pencils of rays proceeding from each point of the object
placed before the eye, are brought to an exact focus on the retina
or not. If they be not brought to an exact focus on the retina,
their focus will be a point beyond the retina, or within it. In
either case, the rays proceeding from any part of the object,
instead of forming a corresponding point on the retina, will form
a spot of greater or less magnitude, according to the distance of
the focus of the pencil from the retina, and the assemblage of
such luminous spots will form a confused picture of the object.
This deviation of the foci of the pencils from the retina is caused
by the refracting powers of the eye being either too feeble or too
strong. If the refracting powers be too feeble, the rays are inter-
cepted by the retina before they are brought to a focus ; if they
be too strong, they are brought to a focus before they arrive at
the retina.

19. The objects of vision may be distributed into two classes,
in relation to the refracting powers of the eye : 1st, Those which
are at so great a distance from the eye, that the pencils pro-
ceeding from them may be regarded as consisting of parallel
rays ; 2ndly, Those which are so near that their rays have sensible
divergence.

55

THE EYE.

It has been stated that the diameter of the pupil varies from
£ to £ an inch in magnitude, the variation depending upon a
power of dilatation and contraction with which the iris is endued.
Taking that diameter at its greatest magnitude of a quarter of an
inch, pencils proceeding from an object placed at the distance of
three feet would have an extreme divergence amounting to less
than half a degree ; and if the pupil be in its most contracted
state when its diameter is only the one-eighth of an inch, then
the divergence of the pencils proceeding from such an object would
amount to about fifteen minutes of a degree. It may therefore
be concluded, that pencils proceeding from all objects more distant
from the eye than two or three feet, may be regarded as consisting
of parallel rays.

20. If the refracting power of the humours of the eye be so
feeble that rays proceeding from such objects, and which enter the
eye in parallel directions, are not rendered sufficiently convergent
to come to a focus on the retina, or on the contrary, are so strong
as to bring them to a focus before they arrive at the retina, the
image produced upon the retina will be confused from the cause
just explained.

21. The remedy for such a defect in vision is supplied by tho
properties of convex and concave lenses.

If the eye possess too little convergent power, a convergent or
convex lens is placed before it, which, receiving the parallel
pencils, renders them convergent when they enter the pupil, and
this enables the eye to bring them to a focus on the retina, pro-
vided the power of the lens be equal to the deficient convergence
of the eye.

If, on the other hand, the convergent power of the eye be too
great, so that the parallel rays are brought to a focus before
arriving at the retina, a divergent or concave lens is placed before
the eye, by means of which parallel pencils are rendered divergent
before they enter the pupil; and the power of the lens is so adapted
to the convergent power of the eye, that the rays shall be brought
to a focus on the retina.

The two opposite defects of vision here indicated are generally
called, the one weak-sightedness or far-siyhtedness, and the other
near- sigh tedn ess.

If the objects of vision be placed so near the eye that the rays
composing the pencils which proceed from them have sensible
divergence, then the foci of these rays within the eye will be at a
distance from the optical centre greater than the principal focus,
which is the name given to the focus of parallel rays. If, there-
fore, in this case, the principal focus fall upon the retina, tho
focus of rays proceeding from sucli near objects would fall
56

FAR SIGHT AND NEAR SIGHT.

beyond it, and consequently the image on the retina would be
indistinct.

22. It follows, therefore, that eyes which see distant objects
at the greater class of distances would see indistinctly all
objects at less distances, unless there were in the eye some
means of self- adjustment, by which its convergent -power may
be augmented. Such means of self- adjustment are provided,
which operate within certain limits, by which we are enabled so
to accommodate the eye to the divergence of the pencils proceed-
ing from near objects, that the same eyes which are capable of
seeing distinctly objects so distant as to render the rays of the
pencils sensibly parallel, are also capable of seeing with equal
distinctness objects at distances varying from ten to twelve inches
and upwards.

23. By what means the convergent power of the humours is
thus varied is not certainly known, but that such means of self-
adjustment exist may be proved by the following experiment : —

Let a small black spot be made upon a thin transparent plate
of glass, and let it be placed at a distance of about twelve inches
from the eye. If the eye be directed to it, the spot will be seen.
as well as distant objects visible through the glass. Let the
attention be earnestly directed to the black spot, so that a distinct
perception of its form may be produced. The objects visible at a
distance will then be found to become indistinct.

But if the attention be directed more to the distant objects, so as
to obtain a distinct perception of them, the perception of the black
spot on the glass will then become indistinct. It is evident,
therefore, that when the eye accommodates itself so as to form.
upon the retina a distinct image of an object at twelve inches
distance, the image produced by objects at great distances will
become indistinct ; and that, on the other hand, when the eye
so accommodates itself as to render the image produced on the
retina by distant objects distinct, the image produced by an
object at two inches distance will become indistinct.

24. It is evident, therefore, that the power of the eye to refract
the pencils of light incident upon it, is to a certain extent under
the control of the will ; but by what means this change in the
refracting power of the organ is made is not so apparent. Various
hypotheses have been advanced to explain it. According to some,
the form of the eye-ball, by a muscular action, is changed in
such a manner as to increase the length of the optic axis, and
thus to remove the posterior surface of the retina to a greater
distance from the crystalline, when it is necessary to obtain a
distinct view of near objects ; and, on the contrary, to elongate
the transverse diameter of the eye, and shorten the optic axis so

57

THE EYE.

as to bring the retina closer to the crystalline, when it is desired to
obtain a distinct view of distant objects.

According to others, this change of form is only effected in the
cornea, which being rendered more or less convex by a muscular
action gives a greater or less convergent power to the aqueous
humour.

According to others, the eye accommodates itself to different
distances by the action of the crystalline, which is moved by the-
ciliary processes either towards or from the cornea, thus transfer-
ring the focus of rays proceeding from it within a certain limit of
distance to and from the retina ; or, by a similar action of the
ciliary processes, the crystalline lens may be supposed to be
rendered more or less convex, and thus to increase or diminish
its convergent power.

25. Whatever be the provisions made in the organisation of the
eJe> by which it is enabled to adapt itself to the reception of
divergent pencils proceeding from near objects, the power with
which it is thus endued has a certain limit. Thus eyes, which
see distinctly distant objects, and which therefore bring parallel
rays to a focus on the retina in their ordinary state, are not
capable of seeing distinctly objects brought nearer to them than
ten or twelve inches. The power of accommodating the vision to
different rays is therefore limited to a divergence not exceeding
that which is determined by the diameter of the pupil compared
with a distance of ten or twelve inches. Now, as the diameter of
the pupil is most contracted when the organ is directed to such
near objects, we may assume it at its smallest magnitude at one-
eighth of an inch, and therefore the divergence of a pencil pro-
ceeding from a distance of twelve inches would be ^th, and the
angle of divergence would therefore be very nearly half a degree.

It may, therefore, be assumed that eyes adapted to the vision of
distant objects are in general incapable of seeing distinctly objects
from which pencils have greater divergence than this, or which is the
same, objects placed at less than ten or twelve inches from the eye.

26. In the case of eyes whose convergent power is too feeble to
bring pencils proceeding from distant objects to a focus on the
retina, they will be in a still greater degree inadequate to bring
pencils to a focus which diverge from near objects; and con-
sequently such eyes will require to be aided, for near as well as
distant objects, by the interposition of convergent lenses. It
would, however, be necessary to provide lenses of different
convergent powers for distant and near objects, the latter requiring
a greater convergent power than the former ; and in general the
nearer the objects viewed, the greater the convergent power
required from the lens.

58

SELF-ADJUSTMENTS OF THE EYE.

27. In the case of eyes whose convergent power is so great as-
to bring pencils proceeding from distant objects to a focus short of
the retina, and which therefore, for such distant objects, require
the intervention of divergent lenses, distinct vision will be attained
without the interposition of any lens, provided the object be placed
at such a distance that the divergence of the pencils proceeding
from it shall be such that the convergent power of the eye bring
them to a focus on the retina.

Hence it is that eyes of this sort are called short- sighted,
because they can see distinctly such objects only as are placed at
the distance which gives the pencils proceeding from them such a
divergence, that the convergent power of the eye would bring
them to a focus on the retina.

28. If it be desired to ascertain the focal length of the divergent
lens which such an eye would require to see distant objects-
distinctly, it is only necessary to ascertain at what distance it is
enabled to see distinctly the same class of objects without the aid
of a lens. A lens having a focal length equal to this distance will
enable the eye to see distant objects distinctly, because such a lens
would give the parallel rays a divergence equal to the divergence
of pencils proceeding from a distance equal to its focal length.

29. Persons are said to be more or less near-sighted, according
to the distance at which they are enabled to see objects with
perfect distinctness, and they accordingly require, to enable them
to see distant objects distinctly, diverging lenses of greater or less
focal length.

As persons who are enabled to see distant objects distinctly
have the power of accommodating the eye so as to see objects at
ten or twelve inches' distance, so short-sighted persons have a
similar power of accommodation, but within proportionally smaller
limits. Thus a short-sighted person will be enabled to see
distinctly objects placed at distances from the eye varying from
four or five inches upwards, according to the degree of short-
sightedness with which he is affected.

30. The two opposite defects of vision which have been mentioned ,
arising from too great or too little convergent power in the eye,
may arise, either from a defect in the quality of the humours or in
the form of the eye. Thus near-sightedness may arise from too
great convexity in the cornea or in the crystalline, or it may arise
from too great a difference of density between the aqueous humour
and the crystalline, or between the crystalline humour and the
vitreous, or both of them ; or, in fine, it may arise from defects
both of the form and of the relative densities of the humours.

31. In a certain class of maladies incidental to the sight, the-
humours of the eye lose in a greater or less degree their trans-

59

THE EYE.

parency, and the crystalline humour is more especially liable to
this. In such cases vision is sometimes recovered by means of the
removal of the crystalline humour, in which case the organ is
reduced to two humours, the aqueous and the vitreous ; but as the
eye owes in a greater degree to the crystalline than to the other
humours the convergent power, it is necessary in this case to
supply the place of the crystalline by a very strong convergent
lens placed before the eye.

32. — 2°. MAGNITUDE OF THE IMAGE ON" THE EETIXA.

In order to obtain a perception of any visible object, it is not
enough that the image on the retina be distinct, it must also have
a certain magnitude.

Let us suppose that a white circular disk, one foot diameter,
is placed before the eye at a distance of 57 £ feet.

The axes of the pencils of rays proceeding from such disk to the
eye will be included within a cone, whose base is the disk, and
whose vertex is in the centre of the eye. .

These axes, after intersecting at the centre of the eye, will form
another cone, whose base will be the image of the disk formed
upon the retina. The common angle of the two cones will in this
case be 1°.

Let A B (fig. 3), be the diameter of the disk. Let c be the
centre of the eye, and let b a be the diameter of the image on the

retina. It is clear, from the perfect similarity of the triangles
A c B and a c b, that the diameter of the image b a will have to
the diameter of the object B A the same proportion as the distance
a c of the retina from the centre c has to the distance A c of the
object from the same centre. Therefore in this case, since one-half
the diameter of the eye is but half an inch, and the distance A c is
in this case supposed to be 57£ feet, the magnitude of the diameter
b a of the image on the retina will be found by the following
proportion : —

a b : A B : : | : 57| X 12 = 690,

Therefore we have

X A B _ _6^ _ 1

"" 690 ~

ab =

690

115

The total magnitude, therefore, of the diameter of the image 01
60

MAGNITUDE OF THE IMAGE.

the retina would in this case be the ^th part of an inch ; yet
such is the exquisite sensibility of the organ, that the object is in
this case distinctly visible.

If the disk were removed to twice the distance here supposed,
the angle of the cone c would be reduced to half a degree, and the
diameter of the image on the retina would be reduced to one-half
its former magnitude, that is to say, to the ^th part of an inch.
If, on the other hand, the disk were moved towards the eye, and
placed at half its original distance, then the angle c of the cone
would be 2°, and the diameter of the picture on the retina would
bo double its first magnitude, that is to say, the jfgth of an inch.

In general, it may therefore be inferred that the magnitude of
the diameter of the picture on the retina is increased or diminished
in exactly the same proportion as the angle of the cone c, formed
at the centre of the eye, is increased or diminished.

33. This angle is called the visual angle or apparent magnitude
of the object ; and when it is said that a certain object subtends at
the eye a certain angle, it is meant that lines drawn from the

. extremities of such object to the centre of the eye form such angle.
The apparent magnitude of an object must not be confounded
with its apparent -superficial magnitude, the term being invariably
applied to its linear magnitude. The apparent superficial magnitude
varies in proportion to the square of the apparent magnitude.

'Thus, for example, when the disk A B is removed to double its
original distance from the eye, the apparent magnitude, or the
angle c, is diminished one-half, and consequently the diameter
a b of the picture on the retina is also diminished one-half; and
since the diameter is diminished in the ratio of 2 to 1, the super-
ficial magnitude of the image, or its area, will be diminished in
the proportion of 4 to 1.

34. It is clear from what has been stated also, that when the
same object is moved from or towards the eye, its apparent
magnitude varies inversely as its distance ; that is, its apparent
magnitude is increased in the same proportion as its distance is
diminished, and vice versd.

It is easy to perceive that the objects which are seen under the
same visual angle will have the same apparent magnitude. Thus
let A' B' (fig. 3), be an object more distant than A B, and of such a
magnitude that its highest point A' shall be in the continuation of
the line c A, and its lowest point B' in the continuation of the line
c B. The apparent magnitude of A' B' will then be measured by
the angle at c. This angle will therefore at the same time
represent the apparent magnitude of the object A B and of the
object A' B'. It is evident that an eye placed at c will see every
point of the object A B upon the corresponding points of the object

61

THE EYE.

A' B'; so that if the object A B were opaque, and of a form similar
to the object A' B', every point of the one would be seen upon a
corresponding point of the other. In like manner, if an object
A" B" were placed nearer the eye than A B, so that its highest
point may lie upon the line c A, and its lowest point upon the line
c B, the object being similar in form to A B, would appear to be of
the same magnitude. Now it is evident that the real magnitudes
of the three objects A" B", A B, and A' B', are in proportion to their
respective distances from the eye ; A' B' is just so much greater
than A B, and A B than A" B", as c B' is greater than c B, and as
c B is greater than c B".

Thus it appears that if several objects be placed before the eye in
the same direction at different distances, and that the real linear
magnitudes of these objects are in the proportion of their distances,
they will have the same apparent magnitude.

35. A striking example of this principle is presented by the
case of the sun and moon. These objects appear in the heavens
equal in size, the full moon being equal in apparent magnitude to
the sun. Now it is proved by astronomical observation that the
real diameter of the sun is, in round numbers, four hundred times
that of the moon ; but it is also proved that the distance of the
sun from the earth is also, in round numbers, four hundred times
greater than that of the moon. The distances, therefore, of these
two objects being in the same proportion as their real diameters,
their visual or apparent magnitudes are equal.

36. It is evident from what has been explained, that objects
which have equal apparent magnitudes, and are therefore seen
under equal visual angles, will have pictures of equal magnitude
on the retina, a fact which proves that the visual angle is the
measure of the apparent magnitude.

37. If the same object be moved successively to increasing
distances, its apparent magnitude will be diminished in the same
proportion, exactly as its distance from the eye is increased.
Thus, if L M (fig. 4), be such an object, its apparent magnitude at

Fig. 4.

the distance E M will be measured by the angle L E M, at the

distance E M' by the angle I/ E M', and at the distance E M" by

the angle L" E M" ; and when the actual magnitude L 3i bears a

62

APPARENT MAGNITUDE.

small proportion to the distance, it is shown by the principles of
geometry that the angle I/ E M' is less than the angle L E H in the
same proportion as E M' is greater than E M, and that the angle
L" E M" is less than L E M in the same proportion as E 3d." is
.greater than E M.

38. Nothing can be more calculated to excite our wonder and
admiration than the distinctness of our perception of visible
•objects, compared with the magnitude of the picture on the retina,
from which immediately we receive such perception.

39. If we look at the full moon on a clear night, we perceive
with considerable distinctness by the naked eye the lineaments of
light and shade which characterise its disk. Now let us consider
only for a moment what are the dimensions of the picture of the
moon formed on the retina, from which alone we derive this
distinct perception.

The disk of the moon subtends a visual angle of half a degree,
and consequently, according to what has been explained, the
diameter of its picture on the retina will be ^th part of an inch,
and the entire superficial magnitude of the image from which we
derive this distinct perception is only the smooth part of a square
inch ; yet within this minute space, we are able to distinguish a
multiplicity of still more minute details. We perceive, for
example, forms of light and shade, whose linear dimensions do
not exceed one-tenth part of the apparent diameter of the moou,
and which therefore occupy upon the retina a space whose
diameter does not exceed the goosoooth part of a square inch.

40. To take another example, the figure of a man 70 inches
high, seen at a distance of 40 feet, produces an image upon the
retina the height of which is about one-fourteenth part of an inch.
The face of such an image is included in a circle whose diameter
is about one-twelfth of the height, and therefore occupies on the
retina a circle whose diameter is about the ^th part of an inch ;
nevertheless, within this circle, the eyes, nose, and lineaments are
distinctly seen. The diameter of the eye is about one-twelfth of
that of the face, and therefore, though distinctly seen, does not
occupy upon the retina a space exceeding the 400^000th of a
square inch.

If the retina be the canvas on which this exquisite miniature is
delineated, how infinitely delicate must be its structure, to receive
and transmit details so minute with such marvellous precision ;
and if, according to the opinion of some, the perception of these
details be obtained by the retina feeling the image formed upon
the choroid, how exquisitely sensitive must be its touch !

41.— 3°. SUFFICIENCY OF ILLUMINATION.

It is not enough for distinct vision that a well-defined picture of

63

THE EYE.

the object shall be formed on the retina. This picture must be
sufficiently illuminated to affect the sense, and at the same time
not be so intensely illuminated as to overpower the organ.

Thus it is possible to conceive a picture on the retina so
extremely faint as to be insufficient to produce sensation, or, on
the other hand, so intensely brilliant as to dazzle the eye, to
destroy the distinctness of sense, and to produce pain.

When we direct the eye to the sun, near the meridian, in an
unclouded sky, we have no distinct perception of his disk, because
the splendour is so great as to overpower the sense of vision, just
as sounds are sometimes so intense as to be deafening.

That it is the intense splendour alone which prevents a distinct
perception of the solar disk in this case is rendered manifest by
the fact that if a portion of the solar rays be intercepted by a
coloured glass, or by a thin cloud, a distinct image of the sun wi 1
be seen.

When we direct the eye to the firmament on a clear night,
there are innumerable stars which transmit light to the eye, and
which therefore must produce some image on the retina, but of
which we are altogether insensible, owing to the faintness of the
illumination. That the light, however, does enter the eye and
arrive at the retina is proved by the fact that if a telescope be
directed to the stars in question, so as to collect a greater quantity
of their light upon the retina, they will become visible.

Fig. 8.— THE THAUMATROPE.

THE EYE.

CHAPTEE II.

42. Power of accommodation of the eye. — 43, 44. Apparent brightness of
luminous objects. — 45-47. Intensity of brightness. — 48-57. The
image must continue a sufficient time upon the retina to enable that
membrane to produce a perception of it — Various illustrations of this.
— 58. Conditions which determine apparent motion. — 59. How
affected by distance. — 60. Example. — 61. When imperceptible. —
62. Motion of the firmament. — 63. Objects in rapid motion invisible.
— 64-66. Duration of the impression on the retina. — 67. Optical toys.
— 68, 69. Coincidence of^ the optical and geometrical centres of the
eye. — 70. Ocular spectra and accidental colours. — 71. Why visible
objects do not appear inverted. — 72. The seat of vision. — 73-75. The
optic nerve insensible to light.

42. THE eye possesses a certain limited power of accommodating
itself to various degrees of illumination. Circumstances which
are familiar to every one render the exercise of this power
evident.

If a person, after remaining a certain time in a dark room,
pass suddenly into another room strongly illuminated, the eye
suffers instantly a degree of inconvenience, and even pain, which

LARDNER'S MUSEUM OF SCIENCE. F 65

No. 59.

THE EYE.

causes the eyelids to close ; and it is not until after the lapse of
a certain time that they can be opened without inconvenience.

The cause of this is easily explained. While the observer re-
mains in the darkened or less illuminated room, the pupil is
dilated so as to admit into the eye as great a quantity of light as
the structure of the organ allows of. When he passes suddenly
into the strongly illuminated room, the flood of light arriving
through the widely dilated pupil acts with such violence on
the retina as to produce pain, which necessarily calls for the
relief and protection of the organ. The iris, then, by an
action peculiar to it, contracts the dimensions of the pupil so
as to admit proportionally less light, and the eye is opened with
impunity.

Effects the reverse of these are observed when a person passes
from a strongly illuminated room into one comparatively dark, or
into the open air at night. For a certain time he sees nothing,
because the contraction of the pupil, which, was adapted to the
strong light to which it had previously been exposed, admits so
little light to the retina that no sensation is produced. The pupil,
however, after a while dilates, and, admitting more light, objects
are perceived which were before invisible.

43. It is sometimes inferred, though erroneously, that the
apparent splendour of the image of a visible object decreases as
the square of the distance increases. This would be the case in
the strictest sense, if, while the object were withdrawn from the
eye to an increased distance, its image on the retina continued to
have the same magnitude ; for, in this ease, the absolute brightness
of each point composing such image would diminish as the square
of the distance increases, and the area of the retina over which
such points are diffused would remain the same ; but it must be
considered, that as the object retires from the eye the superficial
magnitude of the image on the retina is diminished in the same
proportion as the square of the distance of the object from the
eye is increased. It therefore follows that while the points com-
posing the image on the retina are diminished in the intensity of
their illumination, they are collected into a smaller space, so thf/t
what each point of the image on the retina loses in splendour, the
entire image gains by concentration.

44. If the sun were brought as close to the earth as the moon,
its apparent diameter would be 400 times greater, and the area of
its apparent disk 160000 times greater than at present, but the
apparent brightness of its surface would not be in any degree
increased. In the same manner, if the sun were removed to ten
times its present distance, it would appear under a visual angle
ten times less than at present, as in fact it would to an observer

66

BRIGHTNESS OF THE IMAGE.

on the planet Saturn, and its visible area would be a hundred
times less than it is, but the splendour of its diminished area
would be exactly the same as the present splendour of the sun's
disk.

The sun seen from the planet Saturn has an apparent diameter
ten times less than it has when seen from the earth.

The appearance from Saturn will then be the same as would be
the appearance of a portion of the disk of the sun seen from the
^arth through a circular aperture in an opaque plate, which would
exhibit a portion of the disk whose diameter is one-tenth of the
whole.

45. "When the light which radiates from a luminous object has
a certain intensity, it will continue to affect the retina in a
sensible manner, even when the object is removed to such a dis-
tance that the visual angle shall cease to have any perceivable
magnitude. The fixed stars present innumerable examples of
this effect. None of these objects, even the most brilliant of them,
subtend any sensible angle to the eye. When viewed through
the most perfect telescopes they appear merely as brilliant points.
In this case, therefore, the eye is affected by the light alone, and
not by the magnitude of the object seen.

46. Nevertheless the distance of such an object may be increased
to such an extent that the light, intense as it is, will cease to pro-
duce a sensible effect upon the retina.

There are seven classes of the fixed stars, diminishing gradually
in brightness,* which produce an effect on the retina such as to
render them visible to a naked eye. This diminution of splendour
is produced by their increased distance. The telescope brings into
view innumerable other stars, whose intrinsic splendour is as
great as the brightest among those which we see, but which do not
transmit to the retina, without the aid of the telescope, enough of
light to produce any sensible effect. It is demonstrable, however,
that, even without the telescope, they do transmit a certain
definite quantity of light to the retina ; the quantity of light
which they thus transmit, and which is insufficient to produce a
sensible effect, having to the quantity obtained by the telescope
a ratio depending upon the proportion of the magnitude of the
object-glass of the telescope to the magnitude of the pupil.

47. The quantity and intensity of the light transmitted by an
external object to the retina, which is sufficient to produce a per-
ception of such object, depends also upon the light received at the

* The term magnitude is used in astronomy, as applied to the fixed
stars, to express their apparent brightness ; no fixed star, howerer splendid,
subtends any sensible angle.

p 2 67

THE EYE.

same time by the retina from other objects present before the eye.
The proof of this is, that the same objects which are visible at
one time are not visible at another, though equally before the eye,
and transmitting equal quantities of light of the same intensity
to the retina. Thus, the stars are present in the heavens bv day
as well as by night, and transmit the same quantity of light to
the retina, yet they are not visible in the presence of the sun,
because the light proceeding from that luminary, directly and
indirectly reflected and refracted by the air and innumerable other
objects, is so much greater in quantity and intensity as to over-
power the inferior and much less intense light of the stars. This
case is altogether analogous to that of the ear, which when under
the impression of loud and intense sounds, is incapable of per-
ceiving sounds of less intensity, which nevertheless affect the
organ in the same manner as they do when, in the absence of
louder sounds, they are distinctly heard.

Even when an object is perceived, the intensity of the percep-
tion is relative, and determined by other perceptions produced at
the same time. Thus, the moon seen at night is incomparably
more splendid than the same moon seen by day or in the twilight,
although in each case the moon transmits precisely the same
quantity of light, of precisely the same intensity, to the eye ; but
in the one case the eye is overpowered by the superior splendour
of the light of day, which dims the comparatively less intense
light proceeding from the moon.

48. — 4°. THE IMAGE MUST CONTINUE A SUFFICIENT TIME UPON
THE EETINA TO ENABLE THAT MEMBHANE TO PEODUCE A PEE-
CEPTION OF IT.

The velocity with which light is propagated through space is at
the rate of about 200000 miles per second. Its transmission,
therefore, from all objects at ordinary distances to the eye may be
considered as instantaneous. The moment, therefore, any object
is placed before the eye an image of it is formed on the retina,
and this image continues there until the object is removed. Now
it is easy to show experimentally that an object may be placed
before the eye for a certain definite interval of time, and that a
picture may be painted upon the retina during that interval
without producing any perception or any consciousness of the pre-
sence of the object.

To illustrate this, let a circular disk A B c D, fig. 5, about twenty
inches in diameter, be formed in card or tin, and let a circle
A' B' c' D' be described upon it, about two inches less in radius
than the disk, so as to leave between the circle and the disk a
zone about two inches wide. Let the entire zone be blackened,
except the space A M M' A', forming about the one-twentieth of it.
68

CONTINUANCE OF THE IMAGE.

Let the disk thus prepared be attached to the back of a blackened
screen, so as to be capable of revolving behind it, and let a hole
one inch in diameter be
made in the screen at any
point, behind which the
zone A B c D is placed. If
the disk be now made to
revolve behind the screen,
the hole will appear as a
circular white spot so long
as the white space A at
passes behind it, and will
disappear, leaving the same
black colour as the screen
during the remainder of
the revolution of the disk.
The hole will therefore be
seen as a white circular spot
upon the black screen during one-twentieth of each revolution
of the disk. If the disk be now put in motion at a slow rate,
the white hole will be seen on the screen during one-twentieth of
each revolution. If the velocity of rotation imparted to the disk
be gradually increased, the white spot will ultimately disappear,
and the screen appear of a uniform black colour, although it be
certain that during the twentieth part of each revolution, what-
ever be the rate of rotation, a picture of the white spot is formed
on the retina.

49. The length of time necessary in this case for the action of
light upon the retina to produce sensation may be determined by
ascertaining the most rapid motion of the disk which is capable
of producing a distinct perception of the white spot. t This
interval will be found to vary with the degree of illumination.
If the spot be strongly illuminated, a less interval will be suffi-
cient to produce a perception of it ; if it be more feebly illuminated,
a longer interval will be required. The experiment may be made
by varying the colour of the space A M of the zone, and it will be
found that the interval necessary to produce sensation will vary
with the colour as well as with the degree of illumination.

50. Numerous observations on the most familiar effects of
vision, and various experiments expressly contrived for the pur-
pose, show that the retina, when once impressed with the picture
of an object placed before the eye, retains this impression, some-
times with its full intensity and sometimes more faintly, just as
the ear retains for a time the sensation of a sound after the cause
which has put the tympanum in vibration has ceased to act. The

69

THE EYE.

duration of this impression on the retina, after the removal of the
visible object which produced it, varies according to the degree of
illumination and the colour of the object. The more intense tile-
illumination, and the brighter the colour, the longer will be the
interval during which the retina will retain their effects.

51. To illustrate this experimentally, let a circular disk formed
of blackened card or tin, of twelve or fourteen inches in diameter,
be pierced with eight holes round its circumference, at equal dis-
tances, each hole being about half an inch in diameter, as represented
in fig. 6.

Let this disk be attached upon a pivot or pin at its centre o to a
board A B c D, which is blackened everywhere, except iipon a
circular spot at v, corresponding in magnitude to the holes mac.fr
in the circular plate.

Let this spot be first supposed to be white. Let the circukr
disk be made to revolve upon the point o, so as to bring the
circular holes successively before the white spot at v. The retina
will thus be impressed at intervals with the image of this circular
white spot. In the intervals between the transits of the holes
over it, the entire board will appear black, and the retina will
receive no impression. If the disk be made to revolve with a
very slow motion, the eye will see the white spot at intervals,
but if the velocity of rotation be-
gradually increased, it will be found
that the eye will perceive the white
spot permanently represented at v, as
if the disk had been placed with one
of its holes opposite to it without
moving. It is evident, therefore, that
in this case the impression produced
upon the retina, when any hole is
opposite the white spot, remains until
the succeeding hole comes opposite to
** C it, and thus a continued perception of

the white spot is produced.

If the white spot be illuminated in various degrees, or if it bs
differently coloured, the velocity of the disk necessary to produce
a continuous perception of it will differ. The brighter the colour
and the stronger the illumination, the less will be the velocity of
rotation of the disk which is necessary to produce a continuous
perception of the spot.

These effects show that the stronger the illumination and the
brighter the colour, the longer is the interval during which the
impression is retained by the retina.

52. This continuance of the impression of external objects on the
70

Fig. 6.

PEKCEPTION OF A MOVING OBJECT.

retina, after the light from the object ceases to act, is also mani-
fested by the fact, that the continual winking of the eyes for the
purpose of lubricating the eye-ball by the eye-lid does not
intercept our vision. If we look at any external objects, they
never cease for a moment to be visible to us, notwithstanding
the frequent intermissions which take place in the action of light
upon the retina in consequence of its being thus intercepted by
the eye-lid.

53. If a lighted stick be turned round in a circle in a dark
room, the appearance to the eye will be a continuous circle of
light ; for in this case the impression produced upon the retina by
the light, when the stick is at any point of the circle, is retained
until the stick returns to that point.

54. In the same manner, a flash of lightning appears to the
eye as a continuous line of light, because the light emitted at any
point of the line remains upon the retina until the cause of the
light passes over the succeeding points. In the same manner,
any objects moving before uthe eye with such a velocity that the
retina shall retain the impression produced at one point in the line
of its motion until it passes through the other points, will appear
as a continuous line of light or colour.

55. But to produce this effect, it is not enough that the body
change its position so rapidly that the impression produced at one
point of its path continues until its arrival at another point ; it is
necessary, also, that its motion should not be so rapid as to make
it pass from any of the positions which it successively assumes
before it has time to impress the eye with a perception of it ; for
it must be remembered, as has been already explained, that the
perception of a visible object presented to the eye, though rapid,
is not instantaneous.

The object must remain present before the organ of vision a
certain definite time, and its position must continue upon the
retina during such time, before any perception of it is obtained.
Now, if the body move from its position before the lapse of this
time, it necessarily follows that no perception of its presence,
therefore, will be obtained. If, then, we suppose a body moving
so rapidly before the eye that it remains in no position long
enough to produce a perception of it, such object will not be seen.

56. Hence it is that the ball discharged from a cannon passing
transversely to the line of vision is not seen ; but if the eye be
placed in the direction in which the ball moves, so that its angular
motion round the eye as a centre will be slow notwithstanding its
great velocity, it will be visible, because, however rapid its real
motion through space, its angular motion with respect to the eye
(and consequently of the image of its picture on the retina) will

71

THE EYE.

be sufficiently slow to give the necessary time for the production
of a perception of it.

57. The time thus necessary to obtain the perception of a
visible object varies with the degree of illumination, the colour,
and the apparent magnitude of the object. The more intense the
illumination the more vivid the colour, and the greater the appar-
ent magnitude the less will be the time necessary to produce a
perception of the object.

58. In applying this principle to the phenomena of vision, it
must be carefully remembered that the question is affected, not by
the real but by the apparent motion of the object, that is to say,
not by the velocity with which the object really moves through
space, but by the angle which the line drawn from the eye to
the object describes per second. Now this angle is affected by two
conditions, which it is important to attend to : 1°. the direction of
the motion of the object compared with the line of vision; and
2°. by the velocity of the motion compared with the distance of
the object. If the object were to move exactly in the direction of
the line of vision, it would appear to the eye to be absolutely
stationary, since the line drawn to it would have no angular
motion ; and if it were to move in a direction forming an obliq
angle to the line of vision, its apparent motion might be indefini'
slow, however great its real velocity might be.

For example, let it be supposed that the eye being at E, fig. 7,
an object o moves in the direction of o o', so as to move from o to

— j
alar
ique

*

0' in one second. Taking E as a centre, and E o as a radius, let a
circular arc o o" be described. The apparent motion of the object
will then be same as if, instead of moving from o to o' in one
second, it moved from o to o" in one second.

The more nearly, therefore, at right angles to the line of vision
the direction of the motion is, the greater will be the apparent
motion produced by any real motion of an object.

59. A motion which is visible at one distance may be invisible
at another, inasmuch as the angular velocity will be increased as
the distance is diminished.

Thus if an object at a distance of 57| feet from the eye move

at the rate of a foot per second, it will appear to move at the rate

of one degree per second, inasmuch as a line one foot long at 5

72

PERCEPTION OF A MOVING OBJECT.

feet distance subtends an angle of one degree. Now if the eye be
removed from such an object to a distance of 115 feet, the apparent
motion will be half a degree, or thirty minutes per second ; and if
it be removed to thirty times that distance, the apparent motion
will be thirty times slower. Or if, on the other hand, the eye
be brought nearer to the object, the apparent motion will be acceler-
ated in exactly the same proportion as the distance of the eye is
diminished..

60. A cannon-ball moving at 1000 miles an hour transversely
to the line of vision, and at a distance of 50 yards from the eye,
will be invisible, since it will not remain a sufficient time in any
one position to produce perception. The moon, however, moving
with more than double the velocity of the cannon-ball, being at
a distance of 240000 miles, has an apparent motion, so slow as
to be imperceptible,

61. The angular motion of the line of vision may be so dimin-
ished as to become imperceptible ; and the body thus moved will
in this case appear stationary. It is found by experience that
unless a body move in such a manner that the line of vision
shall describe at least one degree in each minute of time, its
motion will not be perceptible.

62. Thus it is that we are not conscious of the diurnal motion
of the firmament. If we look at the moon and stars on a clear
night, they appear to the eye to be quiescent ; but if we observe
them after the lapse of some hours, we find that their positions are
changed, those which were near the horizon being nearer the
meridian, and those which were in the meridian having descended
towards the horizon. Since we are conscious that this change did
not take place suddenly, we infer that the entire firmament must
have been in continual motion round us, but that this motion is
so slow as to be imperceptible.

Since the heavens appear to make a complete revolution in
twenty-four hours, each object on the firmament must move at
the rate of 15° an hour, or at the rate of one quarter of a degree
a minute. But since no motion .is perceptible to the eye which has
a less apparent velocity than 1° per minute, this motion of the
firmament is unperceived. If, however, the earth revolved on its
axis in six hours instead of twenty-four hours, then the sun,
moon, stars, and other celestial objects, would have a motion at
the rate of 60° an hour, or 1° per minute. The sun would appear
to move over a space equal to twice its own diameter each minute,
and this motion would be distinctly perceived.

The fact that the motion of the hands of a clock is not perceived
is explained in the same manner.

