The two rival theories of evaporation, that of _chemical solution_

and that of _independent vapor_, were, in various forms, advocated

by the next generation of philosophers. De Saussure may be

considered as the leader on one side, and De Luc on the other. The

former maintained the solution theory, with some modifications of

his own. De {168} Luc denied all solution, and held vapor to be a

combination of the particles of water with fire, by which they

became lighter than air. According to him, there is always fire

enough present to produce this combination, so that evaporation goes

on at all temperatures.

This mode of considering independent vapor as a combination of fire

with water, led the attention of those who adopted that opinion to

the thermometrical changes which take place when vapor is formed and

condensed. These changes are important, and their laws curious. The

laws belong to the induction of latent heat, of which we have just

spoken; but a knowledge of them is not absolutely necessary in order

to enable us to understand the manner in which steam exists in air.

De Luc's views led him[46\10] also to the consideration of the

effect of pressure on vapor. He explains the fact that pressure will

condense vapor, by supposing that it brings the particles within the

distance at which the repulsion arising from fire ceases. In this

way, he also explains the fact, that though external pressure does

thus condense steam, the mixture of a body of air, by which the

pressure is equally increased, will not produce the same effect; and

therefore, vapors can exist in the atmosphere. They make no fixed

proportion of it; but at the same temperature we have the same

pressure arising _from them_, whether they are in air or not. As the

heat increases, vapor becomes capable of supporting a greater and

greater pressure, and at the boiling heat, it can support the

pressure of the atmosphere.

[Note 46\10: Fischer, vol. vii. p. 453. _Nouvelles Idées sur la

Météorologie_, 1787.]

De Luc also marked very precisely (as Wallerius had done) the

difference between vapor and air; the former being capable of change

of _consistence_ by cold or pressure, the latter not so. Pictet, in

1786, made a hygrometrical experiment, which appeared to him to

confirm De Luc's views; and De Luc, in 1792, published a concluding

essay on the subject in the _Philosophical Transactions_. Pictet's

_Essay on Fire_, in 1791, also demonstrated that "all the train of

hygrometrical phenomena takes place just as well, indeed rather

quicker, in a vacuum than in air, provided the same quantity of

moisture is present." This essay, and De Luc's paper, gave the

death-blow to the theory of the solution of water in air.

Yet this theory did not fall without an obstinate struggle. It was

taken up by the new school of French chemists, and connected with

their views of heat. Indeed, it long appears as the prevalent

opinion. {169} Girtanner,[47\10] in his _Grounds of the

Antiphlogistic Theory_, may be considered as one of the principal

expounders of this view of the matter. Hube, of Warsaw, was,

however, the strongest of the defenders of the theory of solution,

and published upon it repeatedly about 1790. Yet he appears to have

been somewhat embarrassed with the increase of the air's elasticity

by vapor. Parrot, in 1801, proposed another theory, maintaining that

De Luc had by no means successfully attacked that of solution, but

only De Saussure's superfluous additions to it.

[Note 47\10: Fischer, vol. vii. 473.]

It is difficult to see what prevented the general reception of the

doctrine of independent vapor; since it explained all the facts very

simply, and the agency of air was shown over and over again to be

unnecessary. Yet, even now, the solution of water in air is hardly

exploded. M. Gay Lussac,[48\10] in 1800, talks of the quantity of

water "held in solution" by the air; which, he says, varies

according to its temperature and density by a law which has not yet

been discovered. And Professor Robison, in the article "Steam," in

the _Encyclopædia Britannica_ (published about 1800), says,[49\10]

"Many philosophers imagine that spontaneous evaporation, at low

temperatures, is produced in this way (by elasticity alone). But we

cannot be of this opinion; and must still think that this kind of

evaporation is produced by the dissolving power of the air." He then

gives some reasons for his opinion. "When moist air is suddenly

rarefied, there is always a precipitation of water. But by this new

doctrine the very contrary should happen, because the tendency of

water to appear in the elastic form is promoted by removing the

external pressure." Another main difficulty in the way of the

doctrine of the mere mixture of vapor and air was supposed to be

this; that if they were so mixed, the heavier fluid would take the

lower part, and the lighter the higher part, of the space which they

occupied.

[Note 48\10: _Ann. Chim._ tom. xliii.]

[Note 49\10: Robison's _Works_, ii. 37.]

The former of these arguments was repelled by the consideration that

in the rarefaction of air, its specific heat is changed, and thus

its temperature reduced below the constituent temperature of the

vapor which it contains. The latter argument is answered by a

reference to Dalton's law of the mixture of gases. We must consider

the establishment of this doctrine in a new section, as the most

material step to the true notion of evaporation. {170}

_Sect._ 3.--_Dalton's Doctrine of Evaporation._

A PORTION of that which appears to be the true notion of evaporation

was known, with greater or less distinctness, to several of the

physical philosophers of whom we have spoken. They were aware that

the vapor which exists in air, in an invisible state, may be

condensed into water by cold: and they had noticed that, in any

state of the atmosphere, there is a certain temperature lower than

that of the atmosphere, to which, if we depress bodies, water forms

upon them in fine drops like dew; this temperature is thence called

the _dew-point_. The vapor of water which exists anywhere may be

reduced below the degree of heat which is necessary to constitute it

vapor, and thus it ceases to be vapor. Hence this temperature is

also called the _constituent temperature_. This was generally known

to the meteorological speculators of the last century, although, in

England, attention was principally called to it by Dr. Wells's

_Essay on Dew_, in 1814. This doctrine readily explains how the cold

produced by rarefaction of air, descending below the constituent

temperature of the contained vapor, may precipitate a dew; and thus,

as we have said, refutes one obvious objection to the theory of

independent vapor.

The other difficulty was first fully removed by Mr. Dalton. When his

attention was drawn to the subject of vapor, he saw insurmountable

objections to the doctrine of a chemical union of water and air. In

fact, this doctrine was a mere nominal explanation; for, on closer

examination, no chemical analogies supported it. After some

reflection, and in the sequel of other generalizations concerning

gases, he was led to the persuasion, that when air and steam are

mixed together, each follows its separate laws of equilibrium, the

particles of each being elastic with regard to those of their own

kind only: so that steam may be conceived as flowing among the

particles of air[50\10] "like a stream of water among pebbles;" and

the resistance which air offers to evaporation arises, not from its

weight, but from the inertia of its particles.

[Note 50\10: _Manchester Memoirs_, vol. v. p. 581.]

It will be found that the theory of independent vapor, understood

with these conditions, will include all the facts of the

case;--gradual evaporation in air; sudden evaporation in a vacuum;

the increase of {171} the air's elasticity by vapor; condensation by

its various causes; and other phenomena.

But Mr. Dalton also made experiments to prove his fundamental

principle, that if two different gases communicate, they will

diffuse themselves through each other;[51\10]--slowly, if the

opening of communication be small. He observes also, that all the

gases had equal solvent powers for vapor, which could hardly have

happened, had chemical affinity been concerned. Nor does the density

of the air make any difference.

[Note 51\10: _New System of Chemical Philosophy_, vol. i. p. 151.]

Taking all these circumstances into the account, Mr. Dalton

abandoned the idea of solution. "In the autumn of 1801," he says, "I

hit upon an idea which seemed to be exactly calculated to explain

the phenomena of vapor: it gave rise to a great variety of

experiments," which ended in fixing it in his mind as a true idea.

"But," he adds, "the theory was almost universally misunderstood,

and consequently reprobated."

Mr. Dalton answers various objections. Berthollet had urged that we

can hardly conceive the particles of an elastic substance added to

those of another, without increasing its elasticity. To this Mr.

Dalton replies by adducing the instance of magnets, which repel each

other, but do not repel other bodies. One of the most curious and

ingenious objections is that of M. Gough, who argues, that if each

gas is elastic with regard to itself alone, we should hear, produced

by one stroke, four sounds; namely, _first_, the sound through

aqueous vapor; _second_, the sound through azotic gas; _third_, the

sound through oxygen gas; _fourth_, the sound through carbonic acid.

Mr. Dalton's answer is, that the difference of time at which these

sounds would come is very small; and that, in fact, we do hear,

sounds double and treble.

In his _New System of Chemical Philosophy_, Mr. Dalton considers the

objections of his opponents with singular candor and impartiality.

He there appears disposed to abandon that part of the theory which

negatives the mutual repulsion of the particles of the two gases,

and to attribute their diffusion through one another to the

different size of the particles, which would, he thinks,[52\10]

produce the same effect.

[Note 52\10: _New System_, vol. i. p. 188.]

In selecting, as of permanent importance, the really valuable part

of this theory, we must endeavor to leave out all that is doubtful

or unproved. I believe it will be found that in all theories

hitherto {172} promulgated, all assertions respecting the properties

of the particles of bodies, their sizes, distances, attractions, and

the like, are insecure and superfluous. Passing over, then, such

hypotheses, the inductions which remain are these;--that two gases

which are in communication will, by the elasticity of each, diffuse

themselves in one another, quickly or slowly; and--that the quantity

of steam contained in a certain space of air is the same, whatever

be the air, whatever be its density, and even if there be a vacuum.

These propositions may be included together by saying, that one gas

is _mechanically mixed_ with another; and we cannot but assent to

what Mr. Dalton says of the latter fact,--"this is certainly the

touchstone of the mechanical and chemical theories." This _doctrine

of the mechanical mixture of gases_ appears to supply answers to all

the difficulties opposed to it by Berthollet and others, as Mr.

Dalton has shown;[53\10] and we may, therefore, accept it as well

established.

[Note 53\10: _New System_, vol. i. p. 160, &c.]

This doctrine, along with the _principle of the constituent

temperature of steam_, is applicable to a large series of

meteorological and other consequences. But before considering the

applications of theory to natural phenomena, which have been made,

it will be proper to speak of researches which were carried on, in a

great measure, in consequence of the use of steam in the arts: I

mean the laws which connect its elastic force with its constituent

temperature.

_Sect._ 4.--_Determination of the Laws of the Elastic Force of

Steam._

THE expansion of aqueous vapor at different temperatures is

governed, like that of all other vapors, by the law of Dalton and

Gay-Lussac, already mentioned; and from this, its elasticity, when

its expansion is resisted, will be known by the law of Boyle and

Mariotte; namely, by the rule that the pressure of airy fluids is as

the condensation. But it is to be observed, that this process of

calculation goes on the supposition that the steam is cut off from

contact with water, so that no more steam can be generated; a case

quite different from the common one, in which the steam is more

abundant as the heat is greater. The examination of the force of

vapor, when it is in contact with water, must be briefly noticed.

During the period of which we have been speaking, the progress of

the investigation of the laws of aqueous vapor was much accelerated

{173} by the growing importance of the steam-engine, in which those

laws operated in a practical form. James Watts, the main improver of

that machine, was thus a great contributor to speculative knowledge,

as well as to practical power. Many of his improvements depended on

the laws which regulate the quantity of heat which goes to the

formation or condensation of steam; and the observations which led

to these improvements enter into the induction of latent heat.

Measurements of the force of steam, at all temperatures, were made

with the same view. Watts's attention had been drawn to the

steam-engine in 1759, by Robison, the former being then an

instrument-maker, and the latter a student at the University of

Glasgow.[54\10] In 1761 or 1762, he tried some experiments on the

force of steam in a Papin's Digester;[55\10] and formed a sort of

working model of a steam-engine, feeling already his vocation to

develope the powers of that invention. His knowledge was at that

time principally derived from Desaguliers and Belidor, but his own

experiments added to it rapidly. In 1764 and 1765, he made a more

systematical course of experiments, directed to ascertain the force

of steam. He tried this force, however, only at temperatures above

the boiling-point; and inferred it at lower degrees from the

supposed continuity of the law thus obtained. His friend Robison,

also, was soon after led, by reading the account of some experiments

of Lord Charles Cavendish, and some others of Mr. Nairne, to examine

the same subject. He made out a table of the correspondence of the

elasticity and the temperature of vapor, from thirty-two to two

hundred and eighty degrees of Fahrenheit's thermometer.[56\10] The

thing here to be remarked, is the establishment of a law of the

pressure of steam, down to the freezing-point of water. Ziegler of

Basle, in 1769, and Achard of Berlin, in 1782, made similar

experiments. The latter examined also the elasticity of the vapor of

alcohol. Betancourt, in 1792, published his Memoir on the expansive

force of vapors; and his tables were for some time considered the

most exact. {174} Prony, in his _Architecture Hydraulique_ (1796),

established a mathematical formula,[57\10] on the experiments of

Betancourt, who began his researches in the belief that he was first

in the field, although he afterwards found that he had been

anticipated by Ziegler. Gren compared the experiments of Betancourt

and De Luc with his own. He ascertained an important fact, that when

water _boils_, the elasticity of the steam is equal to that of the

atmosphere. Schmidt at Giessen endeavored to improve the apparatus

used by Betancourt; and Biker, of Rotterdam, in 1800, made new

trials for the same purpose.

