Indian Journal of Chemical Technology Vol. II , July 2004, pp 582-592

The nature of heat

Jaime Wisniak Department of Chemical Engineering, Ben-Gurion University of the Negev,

Beer-Sheva, Israel 84 105

T he nature and effects of heat have intrigued philosophers and scientists since ancient times. Different theo['ies were deve loped to exp lain the phenomena, and of these, the wave theory and the ca loric theory were the ones that reillained in force until the second half of the nineteenth century when overwhelming evidence led to the conclusion that heat was not a material substance, that the molecu les of a gas were not stat ionary but could move in space, and that radiation and light were asical ly the

sa ille phenomena.

Key words: Heat, wave theory, materia igni s, undulatory theory, Issac Newton

The Greeks were di vided into two camps regarding the

nature of fire, one of the four e lements that constituted

matte r. For Aristotle air and fire were not sens ible

realiti es because it was through tact that we judged

sensib le rea lity; a ir and fire were weightless and the ir natural p lace was in the periphery of the unive rse. The

supporte rs o f the atom ic theory affirmed the corpora lity, possess io n of weight, and mate ri a lity of fire. T hey

believed that the atoms were much smaller than the other

e lements and located far away from one another, facts that ex plained their ligh tness on the sens ible sca le. In

add iti on, they were prov ided with extreme mobility that increased their spheri ca l shape appropriate to s lide

wit ho ut fri ct io n ; o ur tact translated this ex tre me

move ment into a hea t sensati on . Thus, in the Greek atomism we find together two contrad ictory aspects: heat

as a substance and heat as movement. These two views

wou ld orig inate, in the seventeenth century, two different and rival theori es, the wave theory and the caloric theory.

The \\love theOlY (often ca lled the undulato ry theory)

was based on the fac t that heat and light travelled through space with a definite velocity and that it could not be conceived anothe r way by which an influence, travelling in t ime, could be propagated from one body to another s ituated at a distance. Radiant heat like li g ht , was

supposed to be due to wave moti on in the ethe r. The mol ec ul es of a body were in a state of ve ry rap id v ibrati o n , or were the ce ntre of rapid periodic disturbances of some so rt , and these vibrat io ns or perturbations gave place to waves that travelled through

E-mai l: wisn iak @bgumail.bgu.ae.i l

the ambient ether. These waves moved through the ether

at the speed of light and upon fa lling on the body of a person they were absorbed, generat ing inte rn a l moti o ns

in the mo lecu les and the co rrespotldi n u fee lin u of b b

warmth. The body of a person was exc ited by these heat

waves in the same manner as the eye was exc ited by the waves coming from a luminous body, o r as the ear was

affected by the aeri a l waves or ig inat ing by a sou nding

body. Heat was thus attributed to mot ion. T he kinetics flourished during the first two decades o f the e ighteenth

century, to be ecl ipsed the reafte r by the e the real theo ry of Herman Boerhaave ( 1668-1 738). Boerhaave 's theory

supposed that heat was the vibrati on of the partic les of the heat fluid , o r materia ignis. In his e mphasis on

v ibrati ons, the e the rea l theory was a lso kinetic l.

In the Form in whic h it was genera ll y unde rstood fro m the 1770s until it was fina ll y rejected in the 18S0s

the ca loric theory of gases had two distingui s hing c haracte ri s ti cs. F irs t , the partic les of gases were conceived to be s tati ona ry, being he ld in position by repul sive fo rces that were thought to ex ist between them. Secondly, these rep ulsi ve fo rces we re th e mselves attributed to the presence, e ither round or between the

gas particles, of the subtle, weightless and highly e lastic fluid of heat that from 1787 was known to most sc ientists as caloric . Heat was an imponde rab le e last ic fluid that

permeated th e po res of th e bodi e s a nd f ill ed th e inte rstices between the mo lecul es of the matte r. T he theory negated th at atomic v ibrat io ns a lone co uld

account for the phenomena of heat; th e ro le of the ethe r was essential. In addition , atoms in a gas cou ld not move

EDUCATOR 583

freely through space, they were constrained to vibrate about fixed equilibrium positions. The beli ef that the elastic properti es of gases could be accounted for by suppos ing that gas particles were stationary and subject to mutuall y repul sive forces was wholly Newtonian. In the Prillci/Jio 2 Isaac Newton ( 1642-1727) had shown how Boy le's law could be predicted on such a basis, if it was assumed, that the repulsive force between any two adjacent parti cles of a gas expandin g or contracting isothermall y was in versely proportional to the di stance between them. By the time the caloric theory emerged th ere were already a number of hi ghl y developed theories of electricity, magnetism and light that were based o n th e ex is tence of subtl e, e las ti c, oft en imponderabl e fluid s with properties remarkable similar to those of caloric'.

The ca loric theory came into general use in the eighteenth century and indeed proved to be much more helpfu l in ex plaining the thermal phenomena known that was th e rival and view that hea t was so methin g assoc iated with the motions of the particles of ordinary matter.]n 1779, Willi am Cleg horn extended the material theo ry to take in to accou nt Joseph Black 's ( 1728- 1799) discoveries of spec ific and latent heats. The matter of heat, or ca lori c, as Antoine-Laurent Lavoisier ( 1743-1794) ca ll ed it in 1787 , was now characteri zed by the fo ll ow ing attri butes: (a) ca loric is an elast ic fluid , the parti cles of whi ch repel one another strongly. (b) the particles of caloric are attracted by particles of ordin ary matter, the magnitude of the attract ion being different fo r different subs tances and for different states of aggregati on, (c) caloric is indestructible and uncreatable, (d) ca loric can be either sensible or latent, and in the latter state is combined chemicall y with the parti cles of matter to form the liquid or vapour. Sensible caloric was supposed to form an atmosphere around the parti cles of the body, and (e) ca loric does not have appreciable weighrl.

The caloric theory of heat reached the height of its popularity around 1825, and its supporters included many of th e leading sc ienti sts, espec iall y in Paris. According to Bru sh" it was the keystone of the anti­phlog iston th eo ry and was used in e xplaining phenomena such as thermal expansion , spec ific heat, changes of state, latent heat, and the heat evo lved in chemi cal reactions. The chief opponents of the caloric theory at thi s time were Benjamin Thomson (Count Rumford, 1753- 18 14) and Humphry Davy ( 1778- 1819).

The wave theory was supported by many of the outstanding scientists of that time, among them Franc is Bacon ( 1561 - 1626), Robert Boyle ( 1627- 169 1), Isaac Newton ( 1642-1 727), Sadi Carnot ( 1796-1 832), Joseph Fourier (1768- 1830), Pierre-Simon Laplace ( 1749-1 827), and Thomas Young ( 1773-1 829).

