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Accession w .847u>/<5_ Class
EXPERIMENTAL PHYSICS
BY
WILLIAM ABBOTT STONE, A.B.
INSTRUCTOR IN PHYSICS AT THE PHILLIPS EXETER ACADEMY
BOSTON, U.S.A., AND LONDON
GINN & COMPANY, PUBLISHERS
CTJe &tj)enaettm
1899
COPYRIGHT, 1897, BY
WILLIAM ABBOTT STONE
ALL RIGHTS RESERVED
PREFACE.
THIS book is the result of an experience of nearly ten
years in teaching Experimental Physics to classes consist-
ing of students who were preparing for college and of
students who were not preparing for college.
Most of the experiments are quantitative, some are
qualitative. Qualitative experiments serve to stimulate
the interest of the student, and to prepare his mind for
a better understanding of quantitative experiments. A
beginner in Physics should know something about that
which he is expected to measure before he attempts to
measure it. This knowledge is readily acquired from
qualitative experiments.
To show the aim of the work, I have put at the begin-
ning of each experiment a concise statement, not of the*
result, but of the object of the experiment ; and at the
end of each experiment, questions for the purpose of help-
ing the student unfold the result of the experiment from
his record. The general results of the experiments are
enforced by numerous examples, many of which have been
drawn from Harvard Examination Papers. The experi-
ments are often stepping-stones, each to the next.
The book contains only two or three experiments which
require students to work in groups ; for my experience
IV PREFACE.
has shown that students get the greatest benefit from a
laboratory course in Physics by working each for himself.
My purpose has been not only to teach the student
something about Physics, but also, as Physics yields itself
readily to this purpose, to teach him the importance of
distinguishing between facts and inferences from these
facts, to lead him to weigh facts carefully, and then to
use his judgment impartially in drawing inferences. The
teacher cannot use too much care in impressing upon the
mind of the student the limitations which he must con-
stantly put upon his statements and the danger of mak-
ing generalizations from imperfect data. The student
should not think that he is discovering laws of nature
for himself.
I am under obligations to numerous authors and espe-
cially to my former teacher, Dr. E. H. Hall. Among many
friends to whom my thanks are due are Professor G. A.
Wentworth for his interest, encouragement, and sugges-
tions, Professor J. A. Tufts for valuable assistance in
reading both the manuscript and the proof sheets and for
the great pains he has taken in looking after the English
of the book, and Mr. Frank Rollins for reading the proof
sheets and for valuable suggestions about the experiments.
I shall be grateful for any corrections or suggestions.
EXETER, N. H., February, 1897. W> A< S '
THE LABORATORY AND THE APPARATUS.
THE laboratory should be a well-lighted room, provided with a
sink, tables, and gas or gasoline, if experiments in heat are to 'be
attempted. The room should also contain cases or cupboards, or a
large closet, in which to store the apparatus when not in use. Some
of the more common tools ought always to be at hand, such as a
screw-driver, a hammer, a saw, a vise, a gimlet, a soldering-iron.
An intelligent carpenter can make many of the pieces of apparatus.
In Boston, the L. E. Knott Apparatus Company, 16 Ashburton Place,
are prepared to furnish the apparatus called for in this book. Some
of the apparatus can doubtless be obtained from Walmsley, Fuller
& Co., 134-136 .Wabash Avenue, Chicago ; Eimer & Amend, 205
Third Avenue, New York; Queen & Co., 1010 Chestnut Street,
Philadelphia.
A sufficient supply of apparatus to provide for a division of twelve
students working at a time will cost about $400. This estimate is
based upon the fact that certain pieces of apparatus, such as balances
and air-puinps, can be used in common by two or more students.
Some teachers may find useful the following list, which shows the
experiments in this book that are similar to the exercises in the revised
Harvard list or that are equivalent to them :
HARVARD EQUIVALENT HARVARD EQUIVALENT
KXERCISES. EXPERIMENTS. EXERCISES. EXPERIMENTS.
1. 1, 2, 3. 9. 108.
2. 7. 13. 109.
3. 13. 14. 110.
4. 9. 15. 110.
5- 6. 17. 88, 89.
6. 10. 18. 92.
7. 11, 12. 19. 93.
VI THE LABORATORY AND THE APPARATUS.
HABVABD
EQUIVALENT
HARVARD
EQUIVALENT
EXERCISES.
EXPERIMENTS.
EXERCISES.
EXPERIMENTS.
21.
95.
43.
49.
22.
96, 98.
44.
51.
23.
97.
45.
56.
24.
100.
46.
52.
25.
102.
47.
72.
26.
59, 60.
48.
78.
28.
61.
49.
77.
29.
62.
50.
129.
30.
63, 64, 65.
51.
139,
140, 141.
31.
66, 67, 68.
52.
142.
32.
25.
53.
138.
33.
28.
54.
143.
35.
106.
55.
144,
145.
36.
112.
56.
152,
153.
37.
113.
57.
154.
39.
36, 37, 38.
58.
147,
148, 149, 150.
40.
40.
59.
151.
41.
41.
,
The experiments in the foregoing list are drawn largely from the Har-
vard Pamphlet, but in several cases with modifications. In general,
apparatus has been recommended like that devised by Dr. E. H. Hall.
For the discussion of the experiments valuable suggestions have been
derived from Hall and Bergen's Text-Biok of Physics, Hall's Lessons in
Physics, and Worthington's Physical Laboratory Practice.
EXPERIMENTAL PHYSICS.
CHAPTER I.
MENSURATION, HYDROSTATICS, AND PNEU-
MATICS.
1. Purpose. The purpose of this course in physics
is to lead the student to observe carefully, experiment
intelligently, record accurately, judge impartially, and
infer justly.
2. Directions for Note - Taking-. In a note -book,
which must be his constant companion in the laboratory,
the student should keep a record of the experiments
which he performs. This book must contain the original
records of the work done. No records should be made on
scraps of paper, to be copied later into the note-book.
A blank book about 8f inches long by 7 inches wide, and
containing about 250 pages of good unruled paper, suit-
able for pen or pencil, is recommended. The binding
should be strong, with leather corners for the covers and
a leather back. The first leaf should be left blank for the
name and title, and the remaining pages numbered like
the pages of a printed book, the even numbers on the left-
hand page, the odd on the right.
_84732
2 EXPERIMENTAL PHYSICS.
The records of the measurements and of the obser-
vations should be put on the left-hand pages, while on
the right-hand pages must be put computations and
inferences. The notes, which may be written either with
a black lead-pencil or in ink, should not be altered after
they are made. An obvious error may be corrected by
writing between the lines, but the original record should
not be obscured in any way other than by drawing a line
through the erroneous statement. At the top of the left-
hand page must be placed the number and the object
of the experiment with the date, and also the names of
the pieces of apparatus used. The notes must not be
crowded. It is a good plan to make illustrative diagrams
and sketches. Not more than one experiment should be
recorded on a page.
As long as the student does not depart from the
general rules laid down, he is at liberty to follow any
system of note-taking that may seem best to him. In
developing his method of keeping notes, it is well for him
to ask himself frequently, "Will my notes tell another
person just what I have done ? " Let the student make
his notes concise, yet so clear that another in reading the
record cannot fail to understand it.
3. Directions for Performing- Experiments. Before
beginning work, the student should read with care the
directions which accompany the experiment. In these
directions attention will be called to the precautions
which should be taken in the proper performance of the
experiment. A precaution once noted will be rarely men-
tioned again, but should be taken whenever applicable.
MENSURATION.
All measurements and other necessary data must be
recorded. On the following pages, questions in connec-
tion with the experiments will be frequently asked. The
questions must not be answered by a simple " yes " or
" no," but by a declarative sentence. When the question
is in parentheses, however, the student should not record
the answer in his note-book, but should be able, when
called upon, to give it orally.
4. Mensuration. With a meter stick, having inches
on one side, measure the length, breadth, and thickness,
as accurately as you can, of one of the table-tops in the
laboratory. Get the dimensions in feet and fractions of a
foot, also in meters and fractions of a meter. Record the
measurements in your note-book, on page 2. After con-
sulting your record, answer the following questions :
How many inches are there in each of the three
dimensions ? How many centimeters ? How many milli-
meters ?
In your records of numerical data and results, use
decimal fractions only.
Experiment 1. To find the volume of a solid of regular
Apparatus. A meter stick ; a rectangular block of wood.
Directions. (a) Measure and record the length,
breadth, and thickness of the block in inches and fractions
of an inch, taking four measurements of the length, one
along each of the four edges running in the direction of
the length, four of the breadth, and four of the thickness.
Find the average length, breadth, and thickness.
EXPERIMENTAL PHYSICS.
In making the measurements, place the meter stick on
its narrow side (Fig. 1) to make the ends of the gradu-
m
\ I ! I I i i
1 2 3 4 5 C,
1 1 1 1 1 1 II 1 1 1 1
1 1 I 1 1 ' 1 ' I ! jj
7 8 19 60 1C
l 1 1 1 l 1 1 1 18
;
FIG. l.
ations come close to the block ; do not use the divisions
at the ends of the stick, as the ends may be worn.
Find the product of the numbers that express the
average length, breadth, and thickness. This product
will be the number of cubic inches in the block.
(b) Using the same care as in (a), find the dimensions in
centimeters and fractions of a centimeter.
From the average length, breadth, and thickness, find
the number of cubic centimeters in the block.
NOTE. The block will be needed for the next two experiments.
Experiment 2. To find the weight of a wooden block by
means of a spring balance.
Apparatus. The block of Exp. 1; a spring balance of 8-ounce
capacity (Fig. 2) ; thread.
Directions. Taking care that the balance frame touches
nothing, hang it by its ring from a hook or other suit-
able support. Place your head in such a position that the
line of vision passes by the end of the pointer and is per-
pendicular to the face of the balance. Observe whether
the pointer is opposite the line marked (zero). If the
MENSURATION.
pointer is not opposite the zero line, note how much
above or below it is. By means of a piece of
fine thread hang the block on the hook of the
balance, and observe the new position of the
pointer. In computing the result, make a cor-
rection for the "zero error" of the balance, that
is, the error arising if the pointer, when no
weight is hung on the hook, is not exactly in
front of the zero line. Strive to read carefully
to the tenths of the smallest divisions.
Does the weight of the thread make any
difference in the indications of the balance ?
Making use of the result obtained in Exp. 1
(a), what do you find to be the weight in ounces
of one cubic inch of the block ?
FIG. 2.
Experiment 3. To find the weight of a wooden block
by means of a platform
balance.
Apparatus. The block of
Exp. 1; a platform balance;
metric weights.
Directions. Put the
rider on the zero notch
of the balance scale. Wipe the pans dry and clean. Set
the pans swinging, and add bits of paper till they swing
evenly. On the left-hand pan lay the block ; on the
right-hand pan put weights (Fig. 3). Use the rider in
making the final adjustments. Trust the indications of
a swinging balance only. (Why ? ) Find how many
grams and fractions of a gram the block weighs.
6
EXPERIMENTAL PHYSICS.
Making use of the results obtained in Exp. 1 (5), what
do you find to be the weight in grams of one cubic
centimeter of the block?
Experiment 4. To find the volume of a solid of irregu-
lar shape.
Apparatus. A 100 CC graduate (a cylindrical glass vessel marked
off into cubic centimeters) ; a piece of lead.
Directions. Fill the graduate about half full of water
and note the exact level of the water. Into the
water put the piece of lead (Fig. 4). Be sure
that it is entirely beneath the surface. (Why ?)
If air-bubbles cling to the lead, remove by shak-
ing, but take care not to spill any water. Note
the level at which the water now stands. As
the surface of the water is highest at its edge
where it .meets the graduate, get the level by
sighting along a horizontal line that just grazes
the lowest part of the surface.
How many cubic centimeters of water are
displaced ? Is the volume of water displaced the
same as the volume of the lead ?
How many cubic centimeters does the lead contain ?
5. Quantity ; Unit ; Numerical Value. In the ex-
periments already performed we have made measurements
of length, volume, and weight, and in our subsequent
work, we shall often make measurements of other magni-
tudes, such as temperature, friction, and electrical resistance.
Measured magnitudes are called quantities. Every
quantity is expressed by a phrase consisting of two parts :
one of these is the name of a certain known quantity
FIG. 4.
DENSITY.
which is taken as a standard of reference, and which is of
the same kind as the quantity to be expressed ; and the
other is a number which shows how many times the
standard is to be taken in order to make up the required
quantity. The standard quantity is called the unit, and
the number the numerical value of the quantity.
There are as many units as there are different kinds of
quantities to be measured.
In this book the cubic inch is taken as the unit of
volume and the ounce as the unit of weight for the
English System, except for the measurement of large
quantities, when the cubic foot and the pound are used ;
for the Metric System the cubic centimeter is taken as
the unit of volume and the gram as the unit of weight.
The distance from one end of the Capitol at Washing-
ton to the other is just 751 feet. The phrase " 751 feet "
tells the number of units of a particular kind contained in
the distance mentioned. In this case the foot is the unit,
while 751 is the numerical value of the quantity.
QUESTIONS. What is the unit and what is the numerical value in
each of the following expressions of quantity : 72 feet ? 10 meters ?
202 cubic centimeters ? 8 grains ? 7 ounces ? 100 cubic feet ? 10 inches ?
DENSITY.
6. Density. The final result of Exp. 2 gave the
weight in ounces of one cubic inch of the block, while
that of Exp. 3 gave the weight in grams of one cubic
centimeter of the block.
Definition. By the density of a substance is meant the
weight of one unit of volume of the substance.
8 EXPERIMENTAL PHYSICS.
NOTE. Later in the course we shall limit the meaning of the word
weight in this definition to that expressed by the word mass, and we shall
show that a platform balance and not a spring balance should be used in
our method of getting the density in the English System.
The final result of Exp. 2, then, gave the density of
the block in the English System ; the final result of
Exp. 3, the density in the Metric System.
The student should consult Exps. 1, 2, and 3, and on
the right-hand page of his note-book, the one opposite the
last left-hand page that has been written on, give a brief
account of the method of finding the density of a rect-
angular block of wood, which shall apply to either the
English System or the Metric.
When the Metric. System was planned, it was decided
to take the density of water as unity, that is, to take the
weight of a cubic centimeter of water as the unit of
weight, and to call it the gram, hence
A cubic centimeter of water weighs a gram.
NOTE. Strictly speaking, however, in order that a cubic centimeter
of water may weigh a gram, the water must be pure and it must have a
certain temperature a few degrees above freezing ; but for our purposes
common water at any ordinary temperature will give results sufficiently
accurate.
7. Precautions to be taken in Measurements and
Computations. With a meter stick, such as you have
used, suppose a rectangular block to have been measured
in centimeters with the following results :
MEASUREMENTS MEASUREMENTS MEASUREMENTS
OF LENGTH. OF BREADTH. <u THICKNESS.
cm. cm. cm. .
7.30 6.40 3.12
7.32 6.40 3.10
7.32 6.41 3.11
7.33 6.42 3.14
MEASUREMENTS AND COMPUTATIONS.
It will be noticed that 7.30 cm in the record just given
does not mean exactly the same thing as 7.3 cm . The
former shows that the hundredths of a centimeter could be
estimated, and that you have found that the length is
more nearly 7.30 cm than 7.29 cm or 7.31 cm . The latter
means that the hundredths of a centimeter were not taken
into account. Consequently, unless you are careful to
estimate the hundredths of centimeters, you must write
not 7.30 cm , but 7.3 cm .
If we add each of the columns, and divide each sum by
4 to get the average length, breadth, and thickness, we
have :
4)25.63
6.41
Since the millimeter was the smallest division on the
meter stick, and since we had to estimate the tenths of a
millimeter, the second decimal place in each of the
measurements is in doubt ; hence the second decimal
place in each of the averages is in doubt. Consequently,
in each average, we have discarded as wholly doubtful all
figures after the second place of decimals. It will be
seen, however, by examining the averages, that the last
figure retained has been increased by unity (one) when-
ever the first figure discarded is 5 or greater than 5. It
is not only a waste of time to obtain and to record the
average beyond the first doubtful figure, but is also inac-
curate, since it is understood in physics that the observer
claims as accurate all the figures in the record of a
measurement except the last.
10 EXPERIMENTAL PHYSICS.
We have, then :
Average length = 7.32 cm .
Average breadth =. 6.41 cm .
Average thickness = 3.12 cm .
For the sake of clearness the doubtful figures are
printed in full-faced type.
Let us compute the volume of the block.
Volume of the block = 7.32 X 6.41 X 3.12.
7.32 46.9
6.41 3.12
732 938
2928 469
4392 14O7
46.9212 146.328
The final result is to be entered as 146 CC .
In the future it will be understood that the last figure
recorded in the value of a measurement is in doubt.
Let the student turn back to his record of experiments
performed, and, allowing the old computations to stand,
reckon the results once more in accordance with the
following rules :
1. In all averages keep but one doubtful figure. (If the
figure following the doubtful one is 5 or greater than 5,
increase the doubtful figure by unity.)
2. After multiplying two numbers together, keep in the
result as many figures of the product, counting from the
left, as there are figures in the smaller factor.
SPECIFIC GRAVITY. 11
3. After dividing one number by another, keep in the
quotient, counting from the left, as many figures as there are
in the smaller of the two.
In subsequent experiments, these rules must always
govern your measurements and computations.
SPECIFIC GRAVITY.
8. Specific Gravity. The object of the following
experiment is to make clear to the student the meaning
of the term specific gravity.
Experiment 5. To find how many times as heavy as
an equal volume of water a piece of lead is.
Apparatus. A 100 CC graduate ; a piece of lead that weighs
more than 1008 (grams) ; a platform balance.
Directions. Find the weight in grams of a piece of
dry lead. Find the volume of the lead in cubic centi-
meters (by method of Exp. 4).
With the data obtained, and knowing that a. cubic centi-
meter of water weighs a gram, find how many times as
heavy as an equal volume of water the lead is.
The number thus obtained is called the specific gravity
of lead.
Definition. The number obtained by dividing the weight
of a substance by the weight of an equal volume of water is
called the specific gravity of the substance.
NOTE. For all work in this course use common water at any ordinary
temperature.
12
EXPERIMENTAL PHYSICS.
9. Principle of Archimedes. The next two experi-
ments have for their object the unfolding of the celebrated
Principle of Archimedes. 1 The use of this principle will
enable us to determine
with ease the specific
gravity of substances.
Experiment 6. To
find the relation between
the weight of a body that
will float in water and
the weight of water it
displaces.
Apparatus. A 100 CC
graduate ; a 200 cc beaker ; a
copper vessel with a spout
to which a rubber tube 10 cm
long is attached; a wooden
block whose corners are rounded, if necessary, to allow it to be put
into the vessel ; a platform balance.
Directions. Find the weight of the block in grams.
Fill the vessel with water till some runs off through the
tube attached to the spout. This tube should not be
1 Archimedes (287-212 B.C.), a famous mathematician of Syracuse in
Sicily, was asked, so the story runs, by Hiero, king of Syracuse, to find
whether a certain crown of the king's was of pure gold or of gold alloyed
with silver. Archimedes asked for time to reflect on the problem. Soon
afterwards, when in his bath, he noticed, what he had probably never
carefully observed before, that his body was pressed upwards with a force
which increased the more completely he was immersed in the water ; to
his subtle intellect this discovery suggested a way of solving the king's
problem. By careful experiments he discovered that of equal masses of
gold and silver the silver weighed less in water than the gold. On
making the test, he found the crown to weigh less in water than an equal
mass of gold, so he concluded that the crown was not of pure gold.
FIG. 5.
SPECIFIC GRAVITY.
13
touched during the experiment. When water stops flow-
ing, carefully put the block flatwise into the water
(Fig. 5), and in the beaker catch all the water that flows
out. Measure this water in the graduate.
How many cubic centimeters of water does the block
displace ?
How much does a cubic centimeter of water weigh?
How many grams of water does the block displace ? "
Is the weight of water displaced the same, or nearly the
same, as the weight of the block ?
Can you infer any relation between the weight of a
body that will float and the weight of water it displaces ?
QUESTION. If a wooden
block weighs 100s, how many
grams of water will it dis-
place when floating in water?
Experiment 7. To
find how much less a
body that will sink
weighs in water than
in air.
Apparatus. A spring
balance of 30-pound ca-
pacity ; a heavy iron ball
with a handle to which a
string is attached (an iron
safety-valve weight, weigh-
ing at least 12 pounds) ; a
dipper ; a pail. FIG. 6.
Directions. Perform the experiment at the sink.
By its ring hang the balance to a stout support, and find
the Aveight of the ball.
14 EXPERIMENTAL PHYSICS.
Then, taking care that the ball does not touch the pail,
let it hang by the string, as in Fig. 6, from the hook of
the balance so that it will be completely covered by the
water in the pail in the sink. As it hangs immersed in
the water, find its weight.
Remove the ball from the balance and hang the pail in
its place. With the dipper fill the pail brimful of water,
and get the weight. Now lower the ball into the pail
until it is completely beneath the surface, holding it by
the string till the water stops flowing over the edge of
the pail; then carefully remove the ball, and note the
weight of the pail and the water left.
How much less did the ball weigh in water than in air ?
Did the ball displace its own volume of water?
What is the weight of the water displaced by the ball?
Can you infer any relation between the weight of water
displaced and the apparent loss in weight of the ball ?
The inferences from the results of Exps. 6 and 7 are
together known as the Principle of Archimedes. Try to
frame a concise statement that shall include both of your
inferences.
QUESTION. If a cubic centimeter of iron weighs 7&, what will be
its apparent weight if plunged under water ?
1C. Applications of the Principle of Archimedes.
With one exception, the next six experiments involve the
use of the Principle of Archimedes.
Experiment 8. To find, without the use of a balance,
the specific gravity of a piece of wood.
Apparatus. The same as that used in Exp. 6, without the
balance.
SPECIFIC GRAVITY.
15
Directions. By the method of displacement of water
(see Exp. 6) find the weight of the wood. Then press
the wood down into the water until completely covered.
Catch the water and measure it.
What do you find the volume of the wood to be in.
cubic centimeters ? What, then, is the weight of a volume
of water of the same size as the wood? What is the
specific gravity of the wood ? In what way has the Prin-
ciple of Archimedes helped you in this experiment?
QUESTION. If the specific gravity of white wood is 0.5, how deep
will a rectangular block of white
wood sink in water ?
Experiment 9. To
find, by submersion with
a sinker, the specific grav-
ity of a piece of wood.
Apparatus. A rectangular
block of wood ; a platform
balance standing on a wooden
support ; a piece of lead heavy
enough to sink the block; a
glass jar three-quarters full of
water ; a piece of thread.
Directions. Weigh
the block to O.l g . Over
the left-hand pan of the
balance, as shown in Fig.
7, loop the thread so that it will touch nothing but the pan
and the water. Fasten the lead to the thread, and find how
much the lead weighs when completely submerged in water
without touching either the sides or the bottom of the
jar. If air-bubbles are on the lead, brush them off.
FIG. 7.
16 .EXPERIMENTAL PHYSICS.
Fasten the lead to the block, and, when entirely under
water and touching neither the bottom nor the sides of
the jar, weigh both to O.l g .
If the block were unattached to the sinker, and floating,
by how many grams would the water buoy it up ? (See
your inference from Exp. 6.)
When the sinker is fastened to the wood, and both are
completely submerged, by how many grams more does
the water buoy up the block than it did before ; that is,
what is the difference between the weight of the sinker
alone in water and the joint weight of sinker and block
in water ? What is the weight of a volume of water of
the same size as that of the block ? (In answering this
question, consider carefully your answers to the two
preceding ones.)
What is the specific gravity of the block ?
NOTE. After drying the block, use it in the next experiment.
Experiment 1O. To find, by flotation, the specific gravity
of a piece of wood.
Apparatus. The block used in Exp. 9 ; a meter stick ; a glass
jar nearly full of water.
Directions. By taking measurements at each corner,
get the average thickness of the block. Taking care that
no air-bubbles cling to the under surface or to the sides of
the block, gently lay it on the surface of water in the jar.
If the sides of the block are not oiled, the water will
creep up a little way, but if the block has been oiled, the
water close to the block will be slightly depressed. [This
phenomenon, either the creeping up of the water, or its
SPECIFIC GRAVITY. 17
depression, belongs to a class included under the name
capillary action (from the Latin capillus, hair), as the
phenomenon was first observed in tubes of fine, hair-like
bore.] With the eye on a level with the water, sight,
through the sides of the jar, at the block, and see where
the general level of the water would meet the block.
Remove the block carefully. With a fine pointed lead-
pencil, and guided by the water-line, make a dot at each
corner where the water would have met the block had
it not been for capillary action. Now measure from each
of the dots to the lower surface of the block, and find the
average depth to which the block sank.
The following is the course of reasoning by which the
specific gravity may be found :
Imagine a block of water of the same size as the part of
the wooden block under water.
What relation exists between the weight of this volume
of water and the weight of the wooden block ? (See your
inference from Exp. 6.)
Imagine another block of water of the same size as the
wooden block.
These two blocks of water, which you have imagined,
have equal bases but unequal heights.
Is the weight of the thinner block the same part of the
weight of the thicker that the height of the thinner block
is of the height of the thicker ?
What is the specific gravity of the wood ?
In getting the specific gravity in this case, "have you
made direct use of the weight of the block and the weight
of an equal volume of water?
18 EXPERIMENTAL PHYSICS.
Experiment 11. To find, by the specific gravity bottle,
the specific gravity of a liquid.
. Apparatus. A small bottle having a wide mouth (this is called
the "specific gravity bottle"), with a glass stopple, and of 2-ounce or
3-ounce capacity ; a platform balance ; a piece of cloth or a towel
with which to dry the bottle ; water ; kerosene.
Directions. Wipe the bottle dry both inside and out.
Weigh the bottle together with the stopple, which should
fit tightly. Weigh the bottle full of kerosene. When
putting in the stopple, take care to exclude air-bubbles.
The best way to do this is to fill the bottle brimful, then
push the stopple into place. Weigh the bottle full of water.
What weight of kerosene did the bottle hold ?
What weight of water did the bottle hold ?
Was the volume of kerosene equal to that of the water ?
What is the specific gravity of kerosene ?
In getting the specific gravity in this case, have you
made direct use of the weight of the kerosene and the
weight of an equal volume of water?
Have you made use of the Principle of Archimedes ?
Experiment 12. To find, by means of buoyant action,
the specific gravity of a liquid.
Apparatus. A jar three-quarters full of kerosene ; a jar three-
quarters full of water ; a platform balance with support ; a piece of
lead or iron weighing 100s or more ; a piece of thread.
Directions. Weigh the piece of lead. With the
thread suspend the lead from the balance pan, and weigh
in kerosene. Take the lead from the kerosene, wipe dry,
and find its weight in water.
srtfiv:
SPECIFIC GRAVITY.
What weight of water did the lead displace ? (See
your inference from Exp. 7.) What weight of kerosene
did the lead displace ? Was the volume of kerosene dis-
placed by the lead the same as the volume of water ?
What is the specific gravity of kerosene ?
Have you made use of the Principle of Archimedes ?
Now that you have performed the experiment, what,
should you say, is the meaning of the term "buoyant 1
action " ?
Experiment 13. To find the specific gravity of a solid
that will sink in water.
Apparatua A glass bottle without stopple (the glass bottle used
in Exp. 11 will answer); a platform balance on a support ; a piece
of thread ; a jar of water.
Directions. Weigh the bottle empty. Also weigh the
bottle in water, after filling it with water. See that every
part of the bottle is beneath the surface of the water,
and that there are no air-bubbles in the bottle.
What is the weight of a volume of water of the same
size as the volume of the glass ?
What is the specific gravity of the glass ?
Had the glass forming the bottle been in a solid lump,
would the result have been different ?
Have you made use of the Principle of Archimedes ?
11. Agreement between Specific Gravity and Den-
sity in the Metric System. If the student compares
the result of either Exps. 8 or 9 with that of Exp. 2 and
that of Exp. 3, the specific gravity of wood with its
1 When a word or a term occurs the meaning of which is not perfectly
clear, consult a good dictionary.
20 EXPERIMENTAL PHYSICS.
density in the English System and in the Metric, he
cannot fail to notice that the specific gravity is widely
different from the numerical value of the density in the
English System, while it agrees closely with the numer-
ical value of the density in the Metric. This agreement
does not come by chance, but is the result of the relation
which, in the Metric System of weights and measures,
exists between the unit of volume and the unit of weight.
For example, to get the specific gravity of a piece of
wood, we divide its weight by the weight of an equal
volume of water ; on the other hand, to get the density of
the piece of wood, we divide its weight by the numerical
value of its volume. In the Metric System one cubic
centimeter of water weighs one gram ; so the numerical
value of the volume of a body is equal to the numerical
value of the weight of a like volume of water ; hence,
the quotients resulting from the divisions must be equal
in numerical value.
EXAMPLES.
1. A piece of wood weighs 75&, and its density is 0.5s per cubic cen-
timeter. What is its volume ?
2. A body weighs 100s in air, and 75e in water. What is the specific
gravity of the body ?
3. A body lighter than water weighs lOOg hi air. A sinker, weighing
50s in water, is attached to the body, and their combined weight in water
is 25s. What is the specific gravity of the body ?
4. What is the specific gravity of water ?
5. A cubic decimeter (a cube whose edges are 10 cm ) of wood sinks to
a depth of 6 cm in water. Find the specific gravity of the wood.
6. A specific gravity bottle weighs, when empty, 1000& ; when filled
with kerosene, 1800s ; when filled with water, 2000s. Find the specific
gravity of kerosene.
7. Weight of a sinker in air, 50s ; in kerosene, 42. Is j in water, 40s.
Find the specific gravity of kerosene.
PNEUMATICS.
21
8. A piece of wood of irregular shape floats with - of its volume
under water. What is its specific gravity ?
Solution. If we let 1 represent the weight of a volume of water
equal to that of the wood, the weight of the wood will (by Principle
b
of Archimedes, Exp. 6) be - x 1, or - Hence sp. gr. = y = -
9. An iceberg floats with one-ninth of its volume above the water.
Find the specific gravity of the iceberg.
10. Let us suppose that Hiero's crown (see Art. 9) weighed 10
ounces, and that its specific gravity was 15. If the specific gravity of
gold is 19.3, and the specific gravity of silver is 10.5, find the weight of
silver in the crown.
Solution. Let x denote the weight of silver in the crown.
Then 10 -x will " " " "gold " "
Weight of water whose volume equals that of silver = -
10 x
1 1 u u u u u titt gold.
19.3
By the definition of specific gravity, we have = 15.
X i 1U ~~ C
10.6 10.3
Clearing of fractions, taking out common factors, and combining, we
find 8.8 x = 30.1, whence x = 3.42 ounces.
11. A diamond ring weighs 65 grains in air, and 60 in water. Find
the weight of the diamond, the specific gravity of gold being 17.5, and
that of the diamond 3.5.
PNEUMATICS.
12. Air. The earth on which we live is surrounded by
a gas which we call air. Although we cannot see it, its
existence is proved to us by our being able to feel it.
When we are riding fast we feel the air. The whole
mass of this air is called the atmosphere,
22 EXPERIMENTAL PHYSICS.
We shall now study in the next three experiments
some of the properties of air which come under the head
of Pneumatics.
Experiment 14. To find whether air has weight.
Apparatus. An air-pump; a piece of "pressure" tube with a
pointed glass tube in one end attached to the exhaust nozzle ; a
2-quart glass bottle with a perforated rubber stopple, having a glass
tube thrust through with a piece of pressure tube 10 cm long
attached ; a small brass clamp ; a platform balance ; vaseline.
Directions. Into the mouth of the bottle insert the
stopple slightly smeared with vaseline to make the bottle
air-tight. Over the tubing slip the clamp so that it fits
loosely.
Weigh the bottle together with stopple, tubes, and
clamp. The result is the weight of the bottle filled with
air. Lay the bottle on the table close to the air-pump.
Push the end of the rubber tube over the pointed glass
tube attached to the pump. Without hurrying, make 20
strokes of the pump (a stroke is one complete up-and-
down movement of the handle). Some of the air has now
been pumped out. Screw the clamp tightly on the rubber
tube attached to the .bottle. Remove the bottle and weigh.
If there is a difference between the two weights, how
do you account for it ?
Experiment 15. To find whether the atmosphere presses
equally in all directions.
Apparatus. An air-pump ; a thick-walled " thistle-tube " whose
mouth, about 2.5 cm in diameter, has a , piece of thin sheet rubber,
like that which dentists use, stretched across, and firmly fastened by
a piece of strong thread wound round the tube just back of the lip,
as shown in Fig. 8 (the piece of sheet rubber thus arranged is called
a diaphragm) ; a piece of pressure tube 30 cm long.
PNEUMATICS. 23
Directions. By means of the pressure tube connect
the stem of the thistle-tube with the air-pump. Make
one or two strokes of the air-pump. Take care not to burst
the diaphragm. The diaphragm will be forced into a deep
cup-shape by the pressure of the atmosphere. To prevent
air from leaking into the thistle-tube from the pump,
pinch the tube tightly. Watching the curvature of the
diaphragm, turn the mouth of the tube up, down, and in
many directions.
As you turn the mouth of the tube in different direc-
tions, does the shape
of the diaphragm
change ?
What inference can
you draw ?
Pneumatics is that
branch of physics which
treats of the mechani-
cal properties of air, as weight and pressure.
Experiment 16. To find whether the pressure of the
atmosphere upon a given surface depends on the shape of
the passage by which it reaches the surface.
Apparatus. A small thistle-tube with a rubber diaphragm across
the mouth, about 1.5 cm in diameter, and a piece of rubber tube
5Qcin long attached to the stem.
Directions. With one side of the diaphragm the air
communicates directly, but with the other indirectly
through the tube. If, without compressing the tube,
you bend it into different shapes, you will be able, by
24 EXPERIMENTAL PHYSICS.
watching the diaphragm, to decide whether there is any
change of pressure on the "given surface," the side of
the diaphragm in the thistle-tube.
What inference can you draw from this experiment ?
LIQUID PRESSURE.
13. Liquid Pressure. We shall now study the laws
which govern pressure in liquids.
Experiment 17. To find whether the pressure increases
with the depth below the surface.
Apparatus. A pail three-quarters full of water; a pressure-
gauge.
Directions for Making the Pressure-Gauge. Beneath
the surface of water in the pail dip one end of a piece of
thermometer tube whose length is about 15 cm . When
FIG. 9.
the end is about l cm below the surface, cover it with the
finger and remove the tube. The little thread of water
about l cm long thus caught in the tube is called an index.
Turn the tube into a horizontal position, and remove the
finger from the end. By gentle shaking, get the index
placed at about one-fourth the length of the tube from
one end; over this end, which should have been heated
LIQUID PKESSUKE. 25
and drawn out, carefully slip the rubber tube attached to
the thistle-tube of Exp. 16, and push it on till it covers
about l cm of the glass tube. Take care not to kink, or
bend sharply, or compress the rubber tube, lest you force
the index out. Make a rubber ring by cutting a thin slice
from a rubber tube. Push the glass tube into this ring.
The gauge is now completed, as shown in Fig. 9. In using
it, be sure the tube contain-
ing the index is horizontal.
A convenient form of the gauge is
shown in Fig. 10, where the thistle-
tube and the tube containing the
index are held in position by a metal-
lic frame. By means of the little
crank and a rubber belt, a rotary
motion can be given to the thistle-
tube.
What happens to the index when
you press lightly against the dia-
phragm? If you hold the thistle-
tube clasped in the palm of your
hand, does the index move?
(We shall study this question more care-
fully in the chapter on Heat.)
Directions. Beside the pail upon the table lay the
glass tube of the gauge; along this tube push the little
rubber ring (the "marker") till it is over one end of the
index. With one hand steady the glass tube, with the
other, using great care not to kink, or bend sharply, or
compress the rubber tube, lower the thistle-tube into the
pail (Fig. 11), which should contain water that has stood
26
EXPERIMENTAL PHYSICS.
FIG. 11.
in the room for several hours, to ensure that its tempera-
ture shall be nearly the same as that of the room. As the
thistle-tube goes deeper and deeper below the surface,
watch the index.
How does the index act? What inference can you
draw from this action?
With what are the
thistle -tube and the
rubber tube filled?
By what means is the
pressure sent from
the diaphragm to the
index ?
Experiment 18.
To find whether the
pressure at a given point in a liquid is the same in all
directions.
Apparatus. The same as in Exp. 17.
Directions. On the inside of the pail, a little way
below the surface of the water, make a dot. Keeping its
center on a level with this dot and at a given distance
from the dot, turn the diaphragm so that it will face in
various directions, downwards, horizontally, and obliquely.
What do you infer from the action of the index ?
Compare your inference with that of Exp. 15.
When, as in this experiment, the tube of the gauge is
bent into different curves, what reason have you for
thinking that the pressure transmitted by the air in the
tube does not change in passing round the curves ? (See
your inference from Exp. 16.)
LIQUID PRESSURE.
27
Experiment 19. To find whether the pressure at all
points, in a horizontal plane passing through the liquid, is
equally great.
Apparatus. The pressure-gauge ; two student-lamp chimneys ; a
retort-stand with two clamps each large enough to hold a chimney ;
two good cork stopples to fit the smaller end of each chimney ; a pail
of water ; some cement made by melting together equal parts of
beeswax and rosin.
PART 1. Where it is possible to pass along a straight
line from one point to any other in the plane.
Directions. Dip the stopples into the melted cement
and stop the smaller end of each chimney air-tight. Fill
FIG. 12.
one of the chimneys with water. Placing the hand or a
piece of wet paper over the open end, invert and lower
the chimney into the pail of water. When the covered
end is below the surface of the water, remove the hand or
paper. With its lower end dipping about 6 cm below the
28 EXPERIMENTAL PHYSICS.
surface of the water, clamp the chimney in a vertical
position. (Why the water remains in the chimney you will
learn from Exp. 20.) With its closed end downwards,
and about 6 cm below the surface of water, clamp the other
chimney in a vertical position. Push the diaphragm of
the gauge about 8 cm below the surface of the water.
Sometimes bringing the diaphragm under the chimney
filled with water, as shown in Fig. 12, sometimes under
the chimney whose closed end is in the water, and at
other times under neither, carefully move the diaphragm
about in the same horizontal plane.
Do you observe any change of pressure in going from
one point to another in the same horizontal plane ?
What is your inference ?
As you moved the diaphragm from place to place, the
depth of water over it was sometimes greater and some-
times less. How many different depths of water were
there ?
PART 2. Where it is impossible to pass along a
straight line from one point to another in the plane.
Directions. Push the chimney filled with water down
till its open end is about 10 cm below the level of the
water in the pail. Clamp the chimney. Push the dia-
phragm up inside the chimney about 2 cm . With the
marker note the position of the index. Then, with the
tube bent in as nearly the same shape as before, put the
diaphragm in the water outside, but on a level with its
former position in the chimney. Observe the position of
the index. Great care is necessary to avoid compressing
the rubber tube.
LIQUID PRESSURE. 29
In this part of the experiment, the barrier that has
separated one portion of the horizontal plane from the
other has been the walls of the chimney.
What inference can you draw ?
EXAMPLES.
1. A rectangular vessel, whose interior dimensions are : width 10 cm ,
length 15 cm , and height 20 cm , is filled with water.
a. What is the weight of water in the vessel ?
6. What is the weight of water resting on each square centimeter of
the base ?
c. What is the pressure upon a horizontal square centimeter at the
depth of 2 cm ? At a depth of 10 cm ? At a depth of 15 cm ?
2. Suppose the vessel of the preceding example to be closed by a flat
cover with a hole through its center, into which fits an open tube of
Isq cm cross-section, and also suppose this tube to extend upwards 30 cra
above the top of the vessel. Suppose both vessel and tube filled with
water.
a. What is the total weight of water in vessel and tube ?
6. What is the pressure upon that square centimeter of the base of
the vessel which lies exactly beneath the tube ?
c. Is the pressure upon any other square centimeter of the base of the
vessel greater or less than this ?
d. What is the pressure upon that square centimeter which, at the
top of the vessel, lies exactly beneath the tube ?
e. Is the pressure against each square centimeter of the cover greater
or Jess than this ?
/. What is the total pressure of the water against the cover ?
ff. What is the total pressure of the water against the base ?
h. Subtract the total pressure against the cover from the total pressure
against the base, and compare the result with the weight of all the water
in the vessel and tube.
i. What is the total pressure upon l s i cm of the vertical side of the
vessel, the center of the square being at a depth of 5 cm beneath the
cover ? At a depth of 10 cm ? At a depth of 15 cm ?
30 EXPERIMENTAL PHYSICS.
j. What is the total pressure upon one of the narrow vertical sides of
the vessel ? Upon one of the broad vertical sides ?
k. What is the total pressure upon the base, cover, and sides ?
I. Suppose, by means of a piston, for example, a pressure of 50s is
brought to bear upon the top of the water in the tube. What will now
be the pressure upon that square centimeter which lies at the top of the
vessel, just beneath the tube ?
m. How much will the total pressure against the base of the vessel be
increased by the action of the added pressure ?
n. How much will the total pressure against the base, cover, and
sides be increased by the action of the added pressure ?
ATMOSPHERIC PRESSURE.
14. Pressure of the Atmosphere. In Exp. 19 you
found that the lamp-chimney remained full of water after
it was inverted in the pail of water. In the following
experiment we shall study the cause of this.
Experiment 2<X. To find whether it was the pressure
of the atmosphere that kept the water in the, chimney.
Apparatus. In place of the chimney, a glass tube about 100 cm
long and 0.5 cm in diameter ; a good cork stopple to fit the tube ;
a pail of water.
Directions. With the stopple close one end of the
tube, then fill it with water. Taking care not to shut in
an air-bubble, press the finger firmly against the open end.
Place the end covered with the finger under the surface
of the water in the pail and then remove the finger.
Does the water in the tube fall ?
When you remove the stopple, what is the result ?
Before the stopple was removed, did the atmosphere
get to the water in the tube to press it down ? Did the
atmosphere get to the water in the tube to hold it up ?
ATMOSPHERIC PRESSURE. 31
If the atmosphere did not get at the water in the tube
directly to hold it up, by what indirect means was the
pressure of the atmosphere transmitted to the water in the
tube ? What inference can you draw ?
15. Precautions to be taken in Using- Mercury.
It would bft interesting to find how tall a column of water
the pressure of the atmosphere would support ; unfor-
tunately, however, a tube of sufficient length for the water
would be hard to manage ; so we make use of a short tube
and mercury, a liquid much heavier than water. Mercury,
or quicksilver, as it is often called, has a specific gravity
of 13.6. We shall use mercury in several experiments.
The vapor of mercury is poisonous, hence do not heat
mercury in the room. Before beginning an experiment
in which mercury is used, remove rings from the fingers,
as it badly stains gold. In performing experiments with
mercury, place all the apparatus in a shallow pan to catch
any mercury accidentally spilt.
Experiment 21. To find how tall a column of mercury
the pressure of the atmosphere will support.
NOTE. This is often called the " Torricellian Experiment," in honor
of Torricelli (pronounced tor-re-chel'lee), an Italian who performed the
experiment in 1643.
Apparatus. A piece of thick glass tube, whose bore is about
0.6 cm in diameter, about 80 cm long, closed at one end ; a retort-stand
with clamp ; an iron pan ; a small mortar ; a small funnel'; a piece
of iron wire ; a piece of cloth ; mercury ; a meter stick.
Directions. Make a soft pad of the cloth and lay it
in the pan. On the pad rest the closed end of the tube,
and clamp in a vertical position. By the aid of the funnel
half fill the tube with mercury; then, by twisting the
32
EXPERIMENTAL PHYSICS.
wire in the tube, remove the air-bubbles which adhere
to the sides. Add a little more mercury and again remove
any air-bubbles that you may see. When the 'tube is com-
pletely filled with mercury and contains no
air-bubbles, have ready in the pan the mortal-
filled with mercury to a depth of about 3 cm .
Placing the finger firmly over the open end,
grasp the tube near the top with the right
hand. With the left hand unclamp the tube,
grasp it near the bottom, and in-
verting the tube, place the end in
the mortar below the level of the
mercury. Taking care that no air
enters, remove the finger and again
clamp the tube in a vertical position,
as in Fig. 13.
What happens when the finger is
removed ?
Measure the distance from the
level of the mercury in
the mortar to the top of
the column of mercury in
the tube.
What relation is there between the pressure at a point
on the surface of the mercury in the mortar and the pres-
sure at a point on the same level in the mercury in the
tube ? (See your inference from Exp. 19, Part 2.)
Experiment 22. To find what weight of mercury in
the tube the atmospheric pressure holds up.
Apparatus. The same as that used in Exp. 21 ; a glass beaker :
a platform balance.
FIG. 13.
ATMOSPHERIC PRESSURE. 33
Directions. Using the same care as in Exp. 21, fill
the tube and invert it in the mortar partly filled with
mercury. When the top of the mercury column has
become stationary, find its height as in the last experi-
ment. Over the lower end of the tube put the finger
loosely, and gently raise the tube till its lower end is
just beneath the level of the mercury. Now press the
finger firmly against the end of the tube, lift the tube
out, and incline it in a nearly horizontal position. By
loosening the finger admit the air, a few bubbles at a
time, and allow the mercury to run very gently into
the beaker. Do not spill any of the mercury. Weigh
the beaker with the mercury, and also weigh it empty.
What weight of mercury did the air hold up?
In taking the tube from the mortar, why did you raise
it till its lower end was just beneath the surface of the
mercury before pressing firmly with the finger ?
Making use of the height and weight of the mercury
column, and of the fact that the specific gravity of mer-
cury is 13.6, answer the following questions :
What was the volume in cubic centimeters of the mer-
cury in the tube? What was the area in square centi-
meters of the cross-section of the tube ? What was the
pressure in grams of the atmosphere upon an area of
1 S(1 cm ? What would be the length in centimeters of a
column of water supported by the atmospheric pressure?
16. The Barometer. The barometer is an instrument
for indicating the changes in the pressure of the atmos-
phere. It consists of a cistern filled with clean mercury
into which dips an upright tube of glass containing mer-
cury and closed at the upper end ; the arrangement is
34 EXPERIMENTAL PHYSICS.
like that of Exp. 21. Alongside the tube stands a scale
to measure the height of the mercury column. By watch-
ing the mercury column it has been found to vary in
length not only from day to day, but frequently also
many times a day. This shows that the pressure of the
atmosphere is sometimes greater, sometimes less. The
pressure of the atmosphere is expressed by the length
of the column of mercury which it supports. Thus, if
the column at one time is 72 cm tall, at another 80 cm , we
say that on the first occasion the pressure of the atmos-
phere was 72 cm , on the other 80 cm . The length of the
mercury column is called the height of the barometer.
The average height of the barometer at the sea level
is about 76 cm . In climbing a mountain the atmospheric
pressure becomes less and less the higher you go, so if
you should carry a barometer from the base to the top
of a mountain, the height of the column of mercury would
decrease. The space above the mercury in a barometer
is nearly a perfect vacuum; in honor of Torricelli, who
first observed this, it is called a Torricellian vacuum.
The presence of the vapor of mercury in this space pre-
vents it from being a perfect vacuum.
The term " barometric pressure " is often used in place
of the term " atmospheric pressure."
17. Balancing- Columns. After a liquid has been
poured into connecting tubes (Fig. 14), the column of
liquid in one branch is said to balance the column of
liquid in the other. In order that the results obtained
in experiments with balancing columns may be uninflu-
enced by the capillary action (see page 17), the branches
of the connecting tubes must be sufficiently wide to allow
ATMOSPHERIC PRESSURE. 35
the center of the surface of the liquid in each column to
lie flat.
Experiment 23. To find whether two balancing
columns of water contained in connecting tubes of
unequal cross-section are of equal height.
Apparatus. Two connecting tubes of glass
of unequal cross-section, as shown in Fig. 14, one
about 0.5 cm in diameter, the other about l cm .
Directions. Pour water into the larger
tube.
How does the height of the water in
FIG. 14.
the larger tube compare Avith the height
of the water in the smaller?
If the two columns of Avater are of the same height,
Avhat supports the extra weight of the -column in the
larger tube ?
Could the walls of the tube, where they narrow, support
this weight ?
Experiment 24. To find the specific gravity of a liquid
by balancing columns.
Apparatus. A support consisting of a square base with an
upright rod about 100 cm long, to which is fastened a meter stick ;
a piece of rubber tube ; two glass tubes, each about 100 cm long and
about 0.6 cra in diameter ; a funnel ; a beaker ; two rubber bands.
Directions. To a distance of about l cm over an end
of each of the glass tubes slip an end of the rubber tube.
Place the two glass tubes parallel to each other so that
they with the rubber tube look like a very tall letter U
(we shall call this a U-tube). With the two rubber bands,
as shoAvn in Fig. 15, one near the top, the other about
36
EXPERIMENTAL PHYSICS.
half way down, firmly fasten the U-tube to the upright of
the support. Have the rubber tube so bent as to insure
free communication between the two branches. In order
to read easily the level of the
liquids, have a branch of the
U-tube at either edge of the
meter stick.
Into one branch pour water
through the funnel till it about
half fills both. By drawing
the fingers pressed together
along the rubber tube, drive
out any hidden air-bubbles.
Into one of the branches, very
slowly at first, pour kerosene.
Notice the well-defined bound-
ary between the kerosene and
the water. Continue pouring
kerosene till the top, &, of the
column of kerosene is nearly
on a level with the top of the
meter stick. Be sure, however, that the boundary, /, be-
tween the kerosene and the water does not sink out of
sight into the rubber tube.
How does the pressure at the boundary of the two liquids
compare with the pressure at the same level in the water in
the other tube ? (See your inference from Exp. 19, Part 2.)
How does the weight of the kerosene column, &/, com-
pare with the weight of the water column, Iw, which
stands above the horizontal plane passing through the
boundary of the kerosene and the water ?
FIG. 15.
ATMOSPERIC PRESSURE. 37
What is the length of this column of water ?
What is the length of the kerosene column ?
How does the weight of a certain length of the kerosene
column compare with the weight of an equal length of
the water column ?
What is the specific gravity of the kerosene ?
QUESTION. When the two branches of a U-tube have the same area
of cross-section, suppose a column of water 80 cm tall balances a column
of kerosene 100 cm tall ; how tall a column of kerosene would a column
of water 80 cm tall balance, if the branches of the U-tube were of unequal
area of cross-section ?
18. Inverted TJ-Tube. Even when the liquid will
mix with water, the method of balancing columns can be
used, but in a modified form, as described in the following
experiment.
Experiment 25. To find the specific gravity of a liquid
by means of the inverted U-tube.
Apparatus. The support and the glass tubes of Exp. 24 ; two
small tumblers ; a lead three-way tube ; a pinch-cock ; rubber
tubing ; rubber bands.
Directions. By means of short pieces of rubber tube
couple a glass tube to each of the parallel arms of the
three-way tube. Over the remaining arm .slip a somewhat
longer piece of rubber tube, which is clasped loosely by
the pinch-cock. Fill one tumbler with water, the other
with kerosene, and place them side by side upon the base
of the support, which is not shown in Fig. 16. To this
support fasten, in an inverted position, with rubber bands,
the U-tube that you have just made, with one of the glass
tubes dipping into the water, the other into the kerosene,
38
EXPERIMENTAL PHYSICS.
Record the height to which capillary attraction raises
the liquids in each tube. Then by means of the mouth
draw out some of the air through
the rubber tube till the liquids
rise to a considerable height in
each tube, and, finally, while the
liquids are raised in this way,
clamp the rubber tube with the
pinch-cock.
Record the height of the top of
each column of liquid above the
liquid in the tumbler. In order
to find the heights to which the
liquids actually rose by reason of
removing some of the air from
the tubes, subtract from each of
the recorded heights the amount of
elevation due to capillary attrac-
tion at first observed in each tube.
When thus corrected, what is the
true height of the water column,
and of the kerosene column ?
How does the weight of a certain
length of the kerosene column com-
pare with the weight of an equal
length of the water column ?
What is the specific gravity of the kerosene ?
SPECIFIC GRAVITY OP AIR.
19. Specific Gravity of Air. We have become
acquainted with methods for finding the specific gravity
FIG. 16.
SPECIFIC GRAVITY OF AIR.
39
of solids and of liquids. In the following experiment we
shall get the specific gravity of air by a method that will
serve to illustrate roughly the way in which the specific
gravity of gases may be found.
Experiment 26. To find the specific gravity of air.
Apparatus. An air-pump of simple construction (see Fig. 19);
a dry 2-quart bottle with a perforated rubber stopple, through which
is thrust a piece of glass tube long enough
almost to touch the bottom of the bottle
and to project about 2 cm above the stopple;
a piece of pressure tube about 30 cm long;
a brass clamp ; a 250 CC graduate ; a glass
jar filled with water ; a platform balance.
Directions. Into the mouth of
the bottle insert the stopple slightly
smeared with vaseline to make the
bottle air-tight. Over the end of
the glass tube outside of the bottle
slip the pressure tube and put the
clamp, as shown in Fig. 17, loosely
over the tube.
Weigh the bottle carefully, to-
gether with tubes, stopple, and
clamp. Lay the bottle on its side close to the air-
pump. Over the exhaust nozzle of the pump slip the
end of the pressure tube. Make strokes of the pump to
the number of 20 or 40, or until the air as it escapes
from the pump makes a short, faint hiss. Close to the
end of the pressure tube next to the air-pump make
the clamp fast. Detach the bottle and weigh it carefully.
What weight of air has been removed ? (If less than
FIG. 17.
40 EXPERIMENTAL PHYSICS.
0.7 g has been removed, pump out some more air and weigh
again.)
Near the edge of the table place the bottle and the jar
of water. To a considerable depth beneath the surface
of the water plunge the end of the pressure tube and
loosen the clamp. As the water runs in, hold the bottle
upright at the edge of the table close beside the jar. By
raising or lowering the bottle, keep the surface of water in
it on the same level with the surface of water in the jar.
When the clamp was loosened, what made the water
rush into the bottle? When the water stops flowing
into the bottle, what is the relation between the pressure
of the atmosphere and the pressure of the air in the bottle ?
What is the reason for your answer ?
Clamp the end of the pressure tube and loosen the
stopple. Then raise the tube into a vertical position,
loosen the clamp, and allow the water in the tube to run
into the bottle. (Why ?) Now find how many cubic centi-
meters of water there are in the bottle by measuring this
water with the graduate.
How many cubic centimeters of air at atmospheric
pressure have been removed from the bottle ?
How many grams does this air weigh ? (See answer to
question as to weight of air removed.)
What is the weight of an equal volume of water ?
What is the specific gravity of air ?
NOTE. Keep the bottle and tubes for the next experiment.
Experiment 27. To find what part of 'the air contained
in the bottle was removed.
Apparatus. The bottle, stopple, and tubes used in the last
experiment ; a 250 CC graduate.
BOYLE'S LAW. 41
Directions. Fill the bottle brimful of water. Into
the mouth of the bottle, holding the tube upright, put the
stopple, and press it into place. Then remove the stopple,
and let the water in the tube run into the bottle. (Why?)
With the graduate find how many cubic centimeters of
water there are in the bottle. In the last experiment you
found the number of cubic centimeters of air at atmos-
pheric pressure removed.
What part of the air originally in the bottle was
removed ?
The quotient just found, is called the degree of exhaus-
tion ; hence the
Definition. The degree of exhaustion is a number that
tells what part of the air contained in a vessel has been
removed. This numerical value is expressed as per
cent.
QUESTION. If a vessel of 1000 CC capacity, filled with air at atmos-
pheric pressure, has 950 CC taken out, what is the degree of exhaustion ?
Ans. 95 per cent.
BOYLE'S LAW.
2O. Boyle's Law. When we found the specific
gravity of air, we made no account of the height of the
barometer. The specific gravity of air depends on the
pressure of the atmosphere; so it will be interesting to
find what relation there is between the pressure of the
atmosphere and the volume occupied by a portion of it.
The relation is known as Boyle's Law. 1
1 In honor of Robert Boyle, who discovered the law in 1662.
42
EXPERIMENTAL PHYSICS.
Experiment 28. To find the relation between the volume
of a certain mass of air and the pressure put upon this air.
Apparatus. A wooden support like the one used in Exp. 24 ;
a clean Boyle's tube ; clean mercury ; a medicine dropper ; two
rubber bands.
Directions. Fasten the tube to the support by rubber
bands (Fig. 18). Get the reading of the barometer.
Carefully pour mercury into the
tube till the bend is covered and
the mercury stands about 3 cm
higher in the long arm than in
the short. Tip the tube to al-
low some air to escape from the
short arm; place the tube up-
right again ; note the levels and,
if necessary, repeat the tipping
(in the opposite direction this
time, perhaps) till the mercury
in the closed arm stands l cm or
2 cm above the level of the mer-
cury in the long arm. Then,
by means of the medicine
dropper, cautiously add mercury
till the two levels are the same.
In the subsequent parts of the
experiment the tube must not
be tipped, lest the air in the
closed arm be increased or
FIG. 18. ,. . . , ,
diminished.
Be sure to have the level of the mercury from l cm to 3 cm
above the curve of the tube. Read and record the posi-
BOYLE'S LAW. 43
tion of the top of the meniscus, or rounded part at the end,
of each mercury column above the base of the support.
What is now the pressure on the air in the closed arm ?
[See your inference from Exp. 19, Part 2.]
Now pour in some more mercury, adding the mercury
by means of the medicine dropper, globule by globule
towards the last, till the level of the mercury in the open
arm is half of the barometric height above the level of the
mercury in the short arm.
Record the heights of the tops of the columns above the
base. In this experiment all measurements of length
must be recorded in centimeters.
What is the pressure on the air in the closed branch
now?
Pour more mercury into the tube till the level of the
mercury in the open arm is just the barometric height
above the level of the mercury in the short arm. Record
the heights as before.
What is the pressure on the air in the closed arm now ?
Finally, if the tube is long enough, make the level of
the mercury in the open arm stand one and one-half times
the barometric height above the level of the mercury in
the closed arm. As before, record heights.
What is the pressure on the air in the closed arm now ?
Get the reading of the barometer again. (Why ?)
Measure and record the height of the inside of the top
of the closed arm above the base of the support.
If you divide each of the last three pressures in your
record by the first (the atmospheric) pressure, you can put
the quotients into the following form
44 EXPERIMENTAL PHYSICS.
As the tube is of uniform bore, the volume of air in the
short arm is proportional in each case to the length of
the air column in the short arm, therefore, divide each
of the last three lengths by the first and the quotients
will be the same as those obtained by dividing the actual
volumes. Put these quotients into the fractional form
and see how nearly they agree with
From the results obtained by comparing the quotients
of the pressures with the quotients of the corresponding
volumes, what do you find to be the relation between the
volume of a certain quantity of air and the pressure put
upon this air?
What keeps the mercury from filling the short arm ?
What principles learned in previous experiments have
you made use of in this ?
EXAMPLES.
1. A bent .tube, having one end open and the other end closed, con-
tains mercury which stands 60 cm higher in the open than in the closed
branch. Compare the pressure of the air in the closed branch with that
of the external air ; the barometer at the time standing at 75 cm .
Solution. Since the pressure is equally great at all points in a hori-
zontal plane passing through a liquid (see your inference from Exp. 19,
Part 2), the pressure at the surface of the mercury in the closed branch
(that is, the pressure of the confined air) must equal the pressure at the
same level in the open branch ; but the pressure at this level in the open
branch is the pressure due to the column of mercury 60 cm high plus the
pressure due to the external air bearing down upon the top of this mer-
cury column ; but this air pressure is equal to 75 cm (that is, it will support
a column of mercury 75 cm high) ; so the total pressure will be
60 cm 4- 75 cm = 135 cm .
46
Thus the pressure of the mass of air confined in the closed branch is
135' m .
.-. pressure of confined air : pressure of external air = 135 : 75 = 9 : 5.
That is, the pressure of the air in the closed branch is | as great as
that of the external air.
2. A mass of air occupies 100 CC when the pressure is 60 cm . What
volume will it occupy when the pressure is 120 cm ?