[Note 54\10: Robison's _Works_, vol. ii. p. 113.]

[Note 55\10: Denis Papin, who made many of Boyle's experiments for

him, had discovered that if the vapor be prevented from rising, the

water becomes hotter than the usual boiling-point; and had hence

invented the instrument called _Papin's Digester_. It is described

in his book, _La manière d'amolir les os et de faire cuire toutes

sorts de viandes en fort peu de temps et à peu de frais_. Paris,

1682.]

[Note 56\10: These were afterwards published in the _Encyclopædia

Britannica_; in the article "Steam," written by Robison.]

[Note 57\10: _Architecture Hydraulique_, Seconde Partie, p. 163.]

In 1801, Mr. Dalton communicated to the Philosophical Society of

Manchester his investigations on this subject; observing truly, that

though the forces at high temperatures are most important when steam

is considered as a mechanical agent, the progress of philosophy is

more immediately interested in accurate observations on the force at

low temperatures. He also found that his elasticities for

equidistant temperatures resembled a _geometrical progression_, but

with a ratio constantly diminishing. Dr. Ure, in 1818, published in

the _Philosophical Transactions_ of London, experiments of the same

kind, valuable from the high temperatures at which they were made,

and for the simplicity of his apparatus. The law which he thus

obtained approached, like Dalton's, to a _geometrical progression_.

Dr. Ure says, that a formula proposed by M. Biot gives an error of

near nine inches out of seventy-five, at a temperature of 266

degrees. This is very conceivable, for if the formula be wrong at

all, the geometrical progress rapidly inflames the error in the

higher portions of the scale. The elasticity of steam, at high

temperatures, has also been experimentally examined by Mr. Southern,

of Soho, and Mr. Sharpe, of Manchester. Mr. Dalton has attempted to

deduce certain general laws from Mr. Sharpe's experiments; and other

persons have offered other rules, as those which govern the force of

steam with reference to the temperature: but no rule appears yet to

have assumed the character of an established scientific truth. Yet

the law of the expansive force of steam is not only required in

order that the steam-engine may be employed with safety and to the

best advantage; but must also be an important point in every

consistent thermotical theory.

[2nd Ed.] [To the experiments on steam made by private physicists,

are to be added the experiments made on a grand scale by order of

the governments of France and of America, with a view to {175}

legislation on the subject of steam-engines. The French experiments

were made in 1823, under the direction of a commission consisting of

some of the most distinguished members of the Academy of Sciences;

namely, MM. de Prony, Arago, Girard, and Dulong. The American

experiments were placed in the hands of a committee of the Franklin

Institute of the State of Pennsylvania, consisting of Prof. Bache

and others, in 1830. The French experiments went as high as 435° of

Fahrenheit's thermometer, corresponding to a pressure of 60 feet of

mercury, or 24 atmospheres. The American experiments were made up to

a temperature of 346°, which corresponded to 274 inches of mercury,

more than 9 atmospheres. The extensive range of these experiments

affords great advantages for determining the law of the expansive

force. The French Academy found that their experiments indicated an

increase of the elastic force according to the _fifth_ power of a

binominal 1 + _mt_, where _t_ is the temperature. The American

Institute were led to a _sixth_ power of a like binominal. Other

experimenters have expressed their results, not by powers of the

temperature, but by geometrical ratios. Dr. Dalton had supposed that

the expansion of mercury being as the square of the true temperature

above its freezing-point, the expansive force of steam increases in

geometrical ratio for equal increments of temperature. And the

author of the article _Steam_ in the Seventh Edition of the

_Encyclopædia Britannica_ (Mr. J. S. Russell), has found that the

experiments are best satisfied by supposing mercury, as well as

steam, to expand in a geometrical ratio for equal increments of the

true temperature.

It appears by such calculation, that while dry gas increases in the

ratio of 8 to 11, by an increase of temperature from freezing to

boiling water; steam in contact with water, by the same increase of

temperature above boiling water, has its expansive force increased

in the proportion of 1 to 12. By an equal increase of temperature,

mercury expands in about the ratio of 8 to 9.

Recently, MM. Magnus of Berlin, Holzmann and Regnault, have made

series of observations on the relation between temperature and

elasticity of steam.[58\10]

[Note 58\10: See Taylor's _Scientific Memoirs_, Aug. 1845, vol. iv.

part xiv., and _Ann. de Chimie_.]

Prof. Magnus measured his temperatures by an air-thermometer; a

process which, I stated in the first edition, seemed to afford the

best promise of simplifying the law of expansion. His result is,

that the {176} elasticity proceeds in a geometric series when the

temperature proceeds in an arithmetical series nearly; the

differences of temperature for equal augmentations of the ratio of

elasticity being somewhat greater for the higher temperatures.

The forces of the vapors of other liquids in contact with their

liquids, determined by Dr. Faraday, as mentioned in Chap. ii. Sect.

1, are analogous to the elasticity of steam here spoken of.]

_Sect._ 5.--_Consequences of the Doctrine of

Evaporation.--Explanation of Rain, Dew, and Clouds._

THE discoveries concerning the relations of heat and moisture which

were made during the last century, were principally suggested by

meteorological inquiries, and were applied to meteorology as fast as

they rose. Still there remains, on many points of this subject, so

much doubt and obscurity, that we cannot suppose the doctrines to

have assumed their final form; and therefore we are not here called

upon to trace their progress and connexion. The principles of

atmology are pretty well understood; but the difficulty of observing

the conditions under which they produce their effects in the

atmosphere is so great, that the precise theory of most

meteorological phenomena is still to be determined.

We have already considered the answers given to the question:

According to what rules does transparent aqueous vapor resume its

form of visible water? This question includes, not only the problems

of Rain and Dew, but also of Clouds; for clouds are not vapor, but

water, vapor being always invisible. An opinion which attracted much

notice in its time, was that of Hutton, who, in 1784, endeavored to

prove that if two masses of air saturated with transparent vapor at

different temperatures are mixed together, the precipitation of

water in the form either of cloud or of drops will take place. The

reason he assigned for the opinion was this: that the temperature of

the mixture is a mean between the two temperatures, but that the

force of the vapor in the mixture, which is the mean of the forces

of the two component vapors, will be greater than that which

corresponds to the mean temperature, since the force increases

faster than the temperature;[59\10] and hence some part of the vapor

will be precipitated. This doctrine, it will be seen, speaks of

vapor as "saturating" air, and is {177} therefore, in this form,

inconsistent with Dalton's principle; but it is not difficult to

modify the expression so as to retain the essential part of the

explanation.

[Note 59\10: _Edin. Trans._ vol. 1. p. 42.]

_Dew._--The principle of a "constituent temperature" of steam, and

the explanation of the "dew-point," were known, as we have said

(chap. iii. sect. 3,) to the meteorologists of the last century; but

we perceive how incomplete their knowledge was, by the very gradual

manner in which the consequences of this principle were traced out.

We have already noticed, as one of the books which most drew

attention to the true doctrine, in this country at least, Dr.

Wells's _Essay on Dew_, published in 1814. In this work the author

gives an account of the progress of his opinions;[60\10] "I was

led," he says, "in the autumn of 1784, by the event of a rude

experiment, to think it probable that the formation of dew is

attended with the production of cold." This was confirmed by the

experiments of others. But some years after, "upon considering the

subject more closely, I began to suspect that Mr. Wilson, Mr. Six,

and myself, had all committed an error in regarding the cold which

accompanies the dew, as an _effect_ of the formation of the dew." He

now considered it rather as the _cause_: and soon found that he was

able to account for the circumstances of this formation, many of

them curious and paradoxical, by supposing the bodies on which dew

is deposited, to be cooled down, by radiation into the clear

night-sky, to the proper temperature. The same principle will

obviously explain the formation of mists over streams and lakes when

the air is cooler than the water; which was put forward by Davy,

even in 1810, as a new doctrine, or at least not familiar.

[Note 60\10: _Essay on Dew_, p. 1.]

_Hygrometers._--According as air has more or less of vapor in

comparison with that which its temperature and pressure enable it to

contain, it is more or less humid; and an instrument which measures

the degrees of such a gradation is a _hygrometer_. The hygrometers

which were at first invented, were those which measured the moisture

by its effect in producing expansion or contraction in certain

organic substances; thus De Saussure devised a hair-hygrometer, De

Luc a whalebone-hygrometer, and Dalton used a piece of whipcord. All

these contrivances were variable in the amount of their indications

under the same circumstances; and, moreover, it was not easy to know

the physical meaning of the degree indicated. The dew-point, or

constituent temperature of the vapor which exists in the air, is, on

{178} the other hand, both constant and definite. The determination

of this point, as a datum for the moisture of the atmosphere, was

employed by Le Roi, and by Dalton (1802), the condensation being

obtained by cold water:[61\10] and finally, Mr. Daniell (1812)

constructed an instrument, where the condensing temperature was

produced by evaporation of ether, in a very convenient manner. This

invention (_Daniell's Hygrometer_) enables us to determine the

quantity of vapor which exists in a given mass of the atmosphere at

any time of observation.

[Note 61\10: Daniell, _Met. Ess._ p. 142. _Manch. Mem._ vol. v.

p. 581.]

[2nd Ed.] [As a happy application of the Atmological Laws which have

been discovered, I may mention the completion of the theory and use

of the _Wet-bulb Hygrometer_; an instrument in which, from the

depression of temperature produced by wetting the bulb of a

thermometer, we infer the further depression which would produce

dew. Of this instrument the history is thus summed up by Prof.

Forbes:--"Hutton invented the method; Leslie revived and extended

it, giving probably the earliest, though an imperfect theory;

Gay-Lussac, by his excellent experiments and reasoning from them,

completed the theory, so far as perfectly dry air is concerned;

Ivory extended the theory; which was reduced to practice by Auguste

and Bohnenberger, who determined the constant with accuracy. English

observers have done little more than confirm the conclusions of our

industrious Germanic neighbors; nevertheless the experiments of

Apjohn and Prinsep must ever be considered as conclusively settling

the value of the coefficient near the one extremity of the scale, as

those of Kæmtz have done for the other."[62\10]

[Note 62\10: _Second Report on Meteorology_, p. 101.]

Prof. Forbes's two Reports _On the Recent Progress and Present State

of Meteorology_ given among the _Reports of the British Association_

for 1832 and 1840, contain a complete and luminous account of recent

researches on this subject. It may perhaps be asked why I have not

given Meteorology a place among the Inductive Sciences; but if the

reader refers to these accounts, or any other adequate view of the

subject, he will see that Meteorology is not a single Inductive

Science, but the application of several sciences to the explanation

of terrestrial and atmospheric phenomena. Of the sciences so

applied, Thermotics and Atmology are the principal ones. But others

also come into play; as Optics, in the explanation of Rainbows,

Halos, {179} Parhelia, Coronæ, Glories, and the like; Electricity,

in the explanation of Thunder and Lightning, Hail, Aurora Borealis;

to which others might be added.]