In 1620, Bacon, in his book -NO VUf17 Orgallll/l1 (' ,

analysed all the ava il ab le in fo rmat ion on heat and its effect and stated that it could onl y be ex plained by heat being moti on: "from the instances taken co ll ec ti vely. as well as singly, the nature of whose if heat appears to be motion. This is chiefl y exh ibited in fl ame, which is in constant motion , and in warm or boiling liquids, which are likewise in constant motion. The very essence of heat, or the substanti al se lf of heat is mot ion and nothing else" . According to Bacon a so lid proof of the me­chanical nature of heat could be found in the phenom­enon of fri cti on were it was possible to produce heat without resource to a substance already hot.

Several famous sc ienti sts adopted Bacon's vi ew. Boyle used it7 to try to explain the gain in weight shown by metals on calc in ati ons. Newton bel ieved that heat consisted in a minute vibratory motion of th e particles of bodies, and that thi s motion was communicated through an apparent vacuum, by the undulat ions of an elastic medium, whi ch was also in vo lved in the phenomena of li ght. It was easy to imagine that sLich vibrat ions may be excited in the component parts of bodi es, by percuss ion, by friction , or by destructi on of the equilibrium of cohes ion and repul sion. In hi s book Opricksx Newton wrote : "Do not all fi xed Bodi es, when heated beyond a certain degree, emit li ght and shine, and is not thi s Emission performed by the vibrating motions of the parts? Is not Fire a Body heated so hot so as to emit Light cop iously? Is not the Heat of the warm Room conveyed through the Vacuum by the Vibrations of a much subtl er Medium than Air, which after the Air was drawn out remai ned in the Vacuum? And is not thi s Medium the same with that Medium by which Light is refracted and reflected, and but whose Vibrations Light comlllunicates Heat to Bodies and is put into Fits of easy reflection and easy Transmission? And do not hot Bodies communicate their heat to contiguous cold ones, by the Vibrations of thi s medium propagated from them into the cold ones?" In was Newton's opinion that the vibratory motion of the particles in bodies communicated through an apparent vacuum, by the ondulations of an elast ic med iulll , which was also concerned in the phenomena of li ghtx.

584 INDIAN J. CHEM. TECHNOL., JULY 2004

Cm-not also supported these ideas . According to him "at present , light is generally regarded as the result of a vibratory movement of the ethereal fluid. Light produces hea t, or at least accompanies the radiant heat and moves with the same velocity as heat. Radiant heat is there fore a vibratory movement. It would be ridiculous to suppose that it is an emission of matter while the li ght , which accompanies it, could only be movement. Could a motion (that of radiant heat) produce matter (ca loric)? Undoubtedly not, it can only produce motion . Heat is then the result of a motion"~.

Carnot also referred to th e nature of heat tran smission : "Is heat the result of a vibratory motion of molecules? If this is so, quantity of heat is simply quantity of motive power. As long as motive power is used to produce vibratory movements, the quantity of heat must be unchangeable; which seems to follow from experiments in calorimeters; but when it passes into move ments of sensible extent, the quantity of heat can no longer re main constant"'). A reading ofCarnot's book

Re.flexiolls shows that at that time it supported the caloric theory ; late r documents indicate that Carnot accepted the wave theory of light afterwards".

Fourier in his famous book Analytical Theory of Heot lll stated that "of all the modes of presenting to us the action of heat, that which seemed simplest, and most conformable to observation, consisted in comparing it to that of light. Molecules separated from one another reciprocally communicated across empty space, their rays of heat , just as shinning bodies transmitted their I ight. All bodies had the property of emitting heat through their surface; the hotter they were the more they emitted and th e intens ity of the emitted ray s changed very considerably with the state of the surface".

According to Fourier, " the free state of heat was the same as that of I ight ; the active state of this element was then e ntirely different fro m that of gaseous substances. Heat acted in the same manner in a vacuum, in e lastic tluids, and in liquid or solid masses; it propagated only by way of radiation , but its sensible effects differed according to the nature of bodies. Heat was the origin of all elasticity ; it was th e repul s ive force, which preserved the form of solid masses and the volume of liquids"").

One of the arguments for the material ity of heat at the beg innin g of the nineteenth century was the fact that heat can apparently travel through empty space

without any accompanying movement of matter; hence it could not be simply molecular motion. Attempts to detect the weight ascribed to heat were made at various times during the seventeenth and e ighteenth century by several scientists. For example, in 1665 Boyle had written in New Experiments olld Obser v({ tions Toucliill!!, Cold l

) that water weighed first when frozen and then unfrozen showed "nol one groin dWerence" and in his Essays ofEjjluviuf11:/ afte r showing that a metal gained weight upon calcinations, he suggested that thi s mi ght be due to the addition of " I he material parlicles o.tfire". Up to about 1776, most of the experi ments had been based used in the large amount of heat absorbed by metals (such as iron, copper, gold, and silver) when heated red­hot. The results varied widely because of the experi mental difficulties and the lack of appropriate measuring instruments . In some cases the metal appeared to we igh more when cold ; in other cases, to weigh more when hot; in a few cases, not to change in w~ight. Although good balances for weighing were aV <.: i1 ab le, there were many other possible sources of e rro r when the same object was weighed at widely different temperatures. Although the experimenters were aware of the possible effect of convection currents, different ex pansion of the arms of the balance, or chemical changes in the meta l due to heating (such as oxidation), they e ither were not careful enough or assumed them to e neg li g ibl e~.

In the last quarter of the century the approach to this problem began to be influ enced by Black ' s discoveries of specific and latent heats, particularly the latter. The large size of the latent heat, the fact that a phase change took place at constam temperature and could be realized at room temperature or not much higher, suggested detecting the weight of heat by me lting or freezing a substance. For example, in 1785 , George Fordyce ( 1736-1802) carried out careful experiments to determine whether there was any change of weight when water was frozen l2 His experime nts consisted in weighing a given mass of water after being brought to different degrees of freezing_ He did found an increase in weight of about one part in 129,000. He repeated hi s procedure during five consecutive times; each time more water had frozen and more weight had been gai ned. When the ice subsequently was allowed to me lt , this additional weight was gradually lost.

Particularly ingenious experiments were also pelformed by Joseph-Louis Gay-Lussac (1778-1850) and

EDUCATOR 585

Rumfo rd , as desc ribed below.

The arguments supporting the wave theory led necessaril y to a cha lleng ing question: Were there two d istinct sets of waves in the e the r? Were there heat and light waves, or were these waves of the same nature and type? The fac t that light al so possessed heating power at once led to suspec t that there was no essentia l di ffe rence in characte r between the wave motion that affec ted our sense of heat and that which affec ted our sense of vision 1:\ .