Solution. Boyle's Law states that the volume of a gas varies inversely
as the pressure ; for example, if a mass of air has a volume V\ when the
pressure is PI , and a volume F 2 when the pressure is P 2 , we shall have
the following relation among V\ , F 2 5 PI and Pg :
Fi : F a -= P 2 : PI ;
or, if we call FI the first volume, F 2 the second volume, PI the first
pressure, and P 2 the second pressure, we shall say
1st Volume : 2nd Volume = 2nd Pressure : 1st Pressure.
In the special problem given for solution we have
Fi = 100, PI = 60,
F 2 = x. P 2 = 120.
So 100 : x = 120 : 60,
120 x = 6000,
x-50.
Hence the required volume will be 50 CC .
3. A mass of air occupies 200 CC when the pressure is 76 cm . What
must the pressure be in order that this mass of air shall occupy only
25 CC ?
4. In performing the Torricellian experiment, an inch in length of the
tube is occupied with air at atmospheric pressure before the tube is
inverted. After the inversion, this air expands till it occupies 15 inches,
when a column of mercury 28 inches high is sustained below it. Find
the true barometric height.
Solution. In the statement of the problem nothing is said about the
area of the cross-section of the tube, so we cannot find the volume of the
air that fills an inch in length of the tube ; but let us denote the area of
this cross-section by a, then a will denote the volume of the air in cubic
46 EXPERIMENTAL PHYSICS.
inches. After the hi version of the tube, 15 a will denote the new volume
in cubic inches. If x denotes the true barometric height, that is, the
pressure of the atmosphere, we know, as was stated in the solution of
Example 1, that the pressure at the level of the mercury in the cup, into
which the tube was inverted, is equal to the pressure within the tube on
the same plane. The pressure on the portion of the plane within the
tube is measured by the height of the mercury column above it plus the
pressure of the confined air upon the top of this column. The length of
this mercury column is given in the statement of the problem as 28
inches. Let us denote by P% the pressure of the confined mass of air,
then the pressure on the portion of the plane within the tube is 28 + P% ;
but this has just been shown to be equal to the atmospheric pressure x ;
hence 28 + P 2 - x.
.:P 2 =x-2S.
Collecting what we know to be true about the volumes and the
pressures in this problem, we have
Hence, by Boyle's Law,
a : 15 a = x 28 : x,
ax = 15 a (x 28),
x = 15 (x - 28),
Hence the true barometric height is 30 in.
NOTE. It will be seen that the a, which we introduced for the purpose
of expressing the volume of the air, does not appear in the result. In
other words, it does not matter what the area of the cross-section of the
tube may be.
5. A tube of uniform cross-section, 200 cm long, closed at one end, is
pushed open-end downward into a deep cup of mercury till the air within
it, which originally filled the whole tube, is reduced to one-half of its first
volume. The barometer at the time of performing the experiment reads
76 cm . How far below the surface of the mercury in the cup is the
surface of the mercury in the tube ? How far is the closed end of the
tube above the general surface of the mercury in the cup ?
BOYLE'S LAW. 47
6. A quantity of air is collected in a barometer tube, the mercury
standing 10 in. higher inside the tube than outside, and the correct baro-
metric height being 30 in. If the volume of the air under these con-
ditions is 1 cu. in., what would be its volume at atmospheric pressure ?
Solution. Since the pressure at all points in a horizontal plane passing
through a liquid is equally great, we shall have, denoting by PI the
pressure of the air confined in the tube,
Pi + 10 = 30.
.-. P! = 20.
Collecting what we know to be true about the volumes and the
pressures in this problem, we have
Fi = 1, P! = 20,
F 2 = x. P 2 = 30.
Hence, by Boyle's Law,
1 : x = 30 : 20,
The required volume is, then, f cu. in.
7. A quantity of air occupying 10 CC is admitted to the space above the
mercury column of a barometer, and there expands till it occupies 30 CC .
The column of mercury beneath this air is now 50 cm high. How high
was it before the admission of the air ?
SUGGESTION. Denoting by x the required height, show that the
pressure of the air in the tube is denoted by x 50. Then collect what
you know to be true about the volumes and the pressures, and apply
Boyle's Law.
8. The tube of a barometer has a cross-section of lsqcm } an d when the
mercury column stands at 77 cm , the length of the empty space above it
is 8 cm ; how far will the mercury column be depressed if l cc of air is
passed up into the tube ?
Solution. Suppose the mercury to be depressed through x cm then if
we denote by P 2 the pressure of the air confined in the tube, we shall
have 77-z+P 2 = 77.
.-. Po = X ;
that is, x measures the pressure of this air.
48
EXPERIMENTAL PHYSICS.
Since the cross-section of the tube is l s( i cm , the volume of this air is
(X + 8)cc.
Collecting what we know to be true about the volumes and the
pressures in this problem, we have
Fi = 1, Pi = 77,
r 2 = x + s. P 2 = x.
By Boyle's Law, we have
1 :x + 8 =o;:77,
(x + 8) x = 77,
2 +8x+ 16 = 77 + 16,
(x + 4) 2 = 93,
x + 4 = 9.65,
x = 5.66.
Hence the mercury column is depressed through 5.65 cm .
9. A cylindrical diving-bell, 9 ft. high, is immersed in water so that
its top is 27 ft. below the surface. If the height of the water-barometer
is 34 ft. , find how high the water rises within the bell.
21.
PUMPS.
The Air-Pump. We have already used in the
laboratory (Exps. 14, 15, and 25)
an air-pump of very simple con-
struction. This pump consists
(Fig. 19) of a hollow metallic
cylinder, (7, closed at the bottom,
where it is supported in a vertical
position by an iron foot not shown
in the figure. In the cylinder is a
piston, D, which fits tightly, but
which can readily be pushed down
and pulled up by a handle at-
tached by the rod, F, to the
piston. At the lower end of the cylinder are two nozzles,
PUMPS. 49
E and Cr. When the piston is worked, air is drawn in
through one of these nozzles and pushed out through the
other. On unscrewing the nozzles, a valve will be found
behind each. These valves are made of thin sheet-brass,
and are conical in form. They fit closely into conical
holes communicating with the interior of the cylinder.
The conical holes are called valve seats. In one nozzle
the valve seat tapers towards the end of the nozzle,
while the valve seat behind the other tapers towards the
cylinder.
If the vessel from which the air is to be taken is con-
nected by means of a piece of thick-walled rubber tubing
to the nozzle covering the valve whose sharp end points
outward, and the piston is raised by pulling up on the
handle, the air in the cylinder expands, and thereby its
pressure is diminished ; so the air in the vessel also
expands, and rushes into the cylinder until the pressure
becomes equal in both. When the piston is pushed down,
the air in the cylinder is compressed. This compressed
air closes, by pressing into its seat, the valve by which the
air entered the cylinder ; but it opens the other valve and
escapes into the external air. By repeating the process of
raising and lowering the piston, more air is taken from
the vessel, till, finally, the difference of pressure between
the air in the vessel and the air in the cylinder becomes
so small that it is unable to open or close the valve.
No air-pump has ever been made that will give a perfect
vacuum. In the construction of air-pumps, however, such
skill and ingenuity have been used that with a good pump
one may obtain a nearly perfect vacuum. The bulbs of
incandescent lamps which you see in shops and houses
50
EXPERIMENTAL PHYSICS.
lighted by electricity have the air removed from them by
an efficient pump of peculiar construction. In the side
and near the top of a long upright tube is an opening to
which the lamp-bulb is attached at a certain stage in its
process of manufacture. Mercury is then poured down
the tube. As the mercury passes the opening, the air in
the bulb expands and is swept down the tube.
22. The Common Lifting- - Pump. This pump, so
common in houses and yards, is used for raising water
from a well or cistern to the surface
of the ground. The construction of
this pump is as follows :
A long pipe, A (Fig. 20), extends
from the surface of the ground to some
distance below the surface of the water
in the well. At its upper end the pipe
has a valve, J5, hinged like a trap-door,
opening upwards. To the upper end
of the pipe is fastened a hollow cylin-
der, (7, in which is a tightly fitting
piston, D, that can be raised and
lowered by lowering and raising the
pump-handle to which it is attached
by means of a rod, F. In the piston is
a valve, 6r, opening upwards like
that in the pipe. We shall explain
the action of the pump by supposing the part of the pipe
above the water in the well to be filled with air at the
start. On pushing down the piston by raising the pump-
handle, the air in the cylinder is compressed. This com-
FlG. 20.
PUMPS. 51
pressed air pushes down on the valve, J9, and closes it
more tightly ; but by pushing up on the valve, 6r, in the
piston, the compressed air opens it, and continues to
escape as long as the piston descends. When the piston
is raised, the air in the cylinder becomes rarefied ; the
atmosphere presses down on the valve in the piston and
closes it tightly, but the air in the tube pushes open the
valve, B, and enters the cylinder. By again lowering
the piston and raising it, some more air is taken out. In
the meantime the pressure of the atmosphere on the water
in the well forces the water up the tube, till, as the action
of the pump is continued, the water enters the cylinder.
Now, when the piston is pushed down, the water rises
through the piston-valve, 6r ; when the piston is raised
again, the piston-valve closes, and the valve in the pipe is
pushed open by the water forced into the cylinder by the
pressure of the atmosphere. The piston lifts the water
above it until the spout is reached, whence the water flows
into the pail placed to receive it. Each succeeding stroke
brings a fresh supply of water, which keeps a nearly con-
tinuous stream flowing from the spout.
It frequently happens that the valves do not fit accu-
rately, and in such cases it is necessary, in starting the
pump, to pour some water into the cylinder above the
piston.
QUESTION. When the mercury barometer column stands at a height
of 30 inches (specific gravity of mercury = 13.6), what is the greatest
height to which water can be raised by the common lifting-pump ?
23. The Force-Pump. This is the pump employed
when water is to be raised to a height above the pump, or
when a forcible stream is desired. In construction this
52
EXPERIMENTAL PHYSICS.
pump resembles the lifting-pump, but the piston, instead
of having a valve in it, is solid ; and a valve, (7, is placed
at the mouth of a pipe that leads from a point near the
bottom of the cylinder to the place where the water is to
be delivered. The valve, B, at the top of the pipe is
placed in the same position as the corresponding one in
the lifting-pump. The valve in the
pipe leading from the side of the
cylinder opens away from the cylin-
der (Fig. 21) ; consequently, when
the piston is raised, this valve closes
(Why ?), and the air below the valve,
jB, in the pipe leading into the well
forces its way through and rushes
into the cylinder to equalize the
pressure. By continuing the pro-
cess of pumping, the air is at last
removed from the pipe, and the
water in the well is forced, by the
atmospheric pressure on the surface
of the water in the well, into the
FlG 21 cylinder ; then the piston, when
lowered, pushes down on this water
and forces it through the valve, 6r, into the side-pipe ;
when the piston is again lifted, more water is raised from
the well into the cylinder. (Why does not the water that
has just been forced into the side-pipe run back into the
cylinder?) Then, lowered again, the piston forces the
water in the cylinder into the side-pipe, which conveys
the water, as the pumping goes on, to the place where
it is to be delivered.
THE SIPHON.
53
In the steam fire-engine and other force-pumps the
side-tube leads into a reservoir of air ; the air becomes
somewhat compressed by the water and sends it out in a
continuous stream.
THE SIPHON.
24. The Siphon. The siphon (Fig. 22) in its simplest
form is a bent tube open at both ends. It is used for
transferring a liquid from one vessel to another when it is
not convenient to make .a hole in
the side of the vessel or to tilt it so
that the liquid shall run out. To
make the siphon begin working, one
end is dipped into the liquid which
we wish to remove, and suction, by
means of the mouth or otherwise,
is applied to the other end. When
the liquid is corrosive, like a strong
acid, the method of procedure should
be to fill the siphon with some of
the liquid, close one end, and dip
the other into the vessel of liquid;
on uncovering the end, the liquid will at once begin to
flow. In order that the siphon may work, it is necessary,
if the liquid is discharged into the air, that the end, A,
from which the liquid flows should be below the level,
EF, of the liquid in the vessel, or, if the liquid is dis-
charged into another vessel, the surface of the liquid in
this vessel must be at a lower level than that in the
former.
FIG. 22.
54 EXPERIMENTAL PHYSICS.
The explanation of the action of the siphon, the reason
why the liquid flows first up hill, from E to D, and then
down hill, from D to A, is as follows :
The pressure inside the arm, DA, of the siphon, which
does not dip into the vessel containing the liquid to be
removed, at a point, F, lying in the same plane as the
surface of the liquid, is the same as at the point, E, cor-
respondingly situated in the other arm ; but this pressure
is the same as the atmospheric pressure at a point on the
surface of the liquid in the vessel (Why ? See your
inference from Exp. 19, Part 2). The pressure of the
liquid at the extremity, A., of the arm which is out-
side the vessel is greater than at the point, F, already
spoken of, lying on a level with the surface of the liquid
(Why ? See your inference from Exp. 17) ; but the pres-
sure at this point has already been shown to be equal to
the atmospheric pressure ; hence the pressure at the
extremity, A, of the tube is greater than the atmospheric
pressure, and, consequently, the liquid pressure at this
point overcomes the atmospheric pressure from without,
and the liquid tends to separate at the highest point, D,
of the siphon and to run out. If the height of the bend,
.Z), of the siphon above the level of the liquid in the vessel
is less than the height at which the liquid would stand in
a barometer tube, the pressure of the air will prevent the
liquid from separating at the bend, D, and by forcing
the column of liquid to ascend in the arm dipping into
the liquid, will maintain a continuous flow.
How long will the liquid continue to flow after the level
of the liquid in the vessel into which the siphon discharges
becomes the same as that of the liquid in the first vessel ?
THE HYDROSTATIC PRESS.
55
QUESTIONS. When the barometer stands at a height of 76 cm , what is
the greatest height over which mercury can be carried by means of a
siphon ? When the barometer stands at a height of 30 inches (specific
gravity of mercury = 13.6), show by computation that the greatest height
over which a siphon can raise water will not exceed 34 feet.
THE HYDROSTATIC PRESS.
25. The Hydrostatic Press. The hydrostatic, or, as
it is sometimes called, the hydraulic press, is a machine
FIG 23.
for lifting heavy weights, and for compressing merchan-
dise into small compass. This machine is in its essential
principles constructed as follows :
Two hollow cylinders, A and B (Fig. 23), of iron, each
closed at one end, are set side by side in a vertical position
with their open ends uppermost ; a pipe, (7, of iron con-
nects the two near the bottom, so that water poured into
one cylinder will flow through this pipe into the other.
These cylinders are of unequal area of cross-section, the
56 EXPERIMENTAL PHYSICS.
larger being, perhaps, 1000 times that of the smaller.
From Exp. 23, you already know that if water is poured
into one of the cylinders this water will rise to an equal
height in both. If a pressure be applied by means of a
tightly fitting piston to the top of the water column in
the smaller cylinder, it will take a much greater pressure
applied to the top of the water column in the larger to
balance this pressure; thus, if a pressure of 1 Ib. were
applied to the piston of the smaller cylinder, a pressure of
1000 Ibs. would have to be laid on the piston, Z>, that rests
on the top of the water column in the larger cylinder.
The explanation of this fact is that water transmits a
pressure applied to it with undiminished force in all
directions ; so that when the pressure of 1 Ib. is applied
to the top of the smaller water column, the water trans-
mits this pressure to each portion of the inner surface of
the two cylinders ; consequently each portion of an area
equal to that of the smaller piston has now upon it an
additional pressure of 1 Ib. As the area of the face of the
larger piston is 1000 times that of the smaller, the pressure
on this face will be 1000 Ibs. The larger piston is then
forced upwards with a pressure of 1000 Ibs. Hence, to
keep the larger piston from moving up, it would have to
be loaded with a weight of 1000 Ibs.
A strong framework is built above the larger cylinder,
and the substance that is to be compressed is put between
this and the piston. Had the area of the cross-section of
the larger cylinder been 10,000 times the area of the cross-
section of the smaller, a pressure of 1 Ib. applied to the
smaller piston would produce a pressure of 10,000 Ibs. on
the larger piston.
MARIOTTE S BOTTLE.
57
The hydraulic press is widely used in the arts. It may
be constructed to give pressures of two or three hundred
tons.
MARIOTTE 'S BOTTLE.
26. Mario tte's Bottle. This piece of apparatus (Fig.
24) consists of a bottle having three small holes drilled
through its sides, one near the top, one
near the bottom, and the third half-way
between the other two. A rubber
stopple with one hole has. a glass tube
thrust through it ; this tube is long
enough to reach to the bottom of the
bottle when the stopple is put in place,
and also to project 10 cm above the top
of the stopple. This piece of apparatus
is very useful in fixing the student's
ideas about liquid pressure and its con-
sequences ; so the following experiment
should be carefully performed.
Experiment 29. To find what will
7 . 7 FIG. 24.
happen on removing one or more stopples
in the side of a Mariotte's bottle filled with water.
Apparatus. A Mariotte's bottle ; water.
Directions. After securely stopping the holes in its
sides by means of small cork stopples, as shown in Fig. 24,
fill the bottle brimful of water ; then push the tube and
stopple into place so that the water will rise in the tube
and stand at some distance above the stopple. Be careful
not to have any air-bubbles in the bottle.
58 EXPERIMENTAL PHYSICS.
Before removing any of the side stopples, as you will be
directed to do, call to mind the facts you have already
learned about liquid pressure in Exps. 17, 18, and 19,
and try to predict what will take place ; then, having
made up your mind as to what will take place, remove
the stopple, and see if your prediction is verified.
After placing a vessel to catch the water, take out the
stopple that closes the hole, A, highest up in the side of
the bottle ; then replace this stopple and remove the one
at B ; finally replace the stopple at B and remove the one
at 0.
Does the water run out freely in every case ?
At what level does the water in the tube stand after the
removal of each stopple ?
Now, without removing the large stopple, slip the tube up
till its lower end is on a level with A ; open A and allow
all the water that will run out to do so. Refill the bottle,
push the tube down till its lower end is on a level half
way between A and B, and remove the stopple from A ;
then close A and let the water run from B a short time.
Push the tube down till its lower end is on a level
between B and C ; have the bottle completely filled with
water and remove the stopple at A. Replace the stopple
at A and remove the one at B. Replace the stopple
at B and remove the one at O.
In order to have water flow freely from the bottle, what
relation must there be between the position of the hole
from which the flow takes place and the end of the tube ?
Fill the bottle once more, and keeping the end of the
tube below C remove the stopple at (7, and then take out
also the stopple at A.
GRAPHICAL METHOD. 59
When both stopples are out, what takes place at 0?
When both stopples are out, what takes place at A ?
Write out a brief explanation of the facts you have
observed.
GRAPHICAL METHOD.
27. Graphical Method of Representing Results. In
Exp. 28 we obtained a series of volumes of air, which
decreased in proportion as we increased the pressure
applied to the confined mass of air. Whenever, as in
this instance, we have a series of results which depends
on a uniform variation of some one circumstance in the
experiment, the relation among the results can be clearly
represented to the eye by employing what is known as
the graphical method. To illustrate the application of
this method, let the following be the data obtained, as
in Exp. 28 :
PRESSURE. VOLUME.
1 100 CC
1.5 66.6
2 50
2.5 40
3 33.3
3.5 28.6
4 25
The first column gives in atmospheres the pressures,
which have been increased by the addition of half an
atmosphere at a time ; the second column gives the
volume corresponding to each pressure.
60
EXPEEIMENTAL PHYSICS.
On a sheet of coordinate paper, which is ruled into little
squares by equally spaced lines, a horizontal line is chosen
50
40
30
20
10
10
20
PRESSURES.
FIG. 25.
30
-40
as the " axis of abscissae," and a vertical line as the " axis
of ordinates "; the point at which these two lines intersect
is called the " origin." Starting from the origin, there is
GRAPHICAL METHOD. 61
laid off on the horizontal line a certain distance, equal,
say, to 10 of the divisions, as in Fig. 25, to represent the
first pressure, and from the point thus reached a vertical
distance is measured, equal, say, to 50 of the divisions, to
represent the corresponding volume ; the end of this
vertical line is marked by a point. Each of the remaining
observations is treated in the same way as the first, by
using the same scale as was at first employed for measur-
ing distances in each of the directions (that is, if 10
divisions represent 1 atmosphere, 15 divisions represent
1.5 atmospheres ; if 50 divisions represent 100 CC , 33.3
divisions represent 66.6 CC ). Finally, a strip of hard rubber
or a steel spring is laid edgewise upon the paper, and
made to pass through the points marking the extremities
of the vertical lines. A line is drawn through these
points with a sharp lead-pencil.
This line represents to the eye the relation existing
among the various observations. When the numerical
data employed in the construction of this line have been
carefully determined, and the line itself drawn with pre-
cision, it is possible to obtain with ease and accuracy the
volume the air will occupy for any given pressure between
the extreme pressures made use of in this experiment.
To do this, count from the origin on the horizontal line a
number of divisions corresponding to the given pressure ;
then count the number of divisions in the vertical line
lying between this point and the line joining the extremi-
ties of the vertical lines. The number thus obtained will
represent the required volume on the scale employed in
representing the volumes ; in the present case two divi-
sions on a vertical line represent unit volume.
62 EXPERIMENT AL PHYSICS.
Let the student construct on a piece of coordinate paper
a curve in the manner just described, using the results
obtained in Exp. 28.
EXPERIENCE.
28. Experience ; Observation ; Experiment. At this
stage of our progress it may be well for us to think a little
about the first thing necessary for the successful study of
physics. This necessary thing is experience, which fur-
nishes us with facts. We obtain experience by either
observation or experiment.
In observation we merely note and record phenomena
(that is, things which appear). Thus, a U. S. Signal
Service man observes the ever-changing weather, and
notes the height of the barometer, the temperature and
moisture of the air, the direction and force of the wind,
the height and character of the clouds.
In experiment we vary at will the conditions under
which phenomena occur. We might have to wait years,
or even centuries, to meet with facts which we can readily
produce at any moment in a laboratory.
The work of the U. S. Signal Service man is confined
to pure observation, for he is unable to control any
of the phenomena that he studies. The work of the
physicist and the chemist is not confined to observation
alone ; it also includes experiment, for each is able to vary
at will the conditions under which many of the phenomena
that he studies occur. Where it can be employed, experi-
ment is a fruitful and direct means of getting facts.
Experiments are of two classes : qualitative and quanti-
tative.
EXPERIENCE. 63
A qualitative experiment has for its object the production
and observation of phenomena.
A quantitative experiment has for its object the measure-
ment of the magnitudes of the phenomena produced.
Exp. 19 is a qualitative experiment ; Exp. 21 is a
quantitative experiment. Divide the 29 experiments you
have performed into qualitative and quantitative experi-
ments, and make a list of each group.
29. Facts and Inferences from Facts. On the left-
hand page of his note-book the beginner must constantly
try to record only what his senses have actually observed.
He is apt to record his own character and feelings rather
than the facts, for the mind is like an uneven mirror, and
does not reflect the facts without distortion. Since the
mind by long experience has acquired the power of
judging unconsciously of many things of which his senses
have not actually assured him, the beginner confuses facts
observed with inferences from these facts.
EXAMPLES.
1. Find the specific gravity of a body that weighs 58s in air and 40s in
water.
2. A specific gravity bottle holds 100s of water and 180s of sulphuric
acid. Find the specific gravity of the acid.
3. Find the volume of a solid that weighs 357s in air and 253s in
water.
4. A glass ball loses 33s when weighed in water, and loses 6s more
when weighed in a saline solution. Find the specific gravity of the
solution.
5. A body lighter than water weighs 102s in air ; and when it is
immersed in water by the aid of a sinker, the joint weight is 23s. The
sinker alone weighs 50s in water. Find the specific gravity of the body.
64 EXPEKIMENTAL PHYSICS.
6. Find the specific gravity of kerosene from the following data : In a
U-tube the length of the kerosene column is 100 cm , and the length of the
water column just balancing this is 79 cm .
7. Find the volume of a solid which weighs 458s in air, and 409s in
brine. Specific gravity of the brine = 1.2.
8. How much weight will a body lose whose volume is 47 CC , when
weighed in a liquid the specific gravity of which is 2.5 ?
9. How much water will 1000 CC of oak displace when floating in equi-
librium ? Specific gravity of oak = 0.8.
10. Why is it, in the metric system of weights and measures, that the
specific gravity of a substance and the numerical value of its density are
the same ?
11. Define density ; define specific gravity. A certain solid floats in
water with only two-thirds of its volume submerged. What is the specific
gravity of this solid ?
12. A pump is used to draw water from a well through a vertical pipe.
How long may the pipe be, the barometer reading 76 cm , and the specific
gravity of mercury being 13.6 ? Tell and explain what would happen if
a small hole were bored in the side of the pipe, when full of water, at a
point half-way up.
13. When the height of the column of mercury (sp. gr. = 13.6) in the
barometer is 80 cm , how tall a column of water can the pressure of the
atmosphere support in a tube having a perfect vacuum at the top ?
14. A rectangular block 10 cm thick floats in water with 6 cm of its
depth submerged. Find the specific gravity of the block, showing your
reasoning.
15. From the following data find the specific gravity of sulphuric
acid :
Weight of bottle empty = 5Qg.
Weight of bottle filled with water = 150s.
Weight of bottle filled with sulphuric acid = 234s.
16. How much would the result obtained in the last example have
been changed if l cc of the bottle had been left empty when it was weighed
with water ?
17. A cork of sp. gr. 0.25, the volume of which is 10 CC , floats upon
mercury of sp. gr. 13.6. How great is the submerged part of the cork ?
18. Given that a body appears by the indications of a spring balance
to weigh 15s in air and 10s in water. Answer the following questions :
EXAMPLES. 65
(a) If the balance is correct, what is the specific gravity of the body ?
(b) If each reading of the balance is only T 9 o as large as it should be,
what is the specific gravity of the body ?
19. A cubical vessel, each side of which is 10 cm square, has a tube
Isqcm m cross-section and 20 cm tall rising from the middle of its top.
The tube is open at both ends, and both vessel and tube are full of water.
Neglecting atmospheric pressure and weight of vessel and tube, find
(a) The total pressure which the vessel and tube as now filled exerts
upon the support.
(6) The total pressure exerted against the bottom of the vessel by the
water within it and the tube.
If the pressures are not equal, explain the difference.
20. A vessel is filled with water to a depth of 40 cm . A cylinder of
wood 30 cm long and ICKH cm in area of cross-section, the specific gravity
of which is 0.5, extends upward through a hole in the bottom of the
vessel, the top of the cylinder being 20 cm beneath the surface of the
water. Show whether the cylinder tends to rise or fall, and how great a
force is required to hold it in its present position.
21. A block, the density of which is to be determined, is measured
with a scale the divisions of which are only T % as long as they are sup-
posed to be. How much too small or too large will the value found for
the density be in consequence of this error ?
Solution. Let a, 6, and c denote the true dimensions of the block,
and let W denote its weight. Then the true density, d, will be
abc
As each of the divisions of the faulty scale with which the block is
measured is T 9 T of what it is supposed to be, that dimension of the block
denoted by a will, according to this scale, have a value equal to the
number of times a contains T % , that is,
In like manner, the dimension denoted by b will have a value \- b
when measured by the scale, and the dimension denoted by c will have a
value Y c ' Tne product of - 1 /- a, - 1 / &, and Y- c i tliat is > -V2 9 a&c, will
66 EXPERIMENTAL PHYSICS.
denote the false volume found by using the measurements indicated by
the faulty scale ; and d', the false density, will be
d'= W - 72* W. .
-VV^oftc Tooo a6c
The difference between the true density and the false is
W W W W W
d ~ d/ = tib~c ~ ** ab~c = **** ^te ~ T ^ ^ = T ^ ^ ;
or, in words, the value found for the density will be too small by 0.271 of
the true density.
22. A block, the density of which is to be determined, is measured
with a scale the divisions of which are f as long as they are supposed to
be. How much too small or too large will the value found for the density
be in consequence of this error ?
23. A cube of wood 10 cm on each edge, and of sp. gr. 0.5, is covered
on one side by a piece of metal 10 cm square and l cm thick, of sp. gr. 5.
How deep would the whole mass of wood and metal sink in water ?
Solution. Volume of wood = 1000 CC .
Volume of metal = 100 CC .
Volume of metal and wood 1100 CC .
Weight of wood = 0.5 X 1000 = 500s.
Weight of metal = 5 X 100 = 500&.
Weight of metal and wood = 1000s.
Since the volume of the wood and the metal together is 1100 CC , and
their weight only 1000s, the composite block will float with 1000 CC of its
volume beneath the water. (Why ?)
The composite block would naturally float with the metallic plate
downward ; hence, the outer face of the metallic plate would be 10 cm
below the surface of the water.
24. A cylinder 20 cm long consists of a cylinder of iron, sp. gr. 7, l cm
long, and one of wood, sp. gr. 0.5, 19 cm long. If this cylinder floats up-
right in water, how many centimeters of its length will be above the
water ?
25. A cube of wood, 10 cm on an edge, floats in water with 8.5 cm of its
depth submerged. How many cubic centimeters of its volume will be
under water after kerosene, of sp. gr. 0.8, is poured into the vessel con-
taining the water till the block is completely submerged ?
EXAMPLES. 67
26. A piece of wood, of volume 1200 CC , floats with two-thirds of its
volume beneath the surface of the water. What is the least number of
cubic centimeters of lead, of sp. gr. 11.3, that must be attached to the
block to submerge it completely ?
27. A long tube closed at one end is partly filled with mercury, and
the remainder with air. When this tube is inverted in a deep cup of
mercury and pushed down till there is only 50 cm of its length projecting
above the surface of the mercury in the cup, the level of the mercury in
the tube and in the cup is the same. When the tube is raised till 100 cm
of its length projects above the level of the mercury in the cup, the surface
of the mercury in the tube stands 25 cm above the level of the mercury in
the cup. What is the pressure of the atmosphere ?
28. A barometer which has air in the space above the column reads
65 cm . If the distance from the level of the mercury in the cistern to the
top of the barometer tube is 85 cm , and if the air in the tube has a volume
of l cc when the pressure is 77 cm , find the true barometric height, the area
of the cross-section of the tube being l^qcm.
CHAPTER II.
HEAT.
3O. Some Effects of Heat. We shall begin the study
of heat with some experiments for the purpose of finding
out whether heat will change the size of bodies.
Experiment 3O. To find whether heat will chayige the
size of a volume of water.
Apparatus. A bottle having a wide mouth, like the one used in
Exp. 11 ; a good cork stopple to fit the bottle ; a piece of glass tube
30cm or 4ocm long, and 0.3 cm or 0.4 cm in diameter ; a Bunsen burner ;
a copper boiler ; two little rubber bands ; a jar of cold water.
Directions. Under the boiler half full of water
place the lighted Bunsen burner. While the water
is getting warm, pierce a hole through the stopple
with a cork borer a little smaller than the tube.
Push the tube through the cork. - Fill the bottle
brimful of water, and, taking care not to enclose air-
bubbles, press the stopple into the mouth of the
bottle. If the water fills the tube completely, shake
out some, so that the water will fill less than half
the tube. Around the tube (Fig. 26), at the top of
the water column, slip a rubber band for a marker.
Have the water in the boiler so hot as to be uncom-
fortable to the finger held in it for an instant; if
too hot, add cold water. Put the bottle into the
FIG. ?6. n t water, and for two or three minutes watch the
HEAT. 69
column of water in the tube. At the end of the two or
three minutes, put the other rubber band on the tube, at
the top of the water column.
What have you observed while you have watched ?
What is meant by expansion ?
When heated, does the water in the bottle expand?
Put the bottle into the jar of cold water, and for three
or four minutes watch the water column.
What do you observe ?
What is meant by contraction ?
When cooled, does the water in the bottle contract?
NOTE. This bottle of water with the tube might be used to tell us
which of two liquids is the warmer ; for we might put the bottle first
into one liquid and then into the other, and in each case observe the
height of the water column in the tube. The water column would stand
higher for the warmer liquid. The comparison could be more accurately
made by means of a peculiar instrument, the thermometer (from two
Greek words tJierme, warmth; and metron, a measure), which in action,
and somewhat remotely in form, resembles our bottle and tube.
Experiment 31. To find whether water, alcohol, and
ether, when equally heated, expand equally.
Apparatus. Three bulb-tubes, with two little narrow rubber bands
on each stem as markers ; water, alcohol, ether ; a copper boiler.
. NOTE. The teacher should fill one bulb and a part of its stem with
water, one with alcohol and one with ether, and should clamp the bulb-
tubes in a group, as shown in Fig. 27, to a retort-stand which is firmly
fastened to a table. There should be no flame near this apparatus,
as the vapor of ether is inflammable, and, with air, forms an explosive
mixture.
Directions. Have the copper boiler three-quarters full
of water a little warmer than the air of the room. On
70
EXPERIMENTAL PHYSICS.
each tube, which should have a label as in Fig. 27, adjust
a marker to a level with the surface of the liquid within.
Place the boiler so that the
bulbs shall be beneath the
surface of the water. Move
neither the retort-stand nor the
bulbs. Watch the columns
for two or three minutes.
Make a table, by putting
down the names of the three
liquids, showing the relative
expansion.
Experiment 32. To find
whether heat will make air
FIG. 27. expand.
Apparatus. The bottle, stopple, and tube of Exp. 30 ; a jar of
water.
Directions. Put the
stopple, through which
the tube has been thrust,
tightly into the mouth of
the bottle, which should
contain nothing but air.
Clasp the bottle in the
hand, covering it more
completely than is shown
in Fig. 28, and push the
FIG ' 28< end of the tube about l cin
below the surface of the water in the jar. For one or
two minutes watch the water at the end of the tube.
MERCURY THERMOMETER. 71
What happens in the water at the end of the tube ?
How do you account for what takes place ?
Without removing the end of the tube from the water,
take the hand from the bottle. For one or two minutes
watch the water in the end of the tube.
What does the water in the end of the tube do ?
How do you explain this phenomenon?
MEROTRY THERMOMETER.
31. The Thermometer. Upon the table before you
place a mercury thermometer, and make an accurate sketch
of it in your note-book.
Observe that the thermometer consists of three principal
parts :
1. A spherical or elongated vessel containing mercury.
This vessel, called the bulb, corresponds to the bottle of
Exp. 30.
2. A glass tube of small bore partly filled with mercury.
This tube, called the stem, corresponds to the tube joined
to the bottle of Exp. 30. The thread of mercury partly
tilling the stem is called the column. The position of the
top of the column gives the height of the thermometer.
3. A scale made by scratches on the stem, or made of
paper and enclosed in a glass tube which also contains the
stem. This scale is divided into equal parts, and each one
of these parts is called a degree of temperature.
You will probably notice in some thermometers a little
bulb or slight enlargement at the top of the stem. This
little bulb, if the thermometer is overheated, catches the
mercury, which would otherwise press against the end of
the tube and break it. Before using a thermometer, be
72 EXPERIMENTAL PHYSICS.
sure to examine this place, for, when the thermometer
happens to get turned upside down, a little mercury
frequently lodges here. If there should happen to be
any mercury in the little bulb, grasp the stem at the
end, where the little bulb is, firmly in the hand. Extend-
ing the arm to its full length, raise the hand so that the
large bulb shall point towards the ceiling. Then, carrying
the hand forward, with a quick sweep, bring it to its
natural position by the side, thus making the large bulb
trace out a semicircle in the air. A single energetic treat-
ment is usually sufficient to dislodge the mercury.
Before using a thermometer, look carefully also along
the stem at the column, which is sometimes broken, that
is, separated into two or more parts. In case the column
is broken, firmly grasp the stem, with the bulb downwards,
at its middle part in the fingers of the right hand. Keep-
ing the stem vertical, raise the hand a little way, and then
bring the hand down sharply upon the palm of the left
hand. In most cases this treatment once or twice repeated
suffices to mend the column.
On that part of the scale lying to the right-hand side of
the stem you will notice in many thermometers a column
of ciphers ; while on the left-hand side you will see a
column of figures. A cipher on the right-hand side
belongs with the figure opposite, so we have 10, 20,
30, etc. The space between 10 and 20, 20 and 30, etc.,
is divided into 10 equal parts, or degrees.
The thermometer that we have described is called a
chemical thermometer with a Centigrade scale. This is
the thermometer which we shall use in all our work in
heat.
MERCURY THERMOMETER. 73
Experiment 33. To find what temperature a thermom-
eter indicates when placed in melting ice.
Apparatus. A thermometer ; a beaker full of snow or broken ice.
Directions. In a vertical position, in the beaker of
broken ice, put the thermometer so that its bulb and a
part of its stem shall be covered. Watch the column.
After a time the column ceases to fall and comes to rest.
The column is now said to be stationary. By repeatedly
trying this experiment, physicists have found that the
temperature of clean ice, when melting, is always the same.
Why does the column fall ?
From the position of the column, what symbol should
you infer is used to indicate the temperature of melting
ice?
Experiment 34. To find the temperature a thermom-
eter indicates when placed in boiling water.
Apparatus. A thermometer ; a beaker ; a retort-stand and ring ;
a piece of wire gauze about 15 cm square ; a Bunsen burner.
Directions. After wiping the beaker dry on the out-
side, set it half full of water on the wire gauze laid on the
ring of the retort-stand. Place the lighted Bunsen burner
beneath to heat the water. Dip the thermometer bulb into
the water, and watch the column until the water boils.
Does the column become stationary soon after the water
begins to boil ?
NOTE. Physicists have found that the temperature of boiling water,
or, more accurately, the temperature of the steam from boiling water, is
constant only when certain conditions are fulfilled. These conditions we
shall soon consider.
74 EXPERIMENTAL PHYSICS.
32. The Fixed Points. By Exps. 33 and 34 you have
become acquainted with two remarkable points of the ther-
mometer scale, the melting-point of ice, commonly called
the freezing-point ; and the boiling-point of water. These
two points are called fixed points, as each of them, under
proper conditions, represents an invariable temperature.
On the Centigrade scale, the space between the fixed
points is divided into 100 degrees. Divisions are often
carried along the scale below the freezing-point and above
the boiling-point. Divisions below the point marked zero
(0) are indicated by the negative sign; thus, 10 ^C.
means 10 degrees below the freezing-point (0) on the Cen-
tigrade scale. The mark stands for degree or degrees.
33. Heat and Temperature. The terms heat and
temperature are used in physics so frequently and are of
such importance that particular attention will be given to
the meaning of these terms in the following experiment.
Experiment 35. To find whether heat and temperature
are the same.
Apparatus. A Bunsen burner ; a retort-stand and ring ; a piece of
wire gauze about 15 cm square ; two beakers of equal size ; a ther-
mometer.
Directions. Fill one of the beakers one-third full of
cold water, the other two-thirds full. Place them side by
side on the gauze laid on the ring of the retort-stand.
Put the Bunsen burner beneath, in a position to heat
both beakers equally.
When the water begins to boil in one of the beakers,
find its temperature with the thermometer, and immedi-
TEMPERATURE AND PRESSURE. 75
ately afterward get the temperature of the water in the
other beaker.
Is the temperature higher in one beaker than in the other ?
If the same quantity of heat had entered each beaker,
what inference can you draw ?
Does a thermometer indicate the quantity of heat a
body contains ?
Definition. Heat is that which is capable of producing
in us the sensation of warmth.
Definition. The temperature of a body tells us the
intensity of the heat in it.
TEMPERATURE AND PRESSURE.
34. The Relation between the Temperature at
which Water boils and the Amount of Atmospheric
Pressure. On high mountains, like those in Colorado,
one must boil an egg for five minutes in order to cook it
as hard as if it had been boiled for three minutes at the
seashore. If we really knew that water when boiling on
a mountain has a lower temperature than when boiling at
the seashore, this fact could be easily explained.
As it is not convenient for us to climb a mountain, boil
water on the mountain side, and test the temperature of
this boiling water with a thermometer, we shall bring
about in the laboratory conditions similar to those at
the top of a mountain. The pressure of the air on
a mountain is less than the pressure at the foot of the
mountain, so in the next experiment we shall get the tem-
perature of water when it is boiling under a reduced
pressure.
76 EXPEBIMENTAL PHYSICS.
Experiment 36. To find what influence a diminution
of pressure has upon the boiling-point of water.
Apparatus. A 250 CC Kjeldahl flask ; a rubber stopple with two
holes to fit the flask ; a thermometer ; a piece of glass tube about
15cm long, bent at right angles, and of a size to fit one of the holes in
the stopple ; a piece of pressure tube about 10 cm long ; a Bunsen
burner ; an air-pump ; a piece of pressure tube about 40 cm long, with
a pointed glass tube in one end ; a retort-stand with two rings.
Directions. Place the retort-stand beside the air-pump,
and over the exhaust nozzle slip the end of the pressure
tube. Have the flask half full of water. Through one
hole of the stopple push the bent tube ; through the other,
the thermometer, so that its bulb will be 2 cm or 3 cm from
the bottom of the flask when the stopple is in place.
Insert the stopple, and over .the end of the glass tube
slip the rubber tube. See that there is a free exit through
the tube from the inside of the flask to the open air, lest
there should be a dangerous explosion on heating the flask.
Hold the flask by the extremity of its neck, and, avoid-
ing an exposure to the flame of any part of the vessel not
covered by water, heat gradually. When the water boils,
note the temperature indicated by the thermometer. In
case the neck becomes clouded with mist, making it impos-
sible to read the thermometer, throw a dry cloth or towel
around the flask, and, by tipping it, cause a little water to
run into the neck to wash away the mist. Take the flask
to the air-pump, and support it, as shown in Fig. 29, by
the rings of the retort-stand. By inserting into the piece
of pressure tube on the flask the pointed bit of glass tube
attached by the long rubber tube to the air-pump, connect
the flask and the air-pump.
TEMPERATURE AND PRESSURE. 77
Before you begin to pump, record the temperature of
the water.
Is the water boiling, that is, are bubbles rising through
the mass of the water and breaking at the surface ?
Make one or two strokes of the pump.
What happens in the flask?
After two or three minutes make one or two strokes
more of the air-pump.
What happens in the flask ?
Record the temperature the water now has.
From the facts obtained
in this experiment, what
inference can you draw?
Why does it take a
longer time to cook an
egg on a mountain than
at the sea-level ?
Experiment 37. To
find what influence an in-
crease of pressure has upon
the boiling-point of water. FK ! 29'
Apparatus. With the exception of the air-pump, the same as in
the last experiment ; also, a retort-stand with two rings ; a piece of
wire gauze 15 cm square ; a glass tube bent at right angles', with one
arm about 30 cm long and the other about 5 cm ; an iron pan ; a test-
tube ; mercury ; a cloth ; blotting-paper.
Directions. Put the flask half full of water upon the
wire gauze laid on one of the rings of the retort-stand.
Over the neck of the flask pass the other ring, and clamp
it to the retort-stand to keep the apparatus from tipping
78
EXPERIMENTAL PHYSICS.
over. Slip the short arm of the tube into the bit of pres-
sure tube attached to the stopple. Put the stopple into
the flask, and heat the water to boiling. Record the tem-
perature of the boiling water. If necessary, wash away
the mist as in the last experiment.
Pour mercury into the test-tube to the depth of about
3 cm . When the steam is coming freely from the end of
the glass tube, wrap a cloth round the test-tube, and, hold-
ing it over the pan, not shown in Fig. 30, push the end
of the glass tube to the
bottom of the test-tube.
Have you increased the
pressure in the flask ?
Watch the thermome-
ter.
What is now the tem-
perature of the boiling
water ?
As soon as the mercury
begins to sputter, take
the test-tube away, and
remove the water on
the mercury with blotting-paper.
From the facts obtained by this experiment, what infer-
ence can* you draw ?
35. Boiling-Point of Water. Men of science through-
out the world have agreed to denote by 100 Centigrade
the temperature which a thermometer indicates when
placed in steam from water, which is boiling in an open
vessel when the atmospheric pressure is 760 mm (that is,
FIG. so.
DETERMINATION OF FIXED POINTS. 79
when the atmospheric pressure is sufficient to support a
column of mercury 760 mm high). Hence, the
Definition. Water boils at 100 (7., when the atmos-
pheric pressure is 760 mm .
Careful experiments have shown that the temperature
of water, boiling when the pressure differs but little from
760 mm , may be found by adding 1 for each 27 mm of pres-
sure above 760 nun , or by subtracting 1 for each" 27 mm of
pressure below 760 mm . Examples like those which follow
may make this clearer.
EXAMPLES.
1. When the pressure of the atmosphere is 742 mm , the reading, in
steam, of a thermometer whose scale was not properly adjusted by the
maker is 98. 5. What would be the reading of the instrument for a
pressure of 700 mm ?
Solution. 760 742 = 18 mm . As 27 mm make a difference of 1, 18 mm
would make a difference of |-f of 1, that is, 0.67. Hence, the reading of
the thermometer, when the pressure is 760 mm , would be 98. 5 + 0.67 =
99. 17.
2. In the example just given, if the pressure had been 778 mm and the
thermometer reading 100. 4, what would have been the reading for a
pressure of 760 ml ?
DETERMINATION OF FIXED POINTS.
36. Errors of Thermometer Scale. After the mer-
cury has been put into the bulb, and the stem sealed,
the next step in making a thermometer is to adjust the
scale. In order to adjust the scale, it is necessary to
determine the two fixed points. One of the fixed points
is determined by putting the bulb and a part of the
80 EXPERIMENTAL PHYSICS.
stem into melting ice. By putting the thermometer into
steam coming from boiling water, the other fixed point is
found and marked, as was the first one, upon the stem.
We have already learned that on the Centigrade scale the
freezing-point is marked 0, and the boiling-point 100, and
also that the space between the two points is divided into
100 equal parts.
In adjusting the scale, the maker of a cheap thermom-
eter does not use care ; hence, frequently, the thermom-
eter does not indicate the true temperature. So careful
is a physicist to have his thermometer, though made
by a skilled workman, accurate for delicate work, that he
always tests the scale for himself. He finds the errors of
the thermometer, and in his work makes allowances for
them.
Of the two common errors of a thermometer, one arises
in marking the position of the freezing-point ; the other,
in marking the position of the boiling-point.
To test a thermometer for the accuracy of its freezing-
point and the accuracy of its boiling-point will be the object
of the next experiment.
Experiment 38. To find ivhether the fixed points of a
thermometer have been properly marked on the scale.
(For convenience we shall divide this experiment into three parts.)
PART 1. To find the position of the freezing-point.
Apparatus. A thermometer ; finely broken ice ; a beaker.
Directions. Fill the beaker with clean, finely broken
ice. Add enough water to fill the spaces between the
lumps of ice. Push the bulb of the thermometer vertically
DETERMINATION OF FIXED POINTS. 81
into the middle of the beaker with its stem vertical until
the point marked is only l mm or 2 mm above the surface
of the ice, which should be heaped up in the beaker.
When the column ceases to fall, record the reading. In
this experiment, as well as in other heat experiments, read
the thermometer with care. Try to read to tenths of a
degree. In reading, be careful to place the eye in such
a position that a straight line drawn from the center of the
eye would strike the thermometer at
right angles at the top of the column.
PART 2. To find the position of the
boiling-point.
Apparatus. The thermometer of Part 1 ;
a copper boiler with a copper cone.
Directions. Fill the copper boiler
with water to a depth of 3 cm or 4 cm .
Get a cone that will fit tightly, and put
it in place on the boiler. Into the side
tube leading from the boiler put a cork.
Do not stop up the side tube leading
from the cone. (Why?) Get a cork
stopple that will fit the hole in the top
of the cone. In this stopple, with a
cork borer, make a hole through which
to pass the thermometer. Put the
stopple in place in the top of the cone,
and through the stopple carefully push
the thermometer (Fig. 31) until the
point marked 100 is not more than 2 mm or 3 mm above the
top of the stopple. The bulb, however, must not come
82 EXPERIMENTAL PHYSICS.
within less than 2 cm or 3 cm of the water in the boiler.
Using only one Bunsen burner, keep the water boiling
till the mercury column stops rising ; then record its
position.
We have heated the bulb and a large part of the stem
in the steam. Now draw up the thermometer till the
point marked is just above the stopple. Record the
point at which the column becomes stationary.
If this point is different from the one you found when
the bulb and a large part of the stem were in the steam,
how do you account for the difference ?
SUGGESTION. Consider whether in both cases all the mercury has
been heated to the same temperature.
At the time of performing the experiment, record the
reading of the barometer.
Why is it necessary to know the reading of the barom-
eter? (See Exps. 36 and 37.)
If the atmospheric pressure had been 760 mm when the
bulb and the stem were in the steam, find by computation
where the boiling-point (100) would have come on the
scale of your thermometer. (See Ex. at end of Art. 35.)
We have already done all the .work necessary to find
simply whether the freezing-point and the boiling-point
have been correctly marked on the scale of the thermom-
eter. Part 3 of the experiment is to bring out another
peculiarity of thermometers.
PART 3. To find the position of the freezing-point
again.
Apparatus. The same as in Part 1, with a fresh supply of broken
ice.
DETERMINATION OF FIXED POINTS. 83
Directions. If the thermometer has just been taken
from the steam, let the thermometer remain in the air till
the column has fallen to a height of about 40 or 50.
(Why?) Fill the beaker again with clean, finely broken
ice, and repeat Part 1. After the column ceases to fall,
record its position.
Is the column of mercury shorter or taller than that of
Part 1, and how much?
37. Elevation of the Zero-Point; Temporary Lower-
ing- of the Zero-Point. When the bulb of a thermometer
is put into ice-water, the bulb contracts and a slight eleva-
tion of the column is often observed, followed by a fall of
the column immediately, or as soon as the mercury in the
bulb feels the change in temperature. Even when the
thermometer is kept in a place of uniform temperature,
careful observers have noted that the bulb of a new ther-
mometer shrinks gradually and perceptibly for some weeks
or months. This gradual shrinkage of the bulb raises the
zero-point and introduces an error known as the eleva-
tion of the zero -point.
The cause of this shrinkage is that the bulb, which was
formed by blowing the glass in its plastic state, cooled
before its particles had time to regain the relative posi-
tions which they had before the pressure necessary to the
operation of blowing was applied. As time goes on, these
particles, rapidly at first, but after a while more and more
gradually, begin to accommodate themselves to one another,
and thus produce the shrinkage.
On the other hand, even in good thermometers, the
expansion of the bulb, produced by heating it to the
84 EXPERIMENTAL PHYSICS.
temperature of boiling water, lasts for a little while and
produces a temporary lowering of the zero-point.
In testing a thermometer, why should the operation of
finding the freezing-point come first ?
38. Important Precaution in Testing- the Boiling-
Point of a Thermometer. When testing the boiling-
point of your thermometer, you were directed not to
allow the bulb to dip into the boiling water ; you were to
allow the steam, not the water, to come in contact with
the bulb. The reasons for this precaution will be brought
out in the next experiment and the discussion that comes
after it.
Experiment 39. To find whether salt water will boil at
the same temperature as fresh water.
Apparatus. Two beakers of equal size ; a Bunsen burner ; a
retort-stand and ring ; a piece of wire gauze about 15 cm square ; a
thermometer ; a spoonful of salt.
Directions. Fill each beaker half full of fresh water.
Into one put a spoonful of salt. Set the beakers side by
side on the wire gauze over the flame. When the liquids
are boiling, record the temperature of each.
When boiling, which liquid has the higher temperature ?
In getting the boiling-point of a thermometer, can you
give a reason why it is not best to allow the bulb to dip
into the water?
NOTE. Besides the possibility of impurities in the water, there is
another reason that forbids us to let the thermometer dip into the water.
Gay-Lussac found that, for a given atmospheric pressure, water boils at
different temperatures in different kinds of vessels. For example, he
found the temperature of water boiling in a glass vessel to be higher than
EXPANSION OF A SOLID. 85
that of water boiling at the same time in a metallic vessel. It was shown,
however, by Rudberg that the temperature of the steam which escapes
from boiling water is the same in any kind of vessel, and depends only
on the pressure at the surface of the water. As the result of a large
number of experiments, Rudberg showed that the temperature of steam
coming from impure water was the same as that of steam coming from
pure water.
EXPANSION OF A SOLID.
39. Cubical Expansion ; Linear Expansion. By
Exp. 30 we learned that water (a liquid) expands when
heated, and by Exp. 32 that air (a mixture of two gases)
also expands when heated. When a substance (as the
water in the bottle of Exp. 30) expands in all directions,
\ve have what is called cubical expansion. In general, all
of the solid substances that have been examined expand
in all directions as the temperature rises. Often, how-
ever, the expansion in length only is observed or measured.
This increase in the length is called the linear expansion of
the solid. No two metals expand the same amount for the
same rise of temperature.
The following is an experiment on the measurement of
the linear expansion of a solid.
Experiment 4O. To find by what part of its original
length a rod of brass increases when its temperature is
raised 1.
Apparatus. A Bunsen burner ; the copper boiler with cone (a
sterilizing can makes an excellent steam generator in place of the
boiler and cone); two pieces of rubber tube, one about 60 cm long,
the other about 10 cm ; dividers; a thermometer; a meter stick;
linear expansion apparatus. The linear expansion apparatus consists
of a cylindrical tube, called the jacket, which is made of galvanized
86
EXPERIMENTAL PHYSICS.
iron and is closed at each end with a cork. Through a hole in each
cork runs a brass tube whose expansion is to be measured. Pointing
at right angles to its length, the jacket has two small side tubes, one
near each end and another in the middle. The jacket is set in a
horizontal position upon a wooden frame. On the frame is a vertical
scale and a pointer. The pointer can be moved along the scale by
the expanding rod.
Directions. Lay the jacket (Fig. 32) in its place upon
the frame. Rest one end of the brass tube against the
screw, at the end of the frame remote from the scale.
FIG. 32.
The bit of steel wire soldered to the other end of the brass
tube should press against the hinge of the pointer. Into
the short tube at the middle of the jacket fit a perforated
cork through which the thermometer passes. Over the
end of the little side tube of the jacket next the pointer
slip an end of the long rubber tube ; also slip an end of the
EXPANSION OF A SOLID. 87
short rubber tube over the end of the side tube at the
other end of the jacket. Place a beaker under the end of
this tube in order to catch the condensed steam that would
otherwise drip upon the table. To prevent the jacket from
rotating, make the side tube, having the long rubber tube
attached, rest against the post that supports the pointer.
Measure in centimeters and fractions of a centimeter the
long arm of the pointer, that is, from the center of the
hinge screw (the screw by which the pointer is pivoted)
to the side of the scale facing the cylinder. With a pair
of dividers get in centimeters and fractions of a centimeter
the length of the short arm of the pointer, that is, from the
center of the hinge screw to a point on a level with
that where the bit of steel wire touches the hinge.
See that the end of the brass rod is resting against the
screw at the end of the frame ; if it is not, press it back
till it touches the screw. Take the reading of the ther-
mometer and also the reading of the pointer on the scale.
In taking the reading on the scale, place the eye in such
a position that the line of vision just grazes the upper
surface of the pointer.
Have the boiler one-third full of water. Put the cone
in place and close its top by a stopple, also its side tube.
Do not disturb the frame, pointer, or jacket. By means of
the long rubber tube already attached, join the jacket to
the boiler. Heat the water in the boiler and let the steam
flow through the jacket until the thermometer column
becomes stationary. Record the reading of the thermom-
eter and also the new reading of the pointer. By laying
the meter stick beside the jacket, get the length in centi-
meters of the brass rod in the jacket from the outside
88 EXPERIMENTAL PHYSICS.
of one stopple to the outside of the other. This meas-
urement is, of course, a very rough one, and may be
taken at any stage of the experiment.
From the measurements you have made in this experi-
ment answer the following questions :
(1) What is the distance in centimeters that the pointer
moves over in going from its lowest position to its highest
on the scale ?
(2) How many times does the movement of the pointer
multiply the elongation of the brass rod?
SUGGESTION. Divide the length of the long arm by that of the short
one.
(3) What is the amount computed (from (1) and (2)) of
the elongation of the brass in centimeters ?
(4) Through how many degrees of temperature was the
brass raised?
(5) What is the average amount of elongation of the
brass for 1?
(6) What is the length of the brass rod in centimeters
from the outside of one stopple to the outside of the other ?
(7) By what part of its original length (the length given
in the answer to (6)) has the brass rod increased for an
increase in temperature of 1 ?
The answer to (7) is called the coefficient of linear expan-
sion of brass, hence the
Definition. The coefficient of linear expansion tells by
what part of its length a body has increased for a rise in
temperature of 1.
Is the coefficient of linear expansion a quantity or a
number ?
EXPANSION OF A SOLID. 89
EXAMPLES.
1. A rod of brass at 15 measures 2 ft. in length ; at 95 it measures
2.003 ft. Find the coefficient of linear expansion.
Solution. Increase in length of rod = 2.003 2 = 0.003 ft.
Increase in temperature = 95 15 80.
Increase in length of rod for a rise in temperature of 1 is
0.003 ^ 80 = 0.0000375.
The coefficient of linear expansion = 0.0000375 -r 2 = .000019.
The reason for calling this number a coefficient comes from the fact
that the amount a given length of brass will expand, when its temper-
ature is raised 1, can be found by multiplying the given length by
0.000019, that is, we use it just as in algebra, where a coefficient is a
numerical value multiplied into a quantity.
2. A bar of lead whose length at was 152.32 cm was heated to 100,
when its length was found to be 152.76 cm . Find the coefficient of linear
expansion of lead.
3. A copper rod that was 15 m long at was found to have increased
in length by 2.6 cra , owing to a rise of 100 in temperature. Find the
coefficient of linear expansion of copper.
4. The length of an iron rail at 15 is 30 ft. What will be its length at
10 and at 20 ? The coefficient of linear expansion of this iron is T |off-
Solution. T i^ = 0.0000122.
To find the length of the rail at 10 : In cooling 1 the rail would shrink
by 0.0000122 X 30 ft., or 0.000366 ft.; but in cooling 5 it would shrink
by an amount equal to 5 X 0.000366 ft., or 0.00183 ft. Hence the length
of the rail at 10 would be
30 - 0.00183 = 29.99 ft.
To find the length of the rail at 20 : In having its temperature raised
1, the rail would expand by 0.0000122 X 30 ft., or 0.000366 ft. ; but
in having its temperature raised 5 it would expand by an amount equal
to 5 X 0.000366 ft., or 0.00183 ft. Hence the length of the rail at 20
would be
30 + 0.00183 = 30.00183 ft.
5. What must be the length of a brass rod at 15 in order that at
it may be exactly 2 m long, the coefficient of linear expansion being
0.000019 ?
90 EXPERIMENTAL PHYSICS.
6. Assuming that the maximum temperature of a 30-ft. cast-iron rail
exposed to the sun is 50, and that the temperature of the air at the time
of laying the rail is 10, what must be the minimum distance apart of the
adjacent ends of two consecutive rails ? The coefficient of linear expan-
sion is 0.000012.
7. The distance by rail from San Francisco to Omaha is 1914 miles.
Assuming that the average variation of temperature throughout the
year is 50, what is the variation in the total length of the rails ? The
coefficient of linear expansion is 0.000012.
EXPANSION OF AIR.
4O. Expansion of Air at Constant Pressure ; Dalton's
Law. In Exp. 32 you found that heat makes air expand.
In the experiment just performed, you found by what part
of itself a piece of brass will increase in length for a rise
in temperature of 1. In the next experiment you are to
find by what part of its volume a quantity of air, exposed
to a constant (or uniform) pressure, will expand for a rise
in temperature of 1.
Experiment 41. To find by what part of its volume at
an amount of air, at constant pressure, will expand for a
rise in temperature of 1.
Apparatus. A 250 CC flask fitted with a one-hole rubber stopple,
having a glass tube 3 mm or 4 mm in diameter thrust through, reaching
nearly to the bottom of the flask and projecting about 2 cm above the
stopple ; about 25 cm of pressure tube (to fit the glass tube) and a
pinch-cock to close the end of it; ice-water; a Bunsen burner; a
large glass jar ; a copper boiler.
Directions. Make sure that the flask and all tubes are
dry. Into the flask insert the stopple with glass tube.
Connect the rubber tube with the glass tube. Let the
EXPANSION OF AIR.
91
pinch-cock, as shown in Fig. 33, be placed at the extreme
end of the rubber tube farthest from the stopple. (Why ?)