_Clouds._--When vapor becomes visible by being cooled below its

constituent temperature, it forms itself into a very fine watery

powder, the diameter of the particles of which this powder consists

being very small: they are estimated by various writers, from

1⁄100,000th to 1⁄20,000th of an inch.[63\10] Such particles, even if

solid, would descend very slowly; and very slight causes would

suffice for their suspension, without recurring to the hypothesis of

vesicles, of which we have already spoken. Indeed that hypothesis

will not explain the fact, except we suppose these vesicles filled

with a rarer air than that of the atmosphere; and, accordingly,

though this hypothesis is still maintained by some,[64\10] it is

asserted as a fact of observation, proved by optical or other

phenomena, and not deduced from the suspension of clouds. Yet the

latter result is still variously explained by different

philosophers: thus, M. Gay-Lussac[65\10] accounts for it by upward

currents of air, and Fresnel explains it by the heat and rarefaction

of air in the interior of the cloud.

[Note 63\10: Kæmtz, _Met._ i. 393.]

[Note 64\10: Ib. i. 393. Robison, ii. 13.]

[Note 65\10: _Ann. Chim._ xxv. 1822.]

_Classification of Clouds._--A classification of clouds can then

only be consistent and intelligible when it rests upon their

atmological conditions. Such a system was proposed by Mr. Luke

Howard, in 1802-3. His primary modifications are, _Cirrus_,

_Cumulus_, and _Stratus_, which the Germans have translated by terms

equivalent in English to _feather-cloud_, _heap-cloud_, and

_layer-cloud_. The cumulus increases by accumulations on its top,

and floats in the air with a horizontal base; the stratus grows from

below, and spreads along the earth; the cirrus consists of fibres in

the higher regions of the atmosphere, which grow every way. Between

the simple modifications are intermediate ones, _cirro-cumulus_ and

_cirro-stratus_; and, again, compound ones, the _cumulo-stratus_ and

the _nimbus_, or _rain-cloud_. These distinctions have been

generally accepted all over Europe: and have rendered a description

of all the processes which go on in the atmosphere far more definite

and clear than it could be made before their use.

I omit a mass of facts and opinions, supposed laws of phenomena and

assigned causes, which abound in meteorology more than in any other

science. The slightest consideration will show us what a great {180}

amount of labor, of persevering and combined observation, the

progress of this branch of knowledge requires. I do not even speak

of the condition of the more elevated parts of the atmosphere. The

diminution of temperature as we ascend, one of the most marked of

atmospheric facts, has been variously explained by different

writers. Thus Dalton[66\10] (1808) refers it to a principle "that

each atom of air, in the same perpendicular column, is possessed of

the same degree of heat," which principle he conceives to be

entirely empirical in this case. Fourier says[67\10] (1817), "This

phenomenon results from several causes: one of the principal is the

progressive extinction of the rays of heat in the successive strata

of the atmosphere."

[Note 66\10: _New Syst. of Chem._ vol. i. p. 125.]

[Note 67\10: _Ann. Chim._ vi. 285.]

Leaving, therefore, the application of thermotical and atmological

principles in particular cases, let us consider for a moment the

general views to which they have led philosophers.

CHAPTER IV.

PHYSICAL THEORIES OF HEAT.

WHEN we look at the condition of that branch of knowledge which,

according to the phraseology already employed, we must call _Physical

Thermotics_, in opposition to Formal Thermotics, which gives us

detached laws of phenomena, we find the prospect very different from

that which was presented to us by physical astronomy, optics, and

acoustics. In these sciences, the maintainers of a distinct and

comprehensive theory have professed at least to show that it

explains and includes the principal laws of phenomena of various

kinds; in Thermotics, we have only attempts to explain a part of the

facts. We have here no example of an hypothesis which, assumed in

order to explain one class of phenomena, has been found also to

account exactly for another; as when central forces led to the

precession of the equinoxes, or when the explanation of polarization

explained also double refraction; or when the pressure of the

atmosphere, as measured by the barometer, gave the true velocity of

sound. Such coincidences, or _consiliences_, as I have elsewhere

called them, are the test of truth; and thermotical theories cannot

yet exhibit credentials of this kind. {181}

On looking back at our view of this science, it will be seen that it

may be distinguished into two parts; the Doctrines of Conduction and

Radiation, which we call Thermotics proper; and the Doctrines

respecting the relation of Heat, Airs, and Moisture, which we have

termed Atmology. These two subjects differ in their bearing on our

hypothetical views.

_Thermotical Theories._--The phenomena of radiant heat, like those

of radiant light, obviously admit of general explanation in two

different ways;--by the emission of material particles, or by the

propagation of undulations. Both these opinions have found

supporters. Probably most persons, in adopting Prevost's theory of

exchanges, conceive the radiation of heat to be the radiation of

matter. The undulation hypothesis, on the other hand, appears to be

suggested by the production of heat by friction, and was accordingly

maintained by Rumford and others. Leslie[68\10] appears, in a great

part of his _Inquiry_, to be a supporter of some undulatory

doctrine, but it is extremely difficult to make out what his

undulating medium is; or rather, his opinions wavered during his

progress. In page 31, he asks, "What is this calorific and

frigorific fluid? and after keeping the reader in suspense for a

moment, he replies,

"Quod petis hic est.

It is merely the ambient AIR." But at page 150, he again asks the

question, and, at page 188, he answers, "It is the same subtile

matter that, according to its different modes of existence,

constitutes either heat or light." A person thus vacillating between

two opinions, one of which is palpably false, and the other laden

with exceeding difficulties which he does not even attempt to

remove, had little right to protest against[69\10] "the sportive

freaks of some intangible _aura_;" to rank all other hypotheses than

his own with the "occult qualities of the schools;" and to class the

"prejudices" of his opponents with the tenets of those who

maintained the _fuga vacui_ in opposition to Torricelli. It is worth

while noticing this kind of rhetoric, in order to observe, that it

may be used just as easily on the wrong side as on the right.

[Note 68\10: _An Experimental Inquiry into the Nature and

Propagation of Heat_, 1804.]

[Note 69\10: Ib. p. 47.]

Till recently, the theory of material heat, and of its propagation

by emission, was probably the one most in favor with those who had

studied mathematical thermotics. As we have said, the laws of {182}

conduction, in their ultimate analytical form, were almost identical

with the laws of motion of fluids. Fourier's principle also, that

the radiation of heat takes place from points below the surface, and

is intercepted by the superficial particles, appears to favor the

notion of material emission.

Accordingly, some of the most eminent modern French mathematicians

have accepted and extended the hypothesis of a material caloric. In

addition to Fourier's doctrine of molecular extra-radiation, Laplace

and Poisson have maintained the hypothesis of _molecular

intra-radiation_, as the mode in which conduction takes place; that

is, they say that the particles of bodies are to be considered as

_discrete_, or as points separated from each other, and acting on

each other at a distance; and the conduction of heat from one part

to another, is performed by radiation between all neighboring

particles. They hold that, without this hypothesis, the differential

equations expressing the conditions of conduction cannot be made

homogeneous: but this assertion rests, I conceive, on an error, as

Fourier has shown, by dispensing with the hypothesis. The necessity

of the hypothesis of discrete molecular action in bodies, is

maintained in all cases by M. Poisson; and he has asserted Laplace's

theory of capillary attraction to be defective on this ground, as

Laplace asserted Fourier's reasoning respecting heat to be so. In

reality, however, this hypothesis of discrete molecules cannot be

maintained as a physical truth; for the law of molecular action,

which is assumed in the reasoning, after answering its purpose in

the progress of calculation, vanishes in the result; the conclusion

is the same, whatever law of the intervals of the molecules be

assumed. The definite integral, which expresses the whole action, no

more proves that this action is actually made of the differential

parts by means of which it was found, than the processes of finding

the weight of a body by integration, prove it to be made up of

differential weights. And therefore, even if we were to adopt the

emission theory of heat, we are by no means bound to take along with

it the hypothesis of discrete molecules.

But the recent discovery of the refraction, polarization, and

depolarization of heat, has quite altered the theoretical aspect of

the subject, and, almost at a single blow, ruined the emission

theory. Since heat is reflected and refracted like light, analogy

would lead us to conclude that the mechanism of the processes is the

same in the two cases. And when we add to these properties the

property of polarization, it is scarcely possible to believe

otherwise than that heat consists in {183} transverse vibrations;

for no wise philosopher would attempt an explanation by ascribing

poles to the emitted particles, after the experience which Optics

affords, of the utter failure of such machinery.

But here the question occurs, If heat consists in vibrations, whence

arises the extraordinary identity of the laws of its propagation

with the laws of the flow of matter? How is it that, in conducted

heat, this vibration creeps slowly from one part of the body to

another, the part first heated remaining hottest; instead of leaving

its first place and travelling rapidly to another, as the vibrations

of sound and light do? The answer to these questions has been put in

a very distinct and plausible form by that distinguished

philosopher, M. Ampère, who published a _Note on Heat and Light

considered as the results of Vibratory Motion_,[70\10] in 1834 and

1835; and though this answer is an hypothesis, it at least shows

that there is no fatal force in the difficulty.

[Note 70\10: _Bibliothèque Universelle de Genève_, vol. xlix. p.

225. _Ann. Chim._ tom. lvii. p. 434.]

M. Ampère's hypothesis is this; that bodies consist of solid

molecules, which may be considered as arranged at intervals in a

very rare ether; and that the vibrations of the molecules, causing

vibrations of the ether and caused by them, constitute heat. On

these suppositions, we should have the phenomena of conduction

explained; for if the molecules at one end of a bar be hot, and

therefore in a state of vibration, while the others are at rest, the

vibrating molecules propagate vibrations in the ether, but these

vibrations do not produce heat, except in proportion as they put the

quiescent molecules of the bar in vibration; and the ether being

very rare compared with the molecules, it is only by the repeated

impulses of many successive vibrations that the nearest quiescent

molecules are made to vibrate; after which they combine in

communicating the vibration to the more remote molecules. "We then

find necessarily," M. Ampère adds, "the same equations as those

found by Fourier for the distribution of heat, setting out from the

same hypothesis, that the temperature or heat transmitted is

proportional to the difference of the temperatures."

Since the undulatory hypothesis of heat can thus answer all obvious

objections, we may consider it as upon its trial, to be confirmed or

modified by future discoveries; and especially by an enlarged

knowledge of the laws of the polarization of heat.

[2nd Ed.] [Since the first edition was written, the analogies

between light and heat have been further extended, as I have already

stated. It {184} has been discovered by MM. Biot and Melloni that

quartz impresses a circular polarization upon heat; and by Prof.

Forbes that mica, of a certain thickness, produces phenomena such as

would be produced by the impression of circular polarization of the

supposed transversal vibrations of radiant heat; and further, a

rhomb of rock-salt, of the shape of the glass rhomb which verified

Fresnel's extraordinary anticipation of the circular polarization of

light, verified the expectation, founded upon other analogies, of

the polarization of heat. By passing polarized heat through various

thicknesses of mica, Prof. Forbes has attempted to calculate the

length of an undulation for heat.

These analogies cannot fail to produce a strong disposition to

believe that light and heat, essences so closely connected that they

can hardly be separated, and thus shown to have so many curious

properties in common, are propagated by the same machinery; and thus

we are led to an Undulatory Theory of Heat.

Yet such a Theory has not yet by any means received full

confirmation. It depends upon the analogy and the connexion of the

Theory of Light, and would have little weight if those were removed.

For the separation of the rays in double refraction, and the

phenomena of periodical intensity, the two classes of facts out of

which the Undulatory Theory of Optics principally grew, have neither

of them been detected in thermotical experiments. Prof. Forbes has

assumed alternations of heat for increasing thicknesses of mica, but

in his experiments we find only one _maximum_. The occurrence of

alternate maxima and minima under the like circumstances would

exhibit visible waves of heat, as the fringes of shadows do of

light, and would thus add much to the evidence of the theory.

Even if I conceived the Undulatory Theory of Heat to be now

established, I should not venture, as yet, to describe its

establishment as an event in the history of the Inductive Sciences.

It is only at an interval of time after such events have taken place

that their history and character can be fully understood, so as to

suggest lessons in the Philosophy of Science.]

