Skip to main content

Full text of "Law and theory in chemistry; a companion book for students"

See other formats

^resenteb to 
of the 

Professor J. W. Bain 









All riyhts reserved 




This book contains the substance of a summer-school 
course of eight lectures delivered before an audience 
of school teachers of elementary chemistry at Colorado 
College, Colorado Springs, U.S.A. 

It is not therefore adapted to beginners, but it is 
hoped that it may be found useful by such students 
as wish to recapitulate and co-ordinate the more im- 
portant principles of chemistry before proceeding to 
more detailed and advanced works. 

The qualification companion hook occurring on the 
title-page is used advisedly, for text-book continuity 
and completeness cannot be claimed for the matter 
of the following pages. The seven chapters are in 
reality short and independent essays on the subjects 
of which they severally treat. 

In the choice of subject-matter I was chiefly in- 
tiuenced by the two following considerations. Firstly, 
I desired to treat of those subjects which in my 
opinion are essential to a liberal understandinj^f of 
the science, but which are inadequately treated in, 
or altogether crowded out of, the current text-books 
of elementary chemistry. In the second place, I 


wished to restate and emphasise such points as in 
my experience present especial difficulties to the 

Throughout, the attempt has been made to keep 
the information up to date, and to indicate, with due 
appreciation of perspective, the trend of modern 
research in its relation to the science as a whole. 
In this connection it is perhaps scarcely necessary 
to state that the hope was to excite interest rather 
than to satisfy it. 

I would here express my sincerest thanks to my 
friend, Mr. Pattison Muir, for the very valuable help 
he has piven me. 











SALTS 121 






In the ancient world the only scientific pursuits which 
were considered reputable, and which led to fame or 
distinction, were politics, philosophy, and mathematics. 

Dyeing, tanning, bronze founding, glass making, 
soap making are all industries which boast a remote 
antiquity, but the early practice of these arts was 
confined to the slaves, and the ignominy of attempting 
any adaptation of theory to practice never for a moment 
suggested itself to the noble-born. 

But while the actual practice of what we now under- 
stand by the term commercial chemistry was in the 
hands of the uneducated, and possessed no literature, 
the philosophers theorised on the composition and 
nature of matter, and to trace these theories and their 
consequences is, as we shall find, to trace the early 
history of our science. 

The early Greek philosophers of the seventh to the 

1 V 


fifth centuries B.C. belonged to one or other of two 
schools known as the Ionic and the Eleatic schools 
respectively. The adherents of the Ionic school 
believed that in all the apparently diverse things by 
which they were surrounded there existed a common 
principle or substratum (apxr)), and they sought to 
evolve order and simplicity out of the apparent 
diversity in terms of this common princijjle. Accord- 
ing as the attempt was made to investigate and detect 
this principle by the observation of natural phenomena, 
or by the unaided exercise of the mind, we find Thales 
asserting water to be the substratum of all things, or 
Pythagoras selecting number as the one real thing in 
nature. The attitude of the Pythagorean branch of 
the Ionic school is well illustrated by the following 
quotation from Plato's seventh book of the " Republic " : 
" We shall pursue astronomy with the help of problems 
just as we pursue geometry, but if we wish to become 
thoroughly acquainted with astronomy we will let the 
heavenly bodies alone." 

The disciples of the Eleatic school founded by 
Xenophanes did not attempt to explain the material 
universe, but they espoused a philosophy of an essen- 
tiall}^ negative character. Assuming unity and im- 
mutability in the universe, without attempting to 
further specify or explain either the one or the other, 
they maintain that change and the apparent diversity 
of things are inexplicable delusions of the senses. 
Reason was made the only criterion of i^ruth, and as 
reason apparently led to results at variance with the 


information conveyed by the senses,^ the latter were 
regarded as fallacious. 

To summarise the differences between the two schools 
briefly, we may say that while the Ionic school sought to 
explain the many in the one, the Eleatic school denied 
the real existence of the many and assumed the one. 

The views of Empedocles (440 B.C.) do not, however, 
strictly conform to either of the two schools just de- 
scribed. Unlike the Eleatics, he aimed at a rational 
explanation of the diversity and change in the universe, 
and unlike the Ionic school this explanation was given 
in terms, not of one, but of four common principles, 
viz., earth, fire, air, and water. These substances, to 
which Empedocles assigned mythological names, were 
regarded as the constituents or elements out of which 
everything else was built up. In Empedocles' opinion, 
their association in different proportions sufficiently 
accounted for all the diversities presented by the world 
to the senses. But to account for the continual 
changes that are ever taking place in these diversities, 
Empedocles had to assume the existence of two other 
rival elements, viz., love and strife, ^ the former causing 
the attraction and combination of imlike elements, the 
latter causing their disruption. If we substitute the 
seventy odd elements of to-day's chemistry for the four 
Empedoclean elements first mentioned, and then the 

^ Zeno's well-known paradox of Achilles and the tortoise may here 
be instanced. 

- We should be inclined to regard the " love " and " strife " of 
Empedocles rather in the light of powers or influences than as elements. 
But Burnet (Early Greek Philosophy) .states that Empedocles himself 
regarded them as corporeal elements co-equal with tlie other four. 


term aflfinity for the remaining " love " and " strife," we 
cannot but be struck with the close analogy which the 
views of this early Greek philosopher bear to those held 
in the nineteenth century concerning the composition 
of, and the changes undergone by, the material universe. 

The views of Empedocles were modified, and in their 
modified form popularised by Aristotle (385-322 B.C.). 
The great Stagy rite regarded all substances as portions 
of one and the same fundamental matter, modified by 
the greater or less quantities of the four " elementary 
principles " — earth, fire, air, and water — which it had 
impressed on it. This conception of elementary prin- 
ciples has nothing in common either with our present 
conceptions of the elements or with the original views 
of Empedocles. It is one of those abstract ideas ori- 
ginally borrowed in all probability from India, where 
Buddha taught that in addition to the four principles 
already mentioned, other two — ether and consciousness 
— existed, and it is very difiicult for us to replace our 
clear-cut notions of definite concrete elements by these 
unreal products of the Oriental imagination. 

It must not be supposed that Aristotle intended to 
convey the idea that water, air, fire, and earth, as we 
now understand these terms in a purely materialistic 
sense, constituted the universe by their manifold com- 
binations. The elementary principle of earth implied 
to the Aristotelian school merely the possession by the 
bodies supposed to contain it, of the properties of 
dryness and coldness. Similarly the principle of water 
implied coldness and moistness, the principle of fire, 


heat and dryness, and the principle of steam or air, 
heat and moistness. 

Accordingly it was held that one specific kind of 
matter could be totally changed into another by merely 
altering the proportion in which the principles had 
been impressed on the fundamental matter of the first 
substance — by altering the ratio of its heat, coldness, 
dryness, and moistness. Thus by imparting more heat 
to water (fundamental matter especially richly im- 
pressed with the principle of water) it becomes steam 
or air. By taking away its moisture and cooling it, 
it becomes, as was then taught, rock crystal or petri- 
fied water, — fundamental matter especially rich in the 
principle of earth. 

The important point to note is that the Aristotelian 
doctrine favoured the idea of a possible transmutation 
of any one substance into any other. 

Experiments having as their aim the change of one 
substance into another seem first to have been ex- 
tensively practised in Egypt, which was once called 
Khmi (Greek, ■)(r]/jbLa) on account of the darkness of 
its soil ; Khmi literally meaning black soil. And it 
came about that the art which had as its aim and 
object the transmutation of material things received 
the name of the country where it first flourished — the 
art was called '^rj/,^ just as a certain form of wool- 
spinning is called worsted-making from the village of 
Worsted in Norfolkshire, where the industry had birth. 

1 The use of this term to designate the art first appears, so far as 
we know, in the fourth century. 


In the seventh century the great wave of Islamism 
rolled westward from Arabia towards Europe, and 
the missionaries of Mahomet overran and conquered 


During their sojourn in Egypt, the Arabians found 
the dwellers in the land executing what were then 
regarded as actual transformations of matter.^ For in- 
stance, when molten sulphur was poured into mercury, 
the metallic properties of the latter disappeared and 
the mercury and sulphur changed into a solid substance 
black as the raven's wing. When this black substance 
was heated gently for some time, it changed into the 
beautiful red substance now used as a paint under the 
name vermilion. 

This does not strike us now as a very wonderful 
change, but owing to the way in which the early 
naturalists were wont to symbolise things, it was to 
them a change of the profoundest type. For black 
was with them emblematic of evil, while red denoted 
virtue ; and the change from a black substance into 
a brilliant red one was in their eyes as the miracle 
of an evil tree bringing forth good fruit. 

Bnt the change which appealed most to the Arabian 
conquerors was the, to their minds, less miraculous 
change or transmutation of the base or common metals 
into the noble metals, gold and silver. Though the 

1 It is probable that prior to their invasion of Egypt, the Arabians 
had alread}' learnt something of Egyptian arts through the Nestorians. 
In the fifth century this Christian sect was banished from its home in 
Constantinople to the desert of Thebais in Egypt, whence its followers 
gradually migrated eastwards. 


modus operandi of this transmutation was kept very 
secret,^ yet the possibility of the transmutation was 
regarded as a well-ascertained fact during the first 
centuries of the Christian era. The Arabians carried 
away with them in their western trend this idea of 
the ennobling of the base metals, and introduced it 
into Europe under the title Alchema ; the prefix Al 
being the Arabic for the definite article, and chema 
being the Arabic rendering of XVH-^^' but signifying 
dark in the sense of obscure or secret rather than 
black. In all probability the prefix Al was added 
for the purpose of conferring a dignity and distinction 
on the art as being the highest and most reputable 
of all arts, just as the Spanish discoverers of the New 
World called the American crocodile el Icujarto — the 
lizard — because it was the largest and most formidable 
lizard-like animal they had ever seen. El lagarto 
and alchema persist in the language of to-day as 
the words alligator and alchemy. The word alchemy 
gave rise by apherisis to the word chemist, and this 
in turn to the word chemistry.^ (Cf. poet and 

^ The earliest chemistry of all is to be found in the &yi.a rix^i) or 
holy art, whose secrets were kept sacred under "pain of the peach 
tree" (i.e., under the penalty of being poisoned by hydrocyanic acid), 
whose study was confined to the priesthood and the sons of kings, and 
wliose laboratories were the temples. 

- There are some who, rejecting the derivation of the word Alchemy 
given in the text, would derive XW* from x^'l^^^'^ ('^ in'"o''"o> "'" 
infusion) from xi'M'^5 (j'lice), which in turn is related to Xf^'" (tt> pour). 
Hence the two current methods of spelling the word chemistry = 

Picton in his book The Story of Chemistry rejects both these deriva- 


The Arabian alchemists, as we learn from the writings 
of Geber — works dating from the eighth century and 
constituting the oldest chemical literature extant^ — 
had a theory of their own respecting the nature of 
the metals. Aristotle's theory was wide and applied 
to all kinds of matter, whereas the alchemistic theory 
was specialised and had reference more particularly to 
the metals. The latter theory, moreover, did not re- 
place the former, but only supplemented it. Aristotle's 
elementary principles were still recognised, but regarded 
as the more remote factors in determining the properties 
of matter, while Geber's elements represented the more 
proximate constituents of matter in general and of the 
metals in pai'ticular. 

Geber's idea, which met with a general adoption by 
the alchemists, was that the metals consist of sulj)hur 
and mercury in varying proportions. His sulphur and 
mercury did not, however, mean what these words 
now connote to us — definite chemical individuals with 
invariable properties. The names had for him an 

tions, and asserts that Alexander of Aphrodisia (a great exponent of 
the Aristotelian doctrines in the second century a.D.) invented the 
word chymike for the operations of the laboratory ; but surely it is 
unusual to invent words out of one's inner consciousness without any 
attempt at appropriateness, historical or otherwise, in the resulting 
invention. Though Alexander may have thrown the word chymike 
current on the world, it does not follow that in the selection of the 
word he was uninfluenced by anything save inventive power. 

^ Some philologists would derive the word Gibberish [said to have 
been originally Geberish] from the alchemist Geber, notwithstanding 
the fact that Geber's writings, compared with the inflated and 
unintelligible jargon of other alchemical productions, are models of 
conciseness and clearness. 


abstract meaning ; his sulphur and mercury varied in 
kind and in properties. Thus gold and silver were 
very rich in " pure or perfect kinds " of mercury, but 
the one contained a red sulphur, and the other a 
white. In short, Geber's elements were rather of 
the nature of elementary principles than of the 
nature of elements as we now understand the latter 

Since the change in purity as well as the change 
in relative proportion of these two metallic constituents 
was assumed to be under the control of the experi- 
menter, it is obvious that the attempt to transmute 
the base metals into gold was quite legitimate from a 
theoretical standpoint. 

Further, it was generally believed that the evolution 
of the base metals into the noble ones, gold and silver, 
was a change which was proceeding spontaneously and 
constantly in nature, and that therefore the alchemists' 
task virtually consisted in an artificial acceleration of 
a perfectly natural process. 

Alchemy scarcely merits the dignity of being classed 
as a science. For some of its followers it was a 
transcendental philosophy which amounted almost to 
a religion ; but for the majority it was nothing more 
nor less than an empiric trade. Its chief service to 
science lies in the fact that it stimulated experiment — 
blind and thoroughly haphazard experiment perhaps, 
but still experiment. Its most fatiguing and laborious 
study was prosecuted by the majority, not so much 
out of a desire for scientific triumph or for truth's 


sake, as out of a thirst for that power which the so- 
called philosopher's stone with its Midas touch was to 
confer. The alchemists never dreamed of trying to 
convert gold into lead. 

The philosopher's stone was the name given to a 
mythical theurgic powder^ which was to have the 
power of fermenting millions of times its own weight 
of fused base metal into gold. The strangest and 
most diverse ingredients were mixed together in the 
attempts to prepare this much sought for powder ; 
we read of snails' slime, serpents' teeth, gall stones 
taken from cats, blood, hair, white of egg, &c., in 
addition to the never failing ingredient, mercury. 
The philosopher's stone was generally identified with 
what in more general terms was called the " One 
Thing" — the perfect form of matter which was to 
combine in itself all the properties of all other kinds 
of matter in their highest perfection. Hence we can 
in a measure account for the many and varied in- 
gredients which were believed to be necessary to its 

Many of the receipts for making the philosopher's 
stone that have come down to us are perfectly un- 
intelligible, so allegorical is the language in which 
they are couched. Sometimes the directions seem 
fairly explicit, till one comes to the concluding item 
— "add carefully a sufficiency of you know what.'" 

1 It may here be stated that some philologists find in the generally 
entertained belief that the "stone" would turn out to be a hlack 
powder, a derivation of the word alchemy. See article " Chemie " in 
Ladenburj^'s Handworterbuch der Chemie. 


Several reasons may be assigned for this secrecy and 
mystery, and sometimes one, sometimes another of 
these reasons may have been operative. In the first 
place, the alchemists were undoubtedly desirous of 
keeping their profession strictly limited as to numbers, 
a result which would be effected by the adoption of 
what practically amounted to a private code. Again, 
there were alchemists whose attitudes towards their 
profession are sufficiently expressed in the following 
quotation : — 

"If thou shouldst reveal that in a few words which 
God hath been forming a long time, thou shouldest 
be condemned on the great day of judgment as a 
traytor to the majestie of God." 

Finally, there may have been some alchemists who 
out of vanity or for purposes of self- aggrandisement 
asserted, with intent to deceive, their knowledge of 
the transmuting substance. Obviously it would be 
expedient for such men to express themselves so 
obscurely as to render it impossible for others to 
bring their statements to the test of experiment. 

With the Benedictine monk, Basil Valentine, begins 
the period of iatro — or medical — chemistry, a period 
lasting from the fifteenth to the seventeenth century, 
during which transmutation was in abeyance. Here- 
tofore the apothecaries had prescribed purely vegetable 
preparations only, but now we find mineral specifics 
contesting the field with them and partially re- 
placing them. The true goal of alchemy had come 
to be looked on as the attainment of health, not 


wealth — " a back tougli as Hercules " rather than 
the riches of Solomon — and the philosopher's stone 
was endued with all the attributes of an elixir of 
life in addition to its now secondary transmuting 
powers.^ It was even customary at this period to 
ascribe the great ages of the patriarchs to their 
possession of the health-giving stone. ^ 

It is probable that the idea of the prophylactic 
and life - sustaining function of the stone originated 
in the great projoensity of the alchemists for sym- 
bolism and metaphor. They even went the length 
of constructing their aj)paratus symbolically — retorts, 
for instance, being frequently fashioned so as to 
resemble men, the bulb of the retort being the 
stomach, the crown of the retort being the head, 
and the beak being the nose.^ 

1 Van Helinont (1577-1644), the originator of the generic term gas 
and the discoverer of tlie existence of several distinct kinds of gases, 
believed that the universal solvent or " alkahest," not the philosopher's 
stone, would prove to be the true elixir vitte. 

" See Jonson's Alchemist, act ii. sc. i., where reference is also made 
to the belief that such mythological stories as those of the Golden 
Fleece, the Hesperian Gardens, the Boon of Midas, &c. , were "all 
abstract riddles of the stone." It may be asked how it came about 
that the patriarchs died, seeing that they were possessed of the elixir of 
life. The alchemist would have made answer in this wise. Every 
person has a predestined maximum lease of life — a limit which he 
cannot possibly pass, but a limit to which by reason of disease he 
seldom attains. Now it was not claimed for the magic stone that it 
was more mighty than destiny. All it could do would be, by prevent- 
ing sickness and consequent premature death at three-score years and 
ten or thereabouts, to enable men to enjoy the maximum lease of life 
stretching well up into the hundreds. 

2 See Bolton, Trans. Neio York Acad. Sc, December 1882, March 


In further conformity with this propensity, the alche- 
mists also referred to the base metals as the diseased 
metals, the lepers, &c., and figuratively spoke of their 
transmutation into gold as a healing of their diseases. 
Thus in all probability arose the idea of the alchemist's 
elixir of life. 

In the blind search for this elixir many valuable 
drugs were discovered and fairly fully investigated. 
Valentine busied himself chiefly with the therapeutics 
of antimony and its compounds, and he very thinly 
veiled his impatience with and contempt for " the 
deplorable, putrid, and stinking bag of worms," that 
failed to see the wonderful virtues of antimony as he 
himself saw them. 

In addition to his book. The Triumphal Chariot of 
Antimony/, Valentine left behind him a complication 
in the views which had been current up to his day 
respecting the nature of the metals. This complication, 
which consisted in the assertion of the presence in the 
metals of a third elementary principle, viz., salt,^ did 
not inaugurate any material advance in views respecting 
the composition of matter. This new idea, however, 
was soon generally accepted, and in contemporary 
literature we find all kinds of fanciful analogies in- 
stituted between such diversities as the Trinity, body, 
soul, and spirit, and the trio salt 0, sulphur '^, and 
mercury $. 

^ The principle of salt was represented in that portion of the metal 
which resisted the action of heat, and remained behind as a solid 


Valentine had shown a laudable boldness and inde- 
pendence in ushering in, against strenuous opposition, 
the reign of iatro-chemistry, but his immediate successor, 
Philippus Aureolus Theophrastus Bombastus Paracelsus 
von Hohenheim — that strange character, half scientist, 
half charlatan — carried on the crusade with a vehement 
intrepidity amounting almost to truculence. After 
forcibly expressing his contempt for the old school of 
" medicasters " by a public holocaust of the works of 
the celebrated physicians Galen (second century) and 
Avicenna (tenth century), he continued to work in the 
field first opened up by Valentine, and enriched medicine 
by the knowledge he contributed thereto of many 
valuable mineral specifics ^ (corrosive sublimate, tinc- 
ture of perchloride of iron, &c.), which still figure in 
the pharmacopoeias of to-day. He also substituted the 
more or less pure active principles of plants for the 
crude electuaries of the apothecary, and it is interesting 
to note that it was probably through his introduction 
from the East, and liberal use, not of a mineral, but of 
a vegetable drug, viz., laudandum,^ that Paracelsus 
effected those wonderful cures which gained for him 
his great and widespread reputation.^ 

^ '' The medicines are ranged in boxes according to tiieir natures, 
whether chymical or galenical preparations."- — Quoted in Johnson's 

" Laudandum (of which the modern word for ojjium, viz., laudanum, 
is a contraction) is the Latin gerundive signifying "meet to be 

^ In his poem " Paracelsus," Browning, while making use of incidents 
in the life of the chemist as a mise en scene, sketches the career of an 
ideal Paracelsus. 


Early in his career, Paracelsus devoted himself to an 
ex|3erimental study of transmutation, but it was not 
long before he concluded that it was a chimera. Some 
of the best minds among his contemporaries and im- 
mediate successors were doubtless influenced by the 
conclusions of so great a personality, and renouncing 
alchemy, devoted themselves to medical chemistiy. At 
any rate the decline of alchemy, properly so-called, 
dates from the time of Paracelsus. Most of the so- 
called alchemists of the latter portion of the middle 
ages were in reality frauds of the lowest order, whose 
stock-in-trade consisted in a little Icgcr clc main, and an 
unlimited amount of the inflated and highly allegorical 
language in which the alchemists were wont to give 
their recipes for the elusive stone, and to impress the 
lay mind. 

In the memoirs of the Academy of Sciences for 1772, 
Geoffrey makes an cxposd of the ways and means of 
these pseudo-alchemists. Hollow stirring rods con- 
taining gold, and temporarily stopped with wax, 
crucibles with false bottoms previously charged with 
the precious metals, and composite rods — one half gold 
soldered to the other half iron, and the whole coloured 
uniformly — were among the properties of the craft. 
Thus equipped, the charlatans practised on the cre- 
dulity of the public, easily leading it to believe them 
possessed of clairvoyance, and a supernatural power 
enabling them to control natural agencies. Telling 
fortunes by the stars, dispensing " familiars to rifle 
with at horses and win cups," &c., they pursued a 


royal road to wealth. Instances of such frauds occur 
throughout mediaeval literature and history. One of 
Ben Jonson's best constructed plays — The Alchemist 
— is based on the despicable chicanery of a " cunning 
man," well named Subtle, and his confederate, Face. 
In the Canterhury Tales, again, Chaucer, apparently 
moved by some sudden resentment, departs from the 
order of the poem set forth in the prologue to introduce 
" The Chanones Yemanaes Tale." A yeoman or servant 
falls in with the body of pilgrims on their way to 
Canterbury, and, after detailing to them the seductive 
horrors of alchemy, relates the story of some trickery 
that his late master, the Chanon, had practised on a 

In actual history we find these pseudo-alchemists 
figuring in the retinues of bankrupt kings and spend- 
thrift potentates along with chaplains, jesters, and 
so forth. At the instigation of Edward II., we read 
that John Cremer, Abbot of Westminster, invited 
the famous Spanish chrysopceus} Raymond Lully, to 
come over to England for the purpose of replenishing 
the royal exchequer ; and Henry VI. for long enter- 
tained a firm and costly belief in alchemy, in spite of 
the fact that Henry IV. had passed a law — said to be 
the shortest in the statute-book — making the practice 
of alchemy a felony. Indeed, most of the European 
courts so fostered and encouraged alchemy during the 

^ Chrysopoeia (literally, gold making) was a synonym of the term 
alchemy in use duiiug a long period. See Ben Jonson's Alchemist, 
act ii. sc. i. 


fourteenth and fifteenth centuries that the markets of 
the day were glutted with worthless and counterfeit coin. 
Several coins and medals, which are claimed to be 
products of the alchemical art, are still preserved in the 
Royal Cabinet of Coins in Miinich, and in the Imperial 
Cabinet in Vienna.^ As many of these relics un- 
doubtedly consist of pure gold and silver, one is forced 
to conclude either that the bullion from which they 
were made was produced fraudulently by such tricks as 
Geoffrey has explained (p. 15), or that the noble metals 
resulted from the application of cupellation processes to 
base metals which were believed to be pure, but which 
in reality carried noble metal. In agreement with the 
first conclusion, we read that in 1709 a certain retainer 
alchemist, Domenico Manuel by name, being detected 
in his knavery, experienced the irony of execution on a 
gilded gallows at Kiistrin. In support of the alternative 
conclusion, it may be stated that there is in the British 
Museum a facsimile of a silver medal made by Becher 
(see post, p. 24), which was in all likelihood obtained 
by the cupellation of argentiferous lead supposed by 
Becher to be pure lead.'^ The medal bears on its 
reverse the following inscription : — 

"Anno 1675 mense Julio Ego J. J. Becher Docter 
hanc unciam argenti purissimi ex plumbo arte alchymica 

^ See H. C. Bolton'a Contrihutions of Alchemy to Numismatics ; 
also Reyher, De numis quibusdcm ex chyinico mctallo factis. 

- The original of this interesting medal is in the Vienna Cabinet of 



On the obverse is the usual representation of Saturn 
with his wooden leg, scythe, &c. For the alcheraists 
believed the metals to be under the influences of the 
planets ; and sluggish lead had assigned to it as its 
patron star the planet Saturn — the slowest moving 
planet with which the alchemists were acquainted.^ 

Becher, regarding the production of his medal as a 
bond fide case of transmutation, seems to have valued 
it simply as a chemical curiosity ; for we are told that 
he expressed himself more interested in the solution 
of nature's riddles than in the heaping up of wealth.- 

Even so late as the year 1843 we find one of the 
pseudo-alchemistic cult, one Francois Gambriel, of 19 
Judas Street, advertising in a leading paper his readi- 
ness to teach in a course of nineteen lessons all the 
secrets of the Hermetic Art.^ 

But that the hona fide alchemists themselves tho- 
roughly believed in the possibility of transmutation, 
there can be no doubt.^ Such facts as the following 

1 The personification of Saturn as a lame man with hour-glass and 
scythe, &c., is due to the fanciful identification of the Roman Saturnus 
with the Grecian Cronus during the Hellenising period. 

2 Becher's offer to the Government of Holland to provide it with 
six millions of golden thalers per annum if it would provide a certain 
amount of silver and unlimited sea-sand, does not seem t(j have been 
taken up in spite of the fact that an experiment made in 1679 is said 
to have turned out six times more productive than Becher had 
anticipated ! 

- So called after the mythical Hermes Trismegistos, the reputed 
founder of all arts and sciences, and the Grecian representative of the 
old Egyptian godhead Thoth — the deified intellect. 

* Even such reputed early-day chemists as Davy, Dumas, and 
Bergman, could not bring themselves to utterly reject the idea of the 
possibility of transmutation. Peter Woulfe, a fellow of the Royal 


could not but foster the brightest hopes of men who, 
satisfied with surface views of things, never questioned 
what was under the veneer. Iron plunged into a green 
solution obtained by dissolving certain ores (containing 
copper) in nitric acid, was itself apparently changed 
into the more valuable metal copper ; and copper melted 
with tutty (an impure oxide of zinc) acquired the 
bright rich yellow colour of gold. And in the 
metallurgy of the alchemists much importance was 
ascribed to purely colour changes ; much was supposed 
to have been achieved in making base metals take the 
colour of the noble ones. Indeed, many of the early- 
day alchemists seem to have believed that to give a 
base metal the colour and sheen of gold was in effect 
to change the base metal into gold. In accordance 
with these beliefs, tlie transmuting substance is often 
called a tincture (from tingo, I dye). Thus, on a medal 
of the year 1647 made by one Hofmann, are inscribed 
the letters T G V L, probably an abbreviation of the 
sentence tindurce guttce V lihram, meaning that five 
drops of the tincture used had effected the transmuta- 
tion of a pound of the base metal from which the 
medal had been prepared. 

Again, in the process now known as cupellation, 
lead heated in a vessel made of bone ash, slowly dis- 
appeared and left behind a button of silver. Pyrites 
treated in a similar way often left a legacy of gold. 
Of course the noble metals were ab initio present in 

Society of this century, whose name lives in connection with certain 
pieces of chemical apparatus, was a firm believer in transmutation. 


the lead and the pyrites, but the experiments were for 
the alchemists, who had no notion of what we now 
understand by chemical homogeneity, cases of indubi- 
table transmutation. 

When one recalls the modern work on the marvellous 
effects of "traces of impurities" in altering the pro- 
perties of large masses of matter, one can scarcely be 
surjorised at the attitude of the alchemists. Instance 
in this connection Carey Lea's so-called allotropic forms 
of silver. Carey Lea has recently prepared, among 
others, a blue pulverulent form of silver soluble in 
water, and an insoluble variety of the colour of 
burnished gold. These interesting bodies are not, it 
is true, pure silver ; yet they contain some 98 per 
cent, of the precious metal, and would have been 
startling discoveries in the days when transmutation 
was regarded as a possibility. Reference should also 
be made here to the marvellous effects of great in- 
dustrial significance produced in the properties of iron 
by the addition of mere traces of such substances as 
aluminium, tungsten, &c. 

The transition from the vague and uncurbed fantasies 
of alchemy into the true science of chemistry, was 
marked by the appearance of a work written in the 
form of a discussion conducted by a symposium of 
scientific men, and entitled " The sceptical chymist, or 
chemico-physical doubts and paradoxes touching the 
experiments whereby vulgar spagyrists^ are wont to 

' Chemistry was often referred to as the spagyric art, from <77rdw = 
/ separate, and ayiipw = / unite. 


endeavour to evince their salt sulphur and mercury to 
be the true principles of things." In this work Robert 
Boyle (1626-1691) strongly contests "the doctrines of 
the four elements, and the three chymical principles 
of mixed bodies." From the quotation just made, as 
well as from the remarks of the debaters, it is clear 
that a confusion of ideas had taken place with regard 
to the Aristotelian philosophy, and that actual earth, 
fire, air, and water, had come to be assumed by many 
as being actually present in, and as forming real con- 
stituents of diverse forms of matter — there had been 
in fact a resuscitation of the original Empedoclean 

Boyle, in language which knows nothing of the 
mystic and rococo style of alchemical literature, up- 
holds the modern view of elements, defining them as 
certain jjrimitive and simple bodies which, not being 
made of other bodies or of one another, are the in- 
gredients of which all those called perfectly mixed 
bodies are immediately compounded, and into which 
they are ultimately resolved. 

It is clear that if gold and silver are elements in 
this sense, i.e., simple undecomposable, indestructible 
forms of matter created once for all in fixed and un- 
alterable quantities by a special act of creation, then 
all attempts at transmutation are necessarily in vain. 
The steady growth, since Boyle's day, of the conviction 
that gold and silver, and indeed all the metals, are 
elements in this sense, has been contemporaneous with 
the gradual recognition by the public of the futility 


of alcliemistic aims, and of the deceptions practised 
by the pseudo-alchemists. Yet there still exist a few 
individuals who, rejecting the results and opinions of 
others, and doing their own thinking, entertain firm 
beliefs in such chimeras as the perpetual motion, the 
quadrature of the circle,i and the philosopher's stone.^ 

Boyle maintains that it is impossible to state ofihand 
the number of the elements. He further postulates 
a corpuscular structure of matter, and conceives of 
chemical combination as an approximation of corpuscles 
of different natures ; of decomposition as the result of 
the jDresence of a third kind of corpuscle capable of 
exerting on one of the combined corpuscles a greater 
attraction than that exerted by the corpuscles already 
combined with it. Heretofore the ideas entertained 
respecting chemical combination had in general been 
very fanciful. Although the conclusion was not in 
any way implicated in the Aristotelian conception of 
elementary principles which held sway, yet the forma- 
tion of a new substance had been regarded as a special 
creation following on a real destruction of the combin- 
ing bodies. 

Boyle was the first to distinctly state that the 
peculiar properties of substances disappear on the 
occurrence of chemical combination — or rather become 
merged into the new and unforeseen properties of the 

1 " Quadrature of the circle found. Lessons given. Fee five 
shillings." Extract from advertisement appearing in Nature, August 
17, 1893. 

^ A good picture of this type of man is given in Balzac's V Alchi- 
miste. See also Dumas, Memoirs of a Physician, 


compounds formed. In this connection lie drew a 
hard and fast line between mixtures and true chemical 
combinations — a distinction which will be entered into 
in more detail in Chapter III. 

Boyle further advocated the pursuance of the science 
of chemistry independently of utilitarian ends. He 
combated the view that it was the handmaid of this 
or that science, it was, according to him, a self-con- 
tained and independent part of the great study of 
nature. In the mere advancement of knowledge for 
its own sake he found a sufficient spur to a devoted 
study of chemistry. 

In the next chapter we shall see how Boyle's ideals 
were realised ; how the phenomenon of combustion 
was disinterestedly studied for the sake of the light 
which it was hoped would by this means be shed on 
chemical theory generally ; and how the adoption and 
elaboration of Boyle's conception of the elements was 
one of the chief factors in Lavoisier's happy co-ordina- 
tion of the apparently isolated and vaguely expressed 
items of knowledge of his day into a harmonious and 
perspicuous whole.^ 

^ The reader, who may be incited by the short sketch of the history 
of Alchemy given in tlie text to a deeper study of the subject, is 
referred to the following literature : — 

Article " AXchQmy" Enc. Brit. ; Rodwell, "Birth of Chemistry;" 
Meyer, "History of Chemistry ;" Thomson, " History of Chemistry ;" 
Kopp, " Geschichte der Chemie," and " Die Alchemie in alterer und 
neurerer Zeit ; " Berthelot, " Les origines de L'Alchimie ; " Ben 
Jonson, " The Alchemist." (Morley's Universal Library. ) 



The phenomenon of fire is such an important factor 
in chemical change, both as an agent and as a result, 
that the chemists of the seventeenth and eighteenth 
centuries regarded it as the essential phenomenon of 
chemistry. To found a consistent and competent 
theory of combustion was in their opinion almost 
tantamount to the founding of a satisfactory theor}' 
of general chemistry ; and in the light of modern 
science, which teaches that so many important chemical 
reactions are either changes of the nature of a com- 
bustion (i.e., are oxidations) or changes of the nature 
of the reversal of combustion (i.e., reductions), this 
opinion finds some justification. 

The first theory of chemistry instituted by Beclier 
(1635-1682), and developed by Stahl (1660-1734), 
was essentially a theory of combustion, and is nothing 
else than a special development in one direction of 
Becher's modification of the alchemistic views on the 
nature of matter. 

According to Becher the fundamental constituents 

of inorganic matter were not sulphur, mercury, and 



salt, but the three earths, the mercurial or fluid earth, 
the vitreous or fusible earth, and the combustible or 
fatty earth. The latter was called terra pinguis. 

Stahl especially elaborated this idea of a terra 
pingvis. According to him all combustible bodies (sul- 
phur, phosphorus, carbon, metals, &c.) were compounds 
containing as an essential ingredient a fiery principle 
which he renamed "phlogiston." In the process of 
burning this phlogiston escaped from combination 
often in such quantities and with such intensity as to 
produce the phenomenon of flame. ^ In the case of 
the combustible metals, the residue or earthy powder 
remaining after the phlogiston had escaped was termed 
a calx; hence such metals were regarded as com- 
pounds of calx with phlogiston. In the case of what 
are now generally but loosely known as the non- 
metals, acids resulted from combustion, hence these 
were regarded as compounds of acids and phlogiston. 
It was not at first noticed that the calx or acid, as 
the case might be, weighed more than the substances 
from which they had been produced — chemistry was 
as yet in its purely qualitative stage. - 

When the calx or acid was reheated with a body 
rich in phlogiston, such as charcoal, it combined with 

^ Death by "spontaneous combustion," which was tirnily believed 
in durinj,' the eighteenth century, and has even figured in the fiction 
of the nineteenth (see Bleak House, Preface and chapter xxxii.), 
met with a very simple "explanation" in terms of the phlogiston 

- Boyle seems to have been the first to notice this increase in weight. 
He ascribed it to the combination of the burning body with " igneous 


the phlogiston of the charcoal, reforming the burnt 
substance. Such was the phlogistonist's description 
of reduction. But other bodies rich in phlogiston, 
such as sulphur, flour, sugar, effected the transforma- 
tion of a calx or acid into identically the same metal 
or non-metal as did charcoal.^ Hence it was argued 
that there was but one kind of phlogiston. 

This phlogiston was generally regarded as a definite 
material substance. Stahl looked forward to its isola- 
tion, and seems to have expected a solid earthy body 
insoluble in water. In fact the matter of solubility 
appeared to be merely a question of a greater or less 
amount of combined phlogiston. Phosphorus and 
sulphur, bodies rich in phlogiston, are insoluble in 
water, but the acids produced from these substances 
by the escape of phlogiston are eminently soluble. 
The quantity of phlogiston in a substance was in fact 
believed to condition not only its solubility but all 
its properties — its activity or inertness, its stability 
or instability, its acidity or basicity, &c. 