Have ready warm water in the
boiler. Open the cock and plunge
the flask beneath the water, but
do not get any water into the
flask or tubes. (Why ?) By lay-
ing a piece of wood, with a weight
on it, across the boiler, keep the
flask submerged. Bring the water
to the boiling-point. Boil for
five minutes, so that the tem-
perature of the air in the flask
may become 100. Close the
pinch-cock and remove the flask
from the hot water. Throw a
cloth round the flask, as it may
collapse. (Why?) When cool,
open the pinch-cock under iced water. When as much
water as possible has entered, close the cock. Put the flask
into the jar filled with ice-water, in which there are many
lumps of ice, and keep it submerged five minutes, so that
the temperature of the air in the flask may become 0.
Have at hand a beaker containing ice- water, under the sur-
face of which again open the cock. Make the level of the
water in the flask and that of the water in the beaker the
same, and then close the cock. Remove the flask from
the ice-water. Loosen the stopple, raise the rubber tube into
a vertical position, and open the cock to let the water run
into the flask. (Why ?) Get the volume of water in the flask ;
also the total contents of the flask when the tube is in place.
FIG. 33.
92 EXPERIMENTAL PHYSICS.
From the measurements you have made in this experi-
ment answer the following questions :
(1) What was the volume of air experimented upon at
100?
(2) What was its volume at ?
(3) How much would the volume of air at expand
in having its temperature raised 100 ?
(4) How much in having its temperature raised 1 ?
(5) By what part of its volume at would the air
expand for a rise in temperature of 1 ?
Reduce the decimal fraction, the answer to (5), to a
common fraction with 1 for its numerator.
(For example, the decimal fraction 0.003 is the same as the common
fraction Tff %o- To reduce TT ^^ to a fraction having 1 for its numerator,
divide both numerator and denominator by 3. The result is 3^3, approxi-
mately.)
What is the denominator of the common fraction to
which you have reduced the decimal fraction ?
At what temperature would l cc of air, measured at 0,
become 2 CC ?
At what temperature would l cc of air, measured at 0,
become 0.5 CC ?
The relation which connects the different volumes a
mass of air may have and the corresponding temperatures,
and which enables us to answer questions like those just
asked, is called Dalton's Law.
State Dalton's Law.
NOTE. Dalton's Law is also frequently called the Law of Charles.
Dalton, in 1801, first published the law. Gay-Lussac, independently of
Dalton, published the law in 1802. In his publication, Gay-Lussac states
that Charles (1746-1823), Professor of Physics at Paris, had in 1787 noted
the law, but had never published it.
EXPANSION OF AIR. 93
41. The Air Thermometer; the Absolute Zero.
Careful experiments have shown that not only air but all
gases also expand by ^-^, or 0.00366, of their volume at
for each degree in increase in temperature, and contract
by a like amount (of their volume at 0) for each degree in
fall of temperature. This regularity in the expansion and
contraction of gases has led to the construction of the air
thermometer, in which are observed the changes in volume
of a quantity of air so confined that, no matter how much
it may expand or contract, its pressure will always be
constant. While we shall not describe the construction
of an actual air thermometer, an instrument cumbersome
and, in practice, difficult to use (in fact, it is used only
occasionally as a standard with which to compare mercury
thermometers that are for use in delicate work), we shall
describe an ideal instrument which will make clear the
action of the air thermometer in practice.
This ideal instrument (Fig. 34) consists of a long hori-
zontal glass tube of uniform bore, closed at one end and
graduated in equal parts. It contains a quantity of dry
FIG. 34.
air which, at 0, occupies 273 of these parts, and which is
cut off from the external air by a small pellet of mercury.
As a quantity of air at 0, when heated 1, expands by
2^ f of its volume, it follows that if the air in the tube
has its temperature raised 1, the volume which it will
occupy will be 274 of these parts. Had the temperature
94 EXPERIMENTAL PHYSICS.
been raised to 10, the volume of the air would have been
283 of these parts. As the temperature rises, the air will
occupy more and more of these parts. On the other hand,
had the air in the tube been cooled to 1, the volume
of air would have occupied 272 parts ; if cooled to 10,
the volume occupied would have been 263 parts. As the
cooling continues, the volume of air goes on shrinking;
and Dalton's Law [The volume of a gas measured at
increases (or diminishes) ~by -^^ of itself for every degree
that the temperature increases (or diminishes).] has been
found to hold for the lowest temperatures that we have
obtained. So low a temperature as 273 has never
been reached, but, theoretically, the volume occupied by
a gas at this extremely low temperature would be no space
at all. (In all probability a gas, when cooled, would
become a liquid long before the temperature fell as far
as 273; should the gas have then become a liquid,
Dalton's Law of course would no longer apply.)
The point 273 is called the absolute zero of the
air thermometer, and it is extremely convenient, in deal-
ing with questions relating to gases, to reckon tempera-
tures not from the freezing-point, but from the absolute
zero. The closed end of the tube is marked 0, and the
freezing-point, which is marked on the Centigrade
scale, would be marked 273 on this absolute scale.
(Why?) To get the absolute temperature in Centigrade
degrees, we have only to add 273 to the reading of the
Centigrade scale.
QUESTIONS. What is the absolute temperature, when the temperature
on the Centigrade scale is 0? 10? 100? 273? -10? -100?
-273 ?
EXPANSION OF AIR. 95
Dalton's Law might be stated thus : The volume of a
gas varies directly as its temperature on the absolute scale.
EXAMPLES.
1. If the volume of a certain amount of gas is 500 CC at 50, what would
be its volume at 150 ?
Solution. By Dalton's Law in the form just stated, we have
50 -I- 273 : 150 + 273 = 500 : *,
or 323 : 423 = 500 : z,
whence 323 x = 211500,
.-. x = 654.8".
2. A quantity of oxygen occupies 150 CC at 15. What space will it
occupy if the temperature is reduced to ?
3. A gas has its temperature raised from 8 to 72 ; at the latter tem-
perature it occupies 12 liters. What was its original volume ?
NOTE. 1 liter = 1000 CC .
4. At 0, the space occupied by 1.293s of air is 1 liter. At what tem-
perature will the weight of 1 liter of air be Is ?
42. Problems involving" both Boyle's Law and
Dalton's Law. When the pressure changes and the
temperature does not, Boyle's Law gives us the means
of finding the volume of a gas; on the other hand,
when the temperature changes and the pressure does
not, Dalton's Law gives us the means of finding the
volume of the gas.
There is a class of problems in which we are required
to find the volume after the gas has undergone a change
both in pressure and in temperature. In solving such
problems, first find the volume that would result from a
change in pressure, and then find what this volume would
become when the temperature is changed. In the follow-
ing set of examples, both Boyle's Law and Dalton's Law
are involved.
96 EXPEEIMENTAL PHYSICS.
EXAMPLES.
1. A gas of volume 304 CC , temperature 127, and pressure 75 cm has its
pressure raised to 76 cm and its temperature lowered to 27. Find its
volume after these changes.
Solution. Let x denote the required volume, then collecting what is
given in the problem, we have
V P t
304 75 127
x 76 27
Supposing the temperature to remain constant, let us denote by y the
volume of the gas after the pressure has changed from 75 cm to 76 cm . By
Boyle's Law, we have
304:?y = 76 : 75,
76 y- 22800,
Now find the volume, x, which the volume 300 CC becomes after the
temperature has changed from 127 to 27. By Dalton's Law, we have
300 : x = 127 + 273 : 27 + 273,
300 : x = 400 : 300,
400^ = 90000,
x = 225 CC .
Hence, the volume which results from the change in pressure and the
change in temperature is 225 CC .
2. The volume of a certain quantity of air at 27, and under a pres-
sure of 75 cm , is 1000 CC . What would be its volume at 127 under a pres-
sure of 150 cm ?
3. If a mass of air has a volume of 140 CC when the temperature is
136. 5 and the pressure is 57 cm , what will the volume become when the
temperature is and the pressure is 76 cm ?
4. If a mass of air has a volume of 300 CC when the temperature is
and the pressure 76 cm , what will the volume become when the tempera-
ture is 91 and the pressure is 95 cm ?
5. When the temperature is 99 and the pressure is 95 cm , a mass of
gas has a volume of 320 CC . What must be the temperature in order that
the gas may have a volume of 300 CC , when the pressure is 76 cm ?
TRANSMISSION OF HEAT. 97
6. If a mass of gas has a volume V\ when the pressure is PI and the
temperature is ti , and a volume F 2 when the pressure is P 2 and the tem-
perature is 2 , show that
FiPi = F 2 P 2
Zi T 2
where TI = ti + 273, and T 2 = t z + 273.
TRANSMISSION OF HEAT.
43. Conduction, Convection, and Radiation of Heat.
Heat is communicated from one body to another by one or
more of the three ways, conduction, convection, and radia-
tion. It will be the object of the next five experiments to
make you acquainted with these three ways by which heat
is communicated.
Experiment 42. To find whether wood or copper is the
better conductor of heat.
Apparatus. A match ; a piece of copper wire of the same size as
the match ; a Bunsen burner.
Directions. Between the thumb and the forefinger of
one hand hold the match by its end ; in the same manner
with the other hand hold the copper wire. In the tip of
the flame of the Bunsen burner thrust together the end
of the match and the end of the wire.
Which can you hold the longer ?
Which is a good conductor of heat ?
Which is a poor conductor of heat?
Experiment 43. To find ivliether copper or iron is the
better conductor of heat.
Apparatus. A Bunsen burner ; a copper wire and an iron wire,
each about 10 cm long and as nearly as possible of the same cross-
section.
98 EXPERIMENTAL PHYSICS.
Directions. Hold one wire in each hand so that the
ends shall be together in the top of the flame.
Which is the better conductor?
What is the reason for your answer ?
Why does a piece of oil-cloth feel cold when you step
upon it with the bare feet, while a piece of woolen carpet
feels warm?
Why are wooden handles put on soldering-irons ?
Experiment 44. To find what is meant by convection of
heat.
Apparatus. A Bunsen burner.
Directions. Hold your open hand palm downwards as
high above the flame of the Bunsen burner as you can,
and lower it gradually. Estimate or measure roughly the
distance above the flame at which the temperature becomes
unbearable.
The gases produced by the chemical action in the flame
are hot and expand. The cooler air pushes them up.
They strike the hand and warm it.
Experiment 45. To find whether water is heated by
convection, when heat is applied beneath.
Apparatus. A Bunsen burner ; a retort-stand and ring ; a piece
of wire gauze about 15 cm square ; a beaker ; fine sawdust or bran.
Directions. Into the beaker half full of water sprinkle
a little pinch of sawdust, then place the beaker on the
gauze and heat it over the flame.
By watching the movements of the sawdust, should you
infer that the water is heated by convection ?
TRANSMISSION OF HEAT. 99
What peculiarity in the movements of the sawdust
would lead you to the conclusion that the water in this
experiment is heated by convection ?
Experiment 46. To find what is meant by radiation of
heat.
Apparatus. A Bunsen burner.
Directions. In Exp. 44 you found how close the hand,
when held above, could approach the flame. At this same
distance from the side of the flame hold the hand and
gradually bring it nearer and nearer.
How close can the hand approach ?
Why is not the heat which reaches your hand brought
to it by convection ?
Why is not the heat conducted to your hand ?
Heat that passes through a medium without warming
it, but is capable of warming an object even at a great
distance from the source of heat, is called radiated heat.
The heat which we receive from the sun reaches our
earth through the immense space between the sun and
the earth by radiation.
Point out how the flame of the Bunsen burner illus-
trates the three modes (convection, conduction, and
radiation) by which heat may pass from one point to
another.
By how many of the three modes by which heat is trans-
mitted is your school building warmed ?
In what way do the glowing coals in an open grate
give heat to a room?
Why is an open grate a good means of ventilation ?
100 EXPERIMENTAL PHYSICS.
CALORIMETRY.
44. Measurements of Quantities of Heat. In the
measurements we have made thus far, we have used as
our unit of length the centimeter ; as our unit of weight,
the gram. In measuring quantities of heat, we shall use
a special unit. This unit of heat is named the calorie
(pronounced cal'orie).
Definition. The calorie (the unit of heat) is the amount
of heat required to raise the temperature of I 9 of water 1.
The beginner often asks the question, " How much heat
is there in a calorie ? " Remember that the calorie is a
unit of heat, just as the centimeter is a unit of length.
Experiment 47. To find whether the quantity of heat
given up by a known weight of water in falling through a
certain range of temperature in one part of the thermometric
scale, is able to raise the same weight of water through the
same number of degrees in a different part of the scale.
Apparatus. Two nickel-plated cups ; a copper boiler ; a Bunsen
burner ; a thermometer ; a 100 CC graduate.
Directions. Into one of the cups pour 175 g of cold
water (temperature 5 to 10), into the other pour 175 g of
warm water (temperature 50 to 60). Stir the cold water
with the thermometer and note its temperature ; then,
stirring as before, immediately take the temperature of
the warm water. Before the warm water has had time to
cool below the temperature you have noted, pour it all
into the cold water, stir the mixture well with tKe ther-
mometer, and take the temperature, ,
CALOBIMETKY. 101
Why should a liquid be thoroughly stirred before taking
its temperature ?
How many degrees has the temperature of the hot
water fallen?
How many degrees has the temperature of the cold
water risen?
In what way (conduction, convection, or radiation) does
the cold water receive heat before it is mixed with the
warm?
In what way does the warm water, before mixing, lose
heat?
This experiment leads to the following definition :
Definition. The calorie is the amount of heat which P
of water gives up in cooling 1.
Experiment 48. To find the temperature resulting
from mixing equal weights of water and mercury of different
temperatures.
Apparatus. A copper boiler ; Bnnsen burner ; iron pan ; ther-
mometer ; a 100 CC graduate ; three beakers of nearly equal size ;
broken ice.
Directions. In the graduate, placed in the pan, meas-
ure out 100 g of mercury (sp. gr. = 13.6). Pour the
mercury into the beaker, and put the beaker into the
water in the copper boiler with the lighted burner
beneath. Keep the mercury dry.
Make ready in a beaker 100 g of water 10 colder than
the air of the room. (Why?) Have the mercury 10
warmer than the air of the room. (Why?) Then pour
both, the water first, into the third beaker, which should
have the same temperature as the air of the room, the
102 EXPERIMENTAL PHYSICS.
temperature that it will have, of course, if the beaker has
been standing in the room for a little while. With the
thermometer, stir the two liquids thoroughly, for about
half a minute. Note the temperature of the mixture.
Which liquid appears to have had the greater influence
in producing the final temperature ?
Using the same weights of water and dry mercury as
before, repeat the experiment ; only have the temperature
of the mercury 10 below the temperature of the air of
the room, and the water 10 above the temperature of the
air of the room.
In this case which liquid has the greater effect in pro-
ducing the final temperature ?
Would it take as much heat to warm l g of mercury 1
as to warm l g of water 1?
45. Thermal Capacity; Calorimetry ; Method of
Mixtures. The thermal capacity of a body (solid, liquid,
or gaseous) is the number of calories (see Def., page 100)
necessary to raise its temperature 1. The process of
measuring quantities of heat, for example, the thermal
capacity of a body, is called calorimetry. One of the
methods of calorimetry, called the method of mixtures, is
very common, and is that which you will employ in
your work in calorimetry. The method of mixtures
consists essentially in putting the body to be tested, after
its weight and temperature have been noted, into a quan-
tity of water of known weight, whose temperature is
known but is different from that of the body. The
resulting common temperature, known as the temperature
of the mixture, is noted.
CALOKIMETRY. 103
The body may be a solid, so that it and the water could
not be literally mixed. It is customary, however, to refer
to a solid and the water, when put together in one vessel,
as the mixture.
Experiment 49. To find, by the method of mixtures,
the amount of heat given out by l g of lead in cooling 1.
Apparatus. Lead shot ; a copper dipper to heat the shot in ; a
copper boiler ; a thermometer ; a calorimeter (this is a tall cup of
nickle-plated brass, brightly polished) ; a platform balance ; a little
ice-water a 100 CC graduate ;. a piece of cardboard to cover the
dipper.
Directions. Into the dipper put 500 g of shot. Cover
the top of the dipper with the
cardboard, in order to keep the
shot from being cooled by air
currents. Through a hole in
the cardboard pass the ther-
mometer and plunge its bulb
into the shot. In the boiler
place the dipper with its flange
resting on the top (Fig. 35).
In order that there may be no
danger of boiling the water in
the boiler all away, have the
water reach nearly to the bot-
tom of the dipper at the start.
Close the side tube of the
boiler with a stopple, so that Fl - 35.
the steam will have to pass out under the flange of
the dipper.
104 EXPERIMENTAL PHYSICS.
While the shot are heating, wipe and weigh the calo-
rimeter (pronounced calo-rim f e-ter), and measure out 100 g
of water whose temperature is 6 or 8 colder than the air
of the room, that is, 6 or 8 below the temperature as
indicated by a thermometer near the spot where the
experiment is to be performed. Pour the water into
the calorimeter, and place it conveniently near the heat-
ing apparatus, but shielded from the heat.
When the temperature of the shot has become practi-
cally constant, that is, about 100, remove the thermom-
eter, and allow it to cool till the column stands at about
50 or 40. Then put the thermometer into the calo-
rimeter, stir the water and give the thermometer time
to come to the temperature of the water. Record the
temperature of the water. Meanwhile, stir the shot fre-
quently with an iron rod or any convenient object. Then
take the thermometer out of the water. Take the dipper
from the boiler, remove the cardboard (no time should be
lost in this part of the experiment, for the dipper and its
contents after being taken from the boiler immediately
begin to cool), taking care to spill neither shot nor water,
very quickly pour the shot into the calorimeter. (This can
be successfully done by the student, if he has practised
beforehand pouring some shot from a dipper into an empty
calorimeter.) At once stir the mixture of shot and
water quickly and thoroughly with the thermometer.
Record the reading of the thermometer as soon as the
shot and water have reached a common temperature,
which will probably be a few degrees above the temper-
ature of the room. It is of importance to get this tem-
perature accurately. With vigorous stirring it takes but
CALORIMETRY. 105
a few seconds for the water and the lead to reach a com-
mon temperature. Glance at the thermometer column
frequently ; after the first somewhat violent fluctuations
the mercury will become stationary for an instant and
then begin to fall slowly ; the reading of the column, at
the instant when it becomes stationary, is the one to be
noted.
From the data obtained answer the following questions :
(1) If x denotes the amount of heat given out by l g of
lead in falling 1, how much heat would be given out by
the whole mass of lead in falling 1?
(2) How much heat would be given out by the whole
mass of lead in falling from the temperature it had when
it entered the water to the temperature of the mixture ?
(The heat given out by the lead warmed the calorimeter and the water
in it. Both the water and the calorimeter had the same temperature.)
(3) How much heat does it take to raise l g of water
1? (See Def., page 100.)
(4) How much heat does it take to raise the whole
mass of water 1?
(5) How much heat does it take to raise the whole
mass of water from the temperature it had when the shot
were poured in to the temperature of the mixture ?
(6) If it takes 0.1 of a calorie to raise l g of the sub-
stance of which the calorimeter is made 1, how much
heat will it take to raise the temperature of the whole
calorimeter 1 ?
(7) How much heat will it take to raise the whole
calorimeter from its temperature when the shot entered
to the temperature of the mixture ?
106 EXPERIMENTAL PHYSICS.
When you have answered the questions, make an equa-
tion. On one side put the expression [the answer to (2)]
for the quantity of heat given out by the lead in cooling ;
on the other, the quantity of heat received by the water
[the answer to (5)] plus the quantity of heat received by
ibhe calorimeter [the answer to (7)]. On solving this
equation, you will get the amount of heat given out by
l g of lead in cooling 1.
A special name is given to the numerical value of the
amount of heat yielded by l g of a substance when its
temperature falls 1. This value is called the specific
heat of the substance. The amount of heat necessary
to raise l g of a substance 1 is equal to the amount of
heat given out by l g of the substance when its tempera-
ture falls 1 ; hence,
Definition. The specific heat of a substance is the numer-
ical value of the thermal capacity of I 9 of the, substance.
NOTE. The answer to (6) is called the water equivalent of the calori-
meter. Why ?
QUESTIONS. What is the specific heat of water ? of the calorimeter ?
What was the thermal capacity of the lead used in the preceding experi-
ment ? of the water ? of the calorimeter ?
EXAMPLES.
1. Into 110s of water at 15, contained in a vessel the thermal capacity
of which is equal to that of 10s of water, are put 200s of a certain solid
at 100, and the resulting temperature of the whole is 25. Compute the
specific heat of the solid.
Solution. Let x denote the specific heat of the solid.
Then 200 (100 25) x = the number of calories given out by the lead
in cooling from 100 to 25.
CALOBIMETKY. 107
110 (25 15) = the number of calories received by the water
in having its temperature raised from 15
to 25.
10 (25 15) = the number of calories received by the calo-
rimeter in having its temperature raised from
15 to 25.
Now the number of calories given out by the lead were received
by the water and the calorimeter, so we can add together the calories
received by the water and the calorimeter and form an equation by
putting this sum equal to the number of calories given out by the lead ;
that is,
200 (100 25) x = 110 (25 - 15) + 10 (25 15).
Solving this equation, we have x = 0.08.
2. A coil of copper wire weighing 45. Is was dropped into a calorimeter
containing 52. 5s of water at 10. The copper before immersion was at
99. 6, and the common temperature of copper and water after immersion
was 16. 8. Find the specific heat of the copper wire.
NOTE. When nothing is said about the weight of the calorimeter, as
in the example just given, make no account of the calorimeter in the
computation.
3. Find the specific heat of a substance lOOe of which at 90, when
immersed in 250s of water at 12, gives a resulting temperature of 18.
4. Compute the specific heat of silver from the following data :
Weight of silver = 10.2s
Weight of water = 84s
Temperature of silver = 102
Initial temperature of water = 11. 08
Temperature of mixture = 11. 69
5. If the specific heat of mercury is 0.0333, what will be the temper-
ature of 100s of water taken at 0, into which 1000& of mercury at 100
are poured and thoroughly stirred ?
Solution. Let t denote the required temperature.
Then 1000 (100 t) 0.0333 = number of calories of heat given out by
mercury in cooling from 100 to t.
100 (t 0) = number of calories of heat received by
the water in having its temperature
raised from to t.
108 EXPERIMENTAL PHYSICS.
These two quantities of heat are equal, hence we form the equation
1000 (100 - t) 0.0333 = 100 (t 0).
On solving this equation, t = 25 (nearly).
6. Equal volumes of turpentine at 70 and of alcohol at 10 are
mixed ; find the resulting temperature. (Specific gravity of turpentine,
0.87; of alcohol, 0.80. Specific heat of turpentine, 0.47; of alcohol,
0.62.)
LATENT HEAT.
46. Change of State. Every substance with which
we are acquainted must be in one of the three states, or
forms, the solid, the liquid, or the gaseous. Sometimes
we find a substance in the solid state, sometimes in the
liquid state, and sometimes in the gaseous. For example,
water is a substance with which we are acquainted in the
solid state (as ice), in the liquid state, and in the gaseous
state (as steam). When a solid, such as ice, melts, it passes
from the solid state into the liquid. The solid is said to
have undergone a change of state. On the other hand,
when a liquid, like water, freezes, it has passed from the
liquid *to the solid state. In this case also a change of
state has taken place. When a liquid, like water, passes
into the gaseous form, as steam, or when the gas con-
denses, or passes back to a liquid, there is also a change
of state. In brief, then, when a substance passes from
one of these states to another, a change of state is said to
have taken place.
The next three experiments deal with change of state.
Experiment 5O. To find what changes in temperature
are produced by applying heat to equal weights of ice and
ice-water, contained in separate vessels.
LATENT HEAT. 109
Apparatus. Two similar beakers ; a small pan about 3 inches
deep ; a thermometer ; a Bunsen burner ; a retort-stand and ring ;
ice ; a platform balance.
Directions. Fill one beaker two-thirds full of small
pieces of ice, and put into the other an equal weight of ice-
water. In the pan of boiling water that you have just
removed from the flame, put both beakers, after noting
the temperature of each. Without putting the pan over
the flame again, stir the ice almost constantly, and occa-
sionally stir the water in the other beaker. Let the
beakers stand in the hot water till nearly all the ice has
melted, then quickly note the temperature of each.
Both beakers are of the same size and have stood in the
hot water for the same length of time.
In which one does the temperature remain unchanged,
or almost unchanged ?
As both beakers were at the same or nearly the same
temperature at the start, what has become of the heat
that went to the beaker in which the temperature rose
the least?
In what state were the contents of this beaker before
it was put into the hot water ?
In what state were the contents after it had been sub-
jected to heat?
Definition. The heat required by substances for changing
their state is called latent heat.
A better name is heat effusion, when the change is from
solid to liquid ; heat of vaporization, when the change is
from liquid to vapor. Heat of fusion is sometimes called
latent heat of melting.
110 EXPERIMENTAL PHYSECS.
Definition. The heat that is used in raising the temper-
ature of a body is called sensible heat, as it can be perceined
by the sense of touch.
Experiment 51. To find the amount of heat necessary
to change l a of ice whose temperature is into 1 s of water
whose temperature is 0.
Apparatus. A calorimeter ; a platform balance ; a thermometer;
a piece of cardboard to cover calorimeter ; clear ice.
Directions. Record the weight of the calorimeter.
Put into the calorimeter 20 O g of water whose temperature
is about 55. Cover the calorimeter with the piece of
cardboard, having a notch at one side to admit the ther-
mometer. (The cardboard retards the evaporation of the
water.) Take a lump of clear ice weighing from 140 g to
150 g , which should have been selected before the warm
water was put into the calorimeter, and in an ice-cutting
machine or in a cold box break it up quickly into pieces
about as large as chestnuts. Use neither snow nor snow-
ice. Record the temperature of the water after stirring,
and immediately, avoiding the wetter portions, put into
the calorimeter about 100 g of the ice. Do not weigh out
100 g of crushed ice, but estimate the amount as nearly as
you can. Stir thoroughly, though not violently, with the
thermometer. As the last particles of ice melt, record the
temperature indicated by the thermometer. If so much
ice has been put in as to cool the water below 5, dip out
the ice which remains unmelted, taking out as little water
as possible. Weigh the calorimeter and contents to find
the weight of ice melted.
LATENT HEAT. Ill
By means of the data obtained answer the following
questions, which indicate the course of reasoning that must
be gone through in order to find the number of calories
necessary to melt l g of ice without changing its temperature.
(1) If x denotes the number of calories required to
melt 1 s of ice, how many calories are necessary to melt the
whole weight of ice ?
(2) How much heat is required to raise the temper-
ature of l g of water 1? (See Def., page 100.)
(3) How many calories are required to raise the tem-
perature of the liquefied- ice (ice-water) from to the
temperature of the mixture ?
(4) How much heat is given out by l g of water in
cooling 1? (See Def., page 101.)
(5) How many calories are given out by the warm
water in cooling to the temperature of the mixture ?
(6) In cooling 1, what part of a calorie is given out by
l g of the substance of which the calorimeter is made?
(The specific heat of the calorimeter is 0.1.)
(7) How many calories are given out by the whole
calorimeter in cooling 1?
(8) How many calories are given out by the calorimeter
in cooling from its first temperature to the temperature of
the mixture ?
(The first temperature of the calorimeter is the same as that of the
water in it at the start.)
Make an equation, putting on one side the quantity of
heat necessary to melt the ice [answer to (1)] plus the
quantity of heat necessary to raise the ice-water to the
temperature of the mixture [answer to (3)] ; on the other,
112 EXPERIMENTAL PHYSICS.
put the quantity of heat given out by the water in cooling
to the temperature of the mixture [answer to (5)] plus the
quantity of heat given out by the calorimeter in cooling
to the same temperature [answer to (8)]. On solving this
equation you will get the quantity of heat necessary to
melt l g of ice.
Definition. The latent heat of fusion of a substance is
the number of units of heat required to change 1 of the
substance at its melting-point into liquid at the same temper-
ature.
How many units of heat are required to melt l g of ice ?
How many units of heat will be given out by l g of ice-
water in freezing ?
Which takes the more heat, to melt l g of ice, or to
raise the temperature of l g of water from to 100?
EXAMPLES.
1. From the following experimental data find the latent heat of water :
Weight of water = 200s.
Temperature of water = 58.
Weight of ice = 118s.
Temperature of mixture when all the ice was melted = 8.
(Latent heat of water is another name for latent heat of melting.)
Solution. Let x denote the number of calories necessary to melt IK
of ice.
r
Then 118 x = number of calories necessary to melt the whole
weight of ice.
118 (8 0) = number of calories necessary to raise the liquefied
ice from to 8.
200 (58 8) = number of calories given out by the warm water
in cooling from 58 to 8.
LATENT HEAT. 113
Now the number of calories received by the ice in melting and by the
liquefied ice in having its temperature raised from to 8 was given out
by the warm water when its temperature fell from 58 to 8 ; in other
words, the heat given out by the warm water in cooling went to melt
the ice and to raise the temperature of the liquefied ice, so we have the
equation
118 x + 118 (8 - 0) = 200 (58 - 8).
.-. x 76.7 calories.
2. As the result of experiment, it is found that 25s of copper at the
temperature of 100 are just sufficient to melt 2.875s of ice at 0, so that
the water and the copper are finally at 0. Taking 80 calories as the
latent heat of water, from these data find the specific heat of copper.
3. What quantity of water at 15 will be required to melt 1000s of ice
at 0, so that the resulting mixture shall be at 5 ? (Take the latent heat
of water as 80.)
Experiment 52. To find the number of calories P of
steam, whose temperature is 100, gives up in changing into
water at 100.
Apparatus. A calorimeter ; a thermometer ; a " trap" (consisting
of a side-necked test-tube with a perforated stopple, through which,
and reaching nearly to the bottom of the test-tube, a piece of glass
tube is thrust) ; a copper boiler with a cone (or better a sterilizing
can) ; a Bunsen burner ; a piece of cardboard to cover the calo-
rimeter (this cardboard should have a notch at one edge to admit
the tube conducting the steam, and in the middle a perforation to
admit the thermometer) ; two pieces of rubber tube, one about 50 cm
in length, the other about 10 cm .
NOTE. The object of the trap is to catch the water from the steam
that is condensed, when it passes from the boiler through the long tube ;
the steam must pass through a long tube in order to keep the calorimeter
a long distance from the Bunsen burner, otherwise the contents of the
calorimeter would have its temperature raised by the heat of the flame.
Directions. Fill the boiler one-third full of water.
Fit a cone tightly on the boiler (Fig. 36). Stop the open-
ing in the apex of the cone and also the side tube near
114 EXPERIMENTAL PHYSICS.
the apex. Over the side tube of the boiler slip the longer
piece of rubber tube. Slip its other end over the end of
the glass tube that reaches to the middle of the test-tube.
Over the side tube of the test-tube slip the short piece of
rubber tube with a bit of glass tube in one end.
FIG. 36.
Record the weight of the calorimeter. Then weigh care-
fully in the calorimeter 275 g of water whose temperature
is about 15 below the temperature of the room. When
the steam flows strongly through the trap, the mouth of
the rubber tube, attached to the side tube, should be
plunged beneath the surface of the water in the calorime-
ter, but not so deep as to prevent the steam from con-
densing with a very audible sound. Cover the calorimeter
with the cardboard, and through the opening pass the
LATENT HEAT. 115
thermometer. Frequently stir the water with the ther-
mometer. Screen the calorimeter from the heat radiated
by the flame and other hot objects. When, by the con-
densation of the steam, the temperature of the water has
been raised about 15 above the temperature of the room,
remove the tube from the water. Stir the water thoroughly
with the thermometer and take its temperature.
What was the object in having the final temperature of
the water as much above the temperature of the room as
the initial temperature of the water was below it ?
Weigh the calorimeter and contents, and thus find the
weight of the condensed steam. This weighing is very
important and should be carefully done.
Notice that there are two portions of heat yielded to the
cold water and to the calorimeter ; one coming from the
steam during the act of condensation, the other coming
from the condensed steam (water at 100) while cooling
to the final temperature.
In the computation of the latent heat of vaporization,
take 0.1 as the specific heat of the substance of which the
calorimeter is made.
(1) If x denotes the number of calories given up by l g
of steam at 100 in changing into water at 100, how
many calories are given up by the whole weight of the
steam during this change ?
(2) How many calories are given up by l g of water in
cooling 1? (See Def., page 101.)
(3) How many calories are given up by the condensed
steam (water at 100) in cooling 1?
(4) How many calories are given up by the condensed
steam in cooling to the temperature of the mixture ?
116 EXPERIMENTAL PHYSICS.
(5) How many calories are required to raise the temper-
ature of l g of water 1 ? (See Def., page 100.)
(6) How many calories are required to raise the whole
weight of cold water from its first temperature to the
temperature of the mixture ?
(7) How many calories are required to raise 1 the tem-
perature of l g of the substance of which the calorimeter
is made?
(8) How many calories are required to raise the temper-
ature of "the whole calorimeter 1?
(9) How many calories are required to raise the calo-
rimeter from its first temperature (the temperature of the
water at first) to the temperature of the mixture ?
Make an equation, putting on one side the quantity of
heat given up by the steam in changing into water [answer
to (1)] plus the quantity of heat given up by the condensed
steam in cooling to the temperature of the mixture [answer
to (4)] ; on the other, the quantity of heat necessary to raise
the cold water from its first temperature to that of the
mixture [answer to (6)] plus the quantity of heat required
to raise the calorimeter from its first temperature to the
temperature of the mixture '[answer to (9)]. On solving
this equation you will get the quantity of heat given up
by l g of steam in changing into water.
How many calories would be required to change l g of
water whose temperature is 100 into steam whose temper-
ature is 100 ?
Which would give out the greater amount of heat,
l g of steam whose temperature is 100 in changing into
water, or l g of water in cooling from 100 to 0?
LATENT HEAT. 117
QUESTIONS AND EXAMPLES.
1. Why is steam such an effective agent in heating buildings ?
SUGGESTION. Consider the amount of heat given out by steam in
condensing.
2. Beginning with the fire beneath the steam boiler, describe as fully
as you can the transferences of heat that occur in the process of heating a
room by means of coils of steam-pipe.
3. Using as a model the definition of the latent heat of fusion, page
112, state a definition for the latent heat of vaporization.
4. From the results of the following experiment, allowing for the heat
absorbed by the brass calorimeter, compute the latent heat of steam (the
latent heat of vaporization) :
Weight of calorimeter = 326. 3s.
Weight of calorimeter and water = 757.7s.
Weight of steam condensed = 46.35s.
Temperature of steam = 100.
Temperature of water before experiment = 7. 5.
Temperature of water after experiment = 62. 5.
Specific heat of brass = 0.09.
5. A vessel containing 30s of ice is placed over a Bunsen burner ; how
many calories will be required to melt the ice and to vaporize the water
completely ? (Latent heat of fusion, 80 ; latent heat of vaporization, 536.)
47. Freezing-Mixtures. When ice melts, heat dis-
appears. The form of the ice is changed from the solid
to the liquid, but there is no marked rise in temperature
till all the ice has vanished. The heat that has dis-
appeared in this process has gone to change the form of
the substance, without appreciably raising the temperature
of the water as long as any of the ice remains. When ice
melts, heat passes from surrounding objects that have a
higher temperature than that of the ice to the ice itself ;
consequently, those objects which in this manner part with
118 EXPERIMENTAL PHYSICS.
heat must become colder, unless heat is constantly supplied
to them. When salt is mixed with ice the ice melts more
quickly and so takes heat more rapidly from surrounding
objects. A mixture of ice and salt is called a freezing-
mixture. When this mixture surrounds a freezer full of
cream, the cream freezes. The mixture in becoming liquid
has taken heat from the cream, and the cream has frozen.
Is the freezing-mixture colder than the cream? This is
a pertinent question which the following experiment will
enable you to answer.
Experiment 53. To find whether the temperature of a
mixture of melting ice and salt is different from that of melt-
ing ice.
Apparatus. A beaker ; a thermometer ; a platform balance ;
snow or broken ice ; salt.
Directions. Mix in the beaker one part by weight of
salt and two parts by weight of snow or broken ice. Put
a thermometer into the mixture, and note the temperature.
What conclusion do you reach ?
THERMOMETRIC SCALES.
48. Centigrade, Fahrenheit, and Reaumur Scales.
Besides the Centigrade scale, with which you have become
familiar, there are two others : the Fahrenheit, in use in
England and the United States, and the Reaumur, in use
in Russia and a few places in the north of Germany. The
Fahrenheit scale, named for Fahrenheit, of Dantzig in
Germany, who about 1714 was the first to construct
thermometers whose readings were the same when put
THERMOMETR1C SCALES.
119
into substances having the same temperature, has for its
zero-point the temperature of a mixture of snow and salt.
On this scale the freezing-point is 32 and the boiling-
point 212. On the Reaumur scale the freezing-point is
marked 0, just as on the Centigrade scale, but the boiling-
point is marked 80.
Occasionally you will be required, when given the read-
ing of one of these scales, to find the corresponding
reading of "one of the others. The follow- Q R. F
ing table will help you to understand how
this can be done.
C. F. R.
Freezing-point 32
Boiling-point 100 212 80
C. stands for Centigrade, F. for Fahrenheit,
and R. for Reaumur.
Between the fixed points on the Centi-
grade scale (Fig. 37) there are 100 equal
parts ; on the Fahrenheit, 180 ; on the
Reaumur, 80. Hence a change of 5 C. is
equivalent to a change of 9 F., or 1 C. is
equal to | F. Fahrenheit's zero is 32
below the freezing-point. Hence, to re-
duce Fahrenheit readings to Centigrade
readings subtract 32 from the number of
Fahrenheit degrees and multiply the remainder by |.
(7=f (J--82).
To reduce Centigrade readings to Fahrenheit, multiply
the number of Centigrade degrees by -| and add 32.
JF= 6^+32.
FIG. 37.
f
120 EXPERIMENTAL PHYSICS.
EXAMPLES.
1. Show by a process of reasoning similar to that just given that
E = f (F 32)
F = I R + 32
2. Show that
3. Find the corresponding temperatures on the Centigrade scale of
the following melting points :
Lead, 626 F.; bismuth, 508 F.; tin, 442 F.; Rose's metal, 200 F.
NOTE. Rose's metal is an alloy of the first three.
4. Find the equivalents on the Reaumur scale of the following temper-
atures :
Usual temperature of the human body = 98.4 F.
" " " a common frog = 64 "
" " " a chicken = 111 "
5. In the expedition to China in 1829 the Russian army experienced
for several days a temperature of 32. 8 R. What would this be on
the Fahrenheit scale ?
6. The absolute zero 1 is 273 C. What is this on the Fahrenheit
scale ?
7. At what temperature is the reading of the Centigrade identical
with that of the Fahrenheit ?
FORMATION AND CONDENSATION OF VAPOR.
49. Evaporation ; Boiling*. The object of the next
two experiments is to bring out the distinction between
evaporation and boiling.
Experiment 54. To find whether vapor will form quietly
at the surface of water.
Apparatus. A large test-tube ; a Bunsen burner ; a small piece
of window-glass.
1 See page 94.
FORMATION AND CONDENSATION OF VAPOR. 121
Directions. Hold the test-tube, half filled with water,
above the flame, and warm the water, but do not let it
boil. Above the mouth of the test-tube, and at a little
distance from it, hold the glass plate, which should be
cold, or the experiment may fail.
How did the particles of water which you see get on the
piece of glass ?
If the piece of glass had not been held over the mouth
of the test-tube, what would have become of the water
which now adheres to the glass ?
If the test-tube were allowed to remain uncovered, what
would become of the water in it after a time ?
Definition. Evaporation is the quiet formation of
vapor at the surface of a liquid.
Experiment 55. To find
what phenomena occur when
water is heated gradually to
boiling.
Apparatus. A test-tube, provided
with a small side tube, fitted with a
perforated stopple with a glass tube
thrust through, which reaches almost
to the bottom of the test-tube ; a
bit of rubber tube to fit the side
tube ; a tumbler ; a Bunsen burner ;
a piece of glass tube, bent at right
angles, slipped, as shown in Fig. 38,
into one end of the rubber tube ; a
clasp with which to attach the test-
tube to the tumbler.
FIG. 38.
Directions. Draw some cold water from the tap, and
fill the test-tube nearly to a level with the side tube. Put
122 EXPERIMENTAL PHYSICS.
the stopple with its tube in place in the mouth of the test-
tube. Clasp the test-tube to the tumbler. Let the end
of the glass tube, which you should attach to the side tube
by means of the rubber tube, dip l cm or 2 cm beneath the
cold water, which should nearly fill the tumbler. By
applying heat to the bottom of the test-tube, gradually
warm the water.
Before the water boils, bubbles appear in the test-tube.
Do these bubbles rise to the top of the water in the
test-tube ?
Are they bubbles of steam ?
(It may be best to suspend judgment for a little while before answering
this question.)
Do they burst at the surface ?
Are they large or small ?
As the water becomes warmer, more bubbles form.
In what part of the vessel do they form ?
Do they rise to the surface of the water in the test-tube ?
As they rise, do they grow larger or smaller ?
Are they bubbles of steam ?
(It may be best to suspend judgment for a little while before answering
this question.)
In the upper part of the test-tube, is the water warmer
or colder than at the bottom?
If there is a change of size in these bubbles as they rise,
how do you account for it?
Do any bubbles appear at the end of the glass tube in
the beaker of water? (When bubbles begin to appear
in the beaker at the mouth of the tube, watch them
carefully.)
FORMATION AND CONDENSATION OF VAPOR. 123
As the water in the test-tube gets still warmer, do
bubbles rise to the surface in either vessel?
How do you account for the sharp rattling noise (which
is called singing or simmering) that is heard just before
the water in the test-tube is brought to boiling ?
After the bubbles have begun to come from the glass
tube in the beaker, do they change in character as time
goes on?
At the close of the experiment, do these bubbles detach
themselves from the end of the tube?
After reflecting carefully on what you have observed,
can you tell how to distinguish an air-bubble from a steam-
bubble?
Is steam visible ?
When water is boiling in a tea-kettle, what is the little
cloud seen at the nose ?
Keeping the test-tube in position and letting the end of
the glass tube rest on the bottom of the beaker, remove
the lamp and note what happens as the water begins to
cool.
Do bubbles form ?
Is the water in the test-tube boiling ?
If the water is not boiling, what is the cause of what
you observe ?
Definition. Boiling (or ebullition) is the rapid formation
of vapor in the interior of a liquid.
Experiment 56. To find the temperature at which the
aqueous vapor in the air will condense.
Apparatus. A calorimeter, brightly polished ; a thermometer ;
ice or snow ; salt.
124 EXPERIMENTAL PHYSICS.
Directions. Into the calorimeter pour water drawn
from the tap until it is of a depth sufficient to cover
a little more than the bulb of the thermometer. By
additions of ice-water or ice, with constant stirring, gradu-
ally cool this water until the brightly polished surface of
the calorimeter becomes dimmed with dew. (Should no
dew appear when the thermometer reads 0, add salt and
ice.) If at any time the water in the calorimeter becomes
more than 5 cm deep, pour out the extra water. Record
the temperature as soon as any dew is seen to appear
on the calorimeter. Then allowing the temperature of
the water to rise gradually by receiving heat from the
room, record the temperature at which the dew begins to
disappear.
Care should be taken not to let the breath come upon
the cup, or near it ; for the surface of the cup would
become dimmed by the breath. By keeping some par-
ticular spot of the cup turned from you most of the time,
and glancing at this spot frequently in order to detect
the appearance or disappearance of dew upon it, you will
more easily avoid errors from this source.
The average of the two temperatures recorded is taken
as the dew-point.
Definition. The temperature at which the air deposits
some of its aqueous vapor is called the dew-point.
The dew-point depends upon the amount of aqueous
vapor in the air, and differs greatly from time to time.
In general the dew-point is low in winter, but high in
summer.
PECULIARITY IN THE EXPANSION OF WATER. 125
PECULIARITY IN THE EXPANSION OF WATER
5O. Maximum Density of Water. During the proc-
ess of lowering the temperature of water to the freezing-
point, the water contracts till it reaches a certain tempera-
ture, and then it begins to expand.
Experiment 57. To find the temperature at which
water is at its greatest density.
Apparatus. A 250 CC flask ; a rubber stopple, perforated with two
holes, one to admit a tube 25 cm long of rather fine bore (2 mm or
;3 mm ), the other to admit a thermometer ; a very narrow rubber band
for a marker ; ice or snow.
Directions. Avoiding air-bubbles, fill the bottle com-
pletely with cold water. Put
in place the stopple, through
which you have thrust the tube
and the thermometer. The bulb
of the thermometer should oc-
cupy a position midway between
the bottom of the flask and its
top. Slip the marker over the
glass tube. After packing the
flask in snow or broken ice as
shown in Fig. 39, wait till the
thermometer column becomes
stationary. Bring the marker
to a level with the top of the
water column, which should also
have become stationary. Then
take the flask from the ice, and watch the motion of the
water column as the temperature rises.
Before the column begins to rise, does it sink ?
126 EXPERIMENTAL PHYSICS.
If the column sinks, what is the temperature of the
water as indicated by the thermometer when the column
is lowest?
From the action of the water column and the indications
of the thermometer, what inference can you draw?
51. Results of the Peculiarity in the Expansion
of Water brought out by the Last Experiment. In
winter the surfaces of ponds and lakes lose heat. The
water at the surface being, bulk for bulk, heavier than that
below, sinks ; this sinking of cold water goes on till the
temperature of the whole pond is 4. The surface water
cools, but it is now less dense than the water below ; this
less dense water, therefore, floats, and its temperature falls
till it freezes. The ice, as we know, floats. Deep bodies
of water undisturbed by currents near the bottom or by
springs, like Lake Tahoe in California, show a tem-
perature at the bottom of about 4 all the year round. If
water did not have this peculiarity in its expansion, the
temperature of the whole pond would be reduced to 0.
Then, if the water still continued to contract on freezing,
layer after layer of ice would form only to sink, until the
whole pond would be a mass of solid ice.
In Art. 6 it was stated that a cubic centimeter of water
weighs I 9 ; this statement should now be amended to read
a cubic centimeter of water at 4- weighs l a .
DISCUSSION OF A FEW TERMS.
52. Method. At the end of Chapter I. the meaning
of observation and experiment, and the necessity of dis-
tinguishing between facts and inferences from the facts
DISCUSSION OF A FEW TERMS. 127
were discussed. At this point you should turn back and
review pages 62 and 63.
You have already learned that experiment is a most
fruitful means of ascertaining facts.
The method, that is, the mode or way of accomplishing
an end, differs for different experiments ; but while
experiments are infinite in number, the methods pursued
in performing them are few, so it is possible, by marshall-
ing the experiments each under its proper method, to
bring order out of chaos. A most important method is
known as the method of differences. Its utility depends upon
varying only one condition at a time, while the precaution
is taken to keep all the other conditions unchanged.
Interesting experiments according to the method of
differences are not rare. " In his discovery of the cause
of dew, Dr. Wells made use of this method. If on a
clear calm night a sheet or other covering is stretched
a foot or two above the earth, so as to screen the ground
from the open sky, dew will be found on the grass around
the screen but not beneath it. As the temperature and
moistness of the air, and other circumstances, are exactly
the same, the open sky must be an indispensable antecedent
to dew. The same experiment is indeed tried for us by
nature ; for if we make observations of dew during two
nights which differ in nothing but the absence of clouds in
one and their presence in the other, we shall find that the
clear sky is requisite to the formation of dew." l
53. Empirical Knowledge ; Classified Knowledge.
However useful empirical knowledge, the knowledge gained
1 Elementary Lessons in Logic, by W. Stanley Jevons, p. 244,
128 EXPERIMENTAL PHYSICS.
by experience, may be, its importance is small as compared
with classified knowledge, that is, knowledge well con-
nected and perfectly explained. " He who knows exactly
why a thing happens will also know exactly in what
cases it will happen, and what differences in the circum-
stances will prevent the event from happening. Take, for
instance, the simple effect of hot water in cracking glass.
This is usually learned empirically. Most people have a
confused idea that hot water has a natural and inevitable
tendency to break glass, and that thin glass, being more
fragile than other glass, will be more easily broken by hot
water. Physical science, however, gives a very clear
reason for the effect, by showing that it is only one case
of the general tendency of heat to expand substances.
The crack is caused by the successful effort of the heated
glass to expand in spite of the colder glass with which it
is connected. But then we shall see at once that the
same will not be true of thin glass vessels ; the heat will
pass so quickly through that the glass will be nearly
equally heated ; and accordingly chemists habitually use
thin uniform glass vessels to boil or hold hot liquids with-
out fear of fractures which would be sure to take place in
thick glass vessels or bottles." *
54. Cause ; Hypothesis. By the cause of an event we
mean the circumstances that must have preceded in order
that the event should happen. An event has in general
more than a single cause. " The cause of the boiling
of water is riot merely the application of heat up to
a certain degree of temperature, but the possibility also
1 Elementary Lessons in Logic, by W. Stanley Jevons, p. 257.
THE MOLECULAR HYPOTHESIS. 129
of the escape of the vapor when it acquires a certain
pressure." 1
Hypothesis means in science the imagining of a cause
which underlies the phenomena we are examining, and is
the agent in their production without being capable of
direct observation. In making an hypothesis we assert
the existence of a cause on the ground of the facts
observed, and the probability of its existence depends
upon the number of diverse facts it enables us to explain
or reduce to harmony.
THE MOLECULAR HYPOTHESIS.
55. Molecular Hypothesis of Matter. The follow-
ing brief account of the molecular hypothesis of matter in
its modern form 2 may show more clearly how an hypoth-
esis enables us to harmonize several different facts.
The material substances, as air, metals, wood, glass,
water, and so on, are termed in the language of physics,
matter.
All matter, according to the molecular hypothesis, is
supposed to consist of exceedingly small particles, sepa-
rated from each other by spaces. One of these exceedingly
small particles is called a molecule.
" Every molecule consists of a definite quantity of matter,
which is exactly the same for all molecules of the same
1 Elementary Lessons in Logic, by W. Stanley Jevons, p. 239.
2 The molecular hypothesis is a very old one. Lucretius, a Roman poet
(95-55 B.C.), in his poem De Rerum Natura expounds the molecular
hypothesis, and shows us that even in that remote period philosophers held
the opinion that the observed properties of bodies apparently at rest are
due to the action of invisible molecules in rapid motion.
130 EXPERIMENTAL PHYSICS.
substance. ... The molecules of all bodies are in a con-
stant state of agitation. The hotter a body is, the more
violently are its molecules agitated. In solid bodies, a
molecule, though in continual motion, never gets beyond
a certain small distance from its original position in the
body. The path which it describes is confined within a
very small region of space.
" In fluids, 1 on the other hand, there is no such restriction
to the excursions of a molecule. It is true that the mole-
cule can generally travel but a very small distance before
its path is disturbed by an encounter with some other
molecule. ... In fluids the path of the molecule is not
confined within a limited region, as in the case of solids,
but may penetrate to any part of the space occupied by
the fluid." 2
56. Evaporation and Condensation explained by the
Molecular Hypothesis. The following explanation has
been adapted from that given by Clerk Maxwell in his
Theory of Heat. Some of the molecules of the liquid which
are at the surface and are moving from the mass of the
liquid may, by being struck by other molecules, get such
velocities that they will escape from the forces which retain
the other molecules in the liquid, and will fly about as
vapor in the space outside the liquid. This is the way in
which the molecular hypothesis explains evaporation. At
the same time, a molecule of the vapor striking the liquid
may become entangled among the molecules of the liquid,
and may thus become part of the liquid. This is the
1 The term fluid includes liquids and gases.
2 Theory of Heat, bv J. Clerk Maxwell, p. 306.
THE MOLECULAK HYPOTHESIS. 131
explanation which the molecular hypothesis gives of
condensation. The number of molecules that pass from
the liquid to the vapor depends on the temperature of the
liquid. The number of molecules that pass from the
vapor to the liquid depends on the density of the vapor
as well as on its temperature. If the temperature of the
vapor is the same as that of the liquid, evaporation will
take place as long as more molecules are evaporated than
condensed ; but when the density of the vapor has in-
creased so much that as many molecules are condensed
as evaporated, then the vapor has attained its maximum
density. The vapor is then said to be saturated, and it is
commonly supposed that evaporation ceases. According
to the molecular hypothesis, however, evaporation is still
going on as fast as ever ; only condensation is also going
on at an equal rate, since the proportions of liquid and
gas remain unchanged.
EXAMPLES.
1. When the barometer is 77.8 cm , what is the error of the boiling-
point of a thermometer that in freely escaping steam reads 100. 1 ?
2. Explain why the temperature of boiling water depends upon the
pressure.
3. Show the steps in the process of reasoning by which you found
the coefficient of linear expansion of brass from the results of your
experiment.
4. When the temperature is 0, a copper lightning-rod measures 50 ft. ;
find its length in summer when heated to a temperature of 27. The
coefficient of linear expansion of copper is 0.0000173.
5. The coefficient of linear expansion of steel being 0.000012, what is
the length at of a bar that is just l m long at 20 ?
132 EXPERIMENTAL PHYSICS.
6. A mass of air at measures 200 ; at 100 it measures 27ft cc .
Provided both measurements were taken under the same barometric
pressure, find the coefficient of expansion of air.
7. When the temperature is 20, a mass of oxygen gas measures
500 CC . When its temperature is raised to 40, what will the volume of
the gas become ?
8. When the pressure is 38 cln and the temperature is 68. 25, a certain
mass of air has a volume of 480 CC ; what will this volume become when
the pressure is 76 cm and the temperature is ?
9. Three liters of gas are measured off at 15 and 76.7 cm barometric
pressure. Find the volume of this gas at the standard temperature, 0,
and at the standard pressure, 76 cm .
10. From the following data find the specific heat of nickel :
Weight of nickel = 400s.
" " water = 200s.
" calorimeter = 100s.
Specific heat of calorimeter =0.1.
Temperature of nickel just before entering water = 100.
" " water " " nickel enters = 15.
"the whole after " " = 29. 7.
11. From the following data find the temperature after mixing water
and mercury :
Weight of mercury = 1000s.
" " water = 100s.
Temperature of mercury = 100.
" water = 10.
Specific heat of mercury = 0.0333.
Number of units of heat absorbed by the calorimeter = 80.
12. If the weight of a mass of liquid is 8s, its temperature 80, and its
specific heat 0.24, how many grams of a second liquid, whose temperature
is 10 and specific heat 0.48, must be mixed with the first in order that
the resulting temperature may be 50 ?
13. How many grams of a liquid whose temperature is 70 and whose
specific heat is 0.25 must be poured on 20s of ice at in order to melt
it ? The latent heat of melting is 80.
14. How many grams of steam at 100 will be required just to melt
100s of ice at 0, if the latent heat of vaporization is 537, and the latent
heat of melting is 80 ?
15. What temperature on the Centigrade scale corresponds to 27
on the Fahrenheit ?
CHAPTER III.
ELASTICITY.
57. Correction of the Beading* of a Spring 1 Balance
when used in the Horizontal Position. In the present
chapter the student will find a series of experiments on
elasticity. Some knowledge of elasticity will prove help-
ful to him when he takes up the study of sound in the
next chapter. As frequent use will be made of spring
balances in our work, it will be well to consider the
corrections that must be applied to their readings.
The maker of a spring balance intends to get the weight
of the balance hook and the rod that connects the hook to
the end of the spiral spring, which lies within the balance
frame, so adjusted that, when the balance is hung up by
its ring with no weight suspended from the hook, the
pointer will be just opposite the zero line. Whenever a
balance thus suspended has its pointer not opposite the
zero line, the zero error is found by observing how far the
pointer is above or below this line, as has already been
mentioned on page 5.
In some of the subsequent experiments, however, we
shall have occasion to use the spring balance held not
in a vertical position, as was intended by the maker,
but in a horizontal position. Whenever a spring balance
with nothing hung on its hook is held in a horizontal
position, the hook and the connecting rod no longer pull
on the spring, so the spring contracts and draws the
134 EXPERIMENTAL PHYSICS.
pointer beyond the zero line until the pointer strikes
against the end of the slot in which it moves, or, what
amounts to the same thing, until a projection, near which
the hook is fastened, in the connecting rod comes in con-
tact with the balance frame. If we should lay the balance
upon a table with its ring round an upright rod fastened in
the table-top, and then pull in a horizontal direction on the
hook, the number of pounds' or grams' pull, as registered
by the pointer, would be too small by the weight
of the hook and connecting rod ; by adding, how-
ever, this weight to the amount registered by the
pointer, we should get the number of pounds that
we are really pulling on the hook. The purpose
of the next experiment is to find this correction,
that is, the weight of the hook and connecting rod.
Experiment 58. To find the correction that
must be applied to the reading of a given spring
balance when the pull upon it is to be in a horizon-
tal direction.
Apparatus. Two 30-pound spring balances; two
8-ounce spring balances.
Directions. Suspend by its ring one of the
30-pound spring balances so that it shall hang
freely ; then hang by its hook the other 30-pound
spring balance (see Fig. 40), the correction of
^^ which is to be found, to the hook of the spring
FIG. 4o. i3 a i ance already suspended. Record the reading
of the upper spring balance. This reading is the weight
of the lower spring balance. Record also the reading of
the lower spring balance. This reading is the weight
ELASTICITY. 135
of all of the lower spring balance except its hook and
connecting rod.
What is the weight of the hook and connecting rod of
the lower spring balance ?
Repeat the experiment, using the pair of 8-ounce spring
balances in place of the 30-pound spring balances.
In this case, what is the weight of the hook and con-
necting rod?
EXAMPLES.
1. From a spring balance which is suspended by its ring another
spring balance is hung in an inverted position by its hook. If the spring
balance suspended by its ring reads 3. 7 oz. , and the other spring balance
reads 3 oz., what correction must be applied to the spring balance now
reading 3 oz. , when it is used in the horizontal position ?
2. The spring balance, the correction for which was found in
Example 1, is used in the horizontal position. The spring balance reads
5.3 oz., what is the true reading ?
3. If the readings of two spring balances are the same as in
Example 1, but the zero error of the spring balance which is being tested
is 0.2 oz. (that is, the spring balance when suspended by its ring reads
0.2 oz. above the zero line), what would be the correction for the spring
balance when used in the horizontal position ?
Solution. If the spring balance reads 3.0 oz. , its reading corrected for
the zero error would be 3.2 oz., so the weight of its hook and rod would
be 3.7 3.2 = 0.5 oz. Hence 0.5 oz. must be added to the reading of
the spring balance, when used in the horizontal position.
4. If 0.3 oz. is the zero error of a spring balance (that is, the spring
balance when suspended by its ring reads 0.3 oz. below the zero line), and
this spring balance reads 3.9 oz., when suspended by its hook from the
hook of another spring balance which reads 4 oz., what correction must
be applied when the balance is used in the horizontal position ?
5. A spring balance the zero error of which is 0.4 Ib. is suspended by
its ring, and from its hook is hung in an inverted position another spring
balance the zero error of which is 0.3 Ib. If the reading of the spring
balance suspended by its ring is 3.2 Ibs., and that of the other 3.0 Ibs.,
what correction must be applied to the reading of the spring balance
which has been thus tested, when used in the horizontal position?
136
EXPERIMENTAL PHYSICS.
FORCE.
58. Meaning- of the Term Force. The term force is
important in physics, and it will be our object in the
earlier of the following experiments to make the meaning
of this term clear.
Experiment 59,
a wire.
To find the tension necessary to break
Apparatus. A 30-pound spring balance ; 5 pieces of No. 30
B. & S. spring brass wire, each about l m long ; a wooden guard to
slip on hook of the balance.
NOTE. No. 30 B. & S. means that the size of the wire is number 30,
measured on the Brown and Sharpe wire-gauge.
