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ELEMENTS
PHYSICAL MANIPULATION.
BY
EDWAED C. PICKERING,
Thayer Professor of Physics in the Massachusetts Institute of Technology.
PART II.
MACMILLAN AND CO.
1876.
33
PREFACE.
SINCE the publication of the first Volume of this work, its scope
has been greatly enlarged. It is now made to include, not only
Physics proper, but several kindred branches, and aims to describe
the principal methods of experiment with which every physicist
should be t familiar. As in the first volume, each Experiment is
divided into two parts, a description of the Apparatus, intended
mainly for the instructor, and th^e details of the Experiment, for the
student.
The subject of Electricity is perhaps better adapted than any
other to the laboratory system, and a large amount of space is
therefore devoted to it. Heat follows, not being introduced earlier
on account of its difficulty, The student may thus first acquire
the requisite skill, and this subject then furnishes an excellent test
of his proficiency. To attain accurate results, not only is great
care needed, but very carefully constructed apparatus, and numer-
ous precautions must be taken, and corrections applied. It was
therefore deemed better to select simple and inexpensive forms of
apparatus which should show the student the principles involved,
although not capable of giving very accurate results. If the
latter are desired, the student should be referred at once to the
' : <N s k original memoirs.
V^ The experiments headed Mechanical Engineering, though more
special in their nature, are yet of a kind which is important to
1757G39
IV PREFACE.
every physicist. Physical problems which are to be solved on a
large scale require a thorough knowledge of mechanical engineer-
ing. To this class belong also those which have the greatest
pecuniary value. The methods of conducting such experiments
also are often so faulty, that a brief description of how ti\ef
should be performed will not seem out of place.
The next section is devoted to Meteorology, and contains a brief
description of the principal meteorological and magnetic instru-
ments. No special description of self-registering instruments is
given, on account of the great space and elaborate engravings
required, and because the use of such instruments is, from their
nature, of little value as a means of education, and in general, only
involves replacing a sheet of paper every day ; proper directions
also usually accompany every instrument.
One of the most important features of this volume is the
introduction of a chapter on Astronomy. This subject is so sel-
dom taught practically, except to single individuals as assistants
in an Observatory, that its value as a means of training appears to
have been overlooked. A careful examination of the subject
seems to show that the laboratory method may be used to teach
Astronomy as successfully as Chemistry or Physics. A promis-
ing field is open to any College or School of Science where the
attempt shall be made to teach Practical Astronomy to classes
in a systematic manner; and surely nothing can be more valuable
to the civil engineer or explorer than to be able to determine his
latitude, longitude and time, by the sextant or transit. As this
book is intended to be used in this way, a portion of the smaller
corrections are omitted, as sufficient accuracy is thus attained for
ordinary purposes, and the chapter is not intended as a guide in
an Astronomical Observatory where the greatest possible accuracy
is demanded. The methods of Astronomy, especially as regards the
discussion of results, the determination of errors and the applica-
tion of corrections, are so much superior to those commonly em-
ployed in purely physical work, that they deserve a careful study.
The more exact physical measurements, especially those involving
the accurate determination of angles and time, are, moreover, so
closely akin to those of Astronomy that every physicist should
have some acquaintance with the latter science. In so brief a de-
scription of so vast a science there was little opportunity to add
anything new, and the standard works are so complete that the
professional astronomer would go at once to them. Most of the
methods here given will therefore be found treated more fully in
the works of Chauvenet, Loomis, Coffin and Webb.
As every lecturer on science may derive great aid from the
Lantern, in the projection of illustrations, or in rendering experi-
ments readily visible to an audience, a chapter is added on Lantern
Projections. The aim has been to show how, with simple and
inexpensive means, excellent results may be obtained.
Several subjects of general importance remained which could
not be inserted in the body of the work. These have been incor-
porated in three Appendices, A, B and C. The author, having
experienced a great want of a brief description of the principles
of electrical measurements, prepared a pamphlet for his own stu-
dents which forms Appendix A.
Appendix B gives a series of tables of the numerical constants
most used in physical work. The tables of powers, logarithms
and trigonometrical functions are arranged in a way which is
more brief, and is believed to be more convenient, than that ordi-
narily adopted. A saving of nearly one-third of the time is effect-
ed by the fact that each table covers only two opposite pages, so
it is not necessary to turn the leaves in its use. The method of
using them is also nearly the same for all. The trigonometrical
functions are given to tenths of a degree, as the circles used in the
galvanometers, and most of the other instruments described in
VI PREFACE.
this work, are divided into degrees and read by the eye to tenths.
If the readings are made by verniers to minutes, as in the optical
circle and astronomical instruments, the more extended five or six
place logarithms are required. A great saving of space is effected
by bringing all the principal constants for the metals into a single
table. Similar tables are given for liquids and gases. The blanks
clearly indicate where additional determinations are needed.
In Appendix G are given with some detail directions for the
establishment of Physical Laboratories, on the plan of that under
the charge of the writer. In this Laboratory, about a hundred stu-
dents are instructed every year. It has been in operation with but
little change, except to enlarge its work, for the past six years, and
has therefore had a practical trial on a large scale. A brief list
of works of reference is also added, and a short description of a
hundred additional experiments. These are especially intended
to aid both teacher and student in what should be the aim of
every scientific man, the encouragement of original research. The
wide range of subjects now included in the term physics, shows
that this work is addressed to no narrow circle of readers. The
attention of all persons interested in experimental work of any
kind is solicited, and of all who believe that the practical method
of teaching science, now so largely adopted, is a step in the right
direction.
In conclusion, hearty thanks are tendered to Profs. Trowbridge
and Cross, and especially to Mr. Holman, for careful examination
and revision of the proof sheets of this work.
E. C. P.
February 22nd, 1876.
CONTENTS.
ELECTRICITY.
ELECTRICAL INSTRUMENTS 1
Batteries, 1. Connections, 6. Keys, 7. Plugs, 7. Switches, 8. Com-
mutators, 8.
95. GALVANIC ELECTRICITY .9
96. TELEGRAPH . 15
97. INDUCTION COILS 19
98. LAW OF GALVANOMETER . . . . . . .21
99. GALVANOMETER CONSTANT . . . . . . " 22
100. COSINE GALVANOMETER .25
101. DIFFERENTIAL GALVANOMETER . . . . . 26
102. WHEATSTONE'S BRIDGE 29
103. RESISTANCE COILS . . 36
104. CAPACITY OF CONDENSEKS 37
105. ELECTROMOTIVE FORCE AND RESISTANCE OF A BATTERY. 40
106. RESISTANCE OF BATTERIES . . . . . .41
107. RESISTANCE OF GALVANOMETERS ..... 43
108. MANSE'S METHOD 43
109. WIEDEMANN'S METHOD 44
110. POGGENDORFF'S METHOD 45
111. ELECTROMETERS .46
112. TESTING TELEGRAPHS 49
113. TESTING SUBMARINE CABLES ...... 52
114. FRICTIONAL ELECTRICITY 54
115. INDUCTION MACHINES 62
116. MAGNETISM 64
117. MAKING MAGNETS 65
118. FORCE OF MAGNETS 67
119. LAW OF MAGNETS 68
120. DISTRIBUTION OF MAGNETISM 69
121. MAGNETIC FIELD 71
(yii)
Vlll CONTENTS.
HEAT.
122. TESTING THERMOMETERS 73
123. WEIGHT THERMOMETER 76
124. EXPANSION OF SOLIDS 78
125. EXPANSION OF LIQUIDS 79
126. EXPANSION OF GASES . .80
127. CHANGE OF VOLUME BY FUSION 82
128. CONDUCTION OF SOLIDS . . . . . . .82
129. CONDUCTION OF CRYSTALS . . . . . .82
130. CONTACT THERMOMETER 84
131. RADIANT HEAT . . .84
132. LAW OF COOLING 88
133. PRESSURE OF STEAM 89
134. PRESSURE OF VAPORS 90
135. SPECIFIC GRAVITY OF VAPORS 91
136. DENSITY OF GASES 92
137. MIXTURE OF VAPORS . 93
138. SPECIFIC HEAT 94
139. LATENT HEAT OF FUSION 96
140. LATENT HEAT OF VAPORIZATION 96
141. CARRE" MACHINE 99
142. FREEZING MIXTURES 100
143. PYROMETERS 101
144. HEAT OF COMBUSTION 103
145. EFFICIENCY OF GAS BURNERS . . .' . . .104
146. MECHANICAL EQUIVALENT OF HEAT 105
147. Two SPECIFIC HEATS OF GASES . . . . .106
MECHANICAL ENGINEERING.
GENERAL DIRECTIONS 109
Piping, 109. Steam Boilers, 112. Steam Engine, 115.
148. EFFICIENCY OF BOILERS 117
149. COVERING STEAM PIPES. 1 119
150. COVERING STEAM PIPES. II. . . ... . .121
151. TESTING GAUGES 121
152. PRESSURE AND TEMPERATURE OF STEAM . . .122
153. INDICATOR DIAGRAMS 123
154. FRICTION-BRAKE 126
155. TRANSMISSION DYNAMOMETER 127
156. SPEED OF PISTON RODS 129
157. SPEED OF FLY-WHEELS .130
CONTENTS. x
158. SPEED OF SHAFTING 130
159. STRENGTH OF MATERIALS 132
160. FRICTION OF BELTS 135
161. FRICTION OF PULLIES 136
METEOROLOGY.
162. TEMPERATURE OF THE AIR 139
163. SOLAR RADIATION 143
164. ATMOSPHERIC PRESSURE 145
165. WIND 147
166. MOISTURE 149
167. RAIN AND DEW 152
168. TIDES 153
169. MAGNETIC DECLINATION 154
170. MAGNETIC DIP 157
171A. HORIZONTAL COMPONENT 159
171B. VERTICAL COMPONENT 163
172. ELECTRICITY OF THE AIR 164
PRACTICAL ASTRONOMY.
173.
174.
175
SEXTANT
LATITUDE
TIME
. 166
. 168
. 173
176.
177.
178.
179.
180.
181.
182.
183
LONGITUDE
MERIDIAN
TIME BY TRANSIT
LATITUDE BY TRANSIT ....
TRANSIT CIRCLE
ZENITH TELESCOPE
ALTITUDE AND AZIMUTH INSTRUMENT .
LONGITUDE .....
. . . 174
. . . 176
. 177
. 184
. 186
. 189
. 192
. 195
184.
185.
EQUATORIAL TELESCOPE ....
SPECTRUM TELESCOPE ....
. 197
. 208
LANTERN PROJECTIONS.
186. SUNLIGHT .212
187. ELECTRIC LIGHT 215
188. MAGNESIUM LIGHT 217
189. CALCIUM LIGHT 218
190. LANTERN 225
191. OBJECTS FOR PROJECTION 232
192. TANKS . ... 235
JC CONTENTS.
193. STROBOSCOPE 238
194. VERTICAL LANTERN . . 240
195. LANTERN POLARISCOPE 242
196. LANTERN MICROSCOPE . . . . . . .244
197. OPAQUE OBJECTS 245
198. LANTERN GALVANOMETER 246
, 199. PROJECTION OF LISSAJOUS' CURVES 248
200. PROJECTION OF SPECTRA 250
APPENDIX A. ELECTRICITY.
THEORY OF ELECTRICAL PHENOMENA 253.
Statical Electricity, 254. Induced Currents, 254. Magnets, 255.
Electro-magnetism, 255. Magneto-Electricity, 255. Electrical Meas-
urement, 255. Kirchhoff's Laws, 258. Shunts, 259. Quantity, 259.
Current, 260. Resistance, 260. Capacity, 261. Potential, 262.
APPENDIX B. TABLES.
DESCRIPTION OF TABLES 263
1. SQUARES 268
2. CUBES 270
8. RECIPROCALS 272
4. POWERS 274
5. LOGARITHMS .... 276
6. NATURAL SINES AND COSINES 278
7. NATURAL TANGENTS AND COTANGENTS .... 280
8. LOGARITHMIC SINES AND COSINES 282
9. LOGARITHMIC TANGENTS AND COTANGENTS . . . 284
10. CONSTANTS 286
11. PROPERTIES OF METALS 287
12. PROPERTIES OF LIQUIDS 288
13. PROPERTIES OF GASES AND VAPORS 288
14. HYDROMETER TABLES 288
15. TEMPERATURES 288
16. PRESSURE OF VAPORS 289
17. WET AND DRY BULB THERMOMETERS .... 289
18. SOLAR SYSTEM .289
19. DOUBLE STARS 290
20. CLUSTERS AND NEBULA 291
APPENDIX C. PHYSICAL LABORATORIES.
General Directions, 292. Works of Reference, 296. Additional Ex-
periments, 299.
ALPHABETICAL INDEX ... . 309
ELECTRICITY.
CERTAIN instruments are employed in almost all the applications
of dynamic electricity. The following description of them should
therefore be read carefully before performing any experiments in
this subject.
Batteries. The most common method of generating a current
of electricity is by the unequal action of an acid liquid on two
metals. This may be effected in a great variety of ways, but the
most common forms of galvanic batteries may be divided into the
three following classes. The first class contains those in which a
single liquid is used, the second those of which the Daniell's bat-
tery is the type, with zinc and copper as electrodes, and sulphuric
acid and sulphate of copper as liquids. The third class contains
the other two-fluid batteries like the Grove and Bunsen, a more
intense action being secured by nitric, chromic or other strong
acids. The action of other batteries is readily understood from
them, and therefore need not be described here.
If any two metals, as copper and zinc, are immersed in dilute
sulphuric acid, a decomposition of the liquid takes place, and the
zinc is found to be positively, the copper negatively, electrified.
If they are connected by a wire or other conductor, a continuous
current of electricity will pass through them from the copper to
the zinc. A chemical action now takes place, by which the acid
unites with the zinc, and the hydrogen set free is deposited in
bubbles on the copper. As soon as the circuit, as it is called, is
broken, by removing the wire, this action ceases, and the metals
return to their former feebly electrified condition. If the experi-
ment is made with commercial zinc which contains particles of
iron and other impurities, local action takes place, that is, each
particle acts like the copper plate, and the liquid is decomposed
without sending any current through the wire. To obviate this
2 ELECTRICITY.
difficulty the zinc must be amalgamated, that is, covered with
mercury, which gives it a uniform surface so that it will act only
when the circuit is closed. To amalgamate a plate of zinc, first
scrape off any lumps of salts or dirt that may adhere to it, and
then clean it by immersing in dilute sulphuric acid (1 part to
8 of water). Local action at once ensues, accompanied with a
rapid disengagement of hydrogen with a hissing sound. Then
lay the plate in a wooden trough which will just contain it, and
pour mercury over it, repeating the operation and aiding the
action with a stiff brush. If the mercury does not adhere at
once, dip the plate again in the acid, and repeat until the surface
has a bright silvery lustre, and no effect is produced on immersion
in the acid. Zinc may also be amalgamated by dipping in a solu-
tion of chloride of mercury. The presence of the hydrogen on
the platinum is very objectionable, both because it increases the
resistance, and because it tends with the zinc to form a current in
the opposite direction. The surface of the platinum should there-
fore be roughened either mechanically, or better, by covering it
with a coating of platinum black, to which the bubbles cannot
adhere. To save expense, the plate may be made of silver or lead
covered with platinum black, or a plate of gas carbon may be em-
ployed. The carbon should be first pulverized, then mixed with
molasses, molded under a high pressure, and finally heated to
redness.
A battery known as a Smee, is then easily made by filling a
glass jar half full of dilute sulphuric acid (1 part in 10) and im-
mersing in it two or more plates side by side of amalgamated zinc
and platinum, or carbon. Wires are then connected with the
two plates, and a current sent through any pieces of apparatus by
merely connecting them with it. Such a battery is very clean
and convenient for many purposes, but it is not very powerful,
and rapidly grows weaker when the circuit is closed.
Instead of sulphuric acid, chromic acid is sometimes used,
formed by mixing one part of concentrated sulphuric acid with
four or five parts by volume of a saturated solution of bichromate
of potash ; as the mixture will become very hot, the acid should
be added slowly and well stirred. The zinc is commonly made so
that it can be lifted out of the liquid, as if left standing in it, it is
ELECTRICITY. 6
gradually dissolved. Powerful batteries are made by using several
cells of this form, connecting the plates with a rack and pinion, or
with a wire rope and windlass, so that they may be lifted simul-
taneously by a crank. This battery has a large electromotive
force and small resistance ; it therefore gives a very strong cur-
rent, but like the preceding runs down rapidly.
To remedy the difficulty arising from the weakening of batter-
ies with a single liquid, an important improvement was introduced
by Daniell, in a battery containing two liquids, sulphate of copper
and dilute sulphuric acid, separated by a porous earthenware dia-
phragm. A plate of copper is placed in the former liquid, amal-
gamated zinc in the latter. In one form of this battery the jar
itself is of copper, in which is placed the sulphate of copper, and
in this the earthenware cylinder, called the porous cell. The latter
is filled with dilute sulphuric acid, so that the liquids shall stand at
about the same height inside and out, and the zinc is immersed in
it. When the circuit is closed, the chemical action takes place
through the porous cell, so that the hydrogen set free decomposes
the sulphate of copper and deposits the copper on the copper
plate. The latter therefore becomes heavier and heavier, instead
of being used up. Some crystals of sulphate of copper are placed
in the jar to replace that which is decomposed, otherwise the solu-
tion would grow weaker and weaker. Such a battery gives 'a
very steady or constant current with an electromotive force a little
over 1 volt. Sometimes the copper is placed in the interior, in-
stead of outside the acid, and sometimes a glass balloon, like a
Florence flask, filled with sulphate of copper, is inverted over the
solution in the jar, to replace that which is used up. These bat-
teries work best with the circuit closed when not in use, as the
electricity thus wasted costs less than the injury sometimes done
by a broken circuit. In the latter case, the copper is often depos-
ited on the porous cell in curious lumps not easily removed.
To avoid the trouble arising from a porous cell, gravity batter-
ies are used, in which the cell is dispensed with, and the two
liquids kept apart by the difference in their specific gravity. One
of the best forms of gravity battery is the Callaud, in which the
copper plate is placed at the bottom, and the zinc suspended some
inches above it. Water is then poured in until the zinc is just
4 ELECTRICITY.
covered, and some crystals of sulphate of copper dropped in.
The circuit is then closed over night, and the next day the battery
will be in good working order. By dropping in a little sulphate
of zinc the action may be hastened. The solution of sulphate of
copper being heavier than the acid, will remain at the bottom, as
is easily seen by its color. When the circuit has been closed for
some time the line of demarcation will be well marked, and will
gradually descend as the copper is used up. More crystals must
then be dropped in. On an open circuit the copper, by diffusion,
slowly ascends, the color gradually fading off. Such a battery
will remain in action for months with very little attention, and
gives a very constant current. To prevent evaporation, the surface
of the liquid is frequently covered with oil. It, of course, must
not be moved or the liquids will mix.
Another form of two fluid battery is the Grove, in which the
porous cell contains strong nitric acid and a plate of platinum ;
the outer liquid being dilute sulphuric acid, in which is a plate of
amalgamated zinc. Carbon is, for cheapness, often substituted for
the platinum, the battery then being called a Bun sen. When the
circuit is closed the nitric acid is decomposed, a part of the oxygen
uniting with the hydrogen and setting free binoxide of nitrogen,
which on contact with the air forms dark red fumes of hyponitric
acid. These fumes are very objectionable, as they are hurtful to
breathe, and at the same time rapidly corrode brass, and other
metal surfaces. Various plans have been tried to remedy this
difficulty. For instance, they are rapidly absorbed by alcohol or
by quicklime, and one of these substances is therefore sometimes
placed in flat dishes in the same box as the battery. A mixture
of bichromate of potash and sulphuric acid is sometimes added to
the nitric acid, the chromic acid at once oxidyzing the nitric
fumes. The principal objection to this arrangement is that the
chromium permeates the carbons, forming a disagreeable green
mass in the inner cell. The electromotive force is also less than
that of a Bunsen or Grove cell.
The best remedy is to place the battery out doors, or under a
well ventilated flue, or in an adjacent battery room, where the
fumes will do no harm.
Another form of battery much used at the present time !s the
ELECTRICITY. 5
Leclanche. This consists of a porous cell containing a rod of
carbon tightly packed with pulverized bin oxide of manganese and
placed in a glass jar containing a saturated solution of chloride of
ammonium. The negative electrode is a rod of amalgamated
zinc. These cells are very good when the circuit is closed only
for a few minutes at a time, as the electromotive force is high and
the resistance small, but they run down very rapidly when the
circuit is closed. Many other forms of battery are also in use,
but generally their action is readily understood from the above
examples.
The advantages of a Smee battery are its cheapness, convenience,
cleanliness and the rapidity with which it will work. Its objections,
its small electromotive force, and that it rapidly grows weaker on a
closed circuit. It is, however, much used for electric clocks and
bells. A chromic acid battery is very powerful, but rapidly grows
weaker on a closed circuit, and the zinc must not be left in the
liquid. It is very suitable for the induction coil, or for an electro-
magnet, as it can be set in action by simply lowering the zincs into
the liquid. The Daniell and gravity batteries are well adapted to
giving constant currents for a long time, and, in fact, are the best
for closed circuits. The resistance is, however, considerable. They
are much used on telegraph lines, and for electro-plating. The
Bunsen and Grove batteries are commonly used where a very pow-
erful current is required, as for the electric light, large magnets and
coils. The resistance is small, and the electromotive force large,
but the fumes are very objectionable, and the zincs have to be re-
amalgamated every day. They should always be dismounted and
the parts washed after using. The advantages of the Leclanche
cell are much like those of the Smee, and it is very well adapted
to electric bells, and will keep indefinitely on an open circuit.
Two other sources of electricity are also sometimes employed, the
thermo-battery and the magneto-electric machine. The first of these
consists of a number of pair of strips of different metals soldered
together at the ends, and heated by gas-burners at the inner ter-
minals, the outer ends being kept cool by the air currents circu-
lating around them. To use them, the gas is lighted, and when
they are thoi-oughly heated, a current of great constancy is ob-
tained. The magneto-electric machine consists in substance of a
6 ELECTRICITY.
magnet, in front of which an electro-magnetic armature revolves,
and thus generates a current of electricity as long as the rotation
is maintained. These instruments will be described more in detail
hereafter, in connection with the methods of testing their effi-
ciency.
Connections. To pass a current through any piece of apparatus,
its ends must be connected with the two terminals of the battery
by wires or other good conductors. The circuit is then said to be
closed, and the current will flow from the positive, or carbon pole
of the battery, through the connecting wires to the apparatus, and
through the latter and the second connecting wire back to the
negative pole of the battery. If two connecting wii-es cross each
other so as to touch, or rest against the same metallic body, the
current is liable to pass directly from one to the other, instead of
going through the instrument to which they are attached. It is
therefore common to cover them with some insulating material by
winding them once, or better, twice, with cotton or silk. They
are then called covered wires. To prevent unravelling the thread
is sometimes braided, and to render it more flexible, several fine
wires are sometimes used instead of a single coarse one. The wire
is then often painted, or soaked in parafine to render it impervious
to water, although it is safer to cover wires which are to be used
in water with a layer of rubber. To connect two wires so that the
current shall pass from one to the other, it is only necessary to
scrape their ends clean and twist them together. Or, they may be
cleaned by immersing them in acid and then washing in water and
drying. If the junction is to be permanent, it is better to solder
them. In this case resin should be used instead of soldering acid,
for the latter being hygroscopic, is liable to absorb moisture, keep-
ing the ends of the wire wet, rusting it, and spoiling the connection.
Where the connection has to be made whenever the apparatus
is used, binding screws, or screw cups are more commonly em-
ployed. These consist of little pieces of brass in which a hole is
. bored, into which the end of the wire is inserted, and fixed in place
by a set screw with a milled head, which presses against its side.
Sometimes the screw cups are made with two holes, so that two
wires may be attached at the same time. Generally the binding
screw terminates below in a screw, by means of which it may be
ELECTRICITY. 7
attached to the wooden frame of the apparatus, a connection sol-
dered on below, and connecting wires attached when desired by the
screws. Wires are sometimes connected by double or triple bind-
ing screws, instead of soldering them.
Another method of connecting two wires is to dip both of them
in a small cup containing mercury. The cup may be made by
boring a hole partly through a board and putting a drop of mer-
cury into it, or a metallic cup may be used, and one wire soldered
to its exterior. Mercury cups are convenient from the ease with
which the connections may be altered, but they are objectionable
if they have to be moved, and in accurate experiments the resist-
ance they interpose is found to be variable.
Keys. When a circuit must be broken and closed a great many
times in the course of an experiment, a device called a key is em-
ployed. One of the simplest forms of key is made by fastening
the two wires to a board, and screwing one end of an elastic
piece of brass on to one of them, so that the other end shall be
over the other wire. The circuit is closed by depressing this end
with the finger, while the elasticity of the brass raises it, and
breaks the circuit when the finger is removed. Sometimes a
stiff piece of brass is used, placed between centre-screws, and
raised either by a spring or by a counterpoise on the other end.
The points of contact of the key should be tipped with platinum,
or they will rust or burn away rapidly, especially if the cui'rent is
strong.
Plugs. Two pieces of brass are attached to a base of hard rub-
ber or wood, and separated by a short distance. A conical hole is
then bored between them, so as to form a groove in each. Into this
is fitted a brass conical plug and ground in, so that it shall fit
tightly. When the two brass pieces are connected with the wires
of the circuit, the latter may be closed at will by inserting the plug.
It may therefore with advantage be substituted for a key when
the circuit is to be closed for a considerable time. A plug is also
used when we wish to throw the current out of a piece of appara-
tus without breaking the circuit. The current is here allowed to
pass from one brass piece to the other through the apparatus. On
inserting the plug the resistance of the latter is so small that all
the electricity passes through it.
8 ELECTRICITY.
The great advantage of a plug is the excellence of the contact,
the surfaces being ground together, and any dust or rust being
rubbed off every time the plug is inserted. The surfaces are there-
fore kept bright, and the pressure renders the resistance exceed-
ingly small. Sliding contacts are much to be preferred to simple
pressures, as the latter are liable to introduce considerable resist-
ances, even if the surfaces are protected from rust by platinum.
Switches. When the current, instead of being cut off, is merely
to be diverted into another wire, a switch is used instead of a key.
Let A be a wire connected with one pole of the battery, and B and
C two similar wires connected with the other pole, and with the
two instruments through which we wish the current to pass, and
suppose we wish A connected sometimes with B, and sometimes
with C; the wires JB and O are attached side by side to a small
board, their ends being held down by screws with rounded heads.
A. short distance from them A is similarly attached, the screw
which fastens it passing through a flat strip of brass, which turns
with friction, so that its end may rest on either B or C. Its shape
is such that it always pushes against one of these screw heads,
thus insuring contact, and the friction as it slides over them keeps
the surfaces bright and clean. By merely moving it from side to
side the current may be thrown into one wire or the other.
Commutators. It is frequently necessary to send a current
through a given instrument, first in one direction and then in the
other, and this is done by what is called a commutator. In Fig. 66
let A, B, C, .Z>, represent four quadrants of brass, of
which each is separated from the two adjacent to it
by a short interval, but may be connected by plugs.
Suppose A and J) connected with the positive and
negative poles of the battery, and B and C with the
two terminals of the instrument through which the cur- Flg ' 66>
rent is to be passed. Then if AB and CD are connected by
plugs, as represented by the white circles in the figure, the cur-
rent will pass from the battery to A, by the plug to B, through
the instrument to (7, and back through the second plug to D and
the other pole of the battery. To reverse the currents, change the
plugs so as to connect A C and BD, as shown by the black circles,
when the current will pass, through AC and the instrument to B,
GALVANIC ELECTRICITY. 9
and back to the battery by .Z?, in this case passing from C to ,
and before from B to C. A commutator on the same principle is
made by replacing the four quadrants by four mercury cups, and
connecting them alternately by two bent wires which replace the
plugs. One of the best forms of commutator is shown in plan in
Fig. 67. F is a hard-rubber cylinder, which
may be turned around a horizontal axis so that
it shall rest against the two brass springs A
and D. It is held in place by the supports
B and (7, and carries two strips of brass, one
connected with its axle at the end .Z?,the other
at (7, as shown by the dotted lines. If now,
as in the previous case, A and D are con-
nected with the battery, and and C with the given instrument
the current will pass from A through the cylinder to B, thence by
the instrument to (7, and back by D. When the cylinder is turned
180, the current from A will pass to (7 instead of B, and thus
traverse the instrument in the opposite direction. By turning the
cylinder 90 the current is broken, and may thus be used as a key.
Another commutator is made by connecting the terminals of the
battery with two brass plates, one fastened to the table, the other
held by a spring just above it. The wires attached to the instrument
are fastened to two plates, separated by a piece of hard rubber, and
forming a wedge. When the latter is inserted between the plates
attached to the battery, the current passes and may be reversed by
simply turning the wedge over. Another simple commutator is
made by bringing the two pairs of wires together in a sort of
swivel, so that on turning either around 180 the current is re-
versed.
95. GALVANIC ELECTRICITY.
Apparatus. A battery of three or four Bunsen cells, or of
equivalent strength, an amalgamating trough, some examples of the
screw-cups, plugs, keys, switches and commutators described above,
some fine platinum wire, a coarse galvanometer, an electro-magnet,
electric bells, an electro-magnetic engine, some U-tubes with pla-
tinum terminals, and some chemicals for decomposition.
Experiment. Mount the battery as described above, first amal-
gamating the zincs, and connect the cells for tension, that is, the
10 GALVANIC ELECTRICITY.
zinc of one cell to the carbon of the next. When the experiment
is completed, dismount the battery, pour back the acids and soak
the zincs, carbons and porous cells in water. The connections
must all be made with care, the wires scraped bright, and the
screws turned so that they press hard against the wires. On taking
hold of the terminals, no shock will be felt unless the hands are
moist and the battery powerful ; but touching the wires to the tongue
a slight metallic taste will be noticed, not present when the battery
is not attached. On bringing the terminals slowly together, no
effect is produced until they are in contact or the circuit closed, but
on separating them so as to break the circuit, a small spark will be
noticed. This effect is greatly increased by attaching one terminal
to the end of a file and drawing the other over the roughened
surface, when a series of sparks is produced, due to the combustion
of the minute particles of metal thrown off.
If the terminals are connected with a short piece of fine platinum
wire, the latter is heated, and by diminishing its length, its tem-
perature increases, becoming red, yellow, white, and finally melt-
ing. Such a wire forms an excellent cautery, and would be much
used in surgery but for the difficulty of procuring a sufficiently
powerful and constant source of electricity.
To show the effect of a current on a magnetic needle, connect
the two poles of the battery by a copper wire, so that the current
shall pass through it ; then holding the wire north and south, bring
it down over the needle, when the latter will swing out to one
side. See if the direction is that given by Ampere's law, and by
the laws of currents given in Appendix A. Now place the wire
below the needle, and the latter will turn in the opposite direction.
These effects may be reversed by turning the wire over so that the
current shall flow in the opposite direction. Next, connect the
two battery terminals with two ends of a commutator, and the
terminals of the galvanometer with the other two ends. By
changing the direction of the current, the needle may be made to
deviate to one side or the other. Try the other commutators
in the same way. Place one of the keys in the circuit with the
galvanometer, and notice that the needle deviates only when it is
pressed down ; do the same with a plug. Connect the latter also
so that on inserting the plug in its hole the galvanometer is cut out
GALVANIC ELECTRICITY. 11
of the circuit. Connect two galvanometers, or a galvanometer and
some other instrument described below, with a switch, and see how
the current may be passed through either. Shunt the galvanometer
by connecting its two terminals by double binding screws, both
with the battery and with a wire whose length may be varied.
Notice that in this case the current, and consequently the deflec-
tion, may be reduced as much as is desired.
Next, insert in the circuit a commutator and the electro-magnet,
and notice that the latter has no effect on a piece of soft iron held
near it. Now close the circuit, and the magnet becomes enor-
mously powerful, capable, if large, of supporting several hundred
pounds. It will also hold a heavy bar out horizontally by one
end, or support many small pieces of iron by induction. As
soon as the current is broken, the magnetism instantly ceases.
Holding a basket of nails under the magnet they hang in long
strings from it when the current is closed, and instantly drop when
the circuit is broken. Next, see which is the north end of the
magnet by noticing which end will attract the south pole of the
compass-needle ; the current, as shown by Ampere, will circulate
around this in the opposite direction from the hands of a watch.
Now reverse the current by the commutator, and the magnetism
will be reversed.
An immense number of applications have been made of this
power of producing a powerful attraction, and causing it to cease
instantly. It is difficult to utilize it as a source of power, partly
from the expense and inconvenience of the battery, and partly
because the attraction diminishes very rapidly with the distance.
One of the simplest forms of electro-magnetic engines is that of
Page, in which the current passes through the coil of a small bar
magnet placed between the poles of a permanent horse-shoe mag-
net. The bar magnet is free to turn end for end, and on its axle
is placed a commutator, so that the direction of the current changes
every 180. Placing the bar magnet at right angles to the line
connecting the poles of the horse-shoe magnet, and passing the
current through it, its north end is attracted by, and approaches to,
the south pole of the permanent magnet ; as it revolves past, its
magnetism is reversed, and consequently having the same polarity,
it is now repelled, and attracted by the other pole. A rapid motion
12 GALVANIC ELECTRICITY.
is thus imparted to the bar magnet, which may be reversed by
means of a commutator.
Another important application of electro-magnetism is to electric
bells. These are of two forms, those in which there is a single stroke
when the circuit is made or broken, and those in which the ringing
is continuous as long as the current passes. The first class is very
simply made by attaching a hammer directly to the armature of an
electro-magnet, which is thus drawn up against the bell when the
circuit is made, and pulled back by a spring on breaking the cir-
cuit. If the bell is large, so that the force of the magnet is in-
sufficient, the hammer may be moved by clock-work, which the
electicity serves simply to release. The arrangement for making
a bell ring continuously is shown in Fig. 68. A is an electro-
magnet through which the current passes and
thence through the spring supporting the arma-
ture, and the screw C by a wire to the other
pole of the battery. The first effect is to attract
the armature _S, and bring the hammer in con-
tact with the bell D, striking it. But the cur-
rent is thus broken, the spring supporting B
having been drawn away from the screw C.
consequently the magnet ceases to act, and the
armature flies back until it makes contact again, and is again at-
tracted. These effects succeed each other with great rapidity,
producing a continuous ringing of the bell. C is a screw with a
milled head, so that it is easily brought into exactly the right po-
sition. This arrangement is much used for all kinds of alarm bells,
for hotel annunciators, on telegraph lines to announce that a mes-
sage is to be expected, and in experimental work to denote that a
looked-for event has taken place, since the bell will continue to
sound until the attention of the observer is called, and the circuit
broken. A similar arrangement is also employed to sustain the
vibrations of a tuning-fork, and as an automatic break-piece, to
make and break the current many times a second. This explana-
tion, which is that usually given, does not seem to be adequate,
since there would seem to be no power expended to overcome the
various resistances. After contact the magnet tends to retard the
armature until it comes to rest, as much as it accelerates it before
GALVANIC ELECTRICITY. 13
contact is broken, and hence it would follow that owing to the re-
sistances, the vibrations should become less and less, and soon cease,
while in reality they may increase until they attain a large ampli-
tude, and overcome very considerable resistances. Probably the
true explanation depends partly on the residual magnetism of A,
owing to which the magnet does not begin to retard the armature
until a short time after contact, and continues to accelerate it a little
while after the circuit is broken. Another explanation. is, that the
current does not begin to pass until the instant of contact, while it
continues passing a little while after the spring leaves (7, as is shown
by the spark. Therefore the period of acceleration exceeds that
of retardation. It has been proposed to improve this device by
attaching C also to a spring whose time of vibration is somewhat
less than that of the armature, in which case, when approaching
the magnet, C will follow 1$ and keep the circuit closed, but on
the return, as it vibrates more rapidly, it will break the circuit, so
that the magnet accelerates half the time and does not retard the
other half. Powerful vibrations may be sustained in this way, but
the common method works sufficiently well in ordinary cases.
Connect the platinum electrodes and the poles of the battery with
a commutator, fill the beaker with water and immerse the elec-
trodes. On closing the circuit, little or no effect is produced unless
the battery consists of a great many cells. Now add some sulphu-
ric acid to the water, and immediately bubbles of gas will be given
off from each electrode. By filling some test-tubes with water and
inverting them over the platinum terminals, the gases may be col-
lected. It will be found that the gas given off by the terminal
attached to the negative pole has twice the volume of the other,
and is hydrogen, as is easily seen by igniting it. The other gas is
shown to be oxygen by holding in it a red-hot burnt match, when
it will glow and be relighted. If both gases are collected in the
same vessel, they will explode violently if ignited. This experi-
ment should be tried only with minute quantities of gas, and is
best performed by removing the mixed gases to another larger
and deeper vessel, and allowing a bubble at a time to ascend from
the bottom, and ignite it at the surface. The reason of the effect
of the acid is that the resistance of pure water is enormous, so that
the current with pure water is exceedingly minute, and most of
14 GALVANIC ELECTRICITY.
the gas dissolved as fast as formed. The acid acts merely by ren-
dering it a better conductor. Reversing the current by the com-
mutator, of course reverses the position of the gases disengaged.
When a solution of a salt is acted on by a powerful current of
electricity, a decomposition takes place by which the base is car-
ried to the negative or zinc pole, and the acid to the positive or
carbon pole. This effect is shown by the following experiments.
Fill a U-tube with a solution of sulphate of soda, and tinge it blue
with a little litmus. Place a platinum electrode in each arm of
the tube, and after some time the acid set free at the negative pole
will redden the litmus. This effect is hastened by stirring up the
liquid a little, so that the adhering layer of acid shall mix with the
remainder. If the current is reversed, the blue color will return,
the acid reuniting with the base. If a chloride, as common salt, is
used, the chlorine set free will bleach the solution, removing the
blue tint. By using a solution of iodide of potassium and starch,
the characteristic blue color of iodide of starch is readily pro-
duced. To bring the starch into solution, it should be first soaked
in cold water and then boiled. A similar effect is obtained with
ferrocyanide of potassium, using iron wires as electrodes, instead
of platinum. Prussian blue is then produced at the positive pole.
The presence of the base at the negative pole is best shown by
salts of the metals. Pour a solution of acetate of lead into a
beaker and immerse the two electrodes. The lead will be at once
deposited on the positive terminal, in beautiful crystalline leaf-like
forms. A similar effect is obtained with nitrate of silver. With
sulphate of copper, if the current is not too strong, a smooth coat-
ing of metallic copper is deposited, the electrode, in fact, being
electro-plated. Copper may be deposited on other substances in a
similar manner, but it is better to arrange the apparatus expressly
for the purpose, as follows. A single large DanielPs cell is used as
a source of electricity, and near it is a tank filled with a saturated
solution of sulphate of copper, to which has been added some sul-
phuric acid in the proportion of one part to ten of water. To the
positive terminal of the battery is attached a plate of copper to sup-
ply the metal to be deposited, and to the other terminal is fastened
the object to be plated. This should be cleaned and brightened
to remove the dirt or rust, and if not metallic, covered with a
TELEGRAPH. 15
coating of plumbago or black lead, to render it a good conductor.
To make a copy of a coin, model or other object, two platings
must be made, the first of the object, the second of the first plating.
Or, a cast may be made in plaster or wax rubbed with plumbago
and plated as above. A very constant current should be employed,
and one that is not too powerful, or the metal is liable to be
thrown down in lumps, in a fine powder, or to strip, that is not
adhere. Silver and gold are best deposited from solutions of
their cyanides, and in the case of gold the liquid should be heated
to about 55 C. (130 F.).
96. TELEGRAPH.
Apparatus. The best apparatus for this experiment is a real
telegraph, or tables fitted up like real offices, two for terminals, and
at least one way-station, with relay and local battery.
Experiment. A telegraph may be regarded as composed of four
parts, the source of electricity, the line or conductor for connecting
the two stations, the apparatus for sending the message, and that
for receiving or reading. For a source, a common galvanic battery
is employed, of a strength dependent on the distance and number
of stations, or, more s'trictly, on the resistance of the circuit. For
short distances, two or three Daniell or gravity cells are best.
The line consists of a wire, which should be of iron, galvanized
if the distance is considerable, suspended by glass or other non-
conducting supports, if it passes out doors, but in-doors a copper
wire may be simply tacked along the walls or floor, taking care
that it does not touch any large metallic or other conducting body.
Instead of a second wire to bring back the current, the two ends
may be connected with a gas-pipe, or, much better, a water-pipe.
If these are not available, two large metal plates may be buried
in the ground, and wires connected with them, forming what is
called an earth. The sending instrument is merely a form of key
described above, so that the circuit may be closed for a longer or
shorter time. The instrument for receiving the message, called a
register, consists of an electro-magnet, whose armature is held back
by a spring, and carries a point, which, when the circuit is closed,
is held down on a long strip of paper drawn slowly under it by
clock-work. If the circuit is closed for an instant, a dot will there-
'
t
16 TELEGRAPH.
fore be imprinted on the paper ; if for a longer time, a line. It
was soon found that the dots and lines thus formed could be read
by the sounds produced by the armature, which clicks on being
drawn down to the magnet, and gives a different sound when
drawn back by the spring. Instead of a register, a sounder is
therefore used, which consists of a single electro-magnet and ar-
mature, the latter being drawn back by a spring whose tension
may be regulated by a screw. The object of this screw is to ad-
just the armature with the varying strength of the current, due
either to changes of the battery, leakage along the line, or, in long
lines, to currents of electricity from the air or earth. This is espe-
cially the case during displays of the aurora borealis, and during
thunder storms, when in some cases the battery may be for a time
dispensed with, and the line worked without. In wet weather the
insulators become covered with moisture, and calise a great leak-
age. During violent thunder storms, the line should be attached
directly to the earth wires, taking the instruments out of the cir-
cuit; otherwise there is danger of the lightning entering the build-
ing along the wire, burning up the magnets, and perhaps doing
other injury. The instruments are so connected that the current
passes from the battery, which may be placed at either end of the
line, through the key and sounder, along the line to the other sta-
tion, through its key and sounder to the earth, back through the
ground to the earth of the first station, and thus to the other pole
of the battery. When a message is to be sent from either station,
the key at the other end must be held down or thrown out of the
circuit by a plug or switch, as otherwise the circuit will be, broken,
and no current will pass. For the same reason, after sending mes-
sages, the circuit must be closed at both ends, as if left broken at
either station, the operator at the other end could not give notice
that he wished to send a message.
If the distances to be travelled are considerable, the circuit will
not be powerful enough to work a register or sounder, and there-
fore a relay is used, which resembles a sounder, but contains a mag-
net wound with very fine wire, and is thus sensitive to a very feeble
current. This is connected with a second battery, called a local
battery, and an ordinary sounder, and is so connected that when
the armature of the relay moves, it alternately makes and breaks
TELEGRAPH. 17
the local circuit. The sounder therefore acts with the full effect of
the local battery independently of any leakage or other changes in
the main line, whenever the main current is sufficient to work the
relay. On very long lines repeaters are used, which consist of re-
lays which throw a second main battery into circuit, and thus
repeat the message automatically.
To send a message, therefore, it is necessary first to arrange a
system of long and short currents or dots and lines to represent
each letter of the alphabet; and then any message may be sent by
spelling it out letter by letter with the key, when all the relays and
sounders along the line will move in accord. The alphabet in- use
on the Morse telegraph in this country is given in Fig. 69.
A - Q 4
B R 5
C -- - S --- 6
D T 7
E - U 8
F V 9
G W Comma
H X Semicolon
I -- Y Period
J Z Interrogation
K & - Exclamation
L Parenthesis
M 1 Italics
N 2 Paragraph
O-- 3 Quotation
P
Pig. 69.
Thus the letter A is represented by a dot and line, or by making
the circuit first for an instant, and then for a longer time ; the letter
by a line and three dots, or one long and three short currents,
and so on. The alphabet should not be memorized or practised in
order as given above, but the following system adopted. Two
students should work together at this experiment, and send and
receive alternately. It is well at first to use the register, and record
the letters on the paper, to see that they are correctly formed. The
proper position for the hand, is to hold the button at the end of the
2
18 TELEGRAPH.
key by placing the fore and middle fingers on it, and the thumb
under its edge, nearly closing the other two fingers. Keep the
wrist limber, and rest the arm on the table at the elbow. The
motion must be mainly from the wrist, which should be perfectly
limber, but move up and down with the fingers, and not in the
opposite direction.
Now begin by making a single dot, pressing the key down firmly
and raising it instantly. The line thus made can scarcely be too
short. Next make a series of these dots at regular intervals, grad-
ually increasing the speed until it reaches five or six in a second, at
perfectly equal intervals. Make the letters E, I, , //, P and 6,
which consist of from one to six equidistant dots. In all cases
begin slowly and make them very distinctly, gradually increasing
the speed, until they can be made to follow each other rapidly in
any order, and be read by the sound alone. Make the letters 0,
R, &, (7, Z and Y, formed of dots unequally spaced. The short
interval is called a break, the longer one a space. The former
should have a length about equal to a dot, the latter twice this
amount. The letters of a word should be separated by an inter-
val of four dots, and the interval between words, six dots. The
dashes of the Morse alphabet have a length about three times that
of a dot, except in the case of L or 0, which have double this
length. Originally was made longer still, or equal to nine dots,
but it is now commonly made identical with L. The single dash
representing T should now be practised, also the longer dash, L\
both are liable to be made too short, especially the latter. Make
a series of dashes succeeding each other, trying to bring them as
close as possible, the hand jumping from each to the next. Prac-
tise together the characters T, L,0,M,5 and Paragraph. The
next combination is the dot followed by the dash, as in the letter
A', this must be practised carefully, taking great care not to sep-
arate the two characters, and not to make the dot too long. Prac-
tise T, 0, M, and A ; when these four letters are well written,
practise A, V, V, 4, and W. The dash followed by a dot, as in N,
is a still more difficult combination. There is the same difficulty in
making the interval too great, and the dot and dash of the same
length. Practise together /, 0, M, A and N, until each is clearly
distinguished. Then try JV, D, <?, , 7 and Exclamation. A dash
INDUCTION COILS. 19
between two dots and a dot between two dashes, as F and JT,
should next be practised, and alter them Q, -3^ #> #, JJ Comma, Sem-
icolon and Quotations. The only remaining characters are 1,
Period, Parenthesis, Interrogation and Italics, which may be
learnt next, although the only punctuation marks in common use
on most lines are the comma and period. The alphabet may now
be practised in order, words spelt and messages sent. Let each
student take a book and send a line altei'nately until each has com-
pleted his page.
A convenient method of learning the alphabet is by a little instru
ment formed of a steel spring, which makes a click when bent, or
when allowed to snap back, thus imitating a sounder. A knowledge
of the Morse alphabet will be found useful for signalling in many
cases besides by a telegraph. Thus two persons niay signal to
each other at considerable distances by long and short notes on a
whistle or horn. Again, messages may be sent by waving the
hands or a piece of cloth, agreeing that one position shall repre-
sent a dot and another a line.
97. INDUCTION COILS.
Apparatus. An induction coil, the battery of Experiment 95,
a Leyden jar, some Geissler tubes, terminals of various metals, a
spectroscope, and some fine uncovered copper wire for connections.
Experiment. The induction coil consists of two coils of wire,
the inner or primary consisting of a few turns of stout copper wire,
and the outer or secondary of a very long, fine, carefully insulated
wire. The coils of the primary wire are connected with the bat-
tery, and the instant the circuit is made or broken a current is
induced in the secondary coil, which on account of its great length,
attains a high potential, each coil adding to the effect of the pre-
ceding. When the circuit is made, the secondary current has the
same direction as the primary ; when broken, an opposite direction.
As a current is induced also in the primary circuit which dimin-
ishes the secondary current, a condenser is connected with the
inner coil, formed of alternate sheets of tin foil and oiled silk, by
means of which the current induced in the primary is absorbed.
Inside the inner coil are placed a number of wires, or a bar of soft
iron, by which the effect is greatly increased. In coils used for
20 INDUCTION COILS.
medical purposes, the common method of reducing the current is
by partially withdrawing this core. Its effect is due to the pow-
erful magnetic action induced, which ceases when the primary
circuit is broken. It acts, therefore, by magneto-electricity. Much
depends on the rapidity with which the current is made and
broken. In small coils this is usually done automatically by an
arrangement like that described under Electric JBells, Experiment
95, the iron core being used as the electro-magnet. In larger in-
struments various devices are employed ; sometimes the current is
broken by withdrawing a point from a cup containing mercury,
whose surface is covered with alcohol to protect it from oxidation,
and to render the action more instantaneous. Sometimes a toothed
wheel raises a spring hammer, which by its rapid descent suddenly
breaks the circuit.
The two ends of the primary terminate in screw cups, to which
the battery wires are to be attached. ' The secondary coils
should be connected with brass points, whose distance apart is
readily varied. Making and breaking the circuit a spark will pass
between these points if their distance is not too great. Be careful
not to take the shock, as its effects are very disagreeable, though
not dangerous. All the connections of the secondary coil may be
made with the fine wire, which is convenient from the ease with
which it is bent, while the electro-motive force is so great that the
resistance has little effect.
Separate the points and connect the terminals of the secondary
coil with one of the Geissler tubes. The latter consist of glass tubes
of various, often fantastic, forms, containing gases at extremely
feeble pressures. Platinum wires are sealed in at each end of the
tube, by which the electricity is conveyed to the interior, and
thence passes through the rarefied gas. Now make and break the
primary circuit rapidly, when the whole interior of the tube will
be illuminated with a beautiful light, whose color depends on the
kind of enclosed gas. Sometimes phosphide of calcium, or other
phosphorescent substances are enclosed in the tubes, which then
shine after the current has ceased. The phenomena of fluorescence
are also well shown by placing sulphate of quinine in the tubes,
washing them with uranium salts, or making them of uranium glass.
The light of the spark being intermittent, if a moving body is
LAW OF GALVANOMETER. 21
viewed by it, a large number of images are formed, as with the
stroboscope. This effect is well shown by shaking the hand rapidly
near it, or by moving the head from side to side. Sometimes the
tubes are made to revolve, and beautiful colored stars are thus
produced. If the wires connecting the coil and brass points are
connected, one with the inner, the other with the outer coating of
the Leyden jar, the spark at once changes its character ; it becomes
much more brilliant and dense, but shorter, producing also a much
louder snap, since it now must first, so to speak, fill the jar or con-
denser before it can leap across, a much greater quantity therefore
passing at a time.
Next, view the spectrum of the Geissler tube with the spectro-
scope, as described in Vol. I., Experiment 76, using by preference
tubes contracted along the centre, so that the light is reduced to a
narrow, bright line. The spectra thus obtained consist of several
bright lines, characteristic of the contained gases. Measure the
position of these lines, and determine their wave-length. Replace
the tubes by terminals of various metals, and observe the spectra
as before. The effect is here greatly improved by using the Ley-
den jar. Another method of obtaining the spectrum of a metal is
to make a solution of its chloride or other salt, connect it with one
terminal of the coil, and the other terminal with a platinum wire
brought near its surface, and observe the sparks between them.
98. LAW OF GALVANOMETER.
Apparatus. A battery giving a neai'ly constant current of elec-
tricity, as a Daniell's cell or a thermal battery, a variable resistance,
that is, a set of resistance coils or a rheostat, and the galvanometer
to be tested.
Experiment. Make connections as in Fig. 70, so that the current
shall pass from the battery, J3, through the
resistance, jR, and galvanometer Gf.
Give H various values, and record the
reading of Gr in each case. If a tangent
galvanometer is used, read from both ends
of the needle and take the mean. If the Fig< TO>
galvanometer is very sensitive it should be shunted, that is, its
two terminals connected by a German silver wire, which thus
allows but a small part of the current to pass through it.
22 GALVANOMETER CONSTANT.
Next, construct a curve with abscissas equal to the various val-
ues of H and ordinates to those of the deflections #. Prolong this
curve to the left of the axis of T until the point is reached where
a = 90. The abscissa of this point shows how much the resist-
ance must be diminished to render the current infinite, or to reduce
the total resistance to zero ; it therefore gives the resistance of the
battery and galvanometer. Next construct a second curve, having
ordinates as before, equal to the angles of deflection, and abscissas
to the strength of the current. The latter, since the electromotive
force, E, is constant, by Ohm's law is inversely proportional to
the total resistance, that is, equals the reciprocal of the sum of the
resistances of the rheostat, galvanometer and battery, multiplied
by a certain constant kH. Determine this constant from Ex-
periment 99, and then construct the curve, which will give the
absolute strength of' the current in vebers, directly from the read-
ing of the needle.
If we merely wish to see if the galvanometer follows the law of
the tangents, construct a curve with abscissas equal to the resist-
ance of the rheostat, and ordinates to the cotangent of the angle
of deflection. If the law of the tangents holds, this construction
will give a straight line which will meet the axis of JTat a point
whose distance from the origin will equal the resistance of the
battery and galvanometer.
If the galvanometer is shunted and its resistance is J?, and that
of the shunt r, then the fraction -^ only, will pass through
R-\- T
the galvanometer, and the above results must be multiplied by this
fraction to deduce the strength of current required to produce a
given deflection when the shunt is used.
To measure a current with this instrument is then a very simple
matter. Pass the current through it, note the deflection and find
from the curve the absolute strength of current. If the galvanom-
eter follows the law of tangents, multiply the natural tangent of
the angle of deflection by IcH, and the same result is attained.
99. GALVANOMETER CONSTANT.
Apparatus. One or more galvanometers to be measured, a very
constant battery, a German silver wire, and a beaker containing a
solution of sulphate of copper, in which two copper electrodes
may be placed.
GALVANOMETER CONSTANT.
23
Experiment. Several galvanometers may be measured simulta-
neously by this method almost as easily as a single one. The nee-
dles are brought carefully to
the zero, and they are then all
placed in the circuit as in Figure
71, taking care to place them at
such a distance apart that their
needles shall not affect each
other. Connect the two termi- Fig - 71 -
nals of the battery with the German silver wire S so that it
may be lengthened or shortened, and thus by varying it, the
strength of the current through the galvanometer kept constant.
If either of the galvanometers as 6?" is very delicate, it should be
shunted so that its needle shall be deviated about as much as the
others ; this is easily effected by connecting its terminals with a
wire of German silver, varying its length until the desired deflec-
tion is attained. Next, weigh the electrodes carefully, and con-
nect one with one pole of the battery, the other with the terminal
of the galvanometei'.
So much of the experiment is preliminary, and the remainder
should, if possible, be performed at such a time that observations
may be taken at intervals for several hours ; for instance, starting
early in the morning, and observing them every hour or two, during
the day. Close the circuit by immersing the electrodes in the sul-
phate of copper, and bring them so near each other that the devi-
ation of the needles shall be between 20 and 70. Record the
time and read carefully the deflection of each galvanometer. If
the battery was perfectly constant, it might be left to itself for
several hours, but as it is liable to vary, it should be watched, and
any change in the needle corrected by shortening or lengthening
the wire /$, so that the current through the galvanometer shall be
nearly constant. This should be continued for several hours, and
the circuit then broken by raising the electrodes out of the liquid,
washing them meanwhile with a stream of distilled water from a
wash-bottle. Then wash again in distilled water, and finally
in alcohol. Note the- time when the circuit is broken, and see
if all' the needles retura to* zero. Having dried the electrodes
weigh them carefully, when it will be found that one will have in-
24 GALVANOMETER CONSTANT.
creased, the other diminished, in weight, the copper being removed
from one onto the other. The increase, in, is the most to be relied
on, but it is well to measure the diminution of the other electrode
also, as a check. A current of one veber will deposit .326 milli-
grammes of copper per second. Hence the current in the present
case will be 5^- in which t is the time in seconds. If either
of the galvanometers follows the law of the tangents, JcH is de-
termined directly from the equation C = kH tang v, in which
both C and v are given. In other cases, the observations of Ex-
periment 98 must be employed. Determine from them what total
resistance R f was required to produce the deflection observed in
the present experiment. But the deflection being the same, the
currents also must be equal ; or since E = C r -R', the electromotive
force then employed may be computed. Substituting this value of
E and the observed total resistance in the equation C = -^7, we
obtain a series of values of the current corresponding to various
deflections. A curve should be constructed for each galvanometer
with these quantities as coordinates, and will prove of the greatest
value as it will show the absolute strength of the current in vebers,
corresponding to any given deflection.
The quantity IcH should be frequently determined to test its
constancy, as it varies with the horizontal component of the earth's
magnetism, with changes in the position of the needle in the coil,
and of the distribution of its magnetism. The first of these
causes will alter all the ordinates of the curve in the same ratio,
while the last two will change its form. Variations in the intensity
of the mngnetism of the needle will not affect the curve, since it
changes the component due to the earth and that due to the coil
in the same ratio.
Having found the constant of one galvanometer, that of any
others may be found directly from it. Thus, connect them as in
Figure 71, except that the beaker of sulphate of copper may be
thrown out of the circuit. Alter 8 until the deflection of the
galvanometer previously measured is the same as before. Then
the current is also the same, and hence from the deflections of the
other galvanometers, their constants may be determined as above.
For a Thomson, or other very delicate galvanometer, a simple
COSINE GALVANOMETER. 25
shunt is not sufficient, unless the wire is so short that its resistance
cannot be accurately determined. In this case, after shunting it,
connect one terminal with a large resistance, and then connect
the other terminals of the galvanometer and resistance with a
second shunt. A third reduction may be made if necessary, and
the deflection thus reduced indefinitely. If the galvanometer is
astatic, or has a damping magnet, of course the slightest change in
its magnetism, in that of the earth, or in the position of the mag-
net, will greatly alter its constant. Another method of finding the
constant of a sensitive galvanometer will be given under Experi-
ment 104, and the results should be compared to check each other.
100. COSINE GALVANOMETER.
Apparatus. A constant battery, a commutator, some German
silver wire and a cosine galvanometer. The latter differs only
from a tangent galvanometer in having the coils free to turn
around a horizontal axis, the angle being measured by a graduated
circle and index.
Experiment. Turn the galvanometer around horizontally, read-
ing the two ,ends of the needle to see if they agree. If not, there
is an error of eccentricity, and the mean should always be em-
ployed. .Turn the instrument until the needle points to 0, and
connect with two of the terminals of the commutator, and the
battery with the other two. The current may now be passed in
either direction through the galvanometer, and should give its nee-
dle a deflection of 60 or 70. If, as is probable, the deflection is
greater, shunt the battery by connecting its terminals by the Ger-
man silver wire, and reduce the length until the required deflec-
tion is obtained. This deflection may now be altered from its
greatest value when the coils are vertical, to when they are
horizontal. Bring them into the latter position, or so that their
index reads 90, and see if the needle reads 0. If not, the instru-
ment is not levelled, and one side should be raised or lowered until
the needle is brought to 0. Turn the coils 180 and see if the
needle again points to 0. If the needle is hung by a fibre of
silk this correction may alter its eccentricity. Next, make the
coils vertical, or at 0, and take a series of readings of both ends of
the needle, turning the coils 10 at a time. Calling u the mean
26 DIFFERENTIAL GALVANOMETER.
angle of the needle, and w that of the coils, compute tang v sec w,
which should be a constant in each case.
Turn the coil until the deflection is somewhat less than 45, and
bring the needle to 0, by turning the whole instrument horizon-
tally. Break the circuit, and let the needle come to rest. Its
reading will show the amount the galvanometer has been turned,
and its sine multiplied by the secant of the angle of the coils
should give the same result as before.
It will be seen that the current may be measured in a variety of
ways by this instrument. First, with the coils vertical, as by a
common tangent galvanometer. Secondly, inclining the coils a
series of readings may be taken whose mean gives the strength of
the current with great accuracy. And thirdly, bringing the needle
to by turning the whole instrument, and determining the deflec-
tion by breaking the current. The instrument is then used like a
sine galvanometer.
Comparing the three methods, the tangent galvanometer gives
good results for angles less than about 60 or 70, but above this
point the tangents increase so rapidly that a considerable change
in the current corresponds to but a small alteration in the position
of the needle. The sine galvanometer is more troublesome to
read, and cannot be used for strong currents except by inclining
the coils, as when the deflection exceeds 45 the needle cannot be
brought to coincide with them. In the neighborhood of this
point, however, it is very sensitive, and might be used with advan-
tage when, as in Experiments 99 and 108, we wish to detect a
slight variation in the strength of a current. The advantage of
the cosine galvanometer is that several independent readings may
be taken ; especially in the case of strong currents, when by turning
the coils, the needle maybe brought to that part of its scale where
it is most sensitive. It is open to the objection, however, that if
the coils are very much inclined they tend to make the needle clip,
owing to the large vertical component. It is therefore generally
better with very strong currents to partially reduce the eflect by
shunting the instrument.
101. DIFFERENTIAL GALVANOMETER.
Apparatus. A battery of one Daniell cell, a differential galvan-
ometer, a rheocord, an ohm, an accurate sheet-metal gauge or
DIFFERENTIAL GALVANOMETER. 27
wire gauge, and some copper wire whose resistance is to be de-
termined.
Experiment. A differential galvanometer differs from the ordi-
nary form in having two equal coils, through either or both of
which the current may be passed. It may be used as a common
galvanometer by employing only one coil, or connecting them to-
gether so that the current shall pass in the same direction through
both. Thus calling the coils AB and (7Z), we may use AB or
CD alone, or we may connect B and C and pass the current
through AB CD. In this case we have double the number of coils
of either separately, but double the resistance. Again we may
connect A and C, B and _>, and thus have a galvanometer of
only one-half the resistance of either coil separately. The current
in this case divides, a part going through A C and part through
BD. The differential galvanometer is ordinarily used to test the
equality of two currents by passing them through the coils so that
they shall tend to turn the needle equally in opposite directions,
or leave it at rest. The deflection in any case will equal the dif-
ference of the two currents.
This will only be the case when the two coils have the same re-
sistance, and have the same relative position with regard to the
needle and this must therefore be tested first. Connect the termi-
nals B and D together, and A and C with the battery, so that the
current shall traverse the path ABDC, or the same current go
through both coils in opposite directions. Then if the coils are
rightly placed they will have no effect on the needle, which will
remain at zero. Tf not, one or both of them must be moved until
this condition is fulfilled. Next connect A and Z>, B and (7, and
pass the current through, when it will divide, equal parts going
through each coil if the resistances are equal, and not deflecting
the needle. "When both these tests are satisfied the instrument
is ready for use.
The last connection is that commonly employed when using
the galvanometer, two circuits being formed, one for each coil.
Insert the ohm in one circuit, and the rheocord in the other. The
latter consists of two platinum wires stretched side by side over a
millimeter scale, and connected together by a slide formed of two
thimbles joined together and containing mercury, through which
28 DIFFERENTIAL GALVANOMETER.
the wires pass. By varying the position of the slide, the length
of the wire in the circuit may be altered, and its amount deter-
mined by the scale. Move the slide until the deflection of the nee-
dle is reduced to zero. Then remove the ohm and connect the
wires attached to it directly together. Bring the needle again to
zero, and the difference in reading gives the scale-reading corres-
ponding to 1 ohm. Repeat two or three times, and it will be
found that the results are not wholly concordant, owing to the im-
perfect connection made by the mercury. Now interchange the
rheocord and ohm, and if the galvanometer is correct the same
value of the ohm should be obtained ; if not, the true value will
be the mean proportional of these two.
Place the rheocord in one circuit, and a measured length of the
wire in the other, and bring the needle to zero. This by a simple
proportion gives the resistance in ohms. Repeat with another
piece of different length. Now find the diameter of the wire
by the sheet-metal gauge. For this purpose close the gauge by
turning the milled head and see if the reading is zero ; if not, this
reading must be added to, or subtracted from, the observed read-
ing, according to its sign. Next turn the milled head, insert the
wire, and close the gauge on it. The reading is then taken as
with any micrometer screw. In Brown and Sharpe's gauges one
turn of the screw equals ^ of an inch, or .025, and the head is di-
vided into 25 equal parts, each of which accordingly equals one
thousandth of an inch. The reading should be repeated several
times on different parts of the wire. The resistance of a wire of
pure copper 1 metre long and 1 mm. in diameter at C. equals
.0127 ohms, and for any other wire is proportional to its length,
and inversely as the square of its diameter. This quantity must
be multiplied by (1 + .0038 t) in which t is the temperature of
the room. Compute from this what would be the resistance if the
wire consisted of pure copper, and dividing the observed resist-
ance by this quantity gives the relative conductibility compared
with pure copper.
Various devices have been proposed to remedy the defects of
the rheocord. It may be constructed like a sonometer, the con-
nection being made through the movable bridge. Formerly resist-
ances were generally measured by the rheostat, which consists of
WHEATSTONE'S BRIDGE. 29
two cylinders, one of wood the other of metal, so connected that
a wire may be wound from one on to the other, and the resistance
thus varied at will. In another form the wire is wound on a
wooden cylinder, and the connection made at any desired point
by a sliding elastic strip of brass. None of these instruments,
however, give very satisfactory results.
102. WHEATSTONE'S BRIDGE.
Apparatus. A Wheatstone's Bridge and set of resistance coils,
a Thomson's galvanometer, shunt, lamp and scale, a battery of two
Darnell's cells, some coils of wire whose resistance is to be deter-
mined and some copper wire.
Experiment. These various instruments must be described in
detail beftn-e showing ho\v to use them. The Wheatstone bridge,
though in principle the same as that
given in Appendix A, in its actual con-
struction bears no resemblance to the
figure there given. It is represented
in Fig. 72, and consists of a number of o j
resistance coils connected end to end, p + t tTT' + 'f ' I
with stout brass pieces between them, Fig- 72.
which may be connected together by
plugs, so as to form three continuous lines, CB, BO and OD,
whose total resistance is extremely small. At A, B, C, and D, are
placed screw cups with which wires may be connected, and be-
tween A and C are three resistances of 10, 100, and 1000 ohms,
either of which may be thrown into the circuit by merely drawing
its plug. Three similar resistances are interposed between A and
B, while between and B are coils of 1, 2, 2, 5, 10, 10, 20, 50
ohms, and between and D coils of 100,100, 200, 500, 1000, 1000,
2000 and 5000 ohms. The battery is now connected with A and
Z>, the galvanometer with B and (7, and the resistance to be meas-
ured P, with (7 and D. The current accordingly divides at A,
part passing through M and 0, and the remainder through JVand
P, the galvanometer remaining at rest only when M : N= : P.
M and JVmay evidently have values of 10, 100 or 1000 ohms, and
anything from 1 to 10,000 ohms.
30 WHEATSTONE'S BRIDGE.
The Thomson's galvanometer consists of a long coil of very fine
wire, at the centre of which a minute mirror is hung by a single
filament of silk. To the back of the mirror is attached a little
magnet whose motions are greatly magnified by placing in front of
it a scale of equal parts and a lamp, in such a position that the
image of the flame shall be reflected on to the scale by the mirror.
To render the light as bright as possible, the flame which is formed
by a flat wick, is placed edgewise, and the mirror is slightly con-
cave, or a convex lens is interposed between it and the scale.
Sometimes a narrow slit is interposed in front of the lamp, so as to
form a bright line on the scale, but it is generally better to use a
broader slit with a horse-hair stretched down its centre. A
bright rectangle is therefore projected on the scale with a black
line in the centre, whose position can be read with great precision.
To bring the spot of light to the center of the scale, and to neu-
tralize in part the magnetism of the earth, a magnet is placed
above the coil with its north pole turned towards the north. Grad-
ually lowering this magnet, the effect of the earth will be neutral-
tralized more and more, as is shown by the increased time of
vibration of the mirror and spot of light. Finally, a point is
reached where the needle turns and assumes any position at will.
The earth's magnetism is here neutralized, and if the magnet is
still further lowered the suspended needle will point with its
north pole to the south. Since, with a given current the tangent
of the deflection is always inversely proportional to the horizon-
tal component of the earth's magnetism, if the latter is rendered
very small, the former may be increased indefinitely, so as to pro-
duce a large deviation with even a very feeble current. The
instrument as thus adjusted is very sensitive, so that a slight
current will throw the spot completely off the screen, and an ordi-
nary current might injure the instrument. To reduce its sensibil-
ity a shunt is employed in which its terminals may be connected
by a wire having a resistance of , ^ or v fa of that of the coil.
In the first of these cases, for one part of the current passing
through the galvanometer, nine will pass through the shunt, hence
the galvanometer will receive only one tenth of the whole. The
others, in the same way, cut off all but one hundredth and one
thousandth. These three coils are attached to one terminal of the
WHEATSTONE'S BRIDGE. 31
galvanometer, and are connected with the other when desired, by
a plug. By inserting the latter in another hole, the two termi-
nals are connected directly, so that no current can pass through
the instrument.
To set up the apparatus, place the galvanometer on the table, or
preferably, for greater steadiness, on a bracket attached to the wall,
or on a stone pier, and facing east or west; this direction is to be
pi-eferred as a little more convenient, but it is not indispensable.
Level it by the screws in its base and raise the magnet and mirror
by a little pin just above the coil, so that they shall hang freely
nearly in the centre of the coil. Light the lamp and place it with
its flame edgewise to the galvanometer, and place the scale in front
so that the light shall shine through the slit on to the mirror.
Next, to bring the spot of light to the centre of the scale, raise
the magnet to its highest position and turn its north end to the
noi-th. See now if the mirror swings freely from side to side on
turning the magnet. A bright spot should appear on the scale
and the distance of the latter should be altered until a distinct
image of the slit and vertical hair is formed. Now moving the
magnet slightly, this image will swing from side to side, and may
be brought to any point of the scale. Next, lower the magnet,
turning it, if necessary, so as to keep the spot on the scale, until a
point is reached where the spot goes off" to one end of the scale,
and the mirror tends to turn completely round. The earth's mag-
netism has now been a little more than neutralized by that of the
magnet. The latter should next be raised a little, so that the-
earth's magnetism shall be a little in excess, when the spot will
vibrate slowly over the scale, and on turning the magnet may be
brought back to the centre. As it is difficult to turn the mag-
net slowly enough by hand, a tangent screw is attached, by which
the spot may be brought exactly to any desired point. If the
mirror cannot be brought parallel to the coils by raising the
magnet to its highest position and turning it around, the magnet
should be lowered and turned, if necessary, wholly around until
the mirror is parallel to the coil ; it may then be raised gradually,
and finally left a little below the position of equilibrium. The
above adjustment once made, it should be kept undisturbed except
to bring the spot of light to the centre of the scale, which may be
32 WHEATSTONE'S BRIDGE.
done either by moving the lamp or scale, or turning the tangent
screw slightly. The position of the spot often changes from day
to day, owing either to changes in the torsion of the silk suspend-
ing fibre or in the magnetism of the earth or compensating mag-
net.
A convenient arrangement is to mount the galvanometer so
that the mirror shall be four feet from the floor, and place a table
about three feet in front of it ; on this is placed a strip of ground
glass at the level of the eye, on which the spot of light is received,
and a scale is placed just below to show its exact position. The
battery is placed below the galvanometer, and the other apparatus
on the table; readings can thus be taken with great convenience
and the galvanometer is protected from injury or disarrangement.
To show the extreme delicacy of the galvanometer, remove
the shunt and connect two pieces of copper wire with its termi-
nals. Place the two ends in the mouth, one above, and the other
below the tongue, and a current will be at once formed, often suffi-
cient to throw the spot off the scale. The cause is the different
chemical action of the saliva, from different parts of the mouth.
In the same way a cuiTent is produced by holding the ends with
moist fingers, or dipping both into the same vessel of water, owing
to slight differences in the two surfaces. Holding one terminal in
the teeth and compressing the other with a pair of pincers, pro-
duces a similar effect. These experiments may be varied almost
indefinitely.
The shunt and resistance coils may be placed in any convenient
position, the former being connected by two of its terminals with
the coils at B and C. The battery is also connected with the
coils at A and D. Two keys must be interposed between the
coils and the battery and galvanometer. These should be placed
side by side so that they can be closed by the first and middle
fingers of the right hand. These keys are best made of single
strips of brass screwed down on to the table and insulated at the
ends by rubber buttons. The objection to using a single key con-
nected with the battery is, that currents may be induced in the
coils which will disturb the galvanometer unless the battery cir-
cuit is closed first, and the galvanometer circuit afterwards. This
is easily done with the two keys, after a little practice. Some-
WHEATSTONE S BRIDGE. 33
times a single key is employed, formed of two flexible pieces of
brass, so arranged that on pressing down the upper one, contact
is made between it and the second strip, which closes the battery
circuit, and pressing it still further, closes the galvanometer cir-
cuit by bringing two brass pieces in contact, of which one is at-
tached to the table, the other to the lower surface of the middle
brass strip.
When the instrument is not in use the plug should always be
inserted between the terminals of the galvanometer, so that if the
circuit is accidentally closed no current shall pass through it.
Care should be taken not to send too powerful a current through
the galvanometer, as the needle is then thrown violently to one
side, and its magnetism may be weakened ; for this reason it is
generally best to keep the galvanometer shunted, and pass through
it only T ^ or y^^ of the current. A strong current should never
be passed through the resistance coils for a long time, as it would
heat them, injure the insulation and alter the resistance tempora-
rily, if not permanently.
To measure the resistance of a coil of wire, connect its ends
with G and D and see that the other connections are made as
described above. Shunt the galvanometer so that only -j-^^ of
the current shall pass through it and insert two equal resistances
of 1000 ohms between A and G, A and B. Now close the cir-
cuit for an instant, first pressing down the key under the middle
finger, or that connected with the battery, and then the othej, and
instantly raising them. The spot -of light will probably dart to
one side so rapidly that it is hard to follow it, because the resist-
ance interposed between B and J9, which is very small, is less
than the resistance to be measured. Now draw the plug next D,
which inserts a resistance of 5000 ohms, and again depress the key
when the spot will probably move the other way. If not, the
resistance is either over 5000 ohms, or there is something wrong
in the connections ; to test this, connect the battery with G in-
stead of D, and if the spot moves in the same direction as at
first, there is something wrong in the connections, otherwise the
required resistance lies between 5000 ohms and infinity. In the
latter case, replace the battery connection and draw the other
plugs, and if the spot still moves in the same direction the resis-
3
34 WHEATSTONE'S BRIDGE.
ance is over 10,000 ohms, and the method described below for
very great resistances must be employed. If now the 5000 resist-
ance is too great, replace its plug and draw the 2000 plug; if this
is too small, draw in addition the 1000 plug, if too large replace
the 2000 and draw the 1000. Proceed in this way precisely as in
the method of weighing described in Vol. I, p. 47, always taking
care to introduce the resistances in order. When a near approach
to the correct resistance is obtained the deviations of the spot will
be small, and they may then be increased by altering the shunt so
that T foy or T V of the current passes through the galvanometer.
Finally, removing the shunt plug, employ the galvanometer with
its full sensibility. When the resistance is determined within a
single ohm, a still closer approximation may be obtained by inter-
polation. Thus suppose that with the smaller resistance the spot
comes to rest m divisions to one side of the zero, and when the
resistance is increased one ohm, to n divisions on the other side.
Then the true resistance will equal the smaller resistance, plus
the fraction m divided by m-\-n. Thus, if with 2815 ohms the
deflection is 15 divisions to the right, and with 2816 ohms, 10 to
the left, the true resistance equals 281511 = 2815.6 ohms. Much
time is commonly lost in waiting for the needle to come to rest,
and a great saving may be effected in this respect by closing the
circuit for an instant so as to check the swing. Thus if the current
tends to send the spot to the right, wait till it swings to the left,
and when passing the centre point, close the circuit for an instant.
The magnet receives an impulse in the opposite direction which
may be made to stop it almost entirely. This can be well done
only with practice. It is not generally necessary to wait till the
spot comes to rest, but merely to note the reading of each end of
its swings and take the mean.
If the resistance lies between 1000 and 100 ohms one more
place of decimals may be obtained as follows. Introduce a resist-
ance of 100 ohms between A and C and leave that between A
and B equal to 1000; then- we have as 1000: 100 = 0: the re-
quired resistance, or each resistance coil of O is virtually reduced
to one tenth its previous value. Accordingly 1 ohrn will now
equal .1 ohm and by interpolation, resistances may be measured to
.01 ohm. If the resistance is less than 100 ohms, by making N"
WHEATSTONE'S BRIDGE. 35
equal to 10 ohms, resistances of .01 ohm may be measured, and by
interpolation .001 ohm. If the resistance is over 10,000 ohms
make N= 1000, and M = 100 or 10. In this way resistances up
to 1,000,000 ohms or a megohm may be measured.
Resistances greater than a megohm may be measured approxi-
mately as follows. Make JV= 1000, M= 10 and read the position
of the spot of light, giving various values as 9000, 8000, 7000,
etc., until the spot passes off the scale. Construct a curve which
should be veiy nearly a straight line with abscissas equal to the
deflections, and ordinates to the reciprocal of the resistances, and
prolong it until it meets the axis of IT. At this point the deflec-
tion is zero, and the reciprocal of its ordinate multiplied by 100
gives the required resistance. Another point on this curve is
obtained by making equal to infinity, or connecting the end of
P with the battery terminal, and disconnecting it from D
Another method of measuring a very large resistance, if we have
a coil of large and known resistance as a megohm, is to place
them in turn in circuit with the battery and galvanometer, when
the deflections will be nearly inversely as their resistances. For
these measurements a battery of small cells, connected for tension,
may be employed, as the great resistance prevents injury to the
coils.
The resemblance of this instrument to the chemical balance is
very marked, only it is a balance of prodigious range and possess-
ing many most important advantages. The coils M and N corres-
pond to the arms, to the weights, the spot of light to the index,
and the keys to the supports of the beam and scale-pans. It can
measure from 1,000,000 to .001, a range as great as from 14 tons to
1 grain. Either arm may be made 10 or 100 times as long as the
other, and the index is without weight, and moves over a long scale.
Moreover the shunt enables us to diminish the delicacy of the bal-
ance to -j^, T ^, or T^^J, as if by merely inserting a plug we could
convert a delicate chemical balance into a rough grocer's scale. It
is well to measure several resistances, as described above, some of
them large, and others small, and finally to find the conductibility
of copper as described in Experiment 101. Another excellent
experiment is to measure the resistances of two coils of wire,
and then connecting their ends measure their combined resistance.
36 RESISTANCE COILS.
It should, by the law of divided circuits or shunts, equal their
product divided by their sum. The law for three or more com-
bined resistances may be found in a similar manner.
103. RESISTANCE COILS.
Apparatus. A delicate galvanometer, a British Association
divided-metre bridge, a battery, a standard ohm, some German
silver wire, some small pieces of copper with holes bored through
them, some solder, resin and a Bunsen burner.
Experiment. The B. A. bridge, Fig. 73, consists of a carefully
drawn wire one metre in length, any point of which may be
touched by a sliding key so as to
divide it electrically into two parts.
The current from the battery B then
passes into A, and when the latter is
pressed down it divides, part going
through -4 (7 and the resistance to be
measured J2', and the remainder pass-
ing through AD and the known re-
sistance coil JK, to the other pole of the battery. The four resist-
ances A 6 Y , AD, R f and R correspond to the four resistances of the
common bridge. To measure any resistance J2', connect as in the
figure and press down A ; the needle will in general deviate, but
by sliding A along the wire, a point is easily found where there is
no deviation. In this case the resistance is found from the pro-
portion AD : AC= R : R\ AD and AC being given directly in
millimeters from the divided scale.
Now make a coil whose resistance is 1 ohm. Cut off a piece of
the wire and measure its length and resistance. The resistance
being proportional to the length, a simple proportion gives the
length of the required ohm. To allow for variation of diameter
of the wire and other causes, cut off a piece somewhat too long
(3 or 4 per ct.). Measure its resistance and repeat until the wire is
about an inch too long. Then pass the ends into two of the cop-
per terminals, put on a little resin, heat them in the burner, touch
the ends with a little solder and they are soon fastened firmly in
place. Soldering acid (chloride of zinc) should not be .used, as
CAPACITY OF CONDENSERS. 37
being hygroscopic it attracts moisture and is likely to cause
errors. When the ends are perfectly cool, measure the resistance
which should now be very nearly the required amount. To make
it exact, heat one of the terminals and slide it on or o.ff by the de-
sired amount. When cool, measure again, and repeat until an
exact copy of the standard ohm is attained. To do this with
greater certainty reverse the position of R' and H and see if the
position of A is unchanged when no current passes through the
galvanometer. Any inequality in the two halves of the wire CD
is thus eliminated. An error of .004 will now correspond to a
motion of A of about 1 millimetre. To increase the delicacy
interpose between C and 72', and D and 72, two equal coils of large
resistance. Suppose each has a hundred times the resistance of
CD, then the latter is virtually extended to a length of two hundred
metres, and an error of 1 millimetre is reduced in the same propor-
tion. To make sure that the two coils have the same resistance,
reverse them and adjust the length of K until the mean position
of A, when these two coils are reversed, is the same when JR' and
JK are reversed. If the wire is very long it should be wound oma
bobbin, and to eliminate the induced current we should begin at
the middle and wind the two ends side by side. Instead of a bob-
bin, a common spool may be employed. The whole is then dipped
in melted paraffine, when the air rushes out and is replaced by par-
affine, which' is an excellent insulator. A large rubber tube may
then be stretched over the whole, and on it the resistance marked
in ink. It is also well to mark it with a certain number to refer
to a book giving the date and name of maker, in which may after-
wards be entered the error in the resistance. As the soaking in
paraffine may alter the resistance, this should be done before the
final adjustment of the copper terminals is made. For short coils
the simple wire may be used, and a short piece of fine rubber tub-
ing slipped over it on which to mark its resistance and number.
104. CAPACITY OF CONDENSERS.
Apparatus. Two condensers whose capacities are to be compared,
two switches, a differential galvanometer, a Thomson's galvanome-
ter, two resistances, one of which may be varied at will, and a bat-
tery which need never be closed, but must have a large and nearly
38 CAPACITY OF CONDENSERS.
constant electromotive force. Some Daniell or Leclanche cells may
be used, but the best results will be obtained with a battery of the
form proposed by Latimer Clark, and made with pure mercury for
one element, and pure zinc for the other, the liquid employed
being a paste formed by boiling sulphate of mercury in a satu-
rated solution of sulphate of zinc. The cells may be very small, as
an increased resistance makes but little difference, and their circuit
should never be closed.
Experiment. Connect the inner coatings of the condensers
with the two circuits of the differential galvanometer, and the
other terminals of the later, with one pole of the battery. Con-
nect the outer coatings together, and with a switch, so that
they can be put in contact with either pole of the battery. By
turning the switch in one direction the condensers are charged,
and in the other the two coatings are brought electrically in con-
tact, and hence discharge takes place. If the two condensers have
the same capacities, no effect is produced when the switch is moved,
as equal quantities of electricity in that case pass through each
coil of the galvanometer. If the condensers do not have equal
capacities the needle will swing to one side or the other, accord-
ing as they are charged or discharged. In this case the coil con-
nected with the larger condenser must be shunted, or its terminals
connected with a variable resistance so that a part only of the cur-
rent shall pass through it. By altering this resistance a value
may be found for which there will be no deviation of the needle.
In this case, calling G the resistance of the galvanometer coil, and
S that of the shunt, the current through G will be to the whole cur-
rent as S : G-\- S. But this current equals that in the other coil,
so that, calling the two capacities C and (7', we have C : C' =
Another method of comparing the capacities of two condensers
is by a modification of the Wheat-
stone's bridge. In Fig. 74, let and
P represent the two condensers
whose outer coatings are connected,
and whose inner coatings are attached
to the resistances M and N, and to
the terminals of the Thomson's gal-
vanometer G. A switch 8 is intro-
CAPACITY OF CONDENSERS. 39
duced, as in the other arrangement, so that the outer coating of
the condensers can be connected with the battery, or with their
inner coatings. Now alter one of the resistances M, so that there
will be no deflection of the needle when the circuit is made or
broken. Then the two condensers will be proportional to the re-
sistances M and N. A convenient arrangement is to make the
tAvo resistances Jfand JVthe two parts of the wire of the bridge
employed in Experiment 103, or a set of resistance coils may be
used for M, and a coil of wire for N.
When the condensers have small capacities the following
method is preferable. Connect the Thomson's galvanometer by a
switch with, the two inner coatings and their outer coatings with
a second switch, so that they can be connected either with the bat-
tery or with their inner coatings, through the galvanometer. By
moving the first switch either condenser may be thrown into the
circuit, by moving the second it may be either charged or dis-
charged. Now charge and discharge the first condenser, and
notice the swing of the needle in each case. Do the same with
the second condenser, and the ratio of the mean of their swings
equals their comparative capacity.
If the constant of the Thomson's galvanometer is accurately
known, the capacity of the condenser is readily determined. It is
only necessary to charge it with a battery of known electromotive
force jE 7 , and discharge it through the galvanometer. Then calling
t the time of the swing of the needle, v the amount of swing
caused by the discharge, and c the capacity, we have cE = -
or c := -p. This value of c is correct only if the resistance of
the air is so slight that the needle vibrates for a long time before
coming to rest. If this is not the case, set it swinging, and meas-
ure the extreme amplitude attained during each vibration. The
ratio of two consecutive deflections, or the difference of their loga-
rithms will be nearly constant. Calling I' log v' log v" and
employing the mean value of I, we must in the above value of c
substitute v (1 + Z) for v. The value of kH should be deter-
mined at the time, by comparison with a tangent galvanometer as
40 ELECTROMOTIVE FORCE AND RESISTANCE OF A BATTERY.
described in Experiment 99, or if the capacity of the condenser is
known this method furnishes an easy means of determining kH.
105. ELECTROMOTIVE FORCE AND RESISTANCE OF A BATTERY.
Apparatus. The battery to be tested, a tangent galvanometer,
a plug key, and a resistance coil.
Experiment. If the battery to be tested gives a current which
is nearly constant, the problem becomes a very simple one. Con-
nect the galvanometer Or, Fig. 75, with the
battery J3 and read the deflection of the nee-
dle; then interpose the resistance JR, and
repeat. From the curve accompanying the
Fig. 75. galvanometer determine the absolute cur-
W
^ , Q_
pi
we readily reduce B and E. If the galvanometer
B + G+J?
follows the law of the tangents, C = IcH tang v, from which C is
readily determined. To insure accuracy, the readings of the nee-
dle should lie between 20 and 70, and C should be about double
C'. If the galvanometer is too delicate, it may be shunted, and G-
and kH changed to correspond.
In general, when the circuit of a battery is closed, the current,
at first strong, becomes rapidly weaker and weaker. To deter-
mine the law of this diminution, the current is allowed to pass
alternately through 6r alone, and through Gf and It together,
for intervals of one minute, and the reading of the needle taken
in each case. This is most conveniently done by a switch, plug
key, or other an-angement by which the two terminals of JR are
connected, or short-circuited, as it is called.
Next, construct curves with the times as abscissas, and currents
as ordinates. Two curves are thus obtained, corresponding to the
two positions of the key. From them take values of C and <7',
corresponding to various values of t, and compute the correspond-
T^T
ing values of E and B by the formulas O= , Q and G' =
' *
Finally, construct two curves in which the abscissas
RESISTANCE OF BATTERIES. 41
represent the times, and the ordinates the values of E and B
respectively. From these curves we shall see how much the dimi-
nution of the current is due to the increase of the resistance, and
how much to the diminution of the electromotive force.
106. RESISTANCE OF BATTERIES.
Apparatus. The battery to be measured, a permanent magnet,
a delicate galvanometer, two resistances, one of which may be
varied, and a plug by which three wires may be connected. For
the resistances, two German silver wires may be used, of which
the length of one may be altered by drawing it through a screw
cup.
Experiment. Connect the instruments as in Fig. 76, in which
the battery B, and galvanometer G, are connected with one of the
resistances, JK\ and with the plug. The
third terminal of the latter being connected ,
with the resistance JK, and through it with ,_ L5,1 ^G
the other terminals of the battery and gal- (~JB | R (\)
vanometer. When the plug is out, the cur- ^- 2- _>"
rent passes from B through G and R ', but Fig< 76>
not through R which is then connected only at one end. When
the plug is in, R ' is thrown out of the circuit, its two terminals
being connected by the plug, and R acting as a shunt to G. Evi-
dently the deflection of G is reduced in the first case by the in-
creased resistance R ', and in the second case by the shunt JK. A
certain value of these resistances will therefore produce the same
deflection whether the plug is out or in. This will be the case
7? T? f
when B = -77- On making the connections, the needle will
commonly be deflected entirely to one side, and should then be
brought back by the permanent magnet to the zero. If JK is the
variable resistance make this adjustment with the plug out, and
then inserting the plug, alter JK until the spot is brought back to
the zero. If R ' is variable, make the adjustment with the plug
in, then remove it and alter R' . If the Thomson galvanometer
and set of resistance coils are employed, the same rules must be
followed as in Experiment 102. If German silver wire only is
used, first insert a very short and then a very long piece, when the
42 RESISTANCE OF BATTERIES.
needle should deflect first to one side, and then to the other. By
varying the length, the spot is soon brought to zero. The resist-
ance is then found either by direct measurement or by measuring
the length, and comparing the resistance with that of a known
length of the same wire. Instead of bringing the needle to zero
by the permanent magnet, the method described in Experiment
100 may be employed, using a cosine galvanometer with its coils
placed at right angles to the meridian, arid turning the coils until
the needle is brought to the zero.
7? K f
The formula B = g may be proved either graphically or ana-
lytically. First, lay off in Fig. 77, mn = 3,no = E, op = G, and
erect perpendiculars equal to their po-
tentials, when the plug is out. These
are found by making mm' equal to the
electromotive force of the battery. Then
oo' will equal the difference of potential
of the terminals of the galvanometer,
Fig- 77- and is proportional to the current pass-
ing through it. When the plug is in, the total resistance is much
less, being composed of mn = B and nE' the combined resist-
/^/p
ance of G and 72, or /y _i_ /? The difference of potential of the
two ends of the battery will now be nn", and if this equals oo'
the current through the galvanometer will be the same in the
two cases. The geometrical condition that nn" = oo' follows,
if mn : nR' = mo : op, but mn = B, nE' = Q \ T nio =
B + E' and op = G. Hence B : (^+ R = B + K - & Mul-
tiplying out BG(G + E} = GE(B + E'), or J3G 2 + BGE =
BGE + GEE' .: BG=EE' and B = ^.