In the period 1800-1 835 , ex periments on radiant heat by Will iam Hersche l ( 1738-1 822), John Les lie ( 1726-1 832), Macedoni o Me ll oni ( 1798-1 854), and

others showed th at radi ant heat had most if not all of t he pro pe rti es of li g ht. M e ll o ni , in p a rticul a r, demonstrated that radiant heat shared all the qualitati ve properties of li ght: re fl ecti on, re fracti on, diffrac tion, po lari zation, inte rfe rence, e tc . Thi s led to a widespread be lief that hea t and li ght were essentiall y the same phenomeno n, i.e., superf ic ia lly diffe rent manifestation of the same phys ical agent. M axwell 's electro magnetic theory indicated that heat radiation would be viewed as a spec ia l case o f e lec trom agne ti c waves (infrared radi a ti o n), whi c h p roduced the rm a l effec ts wh e n absorbed by matter' .

By 1830, the wave theo ry of heat was be in g seri ously considered as an a lternative to, or modification of, the caloric theory. The first extended di scuss ion of heat was two papers publi shed by Ampere in 1832 and 1835 I.W. He began hi s memoir by stating that " thanks

to the findings of Edward Young ( 168 1- 1765), Fran c;:o is Arago ( 1785-1 853), and Augustin Fresnel ( 1789-1 827), it is well-kn own that light is produced by the vibrations of a fluid di stributed all over the space and named ether. Rad iant heat, that fo ll ows the same laws in propagating, can be ex pl a ined in the same manner. But, when heat is transferred from the hottest part of a body to that is colder, the propagati on laws are very diffe rent : instead of a vib rational movement transferred by waves (ondes), we have now a movement that propagates graduall y, so that the part that is initia lly hotte r (and consequently, the o ne mo re ag itated w he n heat is ex pl a in ed by vi b ra ti o ns), a lth oug h loos in g heat by deg rees, it conserves more that the parts to which it is transmitting heat. This fact g ives pl ace to an obj ec ti on to heat be ing transferred by vibratory movements" 14.

As more experimental ev idence accumulated it became more and more difficult for the standard calori c

theory to explain the m. Thus it went through a simil ar development stage as the phl ogiston theory had a lready done. Explanation of the wide varie ty of phenomena occun'ing in the generation of heat by fri ction, radiation, temperature, specific heat , expansion , c hange of state, and the repuls ive forces between gas partic les , was done by sui generis variati ons of the theory and the nature of calori c. Caloric was now assumed not onl y to be an e las ti c fluid ; its properties were a lso "elasti c" , they c ha nged accordin g to the ph e no me na in whi c h it partic ipated . Neverthe less, in all ve rsions of the calori c theory only one fluid was concerned and its properti es were merely modif ied by its state of combination with ordinary matte r. For exampl e, according to Joseph­Marie Socquet l 6 caloric could ex ist in four diffe re nt s tat es : ca lo ri c o f co mpos iti o n , of capac it y, of te mpe ra ture , o r as radi a nt ca lo ri c . Ca lo ri c of composition was chemically combined with the ultimate particles of matter, fo rming one essen ti a l constituent of them. A molecule o f a g iven compound , for examp le, w ould contain a ce rtain qu a ntit y of ca lo ri c of compos iti on which would remain unc hanged so long as the molecule continued to exi st, (b) caloric of capacity, on the other hand , was re tained in a body by a pure ly phys ical force (affinity of adhes ion). Particles of calori c, like those of a dissolved gas, were supposed to penetrate any substance and to adhe re to the surface of thei r molecules with a force inversely proportional to the square o f the di stance from the surface , so that the capacity was determined not s impl y by the innate affinity of the molecules for calori c but a lso by the ex tent of the surface area of the molecules to which caloric would adhere . The assumption that every mate rial was formed by a cong lomerate of parti c les meant that it was porous and that the pores were filled by caloric o f temperature, (c) caloric of temperature, unlike a ll o the r types of caloric, could be detected by a thermometer and in this important respect it diffe red from radian.t caloric, which was supposed to move so rapidl y that it was de tectable o nl y if it was s lowed dow n by th e m ate ri a l of a thermometer and essentia lly ceased to be radi ant caloric3

Views of some scientists

In what fo llows we will desc ribe in more deta il the arguments given by some the most famous sc ien­ti sts, in fa vour of one or the other theory.

Lavoisier

Lavoisier, in a first paper presented to the Academie de Sciences l7 suggested that gases and vapours resulted

586 INDIAN J. CHEM. TECHNOL. , JULY 2004

from the combinati on of matter of fire (moliere du f eu

or .lluide igne) with a base, which could be e ithe r a liquid o r a volatile so lid . Tn a following pape r l~, he

s ugges te d that thi s co mbinati o n took place by a mechanism similar to a chemical union. Heating occurred during combu sti on, for example, simply because the base of o il' vilol (oxygen) had a g rea te r affinity for the inflammable substance than for the matte r of fire and so

combined with it, allowing the fire to escape and become free. This explanati on required that the fire should ex ist in two states, combined or free. When fire was combined with o rdinary matte r it was unde tectable, only when it

was free it affected the thermometer and produced the sensa tion of heat·, .

In the ir famous memoir about heat, Lavoisie r and

Laplace ") w rote that physicists were divided regarding

the nature of heat: many of them conside red it to be "un

fl l/ide rep({ndll dans IOlll e la Nalure, &. donI les corps

son l pIlls 0 11 IJ7 0 ins pell elres, ii rais o n d e fe ur

lell1pcmlure. &. leurdisposilion parliculiere iT Ie relenir

(a fluid di stributed in all nature and which penetrated

the diffe rent bodies according to the ir temperature and the ir ability to re tain it ). Heat could combine with bodies and in this state it ceased acting on the thermomete r

and could transfe r from one body to another. Only in th e free state (c holeur fihre) it co uld beco me in

equilibrium with bodies. Other physicists thought that heat is onl y the result of very small movements of the

mo lecul es of matte r. It is known that all bodies, even

the denser of a ll , were full of pores or small e mpty spaces, whose vo lume could be substantially larger that that occupied by the ir matte r; these spaces gave the

partic les the libe rty o f osc illating in a ll directi ons. It was natura l to think that these partic les were always

agitated because if the agitation was inc reased beyond a certain I imit they could di sunite and decompose the

bodies".