Although Stahl seems to have been in favour of 
a solid phlogiston, others regarded it as gaseous, and 
indeed went so far as to identify it with hydrogen. 
When metals dissolve in acids a gas escapes, which 
if collected and heated with the calx recoverable from 
the solution— the calx in this instance really being 

1 In very early times it was known that wheat has the power of 
revivifying a metal from its calx or ashes, and it is said that it was 
partly on account of this property that wheat was made the popular 
symbol of the resurrection. 


a salt — restores the metal. But metal is calx and 
phlogiston ; the gas disengaged on dissolving metals 
in acids is therefore phlogiston. 

The doctrine of phlogiston as just sketched, after 
reigning triumphantly for some half century, finally 
succumbed to the increasing knowledge of the con- 
stitution and nature of the atmosphere. This know- 
ledge shed quite a new and certain light on the 
phenomena of combustion, and was co-ordinated by 
Lavoisier into the theory of combustion held at the 
present day. 

Let us now trace the chief stages in the growth of 
our knowledge of the atmosphere. 

Eobert Hooke (1635-1703), a contemporary of 
Becher, and sometime assistant to Boyle, published in 
1665 his conception of combustion in his Micro- 
(jra'phia. He believed that there existed in air a 
fractional quantity of the same kind of gas as is ob- 
tained by heating saltpetre, or nitre, and that com- 
bustion consisted in the solution of the combustible 
body by this gas. Hooke pointed out many analogies 
between combustion and the solution of solids in liquid 

Mayow (1645-1679), an Oxford physician, worked 
out in more practical detail the ideas of his contem- 
porary Hooke. He showed that when a metal burns 
in air, the volume of air is actually lessened, and that 

' It is interesting to note that Hooke was on the point of anticipating 
Rumford. He clearly stated that fire or flame is not an elemenf, but 
a phenomenon resulting from the agitation of particles. 


the calx residue weighs more than the original metal. 
This he explained by suggesting that the metal had 
combined with the particles of the nitre air, as he 
called it, present in common air, leaving a residue of 
inactive air. The same fact was glossed over by the 
phlogistonists, in terms of the assertion that phlogiston 
was a principle of levity, and that therefore its escape 
from a body during combustion rendered the body 
heavier. And so supremely popular was the phlogis- 
ton theory at the time, that the reasonableness and 
common sense of Mayow's explanation had no weight 
against the transcendental artificiality and uniqueness 
of its own, 

Mayow's experiments were so much to the point, 
that it is hard to see how it came about that their full 
significance was not recognised till they were practi- 
cally rediscovered piecemeal a century afterwards. 

The next advance towards an accurate knowledge of 
combustion was Black's discovery and investigation of 
what he called "fixed air" — the gas now known as 
carbonic acid gas, or carbonic anhydride. 

The attention of the medical world was about this 
time (1728-1799) directed to quicklime, magnesia, and 
allied substances, in the role of efficacious remedies in 
the treatment of stone in the bladder, and Black, being 
greatly interested in medicine, undertook a chemical 
investigation of these new remedies. Up to this time 
the carbonates of lime, magnesia, and the alkalis had 
been regarded as elements, or rather simple bodies, 
which when heated formed quicklime, caustic alkali. 


&c., in virtue of their combination with the phlogiston 
escaping from the burning coal. 

Black chiefly investigated what was then called mild 
magnesia, i.e., magnesium carbonate. He first proved 
that when the carbonate is heated, it loses weight. 
This loss is not due to a combination with phlogiston 
of negative specific gravity, but to the expulsion of a 
gas which he called fixed air, because it could be again 
refixed in a sort of latent condition by the resulting 
caustic magnesia. He showed that the same gas is 
produced when chalk is calcined or treated with acids, 
that it exists in the breath of animals, and is evolved 
in large quantities during fermentation. Further, that 
animals die when placed in it, and that it does not 
support combustion. Nothing regarding the composi- 
tion of this gas was, however, hinted at.^ 

The next step towards the full light was taken by 
the English divine Priestley (1733-1804). Priestley 
did not allow his Calvinistic doctrines to usurp his 
whole interest and leisure, but he gave much attention 
to chemistry, making a speciality of that branch of it 
dealing with the different kinds of air — or as we should 
say now, the different kinds of gases. 

While taking charge of a chapel in Leeds, he hap- 
pened to live near a brewery, in which he spent much 
time studying the properties of fixed air, which Black 
had shown to be produced in large quantities during 
fermentation. On being compelled by circumstances 

^ Black's paper has been republished in convenient pamphlet form 
by the Alembic Club (Sampson & Co.). 


to move from the purlieu of this laboratory, he did not 
drop his interest in fixed air, but began to make it 
artificially from chalk as taught by Black. In order to 
store and examine gases, he made extended use of and 
popularised Mayow's method of collecting them over 
water in what he called a pneumatic trough, a method 
still in vogue. He soon noticed that the fixed air 
dissolved to a considerable extent in water, and that 
the solution had medicinal properties. From this dis- 
covery dates the manufacture of artificial mineral 

Priestley, having fairly exhaustively worked out the 
properties of fixed air, turned his attention to new airs. 
In this investigation he seems to have been guided by 
no principle of selection, but at haphazard he subjected 
to the action of the sun's rays concentrated by a lens 
any compound that he happened to think of or chance 
upon; the gas, if any, produced being collected over 
mercury.^ One of the substances thus experimented on 
was the so-called red precipitate. From this, in 1772, 
he obtained a gas in which inflammable bodies burned 
vigorously, and "which had all the properties of com- 
mon air, only in much greater perfection." He gave it 
the name of dephlogisticated air, and regarded it merely 
as common air quite free of impurities and admixtures. 
He did not regard it as a constituent of air as Hooke 
and Mayow some years previously had done with truer 
insight. Air was to Priestley essentially a simple sub- 

^ A i3tatue of Priestley in Birmingham represents him conducting 
this operation. 


stance, and his dephlogisticated air was merely common 
air in a state of great purity. In 1774, being in Paris, 
he demonstrated to Lavoisier his method of making 
dephlogisticated air. Some years later, as we shall see, 
Lavoisier made great use of this knowledge, and re- 
christened dephlogisticated air, giving it its j)resent 
name, oxygen. 

Priestley was a confirmed phlogistonist. The follow- 
ing is something like his idea of what takes place dur- 
ing combustion. When a substance burns, phlogiston 
escapes from it into the air, which is invested with a 
great affinity or longing for this principle of fire. Sub- 
stances cannot burn out of contact with the air, or other 
substances, such as nitre, which possess this strong 
attraction for phlogiston. But in proportion as the air 
round a burning body becomes more and more charged 
with phlogiston, the poorer a supporter of combustion 
does it become, till finally it may become so phlogis- 
ticated — so noxious, as he expressed it — that it will 
actually quench a flame immersed in it. The air 
obtained from red precipitate was virgin air untainted 
by any phlogiston, and so energetically did it long for 
this principle of fire that even at ordinary temperatures 
it drew it away from several substances, thus causing 
them to tarnish. Iron nails, as we know, soon tarnish, 
i.e., rust, when immersed in impure oxygen. 

If carbon is heated with metallic calx it gives up the 
phlogiston in which it is rich to the calx, reforming 
the pure metal from it. But according to Priestley 
the air that has surrounded a burning body is rich in 


phlogiston ; it then, by a parity of reasoning, ought to 
reduce metals from their calces. If Priestley had but 
tried the experiment here suggested, he would have 
met with such a positive failure that one can hardly 
conceive how he could have continued to cherish his 
views on the nature of combustion.^ It will be noticed 
that Priestley did not attempt to explain why the air 
diminished when combustion took place in a confined 

Priestley, essentially a 'preparateur, also experimented 
in his own casual way on nitrous air (nitric oxide), 
vitriolic acid air (sulphur dioxide), muriatic acid air 
(hydrochloric acid), alkaline air (ammonia), and inflam- 
mable air (hydrogen), which latter had been discovered 
by Cavendish in 1766 and recognised by him as an 
individual gas. 

In his experiments on inflammable air, Priestley very 
nearly anticipated Cavendish's discovery made three or 
four years afterwards, of the composition of water. 
Indeed, Priestley's mind was so saturated with the 
importance of the chimera phlogiston,^ that for once 
at least in his life he failed of a customary good 
fortune to which he alludes in the following words : — 
" In looking for one thing I have generally found 
another, and sometimes a thing of much greater im- 
portance than that which I was in quest of" 

^ It is easy to point out many similar inconsistencies in the theory 
of phlogiston. For instance, the ash from burnt charcoal ought to 
weigh more than the original charcoal. 

- Priestley's last work is entitled The Theory of Phlogiston 


In experimenting with the various airs, Priestley 
always tried their effects on animal and vegetable life. 
For this purpose mice and sprigs of mint seem chiefly 
to have been victimised. In this connection it is 
interesting to recall that he distinctly noted that won- 
derful piece of natural economy whereby the gaseous 
waste-products of animals serve as the food of plants, 
and the atmosphere is maintained in a state of fresh- 
ness and purity compatible with the prolonged existence 
of life. 

It is a great source of regret to read that Priestley, 
who by his blind and undirected enthusiasm for dis- 
covery laid some of the foundation-stones of modern 
chemistry, was so little appreciated by a large section 
of his countrymen that he finally left his native land 
with the remark, "When the time for reflection shall 
come, my countrymen will, I am confident, do me more 

Before we pass on to the brilliant co-ordination of 
the facts of combustion and their true explanation by 
Lavoisier, we must mention briefly the work of that 
peculiarly ascetic philosopher, the Hon. Henry Caven- 
dish — work which furnished Lavoisier with some of his 
most weighty data. 

In 1766 Cavendish discovered that when about two 
volumes of inflammable air are exploded with one volume 
of dephlogisticated air, water is produced. Further, 
if ordinary atmospheric air is used instead of dephlo- 
gisticated air, water is still produced, but a residue 
of phlogisticated air, i.e., what we now call nitrogen, 


always remains. Hence Cavendish ai'gued that air was 
not a simple individual substance, but a mixture of phlo- 
gisticated and dephlogisticated airs. It would seem, 
however, that Cavendish did not clearly grasp what 
seems to us such an evident conclusion from his experi- 
ment, viz., that water is a compound of inflammable 
and dephlogisticated airs.i He had been brought up 
on the phlogiston doctrine, and could never thoroughly 
free himself from its trammels. Although he saw good 
reasons for sujjposing that when a metal burns in the 
air it combines with the dephlogisticated air to form 
a calx leaving the phlogisticated air, yet he could not 
find it in his heart to give support to such a heresy. 
He therefore concluded with Priestley that the metal 
phlogisticated the residual air, but slightly differed 
from that scientist in admitting that some of the air 
in a dephlogisticated state combines with the metal. 
Combustion was a case of a partial combination associ- 
ated with and attended by a contamination ; not of a 
total combination attended by an elimination.^ 

It is remarkable that the most fearful reign of social 
anarchy and bloodshed the modern world has known 
should have bequeathed to us through Lavoisier so 
unexpected a gift as a remodelled and thoroughly 
scientific theory of chemistry. Lavoisier was born in 
Paris in 1743. His peaceful life of scientific research, 
passing amidst all the horrors culminating in the reign 
of terror, was finally ended on the guillotine. 

1 James Watt seems to have been the first to arrive at this conclusion. 
^ The Alembic Club has reprinted in convenient pamphlet form some 
of the more important of Cavendish's papers. 



About the year 1770 Lavoisier turned bis attention 
to combustion. His great success in this field of study 
must be largely attributed to the importance he placed 
on the incessant use of the balance as an instrument of 
research ; an instrument with which he, early in his 
scientific career, established the principle of the con- 
servation of mass ^ — a principle lying at the foundation 
of the science of to-day, and familiar to all. In no 
clicmical change is matter either created or destroyed; 
the sum of the masses of the factor's of a chemical 
change heing identically equal to the su7n of the masses 
of the jjroducts. Tlie form of matter can he changed, 
hut not its quantity. This principle, which strikes the 
materialistic mind of to-day so much in the character of 
a truism, involved quite a revolution in the settled views 
of the end of the eighteenth century. As has before 
been stated, the production of new forms of matter 
was regarded as an act of special creation, having no 
quantitative relation to the destruction or annihilation 
which necessarily preceded it. In Lavoisier's time, too, 
heat or caloric was popularly regarded as material, and 
consequently its greater or less role in any chemical 
change would presumably more or less affect the mass 
relations. But Lavoisier proved that the mass of a 
compound AB is, within the limits of experimental 
error, exactly equal to the mass of A and the mass of 
B combining to form that compound, and is quite 
independent of the heat evolved or absorbed during 
the combination. 

^ This principle was assumed ia many of the ancient philosophies. 


Although Black and Cavendish had done accurate 
pieces of quantitative work, yet it is with Lavoisier that 
chemistry essentially passed from the qualitative to the 
quantitative stage. It was he who ever insisted on the 
paramount importance of the question, "How much?" 
in every chemical inquiry. 

In connection with combustion, Lavoisier first con- 
firmed the fact that when a metal burns it increases in 
weight, and then proceeded to prove in the case of tin 
that the increase in weight is due to air absorbed, and 
is equal to the weight of the absorbed air. He noticed 
that it was not the air as a whole that was absorbed, 
but only a constituent thereof, the unabsorbed con- 
stituent being different from common or fixed airs. 
From classical experiments on red precipitate (HgO), 
suggested by Priestley, he concluded that the con- 
stituent absorbed by burning bodies was nothing else 
than Pi-iestley's dephlogisticated air. 

While this air can be expelled from the red calx of 
mercury by mere heating — a point whose explanation 
had always baffled the phlogistonists — the calces of 
other metals had to be heated with carbon, and the air 
disengaged under these conditions Lavoisier proved to 
be identical with Black's fixed air, which therefore must 
consist of carbon and dephlogisticated air, and which he 
therefore renamed carbonic acid gas. The carbon com- 
bined with the dephlogisticated air of the calx, just as 
it did with that of the atmosphere when burned therein. 
This same carbonic acid gas Lavoisier showed to be 
formed during the respiration of animals, thus trans- 


forming a suspicion which had arisen in the mind of 
Paracelsus into a certainty. Mayow a century pre- 
viously had come to the same conclusion, though not 
iu so definite a manner. 

Since the combination of dephlogisticated air with 
the majority of substances investigated by Lavoisier 
produced acids, he renamed the gas oxygen, or the acid 
producer ; a nomenclature which modern research has 
shown to be not altogether appropriate. 

On burning phosphorus in a confined volume of air, 
Lavoisier found that after about 5 of the air had dis- 
appeared the phosphorus was extinguished, and all 
other combustible substances refused to burn in the 
residual gas. He regarded this noxious air as a true 
constituent of common air actually present therein 
before the burning, and called it first "moufette atmos- 
pherique," and then later "azote," because animals died 
when immersed in it. Rutherford in Ediubursrh simul- 
taneously isolated this gas by treating with caustic 
potash solution air in which animals had been confined 
for some time. He gave it the more popular name 
nitrogen. From his exjjeriment with burning phos- 
phorus, Lavoisier rightly concluded that air was a mix- 
ture of about i oxygen and 4 nitrogen or azote. 

Having given a simple explanation of calcination or 
oxidation and reduction by carbon, Lavoisier now turned 
his attention to the process of reduction, i.e., the re- 
forming of the metals from their calces by means of 
hydrogen. To this end he repeated Cavendish's experi- 
ment on the composition of water, rightly interpreting 


the results and completing the proof by passing steam 
over heated iron, thus obtaining a calx and inflammable 
air which he thenceforward called hydrogen. When a 
calx is heated with hydrogen, the metal reappears, not 
because the calx takes up the phlogiston, in which the 
hydrogen is rich, but because the hydrogen wrests the 
oxygen from the calx and forms therewith invisible 

Lavoisier regarded the solution of a metal in a dilute 
acid as a reaction taking place in two stages. First, 
the metal decomposed the water, setting free the 
hydrogen, and combining with the oxygen to form a 
calx ; and then this calx combined with the acid, form- 
ing a salt soluble in the water holding the acid in 

Here truly was a complete rcnversement of current 
ideas. To the phlogistonist the metal or combustible 
was more complex than the calx or product to which 
it gave rise. The metal or combustible consisted of 
matter plus phlogiston, the calx or product was metal 
or combustible minus phlogiston. To the Lavoisierian 
or antiphlogistic school, however, the calx was more 
complex than the metal — it was a compound, while the 
metal was an element. 

When we look back on Lavoisier's life-work, we see 
it to consist of co-ordination and generalisation rather 
than discovery. He made use of the facts brought him 
by what Huxley has called the hod-carriers of science. 
In making use of these contributions he sometimes, 
unfortunately for his moral reputation, forgot their 


sources, and claimed them as original. Lavoisier's 
attitude towards Priestley, Cavendish, and others, whose 
data he used, is still considered a subject for severe 

Undoubtedly a great factor in Lavoisier's success 
was his unconditional rejection of the old, vague, ele- 
mentary principles of the alchemistic era, and his 
adoption of the conception of elements and compounds 
as developed by Boyle, and now generally received. 

The theory of phlogiston was doomed. Lavoisier's 
explanations steadily gained in favour, and the year 
1785 marked the complete ascendency of his anti- 
phlogistic views. In France his teaching was received 
partly from intellectual conviction, partly from a feel- 
ing of patriotism, stimulated by the title La Chemie 
Frangaise, which Fourcroy was presumptuously pleased 
to bestow on his countryman's theory. 

The majority of British and German chemists also 
expressed their allegiance to the new theory before its 
illustrious founder prematurely passed away. 



The fundamental classification of chemistry is com- 
prised in the two expressions, homogeneous or pure 
bodies, and non-homogeneous bodies or mixtures. 
Everything material necessarily falls into one or other 
of these two classes. 

It is sometimes quite erroneously stated that only 
the homogeneous substances belong to the domain 
of chemistry. This statement probably originates in 
the fact that all the fundamental chemical laws have 
reference to, and are only true for, homogeneous bodies ; 
but homogeneity is the exception, not the rule in 
nature,^ and chemistry is a natural science. Matter 
invariably comes into the laboratory in a state of 
non-homogeneity or mixture, and it is always the 
first and often the most difliicult task of the chemist 
to resolve such a mixture into its homogeneous con- 

' Witness the derivation of the word metal. According to Pliny 

this word is derived from fxer aXKa signifying tor/cthcr with other 

things. There is, however, another possible derivation of the word 

metal, viz., from fxeraWov = a mine, connected with jueraXXdw = I 

search for eliliycntly. 




The study of coal tar, for example, has resulted in 
most important advances in the theory of chemistry. 
Yet the study of coal tar as a whole would have been 
quite barren of valuable results. Tar being a variable 
mixture, the investigation of its properties would have 
led to inconstant results, and made impossible any 
attempts at productive generalisation. But by the 
process of fractional distillation {vide infra), coal tar 
has been sorted into a number of homogeneous con- 
stituents, and it is the study of these constituents 
individually, not of tar as a whole, that has profitably 
engaged the attention of chemists.^ Thus benzene 

1 The following scheme I'epresents the approximate percentages 
obtained, and the stages passed through in the separation (see pod, 
p. 47) of six of the more important homogeneous constituents of coal 
tar : — 

Up to 110° C. 
First Kumiiiigs 



11 ir to 220° c. 

Light Oil. 

210° to 240° 0. 
C.irbolic Oil. 


240° to 270° 0. 
Creosote Oil 

Heavy Oil. 


1(. p. 81° 
1 per cent. 


^ Carbolic Naphtlia- 
/ Acid fe ne 

\ / 1 per ct. 10 per ct. 

Later portion. 
First waslied with 
acid and alkali, 


TT. p. 111° 

cl percent. 

and other 


p. 140° to 150°. 

Solvent Nai)htha 






i to i per ct. 

35 per cent. 


is a definite substance with fixed and invariable pro- 
perties, and its constants determined for a preparation 
from any one coal tar will hold good for a specimen 
obtained from any other tar. 

What, we may now inquire, is the distinguishing 
feature of the class of non-homogeneous bodies ? Briefly 
stated it is this ; a non-homogeneous substance or mix- 
ture can be resolved into unlike portions by processes 
of mere sorting, and the sum of the energies of the 
sorted portions is equal to the energy of the mixture 
from which they were sorted.^ 

If one simply mixes a red powder A with a green 
powder B (no heat evolution or absorption accompany- 
ing the process) the mixture can be resolved into its 
constituents again by patient "hand sorting" under 
the microscope.^ If flour and sugar be mixed, they 
can be separated again by treating the mixture with 
water, in which the sugar alone is soluble. The 
mere mixture of flour and sugar does not alter the 
properties peculiar to each of these substances in the 
pure state. 

Even when all the constituents of a mixture are 
soluble in a given medium, they may often be com- 

^ Mixtures or emulsions of such liquids as are ordinarily spoken of 
as immiscible, e.g., oil and water, are only temporarj'. Such mixtures 
possess more energy than the separated constituents ; but this surplus 
of energy, depending on the area of the surfaces of separation of the 
different liquids, sooner or later runs down into heat, and contem- 
poraneously the mingled liquids sort themselves into easily separable 
layers. [See Maxwell, Theory of Heat, chap, xx.] 

- Dextro- and laevo-tartaric acids were first separated from each 
other and obtained pure by this method. 


pletely separated by repeated crystallisation from that 
medium. Thus when an aqueous solution of potassium 
chloride and potassium chlorate is evaporated, the less 
soluble chlorate crystallises out first, and afterwards 
the more soluble chloride. This method of separation 
is actually adopted in the commercial preparation of 
chlorate of potassium. At Stassfiirt a mineral com- 
posed of potassium and sodium chlorides is found in 
quantity. In order to separate the constituents, a cold 
saturated solution is first made of the mixture. This 
solution is then raised to the boiling point. In pro- 
portion as the water evaporates the sodium chloride 
crystallises out. After a certain time the solution is 
allowed to cool, when potassium chloride separates out. 
For this salt, while much more soluble at high tempera- 
tures than common salt, decreases in solubility very 
rapidly indeed as the temperature is lowered. By 
alternately repeating the boiling and cooling, large 
quantities of the chlorides are separated. 

Again, oxygen and nitrogen are both soluble in 
water, but oxygen to a greater degree. than nitrogen. 
Common air is a mixture of these two gases, conse- 
quently the "air" dissolved by water (which ''air" 
is disengaged again on boiling the water) is much 
richer in oxygen than common air. If the process 
of treating water with air under pressure, and then 
boiling the resulting solution, were repeated often 
enough fairly pure oxygen could be eventually sorted 
out. An investigation of the results of a single opera- 
tion of the above process will be instructive and will 


afford an opportunity of illustrating important laws, 
one discovered by Dalton, and the other by Henry and 
Dalton. The data requisite for this investigation are 
as follows : — 

Per cent. 

Composition of air by volume, oxygen . . 20"9 

„ „ „ nitrogen . . 79-1 

Approximate coefficient of absorption of oxygen . "04 
„ „ nitrogen "02 

The coefficient of absorption of a gas denotes that 
volume thereof (measured at 0° C. and under a pressure 
of 760 mm. of mercury) which is dissolved by one 
volume of water when an excess of the gas is presented 
to the water under a pressure of 760 mm. of mercury. 
Thus one cubic foot of water dissolves '04 of a cubic foot 
of oxygen (measured at 0" C. and 760 mm.) when an 
excess of the gas is allowed to stand over the water 
at normal pressure, 

Dalton's approximative law ^ of partial pressures 
(1802) states that the total pressure of a mixture of 
gases is the sum of the partial pressures exerted by 
the constituents of the mixture in the space occupied 
by the mixture. Suppose the air exerts a pressure 
of 760 mm. Then, from Boyle's law and the above 
data, the partial pressure of the oxygen P^, must be 
given by the equation 

P„ X 100 = 20-9 X 760. 

P„ = 760 X -209 mm. 

Similarly the partial pressure of the nitrogen P^ is 

' " An approximative law exjjresses only a portion of a complex 
phenomenon — the limit towards which the phenomenon aims." 


equal to 760 x "791 inm. In conformity with Dalton's 
law, it will be noticed that P^ + ?„ = 760 mm. 

Henry and Dalton's law (1803-1807) is an approxi- 
mative law which states that the masses of the less 
soluble gases dissolved at ordinary temperatures are 
proportional to the partial pressures exerted by these 
gases.i Let d be the density of oxygen at 0° and 
760 mm. Then one cubic centimetre of water dissolves 
•04fZ grams of oxygen when the pressure is 760 mm. 
By Henry and Dalton's law it will therefore dissolve 

;04tZ_x_760 x_j209 .^^^^ ^ .^qq ^ .qosSG x d grams, 
760 '^ ' 

when the pressure is 760 x '209 mm. The volume of 
this oxygen is •00836 cc. Similarly -02 x '791 cc. of 
nitrogen are absorbed by one cubic centimetre of 
water. Hence the composition of the dissolved air 
is approximately 

Oxygen .... 34'5 per cent. 
Nitrogen . . . . 65"5 per cent. 

In other words, whereas air contains only about 21 
per cent, of oxygen, the dissolved air contains about 
3 1| per cent.^ 

^ It is frequently stated that the law of Henr}- and Dalton furnishes 
a criterion as to whether a gas is physically or chemically dissolved. 
If the law is obeyed, then it is said to be a case of physical absorption, 
otherwise it is chemical change. Such a hard and fast distinction 
cannot be maintained. Solution is a complex phenomenon, and even 
in the simplest cases it seems almost certain that true chemical action 
and simple physical change are inextricably involved (see p. 55). 
Further, it is probable that at low enough temperatures no gas would 
be found to obey Henry and Dalton's law. 

- If the process indicated in the text were to be repeated with this 


Many mixtures may be resolved by taking advantage 
of differences in the volatilities of their constituents. 
When in the analysis of an inorganic substance by 
the usual methods we come to test for potassium, it 
is necessary before performing the test to remove 
the salts of ammonium which have been added earlier 
in the course of analysis. This is effected by eva- 
porating the solution to dryness and then heating 
the residue to low redness, when the more volatile 
ammoniacal salts will pass off, leaving behind the 
less volatile potassium salts. 

A mixture of liquids can often be sorted by frac- 
tional distillation ; that is, by taking advantage of 
differences in the boiling point of its constituents. 
If a mixture of ether (B.P. 35°) and aniline (B.P. 
181°) be heated in a suitable apparatus, the tempera- 
ture of the mixture rises quickly till the neighbour- 
hood of the boiling point of ether is reached, when 
it remains fairly constant till nearly all the ether is 
distilled off. The temperature then rises rapidly to 
the boiling point of aniline, when nearly pure aniline 
is obtained as a distillate. It is not in general pos- 
sible to effect in this way a complete separation of 

air of 34^ per cent, oxygen, the composition of the air resulting from a 
second solution in water would be approximately 

47'5 Oxygen, 
52'5 Nitrogen, 

and a third solution in water would make the composition of the dis- 
solved air approximately 

75 Oxygen, 
25 Nitrogen. 


mixed liquids in one operation, it is only when the 
process has been repeated systematically several times 
that perfect separation is attained. 

This process of fractional distillation is the first and 
most important stage in the resolution of coal tar 
into its homogeneous constituents (see p. 41) ; the final 
isolation of these constituents in a state of complete 
purity being effected by other sorting processes adapted 
to the individual cases. 

As will readily be conceived, a mixture of liquids 
possessing the same or nearly the same boiling points 
does not yield to this method of fractional distillation, 
and indeed in many cases where the boiling points of 
the constituents of a mixture differ fairly widely, 
separation is found to be impracticable. Let A and 
B be the two constituents of a liquid mixture ; then 
it would appear that a separation of A and B by 
fractional distillation is only possible when the boiling 
point of every conceivable mixture of A and B lies 
intermediate between the boiling points of the free 
constituents A and B. This is the case with ether 
and aniline, and therefore all mixtures of these two 
substances can, as already described, be separated by 
fractional distillation. But it is not the case, for 
instance, with ethyl alcohol (B.P. 78°) and water; 
hence mixtures of alcohol and water are not completely 
resolvable by fractional distillation in spite of the large 
difference between the boiling points of the liquids. i 

1 A mixture of 97 per cent, ethyl alcohol with 3 per cent, water 
has a higher boiling point than either pure alcohol or pure water. 


Many mixtures may be resolved by taking advantage 
of differences in the densities of their constituents. 
This principle finds application in the " panning out " 
of gold from its ores, in the sorting of diamonds 
from their specifically lighter matrix in the so-called 
pulsators, and in the resolution of various mixtures 
by centrifugalisation.i In the analysis of a soil the 
clay is separated from the sand by stirring up the 
soil in water. The sand sinks to the bottom of the 
containing vessel, while the clay remains suspended in 
the supernatant liquid, which is poured off and filtered. 
Such methods of resolution, wherein an inert menstruum 
is called into play, are often grouped together under 
the title of elutriation methods.- 

A mixture of gases of different densities can also 
be partially resolved by a process introduced by 
Graham (1805-1869), and called by him atmolysis — 

Hence pure anhydrous alcohol cannot be obtained by fractional 
distillation. Suppose we start with a mixture of 50 parts water and 
50 parts alcohol. Fractional distillation will resolve this into two 
portions : (1) 4S'45 parts of pure water, and (2) 51 '55 parts of 97 per 
cent, ethyl alcohol (50 parts alcohol, and 1"55 parts water). In other 
words, it is fairly easy to get in a pure state some of the water mixed 
with the alcohol, but it is impossible to get alcohol in an anhydrous 
state from an aqueous mixture. To obtain pure anhydrous alcohol 
recourse must be had to distillation of the 97 per cent, alcohol over 
anhydrous baryta. 

^ The centripetal force necessary to keep a particle of mass m 
moving in a circular path of radius r with angular velocity a, is 
numerically equal to the product mra'K Consequently the more 
massive, or rather, the denser particles of a mixture will have a 
greater tendency to fly tangentially off a revolving plate than the less 
dense ones. 

^ For very neat applications of elutriation methods to the proximate 
analysis of minerals see Nature, xliii. p. 404, and xlix. p. 211. 


a rather misleading nomenclature in this connection. 
The lighter a gas is, the more quickly does it pass 
through a porous partition, cceteris paribus. In the 
annexed diagram cc represents a glass tube through 
the axis of which runs a porous tube (e.g., the stem 
of a churchwarden pipe) tt'. The side tube c of the 
glass is in connection with an exhausting pump. If 
electrolytic gas, which is a mixture of hydrogen and 
oxygen in the proportion of two volumes of the former 
to one of the latter, be passed slowly through the tube 


Fig. 1. 

XT', the pump will extract from c a mixture richer in 
the lighter gas hydrogen than the electrolytic gas used, 
while the mixture issuing from tt' will be richer in 
oxygen. Finally a limit will be reached whereat the 
repetition of the process will be unproductive of further 
resolution. The exact statement of the connection 
between the densities of gases and their rates of passage 
through a thin septum of graphite, or better still, biscuit 
ware, is known as Graham's law of diffusion. The 
rates of diffusion of gases under the same pressure 
vary inversely as the square roots of their densities; 
or algebraically stated — 

rate of diffusion of gas x v density of 1/ 
rate of difiiu^ion of gas ij ~ J density oflr' 



This law is not actually realised in practice ; it would 
be absolutely true for "perfect gases" (i.e., ideal gases 
which obey Boyle's law perfectly) diffusing through an 
infinitely thin septum, i 

We may also separate some mixtures by taking ad- 
vantage of their different diffusibilities, as in the process 
of dialysis, also invented by Graham. When substances 
are in solution, the rates at which they pass through 
animal or vegetable membranes- differ widely. Sub- 
stances which can crystallise pass through such mem- 
branes readily.^ On the other hand, solutions of bodies 
which do not crystallise but exhibit conchoidal fracture, 
are either quite incapable of passing, or only pass with 
the greatest difficulty, through such membranes. The 
former readily diffusible class of bodies Graham called 

^ This law, in common with the other gaseous laws of Boyle, Charles, 
and Avogadro (see p. 89), is a necessary consequence of the kinetic 
theory of gases. This theory simply postulates that the pressure of a 
gas is due to the impact on the walls of the containing vessel of the 
small similar particles of which the bulk of the gas is made up. 

Keasoning thence, the expression a / ^ " is arrived at by pure mathe- 

matics for the average velocity of progressional movement of the 
particles of a gas whose density is d, under a pressure of p cm of 
mercury of density D, at a place where the acceleration due to gravita- 
tion is (/. Since the rate of diffusion of a gas varies directly as the 
average velocity of movement of its particles, the law of Graham at 
once follows. 

^ For purposes of dialysis, a parchment made by soaking unsized 
paper in sixty per cent, sulphuric acid for a short time, is in general use. 

•* Striking exceptions to this generalisation are furnished by hsemo- 
globin, the colouring matter of the blood, and vitellin, an albumen 
occurring largely in plants. Both of these substances, though crystal- 
line, are non-diffusible. It has also been stated that egg albumen — 
a colloid almost as typical as glue — can be obtained in the crystalline 



crystalloids ; to the latter non-diffusible class he gave 
the name colloids, from the Greek word {/coWa) for 
glue, their typical representative. As an example of 
the application of the method of dialysis we will take 
the preparation of the important drug "liquor ferri 
dialysati." Like many colloid bodies, ferric hydroxide 
can exist in a soluble or hydrosol form, and in an in- 
soluble or hydrogel form. A solution of the hydrosol 
form constitutes, the drug above mentioned, and it is 
prepared as follows. The 
hydrogel or ordinary form of 
ferric hydroxide is soluble in 
a solution of the crystalloid 
ferric chloride. Such a solu- 
tion is prepared and then 
placed in a dialyser (Fig. 2). 
This consists of a U tube 
uu, made out of parchment 
paper suspended from a rod 
rr in a large vessel contain- 
ing water. The crystalloidal ferric chloride diffuses 
into the surrounding water, which should be frequently 
changed ; while the hydrosol form of the colloidal ferric 
hydroxide 1 remains behind in the U tube in a pure 

This process of dialysis is frequently resorted to in 
toxicological investigations for the purpose of separating 
the crystalloidal poisons from the colloidal contents 

^ It would appear that liquor ferri dialysati is not a solution of pure 
ferric hydroxide, but of ,1 hydrosol fcriic hydroxychloride. 

Fig. 2. 


of the stomach and intestines which would mask the 
reactions of the poisons. 

The method of refrigeration is also largely used in 
the resolution of mixtures. Thus the impure benzene 
obtained by fractionally distilling coal-tar is freed from 
admixed toluene by surrounding it with ice. The 
benzene solidifies, and can be separated from the still 
liquid toluene. Similarly pure sulphuric acid is pre- 
pared from the aqueous product obtained by evapora- 
tion in platinum vessels. Quite recently this method 
of purification by refrigeration has been applied on a 
large scale to the purification of organic bodies, such 
as ether, chloroform, &c., by Pictet and Liebreich, 

So far we have dealt with what may loosely be 
called mechanical methods of resolving mixtures. These 
can, of course, also be resolved by chemical means, but 
in this case one or other of the constituents of the 
mixture necessarily suffers a permanent change. Thus, 
a zinc compound in solution can be freed from an 
admixed copper compound by passing sulphuretted 
hydrogen through the acidulated mixture. The copper 
compound is thus changed into insoluble copper 
sulphide, which can be filtered off, leaving the zinc 
compound in solution. 

A number of very subtle chemical methods of re- 
solving mixtures of very closely allied bodies have 
recently been introduced under the generic title " frac- 
tionation." These methods will receive more detailed 
notice when we speak of the elements. 

It will now be clear that in a mixture the constituents 


conserve the properties peculiar to themselves in the 
free state. Hence it follows that a mixture when 
subjected to certain operations shows in general dif- 
ferential results — part dissolves, part does not; part 
sinks, part floats — so that it can be sorted into its 
constituents by taking advantage of sufficiently pro- 
nounced differences in degree of a common property of 
its constituents. In thus studying the resolution of 
mixtures, we have gained some knowledge of the more 
general and important methods employed by chemists 
for purifying substances. 

Turning now to homogeneous substances. These, as 
was first hinted by Boyle, can be divided into the two 
classes, elements and compounds. The elements are 
practically the units of chemistry ; according to definite 
laws, they unite in manifold combinations and permuta- 
tions to form the now almost infinite number of known 
compounds ; but they defy all attempts to resolve them 
into dissimilar constituents. Mercury, e.g., cannot in 
any known way be split up into dissimilar portions, 
each portion weighing less than the mass started with. 
In short, elements constitute that class of homogeneous 
substances which is amenable to synthesis only ; ele- 
ments cannot be analysed. They constitute what may 
metaphorically be called the alphabet of the science. 