The same formula may be proved analytically by Kirchhoff's
laws as follows^ Let C& C& C R represent the currents in B, G
and J2, when the plug is in, and G the current, which is the same
for all, when it is out. Then C = C . . . (1), since this is the
condition that the deflection of the galvanometer shall be un-
changed. By Kirchhoff's first law, C B =C G + C s ... (2), and by
RESISTANCE OF GALVANOMETER. 43
his second law applied *to the circuit Git, we have GC RC B
= ... (3). Applying the same law to the circuit BG-BJ gives
E= JBC + GC + E'C, and to the circuit BG when the plug is
in, E= BC B + G-CG, and equating these two, BC+ GG-\- R' G
= BC B -f- GC G . . . (4). "We have thus four equations between
the variables C, C B , C G , O R , and substituting (1) and (2) in (4)
gives BG -\- GG -\- R'G = BG + BG B + GO, or reducing
/? K r K Tff
R'G= BGn dividing this by (3) gives jj = <y , or B= & >
107. RESISTANCE OF GALVANOMETERS.
Apparatus. The same apparatus as in Experiment 102, with
the addition of a permanent magnet, and a key.
Experiment. Sometimes as in the last Experiment we wish to
determine the resistance of a galvanometer, and cannot employ
the usual method of measurement since it is needed in the Wheat-
stone's bridge. In Fig. 78, let M, N, G, P,
represent the four resistances, B the battery,
and S the galvanometer, in the usual ar-
rangement of the biidge. If the resistances
are balanced it will make no difference if
the galvanometer is replaced by a short wire,
and key /S, and since no current passes Fig. 78.
through this wire, the current in the four coils will be the same
whether the key is opened or closed. Therefore replace the
resistance to be measured, G, by the galvanometer, and see if the
deflection is unchanged when the key is closed, and if so .ZV : Jf=
P : G or G= ~- If the deflection is not the same, alter P
until it is the same whether the key is up or down. As in the
last Experiment, the spot should be brought to zero by the per-
manent magnet. In the actual case the galvanometer should
be connected with G and Z>, Fig. 72, the key connected with B
and (7, and the resistance altered as in Experiment 102 until no
effect is produced on depressing the key.
108. MANSE'S METHOD.
Apparatus. The battery to be measured, a delicate galvanome-
ter, a magnet, a resistance coil, and a B. A. divided-metre bridge.
44
WIEDEMANN S METHOD.
Experiment. Connect the terminals of ^he battery B, Fig. 79,
with one end of the resistance coil R, and with the sliding key A of
the bridge. Connect the other termi-
nals of B and R with the ends of the
metre and also with the galvanome-
ter, G. The current will now pass
through the galvanometer, deflecting
its needle nearly 90. Lay the mag
net perpendicular to the coils of the
Fig 79. galvanometer, and to the magnetic
meridian, and move it up until the needle is brought to the zero.
Press down the key A when the needle will, in general, be de-
flected. Move A, and find by trial the point at which it has no
effect on the needle. Calling its distance from the two ends a
and 5, the resistance of the battery is given by the equation, b : a
=R-.B.
This may readily be proved if we notice that the electrical con-
ditions are precisely the same as in the last Experiment, except
that the battery and galvanometer have changed places. The four
resistances are a, 5, B and R, and A replaces S.
109. WiEDEMAira's METHOD.
Apparatus. A standard constant battery, B, Fig. 80, a battery,
B 1 , to be compared with it, a tangent galvanometer 6r, and a
commutator, C.
Experiment. The object of this experiment is to measure the
electromotive force of J?', in terms of that of the standard battery,
B. Connect them, so that by turning the
commutator their currents will pass through
the galvanometer either in the same or in
opposite directions as in Figure 80. Read
the deflection of G- in each case, and deduce
the currents C and (7, either from the curve
accompanying the galvanometer, or from the formula, C = kH
tang a, C" = kH tang a'. But by Ohm's law, the current, when
7? -\- V
the effects of the two batteries add, is (7 PIT?'! r* an< ^ wnen
J J' 1 Q
reversed C'= -^ . g 1 \ Q nence &' & '^ * /w from which E is
Fig. 80.
POGGENDORFF S METHOD.
45
deduced in terms of the electromotive force of the standard bat-
tery. If the battery B is not constant, the method given in Ex-
periment 105, should be employed. Connect the batteries for one
minute and read the galvanometer, reverse the commutator during
the second minute and read again. Take in this way a series of
readings until the deflections become sensibly constant. Now
construct curves with ordinates equal to the currents in the two
cases and abscissas equal to the times. Compute a number of
values of E', using the ordinates of points of these curves having
the same abscissas, or equal to the currents which would have
passed had it been possible to make both observations at the same
time. Construct a third curve with the same abscissas and ordi-
nates equal to these computed values of E.
110. POGGENDORFF'S METHOD.
Apparatus. A constant battery to be taken as a standard, the
battery to be tested, a delicate galvanometer, and a variable resist-
JExperiment. First measure the resistance of the standard bat-
tery, which should be the stronger of the two, as described in Exper-
iment 108. Connect the apparatus as in Figure 81, in which the
standard battery B, is connected with the
other battery B' so that they shall tend to
turn the needle of the galvanometer in op-
posite directions. Then connect the termi-
nals of M with those of B. Vary R until the
needle of G- is brought to the zero, when we
7~>
have the equation, E' = E p i p-
To prove this formula graphically, the construction of Fig. 82
may be employed. Make mn = B , the resistance of the stand-
ard battery, mm' = E, its electromotive force,
and no = It, the variable resistance. Then
drawing the straight line mo, mn' will be
the difference of "potential of the ends of -R,
or the tendency of the current to pass
through B and G. If now E ' = pp r , the
Fig. 81.
Fig. 82.
4(J ELECTROMETERS.
electromotive force of the second battery, equals this, or pp' =
TW', no current will pass through the galvanometer. But in this
case mm' : nri = mo : no or B + R : R = E : E' hence
E ' = E B + R'
The same formula may be proved by Kirchhoff's laws as fol-
lows. Call C G , C B and C R the currents in G, B and E, then by
the first law, G G + G R = C & or since C = 0, O R C s .
But in the circuit B'RG, we have by the second law E' =
(B + G) C G 4- C R R, or E' = G B R, since O = ; in the circuit
BE, E=BC B + RC B = (B + R) C* hence E' = %-+-%
111. ELECTROMETERS.
Apparatus. A Thomson's quadrant electrometer, which should
be mounted like the galvanometer, with a lamp and scale in
front of it. Two or three cells of a Clark's battery of constant
electromotive force (Experiment 104), a DanielPs cell, some resist-
ances, and several cells of a water-battery. The latter consists of
small glass vials containing salt water, in which are strips of cop-
per and zinc soldered together, so that the zinc of one cell is
joined to the copper of the next.
Experiment. The principle of the Thomson electrometer is
described in Appendix A. If the more complex form is employed,
it should be carefully adjusted, as described in the pamphlet ac-
companying it, and will then, with care, require but little attention.
When charged by exactly the right amount, the little aluminum
balance in the upper part of the instrument is in equilibrium, so
that on looking through the lens the horizontal hair is midway
between the two dots. If too high, the handle of the replenisher
must be turned in the direction of the hands of a watch until the
hair rises to its proper position. If too low, it must be turned in
the opposite direction. As the balance is liable to adhere to the
stops limiting its movement, the glass above it should be gently
tapped with the finger. Next, light the lamp and see if the image
of the slit and vertical hair falls on the zero of the scale. If not
they must be brought there by turning the screw, moving the
fourth quadrant, and, if necessaiy, the other quadrants. To
measure a slight difference of potential, as that of two metals
ELECTROMETERS. 47
immersed in water, connect them with the studs of the key, the
two springs being attached to the terminals of the galvanometer.
On pressing down the key, the spot of light will be deflected, and
on reversing the key an equal deflection to the other side will be
attained. The instrument is intended to be so adjusted that a de-
flection of 100 scale divisions will correspond to a difference in
electromotive force of 1 volt. To measure large differences of
potential, one of the electrodes should be drawn up from the
quadrant beneath it, and remain in connection only with the
induction plate of the instrument. If this alters the position of
the spot it shows that a charge has been thereby induced, which
must be got rid of by connecting the quadrant with the earth.
For this purpose the milled head of the disinsulator behind the
instrument should be turned until the attached pin points to the
letter "C"' (connect). The spot will thus be brought back, and
the quadrant is again insulated by turning the pin to " D " (dis-
connect). Differences of potential of 100 volts will thus be kept
within the limits of the scale.
The simpler form of electrometer requires to be recharged
every day it is used, and it will not give the same deflection on
different days for the same differences of potential. Like the
other electrometer, a lamp and scale is placed in front of it, so
that the spot of light shall fall at the zero of the scale. It must
next be charged by removing the glass cover and connecting the
brass knob projecting from the interior of the little Leyden jar
with an electrophorus, plate machine, Holtz' machine, or other
source of positive electricity. Care must be taken to make a con-
nection between the ground and the outside of the jar or the
electrometer, as otherwise if the latter stands on a hard wood
table it may not receive a proper charge. If charged too strongly
the needle will swing out so as to touch one of the quadrants
and discharge itself. When properly charged replace the cover
and see if the needle remains at zero. If not, the movable quad-
rant should be drawn in or out until this condition is attained.
Its terminals are then connected with the studs of the key, and
potentials measured as with the other instrument. As it is impos-
sible to charge it twice alike, and as there is no easy means
of altering its charge, the deflections, as stated above, are not
48 ELECTROMETERS.
comparable with one another, and for a given difference of poten-
tial will gradually become less and less.
The instrument having been adjusted, so that the spot stands at
zero, and deviates equally to either side, when the current is re-
versed by the key, a number of measurements of differences of
potential should then be taken. First, connect the terminals with
a Clark's cell which has a electromotive force of 1.457 volts.
With the absolute electrometer this should give a deflection of
145.7 divisions, and with the other instrument it should give a de-
flection from which the constant, or deflection per volt, is readily
determined. Do the same with a second Clark's cell and then
connect them, and see if together they give a double deflection.
Next, measure the electromotive force of the Daniell, and other
batteries, first, when they have been left on an open circuit and
then when the circuit has been closed for some time. The polari-
zation of a single fluid battery is thus well shown. Many simple,
but instructive, experiments may be performed with this instru-
ment. For instance, it may be shown that a zinc and copper plate
when immersed in water assume a difference of potential before
they are connected together, and that on connecting the terminals
of a battery by a long wire, the potential of the various parts will
vary by an amount proportional to the change in resistance, or that
the curve formed by the potentials and resistances is a straight line.
Again, the electrometer may be used like a galvanometer, except
that the circuit through it is always open, instead of closed, and
we may thus approximately measure resistances with a Wheat-
stone's bridge, or determine battery resistance. It forms, in fact,
a galvanometer of infinite resistance.
Another interesting application of the electrometer is to the
examination of condensers. The relative capacity of two con-
densers may be found by charging one, measuring its potential,
and then connecting it with the other so that the charge will be
divided between them, when the potential will be reduced in the
same proportion that the capacity is increased. Again, if a con-
denser is charged and connected with the electrometer, as the elec-
tricity gradually escapes the deflection will diminish. The flow
being always proportional to the electromotive force, by Ohm's law,
if a curve is constructed with abscissas equal to the time and ordi-
TESTING TELEGRAPHS. 49
nates to the logarithm of the deflection, it will give a straight line.
The tangent of the angle, which this line makes with the axis ot
X or the change in the logarithm per second, gives the logarithm
of the rate of diminution of the current per second. Calling this
quantity a, and c the capacity of the condenser, the leakage cur-
rent through the condenser will evidently be JEac, or since by
Ohm's law 12= CR, G CRac, or R = , R is here the insu-
lation of the condenser, and if the latter is in good condition will
be a very large quantity. This is one of the best methods
of measuring a very large resistance. It is only necessary to meas-
ure R and then connect the terminals by the unknown resistance
r and measure again, when the combined resistance R' will
equal , , from which r is readily deduced. Instead of the elec-
trometer, a Thomson's galvanometer may be used, first charging
the condenser for 10 seconds, then disconnecting it for one minute,
and finally discharging it through the galvanometer. In this case
the following formula is more convenient for determining the
resistance. Let d be the deflection when the condenser is dis-
charged directly through the galvanometer, and d' the deflec-
tion when an interval of one minute is allowed to elapse.
1563 6
Then R c (i og ^_ log ^y which gives R in megohms.
112. TESTING TELEGRAPHS.
Apparatus. A telegraph line, the longer the better, but at
least passing to another building and returning through the
ground instead of by a second wire. If no telegraph is available,
any long circuit may be employed, as that of an electric clock, or
electric bell. With this is needed the apparatus described above
for measuring currents, resistances and potentials.
Experiment. This, and the following Experiment, are intended
principally as examples of the previous work, and practical appli-
cations of the methods of measurement there detailed.
First, remove the batteiy and connect the wires attached to it,
and then determine the resistance of the line, magnets, and other
parts of the apparatus, by the methods given above. For this
50 TESTING TELEGRAPHS.
purpose, run wires from the ends of the line to the apparatus for
measurement, find their resistance alone, and when connected with
the line ; the difference equals the resistance of the latter. Meas-
ure in like manner the resistance of each magnet by taking the
difference of the resistances when it is in, and when out of, the
circuit, the last condition being obtained by bringing its two
terminals together. Next, measure the insulation of the line by
breaking the circuit at the further end and measuring the resist-
ance between the nearer end and the ground. This resistance
should be enormously great, unless the line is very "long, and
should be measured by the methods given for determining very
great resistances, Experiment 102.
The next question is, what kind of battery must be used to give
the best effect. To test at any time the condition of the battery
and line, a galvanometer should be employed, which may be inter-
posed in the circuit and the deflection noted. The galvanometer
used in Experiment 98 may be employed, but it is better to use a
less accurate instrument, with the needle on a pivot, instead of
suspended by a filament of silk, as it is then less likely to be in-
jured in moving. It is not necessary that it should follow the
law of the tangents, but the current corresponding to various
deflections should be determined by placing it in the same circuit
with a galvanometer, for which the curve of Experiment 98 has
been constructed, and the current altered by varying the resist-
ance. A curve may then be drawn, in which ordinates shall
equal its deflection and abscissas the absolute current, as deter-
mined by the curve of the other galvanometer.
Connect the galvanometer with the line, and attach a battery
somewhat more powerful than that which is to be used perma-
nently. Now reduce the current by introducing additional resist-
ances, or by shunting the battery, until it is just sufficient to make
the magnets act properly. Then read the galvanometer, and from
the curve determine the strength of current. This gives a mini-
mum, below which the current must not fall. Next, alter the
resistance so that the current shall have such a strength as to give
the best effect. We must now see what battery will best give
this current. In the equation C = , ^, or E = C(B + It),
TESTING TELEGRAPHS. 51
substitute this value for (7, and make R equal to the total resist-
ance of the line and magnets. Then the battery must have such
an electromotive force and resistance that it will satisfy this
equation. If, as is generally the case, we are to use several cells
of resistance B and electromotive force E, we must use the form-
ula for several cells explained in Appendix A, G= p _r -p^
Since the best effect is produced when the inside and outside
resistances are equal, we must have ~ = P. Combining these
two equations, we deduce m and p. It should be remembered that
while the first cost of a battery is proportional to the number of
cells, or to mp, the current expenses or consumption of zinc- or
copper is proportional only to p. Other considerations also enter
in the selection of a battery, according as it is to be used on an
open or closed circuit, as detailed on page 5.
Having thus tested the circuit in its normal condition, if at any
time it will not work properly, the nature of the trouble may be
detected by similar measurements. First, test the battery, and
see if this gives a good current when disconnected from the line,
or better, measure its electromotive force and resistance. If this
is what it should be, measure the resistance of the line and its
insulation. If the line is broken, it is shown by the resistance
becoming infinite. Imperfect connections are also shown by a
great increase of the line I'esistance. If there is a ground, that is,
any part of the wire in contact with the earth, the insulation and
line resistance will become equal, and both less than the normal
line resistance. The position of a fault may also be approximately
found in this case. If the connection with the ground is only
partial, these resistances will be unequal. A defect in any magnet
is shown by first throwing it out of, and then into, the circuit, a
great increase of resistance being produced if the wire is broken,
while if there is a defect in the insulation, so that the cui'rent
passes across, instead of through, the whole coil, the resistance
will be less than when the magnet is uninjured. Duiing damp
weather the supports insulating the line become covered with
moisture, and greatly diminish the insulation. If the wire comes
in contact with the wire of another line, the messages of the latter
will be received on it, though generally feebly. This fault is
52 TESTING SUBMARINE CABLES.
shown by deflections of the galvanometer when no battery is
attached, and by a diminished resistance when the other line is not
in operation. On long lines trouble is sometimes experienced from
earth currents, in which the two terminals assume different poten-
tials, the earth acting precisely like a battery. This is especially
the case during displays of the aurora borealis. It is shown by
deflections of the needle when no battery is attached, the currents
coming without the regularity of those produced by a cross with
another line.
11&. TESTING SUBMARINE CABLES.
Apparatus. Since a real submarine cable is rarely available for
experimental purposes, an artificial cable may be prepared as fol-
lows. Two points are selected for the two terminals, and between
them is placed a vessel of salt water to represent the ocean. The
cable is represented by two coils of known length of fine German
silver covered wire, of two or three thousand ohms resistance
each. A long coil or rubber covered wire is needed, and three of
four shorter pieces, prepared to show the effect of various faults,
in one the wire being broken, in a second the rubber scraped off at
a single point, and in a third the wire being broken, but the rubber
left intact. T\vo very large condensers should be provided, and
this is the greatest difficulty in imitating a cable. For a battery,
several Daniell cells are needed, and a water battery of one or
two hundred cells.
Experiment. To represent the cable when in good condition,
the resistances are connected together, and to the coil of covered
ivire which is then immersed in the vessel of salt water. One end is
then attached to each terminal station, and copper wires, to repre-
sent the ground connections, also pass from the vessel of water to
the same terminals. The condensers are connected with the junc-
tions of the resistance coils, and also with wires passing into the
vessel of salt water. Measure the total resistance of the line by
closing the circuit at the further station, that is, joining the wire
from the vessel of water to the end of the resistance coils, and
determine the resistance by the bridge, as in Experiment 104, by
connecting the wires of the nearer station with the bridge. It is
especially important in this case to close the circuit through the
galvanometer, as otherwise the current from the condenser will
throw a violent current through the galvanometer. An error is
TESTING SUBMARINE CABLES. 53
liable to be introduced from the polarization of the wires in the
salt water, and therefore it is best to use a battery with large elec-
tromotive force, or to measure the resistance at short intervals,
reversing the current each time.
Next, to determine the insulation, break the circuit at the fur-
ther end and measure the current, which will now pass through
the rubber covered wire. The resistance will, in this case, be too
great to be determined by the methods of Experiment 102, unless
the insulation is very poor, or the length of wire very great. In-
stead, therefore, the method given at the close of Experiment 111
should be tried. Another method employed to measure very
great resistances, as that of the junction of two cables, is to allow
the leakage current to flow into a condenser for one minute, and
then discharge it through a galvanometer.
The capacity of the cable is determined precisely as if it was
a condenser, the inner wire and outer covering, or the sea, replac-
ing the two conducting coatings of tin-foil, and the rubber insula-
tor replacing the insulating film of paper or mica. In the present
case, determine the capacity as in Experiment 104. These three
tests should be frequently applied to every cable, and as long as
they give nearly the same results we may infer that the cable is in
good condition.
Now suppose an accident occurs, by which the cable is injured,
and that we wish to determine the kind and position of the fault,
as it is called. This is imitated by disconnecting the resistance
coils and inserting between them one of the rubber covered wires.
When the broken cable is inserted, the resistance is diminished,
and is the same, whether the circuit is made or broken at the
further end. The position of the fault is found from the ratio of
the resistances ; the actual distance in miles is thus determined
by a simple proportion. See how nearly this compares with the
true length of the resistance coils. Precisely the same effect is
produced with the second kind of fault in which the wire is
exposed, but not broken, the resistance of the water being incon-
siderable compared with that of the remainder of the cable. It
is therefore easy to determine the position of a fault if the wire is
in contact with the water. But it very frequently happens that
this is partially protected by the covering, by salts deposited by the
54 FRICTION AL ELECTRICITY.
current, or other causes, so that the current, in passing from the
wire to the water, encounters a certain resistance called the resist-
tance of the fault. This may be represented by leaving the two coils
connected and interposing another coil, which may have any resist-
ance from zero to infinity, between the broken wire just used and the
junction of the two coils. If the position is now measured, as de-
scribed above, too great a result will be obtained, but if intelligible
signals can be sent to the further end, directing those in charge to
first break, and then close their circuit, two measures may be ob-
tained from which the true distance and resistance of the fault may
be approximately determined. Call JR, R' the resistances when the
circuit is open and closed, / the resistance of the fault, I the resist-
tance of the whole cable, and x that of the portion this side of
the fault. Then when the circuit at the farther station is broken,
H = x + /, while when closed the current divides between the
two circuits, / and I x, hence R' = x -f- f \ / -. These
two resistances give /and cc, and from the latter the distance of
the fault is at once determined. The polarization interferes seri-
ously with this measurement, and therefore, if possible, a second
cable should be used instead of the return circuit through the
water. In all these cases the insulation resistance is supposed to
be infinitely great as compared with that of the fault, otherwise
other corrections are necessary.
A fault due to the breaking of the copper wire without injuring
the insulating cover, is comparatively rare, and is illustrated by
the third piece of rubber covered wire. Its effect is to introduce
a very great resistance, which is unchanged, whether the circuit is
open or closed. The position of such a fault cannot be very accu-
rately determined. It may be roughly estimated from the insu-
lation resistance, which is as much greater as the length is less.
The method actually employed, however, is to compare the
capacity of the unbroken portion with that of the whole, regard-
ing them as condensers.
114. FRICTIONAL ELECTRICITY.
Apparatus. A plate electrical machine, a Leyden jar, some
sealing wax, a glass lamp chimney, pithballs, a gold-leaf electro-
scope, a torsion electrometer, and the usual lecture-room appara-
tus for frictional electricity described below.
FRICTIONAL ELECTRICITY. 55
Experiment. Rub the glass chimney on a piece of silk, when
some of the electricity will pass from the silk into the glass. The
latter therefore becomes positively, the silk negatively, electrified.
Now hang a pithball by a thread of silk, and bring the glass near
it. The pithball has appreciable size, and has the same potential
as the air, the glass a higher potential ; therefore attraction takes
place, until the ball strikes the glass, when it receives part of the
excess of electricity, and both now being positively electrified
repulsion takes place. Next, rub the wax with a piece of woollen
and the electricity will pass from the wax to the woollen. If,
then, the wax, which is negative, is brought near the pithball
which is positive, they will attract. If, however, the pithball
touches the wax it gives up its excess to the wax, and both being
then negatively electrified, will repel each other. If a piece of
metal is used instead of the wax, no effect is apparent if the metal
is held in the hand. But this is because, being a conductor, the
surplus electricity passes through it to the hand, and thus escapes.
If the metal is insulated by a glass handle the electricity can no
longer escape, and the above effects ai*e easily obtained.
To determine whether an electrified body is charged positively
or negatively, a gold-leaf electroscope may be employed. This is
easily made of a \ride-mouthed bottle, closed by a cork, through
which passes a brass rod, terminating above in a ball or knob, and
from whose lower end two strips of gold-leaf are hung. When
the brass rod is electrified, these strips repel each other, and sep-
arate at their lower ends. Two strips of tin foil are attached to
the bottle, so that if the gold strips are too strongly charged,
instead of adhering to the glass they will strike the foil and dis-
charge themselves. To use this instrument, bring the body to be
tested near the upper knob, and the gold strips will diverge, the
electricity of the knob passing into the strips, if the body is posi-
tive, and from the strips to the knob, if it is negative. Touch the
knob for an instant, when the strips will come together ; then re-
move the electrified body, when they will again diverge. Now
approaching an electrified glass rod, if the body was positively
electrified the divergence will be increased, if negative, dimin-
ished. Test in this way various substances, rubbing them to-
gether and determining which is positive, and which negative.
56 FRICTION A L ELECTRICITY.
A far more exact instrument than this, is Coulomb's torsion
electrometer, which consists of a cylindrical glass case, in which a
straw with a disk of tin foil at one end is hung horizontally by a
long, fine wire. The upper end of the wire is attached to an
index passing over a graduated circlet which shows the angle
through which it has been twisted. An insulated rod passes into
the interior, so that on turning the index the tin foil may be
brought in contact with it. A graduation outside the glass shows
the angle through which the straw has been deviated. Turn the
index so that the tin foil and ball shall be just in contact. Elec-
trify a glass rod and touch it to them, when they will at once
repel each other, and the straw will swing off through an angle
which we will call a. Bring them nearer by turning the index
through an angle u and call v, the deflection of the straw. Give
u various values, and determine v in each case. If v is small the
distance will be proportional to it, and the force of repulsion to
the torsion, u + v. Assuming that the latter is inversely pro-
portional to some power of the former, we must have (u -\- v)v n
= m. To see if this is the case, construct a curve with coordi-
nates equal to log (u -}- v) and log v, and it should be a straight
line, since log (u -\- v) + n log v = log m. Again, the tangent of
the angle, or n, should equal 2, since the force is inversely as the
square of the distance. If v is not small, the distance must be
taken proportional to sin \ v, or to the chord instead of the arc.
To show the unequal distribution of the electricity on different
parts of a conductor, a proof plane is required. This consists of a
small piece of silvered paper, at the end of a fine glass rod covered
with shellac. To use it, the electrometer is discharged, the straw
.brought to zero, the proof plane touched to the points to be
tested, and the electricity thus removed, transferred to the knob
of the electrometer. A deflection is then obtained, which will be
proportional to the cube of the amount of electricity of the given
point. Charge several conductors, as an ellipsoid, an elongated
cylinder and a circular disk, by rubbing a glass rod and touching
it to them, and measure the amount of electricity of several points
of each.
The electricity resides entirely on the surface of a body. This
may be shown by a hollow sphere with a hole in it. Passing the
FRICTION AL ELECTRICITY. 57
proof plane in, touching the interior and then withdrawing it,
taking care not to touch the edge, it will be found that no elec-
tricity is withdrawn, however highly the sphere is charged. If a
second sphere of the same size, but solid, is allowed to touch the
first, it will also be found that the electricity will be divided
equally between them each taking one half of that on the first
sphere before contact.
The quantity bf electricity obtained as described above, is ex-
ceedingly small ; it may be greatly increased by the use of the
plate electrical machine. This consists of a circular plate of glass,
which may be turned between two pieces of felt covered with an
amalgam of mercury, zinc and tin. An excess of electricity then
passes into the glass, which thus becomes positively electrified,
while the felt or rubber is negatively electrified. A comb of
metallic points is placed opposite the glass, and draws off its
surplus electricity into a large brass cylinder, called a prime
conductor. The latter is supported on a glass pillar to prevent
the escape of the electricity to the ground. On turning the plate
the action soon ceases, because the rubber gives up so much of
its electricity that no further supply can be taken from it. It
should therefore be connected by a chain with the earth, from
which an indefinite amount of electricity is readily drawn. To
use the machine, it is only necessary to connect the rubber with
a gas or water pipe by a chain, and turn the plate by a crank
attached to it. Electricity will then appear on the prime con-
ductor, which will soon attain so high a potential that if the
finger, or other conductor, is brought near, the electricity will at
once overcome the resistance and leap across in the form of a
spark.
When the machine has not been used for some time, or if the
air is moist, it is often difficult at first to obtain electrical effects.
In this case the machine should be carefully dusted and warmed,
as if very cold, dew may be deposited on it, which will form a
conducting surface, over which the electricity will escape rapidly.
Again, the amalgam may not be in good condition, and in this
case the rubber should be removed, the surface roughened by
scraping it with a knife, and, if necessary, fresh amalgam mixed
with lard applied.
58 FRICTION AL ELECTRICITY.
When the machine is in good condition the sparks should fol-
low each other rapidly, and if there is no outlet for the electricity,
a peculiar hissing sound should be produced, due to the escape of
the electricity into the air. In a darkened room pale brushes of
purple light should appear on various parts of the machine.
The phenomena of attraction and repulsion are much better
shown by .the electrical machine than by the simple means de-
scribed above. Pieces of paper or pith are violently attracted
and then repelled. Various electrical toys have been devised to
show these effects, for instance, bells, dancing dolls, the spider, head
of hair, etc. A curious effect, known as philosopher's wool, is
obtained by attaching a little sealing wax to a rod projecting from
the prime conductor and melting it with a candle. As soon as
the machine is charged the mutual repulsion causes the wax to
throw out fine filaments, which may be collected on a sheet of
paper held near it. By electrifying the water contained in a
vessel pierced with a number of fine holes, it will escape in fine
streams instead of in drops. A similar effect is obtained with a
syphon formed of a capillary glass tube. This instrument has a
most important practical application in Thomson's syphon-re-
corder for registering messages received on submarine cables.
Owing to the force of repulsion, the excess of electricity in a
body instantly passes to the surface. For the same reason it col-
lects in greatest quantity on the more curved portions. In elec-
trical apparatus sharp, edges or points are therefore particularly
objectionable, since the electricity collects on them and escapes
more rapidly into the air. The adjacent particles of air becoming
electrified are repelled, and form a current from the point. This
is shown by attaching a pointed wire to the prime conductor
when the current may be perceived by the hand, or by holding
the flame of a candle near it. The electrical flier consists of a wire
with the two, ends bent in opposite directions, like an S, and
balanced like a compass-needle on a pivot. When electrified, it
will revolve rapidly, owing to the reaction of the air on the points,
like a Barker's mill. On viewing a point strongly electrified in a
darkened room, the escape of electricity is readily seen by the
production of a purplish brush of light. If the point is electrified
FRICTIOXAL ELECTRICITY. 59
negatively, the brush is reduced to a simple bright point, although
the escape of electricity is considerably increased.
If the electricity is allowed to pass through a tube from which
the air is partially exhausted, the spark lengthens, and finally
forms a long purple brush-like discharge, resembling the aurora
borealis. A certain amount of gas, however, seems essential, as
with the highest attainable exhaustion no electricity will pass.
The uses of the electrical machine are greatly extended by
the instrument known as the Leyden jar. This is a condenser
formed of a glass bottle coated inside and out with tin-foil
and closed by a wooden stopper, through which passes a brass
rod from which hangs a chain touching the interior of the jar.
To charge it, hold the brass rod, which commonly terminates in
a ball, near the prime conductor, and connect the outer coating
with the earth, or with the rubber. On turning the machine, the
positive electricity will collect on the interior of the jar, and repel-
ling that on the outer coating will cause it to pass off into the
earth. This will go on until a considerable quantity of electricity
is thus stored up in the jar. Then connecting the inner and outer
coatings, or the latter with the brass ball, the whole of the elec-
tricity thus accumulated instantly passes out with a bright spark
and loud snap. If the discharge is through the body, a violent
shock will be felt.
To show that it is indispensible that an outlet shall be afforded
to the electricity on the outer coating of the jar, place the latter
on a plate of glass and try to charge it. In this case the outer
coating will become charged and give sparks, like the prime con-
ductor, while but little electricity will enter the jar, as is proved
by connecting the outer and inner coatings. The electricity
does not reside in the coatings but on the surface of the glass,
as may be shown by means of a jar with movable coatings. A
cylindrical or conical vessel is used for this purpose, the tin-foil
being replaced by closely fitting tin cups. Charge the jar in the
usual manner, then remove the outer coating, place it on the table,
or better on a sheet of glass, and remove the inner coating. Now
place another inner coating in it, and finally replace it in a second
outer coating, taking care during the last operation not to touch
the jar. The latter will be found to be still quite strongly
60 FRICTIONAL ELECTRICITY.
charged. Another evidence that the charge is in the glass, and
not in the metal is, that a few minutes after the jar is discharged
a second feeble spark may be drawn from it, due to the electricity
which has penetrated a little way into the glass. This is known
as the residual charge.
The powerful sparks of a Leyden jar are capable of producing
many effects not readily obtained directly from a machine. This
is especially the case with a battery composed of several jars bav-
in** their inner and outer coatings connected, equivalent in fact to
a single, very large jar. A much longer time is required to charge
such a battery than a single jar and the spark although no longer,
will be much brighter and more intense. It resembles, in fact, a
galvanic battery connected for quantity. Remarkable effects may
be obtained by connecting the outer coating of one jar with the
inner coating of the next, like a galvanic battery connected for ten-
sion. Very long sparks are thus obtained, but the jars should be
disconnected and charged separately.
The simplest way to discharge a Leyden jar or battery is by a
wire bent in the form of a semicircle, and terminating in brass
balls. To avoid receiving any portion of the discharge the wire
should be held by a glass insulating handle. Sometimes the
wire of the discharger is jointed, so as to vary the distance between
the balls. The best instrument for studying the effects of the spark
is the universal discharger, which consists of a small insulated table
and two brass insulated rods mounted on universal joints, so that
they may be brought into any position with regard to one anothei-.
The body to be submitted to the spark is placed between them on
the table, and they are then brought in contact with it, one being
connected with the outer coating of the jar or battery, and the
other with a wire which is connected with the inner coating when
the discharge is to be effected. If a spark is passed through a
thick piece of paper or cardboard, a hole is made with a burr on
each side, which was formerly considered an evidence of two elec-
tric fluids, but is probably due to the sudden generation of steam,
or other explosive action, inside the paper. A plate of glass is
readily penetrated by the spark, if the action is concentrated by
surrounding the wire with some non-conductor, except just at the
end. The best way is to fill a bottle with oil and pass a wire into
FRICTIONAL ELECTRICITY. 61
it so that it shall tcmch the glass ; bringing a second wire near it
on the outside, the spark will pass, producing a hole often too
small to let the oil escape. With a powerful charge, however, the
bottle may be broken. Alcohol, cotton covered with resin, ether
and gas, are readily ignited by an electric spark. The spark gener-
ally scatters gunpowder without firing it, but the latter may be
effected by lengthening the time of the discharge by introducing
into the circuit a large resistance, as a wetted string. To show
the magnetizing power of the current, wind a wire in the form of a
helix, place a steel needle in the interior, discharge a powerful bat-
tery through it, and the needle will be rendered magnetic.
In the above description, we have assumed that the interior of
the jar is electrified positively, the exterior, negatively. It is then
said to be charged positively. The same effects may, however, be
produced by reversing these electrical conditions, or charging the
jar negatively. For this purpose it .is insulated, and the exterior
connected with the prime conductor, and the interior with the
rubber. The difference in the two cases is well shown by the ex-
periment known as Lichtenberg's figures. Charge two jars, one
positively, the other negatively, and draw a series of lines with
the knob of each, on a flat surface of resin or vulcanite. Then
mix some red lead and sulphur, and sift them over it. The sul-
phur in mixing becomes negative, and adheres to the positive lines
in tufts with spreading branches, while the lead, which is positive,
collects in small round spots on the negative lines.
To measure the amount of electricity generated by a machine
the unit jar is sometimes used. This consists of a small Leyden
jar, which is connected with the prime conductor, and a wire at-
tached to the outer coating so bent that it nearly touches the rod
connected with the inner coating. If, now a continuous stream
of electricity is allowed to pass into the jar, it will discharge it-
self at regular intervals whenever the potential of the interior
becomes sufficient to enable the electricity to leap across the in-
terval to the outer coating. To measure by the unit jar the
amount of electricity generated by the machine, connect the inner
coating with the prime conductor, and the outer with the rub-
ber. The number of discharges per hundred turns serves to com-
pare the efficiency of the machine at various times. To deter-
62 INDUCTION MACHINES.
mine how much electricity has passed into a battery, insulate the
unit jar and connect its inner coating with the prime conductor,
and the outer coating with the battery. The outer coating of
the latter is, of course, connected with the ground, or rubber. The
number of discharges, as before, measures the quantity of elec-
tricity.
If pieces of tin foil are attached to a sheet of glass at short dis-
tances apart, a spark will pass from each to the next over a long
series, and by a suitable arrangement of the foil, letters or figures
of light may be thus formed. By scattering iron filings on a glass
plate wet with gum, and when dry discharging a jar over the sur-
face, the electricity passes from point to point in irregular branch-
ing lines, somewhat resembling lightning.
115. INDUCTION MACHINES.
Apparatus. An electrophorus, a piece of fur, a Holtz machine,
an d a piece of vulcanite.
Experiment. The electrophorus consists of a thin disc of some
insulating material, generally resin or vulcanite, resting on a metal-
lic disc connected with the earth. A second metallic disk with a
glass handle may be laid on it, and removed at will. To use the
electrophorus, rub the upper surface of the resin with the fur, by
which the latter is charged positively, the former negatively, or
some electricity is transferred from the disk to the fur. Replacing
the metal disk, its electricity rushes down towards the resin, but
cannot enter, owing to the slight conductivity of the latter. The
disk now becomes positively electrified on the lower surface, and
negatively electrified on the upper surface. Therefore on touching
it with the finger, a spark will be formed, by the electricity enter-
ing it from the hand. But now the upper surface is in its normal
condition, and the lower surface still positively electrified. If,
therefore, the disk is raised by the insulating handle it will be
found to contain more than its normal amount of electricity, or to
be positively electrified, and on touching it a spark will be ob-
tained. By this operation the electrical condition of the resin has
been in no way altered ; it may therefore be repeated indefinitely
without recharging, laying the disk on the resin, touching it with
INDUCTION MACHINES. 63
the finger, lifting the disk, and approaching it to the object to be
charged. This instrument is often very convenient as a source of
electricity, from its simplicity and the ease with which it is used.
The Holtz machine consists of two plates of glass, one of which
is very thin and may be made to revolve rapidly, by a system of
belts and wheels driven by a crank. The second plate is some-
what larger than the first, and is placed as near it as possible.
Two apertures are cut in the second plate, and pieces of paper,
called armatures, glued to the further side. These terminate in
points which project over the apertures, so that when electrified
they will act by induction on the revolving plate. On the other
side of the latter, but opposite the points, are combs of points, like
those of a frictional machine, connected with brass rods and balls,
whose distance may be varied at will, and between which the
spark is to pass. A Leyden jar is hung on each of these rods so
that its inner coating is connected with the rod, and the two outer
coatings are united by a metallic conductor. To charge the ma-
chine, the two brass balls are brought in contact, the movable plate
turned rapidly, and a small electric charge given to one of the
armatures. This is readily done by rubbing a piece of vulcanite
with fur, and touching it to the armature, or by an electrophorus.
Soon an increased resistance will be felt to the motion of the
crank, accompanied by a sort of hissing noise, and on separating
the balls a volley of sparks will pass, of a length which may reach
a foot or over. The machine, as thus constructed, is liable to stop
working suddenly, and requires recharging each time it is used.
These difficulties are remedied by a second pair of combs con-
nected together by a brass rod, placed just opposite the edge of
the armatures to which the points are not attached. The amount
of electricity generated by the Holtz machine is about the same
per turn as that of the frictional machine of the same size, but
since the speed is much greater, much longer sparks, and more
electricity per second is obtained, and the labor of turning it is
much less. It has, accordingly, almost superseded the plate ma-
chine as a source of frictional electricity. Most of the experi-
ments described in connection with the plate machine may be
shown much more satisfactorily with the Holtz machine.
64 MAGNETISM.
If the condensers are removed the sparks are more frequent but
less brilliant, and are accompanied by a sort of brush discharge.
By increasing the size of the jars a shorter, but much more intense
spark is produced, giving a snap, in, some cases almost as loud as
the report of a pistol. The best effect is obtained with the con-
denser attached to the negative pole double the size of the other,
and the ball forming the negative terminal also larger than that
attached to the positive terminal.
116. MAGNETISM.
Apparatus. Some magnets and needles, a stand to which a fine
thread with a wire stirrup may be attached, soft iron armatures, a
piece of cardboard, some iron filings, and two cylinders of wood
or cardboard on which two arrows are painted, to represent Am-
pere's currents.
Experiment. According to the -theory of Ampere, magnetic
phenomena are due to electric currents circulating around the par-
ticles of iron, and the attractions and repulsions are caused by the
effect of these currents on each other. Hold the two wooden
cylinders end to end, and notice that if the N or S poles are
brought together, the currents move in opposite directions, and
hence repel, while if turned so that an N and S pole are brought
together, the currents move in the same direction, and attract ;
this is sometimes expressed by saying that like poles repel, and
unlike, attract. To prove that this is the case with real magnets,
place a bar magnet in the stirrup and hang it from the stand ;
bring the other bar magnet near it and see if the above law holds
in all four cases. The earth also acts like a large magnet with its
south pole to the north, and hence the suspended magnet will
come to rest, only when its north pole is- turned to the north.
This is the principle of the mariner's compass. When a piece of
soft iron is brought near a magnet, induction takes place, and the
iron becomes temporarily a magnet with all its currents flowing in
the same direction, but as soon as the magnet is withdrawn the
currents turn back, and the magnetism ceases. To show this,
bring a magnet near a piece of soft iron, when it at once becomes
magnetic, and will attract a second piece of soft iron, and sustain
MAKING MAGNETS. 65
its weight, if the magnet is strong. On removing the magnet the
second piece of iron at once falls. The same effect is still better
shown by letting the soft iron deflect a compass needle.
Lay a bar magnet on the table, and the sheet of cardboard over
it, supporting the sides so that the card shall be level. Then
sprinkle over it some iron filings, and tap gently on the edge of
the card. The particles will arrange themselves along certain
lines, called magnetic curves, extending from one pole of the mag-
net to the other. The reason is, that each particle is rendered
magnetic by induction, and the direction of the curves is that which
a magnetic needle would assume at that point under the influence
of the two poles of the magnet. By placing a second magnet on
a piece of soft iron near the first, other magnetic curves may be
formed. The object of tapping the card is to neutralize the fric-
tion and enable the particles to assume the positions they would
take if perfectly free to move. The curves may be rendered per-
manent by vising waxed paper instead of cardboard, forming them
as before, and holding a hot piece of metal just above them, when
the wax will melt and hold the filings in place.
117. MAKING MAGNETS.
Apparatus. Some good permanent magnets, ancj some short
bars of hardened steel, such as pieces of stout knitting needles
about two inches long. They should be hardened by heating to
redness, and letting them cool quickly, then drawing the temper
by heat till they acquire a violet straw color. A stand is needed
from which the magnet may be suspended by a filament of silk to
test its strength, and a glass shade to cut off currents of air.
Experiment. The larger the piece of steel the more difficult is
it to magnetize it to saturation. Common needles, or the small
pieces of watch-spring used in galvanometers are easily charged by
merely rubbing the end that is to be north, on the south pole of a
permanent magnet about a dozen times, and the other end the
same number of times on the north pole. For larger bars much
more care must be taken, several methods of rubbing the bar hav-
ing been proposed, some of which will be described below. To
test the magnetism imparted, the magnet must be suspended
freely, as described in Vol. I, Experiment 3. If too heavy to be
66 MAKING MAGNETS.
supported by a single filament of silk, a bundle of several must be
employed, taking care that they are not twisted. To determine
whether the bar is already magnetized, suspend it, cover it with
the glass shade, and see if either end points to the north, and if
when disturbed, it vibrates, and finally returns to its original posi-
tion. If so, measure the time of a number of these vibrations,
fled by division the time of a single vibration, and take the
reciprocal of its square. This gives a measure of the strength of
the magnetism or more strictly of the magnetic moment. Remove
the magnetism by rubbing the north end once or twice on the north
pole of a magnet, and the south end on the south pole. Suspend
it again, and see if the time is increased. If rubbed too much, the
polarity will be reversed, and the other end will now point north.
Repeat until the magnetism is nearly removed, and the time of
vibration is very great. Then magnetize by one of the following
methods, and again take the time of vibration. Remove the mag-
netism, by turning the bar end for end, and repeating, see if
the time can again be rendered very great. Do the same with
the other methods of magnetizing. Finally, compare the results,
and see in which way the strongest magnetism can be induced.
The first method to be described is known as that of single
touch. The bar to be magnetized is fastened to the table, which
is best done by placing its ends on the opposite poles of two
permanent magnets, the end which is to be north against a
south pole, and vice versa ; it is well to mark one end of the bar,
to show which is north. Now bring two permanent magnets
down over the centre of the bar, not quite touching each other,
with unlike poles together and inclined outwards so that each
shall be inclined about 15 to the horizontal. To prevent their
touching, it is well to lay a piece of wood on the centre of the
bar. Now draw them apart, letting them slide over the bar until
they reach the ends, then raise them and bring them back through
the air to a point over the centre and then down into their former
position ; repeat several times, then turn the bar over, and stroke
the other side in the same way. Of course, the north end of the
bar must be stroked by the south pole of the magnet, and the south
end by the north pole.
FORCE OF MAGNETS.
07
By the method of double touch, the two magnets are held ver-
tically, separated by a bit of wood, and brought down onto the
centre of the bar. They are then drawn together to one end of
the bar, and back to the other end, and thus backwards and for-
wards taking care to stop in the middle after stroking each end an
equal number of times. A horse-shoe magnet is particularly con-
venient for this purpose.
A third method of making horse-shoe magnets, proposed by
Jacobi, consists in laying its poles against those of two perma-
net magnets, and drawing a piece of soft iron over it from end to
end.
A still more effective method is to place pieces of soft iron
against its ends, and enclose the whole in a helix of insulated cop-
per wire through which a powerful current of electricity is circula-
ting, making the whole in fact an electro-magnet. In the other
methods the effect is much improved by using electrp-magnets
instead of permanent magnets.
118. FORCE OF MAGNETS.
Apparatus. In Fig. 83, AB C is a small steelyard with a rider
of such a weight that each division of the arm shall correspond to
one tenth of a gramme. Two pins limit the motion so that it
shall only rise or fall by a small amount. D is a soft iron bar, hung
a short distance above the magnet to be tested, E. The latter
rests on a board hinged at G, and which may be raised or low-
ered by the micrometer screw F. The pitch of the latter should
be somewhat over a millimetre, as, for instance, a twentieth of an
inch.
Experiment. In the practical application of magnets it is often
important to know the amount of attraction at various distances.
This is determined with precision by
the following method. Remove the
magnet, and set the rider so that the
piece of soft iron shall be exactly bal-
anced. Then replace the magnet and
set the board FG under D, in such a L
position that the distance of the point
under D from G shall be to the distance FG, in the proportion of
68 LAW OF MAGNETS.
1 millimetre to the pitch of the screw. Thus, if the latter is -fa" t
make Z>G = .7874 FGf. One turn of F will then produce a
motion of the point of the board under X>, of one millimetre.
Turn F so as to raise the board until the magnet is in contact
with D, and its weight removed from the steelyard, so as to bring
C to the lower pin. Read the number of turns and fraction of a
turn, then move F until the bar touches the upper stop, and
read again. If the magnet is very powerful, a plate of glass may
be placed over it, and the thickness added in measuring the dis-
tance of D, or D may be removed, the magnet raised, and then, after
replacing J), lowered into the required position. An undue strain
on the steelyard is thus avoided. Next, lower the board and
move the rider towards the end of the arm one division, or more
if this is not sufficient to bring it against the lower pin. An at-
traction of the magnet of .1 gramme will then be required to
bring th6 tyeam again into equilibrium. Turn F until the bar
rises from the lower pin, and read F. Then turn it back, until the
beam returns to the lower pin. Subtracting the readings just
taken from these, gives two values (one for each pin) of the dis-
tance at which the force of attraction is .1 gramme. Take a series
of readings with various positions of the rider, and read the position
of F for each. Subtracting the first readings from them, gives the
comparative values of the distances x, and forces of attraction y.
To see if these quantities are connected by the relation y = m a",
or if the force is proportional to any power of the distance, con-
struct a curve with coordinates log y and log cc, and if it forms a
straight -line, the tangent of the angle it makes with the axis of X
gives the power n. This experiment may be used to study the best
form of magnet for electro-magnetic engines, or for various other
purposes.
119. LAW OF MAGNETS.
Apparatus. A compass resting on a scale divided into centi-
metres, and placed at right angles to the magnetic meridian, and a
bar magnet.
Experiment. Remove the bar magnet to a considerable dis-
tance so that on turning it end for end, the position of the com-
pass needle will not alter perceptibly. Place the compass over
DISTRIBUTION OF MAGNETISM. 69
the zero of the scale and turn it so that the needle shall point
to zero. Now place the magnet at the further end of the scale
with its centre an exact number of decimetres from the centre of
the compass. Read the change in position of the compass needle,
taking the mean of the two ends. Take a series of readings for
various positions of the magnet, first with one pole and then the
other, turned towards the compass. The tangent of the angle of
deflection equals the ratio of the deflecting force of the magnet to
the horizontal component of the earth's magnetism. Construct a
curve with these tangents as ordinates, and the distances measured
on the scale as abscissas.
If we assume that the effect of a magnet is the same as if its
whole mass were concentrated at the two poles, the theoretical form
of this curve is readily deduced. Let x equal the distance of the
centre of the magnet, and d the distance between its two poles,
which is somewhat less than its length, and y the corresponding
force of attraction. This may be regarded as composed of two
forces, one acting at a distance x d, and the other, which is
weaker, due to the further pole, at the distance x-\-d. These
forces being inversely as the square of the distance, y =. , ,. 2
t x _i_ d\2 = ( X 2 ^2)2- To see if any values of a and d will
satisfy the observations, this equation must be reduced to a linear
form. Solving with regard to (x 2 d' 2 '), we have (x 2 d 2 ) =
or calling d 2 = m and Jkad = n, x 2 = w, and t/ = z,
w m = nz, which is linear, or represents a straight line. Com-
pute, therefore, for each observation w = x 2 , and z */ , and
construct the curve. If the above assumption is correct it will
become a straight line, and the point at which it cuts the axis of
w will give m d' 2 , or the square of the distance between the
poles.
120. DISTRIBUTION or MAGNETISM.
Apparatus. A long iron bar which can be rendered magnetic
at will by two coils of coarse wire, C and 2), Fig. 84, placed near
its ends. A current is passed through the coils by a constant bat-
70 DISTRIBUTION OF MAGNETISM.
tery B, and may be sent through them in either direction by
the commutator E. Soft iron cores are inserted in the coils,
which thus render them powerful bar electromagnets. A thin
coil of fine wire, A> slides over the long bar, and has its ends con-
nected with a reflecting galvanometer G. Its position is meas-
ured by a millimetre scale.
Experiment. Remove one of the coils to a short distance from
the bar, and draw its core out so that it shall have no effect on the
coil A. Then make the circuit by the
commutator, when a current will be sud-
denly induced in the long bar, and by
the latter in A, thus deflecting the gal-
vanometer. Read the extreme deviation
Fi M of the spot of light, and after a few min-
utes break the circuit and read again.
A second current will be induced, this time in the opposite direc-
tion. The magnitude of this deflection affords an excellent meas-
ure of the strength of the induced magnetism. Repeat the
experiment, giving A various positions, and recording the derlec-.
tion in each case. Construct a curve with ordinates equal to the
galvanometer readings, and abscissas to the distance of the coil A
from C. To make sure that the coils have no effect by their
direct action, substitute for the long bar a glass tube, when the
galvanometer needle should remain at rest. The theoretical form
of the curve in the above experiment calling y the deflection and
x the distance, is y = ab* or log y = log a x log #, so that con-
structing a second curve with ordinates equal to log y instead of
y, we should obtain a straight line. Now replace the coil Z>, and
passing the current through C and D in the same direction
observe the deflection for various positions of A. Do the same
with the current passing in opposite directions through the coils.
Construct curves for both cases, also the curve midway between
them. The latter is found by taking the mean of the ordinates
of points having the same abscissa. The last curve will be found
to be coincident with that obtained with a single coil. Moreover,
if a curve is constructed with ordinates equal to the deviation of
the two curves from their mean, and abscissas equal to the dis-
tances of the coil A from Z>, instead of C\ we shall again obtain
MAGNETIC FIELD. 71
the same result as with a single coil. We may therefore conclude
that each coil will produce the same effect as if the other was not
there. This method of studying the distribution of magnetism is
widely applicable ; the coils C and D may be placed directly on
the bar if we repeat the experiment, using a glass tube instead of
the iron bar, and subtract the deflections thus obtained, to elimi-
nate the direct action of the coils. Again, if the coil A is placed
on a permanent bar magnet and a soft iron armature withdrawn, a
deflection is obtained, whose amount will vary with the position
of A.
121. MAGNETIC FIELD.
Apparatus. A constant battery Z?, Fig. 85, a circular coil of
wire, C, about half a metre in diameter, and a compass G. The
needle of the latter is suspended by a filament of silk, and by an
index is read to tenths of a degree. The coil is mounted so that
its position with regard to the compass may be varied, by moving
it either parallel or perpendicular to its own plane by an amount
which may be measured by a millimetre scale.
Experiment. Set the compass so that the reading shall be zero,
then place the coil so that the needle shall lie in its plane, and
their centres coincide, and connect
the terminals of C with the bat-
tery. A tangent galvanometer is
thus formed, and the needle will be
deviated by an angle whose tan-
gent gives the strength of the
magnetic field produced by the
coil compared with that due to rig. 85.
the earth's magnetism. Now
move the coil in its own plane half a decimetre to one side, and
repeat the reading. Take observations in this way at intervals of
half a decimetre until the coil touches the compass, and then con-
tinue the readings with the compass outside the coil. Construct
a curve with abscissas proportional to the distance of the compass
from the centre of the coil, and ordinates to the tangent of the
angle of deflection, or to the strength of the magnetic field.
Replacing the compass at the centre, take a series of readings
72 MAGNETIC FIELD.
of the deflection of the needle when the coil is moved perpendic-
ular to its plane, a decimetre at a time. Construct a curve as
before, and compare it with the result of the following theoretical
considerations. Let y equal the radius of the coil, and x the
perpendicular distance of the needle from its plane. Then the
distance of any point of the coil from the compass, will be
(# 2 -f~y 2 ) a nd the line connecting them will be inclined to the line
connecting the needle and centre of the coil by an angle which
we will call v. Then the effect of each element of the coil will
be inversely proportional to the square of its distance, or to
(a; 2 -j-y 2 ), and its component perpendicular to the coil, is the only
one which will act, since the component in the plane of the coil is
exactly neutralized by an equal and opposite component from the
element of the coil distant from it 180. Since, moreover, the
total effect will be proportional to the number of elements, to
ct/u sin v
2ry, or to y, we may write the strength of field f ^. 3
~, substituting for sin y its value in terms of a; and y, and
calling a the strength of magnetic field at the centre of the coil
where x = 0. Give proper values to a and y, compute f for
various values of x, and construct a curve with f and x as co-
ordinates. It should give the same result as that obtained by
experiment.
If, in the above formula we make f a constant, we obtain
x 2 + y* = by*, in which b is also a constant and equal to v .
Suppose now a galvanometer constructed with a series or shell of
coils of diameters and distances from the needle equal to the val-
ues of y and x taken from this equation. Then evidently all the
coils will produce equal effects, all greater than that of any coil
wound outside of this shell, and less than that of any coil inside
of it. Accordingly, if the whole interior is filled with coils the
greatest effect on the needle will be produced, or we shall have
the greatest deflection for a given current, and the galvanometer
constant will be reduced to a mininum. This equation therefore
is important as giving the best shape for the coils of a delicate
galvanometer.
HEAT.
122. TESTING THERMOMETERS.
Apparatus. The thermometer to be tested, and two tin vessels,
one to contain melting snow, the other boiling water. The first
of these, AB, Fig. 86, is cylindrical, terminating below in an in-
verted cone, with an orifice by which the water may escape.
The second vessel, ABC, Fig. 87, is also cylindrical, and high
enough for the bulb and stem of the thermometer to hang in the
steam. The upper part should be double, so that the steam may
pass up in the centre and down on the outside, otherwise the
upper portion will cool off, and the thermometer reading be too
low. If the tube is to be calibrated, reading microscopes, or the
Dividing Engine, Vol. I, Experiment 21, are also needed.
Experiment. First to determine the error of the zero point,
place the bulb of the thermometer in the first vessel and surround
it with snow, or if this cannot be obtained, with
pounded ice, as in Fig. 86. If the snow is very
dry, wait until it begins to melt, when the reading
of the thermometer should be C., or 32 F. ; the
deviation will be the required error, and should be
read to tenths of a degree. If the position of the
zero is accurately determined, it will be found to
alter continually, especially if the bulb has been jv*"^
recently blown and has not been well annealed.
On this account the best makers keep their tubes months or even
years, before using. The change goes on increasing for years and
may amount, in extreme cases to 1 or 2. Beside this change
there is a temporary change produced whenever the thermometer
is suddenly heated even to the temperature of boiling water.
This effect does not pass off for several days.
74 TESTING THERMOMETERS.
Secondly, to determine the error of the boiling point. Place
a little distilled water in AB, Fig. 87, and heat it to boiling. Pass
the thermometer through the cork closing the top,
and push it down until the boiling point is just out-
side, but not so low that the bulb shall touch the
water, since the temperature of the water changes,
while that of the steam is nearly constant. The
outlet for the steam, C, should be large enough for
its free escape, otherwise a pressure will be pro-
duced inside, which will affect the temperature.
Observe carefully the reading of the thermometer,
and the height of the barometer, H. The true temperature will
equal 100 -|- ^ (H 760). The difference of the observed and
calculated readings equals the error for this point also. For ordi-
naiy work these observations are sufficient, and assuming that the
tube has a uniform diameter throughout, we may determine the
errors for any temperature as follows. Construct the points with
abscissas equal to the zero and computed boiling points, and ordi-
nates equal to the differences between the observed and computed
temperatures enlarged. Connect them by a straight line and it
will give the error for any intermediate point of the scale.
If greater accuracy is desired, the tube must be calibrated, to see
if it is cylindrical. For this purpose a short column of mercury
must be separated from the rest, and its length measured in differ-
ent pails of the tube. To separate the mercury, invert the ther-
mometer, and if the column does not at once descend, tap the
tube on the table. If the mercury descends without breaking, so
as to fill the tube, a small air bubble, will be seen in the bulb. In
this case turn the tube back, when with a little patience the bub-
ble can always be made to ascend to the end of the tube, and
then the mercury will separate at that point. The point of separa-
tion is usually determined by a minute air bubble adhering to the
glass, which expands when the column separates. If the thread
is too long by an amount equal to n degrees, warm the bulb by this
amount after separation has taken place, and the expanding mer-
cury will push the air bubble forward with it. Let the mercury
reunite and cool, when it will contract past the bubble. Now,
make it separate again, and the column will have the desired
TESTING THERMOMETERS. 75
length. If too short, a longer column is obtained by heating the
mercury by the desired amount, then causing the separation to
take place. In this way a thread of any given length is readily
obtained. It is then brought to any required position by inclin-
ing the tube.
Separate a column about 20 in length, and take a series of
readings of the position of each end, to tenths of a degree, as it is
successively moved to various points of the tube. Call I the
reading of the lower end of the column, or that next the bulb,
and u the reading of the upper end, and construct a curve with
abscissas proportional to ?, and ordinates to u I. Since the lat-
ter quantity will vary but slightly it is better to subtract a con-
stant quantity from all the readings, and construct the differences
on an enlarged scale. Determine from this curve the value of
w, when I = 0, and call it u' . Then make I = u f and find the cor-
responding value of u, or u"; make I = u' -\- u" and find u'", then
I =. u' -{- u" -f- u'", and thus proceed until we obtain a series of
values of points of the scale separated by spaces whose volume
will precisely equal that of the mercury column. If now we con-
struct the points with abscissas equal to w', w", ?/", etc., and ordi-
nates to 1, 2, 3, etc., and draw a smooth curve through them, it
will show the true volumes of various portions of the tube, in
terms of the volume of the mercury column taken as a unit. But
as this curve will nearly coincide with a straight line, it is better
to draw a residual curve at once, with abscissas as before equal to
u', u", u'", etc., and ordinates 1 nu', 2 m/', 3 nu" f , etc., n
being so chosen that these quantities shall be as small as possible.
Determine from this curve the volume corresponding to values of
u equal to 10, 20, 30, etc., and divide each by the volume when
u = 100. The results will give the volume in fractions of the
volume between and 100. Multiplying by 100 and subtract-
ing the products from 10, 20, 30, etc., gives the error at these
points. Call e the error thus found, due to the shape of the
tube, and E that determined above from the freezing and boiling
points. Then the entire error will equal e + E and a curve
should next be constructed with temperatures as abscissas, and
the values e -{- E as ordinates. It will be noticed that the values
of e, unlike those of E, need only be determined once for all.
j-g WEIGHT THERMOMETER.
The above method of determining the errors, e, due to the shape
of the tube, may be divided into two parts. First, to find the
points separated by equal volumes, and secondly the computation
from them of the errors. Other methods may be substituted for
either of these; thus the required points may be found directly
by moving the mercury column along by an amount exactly equal
to its length. This is the method commonly employed, but it is
both more troublesome and less accurate than that given above,
and is open also to the serious objection that an error in any one
reading is communicated to all. Instead of the second portion
also, we may assume that the tube is nearly cylindrical for a
length equal to the mercury column, and find the volume of the
intermediate portions by a simple division. But this assumption
is correct only when the column is short, and in that case we can-
not measure the changes in its length with precision.
123. WEIGHT THERMOMETER.
Apparatus. Some test tubes, a piece of the solid and some
of the liquid to be tested, some mercury, some ice, a balance
and. weights.
Experiment. Draw out one of the test tubes in the flame of a
Bunsen burner to a fine point, and bend the end into a hook.
Weigh it and call the weight W. Fill it with mercury, by heat-
ing it and dipping the end into mercury, which will pass into the
tube as the enclosed air cools. Heat again, and repeat until the
tube is full. It may be necessary to boil the mercury, but this
must be done with great care, as it is very liable to break the
glass. A quicker but less exact method is to introduce a drop or
two of ether, which boils much more easily, and can be in a great
measure expelled by heat.
, Cool the tube with its point in mercury, by immersing it in ice
water, and call its weight W. Then heat to a temperature t,
when a portion of the mercury will be driven out of the point of
the tube by its expansion. Collect this overflow, and call its
weight to. The amount of mercury remaining equals W W w^
and if this were heated to t, it would expand by an amount equal
to w. Hence calling m the coefficient of expansion of mercury in
WEIGHT THERMOMETER. 77
glass, we have w = mt( W W w>), from which m is readily
determined. . But this expansion equals the difference between
the absolute expansion of the mercury and that of the glass, or
m = .00018 g, calling g the expansion of the glass. A temper-
ature is now measured by this thermometer by filling it with
mercury at 0, exposing it to the temperature to be tested, and
weighing the amount of mercury expelled. Evidently the maxi-
mum temperature attained is always given. Instead of the over-
flow it is sometimes more convenient, but less accurate, to observe
the weight of the tube and contents after exposure, and determine
the overflow by subtraction.
To measure the expansion of a solid, its weight and volume,
or specific gravity, must first be determined. It is then placed in
a test tube, the latter drawn out to a point, filled with mercuiy at
0, and weighed ; heating to t, the overflow is determined pre-
cisely as before. The coefficient of expansion of the solid, e, is
given by the equation,
w W' W , s /s , W W\
16 = -^6~ mt +p te -(p + ' 13.6 >'
in which s is the weight of the solid, p its specific gravity, TF" the
weight of the tube and solid, and the other quantities the same as
in the last paragraph. It will be noticed that the three terms of
the second member of this equation represent the expansions of
the mercury, solid and glass, respectively, and that each is equal to
the product of the volume by the coefficient of expansion by the
change in temperature. The volumes, moreover, of the mercury
and solid equal their weights divided by their specific gravities,
and for the glass equals the sum of the volumes of the other two.
The expansion of a liquid may be determined precisely like that
of a solid, except that the tube must be inverted so that the liquid
shall not escape. A simpler method, however, is to employ the
above method of determining the expansion of the glass, replacing
the mercury by the liquid. This gives, however, only the average
expansion, and will vary according to the value of t employed.
The expansion of air, or other gases, may also be determined by
this apparatus, and by carefully drying, the gas and taking many
other precautions, very accurate results may be obtained. Heat
the tube when filled with air or gas, to a temperature ", by im-
78 EXPANSION OF SOLIDS.
mersing it in a bath of water or oil carefully stirred. Then seal
the end of the tube in the flame of a Bunsen burner, remove it
and let it cool. Observe also the height of the barometer, P.
Dip the sealed point into a vessel of mercury and break it beneath
the surface. The mercury will immediately rush into the tube
and stand in it at a height p. Observe the temperature, or better,
surround it with a bath of cold water at temperature t f . Invert
the tube, taking care that no mercury shall escape, and weigh it ;
find also the weight when entirely full of mercury, and when
empty. Call these three weights, w', w" and w. Then since the
volumes are proportional to the weights, we see that the volume
w f w a t temperature t' and pressure P />, will expand to a
volume w" w, at a temperature t", and pressure P. Calling W
the weight it would have at the standard pressure H = 760 rams.,
and temperature 0, we have, as shown, Vol. I, p. 51, w' w
JT jjr
W(l + at'} p > and w" w = W(l -f- at')-p whence elim-
inating W and H by dividing and solving with regard to a, we
(W '- W}( P- P )-.( W "- W )P
- (w" w)Ptf (w' w)(P pY''
124. EXPANSION OF SOLIDS.
Apparatus. A long straight bar or wire of brass, or other
metal to be tested, about a quarter of an inch in diameter, and
three or four feet long. A fine line is drawn near each end of the
bar, and it is enclosed in a glass tube through which either water
or steam may be passed continually. A thermometer is inserted
at each end to show the temperature of the interior. Instead of
a glass tube, a rubber or metallic tube may be used with the ends
of the wire and the thermometers projecting. Two reading
microscopes with eyepiece micrometers, which may be fastened
firmly to the table, are also required.
tf Experiment. Place one reading microscope over each end of
the bar, and determine their distance apart, and the magnitude of
one division of each micrometer, as described in Vol. I, Experi-
ment 20. Then pass a stream of cold water through the tube,
measure the temperature of each end, and read the position of
the lines marked on the wire by the micrometers. Call t the
mean of these temperatures, and I the distance between the two
EXPANSION OF LIQUIDS. 79
marks, which is readily determined from the distance of the
microscopes, and the magnitude of the micrometer divisions.
Now pass a current of hot water or steam through the tube and
measure again the mean temperature if' and length I". Then if
I is the length the bar would have at 0, and a the coefficient of
expansion, we have by the law of expansion, I' = I -\- at'l and
I" = I -f- atf'l. Dividing, to eliminate J, and solving with regard
I" i'
to a, we deduce a = .//,/ //. Repeat, and then measure the
expansion of some other metal, or of the same metal between
other limits of temperature.
125. EXPANSION OF LIQUIDS.
Apparatus. A graduated tube closed at one end by a cylin-
drical bulb, whose volume is dependent on the liquid to be used.
If this is water, the volume of the bulb should be about twenty
times that of the tube. A thermometer, some mercury, a bal-
ance and weights are also needed.
Experiment. If the bulb is empty, it should be filled with the
liquid to a point near the bottom of the tube, either by pouring it
down the side of the interior, or if this is too small, by the follow-
ing method. Warm the bulb and dip it into the liquid, when, on
letting it cool, some of the latter will rise into the bulb. Then
invert it and heat carefully until the liquid boils. Dip again into
the liquid, when on cooling, the latter will fill the tube. A por-
tion of the liquid must now be removed, so that its surface shall
be near the lower part of the graduation, either by shaking the
tube, or by inserting a wire. Next, take a series of readings of
the position of the liquid for various temperatures, extending orer
as wide a range as possible, but not approaching too near the boil-
ing point. Construct a curve with temperatures, t, as abscissas,
and the positions of the liquid as ordinates, which we may call I.
To determine the expansion, two quantities must now b
known, the volume of the bulb .2?, in terms of the divisions of its
tube, and the expansion of the glass, g. These quantities maj
be determined once for all, or they may be found as. follows,
Weigh the bulb empty, and when filled with mercury to a point
/', near the bottom of the tube, and again to a point I", near the
80 EXPANSION OF GASES.
top of the tube. Call the three weights w, w r and w". Then if
ni is the weight of mercury required to fill one division of the
tube, evidently w r w m (B + I') and w" w = m (B + I"),
eliminating m by division and solving with regard to B, we deduce
Instead of weighing
rectly, it is better to first obtain w", then remove part of the
mercury and weigh it; w" minus this quantity gives w' more
accurately.
To find <7, partly fill the tiibe with mercury, measure the read-
ing of the surface _Z7 and L" at two temperatures tf and if' which
should by preference be near the freezing and boiling points of
water. Then if L represents what the reading would be at 0,
we have by the law of expansion, L' + B = (L + B} (1 + mtf)
and (L" + B) = (L 4- B)(\ + mti'}, or eliminating, m =
*" j], - j-, - ; m is here the apparent expansion of
the mercury, or its true expansion minus the expansion of the
glass. Since the first of these quantities equals .00018. we have
g = .00018 m.
Returning now to the original curve for the apparent expansion
of the liquid, prolong it, if necessary, to the point where t = 0,
and call the corresponding value of 1, 1 . Find the value of I for
values of t = 10, 20, 30, etc., and the total apparent expansion
from to these points will equal I 1 divided by the volume at 0,
or G -\- 1 . But this is the true expansion minus the expansion of
the glass, hence the true expansion E = , . .. . + tg. To find
the rate of expansion of the liquid at various temperatures, draw
lines tangent to the curve at the points employed above, and find
the increase in volume per degree. Dividing this quantity by the
volume at 0, G + 4 gives the apparent expansion, and adding g
to each, gives the true expansion. Finally, draw curves with
temperatures as abscissas, and expansions as ordinates, and com-
pare the results with those given in the Tables.
126. EXPANSION OF GASES.
Apparatus. A Florence flask, A, Fig. 88, immersed in a vessel
which may be heated, and whose temperature may be measured
EXPANSION OF GASES. 81
by a thermometer, B. The flask is filled with dry air and closed
by a cork through which passes a bent glass tube, (7, serving as a
gauge. The lower part of the tube is filled with mercury whose
height is measured by a scale attached to each arm.
Experiment. Read the height of the barometer, the tempera-,
ture of the w r ater by B, and the difference in level of the mercury
in the arms of C. Then the pressure of the air
in A. will equal the height of the barometer, plus
the height of the mercury in the right hand arm
minus that in the left hand arm; that is, the dif-
erence in the two arms, supposing the pressure
of the air replaced by a column of mercury of
height equal to that of the barometer, added
directly to the mercury in the right arm of the gauge. Heat the
water twenty or thirty degrees, and withdraw the lamp. Stir
briskly with B when it will be seen that the temperature at first
rises, attains a maximum, and then begins to fall. Read the ther-
mometer B and gauge C, and repeat. Four or five readings
should be taken in this way between the freezing and boiling points.
We have thus a number of readings of the corresponding tem-
perature and pressure of a given quantity of gas under nearly
constant volume, since the volume of C is very small compared
with that of A. Call t the temperature, P the pressure, and
JP the pressure it would have at temperature 0. Then P =
P (1 + at) in which a is the required coefficient of expansion.
Apply the method given Vol. I, p. 5, to this case, and determine
the most probable values of a and P . The above equation may
be written = 1 P<rp ^-^Vp ln wm ch P corresponds
to a, -p to x, aP to b, and -p to y. Apply the rule -by sub-
stituting proper values of t and P from the observations taken
above, and thus form as many equations of condition as there
are observations. Then multiply each equation by the values of
p and equate their sum to zero. This gives one normal equation,
and the second is found similarly by multiplying by the various
values of -p. Solving the two normal equations gives P n and
jP , and hence a.
82 CHANGE OF VOLUME BY FUSION.
127. CHANGE OF VOLUME BY FUSION.
Apparatus. A test-tube A, Fig. 89, closed by a cork through
which passes a graduated bent glass tube B. A thermometer,
some mercury, ice and a balance and weights, are also required.
Experiment. Put some dry ice in the test tube, and fill the
remaining space nearly to the top of the graduation with mercury
cooled to C. Bead the position of the top of the mercury,
and let the ice melt. As the water occupies less space than the
ice, the mercury will fall until the fusion is complete. Read the
level at this instant. If the water is allowed to grow warmer, it will
continue to contract, until a temperature of 4 C. is attained, and
then it will expand again. Care must therefore be taken to read
the level as soon as all the ice has disappeared, or else the tube
should be immersed in ice water to prevent its becoming warmed.
Dry the outside of the tube and weigh it. "Weigh the
mercury now in the tube, and weigh the latter, when
empty, when filled to the top, and when filled to the
bottom of the graduation. From the last two weights
the volume of each division of the tube is readily ob-
tained by dividing their difference by 13.6 times the
number of divisions. The volume of the water is also
Fig 89 rea dily deduced from the weight of mercury, of the
tube when full, and the magnitude of the divisions.
The change in volume by fusion is then found from the compara-
tive volumes of the ice and water.
The change in volume of any other substance may be similarly
determined, except that a correction must be applied for tempera-
ture. In the case of fusible metal, or other alloys, water or oil
should be used instead of mercury, to avoid amalgamation, and as
the solid is then rsually heavier than the liquid, the tube B should
be straight, instead of bent.
128. CONDUCTION OF SOLIDS.
Apparatus. In Fig. 90, BC is a bar of the metal to be tested,
with the bulbs of several themometers inserted in it at regular
intervals. A is a vessel which may be filled with boiling water,
and I) is a short piece of the metal, with a thermometer in it to
show what the temperature would be if the bar was not heated.
CONDUCTION OF SOLIDS AND CRYSTALS. 83
This experiment may also be performed with a thermo-pile (Exper-
iment 131) sliding along the bar.
Experiment. Read the thermometers in BG and D, which
should mark the same temperature. Fill A with boiling water,
and at the end of a minute read again. Repeat, at intervals of a
minute, always beginning with the thermometer next B, and
reading them in order, until the temperature has become constant,
and the readings do not alter. Then construct a series of curves,
one for each minute, in which abscissas will represent the inter-
vals between the thermometers,
and ordinates the increase of
reading of each thermometer,
or its reading minus that of
the thermometer D. The final
curve should be such that the Fig. 90.
logarithms of the ordinates will be proportional to the abscissas,
or the latter being taken in arithmetical progression, the former
will vary geometrically. See if this is the case, by using as ordin-
ates the logarithms of the excesses of temperature, and abscissas as
before, when the result should be a straight line. The other curves
will show the gradual progress of the heat along the bar. By
using several bars of various metals, but having the same dimen-
sions and covered with the same varnish, the comparative con-
ductibility may be determined.
If the thermo-pile is used, the temperatui-e of any point of the
bar may be determined, as described in Experiment 131, and the
law of the distribution of its heat tested, as described below.
129. CONDUCTION OF CRYSTALS.
Apparatus. A thin plate of quartz cut parallel to the axis,
with a minute conical hole cut in its centre. Some stout silver
wire ground to a point, some wax and the Dividing Engine, Vol.
I, Experiment 22, are also required.
Experiment. Warm the crystal and touch the wax to it, so. as
to form a thin uniform layer over the surface. Let it cool, and
then heat the wire by a lamp after inserting one end in the hole.
The heat transmitted to the quartz will melt the wax, until the
84 CONTACT THERMOMETER.
loss by radiation will equal that received from the wire. Allow-
ing it to cool, the edge of the fused portion will be marked by a
line whose position is easily observed. To ensure contact of the
wire and crystal, the latter should be turned. Measure the curve
thus obtained with the Dividing Engine, and construct it on an
enlarged scale on paper divided into squares. If quartz conducted
heat equally in all directions, this curve would be a circle ; but as
the conductibility is greatest in the direction of the principal axis,
the curve is found tt> be an ellipse, with its transverse axis parallel
to the principal axis of crystallization. Construct an ellipse which
shall coincide as nearly as possible with the curve, and measure
the ratio of its axes. This curve may be obtained in a more
marked manner by using Meusel's double iodide of copper and
mercury, which changes from red to black on being heated to 70
C., but the curve thus obtained is not permanent, the color return-
ing as the crystal cools.
130. CONTACT THERMOMETER.
Apparatus. A thermometer with its bulb in a small funnel,
the stem passing through the neck, and the larger end being cov-
ered with sheet rubber after filling the funnel with mercury.
Some pieces of cloth, silk, woollen and other fabrics, and a large
surface heated to a constant temperature by boiling water or
steam, are required. The slab of a radiator is well adapted to
this purpose, and to avoid air currents it should be vertical, rather
than horizontal.
Experiment. Measure the temperature of the room as given
by the thermometer, and then hold it against the heated surface
until its temperature becomes stationary. Next, interpose in turn
the various fabrics to be tested, when the maximum temperatures
attained will depend on their relative conductibilities. This
method is not one of precision, and comparative results only can
be expected; but by interposing successively one, two, three or
more pieces of the same material, the law of variation may be
approximately determined.
131. RADIANT HEAT.
Apparatus. A thermo-pile and a delicate short-coil galvanom-
eter, with a mirror and scale, rendered astatic either by a second
RADIANT HEAT. 85
needle, or by a damping magnet. Various sources of heat are
required, as the flame of a lamp, a platinum wire heated to red-
ness, a sheet of hot metal, and a cube containing boiling water,
with one face polished, a second varnished, a third painted white,
and the fourth black. Melloni's therrno-bank may be used to
hold the various portions of the apparatus, but this is not indis-
pensable, as they may be placed in their proper positions on the
table. Plates of glass and of other materials are needed to study
the absorption of heat, and to prove the laws of reflection and
refraction of heat a horizontal graduated circle is required, with a
movable arm and index, to which the thermo-pile may be attached.
The mirror may be placed at the centre of the circle, and its posi-
tion marked by a second index. For the polarization of heat a
number of plates of clear mica, thin glass or collodion, are fast-
ened together and set at an angle of 55, like the bundle of thin
plates in a refracting polariscope. Two sets of such plates are re-
quired, as polarizer and analyzer, and they should be free to turn
by a measured amount around their axes.
Experiment. Light the burner and place it a short distance
from the thermo-pile, whose ends should be covered to protect it
from the heat. Attach the terminals of the pile to those of the
galvanometer, and light the burner connected with the latter, so
as to form a distinct spot of light at the centre of the scale. The
galvanometer must be adjusted, as described in Experiment 102.
Remove the cover of the pile so that the heat of the lamp shall
fall on it, when the spot should at once move nearly to the end
of the scale. It is generally better to note the maximum deflec-
tion rather than wait for the spot to cease vibrating, and much
time will be saved by using a galvanometer of such a form that
the needle will soon come to rest.
Take a series of readings, placing the pile at various distances
from the flame, and see if the deflection is inversely as the square
of the distance. Otherwise a curve may be constructed for the
galvanometer by using as ordinates the deflection, and as abscissas
the reciprocal of the square of the distance. This should give a
straight line ; and if not, all later observations should be reduced
by means of it.
Next, place the thermo-pile at the centre of the graduated circle,
and read the deflection when its face is inclined at various angles
to the incident rays of heat. The total amount of heat which
will fall on the pile will evidently be proportional to the cosine of
86 RADIANT HEAT.
the angle of incidence, and of this the amount absorbed by the
pile will also be proportional to the cosine of the same angle.
Hence the deflection should be proportional to the square of the
cosine of this angle.
To prove the law for the emission of heat, expose the thermo-
pile to the tin cube of boiling water, and note the deflection, as
the cube is inclined to it at various angles. The deflection should
be proportional to the cosine of the angle of emission. This law
is more simply proved by interposing a screen with a hole in it,
when the deflection will remain unchanged when the tin is turned,
as long as the angle of emission is not so great that a line from
the thermo-pile may fall off the heated surface. But the radiat-
ing surface which acts on the pile, will in this case be inversely
proportional to the cosine of the angle, hence the total amount of
heat remaining unchanged, the radiation per square unit must be
proportional to the cosine of the angle. The law of the distance
may be proved in a similar manner.
The transparency of bodies to heat, or their diathermancy, is
measured by placing the pile at such a distance from the flame
that the spot of light will move nearly to the end of the scale.
Now interpose a plate of glass, or other substance to be tested,
when the deflection will be much less, a portion of the heat being
absorbed. The ratio of the two deflections gives approximately
the amount of heat transmitted. Of this, however, a portion is
reflected specularly, in amount depending on the index of refrac-
tion. A loss of about eight or ten per cent may be ascribed to
this cause. After allowing for this error, the absorption by differ-
ent transparent bodies will be found to vary very greatly, espec-
ially when various sources of heat are employed. To show that
this is the case, measure the transmitted heat from the incandes-
cent wire, heated metal and hot water vessel, when it will be found
that while rock salt is almost perfectly transparent or diatherman-
ous to all heat rays, that glass cuts off a large portion, espec-
ially in the case of the heated water, where a plate of glass is
found to be nearly opaque, or athermanous. The reason is, that
each source of heat consists of a bundle of rays of various wave-
lengths, hence accurate quantitative results can be attained only
by separating these rays by a prism, or otherwise, and testing each
RADIANT HEAT. 87
separately. The absorption of two plates of glass is not double
that of a single plate, but follows a more complex law, each addi-
tional plate cutting off less and less, as if it acted like a sieve, and
removed the portions more easily absorbed. The absorption of liq-
uids is measured by two tanks of unequal thickness, the difference
in the transmitted rays in the two cases serving to determine the
absorption. The absorption of gases and vapors may be similarly
determined by a long tube whose absorption is measured when
empty, and when filled with the gas or vapor to be tested. In this
case, as the absorption is generally small, it is well to use a second
cube as a source of heat opposite the other face of the pile, and
measure the deflection before and after the vapor is interposed.
The galvanometer then shows the difference of the two bundles
of radiant heat.
The amount of heat radiated by a given body will depend
greatly on the condition of its surface. Expose the thermo-pile to
the four surfaces of the cube in turn, when it will be found that the
least heat will be received from the polished side, and the most
from that covered with the lampblack. The more heat a surface
radiates the more it will absorb ; but this is not easily shown,
except by covering the face of the pile with various varnishes.
Commonly the pile is covered with lampblack, since this is one of
the best of radiators and absorbers.
When a ray of heat is allowed to fall on a polished surface, the
greater part of it is reflected, as in the case of light, so that the
angle of reflection will equal the angle of incidence. To prove
this, place a mirror of glass or metal at the centre of the gradu-
ated circle, and the thermo-pile on the movable arm. On turning
the latter, little effect is produced, except in a particular position,
and then a marked deflection is obtained. Note the position of
greatest deflection, and read the angles of incidence and reflection,
when they will be found to be equal. Repeat, giving the angle of
incidence various values. For this, and for some of the following
parts of the experiment, the pile should be constructed in the form
of a narrow strip, or line. If care is exercised, it will be found
that some heat will be reflected at other angles than that given by
the law of reflection. This is what is known as diffuse reflection.
It is best seen by using a very intense source of heat.
88 LAW OF COOLING.
Replace the mirror by a prism of rock salt, when it will be
found that heat is refracted like light, the deflection of the gal-
vanometer attaining a marked maximum, in a position nearly
corresponding to that of the red end of the spectrum. Measure
the angles of incidence and refraction and compute from them the
index of refraction of the heat rays, as in Vol. I, Experiment 77.
Rays of heat may be polarized also, like rays of light. For this
purpose interpose the two bundles of plates of mica between the
source of heat and the thermo-pile, when it will be found on turn-
ing one of the bundles, that the deflection will be much greater
when they are parallel, than when at right angles to each other.
Call ra and n the deflections in these two cases, and call A and B
the portion transmitted of the heat polarized in the plane of inci-
dence, and in the plane at right angles to it, when the incident
beams are equal to unity. Then when the plates are parallel we
shall have A transmitted of one ray by one bundle of plates, and
A 2 by both. Of the other ray, B 2 will be transmitted by both, or
of the whole light, A 2 + B 2 . When the plates are crossed, we
shall have of one ray AB, and of the other BA, or 2 AB in all.
Therefore m = A 2 + B\ and n = %A B. But the polarization
effected by one bundle of plates is . . ? or substituting values
, A B Im n
of m and n. 4 j yj = t / ; .
^ A + B \m-\-n
132. LAW OF COOLING.
Apparatus. A large thermometer with a bulb about an inch in
diameter, enclosed in a flask from which the air may be with-
drawn if desired. The whole is immersed up to the neck in a
vessel of water, whose temperature may be kept constant by
stirring.
Experiment. Heat the thermometer very carefully and slowly
over a Bunsen burner, until the reading is about 300 C., then
insert it in the flask and immerse the latter in the vessel of water.
Now take a series of readings as the temperature falls, for every
10, until a temperature of 100 C. is attained, and below this at
the end of every minute. It is well to stir the water occasionally,
and see that its temperature t does not alter. The experiment
maybe varied by exhausting the air or replacing it by another gas,
PRESSURE OF STEAM. y
or by altering the temperature of the water in the containing ves-
sel. To establish the relation between the temperature y and the
time x, the simplest hypothesis that we can make is that the radi-
ation, or rate of cooling, ^r, is proportional to the temperature.
But the surrounding medium radiates back an amount propor-
tional to its temperature t. Hence we may write, -j- = ay at,
or integrating, ax = M log(y t), in which M = .434, the modulus
of the common system of logarithms. This is Newton's law of
cooling, and may be expressed by saying that if the times are taken
in arithmetical progression, the excesses of temperature will vary
geometrically. This law may be tested by constructing a curve
with times as abscissas, and logarithms of the excesses of tempera-
ture as ordinates. If the law is correct, the result should be a
straight line ; but this will seldom be the case, except for small
differences of temperatures.
Dulong and Petit showed that the rate of cooling could be
more correctly represented by the formula :
|| = m 1.0077" m 1.0077' + np\y if**
in which the last term represents the cooling effect of the air. In
this formula m and n are constants, dependent on the volume and
extent of surface of the cooling body, m depending also on the
material of the surface, and n on the nature of the 'gas; b also
depends on the kind of gas present, and p equals its pressure.
133. PRESSURE OF STEAM.
Apparatus. In Fig. 91, A is a flask half full of water, closed
by a rubber cork, through which pass a thermometer, _B, and a
bent tube, CD, serving for a gauge. The water is first boiled for
some time to expel the air, and mercury then poured into the open
end of CD. As the flask cools the mercury will rise, until when
cold the difference of level will be equal to the height of the
barometer within about an inch.
Experiment. Read the height of the barometer, the tempera-
ture of the water, and the difference in level of the mercury in
the two arms of the tube. Heat A carefully, and take a series
of readings of the thermometer B, and difference of level of the
mercury in the two arms of CD. Subtracting the latter from the
90 PRESSURE OF VAPORS.
height of the barometer, gives the pressure of the vapor corres-
ponding to these various temperatures. Construct a curve with
coordinates equal to these pressures and tempera-
tures, and draw a second curve from the results of
Regnault's experiments, as given in the Table of
the pressure of steam. If the observed pressure
at low temperatures is much greater than that
given in the Table, there is probably some air in
A, in which case the mercury should be emptied
F1 ( out of C, and the air expelled by boiling. If time
permits, it is well to observe the pressure as the wa-
ter cools, and compare the curve thus obtained with that given dur-
ing heating. If the water is heated too rapidly it is liable to boil
irregularly, and endanger the flask. This may be avoided by apply-
ing the heat more gradually, or by placing some sand or scraps of
platinum in the flask before sealing. If water collects above the
mercury in (7, it should be allowed for by adding an equivalent
column of mercury, which, since the specific gravity of the latter
is 13.6, is found by multiplying its height by .0735.
Instead of bending the tube GD into a U it may terminate at
D, and dip into a vessel containing mercury. It is then very
easily freed from air at any time by simply boiling the water and
removing the mercury vessel. When taking readings, the position
of the vessel should, however, be constantly altered, so as to keep
the surface of the mercury always at the same height.
134. PRESSURE OF VAPORS.
Apparatus. In Fig. 92, ABCD is a bent glass tube, closed at
A, and filled with mercury, like a siphon barometer. A drop of
water, or other liquid to be tested, is passed through the mercury
into the vacuum, and evaporating, depresses the mercury column
by the pressure of its vapor. The arm AB is enclosed in a large
thin glass tube, which may be filled with hot or cold water, and
the temperature measured by a thermometer, and rendered uni-
form by stirring.
If preferred, a straight barometer tube may be used, instead of
the bent tube, as in the last Experiment. For low temperatures it
is better to use a tube bent at the top, and the end immersed in a
freezing .mixture, as the pressure will be that due to the coldest
part of the space occupied by the vapor.
SPECIFIC GRAVITY OF VAPORS. 91
Experiment. Read the temperature by the thermometer, the
height of the barometer, and the difference in level of the mercury
in the two arms of the tube. Heat *the water grad-
ually, when, owing to the increased pressure of the
vapor the mercury column in AB will descend. Take
a series of readings of the temperatures and corres-
ponding vapor pressures, found by subtracting the dif-
ferences in height of the two columns of mercuiy from
the height of the barometer. Construct a curve with
these quantities as coordinates, and a second curve
with the numbers given in the Table of the pressure
of steam.
135. SPECIFIC GRAVITY OF VAPORS.
Apparatus. In Fig. 93, AB is a graduated glass tube about
2 cms. in diameter and 30 cms. long. G is a larger tube surround-
ing the upper end, which may be filled with hot water, or heated
by steam. The temperature is marked by an immersed thermom-
eter. The liquid to be examined may be enclosed in minute glass
stoppered bottles made for the purpose, or in fragments of glass
tubes drawn out to a point. Some mercury, and a balance and
weights, are also required.