Lavoisier and Laplace be lieved that movements

that did not ex pe rience abrupt changes, were controlled

by the law called conservation of kinetic ene rgy (fo rces

vive). Heat was the kinetic energy that resulted from the subtl e movement of the molecules. Thi s viewpoint of hea t ex plained eas ily wh y th e direct impulsi on (momentum) of so lar rays was inapprec iable, although they produced a large heat. The ir impul s ion was the produc t o f the ir mass by the velocity; although the ir ve­loc ity could be very large the ir mass was ex tremely small so that the product was essentia lly nil.

Lavoisier and Laplace wrote that they would not

make a deci sion regarding which of these hypotheses

was the correct one but that they cou ld enumerate the

principles they had in common, and were independe nt o f th e nature o f heat: ( i) th e quant ity of f ree heat

remained constant during a s impl e mixture o f bodi es,

and ( ii ) if a reacti on o r a change of state occurred w ith a dec rease in free he at , this hea t wo uld reapp e ar

complete ly when the substances returned to their o ri g inal state, and vice versa. The obse rvant reader will rea li ze

immediate ly that Lavoi sie r and Lap lace were already stating in a first approach, the law o f co nse rvati on of

energy.

RIIII~t'(}rd

Rumford carri ed out several expe rime nta l stud ies

of the weight ascribed to hea t, as pa rt of an ex tens ive

program to throw lig ht o n the quest ion of the ultimate nature of heat. M ost o f hi s ex pe ri ments were concerned

with the the rmal pheno mena th at occurred during the

boring of cann ons and he used hi s res ults to attack the ca lo ri c theory from man y po ints of view. ln a paper publ ished in 179910

. Thomson discussed the ex peri ments

he had made to dete rmine the ques tion if heat had weight and concluded that all his results tended to convince

him " th at a body acquired no addit iO nal weig ht upon be ing heated , o r rathe r that heat had no effect w hatsoever

on the we ig hts of bodies". Hi s resul ts led him to support the motion theorl.

Rumford repeated Fordyce's experiments us ing a very sensitive balance that he had borrowed fro m th e Duke of Bavaria and much to hi s ,'u rpri se hi s initial

results corroborated those of Ford yce: freez ing water

resulted in a loss in we ight. He pe rformed another seri es of ex pe riments in whic h he weighed simultaneously identical masses of mercury and wate r before and after

heating the m to the same temperature; this time he found no change in weight. These co nfli c tin g result s led

Rumford to the brilliant idea of performing a third series of ex pe riments , now us ing ide ntica l masses of wate r, spirit of wine, and mercury, cooling them to a temperature at which onl y water froze, and comparing the weig hts before and after cooling. He also took ex treme care in assuring that a ll the three mate rial s are at the same

te mperature as th e surroundings, in itiall y and afte r

cooling. This time he found that none of the materi als showed a change in we ight. After a careful analys is of

EDUCATOR 587

his experiments and results he came to the conclusion

that hi s initial anomalous results were due to the fact that the water was not at a uniform temperature at the time of weighing it. His final conclusion was that "all

attempts to di scover any effect of heat upon the apparent weights of bodies will be fruitless"4.

The most celebrated experiments carried on by

Rumford were those concerned with the heat produced during the boring if canon" l

. Already in 1620, Bacon('

had expressed the idea (that new heat comes into ex istence when an object is rubbed or hammered, and

from this he concluded that " heat itse lf, its essence and

quiddity (identity) , is motion and nothing else". The fact

that heat could be produced without the action of fire and in unlimited quantities presented quite a challer.ge

to the supporters of the caloric theory. The exp lanation given was that the mechanical perturbatiom: modified

the heat capacity of the material ; these perturbations

led the material to behave as a "sponge", forcing more

calori c to leave, without creating it.

According to Rumford"' : " By meditating on the

results of all these experiments we are naturally brought

to that great quest ion which has so often been the sub­ject of speculation among philosophers; name ly : What is heat? Is the re any such thing as an igneous fluid ? Is the re anything that can with propriety be called caloric? We have seen that a ve ry considerable quantity of heat

may be exc ited in the friction of two metallic surfaces and g iven off in a constant st ream or flux , in a ll direc­

tions , without iterati on or intermi ss ion , and without any signs of diminution or ex haust ion. From whence came

the heat, which was cont inually g iven off in thi s man­

ner, in the foregoing experiments? Was it furnished by the sma ll particles of meta l, detached from the larger

solid masses, on their being rubbed together? This, as we have already seen , could not possibly have been the

case. Was it furnished by the air? This coulct not have been the case ; for in three of the experiments, the ma­chinery being kept immersed in water, the access of the

air of the atmosphere was completely prevented. Was it furni shed by the water, which surrounded the machin­

ery? That thi s could not have been the case is ev ident : first, becallse thi s water was continually rece iving heat

from the machinery and could not, at the same time, be giv ing to, and receiv ing heat from , the same body; and secondly, because the re was no chemical decomposi­tion of any part of this water. Had any sllch decomposi­tion taken place (which indeed could not reasonably have

been expected), one of its component elastic fluids (most

probably inflammable air) must, at the same time, have been set at liberty, and in making its escape into the

atmosphere would have been detected ; but though I fre­quently examined the water to see if any air bubbles rose up through it. . . I cou Id perceive none; nor was there

any sign of decomposition of any kind whatever, or other chemical process, going on in the water. Is it possible

that the heat could have been supplied by means of the

iron bar to the end of which the blunt steel borer was

fixed ... ? These suppositions appear more improbable

even than either of these before mentioned; for heat was continually going off, or out of the machinery, by both

these passages, during the whole time the experiment

lasted . And, in reasoning on thi s subjec t, we mu st not forget to consider that most remarkable circumstance,

that the source of the heat generated by friction , in these experiments, appeared ev idently to be inexhaustible.

It is hardly necessary to add that anything which any

insulated body, or sys te m of bodies , can continue to furnish without limitati on cannot possibly be a material

substance: and it appears to me to be extremely difficult,

if not quite impossible, to form any distinct idea of anything, capable of being exc ited and co mmunicated,

in the manner the heat was excited and communication in these, except it be moti on".

Avogadro

In this monumental treati se on mate rial bodies21

Amedeo Avogadro ( 1776-1 856) studied the constituti on

of heavy ordinary bod ies, discussing the nature of molecules , molecular forces , and how phys ica l states

could be interpreted in terms of these forces. E lectr icity and magne ti sm , considered imponde rabl e, were not discussed, and chemistry was touched only peripherally.

