An introduction to scientific chemistry

Front matter

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Introduction

TO

SCIENTIFIC CHEMISTEY;

DESIGNED 70S

THE USE OF SCHOOLS

AND

CANDIDATES FOR UNIVERSITY MATRICULATION

EXAMINATIONS.

BY

F. S. BARFF, M.A.,

€^. €oll,t Cam. ;

London,

SECOND EDITION.

LONDON :

GROOMBRIDGE AND SONS, 5, PATERNOSTEg

MD.CCCLXIX.

[The right of TramslaUon is reserved,']

LONDON :

B. BARBETT AND SONS, PBINTERS,

HABK LANE.

Preface

Thb metliod adopted in this book is somewhat different from that of other elementary treatises. The subject, which extends only to the systematic consideration of what are called the '' non-metallic elements,'' indirectly treats of the more common metals which enter into combination with them, and is divided into two parts. In Part I. no symbols or atomic weights are used, but definite quantities in grammes are employed. I have always found that beginners have great difficulty in conceiving abstract numbers, and that symbols and equations are regarded by many as almost insuperable impediments ; the attepipt to overcome which involves a considerable amount of labour, which might be much more usefully applied.

It has not been my wish to make the subject what is called " easier,'* or to lessen the attention requisite for

IT PREFACE.

acquiring it, l)ut to direct that attention in a way which will render its exercise more profitable. Only a few theoretical considerations are introdaced, and these have been reserved entirely for Part 11. , when the student is supposed to have acquired a knowledge of the facts on which those considerations are founded. Simple examples of calculation, and questions on the matter of each chapter, are given ; and the student is earnestly requested to work out the one, and carefully write out the answers to the other, without referring to the book, and afterwards to compare them with the book, or submit them to his teacher. As only a few can acquire a sound knowledge of Chemistry by themselves, I by no means consider that this book should supply the place of the teacher. Some considerable experience in teaching young persons has proved to me that Chemistry cannot be learnt (it may be "crammed") without experimental illustrations and explanations given by a competent teacher ; nor is even this sufficient without the student be himself exercised in practical work.

I am informed that Professor Bunsen, of Heidelburg, does not allow formtilae or atomic weights to be used during the first three months of a young student's course. It is gratifying to me to find that I have sneh confirmation of the course whicl^ I have for some time adopted.

PREFACE. V

A clergyman, who was a pnpil of Gay Lussac, tells me that that famous chemist neyer nsed formnlsQ, or even mentioned the atomic theory, till he had fully treated of elementary hodles and their compounds ; and that he gave as his reason for so doing, that facts are incontrovertible, but theories may be changed or modified ; and therefore a knowledge of facts should be acquired before theories are considered.

Whilst intending this book to be a manual for candidates for the London University matriculation examination, I have not entirely confined myself to the curriculum at present put forth by that institution, as I hope that it will be found useful generally in schools, and in preparing students for other examinations, as well as in laying a sound foundation for the scientific study of Chemistry. With this view I have endeavoured, as much as possible, to make it an introduction to " Chemistry for Students " by Professor Williamson, whose assistant I have the honour to be, and to whom I am indebted, in great part, for what knowledge of Scientific Chemistry I possess, as well as for many personal favours. I am also indebted to Mr. Temple A. Orme, Teacher of Chemistry in University College School, and to Mr. J. J. Bowrey, late of University College, who have given me many valuable suggestions, which I have adopted ; and to the Eev. Stephen Williams, Professor of Chemistry, Stonyhurst College,

VI PREFACE.

and to Mr. J. Jones, Assistant to Professor Williamson, wbo have helped me with the calculations, and in. revising the proofs.

FKEDK. S. BAKFF.

University College, London, March, i869.

Preface To The Second Edition

In this edition typographical and other errors have heen corrected ; no new matter has been added, except the chemical questions of the Matriculation Examination of the London University for June, 1869, together with the answers to those which involve calculation. The nomenclature adopted in this hook is the same as that now used hy the Examiners at the London University* In the last matriculation paper the terms hydrogen sulphate and nitrate are employed, instead of ^^(^n'c sulphate and nitrate ; this, however, is unimportant. The fact that these bodies are salts is recognised, and this being so, till some other more suitable word is used to designate them, SOg and its analogues must be called acids,

October, 1869,

INTRODUCTION.