Directions. Round some vertical cylindrical object
like a gas-pipe make several turns with one en'd of one of
the pieces of wire, and to prevent slipping
fasten this end to a tack driven into the wood-
work to which the pipe is fastened. Pass the
other end through the eye where the hook is
attached to the balance, and fasten by twist-
ing the wire about itself. Over the hook slip
the wooden guard, and wind the wire round
it several times, as shown in Fig. 41, taking
care there is no slack wire between the hook
and the guard. See that there are no kinks in
Holding the balance in a horizontal position, and
taking care that the rod of the balance to which the hook
is attached does not bind or rub against the frame of the
balance, gradually increase the tension, and constantly
watch the pointer until the wire breaks. When holding
FIG. 41.
the wire,
FOECE. 137
the balance, avoid having the hand near the end to which
the hook is attached, lest the finger be injured by the recoil.
Record the error of the balance when used in the
horizontal position. Also record the number of pounds
the balance indicates when the wire breaks.
Why were you directed to keep the wire free from
kinks, and to wrap it round cylindrical objects like the
gas-pipe and the wooden guard?
Using a new piece of wire each time, make in all five
tests. Record the result of each trial, and find the
average, corrected for the error of the balance.
The tension, or pull, required to break the wire is
called the breaking strength of the wire.
Find the product -of 453.6, and the number that
expresses the average breaking strength. This product
will be the number that expresses the average breaking
strength in grams, as in 1 Ib. there are 453. 6 g .
Experiment 6O. To find how long a wire must be to
break under its own weight, if suspended by one end.
Apparatus. A horn-pan balance ; l m of No. 30 B. & S. spring
1 >rass wire ; a micrometer gauge.
Directions. Measure off accurately l m of the wire.
Weigh it to O.l g on the horn-pan balance.
If the l m of wire were suspended by one end, how hard
\vould it pull down at the point of support ?
Turn back to the last experiment, and get the record
of the breaking strength of the wire in grams.
Knowing the weight of l m of the wire and its breaking
strength, find by computation the length of a piece that
would break of its own weight, if supported at one end.
138 EXPERIMENTAL PHYSICS.
With the micrometer gauge measure the diameter of the
wire ; and find area of cross-section of wire, using formula
A = ^TrD 2 . Knowing that the strength of wires of the
same material as well as their weight, for equal lengths,
is proportional to their area of cross-section, find by com-
putation the breaking strength of a brass wire lsq cm in
area of cross-section.
ELASTICITY OF STRETCHING.
Experiment 61. To find whether a wire will increase
by equal amounts in length for equal additions to the tension
by which it is stretched.
Apparatua About 4 m of No. 27 B. & S. spring brass wire ;
a 30-pound spring balance; two meter sticks graduated in milli-
meters ; a wooden screw and nut ; an iron screw ; two narrow
mirrors.
NOTE. The wooden screw and nut can be readily obtained from a
wooden clamp such as carpenters use. An inspection of Fig. 42 will
show how the screw and nut are arranged. The side of the clamp next
the handle of the screw has a slot cut in it to fit the edge of the table.
The nut is made by sawing off a piece of the side containing the thread
in which the screw works, and should have a strong hook fastened to it.
Directions. Into the top of a table, near one end,
insert the iron screw ; and solder one end of the wire to it.
By passing the other end of the wire through the eye in
which the balance hook is fastened, and twisting this end
round the wire, make it fast. Wind the wire round the
hook of the balance several times.
Put the wooden screw and nut at the end of the table
remote from the iron screw. Put the ring of the balance
over the hook on the nut, and, by turning the screw, make
the balance indicate a tension of 1 Ib. This tension will
ELASTICITY OF STRETCHING. 139
draw the wire straight. Now solder 1 two pieces of fine wire,
each about 0.5 cm in length, across the long wire at right
angles, one near each end, to serve as markers. As shown
in Fig. 42, lay a meter stick lengthwise under each end
of the wire. Lay on each of the meter sticks a narrow
mirror, and adjust each meter stick, by sliding it back
and forth, till the marker under which it lies is exactly
FIG. 42.
over one of the divisions of the meter stick, when the
eye is held, as it should always be held in making read-
ings in this experiment, so that the marker obscures its
own image. Do not allow the meter sticks to be moved
during the experiment.
By turning the screw increase the tension by 2 Ibs.
(The balance now reads 3 Ibs.) Read the position of each
1 In order to solder two pieces of brass, brighten the parts to be joined
by careful rubbing with a file or with emery cloth. Moisten these bright
parts with soldering-fluid, and over each of them pass the tip of a hot
soldering-iron on which is a drop of melted solder to "tin" or coat the
surfaces. Lay the tinned surfaces together, moisten them with soldering-
fluid, and press upon them the hot soldering-iron, from the tip of which
a drop of solder is allowed to flow and to spread round and between
the surfaces. Remove the soldering-iron, and let the solder harden at
the juncture. Do not heat the soldering-iron after a greenish flame
begins to play round it, lest the tinning at its tip be destroyed.
140
EXPERIMENTAL PHYSICS.
marker to quarters of a millimeter ; the difference between
their movements is the amount the portion of the wire
lying between them has stretched. Reduce the tension to
1 lb., and notice whether the wire regains its original length.
Make several trials similar to this, increasing the force
2 Ibs. at a time (making the balance read in addition to
the 1 lb., which is always kept applied, 4 Ibs., and then
6 Ibs.) until the wire fails to return to its original length,
when the tension acting on the wire is reduced to 1 lb.
In recording the results, do not count the force of 1 lb.
applied to keep the wire straight.
The results may be recorded as follows :
MATERIAL, OF WIRE
GAUGE No. .. LENGTH ...
TENSION..
MOVEMENT OF
FIRST MARKER.
MOVEMENT OF
SECOND MARKER.
ELONGATION.
ELONGATION
PER POUND.
lb.
ram.
mm.
mm.
mm.
Measure and record in millimeters the length of the
wire between the two markers.
For what value of the tension does the wire fail to
return to its original length, after the pull on the wire
has been reduced to 1 lb. ?
Does the amount of elongation show any simple relation
to the amount of tension ?
(HINT. In answering this question, look at the first column and at
the fourth of your record.)
ELASTICITY OF STRETCHING. 141
The answer to the last question, which should be
modelled after the statement of Laws 2 and 3 below, con-
stitutes what we shall call Law 1 for the stretching of a
wire.
Law 2. For a given tension, elongation is proportional
to the length of the wire ; that is, the longer the wire, the
greater the elongation.
Law 3. For a given tension, the elongation is inversely
proportional to the area of cross-section of the wire ; that
is, the larger the area of the cross-section of the wire, the
less the elongation.
How could you prove experimentally Law 2 ? Law 3 ?
In Exp. 59 the tension was so great that the wire
broke, while in the present experiment the tension simply
stretched the wire. A tension or pull is called a force.
In Exp. 28 the air confined in the closed branch of the
Boyle's tube was compressed or pushed into a smaller
volume by the weight of the mercury. This compressing
action or push is also called a force.
Definition. A force is a push or a pull.
The power which a body has of recovering, more or less
completely, its original shape after the force which has
changed the shape is withdrawn, is called elasticity of
shape or figure.
Tf stretched or compressed within certain small limits
(that is, stretched or compressed only a little), most solid
bodies will return to their original dimensions, after the
forces, to which they have been exposed, cease to act.
These limits are called the limits of elasticity.
In this experiment, did you stretch the wire beyond its
limits of elasticity?
142 EXPERIMENTAL PHYSICS.
ELASTICITY OF BENDING.
59. Effects of Bending 1 . In the preceding experiment
we observed that a wire had the power of recovering its
original length more or less completely when the force
which stretched it ceased to act. In the next four experi-
ments we shall continue our work in elasticity by study-
ing the effects produced by bending rods of different
dimensions.
Experiment 62. To find the relation between the load
and the amount^ of lending produced in a rod supported at
each end.
Apparatus. A straight rod of clear white pine a little more than
100 cm long, and about l cm wide, and l cm thick; three triangular
prisms of wood ; weights from 100^ to 4008 ; a scale about 10 cm long
with a support to keep it in a vertical position ; a very light, thin
rod of wood about 32 cm long, called a pointer ; a meter stick.
Directions. Lay the rod in a horizontal position on
two of the triangular blocks, placed parallel to each other
with their centers l m apart. The rod should be parallel
to the edge of the table and a little more than 30 cm from
the edge. Place the remaining block opposite the middle
of the rod and parallel to it. The center of this block is
to be 5 cm from the nearer edge of the rod, as shown in
Fig. 43. By placing one end under the center of the rod,
support the pointer on the block, so that it lies across the
block, and at right angles to the rod. Place with its back
turned towards the rod, in a vertical position, the 10 cm
scale at a distance of 30 cm from the edge of the rod, and
close beside the pointer. The movement of the end of
ELASTICITY OF BENDING. 143
the pointer will magnify the bending of the rod five
times. The support on which the pointer rests should
be a little higher than the supports of the rod, so that
the pointer will rest against the front edge of the rod
throughout the experiment, and so continue to magnify
the bending of the rod five times.
Sight carefully across the upper surface of the pointer,
and record its position on the 10 cm scale. Then on the
middle of the rod lay carefully a 100 g weight, and again
FIG. 43.
read the position of the pointer. (If the weights are not
flat, lay the weights in a little pan, as shown in Fig. 43.)
Remove this weight, and read and record again the posi-
tion of the pointer. The weight applied to the rod is
called the load. Now put on 20 O g , and read and record
the position of the pointer. Also take the reading of the
pointer with the load off. Then add 300 g and 400 g in
turn, reading and recording the position of the pointer
every time the load is put on, and also when it is taken off,
144
EXPERIMENTAL PHYSICS.
If permanent bending should be observed, stop recording
the readings.
When weights are put on and taken off, see that the
rod is not shifted on its supports.
The following form for recording observations is sug-
gested :
SUPPORTS 100 cm APART. WIDTH OF ROD
THICKNESS OF ROD
LOAD.
READING
WITH
READING
WITHOUT
AVERAGE
READING
RISE
OF POINTER
DEFLEC-
TION
DEFLEC-
TION
LOAD.
LOAD.
WITHOUT
ON SCALE.
OF ROD.
PER lOOg.
LOAD.
g-
cm.
cm.
era.
cm.
cm.
cm.
3.00
100
3.40
3.00
0.40 -f- 5
= 0.080
0.080
3.00
200
3.75
2.98
0.77 -r 5
= 0.154
0.077
2.96
Find the average of the numbers in the column headed
"Deflection per 100 g ."
Divide each load in the first column of your observa-
tions by the first load (100 g ) ; also divide each deflection
in the sixth column by the first deflection (the deflection
produced by a load of 100 g ).
From the results thus obtained, what should you say is
the relation between the load and the bending produced ?
QUESTION. If a load of 100s produces a bending of 0.25 cm , what will
be the amount of bending produced by a load of 300s ?
NOTE. Sometimes the load is referred to as the transverse force. The
expressions amount of bending and amount of flexure have the same
meaning, signifying the distance through which the middle of the rod is
depressed.
ELASTICITY OF BENDING. 145
Experiment 63. To find the relation between the length
of rods and the amount of bending produced by equal loads.
Apparatus. The same as in the last experiment ; weights from
500s to 20008.
Directions. Arrange the apparatus in all respects as
in the last experiment, with the exception of having the
supports placed at a distance of 50 cm instead of 100 cm
apart. Let the middle portion of the rod be subjected to
the bending, that is, let about 25 cm of each end of the rod
project over each support.
Using the same precautions as already mentioned for
the preceding experiment, and adding 500 g at a time,
load from 500 g to 2000 g . Record as before, and find the
average of the deflections per 100 g .
Divide the average of the deflections per 100 g of the
last experiment by the corresponding average of the
present experiment ; also divide the length (the distance
between the supports) of the longer rod by that of the
shorter.
If the quotients thus obtained are not equal, try to
make them equal by squaring or cubing one of them.
What relation should you say exists between the length
of rods and their amount of flexure ?
QUESTION. If a rod 100 cm long, when loaded with 100s, is bent 0.12 cm ,
how much will the same load bend a rod 50 cm long ?
Experiment 64. To find the relation between the breadth
of rods and the amount of bending produced by equal loads.
Apparatus. With the exception of the rod and weights, the same
as in the last experiment ; a straight rod of clear white pine a little
more than 100 cm long, and about l cm thick and 2 cm wide ; weights
from 2008 to 8008.
146 EXPERIMENTAL PHYSICS.
Directions. Lay the rod on its broad side with the
supports 100 cm apart. Adding 200 g at a time, load from
200 g to 800 g . Record as before.
In this experiment and in Exp. 62 we have rods alike
in all respects except that of width. Divide the average
deflection per 100 g of the rod of Exp. 62 by the corre-
sponding average for the rod of this experiment ; also
divide the width of the rod of the present experiment
by the width of the rod used in Exp. 62.
Are the two quotients equal or nearly equal ?
What relation can you make out as probably existing
between the breadth of rods and the amount of flexure for
equal loads ?
QUESTION. If a rod l cm wide is bent 0.12 cm by a load of 100s, how
much will the same load bend a rod, of equal length and thickness, and
2c
Experiment 65. To find the relation between the thick-
ness (depth) of rods and the amount of bending produced by
equal loads.
Apparatus. With the exception of the weights, the same as in the
preceding experiment ; weights from 500s to 200(K
Directions. Use the broad rod of the preceding experi-
ment. Place this rod on edge with the supports 100 C1U
apart. Adding 500 g at a time, load from 500 g to 2000 g .
Record as before.
This rod is of the same dimensions as that used in
Exp. 62, with the exception of that of thickness (depth).
Divide the average deflection per 100 g of the rod of Exp.
62 by the corresponding average of the rod of this
experiment; also divide the thickness of the rod of this
experiment by that of the rod used in Exp. 62.
ELASTICITY OF TORSION. 147
If the two quotients are not equal, try to make them
equal by squaring or cubing one of them.
What relation can you make out as probably existing
between the thickness of rods and the amount of bending
for equal loads ?
In the experiments on bending, have you tested the
strength or the stiffness of the rods ?
QUESTION. If a load of 100s bends a rod l cm thick 0.12 cin , how much
will the same load bend a rod 2 cm thick ?
ELASTICITY OP TORSION.
6O. Effects of Twisting-. The elasticity of torsion, or
twisting, is shown by the alternate twisting and untwisting
when a weight is suspended from an ordinary string.
Experiment 66. To find the relation between the amount
of twisting of a rod and the force applied.
Apparatus. A rod of clear ash about l m long and by in. in
cross-section ; one end of this rod is fitted into the middle of a circular
board 1 ft. in diameter ; a sheet of cardboard upon which is traced
a circle whose diameter is somewhat greater 'than that of the circular
board, and whose circumference is divided into degrees ; two 8-ounce
spring balances ; a narrow mirror to be used as in Exp. 61.
Directions. Upon a table, having uprights at each end
which support a movable cross-piece, place the cardboard
with the graduated circle uppermost, with the hole in its
center over the hole in a metallic plate set into the table-
top under the cross-piece. Place the rod upright with
the stout pin, which projects from the center of the board,
in the hole in the table-top. Fasten by a clamp, as shown
148
EXPEKIMENTAL PHYSICS.
in Fig. 44, the other end of the rod in the long slot in the
movable cross-piece above the table. The length of the
rod from the top of the circular board to the cross-piece
must be 80 cm . To get the right length, adjust the cross-
piece. Do not let the circular board rub on the cardboard ;
FIG. 44.
do not let the peg bind in the hole. By means of tacks,
fasten the cardboard at the corners to the table. The
circle on the cardboard and circular board must be con-
centric. Have the zero mark on the circle just beneath a
pin driven into the edge of the circular board for an index.
To each of the screws inserted, from diametrically oppo-
site points, into the edge of the circular board, attach a
ELASTICITY OF TO]
piece of flexible string. To each string attach an 8-ounce
spring balance, and with these balances pull horizontally
in opposite directions at right angles to the line joining
the screws. Let the force be the same for each balance,
and, as the rod twists, let the direction of the pull be
changed in such a way as to keep it always at right angles
to the line joining the screws. Use in succession forces of
2, 4, 6, and 8 oz., and record in each case the resulting tor-
sion (that is, the number of degrees) as shown by the read-
ings on the cardboard scale. Of course, as shown in
Exp. 58, a correction must be added to the indication of
the spring balance, when used in the horizontal position,
to get the true measure of the force ; so this correction for
each spring balance must be found and recorded.
The following form of record is suggested :
ROD or CROSS-SECTION BY IN.; LENGTH 80 cm .
AVERAGE
TWISTING
FORCE.
READING
WITH
TWISTING
FORCE.
READING
WITHOUT
TWISTING
FORCE.
READINGS
WITHOUT
TWISTING
FORCE.
TWIST OF
ROD.
TWIST OF
ROD PER
1 oz.
oz.
o
o
1
2
3
1
2
1
1
4
5
1
4
1
1
Divide each twisting force in the first column of your
record by the first twisting force (2 oz.) ; also divide each
twist of rod in the fifth column by the first twist (pro-
duced by the twisting force of 2 oz.).
150 EXPERIMENTAL PHYSICS.
From the results thus obtained, what should you say is
the relation between the force applied and the twisting
produced ?
QUESTION. If a force of 5 oz. twists a certain rod 1.5, through how
many degrees will a force of 12 oz. twist the rod ?
Experiment 67. To find the relation between the amount
of twisting for equal forces and the lengths of rods.
Apparatus. The same as in the preceding experiment, but instead
of the two 8-ounce spring balances, two 4-pound spring balances.
Directions. Arrange everything as in the preceding
experiment, but lower the cross-piece so that only 40 cm of
the length of the rod shall be subject to torsion. Find
and record the corrections for the spring balances, and,
using forces of 4, 8, 16, and 32 oz., proceed as before and
record the results.
Turn back to Exp. 66 to find the average twist of rod
per ounce. Divide this twist by the corresponding aver-
age twist of the rod of the present experiment. Divide
the length of the rod of Exp. 66 by that of the rod of the
present experiment.
Are the quotients equal or nearly equal ?
Can you state a probable relation between the twisting
for equal forces and the length of rods ?
QUESTION. If a force of 8 oz. twists a rod 100 cm long 3, through
how many degrees will the same force twist a rod whose length is 50 cm ?
Experiment 68. To find the relation between the diam-
eters of the cross-section of rods and the amount of twisting
produced by equal forces.
Apparatus. The same as in the preceding experiment, except
that a rod of clear ash of cross-section f by in. is used.
ELASTICITY OF TORSION. 151
Directions. Clamp the rod so that a length of 80 cm
shall be subject to torsion. Find and record the correc-
tions for the spring balances. Apply forces of 1, 2, 3, and
4 Ibs. (that is, 16, 32, 48, and 64 oz.). Record as before.
Divide the average twist per ounce of the rod (whose
diameter is i in.) of Exp. 66 by the average twist of the
rod (whose diameter is f in.) of the present experiment ;
also divide the diameter of the rod of the present experi-
ment by that of Exp. 66.
How nearly do your results agree with the statement,
" The amount of torsion is inversely proportional to the
fourth power of the diameter " ?
QUESTION. If a rod whose diameter is 1 in. is twisted by a certain
force through an angle of 5, through how many degrees would the same
force twist a similar rod whose diameter is 2 in. ?
61. Elasticity of Volume. Besides elasticity of shape
or figure, a body possesses elasticity of volume, or the power
of recovering, more or less perfectly, its original volume
after the force which has changed the volume is withdrawn.
Elasticity of volume is possessed in perfection by liquids
and gases, which recover completely their original volumes
when the compressing forces are removed, no matter how
long they have been applied. In Exp. 28 the weight of
mercury in the open branch compressed the air in the
closed branch, thus making it occupy a smaller volume ;
but when the pressure is removed, the air, by reason of its
elasticity of volume, returns to its former bulk.
62. Strain ; Stress ; Hooke's Law. Any change in
the shape or size of a body is called a strain. Any appli-
cation of force tending to produce a strain is called a stress.
152 EXPERIMENTAL PHYSICS.
In Exp. 61 the elongation of the wire is a strain, and
the tension that produced the elongation is a stress.
In the experiments on bending and twisting, the stu-
dent should point out the strain and the stress.
NOTE. Many years ago an Englishman, named Hooke, discovered
Law I. of stretching ; hence this law is often called Hooke's Law. Hooke
stated his law in the following words : " Ut tensio sic vis."
Using the words stress and strain as just denned, could
Hooke's Law be stated thus ?
" The stress is proportional to the strain."
EXAMPLES.
Before working the following set of examples, collect into a group the
three laws of stretching (see Exp. 61), the four laws of bending (see Exps.
62, 63, 64, and 65), and the three laws of torsion (see Exps. 66, 67, and 68).
1. A balance, the zero error of which is 0.2 lb., weighs 1.7 Ib.
When this balance is suspended by its hook, the pointer indicates 1.5 lb.
What correction must be applied to the reading of the balance when it is
used in the horizontal position ?
2. If a wire 3 m -long and 0.2 6< i mm in area of cross-section is stretched
2.5mm by a force of 2 k e (2000e), how great a force would be required to
stretch by 3 mm a wire of like material 12 m long and 2 s( i nim in area of
cross-section ?
Solution. If a wire 3 m long and 0.2 s< i mm in area of cross-section is
stretched 2.5 mm by a force of 2 k &, a force of l k s would stretch the wire
2 5
one-half as much, or -ir mm (stretching is proportional to the tension)., and
this force of l k s would stretch a length of l m of the wire one-third as
much, or ~;r mm (stretching is proportional to the length). Finally, if the
area of cross-section of the wire were l s i mm , a length of l m of the wire
would be stretched by a force of l k s, two-tenths as much, or ~ = 7^ inm
(stretching is inversely proportional to the area of the cross-section).
EXAMPLES. 153
If by x we denote the force required to stretch the second wire 3 mm ,
we shall find by a process precisely like the one just given that a wire 1
long and isqmm i n are a of cross-section will be stretched mm by a force
zx
Of 1*8.
As the material is the same for each wire, we have
=
2x~ 12
2x= 12
.-.*== 6
Hence, theT force required to stretch the second wire will be 6 k *.
3. If a wire 8 m long and 0.4 s( i mm in area of cross-section is stretched
10 mm by a force of 5 k , how great a force would be required to stretch by
5mm a w i re o f like material 20 m long and 4 8( i mm in area of cross-section ?
4. If a wire 10 m long and l mm in diameter is stretched 10 mm by a force
of 10 k s, ho'w many millimeters would a force of 8 k g stretch a wire of like
material 25 m long and 2 mm in diameter ?
s 5. What is the ratio of the stiffness of a rod 60 cm long to that of
another rod I20 cm long, but of the same width, thickness, and material
as the first ?
6. If a rod 4 ft. long, 2 in. broad, and 0.5 in. thick is bent 0.1 in. by a
weight of 10 Ibs. , how much would a force of 2 Ibs. bend a rod of like
material 12 ft. long, 4 in. broad, and 2 in. thick ?
Solution. It a rod 4 ft. long, 2 in. broad, and 0.5 in. thick is bent 0.1
by a weight of 10 Ibs., a weight of 1 Ib. would bend it one-tenth as much,
or -^r in. (bending is proportional to the load), and this weight of 1 Ib.
would bend a rod 1 ft. long only one sixty-fourth as much, or - in.
o40
(bending is proportional to the cube of the Jength). If the rod were 1 ft.
long and 1 in. wide, the weight of 1 Ib. would bend it twice as much, or
0.2
Trrr in. (bending is inversely proportional to the breadth). Finally, if the
u4U
thickness of the rod were 1 in., its length 1 ft., and its breadth 1 in., a
force of 1 Ib. would bend it one hundred and twenty-five thousandths as
much, or -^ ' = - in. (bending is inversely proportional to the cube of
u40
the thickness).
154 EXPERIMENTAL PHYSICS.
If by x we denote the amount the second rod would be bent by a
weight of 2 Ibs., we shall find by a process precisely like the one just
given that a rod 1 ft. long, 1 in. broad, and 1 in. thick will be bent -
in. by a force of 1 Ib.
As the material is the same for each rod, we have
x 0.1
108 2560
2560 x - 10.8
.-. x = 0.0042
Hence, the amount the second rod would be bent is 0.0042 in.
7. If a rod 4 m long, 6 cra wide, and 8 cm thick is depressed 0.75 cm at its
middle point by a certain load, how much would the same load depress a
rod 3 m long, 3 cm wide, and 4 cm thick ?
8. If a rod 100 cm long, 2n broad, and 3 cm thick is deflected 0.5 cm ,
what would be the deflection, under the same load, of a rod 50 cm long,
2 cra broad, and l cm thick ?
9. If a certain beam 16 ft. long, 4 in. wide, and 6 in. thick is bent
1 in. by a load of 500 Ibs. placed at its middle, how much would a beam
10 ft. long, 8 in. wide, and 12 in. thick be bent by the same load ?
10. A certain beam 4 ft. long is bent downwards 0.5 in. by a load
placed at the middle. If it were 8 ft. long, how far would it be bent by
the same load ?
11. There are two beams of the same length, breadth, and material.
One beam, which is 8 in. thick, is bent 1.6 in. by a certain load, while the
other beam is bent 0.2 in. by an equal load. What is the thickness of
the second beam ?
12. If a rod 80 cm long is twisted through an angle of 1.5 by a force
of 4 oz., through how many degrees will a force of 3 oz. twist a rod
100 cm long, the other dimensions as well as the material being the same
as that of the first rod ?
CHAPTER IV.
SOUND.
63. Wave-Motion. If a stone is dropped into a pool
of calm water, the stone immediately forces down and dis-
places a number of particles of water; consequently the
surrounding particles of water are heaped above the gen-
eral level ; these descend and throw up another wave, and
this in subsiding raises another, until the force of the
original and loftier wave dies away at the edge of the
pool in the faintest ripples. You have probably noticed
the waves that spread in ever-widening circles over a
pool when the water has been disturbed as described.
Did you ever ask yourself the question, " Do the particles
of water forming the first wave, in the center of the pool,
pass to the second wave, and so on to the third, and finally
reach the margin of the pool ? " This question is easily
answered by watching the movements of a bit of wood
floating on the surface. The wood simply bobs up and
down; it does not approach the shore. Since the wood
only rises and falls, we see that the particles of water on
which it rests are not approaching the shore, but are only
moving up and down. Hence it is not the particles of
water, but the wave form that travels from the center to
the margin of the pool. When in summer a wind blows
over a field of grain, we see the wave form advancing, but
we know that the ears of grain are simply nodding.
156 EXPERIMENTAL PHYSICS.
If into a pool of water we drop two pebbles at a little
distance apart, we shall notice that two sets of waves are
produced, each set having for its center the point where
the pebble entered the water. As the waves spread, those
of one set cross those of the other. If we look carefully,
we shall see that where the crest, or top, of one wave
coincides with the crest of another, an elevation higher
than the crest of either wave is produced; also, that
where the trough, or hollow, of one wave coincides with
the trough of another, a depression deeper than the trough
of either is formed; finally, if two waves of equal size
come together in such a way that the crest of one coin-
cides with the trough of the other, there is neither an
elevation nor a depression, but a calm.
The distance from crest to crest, or from trough to
trough, is called a wave-length.
Definition. A wave-length is the distance from any par-
ticle to the next particle that is in a similar position in its
path, and is moving in the same direction. .
In Fig. 45 take the particle a-, b is in the same posi-
tion, but when a is moving downwards b moves upwards.
FIG. 45.
c is the next particle in the same position, but as a moves
downwards c moves downwards. The distance from a to
c measured in a straight line is a wave-length.
THE PENDULUM. 157
Let the student, by dipping his finger into the water
contained in a pail and then quickly removing it, set up a
series of waves as has already been described.
After the waves strike the sides of the pail, are they
sent back towards the center?
By using a finger of each hand, disturb the water in
such a way as to produce two series of waves. One series
mingles with the other.
Do you notice any phenomena of interference (that is,
calms and places of greater or less elevation produced by
the mingling of the waves) ?
You should repeat these observations till the eye becomes
trained to catch the modifications of the wave form.
THE PENDULUM.
64. The Simple Pendulum. When the surface of
water is agitated, the particles of water move up and
down with a rythmic motion. It is important to under-
stand the chief laws this rythmic motion obeys. The
motion of the pendulum is of the same nature as that of
the water particles, so by experimenting with the pendu-
lum, we shall get some knowledge of the motion of the
water particles.
The pendulum we shall use will consist of a lead bullet
attached to a firm support by a thread, which will allow
the bullet to swing freely. The bullet is called the bob of
the pendulum. The fixed point to which the thread is
attached is called the center of suspension of the pendulum.
A motion from side to side is called an oscillation ; a motion
from one side to the other and back again is called a vibra-
158 EXPERIMENTAL PHYSICS.
tion, so that there are two oscillations in one vibration.
The distance the bob swings through, in going from its
middle position to its extreme position, is called the ampli-
tude of vibration. The distance from the center of suspen-
sion to the center of the bob is called the length of the
pendulum. The length of time
a pendulum takes to make an
oscillation is called the time of
oscillation.
Experiment 69. To find /*
whether a change of amplitude _
has any effect upon the num-
ber of vibrations per minute of a pendulum.
Apparatus. The apparatus used is shown in Fig. 46.
A spool is fastened by a screw near the edge of some suitable
support, fastened to the wall a little more than 7 ft. above the
floor. The screw is " set up " till it turns with considerable
friction. A silk thread about 3 m long is wound round the
spool and made to pass through the slot in the head of the
other screw. The lower end of the thread is fastened to a
bullet, the bob. The length of the pendulum may be changed
by turning the spool so as to wind or unwind the thread.
Small adjustments are easily made by gently turning the
spool. To fasten the thread to the bullet, cut a little lip in
the bullet with a knife, place the thread under the lip, and /"~*~\
smooth the lip down with the handle of the knife. Cut off v^ )
the short end of the thread close to the bullet. A watch
, . , . , FIG. 46.
having a second hand is also necessary.
Directions. Taking the lower end of the slot of the
screw as the center of suspension, make the pendulum
36 cm long. Fill the slot with beeswax so that the thread
will not move in the slot. Draw the bob about 5 cm to
THE PENDULUM. 159
one side and release it. The pendulum should swing
parallel to the wall to which the support of the pendulum
is fastened. Glance at the watch and at the pendulum.
When the pendulum is just starting to return from the
end of its swing, take the time. Count accurately for
one minute the number of vibrations. Record the num-
ber of vibrations. Double the amplitude of vibration (by
drawing the bob at the start about 10 cm to one side) and
count the number of vibrations for another minute.
What effect has a change of amplitude on the number
of vibrations performed by a pendulum in a minute ?
Experiment 7O. To find the effect a change of length in
a pendulum has upon the number of vibrations performed
in a- minute.
Apparatus. The same as in the last experiment ; a long pole.
Directions. Place one end of the long pole on the
floor, so that the pole shall stand in a vertical position
with its side against the screw. Mark on the pole the
position of the center of suspension ; then, starting from
this point, measure off on the pole a distance of 225 cm .
Put the pole in the vertical position as before and adjust
the bob till the pendulum is 225 cm long.
Using one amplitude, record, as before, the number of
vibrations for one minute. Then make the length of the
pendulum 100 cm , and record the number of vibrations for
one minute. Finally make the pendulum 25 cm long, and
record as before.
Divide the greatest length of the pendulum by the least.
Divide the largest number of vibrations by the smallest.
Is there any agreement between the quotients ?
160 EXPERIMENTAL PHYSICS.
Does taking the square root of one of the quotients
make the values approximately equal ?
What is the relation between the lengths of pendulums
and the number of vibrations ?
QUESTIONS. From an inspection of your results, answer the following
questions : What is the length of a pendulum that will beat seconds ?
half seconds ?
Experiment 71. To find whether the weight and material
of the pendulum bob have any effect on the number of vibra-
tions in a minute.
Apparatus. The same as in Exp. 69 ; a marble of about the
same size as the bullet.
*
Directions. Jn place of the bullet, fasten the marble
to the end of the silk thread by means of beeswax. Make
the pendulum 36 cm long. Record the number of vibra-
tions per minute.
Compare the result with that recorded in Exp. 69.
What is your conclusion ?
EXAMPLES.
1. If a pendulum makes 30 vibrations in a minute, how many oscilla-
tions does it make in 2 minutes ? How many oscillations does the pen-
dulum make in a second ?
2. If a pendulum makes 40 vibrations in a minute, what is the time
of a single vibration ?
3. If a pendulum 25 cm long makes 60 vibrations in a minute, what
must be the length of a pendulum in order that it shall make 10 vibra-
tions in a minute ?
Solution. As the number of vibrations of two pendulums are to each
other inversely as the square roots of the lengths of the pendulums, we
have, if we denote by x the required length.
VELOCITY OF SOUND. 161
60 : 10 = \lx :
10 Vx = 60 V25
Vz = 6 V25
.-. x = 900
Hence the required length is 900 cm .
4. If a pendulum l m long vibrates once in a second, what must be the
length of a pendulum in order that it shall oscillate once in a minute ?
5. If a pendulum 4 units in length makes a vibration in 0.3 second,
find the length of a pendulum that makes a vibration in 1.8 seconds.
6. If a pendulum 6 units in length makes an oscillation in 5 seconds,
what will be the time of an oscillation of a pendulum 0.54 units in length ?
VELOCITY OP SOUND.
65. The Velocity of Sound in Air. Our next experi-
ment will be for the purpose of getting, roughly, the
velocity of sound in air ; of getting, in other words, the
distance that sound will travel in one second.
Experiment 72. To find the velocity of sound in air.
Apparatus. A wooden support like the one used in Exp. 28 ; a
bullet ; a piece of silk thread ; a stool ; two small boards ; a small
spy-glass.
Directions. This experiment is to be performed out
doors in an open space, where a distance of 500 feet
should be measured off. At the spot from which the dis-
tance is measured the observer with the spy-glass should
stand; at the spot 500 feet away the support should be
placed.
By means of clamps fasten to the support a pendulum
of such length that it will beat half seconds. (See your
record of Exp. 70.) That the bob may be seen as it
swings back and forth, pin a piece of white paper about
162 EXPERIMENTAL PHYSICS.
20cm S q Uare on the upright behind the pendulum. The
student beside the support starts the pendulum swinging,
taking care to have it swing only a little way from side
to side; if it swings off the paper, the observer looking
through the spy-glass cannot see the pendulum. When
the pendulum reaches one extremity of its swing, the
student standing beside the support strikes the boards
together. If the sound reaches the ear of the student
looking through the spy-glass, at the instant in which the
pendulum reaches the other extremity of its swing, then
it has taken the sound just 0.5 second to travel 500
feet. In order that the student at the spy-glass may
have a good many opportunities to observe the pendu-
lum and listen to the sound, the student beside the sup-
port should strike the boards together every time the
pendulum gets to the end of its swing next to him. By
moving the spy-glass from or towards the pendulum, the
distance that the sound will travel in 0.5 second can be
found.
Interchange the spy-glass and the pendulum; then
repeat the experiment, the student who before looked
through the spy-glass now taking his position beside the
support. For the velocity of sound in air, take the aver-
age of the two distances found.
From your observations on the velocity of sound per 0.5
second, what is the velocity of sound per second in feet ?
QUESTION. If there are 15,240 cm in 500 feet, what is the velocity of
sound per second in centimeters ?
Experiment 73. To find whether the air is necessary
for the transmission of sound.
VELOCITY OF SOUND. 163
Apparatus. A Kjeldahl flask ; a one-hole rubber stopple to fit
the flask ; a piece of pressure tube about 30 cm long ; a glass tube
long enough to reach to the middle of the body of the flask ; a little
toy bell ; an air-pump.
Directions. Push the glass tube through the stopple,
and over the end that goes into the flask slip a bit of
rubber tube about 0.5 cm long. With a bit of thread
fasten the bell to the glass tube; the bit of rubber will
keep the thread from slipping off. Over the other end of
the glass tube slip the pressure tube. Put the stopple in
place. Shake the flask, and listen to hear the bell ring.
Connect the flask to the air-pump by means of the rubber
tube. Pump out a little air, and shake the flask.
Is the sound of the bell fainter than before ?
Pump out some more air.
On shaking the flask, can you hear the bell ?
What inference can you draw from this experiment?
Point out in what way you have used the method of
'differences in this experiment.
Can sound pass through a vacuum ?
Experiment 74. To find whether a musical sound can
be produced by a vibrating body beating the air at regular
intervals.
Apparatus. A straight piece of clock-spring about 50 cm long ; a vise.
Directions. Fasten the clock-spring in the vise with
about 45 cm projecting horizontally. Set the spring vibrat-
ing horizontally through a small arc, and record the num-
ber of vibrations made in 0.5 minute. Then set the spring
swinging through a large arc, and record the number of
vibrations made in 0.5 minute.
164 EXPERIMENTAL PHYSICS.
Does the time of vibration of the spring depend upon
the amplitude of vibration ?
Push the spring farther into the vise leaving about 20 cm
projecting. If possible, make observations and record as
before.
What is your inference ?
Leave only about 8 cm projecting, and finally only about
_J.cm
When the spring now vibrates, does it give a musical
sound ?
Does the pitch become higher or lower as the number
of vibrations increases ?
From the results of this experiment, should you say
that a musical sound has been produced by a vibrating
body beating the air at regular intervals ?
TUNING-FORK.
66. The Tuning-Fork. The tuning-fork is an acous-
tic instrument of great interest. The spring of the
preceding experiment serves as a starting-point in the
description of the tuning-fork, which may be looked upon
as an elastic bar bent into a U-shape, free at both ends,
and supported in the middle where the stem or handle is
inserted. Tuning-forks are usually made of steel. The
tuning-fork is excited (set in vibration) by striking the
outside of one of the prongs against a board covered with
leather or flannel, but never against a table or other hard
object. Shortly after the fork has been excited, its tone
becomes pure and simple.
NOTE. The tuning-fork was invented in 1711, by John Shore, a trump-
eter in the service of George I. of England.
TRANSMISSION OF SOUND. 165
TRANSMISSION OF SOUND.
67. Mode of Transmission of Sound in Air. It was
learned in Exp. 73 that the presence of air was necessary
for the transmission of sound from a bell to the ear. But
an inquiry of importance is, how the sound is transmitted
by the air, by a puff, that is, by a small gust of air in
which the air particles are sent from the sounding body
to the ear, or by a pulse, that is, to-and-fro motion, of the
air particles. The object of the next experiment is to
satisfy this inquiry.
Experiment 75. To find whether the movement of air,
when sound passes through it, is of the nature of a puff or of
a pulse.
Apparatus. A long tin tube that tapers at one end ; a candle ;
touch-paper. 1
Directions. Place the tube in a horizontal position on
the table. At the small end put the lighted candle (see
Fig. 47), carefully shielded from air currents, with the
flame opposite the opening and but 2 cm or 3 cra away.
Get a student to strike together two blocks of wood at
the large opening.
What happens to the flame ?
Is the flame affected thus by a puff or by a pulse of air ?
To answer this question, having filled the tube with
smoke by burning touch-paper in it, strike the blocks
together and watch the appearance at the small end of
1 Touch-paper is made by soaking filter paper or blotting paper in a
saturated solution of nitrate of potash, and then drying the paper.
166 EXPERIMENTAL PHYSICS.
the tube. The purpose of the smoke is to make visible
to the eye the currents of air, if any, that are set in
motion by clapping the blocks together. To see what
FIG. 47.
appearance a puff of air would produce, let the student at
the larger end of the tube blow into the tube with a quick
short puff.
From the behavior of the smoke when the blocks are
struck together, should you say that the candle had been
affected by a puff of air or by a pulse ?
68. Is Sound a Wave-Motion of Air ? From Exp. 73
you have already learned that the presence of air is neces-
sary for the transmission of sound, and from Exp. 75 you
have seen that when conveying sound, the particles of air
have a back-and-forth motion. Can this motion be a
wave-motion of air? To prepare yourself for answering
this question, recall your study of water waves and the
idea you gained of what is meant by interference (see
pages 156 and 157). By the interference of two sets of
water waves, there were produced waves of different sizes,
from very small ones up to waves of greater magnitudes
TRANSMISSION OF SOUND. 167
than those of either of the original set of waves; calms
were also produced. If sound is really due to a wave-
motion of the air, phenomena of interference ought to be
observed under suitable conditions. In the interference
of sound waves, silence would correspond to a calm in
the interference of water waves, and varying degrees of
loudness of sound to water waves of different heights.
The object of the next experiment is the study of sound
under different phases, with a view to determining whether
phenomena of interference can occur.
Experiment 76. To find whether the phenomena of inter-
ference can be observed in sound.
Apparatus. A tuning-fork ; a 100 CC graduate ; a cylinder of card-
board about as long as one of the prongs of the tuning-fork and
about 2 cm in diameter ; a tuning-fork, high C.
Directions. By striking one prong of the tuning-fork
against a piece of leather laid upon the table, set the fork
in vibration. Then hold the fork above the graduate in
such a position that the ends of the prongs lie in the axis
of the graduate. Pour water slowly into the graduate.
As the water rises, the sound grows louder; and then as
more water is added, the sound grows weaker. In this
experiment adjust the level of the water till the sound of
the fork is strongly reinforced. Turn the fork slowly
round its axis.
For certain positions of the fork, do the sounds become
nearly inaudible ?
If any such positions are found, hold the fork steadily
in one of them, and then carefully slide the cardboard
cylinder over one of the prongs, as shown in Fig. 48,
168 EXPERIMENTAL PHYSICS.
without allowing the cylinder to touch either prong, as
that would interrupt the vibrations.
Is the sound restored?
Could you account for what you observe by regarding
each prong of the fork as sending out sound, but as one
of the prongs is nearer the mouth
of the graduate than the other,
the sound reflected by the surface of the water
in the graduate interferes with the sound from
the more remote prong?
On the whole, what is your conclusion from
this experiment?
69. Form of a Sound Wave. If a bell is
sounded, the tone of the bell is heard above,
below, at one side, and, in fact, at any point
the ear may be placed. The sound spreads out,
then, in spheres whose common center is the
FIG. 48.
position of the bell. The sound wave is made
up of a condensed portion (where the particles are crowded
together), corresponding to the crest of a water wave, and
of a rarefied portion (where the particles of air are farther
apart than usual), corresponding to the trough of a water
wave. Where a condensed portion of a sound wave coin-
cides with the rarefied portion of another equal wave,
silence results; where the condensed portion coincides
with condensed portion, and rarefied portion coincides
with rarefied portion, a sound louder than that due to
either wave is produced.
Between what points do you measure the length of a
sound wave ?
RAPID VIBRATIONS. 169
The diagram (Fig. 49) represents the concentric waves
of sound spreading from the point of disturbance at the
center. Where the __ _ _
circles of dots are
nearest together,
there is the con-
densed portion of
the wave ; where the
circles of dots are
farthest apart, there
the rarefied por- ^ \ V^Cr.
>n of the wave. \^\\\\ X <^xr~
In the propagation ^x^\ <> ^ *
of water waves the v^^^or- ^i ~ : --
NS^S^-.-^rrr^j
motion of the water ^^T?:3=S^
particles is to and
FIG. 49.
fro at right angles
to the direction in which the wave moves.
In the case of sound waves in air, do the air particles
move to and fro at right angles to the direction in which
the sound travels ?
RAPID VIBRATIONS.
7O. Method of Counting- Rapid Vibrations. In the
experiment with the clock-spring clamped in the vise,
you saw that by shortening the spring the musical sound
emitted increased in sharpness, or pitch, and you also ob-
served that the vibrations became so rapid that the eye
could not follow them quickly enough to count them. In
the next experiment we shall find how many vibrations per
170
EXPERIMENTAL PHYSICS.
second a certain tuning-fork makes. In this experiment
a piece of smoked glass is drawn beneath a vibrating pen-
dulum (Fig. 50) and a vibrating tuning-fork. A little
FIG. so.
style, made of a bristle, is fastened to the pendulum and
another to the fork. These styles trace out curves on the
glass as shown in Fig. 51. The wavy line is traced by
FIG. 51.
the style attached to the tuning-fork, while the other lines
are traced by the style attached to the pendulum.
Experiment 77. To find the number of vibrations made
in a second by a tuning-fork.
RAPID VIBRATIONS. 171
Apparatus. A tuning-fork, middle C ; a piece of apparatus pro-
vided with a support for the tuning-fork and the pendulum ; a watch ;
a bass-viol bow ; rosin ; a rectangular piece of glass.
Directions. Clean the glass, and then slightly smoke
it by holding it in an ordinary flame. Lay the glass on
the carrier beneath the pendulum. To the little rod pro-
jecting from the lower side of the pendulum bob fasten,
by means of thread, a flexible bristle whose end shall
bear lightly on the surface of the glass, so that, as the
pendulum swings, a line shall be traced in the thin layer
of soot which covers the glass. Near the end of one
prong of the tuning-fork a somewhat stiffer bristle should
be fastened by a bit of wax. This bristle should lightly
touch the glass, to whose surface it should, be somewhat
inclined. Find how many vibrations the pendulum makes
in a minute.
How long does it take the pendulum to make one
vibration ?
Now place the tuning-fork, mounted on its support, in
a position to bring the end of the bristle attached to it as
close as practicable beside that attached to the pendulum.
When both pendulum and fork are vibrating, the bristles
should move parallel to each other. When all the adjust-
ments are made, set the pendulum swinging, excite the
fork by drawing the bow, which has been well rosined,
across it; then draw the carrier holding the glass plate
along at right angles to the direction in which the pendu-
lum and fork are vibrating.
Remove the glass, count carefully, using a magnify-
ing glass if necessary, the number of vibrations recorded
by the fork on the glass between the points corre-
172 EXPERIMENTAL PHYSICS.
spending to one vibration of the pendulum. Record
this number.
We already know the time the pendulum takes to make
one vibration, and we have just found the number of vibra-
tions the fork makes in an equal length of time'.
How many vibrations does the middle C tuning-fork
make in a second ?
TUNING-FORK AND RESONATOR.
71. The Determination of the Velocity of Sound in
Air by means of the Tuning-Fork and Resonator. If
we know the number of vibrations which a tuning-fork
makes in a second and the length of a column of air that
will reinforce the tone of the fork as in Exp. 76, we can
compute from these data the velocity of sound in air.
The object of the next experiment is to obtain the data
and make the computation.
Experiment 78. To find, by means of a resonance tube,
the velocity of sound in air.
Apparatus. A glass jar 35 cm or more in depth, and from 3 cm to
10 cm in diameter ; a tuning-fork, middle C ; a thermometer.
Directions. Place the jar on the table, and over its
mouth hold the vibrating tuning-fork with the ends of its
prongs in line with the axis of the jar. Pour water grad-
ually into the jar until the sound of the fork is strongly
reinforced. By pouring in a little more water, or by
pouring out a little, get the length of the air column from
the mouth of the jar to the surface of the water such that
the sound will be the very loudest. Then measure and
TUNING-FORK AND RESONATOR. 173
record in centimeters the distance from the mouth of the
jar (Fig. 52) to the level of the water; also record the
diameter of the jar in centimeters.
Instead of pouring water into the jar, the level of the
water may be readily changed by means of a siphon, con-
sisting of two glass tubes of small bore joined by a rubber
tube. One of the glass tubes is
bent so that it will reach nearly
to the bottom of the jar when hung over its
edge, the other glass tube is bent to hang over
the edge of a jar containing a supply of water.
The rubber tube is long enough to allow the
jar containing the supply of water to be raised
or lowered so that water will flow into the
other jar or out of it, thus raising or lowering
the level.
Record the temperature of the air in the jar.
The forward motion of the fork sent down
the tube an impulse which, at the surface of FlG 52
the water, was reflected in time to reinforce
the impulse given by the fork in its backward motion.
Thus during the forward motion of the fork, that is,
during half a vibration, the sound traveled to the water
and back. When the sound passes through the mouth
of the jar, a spreading of the sound occurs, so it is found
necessary to add to the distance which the sound travels
in one-fourth of a vibration (that is, to the distance from
the mouth of the jar to the level of the water) one-fourth
of the diameter of the jar.
After making this correction, what distance do you find
that sound travels during one vibration of the fork ?
174 EXPERIMENTAL PHYSICS.
From the experiment you have already performed,
how many vibrations does the tuning-fork make in a
second ?
From your data, what is the velocity in centimeters per
second of sound in air?
72. Sympathetic Vibrations. In the last experiment
the fork was able by its vibrations to set into vibration a
column of air of definite length, and thereby the loudness
of its note was greatly increased. The air column, when of
proper length, vibrated in sympathy with the fork; hence
such vibrations are called sympathetic vibrations.
In most sonorous bodies (for example, a tuning-fork)
mechanical movement (the motion of the prongs of a
tuning-fork, for instance) is transformed into sound. It
would be interesting to inquire whether this process has
ever been reversed ; whether, in other words, sound vibra-
tions can generate mechanical motion. There is a little
instrument, known as a sound radiometer, or an acoustic
reaction wheel, which can be kept in motion by sound. It
is made of four small tubes open at one end. These tubes,
made of aluminum on account of its lightness, are accu-
rately tuned to the same note. Two light rods or wires
are fastened together at right angles, making four arms of
equal length. A tube, or resonator, is fastened at the
middle of its length to the extremity of each arm in such
a way that its axis lies in a plane below but parallel to
that of the crossed wires. The whole is delicately poised
on a pivot in a horizontal position. When this instrument
is put near a fork giving the same note as that to which
the resonators are tuned, the little wheel begins to rotate,
TUNING-FORK AND RESONATOR. 175
and continues in rotation as long as the tuning-fork con-
tinues in vibration.
73. Beats. If two tuning-forks, one of which makes
254 vibrations while the other makes 255, are set in
motion, a peculiar palpitating effect results, produced by
bursts of sound, separated from one another by intervals
of comparative silence. These bursts of sound are called
beats. By the principle of interference (see Exp. 76) the
production of beats can be fully explained. Suppose the
forks to be in vibration ; if we start from the time when
the condensed portion of the waves from each fork reaches
the ear at the same instant, that is, when the sound is
loudest, just one second will elapse before the sound
is loudest again. The fork making 255 vibrations per
second gains a vibration in one second over the other fork,
that is, in one second the note from this fork gains one
wave-length ; but since at the middle of the second it has
gained only half a wave-length, the rarefied portion of the
sound wave from this fork combines with the condensed
portion of the sound wave from the other fork, the two
portions neutralize each other, and silence results. Dur-
ing every second, then, that passes while the forks are
vibrating together, there will be one beat and one period of
silence. If one fork had made 254 vibrations per second
and the other 256, two beats and two periods of silence
would have occurred during the second.
If, when two tuning-forks are sounding together, there
are beats, the number of beats per second tells the differ-
ence between the number of vibrations per second of the
two forks ; further, if the number of vibrations per second
176 EXPERIMENTAL PHYSICS.
of one of the forks is known and it is also known which
of the forks gives the higher note, it is possible to find
the number of vibrations per second made by the fork
whose number of vibrations is unknown. For example,
two forks A and B are sounded together, and four beats
per second are counted. If it is known that A makes 256
vibrations per second, and that its note is lower than that
of J&, it follows that B makes in one second 260 vibrations.
74. Octave; Concord; Discord. Two notes are an
octave apart when one is produced by twice as many
vibrations as the other. Thus a tuning-fork that makes
508 vibrations per second emits a note which is the octave
of the note given by a fork vibrating 254 times per second.
When two notes an octave apart are sounded together,
the result is pleasing to the ear, and there is said to be
concord. Besides notes an octave apart, there are others
that produce concord when sounded together; but there
are many notes which, on being sounded at the same time,
produce a disagreeable impression on the ear; such notes
are said to produce discord. The unpleasant, jarring effect
of discord is due to the production of beats.
VIBRATING STRINGS.
75. Pitch of Vibrating Strings. It will be the purpose
of the three following experiments to find what relations
exist between the length, the tension, the thickness of a
stretched wire, and the number of vibrations per second.
Experiment 79. To find the relation between the length
of a stretched wire and the number of vibrations per second.
VIBRATING STRINGS.
177
Apparatus. A spring balance of 30 pounds' capacity ; a piece of
spring brass wire, No. 22 B. & S., 1.5 m long ; two of the triangular
pieces of wood used in Exp. 62 ; a meter stick ; a middle C fork, and
another an octave higher.
Directions. Fasten one end of the wire to a screw in
the table-top, and lay the wire straight on the table;
fasten the other end to the balance. Hook the ring of
the balance to the screw for applying tension, as shown
in Fig. 53. (For Exps. 79 and 80 consider only the bal-
FlG. 53.
ance and wire which, in the figure, is next to the edge of
the table.) Under the wire near the screw fasten by a
brad one of the prisms with its edge at right angles to the
wire. Under the wire lay the other prism parallel to
the first. If the balance, as it should, holds the wire
about as high as the top of the movable prism, this prism
can be moved along under the wire without changing the
tension to any extent.
Allowing for the zero error of the balance, when used
in the horizontal position, stretch the/ wire with a force
of 20 pounds, and, keeping this tension constant, find the
178 EXPERIMENTAL PHYSICS.
lengths that will give notes corresponding to the two
forks respectively. Set the wire into vibration by pluck-
ing it in the middle, and, with the ear close to the wire,
listen for the fundamental note, which may for an instant
be obscured by harsh or grating overtones.
A student who has no keen perception of musical pitch
can secure nearly perfect unison by sounding the wire and
the fork at the same time ; the beats, which become very
apparent when the sounds are near unison, will guide him
in his judgment. It will be well to press the wire with
the finger lightly against the movable prism so as to limit
the vibrations to that part under consideration.
One fork is an octave higher than the other.
Divide the greater number of vibrations by the smaller ;
also the greater length of wire between the prisms by the
smaller.
Are the quotients equal?
The inference you can draw we shall call Law 1.
State Law 1.
QUESTIONS. If a string 100 cm long gives a certain note when plucked,
what must be its length to give the note an octave higher ? What must
be its length to give the note an octave lower ?
Experiment 8O. To find the relation between the tension
of a wire and the number of vibrations per second.
Apparatus. The same as in Exp. 79, without the higher fork.
Directions. Correcting for the zero error of the bal-
ance, when in the horizontal position, make the tension
5 pounds. Find what length of wire will give a note
whose pitch corresponds to that of the middle C fork.
VIBRATING STRINGS. 179
Turn back to your record of Exp. 79 ; you ought to
find there a length recorded equal or nearly equal to the
one just found.
To which fork does the note of the recorded length of
wire correspond?
Divide the number of vibrations of this fork by the
number of vibrations of the fork used in the present
experiment ; also divide the tension used in the last
experiment by the tension used in this experiment.
If the two quotients are not equal, try to make the
second equal to the first by squaring or by taking the
square root.
The relation thus found between the number of vibra-
tions per second and the tension is called Law 2.
State Law 2.
QUESTIONS. If a wire under a tension of 7 pounds gives a certain
note, how much higher would the note become on increasing the tension
to 28 pounds ? How much lower would the note become if the tension
were reduced to 1.75 pounds ?
Experiment 81. To find the relation between the thick-
ness of a wire and the number of vibrations per second.
Apparatus. A piece of spring brass wire, No. 28 B. & S., stretched
as shown in Fig. 53 ; the fork of higher pitch.
Directions. Correcting as before for the zero error of
the balance, when used in the horizontal position, apply to
the wire a tension of 5 pounds. Find what length of wire
will give a note whose pitch corresponds to that of the
fork of higher pitch.
Turn back to Exp. 80 ; you ought to find a length
recorded equal or nearly equal to that obtained in this
experiment.
180 EXPERIMENTAL PHYSICS.
Divide the number of vibrations of the wire of this
experiment by the number of vibrations of the wire of
Exp. 80. The ratio of the thicknesses of the two wires
is as 2 to 1.
If the ratio of the thicknesses is not equal to the ratio
of the number of vibrations, try to make it equal by squar-
ing or taking the square root, inverting if necessary.
The relation thus obtained between the thickness of the
wire and the pitch is called Law 3.
State Law 3.
QUESTIONS. ' If a wire l m long gives a note of a certain pitch, how
much higher will be the pitch of a note given by a wire, of the same
material as the first, of equal length and stretched by the same tension,
but of only one-half the thickness ? How much lower will the note be if
the wire is twice as thick ?
NOTE. The strings or wires which we have considered are supposed
to be of the same material. Whenever the material of two strings, alike
in all other respects, differs in density, there is a fourth law, " The number
of vibrations is inversely proportional to the square roots of the densities."
76. JLoudness ; Pitch ; Quality. The loudness of a
note depends upon the amplitude of vibration. When
a tuning-fork is set in vibration, the note, loud at first,
gradually dies away, becoming fainter and fainter as the
amplitude of the fork's vibrations decreases. The pitch
of a note depends not upon the amplitude of vibration,
but upon the number of vibrations made in a given time :
the greater the number of vibrations, the higher the pitch ;
the smaller the number, the lower the pitch. The quality
of a note depends neither upon the amplitude of vibration
nor upon the frequency of the vibrations, but upon the
peculiar tones which accompany the production of the
fundamental note. On hearing C sounded on a piano
THEORY OF SOUND. 181
and then on a violin, the ear perceives that the pitch is
the same, yet it distinguishes between the note emitted by
the piano and that given by the violin ; a note sounded
on a piano has a different quality from that of the same
note sounded on a violin. To illustrate the modification
the fundamental note undergoes by the peculiar tones,
depending upon the kind of musical instrument used, let
the student imagine, what is so often seen at the sea-
shore, long swelling waves coming from the sea, whose
surface except for these waves is unbroken. These
waves may be taken to represent the fundamental note.
Now suppose a light breath of air disturbs slightly the
surface of these waves, which become dimpled. The
wavelets thus produced modify to a very limited extent
the character of the original waves. So with musical
instruments, each instrument gives out the fundamental
note, C for example, which is the same for them all ; but
each instrument by reason of peculiarities of its construc-
tion gives out little notes, faint to be sure, but sufficient,
nevertheless, to modify the fundamental note and give to
it an appearance or quality different from the correspond-
ing note of some other instrument.
THEORY OP SOUND.
77. Sketch of the Development of the Theory of
Sound. More than two thousand years ago Pythagoras 1
] Pythagoras (pronounced py-thag'o-ras) (about 569-500 B.C.) founded
a school of philosophy whose members in honor of their teacher were
called Pythagoreans (pronounced py-thag-o-re'ans). This school busied
itself with many fantastic mathematical and philosophical speculations,
182 EXPERIMENTAL PHYSICS.
invented the monochord, an instrument similar to that
used in the last three experiments. With this instrument
Pythagoras made several discoveries about the sounds
produced by a stretched string when vibrating. One of
his first discoveries was that a string which gives a cer-
tain note will give a note an octave higher, if the string is
made one-half as long.
Very little advance was made from the time of Pythag-
oras till that of Mersenne, 1 who proved experimentally
that the number of vibrations is inversely proportional to
the length of the string ; that the number of vibrations of
a string is proportional to the square root of its tension ;
and that the number of vibrations is inversely proportional
to the thickness of the string.
The laws of vibrating strings have been determined
mathematically as well as experimentally. It was La-
grange 2 who completed the work from the mathematical
point of view at which his predecessors had labored so
industriously.
It was reserved, however, for Helmholtz, a very emi-
nent physiologist, physicist, and mathematician, to lay
the foundation of musical science, which he accomplished
about the middle of the nineteenth century.
the most famous of which was the doctrine of "the harmony of the
spheres." According to this doctrine, the heavenly bodies in their
motion through the sky give out grand and wonderful music, but so fine
and delicate that our ears, accustomed to the gross sounds immediately
around us, are deaf to this " music of the spheres."
1 Mersenne (pronounced mer-seri) (1588-1648) was a Franciscan friar.
He has been called the " Father of Acoustics."
2 Lagrange (pronounced la-gronzh) (1738-1815) was a celebrated French
mathematician,
LAWS. 183
LAWS.
78. Laws of Nature ; Theory. The laws of nature
are general truths which have been found by diligent
search among the facts obtained by observation and exper-
iment. For example, that " the deflection of a rod is pro-
portional to the load " is a law, or general truth, which all
rods, provided the load is not too great, obey. A law of
nature, it must be remembered, differs from a law for the
government of society; the former is fixed and change-
less, while the latter lasts only till men see fit to repeal
or amend it.