In his approach he was following the theory in vogue

that Newto n' s method of infe rrin g laws from c lose observation of phenomena and then deducing forces from these laws could be applied successfully to phenomena

in which no ponderable matte r figured. In the overa ll context of European physics, Avogadro ' s treat ise was

published too latc. By 1830, new fundamental theori es were unfolding , and as a re sult , the co nce ptual foundations on which mos t of his book rested were obsolete even before the printing had been comp leted . In thi s work, Avogadro continued to support the caloric theory of heat and a distincti ve interpretation of the nature of mo lecular forccs.

588 INDIAN J. CHEM. TECHNOL. , JULY 2004

Like John Dalton (1766-1844), Avogadro believed

that gases were composed of particles of ponderable matter of roughly globular form , whose size was

rep re se nte d by a hard sphere surrounded by an atmosphere of caloric. The particles were separated by

such a distance that their mutual attraction could not be exerc ised. He be lieved that it was " very conceivable

that the mo lecules of gases being at such a distance that th e ir mutual attrac tion could not be exerci sed , their

va rying attraction for caloric limited to condensing the

atmosphere fOllll ed by this fluid , having any larger ex tent

in one case than in the other, and, consequently, without the di stance be tween the molecules varying, or in other

words, without the number of molecules in a given volume be ing different"2, . This claim differed from that of Dalton

for whom the quantity of caloric was always the same for the mo lecul es of all bodi es in the gaseous state and

that the greate r or less attraction for calori c refl ected onl y in a larger or small e r condensation o f the fixed

amount of ca lo ri c; and thus led a varying di stance be tween the mo lecules . For Dalton such decreased rep ulsi o n meant a condensation of volume of the

atmospheres of ca loric and a contraction in the size of the partic les, while no variation occurred in the actual

amount of heat surrounding them. Since diffe rent gases

had diffe rent affinities for caloric, Dalton argued, the ir

particles had to have different sizes, and , the re fore, they mu st be in diffe rent numbers in a g iven volume.

Avogadro discussed the diffe rence be tween hi s ideas and those of Dalton in the introductory part of hi s Essai d 'l/ll e Malliere D and stated if Dalton 's were assumed to be correct then it would be impossible to

ex plain why th e very s imple ratio s found in the combinations of diffe rent gases reported by Gay-Lussac.

According to Avogadro, "in our present ignorance of the manner in which this attraction of the molecules for

caloric is exerted , there is nothing to decide us a priori in favour of one of these hypotheses rather than the other;

and we should rathe r be inclined to adopt a neutral hypothes is, which would make the di stance between the molecules and the quantity of caloric vary according to unknown laws, were it is not that the hypothesis we have just proposed is based on that simplicity of relation between the volumes of gases on combination, which

would appear otherwise inexplicable" . The most likely and logical answer laid in assuming that in a gas the

intermolecular distances were so large that no mutual action between such molecules could take place; under these conditions, a change in the attraction for the caloric

displayed by each molecule might affect the amount of caloric condensing around it , but not the volume. Thus

it was reasonable to assume, that, unde r equal volumes (or equal temperature and pressure) there was always the same number of molecules.

In two foll owing me moirs2-l, he introduced th e additional assumption that the qu ::t ntity of ca lor ic

required to produce a g iven tempe rature inc rement in a unit volume of any gas was de te rm ined solely by the charac teri sti c attractive power of th e mo lecul es. For

Avogadro, it was this quantity, and not spec ific heat, which was conserved in a che mi cal reacti o n.

In a later me mory2), he attempted to corre late the

amount of caloric present in a gas w ith the affinit y of

the same gas for caloric by assumi ng that at a g iven

temperature and pressure the spheres o f the molecules of gases were the same, and th at the same molecules

placed at the centre of these spheres (where the de nsity

o f caloric mu st be inde finite ly large) occupied a certain portion of the ir tota l volume. If now the volume o f the molecules was assumed to be proporti o nal to their mass

then the den sity of the matter of all rno lecules was the same and that they differed onl y by the ir mass inasmuch

as they differed in their volume. Therefore, the vo lume

occupied by each gaseous molecule w ithin the ca lori c

sphere would be proportional to th e mas s of th e molecul es.

Avogadro a lso found, that , the re was a s imilarity between the values of affinities for caloric and the degree

of oxygenicity (affinity for oxygen); th e order of increas in g affinity for caloric , w ith o ne o r two exemptions, resembled that of increas ing affinity for oxygen, i.e., of decreas ing acidity, with the affinity

between hydrogen and caloric on the one hand and th at

between hydrogen and oxygen on the other be ing the greatest of all. Since even oxygen itsel f had affinity for

caloric, it followed that affinities for oxygen and for caloric were of the same nature, that caloric was the

"sostanza ossigen.ica per eccelenw" . In a following paper2-', he was abl e to d eve lop th e foll ow in g

relationship between th e affinity for caloric (A) and refractive power (P):

P = 0.4193 A + 0 . 5807 ~

Ampere

Andre-Marie Ampere (1775-183 ]) recognized at the outset a major difficulty in using the same theory to explain the transmission of radiant heat through space

f:OUCATOR 589

and the co nduct ion of heat through material bodi esl~: "lnstead of a vibratory moti on propagated by waves (olldes) in such a mann er that every wave leaves at rest the fluid which sets it in motion at the in stant of its passage. we have a moti on propagated graduall y in such a manner that the part whi ch ori ginall y was the hottes t. and consequentl y the most ag itated, although loos ing heat by degrees, preserves, however, more that the parts to which it is communicating heat" . In modern terms, the problem was to reconcile the propagati on of heat by waves (second-order d ifferential equation in time) in free space, wi th its propaga ti on as described by Fourier's heat conducti on equati on (first-order time deri vative). But Ampere th ought he could answer thi s and other objecti ons to the theo ryS

Ampere postul ated that the total vis vivo of rhe system was conserved, vis viv(/ bein g defined as the " .'·O/l1l1l e des prodllil s de lo ul es les masses de ses 1I /OIecllles por In carres de I('urs vilesses {I 1111 illSlanl dOlln e. el qll 'O Il v {/joul e Ie dO llhle de I 'ill f(!g role de la SOlllll le des prodllils des fo rces 1I1l111ipliees par les difterell lielles des espaces parc{)urtls dOll S Ie sens de as Forces !}(Ir c/wqlle IIwleCllle, celie illleg ra le qui ne dep'end qlle de 10 posilion re/alive des molecules elOnt prise de IIwlliere qu 'elle soil Ilulle dOllS 1(/ position d 'eqllililJre (lIiIOlir de 10 laqll elle se fail 10 vibratioll" (the summat ion of the prod ucts of the masses of all it s molecul es by the sq uares of their veloc ities at a given moment , adding double the integral of the sum of the prod ucts of the forces multipli ed by the differential s or the spaces described, in the direc ti on of those forces ,

by eac h molec ul e" [l' mv 2 + 2 J l' F . dx ]. T~~i s int egral depended onl y on the relat iv..: positi on of the molecules and was taken in such a manner that it be zero for the eq u i I ibriulTI position about which vi brat ions took place). If the atoms vibrated while immersed in a flui d, they woul d graduall y lose vis viva to it ; ifiniti all y one atom was vibrating and the others were at rest, then the riuid would transfer some vis vivo to these other. However, th e total vis viva of all the ato ms would decreasc as waves were propagated th rough the flui d out of the system. unless we supposed it to be enclosed in a co ntainer of vibrato rs (dioposolI s) , whi ch are maintained in a sla te of vibration at a co nstant vis vivo . Then eventually all the vibrators would approach the samc V I S VIVO .