_Atmological Theories._--Hypotheses of the relations of heat and air

almost necessarily involve a reference to the forces by which the

composition of bodies is produced, and thus cannot properly be

treated of, till we have surveyed the condition of chemical

knowledge. But we may say a few words on one such hypothesis; I mean

the hypothesis on the subject of the atmological laws of heat,

proposed by Laplace, in the twelfth Book of the _Mécanique Céléste_,

and published in 1823. {185} It will be recollected that the main

laws of phenomena for which we have to account, by means of such an

hypothesis, are the following:--

(1.) The law of Boyle and Mariotte, that the elasticity of an air

varies as its density. See Chap. iii., Sect. 1 of this Book.

(2.) The Law of Gay-Lussac and Dalton, that all airs expand equally

by heat. See Chap. ii. Sect. 1.

(3.) The production of heat by sudden compression. See Chap. ii.

Sect. 2.

(4.) Dalton's principle of the mechanical mixture of airs. See Chap.

iii. Sect. 3.

(5.) The Law of expansion of solids and fluids by heat. See Chap.

ii. Sect. 1.

(6.) Changes of consistence by heat, and the doctrine of latent

heat. See Chap. ii. Sect. 3.

(7.) The Law of the expansive force of steam. See Chap. iii. Sect. 4.

Besides these, there are laws of which it is doubtful whether they

are or are not included in the preceding, as the low temperature of

the air in the higher parts of the atmosphere. (See Chap. iii.

Sect. 5.)

Laplace's hypothesis[71\10] is this:--that bodies consist of

particles, each of which gathers round it, by its attraction, a

quantity of caloric: that the particles of the bodies attract each

other, besides attracting the caloric, and that the particles of the

caloric repel each other.

[Note 71\10: _Méc. Cél._ t. v. p. 89.]

In gases, the particles of the bodies are so far removed, that their

mutual attraction is insensible, and the matter tends to expand by

the mutual repulsion of the caloric. He conceives this caloric to be

constantly radiating among the particles; the density of this

internal radiation is the _temperature_, and he proves that, on this

supposition, the elasticity of the air will be as the density, and

as this temperature. Hence follow the three first rules above

stated. The same suppositions lead to Dalton's principle of mixtures

(4), though without involving his mode of conception; for Laplace

says that whatever the mutual action of two gases be, the whole

pressure will be equal to the sum of the separate pressures.[72\10]

Expansion (5), and the changes of consistence (6), are explained by

supposing[73\10] that in solids, the mutual attraction of the

particles of the body is the greatest force; in liquids, the

attraction of the particles for the caloric; in airs, the repulsion

of {186} the caloric. But the doctrine of latent heat again

modifies[74\10] the hypothesis, and makes it necessary to include

latent heat in the calculation; yet there is not, as we might

suppose there would be if the theory were the true one, any

confirmation of the hypothesis resulting from the new class of laws

thus referred to. Nor does it appear that the hypothesis accounts

for the relation between the elasticity and the temperature of steam.

[Note 72\10: Ib. p. 110.]

[Note 73\10: Ib. p. 92.]

[Note 74\10: _Méc. Cél._ t. v. p. 93.]

It will be observed that Laplace's hypothesis goes entirely upon the

materiality of heat, and is inconsistent with any vibratory theory;

for, as Ampère remarks, "It is clear that if we admit heat to

consist in vibrations, it is a contradiction to attribute to heat

(or caloric) a repulsive force of the particles which would be a

cause of vibration."

An unfavorable judgment of Laplace's Theory of Gases is suggested by

looking for that which, in speaking of Optics, was mentioned as the

great characteristic of a true theory; namely, that the hypotheses,

which were assumed in order to account for one class of facts, are

found to explain another class of a different nature:--the consilience

of inductions. Thus, in thermotics, the law of an intensity of

radiation proportional to the sine of the angle of the ray with the

surface, which is founded on direct experiments of radiation, is found

to be necessary in order to explain the tendency of neighboring bodies

to equality of temperature; and this leads to the higher

generalization, that heat is radiant from points below the surface.

But in the doctrine of the relation of heat to gases, as delivered by

Laplace, there is none of this unexpected confirmation; and though he

explains some of the leading laws, his assumptions bear a large

proportion to the laws explained. Thus, from the assumption that the

repulsion of gases arises from the mutual repulsion of the particles

of caloric, he finds that the pressure in any gas is as the square of

the density and of the quantity of caloric;[75\10] and from the

assumption that the temperature is the internal radiation, he finds

that this temperature is as the density and the square of the

caloric.[76\10] Hence he obtains the law of Boyle and Mariotte, and

that of Dalton and Gay-Lussac. But this view of the subject requires

other assumptions when we come to latent heat; and accordingly, he

introduces, to express the latent heat, a new quantity.[77\10] Yet

this quantity produces no effect on his calculations, nor does he

apply his reasoning to any problem in which latent heat is concerned.

{187}

[Note 75\10: P = 2 π H K ρ^2_c_^2 (1) p. 107.]

[Note 76\10: _q_' Π (_a_) = ρ_c_^2 (2) p. 108.]

[Note 77\10: The quantity _i_, p. 113.]

Without, then, deciding upon this theory, we may venture to say that

it is wanting in all the prominent and striking characteristics

which we have found in those great theories which we look upon as

clearly and indisputably established.

_Conclusion._--We may observe, moreover, that heat has other

bearings and effects, which, as soon as they have been analysed into

numerical laws of phenomena, must be attended to in the formation of

thermotical theories. Chemistry will probably supply many such;

those which occur to us, we must examine hereafter. But we may

mention as examples of such, MM. De la Rive and Marcet's law, that

the specific heat of all gases is the same;[78\10] and MM. Dulong

and Petit's law, that single atoms of all simple bodies have the

same capacity for heat.[79\10] Though we have not yet said anything

of the relation of different gases, or explained the meaning of

_atoms_ in the chemical sense, it will easily be conceived that

these are very general and important propositions.

[Note 78\10: _Ann. Chim._ xxxv. (1827.)]

[Note 79\10: Ib. x. 397.]

Thus the science of Thermotics, imperfect as it is, forms a

highly-instructive part of our survey; and is one of the cardinal

points on which the doors of those chambers of physical knowledge

must turn which hitherto have remained closed. For, on the one hand,

this science is related by strong analogies and dependencies to the

most complete portions of our knowledge, our mechanical doctrines

and optical theories; and on the other, it is connected with

properties and laws of a nature altogether different,--those of

chemistry; properties and laws depending upon a new system of

notions and relations, among which clear and substantial general

principles are far more difficult to lay hold of and with which the

future progress of human knowledge appears to be far more concerned.

To these notions and relations we must now proceed; but we shall

find an intermediate stage, in certain subjects which I shall call

the _Mechanico-chemical_ Sciences; viz., those which have to do with

Magnetism, Electricity, and Galvanism.

{{189}}

BOOK XI.

_THE MECHANICO-CHEMICAL SCIENCES._

HISTORY OF ELECTRICITY.

PARVA metu primo: mox sese extollit in auras,

Ingrediturque solo, et caput inter nubila condit.

_Æn._ iv. 176.

A timid breath at first, a transient touch,

How soon it swells from little into much!

Runs o'er the ground, and springs into the air,

And fills the tempest's gloom, the lightning's glare;

While denser darkness than the central storm

Conceals the secrets of its inward form.

{{191}}

INTRODUCTION.

_Of the Mechanico-Chemical Sciences._

UNDER the title of Mechanico-Chemical Sciences, I include the laws

of Magnetism, Electricity, Galvanism, and the other classes of

phenomena closely related to these, as Thermo-electricity. This

group of subjects forms a curious and interesting portion of our

physical knowledge; and not the least of the circumstances which

give them their interest, is that double bearing upon mechanical and

chemical principles, which their name is intended to imply. Indeed,

at first sight they appear to be purely Mechanical Sciences; the

attractions and repulsions, the pressure and motion, which occur in

these cases, are referrible to mechanical conceptions and laws, as

completely as the weight or fall of terrestrial bodies, or the

motion of the moon and planets. And if the phenomena of magnetism

and electricity had directed us only to such laws, the corresponding

sciences must have been arranged as branches of mechanics. But we

find that, on the other side, these phenomena have laws and bearings

of a kind altogether different. Magnetism is associated with

Electricity by its mechanical analogies; and, more recently, has

been discovered to be still more closely connected with it by

physical influence; electric is identified with galvanic agency; but

in galvanism, decomposition, or some action of that kind,

universally appears; and these appearances lead to very general

laws. Now composition and decomposition are the subjects of

Chemistry; and thus we find that we are insensibly but irresistibly

led into the domain of that science. The highest generalizations to

which we can look, in advancing from the elementary facts of

electricity and galvanism, must involve chemical notions; we must

therefore, in laying out the platform of these sciences, make

provision for that convergence of mechanical and chemical theory,

which they are to exhibit as we ascend.

We must begin, however, with stating the mechanical phenomena of

these sciences, and the reduction of such phenomena to laws. In this

point of view, the phenomena of which we have to speak are those in

which bodies exhibit attractions and repulsions, peculiarly

determined by their nature and circumstances; as the magnet, and a

{192} piece of amber when rubbed. Such results are altogether

different from the universal attraction which, according to Newton's

discovery, prevails among all particles of matter, and to which

cosmical phenomena are owing. But yet the difference of these

special attractions, and of cosmical attraction, was at first so far

from being recognized, that the only way in which men could be led

to conceive or assent to an action of one body upon another at a

distance, in cosmical cases, was by likening it to magnetic

attraction, as we have seen in the history of Physical Astronomy.

And we shall, in the first part of our account, not dwell much upon

the peculiar conditions under which bodies are magnetic or electric,

since these conditions are not readily reducible to mechanical laws;

but, taking the magnetic or electric character for granted, we shall

trace its effects.

The habit of considering magnetic action as the type or general case

of attractive and repulsive agency, explains the early writers

having spoken of Electricity as a kind of Magnetism. Thus Gilbert,

in his book _De Magnete_ (1600), has a chapter,[1\11] _De coitione

Magniticâ, primumque de Succini attractione, sive verius corporum ad

Succinum applicatione_. The manner in which he speaks, shows us how

mysterious the fact of attraction then appeared; so that, as he

says, "the magnet and amber were called in aid by philosophers as

illustrations, when our sense is in the dark in abstruse inquiries,

and when our reason can go no further. Gilbert speaks of these

phenomena like a genuine inductive philosopher, reproving[2\11]

those who before him had "stuffed the booksellers' shops by copying

from one another extravagant stories concerning the attraction of

magnets and amber, without giving any reason from experiment." He

himself makes some important steps in the subject. He distinguishes

magnetic from _electric_ forces,[3\11] and is the inventor of the

latter name, derived from ἤλεκτρον, _electron_, amber. He observes

rightly, that the electric force attracts all light bodies, while

the magnetic force attracts iron only; and he devises a satisfactory

apparatus by which this is shown. He gives[4\11] a considerable list

of bodies which possess the electric property; "Not only amber and

agate attract small bodies, as some think, but diamond, sapphire,

carbuncle, opal, amethyst, Bristol gem, beryli, crystal, glass,

glass of antimony, spar of various kinds, sulphur, mastic,

sealing-wax," and other substances which he mentions. Even his

speculations on the general laws of these phenomena, though vague

and erroneous, as {193} at that period was unavoidable, do him no

discredit when compared with the doctrines of his successors a

century and a half afterwards. But such speculations belong to a

succeeding part of this history.

[Note 1\11: Lib. ii. cap. 2.]

[Note 2\11: _De Magnete_, p. 48.]

[Note 3\11: Ib. p. 52.]

[Note 4\11: Ib. p. 48.]

In treating of these Sciences, I will speak of Electricity in the

first place; although it is thus separated by the interposition of

Magnetism from the succeeding subjects (Galvanism, &c.) with which

its alliance seems, at first sight, the closest, and although some

general notions of the laws of magnets were obtained at an earlier

period than a knowledge of the corresponding relations of electric

phenomena: for the theory of electric attraction and repulsion is

somewhat more simple than of magnetic; was, in fact, the first

obtained; and was of use in suggesting and confirming the

generalization of magnetic laws.