But if compounds are composed of and are resolvable 
into elements, how, it may be asked, do we distinguish 
them from mere mixtures? Put briefly, the distinction 
is this : mixtures can be resolved by processes of mere 
sorting; compounds cannot be so resolved. When 


elements combine chemically, the properties of the 
resulting compound are only remotely functions of the 
properties of the elements combining. The altogether 
new properties of the compound are not by any means 
the combined properties of the constituents ; they show 
no partial or differential character. A compound is 
either wholly soluble or wholly insoluble in a given 
menstruum ; it is either wholly magnetic or wholly non- 
magnetic ; under the highest magnifying power attain- 
able it is optically homogeneous. A knowledge of the 
salient physical properties of the free elements consti- 
tuting a compound does not assist us in our endeavours 
to resolve that compound into its constituents, as is the 
case with mixtures. A mixture can be resolved into 
its constituents vdthout involving a simultaneous and 
permanent change in the matter separated or other 
matter ; whereas the analysis of a compound in general 
demands the permanent change of at least one con- 
stituent of the compound as well as of extrinsic 
matter. Thus with respect to the preparation of 
copjser from its compound copper oxide, the knowledge 
that copper is a comparatively non-volatile insoluble 
body, while oxygen is a soluble gas, avails us nothing ; 
and the realisation of the project absolutely demands 
the simultaneous and permanent change of some 
such substance as carbon or hydrogen into oxidised 

Though the distinction between mixture and com- 
pound is in theory easily enough grasped, yet it cannot 
be denied that in practice it is often extremely difficult, 


if not impossible, to state definitely whether in particular 
cases we are dealing with the one or the other class 
of matter. Physiological chemistry furnishes us with 
several examples of this difficulty. Is haBmoglobin a 
" chemical unit " {i.e., homogeneous), or is it a mere 
mixture of the substances globin and hajmatin, which 
it so readily yields ? Is egg albumen — the most 
thoroughly investigated of the proteids — a true 
chemical compound, or is it a mixture of several 
individual but closely allied proteid substances ? Are 
the varying results of its analyses made by different 
experimenters to be ascribed solely to accompanying 
difficultly removable impurities, or to the fact that it is 
essentially a variable mixture ? Is gluten — the sticky 
constituent of dough — a definite substance, or is it a 
mixture of the proteids pre-existent in flour but 
changed by ferment action ? To such questions physi- 
ologists cannot at present vouchsafe definite answers; 
indeed it may be said that one of the most formid- 
able obstacles to the rapid advance of physiological 
chemistry is the uncertainty as to whether many of 
the fundamental substances with which it deals, and 
which have received definite names, are, as a matter 
of fact, " chemical units " (i.e., chemically pure 

Again, the question is often asked, is a solution of 
salt in water really a mere mixture of salt and water 
particles, or does it contain what may be called low- 
grade unstable compounds of salt particles and water 
particles disseminated throughout the general bulk of 


the solution ? Is solutiou a purely physical change 
in aggregation, or does it involve true chemical com- 
binations between the particles of the solvent and 
those of the dissolved substance ? 

The investigation of the nature of solution takes 
a most prominent place in the chemistry of to-day. 
While some chemists are attacking the subject from 
one side by purely physical methods, and summing 
up their results in terms of partial and provisional 
theories involving only physical ideas, others are assail- 
ing the subject from a purely chemical standpoint. 
Yet this statement must not be interpreted as assert- 
ing the existence of two rival and mutually exclusive 
schools on the question of solution. All chemists are 
pretty well agreed that solution is neither a simple 
physical nor a simple chemical change, but that it 
is a very complex process involving simultaneous 
physical and chemical changes. The exact point at 
issue is the actual state of dissolved substances, i.e., 
the constitution of solutions. 

The only satisfactory explanation that has as yet 
been given of the results of investigations of solutions 
from their physical aspect, makes the solvent a passive 
medium in which the discrete molecules of the dis- 
solved substance (or the products of dissociation of 
these molecules, the ions) uniformly distribute them- 
selves. From this point of view the solvent bears 
much the same relation to the dissolved substance 
as the space defined by the walls of a vessel does 
to the gas it contains ; solution, in fact, shows an 


analogy to the evaporation of a liquid in a confined 

On the other hand, investigations carried out from 
a chemical standpoint seem to demand the recog- 
nition of a definite chemical interaction between, as 
distinguished from a mere interpenetration of, the 
molecules of the dissolved substance and those of the 
solvent. When a salt is dissolved in water it appears 
as if the salt molecules combine with the water mole- 
cules to form definite yet very unstable chemical com- 
pounds — true liquid hydrates.^ 

So far then it is clear that the two lines of investiga- 
tion lead to different views regarding the structure of 
solutions and the condition of the dissolved substance. 
But it should be remembered that the more or less 
mechanical conception of solution has arisen from the 
exclusive study of very dilute solutions, while the 
investigations leading to a more chemical rationale 
have been chiefly carried out with strong solutions. 

But little doubt can be entertained that future re- 
search in this field will either establish a continuity 
and relationship between these confessedly partial and 
apparently diverse hypotheses, or by so modifying 
one or both, will fuse them into a consistent and 
comprehensive theory of one of the most common 
but least understood of ]:)]iysico- chemical ])honomena 
— solution. 

Twilight is distinct from daylight, but one would 

^ The constitution of solutions according to this view will be more 
fully developed in the chapter on chemical equilibrinm. 


hardly undertake to say where the one begins and the 
other ends. So is it with the distinction between mix- 
tures and compounds. The extremes of each class 
contrast strongly enough ; but through the inter- 
mediacy of what are called molecular compounds^ — 
a convenient term with as yet a very vague connota- 
tion — the one class merges imperceptibly into, and 
blends with, the other without break of continuity.^ 

The following rough analogy may serve to fix in the 
mind the fundamental differences between mixtures on 
the one hand, and the two classes of homogeneous 
bodies on the other. 

Imagine four heaps, the first of needles only, the 
second of pieces of thread only, the third of needles 
and threads, and the fourth of threaded needles — the 
threads being knotted so as to form loops. The first two 
heaps symbolise elements, say oxygen and hydrogen. 
The third heap symbolises a mixture, say electrolytic 
gas. From this heap unlike heaps can be made by 
mere sorting. The fourth heap resembles a compound, 
say, water, for while mere sorting alone will not resolve 
this heap into two dissimilar ones, yet an isolation of 
its constituents will be practicable after the destruction 
by some extrinsic agency of the continuity of the thread 
loops in the one case, or of the eyes of the needles 
in the other. 

^ See pages 144, 155. 

^ In very interesting communications to the Chemiml Society's 
Journal, vol. Ixi. p. 114, Picton and Linder have shown that there is 
a continuous series of grades of solution passing without break from 
suspension to crystallisable solution. 


But to return to the elements which have also con- 
stituted a field for much of the more recent chemical 
research. The list of elements has undergone many- 
vicissitudes since its first establishment. Until the 
year 1811, when Dav}' introduced the powerful ana- 
lytic method of electrolysis into chemistry, the alkalis 
potash and soda, and the alkaline earths, baryta, 
strontia, and lime, were regarded as elements. On 
the other hand, chlorine up till this date was regarded 
as a compound, being the oxide of a hypothetical 
element. The establishment of the compound nature 
of the alkalis and alkaline earths, and the simple nature 
of chlorine was attended by important modifications 
in the reigning theories of chemistry. Nitrogen was 
for a time deprived of elementary dignity, being 
regarded as the oxide of an unknown element nitri- 
cum, and even the elementary nature of such un- 
doubtedly simple substances as hydrogen, phosphorus, 
and sulphur, was for a time called into question by 

It is perfectly impossible to state definitely the num- 
ber of the elements ; indeed, the practical proof of the 
simplicity of a given matter is one of the hardest tasks 
that falls to the lot of the chemist. Lavoisier's list 
only contained twenty-six members, including what 
are now known to be forms of energy^, heat and 
light, but most chemists are now agreed that the 
number of unequivocal elements lies somewhere be- 
tween sixty-six and seventy. This uncertainty arises 
from the fact that in recent years it has been found 


necessary to open a suspense list for the temporary 
accommodation while suh judice of the many new 
claimants for elementary distinction, and opinion is 
divided as to the exact number of elements which 
ought to be suspended. Even when two naturalists 
agree as to the absolute number of unequivocal elements, 
it does not follow that they favour exactly the same 
elements throughout. One may favour the advance- 
ment of an element A from the suspense to the estab- 
lished list, while the other may think the evidence 
incomplete in the case of A, but satisfactory in the 
case of another claimant B. 

Many of the elements constituting this suspense or 
probationary list are not known in the free state, but 
only in combination with oxygen in the form of very 
refractory (ic, difficultly reducible) oxides. Eefractory 
oxides are generically known as earths, and as the 
particular oxides under consideration are, though 
widely diffused, only met with in nature in very small 
quantities, they are usually referred to collectively as 
the rare earths. Many of these oxides, and therefore 
presumably the metals which they contain, are so 
similar in their chemical properties that they can 
neither be separated nor distinguished from one another 
by ordinary chemical operations or tests. It is not 
improbable that some of them will turn out on nicer 
investigation to be either variable mixtures or allotropic 
forms, while others may prove themselves compounds 
of already known elements and so share the fate of 
Bergman's " siderum," which turned out to be nothing 


else than iron phosjihide, and Richter's "nickolaniim," 
which was merely an impure nickel. 

The most important sources of these rare and doubt- 
ful elements are the minerals gadolinite, cerite, and 

From oradolinite, Bunsen and Bahr isolated the two 
new earths yttria and erbia. These they regarded as 
the pure oxides of new elements which they called 
yttrium and erbium, but they did not isolate these 
elements. Their yttria was pale yellow in colour. 

Soon after this isolation, Smith and Delafontaine 
separated a much darker yellow yttria from samarskite. 
They therefore concluded that it was impure, and suc- 
ceeded in separating from it a new orange-coloured 
earth, terbia. This left a residue of perfectly white 
yttria. Hence they concluded that Bunsen and Bahr's 
yttria was non-homogeneous. Nor did Bunsen and 
Bahr's erbia prove itself a simple substance, for 
Marignac succeeded in resolving it into what he called 
true erbia and ytterbia. Nilson then found that 
ytterbia was non-homogeneous, and split it up into 
true ytterbia and the earth scandia predicted by 
Mendeleeff. Cleve, in making a spectroscopic study 
of Marignac's erbia, came to the conclusion that it 
was not homogeneous, but was a mixture of true erbia 
and two new oxides, holmia and thulia. Finally, de 
Boisbaudran brought forward reasons for suspecting 
the integrity of holmia, which he ultimately resolved 
into true holmia and dysprosia. This little sketch 
does not include all nor nearlv all the rare earths ; 



it is intended to be illiTstrative rather than compre- 
hensive and encyclopsGdic. 

Bunsen and Bahr 

Smith and Delafontaine 



Clfeve . 



Yttria. Terbia. 


Erbia. Ytterbia. 

Ytterbia. Scandin.. 


Holmia. Thulia. 

Holmia. Dysprosia. 

Thus Bunsen and Bahr's original alleged simple earths 
yttria and erbia were far from being homogeneous, as 
they believed ; they were, according to present views, 
mixtures of at least seven discrete oxides. 

The methods which have been chiefly used in re- 
solving these earths are fractional precipitation of 
solutions of the oxides in acids by ammonia ; fractional 
decomposition by heat of the mixed nitrates ; and 
fractional crystallisation as already exemplified in the 
case of potassium chlorate and chloride. 

If to a solution which contains two earths of different 
basicity (and all the earths differ to a greater or less 
degree in this property) insufficient ammonia be added 
to precipitate them both, then the less basic earth yields 
more completely to the precipitant, and can be filtered 
off, while the more basic constituent resists its action 
and remains in solution. Thus after several thousands 
of such fractional precipitations conducted in an orderly 


manner, the two earths may be completely separated 
from one another so far as ammonia can effect this 
separation. The separated products are then ready for, 
and should be subjected to, some other kind of frac- 
tional resolution. If they yield to no other fractional 
methods, then they are pro tern, elements. 

As regards separation by fractional decomposition of 
nitrates, it should be mentioned that here again the 
nitrate formed from the less basic earth yields more 
easily to the decomposing action of heat than the 
nitrate formed from the more basic earth. Let A and 
B be two earths, of which A is more basic than B. 
Form the nitrates of these earths by acting on them 
with nitric acid, and then partially decompose by heat 
the mixed nitrates into their corresponding oxides. 
Take up the residue with water and filter. The residue 
will consist chiefly of the oxide of B and the filtrate of 
the undecomposed nitrate of A. 

In addition to the rare earths already mentioned, the 
following, among others of very doubtful claims, are 
candidates for the class of simple substances : — yttrium, 
ytterbium, zirconium, thorium, decipium, lanthanum, 
samarium, cerium, praseodymium, neodymium. 

The oxides of all the substances so far mentioned 
have been isolated, and the elements of which they 
are oxides have had provisional numbers assigned for 
their atomic weights. These numbers are necessarily 
affected with more or less uncertainty, for in many 
cases they depend on arbitrarily assumed formulae for 
the oxides. 


But even the admission of all the foregoing sub- 
stances into the " elementary hierarchy " does not satisfy 
some chemists, who, either from the spectroscopic ex- 
amination of minerals from different sources, or from 
the results of long-continued and varied fractionations 
in the laboratory, have come to the conclusion that 
most of the above alleged elements are still mix- 
tures. These chemists have not, however, succeeded 
in isolating the constituents of these mixtures ; 
they only find, according to their interpretation of 
spectroscopic phenomena, indications of non-homo- 

Thus Crookes believes yttrium to be a mixture of 
at least five elements, and Kriiss and Nilson would 
find at least nine elements in the once reputed element 
didymium, not two, praseodymium and neodymium, as 
Welsbach thinks. But it should be here emphasised 
that even could these elements be isolated they would 
not be distinguishable from one another chemically. 
Their discrimination would demand the subtile search- 
ing power of the spectroscope, and our most refined 
experimental methods would fail to establish conclusively 
any difference in their atomic weights. As yet, these 
" meta-elements," as they have been called by Crookes, 
are mere possibilities, not certainties, and it may be 
said that their substantiation, while of great specula- 
tive and theoretic interest, would not at all influence 
ordinary practical chemistry, which would still continue 
to regard yttrium, for instance, not its five meta- 
elements, as its working unit. It should also be 


remembered in this connection that as yet spectroscopic 
science "is still, for want of laws, at the epoch of 
accumulation of facts, not of their possession," It 
is as if chemists were making their preconceived 
notions of the nature and number of the elements to 
fit in with spectroscopic phenomena, instead of first 
thoroughly establishing principles of spectroscopy, and 
then using these to interpret the results of their investi- 
gations on the elements. 

Generally speaking, the upholders of the Periodic 
Law 1 — perhaps the greatest chemical generalisation of 
modern times — are averse to the idea of any great 
increase in our commonly accepted number of elements. 
In the tabular scheme which Mendeleeff gives as the 
expression of this law, only six of the rare metals 
are admitted, yttrium, ytterbium, lanthanum, cerium, 
thorium, and zirconium, and there are only, so to 
speak, vacancies left for a very limited number of other 
elements, unless indeed the new elements have atomic 
weights greater than that of uranium, which has the 
highest atomic weight (240) of all known elements. 
None of the above claimants would fall into this 
category, and it seems very improbable that many, if 
any, elements with atomic weights greater than 240 
remain to be discovered. 

This recent work on the rare earths, combined with 
the results of the application of the spectroscope to 
the investigation of the stars and nebulfe, has resulted 

^ See article, "Periodic Law," in Muir and Morley'a new edition of 
Watts' Dictionary of Chemistry. 



in modern views regarding the nature of the elements 
which approximate to those held by the Aristotelian 
school, in so far as they postulate one fundamental 
matter. No longer are the elements universally be- 
lieved to be ultimate and independent in their nature, 
as Boyle and Lavoisier insisted, but the belief is 
growing that they consist of one fundamental matter 
in various stages of condensation, and that the stage 
of condensation is dependent on the temperature, being 
less the higher the temperature — a belief which re- 
invests the alchemistic attempts at transmutation with 
a certain amount of warranty. In 1815 Prout suggested 
that this fundamental matter was hydrogen, but the 
suggestion was shown to be incorrect by the classical 
work of Stas and others. At present the funda- 
mental matter called "protyle," without any further 
attempt being made to characterise it, is, so to 
speak, jjlaced lower down in the scale than hydrogen, 
which is itself regarded as protyle in a certain ad- 
vanced stage of condensation. 

Crookes regards all elements as having been gradu- 
ally evolved from this protyle; the heavier elements, 
such as bismuth, thorium, and uranium, being the 
younger species ; the lighter elements, such as lithium 
boron, &c., being the older. A consequence of the 
adaptation of this theory to the teaching of the 
periodic law, is that what we are accustomed to call 
elements ought really to be called " elementary 
groups " ; that what we are accustomed to regard as 
the atomic weight of an element does not accurately 


represent the weight of each atom constituting that 
element, but the mean of the weights of the atoms 
making up a definite mass of the element, these 
atoms being of slightly different weights. Thus the 
atoms constituting a mass of yttrium have not all 
identically the same weight ; while some, it may be 
the greater quantity, weigh 89 times as much as the 
average weight of the hydrogen atom, a few weigh 
89-01, a few others again 88*99 times as much, and 
so on. As before stated, Crookes believes that there 
exist in the " element " yttrium, at least five different 
kinds of atoms, each constituting what he calls a 
meta-element. These meta-elements are regarded as 
protyle in five very slightly different stages of con- 
densation. He is not quite decided as to whether 
one of these meta-elements largely preponderates over 
the other four as above hinted, but he rather inclines 
to this view. If such is the nature of the yttrium 
commonly accepted as an element, what, he asks, is 
there improbable in the idea that minute investigation 
would result in the assigning of a similar structure to 
the more common and familiar elements — to calcium 
and barium, for instance ? 

If we accept this bold application of the principle 
of evolution to the elements, we are scarcely justified 
in any longer speaking of matter as inanimate. Accord- 
ing to Crookes, the atoms of the elements are born, 
undergo secular vicissitudes, and die ; and the rare 
elements are, in his opinion, strictly comparable to rare 
plants and animals, in that they are simply examples 


of special kinds of atoms that have failed to harmonise 
with their environment.^ 

^ For further details on this abstruse and highly speculative subject, 
reference must be made to Crookes' original papers in the Journal of 
the London Chemical Society, vols. liii. and Iv. In this connection 
Clerk Maxwell's article " Atom " in the Encyclopaedia Britannica should 
also be read. In this article reasons are advanced for the diametri- 
cally opposed belief that the atoms of any one element, hydi-ogen, for 
instance, are eternal and identically similar among themselves, bearing 
the impression, so to speak, of articles stamped by machinery. 



From the beginnings of philosophy the question of the 
constitution of matter ^ has exercised the minds of 
philosophers. Defining matter as that which occupies 
space, it has been asked, does matter completely fill 
the space its outline occupies or not ? Does the gas 
contained in a flask completely fill the space it occupies, 
i.e., the space defined by the sides of the flask, in the 
same way as to our gross senses jelly fills a cup ? Or 
does it, on the contrary, fill the space in much the 
same way as apples fill a barrel, so that with sufiiciently 
magnified vision we could plunge an exceedingly delicate 
style into the flask in such way that the style's point, 
occupying at a given instant an interstice between 
the individual particles of the gas, would not at that 
instant actually touch the gas ? ^ 

^ The implications of the terms constitution <if matter and nature of 
matter must be carefully distinguished. The ultimate nature of matter 
is a metaphysical rather than a chtmico physical question. For a 
resume of the varied views held on this subject see Tait, Properties of 

- It shouhl be remarked that the ([Uestiou of the structure of matter 
is here being developed from tlie conventional chemical standpoint, 
not from the physical. The conception which most chemists, I think, 
have of a piece of chalk, for instance, is a collocation of molecules, each 
made up of hard atoms, each having the incompletely defined composi- 


Stating the question otherwise ; is apparently con- 
tinuous matter really continuous and capable of in- 
finitely small division without losing its individuality, 
or is it really discontinuous and capable of division 
down only to the limit marking the beginnings of dis- 
continuity ? Are geometrical conceptions or arith- 
metical to underlie our theories of the constitution of 
matter ? 

The early Greek philosopher Leukippos (428 B.C.) 
was the first to make answer in a vague way to these 
questions.! He decided that matter is not continuous, 

tion X CaCOs, and each separated from its neighbours by " void." But 
physicists, whilst admitting the ultimate heterogeneousness or grained- 
ness of apparently homogeneous matter, do not deny its perfect con- 
tinuity. The heterogeneity may take the form of alternations of matter 
and void, but it may involve only such differences as exist between 
solid and fluid, or between substances differing enormously in density ; 
or such heterogeneousness as differences in velocity and direction of 
motion, in different positions of a vortex ring in a homogeneous liquid. 
Three points should be noted in this connection — (1) in discussing the 
constitution of matter physicists employ the terms atom and molecule in 
a very loose way ; (2) their connotation of the term heterogeneity is 
quite different from that which the same term bears in Chap. III. ; and 
(.3) although in the restricted domain of chemistry we make provisional 
use of the conception and term atom, yet from a broadly philosophic 
standpoint we do not assert that the chemical atom represents the 
absolute limit to the divisibility of matter. The sociologist adopts as 
his unit the individual, quite regardless of the anatomist's powers. 
The atom is the chemical individual. See Lord Kelvin, PojAdar 
Lectures and Addresses, vol. i., and Maxwell's article "Atom" in the 
EncyclopcBdia Britannica. 

^ Later antiquity chiefly studied the atomic theory in the more 
elaborated form it attained under Demokritos, the pupil of Leukippos, 
and thus the disciple has prett};^ well usurped the place of the master in 
history. For a very concise account of the passage of Eleaticism into 
Pluralism, thence into Atomism, with the fundamental changes of idea 
this passage involved, see Burnet's Early Greek Philosophy. 


but is made up of numerous small separate and in- 
divisible particles called atoms. His views, embraced 
and developed by the Epicurean school, have been pre- 
served for us by the Roman poet Lucretius (b.c. 99) in 
his "De rerum natura," Here is the main argument, 
as presented in the poem. First comes the perfectly 
gratuitous assumption that reproduction — the agglo- 
meration of scattered, invisible particles into visible 
bodies — is slower than decay, the breaking up of bodies 
into invisible particles. From this premise it follows 
that there must be a limit to the breakage ; else the 
decay of infinite past ages would have left nothing 
visible and tangible. This limit to breakage or decay 
involves the idea of a least in things, which least is 
called an atom. Lucretius also taught that there were 
atoms of many different forms and weights — an infinite 
number of each kind ; and that all change consisted in 
the intimate contact or separation from such contact of 
these different kinds of atoms. This view of matter as 
presented by Lucretius is more of a vague poetic cosmo- 
gony than a scientific theory. It had no numerical 
conciseness about it, and was altogether too indefinite 
to be suggestive. It bears to the atomic theory, as 
accepted at present, about the same relation as do the 
scientific dreams and guesses of a Goethe to the experi- 
mentally substantiated inspirations of a Newton. 

Passing over the use which Newton made of an 
atomic conception of the atmosphere to make his 
theoretically derived velocity of sound tally with the 
experimental value — a physical rather than a chemical 


point — we do not find any serious attempt at a strictly 
scientific theory of the constitution of matter till we 
come to the year 1804. In this memorable year 
John Dalton first propounded his atomic theory — a 
"theory which is so fundamental in the chemistry of 
to-day, that were it in any way disproved, the whole 
superstructure of the science would fall in hopeless 
and chaotic ruin. 

Lord Kelvin has said that only when we can measure 
the thing we are speaking about and express it in 
numbers do we begin to know really anything about 
it. Judged by this sentiment, Dalton brought us to 
the beginnings of a true knowledge of atoms, for as 
we shall see his theory was nothing else than that of 
the early Greek philosophers mentioned, founded not 
on fancy, but on the careful observation of the facts 
of nature, and reduced to numerical definiteness. Let 
us see how Dalton was led to embrace the atomistic 
or limited divisibility view of matter. 

The fact that water does not dissolve all gases in 
the same quantities seems first to have suggested to 
Dalton the view that gases consist of large numbers 
of discrete particles, but what in his opinion chiefly 
demanded a resuscitation of the atomic theory was 
undoubtedly his discovery of the law of multiple pro- 
portions taken in conjunction with the previously sub- 
stantiated law of definite proportions. Hence we must 
first glance at these two fundamental chemical laws. 

The discovery of the law of definite proportions 
cannot be ascribed to any particular individual; it 


was arrived at simultaneously by several chemists soon 
after Lavoisier introduced quantitative methods into 
the science. If A, B, &c., represent the masses in 
which definite homogeneous substances interact to 
produce new homogeneous substances represented 
quantitatively by C, D, &c., then this law in its most 
general form states that no matter what the con- 
ditions of reaction or the absolute values of A, B, 

G, D, kc, may be, the ratios -, -, -, -, -, — , &c., 

are all constant. A particular case is when A and B, 
&c., represent elements uniting to form the single 
compound C, and the law is generally enunciated in 
terms of this special case as follows : no matter the 
conditions of formation, or the proportions in which 
the constituents are taken, a given chemical compound 
has always exactly the same percentage composition. 

Most laws (e.^.,the gaseous laws of Boyle and Charles) 
are only true under specified conditions or between 
certain narrow limits, but the law now under observa- 
tion is as far as we can tell an absolute and uncon- 
ditional one. Working with the haloid salts of silver 
— preparing them in many different ways and from 
different proportions of the ingredients — Stas proved 
the law accurate to 1 part in 10,000 parts,i an accuracy 

^ An ordinary chemical balance i.s capable of an accuracy of 1 in 10", 
and Miller in his elaborate construction of the standard pound attained 
an accuracy of 1 in 3 x 10^, but in Stas' experiments errors considerable 
in magnitude when compared witli those involved in mere weighing, are 
incidental to the operations of filtering, washing, incinerating, &c. An 
accuracy of 1 in 10,000 is about that attainable in a simple measure- 
ment of length. 


of high order when we recall the diverse operations 

Yet the law of definite proportions has had its vicissi- 
tudes. In the beginning of this century Berthollet 
denied its truth as above enunciated, asserting that 
the composition of a body might vary within certain 
limits, this variation being dependent on the masses in 
which its constituents were allowed to react ^ — just as 
recipes with slight quantitative differences will give to 
all intents and purposes the same culinary product. 
In this mistaken view he was successfully opposed by 
Proust, who was led to a warm espousal of the law 
by the following experiment. Proust analysed native 
malachite and found that it gave 71 "9 per cent, of cupric 
oxide. He then dissolved the mineral in acid and repr* 
cipitated the malachite in an amorphous form. This 
artificial product gave on analysis 71 "9 per cent, of 
cupric oxide. Hence Proust concluded that no matter 
whether malachite is formed in the crystalline condition 
in the earth's crust, where it is subjected to the influ- 
ence of mighty secular processes of which we know next 
to nothing, or whether it is formed artificially and sud- 
denly in the laboratory, it has in each case identically 
the same composition. He then showed that the 
alleged variable nitrate of mercury which Berthollet 
brought forward to vindicate his attitude, was not a 

^ The influence of mass in causing variations in the relative quantities 
of the products of a change (not of their individual compositions as 
Berthollet supposed) lies at the foundation of the study of chemical 
affinity in the modern acceptation of this term. See Pattison Muir, 
Principles of Chemistry. 


homog-eneous body but a mixture of mercurous and 
mercuric nitrates, in proportions varying according to 
the relative masses of mercury and nitric acid brought 
togrether. Thus arose the distinction between homo- 
geneous substances and non-homogeneoas substances 
or mixtures detailed in Chap. III. 

Passing on now to the law of multiple proportions. 
Before Dalton's time the fact had been recognised that 
a given element A will combine with another element 
B in two or more proportions to form two or more 
compounds, for each of which the law of definite pro- 
portions is true. But up to the year 1803, owing to 
the customary method of stating the results of analysis, 
no regularity had been detected in the values of the 
combination masses of A and B as between compound 
and compound. Dalton analysed the two compounds 
of carbon and hydrogen, methane and ethylene ; as 
also the two compounds of carbon and oxygen, carbonic 
oxide and carbonic anhydride, with these results — 

Ethylene.^ Methane. 

C = 85-71 p.c. H = 14-28 p. c. = 75 p.c. H = 25p.c. 

or approximately or approximately 

0^6 0^6 

H ~ 1 H 2 

Carbonic Oxidk. Carbonic Anhydride. 

C = 42-8f;p.c. = 57-24 pc. C = 27-27p.c. = 72-72 p.c. 

or approximately or api)roximately 

C 6 C 6 

0~8 , It 

^ The percentages here given are not the values actually obtained 
by Dalton. 


No regularity appears between the valves for the two 
hydrides on the one hand, or the two oxides on the 
other, until we consider a constant mass of either of 
the common elements in the two cases, instead of ex- 
pressing the results in the conventional percentage 
form. It is then noticed that the amount of hydrogen 
combined with six unit masses of carbon in marsh 
gas is exactly ^ double (not 1\ times, nor 1 yVo t.i™.es, 
but exactly double) the amount of hydrogen combined 
with six unit masses of carbon in ethylene. Similar 
observations apply to the oxides of carbon, and indeed 
to all cases where two elements combine in different 
proportions to form different compounds. In every 
case the following regularity is observed. If an element 
A combines with an element B in two or more pro- 
portions to form two or more compounds, and if in 
these compounds we consider a fixed mass of either of 
the elements, say A, then the masses of B combined in 
the several compounds with this fixed mass of A, are 
in general so related that the compounds richer in B 
contain of B masses expressible as whole multiples 
of the mass of B, contained in the compound 
poorest in B. This is Dalton's law of multiple pro- 

^ This exactness is never of course attained in practice, on account 
of unavoidable errors of observation, but it is more and more nearly 
realised as we perfect ova- analytic methods. Hence the assumption is 
warranted that the relations in question are in reality absolutely exact. 
The mathematical conception of a limit is here implicated. 

2 Some apology for this diffuse enunciation seems called for. In the 
majority of chemical text-books, the word multiple is never once intro- 
duced in the enunciation of the law of multiple proportions, its place 


What explanation can be adduced of these laws?^ 
Dalton answered, the atomic theory of matter. Admit, 
he said, that simple matter of every kind consists of 
little indivisible particles called atoms, that the atoms 
of one and the same kind of matter have always exactly 
the same weight and the same properties, but that the 
weight and other properties of the atoms differ from 
substance to substance ; that chemical combination 
consists in the coming together into intimate contact 
of definite numbers of simple atoms, to form definite 
compound atoms which in turn are all exactly similar 
for one and the same compound, bearing, so to speak, 
the impress of goods stamped by machinery; then, 
admitting all this, the fundamental laws of chemistry 

being taken by the vague, elastic, yet polarised term "simple ratio." 
In the statement nf the law given in the text the attempt has been 
made to remedy these defects, even at the expense of brevity. 

^ In addition to the two laws given in the text, many add a third — 
the law of reciprocal proportions, or the law of combining weights. 
As a matter of fact, the perception of the numerical relations embraced 
by this law did not antedate and pave the way for the atomic theory, 
but this theory established, certain numerical results necessarily fol- 
lowing from it were grouped together under one or other of the above 
titles, thus : — if AB and AC represent quantitatively two compounds, 
then any compound of B and C will be represented quantitatively by 
nBntC, where n and m are whole numbers, and A, B, C, the com- 
bining weights of the elements. Interpreted in terms of the atomic 
theory, this law may be regarded as stating that the atoms of a given 
element have a fixed and unalterable mass in all the compounds that 
element forms. Agl and AglO;) might each have fixed composi- 
tions without the ratio -^ being identical in the two cases as theory 

demands. Stas, in proving to an accuracy of 1 in W that the 

ratio -^5 is the same in both compounds, has placed the atomic theory 

on a very exceptional experimental basis. 


follow as necessary consequences.^ It is quite easy to 
see how the law of definite proportions follows ; let us 
examine in detail the sequence of the multiple pro- 
portion law. 

Suppose matter to be non-atomic, to be infinitely 
divisible and absolutely continuous. Let the symbol 

represent a definite mass (expressed numerically 

by 6) of carbon on this supposition ; and the symbol 
^ represent under the same conditions a mass of 
hydrogen, numerically expressed by 1. Then ethylene 

might be represented as ® 1|- Now, analysis in 

forms us that methane contains relatively more hydrogen 
than does ethylene. According to the above supposi- 
tion, the mass of hydrogen combined with 6 unit masses 
of carbon in methane might quite easily be li, 1^, li|-, 
or 2ijY, &c. times the mass of hydrogen combined with 
6 unit masses of carbon in ethylene ; for hydrogen is 
jelly-like and structureless, and we can imagine a 

1 Stallo divides the phenomena of chemical change into three classes. 
The first "embraces the persistence of weight and the combination in 
definite proportions ; the second, the changes of volume and the evolu- 
tion or involution of energy ; and the third the emergence of a wholly 
new complement of chemical properties." He asserts that the atomic 
hypothesis is in no sense an explanation of phenomena of the second and 
third classes, nor does it fully explain those of class i. in the sense of 
generalising them and reducing many facts to one. It accounts for 
them by simply iterating the observed fact in the form of an hypo- 
thesis. He admits, however, " the merits of the atomic hypothesis as 
a graphic or expository device — as an aid to the representative faculty 
in realising the phases of chemical or physical transformation," See 
Concepts of Modern Physics, chap. vii. 


quantity of it of any mass whatever. Given 


as representing ethylene, the composition 



a 'priori, be quite as probable for methane as would 

6 m 


But now let us take the atomic theory, and for the 
sake of present argument assume that ethylene con- 
sists of 1 atom of carbon weighing 6 units, and 1 atom 
of hydrogen weighing 1 unit. Then, since methane 
contains more hydrogen relatively than ethylene, it 
follows that per 1 atom of carbon methane must 

contain 2, 3, 4 n atoms of hydrogen ; 

for atoms are the indivisible units of chemistry. 
Since all atoms of the same simple substance have 
exactly the same weight, the law of multiple pro- 
portions necessarily follows ; the amount of hydro- 
gen per given amount of carbon must necessarily 
be in methane a whole multijale of its value in 

To sum up the whole matter ; the existence of a 
multiple law according to the non-atomic theory of 
matter is a possibility among an infinity of other 
equally plausible possibilities ; the odds against its 
existence are infinitely great. But of an atomic theory 
of matter, a multiple law is an absolutely necessary 
consequence. That Dalton clearly saw this consti- 
tutes, perhaps, his greatest claim on the memory of 


We must now follow Dalton in his attempt to find 
the weights ^ of the atoms of elementary bodies. He 
did not, of course, hope to determine the absolute 
weights of the atoms — a determination of which 
even the advanced chemistry of to-day is incapable. 
All he attempted to do was to find the relative weights 
of the atoms. He made the hydrogen atom his standard, 
and arbitrarily called its weight one ; all other atomic 
weights were stated in terms of this standard. Thus 
the statement — the atomic weight of oxygen is 16 — 
simply means that the atom of oxygen is sixteen times 
heavier than the atom of hydrogen, whose absolute 
weight expressed, say in a fraction of a milligram, is 

As an aid to the foundation of a system of atomic 
weights, Dalton framed a series of empirical rules. 
We cannot dissect out the train of reasoning which 
culminated in these rules. They are merely the ex- 
pression of Dalton's own preconceived notions — mere 
guesses, limited only by the condition that compound 
atoms are of simple rather than of complex structure, 
being as a rule made up of very small numbers of 
elementary atoms. Rule 1. If only one compound of 
two elements can be obtained, the compound must be 
assumed a binary '^ one, unless there be good cause for 

^ In some recent text-books, atomic mass replaces the term atomic 
weight. In view of the strict proportionality which exists between 
mass and weight, and in view of the hold the terms weighing and 
weight have in the speech of everyday life, this innovation seems to 
me unnecessary. 

-' A binary compound, according to Dalton, is one whose "com- 


some other conclusion. Rule 2. If two compounds of 
two elements exist, then one is a binary, and the other 
a ternary, compound. Rule 3. If three compounds of 
two elements exist, then one is a binary, and the 
other two are ternary, compounds. Rule 4. If four 
compounds of two elements are known we should 
expect two of them to be ternary, one to be binary, 
and the fourth to be quaternary. Other rules follow, 
dealing with the specific gravities of binary, ternary, 
&c. compounds ; but for these, and indeed for Dalton's 
work on the atomic theory as a whole, the reader is 
referred to Ostwald's Klassihev der exakten Wissen- 
schaften, No. 8, or to the Alemhic Club Reprints} 

To illustrate the application of these rules, we may 
take the case of the atomic weight of oxygen. To 
Dalton only, one compound of hydrogen and oxygen 
was known, viz., water. Hence by Rule 1 the com- 
pound atom of water consisted of one atom of hydrogen 
in combination with one atom of oxygen. Now it is 
found by actual experiments that about 8 grams of 
oxygen combine with 1 gram of hydrogen to form 
about 9 grams of water ; or, what is the same thing, 

8 • 1 

that milligrams of oxygen combine with -— -. mg. 