Ampere rej ec ted firmly a doct rin e that had dominated atomic speculation during the preceding half-

century: "Now, it is clear that if we ad mit the phenomena of heat to be produced by vibrations, it is a contrad icti on to attri bute to heat th e repul sive force of the atoms requisite to enabl e them to vibrate" .

Ampere tri ed to answe r to thi s objec ti on by showin a to whi ch kind of movement "ve re th ese b

phenomena due. Hi s ex planati on was based on the di stincti on that he made among particles, molecules, and atoms. He defined as par/ide an infinite ly small part of a body, hav ing it s same nature, so that a parti cle of a so lid was a so lid , that of a liquid a li qu id , and th at of a gas had the aeriform state. Particles were constituted of molecules maintained at a di stance by attracti ve and repul sive forces; by the repulsion that establi shed among them the vibratory movement of the intercalated ether; and by the attracti on, in direct rati o to their m asses and the inverse of the square of their di stance . Acco rding to A mpere JI1 0lec lJles we re an ass e mbl y of at oms maintained at a distance by the attractive and repUl sive forces proper of each atom, forces th at he accepted were substantially larger than those in the prev ious category. He call ed atom the material points from where these fo rces emanated and stated hi s beli ef th at atoms were abso lute ly indivi s ibl e so th at although space co uld divided infinite ly, matter could not.

Ampere di stin g ui shed be tw ee n mo lec ular vibrations and atomic vibrat ions. In the first , molecul es vibrated in mass when they approached or separated alte rnati ve ly one from the oth er. Molec ul es e ither vibrated or they were at rest. Atoms of eac h molecule we re alway s vibratin g whi Ie th ey approached or separated one fro m the other, but always attached to the same molecules. These latter vibrat ions constituted what he called atomic vibrati ons. He att ribu ted to molecular vibrations and to their spolial propagati on all sound ph e nom ena and to atomi c v ibrat ions a nd th e ir propagation in ether all heat and light phenomena ls

Berlltollel

Claude-Loui s Bertholl et ( 1748- 1822) in hi s Essoi de Stoliqu e Chilll iqlle2() discussed ex tens ive ly th e gaseous state and the chemica l behav iour of gases, using the argument th at only the action of ca loric had effect on th e ir phys ica l changes. Ca lo ri c in c reased th e molecular distance and all gases at the same temperature acquired a quantity of caloric proportional to the vo l­umes determined by the pressure. When two gases com­bined , their properties changed because their mutual at-

590 INDIAN J. CHEM. TECHNOL.. JULY 2004

traction overcame the affinity for ca loric; as a resu lt , a condensation of their volumes occLllTed, followed by new chemica l and physica l characteri stics. Nevertheless, some well-known phenomena did not fit thi s picture, for exampl e, the fact that an increase of ca loric affected the reaction between oxygen and hydrogen whil e the theory required that a great quantity of ca loric shou ld in stead be eliminated. Berthollet overcame this difficult by adopt ing Gaspar Monge's ( 1746- 18 18) twisted argument that the ca loric only caused, by the dilation of one part of the gas, a compress ion of th at which was less heated, so that the total effect was due to the sudden rapproc hement of th e molecul es produced by th e reaction27.

The strength of Berthollet's approach was that the phenomena wi th whi ch he compared the behav iour of ca lori c, fo rmed part of the single coherent system of chemical affi nities that he had recently dev ised: affinities were not constant ; they were variable and re lati ve. If one wa nted to predict the directi on of a reac ti on he had also need to take into account other factors , such as in so lu bi lity, diffe rence in so lubility, vo lat ility, fusibility, and the amounts of the reagents]('. The behaviour of acids provided the model for cal ori c. The quantities of a given ac id required to produce neutrali za ti on va ried according to the base with which the ac id combined. When two acids competed for a given base it was not true that onl y the one having the largest affinity reacted, leav ing the other ac id free. In reality there was a partition of the base between the two acids. Similarl y, different quantities of ca loric were required to produce the same effect (fo r exampl e, a certai n ri se in temperature in d ifferent bod ies), the quantiti es of ca loric (or ac id) in the two cases were proportional to the mass of the body (or base) and to its innate affinity fo r ca loric (or for the acid).

Gay-LlIssac

Durin g hi s lec tures of phys ics at the Paris Faculty of Sciences, Gay Lussac made use of the concept of ca loric, ex plaining to hi s students that the term had been in troduced in order to distingui sh the effect (heat , what is fe lt) from th e cause . Lavo is ier and Laplace had introd uced th e te rm ca lori c in 1783 without takin g positio n regard in g the ques ti on if it was a material substance or merely something associated with motion. Berth oll et too had said that ca loric might be e ither a substance or a force"('. However, it was usuall y treated as a substance or more prec isely as a subtle fluid , which

was mate ri a l and yet did not have weight. Many experiments in which bodies were we ighed first co ld and then hot failed to demonstrate co nc lusive ly th at caloric had weight. To tes t this hypothes is Gay-Lussac propo sed to hi s s tud e nt s a brilli ant and s impl e experiment in which a tightl y stoppered flask containing a layer of sulphuri c acid covered by a layer of water was weighed and then shaken; heat was evo lved and the flask was rewe ighed2x

. This experiment showed th at the heat produced had no weigh t, or as ' Gay-Lussac remarked, " if one wanted to be more prec ise and keep strictly to ex perimental evidence one could say that the caloric produced we ighed less than was poss ibl e to detect even with the most sensitive ba lance".