CHAPTER 1.

DISCOVERY OF LAWS OF ELECTRIC PHENOMENA.

WE have already seen what was the state of this branch of knowledge

at the beginning of the seventeenth century; and the advances made

by Gilbert. We must now notice the additions which it subsequently

received, and especially those which led to the discovery of general

laws, and the establishment of the theory; events of this kind being

those of which we have more peculiarly to trace the conditions and

causes. Among the facts which we have thus especially to attend to,

are the electric attractions of small bodies by amber and other

substances when rubbed. Boyle, who repeated and extended the

experiments of Gilbert, does not appear to have arrived at any new

general notions; but Otto Guericke of Magdeburg, about the same

time, made a very material step, by discovering that there was an

electric force of repulsion as well as of attraction. He found that

when a globe of sulphur had attracted a feather, it afterwards

repelled it, till the feather had been in contact with some other

body. This, when verified under a due generality of circumstances,

forms a capital fact in our present subject. Hawkesbee, who wrote in

1709 (_Physico-Mechanical Experiments_) also observed various of the

effects of attraction and repulsion upon threads hanging loosely.

But the person who appears to have first fully seized the general

law of these facts, is {194} Dufay, whose experiments appear in the

Memoirs of the French Academy, in 1733, 1734, and 1737.[5\11] "I

discovered," he says, "a very simple principle, which accounts for a

great part of the irregularities, and, if I may use the term, the

caprices that seem to accompany most of the experiments in

electricity. This principle is, that electric bodies attract all

those that are not so, and repel them as soon as they are become

electric by the vicinity or contact of the electric body. . . . Upon

applying this principle to various experiments of electricity, any

one will be surprised at the number of obscure and puzzling facts

which it clears up." By the help of this principle, he endeavors to

explain several of Hawkesbee's experiments.

[Note 5\11: Priestley's _History of Electricity_, p. 45, and the

Memoirs quoted.]

A little anterior to Dufay's experiments were those of Grey, who, in

1729, discovered the properties of _conductors_. He found that the

attraction and repulsion which appear in electric bodies are

exhibited also by other bodies in contact with the electric. In this

manner he found that an ivory ball, connected with a glass tube by a

stick, a wire, or a packthread, attracted and repelled a feather, as

the glass itself would have done. He was then led to try to extend

this communication to considerable distances, first by ascending to

an upper window and hanging down his ball, and, afterwards, by

carrying the string horizontally supported on loops. As his success

was complete in the former case, he was perplexed by failure in the

latter; but when he supported the string by loops of silk instead of

hempen cords, he found it again become a conductor of electricity.

This he ascribed at first to the smaller thickness of the silk,

which did not carry off so much of the electric virtue; but from

this explanation he was again driven, by finding that wires of brass

still thinner than the silk destroyed the effect. Thus Grey

perceived that the efficacy of the support depended on its being

silk, and he soon found other substances which answered the same

purpose. The difference, in fact, depended on the supporting

substance being electric, and therefore not itself a conductor; for

it soon appeared from such experiments, and especially[6\11] from

those made by Dufay, that substances might be divided into

_electrics per se_, and _non-electrics_, or _conductors_. These

terms were introduced by Desaguliers,[7\11] and gave a permanent

currency to the results of the labors of Grey and others.

[Note 6\11: _Mém. Acad. Par._ 1734.]

[Note 7\11: Priestley, p. 66.]

Another very important discovery belonging to this period is, that

{195} of the two kinds of electricity. This also was made by Dufay.

"Chance," says he, "has thrown in my way another principle more

universal and remarkable than the preceding one, and which casts a new

light upon the subject of electricity. The principle is, that there

are two distinct kinds of electricity, very different from one

another; one of which I call _vitreous_, the other _resinous_,

electricity. The first is that of glass, gems, hair, wool, &c.; the

second is that of amber, gum-lac, silk, &c. The characteristic of

these two electricities is, that they repel themselves and attract

each other." This discovery does not, however, appear to have drawn so

much attention as it deserved. It was published in 1735; (in the

Memoirs of the Academy _for_ 1733;) and yet in 1747, Franklin and his

friends at Philadelphia, who had been supplied with electrical

apparatus and information by persons in England well acquainted with

the then present state of the subject, imagined that they were making

observations unknown to European science, when they were led to assert

two conditions of bodies, which were in fact the opposite

electricities of Dufay, though the American experimenters referred

them to a single element, of which electrized bodies might have either

excess or defect. "Hence," Franklin says, "have arisen some new terms

among us: we say B," who receives a spark from glass, "and bodies in

like circumstances, is electrized _positively_; A," who communicates

his electricity to glass, "_negatively_; or rather B is electrized

_plus_, A _minus_." Dr. (afterwards Sir William) Watson had, about the

same time, arrived at the same conclusions, which he expresses by

saying that the electricity of A was _more rare_, and that of B _more

dense_, than it naturally would have been.[8\11] But that which gave

the main importance to this doctrine was its application to some

remarkable experiments, of which we must now speak.

[Note 8\11: Priestley, p. 115.]

Electric action is accompanied, in many cases, by light and a

crackling sound. Otto Guericke[9\11] observes that his

sulphur-globe, when rubbed in a dark place, gave faint flashes, such

as take place when sugar is crushed. And shortly after, a light was

observed at the surface of the mercury in the barometer, when

shaken, which was explained at first by Bernoulli, on the then

prevalent Cartesian principles; but, afterwards, more truly by

Hawkesbee, as an electrical phenomenon. Wall, in 1708, found sparks

produced by rubbing amber, and Hawkesbee observed the light and the

_snapping_, as he calls it, under various modifications. But the

electric spark from a living body, which, as {196} Priestley

says,[10\11] "makes a principal part of the diversion of gentlemen

and ladies who come to see experiments in electricity," was first

observed by Dufay and the Abbé Nollet. Nollet says[11\11] he "shall

never forget the surprise which the first electric spark ever drawn

from the human body excited, both in M. Dufay and in himself." The

drawing of a spark from the human body was practised in various

forms, one of which was familiarly known as the "electrical kiss."

Other exhibitions of electrical light were the electrical star,

electrical rain, and the like.

[Note 9\11: _Experimenta Magdeburgica_, 1672, lib. iv. cap. 15.]

[Note 10\11: P. p. 47.]

[Note 11\11: Priestley, p. 47. Nollet, _Leçons de Physique_, vol.

vi. p. 408.]

As electricians determined more exactly the conditions of electrical

action, they succeeded in rendering more intense those sudden

actions which the spark accompanies, and thus produced the electric

_shock_. This was especially done in the _Leyden phial_. This

apparatus received its name, while the discovery of its property was

attributed to Cunæus, a native of Leyden, who, in 1746, handling a

vessel containing water in communication with the electrical

machine, and happening thus to bring the inside and the outside into

connexion, received a sudden shock in his arms and breast. It

appears, however,[12\11] that a shock had been received under nearly

the same circumstances in 1746, by Von Kleist, a German prelate, at

Camin, in Pomerania. The strangeness of this occurrence, and the

suddenness of the blow, much exaggerated the estimate which men

formed of its force. Muschenbroek, after taking one shock, declared

he would not take a second for the kingdom of France; though Boze,

with a more magnanimous spirit, wished[13\11] that he might die by

such a stroke, and have the circumstances of the experiment recorded

in the Memoirs of the Academy. But we may easily imagine what a new

fame and interest this discovery gave to the subject of electricity.

It was repeated in all parts of the world, with various

modifications: and the shock was passed through a line of several

persons holding hands; Nollet, in the presence of the king of

France, sent it through a circle of 180 men of the guards, and along

a line of men and wires of 900 toises;[14\11] and experiments of the

same kind were made in England, principally under the direction of

Watson, on a scale so large as to excite the admiration of

Muschenbroek; who says, in a letter to Watson, "Magnificentissimis

tuis experimentis superasti conatus omnium." The result was, that

the transmission of electricity through a length of 12,000 feet was,

to sense, instantaneous. {197}

[Note 12\11: Fischer, v. 490.]

[Note 13\11: Fischer, p. 84.]

[Note 14\11: Ibid. v. 512.]

The essential circumstances of the electric shock were gradually

unravelled. Watson found that it did not increase in proportion

either to the contents of the phial or the size of the globe by

which the electricity was excited; that the outside coating of the

glass (which, in the first form of the experiment, was only a film

of water), and its contents, might be varied in different ways. To

Franklin is due the merit of clearly pointing out most of the

circumstances on which the efficacy of the Leyden phial depends. He

showed, in 1747,[15\11] that the inside of the bottle is electrized

positively, the outside negatively; and that the shock is produced

by the restoration of the equilibrium, when the outside and inside

are brought into communication suddenly. But in order to complete

this discovery, it remained to be shown that the electric matter was

collected entirely at the surface of the glass, and that the

opposite electricities on the two opposite sides of the glass were

accumulated by their mutual attraction. Monnier the younger

discovered that the electricity which bodies can receive, depends

upon their surface rather than their mass, and Franklin[16\11] soon

found that "the whole force of the bottle, and power of giving a

shock, is in the glass itself." This they proved by decanting the

water out of an electrized into another bottle, when it appeared

that the second bottle did not become electric, but the first

remained so. Thus it was found "that the non-electrics, in contact

with the glass, served only to unite the force of the several parts."

[Note 15\11: _Letters_, p. 13.]

[Note 16\11: _Letters_, iv. Sect. 16.]

So far as the effect of the coating of the Leyden phial is

concerned, this was satisfactory and complete: but Franklin was not

equally successful in tracing the action of the electric matter upon

itself, in virtue of which it is accumulated in the phial; indeed,

he appears to have ascribed the effect to some property of the

glass. The mode of describing this action varied, accordingly as two

electric _fluids_ were supposed (with Dufay,) or one, which was the

view taken by Franklin. On this latter supposition the parts of the

electric fluid repel each other, and the excess in one surface of

the glass expels the fluid from the other surface. This kind of

action, however, came into much clearer view in the experiments of

Canton, Wilcke, and Æpinus. It was principally manifested in the

attractions and repulsions which objects exert when they are in the

neighborhood of electrized bodies; or in the _electrical

atmosphere_, using the phraseology of the time. At present we say

that bodies are electrized _by induction_, when they are {198} thus

made electric by the electric attraction and repulsion of other

bodies. Canton's experiments were communicated to the Royal Society

in 1753, and show that the electricity on each body acts upon the

electricity of another body, at a distance, with a repulsive energy.

Wilcke, in like manner, showed that parts of non-electrics, plunged

in electric atmospheres, acquire an electricity opposite to that of

such atmospheres. And Æpinus devised a method of examining the

nature of the electricity at any part of the surface of a body, by

means of which he ascertained its distribution, and found that it

agreed with such a law of self-repulsion. His attempt to give

mathematical precision to this induction was one of the most

important steps towards electrical theory, and must be spoken of

shortly, in that point of view. But in the mean time we may observe,

that this doctrine was applied to the explanation of the Leyden jar;

and the explanation was confirmed by charging a plate of air, and

obtaining a shock from it, in a manner which the theory pointed out.