-j^Q23 O ./ o 10 

of hydrogen to form - mg. of water. Let us sup- 
pound atom" contains only two simple atoms. In tlie "compound 
atom " of a ternary body there are three atoms, and so on. 

^ These brochures are more generally attainable than the Memoirs of 
the Literary and Philosophical Society of Manchester, m wliich Dalton's 
papers originally appeared. 



pose, simply for tlie sake of clearness, that a hydrogen 

atom weighs -—^ mg.^ 

1 8 

-— lug. H combines with — ^ mg. 0. 

or 1 atom H „ „ ,, 

but, by Rule i., 1 atom H ,, „ 1 atom 0. 

Therefore 1 atom weighs --- mg. 

So if we agree to call the atomic weight of hydrogen 
one, the atomic weight of ox^^gen will equal eight. In 
a perfectly similar manner Daltou arrived at the result ; 
atomic weight of nitrogen = 4f. But 16 (= 8 x 2) 
and 14 (= 4f x 3) are at present regarded as the 
approximately correct values for the atomic weights of 
oxygen and nitrogen respectively. Why these num- 
bers are adopted in j)reference to Dalton's will not be 
apparent till we have treated of Avogadro's hypothesis. 
When we attempt to fix by Dalton's rules the atomic 
weight of such an element as carbon which combines 
with hydrogen, oxygen, &c., in more than one pro- 
portion, we find ourselves on the horns of a dilemma. 
According to Rule 2, either methane or ethylene is a 
binary body, but the rule does not indicate any means 
of assuring ourselves which is the binary body. If 
ethylene be assumed binary, methane will be ternary. 
Ethylene will be CH, methane CHg, and the atomic 
weight of carbon will be 6. If, however, methane be 

1 This very rough approximation is derived from data furnished by 
the kinetic theory of gases. 


assumed binary, ethylene will be ternary. Under this 
assumption, the formula for methane will be CH, that 
for ethylene C.,H, and the atomic weight of carbon 
will be 3. 

Which of these two values for carbon are we to 
select? There is nothing at all in Dalton's rules to 
guide us in such cases as these. Failing inspired arch- 
chemists, one is as justified from the premisses in 
maintaining that the atomic weight of carbon = o as 
another is in championing the value 6. 

This ambiguity in Dalton's rules led to great diffe- 
rences of opinion respecting the atomic weights of 
several of the elements, and ultimately the confusion 
became so great that many advocated the renunciation 
of the atomic theory altogether. The light which it 
indisputably shed on some points did not in the opinion 
of many compensate for the fundamental uncertainties 
with which it was hampered, and which it was power- 
less to resolve. It is, I think, worthy of note that 
the very cases which in the first instance suggested to 
Dalton the law of multiple proportions and the atomic 
theory were exactly those cases in which his elaborated 
system was found wanting, and which led to its un- 
popularity and temporary rejection. 

This indefiniteness, which trammelled the young 
atomic theory, was finally resolved by the knowledge 
accruing from a careful study of the physico-chemical 
properties of gases, to which we now turn. 

In 1805, Gay-Lussac and Humboldt, investigating the 
constancy of the amount of oxygen in the atmosphere, 


employed an analytic method first proposed by Volta. 
This method, which has become classical, consists in 
mixing the air with hydrogen in a eudiometer, ex- 
ploding the mixture by an electric spark, and then 
from the contraction which ensues calculating the 
amount of oxygen present. To apply this method, an 
accurate knowledge of the contraction which occurs 
when liquid water is formed from hydrogen and oxygen 
is obviously essential. After very careful experiments, 
Gay-Lussac and Humboldt found that one volume of 
oxygen combines with two volumes of hydrogen to form 
a drop of water, whose volume in comparison with the 
volumes of the gases exploded is in general negligible. 

2 vols. H + 1 vol. = water with practically negligible vol. 

Hence it follows that 3 volumes of the properly mixed 
gases contract to zero volume on explosion. In other 
words, suppose 2 cubic feet of hydrogen and 1 cubic 
foot of oxygen (measured at atmospheric pressure), 
placed in an air-tight vessel ^ and then exploded, the 
pressure in the vessel would sink from 15 lbs. per 
square inch to nearly zero value. I say nearly, for the 
water formed would vaporise and exert a small pres- 
sure (or as it is currently but unfittingly called, a 
tension) dependent as regards magnitude on the tempe- 

^ This experiment was actually performed by Cavendish, who was 
the first to determine the composition of water by volume (see Chap. 
II. p. 53). Cavendish introduced the gases, hydrogen and oxygen, 
mixed in the proper proportions into a vacuous globe, exploded the 
mixture, and found that the vacuum was re-established, so that several 
successive charges and explosions could be effected with one initial- 
exhaustion of the globe. 


rature. From all of this we conclude that the amount 
of oxygen in a mixed gas is equal in volume to one- 
third the contraction caused by sparking after an excess 
of hydrogen has been added. 

Supposing the water formed from 2 vols, hydrogen 
and 1 vol. oxygen is changed into the gaseous state 
by heating it above 100° C. so as to form super- 
heated steam; or supposing the whole experiment is 
conducted throughout at a high temperature, so that 
the water formed never condenses, what volume-relation 
would the water gas or steam bear to the volumes of 
hydrogen and oxygen which formed it ? In answer to 
this inquiry, Gay-Lussac and Humboldt found that the 
volume of steam formed is exactly equal to the volume 
of the hydrogen (or what is the same thing, to twice the 
volume of the oxygen) exploded. 

Here Gay-Lussac and Humboldt met with a quan- 
titative fact which astonished them by reason of the 
extreme simplicity of the quantities involved. Two 
cubic feet of hydrogen combine with exactly one cubic 
foot of oxygen, not with -9 or li, but according to Gay- 
Lussac and Humboldt with exactly 1 cubic foot, of 
oxygen to form, not 2 x^^y, but exactly 2 cubic feet of 
steam at the same temperature.^ 

' Although we assert in the text the exactness of the ratio 2:1, yet 
it seems well nigh impossible to prove this exactitude experimentally. 
Scott and E. W. Morley, employing all the refinements of modern 
methods, have repeated Gay-Lussac and Humboldt's experiment with 
the following result : — 

2-00245 vols, of hydrogen combine with 1 vol. of oxygen (Scott). 

2-0023 „ „ „ „ (Morley). 

However, in all the theoretical deductions which follow, any slight 


The question suggests itself, does a similar simple 
relationship in the reacting volumes manifest itself in 
other cases of gaseous combination ? It does. 

1 vol. of hydrogen combines with exactly 1 vol. of chlorine 
to give 2 vols, of hydrochloric acid gas. 

1 vol. of nitrogen combines with exactly .3 vols, of hydrogen 

to give 2 vols, of ammonia gas. 

2 vols, of nitrogen combines with exactly 1 vol. of oxygen 

to give 2 vols, of laughing gas. 
1 vol. of carbonic oxide combines with exactly 1 vol. of 
chlorine to give 1 vol. of phosgene gas. 

Several other instances might be adduced of Gay- 
Lussac's Law of Volumes, which states that in homo- 
geneous gaseous reactions (i.e., reactions in which all 
the factors and products of the change are gaseous) all 
the volumes involved are in such simjjle relationship 
that the ratios can in every case be expressed in terms 
of the first six digits.^ 

Just as the law of multiple proportions called forth 
an explanation, so it was not long before the why 
and wherefore of Gay-Lussac's law was under discus- 
sion. The outcome of this discussion was the conjee- 
deviations from simplicity which may possibly exist in the ratios of the 
combining volumes of gases will be disregarded, and the law of volumes 
will be accepted as strictly true. 

^ It should be noticed that when the factors of a homogeneous 
gaseous reaction are elements, the volume of the resulting compound 
is, with very few exceptions, always 2, provided the volume equation be 
throughout reduced to its simplest terms. The formation of phosphine 
from its elements furnishes an example of the exceptions referred to. 

P4 + 6H2 = 4PH3 

1 vol. + 6 vols. — 4 vols. 


tnre ^ accepted by several chemists, but first definitely 
enunciated by Berzelius, that equal volumes of gases 
contain equal numbers of atoms, and hence that the 
atomic weights of gases are proportional to their 
specific gravities.^ In view of the identical behaviour, 
qualitatively and quantitatively, of different gases when 
subjected to pressure and temperature changes, this 
conjecture seemed very plausible. The laws of Boyle 
and Charles seem absolutely to demand some such iden- 
tity in mechanism of the various gases as is implied in 
Berzelius' conjecture. But apart from this considera- 
tion, it cannot be denied that the human mind has a 
peculiar and inherent bias for the uncomplicated, and 
it is probable that the extreme simplicity of the explana- 
tion was one of the most potent factors in securing for 
it a general acceptance. 

Dalton and his school, however, absolutely refused to 
accept Berzelius' interpretation of the law of volumes, 
maintaining that the atomic weights could be deter- 
mined only from " the ponderable relation of elements 

' Berzelius' interpretation of the Law of Volumes seems scarcely to 
merit the title of an hypothesis, which " is any supposition we make in 
order to endeavour to deduce from it conclusions in accordance with 
facts which are known to be real." 

- Since the specitic gravities of oxygen and nitrogen, referred to 
hydrogen as standard, are respectively 16 and 14, it follows that these 
values were adopted b}' Berzelius for the relative atomic weights of 
these elements. It should be remarked that at first Berzelius regarded 
the data derived from the law of volumes as belonging to what he 
called " volume atoms " or "elementary volumes." These he conceived 
of as something fundamentally distinct from Dalton's atoms. After a 
time, however, he returned to the Daltonian conception of atoms and 
applied to these the results following from his hypothesis. See Wurtz, 
T]ic Atomic Theory, pp. 43-48. 


in combination," i.e., from purely analytic data. As an 
argument against this interpretation, those cases of 
gaseous combination which occur without change of 
total volume were adduced. 

1 vol. hydrogen combines with 1 vol. chlorine, forming 
2 vols, hj'drochloric acid gas. 

Assume that the volume of hydrogen considered is so 
small that it contains only one atom ; then, accepting 
Berzelius' conjecture, the equal volume of chlorine 
with which it combines will contain only one atom, and 
the double volume of hydrochloric acid gas formed 
will contain two comjDOund atoms. Now each of these 
compound atoms must contain at least one hydrogen 
atom and one chlorine atom. Therefore the two com- 
pound atoms together must contain at least two atoms 
of hydrogen and two atoms of chlorine. But we only 
started with one atom of hydrogen and one atom of 
chlorine. Therefore matter has been created — an 
absurd conclusion in view of all the proofs that exist 
of the conservation of matter.^ 

Berzelius was bound to admit the justness of this 
reductio ad ahsurdum, and in order to meet it emphasised 
the fact that his so-called hyjjothesis only extended to 
the elementary gases, and not to compound gases and 

^ A neat but indirect proof of the principle of the conservation of 
matter is furnished by the constancy of the length of the year. This 
depends on the masses of the earth and sun. If the masses of the 
earth were continually changing by reason of the chemical changes 
taking place, then some alteration in the length of the year would have 
been produced within historic time. 


vapours. In this form he continued to make a neces- 
sarily restricted use of it for the determination of atomic 
weights. Of Berzelius' work in this direction we shall 
have occasion to speak later. 

Just about this period in the history of the atomic 
theory (18] .3), an Italian chemist, Avogadro, pointed out 
that the whole of the differences between Dalton's and 
Berzelius' attitudes towards the law of volumes would 
disappear if chemistry would but admit into its philo- 
sophy a new order of particles of a higher grade of 
organisation than the atoms. These particles he called 
molecules, and postulated that all the molecules of the 
same substance are identically similar, and in general 
consist of an assemblage of atoms, even in the case of 
simple gases. Heretofore a radical distinction had 
existed between the constitution of a simple, and that 
of a compound, gas. A mass of oxygen was jjictured 
as an assemblage of atoms, each with perfect freedom, 
and completely independent of its neighbours. In a 
compound gas, such as hydrochloric acid, on the other 
hand, the particles enjoying this individuality and 
freed-om were not single atoms — else the gas had been 
a mere mixture of hydrogen and chlorine — but atom 
complexes. Each atom of hydrogen kept perpetual 
company with an atom of chlorine, the combination 
forming a discrete and independent particle of the 

Avogadro asserted that this distinction between the 
simple and compound gases was unwarranted. He 
regarded both hydrogen and chlorine as, in a sense, 


compounds ; the one was to him hydride of hydrogen, 
the other chloride of chlorine. The freely moving and 
independent particle of hydrogen gas was not a single 
atom, it was an atom complex. The only difference 
between a simple and a compound gas is that the atom 
complex of the former is made up of similar, that of 
the latter of dissimilar, atoms. Having premised so 
far, Avogadro then concluded that equal volumes of all 
gases, simple and compound, contain under similar 
conditions of temperature and pressure the same num- 
ber of molecules. This conclusion is generally known 
as Avogadro's "hypothesis."^ As will be readily 
noticed, it is nothing else than Gay-Lussac's conjecture 
with one word changed — molecules replaces atom. 

In 1814, Ampere independently came to precisely 
the same general conclusion with regard to the struc- 
ture of gases, simple and compound. 

It is easy to see that those instances of gaseous 
combination wherewith Dalton combated Berzelius' 
interpretation of the law of volumes involve no in- 
consistencies when interpreted in the light of Avogadro 

^ Avogadro's " hypothesis " is sometimes erroneously stated in the 
form : — All gaseous molecules under like conditions have the same size. 
What is really meant is that all molecules have the same sized spheres 
of action, which they occupy and dominate to the exclusion of other 
molecules. A compact square of fifty soldiers armed with rifles would, 
in a certain sense, dominate the same extent of country as twenty- 
five soldiers armed with the same rifles, although the size of the 
actual squares would be different in the two cases. It may here be 
stated that Avogadro's generalisation is strictly true only for perfect 
gases. The ratio of the number of molecules in equal volumes of 
oxygen and hydrogen at ordinary temperatures and pressures is about 
100,020 : 100,000. 


and Ampere's views. The volumetric relations of 
hydrochloric acid gas merely prove that the molecules 
of hydrogen and chlorine must contain at least two 
atoms each.i 

Yet the times were not ripe for this great generali- 
sation which to-day, under the title Avogadro's law, 
stands the very foundation and framework of theoretical 
chemistry. It attracted but little attention at the time 
of its birth, and soon fell into an oblivion from which 

^ The general introduction of these conceptions of the structure of 
elementary gases at a later period in the history of chemistry, threw a 
new light on the phenomena of substitution which for a time enjoyed 
a special prominence. In the formation ol a halogen derivative of a 
hydrocarbon, it had np to date been necessary to ascribe different 
roles to the admittedly perfectly similar atomic units of the halogen. 
For instance, in the formation of monochlor-niethane, it was held that 
an atom of chlorine first replaced an atom of hydrogen in the hydro- 
carbon — 

CH4 + C1 = CH3C1 f H, 

and then a second atom of chlorine combined with the liberated hydro- 
gen atom — 

H + C1 = HC1. 

In other words, substitution was regarded as a complex chemical change 
taking place in two stages, the chlorine atom in each stage playing a 
different chemical r6lc. But when it was admitted that the smallest 
portion of chlorine entering into chemical reaction is a molecule con- 
taining two atoms, then halogen substitution was seen to be a pure 
case of double decomposition, impossible of resolution into two con- 
secutive stages, and recalling in its main features exactly the substi- 
tution brought about by the action of compound bodies such as nitric 

The two reactions 

CH;;H -f Cl.Cl = CHsCl + HCl. 
CjHsH + OH.NO, = CyHgNOo -F HOH. 

were seen to be quite analogous. It was no longer necessary to ascribe 
difft-i-.iit rules to the smallest individual particles of the halogens. 


it was rescued some forty years afterwards by Gerhardt 
and Laurent. 

In the year 1818, Dulong and Petit, experimenting 
on the specific heats of the elements in a solid state, 
discovered a most striking numerical relation between 
these values and the atomic weights of the respective 
elements. The numerical value of the atomic weight 
of an element multiplied by the value of its specific 
heat gave, in general, a constant product equal to 
about 6"25. The limitation "in general" is advisedly 
introduced, because certain of the current atomic 
weights did not satisfy this relation. On the strength 
of the comparatively large number of atomic weights 
which did satisfy their law, Dulong and Petit pro- 
nounced inaccurate all those which did not, thus 
virtually asserting the universality of their law, and 
establishing it as a powerful instrument for atomic 
weight determinations. They recognised the arbitrari- 
ness of the methods of determining atomic weight 
then in vogue ; for these made the choice of one par- 
ticular value out of a series, bearing a simple multiisle 
relationship to each other, a matter of, we might 
almost say, individual taste. 

In a small annex to a certain kitchen in the city of 
Stockholm, Dulong and Petit's law was warmly wel- 
comed. In this kitchen (which has been referred to as 
one of the magnetic poles of the chemical world), assisted 
by his cook and equipped with culinary utensils rather 
than with what we now understand by apparatus, 
worked one whose name, Johann Jacob Berzelius 


(1779-1848), is one of the greatest on the honour rolls 
of science. From the very beginning of his scientific 
career, Berzelius interested himself chiefly in atomic 
weight determinations. To convert his analytic results 
into values for the atomic weights, he at first made use 
of (1) certain rules recalling in their arbitrariness those 
of Dalton, (2) the law of volumes already mentioned, 
and (3) his so-called oxygen law.i Afterwards he 
employed in addition to these (4) the law of Dulong 
and Petit, and (5) the generalisation of Mitscherlich, 
which has of late years proved itself the very reverse 
of general. 

At the outset, Mitscherlich believed that the correla- 
tion between crystalline form and composition was 
such, that a mere equality in number of the simple 
atoms in the compound atoms of two substances, 
necessitated an identity in the crystal forms, or an 
isomorphism of the two substances ; and vice versa, that 
isomorphism necessarily existed between substances 
whose compound atoms were built up by the same 
number of simple atoms. The discovery of poly- 
morphism (the crystallisation of one and the same 
substance in different forms), however, compelled the 

^ Berzelius regarded salts as dual compounds of acid oxide or 
negative constituent, and basic oxide or positive constituent. Sulphate 

of soda was written -vr q oq The oxygen law stated that in all the 

salts of a given acid the amount of oxygen in the negative constituent 
bore a constant ratio to the amount present in the positive con- 
stituent. This law had been previously recognised by the German 
chemist Richter, who, however, had expressed himself rather obscurely 
on the poiut. 


admission that atomic complexity alone was not the 
whole explanation of isomorphism, but that the arrange- 
ment of atoms must be taken into account. Further, 
the fact had to be admitted that in the majority of 
cases the forms of crystals of similarly constituted 
bodies are only approximately the same, not absolutely 
identical. Indeed, absolutely perfect geometric iso- 
morphism is only found in the cases of bodies crys- 
tallising in the cubic system. Hence Mitscherlich's 
generalisation in its final form was not the clear-cut 
and unequivocal statement that it was in its original 
enunciation. The final statement ran as follows : — If 
the compound atoms of two or more chemically analogoiis 
bodies be composed of the same number of simple atoms 
(no matter the nature of the latter), then the crystals 
of these bodies will have identical or nearly identical 
forms. ^ 

^ Recent research has adduced many exceptions to this elastic gene- 
i-alisation, both in its direct and" converse forms. The three dinitro- 
benzenes belong to the same chemical type, and have all the same 
atomic complexity ; yet they have so little analogy of form that it 
would be an obvious overstretching of the term to call them iso- 
morphous. The exceptions to the generalisation in its converse form 
are grouped together under the titles isogonous or homeomorphous 
bodies. Such bodies, while differing greatly in chemical behaviour 
and even in molecular complexity, are nevertheless isomorphous, e.g., 
PbClj and Sn(CH3)oCl2 are isomorphous, as are also KHSO4 and 
KAlSisOg. It is clear throughout that the term isomorphous, which 
was originally a definite and definable term, is now indefinite and 
undefinable. What degree of similarity in the geometrical forms of 
crystals is necessary in order that the crystals fall in the category, 
isomorphous, is a question which chemists are undecided about. They 
prefer to judge of isomorphism by a series of chemico-physical tests 
rather than by purely crystallographic considerations. Two substances, 
A and B, crystallise in the same system with nearly the same forms 



So marvellously did Berzelius balance probabilities, 
so carefully did he make use of analogy, so skilfully did 
he manipulate his roughly improvised apparatus, that 
his final table of atomic weights (1826), when reduced 
to the hydrogen standard,^ shows remarkable agree- 

and angles. Are they isomorphous '! If they show the same cleavages, 
similar thermal conductivities, similar etched figures, approximately 
equal specific volumes ; if a crystal of A grows regularly in a solution 
of B, or lice vcrsd ; if a crystal of A causes crystallisation in a super- 
saturated solution of B, or vice versa; and if mixed solutions of A and 
B give homogeneous mixed crystals, then the answer is most decidedly 
yes. It is not a sufficient criterion of isomorphism that one only of 
these conditions is satisfied, just as an element cannot in general be 
classified as a metal or a non-metal from the investicration of a single 
property. For a good account of isomorphism, regarded as a branch 
of morphotropy (the general study of the inter-relation of chemical 
composition and crystalline form apart from considerations of similarity 
in the latter), see Hutchinson's article, " Isomorphism," in Watts' 
Dictionary of Chemistry, vol. iii. ; also Mendele'eff, Principles of 
Chemistry, vol. ii. p. 7. 

^ Berzelius regarded oxygen as the most important chemical element 
— the pole of chemistry. He therefore adopted the oxygen atom as 
the basis of his atomic weight system, giving it the arbitrary value 100. 
Modern chemistry has rather favoured Dalton's choice of the hydrorren 
atom as standard atom with the arbitrary value 1. Quite recently, 
however, the question of making oxygen the standard element again, 
assigning it the arbitrary atomic weight 16, has been much discussed. 
There is much to be said in favour of the return. The values of a 
large majority of the atomic weights involve an accurate knowledge of 
the atomic weight of oxygen. Unfortunately the determination of the 
atomic weight of oxygen referred to H = 1 is an extremely difficult 
chemical task, and new results differing often in the first decimal place 
are continually demanding recognition. Every adoption of a new value 
necessitates the alteration of the atomic weights of all those elements 
whose oxy-conipounds have furnished the necessary analytical data. 
If O = 16 were universally adopted as the standard, the only atomic 
weight that need be affected by new data for the coniposition of water 
would be that of hydrogen ; and for all practical purposes the changes 
it would undergo might with safety be overlooked and the value \ 
steadily adhered to. A small change in the accepted value of the 


ments with the values for the atomic weights current 
to-day. To this statement we must, however, make 
three well-defined exceptions, viz., potassium, silver, 
and sodium. Lacking the data for the application of 
the law of specific heat in these three cases, values 
almost exactly twice too great were assigned to the 
atomic weights of these elements. 

I would emphasise the fact that Berzelius made use 
of no one universally applicable guide in constructing 
his system of atomic weights. He applied to the results 
of analysis sometimes one, sometimes another, of the 
five methods above given, and in cases of doubt he 
selected with something akin to inspiration. One is 
almost tempted to say that Berzelius was lucky. 

Despite the great renown of Berzelius as an analytical 

atomic weight of oxygen may involve quite a large change in the values 
of other atomic weights, or it may involve none at all. The following 
approximate values necessary for the determination of the atomic 
weight of barium by Struve's method are instructive. Struve deduced 
the atomic weight of barium from the ratio BaCl2 : BaS04 :: 100 : ] 12"1, 
assuming values for the atomic weights of CI, O, and S. 

(1) Molecular weight of KCl deduced from ] ^ 

reduction of KCIO3 .... 1 

(2) Atomic weight of Ag deduced from ratio 


(3) Molecular weight of AgCl from the reduc- 

tion of AgC IO3 . . • . 

(4) Atomic weight of CI (= mol. wt. AgCl - 

at. wt. Ag) ..... 

(5) Atomic weight of S from ratio Ag : Ag2S04 31 •! 

(6) Atomic weight of Ba .... 

An initial error in the atomic weight of oxygen of ^ per cent, is 
multiplied up into a percentage error of 2*2 in the atomic weight of 
barium as determined by Struve. 

= 16 

= 15-96 














cliemist of the highest rank, many refused to accept his 
estimates of the atomic weights, not only because they 
differed in many instances from those upheld by the 
school of Dalton, but also on account of the discovery of 
inaccuracies and inconsistencies inherent in the system 

Using Berzelius' value for the atomic weight of 
carbon, 12 '2, many anomalies had been noticed in the 
results of organic analysis. The atomic weight of this 
element was therefore redetermined by Dumas and 
others, with the result that the Berzelian value was 
found -2 too high. This discovery not only shook the 
confidence of some of Berzelius' disciples in their master, 
but was made by his opponents the occasion of heaping 
all manner of sarcasm and unjust criticism on the great 
Swedish chemist. 

But perhaps Dumas' work on the vapour densities 
of elements which are solid or liquid at ordinary tem- 
peratures (1827) did more to bring the Berzelian system 
of atomic weights into discredit than did the detection 
of a If per cent, error in the atomic weight of carbon. 
Berzelius had arrived at the values Hg = 200 and 
P = 31 for the atomic weights of these elements 
by a combination of some of the methods above 
indicated. But Dumas found that the vapour of 
mercury is only 100 times heavier than that of hydrogen 
under the same temperature and pressure conditions ; 
while the vapour of phosphorus is 62 times heavier 
than that of hydrogen. Therefore if, as Berzelius 

had maintained, equal volumes of gases contain equal 



numbers of atoms, then the atomic weights of mercury 
and phosphorus must be respectively 100 and 62. If, 
on the contrary, Berzelius' vahies were the true ones, 
then his interpretation of the law of volumes — an inter- 
pretation lying at the very foundations of his atomic 
weight system — must necessarily lack generality. The 
atomic weights of mercury and phosphorus being re- 
spectively 200 and 31, a given volume of mercury 
vapour can only contain half as many atoms as the 
same volume of hydrogen ; while a given volume of 
phosphorus must contain twice as many atoms as the 
same volume of hydrogen. 

The atomic theory now enters upon the most troub- 
lous period of its career. So many different values 
for the atomic weights of the elements were compet- 
ing with each other for general acceptance, and so 
vanishingly small did the chances of any universal 
agreement on the subject appear, that it was proposed 
to do away with the atomic theory and its attendant 
uncertainties altogether, and to return to' a system of 
constants (with suitable notation) for the elements, 
which constants, being simply the numerical expressions 
of ascertained facts, could involve no doubt and admit 
of no uncertainty. 

This new system, which was to bring peace and 
prosperity in its wake, was called the equivalent system, 
and was pioneered by Wollaston. According to Wollas- 
ton the symbol of an element was to represent that 
mass thereof which combines with unit mass of hydrogen 
— a pure number expressing the result of an experi- 


ment, notliincf more.^ The numerical value of this 
mass he called the equivalent number, or simply, the 
equivalent of the element. Just as those quantities 
of acids which neutralise, i.e., combine with, a fixed 
quantity of base are equivalent, so those quantities 
of the elements which combine with a fixed mass of 
hydrogen were also regarded as equivalent. 

Yet this new system, seemingly so simple and un- 
equivocal in its inception, soon had to encounter 
diflSculties as great as any that had ever beset the 
atomic theory. Only a few of the elements could be 
made to combine with hydrogen directly to form 
hydrides ; how then were the equivalents of the 
remaining elements to be determined ? One unit 
mass of hydrogen combines with 35| unit masses of 
chlorine, and chlorine can be made to combine with 
nearly all the elements that do not form hydrides. 
Here then seemed a way out of the difficulty; the 
equivalent of an element was taken to be that 
mass thereof which combines with unit mass of 
hydrogen, or 35| unit masses of chlorine.^ But 
unfortunately in cases where an element combines 

1 As a matter of fact, Wollaston's standard of equivalency was not 
unit mass of hydrogen, but ten unit masses of oxygen. This, however, 
does not in any way affect the line of argument in the text (see note 
1, p. 95). 

- It is to be observed that the equivalent of any element may be 
determined as well by investigating the mass of hydrogen which a 
given mass of the element replaces, as by finding the mass of hydrogen 
with which a given mass of the element conibines. For every combi- 
nation of an element with chlorine, bromine, &c., may be regarded as 
a substitution product of hydrochloric acid, hydrobromic acid, &c. 


with both chlorine and hydrogen, the equivalent de- 
duced from the chloride does not always coincide with 
that deduced from the hydride. Again some elements, 
notably carbon, form numerous compounds with hydro- 
gen (methane, ethane, ethylene, &c., in the case of 
carbon), and each of these compounds would give a 
different value to the equivalent for carbon. Who was 
to decide which particular compound was to be selected 
for fixing the value in question ? That an element 
should be possessed of several equivalents seemed a 
pure contradiction in terms. 

Further complications arose when Gmelin and Gay- 
Lussac attempted to make equivalent the formulae of 
all compound bodies, including the most important 
class of salts.^ As long as the terms equivalent, or 
equivalent weight, are restricted to acids and bases 
among com2)ound bodies, they have perfectly clear and 
definite meanings, and are still employed in this con- 
nection in modern volumetric analysis. But it is hard 
to appreciate the application of the terms to salts. 
However, this application was made in different ways 
by different chemists, with the result that instead of 
applying the equivalents of the elements deduced from 
hydrides, chlorides, &c., to transform the results of 
analysis of compounds into formulge for these com- 

^ Here the idea of equivalency is somewhat changed. "AgO.SOs, 
and NaO, SO3, are equivalent, not because they have equal powers of 
displacement or combination with regard to any criterion, but because 
they are the results of the union of bodies in such proportions that the 
equal powers of combination of the constituent parts were satisfied in 
the act of combining." 


pouDcls, the problem was often reversed, and the 
equivalents of the elements were deduced from pre- 
sumed equivalences between salts. ^ The values obtained 
in this way did not in general agree with those directly 
obtained from analysis of hydrides, chlorides, &c. Thus 
both the values 4f and 14 for the equivalent of nitrogen 
found supporters ; while the equivalent of phosphorus 
was either lOJ, 15-5, or 31. 

It is almost impossible for us now to appreciate 
fully the reasoning of the chemists of this period. The 
confusion of ideas which prevailed, ^ the gratuitous 

^ See Wurtz, The A tomic Theory, p. 71, et seq. 

" Here it may be well to distinguish between the three terms com- 
bining weight, equivalent, and atomic weight. The idea of combining 
weights was associated with, and early recognised as a necessary 
consequence of, the atomic theory (see note 1, p. 77). The atomic 
weights were either numerically equal to, or whole multiples of, certain 
characteristic numbers called combining weights that could be assigned 
to the elements from analyses of their compounds, quite independently 
of any assumptions or suppositions. Hence it would seem that the terras 
combining weight and equivalent mean essentially the same thing ; 
they do. The only difference between them is a chronological one. 
The equivalent notation came after the atomic theory, and was in- 
tended to be independent of it. It was an attempt to replace what up 
to date had proved itself from a chemical standpoint an unsatisfactory 
theory. Combining weights had their names changed to equivalents 
when the atomic theory had been weighed and found wanting. The 
reason for this change in nomenclature is not far to seek. It is an 
epitomised history. The atomic weights of the Daltonian school were 
in many instances numerically efiual to the combining weights assigned 
to the elements, and the two terms, though radically distinct, thus came 
to be used more or less synonymously. Wollaston, in proposing the 
name equivalent weights for the constants of his new system, was 
simply desirous of avoiding a term which had become, quite wrongly, 
more or less identified with a theory. The term equivalent was to 
connote fact, and fact alone. 

The difference between the terms atomic weight on the one hand, 


assumptions which flourished, and the reckless use of 

the analogic method, combine to render its history one 

of the most unsatisfactory and bewildering pieces of 

modern scientific literature. Owing to the numerical 

coincidences in many cases of the atomic weights and 

the equivalents of the elements, the two terms, though 

fundamentally so distinct in their connotations, came 

to be used indifferently and synonymously.^ 

It was Gerhardt and Laurent who, resuscitating the 
long-eclipsed hypothesis of Avogadro, led the way out 
of this confusion worse confounded. The equivalent 
system presented to the mind of Gerhardt great in- 
consistencies, which, in his opinion, could only be 

and equivalent or combining weight on the other, is more fundamental 
than the purely chronological one distinguishing equivalent from com- 
bining weight. The term atomic weight implies a theory of the 
structure of matter, the other two terms do not. The atomic weight 
of chlorine is 35'5 ; its equivalent or combining weight is also 35 "5. 
The former statement calls up the following mental picture. Chlorine 
gas is made up of a number of indivisible ultimate particles called 
atoms equal among themselves, and each 35^ times as heavy as the 
similar ultimate particles of which a mass of hydrogen consists. 
Whereas the latter statement simply implies that a mass of chlorine 
weighs 355 times as much as the mass of hydrogen with which it 
chemically combines. Though all idea of an equivalent notation is 
now abandoned, the terms equivalent and combining weight are still 
used, but now synonymously to denote the smallest mass of an element 
that combines with unit mass of hydrogen, or 35i vmit masses of 
chlorine, or with (ajDproximately) 8 unit masses of oxygen. Indeed 
it will be shown further on that the equivalent, as thus defined, really 
determines the final value adopted for the atomic weight of an element. 
^ Even as late as the year 1834 we find a committee of the British 
Association for the Advancement of Science passing the following reso- 
lution : " We are of opinion that it would save much confusion if 
every chemist would always state explicitly the exact quantities which 
he intends to represent by his symbols." 


removed by a partial return to the Berzelian system 
of atomic weights. The inconsistencies that especially 
appealed to Gerhardt were something of this nature. 
The equivalents of carbonic anhydride and water being 
represented as CO.2 and HO respectively (0 = 6, = 8), 
Gerhardt noticed that when these substances were pro- 
duced in reactions involving organic bodies, they always 
appeared in such relative quantities that the accepted 
equivalents of the organic bodies could never be repre- 
sented as giving rise to a single equivalent, but always 
to 2, 4, or more equivalents of the oxides of carbon 
and hydrogen. 

Thus the interaction of acetic acid and sodium car- 
bonate was represented as follows — 

CgHgOs + 2 NaCOg - CsHgOsNa^ + 2 COg + 2 HO. 

It seemed incongruous and unnatural that organic 
bodies should be so differently constituted from in- 
organic ones as to be incapable of furnishing single 
equivalents of water and carbonic anhydride when 
undergoing chemical transformations. Gerhardt there- 
fore proposed a return to the Berzelian values C = 12, 
= 16, S = 32. Adopting these values, the difference 
noted between organic and inorganic siibstances dis- 
appears. The formula) for the equivalents of water, 
sodium carbonate, and acetic acid become now HgO, 
Na^COg, and C^H^O^ respectively. The formula for 
the equivalent of carbonic anhydride still remains CO.,, 
the equivalent weight being, however, doubled. The 


equation representing the interaction between acetic 
acid and sodium carbonate now takes the form — 

C^HgO^ + Na^COg = CJl(,^ + CO2 + H^O 

involving only single equivalents of carbonic anhydride 
and water. 

But there still remained in Gerhardt's opinion a 
want of uniformity in the equivalent notation. He 
noticed that the current formulse representing the 
equivalent weights of compounds were not strictly 
comparable, in that quantities of bodies correspond- 
ing to their formulse expressed in grams/ say, did not 
occupy the same volume when converted into the 
gaseous state under similar conditions. Thus, CO,, 
C^HjgOg, and C^HgO,^ were the accepted formula for 
the equivalents of carbonic anhydride, alcohol, and 
acetic acid respectively. 

Volume in gaseous state (re- 
duced to 0° and 700 mm.) of 
equivalent weight expressed 
in grams. 

22-4 litres 
44-8 „ 
44-8 „ 

Now Gerhardt proposed to make such alterations as 
were necessary to reduce all formula to a common gaso- 

^ Of course the interpretation of formulaj in grams is quite arbitrary, 
but so long as we are ignorant of the absolute weight of the hydrogen 
atom we cannot fix the absolute weights of compound atoms. What 
we practically do is to make the conveniently simple and concrete 
supposition (which we know to be far from true) that the hydrogen 
atom weighs 1 gram, and the compound atoms of carbonic anhydride, 
alcohol, and ether, 44 grams, 92 grams, and 120 grams respectively. 

Equivalent Weight 

C02 . . 

. • 44 






metric standard. Those masses of substances were to 
be equivalent which occupy the same volume in the 
gaseous state, and the formulee representing the com- 
positions of these masses were to be the equivalent 
formulfe. It is evident that this reform of Gerhardt's 
is nothing else than a return to Avogadro's "hypo- 
thesis." Laurent clearly recognised this, and impressed 
on Gerhardt the advisability of replacing the term 
equivalent by molecule when it has reference to com- 
pounds ; and by molecule or atom, as the case may be 
when it is used in connection with elements. Hence- 
forth Laurent's nomenclature will be observed. 