A significant di scussion on the nature of ca loric and its poss ible ex istence in vacuum took place between Gay-Lussac and Nico las Clement ( 1779- 1842) and Charl es-Bern ard Desormes ( 1777- 18()2) (see below). Accord ing to Gay-Lussac1X there wa~ no truth in the argument that a vacu um contained more cal ori c than when air was present. Clement and Desormes beli eved that vacuum did contain calori c and in the ir entry for the 18 12 pri ze of the Acadellli e de Sciell ces on the spec i fic heat of gases tried to prove the val idity of their assumption. Not onl y their memoir did no t win the prize, it was also rejected for publ icat ion by tlle journal of the Academie. Their paper was publi shed in 1819 by another journal , together with a foll ow-up wo rk2')':;", fac t that brought a sharp repl y from Gay-Lussac.1l . In it Gay­Lussac claimed that the idea that ac uulll contained ca lo ri c was eas il y refut ed by mea ns o f a s impl e experiment: Si nce calori c was assullled to be an elast ic fluid then, similarl y as with a gas, ther . should be a heat change when its volume was changed. S ince an increase or decrease in the volume of a vacuum had no effect on the thermometer, Gay-Lussac conside red that thi s nega­tive result confirmed hi s view.

On the ques ti on of the abso lute quantity of heat in a vacuum Gay-Lussac remarked th at it could not be "reso lved except with the help of nllmeroll s hypotheses wh ich are all the less plausib le as we do not know the nature of heat". According to Cross land.12 , althou gh Gay­Lussac had initiall y thought that calo ri c was a subtle flu id , he now admitted that the nature 01' heat was unclear and now, in hi s physics lec tures, he added an additional ex planation for the nature of ca lori c: "there is a second hypothes is which has also been adopted for a lon u time ;:,

and which beg ins to be he ld in increasin g favour. Thi s second hypothesis is that there ex ists an ex tremely subtle

LDUCATOR 59 1

f luid spread out indefinitely in space, a fluid which was

denoted not very long time ago by the name of ether or ethereal flu id , and it concei ves all molecules of a heated

body in a special state of vibration, of to and fro motion ,

undergo ing a small oscillatory movement which motion

produces the phenomena, the sensations and the effects

of heat" .

CI e me IIt-Des ormes

An inte resting fact is that Desormes and Clement int e rpre te d Gay-Lussac's res ults in a co mpl e te ly

diffe rent manner, arguing that they could actually be

used not only to demonstrate the exi stence of an absolute

zero but al so to calculate it s locatio n. Gay-Lussac had

written that the dete rminati on of the absolute ze ro of heat seemed a co mpl e te fantasy , but according to

Desormes and Clement to support the idea of unlimited

cooling , that is that the temperature could be dec reased

infinite ly, was the same as admitting that the quantity of heat that constitutes this temperature was infinite. If this

were the case, then heat would be unl ike any other meas­

urable thing or quality.

Desormes and Clement presented thei r ideas pa­

per on the subjec t to the French Academy in Septe mber 1812, on occasion of the prize competition for an essay

on th e probl e m o f de termination of specific heats

(competition that was won by Dulong and Pe tit). The pertinent memoir was not accepted for publication in

the j ournal Annale.\· de Chil11ie, but seven years later it was accepted for publication in another j ournar~ ') .

Desonnes and Clement were of the opinion that

the methods and arguments used by others to analjse

the possibility of the ex istence of an ;.;.bsolute zero, as we ll as de te rmining its pos ition , were vitiated by the

lack o f enoug h information about the caloric and the

difficulty of its measurement. For these reasons , they

adopted a complete ly diffe rent approach : "On concevra oiselll cnr que si (Ill lieu de vouloir esrimer Ie calorique qlli forl7le la telllpera rure d es co rps, 0 11. dirig e ses recherches sllr celui qui n 'est engage dans aUCLIIL corps, sllr cellii d'lIll espace vide d 'ail; tous les ill voll veniens d es (fnci enn e s m e thodes inutilernent employees

disparoissent . Nous al/ons don c c herch er tI bien apprecier Ie caloriqlle de /' espace. Cefte conf1oissance nOllr conduira ZI celle dll zero absolll de La temperature, et qll(fnd nOllr l'aurons fixe par cette methode, nous

Ie verifierons par quelques autre,I' moyens" (We real­ize that if instead of trying to determine the caloric that

composes the temperature of a body we address our

research to that that is not held by a body, that of an

empty space, all the inconveniences of old methods dis­

appear. We will estimate the caloric of space. This knowl­edge wi II take us to that of the absolute ze ro of tempera­

ture and once we have dete rmined it by this proced ure we will verify it by other methods) 29

In order to dete rmin e th e caloric of s pa ce, Desormes and Clement utilize d th e well-known

phe nomena that air became heated when it fl owed

suddenly into a space in which the re was abso lute vacuum, or it cooled when dil ated . To them, these results

rdlected the effect of the absolute temperature o f space .

Caloric propagated in vacuum like magnetism and li ght

and elimination of the air did not e liminate the caloric fluid. Thus, when air rushed into empty space its cal ori c

jo ined the one present in the space and, consequentl y, it he ated Up 2') . It was known that te mpe rature was

proportional to the amount of caloric, as long as the re were no phase changes . Since caloric was an elastic fluid , it mu st have similar laws as a gas ; one of the

important properties of gases was that they ex panded in

vacuum at a constant velocity (4 17 m/s ), independent

of their original pressure. Consequentl y, the ir mass fl ow rate was proportional to the ir den sity and not to the ir

speed , a be hav iour substantially diffe rent from that of

liquids, for which the de ns ity was co nstant unde r

different press ures and th e ir m ass fl ow rate was

proportional to the square root o f th e ir pressures. Comparing the cooling of a body to the fl ow of calori c and the temperature to the driving force (pressure drop),

led to the result that for an e lastic fluid the rate flow

should be proportional to the aCTive temperature, that

is, to the temperature difference. Thi s was ex ac tl y what Newton had stated, that the amount of caloric los t was

proportional to the temperature differe nce. Another immediate consequence was that the capac ity of dilated

air for caloric was the mean between that of air at a high pressure and that of pure space (vacuum) ~') .

Using th ese ideas, D eso rm es and Clement performed a se ries of experiments to de te rmine the absolute caloric contained in space by expanding air at atmospheric pressure into an empty vessel maintained

at 12SC. The ir results indicated that " le vide pOifait /t 10 temperature d e 12.5"C con.tien t un e quantite de

coLo rique absolll, capabLe d'elever de 99" un vo l­

ume d 'air atl110spherique qui d 760.8 111111 Hg. seroit egal d lui, et qlli ne choILgeroi( pas" (abso lute vacuum

592 INDIAN J. CHEM. TECHNOL. , JULY 2004

at 12SC contain s a quantity of absolute caloric able of raising by 99"C the temperature of a volume of air hav­ing the same volume at 766 .8 mm Hg). Thi s resul t was the same for dry or humid air. When the temperature

was 18"C (o r 98"C) the corresponding increase in tem­

perature was I 02"C (or I 52"C).