From the results of your work in the laboratory, name
fifteen laws which you have inferred. If now you go
through the process of reasoning by which you arrived
at these laws, is there any instance in which you did
not infer a law from particular cases? For the sake
of illustration take the law just quoted ; by reference to
your record you will see that there were from twelve
to sixteen particular cases among which there seems
to be this bond, or uniform relation, "the deflection of
a rod, in each case, is proportional to the load." Life
would be far too short to test every rod to see if this rela-
tion holds, so from his experience in a few particular cases
the student infers it to be true in all. The belief in the
truth of his inference is strengthened by the answers
given by nature to other inquiring students. The student
must not suppose that the confidence of men of science in
the true statement of the laws of nature rests on infer-
ences from data so imperfect as those obtained in our own
laboratory work. Our data may suggest the possibility
184 EXPERIMENTAL PHYSICS.
of the law, but the physicist is not satisfied with this ;
he makes accurate measurements, he varies the different
cases, he performs different experiments, till he accumu-
lates a large amount of evidence from which to draw his
inferences.
When we speak of the theory of sound, we mean the
general and accurate knowledge of the laws of sound,
just as when we speak of the theory of quadratic equa-
tions we mean the general and accurate knowledge of the
laws which connect the coefficients and the constant term
with the roots.
The term theory, however, is ambiguous; sometimes it
has the meaning just given, at others it is synonymous
with the term hypothesis.
FALLACIES.
79. Fallacies of Observation. In Art. 29 the atten-
tion of the student was called to the importance of dis-
tinguishing between facts and inferences. In this matter
too much attention and care cannot be given to training
the mind to careful habits of discrimination. With the
best of intentions of telling the truth in a court of law,
a witness with little knowledge and little mental culti-
vation, when undertaking to give an account of simple
occurrences that he has seen, often mingles facts and con-
jectures in such confusion, that the lawyer only by skillful
cross-examination and a careful sifting of the evidence
can make the witness separate the facts and the inferences
(false or true) which he has drawn from these facts.
FALLACIES. 185
Even an acute and well-trained mind is not always free
from mistaking an inference for a direct perception. An
amusing instance of this is related of Dr. Wollaston, a
celebrated English chemist. When Sir Humphry Davy
placed in his hand for inspection the scientific curiosity of
the day, a bit of potassium, a substance so light that it
will float on water, Dr. Wollaston carefully examined the
potassium, noted its metallic lustre, and did not hesitate
to declare it a metal. In this philosopher's mind inti-
mately associated with the notion of metal was also the
notion of weight, and the evidence of his sense of touch
was insufficient to separate the two ideas ; so, balancing
the specimen on the tips of his fingers, he exclaimed,
" How heavy it is ! " He mistook his judgment of the
weight of the substance for the sensation itself.
EXAMPLES.
1. The length of the seconds pendulum at Greenwich is 99.413 cm ; find
the length of a pendulum which makes a single oscillation in 1.5 seconds.
2. A tuning-fork makes 256 vibrations per second, and the velocity of
sound in air is 340 m per second; what is the wave-length of the note
produced ?
Solution. If an observer be at a distance of 340 m from the fork,
there will be, between the fork and the ear, 256 condensations and 256
rarefactions ; but a condensation and a rarefaction make up a wave ; so
there will be 256 waves occupying a distance of 340 m , hence, if in 340 m
340
there are 256 waves, the length of one wave will be r^ = 1.33 m .
z5o
3. Find the wave-length of a note making 1000 vibrations per second,
both in air and in water ; the velocity of sound in air being 1100 ft. per
second, and in water 4900 ft. per second.
4. Taking 1120 ft. per second as the velocity of sound in air, find the
number of vibrations which a tuning-fork, vibrating 254 times in a
second, must make before its sound is audible at a distance of 144 ft.
186 EXPERIMENTAL PHYSICS.
5. A stretched string 10 ft. long is in unison with a tuning-fork mak-
ing 256 vibrations per second ; the string is shortened 4 ft. ; how often
will it now vibrate in a second ?
6. A string is fastened at one end to a peg in a horizontal board, and
the other end passes over a pulley and carries 16 pounds. The string
thus stretched gives the note C. What weight must be put in place of
the 16 pounds, so that the string shall give the next lower octave ?
7. Find the distance of an obstacle which sends back the echo of a
sound to the source in 1.5 seconds, when the velocity of sound is 1100 ft.
per second.
Solution. In 1.5 seconds, sound travels 1100 X |, or 1650 ft.; this dis-
tance the sound travels in going to the obstacle and in returning, hence
the distance of the obstacle is 825 ft.
8. The distance from the top of a well to the surface of the water is
210 ft. What time will elapse between producing a sound at its mouth
and hearing the echo ? (Velocity of sound = 1100 ft. per second.)
CHAPTER V.
LIGHT.
80. Self-Lumiiious Bodies ; Non-Luminous Bodies.
When we are in a place exposed to either the sun or any
other glowing body, we become aware of the existence of
objects around us. If the place be securely shielded from
the sun, or if the glowing substance be quenched, then by
the eye we perceive nothing, all is blank ; but when the
substance is kindled again, or the sun shines in once more,
then the sight again perceives the objects which were but
a moment before invisible. This mysterious something
that is necessary to render objects visible is called light.
Bodies like the sun or a lighted lamp, therefore, have the
property of rendering visible not only themselves, but
also the objects on which their light shines. Bodies which
have this power are called self-luminous bodies. On the
other hand, bodies which require the presence of a self-
luminous body to enable us to see them are called non-
luminous bodies.
81. Transparent, Translucent, and Opaque Sub-
stances. If, in a lighted room, we hold a piece of window-
glass before the eyes, we readily see the objects in the room
through the glass. Substances, like glass, through which
objects can be distinctly seen are called transparent. Sub-
stances, like oiled paper, through which, though light pas-
ses, objects cannot be distinctly seen, are called translucent.
188 EXPERIMENTAL PHYSICS.
Substances, like iron, through which no light passes are
called opaque.
Make a list of four transparent substances, another of
four translucent substances, and a third of four opaque
substances.
PHOTOMETRY.
82. Intensity of Illumination. When reading a book
in the evening, you will find it more and more difficult to
see the letters the farther the book is carried from the
lamp. In other words, on carrying a book from the lamp,
the degree to which the lamplight illuminates the page is
diminished. It will be interesting, as an introductory
experiment in light, to find the relation between the
degree to which a lamp or a candle illuminates a given
object, as a screen, and the distance of the object from the
lamp. In the course of the experiment we shall have
occasion to use the term intensity of illumination, and
it is important to understand clearly its meaning, so we
give the following definition :
Definition. By the intensity of illumination is meant
the degree to which a source of light supplies a given body
with light.
Experiment 82. To find the relation between the inten-
sity of illumination and the distance.
Apparatus. A Letheby's photometer; five candles. Letheby's
photometer (Fig. 54), an instrument for measuring the intensity
of illumination, is constructed as follows: there is a long bar or rod
on which a screen of paper, stretched on a frame, is placed in a
vertical position. This screen has a translucent spot of paraffine on
PHOTOMETRY. 189
its center. Two mirrors, one for each eye, are so placed that an
observer may see both sides of the screen at the same time. One of
the lights is placed on one side of the screen ; the other, on the other
FIG. 54.
side. The mode of action of the instrument depends on the fact
that when a piece of paper having a paraffine or other grease spot
on it, is equally illuminated on both sides, the spot becomes nearly, if
not quite, invisible.
Oirectioiis. This experiment is to be performed in
a darkened room. Place in line four candles, all of the
same height, on one of the sliding blocks, in such a way
that the line of candles is at right angles to the bar. On the
other side of the screen place on a sliding block the other
candle. Light the candles and trim the wicks so that the
flames shall be of equal size. In order to let the candles
get well burning, it is best to wait a few minutes before
making any measurements. When trimming the candles,
look at them not with the naked eye, but through col-
ored glasses ; otherwise the eye will not be as sensitive to
the difference of light and shade on the screen. Slide
the block carrying the four candles along the bar till the
middle of the line of flames is at a distance of 80 cm from
the screen. By sliding the single candle back and forth
along the bar, find a position for it such that the spot
shall disappear as you look into the mirrors (or, if the spot
cannot be made to vanish entirely, get the two images of
190 EXPERIMENTAL PHYSICS.
the spot, as seen in the mirrors, of the same shade).
Record the distance of the four candles from the screen ;
also the distance from the screen of the single candle
when placed in the position you have been directed to find.
Next put the four candles at a distance of 160 cm from
the screen, and find the corresponding position of the
single candle. As before, record the distances.
Assuming that each of the five candles gives out the
same amount of light, how does the amount of light given
out by the four candles compare with that given by the
single candle?
In each case, how does the distance of the four candles
compare with that of the single one ?
In this experiment the intensity of illumination on the
screen due to the single candle was equal to the intensity
of illumination due to the group of four candles placed at
a greater distance from the screen on the other side. Now
consider that from the group of four candles, when the
distance has been properly adjusted, three are removed, so
as to leave only one candle ; how much light falls upon
the screen from this single candle as compared with the
amount of light from the group of four ?
Divide the greater distance (the distance of the four
candles from the screen) by the lesser distance (the dis-
tance of the single candle on the other side of the screen);
also divide the intensity of illumination of the single
candle by the intensity of illumination of a single candle
supposed to be placed at a distance from the screen equal
to that of the group of four candles.
If the two quotients are not equal, try to make them
equal by squaring or cubing one of them.
PHOTOMETRY. 191
What relation should you infer holds between the dis-
tance of a light from a screen and the intensity ^ of its
illumination ?
QUESTIONS. How would the distances compare if 9 candles were used
in place of the 4 ? If 16 candles were used ? If 25 candles were used ?
Experiment 83. To find how many candles will give
the same intensity of illumination as a kerosene lamp.
Apparatus. A Letheby's photometer ; a kerosene lamp with a
chimney ; a candle.
Directions. At a distance of 50 cm on one side of the
screen place the candle. On the other side of the screen
place the well-trimmed lamp with its flame turned flatwise
towards the screen. Light the candle and wait till it is
burning well. See that the lamp-flame and the candle-
flame are at equal distances above the table. Move the
lamp till the spot disappears or till both images are of the
same shade. Measure and record the distances.
Denote the power of the candle by 1, and that of the
lamp by x, then by the law brought out in the preceding
experiment :
= intensity of illumination of
(distance of the candle) 2
the candle.
- = intensity of illumination of
(distance of the lamp) 2
the lamp.
But in the present experiment you have adjusted the
distances in such a way as to make the intensity of illumi-
nation of the candle on the screen equal to that of the
lamp, hence,
192 EXPERIMENTAL PHYSICS.
(distance of the lamp) 2 (distance of the candle) 2
_ / distance of the lamp \ 2
\distance of the candle/
Making use of this relation, compute the number of
candles to which the lamp is equivalent.
Definition. Photometry is the art of measuring the
intensity of light.
RAYS.
Experiment 84. To find whether light passes through
the air in straight lines.
Apparatus. A Bunsen burner arranged to give the luminous
flame ; three pieces of cardboard.
Directions. Set up the three cards, through each of
which a pin-hole has been made, in such a way that the
flame or a portion of it can be seen through the holes.
When the flame can be seen, are the three holes in the
same straight line ?
Does, then, light pass through the air in straight lines ?
83. Kay ; Beam ; Pencil. A single ray, or line, of
light (Fig. 55, 1) is represented by a straight line. A beam
of light, that is, a bundle of parallel rays (Fig. 55, 2), is
represented by several parallel straight lines. A pencil
of light, that is, a group of rays converging to or diverging
from a point, is represented by a group of converging or
by a group of diverging lines. Fig. 55, 3, represents a
converging pencil in which the rays proceeding from some
SHADOWS. 193
source of light on the left draw nearer together, so as to
cross each other at the point 0. Fig. 55, 4, represents a
FIG. 55.
diverging pencil in which the rays proceeding from the
source of light 0' spread away from each other as they pro-
ceed to the right.
SHADOWS.
Experiment 85. To find the cause of a shadow.
Apparatus. An opaque cylinder 8 cm or 10 cm in diameter; two
candles ; a piece of cardboard about 20 cm square.
Directions. This experiment is to be performed in a
darkened room. Place the cylinder on a table. Put the
two lighted candles on the table at a distance of 10 cm or
12 cm from the cylinder, making the distance between the
candles equal to the diameter of the cylinder. On the
other side of the cylinder and about 10 cm from it support
the piece of cardboard in a vertical position. Notice a
black band bordered by two lighter ones on the cardboard.
With a pin pierce a hole through the screen where the
black band crosses. Look through this hole towards the
lights.
194 EXPERIMENTAL PHYSICS.
Do you see either or both of the candles ?
Pierce a hole through the screen where one of the
lighter bands crosses. Through the hole thus made look
towards the candles.
Can you see either candle ?
Pierce a hole through the other lighter band.
Looking through this hole, which candle can you see?
Move the screen back and forth to see how the widths
of the bands change.
As you move the screen away, what change is there in
the width of the black band ?
Pierce a hole through a brightly lighted part of the
screen.
Looking through this hole, can you see more than one
candle ?
The black part of the shadow is called the umbra ; the
border is called the penumbra.
From your observations explain the formation of a
shadow, accounting for the umbra and the penumbra.
Does the shadow extend from the cylinder to the screen ?
IMAGES.
84. Formation of Images by Means of Small Aper-
tures. If a hole is made in the shutter of a dark room,
an inverted picture of the scene outside in front of the
window appears on the wall of the room opposite the
shutter. When sunlight passes through the spaces between
the leaves of trees, circular patches of light are seen on
the ground ; if, however, the sun should be partly eclipsed,
the patches of light would be crescent-shaped. The object
IMAGES. 195
of the following experiment will be to study the formation
of images obtained when light passes through small aper-
tures, like the hole in the shutter or the small spaces
between the leaves of trees.
Experiment 86. To find an explanation of the forma-
tion of an image (picture) on the screen of a pin-hole camera.
Apparatus. A pin-hole camera, which consists of a box about
10 cm in width and depth, and 30 cm long, with one end closed and the
other open. In the open end a frame, carrying a translucent screen,
slides. In the center of the closed end is cut a rather large hole,
which is covered by a piece of thin sheet brass, through which a
small hole is pierced.
Directions. Slide the screen into the box, hold the
brass-covered end towards a bright gas-flame in a darkened
room, and look into the open end of the box towards the
flame. At first have the box near the flame, then gradu-
ally take it farther away, always looking in, through the
open end, at the picture on the screen. Also slide the
screen back and forth.
Can you get a position of the screen such that the image
of the flame is very distinct?
Explain, by a drawing, why the image (picture) is
inverted. (See your inference from Exp. 84.)
QUESTIONS. Why are circular patches of light seen on the ground
beneath the trees in summer when the sun is shining ? When the sun is
partly eclipsed, why are these patches crescent-shaped ?
REFLECTION.
85. Reflection of Light ; Angle of Incidence ; Angle
of Reflection. If the eye is in a proper position when
sunlight falls upon a suitable surface, the calm surface of
196
EXPERIMENTAL PHYSICS.
a lake for example, the image of the sun can be seen in
the lake. The rays of light from the sun strike the sur-
face of the water, and some of them are bent back from
the surface and so reach the eye. This bending back of
the rays is called reflection. The rays that strike the sur-
face are. called incident rays (Latin incidere, to fall upon).
The rays that are bent back from the surface are called
reflected rays (Latin reflectere, to bend back).
If a perpendicular be erected to the reflecting surface,
the surface of the lake in this case at a point where an
incident ray falls upon it, the angle between the perpendic-
ular and the incident ray is called the angle of incidence ,*
the angle between the perpendicular and the reflected ray
is called the angle of reflection (Fig. 56).
B
c
FIG. 56.
AS, reflecting surface ; CD, perpendicular (in optics, often called a normal) ; EC,
incident ray; Cf, reflected ray; ECD, angle of incidence ; DCF, angle of reflection.
Experiment 87. To find whether there is any simple
relation between the angle of incidence and the angle oj
reflection.
Apparatus. A small plane mirror ; a sheet of paper 50 cm square ;
a meter stick ; a pin ; a protractor ; two rubber bands ; a block.
REFLECTION. 197
Directions. By means of tacks at the corners, fasten
the sheet of paper to the table. From the middle point
of one side of the paper draw a straight line to the middle
point of the opposite side. Fasten the mirror to a rectang-
ular block, by means of two small rubber bands, so that the
back of the mirror rests against one of the narrow sides of
the block. Place the mirror thus arranged with its edge
along the middle
portion of this
straight line
Have the silvered
part of the mir-
ror over the line.
The reflection
takes place at the
silvered surface.
At some distance
,. * ii FIG. 57.
in front of the
mirror, but to one side of its center, stick a pin upright in
the paper. On the paper lay the meter stick (Fig. 57) in
such a position that its direction makes an acute angle
with the face of the mirror. By sighting along the edge
of the meter stick, point it towards the image of the pin
formed in the mirror. When the meter stick has been
carefully adjusted so as to point accurately towards the
image, and at the same time to make an acute angle with
the face of the mirror, draw, with a sharp pencil, a line on
the paper along the edge of the meter stick to meet the
mirror. Remove the mirror, and produce this line until it
meets the line drawn across the paper. Draw a straight
line connecting the point of meeting of the two lines with
198 EXPERIMENTAL PHYSICS.
the pin. At the point of intersection of the three lines
erect a perpendicular to the line drawn across the paper.
If the mirror were still in position, would the line last
drawn be perpendicular to the surface of the mirror?
With the protractor, measure the angles formed by the
oblique lines with the perpendicular. The angle formed
with the perpendicular by the line from the pin is the
angle of incidence, and the angle formed with the perpen-
dicular by the line from the mirror to the eye (found by
sighting along the meter stick) is the angle of reflection.
After measuring these angles with the protractor, can
you infer a relation between the two angles ?
If you have performed the experiment accurately, your
answer to the question is the statement of the chief law
of the reflection of light.
Make as brief a statement of the law as possible.
Preserve the paper and paste it into your note-book.
PLANE MIRRORS.
86. Images in a Plane Mirror. When you see your
image, or reflection, as it is sometimes called, in a mirror,
doubtless you have noticed that it appears behind the
mirror ; that when you move, the image moves. It will
be the object of the two following experiments to find a
relation between the distance of the object from the mirror
in front and the apparent distance of the image behind the
mirror ; also something about the relative size and shape
of image and object.
Experiment 88. To find what relation holds between the
position of the image of a point and the position of the point.
PLANE MIRRORS. 199
Apparatus. The same as in the last experiment, with a fresh
sheet of paper.
Directions. As in the preceding experiment, fasten
the sheet of paper to the table, draw a straight line across
the sheet, and place the mirror and the pin in position.
Then lay the meter stick on the paper, and by sighting
along its edge, which should be inclined at an acute angle
to the face of the mirror, point it directly towards the
image of the pin (the pin is so small that we shall consider
its position as a mere point). With a sharp lead pencil,
guided by the edge of the meter stick, draw a line on the
surface of the paper directly towards the image. Without
disturbing either the pin or the mirror, sight at the image
of the pin from an entirely different direction, having this
new direction make as large an angle as practicable with
the former line along which you sighted, and as before
draw a line towards the image. Now remove the mir-
ror, and carefully produce the two lines you have drawn
towards the mirror until they cross each other. Also from
the pin draw a line at right angles to the line that the
mirror rested on, and continue it till it crosses the other
two lines.
Now replace the mirror in its old position, change the
position of the pin, and make a new set of observations.
Finally, put the pin in another position and make another
set of observations.
Remembering that the pin is the object, and that its
reflection in the mirror is the image, study the results of
your experiment with a view to answering the following
questions :
How far behind the mirror does the image appear to be
200 EXPERIMENTAL PHYSICS.
as compared with the distance of the object in front of the
mirror ?
For a given position of the object, does the image always
appear at the same place, no matter from what direction
you look into the mirror?
If a line is drawn from the object to the image, is this
line perpendicular to the mirror?
Paste the paper into your note-book.
Experiment 89. To find the relation between the size
and position of an object and its imaye.
Apparatus. The same as that of the preceding experiment, together
with two pins and a fresh sheet of paper.
IMrections. Fasten the paper to the table, draw a line
across it, and on this line stand the mirror. At a distance
of a few centi-
meters in front of
the mirror draw
on the paper a
triangle (Fig. 58)
whose sides are
respectively 6 cm ,
8 cm , and 10 cm long.
By sticking three
pins upright in the
paper, mark the angles of the triangle. By the method
of sighting used in the preceding experiment, find the
position of the image of each of these pins ; that is, find
the positions of the angles in the image of the triangle.
Connect by straight lines the points thus found.
PLANE MIRKOKS. 201
How does the size of the image compare with that of
the object?
How does the distance from the mirror of any point in
the image compare with the distance from the mirror of
the corresponding point of the object?
As compared with the object, is the image inverted,
that is, turned upside down?
SUGGESTION. Call to mind the images of the pins, whether they were
inverted or upright.
Is the image laterally inverted, that is, is the right-hand
side of the object opposite its own reflection ?
Paste into your note-book the sheet on which the
triangle is drawn.
Knowing that a real image can be caught on a screen,
and that a virtual image cannot be caught on a screen^
answer the following questions :
Is the image seen when looking into an ordinary
looking-glass real or virtual?
What kind of image was formed in Exp. 86 ?
87. Multiple Reflections. When, after reflection at
the surface of a plane mirror, a ray of light falls upon a
second plane mirror, the ray is reflected from this second
mirror in such a way as to make the angle of incidence
equal to the angle of reflection. The result of the reflec-
tions of light from one plane mirror to another is a
number of images, the number depending upon the angle
which the two mirrors make with each other. The object
of the next experiment will be to find the number of
images formed when two mirrors are placed at different
angles with each other.
202 EXPERIMENTAL PHYSICS.
Experiment 9O. To find the number of images formed
ly two plane mirrors, when making with each other (a) an
angle of 90, (b) an angle of 60, (c) an angle of 40.
Apparatus. Two plane mirrors ; two rectangular blocks of wood ;
four rubber bands ; a sheet of paper 50 cm square ; a protractor ; a pin.
Directions. Fasten the paper to the table. By means
of the rubber bands fasten the mirrors to the blocks. With
a sharp lead-pencil draw on the paper near the center two
straight lines crossing each other at right angles, that is, 90.
Place the two mirrors (Fig. 59) in such a position that a
long edge of one shall lie along one of these lines, a long
FIG. 59.
edge of the other mirror along the other straight line, thus
making the angle formed by the planes of the mirrors a
right angle. At a distance of- about 4 cm from the place
where the mirrors meet, stick a pin upright in the paper
lying between the mirrors. Record the number of images
of the pin.
Now by the aid of the protractor make the angle
between the two mirrors 60. To do this, draw a line on
the paper, and then measure off with the protractor an
angle of 60 from this line, and then draw a second line,
PLANE MIRRORS. 203
making an angle of 60 with the first ; the mirrors can
now be placed on these lines so as to make an angle of
60 with each other. Stick the pin into the paper as
before, and count the number of its images. Record the
number of images.
Finally, place the mirrors at an angle of 40 to each
other. Record the number of images.
Experiment 91. To find whether the multiple images
formed by two plane mirrors lie on a circumference of which
the intersection of the lines on which the mirrors stand is the
center.
Apparatus. The same as in the last experiment, together with a
long pin.
Directions. Fasten the paper to the table ; draw on it
two lines at 60 to each other. Stick the little pin into
the portion of the paper lying between the two mirrors,
which should have been placed in position on the two
lines. With the long pin locate the position of each
of the images. These images appear to occupy positions
behind the mirrors ; by moving the long pin behind the
mirrors this pin can be made to coincide with the position
of each of the images. This position is secured when on
moving the eye from side to side in front of the mirror the
image and the long pin always occupy the same position.
Mark each of these positions. Mark also the position of
the object, that is, the pin stuck into the paper between
the mirrors. Now clear the paper, and with the inter-
section of the two lines, the point over which the narrow
edges of the mirrors came together, as a center, and a
204 EXPERIMENTAL PHYSICS.
radius equal to the distance of the object from the inter-
section of the two lines, describe a circumference.
Through what points, previously marked on the paper,
does the circumference pass ?
What inference can you draw from this experiment ?
88. Dependence of the Number of Images on the
Angle between Two Plane Mirrors. The relation that
exists between the angle formed by two plane mirrors and
the number of images of an object formed by the mirrors
is as follows :
Provided the number of degrees contained in the angle
between the two mirrors will divide without a remainder
360, the number of degrees in a circumference, the num-
ber of images formed will always be one less than the
value of the quotient thus obtained.
Turn back to your record of Exp. 90, and compare the
number of images obtained in each case with the number
computed in accordance with the foregoing statement.
89. The Kaleidoscope. The fact that two plane mir-
rors placed at an angle of 60 to each other will form
five images of an object, these images being arranged sym-
metrically with respect to the mirrors, has led to the
construction of the kaleidoscope, which in its simplest form
consists of two long, narrow, plane mirrors making an
angle of 60 with each other. These mirrors are con-
tained in a tube, closed at one end by a glass plate
covered by a diaphragm with an aperture in its center; at
the other end by a plate of ground glass, on the inner
side of which lie loose fragments of colored glass. On
looking through the aperture and along the axis of the
tube, an observer sees a design, symmetrical about the
CYLINDRICAL MIRRORS. 205
axis and often very beautiful, formed by the fragments
of colored glass and their five reflections. Whenever the
tube is shaken, the arrangement of the fragments on the
ground glass is changed, and a new design appears.
EXAMPLES.
1. When the distance of a gas flame was 84 cm from the grease spot of
a photometer, and that of a candle 40 cn) on the other side, the grease spot
disappeared. To how many candles is the gas flame equivalent ?
2. An incandescent lamp equivalent to 10 candles is placed at a dis-
tance of l m from a screen. At- what distance from the screen must a
candle be placed in order to give the same intensity of illumination ?
3. An object is placed at a distance of 4 cm in front of a plane mirror.
How far from the object will the image appear ?
4. How many images of an object will be formed by two plane mir-
rors, if they make an angle with each other of 18 ? If they make an
angle of 10 ? If they are parallel ?
5. The aperture of a pin-hole camera is circular in shape, that of
another is triangular, while that of a third is square. What effect has
the shape of the aperture upon the image formed on the screen of the
camera ?
6. If a candle is placed at a distance of 30 cm from an opaque body
12 cm wide, what will be the width of the shadow cast by the opaque body
when the shadow falls upon a screen 100 cm distant from the candle ?
CYLINDRICAL MIRRORS.
9O. Convex and Concave Cylindrical Mirrors. The
polished outside surface of a cylindrical calorimeter, such
as was used in some of the experiments in heat, is a con-
vex cylindrical mirror, while the inner surface, if polished,
is a concave cylindrical mirror. The cylindrical mirrors
usually met with are segments formed by cutting from
a cylindrical surface strips running lengthwise of the sur-
206 EXPERIMENTAL PHYSICS.
face. The center of curvature of a cylindrical mirror is
the center of the circle of which the portion of the mirror
under consideration is the arc.
On looking into a cylindrical mirror, you will see a
distorted image : when the mirror is held in a vertical
position, the image has one form, but when the mirror
is held in a liorizontal position, the image assumes a
different form. It will be the object of the next two
experiments to make you acquainted with the laws of
cylindrical mirrors, and so to help you to understand
better the reason for the formation of the curious images
which cylindrical mirrors give.
Experiment 92. To find how the image in a convex
cylindrical mirror compares with the object in position, size,
and shape.
Apparatus. A convex cylindrical mirror mounted on a semi-
circular support of wood; a small sheet of paper; a small pin;
a meter stick.
Directions. Lay the sheet of paper flat upon a table,
and upon this sheet put the mirror (Fig. 60). With a
sharp-pointed lead pencil draw a line round the support.
Draw on the paper, at a distance of about 5 cm from the
front of the mirror, a straight line about 6 cm long, and
mark the ends and the center of this line with numbers.
We shall call this line the object. Stick the pin upright
into one extremity of the line. In order to get the posi-
tion of the image of the pin, sight at the image along the
edge of a meter stick laid on the table, and, guided by
the edge of the meter stick, draw a line towards this
image ; then move the meter stick to a place widely dif-
CYLINDRICAL MIRRORS. 207
ferent from the first, sight along the meter slick at the
image, and towards it draw another line. Each of the
lines just drawn should be numbered with the same
figure as that which num-
bers the point into which
the pin was stuck. Now
stick the pin into the mid-
dle point, sight at its image,
and, as before, draw lines,
and number each with the
same figure with which you
numbered the middle point.
Finally, stick the pin into
the other extremity of the
line, and again sight at its image, and draw lines.
Remove the mirror from the paper, and get the position
of each of the three images by producing each pair of
lines till they cross. Connect by a line the three points
thus found. This line is the image.
Is the image as far behind the mirror as the object is in
front?
Is the size of the image larger or smaller than that of
the object?
Is the shape of the image the same as that of the object ?
Make a dot at the middle of the straight line forming
one side of the outline of the support. This dot will
mark the center of curvature of the mirror. Join by
lines the center of curvature to each of the points of the
line into which the pin was stuck.
Does each of these lines pass through, or nearly through,
the corresponding points of the image ?
208 EXPERIMENTAL PHYSICS.
Repeat the experiment on a fresh sheet of paper with a
line 5 cm long drawn 6 cm from the face of the mirror.
From the results which you now obtain, do you get the
same answers to the questions as before ?
Did the height of the image seem to be the same as the
height of the pin ? Did the width of the image seem to
be the same as that of the pin?
Hence, should you say that the lines of an object, which
are parallel to the vertical lines of a convex cylindrical
mirror, appear in the image unchanged in length, while
horizontal lines in the object are shortened in the image ?
91. Distance of Image from Convex Cylindrical
Mirror. The law that the angle of reflection equals the
FIG. 61.
angle of incidence a law which holds true for both curved
and plane mirrors will enable the student to see, as is
indicated in Fig. 61, that the image of a point is not, as
in the case of plane mirrors, so far behind a convex mir-
ror as the point is in front, but that the image is at a less
distance from the mirror than is the point itself.
The arc LM represents the mirror. Let be the posi-
tion of the object. Let OL and OM be two rays from
meeting the mirror in L and M. From (7, the center of
CYLINDRICAL MIRRORS. 209
curvature, are drawn the radii CL and CM, which are pro-
duced to D and F. The reflected rays L G- and MK are
drawn so as to make the angles GrLD and KMF equal
respectively to the angles OLD and OMF, as the angle of
reflection is equal to the angle of incidence. When the lines
CrL and KM are produced, they meet in the point /, and
this point gives the position of the image of the object at 0.
In the same way the object at 0' will have its image
formed at I'. The image is nearer the mirror than is the
object.
92. Images formed by a Concave Cylindrical Mirror.
All images formed by a convex cylindrical mirror or by a
plane mirror are
virtual. But
with a concave
cylindrical mir- /^
ror, both virtual
images and real
images can be
formed. Wheth-
er the image formed by a concave cylindrical mirror will
be real or virtual depends upon the distance of the object
in front of the mirror, as indicated by the following con-
struction :
In Fig. 62 the arc LM represents the mirror. Let be
the position of the object. Let OL and OM be two rays from
meeting the mirror in L and M. From (7, the center of
curvature, are drawn the radii CL and CM. The reflected
rays LGr and MK are drawn so as to make the angles
GrLO and KMC equal respectively to the angles OLC
and OMC, as the angle of reflection is equal to the angle
210 EXPERIMENTAL PHYSICS.
of incidence. When the lines G-L and .Of are produced,
they meet in the point J, and this point gives the position
of the image of the object at 0.
If the object is at the point 0', the reflected rays will
actually cross at /' in front of the mirror. It is to be
noted that the
point is at a
distance from
the mirror less
than half the
radius of curva-
ture, while the
point 0' is at a
distance greater than half the radius of curvature. The
image of an object at is virtual, while that of an object
at 0' is real.
Experiment 93. To find virtual images and real images in
a concave cylindrical mirror, and to distinguish between them.
Apparatus. The cylindrical mirror of the preceding experiment
turned so as to present its concave side ; two matches ; a small pin.
Directions. As shown in Fig. 63, two radii should be
drawn from the center of curvature to the mirror, and
between these radii three arrows should be drawn, the
first 1.5 cm from the center of curvature, the second 3.5 CI ",
and the third 4.2 cm .
Holding the mirror about 25 cm from the eye, look at
the images of the three arrows.
Does each of the three images point from left to right
as do the arrows themselves ?
REFRACTION.
211
Stick a -pin into the center of one of the arrows, and lay
the matches, forming a wide angle with each other, so
that they shall point towards the image of the pin. If the
matches, provided they could be produced, are so inclined
to each other as to meet be-
hind the mirror, the image is
virtual; if they are so inclined
to each other as to meet in
front of the mirror, the image
is real. Determine in this
way the nature of each of the
images, whether it is real or
virtual, and record the results.
On a sheet of paper, as
shown in Fig. 63, draw an
arrow about 7 cm distant from
the center of curvature.
Stick a pin into one end of this arrow, and by sighting
as in the last experiment, determine the position of its
image ; stick the pin into the other end of the arrow and
determine the position of its image ; finally, stick the pin
into the center of the arrow and determine the position of
its image. Join the three points thus determined, and
thus form the image of the arrow.
Is this a real or a virtual image ?
REFRACTION.
93. Refraction of Light. The object of the next
experiment will be an examination of the effect produced
upon the direction of a ray of light when the ray passes
from air through a piece of glass and into the air again.
FIG. 63.
212
EXPERIMENTAL PHYSICS.
Experiment 94. To find the shape of the path followed
by a ray of light in passing from an object through a prism
to the eye.
Apparatus. A prism with square ends ; a sheet of paper 50 cm
square ; four tacks ; four long pins.
Directions. Lay the sheet of paper on a table and
fasten it in place by means of the tacks, one at each cor-
ner. On the center of the sheet stand the prism upright
with one of its faces paral-
lel to the right-hand edge
of the paper, as in Fig. 64.
Close to the edge of the
paper farthest from you,
and a little nearer the
right-hand edge of the
paper than the prism,
stick one of the pins up-
right. Mark the position
of this pin by the letter A.
Place the eye a few centimeters above the edge of the
table and look into the prism. Move the eye to the right
or left, if necessary, till the image of the pin at A is seen
through the prism. When the image is seen, stick a pin
upright into the paper near the eye, so that this pin shall
just hide the image when the eye is kept stationary.
Mark the position of this pin by the letter D. Then into
the paper, near the side of the prism next the eye, stick
another pin so that it shall be in line with the pin at D
and with the image. These two pins on the side of the
prism next the eye give the direction in which the ray of
FIG. 64.
REFRACTION. 213
light moves on emerging from the prism. To get the
direction of the ray of light that enters the prism from
the pin at A, stick into the paper on that side a long
pin in such a position that its image hides, when the
eye is in its proper position, the image of the pin at
A. With a fine-pointed lead-pencil draw a line round
the end of the prism on the paper. Remove the prism
and the pins. Lay a meter stick on the paper, and draw a
line from the position occupied by the first pin, A, through
the position of the pin next it on the same side of the
prism until the line meets the line representing the posi-
tion of the side of the prism. This line represents the
incident ray. Then connect by a line drawn from the
side of the prism the positions of the two other pins.
This line represents the emergent ray. As the part of
the ray of light in the prism passes straight from the point
B where the incident ray strikes the side to the point (7,
whence the emergent ray leaves the prism, connect these
two points by a straight line.
From an inspection of your diagram, how many times,
and at what points, is the ray of light bent in passing from
the object (the pin at A) through the prism to the eye ?
From a point outside the prism to a point within the
prism draw, through B, EF perpendicular to the side of
the prism.
Definition. A ray of light that falls upon a substance
is called an incident ray (A B in your diagram) ; if the sub-
stance is one like, glass or water which allows the ray to
enter, the ray after entering is called the refracted ray (BO
in your diagram).
214 EXPERIMENTAL PHYSICS.
The perpendicular to the surface drawn through the
point of incidence, that is, the point at which the ray
strikes the surface, is called the normal.
The angle ABE, between the incident ray and that part
of the normal lying in the medium (air in this case) in
which is the incident ray, is called the angle of incidence ;
while the angle FBC, between the refracted ray and that
part of the normal lying in the medium (glass in this
case) in which is the refracted ray, is called the angle of
refraction. >r \ . v
By inspection of your diagram, which is the smaller,
the angle of incidence or the angle of refraction ?
In the same manner draw at the other face of the prism,
whence the emergent ray leaves, a perpendicular, produc-
ing it a little way into the prism. Letter the end of this
perpendicular which lies within the prism G-, and the end
that lies without H.
Which is the smaller, the angle of internal incidence,
BCGr, or the angle of external refraction, HOD?
When a ray of light passes from a dense medium like
glass into a rare one like air, is the ray bent away from
the normal or towards it ?
Show by a sketch that a ray of light falling obliquely
upon a pane of glass has the same direction after emerging
from the glass as it had before entering it.
Definition. Refraction is the bending of a ray of light
in passing from one medium into another.
94. A Phenomenon explained. When looking into
a clear pool of water perhaps you have tried to touch
REFRACTION.
215
some object at the bottom with a stick ; unless the object
lies directly beneath the eye, the stick to strike the object
must not be thrust straight towards the point where the
object appears to be, but behind it. An oar when dipped
into water appears bent. A straight post standing in
water also presents a very curious phenomenon. To the
observer, shown on the bank in Fig. 65, the part of the
post which is beneath the surface of the water appears to
be shorter than it really is. This phenomenon is due
to the refraction, on emerging into the air, of the rays of
light proceeding from the part of the post under the
water. The eye of the observer is deceived by these
refracted rays. It is unaware of the bending of the rays
at the surface of the water, and so the object appears in
the direction whence the rays come on leaving the water.
216
EXPERIMENTAL PHYSICS.
The apparent bending of an oar, when dipped into
water, is explained in the same manner.
95. Index of Kefractioii. We found, when studying
the subject of the reflection of light, that the angle of
reflection was equal to the angle of incidence ; but on
coming to the study of the refraction of light, we found
that the angle of refraction is not equal to the angle
of incidence, being smaller than the angle of incidence
if the ray passes from a rare
into a dense medium, but
larger if the ray passes
from a dense into a rare
medium.
There is, however, a some-
what remote relation be-
tween the angle of incidence
and the angle of refraction,
which can be illustrated by
the help of Fig. 66. Let
AB represent the surface at
which refraction takes place ; 10 and OR, the incident
ray and the refracted ray ; MN, the normal to AB at 0,
the point where the ray pierces the surface. With as
center and any convenient radius, describe a circumference
AMBN. From I and R respectively draw IE and RH
perpendicular to MN. Let TO represent another inci-
dent ray, and R' another refracted ray, and I'K and
R' G- the perpendiculars.
Now physicists have found by experiment that the ratio
IE
nrrt which is called the index of refraction, is always equal
REFRACTION.
217
to the ratio ^-^, as long as no change is made in the two
-K Cr
mediums ; if one medium is air and the other glass, then
the index* of refraction has a uniform numerical value, no
matter at what angle the incident ray enters; but if for
glass we substitute water, then the index of refraction
assumes a new value.
Turn back to Exp. 94, and in your diagram (which
should have been very accurately constructed; if not
accurately constructed, it must be drawn afresh), with the
point B as a center, describe a circumference which shall
cut the normal in two points, and also cut the incident
ray and the part of the ray in the glass. Draw IE
and RH, and with a pair of dividers carefully measure
the length of each of these lines.
Divide the greater length by the
smaller. Record the result.
Also with O as a center repeat
the process. Record the result.
Experiment 95. To find the in-
dex of refraction from air to water,
by Hall's method.
Apparatus. A glass jar; a brass
partition to fit the jar; a brass index ;
a meter stick ; a sheet of paper.
FIG. 67.
Directions. Put the partition
in place in the jar (Fig. 67), and
also the brass index. Pour water into the jar till its
level comes within 2 mm of the middle tooth of the par-
tition. Then, looking through the side of the jar, add
water cautiously till the level of the water is less than
218 EXPERIMENTAL PHYSICS.
0.5 mm 'from the tooth. With the eye about 25 cm from the
edge of the jar, sighting in a line with the edge of the jar
and the lower edge of the tooth, adjust the index till its
tip seems to lie in this line produced. After these adjust-
ments have been carefully made, look to see whether the
water touches the tooth. In case the water has wet the
lower edge of the tooth, all the adjustments must be made
again.
Then measure and record the internal diameter, and
also the distance of the lower edge of the tooth below the
edge of the jar. Carefully measure, on the outside of the
jar, the distance of the tip of the index below the edge of
the jar.
Having completed the measurements, make carefully
a .full-sized diagram of the sides of the jar, as shown in
Fig. 68. Draw the partition 6r<7, mak-
ing Gr C in length equal to the distance
of the lower edge of the tooth below
the edge of the jar. Produce GrC by
a dotted line. Through C draw a
horizontal line to represent the surface
of the water. Mark the position of
_P, the tip of the index, and draw PC,
which represents the direction of the
ray before leaving the water, and draw CR, representing the
refracted ray. With any convenient radius, as CR, and
with C as a center, describe the arc RI, cutting CR in
R, and PC in I. From R drop the perpendicular RGr
on G-C, and from /drop the perpendicular IE on G-C pro-
duced. Measure carefully IE and R Gr.
LENSES AND PRISMS. 219
TTJ
The ratio - - is the index of refraction from water to
7? ' C 1
air, while the ratio is the index of refraction from air
IJii
to water.
Compute each of these ratios.
It is a good plan to put the index on the side of the jar
opposite the first position of the index, without disturb-
ing the partition, and make a new adjustment. The aver-
age of the two results obtained from the two sets of
measurements will give the index of refraction with
greater accuracy, as by this means errors due to the
unevenness of the edge of the jar and to the position of
the partition will be made very small.
LENSES AND PRISMS.
96. Relation between Lenses and Prisms. Suppose
we have a number of prisms, one of which we place at r ;
then a ray of light, Ar, from a spot of light, J., after
FIG. 69.
passing through the prism, is refracted. If at w a prism
exactly like that at r is placed, as shown in Fig. 69, it
will refract the ray, Aw. Let us denote by B the point
of intersection of the two refracted rays. By using some-
220
EXPERIMENTAL PHYSICS.
what smaller prisms we can, by trial, find positions s and
v, so that these prisms will refract rays from A to B.
Similarly positions for another pair of prisms could be
found; call these positions t and u. Now a lens may
be regarded as made up of so great a
number of prisms that the joinings be-
come smooth, as shown in the diagrams
in Fig. 70.
FIG. 70.
97. Definitions Relating to Lenses.
Lenses are commonly made of glass, and
their surfaces are usually portions of the surfaces of
spheres. In the simplest case the bounding surfaces are
of equal radii.
The centers of curvature of a lens are the points and 0',
that is, the centers of the spheres (Fig. 71) whose inter-
section forms the lens.
The principal axis of a lens is a straight line of indefi-
FIG. 71.
FIG. 72.
nite length drawn through the centers (0, O r ) of curva-
ture. In Fig. 71 AB represents the principal axis.
The optical center of a lens is a point, C in Fig. 72, so
situated that a ray, ABCDE, passing through it has the
LENSES AND PRISMS.
221
FIG. 73.
same direction after leaving the lens as before entering it.
The position of the optical center depends upon the shape
of the lens. For a lens like that represented by the
figure, where the two sides are curved alike, the optical
center of the lens is
at the middle of the
lens.
A secondary axis of
a lens is any straight
line, except the prin-
cipal axis, drawn
through the optical center. In Fig. 72 MM represents
such an axis. There are an infinite number of such axes.
The principal focus of a convex lens is the point at
which the rays, parallel before entering the lens, cross
after passing through the lens.
In Fig. 73 the point F is the principal focus. It will
be noticed that the rays before entering the lens are
parallel, but that the lens bends them so that they meet
after emerging.
98. Names and Properties of Different Kinds of
Lenses. In the following list is given the name, and
after it the description of each
lens. The numbers refer to the
diagrams of Fig. 74.
1. Double convex lens, both
surfaces convex.
2. Plano-convex, one surface
convex, one plane.
3. Concavo-convex, converging, one surface convex, one
concave.
FIG. 74.
222
EXPERIMENTAL PHYSICS.
FIG. 74.
1, 2, and 3 are called converging lenses, because parallel
rays of light, after passing through them, converge. Notice
that they are thickest in the middle.
4. Double concave, both sur-
faces concave.
5. Plano-concave, one surface
concave, one plane.
6. Concavo-convex, diverging,
one surface concave, one convex.
4, 5, and 6 are called diverging
lenses, because parallel rays of light, after passing through
them, diverge. Notice that they are thinnest in the middle.
3 and 6 are also called meniscus lenses.
REAL IMAGES.
99. Focal Length; Conjugate Foci. The object of
the next two experiments will be to make clear the mean-
ing of the terms focal length and conjugate foci.
Experiment 96. To find the focal length of a double
convex lens.
Apparatus. A spectacle lens ; a meter stick ; two blocks each
with a groove to slide on the meter stick ; a piece of cardboard 10 cm
square ; colored glasses.
Directions. Stand the piece of cardboard in the open-
ing in the top of one of the blocks, as shown in Fig. 75,
and the lens with its longest diameter vertical in the
opening in the top of the other block. It is well to
cement the lens in place by dipping the edge in a mixture
of equal parts of melted beeswax and rosin. On the
meter stick place the screen and the lens with its prin-
REAL IMAGES.
223
cipal axis parallel to the length of the rod. Point the
lens toward the sun, so that the sun's rays shall pass
through the lens and fall upon the screen. In order not
to dazzle the eyes, look at the bright spots on the screen
through colored glasses. Move the lens back and forth
on the rod until a position is found that gives on the
screen a sharp image of the sun. The distance from the
lens to the screen as now arranged is called the focal
FIG. 75.
length of the lens. Record in your note-book the position
of the lens on the meter stick, that is, the number of cen-
timeters it is from one end of the rod, and also record the
position of the screen, that is, the number of centimeters
it is from the end of the rod from which you measured
the distance of the lens. You will notice a mark carried
round each block to the meter stick to assist you in mak-
ing these measurements.
What will the difference of these two readings give ?
Make a change in position of the screen on the meter
stick, and adjust the lens till you again get a sharp image
of the sun on the screen. Take the measurements and
record as before. Repeat three times and record, mak-
224 EXPERIMENTAL PHYSICS.
ing five measurements of the focal length in all. Find the
average of the five measurements.
The rays of light from the sun are practically parallel,
and on passing through the lens are bent so as to pass
through the principal focus.
Suppose a luminous point placed at the principal focus,
what effect would the lens have on the rays diverging
from the point?
Experiment 97. To find the relation between conjugate
focal distances of a lens and its focal length.
Apparatus. The same as in Exp. 96, and in addition a small
kerosene lamp. Use the same lens as in Exp. 96.
Directions. Over a smoky flame hold the lamp chim-
ney till its outer surface is covered with soot. Light the
wick of the lamp. Put the chimney in place, and with a
sharp-pointed pin draw an upright arrow, as shown in
Fig. 76, in the soot on the chimney opposite the bright
part of the flame. Have the lines of the arrow very fine.
Perform this experiment in a darkened room.
Place one end of the meter stick as nearly as possible
directly beneath this arrow, and at the opposite extremity
of this stick put the cardboard screen, so that its center
shall be over the end of the stick. Support this end of the
meter stick on a block. Set the lens on the stick near
the lamp, and then slide it away from the lamp till a dis-
tinct image of the arrow (which we call the object) appears
on the screen. Read in centimeters the distance from the
center of the lens to the arrow on the chimney, and
record this distance in a column headed D . (D stands for
distance, and the letter o placed to the right and a little
REAL IMAGES. 225
below stands for object : so D is an abbreviation for " the
distance from the lens to the object.") Measure in centi-
meters, and record, in a column headed D^ the distance
from the center of the lens to the image on the screen.
(Di stands for " the distance from the lens to the image.")
Without moving anything but the lens, slide that along
the stick till it again throws upon the screen a distinct
image of the arrow. Record the distance of the lens from
the lamp in the column headed D , and the distance of
FIG. 76.
the lens from the screen in the column headed D { . Then
place the screen at a distance of 80 cm from the arrow on
the chimney, and proceed as before.
Place the screen at distances of 70 cm , 65 cm , 60 cm ,
from the arrow on the chimney, making records in the
columns headed D and D { , till the lens ceases to throw a
distinct image of the arrow upon the screen. In all, the
screen should be put in five or six different positions. If,
with the lens which you have, you are unable to get dis-
tinct images for five or six different positions of the screen,
start with the screen at a distance of more than 100 cm
from the arrow on the chimney, and then move the screen
towards the arrow about 10 cm at a time.
Let F denote the focal length of the lens as already
found. Express in every case the quantities and as
U f\ -Lr*
226 EXPERIMENTAL PHYSICS.
decimals, then add them (that is, add and expressed
JJ .L/i
as decimals), and see how the sum in each case compares
with expressed as a decimal.
Definition. Conjugate foci of a lens are any two points
so situated with respect to the lens that an object at either of
them will produce an image at the other.
How many conjugate foci can your lens have ?
Look over the results of the experiment just performed,
and answer the following questions :
If the distance between the lens and the object (the
arrow) is increased, does the distance between the image
and the lens increase or decrease ?
When the distance from the lens to the object is large,
is the image large or small ?
When the lens is a long distance from the object, is the
image near the principal focus ?
1OO. Parallax. If the distance of the object from an
ordinary lens is several hundred meters, the image practi-
cally coincides with the principal focus. A second way is
thus suggested of finding the principal focus of a lens, and,
consequently, the focal length. You have already found the
principal focus of a lens in Exp. 96. If you look through
a lens at a distant object such as a chimney, you will see
an inverted image of the chimney. If you can locate the
position of the image (a screen cannot be used for the
purpose in this case), the distance from the lens to the
image will be the focal length of the lens. A peculiar
KEAL IMAGES. 227
means is employed to find the position of the image, which
depends on the following facts :
When traveling by rail and looking from the window
at the distant landscape, you have doubtless observed that
objects at different distances are left behind at different
rates, those not far from the train rapidly, those at a great
distance slowly; consequently, they seem to move past one
another. This apparent relative shift of objects due to a
change in the observer's position is called parallax.
To illustrate the meaning of parallax still further, hold
your two forefingers upright in line with each other and
with the eye. Fix the eye on the nearer finger and slowly
move the head from side to side by slightly bending the
neck. The finger that is farther from the eye will appear
to move in the same direction as the head. Now bring
the more distant finger nearer the other, the relative
motion between them becomes less, and finally, when the
fingers are close together, there is no relative motion. It
will be well to keep in mind the following :
Rule. When two objects are in the same general direction
but unequally distant from an observer, the more distant
object appears to move, with respect to the nearer, in the same
direction as that in which the observer's eye is moving.
Experiment 98. To find, by the method of parallax, the
focal length of a double convex lens.
Apparatus. The lens already used, mounted on a meter stick ;
a block to slide on the meter stick with a long pin stuck in a vertical
position into the middle point of its upper surface.
Directions. Open a window from which you can look
a long distance. Lay the meter stick on the window sill.
228
EXPERIMENTAL PHYSICS.
Put the block carrying the pin in such a position on the
stick that it shall be about as far from the end of the stick
as you are accustomed to hold the printed page of a book
from the eye when reading. Put the lens on the meter
stick (Fig. 77), but not between the pin and the eye. Point
the stick toward some object, as a chimney several hundred
feet away. When you look through the lens, you will
see a little image of the chimney, but inverted. This
FIG. 77.
image is a real one, and exists somewhere in the space
between the lens and your eye. It must be your purpose
now to determine accurately the distance from the lens to
this image. Move the head from side to side, all the while
looking at the image. According to our rule (see page
227), if the image is farther from the eye than the pin is, it
will move with respect to the pin in the same direction as
you move your head ; consequently, in order to get the image
of the chimney to have the same position as the pin, the
lens must be moved towards the pin. On the other hand,
if, when the head is moved from side to side, the image
moves with respect to the pin in the opposite direction to
REAL IMAGES. 229
that in which you move your head, the image is nearer
the eye than the pin, and to make the image coincide
with the pin, the lens must be pushed farther away from
the pin. Adjust the lens till there is no relative motion
between the image and the pin, that is, till the two, on
moving the head, always keep accurately together.
Record the position of the lens and that of the pin.
What is the focal length of the lens in centimeters ?
Repeat the setting and measurements several times.
As before, record these measurements.
How does the average of the results obtained by this
method compare with that obtained in Exp. 96 ?
Experiment 99. To find the position of the real image
of a near object, formed by a double convex lens.
Apparatus. A meter stick ; a double convex lens ; three blocks
with grooves to slide on the meter stick ; two short pins.
Directions. Put the blocks that carry the pins on the
meter stick, with the block carrying the lens between
them, as shown in Fig. 78. Put one pin at a distance,
FIG. 78.
say, 1.5 times the focal length away from the lens. Slide
the other pin along the meter stick, using another meter
stick, if necessary, placed with its end against that of the
first. By the method of parallax, find the position of the
real image of the first-mentioned pin. Changing nothing,
230 EXPERIMENTAL PHYSICS.
sight from the neighborhood of the first-mentioned pin
towards the image of the other.
Does this image coincide with the position of the first-
mentioned pin ?
Measure the distance from the lens to each of the pins.
Make another setting ; measure and record the distances.
From the measurements compute the focal length of
the lens.
Explain how this experiment has illustrated the mean-
ing of the term conjugate foci.
Experiment 1OO. To find the shape and the size of a
real image, formed by a converging lens (double convex), as
compared with the' shape and the size of the object.
Apparatus. The lens mounted on a block; a sheet of blank
paper 100 cm long and 50 cm wide ; a meter stick : two pins, one long,
the other short.
Directions. Spread the paper smoothly on a table, and
fasten it at the corners by means of tacks. Have the
sheet laid with one end near the edge of the table. Draw
a line from the middle of one end of the sheet to the
middle of the other end. At a distance of 2 cm or 3 cm from
that end of the sheet remote from the edge of the table,
draw a line at right angles to the line first drawn. The
line last drawn should be 8 cm long, and should extend 4 cm
on either side of the line first drawn. Mark one end of
this 8 cm line like the tip (Fig. 79) of an arrow. Divide
the arrow thus formed into four parts of equal length by
means of dots.
Lay the block carrying the lens on its side. Have the
edge of the lens rest upon the paper, and the lens so
placed that its axis is parallel to the median line (the line
REAL IMAGES.
231
c
first drawn on the paper). The center of the lens must
be directly over the median line at a distance from the
middle of the arrow about 1.5 times the focal length of
the lens. If the lens should be placed at a distance less
than its focal length from the line, a virtual image would
be obtained. In order to get the center of the lens exactly
over the median line, stick the
short pin upright into the point
3, at the middle of the arrow.
Then stick the long pin upright
into the median line near the
edge of the table. After you
have done this, slide the lens a
little way to the right or to the
left across the median line, till
the image of the small pin is
hidden by the long pin, when
the eye is held near the edge
of the table and in line with the
two pins. The center of the
lens is now over the median line. The lens must not be
moved during the subsequent parts of the experiment.
To locate the position of the image of 3, move the long
pin back and forth till, by the method of parallax, you
make this pin coincide with the image of the short pin.
Mark this position I 3 . (I stands for " image," and the
small number placed to one side and a little below this
letter indicates the point of the arrow into which the pin
is stuck.) Now stick the short pin upright into the arrow
at the tip, which we shall call point 1, and then on the
other side of the lens stick the long pin upright through
FIG. 79.
232 EXPERIMENTAL PHYSICS.
the paper into the table in such a position (found by the
method of parallax) as to make it coincide with the image
of the pin in the tip of the arrow. Mark the position of
the image, that is, the point where the second pin pierces
the paper, I v In the same way locate the points Zj, / 4 ,
etc., corresponding to the points 2, 4, etc., of the arrow.
The student is warned in this experiment not to let
any idea he may have, as to where an image-point
ought to be, interfere with his judgment as to where the
point really is. The five points, I v I v 1%, 7 4 , I 5 , outline
the image of the arrow as the lens would form it if the
lens were lowered until its center was on a level with
the paper. Remove the lens, and mark by a dot the point
on the paper above which the center of the lens was.
Then carefully draw, with a sharp lead pencil, straight
lines joining each of the object-points (1, 2, etc.) of the
arrow with its corresponding image-point (I v I v etc.).
Measure the distance from each object-point to the lens
(that is, to the dot marking the position of the center of
the lens). Measure the distance from each of the image-
points to the lens. Record all of these measurements.
Measure and record the length of the object and that of
the image. If the image is not a straight line, measure
the distance from I straight to 1^ and also the actual
length of the image, whatever its shape.
Measure the distance from point 3 on the object to the
lens, and from the lens to the middle point of the straight
line JjZj. Record the distances.
Call the distance from point 3 on the object to the lens,
D . Call the distance from the middle point of the
straight line I^I b to the lens, D^
REAL IMAGES. 233
Call the length of the object, 0.
Call the length of the line J^, I.
Making use of your measurements, should you say that
D is the same part of D; as is of I?
Repeat your process of reasoning, using the distance
from object-point 1 to lens, and from the lens to I v
together with the values of and / already used.
Can you, as a result of this examination, state any law
for the relation between the several distances and the
dimensions of the object and of the image ?
Can you explain the form of the image ?
SUGGESTIONS. The middle of the object is nearer the middle of the
lens than the ends of the object are. The focal length of a lens, for rays
parallel to a secondary axis, is practically equal to the focal length for
rays parallel to the principal axis. Consequently, a consideration of the
change made in Di by a change in D , in the equation - - + = , will
Jj Ui Jb
be useful in explaining the form of the image.
1O1. Diagram to illustrate the Formation of a Real
Image. The images formed by lenses thus far consid-
ered have been real images, that is, images that can be
caught upon a screen. An inspection of the diagram
(Fig. 80) will show that real images are formed by the
actual crossing of the rays of light.
To construct the real image of an object :
Let AB denote the object, F the principal focus of the
lens, the optical center of the lens, and A'B' the image.
From the point A rays of light are darting out in all
directions ; one of these rays must, then, be parallel to the
principal axis. This ray, lettered AD, after going through
the lens will pass through the principal focus, F. (Why ?)
Another ray, A 0, will pass through the optical center,
234
EXPERIMENTAL PHYSICS.
(see the Def. on page 220), and intersect the ray from
-4, passing through F, at A', forming a real image of the
point A. In like manner a real image of the point B is
formed at B'. Rays of light going from other points of
AB will form, after passing through the lens, images of the
FIG. so.
points whence they start out, so we will connect the points
A* and B', assuming according to the custom of the books
on physics, that the images of all the points of AB will
lie on the straight line A'B'. A B' is called the image of
AB. If the thickness of the lens is small as compared
with the focal length of the lens, there is no great error
in the assumption that A'B' is the image of AB. (Why?)
EXAMPLES.
1. The focal length of a double convex lens is 10 cm . An object is
placed at a distance of 30 cm from the lens ; at what distance from the
lens will the image be formed ?
SUGGESTION. Make use of the relation 4- = =
JJ JJi r
2. The focal length of a double convex lens is 20 cm . The image of an
object is formed at a distance of 100 cm from the lens; how far is the
object from the lens ?
3. The image of an object placed at a distance of 100 cm from a double
convex lens is formed at a distance of 400 cm from the lens. Find the
focal length of the lens.
VIRTUAL IMAGES. 235
4. Show by means of the formula + = what must be the
D Di t
distance, in terms of the focal length, F, of object and image from the
lens in order that they may be of the same size.
5. At what distance from a lens of 36 cm focal length must an object
be placed in order that the dimensions of the inverted image shall be :
(a) Half as large as those of the object ?
(6) Twice as large as those of the object ?
VIRTUAL IMAGES.
1O2. Formation of Virtual Images. The object of
the two following experiments is to show the way of form-
ing virtual images by means of a double convex lens.
Experiment 1O1. To find the relation between the focal
length of a lens and the distance of the object and the dis-
tance of its virtual image.
Apparatus. A meter stick ; a lens ; three blocks with grooves to
slide on the meter stick ; a long pin ; a short pin.
Directions. Mount the lens on one of the blocks, and
put the block on the meter stick at a distance of about
3 cm from one end. Lay the meter stick with its narrow
FIG. 81.