63. If an object which moves very rapidly be not sufficiently

73

THE EYE.

illuminated, or be not of a sufficiently bright colour to impress the
retina sensibly, it will then, instead of appearing as a continuous
line of colour, cease to be visible altogether ; for it does not
remain in any one position long enough to produce a sensible
effect upon the retina. It is for this reason that a ball projected
from a cannon or a musket, though passing before the eye, cannot
be seen. If two railway trains pass each other with a certain
velocity, a person looking out of the window of one of them will
be unable to see the other. If the velocity be very moderate, and
the light of the day sufficiently strong, the appearance of the
passing train will be that of a flash of colour formed by the
mixture of the prevailing colours of the vehicles composing it.

An expedient has been contrived, depending on this principle,
to show experimentally that the mixture of the seven prismatic
colours, in their proper proportions, produces white light. The
colours are laid upon a circular disk surrounding its edge, which
they divide into parts proportional to the spaces they occupy in
the spectrum. When the disk is made to revolve, each colour
produces, like the lighted stick, the impression of a continuous
ring, and consequently the eye is sensible of seven rings of the
several colours superposed one upon the other, which thus produce
the effect of their combination, and appear as white or a whitish
grey colour.

64. The duration of the impression upon the retina, after the
object producing it is removed, varies according to the vividness
of the light proceeding from the object, being longer according as
the light is more intense. It was found that the light proceeding
from a piece of coal in combustion moved in a circle at a distance
of 165 feet, produced the impression of a continuous circle of
light when it revolved at the rate of seven times per second. The
inference from this would be that in that particular case the
impression upon the retina was continued during the seventh part
of a second after the removal of the object.

It is from the cause here indicated that forked lightning pre-
sents the appearance of a continuous line of light.

65. The duration of the impression on the retina varies also
with the colour of the light, that produced by a white object
being most visible, and yellow and red being most in degree of
durability ; the least durable being those tints which belong to
the most refrangible lights.

66. The duration of the impression also depends on the state of
illumination of the surrounding space ; thus the impression pro-
duced by a luminous object when in a dark room is more durable
than that which would be produced by the same object seen in an
illuminated room. This may be ascribed to the greater sensitiveness

74

THATJMATKOPES.

of the retina when in a state of repose than when its entire surface
is excited by surrounding lights. Thus it is found that while the
varying duration of the impression of the illuminated object in a
dark room was one-third of a second, its duration in a lighted
room was only one-sixth of a second.

67. Innumerable optical toys and pyrotechnic apparatus owe-
their effect to this continuance of the impression upon the retina
when the object has changed its position.

Amusing toys, called thaumatropes, phenakisticopes, phantas-
kopes, &c., are explained upon this principle. A moving object,
which assumes a succession of different positions in performing any
action, is represented in the successive divisions of the circumfer-
ence of a circle, as in fig. 8, in the successive positions it assumes.
These pictures, by causing the disk to revolve, are brought in
rapid succession before an aperture, through which the eye is
directed, so that the pictures representing the successive attitudes
are brought one after another before the eye at intervals ; the*
impression of one remaining until the impression of the next is
produced. In this manner the eye never ceases to see the figure,
but sees it in such a succession of attitudes as it would assume if
it revolved. The effect is, that the figure actually appears to
pirouette before the eye. The effects of Catherine-wheels and
rockets are explained in the same manner.

68. The direction in which any part of an object is seen is that
of the line drawn from such point through the optical centre of
the eye. This line being carried back to the retina determines
the place on the retina where the image of such point is found.
If the optical centre of the eye were not at the centre of the eye-
ball, the direction of this line would be changed with every move-
ment of the eye-ball in its socket ; every such movement would
cause the optical centre to revolve round the centre of the eye-
ball, and consequently would cause the line drawn from the
optical centre to the object to change its direction. The effect of
this would be that every movement of the eye-ball would cause
an apparent movement of all visible objects. Now, since there is
no apparent motion of this kind, and since the apparent position
of external objects remains the same, however the eye may be moved
in its socket, it follows that its optical centre must be at the centre
of the eye-ball.

69. Since lines drawn from the various points of a visible
object through the centre of the eye remain unchanged, however
the eye-ball may move in its socket, and since the corresponding
points of the image placed upon these lines must also remain
unchanged, it follows that the position of the image formed on
the eye remains fixed, even though the eye-ball revolve in the

75

THE EYE.

socket. It appears, therefore, that when the eye-ball is moved in
the socket, the picture of an external object remains fixed, while
the retina moves under it, just as the picture thrown by a magic
lantern on a screen would remain fixed, however the screen itself
might be moved.

Thus, if we direct the axis of the eye to the centre o, fig. 9, of
any object, such as A B, the image of the point o will be formed
at o on the retina, where the optical axis D c meets it. The axis
of the pencil of rays which proceed from the point o will pass
through the centre of the cornea D, through the axis of the crys-
talline, and through the centre c of the eye-ball, and the image
of o will be formed at o.

!Now, if we suppose the eye to be turned a little to the left, so

Fig. 9.

that the optical axis will be inclined to the line o c at the angle
D' c o, the image of the point o will still hold the same absolute
position o as before ; but the point of the retina on which it was
previously formed will be removed to o'. The direction of the
point o will be the same as before ; but the point of the retina on
which its image will be formed will be, not at o, at the extremity
of the optic axis, but at o', at a distance o o' from it, which sub-
tends at the centre c of the eye an angle equal to that through
which the optical axis has been turned.

It is evident, therefore, that although the eye in this case be
moved round its centre, the point 0 is still seen in the same direc-
tion as before.

But if the optical centre of the eye were different from the
centre of the eye-ball, the direction in which the point o would
be seen would be changed by a change of position of the eye.

To render this more clear, let c, fig. 10, be the centre of the

Fiar. 10.

eye-ball, and c' the optical centre of the eye. Let the optical
axis c D, as before, be first presented to the point o of the object.
76

OCULAK SPECTRA.

The image of this point will, as before, be formed at o, the point
where the optical axis D c meets the retina. Let us now suppose
the axis of the eye to be turned aside through the angle D c D',
the optical centre will then be removed from c' to c", and the
image of o will now be formed at the point o", where the line o c"
meets the retina. The direction, therefore, in which o will now
be seen, will be that of the line c" o, whereas the direction in
which it was before seen was that of the line c o. The point of
the retina at which the image o was originally formed is removed
to o', while the image is removed to o". Thus there is a displace-
ment not only of the retina behind the image, but also an absolute
displacement of the image, and an absolute change in the apparent
direction of the object. Since no such change in the apparent
direction is consequent upon the movement of the eye in its socket,
it follows that the optical centre c' of the eye must coincide with
its geometrical centre c.

70. The continuance of the effect produced by the image of a
visible object on the retina after such object has been removed
from before the eye, combined with the effect of the image of
another object placed before the eye during such continuance of
the effect of that which was removed, produces a class of phe-
nomena called ocular spectra and accidental colours.

The effect produced by a strongly illuminated image formed on
the retina does not appear to be merely the continuance of the
same perception after the image is removed, but also a certain
diminution or deadening of the sensibility of the membrane to
other impressions. If the organ were merely affected by the con-
tinuance of the perception of the object for a certain time after its
removal, the effect of the immediate perception of another object
on the retina would be the perception of the mixture of two
colours. Thus, if the eye, after contemplating a bright yellow
object, were suddenly directed to a similar object of a light red
colour, the effect ought to be the perception of an orange colour ;
and this perception would continue until the effect of the yellow
object on the retina would cease, after which the red object would
alone be perceived.

Thus, for example, a disk of white paper being placed upon a
black ground, ana over it a red wafer which will exactly cover it
being laid, if, closing one eye, and gazing intently with the other
for a few seconds on the red wafer, the red wafer be suddenly
removed so as to expose the white surface under it to the eye,
the effect ought to be the combination of the perception of
red which continues after the removal of the red wafer, with the
perception of white which the uncovered surface produces ;
and we should consequently expect to see a diluted red disk,

77

THE EYE.

similar to that wliicli would be produced by the mixture of red
with white. t

This, however, is not the case. If the experiment be performed
as here described, the eye will, on the removal of the red wafer,
perceive, not a reddish, but a greenish-blue disk.

In like manner, if the wafer, instead of being red, were of a
bright greenish -blue, when removed the impression on the eye
would be that of a reddish disk.

These and like phenomena are explained as follows : —

When the eye is directed with an intensity of gaze for some
time at the red surface, that part of the retina upon which the
image of the red wafer is produced becomes fatigued with the
action of the red light, and loses to some extent its sensibility to
that light, exactly as the ear is deafened for a moment by an
overpowering sound. When the red wafer is removed, the white
disk beneath it transmits to the eye the white light, which is
composed of all the colours of the spectrum. But the eye, from
the previous action of the red light, is comparatively insensible
to those tints which form the red end of the spectrum, such as red
and orange, but comparatively sensible to the blues and greens,
which occupy the other end. It is therefore that the eye
perceives the white disk as if it were a greenish-blue, and con-
tinues to perceive it until the retina recovers its sensibility for
red light.

71. A difficulty has been presented in the explanation of the
functions of the eye to which, as it appears to me, undue weight
has been given. It has been already explained, that the images
of external objects which are depicted on the retina are inverted ;
and it has accordingly been asked why visible objects do not
appear upside down. The answer to this appears to be extremely
simple. Inversion is a relative term, which it is impossible to
explain or even to conceive without reference to something which
is not inverted. If we say that any object is inverted, the phrase
ceases to have meaning unless some other object or objects are
implied which are erect. If all objects whatever hold the same
relative position, none can be properly said to be inverted ; as the
world turns upon its axis once in twenty-four hours, it is certain
that the position which all objects hold at any moment is inverted
with respect to that which they held twelve hours before, and to
that which they will hold twelve hours later ; but the objects as
they are contemplated are always erect. In fine, since all the
images produced upon the retina hold with relation to each other
the same position, none are inverted with respect to others ; and
as such images alone can be the objects of vision, no one object of
vision can be inverted with respect to any other object of vision ;
78

SEAT OF VISION.

and consequently, all being seen in the same position, that position
is called the erect position.

72. Physiologists are not agreed as to the manner in which the
perception of a visible object is obtained from the image formed in
the interior of the eye. It is certain, however, that this image is
the cause of vision, or that the means whereby it is produced are
also instrumental in producing the perception of sight. It may
also be considered as established that the perception of a visible
object is more or less distinct, according to the greater or less dis-
tinctness of the image. But it would be a great error to assume
that this image on the retina is itself seen, for that would involve
the supposition of a second eye, beyond the first, or within it, by
which such image on the retina would be viewed. Now, no means
of communicating between the image on the retina and the sen-
sorium exist except the usual conduits of all sensation, the nerves.

It has been already explained that the optic nerve, after
entering the eye at a point near the nose, spreads itself over the
interior of the globe of the eye behind the vitreous humour, and
that this retina or network is perfectly transparent, the coloured
image being formed not properly upon it, but upon the black sur-
face of the choroid coat behind it. Now, it has been maintained,
that the functions of vision are performed by this nervous mem-
brane in a manner analogous to that by which the sense of touch
is affected by external objects. The membrane of the retina, it is
supposed, touching the coloured image, and being in the highest
degree sensitive to it, just as the hand is sensitive to an object
which it touches, receives from the coloured image an action
which, being continued to the brain, produces perception there in
accordance with the form and colour of the image upon the choroid.
According to *"his view of the functions of vision, the retina feels,
as it were, the image on the choroid, and transmits to the sen-
sorium the impression of its colour and figure in the same manner
as the hand of a blind person would transmit to the sensorium the
form of an object which it touches.

73. If this hypothesis be admitted, it would follow that the
Tetina itself would be incapable of exciting the sense of sight by
the mere action of light and colours upon it. This is verified by
the fact that when the image produced within the eye is formed
upon a point of the optic nerve which has not the choroid behind
it, no perception is produced.

In order to prove this, let three wafers be applied in a hori-
zontal line upon a vertical screen, each separated from the other
by a distance of two feet. Let the screen be placed before the
observer at a distance of about 15 feet, the wafers being on a level
with the eye ; and let the centre wafer be so placed that a line

79

THE EYE.

Fig. 11.
li

drawn from the right eye to it shall be perpendicular to the screen.
Let the left eye be now closed, and let the right eye be directed to
the extreme wafer on the left, but so that all three wafers may still
be perceived. Let another person now slowly move the screen, so
as to bring it nearer to the observer, maintaining, however, the
middle wafer in the direction of the eye at c. It will be found
that the screen being so moved to a distance of 10 feet from
the eye, the middle wafer will appear to be suddenly extinguished,
and the extreme wafers on the right and left will be seen.

74. This remarkable phenomenon is explained by showing that
in this particular position of the eye and the screen the image of
the middle wafer falls upon the base of the optic nerve when the
choroid coat is not under it.

This will be rendered more intelligible by reference to fig. 11.
where B is the middle wafer, A the left-hand, and c the right-
hand wafer. The image of
A is formed at a, to the
right of the optic nerve ;
and the image of c is
formed at c, to the left of
that nerve. In both these
positions the choroid coat
is behind the retina. But
the image of B is formed at
b, directly upon the point
where the optic nerve
issues from the eye-ball,
and where the choroid does
not extend behind it.

75. Sir Pavid Brewster
gives the following expe-
riment as a further argu-
ment in support of this
hypothesis. In the eye
of the Sepia loligo, or
cuttle-fish, an opaque membranous pigment is interposed between
the retina and the vitreous humour, so that if the retina
were essential to vision, the impression of the image on this
black membrane must be conveyed to it by the vibration of
this membrane in front oi it. Sir David Brewster also mentions
that in young persons the choroid coat, instead of being covered
with a black pigment, reflects a brilliant crimson, like that of dogs
and some other animals ; and imagines that if the retina were
affected by the rays which pass through it, this crimson light
ought to excite a corresponding sensation, which is not the case.
80

THE EYE.

CHAPTEE III.

76. Why objects are not seen double. — 77. Exceptional cases. —

78. The eye has no direct perception of distance or magnitude. —

79. How distances are estimated. — 80. Appearance of the sun and
moon when rising or setting. — 81. How magnitudes are estimated.
— 82. Illusion produced in St. Peter's at Kome. — 83. Magnitude
inferred from distance. — 84. Perception of angular motion. — 85.
How real direction of motion may be inferred. — 86. Examples of the
sun and moon. — 87-90. Effect of the motion of the observer —
Examples. — 91. Angular distance defined. — 92. The eye has no
direct perception of form — How inferred. — 93. Visible area defined.
— 94. Figure inferred from lights and shadows. — 95. Power of dis-
tinguishing colours. — 96, 97. Absence of this power in particular

76. THE question why, having two eyes on which independent
impressions are made by external objects, and on the retina of
each of which an independent picture of a visible object is formed,
we do not see distinct objects corresponding to each individual
external object which impresses the organ, is often asked.

The first reflection which arises on the proposition of this
LARDNER'S MUSEUM OP SCIENCE. a 81

No. 63.

THE EYE.

question, is why the same question has not been similarly pro-
posed with reference to the sense of hearing. Why has it not
been asked why we do not hear double ? why each individual
sound produced by a bell or a string is not heard as two distinct
sounds, since it must impress independently and separately tho
two organs of hearing ?

It cannot be denied, that, whatever reason there be for demand-
ing a solution of the question, why we do not see double 't is
equally applicable to the solution of the analogous question, why
we do not hear double ? Like many disputed questions, this will
be stripped of much of its difficulty and obscurity by a strict
attention to the meaning of the terms used in the question, and in
the discussion consequent upon it. If by seeing double it be
meant that the two eyes receive separate and independent impres-
sions from each external object, then it is true that we see double.
But if it be meant that the mind receives two distinct and inde-
pendent impressions of the same external object, then a qualified
answer only can be given.

If the two eyes convey to the mind precisely the same impres-
sion of the same external object, differing in no respect whatever,
then they will produce in the mind precisely the same perception
of the object; and as it is impossible to imagine two perceptions
to exist in the mind of the same external object which are
precisely the same in all respects, it would involve a contradic-
tion in terms to suppose that, in such case, we perceive the object
double.

If to perceive the object double mean anything, it means that
the mind has two perceptions of the same object, distinct and dif-
ferent from each other in some respect. Now, if this distinctness
or difference exist in the mind, a corresponding distinctness and
difference must exist in the impression produced of the external
object on the organs. It will presently appear, that cases do occur
in which the organs are, in fact, differently impressed by the same
external object; and it will also appear, that in such cases pre-
cisely we do see double, meaning by these terms, that we have two
perceptions of the same object, as distinct from each other as t.re
our perceptions of two different objects.

To render this point more clear, let us consider in what respects
it is possible for the impressions made upon the two eyes by the
same object to differ from each other.

A visible object impresses the eye with a sense of a certain
apparent form, of a certain apparent magnitude, of certain colours,
of a certain intensity of illumination, and of a certain visible
direction. Now, if the impression produced by the same object
upon the two eyes agree in all these respects, it is impossible to
82

WHY WE DO NOT SEE DOUBLE.

imagine that the mind can receive two distinct perceptions of the
object, for it is not possible that the two perceptions could differ
from each other in any respect, except in some of those just men-
tioned. Let us suppose the two eyes to look at the moon, and that
such object impresses them with an image of precisely the same
apparent form and magnitude, of precisely the same colours
and lineaments, of precisely the same intensity of illumination,
and in precisely the same direction. Now, the impressions
conveyed to the mind by each of the eyes corresponding in all
these respects, the object must be perceived in virtue of both
impressions precisely in the same manner, that is to say, it must
be seen in precisely the same direction, of precisely the same
magnitude, of precisely the same form, with precisely the
same lineaments of light and shade, and with precisely the
same brightness or intensity of illumination. It is therefore,
in such a case, clearly impossible to have a double perception of
the object.

It will be observed, that the same reasoning exactly will be
applicable to the sense of hearing. If the same string or the
same pipe affect the tympanum of each ear in precisely the same
manner, so as to produce a perception of a sound of the same pitch,
the same loudness, and the same quality, it is impossible to con-
ceive that two different perceptions can be produced by the two
ears, for there is no respect in which it is possible for two such
perceptions to differ, inasmuch as by the very supposition they
agree in all the qualities which belong to sound.

But, if we could conceive by any organic derangement that the
same musical string would produce in one ear the note ut, and
produce in the other ear the note so/, then the same effect would
be produced as if these two sounds had been simultaneously heard
by the two ears properly organised, and we should have a sense of
harmony of the fifth.

In like manner, if the two eyes, by any defect of organisa-
tion, produced different pictures on the retina, we should then
have two perceptions of the same object having a corresponding
difference.

It has been already shown, that the apparent visual magnitude
of an object, and also that its apparent brilliancy, depend on its
distance from the eye.

Now, assuming, as we shall do, unless the contrary be expressed,
that the two eyes are similarly constituted, it will follow, that an
object whose distance from the two eyes is equal will be seen
under the same visual angle, and will therefore have the same
apparent magnitude ; it will also have the same colour and
intensity of illumination, and, in fine, if the distance between the

G 2 83

THE EYE.

eyes bear an insignificant proportion to the distance of the object
from them, the lines drawn from the centre of the eyes to any
point on the object will be practically parallel ; and. since these
lines, as has been already explained, determine the direction in
which the object is seen, such object will then be seen in the same
direction. Now, since the apparent form, the apparent magnitude,
the apparent colour, the apparent intensity of illumination,
and the apparent direction are the same for both eyes, it is
clear that the same impression must be produced upon the senses,
and the same perceptions conveyed to the mind ; consequently it
follows, demonstratively, that all objects which are placed at a
distance compared with which the distance between the eyes : s
insignificant, will convey a single perception to the mind, and
will consequently not be seen double.

77. But we have now to consider a different case, which will
present peculiar conditions, and consequences of peculiar interest.

Let us suppose an object placed so near the eyes that its dis-
tance shall not bear a considerable proportion to the length of the
line which separates the centres of the eyes. In this case, the
images produced on the retina of the two eyes may differ in
magnitude, and intensity of illumination, and even in form, and,
in fine, it is clear that the apparent direction of any point on the
object as seen by the two eyes will be sensibly different.

In this case, therefore, the two eyes convey to the mind a dif-
ferent impression of the same object ; and we may therefore expect
that we should see it double, and in fact we do so.

But the observation of this particular phenomenon requires
much attention, inasmuch as the perception of which we are con-
scious is affected not merely by the impression made upon the
organ of sense, but by the degree of attention which the mind
gives to it. Thus, if the two eyes be differently impressed either
by the same or by different objects placed before them, the mind
may give its attention so exclusively to either impression, as to lose
all consciousness of the other.

Thus, if two stars be at the same time in the field of view of a
telescope, as frequently happens, and be viewed together by lie
eye, we shall be conscious of a perception of both, so long as the
attention is not exclusively directed to either; but if we gaze
intently on one of them so as to observe its colour, or any other
peculiarity attending it, we shall cease to be conscious of the
presence of the other. The application of this observation to the
question before us will be presently apparent.

Let EL, fig. 12, be the line separating the centres of the two

eyes, u representing the centre of the right, and L that of the left

eye.

84

CASES IN WHICH WE SEE DOUBLE.

Let o be an object, such as the flame of a candle or lamp, seen
at the distance of about 40 feet, so that the lines of direction L o
and K, o converging upon it from the centres of the eyes 19
may be regarded as practically parallel, the distance
being about 200 times greater than the distance L E, °
between the eyes. The object o will therefore be seen in
the same direction by both eyes, and being at a distance
from the two eyes practically equal, will have the same
apparent magnitude, form, colour, and intensity of illu-
mination, and, consequently, will be seen single.

Let a small white rod be held at the distance A, of
about 8 inches from the left eye L, and in the line L o,
so as to intercept the view of the object o from the left
eye. The left eye will then see the rod at A, and not
the object o ; but the right eye will still see the object o,
as before. Now, if the attention be earnestly directed
to the object o, the object A will not be perceived ; but
if the attention be directed to the object A, it will be
perceived distinctly, but the object o will be seen
through it as if it were transparent.

Now, since the object o cannot be seen by the left eye
under the circumstances here supposed, the perception we have of it
must be derived from the right eye ; nevertheless it is seen in the
line L A o, immediately beyond the intercepting wand, and in the
same direction, and in the same manner precisely as it would be
seen by the left eye L if the intercepting wand were removed. It
follows, therefore, that the perception we obtain of the object 0 by
the right eye is precisely the same as that which we should obtain
by the left eye if the right were closed, and the intercepting wand
A removed. This may therefore be taken as an experimental
proof of what, indeed, may seem sufficiently evident, d priori,
that an object, such as o, placed at a distance so great that lines
drawn to it from the centre of the eyes would be practically
parallel, produces precisely the same perception through the vision
of both eyes.

But when the distance of an object from the eye is so small that
the line which separates the eyes bears a considerable proportion
to it, the directions in which such an object is seen by the two
eyes are different, and it is easy to show that in this case such
an object would be seen double.

Let L, and R (fig. 13), as before, be the centres of the two eyes,
and let A B be a white screen placed vertically at a distance of 12
or 14 feet, having upon it a horizontal line on a level with the
eye, upon which is marked a divided scale 1, 2, 3, 4, 5, 6, 7, 8, 9,
10. Let a black wand be held vertically at o, opposite the middle

85

THE EYE.

Fig 13.

e 7 ;ey /o

L II

of the line L E. This wand will be seen by the left eye in the direction
of the division 8, and by the right eye in the direction of the division

4, on the screen, and two images
o the wand will accordingly be
- perceived ; but, according as the
attention is directed to the one or
to the other, a consciousness of
them will be produced. Thus,
by an act of the will we may con-
template only the objects as seen
with the left eye, in which caso
the wand will be seen projected
on the screen perpendicular to
the line A B, at the 8th division ;
and by a like act of the will, the
attention being directed to the
impression produced by the right
eye, the wand will be seen pro-
jected on the screen at the 4th
division of the scale. If the at-
tention be withdrawn from either
of these and the wand be viewed indifferently, we shall be conscious
of the two images, but not with the same distinctness as that with
which we should perceive two wands placed at the 4th and 8th
divisions of the scale. It will follow from this, that when we look
with both eyes at any object, such as the printed page of a book,
at the distance of 8 or 10 inches from the eyes, we have two
images of the different parts of the page placed before the eyes,
which are seen in different directions, and ought therefore to pro-
duce double vision ; but this is prevented by habitually directing
our attention to one of the two, and neglecting the other.

That the perception of an object will be double if the directions
in which it is seen by the two eyes are different, may also be
demonstrated in the following manner : —

It has been already shown that the optical centres of the eyes,
cannot change their position by the mere action of the muscles
which move the eye-balls in their sockets, and that the direction
in which any distant object is seen by both eyes is the same, and
hence it is perceived single ; but if a slight pressure be applied to
the eye with the finger, the optical centre of the eye may bo
moved from its position, so that the direction of the same object
seen by it and the other eye will not be the same. A distant
object will in this case be seen double, being perceived in ono
direction by the eye which retains its natural position, and in
another by that whose position is deranged by pressure.
86

APPARENT DISTANCE.

78. It has been already explained that two similar objects
whose distances from the eye are to each other in the same
proportion as their linear dimensions will have the same apparent
magnitude.

In like manner, if an object, such as, for example, a balloon,
moves from the eye in a direct line, we have no distinct conscious-
ness of its motion, for the line of direction in which it is seen is
still the same. It is true that we may infer its motion through
the air by the increase or diminution of its apparent magnitude ;
for, if we have reason to know that its real magnitude remains
unchanged, we ascribe almost intuitively the change of its
apparent magnitude to the change of its distance ; and we con-
sequently infer that it is in motion either towards or from us,
according as we perceive its apparent magnitude to be increased or
diminished. This information, however, as to the motion of a
body in a direct line to or from the centre of the eye, is not a
perception obtained directly from vision, but an inference of the
reason deduced from certain phenomena. It may, therefore, be
stated generally, that the eye affords no perception of direct
distance, and consequently none of direct motion, the term direct
being understood here to express a motion in a straight line to or
from the optical centre of the eye.

79. The distance of a visible object is often estimated by com-
paring it with the apparent magnitude and apparent distance of
known objects which intervene between it and the eye.

Thus, the steeple of a church whose real height is unknown
cannot by mere vision be estimated either «as to distance or
magnitude, since the apparent height would be the same, provided
its magnitude were greater or less in proportion to its supposed
distance. But, if between the steeple and the eye there intervene
buildings, trees, or other objects, whose average magnitudes may
be estimated, a proximate estimate of the magnitude and distance
of the steeple may be obtained.

For example, if the height of the most distant building between
the eye and the steeple be known, the distance of that building
may be estimated by its apparent magnitude, and the distance of
the steeple will be inferred to be greater than this.

80. A remarkably deceptive impression, depending on this
principle, is deserving of mention here. When the disc of the
sun or moon at rising or setting nearly touches the horizon, it
appears of enormous magnitude compared with its apparent size
when high in the firmament. Now, if the visual angle which it
subtends be actually measured in this case, it will be found to be
of the same magnitude. How, then, it may be asked, does it
happen that the apparent magnitude of the sun at setting and at

87

THE EYE.

noon are by measure the same, when they are by estimation, and
by the irresistible evidence of sense, so extremely different ? This
is explained, not by an error of the sense, for there is none, but by
an erroneous application of those means of judging- or estimating
distance which in ordinary cases supply true and just conclusion!;;.

When the disc of the sun is near the horizon, a number of
intervening objects of known magnitude and known relative
distances supply the means of spacing and measuring a part at
least of the distance between the eye and the sun ; but when the
sun is in the meridian, no such objects intervene. The mind,
therefore, assigns a greater magnitude to the distance, a part of
which it has the means of measuring, than to the distance no part
•of which it can measure ; and accordingly an impression is pro-
duced, that the sun at setting is at a much greater real distanc2
than the sun in the meridian ; and since its apparent magnitud3
in both cases is the same, its real magnitude must be just so much
greater as its estimated distance is greater. The judgment,
therefore, and not the eye, assigns this erroneous magnitude to
the disc of the sun.

It is true that we are not conscious of this mental operation.
But this unconsciousness is explained by the effect of habit,
which causes innumerable other operations of the reason to pass
unobserved.

81. As the eye forms no immediate perception of distance,
neither does it of form or of magnitude, since, as has been already
proved, objects of very different real magnitudes have the same
apparent magnitude to the eye, of which a striking example is
afforded in the case of the sun and moon. Nevertheless, although
the eye supplies no immediate perception of the real magnitude of
objects, habit and experience enable us to form estimates more or
less exact of these magnitudes by the comparison of different
effects produced by sight and touch.

Thus, for example, if two objects be seen at the same distance
from the eye, the real magnitude of one of which is known, that
of the other can be immediately inferred, since, in this case, the
apparent magnitudes will be proportional to the real magnitudes.
Thus, for example, if we see the figure of a man standing beside a
tree, we form an estimate of the height of the latter, that of the
former being known or assumed. Ascribing to the individual
seen near the tree the average height of the human figure, and
comparing the apparent height of the tree with his apparent
height, we form an estimate of the height of the tree.

82. It is by this kind of inference that buildings constructed
upon a scale greatly exceeding common dimensions are estimated,
and rendered apparent in pictorial representations of them

88

ESTIMATE OF REAL MOTION.

On entering, for example, the aisle of St. Peter's at Rome, or
St. Paul's at London, we are not immediately conscious of the
vastness of the scale of these structures ; but if we happen to see
at a distant part of the building a human figure, we immediately
become conscious of the scale of the structure, for the known
dimensions of this figure supply a modulus which the mind
instantly applies to measure the dimensions of the whole. For
this reason artists, when they represent these structures, never
fail to introduce human figures in or near them.

83. It has been explained that the apparent magnitude of
objects depends conjointly on their real magnitude and their
distance. Although, therefore, the eye does not afford any direct
perception teither of real magnitude or distance, we are by habit
enabled to infer one of these from the other.

Thus, if we happen to know the real magnitude of a visible
•object, we form an estimate of its distance from its apparent
magnitude ; and, on the other hand, if we happen to know or can
ascertain the distance of an object, we immediately form some
estimate of its real magnitude.

Thus, for example, the height of a human figure being known,
if we observe its apparent visual magnitude to be extremely small,
we know that it must be at a distance proportionally great. If
we know that at 20 feet the figure of a man will have a certain
apparent height, and that we find that his figure seen at a certain
distance appears to have only one-fifth of this height, we infer that
his distance must be about 100 feet.

In like manner, the real magnitude may be inferred from the
apparent magnitude, provided the distance be known or can be
ascertained. Thus, for example, in entering Switzerland by its
northern frontier, we see in the distance, bounding the horizon,
the line of the snowy Alps, and the first impression is that of
disappointment, their apparent scale being greatly less than we
expected ; but when we are informed that their distance is sixty
or eighty miles, our estimate is instantly corrected, and we
become conscious that the real height of mountains which, seen
at so great a distance, is what we observe it, must be pro-
portionately vast.

84. When an object moves in any direction which is not in a
straight line drawn to or from the centre of the eye, the direction
in which it is seen continually changes, and the eye in this case
supplies an immediate perception of its motion ; but this perception
can be easily shown to be one not entirely corresponding to the
actual motion of the object, but merely to the continual change of
direction which this motion produces in the line drawn from the
object to the eye.

89

THE EYE.

Thus, for example, if the eye be at E (fig. 14), any object which
moves from A to B will cause the line of direction in which it is
seen to revolve through the angle A E E, just as though the body
which moves were to describe a circular arc, of which E is the
centre and E A the radius. But if, instead of moving 'from A to it,
the body were to move from A' to E', the impression which its

motion would produce
upon the sight would
be exactly the same.
It would still appear
to be moving from the

direction E A' A to ths

" " n. ..

direction E B B .

In fine, the eye affording no perception of direct distance,
supplies no evidence of the extent to which the body may change
its distance from the eye during its motion, and the apparent
motion will be the same as if the body in motion described a
circle of which the eye is the centre.

Hence it is that the only motion of which the eye forms any
immediate apprehension is angular motion, that is, a motion
which is measured by the angle which a line describes, one
extremity of which is at the centre of the eye, and the other at
the moving object.

85. Though the real direction in which a distant object moves
cannot be obtained by the direct perception of vision, some
estimate of it may be formed by comparing the apparent angular
motion of the object with its apparent magnitude.

Thus, for example, if we observe that the apparent magnitude
of an object remains constantly the same while it has a certain
apparent angular motion, we infer that its distance must neces-
sarily remain the same, and consequently that it revolves in a
circle, in the centre of which the observer is placed ; or if we find
that it has an angular motion, in virtue of which it changes its
direction successively around us, so as to make a complete circuit of
360°, and that in making this circuit its apparent magnitude first
diminishes to a certain limit, and then augments until it attains a
certain major limit from which it again diminishes, we infer that
such a body revolves round us at a varying distance, its
distance being greatest when the apparent magnitude is least,
and least when its apparent magnitude is greatest. An exact
observation of the variation of the apparent magnitude would in
such a case supply a corresponding estimate of the variation of the
real distance, and would thus form the means of ascertaining the
path in which the body moves.

86. An example of this is presented in the cases of the sun and'
90

APPARENT AND REAL MOTION.

moon, whose apparent magnitudes are subject, during their revo-
lution round the earth, to a slight variation, being a minimum at
one point and a maximum at the extreme opposite point, the
variation being such as to show that their motions are made in an
ellipse in the focus of which the earth is placed.

87. As the eye perceives the motion of an object only by the
change in the direction of the line joining the object with the eye,
and as this change of direction may be produced as well by the
motion of the observer as by that of the object, we find accordingly
that apparent motions are produced sometimes in this manner.
Thus, if a person be placed in the cabin of a boat which is moved
upon a river or canal with a motion of which the observer is not
conscious, the banks and all objects upon them appear to him to
move in a contrary direction. In this case the line drawn from
the object to the eye is not moved at the end connected with the
object, which it would be if the object itself were in motion, but
at the end connected with the eye. The change of its direction,
however, is the same as if the end connected with the object had
a motion in a contrary direction, the end connected with the eye
being at rest ; consequently the apparent motion of the objects
seen which are really at rest, is in a direction contrary to the real
motion of the observer.

88. In some cases the apparent motion of an object is produced
by a combination of a real motion in the object and a real motion
in the observer. Thus, if a person transported in a railway car-
riage meet a train coming in the opposite direction, both extremes
of the line joining his eye with the train which passes him are in
motion in contrary directions ; that extremity which is at his eye
is moved by the motion of the train which carries him, and the
other extremity is moved by the motion of the train which passes
him. The change of direction of the line is accordingly produced
by the sum of these motions ; and as this change of direction is
imputed by the sense to the train which passes, this train appears
to move with the sum of the velocities of the two trains. Thus,
if one train be moved at twenty miles an hour, while the other is
moved at twenty-five miles an hour, the apparent motion of the
passing train will be the same as would be the motion of a train
moved at forty-five miles an hour passing a train at rest.

89. If the line joining a visible object with the eye be moved
at both its extremities in the same direction, which would be the
case if the observer and the object were carried in parallel lines,
then the change of direction which the line of motion would
undergo would arise from the difference of the velocities of the
observer and of the object seen.

If the observer in this case moved slower than the object, the

91

THE EYE.

extremity of the line of motion connected with, the object would
be carried forward faster than the extremity connected vith the
observer, and the object would appear to move in the direction
of the observer's motion, with a velocity equal to the difference ;
but if, on the contrary, the velocity of the observer were greater
than that of the object, the extremity of the line connected with
the observer would be carried forward faster than that connected
with the object, and the change of direction would be the same as
if the object were moved in a contrary direction with the difference
of the velocities.

It is easy to perceive that a vast variety of complicated rela-
tions which may exist between, the directions and motions of the
observer and of the object observed, will give rise to very com-
plicated phenomena of apparent motion. Thus, relations may
be imagined between the motion of the observer and that of th3
object perceived by which, though both are in motion, the object
will appear stationary ; the motion of the one affecting the lino
of direction in an equal and contrary manner to that with which
it is affected by the other ; and, in the same manner, either motion
may prevail over the other more or less, so as to give the lino
of direction a motion in accordance with or contrary to the real
motion of the object.

90. All these complicated phenomena of vision are presented in
the problems which arise on the deduction of the real motion of
the bodies composing the solar system from their apparent motions.
The observer placed in the middle of this system is transported
upon the earth in virtue of its annual motion round the sun with
a prodigious velocity, the direction of his motion changing from
day to day according to the curvature of the orbit. The bodies
which he observes are also affected with various motions at various
distances around the sun, the combination of which with the motion
of the earth gives rise to complicated phenomena, the analysis of
which is made upon the principles here explained.