The present state of chemical science, and the differences of opinion which exist on many important points in connection with it, render it difficult in an elementary work to use terms which will he considered unexceptional hy all. Nor is it desirahle to raise disputed questions where what is asserted will have, to a great extent, to he receiyed hy the student on trust, until his knowledge enables him to grapple with difficulties and form his own opinions. The nomenclature which has heen employed was systematised hy Professor Williamson and is used, to a considerable extent, by Professor Roscoe in his admirable little book, and appears likely to become general, founded, as it is, on a rational principle. The substantive use of the word '^ acid'' is confined to those bodies which have for a short time been called anhydrides. What have been generally termed acids are admitted by all authorities to be hydrogen salts, and they are designated as such whenever it is found necessary to allude to them*

VIU INTRODUOTIOir.

As the elements of beat are not treated of in this book, tbe conditions nnder wbicb all yolumes of gases and raponrs are considered, are tbose of tbe standard temperature and pressure, i.e. at tbe temperature of zero Centigrade and under 760 millimetres of mercury pressure. Tbe young student generally finds considerable difficulty in understanding bow tbe vapour of water (steam) can be measured under such circumstances. It may be well to give as simple an illustration of it as possible. Gases wben beated expand, and tbe rate of tbeir expansion is regular, or very nearly so. If a measure of gas be beated to 1 degree Centigrade, its volume will increase ^^. Now tbis increase is at tbe same rate wbetber tbe measure be large or small. If tben a measure of gas be beated from zero to 273*'C. its volume will be 'doubled, tbus — 1 volume at zero Centigrade, wben beated up to VC, becomes 1 + jify, wben beated to 2°C. it becomes 1 + 5^, to 3**C. 1 + ^, and so on to 273**C., wben it becomes 1 +ff|, or 1 + 1, i.e. 2 volumes ; now tbe volume of 2(11.2) litres of steam at 100°C. is ==» 80.605 litres. So tbat, wben it is said tbat 18 grammes of water in tbe state of steam occupy 2(11.2) litres, it does not mean that they occupy this volume at tbe moment of their formation by the union of oxygen and hydrogen, for at thafc time great beat is evolved and their volume is greater than 30.605 litres; but it

IKTRODUOTIOV. IZ

means that if the volume of the steam could be reduced to zero Centigrade, whilst the barometer indicated a pressure of 760 millimetres of mercuiy, then, under those circumstances, the steam would occupy 2(11.2) litres. Suppose at the time of the union of oxygen and hydrogen in the eudiometer, provision were made for heatings it, so that the steam formed would be at lOO^C, and if it were then found to measure 30.605 litres, its supposed volume at zero would be ascertained as follows : 273 volumes at zero become 373 volumes at 100*0., therefore, inversely, 373 : 273 : : 30.605 : 22.4. But, whatever be the volume of 18 grammes of steam, it is always the same as the volume of 2 grammes of hydrogen under the same circumstances; for it is manifest that if steam obeys the same law as fixed gases, under whatever temperature, and under whatever pressure, hydrogen unites with oxygen to form steam — ^the steam will occupy the same volume as the hydrogen did before its union with oxygen. This will be better understood by the student after he has read to the end of Chapter VII. and should be then referred to.

As it would be injudicious in an elementary work to introduce anything which has not received the public sanction of acknowledged authority, the Author has only stated, to the best of his ability, those opinions which he believes to be generally received. The lumi-

X INTRODUCnOK.

nosity of flame he has explained as owing to the pre* sence in it of solid matter ; he feels it, however, his duty to state that Dr. Frankland is at present engaged in investigating this snbject, and from the able experiments, the results of which he has in part published, it is probable that " the boM particle theory" will have to be modified, if not abandoned. The atomic theory is briefly explained without any allusion to differences of opinion which exist respecting it.

The specific gravities of liquids and solids, and of gases referred to atmospheric air, are only occasionally alluded to in the text^ but a table of those of the most important elements is given at the end of the book.

The decimal system of weights and measures is employed, and a table comparing them with English weights and measures is appended.

The difference between the Centigrade and Fahrenheit thermometric scales is given in Chapter I. ; but afterwards all temperatures are recorded in degrees Centigrade.

By showing young persons the benefits to be derived from the use of a rational metrical system, it is to be hoped that they will, in their time, assist in getting it generally adopted in this country.

Contents

PABT I.

Chapter I. Definition of diemistry Mechanical mixture

Chemical compound . .

Element, defimtion of .

Com}>onnd bodies, ditto .

Density of gases . . .

Stand^d pressore . .

Standard temperature .

Method of weighing gases Thermometers . . .

Decimal weights and mea snres

Chaftek II.

Hydrogen . .