Althouofh Gerhardt returned to the Berzelian atomic 
weights, yet it is interesting to remark that considera- 
tions, not of an atomic structure of matter, but of an 
equivalence, j)hysical rather than chemical in its nature, 
lay at the foundation of his reform, which ultimately 
resulted in the complete abandonment of the equivalent 
system so called. 

The question as to which formula he was to alter 
next presented itself to Gerhardt. Was he to double 
the formula of carbonic anhydride so as to make the 
smallest particle, conserving all the properties of the 
substance in mass, occuj^y the same volume as did 
the accepted molecule of alcohol. Or was he to halve 
the formula of alcohol so as to make its molecule 
occupy the same volume as the accepted molecule of 
carbonic anhydride ? To settle this question he had to 
determine what volume a standard molecule, such as 
that of hydrogen, occupies. From the volumetric com- 


position of hydrocbloric acid gas, it follows that the 
molecules of hydrogen and chlorine must each contain 
an even number of atoms ; two at the least. That the 
hydrogen molecule does not contain more than two 
atoms is proved by the fact that hydrochloric acid is a 
monobasic acid, and only under most exceptional con- 
ditions forms sodium and potassium salts containing 

Hence the molecular weight of hydrogen is 2, and, 
availing ourselves of the convenient supposition for 
theoretical purposes of note 1, p. 104, we may provision- 
ally say that it weighs 2 grams. But it is a well- 
established constant that one litre of hydrogen under 
standard temperature and pressure weighs -0896 ± 
o-rams. Therefore 2 grams of hydrogen will under 
these conditions occupy 22"4 ± litres. 

Hence it follows that carbonic acid has the right 
formula, and that the formulse of alcohol, acetic acid, 
and organic bodies generally must be halved.^ 

^ Suppose for an instant that the molecule of hydrogen is tetratomic. 
Then the formula of hydrochloric acid would be HoCla-, and it would 
necessarily be either a dibasic acid forming two sodium salts or a mono- 
basic acid forming under all conditions salts of the type M'HCl-r, 
where M is a monovalent atom or radicle. 

We have no good proof that the molecule of chlorine is not of higher 
atomicity than 2. However, chlorine is chemically very analogous to 
iodine, and it seems almost certain, from specific gravity determinations 
carried out on the vapour of this body through a wide temperature 
range, that its molecule does not contain more than 2 atoms. 

- The doubled formulae of organic bodies generally was due (1) to 
the fact that these formulae were in many cases derived from analyses 
of silver derivatives, and Berzelius' value for the atomic weight of 
silver was twice too great ; (2) to the fact that certain views (embraced 
under the title dualism) held at this period regarding the constitution 


Gerhardt's proposed reform did not, however, meet 
with general acceptance till after the brilliant work of 
Williamson on the ethers. This research incontestably 
showed by purely chemical reasoning the necessity for 
halving the formula of alcohol in accordance with 
Gerhardt's views, i.e., in accordance with the hypo- 
thesis of Avogadro. 

Starting with ethyl alcohol, Williamson hoped to pre- 
pare therefrom an alcohol of higher molecular weight. 
To this end he first treated ethyl alcohol with potassium 
and then with ethyl iodide. Contrary to expectation, 
the i^roduct was not an alcohol at all, but ordinary 
ether C^H^^O. This is inconsistent with the formula 
C^Hj^O., for ethyl alcohol ; for if the latter body contains 
per molecule twice as much oxygen as ether, then the 
product of the above reactions ought to have contained 
twice as much oxygen as ether, because there has 
simply been replacement of H by CgHg. The only way 
out of this difficulty appeared to be the representation of 
alcohol by the halved formula CoHgO. 

Alcohol. Ether. 

C2H5 ) Q C2H5 ( ^ 

hT^ C,H, i ^ 

of bodies and the mechanism of chemical changes demanded the double 
formulae for their expression. For details, see Meyer, History of 

It follows that Gerhardt's halving of the molecular weights of acetic 
acid, alcohol, &c., necessitated the halving of the Berzelian values for 
the atomic weights of silver and the alkali metals. Unfortunately 
Gerhardt carried his views to an extreme, and, without good warrant, 
halved the atomic weights of twenty-three other elements, an error 
whicli was afterwards pointed out and rectified by Cannizzaro, who 
applied to the cases in question Dulong and Petit's law of specific heat. 


True, a representation of this special formation of 
ether could be given in terms of the doubled formula, 
thus — 

But according to this mode of representation, a 
mixture of methyl and ethyl ethers ought to result 
if methyl iodide were used instead of ethyl iodide. 

C4H10O { ^ ^^-^^j^ ^ (.^jj^^Q _^ ^^jj^^3 ^ 2 j^j 

-'^2 ■' (ethyl ether) (methyl ether) 

As a matter of fact, however, a single ether — a so- 
called mixed ether — and not a mixture of two ethers 
is the result ; and this can only be adequately repre- 
sented in terms of the formula CgHgO for alcohol. 

(ethyl methyl ether) 

Accordingly the molecular weight of alcohol was 
halved, and thereupon the Gerhardt-Avogadro hypo- 
thesis began to grow in general favour, and to acquire 
that recognition which to-day classes it as the most 
important instrument for the determination of atomic 

Before demonstrating the use of the Gerhardt- 
Avogadro generalisation in the determination of atomic 
weights, we must first throw it into a more convenient 
equational form. 




1 gram 
n molecules 

10 grams 
n molecules 

w grams 
11 molecules 

Let H represent a volume of hydrogen weighing 1 
gram. Let X and Y represent equal volumes of other 
gases 0: and y, weighing respectively %v and w' grams. 
Let there be n molecules of hydrogen present in the 
volume H ; then, assuming the truth of Avogadro's 
generalisation, there will be n molecules of x in the 
equal volume X and n oi y in the equal volume Y. 

Now the specific gravity ^ of x (referred to hydrogen 
as standard) is obviously w. 

And the specific gravity of y is w'. 

Further, the weight of one molecule of x must 

be — grams, and the weight of one molecule of y 

must be 


Hence — 

Molecular weight of x 
Molecular weight of y 



w _ Specific gravity of x. 
w' Specific gravity of y. 

In other words, Avogadro's generalisation may be re- 

^ In chemistry, the term "vapour-density" is generally used when 
" specific gravity of vapour " is really meant. Density is simply mass 
per unit volume ; it is of two dimensions. Specific gravity is the ratio 
of thu density of a body to that of some standard substance. The 
number expressing its value for any given substance is a pure number 
and has therefore no dimensions. 


stated in the form : the molecular weights of gases 
vary directly as their specific gravities.^ 

Since x and y are any two gases whatever, let y 
represent hydrogen. 
Molecular weight of a; _ Specific gravity of x. 
Molecular weight of hydrogen Specific gravity of hydrogen. 

Molecular weight of a; _ Specific gravity of x. 

2 ~ i 

or, molecular weight oi x = 2 x specific gravity of x. 

If, as is frequently the case, air be taken as the stan- 
dard of specific gravity, the above equation becomes — 

Molecular weight of « = 2 x 14-44 x specific gravity of a;, 

= 28"88 X specific gravity of x, 

air being, bulk for bulk, approximately 14*44 times 
heavier than hydrogen. 

Having now thrown Avogadro's generalisation into a 
numerical and equational form, we proceed to apply it 

^ Avogadro's law admits of still another mode of expression. The 
gaseous laws of Boyle and Charles are succinctly summed up in the 

pv = RT. 

Where p is the pressure, v the volume, and T the absolute temperature 
of a given mass of any gas, R is a constant depending (1) on the mass 
of the gas taken, and (2) on the nature of the gas. However, if we 
agree to apply the equation in all cases to masses of gases equal to 
their Avogadrean molecular weights interpreted in grams, then R no 
longer varies from gas to gas, but has the constant approximate value, 
84,700 (the pressure being expressed in gravitation units— grams per 
square centimetre). 



to the determination of an atomic weight, say, to the 
determination of the atomic weight of oxygen. 






Carbon monoxide 

42-86 C : 5714 



12 C : 16 

Carbon dioxide 

27-27 C : 72-730 



12 C : 32 

Osmic oxide 

74-93 Os: 25-07 



191-3 Os : 64 

Water . . • . 

11-11 H: 88-89 



2 H : 16 

Arsenious anhydride 

75. 78 As -.24-22 



300-4 As : 96 

Nitric oxide 

46-07 N : 53-33 



14 N -. 16 

Sulphuric anhydride 

40-00 Z : 60-00 



32 S : 48 






Having selected several — the larger the number the 
better — gaseous or gasifiable compounds of oxygen 
(column i.), whose percentage compositions (column ii.) 
are known to a fair degree of accuracy, we find their 
approximate specific gravities in the gaseous state ^ 
(column iii.). From these values we deduce the approxi- 
mate molecular weights ^ (column iv.) by means of one 

^ For practical details see Muir and Carnegie, Practical Chemistry, 
p. 121. 

- The definitions of molecular weight given in many of the text- 
books are exceedingly vague, e.g. : — 

"The moleciilar weights are the weights of two volumes, for mole- 
cules occupy two volumes if an atom of hydrogen occupies one." 

"The molecular weight of a gaseous element or compound is a 
number which tells the weight of two volumes of the gas, that is, the 
weight of that volume of the gas which is equal to the volume occupied 
by two parts by weight of hydrogen." 

In the following definition, the attempt is made to avoid the 
indefinite terms " volumes " and " parts by weight." 

The molecular weight of any substance is that weight thereof 
(expressed in terms of any unit whatever) which in the gaseous state 
occupies the same volume as do two unit weights of hydrogen, the 
same conditions of temperature and pressure and the same weight unit 
being observed in both cases. 


or the other of the equations just developed. Then 
we re-state the percentage compositions in such a way 
as to give the molecular compositions (column v.). 
The ratio 12 : 16 (column v.) is just the same thing 
as the ratio 42-86 : 57-14 (column ii.), but 12 + 16 = 
28 the molecular weight of carbon monoxide. And so 
on for all the other bodies mentioned. 

Now these molecular magnitudes have been deduced 
from equations which are based on the supposition that 
the smallest mass of hydrogen ever found in any 
molecule (■i.e., the atom of hydrogen), is numerically 
represented by unity ; and a glance at column v. con- 
vinces us that the smallest mass of oxygen found in 
the molecule of any compound considered is, in terms 
of the same mass unit, represented numerically and 
approximately by 16. But the least amount of oxygen 
that can by theory exist in a molecule is an atom. 
Therefore the approximate atomic weight of oxygen is 
16.^ The method of procedure in the case of any other 
element is exactly similar. 

It still remains to show how the approximate atomic 
weight assists us to a knowledge of the true atomic 
weight, which now follows upon a very accurate deter- 
mination of the equivalent of the element, i.e., the 

1 We cannot positively and finally assert that the atomic weight of 
oxygen is 16. We can only say that the probability of the approximate 
value = 16 is almost infinitely great. A new substance might be 
discovered whose molecule contained only 8+. unit masses of oxygen 
(H atom = 1 unit mass) ; and there are chemists who, desirous of 
emphasising this vanishing possibility, speak of the maximum atomic 
weight of oxygen being approximately equal to 16. 


smallest mass of the element which combines with unit 
mass of hydrogen, or with that mass of oxygen which 
itself combines with unit mass of hydrogen. 

In the case of oxygen the equivalent is not yet 
definitely agreed upon (see note 1, p. 95). As a 
probable result from all the recent elaborate deter- 
minations of this most important constant, Ostwald 
{Lehrbuch der Allgemeinen Chemie, p. 48) gives the 
value 7'974 [H = 1]. Suppose W,j grams of hydrogen 
combine with W^ grams of an element X, atomic 
weight Z, to form a hydride whose molecular formula 


is H™X „ Then — - is the equivalent of the element 

W„ ^ 

X, and the ratio 

Z X n _ "W3. 


or Z = equivalent number x 


necessarily holds. In other words, the atomic weight 
of any element is numerically equal to its equivalent 
number multiplied by a fraction involving, as a rule, 
only the lower digits. In general, ??i is a whole 
multiple of n, so that the value of the atomic weight 
becomes a whole multiple of the equivalent number, 

Z = r X equivalent number, 

where r = 1, 2, 3, &c. 



In the case of oxygen, then, it follows that the 
atomic weight may be either 

or 15-948 = (7-974 x 2) 
or 23-922 = (7-974 x 3) &c. 

The approximate value 16, already arrived at by 
the application of Avogadro's generalisation, enables 
us to select without any hesitation from these possi- 
bilities the value 15-948 as the interim atomic weight 
of oxygen. 

Until Kaoult's recent work, the constancy in the 
volumes occupied by gaseous molecules (Avogadro's 
generalisation) was the only known example of a 
colligative property.^ Eaoult established the fact that 

^ Following Ostwald, we may divide all chemico-physical properties 
into three classes ; additive, constitutive, and colligative. Weight is 
the one and only true example of an additive property, for the weight 
of a compound is exactly equal to the weights of the elements which 
have reacted to form the compound. The majority of chemico-physical 
properties which have been quantitatively investigated, belong to the 
class of constitutive properties. Let A B D and ABC represent two 
compounds of distinct types, and X', X" the respective values for 
these bodies of some constitutive property, such as molecular volume 

/ ^ mo lecular weight y ^^^^ ^^ ^^ ^ ^^^ ^ represent the atomic volumes 

\ specific gravity / 

/_ atomic weight \ ^^ ^^ -g^ ^ ^^^^ p^ respectively, in the free state. 

\ specific gravity/ 

Then X' and X" are not necessarily equal to a + b + d and a + b + c, 

respectively ; for A B and D in compounds of the type A B D may 

have volumes a' b' and d', while in compounds of the type ABC, 

A and B may have still other values a" and b". Hence 

X' =«' +6' +d' 
X" = a" + b" + c". 

It will be seen, however, that constitutive properties involve an additive 


dilute solutions of indifferent bodies also exhibit well- 
marked colligative properties. 

A given quantity of solvent has its freezing point, or, 
if volatile, its vapour pressure for a given temperature, 
lowered a constant amount in each case, by the solution 
therein of different substances, in quantities propor- 
tional to their molecular weight. Just as the colligative 
property expressed in Avogadro's generalisation gave 
rise to a method for molecular weight determination 
(and thence for atomic weight valuation), so Eaoult's 
results have in the hands of Beckman and others led to 
new practical methods of great utility for the determina- 
tion of molecular weights. These new methods are all 
the more valuable in that they can be applied to bodies 
which cannot be conveniently gasified, or cannot be 
gasified without decomposition, i.e., to bodies which, 
owing either to refractoriness or instability, fall outside 
the pale of Avogadro's generalisation. 

Since Van't Hoff showed that Eaoult's empirical laws 
can be derived by thermodynamical reasoning one from 
the other, and both from a certain theory of solution 
suggested by the phenomena of osmotic pressure, they 
have been very widely and generally applied to the 
determinations of molecular weights in cases unsuited 
to the gaseous specific gravity method. 

element ; and indeed, as soon as we know the values of any property 
peculiar to the atoms in a given class of compounds, the evaluation of 
constitutive properties for bodies of that class is a matter of pure addi- 
tion. Avogadro's generalisation is the expression of a colligative pro- 
perty. No matter what the composition or complexity of a gaseous 
molecule may be, it will occupy under given conditions a given deter- 
mined space. 


Of the two methods due to Raonlt, that founded on 
the lowering of freezing point seems the most practical 
and popular ; it has therefore received a special name, 
being known as the cryoscopic method. For the details 
of the practice and theory of these methods the reader 
is referred to Ostwald's Solutions, translated from the 
Lehrhiich der Allgemeinen Chemie. 

It cannot be too strongly emphasised that chemists, 
in applying to bodies in the solid and liquid states the 
constants determined for the molecules of these bodies 
in the gaseous state, do not thereby intentionally commit 
themselves to any theory of the molecular structure of 
solids and liquids. Chemical changes find adequate 
interpretation in terms of the formula derived from a 
study of gases ; indeed, it seems as if the complex mole- 
cules of solids and liquids, under the necessary condi- 
tions for chemical change, and prior to such change, 
break down into simpler molecules, comparable, if not 
identical in magnitude, with the gaseous molecules.^ 
In other words, it happens that the gaseous molecule 
remains the chemically reacting unit in the solid or 
liquid state, although the physical molecules (i.e., the 
smallest masses of solids and liquids which exhibit all 
the properties, physical and chemical, of the substances 

^ Seeing that the unit of chemical activity of a solid or liquid is not 
necessarily the physico-chemical molecule of that substance, but may be 
only a dissociation product thereof, comparable in magnitude with the 
true gaseous molecule, there are those who advocate the restriction 
of the terms molecule and molecular weight to purely gaseous pheno- 
mena, using the non-committal terms, reacting unit and reacting 
weight, in describing the interactions of solids and liquids. 


peculiar to their solid or liquid states), are almost 
certainly polymers of the gaseous molecules. 

If MN be the formula of the gaseous molecule, then 
(M^N^) and (Mj^N^,) represent the physical molecules of 
the same substance in the liquid and solid states re- 
spectively ; X and y being whole numbers, and y in all 
probability greater than x. 

It may be that the time is coming when we shall ex- 
press more in our equations than we do at present, this 
increased information involving the true molecular 
magnitudes of the solids and liquids (or dissolved 
substances) interacting, i.e., the absolute values of x 
and y. 

That this polymerisation, or condensation of the 
simpler into more complex molecules, does often take 
place as a substance passes from the gaseous into the 
liquid state is certain, if we are justified in the universal 
application to vapours of Avogadro's generalisation. 
With many substances it makes itself evident even 
before the liquid state is reached. At high tempera- 
tures and low pressures gaseous nitric peroxide has 
the triatomic molecule NO2 ; at lower temperatures 
and higher pressures these simpler molecules combine 
in pairs to form hexatomic molecules N2O4. Again, 
acetic acid vapour at high temperatures is made up of 
molecules CgH^Og, while at temperatures near its con- 
densing point the molecules have the niore complex 
formula C^HgO^. Indeed in many cases the specific 
gravities of the vapours of substances gradually increase 
as the temperature of the boiling-point is approached, 


indicating a gradual increase in complexity of the 
molecules. 1 

Now the gaseous and liquid states are really continu- 
ous, despite the apparent discontinuity which appears 
in the majority of cases under ordinary conditions of 
temperature and pressure. Hence we are led to the 
conclusion that the molecular condensation which ap- 
pears in some cases as the liquid state is approached 
(but in other cases is so delayed as not to manifest 
itself until the upper limiting temperature of the liquid 
state has been actually passed) will continue to take 
place in increasing degree as the temperature is lowered 
after the liquid state is reached. 

That this conclusion is just has been verified in 

^ The variability in the values of specific gravity determinations 
of vapours at different temperatures is well manifested in the case of 
the chlorides of aluminium and iron, and in this connection has caused 
much discussion. Grtinewald and Meyer hold that the specific gravity 
of ferric chloride does not become approximately constant for any con- 
siderable temperature interval until a temperature of over 700° has 
been reached, when the vapour consists of molecules having the composi- 
tion FeClg. On the other hand, Nilson and Pettersson maintain that the 
specific gravity of the vapour is constant for quite a large temperature 
interval, with 321° as its lower limit. Their experiments led to the 
molecular formula FeoClf,. Again, while Friedel and Crafts upheld the 
formula Al.;Cl(j for aluminic chloride, Nilson and Pettersson are led by 
their experiments to support the formula AICI3. It seems necessaiy 
to admit that in both cases molecules of the types MoCle and MCI3 
exist ; an admission which surrounds the expression "molecular weight 
of a gas " with indefiniteness. For all purely equational purposes it 
matters little which formula we use; but the true molecular formula, 
if indeed we can speak of a true molecular formula in these cases, is a 
point of great moment regarded from the standpoint of the valency 
theory (see Chapter VI.). Obviously the whole discussion turns on the 
difficulty of proving the existence and nature of the decompositions 
and dissociations taking place in a gas at high temperatures. 


several cases by the application of Raoult's cryoscopic 
method of molecular weight determination.^ Yet it must 
be remembered that the cryoscopic method can only be 
applied to fairly dilute solutions, and it is almost cer- 
tain that in such solutions the molecule of a dissolved 
solid or liquid .is smaller than it would be in the homo- 
geneous solid or liquid state. The mere act of solution 
often dissociates the molecules of the solid or liquid, 
to such an extent that the dissociated molecules are of 
the same magnitude as the gaseous molecules ; some- 
times, however, the dissociation does not proceed so far, 
the extent of the dissociation being dependent on the 
nature of the indifferent solvent used. Acetic acid, 
used as a solvent, seems to have a great dissociating 
tendency ; hydrocarbon solvents, on the other hand, 
manifest this property in a much less pronounced 
degree.^ In short the cryoscopic method can only 

^ Measurements of other physical quantities also point to the exist- 
ence of complex liquid molecules. Eot\ 6s finds it impossible to explain 
certain observations of his on surface tension, unless it be admitted 
that molecules of liquids are from case to case more complex in vary- 
inw decree than the molecules of the same substances in the sraseous 
state. Recently Ilamsay and Shields have come to similar general 
conclusions. See Chemical Society's Journal, Ixiii. p. 1089. 

- Because certain liquids {e.g., acetic ether) possess in all solvents the 
same molecular weight as they do in the gaseous state, it has been 
suggested that the gaseous molecules of such bodies do not polymerise 
vrhen liquefaction takes place. This seems quite a misleading sug- 
gestion. It is not probable that the dissociation tendency is a function 
only of the solvent ; the greater or less stability of the molecular 
complex of the dissolved substance itself must also be a factor. And 
surely it is not improbable that in some bodies the molecular com- 
plexes peculiar to the liquid state may be held together so loosely that 
they break down even under the influence of comparatively inert 
hydrocarbon solvents. 


furnish us with a minimum value for the molecular 
weight of a solid or liquid body. 

Of the true molecular weight of solids nothing is 
known. It is supposed that the polymerisation of the 
molecules in the solid state is o^reater than it is in the 
liquid state — that the molecule of ice is heavier than 
the molecule of water. Perhaps one and the same solid 
substance can have different weighted molecules accord- 
ing to the conditions of its formation and existence, 
and with this difference may, perhaps, be associated 
the phenomena of allotropism (or physical isomerism) 
and polymorphism (see p. 93, and Chap. VI.). 



Before dealing with the more important classes of 
compounds, it is advisable to jjreface a few remarks 
on a classification of the elements which, in spite of 
indefiniteness and artificiality, still enjoys a greater or 
less degree of popularity. 

At one time it was believed that chemical action 
is essentially electrical in its nature, and that every 
chemical change is the result of the play of the stronger 
or weaker attractions of oppositely electrified atoms or 
groups of atoms. Berzelius especially developed this 
view of the electrical nature of chemical affinity. He 
believed each atom to be electrically bipolar — each 
atom to have a definite charge of positive, and a 
definite charge of negative, electricity.^ Since these 
charges were in general supposed to be unequal in 
amount, the charge present in greater amount gave a 
more or less positive or negative character to the atom 
as a whole. In accordance with the results of experi- 
ments on the behaviour of several compounds when 

^ If Berzelius had expressed himself in terms of electric potential, 
the necessity for assuming a bipolar electrical distribution in the atom 
would have been obviated. 


electrolysed (i.e., when decomposed by the electric 
current), Berzelius arranged the elements in an electro- 
chemical series such that the element with the most 
negative atoms stood at the head, and the element 
with the most positive atoms at the bottom, of the 
series, any intermediate element being more negative 
than those below it in the series, and more positive 
than those above it. 

It was soon recognised that the elements towards 
the electro-negative end of the series thus constructed 
had properties in common which were different from 
those common to the elements towards the electro- 
positive end of the series. The electro-negative ele- 
ments are, as a rule, of comparatively low specific 
gravity, bad conductors of heat and electricity, and 
more or less transparent. Their oxides are for the 
most part readily soluble in water, and produce solu- 
tions with a sour taste and great solvent and corrosive 
powers. The elements themselves show an aptitude 
for combining with hydrogen to produce hydrides and 
decompose water, combining with its hydrogen and 
setting free its oxygen. 

The electro-positive elements, on the other hand, 
have as a class relatively high specific gravities, and 
possess a peculiar lustre. They are good conductors 
of heat and electricity, and are translucent only when 
reduced to very thin layers. Their oxides are for the 
most part insoluble in water, but they have the power 
of reacting with the solutions of the oxides of the 
electro-negative elements so as to destroy all the char- 


acteristic properties of the latter. Further, the electro- 
positive elements do not readily form compounds with 
hydrogen, and decompose water, combining with its 
oxygen and liberating the hydrogen. 

It seemed good therefore to divide the elements 
into two classes.^ — 

(1) The electro-negative elements or the non-metals.^ 

(2) The electro-positive elements or the metals. 

If this classification enabled us to make anything 
approaching to a satisfactory definition of acids, bases, 
and salts, it might despite its indefiniteness 2 be re- 
tained. But we shall show further on that it does not 
possess this much to be desired merit, and may also 
remark here that the only satisfactory classification of 
the elements — that afforded by the periodic law — does 
not favour any such simple and fundamental division as 
is embraced in the terms metal and non-metal. 

Before passing on to acids, bases, and salts, it is also 

^ By some the word "metalloid" is used in preference to "non- 
inetal." In view of the significance of the termination — oid as 
generally used, this preference is scarcely justified. 

2 This indefiniteness is a necessary accompaniment of all classi- 
fications which are not based on one definite criterion. A number 
of properties are currently regarded as metallic, a number of other 
properties as non-metallic. These properties in each case are not con- 
sidered of equal value inter se in deciding as to the metallic or non- 
metallic character of the element possessing them, but yet there exists 
no authoritative conventional scale of values. An element as a rule 
possesses properties falling under each category', and the non-metallic 
properties have to be weighed against the metallic ones in the un- 
adjusted balances of private opinion. In the absence of all convention 
it is impossible to give a final and indisputable answer to the question, 
" Is tellurium a metal or a non-metal ? " 


necessary to say a few words on a thorouglily arbitrary 
classification of compounds which is in vogue. All 
compounds, by convention, fall under one or other of 
the two headings — organic and inorganic; and hand 
in hand with this classification goes a division of the 
science at large into two branches — organic and in- 
organic chemistry. But "carbon compounds" and 
"the chemistry of carbon compounds " are undoubtedly 
much more appropriate titles than "organic compounds" 
and " organic chemistry " respectively. For compara- 
tively very few of the bodies treated in this main 
subdivision of compounds are, as the latter titles seem 
to imply, products of organisms, i.e., of life ; while, on 
the other hand, some substances included among in- 
organic compounds are products of vital metabolism. 

Since L(5mery's time (1645-1715) up till the be- 
ginning of this century, chemists were possessed of the 
idea that the products of organisms — most of which 
are compounds of carbon — could not be made artifi- 
cially, but that their production absolutely demanded 
the intermediacy of life — the operation of the so-called 
vital force. "Operations of chymistry fall short of 
vital force; no chymist can make milk or blood of 
grass." Further, it was the custom to ascribe the 
variable results obtained in analyses of animal and 
vegetable products to the fact that such bodies did 
not conform to the fundamental law of chemistry (law 
of fixity of composition), and not to the difficulties 
attendant on the analytical methods and the purifica- 
tion of complex carbon compounds. Hence a very 


sliaqj distinction was made between organic and in- 
organic or mineral compounds. 

But the distinction is now recognised as existing 
for convenience only.^ Exactly the same laws hold 
in the case of carbon compounds as in the realm of 
mineral or inorganic chemistry, and many of those 
carbon compounds which are products of the life of 
organisms have been synthesised independently of the 
living laboratory, i.e., of vital force so called. Thus 
there exists no better reason than convenience to be 
adduced for this primary division of compounds, and 
no valid excuse exists for retaining the effete and mis- 
leading term "organic compounds" in preference to 
the more fitting title " carbon compounds." The com- 
pounds of nitrogen are increasing so rapidly, that 
before long it may be advisable to study them as a 
class apart, just as has been the case with carbon 

In discussing acids, bases, and salts, it will be only 
too apparent that we are unable to give satisfactory 
definitions of these classes of compounds, and farther, 
that any of the attempts at definition that may be 
advanced are not independent one of another. In 
other words, we cannot attempt to define one of these 
classes of compounds without implying or assuming 
the definitions of the other classes. In physics all 
definitions can be expressed quite independently of one 

^ A sign of the extremely arbitrary nature of this classification is 
seen in the fact that the oxides of carbon, together with the bodies 
they form by direct combination, are included in inorganic chemistry. 


another in terms of powers of three fundamental units, 
but in chemistry we have no approach to such definition. 

Acids. — Probably the first acid known to the ancients, 
certainly the one best known to them, was vinegar. 
Regarding the solvent powers of this comparatively 
feeble acid, most exaggerated notions were entertained ; 
witness the belief that Hannibal therewith etched a 
passage over the Alps for his army. The alchemists, 
however, knew most of the mineral acids. Geber (eighth 
century) describes the preparation of aquafortis (nitric 
acid) and also of aq^^a regia, which he obtained by 
dissolving sal ammoniac in aqtia fortis. Geber also 
knew of oil of vitriol. The iatro-chemist Valentine 
(beginning of the sixteenth century) first made spiritus 
salis (hydrochloric acid), and showed that aqua regia 
can be made by mixing this new spiritus with aqua 
fortis. Later iatro-chemists, Libavius and Glauber, 
contributed much to an increased knowledge and more 
extended use of the acids by introducing improved 
methods of preparation. 

But as yet no attempt at the classification of bodies 
by their properties had been made, and the generic 
term acid had not arisen, 

Boyle was the first to group together into one class 
all substances which have the following properties : 
(1) a sour taste, (2) a great solvent action, (3) the 
power of precipitating sulphur from alkaline solutions 
of this substance, (4) a reddening action on many 
vegetable blues such as litmus, (5) the power of acting 
on wood ashes to produce substances without either 


the astringent solvent properties of acids or the soapy- 
cleansing properties of solutions of wood ashes. Bodies 
possessing these properties were called collectively acids. 
Even down to the beginning of the eighteenth century- 
most chemists were satisfied with the explanation that 
all substances possessing these properties did so in 
virtue of a greater or less amount of a common con- 
stituent which was called the "primordial acid." Such 
a vague explanation did not however satisfy Lavoisier, 
who renounced all alchemistic fancies of "primordial 
acids" and "principles of acidity." He thought, as 
we have seen, that oxygen was the acid producer, and 
that therefore every acid owes its acidity in some way 
to the oxygen which it necessarily contains. It must 
be here emphasised that Lavoisier did not regard the 
elements of water, and therefore hydrogen, as necessary 
constituents of acids. His acids were mere dissemi- 
nations in water of our acid anhydrides (or acidic 
oxides) — binary compounds of some non-metal with 
oxygen. Thus to Lavoisier sulphuric acid was SO3, 
and not H2O, SO3, or U^O^} 

Up to the year 1787 all the substances known to 

^ It is now believed that after their solution in water, the acid 
anhydrides as such lose their identity ; a new class of bodies called 
hydroxides being formed. These bodies contain as proximate parts of 
their molecules one or more hydroxyl (OH) radicles. Thus when SO3 
reacts with H.,0, a rearrangement of atoms is believed to accom- 
pany combination, so that the resulting compound is represented as 
S02(OH)2 (sulphuryl di-hydroxide), and not as SO3, H-jO (hydrated 
sulphuric oxide). Similar remarks apply to the solutions of the oxides 
of certain metals known as the alkaline oxides, and the alkaline-earth 
oxides. Thus potassium oxide KjO reacts with water in the process 
of dissolving in it to form potassium hydroxide K(OH). 


have the properties of acids as laid down by Boyle 
were products of the interaction of water with the 
oxides of non-metals ; hence the oxides of the 
non-metals were called acid (acidic) oxides. In 
the year just mentioned Berthollet took up the in- 
vestigation of prussic acid (discovered some three or 
four years previously by Scheele), and came to the 
conclusion that it had true acid properties but yet was 
entirely free from oxygen. In 1796 he came to the 
same conclusion for sulphuretted hydrogen, or sul- 
phydric acid, as it may be called. Lavoisier's reputa- 
tion was, however, more mighty than Berthollet's facts, 
and as regards acids, matters remained in statu quo 
until Davy in 1810 clearly proved that hydrochloric 
acid does not contain any oxygen, but is a compound 
of hydrogen with an element chlorine. Further, in 
1813, hydriodic acid was shown to be altogether free 
from oxygen, and it was remarked that iodic anhy- 
dride shows no acid properties until it is dissolved in 
water, i.e., until the element hydrogen is introduced. 
Davy then began to recognise that there is no one 
particular acid-forming element. He noticed that 
hydrogen is a universal constituent of acids, but he 
did not rush over to the converse and say that all 
hydrogenised bodies are necessarily acids. On the 
contrary, he regarded the existence of acid properties 
as depending chiefly on the other elements combined 
with the hydrogen, and not on the hydrogen itself. 
The result of Davy's work was that acids came to 
be classed as hydracids (acids free from oxygen) and 


osyacids (acids formed from acidic oxides). Shortly 
afterwards Liebigr came to the same conclusions as 
Davy, ■ and defined acids as particular compounds of 
hydrogen in which the latter can be replaced by 

The growth, of our knowledge since Davy's time 
has not brought us a satisfactory expression of any 
generalisation as to the particular compounds of 
hydrogen enjoying this property. We are in fact 
bound to admit that an acid belongs to that category 
of things which are perfectly conceivable but indefin- 
able. With Boyle and Liebig we can enumerate the 
properties which we agree shall be connoted by the 
term acid — we can agree as to what are to be regarded 
as acidic functions, but that is all. The diflSculty 
remains that several bodies possessing some, or may 
be all, of these properties are, for other reasons, not 
regarded as acids. We have no one property which we 
can use as an absolute criterion of acidity. Thus the 
salt copper sulphate turns blue litmus red, and causes 
an effervescence of carbon dioxide when mixed with 
a soluble carbonate. Bisulphate of sodium turns blue 
litmus red, causes effervescence with soluble carbonate, 
and contains hydrogen which is replaceable by metals ; 
yet on account of the method of its formation it is not 
regarded as an acid. It seems hopeless then to attempt 
any definition of the term acid in terms of chemical 

If we attempt a definition from the point of view 
of composition rather than properties, we meet with 


equally great difficulties. As Davy and Liebig saw, 
all bodies regarded as acids contain hydrogen, but 
all hydrogenised bodies are not acids. Evidently the 
hydrogen must be combined with certain elements, 
and in a definite manner, to produce an acid. Let 
us try to generalise in this direction. The oxides 
of the non-metals react with water to produce 
hydroxides which are called acids (see note, p. 127). 
Therefore we might attempt to define acids as the 
hydroxides of the non-metals [Cl(OH)] or of non-met- 
allic groups [S02(OH)2]. iBut the bodies HCl, HBr, HI, 
&c., are called acids. Hence we must enlarge our 
definition to include these hydracids. Acids are the 
hydrides and hydroxides of non-metallic elements. 
But this is not a successful definition ; for nitrogen 
and phosphorus are generally regarded as non-metals 
by those who employ the latter term, yet their hydrides 
are not acidic.^ Again, the bodies HgPtClg and 
H^FeCgNg are acids, but neither PtClg nor FeOgN^ 
can be called groups of non- metallic elements. It 
seems hopeless then, even had the title non-metal 
a strict connotation, to attempt to satisfactorily define 
an acid in terms of its qualitative composition. We 
cannot define an inorganic acid in terms of its pro- 
perties alone, nor in terms of its composition alone, 
nor in terms of both together; composition, properties, 
and synthetical history must all be taken into account 
in deciding a body's claim to rank as an acid. 

^ Ammonia nevertheless contains liydrogen directly replaceable by 
the metals K, Na, 



Acids are classified according to their strengths or 
affinities, and also according to their basicities. The 
former classification will be taken up in the chapter on 
chemical equilibrium. The latter classification is due to 
Liebig, who distinguished acids as mono-, di-, tri-, tetra- 
basic, &c., according as they possessed one, two, three, 
four, or more atoms of hydrogen per molecule replace- 
able by metals. It is not always true that the replace- 
able hydrogen atoms are coequal in number with the 
total hydrogen atoms present in the molecule. In cases 
where this equality exists the basicity of the acids can 
at once be determined from their formulae ; but the 
equality must have been proved by experiment to exist. 
The ex|Derimental investigation of basicity takes the 
form of a determination of the maximum number of 
stable potassium or sodium salts the acids can form.^ 

Bases. — From early times it had been noticed that the 
extracts of the ashes of burnt plants possessed certain 
characteristic properties. For example, these extracts 
have great cleansing power, apparently dissolving 
grease and fat ; they are soapy to the touch, and have 
the property of restoring to their normal colours vege- 
table blues which have been reddened by acids. The 
active principle of these extracts was called an alkali, 
this title first appearing in Geber's writings, and liter- 
ally meaning the ash.- Soon it was discovered that a 

^ For practical details see Muir and Carnegie, Practical Chemistry, 
p. 38 rt seq. 