91. It is usual to express the relative position in which objects
are seen by the relative direction of lines drawn to them from the
eye ; and the angle contained by any two such lines is called tho
angular or visual distance between the objects. Thus, the angular
distance between the objects A and B, fig. 14, is expressed by the
magnitude of the angle A E B. If this angle be 30°, the objects
are said to be 30° asunder. It is evident from this that all objects
which lie in the direction of the same lines will be at the same
angular distance asunder, however different their real distance
from each other may be. Thus, the angular distance between A
and B, fig. 14, is the same as the angular distance between
A' and B'.

92

PERCEPTION OF BULK AND FOltM.

92. Sight does not afford any immediate perception either of the
volume or shape of an object. The information which we derive
from the sense, of the bulk or figure of distant objects, is obtained
by the comparison of different impressions made upon the sense of
sight by the same object at different times and in different posi-
tions. A body of the spherical form seen at a distance appears to
the eye as a flat circular disk, and would never be known to have
any other form, unless the impression made upon the eye were
combined with other knowledge, derived from other impressions,
through sight or touch, or both these senses, and thus supplied
the understanding with data from which the real figure of the
object could be inferred. The sun appears to the eye as a flat,
circular disk ; but, by comparing observations made upon it at
different times, it is ascertained that it revolves round one of its
diameters in a certain time, presenting itself under aspects in-
finitely varying to the observer ; and this fact, combined with its
invariable appearance as a circular disk, proves it to be a sphere ;
for no body except a sphere, viewed in every direction, would
appear circular.

Although we do not obtain from the sense of sight a perception
of the shape of a body, we may obtain a perception of the shape
of one of its sections. Thus, if a section of the body be made by
a plane passing through it at right angles to the line of vision,
the sight supplies a distinct perception of the shape of such section.
Thus, if an egg were presented to the eye with its length in the
direction of the line of vision, it would appear circular, because a
section of it made by a plane at right angles to its length is a
circle ; but if it were presented to the eye with its length at right
angles to the line of vision, it would appear oval, that being the
shape of a section made by a plane passing through its length.

If a body, therefore, presents itself successively to the eye in
several different positions, we obtain a knowledge by the sense of
sight of so many different sections of it, and the combination of
these sections may in many cases supply the reason with data by
which the exact figure of the body may be known.

93. As the term " apparent magnitude " is used to express the
visual angle under which an object is seen, we shall adopt the
term visible area to express the apparent magnitude of the section
of a visible object made by a plane at right angles fo the line of
vision, that is to say, to the line drawn from the eye to the centre
of the object.

94. Besides receiving through the sight a perception of the
figure of the section of the object which forms its visible area, we
also obtain a perception of the lights and shades and the various
tints of colour which mark and characterise such area. By

93

THE EYE.

comparing the perception derived from the sense of touch with those
lights and shades, we are enabled by experience and long habit
to judge of the figure of the object from these lights and shades
and tints of colour. It is true that we are not conscious of this
act of the understanding in inferring shape from colour and from
light and shade ; but the act is nevertheless performed by the
mind. The first experience of inference is the comparison of the
impressions of sight with the impressions of touch ; and one of the
earliest acts of the mind is the inference of the one from the other.
It is the character of all mental acts, that their frequent per-
formance produces an unconsciousness of them ; and hence it is
that when we look at a cube or a sphere of a uniform colour,
although the impression upon the sense of sight is that of a nab
plane variously shaded, and having a certain outline, the mind
instantly substitutes the thing signified for the sign, the cause
for the effect ; and the conclusion of the judgment, that the object
before us is a sphere or a cube of uniform colour, and not as it
appears, a flat plane variously shaded, is so instantaneous, that
the act of the mind passes unobserved.

The whole art of the painter consists in an intimate practical
knowledge of the relation between these two effects of perception
of sight and touch. The more accurately he is able to delineate
upon a flat surface those varieties of light and shade which
visible objects immediately produce upon the sense, the more
exact will be his delineation, and the greater the vraisemblance
of his picture.

What is called relief in painting is nothing more than the exact
representation on a flat surface of the varieties of light and shade
produced by a body of determinate figure upon the eye ; and it is
accordingly found that the flat surface variously shaded produced
by the art of the painter has upon the eye exactly the same effect
as the object itself, which is in reality so different from the coloured
canvas which represents it.

95. The immediate impressions received from the sense of sight
are those of light and colour. The impressions of distance, mag-
nitude, form, and motion are the mixed results of the sense of
sight and the experience of touch. Even the power of distinguish-
ing colours is not obtained immediately by vision without some
cultivation of this sense. The unpractised eye of the new-born
infant obtains a general perception of light ; and it is certain that
the power of distinguishing colours is only found after the organ
has been more or less exercised by the varied impressions produced
by different lights upon it. It would not be easy to obtain a
summary demonstration of this proposition from the experience;
of infancy, but sufficient evidence to establish it is supplied b}-
94

PECULIAR DEFECTS OF VISION.

the cases in which sight has been suddenly restored to adults blind
from their birth. In these cases, the first impression produced by
vision is that the objects seen are in immediate contact with the
eye. It is not until the hand is stretched forth to ascertain the
absence of the objects seen from the space before the eye that this
optical fallacy is dissipated.

The eye which has recently gained the power of vision at first
cannot distinguish one colour from another, and it is not until
time has been given for experience, that either colour or outline
is perceived.

96. Besides that imperfection incident to the organs of sight
arising from the excess or deficiency of their refractive powers,
there is another class which appear to depend upon the quality of
the humours through which the light proceeding from visible
objects passes before attaining the retina. It is evident that if
these humours be not absolutely transparent and colourless, the
image on the retina, though it may correspond in form and outline
with the object, will not correspond in colour ; for if the humours
be not colourless, some constituents of the light proceeding from
the object will be intercepted before reaching the retina, and the
picture on the retina will accordingly be deprived of the colours
thus intercepted. If, for example, the humours of the eye were
so constituted as to intercept all the red and orange rays of white
light, white paper, or any other white object, such as the sun,
for example, would appear of a bluish-green colour ; and if, on
the other hand, the humours were so constituted as to intercept
the blues and violets of white light, all white objects would ap-
pear to have a reddish hue. Such defects in the humours of the
eye are fortunately rare, but not unprecedented.

97. Sir David Brewster, who has curiously examined and col-
lected together cases of this kind, gives the following examples
of these defects : —

A singular affection of the retina in reference to colour is shown
in the inability of some eyes to distinguish certain colours of the
spectrum. The persons who experience this defect have their
eyes generally in a sound state, and are capable of performing all
the most delicate functions of vision. Mr. Harris, a shoemaker
at Allonby, was unable from his infancy to distinguish the cher-
ries of a cherry-tree from its leaves, in so far as colour was
concerned. Two of his brothers were equally defective in this
respect, and always mistook orange for grass-green, and light
green for yellow. Harris himself could only distinguish black
and white. Mr. Scott, who describes his own case in the Phi-
losophical Transactions, mistook pink for a pale blue, and a full
red for a full green.

95

THE EYE.

All kinds of yellows and blues, except sky-blue, he coulc
discern with great nicety. His father, his maternal uncle, one
of his sisters and her two sons, had all the same defect.

A tailor at Plymouth, whose case is described by Mr. Harvey,
regarded the solar spectrum as consisting only of yellow and
light blue ; and he could distinguish with certainty only yellow,
white, and green. He regarded indigo and Prussian blue as
black.

Mr. II. Tucker described the colours of the spectrum as
follows : — •

Hed mistaken for .
Orange ,,
Yellow sometimes
Green ,,
Blue „ .

Indigo , ,
Violet

brown.

green.

orange.

orange.

pink.

purple.

purple.

A gentleman in the prime of life, whose case I had occasion to
examine, saw only two colours in the spectrum, viz. yellow and
blue. When the middle of the red space was absorbed by a blue
glass, he saw the black space with what he called the yellow oa
each side of it. This defect in the perception of colour was ex-
perienced by the late Mr. Dugald Stewart, who could not perceive
any difference in the colour of the scarlet fruit of the Siberian
crab, and that of its leaves. Dr. Dalton was unable to distinguish
blue from pink by daylight ; and in the solar spectrum the red
was scarcely visible, the rest of it appearing to consist of two
colours. Mr. Troughton had the same defect, and was capable of
fully appreciating only blue and yellow colours ; and when he
named colours, the names of blue and yellow corresponded to the
more and less refrangible rays ; all those which belong to the
former exciting the sensation of blueness, and those which belong
to the latter the sensation of yellowness.

In almost all these cases, the different prismatic colours had
the power of exciting the sensation of light, and giving a distinct
vision, of objects, excepting in the case of Dr. Dalton, who was
said to be scarcely able to see the red extremity of the spectrum.

Dr. Dalton endeavoured to explain this peculiarity of vision by
supposing that in his own case the vitreous humour was blue, and
therefore absorbed a great portion of the red and other !
refrangible rays ; but this opinion is, we think, not well founded.
Sir J. Herschell attributes this state of vision to a defect in the
sensorium, by which it is rendered incapable of appreciating
exactly those differences between rays on which their colour
depends.
90

Fig. 6.— AIR-PUMP.

THE ATMOSPHERE.

1. Experimental proofs of the weight of the atmosphere.— 2. The bladder
glass. — 3. Pressure equal in all directions. — 4. Pressure of air in a
room explained. — 5. Magdeburg hemispheres. — 6. Suction with tube.
— 7. Pascal's experiment at Rouen. — 8. Horror of a vacuum. — 9.
Galileo and the pump-makers. — 10. Torricelli's celebrated experiment.
— 11, Pascal's experiment on the Puy-de-d6me. — 12. Actual pressure
of atmosphere ascertained. — 13. Height of an atmosphere of uniform
density. — 14. Vastly greater height of an elastic atmosphere. — 15.
Air less and less dense in ascending. — 16. Effects of atmospheric
pressure. — 17. Boy's plaything of a sucker. — 18. Flies walking on
ceiling. — 19. Respiration. — 20. Action of bellows. — 21. Ventpeg — lid
of tea-pot. — 22. Pneumatic ink-bottle. — 23. Syringes. — 24. Ex-
hausting syringe. — 25. Rate of rarefaction. — 26. Absolute vacuum
cannot be obtained. — 27. But may be indefinitely approached. — 28.
Air-pump. — 29. Condensing syringe. — 30. Condenser.

1. IN a former part of this series some of the most conspicuous
properties of the atmosphere were explained, and among these its
weight and pressure.* "We now propose to resume this subject,
and to explain the expedients by which the weight, elasticity, and
other mechanical properties of the atmosphere are ascertained.

* Common Things — Air, vol. ii. p. 1.

LARDNER'S MUSEUM OF SCIENCE. H 97

No. 55.

ATMOSPHERE.

2. One of the most direct demonstrations of the weight of tl
atmosphere is aiforded by the experiment, shown in all popular
lectures on physics, made with the apparatus called the Bladder
Glass. This is a glass cylinder of four or five inches in diameter,
open at both ends, upon one end of which a piece of bladder —
rendered soft and pliable by being soaked in water, is firmly
tied, the wet edges of the bladder adhering to the outside surface of
the glass, and to its edge, so as to be in complete air-tight contact
with it. The end of the cylinder which remains uncovered is
then smeared at the edges with lard, and placed upon the plate of
an air-pump, the lard rendering its contact with the plate air-
tight. The air-pump, which will be described in another part
of this number, is nothing more than a syringe conveniently
mounted, by which the air can be partially or almost wholly,
extracted from any close vessel, the mouth of which is applied
upon the plate.

Let us suppose then, that by the action of the pump, a part of
the air included under the bladder is withdrawn, the pressure of
the air thus rarefied will be less than that of the external air,
which is not so rarefied, and consequently the bladder being
pressed with more force downwards than upwards, will yield to
the excess of downward force, and will become concave. If by
the constant action of the pump more and more of the air bo
withdrawn, the excess of the downward force becoming greater
and greater, the bladder, if it have not sufficient strength to
support the increased pressure, will burst inwards with an
explosion as loud as that produced by the discharge of a large
pistol.

3. The same effect will be produced in whatever direction the
mouth of the bladder-glass be presented, showing that the
pressure of the external atmosphere acts upon the bladder equally
in all directions downwards, laterally, obliquely, and upwards.

4. Even to those who admit the great weight of a column of the
atmosphere, extending from the surface of the earth to the highest
limit of that fluid, this experiment performed in a room often
seems astonishing and inexplicable ; for however weighty may be
a column of air which extends upwards to the top of the atmos-
phere, it cannot be understood how a column extending upwards
only to the ceiling of the room can have so great a weight. It is
certain that water is much heavier than air, and that a column of
that liquid as high as the ceiling would not have a weight at all
comparable to that which bursts the bladder.

This difficulty is explained by the common effect of fluidity, by
which pressure is equally and freely transmitted in all directions
through the fluid, which property was illustrated by the experiment

'

BLADDER GLASS — MAGDEBURG HEMISPHERES.

with the bottle described in our Tract on Air,* already quoted.
The air included in a room is not directly under the pressure of a
column of atmosphere extending indefinitely upwards ; but it is
compressed at all the openings by which it enters the room^by the
external air, and this pressure, which proceeds from the incum-
bent weight of such an atmospheric column outside the room or
building, being freely transmitted inwards, the air in the room is
affected by it in exactly the same manner, and to exactly the
same degree, as if it were placed immediately under the incumbent
weight of a column extending to the top of the atmosphere.

5. There is another familiar experiment which illustrates in a
striking and instructive manner the atmospheric pressure, and
which is known as that of the Magdeburg hemi-
spheres. The apparatus known by this title is
represented in fig. 1. It consists of two hollow
brass hemispheres with evenly ground edges,
which admit of being brought into air-tight con-
tact when smeared with lard. The apparatus
when secured upon the plate of an air-pump may
be exhausted, so that the space within the hemi-
spheres may be rendered a partial vacuum. The
external air will thus press the two hemispheres
together with a force proportional to the difference
between the pressure of the external air and the
pressure of the rarefied air within. When a
sufficient exhaustion has been produced, the stop-
cock attached to the lower hemisphere is closed,
the apparatus is unscrewed from the pump-plate,
and a handle screwed upon the lower hemisphere. It will be
found that two of the strongest men will be unable to tear the
hemispheres asunder, provided they are of .a moderate magnitude,
owing to the amount of the pressure with which they are held
together. If, for example, the pressure of the rarefied air
within is equivalent to a column of two inches of mercury,
while the external air has a pressure represented by 30 inches of
mercury, there will be a force amounting to 14 Ib. per square
inch on the section of the hemispheres.

If the hemisphere have 4 inches diameter, the area of their
section will be 1 2| square inches, and consequently the force with
which they will be pressed together will be
12£ X 14 = 175lb.

This apparatus derives its name from the place where the
inventor of the air-pump, Otto Guericke, first exhibited the

* Vol. ii., p. 4.

H2

THE ATMOSPHERE.

experiment, in the year 1654. The section of the hemispheres
employed by him measured 113 square inches, and they were held
together by a force equal to about three- fourths of a ton.

Since the atmosphere envelopes the earth, extending, e very wh
above its surface to nearly the same height, it presses upon every
part of the surface, upon the surfaces of extensive continents and
islands, as well as upon those of oceans and seas, with the same
force as that which it is shown to exert upon the bladder-glass,
and the Magdeburg hemispheres.

6. Let one end of a glass tube be plunged in a vessel of water,
and let the air be partially drawn from the other end by the
suction of the mouth applied to it. It will be immediately
observed that water will enter the tube, and will rise in it higher
and higher the more air is drawn from it by the mouth. This simple
experiment, so often made in the sport of children, supplies means
of weighing a column of air extending from the surface of the earth
to the top of the atmosphere, with as much precision as if that
column could be placed in the dish of a balance, and counter-
poised by equivalent weights. The water ascends in the tube,
because the pressure of the air within the tube being diminished
by the suction of the mouth, is less than the pressure of the air
upon the surface of the water in the vessel. This latter pressure
therefore predominating, forces the water up to a certain height
in the tube. The weight of the column of water which thus
ascends in the tube, is exactly equal to the excess of the weight of
a corresponding column of air, extending from the surface to the
top of the atmosphere, over the pressure of the air remaining in
the tube ; and it follows, that if the tube were long enough, and if,
by the suction of the mouth, all the air could be withdrawn from
it, a column of water would rise in the tube whose weight would
be exactly equal to that of a corresponding column of the air,
extending from the surface to the top of the atmosphere.

7. Now this experiment was actually made by Pascal, at
Houen, in 1646. A tube was procured, measuring 46 feet in
length, but as the suction of the air from it was then considered
impracticable, the difficulty was surmounted by first closing the
tube at one end, and then completely filling it with water. The
upper end being then well corked, so as to prevent the escape of
the water, the tube was inverted by means of ropes and pulleys
properly attached to it, and the corked end being immersed in a
reservoir of water, and the tube being erected to the vertical
position, the cork was taken out. Immediately the column of
water in the tube subsided ; but instead of falling altogether out
of it into the reservoir, as many expected would happen, it
remained suspended at a height of about 34 feet above the level of

100

WATER BAROMETER.

the water in the reservoir; the other 14 feet of the tube remaining
empty.

It followed, therefore, that the column of water, 34 feet high,
exactly balanced a corresponding column of air extending from
the surface to the top of the atmosphere.

It appears, therefore, from the result of this celebrated experi-
ment, that every part of the surface of the globe, whether it be
land or water, and of the surface of every object upon the globe,
is subject to the same pressure as if it were at the bottom of a
reservoir of water 34 feet deep.

8. When we look back upon the progress of physical discovery
during former ages in this department of knowledge, and consider
the numerous phenomena which were constantly offered by Nature
herself to the least attentive and the least acute, it cannot fail to
excite surprise, that the grosser and more obvious properties of
that universally diffused fluid which everywhere surrounds us, and
of which mankind in every age and country have so largely availed
themselves for the uses of life, should remain not only undiscovered
but altogether misapprehended. Even those who claimed the
rank and title of philosophers seemed to have turned aside from
the plain path of discovery pointed at by the finger of Nature, and
with a perverseness and fatal obstinacy devoted their faculties to
the invention of fanciful theories and hypotheses, having so little
analogy to truth or nature, that the bare statement of them now
seems grotesque.

The ancient philosophers observed, that in the instances which
commonly fell under their notice space was always filled by a
material substance. The moment a solid or a liquid was by any
means removed, immediately the surrounding air rushed in and
filled the place which it deserted : hence they adopted the physical
dogma that Nature abhors a vacuum. Such a proposition must be
regarded as a figurative or poetical expression of a supposed law
of physics, declaring it to be impossible that space could exist
unoccupied by matter.

Probably one of the first ways in which the atmospheric pressure
presented itself was by the effect of suction with the mouth, above
described. This phenomenon was accounted for by declaring
that "nature abhorred a vacuum," and that she therefore com-
pelled the water to enter the tube and fill the space deserted by
the air.

The effects of suction by the mouth led by a natural analogy- to
suction by artificial means. If a cylinder be open at both ends,
and a piston playing in it air-tight be moved to the lower end,
upon immersing this lower end in water, and then drawing up
the piston, an unoccupied space would remain between the piston

101

THE ATMOSPHERE.

and the water. " But nature abhors such a space," said the
ancients, "and therefore the water will not allow such a space
to remain unoccupied : we find accordingly that as the piston rises
the water follows it." By such fantastical theory pumps of various
lands were constructed.

9. The antipathy entertained by Nature against an empty space
served the purposes of philosophy for a couple of thousand years,
when it happened in the time of Galileo, that is, about the middle
of the seventeenth century, that some engineers near Florence,
being employed to sink a pump to an unusual depth, found they
could raise by no exertion the water higher than 32 feet in the
barrel. Galileo was consulted, and it is said, that he answered,
half seriously, half sportively, that nature's abhorrence of a
vacuum extended to the height of 32 feet, but that beyond this
her disinclination to an empty space was not carried. The answer,
however, whatever it was, does not appear to have been satis-
factory, and the question continued to excite attention.

10. After the death of Galileo, Torricelli, his pupil, since become
so celebrated, directed his attention to its solution. He argued,
that whatever be the cause which sustains a column of water in a
pump, the measure of the power thus manifested must be the
weight of the column of water sustained : and, consequently, if
another liquid were used, heavier bulk for bulk than water, the
same force would sustain a column of that liquid, having less
height in proportion as its weight would be greater. By using a
heavier liquid, therefore, such as mercury, for example, the column
sustained would be much shorter, and the experiment would
be more manageable. The weight of mercury being bulk for
bulk about 13| times that of water, it followed that, if the force
imputed to a vacuum could sustain 34 feet of water, it would
necessarily sustain 13^ times less, or about 30 inches of mercury.'
Torricelli therefore made the following experiment, which has
since become so memorable in the history of physical science.

He procured a glass tube A B, fig. 2, more than 30 inches long,
open at one end, A, and closed at the other, B. Filling this tube
with mercury, and applying his finger at the open end A, so as t>
prevent its escape, he inverted it, plunging the end A into mercury
contained in a cistern, c D, fig. 2.

On removing the finger, he observed that the mercury in the
tube fell, but did not fall altogether into the cistern ; it only sub-
sided until its surface E was at a height of about 30 inches above
the surface of the mercury in the cistern.

This result, which was precisely what Torricelli had anticipated,
clearly demonstrated the absurdity of the statement imputed to
Galileo, that Nature's abhorrence of a vacuum extended to the
102

TORKICELLIS EXPERIMENT.

Fig.

height of 32 feet, since in this case her abhorrence was limited
to 30 inches? In fine, Torricelli soon perceived the true cause
of this phenomenon.

The weight of the atmosphere acting upon the surface of the
mercury in the cistern supports the liquid in the tube. But the
surface E being excluded from contact with the atmosphere, is free
from the pressure of its weight ; the
column, therefore, of mercury F, being
pressed upwards by the weight of the
atmosphere, and not being pressed down-
wards by any other force, would stand
in equilibrium.

This explanation was further con-
firmed by the fact, that on admitting
the air to the upper end of the tube B,
by breaking off the glass at that point, or
opening a stop-cock placed there, the
column of mercury in the tube instantly
dropped into the cistern. This was
precisely the effect which ought to ensue,
inasmuch as the admission of the pres-
sure of air upon the column E balanced
the pressure on the surface in the
cistern, and there was no longer any
force to sustain a column of mercury in
the tube, and consequently it fell into
the cistern.

11. This experiment and its explana-
tion excited, at the epoch we refer to, the greatest sensation
throughout the scientific world, and, like all new discoveries
which have a tendency to explode long-established doctrines,
was rejected by the majority of scientific men. The celebrated
Pascal, wl^o flourished at that epoch, however, had the sagacity
to perceive the force of Torricelli' s reasoning, and proposed to
submit his experiment to a test which must put an end to
all further question about it. " If," said Pascal, "it be really
the weight of the atmosphere under which we live that sup-
ports the column of mercury in Torricelli' s tube, we shall
find, by transporting this tube upwards in the atmosphere,
that in proportion as it leaves below it more and more of the
air, and has consequently less and less above it, there will be
a less column sustained in the tube, inasmuch as the weight
of the air above the tube, which is declared by Torricelli to be
the force which sustains it, will be diminished by the increased
elevation of the tube."

103

THE ATMOSPHERE.

Pascal therefore caused Torricelli's tube to be carried
top of a lofty mountain, called the Puy-de-d6me, in Auvergne,
and the height of the column to be correctly noted during the
ascent. It was found, in conformity with the principle announced
by Torricelli, that the column gradually diminished in height as
the elevation to which the instrument was carried increased.
The experiment being repeated upon a high tower in Paris with
like success, there no longer remained any doubt of the fact, that
the column of mercury in the tube, as well as the column of water
in common pumps is sustained, not by the force vulgarly called
suction, nor by Nature's abhorrence of a vacuum, but simply by the
weight of the incumbent air acting in one case on the surface of
the mercury, and in the other on the surface of the water in the
well, in which the pump terminates.

12. The instrument which we have here described, as used in
the experiment of Torricelli, is nothing more than the common
barometer.

The methods of constructing and mounting it so as to adapt it
for use, and the precautions necessary to ensure the certainty and
precision of its indications, will be explained in another number
of this series ; meanwhile it will be sufficient for the present to
assume generally, that the mercurial column E F, suspended in the
glass tube equilibrates with, and therefore measures the weight of
a corresponding column of the atmosphere, extending from the
surface, c F, of the mercury in the cistern indefinitely upwards.

It has been shown,* that air in its usual state is 772^ times
lighter than water. But water being 13| times lighter than
mercury, it follows that air must be 13^ times 772| times lighter
than mercury. By multiplying 772| by 13|, we obtain 10429.
It follows, therefore, that 10429 cubic inches of air are equal in
weight to 1 cubic inch of mercury.

13. If the atmosphere, in ascending from stratum to stratum,
had constantly the same density, so that each cubic inch of air, at
all heights, would have the same weight, we could at once deter-
mine its entire height by the preceding experiment ; for since a
column of mercury, 30 inches, or 2| feet high, has the same
weight as a column of air extending from the surface of the
ground to the top of the atmosphere, and since the weight of the
mercury, bulk for bulk, is 10429 times greater than that of air,
it is evident that the height of a column of air as heavy as the
column of mercury, must be 10429 times greater than that of the
column of mercury, and would therefore be 10429 times

that is 26072 feet, or 5 miles very nearly.

104

Vol. ii., p. 3.

VARYING DENSITY OF ATMOSPHEKE.

Are we then to infer, that the height of the atmosphere is
really not more than 5 miles ? We have a thousand evidences to
the contrary. The height of the summit of the mountain called
Dhwalagiri, one of the Himalaya chain, has been ascertained
to be 28000 feet, and clouds are seen suspended in the air far
above it. The atmosphere therefore extends to a height far above
26000 feet.

14. This height of 5 miles is that which would limit the atmos-
phere, if air were such a fluid as water, so that stratum might be
heaped upon stratum to any height, without producing any com-
pression in the lower strata by the effect of the weight of the
superior strata. Air, however, is not such a fluid. It is, as has
already been shown,* compressible without limit, and not only
compressible but expansible. The air around us which composes
the lowest stratum of the atmosphere, is compressed by the entire
weight of the series of strata of air which are above it, and this
weight, as has been already shown, amounts to 15 Ib. upon a
square inch of surface. Now, if any portion of this air be sub-
jected to double that pressure, it will be contracted into half its
bulk, and will consequently have twice its density ; and if, on the
other hand, it be relieved of half the pressure, it will expand into
twice its bulk, and will consequently have only half the density.
In a word, the state of air as to density will depend upon the
pressure to which it is subjected. If that pressure be augmented
or diminished, the density of the air will be augmented or
diminished in exactly the same proportion.

15. Air being therefore elastic, and consequently indefinitely
compressible and expansible, it follows that, as we ascend in the
atmosphere from stratum to stratum, the density must be con-
tinually diminished, because the quantity of air above each
successive stratum, being continually less, the weight pressing on
the strata is continually less, and consequently the density must
be proportionally less.

Hence it is apparent that the actual height of the atmosphere
must be vastly greater than five miles. If the atmosphere, in
ascending, were imagined to be resolved into a number of layers,
each of which would contain the same weight of air, these layers
would increase in thickness in ascending. Thus, if the lowest layer
were 10 feet thick, a layer at such a height that half the entire
atmosphere was below it, would be 20 feet thick, because being
subject to only half the pressure it would have only half the density,
and would therefore occupy twice the bulk . In like manner, a layer
at such a height as would leave three-fourths of the atmosphere

* Yol. ii., p. 5.

105

• THE ATMOSPHERE.

below it, being pressed upon by the weight of only one-i
would have a thickness of 40 feet, and so on.

The air, therefore, in ascending, becomes continually and
indefinitely thinner and rarer. Persons who have ascended to
great heights in balloons or on mountains, have accordingly found
themselves in an atmosphere so rarefied as to derange seriously
the vital functions.

16. The various phenomena vulgarly called suction are nothing
more than so many various effects of the atmospheric pressure.

17. If a piece of moist leather be placed in close contact with
any heavy body having a smooth surface, such as a stone or a
piece of metal, it will adhere to it ; and if a cord be attached to
the leather, the stone or metal may be raised by it.

This effect arises from the exclusion of the air from between
the leather and the stone. The weight of the atmosphere presses
their surfaces together with a force amounting to 15 Ib. on a
square inch of the surface of contact.

18. The power of flies, and other insects, to walk on ceilings,
smooth pieces of wood, and other similar surfaces, in doing which
the gravity of their bodies appears to have no effect, is explained
upon the same principle. Their feet are provided with an appa-
ratus similar exactly to the leather applied to the stone.

19. The pressure and elasticity of the air are both called into
effect in the act of respiration. When we inspire the atmosphere,
we make by a muscular exertion an enlarged space within the
chest. The atmospheric pressure forces the external air into this
space. By another and contrary muscular exertion, the chest is
then contracted, so as to squeeze out the air which has been
inhaled, and which, by compression, acquires an elasticity greater
than the atmospheric pressure, in virtue of which it is forced out
at the mouth and nostrils.

20. The action of a common bellows is precisely similar, except
that the aperture through which the air enters is different from
that by which it is expelled. The analogy, however, would be
complete if we inspired by the mouth and expelled by the nose.
When the boards of the bellows are separated, the inner chamber
is enlarged, and the air is forced in by the external pressure
through the aperture governed by the leather valve or clack.
The boards being then pressed together, and the escape of the
air being stopped by the closed valve, it is compressed until it
acquires an elasticity greater than the atmospheric pressure, and
is forced out.

Bellows on a large scale are constructed with an intermediate
board, so as to consist of two chambers, and to produce a con-
tinued instead of an intermittent blast. This is nothing more
106

BELLOWS-PNEUMATIC INK-BOTTLE.

than a double bellows, one forcing air into the chamber of the
other, and the second being urged by an uninterrupted pressure
produced usually by a weight suspended from the upper board.

21. The effect produced by a vent-peg in a cask of liquid is
explained by the atmospheric pressure. The cask being air-
tight, so long as the vent-peg is maintained in its position, the
-surface of the liquid in the vessel will be excluded from the
atmospheric pressure, and it can only floAV from the cock in
.virtue of its own weight. If the weight of the atmosphere be
greater than the weight of a column of the liquid, corresponding
with the depth of the liquid in the vessel, the liquid cannot flow
from the cask; but the moment the vent-peg is removed, the
-atmospheric pressure being admitted above the level of the liquid in
the cask, the liquid flows from the cock in virtue of its own weight.

If the lid of a teapot or kettle were perfectly close, the liquid
would not flow from the pipe, because the atmospheric pressure
would be excluded from the inner surface. A small hole is there-
fore usually made in the lid to admit the air and allow the liquid
to flow freely.

22. Ink-bottles are sometimes so constructed as to prevent the
inconvenience of the ink thickening and drying. Such a bottle
is represented in fig. 4 : A B is a close glass
vessel, from the bottom of which a short
tube B c proceeds, the depth of which is
sufficient for the immersion of a pen. When
. ink is poured in at c, the bottle being placed
in an inclined position, is gradually filled
up to the knob A. If the bottle be now placed
in the position represented in the figure, the
chambery A B being filled with the liquid,
the air will be excluded from it, and the
pressure tending to force the ink upwards in
the short tube c, will be equal to the weight of the column
of ink, the height of which is equal to the depth of the ink
in the bottle A B, and the bore of which is equal to the section
of the tube c. The ink will be prevented from rising in the tube c
by the atmospheric pressure, which is much greater than the
pressure of the column of liquid in the bottle. As the ink in the
short tube c is consumed by use, its surface will gradually
fall to a level with the horizontal tube B, a small bubble of air
will then insinuate itself through B, and will rise to the top
of the bottle A B, where it will exert an elastic pressure, which
will cause the surface of the ink in c to rise a little higher ; and
this effect will be continually repeated, until all the ink in the
bottle has been used.

107

THE ATMOSPHERE.

Birdcage fountains are constructed on the same principle.

The peculiar gurgling noise produced in decanting wine arises
from the pressure of the atmosphere forcing air into the interior of
the bottle to replace the liquid which escapes.

23. The common syringe by which air is withdrawn from or
condensed in any vessel derives its efficacy altogether from this
property of the elasticity of air.

The instrument is called an exhausting or condensing syringe,
according as it is adapted to extract air from a vessel, or to force
air into it.

24. To explain the principle of the exhausting syringe, let A B
(fig. 5) represent a cylinder having a solid piston r, moving-
air-tight in it. Let c be a tube proceeding
from its lower end, furnished with a stop-cock
c, and let B be another tube furnished with a,
stop-cock D. Let the tube c be screwed upon
any vessel such as n, from which it is desired
to extract the air.

If the piston be now raised in the cylinder,
the cock D being closed and the cock c being-
open, the air in B, will necessarily expand, in
virtue of its elasticity, so as to fill the enlarged,
space provided by raising the piston. The
air which previously filled the vessel R and the
connecting tube will, in fact, now fill these,
and also the enlarged space in the cylinder.
When the piston is brought to the top of the
cylinder, let the cock c be closed and the cock
D be opened. Upon driving down the piston,
the air which fills the cylinder will be expelled
from the tube B through the open stop-cock D.
When the piston has reached the bottom of
the cylinder, let D be closed and c opened,
and let the same process be repeated ; the air filling the vessel K
will, as before, dilate itself, so as to fill such vessel and the
cylinder. The cock c being again closed, and D opened, and the
piston driven down, the air which fills the cylinder will be again
expelled. This process being continued, any desired quantity of
air can be taken out of the vessel n and expelled into the
atmosphere.

It is evident that the escape of the air from B, into the cylinder
is effected in virtue of its elasticity ; while its escape from the
stop-cock D into the atmosphere is effected in virtue of its com-
pressibility.

25. It is easy to explain the rate at which the air is drawn
108

EXHAUSTING SYRINGE.

from the vessel K by this process. If we suppose the volume of the
cylinder through which the piston passes to be j^th, for example,
of the entire volume of the cylinder the tube and the connecting
pipe taken together, then it is clear, that on completing the first
downward stroke of the piston, ith of all the air included between
the piston and the surface of the vessel K will be expelled, and
reQths will consequently remain.

At every succeeding stroke, ^th of what remained after the
preceding stroke will be expelled, and in the same way T95ths
will remain.

If we suppose the vessel R and the connecting tube to contain
ten million grains weight of air, the quantities expelled at each
successive stroke, the quantities remaining, and the total quan-
tities expelled from the commencement of the operation, will be
thus exhibited in the following table : —

No. of Strokes.

Graius expelled
at
each stroke.

Grains remaining
under
pressure.

Total number
of
grains expelled.

I

I,oooooo

9,000000

I,oooooo

2

900000

8,100000

1,900000

3

810000

7,290000

2,710000

4

729000

6,561000

3,439°°°

5

656100

5,904900

4,095100

6

590490

5,3r4410

4,685590

7

53I44I

4,782969

5,217031

8

478297

4,304672

5,695328

9

430467

3,874205

6,125795

10

387421

3,486784

6,513216

ii

348678

3,138106

6,861894

12

3l38n

2,824295

7,i757°5 1

Thus, in twelve strokes of the syringe, of the ten million of
grains of air originally included, something more than seven
million, or seven-tenths of the whole, have been withdrawn, and
something less than three-tenths remain.

26. A rarefaction has been therefore produced in the pro-
portion of something more than three to ten. But it will be
apparent, that although by this process the rarefaction may be

109

THE ATMOSPHERE.

continued to any required extent, a literal and absolute vacuum
can never be produced, because some quantity of air, however
small, must always remain in the vessel E. After every stroke
of the piston, nine-tenths of the air which is in the vessel
before the stroke remains in it. Now it is evident, that if wo
successively subtract one-tenth of any quantity, we must always
have some remainder, however long the process be continued :
and the same will be true, whatever proportion be thus continually
subtracted.

27. Nevertheless, although an absolute vacuum cannot be
obtained by such means, we can continue the process until the
rarefaction shall be carried to any required extent.