E, position of eye ; L, position of lens ; S, position of short pin ; T, position
of long pin.
edge on the table and with the end carrying the lens next
to you. Into the center of the top of another block stick
the short pin. Place this block, as shown in Fig. 81, on
236 EXPERIMENTAL PHYSICS.
the meter stick so that the pin shall be between the lens
and its principal focus. The pin must, however, be on
the side of the lens remote from the eye.
The long pin, stuck upright into the top of the third
block, is placed on the meter stick beyond the short pin.
As you look through the lens you will see a virtual image
of the short pin. By moving the long pin towards you
or by pushing it further away, try to locate the position of
the image of the short pin by the method of parallax
already explained. The eye should be held in a position
which will not allow a view of any part of the short pin
over the top of the lens. The long pin is to be looked
at over the lens, not through it. When the long pin,
seen over the lens, and the image of the short pin keep
together as the head is moved from side to side, measure
and record the distance from the lens to the short pin, and
also the distance from the lens to the long pin (the position
of the virtual image). Then make a new setting of the
short pin, and by adjusting the position of the long pin,
again find the position of the image. As before, record
the readings.
In Exp. 97 you found, by substituting the proper
quantities, that --{-- = , that is, the reciprocals of
D JJi 1
the object-distance and image-distance added produce the
reciprocal of the focal distance.
In the present experiment the object-distance has always
been less than the focal distance, but the image-distance
always greater than the focal distance.
Take the difference between the reciprocal of the object-
distance and the reciprocal of the image-distance, that is,
VIRTUAL IMAGES.
237
, and see how this difference compares with the
reciprocal, , of the focal distance.
Jb
The difficulty often met with in getting the position of
the virtual image in the experiment just performed intro-.
duces an uncertainty into the value of the focal length
calculated from the data obtained.
Experiment 1O2. To find the shape and the size of a vir-
tual image, formed by a converging lens (double convex), as
compared with the shape and the size of the object.
Apparatus. The same as that used in Exp. 100 with a fresh sheet
of paper.
Directions. Fasten the paper on the table in the same
position as for Exp. 100. Draw a median line lengthwise
of the paper. Place the lens on
its side, as in Exp. 100, but at
a distance of about 20 cm from
the end of the paper nearest
the edge of the table. On the
median line, on the side of the
lens remote from the edge of
the table, make a dot at a dis-
tance from the lens equal to
about two-thirds its focal length.
Through this dot draw a line at
right angles to the median line.
This line should be 5 cm long and
should be bisected by the median
line. Mark one end of this line like the tip of an arrow.
Divide the arrow into five equal parts, as indicated in Fig. 82.
238 EXPERIMENTAL PHYSICS.
In order to get the center of the lens over the median
line, stick the short pin upright into the middle of the
arrow, at the point where it crosses the median line.
Stick the long pin upright into the median line, at the
end of the paper remote from the lens. Look through
the lens with the eye in line with the two pins, and slide
the lens a little way to the right or to the left, across the
median line, till the image of the short pin is in line with
the two pins. When the image is in line with the two
pins, the center of the lens is over the median line.
Stick the short pin upright through point 1. Look
through the lens and locate, by means of the long pin, the
position of the image of the short pin. As this image is
virtual, it will appear on the same side of the lens as is
the object.
In this manner locate the position of the image of the
short pin for each of the remaining five points. Draw
lines and make measurements similar to those of Exp. 100.
Is there any distinction between the form of the image
obtained in this experiment and the form of the image ob-
tained in Exp. 100 ?
What relations can you make out, from your measure-
ments, between the distance of object and image from the
lens and their lengths ?
1O3. Diagram to illustrate the Formation of a Vir-
tual Image. By an inspection of the diagram (Fig. 83)
it will be seen that a virtual image is formed not by the
actual crossing of the rays of light, but by their apparent
crossing.
To construct the virtual image of an object:
VIRTUAL IMAGES. 239
Let AB denote the object, F the principal focus of the
lens, the optical center of the lens, and'^L'.B' the image
which we wish to find. From A rays of light are darting
out in all directions; one of these rays must, then, be
parallel to the principal axis. This ray, lettered AD,
after going through the lens will pass through the princi-
pal focus, F. (Why?) Another ray, A C, will pass through
the optical center, 0. (See the Def. on page 220.) The
bending of the ray, ADKF, deceives the eye, and the point
FIG. 83.
A appears to lie on the prolongation of FK-, the point A
also lies on the line J(7, hence the point A appears to lie
at the intersection of FK produced and 1C produced, or
at A'. A' is the virtual image of A. The point A' is
not the point from which the rays of light actually come,
but it is the point from which to the eye they appear to
come.
By a similar process B' is found to be the virtual image
oiB.
The image, A'B', is larger than the object, AB. When-
ever an object is placed between a convex lens and its
principal focus, a virtual image is seen on looking in from
the other side of the lens. As the image is always mag-
240 EXPERIMENTAL PHYSICS.
nified, or enlarged, the name magnifying glass is commonly
given to a lens used in this way.
In order that the straight line A'B' may represent the
image, with very small error, must the thickness of the lens
be large or small as compared with the focal length of
the lens?
104. Velocity of Light. There are four moons which
revolve about the planet Jupiter. At times a moon will
be visible, at others eclipsed. The exact time can be cal-
culated at which an eclipse can be seen from the earth,
when the earth is in that part of its orbit nearest Jupiter;
but as the earth recedes from Jupiter, the eclipses do
not occur on time, but occur later and later till the
earth reaches that part of its orbit most distant from
Jupiter, when the eclipses are 16 minutes and 36 seconds
behind time. As the earth sweeps round in its orbit and
approaches Jupiter, the eclipses occur more and more
nearly on time, and when the earth and Jupiter are near-
est each other, the eclipses are once more precisely on
time. This discrepancy between the computed time at
which the eclipse should take place and the actual time
at which the eclipse is seen, when the earth is most remote
from Jupiter, is due to the fact that the light has taken
16 minutes and 36 seconds in crossing the earth's orbit,
a distance of about 190,000,000 miles. This gives, by
dividing 190,000,000 by 996 (the number of seconds in
16 minutes and 36 seconds), the velocity of light to be
about 190,000 miles per second.
105. Nature of Light. All men of science are agreed
that a ray of light represents a motion of some kind.
VIRTUAL IMAGES. 241
Whenever a stone is thrown from the hand, or an arrow
shot from a bow, we know that either of them will be pro-
pelled through the air with a velocity which depends upon
the weight and the shape of the object, and also upon the
force employed in its discharge. When we hear that light
has a velocity of about 190,000 miles per second, we feel a
keen interest to know what is the nature of the motion
that is propagated through a distance so great in so short
a period of time.
Two hypotheses have been advanced for explaining the
nature of light, the corpuscular hypothesis and the wave
hypothesis.
The corpuscular hypothesis, long supported by the author-
ity of Sir Isaac Newton, supposes, in brief, that particles,
called corpuscles, so very minute that they cannot be
weighed are given out bodily, like sparks, from the sun,
the fixed stars, and all luminous bodies. It is further
supposed that these particles travel with enormous veloc-
ity, and excite the sensation of vision by striking against
the eye.
As this hypothesis failed to explain all the facts known
about light, the hypothesis was abandoned early in the
nineteenth century in favor of the wave hypothesis, which
has not only explained all the facts about light with
which we are acquainted, but has also made predictions
about light which have subsequently been verified by
experiment. The wave hypothesis supposes the existence
of a substance, called the ether, which occupies all space,
not only the regions between the stars, but also the spaces
between the molecules of all bodies. This hypothesis also
supposes that a luminous body has the power to cause
242 EXPERIMENTAL PHYSIOS.
waves in the ether, which travel with great rapidity, and on
striking the eye produce the sensation which we call light.
When we studied the subject of wave-motion, we found
that it was possible for two water waves of equal size to
interfere in such a way as to produce a calm. In the sub-
ject of sound we found that two equal sound waves could
interfere to produce silence. In light, two light waves
can interfere and produce darkness, as can be readily seen
by looking at a flame through a narrow slit cut by a pen-
knife in a card. Very narrow black bands will be seen
running parallel to the slit on each side of it. These
black bands are formed by the interference of the light
which is reflected from the edges of the slit. These edges
correspond to the two centers of disturbance that we con-
sidered when examining the interference of two sets of
water waves.
As an example of one of the remarkable predictions of
the wave hypothesis of light, perhaps the following will
serve as well as any. By a mere manipulation of the
mathematical symbols by which the wave hypothesis is
expressed, it was shown that by stopping, in a certain
way, a portion of the rays of light passing through a
circular opening, the illumination of a point upon a screen
behind the opening would be greatly increased. On per-
forming the experiment which the mathematical formulae
suggested, the prediction about the increase of illumina-
tion was verified.
We must bear in mind, however, that, although the
hypothesis of the existence of the ether has enabled us to
explain the known facts about light, it does not by any
means follow that the ether has an actual existence, not
VIRTUAL IMAGES. 243
even if facts have been predicted by its' aid. For when-
ever a mass of facts, like those connected with the phe-
nomena of light, is collected, and a means found to bind
the facts together and to explain them, it cannot be at all
surprising, if certain facts, of which we were ignorant,
should be included in the collection. These facts of
which we were ignorant will be found when we carefully
examine the collection.
EXAMPLES.
1. In determining the illuminating power of a gas flame by Bunsen's
photometer, the distance from the gas flame to the grease spot was 90 cm ,
and from the grease spot to the standard candle 35 cm . What was the
candle power of the gas flame ?
2. If a plane mirror recedes from a fixed object at the rate of 10 ft. a
second, at what rate will the image recede from the mirror ? From the
object ?
3. What must be the length of a plane mirror in order that an observer
may see his whole length therein, the mirror being placed parallel to the
observer ?
4. When a real image is thrown upon a screen it can be seen from all
points from which the face of the screen can be seen. When the image
does not fall upon a screen, the region from which it can be seen is much
more restricted. Explain this difference by means of a diagram showing
the course of the light rays.
5. The image of a clock face is thrown upon a screen. The time is
12.30. Make a diagram of the image as seen by an observer looking from
the lens.
6. In a photographic camera, using a single lens, let the plate be so
placed that the center only of the picture is distinct. Must the plate be
pushed nearer the lens or pulled further away in order that the edges of
the picture may become distinct ?
7. An object is placed at a distance of 8 cm from a lens, the focal length
of which is 24 cm ; will the image be real or virtual ? Erect or inverted ?
At what distance will the image be from the lens ?
244 EXPERIMENTAL PHYSICS.
8. An object 7 cm high is placed at a distance of 50 cm in front of a lens ;
the image is l cm high ; what is the focal length of the lens ?
9. At what distance from a lens must an object be placed so that the
image shall be erect and twice as high as the object ?
10. An object placed 5 cm before a lens has its image formed 15 cm from
the lens on the same side ; what is the focal length of the lens ?
11. An object placed 5 cm before a lens has its image erect and of three
times its linear magnitude ; what is the focal length of the lens ?
12. A candle and a gas flame are placed 180 cm apart. If the gas
flame is equivalent to four candles, where must a screen be placed on
the line joining the candle and the gas flame, in order that it may be
equally illuminated by each of them ?
13. Two parallel plane mirrors, A and B, face each other at a dis-
tance of 5 ft., and a small object is placed between them at a distance of
2 ft. from J., and, consequently, 3 ft. from B. Calculate the distances
from A of the two nearest images that are seen in J., and also calculate
the distances from A of the two nearest images that are seen in B.
14. Two plane mirrors, resting in a vertical position upon a horizontal
table, make an angle, A, with each other. A ray of light from the point
P strikes one of the mirrors at the point 5, whence the ray is reflected
to the other mirror which it strikes at the point (7, and is then reflected
in the direction CQ. Prove that the angle made by CQ and PB is two
times the an.srlc A .
CHAPTER VI.
MECHANICS.
106. Mechanics defined. Mechanics is that branch
of physics which deals with the effects of force upon
matter. Whenever several forces act upon a body at
rest, one of two things happens, either the body remains
at rest, or else the body moves. For convenience, the
subject of mechanics is divided into two parts, according
as the forces produce rest or motion. All cases of forces
producing rest are grouped under the head of statics, while
all cases where motion is produced are grouped under the
head of kinetics. In the greater part of this chapter,
experiments in statics only will be considered.
107. Mass; Unit of Force; Weight. A force has
already been denned on page 141 as a push or a pull.
Before defining the unit of force, which we shall use in
a good deal of our experimental work, it will be well to
discuss the meaning of the term mass, a term which we
shall find useful in defining the unit of force.
The mass of a body is usually defined as the quantity of
matter the body contains. To illustrate this definition of
mass, suppose two pieces of iron of equal size and alike
in every particular be placed together; then the mass
of the two combined will be twice the mass of either. If
three pieces of iron of the same size and alike in every
particular be placed together, the mass of the three com-
bined will be three times the mass of any one.
246 EXPERIMENTAL PHYSICS.
The study of physics has already brought before us the
necessity of having units to measure various quantities,
as length, volume, and heat, so it will not seem strange
to look about for some unit of mass.
There is a piece of platinum which is the standard for
mass. Copies of this standard have been made. The name
of this unit of mass is the pound. In a grocery shop you
may see lying on the counter pieces of iron with numbers
upon them. These pieces of iron are the pounds and
multiples and fractions of the pound. They have been
made by placing one of the standard units of mass in one
pan of a balance and a piece of iron in the other pan, the
piece of iron being filed .till it just balances the standard
unit. The piece of iron is then said to be of the same
mass, that is, it contains the same amount of matter as
the standard. The grocer in selling his goods puts one of
the pieces of iron, the pound, for example, into one pan
of the balance ; into the other, the article to be sold.
When a sufficient amount of the article, tea, for instance,
is put into the pan, the unit of mass, the pound, is bal-
anced by the tea. Having stated what the unit of mass
is, the unit of force is given by the following :
Definition. The unit of force, the pound, is the pull of
the earth on the unit of mass, the pound.
It is unfortunate that the unit of force has the same
name as the unit of mass.
We shall measure forces by means of the spring balance,
an instrument made of a spiral spring fastened at one end
to a support, the inner side of the frame ; at the other
end of the spring is a little index, or pointer, which moves
REPRESENTATION OF FORCES. 247
in front of a scale. If it were not already constructed, we
might make the scale of the balance in the following way :
Upon the hook of the balance hang a mass of 1 Ib. Mark
the place at which the pointer comes to rest. Then hang
on 2 Ibs., and mark the position of the pointer. Proceed
in this way till the scale is completed. We could, if we
wished, subdivide the pound divisions into halves and
quarters, and thus obtain the fraction of a pound. Would
this method of making the subdivisions be accurate ? (See
Hook's Law, page 152.)
Definition. The weight of a body is a force, the earth's
putt upon the body.
NOTE. The word " weight ' ' as commonly used is ambiguous. We speak
of a certain weight of tea. If the tea has been weighed with a spring
balance, the use of the word " weight" in the preceding sentence is cor-
rect. (Why ?) On the other hand, if a beam balance (platform balance)
had been used, the use of the word "weight" in the sentence is, strictly
speaking, incorrect. (Why ?)
If we could restrict the word " weighing" to the operation performed
with the spring balance, and could use the word "massing" to mean
the operation performed with the beam balance, what would be the
advantage ?
REPRESENTATION OF FORCES.
1O8. How Forces are represented. It has been found
convenient to represent forces by straight lines. Thus if
a force of 5 Ibs. is made to act in a northerly direction
upon a body, mathematicians represent this force by a
straight line drawn toward the north. Then to show
that the line represents a force of 5 Ibs., the line is made
five times the length of a line representing a force of 1 Ib.
(The length of the line representing 1 Ib. is chosen at
pleasure.)
248
EXPERIMENTAL PHYSIOS.
1O9. Illustration of liow a Line may be used to
represent a Force. Let us suppose a line 0.5 cm long
to represent in magnitude a force of
1 Ib. The irregular outline of Fig. 84
representing the body, the line AB,
2.5 cm in length, drawn toward the top
of the page represents both the direc-
tion of the force and also its magnitude,
or size. It is convenient to indicate the
direction in which a force acts by an
arrowhead, as in the figure. The point
B of the body at which the force is ap-
plied is called the point of application
of the force. The line of indefinite
length, of which AB is a limited por-
tion, is called the line of action of the
force. In order to represent completely
a force on paper, three things must be known :
(1) The magnitude of the force ;
c (2) The direction of
force ;
(3) The point of application.
The line AB (Fig. 85) represents a rod. A force
of 5 Ibs. applied at A acts downwards ; a force of
10 Ibs. applied at (7, the middle point of AB, acts
upwards ; a force of 5 Ibs. applied at B acts down-
wards.
In representing the force at J., what unit of length has
been taken to represent the magnitude of 1 Ib. ?
FIG. 84.
the
FIG. 85.
HINT. Measure the line with a meter stick.
EQUILIBRIUM. 249
Using the same unit of length to represent the magni-
tude of a force of 1 Ib. as was used in representing the
same force at A, draw lines to represent the force acting
at C and the force acting at B.
EQUILIBRIUM.
11O. Conditions of Equilibrium. Two or more forces
are said to be in equilibrium, or to balance, when they are
so opposed to each other that their combined action on
a body produces no change in its rest or motion.
To determine what relation must exist among a set of
forces in order that the forces may neutralize each other
in their action on a body to which they are applied will
be our immediate task. These conditions are called the
conditions necessary for equilibrium, or, more briefly, condi-
tions of equilibrium.
The purpose of the next experiment is to find the con-
ditions of equilibrium of three parallel forces whose lines
of action all lie in one plane, and whose points of applica-
tion lie in the same straight line which is at right angles
to the line of action of the forces.
In trying to discover and state these conditions, the
student must keep in mind: (1) the magnitudes of the
forces under consideration, (2) their directions, (3) their
points of application.
There are various forms in which the conditions of
equilibrium may be stated; one of these forms, good,
although not the most concise, consists of answers to the
following questions :
(1) How does the magnitude of the largest force compare
with the sum of the magnitudes of the other two forces ?
250
EXPERIMENTAL PHYSICS.
(2) How does the direction of the largest force compare
with that of the other two forces ?
(3) What is the position of the point of application of
the largest force with respect to the position of the
points of application of the other two forces?
Experiment 1O3. To find the conditions of equilibrium
of three parallel forces which act in one plane, and whose
points of application all lie in the same straight line.
Apparatus. Three 30-pound spring balances ; a board 1 ft. square
protected from warping by pieces fastened to the edges ; the top of this
board is divided into squares each 2 in. on a side ; at the corner of
each is a hole, and the holes are numbered (Fig. 86) from 1 to 49
inclusive; several iron pegs to fit the holes rather closely; three
marbles equal in size ; three wooden screws with attachments to fit
the edge of the table; supports for the balances; a large sheet of
common window glass.
Directions. On the top of a table lay a sheet of win-
dow glass, in order to have a smooth surface, and put the
marbles on the glass at equal
distances from one another, so
that they shall be at the vertices
of an equilateral triangle. Put
a peg into hole 27, one into hole
25, and one into hole 23. Lay
the board, marked side up, on
the marbles. At one end of the
table put two of the wooden
screws, as shown in Fig. 87,
JblG. OD.
fitting them to the table by
slipping the slot, cut in the piece of wood attached to the
screw, over the edge of the table. When attached to
EQUILIBRIUM.
251
the table, the centers of these pieces through which the
screws pass should be as far apart as the holes (23, 27)
in the board are distant from each other. At the other
end of the table, and directly opposite the portion of the
table midway between the two wooden screws already in
position, place the remaining wooden screw. Find and
FIG. ST.
record the correction of each balance (see Exp. 58). Place
the ring of a spring balance over the hook that projects
horizontally from the top of the little nut on the screw.
Lay the spring balance on its back, and support the balance
frame near each end by little pieces of wood, as shown in
the figure. In like manner fasten the other two balances
to the other hooks, and support them in the little rests.
Have the nuts near the ends of the screws. By means
of strings, not doubled, but with loops in their ends, attach
252 EXPERIMENTAL PHYSICS.
the hooks of the spring balances to the pegs in such a way
that the strings shall be parallel to each other. The hooks
of the balances must not touch the board ; the strings must
not press down on the edge of the board ; but the end of
each string which passes over the peg must rest on the
board. There must be no friction in any of the balances.
(Why?) By turning the screws, the strings attached to
the balances can be brought directly over the lines traced
on the board at right angles to the line in which the pegs
stand. In order to effect this, it may be found necessary
to move one of the screws along the edge of the table for
a little distance.
When this adjustment has been completed, turn the
screws, keeping the strings over the proper lines, until
the balance . attached to hole 25 registers 14 Ibs., when
the correction for the error due to its horizontal position
is taken into account. In all work involving the use of
one or more spring balances in the horizontal position, a
correction must be applied to the reading of each spring
balance.
A record should be made in the note-book of the
magnitude of each force, its direction, and its point of
application. For ready reference, a diagram of the board
should be made in the note-book, and the points indicat-
ing the holes should be numbered from 1 to 49, like the
holes on the board. A brief and clear record can be made
as indicated below :
HOLE. FORCE. DIRECTION.
23, 25, 27, 14, - V i V
EQUILIBRIUM. 253
The space on each side of the 14 should be filled with
the numbers representing the magnitudes of the forces
whose points of application are at 23 and 27. The first
arrow indicates the direction of the force applied at 23 ;
the second arrow that of the force at 25 ; and the third
arrow that of the force at 27.
Next, having slackened the balances, take the peg out
of hole 27 and put it into hole 26, and move the screw
along the edge of the table till it is opposite hole 26.
Proceed as before, but apply a force of 15 Ibs. to the peg
at hole number 25. Record as before.
Slacken the spring balances. Take the peg out of hole
23 and put it into hole 22. Move the screw along the
edge of the table till it is opposite hole 22. Apply 16 Ibs.
to the peg in hole 25. Record as before.
Answer the following questions :
In each case, how does the magnitude of the largest
force compare with the sum of the other two forces ?
What is the direction of the largest force as compared
with the direction of the other two forces ?
Is the point of application of the largest force always
between the points of application of the other two forces ?
Divide the greater outside force by the smaller ; also the
greater distance from the middle force by the smaller
distance. (The "middle force" is the force whose point
of application is anywhere between the two outside forces.)
State the relation between the two outside forces and
their distances from the middle force.
Divide any one of the three forces in one of the groups
by either of the other forces. Divide the distance of this
last chosen force, from the force not chosen, by the
254 EXPERIMENTAL PHYSICS.
distance of the first chosen force, from the force not
chosen.
State the relation between any two forces and their
respective distances from the remaining force.
State in as few words as possible the three conditions of
equilibrium which must hold in order that any group of
three parallel forces may balance.
RESULTANT AND BQUILIBRANT.
111. Resultant and Equilibraiit defined. The result-
ant of two or more forces is a single force that will exactly
replace them in its action on a body.
Thus, in Exp. 103, the resultant of the two outside
forces in any case would be a force which has the same
direction as the two outside forces, which is equal to their
sum, and which is applied at the peg in hole 25.
The resultant of one of the outside forces and the
middle force would be a force equal to their difference,
applied at the peg to which the other outside force is
applied, but in the opposite direction, that is, in the direc-
tion of the greater force.
The equilibrant of a set of forces is a single force that
will exactly neutralize their action.
Thus, in any one of the cases of Exp. 103, the middle
force is the equilibrant of the two outside forces. Either
outside force is the equilibrant of the middle force and the
other outside force.
To find the resultant of a group of any number of
parallel forces, we must replace two of the forces by
their resultant, then replace the resultant just found
and one of the remaining forces by their resultant, and
RESULTANT AND EQUTLIBRANT. 255
proceed in this manner till the resultant of the group is
obtained.
The special name of couple is given to a group consist-
ing of two parallel forces, equal in magnitude, but acting
in opposite directions. The perpendicular distance be-
tween the lines of action of the couple is called the arm
of the couple. The effect of a couple is to rotate the
body to which it is applied.
EXAMPLES.
1. A force of 6 Ibs. acts due north and a force of 15 Ibs. acts due
south. If both forces have the same point of application, find the direc-
tion and magnitude of their equilibrant ; of their resultant.
2. A rod extends east and west. A force of 10 Ibs. and a force of
5 Ibs. , both acting due south, are applied to the rod at points 6 ft. apart.
Find the equilibrant of the two forces and also their resultant, stating
the direction, magnitude, and point of application of the equilibrant and
of the resultant.
Solution. From the conditions of equilibrium which we have found, it
follows that the direction of the equilibrant must be due north. (Why ?)
It also follows that the magnitude of the equilibrant must be 10 -I- 5 = 15 Ibs.
(Why ?) To find the point of application of the equilibrant, a little more
work is necessary. From the remaining ^
conditions of equilibrium, if C (Fig. 88) is
the point of application of the equilibrant,
we have
10 : 5 = CB : CA.
But AB = 6 ft.
Consequently CB = 6 CA ;
hence 10 : 5 = 6 - CA : CA.
10 CA =30-5 CA.
15 (M = 30.
' CA = 2 " FIG. 88.
Hence CA = 2 ft., that is, the point of application of the equilibrant
is 2 ft. from the point at which the force of 10 Ibs. is applied.
The point of application of the resultant, as well as its magnitude, is
the same as for the equilibrant, but its direction is due south. (Why ?)
256 EXPERIMENTAL PHYSICS.
3. A rod extends east and west. To this rod a force of 15 Ibs. is
applied due north and 5 Ibs. due south. If the points of application are
9 ft. apart, find the direction, magnitude, and point of application of
their equilibrant ; of their resultant.
4. To a rod extending east and west are applied four forces : a force
of 5s due north, a force of 10s due south, a force of 15s due north,
and a force of 20s due south, at distances of 10 cm , 20 cm , 30 cm , and
40 cm , respectively, from the western end of the rod. Find the direc-
tion, magnitude, and point of application of their equilibrant; of their
resultant.
5. A rod extending east and west is acted upon by a force of 20s due
north and by a force of 20s due south. If the points of application are
90 cm apart, find their equilibrant.
Solution. The two forces given in the example form a couple. There
is no single force that will balance a couple. This statement may be bet-
ter understood by the student after examining the following investigation :
If the force acting toward the south is a little less than 20s, the
equilibrant will be a small force acting toward the south, but having its
point of application a long distance from the middle force. (Why ?) As
the force acting due south approaches 20s as its limit, the equilibrant
approaches zero as its limit, and its point of application moves farther
and farther away along the line. Hence, mathematicians say that the
equilibrant of a couple may be regarded as a zero force acting at an
infinite distance.
6. Find the directions, magnitudes, and points of application of two
forces that will just neutralize the tendency of the pair of forces given
in Example 5 to rotate the rod.
EQUILIBRIUM.
112. Points of Application not all in the Same
Straight Line. For each case of equilibrium that we
have tried, the points of application of the forces have
been in a straight line, which was perpendicular to the
direction of the forces. In Exp. 104 we shall examine
cases in which the points of application of the forces are
not all in the same straight line,
EQUILIBRIUM. Nsgf CALlfO^ 257
Experiment 1O4. To find, provided three given parallel
forces are in equilibrium when their points of application lie
in the same straight line, whether the forces will sfyll be in
equilibrium when their points of 'application lie , in a broken
line.
Apparatus. The same as in Exp. 103.
Directions. Set up the apparatus, using one of the
cases of equilibrium already recorded in Exp. 103. Then
keeping two points of application unchanged, vary the
place of tlie third with a view of finding any positions it
may have such that when the forces are just the same in
magnitude and direction as at first, they shall still be in
equilibrium. Experiment with each point of application
in turn, and, using the form suggested in Exp. 103, record
the result of the trials in your note-book.
From an inspection of your record, what inference can
you draw?
SUGGESTION. If points are found at which the forces may be applied
and the equilibrium holds, consider how these points are situated with
respect to each other and with respect to the line in which they at first
had their places.
Experiment 1O5. To find, provided three given parallel
forces are in equilibrium, whether they will remain in equi-
librium when they are kept parallel, but veered round in
a new direction.
The question we wish to settle may be made a little
clearer by an inspection of the diagrams on the following
page.
258
EXPERIMENTAL PHYSICS.
/
FIG. 89.
We wish to find, provided the forces in 1 and 3 (Fig.
89) are in equilibrium, whether they will remain in equilib-
rium when veered round as in 2 and 4.
Apparatus. The same as in Exp. 103.
Directions. Set up the apparatus, making use of one of
the cases of equilibrium found in Exp. 103. Then, keep-
ing the magnitude and point of application of each force
unchanged, veer the forces round, with respect to the
board, into a new direction, but keep them parallel to
MOMENT OF A FORCE.
259
each other. The easiest way to veer them round is to
tighten one of the screws, and to loosen the others till
the strings, remaining parallel to each other, no longer
lie along the lines traced upon the board. Record the
trials and the results in your note-book.
What conclusion do you draw from the experiment as
thus far performed?
Repeat the experiment, using any case of equilibrium to
begin with found in Exp. 104, where the points of appli-
cation do not lie in the same straight line. Record the
trials and the results.
Do you find the same result as in the first part of the
experiment ?
What general conclusion can you draw from this experi-
ment?
MOMENT OF A FORCR
113. Definition of the Moment of a Force. Before
discussing the record of the results of
Exp. 105, we will define the meaning of
the term moment of a force.
The moment of a force is the power the
force has to rotate the body, to which it is
applied, about some selected axis. This
power depends not only upon the magni-
tude of the force, but upon its position.
A force applied to the middle of a door
has less power to turn the door on its
hinges than if it were applied to the side
of the door remote from the hinges. The
" selected axis " in this case is the line FIG. 90.
260 EXPERIMENTAL PHYSICS.
running through the hinges about which the door turns,
as shown in Fig. 90.
Definition. The numerical measure of the moment of a
force, with, respect to an axis, is the product of the force and
the perpendicular let fall on its line of action from the axis.
Let the irregular outline represent a body ; let a force,
F, act on the body in the plane of the paper; let an axis,
perpendicular to the paper, pierce it at 0. Then the
moment of the force, F, about
the axis through the body at
is F X OM, where OM is the
length of the perpendicular let
fall from upon the line of
action of F.
Now work out in vour note-
FlG. 91. J
book the moments for two
cases of equilibrium in Exp. 103, for two cases in Exp.
104, and for two cases (if you found as many) in Exp. 105.
In each case take in turn for the axis each of the three
pegs used in that case, and at least one other peg. This
will make twelve moments calculated for each case of
equilibrium. The calculations, however, are extremely
simple. Call a moment positive if it tends to produce
rotation round the given axis in the direction of the motion
of the hands of a watch. Call a moment negative if it
tends to produce rotation in the opposite direction round
the axis.
Is there anything in the nature of the case why we
should regard one direction of rotation positive rather
than the other?
MOMENT OF A FORCE.
261
We can now replace the set of three conditions, for the
equilibrium of parallel forces, suggested on pages 249 and
250 by a set of two conditions only :
(1) The algebraic sum of the forces must be zero ; that
is, the sum of the forces in one direction must be equal to
the sum of the forces in the opposite direction.
(2) The algebraic sum of the moments of the forces
must be zero; that is, the tendency for rotation in one
direction must be equal to the tendency in the opposite
direction.
NOTE. The algebraic sura of two or more quantities is the result
obtained by adding them according to the rules of algebra, which take
into account the signs of the quantities.
The set of conditions given above is true for the equi-
librium of any number of parallel forces in one plane.
To illustrate the
applications of the
conditions of equi-
librium just stated,
let us find the equi-
librant of the set of
forces described in
Fig. 92, and conse-
quently the result-
ant which always
has the same mag-
nitude as the equi-
M
12
10
FIG. 92.
librant, but the
opposite direction.
We will call forces acting upwards positive, and those
acting downwards negative,
262
EXPERIMENTAL PHYSICS.
The distance KL LM= 2, and MN= NO = 4.
Making use of condition (1), that is, in order to have
equilibrium, the algebraic sum of the forces acting on a
body must be zero, we find, x being the magnitude of the
equilibrant,
x 6 + 8 1 + 1 2 = , or x = 4 .
12
The magnitude of
the equilibrant
is then 4. The
minus sign denotes
that the equili-
brant acts down-
M_ _ | _ o wards. (Why ?)
To make use of
condition (2), let
us first calculate
the moments with
10 respect to an axis
passing through
K.
Moment of 6 about K= (6x0) = 0.
" " 8 " "= (8x2) = 16.
" " 10 " " = (10 X 4) = 40.
" "12 = (12 x 8) = 96.
Moment of the equilibrant, 4, at the unknown distance y
from K = 4 X y= ty*
Hence, 4y + 16 + 40 96 = 0, or 4y = 72.
Hence, y = 18 units to the right from K. Why is not
the distance 18 units to the left from J5T?
We see that the first condition gives us the direction
MOMENT OF A FORCE. 263
and magnitude of the equilibrant ; the second condition,
the point of application of the equilibrant.
Let us now take moments about M, that is, apply the
second condition with respect to an 'axis through M.
Moment of 6 about M= -(G X 4) = 24.
8 " " = (8x2) = 16.
" 10 " (10 X 0) = 0.
"12 " "= (12 X4) = 48.
Moment of the equilibrant, 4, at the unknown distance
z from M= 4 X z = 4z.
Then 4z 24 + 16 + 48 = 0, or 4z = 56.
Hence, z = 14, that is, the point of application of the
equilibrant is 14 units to the right from M ; but 14 to
the right from Mis equal to 18 to the right from K, so the
result reached is the same as before.
Compute the moments about 0.
Will the direction, the magnitude, and the point of
application of the resultant of the four forces be the same,
no matter what point is taken to pass an axis through
about which to compute moments ?
Experiment 1O6. To find what relations must exist
among four forces (one acting north, one south, one east,
one west) in one plane, in order that they may be in
equilibrium.
Apparatus. The same as in Exp. 103, but with one more spring
balance.
Directions. Perform this experiment on a wide table.
With the four spring balances, each pulling in a different
direction, but always along some line marked on the board,
as shown in Fig. 93, make three cases of equilibrium.
264
EXPERIMENTAL PHYSICS.
Take new points of application and new magnitudes of
forces for each case. Record in a manner similar to that
suggested in Exp. 103.
In each case, is there any fixed relation between the
magnitude of a force acting in one direction and the mag-
nitude of a force acting in the opposite direction ?
Selecting one of the cases of equilibrium you have
made, compute the moments of its forces with respect to
one of the pegs used in this case.
Then for this same case make
three more computations, one with
respect to each of the three re-
maining pegs. Finally, compute
for this case the moments of its
forces about some peg put at ran-
dom into any hole in the board.
In each set of moments thus
computed, does the algebraic sum
of the moments equal zero ?
Calling forces acting east positive, those acting west
negative, forces acting north positive, those acting south
negative, state carefully two general laws modeled after
those given on page 261.
QUESTIONS. When any number of forces are acting upon a pivoted
body, what is the necessary condition for their causing no rotation ?
When a body is subjected to forces acting in one plane only, what con-
ditions must be fulfilled in order that the body may neither slide nor
turn?
GRAVITY.
114. Center of Gravity. The earth pulls downward
on each of the many particles of which a body is com-
FlG. 93.
GRAVITY. 265
posed. This downward pull of the earth is called gravity.
In the next experiment we shall take as the body to be
considered a piece of cardboard. Since the cardboard is
composed of a great number of particles, there are a vast
number of forces acting downward upon the body. All
these forces are practically parallel. (Why?) The object
of the experiment is to find whether the resultant of these
parallel forces passes through a fixed point about which
the cardboard will balance, if supported at this point.
Experiment 1O7. To find the center of gravity of a
piece of cardboard of triangular shape.
Apparatus. A triangle of cardboard whose sides, for example,
are 10 cm , 20 cm , and 25 cm long ; a piece of thread ; a pin ; a bit of
sheet lead.
Directions. Through the cardboard, very near one
corner, stick a pin, and enlarge a little the hole thus
made, so that when the pin is stuck horizontally into the
edge of the table, the cardboard will swing freely with but
little friction at the hole. When the card-
board, thus suspended, comes to rest, " the
resultant force of its weight is balanced
by the upward elastic resistance to bending
exerted by the pin ; and a plumb line, made
of a bit of lead fastened to the end of a
piece of thread, hung over the pin, will
give the direction in which either force
acts." Hang the plumb line over the pin
by a loop, as shown in Fig. 94. Have the plumb line long
enough to reach more than across the cardboard. Mark
the point where the plumb line crosses the lower edge of
266 EXPERIMENTAL PHYSICS.
the cardboard. Now take down the cardboard and draw
on it, with a sharp-pointed lead-pencil, a line from the pin
hole to the point where the plumb line crosses the edge of
the cardboard; this line, thus drawn, gives the direction
of the resultant force of gravity on the cardboard.
Hang the cardboard from another corner, and repeat the
process. A second line for the direction of the resultant
force of gravity is thus obtained. Call the point in which
the second line cuts the first one, G-. Now suspend the
cardboard from its third angle.
Does the plumb line cross the point G- ?
Lay the cardboard in a horizontal position on a pin-
point, so that G- shall rest upon the pin-point.
Does the card balance ?
Does the resultant of all the parallel forces constituting
the weight of a body pass through a fixed point ?
Why is this point called the " center of gravity " ?
Does the center of gravity of the piece of cardboard lie on
one of the surfaces, or midway between the two surfaces ?
Can we regard the weight of a body as collected at its
center of gravity (that is, if we could replace all the paral-
lel forces which constitute the weight of the body by a
single force equal to the sum of this great number of
parallel forces, would the line of action of this single
force pass through the center of gravity of the body) ?
This question we shall try to answer in the next
experiment.
Experiment 1O8. To find whether the weight of a body
acts just as if it were all collected at the center of gravity of
the body.
GRAVITY. 267
Apparatus. A wooden stand like that used in Exp. 24 ; a heavy
iron ball ; a triangular prism of wood ; a 30-pound spring balance.
Directions. Record the weight of the ball in pounds,
and also that of the stand. On a table, near the corner,
lay the triangular piece of wood, and on this lay the stand
(Fig. 95) to which the
iron ball is hung by a
loop of string. Have ^ ^
the edge, not the face, I
of the meter stick, Jk
which is fastened to
, , , FIG. 95.
the stand, rest on the
triangular piece of wood. On the triangular piece of wood
balance the stand with the weight attached. Then record
the distance from the end, A (Fig. 95), to the point of
application, P, of the weight; also record the distance
from A to the fulcrum, 8.
What is the distance in centimeters from P to SI
Considering the weight of the ball as one downward
force, and the weight of the stand, the body, as the other
downward force, find, by applying the principle of moments,
at what distance from the fulcrum, S, the weight of the
stand, if collected at one point, would have to be applied in
order to produce the state of equilibrium that is observed.
Apply the principle of moments in the following way:
Multiply the weight of the ball by its distance from the
fulcrum ; also, denoting by x the distance from the ful-
crum to the point where the weight of the stand would
have to be collected in order to produce the state of equi-
librium observed, multiply the weight of the stand by x.
Put the two products thus obtained equal to each other
268 EXPERIMENTAL PHYSICS.
(we have a right to do this by the second condition of
equilibrium, page 261), and solve the equation thus ob-
tained to get the value of x. Add to x the distance, SA,
from the fulcrum to the end, A, of the stand.
What is the distance from A of the point obtained by
this computation?
Now change the position, P, of the ball on the stand, and
balance again. Make measurements and record as before.
What is the distance from A of the point obtained by
this computation?
Finally, remove the ball, and balance the stand alone
on the triangular piece of wood.
What is the distance in centimeters from the end, A, to
the balancing-point, the center of gravity, the present
position of the fulcrum?
How does the distance just obtained compare with the
two computed distances from A ?
Has or has not the weight of the stand acted as if
collected at the center of gravity?
How great a pressure has been exerted upon the sup-
port, that is, upon the triangular piece of wood, in each of
the three oases?
Can you always regard the weight of a body as a force
applied at the center of gravity of the body?
How could you find, by applying the teachings of this
experiment, the weight of the stand, if the position of its
center of gravity, the position of the fulcrum, the position
of the iron ball, and also the weight of the iron ball Avere
given ?
How could you find by experiment the center of gravity
of the stand?
GRAVITY. 269
EXAMPLES.
1. A uniform straight lever 10 ft. long balances at a point 3 ft. from
one end, when 12 Ibs. are hung from this end and an unknown weight
from the other. The lever itself weighs 8 Ibs. Find the unknown weight.
Solution. Denoting by x the unknown weight in pounds, and regard-
ing the weight of the lever as a force applied at its center of gravity, take
moments about the point of support thus :
12 X 3 8 X 2 + x X 7,
or 7z = 36 - 16 = 20.
.-. x = 2f.
Hence, the weight which was to be found is 2f- Ibs.
NOTE. Whenever we say a lever is uniform, we mean that its center
of gravity is the center of its length.
2. A straight lever 6 ft. long weighs 10 Ibs., and its center of gravity
is 4 ft. from one end. What weight at this end will support 20 Ibs. at
the other, when the lever is supported at a distance of 1 ft. from the end
nearer the center of gravity ?
3. A telegraph pole is made of three hollow iron cylinders joined end
to end. Each cylinder is 4 m long; the lowest weight 250 k s, the middle
one 150 k e, and the uppermost 50 k s. Find the center of gravity of the
pole.
SUGGESTIONS. Regard the weight of each section as applied at the
center of gravity of the section to which it belongs. Imagine the pole
placed in a horizontal position. Find where a prop would have to be
placed to produce equilibrium.
4. A cube of wood, 10 cm on each edge and of specific gravity 0.5, is
covered on one side by a plate of metal 10 cm square, l cm thick, of specific
gravity 5. How far from the outer surface of the metal plate is the
center of gravity of the whole ?
5. Two uniform cylinders of the same diameter, whose lengths are 1 ft.
and 7 ft., respectively, and whose weights are in the ratio of 5 to 3, are
joined together so as to form one cylinder. Find the position of the
fulcrum about which the whole will balance.
270 EXPERIMENTAL PHYSICS.
LEVERS.
115. Classes of Levers. A lever is a rod, or bar, by
means of which a force can be applied more advanta-
geously than it otherwise could in moving a body. A
crowbar is a lever. It is rested, near one end, on a piece
of stone or other firm support, called a fulcrum. The end
near the fulcrum is placed under the body to be raised,
and a force is applied at the other end tending to bring
this end downward. The body to be moved is called the
weight, and the force applied at the other end of the crow-
bar is called the power. There are three classes of levers.
A lever like the one just described, where the fulcrum is
between the weight and the power, is called a lever of the
first class.
An oar, when used in rowing a boat, is a lever. The
water into which the blade of the oar dips is the fulcrum,
the resistance of the boat to being urged forward is the
weight, which meets the oar at the rowlock, and the force
of the rower's arm is the power. When the weight is
between the fulcrum and the power, as in the case of an
oar, the lever is called a lever of the second class.
A pitchfork, when used in lifting hay, is a lever. One
end is held firmly in the hand, which is the fulcrum, the
hay at the other end is the weight, and the force, applied
by the other hand to the pitchfork somewhere between
the fulcrum and the weight, is the power. When the
power is between the fulcrum and the weight, the lever is
called a lever of the third class.
In many problems concerning levers, the weight and
the power are supposed to act at right angles to the lever,
NON-PARALLEL FORCES. 271
and the distance measured along the lever from the ful-
crum to the weight is called the weight-arm, while the
distance from the fulcrum to the power is called the power-
arm. By applying the principle of moments we have :
power X power-arm = weight X weight-arm.
QUESTIONS. Which is the greater, the power or the weight in a lever
of the first class ? In a lever of the second class ? In a lever of the
third class ?
NON-PARALLEL FORCES.
116. Concurrent Forces. We have given consider-
able study to cases of equilibrium where we have had
three parallel forces acting on a body, and we have found
the resultant and the equilibrant of groups of parallel
forces.
It now remains for us to study the conditions of equi-
librium of three concurrent forces, that is, forces whose
lines of action meet in a point.
Experiment 1O9. To find the condition for equilibrium
of three concurrent forces.
Apparatus. Three 30-pound spring balances ; two pieces of slen-
der, strong, hard-twisted string 70 cm or 80 cm long ; a wooden block
like the one whose specific gravity you found ; a meter stick.
Directions. The experiment is to be performed on
a table with a smooth top. Note the error of each bal-
ance when in the horizontal position. Tie a loop in each
end of one string. Do the same to the other string,
only make one of the loops 10 cm long. Pass the first-
mentioned string through the large loop, so that the large
loop lies between the loops in the ends of this string, each
of which loops should be slipped on the hook of a spring
272
EXPERIMENTAL PHYSICS.
balance, one loop only on one hook. The spring balances
should be kept in place by having their rings fastened to
the screws in blocks clamped near two corners of the
table, shown in Fig. 96, but the balances should be able
to swing freely round the screws in any horizontal posi-
tion. Slip the remaining loop of the second string over
FIG. 96.
the hook of the remaining spring balance. Now pull the
third spring balance by its ring in any desired direction
and with such a force as to draw the strings tight, and
make each balance point in the same direction as the
string attached to its hook. By means of a clamp, fasten
the balance by its ring. Make a careful reading of each
balance, taking care to apply the proper correction to
each. Put the open note-book beneath the junction of
the strings, and on the page, with the block as a guide,
TRIANGLE OF FORCES. 273
draw, with a sharp lead-pencil, a line a few centimeters in
length parallel to each string and beneath it. From the
point where these lines meet, when produced if necessary,
lay off on each line an arrow proportioned in length to the
reading of the balance whose pull was directed along the
line, the tip of the arrow in each case pointing away from
the junction. From the tip of any arrow lay off a line
parallel and equal to one of the other arrows, and from
the end of the line thus drawn draw another line parallel
and equal in length to the remaining arrow. (It is not
impossible that the line last drawn will coincide with the
line to which it is drawn parallel.)
What is the name of the geometrical figure formed by
the two lines just drawn and the selected arrow.
Point out how the following statement agrees with the
result of the experiment:
If three forces acting upon a material point are in equi-
librium, and three lines be drawn, without taking the
pencil off, parallel to the successive forces acting on the
point and in the same direction with them, and propor-
tional to them in magnitude, a triangle will be formed.
The triangle thus formed is called the triangle of forces.
If the three forces are not in equilibrium, the lines will
not form a triangle.
TRIANGLE OP FORCES.
117. Principle of the Triangle of Forces. If three
forces are in equilibrium, and any triangle be drawn with
its sides parallel to the lines of action of the forces, the
lengths of these sides will represent the relative magni-
tudes of the corresponding forces.
274
EXPERIMENTAL PHYSICS.
Test the statement just made by drawing a triangle on
the page of your note-book, the sides of the triangle being
drawn parallel to the direction of the forces recorded in
Exp. 109.
On two of the arrows, in your original figure, as sides,
construct a parallelogram. Produce the remaining arrow
backwards by its own length from the point whence the
three original arrows spring.
Does the line you have just drawn
coincide or nearly coincide with the
diagonal of the parallelogram ?
In the case of three concurrent
forces, as A, B, and C of Fig. 97, in
equilibrium, we have the following
relations :
A is the equilibrant of B and C.
B " " " " A " C.
C " " " " A " B.
a " " resultant " B " 0.
b " " " " A " C.
c " " " " A " B.
QUESTIONS. What is the condition that must hold in order that three
concurrent forces shall be in equilibrium ?
A force of 10 Ibs. acts due east, and a force of 10 Ibs. acts due north,
at the same point. What is the magnitude of their resultant ? Of their
equilibrant ? In what direction does the resultant act ?
EXAMPLES.
1. A ball, of weight 2 Ibs. and of radius 4 in., is suspended by a string
fastened to a vertical wall. The ball rests against the wall, and the direc-
tion of the string passes through the center of the ball. If the distance
of the point at which the string is fastened to the wall is 6 in. above the
EXAMPLES. 275
point where the ball touches the wall, find the pressure of the ball against
the wall.
Solution. In Fig. 98 let P be the point at which the end of the string
is fastened to the wall ; let M be the point at which the ball touches the
wall. We are asked to find the pressure of the ball
against the wall. This pressure will be equal to the
push of the wall against the ball. There are three
forces which keep the ball in equilibrium, the weight
of the ball, the push of the wall, and the tension of
the string; but these three forces pass through a
single point, C, so let us denote the weight by CW,
the push by CjR, and the tension by CT. These
three forces are in equilibrium, and are parallel,
respectively, to PM, JfO, and CP, the sides of the
right triangle, PMC. Hence, by the principle of the triangle of forces,
CW = PM
CR MG'
By the conditions of the problem, CW = 2 Ibs., PM = 6 in., and
MG = 4 in., consequently, if we denote by x the required force, CR,
2 _6
z~4
Hence, the pressure of the ball against the wall is 1.33 Ibs.
2. Find the tension of the string in Ex. 1.
3. A picture frame weighing 10 Ibs. is hung by a cord passing over
a nail, the two parts of the cord making an angle of 90 with each other.
Find the tension in the cord.
4. A uniform pendulum rod is pulled aside from the vertical by a
horizontal force applied to the lower end. If the pendulum rod weighs
10s, what must be the horizontal force in order that the pendulum rod,
when in equilibrium, shall make an angle of 45 with its former position ?
5. An isosceles triangle, the vertical angle of which is equal to 120,
is drawn on a vertical wall with its base horizontal and its vertex down-
wards. At each corner of the triangle a smooth peg is driven into the
wall at right angles. A thread with 12s attached to each end is passed
under the lower peg and over the other two pegs. Find the pressure on
each peg. Find also the vertical and the horizontal pressure on each peg.
276
EXPERIMENTAL PHYSICS.
COMPOSITION AND RESOLUTION.
118. Composition and Resolution of Forces. The
process of finding the resultant of a group of forces is called
the composition of forces, while
the process of finding two
forces which will exactly re-
place a single force in its action
upon a body is called the reso-
lution of forces.
In the composition of forces
we get one definite answer to
the problem.
In the resolution of forces
we get an _ indefinite number
of answers, for upon a given
force, AB, as diagonal we can
construct an indefinite number
of parallelograms, a few of
which are shown in Fig. 99.
The two forces into which a
single force is resolved are
called components. It is often
convenient to resolve a force
into two components at right angles to each other.
FIG. 99.
FRICTION.
119. Friction a Force ; Coefficient of Friction. Fric-
tion is the force which opposes the sliding of one body
over another.
FRICTION. 277
If R denotes the perpendicular pressure between two
surfaces which slide over each other, and F denotes the
F
friction, the quotient of has been found to be a con-
H
stant number for any two given surfaces, provided the
corresponding surfaces are of the same material and in
the same condition, and is called the coefficient of friction.
The coefficient of friction is denoted by the Greek letter
F
p, that is, = JJL, and consequently F = pR.
R
Does the last equation suggest to you the propriety of,
calling ft the " coefficient of friction " ?
Experiment 11O. To find the coefficient of friction of
wood sliding on paper.
Apparatus. A smooth board, about 50 cm long ; a block of wood
such as you got the specific gravity of ; an 8-ounce spring balance ;
a sheet of paper about 25 cm long and a little wider than the board.
PART 1. Where the sliding is on a horizontal plane.
Directions. Find what fraction of an ounce it takes
to draw the pointer down to the zero line, when the
balance is in a horizontal position. Spread the paper
smoothly on the board, fold the edges of the paper over
the sides of the board, and fasten by tacks. Lay the board
horizontally. Place the block on one of its narrowest
sides on the paper. Tie a thread round the block, but
in such a way that no part of the thread shall come
between the block and the paper. Fasten the end of the
thread to the hook of the spring balance, and pull with
the spring balance held in a horizontal position with a
278 EXPERIMENTAL PHYSICS.
force sufficient to keep the block moving with uniform
velocity along the paper. Record the force indicated by
the balance, and correct this force for the error of the
balance when held in the horizontal position.
Then, taking care as before that the thread does not
lie between the block and the paper, lay the block on its
broad side, and record as before the force necessary to
maintain uniform motion.
From the two cases just tried, should you say that the
amount of friction depends upon the extent of surface in
contact ?
Now load the block, still on its broad side, with 200 g
and 400 g in turn, recording in each case the force required
to maintain uniform motion. Weigh the block itself in
ounces ; and also find the weight in ounces of the two
weights, the 200 g and the 400 g . Then calculate the
coefficient of friction for each of the four cases tried. To
compute the coefficient of friction, divide the friction (the
number of ounces the spring balance indicated when
corrected for the zero error) by the perpendicular pressure
(the weight of the block in ounces plus the weight in
ounces of any load put upon the block).
What value do you get for the coefficient of friction ?
PART 2. Where the sliding is on an inclined plane.
Raise one end of the board until the unloaded block,
once started, will slide along the paper with uniform veloc-
ity. Then, keeping the board fixed in this position, meas-
ure the vertical distance from the under (Why?) side of
the raised end to the table, and the horizontal distance
from the foot of this vertical line to the point where the
FRICTION. 279
lower end of the board rests upon the table. The co-
efficient of friction can be calculated by dividing the
vertical distance by the horizontal.
Does the numerical value which you get equal that
which you got by the other method?
NOTE. The angle which the inclined plane makes with the horizontal
plane, when the body is just about to slide, is called the angle of repose,
or the angle of friction.
The proof of the statement that the coefficient of
friction can be obtained by dividing the vertical distance
by the horizontal is given in the demonstration of the
following :
Theorem. When a body slides with uniform velocity
down an inclined plane, the coefficient of friction is equal
to the height of the plane divided by the base.
Let (Fig. 100) be a body sliding with uniform veloc-
ity down the inclined
plane, BA.
T OB
1 o prove /u, = :
Let OW, OF, and
OR represent weight
of 0, friction, and per- FIG. 100.
pendicular pressure respectively.
From C draw CD \\ OR.
CD, DB, B C are || resp. to OR, OF, OW.
~r\~ip> f)TP
= -jyp (by the principle of the A of forces).
A ABC is art. A.
280 EXPERIMENTAL PHYSICS.
CD JL AB (by the principle that a st. line J_ to one of
two || 's is _L to the other).
. . A CBD and AB C are similar.
CB _ DB
''' AC~ CD'
OF _ DB
~0*-~CD'
OF
And ^ = - (by definition).
CB
EXAMPLES.
1. The coefficient of friction for wood on wood is 0.33. How great a
force must be applied to a block of wood weighing 100 Ibs. in order to
drag it along a wooden plank ?
2. A body slides with uniform velocity down a plane inclined at an
angle of 30 to the horizon. What is the coefficient of friction between
the body and the plane ?
HINT. The hypotenuse is twice the length of the side opposite the
angle of 30.
3. A body, the weight of which is 10 Ibs., rests upon a plane inclined
at an angle of 30 to the horizon ; find the pressure at right angles to the
plane, and the force of friction exerted.
4. If the height of an inclined plane be to the length as 3 is to 5, and
a body the weight of which is 15 Ibs. be supported by friction alone, find
the force of friction in pounds.
WORK.
12O. Work defined ; Unit of Work. One important
object of the next experiment is to illustrate and enforce
the meaning of the term work as used in physics. Work
z's the overcoming of resistance through space.
WORK. 281
According to the meaning given in physics to the term
work, the mere supporting of a book by the hand is not
work; but if the book is raised, work is done, for a resist-
ance, the weight of the book, is overcome (through a
space).
The unit of work, among English-speaking engineers, is
the foot-pound (ft. lb.). The foot-pound is the amount of
work done in overcoming the resistance of a force of one
pound through a distance of one foot.
If you should lift a pound-mass vertically a distance of
one foot, the amount of work done would be one foot-
pound.
QUESTIONS. How many foot-pounds of work must be done in dragging
a 20-lb. weight a distance of 15 ft. along a horizontal plane, if the coeffi-
cient of friction is 0.4 ? If the coefficient of friction is 0.5 ?
Experiment 111. To find the amount of work done in
dragging a body up an inclined plane.
Apparatus. An inclined plane, a stout plank with a long slot cut
through it, one end resting on the floor, the other end raised above
the floor, as shown in Fig. 101 ; a 4-pound spring balance ; a small,
strong carriage ; four 200s weights, with which to load the carriage.
PART 1. To find the work done, apart from that
employed in overcoming friction, by a force parallel to
the incline, in drawing the loaded carriage (Fig. 101) such
a distance up the plane as to make the vertical rise 2 ft.
Directions. Along the incline measure the distance,
AB, corresponding to a vertical rise of 2 ft. ; then find
the force parallel to this incline which would be neces-
sary to move the loaded car with uniform velocity up
the incline, if there were no friction. To determine and
eliminate the friction at any part of the incline, find the
282
EXPERIMENTAL PHYSICS.
pull on the balance parallel to the incline required to
move the carriage at a uniform velocity up the incline at
this part, and then the pull in the same direction which
will allow the carriage to move with uniform velocity down
FIG. 101.
the incline at the given part. The average of the two
pulls will be the pull that would be required if there were
no friction, and half the difference between the two forces
will be the force required to overcome the friction at the
spot in question. The diagrams and the following dis-
cussion will, perhaps, make this clearer.
In the first diagram (Fig. 102) the car is supposed to
be moving up the in-
cline. The friction,
F, and the resolved
part, #, of the force
of gravity oppose the
motion. If the spring
balance reads a Ibs.,
we have
(1)
FIG. 102.
WORK.
283
In the second diagram (Fig. 103) the car is supposed to
be moving down the plane. The friction, JP, acts in a
direction opposite to
the motion, so we ,
have, if the balance
now registers b Ibs.,
2? = JF+5, or,
= b. (2)
By adding (1) and (2) we have, FlG - 103 -
2x a b,
Hence, the force necessary to keep the car moving up the
incline, if we leave friction out of account, is - - Ibs.
2
a _ 5
By subtracting (2) from (1) we find, F= - . If
2
the plane were uniform, it would be necessary to deter-
mine the force at one place only ; but as the incline may
vary slightly, it is best to determine the force at three or
four places and take the average.
Multiply this average force, a;, by the distance, measured
along the plane through which the force would have to
act in order to draw the car up the plane so that its
vertical rise would be 2 ft.
How many foot-pounds of work are required?
PART 2. To find the work, friction aside, done by a
force acting parallel to the base of the incline, in drawing
the loaded car such a distance up the incline as to make
the vertical rise 2 ft.
284 EXPERIMENTAL PHYSICS.
Directions. Let the string that attaches the carriage
to the balance pass through the slot cut in the plane, as
shown in Fig. 104. Then draw the carriage up the plane,
always pulling horizontally on the balance. Do not let
the string rub on the sides of the slot. By observing the
pull going up and the pull coming down, eliminate fric-
tion, as in Part 1. Measure the horizontal distance, AC,
corresponding to a vertical rise of 2 ft. Multiply the force
by the distance, AC.
How many foot-pounds of work are necessary ?
PART 3. To find the amount of work done in raising
the carriage and contents through a vertical distance of
2ft.
Directions. Weigh the carriage and its load together
on the same balance.
How many foot-pounds of work would it take to raise
the carriage and its load through a vertical distance of
2ft.?
How do the amounts of work in the three cases compare
with each other?
WORK. 285
121. Law of the Inclined Plane. The teachings of
the preceding experiment lead to a very important result,
known as the law of the inclined plane.
The amount of work done in dragging a body up an
inclined plane is equal to the weight, W, of the body mul-
tiplied by the height, OB, of the plane (Fig. 105), whether
the force used to drag the body acts parallel to the in-
cline, AB, or parallel to the
base, AC, consequently, if
P denotes the force par-
allel to AB necessary to
drag the body, and Q the
force parallel to AC,
P x AB = W X CB, "
QXAO =WXCB,
that is, the force required to draff the body multiplied by the
distance through which it acts is equal to the weight of the
body multiplied by the vertical distance through which it is
raised.
EXAMPLES.
1. A body weighing 100 Ibs. rests upon an incline, (a) How much
work must be done in drawing the body 10 ft. up this incline, the vertical
ascent being 6 ft. ?
Solution. 100 X 6 = 600 ft. Ibs.
(6) What force is necessary to draw the body up the incline, if applied
parallel to the incline ?
Solution. P X 10 = 100 X 6 ; hence, P = 60 Ibs.
(c) What force is necessary to draw the body up the incline if applied
parallel to the base ?
Solution. Q x V~10 2 - 6 2 = 100 X 6 ; hence SQ = 600, .-. Q = 75 Ibs.
(d) How much work must be done if the coefficient of friction is 0.2 ?