Preparation of Weight of .

Collection of Flame of . .

QnestionB on

PAGE

1 2 2 2 2 3 5 6 6 7

11 12 14 15 16 16

Chapter III. Discovery of .... 18

Mannfactnre of ... 19

Composition of potassio

chlorate 19

Cfdcnlations 20

Oxygen, density of . . . 21

Volnmeof 22

Oxygen — continued. paqb A supporter of combustion 23

Questions on .... 24

Chapter IV. Nitrogen 25

Obtained from air . . . 25

Density of . . . . . 20

Qliestions on .... 26

Chapter V. Carbon 27

Allotropic modificationfl of . 27

Charcoal and coal ... 28

Carbon not volatile ... 28

0HAPTER VI.

Combustion . . . . . 80 Heat evolved by chemical

union 31

Flame, construction of . . 33

Luminosity of flame . . 84

Unbumt gases in flame . . 35

Bansen burner . . . . 36

Combustion, chemical action 87

Questions on combustion * 38

Chapter VII. Water, its composition . * 39

Besutt of combustion • 40

Xll

COKTBNTB.

PAGE

. 41 . 45 . 44 . 45

Water— continiied

GompoBitLon by weight .

Synthesis of ....

Calculations . ....

Water, electrolysis of . .

Combination of oxygen and

Eudiometer 48

Steam, absolute volume of . 48 Questions on water ... 49

Chapteb VIII.

Water, its impurities'. . . 52

Hardness of water ... 52

Clarke's test 53

Water of crystaUisation . 54

Sea water 54

Lime in Water .... 56 Questions on impurities in

water 56

Chapteb IX.

Atmospheric air . . . . 57

Air a mixture of gases . . 57

Not a chemical compound 58

Carbonic acid in air . . . 59

Water vapour in air « . . 60

Ozone 61

Purification of air . . . . 61

Analysis of air 62

Eudiometrio analysis of air. 63

Eespiration of animals . . 64

Office of plants .... 65

Density of air . . . . • 65 Questions on atmospheric

air .66

Chapter X.

Diflftision of gases Hates of diffusion Questions on diffusion

68 69 70

Chapter XI.

Carbonic acid .

Preparation of

71 73

PAGE

Carbonic acid, how obtained from air ... 74 Liquefaction of ... 75 Solid carbonic acid ... 76 Tests for carbonic acid . . 77 QuestionB on carbonic acid 78

Chapter XII.

Carbonic oxide .... 80

Composition of ... 81 Combustion of an ordinary

fire 82

Questions on carbonic oxide 83

Chapter XIII.

Harsh gas 85

Fire-damp 85

Davy lamp 86

Marsh gas, preparation of 87

Questions on marsh gas . 88

Chapter XTV.

defiant gas 90

Preparation of .... 91

Dutch Hquid 92

Questions on defiant gas . 92

Chapter XV.

Coal gas 94

Impurities of .... 96

Questions on coal gas . • 97

Chapter XVI.

Oxides of nitrogen ... 98

Nitrous oxide 99

Liquefeiction of ... 100

Nitric oxide 101

Nitrous acid 102

Nitric peroxide . . • .103

Nitric acid 104

Nitrates 108

Tests for a nitrate . . .110

Questions on hydric nitrate 111

CONTENTS.

ZUl

Chjlpter XVII.

PAGE

Freparation of ... 114 Ammonic hydrate . . .115 Ammonia, composition of . 116 Liquefaction of . . .117 Dry ammonia gas . . . 118 Tests for ammonia . . .119 Questions on ammonia . .119

chaptek xvm.

Chlorine 121

Combustions in chlorine . 122 Chlorine, preparation of . 123

Calculations 124

Chlorine action on ammonia 125 Questions on chlorine . .125 Compound of oxygen and

chlorine 127

Hypochlorous acid . . .127 Hydric hypochlorite . .128 Bleaching powder . . .129

Bleaching 130

Potassic chlo^te . . . .181 Hydric chlorate .... 182 Tests for a chlorate . . . 183

Chlorous acid 184

Chloric oxide 184

Perchloric acid .... 185 Questions on hypochlorous

add 136

Do. hydric hypochlorite 186

Chapter XIX.

Hydric chloride .... 138 Graham's experiment . . 189 Hydric chloride, solution of 140 Preparation of ... . 141 Tests for chlorides . . . 142 QuestiGns on hydric chloride 148

Chapter XX.

Bromiiie 148

Freparation of .... 147

Hydric hypobromite

Hydric bromate • . .