In practice, the stop-cocks D and c are replaced by valves. A
valve is placed at D which, opening outwards, is forced open by
the elasticity of the air compressed under the piston when
depressed, but is kept closed by the external pressure of the
atmosphere when the piston is raised. The valve at c opens
upwards, and is opened by the elasticity of the air in E when the
piston is raised, and kept closed by the elasticity of the com-
pressed air in the cylinder when the piston is depressed. Instead
of placing a tube and valve at B, it is usual to make the valve in
the piston itself, opening upwards; but the action is still the
same. An exhausting syringe, therefore, may be shortly described
to consist of a cylinder with two valves, one in the bottom,
opening upwards, and one in the piston, also opening upwards.
When the piston is drawn upwards, the valve in the bottom of
the cylinder is opened by the pressure of the air under it, and the
air passes through it. When the piston is driven downwards, the
valve in the piston is opened by the elasticity of the air com-
pressed under it, which rushes through it.

• 28. The air-pump is an apparatus consisting usually of two
exhausting syringes, B B', fig. 6, mounted so as to be worked by
a single winch and handle, as represented at D, and communi-
cating by a common pipe T with a glass vessel E, in which may bo
placed the objects of experiment. The vessel E, called a receiver ,
has an edge s, ground smooth, resting upon a plate, also ground
smooth, and kept in air-tight connection with it by being smeared,
with hog's lard. A stop-cock c is provided in the pipe T, by which
the communications between the receiver E and the syringes can
be made and broken at pleasure. Another stop -cock is provided
elsewhere, by which a communication can be made at pleasure
between the interior of the receiver E and the external air. To
indicate the extent to which the rarefaction is carried from time
to time by the operation of the syringes, a mercurial gauge
ir Q M is provided, constructed in all respects similar to a
110

ATE PUMP.

barometer. The atmosphere presses on the surface of the-
mercury in the cistern M, while the column of mercury in
the tube H G is pressed upon by the rarefied air in E. The
height of the column, therefore, sustained in the tube, indicates
the difference between the pressure of the external air and the air
in the receiver.

When a gauge, of the form represented in fig. 6, is used, it
is necessary that it should have the height of about 30 inches,
since, when a high degree of rarefaction has been effected, a
column of mercury will be sustained in the tube H G, very little
less than in the common barometer. In small pumps, where
this height would be inconvenient, a siphon-gauge, such as that
represented in fig. 7, is used. This gauge is screwed on to a pipe
communicating with the receiver. Mercury fills the leg A B,
which is closed at the top A, and partially fills the legs s.
"When the atmosphere communicates freely with the tube D c,
the surface of the mercury in s being pressed by its
full force, sustains all the mercury which the tube
B A can contain, and this tube, consequently,
remains completely filled ; but when the pipe DCS
is put in communication with the exhausted receiver,
the surface of the mercury in s being acted upon only
by the pressure of the rarefied air in the receiver,
the weight of the higher column in B A will pre-
dominate, and the mercury will fall in it, until the
difference of the levels in the two legs shall be equal
to the pressure of rarefied air in the receiver.

29. The condensing syringe differs from the ex-
hausting syringe only in the direction in which the

valves are placed. It consists of a cylinder and piston, as repre-
sented in fig. 5. When the piston is drawn upwards, the cock
D is open, and c is closed, and the cylinder is filled with air
proceeding from the external atmosphere. ; When the piston is
pressed downwards, the cock D is closed and c is opened, and
the air which filled the cylinder is forced into the vessel E. On
raising the piston again, the cock c is closed and D is opened,
and the effects take place as before. It is evident that, by every
stroke of the piston, as much air as fills the cylinder is driven
into the vessel E.

In practice, the cocks D and c are replaced by two valves, one
in the bottom of the cylinder, and the other in the piston, both
opening downwards, contrary to the valves in the exhausting
syringe.

The operation is explained in the same manner.

30. The condenser is an apparatus which bears to the con-

Hi

THE ATMOSPHERE.

densing syringe precisely the same relation which the air-pump
bears to the exhausting syringe. It consists of one or two
condensing syringes, mounted so as to be conveniently worked by
a winch, and communicating with a strong reservoir, which is
fastened down upon a plate, so as to be maintained in air-tight
contact with it, notwithstanding the bursting pressure of air con-
densed within it. By the operation of syringes, volumes of air
corresponding to their magnitude are forced continually into the
reservoir, which becomes therefore filled with an atmosphere pro-
portionally more dense than the external air.

112

COMMON THINGS.

TIME.

LARLNER'S MUSEUM OF SCIENCE. i

No. 56.

113

CHAPTER I.

1. Simple notions difficult to define. — 2. Conception of Time, how obtained.
— 3. By succession of sensible impressions. — 4. Proof that such
succession is necessary. — 5. Time passes faster with soine than with
others. — 6. Is measured only by a regular and uniform succession. —
7. Periodic phenomena which may measure time. — 8. Natural
appearances intended for that purpose. — 9. Significations of the
word "day." — 10. Hours. — 11. Their length in certain cases
variable. — 12. Vulgar and equinoctial hours. — 13. Commencement
of the day with different nations. — 14. Italian time. — 15. Incon-
venience of such a mode of reckoning. — 16. Modern method. —
17. Civil and astronomical time. — 18. The day the standard unit.
— 19. Necessary to determine it rigorously. — 20. What is a day ? —
21. Diurnal rotation of the heavens. — 22. Its constancy an<l
uniformity. — 23. Nevertheless not fitted to be the unit of civil time.
24. The meridian. — 25. Diurnal motion of the sun — means of
observing it. — 26. Transit instrument. — 27. Method of observing
with it. — 28. Sidereal day — its subdivisions. — 29. Its permanency
and uniformity — unfit, nevertheless, for a measure of time. — 30. Why
the sun is not fit.

I. — TIME IN GENERAL.

t. THE most simple of our notions are those which it is most
difficult to describe or define. It is fortunate that they are pre-
cisely those which least need definition. Geometers have failed
in defining a straight line, or a plane surface, but no persons
differ in their conceptions of the meaning of these terms. Locke
observes, with his usual felicity and clearness, that a word which
expresses a simple idea, does not admit of definition, inasmuch as
a definition being a sentence composed of two or more words
having different significations, cannot collectively express one
idea which has no composition at all. The only way to convey
to the mind of another, the meaning of such a word, is by pre-
senting to his senses the object or the quality which it expresses.
In that case, if he possess the necessary organ of sense, he will
immediately obtain the perception ; if he do not all the words in
the world will not convey it to him. A person blind or deaf from
infancy can never acquire any perception of colours or sounds.
A. blind man after listening attentively to an elaborate description
of the colour scarlet, declared that he had a very clear and satis-
factory notion of it, and that he considered it like the sound
of a trumpet !

2. Time is a word about the meaning of which it would seem
that there could be no disagreement; yet we cannot as in the
case of words expressing sensible ideas refer to any external
object from which we can immediately receive the perception
which that word expresses. Although we cannot define by words
114

ORIGIN OF THE NOTION OF TIME.

the meaning of the terms white or red, we can point to the lily
and the rose, and thus supersede verbal definition. We cannot
define the notes of the nightingale or the lark, but if we walk
forth in the night or at the early dawn, the one or the other will
discourse music more eloquent than definition.

Can we then, by a like appeal to the senses, obtain a notion of
what is expressed by the word TIME ? Which organ does it
address ? Time cannot be seen, heard, felt, tasted or smelled.
It cannot be seized and submitted to observation and analysis.
It is the most fleeting of all perceptions. Moment follows
moment in never ceasing succession, but no moment can be said
to have any continued existence, so as to be submitted to
contemplation.

3. Metaphysicians differ as to the mental process by which we
acquire a perception of duration, but they agree generally that its
origin is closely connected with the succession of our thoughts and
ideas. From our observation and consciousness of this succession,
and from that alone, does our original conception of time proceed.
When the mind has once been stored with ideas and perceptions
derived by the senses from external objects, the memory can at will
reproduce them and marshal them in infinitely various series before
the imagination. Of such succession of thoughts and feelings
thus evoked by memory we are as distinctly conscious as we are
of those derived directly from external objects, and by that con-
sciousness we acquire a perception of time when no external
objects are presented to the senses. Thus if during the darkness
of night we lie awake, a constant succession of thoughts and
images pass through the mind, consisting altogether of various
ideas and combinations supplied by the memory. This succession
of notions creates a consciousness from which we derive a per-
ception of a certain lapse of time.

4. That an actual succession of thoughts, emotions, ideas or
images, whether they proceed directly from external objects or
arise from the operations of memory, reflection, or imagination,
is absolutely necessary to our perception of time is demonstrated
by the fact that whenever such succession ceases, our percep-
tion of time ceases with it. Thus in profound sleep without
dreaming, we have no perception whatever of duration. Having
gone to sleep at night, and waking, in the morning it is true that
we know that a certain definite interval has elapsed, but we
derive this knowledge by inference from external phenomena and
not at all from consciousness. We see that the darkness of night
has changed to the light of day ; that the sun which was below
the horizon is above it, and we know by past experience that
these changes are only produced in a certain interval of time, and

i 2 115

COMMON THINGS — TIME.

lat such interval of time must have elapsed since we fell asleep.
But if we fall asleep in tne evening and do not awaken until the
next day but one, we are unconscious of the lapse of more than
one night. Robinson Crusoe, alone on the desert island, being
indisposed, swallowed a narcotic composed of rum and the infusion
of tobacco, which threw him into a profound sleep that continued
from the night until the afternoon of the next day but one, and
he was unconscious of the lapse of more than a single night. He
found accordingly, when liberated from his solitary abode, upon
comparing his journal with the actual dates, that he had lost a
day in his account.

5. It might, therefore, be naturally inferred that the succession
of our thoughts or mental impressions, being the origin of ou:
perception of duration, would be necessarily a measure of dura-
tion, and indeed the only measure of it. It is easy, nevertheless,
to see that such an inference can only be admitted with consider-
able qualification. The succession of sensible impressions pro-
duced by certain regular and uniform series of external appear-
ances is unquestionably an exact and the only exact measure of
time, but it would be, on the other hand, a grave error to assume
that such a just measure of duration can result indifferently from
every series of mental impressions. Who does not know that a
series of agreeable thoughts and brilliant ideas has the effect of
making time pass with unwonted rapidity ?

" Too late I stayed. Forgive the crime !

Unheeded flew the hours.
How noiseless falls the foot of Time
Which only treads on flowers !

" Ah ! who with clear account remarks

The ebbing of his glass,
When all its sands are diamond sparks,
Which dazzle as they pass ? "

Again, — the series of our thoughts becomes a most fallaciou
measure of time when we are the sport of the more exciting
passions and emotions, such as hope, fear, or despair.

"Rosalind. Time travels in divers paces with divers persons; I'll tell
you who time ambles withal, who time trots withal, who time gallops
withal, and who he stands still withal.

' ' Orlando. I prythee, who does he trot withal ?

" Ros. Marry, he trots hard with a young maid, between the contract
of her marriage, and the day it is solemnised. If the interim be but a
se'nnight, time's pace is so hard, that it seems the length of seven years.

" Orl. Who ambles time withal ?

"Ros. With a priest that lacks Latin, and a rich man that hath not
the gout : for the one sleeps easily, because he cannot study, and the other
lives merrily, because he feels no pain ; the one lacking the burden of lean
116

MEASURES OF TIME.

and wasteful learning, the other knowing no burden of heavy tedious
penury. These time ambles withal.

" Orl Who doth he gallop withal ?

11 Ros. With a thief to the gallows : for though he go as softly as foot
can fall, he thinks himself too soon there.

" Orl. Who stays it withal ?

" Ros. With lawyers in the vacation : for they sleep between term and
term, and then they perceive not how time moves."

SHAKSPEARE, As You Like It, Act III. Scene 2.

6. A succession of thoughts and perceptions floating at hazard
through, the mind, or excited casually and without regularity hy
external objects, produces a perception of time, but affords no
measure of it ; just as the general view of a landscape produces
the impression of a certain progression of distances among the
objects composing it, without, however, supplying the means of
estimating with numerical precision such distances.

A progression of events or perceptions . which would supply a
measure of time, must be absolutely uniform and regular. In
such case the number of repetitions of the same event or pheno-
menon found between any two points of the series becomes
the measure of the interval of time which has elapsed between
them.

7. The series of phenomena adopted by mankind as measures
of time have been either natural or artificial. Natural measures
of time consist of regularly recurring periodical phenomena,
which are easily and universally observable by all the world, and
which never cease to be reproduced with the same uniformity in
all parts of the inhabited globe. Artificial measures are usually
motions which are so contrived as to be uniform so long as they
continue, and which, when exhausted, admit of being restored.

Any regular periodical change, however, may serve as a
measure of time. Thus woodmen ascertain the age of certain
trees by marks upon their trunks. The ages of certain species of
cattle are indicated by the successive formation of rings on their
horns. The age of horses is ascertained by the successive dis-
appearance of marks from their teeth.

If a candle in burning were consumed uniformly its decrease
of ^ length might be used as a measure of time. In certain sales
by auction, the continuance of the bidding was limited by "inch
of candle."

8. But the periodical phenomena which have been most univer-
sally adopted in all ages and all countries as measures of time,
are those which were expressly assigned for that, among many
more important purposes, by the Omniscient, who, when he "made
the firmament and saw that it was good," said —

"Let there be light in the firmament of the heaven, to divide

117

COMMON THINGS — TIME.

the day from the night; and let them be for signs, anc
seasons, and for days, and years :

"And God made two great lights; the greater light to rule
the day, and the lesser light to rule the night." — Gen. i. 14, 16.

Days, weeks, months, and years, and the subdivisions of a
day, hours, minutes, and seconds, having then been adopted by
mankind in general as the measures of time, and as the land-
marks of history and chronology, it may perhaps be thought that
little more remains to be said about the matter; that these
chronometric terms used in the common intercourse of life by all
peoples —

" Familiar in their mouths as household words,"

have significations so clear, distinct, and unequivocal as to super-
sede the necessity of all exposition and discussion. All the
world knows what a day is, and that weeks, months, and years
are composed of so many of these days. We shall, nevertheless,
soon render it apparent that the import of these very familiar
terms is not quite so clear even in the minds of moderately well-
informed persons as it is supposed to be.

II. — THE HOURS.

9. The term DAY has two distinct significations* As opposed
to night, it means the interval during which we receive light from
the sun. Now this interval is not very definite. According to
some, it means the interval between sunrise and sunset. But
according to others, it signifies the interval between the morning
dawn and the termination of the evening twilight ; or from the
disappearance of the stars before sunrise to their reappearance after
sunset.

The other sense of the word DAT is that in which it is used as
a chronometric term. It is the interval of time which elapses
between two successive appearances of the sun at the same point
of the heavens with relation to the horizon. This interval evi-
dently includes a day and a night.

The Greeks used a word, for which there is no English equi-
valent, to express this latter sense of the term DAY. This word
was wxefaepov (nukthemeron,} a compound of the terms night
and day.

10. From time immemorial a duodecimal division of the day
has been adopted by all nations. Some peoples have counted the
hours consecutively, from one to twenty-four. Others have divided
the day into two series of twelve hours. It may perhaps be a
legitimate subject of regret that the same system of decimal reckon-
ing, which has conferred, such simplicity upon the arithmetical

118

THE HOUES.

notation and terminology, should not have been applied to the
counting of time. When the spirit of innovation was in the
ascendant in France in 1793, such an attempt was made, the day
being divided into ten hours, the hour into an hundred minutes,
and the minute into an hundred seconds. The power of custom,
however, prevailed over even the domination of terrorism and the
project signally failed.

11. The hours into which the day was resolved were generally
intended to be equal, each being the twenty-fourth part of the
entire interval called a day. Nevertheless, there were some
exceptions to this. Thus, at a certain epoch in Greece, the
interval between sunrise and sunset was divided into twelve
equal parts called hours of the day, and the other interval, be-
tween sunset and sunrise, was also divided into twelve equal
parts, called hours of the night. It is evident that the diurnal
hours were equal to the nocturnal hours only at the equinoxes,
and that from the spring to the autumnal equinox the diurnal
were longer than the nocturnal hours, and from the autumnal to
the spring equinox the nocturnal were longer than the diurnal
hours. The hours, both diurnal and nocturnal, were also subject
to continual variation of length. From the first day of winter,
or the shortest day, to the first day of summer, or the longest day,
the diurnal hours constantly increased, and the nocturnal hours
constantly decreased in length ; and from the first day of summer
to the first day of winter, the nocturnal hours constantly increased,
while the diurnal hours constantly diminished.

Such a system could not be properly denominated chronometric
at all, since the interval of time called an hour was different at
different seasons.

12. Defective as such a method of counting time must have
been for the purposes of common life, it was utterly inadmissible
for any scientific investigations ; and Ptolemy, in his astronomical
observations, was always obliged to transform the vulgar hours
into equinoxial hours ; so called, no doubt, because it was only at
the equinoxes that the vulgar diurnal were equal to the noc-
turnal hours.

How imperfect the art of measuring time was in that age, may
be imagined when it is stated that, in the observations of Ptolemy,
the time of astronomical phenomena is never indicated nearer the
truth than a quarter of an hour. At present it is determined in
good observations to less than the tenth of a second.

13. For chronometric purposes, it is not enough to fix the value
of the standard unit of time. It is necessary also to establish a
convention as to the moment at which each successive unit com-
mences, and the preceding one terminates. In a word, a point of

COMMON THINGS — TIME.

departure must be agreed upon for each clironometric unit ; and
this, as will be seen, is a subject upon which much disaccord has
prevailed, and the establishment of which, with all the aids
afforded by the advanced state of astronomical science, has been
a matter of the greatest difficulty and delicacy.

The Jews, the ancient Athenians, the Chinese, and other
Oriental nations, as well as the Italians, fixed the commencement
of the day at sunset. According to the Italians, even to the pre-
sent times, the day is divided into twenty-four successive hours,
reckoned continuously from sunset to sunset. Thus, at an hour
before sunset, it is said to be twenty-three o'clock, at two hours
before sunset it is twenty- two o'clock, and so on.

According to this system, the hour of sunrise varies from day
to day, and from season to season, but the hour of sunset is con-
stant, being 24 o'clock or 0 o'clock. At the equinoxes, the sun rises
at twelve o'clock. From the spring to the autumnal equinoxes, it
rises before twelve, and from the autumnal to the spring equinoxes,
it rises after twelve.

It is evident that a clock to indicate such time must be set from
day to day, or at least from week to week, since the hour of sunset
would be constantly later during one half-year, and constantly
earlier during the other.

14. At some places in Italy, and more particularly at Eome,
public clocks are set according to this system, and others placed
near them according to the common system, the indications of the
one being called ITALIAN, and those of the other, FRENCH TIME.

The system of Italian time has been defended upon the ground
of the convenience it affords, of always telling the hour of sunset,
so as to show to travellers and those who are occupied in out- door
employments the time they have at their disposition before night-
fall. Against this convenience, such as it is, however, is to be
considered the constant necessity from day to day of setting all
the watches and clocks — an operation called by the Italians
TOCCAKE IL TEMPO — to touch the time. There are other obvious
inconveniences, however, attending such a system, such as the
constant variation of the hours of meals, of going to bed and rising,
of all descriptions of regular labour, the hours of opening and.
closing all public offices, of commencing and terminating all public
business, &c. Nevertheless, such is the force of established custom,
that this mode of reckoning time still prevails to a great extent in
the Italian peninsula.

The Babylonians, Syrians, Persians, the modern Greeks, and
the inhabitants of the Balearic Isles, took the moment of sunrise
for the commencement of the day.

15. Whether the commencement of the day be fixed at sunset
120

THE HOURS.

or sunrise, the disadvantages indicated above must attend such a
mode of reckoning time ; to which it may be added, that of all
diurnal phenomena, there is not one of which the observation is
attended with more uncertainty and risk of error than sunrise
and sunset.

16. The English, French, Germans, and generally the moderns
in all the more civilised parts of the globe, commence the day at
midnight, and divide it into two equal series of twelve hours, so
that midday is twelve o'clock as well as midnight. According to
this system of reckoning, it is necessary, whenever an hour is
named, to indicate its relation to noon. The hours before noon
are indicated by the letters A.M., and those after noon by P.M.,
being the initials of the Latin words ante meridiem (before mid-
day), and. post meridiem (after midday).

Among ancient astronomers who adopted this mode of reckoning,
may be mentioned Hipparchus, who flourished about a hundred and
fifty years before our era, and among moderns Copernicus.

The ancient Egyptians began the day at noon, in which they
were followed by Ptolemy, a celebrated astronomer, who nourished
at Alexandria in the second century of our era. This diurnal
epoch has been by general consent adopted by modern astronomers,
who divide the day into twenty-four successive hours, reckoned
from noon to noon. Thus, according to their manner of reckoning,
twenty minutes and an half after ten o'clock in the morning,
would be 22h 20m 30s.

17. Civil or common time, therefore, is half a day before
astronomical time, a circumstance which must always be carefully
allowed for in the comparison of dates expressed according to the
two modes of reckoning.

Thus, for example, the first day of the year 1854, according to
civil reckoning, commenced at the moment of midnight, between
the 31st December, 1853, and 1st January, 1854. But according
to astronomical reckoning it commenced at midday on 1st January,
1854. It follows, therefore, that the twelve hours which pre-
ceded the noon of "1st January, 1854, were according to astrono-
mical reckoning the last twelve hours of the year 1853.

In like manner, a certain hour of the forenoon, 5 A.M. of a day
(Tuesday, for example), according to civil time, is 17h Om 0s of
the preceding day (Monday), according to astronomical time.
From noon, however, till midnight of any given day, the civil
and astronomical dates are exactly the same.

III. — THE DAY.

18. A day then being adopted by common consent, and indeed
by the force of things, as the standard unit for the measure of

121

COMMON THINGS — TIME.

time, all longer intervals being expressed by its multiples, and
all shorter ones by its fractional subdivisions, it is above all things
indispensable that its absolute length should be understood with
perfect clearness, and ascertained with the most rigorous precision.
Like all standard measures, it is necessary that it should have
one invariable length, and that this length should be at all times
capable of verification by comparison with some natural pheno-
mena, observable at all times and places, and which, during
an endless succession of ages, past and future, is subject to no
change.

19. It may perhaps be thought that such extreme precision and
permanency is needless, and that a departure of the standard from
exactness by a very minute fraction would be for all practical
purposes unimportant. If the standard, whatever it be, were
only applied to the measurement of quantities which are not large
multiples of itself, this might be admitted. But it is otherwise,
when it forms a very minute fraction of that which it is applied
to measure. An error of the ten-thousandth part of an inch in a
foot maybe unimportant, so long as short spaces — as, for example,
the length of a room — only are in question. But, if we attempt
to apply the foot to measure great distances, the small error
multiplied until it swells into one so great as utterly to vitiate
the results. Thus an error of the ten-thousandth part of an inch
in a foot becomes an error of more than an inch in two miles ; of
more than a foot in twenty -four miles ; of more than a mile in
120000 miles, and so on.

If in the measurement of distance vast errors may thus arise
from the indefinite increase of small inaccuracies of the standard
units by multiplication and accumulation, it is much more so
with respect to the measures of time, errors in which, even of the
smallest amount, accumulating for ages, would involve not only
astronomy but history and chronology in complete confusion. It
will therefore be understood how important it is in many points
of view, that we should obtain clear, distinct, and settled notions
of the import of these terms, — days, weeks, months, and years, —
which constitute our chronometric nomenclature.

20. "What is a day, the fundamental unit of all time ? In a
rough and general way we have defined it to be the interval of
time which elapses between two successive returns of the sun to
the same point of the firmament. But to observe and ascertain
with the necessary precision this interval, it is necessary to have
some means of marking a certain point of the firmament ; and,
when so marked, of observing the exact moment at which the
sun arrives at it. The sun, however, not being a mere point, but
a circular space or disc, as it is called, of considerable apparent

122

)pa,ruiii;

THE DAY.

magnitude, covers a certain part of the Leavens, and different
points of this disc arrive at a given point of the firmament at
different moments ; so that when we speak of the moment the sun
passes any given point of the heavens, our words have no definite
meaning unless we specify what point of the sun's disc our obser-
vation is applied to. The point in question is of course the centre
of the disc, the successive returns of which to a certain position
in the heavens must be observed.

The point most convenient in all respects for such an observa-
tion is the highest to which the sun rises in its diurnal course
across the heavens. But to render this position of the sun's
centre, and the means of observing it intelligible, it will be
necessary to consider the apparent diurnal motion of the heavens
under a much more general point of view.

21. If we suppose an observer to stand with his back to the
north, looking to the south, and consequently having the east
upon his left, and the west upon his right, the sky being supposed
to be cloudless for a day and a night, a remarkable spectacle will
be presented to his view, the imposing grandeur of which con-
tinues to excite our admiration in spite of the familiarity which
is produced by its never-ceasing presence.

The celestial vault presents the appearance of a vast hollow
sphere, one half of which only is presented at any one moment to
our view, the base of this visible hemisphere being the plane of
the horizon, in the centre of which we stand. This hollow sphere
appears to have a motion of rotation round a certain diameter as
an axis, carrying with it as it revolves the countless objects, stars,
planets, sun, and moon, which appear in various positions upon
its stupendous concave surface. Standing in the position here
described the sphere seems to revolve from left to right round an
axis inclined to the horizon in a vertical plane, directed north and
south. This apparent motion causes all the celestial objects to
rise in succession on the left, that is on the east, and gradually
rising they approach to and pass the vertical plane directed north
and south, and after passing it, they descend upon the right, that
is on the west, and in fine disappear below the horizon.

22. This diurnal motion of the celestial sphere is characterised
by the most rigorous and absolute uniformity and constancy. It
is never faster, never slower, and never stops. It has continued
thus to move from time immemorial, and according to all appear-
ance, and subject to the existing laws of nature, will continue so
to move as long as the globe of the earth endures.

23. Such constancy and uniformity, combined with the fact
that it is universally observable, would render such an apparent
motion eminently fitted as a measure of time. Nevertheless as

123

COMMON THINGS — TIME.

will presently appear, it is attended with other circumstances
which make it unsuitable for that purpose.

24. The vertical plane directed north and south, of which we
have spoken, if supposed to be extended upwards to the firmament,
will meet the visible hemisphere in a semicircle which, passing
through the zenith, as the point directly over the observer is
called, descends to the horizon at the north and south points.
This semicircle is called the MERIDIAN. It divides the visible
hemisphere into two equal parts, the eastern on the left of the
observer, and the western on his right. By the diurnal rotation
of the celestial sphere, all objects upon it rising in the east
ascend to the meridian, where they attain their greatest altitude',
and then descend to the west and disappear. The interval
during which each of them is visible is divided into two exactly
equal parts by the meridian, the time which elapses between tho
moment at which it rises and that at which it passes the meridian
and attains its greatest altitude, being equal to that which
elapses between the latter moment, and that at which it
disappears.

This movement of the heavens is more observable by night than
by day, because it is then shared by a vast number of objects,
having positions infinitely various upon the celestial vault.
Countless numbers are every moment rising or ascending towards
the meridian, passing it, or descending from it, or setting.
Although the objects upon the firmament by day are not leas
numerous, they are rendered invisible by the superior splendour
of the sun. They may nevertheless be seen even then with suffi-
ciently powerful telescopes, and they present exactly the same
apparent motion, being still carried round with the common
motion imparted by the celestial sphere.

25. The sun like the rest is carried round with the diurnal
motion, and its continuance above the horizon is divided into
equal parts by the meridian. Hence it appears that when its
centre is on the meridian, it is midday or noon, and at that
moment it has its greatest altitude.

This moment then being the epoch upon which the fundamental
unit of time is based, it becomes of great importance to com-
prehend the means which have been contrived for accurately
observing it. If the meridian were traced by a visible line upon
the heavens, the observation of the moment at which any celestial
object crosses it would be easy. But that not being the case, it
may be asked how the moment at which the sun's centre passes a
merely imaginary line, can be ascertained with the ext
precision necessary in this case.

26. Astronomers have accomplished this by a very simple
124

THE TRANSIT INSTRUMENT.

admirable contrivance. They have enabled observers to mark for
themselves the meridian upon the firmament with such distinct-
ness and precision, that the moment at which any celestial object
passes it can be ascertained to a small fraction of a second by
direct observation.

One of the forms of instrument most easily understood by which
'this is accomplished is shown in fig. 1 (p. 113). The passage of any
celestial object across the meridian being called a TRANSIT, in-
struments adapted to ascertain the moment such transits take
place are called TRANSIT INSTRUMENTS. The particular form
shown in fig. 1 is called a TRANSIT CIRCLE.

The instrument is mounted on two pillars, A c and B D, of solid
stone, erected on a foundation of masonry presenting all the con-
ditions necessary to guarantee the greatest firmness and solidity.
These pillars stand east and west, the space between them there-
fore,- looking north and south. A telescope E F is supported
upon an horizontal axis A B, the ends of which rest in angular-
shaped supports, called from their form Y's, which are established
upon the summits of the two stone pillars. These supports being
rendered by suitable adjustments truly horizontal, and the line
joining them being directed truly east and west, the telescope
when placed in an horizontal direction will point exactly north
and south, and if it be turned upon its axis, so as to be succes-
sively directed to different points of the firmament, it will sweep
over the celestial meridian.

Attached to the telescope is a graduated circle, consisting of two
flat rims of metal, connected together in a firm manner by a
system of spokes and diagonal braces. By means of this circle the
altitude of any object to which the telescope may be directed can
be measured ; but this not being connected with our present pur-
pose need not be further noticed. All that is now necessary to
be understood is that when it is turned upon its axis, the telescope
is successively directed to all points of the meridian.

When we look through the telescope, we behold a circular space
upon the heavens of a certain magnitude. This space is called

the FIELD OF VIEW.

The meridian is in the direction of a line which would pass
vertically through the centre of this circular space, dividing it
into two equal parts, one to the right, and the other to the left.
The celestial objects, as they are carried by the diurnal motion of
the sphere, pass from east to west across the meridian, moving in
a direction apparently horizontal. Such of them, therefore, as
may come within the limits of the field of view, in any one posi-
tion of the telescope, will appear to pass across the field in
horizontal lines ; and if the observer were provided with any means

125

COMMON THINGS — TIME.

ascertaining the moment at which an object is precisely J
way between the point at which it enters and that at which it
leaves the field of view, he would know the moment at which
it passed the meridian.

This is accomplished by a very simple and admirable con-
trivance. In the eye-piece of the telescope is fixed a small frame ,
across which are extended vertically five or seven fine wires or
filaments at equal distances apart, the centre one passing through
the middle of the field of view, and one horizontal wire also
passing through the centre, and therefore dividing all the vertical
wires equally.

The field of view and the system of wires are shown in fig. 2,
(p. 129), where E w is the horizontal, and IT s the middle vertical
wire. It must be observed that the wires are so extremely fine that
even when they are magnified by the eye-glass of the telescopo
they still appear like mere hairs. The number of vertical wires
being always odd, one of them will necessarily pass through the
centre. The instrument represented in fig. 1 is provided with
such adjustments, that the middle wire N s, can be brought to
coincide with the utmost precision with the meridian.

The magnifying power of the telescope has the same effect upon
the apparent motions of objects as upon their apparent magnitude.
It increases the one in the same proportion as the other. The
consequence is that, although the apparent diurnal motion of
celestial objects is no more perceptible to the naked eye than is
the motion of the hour-hand of a watch, yet when viewed with
the telescope, this motion is very distinctly perceptible. The
stars seem like so many luminous insects, creeping with a visible
motion across the field in horizontal directions, and passing in
succession behind each of the parallel vertical wires.

27. So rapid is this apparent motion of the celestial objects
across the field of the telescope, that a star is- seen to pass from
one side to the other of one of the vertical wires between two suc-
cessive beats of the clock. Thus it may be seen at o, fig. 2, at
the moment marked by one beat, and at o', at the moment marked
by the next. Practised observers are in such case able t>
determine to the tenth of a second, or even less, the instant of its
transit over the wire. Thus if the moment it is at o, be 10h 20m
20s, and that at which it is at o', be 10h 20m 21% the observer will
be able to say for example that the instant at which it has passed
the wire N s is more than 10h 20m 21s -4, and less than 10h 20m
218>5, and he may assign the time as 10h 20ra 21s-45. Different
observers acquire, according to their respective aptitudes, different
degrees of skill in such observations, and in all cases the results
of their observations can be checked by comparing those obtained
126

SIDEREAL DAY.

by two or more observers observing the same transit at the same
place.

28. If the transit of the same star be observed for two or more
successive nights, the interval which elapses between any two-
successive transits can thus be determined. Now it has been
found that this interval is absolutely the same, not only for all
stars whatever, but also that it is the same at whatever part of
the earth the observation may be made. By comparing the
results of ancient with modern observations, it has also been
found that this interval has not undergone the least change.

It is well known that this apparent diurnal rotation of the
heavens, by which a common motion is thus imparted to all
celestial objects, is the optical effect produced by the rotation of
the earth upon its axis, and the time of that rotation is conse-
quently the interval which elapses between two successive
meridional transits of any fixed star.

Such is the constant and invariable character of this motion r
and its absolute uniformity, that Laplace has shown, independently
of all theory, that, as a matter of fact, the time of this apparent
rotation of the heavens cannot have suffered any change amounting
to so much as the hundredth part of a second since the time of
Hipparchus, being an interval of twenty centuries.
This interval is called a SIDEREAL DAY.

The sidereal day is subdivided into hours, minutes, and seconds,
in the manner already explained.

The circumference of the celestial sphere being supposed to be
divided into 360°, through which it revolves in 24 hours, it
follows that it turns through 15° per hour, 15' per minute, and
15" per second.

It is perhaps to be regretted that the terms minutes and
seconds have been used in two different senses, the more especially,
as their application in both these senses is constantly necessary in
all astronomical works. As applied to the arcs of circles, or to
angular measurement, a MINUTE signifies the sixtieth part of a
degree, and a SECOND the sixtieth part of a minute. As applied
to time a MINUTE signifies the sixtieth part of an hour, and a
SECOND the sixtieth part of a minute.

The confusion which might arise in calculations in which
both time and angular measures are involved, is prevented by the
adoption of the letters m and s, to express minutes and seconds
of time, and the signs ' and " to express angular minutes and
seconds. Thus — 8h 30m 25-6"

expresses an interval of time consisting of 8 hours, 30 minutes,
25 seconds, and 6-tenths of a second ; while
8° 30' 25-6"

127

COMMON THINGS — TIME.

expresses an angle or circular arc, the magnitude of which is
8 degrees, 30 minutes, 25 seconds, and 6-tenths of a second.

29. The absolute uniformity and permanency which thus
characterise the diurnal rotation of the heavens, combined with
the fact that it is observable at all parts of the earth, would
render it eminently suitable as a measure of time. It wants,
nevertheless, one condition which is quite as essential for the
purposes of civil life as uniformity and permanence. It is not
marked and limited by any conspicuous phenomena which strike
the senses of all mankind. It does not correspond with the
periodical returns of light and darkness, nor with the successive
returns of the sun to the meridian. It does not even fall into
accordance with the conspicuous lunar phenomena; so that,
although it be true that it is observable alike in all parts of the
earth, the phenomena by which it is marked are such as can only
be observed with the aid of astronomical instruments, and such as
do not address themselves to mankind in general.

30. To obtain, therefore, a fit measure of time for civil purposes,
some measure must be found which will fall into such accordance
with the periodical vicissitudes of light and darkness and the
successive meridional transits of the sun, that the chronometric
unit may correspond either exactly, or nearly enough, for all
practical purposes with those diurnal appearances by which the
records of mankind have in all ages and countries been made.

And why, it may naturally enough be asked, may not the
successive returns of the sun to the meridian serve the purpose ?

It may be stated briefly but distinctly that the solar diurnal
phenomena, as they are actually presented in the heavens, do not
answer as a measure of time even for civil, to say nothing of
scientific purposes. Why they are unsuitable, and what sub-
stitute has been contrived for them, will require some words of
explanation.

128

COMMON THINGS.

TIME.

CHAPTEE II.

31. How to observe the sun's transits. — 32. Interval between them variable.
— 33. Mean and apparent time. — 34. Relative changes of mean
and apparent time. — 35. The days on which they coincide. —
36. The Equation of time. — 37. Further explained. — 38. Its
extreme error. — 39. Mean time adopted in France. — 40. Un-
iitness of apparent time. — 41. Local time varies with longi-
tude.— 42. Equalisation of local time proposed. — 43. How time-
pieces are regulated. — 44. Mean solar hours, minutes, and seconds. —
45. Length of sidereal day. — 46. The week. — 47. Opinions as to its
origin. — 48. Both opinions erroneous. — 49. Origin of the names of
the days. — 50. First day of the week. — 51. The month.