Solution. 100 X 6 + 80 X 0.2 X 10 = 760 ft. Ibs.
286 EXPERIMENTAL PHYSICS.
NOTE. In the solution of (d), the expression 80 X 0.2 X 10 is obtained
by applying the principle of the triangle of forces.
2. A block weighing 10 Ibs. rests on an incline such that the block
must move 5 ft. in order to rise 3 ft. The pressure of the block against
the incline is in this case 8 Ibs. The coefficient of friction is 0.25. How
much work must be done against gravity by a force parallel to the incline
in drawing the block up 5 ft. How much work against friction ?
3. An inclined plane rises 3.5 ft. for every 5 ft. of length. Find what
force in pounds must be applied parallel to the incline to drag up a
weight of 200 Ibs.
4. A railway train weighing 30 tons is drawn up an inclined plane of
1 ft. in 60 by means of a rope and a stationary engine ; find what num-
ber of pounds at least the rope should be able to support.
5. If the base of an inclined plane is to the height as 24 is to 7, find
the force necessary to drag a body weighing 48 Ibs. up the plane.
(a) When the force acts parallel to the incline.
(&) When the force acts parallel to the base.
6. While a car moves along a track a distance of 10 ft. , a man pushes
with a force of 25 Ibs. against the side of the car in a direction at right
angles to the track. Does the push of the man on the car assist its
motion? Does his push, except by possibly increasing the friction,
retard the motion of the car ? How many foot-pounds of work does the
man do upon the car during its motion ?
INERTIA.
122. Inertia a Property of Matter. There is an
inherent property of matter called inertia, which makes
the application of a force necessary to bring about any
change in the direction or magnitude of a body's motion.
To start a body requires the application of force; to
stop a body requires the application of force ; to deflect
a moving body from its path also requires the application
of force.
In brief, to start a body, to stop it, to increase its veloc-
ity, to diminish its velocity, or to deflect it from its path,
INERTIA. 287
the application of a force is required. The property of
matter that makes this application of force necessary is
called inertia.
To get the quantity of matter in a body, we have com-
pared the body, by means of a pan balance, with a stand-
ard mass. Since the attraction of the earth becomes greater
as we approach the polar regions from the equatorial, a
mass of matter would weigh more at the pole than at the
equator. The spring balance does not measure the mass,
that is, the quantity of matter a body contains, but it does
measure the force of gravity at different parts of the
earth's surface.
123. Definition of the Equality of Two Masses. In
our discussion of the term mass in the early part of this
chapter we tacitly assumed that two bodies have the same
mass, no matter how much they may differ in substance,
provided they are in equilibrium when placed in the
opposite pans of a balance.
The idea of inertia, however, gives us a means of com-
paring two masses for equality without the use of a
balance of any description. The method holds not only
for the earth, but for all the heavenly bodies also, as well
as for all regions of space. In the following experiment
we shall apply this "inertia test" for the equality of two
masses.
Experiment 112. To find, without the use of a balance,
whether two masses are equal or not.
Apparatus. The mass-tester (Fig. 106), consisting of a vertical
axis with two horizontal arms to carry cups (nickel-plated calorime-
ters), and a spiral spring with one end fastened to the axis and
288
EXPERIMENTAL PHYSICS.
the other fastened to the support in which the upper end of the axis
is pivoted ; two 100s weights ; some lead shot ; a platform balance.
Directions. In each of the cups put a 100 g mass, turn
the axis through 180, and find accurately the time of
six vibrations. Then take out the 100 g mass and put in
place of it lead shot ; try to have equal
amounts of shot in each of the cups so
that the axis shall not bind where it is
pivoted. By varying the amount of shot
(adding more if the apparatus moves too
fast, taking out some if the apparatus
moves too slowly), get the apparatus to
make the same number of vibrations in
the same time as when the iron occupied
the place of the lead. Find how many
grams the shot weighs.
VELOCITY.
FIG. 106.
124. Measure of the Velocity of a
Body. Whenever a body moves (that
is, changes its position) it either passes
over equal spaces in equal times, like the hand of a clock,
and is said to have constant velocity, or else passes over
unequal spaces in equal times, like a stone falling from
a height toward the ground. From the instant the stone
begins its downward motion, it falls with greater and
greater swiftness until it rests upon the ground. When
the body passes over unequal spaces in equal times, its
velocity is said to be variable.
^Definition, Velocity is the rate of motion of a body.
ACCELERATION. 289
The velocity of a body is measured by the distance
traversed divided by the time that elapses during the
journey.
If we denote by s the distance traversed in time, t, by
a body moving with constant velocity, v, we have
EXAMPLES.
1. If the tip of a clock-hand moves a distance of 30 cm in 20 minutes,
what is the velocity ?
Solution. We are to find the number of units of length traversed in
a unit of time. If we take as our unit of length the centimeter, and as
30
our unit of time the minute, the required velocity will be = 1.5 cm per
zo
minute.
If we take as our unit of length the centimeter, as before, and for our unit
30 1
of time the second, the required velocity will be = = 0.026 cm
^U X ou 4U
per second.
O 1
2. Is a velocity of - cm per minute the same as a velocity of cra per
second ?
3. If a tortoise walk at the rate of 3 in. a second, how many feet will
he go in an hour ?
4. How many seconds would a train take to go 0.2 of a mile at the
rate of 20 miles per hour ?
5. With what velocity must a horse trot in order to .go 780 yds. in
1 minute ?
ACCELERATION.
125. Measure of Acceleration. When a body is mov-
ing with a variable velocity, the rate at which the velocity
changes is called acceleration. It is measured by the
290 EXPERIMENTAL PHYSICS.
velocity gained by the body in a certain time, divided by
the time taken to gain it.
Acceleration is said to be constant when the velocity
gains equal additions of acceleration in equal times.
Variable acceleration, which we shall have no occa-
sion to consider, results when the velocity gains unequal
additions of acceleration in equal times.
For each second the acceleration of a body falling in
a vacuum near the surface of the earth is constant, and
is equal to about 980 cm per second.
If a body moving with a velocity which has a constant
acceleration, , has a velocity of V Q at the beginning of the
time, , and a velocity of v at the end of this time, we
have _ _
(2)
EXAMPLES.
1. If the velocity of a falling body after 3 seconds is 2840 cm per second,
what is its acceleration ?
Solution. We are to find the number of units of velocity acquired in
a unit of time. If we take as our unit of velocity the centimeter per
second, the acceleration in 1 second will be
2840
= 980 cm per second,
o
2. If a body is thrown downward with an initial velocity of 100 cm per
second from a balloon, and after the lapse of 3 seconds its velocity is
2940 cm per second, what is its acceleration ?
Solution. As acceleration is the gain in velocity divided by the time
taken, in this case 3 seconds, in making this gain we have for the accelera-
tion in 1 second
2940 - 100 2840 non
= = 980 cm per second.
3 o
3. A body starts from rest and acquires a velocity of 1200 cm per second
in half a minute ; what is its acceleration ?
-DISTANCE TRAVERSED. 291
4. A body starts with a velocity of 75 cm per second, and 5 seconds
afterward is moving with a velocity of 97 cm per second; what is its
acceleration in 1 second ?
5. Starting with a velocity of 25 cm per second, a body for every sec-
ond it moves has an acceleration of 980 cm per second ; what will be its
velocity in 1, 2, 3, and 6 seconds, respectively ?
DISTANCE TRAVERSED.
126. Distance traversed by a Moving Body. If the
initial velocity of a moving body is v , and the velocity it
has at the end of the time, , is v v its average increase of
velocity will be
2
and denoting by s the distance passed over by the body
by reason of the increase of velocity from V Q to v v we have
(3)
But v l V Q = at by (2),
EXAMPLES.
1. How far will a body fall in 2 seconds ?
Solution. The relation existing between the time during which a
body moves, under a constant acceleration, and the distance traversed
by the body in this time is
2. How much farther will a body fall during the second second of its
fall than during the first ?
292 EXPERIMENTAL PHYSICS.
980 X 2^
Solution. The distance fallen in 2 seconds = - - - = 1960 cm .
,., = 980 XI' =490cm
Hence, the distance traversed during the second second will be
1960cm _ 4900 = 1470cm.
3. Show that the distance passed over in the (t + 1) second by a body
acted upon by a constant acceleration, a, is f (2t + 1).
cifi
Solution. Distance traversed in t seconds = .
Hence, the distance traversed in the (t + 1) second is
4. Show that the distance passed over during the 2 seconds immediately
following the Zth second by a body starting from rest and moving under
a constant acceleration, a, is 2a (t + 1).
5. How many seconds will a falling body, starting from rest, require
to fall 490' m ?
6. Two bodies are let fall from the same point at an interval of
2 seconds ; find how many centimeters they will be apart at the end of 6
seconds from the fall of the first, the acceleration of gravity being 981 cm
per second.
QUANTITY OF MOTION.
127. Momentum. If two bodies, one having twice
the mass of the other, are moving with equal velocity, the
greater mass has the greater quantity of motion. If the
bodies of equal mass are moving with unequal velocities,
the body moving with the greater velocity has the greater
quantity of motion. The quantity of motion, then, which
a body has, depends upon the mass of the body and upon
the velocity with which it is moving ; so we define the
QUANTITY OF MOTION. 293
momentum (which means, simply, quantity of motion) of
a body as the product of the mass of the body and its
velocity. If the mass of a body is m and its velocity v,
its momentum is mv.
The meaning of momentum will be illustrated by the
next experiment, which has for its object the comparison
of the total amount of momentum of two masses before
colliding with each other, and the total amount of momen-
tum of the two masses after collision.
Experiment 113. To find how the total amount of
momentum of two masses before collision compares with the
total amount of momentum after collision.
Apparatus. Two ivory balls, one weighing about 50s, the other
about 200 ; a flat bar of wood about 50 cm long, and of a width
somewhat greater than the sum of the radii of the balls ; a piece of
apparatus like that shown in Fig. 107 ; fine iron wire, No. 33 B. & S.
PART 1. When the larger ball strikes the smaller at
rest.
Directions. Fasten the flat bar, in a horizontal position,
as high above the floor as practicable. Into each end of
the bar drive two tacks, whose distance apart shall equal
the sum of the radii of the balls. To one of these tacks
fasten one end of a long piece of fine iron wire, pass the
other end through a little screw-eye in one of the ivory
balls. Then carry this end to the tack driven into the
other end of the board directly opposite the first, and
there fasten the wire, after drawing it up till the ball,
when hanging freely, almost touches the center of the
scale, which is shown in Fig. 107. The other ball should
294 EXPERIMENTAL PHYSICS.
be suspended in the same way. The positions of the
balls should then be adjusted till their centers are in a
horizontal line, and directly over the scale. Record the
weight of each ball, and also the weight of the wire which
supports each.
Allowing the smaller ball to hang at rest, draw the
larger ball through an arc of about 10, keeping it over
FIG. 107.
the scale. Record the reading on the scale directly
beneath each ball. Then release the larger ball, and
again observe and record the readings, when the balls
have swung as far as they will after collision.
Through how many centimeters, as measured on the
scale, did the larger ball move before collision ?
Through how many centimeters did the larger ball
move after collision ?
Through how many centimeters did the smaller ball
move after collision?
Make this trial several times, always drawing the larger
ball through the same arc, and take the average of the
corresponding readings in the several trials.
When experimenting with the simple pendulum, you
found that the length of the arc through which the pen-
dulum swung made no perceptible difference in the time
QUANTITY OF MOTION. 295
of an oscillation. In the present case, the velocity with
which the larger ball is moving, when it hits the smaller,
is proportional to the distance through which it has
moved ; also the velocity with which the smaller ball starts
after it has been hit by the larger is proportional to the
distance it moves until it starts to swing back ; and the
distance the larger ball moves after the collision is pro-
portional to the velocity which it had just after the colli-
sion. As we wish only to compare the momenta of the
balls before impact with the momenta after impact, we
shall use these distances in place of the actual velocities
to which they are proportional.
The following questions will show the line of reasoning
by which the result is reached :
(1) What is the product of the mass of the larger
ball plus half the mass of its supporting wire, and the
distance through which it moved before striking the
smaller ?
(2) Calling the product, asked for in the preceding
question, momentum, what was the momentum of the
smaller ball before it was struck by the larger ?
(3) What was the momentum of the larger ball after
collision ?
(4) What was the momentum of the smaller ball after
collision ?
(5) How does the sum of the answer to (1) and the
answer to (2) compare with the sum of the answer to (3)
and the answer to (4) ?
Why was only half of the weight of the suspending
wire added in each case to the weight of the ball ?
296 EXPERIMENTAL PHYSICS.
PART 2. When the smaller ball strikes the larger at rest.
Directions. The apparatus should be arranged as for
Fart 1.
Proceed as in Part 1, but allow the larger ball to hang
at rest, and draw the smaller one through an arc of about
10 and then release it. As before, repeat the trial and
record the readings.
Through how many centimeters did the smaller ball
move before collision?
Through how many centimeters did the smaller ball
move after collision ?
Through how many centimeters did the larger ball
move after collision?
(1) What was the momentum of the smaller mass
before collision ?
(2) What was the momentum of the larger mass before
collision ?
(3) What was the momentum of the smaller mass after
collision ?
(4) What was the momentum of the larger mass after
collision ?
(5) How does the sum of the answer to (1) and the
answer to (2) compare with the sum of the answer to (3)
and the answer to (4) ?
NOTE. When a ball, as the smaller one in this case, moves after
collision in the opposite direction to that in which It was moving before
collision, its velocity is negative, and therefore its momentum is also
negative ; so when we get the sum of the answers to (3) and (4), it is the
algebraic sum which is required.
PART 3. When the balls, moving from opposite direc-
tions, meet at their point of rest.
QUANTITY OF MOTION. 297
Directions. Draw each of the balls through an arc of
about 10 and release them, taking and recording as
before the readings of their various positions.
Through how many centimeters did the larger ball
move before collision ?
Through how many centimeters did the smaller ball
move before collision ?
Through how many centimeters did the smaller ball
move after collision ?
Through how many centimeters did the larger ball
move after collision ?
Remembering that, if velocity in one direction is con-
sidered positive, velocity in the opposite direction is nega-
tive, find the algebraic sum of the momenta of the two
masses before collision; also the algebraic sum of the
momenta of the two masses after collision.
How does the first sum compare with the second ?
EXAMPLES.
1. A ball weighing 20s moving north with a velocity of 50 cm per sec.
strikes centrally a ball weighing 100s which is at rest. After the collision
the larger ball moves north with a velocity of 12 cm per sec. What velocity
has the smaller ball after the collision, and in what direction is it moving ?
Solution. Let x denote the velocity of the smaller ball after the colli-
sion. We have
100 X = momentum of larger ball before collision.
20 X 50 = 1000 " " smaller " " "
100 X 12 = 1200 " " larger " after "
20x-x= 20x " "smaller " " "
But the total momentum before collision is equal to the total momentum
after collision ; hence
0+ 1000= 1200 + 20 x
298 EXPERIMENTAL PHY-S1CS.
That is, the smaller ball is moving after the collision with a velocity of
10 cm per sec. towards the south. The minus sign denotes that the direc-
tion of motion is opposite that which the ball had before the collision.
2. If a ball of mass 25s moving with a velocity of 60 cm per sec. strikes
centrally another ball at rest the mass of which is 100?, and then rebounds
with a velocity of 20 cm per sec., with what velocity does the larger ball
move after the collision ?
3. A ball of mass 200s moving with a velocity of 30 cm per sec. strikes
centrally another ball of mass 65s at rest. After the collision the larger
ball moves on with a velocity of 17 cm per sec. With what velocity does
the smaller ball move after the collision ?
4. A ball of mass 75s moving north with a velocity of 200 cm per sec.
strikes centrally another ball of mass 60s moving south with a velocity of
100 cm per sec. After the collision the larger ball moves on with a velocity
of 30 cm per sec. What is the velocity of the smaller ball after the collision,
and in what direction is it moving ?
ABSOLUTE UNIT OP FORCE.
128. The Dyne. The units of force which we have
used in our work in the laboratory have been gravitational
units, or units of force depending for their value upon the
pull of gravity. As the force of gravity is not constant,
but increases in strength as we go from the equator
towards either pole, a unit of force has been adopted
called the dyne, which is independent of the earth's
attraction, and remains constant for all parts of the uni-
verse. The dyne is a unit of force which depends upon
the inertia of matter. (See definition of inertia, page 286.)
Definition. The dyne is that force which, acting upon a
mass of I 9 for one second, gives it a velocity of l cm per second.
If the dyne acts for 2 sec. on a mass of l g , the velocity
imparted will be 2 cm per sec. ; for 3 sec., 3 cm per sec.; and
so on.
ABSOLUTE UNIT OF WOIiK. 299
If a force of 2 dynes acts for 1 sec. on a mass of l g , the
velocity imparted will be 2 cm per sec. ; for 3 dynes, 3 cm
per sec.
If the dyne acts on a mass of 2 g for 1 sec., the velocity
imparted will be J- cm per sec. ; on a mass of 3 g , ^ cm per sec.
If / denotes the number of dynes, m the number of
grams acted upon, t the number of seconds the action
lasts, and v the velocity acquired,
,=i ( 4)
m
Equation (4) on clearing it of fractions takes the form
mv = ft.
This equation expressed in words is : " The momentum
of a body is equal to the force acting upon it multiplied
by the time the force has been acting."
ABSOLUTE UNIT OF WORK.
129. The Erg 1 . Work has already been defined as
the overcoming of resistance ; and work is measured by
the product of the force (used in overcoming the resist-
ance) and the distance through which the force acts.
If the dyne be taken as the unit of force and the centi-
meter as the unit of distance, then the unit of work is the
work done by one dyne acting through a distance of l cm .
This unit of work is called the erg (from the Greek ergon,
work). The erg is an absolute unit of work, while the
foot-pound is a gravitational unit of work. The erg is a
unit, the magnitude of which remains unchanged in what-
ever part of the universe it may be employed ; while the
foot-pound could be used nowhere except upon the surface
300 EXPERIMENTAL PHYSICS.
of the earth, and even then it would have different values
at different parts of the earth's surface.
SYSTEMS OF UNITS.
13O. The English System; the Ceiitimeter-gram-
second System. In the English System the foot is
taken as the unit of length, the pound as the unit of
mass, and the second as the unit of time, while in the
Centimeter-gram-second System (often written in the ab-
breviated form C.G.S. System), the centimeter is taken as
the unit of length, the gram as the unit of mass, and the
second as the unit of time.
The following list of units with their definitions is
important :
UNITS OF FORCE.
ENGLISH SYSTEM. C.G.S. SYSTEM.
Gravitation, Pound, Gram.
Absolute, Poundal, Dyne.
UNITS or WORK.
ENGLISH SYSTEM. C.G.S. SYSTEM.
Gravitation, Foot-pound, Gram-centimeter.
Absolute, Foot-poundal, Erg.
The gravitation unit of force, the pound, is the pull of
the earth upon a mass of one pound.
The absolute unit of force, the poundal, is that force
which, acting upon the pound-mass for one second, will
give it a velocity of one foot per second.
The gravitation unit of work, the foot-pound, is the
amount of work done in lifting the pound-mass one foot
high in opposition to the force of gravity ; or, what is the
SYSTEMS OF UNITS. 301
same thing, the foot-pound is the amount of work done in
overcoming the force of one pound through a distance of
one foot.
The absolute unit of work, the foot-poundal, is the
amount of work done in overcoming a resistance of one
poundal through a distance of one foot.
The gravitation unit of force, the gram, is the pull of
the earth upon a mass of one gram.
The absolute unit of force, the dyne, is that force
which, acting upon the gram-mass for one second, will
give it a velocity of one centimeter per second.
The gravitation unit of work, the gram-centimeter, is
the amount of work done in lifting the gram-mass one
centimeter high in opposition to the force of gravity ; or,
what is the same thing, the gram-centimeter is the amount
of work done in overcoming the force of one gram through
a distance of one centimeter.
The absolute unit of work, the erg, is the amount of
work done in overcoming a resistance of one dyne through
a distance of one centimeter.
131. Energy. Energy is the ability of doing work,
and is measured by the work done.
Thus, if a force of / dynes is overcome through a dis-
tance of s cm , the work done = fs ergs, fs is also the
measure of the energy expended.
-^ ,. mv
From (4) / = .
But * =
mv 1 mvat
302 EXPERIMENTAL THYSICS.
But at = v.
(5)
997?)
The quantity - - is denoted by the expression "the
Z
kinetic energy of the body." So we may say that the
kinetic energy of a body is found by multiplying the
mass of the body by the square of the velocity, and taking
half the product.
132. Conservation of Energy. A body raised above
the surface of the earth has potential energy, or energy of
position ; but when the body falls, it will perform just as
much work as was necessary to raise it. In the act of
falling, the body's potential energy will be changed into
kinetic energy, or energy of motion ; consequently what
the body loses in potential energy, it gains in kinetic.
On the instant of striking the ground, all the body's
potential energy has been changed into kinetic energy.
When the body was falling, the total amount of energy
it possessed, considering both potential and kinetic, was
no more, no less, but always the same. It is true that the
form of the energy was always changing, a greater and
greater quantity becoming kinetic at the expense of the
potential ; the sum total, however, of all the energy pos-
sessed by the body remained constant. This doctrine of
the preservation or indestructibility of energy, usually
called the conservation of energy, is of the greatest impor-
tance in physics. Just as water may exist in any one
of the forms, solid, liquid, or gaseous, and yet remain
water, just so may energy exist in various forms and still
THERMODYNAMICS. 303
remain energy. Heat, light, and sound are forms of
energy. When the falling body, about which we have
been speaking, strikes the ground, there is a change of
form of its kinetic energy: a part appears as heat, causing
an increase in the temperature of the body ; another part
produces vibrations of the air, which reach the ear as
sound, and if the body is of sufficient hardness, a flash of
light may be seen. The body may, too, throw up a little
earth when it strikes the ground, and also produce tremors
and vibrations in the ground where it falls, so the kinetic
energy which the body had in striking the ground has
been changed from the kinetic form into that of heat,
sound, etc.; but the sum of the amounts of energy in each
of the separate forms is equal to that in the kinetic form.
Though its form may change, energy itself is indestruc-
tible ; its amount in the universe is always the same.
THERMODYNAMICS.
133. Mechanical Equivalent of Heat. Whenever
one body is rubbed by ariother, heat results ; also whenever
a piece of metal is hammered, the metal grows hot. In
each of these cases mechanical action has been expended,
and heat has been a result. In brief, then, heat has been
a result of work. We have already become acquainted
with a unit, the calorie, with which to measure quantities
of heat, and also with the gram-centimeter, with which to
measure work. It will be the object of the present article
to give a concise account of the method of finding the
relation between the unit of heat and the unit of work ; in
other words, of finding how many gram-centimeters are
equivalent to one calorie.
304 EXPERIMENTAL PHYSICS.
The first precise numerical determination of this rela-
tion was made by Joule, in the following manner :
An upright cylindrical vessel is filled with water of a
known temperature. A vertical shaft stands in the vessel.
Extending from the sides of this shaft, in a horizontal
direction, are paddles, which, when the shaft is turned,
pass between stationary vanes projecting from the sides of
the vessel. The paddles and the vanes keep the water
thoroughly stirred when the shaft is turned. By means
of an arrangement of wheels and a flexible string, the
shaft is kept turning by a heavy body of known weight
attached to the end of the string, and allowed to descend
like a clock-weight.
As time goes on, and the water continues to be stirred,
the temperature of the water rises. At the end of the
experiment, the number of degrees through which the
temperature of the water has risen is noted; also the
distance through which the heavy body has fallen. After
making necessary corrections for friction, the weight of
the heavy body multiplied by the distance through which
it has descended gives the amount of work expended in
raising the temperature of the water. After making neces-
sary corrections for the loss of heat from the water, the
weight of the water multiplied by the number of degrees
through which its temperature has been raised gives the num-
ber of units of heat received by the water during the process
of stirring. By repeated experiment it has been found that
one calorie is equivalent to Jj,%,730 gram-centimeters.
Definition. The mechanical equivalent of heat denotes
the amount of mechanical energy which must be transmuted
into heat in order to yield one unit of heat.
THERMODYNAMICS. 305
134. The Steam Engine. Mechanical energy can be
transformed into heat; The process can be reversed ; that
is, heat can be transformed into mechanical energy. The
steam engine is a contrivance for transforming heat into
mechanical energy. Coal is burned on the grate beneath
a boiler containing water. A large amount of the heat is
wasted, but some of it vaporizes the water, turning it into
steam. This steam is conveyed to a cylinder, and is
alternately admitted automatically above and below a
piston which is pushed back and forth by the expansion
of the steam. A rod attached to the piston communicates
its motion to a wheel which is kept revolving as long as
the piston continues to move. By means of a belt, pass-
ing around this wheel, machinery can be kept in motion.
EXAMPLES.
1. Two men carry a weight of 152 Ibs. between them on a pole, rest-
ing on one shoulder of each ; the weight is three times as far from one
man as from the other. Find how many pounds each supports, the
weight of the pole being disregarded.
2. A man supports two weights slung on the ends of a stick 80 cm long
placed across his shoulder. If one weight be two-thirds of the other, find
the point of support, the weight of the stick being disregarded.
3. A man carries a bundle at the end of a stick over his shoulder. As
the portion of the stick between his shoulder and his hand is shortened,
show that the pressure on his shoulder is increased. Does this change
alter his pressure upon the ground ?
4. If the forces at the ends of the arms of a horizontal lever be 8 Ibs.
and 7 Ibs., and the arms 8 in. and 9 in. long respectively, find at what
point a force of 1 Ib. must be applied at right angles to the lever to keep
it at rest.
5. A uniform rod 3 ft. long and weighing 4 Ibs. has a weight of 2 Ibs.
placed at one end. Find the center of gravity of the system.
306 EXPERIMENTAL PHYSICS.
6. A heavy beam is made up of two uniform cylinders whose lengths
are as 3 is to 2, and whose weights are as 3 is to 5. Determine the posi-
tion of the center of gravity.
7. A door 10 ft. tall, 5 ft. wide, and weighing 100 Ibs. is attached to
a wall by one edge in an upright position at two points, the first 1 ft.
above the bottom, the other 1 ft. below the top. How great is the total
downward pull upon the wall at the two supporting points ? How great
is the horizontal force exerted upon the wall at each point, and is this
force a push or a pull ?
8. A uniform bar 10 ft. long leans with one end against a vertical wall
at an angle of 45; the other end rests upon the ground. The bar weighs
20 Ibs. There is no friction between the bar and the wall, so that the
force there exerted is entirely horizontal. How great is this force ?
9. A cord is fastened at each end, and a weight is suspended from it
at a certain point, where the cord bends at a right angle. The pull
exerted at one end of the cord is 3 pounds, and at the other end 4 pounds.
How heavy is the suspended weight ? (The weight of the cord is neglected.)
10. A balance has arms of unequal length, but the beam assumes the
horizontal position when both scale-pans are empty. Show that if the
two apparent weights of a body are observed when it Is placed first in one
pan and then in the other, the true weight will be found by multiplying
these together and taking the square root.
Solution. Let a and b denote the lengths of the arms of the balance,
and x the true weight of the body. If a weight, 101, must be put into the
pan attached to the arm whose length is a when the body is put into the
other to produce equilibrium, we have, by the principle of moments,
bx oi0i. (I)
If, when the body is transferred to the other pan, a weight, w%, must
be put into the pan which before contained the body to produce equi-
librium, we have
ax 6w> 2 . (2)
From (1) a _ x_
b wi
From (2) a _ w> 2
x =
EXAMPLES. 307
Hence, the true weight is equal to the square root of the product of
the apparent weights.
11. The arms of a balance are in the ratio of 19 to 20 ; the pan in
which the weights are placed is suspended from the longer arm. Find
the real weight of the body which apparently weighs 38 Ibs.
12. Two weights of 2 Ibs. and 5 Ibs. balance on a uniform heavy lever,
the arms being in the ratio of 2 to 1. Find the weight of the lever.
13. In a hydraulic (or hydrostatic) press the area of the small piston
face is 1 square inch and that of the large piston face is 50 square inches.
(a) If a force of 50 pounds is applied to the small piston, how great is
the force exerted upon the large piston, provided there be no friction ?
(6) How much work is done upon the small piston while it moves
6 inches, and how much is done at the same time upon the large piston ?
Name the unit in which the work is reckoned.
14. A trap-door of width 4 ft. and weight 8 Ibs. has a load of 16 Ibs.
applied to the edge remote from the hinge. s. How many foot-pounds of
work will be done in raising the trap-door till the edge remote from the
hinges is 2 ft. above the floor ?
15. A uniform plate of metal 10 cm square has a hole 3 cm square cut
out of it, the center of the hole being 2.5 cm distant from the center of the
plate. Find the position of the center of gravity of the plate.
16. A ladder, 30 ft. long and weighing 48 Ibs. , rests against a smooth
wall, with its foot 15 ft. from the bottom of the wall. Find the pressure
on the wall and on the ground, taking the center of gravity of the ladder
as one-third of its length up.
17. A stone is thrown vertically upwards with a velocity of 192 ft. a
second. Find how high it ascends, and how long it takes before returning
to the hand.
CHAPTER VII.
MAGNETISM.
135. Magnets. The object of the experiments in this
article will be to make clear the nature and the properties
of magnets.
Experiment 114. To find what happens on touching a
magnet to different kinds of substances.
Apparatus. A bar magnet ; bits of wood, paper, glass, and also
bits of iron and copper wire, or tacks.
Directions. Touch one end of the magnet to the
various substances, one after another-, with which you
have provided yourself.
What happens in each case ?
The effect which you observe on touching the magnet
to a bit of iron is called attraction, and we say that the
magnet attracts the bit of iron.
Experiment 115. To find whether the magnet will
attract a bit of iron without actually touching it.
Apparatus. A bar magnet and a bit of iron.
Directions. Make the end of the magnet approach the
iron very slowly.
Does the iron move before the magnet actually touches
it?
Does the magnet exert its influence through the air ?
POLES. 309
Experiment 116. To find whether the magnet will
attract a bit of iron when the end of the magnet is covered
with a piece of paper.
Apparatus. A bar magnet ; a bit of iron ; paper.
Directions. Wrap one end of the magnet in a piece
of paper.
Will the end thus wrapped attract the iron ?
Experiment 117. To find whether the attraction of the
magnet in the preceding experiment acted through the paper
or around it.
Apparatus. The same as in the preceding experiment.
Directions. Wrap the whole magnet in paper.
Will the magnet now attract the iron ?
Does the magnet exert its influence through the paper?
POLES.
136. North-Pointing- Pole; South-Pointing Pole.
In the next four experiments the poles, or parts of the
magnet where the attraction is strongest, will be found,
as well as the direction which the magnet will take when
suspended so that it can be free to turn.
Experiment 118. To find whether the magnet will
attract at the center of its length.
Apparatus. A bar magnet ; an iron tack.
Directions. Touch the central portion of the length
of the magnet to the tack.
Does the central portion of the magnet attract?
310 EXPERIMENTAL PHYSICS.
Experiment 119. To find at what parts of a magnet the
attraction is the strongest.
Apparatus. A bar magnet ; iron filings, fine and clean.
Directions. Lay the magnet on a sheet of paper.
Sprinkle iron filings over the magnet ; then grasping the
magnet in the middle, carefully raise it from the paper.
What portions of the magnet attract the strongest?
How does this experiment enable you to tell?
How many poles has the magnet with which you have
experimented ?
Experiment 12O. To find whether one end of the mag-
net will point north.
Apparatus. A bar magnet ; a piece of fine silk thread.
Directions. Tie one end of a piece of thread about 1
ft. long round the middle of the magnet. Tie the free end
of the thread to some support that will allow the magnet
to hang freely. The support must not be in the neighbor-
hood of any iron. Now adjust the loop round the magnet
so as to make the magnet hang in a horizontal position.
When the magnet is first hung up, the thread may twist
a little and set the magnet spinning. If the magnet spins
round two or three times, stop its motion with the hand,
or else the thread will become twisted the other way, and,
after a time, set the magnet spinning in the opposite direc-
tion, and thus cause loss of time.
When the magnet comes to rest, does one end point
towards the north?
If so, mark this end with a piece of chalk. Hang the
magnet up in a different part of the room, but not in the
neighborhood of any iron.
ATTRACTION AND REPULSION. 311
In each part of the room where you hang the magnet
up, does the marked end point north?
NOTE. In trying experiments with magnets, see that there are no
pieces of iron or other magnets, in the neighborhood of the place where
you are making the experiments ; iron weights, retort-stands, keys,
knives, etc., must be removed.
Experiment 121. To find whether one end of another
magnet will point north.
Apparatus. Another bar magnet ; a piece of fine silk thread.
Directions. Hang up the new magnet and repeat with
it Exp. 120.
What is the result?
If one end points north, mark this end with chalk.
In a magnet, the pole that points north is called the
north-pointing pole ; the pole that points south is called
the south-pointing pole. We shall write N-pointing pole
for north-pointing pole, and S-pointing pole for south-
pointing pole.
ATTRACTION AND REPULSION.
137. Attraction and Repulsion of Magnetic Poles.
We shall now try some experiments for the purpose of
getting a rule for predicting whether there will be attrac-
tions or repulsions when like poles of two magnets are
brought near each other ; also when unlike poles are
brought near each other.
Experiment 122. To find whether an N-pointing pole
will attract an N-pointing pole.
Apparatus. Two bar magnets.
312 EXPERIMENTAL PHYSICS.
Directions. Mark the N-pointing pole of each magnet
with chalk. Hang up one of the magnets as in Exp. 121.
When the magnet has come to rest, bring near its N-point-
ing pole the N-pointing pole of the other magnet.
What takes place ?
Experiment 123. To find whether an S-pointing pole
will attract an S-pointing pole.
Apparatus. The same as before.
Directions. Repeat Exp. 122, making use of the
S-pointing poles instead of the N-pointing poles.
What takes place?
Experiment 124. To find whether an N-pointing pole
will attract an S-pointing pole.
Apparatus. The same as before.
Directions. Repeat Exp. 122, but bring an N-pointing
pole near an S-pointing pole.
What is the result?
From the results of Exps. 122, 123, and 124, state a
rule for predicting what will take place when a pole of
one magnet is brought near the a pole of another magnet.
138. The Compass. In the construction of the com-
pass advantage has been taken of the fact that a bar
magnet, when suspended in a horizontal position, points
towards the north. A thin piece of steel that has been
hardened and magnetized is poised upon a fine point of
hard steel, such as the point of a needle. The thin piece
of magnetized steel, called a magnetic needle, will move
freely round on this point, but if left to itself, will always
METHOD OF MAKING A MAGNET. 313
come to rest with its poles pointing nearly north and
south. The magnetic needle is indispensable in naviga-
tion, as thereby it is possible to ascertain the direction of
the north pole of the earth, and, consequently, to direct
a vessel's course by the chart.
METHOD OF MAKING A MAGNET.
139. Natural Mag-nets ; Artificial Magnets. Besides
the artificial magnets which you have been using, there
are lodestones, or natural magnets, which have the same
properties that you have already observed in magnets.
The lodestone is an ore of iron, black and hard. This
ore of iron is called magnetite, and is found in Asia Minor,
Sweden, Arkansas, and in other parts of the world. The
purpose of the next experiment is to make a magnet.
Experiment 125. To find whether a magnet can be made
from a piece of steel.
Apparatus. A piece of watch spring about 8 cm long; a bar
magnet; a compass.
Directions. Heat the bit of watch spring in a flame
till it is just red hot. Take the spring from the flame and
let it cool. You will now be able to straighten the spring.
Heat the spring once more in the flame, and when it is
red hot, plunge it quickly into cold water. The bit of
steel is now hard and very brittle.
Stroke the bit of steel lengthwise with one pole of a
strong magnet. Always make the strokes from one end
of the steel, but never make back strokes. From time to
time turn the steel so as to stroke the other side. By
314 EXPERIMENTAL PHYSICS.
using the compass, find which end of the little magnet
you have made is the N-pointing pole. Keep this magnet
for the next experiment.
Experiment 126. To find, if a magnet be broken,
whether the parts into which it is broken are magnets.
Apparatus. The little magnet you made in the last experiment.
Directions. Break the magnet in the middle.
Is each part a magnet ?
By breaking the magnet thus, have we succeeded in
separating the. poles so that there is an N-pointing pole,
and an N-pointing pole only, on one of the pieces, and an
S-pointing pole, and an S-pointing pole only, on the other
piece ?
Carefully considering what you have learned about
magnets from the experiments you have performed, give
as good a definition as you can of a magnet.
MAGNETIC INDUCTION.
14O. Induced Magnetization. Whenever a magnet
by its action produces magnetization in a piece of metal,
this magnetization is called induced magnetization. The
following experiment will make clearer the meaning of
the term induced magnetization.
Experiment 127. To find what is meant by magnetic
induction.
Apparatus. A bar magnet ; a short cylinder of soft iron ; a small
iron tack.
MAGNETIC CURVES. 315
Directions. Touch the cylinder of soft iron to the tack.
Does the iron attract the tack?
Now put one end of the soft iron cylinder against one
end of the magnet, and holding the two together, touch
the other end of the soft iron cylinder to the tack.
Is the tack attracted?
Remove the magnet from the soft iron.
What does the tack do ?
Put a piece of paper between the end of the magnet
and the cylinder of soft iron.
Will the soft iron now attract the tack?
Does the piece of soft iron become a magnet while the
bar magnet is near it?
If the soft iron does become a magnet, can you say it
becomes a magnet by induction?
MAGNETIC CURVES.
141. Curves formed by Iron Filings about a Mag-
net. Whenever iron filings are sprinkled upon a magnet,
the filings arrange themselves in clusters at the poles of
the magnet, and if the magnet is lying on a table, the
filings, which fall upon the table in the neighborhood of
the magnet, unite in lines and assume the form of curves.
Experiment 128. To find the general form of the curves
of iron filings sprinkled near a magnet.
Apparatua A bar magnet ; iron filings ; a muslin bag ; a. sheet
of paper 20 cm square.
Directions. Lay the bar magnet on the table, and over
it lay the sheet of paper, which should be supported by
316 EXPERIMENTAL PHYSICS.
pieces of wood so as to make the surface level (meter
sticks are good for this purpose). Holding the muslin
bag filled with iron filings about a foot above the paper,
sift the iron filings over the paper. Tap the paper lightly
till the filings set themselves along lines. These lines are
called magnetic curves. Avoid getting too great a quan-
tity of filings on the paper. Sketch in your note-book
the outline of the magnet and the magnetic .curves.
Definition. The space through which the magnetic in-
fluence of a magnet extends is called the magnetic field of the
magnet.
142. Lines of Magnetic Force. The preceding ex-
periment helps us to see what is meant by the term
magnetic field. " This expression merely denotes the space
all round a magnet through which it is capable of exerting
an influence upon soft iron or upon other magnets. The
magnetic curves by which the magnetic field may be
mapped out represent, in the first place, ropes or chains
more or less continuous, into which the iron filings
arrange themselves when they are rendered free to turn
by the influence of tapping." The iron filings, in fact,
become little magnets by induction. Had we used, in-
stead of iron filings, a series of very small magnetic
needles free to move, these would have similarly arranged
themselves along the magnetic curves. These magnetic
curves are called lines of magnetic force.
Definition. A line of magnetic force is a line or path in
a magnetic field, such that if we walk along it with a little
magnetic needle suspended from our hand, this needle will
always point along the path.
MAGNETIC CURVES. 317
The earth is a huge magnet having its magnetic poles
comparatively near its geographical poles, but not coinci-
dent with them. The lines of magnetic force of the
earth's magnetic field curve round over the surface of the
earth from pole to pole and act on a freely suspended
magnet, that is, a magnet that can turn to the right or
left, also up or down, in such a manner that the magnet
turns till it lies as nearly as possible along one of these
lines.
Using a magnetic needle as suggested in the definition
of a line of magnetic force, we shall now take up some
experiments on tracing lines of magnetic force.
Experiment 129. To find the shape of the lines of
magnetic force about a bar magnet whose N-pointing pole is
turned towards theyiorth.
Apparatus. A bar magnet ; a small compass ; a sheet of paper
about 50 cm square ; seven copper tacks.
Directions. Fasten the sheet of paper on the table
with copper tacks, not with iron tacks, at each corner.
Remove all iron from the neigborhood. (Why?) Draw
a line extending across the paper and pointing north.
This is done by laying a meter stick on the paper, placing
the compass on the stick, and turning the stick till the
compass needle is parallel with the sides of the meter
stick. Then with a pencil draw a line beside the meter
stick. Lay the bar magnet on the middle portion of this
line with the N-pointing pole pointing north. Fasten the
magnet in place by sticking two tacks into the table on
one side, and a third tack on the opposite side, as shown
in Fig. 108. Mark the outline of the magnet on the
318 EXPERIMENTAL PHYSICS.
paper. Place the compass at point 1, Fig. 108, of the
magnet, and then move it away in the exact direction in
which the compass needle points. A good way to do this
is to make a dot on the paper just at the end of the
compass opposite the end of the needle that is turned
away from the N-pointing pole of the magnet. Then
move the compass till the end of the needle that is
next to the magnet is over this dot. Make a dot at
FIG. 108.
the other end of the needle on the paper, and continue
this process till the path reaches the edge of the paper or
returns to the magnet.
Trace upon the paper the lines thus followed by the
compass, putting arrowheads at several points to indicate
the direction in which the N-pointing pole of the compass
needle points at these places. Then place the compass a
little nearer the middle of the magnet (at 2), and starting
anew trace another line and mark it as before. Then,
beginning still farther (at 3) toward the middle of the
magnet, do as before. Finally, start not more than 3 cm
or 4 cm from the middle of the magnet and trace a line.
Trace an equal number of lines on the western side of
the magnet. There should be traced in all eight lines.
Paste the paper into your note-book.
MAGNETIC CUBVES.
/; <.
Experiment 13O. To find the shape of the lines of
magnetic force about a bar magnet whose N-pointing pole is
turned towards the south.
Apparatua The same as in the last experiment, with a fresh
sheet of paper.
Directions. Fasten the sheet of paper to the table.
Draw a line across it towards the north. Put the magnet
on the line and fasten the magnet with its N-pointing
pole pointing south. Draw an outline of the magnet on
the paper. Then use the compass and trace lines as before,
marking them all with arrowheads to indicate the direction
in which the N-pointing pole of the compass needle points.
Start from the same points of the magnet as in the last
experiment. Draw eight lines in all. Paste the paper
into your note-book.
Experiment 131. To find the shape of the lines of
magnetic force about two bar magnets placed side by side,
parallel, and with their N-pointing poles pointing north.
Apparatus. The same as in the last experiment, with an additional
magnet and a fresh sheet of paper and three more copper tacks.
Directions. Fasten the paper to the table ; draw the
line towards the north ; lay the two magnets parallel on
the paper (Fig. 109), the N-pointing poles pointing north
and about 15 cm apart, measured on an east and west line.
Trace the outline of each magnet. Proceed to trace the
lines of force as in the experiments already performed.
Start from the positions indicated by the figures in the
diagram. Trace the lines followed by the compass needle,
and paste the paper into your note-book. When you are
320
EXPERIMENTAL PHYSICS.
tracing the lines of force in the space between the magnets,
be careful not to move the compass from the field of one
magnet into that of the other.
Examine the three diagrams which you have made in
1 2 3 4
FIG. 109.
Exps. 129, 130, and 131, and then answer the following
questions :
Is there any case in which all the lines of force return
to the magnet?
Is there any case in which none of the lines of force
return to the magnet?
Is there any case in which some, but not all, of the
lines of force return to the magnet?
Can you account for the shape of the lines of force ?
SUGGESTION. Keep in mind that for certain positions of the magnet
the magnet's action and the earth's action upon the compass needle
oppose each other, while for other positions these actions assist each other.
MAGNETIC CUBVES.
321
In the case where you had the two magnets side by
side, were the curves between the magnets crowded more
closely together than the corresponding curves on the
outside ?
Did you find in the case of the two magnets a neutral
region, that is, a place where the compass needle could,
by a very slight variation of its position, be made to point
in an entirely new direction?
143. Theory of Magnetism. Keeping in mind what
our experiments in magnetism have taught, let us try to
frame a theory of magnetism. The. fact that lines of force
leave an ordinary bar magnet at its ends, and that they
also return to its ends, might lead us at first thought to
conclude that magnetism exists only at the ends of a
magnet ; but when we call to mind the fact that a magnet
may be broken into many pieces which have each an
N-pointing pole and an S-pointing pole of equal strength,
we infer that, could we continue this subdivision of the
magnet till its ultimate particles, or molecules, were
reached, each particle would be found to be a magnet
with an N-pointing pole and an S-pointing pole of equal
strength. When to make a magnet of a bar of steel we
stroke it with a magnet, we find that the magnet loses
none of its magnetism (it can lift as heavy a weight after
we have stroked the steel as before) ; so we look upon a
piece of unmagnetized steel as consisting of particles, each
a magnet in itself, but arranged in such a way as to
neutralize each other ; and we look upon the process of
magnetization as consisting in a rearrangement of the
particles, so that all the N-pointing poles shall be turned
322 EXPERIMENTAL PHYSICS.
in one direction, and all the S-pointing poles in the
opposite direction. In a bar magnet, then, the layers of
particles forming the ends would be the only particles the
magnetism of which is not completely neutralized by their
neighbors. The outer face of the layer of particles at one
end of the bar would have free N-pointing magnetism ;
the outer face of the layer at the other end, free S-pointing
magnetism.
144. Coercive Force ; Residual Magnetism. A piece
of hardened steel is more difficult to magnetize than a
piece of soft iron ; but, on the other hand, the piece of
steel retains its magnetism, while the soft iron quickly
loses all but a trace. These facts are explained by saying
that the particles composing the steel bar are difficult to
turn out of the positions which they have when the bar
is in its ordinary unmagnetized state ; but after the
bar has been magnetized, it is difficult for them to return
into their old positions, consequently, the bar of steel
remains magnetized. In the case of a bar of soft iron,
however, the particles composing it are easily turned out
of their positions ; but after the source of magnetization is
removed, these particles readily return very nearly to
their former positions, and all but a trace of magnetism
disappears. The power of resisting magnetization or
demagnetization is called coercive force, or better, reten-
tivity. Thus, hardened steel has great retentivity; soft
iron, little.
The trace of magnetism that remains in a piece of soft
iron, after its temporary magnetism has disappeared, is
called residual magnetism.
CHAPTER VIII.
ELECTRICITY.
145. Effects due to Electricity. We shall begin our
study of the subject of electricity with a few simple experi-
ments for the purpose of observing some of the effects due
to electricity. To produce the electricity, we shall use a
Bunsen cell. The Bunsen cell is a contrivance for obtain-
ing electricity ; it consists of the following parts :
(1) A glass jar (Fig. 110, 1), containing dilute sulphuric
acid 1 to a depth of a few inches.
(2) A hollow cylinder of zinc (Fig. 110, 2), to be placed
in the glass jar.
(3) A porous cup (Fig. 110, 3) of unglazed earthen-
ware, containing a mixture of sulphuric acid, water, and
bichromate of potash. 2
(4) A prism of carbon (Fig. 110, 4), to be placed in the
porous cup.
(5) Two brass clamps, not shown in the figure. One
of these clamps is fastened to the zinc cylinder, the other
to the end of the carbon prism.
The porous cup containing the liquid and the carbon, is
placed within the hollow of the zinc cylinder contained
in the glass jar. Fig. 110, 5, represents a section of the
cell when all the parts have been brought together and
1 Consisting of one part by weight of sulphuric acid and twelve parts
of water.
2 Consisting of eight parts by weight of water, two parts of sulphuric
acid, and one part of bichromate of potash.
324
EXPERIMENTAL PHYSICS.
arranged in the proper manner. The different parts
shown in the section of the cell can be easily distin-
guished by noting that the first, the upper, arrow touches
the glass jar, the second arrow touches the zinc, the third
arrow touches the porous cup, and the fourth arrow touches
1
FIG. no.
the carbon prism. The horizontal line marks the surfaces
of the liquids, which should be at the same level in both
the jar and the porous cup. Be careful not to spill any
of the acid upon the clothing or upon the table.
Experiment 132. To find whether electricity produces
a physiological effect.
Apparatus. A Bunsen cell ; two copper wires, each about 40 cm in
length, with ends brightly polished with sandpaper.
Directions. Attach one end of one wire to the clamp
fastened to the zinc ; there is a little hole in the top of
the clamp into which the end may be slipped and then
firmly fastened in place by means of a screw. In the
same manner attach the end of the other wire to the
clamp which is fastened to the carbon.
ELECTRICITY. 325
Touch the free end of one of the wires to the tip of the
tongue.
What is the sensation ?
Touch the end of the other wire to the tip of the
tongue, after removing the first wire from the tongue.
What is the sensation ?
Touch both wires to the tongue, so that the ends of the
wires are about l cm apart.
What is the sensation?
Which wire seems to cause the sensation ?
The sensation you have felt is called a " physiological
effect of the electric current." It is customary to speak
of electricity as flowing, and this flow of electricity is
called an electric current. Furthermore, the current is
spoken of as flowing from the carbon, through the wire
joining the carbon, to the zinc ; when the current reaches
the zinc, it flows through the liquids in the cell back to
the carbon again. This process goes on till the cell
becomes exhausted, by reason of some of the materials
which compose it becoming used up, or till the wire is
disconnected from either the zinc or the carbon. In the
experiment you have just performed the current flowed
through the tip of the tongue from one wire to the other.
Experiment 133. To find whether electricity can pro-
duce light.
Apparatus. Two Bunsen cells ; three pieces of copper wire, each
about 40 cm long ; a file.
Directions. By means of one of the wires join the
zinc of one cell to the carbon of the other. Join an end
of one of the remaining pieces of wire to the free clamp of
326 EXPERIMENTAL PHYSICS.
one cell, and an end of the other wire to the free clamp
of the other cell. To the end of either of the two wires
last mentioned attach the file, and rub the end of the
other wire along the file.
What do you see ?
NOTE. An arrangement of two or more cells is called a battery ; just
as in military science a battery of guns means an arrangement of two or
more guns.
Experiment 134. To find whether the electric current
can produce heat.
Apparatus. A Bunsen cell; a piece of iron wire, No. 30 B. & S.;
a piece of copper wire of the same size as the iron.
Directions. Twist one end of the iron wire round the
end of one of the copper wires leading from the cell ; then
move the end of the other copper wire leading from the
cell along the iron wire.
Does the iron wire grow warm ?
In place of the iron wire use the piece of copper wire.
Does the copper wire grow as warm as the iron wire ?
In the experiments on heat, which did you find to be
the better conductor of heat, iron or copper?
If a poor conductor of electricity is drawn out into a
wire it will be heated a good deal.
Hence, which is the better conductor of electricity, iron
or copper?
Experiment 135. To find what effect is produced on a
magnet ly an electric current in its neighborhood.
Apparatus. A Bunsen cell ; a small compass.
Directions. Join the ends of the wires leading from
the cell by twisting them together. Bring the loop of
ACTION OF CURRENTS ON MAGNETS. 327
wire thus formed close to the face of a compass. What
happens to the compass needle?
Does the electric current act in any way like a
magnet ?
146. The Measurement of the Strength of an Elec-
tric Current. In order to measure the strength of an
electric current, you might make use of any one of the
effects you have studied in Exps. 132, 133, 134, and 135,
thus :
(1) The greater the physiological effect, the stronger
the current.
(2) The greater the luminous effect, the stronger the
current.
(3) The greater the heating effect, the stronger the
current.
(4) The greater the magnetic effect, the stronger the
current.
For the purpose of measuring the strength of a current
of electricity it has been found best to make use of its
magnetic effect. Hence we shall make a careful study
of the magnetic effect of the electric current.
ACTION OF CURRENTS ON MAGNETS.
147. Magnetic Field produced by an Electric Cur-
rent. Whenever a current of electricity flows through
a conductor, a magnetic field is produced, by the current,
in the neighborhood of the conductor. It will be our
purpose to find out something about the lines of force
in a magnetic field which is produced in this way.
328 EXPERIMENTAL PHYSICS.
Experiment 136. To find the shape of the lines of force
when a magnetic field is produced in the neighorhood of a
conductor by a current of electricity flowing through.
Apparatus. Two Bun sen cells ; a stout copper wire ; a piece of
cardboard about 20 cm square ; fine iron filings ; pieces of copper wire
for connecting the cells.
Directions. Join the zinc of one cell to the carbon of
the other by a piece of wire. Pierce the cardboard at its
center with a hole large enough for the stout wire to pass
through. Place the cardboard in a horizontal position
with the stout wire protruding vertically through the hole
both above and below. To one end of this stout wire
join, by means of a piece of wire, the free carbon, and to
the other end of the stout wire, also by means of a piece
of wire, join the free zinc. A current is now flowing
through the stout copper wire. Sprinkle on the card-
board a few iron filings, and gently tap the cardboard.
In what form do the filings arrange themselves on the
cardboard ?
What is the form of the lines of force in the magnetic
field surrounding the conductor?
Experiment 137. To find the relation between the
direction of the electric current and the direction in which a
compass needle points, when placed in the neighborhood of
the current.
Apparatus. A Bunsen cell ; a compass ; a piece of copper wire
2 m or 3 m long ; two connecting cups ; five copper tacks.
Directions. Bend the piece of wire into the form of a
square (Fig. Ill), and have the ends of the wire project
ACTION OF CURRENTS ON MAGNETS. 329
5 cm or 10 cm from the corner of the square. Place this
square on the table so that two sides shall run east and
west, and the other two north and south. You can make
sure that the square is placed correctly by means of a
compass, adjusting the square till the sides that are to run
north and south are parallel to the needle. Join (Fig. Ill),
by means of connecting cups, the ends of the wire forming
the square to the ends of the wires from the cell. Be care-
ful to scrape the insulating material from the ends of the
wires, in order to get good contact. Fasten the corners
of the square to the table with cop-
per tacks. The figure represents
the arrangement. The arrowheads
denote the direction in which the
current flows in going from the
carbon of the cell through the wire
back to the zinc of the cell. Call
the side of the square through which the current, on its
way from the carbon to the zinc, flows east, E, that in
which it flows west, W, etc.
Draw in your note-book a diagram similar to the figure.
Now place the compass on the wire at the middle of the
side E, and indicate, by drawing a straight line through
the middle point of the line E in your note-book, the
general direction in which the N-pointing pole of the
compass needle turns. At one end of this line put an
arrowhead, to show which end represents the N-pointing
pole of the needle.
Now draw another diagram in your note-book just like
the one you have already drawn. Lift the wire a little
way on the side E, without detaching it from its fasten-
330 EXPERIMENTAL PHYSICS.
ings, and slip the compass underneath the middle of the
side JE. In the new diagram, by drawing a line as before,
indicate the direction in which the needle points. Do the
same thing with each of the sides $ W, and JV, marking
in one diagram the position of the needle when placed
above the middle point of each side, and in the other
diagram the position of the needle when the compass is
placed beneath the middle point of each side.
QUESTIONS.
By referring to your diagrams, answer the following questions :
1. A wire is stretched north and south, and a current runs from south
to north in the wire ; if a compass is placed above the wire, will the
N-pointing pole of the needle be on the east or on the west side of the
wire ?
2. Suppose the conditions mentioned in 1 remain the same in all
respects, except that the compass is placed under the wire ; on which side
(east or west) will the N-pointing pole of the needle lie ?
3. Suppose all the conditions mentioned in 1 remain unchanged,
except that the current flows from north to south ; what will be the posi-
tion of the N-pointing pole of the needle ?
4. If in the last question the compass had been placed under the wire,
everything else remaining the same as before, what position would the
N-pointing pole of the needle have taken ?
5. In a wire stretched east and west a strong current of electricity
flows from east to west ; if a compass is placed above the wire, will the
N-pointing pole turn to the north or to the south side of the wire ?
6. Suppose all the conditions of 5 remain unchanged, except that the
compass is placed underneath the wire ; what position does the N-pointing
pole of the needle take ?
7. Suppose all the conditions mentioned in 5 remain unchanged,
except that the current flows from west to east ; in what position will
the N-pointing pole of the compass needle point ?
8. Suppose all the conditions mentioned in 7 remain unchanged,
except that the compass is placed below the wire ; what position will the
N-pointing pole of the needle now take ?
LINES OF FORCE ABOUT A COIL. 331
148. Rule for Direction of Deflection of Magnetic
Needle by Electric Current. A line of force is said to
have the direction in which the N-pointing pole of a com-
pass needle points, when placed on the line of force ;
bearing this in mind, answer the following question :
If you look along the wire in the direction in which
the current flows, will the lines of force run round the
wire in the same direction as the hands of a clock move?
Your answer to this question gives the rule for finding
the direction of deflection of a magnetic needle by an
electric current.
LINES OF FORCE ABOUT A COIL.
Experiment 138. To find the positions of the lines of
force surrounding a conductor which consists of a coil of wire.
Apparatus. A wooden ring, round which is wound 15 turns of
insulated copper wire, mounted on a base (this wire is wound with
cotton or silk to keep the electricity from going across from one spire
to the next ; a wire thus covered is called insulated wire) ; a Bunsen
cell ; a compass ; a meter stick.
Directions. To each of the outer binding posts join a
wire from the cell (Fig. 112). By counting the coils of
wire you can assure yourself that there are 15 turns on the
wooden ring, and by carefully examining the apparatus you
will see that there are 15 turns of wire " in circuit," which
is a brief form of saying that all these 15 turns of wire are
traversed by the current. Place the ring so that the plane
of its coil shall be east and west, and so that the current
shall flow from east to west through the wires on the top
of the circle. To find whether the current is flowing in
332 EXPERIMENTAL PHYSICS.
the way described, place the compass on the top of the
circle, observe the position of the needle, and refer to the
rule about the deflection of a magnetic needle which you
were asked to state. On the cross-piece place a meter
stick with its center on that of the cross-piece, and have
the meter stick at right angles to the plane of the coil.
Support the ends of the meter stick by
means of blocks to keep the stick steady.
The stick should be pointing north and
south. On the meter stick place the
compass 10 cm south of the center of the
coil, and record in a diagram, by means
of a straight line, the direction in which
the needle points. Now move the com-
pass north along the meter stick 5 cm ; record as before the
position of the needle. Then move the compass 5 cm north
to the center of the coil ; record. Again move the compass
5 cm north ; record. Finally, move the compass 5 cm north
from the last stopping-place, and record the position of
the needle.
Place the compass within the coil, but close to its east-
ern side. Record, by means of a diagram, the direction
of the needle. Then place the compass in turn north,
east, and south of this portion of the coil (and all the time
close to it), recording the direction in which the needle
points for each position of the compass. Carrying the
compass round the western side of the coil, make and
record similar observations. Fig. 113 may help to make
the meaning of this paragraph clearer. The shade lines
represent the part around which the compass is carried ;
the circles, the positions of the compass.
o + o
o o
CHEMICAL ACTION IN THE CELL. 333
Now reverse the current in the coil. This is done by
changing the connections with the cell, putting the wire
attached to the zinc in the binding post that before held
the wire from the carbon, and the wire from the carbon
into the binding post that
before held the wire from the
zinc. Repeat all the opera-
tions described in the preced-
ing part of this experiment, (j|[) Cj J
and make new diagrams.
Compare the diagrams ob-
tained by moving the compass
/ FIG. 113.
round the east and west sides
of the coil with those obtained in Exp. 131 in magnetism,
when the two magnets were placed parallel to each other.
In this comparison, point out the differences and the like-
nesses in the arrangement of the lines of force about the
magnets and about the coil.
In this experiment, have you noticed anything in the
course of your work that would make it appear as if the
coil acted as a magnet, having one pole at one face of
the coil and the other pole at the other face ?
CHEMICAL ACTION IN THE CELL.
149. Study of the Action that takes Place in the Cell.
As we have now studied some of the effects of electricity,
we are in a better position to study the action that goes
on in the cell. In beginning the study of the cell, we
shall take the simplest form, not the complicated arrange-
ment that we have been using.
334 EXPERIMENTAL PHYSICS.
Experiment 139. To find what action dilute sulphuric
acid has upon a strip of zinc and upon a strip of copper
placed in it.