Before we proceed to the history of the theory, we must mention some

other of the laws of phenomena which were noticed, and which theory

was expected to explain. Among the most celebrated of these, were

the effect of sharp points in conductors, and the phenomena of

electricity in the atmosphere. The former of these circumstances was

one of the first which Franklin observed as remarkable. It was found

that the points of needles and the like throw off and draw off the

electric virtue; thus a bodkin, directed towards an electrized ball,

at six or eight inches' distance, destroyed its electric action. The

latter subject, involving the consideration of thunder and

lightning, and of many other meteorological phenomena, excited great

interest. The comparison of the electric spark to lightning had very

early been made; but it was only when the discharge had been

rendered more powerful in the Leyden jar, that the comparison of the

effects became very plausible. Franklin, about 1750, had offered a

few somewhat vague conjectures[17\11] respecting the existence of

electricity in the clouds; but it was not till Wilcke and Æpinus had

obtained clear notions of the effect of electric matter at a

distance, that the real condition of the clouds could be well

understood. In 1752, however,[18\11] D'Alibard, and other French

philosophers, were desirous of verifying Franklin's conjecture of

the analogy of thunder and electricity. This they did by erecting a

pointed iron rod, forty feet high, {199} at Marli: the rod was found

capable of giving out electrical sparks when a thunder-cloud passed

over the place. This was repeated in various parts of Europe, and

Franklin suggested that a communication with the clouds might be

formed by means of a kite. By these, and similar means, the

electricity of the atmosphere was studied by Canton in England,

Mazeas in France, Beccaria in Italy, and others elsewhere. These

essays soon led to a fatal accident, the death of Richman at

Petersburg, while he was, on Aug. 6th, 1753, observing the

electricity collected from an approaching thunder-cloud, by means of

a rod which he called an electrical gnomon: a globe of blue fire was

seen to leap from the rod to the head of the unfortunate professor,

who was thus struck dead.

[Note 17\11: Letter v.]

[Note 18\11: Franklin, p. 107.]

[2nd Ed.] [As an important application of the doctrines of

electricity, I may mention the contrivances employed to protect

ships from the effects of lightning. The use of conductors in such

cases is attended with peculiar difficulties. In 1780 the French

began to turn their attention to this subject, and Le Roi was sent

to Brest and the various sea-ports of France for that purpose.

Chains temporarily applied in the rigging had been previously

suggested, but he endeavored to place, he says, such conductors in

ships as might be fixed and durable. He devised certain long linked

rods, which led from a point in the mast-head along a part of the

rigging, or in divided stages along the masts, and were fixed to

plates of metal in the ship's sides communicating with the sea. But

these were either unable to stand the working of the rigging, or

otherwise inconvenient, and were finally abandoned.[19\11]

[Note 19\11: See Le Roi's Memoir in the _Hist. Acad. Sc._ for 1790.]

The conductor commonly used in the English Navy, till recently,

consisted of a flexible copper chain, tied, when occasion required,

to the mast-head, and reaching down into the sea; a contrivance

recommended by Dr. Watson in 1762. But notwithstanding this

precaution, the shipping suffered greatly from the effects of

lightning.

Mr. Snow Harris (now Sir William Snow Harris), whose electrical

labors are noticed above, proposed to the Admiralty, in 1820, a plan

which combined the conditions of ship-conductors, so desirable, yet

so difficult to secure:--namely, that they should be permanently

fixed, and sufficiently large, and yet should in no way interfere

with the motion of the rigging, or with the sliding masts. The

method which he proposed was to make the masts themselves conductors

of electricity, {200} by incorporating with them, in a peculiar way,

two laminæ of sheet-copper, uniting these with the metallic masses

in the hull by other laminæ, and giving the whole a free

communication with the sea. This method was tried experimentally,

both on models and to a large extent in the navy itself; and a

Commission appointed to examine the result reported themselves

highly satisfied with Mr. Harris's plan, and strongly recommended

that it should be fully carried out in the Navy.[20\11]]

[Note 20\11: See Mr. Snow Harris's paper in _Phil. Mag._ March, 1841.]

It is not here necessary to trace the study of atmospheric

electricity any further: and we must now endeavor to see how these

phenomena and laws of phenomena which we have related, were worked

up into consistent theories; for though many experimental

observations and measures were made after this time, they were

guided by the theory, and may be considered as having rather

discharged the office of confirming than of suggesting it.

We may observe also that we have now described the period of most

extensive activity and interest in electrical researches. These

naturally occurred while the general notions and laws of the

phenomena were becoming, and were not yet become, fixed and clear.

At such a period, a large and popular circle of spectators and

amateurs feel themselves nearly upon a level, in the value of their

trials and speculations, with more profound thinkers: at a later

period, when the subject is become a science, that is, a study in

which all must be left far behind who do not come to it with

disciplined, informed, and logical minds, the cultivators are far

more few, and the shout of applause less tumultuous and less loud.

We may add, too, that the experiments, which are the most striking

to the senses, lose much of their impressiveness with their novelty.

Electricity, to be now studied rightly, must be reasoned upon

mathematically; how slowly such a mode of study makes its way, we

shall see in the progress of the theory, which we must now proceed

to narrate.

[2nd Ed.] [A new mode of producing electricity has excited much

notice lately. In October, 1840, one of the workmen in attendance

upon a boiler belonging to the Newcastle and Durham Railway,

reported that the boiler was full of fire; the fact being, that

when he placed his hand near it an electrical spark was given out.

This drew the attention of Mr. Armstrong and Mr. Pattinson, who made

the circumstance publicly known.[21\11] Mr. Armstrong pursued the

investigation {201} with great zeal, and after various conjectures

was able to announce[22\11] that the electricity was excited at the

point where the steam is subject to friction in its emission. He

found too that he could produce a like effect by the emission of

condensed air. Following out his views, he was able to construct,

for the Polytechnic Institution in London, a "Hydro-electric

Machine," of greater power than any electrical machine previously

made. Dr. Faraday took up the investigation as the subject of the

Eighteenth Series of his _Researches_, sent to the Royal Society,

Jan. 26, 1842; and in this he illustrated, with his usual command of

copious and luminous experiments, a like view;--that the electricity

is produced by the friction of the particles of the water carried

along by the **steam. And thus this is a new manifestation of that

electricity, which, to distinguish it from voltaic electricity, is

sometimes called _Friction Electricity_ or _Machine Electricity_.

Dr. Faraday has, however, in the course of this investigation,

brought to light several new electrical relations of bodies.]

[Note 21\11: _Phil. Mag._ Oct 1840.]

[Note 22\11: _Phil. Mag._ Jan. 1848, dated Dec. 9, 1841.]

CHAPTER II.

THE PROGRESS OF ELECTRICAL THEORY.

THE cause of electrical phenomena, and the mode of its operation,

were naturally at first spoken of in an indistinct and wavering

manner. It was called the electric _fire_, the electric _fluid_; its

effects were attributed to _virtues_, _effluvia_, _atmospheres_.

When men's mechanical ideas became somewhat more distinct, the

motions and tendencies to motion were ascribed to _currents_, in the

same manner as the cosmical motions had been in the Cartesian

system. This doctrine of currents was maintained by Nollet, who

ascribed all the phenomena of electrized bodies to the

contemporaneous afflux and efflux of electrical matter. It was an

important step towards sound theory, to get rid of this notion of

moving fluids, and to consider attraction and repulsion as statical

forces; and this appears to have been done by others about the same

time. Dufay[23\11] considered that he had proved the existence of

two electricities, the vitreous and the resinous, and conceived each

{202} of these to be a fluid which repelled its own parts and

attracted those of the other: this is, in fact, the outline of the

theory which recently has been considered as the best established;

but from various causes it was not at once, or at least not

generally adopted. The hypothesis of the excess and defect of a

single fluid is capable of being so treated as to give the same

results with the hypothesis of two opposite fluids and happened to

obtain the preference for some time. We have already seen that this

hypothesis, according to which electric phenomena arose from the

excess and defect of a generally diffused fluid, suggested itself to

Watson and Franklin about 1747. Watson found that when an electric

body was excited, the electricity was not created, but collected;

and Franklin held, that when the Leyden jar was charged, the

quantity of electricity was unaltered, though its distribution was

changed. Symmer[24\11] maintained the existence of two fluids; and

Cigna supplied the main defect which belonged to this tenet in the

way in which Dufay held it, by showing that the two opposite

electricities were usually produced at the same time. Still the

apparent simplicity of the hypothesis of one fluid procured it many

supporters. It was that which Franklin adopted, in his explanation

of the Leyden experiment; and though after the first conception of

an electrical charge as a disturbance of equilibrium, there was

nothing in the development or details of Franklin's views which

deserved to win for them any peculiar authority, his reputation, and

his skill as a writer, gave a considerable influence to his

opinions. Indeed, for a time he was considered, over a large part of

Europe, as the creator of the science, and the terms[25\11]

_Franklinism_, _Franklinist_, _Franklinian system_, occur in almost

every page of continental publications on the subject. Yet the

electrical phenomena to the knowledge of which Franklin added least,

those of induction, were those by which the progress of the theory

was most promoted. These, as we have already said, were at first

explained by the hypothesis of electrical atmospheres. Lord Mahon

wrote a treatise, in which this hypothesis was mathematically

treated; yet the hypothesis was very untenable, for it would not

account for the most obvious cases of induction, such as the Leyden

jar, except the atmosphere was supposed to penetrate glass.

[Note 23\11: _Ac. Par._ 1733, p. 467]

[Note 24\11: _Phil. Trans._ 1759.]

[Note 25\11: Priestley, p. 160.]

The phenomena of electricity by induction, when fairly considered by

a person of clear notions of the relations of space and force, were

seen to accommodate themselves very generally to the conception

{203} introduced by Dufay;[26\11] of two electricities each

repelling itself and attracting the other. If we suppose that there

is only one fluid, which repels itself and attracts all other

matter, we obtain, in many cases, the same general results as if we

suppose two fluids; thus, if an electrized body, overcharged with

the single fluid, act upon a ball, it drives the electric fluid in

the ball to the further side by its repulsion, and then attracts the

ball by attracting the matter of the ball more than it repels the

fluid which is upon the ball. If we suppose two fluids, the

positively electrized body draws the negative fluid to the nearer

side of the ball, repels the positive fluid to the opposite side,

and attracts the ball on the whole, because the attracted fluid is

nearer than that which is repelled. The verification of either of

these hypotheses, and the determination of their details, depended

necessarily upon experiment and calculation. It was under the

hypothesis of a single fluid that this trial was first properly

made. Æpinus of Petersburg published, in 1759, his _Tentamen Theoriæ

Electricitatis et Magnetismi_; in which he traces mathematically the

consequences of the hypothesis of an electric fluid, attracting all

other matter, but repelling itself; the law of force of this

repulsion and attraction he did not pretend to assign precisely,

confining himself to the supposition that the mutual force of the

particles increases as the distance decreases. But it was found,

that in order to make this theory tenable, an additional supposition

was required, namely, that the particles of bodies repel each other

as much as they attract the electric fluid.[27\11] For if two

bodies, A and B, be in their natural electrical condition, they

neither attract nor repel each other. Now, in this case, the fluid

in A attracts the matter in B and repels the fluid in B with equal

energy, and thus no tendency to motion results from the fluid in A;

and if we further suppose that the _matter_ in A attracts the fluid

in B and _repels the matter_ in B with equal energy, we have the

resulting mutual inactivity of the two bodies explained; but without

the latter supposition, there would be a mutual attraction: or we

may put the truth more simply thus; two negatively electrized bodies

repel each other; if negative electrization were merely the

abstraction of the fluid which is the repulsive element, this result

could not follow except there were a repulsion in the bodies

themselves, independent of the fluid. And thus Æpinus found himself

compelled to assume this mutual repulsion of material particles; he

had, in fact, the {204} alternative of this supposition, or that of

two fluids, to choose between, for the mathematical results of both

hypotheses are the same. Wilcke, a Swede, who had at first asserted

and worked out the Æpinian theory in its original form, afterwards

inclined to the opinion of Symmer; and Coulomb, when, at a later

period, he confirmed the theory by his experiments and determined

the law of force, did not hesitate to prefer[28\11] the theory of

two fluids, "because," he says, "it appears to me contradictory to

admit at the same time, in the particles of bodies, an attractive

force in the inverse ratio of the squares of the distances, which is

demonstrated by universal gravitation, and a repulsive force in the

same inverse ratio of the squares of the distances; a force which

would necessarily be infinitely great relatively to the action of

gravitation." We may add, that by forcing us upon this doctrine of

the universal repulsion of matter, the theory of a single fluid

seems quite to lose that superiority in the way of simplicity which

had originally been its principal recommendation.

[Note 26\11: _Mém. A. P._ 1733, p. 467.]

[Note 27\11: Robison, vol. iv. p. 18.]