31. THE sun presenting to an observer not merely a brilliant
point, as is the case with a fixed star, but a circular luminous
space called a DISC, of considerable magnitude, the various parts
of which pass the meridian at different moments of time, it is
LARDNER'S MUSEUM OF SCIENCE. K 129

No. 58.

COMMON THINGS — TIME.

necessaiy to define what is meant by the meridional transit of th e
sun with more precision, and to show by what sort of observation
the moment of such transit can be ascertained.

It has been agreed, that by the meridional transit of the sun,
that of the centre of the solar disc is to be understood.' But as this
centre is not marked by any visible or observable point by which
it can be distinguished from other points of the sun's disc, its
transit cannot be directly observed.

The difficulty arising from this circumstance has been overcome
by a very simple expedient.

As the solar disc enters the field of view from the east side it
approaches gradually the meridional wire, N s, and at length
touches it, as shown in fig. 2, with its western edge, w, cr
LIMB, as it is called by astronomers. The moment of this contact
is observed in the manner already described in the case of
a star. The solar disc then continues to move across the field
until it takes the position indicated by the dotted circle, in.
which the eastern limb touches the meridional wire, K s. The
moment this takes place being also observed, the middle of the
interval is calculated, which is the instant at which the centre of
the disc passed the meridian.*

32. If the sun were stationary in the firmament, it is evident
that the interval between its successive meridional transits would
be the same as that of the successive transits of a fixed star, and
in that case the SIDEREAL DAY would be identical with the SOLAR
DAY. But it is well known that the sun is not thus fixed. On
the contrary, it moves constantly in the firmament, making a
complete circuit of the heavens in a year. If this motion were
uniform, the daily displacement of the sun would be 0° 59' 8-2".

Now let us consider what effect such a displacement, being
always eastward, would produce upon the interval between the
successive transits of the sun compared with that of the transits of
a star which suffers no such displacement.

Let s (fig. 3) represent the sun at the moment its centre is on the
meridian, :N s, on any given day, and let o represent a fixed star
which is on the meridian at the same instant. After the lapse of
24 sidereal hours the star, o, will be again upon the meridian, N s ;
but during these 24 hours the sun, s, will have moved towards ]•;,
that is, eastward to the position, s', the distance, s s', being

* In fig. 2 the motion of the celestial objects and their position is repre-
sented as they are seen by the naked eye, or by a terrestrial telescope.
But all objects are inverted and reversed by the astronomical telescope,
so that the top is seen at the bottom, and the east seen at the west, and
vice versa. It has been thought better for the present purpose to represent
the points and motions as they are naturally seen.
130

SUN?S TEANSITS.

0° 59' S'2". The sun, therefore, will not yet have come to the
meridian, and will not arrive at it until it is carried by the
diurnal motion of the firmament through this space Fig. 3.
of 0° 59' 8 "2". But since the firmament moves at N

the rate of 15' in each minute of time, it will take
3m 56s to carry the sun, s' to the meridian. It
follows, therefore, that, supposing the sun to move
daily 0° 59' 8-2" eastward at right angles to the
meridian, a solar day would exceed a sidereal day
by 3-" 56". E

If the eastward daily motion of the sun, measured
at right angles to the meridian, were uniform there-
fore, the interval between its successive transits
would possess all the requisites for a chronometric
unit, and although the solar day would not be
equal in length to the sidereal day, it would, nevertheless, be of
invariable length, and would besides be in complete accordance
with those periodical vicissitudes of light and darkness which
have been, by common consent, used by mankind in all countries
and in all ages as the measures of time.

But the solar day is wanting in fact in this essential condition ;
it is not invariable in length. Its variation, though not great, is
nevertheless such as to render it unsuitable as an unit of time,
even for civil, to say nothing of astronomical, uses. No clock or
watch could be constructed which would continue to go with the
sun. A clock, which at one time of year would correspond with
the meridional transits, would at another either anticipate them,
or fall behind them.

The variation in the rate at which the sun is displaced daily
towards the east, and at right angles to the meridian, arises from
several causes. First, the rate at which the sun moves upon the
firmament is subject to variation. While its average daily dis-
placement is, as we have stated, 0° 59' 8*2", it amounts at the
beginning of the year to 1° V 9'9", and at the middle of the year
to only 0° 5V 11-5". Although we are not directly concerned here
with the cause of this variation, it may be as well to observe, that
it arises from the fact that the earth does not revolve in an exact
circle with the sun in the centre, which it must have done if its
motion were uniform, but in an oval, the sun being nearer to one
end than to the other, and the rate of the motion increasing as the
distance of the sun decreases. Secondly, the motion of the sun is
not generally at right angles to the meridian, but more or less
oblique to it at different seasons, and the more oblique it is
to the meridian, the less does a given displacement affect its
eastward motion at right angles to the meridian. Thirdly, the

K2 131

COMMON THINGS — TIME.

sun is at different seasons at different distances from the celestial
equator, and the more remote it is from the equator the more
does a given displacement aifect its return to the meridian, for the
same reason exactly as that for which two places on the earth, at
a given distance east and west of each other, will have a greater
difference of longitude the farther they are from th£ line.

33. Seeing, then, that the interval between the successive
meridional transits of the sun is subject to variation, and therefore
unsuitable for a chronometric unit, but that it would be suitable
if the sun's daily easterly displacement were always the same,
astronomers have imagined an expedient, which, without sacrificing
the advantage of an accordance with the periodical vicissitudes of
light and darkness, secures the advantage of complete uniform: ty
as to the length of the chronometric unit.

This is accomplished by the substitution for the real of a
fictitious sun, whose daily easterly motion is always the same, and
exactly equal to the average daily easterly motion of the real sun,
that is, to 0° 59' 8'2". The time, as indicated by this fictitious
sun, is called MEAN TIME, the moment when its centre passes the
meridian is called MEAN NOON, and the fictitious sun itself is
sometimes called the MEAN SUN.

The variable and unavailable time indicated by the motion of
the real sun is called APPARENT TIME, and the moment of the
meridional transit of the real sun is called APPARENT NOON.

34. From what has been stated, it will therefore be understood
that the mean and the real suns make a complete circuit of the
heavens in exactly the same time, that is, in a year ; so that,
starting together from a given point, they will arrive together at
the same point at the instant which terminates the year ; but
while the easterly daily displacement of the one is always
absolutely the same, being 0° 59' 8-2", that of the other is
variable, being sometimes greater than 0° 59' 8 '2", sometimes less,
and at certain times the same.

To illustrate the changes of the relative position of the two suns,
let us imagine two railway trains to start from London at the same
moment, side by side, on two lines of rails, making a trip to
Liverpool and back, and to arrive at London, on their return,
precisely at the same moment ; but let the speed of one be
absolutely uniform, at 30 miles an hour, during the entire
journey, while that of the other is subject to variation, being
slower in ascending inclines, and faster in descending them. The
latter will at some places outstrip, and at others fall behind, the
former, and at certain points they will be for a 'moment side by
side. The variable train will represent the real, and the uniform
train the fictitious or mean SUE.
132

MEAN AND APPARENT TIME.

The two trains throughout their trip would, in such case, never
be found very far asunder. Neither will the two suns separate to
any great distance. If they did so, the expedient of the fictitious
sun as a measure of time for civil purposes would fail, inasmuch
as the civil day would fall into perceivable disaccord with the real
day.

35. The days of the year at which the true and fictitious suns
come together, and on which the mean and apparent time agree,
are subject to a very slight variation ; but in the year 1855, this
coincidence takes place on the 15th April, 15th June, 1st
September, and 24th December.

To trace the relative positions of the mean and real suns,
we are to consider that on the 15th April they are on the
meridian together, or very nearly so. The next day the mean
sun will have passed to the east of the real sun, so that the latter
will arrive at the meridian first, and when the mean sun
comes upon the meridian, that is, at the moment of mean noon,
the real sun will be to the west of it. Each succeeding day the
real sun will fall back more and more to the west of the
mean sun, and the apparent noon will precede the mean noon
by a constantly increasing interval. Thus, on the 16th April,
the apparent precedes the mean noon by 8s, on the 17th by
22-4% on the 18th by 36-4% on the 19th by 50s, and so on; this
gradual increase going on until the 15th May, on which day the
apparent precedes the mean noon by 3m 53-87% and the distance
of the true sun, west of the mean sun, is then 58' 28", a space
equal to nearly twice the apparent diameter of the sun.

After the 15th May the real sun falls less and less west of the
mean sun, so that the two suns approach each other closer and
closer until the 15th June, when they again coincide. Thus,
from the 15th April to the 15th June, the apparent time precedes
the mean time by a quantity which varies from 0 to 3ra 53 '87s,
and the distance of the real sun to the west of the mean sun
varies from 0° to 58' 28".

As the time shown by the mean sun is the time shown by a
properly regulated clock, it follows that during this interval the
sun passes the meridian before noon — a fact which is commonly
expressed by saying that the sun is FAST.

36. The interval of time between the meridional transits of the
real and fictitious suns, or what is the same, the interval between
the apparent noon and the mean or civil noon, or the noon shown
by a properly regulated clock, is called the EQUATION OF TIME.

37. Between the 15th April and the 15th June it appears,
therefore, from what has been explained, that the time of mean
noon can be deduced from that of apparent noon by subtracting

138

COMMON THINGS TIME.

from the latter tlie equation of time, and on the other hand, tl
time of apparent noon is deduced from that of mean noon by
adding to the latter the equation of time.

But to trace further the relative positions of the true and
mean suns. After the 15th June the real sun falls to the east
of the mean sun, and consequently does not come to the
meridian until after the mean sun has passed it, that is, until
after noon. On the 16th June the real sun passes the meridian
13-53" later than the mean sun ; on the 17th, 26-439 ; on the 18th,
39*42S ; on the 19th, 52-44s ; and so on, passing it each day later
and later in the afternoon, until the 26th July, when it passes the
meridian 6m 12-68" later. After that day it begins to pass the
meridian at earlier intervals after the mean sun, and the intervals
become less and less until the 1st September, when it coincides
with the mean sun.

On the 26th July the apparent noon being 6m 12 -68s later
than mean noon, the centre of the real sun must be 1° 33' 10-2"
east of the centre of the mean sun, which is a space equal to about
three times the apparent diameter of the sun.

Thus it appears, that from the 15th June to the 1st September,
the apparent time follows the mean or civil time, that is to say,
the sun passes the meridian at times varying from 0 to Oh 6m 12-68*
in the afternoon. This fact is usually stated by saying that the
sun is SLOW.

During this interval the apparent time is found by subtracting
the equation of time from the mean time, and the mean time by
adding it to the apparent time.

After the 1st September the real sun again passes to the west of
the mean sun, and consequently passes the meridian before it.

Thus, on the 2nd September, its meridional transit takes place at
19-688 before noon ; on the 3rd at 38'77S ; on the 4th at 58-11* ;
and so on, the transit being earlier and earlier until the 3rd
November, when it takes place at 16™ 18 -5 1s before noon, Avhich
is therefore the greatest amount of the equation of time, and the
greatest departure of the time of the sun from the time of tl
clock. The sun is in this case 16m 18-51* fast.

38. Since the firmament moves at the rate of fifteen minutes
arc for every minute of time, it follows that in 16m 18-51S before
the meridional transit of the sun, its departure from the meridian
must amount to 4° 4' 37 -65", a space equal to nearly eight times
the sun's apparent diameter.

From the 3rd November to the 25th December the distance of
the real sun west of the mean sun constantly decreases, and they
coincide on the 25th December.

It follows, therefore, that from 1st September to the 23th.
134

:

MEAN AND APPARENT TIME.

December, the sun is fast by an interval which varies from 0 to
16m 18'518.

After 25th December the real sun once more falls to the eastward
of the mean sun, and consequently it does not arrive at the
meridian until after the mean sun has passed it, that is until
some time after the mean noon. On the 26th December it passes
the meridian at 40 -45s ; on the 27th at lm 10- 15s ; on the 28th
at lm 39- 71s after noon, and so on, the lateness of its transit
increasing until the llth February, 1856, when it passes the
meridian at 14m 32*36S after noon. After this its transit is less
and less late until the 15th April, when it again coincides with
the mean sun.

It appears, therefore, that from the 25th December to the 15th
April the sun is always slow, its deviation from the time of the
clock being greatest on the llth February, when it amounts to
14m 32 '36s. The distance of the true sun from the mean corre-
sponding to this interval, computed as before, is 3° 38' 5 '4". On
the llth February, therefore, the true sun is at this distance east
of the mean sun. This distance is not quite seven times the
diameter of the sun's disc,

39. The real interval between two successive transits of the
sun being variable, it is evident that no piece of mechanism could
be constructed which, without adjustment, would point daily to
12 o'clock at the moment of apparent noon. So long, therefore,
as the mean time was not adopted as the chronometric measure
for civil purposes, it was necessary daily, or at least weekly, to
regulate all the clocks, public and private, according to the vary-
ing time of apparent noon. This was the practice even in a
country so enlightened as France until an epoch so recent as 1816.
Before this time the most remarkable disagreement constantly
prevailed among the public clocks of Paris, few of which were
regulated sufficiently often by observations of the sun. M. Arago
relates, that Delambre, the celebrated French astronomer, told
him that he frequently heard the public clocks, one after another,
striking the same hour during half an hour.

At the time of introducing the change in the regulation of the
clocks of Paris from apparent to mean time, the prefect of the
Seine (which is the title of the chief of the municipality, or mayor
of Paris,) entertained such serious fears that an insurrectional
movement might be excited among the working classes, who, it
was supposed, would revolt against a noon which did not corres-
pond with the noon of the sun, or mid-day, and which conse-
quently would divide the day, from sunrise to sunset, into two
unequal parts, that he refused to sign the ordonnance for the
change unless it was accompanied by a formal report of the Board

135

COMMON THINGS — TIME.

of Longitude to sanction it. These apprehensions, however, proved
groundless, for the change took place unperceived by the great
mass of the people.

Meanwhile the watch and clockmakers rejoiced at the change
which established a sort of civil time, in accordance with which
it was mechanically possible to construct timepieces. Such a
change relieved them from the annoyance produced by the remon-
strances of their customers complaining of their best constructed
watches losing or gaining as much as a quarter of an hour, or
even more, upon the sun. It was in vain that the celebrated
Breguet, and his colleagues of the trade, assured them that the
sun and not the watch was too fast or too slow.

40. It may be easily imagined how utterly incompatible with the
management of public business as now conducted such an imperfect
system of chronometric regulation would be, when it is considered
what disastrous consequences might arise upon railways, if the
starting, stopping, and arrival of trains, were not subject to greater
precision than could be attained under such circumstances.

41. However exactly the chronometric measures in a given
place may be regulated, their indications will necessarily differ
from those of similar chronometric measures in other places
having different longitudes. The cause of this difference is
the successive arrival of the mean sun at the several meridians
of such places. By the apparent diurnal motion of the heavens,
the sun, earned round the globe, arrives in succession, from hour
to hour, at the meridians of places situate one westward of the
other, and as the sun thus carried round makes a complete revolu-
tion in 24 hours, it moves from meridian to meridian at the rate
of 360° in 24 hours, or 15° per hour, or 1° in four minutes. Thus,
at two places differing in their longitude by 1°, the local time will
differ by four minutes, that which is east being four minutes
earlier than that which is west.

In consequence of this the clocks in different towns of the
United Kingdom show at the same moment of absolute time
different hours. Liverpool, for example, being 3° west of London,
and 1° being equivalent to four minutes, it follows that the sun
passes the meridian of London twelve minutes before it passes
that of Liverpool ; and as this is equally true of the fictitious sun
which regulates civil time, it follows that mean noon at London,
and therefore all other hours determined with relation to mean
noon, precede the corresponding hours at Liverpool by twelv
minutes.

42. It has been lately proposed to assimilate the chronome
epochs at all parts of the United Kingdom, by means of cloc
which are moved with a common motion, so that their han

136

CIVIL TIME.

however distant they may be one from another, must always
point at the same moment to the same honr. Such a common
motion may be imparted to them by means of an electric current
transmitted along conducting wires, similar to those iised for the
electric telegraph. In this way all clocks in all parts of the king-
dom could be made to indicate the Greenwich time.

If this measure should be adopted the civil time will have
undergone another change, and instead of being the mean time
proper to the place, it will be the mean time at Greenwich.
Thus the civil time at Liverpool, for example, would differ from
the mean time there by twelve minutes. And as the mean time
at certain epochs already differs from the apparent time by more
than a quarter of an hour, it will sometimes happen that the civil
time will differ from the apparent time by nearly half an hour.
Thus the sun may be on the meridian of Liverpool, and conse-
quently the real mid-day may take place at about half-past
eleven o'clock.

Such a circumstance, however contradictory and anomalous it
may appear when considered astronomically, would, however, be
attended with no inconvenience in civil life.

43. The length of a mean solar or civil day, and the method of
denning the moment of its commencement, being well understood,
it remains to show how the motion of a timepiece is regulated so
as to represent it.

Let us suppose a clock, the pendulum of which is intended to
beat seconds, to be roughly regulated, so that its hour-hand shall
make two complete revolutions in a day. This approximation to
an exact movement may be easily accomplished by many obvious
expedients, one of which would be to set it to twelve o'clock when
the sun appears to have attained its greatest altitude.

The clock, thus approximately regulated, being placed near a
transit instrument, such as that already described (26), let the
observer, as the sun approaches the meridian, direct the telescope
to the point of the meridian over which it is about to pass. When
the disc of the sun enters the field of view, and is approaching the
wire, N s, fig. 2, let the observer look at the clock, and observe
the exact time, and let him count the time from that moment by
his ear as he listens to the successive beats of the clock. Con-
tinuing thus to count, he will find that the western edge of the
sun's disc will touch the wire N s at a certain moment between
two successive beats, and by practice he will be able to assign the
moment of contact between the beats. As the disc of the sun takes
about two minutes to pass across the wire, he will have sufficient
time to write down the exact time of the transit of the western
edge and to return to the telescope before the eastern edge comes

137

COMMON THINGS — TIME.

near the wire. Again observing the time shown by the clock,
again counting the beats he observes, in like manner, the moment
at which the eastern edge touches the wire.

Now let us suppose the times of contact to be as follows : —

Contact of Western limb
Contact of Eastern limb

Transit of sun's centre

H.
12
12

M.

10

11

24 22

12 11

As has been already explained, the time of the transit of the
-centre of the sun's disc is found by adding together the times of
the transits of the eastern and western limbs, and dividing the
sum by two.

It would then appear from this that the time shown by the
•clock at the moment of apparent noon is eleven minutes and three
seconds, and nine-tenths of a second after twelve.

Let us suppose that the observer then refers to the table of the
equation of time for the day of the observation, and finds there
that the moment of mean noon was 3ra 32^ earlier than the
apparent noon. To find the time of mean noon, therefore, as
shown by the clock, he performs the following arithmetical
operation : —

From apparent noon .
Subtract the equation of time

H. M.

12 11
3

12

From which it appears that the clock is 7m Sl^5 fast.

Leaving the clock unaltered, the same observations and calcu-
lations are made the following or any succeeding day, and if the
clock gives a later hour than 12h 7m 31^8 for mean noon, its rate
is too fast, or it "gains." If it gives an earlier hour, its rate
is too slow, or it " loses." Let us suppose, for example, that after
the lapse of five days the clock gives 12h 8m 25^s for mean noon,
we shall have

Mean noon — sixth day
,, first day .

Clock gains in five days

H. M.
12 8
12 7

0 0 53/5

The clock therefore gains at the rate of 10-^ seconds per day.
The method of correcting the rate is by lengthening the
138

MEAN NOON.

pendulum, as will be explained in a future number of the
MUSEUM.

44. When the pendulum has been exactly regulated, it will
swing 86400 times between the moments of mean noon on two
successive days. The time of 60 swings will be a mean solar
minute, and the time of 3600 will be a mean solar hour. The
olock thus regulated, being set to 12 at the moment of mean
noon, will again point to 12 at mean midnight, and again at
the succeeding mean noon, and so on.

45. From what has been explained, it will be understood that a
sidereal day, or the time of the rotation of the earth upon its axis,
is somewhat shorter than a common civil day. The exact propor-
tion between these chronometric units, which is by no means an
easy problem, has, however, been solved by astronomers, and it
is found that 100,000000 common or civil days are equal to
100,273791 sidereal days, or, if less extreme arithmetical precision
be sufficient, it may be stated that in a thousand common days
the earth makes 1002| rotations on its axis.

From these numbers it is easy to express the time of rotation
in hours, minutes, and seconds of civil time. To do this we have
the proportion

100,273791 : 100,000000 : : 24 : the time of rotation.

By the rule of three, therefore, the time of rotation will be

hours.

2400,000000 _
T007273W '

It appears, therefore, that the time of the earth's rotation falls
short of 24 hours, such as those shown by well regulated clocks,
by three minutes, fifty-five seconds, and ninety-one hundredths
of a second.

IV. — THE WEEK.

46. Having thus explained fully the meaning of a day, con-
sidered as the standard unit of time, and of the subordinate and
lesser divisions of hours, minutes, and seconds, it will now be
necessary to notice the larger chronometric units.

The chronometric unit, in the ascending order, which comes
next to the day, is the WEEK.*

47. The opinions of historians and antiquarians are much
divided as to the date and prevalence of the custom of counting
time by periods of seven days. It is certain, however, that among
the oriental nations such a period has been in use from time
immemorial. Philo Juda3us, Josephus, and St. Clement of

* From the Saxon word WEOC, having the same signification.

139

COMMON THINGS — TIME.

Lexandria, maintained that the period of a week was in us
among all ancient peoples. Goguet, a modern French authorit
adopts the same opinion. Others, on the contrary, among whom
may be mentioned Costard and Maiiry,* contend that no ancient
use of the period of seven days prevailed except among the Jews,
who took it of course from the traditions of the creation, given in
the Pentateuch.

48. Both these extreme opinions, but especially the latter, are
erroneous. The week, as a division of time and multiple of a day,
was in general use among the ancient Chinese, the Egyptians,
the Chaldeans, and the Arabs, as well as among the Jews. It
was not in the calendar of the Greeks, who divided the month
into three periods of ten days, and it was not adopted by the
Romans until the time of Theodosius, who reigned in the latter
part of the fourth century of our era. There is properly no word
in the Latin classics equivalent to the term WEEK. Jfebdomas
signified seven of anything, and when applied to days had
reference to diseases, in which the physicians held (as now
appears erroneously) that crises were manifested of which the
periods were 7, 14, and 21 days.

"While most authorities trace the use of weeks to the Mosaic
account of the creation, others ascribe it to the phases of the
moon, and others again to the planets as known to the ancients.
The lunar phases not being even nearly commensurate with the
week, they can scarcely be regarded as the origin of this chrono-
metric unit, and the denomination of the days having in all
languages more or less reference to the celestial objects, the latter
opinion seems to be most generally entertained.

49. In the ancient Egyptian astronomy, the sun and moon being
included among the planets, and of the bodies properly called
planets, five only being known, Mercury, Yenus, Mars, Jupiter,
and Saturn, the total number of planets was taken to be seven.
They were ranked in the order of their supposed distances from
the earth as follows : —

1. SATURN

2. JUPITER,

3. MARS

4. THE SUN

5. VENUS

6. MERCURY

7. THE Moux.

ia jrum

Dion Cassius, an eminent historical writer of Home, who was
consul about 220 A.D., gives the following explanation of
manner in which the Egyptians derived the names of the days
the week, and their order, from those of the seven planets.

* See dissertation Ly M. Biot upon the astronomical chronology. — Mt
Acacl. Sc. tome xxii.
140

THE WEEK.

The series of HOURS without reference to days were resolved
into periods of seven, each dedicated to a planet. Thus the first
hour was dedicated to SATURN", the next to JUPITER, the third to
MARS, and so on. The day, however, being divided into twenty-
four hours, which is not a multiple of seven, it followed necessarily
that each successive day would begin with an hour dedicated to a
different planet. Let us see then how the days would, according
to such a system, succeed each other.

The day which begins with the hour dedicated to Saturn would
evidently end with the hour dedicated to Mars, for the twenty-
four hours would consist of three complete periods of seven, and
the twenty-fourth hour would be the third of the fourth period and
would consequently be the hour dedicated to Mars. The first hour
of the next day would be that dedicated to the Sun. In like
manner this day beginning with the hour dedicated to the Sun,,
and consisting of three hours more than three complete periods,
would end with the hour dedicated to Mercury, and the next day
would begin with the hour dedicated to the Moon.

The succeeding day would in like manner commence with the
third in order from the Moon, that is, Mars ; the next with the
third in order from Mars, that is Mercury ; the next with the
third in order from Mercury, that is Jupiter ; the next with the
third in order from Jupiter, that is Venus ; and after Venus the
series would recommence with the hour dedicated to Saturn.

Thus in each successive period of seven days, the first hour of
each successive day of the period would be dedicated to the
planets in the following order : —

1. SATURN

2. THE SUN

3. THE MOON

5. MERCURY

6. JUPITER

7. VENUS.

4. MARS

The Latin names of the days are in accordance with this,

1. DIES SATURNI (Satiirn's day)

2. DIES SOLIS (Sun's day)

3. DIES LUNAB (Moon's day)

4. DIES MARTIS (Mars' day)

5. DIES MERCURII (Mercury's day)

6. DIES Jovis (Jupiter's day)

7. DIES VENERIS (Venus' day).

These names are retained in the English language for SATUR-
DAY, SUNDAY, MONDAY. The names for the days dedicated to
Mars, Mercury, Jupiter, and Venus have been taken from Saxon
divinities.

141

COMMON THINGS — TIME.

The days of Mars, Jupiter, and Venus have been called TUES-
DAY, THURSDAY, and FRIDAY, from TUESCO, THOE, and FRIGGA,
the Mars, Jupiter, and Yenus of the Scandinavian mythology. The
day of Mercury has been called WEDNESDAY, from WODIIT or
ODIIT, the chief of the gods.

In all legislative and judiciary acts and documents, the Latin
names of the days of the week are still retained.

Derivations of the Latin names, with one or two exceptions,
are used in the languages of "Western Europe. SUNDAY is an
exception, the name of which is a derivative of DIES DOMINICA,
the LOED'S-DAY, and SATURDAY, in Italian, is SABBATO, the
SABBATH, that day being the Jewish Sabbath.

There is another method of connecting the series of days of the
week with the seven celestial objects from which their names have
.been taken, so as to explain the order in which they succeed each
other, which if it be only from respect to its antiquity may be
worth mentioning here.

The ancient astrologers, among whom were included a large
number of astronomers, properly so called, imagined a mystical
figure, in the centre of which the earth was placed, surrounded by
the seven celestial bodies dividing the circular space as shown in
fig. 4, into seven equal arcs. From each planet's place two straight
lines were supposed to be drawn to the places of the two most
remote planets in the circular order, so as to form seven triangles,
each of which has two rectilinear sides and an arc of the circle as
its base. The planets succeed each other round this circle in the
order of their then supposed distances, in the same manner as
already explained. Thus Saturn is succeeded by Jupiter, which
is followed by Mars, and so on as in the former case.

Now let us suppose that commencing from any one planet, the
moon for example, we follow in regular succession the intersecting
straight lines, we shall find that the planets succeed each other in
the same order as that of the days of the week, or in the contrary
order. Thus proceeding from A, we pass to B, from B to c, and so
on, following the course indicated by the arrows, and the names of
the planets at A, B, c, D, E, F, and G are precisely those from which
the names of the days of the week, beginning from Monday and
ending with Sunday, are taken. If we had followed the other
course against the direction of the arrows, we should have obtained
the names in a contrary order, as if we went backwards through
the week.

In the cabalistic doctrines of astrology there were various
influences imputed to the succession of planets thus obtained, with
which we have however here no concern.

In both systems the number seven which forms the basis of the
142

NAMES OF WEEK-DAYS.

chronometric period of a week had its origin in the supposed
number of the planetary bodies. This number seven was in other
respects regarded by the ancients as being invested with various
mystical influences, and as being reproduced in forms infinitely
various, not only in the natural objects and phenomena, but even
in human events. There were the seven stars, the seven cardinal
sins, the seven wonders of the world, the seven critical days in
human maladies, the thrice seven years which converted a youth
into a man, and so on. In short the number seven was regarded
with a sort of religious veneration, so that the announcement of
an eighth or ninth planet in Egypt, Greece, or Home would, as
Arago wittily observed, have been regarded as such a heresy as to
bring upon the unhappy discoverer the maledictions of the priests-
and even the punishment of death instead of the honours and
rewards of academies and universities.

50. The week being an arbitrary and conventional chronometric
period, having no relation to any natural phenomenon, the day
which begins it is equally so. In the Hebrew Scriptures its origin
being connected with the narrative of the creation, and the institu-
tion of the Sabbath being a perpetual commemoration of the
succession of divine acts by which the present state of the earth
and the creatures which inhabit it were called into being, the
seventh, or last day of the week, would naturally be that upon
which the Sabbath is celebrated, and according to this principle
Sunday would be the last and Monday the first day of the week.
Such, however, has not been the conventional arrangement. The
Sabbath, or seventh-day of the Jews, was the morrow of the Cruci-
fixion, and was Saturday ; the succeeding day being that of the
Resurrection, was consequently the first day of the Jewish week.

Among Christians, this first day has accordingly been celebrated
as Sunday, or the day of rest and prayer, the Jews still of course
observing Saturday as their Sabbath.

It has therefore been generally agreed to call Sunday the first
day of the week, but to invest it with those sacred attributes and
characters which in the fourth commandmenf were conferred upon
the seventh day.

V.— THE MONTH.

51. The next chronometric Unit is the month, a name which
implies some correspondence with lunar phenomena. The relation
of this division of time to the moon is apparent in all languages.
Thus, while in Greek wv (men) is month, id\vr\ (mene) is moon,
both being derived from the Sanscrit Ml, measure, the Persian
M!H signifying also month.

143

COMMON THINGS — TIME.

The sun and moon move round the celestial sphere in the same
direction from west to east, but the moon moves more than thirteen
times faster than the sun, and consequently makes more than
thirteen revolutions of the heavens while the sun makes one.
The moon is therefore constantly either departing from or
approaching to and overtaking the sun. At the moment it over-
takes the sun it is said to be in CONJUNCTION, and is called NEW
MOON. At the moment it is in the opposite part of the heavens,
and when therefore it is 180° removed from the sun, it is in
opposition ; and as it then presents its enlightened hemisphere
directly towards the earth, it appears with a complete circular
disc, and is called FULL MOON. "VVhen it is a quarter of the
heavens, or 90°, before or behind the sun, it is said to be in the
QUARTERS, and appears as an enlightened semicircle, and is call
HALF MOON.

The time which the moon takes to make one complete revolution
of the heavens, is called the moon's "period," or "periodic
time," and is found by the most exact modern observations to be

27-32166 days

expressed in decimals. If expressed in hours, minutes,
seconds it is

97d 7h 43m HAS
. 10 •

The moon's period is unsuitable for a measure of civil time for

two reasons : first and chiefly because the moment which terminates
one period and begins the next, is not marked by any conspicuous
and generally observable phenomenon, and can only be ascertained
by astronomers ; and secondly, because it is incommensurable with
the fundamental chronometric standard, the day, and as will
hereafter appear, equally so with the year. For these reasons it
has never been adopted as a chronometric unit either for civil or
astronomical purposes^

144

Fig. 4.

COMMON THINGS.

TIME.

CHAPTER III.

The month (continued). — 52. Not conformable with lunar periods. — 53.
Difficulty of subdividing the year. — 54. Division unequal. — 55. Egyp-
tian months. — 56. Greek. — 57. Solon's months. — 58. Roman months.
— Romulus. — 59. Origin of names of months. — 60. Additional months
of Numa.— 61. Origin of their names. — 62. Their lengths. — 63.
Superstition in favour of odd numbers — methods of remembering the
lengths of the months. — 64. Calends. — 65. Greek Calends. — 66.
Nones. — 67. Ides. — 68. Practice of counting backwards. — 69. Dis-
cordance of the Roman year with the seasons. — 70. Month Mercedo-
nius. — 71. Legal meaning of "month." — 72. The year. — 73. What
is a year ? — 74. Egyptian. — 75. Only a rude approximation to the
course of the seasons. — 76. The vague year and Sothic period. — 77.
Advantage of Egyptian year. — 78. Greek year. — 79. Meton and his
cycle. — 80. Origin of Golden Number. — 81. Meton ridiculed by Aris-
tophanes.— 82. Near accordance of the lunar phases with the Metonic
cycle. — 83. Roman year. — 84. Pontifical abuses. — 85. Julian Calendar.
— 86. Bissextile years.
LARDNER'S MUSEUM OP SCIENCE. L 145

No. 62.

COMMON THINGS — TIME.

THE interval between two successive conjunctions of the moon
with the sun, or between two successive new moons, is greater
than the moon's period. If we suppose the sun and moon to start
together from conjunction, the moon moving more than thirteen
times faster, immediately goes before the sun; and- as the sun
moves at the rate of about 1° per day, the moon must move at the
rate of more than 13° per day, and consequently departs from the
sun at the rate of more than 12° per day. When the moon has
made a complete revolution, that is at the end of 27*32166 days
from conjunction, the sun will have advanced about 27° from the
place at which the moon arrives after having completed its revo-
lution. The next conjunction or new moon cannot take place
therefore until the moon overtakes the sun, and as it advances upon
the sun at the rate of a little more than 12° per day, it will tako
somewhat more than two days to come up with it. In fine, by
the most exact observations and calculations, it has been found
that the interval between two successive conjunctions is

29-530589 days
expressed decimally, or in hours, minutes, and seconds

29d 12h 44m 2-89s.

This interval is called a LUNATION, and it exceeds 29| days, as it
appears, by a little less than three quarters of an hour.

Although the lunation is not commensurable with either ths
day or the year, yet its recurrence, and even its fractional parts,
are marked by phenomena so striking and so universally observable
without instruments, that in all ages and all countries it has by
common consent been used to measure time, the fractional parts
by which it exceeds 29 and falls short of 30 days, being com-
pensated by various expedients.

The evident object to which the adoption of months was directed
was to establish a convenient chronometric unit, holding an inter-
mediate place between the week and the year ; such unit to consist
of a complete number of days without a fraction, and to be at the
same time an exact submultiple of the year ; that is, such an
interval that the year should be an exact multiple of it, and finally
that it should be in as near accordance as might be found prac-
ticable with the period of the lunar changes.

That various nations in different ages should be found incomplete
disaccord in their attempts at the satisfaction of these several con-
ditions, and that the usages and chronological forms into which
these attempts resolved themselves should exhibit much confusion,
will not be at all surprising when it is considered that the condi-
tions themselves are not only incompatible one with another, but
their satisfaction utterly impracticable.

These conditions involve the consideration of three distinct
14G

THE MONTHS.

chronometric periods, the diurnal, the lunar, and the solar or
annual. The lunar period, whatever be the phenomena on which
it is based, whether it be the actual time of the revolution of the
moon round the earth, or the interval between its phases, that is
between full moon and full moon, is neither a multiple of the day
nor a submultiple of the year. A month therefore, determined by
the lunar period in whatever way it be considered, could not
consist of an exact number of days, nor be so taken that the
year should consist of an exact number of months.

52. All real conformity therefore between the chronometric
periods derived from the sun and moon must very soon have been
found to be unattainable, and the problem was therefore limited
to the establishment of a convenient subdivision of the year,
holding a place between the day and the year, dividing the year
into an exact number of equal parts, which should be neither too
great nor too small for social convenience.

53. Now let us consider how far these several conditions were
attainable.

A year, as will presently appear, consists of 365 days and a
fraction. In its chronological effects this fraction is attended
with many inconveniences of its own, but we shall for the present
disembarrass ourselves of it and consider the year as the ancients
did, to consist of the round number of 365 days.

This number is somewhat unmanageable when the object is to
resolve it into equal parts, each of which, shall be a whole
number. It is divisible without a remainder by 5 and by 73, but
by no other whole number.