Experiment. Close a thin glass tube at one end, and draw out
a small piece, so as to form a minute bulb terminating in a fine
point. Weigh it and fill with the liquid whose va-
por is to be measured, by warming and dipping the
end in the liquid, and as it cools a drop will be driven
inside by the pressure of the outer air. Heat the
glass carefully, so as to boil the liquid, and immerse
the end again, when, on cooling, it will be completely
filled. Close the end by holding it for an instant
in a gas flame, and then weigh it. The increase
of weight gives the amount of enclosed liquid. If the small glass
stoppered bottles are used, it is easy to weigh them empty and
full, taking care, in the second case, that the exterior is dry and
clean. Now fill the graduated glass tube with mercury, and in-
vert it over the vessel Z>, taking care that no air bubbles remain
inside. Pass the bulb containing the liquid under its edge, when
it will rise to the top and float on the mercury. Warm the tube
92 DENSITY OF GASES.
by steam or warm water, when the liquid will expand, break the
bulb, and being converted into vapor, will displace the mercury.
The temperature maintained must be sufficient to evaporate all
the liquid, which is known by the surface of the mercury appear-
ing dry. Observe the height of the barometer, and the height of the
mercury inside the tube, above that outside. The temperature is
then read by the thermometer, and the volume by the graduation.
This must be reduced to the standard temperature and pressure
oyo p
by the formula, V m = ^(273 -|-V)760' as ex P lained in Vol. *i
p. -51, in which P equals the height of the barometer minus the
difference of level of the mercury inside and outside of the grad-
uated glass tube. The specific gravity compared with water will
then equal the weight of liquid employed, divided by the volume
computed as above. Its specific gravity compared with air is
found by dividing this quantity by .001293, the specific gravity
of air. If the liquid has a known chemical composition, its two
specific gravities are found by dividing its atomic weight by 28.88
and .0373, respectively.
136. DENSITY OF GASES.
Apparatus. A delicate balance and weights, a thin glass globe
closed by a stopcock, an air pump, drying tubes, and a supply of
the gas to be examined.
Experiment. Exhaust the globe as completely as possible, and
measure the pressure of the air remaining. Then weigh it, or
rather place a somewhat heavier weight in the other scale pan,
and counterpoise very exactly by weights in the pan over the
globe. Read also the height of the barometer and the tempera-
ture of the air of the room. Connect the drying tubes with the
globe and allow the air to enter very slowly. Weigh a second
time by counterpoising again, and the change in weight equals the
weight of the air required to fill the globe. Exhaust again, and
fill with the gas to be tested. This is done by passing the gas
through the drying tubes to expel the air they contain, and then
allowing it to pass into the globe by partially opening the stop-
cock. To get rid of the small remaining amount of air, it is
best to exhaust and refill a second time. Weio-h the flask as
MIXTURE OF VAPORS. 93
before, and the increase compared with that when filled with air,
gives approximately the specific gravity of the gas, as in Vol. I,
Experiment 46. The absolute density of the gas may be found
by reducing its volume to and 760 mms. pressure, Vol. I, p. 51,
and recollecting that 1 litre of dry air weighs 1.293 grammes.
A much more accurate method, however, is to fill the globe with
mercury or water, measure the increase of weight, and thus de-
duce the volume in centimetres.
The preceding method can also be applied to finding the density
of a vapor ; a few grammes of the liquid, very pure and carefully
distilled, must be poured into the globe, and the latter then im-
mersed in a bath of water or oil, and raised tc a temperature con-
siderably above the boiling point of the liquid. The stopcock is
of course left open, and the vapor will rapidly escape, carrying
the air with it. When all the liquid has been converted into
vapor, which is known by the escape of vapor ceasing, the stop-
cock is closed, the temperature of the bath and the barometiic
pressure being first noticed. The globe is then removed from the
bath, allowed to cool, and the exterior carefully dried and weighed.
The computation is made precisely as in the last Experiment, ex-'
cept that the volume of a given weight is measured, instead of
the weight of a given volume.
137. MIXTURE OF VAPORS.
Apparatus. In Fig. 94, AB is a glass tub.e closed above and
below with stopcocks, a third stopcock C being added above, in
which the hole passes only part way through the plug, thus allow-
ing a liquid to be added, a drop at a time. A second tube, D, is
connected with the first, and serves to measure the pressure of the
enclosed gas.
Experiment. The tube must first be dried, which is best done
by unscrewing C, opening A and B and blowing dry
air through the tubes. Then close A and pour mercury
into the open tube till it stands at a point marked on
the tube AB. Read the height of the mercury in the
open tube, and screw C in place. Pour some water
into the end of C and turn its plug around once.
When the aperture in the latter is up, it fills with
water which escapes into the tube as the plug is turned
94 SPECIFIC HEAT.
over. The water evaporating will increase the pressure and make
the .mercury fall in AH, and rise in D. Add more mercury, there-
fore, through the open tube, until it stands exactly at the mark in
the closed tube. This is best done by adding an excess of mercury
and letting it slowly escape through A. The increased height of
mercury in D represents the pressure due to the water, and will
be found to be nearly the same as that formed at the same tem-
perature in a vacuum.
138. SPECIFIC HEAT.
Apparatus. A cylindrical vessel of thin sheet copper silvered,
supported in a second similar vessel of the same material, by rest-
ing it on three wooden points, or on two strings stretched inside
the outer vessel, near the bottom. Two thermometers, one for
measuring small changes of temperatures, the other graduated up
to 100 C., a balance and weights, a vessel in which water may be
heated, and some mercury and sand, are also required. Instead
of the copper vessels, common glass beakers may be employed, if
great accuracy is not required.
Experiment. Weigh the inner copper vessel, or calorimeter, as
it is called, and then partially fill it with cold water, and weigh
again. Heat some water and notice its precise temperature, also
that of the cold water and of the room. Then pour part of the
hot water into the calorimeter, stir briskly, and read the tempera-
ture of the mixture, as soon as it has become uniform. The suc-
cess of the experiment depends, in a great measure, on this opera-
tion, which requires much care. It is well first to take the tem-
perature of the cold water, at the beginning of a minute read the
thermometer in the hot water, then pour quickly and take a series
of readings as the calorimeter cools. Now weigh the calorimeter
with the mixture, and call its weight when empty, w, when con-
taining cold water, w', and after the hot water is added, w". Call
T the temperature of the hot water, t that of the cold water, and
if that of their mixture ; also call c the specific heat of the cal-
orimeter, and S that of the hot water, which should equal unity
if the experiment is correctly performed. Then the weight of
hot water added is w" w', and its fall in temperature T t' ;
hence the amount of heat it gives up is S(w" /)( T '), since
SPECIFIC HEAT. 95
the specific heat equals the amount of heat given out by a unit of
weight of the substance in cooling 1 C. The cold water, on the
other hand, gains in temperature (t' ), and in weight (w' w) ;
to the latter must be added the water-equivalent of the calorime-
ter, or weight of water which would require the same amount of
heat as the calorimeter to warm it 1. But for every gramme of
the calorimeter we must have c grammes of water ; hence for w
grammes we must have we grammes of water. Accordingly the
total amount of heat received will equal {t r t) (w r w + toe),
or since this must equal the heat given out by the hot water,
#(/' to') ( T tf) = (if t) (w' w + toe), or 8 =
( w r w -f wc ) (t' t) T
( t\-rrjr 3i I* no errors were committed, 8 should
(* w ) (T t)
equal unity, and it is well to repeat the experiment two or three
times, or until a value closely approaching this, is attained.
One of the principal sources of error is the loss due to radi-
ation from the hot water after its temperature is taken, and
before that of the mixture is observed. The readings taken dur-
ing the cooling of the mixture are designed to correct this error.
Construct a curve with abscissas equal to the times, and ordinates
to the logarithms of the excesses of temperature above that of
the room. This, by Newton's law of cooling (Experiment 132),
will be very nearly a straight line, and continuing it back to the
point where the hot water was poured into the calorimeter, will
give the temperature which would have been attained had there
been no loss of radiation, or could we have mixed the liquids in-
stantly and read the temperature at once. The value of if thus
obtained is that which should be used in the above formula. To
still further reduce this source of error, the water in the calorimeter
should be somewhat colder than the air of the room, and the amount
of hot water added should be such as to bring the temperature of
the mixture about as much above that of the surrounding air.
This same method may be used for such other liquids as do not
undergo a chemical change on contact with water or with the
calorimeter; solids in powder may be similarly treated. Find in
this way the specific heat of sand, heating it for some time in a
vessel surrounded by boiling water, to be sure that its temperature
is uniform. Find also the specific heat of mercury, replacing the
96 LATENT HEAT OF FUSION.
copper calorimeter by one of glass. The mercury must not be
heated over 100 C., or it will convert some of the water into
steam, and create a great loss, due to its latent heat.
139. LATENT HEAT OF FUSION.
Apparatus. The same as in the last Experiment, except that
some fresh, dry snow is needed, instead of the mercury and sand.
Experiment. Latent heat is measured almost precisely like
specific heat, and the same precautions are necessary in both cases.
The calorimeter is weighed empty, and when partly filled with
warm water ; the temperature of the latter and of the room is
then observed. Take the temperature of the snow, and put some
of the dryest portions into the calorimeter ; stir briskly, and as
soon as all is melted, take a series of readings of the temperature
every half minute. The correction for radiation is here much
greater than in finding the specific heat of liquids, since a much
longer time will elapse before all the snow is melted. Finally,
weigh the calorimeter and contents, to determine the amount of
snow added.
To compute from these observations the latent heat, call, as be-
fore, w, w' and w' r , the three weights of the calorimeter, T,
which will always be negative, the temperature of the snow, and
t and if the temperature of the calorimeter, before and after add-
ing the snow. Call L the latent heat, and S the specific heat of
the snow, which is about .5. Then the weight of the snow will
equal w" w', and its gain in heat may be divided into three
parts. First, heating the snow from Tto 0, its melting point ;
secondly, the latent heat L, and thirdly, after fusion, warming the
water from to if. The sum of these three will be (w" w)
(ST + L + t'\ or (w" w') (5T + L -f f\ since the specific
heat of water is unity. The heat given out by the calorimeter
will be (t tf)(w' w -j- cw>), and equating these two, and solv-
(t t?)(w' w + cw)
ing, gives L= ^ _ w ^ ] --ST-t'.
140. LATENT HEAT OF VAPORIZATION.
Apparatus. In Fig. 95, A is a tubulated retort, with a ther-
mometer B passing into it to mark the temperature of the vapor,
LATENT HEAT OF VAPORIZATION.
97
Fig, 95.
and C is a Florence flask, into which passes a second thermometer,
7>, to mark the temperature of the enclosed water. A screen, E,
serves to prevent the heat from passing directly to C by radiation.
A balance and weights should be provided, and a Bunsen burner
to boil the water in A.. -
Experiment. Fill A half full of water, and heat it by lighting
the burner under it. Disconnect C and weigh it, first when empty,
and then when partly full of water. Let
the water in A boil for some minutes, and
observe the temperature of the air of the
room, of the water in C, and of the steam
in A. Then connect A and 6 r , so that
the steam from the former shall pass over
into the latter, condensing and giving up
its latent heat. Observe the temperature
of the water in C by the thermometer JJ,
every minute for ten or fifteen minutes, then disconnect, and ob-
serve the temperature as C slowly cools. To keep the tempera-
ture of the water in C uniform throughout, it should be stirred
continually with the thermometer, or by a metallic stirrer raised
and lowered by a wire handle. Weigh C with its contents,
and the increase of weight will equal the amount of steam re-
ceived from A. Now construct a curve with abscissas equal to
the times, and ordinates to the temperatures, as given by D,
minus that of the air of the room. The curve thus drawn will
consist of two parts, one representing the heating, the other the
cooling of the water. Were there no loss by radiation, or other
causes, the first of these would become sensibly a straight line,
inclined to the axis by an amount proportional to the rate at
which the heat is conveyed from A to (7, and the second curve
would become a horizontal straight line, since the temperature
would remain unchanged. Owing to radiation, however, the
water is continually losing heat, and a very considerable error is
introduced if this loss is neglected. To apply a correction, we
must know the rate at which the temperature would fall if C was
heated 1 above the surrounding air. By Newton's law of cool-
ing, which will be sufficiently exact in the present case, the rate at
any temperature will be proportional to that temperature. Hence
7
98 LATENT HEAT OF VAPORIZATION.
if we draw tangents to the curve representing the cooling of O
at two or three points, then determine how much the loss is per
minute at these points, and divide this loss by the ordinate, or
excess of temperature of the point, we obtain values of the re-
quired rate of cooling for an excess of 1. A more accurate
method of determining this quantity is the following. As shown
dy
on page 89, the rate of cooling is -^ = ay at, in which a is
the quantity we wish now to determine, and integrating, ax =
Mlog (y t). Accordingly, if we construct a curve with ab-
scissas, as before, equal to the times, and ordinates to the loga-
rithms of the excesses of temperature over that of the air, we
obtain a straight line, and the tangent of the angle it makes
with the axis of Y multiplied by M, gives a, the required rate
of cooling. See if similar results are found by both methods.
The loss by cooling during any short time, dx, will evidently
equal a(y fydx, since it is proportional to the rate of cooling,
the excess of temperature, and the time. Hence the total loss
while the water is being heated will be proportional to the total
area included between the curve and the line y = t. This is com-
monly found with sufficient accuracy by multiplying the total
time of heating by the average of the initial, and final tempera-
tures. Multiplying this product by , and adding the result to the
final temperature gives the temperature which would have been
attained had there been no loss. To make this correction as small
as possible, it is well to begin with water in C as cold as possible,
so that the gain of heat by radiation from the outer air may in
part compensate for the loss, as C becomes heated.
To determine the latent heat from the quantities thus obtained,
let T equal the temperature of the steam, t and if the initial and
final temperatures of the water after correcting for loss by radia-
tion, to, w' and w", the weights of C when empty, after the water
is added, and at the end of the experiment, so that w' w will
equal the weight of water in C, and w" ID' the weight of steam
passed from A to C. Then the heat given out by the steam will
consist of two parts, that due to its latent heat in converting it
into water, and to its sensible heat given out as the water so pro-
duced cools from T to *', or (w" w')\_L + T tf~\ The heat
CARRE MACHINE. 99
received by the water equals the water equivalent of C, and its
contents, or (w' id) + sw, calling s the specific heat of O, or .2,
multiplied by the increase of temperature, if t. Equating these
two quantities (w" w'}\_L + T 1~] = (/ w + sw)(lf t),
T (w' w -\-swVtf t)
and solving with regard to L gives L = ; '
T+ t'.
141. CARKE MACHINE.
Apparatus. A Carre ice machine, such as is represented in Fig.
96, in which AB is an iron boiler containing ammonia and water,
and connected with a double cylindrical vessel, (7, by an iron tube.
In the upper part of A a tube is inserted, in which a thermome-
ter is placed, and surrounded by oil so as to take the temperature
of the tube. A cylindrical tin vessel is inserted in (7, and contains
the water to be frozen. A little alcohol is poured around it to
prevent its adhering to C. A must be heated in a small furnace,
and an abundance of cold water is needed to carry off the heat
from C.
Experiment. Set the Carre machine on end for five or ten min-
utes, so that C shall be uppermost, and all the liquid in it driven
into A. This is very essential to the success of the operation. Then
place A on the furnace, and C in a tub of
water at as low a temperature as is readily
attained. The tin vessel is of course taken
out, and C is placed entirely under the wa-
ter. A moderate and constant heat is now
applied, first pouring a little oil into the
tube in the upper part of A, and inserting
the thermometer. The temperature will
gradually rise, the ammonia separate from
the water and distil over into C, where it * '
will condense in the liquid form. Its latent
heat will thus be given up to the surrounding water, which must
therefore be constantly changed, or it will soon become warm.
The thermometer should be watched, as it gradually rises, until it
attains 130 C., when the heat should be withdrawn and A al-
lowed to cool. This concludes the first part of the operation, the
ammonia being converted into a liquid form, and its latent heat
carried off by the water. Now turn the Carre machine around,
100 FREEZING MIXTURES.
so that A shall be in the water instead of C, taking care not to
cool A too suddenly. Fill the tin vessel with the water, or other
substance to be frozen, close the hole in the bottom of O with a
cork, insert the tin vessel and pour a little alcohol or brandy
around it to prevent its freezing to C. Wrap a woollen cloth
around C to protect it from the air, and renew the water around
A as it grows warm. The liquid ammonia will now evaporate
rapidly, pass over into A, and be absorbed by the water ; the only
source from which it can obtain the heat needed to vaporize it will
be C and the water, which will consequently soon begin to freeze.
The heat given up by the absorption in A will be carried off by
the surrounding water, which must therefore be changed to keep
it cool. After some time the water in the tin will be found to be
completely frozen, and may then be extracted by simply dipping
the tin in water.
142. FREEZING MIXTURES.
Apparatus. Some snow or ice, salt, nitrate of ammonia, sul-
phate of soda and chlorhydric acid, a beaker suiTounded with
wool or other non-conductor, and a thermometer.
Experiment. A great variety of freezing mixtures have been
employed, all dependent on the formation of a liquid from the
mixture of a solid and liquid, or of two solids, where the heat
required to effect the change, being withdrawn from the substances
themselves, lowers their temperature. In each of the following
cases, measure the temperature of the substances employed before
and after mixture. The most common freezing mixture is formed
by adding one part of common salt to two of snow or pounded
ice, when the temperature will fall nearly 20 C. The cold thus
produced was supposed by Fahrenheit to be the absolute zero of
temperature, and was hence selected by him as the starting point
of the thermometer which bears his name. Mix equal parts of
water and nitrate of ammonia, when the temperature will fall 26 ;
again, to five parts of chlorhydric acid add eight parts of sul-
phate of soda, when the temperature will fall 27. By distillation
the salt may be recovered in each of these cases.
Far lower temperatures than these may be obtained by the
vaporization of liquified gases, as in Experiment 141, but the ap-
PYROMETERS. 101
paratus required is generally not adapted to daily laboratory work.
Liquid carbonic acid and protoxide of nitrogen are most com-
monly employed, and act both by their latent heat and by the
heat absorbed on the enormous increase of volume when the gas
is allowed to expand into the open air. If liquid carbonic acid is
allowed to evaporate, the temperature will fall to 70 C., and a
portion of the remainder will be frozen. If a jet of carbonic acid
under high pressure is allowed to escape, a temperature of 93
may be attained. A portion of the gas is, in this case, frozen into
flakes, like snow. Mixing some of this snow with liquid protoxide
of nitrogen and ether, so as to form a paste, and placing the whole
under the receiver of an air-pump, so as to accelerate the evapo-
ration, gives a temperature of 110 C., the lowest yet obtained.
143. PYROMETERS.
Apparatus. The various pyrometers described below, including
a mercury thermometer, graduated to 360 C., and an air thermom-
eter formed of a glass, or better, a porcelain, bulb, filled with dry
air, and connected by a fine tube with a gauge containing mer-
cury. A Wedgewood pyrometer and some clay cylinders, a piece
of platinum, or of iron, if platinum is too expensive. A thermo-
electric pile, formed of two wires of platinum and indium welded
together at the ends, and connected with a delicate galvanometer,
also a Siemens' resistance pyrometer, consisting of a coil of fine
platinum wire, forming one side of a Wheatstone's bridge. As
sources of heat we may use boiling water, oil, sulphur, cadmium
or zinc, baths of various alloys at their melting points, and for
higher temperatures any form of furnace or gas-flame.
Experiment. The following are the more common methods of
measuring very high temperatui-es. Try each in turn with those
temperatures to which it is applicable, and compare the results.
Measure the temperatures of the water, oil and alloys, with the
thermometer, taking care that it is not heated above 360. Do
the same with the air-thermometer, immersing the bulb in the
bath to be tested, and reading the difference in level of the mer-
cury in the gauge. Read also the height of the barometer, and
adding it to the level of the mercury in the outer arm of the
gauge, the difference will give the true pressure of the enclosed
air. This pressure will then be proportional to the absolute tern-
102 PYROMETERS.
perature, or temperature above 273 C. Calling P the pres-
sure, and P the pressure at 0, we may write P P (l + <) m
which t is the temperature, and a equals ^}^ the coefficient of ex-
pansion of gas. A correction may be applied for the increased
volume, as the mercury is driven down in the gauge, but this may
be neglected if the tube is small and the bulb large. If a glass
bulb is used, temperatures ,up to 800, or nearly the softening
point of glass, and with a porcelain bulb, much higher tempera-
tures may be measured.
Wedgewood's pyrometer depends on the principle that dried
clay contracts when exposed to heat, by an amount nearly propor-
tional to the temperature. A number of short clay cylinders are
accordingly made of precisely the same diameter, and this diame-
ter is measured by placing them in a wedge-shaped cavity with
graduated sides, formed of two graduated metallic rods slightly
inclined to one another. The distance to which the clay may
be inserted will mark, on an enlarged scale, its diameter. Ex-
pose a cylinder to the temperature to be measured, and after
cooling insert it in the wedge-shaped cavity. The distance to
which the cylinder will enter shows the temperature. The scale
must be reduced to degrees empirically, and will vary with the
kind of clay. It is found that on a long exposure to high temper-
ature the clay continues to contract, and thus very accurate read-
ings cannot be obtained with this pyrometer.
Another method of measuring temperatures is dependent on the
specific heat of platinum. A piece of this metal is exposed to the
temperature to be measured, and then dropped instantly into a
calorimeter, as if measuring its specific heat, Experiment 138.
The same formula is employed, except that instead of knowing
the upper temperature and determining the specific heat, we now
have the latter given as equal to .032, and therefore T =
W -\- WC)
w f ) --- rf- If iron is used, .114 must be taken
for the specific heat. The great difficulty with this method is the
loss of heat in transferring the metal to the calorimeter, and also
that a portion of the water is converted into vapor, causing a
large loss, due to the latent heat absorbed by the steam.
The thermo-pile affords an easy means of measuring high tern-
HEAT OF COMBUSTION. 103
peratures. It is only necessary to connect its terminals with the
galvanometer and expose its junction to the temperature to be
measured, which will be nearly proportional to the deflection of
the galvanometer needle. It is better to immerse the other termi-
nal of the thermo-pile in cold water, when the electromotive force,
and consequently the current and the deflection, will be propor-
tional to the diiference in temperature.
Siemens' resistance pyrometer depends on the change in electri-
cal resistance in a platinum wire when exposed to changes of tem-
perature. It is merely necessary to make the coil one side of a
Wheatstone's bridge, or connect it with one coil of a differential
galvanometer, and measure its resistance when exposed to changes
of temperature. It may also be used to measure ordinary tem-
peratures of inaccessible places, as in deep sea-soundings, by inter-
posing as the second arm of the bridge a similar coil immersed in
water, which may be warmed or cooled at will. The temperature
is altered until no current passes through the galvanometer, when
the temperature will equal that of the other coil, and may be
measured directly with a thermometer. When the point whose
temperature is to be determined is very distant, the unknown
temperature of the connecting wires is likely to introduce a large
error. This may be avoided by inserting in the circuit of the
other arm of the bridge a second wire running side by side with
that connected with the platinum. The temperature is thus al-
ways the same for both, and the error thereby compensated.
144. HEAT OF COMBUSTION.
Apparatus. A Dulong calorimeter, which consists of a vessel
in which the combustion takes place, with four outlets. One is
connected with a long spiral tube, like the worm of a still, through
which the products of combustion are drawn ; a second aperture
serves to admit the substance to be burned, a third admits the air
or oxygen, and the fourth, closed by a plate of glass, enables the
observer to watch the combustion and see that it is complete.
The whole is contained in a larger vessel containing water, whose
temperature is rendered uniform by a stirrer, and is measured by a
thermometer. A second thermometer serves to measure the tem-
perature of the escaping gases. The latter should pass through
a meter into an aspirator, and if the substance to be tested is a
gas, a second meter should be inserted to measure its volume.
104 EFFICIENCY OF GAS BURNERS.
Experiment. Measure the temperature of the air of the room,
of the water of the calorimeter, and the height of the barometer.
Light the gas burner, place it inside, and regulate the flow from
the aspirator, so that the combustion shall be complete. Read the
temperature at regular intervals, keeping the water well stirred.
Extinguish the light and letting the calorimeter cool, determine
the correction for loss by radiation precisely as in Experiment 140.
Call w the weight of gas burnt, w' the weight of air used to con-
sume it, TFthe water equivalent of the calorimeter and contents,
If the required heat of combustion, t the corrected increase of
temperature, and tf the excess of temperature of the escaping
gases above the air of the room. Then wH = Wt' + (w -}- w')t.
The weights of the gases are determined from their volumes and
specific gravities, correcting for temperatures and pressures. If a
solid or liquid combustible is employed it must be weighed directly.
145. EFFICIENCY OF GAS BURNERS.
Apparatus. A Bunsen burner, whose consumption is measured
to thousandths of a foot by a meter, or an alcohol lamp which
may be weighed while burning, a tin vessel containing water to be
heated, a thermometer and a balance and weights.
Experiment. Weigh the tin vessel empty, and when partly
filled with water, and observe the temperature of the room and
of the water. Light the gas, and take a series of readings of the
temperature of the water at the beginning of every minute, and
thirty seconds later of the meter, as described in Vol. I, Experi-
ment 57. When the water begins to boil weigh again, then let it
boil for ten minutes and make a final weighing. The average of
each two consecutive readings of the meter may be taken as its
true reading at the beginning of the minute. Construct a curve
with these readings as abscissas, and temperatures as ordinates.
The tangent of the angle this curve makes with the axis of J^
gives the increase of temperature per cubic foot consumption of
gas. Multiplying the number of degrees thus obtained by the
water equivalent in kilogrammes of the tin vessel and contents,
gives the number of units of heat evolved per cubic foot of gas
burned. 4 This same quantity divided by the consumption per
minute, will give the number of units of heat per minute with the
MECHANICAL EQUIVALENT OF HEAT. 105
particular burner employed. From the loss of weight of the wa-
ter during boiling, the heat received may also be determined, call-
ing the latent heat of vaporization 537. This method is much less
delicate than the other, unless the source of heat is very powerful.
Compare the effect of placing the tin vessel at different distances
from the lamp, and also of using a luminous, instead of a non-
luminous flame. Comparing the results with those obtained in
Experiment 144, we see how small a portion of the whole heat of
the flame is utilized.
146. MECHANICAL EQUIVALENT OF HEAT.
Apparatus. In Fig. 97, A, JB, are two hollow iron cones, of
which the outer and lower one may be kept revolving with a
constant velocity by a belt passing over a pulley C. Any small
motor, as a steam or electric engine, clockwork, or even a crank,
may be used to maintain this motion, which should be as uniform
as possible. The upper cone is filled with mercury, and contains a
thermometer to measure its temperature; a light arm, ED, is at-
tached above, to whose ends cords are fastened over pulleys, and
equal weights are hung at the ends to tend to turn it in the
opposite direction from that in which C is turning. Stops should
be placed on each side of ED to prevent its turning too far.
Experiment. Start the motor so that C, and with it the lower
cone J3, shall revolve at a uniform rate, and see what loads must
be attached to the pulleys to hold the beam in equilibrium. It is
well to use somewhat too small a load, and check the motor with
the finger, so as to keep the beam bal-
anced between its two stops. Every-
thing being in readiness, read the
temperature of the mercury by the
thermometer F, start the motor, keep
the beam between the two stops, and
observe the speed. This may be done Fi ^
by a shaft-speeder, OP better, by the ar-
rangement described in Experiment 158. The work required to
overcome the friction between A. and JS will now be converted
into heat, and the thermometer will accordingly rise steadily.
Read the temperature every minute for five or ten minutes, and
then determine the correction for radiation by stopping the motor
106 TWO SPECIFIC HEATS OF GASES.
and taking readings as the cones cool. Determine the increase in
temperature, t, correcting for radiation, as in Experiment 140.
The water equivalent of the two cones will equal their weight
multiplied by .114, the specific heat of the iron, and to this must
be added the weight of mercury multiplied by .033, its specific
heat, or w's' + w"s" ; multiplying this quantity by t gives the
amount of heat generated. To determine the amount of work
expended, call W the weight on the strings over each pulley, 21 the
length of ED, or perpendicular distance between the two horizon-
tal strings, and n the number of turns per minute of the pulley C.
Then the work done will be the same as if a force TF on each end
of ED, or 2 W on one end, turned it round n times, or traversed
a distance of 1-ln. The work done is accordingly 4~ln W. If
then Jf is the mechanical equivalent of heat, or work which may
be done by one unit of heat, we must have M(w's f + w"s")t =
krdn W, or M = , fg / , w s "\ in which care must be taken to
use as units the kilogramme and metre. This experiment should
be repeated several times, and also varied by placing a load on the
inner cone, A, thereby increasing the friction, and consequently
the rate of heating.
147. Two SPECIFIC HEATS OF GASES.
Apparatus. In Fig. 98, A is a large flask closed by a cork,
through which pass a tube with a large stopcock, _Z?, and a bent
tube forming a gauge, CD. A large rubber tube may be attached
to B so as to partially exhaust the air.
Experiment. The theoretical determination of the mechanical
equivalent of heat and of the velocity of sound in gases, depends
on the accurate determination of the ratio of the specific heat
of gases under constant pressure to that under constant volume.
Evidently the former quantity must be the greatest, since when
a gas is heated under constant pressure, besides warming the
gas, a certain amount of energy must be expended in over-
coming the pressure, so as to allow the expansion to take place.
The ratio of these specific heats is best determined by the appa-
ratus of Clement and Desormes, represented in Fig. 98. Con-
nect the rubber tube with B, open the stopcock and partially
TWO SPECIFIC HEATS OF OASES. 107
exhaust the air, either by the mouth or by an air pump, so that
the water shall rise nearly to the top of CD. Close the stop-
cock and disconnect the rubber tube, when,
even if there is no leak, the liquid will slowly
descend, because the gas cooled by the rare-
faction gradually recovers the temperature of
the surrounding medium. Wait until it comes
to rest, and read the exact level of the water.
Open the stopcock for just one second, close
it and take readings every five or ten sec- Fj 9g
onds, as the water rises in the gauge, until
it comes to rest. When the cock is open, air rushes in, heating
the enclosed air, so that when the cock is closed and the air has
time to give up its heat to the surrounding bodies, it is found that
the exhaustion is still about a third of what it was at first. To
determine this fraction with precision, or rather, what it would be
were there no loss by radiation while the stopcock was open, con-
struct a curve with abscissas equal to the times, and ordinates to
the height of the water level in CD. This curve forms a nearly
horizontal line before the stopcock is opened, then is nearly vertical
until it reaches the axis, then a sinuous line, owing to the vibra-
tions of the air at the orifice, and finally a smooth curve after the
stopcock is closed. Only the first and last of these forms can be
observed. Prolong the curved portion until it meets the vertical
line, and repeat the experiment, if necessary, until the time during
which the stopcock is left open is such as to bring this point near
the surface of the water.
Call p' the height of the water before the stopcock is opened,
and p" the height it finally attains, so that it first descends
through p', and then rises through p". Then the ratio of the
specific heat under constant pressure, to that under constant
volume will equal /
To prove this formula,, suppose a given mass of gas confined, so
that its volume cannot alter, and placed in a medium, whose
temperature is somewhat greater than its own. It will gradually
be heated, and an amount of energy which we may call A will
thereby be transferred from the medium to it. Its pressure also
108 TWO SPECIFIC HEATS OF GASES.
will be increased. Now suppose that it is allowed to expand, until
its pressure becomes the same as at first. The first effect would be
to cool it, but soon it will absorb enough heat from the surround-
ing medium to render the temperature the same as that of the
medium. Call B the additional amount of enei'gy.thus absorbed.
Evidently the ratio of the specific heat under constant pressure,
to that under constant volume will be as A -\- B is to A. If now
we compress the gas to its original volume, the energy B will be
set free as heat, and will soon be lost by radiation to surrounding
objects, while the energy A will remain and may be recovered if
the gas is cooled down to its original temperature.
Now in the experiment just performed, when the gas is
compressed by an amount which may be represented by />', cor-
responding to* A -\- B, the quantity of heat set free will be repre-
sented by p" corresponding to B, or since for these small changes,
the energy maybe taken as proportional to the change in pressure,
we shall have A -}- B : B = p' : p". This may also be written
A : B =-p' p" : p" or A + B : A p' \p' p", hence the ratio
of the two specific heats, -T = / ??
MECHANICAL ENGINEERING.
The number of experiments a Mechanical Engineer is called
upon to perform, is generally small, but their importance can
scarcely be overestimated, as no other branch of Physics has so
great a value, both as a saving of money, and as a protection to life
and limb. The following Experiments require little apparatus be-
yond that usually accompanying a furnace, a boiler and engine, and
a dynamometer. The large original cost of the engine is, in part,
compensated by its value in a technical school or college as a
source of power, on which account alone it is considered a neces-
sity in many such institutions. A knowledge of piping, or carry-
ing steam in pipes, and of running a boiler or engine, is so requisite
to the following work, that a special description of them is pre-
fixed. The proper method of taking care of a boiler or engine
can, however, be learned only by experience, and no one should
be entrusted with either, for the first time, except in the presence
of an experienced engineer. The instructions given below must
therefore be regarded merely as aids to the pupil, and to simplify
the work of the instructor.
Piping. To understand the proper method of conveying steam
from one point to another, a short description is here given of
piping, and applies, with slight changes, to the conveyance of
any other fluid, as air, gas or water. Pipes from 15 to 20 'ft. in
length are used, and of diameters reckoned in eighths of an inch,
as , , |, , f, 1, l, l, 2, 2^, and 3 inches. The intermediate
sizes are not in use. These distances denote interior diameters,
but they are really too small, the actual diameter of a pip e
being .28 in., of a J pipe .62 in., and of a 1 inch pipe 1.05 ins. To
connect two pipes of the same size, a screw thread is cut on the
end of each with a die, and a coupling, or short piece of larger and
thicker pipe with a thread inside of it, is screwed on one, first
interposing a little red lead. The other pipe in then screwed into
(109)
110 PIPING.
it until a tight joint is obtained. The red lead serves to lubricate
the joint, and at the same time renders it tighter ; without the red
lead the pipes could be turned only with great difficulty, and it
would be almost impossible to take them apart. A rusted joint is
made by wetting the ends and screwing them together, when the
iron rusts, and it becomes almost impossible to separate them.
When a screw thread is cut on the outside of a pipe it is called
an outside or male screw ; when cut in the interior, an inside or
female screw. A die cuts a male, a tap a female screw. The lat-
ter are never cut on common steam pipes as they weaken them
too much, and render them liable to split.
If the pipes are not of the same size, reducing couplings are
used, or thick tubes with inside screws of different sizes cut in the
two ends. If the difference in size is very great, a bushing must
be inserted in the smaller end of the coupling. This consists of a
short tube with an outside thread to fit into the coupling, and an
inside thread to fit on to the pipe. If two couplings have to be
connected, nipples are used, or short pipes with outside threads on
both ends. To close a pipe a cap is employed, made like a coup-
ling, except that it is closed at one end. A coupling may, in the
same way, be closed by a plug, a piece of iron with an outside
screw on one end, and cast square at the other, for convenience
of turning it with a wrench. When two pipes are already laid,
they cannot be connected as described above, since one must be
turned around in order to screw it into the coupling. What is
called a right and left is then used ; that is, a coupling with a
right handed screw cut in one end, and a left handed screw in the
other. Right and left handed screws are cut on the pipes, and the
coupling turned into place without disturbing them. Of course,
if there is a space between the two pipes, an additional pipe and
coupling must be inserted. Rights and lefts when larger than
inch are marked by a number of ridges on the outside, so that
they may be recognized at a glance. Two pipes are connected at
right angles by an elbow, or L, which looks like a coupling bent at
right angles. If the pipes are to be inclined at any other angle,
an L must be screwed on the end of each, and the two Ls con-
nected by a nipple. In this case, the two pipes will not lie in the
same plane, one being above the other.
PIPING. Ill
When a branch is to be inserted in a pipe, a T is employed.
This resembles a coupling with a short pipe on one side with an
inside screw, forming, in fact, a combination of an L and coupling.
The three ends may be either of the same, or of different sizes.
For convenience of fastening pipes to woodwork, JJs and Ts are
sometimes made with projections cast on the side, with holes
through which screws may be passed ; such fittings are called drop
Ls, and drop Ts. Larger pipes are held in place, when neces-
sary, by clips, or pieces of sheet metal bent around the pipe, and
fastened down by screws. To insert two branches into a pipe at
the same point, or to make a pipe divide into three, a cross is used,
which is a T with two branches instead of one, that is, a short
pipe on each side.
The above are the most common fittings, and with them almost
all connections can be made ; it will be noticed that couplings,
caps, Ls, TS, and crosses have only inside screws, pipes, plugs and
nipples only outside, and bushings both. Evidently the inside
and outside screws must always come alternately. Where there
is any probability that additional connections will have to be
made, it is best to put in Ts frequently, instead of couplings and
Xs, plugging the extra holes. The additional expense is small,
while the saving effected may be very great. In long pipes it is
also often better to insert plugged Ts at short intervals, or rights
and lefts. If this is not done, and a branch must be inserted,
it is either necessary to take the fittings all to pieces at one end,
so that the pipe will turn 'round, or else to cut the pipe in two, re-
move a piece, and insert a T, making the last joint by a right and
left. If a right and left has been already inserted, it may be dis-
connected at once at this point, while if a plugged T had been
used, it would only be necessary to remove the plug and screw
the pipe in, in its place. If the pipe is used for gas, it is not even
necessary, in this case, to shut the latter off.
To avoid turning the pipe, unions are sometimes used. In
these, two planed surfaces are screwed on to the pipes to be
joined, a washer interposed and then brought together by an out-
side screw cut on one end, and a loose nut fitting over the other.
Screwing the nut in place fastens the pipes together, and they are
easily separated or turned at any time.
112 STEAM BOILERS.
To cut off communication through a pipe, either wholly or in
part, a cock or valve is used. The former, of which we have
examples in common gas and water fixtures, consists of a plug
passing through the pipe at right angles, and with a hole through
it, which may be turned either in the direction of the pipe or
across it. If the pipe is large or the pressure great, valves are
much better. They consist of cast iron boxes, in which a screw
turned by a small wheel forces a conical plug against a partition
in the box so as to close a hole bored in it, thus cutting off com-
munication between the upper and lower parts, which open on op-
posite sides of the valve. The valve is connected with the pipes
by two female screws, like a coupling. Other forms of valves are
sometimes used, as for instance, one in which a screw forces a
diaphragm at right angles to the pipe. This valve has the ad-
vantage, when open, of opposing much less resistance to the flow
of the fluid, but it is much more liable to leak.
The tools used for piping are few in number. To divide a
pipe at any required point, it is held in a stout vice, and cut by
turning around it a cutter in which a sharp edged steel wheel is
forced by a screw against the pipe. Care must be taken to turn
the screw gradually, or the pipe will be flattened or bent, and to
hold it at right angles to the axis, or a screw-like cut will be made.
Outside screw-threads are cut on pipes by a die turned in the
usual way, by two long handles. Inside screws are never cut on
pipes, and connections always come with the screws cut. To
screw the parts together, pipe-tongs are used, made somewhat like
pliers, only so arranged that they wedge on the pipe, holding
tighter the harder they are turned. For unscrewing they must be
turned over. For different sized pipes different tongs must be
used, or they are sometimes made adjustable with a screw to fit
any size. To turn the Ls, Ts, plugs, etc., a monkey-wrench is
most convenient.
Steam Sailers. Boilers are made in a great variety of forms,
but are generally of sheet iron or boiler plate, held together with
rivets. The tubular form is the most common, in which the hot
air and gases from the fire are carried in tubes through the centre
of the boiler. Being thus completely surrounded with water, the
heat is rapidly transmitted to it, producing steam quickly and
STEAM BOILERS. 113
preventing much of the heat from escaping with the products of
combustion. Cast iron is sometimes employed, the earliest and
best known form being the Harrison boiler, which consists of a
series of cast iron spheres like bomb-shells. This is one of the
safest forms of boilers, but is heavy and sometimes gives trouble
from collecting scale, as described below.
A pipe is connected with the upper part of the boiler to carry
off the steam as it is generated, and the space not filled with
water, called the steam space, should be considerable, otherwise
when the water is boiling violently, it will be carried off with the
steam, which is called foaming or priming. Sometimes a projec-
tion, called a steam dome, is made in the boiler to avoid this diffi-
culty. The water is admitted by a second pipe, which may be
connected directly with the hydrant if the pressure is sufficient,
or with a force pump driven by hand or by an engine. To show
the height of the water in the boiler, one or more vertical glass
tubes or water gauges are connected below with the water, and
above with the steam in the boiler. Great care must be taken
when cleaning them, which should be done Only when necessary,
and then by pushing a cloth through them with a stick, as metal
is liable to produce a scratch which will eventually cause the tube
to break. Three or four outlets closed by valves are commonly
placed at different heights in the side of the boiler, and the height
of the water detei-mined by opening them in turn. Steam will
come from those above, and water from those below the water
line. Unfortunately, owing to the foaming of the boiler, it is
sometimes very difficult to determine the true amount of water in
the boiler when steam is made very rapidly, as the water in the
glass gauge will be in constant motion, and both water and steam
will come from all the valves. To measure the pressure in the
boiler a gauge is connected with it by a pipe, showing the pres-
sure in pounds by the motion of an index. To obtain the real
pressure, 15 pounds must be added for the pressure of the atmo-
sphere. To empty the boiler another pipe enters near the bottom
through which the water may be drawn out. A large hole, called
a manhole, is also commonly made in the top, so that a man can
get inside for repairs or other purposes. Every boiler should also
be provided with a safety valve, or a hole closed by a plate pressed
114 STEAM BOILERS.
against it by a weight, such that if the pressure is too great it is
lifted and the steam escapes.
Every boiler, after it is set, should be tested by what is called
the cold water test, to see that it is strong enough, and that it
does not leak. For this purpose it is completely filled with water
and connected with a small force pump worked by hand. Work-
ing the pump gradually, the gauge at once rises and should be
carried considerably above the pressure at which it is to be used.
Communication being then cut off between the pump and boiler
by a valve, if there is no leak the index should remain unchanged.
With small boilers the plan has been tried of inserting a metallic
plate inside the boiler, and connecting it with the positive pole of
a powerful galvanic battery by an insulated wire. Connecting the
other pole with the boiler, decomposition of the water will take
place, and the gases thus set free will produce the required pres-
sure. The conductibility of the water should be increased by
adding a little salt.
In running the boiler, care should be taken that the water does
not get too low. Of course the fire must never be made when
the boiler is empty, or it would soon destroy it. After the boiler
has been used for some time much trouble is often experienced
from a stony sediment or coatingof the interior of the boiler,
called scale. The non-volatile salts remaining in the water as it is
boiled away, collect, often in large quantities, especially when the
water contains much lime. This prevents the heat from being
transmitted freely to the water, and hence the iron is overheated
and soon burnt out. To avoid this difficulty, the same water
should be used over and over again if possible, as with a condens-
ing engine, or in buildings heated with steam. Sometimes, also,
the water should be partly blown out from the lower aperture by
the steam pressure. The mechanical disturbance thus carries off
much of the scale. Various other remedies are recommended,
but if the scale still collects, a man should occasionally be sent
inside to chip it off with a hammer and cold chisel.
The management of the fire is much the same as that of a
common house furnace. There are two doors, one above through
which the coal is thrown, and one below, for removing the ashes.
In each door is a slide by which a small aperture may be closed to
STEAM ENGINE. 115
a greater or less extent, as desired. When the lower door is open,
the draft in the chimney draws air through it and through the
coal, producing an intense combustion. When the upper door is
open the cold air is drawn above the coal, cooling it and deaden-
ing the fire. The draft in the chimney may be regulated either
by dampers which close it to a greater or less extent, or by a slide
which admits cold air, cooling it and 'thus lessening the draft.
There are therefore three ways of increasing the heat ; closing the
upper door, opening the lower door, and opening the damper, or
closing the slide which admits cold air into the chimney. When
the fire is low, and fresh coal has been put on, or when starting
the fire, the upper door should be closed and the lower opened,
but when under way it can generally be completely regulated by
the slides. No definite rules can be given, as every thing depends
on the particular conditions in each case, as draft, kind of fuel, size
of furnace, heat required, etc. On leaving the furnace for the
night, or when not wanted for some time, the slide in the upper
door should be opened, the lower one nearly or quite closed, and
the draft lessened.
When the pressure of steam is just equal to that due to its tem-
perature, as is the case when it is in contact with the water of the
boiler, it is said to be saturated, and it will begin to condense at
once if cooled, or if the pressure is at all increased. If heated
above this point it is said to be superheated. If much water is
carried over in drops with the steam, the latter is said to be wet,
while if no water is present, it is called dry steam. Dry, super-
heated steam is easily recognized by its bluish color, and the
hand may be held in a jet of it with impunity.
Steam Engine. The most essential part of an engine is a
cylindrical iron box called the cylinder, in which is a movable
partition called the piston. Steam is admitted on one side of this,
driving it to the other end, and then on the other side driving it
back. This rectilinear motion is converted into a circular motion
by means of a crank, and is rendered nearly uniform by a heavy
cast iron wheel, called a fly-wheel. The steam is directed by
means of a slide valve, so that it shall be admitted first on one
side and then on the other of the piston, which is done automati-
116 STEAM ENGINE.
cally by moving the valve by an eccentric on the axis of the fly-
wheel.
To start the engine, it is merely necessary to turn on steam,
when the engine will begin to move, unless the piston is at the
dead point, that is, at the end of its stroke. In this case, the fly-
wheel must be turned slightly, by hand, when the steam will
carry it round. If the steam is turned on at once, it will rush
into the cold cylinder, and condense, forming water, which being
almost incompressible, and coming between the piston and the
end of the cylinder, is likely to break off the cylinder-head. Ac-
cordingly an outlet is made in the cylinder which should always
be opened before the steam is admitted, and closed when the
engine has run for some time, and the cylinder heated so that
the condensation is slight. To prevent the engine from going too
fast, when it is doing no work but overcoming the friction of its
parts, a governor is attached, which commonly consists of two
balls turned by the flywheel, forming a conical pendulum, and
which if the speed becomes too great, fly apart and cut off the
steam. The pipe by which the steam is admitted into the cylin-
der is called the supply pipe, that by which it passes off, the
exhaust. A great deal of power is lost in driving the piston back
against the steam on the other side and forcing it through the
exhaust. To diminish this loss, the exhaust is sometimes con-
nected with a condenser, or cold space, by which the steam is
reduced to water, and its pressure greatly diminished. This form
of engine is called a condensing engine, but is not much used, on
account of the expense and bulk of the condenser, except to avoid
using salt-water at sea. Again, there is a great loss, since the
steam is admitted at high pressure, and when the exhaust is
opened, allowed to expand until its pressure is no greater then
that of the atmosphere, without doing any useful work. A part
of this loss is prevented by a cut-off, by which the steam is ad-
mitted into the cylinder until the piston has performed part only
of its work, communication with the boiler is then interrupted and
the piston is forced on by the expansion of the steam. The cut-
off is accomplished in various ways, but generally by giving a
proper motion to the slide-valve.
EFFICIENCY OF BOILERS. 117
148. EFFICIENCY OF BOILERS.
Apparatus. The furnace and boiler, a large graduated vessel
to measure the water, and a platform balance to weigh the coal.
Experiment. The most important experiment that a mechani-
cal engineer is called upon to perform, is to determine how much
coal is required to evaporate a pound of water in a given boiler.
Its pecuniary value often represents many thousands of dollars,
and therefore too great care cannot be taken with it. The trial
should last at least twelve hours, and better thirty-six, or even a
longer time. A large number of students may participate in the
trial, and watching by turns, render the work less laborious. It is
best to combine this experiment with Nos. 153 and 154, as there
will be ample time for all without interfering.
Different results are obtained with different pressures, and
changes in the intensity of the fire. Accordingly, both must be
kept as nearly constant as possible. The best effect is generally
attained with a moderate fire, and less if the combustion is very
rapid or very slow. The coal is weighed directly by shovelling it
on to the platform scale, and thence into the furnace. To meas-
ure the amount of water converted into steam, is more difficult. It
is best done by a condenser, as in a condensing engine. A tem-
porary substitute is a steam coil, such as is used for heating build-
ings, immersed in water, and collecting the water as it condenses.
Approximate results may be obtained by measuring the water
admitted, but it is then essential that the water level shall be the
same at the beginning and end of the measurement, a condition
not easily attained. The amount of water admitted may be
measured by a water meter, by counting the number of strokes of
the force pump, or by connecting a strong, iron vessel with the
boiler, by two pipes which may be closed by valves. A third pipe
and valve serves to admit the water. The latter valve is then
closed, and the other two opened when the steam displaces the
water, and lets it run into the boiler.
The day before the experiment is to be performed the boiler
should be filled until the water stands exactly at a height marked
on the glass gauge tube, and the amount measured. The fuel
should also be weighed and put in the furnace ready to be kin-
118 EFFICIENCY OF BOILERS.
died. Early the following morning the fire is lighted, the time
noted, and if a thermometer is in the boiler, its rise in tempera-
ture per minute observed. The gradual rise in the pressure of the
steam should also be recorded. When the desired pressure is
reached, the steam is allowed to escape, and this pressure main-
tained. A careful record is then kept of the amount of coal and
water used, and the time at which each is added. The level of
the water in the boiler should be kept nearly constant, though,
owing to the foaming, this cannot be done with any accu-
racy, when steam is generated very rapidly. The real commence-
ment of the experiment is when the steam begins to escape, and
at the end of the time everything should be brought as far as
possible into the same condition as at the beginning, that is, the
fire about equally intense, and the water level and steam pressui'e
the same. Then draw the fire, measure the amount of steam
generated, and the lowering of temperature as the water cools.
If the water entering the boiler is measured it is better on draw-
ing the fire to shut off steam, if this can be done without unduly
increasing the pressure, and measuring the amount of water which
must be added, or withdrawn, to bring the level to the same
height as at first.
The observations made before the steam was allowed to escape
from the boiler, serve to show how much time is required to fire
up, and the amount of fuel used. The amount of fuel wasted in
heating the furnace, boiler and chimney, and escaping up the lat-
ter, is then easily calculated, as follows. Let W be the weight of
coal burnt, and h its heat of combustion, then Wh will be the total
amount of heat generated, if the combustion is complete. Again,
let w be the weight of water in the boiler, and t the difference in
temperature of the water when admitted to the boiler and that
due to the pressure at which the steam is blown off. Then wt is the
amount of heat employed usefully in heating the water, and the
remainder, or Wh wt, the amount lost. The most important
observations, however, are those taken while the steam is passing
off, and hence often these only are taken, beginning and ending
the trial with a good fire of equal brightness at each time. The
weight of water evaporated during the whole trial divided by the
amount of coal burnt, gives directly the evaporation per pound of
COVERING STEAM PIPES. I. 119
coal. It is very instructive to construct curves showing the rela-
tion of each two of the three quantities, time, weight of coal,
and weight of water. All should be approximately straight lines,
and the inclination of that showing the relation of the coal to the
water, gives the weight of water to the pound of coal. The theo-
retical amount, calling W the weight of the coal burnt,= TP"'A,
and the amount usefully expended equals w r (t -f- i), calling w'
the amount of water evaporated and L its latent heat at the pres-
sure of the steam. If T is the temperature of the steam,
L = 606. +.3 Tfrom which L is readily determined. The ratio
Wh
of the heat received to that expended or ,, . ^ \ equals the effi-
ciency of the boiler. For good coal, h will equal about 8000, or
the same as pure carbon, the presence of foi'eign matters being
compensated by the small amount of hydrogen, whose calorific
power is much greater. Accordingly the maximum amount of
water at 20 which could be evaporated, would be VW = 11
pounds, while in actual practice, 5 to 7 pounds, are very high
results.
One of the principal difficulties to be apprehended in this exper-
iment is that some of the water will escape in the liquid form,
being carried over mechanically by the stream. This of course
greatly increases the apparent evaporation, while in reality it is a
serious defect in a boiler, throwing much water into the engine.
On this account a boiler which appears to give most excellent
results by this test, may be in fact, only one which foams very
badly. Great care should therefore be taken at intervals during
the test to let a little steam escape, and see that it is dry.
149. COVERING STEAM PIPES. I.
Apparatus. A number of 1" steam pipes OD, C'l?, Fig. 99,
about 8 or 10 ft. long, closed below by small stopcocks D, D',
called pet-cocks, and above by steam valves, (7, C", are connected
with the boiler so that they shall be vertical. The best way is to
bring a pipe A horizontally from the boiler, and then vertically to
the required height B \ on the end of this, put a T and hang the
pipes from the branches. Two pipes only need be used at a time,
but it is in some respects better to use four. All should be
arranged symmetrically from the central pipe which should be
well covered to prevent loss by radiation. The vertical pipes
120 COVERING STEAM PIPES. I.
are precisely alike, but are covered in various ways, one with plaster
or cement, a second with felt, a third with felt covered with canvass
and painted, and the fourth left in its ordinary condition. E, E,
are two similar graduated vessels to collect the condensed water.
Experiment. When steam is conveyed through a long un-
covered steam pipe, the loss of heat by radiation and condensation
of the water is far greater then is ordinarily supposed. A great
saving may often be effected by covering the pipe with felt or
other material, and the object of the following experiment is
to determine the comparative efficiency of different coverings.
The fire during the experiment should be kept as nearly as pos-
sible the same so that the pressure may be unchanged, and the
steam in the boiler should be very dry. Every
tn i n g being in readiness, open the pet -cock D
slightly, to let the water escape as it condenses,
and at the beginning of a minute open (J wide.
The steam rushing into the cold pipe will rapidly
condense so that a considerable amount of water
will be forced into the graduated vessel. Open the
pet-cock so as to allow the water to escape freely,
but not so wide as to let out much steam. Read
1 the volume of water collected at the end of every
jf[ s jfp' minute, and construct a curve with abscissas equal
. gg to the times, and ordinates to the volume of water
condensed. Repeat the experiment with the other
pipes closing the valve of each when its test is complete. A series
of curves is thus obtained, and a comparision shows the relative
efficiency of the various coverings. These curves first rise rapidly
until the pipes are well heated, and then become nearly straight
lines, their inclination showing the relative efficiency.
From them it will be noticed that while the loss from an un-
covered pipe is the greatest, that it takes longer to heat up a
covered pipe, so that sometimes when the steam is required very
quickly, or for a very short time, the uncovered pipe may be the
most effective. To determine the actual condensation per foot of
length, a straight line must be drawn nearly coinciding with the
curve, and the increase of volume of the water per hour, noted.
Dividing this by the length of the pipe in feet, gives the rate of
TESTING GAUGES. 121
condensation. From the latent heat, it is easy to reduce to actual
heat units. The experiment may be varied, not only by using
different coverings, but by varying the pressure of the steam, or
the temperature of the surrounding air.
If the pressure of the steam is liable to vary, a valve should be
inserted in A and a steam gauge connected with JB. The reading
of the gauge is then kept constant by opening or closing the
valve.
150. COVERING STEAM PIPES. II.
Apparatus. A number of pieces of steam pipe of the same
diameter and length, closed at one end by caps, and at the other
with corks, through which thermometers pass. The pipes are
covered, as in the last Experiment, with various substances to be
tested, and are all placed side by side on the table but far enough
apart not to heat each other.
Experiment. Fill each tube with boiling water, insert the cork
and note the temperature every minute, as in Vol. I, Experiment
5. If four thermometers are to be observed, read one at the
beginning of each minute, a second, quarter of a minute later, the
third at the half minute, and the fourth at the three quarters, so
that they shall be read in turn, each one at intervals of precisely
one minute. Next, construct curves with ordinates equal to the
logarithms of the excess of temperature above the surrounding
air, and abscissas to the time. The relative inclination of the
various lines gives the comparative rate of cooling.
151. TESTING GAUGES.
Apparatus. The apparatus described in Vol. I, Experiment 55,
and represented in Fig. 44, is well adapted to this experiment. If
an open mercury gauge is not available, a T may be screwed on
to the outlet of a small force pump, the gauge to be tested at-
tached to one branch, and a standard gauge to the other. The
best form of gauge for a standard, next to an open mercury column,
is a graduated glass tube closed at one end and containing air, the
lower part of the tube being filled with mercury. After calibrat-
ing the tube the graduation may be reduced to millimetres of
mercury by Mariotte's law. Any good gauge may be employed as
a standard, if its errors are first determined by comparison with
one known to be correct. A still simpler method of comparing
two gauges is to connect both with the same steam-pipe, and com-
pare the readings under various pressures.
122 PRESSURE AND TEMPERATURE OF STEAM.
Experiment. By working the pump, any desired pressure may
be applied to the gauges, and they may thus be compared directly.
The readings with the mercury gauge may be reduced to pounds
to the inch, by the rule that 51.7 mms. of mercury produce a
pressure of one' pound per inch, hence, the readings in millimetres
must be divided by this number to give the pressure in pounds.
To obtain the total pressure, the height of the barometer should
be added, but it is generally sufficiently exact to add 15 Ibs.
Care must be taken that the joints are tight, and that the pres-
sures when high, remain constant long enough to read the gauges
accurately. Metallic gauges often give erroneous readings when
exposed to sudden changes of pressure owing to their imperfect
elasticity, and a similar effect is observed with air-gauges, owing
to the change in temperature due to sudden condensation or rare-
faction. Time should therefore be allowed for the readings to
become constant.
Take a series of simultaneous readings, of both gauges, and
construct a curve with abscissas equal to the true reading and
ordinates to their difference, or the error. This curve may be
used directly to correct all readings taken with this gauge, and as
the error is likely to alter from time to time it is well occasionally
to repeat this experiment.
152. PRESSURE AND TEMPERATURE OF STEAM.
Apparatus. Besides the furnace, boiler, and pressure gauge the
only other apparatus needed is a thermometer which can be
placed inside the boiler. The best way to insert a thermometer in
the boiler, is to bore a hole in the side and cut a thread in it, then
screw in a tube from the inside, and close the inner end with a
cap. The thermometer is then placed in this tube, and soon attains
the interior temperature without being subjected to the pressure of
the steam. To ensure good contact, the tube should be filled witk
mercury or oil. Other methods of determining the temperature
may also be employed, as an air thermometer, a thermo-electric
pyrometer, or a Siemens' electric resistance thermometer.
Experiment. Start the fire, and as steam is formed, note the
corresponding temperatures and pressures. Construct a curve
with these quantities as coordinates, and compare it with the
INDICATOR DIAGRAMS.
123
results found by Regnault, and given in the table of the pressure
of steam at various temperatures.
153. INDICATOR DIAGRAMS.
Apparatus. The steam engine described above, and a steam
indicator.
Experiment. The steam indicator consists of a small cylinder
whose piston is held down by a spring like that of a spring bal-
ance, so that the height to which it rises at any instant, is propor-
tional to the pressure of the enclosed gas or steam. A hole is
bored in the cylinder head, and the indicator attached by a pipe
with a valve, so that when the valve is opened, the height to
which the piston rises, denotes the pressure at the instant, in the
cylinder. To record this pressure, a pencil, or metallic point, is
attached to the piston and moves over a cylinder on which is
stretched a piece of paper, so prepared that the passage of the
point will make a black mark. The cylinder is connected with
the piston of the engine, by a string and lever, so that it shall turn
by an amount proportional to the distance traversed by the piston.
A spring keeps the string tight and turns the cylinder back when
the piston returns. Evidently as the piston moves, the pencil
will describe a curve whose abscissas show the position of the
piston, and ordinates the pressure throughout the stroke. To
draw the curve, or indicator diagram, attach the paper to the cylin-
der, and open the indicator valve without connecting the string
with the piston. The pencil will then simply rise and fall during
each stroke, drawing on the paper the axis of Y. Now close the
valve and attach the string to the piston. The cylinder will then
turn forwards and backwards, and the pencil will describe the
axis of X. Now after seeing that the engine is running as uni-
foi'mly as possible, open the valve, and the pencil will at once
describe a diagram, and repeat it again and again as long as the
engine continues to work uniformly. After drawing the curve
once, renew the paper and repeat ; after a few trials a good curve
will be obtained. Record the time, pressure of steam in the
boiler, and number of revolutions per minute. To reduce the
result we must also have the interior diameter of the cylinder and
the length of stroke.
124 INDICATOR DIAGRAMS.
The indicator is a most important instrument in studying the
steam engine, as almost all the defects or peculiarities of the lat-
ter are rendered visible by it. On this account it is necessary to
study the form of its diagrams a little more in detail. At the
beginning of the stroke the steam enters and the pressure rises
almost immediately to that in the boiler, forming a line nearly
vertical ; it then becomes horizontal till the end of the stroke,
when it quickly descends to the line of atmospheric pressure and
remains there during the return stroke. If there is a cut-off the
pressure begins to descend at the point of cutting off, at first
rapidly, and then more slowly, forming, by Marietta's law, a curve
nearly coinciding with a hyperbola. If a condenser is used, the
line on the return stroke descends below the atmospheric line
approaching the true zero of pressure.
In practice these forms are never perfectly attained, and all the
corners of the diagram are rounded, instead of angular. Often,
especially at high speeds, the pressures seem to alternately in-
crease and diminish, an effect really due to the vibrations of the
spring. The area, however, is sensibly unchanged, and may be
found by drawing a line through the centre of the vibrations.
The work done by the steam during any short portion of its
stroke equals its length multiplied by the total pressure, or pres-
sure per square inch multiplied by the area of the piston. Hence,
it may be measured by the area included between the curve and
the axis of .3^ or line of no pressure. Since the pressure on the
back stroke is prejudical, the area between the lower part of the
curve, and the axis must be subtracted. Therefore the area en-
closed within the complete curve is a measure of the total work
done. To obtain this in foot-pounds, the area of the diagram
must be divided by the area of a rectangle whose height is one
pound, and whose length is one foot, on the scale to which the
diagram is drawn. Multiplying this quotient by the area of
the piston in inches, gives the total work done by the piston in
one stroke. To reduce this to horse-power, multiply by the num-
ber of single strokes per miuute, and divide by 33,000. To ex-
press it mathematically, let r be the radius of the cylinder, n the
number of double strokes, which are more easily counted than
single strokes, A the area of the diagram in inches, d the distance
INDICATOR DIAGRAMS. 125
on the diagram representing 1 pound, d' that representing a mo-
tion of 1 inch of the piston. Then the work of each stroke in
foot-pounds, will equal i^d'd 1 anc * tne norse -P ower
A 2n7rr 2 2* r>_
33000 12 X 33000 X dd' X nA "
In which, with the same engine and indicator, nA is the only
variable.
Any of the methods mentioned in Vol. I, p. 22, may be em-
ployed to determine the area of an indicator diagram, the most
common being to draw equidistant vertical lines and take the sum
of the trapezoids thus formed. This equals the product of their
common distance apart, multiplied by the mean of the first and
last, plus the sum of all the others. A much more accurate way
is to divide the whole length into an even number of equal parts.
Then calling 1? a^ a s . . . a n the various ordinates, and b their mu-
tual distance apart, the area by Simpson's rule will be
A = b (a, + 4a 2 + 2a, + 4a 4 + 2a 5 + ---- aj.
Many of the defects of an engine are shown by an indicator
diagram. Thus if the supply pipe is too small, or the steam wire-
drawn, as it is called, the curve will not attain its full height
until the piston has moved some distance. To show this, takte a
diagram when the engine is doing a large amount of work, with
the valve in the steam pipe opened to the full, and again, when
doing no work, the steam being cut off either by the governor or f
by partly closing the valve. If the exhaust is too small there is a
back pressure during the return stroke. If the exhaust is opened
too soon, the pressure falls before the end of the stroke ; if too
late, an increased back pressure is shown at the end of the return
stroke. To show this, take diagrams, changing the position of the
eccentric, when its best position is readily deduced. If the
engine has a variable cut-off, take a series of readings with it in
various positions, and compare in each case the amount of work
done with the steam employed. Although diagrams properly
taken show many peculiarities in an engine which cannot other-
wise be well detected, yet too much reliance must not be placed
on them, as it is possible to make an engine give diagrams of
almost any desired shape without thereby rendering it very effi-
cient.
126 FKICTION-BRAKE.
154. FKICTION-BKAKE.
Apparatus. The steam engine, or any motor, as a gas, hot-air
or electro-magnetic engine, a turbine, or water wheel, may be used
for this experiment. On the main shaft, the brake represented in
Fig. 100 is attached. AB is a piece of wood which may be
screwed against the shaft by two bolts which pass through it and
CD. It is upheld at B by a spring balance E, and is prevented
from vibrating by a disk G which passes into a vessel of water.
A tube H allows a small stream of oil to flow over the axle to
prevent its becoming heated. To prevent B from rising when
the engine is started, weights F are applied to hold it down, and
two stops should be inserted to limit its motion.
Experiment. The friction-brake affords a means of measuring
directly the amount of work done by an engine or other motor.
Unscrew the bolts holding CD,
remove the weights F, and read
the spring-balance. The reading
is that due to the weight of the
beam AB, and 'must be sub-
tracted from all the following
readings. Suppose now we wish
to determine the greatest amount
of work which can be obtained
from the engine when running
100 at a given speed under a given
steam pressure. Start the en-
gine, screw CD against AB, and allow oil to flow from 6r on to
the axle, or it will be heated by the friction. If water is used
instead of oil the brake is liable to chatter, making such a jar-
ring as to endanger the machine. The direction of the motion,
if the brake is placed as in Fig. 100, must be that of the hands of
a watch, so that B will tend to rise and press against its upper
stop. The amount of this upward pressure may be regulated by
the bolts pressing CD against AB and will be proportional to the
friction around the axle. Continue to tighten the bolts until the
full power of the engine is expended in overcoming the friction,
which is shown by its beginning to labor and run more slowly,
although the governor allows the full supply of steam to pass.
Now add weights to F until the beam is held balanced between
TRANSMISSION DYNANOMETER. 127
the two stops. If no spring balance is used it will be impossible
to attain this condition perfectly, as, owing to continual variations
in the friction, the beam will sometimes rise and sometimes fall
with the same weight ; while if we depend wholly on a spring-
balance, instead of on the weights, it will begin to vibrate, and the
hand will not come to rest. It is best therefore to depend mainly
on the weights, adding the spring to enable us to judge better of
the mean value of the friction. The reading of the balance is of
course always subtracted from the weight to obtain the ' upward
tendency of JB. The vibrations of the beam are materially
checked by the disk Gr which can move but slowly, owing to the
liquid resistance. A number of readings should now be taken
of the balance and weights, and the speed of the shaft observed,
as in Experiment 158, loosening the bolts and again tighten-
ing them after each observation. To determine the work in foot-
pounds let n be the number of revolutions of the shaft per min-
ute, P the change in the force, acting on the end of the beam JB,
that is the first reading or downward pull of the beam added to the
force required to hold it down during the experiment. Call d the
perpendicular distance, in feet, from JS to the centre of the shaft,
and H the required horse-power. Then the work expended in
friction, per minute, is evidently the same that would be required
to pull JB around n times with a force P, or exert a force P
through a distance 2;m. This amount of work equals 2?mP foot-
pounds and since 33,000 foot-pounds equal one horse-power, we
2~ n f>
must have 11= qo nnrp r proportional to n and to P. If the
engine can be run at various speeds, measure the amount of work
it will do at these speeds, taking care that the full pressure of
steam is attained in the cylinder, and that it is not reduced by the
governor or by a valve. It must be remembered, however, that a
large engine cannot be run above a moderate speed without
danger.
155. TRANSMISSION DYNAMOMETER.
Apparatus. Any form of transmission dynamometer may be
employed, but that represented in Fig. 101 is cheap and conven-
ient when the power to be transmitted is not very great. The
arrangement is similar to that devised by Huyghens for winding
128 TRANSMISSION DYNANOMETER.
astronomical clocks without stopping them. A is a pulley driven
by the engine, or other source of power, B a second similar pul-
ley to drive a lathe, planer, or other machine to be tested. An
endless belt passes over both, and also over the two pulleys C
and D. G is held down by a weight E which measures the force
tending to pull it up, and a weight F is attached to D to keep
the belt stretched and prevent its slipping on A. or B. A better
arrangement is to use a chain like that used with large clocks, and
for A and J5, wheels with projections to fit the chain instead of
pulleys. All slip is thus avoided. Another plan is to use bevel
wheels instead of A and B, and connect them by an axle also
carrying two bevel gears. The latter turn in opposite directions,
and tend to turn their axle, end for end, with a force- whose mo-
ment equals that of the transmitted force. This may then be
easily measured by a lever-arm with weights holding the axle at
rest. In a third form of dynamometer, the driving and driven
pulleys are on the same shall, one attached to it, the other free to
turn ; they are connected by some form of spring, and its amount
of deflection serves to measure the moment of the transmitted
power.
Experiment. When power is furnished to run several machines,
it is often desirable to know how much is required for, or con-
sumed by, each. A transmission dynamometer
is used for this purpose, and in its simplest form
merely shows how much the driving axle is
twisted. Other dynamometers do more than
this, and record the product of the twisting
force by the distance traversed, and thus give
the work done directly. - To measure the
amount of work required by any machine,
connect it by a belt with a pulley to the right
Fig 101 ^ -^' an< ^ ^e en g me with a similar pulley to
the left of A. The connection must be such
that C shall tend to rise and D to descend. Vary the weight E,
until it is just sufficient to balance F, or until its moment equals
that of F, plus the moment of the force transmitted by the shaft.
Then calling P the difference of E and F, and r the radius of
A or B, the moment of torsion will equal Pr, and if the shaft
makes n turns per minute, the work transmitted will equal xrnP,
which represents the amount of work required to run the machine
at the given speed. This may be reduced to horse-powers by di-
SPEED OF PISTON ROD. 129
viding by 33,000. Now make the machine do work, and F will
at once rise, and must be increased to balance the increased mo-
ment. The increased work represents that done by the machine.
Determine in this way the work done by a lathe when a shaving
is being cut, of a planer when at work, and of a circular saw
when cutting a board. We see also by these measurements how
much of the power is lost by friction.
It is sometimes more convenient to combine the preceding
Experiment with this, and let the friction brake absorb the power
transmitted by the dynamometer described above. One instru-
ment may then be tested by the other, and the two measures of
the power compared. By varying the tightness of the screws
various readings of both may be obtained without altering the
engine or other motor driving them.
156. SPEED OF PISTON ROD.
Apparatus. A table is placed in line with the piston of the
steam engine, and on it is a sheet of paper over which a small
carriage may be drawn by a string attached to the piston. On
the carriage is a small electro-magnet to whose armature a pencil
is fastened, which makes a dot whenever the circuit is closed. A
galvanic battery is connected with the magnet and a tuning fork
inserted in the circuit so as to make and break the circuit 100
times a second. Instead, a tuning fork and style may be drawn
over a long strip of smoked glass or paper precisely as in Vol. I,
Experiment 64. A second string is attached to the carriage and
passing over a pulley on the edge of the table, carries a heavy
weight at the other end. By the motion of the piston, therefore,
the carriage is drawn over the table, and is carried back by the
weight.
Experiment. See that the pencil is so adjusted as to make
dots when the circuit is closed through the magnet, and, after con-
necting the string with the piston, that the carriage moves
smoothly over the table. When the piston is nearly at the end
of its stroke, close the circuit, and a series of dots will be formed
on the paper near together at the ends, and far apart in the centre.
Break the circuit at the end of the stroke, move the paper a short
distance sideways, and repeat. Measure the distance of each dot
from the end one, and write the results in a column. Write the
Qrst differences in a second column, and the mean of each two
130 SPEED OF SHAFTING.
consecutive numbers in the third. Construct a curve with abscis-
sas equal to column three, and ordinates to column two enlarged.
The result shows the velocity at any point of the stroke. A more
accurate method theoretically, is given in the next Experiment,
but that given above is sufficiently exact unless the speed of the
piston rod is veiy great so that the number of dots is small. This
experiment has great value also in a steam pump or water-pres-
sure engine, to see if the delivery is uniform.
157. SPEED OF FLY-WHEELS.
Apparatus. A spur-wheel with 36 teeth is placed on the same
shaft as the fly-wheel, and a metal bar allowed to press against it.
A chronograph and galvanic battery are the only other instru-
ments needed for this experiment.
Experiment. Connect one pole of the battery with the metal
bar and the other with the spur-wheel, or with the engine, inter-
posing the magnet of the chronograph in the circuit. As now the
engine turns the fly-wheel, the circuit will be made and broken 36
times in every revolution, or every 10. If the motion is uniform,
the marks on the chronograph should correspond to equal inter-
vals of time, and a curve constructed with these angles as ordi-
nates, and times as abscissas, should be a straight line. If not, the
inclination of the curve to the axis of ^"at any point, gives the
velocity at that point. To find this, draw a tangent at the point
and measure its inclination, or the change in ordinates, when the
abscissas alter by unity. Make this measurement for every 30
and construct a new curve with angles as abscissas, and velocities
as ordinates. It is very well to combine this experiment with the
last and see if they agree, as in Vol. I, Experiment 28.
158. SPEED OF SHAFTING.
Apparatus. A shaft-speeder, and two shafts connected by a
belt and revolving uniformly. To test the results the following
apparatus will be found extremely convenient. Three vertical gas-
pipes are connected together below, and to the centre one a glass
tube is attached. They are then filled half full of mercury, and
some colored water poured into the glass tube until it is nearly
full. If now the tubes are attached to a vertical shaft so that the
centre tube shall lie in the axis, and the shaft is caused to revolve,
SPEED OF SHAFTING. 131
the mercury will, by centrifugal force, be thrown into the outer
tubes, and the water-level will descend. A suitably graduated
scale is then placed near the revolving glass tube, when the posi-
tion of the water-level will mark the rate at which the tube is
turning. As the centrifugal force increases as the square of the
velocity, the divisions of the scale for high speeds will be much
larger than those for low speeds. To render them more nearly
uniform, and also to prevent the mercury from being thrown out
of the outer tubes, the latter should be bent in towards the centre.
To measure the speed of a horizontal shaft the tubes should be
mounted so that they are free to turn, and connected with the
shaft by a flexible spring like that of a dental lathe, by a pulley
and belt, or better still, by bevel-gears.
Experiment. A shaft-speeder consists of a steel rod with a
sharp three-sided point, free to turn, and whose revolutions are
marked by one or more indices like those of a gas-meter or sirene.
It will be noticed that there is a depression in the end of every
shaft, called a dimple, by which it is held while made. To meas-
ure its speed, the point of the shaft-speeder is inserted in this dim-
ple for one minute, and, being pressed against it, turns, owing to
the friction. The number of revolutions, a$ given by the index,
gives the speed of the shaft. As it is a little difficult to bring the
point in place exactly at the beginning of a minute, it is more
accurate to hold it against the shaft, and note the reading exactly
at the beginning and at the end of the minute ; or, at the end of
the time suddenly remove it, and read the position in which the
index has stopped. Greater accuracy is attained by prolonging
the time, if the shaft moves uniformly. Measure the speed of the
two connected shafts, and also the radii of the pullies over which
the belt connecting them passes; or more simply, measure the
circumference of each pulley by passing a steel tape around it.
If there was no slip of the belt, the ratio of the speeds of the shafts
would be the same as that of the radii or circumferences of the
pullies. The difference between the observed and computed speed
of the driven shaft will therefore measure the slip. These results
are easily tested by the liquid speeder. It is only necessary to
observe the height of the liquid when the scale gives the speed at
once. To make, or test, the graduation, a scale of equal parts
should be placed against the glass tube and the shaft run at vari-
ous speeds. The number of turns per minute is then carefully
132
STRENGTH OF MATERIALS.
measured in each case with the ordinary shaft-speeder, and the
corresponding level of the liquid observed. A curve is now con-
structed with ordinates equal to the scale readings, and abscissas
to the speed of the shaft. From this, the correct scale is easily
constructed by graphical interpolation.
159. STRENGTH OF MATERIALS.
Apparatus. In Fig. 102, AB is a large screw by which any
object to be compressed may be forced against the steel plate (J.
EG is a steel lever with two knife-edges resting against 1) , which
forms the bed-plate of the dynamometer, and to which the nut,
through which the screw passes, is fastened. Two other knife
edges also rest against (7, and take u"p the pressure from it. To E
is attached a stout wire, by which it is hung from the short end of
the steelyard FGH. To His fastened the spring balance^ capa-
ble of reading to 30 Ibs. by single ounces. Any similar form of
lever balance may be employed, but that here shown is simple and
inexpensive. If the proportions are such that one pound on I cor-
responds to ten on EF, and to one hundred on B C, forces up to
3000 Ibs. may be measured. J is a small reading microscope with
an eye-piece micrometer to measure changes in form of BC. Be-
sides the various objects to be tested which will be described
below, a stiff bar K, Fig. 103, with two knife edges on it, and a
curved piece of cast iron M are also needed.
JExperiment. The dynamometer here described may be ap-
plied to a great variety of purposes which will be described below
in order. First, to meas-
ure the compressibility of
any substance, prepare a
cylindrical bar of it with
flat ends, and placing it
between B and C hold it
by turning the screw.
Mark a point on the bar
and read its exact position
Fig. 102. with the microscope J, or
better use two micro-
scopes, and observe the change in distance of two points one
near each end of the bar, when compressed. Now remove the
spring balance and apply a weight of five pounds to H. It
STRENGTH OF MATERIALS. 133
will probably at once descend against its stops. Turn the screw
until H rises and remains balanced, when the pressure will equal
that due to the weight. Observe the distance apart of the points
as in Vol. I, Experiment 20. Take in this way a series of read-
ings of the distances corresponding to various pressures. Deter-
mine from them the most probable value of the compressibility
by the method given in Vol. I, p. 4, assuming that I = 1 Q -J- ap, in
which / is tne length when no pressure is applied, I the length
under the pressure jp, and a the coefficient of compressibility. The
various observed values of I and p must be substituted in this
equation and from them the best values of / and a deduced. A
simple, but less accurate method, is to construct a curve with ordi-
nates equal to the pressures, and abscissas to the lengths, which
should give a nearly straight line ; a is then equal to the tangent
of the angle this line makes with the axis of IK. We must next
determine the modulus of compression, C. For moderate pres-
sures, the diminution in length of a bar is proportional to the pres-
sure. Hence if this law held at all pressures, a certain force per
square unit would reduce its length to zero, although there is no
substance for which this is actually the case, since crushing takes
place or the law changes, long before this limit it reached. Call-
ing s the cross-section of the bar, P the load per square inch, 1
its length under no pressure, and I its length under pressure Ps,
we must have I 1 asP in which, if we make I = 0, P will
equal <7, or C = -
With a large pressure it will be found that the two points in
the bar gradually approach each other, and observing their dis-
tance at various times we may construct a curve which will repre-
sent the permanent set. By using bars of various lengths and
cross-sections, we may prove that, for a given pressure, the change
in length is with cylindrical or prismatic bars proportional to the
length and cross-section, whatever may be their shape. In all the
above work it is essential that the section shall be sufficient to
prevent the bar from bending under the pressures employed.
To determine the laws of crushing, replace the spring-balance,
and observe its index, as the pressure is gradually applied by the
screw. When the pressure is considerable, the reading of the bal-
134 STRENGTH OF MATERIALS.
ance will begin to diminish as soon as the screw stops, owing to
the permanent set, until finally a point is reached beyond which
the index will not move, and the body breaks. This maximum
position of the index marks the breaking weight, and is simply
proportional to the cross - section of the body. Different sub-
stances break very differently, some are brittle, give way suddenly,
and the index going down at once to zero, the beam falls against
its stop. With a sudden jar, their fracture often takes place at
much lower pressures. Other bodies are plastic, yield slowly, and
often have no definite breaking points, but will support a much
larger weight for a short time than if it has to be sustained very
long.
If the length of the body is great compared with its diameter
other laws hold. The strength of a column built in at both ends,
built in at one end and simply supported so that it is free to turn
at the other, and simply supported at both ends, are readily com-
pared by similar rods flat at both ends, rounded at one end, and
rounded at both ends. The laws of the length, of the diameter,
and the superiority, for a given weight, of hollow columns, are also
readily found.
The laws of transverse elasticity may be tested on a much
larger scale than in Vol. I, Experiment 35, by the help of 1C, Fig.
103. A stout bar is laid against C, and two
knife - edges slide over it, while a third knife-
& edge rests against B. The bar to be tested is
placed between the three knife-edges and bent
by the screw. The pressure is measured by the
steelyard as before, and the amount of pressure
by the microscope J. Metal bars of consider-
able size may thus be used and the laws for the
Fig. 103. length, thickness and width, tested. Castings
may also be made of various forms of girders
at a cost little above that of the patterns, and the metal used over
and over again. The shearing strength of various kinds of glue, ce-
ment, mortar or other similar substances, is readily found by join-
ing three blocks of wood, metal or stone as in L, inserting them
between B and (7, and measuring the force required to make them
elide over each other. Still another application of this dynamom-
FRICTION OF BELTS. 135
eter is to testing the strength of various forms of teeth for wheels.
Castings are made of the form shown in M and the curved piece
being placed against j&, and the casting against (7, the screw is
turned until the teeth are broken.
160. FRICTION OF BELTS.
Apparatus. A shaft on which are several pulleys of various
sizes, either of wood or metal, and which may be turned very
slowly by power or by hand. Several belts of various widths and
material are also needed, some Krlb. weights, a spring balance read-
ing to 30 Ibs. by single ounces, and a clinometer or level with a
graduated circle attached for measuring slopes.
Experiment. Pass one of the belts over a pulley, attach a 10 Ib.
weight to one end, and the hook of the spring balance to the
other. Fasten the other end of the balance to the floor so that it
shall hang vertically. If there was no friction of the bearings of
the shaft, the reading of the balance should now be 10 Ibs. but it
may in any actual case be greater or less than this amount by any
quantity less than the friction. Now turn the wheel so that the
belt shall be carried from the balance. The reading will in-
crease until it equals 10 Ibs. plus the friction of repose; the belt
will then begin to slip, and as the wheel continues to turn, the
reading will remain equal to 10 Ibs. plus the friction of motion.
See whether the friction is dependent upon the velocity.
Next, turning the wheel backwards the reading equals 10 Ibs.
minus the friction. Care must be taken that the reading of the
balance is zero when no weight is applied, or if not, a correction
is necessary. Repeat the experiment, adding, a 10 Ib. weight to
each side so that the strain shall be 20 Ibs. on one side, and 10 Ibs.
plus the reading of the balance on the other. Do the same with
heavier weights, also with other pullies and belts. In the case of
leather belts try both sides and see which gives the greatest fric-
tion. The friction when the belt touches a greater or less
portion of the circumference of the pulley is found in a similar
manner, by fastening the balance in such a position that the two
parts of the belt shall be inclined at the required angle. Adjust
this angle by the clinometer, which consists of a spirit-level free to
turn in a graduated circle, so that it may be inclined at any angle
136 FRICTION OF PULLIES.
to one side of the instrument which is planed smooth. Make this
angle 60, and set the balance in such a position that, when the
clinometer is laid on the belt, the bubble of the level will be in
the middle. The other part of the belt being vertical, the two
sides will be inclined at an angle of 30, or 150 of the pulley will
be covered. Make a series of measurements with angles of 30,
60, 90, 120, 150 and 180. For larger weights a stronger bal-
ance must be employed, or a cord passing over a pulley attached
to the end of the belt and the weights hung to it. This is, how-
ever, open to the objection that an error is introduced due to the
fiiction of the pulley. Care should be taken not to turn the shaft
too rapidly, or the belt will heat.
To compare the results with theory, let t be the tension of any
part of the belt, v the corresponding angular distance from the
point where the belt touches the pulley, and f the coefficient of
friction. Then the normal pressure dp of the belt on the minute
portion dv of the pulley will be the resultant of two equal forces
t, inclined at an angle of 180 dv, or dp = tdv. The increase of
tension dt equals dp multiplied by the coefficient of friction, or
fa =fdp =ftdv, and integrating, log t = Mfa. When the belt
covers 180, v \n and calling if and if' the tensions at the ends,
log if log if' = log y/ = i vfM.
161. FBICTION OF PULLIES.
Apparatus. Several pullies of various sizes and materials
placed on a shaft which replaces their pins, and which may be
turned in either direction. A set of weights, a spring balance,
a flexible cord and a clinometer.
Experiment. This experiment is nearly the same as the last,
the cord is used like the belt, and the difference in the tension of
its two ends is measured when the axle is turned. The calcula-
tion is, however, quite different, as the friction depends only on
the resultant of the two tensions. The magnitude of this equals
the sum of the tensions if the cords are parallel, otherwise, it is
found by the parellelogram of forces. If the pulley is large its
weight should be included in finding this resultant. The ratio of
the difference in tension to the resultant pressure may be called
the coefficient of friction of the pulley, and should be constant.
METEOROLOGY.
The science of Meteorology treats of the heat, pressure, mois-
ture and other properties of the atmosphere with which our globe
is surrounded. To determine its laws, observations have been
made at various points of the earth at regular intervals for long
periods of time. The graphical method is largely used in the dis-
cussion of the results. This is most readily done by drawing a
curve with abscissas proportional to the times, and ordinates to
the temperature or other quantity measured. Sometimes this
curve is drawn automatically and the instrument is then called
self-registering. The general method in this case is to move the
paper uniformly by clock-work, and give the pen or pencil a mo-
tion at right angles to it by the thermometer or other instrument
to be recorded, taking care that the motion of the pencil shall be
proportional to the change in reading. This is easily accom-
plished with a metallic thermometer or aneroid barometer by
allowing them to move the pen or pencil directly. In some cases,
however, this cannot be done, and it is always objectionable on
account of the friction. It is therefore more common to employ
an electrical attachment for which the mercury of the thermome-
ters and barometers is especially convenient in effecting electrical
contact. Sometimes, as with magnetic observations, even this
method is not available on account of the minuteness of the forces
to be observed. In this case a spot of light from a lamp is re-
flected by a mirror attached to the instrument on to the paper
which is rendered sensitive photographically. The slightest mo-
tion is thus made visible and recorded permanently without in the
least interfering with the action of the apparatus. Self-registering
records are much more valuable than those obtained by single
observations since they are much more complete, and give all
the variations of short duration which occur in all meteorological
(137)
138 METEOROLOGY.
phenomena and quite escape a common observer. They effect also
a great saving in time both in taking the observations and in
constructing the curves. To give the results in numbers they
sometimes also print the results (Dudley Observat., Rep. II, p. vii).
The most complete self-registering instrument is the Meteoro-
graph of Secchi, exhibited at the Paris Exposition of 1867 (Bar-
nard's Report, p. 571) in which various meteorological phenomena
are recorded side by side on the same sheet.
To eliminate the effects of the small variations, the average or
mean of a long series of observations is taken. In the same way
to determine the changes due to any cause we group together
those observations where this cause should have its greatest effect,
and in a second group those where the effect is least, and so on
for each intermediate value. For instance, suppose we have a
series of observations of the temperature of a given place for
every hour for ten years. The mean of all these, or their sum
divided by their number gives the mean temperature. Now sup-
pose we wish to know if the height of the barometer affected the
thermometer. We should group together and take the mean of
all these observations of the thermometer taken when the barom-
eter stood between 700 and 710, form a second group of all those
between 710 and 720, a third between 730 and 740, and so on, and
then see if these means seemed to follow any definite law. This
would be done most easily by drawing a curve with abscissas
equal to the pressures 705, 715, etc., and ordinates to the ob-
served means. If the variations from a horizontal straight line did
not much exceed the accidental errors, we should conclude that
there was no relation, or at least that the effect was too small to be
shown without a still greater number of observations. Generally
the cause is periodic, as the motion of the sun or moon. Thus to
find the effect of the rotation of the earth we group all the ob-
servations at the same hour of the day and compare their mean
with those taken at other hours. The effect of the motion of the
earth around the sun is similarly shown by comparing the mean
temperature for each month.
The true mean for any given time is of course obtained more
accurately from the curve of a self-registering instrument. In this
case the area of the space included between it and the horizontal
TEMPERATURE OF THE AIR. 139
axis must be determined and divided by its length, that is, by the
time ; the result is the required mean.
Another most important application of the Graphical Method is
to represent the conditions at different places. The method of
contours, Vol. I, pp. 14 and 34, is here used, all the points where
the quantity observed is the same being connected with a curved
line like a contour line. This plan is largely used by the Signal
Service Office in predicting the weather and marking the progress
of storms. These lines have different names according to the
phenomena they represent.
Isothermal lines are those of equal temperature.
Isochimenal lines are those of equal winter temperature.
Isotheral lines are those of equal summer temperature.
Isobaric lines are those of equal barometric pressure.
Isogonal lines are those of equal magnetic declination.
Isoclinal lines are those of equal magnetic dip or inclination.
Isodynamic lines are those of equal magnetic intensity.
162. TEMPERATURE OF THE AIR.
Apparatus. A good thermometer, the various maximum and
minimum thermometers described below, and Joule's arrangement
for determining the temperature of the air. This consists of two
thin copper tubes, one inside of the other, so connected that the
intermediate space may be filled wi'th water, whose temperature is
measured by a good thermometer. In the interior a spiral wire
with a mirror attached, is hung bv a filament of silk to show if the
air currents make the wire twist. The tube may be closed by a
cap placed over the lower end. The thermometers should be pro-
tected from radiation and be hung at least ten feet from the
ground, and a foot from the wall. The arrangement employed at
the Greenwich observatory consists of a stand which somewhat
resembles a high writing desk, and consists of an inclined board
on a support, to the upper edge of which the thermometers are
hung. To prevent the board from becoming heated by the sun's
rays a second board is placed parallel to it, an intervening space
being left to allow the air to circulate and an inclined roof is at-
tached over the thermometers to protect them from rain. The
whole is free to turn and should always be placed with the first
board towards the sun.
^Experiment. The most prominent meteorological phenomenon,
and that most commonly measured, is the temperature of the air.
140 TEMPERATURE OF THE AIR.
This may be determined by a thermometer whose correctness is
tested and its errors determined as described in Experiment 122.