- The active principle of wood ashes is in reality potassium carbonate. 
This is no longer classed as an alkali ; it is a salt with alkaline pro- 



solution of the highly volatile ammonia or hartshorn 
also possessed the above properties. Hence a distinc- 
tion was made between fixed and volatile alkalis. It 
was Stahl who first noticed that, in addition to the 
above enumerated properties, alkalis have the power of 
reacting with acids to produce indifferent substances. 
It was as if the properties of acids and alkalis were 
diametrically opposed, and in combination mutual 
neutralisation took place, just as would be the case 
with two equal and opposite magnetic poles — a sort of 
cancelling out of positive and negative. 

So far the substances which had the power of thus 
neutralising acids were all soluble in water. Sometime 
later it was found that certain almost insoluble sub- 
stances which are very fixed in the fire, i.e., do not 
melt nor change in any way, have the same property. 
These were called the earths, and Eouelle in 1744 
combined alkalis and earths into the one class hase, 
defining a base as any substance which combines with 
and neutralises an acid. 

It is almost impossible to give a concise and 
exact definition of base as that term is now applied. 
Speaking loosely, the oxides of the metals, and the 
hydroxides they form when they are made to combine 
directly or indirectly with water, are regarded as bases ; 
hence metallic oxides are often spoken of as basic 
oxides. May we not then define a base as the oxide 
or hydroxide of a metal ? Such a definition does not 
include hydrides of certain non-metals (ammonia NH3, 
phosphine PH3, &c.), which are established as bases ; 


and, further, it does not indicate that the higher oxides 
of some metals have acidic functions. We are equally 
unsuccessful when we try to frame a definition in 
terras of properties. All bases do not react with acids 
so as to neutralise the latter, i.e., completely destroy 
their characteristic properties, as Rouelle, to whom 
only the strongest bases were known, believed. The 
solution obtained when sulphuric acid is treated with 
an excess of the base copper oxide still possesses acid 
characters. Again, while some bases act on vegetable 
colouring matters, others do not. Nor can bases be 
said to be bodies which in reacting with acids cause a 
replacement of the hydrogen of the acids by metals, for 
the bases N2H4, NH3, PH3, &c., do not contain metals, 
and the |)roducts of their interaction with acids are 
of the nature of additive, not substituted, compounds. 
True, the definition, " A base is a substance which 
reacts with acids to produce a salt and water at most," 
holds good, but it is a definition in terms of acids which 
cannot be defined, and involving a new class of bodies, 
salts which themselves require definition. Hence we 
must conclude that while it is possible to lay down 
what we mean by basic characters or functions, it is 
impossible to define bases ; for many bodies which are 
not regarded as bases exhibit basic characters, and 
many bases exhibit only a few of what are all admittedly 
basic functions. 

A rough classification of the more important inor- 
ganic bases follows. The table clearly shows the true 
relation of the terms alkali and base. In some elemen- 



tary text-books the terms are used as if they were 
synonymous. This is not the case. An alkali is a 
particular kind of hydroxide which is a particular kind 
of base. Every alkali is a base, but every base is not 
an alkali. 

'Alkaline oxides (KoO, Na<.0, 
RboO, CsoO, RboO, Li.O) 
form very soluble hydroxi- 
des with marked basic char- 
acters called alkalis. 
Alkaline earth ■ oxides (CaO, 
SrO, BaO) form slightly 
soluble hydroxides with 
less pronounced bisic char- 
acters than the alkalis. 
The lower oxides of the re- 
maining metals fall under 
this heading. The hy- 
droxides of these oxides 
are formed by adding an 
alkali, or alkaline earth 
hydroxide, to solutions of 
the oxides in acids. 

/-Oxides and hy- 
droxides of 
the metals. 

,- Oxides which directly 
react with water J 
to produce hy 


Oxides which do not 
directly react with"^ 
\^ water. 

Hydrides of 
certain non- 
metals, and 
their deriva- 
^ tives. 

Ammonia NH".,, amidogen N0H4, hydroxylamine 
' NHoOH, phosphine PH3, &c.' 

However convenient classifications of oxides into 
acidic, basic, intermediate, and indifferent varieties 
may be for an elementary presentment of chemistry, a 
glance from the vantage-ground of facts which are not 
usually referred to in elementary courses, but which 
are none the less facts on that account, shows such 
classifications to be imperfect and arbitrary to a degree. 
New reactions and new substances are continually 
being discovered, which testify to the fact that oxides 
generally are capable of exhibiting under one set of 
conditions what are currently accepted as acid char- 
acters ; under another set of conditions, what are 


currently accepted as basic characters. For instance, 
chromium trioxide is usually classed as an acidic oxide, 
because it reacts readily with the alkalis, partially 
destroying the characteristic properties of the latter. 
But it also reacts with sulphuric acid, destroying its 
characteristic properties, and surely this is a basic 
function. True, the salt formed in this latter case 
does not correspond to CrOg, but it has not yet been 
authoritatively laid down that such correspondence is 
an essential feature of acids, or bases as the case 
may be. 

It seems, however, to be tacitly assumed that 
an oxide has no claim to rank as acidic or basic 
until it can be proved to produce corresponding salts. 
Thus, true basic rank was denied to Pb02 until the 
recent preparation of the corresponding salts PbCl^, 
Pb(C2H30.,)^, &c. In spite of its reaction with hydro- 
chloric acid, it was regarded as a feeble acidic oxide 
destitute of true basic properties. Now in virtue of 
these new salts it ranks as an intermediate oxide.i 

^ When an acid and base interact to produce a salt- only, or a mix- 
ture of salt and water only, the salt ,is said to correspond to both the 
acidic oxide of the acid and the basic oxide of the base. 

BaO + H.,S04 = BaS04 + H,0 

2 BaOo + 2 H0SO4 = 2 BaSO^, + 2 H,0 + Oo. 

According to definition, BaS04 corresponds to the oxides SO3 and 
BaO, but it does not corresj^ond to the oxide BaOj. If other factors 
{e.g., oxygen from the air) than the acid and base be involved, the 
resulting salt is not regarded as corresponding to one or other of the 
oxides involved. Thus potassium manganate K2Mn04 (regarded as 
KoO MnOa) does not correspond to the oxide MnO^ from which it is 


Even if the restriction of correspondence (as defined 
in the note) were imposed, the difiiculties attendant on . 
the classification of oxides would not be greatly lessened. 
Barium peroxide, for example, though it reacts readily 
with H2S0^ (SO3) does not form a corresponding salt 
therewith. Hence it ought not to rank as a basic 
oxide. But barium peroxide reacts readily with the 
acidic oxide SOg, giving as sole product the salt BaSO^ ; 
therefore, from this point of view, the peroxide is a 
basic oxide. 

When manganese dioxide is heated with potash in 
the presence of air, a salt K, MnO^ is formed. This is 
said not to correspond to the dioxide MnOg, but to the 
trioxide MnOg, and its formation under these conditions 
is not regarded as any proof of acidic properties in 
MnOg. This seems to imply that the MnO, is first 
oxidised to MnOg by the oxygen of the air, and this 
acidic oxide then reacts with the potash to form the 
corresponding salt potassium manganate. But we have 
no proof that the Mn02 does not itself first combine 
with the 23otash to form a corresponding manganite, 
which as soon as it is formed oxidises to manganate. 
Or, since KgO is known to be peroxidised when heated 
in the air, it may be that the exceedingly un- 
stable salt K2MnO^ results from the interaction of 
the acidic oxide MnOa and the basic oxide K2O2. 
But enough has been said to indicate some of the 
difiiculties attendant on the attempt to rigidly classify 
the oxides. 

Before treating of salts, the subject of neutralisation 


merits a passing notice. When an alkali in aqueous 
solution is added to an aqueous solution of a strong 
acid in just the right quantity to destroy completely 
both the characteristic joroperties of the acid and the 
alkali — for the two sets of properties disappear simul- 
taneously — the .acid is said to be neutralised by the 
alkali, and vice versd. 

We might employ the disappearance of any one of the 
characteristic properties of acids or alkalis as an index 
of the realisation of complete neutralisation, but the 
property hitherto almost universally selected for this 
purpose is the reddening action of acids, and the blueing 
action of alkalis on the vegetable colour litmus — the 
tinctorial matter of a certain species of lichen. The 
normal hue of this substance is puq^le, but it turns 
red when treated with acids, and blue when treated 
with alkalis. Suppose then we have an acid solution 
which we wish to exactly neutralise with a solution of 
alkali, we add a few drops of litmus solution to the 
acid, and then add the alkali solution cautiously till 
the red solution containing the acid becomes purple. 
The neutralisation is then considered to be exact, 
whereas, if too much alkali had been added, the solu- 
tion would be blue, if too little, red. Processes of this 
kind are known generally as processes of titration, for 
they are usually carried out with, or rather involve 
somehow, solutions whose strength or titre is known 
beforehand ; and colouring matters like litmus used as 
aids to exact titration are called indicators. But the 
introduction of numerous coal-tar products which give 


colour changes with acids and alkalis ^ leads us to ask 
if the neutral tint of litmus is an index of exact 
neutralisation, i.e., the presence of acid and alkali in 
precisely the quantities theoretically necessary for com- 
plete combination. 

These new artificially prepared indicators are so 
sensitive that they do not show intermediate neutral 
tints as is the case with litmus. They not only differ 
among themselves in sensitiveness to, but also in their 
qualitative attitudes towards, one and the same solu- 
tion. Thus, potassium sulphite solution is neutral to 
phenolphthalein, but changes violet litmus to blue just 
as an alkali does. Copper sulphate solution is acid 
as tested by litmus, but neutral in its behaviour to 
lacmoid. Saliva, which is normally neutral to litmus, is 
strongly alkaline to lacmoid and acid to turmeric ; and 

-* Among these new indicators may be mentioned — 

Phenolphthalein : with acids, colourless ; with alkalis, purple red. 
Methyl orange : with acids, pink ; with alkalis, pale yellow. 
Lacmoid : with acids, red ; with alkalis, blue. 
Rosolic acid : with acids, pale yellow ; with alkalis, violet red. 

The behaviour of a substance in the role of indicator, seems to be 
determined by the balance of acidic and basic characters in its mole- 
cule. If the acidic properties are relatively strong, the indicator is 
especially sensitive to bases, and can be successfully used in the 
titration of salts formed from weak acids, such as carbonates, sul- 
phides, borates, &c. For carbonic, sulphydric, and boric acids, which 
are liberated during the process of such titrations, are unable to affect 
the colour of the indicator. If, on the other hand, basic characters 
have the predominance in the molecule, then the indicator, being very 
sensitive to acids, is useless for titrations wherein even such feeble 
acids as carbonic, sulphydric, &c., are produced. The differences in 
sensitiveness of these indicators have been applied to the simplification 
and shortening of many processes of volumetric analysis. 


so on. Indicators, then, differ among themselves in their 
testifications as to acidity, alkalinity, and neutrality, 
and there is no reason why the indications of litmus 
should be accepted in preference to those of other 
colouring matters. 

Salts. — The term salt did not always have its present 
connotation. It was at one time loosely applied to 
all substances which tasted like sea-salt, were easily 
soluble in water and recoverable from their solutions 
by evaporation. Of these characteristics solubility was 
regarded as the most important ; hence among the 
alchemists we find an acid referred to as sal acidum, 
an alkali as sal alkali, while a salt proper was 
distinguished as sal salsum. It was Rouelle who, 
totally disregarding solubility relations, appropriated 
the term salt for the product of the interaction of 
an acid with a base or metal. The essential feature 
of an interaction of this kind is the replacement, total 
or partial, of the replaceable hydrogen of the acid 
by equivalent quantities of metals. If the whole of 
the replaceable hydrogen of an acid is displaced by 
a metal, the resulting salt is in general called a normal 
salt. Thus Na^COg (from the acid H^COgAq) CuSO^ 
(from H2SOJ and NagPO^ (from H3POJ are all normal 
salts. The normal salts formed by the interaction of 
the strong acids (HCl, HgSO^, HNO3, &c.) and the 
strong bases (KOH, NaOH) were the first to be 
investigated. As such salts (e.(/., K^SO^, NaCl, KNO3, 
&c.) were all neutral to litmus, it was once customary 
to regard as synonymous the terms neutral salt and 


normal salt. But it is now known that many normal 
salts are not neutral. When the metal of a weak base, 
e.g., Fe(0H)3 replaces all the hydrogen of a strong acid, 
e.g., HCl, a normal salt with acidic properties results, 
e.g., FeClg. On the other hand the interaction of a 
strong base, e.g., KOH and a weak acid, e.g., HgCOg 
gives a normal salt with alkaline properties, e.g., 

If only a portion of the replaceable hydrogen of the 
acid is replaced by metal, as in the compounds NaHSO^, 
NaHCOg, Na^HPO^, the resulting salts are called acid 
salts. This title does not necessarily imply the posses- 
sion of any other acidic property than the presence of 
one or more hydrogen atoms replaceable by metals ; as 
we shall see presently, it does not always imply even 
this characteristic. It denotes a particular composition 
rather than a definite set of properties. Thus the 
slightly alkaline body Na,HPO^ is in terms of our 
definition an acid phosphate of sodium, while acid 
sodium carbonate NaHCOg possesses very pronounced 
alkaline properties. ^ 

But it is necessary to enlarge our ideas of acid salts. 
If acid salts were nothing else than acids in which 
part of the replaceable hydrogen is substituted by an 
equivalent quantity of metal, then it follows that a 
dibasic acid like carbonic acid (HgCOgAq) should be 
capable of forming only one acid sodium salt NaHCOg. 

^ Acid salts containing replaceable hydrogen and formed from dibasic 
acids are often distinguished from the normal salts formed from the 
same acid and base by the prefix bi-. Thus NaHS04 is bisulphate of 
sodium ; NaHCOs bicarbonate of sodium, and so on. 


But there is another way of looking at, and defining, 
acid salts. In the normal sodium salt of carbonic acid 
NagCO^ or Na.O.COg 

the acid oxide : the basic oxide : : one reacting weight : 
one reacting weight. 

In the acid salt SNaHCO^ or Na,0.2C02.H,0 

the acid oxide : the basic oxide : : two reacting weights : 
one reacting weight. 

In other words an acid carbonate of sodium is a 

1^ . ,. , ,, ,. reacting weights of acidic oxide 

salt in which the ratio ,. ^.— ,- — t^ — ■ ^^ — 

reacting weights 01 basic oxide 

exceeds the value unity. This is a wider definition 

than the one previously given, in that it does not point 

to any limit for the number of possible acid salts. 

It prepares us for the statement that a second acid 

carbonate of sodium exists. This is the so-called 

sesquicarbonate of sodium which has the composition 


Every oxy-salt can be conventionally regarded as a 

compound of basic with acidic oxide. Let us suppose 

that in the normal salt of a given metal the ratio 

reacting weights of acidic oxide 

reacting weights of basic oxide 

then if other salts formed from the same acid and 
base or metal exist in which the above ratio has 
a greater value than n, they must be regarded as 
acid salts. 


We see then that it is not necessary that every acid 
salt should contain replaceable hydrogen. Thus, in 
addition to the normal sulphate of antimony Sbg (SO^)^ 
[Sb.^Og.SSOy], a sulphate having the composition 
SbgS^Ojg [Sb203.4S03] is known. It is therefore 
in terms of our latest definition an acid salt, and as 
such it is commonly regarded, though it does not 
contain replaceable hydrogen. 

Why then, it may be asked, should it not be called 
a normal salt, seeing that all the hydrogen of the acid 
from which it has been formed (H.^SO^) has been re- 
placed? The answer is, that by tacit consent only 
those salts are called normal which, in addition to the 
absence of replaceable hydrogen, can be represented 
as containing whole multiples of the radicles of the 
acid forming them.^ Thus all normal sulphates can be 
represented as containing electro-positive element united 
with ^(SO^) ; all normal carbonates will contain ^(COg) ; 
all normal phosphates n (t'O^) ; and so on. 

T p , 1 , . reacting weights of acidic oxide „ 

If the ratio -~ r^- — -^, — -. -, — for a 

reactmg weights oi basic oxide 

particular salt fall below the value n peculiar to the 

normal salt, then the salt is called a basic salt. In 

normal mercuric sulphate HgSO^ [HgO.SO.^] n = 1\ 

in the sulphate HggSOg [SHgO.SO^] n equals only \. 

This latter compound is therefore a basic sulphate of 

mercury. These basic salts constitute quite a large 

^ The molecular formula of acids may be conceived as made up of 
two parts ; one part consisting of the whole of the replaceable hydrogen, 
the residue constituting the other part being called the acid radicle. 


aucl important class of bodies. They are for the most 
part insoluble substances formed when excess of water 
acts on the normal salts formed from weak bases, or 
when excess of weak base is allowed to interact with 
acid and a strong acid. 

From the fact that there are several acids which 
do not contain oxygen and have thei^efore no corre- 
sponding acidic oxides, it follows that our definitions of 
acid and basic salts in terms of the ratio 

reacting weights of acidic oxide 
reacting weights of basic oxide 

lacks generality. We can, however, regard all acid and 
basic salts from one common standpoint, provided we 
apply a vaguely extended meaning to the word neutra- 
lisation. When a weak base interacts with a strong- 
acid, the resulting normal salt as we have seen has 
in general distinctly acid properties. In virtue of 
these properties it can interact with more basic oxide, 
producing what we may conceive of as a nearer 
approach to absolute neutralisation in the form of a 
basic salt. According to this view, the weaker bases 
should show themselves particularly prone to form basic 
salts with strong acids ; and this is known to be 
actually the case. 

Again, when a strong base interacts with a weak 
acid, basic properties predominate in the normal salt, 
in virtue of which it is capable of further interaction 
with more acid or acidic oxide, with the realisation of 
more perfect neutralisation in the form of an acid salt. 


Thus it follows that acid salts are formed chiefly from 
the strong bases. 

It has been customary to regard the excess of acid 
in an acid salt over and above that necessary for the 
production of a normal salt, as less intimately com- 
bined or associated with the base than that portion of 
the acid which just suffices for conditions of normality. 
Similar remarks apply to excess of base in basic salts. 
In conformity with these unsubstantiated views, acid 
and basic salts are often represented as molecular com- 
pounds of normal salt and acid on the one hand, and of 
normal salt and base on the other. Thus basic bismuth 
chloride is sometimes written Bi^Og.BiClg [3 BiOCl] ; 
sesquicarbonate of sodium, according to this method 
of representation, becomes 2Na2OO3.H2CO3.2H2O, and 
acid sulphate of potassium, KgSO^.HgSO^.^ 

But if normal salts still retain acid and basic func- 
tions, enabling them now to combine with more base, 
now with more acid, the question naturally arises, why 
should not normal salts with residual acidic functions 
combine with normal salts possessed of residual basic 
functions? This question introduces us to the class 

^ According to this view of the matter, the so-called hyperacid salts 
formed by monobasic acids, e.g., KCl.HCl or KHCU, KF.HF or 
KHFo &c., ought not to be distinguished from the ordinary acid salt 
such as Na2s64. H0SO4. The term "hyperacid salts" for these com- 
pounds is an outgrowth of the primitive views on acid salts, which 
represented them as acids in which only part of the replaceable hydro- 
gen is replaced by metals. According to these views it is, of course, 
impossible for a monobasic acid to form acid salts ; and hence the 
introduction of the term " hyperacid salts " to meet the necessities of 
such cases as KHClo, KHFo &c. 


of double salts which is at present receiving a good 
deal of attention. 

Normal sulphate of sodium, Na2S04, exhibits re- 
sidual basic properties in its interaction with sul- 
phuric acid to produce the acid sulphate of sodium 
Na^SO^.H^SO^. (2 NaHSOJ. To zinc sulphate, by 
reason of the existence of such basic salts as 
SO3.2 ZnO, SO3.4 ZnO,.2 H2O, SO3.6 ZnO.lOH^O, 
and SO3.8 ZnO. 2 HoO must be ascribed residual acidic 
properties. What wonder then that basic Na^SO^ 
combines with acidic ZnS04, forming the double sul- 
phate Na2SO,.ZnS04.4H.20? 

The double halides are an especially important class 
of bodies, and much is to be hoped from their further 
investigation. Their formation and existence admit of 
a provisional explanation similar to that just employed 
in connection with the double sulphates. 

By reason of the existence of the unstable hyperacid 
salts having the general formula MX.HX, where X is 
a halogen and M the metal of an alkali, slight basic 
properties must be allowed to the alkaline halides. 
But the normal salts formed by the interaction with the 
haloid acids of the weaker bases {i.e., the oxides and 
hydroxides of the heavy metals) have a surplus of acidic 
characters. Hence we have a large series of com- 
pounds, called double halides, of the general formula 
n (MX) 111 (M'X^) where MX represents alkaline halide 
and M'X^ the halide of some element other than the 
metal of an alkali. The following are a few examples, 
picked at random, of such double halides BeC1.2.2KCl, 


MgFg-NaF, Pblg-oNH^Cl. In accordance with the 
manner of regarding double salts here developed, it is 
found that these are most readily formed by halides 
corresponding to those oxides which in turn most 
readily form basic salts. Attempts have been made 
from time to time to remove the so-called double 
halides from the ill- defined and artificial class of 
molecular compounds by assigning to them normal 
unitary atomic structures.^ These attempts necessi- 
tated certain extensions of our ideas of valency (see 
next chapter) which have not met with general 
acceptance ; and until some more satisfactory theory 
of the structure of the double halides is framed, these 
bodies will, in all probability, continue to be empiri- 
cally regarded as molecular compounds of the simple 
metallic halides from which they are prepared. 

Inorganic compounds are not all included under the 
titles acids, bases, and salts. There is in addition a 
large and rapidly growing number of little-investigated 
binary bodies, such as the phosphides, the borides, the 
nitrides, the silicides, the carbides, the selenides, the 
tellurides, the arsenides, and the antimonides. Most of 
these substances (which may for the present be classed 
together under the heading indifferent todies -) are 
formed by direct union of the elements at high tem- 

^ For the distinction between molecular and atomic compounds see 
p. 155. 

2 The oxide NO together with several hydrides, e.g., SiKj, P.,H4, 
would also fall under this category of indifferent bodies. For an 
exhaustive list of these indifferent bodies, the reader is referred to 
Ramsay, System of Inorganic Chemistry, p. 497 ct seq. 


peratures and are decomposed by water. Though in 
several cases the phosphides, &c., of an element M are 
of the- same type as the phosphides, &c., of the element 
hydrogen {e.g., PaHg and PgZn'g), yet they cannot be 
regarded as salts of the latter. For the hydrogen 
compounds do. not exhibit the most universal of acid 
properties — the possession of hydrogen atoms directly 
replaceable by equivalent quantities of other elements. 



With respect to the arrangement of the simple atoms 
in the compound atom (molecule) the earlier chemists 
did not concern themselves. The determination of the 
mere composition and formula of the compound atom 
was a problem more than sufficient for their day. But 
during the years 1820-25 the discovery and investi- 
gation of cyanic, fulminic, and cyanuric acids forced 
chemists to face the question of the mutual relations 
of the atoms in the molecule. These three acids were 
found to have identically the same percentage composi- 
tion, and yet the properties of the three bodies differed 
most pronouncedly. 

So foreign did the possibility of the existence of two 
or more different bodies of the same percentage com- 
position appear to the early chemical philosophy, that 
Berzelius for long refused to admit it. Finally, how- 
ever, the accumulation of well-authenticated instances 
of the phenomenon, among which the different tartaric 
acids may especially be mentioned, not only forced 
Berzelius to an admission, but led him to introduce the 
general term "isomerism"^ for the class of facts 
under observation. 

^ Much confusion exists in regard to the precise use of the terms 

isomerism, metamerism, &c. Some, regarding identity of percentage 



What explanation of isomerism could there possibly 
be other than a difference in atomic arrangements in 
the molecules of isomeric bodies ? Henceforth it was 
acknowledged that the properties of a substance depend 
not only on its composition but also on the atomic 
architecture of- its molecules. Now the architecture of 
two molecules having identical atomic compositions can 
differ in two ways. The relative positions of the atoms 
remaining the same, their distances apart may differ ; 
or the atomic distances being constant or without in- 
fluence, the relative positions may differ. It is be- 
lieved, not without strong evidence, that differences in 
the relative positions of the atoms constitute the sole 
determining cause of isomerism ; differences in atomic 
distances, if indeed such exist, being without influence. 

composition as the sole condition of isomerism, divide isomers into the 
two classes polymers and metamers ; pol3Mners having different mole- 
cular weights, metamers the same molecular weight. 

Others again give two meanings — a wide and a restricted one — to 
the term isomer. As before, all bodies having the same percentage 
composition are isomers in the wide sense. Such isomers are then 
classified into (a) bodies of different molecular weights, (/3) bodies of 
the same molecular weight. Bodies of the former class are polymers. 
The latter class is further subdivided into (a') bodies of the same type 
or isomers in the restricted sense, and (,3') bodies of different types or 

Throughout this chapter the terms will be used in accordance with 
Berzelius' first suggestion, viz. : — 

Polymers — bodies of the same percentage composition and different 

molecular weights. 
Isomers — bodies of the same percentage composition and the same 

molecular weight. 
Metamers — closely related isotners which are capable of very readily 

changing one into another. 

(See article "Isomerism" in Watts' Dictionary of Chemistry.) 


At any rate, all known cases of isomerism can be ex- 
plained in terras of differences in atomic arrangement 
alone. ^ 

Two, and only two isomers of the formula 02HgO are 
known ; all attempts to produce a greater number have 
been futile. But it is obviously possible to arrange the 
nine atoms in a multitude of different ways. Why then 
does not a multitude of isomers exist ? There must be 
a something limiting the possible groupings of a num- 
ber of atoms in a molecule, whose cause must surely be 
sought for in the nature of the atoms themselves. 

To take an analogy. Imagine a number of athletes 
of widely varying strength or holding power. So long 
as we pay no regard to their holding powers it is 
evident that we can arrange these athletes in a large 
number of different groups — in each group the relative 
positions of the athletes being different. 

But the number of possible arrangements is very 
much diminished as soon as we make the stipulation 
that the groups are to be conditioned by, and exist in 
virtue of, the holding powers of the individual athletes 
— groups such as the "human trees" which so fre- 
quently form one of the items in a circus programme. 

So it is with the atoms in a molecule ; they are not 
thrown together "higgledy-piggledy" and without any 
dependence on the intrinsic peculiarities of the atoms, 

^ The distances between those atoms of a molecule which have 
" strong affinities " for each other may be a determining cause in 
isomeric change. But the isomctnc change from one body A to another 
body 5 is a very different thing from the isomerism of A and B. (See 
p. 183). 


but the molecule owes its continued existence to the 
definite holding or linking power of its constituent 
atoms; To this property or power of atoms the general 
term valence or valency has been applied. 

As at the birth-time of the recognition of valency, 
no molecules were known containing per one atom of 
hydrogen more than one atom of any other element 
X (i.e., as there were no bodies of the type HX^), and 
as the hydrogen atom had already been chosen as the 
standard for atomic weights, it seemed well to make it 
also the standard for valencies. Any atom X which 
held in combination one atom of hydrogen, and formed 
a molecule HX, was called a monovalent atom. The 
existence of the molecule H^Y established the diva- 
lency of Y, and so on. 

It will readily be seen that valency is nothing else 
than a special name given to equivalency when this 
is applied to atoms, and it is not therefore surprising 
that the same difficulties as beset the attempt to 
establish an equivalent system appear again in the 
later attempts to fix the valencies of the elementary 

Only a few elements combine with hydrogen to 
form gasifiable molecules, and had we to rely only on 
hydrides, our knowledge of the valencies of the atoms 
of the elements would be very incomplete. Fluorine, 
chlorine, bromine, and iodine, however, combine atom 
for atom with hydrogen, hence they are univalent atoms, 
and may be used as middlemen to fix the valencies of 
elements which do not form hydrides. Unfortunately 


the valency of an atom as derived from a study of the 
halides of the element does not always agree with the 
valency as fixed by the hydride, e.g., PH^, PFg. More- 
over, many elements form at least two gasifiable halides 
with the same halogen, e.g., HgCl, HgOl2. Which 
particular halide is to determine the valency of the 
atom in question ? Can we, indeed, correctly speak of 
the valency of an atom ? ^ 

This question has given rise to two opposing schools. 
One school, vaguely referring the phenomena of valency 
back to some objective attribute of the atom, asserts 
the necessary constancy of valency. The valency of an 
atom is, according to this school, as constant as its 

^ From a study of the periodic law, Mendel(^eff arrived at the follow- 
ing generalisation : The sum of the " equivalents " of oxygen and 
hydrogen with which a single non-metallic atom is combined in its 
highest salt forming oxide on the one hand, and in its maximum 
hydride on the other, is constant for all non-metallic atoms, and is 
equal to 8. Thus, the highest salt-forming oxide of carbon is COo ; the 
maximum hydride of carbon is CH4. In each case the carbon atom is 
combined with four "equivalents," and 4 + 4=8. The pairs of com- 
pounds PH3, PoOg; AsHs, AsoO^; TeOg, TeHo, illustrate the same 
principle. It is obvious that by " equivalents," Mendeleeff here means 
something very much akin to valencies ; and in this connection he asks 
why the valency of an atom should be gauged by its hydrides rather 
than by its oxides. It should be noted that Mendeleeff 's generalisa- 
tion is founded on the assumption that peroxides (i.e., oxides of higher 
types than the so-called group oxides) are not strictly salt-forming — do 
not form corresponding salts. The recent isolation of salts MoSoOg 
(where M = monovalent atom) corresponding to sulphur peroxide S2O7 
is at variance with this assumption. The sum of the "equivalents" of 
sulphur in S0O7, and SHo is 9, and not 8. Some other criterion than 
the power of forming corresponding gaits must lie at the basis of a 
classification of oxides adapted to Mendeleeff 's generalisation. Further, 
the partiality of the generalisation, including as it virtually does only 
the non-metals, is against it. See Mendele'eff 's Principles of Chemistry, 
vol. ii., appendix 1. 


weight, although under certain conditions it is not 
wholly in evidence. Among modern chemists, van't 
Hoff may be cited as an adherent of this school. He 
assumes that the attractions in virtue of which the 
atoms of a molecule hold together, are of the same 
order as the gravitative attractions of ponderable masses. 
This being the case, he shows that the intensity of 
the attraction over the surface of an atom would be 
constant only if the atom were truly spherical. If, on 
the contrary, the atom had any other figure than the 
sphere, then at certain points on its surface the attrac- 
tive forces would have maximal values — these values 
being unequal ijiteo- se. According to van't Hoff 's view, 
then, the valency of an atom expresses the total number 
of points of maximal attraction — this number being 
dependent on the form of the atom. As the form of 
the atom is presumably constant, the valency is also 
constant. If, however, under certain conditions the 
movements of the atoms conditioning the temperature 
of the gas become so energetic that only the higher 
maxima of attraction are powerful enough to come 
into effective operation, the atom will apparently pos- 
sess a valency lower than its actual valency.^ 

' In view of the fact that Faraday's law of electrolysis can be 
stated ill terms of valency data, it may seem somewhat surprising that 
no satisfactory electrical theory of the cause of valency has appeared. 
Yet it should be remembered that valency had its origin, and finds 
its chief application, in organic chemistry, and the great majority of 
organic compounds, i.e., all oi'ganic compounds which are not salts nor 
acids, are non-electrolytic. In electrolysis the positive electricity may 
be regarded as conveyed through the electrolyte from anode to kathode 
by the metallic atoms, the negative electricity from kathode to anode 


The opposing school, most non-committal and un- 
imaginative, does not attempt to theorise on, or explain 
in any way, the phenomena of valency. It does not 
speak of the absolute valency of any atom, but only 
of the maximum known valency of an atom or, less 
general still, of the valency of an atom in a particular 
compound. 1 

The history of the school of constant valency is an 
instructive one. Its attempts to vindicate its tenets 
gave rise not only to such familiar distinctions as those 
involved in the terms saturated and unsaturated bodies, 
atomic and molecidar compounds, but also to the cele- 
brated so-called theory of bonds. 

by the non-metallic atoms or acid radicles. Atoms and radicles in 
their capacity as carriers of electricity during electrolysis are called 
ions. Faraday's law can be stated in the following form : — The elec- 
trical carrying power of an ion is directly proportional to its valency. 
In other words, a quantity of electricity, positive or negative, which 
is conveyed through a salt solution by an ?i-valent atom or radicle, 
would require for its convection n monovalent atoms or radicles. If a 
current of electricity be passed through two electrolytic cells in suc- 
cession, the amount of electricity passing through each cell in a unit 
of time is the same. If in the first cell we have a salt of a divalent 
metallic atom, in the second a salt of a monovalent metallic atom, 
then for every atom (or what is the same thing, for every atomic 
weight expressed in any mass unit) of the divalent metal deposited in 
the first cell we shall have two atoms (two atomic weights in the same 
mass unit) of the monovalent metal deposited in the second cell. See 
Lodge, Modern Views of Electricity, p. 72 et seq. 

The table given in note 1, p. 159, could quite well be constructed 
from quantitative electrolytic determinations alone. 

^ Apropos of the attitudes of these rival schools, Ostwald writes : — 
" Fragt man nach dem Wege, auf welchem eine Entscheidung zu treffen 
wore, so kann eine solche nur auf Grundlage einer bestimmten, wohl 
begriindeten Hypothese iiber die Natur dessen, was wir Valenz nennen, 
erlaugt werden." 


The nitrogen atom combines with three atoms of 
hydrogen to form ISTHg ; therefore nitrogen is trivalent. 
In order to express this fact clearly and succinctly, the 

notation -YnV '^^^ employed. At first the lines proceed- 
ing from the circle enclosing the symbol for nitrogen 
were regarded in their true light — simply as a species 
of chemical shorthand ; but soon they came to be 
regarded as symbolising some objective characteristics 
of the atoms called bonds or units of affinity. The 
nitrogen atom was trivalent, because it was possessed 
of three bonds or units of affinity. It did not hamper 
the advance of the school, that for long no satis- 
factory answer could be given to the question, what 
is the nature of a bond or affinity unit ? But chemists 
are not the only people who have at times deceived 
themselves into the belief that to name the unknown 
is to explain and progress. ^ 

But if nitrogen is trivalent, and hydrogen and iodine 
both monovalent, how, it was asked by the opponents of 
the school, could the existence of the molecule NH^I be 
explained ? In terms of the difference between atomic 
and molecular compounds, was the answer. Only in the 
former class of bodies, it was said, is valency operative. 
Ammonium iodide is a loose molecular compound of 
the two atomic compounds NH3 and HI, in the former 
of which the nitrogen atom displays its customary 

1 Thanks to van't HoflE's theory of valency, we may now, without 
bfinj,' accused of a mere glossing of our ignorance, employ the term 
"bond." Some such term, properly understood, is not only generally 
useful, but it is absolutely indispensable in describing the results of the 
new stereo-chemistry (vide infra). The word bond is much to be pre- 
ferred to its once synonymous term " unit of aflBnity." 


trivalencj. The attraction (or energy degradation), in 
virtue of which the atomic compounds HI and NH^ 
mutually hold each other in combination, is not only 
independent of, but of a quite different order from, 
the attractions associated with the valencies of the 
atoms, and instrumental in holding together the parts 
of atomic compounds. The former attractions are 
attributes of the molecules as wholes, and are of a 
physical rather than a chemical nature. 

However, experiments on the substituted ammonium 
iodides (NH^I in which the H atoms are replaced by 
different monovalent organic radicles) showed in this 
special case the artificiality of the distinction between 
atomic and molecular compounds, and the necessity of 
regarding ammonium iodide as a true atomic com- 
pound in which the nitrogen atom, holding in direct 
combination the four atoms of hydrogen and the one 
atom of iodine, must be pentavalent.^ 

The school of constant valency was bound to recog- 
nise the justness of these conclusions, to which it 
immediately adapted itself by instituting a distinction 
between saturated and unsaturated compounds, main- 
taining the while that the nitrogen atom was constantly 
pentavalent instead of trivalent, as hitherto upheld. 

Here will be observed a slight departure from the 
original signification of valency ; the valency of an atom 
is now measured by the number of bonds it possesses. 

^ The behaviours of such presumed inorgauic molecular compounds 
as KTII4 [KI.TII3], K^SbBiyCl.-i [SbBrs.SKCl], &c., are also not in 
harmony with the deductions which necessarily flow from the admission 
of molecular combination as distinguished from true atom linking. 


It at first sight seems more definite than the original 
signification in that a cause for the phenomena is 
assigned. But phenomena which are not understood 
are not cleared up by the mere assigning of causes 
whose natures are themselves darkly obscure. It is 
worthy of remark that till van't Hoff' s time no satis- 
factory explanation was advanced of the reason why 
an atom forms sometimes a saturated, sometimes an 
unsaturated molecule. 