Apparatus. A small glass tumbler ; a strip of sheet zinc and a
strip of sheet copper, each about 10 cm long and 1.5 cm wide, and each
having about 50 cm of insulated copper wire (size about No. 20 B. & S.)
soldered to one end.
Directions. At the sink, fill the tumbler to within l cm
of its top with dilute sulphuric acid (1 part by volume of
acid to 20 parts by volume of water). Do not let any of
the acid fall upon the floor, table, or clothing. Put into
the tumbler, close to one side, the
strip of clean zinc, and close to
the other side the similar strip of
copper; each strip should rest on
the bottom of the tumbler, and
the upper end of each should be
Fio j bent so as ,to clasp the edge of
the tumbler, as shown in Fig.
114. Now observe for about a minute what happens at
the surface of each strip, taking care that the strips do not
touch each other.
What happens at the surface of each strip ?
Experiment 14O. To find what happens when a strip-
of zinc and a strip of copper, plunged into dilute sulphuric
acid, are joined by a piece of copper wire.
Apparatus. The same as in the preceding experiment; also a
compass and a coil mounted on a base as shown in Fig. 112; mercury.
Directions. Having the tumbler, plates, and acid
arranged as in the last experiment, put the two strips into
metallic connection, by attaching their wires to the ends
CHEMICAL ACTION IN THE CELL. 335
of the 15-turn coil. Before the wires are attached, how-
ever, the compass should be placed on the center of the
shelf running across the coil, and the coil turned round
till the needle of the compass lies in the plane of the coil.
The little instrument thus arranged, consisting of the
compass and the coil, is called a galvanoscope. It enables
us to detect the presence of an electric current; for, as
we already know, if a current flows through the coil, the
needle is deflected from its natural position ; if the current
is strong, the needle will be deflected a good deal ; if the
current is weak, the needle will be deflected only a little.
Whenever the galvanoscope is used, it must be placed in a
position to make its coil lie in the magnetic meridian; that
is, the needle of the compass on the little shelf running
through the center of the cx)il must lie in the plane of the
coil. After the galvanoscope has been placed in position, on
no account must its position be changed till the experiment is
completed.
Observe for a short time what happens at the surface of
each of the strips in the acid.
Do any bubbles form and rise ? Do more rise from one
strip than from the other?
Observe, too, the behavior of the galvanoscope needle.
After tapping the instrument lightly to make sure that
the needle has not through friction on the pivot come to
rest in the wrong position, record the number of degrees
through which the tip of the needle has turned.
Disconnect the zinc strip, and plunge into mercury that
part only which has been under the acid. Then, after
wiping from the zinc any loose drops of mercury, replace
it in the acid.
336 EXPERIMENTAL PHYSICS.
What happens now at the surface of the zinc ?
Now connect, as before, with the galvanoscope.
What happens at the surface of the zinc ?
Be careful that the two strips are as far apart and
immersed to the same depth as before.
What position does the galvanoscope needle take ?
What happens at the surface of the copper strip ?
Experiment 141. To find whether the strength of the
current from the single-fluid cell changes as time goes on.
Apparatus. The same as in the last experiment.
Directions. Wipe the plates dry and clean. Then
put them into the liquid and immediately get the reading
of the galvanoscope, that is, the number of degrees through
which the N-pointing pole of the needle is deflected.
Readings should then be taken every two minutes for a
period of ten minutes. If at the end of ten minutes there
are any bubbles on either of the strips or on both, rub off
these bubbles with a bit of wood without removing the
strips from the acid, talcing care to have no mercury come in
contact with the copper. Record the position of the needle
in every case.
Finally, try the effect of amalgamating (covering with
mercury) the copper ; the zinc has been amalgamated.
How do you account for the position of the needle ?
15O. Discussion of the Chemical Action that takes
Place in the Cell. Chemists teach that a molecule of sul-
phuric acid consists of two parts of hydrogen (the bubbles
that you saw rising from the zinc before the circuit was
closed were bubbles of hydrogen), one part of sulphur,
CHEMICAL ACTION IN THE CELL. SB 7
and four parts of oxygen. When this molecule of sul-
phuric acid comes in contact, under proper conditions,
with zinc, chemical action takes place and the two parts
of hydrogen in the molecule are pushed or crowded out
by one part of zinc, and the hydrogen passes off in the
form of bubbles, while the compound formed with the zinc
remains behind ; this compound is called zinc sulphate.
151. The Reason for Amalgamating the Zinc. If
the zinc is acted upon by the acid when the battery is
not in use, a waste of zinc takes place ; pure zinc, when
placed in sulphuric acid, is but little affected. Pure zinc,
however, is expensive, so we use impure, but amalga-
mated, zinc. Impure zinc when amalgamated behaves in
sulphuric acid much like pure zinc; the mercury dissolves
the zinc, leaving the impurities unchanged, thus spread-
ing a coating of pure zinc over the surface of the plate.
Under ordinary circumstances, sulphuric acid acts but
slightly upon copper. Any action seen at the surface of
the copper strip in Exp. 140, even when the circuit was
closed, was due to hydrogen bubbles, set free by a chem-
ical action that did not affect the copper.
152. Polarization of the Cell. The weakening of the
current of a single-fluid cell after the circuit is closed,
and the recovery of strength by the current when
the plates are thoroughly rubbed, are phenomena that
demand our attention. This weakening of the current is
evidently not due to an exhaustion of the fluids in the
cell, but rather to the condition produced at the surface
of one or both of the metallic strips by the action of the
cell. In fact, the weakening of the current is due to
338 EXPERIMENTAL PHYSICS.
the deposition of bubbles of hydrogen upon the plate of
copper ; for when the bubbles are removed, the strength
of the current returns. This deposition of hydrogen
bubbles upon the copper plate is called polarization of
the cell. The coating of hydrogen bubbles upon the plate
acts in two ways to weaken the current :
(1) Since the hydrogen is a poor conductor of elec-
tricity, it opposes the flow of the current ;
. (2) When the copper strip is covered with a film of
hydrogen, we have practically a plate of hydrogen exposed
to the action of the acid; the result is the starting of a
current in the opposite direction, that tends to neutralize
the first, which flows in the cell from the zinc to the
copper. The more the copper plate gets covered with
the hydrogen bubbles, the stronger does this neutralizing
tendency become, until the first current is overpowered ;
then the galvanoscope indicates no current in either direc-
tion.
In order to avoid the formation of hydrogen bubbles
upon the copper plate, use is made of the two-fluid cell.
In this cell the copper plate is immersed in a liquid
which does not allow hydrogen to reach the copper plate.
Just how this is done will become clearer after perform-
ing the following experiment with a two-fluid cell.
Experiment 142. To find what action goes on in the
two-fluid cell.
Apparatus. A large tumbler ; a small porous cup that will sit
easily into the tumbler ; a piece of zinc 10 cm long, 2.5 cm wide, 0.4 cm
thick, with a piece of copper wire 40 cm long soldered to it ; a piece of
sheet copper 10 cm square, with a copper wire 40 cm long like that of
CHEMICAL ACTION IN THE CELL. 339
the zinc ; a galvanoscope ; dilute sulphuric acid (one part by volume
of acid to twenty parts by volume of water); a saturated solution of
sulphate of copper ; mercury.
Directions. Put the zinc into the porous cup, and then
fill this cup with diluted sulphuric acid to within 2 cm of
its top. Put the cup containing the zinc and acid into
the tumbler, and then pour into the tumbler sulphate of
copper solution till this liquid stands as high in the tum-
bler as the acid stands in the porous cup. Then remove
the zinc from the acid. The zinc is now in a condition to
be amalgamated, which should be done by dipping it into
the mercury. After amalgamation, wipe the zinc to re-
move loose drops of mercury (do this over an iron pan to
save the mercury), and then weigh the amalgamated zinc
to O.l gm . Wash, dry, and then weigh with equal accuracy
the copper sheet. Bend the copper plate somewhat so
that it may partly encircle the porous cup, and put the
plate thus bent into the sulphate of copper in the tum-
bler. Replace the zinc in the porous cup. You already
know that if one wire from a cell is joined to one of the
outside posts of the galvanoscope and the other wire from
the cell to the other outside binding-post, then the current
from the cell will flow through 15 turns of the galvano-
scope coil. On the other hand, if one of the wires from
the cell is joined to the middle post and the other wire
to one of the outside posts, the current from the cell will
flow through 5 or 10 turns of the galvanoscope coil, ac-
cording to which of the outer posts the wire is attached to.
Join the cell to the galvanoscope so that the current shall
flow through the 5-turn section. As soon as the needle
comes to rest (before reading the instrument, it should be
340 EXPERIMENTAL PHYSICS.
lightly tapped so that the needle may disengage itself if
caught by friction on the pivot), record its position, stat-
ing how many degrees it is deflected from the magnetic
meridian, and also whether this deflection is towards the
east or towards the west. Readings should be taken and
recorded at 5-minute periods for half an hour. Then dis-
connect the cell, remove both the zinc and the copper,
rinse each gently, taking care not to remove any deposit
that may have formed ; and then, without rubbing, dry
the plates, and weigh them again.
What has been the gain or loss in weight for each
plate?
From an inspection of the record of the galvanoscope
readings, should you say that the current had become
and remained constant soon after the beginning of the
experiment?
At the beginning of the experiment the walls of the
porous cup are often not thoroughly wet. After a little
while, however, the liquids soak in and the walls become
moist. The current flows more easily through a substance
thoroughly wet than through the same substance when
only moist.
NOTE. This two-fluid cell with which you have experimented is
called, from the name of its inventor, the Daniell cell.
153. Chemical Action in the Two-Fluid Cell. With-
in the porous cup, in Exp. 142, the zinc pushes out the
hydrogen in the sulphuric acid and takes its place.
The hydrogen thus set free does not appear in the form
of bubbles, but in the part of the cell outside the porous
cup, it pushes out the copper of the copper sulphate
CHEMICAL ACTION IN THE CELL. 341
(copper sulphate consists of 1 part of copper, 1 of sul-
phur, and 4 of oxygen). The copper freed in this manner
is deposited upon the copper plate. Instead of hydrogen
being deposited upon the copper plate, copper is depo-
sited and polarization is prevented. The cell gives a
steady current till the materials (generally the copper
sulphate) of the cell become exhausted. The Bunsen 1
cell is a two-fluid cell.
154. The Ampere. Exp. 142 gives a means of under-
standing clearly what is meant by the ampere, the unit of
current strength.
Definition. An ampere is a current of such strength as
to set free from its chemical combinations 0-0003281 of a
gram of copper in one second.
The usual strength of current for an arc-lamp is about
10 amperes.
Turn back to your record of Exp. 142, and with the data
there furnished, compute the weight in grams of copper set
free (that is, deposited on the copper plate) from the sul-
phate of copper solution in one second by the current.
If a current of one ampere sets free in one second
0.0003281 8 f copper from its chemical combinations, what
was the average strength in amperes of the current pass-
ing through your Daniell cell during the half-hour test?
155. The Commutator; the Rheostat. In the next
experiment you will have occasion to use two pieces
1 It is better to call the cell you used in the first experiments in elec-
tricity the Poggendorff cell. The true Bunsen cell has nitric acid in the
porous cup instead of the mixture of water, sulphuric acid, and bichro-
mate of potash which you used.
342 EXPERIMENTAL PHYSICS.
of apparatus, a description of which is here given for
convenience.
Hitherto, when you wished to change the direction of
a current through a conductor (the galvanoscope coil, for
instance), the ends of the wires from the cell were inter-
changed at the ends of the conductor. This changing of
connections was troublesome and took time. To effect
this change quickly and conveniently, a piece of apparatus
called a commutator has been contrived.
The commutator (Fig. 115) consists of a block of wood
in one side of which four holes, called cups, are made.
There are four binding-posts screwed
into tlie sides of the block, one enter-
ing each cup. The cups are partly
filled with mercury. There are also
two wires passing through a disc of
wood and bent at the ends, by means
of which the cups can be connected in
no. 115. pairs>
The cell must always be joined to a pair of opposite
binding-posts, and the galvanoscope wires must be joined
to the other pair of binding-posts.
If the set of movable wires, carried by the wooden disc,
dip into the cups, the current flows from the cell through
the galvanoscope. If the disc is raised, given a quarter
turn and then lowered, the current will flow in the op-
posite direction through the galvanoscope.
The rheostat, shown in the upper part of Fig. 116, con-
sists of a frame made by attaching an upright at each end
of a piece of plank about a meter long, and joining the
upper ends of these uprights by a meter stick parallel to
ELECTRICAL RESISTANCE. 343
the plank. On one of the uprights are placed four hori-
zontal rows of binding-posts. Each row consists of two
posts. On the other upright, near its lower end, is placed
a horizontal row of two binding-posts. Between the two
uprights is stretched a piece of No. 30 German silver
wire, held in place at its ends by the binding-posts which
are nearest the plank and are placed nearest the inside
edge of each upright. Another piece of No. 30 German
silver wire is fastened to the outer binding-post of the
lowest row. This wire is then carried round the outer
edge of the upright and brought to the other upright
round whose outer edge it is carried and fastened to the
binding-post nearest this edge. Another piece of No. 30
German silver wire is fastened to one of the binding-posts
in the next row above, is carried once round the supports,
and fastened at its end to the other binding-post of the
pair. The same thing is done for the next pair of posts,
only a No. 28 German silver wire is used. Finally, round
the upper part of the rack are wrapped 20 m of silk-cov-
ered, No. 30, copper wire ; an end of this wire terminates
at each of the upper pair of binding-posts.
ELECTRICAL RESISTANCE.
156. Electrical Resistance of Wires. When water
runs through a pipe, the friction between the walls of
the pipe and the flowing water resists the flow. The
current of water is not so strong as it would be were
the impeding effect of friction removed. The resistance
to a flow of water in two pipes of the same diameter, but
of unequal lengths, is greater in the longer pipe. On
344 EXPERIMENTAL PHYSICS.
the other hand, in two pipes of the same length, but of un-
equal diameters, the resistance is greater in the smaller.
Thus, just as a pipe through which water runs offers
to the flow a resistance, which depends upon the size and
length of a pipe, so a wire offers resistance to the flow of
electricity. It will be the object of the next two experi-
ments to find, if possible, some relation between the length
of the wire and the amount of resistance (Exp. 143); also
between the area of cross-section of the wire and the
amount of resistance (Exp. 144).
Experiment 143. To find what effect the length of a
wire has upon its resistance to the flow of an electric current.
Apparatus. A Daniell cell ; a rheostat ; a commutator ; a gal-
vanoscope ; an " English " binding-post.
Directions. By means of a bit of copper wire connect
the pair of binding-posts at the bottom of the left-hand
upright (Fig. 116) ; thus the two pieces of German silver
wire attached to these binding-posts are united. Then
arrange the apparatus, as shown in Fig. 116. The lower
part of this figure is supposed to join the upper part at
the line AB. The current is made to run through 15
turns of the galvanoscope. By means of the commutator
the current can be easily and quickly reversed through
the galvanoscope. Before beginning the experiment, the
porous cup should have been soaked through by the acid.
This can best be done by pouring the acid into the porous
cup a few minutes before the cup is put into the sulphate
of copper solution. As the rheostat is now arranged, the
current is flowing through 2 m of German silver wire (the
resistance of the short piece of copper wire you inserted
ELECTRICAL RESISTANCE.
345
between the two binding-posts may be neglected). Read
and record the position of the compass needle, which
should be placed at the center of the shelf ; the coil
itself, before the current is allowed to flow through,
should be placed nearly in the magnetic meridian. Now,
by means of the commutator, reverse the current through
FIG. 116.
the galvanoscope, and again record the reading. Take the
average of the two deflections. For example, suppose
the N-pointing end of the needle to have come to rest at
42 east of north before the reversal of the current, and
at 38 west of north after the reversal, the average, or 40,
should be taken as the true deflection. This method of
reversal and averages renders it unnecessary to place the
coil accurately in the magnetic meridian. (Why?)
Now remove the bit of copper wire which you inserted
to connect the two pieces of German silver wire. Con-
nect these same two German silver wires by means of '
the English binding-post, which should be placed directly
346
EXPERIMENTAL PHYSICS.
beneath the 90 cm mark on the meter stick. The current
will now pass through 180 cm of the wire.
Read the galvanoscope, which, when you have once
begun the experiment, you must not disturb till the
experiment is completed. Reverse the current, and read
again. Shift the English binding-post to a position under
the 80 cm mark of the meter stick, so that now the current
will flow through 160 cm of the wire. Read the galvan-
oscope ; reverse the current, and read the galvanoscope
again. By shifting the English binding-post, make the
current flow in turn through 140 cm , 120 cm , 100 cm , 80 cm ,
and 60 cm of the wire. For every change in position of
the English binding-post, read the galvanoscope, reverse
the current, and read the galvanoscope again. To make
sure that the strength of the cell has not changed during
this series of observations, take off the English binding-post
and insert, as you did at the start, the bit of copper wire,
so that the current may flow through the 2 m of the wire.
Read and reverse as before. If the strength of the cell is
the same as at the start, the average deflection just obtained
will be the same as the average deflection obtained at the
beginning of the experiment.
A convenient form in which to enter the measurements
in your note-book is the following :
cin.
200
180
160
140
120
100
80
60
200
EAST
o
o
o
o
o
WEST
AVERAGE
ELECTKICAL RESISTANCE. 347
From an inspection of your measurements, can you see
any indication of what change in the resistance of a wire
an alteration in its length makes ; that is, does a long wire
offer more or less resistance than a short wire of the same
thickness ?
From the measurements you have made, the exact law
stating the dependence of resistance upon the length of
wire cannot be inferred. The following is a statement of
the law :
The resistance of a wire varies directly as its length.
QUESTION. If there are two wires of the same thickness and material,
but one twice as long as the other, how many times as much resistance
will the longer wire have than the shorter ?
Experiment 144. To find what influence the area of
cross-section of a wire has upon its resistance to the flow of
an electric current. 1
Apparatus. The same as in the preceding experiment, without
the English binding-post.
Directions. Arrange the apparatus as in the preceding
experiment, only shift the wires leading from the apparatus
to the rheostat from the lower pair of binding-posts to the
second pair above, thus putting in continuous circuit with
the galvanoscope the 2 m of No. 28 German silver wire.
This experiment is a very brief one. Simply read the
galvanoscope, reverse the current, read again, and record.
Compare the average deflection thus obtained with the
1 If this experiment is not performed on the same day as the preceding
experiment, it will be necessary to take some of the measurements of that
experiment over again to make sure that the cell has undergone no
change in strength.
348 EXPERIMENTAL PHYSICS.
deflections obtained with various lengths of No. 30 German
silver wire in the last experiment.
What length of No. 30 is equivalent in resistance to
2 m of No. 28 ?
The area of cross-section of No. 28 wire is about 1.46
times that of No. ,30 ; so if we call the area of the cross-
section of No. 30, 1, that of No. 28 will be 1.46.
Divide the length of No. 28 wire (2 m ) by 1.46.
Divide the length of No. 30 wire (of equal resistance)
by 1.
Are the two quotients equal or nearly equal ?
What relation should you infer exists between the area
of cross-section of a wire and its resistance ?
157. Divided Circuit. Suppose a branch pipe springs
from the side of a main pipe and joins the main pipe
again at some distance from the starting-point, the branch
thus forming a loop with the main pipe. If water flows
along the main pipe, the circuit of water divides when it
reaches the point of branching, one part continuing in the
main pipe, the other turning aside into the branch, through
which it flows till it re-unites with the current in the main
pipe. Each part of the loop, the main pipe and the branch,
offers resistance to the flow of water ; but the combined
resistance of both parts of the loop is less than that offered
by either alone, so that by both branches of the loop taken
together less resistance is offered to the flow than by an
equal length of the main pipe. In place of a simple loop
of two branches we might insert one or more additional
branch pipes, and thus* have a loop of three branches or
more. The current would then divide itself among all
ELECTRICAL RESISTANCE.
349
these branches. Just as a current of water divides in
branched pipes, so a current of electricity divides in a
branched or divided circuit, consisting of two or more
wires all springing from the same point and all coming
together again at another point. The current of electricity
on entering this system of wires at one of these two meet-
ing-points divides itself into smaller currents among the
wires, each smaller current flowing along its wire till it
is reunited at the other junction with the other smaller
currents. The next experiment has for its object the study
of resistance in a divided circuit.
Experiment 145. To find how the resistance of a
divided circuit consisting of one loop compares with the
resistance of half the loop.
Apparatus. The same as in the last experiment.
Directions. Connect the two pieces of German silver
wire that have already been used on the rheostat by a bit
of copper wire as before. Then join
this united wire with the other 2 m of
No. 30 German silver wire in " mul-
tiple arc " circuit ; that is, join in
divided circuit in such a way that
part of the current will go through
one of the 2 m pieces of wire, the other
part of the current through
" the other 2 m pieces of wire
. as shown in Fig. 117.
Read the galvanoscope, re-
verse, and read the galvanoscope again ; record.
By reference to the record of Exp. 143, what length of
350 EXPERIMENTAL PHYSICS.
No. 30 German silver wire, as used in that experiment,
has a resistance equal to that of the two 2-meter pieces of
No. 30 German silver wire joined in multiple arc as in the
present experiment?
What part, then, of the resistance of a single 2-meter
piece of No. 30 wire is the resistance of two 2-meter pieces
of No. 30 wire joined in multiple arc ?
158. The Ohm. In order to measure resistances, a
unit of resistance, called the ohm, has been established.
Definition. The resistance equal to that offered by a
column of mercury of uniform cross-section, at 0, 106.3 CI *
long and of mass 14-.^521 & ', is called the ohm.
Copper is a much better conductor of electricity than
mercury is. A copper wire whose area of cross-section is
I 8qmm would have to be about 45 m long in order to have a
resistance of one ohm. Among metals German silver has
a high resistance, and its resistance varies only slightly
with the temperature. For these reasons German silver
wire is employed in the construction of resistance coils,
which are introduced frequently into electrical circuits to
modify the strength of the current.
Experiment 146. To find what length of Grerman silver
wire is equivalent in resistance to 20 m of copper wire. 1
Apparatus. The same as in the preceding experiment.
Directions. Put the 20 m of copper wire, No. 30, into
continuous circuit with the galvanoscope. Read the gal-
vanoscope, reverse the circuit, and read again ; record.
1 See note at bottom of page 347.
ELECTRICAL RESISTANCE. 351
Compare the average deflection obtained with those
obtained in Exp. 143, and so find the length of German
silver wire equivalent to that of the copper. Record.
EXAMPLES.
1. If a wire l m long has a resistance of 1 ohm, what will be the
resistance of a wire of the same material and of the same thickness 2 m
long ? 10 m long ? 0.5 m long ?
2. If a wire of Isqmm area of cross-section has a resistance of 1 ohm,
what will be the resistance of a wire of the same material and length, but
of 0.5 8< i mm cross-section ? 2 8< i mm area of cross-section ? 10 8 i mm area of
cross-section ?
3. If a wire l m long and I 8( i mm area of cross-section has a resistance of
1 ohm, what will be the resistance of a wire of the same material 2 m in
length and 2 s i mm in area of cross-section ?
4. If a wire 2 m long and l mm in diameter has a resistance of 3 ohms,
what will be the resistance of a wire of the same material 4 m long and
2 ram in diameter ?
Solution. If a wire 2 m long and l mm in diameter has a resistance of
3 ohms, a wire l m long and l mm in diameter will have a resistance of
1.5 ohms. If x denotes the resistance in ohms of a piece of wire 4 m long
and 2 mm in diameter, - will denote the resistance of a wire l m long and
2mm m diameter. A wire 2 mm in diameter has four times the area of
cross-section of a wire l mm in diameter, since the areas of circles are to
each other as the squares of their diameters ; consequently a wire l m long
and l mm in diameter would have a resistance of X 4 = x. But the
4
resistance of a wire l m long and l mm in diameter has previously been
found to be 1.5 ohms ; hence x=l.b.
That is, the resistance of the wire which is 4 m long and 2 mm in diameter
is 1.5 ohms.
5. A wire 10 m in length and l mm in radius has a resistance of 2 ohms ;
what must be the radius of another wire of the same material whose length
is 5 m , in order that it may have the same resistance as the first wire ?
6. A wire of length V and diameter d' has a resistance of r ohms;
what is the resistance of a wire of the same material of length I " and
diameter d" ?
352 EXPERIMENTAL PHYSICS.
ELECTRO-MOTIVE FORCE.
159. The Volt. The term electro-motive force is one
which often occurs in books on the subject of electricity.
The term may best be explained for the beginner by
analogy, thus : " Just as in the water pipes a difference of
level produces a pressure, and the pressure produces a flow
as soon as the tap is turned, so difference of electrical level
produces electro-motive force, and electro-motive force sets
up a current as soon as a circuit is completed for the
current to flow through." The unit of E.M.F. (electro-
motive force) is called the volt, in honor of Volta, an
Italian physicist.
The E.M.F. of the Daniell cell is about 1.1 volts.
It has been proved on investigation that the E.M.F. of
a cell depends not upon the size of the plates, but upon
the materials comprising the cell.
160. Ohm's L.aw. Ohm, a German physicist, discov-
ered that the strength of a current of electricity is equal
to the E.M.F. driving the current, divided by the resist-
ance which the. current encounters ; that is,
, . E.M.F.
strength 01 current = r
-../-kOT
resistance
For the sake of brevity the law is usually stated in the
following form :
where O stands for strength of current,, j& for E.M.F., and
R for resistance.
QUESTIONS. What is the name of the unit of current strength ? Of
the unit of E,M.F, ? Of the unit of resistance ?
BATTERY RESISTANCE. 353
If there is a circuit in which the E.M.F. is 1 volt, and the resistance
1 ohm, what is the strength of the current ?
If a battery having an E.M.F. of 5 volts is placed in a circuit of which
the total resistance is 100 ohms, what will be the strength of the current ?
BATTERY RESISTANCE.
161. Resistance to the Current in the Cell. The
liquids in a cell offer to the flow of the electric current a
resistance whose magnitude depends, not only upon the
character of the liquids, but also upon the size of the
plates and their distance, apart.
In writing Ohm's Law in the literal form, it is customary
to denote by R the resistance in the part of the circuit
that lies outside the battery, and by r the resistance
offered by the cell itself ; so we have
.Jf.
' +
R for brevity is called the external resistance; r is called
the internal resistance.
Experiment 147. To find whether a difference in size
and position of the plates of a cell produces a variation in the
strength of a current.
Apparatus. Two Daniell cells with the liquids equally deep in
both, one furnished with a plate of zinc and a plate of copper of the
same size as in Exp. 140, the other with plates 10 cm long and 0.5 cm
wide, each plate having a wire soldered to it for making electrical
connections ; a galvanoscope ; a rheostat ; a commutator.
PART 1. When the cell with large plates is used.
Directions. Before making any measurements, see that
the porous cups are thoroughly soaked by the solutions.
354 EXPERIMENTAL PHYSICS.
Join the cell having the large plates to the commu-
tator ; also join the 5-turn section of the galvanoscope
to the commutator. By this arrangement the current
through the galvanoscope can be readily reversed. Read
the galvanoscope, with the plates as far apart in the cell
as possible. Then, by means of the commutator, reverse
the current, and read the galvanoscope again. Record the
readings, and find their average.
PART 2. When the cell with small plates is used.
Directions. Now disconnect the cell from the galvan-
oscope, and put the cell with small plates into the circuit.
Put the plates as far apart as the large plates of the other
cell were placed, read the galvanoscope, reverse the cur-
rent, and read the galvanoscope again. Record the read-
ings, and find their average. In this and subsequent
experiments, whenever you are directed to read the gal-
vanoscope, bear in mind that the readings are to be taken
one before and the other after the current has been
reversed. Put the plates as near together as possible,
and read again.
After an inspection of your record, answer the following
questions :
With the small cell, do you get the stronger current
when the plates are far apart or when they are close
together ?
Do you get a stronger current with the cell having
large plates or with the cell having small plates placed
as far apart as those of the large-plate cell are ?
NOTE. When the plates in the small-plate cell are put nearer together,
the liquid path, which the current in its passage from one plate to the other
BATTERY RESISTANCE. 355
traverses, is shortened ; consequently, the internal resistance of the cell
is diminished. When the plates of two cells, as in the experiment just
performed, are of different sizes, but the length of the liquid conductor
between them is the same, the cross-section of the liquid conductor in
the cell having the larger plates is larger than that of the other cell ;
hence, the internal resistance of the large-plate cell is less than that of
the small-plate cell.
In the experiment just performed the external resistance was small.
The next experiment differs only in this respect, that the external resist-
ance is to be made larger.
Experiment 148. To find whether a difference in size
and position of the plates of a cell produces the same
variation in the strength of the current when the external
resistance is large as it does when this resistance is small.
Apparatus. The same as in the previous experiment together
with a rheostat.
Directions. Put the narrow-plate cell into circuit with
the 15 turns of the galvanoscope, and 2 m of the No. 30
German silver wire in the rheostat, inserting the commu-
tator in order to reverse the current through the galvan-
oscope. With this arrangement repeat Part 2 of the
preceding experiment.
Then disconnect the narrow-plate cell, and put in its
place the large-plate cell. Then with this arrangement
take readings, as in Part 1 of the preceding experiment.
Has the current, in this experiment with the added
external resistance, shown more or less fluctuation for
change in size and position of the plates than when, as
in the preceding experiment, the external resistance was
smaller ?
Ohm's Law may help you in understanding the results
you have obtained.
356 EXPERIMENTAL PHYSICS.
By inspection of the literal form of Ohm's Law it will
be seen, after a little consideration, that when the external
resistance, R, is small, a variation in the internal resist-
ance, r, will sensibly affect the value of (7; on the other
hand, when R is large and r small, a variation in r will
produce no sensible change in the value of C.
To make this clearer, let us take a numerical example.
(1) When the external resistance, R, is small.
Let R = \, r2.
c =fT2 = f-
Change the value of r from 2 to 3.
^iff-f
Hence, in this case, by increasing r by 1, the value of
pi -pi
the current, (7, is diminished from to , or, expressed
o 4
in decimal form, from 0.33 E to 0.25 E.
(2) When the external resistance, R, is large.
Let 12 = 100, r=2.
Change the value of r from 2 to 3.
The " =Io5T8 = iS-
Hence, by increasing r by 1, the value of the current, (7,
pi -pi
is diminished from to , or, expressed in decimal
10.2 lOo
form, from 0.0098 E to 0.0097 E,
ARRANGEMENT OF CELLS. 357
ARRANGEMENT OF CELLS.
Experiment 149. To find, provided the external resist-
ance is small, which is the stronger, the current from two
cells joined abreast or from two cells joined in series.
Apparatus. Two Daniell cells provided with full-sized plates (such
plates as used in Exp. 147, Part 1) ; a galvanoscope ; a commutator.
PART 1. When the cells are joined abreast.
Directions. Join, so as to make good metallic contact,
the ends of the wires leading from the zinc plates of the
two cells ; also join the wires leading from the coppers of
the two cells. Put the cells thus joined into circuit with
the 5-turn section of the galvanoscope. Cells joined in
this way are said to be joined abreast. Insert a commu-
tator into the circuit for reversing the current through
the galvanoscope. Read the galvanoscope, and record the
deflections.
PART 2. When the cells are joined in series.
Directions. Now disconnect the cells, and join the
wire from the zinc of one cell to the copper of the other
cell. Put the battery into circuit with the 5-turn section
of the galvanoscope ; insert the commutator to change the
current through the galvanoscope. When arranged in
this way, the cells are said to be joined in series.
Read the galvanoscope, and record the deflections.
With which arrangement of cells did you obtain the
stronger current?
Experiment 15O. To find, provided the external resist-
ance is large, which is the stronger, the current from two
cells joined abreast or from two cells joined in series*
358 EXPERIMENTAL PHYSICS.
Apparatus. The same as in the last experiment together with a
rheostat.
PART 1. When the cells are joined abreast.
Directions. As in Part 1 of the last experiment, join
the cells abreast, and then put them in circuit with the
15 coils of the galvanoscope and the 2 m piece of No. 30
German silver wire in the rheostat ; insert the commutator
to change the current through the galvanoscope. Read
the galvanoscope ; record its deflections.
PART 2. When the cells are joined in series.
Directions. Now join the cells in series, and put them
in circuit with the 15 coils of the galvanoscope, 2 m No. 30
German silver wire, and commutator. Read the galvano-
scope ; record its deflections.
With which arrangement of cells did you get the
stronger current?
162. Arrangement of Cells Abreast and in Series.
From your experiments you have been led to the con-
clusion that when the external resistance is small, the
internal resistance must be small ; and, on the other hand,
when the external resistance is large, the internal resistance
must be large.
Careful experiments have shown that the E.M.F. of a
battery depends upon the number of cells, joined in series ;
a battery of two cells, joined in series, has an E.M.F.
equal to the sum of the E.M.F. of each ; if the E.M.F. is
the same for each cell, then of course the E.M.F. of the
battery is twice that of one of the cells ; the E.M.F. of a
battery consisting of five cells of the same strength, joined
in series, is five times that of a single cell ; finally, the
ARRANGEMENT OF CELLS. 359
E.M.F. of a battery composed of n cells of equal strength,
joined in series, is n times that of a single cell.
It has also been shown that a battery of two cells of
equal strength, joined abreast, has the same E.M.F. as a
single cell ; a battery of five cells of equal strength, joined
abreast, has the same E.M.F. as a single cell ; and, finally,
a battery consisting of n cells of equal strength, joined
abreast, has the same E.M.F. as a single cell.
Accurate experiments have also shown that the internal
resistance of a battery of ten cells joined in series is equal
to the sum of the internal resistances of the cells ; or if the
cells are of equal internal resistance, the internal resist-
ance of a battery composed of two cells joined in series is
twice that of one cell. In fact, if cells of equal resistance
are joined in series, the internal resistance of the battery
thus formed is equal to the resistance of one cell multi-
plied by the number of cells.
If two cells of equal internal resistance be joined abreast,
the internal resistance of the battery thus formed would
be one-half the resistance of a single cell. If n cells of
equal internal resistance be joined abreast, the internal
resistance of the group would be - of the resistance of a
n
single cell.
Whenever you desire to group a given number of cells
in order to form a battery that will give the maximum,
or strongest, current through a known external resistance,
you should be guided by the following
Rule. Join the cells in such a way as to make the inter-
nal resistance of a battery equal, as nearly as possible, to the
external resistance.
360
EXPERIMENTAL PHYSICS.
We shall illustrate this rule by the following example :
There are 12 cells, each of E.M.F. 1 volt and internal
resistance i ohm, and there is a wire the resistance of
which is 2 ohms. How must the cells be arranged in
order to yield the maximum current through the wire ?
Let us arrange the cells in various ways and compute
the strength of the current.
(1) All the cells in series (Fig. 118).
FIG. 118.
By Ohm's Law we can find the strength of the current
with this arrangement :
E 12 X 1 12
C= - - = -- - = = 1 .5 amperes.
E r 2 12x 8
FIG. 119.
ARRANGEMENT OF CELLS.
361
(2) 2 cells abreast and 6 in series (Fig. 11-9).
0= ^-^ = = 1 .71 amperes.
2+1x6x1 7
(3) 3 cells abreast and 4 in series (Fig. 120).
R
R
H
FIG. 120.
FIG. 121.
=
4X1
12
= - = 1.5 amperes.
2+1X4X \
(4) 4 cells abreast and 3 in series (Fig. 121).
0=- - = ?i = 1.26 amperes.
2 X3x 19
362
EXPERIMENTAL PHYSICS.
(5) 6 cells abreast and 2 in series (Fig. 122).
C=- = if =r 0.95 ampere.
2 + J X 2 X \ 13
(6) All the cells abreast.
c _ I _ 24 _ Q19
We have grouped the cells in many differ-
ent ways, and find that the strongest current
is obtained in the second arrangement, when
the internal resistance and the external re-
sistance are as nearly equal as possible. It
can be proved by algebra that the strongest
current is obtained when the external resist-
ance and the internal resistance are equal ;
but such a proof is beyond the scope of
this book.
EXAMPLES.
1. How should 10 cells, each having an internal
resistance of 1 ohm, be arranged in order to send the
strongest current possible through a resistance of 12
ohms ?
2. How should- 12 cells, each having an internal
resistance of ohm, be arranged in order to send the
strongest current through a resistance of 1 ohm ?
Solution. If x denotes the number of cells in series,
then 12 -j- x will denote the number of cells abreast,
and the internal resistance of the battery will be t ;
i ~T~ &
x must have such a value as to make this resistance
FIG. 122. e< l ual ! hence ^
12
tn
R
nnn
l-l
r^
1
H
i
1
1
i
i
1
_i
i
1
_i
i
n
J
i
i
= 12,
= 16,
ELECTRO-MAGNETISM. 363
That is, the battery must be arranged with four cells in series and con-
sequently with three cells abreast.
3. Four cells, each of E.M.F. 1 volt and internal resistance 2 ohms,
are to be arranged to send the strongest current possible through an
external resistance of 2 ohms ; what must the arrangement be ?
4. There are two cells, each having a resistance of 2 ohms ; how should
the cells be arranged in order to get the strongest current when the ex-
ternal resistance is 1 ohm ? 2 ohms ? 4 ohms ?
5. How should 20 Daniell cells, each with a resistance of 1 ohm, be
grouped in order to send the strongest current through a resistance of
0.9 ohm?
ELECTRO-MAGNETISM.
163. The Electro - Magnet ; Telegraph Key and
Sounder. The object of the next experiment will be to
bring out the properties of the electro-magnet, and also
to show how the electro-magnet can be used to reproduce
signals made at a long distance from the electro-magnet.
Experiment 151. To find what influence a current of
electricity has upon a piece of iron, when flowing through a
wire wound round the iron.
Apparatus. A Daniell cell ; a cylinder of soft iron about 7 cm long
and 0.7 cm in diameter ; insulated copper wire, No. 30 B. & S. ;
a piece of pine wood about 20 cm square ; sheet spring brass about
0.5 mm thick ; a disc of soft iron 0.3 cm thick and 0.7 cm in diameter.
PART 1. The electro-magnet.
Directions. Wind the wire upon the cylinder of soft
iron, just as thread is wound upon a spool, making one or
two layers.
When the ends of the wire are joined to the cell, and
the disc of soft iron is brought near one end of the iron
cylinder, what is the result ?
364 EXPERIMENTAL PHYSICS.
When the circuit is broken, that is, when one end of
the wire is disconnected from the cell, what happens to
the iron disc?
What is an electro-magnet?
PART 2. The electro-magnet used in the construction
of a telegraphic key and sounder.
Directions. Cut from the sheet brass a strip about
10 cm long and about 0.7 cm wide. Solder the iron disc flat-
wise to the side of the brass strip near one end (see note
on page 139); to the other end solder a flat-headed screw,
so that the length of the screw shall be at right angles to
the length of the strip, and one edge of the strip shall
touch the under side of the head of the screw. Insert the
screw into the board at a point on a diagonal about 6 cm
from the corner, turning the screw till the strip is parallel
to the side of the board and the center of the disc is about
on a line with the center of the electro-magnet which you
have made, when the electro-magnet is laid upon its side
on the board. Fasten the electro-magnet in place by a bit
of leather laid over the magnet and tacked to the board at
each end. Cut another strip from the brass. This strip
should be about 12 cm long and 1.5 cm wide, and should be
bent at right angles to its length at a distance of about
3 cm from one end, and again at right angles, but in the
opposite direction, at a distance of l cm from the same end.
Through the center of this bent end, which is l cm long, a
hole should be made. A screw should be inserted through
this hole into the board. Some of the insulating material
should be removed from one end of the magnet wire.
This end should be wound round the screw, passing
GALVANOMETERS. 365
through the brass, two or three times, and then the screw
should be "set up" till everything is fast. A screw
should be inserted into the board, under the free end of
the brass strip, to such a distance as to allow a space of
about l cm between the head of this screw and the under
side of the brass strip. When a wire from the cell is
joined to this screw, and the other end of the magnet wire,
from which the insulating material has been removed, is
also connected to the cell, the apparatus is completed.
When the brass strip, called the key, is pressed down till
it touches the screw, the circuit through the electro-
magnet is completed, and the little disc of iron, called the
armature, fastened to the end of the horizontal strip, is
attracted to the electro-magnet. The electro-magnet and
the armature are together called a sounder. Before the
sounder will work in a satisfactory manner, the armature
may have to be adjusted by turning the screw so as to
bring the armature nearer the magnet or to carry it far-
ther away. When the suitable adjustments have been
made, the armature will strike the electro-magnet with
a sharp click whenever the key is depressed.
Join your instrument to that made by some other
student, and try to transmit signals from one instrument
to the other.
State how a method might be devised for sending
signals from one house to another, by means of an instru-
ment similar to that which you have made.
GALVANOMETERS.
164. The Tangent Galvanometer; the Astatic Gal-
vanometer. The galvanoscope which we have used in
366 EXPERIMENTAL PHYSICS.
testing the presence of a current of electricity might
also be used to measure the strength of the current, the
strength of the current being proportional, not to the
angle through which the needle is deflected, but to the tan-
gent 1 of the angle through which the needle is deflected.
In the tangent galvanometer, the current passing through
the coil tends to deflect the needle,
while the earth's magnetic force re-
sists this tendency; consequently,
whenever a very weak current flows
through the coil, there is little or no
deflection of the needle to be observed.
To indicate the presence of a weak
current, we must use a more delicate
instrument, called an astatic galvan-
ometer.
This instrument, 2 as shown in Fig.
123, consists of a flat coil of insulated
FIG. 123.
wire, placed m a horizontal position,
over which is laid a circular card graduated in degrees.
From an upright support is hung, by a delicate fiber, a
little contrivance, resembling the letter H turned on its side
with the cross line carried beyond one side, as shown in
Fig. 124. This H-shaped contrivance is made of alumi-
num, or some other light and rigid substance. On each
of the sides of the H is fastened a magnet, indicated by
the heavy black lines in the figure. - These magnets are
1 If from any point in one side of an angle a perpendicular is dropped
to the other side, the tangent of the angle is equal to the ratio of the
perpendicular and that part of the side included between the vertex of
the angle and the foot of the perpendicular.
- 2 Devised by Dr. E. H. Hall.
GALVANOMETERS. 367
turned in opposite directions, so that the N-pointing pole
of the upper magnet is directly over the S-pointing pole
of the lower magnet, and the magnets are of nearly equal
strength. Consequently, the earth's action upon this
combination of two magnets has but little effect in
making it take a definite direction. In Fig. 124, E repre-
sents the fiber which
supports the mag-
nets, D represents
the graduated scale
over which the side
of the H carrying
the upper magnet
moves, C represents
the coil through
, . , ,, FIG. 124.
which the current
of electricity flows. The arrows denote the direction in
which the current is supposed to be flowing. If the
N-pointing pole of the lower magnet is pointing to the
right, the action of the current upon this magnet will
be to turn its N-pointing pole away from the observer,
in consequence of the magnetic action of currents on
magnets which you have already examined in Exp. 137.
The effect of the current, in the upper half of the coil, on
the upper magnet will be to turn it in the direction in
which the lower magnet is turned ; the effect of the lower
half of the coil will be to turn the upper magnet in the op-
posite direction. This effect, however, is slight, because
the lower half of the coil is so far from the magnet. The
current acts strongly upon the magnets to turn them in the
same direction, while the earth's action upon them is very
368 EXPERIMENTAL PHYSICS.
slight. The H-shaped piece to which the magnets are
fastened is very easy to move, since the fiber offers little
resistance to twisting. Hence, this arrangement of the
magnets and the coil gives an excellent means of detect-
ing the presence of feeble currents.
On the base of the support (Fig. 123) on which the
coil rests are leveling screws. By turning these screws,
the instrument can be adjusted so that the H-shaped piece
will hang freely without touching either the sides of the
slot in the cardboard scale or the coil itself. At the upper
end of the support to which the end of the fiber is attached
is a little screw. By loosening this screw, the magnets can
be raised or lowered, thus bringing the upper side of the
H-shaped piece the proper distance from the scale. A glass
shade covers everything in order to keep out currents of
air, which would set the magnets swinging. Two binding-
posts in front serve to connect the coil with the wires
carrying the current of electricity.
MEASUREMENT OF RESISTANCE.
165. Method of Substitution ; Bridge Method. In
our experiments on electrical resistance, Arts. 151, 152,
we made use of the method of substitution. We allowed a
current of electricity to flow through a wire, and noted
the deflection of the galvanoscope needle ; then we found
another wire which would offer the same resistance to
the current which the first wire offered, that is, when a
current of the same strength flowed through the second
wire as through the first, the needle would be deflected
equally. If we had actually known the resistance of the
MEASUREMENT OF RESISTANCE. 369
second wire in ohms, we should, also know the resist-
ance of the first wire. To measure resistances by this
method, then, we should have to note the deflection
produced in the needle of the galvanoscope when a
current was flowing through the wire the resistance
of which we wish to get; then we should have to
substitute, for the wire of unknown resistance, wires of
known resistance till the current gave the same deflection
as before. This method is not as good as the bridge
method, in which use is made of an instrument called
Wheatstone's bridge.
Before describing this instrument, we must examine
the meaning of the term equipotential points.
166. Electrical Potential; Equipotential Points. In
order that water may flow from one point to another,
there must be a difference of level. In order that elec-
tricity may flow, there must be a difference of potential, or
electrical level. Whenever two points have the same level,
water cannot flow from one to the other ; whenever two
points have the same potential, a current of electricity
cannot flow from one to the other through a wire joining
them. Two points which have the same potential are
called equipotential points. The following experiment will
make clearer the term equipotential points.
Experiment 152. To find the relation between the
length* of the segments of a wire divided by a point and
the resistances of the segments of another wire divided by a
point which has the same potential as the first.
Apparatus. A frame on which is stretched a German silver wire ;
a Daniell cell; an astatic galvanometer; a piece of copper wire a
370 EXPERIMENTAL PHYSICS.
little more than 100 cm long ; insulated copper wires for making
connections.
Directions. Fasten one end of the copper wire and
also the end of one wire from the cell in one of the front
binding-posts in the frame (Fig. 125). Draw the copper
wire straight, and fasten it in the other binding-post
together with the end of the other wire from the cell.
The current on leaving the wire from the cell enters the
brass strip to which the two wires are attached, where it
divides, one part flowing along the copper wire, the other
FIG. 125.
part along the German silver wire, as shown by the arrows.
These currents unite when they reach the other brass
strip to which the wires are attached, and the united
currents return to the cell. Connect by a thin wire some
point, as P 1 , in the copper wire with the galvanometer,
and touch the wire leading from the other binding-post of
the galvanometer to the German silver wire at various
points till a point is found which has the same potential
as the point P', so that no current flows through the gal-
vanometer. Call this point P. Measure and record the
lengths, a and 5, c and d, of the segments of the two
wires. Then change the position of P r and find the
corresponding position of P. Record the measurements
as before. Again change the position of P r ; make measure-
ments and record*
MEASUREMENT OF RESISTANCE. 371
In every case which you have tried, is the following
proportion true? a : b = c : d.
If you denote the resistances of the segments, a, 6, e,
and c?, by A, B, C, and D, respectively, knowing that the
resistance of a wire is proportional to its length, are the
following proportions true ?
a : b = A : B,
c: d = C: D.
Is the following proportion true ?
C a
r =
167. Theory of Wheatstone's Bridge. Fig. 126 rep-
resents a Wheatstone's bridge in the form of a diagram.
The horizontal line represents a wire of German silver;
the curved line represents another
conductor ; the wavy lines repre-
sent the wires which connect the
bridge to the cell; the arrows
represent the direction of the cur-
rent in each conductor ; Cr is the
galvanometer connected by wires
to the equipotential points R and S. The point S has
been found by sliding the end of the wire joined to the
galvanometer along the German silver wire till no current
is indicated by the galvanometer. From the results of the
preceding experiment we know that
r : x = a : 6,
x b b
or - = - .-. x= - X r.
r a a
372
EXPERIMENTAL PHYSICS.
Experiment 153. To find, by the bridge method, the
resistance of a piece of wire.
Apparatus. A Wheatstone's bridge (Fig. 127) ; an astatic gal-
vanometer ; a Daniell cell ; a box of resistance coils, that is, coils of
FIG. 127.
wire of known resistance which can readily be put in circuit ; a piece
of insulated copper wire, No. 30 B. & S., 200 cm or 300 cm long.
Directions. By means of short, thick, copper wires,
whose resistance may be neglected, join the resistance box
to the binding-posts on each side of the left-hand gap in
the brass strip which nearly surrounds three sides of the
instrument, as shown in Fig. 127. Join the resistance to
be measured to the binding-posts on either side of the
right-hand gap. Connect one wire from the galvanometer
to the binding-post at R, and the other wire to the bind-
ing-post on the piece which slides along the scale over
which the German silver wire is stretched. Connect the
cell to the binding-posts as shown in the figure. When
MEASUREMENT OF RESISTANCE. 373
everything is ready, touch the sliding part to the German
silver wire and quickly remove it, noting in which direc-
tion the vane of the galvanometer moves. Then, when
the vane has settled somewhat, touch the sliding part
again to the German silver wire, but at a different point,
and note the direction in which the vane is deflected.
The object at first is to get two positions for the sliding
part which will deflect the vane in opposite directions.
The point on the German silver wire equipotential to R
lies somewhere between these two positions, and can now
be readily found. If the point S thus found should
happen to be near the end of the German silver wire,
change the resistance r, by adding resistance or diminish-
ing it, till 8 is at least 20 cm from the end of the wire.
When S has been found so that no current flows
through the galvanometer, record the length of a and
of 5; also record the resistance r. Compute the resist-
ance x.
TEMPERATURE AND RESISTANCE.
168. Temperature Coefficient of Resistance. When-
ever a copper wire is heated, its resistance increases. In
fact, the resistance of all metals increases with an increase
of temperature. The object of the following experiment
is to measure the resistance of a copper wire at 0, and
also at 100, and then to determine what is known as the
temperature coefficient of resistance for copper.
Experiment 154. To find by what part of its resistance
at a copper wire increases in resistance for a rise in
temperature of 1.
374 EXPERIMENTAL PHYSICS.
Apparatus. In addition to that of Exp. 153, a jar of ice-water
with many pieces of floating ice ; a copper boiler ; a Bunsen burner ;
a thermometer ; a glass tube of rather large diameter.
Directions. Wind the wire rather openly round the
glass tube, and put the tube thus wound with the wire
into the jar of ice-water. Connect the ends of the coil to
the bridge by short, thick, copper wires, in the place in
which the resistance x (Fig. 127) occupied in Exp. 153.
Arrange the other parts of the apparatus as you did in
Exp. 153, and find the resistance of the copper wire,
after thoroughly stirring the ice and water with the ther-
mometer. Transfer the coil of wire from the ice-water
to the copper boiler partly filled with water, and heat this
water to boiling. Then find the resistance again of the
wire.
From the results which you have obtained, answer the
following questions :
(1) What is the resistance of the wire at ?
(2) What is the resistance of the wire at 100 ?
(3) What is the increase in the resistance of the wire
for a rise in temperature of 100 ?
(4) What is the average increase in the resistance of
the wire for a rise in temperature of 1?
(5) What part of the resistance at is the increase in
resistance for 1?
Definition. The temperature coefficient of a conductor is
a number which tells by what part of itself the resistance at
has increased for a rise in temperature of 1.
I JST D E X
Absolute temperatures, 94 ; units,
300 ; zero, 94.
Acceleration, 289.
Air, 21 ; specific gravity of, 39.
Air thermometer, 93.
Algebraic sum, 261.
Amalgamating zinc, 337.
Ampere, the, 341.
Amplitude, 158.
Angle of incidence, 196; of fric-
tion, 279; of reflection, 196;
of refraction, 214; of repose,
279 ; tangent of an, 366.
Apparatus, manufacturers of, v.
Arrangement of cells abreast, 357 ;
in series, 358 ; rule for, 359.
Astatic galvanometer, 366.
Atmosphere, 21 ; pressure of, 30.
Axis of abscissae, 60 ; of ordinates,
60 ; principal, 220 ; secondary,
221.
Balance, corrections of, 133 ; zero
error of, 5.
Barometer, 33.
Battery,. 326 ; resistance of a, 353.
Beats, 175.
Boiling, 123.
Boiling-point of water, 79.
Boyle, Robert, 41.
Boyle's Law, 45.
Bunsen cell, 323.
Calorie, 100, 101.
Calorimetry, 102.
Camera, pin-hoie, 195.
Capillary action, 1 7.
Cause, 128.
Center of curvature, 206, 220 ; of
gravity, 266; of suspension,
157 ; optical, 220.
Circuit, divided, 348.
Charles, Law of, 92.
Chemical action in cells, 336, 340.
Coefficient of friction, 277, 279 ; of
linear expansion, 88.
Coercive force, 322.
Commutator, 342.
Concord, 176.
Condensation explained, 130.
Conduction of heat, 97.
Conjugate foci, 226.
Conservation of energy, 302.
Convection, 97.
Couple, 255 ; arm of, 255.
Current, electric, 325; action on
magnets of, 327 ; strength of,
327.
Dalton, 92 ; Law of, 94, 95.
Daniell cell, 323.
Density, 7.
Dew-point, 124.
Directions for note-taking, 1 ; for
performing experiments, 2.
376
INDEX.
Discord, 176.
Dynamics, 245.
Dyne, 298.
Elasticity, limits of, 141 ; of bend-
ing, 142 ; of stretching, 138 ; of
shape, 141 ; of twisting, 147 ;
of volume, 151.
Electric current, 325.
Electro-magnetism, 363.
Electro-motive force, 352.
Energy, 301 ; conservation of, 302 ;
kinetic, 302 ; potential, 302.
Equilibrium, 249; of concurrent
forces, 273 ; of parallel forces,
249, 261.
Equipotential points, 369.
Erg, 299.
Ether, 241.
Evaporation, 121; explained, 130.
Exhaustion, degree of, 41.
Expansion, cubical, 85; linear, 85;
of air, 90.
Experience, 62.
Experiment, 62; qualitative, 63;
quantitative, 63.
Facts and inferences, 63.
Fixed points, 74.
Fluid, 130.
Focal length, 223.
Foci, conjugate, 226.
Focus, principal, 221.
Foot-pound, 281 ; -poundal, 301.
Force, 141 ; components of a, 276 ;
of friction, 276 ; line of, 316;
moment of a, 260 ; transverse,
144 ; units of, 246, 298, 300.
Forces, composition of, 276 ; con-
current, 271 ; equilibrant of
concurrent, 274; resultant of
concurrent, 274; representa-
tion of, 247 ; resolution of,
276; triangle of, 273.
Freezing mixtures, 117 ; point, 74.
Friction, 276.
Fulcrum, 270.
Fusion, latent heat of, 112.
Galvanometer, tangent, 366 ; astat-
ic, 366.
Galvanoscope, 335.
Gay-Lussac, 84, 92.
Gram, 8, 301.
Graphical method, 59.
Gravity, 265 ; center of, 266.
Heat, 75 ; conduction of, 97 ; con-
vection of, 97; latent, 109;
measurement of, 100 ; mechan-
ical equivalent of, 304; of fu-
sion, 112 ; of vaporization, 117 ;
radiation of, 97; sensible, 110;
specific, 106 ; unit of, 100, 101.
Helmholtz, 182.
Hiero, 12.
Hooke's Law, 152.
Hydrostatic press, 55.
Hypothesis, 129; molecular, 129.
Illumination, intensity of, 188.
Images, construction for real, 233 ;
for virtual, 238 ; formation of,
by small apertures, 194, by
cylindrical mirrors, 208, 209,
by lenses, 222, 235, -by plane
mirrors, 198 ; number of, 204 ;
real, 201; virtual, 201.
Inclined plane, 285.
Index of refraction, 216.
Inertia, 286.
Inferences, 63.
INDEX.
377
Interference of light, 242; of
sound, 167.
Jevons, W. Stanley, 127, 129.
Joule, 304.
Kaleidoscope, 204.
Kinetic energy, 302.
Kinetics, 245.
Knowledge, classified, 128 ; empiri-
cal, 127.
Lagrange, 182.
Latent heat, 109; of fusion, 112;
of vaporization, 117.
Laws of nature, 183.
Lenses, 220 ; definitions relating to,
220 ; names and properties of,
221, 222 ; focal length of, 223 ;
relation of, to prisms, 219.
Levers, classes of, 270 ; influence
of weight of, 266 ; law of, 271.
Light, beam of, 192 ; interference
of, 242 ; nature of, 240 ; pencil
of, 192; rays of, 192 ; reflection
of, 196; refraction of, 211, 123 ;
velocity of, 240.
Liquid pressure, 24.
Lodestones, 313.
Lucretius, 129.
Magnets, action of currents on,
327 ; poles of, 309.
Magnetic attractions and repul-
sions, 311; compass, 312;
curves, 316 ; field, 316 ; force,
line of, 316; induction, 314;
needle, 312.
Magnetism, theory of, 321.
Magnetite, 313.
Magnifying glass, 240.
Mariotte's bottle, 57.
Mass, 245 ; unit of, 246.
Maxwell, J. Clerk, 130.
Measurements and computations, 8.
Mechanical equivalent of heat, 304.
Mersenne, 182.
Method, bridge, 369; graphical, 59 ;
of differences, 127 ; of mix-
tures, 102 ; of substitution, 368.
Mirrors, cylindrical, 205; plane, 198.
Molecule, 129.
Moment of a force, 259, 260.
Momentum, 292.
Newton, 241.
Note-taking, directions for, 1.
Numerical value, 5.
Observation, 62 ; fallacies of, 184.
Octave, 176.
Ohm, the, 350.
Ohm's Law, 352.
Optical center, 220.
Oscillation, 157.
Parallax, 227.
Pendulum, 157 ; length of, 158.
Penumbra, 194.
Photometry, 192.
Pitch, 180.
Pneumatics, 23.
Poggendorff cell, 341.
Polarization, 337.
Potential, 369.
Pound, 246.
Poundal, 300.
Prisms and lenses, 219.
Pump, air, 48 ; force, 51 ; lifting, 50.
Pythagoras, 181.
Quality of sounds, 180.
Quantity, 5.
378
INDEX.
Radiation of heat, 97.
Reflection of light, 196.
Refraction, index of, 216 ; of light,
211, 214.
Residual magnetism, 322.
Resistance battery, 353 ; external,
353; internal, 353; of wires, 343.
Retentivity, 322.
Rheostat, 342.
Rotation, negative, 260; positive,
260.
Rudberg, 85.
Shadows, 193.
Shore, John, 164.
Siphon, 53.
Soldering, 139.
Sound, interference of, 167 ; loud-
ness of, 180 ; pitch, 180 ; trans-
mission of, 165; theory of,
181 ; velocity of, 161 ; quality
of, 180 ; wave, form of, 168.
Sound radiometer, 174.
Specific gravity, 11 ; and density,
19 ; of air, 38 ; of a liquid, 18,
35 ; of a solid, 15, 19.
Specific heat, 106.
Statics, 245.
Steam engine, 305.
Strain and stress, 151.
Sympathetic vibrations, 174.
Temperature, 75 ; absolute 94 ; and
pressure, 75 ; and resistance,
373.
Temporary magnetism, 322.
Theory, 184.
Thermal capacity, 102.
Thermometer, air, 93 ; mercury, 71.
Torricelli, 31 ; experiment of, 31.
Triangle of forces, 273.
Tuning-fork, 164.
Umbra, 194.
Unit, 7.
Units, absolute, 300; gravitation,
300.
Vapor, saturated, 131.
Velocity, 288; of light, 240; of
sound, 161, 172.
Vibration, 157 ; of strings, 176.
Volt, the, 352.
Water, boiling-point of, 79 ; freez-
ing-point of, 74; maximum
density of, 125.
Wave crest, 156; length, 156; mo-
tion, 155; motion of sound,
166; trough, 156.
Weight, 247.
Wheatstone's bridge, 369; theory
of, 371.
Wollaston, 185.
Work, 280.
Zero, absolute, 94; error of bal-
ance, 5.
Zero-point, elevation of, 83 ; lower-
ing of, 83.
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