Asuming however, that the thermometer is exact, it is not an easy
matter to determine the true temperature of the air. Of course
the thermometer must be protected from the sun, and observed in
the shade, and care should be taken that it is not exposed to other
radiations, as that of a brick or white-washed wall on which the
sun is shining, or to light reflected from the water or ground.
Exposure to the sky when clear, is nearly as bad, though the effect
is the opposite, since the thermometer then radiates its heat into
space and its temperature, especially after sunset, is often lowered
several degrees. The effect is diminished by the black tin stand
which partially covers the bulb, but if this is unduly heated or
cooled by radiation the bulb is affected also. Holding the ther-
mometer in the hand or breathing on it also soon alter its tem-
perature.
To determine the temperature of the air by Joule's method, fill
the space between the copper tubes with water, and close their
lower end by the cap. The air currents are thus cut off and the
spiral wire inside will now come to rest so that there shall be no
torsion of the suspending fibre. Mark the position of the mirror
either by a scale and spot of light, or simply by the eye. Now
move the cap, and if the water is warmer then the surrounding
air, the tubes will act like a chimney and the ascending air current
will twist the spiral wire, and with it the mirror. If the water is
colder than the air the mirror will turn in the opposite direction.
Observe the effect with cold and warm water, then vary the tem-
perature of the latter until the mirror remains in the same posi-
tion, whether the cap is on, or off, taking care to stir the water
briskly so that its temperature shall be uniform. The reading of
the immersed thermometer will then give the true temperature of
the air.
We often wish to know, not only the actual temperature at any
given time, but the highest and lowest temperature attained dur-
ing the day or other interval. Maximum and minimum thermom-
eters are employed for this purpose. Rutherford's maximum
thermometer consists of a common mercury thermometer placed
horizontally, with a small index of steel or graphite in the tube
TEMPERATURE OF THE AIR. 141
above the mercury. If the temperature increases, the mercury
pushes the index in front of it, but as it cools leaves it behind,
since there is little adhesion between the mercury and index.
The latter, therefore, remains at the point where the temperature
was highest. To bring the index back to the mercury or to reset
the instrument it is only necessary to incline the thermometer and
tap it, or if the index is of iron, draw it back with the magnet.
Phillips' maximum thermometer differs from the above in replacing
the index by a small bubble of air which separates a part of the
mercury column from the remainder. When the mercury expands^
it pushes the column in front of it, but when it contracts the
elasticity of the air prevents the motion of the detached portion.
Rutherford's minimum thermometer is filled with alcohol, and
carries an index of glass which remains in the liquid, allowing the
latter to expand past it when the temperature rises, but by capil-
larity being drawn back when the surface touches it, owing to the
contraction of the liquid. It is set by inclining the tube and
tapping it until the index slides down to the surface. Commonly
the maximum and minimum thermometers are placed on a board
side by side, their bulbs turned in opposite directions so that both
may be set by inclining the board the same way.
To avoid the trouble of a index, which sometimes sticks to the
mercury or catches and cannot be moved along the tube, Negretti
and Zambra make a maximum thermometer with the tube bent at
right angles near the bulb, and partially contracted at this point.
The tube is then inclined downwards and when the mercury ex-
pands it forces itself past the contracted part, while when the
temperature falls, separation takes place there. The reading is,
therefore, that of the highest temperature attained since the in-
strument has been set. The latter operation is performed as be-
fore by inclining the thermometer.
Sixe's maximum thermometer consists of a U-tube closed at
one end and terminating at the other in a large bulb filled with
alcohol. The U is half filled with mercury over which are two
steel indices with little hair springs which hold them in place
when left to themselves. As the temperature rises, the alco-
hol expands and pushes the mercury down on one side and up on
the other. The first index, therefore, being held by the spring, is
142 TEMPERATURE OF THE AIR.
left hanging in the tube, the alcohol passing it freely, while the
second index is pushed up by the mercury column until the maxi-
mum is reached. When the temperature is lower than it has
been since the instrument was set, the opposite effect is produced,
the first index being pushed up by the mercury, and the second
left hanging by its spring. The indices are drawn back to the
mercury by a magnet, and the position of their lower ends de-
notes the maximum and minimum temperatures attained.
One of the best forms of maximum thermometer is Walferdin's,
in which the upper end of the tube terminates in a fine point
enclosed in a small glass chamber. If now the temperature rises,
part of the mercury overflows into the chamber and remains there
when the temperature falls. The maximum temperature is de-
termined by immersing the thermometer in a vessel containing
water, and heating the latter until the mercury again reaches
the top of the tube, when the temperature of the water as shown
by a common thermometer equals the required maximum. Or,
the tube may be graduated from the point, and the maximum tem-
perature attained equals the reading of the thermometer plus its
temperature, Avhich is readily found by placing it with another
thermometer in a vessel of water. To set the instrument, warm
it until the tube is full and invert, when as it cools, the mercury
is drawn back into the bulb.
A minimum thermometer is made by slightly altering this and
inverting it, filling the bulb, which is now uppermost, partially
with alcohol and the lower part with mercury and alcohol. The
stem is filled partly with mercury and partly with alcohol by
warming and inverting it. As the temperature falls, the mercury
is drawn out of the tube, but as it rises is replaced by alcohol.
To compare the climate of different places, and for other pur-
poses, it is often desirable to compare their average or mean tem-
perature. If observations are made at short and equal intervals,
as every hour, it is seen that the temperature attains a maximum
at about 2 p. M., and a minimum shortly before sunrise. The
mean temperature of the day may then be found by taking the
sum of all the observations and dividing by their number. Such
observations, however, are exceedingly laborious, unless made with
a self-registering instrument, and other less accurate methods are
SOLAR RADIATION. 143
therefore generally preferred. The mean of the maximum and
minimum temperatures gives approximately the mean tempera-
ture, but the result is generally a little too high. Evidently twice
during the day the temperature must coincide with the mean, but
the hour will vary with different localities. It is generally about
8 or 9 in the morning and evening. The mean of two observa-
tions at intervals of twelve hours gives nearly the mean, the best
hours being 10 A. M. and 10 p. M. Still better results are attained
by three daily observations, at 7 A. M., 2 p. M., and 9 P. M., and add-
ing the sum of the first two to twice the last, and dividing by four.
To determine the mean temperature during any given time an
ingenious device has been proposed by Jurgensen. A watch is
made in which the balance wheel instead of being compensated,
has the two metals reversed, so that a slight increase of tempera-
ture makes it run very slowly, and a decrease makes it gain
rapidly. It is now kept first at a high, and then at a low tempera-
ture, and its rate being accurately determined in each case, gives
nearly the temperature necessary to produce any required rate.
Now deduce the mean rate during the given time, and from it we
obtain the mean temperature with great exactness, since it allows
for every change in temperature of the balance wheel even if last-
ing for but a few seconds.
Another method of determining the mean annual temperature
is from the temperature of deep wells or springs or from the tem-
perature of the ground at considerable depths.
Besides measuring the temperature of the air in the shade,
many observations have been made to determine the relation of
the temperature to the height, its variations at different depths at
sea and in the ground. It is found that at great depths the tem-
perature rises in the earth about 1 C. for every fifty to one hun-
dred feet, but at small depths the temperature is affected by the
diurnal and annual variation at the surface, being, however, behind
them in time, so that at a depth of about twenty-five feet the
changes are six months behind hand, or the temperature is greatest
in winter, and least in summer.
163. SOLAR RADIATION.
Apparatus. A solar radiation thermometer, a Pouillet's pyr-
heliometer, and a lens pyrheliometer, or a large burning-glass and
a thermometer with blackened bulb.
144 SOLAR RADIATION.
Experiment. The solar radiation thermometer consists of a
mercury maximum thermometer with a blackened bulb, contained
in a larger bulb from which the air has been completely exhausted.
To use it, expose it to the sun's rays, and record the maximum tem-
perature attained ; observe also the temperature of the air in the
shade. The most common method of determining the absolute
amount of heat received fi'om the sun is Pouillet's pyrheliometer.
This consists of a flat circular tin box, blackened on one side and
filled with water in which is immersed the bulb of a thermometer.
The instrument is placed on a universal joint so that it can be
turned in any direction. To make a measurement, the water be-
ing nearly at the temperature of the air is placed in the shade for
four minutes and exposed to the radiation of the sky ; during the
next minute remove it into the sunlight and adjust it so that its
face shall be perpendicular to the rays of the latter, but so covered
that it shall be protected from its heat. Call the change of tem-
perature during these five minutes, t. To adjust the position of the
instrument a circular disk is placed behind the box and parallel to
it, so that it is set in position by merely turning the instrument
until the shadow of the box shall exactly cover the tin disk.
Now expose the blackened surface of the box to the sun for five
minutes, call the change of temperature s, and again place it for five
minutes in the shade, and call the change of temperature if. Then
the true increase may be taken equal to s ^ (t -\- t'). If w is
the weight of water, w' the weight of the tin box containing it,
and s' its specific heat, w -f- w' s' will be its water-equivalent, and
if r is the radius of the circle exposed to the sun the number of
units of heat received from it per minute will be nearly equal to,
^ ^ r2 This forms a standard by which
any solar radiation thermometer may be graduated. The lens
pyrheliometer consists of a calorimeter in which the water is
heated by a large burning-glass. The change' in temperature is
here much greater, but a correction must be made for the heat
lost by the lens. By simply placing a thermometer with a black-
ened bulb a short distance within the focus of a large burning-
glass, the comparative heat of the sun, at different times, is read-
ily observed. The variations with its altitude, and during the
progress of an eclipse, are thus well studied.
ATMOSPHERIC PRESSURE. 145
164. ATMOSPHERIC PRESSURE.
Apparatus, Examples of the various barometers described
below, and a thermometer for determining the temperature of the
air. While most meteorological observations must be made in the
open air, that of atmospheric pressure is made equally well in-
doors, as the pressure is easily transmitted through the cracks in
the doors and windows.
Experiment. A standard barometer consists of a glass tube at
least a centimetre in diameter, filled with mercury from which the
air has been expelled by boiling, and the tube is then inverted over
a cistern containing mercury. The height is read as described in
Vol. I, Experiment 12, or the scale may be attached directly to
the steel point. The latter is then screwed down until it just
touches its reflection, and the height of the column read by a
vernier or cathetometer telescope. To determine from this read-
ing the true height of the barometer, corrections must be applied
for capillarity, for temperature of the mercury, and for latitude, as
described in Vol. I, Experiment 58. The formula there given may
also be employed to correct the elevation above the sea-level, since
having E and p we may determine p'. Generally, however, it will
be sufficiently exact, if the height is not very great, to subtract a
certain constant quantity from all the readings, and thus correct
for elevation and capillarity.
The principal objections to this instrument are, that it is not
portable, and that an error is likely to occur in making the point
coincide with the surface of the mercury. One method of rem-
edying this difficulty is to attach a plunger to the vernier, so that
raising the latter depresses the former, by an equal amount, into
the mercury of the cistern. The surface of the latter will always
remain at the same height when the vernier is set, if the plunger
has the same diameter as the tube.
Another form of barometer, known as the Kew standard ba-
rometer, has a cistern with a cross-section precisely 25 times that
of the tube. The scale on the latter is made f f of its true size,
hence the rise of the mercury in the cistern is corrected at once
by the scale. Each inch on the scale is divided into twenty parts
or to .05" and the vernier divides these into 25 or reads to .002".
10
146 ATMOSPHERIC PRESSURE.
To set the instrument, raise or lower the vernier by the milled
head on one side, until the top of the mercury seems just to touch
the lower edge of the vernier, when the eye is brought on a level
with it. The reading of the latter then gives the height.
Gay Lussac's siphon barometer consists of a bent glass tube of
which the larger end is closed and forms the barometer tube while
the shorter end is open and forms the cistern. Evidently as the
mercury falls in the long tube it will rise a nearly equal amount
in the short one, hence, the range of either end is only about one
half that of the common barometer. The scale is divided both ways
from the centre, and there is a vernier to read each mercury sur-
face; the height equals the sum of the two readings. This ba-
rometer may be carried by inclining it until the mercury reaches
the top and then inverting it. The tube being then full of mer-
cury there is little danger of injury, while if carried right side up
the mercury rises and falls and is very liable to break the tube.
One of the most common forms of barometer is Fortin's, in
which the cistern is closed below by a leather bottom, which may
be raised by a screw. The sides are of glass and an ivory point
dips down so that it may be made to touch the mercury by turn-
ing the screw. To take a reading, turn the screw until the point
touches its reflection, and read the verniers. It may be trans-
ported by turning the screw until the mercury is pushed up to the
top of the tube and then inverting the instrument. This makes
an excellent mountain barometer. When used for very great
heights only, the tube is sometimes made shorter, thus rendering
it more portable.
The aneroid barometer is constructed on a wholly different
plan from the above. A circular metallic box is closed above with
a cover of corrugated metal and exhausted of air. As the pres-
sure of the outer air varies, the cover rises or falls and its motion
is magnified by an index moving over a scale. The latter is
divided arbitrarily and the index is turned by a screw in the back
of the instrument until it agrees with the reading of a standard
barometer. Both are then subjected to a different pressure and the
length of the short arm of one of the levers altered until the reading
is. again the same. In this way it may be made to agree very nearly
with the standard, as long as the temperature is unchanged. If
WIND. 147
now the temperature rises, the elasticity of the metal diminishes,
and the cover sinks in, as if the pressure had increased. To rem-
edy this source of error a little air is admitted into the box which,
when heated, expands, and increasing the interior pressure tends
to counteract the effect of the diminished elasticity of the metal.
Evidently by varying the amount of air, which is easily meas-
ured by the pressure it produces, we can compensate almost
exactly for the changes in temperature. An aneroid is read
directly from the position of its index, and gives the pressure ap-
proximately without correction.. The best instruments are, how-
ever, liable to an error of some hundredths of an inch. They will
generally give different results when hung up and when laid
down, and also alter if tapped with the finger. In the latter case
the reading may be greater or less than the true reading by an
amount not exceeding the friction of motion, while if not tapped,
it may vary as much as the friction of repose.
165. WIND.
Apparatus. A weathercock to show the direction of the wind,
and various anemometers to measure its velocity. They should
be raised above surrounding objects, otherwise eddies will be
formed, and errors thus introduced.
Experiment. The direction of the wind is most easily shown
by an ordinary weathercock. The centre of gravity of the vane
should lie in its axis and the surface exposed to the wind be as
large at one end and as small on the other as possible. The friction
also must be reduced to a minimum. The direction of the wind
in the upper part of the atmosphere may sometimes be measured
by the motion of the clouds.- For this purpose lay a sheet of look-
ing-glass horizontally, and observe the reflection of a cloud in it.
Then lay a ruler on the glass and holding the head perfectly still,
turn the ruler until it coincides with the direction in which the
cloud appears to move. Its position may then be measured by a
compass, and gives, after correcting for the magnetic variation, the
direction of the wind.
In determining the velocity of the wind, much will depend on
the height of the anemometer above the ground or surrounding
objects. At the height of eight feet, the velocity is often double
148 WIND.
that within a foot of the ground. Most of the following anemom-
eters must be kept turned towards the wind, and this is most eas-
ily effected by attaching them to the weathercock. One of the
simplest anemometers is that of Lind, whick consists of a simple
U tube with one end bent down horizontally and turned towards
the wind. When half filled with water the liquid will be pressed
down on the side towards the wind, and the difference in level x
gives the velocity v of the wind by the formula v = 3.26 V-c 5 x
is here given in inches, and v in miles per hour. To reduce the
oscillations, the tube may be contracted at the lower part, and for
observations at sea, a valve is sometimes connected with the tube
so that when the liquid has attained its proper position, the valve
may be closed so that it will not return, and the reading then taken
at leisure. The maximum pressure is readily obtained by making
a small hole in the leeward arm of the tube at the water line. As
the pressure increases, the water is forced out and the level of the
remaining liquid shows the maximum pressure attained.
Bouguer's anemometer consists of a single plate held at right
angles to the direction of the wind, and the pressure measure 1
directly by a spring. The velocity is then given by the formula
v = 1.3 Vjt> in which v is the velocity in miles per hour, and p the
pressure in pounds per square foot. A modification of this instru-
ment is that of Taupenot, in which a board is allowed to swing out
at an angle, whose magnitude measures the pressure. Both these
instruments are especially open to error from the varying strength
of the wind, which is liable to set them vibrating.
One of the most common forms of anemometer is that of Rob-
inson, which consists of four sheet-metal hemispheres connected
together so that they can turn around a vertical axis. As the
pressure is always greater on the concave than on the convex side,
they will continue to revolve in the same direction, whatever is
the direction of the wind. The velocity of each hemisphere will
be one third of that of the wind, so that if placed at a distance
of 6.72" from the axis, 500 revolutions will equal one mile. A set
of wheels and indices serve to measure the total number of turns.
The total distance traversed by the wind is given by subtracting
the reading at the beginning from that at the end of the time, and
the average velocity by dividing this distance by the time. An-
MOISTURE. 149
other excellent anemometer is that described in Vol. I, Experi-
ment 60. All anemometers should be tested before relying too
implicitly on their readings, by carrying them on a calm day either
on a railroad car or in a wagon at various known velocities, or
attaching them to a long' arm free to revolve around a vertical
axis. A curve may then be constructed which will give the read-
ing in terms of the velocity.
The direction and velocity of the wind is so constantly chang-
ing that self-registering instruments are needed to give really satis-
factory results. A great variety of methods have been employed
and will be found described in detail in the proper works, but as
they are of special, rather than general interest, they need not be
enumerated here.
166. MOISTURE.
Apparatus. A hair-hygrometer, wet and dry bulb thermometers,
a hygrodeik, Daniell's hygrometer, Regnault's hygrometer, an as-
pirator, some drying tubes, a balance and weights.
Experiment. The amount of moisture in the air may be stated
in three different ways. First, the absolute amount rnay be given,
as so many grammes per cubic metre, or grains per cubic foot ;
secondly, by giving the pi'essure of the vapor in millimetres or
inches ; and thirdly, the amount may be compared with that re-
quired to produce saturation. Thus if the air contains half as
much moisture as is needed to saturate it, or produce condensation,
the moisture is said to be 50 per cent. Since cold air will hold less
moisture than warm, if the latter is cooled, a temperature, called
the dew-point, is soon reached at which the moisture is deposited
as dew.
The simplest instrument for measuring moisture is Saussure's
hair hygrometer. This consists of a hair fastened at one end and
carrying an index at the other. When exposed to moisture it
expands, and the index shows the change. Unfortunately, the
motion of the index is not proportional to the amount of moist-
ure, and what is worse, is not the same for any two hairs. Accord-
ingly, a table must be detennined for each instrument, or when-
ever the hair is changed. Even then, accurate results cannot be
150 MOISTURE.
obtained, since, if exposed to a perfectly dry atmosphere, the zero
point will slowly change. To obtain the best results the hair must
be steeped in ether or boiled in carbonate of soda, to remove all
traces of grease.
The most common method of measuring moisture is by means
of the wet and dry bulb thermometer. This method depends on
the principle that the dryer the atmosphere, the more rapid the
evaporation of water, and hence the colder the water becomes, from
the absorption of the heat required to vaporize it. The arrange-
ment employed consists of two similar thermometers placed side
by side, one being covered with a piece of cloth kept wet from a
vessel below containing water. The wet bulb thermometer will
now always read lower than the dry bulb, and by the two readings
the amount of moisture may be determined from a table. To
measure the moisture therefore, it is only necessary to see that one
bulb is wet, to read the two thermometers, and determine the
moisture from the table. Care should be taken that the wet bulb
is not exposed to a current of air, as this accelei-ates the evapora-
tion and diminishes the apparent amount of moisture.
An ingenious modification of the wet and dry bulb thermome-
ters is the hygrodeik. In this instrument the two thermometers
are placed side by side on a stand, and carry two indices of which
one is brought to the level of the mercury in the dry bulb by
raising or lowering a milled head, and the other is brought to
coincide with the wet bulb by turning the milled head. A
pointer is attached to the latter which may thus be directed to
any part of the space between the two thermometers. In this
space a card is placed on which are drawn three sets of curves of
such a form as to show the amount of moistui'e corresponding to
any readings of the two thermometers. One set of curves gives
the absolute amount of moisture and its pressure, the second the
relative humidity, and the third shows the dew-point. To make
a reading, raise or lower the milled head until the index is oppo-
site the mercury of the dry bulb thermometer, then turn it until
the second index coincides with the mercury of the wet bulb,
and the position of the pointer shows by inspection the amount
of moisture.
All the above instruments give results which have to be re-
MOISTURE. 151
duced by the aid of previous experiments, and cannot be relied
upon when great accuracy is required. These objections are
avoided in hygrometers depending on the determination of the
dew-point. Daniell's hygrometer consists of a glass tube bent at
right angles, with a bulb at each end, one of blackened glass, the
other covered with muslin. A thermometer is enclosed in this tube
with its bulb in the black glass, which is half filled with ether and
the air expelled by boiling it before sealing. If now a little ether
is poured upon the muslin, by its rapid evaporation and conse-
quent absorption of heat from the glass, the latter is cooled. Con-
densation, therefore, of the ether vapor inside of it takes place,
and evaporation of the ether in the black glass, which in turn is
cooled as in a cryophorus. The thermometer, therefore, begins to
fall, and descends until it has so far cooled the surrounding air, that
the dew-point is reached and condensation takes place on the sur-
face of the glass. The temperature is then read by the thermom-
eter but will be somewhat below the dew-point, since the dew is
probably not noticed at first. In a few seconds the glass will be-
come warmed and the condensed dew will evaporate ; read the
temperature which may be a little above the dew-point, add more
ether, and repeat until the dew-point is determined exactly. Care
must be taken not to breathe on the blackened bulb or to allow
the moisture of the body to be deposited on it. In warm cli-
mates, alcohol may be used instead of ether.
Regnault has modified the above instrument so as to render it
much more accurate. Two thin polished silver tubes, like test
tubes, are closed by corks through which pass the stems of two
similar thermometers. One of the tubes is partly filled with ether,
and through its cork pass two glass tubes, one opening in the up-
per, the other in the lower part of the silver tube. The first glass
tube is connected with an aspirator by which air may be drawn
through the ether. When this is done the latter evaporates rap-
idly, and its temperature falls until dew is deposited on the silver.
The air-current is then stopped, the ether grows warmer and the
dew evaporates; the true dew-point is thus determined with great
accuracy. When an aspirator cannot be conveniently used, a rub-
ber tube is connected with the glass tube passing to the bottom
of the silver tube, and the ether cooled by blowing air through it.
152 RAIN AND DEW.
The ether vapor escaping from the other tube should in this case
be carried off and down by a second rubber tube so as not to in-
terfere with the deposition of the dew. The advantages of this in-
strument over Daniell's hygrometer consist in the ease with which
the dew can be detected on the surface of the silver, the more so
from the presence of the second silver vessel, which is always dry ;
again, the passage of the air through the ether stirs it up
thoroughly, and renders -its temperature very nearly uniform
throughout.
The most accurate method of determining the moisture in the
air and that with which' all others are compared to see if they are
correct, is the chemical method. In this, a known volume of the
air to be measured is drawn by an aspirator through three tubes
filled with some drying substance, as pumice stone moistened with
sulphuric acid. The first tube collects the moisture, or if any
escapes this, it is stopped by the second, and the third prevents
moisture from passing back from the aspirator. The amount of .
moisture is found from the increase of weight of tubes one and
two.
167. RAIN AND DEW.
Apparatus. A rain gauge, a vessel for determining the evapor-
ation, some cotton wool, thermometers, an aethrioscope and an acti-
nometer.
Experiment. A rain gauge may be made of a simple funnel in-
serted in a graduated vessel so that the rain falling on it may be
collected and measured. It should be placed within a few inches
of the ground, as the quantity of rain received diminishes rapidly
with the height, and it should be placed as far as possible from all
buildings and other objects liable to produce eddies. By a simple
proportion, the water received is reduced to the depth it would
have if distributed uniformly over the exposed surface. To com-
pare the amount of rain received, with the moisture passing into
the air by evaporation, a cylindrical vessel containing water is ex-
posed directly to the air. The lowering in level from day to day
measures the evaporation, and may be observed directly. To
prevent birds and other animals from drinking the water, it is
customary to surround the vessel with sharp pointed wires. This
TIDES. 153
instrument is called an atmidometer. To measure the evapora-
tion with precision, the apparatus desciibed in Vol. I, Experiment
13, may be used.
Many objects exposed to the sky on clear nights, especially in
the summer and autumn, cool by radiation until their temperature
is below the dew-point of the air. Moisture is then deposited on
them, and is called dew. The amount may be measured by ex-
posing a plate of glass or metal painted black to the sky and col-
lecting the water deposited. Or, pieces of cotton wool may be
employed, and the increase in weight observed. Such an arrange-
ment is called a drosometer. To measure the amount of noctur-
nal radiation a thermometer with blackened bulb is exposed to the
air and protected from radiation from the earth by placing under
it a box tilled with eider-down. This instrument is called an ac-
tinometer. The radiation to the sky may also be measured by
the aethrioscope, which consists of a vertical glass tube terminat-
ing in bulbs, of which the lower takes the temperature of the air,
and the upper is blackened and exposed to the sky. A concave
mirror cuts off radiation from the earth and an index of water in
the tube shows the relative temperatures of the two bulbs. When
the upper bulb is covered, both take the same temperature, and
the drop of water comes to the zero point, but on exposing the
upper bulb to the sky, the drop at once rises.
168. TIDES.
Apparatus. A tide-gauge, which may consist of a simple float
attached to a cord passing over a wheel whose position marks the
level of the water. Or a flexible rubber bag sunk below low-water
mark, and connected by a tube with a mercury column or steam
gauge may be employed.
Experiment. Although not strictly a meteorological phenomenon
the rise and fall of the tide is often associated with Meteorology,
and this is especially the case, from their close connection with the
rain fall and evaporation, with the variations of level of lakes and
rivers, which are observed in precisely the same way. To ob-
serve these changes of level, it is only necessary that the water
should communicate with an adjacent well or pit, and that sudden
variations of level due to waves or other disturbing causes should
154 MAGNETIC DECLINATION.
be cut off by diaphragms or by contracting the connecting pipe.
The simplest way to measure the level of the water is by a verti-
cal graduated rod immersed in the water, from which the level is
read directly. Another method is to use a float with a cord pas-
ing over a pulley and stretched by a weight at the other end.
The position of the wheel, which may be transmitted to indices,
marks the height of water.
An ingenious form of tide-gauge has been used by the Coast
Survey, for measuring the rise and fall of the tide when observa-
tions could not be made on shore but only by vessels at anchor.
It consists of a flexible air-tight bag which is filled with air and
thrown overboard, being weighted so that it will sink, and con-
nected with the surface by a long flexible tube. To the upper
end of the latter is attached 'any form of pressure-gauge, and from
its reading the depth of water is at once deduced. As, therefore,
the vessel rises and falls with the tide, the index of the gauge
moves to correspond. The same instrument is well adapted to
taking soundings, if the water is not too deep. The bag is
thrown overboard and towed by the boat, when the index always
denotes the vertical depth of water above the bag.
169. MAGNETIC DECLINATION.
Apparatus. In this experiment, and in the three that follow
it, all the observations should, if possible, be made in a small de-
tached building or magnetic observatory, constructed entirely
without iron, and the instruments should be mounted on stone
piers disconnected from the rest of the building, to protect them
from jars. When this cannot be done, a room should be assigned
to them, preferably in the cellar, to secure a uniform temperature
and a steady foundation. All iron must be removed to a distance,
especially when determining the absolute magnitude of the ele-
ments, and the observer should take care that he has no iron about
his person, as a pocket knife, keys, or steel-mounted eye-glasses.
The instruments should be protected by cases with plate glass
windows through which they may be observed.
To measure the magnetic declination, a common surveyor's tran-
sit is needed, -which may be placed near a northern window so that
the pole star shall be visible. A vertical mirror is attached to the
wall opposite it in such a position that ,the observer on looking
through the telescope will see its reflection in the mirror. Instead
of the mirror a collimator may be used, or telescope without an
MAGNETIC DECLINATION. 155
eyepiece having cross-hairs illuminated by a light placed behind
them. A still simpler substitute is a very distant object. The di-
rection of the meridian must be determined once for all, as ex-
plained in Experiment 182, and the reading of the horizontal circle
of the transit observed. The telescope is then turned towards the
mirror until, on looking through it, its cross-hairs bisect the reflec-
tion of its end. This may be determined more precisely by hang-
ing a plumb line in front of its centre, or if a collimator is used,
bringing the two sets of cross-hairs to coincide. The horizontal
angle will now give the direction of the line normal to the mirror.
North or south of the transit a bar magnet is hung by one or more
filaments of silk, the upper end lying in the thread of a horizontal
screw turning in a fixed nut, so that the magnet may be raised or
lowered in a perfectly vertical direction. To remove the twist,
the screw and nut may be turned around a vertical axis over the
silk fibres. To one end of the magnet a lens is attached and, at a
distance equal to the principal focal distance, a set of cross-hairs.
The magnet is hung from the silk by a stirrup so that it may be
turned over at will. A brass bar of the same weight as the mag-
net should also be provided.
To measure changes in the magnetic declination, a mirror is at-
tached to a small magnet suspended by a long filament of silk and
its motion observed by a telescope and scale.
Experiment. In studying the magnetic condition of the earth
we find that its total effect is equivalent to two equal and opposite
forces acting on the two poles of the magnet. To determine the
direction of this force we must measure its declination, or varia-
tion to the east or west of the true meridian, and its dip or incli-
nation to the vertical. Then, finding the magnitude of the force
or the magnetic intensity, the magnetic condition is fully deter-
mined. The three quantities, the declination or variation, the
inclination or dip, and the intensity, are called the magnetic ele-
ments. On measuring them, it is found that they vary not only
in different parts of the earth, but also with the time, undergoing
variations with the hour of the day, the season of the year and
from year to yeai\ These variations are called diurnal, annual and
secular. Besides these there is a fourth, irregular variation which
cannot be predicted, keeping a suspended magnet in constant mo-
tion, the changes sometimes being very great. The latter are
called magnetic storms. Two classes of instruments are therefore
required, the first to determine the absolute magnitude of the
three elements, and the second to study their changes.
156 MAGNETIC DECLINATION.
Set up the transit, so that it shall lie in the same meridian as
the suspended bar magnet and in the line perpendicular to the
mirror. Turn the telescope towards the latter -until the cross-hairs
coincide with the reflection of the centre of the end of the tele-
scope, or of a plumb line hung in front of it, and read the horizon-
tal an^le. To eliminate torsion replace the magnet by the brass
bar and turn the suspending fibre by its support at the upper end
until the stirrup points directly towards the transit. Then replace
the magnet and placing a light behind its cross-hairs, turn the teles-
cope towards it and. bring the two sets of cross-hairs to coincide.
Turn the magnet over in its stirrup and repeat. The mean of
these two readings gives the true direction of the magnetic me-
ridian, since it eliminates any error due to deviation of the mag-
netic axis from the line connecting the cross-hairs and centre of
the lens attached to the magnet. If now we call a the angle be-
tween the true meridian and the line perpendicular to the mirror,
and b the angle between the mirror and the mean position of the
magnet, a b will equal the magnetic declination.
To determine the variations of the declination, it is only neces-
sary to observe, with the telescope, the reading of the scale re-
flected from the mirror. To reduce these readings to absolute
angular readings, we must know the distance of the nearest point
of the scale from the magnet-mirror and the scale reading of this
point. For this purpose hang a plumb line over the centre of the
telescope, and turn the mirror until its reflection where crossing
the scale is visible in the telescope. The scale reading /, gives
the required point. Its distance d, from the mirror is then meas-
ured directly by a millimetre scale. Call s the scale reading cor-
responding to any angle a, and a' the declination when the scale
o' o
reading is s'; then ^ tang 2 (a' a). To determine a',
measure the absolute declination by the instrument described
above, and read s at the same time. Then substituting the value
of a deduce a'. As the declination varies but a small amount it
will generally be sufficiently accurate to assume that the tangent is
proportional to the arc, in which case each scale division will equal
J)
jYjg minutes, or if D = 1719 mms., 1 division will equal a minute.
If the scale is observed continuously, it will be seen to be con-
MAGNETIC DIP. 157
stantly in motion, and this is the case to a surprising extent dur-
ing displays of the aurora borealis.
170. MAGNETIC DIP.
Apparatus, A dipping needle, of which the best form is that
proposed by Joule, and a magnet to reverse the polarity of the
needle.
Experiment. If a piece of steel is placed north and south, bal-
anced on a knife-edge and then rendered magnetic, the north end
will seem to have become heavier than the so.uth, owing to the
inclined direction of the magnetic force of the earth. In the
southern hemisphere, however, the other end descends or dips.
To measure the angle of inclination, a dipping needle is employed.
This consists of a magnetic needle resting on a circular axis so
that it can move very freely in a vertical plane. The ends are
pointed, and a vertical graduated circle is placed near them to
show the angle of dip. Sometimes a plate of looking-glass is
placed behind the needle, and the graduation etched on it. The
parallax is eliminated by bringing the needle to coincide with its
reflection. The friction should be reduced to a minimum by using
a very small axis of hardened steel, resting either on two knife-
edges, or on friction rollers. The whole is mounted on a verti-
cal axis free to turn, the angle of rotation being, measured by a
horizontal graduated circle. It should also carry a level, and be
mounted on levelling screws.
In Joule's dipping needle, the axis, instead of resting on steel
supports hangs on two loops formed by hanging filaments of silk
from the ends of a delicate balance. The friction is thus reduced
to a minimum and alters the position of the needle by less than a
minute of arc. Maxwell proposes to read the position of the
needle, by placing two prisms acting like mirrors in front of the
telescope, so that they shall reflect the two ends of the needle into
the field at the same time, and to take the reading by measuring
the angle through which they must be turned in order that the
two ends may coincide.
To measure the dip, level the instrument in the usual way, by
bringing the level parallel to two of the levelling screws, and turn-
ing one of them until the bubble is in the middle ; then turn the
158 MAGNETIC DIP.
level 90, or until it is perpendicular to these screws, and again
bring the bubble to the centre by the third screw. Repeat until the
bubble remains in the centre, however the vertical circle is turned.
If, now, the needle is set vibrating, it should continue to move for
a long time, and finally always come to rest at the same point.
Place the circle in the magnetic meridian, read the position of the
two ends of the needle, and their mean will equal the dip. The
circle may generally be set in the proper position by a common
compass, but the following method is more common. If the circle
is turned completely around, it will be noticed that in two posi-
tions, when at right angles to the magnetic meridian, the needle
is vertical, and when in the meridian its reading is least. The
proper position may therefore be found by turning the circle until
the needle is vertical, then turning it exactly 90. When the
needle is in the meridian it is acted by the two components IT=
/cos i acting horizontally, and V=Ts\n i acting vertically, calling
/the total force, Hand. F'its two components, and i the angle of
inclination or dip. - If the needle is turned into a plane inclined
by the angle v to the magnetic meridian, the vertical component is
unchanged, while the horizontal component is reduced to H' =
/Tcos v = /cos i cos v. Hence, if i' is the angle of inclination of
the needle in its new position, we shall have,
., /sin i tang i
~ /cos i.cos v cos v '
Evidently the minimum value of i' is t, when v = 0, and i =. 90
when v = 90, as stated above. If two readings i' and i", are
taken when the circle is turned 90, we have cot i' = sin v cot i
and cot i" = cos v tang t, or cot 2 i' + cot 2 i" = cot 2 i, which fur-
nishes a third method of determining i.
In the above measurement of the dip we have made two as-
sumptions, neither of which is likely to be correct. First, that the
centre of gravity coincides with the centre of the axis supporting
the needle, and secondly, that the line connecting the north and
south poles of the needle, is parallel to that connecting the two
ends, which serve as pointers to read the graduated circle. The
first source of error is eliminated by turning the vertical circle
180, when the needle turns over, so that the other side is upper-
most. If, then, in the first case the centre of gravity is below the
HORIZONTAL COMPONENT. 159
axis and tends to diminish the inclination, in the second it is above
it, and increases the inclination by nearly the same amount.
Hence, the mean of the two gives very nearly the correct reading.
To eliminate differences in the pivots the needle should also be
turned over, and the readings repeated in that position. To elimi-
nate the incorrect position of the magnetic axis, the magnetism
must be reversed. This is done by stroking the needle several
times, from the centre outwards, first on one end and then on the
other, with a permanent magnet. As the polarity is to be re-
versed, the north end of the needle must be stroked with the
north pole of the magnet, and the south end with the south pole.
After reversal, the dip is again observed, the other end of the nee-
dle now pointing downwards.
The dip may also be found from the time of vibration of a dip-
ping needle, when placed first in the meridian, and then, in
plane at right angles to this. The force acting on the needle will
be, in the first case, the total magnetic force I, and secondly its ver-
tical component only, or I sin '. But if n and n' are the number
of vibrations the needle makes in a given time in the two cases,
the forces will be proportional to n* and n'\ or I : I sin i =
n' 2
n 2 : n' 2 , hence, sin i = 5, or the sine of the dip equals the square
of the ratio of the number of vibrations.
17lA. HORIZONTAL COMPONENT.
Apparatus. A mirror is attached to a rectangular steel magnet
about a decimetre long, which may be suspended by a bundle of
filaments of silk. A telescope and scale serve to mark the motions,
as in Experiment 169. To determine the moment of inertia, two
cylindrical brass weights may be attached to the magnet at known
distances from its end ; a good compass, a wooden or brass bar a
metre in length and divided into decimetres, and a bifilar magne-
tometer are also needed.
Experiment. If a dipping needle is moved from its position
of equilibrium, it will vibrate under the influence of the magnetic
attraction of the earth, like a pendulum, and the square of the
time will be inversely proportional to the magnitude of this force.
Owing to friction, however, an accurate measurement cannot be
obtained in this way, and accordingly its horizontal component and
160 HORIZONTAL COMPONENT.
direction are determined instead. The total force equals its
horizontal component divided by the cosine of the dip. The
horizontal component is measured as follows. A magnet is sus-
pended by a bundle of filaments of silk, and its time of vibration
determined. This gives the product of H, the horizontal com-
ponent of the earth's magnetism, by M, the magnetic moment
of the magnet, if we know I the moment of inertia of the latter.
The ratio of M to H is next determined by seeing how far the
magnet will deviate a compass needle from the meridian. Having
thus determined MH and 7^ we readily deduced Let us now
see more exactly how these two experiments are made, -and then
how the value of If is computed from them.
To determine its time of vibration, the magnet is placed in its
stirrup, a black thread is hung over the scale near the point marked
by the cross-hairs of the telescope, and the magnet set in vibra-
tion, by holding another magnet near it for a few seconds. Care
must be taken not to touch it, or it will be set swinging like a
pendulum. The time of transit of the thread past the cross-hairs
is next taken, as in Vol. I, Experiment 15. Six transits are thus
observed to the nearest tenths of a second, an interval of several
minutes is then allowed to elapse, and a second series of transits
taken. From these the true time of transit may be determined
with great accuracy. For this purpose, take the mean of the first
and second, the third and fourth, and the fifth and sixth observa-
tions of each series. This will give the turning points of the mag-
net. Then take first differences, which will equal approximately the
time of vibration. Take the mean of the four times thus obtained
and call it t. Then take the mean of the six original observations
of the first and of the second series, and call their difference T.
Dividing T by t gives the number of intermediate vibrations,
which should be a whole number. Owing to slight errors in t, it
will not come out exact, but dividing T by the nearest whole
number gives the time with great accuracy. Care must be taken
not to make T so great as to render the number of vibrations
doubtful, or other intermediate observations become necessary,.
Often sufficient accuracy is attained by observing two transits of
the thread past the cross-hairs in the same direction with an
HORIZONTAL COMPONENT. 161
interval of several minutes between them, and counting the inter-
mediate passages. The time is then found by a single division.
To determine the ratio of M to H, two observations are taken
with the magnet placed at different distances from the compass
needle. The compass is placed in the centre of the divided bar,
which is turned at right angles to the magnetic meridian. The
magnet is then placed with its centre on the 1, 2, 8 and 9 dms.
points, its north pole being turned first toward the compass, and
then in the other direction. All the deflections of both ends of the
compass needle are measured, and the mean of those produced
when the magnet is distant 3 dm. taken, also when 4 dm. distant.
It is only absolutely necessary to take two readings at different
distances, but by the repetition recommended above, errors of ec-
centricity and want of symmetry of the magnet or compass nee-
dle are eliminated. The deflection should be as great as possible,
but the least distance of the magnet should be at least three times
its length, and ten times that of the compass needle. The greatest
accuracy is attained when the greater distance is to the smaller, as
four is to three. Instead of placing the magnet east and w"est, it
may be placed north and south of the compass, and the observa-
tions made as before, only the result, if the same formula is used,
will be twice as great as in the first case, that is will equal 2 M
divided by H. Of course the bar must now be turned east
and west, as, if placed north and south no deflection will be pro-
duced.
The horizontal component H of the earth's magnetism is next
computed as follows. Let M be the magnetic moment of the
magnet, or the intensity of magnetism of the poles multiplied by
their distance apart. For any pendulum, = it t/ in which tf is
the time of vibration, I the radius of gyration or length of an
equivalent simple pendulum, and a the acceleration of the force
causing it to vibrate. From this we deduce, a = %- or multi-
m**l 2
plying each side by the mass m, and by Z, we obtain mla = ^
But mla = MIT, since it equals the force tending to bring the
162 HORIZONTAL COMPONENT.
magnet into the meridian from a position at right angles to it, or
replacing ml 2 by the moment of inertia I, we obtain MH = -^
Commonly we have given the weight w, length Z, and breadth 5,
of the magnet, and in this case,
If the magnet, instead of being rectangular, is of such a shape that
its moment of inertia cannot be computed, it may be determined
experimentally by hanging two cylindrical weights at equal dis-
tances from the centre and observing the new time of vibration.
Calling t' this time of vibration, 2w' the weight of the cylinders,
and I their distance from the centre, we have the proportion,
Having thus computed MH^ we must next determine -jr from
the second observation. Calling r and / the two distances at
which the magnet is placed, or 3 and 4 decimetres in the above
example, and v, v f the corresponding mean deflections of the com-
M r 5 tang v / 5 tang v'
pass needle, it may be proved that -jf = ~ ^( 2 /-^ - .
As stated above, if the deflecting magnet is placed north and south
M r 5 tang v" r' 5 tang v"'
of the compass, -JT - 2 , 2 - - - > v and v being
the corresponding deflections. Having thus determined MH and
jur i - - jTf-
jj we readily deduce JI=\/ Mil -7- -jr. Great care must be
taken to reduce all measures to the same units, or to centimetres,
grammes and seconds.
To measure the changes in the horizontal component, of the
earth's magnetism, a bifilar magnetometer is commonly employed.
This instrument differs from that used to measure variations in
the declination, mainly in having the magnet suspended by two
bundles of filaments of silk instead of by one. Their distance below
is regulated by two screws, and above by two pulleys between
which they pass. The two threads are connected together above
and pass over a pulley, so that the tension of both may be the
same. The upper suspending pulleys are turned until the magnet
is nearly perpendicular to the magnetic meridian, and the length
of the threads, and their distance apart should be such, that they
VERTICAL COMPONENT. 163
will thus be twisted through an angle of about 45. Evidently
when the threads are turned so that they hang obliquely, as their
length remains unchanged, the magnet is slightly raised, so that
the directive force of the earth's magnetism is balanced against
the weight of the magnet. The observations are made by the
telescope and scale in the usual manner, the scale readings
being very nearly proportional to the changes in the horizontal
intensity. To reduce them to absolute measure, a magnet of
known magnetic moment Jf is placed north or south of the suspen-
ded magnet, at the same height, and at a distance d. The change
in the magnetic field will then equal ig-, and, as this corresponds
to a change of reading of n divisions, the value of one division is
readily obtained. The zero of the scale is at once found by meas-
uring the component by the method given above, and by the bifilar
magnetometer simultaneously. This comparison should be made
frequently as the readings are liable to vary, owing to changes in
the magnetic moment of the suspended magnet, and to altera-
tions in the length and distance apart of the two suspending
threads, due to changes of temperature. To measure very minute
changes in the horizontal intensity, the magnet is sometimes
turned 180 into the magnetic meridian with its north end to the
south. The delicacy may then be increased indefinitely by vary-
ing the distance of the suspending filaments. If they are brought
too near together, however, the magnet will be in unstable equilib-
rium.
17 IB. VERTICAL COMPONENT.
Apparatus. The only instrument required, is a magnetometer
balance with a telescope and vertical scale for measuring devia-
tions.
Experiment. The absolute value of the vertical component of
the earth's magnetism is not readily measured directly, but is more
commonly deduced from the other magnetic elements. Its varia-
tions are, however, easily observed by the magnetometer balance,
which consists of a magnet placed in the magnetic meridian, and
balanced on knife-edges like the beam of a chemical balance. A
mirror is attached, from which the deviations may be observed in
the usual way, by a telescope and vertical scale.
164 ELECTRICITY OF THE AIR.
The magnitude of the divisions of the scale may be reduced to
absolute measure by placing a vertical magnet of known moment
M at a distance d above or below the balance, and noting the
change in scale reading n. The corresponding change in the mag-
netic field will be -- and dividing this'by n will give the value
of one scale division as in the case of the bifilar magnetometer.
The zero of the scale is then determined by comparison with the
absolute vertical component, which is deduced by multiplying the
horizontal component by the tangent of the dip. The absolute
magnitude of the divisions may also be determined by measuring
the force required to balance the beam when turned horizontally
90 or 270, and comparing it with the deflection produced by
one milligramme placed at the same distance from the knife-edges.
The small magnitudes of the forces to be measured, renders this
method unsatisfactory.
The horizontal and vertical components, H and V^ the total
intensity /, and the inclination i are connected together by the
y
two equations, I 2 = If 2 -{- F 2 , and tang i = -g- Hence, if
either two are known the other two may be deduced. It will be
seen from the above that it is difficult to measure directly the
total intensity I, or its variations, the vertical component V, or
the variations of the dip i.
172. ELECTRICITY OF THE AIR.
Apparatus. Two instruments are required in this experiment
of which one assumes the same electrical potential as the air, and
the second measures this potential. For the first of these a
water-dropping collector is commonly used, or an insulated vessel
of water, with a small tube leading from it through which the
liquid escapes in a fine stream breaking into drops. A burning
match made of a roll of blotting paper dipped in nitrate of lead
may be used for the same purpose, or a metallic vessel containing
ether, whose vapor escapes through a small aperture in the top.
To measure the potential, any electrometer of sufficient range and
delicacy may be used. Generally Thomson's quadrant electrome-
ter is to be preferred ; or his portable electrometer, if observations
are to be made at various places. Peltier's electrometer is also con-
venient, if less accuracy is required.
ELECTRICITY OF THE AIR. 165
Experiment. If the electrical potential of the earth is com-
pared with that of the air, it will be found that the latter is com-
monly in excess in pleasant weather, or the earth is negative. In
stormy weather, especially during thunder-storms, the potential of
the air varies very irregularly, being sometimes positive and
sometimes negative ; even in calm, clear weather the variation per
minute often amounts to five or ten per cent. To measure the
potential of the air, fill the water-dropping collector, and connect
it with one terminal of the electrometer, the other terminal being
connected with the earth. If the surface of the stream of water
has a potential greater than that of the surrounding air, the ex-
cess of electrictity is rapidly carried off by the falling drops. The
potential measured, therefore, is that of the air at the point where
the stream divides into drops. The heated air from the match and
the ether vapor, act in a similar manner.
The method of using the quadrant electrometer is given in Ex-
periment 111. In the portable electrometer, the electrified needle
is attached to the centre of a stretched platinum wire, and the
angle through which the latter must be twisted to bring the nee-
dle into a given position, is noted. The difference of potential is
proportional to the square root of the angle of torsion. Peltier's
electrometer consists of an insulated compass needle resting
against a wire parallel to it. When both are electrified, repulsion
takes place and the needle swings off at an angle which may be
measured by a graduated circle placed below.
Measure the potential at various heights above the'surface of the
earth and it will be found that the changes are nearly proportional
to the height. Take also a series of readings every minute, and
construct a curve with times as abscissas, and potentials as ordi-
nates. It is curious to notice the electrometer, during the pro-
gress of a distant thunder-storm, as after each flash of lightning
the electrometer will mark a sudden change of potential.
PRACTICAL ASTRONOMY.
173. SEXTANT.
Apparatus. The only instrument needed for this experiment
is a sextant ; and, although the adjustments are best made by means
of a star, the sun or any well defined distant terrestrial object may
be employed. A star catalogue is needed for the latter part of
the experiment.
Experiment. A sextant consists of a sixth of a graduated cir-
cle with each division exactly one half of its usual size. A small
telescope is attached to one side, and opposite is placed a mirror,
called the horizon-glass, of which one half only is silvered. The
angles are measured by a vernier reading to 10", attached to an
arm free to revolve around the centre of the circle. Upon this
arm, and in the same plane as the axis, is attached a second mirror
called the index-glass. The arm may be set exactly in any required
position by a clamp and tangent screw. A magnifying glass is
attached, to read the vernier, and a handle is placed behind the in-
strument by which it may be held. A set of four colored glasses
may be inserted between the two mirrors to moderate the light,
when directed towards the sun. A second set of three glasses may
be interposed behind the horizon-glass to moderate the light of the
direct image. When the sun is partially obscured, one or more
of these glasses may be used. The telescope has two horizontal
and two vertical cross-hairs in its focus, forming a square in the
centre of the field of view, and is directed towards the horizon-
glass, which is so placed that it will reflect light received from the
index-glass into the telescope. On looking through the latter,
therefore, two objects may be seen simultaneously, one through the
unsilvered portion of the horizon-glass, the other by reflection
(166)
SEXTANT. 167
from both nfirrors. From the law of reflection it follows that
when the two images coincide, the angle will be double that
between the two mirrors. That this condition may hold, it is
essential that both mirrors should be perpendicular to the plane of
the graduated circle, and the telescope parallel to it. Before using
a sextant, therefore, it should be subjected to the following tests,
and the error, if any, corrected.
1st. Index-glass perpendicular to circle. Turn the sextant
around so that the graduation is away from the observer, and hold-
ing the index-glass near the eye, observe the reflection of the
graduation in it. If the image coincides in direction, and appears
to form a continuation of the circle itself, the mirror is in its
proper position. There is no provision for adjusting this mirror
as it is not often necessary. It may be adjusted by unscrewing
the index-glass, and inserting paper, or tiu-foil, under one edge of
its support, or by filing down the pins against which the mirror
rests.
2d. Horizon-glass perpendicular to circle. Bring the vernier
near the zero and turn the telescope towards a star or other
well-defined distant object. If the images can be brought to coin-
cide by moving the index, no correction is necessary. Otherwise,
turn a screw above or below the horizon-glass until this condition
is fulfilled.
3d. Telescope parallel to plane of circle. Bring two of the
wires in the telescope parallel to the circle, and set the index so
that the two images of the star shall coincide with the wire near-
est the circle. Turn the instrument until they fall on the other
wire, and if they still coincide, the adjustment is exact. Other-
wise, move the two screws which fasten the collar holding the
telescope to the frame of the instrument.
4th. Index Error. Make the two images coincide exactly by
the tangent screw, when the reading of the arc will give the index
error. The graduation is extended beyond the zero, forming what
is called the arc of excess, and if the reading falls on this, it must
always be added, otherwise, subtracted from the observed reading.
The index error may be found in the day time by viewing the two
images of the sun, first interposing both sets of colored glasses.
Bring the two images so that they shall just touch, first with one
168 LATITUDE.
uppermost, and then the other. One half of the difference of the
two readings equals the index error. This is the most important
error of all, and should always be observed before using the instru-
ment.
Now measure the distance between two bright stars at least 45
above the horizon. For this purpose hold the sextant by its han-
dle in the right hand with its plane parallel to the rays coming
from both stars, and the telescope turned towards one of them.
Then turn the movable arm until the second star is seen at the
same time, clamp it and bring the two images together with the
tangent screw. The reading of the vernier, when corrected for
index error, will equal the required distance. Take from the star
catalogue the right ascensions and declinations of the stars. Then
in the spherical triangle they form with the pole, we have given
two sides and the included angle ; for 90 minus the declination
of each gives a side, and the difference in right ascension gives the
angle between them. From these, compute the third side or dis-
tance apart of the two stars and see how nearly it coincides with
observations. Calling 8,/S' and P the two stars and the pole, and
D the point where a perpendicular from /S will meet S'P, we have
tan PD=cos SPS' tang #'P and cos SS'= cos S'D cos SP
sec PI). If stars near the horizon are observed, an incorrect re-
sult is obtained owing to the refraction of the air, but above
45 this error will be small.
174. LATITUDE.
Apparatus. A sextant and artificial horizon which consists of
a vessel containing mercury, protected from currents of air by a
roof formed by two pieces of plate glass. To prevent the mer-
cury from becoming tarnished, a small piece of tin-foil maybe
added to it, which, being dissolved, forms a film covering its sur-
face. If this film is removed, the liquid beneath will be bright
and clear. Glycerine is also recommended for the same purpose,
and to diminish the motion caused by slight jars. Another form
of artificial horizon consists of a piece of black glass ground per-
fectly plane and resting on three levelling screws. A very deli-
cate spirit-level resting on three points, one of which may be raised
or lowered, serves to render the plate horizontal. It is desirable,
though not essential, to have a sea-horizon to the south, and a
chronometer giving Greenwich mean time.
LATITUDE. 169
Experiment. The most common method of determining the lat-
itude is by measuring the altitude of the sun or of a star when on
the meridian. If the observation is made at sea, the telescope of
the sextant is directed towards the horizon beneath the object, and
the image of the latter brought to coincide with it by moving the
index. The sextant is then turned from side to side, when the
object will appear to describe a line convex downwards. Turn
the tangent screw until at its lowest point the image will just touch
the horizon, and take the reading. If the observation is made on
land, the artificial horizon is more commonly employed. In this
case the telescope is turned down until the reflection of the object
in the mercury is seen, the index is then moved until the second
image is brought into the field, the instrument clamped and the
images brought to coincide by the tangent screw. The angle as
given by the vernier is that between the object and its reflection,
or twice the altitude. If practicable, and always where the greatest
accuracy is required, two observations should be made, turning
the artificial horizon around 180, so as to eliminate want of paral-
lelism of the plates of glass.
If the glass horizon is used, it must be levelled as follows. Place
the level parallel to two of the screws, and raise or lower one of
them until the bubble is in the centre. Turn it end for end, and if
the bubble goes toward one end of the tube, bring it half way
back by the adjustable point on which one end of it rests, and
level the glass plate again. Now turn the level 90, and turn the
third screw until the bubble is in the middle. It should remain in
this position however the level is turned.
The observed altitude by no means equals the true altitude, but
should be corrected as follows. The order, though not essential
at sea, or when great accuracy is not required, should be strictly
that given below.
. Index-Error. Add or subtract the index-error according to its
sign.
Dip. Owing to the sphericity of tne earth, the sea-horizon
appears below the' true horizon or great-circle with the zenith as
a centre. The magnitude of the dip in seconds is D = 59"-y/A,
in which h is the height of the point of observation in feet, or
log D = 1.77115 + \ log h. This correction must always be sub-
170 LATITUDE.
traded from the observed altitude. If an artificial horizon is used,
this error is reduced to zero.
Refraction. Owing to the refraction of the light passing through
the air, objects always appear above their true position. This cor-
rection is a large and uncertain one, unless the altitude is consid-
erable, and, on account of it, observations of the heavenly bodies
should never be taken near the horizon. The magnitude of
the refraction is approximately given by the equation J? = 57"'
tang (Z 372), in which _B is the required refraction, and Z the
apparent zenith distance or 90 minus the altitude. To determine
7?, make it equal to zero in the second side of the equation and
thus determine Jt approximately, then substituting this value gives
the more accurate value, B = 57" -tan (Z 3 X 57"- tang Z).
This correction, like that of dip, must always be subtracted from
the observed altitude.
Parallax. An error is due to the apparent change in position
of the body, since the observer is not at the centre of the earth.
The amount of the error equals the angular interval, as seen from
the object, between the observer and the centre of the earth. It
T>
is called the parallax P, and equals -j^ cos A, in which A. equals
the altitude, R the radius of the earth, and D the distance of the
object. The quantity -jy is called the horizontal parallax, and is
usually given in the Nautical Almanac. Except in the case of the
moon, this correction is small, and with the sun never exceeds 8".
It is always to be added to the observed altitude, and in the case
of the fixed stars is always zero.
Semi-diameter. When the lower edge of the sun or moon is
observed, the true altitude is determined by adding the semi-diame-
ter, which is given in the Nautical Almanac. This correction is
small with the planets, and imperceptible with the fixed stars. In
the case of the moon, the semi-diameter must be increased, owing
to the observer being nearer than the centre of the earth, the
amount of the correction, or the augmentation, equalling 15."65
sin A.
When the object is on the meridian, the latitude is given by the
formula L = A -f- D 90, in which L is the latitude, A the
altitude, and D the declination of the object, south declinations
LATITUDE. 171
being always regarded as negative. In the case of the sun, D is
found by interpolation from the Nautical Almanac, which gives
the declination every day at Greenwich apparent noon. To this
must be added the Greenwich time of the observation multi-
plied by the hourly change of declination, or subtracted if the de-
clination is diminishing. The Greenwich time is either taken
directly from a chronometer or it will equal the longitude west of
Greenwich added to the equation of the time. The time need not
be found with great accuracy, since an error of a minute will at the
most only cause an error of about 1" in the latitude. The observa-
tion should be made within a minute or two of apparent noon, that
is, twelve o'clock plus the equation of time. At sea, however, it is
customary to begin to measure the altitude some minutes before
noon, and follow the sun with the tangent screw until it begins to
descend or dip. The greatest altitude is that employed. If the
sun passes near the zenith, its altitude will alter rapidly from east
to west. In this case, its distance from the north or south point
of the horizon should be measured.
The observation of a star is more difficult on account of its fee-
ble light, but greater accuracy is attainable, and the calculation is
much simpler.
If the time is known with accuracy, either by a chronometer or
as described in the next Experiment, the latitude may be deter-
mined approximately by a single observation of any known
heavenly body. This involves our first solution of a spherical
triangle which is so frequently employed in astronomy that it is
known as the astronomical triangle or as the ZPS triangle, Fig.
104, since it is formed by the zenith Z, the
pole P, and the star or other object S. In
this triangle ZP equals 90 minus the lati-
tude of the place, PS the north polar dis-
tance, or 90 minus the declination, and ZS
the zenith distance, or 90 minus the altitude.
The angle PZS or angular distance from
the meridian is known as the azimuth, or, F . 104
with terrestrial objects, as the bearing. The
angle ZSP is rarely used, it is sometimes called the parallactic or
position angle. The third angle ZPS is called the hour angle, and
172 LATITUDE.
equals the time which has elapsed since the star has culminated
or crossed the meridian. For objects west of the meridian, this an-
gle will be positive, for those east, negative. When the star cul-
minates, the sidereal time will equal its right ascension, hence the
sidereal time minus the right ascension will equal the hour-angle
at any instant.
If the mean time t, and the longitude L are known, the sidereal
time must be computed from them. A clock giving mean solar time
will gain on a clock giving sidereal time 9.8565 sidereal seconds per
hour, or 236.5553 per day. The rate of gain may be expressed by
the fraction .0027379 of the whole solar interval. Hence any
mean solar interval T is reduced to sidereal time, by adding
.0027379 T or sometimes more conveniently by redqcing it to
hours A, and adding 9.8565 seconds. Sidereal time is in like man-
ner reduced to solar, by subtracting .0027304 T or 9.8296 seconds
per hour. If s is the sidereal time of mean noon at Greenwich as
given in the Almanac, the required sidereal time,
t f = t + E+ .0027379 (t + Z),
and the hour angle is found as before by subtracting if from the
right ascension.
If now any three of the parts of the ZP8 triangle are given,
the other three may be computed. Thus, in the present case,
we determine from the Almanac PS and ZPS, and the alti-
tude as measured by the sextant subtracted from 90, gives ZS.
From these, PZ may be computed by letting fall a perpendicular
SD from S upon the meridian PZ, when tang PD = cos 8PZ
tang &P, and cos DZ cos PD cos 8Z sec SP\ again, PZ =
PD + ZD and the latitude equals 90 PZ. Greater accuracy
is attained and the calculation simplified by using the pole star, in
which case P/8 is only 1 25'.
In all ordinary cases, the star should be observed near the me-
ridian, and the calculation may then be greatly simplified. Call a
the change in altitude during the first minute after culmination;
1".9635 cos L cos d
sin , L ^ ,m which L is the latitude and d the
declination. Then for a small hour-angle , the change in alti-
tude will be proportional to 2 ,or A = A' -J- at 2 in which A is the
true, and A' the observed altitude. The common method of find-
ing the true altitude of a star at culmination, is to observe its
TIME. 173
altitude at short intervals, before and after, and reduce them by
the formula,
. A' -h A" -f A'" + &c. f* + tf' 2 + t"" i + &c.
A =- ^ r + - ~ir-
in which w is the total number of observations. The value of A is
then corrected and used as an ordinary meridian altitude. It
will be noticed that a becomes very large when L nearly equals
d, or the star is near the zenith. Stars, therefore, should be se-
lected which do not culminate too near the zenith, since their
altitude varies too rapidly.
175. TIME.
Apparatus. A sextant, an artificial horizon, and a clock or
chronometer.
Experiment. In the ZPS triangle, if we know the latitude of
the place of observation, the declination and right ascension of
the sun or a* star $, and measure the altitude, or 90 ZS, the
triangle is readily solved. Having the three sides, we may deter-
mine the hour-angle ZPS and hence the time, by the formula,
cos ZS cos PS cos PZ
cos ZPS = sin PS sin PZ ' or more convementl y
calling M= \ (PZ + PS + SZ), by the formula,
//sin M sin (M ZS)\
cos i ZPS = Y/( gin p^ rinjPZ ')
If the star is near the horizon the error from refraction is large and
variable ; if near the meridian, the change in altitude is too slow,
and a slight error in altitude will produce a large error in the time.
Hence the observations should generally be made two or three
hours before or after the star culminates. As a single observation
is always uncertain, it is best to take a series of readings by set-
ing the index to some even division of the graduation, and observe
by a watch or clock the time at which the two images of the star
coincide, then move the index exactly 10' or 20' and observe the
time again. Having thus obtained a number of observations, take
the mean of the angles and the mean of the times, and treat them
like a single observation.
If the object observed is a star, the sidereal time is very simply
found from the hour-angle H. Calling B, the right ascension of
174 LONGITUDE.
the star, the sidereal time T E + H, taking care to make H
negative if the object is east of the meridian. This equation is
readily proved by recollecting that H hours before the observa-
tion, the star was on the meridian, when the sidereal time by defi-
nition equalled its right ascension. The local time T' = T S t
in which S is the right ascension of the sun at the time of obser-
vation, obtained from the Nautical Almanac by interpolation, as in
the last Experiment. In the case of the sun, the mean time may be
determined directly by the equation, T'= II-}- E .0027304 H
in which JEJis the equation of time.
A much more accurate method than that of single altitudes,
given above, is the method of equal altitudes, in which the star is
observed before and after passing the meridian. Clamp the index
of the sextant and take a series of readings at intervals of 10' or
20', when the star is east of the meridian, then, without unclamp-
ing the index, wait until the star has culminated, and attained
nearly the same altitude west of the meridian. Now tak a sec-
ond series of altitudes, of course in inverse order, as 'the star de-
scends. The mean of the times, when the star has the same
altitude east and west of the meridian gives the time of culmina-
tion. The advantage of this method is that it eliminates index
error, error in graduation, eccentricity, 1'efraction, dip and parallax,
since these quantities are the same in both cases. The calculation,
also, is extremely simple and requires no logarithmic tables.
"When the sun or a planet is observed, a correction must be ap-
plied, since there is generally an appreciable change in declination
between the morning and afternoon observation. Calling L the
latitude of the place, D the declination of the sun, d its change in
declination between the time of culmination and that of the last
observation, H the hour-angle, or half the interval between the
two observations, and h the correction to be applied. Then it
may be proved that h = ^d (tang L cosec H tang D cot //)
which is to be added to the computed time of culmination if the
object is moving northward, and subtracted if it is moving south-
ward.
176. LONGITUDE.
Apparatus. The sextant, artificial horizon, and a chronometer
regulated to Greenwich mean time.
LONGITUDE. 175
Experiment. Various methods are employed for finding the
longitude, which will be described in detail in Experiment 185.
At sea it is most commonly found by determining the local time
as described in the last Experiment, and comparing it with a
chronometer carefully regulated to Greenwich time. The error
and rate of the chronometer must be determined as frequently as
possible by comparison with other chronometers, or by determining
the local time at points whose longitude is known. The longi-
tude then equals the difference between the local time and Green-
wich time.
When the Greenwich time is not known, the longitude may be
determined from the position of the moon. The most common
method is that known as "Lunar Distances." In the Nautical
Almanac, the distance of the moon from several stars is given
every day, at Greenwich noon. The motion of the moon is,
however, so great, over half a degree an hour, that this distance is
constantly altering rapidly. If, then, the distance is observed at
any other point, the Greenwich time at that instant may be com-
puted, and comparing it with the local time, gives the longitude.
Several corrections, however, have to be applied on account of the
small distance of the moon, and hence, this method in practice is
both laborious and inexact.
The observations consist in the determination of the local time,
a series of readings of the distances of the moon and star, and their
altitude found by interpolation from observations before and after.
The mean of the distances and of the times is to be used as a sin-
gle observation and the altitude at this instant determined. The
approximate latitude and longitude must also be known. If the
latter cannot be otherwise obtained, the method of successive ap-
proximations may be used (Vol. I, p. 10). Find from the Nautical
Almanac the semi-diameter and parallax of the moon and of the
other body, if it is not a star. Add to the moon's semi-diameter
its augmentation, or 15."65 sin A, in which A is its altitude. If
the altitude is small, the contraction due to refraction must be
subtracted from the semi-diameters of the sun and moon. The
observed distance must be corrected for index error and for semi-
diameter of the moon, and of the sun also, if the latter is ob-
served. Correct the observed altitude of each body for index
176 MERIDIAN.
error, dip and semi-diameter, to find the apparent altitude. Find
also the true altitude by subtracting the parallax and adding the
refraction. Call M and S, Fig. 105, the appar-
ent positions of the centre of the moon and star,
and M' and & their true positions. Then, in the
triangle MSZ, we have given the three sides,
hence we can compute the angle at Z. But in
the triangle M'S'Zwe have given M'Z and
S' Z, equal to the complements of the true alti- s 'l
tudes, and the angle M'ZS' = MZS, since Fig. 105.
both parallax and refraction act only in vertical
circles. Accordingly we can solve the triangle M'ZS' and de-
duce M 1 S', the true distance of the moon and star, as seen from
the centre of the earth. This is most conveniently done by the
following formulas. Call A = 90 MZ, and A' = 90 M'Z,
the apparent and real altitudes of the moon, B 90 SZ and
B' ' =2 90 S'Z, the apparent and real altitudes of the star, and
D = MS, J} f = M'S' the apparent and real angular distance
apart of the star and moon. Make N= \ {A -f- B -\- D) and
cos ~
%(.' + B' -\- ), we have, sin \D' J cos NCOS (Wv). Sev-
eral other solutions may be used, but these have the advantage
that, having only cosines in their second members, they are readily
remembered.
177. MERIDIAN.
Apparatus. The sextant, an artificial horizon, chronometer, and
a distant terrestrial object. At night a distant lighthouse or other
light answers well.
Experiment. The true bearing of any terrestrial object may be
determined by the sextant, if we know the latitude and longitude
of the place of observation and the local time. Let Z be the
zenith, P the pole, the object, and S the sun or any star whose
right ascension and declination are known.
Measure the distance SO by the sextant, or better, set the index
at any even division and notice the time at which the two images
touch. Increase or diminish the angle 10' or 20' and read again.
TIME BY TRANSIT. 177
Take a series of readings in this way and compute the mean of
the distances, and the mean of the times.
The altitude of S must also be determined either from simultan-
eous measurement by another observer, or from measurement of
the altitude before and after, from which the true altitude may be
found by interpolation. The altitude may also be found from the
ZPS triangle in which we have given ZP, PS and ZPS. Call D
the point where a perpendicular from S meets PZ, then tang
PD = cos ZPS tang PS, cos DZ = cos PD cos 8Z sec PS, and
PZ = PD i ZJ). This must be corrected for refraction so as to
give the apparent altitude. Again, compute the azimuth PZS by
the proportion, sin ZS : sin P/S = sin ZPS : sin PZS. Measure
the altitude of or 90 OZ, and in the triangle OZS we have
given the three sides OZ, OS, and ZS; from these compute OZS
as in Experiment 175. Adding OZS to PZS gives the required
azimuth PZO.
The azimuth of any other terrestrial object, O, is found directly
from that of 0, by measuring 00' and the altitudes of and O r ,
we then have the three sides of the triangle OZO and can, hence,
readily compute the angle at Z, as above. In selecting S and 0,
we must take care that the angle SOZis not too nearly or 180
as, otherwise, a slight error in /SO may make a large error in the
azimuth.
To determine the direction of the meridian subtract PZO from
180, and set the sextant at this angle. Then move a meridian
mark until its image 0" is brought to coincide with that of 0. If
and O" are not in the horizon, the angle between them must be
computed from the spherical triangle 00" Z.
178. TIME BY TRANSIT.
Apparatus. A portable transit instrument, a chronometer, and
a vessel of mercury. If the transit is mounted permanently, two
collimators are convenient, though not essential ; a surveyor's tran-
sit may be used in this and the three following Experiments, if
great accuracy is not required.
Experiment. The most important instrument in an Astronomi-
cal Observatory, as far as measurements of precision are concerned,
is the transit. This consists of a telescope mounted so that it is
12
178 TIME BY TRANSIT.
free to revolve in the plane of the meridian. Its axis, which con-
sists of two cones to ensure stiffness, terminates in carefully turned
cylindrical steel pivots which rest in metallic Vs, resting on sub-
stantial stone or iron piers. To adjust the position of the axis,
one Fmay be raised or lowered, and the other moved horizontally
by screws. In large instruments most of the weight is taken off
the pivots by levers and countei-poises. The observation consists
in noting the time at which various celestial objects transit, or
cross the spider-lines placed in the focus. Generally five or seven
vertical equidistant wires are used, and one horizontal wire. A
thread, movable by a screw forming a spider-line micrometer is
also inserted in the focus, and may be parallel to either the verti-
cal or horizontal wires, according to the use to which it is to be ap-
plied. To level the axis, a delicate spirit-level terminating in Vs
may be laid across from one pivot to the other. To point the tel-
escope at any desired altitude, a small graduated circle is attached
either to the axis of the instrument or to the eye end of the tele-
scope. The angle in the latter case is read by an index and ver-
nier with a level, attached. The vernier is set to the required
angle, and the telescope then inclined until the bubble of the level
is brought to the middle of the tube.
At night the cross-hairs will not be visible on account of the
darkness of the sky ; some method of illumination must therefore
be employed, of which the simplest is to place a lamp nearly in
line with the telescope, but a little to one side so that its light
shall not fall directly into the field. The latter is thus illumi-
nated so that the wires appear dark on a light back ground. A
better and more common method of illumination is to place an
inclined plate of metal in front of the telescope so as to reflect
the light down the tube, and to perforate it so that it shall not cut
off the light passing directly into the telescope. In larger instru-
ments, a hole is cut in the tube of the telescope, or the axis is per-
forated and the light thus admitted, the metallic plate being
placed inside. For faint objects a glass plate is inserted in one
side of the eyepiece, and the light allowed to shine directly on the
wires, which thus appear bright on a dark ground.
Place the instrument approximately in the meridian where there
is a clear view to the north and south, focus the eyepiece on the
TIME BY TRANSIT. 179
cross-hairs and then turning the telescope towards a star, move the
eyepiece and cross-hairs together until a distinct image is formed.
This must be done with care, until, when the horizontal cross-hair
is brought over a star, the latter will remain bisected when the
eye is moved up and down.
Next, level the axis by placing the spirit-level astride from one V
to the other, and turn the screws, altering the height of the V,
until the bubble is in the centre, that is, until the reading of both
ends of the bubble is the same. Then reverse the level end for
end, and, if the bubble remains in the centre, the adjustment is
correct, if not, alter the screws of the level until the bubble is
brought half way back, and the screw of the transit V until the
bubble returns to the centre. Reverse again, and repeat until the
adjustment is exact. The level does not now necessarily lie in
the same vertical plane as the axis of the transit, and this should
next be tested by swinging the level backward and forward so
that its Vs will slide over the pivots. If the bubble moves, the
level must be adjusted by the screws by which one end is moved
laterally. It is important to know the angular magnitude of the
divisions of the level. For this purpose it is laid on a long rod,
one end of which may be raised or lowered by a micrometer-
screw, and the other rests on two points at right angles to its
length. Bring the bubble first to one end and then to the other
of the graduation of the tube, and read the position of the screw
in each case. Take the mean of the two ends of the bubble, and
call the change in position, in divisions, n. Call a the change in
reading of the micrometer-screw, and I its perpendicular distance
from the line connecting the two points. Care must be taken to
measure both a and I in the same unit, as the centimetre or inch.
If s is the number of seconds corresponding to each division of the
level, since the length of the radius in seconds is 206265, we must
have the proportion, I : a = 206265 : ns. A simple method of
measuring the divisions of a level is to lay it on a straight-edge
set on edge, and raise either end by inserting under it a wire
whose diameter is then measured by a sheet-metal gauge.
If the level is not very sensitive, its form is readily investigated
by attaching it to a telescope with cross-hairs, and directing the
latter towards a distant vertical scale of equal* parts. The tele-
180 TIME BY TRANSIT.
scope is then inclined so that the bubble shall rest in different
parts of the tube, and a curve constructed with the scale-readings
of the cross-hairs as ordinates and the positions of the centre of
the bubble as abscissas. If the scale is of millimetres and is dis-
tant 20.6265 metres from the object-glass of the telescope, each
division will equal 10". For other distances the readings may be
reduced to seconds by a simple proportion. Instead of the scale,
the telescope may be directed towards any distant object, and its
angular position as the bubble is moved along the tube, measured
by a spider-line micrometer.
The cross-hairs should be exactly vertical, and this is effected
by turning the ring carrying them until when a distant object is
covered by one, it will remain covered, as the telescope is raised
or lowered. The horizontal wire may also 'be tested when the
instrument is completely adjusted, by seeing if a star near the
equator, when bisected by the horizontal wire, neither appears
above or below it, as, by the diurnal motion, it moves slowly across
the field.
The next adjustment is to bring the central cross-hair into the
plane perpendicular to the axis, otherwise, it will describe a small
circle parallel to the meridian. This is called the collimation ad-
justment. Point the telescope towards any terrestrial object at
least a mile distant, so that its focus shall be the same as that of a
star, and note the exact point covered by the central hair. Then
reverse the telescope, by raising it out of its Vs and turning its
axis end for end. Point the telescope in the same direction as
before and see if the central hair coincides with its former position.
If not, move the ring carrying the cross-hairs, sideways over half
this distance, and repeat until the adjustment is exact. As it often
is not convenient to use a distant terrestrial object, a vessel of
mercury may instead be placed under the telescope and the latter
pointed down vertically towards it. A collimating eyepiece is
now employed in which light is thrown down the tube of the tele-
scope through a hole in the side of the eyepiece by a mirror inside.
A simple substitute for this is to gum a little piece of mica or
glass to the eyepiece so as to reflect the light of a lamp down the
tube. On looking through the telescope an image of the cross-
hairs will be seen reflected in the mercury, and coinciding with
TIME BY TRANSIT. 181
the hairs themselves if the adjustment is exact. Since the mer-
cury surface is always perfectly level, this adjustment, if the tran-
sit is reversed, serves also to show whether the axis is horizontal.
The transit is brought nearly into the meridian, by pointing it
towards the pole star at its culmination. This is shown by its
right ascension, the longitude and the time as given by a common
watch ; or more roughly, by noticing when the star C Ursce ]\fa-
joris, in the middle of the handle of the Dipper, lies in the same
vertical plane as the pole star. A slight deviation from the meri-
dian will be quite imperceptible for stars near the zenith, and the
transit of a zenith star may therefore now be observed with preci-
sion. Wait until some known star culminates near the zenith and
pointing the telescope towards it, count seconds with the clock or
chronometer as the star approaches the first thread. Note men-
tally the position at the beginning of the second preceding and that
following its transit and divide the interval into tenths by the eye.
This gives the time to tenths of a second. Do the same with the
other threads and take their mean. The difference between this
time and the star's right ascension gives the error of the clock
which should be set to the nearest minute. Next, observe the
transit of the pole star and as the time approaches, as given by
the clock, move the transit horizontally by the screws, moving one
of the Vs so as to follow the star until the time is the same as its
right ascension.
Before preceding further, we must determine the relative posi-
tions and distances apart of the threads or vertical cross-hairs.
Since a star crosses the meridian but once in twelve hours, to in-
crease the number of observations, several threads are used, and
the time of transit over each observed. Instead of reducing them
to the middle thread, an imaginary thread called the mean thread
is used, corresponding in position with the mean of the real
threads, and, therefore, very nearly coinciding with the central
thread. To measure the position of the threads, observe the time
of transit of a star over each, and the mean of all gives the time
of transit over the mean thread. Subtract from each of the transits
that of the mean thread, and divide the differences by the cosine of
the star's declination. This is to reduce the interval to that which
it would be if the star was on the equator, and is called the equato-
182 TIME BY TRANSIT.
rial interval of the thread. The best results are obtained with a
star near the pole, since, in this case, the intervals become large,
and hence may be measured more accurately, but in this case a
correction must be applied for the curvature of the path. This is
readily done by dividing the sine of the observed interval by the
cosine of the declination, which will give the sine of the required
equatorial interval. If in any case we fail to obtain transits over
all the wires, the mean of the observations may be obtained and
corrected by subtracting from this mean the equatorial intervals
of the wires used, divided by the cosine of the declination.
Owing to unequal expansion by changes of temperature and to
other causes, it is impossible to keep a transit in perfect adjust-
ment. It is therefore found to be better to adjust it once as nearly
as possible, and afterwards measure its deviations and apply cor-
rections. These are three in number, for azimuth, for level, and for
collimation. The correction for azimuth may be found by observ-
ing the transit of the pole star at its upper and lower culmination.
If the transit is precisely in the meridian, the difference in time
should be exactly twelve hours. If the time differs from this by
an amount d it may be shown that the deviation in azimuth a =
%d sec L cot D, in which L equals the latitude, and D the decli-
nation of the pole star. A second method is to observe the transit
of two stars differing considerably in declination, when the differ-
ence in time should equal the difference in right ascension. Calling
cos J) cos jy
d, as before, the error in time, a = d cos s [ n (jy_ j)y One of
the stars should be near the pole, the other at some distance from
it, and it is more convenient to select two stars differing but little
in right ascension ; 51 Cephei and 8 Ursce Minoris are well
adapted to this purpose, only, in this case, as they culminate on
opposite sides of the pole, we must give D a negative sign in the
above formula, so that we shall have in the denominator D' -|- U
instead of D' D.
The error in level is found by observing the bubble of the spirit-
level in its two positions, when turned end for end ; multiplying
the mean deviation from the centre by the value of one division,
gives the angular deviation b, in seconds.
TIME BY TRANSIT. 183
Reverse the telescope and repeat, and if a different result is at-
tained, it shows that the two pivots are unequal, the error equal-
ling one half the difference in the readings. As the pivots may be
irregular in shape, readings of the level should be taken with the
telescope turned 10 at a time on each side of the zenith ; a cor-
rection may then be applied for any given position of the tele-
scope.
The error in collimation may be found directly with the spider-
line micrometer, first measuring the angular magnitude for one
turn of the screw as described in Experiment 180. Direct the
telescope towards any well defined object and measure its distance
from the central thread ; then reverse the telescope, and measure
again. The difference will equal twice the error of collimation.
A more accurate method is to observe the transit of the pole star
over two of the wires, then reverse the telescope and observe the
transit over the same two wires, which will now be on the other
side of the field. Reduce each to the mean thread, when the re-
sults will differ by twice the error. Multiplying this by the cosine
of the declination, gives c. Another method is to direct the tele-
scope towards its reflection in the vessel of mercury. Bring the
movable wire to coincide with its reflection, or with that of the
central thread and divide by two, and the distance from the cen-
tral thread, correcting for level, gives c. The error in level may
also be found by reversing the transit, when in one case the inter-
val between the thread and its image will equal the sum, and in
the other the difference of the errors of collimation and level. If
the pivots are unequal, the error must be determined by the level,
and a correction be applied. If the movable thread is parallel to the
horizontal wire a measurement may still be made by forming a
small square by the vertical thread, its reflection, the horizontal
thread and the movable thread, as a slight deviation from equality
in the sides is readily detected by the eye. If collimators are pro-
vided, their cross-hairs are used like the distant object in the first
method. Two are employed to avoid reversing the telescope.
Their cross-hairs are brought to coincide, after removing the tran-
sit telescope. To avoid the difficulty of superposing two vertical
hairs, one collimator may have two parallel threads very near to-
gether, the other, two threads inclined at an angle.
184 LATITUDE BY TRANSIT.
Having thus found the values of a, b and c, we may determine
the right ascension R.A. of any body by the following formula, in
which Tia the time as given by the clock, E the error of the lat-
ter, L the latitude of the place of observation, Z the zenith dis-
tance of the object observed, and D its declination. Z is readily
obtained from the latitude and declination,
M.A. = T -}- E -}- a sin Z sec D -\- b cos Z sec D -\- c sec D.
To adjust the finding circle, set the telescope vertical, by view-
ing its reflection in the mercury surface, set the index at the lati-
tude of the place and move the level of the finder by the adjusting
screws until the bubble is in the middle. The index will then
mark the declination of any object to which the telescope is
pointed. If we wish to have the finder give zenith distances, the
index should be clamped at instead of at the latitude. If pre-
ferred, the telescope may be pointed towards any star whose dec-
lination is known, and the finder set to correspond, after correcting
for refraction.
To find the time by the transit instrument it is only necessary
to observe the transit of any known star, preferably one not too
near the pole, and the mean of all the wires, after applying the
above corrections, gives the sidereal time. The difference between
this and the time as given by the clock gives its error. This
should be determined frequently, and the error and rate thus
deduced. The mean time may be deduced from the sidereal time
and the sun's right ascension, or it may be observed at noon by
observing the transits of both edges of the sun. Correcting this
by the amount that the sun is slow or fast, as given in the Nauti-
cal Almanac, gives the mean time directly.
179. LATITUDE BY TRANSIT.
Apparatus. A transit instrument which may be set with its
axis north and south, and a clock giving sidereal time.
Experiment. One of the best methods of determining the lati-
tude of a place is by a transit set in the prime vertical, that is, in a
vertical plane at right angles to the meridian, or with its axis
north and south. To adjust it in this position, after setting the
axis nearly north and south, it is levelled and the central cross-
LATITUDE BY TRANSIT. 185
hair brought into the plane of collimation as in the last Experi-
ment. It is then brought into the proper azimuth by observing
the transit of a star near the horizon, that is, one whose declina-
tion is small. The time of transit is first computed by the tri-
angle ZPS formed by the zenith, star and pole, in which the angle
at Z equals 90, ZP equals 90 Z, where L is the approximate
latitude, and PS equals 90 D, or the star's north polar distance.
The hour angle ZPS or II, is given by the formula, cos H=
tang D cot Z, and subtracting or adding this to the star's right
ascension, according as the observation is towards the west or east,
gives the sidereal time of transit of the star. At this instant
bring the middle, cross-hair to coincide with the star, and if the
other adjustments have not been disturbed the instrument will be
in position. Generally the axis will be no longer horizontal, and
it is therefore necessary to repeat with a second star. If the tele-
scope has a horizontal circle like an altitude and azimuth instru-
ment, it is most easily adjusted by placing it in the meridian and
then turning it exactly 90. To find the latitude it is now only
necessary to observe the two transits of a star which culminates a
little south of the zenith, and calling one half of this time, or the
hour angle, H, we have in the ZPS triangle, PZS 90, P/S
90 D and ZPS = H, whence we deduce the latitude L =
90 PZby the equation tang L tang D sec H. The advan-
tage of this method is that, if the star culminates near the zenith,
a small error in If will make an almost imperceptible error in the
latitude. If the only error of adjustment is that the axis is not
horizontal, a correction is simply applied by adding to the latitude
the inclination, if the north end is highest, and subtracting it, if
lowest. The error in azimuth is found by observing the east and
west transits of the same star, not too near the zenith, and the
mean of the two times, after correcting for error of the clock,
minus the right ascension of the star, equals the error in azimuth
a. To correct for this error, we must multiply the second mem-
ber of the equation given above by cos a, or write tang L
tang D sec IT cos a. If the telescope is reversed, the values of the
latitude will in one case be too great and in the other too small by
an amount equal to the error of collimation. Hence, if the same
star is observed on two successive nights with the telescope re-
186 TRANSIT CIRCLE.
versed, the mean result will eliminate this error. The latitude
may be determined from two stars observed on the same night with
the telescope in reversed positions, if their declinations are known
with precision. Of course in practice a large number of stars
should be observed, and the mean result employed, as no single
observation should ever be relied upon.
180. TRANSIT CIRCLE.
Apparatus. A transit circle, clock, and vessel of mercury.
Experiment. A transit circle consists of an transit instrument
to which is attached a large, finely graduated, vertical circle. Two
or more reading microscopes serve to read the position of the cir-
cle, and to show the altitude of the object to which the telescope
is pointed. Each microscope contains a spider-line micrometer,
and the distance of their objectives from the spider-lines and from
the graduated limb should be such that one revolution of the
screws shall equal one minute. If the head is divided into sixty
parts the reading may be made to single seconds, or by estimation,
to tenths of a second. As it is difficult to keep the microscopes
at precisely the right distances, the magnitude of one division of
the circle should be measured by each micrometer occasionally,
and the readings corrected if necessary. The eccentricity should
also be examined as explained in Vol. I, Experiment 7.
A number of parallel vertical threads, a fixed horizontal thread,
and three equidistant horizontal threads moved by a screw and
forming a spider-line micrometer are inserted in the eye end of
the telescope. We must now determine with precision the
angular magnitude of one turn of the screw. This may be done
in several ways ; first, by measuring the distance from the optical
centre of the lens, or its focal distance F, and the pitch of the
screwy in centimetres or inches; then a = Jf 206265, in which a
is the required angular magnitude in seconds. Secondly, measure
any known angular magnitude, as the diameter of the sun, and
divide the diameter, as given in the Nautical Almanac, by the
number of turns. Thirdly, turn the threads around 90 so that
they shall coincide with the meridian, and note the time of transit
TRANSIT CIRCLE. 187
of a star over them when they are moved across the field by a
known amount. If the screw has been turned n times and the
star has a declination D and occupies a time t in traversing this
distance, we must have na = t cos D. The best results are ob-
tained with the pole star, in which case, owing to the curvature of
its path, we must write sin na = t cos D. Irregularities in the
screw may thus be detected. Again, the telescope may be directed
towards any well defined distant terrestrial object, the latter bi-
sected by the cross-hairs, and the reading of the circle and of the
micrometer observed. Move the telescope slightly and again
bring the cross-hairs to coincide with the object, when the change
in reading of the circle and micrometer serves to compare them;
the cross-hairs of a collimator form an excellent object in this case.
Finally, the telescope may be directed toward a theodolite and the
angular distance corresponding to n turns of the screw measured
directly.
The instrument is first adjusted precisely like a transit, and may,
in fact be used like it to determine time and right ascensions. In
determining the error of collimation, the movable thread is
brought into such a position as to form a square with the central
vertical thread, its reflection and the fixed horizontal thread.
Then move the thread over its reflection, so as again to form a
perfect square, when the distance it has been moved will equal
twice the interval between the vertical thread and its image, or
four times the error in collimation. Since the square should al-
ways be very small, its sides may be rendered equal by the eye
with great precision.
The zero point of the circle must next be found by setting the
micrometer at zero, and moving the telescope until the thread
coincides with its reflection in the vessel of mercury placed be-
neath it. The reading of the circle then gives the position of the
nadir or point 180 distant from the zenith. The horizontal points
may also be determined by observing a star and its reflection in a
vessel of mercury, and bisecting the angle between them. Unless
the star is near the pole, its motion will be too rapid to enable the
circle to be read during its transit across the field of view. The
circle should therefore be set approximately in the right position
and read beforehand, and the star as soon as it appears, bisected
188 TRANSIT CIRCLE.
and the micrometer read two or three times. The telescope is
then directed towards the image in the mercury, clamped, and the
micrometer again read after turning it on the star. The second
position'of the circle may then be read at leisure. If a spirit-level
finder is attached to the telescope, still more time may be saved
by setting it beforehand so that the telescope can be set by sim-
ply turning it until the bubble moves from end to end. The
. mean of the readings of the star and its reflection gives the hor-
izontal point of the instrument, and should differ by 90 from the
nadir found above.
The advantage of this method is, that by using different stars,
we can obtain various independent determinations of the zero
point.
The apparent altitude of any star when on the meridian is' de-
termined directly from the graduated circle and micrometer. The
circle may be set so that the star shall transit across the field of
the telescope, damped, and the circle read by the microscopes.
When the star enters the field it is bisected by the micrometer
wire and several readings taken. From the mean of these, the
reading of the circle and the magnitude of the micrometer divi-
sions, we deduce the corrected reading of the circle, and subtract-
ing from this the zero point as found above, we obtain the apparent
altitude. The true altitude equals the apparent altitude minus
the refraction, and in this case the simple formula r = 57" tang
(Z 3r) given in Experiment 174, is not sufficiently exact.