[Note 28\11: _Mém. Ac. P._ 1788, p. 671.]

The mathematical results of the supposition of Æpinus, which are, as

Coulomb observes,[29\11] the same as of that of the two fluids, were

traced by the author himself in the work referred to, and shown to

agree, in a great number of cases, with the observed facts of

electrical induction, attraction, and repulsion. Apparently this

work did not make its way very rapidly through Europe; for in 1771,

Henry Cavendish stated[30\11] the same hypothesis in a paper read

before the Royal Society; which he prefaces by saying, "Since I

first wrote the following paper, I find that this way of accounting

for the phenomena of electricity is not new. Æpinus, in his

_Tentamen Theoriæ Electricitatis et Magnetismi_, has made use of the

same, or nearly the same hypothesis that I have; and the conclusions

he draws from it agree nearly with mine as far as he goes."

[Note 29\11: _Ac. P._ 1788, p. 672.]

[Note 30\11: _Phil. Trans._ 1771, vol. lxi.]

The confirmation of the theory was, of course, to be found in the

agreement of its results with experiment; and in particular, in the

facts of electrical induction, attraction, and repulsion, which

suggested the theory. Æpinus showed that such a confirmation

appeared in a number of the most obvious cases; and to these,

Cavendish added others, which, though not obvious, were of such a

nature that the calculations, in general difficult or impossible,

could in these instances be easily performed; as, for example, cases

in which there are plates or globes at the two extremities of a long

wire. In all these cases of {205} electrical action the theory was

justified. But in order to give it full confirmation, it was to be

considered whether any other facts, not immediately assumed in the

foundation of the theory, were explained by it; a circumstance

which, as we have seen, gave the final stamp of truth to the

theories of astronomy and optics. Now we appear to have such

confirmation, in the effect of points, and in the phenomena of the

electrical discharge. The theory of neither of these was fully

understood by Cavendish, but he made an approach to the true view of

them. If one part of a conducting body be a sphere of small radius,

the electric fluid upon the surface of this sphere will, it appears

by calculation, be more dense, and tend to escape more

energetically, in proportion as the radius of the sphere is smaller;

and, therefore, if we consider a point as part of the surface of a

sphere of imperceptible radius, it follows from the theory that the

effort of the fluid to escape at that place will be enormous; so

that it may easily be supposed to overcome the resisting causes. And

the discharge may be explained in nearly the same manner; for when a

conductor is brought nearer and nearer to an electrized body, the

opposite electricity is more and more accumulated by attraction on

the side next to the electrized body; its tension becomes greater by

the increase of its quantity and the diminution of the distance, and

at last it is too strong to be contained, and leaps out in the form

of a spark.

The light, sound, and mechanical effects produced by the electric

discharge, made the electric _fluid_ to be not merely considered as

a mathematical hypothesis, useful for reducing phenomena to formulæ

(as for a long time the magnetic fluid was), but caused it to be at

once and universally accepted as a physical reality, of which we

learn the existence by the common use of the senses, and of which

measures and calculations are only wanted to teach us the laws.

The applications of the theory of electricity which I have

principally considered above, are those which belong to conductors,

in which the electric fluid is perfectly moveable, and can take that

distribution which the forces require. In non-conducting or electric

bodies, the conditions to which the fluid is subject are less easy

to determine; but by supposing that the fluid moves with great

difficulty among the particles of such bodies,--that nevertheless it

may be dislodged and accumulated in parts of the surface of such

bodies, by friction and other modes of excitement; and that the

earth is an inexhaustible reservoir of electric matter,--the

principal facts of excitation and the like receive a tolerably

satisfactory explanation. {206}

The theory of Æpinus, however, still required to have the law of

action of the particles of the fluid determined. If we were to call

to mind how momentous an event in physical astronomy was the

determination of the law of the cosmical forces, the inverse square

of the distance, and were to suppose the importance and difficulty

of the analogous step in this case to be of the same kind, this

would be to mistake the condition of science at that time. The

leading idea, the conception of the possibility of explaining

natural phenomena by means of the action of forces, on rigorously

mechanical principles, had already been promulgated by Newton, and

was, from the first, seen to be peculiarly applicable to electrical

phenomena; so that the very material step of clearly proposing the

problem, often more important than the solution of it, had already

been made. Moreover the confirmation of the truth of the assumed

cause in the astronomical case depended on taking the right law; but

the electrical theory could be confirmed, in a general manner at

least, without this restriction. Still it was an important discovery

that the law of the inverse square prevailed in these as well as in

cosmical attractions.

It was impossible not to conjecture beforehand that it would be so.

Cavendish had professed in his calculations not to take the exponent

of the inverse power, on which the force depended, to be strictly 2,

but to leave it indeterminate between 1 and 3; but in his

applications of his results, he obviously inclines to the assumption

that it is 2. Experimenters tried to establish this in various ways.

Robison,[31\11] in 1769, had already proved that the law of force is

very nearly or exactly the inverse square; and Meyer[32\11] had

discovered, but not published, the same result. The clear and

satisfactory establishment of this truth is due to Coulomb, and was

one of the first steps in his important series of researches on this

subject. In his first paper[33\11] in the _Memoirs_ of the Academy

for 1785, he proves this law for small globes; in his second Memoir

he shows it to be true for globes one and two feet in diameter. His

invention of the _torsion-balance_, which measures very small forces

with great certainty and exactness, enabled him to set this question

at rest for ever.

[Note 31\11: _Works_, iv. p. 68.]

[Note 32\11: _Biog. Univ._ art. _Coulumb_, by Biot.]

[Note 33\11: _Mém. A. P._ 1785, pp. 569, 578.]

The law of force being determined for the particles of the electric

fluid, it now came to be the business of the experimenter and the

{207} mathematician to compare the results of the theory in detail

with those of experimental measures. Coulomb undertook both portions

of the task. He examined the electricity of portions of bodies by

means of a little disk (his _tangent plane_) which he applied to

them and then removed, and which thus acted as a sort of electric

_taster_. His numerical results (the intensity being still measured

by the torsion-balance) are the fundamental facts of the theory of

the electrical fluid. Without entering into detail, we may observe

that he found the electricity to be entirely collected at the

surface of conductors (which Beccaria had before shown to be the

case), and that he examined and recorded the electric intensity at

the surface of globes, cylinders, and other conducting bodies,

placed within each other's influence in various ways.

The mathematical calculation of the distribution of two fluids, all

the particles of which attract and repel each other according to the

above law, was a problem of no ordinary difficulty; as may easily be

imagined, when it is recollected that the attraction and repulsion

determine the distribution, and the distribution reciprocally

determines the attraction and repulsion. The problem was of the same

nature as that of the figure of the earth; and its rigorous solution

was beyond the powers of the analysis of Coulomb's time. He obtained,

however, approximate solutions with much ingenuity; for instance, in a

case in which it was obvious that the electric fluid would be most

accumulated at and near the equator of a certain sphere, he calculated

the action of the sphere on two suppositions: first, that the fluid

was all collected precisely at the equator; and next, that it was

uniformly diffused over the surface; and he then assumed the actual

case to be intermediate between these two. By such artifices he was

able to show that the results of his experiments and of his

calculations gave an agreement sufficiently near to entitle him to

consider the theory as established on a solid basis.

Thus, at this period, mathematics was behind experiment; and a problem

was proposed, in which theoretical numerical results were wanted for

comparison with observation, but could not be accurately obtained; as

was the case in astronomy also, till the time of the approximate

solution of the Problem of Three Bodies, and the consequent formation

of the Tables of the Moon and Planets on the theory of universal

gravitation. After some time, electrical theory was relieved from this

reproach, mainly in consequence of the progress which astronomy had

occasioned in pure mathematics. About 1801, {208} there appeared in

the _Bulletin des Sciences_,[34\11] an exact solution of the problem

of the distribution of electric fluid on a spheroid, obtained by M.

Biot, by the application of the peculiar methods which Laplace had

invented for the problem of the figure of the planets. And in 1811, M.

Poisson applied Laplace's artifices to the case of two spheres acting

upon one another in contact, a case to which many of Coulomb's

experiments were referrible; and the agreement of the results of

theory and observation, thus extricated from Coulomb's numbers,

obtained above forty years previously, was very striking and

convincing.[35\11] It followed also from Poisson's calculations, that

when two electrized spheres are brought near each other, the

accumulation of the opposite electricities on their nearest points

increases without limit as the spheres approach to contact; so that

before the contact takes place, the external resistance will be

overcome, and a _spark_ will pass.

[Note 34\11: No. li.]

[Note 35\11: _Mém. A. P._ 1811.]

Though the relations of non-conductors to electricity, and various

other circumstances, leave many facts imperfectly explained by the

theory, yet we may venture to say that, as a theory which gives the

laws of the phenomena, and which determines the distribution of

those elementary forces, on the surface of electrized bodies, from

which elementary forces (whether arising from the presence of a

fluid or not,) the total effects result, the doctrine of Dufay and

Coulomb, as developed in the analysis of Poisson, is securely and

permanently established. This part of the subject has been called

_statical electricity_. In the establishment of the theory of this

branch of science, we must, I conceive, allow to Dufay more merit

than is generally ascribed to him; since he saw clearly, and

enunciated in a manner which showed that he duly appreciated their

capital character, the two chief principles,--the conditions of

electrical attraction and repulsion, and the apparent existence of

two kinds of electricity. His views of attraction are, indeed,

partly expressed in terms of the Cartesian hypothesis of vortices,

then prevalent in France; but, at the time when he wrote, these

forms of speech indicated scarcely anything besides the power of

attraction. Franklin's real merit as a discoverer was, that he was

one of the first who distinctly conceived the electrical _charge_ as

a derangement of equilibrium. The great fame which, in his day, he

enjoyed, arose from the clearness and spirit with which he narrated

his discoveries; from his dealing with electricity in the imposing

form of thunder and lightning; and partly, perhaps, from his

character as an {209} American and a politician; for he was already,

in 1736, engaged in public affairs as clerk to the General Assembly

of Pennsylvania, though it was not till a later period of his life

that his admirers had the occasion of saying of him

Eripuit cœlis fulmen sceptrumque tyrannis;

Born to control all lawless force, all fierce and baleful sway,

The thunder's bolt, the tyrant's rod, alike he wrenched away.

Æpinus and Coulomb were two of the most eminent physical

philosophers of the last century, and labored in the way peculiarly

required by that generation; whose office it was to examine the

results, in particular subjects, of the general conception of

attraction and repulsion, as introduced by Newton. The reasonings of

the Newtonian period had, in some measure, anticipated all possible

theories resembling the electrical doctrine of Æpinus and Coulomb;

and, on that account, this doctrine could not be introduced and

confirmed in a sudden and striking manner, so as to make a great

epoch. Accordingly, Dufay, Symmer, Watson, Franklin, Æpinus and

Coulomb, have all a share in the process of induction. With

reference to these founders of the theory of electricity, Poisson

holds the same place which Laplace holds with reference to Newton.

The reception of the Coulombian theory (so we most call it, for the

Æpinian theory implies one fluid only,) has hitherto not been so

general as might have been reasonably expected from its very

beautiful accordance with the facts which it contemplates. This has

partly been owing to the extreme abstruseness of the mathematical

reasoning which it employs, and which put it out of the reach of

most experimenters and writers of works of general circulation. The

theory of Æpinus was explained by Robison in the _Encyclopædia

Britannica_; the analysis of Poisson has recently been presented to

the public in the _Encyclopædia Metropolitana_, but is of a kind not

easily mastered even by most mathematicians. On these accounts

probably it is, that in English compilations of science, we find,

even to this day, the two theories of one and of two fluids stated

as if they were nearly on a par in respect of their experimental

evidence. Still we may say that the Coulombian theory is probably

assented to by all who have examined it, at least as giving the laws

of phenomena; and I have not heard of any denial of it from such a

quarter, or of any attempt to show it to be erroneous by detailed

and measured experiments. Mr. Snow Harris {210} has recently[36\11]

described some important experiments and measures; but his apparatus

was of such a kind that the comparison of the results with the

Coulombian theory was not easy; and indeed the mathematical problems

which Mr. Harris's combinations offered, require another Poisson for

their solution. Still the more obvious results are such as agree

with the theory, even in the cases in which their author considered

them to be inexplicable. For example, he found that by doubling the

quantity of electricity of a conductor, it attracted a body with

four times the force; but the body not being insulated, would have

its electricity also doubled by induction, and thus the fact was

what the theory required.