Conceptions of valency had their origin in the study 
of carbon compounds, and it is in the field of carbon 
compounds that the developed theory to-day finds its 
most successful applications.^ The reasons for this are 
not far to seek. The carbon atom is peculiar in that its 
valency determined from all its highest forms of com- 
bination containing only a single carbon atom in the 
molecule, is constant. The molecules CH^, CHCI3, 
CHBr^, CCI4, CS2, and CO, all point to the tetravalency 
of carbon. 2 Again, carbon compounds are for the 
most part easily vaporised, and hence the molecular 

^ It should be particularly noted that organic chemistry, though 
largely indebted to, is nevertheless quite independent of, the theory 
of valency. Mendeleefif has shown that the application of Newton's 
third law of motion in the form in which it appears when regarded as 
a corollary of the first law, combined with the principle of substitution, 
is capable of effecting all that the doctrine of valency really effects, viz., 
the limitation of the number of isomers possible for a given atomic com- 
plex, and the provision for each isomer of an appropriate molecular 
ground plan. (See Mendeldeff, Nature, vol. xl. No. 1032, and Carnegie, 
American Chemical Journal, vol. xv. No. 1.) 

^ It may be that some day this series will be rendered complete by 
the discovery of a substance having the molecular composition CN-> ; 
the group N2 being tetravalent, as in the molecule of hydrazine 
H2 = N2 = Ho. 


weights of the majority of carbon compounds are 
known. On the other hand, of only some sixty inorganic 
compounds of the type MX„ are the true molecular 
weights known, and it is impossible to draw unequivocal 
conclusions regarding the valency of an element M 
which does not from gasifiable compounds of the type 
MX„, where X represents some monovalent atom or 
group. No compound of sodium has been vaporised. 
Sodium chloride may have the molecular composition 
NaCl, in which case sodium is a monovalent atom ; but 
there is no a priori reason why the molecular composi- 
tion of salt should not be NagClg . . . Na„01„, in which 
cases the sodium atom may be respectively di- tri- 
. . . n . . . (2n — 1)- valent. 

Further, of the elements with gasifiable compounds 
of the type MX„ none except silicon, which is very 
closely related to carbon, shows a constant valency as 
X is varied. Thus, the phosphorus atom is trivalent 
in phosphine PH3, and pentavalent in phosphorus pen- 
tafluoride PF^. Nor, by reason of the comparative 
simplicities of the molecules of inorganic bodies, the 
thorough and so to speak annihilatory nature of the 
changes they undergo, and the absence of marked 
cases of isomerism among them,i are questions rela- 

^ The only well-marked cases of isomerism (it inaij, however, be 
polymerism) in inorganic chemistry are afforded by the so-called 
inorganic amines — the numerous and complex bodies which are formed 
by the action of ammonia, under varied conditions, on the salts of such 
metals as platinum, cobalt, chromium, and rhodium. See Ramsay, 
System of Inorganic Chemistry, p. 524, et seq. The structural formulse 
which have in some cases been assigned to these inorganic isomers are 
open to great doubt and uncertainty. 


ting to stracture of so much importance in inorganic 
chemistry as they are in the domain of carbon com- 

For all these reasons the theory of valency admits of 
much more definite and productive application to carbon 
compounds than to inorganic bodies; indeed it may 
seriously be questioned whether the necessarily loose 
and gratuitous applications of considerations of valency 
to inorganic compounds have not impeded the progress 
of the science at large.^ That such applications brought 
discredit on the theory itself will be admitted by most. 

1 The valency data of greatest practical importance in inorganic 
chemistry are here tabulated — 

I. Metals and basic radicles — 

(a) monovalent, K, Na, Li, Rb, Cs, NH4, Ag, Hg""', Cu"»^ 

Au""S T1""S BiO. 
(,3) divcdent, Ca, Sr, Ba, Pb, Mg, Zn, Cd, Hg'^ Cu"', Sn<">^ 

Fe""% Cr™', Mn""^, Co, Ni, Be, Pt<'"^ UO.,. 
(7) trivalent, Au"=, Al, Bi, Fe'', Cr"=, Tl"=. 
(5) tetravalent, Sn'S U""S Pt'". 
II. Non-metals and acidic radicles — 

(a) monovalent - CI, - Br, - 1, - F, nitrites - NO.,, nitrates - 

NO3, hypochlorites - CIO, chlorates - CIO3, cyanides - CN, 

cyanates - CNO, thiocyanates - CNS, metaphosphates - 

PO3, perchlorates - .C IO4. 
(^) divalent - O, - S, sulphites - SO3, sulphates - SO4, thiosul- 

phates - S2O.!, carbonates - CO3, silicofluorides-SiFg, chro- 

mates - Cr04, dichromates - Cr207, orthomolybdates - 

M0O4, tungstates — WO4, metaborates - B2O4, pyroborates - 

B4O7, metasilicates - SiOy. 
(7) trivalent, phosphites - PO3, phosphates - PO4, ferricyanides 
- Fe(CN)6, arsenites - AsOs, arseniates - ASO4, ortho- 

borates - BO;;. 
(5) tetravalent, ferrocyanides - Fe(CN)(i, pyrophosphates - P2O7, 

orthosilicates - Si04. 

By means of this table, the formula of any common inorganic salt 
can be found. Place the symbols for the metal and acid radicle of the 


The chief services that the theory of valency has ren- 
dered the chemistry of carbon compounds have been in 
the domain of isomerism. The theory enables us to pre- 
dict with absolute certainty the number of isomers con- 
sistent with a given molecular composition. The general 
idea one is apt to glean from much of the literature 
on the subject is that valency lies at the basis of the 
so-called constitutional or structural formulge. This is 
not the case. What does lie at the basis of structural 
formulee is merely the conception of definite atomic 
linkage — a conception of lower order than that of 
valency. It is quite possible to symbolise succinctly the 
chemical relations of a body — to give it a structural 

salt in juxtaposition ; then multiply one or other of these symbols, or 
it may be both, so that the metallic atoms and acid radicles become 
equivalent. Express these multiples in small subscripts placed after 
the respective symbols, and the result is the formula required. Thus 
calcium phosphate is Cag (P04)2 ; for we must take three divalent atoms 
and two trivalent radicles in order to get a balance of the valencies of 
the two constituent parts of the salt. 

The table is necessarily incomplete. Elements which form halides 
of several types, but no stable oxy salts, e.g., W and Mo, have been 
omitted. As regards the formulae of oxides, the table is only available 
for those markedly basic oxides which form corresponding salts ; it 
correctly gives the formulae for such oxides as ferrous oxide, baric 
oxide, (Sec, but it does not help us in the cases of the magnetic oxide 
of iron, baric peroxide, &c. Further, it only gives the formula) for 
normal salts ; the complex poly-salts formed by weak acids such as 
boric, molybdic, tungstic, silicic, &c., are most simply represented, not 
as made up of metal and acid radicle, but of acidic and basic oxide, 
thus — n BO in AO, where BO is the oxide of a metal, AO the oxide of 
a non-metal, and m n are whole numbers. However, these complex 
salts can also be represented as derived from the normal salts. Thus 
the mineral serpentine usually written 2Si02.3MgO, may also be 
regarded as a dehydrated acid magnesium ortho-silicate, MgsHj 
(Si04)., -H.iO = Mg3Si207. Obviously, the table does not inform us as 
to the possible number or the limit forms of such complex salts. 


formula recalling its mode of formation, suggesting its 
decompositions, &c., — by means of certain conventions 
respecting the written arrangements and groupings of 
the constituent atoms, and without in any way having 
recourse to the teachings of valency. Thus, the symbol 

HO . S . OH conveys much information concerning sul- 

phuric acid, and yet is framed without any regard to 

the doctrine of valency. This symbol pictures the fact 

of the symmetry of the sulphuric acid molecule, and 

therefore the impossibility of the existence of isomeric 

forms of the derivatives HBSO^ and ER'SO^. 

Further, knowing the equal value, substitutionally, 

of CI and (OH), of H and K, &c., and also the readiness 

with which hydroxyl groups linked to the same atom 

interact, the following transformations are at once 

suggested by the symbol given — 

Cl.S.Cl Cl.S.OH Cl.S.OK KO.S.OK S.O 

To argue whether the sulphur atom is tetra- or hexa- 

valent in sulphuric acid is profitless. The formulae 


HO — S — OH / S 

do not convey any more information about the pro- 
perties of sulphuric acid than does the simple 

representation HO . 8 . OH. 


Before proceeding to illustrate the applications of 
considerations of valency to organic bodies, it is first 
necessary to speak of the valencies of compound 
radicles. A compound radicle is a group of atoms 
which, like a single elementary atom (simple radicle) 
appears as an undecomposed whole throughout a large 
series of compounds or transformations. Like an atom, 
too, a compound radicle has a definite valency. These 
compound radicles, or stable atom complexes, play so 
conspicuous and important a role in the field of carbon 
compounds that they were once regarded as the true 
atoms of organic chemistry, which itself was supposed 
to be adequately defined as the chemistry of compound 
radicles. As random examples of these compound 
radicles we may cite ethyl CgH^, ethyoxyl CgH^O, 
hydroxyl OH, carboxyl COOH, and amidogen NHg 
— all monovalent radicles, for each combines with a 
single atom of hydrogen to form a gaseous mole- 
cule ; the divalent radicles ethenyl CgH^, carbonyl 
CO, and the trivalent radicles, glyceryl C3H5 and 
methenyl OH. 

Now, if the carbon atom can hold in combination 
four hydrogen atoms, it will also hold in combination 
four monovalent compound radicles, and therefore such 
molecules as 

OC..H5 H NH2 

I I I 

CHjO - C - OC0H5 HOOC - C - COOH H - C - COOH, &c. 

I I I 

OC2H5 H H 

ought to, and do, exist. 


Hence we are bound to give an extended significance 
to the statement — the carbon atom is tetravalent. Not 
only does it imply that the carbon atom combines with 
four atoms of hydrogen to form a gaseous molecule, 
but further that in any molecule a carbon atom is 
capable of directly interacting with four, but no 
more than four, other atoms, the particular valencies 
of these atoms being a matter of indifference. 
Thus in the ethyl ether of ortho-carbonic acid, 
C(0C2H.)^, the heavily printed carbon atom directly 
interacts with four divalent oxygen atoms, each of 
which again directly interacts with a monovalent 
ethyl group. In glycocine 


the heavily printed carbon atom acts on two mono- 
valent hydrogen atoms, one trivalent nitrogen atom, 
and one tetravalent carbon atom — four atoms in all. 

Let us now proceed to apply these considerations to 
isomerism. A body is discovered having the molecular 
composition CoHgO. Can it have isomers, and if so, 
how many? The answer returned by the valency 
theory is this. If the constituent atoms can be arranged 
in n different ways so that each of the carbon atoms 
never interacts directlv with more than four other 
atoms, and each of the oxygen atoms with more 
than two other atoms, then n isomers, all told, are 
possible. As a matter of fact, it is found on trial 
that the atoms CgHgO can be arranged in only 


two ways, subject to the restrictive conditions just 
stated — 

H— C— 0— C— H H— C— C— 0— H 



H H 


C H 


C C 



H H 

In strict accordance with this result, all attempts to 
prepare more than two isomers of the composition 
OgHgO have failed. The two known substances having 
this formula are methyl ether and ordinary alcohol. 

The problem next rises, which of these formulae are 
we to ascribe to methyl ether ; which to alcohol ? This 
is solved by the knowledge of the fact that one atom 
of hydrogen in the alcohol molecule differs from the 
remaining five in that it alone can be replaced by 
alkali metals. Now, in the left-hand formula all the 
atoms of hydrogen are similarly related to the molecule, 
but in the right-hand formula five atoms of hydrogen 
directly interact with carbon atoms (i.e., are directly 
linked to carbon atoms), while the sixth hydrogen atom 
acts only indirectly on a carbon atom through the 
oxygen atom. Therefore the right-hand formula belongs 
to the molecule of alcohol, and therefore by exclusion 
the left-hand one represents methyl ether. Further, 
the syntheses and all the known transformations of 
methyl ether, and ethyl alcohol, are in strict conformity 
with, and indeed are deducible from, their appropriate 
symbols thus arrived at. 

Although in many cases more isomers ought to exist 


according to the teachings of valency than are at 
present known, ^ yet in no case is a greater number of 
isomers known than is provided for, and anticipated 
by, the valency theory. 

Till within quite recent years this statement could 
not have been made. 

It would seem to follow from the simple case already 
considered, that isomerism ought always to be accom- 
panied by differences in chemical properties, these 
differences finding expression in, and being due to, 
the differing molecular architectures of the isomers. 
Yet bodies are known which, having the same molecular 
weight and the same composition, undergo precisely 
the same chemical transformations, and are yet quite 
different in such physical properties as crystalline form, 
solubility, action on polarised light, &c. Such bodies, 
on account of the identity of their chemical transfor- 
mations, must be assigned identical formulae — identical 
molecular architectures ; and for this reason they were 
for long regarded as forming exceptions to, or at least 
falling outside the pale of the province of the "theory " 
of valenc}^. Hence they were relegated to a kind of 
suspense class, bearing the title physical isomers. 

We now know, thanks to the researches of van't 
Hoff and Le Bel, that these are not exceptional pheno- 
mena, but are fully provided for by the theory of 
valency, if we do not limit the possible different 

^ For instance, nine heptanes having the composition C/Hm, ought 
to exist according to the teachings of valency ; as yet, however, only 
four bodies having this composition have been isolated. 


arrangements of atoms in space by the different arrange- 
ments possible in a plane. 

It is not irrational to assert that two isomers of the 
formula CHgClg should exist. For the formulse — 

H H 

I I 

CI — C — CI CI — C — H 

I I 


while both in accordance with the dictates of valency, 
obviously differ. In the right-hand formula the two 
chlorine atoms are not related to the rest of the mole- 
cule in the same way as they are in the left-hand 
formula. Why should not this difference entail a 
difference in properties — a possible isomerism of the 
molecule CHgClg ? It evidently does not, for all 
attempts to prepare two different bodies of the formula 
CHgClg (and Henry has made many such) have failed. 
We are therefore compelled to still further enlarge 
our conceptions of valency by the conclusion that there 
is really no difference between the above formulge — that 
the order of cyclical arrangement of the atoms round 
the central carbon atom is, in effect, immaterial. Con- 
sequently, no isomeric molecules of the types CHR'3, 
CHR'R"^' CHR'R"R'", 0R'2R"2, CR'gR", CR^R"R"'R", 
should exist. In partial accordance with this con- 
clusion, no isomers of the first five types are known, 
but, contrary to the conclusion, all the simplest of the 
so-called physical isomers conform to the sixth type. 



CR'R"R'"K"' — possess what is called an asymmetric 
carbon atom. 

Van't Hoff and Le Bel showed the way out of this 
difficulty by reminding us that molecules are tri- and 
not di-dimensional entities. 

We get a spatial conception of molecules in accord- 
ance with the limitations of valency, if we conceive the 
carbon atom placed at the centre of a tetrahedron, its 
four "valencies" or "bonds" being directed towards 
the four solid angles a, h, c, 
d, of the tetrahedron. 

So lonof as the monovalent 
atoms or radicles on which 
the carbon atom directly in- 
teracts are not all different, 
then it is impossible to 
place them at the angles a, 
b, c, d, so as to occupy in dif- 
ferent dispositions different 

spatial relations to the central carbon atom. Let A 
stand for one of the disjoositions, and B for another, 
and suppose the two tetrahedra interpenetrative, then 
it will always be possible, no matter the dispositions, so 
to place A inside B, or vice versd, that the similar atoms 
or radicles attached to the central carbon atoms will 
fall together and occupy the same region of space. 
In short, the two dispositions will always be super- 

But when the atoms or groups at the angles a, h, c, d, 
are all different from one another, then it is possible 

Fig. 3. 


to get two dispositions which are uon-siiperposable — 
the one disposition bearing to the other the same rela- 
tion as does an object to its image in a plane mirror ; 
the same relation as a left-hand glove bears to a right- 
hand one. In crystallography this would be called an 
enantiomorphous relationship. In other words, if in 
one molecule the atoms or radicles are regarded as 
disposed around the central carbon atom in a right- 
handed spiral, then in the other molecule the disposition 
is a left-handed spiral. 

Let us illustrate this last case by the lactic acids 
which indeed first suggested to Wislecenus the neces- 
sity of introducing stereometric conceptions into the 
domain of molecular architecture. 

Three lactic acids are known ; they have all practi- 
cally identical chemical properties, but differ from each 
other in their action on polarised light, and in the 
solubilities of their salts. Dextrolactic acid turns the 
plane of polarisation to the right; sarcolactic acid to 
the left; while fermentation lactic acid is optically 
inactive. The molecules of these lactic acids must, from 
their chemical relationships, have the structure 


HOOC — C — H 


The heavily printed carbon atom in the above symbol 
is obviously asymmetric. Therefore there are possible 



two different dispositions around it of the radicles it 
holds in combination, viz. : — 





Fig. 4. 

Fig. 5. 

One of these dispositions must characterise dextrolactic 
acid ; the other, sarcolactic acid. Yet in the present 
state of our knowledge it is impossible to definitely 
allocate them. 

But what of the third lactic acid — the inactive 
modification ? The theory at first sight does not seem 
to provide for it. 

It has now been definitely proved that inactive or 
ordinary lactic acid is not a true chemical unit, but 
a mixture in compensating quantities of the dextro 
and laevo modifications. Its formula would be given 
by placing a plus sign between the above two figures,^ 

Attempts have recently been made to find some con- 

^ For the further development of stereometric ideas we would refer 
the reader to Marsh, Cheniistri/ in Space, and Auwers, Die Enticickeluncf 
der Stercochemie. 

Suffice it here to say that there are no known instances ()f physical 
isomersion of carbon compounds which do not receive full and adequate 
interpretation iu terms of the attributes of the asymmetric carbon atom. 


nection between the masses of the radicles, B,\ W\ R'", 
and R'^, held in combination by an asymmetric carbon 
atom, and the nature and amount of the optical activity 
which, unless compensatory influences come into play, 
is invariably associated with asymmetric carbon atoms. 
A regular tetrahedron has six planes of symmetry ; 
a plane of symmetry bisecting each of the sis inter- 
facial angles of the figure.^ Let us suppose that the 
centre of such a tetrahedron is occupied by a carbon 
atom, and that four atoms or radicles are disposed round 
the carbon atom so that their masses are concentrated 
at the apices of the four solid angles of the tetrahedron. 
So long as these four radicles are not all dissimilar, the 
centre of gravity of the whole system will be ia one 
or other of the six planes of symmetry of the tetra- 
hedron, and there will be no optical activity. But 
when all the radicles or atoms differ among themselves, 
the centre of gravity of the system no longer falls 
within any of the planes of symmetry, and optical 
activity makes its appearance. Let the perpendicular 
distances of the centre of gravity of the system in 
this latter case from the six planes of symmetry be 
d^, d^, d^, d^, d^, and d^. Then the product V = d^ x d^ 
X d^ X d^ X d^ X d^ is, according to Guye, a measure of 

■^ " A plane of symmetry may be defined as a plane which is capable 
of dividing a body into two halves which are related to each other in 
the same way that an object is to its reflection in a mirror. More 
exactly we may say : two objects or two halves of the same object are 
symmetrical with reference to a plane placed between them, when from 
any point of one object a normal to this plane, prolonged by its own 
length on the opposite side of the plane, will meet the corresponding 
point of the other object." — Williams, Elements of Crystallography. 


the asymmetry of the molecule, and should therefore 
be proportional to the optical activity of the substance. 
If plus and minus signs be conventionally applied to the 
distances d-^, d^, d^, &c., according as they are measured 
from one side or the other of each plane of symmetry, 
P may be either positive or negative according to 

Guye has shown how P may be calculated before- 
hand for any meditated derivative of a given optically 
active substance. If the passage from an optically 
active body A to an optically active substitution 
derivative A' would involve an increase in the value 
of P, then, according to Guye, we may predict that 
A' will be more active optically than the parent 
substance ; if the transformation would involve a 
diminution in the value of P, then the new body 
will be less active than the orioinal one from which 
it was derived. Finally, if the passage from A to 
A' is accompanied by a change of sign of P, then 
the parent substance and its derivatives will produce 
opposite rotations ; one will be a dextro-rotatory sub- 
stance, the other a laevo-rotatory substance. 

In the following symbol for active amyl chloride, 

it can readily be shown that „^ 

the centre of gravity of the 
system falls on the CH^Cl \ \ J^fa*^^ 

side of the dotted j^lane of 
symmetry CJS^^mH. If there- 
fore the chlorine atom in the 
CHgCl group be replaced by a heavier atom, the 




centre of gravity of the system must still remain on 
the same side of the plane C^H^mH, but will be 
further removed from it. Accordingly it is found 
that amyl bromide has higher optical activity than 
the chloride ; and amyl iodide in turn higher activity 
than the bromide.^ 

Let us take another illustrative application of Guye's 

In the accomj)anying symbol for dextro-tartaric acid, 

the centre of gravity would 
lie on the CO^H side of the 
dotted plane Hmm'JI. Let 
us now replace the H atoms 
of the hydroxyl groups by 
acetyl radicles (acetyl = 
CH3CO). This substitution 
carries the centre of gravity 
over to the other side of the 
plane Hmm'H ; and it is 
found as a matter of fact 
that diacetyl tartaric acid is 
Now let us form etherial salts of diacetyl tartaric 

■* The values are as follows : — 

[o]d = 1° 6' for the chloride. 
— 4° 24' for the bromide. 
= 8° 20' for the iodide. 

In these equations [ajn may be taken to represent the angle through 
which the plane of a polarised ray of sodium light would be turned if 
it were made to pass through a tube of ^u square centimetre cross 
section, and of just sufficient length to hold exactly one gram of the 
substance under examination. 


Fig. 7. 



acid by replacing the H atoms of the carboxyl groups 
with alkyl monovalent radicles E {e.g., CgHg, C3H7, &c.). 
This brings the centre of gravity of the system back 
towards the COgR side of the plane Hiimi'H, and 
consequently we find that the Isevo-rotatory power 
of the etherial. salt diminishes as the weight of R 
increases, until finally the rotation changes sign and 
the higher etherial salts of diacetyl tartaric acid are 

Diacetyltartaric acid [aj^ = 

- 23-14° 

Methyl-diacetyl-tartarate „ 

- 14-29° 


+ 1-02° 


+ 6-52° 

Although many facts are in harmony with pre- 
dictions founded on Guye's views of the relations 
between optical activity and molecular asymmetry, 



£ 6 


2 5 

Fig. 8. 

Fig. 9. 

yet isolated instances of exceptions to his generalisa- 
tions are not wanting. Thus from the accompauyin<i- 
diagrams it is easy to see that ethyl glycerate (Fig. 9) 


should have higher optical activity than ethyl lactate 
(Fig. 8) ; but as a matter of fact the optical constants 
for these two bodies are as follows : — 

Ethyl lactate [«]„ = - 14-19° 
Ethyl glycerate [«]„ = - 9-18° 

Again, such a body as ethylic diacetyl glycerate 

CHgO . C2H3O 

H . c . o . an.o 


C • OOC2H5 

should be optically inactive if mass were the only factor 
determining optical asymmetry ; for the two isomeric 
radicles OHg . . O2H3O and COOC2H5 have equal 
masses, and when this is the case P must be zero. For 
if a, h, c, d represent the masses of the radicles held in 
combination by an asymmetrical carbon atom in such 
a way that these masses are concentrated at the apices 
of a regular tetrahedron, then one of the factors in 
determining the value of P is — 

{a - b)(a - c) (a - d) (b - r.) (b - d) (c - d) 
{a + h + c + df 

It is clear that if any two of the masses a, h, c, d 
become equal in value, then P — the product of 
asymmetry — must also become zero. When this is the 
case, the optical activity which is supposed to accom- 
pany asymmetry in Guye's sense, should disappear. 
Hence it would appear that in addition to mere mass 


relationships, consideratious of structure must also find 
a place in future attempts to quantitatively link to- 
gether optical activity and molecular asymmetry. 

So far we have only dealt with what were once 
regarded as exceptional isomerisms among saturated 
carbon compounds. We now turn to peculiar cases of 
isomerism presented by unsaturated carbon compounds 
of , ethylenic and acetylenic types, i.e., compounds in 
whose molecules one or more o£ the carbon atoms 
directly acts on less than four other atoms or radicles.^ 
Many of the isomeric bodies of this class, while on 
the whole resembling each other chemically, yet in addi- 
tion to purely physical differences manifest also minor 
chemical contrasts. It is of especial significance that 
the physical differences alluded to do not, as in the 
case of saturated bodies, involve optical activity. 

1 The carbon atoms in ethylene and acetylene are often said to be 
doubly and trebly linked respectively, and the two substances are 
represented as follows — 

H-C-H C-H 

II - 111 

H-C-H C-H 

If I symbolises a certain interaction between a pair of carbon 

C C 

atoms, II and ||| certainly suggest interactions of double and treble 

C C 

intensity ; but Thomsen's thermocheniical studies in this direction, as 
well as the salient chemical characteristics of ethylene and acetylene, 
are at variance with such a state of things. That all the four points of 
maximal attraction ("bonds") of the carbon atom must always be in 
active operation is an unwarranted assumption passed down from the 
early school of constant valency. The intra-molecular movements of 
ethylene may be of such a nature that only the three greatest maxima 
of attraction are able to effectually assert themselves. 


Moreover, these cases of isomerism, unlike the optical 
isomerism just discussed, are not inconsistent with the 
two-dimensional expression of the doctrine of valency. 
As illustrative, let us take the case of the isomerism of 
maleic and fumaric acids. 

These two acids differ in their physical properties as 
follows. While fumaric acid sublimes on being heated, 
maleic acid has a definite melting point, 130° ; and the 
latter acid is much more soluble than the former. 

While the chief reactions ^ of the two acids demand 
in each case the same rational formula, viz. — 

t C . H . COOH 

yet the following minor differences between the two 
acids may be cited. Fumaric acid is more stable than 
maleic, so that reactions which take place with maleic 
acid, under ordinary conditions, require high tempera- 
tures and high pressures in the case of fumaric acid. 
Some reactions, e.g., etherification, proceed in the case 
of both acids under the same conditions, but at a slower 
rate with fumaric than with maleic acid- Maleic acid 
readily yields an anhydride, fumaric acid does not. The 
action of bromine on the two acids gives rise to different 
products; from fumaric acid dibromo succinic acid re- 
sults ; from maleic, iso-dibromosuccinic acid. Another 
peculiarity of these isomers is the readiness with which 
fumaric acid can be changed into maleic acid derivatives, 

^ Both acids are dibasic, and are formed from malic acid by dehydra- 
tion. Reducing agents convert both acids into succinic acid. 


and maleic acid into fumaric acid derivatives. Thus, 
if maleic acid is treated with bromine, and then the 
elements of hydrobromic acid are subsequently removed 
by the action of water, the result is bromofumaric acid. 
Conversely, bromomaleic acid can be obtained by a 
similar series of operations from fumaric acid. 

Enousrh has been said to indicate that we have here 
a much more pronounced kind of isomerism than that 
which the lactic acids presented. Moreover, in this 
case different di-dimensional arrangements of the 
atoms in the complex C2B[2(COOH)2 are consistent 
with the tetravalency of the carbon atom. Hence 
numerous attempts have been made to assign to the 
two acids di-dimensional structural formulae. Such 
structural formulee necessarily involve different radicles 
in the two cases, despite the great chemical similarity 
of the acids. Thus, Anschlitz, while retaining the 

COOH — C — H 
COOH — C — H 

for fumaric acid, advocates 

CH. C(0H)2- 



as best representing the molecular structure of maleic 
acid. But these di-dimensional representations met 




with so little favour generally that the term alio 
isomerism was provisionally introduced to group to- 
gether such apparently inexplicable cases of isomerism 
among unsaturated bodies as are typified by the acids 
under discussion.^ 

When recourse is had to spatial considerations we 
find that all difiiculty disapjoears, and that the reten- 
tion of the term allo-isomerism is needless. For there 
are two, and only two, tri-dimensional arrangements 





Fig. 10. 

Fig. 11. 

of the atom complex C.^HoiGOOH^, in each of which 
essentially the same structural units obtain, i.e., the 
same radicles are involved in each case. These two 
arrangements will be sufficiently obvious from the 
accompanying plane projections. 

So far our conceptions of valency have been purely 

1 There are, however, many who still maintain that the di-dimen- 
sional formulse represent the properties and peculiarities of the two 
acids better than do the accepted tri-dimensional ones. 


statical, but Wislicenus, by introducing dynamical 
ideas, has much extended the original theory of van't 
Hoff and Le Bel. According to Wislicenus, the atoms 
in a molecule exert influences on each other even when, 
according to the teachings of valency, they do not 
diredlij interact, i.e., link each other. The negative 
or chlorous atoms have a great attraction or affinity 
for the positive or basylous atoms, and this attrac- 
tion is either partially satisfied in the molecule 
by the chlorous atoms swinging themselves as near 
as possible to the basylous atoms ; or it may be 
that the attraction only sets up an intra-molecular 
stress which, under favourable conditions of tempera- 
ture, &c., asserts itself, and causes such a rotational 
movement in the molecule that the mean distance 
between the mutually attracting atoms is made as 
small as possible. 

In terms of these views, not only is it possible in 
many cases to assign the appropriate formula to a 
given isomer, but obscure chemical transformations, 
such as the before-mentioned mutual convertibility 
of fumaric and maleic acid derivatives, find a full 
explanation. Indeed Wislicenus' views have raised 
the van't Hoff-Le Bell hypothesis from the level of 
mere co-ordination and explanation of known facts, 
to the higher level of prophecy ; it now not only 
explains, but anticipates facts. For a complete exposi- 
tion of Wislicenus' views we would refer the reader 
to the pamphlet Uher die rdumliche Anordnung der 
Atome in oi^ganischen MoJehulen (Hirzel, Leipzig). 


All we can do here is to exemplify these new views 
very briefly as they bear on the isomerism of maleic 
and fumaric acids. 

The first question to be settled is — Of the two 
formulae, which is to be assigned to fumaric, which 



nil ■ 

Fig. 12. Fig. 13. 

to maleic acid ? The left-hand formula figures a 
more stable system than does the right-hand one, 
for in the former the chlorous carboxyl groups are 
as near as is possible to the basylous hydrogen atoms. 
But fumaric acid is, as we have said, a more stable 
acid than maleic ; hence the left-hand formula sym- 
bolises fumaric acid, and, by exclusion, the right-hand 
formula maleic acid. The constitution of maleic acid 
explains its ready dehydration. The water which 
splits off during the formation of an anhydride from 
an acid is known to result from the hydroxy 1 portions 
of carboxyl groujjs, and it is but natural to assume 



that the proximity in the molecule of these groups 
would favour a reaction in which both are simul- 
taneously implicated. 

Let us now explain by a typical example the rationale 
of the formation of maleic acid derivatives from f umaric 
acid. When bromine and f umaric acid are heated to- 
gether, each molecule of the acid takes up two atoms 
of halogen. This, in terms of stereometric formula?, can 
only take jolace in one way : — 



+ Br2 = 



Fig. 14. 

But the resulting molecule pictured is in a state of 
internal stress by reason of the attractions of the 
strongly positive hydrogen atoms for the strongly 
negative bromine atoms. As a result of this stress, 
an intra-molecular rotation around the axis joining the 
two asymmetric carbon atoms ensues, so as to bring 
the hydrogen atoms into as close proximity as possible 



to the bromine atoms, i Hence, when by the subse- 
quent action of water a molecule of hydrobromic acid 






Fig. 15. 


is removed, the only possible result is bromo-maleic 

' From the phenomena presented by the isomerism of the three 


benzil dioximes, all of which have the formula | Meyer 

and Auwers concluded that carbon atoms may be linked in two ways ; 
cue way admitting of free rotation of the parts of the molecule round 
the joining axis, and another way inconsistent with any rotational 
movement. It has, however, been pointed out, that the exceptional 
isomerisms exhibited by the benzil dioximes might be explained 
without having recourse to the idea of non-rotational, singly linked, 
carbon atoms, by applying stereometric considerations to the nitrogen 
atom — cy., regarding it as occupying one angle of a tetrahedron, its 
three " valencies " or " bonds " being directed towards the other three 
angles. But as yet nothing very definite can be said concerning the 
stereochemistry of the nitrogen atom ; the whole subject has not yet 
emerged from the purely tentative stage. It may here be stated that 
an attempt has quite recently been made to account for the isomerism 
exhibited by amido-platinum compounds of the type PtX^NHsjo (see 


Many substances are known, to each of which it 
seems necessary to assign more than one formula. 
Such substances therefore exhibit a peculiar kind of 
isomerism which has been called tautomerism. Some 
of the reactions of such a tautomeric body suggest 
one structure for it, while other of its reactions seem 
to demand quite another structure. It has been pro- 
posed to call the alternative structures of a tautomeric 
body its desmotropic forms or states. 

Laar, who first drew attention to this form of 
isomerism, is inclined to think that the molecular 
architecture of a tautomeric body is changing from 
moment to moment — that the structure of hydrocyanic 
acid is at one instant 

and at the next instant 


Others, however, are of the opinion that one of the 
structures, being a more stable configuration than the 
other, really represents the body in the free state, 
but that this stable form is under certain conditions, 
and by the action of certain reagents, primarily trans- 
formed into the less stable, pseudo, or lahilc form 
which then undergoes further change. Thus phloro- 
glucone behaves sometimes as a phenol giving metallic 
derivatives and methyl ethers, at other times as a 

note, p. 158), by applying spatial considerations to the platinum atom. 
The latter is regarded as occupying the centre of a regular octahedron, 
at the six solid angles of which are placed the atoms and radicles 
constitutini/ the molecule. 

1 84 


ketone or carboxyl compound giving oximes. The 
formula appertaining to its stable phenolic form, i.e., 
to phloroglucone properly so-called, is 




while its ephemeral labile ketonic form demands the 



In some instances, both desmotropic forms are 
capable of continued and well differentiated existence 
in the free state and even in solution. Thus succino- 
succinic ether exists in both a colourless and a yellow 

It should be remarked that, so far as is known, all 
cases of tautomerism depend on the mobility in the 
molecule of hydrogen atoms ; the passage from one 
desmotropic form to another being effected by the 
wandering of one or more hydrogen atoms. 

These new views may perhaps be adduced to account 


for the curious transformations exhibited by cyanogen 
compounds. Potassium cyanate NCOK prepared from 
cyanic acid NCOH, when treated with ethyl iodide 
O0H5I gives ethyl isocyanate OCNC^Hg, and not ethyl 
cyanate as would naturally be expected. Yet isocyanic 
acid OCNH, the desmotropic form of cyanic acid 
NCOH, is not known in the free state ; the ethyl 
radicle is required to confer stability on the apparently 
extremely labile configuration OCNH. 

Similar considerations may be applied in explanation 
of the behaviour of cyanuric and thiocyanic acids. 



Although the occurrence of chemical interaction 
between solutions of sodium sulphate and hydrochloric 
acid is not manifest to the unaided senses by reason of 
the fact that all the factors and products of the inter- 
action are soluble colourless bodies, yet we have con- 
vincing indirect proofs that such an interaction does 
actually take place.^ Moreover, the evidence in favour 
of the occurrence of chemical change between solutions 
of sodium sulphate and hydrochloric acid is of such a 
nature that we are forced to conclude that the interac- 
tion is not correctly represented by the equation 

Na^SO^Aq + 2HClAq = 2]SraCl Aq + H^SO^Aq. 

For, by convention, this equation when interpreted 
into words would run : — Dilute solutions of sodium 

1 As dissociation phenomena are generally fully treated in elementary 
text-books, this chapter has been almost wholly devoted to a study 
of those equilibria which are established in solutions of chemically 
interacting substances at ordinary temperatures. 

" See note, p. 193. It is very easy to prove the occurrence of 
chemical change in the particular system MgS04Aq + 2NaClAq, 
although the interaction is not accompanied by visible changes under 
ordinary conditions. It is only necessary to cool a mixture of the solu- 
tions of the two salts, when the very slightly soluble sodium sulphate 

will partially crystallise out in a hydrated form. 



sulphate and hydrochloric acid when brought together 
in equivalent quantities^ completely decompose each 
other with the formation of equivalent quantities of 
sodium chloride and sulphuric acid which both remain 
in solution. 