Hydric bromide . . .

Tests for bromides . .

Questions on bromine .

Chapter XXI.

PAGR

Iodine • • 168

Iodides, action of chlorine

Iodic acid 165

Hydric iodate 165

* Potassic iodate . . . .155 Questions on iodine . . .156

Hydric iodide 167

Potassic iodide . . . .158 Tests for iodides . . . .159 Questions on hydric iodide 160 Questions on potassic iodide 160

Chapter XXII.

162 162 164 165

Hydric fluoride . . .

Tests for a fluoride . .

Questions on fluorine

Chapter XXHI.

Sulphur at diffetent temperatures 167

Sulphur, its solubility . .168 Questions on sulphur . .169 Sulphurous acid . . . .170 Tests for sulphurous acid . 171 Questions on sulphurous

acid 172

Sulphuric acid .... 172- Questions on sulphuric add 175 Hydric sulphate . . . .175 Questions on hydric sulphate 179 Hydric sulphide . . . .180 Tests for hydric sulphide . 182 Questions on hydric sulphide 188 Carbonic sulphide . • •184

OONTEKTB.

Chapter XXIV.

PAGE

FhoBphoros 185

Questioiis on phosphorus . 187 Fhosphorio a<oid . . . .187

Questions on phosphorioaoicl 188 Trihjdrio phosphibte . . 189 Tests for phosphates . . 191 Questions on izihjdric phosphate . ... . .193

Phosphorous add . . .193 Hydno phosphite .... 194

Questions on phosphorous

add 194

Hydric phosphide . . .195 Questions on hydric phos-

OhapteeXXY,

PAGE

Boradc acid 196

Tests for borates .... 197 Questions 198

Chaptee XXVI.

SiUcon 199

SiHdc add 200

Difiadon of liquids . . . 201

Silidc chloride .... 202

Glass 202

Tests for silica .... 204

Questions 205

PAET II.

Chaptee I.

Combination by weight . . 206 Equivalent definition of . 208

Chaptee II.

Atomic theory 209

Valency 210

IColecules 211

Table of atomic weights . 212

Chapter III.

Symbols 214

Formuln for reactions . .215

Nitrogen 218

Water 218

Chapter IV.

Carbonic acid 219

Carbonic oxide .... 220

Harsh gas 221

defiant g(M 222

Chapter V.

Oxides of nitrogen . . . 223

Nitrous oxide 223

Nitric oxide 228

Nitrous add 226

Nitric peroxide .... 225

Nitnc add 226

Chapter VI.

Water type 228

Chapter VH.

Chlorine . . .

Hypochlorous add Hydric hypochlorite Hydric chlorate .

Chlorous add . .

Chloric oxide . .

Hydric perchlorate Hydric chloride .

Tests for chlorides

CONTENTS.

XT

Bromine . . .

Hydric hypobromite

Hydric bromate .

Hydric bromide .

Hydric iodate

Potassic iodate • Hydric iodide Potassic iodide

Fluorine . . .

Ghafteb VIII.

Sulphnroxis acid . .

Sidphites ....

Sulphnric acid . .

Hydric snlphate . .

Sulphates ....

Hydric hyposulphite .

Hydric sulphide Decomposition of

sulphide .

Gathonic sulphide Si^phur and oxygen

pared ....

Hydric sulphocarbonate

Chapter IX

hydric

PAGB

Fhosphoros ....

Phosphoric acid . .

Trihydric phosphate Hicrocosmic salt . .

Tetrahydric diphosphate Hydric metaphosphate Phosphorous acid Hydric phosphite Hydric phosphide Phosphorous chloride Phosphoric chloi^de •

246 247

247 248

PAGB

Phosphoric oxyohloride . . 255

Chafteb X.

Boracic acid ..... 266 Silicic acid 256

Silicic chloride Silicic fluoride

267 268

Ohaptbb XI.

Changes in ralenoy . . . 260 Molecular formulsB . . .261 Adds, bases, salts . . . 262

Chapter XII.

Specific weights of gases . 265 Specific weights of solids

and liquids . . . , 265 Metrical weights and measures 266

Chapter XIII.

Questions on Part II. . . 270 Answers to some of the questions on Part II. 277

Chapteb XIV.

Advice to candidates under examination . .

Chapter XV.

London Uniyersity examination papers. Matriculation 288

Answers to calcxdations in matriculation examination papers .... 296

MODEEN CHEMISTEY.