It follows from this that the year admits of only two subdivisions
fulfilling the prescribed conditions. It may be divided into 73
intervals of 5 days, or into 5 intervals of 73 days,

The former subdivision being less than a week, would be obvi-
ously inadmissible. By the latter the year would consist of 5
equal divisions of 73 days.

Would such a division fulfil the conditions ? Would it be too
great for social convenience ?

The most conclusive practical answer to this question may be
derived from the concurrent testimony of all nations sufficiently
advanced to know that the year consists of 365 days. It must
have been evident that a division into 5 equal periods of 73 days
could be made. Nevertheless no such division of the year was
ever proposed. By this common consent therefore such a subdivi-
sion has been tacitly but unequivocally pronounced to be unsuitable
to the purposes of mankind.

54. Seeing then that no division of the year into equal periods
was practicable, two expedients only were presented ; jfirst, to

L 2 147

COMMON THINGS — TIME.

divide the year into a certain number of equal parts, with a
remainder, and to count that remainder as a supplemental part,
just as in arithmetic, when the dividend is not exactly divisible
by the divisor, we give the quotient, and name the remainder ; or,
secondly, to resolve the year into some convenient number of
unequal parts, which would be effected by distributing the days
composing the remainder between the equal divisions obtained by
the former expedient.

Both of these expedients have accordingly been adopted by
different nations in different ages, but the latter has eventually
received the general preference, and the year is now, by all the
more civilised nations of the world, divided into twelve unequal
parts, called, somewhat inappropriately, MOXTHS.

55. The Egyptians, adopting the first of the expedients above
stated, divided the year into twelve equal months of thirty days.
The remaining five days formed a complementary division at the
end of the year, and were intercalated before the commencement
of the next year.

56. The division of the year into months by the Greeks was not
only incongruous and obscure, but no two states of the confedera-
tion agreed either in the number, or the lengths, or the names of
their months, nor even in the beginning of their year. Generally,
however, all agreed in resolving the year into twelve months of
unequal lengths. Some states commenced the year at the summer
solstice, some at the winter solstice, and some at or near the
autumnal equinox. A dozen or more separate states called the
months by different names. Some months were designated by
specific names, while others were indicated only by their nume-
rical order, counting from the beginning of the year ; but as the
states did not begin their years from a common epoch, months
having the same numerical designation in different states corre-
sponded to different seasons. Thus, the fifth Attic month
corresponded with November, the fifth Lacedemonian with
February, the fifth Boeotian with May, the fifth Delphic witli
January, and so on. The enormous confusion which must arise
from such discordance between different provinces of a nation,
having the same language, and the numerous and perplexing
difficulties of interpretation of Greek authors, writing according
to such different customs, can be easily imagined.

"We forbear to encumber our pages with the eleven series of
names of these months, which, being all obsolete, would have no
other utility than to aid the interpretation of the Greek authors.
Those who desire such information, will find sufficient for their
purpose in the " Dictionary of Greek and Roman Antiquities" of
Dr. Smith, Art. Calendarium.
148

THE MONTHS.

57. Notwithstanding the discordancy and obscurity which sur-
round the records and usages of the Greeks, in relation to their
calendar, their knowledge of the period of the lu*nar phases which
served as the basis of their chronometric system, attained at an
early epoch of their history extraordinary precision. The lunation
was estimated at 29| days, which is within three quarters of an
hour of its exact length, and it was assumed as their month.
Solon went even so far as to make the month exactly conformable
to it. The thirtieth day was divided between two successive
months ; the first half, from sunrise to sunset, being given to the
expiring month, and the other from sunset to sunrise to the
new month. The day thus shared between two different months
was called eVij ttal vea, the old and new day. This correction,
however, was only applied to every other month, the intermediate
months being limited to twenty-nine days.

At a later period, when this had fallen into disuse, the
same name, *vt\ /col yea, was applied to the last day of the month
generally.

58. If any evidence were sought to illustrate the difficulty
which has attended the attainment of a degree of perfection in
{he art of counting and recording time, it would be found in a
review of the state of that art among the Greeks and Romans, the
two most enlightened and civilised nations of antiquity, to whose
labours in literature and the sciences the moderns are so largely
indebted.

Nothing that can be imagined can exceed the confusion and
absurdity which prevailed in the Roman chronometric conventions
before a very late period in the progress of the empire.

Romulus, the founder of Rome, established a year, consisting of
ten months, six of which had thirty, and four thirty-one days,
making the year 304 days.

Since the names given to these months have, for the most part,
come down to modern times, and have been adopted in our own
nomenclature, it will be useful here to state them, and notice their
origin.

The first four months of the year of Romulus were called,
MAES, APRILIS, MAIA, and Julius, from whence our names
MARCH, APRIL, MAY, and JUNE.

59. The first took its name from Mars, the father of Romulus,
according to the Roman fable.

The origin of the second is somewhat uncertain, some deriving
it from the Latin word aperire, to open, allusive to the state of
vegetation in spring ; and others from Aphrodite, one of the Greek
names of Yenus.

The names of May and June were taken obviously enough

149

[ON THINGS — TB:

from Mai'a, the mother of Mercury, and Juno, the queen ol
gods.*

The names of the other six months, expressing merely their
numerical order, were —

Quintilis (the fifth)
Sextilis (the sixth)
September (the seventh)

October (the eighth)
November (the ninth)
December (the tenth).

60. A year of 304 days could not long endure, since it would be
soon thrown into discordance with the nature of things. It was,
accordingly, no later than the succeeding reign, that of Numa,
that two months were added to the year. These were called
JANUARY and FEBRUARY.

In the first instance, February stood before January, the formei
being put at the end, and the latter at the beginning of the year.
This order was, however, subsequently reversed, and January
remaining the first month of the year, February became the
second, March being the third, and so on. This will explain,
a circumstance, which often excites inquiries in relation to the
last four months of the year, which appear to hold an order in the
series of months different from that indicated by their names. It
must be remembered, that when they received their names March
was the first month.

61. JANUARY, the first month of the year, took its name from.
JANUS, a divinity who held an important place in the Roman
religion. Janus presided over the beginning of every thing ; he
was the guardian deity of gates, and was represented with two
faces looking to opposite sides. He was on this account selected
to preside over the first month.

FEBRUARY took its name from FEBRUUS, an ancient Italian
divinity, whose rites were celebrated during the latter part of that
month. This divinity also presided over the dead, whose festival,
called FERALIA, was celebrated about the same time.

At a later period, the names of the months Q.UINTILIS and
SEXTILIS were changed to those of JULIUS and AUGUSTUS, to
commemorate these Emperors, the former of whom, as we shall
see, was signalised by a most important reform of the methods of
recording time. These names are continued by us for the months
of July and August.

Such was the origin of the present names of the twelve months
of the year.

* Ovid gives a different derivation of the names of May and Jum
namely, that they are the months of the old (majores) and young (juvei

" Tertius a senibus, juvenum de nomine quartus."

Fasti, Book I. line 41.
150

THE MONTHS.

62. Unequal as were the lengths of the months instituted by
Romulus, still greater inequality, irregularity, and confusion,
were introduced by his successors. In the Romulian year of
ten months, the months of March, May, Quintilis (afterwards
July), and October, had each thirty-one days, all the others
having thirty. When it was decided to render the year more
conformable to the solar phenomena, by increasing its length,
it was resolved to add fifty-one days to it; but this being
considered too much for one month, and too little for two, one
day was taken for each of the six months having thirty days ;
and the fifty- seven days thus obtained were divided into two
months, twenty-nine being given to January, and twenty-eight
to February.
The months then stood as follows : —

January .
February .
March .
April

May if,.-'
June.

Days.
29
28
31
29
31
29

July (then Quintilis)
August (then Sextilis)
September.
October .
November .
December

Days.
31
29
29
31
29
29

The practice of such arithmetical caprices in dealing with
matters upon which all chronological and historical records must
more or less depend, would seem inexplicable if tradition had not
supplied a clue to it. Why, for example, take a day from each
of the months of thirty, instead of the obvious expedient of taking
the odd day from each of those having thirty-one days ?

63. It appears that in these times odd numbers were regarded
as lucky or auspicious, even ones unlucky or inauspicious. A
point was therefore made to create divisions of time, consisting,
as far as possible, of odd numbers of days ! Months of twenty-nine
and thirty-one days were, therefore, preferable to months of thirty
days. Fifty-one days being added to 304, gave a year of 355
days, which, being an odd number, answered very well. But it
was impossible to divide an odd number into twelve parts, all of
which are odd, since twelve odd numbers added together would
make an even number. One of the twelve months was doomed,
by the very nature of things, and the laws of number, to consist
of an even number of days. This unlucky number was, therefore,
as a matter of course, assigned to February, over which the Genius
of Death presided, and which was appropriated to the celebration
of the Festival of the Dead. Hence it arose that February has
the exceptional number of twenty-eight days.

Before we hastily visit with harsh censure this most absurd
superstition, let us pause, and look at home, and see if we be

151

COMMON THINGS — TIME.

ourselves totally exempt from ideas altogether as absurd, it not
quite as mischievous. Who has not met with persons professing
some claims to education and intellectual position, who object to a
dinner party composed of thirteen, and to an odd, number of
candles being lighted on certain occasions? How many who
would consider themselves insulted if they were charged with
ignorance, object to start upon a journey, or to commence any
serious enterprise on a Friday ?

The difficulty of recollecting which months have thirty-one and
which only thirty days, has been so generally acknowledged, that
various technical aids to the memory have been contrived by which
they may be at any moment ascertained.

If the months be reckoned in numerical order from tht;
beginning of the year, the odd months, as far as the seventh, and
the even ones afterwards, are those which have thirty-one days.
Thus, they are the first, third, fifth, seventh, eighth, tenth, and.
twelfth, which are January, March, May, July, August, October,
and December.

When we close the hand there are four projecting knuckles of
the four fingers, with depressions between them. If we give the
knuckles and intermediate depressions the names of the successive
months, recommencing from the first knuckle, after having once
gone over them, we shall find that the months of thirty-one days
are those which fall upon the knuckles. Thus, the knuckle of the
first finger is January, that of the second March, that of the third
May, and that of the fourth July. Recommencing then, that of
the first is August, that of the second October, and that of the
third December.

Every one is familiar with the lines —

" Thirty days hath November,
April, June, and September ;
February hath twenty-eight alone,
And all the rest have thirty-one."

64. The first clay of a month was called by the Romans CALENDS,
a name which was also applied to the months themselves. Hence
it came that a table, showing for the current year the succession
of months, and of the days in each month, came to be called a
CALENDAR.

65. The name Calends was not used by the Greeks. Hence
arose a saying when any thing was indefinitely adjourned, that it
was postponed to the " Greek Calends."

66. The seventh days of the four great months, as those con-
sisting of thirty-one days were denominated, and the fifth days
of all the lesser months, consisting of twenty-nine days, were called
NOXES.

THE YEAR.

67. In like manner, the fifteenth days of all the great months,
and the thirteenth of all the lesser months were called IDES.

68. The cause of this difference of position of the ides and nones
in the greater and lesser months is to be found in the Roman
custom of counting time backwards. Thus, in all months, greater
or lesser, the ides were the seventeenth days, and the nones the
twenty-fifth days, counting backwards from the last day inclusive.

It was not only the nones and ides themselves that were
counted backwards, but also the intermediate days. Thus, in a
month of thirty-one days, the first six days were called succes-
sively as follows : —

1st day

2nd

3rd

4th

5th

6th

7th

Calends

Sixth before the nones

Fifth

Fourth ,, ,,

Third „

The eve of the nones

The nones.

In the same manner, the days succeeding the nones were
counted backwards from the ides, and those succeeding the ides
counted backwards from the calends of the next month.

Although carried to such an extent, the practice of backward
reckoning was absurd ; the method is, in certain cases, obviously
convenient, and is still in general use. "When remarkable festival
days and anniversaries occur, we all find it convenient to name
the preceding day their eve, and we even sometimes refer to the
second or third day before such or such a remarkable epoch.

69. The periodic returns of the seasons taking place at intervals
of about 365 days, could not remain long in accordance with a
year of 355 days. This was soon perceived; and of all the
inexplicable expedients of which the management of chronometric
regulation affords any example, certainly the most curious by far
was that by which it was attempted to bring the civil iato accord-
ance with the natural year.

Imperfect as the knowledge of astronomy was in these times,
the mere observation of the returns of the seasons, such as all
agriculturists in the rudest state would have made, was enough
to show that 355 days was ten or twelve days less than the period
of the seasons ; and, therefore, that by continuing to count time
by such a year, the seasons would return ten or twelve days later
from year to year.

70. Numa, the successor of Romulus, who, as has been already
stated, modified the calendar, decided that the civil year should
be brought into accordance with the period of the seasons, by
introducing into every other year a thirteenth month, called

153

COMMON THINGS TIME.

MEKCEDONITJS, consisting alternately of twenty-two and twenty-
three days. So far the expedient presented nothing very
singular, but the manner in which this supplemental bi-annual
month was introduced was most curious. It was decreed that
the progress of the month of February in every other year should
be suspended at the end of the twenty-third day, and that then
the month Mercedonius should commence, and that, when it was
completed, the month of February should be continued to its last
day ! Thus Mercedonius was wedged in between the 23rd and
24th of February. In these alternate years, the day after the
23rd February was the 1st Mercedonius, and the day after the
22nd or 23rd Mercedonius, as the case might be, was the 24tl
February, and the succeeding days the 25th, 26th, 27th, and 28tL
of February ! ! !

71. The term month has been used in different senses, one oi'
which is the interval during which the moon makes a complete;
revolution round the earth.

Four weeks exceeding this interval by no more than sixteen
hours, that period of time has been also called a month. Accord-
ing to Blackstone, this is the legal sense of the term, unless
a different meaning be expressly given to it. A lease for twelve
months is a lease for forty-eight weeks.*

VI. — THE TEAK.

72. This is the largest of the chronometric units, and is con-
sequently that by which all long periods are expressed.

73. What is a TEAK ? To most persons it may seem that such
a question is superfluous, forasmuch as every one must very well
know what a year is. If we press for an answer, and sift such
as are given, the matter will not, however, prove to be so plain
and so easy.

Some may reply that it is the interval of time during which
the sun makes a complete revolution of the heavens.

Others will say that it is the interval determined by the
periodical recurrence of the seasons.

The question would be stripped of part of its difficulty if these
two intervals were the same. But they are not. If it be replied
that their difference is not great, we may rejoin that the difference,
however small it may be, will become great by accumulation, and
that when the question relates to centuries it may be such as to
throw the two definitions into utter discordance.

In explaining the circumstances attending the diurnal unit, we
showed that one essential condition attending it was, that it
should be invariable ; in other words, that every succeeding day

* Blackstone, ii. chap. 9.
154

THE YEAR.

should have exactly the same length. The same condition is
indispensable ; and for the same, and even stronger, reasons in
the case of the annual unit. Yet the natural standard from
which that unit is taken, the periodical return of the seasons, like
the periodical return of the sun to the meridian, is subject to a
certain variation. It is on that account unsuitable for a standard
measure of time. This defect, however, is removed by an expe-
dient similar to that by which the mean solar day was substituted
for the apparent solar day. A fictitious period is assigned to the
return of the seasons, which is a mean between the extreme
variations of the actual period which marks their successive
returns, and this fictitious period, which is invariable and never
differs much from the real period, being sometimes a little more
and sometimes a little less, is adopted as the chronological year.

Unfortunately for the facility of chronology, however, neither
this nor any other standard measure of time based upon the
succession of seasons, consists of an exact round number of days
without a fraction ; nor has the fractional part remaining over a
whole number of days the advantage of amounting by any extent
of repetition to a day, or even to any whole number of days.

This circumstance, "as will presently appear, has been productive
of grave inconvenience in history and chronology.

74. In their first rough attempt at the establishment of the
annual standard of time, the Egyptians gave the year 360 days,
divided into twelve equal months of 30 days.

This is supposed to have been the origin of the division of the
circle into 360 degrees, and indeed of the prevalence of a duode-
cimal modulus in many other popular measures.

The subsequent addition of the five complementary days is
attributed to an Egyptian god or hero called by the Greeks
HEKMES, with the distinguishing appellation of TEISMEGISTOS,
thrice-greatest.

75. This interval of 365 days was as near an approximation to
the period of the seasons as could be made in round numbers.
Nevertheless its continuance would, after the lapse of a certain
time, have been the cause of inextricable confusion. Let us see
whether we cannot make this apparent.

The true period marked by the return of the seasons is now known
to differ from 365| days by a little more than eleven minutes. This
difference, minute as it is, has been the cause of great difficulties
in history and chronology. Let us, however, for the present put
it out of view, and take the year as being 365| days exactly.

After the lapse of one year of 365 days the seasons would,
therefore, return a quarter of a day later than in the preceding
year. After another year of 365, they would return half a day

155

COMMON THINGS— TIME.

ber,
bion

LSUO

later; after another, three -quarters of a day later; and after four
years they would be an entire day later. Thus if spring began
in the first year on the 21st March, it would begin in the fourth
year on the 22nd March. In like manner it would begin in the
eighth year on the 23rd, in the twelfth, on the 24th, and so on ;
being one day later every fourth year. In 30 times four years
it would be a month later ; and in 182| times four years — that is
in 730 years — it would be just six months later, so that Spring
would commence on the 21st September, and Autumn on the
21st March. The first day of Summer would be 21st December,
and the first day of Winter would be 21st June.

Such would be the ultimate effects ensuing from the adopti<
of a year of 365 days. ^^^^^~

The confusion, historical and chronological, which would ensue
from such a method of recording time must be obvious. If we
found any event recorded in remote times which might have been
affected by the season of the year at which it occurred, its date would
supply no immediate indication of that. For anything indicated
by the month in which it took place, it might have been in any
season whatever, Spring, Summer, Autumn, or Winter. It is true,
however, that the season might be discovered from the date, by
calculating backwards, and allowing a day for every four years.

It is clear that after a period of four times 365 years — that is
1460 years — the seasons would return to the same days, having
in the interval commenced upon every day of the year from the
first to the last.

76. This discordance between the year of 365 days and the
period of the seasons caused the former to be called the Vague
year ; the period of 1460 years, after which the seasons would
return to the same days, was called the SOTHIC TEEIOD, from
some supposed relation to the dog-star, called SOTHIS.

77. However obvious were the objections attendant on the
adoption of the year of 365 days it was not without defenders
and partisans. The advantage claimed for it will, in our times,
appear curious. It was said that such a year would cause all the
festivals to fall successively upon every day in it, and would thus
sanctify the entire year ; just as if a Christian would at present
advocate it on the ground that Christmas would in the course of
fourteen or fifteen centuries fall upon every day in each season, of
spring, summer, autumn and winter !

78. The Greeks, as we have seen, first measured time by months
consisting alternately of 29 and 30 days, giving an average of
29| days, a very close approximation to the true mean length of a
lunation, and their year consisted of twelve such months. Such
a year, however, consisting of only 354 days, deviated from the

]56

THE YEAR.

periodic return of the seasons by more than eleven days, and
after the lapse of no more than three years the seasons were put
back more than a month ; and after a period of eighteen years
they were actually reversed, midsummer taking the place of mid-
winter, and vice versa. The return of the seasons constituted so
obvious and so natural a measure of the year, and was so inti-
mately connected with the prosecution of human affairs, and
especially with agriculture, that no measure of the year which
varied so much from it could be long maintained ; and, as we
have already stated, attempts were soon made in all the provinces
of Greece to bring the series of twelve months into accordance
with the period of the seasons, by adjusting their several lengths
so as to make a total of 365 days : an interval so near the true
succession of the seasons that an age must elapse before any
important discordance would have been rendered manifest.

Religious questions, however, intervened and raised serious
difficulties among the Athenians. The festivals and ceremonies
connected with the worship of the gods all originated at an early
epoch when the lunar phenomena alone formed the basis of their
chronology. Certain observances were required to be made in certain
phases of the moon, and when those phases, by the changes in the
lengths of the months, no longer recurred upon the same days of
the year, but assumed a character similar to that of the moveable
feasts of the Christian church, it became necessary in order to fix
beforehand the times of their celebration, to calculate the days of
the lunar phases, and, in a word, to create a calendar.

The difficulties which thus arose in the imperfect state of
astronomical science at that epoch were seriously aggravated by
a command proceeding from an oracle, to the effect that certain
festivals appointed to be celebrated under particular lunar phases
should be also held at certain seasons of the year. This at once
rendered necessary the solution of the problem to bring into
numerical accordance the series of lunations and the succession
of the seasons, a problem which was at the time as far removed
beyond the skill of the astronomers as that of the priests.

79. At length, about 432 B.C., Meton, an ancient astronomer,
succeeded in obtaining a solution of it which, if not absolutely
complete, was regarded as so satisfactory as to excite an outburst
of popular enthusiasm. He stated that 235 lunations were
exactly or so nearly equal to nineteen years that at the end of
that period the full moons would again fall upon the same days of
the year, and that, consequently, if the series of full moons were
recorded for any single period of nineteen years, indicating the days
upon which they severally took place in each year, they must recur
upon the same days in every succeeding period of nineteen vears,

157

COMMON THINGS — TIME.

and must have in like manner occurred upon the same days in
every past period of nineteen years. Thus all calculation of the
recurrence of the lunar phases was rendered unnecessary. The
lunar calendar of any interval of nineteen years was merely :i
reproduction of the lunar calendar of the preceding interval.

This period of nineteen years was, and is still, called the
METONIC CYCLE.

80. This discovery which was made public by Meton on the
occasion of the celebration of the Olympic games in 432 B.C., ex-
cited such unbounded enthusiasm and admiration, and the benefits
it conferred upon chronology were so highly appreciated, that the
numbers expressing the dates of the full moons in a cycle wero
ordered to be inscribed in letters of gold upon the public monu-
ments, and upon tablets in the temples of the gods. It is to thif
circumstance that is ascribed the fact that these numbers were after-
wards usually written in the almanacks in gilt characters, and.
later when printing had been invented, they were distinguished
by being printed in red ink, and they .thus acquired the name of
golden numbers, by which they are distinguished in the calendars
of the present day.

81. Neither the brilliancy of this discovery, nor the glory of
the Olympic crown, nor the great popularity with which he was
surrounded, protected Meton from the shafts of his illustrious
contemporary Aristophanes, who attempted to turn him into
ridicule and bring him into discredit by introducing him among
a group of charlatans in the well-known comedy entitled "The
Birds" (o/wi0es).

82. It is a curious fact that the accordance of the succession of
the lunar phases with the Metonic cycle has become more and
more precise, as the motions of the sun and moon in the heavens
have been more exactly ascertained. The mean length of a
lunation, which was already known in Meton's time with great
precision, is 29*530589 days, and consequently 235 lunations
consist of

29-530589 x235d=6939d 16h 31m 19s. ,/>

The mean length of the year, which was not so well ascertained
in Meton's time, is now known to be 365-24224 days, or

365d 5h 48m 49-5%
and consequently nineteen such years consist of

(365d 5h 48m 49-5')xl9=6939d 14h 27m 41%
from which it appears that 235 lunations exceed nineteen y
by 2h 3ra 38s.

After each interval of 1 9 solar years, therefore, the successi
lunations would commence 2h 3m 38s later.

83. It has been already stated that the Roman year consisting
158

LUWU

aive

THE TEAK.

first of '304 days, was immediately increased to 355 days; and that
ultimately, by tjie complementary month called Mercedonius,
45 days were added to every fourth year. Thus each series of
four years consisted of

DAYS.

1 355

II 355

III 355

IV. . . . . . 400

1465'

So that the four years consisted of 1465 days.

The true length of four solar years being, however, only 1461
days, four Roman years as thus established would be four days
too long ; so that every four years the seasons would fall four
days earlier in the year, and in the short period of thirty years,
they would be severally moved back a month.

84. This consequence being soon rendered apparent, a remedy
for it became necessary, and that which was first adopted was one
of the worst expedients that could have been imagined. A dis-
cretionary power was given to the nontiffs to intercalate as many
days as they might consider necessary to bring the year into
accordance with the succession of seasons.

As might have been foreseen, this measure speedily gave rise to the
most gross system of abuses. Accounts being made up, payments
made, and interest computed for all affairs private and public to
the first days of the months, the pontiffs prostituted the powers
conferred upon them to the most corrupt purposes. The temporary
magistracy of those whom they favoured was prolonged, and that
of those whom they opposed was abridged ; payments to be made
by their friends were postponed, those due by their opponents
accelerated ; the profits of the farmers of the revenue were aug-
mented or diminished at their good will and pleasure, by the
adroit management of the arbitrary intercalary days by which
they were enabled to prolong or to abridge any months of the
years. The disorders thus produced attained at length to such a
pitch, that the festivals of autumn were celebrated in spring and
vice versa.

VII.— THE JULIAN REFORM.

85 •. It was reserved for Julius Csesar not only to put an end to
this confusion and the abuses in which it originated, but to esta-
blish a system of recording time, which has come down to our own
epoch, and is denominated from its founder the JULIAN CALENDAR.
He was aided in this great reformation by Sosigenes, an eminent

159

COMMON THINGS — TIME.

Egyptian astronomer of that day. He was, according to the laws,
authorised to accomplish this, being himself chief pontiff.

Astronomical science had so far advanced, that the length of the
period determined by the succession of the seasons was known
to be about 36o| days. But the adoption of a civil year con-
forming to this would have involved consequences of a highly
impracticable kind. Thus, if we suppose such a year to commence
at midnight, between the 31st December and 1st January, the
succeeding year would commence at six A.M. on the next
1st January; the next at noon, on the following 1st January;
the next at six P.M., on the 1st January of the third year; and,
in fine, the next at the midnight between the 1st and 2nd January
on the fourth year. Thus, in a series of four years, the first day
of January would be transferred piecemeal, quarter by quarter,
backwards to the preceding year.

This was evidently an impracticable measure. Julius Cocsar,
who in the eminently practical character of his genius closely
resembled Napoleon, resolved upon surmounting the difficulty by
an expedient as simple in its execution as it was happy in its
conception.

86. It was decided to adhere to years consisting of a whole
number of days, and to allow the fractions to accumulate from
year to year, until they should make up an entire day, and then
to add that as a supplemental day to the year in which the accu-
mulation should arrive at its limit. Since therefore the fraction
over the round number of 365 days was assumed to be a quarter of
a day, it would at every fourth year amount to a day. It was,
therefore, decided to accomplish the object by giving one addi-
tional day to such fourth year. These four successive years were
to be thus composed : —

1 365

II 365

III 365

IV 366

Mean length .

The object was, therefore, attained without annexing fractional
parts of a day to the year.

The additional day given to the fourth year was introduced
into the month of February, making that month 30 instead of
29 davs.

160

COMMON THINGS.

TIME.

CHAPTEE IY.

87. Year of confusion. — 88. New arrangement of the months. — 89.
Mistake of the Pontiffs.— 90. Leap-years.— 91. Historical dates.—
92. Day of the equinox. — 93. What is the equinox ? — 94. The two
equinoctial points. — 95. Sidereal year. — 96. Precession of the equi-
noxes.— 97. Equinoctial year. — 98. Civil year. — 99. Difference
between it and the Julian year. — 100. Effect of this difference. —
101. Cause of the reformation of the Calendar. — 102. Discordance
between the real and ecclesiastical equinox. — 103. Gregorian reform.
— 104. Gregorian Calendar. — 105. Its compensating effect. — 106. Re-
sistance to its adoption. — 107. Dates of its adoption in different
countries. — 108. In England. — 109. Its reception there. — 110. Occa-
sional agreement of the new and old styles. — 111. Anecdotes relating
to the change. — 112. Russia adheres to the old style. — 113. Com-
mencement of the year. — 114. Various in different countries. —
115. In England. — 116. Old and new style in England. — 117. Tem-
porary inconvenience attending it.

LARLNER'S MUSEUM OP SCIENCE.
No. 64.

161

COMMON THINGS — TIME.

IT will bo remembered that tlie Eomans counted the days of
the month backwards, and that those of the latter part were
reckoned from the calends or first day of the next month. Now
it happened that the sixth day of February, counting backwards
from 1st March, called the sexto-calendas was consecrated to a
festival celebrating the expulsion of the Tarquins. It was
resolved to place the supplementary day of the fourth year imme-
diately before this sexto-calendas, and to avoid changing the
denomination of the other days it was decided to call it a second
sexto-calendas. It was therefore denominated BISSEXTO-CA-
LENDAS, and the year in which this additional day was intercalated
was and still is called A BISSEXTILE YEAH.

The commencement of the year was ordered to take place on
the day of the new moon, which occurred next after the winter
solstice of the preceding year. This day was accordingly called
the 1st January, 709, from the foundation of Eome, and as t'ie
commencement of our era was the year 754 from the foundation
of Eome, it follows that the date of the Julian reform was 45 B.C.
and consequently the year preceding the murder of Csesar.

87. This admirable arrangement provided for the future, but it
did not repair the consequence of the past abuse and disorder.
The complementary month called Mercedonius had been the sub-
ject of constant maltreatment by the pontiffs, having been
abridged and extended in the most capricious and arbitrary
manner, so as completely to derange the position of the seasons,
relatively to the commencement and the close of the year. To
rectify this some bold and exceptional temporary measures were
indispensable. Ca3sar being chief pontiff exercised the power
which his predecessors in that office had so grossly abused to
rectify these disorders, and restored by a violent and exceptional
measure the day of the spring equinox to the 25th March, the
date which it held in the time of Numa, To accomplish this, he
decreed that the year 708 from the founding of Eome should
consist exceptionally of 445 days. These 445 days were com-
posed in the following manner : — -

Days.
The common year . . . . .. . .355

Month Mercedonius . . . . . 23

Two extraordinary months between November and

December : * First .... 33

Second . . . . 34

445

The year in which these changes were introduced came to be
called the " YEAH OF CONFUSION." This year was 46 B.C.

88. Besides thus re-adjusting the place of the equinoxes, the
1G2

THE JULIAN KEFOEM.

distribution of the 365 days among the twelve months was re-
arranged. It was ordered that the odd months, counting from
the beginning "of the year should contain 31 days each, and that
the others should contain 30, except February, which in common
years was to contain 29, and in bissextile years 30 days.

This natural and easily remembered distribution was disarranged
soon after to gratify the frivolous vanity of Augustus. It has been
already stated that the month Sextilis had its name changed to
Augustus in compliment to that emperor. Not satisfied with thus
having his name perpetuated, he insisted that the number of days
in his month should not be less than in Caesar's. The day added
to August was therefore taken from February, which was thus
reduced to 28 days for common, and 29 for bissextile years. The
months definitively stood as follows : —

January
February
March .
April
May .
June

Days.
31

28 or 29
31
30
31
30

'July .
August
September
October .
November
December .

Days.
31
31
30
31
30
31

The alternation of 30 and 31 days proposed by Caesar is there-
fore preserved with the exception of July and August, two months
of 31 days in immediate succession.

It was attempted at later periods of the empire to prostitute the
calendar by changing the names of the latter months of the year
into those of Tiberius, Claudius, Nero, and Domitian ; but the
good sense of the Roman public resisted such an ignominy.

89. The death of Caesar in the year after this reform had been
decreed, threw the task of its realisation into the hands of the
pontiffs, whose very first act betrayed a total misapprehension of
the meaning of the most important of the conditions of the new
system. The terms of the Julian edict, by which the recurrence
of the bissextile year was defined, have not come down to our
times ; but it is certain that the pontiffs interpreted the periodic
addition of the intercalary day as designed for every third year,
and not every fourth year. That they were not set right by any
contemporary authority like Sosigenes, who, knowing the object
to be accomplished by the expedient, might have demonstrated
the sense of the edict, if the words in which it was expressed
were equivocal, only shows in a striking point of view how rare
this sort of knowledge must have been in that age. However, it
is certain that for the first 36 years after the reformation, every
third, instead of every fourth year, was taken as a bissextile year,
and consequently that these 36 years, including 1 2 instead of 9

at 2 163

COMMON THINGS — TIME.

intercalary days, had a total length greater by 3 days than
due to them by the Julian system rightly understood. "When
this error was at length perceived, the consequence of it was
rectified by order of Augustus, who decreed that for three succes-
sive periods of four years, the intercalary day due to every fourth
year should be omitted, so that the excess given to the preceding
36 years was compensated by an equal deficiency in the 12
following years, after which the regular recurrence of bissextile
years was observed.

The mistake is known to have arisen thus— In Roman COT
every fourth is our third,

1234 12

A B C D E P 0 H I J K &o.

1234 1234

Livy describes the cycle of 19 years as one which begins
twentieth year.

90. The common name given to bissextile years in our language
is LEAP YEAES, which the dictionaries explain by stating that
" every fourth year leaps over a day more than a common year."
It is, however, objected by some that the term LEAP year is inap-
propriate, inasmuch as leaping over a day would imply its omis-
sion, instead of which in such years an extra day is thrust in.

The term is also explained by stating, that it implies that a day
is leaped over in the calendar without giving it a distinct name.

It is worthy of remark that in the ecclesiastical calendar of
foreign countries, the day called " intercalary " in bissextile or
leap years, is not the 29th but the 24th of February.

91. It will be perceived from what has been stated, that some
confusion prevailed for nearly forty years from the date of the
Julian reform, that is until very near the commencement of the
Christian era ; nor is there any historical certainty as to the
regular observance of the new method until the commencement of
our era. It is certain, however, that the Roman years 761, 765,
769, &c., which were the years A.D. 8, 12, 16, &c., were counted
as leap years, and about all succeeding dates there is no doubt.

From these dates, historians and chronologists have reckoned
not only forwards but backwards, so as to reduce all historical
events to the position in respect to the order of time which they
would have held, if the Julian system had always existed. When
we read of historical events, occurring in distant ages before these
reforms in the methods of recording time, we are to understand
that the dates assigned to them are by no means those which they
bore at the time, and in the nation of their occurrence ; but that
by the labours of chronologists, the local dates given to them by
164

LEAP YEAR.

the contemporary annalists, dates varying not only in different
countries according to their different usages, but even in the same
country in different ages, have been changed into those dates
which they would have had if the Julian chronology had prevailed
then.

It is evident that without this simplification and assimilation,
historical dates would present a mass of confusion, which would be
inextricable to all ordinary readers.

92. It has been already stated that the interval of 365| days,
assumed in the Julian reformation as the length of a year, is not
its true length, but differs from it by a very small fraction of a
day. As we have now to explain the part which this very
minute fraction has played in chronology, it will be necessary to
convey to the reader a more clear and distinct notion of the
meaning of the word year, than that which is included in the
general statement that a year is the period after which the seasons
are reproduced ; for it may fairly be asked what determines the
limits of the seasons ? how are the exact moments of time at
which they severally begin or end defined ? For it must be observed
that our enquiries now involving not whole numbers of days, but
small fractions of a day, it is not enough to know that this or that
season begins or ends on this or that day; we must know the
hour, minute, second, — nay even the fraction of a second, which
marks the epoch we desire to determine.

It is customary then to define the course of the seasons by the
moment at which spring begins. It has been agreed to take for
this the moment at which the centre of the sun's disc has such a
position in the heavens, that if it were stationary there, day and
night would be exactly equal, that the sun would be in short
exactly twelve hours visible, and twelve hours invisible : twelve
hours above, and twelve hours below the horizon.

It may be said that this definition is needlessly verbose and
complex, inasmuch as it would be more simple and intelligible to
say at once that spring begins on the day of the equinox.
' Undoubtedly such a summary statement would be much
shorter and more simple, and provided that it be clearly under-
stood, and that it be sufficiently definite, it can be subject to no
objection. But what is meant by the " day of the equinox?"
We shall, of course, be answered that it is that day on which the
sun is twelve hours above, and twelve hours below the horizon.

Yery well ! let us go to the almanac, and search for such a
day. We take the almanac of 1854, and find that on 19th
March the sun was twelve hours and one minute above, and
eleven hours and fifty-nine minutes below the horizon. On the
20th it was twelve hours and six minutes above, and eleven hours

165

COMMON THINGS — TIME.

and fifty-four minutes below the horizon, while oil the 18th it
was eleven hours and three minutes above, and twelve hours and
fifty-seven minutes below the horizon. On no day of the month
was it exactly twelve hours above, and twelve hours below the
horizon ; and the same result would be found by examining in the
same manner the almanacs for other years.