In a second paper'o, Desormes and Clement pre­

sented the objections that had been raised against the

doctrine o f abso lute te mperature, and the ir refutations

to the same: (a) Assumpt ion of the existence of caloric

in space free of matte r (vacuum) , (b) The possibi lity of measurin g the caloric o f space, and (c) The possibi lity o f de te rmining the absolute zero of temperature. ]n ad­

dition , they provided two additional procedures to deter­

mine the position of the absolute zero of temperature".

The demise of the theory

In 1845 E rn s t Wilhelm Brucke ( 18 19-1892)

publi shed a critical rev iew of the ev idence against the

identity o f heat and li ght, in connection with hi s s tudies o n the phys ical properties of the eye; he apparently

wanted to be lie ve in this identity and to accept the wave theory o f hea t3

-1. Hermann von Helmho ltz ( 182 1- 1894),

in a me mo ir published in 1847 on the conse rvation of force, conc luded that heat must be explai ned in terms

of motion , preferably by a wave theory such as that of Ampere·1s Be fore th e 1850s, gases were norma ll y

thought to be composed of stationary, equally spaced

part ic les between wh ich repulsive forces were postu­

lated in order to account for pressure and other charac­

te ri stic properties associate with the gaseous state. One

of the most important events in the hi story of nineteenth

century phys ical sc ie nce was the emergence in the late

1850s , of a wel l- founded and genera ll y acceptable kineti c theory of gases, the proof of the equivalence of heat and work, and the law of energy conservation:l,37.

Subsequent development of be tte r ex perimental techniques to understand the structure of radiant heat, the application of thermodynamic princ iples , the proof that ethe r did not ex is t, and research on thermal black

body radiation led to the quantum theory at the beginning of the twentie th century and to demise 01 the wave theory.

Refe rences I Mel h,ldo E M, Hisl S Il/{l Ph),s Sci, 13 ( 1983) 3 1 I. 2 Newton I, Philosophiae Naluralis Prillcipia Ma1helllalica (Lon­

don), 161:\7, 30 I, Book II , proposition xxi ii . 3 Fox R, The Caloric Theory of Gases - Frolll La vois ier 10

Regllaul (Clarendon Press , Oxford ), 1971 . 4 Roller D, The Rise ami Declille or lhe Caloric Theo n ' (Harvard

Un iversity Press, Cambridge) , 1950. 5 Bacon F, NOVUIII OIRalllllll , in Francis Baco n, Great Books of

th e Western World, Robe rt Maynard Hut chins , Ed itor , Encyclopaedia Britannica, Chi cago, 1955, vol. 30; Book 2.

6 Boyl e R, Essays of Ih e Slrall ge SUh li/ll', G rea l E.lficac.\', Delerlllilwle Nalure of Eflluviwils E.rperilll ellls Iv Make Fire

Cl lld Flalll e POllderable, Tog elher IVilli it Discoven ' or Ih e Perviousll ess oj' Glass (M. Pill , London), 1673.

7 Newton I, Oplicks, London , 1730. Republi shed by Do ver Publi cations , New York , 1952; Book II , P",rlIV, questions vi ii , xviii , and xxi.

8 Mendoza E (Ed .) Rejlecl iolls Oil Ih e lIIolive p()lver of .lire 1>.1'

Sadi CarllOl , Ci lld o lh e r Iwpers on Ihe sec olld lOll' of

IhenllodYIICllllics by Clapeyron E & Clausius R (Do ve r Publi ca­ti ons: New York), 1960.

9 Brush S, Bril J HisIOJ)' Sci,S ( 1970) 145. 10 Fourier J, Ana/.l'lical Th eon' or Heal , in Great Books of the

Wes tern World, edit ed by Ad ler M .I . Associate Editor, Encyclopaed ia Britannica, Toronto , 1952.

II Boyle R, New Experiments and Obser vations Touching Cold ( 1665), in Th e Works oj' Roberl Bo\'le , voluille 4, edited hy Hu nter Michael & Davis Edwa rd D (Pickering & ChalO. Lon­don), 1999 , 203-575.

12 Fordyce G, Phil Tmns , 75 ( I 7l:<5) 36 1. 13 Preston T, The Th eory of Hell! (MacM illan. London ). 1029. 14 Ampere A M, Bibliolheq/l(:, Universe//,' (Gencve), 49 ( I H]2)

225. IS Ampere A M, Ann Chinl , 58 ( 1835) 432. 16 Socquet J M, Essai sur Ie Ca loriqlle (D e.l'my. Paris), 180 I. 17 Lavoisier A, Melli Acad Sci , ( 1777) 420. 18 Lavoisier A, Melli Acad, Sci, ( 1777) 592. 19 Lavoisier A & Laplace P S, Melli Acad Sci , ( 1780) 355. 20 Thomson B. Phil TrailS, 89 ( 1799) 17') . 2 1 Thomson B, Phil Trans, 88 ( 1798) 80. 22 Avogadro A, Fisica dei C0I1,i Pondera/;ili (Stamperia Rea le,

Turin) 1837. 23 Avogadro A, J Phys, 73 (18 II ) 58. 24 Avogadro A. Bihlioleca Iialiww, 5 ( 18 16) 47<.1; 4 ( 11:\ 15 ) 73. 25 Avogadro A, Mellloire MlII Fis Soc 11(11 Sci, 18 ( 1820) 153. 26 Berthollet C L, Es.wi de S/(lIiqlle Ch illl:l/lle (Demonville, P,l ri s)

1804; in two volumes. 27 Morselli M, Allledeo Avogadro (D Re idel Publi sh ing Co.:

Dordrecht , Holl and), 1984. 28 Gay-Lussae J L, Mellloires de PhYsiqlle ('/ de Chilllie de /a

SOCiele d'ArClleil , I ( 1807) 180. 29 Desormes C B & Clement, N . .1 Phys, 89 ( 18 15) 320. 30 Desormes C B & Clement , N, J Phys . 89 ( I HIS) 428. 3 1 Gay-Lussac J L, Ann Chilli Ph),s, 13 ( I H20) ]04. 32 Crosland M, Gav-LlIs.m c Scienlisl and I}(Jl lI geois (Cambridge

University Press), 1978. 33 Costabel P, Archives IlIIem alionale d 'His loire des Sciences ,

2 1 (1968) I. 34 Brucke E, Ann Ph),s 12], 65 (1845) 5')3. 35 Helmholtz H, Ueber dir Er/wlllln g del' Kmji , (Berlin ) I X47.

36 Maxwell J C, J Chelll Soc, 21:\ ( 1875) 493.