Chapter I

Clieniistry treats of the changes which take place when one substance acts upon another so as to form new bodies, having different properties from either of the substances employed. In order that substances may act chemically on one another, the particles of which they are composed must come into, what is ordinarily called, actual contact. Sometimes two solid bodies may be mixed together in a mortar, as, for instance, sodic carbonate, commonly called soda, or carbonate of soda, and hydric tartrate, commonly called tartaric acid, and if both be dry no action takes place ; but if water be added, effervescence occurs, bubbles are formed, and a gas escapes, and a new substance is left behind, which is altogether different from either hydric tartrate or sodic carbonate. If these substances have been mixed in proper proportions, the gas which escapes is carbonic acid, and the substance which remains dissolved in the water is sodic tartrate. Here the water has brought into close contact the particles of the two substances. Again, if fine copper filings be mixed with finely-powdered brimstone — the chemical name is sulphur — there will be a mixture of copper and sulphur, small

2 MECHANICAL MIXTURE, CHEMICAL COMPOUND.

pieces of red copper with small pieces of yellow sulphur, and the sulphur and copper can be completely separated from one another : but if they be heated together, a new substance is formed, of a black colour ; no copper remains as such, if the heat has been applied long enough ; the heat has melted the sulphur and has brought the particles of sulphur and copper into close contact, and chemical action has taken place, and cupric sulphide has been made. You will be expected to know the difference between a mechanical mixture and a chemical compound, and this is a good illustration of it ; when the copper and sulphur were first mixed, and until heat was applied, the mixture was called a mechanical mixture; but after the action of heat it became a chemical compound. In like manner the sodic car« bonate and hydric tartrate, as long as they were kept dry, formed a mechanical mixture, but when water had been added, chemical action took place, and new chemical compounds were formed. We will take one more illustration. If sodic carbonate be mixed with sand, no change takes place, and the sodic carbonate can be washed away entirely from the sand ; but if they be heated together, carbonic acid escapes and a kind of glass is formed. This is a chemical compound quite different from sand or sodic carbonate.

Simple bodies which are believed to consist of only one substance are called elements, such as iron, silver, gold, charcoal, sulphur, &c.

Compound bodies are made up of two or more elements chemically combined, as cupric sulphide.

Some substances are more dense than others ; that is, their particles are heavier. For instance, take two

DENSITIES OF GASES. 6

marbles of exactly the same size, one of clay, the other of stone or marble ; that of stone or marble is the heavier of the two, that is, it is more dense. If quicksilver be poured into water it sinks to the bottom, because it is more dense than water; and oil floats on the surface of water, because it is less dense than water.

Again, some gases are more dense than others Common air is a mixture of two gases. And the gas (coal gas) which we bum is also a mixture of gases ; but this gas is lighter than air, as is proved by the fact that a balloon filled with coal gas will rise in the air. If you take two thin india-rubber air-balls of equal size, and fill one with air and the other with coal gas, that filled with air will fall to the floor, while that filled with coal gas will go up to the ceiling. In equal measures of coal gas and air, the coal gas is lighter than the air. There are other gases besides those we have mentioned which are heavier than air. Now it is necessary that we should be able to compare the densities of different bodies, and in order to do this we take one body as a standard, and then find out how much heavier other bodies are than it is : we take water as the standard for solids and liquids.

Thus, if we weigh a measure of water and then weigh a measure of iron of exactly the same size, we shall find that the iron is nearly eight times as heavy au the water. We shall not, however, consider the relative weights of solids and liquids here, as it belongs to what is usually considered another branch of the subject ; but we shall have to consider the densities of gases and vapours, and to do so properly, we must at the commencement settle upon a definite standard of

4 DENSITIES OF GASES.

weight and measure. We shall take the lightest gas known, viz. hydrogen, as our standard of reference, and with it we shall compare all other gases and vapours. The quantity by weight of this gas which we shall take as our standard will be one gramme, and the quantity by measure will be eleven decimal two litres — and the reason why this weight and this measure are taken is, because that quantity which will fill a measure containing 11.2 litres, weighs 1 gramme at the temperature of melting ice, that is zero on the Centigrade scale, and under the pressure of a column of mercury 760 millimeti'es high, and this is called the standard temperature and pressure.

The gases and vapours must always be weighed at the same temperature, because heat causes gases to expand, as may be clearly seen if a bladder about two-thirds full of air be warmed before a fire ; before warming, the bladder, not being full of air, is loose, but when it is warmed the air expands and fills it, and the bladder becomes quite tight. The air has been made by the heat to fill a larger space, but its weight is the same as it was before heating. If therefore we were to let off half the air in the bladder, when heated, into a vessel and measure it, keeping it all the time at the same temperature, and if we were to allow it to cool down, we should find that it would, when cool, occupy a smaller space ; and it would therefore weigh less than it did at the original temperature.