It appears then that rigorously equal day and night is a phe-
nomenon that never exists. It is no answer to this to say that
the day and night in the instance produced and others differ only
by a minute or two, because the question here involves only the
consideration of those very minute intervals.

Since then the "day of the equinox" cannot mean a day on
which day and night are equal, what is its exact meaning ? "We
reply that it means very obviously the day on ivhich the equinox
takes place. But then what is in that case meant by the word
equinox? We reply by turning back upon the explanation
already given, that the equinox is that precise moment when the
centre of the sun's disc has such a position that, supposing it 1o
retain that position unchanged, it would be twelve hours above, and
twelve hours below the horizon, during a revolution of the heavens.

93. But since the sun's disc has a continual easterly motion
upon the heavens, moving at the rate of nearly 1° per day, or 2|'
per hour, it does not retain the position in question more than an
instant. It moves round the heavens as the hand of a clock
moves round its dial, passing incessantly from point to point.
The exact point at which the centre of the sun is at the moment
above described, is therefore called the equinoctial point, as the
moment of time at which it passes through that point is called
the equinox.

94. There are two equinoxes and two equinoctial points. The
first takes place about the 21st March, and the other about the
23rd September.*

The former is called the vernal equinox, and the latter the
autumnal equinox, because it has been agreed to fix the beginning
of spring at the one epoch, and the beginning of autumn at the
other.

The two equinoctial points are situate at opposite sides of the
heavens, separated one from the other by an entire hemisphere, r.s
must be evident when it is considered that the sun takes six
months to move from the one point to the other.

95. Having thus conveyed a distinct notion of the meaning of
the equinoxes, and of the equinoctial points, we shall find less

* In the tables of sunrise and sunset given in the almanac, the effects of
refraction are taken into account. These are omitted, however, in fixing
the position of the equinoxes.
160

THE EQUINOXES.

difficulty in explaining the different senses in which the word
YEAR is used.

If the equinoctial points maintained a fixed position on the
heavens, the interval between the moments at which the centre
of the sun's disc would pass twice successively through either of
them, would be in fact the interval during which the sun makes
or appears to make a complete revolution of the heavens.

This interval is called the SIDEREAL YEAR.

Astronomers have ascertained the exact length of this year
to be 365d 6h 9ra 10-388.

It appears, therefore, that this long interval has been ascertained
to within the hundredth part of a second of its true value.

96. But the equinoctial points have not a fixed position on the
heavens. They are on the contrary, subject to a slow displace-
ment from year to year in a direction contrary to the motion of
the sun. The amount of this annual displacement is small, being
a little less than one minute of a degree, — that is, about the
thirtieth part of the breadth of the sun's disc.

Small as this displacement is, it has been very precisely mea-
sured ; and its effects, which are of the highest importance, as
well in chronology as in astronomy, have been exactly appreciated.

On account of this removal of the equinoctial point backward,
the sun arrives at it after making a revolution of the heavens,
sooner than it would have done if it had not been displaced.
This must be evident when it is considered that the equinoctial
point, displaced in a direction contrary to that of the sun's
motion, advances to meet the sun on its return. The sun there-
fore arrives at it before it makes a complete revolution of the
heavens, and the time of each successive equinox precedes the
time at which it would have taken place if the equinoctial point
had been stationary.

This phenomenon has for that reason been called the PRE-
CESSION OF THE EQUINOXES.

97. The effect therefore obviously is, that the interval between
two successive equinoxes is less than the sidereal year.

This interval between two successive equinoxes is called the

EQUINOCTIAL Or TROPICAL YEAR.

The sidereal year is of invariable length, and would on that
account be well suited to be a standard measure of time. But it
has one capital defect, which renders it totally unfit for civil
purposes. It is not in accordance with the periodic returns of the
seasons by which all mankind measure the year.

If the equinoctial points were stationary, the sidereal year
would also be the equinoctial year, and in that case it would be
coincident with the return of the seasons. But in consequence of

167

COMMON THINGS — TIME.

the displacement of the equinoctial points, the commencement of
the equinoctial anticipates that of the sidereal year ; the extent
of this anticipation, though very small at first, accumulating for
long series of years, causes the seasons to take place successively
at all imaginable parts of the sidereal year.

For these reasons the sidereal year has never been adopted as
the civil year.

If the annual displacement of the equinoctial point were
regular and constant, the precession of the equinoxes would bo
also constant ; and the equinoctial year, differing from the side--
real year by an invariable quantity, would itself be invariable, and
as it is in accordance with the succession of the seasons, it would
be in all respects eligible as a standard measure of civil time.

But it so happens that this displacement is rendered variable by
the operation of several causes. Its variations, however, are
circumscribed within narrow limits. It alternately increases and
decreases, and has a certain ascertainable average amount. On
account of this variation, the equinoctial year is of slightly variable
length, and is therefore not fit for a standard measure of time.

98. This being the case, and the mean annual displacement of
the equinoctial point being accurately ascertained, a fictitious
equinoctial point is supposed to exist, which has this mean annual
displacement, and the interval between two successive returns of the
sun to this fictitious equinoctial point being invariable, is adopted
as the standard, and is called the MEAN SOLAR or CIVIL YEAR.

Although rigorously this year does not therefore correspond
with the returns of the seasons, it never varies from them by any
interval great enough to be perceived or appreciated by any but
astronomers.

The exact length of the mean solar or civil year is

365d 5h 48m 49s-54,
being less than the sidereal year by 20M 20s -8.

99. Such being then the actual length of such a year as would
always remain in accordance with the successive returns of the
seasons, let us see to what extent the year of the Julian calendar
differs from it, and how such difference would affect chronology.

The Julian year being 365| days, the difference between it and
the mean solar year is easily found.

D. H. M. S.

Julian year 365 6 0 O'OO

Mean solar year . .. 365 5 48 49 '54

Difference . . . . 11 10-46

100. It appears, therefore, that the Julian years would depart
from the course of the seasons at the rate of llm 10"4G, or about
168

• THE GREGORIAN REFORM.

tlie 129th part of a day per annum. The departure accumulating
from year to year would amount to a whole day in 129 years, to
two whole days in 258 years, to three in 387 years, and so on.

Now, although such a departure would not be perceptible during
the lives of a single generation, it must evidently become so after
some centuries. The equinox falling back towards the beginning
of the year at the rate of one day in 129 years, was in the fifteenth
century thus thrown back as much as eleven days.

It is evident that the continuance of this from century to
century would have thrown the equinox back from day to day
until it, and consequently the seasons, would have successively
assumed every possible position in the year.

VIII. — THE GREGORIAN" REFORM.

101. Although in a more civilised and enlightened age this
would have been a reason sufficiently urgent to undertake a
revision and correction of the calendar, we are indebted for the
reform which took place to other and different causes.

102. It was the rule of the Church to celebrate the festival of
the Resurrection at a time not far removed from the 21st March,
which was taken to be the day of the equinox, depending how-
ever also upon conditions connected with the lunar phenomena
with which we are not at present concerned, but which we shall
explain fully on another occasion. If therefore the real equinox
were subject, as we have stated, to a gradual change, which would
throw it back from year to year, so that it would fall each
successive year earlier and earlier, while the festival of Easter,
still related to the 21st March, would necessarily be farther and
farther removed from the equinox, it must obviously happen
in the course of time that the festival would fall successively
in every season of the year, and indeed on every day of the year.

The Roman ecclesiastical authorities of the day becoming pain-
fully aware of this, and sensible that no decree of pope or council
could accelerate the motion of the equinox for the future, or
carry it forward from the llth to the 21st March; to repair the
error of the past, resolved that since they could not bring the
equinox to the 21st March, they would bring the 21st March to
the equinox.

103. This change, with the others necessary to prevent the
recurrence of a like discordance between the ecclesiastical year
and the seasons, took place in the latter part of the sixteenth
century, in the pontificate of Gregory XIII., from whom the
reformed calendar came to be called the Gregorian calendar.

As at the epoch of the Julian reform, two errors were to be
corrected, those of the past and those of the future. The accu-

169

COMMON THINGS — TIME.

mulated effect of the past errors was that the real epoch of the
spring equinox had fallen ten days behind the nominal day of its
occurrence, which was the 21st March. The future cause of error
was that an additional day every fourth year was too much, but
that 129 years must elapse before the redundancy would cause the
equinox to be one day behind its time.

104. To remedy the consequence of past errors, it'was decreed
that the days of the months should be all expressed by number;-;,
greater by 10 than those by which, according to the succession of
time, they were expressed. Thus the llth March, 1582 (the year
in which the reform took place) was decreed to be the 21st March,
and in like manner all the other days of the year were augmented
by 10. By this expedient the last ten days of 1582 were thrown
over into 1583, inasmuch as the 21st December, 1582, became
31st December, 1582, and consequently 22nd December, 1582,
became 1st January, 1583.

The day of the vernal equinox thus recovered the date - of
21st March. How it was secured in the undisturbed possession of
that date, we shall now see.

By following the established rules of the Julian calendar, it
would have been one day behind its date in 129 years from 1582,
that is in 1711. To prevent this, it was decreed that the year
1700, which would by the Julian calendar be a leap year, should
be a common year. One day being thus omitted, the equinox of
1711 would be restored to its date of 21st March. In like manner
it would be again a day behind in 1840. This was in like
manner to be prevented by making 1800 a common year, which
ought to be a leap year. Again it would be a day behind its
time in 1969, which would be set right as before by making 1900
a common instead of a leap year. Another period of 129 would
go to 2098, which was remedied by making 2100 a common instead
of a leap year.

Thus the equinox would be kept right by making three suc-
cessive secular years 1700, 1800, and 1900 common years instead
of leap years, leaving 2000 a leap year, but making 2100 a
common year instead of a leap year, and going on from century to
century in the same manner, leaving every fourth secular year a
leap year, but making all the others common years. The series
of secular years would therefore be as follows : —

1700 Common 2300 Common

1800 ,, 2400 Leap

1900 ,, 2500 Common

2000 Leap 2600 ,,

2100 Common 2700 ,,

2200 ,, 2800 Leap,
170

THE GREGORIAN REFORM.

and so on. The secular leap years will always be those of which
the first two figures are exactly divisible by 4 without a remainder,
as 2000, 2400, 2800, 3200, 3600, &c., all the other secular years
being common years.

105. Let us see whether the compensation thus produced for
the errors of the Gregorian calendar is practically sufficient,
for perfect it is not, nor is it possible for any such compensation
to be so. It has been shown, that the Julian year was too long
by the 129th part of a day very nearly. To compensate for this
Pope Gregory XIII. does what ? He takes away three days from
400 years, which is equivalent to taking ^th part of a day
from one year, whereas the quantity required to be deducted is
the 129th part of a day, which is greater than the 5§oth part.
The compensation of Pope Gregory is therefore short of the
requisite quantity by the difference between the 129th and the
^th part of a day, that is by the 3969th part of a day.

Thus it appears that by following the Gregorian calendar the
equinox will not be so much as one day behind its time until an
interval of 3969 years elapses, counting from the year 1582, that
is until the year of our Lord 5551. When that time arrives the
evil maybe staved off for another period of 3969 years, by declaring
the year 5600 a common, instead of a leap year. We may, how-
ever, safely leave to the inhabitants of the earth at that epoch the
management of the affair. Sufficient for the day is the evil thereof.

106. Notwithstanding the undeniable reasonableness of this
reform of the calendar, and the manifest absurdity of persevering
in calling the 21st March the vernal equinox, when all the world
had the evidence of their senses to prove to them that the
equinox had really taken place ten days earlier, the change pro-
posed was not generally adopted. Protestant States were opposed
to it because it emanated from Catholic ecclesiastical authorities,
and as was wittily observed, they preferred rather to be in oppo-
sition to the sun than in accordance with the Pope. The nations
professing Greek Catholicism were opposed to it because it
emanated from the head of the branch of their Church which
they denied to be orthodox.

The papal decree fixed the exact date of the commencement of
the reform at the 5th October, 1582, according to the former
style, which day was decreed to be called the loth October.

107. In France the change was adopted on the 10th December,
next following, which was called 20th December.

In the Catholic States of Germany it was adopted in 1584.

The Protestant German States, having resisted the reform for
nearly twenty years, at length yielded, and accepted it in 1600,
in which year the 19th February was declared to be 1st March.

171

Denmark, Sweden, and Switzerland, were later in the adoption
of the change, but soon followed the example of Germany.
Some Swiss towns nevertheless offered such vigorous opposition to
the measure, that the intervention of the military was necessary
to enforce it when adopted by the authorities.

In Poland, where it was adopted by the government as early as
1586, it encountered considerable opposition in certain towns,
and even excited a serious insurrection at Eiga.

108. The anti-papal spirit being much more dominant in
England than common sense or scientific authority, the reform,
was resisted for nearly two centuries, so that the real had fallen
above eleven days behind the legal date of the equinox. In 1752,
however, the force of things at length prevailed over this dis-
creditable bigotry, and the reform was introduced into the
calendar, by declaring the 3rd to be the 14th September.

109. A measure of which the effect was to overturn the long
established landmarks of time, and to substitute for them others,
new and altogether strange to tradition and usage, could not be
supposed to pass without exciting many reclamations among
persons of all classes from the peer to the peasant. Personal
feelings were excited at the unceremonious perturbation of
birthdays and of marriage anniversaries. Eeligious exasperation
was produced by the arbitrary transposition of the most solemn
festivals. Even the moveable feasts already surrounded with
some confusion, became for the moment confusion worse con-
founded. Political celebrations and the dates of historical events
shared in the general disturbance.

In an essay on the ecclesiastical calendar, by Professor De
Morgan, which was published in the Companion to the British
Almanac, for 1845, some amusing examples of this are collected.
A friend of the author, an eminent scientific man, not long since
deceased, related of his own knowledge, when a boy, that a
worthy couple in a country town, scandalised at the change of
style in 1752, continued to attempt the observance of Good
Friday on the old day. To this end they used to walk seriously,
and in holiday costume, to the church door, at which the gentle-
man used to knock for a certain time with his cane, demanding
admittance. On finding no admission, they walked as solemnly
home again, and read the Church service appointed for the day.
On the new and, as they regarded it, spurious Good Friday, they
ostentatiously acted as if it either preceded or followed the genuine
day, as the case might be, so as to render it manifest to their
neighbours and friends, that they at least totally rejected the new
style.

110. In the 48 years, between 1752, the date of the change of
172

POPULAR SUPERSTITIONS.

style, and the end of the century, there were, however, 18 years
in which harmony must have been re-established between the
partisans of the new style and those who reverenced tradition, for
in these years it chanced that the moveable feasts, according to
both styles, fell upon the same days. " This," observes Professor
De Morgan, " happens still occasionally, and will do so, though
less and less frequently, until 2698 A.D., when it will happen for
the last time."

Even still, after the lapse of more than a century, the Christmas
Day of the old style is celebrated under the name of Twelfth
Day, and the name of " Old Christmas Day" is still given to it in
the calendar. It falls on the Feast of Epiphany.

111. Before the change of style, a popular belief prevailed in
England, that at the moment of the midnight with which Christ-
mas Day began, the cattle always fell on their knees in their
stalls. Now when the change of style took place, it could scarcely

. have been expected that the arbitrary will of the legislature would
be respected by these dumb animals, and it was accordingly found
that they continued to perform the act of reverence, not on the
Christmas Day of the law, but on that of the old style ! The best
of this joke was, however, that the Christmas Day of the law was
a Popish institution, forced upon England by circumstances,
and it was maintained that these Protestant cattle were all the
more obstinate in their dumb protestation against the Romish
innovation.

It appears, nevertheless, that in Catholic countries which
acknowledged the authority of the See of Rome, in changing the
style in 1582, inanimate things, not to say cattle, acknowledged
the validity of the decree ; for we have the high authority of the
truly learned Riccioli, to whose astronomical works the scientific
world is so largely indebted, to assure us that the blood of St.
Januarius, which previously used to liquefy punctually on the
19th September, immediately changed the day of its miraculous
liquefaction to the 19th September of the new style, which was
the 9th September of the old style. Like the day of the nominal
equinox, that of the miracle was accordingly put back ten days,
in obedience to the papal bull. '

Riccioli also mentions the case of a certain supernatural twig,
which had been accustomed to put forth miraculous buds on
Christmas Day. This Romish twig, unlike the Protestant cattle,
as the astronomer assures us, was found to bud on the new
Christmas Days which followed the publication of the Papal
bull.

112. Of all Christian States, Russia alone still insists on
adhering to the Julian calendar, and accordingly, by the further

173

COMMON THINGS — TIME.

accumulation of the effects of the erroneous length assigned to the
year, the Russian legal equinoxes are now twelve days in advance
of the real equinoxes.

113. The influence which long continued usage exercises upon
the mind is such that we are always disposed to think, that what
has been long established has been so by the nature of things,
and therefore of necessity, and not at all by the arbitrary appoint-
ment of local and temporary authorities, or by the voluntary
choice of the people. Thus, who does not imagine that it is for
some natural and necessary reason that the year begins on the
1st of January ? January is the first of the series of twelve months,
and what can be more natural than to take its first day as the
commencement of the year? But why is January the first
month ? It is marked by no peculiar or universally observable
phenomenon. If the sun, on its first day, were seen to occupy
any remarkable position, as, for example, that which it has at
the equinox, or if the sun and moon were always found together
on that day, or if a conspicuous eclipse, or any other striking
phenomenon periodically presented itself on that day, a reason
would be found why January is the first month, and why
its first day is the first day of the year. But neither the month
nor the day is signalised by such phenomena, nor by any which
can be supposed to mark it by nature as the commencement of a
chronometric period.

It might be imagined that at all events the first day of some
montli would be selected as the commencement of the year. No
reason, as it would appear, could induce people to begin the year
in the middle of a month, so that one part of that month should
be in one year and the remainder in the other. Nevertheless,
obvious as these considerations now appear, it is certain that they
have had no weight with mankind. Other considerations of
another order, exercising over the mind much more potent
influences, have predominated, and years, accordingly, with
different nations and in different ages, have had their commence-
ment fixed upon days whicli have no reference either to astro-
nomical phenomena, or the order or limits of the months.

114. Religious anniversaries, as might naturally have been
expected, have played a prominent part in this chronological
element. Christmas Day, Easter Day, and the Festival of the
Annunciation, commonly called Lady Day, have been, in different
countries and at different ages, selected as the first day of the
year. Among the French, at the time of Charlemagne, the year
commenced on Christmas Day. It commenced on Faster Day
among the same people under the Capet monarchs, and this prac-
tice was very general in the twelfth and thirteenth centuries. In

174

CHANGE OF STYLE.

England the year commenced on Lady Day (25th March) until
1752.

It must not be understood that this commencement of the year
involved any change either in the months or in the order of their
days. Thus when the year commenced on Christmas Day, that
day was still called the 25th December, and was preceded by the
24th and followed by the 26th December ; but the 24th December
belonged to one year and the 25th to the next. In like manner,
the two days which we now refer back to as the 24th and 25th
March, 1751, were, at the time they actually occurred, called the
24th March, 1750, and 25th March, 1751. Thus 24 days of
March belonged to 1750, and the remaining 6 days to 1751.

115. To us at present, with the habits of counting the years,
months, and days to which we have been accustomed, such a
method of commencing the years appears so absurd and attended
with such strange confusion and disorder that we find it difficult
to imagine how a people could ever continue the practice of it.
Nevertheless it is certain, so far from any such impression
existing at the time this usage prevailed, the announcement of the
change of style, as it was called, which was decided upon by the
legislature in 1751-2, encountered the most serious resistance,
and excited popular disturbances of grave importance. The
transfer of the beginning of 1752 from the 25th of March to the
1st of January, immediately preceding it, deprived the year 1751
of the months of January, February, and twenty-four days of
March, nearly the whole of its three last months.

This change and the apparent sponging out from the course of
time of eleven days exasperated the populace, who, assembled in
the streets of London, and pursued the members of the government
(among whom was the celebrated Lord Chesterfield) when they
appeared, with cries and imprecations, demanding that their
eleven days should be given back to them.

The traces of this custom in our country are still apparent in
various practices. Leases are commenced and determined by
Lady Day. The quarter days on which rents become due are
regulated in the same manner. All rents are payable on Lady
Day and Michaelmas Day, and not, as might naturally be expected,
on the last days of June and December.

116. Until the adoption of the Gregorian calendar in England
in 1752, the years, as has been already stated, commenced upon the
25th March, so that the year 1751 began on the 25th March, 1751,
and ended upon the day now called the 24th March, 1752, while
the year 1752 ended on the day now called the 24th March, 1753.
Independently of the other obvious objections to such a system, it
was out of all accordance with the mode of reckoning time prac-

175

COMMON THINGS — TIME.

tised by other nations of Europe, and great inconvenience and
some confusion prevailed in the adjustment of dates in all inter-
national transactions. It was therefore resolved to include in the
reformation of the calendar the change of the commencement of
the year, from the 25th March to the 1st January, which was
accomplished by declaring that the days, from the 1st January,
1751 (as formerly counted) should be taken as belonging to 1752,
and that 1752 should end on the 31st December, and 1753 begin
on the day formerly called the 1st January, 1752. Thus, in fact,
the months of January, February, and twenty-four days of March,
were transferred from each year to that which succeeded it.

This will explain the peculiar way of expressing dates which is
found in all documents and printed works which appeared at, and
for some time after the reform was adopted. Both dates, the
new and the old, according to the reformed and unreformed style,
were usually expressed, the old above and the new below a line,
like the numerator and denominator of a fraction. Thus, for
example, the day which was the 19th June, 1753, in the old style,
being the 30th June, 1753, in the new style, the date was written

19

thus, -_ June, 1753. In other cases the month was changed as
oil

well as the day ; thus the day which was the 30th June, 1753, old
style, became the llth July, new style, and the date was written

30th June, 7
l

In other cases again, the day, month, and year were all
changed, as, for example, the day which, in the old style, was
the 23rd February, 1753, in the old style, became the 6th March,
1754, in the new style, and was thus written : —

23rd February, 1753.
6th March,! 7 -34.

117. The difficulties which such a change at first produced
among the great mass of the population of the country, who, from
their limited education and information, must have been unaware
of the many important grounds on which the reform was based,
can be easily conceived.

Happily, however the reform was realised, and the incon-
veniences which first attended it disappeared after a few years, so
that the English dates were not only brought into accordance with
the course of the seasons, but with those adopted by other civilised
nations.

FORCING PUMP

COMMON THINGS.

PUMPS.

1. Earliest methods of raising water. — 2. Bucket in a well. — 3. By
windlass and rope. — 4. By two buckets balanced over a pulley. —
5. Method of working these by animal power. — 6. The rope in this
case balances itself. — 7. The lifting pump. — 8. Double lifting pump
worked by animal power. — 9. Various forms of valves. — 10. Clack
valves. — 11. Conical spindle valves. — 12. Ball valves. — 13. The
suction pump. — 14. Analysis of its action. — 15. Forcing pump. —
16. Same with air vessel. — 17. Same with solid plunger. — 18.
Double action forcing pump. — 19. Garden watering pumps. — 20.
Fire-engine. — 21. Chain pump. — 22. Drainage of mines.

1. As water is one of the most universal necessaries of life, and
abundant as it is in nature, is not always found in the localities
where circumstances oblige us to fix our habitations, expedients
by which it can be obtained in sufficient quantity, and of the

LARDNER'S MUSEUM OP SCIENCE. N 177

No. 60.

COMMON THINGS — PUMPS.

necessary purity, have been among the earliest mechanical and
physical inventions in every country. Natural springs showed
that sources of water existed in the lower strata of the earth.
This suggested the process of well-sinking or boring for water.
But the water when thus found rarely rises to the surface spon-
taneously. It does so in those deep springs called artesian
wells ; but in all ordinary cases where a shaft has been sunk
deep enough to find water, the water collects in the bottom
of the shaft, and never rises above a certain level. Expedients
are therefore necessary in all such case? to raise it to the
surface.

2. The first and rudest of these contrivances, is to let down a
bucket by means of a rope, and thus to draw up one bucket-full
after another. The rope by which the bucket is elevated, when
the well is not very deep, is sometimes attached to the long ar:n
of a lever (fig. 1) the shorter arm being pulled down when
the bucket is drawn up full. This is perhaps the rudest and

Fig. 1.

most inartificial of all contrivances for the elevation of the
water. A pulley established over the mouth of the well is one
degree more efficient.

The bucket being let down and dipped in the water, is drawn
up by pulling the rope.

In this case the labour is expended not only in raising the
weight of the water and of the bucket which contains it, but also
that of the rope, which, if the well be deep, is not inconsiderable.
Besides this a certain force must be exerted to bend the rope con-
tinually over the groove of the pulley, and to overcome the
friction of the pulley itself in moving upon its axle.

3. A windlass established over the mouth of the well (fig. 2) is
one degree, and only one degree, more efficient than these rude
178

RAISING WATER.

expedients. In this case the bucket is raised by turning the

winch of the windlass, so that the rope is gradually wound upon

its axle. The power has Fig. 2.

still to raise the weight of

the rope, to produce its

flexure on the axle, and to

overcome the friction of

the axle of the windlass in

its bearings.

In the contrivance of
mechanical agents, the first
object is always to remove
as much as possible all
sources by which the moving power is absorbed upon useless
objects. In the present case the only useful exertion of the
moving force is that which is engaged in raising the water.
The useless parts of the force expended, are, first, that
absorbed by the weight of the bucket ; secondly, that absorbed
by the weight of the rope ; thirdly, that absorbed in bending
the rope over the groove of the pulley, or the curvature of the
axle ; fourthly, that which is expended on the friction of the
axle in its bearings ; fifthly, that which is expended in drawing
the bucket aside when it has been elevated, and discharging
the water from it into the vessel or reservoir destined to receive
it ; and, sixthly, that which is expended in letting down the
bucket into the well to be refilled.

Now when all these sources of waste of power are considered
and estimated, and their aggregate amount determined, it will be
apparent that they greatly exceed the
force expended upon the mere elevation
of the water.

4. A part of the loss of power arising
from these causes is sometimes removed
by the simple expedient of attaching two
buckets to the extremities of the rope
which passes over the pulley (fig. 3)
established above the well. By these
means, while the full bucket is drawn up
the empty one descends, and by its weight
and that of the rope which descends with
it, the weight of the full bucket and the
rope which ascends with it is balanced, so
that the power has only to act against the .
weight of the water, the friction and the
resistance to flexure presented by the rope.

N 2 179

COMMON THINGS — PUMPS.

o. Animal power may be applied to this method of raising
[ water by such an arrangement as is represented in fig. 4. This is

Fi<r. 4.

the method generally used in France by the market gardeners, in
the environs of large towns, to raise water for irrigation. Two
pulleys are established side by side, over the well, at such a dis-
tance asunder that two buckets or barrels suspended from them
may pass each other as one ascends and the other descends, with-
out mutual collision or obstruction. The rope supporting one
bucket, after passing over one of these pulleys, is carried two or
three times round a large vertical drum erected near the well,
and then passing over the other pulley is let down into the well
with the other bucket attached to it.

The semicircular handles to which the rope is attached, are con-
nected with the barrels, not at the edge of the mouth, but at two
points in their sides, a little above their middle point, so that when
filled they will maintain themselves steadily in the vertical position,
but when empty they will easily be turned upon their sides by mere
contact with the surface of the water so as to fill themselves, when
let down empty.

A horse or ox yoked to a lever of considerable length, projecting
from the vertical shaft, turns it, and with it the drum, and con-
tinues to go round in the same direction, until one barrel is raised to
the mouth of the well and the other is plunged in the water below
and filled, the contents of this barrel being discharged into a reser-
voir or vessel destined to receive it. The animal is then yoked
in the other direction, and again travels round until the other
barrel is raised, and that which was just discharged let down.

6. It is evident that in this and all similar arrangements the
weight of the rope on the whole balances itself ; for although it
preponderates against the power when the full barrel begins to
180

LIFTING PUMP.

Fig. 5.

ascend, the ascending part of the rope being then longer than the
descending, this preponderance gradually decreases until the
ascending meets the descending barrel. At this point, the ascend-
ing and descending parts of the rope being equal, balance each
other, and after this the descending part, preponderating, aids the
power just as much as the ascending part previously opposed it.
There is, therefore, so far as relates to the weight of the rope, a
perfect compensation.

The same apparatus is much used in France, in raising stone
through vertical shafts from subterranean quarries, and other
mining operations.

7. If, instead of a rope and bucket, a pipe or tube be let down
into the well, and in this pipe a piston be provided, having a valve
in it opening upwards, this piston being worked in the usual
manner upwards and downwards, the water would be lifted in the
pipe. Such an apparatus is called a lifting-pump, and is repre-
sented in fig. 5 : w is the water, c d the piston, u the valve in it
which opens upwards. When the piston is moved downwards,
this valve opens, and the water passes

through it. When the piston is moved
upwards, the column of water is pushed
up, and the valve is kept closed by the
pressure of the water upon it. A valve
x is placed at c D in a fixed position,
through which the column of water
passes when the piston rises, and which
prevents the return of such water down-
wards, the valve being kept closed by
the weight of the water above it. The
column of water driven upwards by the
piston is pushed to any required height,
through the pipe E r. In such an ap-
paratus, the moving power must be equal
to the weight of the water raised,
together with the weight of the pump-rod
and frame by which the piston is worked,
as well as the friction of the moving
parts.

8. A very ingenious form of pump which, though differing
altogether in appearance from the lifting pump, acts nevertheless
upon precisely the same principle, is shown in fig. 6. It has the
advantage of being nearly free from friction, and of being capable
of being worked by the weight of an animal walking up an inclined
plane, which is the most advantageous manner in which animal
power can be applied.

181

COMMON THINGS — PUMPS.

Let D c be a wooden tube of any shape, round or square,
which descends to a depth in the well or reservoir equal to the
F. height above the surface of the reservoir to which

the water is required to be raised. Thus if D o be
the height to which the water is to be raised above
the level of the well, then the depth o c must be at
least equal to D o. L M is a heavy beam Or plunger,
suspended from a chain, and capable of descending
by its own weight in water, and passing water-
tight through the collar F E. A valve, v, covers an
opening placed at the bottom of the tube. By the
hydrostatic pressure the water will enter the valve v,
and fill the barrel to the level o G of the water
in the cistern. G I is a short tube proceeding from
the side of the barrel,v at the surface of the water,
and communicating with the vertical tube EN by a
valve I, which opens upwards. K is the spout of
discharge. The plunger L M hangs loosely in the tube,
so that it moves upwards and downwards perfectly free
from friction, except that of the collar F E, where it is
properly lubricated. "When this plunger is allowed to
descend by its weight into the water which fills the
lower part of the tube, the valve v is closed, and the
water displaced by the plunger is forced through the
valve i into the tube E JST. When the plunger is raised
the valve I is closed, and the water thus forced into
the tube E x cannot return. The water from the
cistern then flows through the valve r, and rises in the tube to the
level G. The next descent of the piston propels more water into the
tube E x, and this is continued so long as the piston is worked.

The manner in which such an apparatus is worked by the weight
of a man, or any animal, is represented in fig. 7, p. 183. Two
pumps are used, such as that just described, and when the plunger
descends in one it rises in the other. The two pumps communicate
with one vertical pipe, which therefore receives a continual, supply
of water ; for while the action of one pump is suspended the other
is in progress. A man walks from one end of an inclined piano
to the other, and by his weight upon one side or the other of the
fulcrum causes the plungers alternately to rise and fall.

9. Valves are of such constant use in all forms of pump, that it
will be useful here briefly to explain their principal varieties.

A valve in general is a contrivance by which water or other

fluid flowing through a tube or aperture is allowed free passage

in one direction, but is stopped in the other. Its structure

is such, that while the pressure of the fluid on one side has a

182

VALVES.

tendency to close it, the pressure on the other side Jias a tendency
to open it.

As in all forms of pump the water is required to be moved upwards,
all the valves necessarily open upwards and close downwards.

Fig. 7.

There are several varieties of form.

10. The clack valve is like the lid of a box (fig. 8).
upwards, playing upon a hinge, and when
the water presses it downwards it is closed.

The single clack valve is the most simple
example of the class. It is usually constructed
by attaching to a plate of metal larger
than the aperture which the valve is intended to stop, a piece
of leather, and to the under side of this leather another piece of
metal smaller than the aperture. The leather extending on one
side beyond the larger metallic plate, and being flexible, forms
the hinge on which the valve plays. Such a valve is usually
closed by its own weight, and opened by the pressure of the fluid
which passes through it. It is also held closed more firmly by
the pressure of the fluid whose return it is intended to obstruct.

The extent to which such a valve should be capable of -pig. 9.
opening, ought to be such that the aperture produced by
it shall be equal to the aperture which it stops. This will
be effected if the angle through which it rises be about 30°.
A double clack consists of two semicircular plates,
having the hinges on the diameters of the semi-
oircles, as represented in fig. 9.

183

COMMON THINGS — PUMPS.

Of the valves which are opened by a motion perpendicular tx>
their seat, the most simple is a flat metallic plate, made larger
than the orifice which it is intended to stop, and ground so as to
rest in water-tight contact with the surface surrounding the
aperture. Such a valve is usually guided in its perpendicular
motion by a spindle passing through its centre, and sliding in holes
made in cross bars extending above and below the seat of the
valve.

11. The conical valves, usually called spindle-valves (fig.
10), are the most common of this class. The best angle to

Fig. 10. ke given to the conical seat is found in

practice to be 45°. With a less inclination
the valve has a tendency to be fastened in
its seat, and a greater inclination would,
cause the top of the valve to occupy unne-
cessary space in the valve-box. The area, or transverse sectioc
of the valve-box, should be rather more than double the magni-
tude of the upper surface of the valve, and the play of the valve
should be such as to allow it to rise from its seat to a height not
less than one-fourth of the diameter of its upper surface.

12. The valves coming under this class are sometimes formed as

spheres or hemispheres (fig. 11) resting in a
conical seat, and in such cases they are
generally closed by their own weight, and
opened by the pressure of the fluid which passes
through them.

13. The several expedients already described
'are, however, greatly surpassed in convenience
by the form of pump almost universally used
in domestic and general economy, and known as
the sucking or suction pump.

A section of this useful apparatus is shown in fig. 12, p. 169.
It consists of a pipe or barrel, s o, which descends into the
well, and the length of which must not exceed 32 feet. Attached
to the top of this pipe, which is called the suction-pipe, is a large
syringe, acting precisely on the principle of a common exhausting
syringe.

At the commencement of the operation, the pipe s E is filled with
air to the level of the water in the well. The operation of the
syringe draws the chief part of the air out of this pipe s E. When
the water within the pipe is partially relieved from the atmospheric
pressure, the weight of the atmosphere, acting upon the external
surface of the water in the well, forces it up in the pipe s E ; and
according as the air is withdrawn by the syringe, the water con-
tinues to rise, until it passes through the valve x. This valve
184

SUCTION PUMP.

Fig. 12.

opening upwards, prevents its return, since the weight of the column

above it will keep it closed. When the barrel A c becomes filled

with water, the syringe no longer acts as

such, but works on the principle of the

lifting pump, already explained. When

the piston descends, the valve x is closed

and the valve v opened, the water passing

through the piston. When the piston is

raised, the valve v is closed, and the column

of water above the piston is projected

upwards.

Meanwhile the pressure of the atmo-
sphere on the water in the well causes more
water to rise in the pump-barrel following
the piston.

The atmospheric pressure is capable of
supporting a column of about 34 feet of
water.* It is evident, therefore, that such a
pump as is here described can only be efficient
when the piston is at a height of less than
34 feet above the surface of the water in
the well, since otherwise the atmospheric
pressure would not keep the water in
contact with the piston.

The suction-pump, therefore, as com-
pared with the lifting-pump, saves 34 feet
length of pump rod ; but otherwise there
is no comparative mechanical advantage.

It might appear at first view that the pressure of the atmosphere
sustaining a column of water in the suction-pipe, supplies aid to
the power that works the pump, and spares an equivalent amount
of that power.

This, however, is not the case, as will appear from a due
consideration of all the forces which are in operation.

14. Of these forces there are some which are directed down-
wards from the top of the column raised by the piston towards the
bottom of the well, and others which are directed upwards. Now
it is evident that the mechanical power applied to draw the piston
up will have to overcome all that excess by which the forces
downwards exceed the forces upwards. Let us suppose a column
of water resting on the piston, after having passed through
the valve v. The upper surface of this column is pressed upon by
the weight of the atmosphere ; the piston has, therefore, this

See Tract on Barometer (10).