Recourse must therefore be had to Tables, of which those of
Bessel agree best with observation. These are based on the for-
mula, r =. ab m c 71 cot A, in which r is the refraction, and A the
apparent altitude ; a, m, and n vary slowly with A and their values
are accordingly given in a table with A as an argument ; b de-
pends on the pressure of the air, and is equal to the product of two
factors, one dependent on the height of the mercury column, the
other on its temperature ; finally, c depends on the temperature of
the air.
The latitude is readily found by this instrument by observing
the altitude of any star at its upper and lower culmination. Evi-
dently the first will equal the sum, and the second the difference
of the altitude of the pole or the latitude, and the north polar
ZENITH TELESCOPE. 189
distance. The mean of the two altitudes will therefore give the
latitude, and this method has the advantage that it is wholly inde-
pendent of all previous determinations of the position of the star,
depending only on the accurate graduation and adjustment of
the instrument. The principal use of the transit circle is, however,
the measurement of the exact position of the stars. Their right
ascensions are found from the times of transit, as with the transit
instrument, and their declinations from the latitude and altitudes.
The fixed stars, if carefully observed, will be found, their name
notwithstanding, constantly changing their position. These mo-
tions are due in part to changes in position of the axis of the
earth (precession and nutation), and to the velocity of light (aber-
ation), also partly to their real motions with regard to the sun, or
their proper motion. The position of two hundred of the bright-
est stars is given for every ten days in the Nautical Almanac.
For the others, a star catalogue must be consulted, which gives
not only their right ascensions and declinations at a given time or
epoch, but also for each star certain constants for computing their
position at any future time. Let t be the time expressed deci-
mally in years after that for which the catalogue is computed, k
the correction to be applied to the given right ascension, and W the
correction in declination ; p and p' the proper motion in right
ascension and declination, and a, b, c, <?, and a', >', c', <?', con-
stants dependent on the position of the star, given by their loga-
rithms in the catalogue. -4, B, (7, D and E are constants de-
pendent on the time, and are given in the Nautical Almanac. E
can generally be neglected, as it never exceeds .05". Then the
values of k 1 and k may be computed by the formulas,
K = tp' + Aa! + BV + Cc' + Dd', and
k = tp + Aa + Bb + Cc + Dd + E.
If a, , c, etc., are not given, they may be computed trigonomet-
rically, or the change in position determined from six other so-
called independent constants.
181. ZENITH TELESCOPE.
Apparatus. A zenith telescope, or, if this is not available, a
transit, or an altitude and azimuth instrument may be used, if a
micrometer and sensitive level are attached, as described below.
190 ZENITH TELESCOPE.
Experiment. A zenith telescope consists of a telescope mounted
so that it can turn either around a horizontal or a vertical axis and
supported on a tripod with levelling screws. A very delicate
level is attached to the telescope, and may be turned around an
axis coinciding with, or parallel to, the horizontal axis of the in-
strument. A small graduated circle is commonly attached, like
the finder of the transit instrument, to show the angle between the
level and telescope, or the inclination of the latter. The eyepiece
has a spider-line micrometer like that of the transit circle, and
some fixed equidistant vertical hairs are also usually added for
observing transits. Two stops are commonly attached to the hor-
izontal circle so that the instrument can be turned in azimuth just
180.
This instrument is intended to determine the latitude, which
can thus be obtained with an accuracy at least equal to that of any
other method. Two stars are selected differing but little in right
ascension so that they shall culminate within a few minutes of
each other, and with declinations such that they shall culminate,
one north and the other south of the zenith by nearly equal
angles, that is, so that the mean of their declinations shall nearly
equal the assumed latitude of the place. Having selected several
suitable pairs of stars, the instrument is placed with one of its legs
to the north and the other two east and west. The level attached
to the stand is now placed east and west, and the bubble brought
to the centre, then turned north and south, and again levelled by
the north screw, and this operation repeated until the bubble re-
mains in the centre, while the telescope is turned completely
around. If there is no level, except that attached to the telescope,
it is set so that, when levelled and turned horizontally 180, the
bubble will remain nearly in the middle. The level is now per-
pendicular to the vertical axis and the instrument may be ad-
justed as before. The magnitude of the divisions of the level and
of the micrometer must next be determined in angular measure,
and the telescope then brought nearly into the meridian by turning
it towards any known star, and bringing the central vertical cross-
hair to coincide with it at the computed time of transit. The
stops are set on the horizontal circle so that the telescope may be
quickly set in the meridian, and the finding circle set to one half
ZENITH TELESCOPE. 191
the difference of the declination of the first two stars to be ob-
served. The telescope is then turned to the north or south ac-
cording to which star culminates first, and, as the star approaches
the meridian, the telescope directed towards it. The level is then
clamped to the telescope, the bubble is brought nearly to the
centre and the reading of each end taken. The micrometer wire
is now made to cover the star and bisect it at the instant of transit
as given by the clock. Or, if this is missed, to bisect it at a known
time after transit. The micrometer reading is then taken and the
telescope turned 180. When the second star enters the field,
the micrometer wire is brought over it and a second bisection
made at the instant of transit. The position of the ends of the
bubble of the level is also taken. It may be remarked that while
it will not do to alter the angle between the telescope and level
during the observation, there is no objection to moving both to-
gether, if the vertical axis of the instrument is not properly ad-
justed. If then, on reversing the telescope, the bubble moves to
the end of the tube, it may be brought back by moving the tele-
scope. The difference in altitude of the two stars will now equal
the difference in the micrometer readings, after adding or subtract-
ing the error of level. Calling D the mean of the declinations of
the two stars, a their difference in altitude, the latitude L = D 4=
% a, using the plus sign if the altitude of the northern star is great-
est, and the negative sign if it is the least.
The great advantage of this method is that it is so free from
almost all instrumental errors, and depends only on the rigid con-
nection of the telescope and level, and on the correctness of the
micrometer screw. It is also, in a great measure, independent of
refraction, since both stars, having about the same altitude,
are affected nearly alike. To still further reduce this error, stars
should always be selected culminating within 25 of the zenith.
Evidently, any error in the position of the stars will affect the lat-
itude, and it is therefore essential to use a number of pairs of stars,
selecting by preference the brighter ones, since the position of
these is more accurately known.
Since the measurement depends wholly on the rigid connection
of the telescope and level, evidently a transit, or altitude and
azimuth instrument may be used almost precisely like a zenith tel-
192 ALTITUDE AND AZIMUTH INSTRUMENT.
escope, and nearly the same directions apply to all. It is only nec-
cessary that a delicate level should be attached to the finding cir-
cle, or otherwise connected with the telescope, so that it can be
set 'at any angle.
182. ALTITUDE AND AZIMUTH INSTRUMENT.
Apparatus. An altitude and azimuth instrument, or a survey-
or's transit, a chronometer and an artificial horizon.
'Experiment. An altitude and azimuth instrument or an altazi-
muth, resembles a surveyor's transit enlarged, and is used to meas-
ure simultaneously both horizontal and vertical angles. It is not
much used in Observatories, as it is difficult to attain as accurate
results with it, as with the simpler instruments, each additional
complication being a new source of error. It has, however, been
used for special purposes, as for studying the refraction, and for
observing the moon when not on the meridian. In the field, on
the other hand, the observer is much more likely to be able to
procure a surveyor's transit than any astronomical instrument, and
it seems therefore desirable to show how the latitude and time
may be determined by it.
The instrument, if large, is mounted on three legs with level-
ling screws resting on a point, line and plane as described in Vol.
I, Experiment 77. One leg is turned to the north, the other two
east and west, and the instrument is levelled as described in the
last Experiment. Smaller instruments, such as are used by 8mv
veyors, are supported on tripods and are levelled by four screws.
The horizontal circular plate is turned until one of the levels is
parallel to two of the screws, diagonally opposite each other, and
the bubble brought to the centre by turning them in opposite di-
rections, i.e., turning both thumbs in, or both out. The other
screws are then turned until the other level is horizontal. By a
little practice the screws will be turned together so that the in-
strument shall be neither loose nor wedged too tightly. Before
using the instrument it should be carefully adjusted as follows.
First, see that the plane of the levels is perpendicular to the axis
of the instrument. Clamp the plate carrying the graduated cir-
cle, and, after levelling the instrument as directed above, turn the
ALTITUDE AND AZIMUTH INSTRUMENT. 193
upper plate carrying the cross-hairs 180, and see if the bubbles
remain in the centre of the tubes. If not, turn the screws sup-
porting the levels so as to bring the bubble half way back, level
the instrument again, reverse it, and repeat until the bubble re-
mains in the centre in every position of the plate. Now clamp
the upper plate and turn the plate carrying the graduated circle.
If the bubble now moves from side to side, the axes of the two
plates do not coincide, a defect not easily remedied. If however,
the instrument is used as described below, keeping the lower plate
clamped, no error is introduced by this deviation of the two axes.
The telescope may now be adjusted for level, collimation and azi-
muth like a transit. In making the last adjustment, or bringing it
into the meridian, the vernier should be set at zero, the lower
plate tightly clamped, and the adjustment effected by its tangent
screw. The time may now be found at night by observing the
transit of any known star, or at noon by observing the transit of
both limbs of the sun as described in Experiment 178. Turning
the instrument so that the vernier shall be at 90, the telescope
will be in the prime vertical and the latitude may be determined
as in Experiment 179. By making the proper adjustments the
altzimuth may also be used as a transit circle as described in Ex-
periment 180, though in this case a spider-line micrometer should
be inserted in the eye-piece. By adding a sufficiently delicate
level to the vertical circle, it may be used as a zenith telescope,
Experiment 181. From these varied uses the altazimuth is some-
times called the universal instrument.
Altitudes and azimuths may now be observed directly, the for-
mer by the vertical, and the latter by the hoiizontal circle. An
interesting application of this instrument is to finding a star in the
day time. The altitude and azimuth are first computed in ad-
vance allowing time for the accurate adjustment of the instru-
ment. In the ZP8 triangle, PZ = 90 L, the co-latitude,
PS = 90 Z>, or the star's north polar distance, and ZPS = H
its hour angle. The latter is found by subtracting the sidereal
time from the right ascension of the star. If the mean solar time
only is given, it must be reduced to sidereal time as in Experi-
ment 174. PZ, or the zenith distance, and the azimuth PZS are
then computed as in Experiment 177, and the former corrected for
194 ALTITUDE AND AZIMUTH INSTRUMENT. <
refraction. Set the telescope to this altitude and azimuth, and on
looking through it at the proper time, the star should be seen at
the intersection of the cross-hairs. Move the telescope if necces-
sary, so as to bisect it at the given instant and reading the alti-
tude and azimuth, determine the error. The star most readily
seen in the day time is the planet Venus, if not too near the sun.
Its position must be determined from the Nautical Almanac, and
corrected for parallax. By looking along the telescope, so as to
obtain the right direction, it can often be seen by the naked eye.
Of the fixed stars, of course Sirius, as the brightest, is most easily
found ; but when the sky is dark blue any first magnitude star is
readily seen with a common surveyor's transit.
It frequently happens, when portable instruments are used, that
great accuracy is not needed, and that the time is limited. In
this case the direction of the meridian may be determined by a
single observation of any known star, since in the ZPS triangle
we have given ZP, PS and ZPS. "We can therefore compute
PZS, and turning the telescope horizontally through this angle
brings it into the meridian. The star best suited to this observa-
tion is the pole star, and, if the hour-angle is about six hours, a
slight error in the clock will not introduce any appreciable error
in the result. The meridian may also be determined, without ob-
serving the time, by setting the telescope on any star, observ-
ing the horizontal angle, and when the star again attains the same
altitude- on the other side of the meridian, observing its azimuth
again. The mean of the two azimuths gives the direction of the
meridian. This method may be applied in the day time to the
sun, if we correct for its change in right ascension, but it is gener-
ally better to observe the position of the sun at noon by comput-
ing the time when the westerly limb will cross the meridian, and
bringing the telescope to coincide with it, The result may be ver-
ified by observing the transit of the other limb of the sun.
The latitude may also be determined by an altazimuth precisely
as with a sextant, from the altitude of the pole star, or of the sun
at noon.
After finding the direction of the meridian it is well to measure
the azimuth of some distant terrestrial object so that the meridian
can be again determined from it at any time. A more convenient
LONGITUDE. 195
method, in some cases, is to fasten a plane glass mirror to the wall,
and placing the instrument opposite it, turn it until its cross-hairs
coincide with their reflection. This gives the angle between the
normal to the mirror and the meridian.
183. LONGITUDE.
Apparatus. A transit and chronometer at the two points
whose longitude is to be compared. A telegraph connecting
them and a chronograph is also desirable, though not essential.
Experiment. The correct determination of the longitude is a
matter of much greater difficulty then the corresponding measure-
ment of the latitude. By the longitude of a place is meant the
angle between its meridian and that of some other place assumed
as a starting point, for which the Observatory at Greenwich is
commonly employed. To determine the difference of longitude
of two stations, it is only necessary to observe the time of occur-
rence of the same event at each, when the difference in the times
will equal the difference in the longitude. For short distances we
may use the flash of a cannon, the explosion of a rocket, or other
similar effect, but generally in such cases the difference in longi-
tude can be much more accurately determined trigonometrically.
For more distant places we require some event visible over a large
part of the earth, and must seek for this among the heavenly
bodies. The entrance of the moon into the shadow of the earth
during a lunar eclipse would satisfy these conditions, biit unfortu-
nately, owing to the refraction of the earth's atmosphere and the
penumbra caused by the large angular dimensions of the sun, this
effect is not sharply defined, so that its exact time cannot be ob-
served. The motions of Jupiter's satellites are better adapted to
the purpose and may be observed with any telescope of moderate
power. The phenomena to be observed consist of the eclipses, or
passages of the satellites into the shadow of the planet, transits or
passages of the shadows of the satellites across the face of the
planet, and occultations, or disappearances of the satellites behind
the planet. The necessity of a telescope, however, precludes then-
observation at sea, and unfortunately the times are not suffi-
ciently instantaneous for accurate observation. They differ more-
196 LONGITUDE.
over, as seen with telescopes of different sizes and poweis. Ap-
proximate results may, however, be attained by merely subtracting
the observed local time from that given in the Nautical Almanac.
From the ease of the observation and calculation, this method,
is sometimes valuable to travellers.
The longitude may be determined with precision from the in-
stants of contact during eclipses of the sun, from transits of Mer-
cury or Venus, or from the instant of occultation of stars by the
moon, but the rarity of these events and the difficulty of the com-
putation involved, render it undesirable to discuss them here.
The motion of the moon in right ascension is so rapid that it
may be used to determine the longitude. Its time of transit and
that of some known star are observed, and the time at which its
right ascension at Greenwich would have been the same, is then
determined by interpolation from the Nautical Almanac. The
great objection to this method is that an error in the position of
the moon as computed or as observed is increased about twenty-
seven times in the final result. Hence it is impossible by this
method to obtain the longitude nearer then within about one sec-
ond, however frequently the observations are repeated.
A better method of determining the longitude, and the one
generally employed until within a few years, is by the transporta-
tion of chronometers. If, at the first station, we observe the transit
of several stars by means of a chronometer giving sidereal time,
we obtain its error directly by subtracting their right ascension.
If this is repeated on several days we obtain its rate. Now carry
the chronometer to the second station whose difference of longi-
tude is to be determined, and observe the transit of the same stars
there. Evidently the difference in time of the chronometer, after
allowing for its changed error, will equal the longitude. To avoid
accidental errors and the change in rate when the chronometer is
carried from one point to the other, it should be sent back and forth
m several times, or better, the comparison should be made by several
chronometers. Generally, instead of observing the transits di-
rectly by the chronometer it is compared at each station with the
observatory clock and the longitude thus determined, after allow-
ing for the errors. To compare a chronometer with a clock or
with another chronometer, the minutes and seconds are read off
EQUATORIAL TELESCOPE. 197
directly, and the fraction of a second between their ticks esti-
mated. If the chronometers have very different rates, or better,
if one gives sidereal and the other solar time, the difference can
be determined with much greater accuracy. Since 367 sidereal
seconds equal very nearly 366 solar seconds, it follows that in every
3 in. 3 s., the solar chronometer will gain half a second or one beat
on the other. Accordingly every three minutes their ticks will
coincide, and, observing by the ear their time of coincidence, the
difference between them may be determined within about .05 of a
second.
The best method of determining the longitude is, however, by
means of the electric telegraph and chronograph as described in
Vol. I, p. 17. The principal error in this case is the personal equa-
tion of the observers, or interval between the instant of transit of
the star and the depression of the finger key. To eliminate it,
the observers should change places, or determine their personal
equations directly. The absolute personal equation may be found
by observing the transit of an artificial star which records its cor-
rect time of transit automatically on the chronograph. The dif-
ference between the observed and true times equals the personal
equation. The difference in personal equation of two observers
may be found by letting one observe a transit over three or four
wires of a transit instrument and the other over the remaining
wires. Do this with twenty or thirty stars and reduce each to the
mean thread by multiplying the equatorial interval by the secant
of the star's declination. The difference between the mean of their
results will equal their personal equation. To avoid the difficulty
of the second observer being hurried in taking the place of the
first, which may affect his personal equation, each may observe
the clock error by several well known stars, and the difference will
equal their personal equation. The determination of the personal
equation is of even more importance in ascertaining longitudes by
chronometers, unless the same observer determines the clock error
at both stations.
184. EQUATORIAL TELESCOPE.
Apparatus. A telescope mounted equatorially with a spider-
line and position micrometer. For class purposes, and when the
198 EQUATORIAL TELESCOPE.
most perfect results are not needed, the siderostat will form a most
convenient substitute for an equatorial mounting. A sidereal
clock, a lantern, a good stellar map or globe, and Webb's Celestial
Objects, or some similar book, are also needed.
Experiment. A great difficulty in the observation of celestial
objects with large telescopes, especially with high powers, is that,
owing to the motion of the earth, they move rapidly out of the
field of the telescope. To avoid this difficulty, telescopes intended
especially to study the physical aspects of the stars are mounted
equatorially, as it is called, so that this motion is readily followed.
One axis, called the polar axis, is directed toward the pole, that is,
set in the meridian and inclined by an angle equal to the latitude
of the place. At right angles to this is placed a second axis, called
the declination axis. At one end of the latter, and at right an-
gles to it, is placed the telescope, counterpoised by a weight at
the other end. The amount that each axis turns is shown by a
graduated circle and vernier. If the telescope is directed towards
a star and slowly turned around the polar axis it will evidently
describe the same path as the star, and may be made to follow it
readily by hand. If clockwork is attached so as to make the axis
turn once in twenty-four sidereal hours, the telescope will remain
directed towards the star and will follow it indefinitely. Thus
the hour angle of the star may be read off directly from the
circle attached to the polar axis, and the north polar distance or
declination, from the circle on the declination axis. Hence there
are two positions of the telescope obtained by turning it around
each axis 180, in which it can be directed to any part of the
heavens.
To adjust the equatorial, we must first bring the polar axis into
the meridian. Set the declination axis horizontal and move the
telescope and stand until it is directed to a star at the instant of
culmination, as given by its right ascension and the clock. To
incline the polar axis by the right amount, direct the telescope to
any known star when near the meridian and read the polar dis-
tance by the declination circle. Reverse the telescope and read
again. The mean of the two readings, corrected for refraction,
gives the north polar distance, and this should be rendered the
same as the true north polar distance, by raising or lowering the
EQUATORIAL TELESCOPE. 199
axis. The difference in these readings divided by two gives the
error of the vernier of the declination circle. To find the error
in position of the vernier of the hour circle, set the telescope near
the meridian and observe the transit of any known star not too
near the pole. The difference between the hour angle as given
by the clock and that given by the hour circle, shows the error in
position of the latter. To see if the axis of the telescope is at
right angles to the declination axis, observe the transit of an equa-
torial star, reverse the telescope and observe its transit again, when
the difference between the interval as given by the clock and as
given by the hour circle equals twice the error of collimation.
To the eye end of the telescope is attached a spider-line mi-
crometer free to turn around an axis coincident with that of the
telescope, forming what is called a position micrometer. The an-
gle is measured by a graduated circle and vernier. A small tele-
scope called a finder is attached to the side of the large telescope,
and is set parallel to it. It carries cross-hairs in its focus, by
which minute objects are more readily brought into the field of
the larger instrument. To adjust the finder direct the large
telescope towards any convenient object and, bringing it to the
centre of the field, move the cross-hairs of the finder until they
cover it.
The siderostat consists of a plane silvered-glass mirror mounted
on two axes at right angles to each other, one being brought paral-
lel to the axis of the earth, like an equatorial. The telescope is
fixed parallel to the earth's axis and is directed down towards the
mirror. Evidently if the mirror is turned so as to reflect a star
into the telescope it will follow it in its motion like an equatorial.
The advantages of this instrument for certain purposes are very
great, especially where, as in the next Experiment, much apparatus
is to be attached to the eye end. As the latter is fixed, the obser-
vations may also be made much more conveniently, especially
where an object is to be shown to a class, since the observer al-
ways remains in the same position. The difficulties of a dome,
otherwise necessary, are also avoided. The objections to this ar-
rangement are the difficulty of making, and keeping, a surface
perfectly plane, the loss of light, and the inconvenience in finding
objects.
200 EQUATORIAL TELESCOPE.
To find an object when its right ascension and declination are
given, set and clamp the telescope to the proper declination by
the declination circle. Subtract the right ascension of the object
from the sidereal time, and set and clamp the hour circle to the
difference, or the hour angle. Now on looking through the finder
the object should be in the field, and may be brought by the tan-
gent screws to the intersection of the cross-hairs. It will then be
seen in the field of the larger telescope. No correction is here
made for refraction owing to which the star will appear above, or
since the telescope inverts, apparently below its predicted place.
Unless the altitude is small, however, this will give little trouble.
If the object is to be measured or observed for some time, the clock
should be started so that it may be followed continuously. This
is almost indispensable when high powers are used. Try finding
soine of the brighter stars in the day time, and see how nearly the
predicted and observed places agree. Evidently the inverse
method of pointing the telescope towards any unknown object,
reading the two circles and observing the time, furnishes an easy
means of determining its right ascension and declination after cor-
recting for refraction, but it will not compare in accuracy with the
methods of Experiment 183 and 185.
The position of an object is determined by the micrometer as
follows. Light the lamp illuminating the cross-hairs, put on a low
power eyepiece and turn the telescope so that two or three known
stars shall be in the field at the same time. Regard one of them
as unknown and measure its distance and direction from each of
the others. To determine the direction, clamp the telescope so
that it shall not be carried by the clock work and turn the microm-
eter until when the wire which is parallel to the screw is brought
over the star, the latter will remain bisected as by the earth's mo-
tion it passes out of the field. The index of the position circle
should now read zero. Connect the telescope with the clock, and
turn the wire until parallel to, or rather until it covers, both stars.
The angle through which it is moved is known as the position an-
gle. Now determine the distance of the stars as described in Vol.
I, Experiment 77. To eliminate the error due to the wires not
coinciding, when the screw is set at zero, it is well to take two
readings, one with the movable wire on each side of the fixed one,
EQUATORIAL TELESCOPE. 201
and employ their mean. The difference in declination of the two
stars will equal the reading of the micrometer, reduced to angular
interval as in Experiment 181, multiplied by the sine of the posi-
tion angle. The difference in right ascension will in like manner
equal the distance multiplied by the cosine of the mean declina-
tion of the two stars. These formulas neglect the curvatures of the
heavens between the two stars, and, if the distance is considerable,
or great accuracy is required, a more accurate value must be de-
duced by spherical trigonometry. The position of any object is
fixed by measurement from a single star, but greater accuracy is
attained by comparison with two or three. To test the work,
measure also the difference in right ascension and declination by
the following method, which has the advantage that clockwoVk
moving the telescope is not needed. Make the position angle 0,
so that the movable wire is parallel to the star's path, and, clamp-
ing the telescope a little to the west of both s'tars, observe the dif-
ference in the time of their transits over the vertical wires of the
micrometer. Move the telescope again in advance of the stars and
observe the transits a second time. The interval of the Jtime will
equal the interval of right ascension. The difference in declination
may also be found by bringing the movable wire to coincide first
with one star and then with the other, when the difference in read-
ing will give the difference in declination.
Let us now consider, in order, the principal objects to be
observed.
The Sun. To moderate the intense heat when the telescope
is turned directly towards the sun, a cap with an aperture is
sometimes placed over the object glass. The spherical and chro-
matic aberration is also thus diminished, but the aperture must
not be too far reduced, or owing to diffraction the definition will
be injured. A plate of smoked or colored glass is interposed be-
tween the eye and eye lens to cut off the light, and in this position
its irregularities do not affect the image. It will be noticed that
the centre of the sun's disk is much brighter than the edge, and
that generally a number of dark spaces, or spots, are visible. The
larger spots are surrounded by areas less bright than the sur-
rounding surface which are called penumbrce. Spaces brighter
than the disk called faculce are also commonly seen. If the sur-
202 EQUATORIAL TELESCOPE.
face is carefully examined with a good telescope, it is seen to be
covered with a multitude of objects, resembling willow leaves or
rice grains in shape. The spots are more frequent in the equato-
rial portions of the sun, or at least in latitudes 10 to 30, and if
watched from day to day will be seen to alter their shape and
gradually move from west to east owing to the sun's rotation.
During an eclipse of the sun, the principal phenomena to be
looked for are the following. Approaching disk of the moon before
contact, instant of first contact, measurement of obscured portion
of sun at known times during first few minutes after contact.
Appearance of sun's surface adjacent to moon's limb which would
be altered if any lunar atmosphere existed. Time of moon's limb
reaching any marked spots. Breadth of crescent at observed times
when most of the disk is eclipsed. If the eclipse is annular, the
time of formation and rupture of the ring should be observed, and
the appearances when the narrow line of light breaks. If the
eclipse is total, too great care cannot be taken in preparation for
its accurate observation. The colored glass should be arranged so
that it may be instantly removed, as it will not then be needed
during totality nor by the unaided eye for a few minutes before or
after. Care should be taken that the eye is not dazzled by look-
ing too much at the sun before totality, or, if the weather is cool,
that the hands do not become numb du'ring the chill accompanying
the cutting off of the sun's heat. The appearance during totality
is indescribably grand, and the aspect, both of the sun and of
surrounding objects, is extremely difficult to depict. Observations
may be made on the approach of the shadow by looking towards
the western horizon, and, during totality, of the form, structure and
polarization of the corona. The protuberances can be well ob-
served when there is no eclipse, and therefore much time should
not be spent on them. The light will be, roughly speaking, about
that of twilight when the sun is 5 below the horizon, or that of a
candle distant about fifty cms. as shown by the photometer, Vol. I,
Experiment 68. Beside these observations others may be made
with the spectroscope as will be described in the next Experiment.
As the eclipse passes off, similar observations may be made. During
the eclipse, observations may be also made with advantage on the
variation of the light, on the temperature of the air, on the radiant
EQUATORIAL TELESCOPE. 203
heat from the sun, and on the changes in polarization of the sky.
Since the direct light of the sun is too intense to be observed di-
rectly by the photometer, it may be reduced by covering the front
portion by a box arid allowing only a small part to pass through a
lens of short focus.
The Moon. As seen through a small telescope, no heavenly
body shows to greater advantage than the Moon, both on account
of the number of objects to be examined and the changes they
undergo with variations of illumination, or when the Moon is in
different phases. A good map is essential, of which the best is
that of Beer and Madler, its reduced copy in Webb's Celestial
Objects, or the elaborately illustrated work of Carpenter and Nas-
myth. The photographs of Rutherford and De la Rue may also
be used for comparison. As one side only of the Moon is always
directed towards the Earth, lunar objects always retain the same
apparent relative positions and vary only with changes in illumina-
tion. The best effect is generally obtained when the light falls
obliquely, or when the irregular edge of the illuminated portion
called the terminator is near the object to be studied. If the Moon
is observed when full, it is seen to consist of light and dark por-
tions, the latter being designated by the Latin prefix Mare, as they
were formerly supposed to be seas. Many parts of the surface are
covered with circular rings of various sizes, which are supposed to
be the craters of extinct volcanoes. Near the southern portion^
which, since the telescope inverts, will be at the top, is a marked
circle called Tycho, which seems to form the centre of the most
disturbed portion of the moon's surface. Yarious lines extend
from this crater several hundred miles in length, one of them pass-
ing over the centre, reaching nearly across the disk and bisecting
the dark space known as Mare Serenitatis. In the northern portion
is a dark elliptical spot about sixty miles in diameter, surrounded
with walls nearly 4,000 high, known as Plato. South of this
about quarter way to Tycho is another conspicuous crater, Archim-
edes, south east of this is Copernicus, and a little south of west
from the latter is Kepler. Returning now to the north and a little
to the east we reach Aristarchus, the brightest point of the moon's
surface. A long precipitous range of mountains extending from
Mare Serenitatis toward Copernicus is called the Appenines and
204 EQUATORIAL TELESCOPE.
is a beautiful object when the moon is at the quarter. The small
dark patch in the north eastern part of the moon's disk is called
Mare Crisium. Near its centre will be noticed a curious pair of
volcanic craters.
Mercury. On account of the short distance of Mercury from
the sun, it can never be observed when the latter is far below the
horizon, and rnay sometimes be seen by the naked eye, as a star
near the horizon soon after sunset. The distortion due to the
atmosphere is then so great and the intrinsic brightness of its disk
so considerable, that it is best observed before sunset, pointing the
telescope in the right direction from its right ascension and decli-
nation as given in the Nautical Almanac. It will then be seen to
undergo the same changes of phase as the moon, according to its
position with regard to the sun and earth. Its apparent diameter
varies from 4" to 12", and its greatest distance from the sun never
exceeds 30.
Venus. The same remarks apply, though with less force, to
Venus, which is best observed about sunset. With even a moder-
ate magnifying power it will look larger than the moon to the
naked eye, though it is difficult to convince one's self that this is
the case unless the moon is near and seen with one eye, while the
other is directed towards Venus. The angular diameter of Venus
varies from 9" to 62" and its greatest elongation from the sun is
47.
Mars. As seen through a telescope, Mars presents a nearly cir-
cular disk of a reddish or ruddy hue, having a diameter of from 3"
to 18", or occasionally 23". Certain markings may be seen upon
its surface, and a whiteness is seen at the polar portion extending
as the pole is turned from the sun, and which has been supposed
to be snow. When Mars is not in the same line as the earth and
sun, it assumes a gibbous form like the moon, the ratio of the two
diameters amounting in some cases to 10 : 9.
Asteroids. Any of the larger Asteroids are easily found from
their right ascensions and declinations as given in the German
Nautical Almanac. They appear precisely like minute stars, but
are readily distinguishable by their motion which is perceptible in
the course of a few hours by a spider-line micrometer.
EQUATORIAL TELESCOPE. 205
Jupiter. The largest of the planets, and the brightest, with the
exception of Venus, is Jupiter, which in the telescope presents
an elliptical disk, the ratio of the equatorial to the polar diameter
being about as 17 : 16. The angular diameter varies from 30" to
46". It is accompanied by four satellites or moons, which appear
as minute stars, readily seen in a small telescope or even with a
large opera-glass. They frequently are eclipsed in traversing the
shadow of the planet or occulted in passing behind its disk.
When passing in front of it, or transiting across the planet, they
are visible as bright spots, and the transits of their shadows, caus-
ing eclipses of the sun on Jupiter, are also visible as black spots.
The times of all these phenomena are recorded in the Nautical
Almanac. The satellites are generally seen in a line approxi-
mately coinciding with the path of Jupiter and the greatest angu-
lar elongation of the furthest satellite is about 10'. When Jupi-
ter's disk is carefully examined it is seen to be traversed by two or
three dark lines or belts, nearly parallel to its equator.
Saturn. The second in size of the planets is Saturn, which
presents a disk of about 14" to 21" diameter. Its most remarkable
peculiarity is the ring with which it is surrounded and which con-
sists of three concentric annular disks, of which the two outer only
are visible with ordinary telescopes. The plane of the rings is
inclined 28 11' to the plane of the orbit of Saturn, and hence,
twice during Saturn's revolution they are seen edgewise and disap-
pear. This will be the case in 1877 and 1892.
Eight satellites surround Saturn, one, Titan, being of considerable
size and appearing as an eighth magnitude star. The next largest
is the outer satellite, lapetus, whose light is, however, variable,
probably owing to its surface being spotted. The third, fourth
and fifth from the centre are visible with a good telescope, but the
others can only be seen by the largest instruments. The greatest
elongation of the outer satellite is about 10', which, with their
motion, serves to distinguish them from stars.
Uranus. This planet may be seen by the naked eye as a sixth
magnitude star, and in the telescope presents a dim disk 4" in
diameter. Its satellites are beyond the reach of ordinary tele-
scopes. Its place is given in the Nautical Almanac, and during
206 EQUATORIAL TELESCOPE.
the remainder of the century it will be well situated for observa-
tion in the evening in the spring and summer.
. Neptune. But little can be seen of Neptune except as a dim
ill defined eighth magnitude star. Its position during the rest of
the century will be in Aries and Taurus, and it may be most
favorably observed during the winter.
Comets. In the observation of comets, low powers only can be
used, and the tail can generally be seen better with the naked eye
or with an opera-glass, than with a telescope. If the position is
not accurately known, it may sometimes be found by sweeping.
Point the telescope above and to one side of the supposed place,
swing the telescope horizontally, then lower it a distance about
equal to half the breadth of the 'field, and thus go on until the
comet is found or the limits of its possible position passed. The
lowest power should be used, to secure the greatest light and the
largest field.
When a very minute or faint object is to be observed it may
sometimes be seen more readily by looking to one side of its sup-
posed place, so that its image shall be formed on one side of the
centre of the retina.
Double Stars. The real angular diameter of a fixed star is so
small, probably only a few hundredths or thousandths of a second,
that their true shape is never perceptible, even in the most power-
ful telescopes. With the best instruments they present small
circular outlines called spurious disks, due to diffraction, whose
diameter increases as the aperture of the telescope diminishes.
If we examine a large number of stars we find that many of them
are double or consist of two very near together, and the propor-
tion is much greater than could be accounted for by mere acciden-
tal juxtaposition. Where the interval is small, the pair are found
to revolve around their centre of gravity in accordance with the
law of gravitation. This cannot be verified in the case of the
more distant components, on account of the immense interval of
time which would be required to produce a perceptible motion.
There are several examples among stars visible to the naked eye
of the close approach of two, and presenting, therefore, the same
appearance as close double stars seen through a telescope. Of
these may be mentioned the two components of a Capricorni, of
EQUATORIAL TELESCOPE. 207
f Leonis, and of e Lyrce. The distances in the three cases are
873", 337" and 207". The star Alcor, I Ursce Majoris, in the
middle of the handle of the Dipper, has a small star 690" distant
from it, and resembling a double star with components of different
sizes. The star e Lyrce is valuable as a test of the eye. The
vision is not perfect if the two stars cannot be distinguished.
They are easily found as forming a small equilateral triangle with
another star of equal brightness and with a Lyrce, the very bright
star in the zenith in summer. A list of the more easily resolved
double stars is given in Appendix B, Table 19. Find a number of
them and measure their distance apart and position-angle by the
micrometer.
Many of the stars when viewed with a sufficiently powerful tel-
escope are seen to consist of three or more components. They are
then called triple or multiple stars. As examples of these objects
may be mentioned 14 Can. Min., O 2 Sagit., o and y Cyg., 90 Leo^
11 JS/bnoc., 65 Urs. Maj., , t, o and 6 Orionis.
The color of the fixed stars varies very greatly, and this is es-
pecially noticeable with the double stars, since the two compo-
nents are readily compared with each other. Besides these there
is a small class of bright red stars of which those located in
xvm h. 57 m., S 5 53', xx h. 10 m., S 21 45', and xxm h. 51 m.
JV50 40' are good specimens. Several other red stai-s will also
be noticed in Persus, Auriga and Cygnus. The brightness of
many of the fixed stars has been observed to alter periodically.
Among the most remarkable of these variable stars are o Ceti, ft
Persei and y ArgHs.
Clusters and Nebulas. A further examination of the heavens
shows a tendency of the stars to collect in groups, of which, among
stars visible to the naked eye, the Pleiades are the best example.
Next to these is a misty whitish spot in Cancer known as Prcese-
pe, which, with a telescope or even an opera-glass, is seen to con-
sist of a group of small stars. Another example is in the so-called
sword handle of Perseus which, under the slightest optical aid, is
in a great measure resolved into stars. The Milky Way, a white
cloudiness extending completely around the heavens, also under a
sufficient magnifying power is resolved into stars. Besides these
there are many objects presenting a similar appearance in the tele-
208 SPECTRUM TELESCOPE.
scope which are known as nebulae. As a large part of them are
resolved into clusters of stars in the most powerful instruments,
and as a bright cluster in a small telescope looks exactly like a
faint nebula in a large instrument, it was at one time supposed
that all nebulae might be resolved if sufficient optical power could
be brought to bear on them. Later observations with the spec-
troscope have, however, proved that some of them consist of gas-
eous matter, and can never be resolved into stars.
A list of the most remarkable cluster^ and nebulae is given in
Table 20. Prominent among them is the great nebula of Orion,
visible to the naked eye as a misty star in the middle of the sword
handle. As seen through the telescope this star is resolved into
four, surrounded with a bright hazy luminosity. This is a real
nebula as shown by the spectroscope. The nebula in Andromeda
almost equally bright, is large and oval, and, though not yet satis-
factorily resolved, doubtless consists of stars, as it gives a continu-
ous spectrum. The cluster in Hercules is also very bright, and in
a large telescope is a superb object. Nebula3 often assume certain
definite forms, as a ring, of which the only example accessible to
small telescopes is that in Lyra, nearly midway between |3 and f.
Another form is the planetary nebula, which presents a small
sharply defined circular disk, like a planet ; the largest of these is
97J/in Ursa Major, which has a diameter of 2' 40". Others are
spiral in structure, of which the most remarkable is 51 M. in Canes
Venatici.
185. SPECTRUM TELESCOPE.
Apparatus. The equatorial or siderostat, described in the last
Experiment, and a spectroscope to replace its eyepiece, which for
observations on the sun should have a very great dispersion, either
by using a large number of prisms, or better by a diffraction grat-
ing. For other purposes, a direct vision spectroscope or other
form giving a smaU dispersion is preferable. Very good results
may be attained with a large cosmorama lens as an objective, since
sharp definition is not needed, but a large amount of light is
indispensable.
Experiment. When the object to be observed has a consider-
able angular aperture, good results are attained by directing a
simple one prism chemical spectroscope towards it without using
SPECTRUM TELESCOPE. 209
the telescope. This is the case in studying the spectrum of the
sky, of clouds, of the aurora borealis and of the zodiacal light. In
all cases the wave-length must first be determined in terms of the
scale-reading as described in Vol. I, Experiment 77. A direct-
vision spectroscope may be used if a scale is inserted in its eye-
piece, but with faint objects the loss of light is an objection.
The solar spectrum may be observed as described in Vol. I, Ex-
periment 77. No limit has yet been reached to the dispersion
which may be used with advantage. The best results seem to
have been attained with a diffraction grating formed of fine lines
ruled with a diamond on speculum metal or silvered glass. By
observing a spectrum of a higher order an enormous dispersion
may be obtained. The plate should be set at right angles to the
observing telescope. The light of the sun being reflected di-
rectly by means of a mirror, we obtain rays from all parts of the
sun's disk. If, however, a carefully corrected lens is interposed
at a distance from the slit equal to its focal length, a well defined
image of the sun will be formed upon the slit, and accordingly the
spectrum of any portion of the sun's disk may be observed.
Carrying this a step further by enlarging the lens, we have the
more common arrangement of a telescope with the eyepiece re-
placed by a specti'oscope. If the spectrum of the space just
beyond the edge of the sun is observed with a high dispersive
power, the image of the sun being carefully focussed, the lines C
and F will sometimes appear bright instead of dark, owing to the
presence of protuberances such as are described in the last Experi-
ment in connection with eclipses of the sun. If now the slit is
gradually opened, the true shape of the protuberance will be seen
in red or green on a dark background. Under favorable circum-
stances many other lines have been seen reversed, but the line
C'is most favorable for ordinary observation. The reason that
the protuberances are thus rendered visible is that by dispersion
the light of the sun may be 'indefinitely diminished, while that of
the protuberances, consisting of a limited number of monochromatic
rays, retains nearly its original brilliancy. Accordingly, with a
sufficient dispersion, the light of the protuberance becomes brighter
than that of the sun itself.
During an eclipse of the sun, many of the phenomena may be
14
210 SPECTRUM TELESCOPE.
studied to advantage with the spectroscope. If directed to a
protuberance near the point of first contact, the approach of the
moon is marked by the gradual covering up of the protuberance.
The instant of first contact is thus well observed. During the
partial phase the change, if any, along the edge of the moon may
be looked for, and during totality the spectrum of the corona may
be observed. This is best seen with a moderate dispersion or by
a simple chemical* spectroscope with no lens in front of the slit.
The spectrum of the whole light around the sun is in this case
observed.
The spectrum of the stars is best seen with a spectroscope con-
sisting of but one or two prisms, as the light is generally too fee-
ble for a greater dispersion. As the image of a star is a minute
point, if allowed to fall directly on the slit its spectrum would be
a narrow luminous line in which it would be difficult to distinguish
the dark lines. To remedy this inconvenience a cylindrical lens
is interposed in such a position as to form a line of light on the
slit. A spectrum of less brilliancy but greater breadth is thus
formed. The slit may be either parallel or perpendicular to the
axis of the lens according to the distance at which it is placed.
The latter position is, however, generally preferable, since, if the
two are parallel, the spectrum will not be of equal breadth through-
out, owing to the aberration of the lens. The fixed stars give
spectra resembling that of the sun, and consisting of continuous
spectra crossed by dark lines. Clusters of stars give similar spec-
tra, though they are so faint that the lines are not visible, and
the spectra appear continuous. Nebulae, on the other hand,
give spectra composed of three or four bright lines, a charac-
teristic property of luminous gases, consequently such nebula3 can
never be resolved into stars. This is the best if not the only cer-
tain means of distinguishing between faint clusters and nebulas.
Much interest has been excited by the observation of the mo-
tion of the stars by the spectroscope. If the latter is rapidly
approaching a luminous body the waves of light fall upon its slit
at shorter intervals, and hence the wave-length appears to dimin-
ish. In the same way an increase in distance of the light and slit
appears to increase the wave-length. Owing to this action the
lines in a spectrum would move towards the red end by an amount
SPECTRUM TELESCOPE. 211
proportional to the velocity of recession of the light observed, or
towards the violet end if the distance was diminishing. This
method has the advantage that it measures the velocity of motion
quite independently of the distance of the object, but the velocity
of light is so great that it is only capable of measuring velocities
amounting to several miles per second. On observing the spec-
trum of Sirius with a large dispersion, Mr. Huggins noticed that
the F line in its spectrum was a little less refrangible than that
given by a Geissler tube containing hydrogen. From this he in-
ferred that Sirius was receding at the rate, of 41 miles per second,
or allowing for the motion of the earth 30 miles per second.
Similar observations have been made on many other bright stars,
but to attain accuracy a telescope of the largest size is indispensa-
ble on account of the feeble light. The velocity is readily com-
puted as follows. Determine by a micrometer the change in
wave-length I of the hydrogen line F compared with that of a
Geissler tube. Then we have the proportion A : I =. V : v, in which
X is the wave length = .0000004861, for the .Fline, F the velocity
of light = 300400000, and v the required velocity, all being given
in metres. From this we deduce, v = 618000000000000 I, or if I
is given in millionths of a millimetre and v in kilometres, v = 618?.
This method of measuring velocity is not, however, universally
admitted, as certain considerations, both theoretical and experi-
mental, seem to show that the motion of the light may have no
effect on its wave-length.
LANTERN PROJECTIONS.
During the past ten years a new era has arisen in the illustra-
tion of lectures, by the general introduction of the magic lantern
as a means of demonstration. Not only in science, but in the
mechanic arts, in architecture, and in fact in any subject suscepti-
ble of illustration by engravings or photographs, a few glass plates,
which may be carried in the hand, will interest and instruct an
audience more than the finest diagrams, which are, moreover, far
more cumbrous and expensive. It is, therefore, desirable that
every one who may have occasion to address an audience should
be able to manage a lantern and to project photographs on the
screen. Again, especially in physical experiments, many objects
are so minute that they cannot well be shown to a large number
of persons, and an enlarged image of these may often be thrown
on the screen and thus be seen by hundreds at a time.
The method employed is to illuminate the photograph or other
object as strongly as possible by a very brilliant light, and then in-
terpose a convex lens at such a distance that an image shall be
formed at its conjugate focus on a large white screen stretched
over the opposite wall. The sources of light most commonly em-
ployed are sunlight, the electric light, the magnesium light and the
calcium light, which will be considered in turn.
186. SUNLIGHT.
Apparatus. A window facing to the south is desirable, which
may be closed by a shutter with a circular aperture. The other
windows should be provided with shutters or opaque curtains so
as to exclude all light. A porte-lumiere may be fitted into the
hole in the shutter or a heliostat may be placed on a shelf, outside
212
SUNLIGHT. 213
so as to reflect a ray of light into the room. The hole in the
shutter is commonly closed by a board, which *may be removed
and the porte-lumiere fastened in its place by screws or buttons.
Experiment. If always available, no source of light could com-
pare with the sun for almost all projections. Its advantages are
steadiness and great intensity, especially when a parallel beam is
required. The porte-lumfere consists of a mirror which may be
turned around either of two axes at right angles to each other.
These motions can be effected by handles inside the room so that
the mirror may be turned in any desired direction. This is nec-
cessary, as, owing to the apparent motion of the sun, the direction
of the light is constantly changing, and the mirror must be moved
at intervals to correspond.
A simple form of porte-lumi&re may be made by passing a tin
tube about four inches in diameter and six inches long through
the shutter, making it free to turn, but held in place by friction.
The lower end of the mirror is hinged to this tube, and the upper
end is held by a cord which passes through the tube around a
violin peg attached to the tube, inside the shutter. The string is
kept tight by the w r eight of the mirror, and the latter may be
raised or lowered by tu'rning the peg. Turning the tube gives it
a second motion at right angles to the first. Sometimes the proper
motion is given to the mirror by clock-work, forming the instrument
known as the heliostat. The apparent motion of the sun is a cir-
cle with the rforth pole of the heavens as a centre, or around the
axis of the earth, and with a radius varying from 67 in summer
to 90 in spring or autumn and to 113 in winter. Suppose now
we place a rod parallel to the axis of the earth, that is, running
north and south and inclined to the horizon by an angle equal to
the latitude of the place, and that we cause it to revolve uniformly
once every twenty-four hours, by clock-work. Every point of
this will retain the same relative position with regard to the sun
during the day ; or, if an arm is attached pointing towards the
sun it will follow the latter in its motion. Now suppose a mirror
attached to the rod and turned through such an angle as to reflect
the light in the direction of the rod, or parallel to the earth's axis.
As the sun moves, the mirror will turn with it, and always throw
the light in the same direction. The direction of the beam will
214 SUNLIGHT.
thus be fixed, and by a second mirror may now be turned in any
desired direction. This is known as Fahrenheit's heliostat. To
avoid using two mirrors a more complex arrangement is some-
times employed. In Silbermann's heliostat the mirror is attached
at right angles to the diagonal of a parallelogram, one side of
which is by clock-work kept turned towards the sun, while the
other is fastened in the direction in which the light is to be thrown.
The mirror is thus kept equally inclined to this direction and to
the sun, the required condition. The principal objection to this
instrument is that the joints give a jerking instead of a steady
motion to the mirror. Foucault's heliostat consists of a rod
turned by clock-work so that it shall always point towards the
sun, with one end attached to the edge of the mirror and the
other to a rod normal to the surface. The mirror is mounted on a
universal joint and may be placed alj any desired angle with
the revolving rod. Its direction, and the revolving rod, will now
always be equally inclined to the normal to the mirror, which is
the required condition that the light shall always be thrown in
the same direction as long as the rod is made to follow the sun.
To obtain a beam of sunlight, remove the board from the shut-
ter and replace it by the porte-lumidre, which may then be fas-
tened in place. Turn the mirror until the light reflected from its
surface falls upon the opposite wall, where, if the aperture is re-
duced, it will form a bright circular image of the sun. If the two
surfaces of the mirror are not exactly parallel, a series of images
is seen, their number and distance apart increasing with the
angle of incidence. The first image formed by the front surface
of the glass is generally fainter than the second formed by its rear
surface, the others are due to continued internal reflection. If the
position of these images is noticed, it will be seen that they are
moving slowly over the wall, so that the mirror must be turned
occasionally to keep them near the same point. If the heliostat is
used, it must be adjusted so that its axis is parallel to the earth's
axis. It should be fastened permanently at an angle equal to the
latitude, and then turned into the plane of the meridian. The
mirror is then moved until the light is reflected in the proper
direction, and the clock-work started.
ELECTRIC LIGHT. 215
Great care must be taken always to bring the porte-lumfere or
heliostat inside after using, as exposure to the weather for even a
single night may cause serious injury.
187. ELECTRIC LIGHT.
Apparatus. A magneto-electric machine or a powerful battery,
connecting wires and an electric light regulator. If the current is
to be generated by a magneto machine, an engine is needed as
a motor. The power and speed required will depend on the
strength of current desired and the kind of machine used. Gener-
ally an engine of at least three or four horse-power is needed, and
a speed of five to fifteen hundred turns per minute. The machine
should be driven in the usual way by a belt and pulley. If a bat-
tery is employed it should be set up in an adjoining room with
the windows open, or under a hood, to carry off the fumes.
Experiment. The brightest light that can be obtained artifi-
cially is the electric light, and but for its expense and the trouble
of production, it would probably supersede other sources for pro-
jections. It is generated by passing a powerful current of elec-
tricity between two carbon points, which when separated by a
short distance become heated to incandescence and give out an
intense white light. Two methods are employed for producing
the current, a magneto-electric machine and a galvanic battery. In
the first of these an electro-magnet is caused to revolve rapidly
past the poles of a permanent magnet, and the current thus gener-
ated excites a second much larger electro-magnet. A greatly
increased current is now obtained by revolving another electro-
magnetic armature in front of the latter. This is the principle
employed in the Wilde machine, but in later forms no per-
manent magnet is used, the current being produced in the first
magnet by induction or otherwise, and then maintained by the
current itself. The current is rendered continuous in the form
proposed by Gramme, in which a large number of coils are used in
the revolving armature, and with which extraordinary effects are
produced. A steam engine is required to drive these machines,
but notwithstanding their large first cost, they form the cheapest
Bource of powerful currents of electricity, and are now coming into
general use for industrial purposes.
216 ELECTRIC LIGHT.
The more common method of producing the electric light is by
means of a battery of from 40 to 60 large Bunsen or Grove cells.
These are mounted as described on page 1, and give a current of
sufficient power to generate an excellent light. The advantage
over the previous method is that no engine is required, and the
first cost is comparatively small ; but the labor of amalgamating
the plates and mounting the battery is very considerable, the con-
sumption of acid great, the current rapidly grows feebler, and the
fumes require a separate, well ventilated battery room.
The current thus generated and having an electromotive force
of 50 to 100 volts, is passed between two terminals of gas coke
which are then separated by a small amount. If this distance
becomes too great the light flickers and is liable to go out, the
current then ceasing and not flowing again until the carbons have
been brought in contact ; if it becomes too small the light is also
enfeebled. Owing to the intense heat, both carbons are gradu-
ally volatilized, and, as the distance thus increases, a regulator is
required to keep this distance constant. The positive terminal,
which should be placed uppermost, wears away more rapidly than
the other, in the ratio of about two to one. Much ingenuity has
been expended on the regulators designed to render this distance
constant. The form in most common use is that of Foucault. In
this the current passes around an electro-magnet whose armature
is adjusted against a spring, so that if it is drawn towards the
magnet it releases a train of clock-work which separates the car-
bons, and if the armature recedes from the magnet, a second train
of clock-work makes the carbons approach. If the current is
passing the carbons wear away, and the resistance increases with
the distance between them ; as the current by Ohm's law becomes
feebler the magnet is weakened, the spring overcomes the at-
traction on the armature, the latter recedes and the clock-work
brings the carbons nearer together. If the light from any cause
is extinguished, the same action goes on until the carbons are in
contact. The current then passes with its full strength, the
armature is drawn down, releases the other train of clock-work,
and the action proceeds as before. A tolerable degree of steadi-
ness is thus attained, and if extinguished the lamp will relight
itself. An objection to this regulator is that, if the electromotive
MAGNESIUM LIGHT. 217
force of the current is insufficient, it is liable to take on an oscillat-
ing motion ; the carbons separate so far as to break the circuit,
then rush together and again separate. This is especially objec-
tionable with the magneto machines, as in the best forms the work
required to drive them is small when the current is broken, and
accordingly each change in the current produces a violent strain
on the engine.
A much simpler regulator is that of Browning, in which the
upper carbon is attached to an electro-magnet traversed by the
current and free to slide down a vertical rod. As long as the
current is strong the magnet attracts its armature, which acts as a
brake and prevents its sliding down, but as soon as the current is
weakened by the wearing away of the carbons the magnet de-
scends and the carbons approach. A screw serves to regulate the
position of the lower carbon.
To produce the light, start the engine, if the magneto machine
is to be employed, or set up the battery, and connect the terminals
with the binding screws on the regulator. If the carbons are not
in contact the circuit will be broken. If the Foucault regulator is
employed, it should first be wound up and the pointer in front
turned from " Arret " to " Marche. " The carbons will then
slowly approach until they touch, when the armature will be
drawn down and they will separate, and if all is right a brilliant
light will be produced between them. To obtain the best effect,
the spring regulating the force with which the armature is held in
place must be carefully adjusted by the screw near the base of the
regulator. When the carbons are consumed they are removed by
unscrewing the carbon holder by a small wrench.
188. MAGNESIUM LIGHT.
Apparatus. A magnesium lamp and cloth chimney by which
the smoke may be carried upwards out of the window or into a
flue.
Experiment. The metal magnesium when ignited burns with
intense heat, raising to whiteness the oxide formed. The simplest
way of employing it as a light is to pass the metal in a finely
divided state through the flame of a spirit lamp, when it emits an
intense- white light in burning. The more common method, how-
218 CALCIUM LIGHT.
ever, is to burn it in the form of ribbons. Two coils of this
are placed on reels on top of the lamp ; their ends are drawn
between rollers turned by clock-work, and two rollers placed
below serve to cut off the ends of the burnt magnesium. Care
should be taken in putting on the ribbons to pass them through
the rollers in such a way that the ends shall curl outwards, that is,
from each other. The brillancy and steadiness of the light
depend in a great measure on the proper supply of air. To ef-
fect this, a chimney is provided carrying off the burnt magnesium
which otherwise would soon fill the room with a white impalpable
powder consisting of calcined magnesia. The chimney is com-
monly made of a cloth tube distended by a flat helical wire and
should be carried upwards into the open air or into a flue. The
upward direction is essential or the draught will be checked.
Sometimes the tube terminates in a large bag which allows the air
to pass and retains the magnesia, but the air-currents are thus
checked. To light the lamp, open the damper in the back part
and turn the detent which releases the clock-work until about two
inches of the magnesium protrudes below the rollers, then stop it
and light the ends by holding under them a match, or better an
alcohol lamp, and as soon as they light start the clock-work again.
If the wire is fed too slowly the flame will burn too high. This
may be remedied by moving the vanes of the clock-work, or by
keeping the latter well wound up, turning the key a little every
few minutes. The opposite plan is to be adopted if the clock-
work goes too rapidly. The position of the light may be viewed
either through colored glass, or, if the lamp is used in a lantern, by
observing from behind the reflection of the flame in the lens in
front.
The advantage of this light is its portability, and that it is
always ready at a moment's notice. The objections are its ex-
pense, which is considerable, the variability and insufficient inten-
sity of the light.
189. CALCIUM LIGHT.
Apparatus. Two holders, bags or reservoirs to contain the
gases, a burner and some lime cylinders. If the oxygen is to be
made, a retort, gas furnace, some black oxide of manganese, chlo-
rate of potash, caustic potash and a wash-bottle are required.
CALCIUM LIGHT. 219
Experiment. The light in most common use for lantern projec-
tions, on account of its cheapness and convenience, is that obtained
by inserting a cylinder of lime in the flame of the oxy-hydrogen
blowpipe.
The gases may be kept in holders over water, a greater or less
pressure being produced by weights. Great care must be taken
that they do not get mixed or there is danger of a most violent
explosion on the approach of a flame. They should, therefore,
never be interchanged, and care must be taken on first admitting
the hydrogen that no air remains in the holder. Rubber bags are
often used instead of holders as they are less expensive and much
more portable, but they are more liable to leak, and therefore the
hydrogen should never be kept long, if it can be avoided ; it is
also best to subject it to a small pressure that the leak, if any,
may be outwards. Copper cylinders are now, however, frequently
employed, in which the gases are confined under great pressure
and thus preserved indefinitely and burned at a moment's notice.
The current expense is comparatively small, as the gases are man
ufactured and compressed by a company and sent by express to
any part of the country. It is better that the pressure should be
the same for both gases, and it may be readily tested by attaching
a common steam pressure gauge.
Pure hydrogen is now seldom used for the calcium light, coal
gas being much cheaper and sufficiently good for the purpose.
For any special purpose hydrogen may be made in large quanti-
ties from iron filings and dilute sulphuric acid much more cheaply
than from zinc. Where coal gas is not easily obtained, the hydro-
gen maybe replaced by an alcohol lamp, though the flarne of which
the oxygen is blown as in a common blowpipe. The light thus,
formed is called the Bude light.
As many persons prefer to make their own oxygen, the details
are given below somewhat fully. A mixture of binoxide of man-
ganese and chlorate of potash is heated in a flask which may be
of copper, cast iron or sheet iron. The first is the most expensive
and burns through in time, the second is the most durable but
requires a furnace or stove, and hence the third is -generally the
most convenient. To render the joints gas-tight when first used,
a little thin luting clay or plaster of Paris should be poured in and
220 CALCIUM LIGHT.
the flask then heated. The cover may be screwed on or held in
place with a gallows-screw connection and luting clay. The
tightness of the joint may be tested by attaching a short rubber
tube to the outlet, blowing into it, pinching it with the fingers and
then seeing if the pressure is maintained. Oxygen may be made
by heating either binoxide of manganese or chlorate of potash
alone, but the former requires a high temperature and leaves a
very disagreeable black mass, which is not easily removed, and the
latter is very dangerous if heated too rapidly. It is therefore
better to mix them, when the manganese seems to modify the
decomposition of the chlorate so as to render the action more uni-
form. The proportion may be varied very greatly, equal parts
may be used at first, and one part of manganese to two or four of
potash when the experimenter is familiar with the process. Great
care should be taken that the chlorate is pure and that no dust or
organic matter is present in the flask, or it may cause a violent
explosion. It is safest always to test the potash and manganese by
heating a little in a glass tube. The greatest danger is that sul-
phide of antimony may be mistaken for the manganese, which it
greatly resembles.
The oxide and chlorate should be finely powdered and well mixed
by rolling them in a piece of paper or shaking them together in
a bottle. It is better to mix them shortly before using, rather
than in large quantities at a time, as in the latter case there is a
little liability to clog and form lumps, from which the gas is given
off" with too great rapidity. About a pound of the mixture is
placed in the flask, the cover fastened on and rendered air-tight as
described above. It is then placed over a gas-stove, such as is
used for cooking purposes, and connected by a short rubber tube
with the wash-bottle. This consists of a large bottle closed by a
cork or rubber stopper through which pass three tubes, one from
the flask passing nearly to the bottom, through which the gas
enters, a second ending just below-the cork and a third, or safety
tube, reaching nearly to the bottom of the bottle and with a rub-
ber tube connected above and bent over into a vessel to catch the
liquid if thrown out. The bottle is then about one-third filled
with strong caustic soda or potash. The gas from the flask will
now pass through the soda which will absorb any chlorine or other
CALCIUM LIGHT. 221
impurity, and the remaining pure oxygen may then pass through
a long rubber tube to the holder or bag. The object of having
the rubber tube connecting the flask and wash-bottle short, is
that if heated by the oxygen it may be decomposed, and the
hydrocarbon vapors given off uniting with the oxygen cause an
explosion, as accidents have occurred which seemed due to this
cause. If, therefore, the tube becomes too hot, it is well to cool it
with a wet cloth. The tube connecting the retort and wash bottle,
and the outlet of the latter, should be as large as possible, as one
of the most common causes of accident is the stoppage of these
tubes during a violent formation of the gas, by the manganese or
soda collecting in them.
Everything being in readiness, the gas may be lighted and
turned on to the full. The flow is rather more uniform in this
case than if heated up slowly, as the whole mass then reaches the
point of decomposition at about the same time, and the gas is
liable to be given off suddenly in great quantity, while if the heat
is strong at first, the lower part of the mixture is decomposed
before the upper part has been strongly heated. Owing to the
expansion of the air, bubbles will appear in the wash-bottle almost
immediately, which will increase in number as the gas is given off.
The first portions should be allowed to escape, and then the tube
should be connected with the holdter or bag and the gas will pour
into them. With a little supervision the process will now go on
of itself, but it should be watched, or accidents may happen. The
liquid will rise in the safety tube to a height dependent on the
pressure in the holder, and the resistance of the tubes. If there
is any stoppage, the safety tube will fill and run over, emptying
the wash-bottle in a few seconds. This is avoided by instantly
breaking the connection between the flask and bottle by the rub-
ber tube. This should be done, in fact, in case of any accident.
If the gas is generated too rapidly, the burner should be turned
down, but as this will not produce an effect immediately, the
bubbles should be watched so as to anticipate too violent an
action. The danger from too rapid a flow of gas, is that the
liquid in the wash-bottle will be thrown up into the outlet tube,
and, running down into the rubber tube, close it and stop the flow
of gas. The burner should not be extinguished until the wash-
222 CALCIUM LIGHT.
bottle is disconnected, or the liquid in the latter may be drawn
back into the retort, converted into steam and produce an explo-
sion. A pound of the chlorate should generate about four cubic
feet of gas, and when nearly this amount has* been given off, the
bubbles begin to come more slowly, the wash-bottle should then
be disconnected from the flask, and the burner extinguished.
When the flask is cold, the cover should be taken off and cold
water poured in. After some time the water softens the potash
and manganese, and they may then be easily removed.
When the gas is required in larger quantities the following
method is more convenient. A common cast iron retort is sup-
plied with two tubes, an outlet for the gas and an inlet termina-
ting above in a large tin funnel in which is placed a quantity of
chlorate of potash. To prevent the latter from passing directly
into the retort, a stop-cock is interposed whose plug is not perfora-
ted, but has a cavity in it so that on turning it, a little of the
chlorate passes each time into the retort. The latter being heated
nearly to redness the plug is turned, when the gas is instantly
liberated and passes over into the holder ; this operation is re-
peated until a large quantity of gas has been generated. Instead
of the funnel, a conical hopper closed above may be used, and the
chlorate supplied by a revolving fan-wheel. Another method of
generating the gas is by Edgerton's cylinders, which consist of
wrought iron cylinders in each of which are placed a pound of
chlorate of potash and four ounces of binoxide of manganese.
The cylinder is then heated over a stove, taking care that it does
not become red hot. The oxygen is thus generated under pres-
sure and may be used as soon as the cylinder is cool, or kept
indefinitely. A second cylinder lined' with vulcanized rubber
serves to prepare the hydrogen from sulphuric acid and zinc.
To burn the gases, they are brought by rubber tubes to the jet,
which is made of various forms. The simplest and most efficient
method would be to mix the gases in bulk and then burn them
from a simple tube like a blow-pipe. But this method is never
employed on account of its danger. The mixed gases in any
considerable quantity explode with extreme violence, and the
flame is liable to travel back through even a small tube. For-
merly safety tubes were much used, consisting of tubes filled with
CALCIUM LIGHT. 223
fine wires, inserted between the burner and holder, but these are
not always effective, and the consequences of an explosion are so
disastrous as never to justify mixing the gases in bulk.
The same effect may be obtained by making the jet terminate
it a small copper chamber in which the gases mix and' are
burnt through a small hole in the end. The cap of a copper cart-
ridge is sometimes used for this purpose. The hydrogen should be
turned on first and lighted, and then the oxygen, taking care that
there is not too much of the latter, as in that case, the flame is
extinguished with a loud snap due to the explosion of the little
mass of gas in the copper chamber. The blue part of the flame
shortens when the oxygen is in excess, and just before the explo-
sion, draws back till it reaches the orifice, so that with a little
care, if the pressure is constant, this snapping is easily foreseen
and avoided.
Another form of burner is made like a common blast lamp, the
hydrogen being burnt through a large orifice, while the oxygen is
supplied through a small tube opening in its centre. This form
has the advantage of perfect safety, as it is almost impossible for
the two gases to be mixed, and there can therefore be no explo-
sion. The light, however, is not as intense, since the gases do not
unite as completely, and if the oxygen is delivered under too
great a pressure it is liable to cool the lime, forming a dark spot
in the centre of the light. A third and still simpler form consists
of a large orifice for the hydrogen, and a small one for the oxygen,
arranged like a common blow-pipe, so that the oxygen is blown
through the large flame of the hydrogen. The last two forms of
burner do not require a high pressure for either gas, but in the
first form a pressure of a foot or more is needed or the gases may
snap.
The oxy-hydrogen flame, although colorless, has a most intense
heat. This may be seen by holding a piece of steel, as a watch
spring, in it, which will be burnt off with a shower of sparks, or by
a piece of platinum wire which will be heated to whiteness, and
then melted. If now a piece of quick-lime is placed in the flame,
it is heated to such intense whiteness as to afford a brilliant light.
The limes, as they are called, are made in the form of cylinders,
and are either held in small cups, or sometimes have holes bored
224 CALCIUM LIGHT.
through them, and are mounted on vertical wires. They tend to
absorb moisture and when not in use should, therefore, be kept
in glass stoppered bottles containing quick-lime, otherwise they
are liable to crack and fall to pieces. When the flame has played
for a considerable time on the same point of the lime, the light .
becomes less intense, and the lime should, therefore, be turned.
To obtain a very uniform light, clock-work is sometimes attached,
by which the lime is caused to revolve slowly so as continually
to expose a fresh portion of its surface.
To avoid the difficulty of the wearing away of the limes and
their hygroscopic nature, cylinders of zirconia have been employed
but the light they emit is less brilliant.
To produce the light, therefore, take a lime from the stoppered
bottle in which it is contained, and place it in its cup. Wind up
and start the clock-work, if any is used. Close the stop-cocks for
both oxygen and hydrogen at the burner and open them at the
holders. To make sure that there are no mixed gases, it is well to
allow a little of each gas to escape through its tube before ignit-
ing them. A considerable weight must be placed on each holder
or bag to produce the requisite pressure; thus to obtain a pressure
of a foot a weight of sixty-two pounds per square foot is required.
If two bags are used they should be placed between three boards
hinged so as to form a Z. One bag is placed on each side of the
inclined board, and the weights on top. Moving the weights to
one side or the other any desired pressure can be exerted on
either bag. If the gas is contained in cylinders under pressure, it
must be regulated only by the valves on them, and the stopcocks
on the burner kept wide open all the time, or the connecting
tubes will be burst by the pressure. The cylinders are closed by
conical valves operated by a long handle which may be very
exactly adjusted by gentle blows with the hand. Turn on the
hydrogen and light it, and after the lime has become somewhat
warmed admit the oxygen carefully. A rustling, hissing sound is
produced if the latter is in excess, or with the first kind of burner
a violent snap extinguishing the light. The appearance of the
flame when the gases are in the right proportion is soon learned.
The brilliancy of the light also affords an excellent test of the
correct proportion of the two gases. If the light becomes dim
LANTERN. 225
see if the pressure of either gas has altered so that they are not
in the right proportions and try turning the lime so as to expose a
fresh surface.
Finally, the advantages of the calcium light are its cheapness
and its great steadiness, in which latter respect it has a great
advantage over both the electric and magnesium lights.
Although the above description has been confined to the
brighter lights, yet for many purposes excellent effects are obtain-
able with an oil lamp, especially in a small room. The flame
should be as intense as possible and not very large. For this
reason a kerosene lamp placed edgewise gives good results.
190. LANTERN.
Apparatus. For the lantern a simple wooden box about a foot
on a side may be employed. It should be blackened inside and
have a hole in the top to allow the hot air to escape. In front is
a circular hole four or five inches in diameter, and on each side
and behind larger apertures closed by curtains or doors. If the
latter are used, that in the rear should be hinged above, and the
others hinged in front, so that, when open, the light will not fall
on the screen. The whole is placed on a long board on which
may be placed the lenses and other apparatus employed, or a stand
like the bed-plate of a lathe may be placed in front of the lantern
and the various instruments attached to this. For the simple
projection of pictures, however, it is more convenient to have
the condensers and projecting lenses attached directly to the lan-
tern, and between them and close to the condensers, a place for
inserting the picture-holder. The construction of these will be
given below. The projecting lenses are movable and may be
slid in or out by the hand or better by a rack and pinion.
The pictures may be projected directly on a white wall, or, if
this is not available, upon a screen of white cloth. If the latter is
to be used permanently it should be moistened, stretched and held
in place by tacks and then painted. Good results may also be
obtained with a white curtain. Cloth may be obtained eleven feet
wide, and, therefore, a seam is unnecessary except in large halls,
where if well made, it is not likely to be very noticeable.
Experiment. The method of projecting objects on the screen is
shown in Fig. 106. A represents the source of light and BB' a
lens at a distance from it equal to its focal distance, so that the
emergent rays shall be parallel. GO' is a second lens which
15
226 LANTERN.
brings the rays to a focus at D where the projecting lens is placed.
The object is placed at FF' at such a distance from D that its
conjugate focus shall fall upon the screen EE'.
The lenses BB' and CO' are called the condensers, and D the
projecting lenses. Evidently the diameter of the circle of light
upon the screen
will be EE', and
that of the field
or of the largest
object that can be
projected, FF'.
Since the image
of F is formed at Fig. loe.
E' and of F' at
E, the upper part of the object will appear at the lower part of
the screen and vice versa. By similar triangles it follows that
FF' : EE' = DF: DE' or since DE' is generally very large
compared with FD, the latter will nearly equal the focal dis-
tance of the lens D. Hence it follows that the size of the object :
size of the image = focal distance of D : distance of the screen.
The ratio of the diameter of the circle on the screen to the dis-
tance of the latter should not exceed one to two, and should
generally be one to three or four. The advantage of the latter
ratio is that the aberration is diminished, but it renders it nec-
essary that the lantern should be placed at a greater distance
from the screen. A convenient arrangement is to place the lan-
tern behind the spectators, and throw the light over their heads.
An imperfect image of the light A will be formed at D, whose
size will bear the same ratio to that of A as their distances from
the condenser. As the aberration will still further increase the
size of the image, it is evident that if the screen is placed a
long way from the lantern, to have a field and image of the same
size, the focal length of D and its diameter must both be in-
creased, or part of the light will be lost by not passing through it.
As the object of D is simply to form an image of FF', it must
be carefully corrected both for spherical and chromatic aberration.
Other defects, however, such as striae, dust on the surface or even
cracks, do little harm except so far as the small loss of light is
LANTERN. 227
concerned. The condensers, on the other hand, are designed
simply to collect as much light as possible so that it shall pass
through the lens D. For ordinary projections, therefore the
spherical and chromatic aberration are unimportant so long as
they are not sufficient to throw the light outside of the lens D.
Any striae, dust or cracks are, however, liable to show upon the
screen, especially if, as is commonly the case, the field of view FF'
lies near the condenser. On the other hand if this distance is
considerable, the field of view is reduced, or larger condensers are
required.
In the most perfect instruments a large part of the light is lost.
Let A be a luminous point radiating light equally in all direc-
tions, and let the distance of BB r equal one third of its diame-
ter. Then a little more than a fifth of the whole light, or 22.3 per
cent will fall on it. The condensers consist of from two to five
lenses, the projecting lenses of from two to six, and the object
ordinarily consists of one or two plates of glass. Therefore the
light has to traverse from four to thirteen pieces of glass. Taking
six as the most common number, and recollecting that .90 only is
transmitted by a clear glass plate, we see that .90" = .53 of 22.3
or 11.8 per cent only is received on the screen. A portion of this
light might be saved by a reflector, and this is sometimes done with
the electric light, but with the calcium light the front portion
only of the lirne is illuminated. The reflector should be spherical
with the light at the centre, and in this case were there no loss
the light would be doubled. In practice, however, the gain is
much less.
The most obvious way to increase the light is to bring the con-
densers nearer the light. But the limit is soon reached, owing to
the heat, if this distance is reduced below three inches. On this
account a piece of glass is sometimes interposed between the
light and the first condenser. If cracked it is easily replaced and
the lens is protected. This is especially desirable with the elec-
tric light since minute pieces of incandescent qarbon are liable to
snap off and fuse into the glass.
Condensers are made of various forms; the simplest is that
shown in Fig. 106, and consists of two plano-convex lenses with
their curved surfaces turned towards each other. In this position
228 LANTERN.
the aberration is least, according to the rule that the most curved
face should be turned towards the least convergent beam. For-
merly condensers were made of three equal double convex lenses,
but the increased loss of light was an objection. A form much
used at present is the Cresson condenser formed of four lenses,
three designed to render the rays parallel, and the fourth to con-
verge them to D. The first lens is 4.5 inches in diameter, the
others 5 inches. The radii of curvature of the first six surfaces
are oo, 4.5, 30, 6, 52, 8.75 inches respectively. Evidently the
first lens is plano-convex, the second a meniscus and the third a
double convex lens. They are placed near together, and united
are equivalent to a single lens with but little aberration, having a
focus only three inches distant from the plane surface of the first
lei^s. The light being placed at this point the rays emerge very
nearly parallel. They are concentrated by a double convex lens
whose two surfaces should have curvatures in the ratio of one to
six, since this form gives the least aberration. For use in large
halls the Morton condenser is preferable to the Cresson. It con-
sists of three plano-convex lenses with radii 4.5, 3.5 and 4 inches,
and diameters 4.5, 5 and 5 inches. Its focal distance is only 2
inches, so that it takes in nearly twice as much light as the Cresson
and produces a proportionately brilliant image, but the aberration
is also much greater.
To project large objects, large condensers are needed. These
have the advantage when a very intense light is used that they
are less liable to crack, since they must be placed farther from the
light. A simple and quite efficient arrangement is to bring BE'
Fig. 106, somewhat nearer to A, so that the light shall diverge
after passing it. CO' is then replaced by a plano-convex lens
seven or eight inches in diameter placed at such a distance that it
shall be wholly within the cone of rays. A projecting lens of
suitable focus is then placed at D and an object as large as the
lens replacing CO' may thus be projected. By this arrangement
but one large lens is required. For most purposes, however, con-
densers four or five inches in diameter are most convenient, as,
when -greater than this the image at D is enlarged, and conse-
quently a larger projecting lens is required.
The conditions of excellence in the projecting lenses are nearly
LANTERN. 229
the same as those for the portrait lenses of a photographic camera,
and hence such lenses are much used for projections. A dia-
phragm cannot, however, be used, on account of the loss of light.
When sunlight is used the conditions are much simplified, since
the beam is already parallel. The condenser may consist of a
simple convex lens of diameter a little greater than that of the
object to be projected, and of focal length as much less than the
distance of the screen as the diameter of the lens is less than that
of the desired circle of light. The light will form a cone at the
apex of which is placed the projecting lens, which may consist of
a simple convex lens of small diameter with a focus somewhat
less than that of the condenser. The aberration will be small,
since all the light will pass very near the centre of the projecting
lens, and excellent projections may accordingly be obtained by very
simple means.
In a. lecture room accommodating a hundred persons, a screen
of eight or ten feet square is most convenient. The lantern
should be placed opposite the centre of this, on a table three feet
high, the whole being raised on a platform so that the light shall
pass entirely over the heads of the spectators. The lenses being
placed in position in front of the lantern, the room is darkened
and. the calcium or other burner inserted in the lantern and
lighted. A circle of light will now be formed on the screen which
may be rendered concentric with it by inclining or turning the
lantern. To see if the light is at the proper distance from the
condenser, remove the front lens of the latter and the projecting
lens and move the light until the emergent rays are approximately
parallel, or until an inverted image of the light is formed upon
the screen. Replace 'the front lens of the condenser and, where
the emergent cone of light has the smallest cross-section, in-
sert the projecting lenses. If now any object, as a pencil, is
interposed near the condenser, an enlarged inverted image of it
will be formed on the screen. This marks where the objects
should be placed. As the latter are commonly photographs on
glass, a wooden holder is convenient in which they may be held
and brought into position by sliding them along a groove in front
of the condensers. Having once adjusted the apparatus, the light
is brought into position, without altering the lenses, by moving it
230 LANTERN.
until the circle on the screen is bright and uniform. The presence
of irregular bluish patches generally denotes that the light is
too near the condensers, but if, on removing it, the top of the
circle remains dark the light is too high and should be lowered,
and raised if the upper part is dark. If the right hand portion is
dark the light must be moved to the right, and vice versa. If the
light is too far, the field will be bordered with a reddish fringe.
Finally, the picture being placed in position, it is carefully focussed
by moving the projecting lenses until the image on the screen is
as distinct as possible.
By observing a few simple precautions the effect of the pictures
may be greatly improved. Thus in the presence of an audience
the bright circle of light should not be formed on the screen
before showing a picture, or the latter will look dark by contrast.
Never allow the light to shine directly on the audience, or their
eyes will be dazzled and the effect of the pictures diminished.
Two picture-holders are needed so that one picture may be put in
place while the other is being exhibited. Holders are sometimes
made with places for two pictures and slide back and forth, each
picture after it is shown being replaced by another without remov-
ing the holder. Sometimes the pictures slide in a groove and are
pushed in, one in front of the other.
Before the exhibition, the pictures should be arranged in order,
all turned in the same way, so that they may readily be placed
in the holder, inserted in the lantern upside down, and turned so
that the right side shall be towards the light. If the last condi-
tion is not fulfilled, letters and numbers will be read backwards,
and views will appear turned end for end. The rule is that the
lettering must read correctly as seen from the light. The first
picture to be shown should be tried in the lantern beforehand, the
position of the light adjusted and the projecting lens very care-
fully focussed. The light is then extinguished and a black cloth
thrown over the -projecting lens. .When the picture is to be
shown, the light is produced, the room darkened and the cloth
then removed. Place the second picture in its plate-holder and
when the first has been seen long enough, replace it quickly by the
other. It is a good plan to cover the projecting lens with the
black cloth when changing the pictures, so that the audience shall
LANTERN. 231
not see them move. The brightness also appears greater, by con-
trast with the intervening darkness. If the light is very bright it
will be found to be more 'agreeable and much less trying to the
eyes not to render the room entirely dark.
Sometimes the lantern, instead of being placed in front of the
screen, is placed at an equal distance on the other side of it. The
screen should be free from seams, and moderately transparent.
There is always, however, a great loss of light, and an assistant is
needed to manage the lantern. Another objection is, that, if the
spectators are directly in front, they will see the light through the
screen as a brilliant spot of light. The advantage, however, is
that the lantern is out of the way and does not obstruct the view
or otherwise disturb the spectators.
Dissolving views are rarely employed in scientific work, except
in showing some of the phenomena of color. They are produced
by two lanterns adjusted so as to throw similar pictures, as a
summer and winter view of the same landscape, on the same part
of the screen. The light is wholly cut off from one lantern, and
this is gradually uncovered while the other is obscured, so that
one picture gradually fades into the other. The change may be
effected by two sets of wedge-like points attached to a rod which
may be moved laterally. In one position the light is completely
cut off where the bases of the wedges come together, and, as the
rod is moved, more and more light passes between the points
until they are entirely removed. Another form of screen is circu-
lar, with an aperture formed of two circles whose centres do not
coincide. As this screen is turned, the light is admitted in vary-
ing amounts from one or the other lantern. Sometimes a single
lantern is used with two condensers at right angles to each other,
the two beams being rendered parallel by reflection from mirrors.
The phantasmagoria might have application in scientific work,
though now only used as a toy. The lantern in this case is
placed behind the screen, and the pictures are commonly painted
in bright colors on a dark background. The lantern is first placed
close to the screen forming a very minute picture, which enlarges
and therefore seems to approach as the lantern is withdrawn.
The light should be much reduced at first and gradually increased,
232 OBJECTS FOR PROJECTION.
and the focus altered as the lantern is moved. Both these ad-
justments may be effected automatically.
191. OBJECTS FOR PROJECTION.
Apparatus. The lantern and the various objects suitable for
projection described below.
Experiment. The most common objects for the lantern are
photographs of the form known as glass positives described Vol. I,
p. 187. Almost any known object may thus be shown to an audi-
ence, for instance, landscapes, buildings, sculpture, machinery, and
especially engravings and woodcuts. The latter form an excellent
substitute for diagrams, and by collecting the best illustrated books
and selecting cuts from them, a set of excellent diagrams is
obtained at a trifling expense, with the advantage of furnishing per-
fect fac-similes of the originals. In copying woodcuts they must
be very sharply focussed and not exposed too long, so as to give a
density between an ambrotype and a negative. The size of plate
commonly used is 3"by 4" known to photographers as quarter
plates. Sometimes double this or "half size" is employed. To
protect the negative, it is sometimes covered by a second plate of
glass held in place by strips of paper around the edges. If, how-
ever, the plates are varnished they are not very liable to injury,
especially if kept in boxes with saw-cuts in the sides to prevent
their surfaces from touching. If thick paper is pasted on the side
on which the photograph is taken, they may be laid upon each
other without danger. This also renders it easier to label and
number them. If the picture does not fill the plate, the blank
edges must be covered either with paper or black paint, as a broad
white border will make the picture look much fainter.
Many other objects may be shown in the same way, for instance,
acoustic curves on smoked glass or collodion, or any thin object
whose outline is characteristic. A great field is opened by using
the -screen as a blackboard. For this purpose a common smoked
glass may be employed, the drawing being prepared beforehand or
even in the presence of the audience. An excellent surface is ob-
tained by preparing a plate for a photograph, exposing to a strong
light, developing and fixing ; drawings of great delicacy may be
OBJECTS FOR PROJECTION. 233
made on this by removing the film with a sharp point. As it is a
little difficult in this case to draw so well on a vertical surface, the
vertical lantern described below is often more convenient. To draw
objects in dark lines on a bright ground, thin sheet gelatine may
be employed or a simple sheet of glass, first covering it with a
thin coating of gum by pouring dilute gum water over it, and
then letting it dry. Glass perfectly free" from grease may also be
employed, but less conveniently. India ink should be used, as it
adheres better than common ink.
A great variety of models may be well shown by projection if
care is taken to make them of suitable size and so that they will
lie in one plane. For instance clock escapements, electro-mag-
netic engines and various forms of telegraph. A thermometer is
another good object, and small variations in temperature are thus
readily shown.
Many of the laws of animal electricity may be shown to an
audience by projecting a frog's legs on the screen, and showing
the twitching caused by electrical excitations. If large condensers
are employed, the whole frog may be shown, thus rendering the
experiment much more intelligible.
An interesting experiment, especially with the electric and
magnesium lights, is to project the light itself upon the screen.
This is easily accomplished by removing the condensing lenses
and bringing the projecting lenses nearer, until a distinct inverted
image of the light is seen. With the electric light the wearing
away of the carbons, and the action of the regulator is clearly
shown. When sunlight is used, the sun itself may be projected on
the screen if the mirror of the porte-lumidre is plane. The best
effect is obtained by placing a telescope horizontally as if we
wished to look at the image in the mirror, and drawing out the
eyepiece somewhat beyond the position of distinct vision for
parallel rays. The image formed at the focus of the objective will
then be projected on the screen. The sun spots may thus be well
shown, and during a partial eclipse the phenomena may be
watched by a large number at a time.
Some interesting effects may be obtained with the direct light,
removing both condensing and projecting lenses. Thus if any
large object is interposed, its shadow will be projected very
234 OBJECTS FOR PROJECTION.
sharply on the screen. If now a plate of ground glass is inserted,
the shadow becomes hazy, the change increasing with the distance
of the glass from the light. The difference between a penumbra
and shadow is thus well shown. With sunlight a condensing lens
should be interposed to bring the parallel rays to a focus.
The effect of a mirage may be shown on the screen by inserting
as an object a metallic plate with a small hole in it, or better,
removing the condensers, interposing the plate, and projecting the
aperture on the screen as when projecting the image of the light.
Now interpose in the beam of light a nearly horizontal plate of
metal heated below by a gas burner. The hot air in contact with
the plate will reflect a portion of the light forming an irregular
image of the aperture above the other image and readily distin-
guished from it by its irregular waving motion.
Another interesting class of phenomena are those of phosphor-
escence and fluorescence. Many solids, especially the phosphides,
if exposed to a strong light, continue to shine in the dark. Sets of
tubes are sometimes prepared with substances which emit various
colors after such an exposure. The electric and magnesium lights
are particularly adapted to produce these effects, owing to the pre-
dominance of the more refrangible rays. It is only necessary to
expose the tubes to the light for a few seconds, taking care to
interpose a screen to cut off the light from the eyes of the audi-
ence ; then holding the tubes up they will shine for some time
quite brightly. The fluorescence of sulphate of quinine and other
substances is well shown by painting a flower or other object
with their strong solutions on a sheet of white paper. It will be
almost invisible by ordinary light, or, if hung against the screen,
by the circle of light from the lantern. If, however, a piece of
violet glass or even blue cobalt glass is interposed, the portions
covered with the fluorescent substance will shine brightly.
The curious change of color of some cobalt salts with heat is
well shown by covering a piece of glass with a strong solution of
chloride of cobalt and gelatine. If projected on the screen it
will give a pink tint to the light which will gradually change to
deep blue under the influence of the heat. The pink color will be
restored if the plate is left in a cool, moist place:
The cbromatrope consists of a disk of glass mounted so that it
TANKS. 235
can be made to revolve rapidly in its own plane, and used as an
^object in the lantern. In the best form, the glass is ground to a
circular disk and made to revolve on wheels covered with rubber.
By using circles covered with glass or gelatine of different colors
the effect of their combination is readily shown to an audience.
Among the best effects are those of yellow and blue glass which
produce white when combined, and red and green which produce
a yellow circle on the screen, when the disk revolves rapidly.
Colors may also be combined by partially covering the projecting
lens with pieces of glass of various colors taking care that they do
not overlap. Chinese fireworks are formed of two disks of glass
painted in various colors, and so mounted that they shall turn in
opposite directions. The motion should be comparatively slow,
and by varying the colors, forms and positions of the figures, great
variety is attainable. Two sets of circles with centres on one
side of the centre of motion give good results. Replacing the
colored glases by perforated cards, wire gauze, or lace, curious in-
terference figures are obtained.
The formation of crystals are among the most beautiful of
objects for the lantern. Prepare a hot saturated solution of the
salt to be shown, pour it on a plate of glass and insert in the
lantern. As the water evaporates the crystals will be formed
covering the screen with forms of great beauty and variety. The
rapidity of formation may be increased by using alcohol instead of
water. Almost any crystallizable salt may be employed, but
among the best objects may be mentioned urea, which forms
beautiful needles, also oxalate and chloride of ammonium and ni-
trate of potash.
The effects of a kaleidoscope may be obtained on a screen by
inserting the instrument between the condensers and projecting
lenses after removing the plate of ground glass. The great
difficulty is the loss of light and unequal brightness of the re-
flected image.
192. TANKS.
Apparatus. The lantern and two or three tanks, each formed
of two pieces of plate glass held together by four clamps and
separated by a strip of rubber half an inch thick. The rubber is
cut straight and bent so as to form the bottom and two sides of
236 TANKS.
the tank. Notches should be cut in one side that it may bend
more easily. Liquids may be added drop by drop by pipettes, of ^
which the most convenient form consists of pointed glass tubes
terminating above in elastic rubber balls. A galvanic battery of
sufficient power to decompose water is also needed, and the fol-
lowing chemicals ; litmus, cochineal, red cabbage, alcohol, some ani-
line color, sulphuric acid, ammonia, sulphate of copper, acetate of
lead, ferrocyanide of potassium, perchloride of tin and lime water.
In the bottom of one tank a small coil of platimum wire is placed
which may be heated by the battery, and in another tank are
two platinum electrodes. Some small test tubes, U tubes and glass
rods are also needed. Various small living animals as minnows,
larvse, etc., may also be shown on a large scale upon the screen.
To erect the image a right angled or erecting prism is required.
Experiment. A great variety of chemical and electrical ex-
periments may be shown by the use of tanks. Place one of
these in the lantern as an object and
half fill it with water. The inversion
of the image is here an objection, as
the water will appear on the upper
part of the screen and the air below.
It may be obviated by placing the light
angled prism in front of the projecting lens, with its hypothenuse
horizontal. The image will then be reflected from the latter and
being inverted a second time will represent the object as erect, as
is shown in Fig. 107. It is evident that the ray A. will be re-
flected to A', and JB to B', i.e., the image inverted. Zentmayer's
erecting prism differs from this in having the angles 27, 27 and
126, as shown by the broken lines, so that the rays will pass
through the prism parallel to its faces. It has the advantage that
no glass is wasted and with glass of given thickness a broader
beam is transmited in the ratio of 1.44 to 1.
The convection currents produced by heat are well shown" by
filling the tank containing the platinum coil with water, and con-
necting it with the galvanic battery. Immediately a current of
warm water will rise from the platinum and spreading over the
surface descend on the sides. These currents are rendered much
more visible by adding to the water a little strong solution of
cochineal which will at once fall to the bottom of the tank and be
raised by the heat to the surface. A similar convection due to
TANKS. 237
their difference of density is well shown by adding to a tank con-
taining water a little perchloride of tin. Quite a different effect
is obtained by adding to a tank filled with alcohol a drop at a
time of one of Judson's aniline colors which, as it falls, will divide
up into root-like threads.