When gases are compressed they occupy a smaller space than they did before ; thus, in the air-gun, air is pumped into a metal ball, and prevented from escaping by a stopcock — when the stopcock is turned the air

DENSITIES OF OASES.

rushes out violently, and the air pumped into the small metal ball would, if allowed to escape into a vessel where it could be measured, measure very much more than it did when in the ball.

Now the atmosphere which surrounds the earth extends to about 44 miles above its surface, and, consequently, the air near the earth, being pressed upon by the air above it, is more dense than the air higher up, which has less air above it — so that a pint of air on the surface of the earth weighs heavier than a pint of air on the top of a high mountain. Suppose a column of air 1 inch square and 44 miles high, that is as high as the air extends from the earth in an upward direction, could be separated out from the atmosphere and weighed, it would weigh about 15 lbs. Therefore it presses on a piece of the earth's surface of 1 inch square with a pressure of 15 lbs. If we take a glass tube about a yard long and with an area equal to 1 square inch, and seal up one of its ends, and, after filling it with mercury, place it with its open end in a vessel containing mercury, the mercury in the tube will fall till the top of the column in the tube is 30 inches above the surface of the mercury in the vessel — and this is because a column of air 44 miles high and 1 inch square is pressing upon the lower end of the column of mercury, and as long as the column of mercury weighs as much as the column of air, the air can support it in the tube. Now this column of mercury 30 inches high is found to weigh 15 lbs. — and therefore we know that the pressure of the column of air is 15 lbs. If any circumstances cause the column of air to be lighter than 15 lbs,, then the column of b METHOD OF WEIGHING GASES.

mercury will be less than 30 inches ; and if the colnmn of air is brought to weigh more than 15 lbs. then the column of mercury in the tube will be longer than 30 inches. Now such circumstances do occur, and therefore the air is more dense at one time than at another. (This we know from the barometer ; sometimes the mercury in it stands high, and then the air is dense ; sometimes it stands low, and this shows that the air is light.) And therefore gases which are pressed upon by the air will be more dense when the air which presses on them is heavier or more dense ; and if a gas is more dense at one time than another, the same measure of it will weigh heavier. We see, therefore, that it is necessary to measure gases under the same pressure.

A simple method of weighing gases is to get two glass globes of equal capacity, and of as nearly equal external dimensions as possible. These globes should be supplied with stopcocks. Both should be exhausted of air by the air-pump, and should be made to weigh exactly the same weight in a very delicate balance. One of these globes should be removed from the balance and be filled with hydrogen and weighed, and its weight noted carefully. It should then be emptied, exhausted, and filled with, say, oxygen, and weighed again ; this time it will be found to weigh 16 times as much as it did before, and in this way the relation between the density of any gas and hydrogen can be obtained, or that existing between the densities of any two gases.

The temperature at which gases are measured is zero Centigrade. There are three kinds of thermo-

THEBHOMETEBB^ COMPARISON OF SCALES. 7

meters by which the temperature is measured, — Fahrenheit, which is used in this country, Centigrade, and Reaumur, which are used on the continent. The Centigrade thermometer is almost invariably employed in scientific experiments, and is generally quoted in scientific works ; we shall therefore use it in this book. All thermometers are marked with divisions which are called degrees. In a Fahrenheit thermometer the point called freezing-point is at 32°, and a point 32° below this is called zero. The freezing-point in a Centigrade thermometer is called zero ; the zero of Centigrade, therefore, corresponds with 32° of Fahrenheit. In a Fahrenheit thermometer the boiling-point is 212°, but in the Centigrade it is 100°. Now, between the freezing-point in Fahrenheit and the boiling-point there are 180 degrees, because there are 212 degrees from the zero, and this is 32 degrees below the freezing-point, and 32 subtracted from 212 give 180. In Centigrade the number of degrees between the freezing and boiling points is 100, therefore, in the two thermometers the same space is divided into 180 and 100 parts respectively, consequently a degree Centigrade is larger than a degree Fahrenheit, in the proportion of 180 to 100, or 9 to 5. We can find out to what degree Centigrade any given degree of Fahrenheit corresponds if we firs't subtract from it 32, because the zero of Fahrenheit is 32 degrees below the freezing-point, and then multiply the remainder by 5 and divide by 9.