155

COMMON THINGS — PUMPS.

weight to sustain. It lias also to sustain the weight of the water
which is above it. The atmospheric pressure acting also on the water
in the well, is transmitted by the water to the bottom of the piston;
but this effect is diminished by the weight of the column of water
between the surface of the water in the well and the bottom of the
piston, for the atmospheric pressure must, in the first place,
sustain that column, and can only act upon the bottom of the;
piston in the upward direction with that amount of force by which,
it exceeds the weight of the column of water between the piston
and the well. The effect, therefore, on the piston is the same as
if it were pressed downwards by the weight of the column of
water between the piston and the well, and at the same time
pressed upwards by the atmospheric pressure. Thus the piston
may, in fact, be regarded as being urged downwards by the
following forces, — the atmospheric pressure, the weight of the
water above the piston, and the weight of the water between the
piston and the well ; that is to say, in fact, by the atmospheric
pressure, together with the weight of all the water which has been
raised from the well. At the same time, it is pressed upwards by
the atmospheric pressure transmitted from the surface of the water
in the well. This upward pressure will destroy the effect of the
same atmospheric pressure acting downwards on the surface of
the water above the piston, and the effective downward force will
be the weight of all the water which is contained in the pump.

By this reasoning, it appears that the pump must be worked
with as much force as is equal to the weight of 'all the water
which is in it at any time, and, therefore, that the atmospheric
pressure affords no aid to the working power.

Since the action of the pump in raising water is subject to inter-
mission, the stream discharged from the spout will necessarily flow
by fits and irregularly, if some means be not adopted to prevent this.
At the top of the pump a cistern may be constructed, as shown in
£g. 12, with a view to remove this inconvenience. If the pump be
worked, in the first instance, so as to raise more water in a given
time than is discharged at the spout, the column of water will
necessarily accumulate in the barrel of the pump above the spout.
The cistern Ji N will, therefore, be filled, and this will continue
until the elevation of the surface of the water in the cistern above
the spout will produce such a pressure, that the velocity of
•discharge from the spout will be equal to the velocity with which
the water is raised by the piston. The level of the water in the
cistern will therefore cease to rise. This level, however, will be
-subject to a small variation as the piston rises; for while the
piston is descending, the water is flowing from the spout, and no
water is raised by the piston, consequently the level of the water
186

COMMON HOUSE PUMP.

in the cistern falls. When the piston rises, water is raised, and
the quantity in the cistern is increased faster than it flows from
the spout, consequently the level of the water in the cistern rises,
and thus this level alternately rises and falls with the piston.
But if the magnitude of the cistern be much greater than the
section of the pump-barrel, then this variation in the surface will
be proportionally small, for the quantity of water which fills a
part of the barrel, equal to the play of the piston, will produce
a very slight change in the surface of the water in the cistern.
The flow, therefore, from the spout will be uniform, or nearly so.
The action of this sort of pump will be rendered still more easily
intelligible by fig. 13, which represents the working model of a

Fig. 13.

suction-pump usually provided for demonstrations in popular
lectures. The pump-handle H H' raises and lowers the piston
rod a. The pump-barrel is formed of glass, so as to show the

187

COMMON THINGS— PUMPS.

Fig. 14.

II

piston within it, having a valve opening upwards. The other
parts of the apparatus are marked with letters corresponding with
those of fig. 12.

15. Another form of pump, called the forcing-pump, is attended
with many advantages, and is extensively used. This instrument

is represented in fig. 14. The suction-
pipe c E is similar to the suction-pump.
The piston c d is a solid plug without
a valve.

The forcing-pipe G n has at its base
e f a valve v' which opens upwards.
When the piston c d is raised, the valve
v is opened, and the water rises from
the suction-pipe into the pump-barrel.
When the piston c d is pressed down-
wards, the valve v is closed, and the
water is forced by the pressure of the
piston through the valve v' into the force-
pipe, and thus while the operation is
continued, at each upward motion of the
piston, water is drawn from the suction-
pipe into the pump-barrel, and at each
downward motion it is forced from the pump-barrel into the force-
pipe.

16. In order to produce a continued flow of water in the force-
pipe, an air-vessel is often attached to force-pumps. Such an ap-
pendage is represented in fig. 15.

When the piston descends, the water
is driven through the valve V into the
vessel which is closed and contains air.
The force-pipe G H descends into this vessel,
and terminates near the bottom. The
water which is forced in rises in it to a
certain level, w w'} the air above it being
compressed. The return of the water
through the valve v' being stopped, it is
subject to the elastic pressure of the air
confined in the air-vessel M ]ST. This pres-
sure forces the water through the tube n G
from the top of which it issues in a con-
stant stream.

The forcing-pump with its air-vessel, as constructed for demon-
stration at popular lectures, is shown in fig. 16, p. 189, where all
the parts are indicated by the same letters as in figs. 14 and 15.
The water which flows in a continual stream from the force-
188

FORCING PUMP.

pipe G returns by the pipe P to the reservoir K, from which it is
again raised by the pump.

Fig. 1C.
H'

17. In the force-pump, where the water acts upon the piston
with a great pressure, it is very important that the piston should
move in complete water-tight contact with the pump-barrel. This
is best accomplished by an accurately formed metallic plunger, P,
fig. 17, working through a collar of leather, A B, which is exactly
fitted to it, and with which it is made air-tight and water-tight,
by behig lubricated with oil or tallow. When this plunger is raised,
the space it deserts is filled by the water which rises through the
valve v, and when it descends, the water which filled the space
into which it advances, is driven before it through the valve v
into the force-pipe.

18. If the forcing-pump, represented in fig. 16, be attentively
considered, it will be perceived that the principles on which the
piston acts, in its ascent and descent, are perfectly distinct. In

189

COMMON THINGS — PUMPS.

its ascent it is employed in drawing the water from the suction-
pipe into the pump-barrel, and in its descent it is employed in
forcing that water from the pump- barrel
into the force-pipe. Now the piston being1
solid, and not furnished with any valve,
there is no reason why its upper surface
should not be employed in raising or pro-
pelling water as well as the lower. While
the lower surface is employed in drawing
water from the suction-pipe, the upper
surface might be employed in propelling
water into the force-pipe ; and, on the
other hand, in the descent of the piston,
when the lower surface is employed in.
propelling water into the force-pipe, the
upper surface might be engaged in draw-
ing water from the suction-pipe. To
accomplish this, it is only necessary that
the top of the cylinder should be closed,
and that the piston-rod should play
through an air-tight collar, the top of

the cylinder communicating with the force-pipe and the suction-
pipe, as well as the bottom.

Such an arrangement is represented in fig. 18. "When the
piston ascends, the suction-valve F is opened, and water is drawn
into the pump-barrel below the piston;
and when the piston descends, the suction-
valve F is closed, and the pressure of the
piston on the water below it opens the
valve c, and propels the water into the
force-pipe c G. Also, while the piston is
descending, water rises through the suc-
tion-valve E into the barrel above the
piston ; and when the piston ascends, the
water being pressed upwards keeps the
valve E closed, and opens the valve D, and
is thus propelled into the force-pipe. By
this arrangement the force-pipe receives a
continual supply of water from the pump-
barrel without any intermission; and in
like manner the pump-barrel receives an
unremitting flow from the suction-pipe.
This will be distinctly seen, if it is con-
sidered that either of the two valves E
or r must always be open. If the piston go down E is open and F
190

Fig. IS.

FIRE-ENGINE — CHAIN PUMP.

closed ; if it go up E is closed and F open. A stream, therefore,
continually flows through one valve or the other into the pump-
barrel. In like manner, whether the piston ascend or descend,
one of the valves, c or D, must be open.

19. The simple pumps used for watering gardens are shown in
fig. 19, at the head of this tract, a single or double-action force-
pump projecting a jet of water over the ground to be irrigated.

20. The fire-engine is a double forcing-pump, each barrel of
which acts upon the principle explained above.

A section of such an engine, in its most usual form, is represented
in fig. 20.

The solid pistons a a are alternately forced down upon the water
which has been drawn into the barrels upon the principles already
explained, and the water is thus forced into the air vessel e. The-
reaction of the compressed air drives the water with a proportion-
ate force through the force-pipe d into a long, flexible, leathern
hose, upon the end of which a large jet-pipe is screwed. The
firemen carry this jet-pipe near to or into the building on fire,
and with it throw up to great heights a constant stream of water,
which, falling on the burning bodies, extinguishes the fire.

Fig. 20.

21. A form of lifting-pump, called the chain-pump, is commonly
used to discharge the water from the hold of ships of war and
other vessels of the large class. This pump consists of an endless
chain which passes over two rollers, one of which is established on
the deck, above the level at which the water is to be discharged,
and the other at the bottom of the hold. Attached to the chain,
and placed at right angles with it, are a series of saucers, or'a sort

191

COMMON THIXGS — PUMPS.

of flat circular plates, one above the other, by which the water is
lifted. These saucers lift the water and press it up through a
vertical pipe placed near the ascending side of the chain. The
water, rising through this pipe, is discharged into a cistern on the
deck, from which it flows off into the sea through a waste pipe
called the pump-dale.

There are two hollow vertical barrels, or cases, through one of
which the chain ascends, and through the other it descends. The
chain is worked by means of a winch attached to the upper roller,
over which it passes. This winch receives a continual motion of
rotation, by the power of men applied to its handles, which are
so formed that several men can work them simultaneously.

In large vessels these pumps are constructed upon a scale suffi-
cient to enable them to raise a ton of water, or about 250 gallons
per minute.

22. The purpose to which pumps are applied on the most vast
scale is in the drainage of mines. In that case the power required
far exceeds the limit to which animal power is practically available,
and even steam-power, by which such pumps are worked, requires
to be applied on a scale far exceeding every other form in which
it has been applied in the industrial arts.

192

COMMON THINGS.

SPECTACLES.

1. Their general utility. — 2. Should therefore be generally understood. —
3. Vision. — 4. Blindness. — 5. Defective sight. — 6. Long and short
sight. — 7. Remedy. — 8. Spectacles. — 9. Effect of convex lenses. —
10. Of concave lenses. — 11. Focal length of a lens. — 12. Varies with
distance of object. — 13. Peculiarities of vision in short sight explained.
— 14. In long sight. — 15. The mounting of spectacles. — 16. Periscopic
spectacles. — 17. Both eyes have not always the same power of vision.
— 18. Ophthalmometer. — 19. Application of it in selecting glasses. —
20. Curious defects of vision.

1. SPECTACLES are incontestably the most universally useful gift
which, optical science has conferred on mankind. More wonderful
instruments abound. The miracles disclosed to human vision by
the telescope and the microscope are known to all. To such
marvels, spectacles lay no claim. But to compensate for this
LARDNER'S MUSEUM OF SCIENCE. o 193

No. 65.

COMMON THINGS— SPECTACLES.

their utility is ubiquitous. In the palace of the monarch and in
the cottage of the peasant their beneficent influence is equally
diffused. It is remarkable also, that, unlike most other produc-
tions of art and science, cost can add nothing to their perfection.
Those of the millionaire may be mounted in gold, and those of the
humble labourer in iron ; but the optical medium, the glass lenses
to which they owe their perfection, must be the same.

2. It is good that an object of such unbounded usefulness
should be generally understood. The more completely and
clearly the principles on which the application of the instru-
ment depends are comprehended, the greater will be the extent
of the benefit which each individual will derive from them, and the
less frequent will be the inconveniences and evils resulting from
their abuse.

Before it is possible, however, to comprehend the principle and
the right use of spectacles, it is indispensably necessary to be
acquainted with the structure and functions of the eyes, and such
readers as have not already obtained that preliminary knowledge
are referred for it to our tract on that subject.

The defects incidental to the sense of sight have been briefly
noticed in that tract, and the optical expedients by which
remedies have been obtained for them have been stated. We
propose here to resume that subject, and to present other and
more developed illustrations of it.

3. When an object is placed at a certain distance from the eye,
a small picture or image, as it is called, of the object is produced
upon the posterior surface of the coating which lines the inside of
the spherical shell, called the eye-ball. This coating, upon which
the picture is thus formed, is called the retina.

It is this picture on the retina which enables us to see the object.
If this picture be obscure, falsely coloured, confused, or indistinct,
our vision of the object will also be obscure, falsely coloured, con-
fused, or indistinct.

In its natural and healthy state the structure of the eye is such
that the pictures of all objects presented to it thus formed upon
the retina, are clear, rightly coloured, and perfectly distinct in
form and outline. In individual cases, however, eyes are vari -
ously defective.

4. If the coats and humours, through which the rays of light,
proceeding from external objects ought to pass, be not in any
degree transparent, no picture whatever is formed on the retina,
and the subject is blind.

5. If the coats and humours are imperfectly transparent the
picture will be obscure, being formed only by the rays of light
partially transmitted through the humours.

194

SHORT SIGHT — WEAK SIGHT.

It sometimes happens that the humours, like coloured glass or
coloured liquids, transmit only light of a particular colour. In
that case the image on the retina is falsely coloured, the false
colours depending on the colour of the humours.

For these several classes of defects spectacles are wholly ineffi-
cacious.

6. When the humours are perfectly transparent and free from
colour, the picture which they would produce may fall not imme-
diately upon the retina, hut at a distance more or less considerable
before or behind it. In that case the effect produced upon the
retina will be a picture more or less confused and indistinct. It
will be so much the more indistinct as the place where the dis-
tinct picture would be formed is more distant from the retina.

If the place of the distinct picture be before the retina, the
defect is owing to the eye having too great refracting power upon
the rays of light. If it be behind the retina, it is owing to the
refracting power being too feeble.

The former is called SHOKT SIGHT, and the latter LONG SIGHT,

Or WEAK SIGHT.

7. For these defects of vision, which are by far the most
common, spectacles supply a perfect remedy.

They accomplish this by the effect they are capable of producing
upon the place of the picture. If the eyes be weak-sighted, and
consequently the picture is formed behind the retina, spectacles
are applied which have the effect of bringing forward the picture
to the retina. If they be short-sighted, so that the picture is
formed before the retina, spectacles are applied which have the
effect of throwing it back to the retina.

8. Spectacles consist of circular discs of glass called lenses,
the surfaces of which are brought by grinding and polishing to a
convex or concave form.

9. If a convex lens of this kind be placed before the eye, it will
have the effect of bringing forward the picture formed within the
eye. A concave lens, placed in the same manner, will have the
contrary effect of throwing it backward.

It will be easy for any person to convince themselves that such
glasses have the properties here described.

Let a convex disc of glass or lens, G G, fig. 1, be placed before a
candle, c, and let a white paper screen be placed behind G G, and
moved towards and from it until a position is found, such as s s,
in which a distinct inverted picture of the candle will be seen
upon it. If the screen^be now moved to s' s', a little nearer to G G,
so that the place of the distinct picture shall be behind it, an
indistinct picture of the candle will be seen upon the screen.

In' this case the lens G G may be imagined to represent the eye of
o2 195

COMMON THINGS SPECTACLES.

a weak-sighted person, the candle c a visible object, and the
screen s's'the retina, upon which an indistinct image of the object

G'

(V

S'

5'

-

s depicted, and s s the place behind the retina, at which the
picture would be distinct.

Now if another convex lens, G'G', which may represent
a spectacle glass, be placed before G G, it will have the effect of
bringing forward the place of the distinct image, and it will bring
that place more or less forward according as G' G' is more or less
convex. It is easy to conceive that its convexity may be such
that the image of the candle will be brought exactly to the position
of the screen s' s'.

Thus it appears, that if the screen be misplaced, with relation
to the distinct picture of the candle, so as to be before it, a glass
G' G' of suitable convexity, placed before G G, will bring the dis-
tinct picture forward to the position of the screen, upon which it
will then be seen.

This is a simple experiment which any one can try with a
candle, a sheet of paper, and two spectacle glasses.

It perfectly represents the case of a weak-sighted person, and
the benefit they derive from convex spectacle glasses.

If, however, the lens G' G' be too convex, the picture will be
brought too much forward, and it will be formed not on the screoii
s' s', but before it, and will consequently be indistinct. If, on the
contrary, the lens G' G' be not sufficiently convex, the picture will
not be brought so forward as the screen s' s', and will still be
indistinct upon it.

Thus, between the relative positions of the distinct picture of
the candle, that of the screen s' s', and the convexity of the lens
196

CONVEX AND CONCAVE GLASSES.

G' G', there is a certain relation, such that only one particular
degree of convexity will bring the distinct picture upon the
screen.

In the same manner, it follows that between the relative
positions of the retina, of the distinct picture formed behind it,
and the convexity of the spectacle glasses, there is a certain
fixed relation, such that such glasses only as have a particular
convexity will bring the distinct picture on the retina, and pro-
duce clear and distinct vision.

10. Let us suppose now that the screen is placed as at s's',
fig. 2, behind the position at which the distinct picture of the
candle is formed. In this case it is required to throw the

G'

distinct picture backwards, and as it was brought forwards by
the interposition of a convex glass, it will be thrown backwards
by the interposition of a concave glass. Such a lens, G'G',
having the proper degree of concavity, being therefore placed
before G G, the distinct image will be seen upon the screen s' s'.

As in the former case, there is a certain relation between the
relative positions of the distinct picture of the candle, of the
screen s' s', and the concavity of the lens G' G', so that only one
particular degree of concavity will throw back the distinct picture
to the screen.

As in the former case, this experiment illustrates the case of a
short-sighted eye, and the remedy aflixed by the interposition of
a concave glass. The lens G G represents the eye, s' s', the retina,
and s s the place before it where the distinct picture is formed

197

COMMON THINGS — SPECTACLES.

when no glass is used. When G'G' is interposed between tho
object and the eye, the distinct image is thrown back to s' s', the
place of the retina.

11. The place at which the distinct image of a distant object is
formed by a lens, or by any other optical medium equivalent to a
lens, is called the FOCUS of the lens, and the distance of the focus
from the lens is called the FOCAL LENGTH of the lens.

When the structure of the eye is perfect, therefore, its focus
must be on the retina, and its focal length will be the interior
diameter of the eye-ball. When the focal length of the eye is
greater than this the focus is behind the retina, and the eye
is weak-sighted or long-sighted. When the focal length is less,
the focus is before the retina, and the eye is short-sighted.

12. If an object, a candle for example, placed before a convex
lens, be moved towards the lens, the place at which its distinct
picture is formed, that is its focus, will move from the lens,
so that the nearer the object is to the lens the further will its
picture be from it. It is easy to verify this by means of the
candle, the lens, and the screen. As the candle is moved nearer
and nearer to the lens, the place at which the screen will receive
a distinct picture of the flame will be farther and farther from the
lens, and in the same manner if the candle, being placed very
near the lens, be gradually removed farther and farther from it,
the place at which the screen will receive a distinct picture will
be nearer and nearer to the lens.

This will explain some circumstances attending the vision of
near-sighted and weak-sighted persons, which are familiar to
every one.

13. When a near-sighted person looks at a distant object, its
focus is within the eye-ball, before the retina, on which, conse-
quently, the picture is indistinct. But if the object be brought
gradually nearer and nearer to the eye, its distinct picture will
move more and more backward, according to what has been just
shown, and it will consequently approach nearer and nearer to the
retina, until at length the object is brought so near the eye, that
the distinct picture exactly falls upon the retina. The vision is
then perfect.

It will thus be understood why near-sighted persons can see
objects distinctly, only when they are brought within a certain
distance of the eye. The more removed the focus of their eye is
from the posterior part, the nearer an object must be brought
before the picture is thrown back to the retina, and the person is
said to be so much the more near-sighted.

Concave spectacle- glasses, in this case, have the same effect in

throwing back the picture as the proximity of the object, and with

198

EFFECTS OF SHORT AND LONG SIGHT.

such, spectacles the object can consequently be seen distinctly
without being brought near to the eyes. If, when the spectacles
are interposed, the object be brought as near the eyes as would be
necessary for distinct vision without spectacles, the vision will be
indistinct ; because, in that case, the effect of the glasses will be
to throw the distinct picture behind the retina, which, without
the glasses, would have been upon it.

When persons are not very short-sighted, they generally read
or work without spectacles, but require their aid when they walk
abroad or move in society in large rooms, because the book or the
objects of their work can, without inconvenience, be placed at the
moderate distance from their eyes which is sufficient to throw the
focus back upon the retina, but the more distant objects at which
they look when walking abroad or in large rooms are beyond the
proper limit of distance, and the focus, being before the retina,
must be thrown back by concave spectacles.

14. When an object is placed near the eyes of a weak-sighted
person, the focus is behind the retina, and the picture on the retina
is consequently indistinct. If the object be gradually removed
to a greater and greater distance, the focus, according to what
has been explained, will approach the retina nearer and nearer,
and, if the sight be not too weak, it will come upon the retina
when the object is removed to a certain distance from the eye.
In this case, however, owing to the greater distance of the object,
stronger illumination is required, and it is found, accordingly,
that when weak-sighted persons hold a book at arms-length from
the eyes, they are obliged, at the same time, to place a strong
light near the page.

Eyes, which are not of very weak sight, have sufficient power to
bring the picture of all objects, whose distance exceeds three or
four feet, upon the retina. But for nearer objects, the picture,
being behind the retina, requires to be brought forward by the
interposition of convex spectacles. The nearer the object looked
at is, the more convex ought the glasses to be, and hence it comes
that very weak-sighted persons require to be provided with more
than one pair of spectacles, those adapted to more distant objects
being less convex, and those adapted to nearer objects more so.

When the weakness of sight is so limited that the pictures of
distant objects fall upon the retina, those only of nearer ones
being behind it, the eye is said to be FAB-SIGHTED, in contra-
distinction to the opposite defect, by which distinct vision is only
obtained by the closer proximity of the object.

15. Spectacles consist of two glass lenses mounted in a frame so
as to be conveniently supported before the eyes, and to remedy
the defects of vision of naturally imperfect eyes.

199

COMMON THINGS — SPECTACLES.

Whatever be the defects of sight which they may he used to
remove, it is evident that the lenses ought to be so mounted that
their axes shall be parallel, and that their centres shall coincide
with the centres of the pupils when the optical axes are directed
perpendicular to the general plane of the face, that is to say, when
the eyes look straight forward.

These conditions, though important, are rarely attended to in.
the choice of spectacles. If spectacles be mounted in extremely
light and flexible frames, the lenses almost invariably lose their
parallelism, and their axes not only cease to be parallel, but are
frequently in different planes. Spectacles ought therefore to be
constructed with mounting sufficiently strong to prevent this
derangement of the axes of the lenses, and in their original
construction care should be taken that the axes of the lenses be
truly parallel.

In the adaptation of spectacles it is necessary that the distance
between the centres of the lenses should be precisely equal to the
distance between the centres of the pupils. The clearest vision
being obtained by looking through the centres of the lenses, the
eyes have a constant tendency to look in that direction. Now if
the distance between the centres of the lenses be greater than the
distance between the centres of the pupils, the eyes having a ten-
dency to look through the centres of the lenses, their axes will
cease to be parallel, and will diverge as in the case of an outsquint.
On the other hand, if the distance between the centres of the
lenses be less than the distance between the centres of the
pupils, there will, for a like reason, be a tendency to produce
an insquint.

I have myself known persons of defective sight, who had never
been able to suit themselves with spectacles, and concluded that
they had some defect which spectacles could not remedy. Upon
observing the form of their heads, I found, in each case, that the
eyes were more distant asunder than eyes generally are, while
the spectacles they used, being those made with the lenses at the
usual distance, were never, and never could be, so placed as to be
concentrical with the eyes, and hence arose the discomfort attend-
ing their use. In all such cases I removed the inconvenience by
measuring the distance between the centres of the eyes, and caus-
ing proper glasses to be mounted in frames, so that the distance
between their centres should correspond with the distance between
the centres of the eyes.

I would therefore advise every one who uses spectacles to cause
the distance between the centres of their eyes to be exactly mea-
sured, and to select for their spectacles mountings corresponding
with this distance.
200

PERISCOPIC SPECTACLES.

16. The most perfect vision with spectacles is produced when
the eye looks in the direction of the axis of the lenses, and more
or less imperfection always attends oblique vision through them.
Persons who use spectacles, therefore, generally turn the head,
when those whose sight does not require such aid merely turn the
eye.

To diminish this inconvenience, the late Dr. "Wollaston sug-
gested the use of menisci, or concavo-convex lenses, instead of
double concave or double convex lenses with equal radii, which
up to that time had been invariably used.

Sections of lenses of this kind are given in figs. 3 and 4. In fig.
3, the convexity A' B' c', of which the centre is o', is greater than

Fig. 3.

the concavity ABC, of which the centre is o, and the effect of the
lens is the same as that of a convex lens. Such glasses are there-
fore adapted for weak sight. In fig. 4, on the contrary, the con-
cavity A B c, of which the centre is o, is greater than the convexity

Fig. 4.

C'

A' B' c', of which the centre is o', and the effect of the lens is the
same as that of a concave glass. Such glasses are therefore
adapted to short sight.

The effect of these, as compared with double convex and double
concave glasses, is, that objects seen obliquely through them are
less distorted and, consequently, that there is a greater freedom
of vision by turning the eye without turning the head, from which
property they were named periscopic spectacles.

17. In the selection and adaptation of spectacles, it is invariably
assumed without question, that the two eyes in the same indi-

201

COMMON THINGS — SPECTACLES.

vidual have exactly the same refracting power. That this is the
case is evident, from the fact that the lenses provided in the same
spectacles have invariably the same focal length.

Now although it is generally true that the two eyes in the
same individual have the same refractive power, it is not invari-
ably so ; and if it be not, it is evident that lenses of equal focal
length cannot be at once adapted to both eyes.

"When the difference of the refractive power of the two eyes i»
not great (which is generally the case when a difference exists
at all), this inequality is not perceived. By an instinctive act of
the mind, of which we are unconscious, the perception obtained by
the more perfect of the two eyes in case of inequality is that to
which our attention is directed, the impression on the more defec-
tive eye not being perceived.

It might be expected, however, that the inequality woulc.
become apparent, by looking alternately at the same object with
each of the eyes, closing the other ; but it is so difficult to compare
the powers of vision of the two eyes when they are not very
unequal, by objects contemplated at different times, even though
they should be exhibited in immediate succession, that this
method fails.

18. My attention having been directed to this question, I
contrived an apparatus, which may not inaptly be called an
Ophthalmometcr, by which the least difference in the powers of
vision of the two eyes may be rendered immediately apparent.

The principle I adopted for this purpose, resembles that which
has been otherwise applied with success in photometers. I have so
arranged the apparatus, that two similar objects similarly illumi-
nated shall be at the same time visible in immediate juxtaposition,
the one by the right eye being invisible to the left eye, and the
other by the left eye being invisible to the right eye.

This apparatus consists of a small box, A B c D, fig. 5, about
five inches in width, A D, ten inches in length, A B, and six inches
in height. "Within this there slides another box, A' B' c' D', made
nearly to fit it, but to move freely within it, the interior of this
box being blackened, or lined with black velvet. In the end, B' c',
is a rectangular aperture, the length of which M N is about an
inch, and the height about half an inch ; the length, however,
being capable of being augmented and diminished by slides.
Opposite to the end of the box B c is a white screen, on which is
traced a horizontal line parallel and opposite to the opening M N,
and marked with a divided scale, the 0 of which is opposite to the
centre of the aperture M x, and the divisions upon which are
numbered in each direction from 0 by 1, 2, 3, 4, 5, 6

Let us suppose the eyes now applied at B. and L. Let the
202

EYES USUALLY UNEQUAL.

sliding interior box B' c' be moved until, on closing the left eye,
the division 0 of the scale coincides with the edge M of the open-
Fig. 5.

ing, and at the same time, by closing the right eye, the same
division 0 of the scale coincides with the edge N of the opening.
It will be always possible to make this adjustment, provided the
eyes are placed centrally opposite the opening M N, which may be
easily managed by cutting in the edge of the box A D an opening
to receive the bridge of the nose. This arrangement being made,
it is clear that if we close the left eye we shall see the space
upon the scale included by the lines E, N and E if continued
to the screen R' if. Let us suppose this space to include the six
divisions of the scale from 0 to 6. If we close the right eye,
we shall see with the left eye the six divisions' of the scale to
the right of 0. Now if we open both eyes and look steadily with
them through the aperture M N, giving no more attention to the
impression on the one than on the other, we shall see the twelve
divisions of the scale, six to the right and six to the left of 0 ;
the six divisions to the left of 0 being seen only with the right
eye, and the six divisions to the right of 0 being seen only with
the left eye.

In this way we have two similar objects, similarly illuminated
and of equal magnitude, in immediate juxtaposition, the one seen
by the right and the other by the left eye ; and any difference in
their distinctness, quality, brilliancy, or colour, will be as clearly
and instantly perceivable as the comparative brilliancy of spaces
illuminated by two different lights in the photometer. I have
already experimented with this apparatus upon my own eyes, the
result of which is, that I find that the sight of the right eye is
much better than that of the left, the figures to the left of 0 being
always more distinct than those to the right of it : but, what is
more remarkable, I find that the transparency of the humours of

203

COMMON" THINGS — SPECTACLES.

the right eye is more perfect than that of the humours of the left
eye, for the space to the right of 0 always appears less bright
than the space to the left of it.

19. To apply this instrument for the purpose of adapting spec-
tacle lenses to eyes of unequal powers of vision, it is necessary
first to ascertain the existence of the inequality of power in the
manner already explained. It would then be necessary to provide
two distinct screens on which similar scales might be drawn, so
that they might be placed at different distances from the aperture
M N. Let their relative distances be then determined, so that
the two eyes would see the scales with equal distinctness. These
distances will then represent the focal lengths of the divergent
lenses which it would be necessary to provide for the eyes, so as.
to make them see different objects with equal distinctness.

In the case of weak-sighted eyes, this method will not be appli-
cable. In that case let the two screens be placed at equal dis-
tances from the aperture M N, and let lenses be selected for each
eye separately, closing the other, so as to give a distinct perception
of the scales. The two lenses being then simultaneously applied
to the eyes, let the scale be viewed with both eyes open. If the
lenses be adapted to correct the defect of vision, the two parts of
the scale to the right and to the left of 0, seen at the same time by
each eye alone, will appear of uniform brilliancy and distinctness.

If defective eyes were tested by this method, I believe it would
be found that inequality of vision would be much more common
than is generally supposed, and accordingly the adaptation of
spectacles would be considerably improved.

20. Cases occur not only in which the comparative powers of
vision of the two eyes differ, but in which the power of vision,
even of the same eye, is different when estimated in different
directions.

I have known short-sighted persons who were more short-
sighted for objects taken in a vertical than in a horizontal direc-
tion. Thus with them the height of an object would be more
perceptible than its breadth, and in general, vertical dimensions
more clearly seen than horizontal. This difference arises from
the refractive power of the eye taken in vertical planes being
different from the refractive power taken in horizontal planes ;
and the defect is accordingly removed by the use of lenses whose
curvatures, measured in their vertical direction, is different from
their curvature measured in their horizontal direction. The
lenses, in fact, instead of having spherical surfaces, have elliptical
surfaces, the excentricities of which correspond with the varia-
tion of the refractive power of the eye.

THE KALEIDOSCOPE.

1 Origin of the name.— 2. Structure of the instrument.— 3. Its optical
effect.— 4. Varieties of its form.— 5. Its occasional use in the arts.—
6. Another optical toy depending on two reflections.

1. THIS pretty optical toy, which is named from three Greek
words, Ka\ov etios (Kalon eidos), a beautiful form, and MOW
(skopeo) I see, depends upon the properties of the looking-glass.

2. Two oblong slips of looking-glass, A ace, and AabB, fig. 1, are
placed edge to edge at A a, inclined to each other at an angle of 60°.

Fig. i.

Thus placed, they are fixed in a tube of tin or brass of correspond-
ing size, one end view of which is shown in fig. 2, where the circle
A c B represents the tube, and A B and A c the edges of the plates
of glass. One end of the tube is covered by two discs of glass,
between which broken pieces of coloured glass or other transparent
coloured object are placed loosely, so that they can fall from side
to side, and take an infinite variety of casual arrangements. The
external disc is ground-glass, to prevent the view of external
objects disturbing the effect. The other end of the tube is covered
by a diaphragm, with a small eye-hole in its centre, through
which the observer looks at the coloured objects contained in the
cell at the other end. He not only sees these objects, but also
their reflection in each of the inclined glasses ; and when the angle
of inclination is 60°, the object will be seen five times repeated in
positions regularly disposed round the line formed by the edges
at which the glasses touch each other.

3. The angular space, B A c, included between the glasses, and
every object within it, will be seen reflected in each glass. Thus
B A c will be seen in the glass B A, as if it were repeated in the

205

THE KALEIDOSCOPE.

space B A c', and in the glass A. c, as if it were repeated in the
space c A c". But this is not all. The reflection B AC/ becomes
an object before the glass A c, and being reflected by it, is repro-
duced in the space c" A c"", and the reflection c A c" being reflected
by the glass A B, is reproduced in the space c' A c"'. Thus besides

Fig. 2.

the view of the objects themselves which are between the glasses,
and which would be seen if there were no reflection, the observer
will see the four reflections, two c A c" and c" A c"" to the right,
and two B A c' and c' A c"' to the left.

But the reflection c' A c'" is again reflected by the glass A c,
and is seen in the space c'" A c"", and at the same time the reflec-
tion c" A c"" is reflected in the glass A B, and is also reproduced
in the same space c" A c."" Thus it appears that this space c" A c""
receives the reflection of both glasses.

The observer looking through the eye-hole of the kaleidoscope
sees a circle whose apparent diameter c c'" is twice AC the breadth
of the reflector. This circle is divided into six angular spaces, two
of which are the first reflections, and other two the second reflections
of the inclined glasses. The other two consist of the actual space
included between the glasses, and a similar space opposite to it
which receives at once the third reflection of both glasses.

Since looking-glasses never reflect all the light incident
206

lent upon

THE KALEIDOSCOPE.

them, these reflections will not be as vivid as the direct view of
the space B c; nor will they, compared one with another, be
equally vivid. The reflections B c' and c' c" will be less vivid than
the object B c, but more so than the second reflections c' c'" and
c" c"". The third reflection c'" c"" would be less vivid than the
second c' c'" and c" c"", if it proceeded only from one glass as do
the latter. But it must be remembered that being the combined
reflection of both glasses, the loss of brightness by the multiplied
reflections of each glass is to some extent compensated.

4. We have here supposed that the glasses are inclined at 60°,
but they may be inclined at any angle which is an aliquot part of
360°. Thus if they are inclined at 90°, the circular space or field
of view round A will be divided into four angular parts, and the
same observations are applicable. If the glasses are inclined at
an angle of 45°, the field of view will be divided into eight equal
angular spaces, seven of which will be filled by the reflections.

From what has been here explained, the unequal brightness of
the angular spaces seen in the kaleidoscope will be understood.
If, as is most common, the angle of the glasses be 60°, this is per-
ceptible, but if it be 45°, the repeated reflections so reduce the
brightness as to impair the beauty of the effect.

5. The effects of the kaleidoscope are very striking, in conse-
quence of the endless variety of which they are susceptible, even
with a single cell at the object end of the instrument ; but it may
be so arranged that several cells, including different collections
of coloured objects, may be provided, and may be changed one
for another, fitting on the end of the tube like the cover of the
object glass of a telescope.

The effects of this pretty little optical contrivance have been
occasionally rendered useful in the industrial arts, in suggesting
patterns for carpets and other products of the loom.

6. An amusing optical toy is represented in fig. 3, by means of

which objects may be seen, notwithstanding the interposition of
any opaque screen between them and the eye. The rays proceed-
ing from the object P entering the tube d strike on the mirror I

207

THE KALEIDOSCOPE.

placed at an angle of 45°, and are reflected downwards vertically
to the mirror h, also placed at 45°, from which they are reflected
horizontally to the mirror g placed at 45°, from which they are
again reflected vertically to the mirror k placed at 45°, from which
they are reflected horizontally to the eye at A. The eye thus sees
the object after four reflections, the rays which render it visible
having travelled round the rectangular tube I h g k.

203

LONDON, February, 1855.

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