[Note 36\11: _Phil. Trans._ 1834, p. 2.]

Though it is thus highly probable that the Coulombian theory of

electricity (or the Æpinian, which is mathematically equivalent)

will stand as a true representation of the law of the elementary

actions, we must yet allow that it has not received that complete

evidence, by means of experiments and calculations added to those of

its founders, which the precedents of other permanent sciences have

led us to look for. The experiments of Coulomb, which he used in the

establishment of the theory, were not very numerous, and they were

limited to a peculiar form of bodies, namely spheres. In order to

form the proper _sequel_ to the promulgation of this theory, to give

a full _confirmation_, and to ensure its general _reception_, we

ought to have experiments more numerous and more varied (such as

those of Mr. Harris are) shown to agree in all respects with results

calculated from the theory. This would, as we have said, be a task

of labor and difficulty; but the person who shall execute it will

deserve to be considered as one of the real founders of the true

doctrine of electricity. To show that the coincidence between theory

and observation, which has already been proved for spherical

conductors, obtains also for bodies of other forms, will be a step

in electricity analogous to what was done in astronomy, when it was

shown that the law of gravitation applied to comets as well as to

planets.

But although we consider the views of Æpinus or Coulomb in a very

high degree probable as a _formal theory_, the question is very

different when we come to examine them as a _physical theory_;--that

is, when we inquire whether there really is a material electric

fluid or fluids.

_Question of One or Two Fluids._--In the first place as to the

question whether the fluids are one or two;--Coulomb's introduction

of {211} the hypothesis of two fluids has been spoken of as a reform

of the theory of Æpinus; it would probably have been more safe to

have called his labors an advance in the calculation, and in the

comparison of hypothesis with experiment, than to have used language

which implied that the question, between the rival hypotheses of one

or two fluids, could be treated as settled. For, in reality, if we

assume, as Æpinus does, the mutual repulsion of all the particles of

matter, in addition to the repulsion of the particles of the

electric fluid for one another and their attraction for the

particles of matter, the one fluid of Æpinus will give exactly the

same results as the two fluids of Coulomb. The mathematical formulæ

of Coulomb and of Poisson express the conditions of the one case as

well as of the other; the interpretation only being somewhat

different. The place of the forces of the resinous fluid is supplied

by the excess of the forces ascribed to the matter above the forces

of the fluid, in the parts where the electric fluid is deficient.

The obvious argument against this hypothesis is, that we ascribe to

the particles of matter a mutual repulsion, in addition to the

mutual attraction of universal gravitation, and that this appears

incongruous. Accordingly, Æpinus says, that when he was first driven

to this proposition it horrified him.[37\11] But we may answer it in

this way very satisfactorily:--If we suppose the mutual repulsion of

matter to be somewhat less than the mutual attraction of matter and

electric fluid, it will follow, as a consequence of the hypothesis,

that besides all obvious electrical action, the particles of matter

would attract each other with forces varying inversely as the square

of the distance. Thus gravitation itself becomes an electrical

phenomenon, arising from the residual excess of attraction over

repulsion; and the fact which is urged against the hypothesis

becomes a confirmation of it. By this consideration the prerogative

of simplicity passes over to the side of the hypothesis of one

fluid; and the rival view appears to lose at least all its

superiority.

[Note 37\11: Neque diffiteor cum ipsa se mihi offerret . . . . me ad

ipsam quodammodo exhorruisse. _Tentamen Theor. Elect._ p. 39.]

Very recently, M. Mosotti[38\11] has calculated the results of the

Æpinian theory in a far more complete manner than had previously

been performed; using Laplace's coefficients, as Poisson had done

for the {212} Coulombian theory. He finds that, from the supposition

of a fluid and of particles of matter exercising such forces as that

theory assumes (with the very allowable additional supposition that

the particles are small compared with their distances), it follows

that the particles would exert a force, repulsive at the smallest

distances, a little further on vanishing, afterwards attractive, and

at all sensible distances attracting in proportion to the inverse

square of the distance. Thus there would be a position of stable

equilibrium for the particles at a very small distance from each

other, which may be, M. Mosotti suggests, that equilibrium on which

their physical structure depends. According to this view, the

resistance of bodies to compression and to extension, as well as the

phenomena of statical electricity and the mutual gravitation of

matter, are accounted for by the same hypothesis of a single fluid

or ether. A theory which offers a prospect of such a generalization

is worth attention; but a very clear and comprehensive view of the

doctrines of several sciences is requisite to prepare us to estimate

its value and probable success.

[Note 38\11: _Sur les Forces qui régissent la Constitution

Intérieure des Corps._ Turin. 1836.]

_Question of the Material Reality of the Electric Fluid._--At first

sight the beautiful accordance of the experiments with calculations

founded upon the attractions and repulsions of the two hypothetical

fluids, persuade us that the hypotheses must be the real state of

things. But we have already learned that we must not trust to such

evidence too readily. It is a curious instance of the mutual

influence of the histories of two provinces of science, but I think

it will be allowed to be just, to say that the discovery of the

polarization of heat has done much to shake the theory of the

electric fluids as a physical reality. For the doctrine of a

material caloric appeared to be proved (from the laws of conduction

and radiation) by the same kind of mathematical evidence (the

agreement of laws respecting the elementary actions with those of

fluids), which we have for the doctrine of material electricity. Yet

we now seem to see that heat cannot be matter, since its rays have

_sides_, in a manner in which a stream of particles of matter cannot

have sides without inadmissible hypotheses. We see, then, that it

will not be contrary to precedent, if our electrical theory,

representing with perfect accuracy the _laws_ of the actions, in all

their forms, simple and complex, should yet be fallacious as a view

of the _cause_ of the actions.

Any true view of electricity must include, or at least be consistent

with, the other classes of the phenomena, as well as this statical

electrical action; such as the conditions of excitation and

retention of {213} electricity; to which we may add, the connexion

of electricity with magnetism and with chemistry;--a vast field, as

yet dimly seen. Now, even with regard to the simplest of these

questions, the cause of the retention of electricity at the surface

of bodies, it appears to be impossible to maintain Coulomb's

opinion, that this is effected by the resistance of air to the

passage of electricity. The other questions are such as Coulomb did

not attempt to touch; they refer, indeed, principally to laws not

suspected at his time. How wide and profound a theory must be which

deals worthily with these, we shall obtain some indications in the

succeeding part of our history.

But it may be said on the other side, that we have the evidence of

our senses for the reality of an electric fluid;--we see it in the

spark; we hear it in the explosion; we feel it in the shock; and it

produces the effects of mechanical violence, piercing and tearing

the bodies through which it passes. And those who are disposed to

assert a real fluid on such grounds, may appear to be justified in

doing so, by one of Newton's "Rules of Philosophizing," in which he

directs the philosopher to assume, in his theories, "causes which

are true." The usual interpretation of a "vera causa," has been,

that it implies causes which, independently of theoretical

calculations, are known to exist by their mechanical effects; as

gravity was familiarly known to exist on the earth, before it was

extended to the heavens. The electric fluid might seem to be such a

_vera causa_.

To this I should venture to reply, that this reasoning shows how

delusive the Newtonian rule, so interpreted, may be. For a moment's

consideration will satisfy us that none of the circumstances, above

adduced, can really prove material currents, rather than vibrations,

or other modes of agency. The spark and shock are quite insufficient

to supply such a proof. Sound is vibrations,--light is vibrations;

vibrations may affect our nerves, and may rend a body, as when

glasses are broken by sounds. Therefore all these supposed

indications of the reality of the electric fluid are utterly

fallacious. In truth, this mode of applying Newton's rule consists

in elevating our first rude and unscientific impressions into a

supremacy over the results of calculation, generalization, and

systematic induction.[**39\11] {214}

[Note **39\11: On the subject of this Newtonian Rule of

Philosophizing, see further _Phil. Ind. Sc._ B. xii. c. 13. I have

given an account of the history and evidence of the Theory of

Electricity in the _Reports of the British Association_ for 1835.

I may seem there to have spoken more favorably of the Theory as a

Physical Theory than I have done here. This difference is

principally due to a consideration of the present aspect of the

Theory of Heat.]

Thus our conclusion with regard to this subject is, that if we wish

to form a stable physical theory of electricity, we must take into

account not only the laws of statical electricity, which we have

been chiefly considering, but the laws of other kinds of agency,

different from the electric, yet connected with it. For the

electricity of which we have hitherto spoken, and which is commonly

excited by friction, is identical with galvanic action, which is a

result of chemical combinations, and belongs to chemical philosophy.

The connexion of these different kinds of electricity with one

another leads us into a new domain; but we must, in the first place,

consider their mechanical laws. We now proceed to another branch of

the same subject, Magnetism.

{{215}}

BOOK XII.

_MECHANICO-CHEMICAL SCIENCES._

(CONTINUED.)

HISTORY OF MAGNETISM.

EFFICE, ut interea fera munera militiaï

Per maria ac terras omneis sopita quiescant.

Nam tu sola potes tranquilla pace juvare

Mortales; quoniam belli fera munera Mavors

Armipotens regit, in gremium qui sæpe tuum se

Rejicit, æterno devictus vulnere amoris;

Atque ita suspiciens tereti cervice reposta,

Pascit amore avidos inhians in te, Dea, visus,

Eque tuo pendet resupini spiritus ore.

Hunc tu, Diva, tuo recubantem corpore sancto

Circumfusa super, suaves ex ore loquelas

Funde, petens placidam Romanis, incluta, pacem.

LUCRET. i. 31.

O charming Goddess, whose mysterious sway

The unseen hosts of earth and sky obey;

To whom, though cold and hard to all besides,

The Iron God by strong affection glides.

Flings himself eager to thy close embrace,

And bends his head to gaze upon thy face;

Do thou, what time thy fondling arms are thrown

Around his form, and he is all thy own,

Do thou, thy Rome to save, thy power to prove,

Beg him to grant a boon for thy dear love;

Beg him no more in battle-fields to deal.

Or crush the nations with his mailed heel.

But, touched and softened by a worthy flame,

Quit sword and spear, and seek a better fame.

Bid him to make all war and slaughter cease,

And ply his genuine task in arts of peace;

And by thee guided o'er the trackless surge,

Bear wealth and joy to ocean's farthest verge.

{{217}}

CHAPTER I.

DISCOVERY OF LAWS OF MAGNETIC PHENOMENA.

THE history of Magnetism is in a great degree similar to that of

Electricity, and many of the same persons were employed in the two

trains of research. The general fact, that the magnet attracts iron,

was nearly all that was known to the ancients, and is frequently

mentioned and referred to; for instance, by Pliny, who wonders and

declaims concerning it, in his usual exaggerated style.[1\12] The

writers of the Stationary Period, in this subject as in others,

employed themselves in collecting and adorning a number of

extravagant tales, which the slightest reference to experiment would

have disproved; as, for example, that a magnet, when it has lost its

virtue, has it restored by goat's blood. Gilbert, whose work _De

Magnete_ we have already mentioned, speaks with becoming indignation

and pity of this bookish folly, and repeatedly asserts the paramount

value of experiments. He himself, no doubt, acted up to his own

precepts; for his work contains all the fundamental facts of the

science, so fully examined indeed, that even at this day we have

little to add to them. Thus, in his first Book, the subjects of the

third, fourth, and fifth Chapters are,--that the magnet has

poles,--that we may call these poles the north and the south

pole,--that in two magnets the north pole of each attracts the south

pole and repels the north pole of the other. This is, indeed, the

cardinal fact on which our generalizations rest; and the reader will

perceive at once its resemblance to the leading phenomena of

statical electricity.