The rise of water in capillary tubes is readily shown on the
screen by dipping a fine glass tube into the tank, and the hyper-
bolic curve between two plates, by holding a plate against one
side of the tank. The liquid in this case should be colored.
Three methods are available for showing chemical decomposi-
tions on the screen. First, mixing the substances directly in the
tank. This is generally the best method, but, since the tank must
be washed out after each decomposition, much time is required.
In the second method the decompositions are effected in test
tubes immersed in the water of the tank. They may, therefore,
be changed rapidly and the appearance more nearly resembles a
real chemical analysis. The third method will be described in
connection with Experiment 194. Fill a tank with water and
color it blue with a little litmus. Add a few drops of acid and
Stirling with a glass rod the color will change to red. The blue
color may be restored by a little ammonia, and the effect repeated
indefinitely. If cochineal is used instead of litmus the acid will
turn it yellow, and ammonia, purple. A solution of red cabbage
in boiling water is blue, but will change to red with acids, to green
with alkalies, and to purple with alum. Wash out the tank and
fill with a dilute solution of sulphate of copper, which is a pale blue.
A little ammonia produces a white opaque precipitate appearing as
a black cloud, which, on adding more ammonia, dissolves into a
clear deep blue liquid. A little acid makes the precipitate reap-
pear. To the clear liquid add a drop of ferrocyanide of potassium.
Instantly clouds of the dark brown ferrocyanide of copper appear.
Place a test tube in the tank after refilling with water ; it will look
like 'a polished metallic rod, owing to total reflection. On filling it
with water, however, it will nearly disappear. Chemical reactions
in such a tube may be shown to an audience very much as they
are ordinarily seen by a single individual, and a complete course in
qualitative analysis may be thus illustrated. The great difficulty
is, that all opaque precipitates, whatever their color, will appear
238 STROBOSCOPE. 4
black. Thus sulphate of baryta and oxalate of lime appear black
instead of white. The generation of hydrogen or carbonic acid is
well shown on the screen, also the turbidity of lime water on add-
ing carbonic acid. To effect the latter, it is only necessary to fill
the test tube with lime water and blow through a tube immersed
in it, when the carbonic acid of the breath will precipitate the
lime.
Electrical decompositions may also be shown in two or three
ways. Place in the lantern the tank having two platinum elec-
rodes, fill it with dilute sulphuric acid and connect the battery. A
torrent of bubbles will at once ascend from each electrode, the
hydrogen being given off from the negative, the oxygen from the
positive terminal. They may be distinguished by the greater
volume of the hydrogen which, when the current is reversed will
appear at the other electrode. If the negative electrode is pallad-
ium instead of platinum, the hydrogen will be absorbed instead
of set free. If then the current is reversed, the gas will be set free
tumultuously, the palladium twisting and turning like a serpent.
The other decompositions described in Experiment 95 may be
shown similarly. That of acetate of lead is especially beautiful,
the deposited lead resembling a tree and growing rapidly on the
screen while bubbles of oxygen are set free at the other pole.
When the current is reversed the tree appears to wither, and is
gradually absorbed or dissolved, no bubbles appearing until all the
lead has disappeared. Meanwhile a second tree is forming on the
other platinum terminal. The other decompositions are better
shown in a U tube immersed in a tank of water, one electrode
being placed in each arm of the tube.
In lectures on natural history a great variety of minute marine
animals may be projected living on the screen by placing them in
tanks containing water.
193. STROBOSCOPE.
Apparatus. The lantern and a circular disk of tin perforated
with several equidistant holes, and mounted so that it may be
turned uniformly by some small motor, or by hand. Its weight
should be considerable that it may run uniformly like a fly-wheel.
As objects we may use a tuning fork whose vibrations are sus-
tained electrically, an electro - magnetic engine or a fan wheel
STROBOSCOPE. 239
regulating clockwork. One of the best objects is a large wooden
wheel painted in radial stripes, which may be turned uniformly,
but almost any moving objects may be employed.
Experiment. The effect of the stroboscope depends on the
persistence of vision, or the fact that the image of an object on the
retina, even if seen but for an instant, will remain for quite a frac-
tion of a second. Accordingly if the object is seen at very short
intervals, it will appear to be visible continuously. Project the
circle of light on the screen and interpose the edge of the tin disk
at the point where the cone of rays is smallest. As this point
coincides with the projecting lens, the latter should be altered,
since freedom from aberration is not very important in this ex-
periment, while if the disk is not properly placed the edges of the
objects shown will appear indistinct. If now the disk is turned,
the screen will appear alternately light and dark, but if the mo-
tion is rapid the light will appear to be continuous. When, how-
ever, any moving body is introduced in the beam of light, a
number of images are seen. This is well shown by letting a
person walk in front of the screen or by shaking the hand near
the projecting lens. In the latter case, the number of fingers will
seem to be enormously increased. To study the effect more care-
fully, remove the tin disk, place the large wheel against the screen,
and set it in motion. It will now appear as a circle of uniform
grayish color. Replacing the tin disk and turning it, a certain
speed will be found at which the large wheel will turn through an
angular distance just equal to that between its spokes while the
tin wheel passes from one aperture to the next. The large wheel
will then appear to be at rest, although really revolving very
rapidly. If the motion of either wheel is altered, the large wheel
may be made to appear to turn slowly in either direction, accord-
ing as the interval between the flashes of light is a little greater
or a little less than that between the passage of one spoke of the
large wheel to the place occupied by the next preceding. This
explanation may be tested by attaching a piece of white paper to
one spoke of the wheel, when it will be seen to be in rapid motion
although the wheel may appear to be at rest. By increasing the
speed of the tin disk exactly two or three times, the number of
spokes will appear to be increased in the same ratio. This effect
240 VERTICAL LANTERN.
*
is best seen if the wooden wheel has but few spokes. The tuning-
fork or electro-magnetic engine form excellent objects for the stro-
boscope. If large, they may be placed near the screen, and in this
case the projecting lenses should be dispensed with, but if small
they are best seen when projected in the usual way. Any other
object, whose motion is too rapid to be easily followed by the eye,
may be shown in the same manner.
Excellent stroboscopic effects may also be obtained by a Holtz'
machine or an induction coil and condenser, with the advantage
that, as the spark is instantaneous, the image of the moving object
is perfectly distinct.
194. VERTICAL LANTERN.
Apparatus. A vertical lantern and various objects for projec-
tion, several plates of glass, some camphor and essential oils, a small
magnet, iron filings, a sieve, a magnetic needle, which may be bal-
anced on a needle point fastened to a plate of glass by a drop of
sealing-wax, and a tank formed by cementing a ring of glass to a
glass plate are required.
Experiment. Many objects may be brought into a horizontal
plane much more conveniently than into a vertical plane, and
these may be projected by the arrange-
ment represented in Fig. 108 and known
as the vertical lantern. A is the source
of light, JS' the first lens of the con-
denser or portion rendering the rays
parallel, and GG' a plane glass mirror
which reflects the parallel beam of light
vertically. CC' is the front lens of the
condenser which brings the light to a
focus at Z> where the projecting lens is
Kg log placed. It is then reflected horizontally
to the screen by the right angled prism
or plane mirror E. Although the prism reflects more light than
the mirror, yet it is open to the objection that, unless the screen is
much above it, the lower portion of the circle of light will be
darker than the rest, because the light is not totally reflected ; the
two parts will be separated by a colored curved line, and the
portion not totally reflected will, if not intercepted, form an
VERTICAL LANTERN. 241
image on the ceiling. The mirror has the further advantage that
its size may be increased much more readily than that of the
prism.
Any object may now be projected by merely laying it on (7(7,
focussing by raising or lowering Z>, and bringing the circle to the
centre of the screen by moving E. Since E inverts the image,
the object should be so placed that the top shall be towards the
light, and that lettering shall read correctly when seen from above.
Project in this way some photographs and other objects. The
principal objection to this arrangement is that there is a consider-
able loss, of light by the two reflections, and that, consequently,
the projections are less bright. It is, however, particularly con-
venient for making drawings or writing on the screen, since the
prepared surface is horizontal, and the letters need not be written
backwards.
The simpler laws of magnetism may be admirably shown in the
vertical lantern. Placing the compass needle on its pivot in the
field, it will point north and south, and approaching a second
magnet or needle, their attractions and repulsions are well shown.
Bringing a second suspended needle into the field near the first,
and setting one of them swinging, their complex mutual action is
well seen. The formation of magnetic curves, described in Experi-
ment 116, is admirably adapted to the vertical lantern. It is only
necessary to form them on a plate of glass instead of on card-board.
The attraction and repulsion of parallel currents, of solenoids,
and the effect of the wire conducting a current on a magnetic
needle, all form excellent objects for the vertical lantern.
Chemical and electrical decompositions may be well exhibited
in the vertical lantern. The simplest way is to pour a few drops
on a plate of glass or into a watch glass, when effects similar to
those of Experiment 19 may be obtained, with the advantage that
the .plates may be almost instantly cleaned. Almost any delicate
experiment can be better shown in the vertical lantern, since
where careful manipulation is required, it is generally much easier
to work with the object in a horizontal, then in a vertical plane.
Living objects may also be thus projected more conveniently.
When we wish to employ a considerable quantity of water, the
tank is used. The motion of fragments of camphor on the sur-
242 LANTERN POLARISCOPE.
face of water and Toralinson's cohesion figures may also be best
presented to an audience by the vertical lantern. The tank,
must be perfectly clean, washed with potash, then with distilled
water and allowed to dry, but not be wiped. Fill it with water and
add a drop of almost any of the essential oils, as cinnamon or
coriander, when various curious forms are obtained as it spreads over
the surface.
The transmission and interference of waves are well shown by
such a tank filled with alcohol, in which the motion is slower
than in water. The waves may be excited by touching the
surface with a sharp point, or allowing drops of liquid to fall upon
it. The foci of an elliptical tank are shown by immersing an
elliptical diaphragm within the glass circle. The best effect is ob-
tained by placing the lens at double the distance required to
produce an image of the surface of the liquid on the screen, or
more properly by using a lens of one half the usual focal length.
Wave motion may also be shown by reflection from the surface of
mercury. A fine tube is placed nearly in contact with the surface
and connected with a cavity covered with a piece of sheet rubber.
Tapping on the latter sends a puff of air upon the mercury, gener-
ating a wave. A series of waves may be maintained by a current
of air passed through the tube, which should then be made to
touch the liquid.
Waves may be admirably shown by Crova's apparatus, which
depends, however, on a wholly different principle. A number of
curves are drawn on a circular disk of blackened glass and a dia-
phragm interposed with a slit in it. Projecting this as an object,
a series of dots appear which alter their position as the disk is
turned. By employing suitable curves various forms of wave
motion may thus be shown. Transverse vibrations are also illus-
trated by a disk with a series of parallel slits through which differ-
ent parts of the curve are projected.
195. LANTERN POLARISCOPE.
Apparatus. The usual method of projecting the phenomena of
polarized light is readily understood from Fig. 108, if we slightly
modify it and regard it as a horizontal, instead of a vertical sec-
tion. The light being rendered parallel by BBj falls on G &
LANTERN POLARISCOPE. 243
which now represents a bundle of thin plates of glass inclined at
an angle of 55 instead of 45 so that the light will be turned 110
and then fall on the lens CC' which is placed at right angles to
the reflected beam. The light is brought to a. focus at D where it
passes through a large Nicol's prism, the projecting lens being
placed between it and CC'. The reflector E is not used. A large
Nicol's prism forms a better polarizer than the bundle of plates, as
it gives a brighter image, but the expense is much greater.
Experiment. Turn the lantern nearly at right angles to the
screen, so that when the plates of glass are set at an angle of 55
to the incident light the reflected beam shall be thrown on the
screen. Then interpose the lens CC' and the projecting lens,
when a circle should be formed on the screen as usual, only some-
what less bright. To see if the light is totally polarized place the
Nicol's prism in front of the projecting lenses, taking care that it
shall be at the point where the beam of light has the smallest
cross-section. This is essential to save as much light as possible.
The projecting lenses may be of larger size than usual, a simple
plano-convex lens giving good results. On turning the prism, the
brightness of the circle of light on the screen will vary, and it
will disappear completely if the polarization is total. If this is
not the case, the angle of the plates must be altered until this
condition is fulfilled. The simple laws of polarized light may now
be demonstrated; for instance, using as an object a diaphragm with
a small hole in it, and inserting a double image prism, two images
will be formed whose intensities will vary as the prism is turned.
The eifect of other analyzers, as a tourmaline or bundle of glass
plates, may also be tested.
Any of the phenomena of polarized light requiring a parallel
beam may next be shown by placing the object near the front lens
of the condenser and forming an image of it on the screen with
the projecting lens, when, if doubly refracting, it will appear of a
color dependent on the position of the Nicol's prism and its own
thickness. If the object is too small to be shown well in this way,
a projecting lens of shorter focus may be used. Project in like
manner some selenite figures, compressed and bent glass and
unannealed glass. Interposing a plate of mica near the projecting
lens, it will render the light circularly or elliptically polarized.
Rotary polarization, Babinet's wedges and a bi-quartz may be
244 LANTERN MICROSCOPE.
similarly projected. Generally the most striking effect is obtained
by crossing the analyzer and polarizer so that the field shall be
perfectly dark until the object is inserted.
Objects requiring a converging beam are readily projected by
placing them near the analyzer, and the light will be increased by
removing the projecting lens, though the circle on the screen will
no longer have a distinct border. Try in this way objects 1 to 8
in Vol. I, Experiment 92. The rings will appear colored, since the
light is not monochromatic. If the lime light is used, remove the
lime cylinder and replace it with a glass rod or a stick dipped in
salt as described in Experiment 200, when the rings will appear in
vastly increased number and extent. They will be alternately yel-
low and black.
The field of view is not very large in this case, that is, the angle
between the extreme rays passing through the crystal is compara-
tively small. To remedy this difficulty, two very convex lenses
are sometimes inserted, in the place of the projecting lens, at a
distance apart equal to the sum of their focal distances, and the
objects interposed between them. The two systems of rings of a
biaxal crystal may thus be shown, even if the angle between the
axes equals 60.
196. LANTERN MICROSCOPE.
Apparatus. The lantern with a projecting lens, an objective
of short focus, and a stand for the object by which its position may
be carefully adjusted. A tank of water or solution of alum is
needed to cut off the heat, and should be placed near the conden-
sers. Any objects, if not too small, may be employed, but the
best are preparations of whole insects, injected tissues, and minute
living animals.
Experiment. The conditions for success in projecting minute
objects on the screen are very simple. The light should be very
bright but small, and the condensers as free from spherical aberra-
tion as possible, so as to concentrate the light at the projecting
lens into a very small space. The diameter of the objective
should be large, so that it may take in as much of the light as
possible, and on this account microscope objectives, except for very
low powers, seldom give satisfactory results. An objective of
much shorter focus than an inch is rai'ely desirable, on account of
OPAQUE OBJECTS. 245
the loss of light ; with sunlight, however, where the rays are
already very nearly parallel, the aberration is small, and magnifi-
cent effects are obtainable with common microscope objectives.
The light after leaving the condenser should pass through a tank of
water or alum which absorbs almost all of the heat, otherwise the
object is liable to be injured by the Canada balsam becoming
softened.
The magnifying power is much less than is ordinarily supposed ;
the angular enlargement, as seen from a distance equal to that of
the lantern, being only about eight or ten times with a one inch
objective. Hence, but little more can be shown than is visible to
a single observer with a common pocket magnifying glass. The
linear enlargement is much greater than this, being equal to the
ratio of the distance of the lantern from the screen, divided by
the focal distance of the objective. Thus, with a one inch objec-
tive, and a screen twenty-five feet distant, the linear enlargement
is three hundred diameters. But if we approach within a few
inches of the screen to get the full effect of this enlargement, the
irregularities of the surface and aberrations neutralize in a great
measure the advantage thus gained. With sunlight, however,
much higher powers may be used.
To project an object, see that everything is in proper adjust-
ment, the light burning its brightest, all the surfaces of the lenses
clean, and that the liquid in the tank is transparent. After some
time the bubbles that collect in the water should be removed, as
they reduce the light. The objective must be so placed that as
much light as possible shall pass through it, and the object placed
at the proper distance and carefully focussed. Objects of consid-
erable size will then show to great advantage, but those of greater
delicacy cannot be shown satisfactorily.
Effects of great beauty may be obtained, without reducing the
light too much, by combining the polariscope and microscope if
large objects are employed
197. OPAQUE OBJECTS.
Apparatus. A large lantern in which the doors are replaced
by curtains, or two smaller lanterns without projecting lenses, by
which the light is directed upon the object which is placed in a
246 LANTERN GALVANOMETER.
small dark box. An image is then thrown on the screen by a
projecting lens.
Experiment. Very many small objects cannot be projected on
the screen on account of their opacity, and the fact that their
shadows are not sufficiently characteristic. Accordingly various
plans have been tried to project objects on the screen as we
ordinarily see them, that is, by reflected light. The great trouble
is the want of sufficient brightness, and, but for this difficulty,
this method would doubtless be very largely used.
The simplest method of projecting opaque objects on the screen
is to remove the projecting lenses and condensers, and replace the
latter by a large, short focus, convex lens. The light is then turned
around, withdrawn to one side, and shaded so that it shall not
shine on the lens. If now any object, as the hand, is introduced
into the lantern near the focus of the lens, it will be strongly illu-
minated by the light and an enlarged inverted image of it will be
thrown on the screen. The best objects for such projections are
plaster-casts, jewelry, a watch open and closed, glass ware, flow-
ers, and any bright or sparkling objects. Unfortunately objects
are turned right for left so that print reads backwards. Paper
photographs do not show to great advantage,
probably because we involuntarily compare
them with the far more brilliant glass trans-
parencies.
Another method of projecting opaque objects
is shown in Fig. 109. A, A t are two calcium
or other lights, and -5, B' condensers rendering
their rays parallel. E is the object to be pro-
jected which is thus strongly illuminated. D
is a projecting lens by which an image of E
is formed on the screen. The advantage of this method is, that
two lights are used instead of one, thus producing a stronger
illumination, but the cross light thus thrown reduces the shadows
and thus destroys in a great measure the effect of relief.
198. LANTERN GALVANOMETER.
Apparatus. The lantern and the various forms of galvanome-
ters described below. For projecting the deflections of the mirror
LANTERN GALVANOMETER. 247
galvanometers, a convex lens of about a foot focus, and a dia-
phragm with a small circular hole are required. The diaphragm
should be so mounted that it may be inserted in the place of the
condensers.
Experiment. A large part of the various measurements of elec-
trical quantities depends on the deflection of a galvanometer nee-
dle. There are various ways in which this may be shown on the
screen. A simple and convenient galvanometer is made by sus-
pending a small piece of magnetized watch spring by a filament of
silk from a plate of glass, attaching a fine wire as a pointer, and
introducing it as an object in the vertical lantern. The upper
plate may be sustained by a ring of wood, forming a circular box.
Another plate of glass on which is photographed a graduated
circle forms the bottom of the box. The difference in level is so
slight that if the circle is focussed on the screen the image of the
index is still distinctly visible. Two coils of covered wire are
now wound on each side of the box just outside of the graduated
circle and a galvanometer is thus obtained of considerable delicacy,
while at the same time, owing to the short length of the magnet,
it will follow very nearly the law of the tangents. It is, there-
fore, possible to make quantitative measurements with consider-
able precision from readings on the screen. Various devices may
be employed to obviate the difference in focus of the needle and
graduated circle. Thus, two lanterns may be employed, one pro-
jecting the needle and the other the circle so that they shall be
concentric. Again, for the mirror of the vertical lantern a piece of
plate glass maybe used, and part of the light passing upwards
will form an image of the needle, while the remainder and larger
portion will pass through, and may be concentrated by an addi-
tional lens and an image of the circle projected like any other
object. The difficulty of want of delicacy from the distance of
the coils is sometimes obviated by drilling a hole through the
lens beneath the graduated circle and the mirror, and attaching
to the index a vertical wire, to the lower end of which and below
the mirror, is attached a second needle. The galvanometer is thus
rendered astatic and great delicacy may be attained, since the coil
surrounding the needle may be brought veiy close to it and may
be made of great length. The vibrations of the needle may also
243 PROJECTION OF LISSAJOUS CURVES.
be checked by attaching an air vane, or by allowing the lower end
of the wire to dip in a liquid.
The greatest delicacy is, however, attainable with the mirror
galvanometer, and it becomes desirable to consider how the deflec-
tions of such an instrument may be projected on the screen, since
it is equally applicable to electrometers, the horizontal pendulum,
and various other instruments designed to measure minute forces
or alterations in form.
Turn the lantern away from the screen, remove the condensers
and projecting lenses and insert the diaphragm. Place the galvan-
ometer in line so that the light shall shine through the circular
aperture upon its mirror. Interpose the lens and form a distinct
image of the circular aperture on the wall. A slight motion of
the mirror will now produce a large deviation of the spot of
light. If quantitative measurements are to be made, a large scale
must be hung on the screen or projected by a second lantern.
But generally the direction of the deviation is all that is needed,
and this is shown by merely resting a pointer against the wall
under the spot when no current is passing.
That the spot may be distinct and have the greatest brilliancy,
several precautions are necessary. The light is commonly first
reduced to a parallel beam by the condensers, and the diaphragm
then interposed ; but this arrangement seems to have no advan-
tages if the aperture is small, while there is considerable loss from
the reflection and absorption by the condensers. If a large aper-
ture is used the condensers become necessary to secure a uniform
illumination of the image.
199. PROJECTION OF LISSAJOUS' CURVES.
Apparatus. The lantern, a diaphragm with holes of various
sizes which may replace the condenser, a convex lens of about two
feet focus and two tuning forks with adjustable weights and with
mirrors attached to the ends of their prongs, are needed. The
curves may also be projected by the other instruments described
below.
Experiment. The curves of Lissajous are described in full in
Vol. I, Experiment 65, and their importance and beauty render it
desirable that they may be shown to many persons at a time.
PROJECTION OF LISSAJOUS* CURVES. 249
Remove the condenser and place the diaphragm near the light, so
that it shall shine through a small circular aperture. Form a
bright image of this on the screen by means of the lens. Then
interpose the fork, so that the light shall fall on one mirror, be
reflected from this to the other mirror, and thence upon the
screen. There it will form a bright spot, and, vibrating one or
both of the forks, the various curves will be produced. With sun-
light the curves will be very bright, but with the calcium light it
is quite difficult to obtain satisfactory effects. The mirrors should
be near each other and near the lens to give the best results. The
size of the curve will be proportional to the distance of the screen
from the mirrors and to the amplitude of the vibrations of the
fork. On the other hand, the spot, which should be as bright and
small as possible, will have a diameter proportional to the distance
of the screen. The diameter may be diminished by using a long
focus lens, but the mirrors must then be further from the lantern
and the size of the curves thereby diminished.
The curves of Lissajous may be shown on the screen on a much
larger scale by various mechanical devices. One of the best
of these consists of two pendulums vibrating in planes at right
angles to each other, their lengths being adjustable by raising or
lowering the weights forming their bobs. To one is attached a
plate of smoked glass which is placed as an object in the vertical
lantern, and to the other a metallic point which by its motion
scratches a line on the smoked surface. If now both are set in
motion together, a line resembling the curves of Lissajous will be
obtained, except that as the amplitude of the vibrations diminish
the curve will continually approach the central point. This diffi-
culty may be avoided by maintaining the motion of the pendulums
by clock-work or electricity.
Another arrangement consists of two sets of strong clock-work
by which two wheels can be driven at any desired speed. The
latter is varied by partially winding up the spring, if this is used
as a motor, or by altering the driving weights. On the face of
each wheel a pin projects, one of which moves in a horizontal, the
other in a vertical slit. These pins form two opposite comers of a
parallelogram of which the third corner is fixed, and the fourth
carries a plate pierced with a small hole which forms the object in
250 PROJECTION OF SPECTRA.
the ordinary lantern. Evidently this hole will rise and fall with
one wheel and move backward and forward with the other. By
varying the rate of motion of the two wheels all the curves of
Lissajous may be shown on a large scale, and the changes may be
made to take place continuously so that in a few minutes we may
show all the possible notes in the gamut. Two plates with
horizontal and vertical slits may also be used as an object, and
one raised and lowered, the other moved horizontally by two pins
attached to revolving wheels.
200. PROJECTION OF SPECTRA.
Apparatus. The lantern, a convex lens, and two large flint
glass or bisulphide of carbon prisms, or an Eaton's prism,
various metals whose spectra are to be shown, solutions of the
chlorides of the alkalies, some sodium, a platinum spoon, and some
sticks about quarter of an inch square are needed.
Experiment. To project a spectrum on the screen, the conden-
sers are replaced by the diaphragm with adjustable slit, and an
image of this formed on the wall with a lens. A prism is then
introduced in the path of the rays when a spectrum will at once
be formed to one side. Various precautions must be taken *to
secure satisfactory results. The breadth, or distance from the top
to the bottom, of the spectrum will bear nearly the same propor-
tion to the length of the slit, that its distance bears to the focal
distance of the lens. If this breadth is considerable, the condenser
should be placed between the slit and light, otherwise the edges
of the spectrum will be indistinct, the slit not being uniformly illu-
minated. With a long slit the colors will be curved owing to the
light passing obliquely through the prism. This is best remedied
by a curved slit turned the other way. The form should be para-
bolic and the amount of curvature should be the same as that of
the colors. As the prism is turned, the spectrum will attain a
minimum of deviation and the red end will move towards the
violet whichever way the prism is turned from this. It will be
noticed, however, that while when the edge of the prism is turned
away from the light the spectrum will shorten, when turned to-
ward the light the spectrum will increase greatly in length. This
method of lengthening the spectrum must be employed with mod-
PROJECTION OF SPECTRA. 251
eration, as the light rapidly diminishes and the change in focus
necessitates a change in position of the lens. This principle is
made use of in Eaton's prism, in which the deviation of a bisul-
phide of carbon prism turned so as to give a very long spectrum
is compensated by a crown glass prism turned the other way. A
long spectrum is thus produced directly on the screen, while with
an ordinary prism the lantern must be turned. Prisms are made
of flint-glass and bisulphide of carbon, the latter having a decided
advantage in the great dispersion they produce. Diffraction grat-
ings do not give satisfactoiy results from the want of light.
Some persons prefer to use a condenser and converge the light
upon the slit, inserting just in front of it a concave lens. This
method, which would have great advantages were the source of
light a point, loses much of its efficiency from the reflection,
absorption and aberration of the lenses.
A convenient arrangement for imitating various spectra is to
hang up a curtain of black lace and project the spectrum on it,
taking care that no bright objects are behind the lace or they will
be illuminated and rendered visible to the audience. Any spec-
trum may now be closely imitated by attaching strips of white
paper to the lace in such positions that they shall be illuminated
by light of the proper olor. A long strip of paper will represent
a continuous spectrum on which dark lines may be drawn if de-
sired. Faint lines or bands may be represented by darker paper
and very faint continuous spectra by white lace.
With sunlight, brilliant spectra may be obtained, but of course
they always contain the solar lines. The latter are so fine that it
is difficult to render them visible to an audience, and requires
careful focussing. They are best seen with a lens having a focal
length of two feet, or even more.
With the calcium light the spectra of the alkalies and alkaline
earths may be shown on the screen by removing the lime and
holding in its place in the flame a stick quarter of an inch square,
previously soaked in a saturated solution of the chloride of the
metal to be shown. A brilliant colored flame is thus produced,
and the wood chars slowly if dipped frequently in the liquid. A
rod of soda glass may be used in the same way to produce the
252 PROJECTION OF SPECTRA.
yellow line of soda, and this forms one of the best sources of
intense monochromatic light.
The reversal of the sodium line may be shown by producing the
continuous spectrum of the lime light, and interposing the flame
of a Bunsen burner in which a platinum spoon is held containing a
small piece of sodium. The latter bursts into flame, giving out
dense yellow clouds of sodium vapor which cut off the yellow
light, and form in the spectrum a black line in the yellow.
The spectra obtained by the electric arc are much brighter
owing to its intensity. The heat is so great that not only the
alkalies but many other metals are readily volatilized by it and their
spectra shown, for instance, cadmium, zinc, copper and lead. The
lower carbon is replaced by a number of carbon cups which may
be brought in turn under the upper cai'bon. A little of the metals
is placed in each cup and after adjusting the apparatus by the con-
tinuous spectrum of the carbons, the latter are somewhat more
widely separated so as to throw the continuous spectrum out of
the field. The spectrum of the incandescent metal vapor is then
projected on the screen, in some cases with great brilliancy.
The soda spectrum may be reversed as with the calcium light,
or less easily by placing some sodium on the carbons which are
then brought near together. The sodium vapor surrounding the
incandescent carbon cuts off the yellow light.
The absorption bands of dried blood, colored glass, or other
bodies, are well shown by interposing these substances in the
beam, when the continuous spectrum is formed on the screen.
For liquids, as solutions of didymium salts and permaganate of
potash, a wedge-shaped cell may be used. For gases and vapors,
as nitrous fumes and iodine, a globe with plane glass faces is inter-
posed in the same manner.
Appendix A..
ELECTRICITY.
ELECTRICAL phenomena may be explained according to various theo-
ries. One of the simplest, and for purposes of instruction, one of the
most convenient, is that which regards electricity as a material substance
devoid of weight, and infinitely more subtle than the most rarefied gas.
All space is supposed to be filled with this substance, and electrical
phenomena to be due to changes in its distribution. A prominent theory,
that of Edlund, assumes that it is identical with the ether by which
vibrations of light are transmitted. Electricity passes through some
bodies much more readily than through others. The latter are said to
have a much greater electrical resistance than the former. When the re-
sistance is small, the body is said to be a good conductor, when large, a
non-conductor or insulator. These terms are only relative, as there are no
perfect conductors or perfect insulators; that is, the resistance is never
either zero or infinity. When a body has more than its normal quantity of
electricity it is said to be positively electrified, and when less, negatively
electrified. It is by no means certain that these terms are not reversed,
as we have no certain means as yet, of distinguishing which is which.
As in the case of gases, the particles of electricity are supposed to be
mutually repulsive; hence when two bodies, one electrified positively,
the other negatively, are brought in contact, the electricity always tends
to pass from the former into the latter. This tendency is said to be
due to the difference in potential of the two bodies, or, in common lan-
guage, difference in tension. The term electromotive force is used to
denote the force which produces a difference in potential. The absolute
potential of a body is not used, since we have no standard with which to
compare it; and when a body is said to be electrified positively or nega
tively we mean with regard to the surrounding medium, or the part of the
earth in which it is placed. The passage of electricity from one body to
another having a less potential, is called a current, as in the case of gases
or liquids. The discussion of the phenomena due to electricity when at
rest, is called statical electricity, the phenomena of electrical currents,
dynamical electricity. In the former, as in frictional electricity, we have
commonly small quantities, but enormous differences in potential. In
dynamic as in galvanic electricity, very large quantities, but slight differ-
ences of potential.
Statical Electricity. The law for the amount of electrical repulsion is sim-
ilar to that of gravitation, being proportional to the product of the amounts
of electricity in the two bodies, and inversely as the square of the distance.
(253)
254 APPENDIX A.
If, now, two particles A and B are positively electrified with regard to the
surrounding medium, they mutually repel each other, since the repulsion of
the particles they contain is greater for each other than for the medium
which they displace. In general, then, two positively electrified bodies
repel each other. Now suppose the potential of the medium increased
until it is equal to that of the particle B, which contains the least electricity
of the two. Evidently now no action will take place, since the repulsion
of A on the surrounding medium is for equal volumes precisely the same as
that on B. The effect of A is composed of two parts, that on B, and that
on the medium surrounding it. These two must be just equal and oppo-
site, since their resultant is zero. Again, A' a effect on B alone would be a
repulsion, hence its effect on the surrounding medium would be to attract
B. Suppose, now, the electricity in B is diminished, or it is electrified neg-
atively with regard to the surrounding medium. The force of repulsion is
thus diminished, while the attraction due to the surrounding medium is
unchanged. The latter, therefore, is in excess, and the particles tend to
approach, or attract each other. Two bodies, one positive the other nega-
tive, therefore attract each other. Next, suppose the potential of the
medium equal to that of A, so that 5, which has a less potential, appears
negatively electrified. As before, the effect is zero, being composed of the
two equal and opposite effects, the effect of B and the medium surrounding
it on A, and that on the medium around A. But the first of these has been
shown above to be an attraction, hence the second must be a repulsion.
Now diminish the potential of A so that it will be less than that of the
medium. Evidently the force of attraction will be diminished, while the
repulsion will be unchanged. But now both A and B are negatively elec-
trified, hence two negatively electrified bodies repel each other.' These
laws are briefly expressed by saying that bodies containing like kinds of
electricity repel each other, while unlike, attract.
When B is a conductor of appreciable size at the same potential as the
surrounding medium, and A is positively electrified, a different effect is pro-
duced. The electricity in the part of B nearest A is repelled and driven
to the further end, so that the latter becomes positively electrified, the
nearest end negatively. One end is therefore repelled, the other attracted,
but the attraction is the greatest, since the distance is less. In the same
way, if A is negatively electrified the electricity in B will rush to the part
nearest it, being repelled by the surrounding medium least on that side.
The part next A will therefore be electrified positively, the further parts
negatively. As before, attraction will take place. If, then, a body electri-
fied either positively or negatively is brought near a conductor at the same
potential as the surrounding medium, attraction will take place, and the
further end of the conductor will be electrified the same way as the first
body, its near end oppositely. This phenomenon is known as induction.
Induced Currents. When currents of electricity flow in the same direc-
tion through two parallel conductors, attraction takes place; when in oppo-
site directions, repulsion. It may be proved mathematically that this law
follows from the above properties of electricity, if it is assumed that a
certain time is required for the force of repulsion to act between two parti-
cles at a distance. If, when the currents are passing in the same direction,
the conductors yield to the attraction and approach, a part of the energy of
the currents is lost, and they become weaker. On the other hand, if sud-
denly separated, the currents will be strengthened, the work done being
converted into electricity. If no current is passing through one of the
conductors, suddenly withdrawing the other will create one, while suddenly
ELECTRICITY. 255
approaching it will produce a current flowing in the opposite direction.
The more rapidly the conductor is approached or withdrawn the more
marked the effect. Hence the best result is attained by suddenly making
or breaking the circuit, as this has the same effect as instantly bringing
the conductor from an infinite distance, and again removing it to infinity.
The conductors are commonly wound in coils in order to obtain a great
length in a small space. By making the second coil of fine wire of great
length, a current may be induced in it of high potential, since each coil
will add to the effect of the others.
Magnets. Ampere explained all the phenomena of magnets by supposing
that an electric current flows around each particle of iron. In a magnet
all these currents flow in the same direction, which is, at the south end,the
same as the hands of a watch. The currents in the interior neutralize each
other, those only on the exterior being perceptible. In soft iron the cur-
rents flow in all directions, but are easily brought into the same plane on
the approach of a magnet. In hardened steel, on the other hand, this
change takes place only with difficulty, but is permanent when the magnet
is removed. When the opposite ends of two magnets are brought near
each other the currents flow in the same direction, and hence attract. If
the ends are alike the currents are in opposite directions, and hence repel.
Other magnetic phenomena are simply explained in the same manner.
. Electro-Magnetism. When a current traversing a conductor is brought
near a magnet, it attracts its currents and tends to make them parallel to
itself, in which case the magnet will assume a position with the line con-
necting its poles at right angles to the current. The side to which the
north end will be diverted may be determined from the rule given above,
or it may be remembered by the law given by Ampere, that if the observer
imagines himself placed in the conductor facing the magnet and the current
entering at his head, the north pole will always turn to the right. If soft
iron is used instead of a magnet, all the currents will be turned in the same
direction parallel to the conductor, and it will become magnetic. The con-
ductor is commonly wound in a coil around the soft iron, and the poles are
readily distinguished by recollecting that the end around which, when we
face it, the current flows in the direction of the hands of a watch, is the
south pole.
Magneto-Electricity. A current may be induced in a conductor by the
currents of a magnet, precisely as by a current in a second coil. It is
only necessary to insert the magnet in the coil, or withdraw it rapidly, that
the distance between the conductors may be suddenly altered, and a cur-
rent induced.
Electrical Measurement. In studying electrical phenomena, several dis-
tinct quantities present themselves for measurement. Prominent among
these are quantity, resistance and potential, each of which require the
accurate establishment of a unit. As in the English system of weights and
measures, originally units were adopted having no simple relation to each
other, the unit of quantity being the amount required to generate 1 cm. 8
of mixed oxygen and hydrogen from the decomposition of water. The
unit of resistance was that opposed by a cylinder of mercury having a
length of one metre and cross-section of one square millimetre. The
failure of the first Atlantic Cable in 1858, was felt to be due in a great
measure to the insufficient knowledge of the proper electrical conditions
and insufficient means of accurate measurement. Recognizing this diffi-
culty, a Committee was appointed by the British Association, of the most
eminent electricians of England, with Prof. Williamson as chairman.
256 APPENDIX A.
They devoted several years to the task, and as a result, proposed a system
of electrical units which has been generally adopted. Two conditions
were assumed by the Committee in selecting the units. First, that they
should be absolute units, that is, dependent on no arbitrary conditions, but
derived' directly from the centimetre, gramme and second; and secondly,
that they should be so connected together that, as in the metric system, re-
ductions may be made from one to another without employing any other
factor than unity.
The following equations show the relation these quantities bear to one
another. Faraday proved that Q =. CT . . . (1), or the quantity trans-
mitted by a conductor equals the product of the time by the strength of the
current. Joule showed that W = C 2 RT . . . (2), or the work done by a
current equals the product of the time by the resistance, by the square of
ET
the current. Finally, by Ohm's law, C= -^, or E = CR . . . (3), the
electro-motive force equals the current multiplied by the resistance. If,
now, either one of the units is determined, with the units of time and
space, all the others can be deduced. Thus having given the unit of re-
sistance, the unit of current is deduced from (2)" by making W, R and T,
equal to unity, and equals that required to do a unit of work per second
in overcoming a resistance of unity. Again, (3) gives the unit of potential
or electro-motive force, by making C and R equal to unity, and equals
the electro-motive force required to force a unit current through a unit of
resistance. Finally, the unit of quantity is given by (1) making C and T
equal to unity, in which case the unit of quantity equals the amount trans-
mitted by the unit of current per second. It therefore only remained to
determiae one of these units to define all the rest, and for this purpose the
unit of resistance was selected as more easily determined, and more easily
constructed in a permanent form.
Two systems of measurement may be employed to connect electrical units
with those of time, space and mass. First, the electro-static system, in
which the unit quantity would be defined as that required to produce a
repulsion of unity between two particles at distance unity, and secondly
the electro-magnetic system, in which the units are defined by the effect
of a current on a magnet. The second of these systems is adopted as
more convenient in practice, and the ratio between the two units of quan-
tity is found to be equal to 28 billion centimetres, or the velocity of light
within the limits of errors of observation. The two systems may also be
compared as follows. In both, 1st, the unit current conveys the unit quan-
tity per second; 2d, the unit current in a conductor opposing a unit's
resistance will do a unit's work; and 3d, the unit current will be trans-
mitted by a conductor opposing a resistance of unity, if the difference of
potential of its two ends is unity. But in the electro-static system the unit
quantity will repel a similar quantity at a unit's distance with unit force;
while, in the electro-magnetic system, the unit current flowing through a
conductor of unit length will create a unit force on a unit magnetic pole at a
unit distance. By a unit pole is meant that which repels an equal pole at a
distance unity with force unity.
The following method was employed to establish the relation between
the unit of resistance and the units of time, space and mass. A coil of
wire was caused to revolve with uniform velocity around a vertical axis.
At the centre of the coil was placed a small magnet delicately suspended
by a filament of silk, and carrying a mirror by which its motion could be
measured by a telescope and scale. When the coil is turned a current is
ELECTRICITY. 257
induced in it by the magnetism of the earth, and the needle deviates from
the magnetic meridian. From the dimension of the coil, its velocity, and
the deviation of the needle, a relation is established between the resist-
ance of the coil and the absolute unit. Measurements were made in this
way in 1863 and 1864, and the probable error of the final result amounted
to only .08 of one per cent. A number of copies of the standard unit
were then made, formed of coils of wire of 1 part platinum and 2 parts
silver, the whole imbedded in parafine, and enclosed in a thin copper
case. The resistance alters about 3.2 percent, between and 100 C., and
the temperature at which they are exact is marked on each. The error
amounts to less than .01 of one per cent. To use them, they are imm'ersed
in water which is then brought to the required temperature.
When, as in the present case, quantities of very different Orders of
magnitudes are to be dealt with, either enormously great or exceedingly
minute, instead of writing out a large number of ciphers before or after
each, they may be replaced by writing 10", in which n is a whole number,
either positive or negative, according as the quantity is very great or very
small. Thus for a million we may write 10 6 , for one millionth 10~ 6 . For
brevity 10", when n is positive, is denoted by appending the cardinal num-
ber, and when n is negative, prefixing the ordinal number. For example,
the velocity of light is about 3 X 10 10 centimetres, or 3 centimetre-tens,
the wave-length of yellow light about 5 X 10~ 5 centimetres, or 5 fifth-
centimetres, and hence a yellow body vibrates 6 X 10 14 times per second.*
The absolute unit of resistance, as found above, is an exceedingly small
quantity, hence it is multiplied by a billion to make it of a convenient
size, or the adopted unit := 10 9 absolute units. In the same way the abso-
lute unit of capacity is enormous, and the adopted unit = 10~ 9 absolute
units. The unit of quantity =z- 10" 1 absolute units, and the unit of poten-
tial = 10 8 absolute units.
These units are often called, from the name of the Committee, the B. A.
Units; but since they depend only on the centimetre, gramme and second,
the Committee recommend that they should be called the C. G. S. Units.
Names are given to each, after the physicists who have distinguished them-
selves in the branch of electricity to which they relate. Thus the unit of
quantity is called a veber, the unit of capacity a farad, the unit of resist-
ance an ohm, and the unit of potential a volt, after Weber, Faraday, Ohm
and Volta. To denote quantities very much greater or less than the units,
the prefixes mega- and micro- are used, the former denoting a million times,
the latter a millionth part; thus a megohm equals 1,000,000 ohms, a micro-
farad .000001 farad. The following examples will serve to show the mag-
nitude of these various units. A piece of No. 16 copper wire (diameter
.06 inches) 60 ft. long has a resistance of about 1 ohm. A Smee cell
has an electro-motive force of about 0.25 volts, a Daniell cell about 1.1 volts,
and a Grove or Bunsen abjut 1.8 volts. The capacity of the Atlantic
cable is only 800 microfarads, and its resistance 8000 ohms.
Kirchhojfs Laws. The magnitude of the currents in a system of con-
ductors is'often readily determined by the two following laws discovered by
Kirchhoff. 1st. When any number of conductors meet in a point the sum
of the currents flowing tow'ards it equals the sum of those flowing from it.
This is obvious, as otherwise the quantity of electricity in the point would
alter, and it would constantly become more and more positively or nega-
tively electrified. 2d. In any closed circuit the sum of the products of the
resistances by the currents equals the sum of the electro-motive forces in
the circuit. Ohm's law follows as a special case of this.
17
258 APPENDIX A.
Batteries. A most valuable application of Ohm's law is to determine the
strength of the current which will flow through a given piece of apparatus
with "different forms of battery, thus enabling us to decide which is best
7^
adapted to our purpose. In the equation C = n, let E denote the electro-
motive force of the battery, and R the total resistance of the circuit, which
consists of two parts, the resistance of the battery B, and that of the instru-
ment and connecting wire. The latter is constant, and may be called P, so
T^T
that C = p _i_ p- If) now, the battery consists of n cells, each having an
electro-motive force E and resistance B, and they are connected for ten-
sion, or thje zinc of one connected with the carbon of the other, evidently
the total electro-motive force will be nE. The total resistance also will be
nB, since all the electricity has to pass through each cell. The current
then, C = j, . p. Next, suppose the cells connected for quantity, or
all the zincs connected together, and all the carboas connected. The
electro-motive force will be only E, but the resistance will be much less
than that of a single cell. It will in fact be only B -f- , since in-
stead of one passage for the current, n are open. In this case, multiply-
ing both numerator and denominator of the fraction by n, we deduce
C = , J p. As a third case, suppose the battery divided into p sets
of m cells, and that in each set all the zincs and all the carbons are con-
nected together, while the sets are connected for tension, or one set of car-
bon with the next set of zinc. The battery is then said to be connected
for quantity m and tension p, and is equivalent to p large cells of electro-
motive force E and resistance B -J- m. The current, therefore, C
v , D- It mav De proved mathematically that with a given battery the
pB -\- mP J B
strongest current is obtained when the resistance of the battery, or is
most nearly equal to P, or as it is commonly expressed, the resistances
inside and outside the battery are equal. Generally the outside resistance
is much the greatest, and therefore the best effect obtained when the bat-
tery is connected for tension.
Two special cases should here be considered. First, if the outside resist-
ance P is very great, so that B can be neglected compared with it, the first
equation becomes C = -p-, or in this case, n cells connected for tension
give n times the current of one cell. If connected for quantity, however,
C = -^p = p-, or there is no gain by increasing the number of cells, a
hundred giving no greater current than one. Next, if P is very small the
opposite result is obtained, the first equation becoming C 5 = ^, and
the second C = TT. Hence with a small resistance the cells should be
connected for quantity, for if connected for tension there is no stronger
current than with a single cell.
The electro-motive force of a battery is wholly independent of the size
of the plates, and depends only on the difference of the chemical action on
them. The resistance of the battery, on the other hand, is nearly inversely
as their cross-section, and proportional to their distance apart, and it is
ELECTRICITY. 259
only on account of the diminished resistance, that large cells are to be pre-
ferred to small. The consumption of zinc is proportional to the number of
cells connected for tension, or to p in the above formula. A battery con-
nected for quantity is therefore much less expensive than when connected
for tension.
Shunts. Sometimes we wish to allow a portion only of a current to pass
through a given instrument. This is particularly the case with galvanom-
eters, which are often made so delicate that they would be easily injured
if subjected to too powerful a current. In this case a second passage is
opened to the current called a shunt, since it allows part of the electricity
to shun the original circuit. In Fig. 110, let R' be the resistance of the gal-
vanometer, or other instrument to be shunted, and R" the resist-
ance of the shunt. Then calling C, C' and C" the currents in
the circuit outside the. shunt, in R f , and in R' r , we have by Kirch-
hoff's first law C=C'-\-C", and by his second law C'R'=C"R".
Hence C'=:CV /f' from which we see that by making R"
small enough we may reduce the current in R' as much as we
please. Fig . no.
The combined resistance R, of R' and R", or in any other
case of a divided circuit, is found as follows. Let E be the difference of
potential of the two junctions of R f and R", then by Ohm's law C' = !
C " = IF" or the whole CUrrent C ' + C "= E (ft + >/) Now R
must have such a value that if it replace R' and R" the current will be
unchanged, or C = -^=zE (]5> -f- 577 ), hence R n/ i p//
Quantity. 1. Voltameter. Two platinum electrodes are immersed in a
vessel containing dilute sulphuric acid, and a glass tube graduated to cubic
centimetres is placed over them to collect the gases set free. The current
is allowed to pass, and the volume of gas collected is then corrected for
temperature, pressure and moisture. Then we have Q = .I7v, in which Q
is the required quantity in vebers, and v the corrected volume in cm*.
The principal objections to this method are the difficulty of determining
the correct volume of the gases, and their solubility in the liquid.
2. Deposition of Copper. Two copper electrodes are placed in a beaker
containing a saturated solution of sulphate of copper. They are inserted
in the circuit, and the increase of weight of that attached to the negative
or zinc pole of the battery is noted. Then Q = .32w, in which w is the
increase of weight in milligrammes. This method is much to be preferred
to the preceding.
Current. 1. Tangent Galvanometer. A compass needle is hung at the
centre of a coil of insulated wire, whose radius is at least three times its
length. Sometimes two parallel, vertical coils are used,
wound so that their depth shall be to their breadth as 1 :
.928 and separated by an interval equal to their radius.
The instrument is so placed that the coils shall lie in the
magnetic meridian, and the needle be parallel to them, or at
zero. The current is then passed through them, when the Fig. 111.
needle will be acted on by two forces, H the horizontal com-
ponent of the earth's magnetism, which tends to keep it parallel to the
plane of the coils, and C' the effect of the current tending to turn it at
right angles to the coils, as shown in Fig. 111. For equilibrium, the needle
260
APPENDIX A.
must coincide with the resultant of these forces, when a simple construction
shows that C' = H tang v, in which v is the angle of deviation of the nee-
dle. But the current C is proportional to C", or equals kC f , in which k is
the galvanometer constant, and depends only on the form of the instrument.
Therefore C = kH tang v, in which kH must be determined by the method
of depositing copper, after which the instrument may be used directly for
measuring currents. The galvanometer constant may also be determined
by computation, from the dimensions of the coil. Let y be the radius of
the coil, x the distance of its centre from the magnet, and I the length of
the wire. Then k = "T ' from which k is readily computed.
2. Sine Galvanometer. In this instrument the coils may be of any de-
sired form, and no graduation is needed for the needle, which is always
brought to the same point, or to the zero. A graduated circle is, however,
attached to the coils so that the angle through which thev are rotated may be
measured. The coils are first turned so that the needle points to zero, the
current is then passed through them and they are again turned until the
needle points to zero. Call v the angle through which they
Vc'TX have been moved, then C' = H sin v, since constructing
\ .\ \ the parallelogram of the forces acting on the needle, as in
Fig. 112, we find that H is now the hypothenuse of a right-
angled triangle, of which C' is the side opposite v. As
before, C = kC f , and hence C = kH sin v irt which kH is
determined as in the case of the tangent galvanometer.
8. Cosine Galvanometer. If the coils of a tangent galvanometer are
free to turn around a horizontal axis, their effect on the needle may be di-
minished at will. For since their effect is always equivalent to a force
acting at right angles to their plane it may be decomposed into two; one, the
vertical component equal to C' sin w, the other acting horizontally, equal to
C' cos w, in which w is the angle of inclination of the coils. The first of
these components tends only to incline the needle or to make it dip, and
the second only to deviate it. The strength of the current therefore is
measured by the equation C = kC' = = ', in which by giving differ-
ent values to v and w many readings may be obtained for the same current.
Moreover it may be used on currents too powerful to give good results with
the tangent galvanometer by merely making w nearly 90, when v may be
made as small as is desired.
Resistance. 1. Differential Galvanometer. The simplest method of
measuring resistances is by a differential galvanometer, in which two equal
coils are wound around the needle. If equal currents pass through these
in opposite directions, the deviation of the needle will be nothing. To
measure a resistance, the current of the battery is divided, so that part will
pass through one coil and a set of resistance coils, or other arrangement for
varying the resistance, and the remainder through the other coil, and the
resistance to be measured. The variable resist-
ance is then altered until the needle is brought
to zero, when its amount equals the required re-
sistance, since the two currents will be equal only
when the two circuits oppose the same resistance.
2. Wheatstone's Bridge. The principle of this
most valuable instrument is shown in Fig. 113.
Four resistance coils, M, TV, O and P, are con-
Fig. 113. nected together end to end, and the opposite junc-
tions connected with the battery B and galvan-
ELECTRICITY. 261
ometer G, as in the figure. The current from B divides, part ooinr through
M and O, and the remainder through N and P. If the resistances are so
related that M : N = : P, no current will pass through the galvanome-
ter, since its two terminals will have the same potential. Accordingly
having given three of the resistances, the fourth may be determined with
great accuracy if a delicate galvanometer is used. If M = N, O will equal
P, and thus a resistance may readily be copied.
The formula M : N = : P, may be proved as follows. In Fig. 114 let
abscissas represent resistances, and ordinates the excess of potential above
that of the negative pole of the battery. Lay off four distances equal to
M, N, and P, and erect a perpendicular at each junction equal to its
potential. This will be greatest at the junc-
tion MN, and zero at the junction OP. At
any intermediate point it is found by drawing
straight lines from the ends of O and P to the
perpendicular at MN, since the potential will
diminish continuously by an amount propor-
tional to the change in resistance. From the
figure it is obvious that the perpendiculars at Fig. 114.
the junctions M O and NP will be equal only
when M : N = : P; but when this is the case, no current will pass
through the galvanometer, since its terminals will have the same potential.
This same proposition may be proved by KirchhofFs laws. Calling the
current in M, C M the current in N, C^ etc., we have by the first law
CM + C C = 0, since M, G and O meet in a point; but C = 0,
since no current passes through the galvanometer, hence C x = C . In the
same way, C y '= C P . Now in the closed circuit MNG, we have by the
second law, C M M 4- C G C y N = 0, and in the circuit OPG we have,
C C G G C P P 0, giving the negative sign when the current
Hows in the opposite direction. Dividing the first of these equations by the
second, and recollecting that C = 0, we have .f ,. = J v , or -^=-5 ,
since Cx C , and C y = C P .
Capacity. Condensers. Capacities are usually measured by condensers
formed by separating two good conductors by a thin insulating film, as in
the case of a Leyden jar. They are commonly made of alternate sheets
of tin foil and oiled-silk or waxed paper, connecting the alternate sheets of
foil together. A very important example in practice of a condenser, is a
submarine cable, in which the insulating covering replaces the paper, and
the core and outer covering, or water, the two conductors. The relative
capacities of two condensers may be measured precisely like resistances,
with a Wheatstone's bridge. They are inserted in the place of two of the
resistances, as and P. They are then charged by connecting the bat-
tery, when the needle will deviate unless their capacities bear the same
ratio as M and N. They are next discharged by connecting their inner and
outer surfaces together, or replacing the battery by a conductor, when the
electricity flowing out of them will deviate the needle in the opposite direc-
tion. By changing M or N the ratio of the two capacities is readily found.
A second method is to use a differential galvanometer, connecting the two
condensers with the two coils, and connecting a variable shunt with the
coil to which the largest condenser is attached. A third method is, to
charge the condensers in turn from the same battery, interposing a galvan-
ometer, and noticing the swing of the needle in each case, as it shows the
amount of electricity which must pass into the condenser to bring it to the
same potential as the battery.
262 APPENDIX A.
Potential. Electrometers. Electro-motive forces or differences of potential
are measured by electrometers, of which the most perfect is Thomson's
quadrant electrometer. In its simplest form this consists of four quadrants
of sheet brass, over which hangs an aluminum needle connected with the
interior of a Leyden jar. The latter is charged so that the needle is posi-
tively electrified. If, now, two opposite quadrants have a higher potential
than the other two, the latter will attract the needle, and cause it to tend
to become parallel to the line bisecting them. A mirror and scale serves
to show the amount of the torsion. The quadrants are first connected
with the poles of a standard battery, and then with the two bodies whose
difference of potential is to be determined. The comparative deviations
show the required difference. The whole instrument is covered with a
glass shade and kept perfectly dry by sulphuric acid. In the more complete
form of the instrument the Leyden jar is charged by a little replenisher,
somewhat like a Holtz machine, until it is capable of exerting a known
attraction, it therefore always gives constant results, and from it the poten-
tial is obtained directly.
.A-ppenclix B.
TABLES.
Tables 1 to 9 give the tabular numbers most commonly required in com-
putation and are all arranged according to the same plan, so that the method
of using them shall be as' nearly as possible alike. Each right hand page
should properly be placed immediately below that opposite it, but since
this was impracticable they are placed side by side. To render the tables
more legible the units when repeated are in some cases omitted, and given
only for every fifth number and when they change. They may always be
correctly inserted by taking the units just above.
Table 1 gives the Squares of numbers from 1.00 to 9.99, differing by
hundredths of a unit. To find the square of any number, as 3.27, take
the column headed 3 and follow it down to the number opposite .27 where
we find 10.6929, the required square, retaining the 10 from the number,
above. If the second figure is less than 5 the result should be taken from
the left hand page, otherwise, from the right hand page. Thus, the square
of 7.89 is 62.2521. If the number contains more than three significant figures
the result is obtained more accurately by interpolation. Generally first dif-
ferences only need be used, and since the numbers follow each other in
order vertically, the subtraction is readily made. Thus, to find the square
3.276; the square of 3.27 is 10.6929, of 3.28 is 10.7584, and their difference
.0655; .6 of this equals .0393 which added to 10.6929 gives 10.7322. If the
decimal point of the number is moved, that of the square must be moved
twice as many places; thus, the square of 3.27 is 10.6929, of 327 is 106929,
and of .03 2 7 is .00 1069 2 7.
This table may be used to extract square roots approximately. Thus, to
find the square root of 2 or the number whose square is 2, we find by fol-
lowing down the columns that it is contained between 1.41 and 1.42.
Moreover, the difference between their squares, or 2.0164 1.9881 .0283.
and dividing 2. 1.9881 =.0129 by this, gives .4205, which multiplied by
.01 and added to 1.41 gives 1.414205 as the square root of 2. Its true value
is 1.414214. The square root of 200 is in like manner 14.142 and of .02 is
.14142, moving the decimal point of the square root one half as far as that
of the number. To find the square root of .2 move the decimal point two
places, when the square root of 20 is given in the table as 4.47, and that of
.2 is .447.
Table 2 gives in precisely the same manner the Cubes of numbers from
1.00 to 9.99. Thus, the cube of 8.32 is 575.930, of 8.324 is 576.76 and of
(263)
264 APPENDIX B.
478 is 109.215. If the decimal point must be moved, that of the cube must
be moved three times as far; thus the cube of 832 is approximately
575930000, of .832, .00057593. Similarly, cube roots may be extracted.
The cube root of 3 is 1.44, or interpolating, 1.4422. The cube root of
3 is one tenth that of 300 or .6694, of .03, a tenth of the cube root of 30 or
.3107.
Table 3 gives the Reciprocals of the same numbers from 1.00 to 9.99,
and is used in the same way. Thus, the reciprocal of 1.28 is .78125, of
1.284, .7788. If the decimal point has been moved, that of the reciprocal
must be moved an equal amount in the other direction ; thus the reciprocal
of 12.84 is .07788, of .1284, 7.788, of .01284, 77.88.
Table 4 gives various powers of a hundred numbers from to 10,
varying by tenths. These numbers are very useful in testing observations
to determine the law connecting them. Thus, to see if one quantity varies
inversely as the square of another we use the values of x ~ 2 . Similarly
the square root, cube root, inverse square, cube, square root, cube roots,
fourth and fifth powers are given. Combining this with Tables 1, 2, and 3
we may find at once the value of x raised to the powers 3, 2, 1 , ,
|, |, \, 2, 3, 4 or 5. If the decimal point is different, the powers may
still be found approximately by changing the decimal point as in the pre-
vious Tables. The fraction and its square are frequently employed,
the first, for instance, in the British Association Bridge and the second in
ited in
the relative
stands
72 inches from one of the lights, their ratio is 6.612.
Table 5 gives the logarithms of numbers from 1.00 to 9.99, to four
places of decimals. The arrangement differs from the common tables since
the tabular numbers follow each other vertically instead of horizontally, but
it is believed that this is an undoubted improvement from the ease in in-
terpolation, the diminished liability to error, and a uniformity with tables
of the other functions. As in Table 1, take the column with the same
heading as the left hand figure and follow it down to the number opposite
the second and third figures. If the second figure exceeds 4, use the right
hand page. If the number is contained between 1 and 10 its characteris-
tic will be 0. Increase it by unity for each place to the right that the
decimal point is moved, and if a fraction, or the decimal point moved to
the left, call the characteristic 10 and diminish it by the same amount.
Thus, log 438 = 0.6415, log 4.387 = 0.6415 -f- .0007 = 0.6422, log 438 =
2.6415, log .0438 = 8.6415.
Table 6 gives the Natural Sines and Cosines of angles for every tenth
of a degree. Each column contains the sines for five degrees, the tens
being given at the top of the page, and the units and tenths in the left
hand column. When the units exceed four the right hand page must be
used. Thus n at sin 62. 7 =.8886 and nat. sin 18.3 =r .3140. If the
angles are given in single minutes the sines may be obtained by dividing
'by six and, if necessary, interpolating. By the inverse process the angle
corresponding to any sine is found; thus, sin" 1 . 2 r= 1132'. Cosines are
found in the same way. reading from the bottom and right hand column.
Thus, cos 18.6 =.9478', cos 72 28' =.3013, cos- 1 .9 = 25 51'.
TABLES. 265
Table 7 gives Natural Tangents and Cotangents of angles for every
tenth of a degree and is used precisely like Table 6. Thus, tang 5 2. 4 =
1.2985, cot" 1 .4376 =r 66 22'.
Table 8 gives Logarithmic Sines and Cosines of angles for every tenth
of a degree and is used precisely like Table 6. Thus, log sin 3.6 = 8.7979,
log cos" 1 9.00 = 84 16'.
Table 9 gives the Logarithmic Tangents and Cotangents of angles for
every tenth of a degree and is used precisely like Table 6. Thus, loo- tana-
22.4 = 9.6151 log cot- 1 0.2368 = 59.9.
Table 10 gives the numerical constants and ratios most used in physics.
The first column defines the constant, the second gives its numerical value,
the third gives its reciprocal and the fourth its logarithm. Thus the line
4 Grain in grammes ' shows that .0648 grammes make a grain, and 15.432
grains make a gramme. The logarithm is useful in reducing from one unit
to another. In this, as in several of the following tables, the decimals are
not carried as far as is customary, but all figures having any significance
are here retained and those omitted are liable to mislead, as implying a
greater accuracy that has really been obtained in their determination.
Thus a metre is commonly stated to equal 39.37079 inches, but different
measurements differ greatly in the last two places. Where the right hand
figures are known to be zero they are retained, thus 1 inch equals 2.5400
cms. more nearly than 2.5399 or 2.5401.
Table 1 1 gives the Properties of the Metals whose names are in the
first column. The next column gives their chemical symbols; the third
column gives their atomic weights, and the fourth their specific gravities;
the values given in this column are taken from Clarke's Constants of Na-
ture. Only one place of decimals is retained, since the values commonly
vary by at'least one tenth in different specimens. As exceptions we might
give, Hg= 13.596, Li =.58, Na =.97, K .87. The next column gives the
moduli of ela'sticity, oV forces in kilogrammes required to double the length
of a bar having a cross section of 1 mm. if the same law of elasticities
continued to hold for such large extensions as for small. This modulus
may also be defined as the ratio of stress to strain for moderate strains.
Following this are the hardness according to Bottone (Les Mondes, xxxi,
720), and the specific heats, mostly taken from Watts' Diet., Supplement I, p.
665. The points of fusion follow, taken from Clarke's Constants of Nature.
The coefficients of expansion are Fizeau's results ( Watts' Dict.,Supplement I,
p. 680) ; they must be divided by 10 8 to give the coefficient per degree C. or
they equal the change in length in ten millionths, per degree. Conduct, gives
the conductivities according to Wiedemann and Franz (Pogg. Ann., Ixxxix,
497) reduced to absolute units. Electrical Resist, gives the resistance in
ohms of a wire of the metal one metre in length, and having a cross section
of one millimetre, according to the observations of Matthiessen , except for
cadmium, palladium and thallium, where Benoit's results (Bib. Univ., cciii.
284) are given. Thermo-Elect. gives the thermo-electric position of the
metals at 20 C. per degree C. in microvolts compared with lead, according
to the observations of Matthiessen. Thus, a pair composed of nickel and
iron with its terminals differing 5 will give a electromotive force of 5
[11.4 ( 17.5)] = 144.5 microvolts or .0001445 volts. The last column
gives the refractive equivalents, or indices of refraction minus one, divided
by the densities, according to Gladstone (Phil. Trans., 1870, p. 9).
266 APPENDIX B.
Table 12 gives the Properties of the most common Liquids whose
names are given in the first column. .The next column gives their chemi-
cal symbols; the next, their specific gravities; Capillarity gives the height
to which the liquid will rise in a tube of diameter 1 mm. according to
Frankenheim (Pogg. Ann., Ixx, 515). Compress, gives the compressibility
multiplied by 10 6 or diminution in volume in millionths per atmosphere.
The next column gives the velocity of sound in an unlimited mass of the
liquid according to Wertheim (Ann. Chim. Phys., Ill, xxiii, 434). Then
follow the specific heat, the total expansion in heating the liquid from
to 100, the boiling point, and the latent heat. The next two col-
umns give the index of refraction for the sodium line, and the disper-
sion or difference in index of the red and violet rays. The last column
gives the magnetic power compared with water, according to Faraday
(Bib. Univ., xxiii, 105).
Table 13 gives the Properties of the most common Gases whose names
are given in the first column. In the next columns are given their chemi-
cal symbols, their molecular weights, and their densities or specific gravities,
air being taken as unity. Then follow the weight in grammes per litre ;
the specific heat for equal weights; the specific heat for equal volumes ; the
boiling points or temperature necessary to reduce them to the liquid form;
the velocity of transpiration according to Graham (Phil. Trans., 1846, p.
573, 1849, p. 349) ; the velocity of sound according to Dulong; the index of
refraction for the sodium-line minus one, multiplied by a thousand. Thus
the index for air = 1.0002923. Where four places of decimals are given
the results are those of Mascart (Comptes Rendus, Ixxviii, 801), the others
are those of Dulong (Ann. Chim. et Pkys., II, xxxi, 154). The last
column gives the dispersion, or value of B in the formula of Cauchy,
Table 14 serves to reduce various hydrometer readings. The first
column gives the reading or point to which the hydrometer sinks in the
liquid. The second column gives the corresponding specific gravity, if the
hydrometer is graduated according to Baume's scale for liquids heavier
than water. The third column corresponds to Baume's scale for liquids
lighter than water ; columns four and five give the similar readings on
Beck's scale, column six on Cartier's, and column seven on Twaddell's. The
latter may also be computed by the formula g 1-4-.005 r in which r is the
reading and g the required specific gravity.
Table 15 gives the temperatures in Centigrade and Fahrenheit degrees
of various phenomena. The first column describes the effect, the second
gives the temperature on the Centigrade and the third that on the Fahren-
heit scale.
Table 16 gives the pressure of Vapors according to the experiments of
Regnault (Memoirs of the French Acad., xxi, 624; xxvi, 374). The first
column gives the temperature, the others the pressure in millimetres of the
liquid whose name heads the column.
Table 1 7 furnishes the means of determining the amount of moisture
in the ah;, from the readings of the Wet and Dry Bulb Thermometers.
Column one gives the temperature of the air as given by the dry bulb
TABLES 267
thermometer, and the other columns give the pressure of the aqueous vapor
in millimetres corresponding to a difference in reading of the two ther-
mometers, by an amount equal to the number heading the column. Thus,
if the dry bulb reads 16 and the wet bulb 10, or their difference 6, we
follow down the first column to the point 16 and then horizontally to the
column headed 6 where we find the number 9.9 which equals the required
amount of moisture in the air. The second column gives the amount of
moisture if the difference in the two thermometers is zero, or the air sat-
urated. It may therefore be used in connection with Table 16 for the
pressure of steam at intermediate pressures. The relative humidity may
be found by dividing the actual amount of moisture in the air, by that
which would be required to saturate it. Thus in the above example at 16,
13.5 mm. would saturate air, or the relative humidity is 9.9 divided by
13.5 or .73. The dew point also is found by noting the temperature at
which the observed moisture would saturate the air, or from the first col-
umn the reading corresponding to a value of 9.9 in the second column.
In the present case this lies between 10 and 12, or is about 11.1C.
Table 18 gives the principal elements of the Solar System, assuming
the solar parallax to be 8.94". Most of these numbers are taken from
Lockyer's Astronomy. They give the names of the planets, their symbols,
distances from the sun in miles, distances compared with that of the earth,
the times of revolution, the eccentricity of the orbit, its inclination to the
tcliptic, the longitude of the ascending node, the diameter in miles, masses
compared with that of the earth and specific gravities. Corresponding
elements are also given for the sun and moon.
Table 19 gives the position of some of the most conspicuous of the
Double Stars. Those are selected which are of sufficient size to be easily
seen by the naked eye, that they may be observed by those whose teles-
copes have no equatorial mounting. For the same reason only those are
given, both of whose components are readily seen with telescopes of mod-
erate power. They are arranged in the order of their right ascensions,
which are given in the first column. The declination is given next, then
the constellation in which they are situated, their specific name or letter,
the magnitude of the larger and then of the smaller component, their dis-
tance apart in seconds and their position angle in degrees and tenths. The
last column gives their color, using the following abbreviations, p. pale,
d. deep, bl. blue, gr. green, lil. lilac, pur. purple, r. red, vi. violet, and
w. white. When no color is given the authorities differ. When the star
has three components it is marked T., and B. denotes that it is binary.
This Table and the following are compiled in a great measure from Webb's
Celestial Objects for Common Telescopes.
Table 20 gives similarly a list of the more conspicuous Clusters and
Nebulae. The first column gives the number in the Catalogue of the Brit-
ish Association, the second the right ascension, the next the declination,
then the Constellation and specific name; $ denotes the catalogue of the
elder Herschel, and M that of Messier. The last column serves to describe
the object ; E., denotes that it is visible as a misty spot to the naked eye.
O., that a small optical power only is needed, as a finder or opera glass, to
recognize its place. C., denotes that the spectrum is continuous, or that
the object is probably a cluster composed of stars, and G., that it is gaseous
or a nebula. The other abbreviations are clust. and cl. for cluster, neb. for
nebula, plan, for planetary, resolv. for resolvable, and diam. for diameter.
268
1. Squares.
n
1.
2.
3.
4.
5.
6.
r*
8.
9.
.00
I.OOOO
4.0000
9.0000
16.0000
25.0000
36.0000
49-0000
64.0000
Si.oooo
.01
.0201
.0401
.0601
.0801
.1001
.1201
.1401
.1601
.1801
.02
.0404
.0804
.1204
.1604
.2004
.2404
.2804
.3204
3604
.03
.04
.0609
.0816
.1209
.1616
.1809
.2416
.2409
3216
.3009
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.3609
.4816
.4209
.5616
.4809
.6416
5409
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.05
.06
1.1025
.1236
4.2025
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9-3025
3636
16.4025
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36.6025
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49.7025
.8 43 6
64 S
81.9025
82.0836
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65.1249
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.1664
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.9664
CO.I264
.2864
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.09
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3681
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37.0881
.2681
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.10
I. 2100
4.4100
9.6100
16.8100
26.0100
37.2100
50.4IOO
65.6100
82.8100
.11
.2321
.4521
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.8921
.1121
3321
5521
7721
.9921
.12
2544
4944
7344
9744
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.6944
9344
83.1744
.13
.2769
5369
.7969
17.0569
.3169
5769
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66.0969
.3569
14
.2996
5796
8596
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9796
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5396
.15
I-322C
4.6225
9.9225
17.2225
26.5225
37.8225
51.1225
66.4225
83.7225
.16
3456
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3056
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5856
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.17
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10.0489
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38 . 0689
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7489
84.0889
.18
3924
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55 2 4
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.19
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.7961
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67.0761
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1.4400
4.8400
10.2400
17.6400
27 . 0400
38.4400
51.8400
67.2400
84.6400
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.8841
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52.1284
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85.0084
.23
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43 2 9
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3529
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7329
. 1929
.24
5376
5.0176
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':$
5.0625
.1076
10.5625
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2 7-5625
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39.0625
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68.0625
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.30
.31
1.6900
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5.2900
336i
10.8900
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18.4900
576i
28.0900
.1961
39.6900
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53.2900
68.8900
69.0561
86.4900
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.32
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11.0224
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t;824
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87.0489
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7956
475 6
I 556
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5^6
.1956
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5556
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1.8225
S-5225
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18.9225
28.6225
40.3225
54.0225
69.7225
87.4225
.36
.8496
. 5696
. 2896
19.0096
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5769
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70.0569
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.38
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4244
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4644
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9844
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.4921
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29.0521
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88.1721
.40
.41
1.9600
.9881
5.7600
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11.5600
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19.3600
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29.1600
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40.9600
41.0881
54.7600
.OX>8l
70.5600
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88.3600
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2.0164
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3449
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71.0649
7364
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9536
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89.1136
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2.1025
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6.0025
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11.9025
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19.8025
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29.7025
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41.6025
73i6
55-5025
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71.4025
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12.0409
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.48
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20.0704
30.0304
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9504
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.49
.2201
.2001
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42. 1201
^6. loor
72.0801
90.0601
1. Squares.
269
n
1.
2.
3.
4.
5.
6.
7.
8.
9.
.50
2.2500
6.2500
2.2500
0.2500
30.2500
2.2500
56.2500
2.2500
90.2500
.51
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3201
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354
3904
434
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5904
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3409
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8516
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91.0116
.55
.56
2.4025
4336
6. 5025
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2.6025
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0.7025
7936
30.8025
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2.9025
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57.0025
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3.1025
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91.2025
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31.0249
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8881
21.0681
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.60
2.5600
6.7600
2.9600
21. 1600
31.3600
43-5600
57.7600
73.9600
92.1600
.61
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3-0321
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94.0900
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3.0276
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3.6100
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48 . 0249
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63.0436
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3.8025
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15.6025
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24.5025
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35-4025
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.7604
.7204
.6804
.6404
.6004
99
9601
.9401
.9201
.9001
.88or
.8601
.8401 i
.8001
270
2. Cubes, y = x 3 .
X
1.
2.
3.
4.
5.
6.
7.
8.
9.
.00
.000
8.000
27.000
64.000
125.000
216.000
343-000
512.000
729.000
.01
.030
8. 121
27.271
64.481
25-752
17.082
44.472
13.922
3!-433
.02
.061
8.242
27-544
64.965
26.506
18.167
45.948
15-850
33-871
.03
.04
093
.125
8-365
8.490
27.818
28.094
65-45 1
65-939
27.264
28.024
19.256
20.349
47.429
48.914
17.782
19.718
36-3M
38-763
.05
.158
8.615
28-373
66.430
128.788
221.445
350-403
521.660
741.218
.06
.191
8.742
28-653
66.923
2 9-554
22-545
51-896
23.607
43 -'677
.07
.225
8.870
28.934
67.419
30-324
23.647
53-393
25.558
46. 143
.08
.260
8.999
29.218
67.917
3I-097
24-756
54-896
27. 514
48.613
.09
.295
9.129
29.504
68.418
31-872
25.869
56.401
29.475
51.089
.10
-331
9.261
29.791
68.921
132.651
226.981
357-9II
53I-44I
753-571
.11
.368
9-394
30.080
69.427
33-433
28.099
59-425
33-412
56.058
.12
405
9.528
30-371
69^35
34-218
29.221
60.944
35-387
58.551
.13
443
9.664
30.664
70-445
35.006
30-346
62.467
37-368
61.048
.14
.482
9.800
30.959
70.958
35-797
31-476
63.^4
39-353
63-552
.15
.521
9-938
31-256
71-473
136.591
232.608
365.526
541-343
766.061
.16
.561
10.078
3 I -554
71.991
37-388
33-745
67.062
43.338
68.575
.17
.602
10.218
31-855
72.512
38.188
34-885
68.602
45-339
71.095
.18
.19
-643
685
10.360
10.503
32.157
32.462
73-035
73-560
38.992
36.029
37-177
70.146
71.695
47-343
49-353
73.621
76.152
.20
.728
10.648
32.768
74-088
140.608
238.328
373.248
55I-368
778.688
.21
772
10.794
33-076
74-618
41-421
39-483
74-805
53-388
81.230
.22
.816
10.941
33-386
75- I 5 I
42.237
40.642
76.367
55-412
83.777
.23
.861
11.090
33-698
75-687
43-056
41.804
77-933
57-442
86.330
.24
.907
11.239
34-012
76.225
43.878
42.971
79-503
59.476
88.889
.25
953
11.391
34.328
76.766
144.703
244.141
381.078
561.516
791-453
.26
.27
.000
.048
"543
11.697
34.646
34.966
77 309
77-854
45-532
46.363
45-3H
46.492
82.657
84.240
63.560
65.609
94.022
96.598
.28
.097
11.852
35-288
78.403
47-198
47-673
85.828
67.664
99.179
.29
.147
12.009
35-611
78.954
48.036
48.858
87.420
69.723
801.765
.30
.197
12.167
35-937
79.507
148.877
250.047
389.017
571-787
804.357
.31
.248
12.326
36.265
80.063
49.721
51.240
90.618
73-856
06.954
.32
.300
12.487
36.594
80.622
50.569
52-436
92-223
75-930
09-557
.33
353
12.649
36.926
81.183
51.419
5 7 636
93 * ^ 1 3
78.010
12.166
.34
.406
12.813
37.26o
81.747
52-273
54.840
95-447
80.093
14.780
.35
.460
12.978
37-595
82.313
153- *30
256.048
397.06?
582.183
817.400
.36
5'5
13-144
37-933
82.882
53-991
57-259
98.688
84.277
20.026
.37
.571
13-312
83-453
54-854
58-475
400.316
86.376
22.657
.38
.628
13.481
38.614
84.028
55-721
59.694
01.947
88.480
25.294
.39
.686
13-652
38.958
84.605
56.591
60.917
03-583
90.590
27.936
.40
744
13.824
39.304
85.184
157.464
262.144
405.224
592.704
830.584
.41
.42
.803
-863
I3.998
14.172
39-652
40.002
85-776
86.351
58.340
59-220
63.375
64.609
06.869
08.518
94-823
96.948
35.897
.43
.924
14-349
40.354
86.938
60.103
65.848
10.172
99.077
38-562
.44
.986
14-527
40.708
87.528
60.989
67.090
11.831
601.212
41.232
.45
3-049
14.706
41.064
88.121
161.879
268 . 336
4I3.494
603.351
843-908
.46
3.112
14.887
41.422
88.717
62.771
69.586
15.161
05.496
46. 590
.47
3-177
15.069
41.782
89-315
63.667
70.840
16.833
07.645
49.278
.48
3.242
15-253
42.144
89.915
64.567
72.098
18.509
09.800
5i-97i
.49
3-308
15-438
42.509
90.519
35.469
73-593
20.190
11.960
54.670
2. Cubes. y=x 3 .
271
X.
1.
2.
3.
4.
5.
6.
7.
8.
9.
.50
3-375
15.625
42.875
91.125
66.375
74.625
21.875
14.125
57-375
.51
.52
3-443
15.813
16.003
43.244
43.614
91-734
92-345
67.284
68.197
75.894
77.168
23-565
25.259
16.295
18.470
60.085
62.801
.53
3- 582
16.194
43.987
92.960
69.112
78.445
26.958
20.650
65-523
.54
3.652
16.387
44.362
93-577
70.031
79.726
28.661
22.836
68.251
.55
3-7 2 4
16.581
44-739
94.196
70.954
81.011
30.369
25.026
70.984
.56
.57
3-796
3.870
16.777
16.975
45.118
45-499
94.819
95-444
71.880
72.809
82.300
83-593
32.081
33-798
27.222
29.423
73-723
76.467
.58
3-944
17.174
45.883
96.072
73-741
84.890
35-520
31.629
79.218
.59
4.020
17-374
46.268
96.703
74.677
86.191
37-245
33-840
8i.974
.60
.61
4.096
4-173
I7.576
17.780
46.656
47.046
97.336
97-972
75.616
76.558
:8l
438.976
40.711
636.056
38-277
884.736
87.504
.62
4.252
17.985
47-438
98.611
77-5 4
90.118
42.451
40.504
90.277
.63
4-331
18.191
47-832
99-253
78.454
91-434
44.195
42.736
93-056
.64
4.411
18.400
48.229
99-897
79.406
92-755
45-944
44-973
95.841
.65
4.492
18.610
48.627
00.545
180.362
94.080
447.697
647.215
898.632
.66
.67
4-574
4-657
18.821
19 '034
49 . 028
49- 43 1
01.195
01.848
81.321
82.284
95.408
96.741
49-455
51.218
49.462
51.714
901.429
04.231
.68
.69
4.742
4.827
19.249
19.465
49.836
50.243
02.503
03.162
83.250
84.220
98.078
99.418
52.985
54-757
53-972
56-235
07.039
09-853
.70
4-9I3
19.683
50-653
103.823
185.193
300.763
456-533
658.503
912.673
.71
5.000
19-903
51.065
04.487
86.169
02.112
60.776
15.499
.72
.73
5.088
5-178
20.124
20.346
Si-479
51-895
05-I54
05.824
87.149
88.133
03.464
04.821
60.100
61.890
63-055
18.330
21.167
.74
5.268
20.571
52-3H
06.496
89.119
O6.l82
63.685
67.628
24.010
.75
5-359
20.797
52.734
107.172
190.109
307.547
465-484
669.922
926.859
.76
.77
.78
5 "45 2
5.640
21-025
21.254
21.485
53-157
53:583
54.010
07.850
08.531
09.215
91.103
92.100
93.101
08.916
10.289
11.666
67.289
69.097
70.911
72.221
74-526
76.836
29.714
32-575
35-441
.79
5-735
21.718
54.440
09.902
94.105
I3-047
72.729
79- I 5 I
38-314
.80
.81
5.832
5-930
21.952
22.188
54-872
55-306
110.592
11.285
195.112
96.123
3 r 4-43 2
15.821
474-552
76.380
681.472
83-798
941.192
44.076
.82
6.029
22.426
55-743
11.980
97 -!37
17.215
78.212
86.129
46.966
.83
6.128
22.665
56.182
12.679
98-155
18.612
80.049
88.465
49.862
.84
6.230
22.906
56.623
13-380
99.177
20.014
81.890
90.807
52.764
.85
6-332
23.149
57-067
114.084
200.202
321.419
483-737
693.154
f.672
.86
6-435
23 39^
57-5 12
14.791
01.230
22.829
85.588
95-506
585
.87
6-539
23 . 64(
57-96i
I5-5 01
02.262
24.243
87-443
97.864
-505
.88
6.645
23 . 88S
58.411
16.214
03.297
25.661
89-304
700.227
64.430
.89
6.751
24.138
58.864
16.930
04-336
27.083
91.109
02.595
67.362
.90
6.859
24.389
59-3*9
117.649
205.379
328.509
493-039
704-969
970.299
.91
6.9$
24.642
59-776
18.371
06.425
29-939
94.914
07.348
73-242
.92
7.078
24.897
60.236
19.095
07.475
3'-374
96.793
09.732
76.191
.93
7.189
25- I 54
60.698
19.82
08.528
32-813
98.677
12.122
79- J 47
.94
7-301
25.412
61 . 163
20.554
09.585
34-255
500.566
14.517
82.108
.95
7-4I5
25.672
61.630
121.287
210.645
335-702
502 . 460
716.917
985.075
.96
.97
7-530
7-645
25.934
26.198
62.099
62.57
22.024
22.76;
ii.7oc
12.776
37-154
38.609
04-358
06.262
I9-323
21-734
88 . 048
91.027
.98
7.762
26.464
63.045
23-506
13-847
40.068
08.170
24.151
94.012
.99
7.881
26.73
63-52
24.25
14.922
4L53 2
10.082
26.573 97- 00 3
272
Reciprocals, y = x' ]
X.
1.
2.
3.
4.
5.
6.
7.
8.
9.
.00
1. 00000
0.50000
0-33333
0.25000
0.2000O
0.16667
0.14286
0.12500
O.IIIII
.01
0.99010
4975 1
.33223
2493 8
.19960
.16639
.14265
.12484
.11099
.02
.98039
4955
33"3
.24876
.19920
.16611
.14245
.12469
.11086
.03
.97087
.49261
33003
.24814
. 19881
16584
.14225
I2 453
.11074
.04
.96154
.49020
32895
24752
.19841
.16556
.14205
.12438
.11062
.05
0.95238
0.48780
0.32787
o 24691
o. 19802
0.16529
0.14184
0.12422
0.11050
.06
-94340
.48544
.32680
.24631
19763
. 16502
.14164
.12407
. i 1038
.07
.08
93458
92593
.48309
.48077
32573
32468
.24570
.24510
19724
.19685
.16474
.16447
.14144
.14124
.12392
.12376
.11025
.11013
.09
91743
.47847
.32362
.24450
.19646
. 16420
.14104
.12361
.IIOOI
.10
0.90909
0.47619
0.32258
0.24390
0.19608
o. 16393
0.14085
0.12346
0.10989
.11
.90090
47393
32154
24331
19569
16307
.14065
.12330
10977
.12
.89286
.47170
32051
.24272
J 953i
16340
.14045
.12315
.10965
.13
.14
.88496
.87719
.46948
.46729
31949
31847
.24213
24155
19493
!9455
16313
. 16287
. 14025
. 14006
.12300
.12285
10953
.10941
.15
0.86957
0.46512
0.31746
0.24096
0.19417
0.16260
0.13986
0.12270
0.10929
.16
.86207
.46296
.31646
.24038
19380
.16234
.13966
.12255
.10917
.17
.85470
.46083
31546
.23981
19342
.16207
13947
.12240
. 10905
.18
.19
.84746
.84034
.45872
.45662
31447
31348
1930S
. 19268
.16181
.16155
.13928
.13908
.12225
.I22IO
:S
.20
0-83333
0-45455
0.31250
0.23810
0.19231
o. 16129
o. 13889
O.I2I95
0.10870
.21
.82645
45249
3"53
23753
.19194
.16103
.13870
.I2l8o
.10858
.22
.81967
4545
31056
23697
i9i57
.16077
13850
.12165
. 10846
.23
.81301
.44843
.30960
23641
.19120
.16051
13831
.12151
.10834
.24
.80645
44643
.30864
23585
.19084
.16026
.13812
.12136
.10823
.25
0.80000
0.44444
0.30769
0.23529
0.19048
0.16000
0-13793
O. 12121
o.ioSn
.26
79365
.44248
30675
23474
.19011
15974
13774
.12107
.10799
.27
.78740
44053
.30581
.23419
18975
I S949
I 3755
. I2O92
.10787
.28
.78125
.43860
.30488
23364
18939
.15924
13736
.12077
.10776
.29
775 I 9
.43668
30395
23310
.18904
.15898
i37i7
.12063
.10764
.30
0.76923
0.43478
0.30303
0.23256
0.18868
0.15873
0.13699
O.I2O48
0.10753
.31
76336
.43290
.30211
.23202
. 18832
.15848
.13680
.12034
.10741
.32
75758
43103
.30120
.23148
18797
.15823
.13661
.I2OI9
10730
.33
.75188
.42918
30030
23095
.18762
15798
13643
.12005
.10718
.34
.74627
42735
.29940
.23041
.18727
15773
. 13624
.11990
. 10707
.35
0.74074
-42553
0.29851
0.22989
0.18692
0.15748
0.13605
O.II976
0.10695
.36
73S 2 9
42373
. 29762
.22936
.18657
15723
13587
.11962
.10684
.37
72993
.42194
.29674
.22883
. 18622
15699
I 3569
.11947
. 10672
.38
.72464
.42017
.29586
.22831
18587
.15674
T 355o
"933
.10661
.39
.71942
.41841
29499
.22779
18553
.15649
13532
.11919
. 10650
.40
0.71429
0.41667
0.29412
0.22727
0.18519
0.15625
o-iSSH
0.11905
0.10638
.41
.70922
.41494
.29326
.22676
. 18484
.15601
I 3495
.11891
. 10627
.42
70423
.41322
. 29240
.22624
18450
- I 5576
J 3477
.11876
.10616
.43
69930
.41152
2 9i55
22573
.18416
I 5552
13459
.11862
.10604
.44
.69444
.40984
.29070
.22523
. 18382
.15528
.13441
. 11848
- !0593
.45
0.68966
0.40816
0.28986
0.22472
0.18349
0.15504
0- 13423
0.11834
0.10582
.46
68493
.40650
.28902
.22422
.18315
.15480
13405
.11820
.10571
.47
.68027
.40486
.28818
22371
.18282
.I545 6
13387
.11806
.10560
.48
.67568
40323
28736
.22321
. 18248
I 543 2
13369
.11792
10549
.49
67114
.40161
28653
22272
.18215
.15408
I 335 I
.11779
10537
3. Reciprocals, y = x~i.
273
X.
1.
2.
3.
4.
5.
6.
7.
8. 1 9.
.50
.66667
.40000
.28571
.22222
.18182
0-I5385
J 3333
0.11765
D.I0526
.51
.66225
.39841
.28490
22173
.18149
.15361
I33i6
"75 1
.10515
.52
.65789
39683
.28409
.22124
.18116
15337
.13298
"737
.10504
.53
.54
65359
64935
.39526
39370
.28329
.28249
.22075
.22026
. 18083
.18051
I53I4
.15291
.13280
.13263
.11723
.11710
10493
. 10482
.55
.56
.64516
.64103
.39216
39062
.28169
.28090
.21978
.21930
o. 18018
.17986
0.15267
.15244
0.13245
.13228
0.11696
.11682
O.I047I
.10460
.57
.63694
.38911
.28011
.21882
!7953
.15221
.13210
.11669
. 10449
.58
.63291
38760
27933
.21834
.17921
.15198
I 3 I 93
.11655
10438
.59
.62893
.38610
27855
.21786
.17889
W7S
W7S
.11641
. 10428
.60
0.62500
0.38462
0.27778
0-21739
0.17857
0.15152
0.13158
0.11628
O.I04I7
.61
.62112
383H
.27701
.21692
.17825
.15129
.13141
.11614
.10406
.62
.61728
.38168
.27624
.21645
17794
.15106
i3 I2 3
.11601
I0 395
.63
61350
.38023
.27548
.21598
.17762
15083
.13106
.11587
.10384
.64
.60976
37879
27473
21552
17730
.15060
.13089
.11574
10373
.65
0.60606
0.37736
0.27397
0.21505
0.17699
0.15038
0.13072
0.11561
o. 10363
.66
.60241
37594
.27322
.21459
. 17668
'SQ'S
'3055
"547
10352
.67
.59880
37453
.27248
.21413
17637
.14992
13038
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10341
.68
595 2 4
373 3
.27174
.21368
.17606
H970
.13021
.11521
10331
.69
59172
37175
.27100
.21322
'7575
. 14948
.13004
.11507
. 10320
.70
0.58824
0.37037
0.27027
0.21277
0-17544
0.14925
0.12987
0.11494
0.10309
.71
.58480
.36900
.26954
.21231
W3
.14903
.12970
.11481
.10299
.72
.58140
36765
. 26882
.21186
17483
. 14881
!2953
.11468
. 10288
.73
57803
36630
.26810
.21142
.17452
14859
12937
"455
.10277
.74
57471
.36496
26738
.21097
. 17422
14837
.12920
.11442
. 10267
.75
0.57143
0-36364
0.26667
0.21053
0.17391
0.14815
0.12903
0.11429
0.10256
.76
.56818
36232
.26596
.21008
.17361
H793
.12887
.11416
. 10246
.77
56497
.36101
.26525
. 20964
i733i
.14771
.12870
.11403
JQ235
.78
.56180
35971
26455
.20921
.17301
H749
.12853
.11390
.10225
.79
55866
.35842
.26385
.20877
.17271
. 14728
.12837
"377
.10215
.80
0.55556
0-357*4
0.26316
0.20833
0.17241
0.14706
0.12821
0.11364
0.10204
.81
55249
S55 8 7
.26247
.20790
.17212
.14684
.12804
"35 1
.10194
.82
54945
3546i
.26178
20747
.17182
.14663
.12788
"338
.10183
.83
54645
35336
. 261 10
. 20704
I7I53
.14641
.12771
"325
.10172
.84
54348
.35211
.26042
.20661
.17123
.14620
12755
.11312
.1016;
.85
0.54054
0.35088
0.25974
O.206I9
0.17094
0. 14599
0.12739
0.11299
0.10152
.86
53763
34965
.25907
20576
.17065
14577
.12723
.11287
.10142
.87
53476
.34843
.25840
20534
.17036
14556
.12706
.11274
.10132
.88
53i9i
34722
25773
. 20492
.17007
H535
.12690
.11261
.IOI2I
.89
.52910
34602
25707
. 20450
.16978
HSU
.12674
.11249
.10111
.90
0.52632
0.34483
0.25641
O.2O4O8
0.16949
0.14493
0.12658
0.11236
O.IOIOI
.91
52356
34364
25575
.20367
.16920
.14472
.12642
.11223
.10091
.92
.52083
34247
25510
20325
. 16892
H45I
.12626
.11211
.10081
.93
.5181:
3413
25445
. 20284
.16863
14430
.12610
.11198
.10070
.94
5 I 546
-34014
25381
. 2O24;
16835
.14409
.12594
.11186
.10060
.95
0.51282
0.33898
0.25316
0.20202
0.16807
o. 14388
0.12579
O.IH73
0.10050
.96
.51020
.33784
25253
.20l6l
16779
.14368
.1256^
.IIl6l
.10040
.97
50761
33670
.25189
.2OI2I
.16750
14347
.12547
.11148
.10030
.98
505 5
33557
.25126
.20080
.16722
14327
12531
.11136
.10020
.99
5 2 5
33445
25063
.2O040
.16694
. 14366
.12516
.11121
.IOOIO
274
4. Powers. y = x
-a
-3
y*.
J
-y*
-^
4
5
X
/ X
lO-x
\10-x
0.0
00
oo
0.0000
O . OOOO
00
00
0.0000
.OOOOO
.OOOO
O . OOOO
O.I
IOO.OO
IOOO.O
.3162
.4642
3.1623
2.1544
.000
.00001
.0101
.0001
0.2
25.00
125.0
4472
'I 8 ; 48
2.2361
1.7100
.0016
.00032
.0204
.0004
0.3
II. II
37-o
-5477
.6694
1.8291
1.4938
.008
.00243
.0309
.0009
0.4
6.25
15.6
.6325
.7368
1.5811
1-3572
.0256
.01024
.0416
.0017
O.5
4.0000
8. oooo
0.7071
0-7937
1.4142
1.2599
0.0625
.03125
.0526
0.0028
0.6
0.7
O.8
2.7778
2.0408
1.5625
4.6296
2-9I55
7746
.8367
.8944
8434
.8879
.9283
1.2910
1.1952
1.1180
1.1856
1.1262
1.0772
.1296
.2401
.4096
.07776
.16807
.32768
.0638
.0752
.0869
.0041
.0057
.0071
0.9
1.2346
I-37I7
9487
9655
1.0541
1-0357
.6561
59049
.09890
.0098
1.0
I.OOOO
I.OOOO
I . OOOO
I.OOOO
I.OOOO
I.OOOO
I.OOOO
I.OOOO
.mi
0.0123
1.1
0.8264
0.7570
.0488
3 2 2
0-9535
.9687
1.4641
1.6105
.12360
.015;
1.2
.6944
5787
0954
.0627
.9129
.9410
2.0736
2.4883
.13636
.0106
1.3
1.4
59*7
5 I0 5
4552
3644
.1402
.1832
.0914
.ii87
.8771
.8452
.9163
8939
2.8561
3.8416
3-7129
5-3782
M943
.16279
.022;
.0265
1.5
0.4444
0.2963
1.2247
i 1447
0.8165
0.8736
5.062
7-594
.17647
0.0311
1.6
.3906
.2441
.2649
.1696
.7906
.8550
6.554
10.486
. 19048
.0363
1.7
.3460
.2035
3038
1935
7670
8379
8.352
4-199
.20482
.0420
1.8
.3086
1715
.3416
.2164
7454
.8221
0.498
8.896
.21951
.0482
1.9
.2770
.1458
.3784
.2386
7255
.8074
3-032
24.761
23457
.0550
2.0
0.2500
0.1250
1.4142
1-2499
0.7071
0-7937
6.000
12.000
25000
0.0625
2.1
.2268
.1080
.4491
2806
.6901
.7809
9.448
0.841
.26582
.0707
2.2
2.3
.2066
.1890
0939
.0822
.4832
.5166
.3006
.3200
.6742
6594
.7689
7576
3.426
7.984
S.'S-j
.28205
.29870
.0892
2.4
1736
.0723
5492
3389
6455
.7469
3.178
9.626
31579
.0997
2.5
0.1600
o . 0640
1.5811
3572
0.6325
0.7368
9.062
97-66
33333
O.IIII
2.6
.1479
.0569
6125
375 1
.6201
7272
5.698
18. 81
1234
2.7
1372
.0508
.6432
3925
.6086
.7181
3-144
43-49
3698^
. i^6
2.8
.1276
.0456
6733
4095
.5976
7095
1.466
72.10
38889
.1512
2.9
.1189
.0410
.7029
.4260
5872
.7012
0.728
05.,!!
.40845
.1668
3.0
3.1
O.IIII
.1041
0.0370
0336
.7607
.4422
.4581
0-5774
56/9
0.6934
.6858
81.00
92,35
86.29
42857
44928
0.1837
.2019
3.2
.0977
0305
.7889
.4736
5592
.6786
04.86
35-54
47059
2215
3.3
.0918
.0278
.8166
.4888
555
.6717
18.59
9i-35
.49254
.2426
3.4
.0865
.0254
8439
537
5423
.6650
33-63
54-35
2654
3.5
0.0816
0.0233
1.8708
.5183
0-5345
0.6586
50.06
25.22
.53846
0.2899
3.6
.0772
.0214
.8974
.5326
.5270
.6525
67.96
604.66
.56250
.3164
3.7
0730
.0197
9235
.5467
5*99
.6466
87.42
593-44
58730
3449
3.8
3.9
.0693
.0657
.0182
.0169
9494
9748
.5605
5741
5130
.5064
.6408
6353
08.51
31-34
92-35
?02.2 4
61290
63934
3756
.4088
4.0
0.0625
0.0156
2. OOOO
.5874
0.5000
0.6300
56.00
024.O
.66667
0.4444
4.1
4.2
4.3
0595
.0567
.0541
.0145
0135
.0126
.0248
.0494
.0736
6005
6134
.6261
4939
.4880
.4822
.6248
.6198
.6150
82.57
11.17
41.88
158.6
306.9
470.1
69492
72414
75439
.4829
-5244
.5691
4.4
0517
.0117
.0976
.6386
4767
6103
74.81
6 49 .2
.78571
y -*
.6175
4.5
4.6
0.0494
.0473
O.OIIO
.0103
2.I2I3
.1448
.6510
.6631
0.4714
.4662
6057
.6013
10.06
47-75
845-3
059.6
81818
8^185
.6694
.7256
4.7
4.8
4.9
0453
0434
.0416
.0096
.0090
.0085
.1679
.1909
.2136
6751
.6869
-6985
.4613
4564
4517
5970
5928
.5888
87-97
30.84
76.48
33.1
824. 8|
88679
92308
96078
.7864
.8521
.9231
4. Powers, y = x 1
275
X
-2
-3
K
%
-*
- 1 A
4
5
x
r x y
5.1
04000
3845
.00800
0754
2.2361
-2583
1.7100
.7213
0.4472
.4428
0.5848
.5810
625.00
676.52
3125.0
3450-3
I .0000
.0408
I.OOO
.083
r'o
3698
0711
.2804
7325
4385
5772
731.16
3802 . o
0833
.174
5.4
3429
06 7 2
0635
.3022
3238
7435
7544
4344
4303
5735
5695
789.05
850-31
4182.0
4591-7
.1277
1739
.272
.378
5.5
5.6
5.7
5.8
5.9
03306
3^9
3078
2973
2873
.00601
0569
0540
0487
2 -3452
.3664
3875
-4083
.4290
1.7652
7758
.7863
7967
.8070
0.4264
.4226
.4189
.4152
.4117
0.5665
8
5534
9I5- 1
1055-6
1131.6
1211.7
5032.8
5507.3
6016.9
6563.6
7149.2
1.2222
.2727
3256
.3810
4390
1.494
.620
757
.907
2.071
6.0
.02778
.00463
2-4495
1.8171
0.4082
0-5503
1296.0
7776
1.5000
2.250
6. 1
6.2
2687
2601
0441
0420
.4698
.4900
.8272
8371
.4049
.4016
5473
5443
1384.6
1477.6
8446
9161
6316
.446
.662
6.3
2520
0400
.5100
.8469
3984
54H
r 575-3
9924
.7027
.889
6.4
2441
0381
5298
.8566
3953
5386
1677.7
10737
.7778
6.5
ft tt
-02367
.00364
2-5495
1.8663
0.3922
0.5358
1785.1
11603
I.857I
3-449
[>.O
2296
0348
.5690
8758
.3892
533 1
1897-5
12523
.9412
3.768
6.7
6.8
2228
2163
0332
0318
.5884
6077
.8852
.8945,
3863
3835
534
.5278
J 4539
2.0303
.1250
4-122
4.516
6.9
2100
0304
.6268
.9038
3807
5253
2266.7
15640
2258
4-954
7.0
7.1
.02O4I
I98 4
.00292
0279
2.6458
.6646
1.9129
.9220
0.3780
3753
0.5228
5203
2401.0
2541.2
16807
18042
2-3333
4483
5-444
5-994
7.2
1929
0268
6833
.9310
3727
5 J 79
2687.4
19349
5714
6.612
7.3
7.4
I8 77
1826
0257
0247
.7019
.7203
9399
9487
3701
3675
5132
2 839- 8
2998-7
20731
22190
737
.8462
7.3
8.101
7.5
.01778
.00237
2.7386
1-9574
0-3651
0.5109
3164.1
2373
3.0000
9.00
7.6
1731
0228
7568
.9661
3627
.5086
.1667
10.03
7.7
1687
0219
7749
9747
.3604
.5064
35I5-3
27068
3478
II. 21
7.8
1644
O2II
.7928
.O872
.5042
3701-5
28872
5455
12-57
7.9
I6O2
0203
.8107
.9916
3558
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3895.0
30771
.7619
8.0
.01562
.00195
2.8284
2.00OO
0.3536
0.5000
4096.0
32768
4.0000
16.00
8.1
1524
0188
.8460
.0083
35 r 4
4979
4304.7
34868
4.2632
18.17
8.2
1487
0181
.8636
.0165
3492
4959
4521.2
37074
4-5556
.20.75
8.3
1452
0175
.8810
.0247
3471
4939
474 I- 8
39390
4.8824
23.84
8.4
1417
0169
.8983
0328
3450
.4919
4978.7
41821
5.2500
27.56
8.5
.01384
.00163
2-9^55
2.0408
0-343
0.4900
5220.1
44371
5.6667
32.11
8.6
1352
0157
-9326
.0488
.3410
.4881
5470.1
47043
6.1428
37-73
8.7
8.8
8.9
1321
1291
1262
0152
0147
0142
.9496
-9665
9833
.0567
.0646
.0724
3390
3371
3352
.4862
.4844
.4826
5729.0
5997-0
6274.2
49842
52773
55841
6.6923
7-3333
8.0909
44-79
I 3 ' 7 !
65.46
9.0
.01235
00137
3.0000
2.0801
0-3333
0.4808
6561.0
59049
9.000
81.0
9.1
1208
.0166
.0878
33*5
4790
6857-5
62403
10. Ill
102.2
9.2
9.3
1181
1156
0129
0124
0332
.0496
.0954
.1029
3297
3279
4772
4755
7163.9
7480.5
69569
11.500
I3 . 2 86
132.2
176.5
9.4
1132
OI2O
.0659
.IIO5
.3262
4738
7807.5
73390
15.667
245.4
9.5
.01108
-OOII7
.0822
2.II79
0.3244
0.4722
$145.1
77378
19.000
361.0
9.6
9.7
1085
1063
OHO
.0984
.1145
1253
1327
3227
.3211
.4705
.4689
8852.9
8i|37
85873
24.000
32.333
576.0
1045.0
9.8
1041
OIO6
^305
.I4OO
3 r 94
4673
9223.7
90392
49.000
2401.0
9.9
IO2O
OIO3
.1464
.1472
3178
4657
9606.0
9599
99.000
98OI.O
276
5. Logarithms, y logx.
X.
1.
2.
3.
4.
5.
6.
7.
8.
9.
N.LlOx
.00
o.oooo
0.3010
0.4771
0.6021
0.6990
0.7782
0.8451
0.9031
0.9542
infin.
.01
.0043
3032
.4786
.6031
.6998
7789
8457
.9036
9547
7.6974
.02
.0086
3054
.4800
.6042
.7007
.7796
.8463
.9042
95S 2
8.3906
.03
.04
.0128
.0170
3075
.3096
.4814
.4829
:
.7016
.7024
.7803
.7810
.8470
.8476
.9047
9053
9557
.9562
8.7960
9.0837
.05
O.02I2
0.3118
0.4843
0.6075
0.7033
0.7818
0.8482
0.9058
0.9566
9.3069
.06
0253
3 J 39
.4857
.6085
7042
.7825
.8488
.906"
957 1
.4892
.07
.08
.0294
0334
.3160
.3181
.4871
.4886
.6o 9 6
.6107
.7050
759
.7832
7839
.8494
.8500
.9060
.9074
9576
.9581
6433
.7769
.09
0374
.3201
.4900
.6117
.7067
.7846
.8506
.9079
9586
.8946
.10
0.0414
0,3222
0.4914
0.6128
0.7076
0.7853
0.8513
0.9085
0.9590
o.oooo
.11
0453
3243
.4928
.6138
.7084
.7860
.8519
.9090
9595
0953
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.0492
3263
4942
.6149
7093
.7868
.8525
.9096
.9600
.1823
.13
053 1
.3284
4955
.6160
.7101
7875
8531
.9101
.9605
.2624
.14
0569
334
.4969
.6170
.7110
.7882
8537
.9106
.9609
3365
.15
0.0607
0.3324
0.4983
0.6180
0.7118
0.7889
0-8543
0.9112
0.9614
0.4055
.16
.0645
3345
4997
.6191
.7126
.7896
8549
.9117
.9619
.4700
.17
.18
.0682
.0719
3365
3385
5024
.6201
.6212
7135
7143
7903
.7910
8555
.8561
9122
.9128
.9624
.9628
.19
0755
3404
5038
.6222
7152
7917
.8567
9133
9633
.6418
.20
0.0792
0.3424
0.5051
0.6232
0.7160
0.7924
0-8573
0.9138
0.9638
0.6931
.21
.0828
5065
.6243
.7168
793 1
.8579
9H3
9643
7419
.22
.23
.0864
.0899
3483
579
.5092
^
.6263
.7177
7185
7938
7945
8585
.8591
.9149
9154
.9647
.9652
7885
8339
.24
0934
35 02
5 I0 5
.6274
7193
7952
.8597
9159
9657
8755
.25
0.0969
0.3522
0.5119
0.6284
0.7202
0-7959
0.8603
0.9165
0.9661
0.9163
.26
.1004
3541
5132
.6294
.7210
.7966
.8609
.9170
.9666
9555
.27
.1038
.3560
SMS
.6304
.7218
7973
8615
9*75
.9671
9933
.28
.1072
3579
5 J 59
.6314
.7226
.7980
.8621
.9180
9675
i . 0296
.29
.1106
3598
5172
6325
7235
.7987
.8627
.9186
.9680
.0647
.30
.31
.32
0.1139
.1206
-36i7
3636
3655
0.5185
5198
.5211
0.6335
6 345
6355
0.7243
7251
7259
0-7993
.8000
.8007
0.8633
.8639
.8645
0.9191
.9196
.9201
0.9685
.9689
.9694
1.0986
'$&
.33
1239
3674
.5224
6365
7267
.8014
8651
.9206
.9699
1939
.34
.1271
.3692
5237
6375
7275
.8021
8657
.9212
9703
.2238
.35
0-1303
0.3711
0.5250
0.6385
0.7284
0.8028
0.8663
0.9217
0.9708
1.2528
.36
3729
5263
6395
.7292
8035
.8669
.9222
9713
.2809
.37
^67
3747
.5276
.6405
.7300
.8041
8675
.9227
.9717
3083
.38
1399
.3766
5289
.6415
.7308
.8048
.8681
.9232
.9722
3350
.39
.1430
3784
53 02
.6425
8055
.8686
9238
9727
..3610
.40
0.1461
0.3802
o.53i5
0.6435
0.7324
0.8062
0.8692
0.9243
0-973 1
1-3863
.41
.1492
3820
5328
.6444
733 2
.8069
.8698
.9248
9736
.4110
.42
i5 2 3
3838
5340
6454
7340
.8075
.8704
9253
.9741
435 1
.43
1553
3856
5353
.6464
7348
.8082
.8710
9258
9745
.4586
.44
.1584
3874
5366
.6474
,7356
.8089
.8716
9263
9750
.4816
.45
0.1614
0.3892
0.5378
0.6484
0.7364
0.8096
0.8722
0.9269
0-9754
1.5041
.46
.1644
399
5391
6493
7372
.8102
8727
.9274
9759
.5261
.47
1673
3927
5403
.6503
738o
.8109
8733
.9279
5476
.48
i73
3945
.5416
6513
.7388
.8116
8739
.9284
.9768
.5686
.49
1732
.3962
.5428
.6522
7396
.8122
8745
.9289
9773
.5892
5. Logarithms, y = log; x.
277
X.
2.
3.
4.
5.
6.
7.
8.
9.
\.LlOx
.50
.1761
3979
.5441
6532
.7404
0.8129
3-8751
0.9294
3-9777
i .6094
.51
.52
.53
.1790
.i8i8
.1847
3997
.4014
.4031
5453
5465
5478
.6542
6551
6561
.7412
.7419
.7427
.8136
.8142
.8149
.8756
.8762
.8768
9299
9304
9309'
.9782
.9786
.9791
v/wx/if.
.6292
.6487
.54
1875
.4048
5490
6571
7435
8156
.8774
93 r 5
9795
^6864
.55
0.1903
0.4065
0.5502
0.6580
7443
0.8162
3.8779
0.9320
3.9800
I . 7047
.56
I93 1
.4082
55H
.6590
745i
.8169
.8785
9325
.9805
.7228
.57
.58
.1959
.1987
.4099
.4116
5527
5539
;^
7459
.7466
.8176
.8182
.8791
8797
6330
9335
.9809
.9814
7405
7579
.59
.2014
4133
5551
.6618
7474
.8189
.8802
9340
.9818
7750
.60
0.2041
0.4150
0-5563
0.6628
0.7482
0.8195
3.8808
0-9345
0.9823
1.7918
.61
.2068
.4166
5575
.6637
7490
.8202
.8814
935
.9827
.8083
.62
.63
.64
.2095
.2122
.2148
.4183
.4200
.4216
.5587
5599
.5611
.6646
.6656
7497
755
75*3
.8209
.8215
.8222
.8820
.8825
.8831
9355
936o
9365
.9832
8245
.8405
.8563
.65
0.2175
0.4232
0.5623
0.6675
0.7520
0.8228
0.8837
0.9370
0.9845
1.8718
.66
.67
.22OI
.2227
4249
4265
5635
.5647
'6693
7528
7536
.8235
.8241
.8842
.8848
9375
938o
.9850
9854
.8871
.9021
.68
2253
.4281
.5658
.6702
7543
.8248
.8854
9385
9f59
.9169
.69
.2279
.4298
.5670
.6712
7551
.8254
.8859
9390
.9863
9315
.70
.71
0.2304
2330
0.43M
4330
0.5682
.5694
0.6721
.6730
0-7559
.7566
0.8261
.8267
0.8865
.887?
0-9395
.9400
-$f 2
1.9459
.9601
.72
2355
4346
5705
.6739
-7574
.8274
.8876
9405
9877
.9741
.73
2380
.4362
5717
.6749
.7582
.8280
.8882
.9410
.9881
.9879
.74
2405
4378
5729
.6758
.7589
.8287
.8887
.9415
.9886
2.0015
.75
0.2430
0-4393
0.5740
0.6767
0-7597
0.8293
0.8893
0.9420
0.9890
2.0149
.76
.77
2455
. 2480
4409
.4425
5752
5763
.6776
.6785
7604
.7612
.8299
.8306
.8899
.8904
9425
943
.9894
.9899
.0281
.0412
.78
.2504
.4440
5775
6794
.7619
.8312
.8910
9435
9903
.0541
.79
.2529
4456
5786
.6803
7627
.8319
8915
9440
.9908
.0669
.80
0-2553
0.4472
0.5798
0.6812
0.7634
0.8325
0.8921
0.9445
0.9912
2.0794
.81
.2577
4487
.5809
.6821
7642
.8331
8927
.9450
.9917
.0919
.82
.83
.84
.2601
.2625
.2648
.4502
.4518
4533
.5821
5832
5843
.6830
.6839
.6848
.7649
.7657
.7664
8338
.8344
8351
-8932
-8938
8943
9455
.9460
9465
.9921
.9926
9930
.1041
.1163
.1282
.85
0.2672
0.4548
0.5855
0.6857
0.7672
0.8357
0.8949
0.9469
0-9934
2.1401
.86
.2695
4564
.5866
.6866
7679
8363
.8954
9474
9939
.1518
.87
.88
.2718
.2742
4579
4594
5877
.5888
6875
.6884
.7686
.7694
8370
8376
.8060
.8965
9479
.9484
9943
.9948
1633
.1748
.89
.2765
.4609
.5900
.6893
.7701
-8382
.8971
9489
9952
.1861
.90
0.2788
0.4624
0.5911
0.6902
0.7709
0.8388
0.8976
0.9494
0.9956
2.1972
.91
.2810
4639
5922
.6911
.7716
8395
.8982
9499
.9961
.2083
.92
-2833
5933
.6920
.7723
.8401
.8987
9504
9965
.2192
.93
-2856
.4669
5944
.6928
773 1
.8407
-8993
.9509
.9969
.2300
.94
.2878
.4683
5955
6937
.7738
.8414
.8998
95!3
9974
.2407
.95
0.2900
0.4698
0.5966
0..6946
0-7745
0.8420
0.9004
0.9518
0.9978
2 - 2 5'3
.96
.2923
4713
5977
6955
775 2
.8426
.9009
9523
.998"
.2618
.97
2945
.4728
.5988
.6964
.7760
.8432
.9015
9528
9987
.2721
.98
.2967
4742
5999
.7767
8439
.9020
9533
.9991
.2824
.99
.2989
4757
.6010
.6981
7774
.8445
9025
9538
.9996
2925
278
6. Natural Sines. y = sin x.
X.
O
10
200
300
40o
500
60o
700
8O
0.0
3.OOOO
3.1736
3.3420
3.5000
.6428
0.7660
3.8660
3-9397
3.9848
0.1
.OOI7
1754
3437
5015
.6441
.7672
.8669
9403
.9851
9.9
0.2
.0035
.1771
3453
6455
7683
.8678
.9409
9854
9.8
0.3
.0052
.1788
3469
545
.6468
7694
8686
.9415
.9857
9.7
0.4
.0070
.1805
.3486
.5060
.6481
.7705
8695
.9421
.9860
9.6
0.5
3.0087
3.1822
3.3502
3.5075
.6494
0.7716
3.8704
3.9426
3.9863
9.5
0.6
.0105
.1840
35'8
.5090
.6508
.7727
.8712
943 2
.9866
9.4
0.7
.OI22
i857
3535
5 I0 5
.6521
-7738
.8721
9438
9869
9.3
0.8
.OI40
.1874
3551
.5120
6534
7749
.8729
9444
.9871
9.2
0.9
0157
.1891
3567
5*35
.6547
776o
.8738
9449
.9874
9.1
1.0
0.0175
0.1908
0.3584
0.5150
.6561
0.7771
3.8746
3-9455
3.9877
9.0
1.1
1.2
.0192
.0209
.1925
.1942
.3600
.3616
.5180
6574
6587
.7782
7793
8755
8763
.9461
.9466
.9880
.9882
8.9
8.8
1.3
0227
.1959
3 6 33
5 l6 5
.6600
.7804
.8771
.9472
.9885
8.7
1.4
.0244
1977
3649
.5210
.6613
.7815
.8780
.9478
.9888
8.6
1.5
0.0262
0.1994
0.3665
0.5225
0.6626
0.7826
0.8788
0.9483
3.9890
8.5
1.6
.0279
.2011
.3681
.5240
.6639
7837
.8796
.9489
.9893
8.4
1.7
.0297
.2028
3697
5255
.7848
.8805
9494
.9895
8.3
1.8
.0314
.2045
37H
.5270
.6665
7859
.8813
.9500
.9898
8.2
1.9
0332
.2062
3730
.5284
.6678
.7869
.8821
9505
.9900
8.1
2.0
2.1
0.0349
.0366
0.2079
.2096
0.3746
.3762
0.5299
0.6691
.6704
0.7880
.7891
0.8829
.8838
95"
.9516
0-9903
9905
8.0
7.9
2.2
.0384
.2113
-3778
5329
.6717
.7902
.8846
9521
.9907
7.8
2.3
.0401
.2I3O
3795
5344
.6730
.7912
.8854
.9527
.9910
7.7
2.4
.0419
.2147
.3811
5358
6743
7923
.8862
9532
.9912
7.6
2.5
0.0436
O.2l64
0.3827
0-5373
0.6756
0-7934
0.8870
0-9537
0.9914
7.5
2.6
.0454
.2l8l
3843
.5388
.6769
7944
.8878
.9542
.9917
7.4
2.7
.0471
.2198
3859
.5402
.6782
7955
.8886
9548
.9919
7.3
2.8
2.9
.0488
0506
.2215
2233
.3f75
.3891
5417
5432
.6794
.6807
7965
.7976
.8894
.8902
9553
9558
.9921
9923
7.2
7.1
3.0
0-0523
0.2250
0.3907
o. 5446
0.6820
0.7986
0.8910
0.9563
0.9925
7.0
3.1
.0541
.2207
3923
-5461
-6833
7997
.8918
.9568
.9928
6.9
3.2
0558
.2284
3939
5476
.6845
.8007
.8926
9573
9930
6.8
3.3
.0576
.2300
3955
5490
.6858
.8018
8934
9578
993 2
6.7
3.4
0593
2317
3971
5505
.6871
.8028
.8942
9583
9934
6.6
3.5
0.0610
0.2334
0.3987
o-55 T 9
0.6884
0.8039
0.8949
0.9588
0.9936
6.5
3.6
.0628
235 1
.4003
5534
.6896
.8049
8957
9593
.9938
6.4
3.7
0645
2368
.4019
.5548
.6909
.8059
.8965
9S9^
.9940
6.3
3.8
.0663
2385
4035
55 6 3
.692?
.8070
8973
9603
.9942
6.2
3.9
.0680
.2402
.4051
5577
6934
.8080
.8980
.9608
9943
6.1
4.0
0.0698
0.2419
0.4067
0-5592
0.6947
0.8090
0.8988
0.9613
0.9945
6.0
4.1
.0715
.2436
.4083
.5606
.6959
.8100
.8996
.9617
9947
5.9
4.2
.0732
2453
.4099
.5621
.6972
.8111
.9003
.9622
9949
5.8
4.3
.0750
247
.4115
5635
.6984
.8121
.9011
995 1
5.7
4.4
0767
.2487
4I3 1
5650
.6997
.8131
.9018
.9632
9952
5.6
4.5
0.0785
0.2504
0.4147
0.5664
0.7009
0.8141
0.9026
0.9636
0.9954
5.5
4.6
.0802
2521
.4163
5678
.7022
.8151
9033
.9641
9956
5.4
4.7
.0819
2538
.4179
5693
7034
.8161
.9041
.9646
-9957
5.3
4.8
.0837
2 554
.4195
5707
.7046
.8171
.9048
.9650
9959
5.2
4.9
.0854
.4210
5721
7059
.8181
.9056
9655
.9960
5.1
5.0
.0872
.2588
.4226
5736
.7071
.8192
.9063
9659
.9962
5.0
80o
7O
60
50
40
3O
200
100
Z.
6. Natural Cosines. y = cos z.
6. Natural Sines, y sin x.
279
X.
20
30
4O
50
60
70
80
5.0
0.08 7 2
0.2588
0.4226
0.5736
0.7071
0.8192
0.9063
0.9659
0.9962
5.O
5.1
.0889
.2605
4242
575
7083
.8202
.9070
.9664
9963
4.9
5.2
.0906
.2622
.4258
5764
.7096
.8211
.9078
.9668
9965
4.8
5.3
.0924
2639
4274
5779
.7108
.8221
.9085
9673
.9966
4.7
5.4
.0941
.2656
.4289
5793
.7120
.8231
.9092
9677
.9968
4.6
5.5
0.0958
0.2672
0.4305
0.5807
0.7133
0.8241
0.9100
0.9681
0.9969
4.5
5.6
.0976
.2689
4321
.5821
7145
.8251
.9107
.9686
.9971
4.4
5.7
5.8
0993
.1011
.2706
2723
4337
4352
5f35
5850
7157
7169
.8261
.8271
.9114
.9121
.9690
.9694
9972
9973
4.3
4.2
5.9
.1018
.2740
.4368
.5864
.7181
.8281
.9128
.9699
9974
4.1
6.0
0.1045
0.2756
0.4384
0.5878
0.7193
0.8290
0.9135
0.9703
0.9976
4.0
6.1
.1063
2773
4399
.5892
.7206
.8300
9143
.9707
9977
3.9
6.2
.1080
.2790
.4415
.5906
.7218
.8310
.9150
97"
.9978
3.8
6.3
.1097
.2807
4431
.5920
.7230
8320
9157
9715
9979
3.7
6.4
.1115
2823
.4446
5934
7242
.8329
.9164
9720
.9980
3.6
6.5
o. 1132
0.2840
0.4462
0.5948
0.7254
0-8339
0.9171
0-9724
0.9981
3.5
6.6
"49
.2857
4478
.5962
.7266
.8348
.9178
.9728
.9982
3.4
6.7
.1167
.2874
4493
5976
.7278
.8358
.9184
9732
9983
3.3
6.8
.1184
.2890
.4509
5990
.7290
.8368
.9191
9736
.9984
3.2
6.9
.1201
.2907
4524
.6004
.7302
8377
.9198
.9740
.9985
3.1
7.0
o. 1219
0.2924
0.4540
0.6018
0.73M
0-8387
0.9205
0.9744
0.9986
3.0
7.1
.1236
.2940
4555
.6032
7325
8396
.9212
9748
.9987
2.9
7.2
1253
.2657
4571
.6046
7337
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.9219
975 1
.9988
2.8
7.3
.1271
.2974
.4586
.6060
7349
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9225
9755
.9989
2.7
7.4
..1288
.2990
.4602
.6074
73 61
.8425
9232
9759
.9990
2.6
7.5
0-1305
0.3007
0.4617
0.6088
0-7373
0-8434
0.9239
0.9763
0.9990
2.5
7.6
1323
3024
4633
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7385
8443
9245
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2.4
7.7
.1340
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7396
8453
9252
9770
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2.3
7.8
1357
3057
.4664
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.7408
.8462
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9774
9993
2.2
7.9
1374
30/4
4679
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.8471
.9265
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9993
2.1
8.0
0.1392
0.3090
0.4695
0.6157
0-743 1
0.8480
0.9272
0.9781
0.9994
2.0
8.1
.1409
3 IQ 7
.4710
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7443
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.9278
9785
9995
1.9
8.2
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3123
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7455
8499
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9995
1.8
8.3
.1444
.3140
.4741
.6198
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9792
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1.7
8.4
.1461
3156
4756
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.7478
8517
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1.6
8.5
0.1478
0-3173
0.4772
0.6225
0.7490
0.8526
0.9304
0.9799
0.9997
1.5
8.6
.1495
.3190
.4787
.6239
7501
8536
93"
.9803
9997
1.4
8.7
I 5 I 3
.3206
.4802
.6252
75*3
8545
93 1 7
.9806
9997
1.3
8.8
1530
3223
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7524
8554
9323
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1.2
8.9
1547
3239
4833
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7536
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9330
.9813
.9998
1.1
9.0
0.1564
0.3256
0.4848
0.6293
0-7547
0.8572
0.9336
0.9816
0.9998
1.0
9.1
.1582
4863
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7559
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9342
.9820
9999
0.9
9.2
.1599
.3289
.4879
.6320
7570
.8590
.9348
9823
9999
0.8
9.3
.1616
3305
.4894
6334
7581
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9354
.9826
9999
0.7
9.4
1633
3322
.4909
6347
7593
.8607
.9361
.9829
9999
O.6
9.5
9.6
:;is
0.3338
3355
0.4924
4939
0.6361
6374
0.7604
7615
0.8616
.8625
0-9367
9373
0-9833
.9836
.0000
.0000
0.5
0.4
9.7
!i685
3371
4955
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.7627
.8634
9379
9839
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0.3
9.8
.1702
3387
.4970
.6401
.7638
.8643
9385
.9842
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0.2
9.9
.1719
3404
4985
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7649
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9391
9845
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0-1
1736
.3420
. 5000
.6428
.7660
.8660
9397
.9848
.0000
0.0
80
70
60
50
40
3O
20
10
o
z.
6. Natural Cosines, y = cos z.
280
7. Natural Tangents. y = tang x.
X.
10
20
30
40
50
60
7O
80
0.0
o.oooo
0.1763
0.3640
0-5774
0.8391
1.1918
1.7321
2 -7475
5-67I3
O.I
0.2
.0017
35
.1781
.1799
3659
3 6 79
-5797
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.8421
.8451
.1960
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7391
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7776
7297
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9.9
9.8
0.3
.0052
.1817
3699
.5844
.8481
.2045
7532
.7929
.8502
9.7
0.4
.0070
1835
3719
.5867
.8511
.2088
.7603
.8083
-9124
9.6
0.5
0.0087
0-1853
0-3739
0.5890
0.8541
1.2131
1-7675
2-8239
5-9758
9.5
0.6
0.7
.0105
.0122
.1871
.1890
3759
3779
5914
5938
8571
.8601
.2174
.2218
7747
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8397
8556
6.0405
.1066
9.4
9.3
0.8
.0140
.1908
3799
.5961
.8632
.2261
7893
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1742
9.2
0.9
0157
.1926
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5985
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.2305
.7966
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2432
9.1
1.0
O.OI7C
0.1944
o-3 8 39
0.6009
0.8693
i . 2349
1.8040
2.9042
6-3138
9.0
1.1
1.2
.0192
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.1962
.1980
.3859
3879
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.6056
.8724
.8754
2393
2437
.8115
.8190
.9208
9375
3859
4596
8.9
8.8
1.3
.O227
.1998
3899
.6080
.8785
.2482
.8265
9544
535
8.7
1.4
.0244
.2016
3919
.6104
.8816
2527
.8341
.9714
-6122
8.6
1.5
O.O262
0.2035
0-3939
0.6128
0.8847
1.2572
1.8418
2.9887
6.6912
8.5
1.6
.0279
.2053
3959
6152
.8878
.2617
8495
3.0061
7720
8.4
1.7
.02 9 7
.2071
3979
.6176
.8910
.2662
8572
.0237
8548
8.3
1.8
.0314
.2089
.4000
.6200
.8941
.2708
.8650
.0415
9395
8.2
1.9
0332
.2107
.4020
.6224
.8972
2753
.8728
595
7 0264
8.1
2.0
0.0349
0.2126
0.4040
0.6249
0.9004
1.2799
1.8807
3-0777
7-1154
8.0
2.1
.0367
.2144
' .4061
.6273
.9036
.2846
.8887
.0961
.2066
7.9
2.2
.0384
.2162
.4081
.6297
.2892
.8967
.1146
.3002
7.8
2.3
.O402
.2180
.4101
.6322
.9099
2938
.9047
1334
.3962
7.7
2.4
.0419
.2199
.4122
6346
9*3!
2985
.9128
1524
7-4947.
7.6
2.5
0.0437
0.2217
0.4142
0.6371
0.9163
1-3032
1.9210
3.1716
7-5958
7.5
2.6
.0454
.2235
.4163
6395
.9195
3079
.9292
.1910
.6996
7.4
2.7
.04 7 2
.2254
.4183
.6420
.9228
3 J 27
9375
.2106
.8062
7.3
2.8
.0489
.2272
.4204
.6445
.9260
3 J 75
.9458
.2305
.9158
7.2
2.9
.0507
.2290
.4224
.6469
9293
.3222
.9542
.2506
8.0285
7.1
3.0
0.0524
0.2309
0.4245
0.6494
0-9325
1.3270
1.9626
3.2709
8.1443
7.0
3.1
.0542
.2327
.4265
.6519
9358
33i9
97"
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6.9
3.2
0559
2345
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6544
9391
3367
9797
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3863
6.8
3.3
0577
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4307
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3332
5 I2 6
6.7
3.4
0594
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4327
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9457
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3544
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6.6
3.5
0.0612
0.2401
0.4348
0.6619
0.9490
I -35 I 4
2.0057
3-3759
8.7769
6.5
3.6
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4369
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9523
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3977
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6.4
3.7
.0647
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4390
.6669
.9556
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0233
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9-0579
6.3
3.8
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44"
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9590
3663
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6.2
3.9
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2475
4431
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3713
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3572
6.1
4.0
0.0699
0.2493
0.4452
0.6745
0-9657
1-3764
2-0503
3-4874
9-5 x 4
6.0
4.1
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4473
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5 I0 5
677
5.9
4.2
0734
2530
4494
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9725
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5339
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5.8
4.3
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45'5
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9759
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5576
0.019
5.7
4.4
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4536
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9793
3968
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-.199
5.6
4.5
0.0787
0.2586
0-4557
0.6873
0.9827
1.4019
2.0965
3-6059
0-385
5.5
4.6
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. 2601;
4578
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6305
579
5.4
4.7
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4.8
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9965
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1.205
1
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1. 0000
.4281
.1445
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430
5.0
80
7O
00
5Oo 40
30
20
1O
Z.
7. Natural Cotangents, y = cot z.
. Natural Tangents, y tang x.
281
X.
Oo
100
20
40
50
60
70
80
5.0
0.0875
0.2679
0.4663
0.7002
I. 0000
1.4281
2.1445
3-73 21
u.4Jb
5.0
5.1
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4335
7583
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4.9
5.2
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7054
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4388
. 1642
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909
4.8.
5.3
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-2736
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.4442
.1742
.8118
12.163
4.7
5.4
.0945
.2754
.4748
.7107
.0141
4496
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.8391
.429
4.6
5.5
0.0963
0.2773
0.4770
0.7133
1.0176
1-4550
2.1943
3.8667
12.706
4.5
5.6
.0981
.2792
.4791
.7159
.0212
.4605
.2045
.8947
.996
4.4
5.7
.0998
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.7186
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.4659
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.9232
13-300
4.3
5.8
.ioi6
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-4834
.7212
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4715
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.9520
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4.2
5.9
I0 33
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7239
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"4770
2355
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4.1
6.0
0.1051
0.2867
0.4877
0.7265
1-0355
1.4826
2.2460
4.0108
14.301
4.0
6.1
6.2
.1069
.1086
.2886
2905
.4899
.4921
.7292
73*9
0392
.0428
.4882
.4938
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-2673
.0408
0713
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15-056
3.9
3.8
6.3
.1104
.2924
.4942
7346
.0464
4994
.2781
.1022
464
3.7
6.4
.1122
2943
4964
7373
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5051
.2889
!335
895
3.6
6.5
O.II39
0.2962
0.4986
0.7400
1.0538
1.5108
2.2998
4-1653
16.350
3.5
6.6
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.2981
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7427
0575
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.832
3.4
6.7
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7454
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2303
17-343
3.3
6.8
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5051
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3332
2635
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3.2
6.9
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3038
5073
7508
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5340
3445
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8.464
3.1
7.0
0.1228
0.3057
0.5095
0.7536
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1-5399
2-3559
4.3315
9.081
3.0
7.1
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5"7
7563
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5458
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740
2.9
7.2
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5 r 39
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55*7
3789
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0.446
2.8
7.3
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3"5
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5577
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4373
1.205
2.7
7.4
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3134
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.0875
5637
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4737
2. 022
2.6
7.5
O.I3I7
3.3153
0.5206
0-7673
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5697
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5107
2.904
2.5
7.6
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3172
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5757
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3.859
2.4
7.7
5250
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5864
4.898
2.3
7.8
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5272
7757
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4504
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6.031
2.2
7.9
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5295
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5941
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7.271
2.1
8.0
3.1405
3.3249
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3.7813
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475 1
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8.636
2.0
8.1
M23
3269
534
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7453
0.145
1.9
8.2
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5362
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I.82I
1.8
8.3
8.4
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3307
33 2 7
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5407
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6191
6255
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5257
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5-8oi
1.7
1.6
8.5
3.1495
3-3346
5430
3-7954
i3 3
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9152
8.188
1.5
8.6
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3365
5452
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J 343
6383
55 J 7
9594
0.917
1.4
8.7
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3385
5475
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1383
6447
5649
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4.066
1.3
8.8
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3404
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.6512
5782
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7.740
1.2
8.9
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3424
5520
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.6577
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2.o8l
1.1
9.0
9.1
9.2
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3-3443
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3482
0-5543
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3.8098
.8127
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1585
6643
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6775
6051
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6325
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7-200
3.657
1.615
l.O
0.9
O.8
9.3
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1.847
0.7
9.4
1655
3522
5635
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5.489
0.6
9.5
9.6
9.7
9.8
9.9
0.1673
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1745
3-3541
3561
3581
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5704
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575
0.8243
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8332
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1833
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7045
7"3
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7034
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5578
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14.59
43-24
90.98
86.48
72.96
0.5
0.4
0.3
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1763
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5774
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7475
6713
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uu
8O
7O
60
50
JO
3O
20
100
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7. Natural Cotangents. y=cotz.
282
. Logaiithmic Sines. y=logsinx.
X.
GO
10
2O
30
40o
500
60 i 7O
80
o.o
oo
9-2397
9-5341
9.6990
9.8081
9-8843
9-9375
9-9730
9-9934
0.1
7.2419
. 2439
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9733
9935
9.9
0.2
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5382
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8855
9384
9735
9936
9.8
0.3
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2524
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9738
9937
9.7
0.4
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2565
5423
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9393
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9939
9.6
0.5
0.6
0.7
7.9408
8 . O200
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9.2606
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9- 5443
5463
5484
9-7055
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.7080
9.8125
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9.8874
.8880
.8887
9-9397
.9401
.9406
9-9743
9746
9749
9.9940
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9943
9.5
9.4
9.3
O.8
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554
7093
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8893
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9751
9944
9.2
0.9
.1961
.2767
5523
.7106
.8161
.8899
.9414
9754
9945
9.1
1.0
8.2419
9.2806
9- 5543
9.7118
9.8169
9-8905
9.9418
9-9757
9-9946
9.0
1.1
.2832
.2845
5563
7I3 1
.8178
.8911
.9422
9759
9947
8.9
1.2
.3210
.2883
5583
.7144
.8187
.8917
9427
.9762
9949
8.8
1.3
.3558
.2921
.5602
7156
.8195
.8923
9431
9764
.9950
8.7
1.4
3880
2959
.5621
.7168
.8204
.8929
9435
.9767
.9951
8.6
1.5
8.4179
9.2997
9.5641
9.7181
9.8213
9-8935
9-9439
9.9770
9-9952
8.5
1.6
4459
3034
.5660
7193
.8221
.8941
9443
.9772
9953
8.4
1.7
4723
.3070
.5679
.7205
.8230
.8947
9447
9775
9954
8.3
1.8
.4971
.3107
.5698
.7218
.8238
8953
9451
9777
9955
8.2
1.9
.5206
3143
5717
.7230
.8247
8959
9455
.9780
9956
8.1
2.0
2.1
8.5428
.5640
9-3I79
.3214
5754
9.7242
7254
9-8255
.8264
9.8965
-.8971
9-9459
9463
9.9782
9785
9.9958
-9959
8.0
7.9
2.2
.5842
3249
5773
.7266
.8272
8977
.9467
.9787
.9960
7.8
2.3
.6035
.3284
5792
.7278
.8280
.8983
.9471
-9789
.9961
7.7
2.4
.6220
3319
.5810
.7290
.8289
.8989
9475
.9792
.9962
7.6
2.5
2.6
8.6397
.6567
9-3353
3387
9. 5828
5847
9.7302
7314
9.8297
.8305
9.8995
.9000
9-9479
-9483
9-9794
9797
9-9963
.9964
7.5
7.4
2.7
-6731
3421
5865
.7326
8313
.9006
-9487
9799
.9965
7.3
2.8
.6889
3455
5883
7338
.8322
.9012
.9491
.9801
.9966
7.2
2.9
.7041
-3488
.5901
7349
8330
.9018
9495
.9804
.9967
7.1
3.0
8.7188
9-3521
9.5919
9-736i
9.8338
9.9023
9.9499
9.9806
9.9968
7.0
3.1
7330
3554
5937
7373
.8346
.9029
9503
.9808
.9968
6.9
3.2
3.3
.7468
.7602
.3618
5954
5972
.7384
7396
8354
.8362
9035
.9041
.9506
.9510
.9811
.9813
.9969
.9970
6.8
6.7
3.4
7731
.3650
5990
.7407
.8370
.9046
.9514
.9815
.9971
6.6
3.5
8-7857
9.3682
9.6007
9.7419
9.8378
9.9052
9.9518
9.9817
9.9972
6.5
3.6
7979
3713
6024
743
.8386
9057
9522
.9820
9973
6.4
3.7
.8098
3745
.6042
7442
.8394
.9063
9525
.9822
9974
6.3
3.8
8213
3775
.6059
7453
.8402
.9069
9529
.9824
9975
6.2
3.9
.8326
.3806
.6076
.7464
.8410
.9074
9533
.9826
9-9975
6.1
4.0
8.8436
9 3837
9.6093
9.7476
9.8418
9.9080
9-9537
9.9828
9.9976
6.0
4.1
8543
.3867
6110
7487
.8426
.9085
9540
.9831
9977
5.9
4.2
.8647
3897
.6127
.7498
8433
.9091
9544
.9833
.9978
5.8
4.3
8749
3927
.6144
759
.8441
.9096
9548
9835
.9978
5.7
4.4
.8849
3957
.6161
7520
.8449
.9101
955 1
.9837
9979
5.6
4.5
8.8946
9.3986
9.6177
9-7531
9.8457
9:9107
9-9555
9.9839
9.9980
5.5
4.6
.9042
.4015
.6194
.7542
.'8464
.9112
9558
.9841
.9981
5.4
4.7
4.8
9135
.9226
.4044
4073
.6210
.6227
7553
.7564
.8472
.8480
.9118
.9123
9562
.9566
9843
-9845
.9981
.9982
5.3
5.2
4.9
9315
.4102
.6243
7575
.8487
.9128
.9569
-9847
9983
5.1
5,O
9403
.4130
.6259
7586
.8495
9i34
9573
.9849
9983
5.O
800
70
600
500
400
3O
200
100
O
Z
. Logarithmic Cosines.
log cos z.
. Logarithmic Sines. y=log sin x.
283
X. 0<=
10
20
30
40
50
60
7O
80
5.0
8.9403
9.4130
9.6259
9.7586
9.8495
9-9I34
9-9573
9.9849
9-9983
5.O
5.1
9489
.4158
.6276
7597
.8502
9139
.9851
.9984
4.9
5.2
9573
.4186
.6292
.7607
.8510
.9144
.9580
9853
9985
4.8
5.3
9655
.4214
.6308
.7618
.8517
.9149
9583
9855
9985
4.7
5.4
9736
.4242
.6324
.7629
.8525
9155
.9587
9857
.9986
4.6
5.5
8.g8i6
9.4269
9.6340
9.7640
9-8532
9.9160
9.9590
9-9859
9.9987
4.5
5.6
.9894
.4296
.6356
.7650
.8540
.9165
9594
.9861
-9987
4.4
5.7
.9970
4323
6371
.7661
8547
.9170
9597
.9863
.9988
4.3
5.8
5.9
9.0046
.0120
435
4377
.6387
.6403
.7671
.7682
8555
.8562
9175
.9181
.9601
.9604
.9865
.9867
.9988
9989
4.2
4.1
6.0
9.0192
9.4403
9.6418
9.7692
9.8569
9.9186
9.9607
9.9869
9.9989
4.0
6.1
.0264
4430
6434
7703
8577
.9191
.9611
.9871
9990
3.9
6.2
334
4456
.6449
7713
.8584
.9196
.9614
9873
.9990
3.8
6.3
.0403
.4482
.6465
7723
.8591
.9201
.9017
9875
.9991
3.7
6.4
.0472
.4508
.6480
7734
.8598
.9206
.9621
.9876
.9991
3.6
6.5
9-0539
9-4533
9.6495
9-7744
9.8606
9.9211
9.9624
9.9878
9.9992
3.5
6.6
6.7
.0605
.0670
4559
.6510
.6526
-7754
.7764
.8613
.8620
.9216
.9221
.9627
.9631
.9880
.9882
.9992
9993
3.4
3.3
6.8
0734
.4609
.6541
7774
.8627
.9226
9634
.9884
9993
3.2
6.9
.0797
4634
.6556
7785
.8634
.9231
9637
.9885
9994
3.1
7.0
9-0859
9.4659
9.6570
9-7795
9.8641
9.9236
9.9640
9.9887
9.9994
3.0
7.1
.0920
.4684
.6585
-7805
.8648
.9241
9643
.9889
9994
2.9
7.2
.0981
.4709
.6600
-7815
.8655
.9246
.9647
.9891
9995
2.8
7.3
.1040
4733
.6615
7825
.8662
.9251
.9650
.9892
9995
2.7
7.4
.1099
4757
.6629
7835
.8669
9255
9653
.9894
.9996
2.6
7.5
9- "57
9.4781
9.6644
9.7844
9.8676
9.9260
9.9656
9.9896
9.9996
2.5
7.6
.1214
.4805
-6659
7854
.8683
.9265
9659
9897
.9996
2.4
7.7
.1271
.4829
.7864
.8690
9270
.9662
.9899
.9996
2.3
7.8
.1326
-4853
.6687
.7874
.8697
9275
.9665
.9901
9997
2.2
7.9
-1381
.4876
.6702
.7884
.8704
9279
.9669
.9902
9997
2.1
8.0
9.1436
9.4900
9.6716
9.7893
9.8711
9.9284
9.9672
9.9904
9.9997
2.0
8.1
8.2
.1489
.1542
-4923
.4946
.6730
.6744
7903
.8718
.8724
.9289
9294
9675
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1.9
1.8
8.3
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6759
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1.7
8.4
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6773
793 2
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933
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1.6
8.5
9.1697
9-5 OI 5
9.6787
9-7941
9.8745
9.9308
9.9687
9.9912
9-9999
1.5
8.6
1747
537
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795 1
875 1
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99 I 3
9999
1.4
8.7
1797
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9317
9693
9915
9999
1.3
8.8
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.7970
.8765
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9999
1.2
8.9
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7979
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9999
1.1
9.0
9-1943
9.5126
9.6856
9.7989
9.8778
9-933 1
9.9702
9.9919
9-9999
1.0
9.1
.1991
.5148
.6869
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.8784
9335
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9999
0.9
9.2
.2038
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.8791
9340
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o.oooo
0.8
9.3
.2085
5 I 92
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8797
9344
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0.7
9.4
2131
5 2I 3
.6910
.8026
.8804
9349
9713
9925
.0000
0.6
9.5
9.2176
9-5235
9.6923
9.8035
9.8810
9-9353
9.9716
9.9927
o.oooo
O.5
9.6
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6937
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9358
9719
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0.4
9.7
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-5278
.6950
.8053
.8823
.9362
.9722
.9929
.0000
0.3
9.8
.2310
.5299
.6963
.8063
.8830
9367
.9724
993 1
.0000
0.2
9.9
2353
.5320
.6977
.8072
.8836
9371
.9727
9932
.0000
O.I
2397
5341
.6990
.8081
8843
9375
973
9934
.0000
0.0
8O
70
60
50
40
30
20
10
Z.
. Logarithmic Cosines.
log cos z.
234
9. Logarithmic Tangents, y = log tang x.
X.
10
20
30
40
50
60
70
80
0.0
00
2463
.5611
.7614
.9238
.0762
.2386
.4389
7537
O.I
0.2
0.3
0.4
.2419
5429
.7190
8439
2507
2551
.2594
.2637
5634
.5658
5681
5704
.7632
.7649
.7667
.7684
.9254
.9269
.9284
.9300
-0777
0793
.0808
.0824
.2403
.2421
.2438
2456
4413
-4437
.4461
4484
75 8r
.7626
.7672
.7718
9.9
9.8
9.7
9.6
0.5
9409
9.2680
-5727
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93* S
0.0839
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0.4509
0.7764
9.5
O.6
0.7
0.8
.0200
.0870
.1450
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.2764
.2805
5750
5773
5796
7719
7736
7753
933
.9346
.9361
.0854
.0870
.0885
.2491
-2509
2527
4533
4557
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.7811
.7858
.7906.
9.4
9.3
9.2
0.9
.1962
.2846
.5819
7771
9376
.0901
2545
.4606
7954
9.1
1.0
.2419
9.2887
.5842
.7788
9.9392
0.0916
0.2562
0.4630
0.8003
9.0
1.1
1.2
1.3
2833
.3211
3559
.2927
.2967
.3006
.5864
.5887
5909
-7805
.7822
.7839
.9407
9422
.9438
0932
.0947
.0963
.2580
.2598
.2616
4655
.4680
4705
.8052
.8102
.8152
8.9
8.8
8.7
1.4
.3881
.3046
593 2
.7856
9453
.0978
.2634
4730
.8203
8.6
1.5
1.6
.4181
.4461
9.3085
9-5954
5976
9.7873
.7890
9-. 9468
9483
0.0994
.1010
0.2652
.2670
0-4755
.4780
0.8255
.8307
8.5
8.4
117
.4725
.3162
5998
.7907
9499
.1025
.2689
.4805
.8360
8.3
1.8
4973
.3200
.6020
.7924
.9514
.1041
2707
.4831
.8413
8.2
1.9
.5208
3237
.6042
.7941
9529
.1056
2725
4857
.8467
8.1
2.0
5431
9-3275
9.6064
9.7958
9.9544
0.1072
0.2743
0.4882
0.8522
8.0
2.1
5643
33"
.6086
7975
.9560
.1088
.2762
.4908
8577
7.9
2.2
.584^
3349
.6108
.7992
9575
.1103
.2780
4934-
-8633
7.8
2.3
.6038
.3385
.6129
.8008
959
.1119
.2798
.4960
.8690
7.7
2.4
.6223
.3422
.6151
.8025
.9605
"35
.2817
.4986
.8748
7.6
2.5
8.6401
9-3458
9.6172
9.8042
9.9621
0.1150
0.2835
0.5013
0.8806
7.5
2.6
2.7
2.8
57i
.6736
.6894
3493
3529
3564
.6194
.6215
.6236
.8059
.8075
.8092
.9636
.9651
.9666
.1166
.1182
.1197
.2854
.2872
.2891
5039
.5066
5093
.8865
.8924
8985
7.4
7.3
7.2
2.9
.7046
3599
6257
.8109
.9681
.1213
.2910
.5120
.9046
7.1
3.0
8.7194
9-3634
9.6279
9.8125
9.9697
0.1229
0.2928
0.5147
0.9109
7.0
3.1
7337
.3668
.6300
.8142
.9712
1245
2947
5174
.9172
6.9
3.2
7475
3702
.6321
.8158
.9727
.1260
.2966
.5201
.9236
6.8
3.3
.7609
3736
.6341
-8175
974 2
.1276
.2985
.5229
.9301
6.7
3.4
7739
3770
.6362
.8191
9757
.1292
.3004
.5256
9367
6.6
3.5
8.7865
9.3804
9-6383
9.8208
9.9772
0.1308
0.3023
0.5284
0-9433
6.5
3.6
.7988
3837
.6404
.8224
.9788
1324
.3042
S3 12
.9501
6.4
3.7
.8107
.3870
.6424
.8241
.9803
.1340
.3061
5340
9570
6.3
3.8
3.9
.8223
8336
3903
3935
6445
.6465
8257
.8274
.9818
9833
.3080
3099
-5368
5397
.9640
.9711
6.2
6.1
4.0
8.8446
9.3968
9.6486
9.8290
9.9848
0.1387
0.3118
0.5425
0.9784
6.0
4.1
8554
,4000
.6506
.8306
.9864
.1403
3 T 37
5454
.9857
5.9
4.2
.8659
.4032
6527
8323
.9879
.1419
.3157
5483
9932
5.8
4.3
.8762
.4064
654
8339
.9894
1435
.3176
5512
1.0008
5.7
4.4
.8862
4095
.656
8355
.9909
.1451
.3196
5541
.0085
5.6
4.5
8.8960
9.4127
9.658
9-8371
9.9924
0.1467
0.3215
0.5570
1.0164
5.5
4.6
.9056
.4158
.660
.8388
9939
.1483
3235
. 5600
.0244
5.4
4.7
.9150
.4189
.662
.8404
9955
.1499
3254
5629
.0326
5.3
4.8
.9241
.4220
.664
.8420
.9970
.1516
3274
5659
.0409
5.2
4.9
933 1
.4250
.666
.8436
9985
1532
3294
-5689
0494
5.1
5.0
.9420
.4281
.668
.8452
o.oooo
.1548
5719
.0580
5.0
80
70
6O
50
40
3O
20
10
Z.
9. Logarithmic Cotangents.
Iog cot z.
9. Logarithmic Tangents. y = log tan x.
285
X.
Oo
100
20
30
40
50
60
70o
800
5.0
5.1
8.9420
.9506
9.4281
43"
9.6687
.6706
9-8452
.8468
o.oooo
.0015
0.1548
.1564
0-33I3
3333
0-57J9
5750
1.0580
.0669
5.0
4.9
5.2
5.3
5.4
.9591
.9674
9756
4341
4371
.4400
-9726
.6746
6765
.8484
.8501
.8517
.0030
.0045
.0061
.1580
.1596
.1612
3353
3373
3393
.5780
.5811
5842
759
.0850
944
4.8
4.7
4.6
5.5
8-9836
9-443
9.6785
9-8533
0.0076
0.1629
0-3413
0.5873
I . 1040
4.5
5.6
5.7
.9915
.9992
4459
.4488
.6804
.6824
-8549
8565
.0091
.0106
.1645
.1661
3433
3453
-"38
.1238
4.4
4.3
5.8
9.0068
45*7
.6843
.8581
.0121
*677
3473
1341
4.2
5.9
.0143
.4546
.6863
8597
.0136
.1694
3494
.1446
4.1
6.0
9.0216
9-4575
9.6882
9.8613
O.OI52
0.1710
0.3514
0.6032
I - I 554
4.0
6.1
.0289
-4603
.6901
.8629
.0167
.1726
3535
.6065
.1664
3.9
6.2
6.3
.0360
.0430
.4632
.4660
.6920
6939
.8644
.8660
.0182
.0197
-1743
!759
3555
3576
.6097
.6130
1777
.1893
3.8
3.7
6.4
0499
.4688
.6958
.8676
.O2I2
.1776
3596
.6163
.2012
3.6
6.5
9.0567
9-4716
9.6977
9.8692
0.0228
0.1792
0-3617
0.6196
I.2I35
3.5
6.6
0633
4744
.6996
.8708
.0243
.1809
3638
.6230
.226l
3.4
6.7
.0699
.4771
7015
.8724
0258
.1825
3659
.6264
.2391
3.3
6.8
.0764
4799
7034
.8740
.0273
.1842
3679
.6298
2525
3.2
6.9
.0828
.4826
7053
8755
.0288
.1858
.3700
-6332
.2663
3.1
7.0
7.1
9.0891
0954
':$?
9.7072
.7090
9.8771
.8787
0.0303
.0319
0.1875
.1891
0.3721
3743
0.6366
.6401
1.2806
2954
3.0
2.9
7.2
.1015
.4907
.7109
.8803
334
.1908
3764
.6436
.3106
2.8
7.3
.1076
4934
.7128
.8818
0349
.1925
.6471
.3264
2.7
7.4
"35
.4961
.7146
.8834
.0364
.1941
.3806
6507
3429
2.6
7.5
9.1194
9.4987
9 7^65
9.8850
0.03 79
0.1958
0.3828
0.6542
3599
2.5
7.6
1252
.5014
7183
.8865
0395
1975
3849
.6578
3777
2.4
7.7
.1310
.5040
.7202
.8881
.O410
.1992
3871
.661 5
3962
2.3
7.8
1367
.5066
.7220
.8897
0425
.2008
.3892
.6651
4155
2.2
7.9
1423
.5092
-7238
.8912
.0440
.2025
39H
.6688
4357
2.1
8.0
9.1478
9.5118
9-7257
9.8928
.0456
0.2042
0-393 6
6725
4569
2.0
8.1
1533
5*43
7275
.8944
.0471
2059
3958
.6763
4792
1.9
8.2
.1587
.5169
7293
.8959
.0486
.2076
.3980
.6800
.5027
1.8
8.3
.1640
5 J 95
73"
8975
.0501
.2093
.4002
.6838
5275
1.7
8.4
.1693
5220
7330
.8990
.0517
.2110
.4024
6377
5539
1.6
8.5
3-1745
3-5245
9-7348
9.9006
0532
.2127
.4046
.6915
.5819
1.5
8.6
1797
.5270
7366
.9022
0547
2144
.4068
6954
.6119
1.4
8.7
8.8
.1848
.1898
5295
.5320
7384
7402
9037
953
.0562
.0578
.2l6l
.2178
.4091
4"3
6994
7033
.6441
.6789
1.3
1.2
8.9
.1948
5345
.7420
.9068
0593
2195
.4136
7073
.7167
1.1
9.0
9.1997
3-5370
9-7438
9.9084
.0608
O.22I2
.4158
7"3
.7581
1.0
9.1
.2046
5394
7455
.9099
.0624
.2229
.4181
7154
.8038
O.9
9.2
.2094
5419
7473
9"5
.0639
.2247
.4204
7195
.8550
0.8
9.3
9.4
.2142
.2189
-5443
.5467
.7491
7509
.9130
.9146
.0654
.0670
.2204
.2281
.4227
.4250
7236
7278
.9130
.9800
0.7
0.6
9.5
9.6
9.7
9.8
9.2236
.2282
.2328
2374
3-5491
55 l6
-5539
5563
9-7526
7544
7562
7579
.9161
.9176
.9192
.9207
.0685
.0/00
.0716
0/31
0.2299
.2316
2333
.2351
-4273
.4296
43 '9
4342
.7320
7363
.7406
7449
.0591
.1561
.2810
-4571
0.5
0.4
0.3
0.2
9.9
.2419
5587
7597
.9223
.0746
.2368
.4366
7493
.7581
O 1
2463
.5611
.7614
.9238
.0762
.2386
4389
7537
CO
oo
80
70
60
5O
40
30
20
10
z.
9. Logarithmic Cotangents, y = log cot z.
286
1O. Constants.
Num.Val
. Recip.
Log.
Circumference in diameters, TT
71-2 = 9.8696044,^=1.7724538
3.141592
2.718281
434294
1.414213
1.7320508
.6744
57.29578
3437.7468
206264.8
8". 94
20". 4.1
.9972696
365.24221
23027/24'
I?.'?
978.0
983.2
99.09
99.62
39- 1393
194.897
2.5400
30.480
1.6093
6.451
16.387
i-i355i
.0036075
.06480
45359
37324
252-458
1.293
13825
.00102
.00102
7.46
70,308
13-596
1.05949
33030
300400
00005895
21. 67
425
773
41.6
.003665
XSl
79-4
537
9536
.01024
1.079
.001516
.318309
.367889
2.30258
.707106
0174532
. 0002908
.0000048
1.0027379
.0027379
.0001568
.0001573
.001022
.001917
.01009
.0100^
02555
.0051309
39370
.03281
1550
.061025
.88066
277.274
15-432
2 . 20462
2.67951
.003961
7734
7-233 1
980
980
134
.01422
07355
.94386
16963.5
.04615
.00235
.00129
.02404
273
7057
03463
.0126
.001862
1.0487
97.656
.9268
659.6
0.49715
0.43429
9.63778
0.15051
0.23856
9.82898
1.75812
3-53627
5-3I443
0-9523
2.56258
3-80464
3.80319
2-9903
2.9926
1.9960
1.9983
1.59261
2.28981
0.4048
1.4840
0.2066
0.8097
2145
0.0552
9. '6566?
57198
.40219
. 1116
.1407
.009
.009
873
.8470
I334I
.02509
.5189
4777
7705
3359
.6277
.8882
.619
.5641
1514
.4606
.900
73
9794
.0107
0330
.1807
Modulus of common logarithms, M .
Square root of 3. ... .'....
Ratio of probable to mean error
Radius in degrees
Mean time in sidereal time
Tropical year in mean days = 36$d. e,h. 48m. 463
Dbliquity of ecliptic 1877
Equatorial radius of earth in kilometres
Polar radius of earth in kilometres ....
Force of gravity at equator in centimetres . .
Force of gravity at pole in centimetres ....
seconds pendulum at equator in centimetres .
Seconds pendulum at pole in centimetres .
Seconds pendulum at London in inches (Kater) .
Toise of Peru in centimetres
'nch in centimetres
Statute miles in kilometres
^ubic inch in centimetres
Imperial gallon in cubic inches
'ound Avoirdupois in kilogrammes
} ound Troy in kilogrammes
Weight of i cu. inch of water in grains at 62F.
Veight of i litre of air in grammes ....
r oot-pound in kilogrammetres
Dyne in grammes, approx
rg in gramme-centimetres, approx
lorse power in erg-nines, approx
5 ound per sq. inch in grammes per sq. centimetre
Specific gravity of mercury
nterval of semitone in isotonic scale ....
Velocity of sound in air in centimetres at o C. .
Velocity of light in vacuo in kilometres
Wave-length of sodium line D in centimetres .
dotation of I mm. of quartz (D line) ....
Mechanical equivalent of heat in French units
Mechanical equivalent of heat in English units
Mechanical equivalent of heat in megalergs, app. .
Expansion of gases per degree Centigrade.
,atent heat of fusion of ice
^atent heat of vaporization of steam at 100 C. .
r arad liberates of H in milligrammes ....
Electromotive force of a Daniell's cell in volts .
lesist. of Cu. wire I inch long, wt. I gnu, in ohms
11. Properties of the Metals.
287
1
fe
Symbol. 1
1 Atomic 1
Weight. 1
1 Modulus 1
of Elast. 1
=
II
cc
1 Point of I
| Fusion. 1
H
1
Electrical!
Resist. 1
Thermo- 1
Electric. 1
a
Aluminum
Al
27.4
2.6
.0821
.214
2336
.030
_|_ -
8.4
Antimony
SI)
122.0
6.7
.051
450
1055
359
-2.8
24-5
Arsenic
As
75-o
5-7
.081
602
-13.6
'5?
Barium
Ba
4-
15.8
Bismuth
Bi
2IO.O
9.8
031
270
1316
2.4
*33
4-89
39.2
Cadmium
Cd
112.
8.6
.0700
054
3 20
3102
.068
3-9
13.6
Caesium
Cs
J 33-
13?
Calcium
Ca
40.0
1.6
.0405
.167
.036
'5- 1
10.4
Cerium
Ce
42.
5-5
13?
Chromium
Cr
52.2
7-3
.1450
18?
Cobalt
Co
58.8
8-5
.1360
.107
1250
1244
+22.4
10.8
Copper
Cu
63-4
8.9
I20OO
.094
IIOO
1698
100
.017
ii. 6
Didymium
Erbium
D
E
95.0
112. 6
16?
Gallium
Ga
Glucinum
Gl
9-4
2.1
5-7
Gold
Au
197.0
19-3
8000
.0979
.032
1250
I45 1
72
.021
1 .2
24.0
Hydrogen
11
I.O
3-41
i?
Indium
In
198
7-2
.0984
057
176
4594
Iridium
Ir
198
22.4
033
708
2.5
Iron
Fe
56.0
7-7
2OOOO
'375
"3
1500
1228
1 6
.098
17-5
12?
Lanthanum
La
93- 6
Lead
207.0
11.4
I70O
0570
.031
33
2948
II
.198
o.o
2 4 .8
Lithium
U
7.0
.6
.941
180
.080
13-7
3-8
Magnesium
24.0
1-7
0726
.247
2762
.031
+ 4
70?
Manganese
Mr
55-
7-
1456
.122
1600
12?
Mercury
Molybdenum
Mo
200.
96.0
13.6
8.6
033
.072
39
1600
.956
+ 4.2
21 ?
Nickel
Ni
58.8
8-3
1410
.109
1286
+ii. 4
10.4
Niobium
Xb
94-0
7-
Osmium
Os
21.4
.031
679
Palladium
Pel
106.0
11.7
10000
1 200
059
1190
8.6
.138
+7.2
22.2
Platinum
Pt
197.4
21.5
16000
1107
.032
907
ii
.092
9
26.0
Potassium
K
39- *
9
0230
.170
60
.072
+12.7
8.1
Rhodium
R
104.4
II. 2
.058
858
24? .
Rubidium
Kb
85-4
1.5
38
I 4 .0
Ruthenium
Ru
104.4
II .2
.O6l
991
Selenium
Se
79-4
4-8
0990
.084
217
807
Silver
As,
108.0
10-4
7OOO
0400
.057
IOOO
'935
136
015
3
13?
Sodium
Strontium
Xa
Sr
23.0
87.6
I.O
2-5
293
96
.021
.227
+5-9
8.7
4 .8
I 3 .6
Tantalum
Ta
182.0
10.5
Tellurium
Te
128.0
6.2
.047
500
1732
502
Thallium
Tl
204.0
ii. 8
0565
034
290
.183
21.6
Thorinum
Th
57-9
7-7
Tin
Sn
118.0
7-2
4OOO
0651
.056
230
2270
20
134
.1
27?
Titanium
Ti
50.0
25?
Tungsten
W
184.0
17.4
.033
Uranium
U
240.0
18.4
.O2
10.8
Vanadium
V
Si-2
5-5
25?
Yttrium
Y
61.6
Zinc
Zn
65.2
6.8
9OOO
.1077
093
420
2905
26
057
-3-7
10?
Zirconium
Zr
89.6
4.1
22?
Steel
7.8
20OOO
1400
1 200
1 6
Brass
8.3
9OOO
.094
900
1900
32
.058
288
12. Properties of Liquids.
i
If
J!
g
"3 s
H
MIlMlX
JN
11
II
S
11
1
1
off
cctf
W
i
> Vi
H
Hft
A
S
W T ater
H,O
I.OOO
29-3
477
1437
I.OOO
.0466
100
536
334
.012
I .OO
Alcohol
C 2 H 6
792
11.4
004
1160
595
.III
78
20C)
372
.Oil
.81
Ether
C 4 H I0
715
9-5
IIIO
1160
.540
.0714
35
91
.OI2
.80
Bisulph. Carb.
Turpentine
cX
1.263
.86q
9-7
12.7
7H
1212
238
432
.0714
4 6
159
60
474
.077
.022
1.0 3
Mercury
Hg
13.60
9.2
3
033
.0182
357
Bromine
Br
2.966
9.0
"3
47
Sulph. Acid
H 2 SO 4
1.841
320
343
.0588
434
.014
1. 08
Nitric Acid
H 2 N0 6
!-55
322
.III
86
.410
.019
.91
13. Properties of Oases.
i
1
%
1
S
II
|a
.
0,0"
!.!
jftj
If
||
J]
1
*
I
1
1
&t
s*
"3 *
*1
5
Hydrogen
H 2
2
.069
.089
3-409
.236
_
2.288
^69"
1388
.0044
Marsh Gas
Ammonia
CH 4
NH 3
16
17
555.
.717
.770
593
.328
.300
-38-5
815
955
443
385
Steam
H 2 O
18
.623
.805
.480
2 99
100
Carbonic Ox.
CO
28
957
236
245
237
.145
337
3336
.0075
Nitrogen
Ethylene
N 2
C 2 H 4
28
28
.972
.978
.256
263
244
.404
237
.411
.141
.980
34
2972
.678
.0069
Air
I.OOO
.292
237
2 37
.107
33
2923
.0058
Binox. Nit.
NO
30
1.039
342
.231
2 3 8
.141
.2967
Oxygen
Sulph. Hyd.
2
H 2 S
32
1.106
1.191
.218
243
.240
.286
61.8
.000
.614
37
.272
.644
Nitrous Oxide
Carbonic Acid
Cyanogen
N 2 O
C 2 N 2 2
44
48
54
1.520
i . 529
i. 806
'$?
.224
.217
245
331
87-9
-78.2
35
335
370
.976
262
262
.5084
4494
.8202
.0127
.0052
.0100
Sulph. Anhyd.
S0 2
64
2.234
.886
154
341
IO. I
538
.6820
Chlorine
C1 2
7i
2.470
3-!9i
.121
.296
-33-6
.500
14. Hydrometer Tables.
15. Temperatures.
- >1
If
o*
>>
*
1
1
Absolute zero
C,
273
F.
460
18
i|
9 >
" ~
$
t;
"S
Lowest temperature yet attained.
140
22O
8|
w s
3
a
5
1
Lowest observed temp, of air .
60
76
H
Mercury freezes
39
-jg
.000
.000
I.OOO
.00
Water freezes . . . .
+32
5
35
.030
.971
.02
Average temp, of earth's surface.
-(-15
60
10
073
I.OOO
.062
944
5
Temperature of human body .
37
99
15
.114
.967
.097
.919
.970
.07
Highest observed temp, of air .
56
133
20
.158
936
X 33
895
936
.10
Wood's metal, i Cd, 2 Sn, 4 Pb,.
70
158
-5
.205
.907
.172
.872
95
.12
Rose's metal, 4 Bi, i Pb, i Sn, .
94
200
2 57
.880
.214
.850
.876
.15
Boiling point of water . . .
IOO
212
35
.854
259
.829
.849
17
Highest temp, sustained by man.
129
264
40
375
.830
.308
.810
.824
. 20
Boiling point of mercury.
357
677
45
.442
.807
360
.791
.22
Boiling point of sulphur .
440
824
^o
.517
785
.417
773
2 5
Dark red heat (Draper) . . .
525
977
55
599
.764
.478
.756
.27
Boiling point of cadmium
860
1580
00
601
CAC
Cherry red
900
1650
65
. uyi
795
745
.619
723
3
32
Boiling point of zinc .
1040
1900
7
.912
.700
.708
35
Yellow heat
1 200
2200
75
045
.790
37
White heat
1300
24OO
16. Pressure of Vapors.
289
T.
Water.
Alcohol.
Etlier.
C 2 S
OilTurp.
S0 2
NH 3
C0 3
>Hg
2O
9.1
3-34
68.90
47-30
479.46
1392.1
15142.4
10
2.08
6.47
114.72
79-44
762.49
2144.6
20340.2
4.60
12.70
184.39
127.91
2.07
1165.06
3I83-3
26906.6
.02
+10
20
9.16
17-39
24.23
44.46
286.83
432.78
198.46
298.03
2-94
4-45
1799-55
2462.05
4574-0
6387.8
44716.6
56119.0
03
.04
3
31-53
78.52
634.80
434.62
6.87
3431.80
8700.9
69184.4
05
40
54.91
I33-69
907.04
6i7-53
10.80
4670.23
"595-3
.08
50
91.98
219.90
1264-83
857-07
16.98
6220.01
15158.3
.11
60
148.79
350-21
1725.01
1164.51
26.46
8123.80
19482.1
.16
70
233- 9
5,4i-i5
2304.90
1552.09
.40.64
24675-5
.24
80
354-64
812.91
3022.79
2032.53
61.30
30843.1
35
90
52S-4S
1189.30
3898.26
2619.08
90.61
38109.2
5 1
100
760.00
1697.55
4953-30
3325-I5
131.11
46608.2
75
120
140
1491.28
2717.63
523I-73
5 6 74.59
7719.20
5148.79
7603.96
257.21
464.02
I'M
1 60
4651.62
775-09
5-90
1 80
7546.39
1207.92
11.00
2OO
11689.0
1771.47
19.90
220
17390.4
34 -7C
17. Wet and Dry Bulb.
T.
1
3
3
40
5
6
70
8
9
10
11
12
14o
10
2.1
1.6
I.O
5
4
8
2-5
1.9
1.4
9
4
6
2-9
2.4
1.8
i-3
.8
3
4
3-4
2.9
2-3
1.8
1.3
.8
3
2
4.0
3-4
2.9
2.4
1.9
1.4
9
4
O
4.6
4.0
3-4
2.8
2.2
1.6
I.O
4
+ 2
5-3
4-7
4.1
3-5
2. 9
2-3
1.7
i.i
5
4
6.1
5-5
4-9
4-3
3-7
3- 1
2.5
1.9
7
.1
6
7-o
6.4
5-8
5-2
4.6
4.0
3-4
2.8
2.2
1.6
I.O
4
8
10
12
.8.0
9.2
10.5
U
9.8
6.8
8.0
9.2
6.2
i:l
5-6
6-7
8.0
K
7-4
4-4
1:1
3-8
4-9
6.2
3-2
*i
2.6
3-7
5-
2.0
3- 1
4-4
1.4
ii
.8
1.9
3-2
.2
1:1
M
16
11.9
"3
12.9
10.7
12.3
IO.I
11.7
9-5
ii. i
8.9
10.5
8-3
9-9
7-6
9-3
7-
8-7
6.4
8.0
5-8
7-4
il
4.6
6.2
4 .o
5-6
18
15-4
14.7
14.1
"3-5
12.9
12.3
11.7
n. i
10.5
9.8
9.2
8.6
8.0
7-4
20
17.4
16.8
16.2
J 5-5
14.9
14-3
13-7
I 3- I
12.5
11.9
II. 2
10.6
IO.O
9-4
22
19.7
19.0
18.4
17.8
17.2
16.6
16.0
J 5-3
14.7
14.1
13-5
12.9
12.3
ii. 6
24
22.2
21.6
20.9
20.3
19.7
19.1
18.5
17.9
17.2
16.6
16.0
15-4
14.8
14.2
26
25.0
24-4
23-7
23.1
22.5
21.9
21.3
20. 6
20.
19.4
18.8
18.2
17-5
16.9
28
28.1
27-5
26.9
26.2
25-6
25.0
24.4
23-7
23.1
22.5
21.8
21.2
20. 6
30
31-5
30-9
30-3
29.7
29.0
28.4
27.8
27.2
26.5
25-9
25-3
32
35-4
34-7
34-1
33-5
32-8
32.2
31.6
31.0
30-3
34
39-6
38-9
38.3
37-7
37-o
36-4
35-8
i
1. Solar System.
Name.
Sy.
Miles dist.
E = l.
Time rev.
Kc'O,
Incl.
Asc.node
Diam,
Mass.
S.G.
Sun
n
o /
/
852584
314760
i-4
Mercury
S
35393000
3871
87-97
.2056
7 0.4
45 57-5
2962
.065
6.8
Venus
66131000
7233
224.70
.0068
3 23-6
74 54-2
7510
7^5
5- 1
Earth
91430000
I.OOOO
365-26
.0168
O.O
oo.o
7901
I.OOO
5-5
Moon
238800
.0026
27.32
.0^48
5 8.8
13 53-3
2153
.on
3'i
Mars
$
139312000
1 5237
686.98
0933
i 51.1
480-5
4920
.124
5-i
Jupiter
Saturn
Uranus
n
h
w
475693000
872135000
1753851000
5.2028
9.5388
19.1824
4332-53
10759.22
30686.82
.0482
.Oi;6o
.0466
i 18.5
2 29.4
o 46.9
98 26.3
in 56.6
72 59.6
85390
71904
33094
300.86
90.032
12.641
1.2
-7
I ..0
Neptune
2746270000
30-0363
60126.71
.0087
I 47.0
13 05.2
36620
16.761
-9
290
19. Double Stars.
R. A.
Dec.
Constellation.
Name
Mags.
Dist.
Angle
Color.
h. m.
o 30
N 33 o
Andromeda
7T
4-5
9
36
173-9
w. bl.
I 12
N 88 37
Ursa Minor
a
2-5
9-5
18.6
210. I
ye. 1 bl.
I 17
N 67 27
Cassiopea
i/>
4-5
9
29
106
d ye. w.
I 46
N 18 40
Aries
7
4-5
5
8.8
359-8
I S 6
N 41 42
Andromeda
7
3-5
5.-S
ii
61.6
d ye. gr.
II 41
N 55 21
Perseus
n
5
8-5
28
300.4
o. bl.
III 48
S 3 20
Eridanus
3 2
5
7
6.6
346.5
d ye. d gr.
III 49
N 39 38
Perseus
e
3-5
9
8.4
9.1
w. lil. '
IV 10
S 7 5
Eridanus
o 2
5
9-5
82
107.6
o. bl.
IV 28
N 16 14
Taurus
a
i
12
108
35-9
IV 29
N 9 54
Taurus
88
5
8-5
68
300.4
B.? w. bl.
IV 34
N 22 42
Taurus
T
5
8
62
209.8
w. vi.
IV 50
N 37 42
Auriga
G)
5
9
7
352-6
w. 1 bl.
V 7
N 32 32
Auriga
14
5
7-5
13.5
224.5
V 8
S 8 21
Orion
(8
i
9
9-5
199.4
p ye. d bl.
V 16
N 3 25
Orion
2 3
5
7
3 2
27.9
w. 1 bl.
V 25
S o 24
Orion
d
7
53
359-9
w. vv.
V 28
V 29
N 9 51
S 6 o
Orion
Orion
Z
i
4
3-5
6
8-5
4-5
"5
43-o
141.7
p ye. pur.
T. w. bl. r.
V 3 o
N 30 25
Auriga
26
5
8
12.3
267.8
w. p bl.
V 32
S 2 40
Orion
a
4
8
12.5
84.2
T. w. bl. r.
V 39
S 22 29
Lepus
7
4
6-5
93
349-o
p ye. p gr.
VI 36
N 25 15
Gemini
E
3
9-5
in
94.1
w. d bl.
VII 12
N 22 13
Gemini
6
3-5
9
7.2
200
w. pur.
VII 26
N 32 10
Gemini
a
3
3-5
5
240
B. w. w.
X 49
N 25 29
Leo
54
4-5
7
6.2
102.7
X 56
N 62 27
Ursa Major
a
8
381
203.8
XII 16
N 26 34
ComaBerenices
12
5
8
66
168.2
y. r.
XII 23
S 15 47
Corvus
6
3
8.5
24
210.9
1 ye. pur.
XII 35
S o 44
Virgo
7
4
4
5
150
B. w. p gr.
XII 50
N 39 4
Canes Venatici
12
2-5
6-5
19.8
227.0
w. lil.
XIII 19
N 55 36
Ursa Major
c
3
5
14.4
147.4
w. gr.
XIV 12
N 51 58
Bootes
I
4-5
8
38
33-4
1 ye. w.
XIV 35
N 16 59
Bootes
7T
3-5
6
6
102
w. p ye.
XIV 44
s 15 30
Libra
a
3
6
229
314.3
P ye- gr.
XIV 45
N 19 39
Bootes
3-5
6-5
5
290
B.
XV 10
N 3348
Bootes
6
3-5
8-5
no
75-o
ye. lil.
XV 34
N 37 4
CoronaBorealis
5
6
6.1
301.2
w. gr.
XV 58
S 19 27
Scorpio
/?
2
5-5
13.1
24.9
p ye. lil.
XVI 4
S 19 7
Scorpio
V
4
7
40
338- 5
p ye. w.
XVI 13
S 25 17
Scorpio
ff
4
9-5
20
271.6
w. r.
XVII 3
N 54 39
Draco
u
4
4-5
3
180
B. w. w.
XVII 7
XVII 9
S 26 24
N 1432
Ophiuchus
Hercules
36
a
4-5
3-5
6-5
5-5
5
4-5
200
118.7
B. p r. p ye.
o. gr.
XVII 10
N 25 o
Hercules
6
4
8.5
19
180
XVII 14
S 12 43
Serpens
V
4-5
9
5 1
3 I -3
P gr- lil-
XVII 19
N 37 16
Hercules
P
4
5-5
3-7
308.9
w. p gr.
XVII 30
N 55 16
Draco
v i
5
5
62
311.8
w. w.
XVII 54
XVII 59
N 2 56
N 232
Ophiuchus
Ophiuchus
67
70
4
4-5
8
7
55
4
143.6
90
p ye. pur.
B. pur.
XVIII 33
N 38 40
Lyra
a
i
ii
47
152.0
w. bl.
XVIII 40
XVIII 40
N 37 28
N 39 32
Lyra
Lyra
c
et
5
l\\
44
3
149.6
18
ye. p gr.
B. ye. p r.
XVIII 40
N 39 32
Lyra
e 1
5
5-5
2 -5
'45
B. w. w.
XVIII 50
XIX 9
N 4 2
N 38 55
Serpens
Lyra
e
4-5
5
5
9
22
28
'g-jj
Od. f O
p ye. d ye.
bl. vi.
XIX 25
N 2741
Cygnus
^
3
7
34
55-6
d ye. d bl.
XIX 41
N 33 26
Cygnus
X
5
9
26
72.9
d ye. p bl.
XIX 43
N 18 49
Sagitta
I
5
9
8.6
312.3
w. bl.
19. Double Stars (continued).
291
R. A.
Dec.
Constellation.
Name
Mags.
Dist.
Angle
Color.
XX 10
N 46 21
Cygnus
o 2
4
7-S
107
174-1
T. o. bl. bl.
XX 13
N 77 19
Cepheus
K
4-5
8-S
7-5
123.8
p ye. bl.
XX 14
S 15 ii
Capriconus
P
7
205
267.2
o. bl.
XX 41
XXI i
N 15 40
N 38 5
Delphinus
Cygnus
L
4 '
5-5
1 1. 8
20
273-3
120
ye. p gr.
B. ye. d ye.
XXI 16
N 19 15
Pegasus
I
4
9
36
3^0.8
d ye. lil.
XXI 27
N 70 o
Cepheus
(3
8
251.0
w.bl.
XXI 38
XXI 38
N 9 17
N 28 10
Pegasus
Cygnus
e
/*
2-5
<,
1
138
5-4
324-3
"4-3
ye. bl.
T. w. bl. bl.
XXII o
N 64 o
Cepheus
7
6
286
XXII 24
N 57 45
Cepheus
6
4-5
7
4i
192.2
d ye. d. bl.
2O. Clusters
Nebulae.
No.
R, A,
Dec.
Constellation,
Name.
Remarks.
116
h. m.
36
N 40 30
Andromeda
M 31
1. E. large, oval.
352
I 2 7
tf 30 i
Mangulum
M 33
). large, faint cluster.
392
I 37
N 60 35
Cassiopea
VI 31
). cluster.
5 12
II 10
^ 5 6 34
'erseus
VI 33
L brilliant cluster.
584
II 34
N 42 ii
3 erseus
M 3 4
L fine.
III 40
* 23 45
Taurus
'leiades.
826
1157
IV 8
V 27
S 13 4
N 21 56
iridanus
Taurus
IV 26
M i
Z. planetary nebula.
Crab nebula.
"79
V2 9
S 5 29
Orion
M 42
G. E. brightest nebula.
I2 95
V 4 4
N 32 31
Auriga
M 37
T ine. 500 stars.
1360
VI i
N 2.4 21
jemini
M 35
L cluster stars uniform.
1424
VI 24
N 5 2
VIonoceros
VII 2
L cluster.
1454
VI 41
S 20 37
Canis Major
M 41
. fine group.
i!8
VII 31
VII 36
S 14 12
S 14 31
Argo Navis
Argo Navis
VIII 38
M 46
E. large group.
Circular clust. diam. 30'
I 57 I
VII 39
S 23 33
Argo Navis
M 93
3right cluster.
1611
VII 54
S 10 25
Argo Navis
VI 37
Fine vicinity.
1681
VIII 33
^ 20 24
Cancer
M 44
Praesepe.
1712
VIII 44
tf 12 17
Cancer
M 67
3. cluster.
2I 2
X 18
S 18 o
Hydra
IV 27
Plan. neb. like Jupiter.
2 343
XI 7
N 55 43
(Jrsa Major
M 97
Plan. neb. diam. 2'4o"
2838
XII 12
N 15 15
Virgo
M 99
Spiral nebula.
349
XII 25
N 15 8
Virgo
M 88
Dull, fine neb. vicinity.
3I3 2
XII 33
S 10 54
Virgo
I 43
Elongated.
XIII 34
N 47 S 2
Canes Venatici
M 51
C. O. spiral.
3636
XIII 36
N 29 i
Canes Venatici
M 3
C. cluster.
4173
XVI 9
S 22 40
Scorpio
M 80
Like a comet.
4230
XVI 37
N 36 42
Hercules
M 13
C. E. cl. finest of kind.
4294
XVII 13
N 43 16
Hercules
M 92
C. E. cl. like M 13.
4346
4361
4373
4397
XVII 49
XVII 56
XVII 59
XVIII ii
S 18 59
S 24 21
N 66 38
S 18 27
Ophiuchus
Sagittarius
Draco
Clypeus
M 23
M 8
IV 37
M 24
Fine vicinity.
E. bright part Galaxy.
G. plan. neb. diam. 35"
G. E. fine vicinity.
4400
XVIII ii
S 13 5
Clypeus
M 16
Fine cluster.
4401
4403
XVIII 12
XVIII 13
S 17 ii
S 16 15
Clypeus
Clypeus
M 18
M 17
Fine vicinity.
G. O. Horseshoe neb.
4410
XVIII 21
N 6 29
Serpens
viii 72
E. fine.
442^
XVIII 28
S 24 o
Sagittarius
M 22
Br. cl. stars ii mag.
4432
4447
XVIII 38
XVIII 49
XIX 54
S 932
N 32 52
N 22 22
Scutum
Lyra
Vulpecula
M 26
gg
Coarse cluster.
G. finest annular neb.
G. O. Dumb-bell neb.
4628
4670
4678
XX 57
XXI 24
XXI 27
S ii 52
N ii 3
S i 24
Aquarius
Pegasus
Aquarius
5.i
M 2
G. plan. neb. diam. 20"
C. insulated resolv. cl.
C. structure granulated.
4687
XXI 33
S 23 44
Capricornus
M 3 o
Cluster.
O.
PHYSICAL LABORATORIES.
IN the Preface to the first volume of this work is a brief description of
the method recommended for conducting a Physical Laboratory. It is
believed, however, that some suggestions regarding details, may prove of
value. If the Laboratory is to be used simply for the current instruction
of large classes it should consist of a large room with two or three of
smaller size adjacent. One of the latter should be arranged so that it may
be completely darkened for the Photometers, Expts. 67 and 69; another
should be partially dark for Expts. 65, 72, 76, 78, 88, 94, 103, 104, 111
and 113, while a third room should be provided with a porte-lumiere and a
southern window for Expts. 77, 89, 90, 91, 131 and for Lantern Projections.
In the larger room some of the experiments require a good light, which is
best attained by tables in front of a northern window which the student
faces. Expts. 71, 79, 92 and 93 should be so placed. Most of the other
experiments may be performed on tables placed in the centre of the large
room, so that students may work on both sides of them. They should be
three feet high that the students may stand, or sit on high stools. Four
feet is a convenient width, and the length will depend on the location.
The space beneath them may be made available by drawers and cupboards.
Most of the tables should be provided with gas and, for some, water is
needed, as in a chemical laboratory. A considerable amount of wall space
should be left free and covered with wood rather than plaster, as it is very
convenient for Expts. 23, 24, 26, 27, 34, 39, 41, 42, 49, 50, 55, 63, 121,
and 128. Curves, drawings and photographs may also be hung up on the
wall for examination or consultation.
The indicator board, to show what work each student is doing, may be
made of various forms. A convenient plan is to drive pins obliquely into
a drawing board in rows so that they shall be separated about three inches
horizontally, and two inches vertically. The heads of the pins are then
cut off, and cards hung on them, those in the first vertical row bearing the
names of the experiments, those in the other rows giving the names of the
students. The class should be divided into sections of from fifteen to
twenty-five students, though the smaller number is much to be preferred.
The number of experiments should be considerably greater, that there may
be no delay, and the simpler experiments should gradually be replaced by
those of greater difficulty. The following list is a good one to begin with :
Expts. 1, 2, 3, 4, 5, 7, 10, 11, 12, 13, 14, 15, 17, 18, 20, 23, 24, 25, 26, 28,
29, 30, 35, 36, 41, 42, -15, 46, 70, and 78. If the class is small, every student
(292)
PHYSICAL LABORATORIES. 293
may be required to perform the following Expts., 3 or 4, 10 or 11, 12, 14,
15, 23 or 24, 25 or 26, 28 or 29, 35, 41, 45, 46 and 78, all of which work
well in practice. When the student has acquired some skill with these
experiments, the following may be added, 19, 21, 44, 48, 67, 69, 71, 72, 76,
77, 79, 88, 91, 92, 93 and 94. Some experiments should next be given
from the second volume, as 95, 96, 97, 98, 101, 102, 103, 104, 105, 109, 110
111, 112, 114, 119, 120, 122, 126, 131, 133, 134, 138, 145 and 147. The
later experiments should be taken up by the older students according to
their respective wants, and form, in fact, several distinct courses.
The Graphical Method is used very largely in the discussion of the
results of these experiments, as it possesses great advantages in many ways.
It shows at a glance the accuracy of the work, and as modified, is exact
enough to show the errors of the most carefully conducted experiments.
The paper on which the curves are drawn may be prepared in various
ways. It should be divided into squares by two sets of parallel lines of
which every fifth should be more marked than the rest. The interval
between the lines may be one millimetre, but generally a coarser ruling, as
two millimetres or a tenth of an inch, is more convenient. The absolute
interval is unimportant, but regularity is desirable, though by the method of
residual curves the errors may be rendered so large that defects in the
ruling will be quite imperceptible. The squares may be engraved on
metal or stone, and the paper printed as in line engraving or lithography,
but since the paper must be wet in these processes, the irregular contrac-
tion will introduce errors. A number of printer's rules may also be set up
at the required intervals, and the lines printed from them on a common
printing press. By taking two impressions on the paper, turning it 90, the
squares are formed by the intersection of the two sets of lines. This
method would be cheap for a very large number of copies, but if the
squares are not to be very small the best, method seems to be to rule the
paper like writing paper. A set of pens is obtained properly spaced and
every fifth one is spread slightly, so that it shall make a broader line. The
paper is then ruled twice at right angles. The sheets should be about
16 X 21 inches, and be cut into six parts, 7X8 inches. Each student
should be provided with a note book, on the cover of which, his name should
be marked . A convenient size of page is 7 X 8 inches so that the paper
on which the curves are drawn, may be pasted into the book. Students
in taking notes may follow the rule that the observations, method of dis-
cussing them, and the results, should be entered in full, so that any one
understanding the experiment may see exactly what has been done. Each
student, after performing an experiment, should check it off in the Index, as
it is thus easy to see at a glance what others he must still perform.
The cost of establishing a Physical Laboratory need not be very great,
and a prominent object throughout this work has been to devise apparatus
which will be efficient, without being expensive. A large portion of it may
be made by any carpenter, and the expense should be mainly in the mov-
ing portions, as the micrometer screws, joints and slides. A great saving
may also be effected in the graduations, which may be made in many cases
on paper instead of on metal. When great accuracy is essential, steel
scales may be procured divided either into millimetres or fractions of an
inch. Where, however, the readings are made simply by the eye, sufficient
accuracy is often attainable with paper or cardboard scales. If these are
lithographed or engraved, an error is introduced from the shrinkage of the
paper, since it must be printed wet. A better method, therefore, is to cut
out the scale from a plate of type metal or set it up with printer's rules.
294 APPENDIX C.
Great care must be taken as regards the intervals, which may be adjusted
with sheet-metal or tinfoil and the whole justified, or continually compared
with a steel graduated scale. The scales may then be printed at trifling
expense on a common printing press on dry paper.
Graduated circles may also be printed on paper or cardboard at small
expense; but a simple and inexpensive way to graduate metallic circles is on
a lathe with the index wheel used for cutting gears. The average error in
this case is only about 2' which is of no consequence when the readings are
made by the eye to tenths of a degree only.
Small microscopes and telescopes are required in many of the experi-
ments for reading scales and for other purposes. These instruments are
made very cheaply in France, and though not suitable for the most accu-
rate work, yet for ordinary purposes are all that is required.
By adopting the method of weighing described in Experiment 19, great
accuracy is attainable at small expense. With large balances the index
may be replaced by a spirit-level attached to the beam, which will show
very small variations in the load. The knife edges may also be replaced
by pieces of steel watch spring, like the suspension of a pendulum, with the
advantage of freedom from friction. This is especially convenient where
acids are to be weighed, since their fumes would soon dull the knife edges,
while, as the springs are straight, when the beam is level, variations in
their elasticity will not affect the result.
Reference has frequently been made to a simple form of galvanometer
which combines at the same time efficiency and cheapness. A circular box
is turned out of wood, having an interior diameter of about four inches and
a depth of an inch and a half. On the bottom of this is placed a circular
piece of looking-glass and on it a cardboard graduated circle, with the
central portion removed. The top of the box is formed of a circular plate
of glass sunk in the wood so that its upper surface shall be flush with the
top of the box. The magnet consists of a piece of watch-spring about
three eighths of an inch long, straightened by bending, and magnetized
by rubbing it on a powerful magnet. A piece of fine wire nearly four
inches long, is now straightened by rolling it between two plates of glass
and is attached to the magnet by enclosing both in a small stirrup of paper.
The latter is then suspended by a single filament of silk from the centre of
the glass at such a distance that as the magnet turns it will approach but
not touch the graduated circle. To find the centre of the glass, or point
exactly over the centre of the graduated circle, lay a rule on the glass so
that when the eye is brought into the plane passing through its edge and
its reflection, the reading of both ends shall be the same. Draw a short
line near the centre of the circle on the glass with common ink. Repeat,
turning the ruler nearly at right angles. The intersection will give the
required centre. Now turn the glass over, put a drop of varnish on the
centre, dip the end of the filament of silk in it, and fasten it in place with a
small piece of paper bringing its edge just over the cross. The exactness
of the centering may be tested by Expt. 7. In this form the instrument
makes an excellent compass. The reading may be taken to tenths of a
degree by placing the eye so that the wire index shall just cover its reflec-
tion, and estimating the tenths. To convert this into a galvanometer a
piece of covered wire is wound on a flat, square block of wood, and inserted
in a square hole or mortise cut in the bottom of the box. The ends of the
wire are then connected with binding screws in the sides of the box. The
advantages of this instrument are, that, as there is no friction, minute deflec-
tions may be observed with accuracy, the error from parallax is eliminated
PHYSICAL LABORATORIES. 295
by the mirror, and the tangents of the angular readings are nearly propor-
tional to the currents on account of the short length of needle. The lower
half of the coil tends to counteract the effect of the upper portion, but its
distance being greater the effect ic slight. The principal objection to this
instrument, if great accuracy is required, is the torsion of the silk fibre
which introduces an error. To avoid tbis, the needle should never be
allowed to swing completely around, and if it deviates from the magnetic
north, the cover should be turned until the filament is untwisted.
The current expenses of the Laboratory need not be great, since the
apparatus is easily replaced and not easily injured. It was anticipated
that the loss by breakage would be considerable, but in practice it has proved
to be very trifling, in fact, almost nothing, except from causes beyond the
control of the student. The annual expenses compare very favorably with
those of a chemical laboratory, as so little material is consumed, and the
apparatus can in general be used over and over again.
Where the more advanced work of the second volume is to be done, a
number of small rooms are much more convenient than a single large lab-
oratory. One is needed as a workshop, and should be provided with car-
penter's tools, a lathe, a table with blast-lamp for glass-work, and tools for
working in metal, soldering and other similar work. Another room is
needed for experiments in Mechanical Engineering, which should be, if
possible, on the ground floor, and should contain an engine and boiler.
The measurements of terrestrial magnetism should also be made on the
ground floor, or at least on stone piers disconnected from the building, or
preferably in a small separate building. Great care should be taken that
no iron is near, especially if it is liable to be moved. The astronomical
work should be done in an observatory which may be on top of the build-
ing if the instruments rest on stone piers. It is difficult, however, to attain
steadiness at a great height. The need of a clear horizon is much less than
is commonly supposed, except in special cases. Generally if we can
observe to within 20 or 30 of the horizon to the south, and even to
within 30 or 40 in other directions, it is all that is really needed. The
effect of the heated air from chimneys, etc., however, extends much beyond
their apparent altitude. The Lantern Projections should be conducted in
a lecture room, and students may acquire practice in addressing an audi-
ence and performing experiments in their presence, by inviting their
friends to an exhibition of the various phenomena at the close of their
course.
One of the principal objections made to the introduction of the Labora-
tory method of teaching Physics, was the amount of time that would be
required for each experiment. It was said that as it takes an entire day to
measure a temperature accurately with the air thermometer, that in a whole
term the student would become familiar with but very few methods of ex-
periment. While this might be the case with a certain class of experi-
ments, it is wholly different with the work described in this book. When
the students first entered our Laboratory, the average time per experiment,
including absences, was 1.8 hours. By the introduction of Volume I, so
that they could read over the descriptions of the experiments at home, and
by the gradual improvement in the apparatus, the average time has been
materially reduced. Probably with small sections and abundant means
for keeping the apparatus in perfect condition, the time would not greatly
exceed one hour.
296
APPENDIX C.
BOOKS OF REFERENCE.
A good Library, even if not very extensive, is an exceedingly valuable
al Laboratory, provided the selection is properly
ly appended of a few books useful for freuent
ence and forming a working library, such as should be at the command of
every physicist. First are given the principal German, French, English
and American periodicals, that relate to physics; y. denotes that the num-
bers are published yearly, q. quarterly, m. monthly, w. weekly, and i. at
irregular intervals. Then follow works on general physics and its branches,
works on kindred subjects, and finally the catalogues of instrument mak-
ers, which are sufficiently complete to render them valuable for reference.
To these should be added a good Encyclopaedia, German, French and Eng-
lish dictionaries, an atlas and seven-place logarithmic tables.
Periodicals.
PoggendorfPs Annalen. m.
Fortschrifte der Physik. y.
Carl's Repetitorium. m.
Astronomische Nachrichten. w.
Bulletin of the Royal Academy of
of St Petersburg, q.
Memoirs of the Royal Academy of
Vienna, i.
Memoirs of the Swedish Roy. Acad. .
Bibliotheque Universelle. m.
Comptes Rendus. w.
Memoirs of the French Academy, i.
Annales de Chim. et de Physique, m.
Journal de Physique, m.
Annales de 1'Ecole norm, super, m.
Les Mondes. w.
London Philosophical Magazine, m.
Philosophical Transactions of the
Royal Society, i.
Nature, w.
Report of the British Association, y.
Quarterly Journal of Science, q.
Quarterly Journal of Microscopical
Science, q.
Monthly Microscopical Journal, m.
Astronomical Register, m.
Symons' Meteorological Journal, m.
Electrical News. w.
Photographic News. w.
Amer. Journ. of Arts and Sci. m.
Journal of the Franklin Instit. m.
Proc. of the Amer. Association, y.
Proc. of the American Academy, i.
Proc. of the Amer. Philos. Soc. -|y.
Smithsonian Reports, y.
Coast Survey Reports, y.
Annual Reports of the Signal Ser-
vice Department.
Popular Science Monthly, m.
The Lens. q.
The Magic Lantern, m.
The Telegrapher, m.
General Physics.
Wiillner. Lehrbuch des Exper.
Physik. 4v.
Hessler, Pisko. Lehrbuch der
Technische Physik. 2v.
Verdet. (Euvres. 8v.
Jamin. Cours de Physique. 3v.
Jamin. Petit traite de Physique.
Daguin. Traite elementaire de Phys-
ique. 4v.
Boutan, Almeida. Cours elem. de
Physique. 2v.
Pouillet. Elemens de Physique. 3v.
Deschanel. Elementary Treatise on
Nat. Philos. 4v.
Ganot. Elem. Treatise on Physics.
Muller. Lehrbuch der Physik und
Meteorologie. 3v.
Mayer. Lecture Notes on Physics.
Stewart. Lessons in Elementary
Physics.
Lardner. Handbook of Natural
Philosophy. 4v.
Silliman. Principles of Physics.
BOOKS OF REFERENCE.
297
Mechanics.
Thomson, Tait, Treatise on Nat-
ural Philosophy.
Weisbach. The" Mechanics of En-
gineering and Machinery.
Rankine. A Manual of Applied
Mechanics.
Todlumter. Analytical Statics.
Tait, Steele. Dynamics of a Particle.
Goodie. Principles of Mechanics.
Goodeve. Elements of Mechanism.
Cross. Course in Elemen. Physics.
Smith. An Elem. Treatise on Me-
chanics.
Ball. Experimental Mechanics.
D'Aubuisson. Hydraulics.
Francis. Lowell Hydraulic Exper.
Bunsen. Gasometry.
Williamson. Use of the Barometer.
Clegg. Treatise on the Manufac-
ture of Coal Gas.
Sound.
Helmholtz. Die Lehre von den
Tonempfindungen.
Tyndall. On Sound.
Airy. On Sound and Atmos. Vibrat.
Donkin. Acoustics.
Taylor. Sound and Music.
Peirce. An Elem. Treatise on Sound.
Radau. Wonders of Sound.
Hopkins and Rimbault. The Organ.
Light.
Billet. Traite d'Optique phys. 2v.
Moigno. Repertoire d'Optique mod-
erne. 4v.
Nugent. Treatise on Optics.
Parkinson. A Treatise on Optics.
Airy. Undul. Theory of Optics.
Fresnel. (Euvres completes. 3v.
Potter. An Elem. Treat, on Optics.
Potter. Physical Optics.
Brewster. A Treatise on Optics.
Brewster. New Philos. Instruments.
Tyndall. Light and Electricity.
Tyndall. Six Lectures on Light.
Lommel. Light. (Int. Sci. Ser.)
Helmholtz. Physiological Optics.
Kirchhoff. Researches on the Solar
Spectrum.
Angstrom. Spectre Normale.
Schellen. Spectrum Analysis.
Roscoe. Spectrum Analysis.
Watts. Index of Spectra^
Lockyer. The Spectroscope and its
Applications.
Grandeau. Instruction pratique sur
1'Analyse Spectrale.
Electricity.
De la Rive. A Treatise on Elec. 3v. Maxwell. Electricity and
Faraday. Experimental Researches
in Electricity. 3v.
Becquerel. Traite d'Elect. et de
Magnetisme. 3v.
Chevreul. De la loi du contraste
simultane des Couleurs.
Bezold. Die Farbenlehre.
Briieke. Die Physiol. der Farben.
Pereira. Lectures on Polar. Light.
Spottiswoode. Polariz. of Light.
Woodward. Familiar Introduction
to the study of Polarized Light.
Carpenter. The Microscope and
its Revelations. ,
Beale. How to work with the Mi-
croscope.
Griffith, Henfrey. The Micrographic
Dictionary.
Hogg. The Microscope.
Moigno. L'Art des Projections.
Monkhoven. A Popular Treatise on
Photography.
Sutton. A Dictionary of Photog.
Hunt. A Manual of Photography.
Stillman. Photography.
Vogel. The Chemistry of Light
and Photography (Int. Sci. Ser.)
Phipson. Phosphorescence.
Thomson. Papers on Statical
tricity and Magnetism.
Wiedemann. Die Lehre von Gal-
vanismus.
298
APPENDIX C.
Electricity (Continued).
Jenkin. Electricity and Magnet.
Noad. A Manual of Electricity.
Noad. Student's Text Book of Elec-
tricity.
Guthrie. Electricity and Magnetism.
Jenkin. Reports on Elect. Standards.
Du Moncel. Applications d'Elec-
tricite. 4v.
Dub. Electromagnetismus.
Blavier. Nouveau Traite de Tele'g.
Schellen. Der electrom. Telegraph.
Sabine. The Electric Telegraph.
Culley. A Handbook of Practical
Telegraphy.
Russell. History of the Elect. Teleg.
Russell. The Atlantic Telegraph.
Watts. Manual of Electro-Metal.
Napier. Electro-Metallurgy.
Rosaline. Galvanoplastic Manip.
Lamont. Der Erdstrb'm. %
Airy. A Treatise on Magnetism.
Harris. Rudimentary Magnetism.
Tyndall. Researches on Diamag.
Heat.
Regnault. Memoirs of the French
Academy. Vols. xxi, xxvi.
Him. Theorie mecanique de la
Chaleur.
Zeuner. Theorie mecanique de la
Chaleur.
Clausius. The Mechanical Theory
of Heat.
Rankine. Steam Engine and other
Prime Movers.
Briot. Theorie mecanique de la
Chaleur.
Melloni. La Thermochrose.
Tait. Thermodynamics.
Maxwell. Theory of Heat.
Stewart. An Elementary Treatise
on Heat.
Stewart. Conservation of Energy.
Tyndall. Heat as a Mode of Mo-
tion.
Tyndall. Contrib. to Molec. Sci. in
the Domain of Radiant Heat.
Tyndall. On Radiation.
Peclet. Traite de la Chaleur. 3v.
Astronomy.
Watson. Theoretical Astronomy.
Chauvenet. Manual of Spherical
and Practical Astronomy.
Loomis. An Introduction to Practi-
cal Astronomy.
Briinnow. Spherical Astronomy.
Coffin. Navigation and Nautical
Astronomy.
Bowditch. Practical Navigator.
Grant. History of Physical Astron.
Arago. Popular Astronomy.
Chambers. Descriptive Astronomy.
Herschel. Outlines of Astronomy.
Loomis. A Treatise on Astronomy.
Lockyer. Elem. Lessons in Astron.
Guillemiu. Le Ciel.
Smyth. Cycle of Celestial Objects.
Webb. Celestial Objects for Com-
mon Telescopes.
Secchi. Le Soleil.
Lockyer. Contrib. to Solar Physics.
Beer, M'adler. Der Mond.
Beer, M'adler. Mappa Selenograph.
Nasmyth, Carpenter. The Moon.
Proctor. Saturn and his System.
Heis. Atlas ccelestis novus.
Tables.
Hutton. Mathematical Tables.
Barlow. Tables of Squares, Cubes.
Crelle. Rechentafeln.
Clarke. Constants of Nature.
Rankine. Rules and Tables.
Guyot. Tables, Meteor, and Phys.
Sharpies. Chemical Tables.
Sabine, Clark. Electrical Tables.
Hirsch. Definite Integrals.
Alexander. Universal Dictionary of
Weights and Measures.
ADDITIONAL EXPERIMENTS. 299
Catalogues.
Salleron. Paris. Negretti and Zambra. London.
Deleuil. Paris. Elliott Brothers. Electrical. Lond.
Alvergniat. Paris. Casella. Meteorological. London.
Hoffman. Optical. Paris. Griffith. Chemical. London.
Kcenig. Acoustic. Paris. Queen. Philadelphia, New York.
Beck. Optical and General. Lond.
Miscellaneous.
Royal Society. Catal. of Sci. Papers. Eliot, Storer. Manual of Chemistry.
Poggendorff. Handwb'rterbuch Biog. Helmholtz. Popular Lectures.
Karmarsch. Technolog. Dictionary. Youmans. Conservation and Cor-
Whewell. Hist, of Induct. Sci. 2v. rellation of Forces.
Kohlrausch. Phys. Measurements. Barnard. Report on the Indus-
Frick. Physical Technics. trial Arts, Paris Expos., 1867.
Nicol. Cyclopaedia of Sciences. Barnard. The Metric System.
Davies, Peck. Mathemat. Diction. Brook. French Measures and Eng-
Wurtz. Dictionaire de Chemie. lish Equivalents.
Watts. Dictionary of Chemistry. Gillespie. Land Surveying.
Taylor. Scientific Memoirs. Buchan. Handy Book of Meteorol.
Miller. Elements of Chemistry. Dove. Law of Storms.
Cooke. Chemical Physics. Herschel. Meteorology.
Cooke. The New Chemistry (Int. Loomis. A Treatise on Meteorology.
Sci. Ser.)
ADDITIONAL EXPERIMENTS.
One of the greatest advantages of a Physical Laboratory would, how-
ever, be lost if the work should be confined to what has been already
described. ' The highest aim of every physicist should be to direct, not
only his own utmost efforts, but those of his students, toward original inves-
tigations or the determination of new facts and laws. Without this, he is
liable to become a mere machine, disseminating knowledge, but never
advancing it. The whole aim of this book has been in this direction, and
without it, we may educate followers, but never leaders in science. Origi-
nality is not, however, easily acquired, and seems to come to many persons
as a natural gift. Nothing appears to be more difficult to many students
than to attempt something new. Much, however, may be acquired by
practice ; the student should first be required to carry out some simple
details, then to devise and plan an instrument of a given construction, and
next to devise apparatus for producing some required effect. Much aid
may often thus be obtained from students in planning and carrying out a
Laboratory, or in increasing the number of experiments. Some problems
should now be proposed to ihe student which he should be required to
solve experimentally; and generally by this time his tastes will lead him
towards some branch of the subject, or some difficulty will present itself
which he should attempt to solve himself. He will now have attained the
position of a true student of science, one who aims to study the unknown,
as well as the known. Such work is, however, by no means easy for the
instructor, especially when he has a large number of students to direct. It
is believed that the following list of one hundred additional experiments
will materially aid him in this matter. They cover a broad range of sub-
300 APPENDIX C.
jects and serve as suggestions of problems for the student. Some of them
are extremely simple, and serve as examples for the student to describe
clearly and concisely how they should be performed. They may also be
used where large classes are to be taught and a larger number of very
elementary experiments are required. Others again are taken from pub-
lished memoirs, and include various suggestive methods, as yet by no
means exhausted. A thoughtful student will often, from an examination
of these, see some new application or extension which may lead to most
valuable results. These may be increased almost indefinitely, in fact, the
current numbers of the scientific periodicals, especially PoffgendorflPf
Annalen and the Complex Rendus are full of them. Others again are new,
and contain suggestions of valuable work which might be done by any one
who will devote sufficient time and labor to them. The tables of Appen-
dix B, especially Nos. 10, 11, 12, and 13, suggest many constants which
need to be more accurately determined and point out many gaps which
need to be filled. Enough has been said to show how vast the field is, and
that the following list might have been almost indefinitely extended.
201. Measure any distance in metres and in inches, and reducing both
to the same unit, determine the error of the scales. Place English and
French scales edge to edge, and noting where the divisions coincide, as in
the vernier, determine the ratio of the metre to the inch.
202. Weigh a pound Troy in grammes and determine the error, meas-
ure- also the weight of a kilogramme ingrains. Weigh any convenient
object with French and with English weights, and, reducing the latter to
grammes, determine the error.
203. Cut out a circle of cardboard and determine its area by the formula
~r 2 , by drawing parallel lines and applying the formula A = \a (b 1 -J- 26,
-f 26 3 + &c. ... &) and A la (^ + 46 2 + 26 8 -f 46 4 + 26 5 + &c.,
. . . . b n ). Determine also the area by weighing the cardboard, and by
drawing the circle on rectangular paper and counting the squares as in Vol.
I, p. 22.
204. Form a triangle by making three pin holes in a sheet of card-
board. Measure the three angles by a table of chords, and by a protractor,
and see if the sum equals 180. Compute the angles also trigonometric-
ally, after measuring the three sides.
205. Measure the thickness of some sheet-metal, the diameter of wires,
and the exterior and interior diameters of tubes with gauges and calipers.
Determine from this the numbers of the Birmingham and American wire
gauges in inches or millimetres.
206. Measure the thickness of thin plates with Cornu's reflecting spher-
ometer and compare the results with those obtained by a sheet-metal gauge
(Journ. de Phys., iv. 7).
207. Form a simple pendulum by suspending a heavy ball from the end
of a string. Measure the time of a hundred vibrations, giving the string
various lengths. Find the relation of the time to the length, by construct-
ing a line with coordinates equal to the logarithms of these quantities.
Finally, deduce the value of g from each observation.
208. Measure the force of gravity by Kater's pendulum, determining the
time of vibration, as in Experiment 41, and the distance between the knife-
edges by Experiment 20.
ADDITIONAL EXPERIMENTS. 3Q1
209. Measure on the floor of the laboratory a distance of twenty metres
with the greatest possible accuracy, by the method of measuring base-lines,
Vol. I, p. 21, or by Experiment 20. Mark each five metre point by a nail
with a fine cross scratched upon it. Determine the variation of length of a
steel or linen tape-measure when subjected to various strains. Measure
also the sag when it is hung freely at both ends under various tensions and
compare the observed length of the catenary with that given by theory.
210. Measure the strength of different kinds and sizes of thread and of
. various kinds of knots, by the following apparatus. Suspend a cannon ball
by a fine wire and attach the thread to be tested to its centre. Draw the
ball from the vertical by the thread, until the latter breaks. Its strength
will then be nearly proportional to the distance through which the ball has
been moved. This distance may be accurately measured by allowing a
bent wire to trail from the ball, dragging a second wire while the ball moves,
but detaching itself when the ball swings back on the breaking of the
thread.
211. Find the position of the neutral axis of a bar bent transversely, by
measuring the distance between two pairs of points near the upper and
lower surfaces before and after the load is applied.
212. Determine the laws of torsion by suspending a magnet by a fine
wire. Determine the angular deviation of the upper end by a graduated
circle, and of the lower end by a mirror and graduated circle below the
magnet. Measure the magnetic moment of the magnet, and determine its
deviation as the upper end of the wire is turned. Repeat with wires of
other lengths, diameters and materials. The torsion of a spider's thread, or
filament of silk may be similarly measured. The compass described on p.
266 is well adapted to this experiment. . Turn the magnet 360 by a large
magnet, and notice the change of reading. Repeat until it is twisted
nearly at right angles to the meridian. It will now slowly return owing to
the permanent set of the fibre.
213. Hang two ivory balls, side by side, in front of a graduated scale.
Draw one aside a known distance, and letting it fall back observe the
motion of each ball after impact. Compare the.results with theory, using
balls first of the same, and then of different, sizes. Deduce thus the coeffi-
cient of elasticity.
214. Measure the velocity of the bullet from a revolver, parlor rifle,
cross-bow or catapult with a ballistic pendulum. If the catapult is used
attach it to the table, and determine the effect of drawing the spring by
known amounts, and also by varying the weight of the ball.
215. Test the laws of impact in the case of a pile driver. The pile may
be a stick an inch in diameter and be driven by a weight of 10 Ibs., falling
from various heights. Measure the height of fall, and descent of the pile
after each blow and compare with the weight required to depress the pile
by a dead pressure. The pile may be driven into clay, or the resistance
may be produced by clamping it between two boards.
216. Cut a hole in the bottom or side of a box, and close it by a board
fitting loosely. Fill the box with sand and measure the magnitude and
point of application of the force required to prevent the sand from forcing
the board outwards.
217. Make four pin holes in a sheet of drawing paper forming a square,
and measure the distances of each from the others very exactly, btretcn
302 APPENDIX C.
the paper on a drawing-board and measure again. Repeat after cutting
the paper off the board, and then measure the variations, both parallel and
at right angles to the fibre with various conditions of temperature and
moisture.
218. Repeat the experiments of Clarke on the pressure of sap in plants
(Amer. Journ. Sci., cvii, 522).
219. Allow a stream of water to impinge upon a vertical disk attached
to one end of a suspended beam, and measure the pressure exerted by the
weight which must be added to the other end to keep the beam horizon-
tal. Repeat, directing the stream at various angles and varying the pres-
sure or velocity, the diameter of the stream, the size of the disk, and mak-
ing it concave or convex.
220. Measure the flow of liquids through capillary tubes by the method
of Poiseuille (Ann. Chim. Phys., Ill, xxi, 76).
221. Determine the laws of osmotic action of liquids by the method of
Graham (Phil. Trans., 1854 and 1861).
222. Determine the amount of air carried down by adhesion to rain-
drops.
223. Measure the resistance of the air by making a disk of cardboard
revolve at the end of a horizontal bar, and measure the force required on
varying the size and form of the disk and its velocity.
224. Determine the flow of gases through small apertures by measuring
the variation of pressure of a receiver from which the air has been ex-
hausted, and into which it is allowed to return through a pin hole in a
platinum plate.
225. Determine the flow of gases by Bunsen's method of determining
the density of gases.
226. Determine the transpiration of gases by the method of Graham
(Phil. Trans., 1846 and 1849).
227. Determine the viscosity of gases by the method of Meyer (Pogg.
Ann., cxxv, 177), and Maxwell (Phil. Trans., 1866, 249).
228. Study the laws of the passage of gases through porous plates.
Suitable plates of any desired thickness may be made by moulding plaster
of Paris between two plates of glass. Close a glass tube by such a plate,
and immersing the open end in water measure the changes in level under
different pressures. Repeat, filling the tube with other gases instead of air,
and also replacing the plaster with rubber or bladder.
229. Measure the length of a rectangular organ pipe and add twice its
depth. See how the result agrees with the wave-length computed from the
velocity of sound and the pitch. Repeat with other pipes and with cylin-
drical pipes, adding to their length five-thirds of their diameter.
230. Measure on the monochord the length of string corresponding to
the various notes of the scale, and compare with the computed pitch.
231. Repeat Melde's Experiment as modified by Lowery (Amer. Journ.
Sci., cvii, 493). See Experiment 63.
232. Determine the number of vibrations of a tuning fork from its di-
mensions, by the formulas of Mercadier. (Comptes Rendus, Ixxix, 1001,
1069). Determine also the law connecting the position and magnitude of a
weight on the prongs with the number of vibrations as given by Lissajous'
method.
ADDITIONAL EXPERIMENTS. 303
233. Measure electrically the number of vibrations of each string of the
middle octave of a well-tuned piano by the method of Cooley(/ourn.
Frank. Inst., Ixxxvii, 44; Ixxxviii, 341).
234. Determine by Lissajous* curves the number of vibrations of each
reed of a well-tuned cabinet organ. A comparateur should be used, kept
vibrating electrically, whose pitch may be slightly altered, without stopping
it, by moving a weight.
235. Determine the relation between the velocity of translation of a
moving sound and its change in pitch, as proposed by Mayer (Amer. Journ.
Set., ciii, 267).
236. Determine the phase of vibration of the air surrounding a sound-
ing body, as proposed by Mayer (Amer. Journ. ScL, civ, 387, 504).
237. Measure the wave-lengths of sounds in air, and test the applications
of the method, as proposed by Mayer (Amer. Journ. Sci., civ, 425).
238. Measure the relative intensities of sounds, as proposed by Mayer
(Amer. Journ. Sci., cv, 44, 123).
239. Compare the methods of sonorous analysis proposed by Mayer
(Amer. Journ. Sci., viii, 170).
240. Measure the relative brightness of two lights by the Rumford
photometer. ,
241. Devise a form of photometer for measuring the amount of light
reflected at various angles by polished surfaces, in which a single light
only shall be used, as in Expt. 6 7.
242. Determine the law of concave mirrors (see Expt. 78), and measure
the size of the images as well as -their position.
243. Determine the law of the enlargement of the images and positions
of the conjugate foci of a combination of two lenses not in contact. (See
Expt. 78.)
244. Measure the change in focus of a lens placed obliquely both for
horizontal and vertical beams (Proc. Amer. Acad., x, 300), and apply the
same method to the case of mirrors.
245. Determine the distortion produced by the lens of a photographic
camera by taking a picture of a scale of equal parts, and measuring by Expt.
21 the position of the divisions. The distortion may then be shown by a
residual curve. Instead of a scale the equidistant vertical posts of a dis-
tant iron fence may be used, taking care to turn the plate exactly parallel
to the fence.
246. Arrange a spectroscope so that the relative brightness of different
portions of two spectra may be compared by the method of Vierordt,
(Amer. Journ. Sci., cii, 139), or by that of Trannin (Comptes Rendus,
Ixxvii, 1495). Determine the relative distribution of the light of the sky,
of a white cloud, of a platinum wire heated to incandesence, of various
flames, of various absorption spectra, and of the different lines of an incan-
descent metal or gas.
247. Measure the relative actinic effects of different parts of various
spectra (See Expt. 246) by the method of Bunsen and Roscoe (Phil.
Trans. 1863, 139).
248. Form Newton's rings between a lens and plane surface with mono-
chromatic light, and measure the diameter of the rings accurately by the
304 APPENDIX C.
Dividing Engine, Expt. 21. From this deduce the curvature of the surface
and its distance from the lens under various pressures.
249. Measure the dispersion of thin plates of various materials by form-
ing Talbot's bands with them in a spectroscope. The number of bands
between any two solar lines of known wave-length serves to determine
the difference in index of refraction. By turning the plate a known angle
a second equation of condition may be formed. By polarizing the. light
the ordinary and extraordinary indices of doubly refracting media may be
measured. The same method may be applied to liquids by using thin
tanks partly filled with the substance to be examined.
250. Repeat the experiments with the interferential refractor, and apply
this instrument to testing Mariotte's law and measuring the ratio of the two
specific heats of gases.
251. Set a strip of thick glass on edge, support it at the ends and load
it in the middle. Determine the strain of the different portions by their
effect on polarized light.
252. Repeat Maxwell's experiments on the three primitive colors and
their combinations (Roy. Edin. Trans., xxi, 275; Phil. Trans., 1860, 57).
253. Measure the variations in resistance of crvstallized selenium when
exposed to light (Phil. Mag., xlvii, 216, xlviii, "l61, 1; 416). Test the
results by the law that the intensity of light is inversely as the square of
the distance, and apply this method of measurement to the spectra of
Expt. 246.
254. Measure the resistance of liquids by the electrodynamometer as
used by Kohlrausch and Nippoldt (Pogg. Ann., cxxxviii, 280, 370). The
polarization is eliminated since the current? are rapidly reversed.
255. Determine the forms of equipotential curves and surfaces by the
method of Adams (Proc. Roy. Soc., xxiv, 64; Phil. Mag., 1, 548).
256. Prove the laws of the attraction of currents and of solenoids by
the horizontal pendulum.
257. When a circuit is closed through a very long wire, the current
does not instantly arrive in its full intensity at the further end. Determine
the form of the arrival wave. Study in the same way the form of induced
currents.
258. Determine the magnitude of the ohm by the method of Weber
. Ann., Ixxxii, 337; Rep. Brit. Assoc., 1863, 163 and 1864, 345; Jen-
Elect. Stand., 96).
259. Determine the ratio of the electrostatic, to the electrodynamic
unit (Rep. Brit. Assoc., 1869, 434; Jenkin's Elect. Stand., 186).
260. Repeat the experiments of Lippman on the effects of electricity on
capillarity (Pogg. Ann., cxlix, 546).
261. Study the laws of electro-torsion by the method of Gore (Proc.
Roy. Soc., xxii, 57; Amer. Journ. Sci., cvii, 418.)
262. Determine the specific inductive capacity of various di-electrics,
by the method of Gibson and Barclay (Phil. Trans., 1871, 573).
263. Study the laws of the electricity generated by belts. (See Joulin,
Ann. Chim. Phys., Ill, ii, 5.)
264. Repeat the experiments of Angot on the distribution of statical
electricity.
ADDITIONAL EXPERIMENTS. 305
265. Measure the electromotive force required to produce sparks of
various lengths (Proc. Roy. Soc., x, 326; Reprint of Papers on Elect.,
Thomson, 247).
266. Measure the change in length and in volume of an iron bar when
magnetized (Phil. Mag., xxx, 76, 225, xlv, 350).
267. Measure the comparative efficiency of different cores for electro-
magnets by the method of Mayer (Amer. Journ. Sci., 1, 195).
268. Measure the distribution of magnetism in soft iron by the method
of Jamin (Comptes Renclus Ixxviii, 95 et seq.).
269. Measure the distribution of magnetism in soft iron by the method
of Rowland (Amer. Journ. Sci., ex, 334).
270. Repeat the experiments of Bouty on the magnetic moments of
minute magnets (Phil. Mag., xlix, 81, 186).
271. Measure the strength of the various parts of the field of an electro-
magnet by the magnetic proof plane of Rowland (Amer. Journ. Sci., ex, 14).
272. Determine the coefficient of magnetism of various substances as
proposed by Rowland (Amer. Journ. Set., cix, 358).
273. Determine the absolute conductibility of metals for heat by the
method of Peclet (Ann. Chim. Phijs., Ill, ii, 107).
274. Measure the temperature of maximum density of water by the
method of Joule (Phil. Mag., xxx, 41).
275. Measure the velocity of evaporation of volatile liquids by the
method of Stefan (Phil. May. xlvi, 483>
276. Repeat Expt. 246, using a thermopile instead of the photometer,
and compare the relative amounts of heat of the various spectra with their
relative amounts of light (Expt. 131).
277. Repeat Crooke's experiments with the radiometer (Quart. Journ.
Sci., xlii, 274, xlvii, 348; Phil. Mag., xlviii, 65, 81, 1, 177, 245) and apply
this instrument to the accurate measure of radiant energy in Expt. 246.
278. Measure the specific heat of various substances 'by the mercury
calorimeter of Favre and Silbermann (Ann. Chim. Phys., Ill, xxxvi, 33).
279. Measure the specific heat of various substances by Bunsen's ice
calorimeter (Pogg. Ann., cxl, 1).
280. Measure the flow of coal gas through apertures of various forms
and sizes and under different pressures, first when burning, and then when
extinguished.
281. Determine the mechanical equivalent of heat by the methods of
Joule and Hirn.
282. Determine the dynamical equivalent of heat from the thermal
effects of electric currents by the method of Joule (Brit. Assoc. Rep., 1867,
512; Jenkin's Elect. Standards, p. 175).
283. Measure the thermal equivalent of magnetism from the heating of
the core of an electro magnet by the method of Cazin (Ann. Chim. Phys.,
Ill, vi, 493).
284. Determine the relative efficiency or ratio of energy consumed to
energy generated in a waterwheel, turbine or water-pressure engine.
Measure the height of fall or pressure, the water employed, by Expt. 48,
the number of turns per minute by Expt. 158, and the power generated, by
Expts. 153, 154 and 155.
306 APPENDIX C.
285. Determine the relative efficiency of a steam, gas or hot-air engine
by Expts. 148, 153, 154, 155 and 158.
286. Determine the relative efficiency of an electro-magnetic engine,
measuring the resistance by Expt. 102 and the current employed by Expt.
98. If the circuit is closed during a portion only of the revolution, a suit-
able allowance must be made. We can, by varying the number of cells of
the battery, determine how many would be required to produce any given
effect. Finally measure the power by Expts. 154, 155 and 158. Measure
also by a spring balance the dead pull on the fly wheel in different portions
of its revolution and by integration deduce the total value. See how this
compares with that previously determined.
287. Determine the efficiency of a thermal battery, measuring the con-
sumption of g^s by a meter, and the quantity of electricity by Expt. 98.
The experiment may be divided into three parts, while heating, after the
temperature has become constant, and while cooling after the gas is extin-
guished. See how far the result will vary with changes in the rate of con-
sumption of gas and in the outside resistance.
288. Determine the efficiency of a Plante battery (Les Mondes, 1873,)
measuring the current which passes into it from the charging battery
(Expt. 98), and again that which returns. Measure also the variations in
electromotive force and resistance (Expt. 105).
289. Determine the efficiency of a magneto-electric machine. (Proc.
Amer. Acad., x, 432).
290. Determine the efficiency of a Holtz machine (Ann. Chim. Phys.,
Ill, ii, 5). Measure by a transmission dynanometer, Expt. 155, the power
required to drive the machine, the speed by Expt. 158, and the current by
Expt. 98, using the secondary coil of an induction coil with a mirror
and magnet hung inside, as a galvanometer.
291. Measure the height of clouds and the velocity of the winds mov-
ing them, compared with that on the earth's surface as described in the
Proc. Amer. Acad., xi.
292. Measure the density of fog, or the amount of light absorbed by
layers of various thicknesses.
293. Suspend a Foucault's pendulum and measure the angular deviation
per minute. See how much it differs from its theoretical value of 15' sin L,
in which L is the latitude.
294. Determine the density of the earth by the method of Cavendish.
295. Repeat the experiments of Zollner with the horizontal pendulum
(Pogy. Ann., xl, 134, 140).
296. Determine the limit of resolvability of close double stars by the
following apparatus. A miniature telescope is formed with a microscope
objective and a position and spider-line micrometer. By the side of this
are placed two artificial stars formed of needle holes in sheet metal strongly
illuminated by a light behind, and whose position and distance may be
varied at will and measured by a micrometer screw and graduated circle.
A vertical mirror of plane glass is placed opposite so as to reflect the image
of the stars into the telescope. Determine the probable error of the posi-
tion angle and distance of the stars when variously set.
297. Measure the light of the sky at different distances from the sun.
This may be done by the photometer of Expt. 68, or better, by illuminat-
ing the two halves of the field of view of an eyepiece by allowing the light
ADDITIONAL EXPERIMENTS. 307
of the sun, reduced by a lens, to fall on one, and then reflecting into the
other half, the light of the sky. The position of the lens may then be
varied until equality is obtained.
298. Compare the light of the sun with that of a candle by the photo-
meter of Expt. 68. The light of the sun is easily reduced sufficiently by
passing it through a short focus lens.
299. Measure the brightness of different portions of the sun's disk,
as described in the Proc. Amer. Acad., x, 428.
300. Determine the relative brightness of various portions of the larger
nebulae by attaching a Rood's photometer (.4 mer. Journ. ScL, xlix,) to
the eyepiece of a telescope and allowing the light to pass through a small
hole in a diaphragm filling the field of view. A large telescope is needed
for this experiment, or if this is not available, a large cosmorama lens of
long focus may be used for an objective. Similar observations may also be
made to excellent advantage on any bright comet.
INDEX.
ABERRATION, 1, 178.
Absorption, dynamometer, II, 126; pho-
tometer, 1, 132 ; of heat, H, 86; spectra,
projection of, II, 252.
Achromatic condenser, 1, 160.
Acoustics, I, 122.
Acoustic curves, 1, 125.
Actinometer, II, 153.
Adams, equipotential curves, II, 304.
Adapter for microscope objectives, 1, 156.
Additional Experiments, II, 299.
Aethrioscope, II, 153.
, , .
Air, electricity of the, II, 164; metre, 1, 120;
pressure of the, II, 145; pump, I, 103;
temperature of the, II, 139; thermome-
ter, II, 101.
Albumenized paper, 1, 188.
Alphabet, Morse, II, 17.
Altitude, and azimuth instrument, II, 192 ;
by sextant, II, 169; by transit circle, II,
188.
Amalgamating zinc, II, 2.
Amber varnish, 1, 127.
Ambrotypes, I, 187.
American method of determining longi-
tude, 1, 18; 11,197.
Amici'sprism,!, 159.
Ammonia, used for making ice when lique-
fied, II, 99.
Ampere's law, II, 10; theory, II, 64, 255.
Analytical method, I, 3.
Analyzer, I, 160, 208, II, 243.
Anemometer, II, 147.
Aneroid barometer, 1, 116, II, 146.
Angles, measurement of, I, 23, II, 300 ; of
crystals, I, 139; of friction, I, 71; of
prisms, 1, 141.
Angot, distribution of electricity, II. 301.
Angstrom's map of solar spectrum, 1, 154.
Angular aperture of microscope objectives,
if 159, 173.
Aniline colors for showing convection, II,
237.
Animalculae-cage, 1, 169.
Animals shown by lantern, II, 238.
Annual variations of magnetic needle, II,
155.
Aperture of microscope objectives, 1, 159,
173.
Approximations, successive, 1, 10.
Aqueous vapor, lines in spectrum of, I.
153; pressure of, II, 289.
Arago's polariscope, I, 217.
Archimedes, principle of, I, 89.
Areas, measurement of, I, 22, II, 300.
Arrival wave, II, 304.
Artificial horizon, II, 168.
Ascending node, longitude of, II, 289.
Aspirator, II, 151.
Astatic, rendering galvanometer, H, 31
Asteroids, II, 204.
Astigmatism, 1, 191.
Astronomy, II, 166 ; books on, II, 298.
Astronomical triangle, II, 171.
Athermancy, II, 86.
Atlantic Cable, II, 255.
Atmospheric pressure, II, 145.
Atomic weights, II, 287, 288.
Aurora borealis, telegraphs disturbed by,
II, 16.
Automatic break-piece, II, 12.
Axis, neutral, II, 301.
Azimuth, II, 171, 177, 192.
B. A units, II, 255.
Babinet's goniometer, I, 141; wedges, I,
217; II, 241.
Bag for holding gas, II, 219.
Balance, chemical, I, 19, 47, II, 294; hydros-
tatic, I, 93; magnetometer. II, 163; re-
semblance to Wheatstone's bridge, II, 35.
Ballistic pendulum, II, 301.
Barometer, I, 114, II, 145; filling, I, 115
heights measured by, 1, 116.
Base, apparatus. I, 21 ; line, II, 301.
Batteries, II, 1, 9, 258; resistance pf, II, 40,
41,43; Clarke's, II, 48.
Battery room, II, 216.
BaunuS's hydrometer, II, 288.
Bead of borax, I, 155.
Beams, deflection of, I, 77, 79, II, 134.
Bearings, II, 171.
Beck's hydrometer, II, 288 ; microscope, I,
156. '
Belladonna, used in enlarging retina, 1, 197.
Bells, electric, II, 12.
Belts, friction of, 11,12; electricity of , II,
Bible, written microscopically, I, 21.
Bifilar magnetometer, II, 162.
Binding screws, II, 6.
Binocular microscope, 1, 156, 161.
Biprism, 1, 199.
Biquartz, I, 217; projection of, II, 241.
Blood, circulation of in frog, 1, 169; corpus-
cles, 1, 169; spectrum of, 1, 166.
Boilers, 11,112,117.
Boiling point of gases, II, 288 ; of liquids,
II 288; of thermometers, II, 74.
Bond's spring governor, 1, 19.
(309)
310
INDEX.
Books of reierence, II, 296.
Borax bead, 1, 155.
Borda's pendulum, I, 85.
Bougeur s anemometer, II, 148.
Bouty's measurement of magnetic mo-
ments, II, 305.
Bow of violin, tuning forks sounded by, I,
122, 124.
Brake, friction, II, 126.
Break-piece automatic, II, 12.
Bridge, Wheatstpne's, II, 29, 36, 43, 261.
British Association, bridge, II, 36,43; re-
port on electrical units, II, 255.
Brown and Sharpe's sheet-metal gauge, I,
73.
Browning's regulator for electric light, II,
217.
Bude light, II, 219.
Bundle of glass plates as polarizer, I, 208 ;
II, 243.
Bunsen's, disk, I, 132; ice calorimeter, II,
305; method of measuring density of
gases, II, 302; photometer, 1, 135; pump,
1, 118.
Burners, for calcium light, II, 222; effi-
ciency of gas, 1, 135, II, 104.
Bushings, II, 110.
CABLES, telegraph, testing, II, 52.
Cage, animalculae, 1, 109.
Calcium light, II, 218.
Calibration, by mercury, I, 37; by water, I,
39 ; of thermometers, II, 74.
Callaud battery, II, 3.
Calorimeter, II, 94; Bunsen's ice. II, 305.
Camera, eye a, I, 191; lucida for micro-
scopes, I, 164; photographic, 1, 182.
Camphor, motion of, projected, II, 41.
Cams, laws of, I, 70.
Caudle-balance, 1, 136.
Cap, II, 110.
Capacity, electrical, II, 261 ; of condensers,
measured, II, 37; of telegraph tables, II,
53.
Capillarity, 1, 100, II, 288; correction for, in
barometer, I, 117; relation to electricity,
II, 304 ; shown by lantern, II, 237.
Capillary tubes, flow of liquids through, II,
Carbons, for batteries, II, 2 ; projection of,
11,233.
Cam ice machine, II, 99.
4 Cartier's hydrometer, II, 288.
Casella's air-meter, I, 120.
Cascade, charging Leyden jars in, II, 61.
Cassia, oil of, for depositing silver, 1, 178.
Catalogues of instrument makers, II, 299.
Catenary, I, 67, II, 301.
Cathetometer, I, 22, 39.
Cauchy, formula of, for dispersion, 1, 153.
Cautery, platinum wire for, II, 10.
Cazin, thermal equivalent of magnetism,
II, 305.
Cement, strength of, II, 134.
Centering of telescope lenses, 1, 178.
Centre of gravity, I, 66.
Centrifugal shaft-speeder, II, 130.
C. G. S. units, centimetre, gramme and sec-
ond units, II 257.
Change of color by heat, II, 234; of vol-
ume by fusion, II, 82.
Chemical, decomposition shown by lantern,
II, 237, 241 ; spectroscope, I, 148.
Chemistry, books on, II, 299.
Chinese fireworks, II, 235.
Chladni'9 experiment, 1, 130.
Chromatic aberration, 1, 178.
Chromatrope, II, 234.
Chromic acid battery, II, 2.
Chromograph, 1, 17.
Chronometers, comparison of, II, 196; find-
ing longitude by, II, 196; rating, I, 44.
Ciliary motion, I, 169.
Circum-meridian altitudes, II, 172.
Clarke, experiment of, on pressure of sap,
Clark's battery, II, 48.
Cle'ment and Desormes' experiment, II, 106.
Clouds, height of, II, 306.
Clusters of stars, II, 207, 291.
Coatings of Leyden jar, function of, II, 59.
Cobalt chloride, change of color by heat,
II. 234.
Cock. II, 112.
Coefficient of efflux, I, 95, 99 ; of friction, I,
Cohesion figures, II, 242.
Coils, induction, II, 19 ; resistance, II, 21,
99.
Coincidences, method of, I, 86.
Cold, artificial production of, II, 99, 100.
Collirnation adjustment, II, 180.
Collimator, 1, 141.
Collodion, 1, 126, 183: curves on, projected,
II, 232.
Color, changes in, by heat, II, 234; of fixed
stars, II, 207.
Colored stars. II, 207.
Colors, combination of, II, 235, 304.
Columns, strength of, II, 134.
Combination of colors, II, 235, 304.
Combustion, heat of, II, 103.
Comets, II, 206.
Commutators, II, 8.
Compass, mariner's, II, 64; projected on
screen, II, 41.
Composition of forces, I, 62.
Compressibility of liquids, II, 288.
Compression, modulus of, II, 133.
Condensation of steam in pipes, II, 120.
Condenser, Wenham's parabolic, I, 160;
achromatic, 1, 160.
Condensers, II, 227, 261; capacity of, II,
37,39; lantern, II, 227.
Conductibility of metals, II, 287, 305.
Conduction of heat by crvstals, II, 83 ; by
fabrics, II, 84; of solids, II, 82.
Conductors, II, 253; distribution of elec-
tricity on, II, 36, 304.
Connections, electric, II, 6.
Constant, level, I, 99 ; of galvanometer, II,
22.
Constants, table of, II, 286.
Contact, level, I, 21 ; thermometer, II, 84.
Contours, 1, 14, 34.
Convection, II, 236.
Cooley's experiment on temperature, IL
302.
Cooling, law of, II, 88.
Copper, deposition of, II, 14, 23, 259.
Cornea, I, 198.
Corner pieces, tin, I, 82.
Cornu's reflecting spherometer, II, 300.
Corpuscles, blood, I, 169.
Correction of lenses, I, 178.
Cosine galvanometer, II, 25, 260.
Cosines, table of logarithmic, II, 282; of
natural, II, 278.
Cotangents, table of natural, II, 280; of
logarithmic, II, 284.
Coulomb's torsion electrometer, II, 56.
Couples, I, 65.
311
Couplings, II, 109.
Covered wire, II, 6.
Covering steam pipes, II, 119, 121.
Cramer and Helmholtz. experiment of, I,
191.
Crank-motion, I, 68.
Cresson's condensers, II, 218.
Criterion for rejecting doubtful observa-
tions, I, 6.
Crookes' radiometer, II, 306.
Crova's wave apparatus, II, 242.
Cross, II, 111; hairs, forms of, I, 23; illu-
minated, II, 178 ; insertion of, I, 29.
Crushing, laws of, II, 133.
Crystals, angles of, I, 139; formation of,
under microscope, I, 169; formation of,
projected, II, 235; formation of, electri-
cally, II, 14; projection with polarized
light, II, 244.
Cube root,-, table of, II, 274.
Cubes, table of, II, 270.
Cup, screw, II, 6; mercury, II, 7.
Current, electric, II, 260; measurement of,
II, 21, 25.
Curvature, measurement of, I, 23, 42, 175,
II, 303.
Curves of error. I, 14.
Cy.-loid. for gasholder, 1, 109.
Cylinders, for holding gas, U, 217; steam,
II, 219.
DALTON'S law of mixture of gases and
vapors. II, 93.
Darnell's battery, II, 3; hygrometer, II, 151.
Dashpot, II, 126.
Daylight photometer, I, 134.
Decanting gases, I, 50.
Declination, II, 154.
Decompositions, electric, II, 13; as a meas-
ure, II, 23 ; as a test of boilers, II, 114.
Defects of engine tested by indicator, II,
123 ; of eye, 1, 191, 196 ; of telescopes, 1, 178.
Deflection of beams, I, 77, J9, II, 134.
Density of gases, U, 92, 288. See Specific
Gravity.
Deposition of copper, II, 14, 23, 259.
Developing photographs, 1, 184.
Dew, II, 152; point, II, 149.
Diagrams, indicator, II, 123.
Diamonds, circles cut by, I, 170; used in
ruling glass scales, I, 20-.
Diaphragm for microscope, 1, 158.
Diathermancy, II, 86.
Differences, method of, I, 6.
Differential galvanometer, II, 26, 260.
Diffraction, I, 152; bank, I, 199, 202.
Diffuse reflection, II, 89.
Dimple, II, 131.
Dip, of the horizon, II, 169; magnetic, II,
159.
Dipping needle, II, 157.
Direct light for microscope objects, I, 159.
Discharge, universal, II, 60.
Dispersion of light, I, 153; in liquids, II,
288 ; in gases, II, 288.
Dissolving views, II, 31.
Distances, lunar, II, 175; measurement of,
II, 300.
Distortion of photographic lenses, II, 303.
Diurnal variation of magnetic needle, II,
155.
Divided metre bridge, II, 36.
Dividing engine, I, 20, 56, 59.
Dot and line alphabet, II, 17.
Double, stars, II, 206, 290; touch, 11,67;
weighing, 1, 19.
Drawing paper expansion of, II, 301.
Drop, Ls and Ts. II, 111..
Drymg, sulphuric acid for, 1, 106.
Dulong and Petit's, law of cooling, II, 89 ;
calorimeter, II, 103.
Dynamometer, absorption, II, 126; polar-
ized light, II, 304; transmission, II, 127.
EARTH, density of, 11,306; in electricity,
II, 15 ; magnetism of, II, 154.
Eaton's prism, II, 250.
Eccentricity, of graduated circles, I, 33 ;
corrected by second vernier, 1, 142 ; of or-
bits, II, 2891
Eclipse, light of, 1, 135; solar, II, 202.
Edlund, theory of, II, 253.
Efficiency of gas-burners, II, 104; of ma-
chines, II, 305, 306.
Efflux of liquids, I, 94, 99; of gases, I, 113.
Elasticity, modulus of, I, 80; of metals,
II, 287 ; transverse, II, 134.
Elbow, II, 110.
Electric, bells, II, 12; decompositions, II,
13,238, 241; light, II, 215; resistance of
metals, II, 287; telegraph, II, 15; tele-
graphic longitude, II, 197.
Electrical, machine, II, 57; flier, II, 58.
Electricity.il, 1, 253; book on, II, 297; of
the air, II, 164.
Eleetrodynamometer, II, 304.
Electromagnet, II, 11.
Electromagnetic engine, II, 11; shown by
stroboscope, II, 240.
Electromagnetism, II, 255.
Electrometers. 1 1 , 4(,. 1:1,1! : Coulomb's, II, 56.
Electromotive force of batteries, II, 40, 41 ;
Poggendorffi's method, II, 45; VViede-
mann's method, II, 44.
Electroplating, II, 14.
Electroscope, gold-leaf, II, 55.
Electrostatic unit, ratio to electrodynamic
unit, II, 304.
Electro-torsion, II, 304.
Elements, properties of metallic, II, 287; of
solar system, II, 289.
Emission of heat, II, 86.
Emmetropic eye, 1, 198.
Energy, conservation of, II, 105, 107, 305.
Engineering, Mechanical, II, 109.
Enlargement of lantern microscope, II, 245.
Equatorial, interval of threads, II, 181;
telescope, II, 197.
Equipotential curves, II, 304.
Equivalent, mechanical, of heat, II, 105, 305.
Erecting prism, II, 236.
Errors, I, 2; clock, I, 45; curves of, 1, 14,
34 ; probable, I, 3.
Etching, I, 61.
Evaporation, measured by hook gauge, I,
41 ; rapidity of, II, 305.
Exhaust, II, 116.
Expansion, of gases, II, 288 ; of liquids, II,
77, 79, 288; of solids, II, 77, 78, 287.
Eye and ear method, 1, 18, II, 181 ; testing,
1, 191.
Eyepieces, I, 30 ; microscope, 1, 156.
A, I, 201.
Fahrenheit's heliostat, II, 213.
Filling bodies, I, 84.
Fault in telegraph cables, II, 53.
Field, magnetic, II, 71.
Fifth powers, table of, II, 274
Figures of Lichtenberg, II, 61.
Films, soap-bubble, I, 101.
312
Finder, Maltwood's, 1, 161.
Fireworks, Chinese, II, 235.
Fixed stars, color of, II, 207 ; motion of, 211.
Flier, electrical, II, 58.
Floating bodies, I, 90.
Flow of liquids, I, 94.
Fluorescence, II, 234.
Fluorhydric acid for etching, I, 61.
Fly, eye of a, for the microscope, 1, 158.
Fly-wheel, II, 114; speed of, II, 130.
Foaming of boilers, II, 112.
Foci of objectives, I, 173.
Fog, density of, II, 306.
Fogging, photographic, 1, 187.
Forces, composition of, I, 62 ; parallel, 1, 64.
Fork, tuning, 1, 124, II, 302 ; see Tuning fork.
Fortin's barometer, II, 146.
Foucault's heliostat, II, 214 ; pendulum, II,
306; regulator, II, 216.
Fourth powers, table of, II, 274.
Fraunhof er lines, 1, 152.
Freezing mixtures, II, 100.
Friction, angle of, I, 71; brake, II, 136;
coefficient of, I, 70; heat developed by,
II, 105 ; of belts, II, 135, 304 ; of pullies,
II, 136.
Frictional electricity, II, 54.
Frog, projected, II, 233.
Fusion, change of volume by, II, 82 : latent
heat of, II, 96 ; of inetals, temperature of,
II, 287.
GALVANOMETER, II, 260, 294 ; best form of,
II, 72; constant of, II, 22; cosine, II,
25; delicate, II, 36; differential, II, 26;
lantern, II, 246 ; law of, II, 21 ; projection
of, II, 248; resistance of, II, 43; Thom-
son's, II, 30.
Gas, burner, efficiency of, II, 104; holder,
I, 109, II, 219; meters, 1,111; pipes, II,
109.
Gases, decanting, I, 50 ; density of, II, 92 ;
efflux of, I, 113; expansion of, II, 80;
measurement of, 1, 109;, Mechanics of, I,
89; properties of, II, 286; reduction, I,
51.
Gauge, flask, I, 92; hook, I, 41; mercury, I,
107; rain, II, 152; sheet metal, I, 73; tide,
11,153; vacuum, 1, 104.
Gauges testing, II, 121.
Gav Lussac's syphon barometer, II, 146.
Geissler tubes, II, 20.
Gibson and Barclay's experiment, II, 304.
Glass, drawing on, II, 233 ; smoking, I, 126.
Glaucoma, 1, 198.
Gold-leaf electroscope, II, 55.
Goniometer, Babinet's, 1,141; microscope,
1, 163; Wollaston's reflecting, 1, 139.
Gore, electro-torsion, II, 304.
Graduating, circles, I, 23; lines, I, 58.
Graham, experiments of, II, 302.
Gramme, machine, II, 215 ; relation to me-
tre, I, 90.
Graphical method, I, 3, 11, H, 293.
Gravity, action of, I, 84; battery, II, 3;
centre of, I, 66 ; force of, H, 300.
Greenwich time, II, 171.
Grove's battery, II, 4.
HAIR hygrometer, II, 149.
Hardness of metals, II, 287.
Hartnack's microscope, 1. 156.
Heat, II, 72; books on, II, 298; change of
color by, II, 84, 234; conduction of, II,
287; latent, II, 96 ; mechanical equivalent,
II, 105,305; of combustion, II, 103; radi-
ant II. 84 ; specific, II, 94.
Heights, measured by barometer, 1, 116.
Heliostat, I, 151, II, 213.
Helmholtz, experiment of, 1, 191 ; of opthal-
moscope, 1, 196.
Holders, gas, 1, 109, II, 219.
Holtz' machine, II, 62, 306.
Hooke's joint, I, 69.
Hook gauge, I, 41, 95.
Horizon, artificial, II,- 168; dip of, II, 169;
glass, II, 166.
Horizontal, component of earth's magnet-
ism, II, 159; pendulum, II, 306.
Hour angle, II, 171.
Huyghens' arrangement for winding clocks,
Hydrogen, lines in spectrum, I, .153, II, 209.
Hydrometer, I, 91; tables, II, 288.
Hydrostatic balance, I, 93.
Hygrodeik, II, 150.
Hygrometers, II, 149.
Hypermetropic eye, 1, 198.
IAPETUS, satellite of Saturn, II, 205.
Ice, calorimeter, II, 305 ; machine of Carre",
II, 99.
Impact, II, 301 ; of water, II, 302.
Index, error, II, 169: glass, II, 166; of re-
fraction, 1, 43, 145, 146, 147. 151, II, 288, 304.
Indicator, board, II, 292; diagram, II, 123.
Induced currents, II, 254.
Induction, coil, II, 19; electric machines,
II, 62.
Inductive capacity, II, 304.
Insulated wires, II, 6.
Insulation, defect in, of cables, II, 54.
Insulators, II, 253.
Intense cold, 1, 107, II, 100.
Intensity, magnetic, II, 159; of sound, II,
Interference of light, 1, 199.
Interferential refractor, II, 304.
Interpolation, analytical, I, 7 ; graphical, I,
12; inverse, I, 8.
Investigation, original, 1, 1, II, 299.
Involute for gasholder, 1, 109.
Iris, 1, 191.
Isobaric lines, II, 139.
Isochimenal lines, II, 139.
Isoclinal lines, II, 139.
Isodynamic lines, II, 139.
Isogonal lines, II; 139.
Isotheral lines, II, 139.
Isothermal lines, II, 139.
JACOBI'S method of making magnets, II,
Jar,'Leyrten, II, 59; unit, II, 61.
Jet for calcium light, II, 222 ; of water, 1, 97.
Joint, Hooke's universal, I. 69.
Joule's, dipping needle, II, 157; equiva-
lent, II, 105 ; method of measuring the
temperature of the air, II, 144 ; method
of finding the temperature of maximum
density, II, 305.
Joulin's experiment, II. 304.
Jupiter, II, 205; satellites, eclipses of, II,
195.
Jurgensen's mean, temperature thermome-
ter, II, 143.
KALEIDOSCOPE, II, 235.
Kater's pendulum, II, 300.
Kew barometer, II, 145.
Keys, electric, H, 7.
KirchhofTs, laws, II, 42, 46, 257; map of
spectrum. 1, 152.
Knobs of glass, 1, 184.
INDEX.
313
KoLlrausch's experiment, II, 301.
Kundt's experiment, 1, 123.
L or elbow, II. 110.
Lace, spectra imitated by, II, 251.
Lantern, II, 212 ; construction of, II, 225 ;
galvanometer, II, 246; microscope, II,
244; polaitooope, II, 242; vertical, II, 240.
Latent heat, of fusion, II, 96 ; of liquids,
II, 283; of vaporization, il 96.
Latitude, barometric correction for, 1, 118;
by sextant, II, 168 ; by transit, II, 184 ; by
transit circle, II, 188; by zenith teles-
cope, II, 189.
Lavender, oil of, for depositing silver, I,
178.
Lengths, measurement of, I, 19. See Wave-
lengths.
Lenses, condensing, II, 227 ; law of, I, 155 ;
oblique, II, 303; projecting, II, 226.
Level, adjustment of, II, 179; contact, I,
21 ; tester, II, 179.
Leyden jar, II, 21,59.
Lichtenberg's figures, II, 61.
Lieberkuhn, I, 160.
Light, I. 132 ; books on, II, 297 ; electric. II,
215; lime, II, 218; magnesium, II, 217; of
sun, II. 212.
Lime light, II, 218.
Lippmann's experiment, II, 304.
Liqueh'ed gases, II, 100.
Liquids, efflux of, I, 94 ; expansion of, II,
79 ; flow through small orifices, I, 99 ; jets
of, I, 97 ; Mechanics of, I, 89 ; properties
of, II, 288.
Lissajous' experiment, I, 128,11,302; pro-
jected. II, 268.
Logarithmic sines and cosines, II, 282; tan-
gents and cotangents, II, 284.
Logarithms, table of, II, 274 ; Naperian, II,
274.
Longitude, II, 174, 195 ; of ascending nodes,
117289.
Lowery's experiment, II, 302.
Lucida, camera, I, 164.
Lunar distances, II, 175.
Lycopodium powder, 1, 123.
MACHINE, electrical, II, 57.
Magdeburg hemispheres, I, 105.
Magnesium light, II, 217.
Magnetic, curves, II, 65,241; declination,
II, 154; dip, II, 157; field, II, 71; intens-
ity, II, 159, 163; storms, II 155.
Magnetism, II, 64, 305; horizontal compo-
nent of earth's, II, 159; vertical compo-
nent of earth's, II, 163; distribution of,
II, 69; of liquids, II, 288; shown by lan-
tern, II, 241.
Magneto-electricity, II, 255; electric ma-
chines, II, 5, 215, 306.
Magnetometer, balance, II, 163 ; bifllar, II,
162.
Magnets, II, 64, 255; electro-, II, 11 : force
of, II, 67; law of, II, 68; making, II, 65.
Maltwood's finder. 1, 161.
Manse's method, II, 43.
Mariner's compass, II, 64.
Mariotte's, flask, I, 99; law, I, 107, II, 304.
Mars, II, 201.
Massachusetts, law for gas in, I, 136.
Materials, strength of, II, 132.
Maximum, density, II, 305; thermometers,
II, 140.
Maxwell, experiments of, II, 302, 304.
Mayer, experiments of, II, 303, 305.
proper-
Mean, I, 3 ; temperature, II, 143 ; time, II,
Mechanical, engineering, II, 109; equiva-
lent of heat, II, 105, 305.
Mechanics, book on, II, 297; of gases, I,
89; of liquids, I, 89; of solids, I, 62.
Mega-, II, 257.
Megohm, II, 35.
Melde's experiment, 1, 124, II, 302.
Melloni's thermo-bank, II, 85.
Mercadier's experiment, II, 302.
Mercury, II, 204; cleaning, 1,35; transits
of, II, 196.
Meridian, found by altitude and azimuth
instrument II, 191 ; found by a sextant,
II, 176; marked by mirror, II, 194.
Metallic spectra, projection of, il, 252.
Metals, conductibility of, II, 305; pro
ties of, II, 287.
Meteorograph, II, 138.
Meteorology, II, 137.
Meters, air, I, 120; gas, I, 111.
Metronome pendulum, I, 85.
Meusel's double iodide of copper and mer-
cury, II, 84.
Micro-, II, 257.
Micrometer, for microscope, 1, 162; screw,
I, 20, 77; spider-line, I, 154, II, 199; stage,
I, 163.
Microscope, I, 156; lantern, II, 244; read-
ing, I, 21.
Minimum thermometer, II, 140.
Mirage, shown on screen, II, 234.
Mirror, and scale, I, 21, 24, 77; galvanome-
ter, II, 30, 247.
Mirrors, law of, II, 303; of silver and plati-
num, I, 178; silvering mercury, 1, 177.
Mixture of vapors, II, 93.
Modulus of compression, 11,133; of elas-
ticity, I, 80.
Moisture, II, 149.
Moments, I, 63 ; magnetic, II, 160, 305.
Monochord, II, 302.
Monochromatic light, II, 244.
Moon, II, 203; light of, I, 135.
Morse alphabet, II, 17.
Morton's condensers, II, 228.
Motion, friction of, II, 135; of stars, II, 210.
Myopia, 1, 197.
NACHET'S microscope, 1, 156.
Naperian logarithms, table of, II, 274.
Nebula;, II, 207, 291 ; brightness of, II, 307;
spectrum of, II, 210.
Needle, dipping, II, 157.
Negatives, photographic, I, 181.
Negretti and Zauibra's thermometers, II,
141.
Neptune, II, 205.
Neutral axis, II, 301.
Newton's, law of cooling, II, 88, 95, 97 ; rings,
1, 177, II, 303.
Nicholson's hydrometer, I, 91.
Nicol's prism, 1, 160, 180.
Nipples, II, 110.
Nobert's lines on glass, I, 20, 167.
Nodes, longitude of ascending, II, 289.
Non-conductors, II, 253.
North polar distances, II, m.
OBJECTIVES, foci and aperture, 1, 173; mi-
croscope, 1, 156.
Objects, for microscope, 1, 156 ; for projec-
tion, II, 232 ; mounting of, I, 170 ; perfo-
Oblique' illumination, 1, 159; lenses, II, 30a
314
Ohm. II, 257; determination of, II, 304;
melting, II, 36; standard, II, 256.
Oleate of soda, I, 101.
Opaque objects, projected, II, 245; exam-
ined under microscope, 1, 159.
Opthalmoscope, I, 196.
Optical circle, 1, 141.
Optics, 1, 132 ; books on, II, 297.
Optometers, 1, 191.
Organ-pipes, I, 122.
Original investigation, 1, 1, II, 299.
Osmose, II, 302.
Over-corrected lenses, test for, 1, 178.
Orifices, flow of liquids through, I, 99.
Oxygen, making, II, 220.
Oxyhydrogen blowpipe, II, 222.
PALM-GLASS, 1, 105.
Papilla, 1, 198.
Parabolic condenser, 1, 160; form of jet, I,
Parallactic angle, II, 171.
Parallel forces, I, 64.
Parallelism, adjustment of collimator for,
I, 143.
Peclet's determinations of conductibility,
II, 305.
Peirce's criterion, I, 6.
Peltier's electrometer, II, 164.
Pendulum, II, 400; ballistic, II, 301;
Borda's, I, 85 : compound, II, 251 ; met-
ronome, I, 85; torsion, I, 87; viewed by
stroboscope, II, 240.
Penumbra, II, 201 ; projected, II, 234.
Perforating glass by spark, II, 60.
Periodicals, II, 296.
Personal equation, II, 197.
Peter's microscopic writing, I, 20.
Phantasmagoria, II, 231.
Phase of vibration, II, 303.
Philosopher's wool, II, 58.
Phosphorescence, II, 234.
Photographic registration, II, 137.
Photography, I, 181.
Photometer, absorption, I, 132; Bunsen, I,
135; clock, I, 136; daylight, I, 134: disk,
1, 132; Rumford, 11,303; selenium, 11,304.
Physical, investigation, I, 1, II, 299; labora-
tories, I, vi, II, 292; measurement, 1, 16.
Physics, books on, II, 296.
Picture-holders, II, 228.
Pictures for lantern, II, 230, 232; photo-
Pole star, II, 181.
Porcelain, photographs on, 1, 17.
Porte-lumiere, II, 212.
Position, angle, II, 171, 290; micrometer,
II, 199.
Positives, photographic, I, 187.
Positives, photographi
Potential, II, 262.
graphic, I, 184.
ile-driver, II, 301.
-, , .
Pipes, organ, I, 122; resistance of, I, 98.
Piping, fl, 109.
Piston, II, 115; speed of, II, 129.
Plane surfaces, testing, 1, 175.
Planets, II, 204; elements of, II, 289.
Plante's battery, II, 306.
Plate electrical machine, II, 57.
Plateau's experiment, I, 101.
Plates, vibrations of, 1, 130.
Plating, electro-, II, 14.
Platinizing mirrors, I, 178.
Pleiades, II, 207.
Plugs, electric, II, 7; for resistance coils,
II, 29 ; steam fittings, II, 110.
Pneumatic trough, I, 50.
Pneumatics. 1, 103.
Poggendorff's method, II, 45.
Poiseuille's experiment, II, 302.
Polariscqpe, forms of, I, 217; lantern, II,
242 ; microscope, 1, 160.
Polarization of heat, II, 87; of light, I, 208;
of telegraph cables, II, 53.
Polarized light dynamometer, II, 304.
Pouillet's pyrheliometer, II, 143.
Power, of engines, measured, II, 123, 12G.
Powers, table of, II, 274.
Practical Astronomy, II, 166.
Pressure, atmospheric, II, 145; gauge, II,
154; of sand, II, 301; of sap, II, 301 ; of
steam, II, 89, 122; of vapors, II, 90, 289.
Priming of boilers, II, 112.
Prime vertical, transit in, II, 184.
Prisms, angles of, I, 141 ; erecting, II, 236 ;
total reflecting, II, 240.
Probable error, I, 3.
Projectiles, laws of, I, 97.
Projecting lenses, II, 226.
Projections, Lantern, II, 212; objects for,
11,232.
Properties, of gases, II, 288; of liquids, II,
288; of metals, 11,287.
Pullies, friction of, II, 136.
Pump, air, 103; Bunseu, I, 118.
Pupil, I, 191.
Pyrheliometer, II, 143.
Pyrometers, II, 101.
P. Z. S. triangle, I, 45.
QUALITATIVE investigation, 1, 1.
Quantity, batteries connected for, II, 258 ;
electric, II, 259.
Quantitative investigation, I, 1.
Quartz prism, I, 154; polarization of, I, 216.
RADIANT heat, II, 84.
Radiation, II, 84, 143; correction for, II,
105; loss due to, II, 88, 95, 97.
Radiometer, II, 305.
Rain, II, 152; drops, adhesion of air to, II,
302.
Rating thermometers, I, 44, II, 196.
Reading microscopes, I, 21, 55, II, 186.
Receivers, for air pump, I, 104.
Reciprocals, table of, II, 272.
Reducing couplings, II, 110.
Reference, books of, II, 29t>.
Reflecting, goniometer, I, 139 ; spherometer,
II, 300
Reflection, law of , I, 138, 144; of heat, II,
87 ; photometer for measuring, II, 303.
Reflectors of silver and platinum, I, 178.
Refraction, correction for, II, 70, 188 ; index
of, I, 43, 147, 157, II, 288 ; law of, 1, 145,
146; measured, II, 304; of heat, II, 88.
Refraction equivalent, II, 287.
Register, telegraph, II, 15.
Registering instruments, II, 137.
Regnault's experiments on Mariotte's law,
1,107: hygrometer, II, 151; experiments
on vapors, II, 90, 28.
Regulator, for electric light, II, 216 ; gas,
Relay, telegraphic, II, 16.
Repeater, telegraphic, II, 17.
Repose, friction of, II, 135.
Residual curves, 1, 12.
Resistance, coils, II, 21, 29; electric, II,
260; making coils, II, 36; measurement
of, II, 30 ; of air, II, 302 ; of batteries, II,
40, 41, 43; of galvanometers, II, 43; meas-
urement of great, II, 35; of metals, II,
287; of pipes, I, 98; of selenium, II, 304.
Resolvability, II, 306.
INDEX.
315
Retina, I, 191.
Reversal of sodium line, II, 252.
Revolving wheel run by stroboscope, II ,239.
Rheocord, II, 28.
Hheostat, II. 22, 28.
Right and left steam fitting, II, 110.
Rings, Newton's, I, 177, II, 303.
Robinson's anemometer, II, 148.
Rods for trusses, I, 80.
Rood's photometer, II, 307.
Rotary polarization, I, 222, II, 243.
Rowland, expei-inn-nts uf. II, 305.
Rubber bag for holding gas, II, 329.
Ruhmkorff's coil, II, 19.
Rumford's photometer, II, 303.
Rusty glass, I, 184.
Rutherford's thermometers, II, 140.
SACCHARIMETER, I, 222.
Sand, pressure of, It, 301.
Sap, pressure of, II, 301.
Satellites of Jupiter, eclipses of, II, 195.
Saturn, II, 205.
Sau-iiire's hair hygrometer, II, 149.
Savart's bands, I, 20,8, 217.
Saxton's hygrometer, I, 21, 24, 79.
Scale in boilers. II, 114.
Scales, ruling, I, 69. II, 293.
Screen for projections, II, 225 ; as a black-
board, II, 232.
Screw cups, II, 6.
Screws, inside and outside, II, 110.
Secchi's meteorograph, II, 138.
Secular variations of magnetic needle, II,
158.
Selenite, cause of color, I, 214 ; figures pro-
jected, II, 243.
Selenium, resistance of, II, 304.
Self-registering instruments, II, 137.
Semi-diameter, correction for, II, 170.
Sextant, I, 45, II, 166 ; glass, I, 175.
Shadows, shown on screen, II, 233.
Shafting, speed of, II, 130.
Shearing strains, II, 134.
Sheet metal gange, I, 73, II, 300.
Shunts, II, 259.
Short circuited, II, 40.
Shunt for galvanometer, II, 30.
Sidereal interval of threads, II, 181 ; time
defined, II, 172: time found by sextant,
II, 173; time found by transit, II, 177.
Siderostat, II, 199.
Siemens' resistance pyrometer, II, 103.
Significant figures, I, 10.
Silbermann's heliostat, II, 214.
Silk fibres, suspension by, I, 31.
Silver, deposition on glass, I, 178; photo-
graphic bath, 1, 183.
Simon's method of studying capillarity, I,
100.
Simpson's rule, I, 22.
Sine galvanometer, II, 260.
Sines, table of logarithmic, 11,282; table
of natural, II, 278.
Single touch, II, 66.
Sirene, I, 122.
Sixe's thermometers, II, 141.
Sky, light of, II, 306.
Slide valve, II, 115.
Smee's batteries, II, 2.
Smoked glass, I, 126; curves on, projected,
II, 232.
Soap-bubble films, 1, 101.
Sodium, lines in spectrum of, 1, 153.
Solar, microscope, II, 244; radiation, II,
143; spectroscope, 1, 151; system, II, 289;
time, II, 172.
Soldering, II, 6, 36.
Soleil's saccharimeter, I, 222.
Solenoids, attraction of, II, 254, 304.
Solids, conduction of, II, 82; expansion of,
11,78; mechanics of, 'I, 62.
Sorby's spectrum microscope, 1, 165.
Sound, I, 122; books on, II, 297; velocity
. of, I, 123, II, 288.
Sounder, telegraphic, II, 16.
Sparks, effect of electric, II, 60.
Specific gravity, bottle, 1,92; by hydrom-
eters, I, 91; of gases, 11,91,288; of liq-
uids, II, 288; of metals, II, 287.
Specific heat, II, 94; as a measure of tem-
perature, II, 102 ; of gases, II, 106, 288 ; of
liquids, II, 288; of metals, II, 287.
Spectra, electric, II, 21; projection of, II,
250.
Spectrometer, 1, 141.
Spectroscope, chemical, 1, 148; for compar-
isons, II, 303; solar, 1, 151, II, 208.
Spectrum, lines of, 1, 148, 152 ; microscope,
1, 1G5; telescope, II, 208.
Speed, of fly-wheels, II, 130 ; of piston rod,
11,129: of shafting, II, 130.
Spherical aberration, 1, 178.
Spherometer, I, 25, 42 ; Cornu's reflecting,
II, 300.
Spider line micrometer, I, 25, II, 199.
Spring candlestick, 1, 132.
Square root, table of, II, 274.
Squares, table of, II, 268.
Stage micrometer, I, 163; microscope-. I,
160.
Standards of volume, I, 52.
Staphyloma, 1, 198.
Stars/clusters of, II, 207,291; double, II,
290; spectrum of, II, 208; motion of, II,
210.
Statical electricity, II, 253.
Steam, boilers, II, 112; pipes, covering, II,
119, 121; engine, II, 115; pipes, II, 109;
pressure, II, 89, 122.
Stefan's experiment, IT, 305.
Stimpson's caudle-balance, 1, 136.
Storms, magnetic, II, 155.
Strength, of materials, 11,132; of thread,
11,301.
Stria;, II, 178, I, 226.
Stroboscope, II, 238.
Student's microscope, 1, 156.
Submarine telegraph, II, 52.
Sugar, rotary polarization of, I, 222.
Sulphuric acid for drying, I, 106.
Sun, II, 201; light of, II, 212,307; image
of, projected on the screen, II, 233.
Supply pipe, II, 116.
Surfaces, testing plane, 1, 175.
lymtofs 8 ; of' g'ases, II, 288; of liquids, II,
288; of metals, 11,287.
Syphon, barometer, I, 104; recorder, II,
58; vacuum gauge, 1, 104.
T or Tee, II, 111.
Tables, II, 263; books, II, 298.
Talbot's bands, II, 304.
II, 284;
table of natural, II, 280.
Tanks, II, 235.
TeeorT, II, 111.
Telegraph, II, 15 ; testing, II, 49.
Teefcope, equatorial, II, 197 ; spectrum, It
207; testing, 1, 178 ; zenith if, 189.
Temperament, musical, II, 302.
316
INDEX.
Temperature, II, 288; curve, 1,31; of the
air, II, 139; of steam, II, 122.
Tension, I, 73 , batteries connected for, II,
9, 258 ; change of volume by, I, 75.
Tenths, estimation of, I, 27, 44.
Testing, gauges, II, 121; telegraphs, II, 49,
52; telescopes, I, 178; the eye, I, 191;
thermometers, I, 32, II, 72.
Test objects for microscopes, 1, 166 ; types,
1, 191.
Thermal equivalent of magnetism, II, 395.
Thermo, -battery, II, 5; -electric position
of metals, II, 27; -pile, II, 83, 84.
Thermometers, I, 32, II, 73, 139; air, II,
101; contact, II, 84; projected, II, 233;
weight, II, 76.
Thickness, measurement of, II, 300.
Thomson's, electrometer, II, 46, 262; gal-
vanometer, II, 30, 37, 248; syphon vender,
II, 58.
Thread interval, II, 181.
Thunder storms, telegraphs disturbed by,
II, 16.
Tide, II, 153.
Time, 171 ; found by sextant, II, 173; found
by transit, II, 177 ; measurement of, 1, 16.
Titan, satellite of Saturn, II, 205.
Tolles' microscope, I, 156.
Tomlinson's cohesion figures, II, 242.
Toning paper photographs, 1, 189.
Torricelli, theorem of, I, 97 ; vacuum of, I,
115.
Torsion, electro-, II, 301 ; electrometer, II,
56; laws of, I, 82, 85, II, 301.
Total reflection, in vertical lantern, II, 240;
index of refraction measured by, 1, 147.
Touch, single, II, 66; double, II, 67.
Tourmaline, I, 208.
Trannin's spectroscope, II, 303.
Transmission dynamometer, II, 127.
Transit, II, 177; circle,' II, 186.
Transits, method of observing, I, 44, 45: for
finding longitude, II, 196.
Transparency of flame, I, 133 ; of bodies for
heat, II, 86.
Transpiration of gases, II, 288, 302.
Transverse elasticity, I, 77, 79, II, 134.
Tripod, proper method of supporting, I,
Trusses, I, 80.
Tuning fork, I, 124, II, 352; curves of , I,
125; Lissajous', I, 128, II, 248,302; seen
by stroboscope, It, 240 ; vibrations main-
tained electrically, II, 12.
Twaddell's hydrometer, II, 288.
UNDER-CORRECTED lenses, test of, 1, 178.
Units, electrical. II, 255.
Universal joint, I, 69.
VALVE, II, 112; slide, II, 115.
Vaporization, latent heat of, II, 96, 288.
Vapors, mixture of, II, 93; pressure of, II,
90, 289; properties of, II, 288; specific
gravity of, II, 91.
Variations of the magnetic needle, II, 155.
r, II, 257.
Velocity of motion, ofi fly-wheel, II, 130;
of piston rod, II, 129*
Velocity of sound, I, 123; in liquids, II,
288 ; in gases, II, 288.
Velocity of wind, 1, 121.
Venus, II, 204; seen in daytime, II, 194;
transits, II, 196.
Vernier, 1, 19, 28.
Vertical, component of earth's magnetism,
II, 113; lantern, II, 240.
Vibration, curves of, 1, 125; of cards, 1, 124;
of forks, 1, 128; of plates, I, 130.
Vierordt's spectroscope, II, 303.
Violin bow, forks sounded by, 1, 122, 124 ;
plates sounded by, 1, 130.
Viscosity of gases, II, 302.
Volt, II, 257.
Voltameter, II, 259.
Volumes, change of, by fusion, II, 82;
change of, by tension, I, 75; measure-
ment of, I, 22; of surfaces of revolution,
I, 67.
WALFERDIN'S thermometer, II, 142.
Water-dropping collector, II, 165.
Wave, lengths of light, I, 153, 201, 205;
lengths of sound, 11,303; motion, II, 242.
Weathercock, II, 147.
Wedgewood pyrometer, II, 102.
Weighing, double, 1, 19, 53 ; proper method
Weights, I, 4, II, 300 ; breaking, I, 72 ; com-
parison of, I, 48; making, I, 49; measure-
ment of, I, 49 ; relation of, to measures,
1,90.
Wenham's parabolic condenser, 1, 160.
Wet and dry bulb thermometers, II, 150,
289.
Wheatstone's bridge, II, 29, 261; British
Association, II, 36 ; condenser's compared
by, II, 38.
Wiedemanu's method, II, 44.
Wilde's machine, II, 215.
Wind, II, 147; velocity of, 1. 121, II, 306.
Wollaston's goniometer, I, 139 ; instrument
for measuring indices of refraction, I,
147.
Wool, philosopher's, II, 58.
ZENITH, distance, II, 171 ; telescope, II, 189.
Zentmayer's microscope, I, 156.
Zero point of thermometers, II, 73.
Zinc, for batteries, II, 1.
Zirconia cylinders, II, 224.
Zolluer's horizontal pendulum, II, 304, 306.
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