Now, as a matter of fact, such a complete decomposi- 
tion of the sodium sulphate and hydrochloric acid does 
not take place under the specified conditions (dilute 
solution, and equivalent quantities of the reagents). 
Only a portion of the system Na.,SO^ + 2HC1 + Aq is 
changed into the system 2NaCl + H.^SO^ + Aq. This 
fact might be adequately represented in the following 
manner — 

{m + n) ]S'a.2S04Aq + {m + n) H^d.^Aq = m ISTagCloAq + 
m H2S0j,Aq + n ISTa^SO^Aq + n H^CloAq 

From this representation we learn that when {m + n) 

^ Those quantities of acids which neutralise a fixed quantity of 
any base are equivalent. Conversely those quantities of bases which 
neutralise a fixed quantity of any acid are equivalent. This was the 
original and most obvious meaning of equivalencj', but the original 
meaning of the term has been widened so that it nuw applies to salts 
as well as to acids and bases. A quantity, x grs., of a salt (MA) is 
said to be equivalent to a quantity y grs. of an acid A', if the quantity 
of acid A necessary to produce x grs. of the salt MA is equivalent in 
the original acceptation of the word to y grs. of the acid A'. Thus the 
molecular weight of sodium sulphate interpreted in grams [1413 grs.] is 
formed from the molecular weight in grams [98 grs.] of sulphuric acid. 
But 98 grs. of sulphuric acid is equivalent to, i.e., will neutralise the 
same quantity of any base as, 73 grs. of hydrochloric acid or two molecu- 
lar weights of hydrochloric acid expressed in grams. Therefore in 
accordance with the widened significance of the term equivalence now 
in vogue, 2HC1, H0SO4, Na-2S04 represent equivalent ([uantities of the 
substances formulated no matter what mass units be used. 


equivalents of sodium sulphate are brought together 
with an equal number of equivalents of hydrochloric acid 
in dilute aqueous solution, only m equivalents of the 
two substances undergo chemical change, the residual 
n equivalents of each substance remaining unchanged. 
But this is not a perfectly satisfactory method of repre- 
sentation, for this reason. It suggests that the mole- 
cules of each of the reacting substances must differ in 
some way or other among themselves, seeing that some 
enter into chemical reaction under the conditions, while 
others apparently do not. And this is not in con- 
formity with the fundamental principle of the atomic- 
molecular theory, which principle asserts that the 
molecules of a substance are all precise replicas one 
of another, both in structure and attributes. If one 
molecule of sodium sulphate reacts under certain con- 
ditions, then we should expect all the molecules of 
sodium sulphate to react under these conditions. 

The difficulty disapj)ears at once if we regard re- 
actions like the one under consideration as the result of 
two independent and antagonistic chemical changes 
proceeding simultaneously within the system.^ 

When hydrochloric acid is added to an equivalent 
quantity of sodium sulphate in dilute aqueous solution, 

^ That two or more reactions can proceed within a system simul- 
taneously and independently one of another is the enunciation of the 
principle of the coexistence of reactions — a principle which bears much 
the same relation to chemistry as does Newton's second law of motion 
to dynamics. This principle has never been dh'cctly proved ; but 
reasoning founded on the assumption of such mutual independence of 
reactions has led to results in harmony with experimental fact, and 
thus the truth of the principle is established. 


molecules of sodium chloride and sulphuric acid are 
formed at a gradually diminishing velocity as time goes 
on.^ The new molecules thus formed do not, however, 
remain inert, but interact to reproduce molecules of the 
original substances at a gradually increasing velocity. 
Let us call the passage from Na2S0^Aq + HgClgAq to 
Na.,CloAq + HoSO^Aq the direct partial change, and 
the passage in the opposite direction the reverse partial 

What causes the velocities of the two changes thus 
defined to vary from moment to moment ? Guldberg 
and Waage first definitely answered this question, by as- 
serting that the velocity of every change at any moment 
varies directly as the product of the number of the 
equivalents of the factors of the change present in unit 
volume of the medium of change. As this number is 
continually varying, owing to the occurrence of change, 
it follows that the velocity must also continually vary. 

^ No chemical change is instantaneous, but every change requires for 
its occurrence a period of time varying from a fraction of a second too 
small to measure, to several years. The reactions between various acids 
and alkalis {i.e., neutralisation) take place in so short a time that it has 
not been possible to measure their absolute durations. Estimates of 
their relative durations have, however, been indirectly obtained. On 
the other hand, many of the reactions between organic bodies proceed 
very slowly indeed. Witness in this connection the slowness of the 
chemical changes occurring in the so-called ageing of wine. The use 
of the word velocity in connection with chemical reactions as introduced 
by Wenzel in 1777 demands explanation. The original dynamical 
meaning of the term is space passed over per unit time. But the idea 
of space does not enter into the definition of the term in its chemical 
acceptation. The velocity of a chemical reaction at any moment 
simply denotes the quantity of substance (expressed in equivalents) that 
undergoes change per unit of time at that moment. 


Suppose the two substances A and B combine com- 
pletely to form a third body C. Let us bring together 
solutions of A and B, such that 2^9 equivalents of A 
and 2^' equivalents of B are contained in unit volume 
of the resulting solution. Then the velocity, V, of the 
reaction {i.e., the rate at which C is formed) will vary as 
2p X 2q. Or stated algebraically — 

Voo 4pg 
V = 4Kpg. 

Where K is a constant called the velocity constant for 
the change.^ After a certain time there will be left only 
23 equivalents of A, and q equivalents of B in unit 
volume of the medium of change. The velocity of 
formation of at this epoch, according to Guldberg 
and Waage, would be 'Kpq — only f th its original value. 
The principle here illustrated is often referred to as 
Guldberg and Waage's law of mass action.^ 

To return now to the interaction of hydrochloric 
acid and sodium sulphate. The number of equivalents 

1 The velocity constant K must be carefully distinguished from the 
velocity V. Under given conditions K is constant for any given change, 
but V of course varies from moment to moment. 

'^ The first to prove the influence of mass in chemical changes was 
Wenzel, 1777. Wenzel, however, confined his investigations to a single 
class of changes, viz., the interaction of metals with acids of various 
strengths. In the beginning of this century, Berthollet asserted the 
influence of mass in chemical changes in general terms. "Every 
chemical change is essentially of the nature of a combination, and the 
power of any substance to enter into combination is proportional to its 
affinity and to its mass." This is practically the text of Berthollet's 
famous work, Ussai de Statique Chimique. According to Berthollet, a 
small affinity can be compensated by a large mass, and hence complete 
reactions are the exception and not the rule in chemistry. Suppose 


expressed in grams or otherwise (i.e., the masses) of 
NaCl and HgSO^ resulting from the direct change 
depends not only on the velocity constant peculiar to 
the change, but also on the numbers of the equiva- 
lents (i.e., the masses) of HCl and Na^SO^ in unit 
volume of the solution. As these latter numbers are 
continually decreasing, the velocity of the direct partial 
change must continually decrease from a maximum value 
downwards. But as the numbers of the equivalents 
per unit volume of the factors of the direct partial 
change decrease, the numbers of the equivalents of 
the factors of the inverse partial change ^:)art passu 
increase, consequently the velocity of this change is 
continually increasing from zero upwards. Hence it 
necessarily follows that a state of what has been 
called mobile equilibrium between the direct and re- 
verse partial changes must finally be reached, whereat 
the velocities of the two changes being exactly equal, 

the body C has a stronger affinity for A than has B. Then if C be 
added to AB in equivalent quantity, the reaction 

AB + C = AC + B 

will proceed, but not to completion, for the gradually increasing mass 
of B will eventually compensate its smaller affinity, and make it for- 
midable enough to contest successfully the diminishing quantities of C 
Before Berthollet's time it had been held that reactions are determined 
entirely by the stronger affinities ; to which view the idea of incomplete 
reactions was quite foreign. From his fundamental premiss, however, 
Berthollet made deductions which Proust proved to be incorrect (see 
p. 74), and this overthrow of the incorrect deductions unfortunately 
brought the correct premiss from which they were derived into dis- 
repute and temporary oblivion. Guldberg and Waage's law of mass 
action is nothing else than Berthollet's views reinstated and thrown 
into mathematically exact form. 


effective chemical change one way or the other ceases. 
When this permanent equilibrium point is arrived 
at, as many equivalents of HCl and Na^SO^ are de- 
composed by the direct partial change per vmit time 
as are formed by the reverse partial change in the 
same time unit ; but the molecules of NagSO^, HOI, 
HNO3, and NaCl existing at one epoch are not 
necessarily the same ones which will be present at 
another subsequent epoch. If they do chance to be 
identically the same molecules at the two epochs, we 
can assert that they have not had a continued exist- 
ence in the interim. 

In the representation of these so-called incomplete 
reactions, wherein a state of equilibrium is finally 
reached, van't Hoff has proj)Osed to replace the sign 
of equality in the ordinary equations by a pair of 
oppositely directed arrows, thus — 

H2Cl2Aq + NaoSO^Aq t^ Na^Cl^Aq + H^SO^Aq. 

Now, thoroughly appreciating the nature of the 
dynamical equilibrium which marks the cessation, not 
of chemical change, but of effective chemical change, 
in these incomplete reactions, we will return to that 
method of their representation which we first gave, 
and which for the immediate purpose in hand is more 
convenient than the one proposed by van't Hoff, 

Let us suppose that in the general equation 

{m + w)Na2S04Aq + (m + 11)11^01 ^A.(i = mNagClaAq + 
mHoS04Aq + ?^NaoS04Aq + wHoClgAq 

m -)- n equals 100. The question arises, what are the 


individual values of m and n ? This question has been 
submitted to experiment, and it has been ascertained 
that irv and n in the above reaction have the approxi- 
mate values 66f and 33|- respectively.^ Moreover, 
exactly the same state of final equilibrium is arrived 
at if, instead of setting out with hydrochloric acid and 
sodium sulphate, we start with hydrochloric acid and 
the proximate constituents of sodium sulphate, viz., 
caustic soda and sulphuric acid, in accordance with 
the following equation — 

{yn + n) NuoO^HgAq + {in + n) HgSO^Aq + {m + n) 
HaClgAq = m NagCl^Aq + m HgSO^Aq + n jS^a2S04Aq 
+ 7iH,CloAq. 

This latter method of regarding the reacting system 
emphasises the fact that the reaction virtually consists 
in a strife between two equivalent quantities of acids 
to appropriate a quantity of base only just sufficient 
to neutralise either acid separately. As a result of 
this competition the base divides itself between the 
two acids, twice as much base (i.e., 66f equivalents) 
combining with the hydrochloric acid as combines with 
the sulphuric acid (3 3 J equivalents). 

In accordance with the results o.f such investigations 
as the one just described, acids are classed as weak or 
strong. When two acids in equivalent quantities and 

^ For the actual carrying out of metliods suited to the investigation 
of equilibria see Muir and Carnegie's Practical Chemistry, pp. 141-146, 




in dilute aqueous solution are presented to a dilute 
aqueous solution of a quantity of base just sufficient 
to neutralise either acid separately (or what amounts to 
the same thing, when an acid is allowed to react with 
an equivalent quantity of the salt of another acid in 
dilute aqueous solution) the base is in general divided 
between the two acids, and the strengths (or affinities, 
or avidities) of the two acids are proportionate to the 
quantities of base each appropriates. Thus it follows 
that sulphuric acid is a weaker acid than hydrochloric, 
the latter acid being approximately twice as strong as 
the former. By conducting numerous quantitative ex- 
periments, involving different pairs of acids, we can 
obtain a table of the relative affinities or strengths of 
the acids, such as the following one, in which, however, 
the values assigned the various acids are admittedly 
only approximate : — 

Nitric acid 

. 1-00 

Hydrochloric acid 

. 1-00 

Hydrobromic acid 

. -89 

Hydriodic acid . 

. -70 

Sulphuric acid . 

. -49 

Selenic acid 

. -45 

Trichloracetic acid 

. -36 

Orthopho.splioric acid 


Oxalic acid 


Hydrofluoric acid 


Citric acid 


Acetic acid 


Boric acid .... 


Silicic acid 

. -00 



As will be seen nitric and hydrochloric acids are the 
two strongest acids, being approximately equal in 
strength. Compared with either of these, acetic acid 
is seen to be a very feeble one. If equivalent quan- 
tities of hydrochloric acid and acetic acid were added 
to a dilute aqueous solution of caustic soda, contain- 
ing just enough caustic soda to neutralise either acid 
separately, the caustic soda would divide itself between 
the hydrochloric and acetic acids in the ratio of 1 : 03, 
i.e., about 2'91 per cent, of the soda would combine with 
the acetic acid and 97 "09 per cent, with the hydrochloric 
acid. In a precisely similar way bases have been classed 
as weak or strong. Of a pair of bases presented in 
dilute aqueous solution to an acid only just sufficient 
to neutralise either base separately, that base wliich 
appropriates, or combines with, the greater part of the 
acid is the stronger base. The following table gives 
the relative strengths of a few of the better investi- 
gated bases in terms of the arbitrary value unity 
assigned to the strongest base, lithium hydroxide : — 

Lithium hj'droxide 
Sodium hydroxide 
Potassium hydroxide 
Thallium hydroxide 
Piperidin . 
Ammonia . 



We have seen that hydrochloric acid is approximately 
twice as strong as sulphuric acid if the criterion be a 
tug-of-war for a quantity of soda insufficient to meet 


the conjoint demands of the two acids. It has been 
found that approximately the same relation holds 
between the strengths of the two acids whatever base 
be made the object of competition, whether potash, or 
soda, or lime, &c. Moreover, as is well known, acids 
have the power of inverting cane sugar, that is, of 
transforming it in the presence of water into a mixture 
of dextrose and Isevulose ; and also in this transforma- 
tion hydrochloric acid is found to act twice as ener- 
getically as sulphuric acid. Numerous other reactions 
might be adduced which are either brought about or 
accelerated by acids, and in all of them hydrochloric 
acid is approximately twice as effective as sulphuric 

Similar remarks apply to changes induced or acceler- 
ated by bases. If lithium hydroxide is fifty times as 
strong as ammonia when the struggle for a particular 
acid is the criterion, then it is found to be approxi- 
mately fifty times as effective as ammonia in bringing 
about any other change demanding the intervention of 
a basic substance. 

On the basis of the approximately concordant results 
for the strengths of acids and bases derived from the 
investigation of such diverse changes as we have hinted, 
it was at one time claimed that the values thus assigned 
to the acids and bases as representing their strengths, 
could they be freed from all experimental error, would 
be perfectly characteristic numbers for the respective 
acids and bases, quantitatively conditioning all the 
reactions brought about by them. In pursuance of 


these views, it was proposed to give the generic name 
of specific afinity constants to the numbers represent- 
ing the strengths of the acids and bases. 

On fuller investigation, however, it appeared that 
neither the claim nor the proposal could be admitted ; 
for the partition of a base between two acids depends 
not only on the nature of the contending acids, but 
also on the quantity of . water present. A table of 
strengfths or affinities constructed from the results of 
experiments on the partition of a base between acids 
in normal solution,^ does not present the acids in 
the same order as a table founded on the results of 
investigations of deci-normal acid solutions. In other 
words, water cannot be regarded as a merely passive 
medium when the power of acids is in question ; " the 
power of an acid to do " is a function of the state of 
dilution of the acid. For instance, in the system acid 
A, acid A', 'base, water, we have not merely a tug-of- 
war of the two acids A and A' for the base, but the 
final equilibrium is the expression of the resultant of 
(1) the " affinity " of A for water, (2) the " affinity " 
of A' for water, (3) the " affinity " of the base for 
water, (4) the " affinity " of A for the base, and 
(5) the "affinity" of A' for the base; and in con- 

1 Let the numerical value of the quotient — 
molecular weight of acid 

number of replaceable H atoms in molecule 

be called n. Then a normal solution of an acid contains n grams of 
the pure acid per litre of solution at a specified temperature. A deci- 
normal solution has ^^th the concentration of a normal one. 


formity with the law of mass action, every alteration 
in the quantity of water present necessarily alters 
the final distribution of matter marking the state of 
equilibrium from which the strengths of the acids are 

Quite recently, however, it has been found possible 
to obtain for the acids characteristic numbers which 
are independent of their greater or less dilution, and 
of the particular reactions in which the acids may 
be implicated. These numbers are now regarded as 
the true affinity constants of the acids, but they 
necessarily have quite a different significance from the 
old system of supposed constants derived from the 
study of the partition of acids between bases, &c., 
seeing that they are independent of dilution. 

When an acid is dissolved in a large quantity of 
water, it behaves in many respects as if it were (and 
is accordingly by some believed to be) partially decom- 
posed into its ions (see note, p. 153). Thus a dilute 
solution of hydrochloric acid behaves as if it contained, 
in addition to molecules of HCl, ions of hydrogen and 
chlorine. If at a certain dilution K the number of 
undecomposed molecules is just equal to the number 
decomposed into ions, then K is taken as a measure of 
the true specific affinity constant of the acid. 

The investigation of affinity in accordance with these 
conceptions has as yet been chiefly confined to organic 
acids, and it is found that the order of the acids in a 
table of affinities, according to the new definition of 
affinity, is practically the same as the average order in 


the old tables of supposed affinity constants which 
were derived from the results of "different reactions 
brought about by acids of varying concentration.^ 

We have seen (page 57) that certain phenomena 
exhibited by fairly strong aqueous solutions point to 
definite combinations between water molecules and 
molecules of dissolved substance, i.e., to the existence 
in solutions of definite liquid hydrates. It is supposed 
that these liquid hydrates are very unstable bodies 
which at ordinary temperatures are partially dis- 
sociated,- the original hydrates forming with the 
products of their dissociations mobile equilibria as 
represented in the following equations : — 

m (A?^ HoO) ^^ 7nn H^O + m A 

m' {An' H^O) :;^ m'n' H^,0 + m' A &c., 

where (m + ni + &c.) A represents the salt dissolved 
in 77in — m'n = &c. molecules of water. The inter- 
pretation of the above symbolism is that in a solution 
of A of determined concentration, the hydrates A'/iH.,0, 
A7i'H20 &c. are present, but that these hydrates 

^ In the algebraical expression through which the desired affinity 
constants are obtained from the results of experiment, there is an 
inherent weakness which makes itself especially felt in the case of 
the stronger inorganic acids. For further details on the subject 
of affinity constants the reader is referred to the Lehrbuch der AUge- 
mcincn Chcmie of Ostwald, to whom we owe much of the best work 
that has been done in the direction of raising affinity to a quantitative 

- A dissociation is a reversible decomposition. When KCIO3 is 
heated it decomposes into KCl and 30, for these two substances do not 
recombine on cooling to reform potassium chlorate. When PCI-, is 
heated, it dissociates into PCl:j and Clo, because these two gases as 
they cool in contact combine together completely to reform PCI5. 


partially dissociate into anhydrous salt,^ (??iA, m'A. &c.) 
and water (iniiR.^O, m'n'R^O &c.) till mobile equilibria 
are established for each system, i.e., until in each system 
as many molecules of the hydrate are dissociated as are 
reformed per unit of time. As the concentration of 
the solution is varied, the ratios in which the various 
dissociating hydrates are present also varies, and at 
certain stages in the concentration new dissociating 
hydrate systems would make their appearance, while 
pre-existing systems would disappear. According to 
the views here illustrated, solutions have been defined 
as " fluid and unstable, but definite chemical compounds 
in a state of dissociation." 

All the incomplete reactions we have already con- 
sidered have been homogeneous,^ but homogeneity in 

' Or it may be, into a hydrate of lower hydration in accordance 
with the equation 

m (A n H.O) •^m(^A'^H.o\ + ( mn - ''^ \ HoO, 

where m, n, and x are integers. 

- When all the products and factors of a reaction are in the same 
physical state (same state of aggregation), the reaction is said to be 
homogeneous. The following are examples of homogeneous reactions : — 

Cl.> + Ho = 2HC1. NaCl Aq + KNOgAq t^. KCl Aq + NaNOg Aq. 

^ '■ 

gases. solutions. 

Fe + S = FeS. 


The combination of gaseous SOo with solid PbO^ to form solid 
PbS04 is illustrative of non-homogeneous reactions. The significance 
of the terms homogeneous and non-homogeneous used in connection 
with reactions or systems must be carefully distinguished from the 
significance of the same terms when used, as in Chap. III., in con- 
nection with substances. 


this sense is not an essential condition of incomplete 
reaction. The very familiar reaction between solutions 
of common salt and silver nitrate is not correctly repre- 
sented in the equation 

AgNOgAq + Is^aCl Aq = AgCl + NaXO.Aq, 

for when effective chemical change between strictly 
equivalent quantities of AgNOg and NaCl has ceased, 
it is easy to prove the presence in the non-homogeneous 
system of traces of undecomposed AgNOg and NaCl. 
In other words, a condition of equilibrium finally 
supervenes, the equilibrium in this case, however, being 
so much in favour of the direct partial change, that 
unless for very accurate work, the decomposition of 
AgNOg by an equivalent quantity of NaCl may be 
regarded as practically complete. 

The interaction of steam and heated iron is another 
familiar instance of an incomplete reaction taking place 
in a non-homogeneous system. 

3Fe + 4H2O -^ FegO^ + 4H, 
(solid) (gas) (solid) (gas) 

The sole condition for incompleteness of reaction 
between equivalent quantities of interacting substances 
resulting in mobile equilibria is that the products of 
the change must be of such a nature that they are all 
retained within the sphere of action of the system 
considered.^ If by any means removal from the sphere 

^ It follows that the salts in solution in mineral waters, &e. , nmst 
constitute very complicated dynamic equilibria. The schemes in which 
analysts are wont to express tiie results of their analyses are mislead- 


of action of one or more of the products of the change 
is effected, the reaction proceeds to completion. Thus, 
if in the interaction of steam and heated iron it were 
possible to allow the hydrogen to escape as soon as 
formed, without at the same time permitting any steam 
to escape, then three atoms of iron would completely 
decompose four molecules of steam. One of the factors 
necessary to the reverse partial change being removed, 
that change cannot take place, and the direct partial 
change meeting with no opposition proceeds to comple- 
tion. To take another instance actually realised by 
Berthelot and St. Gilles. When benzoic acid and 
alcohol are brought together they slowly interact with 
the production of benzoic ether (ethyl benzoate) and 
water, which in turn simultaneously interact, reforming 
the original factors of the change. 

C,,H5C00H + C2H5OH t^ CeH^COOC^Hg + HgO. 

Under ordinary conditions effective chemical change 
ceases when about 66 per cent, of the benzoic acid and 
alcohol have been transformed into benzoic ether. But 
when the water resulting from the change is removed 
from the sphere of action, the whole of the benzoic acid 
and alcohol is forthwith etherified. This removal of 
the water from the sphere of action is effected by the 
addition of barium oxide to the system. As soon as 

ing. The bases in a homogeneous system can be accurately determined 
and also the acids, but it is impossible from the results of the quanti- 
tative analysis only to apportion the acids to the bases so as to represent 
the actually existing constitution of the system. 


any water is formed it combines with the oxide forming 
inert barium hydroxide. 

It is to be noted that the same state of equili- 
brium is reached whether we set out with the system 
C^H^COOH + C.H^OH or with the system C^jH^COOaHg 
+ H.^O. In the former case effective change proceeds 
till 6Q per cent, of the benzoic acid and alcohol have 
been transformed into benzoic ether and water; in the 
latter case effective change proceeds until 66 per cent, 
of the ether and water remain undecomposed. This 
is a perfectly general characteristic of these mobile 
equilibria. Eepresenting incomplete reactions by the 
general equation 

AB + A'B' :; A'B + AB' 

' 00 (2) 

we may say that in all cases the distribution of 
matter which obtains when equiUbrium is established 
is independent of whether the point of departure be 
made the system (1) or (2). In a few particular cases 
this statement admits of very simple proof. For 
instance, a mixture of equivalent quantities of KClAq 
and NaNOgAq gives exactly the diffusate as a mixture 
of equivalent quantities of KNOgAq and NaClAq, 
showing that in both cases the same equilibriated 

xIs^aClAq + ^t-Km^Aq + (1 - a;) KClAq + 
(1 - ./^NaXOgAq 

is undergoing dialysis. 


Another method of rendering an incomplete reaction 
practically complete as regards some one or more of 
the members constituting the system will at once be 
evident on referring to Guldberg and Waage's law of 
mass action. This method consists in largely increas- 
ing the mass of one of the factors of the change rela- 
tively to the other. Thus, if in the etherification of 
alcohol by benzoic acid we largely increase the number 
of equivalents of alcohol relatively to the number of 
equivalents of benzoic acid, or vice versd, then, in either 
case, we approach indefinitely close to a state of com- 
plete etherification of the acid on the one hand, or the 
alcohol on the other. 

It is in virtue of the action of mass that we are 
able to completely convert NaOl into NaNOg by means 
of HNOgAq, or conversely to change NaNOg into NaCl 
by means of HClAq. When NaCl, for instance, is 
treated with HNOgAq a partial change takes place, and 
NaCl, HCl, NaNOg, and HNO3 are all present. If the 
system be now heated, the free acids owing to their 
volatilities pass away, leaving non-volatile NaCl mixed 
with a little non-volatile NaNOg. If more HNOgAq is 
added to this residue, and the system again heated, a 
second residue richer in NaNOg will result ; and so 
by repeating the operations of adding HNOgAq and 
evaporating often enough (i.e., by using a large enough 
relative mass of HNO3), the NaCl can be completely 
changed into NaNOg. The case of the converse trans- 
formation of NaNOg into NaCl by means of a large 
excess of HCl is quite similar. 


In the light of the facts just treated, a reference to 
the remarks made on solution both in this chapter and 
in Chapter III. leads us into difficulties. 

If a substance in solution be largely diluted, i.e., if 
the relative mass of water be largely increased, we 
should expect, in accordance with what precedes, that 
the excess of water would lead to a great increase in 
the amounts and stabilities of the higher hydrates of 
the dissolved substance. But those who have experi- 
mented most with very dilute solutions, find that their 
.results are best summarised in terms of the hypothesis 
that hydrates do not exist at all in dilute solutions. 
It appears as if the increased dilution not only breaks 
up the molecular complexes of water molecules and 
salt molecules constituting the hydrates, but actually 
destroys the integrity of the salt molecules themselves, 
resolving these into their ions.i For the present, until 
more light is shed on the vexed question of solution, 
we must be content to remember that tliis difficultv 
exists without attempting to decide it one way or the 

The question now arises for discussion, are all re- 
actions between equivalent quantities of mutually 
interacting bodies incomplete ? May not one or more 
of the products of certain changes be of such a nature 

' See note, p. 153. An ion may consist of a group of atoms, e.g., 
SO4, or of a single atom, c.(j., Na. In the latter case the ion and the 
atom are supposed not to be identical. For the present it is customary 
to attribute the assumed difference between them to the possession by 
the ion of a certain charge of electricity proportional to the valency of 
the atom. 


that they are removed from the system's sphere of 
action as quickly as they are formed, in virtue of their 
own peculiar jDroperties ? Changes giving rise to 
bodies with such properties, would proceed to comple- 
tion even although their factors were brought together 
in strictly equivalent quantities. 

Stas has shown that AgBr is not acted on at all by 
a solution of NaNO^, or that if there be any action it 
is too slight to be detected by the analytic means at 
our disposal. Hence it follows that the reaction between 
AgNOgAq and NaBrAc[ is, so far as we can tell, a 
complete one, and that the equation — 

AglSTOgAq + NaBrAq = AgBr 4- NaNOgAq 

is experimentally realised. 

There are many well-known reactions, such as that 
between HgSO^Aq and BaC^Aq, viz., 

HgSO^Aq + BaCl^Aq = BaSO^ + 2HClAq, 

which are for practical purposes regarded as complete, 
but which, as a matter of fact, are incomplete reactions 
in which the distribution of matter marking the attain- 
ment of equilibrium is overwhelmingly in favour of the 
direct partial change. The BaSO^, formed in the above 
reaction, is slightly soluble in (i.e., interacts with) 
dilute solutions of HCl, and, in virtue of this slight 
solubility, there is a reverse partial change, which is 
the condition for incompleteness of reaction and the 
establishment of an equilibrium. But the reverse 
partial change in this case is of very small moment. 


The subject of neutralisation calls for a word or two 
here. Those particular and important branches of 
volumetric analysis known as alkalimetry and acidi- 
metry are founded on the assumption of the absolute 
truth of such equations as — 

H^SO^Aq + 2NH40HAq = (NH4)2S04Aq + 2H2O 
HClAq f NaOHAq = NaClAq + H,0. 

That is to say, these reactions are regarded as complete 
although there is evidently no removal from the sphere 
of action, artificial or otherwise, of the products of the 
neutralisations of equivalent quantities of acids and 
bases. Here, again, it is probable that we have in- 
stances of incomplete reactions in which the reverse 
partial change is so insignificant as to be negligible. 
That ammonium sulphate is slightly decomposed by 
water with the formation of free acid and ammonia is 
probable from the fact that air when passed through 
solutions of (NH4)2SO^ acquires alkaline properties — 
the solutions themselves meanwhile developing acid 
characters. This behaviour of ammonium sulphate 
solution has been adduced to explain the completeness 
of the interaction of equivalent quantities of ammo- 
nium sulphate (NH^)2S0^Aq and potassium carbonate 
K.jCOg Aq. Seeing that both the factors of this inter- 
action, and all the possible products formed by double 
decomposition, are soluble in water and therefore remain 
within the sphere of action, one would be inclined, 
off-hand, to class this particular change with the in- 
complete reactions. 


According to Berthelot the completeness of the inter- 
action finds an explanation in terms of the partial 
decomposition of one of the interacting factors. The 
ammonium sulphate and water may be regarded as 
giving rise to some such equilibrium as is represented 
in the following equation — 

(NH4)2S04Aq + 2H20Aq 1; 2NH,0HAq + HoSO^Aq. 

The potassium carbonate destroys this equilibrium by 
neutralising (and so removing from the sphere of action) 
the free sulphuric acid present at any moment ; more 
ammonium salt reacts with water in the tendency to 
again establish the primitive equilibrium, and so the 
cycle repeats itself until practically the whole of the 
ammonium sulphate is decomposed. 

The experimental investigation of the possibility of 
the establishment of equilibria in the cases of reactions 
evolving gases (which under ordinary circumstances 
escape from the sphere of action) is a very difficult 
matter. A definite answer has as yet not been furnished 
to the question, is the equation 

Zn + H^SO^Aq 1; ZnSO^Aq + K,, 

a correct representation of facts, provided the hydrogen 
evolved is prevented from leaving the system — would 
the reaction under such conditions be found to be 
actually incomplete ? In the meantime one has little 
hesitation in giving a theoretical answer in the affirma- 
tive to such a question. 

The existence of such equilibria as we have been 


discussing disproves a principle which was enunciated 
by Thomsen in 1854?, and again in 1864 by Berthelot. 
The latter naturalist has done so much work in the 
attempt to establish the principle on an experimental 
basis that it is now generally referred to as Berthelot's 
Imv of maximum work, although priority in the matter 
undoubtedly belongs to Thomsen.^ Berthelot enunci- 
ated his " law " in the following terms : — 

Every chemical change realised without the intervention 
of external energy tends to the formation of that hody or 
system of bodies, the production of which is accompanied 
by the development of the greatest quantity of heat. 

This statement, which simply asserts that every 
chemical reaction tends to make the system assume 
that state, in the attainment of which it liberates most 
heat, further implied to Berthelot the necessity for the 
occurrence of every transformation that would involve 
an evolution of heat, and the impossibility of the 
spontaneous occurrence of every transformation that 
would involve an absorption of heat."^ And it is this 

^ Berthelot called his principle the "Law of maximum work," from 
its analogy to a well-established principle in mechanical energetics. 
If a raised stone be allowed to fall, it falls vertically to the earth's 
surface, and never in a direction inclined to the plumb line. The 
vertical direction is the one in which occurs a maximum change of 
potential into kinetic energy per unit time. This is an instance 
illustrating the so-called maximum principle which asserts that of all 
possible changes that one will take place which involves the greatest 
transformation of energy per unit time. (Throughout the remainder 
of this chapter it is assumed that the reader has an elementary know- 
ledge of general energetics.) 

- As a corollary to this "law," Berthelot stated his theorem of the 
necessity for reactions as follows : — " Every chemical change which 


practical aspect of the " law " that has chiefly appealed 
to, and engaged the attention of, chemists generally. 

Suppose we have a substance quantitatively repre- 
sented by AB, and we wish to know whether it will 
interact with a third body quantitatively represented 
by C to form either the bodies AC + B or the bodies 
BO + A. We may provisionally regard such an inter- 
action as taking place in two consecutive stages ; in 
the first stage AB is decomposed into A and B, and 
then in the second stage A combines with B or C, as 
the case may be. If A and B combine together to 
form AB with the evolution of a quantity of heat 
energy h, we know that exactly the same quantity of 
energy h must be added in order to reverse the change 
and resolve AB into A and B.^ Suppose that the 
combination of A and C gives rise to an evolution of 
heat energy represented by H, and that the combina- 
tion of B and C is attended by an evolution of heat H'. 

can be accomplished without the aid of a preliminary action or the 
addition of energy from without the system, necessarily occurs if it is 
accompanied by disengagement of heat." This theorem seems to have 
been generally applied without regard to the significance of the some- 
what indefinite qualifications " which can be accomplished . . . from 
without the system." 

1 The principle, that the quantity of heat energy absorbed in de- 
composing a given mass of a compound into its elements is exactly 
equal to the heat energy evolved when the elements combine to form 
the siven mass of the compound, was first given by Lavoisier and 
Laplace. This principle, which is a necessary consequence of the 
more general principle of the conservation of energy, is also true for 
chemical changes other than mere synthesis and analysis. If the 
passage of a complex system from any state A to any other state B, 
by any path whatsoever, absorbs a quantity of heat energy H, then 
the reverse passage from B to A by any path will be attended with 
the evolution of H heat units. 


The following cases must be considered : — 
(1.) H and H' may both be less than li, in which 
event the " law," or rather its popularised implication, 
pronounces against the spontaneous occurrence of either 
change, seeing that both changes under these conditions 
would be endothermic.i (2.) H and H' may both be 
greater than h, in which case both reactions are exo- 
thermic, and therefore possible under the conditions. 
The relative magnitudes of H and H' according to the 
" law " decide as to which of the two possible changes 
will actually occur. If H > H', then AC + B will be 
formed exclusively ; if H' > H, then BC + A will be 
the sole products of the reaction. 

When steam is passed over hot iron, chemical change 
ensues, resulting in the production of magnetic oxide 
of iron and hydrogen 

3Fe + 4H,0 = FegO^ + iB.^, 
but if retaining the same conditions copper be substituted 
for iron, the steam is not decomposed with the production 
of copper oxide and hydrogen in accordance with the 


Cu + H,0 - CuO + H^. 

These facts and many others of a similar nature might 
be adduced as confirmations of Berthelot's "law." 

1 It is to be regretted that the application of so many different 
significations to the terms exothermic and endothermic has led many 
chemists to avoid their use altogether. Rigidly defined they are 
exceedingly convenient terms for the description of thermo-chemical 
phenomena. In the text an endothermic reaction is taken to mean 
any reaction which is accompanied by an absorption of heat ; an exo- 
thermic reaction, any reaction which is accompanied by an evolution 
of heat. The terms as thus used have no quantitative significance. 


For since the formation of a gram molecule (232 grs.) 
of Fe^O^ from its elements is accompanied by an 
evolution of 264,700 heat units, while the resolution 
of four gram molecules (72 grs.) of steam into its 
elements is attended by the absorption of only 232,000 
heat units, it follows that the realisation of the first 
change will be attended by the evolution of heat energy 
to the extent of 32,700 units. On the other hand, 
the 37,200 units of heat evolved when a gram molecule 
(80 grs.) of copper oxide is formed from its elements 
is less than that required, 58,000 units, to resolve a 
gram molecule (18 grs.) of gaseous water into its 
elements, and so the realisation of the second reaction 
would involve an absorption of heat.^ 

Further, the generalisation that the readiness and 
intensity with which reactions take place increase with 
the thermal values of the reactions, is also in accordance 
with Berthelot's "law." 

But on the other hand there are very many facts 
which are at variance with the "law." Suppose we 
wish to know, without actually trying the experiment, 
whether hydrochloric acid gas acts on silver in accor- 
dance with the empirical equation 

HCl + Ag - AgCl + H. 

Looking up the heat of formation of HCl {i.e., the 

^ The possibility that reactions could take place in such way that 
the hydrogen of the water combines with the metals and the oxygen 
is set free, is presumed to be precluded by the fact that such changes 
would be strongly endothermic, though through lack of data the 
exact values of the heat absorption in each case cannot be given. 


beat evolved when a gram molecule of hydrochloric acid 
gas is formed from its elements), we find it to be 
220,000. The heat of formation of AgCl is 291,000. 
Now, applying Berthelot's " law " to these data, we 
are led to the conclusion that silver will be attacked 
by hydrochloric acid. But this conclusion is false, for 
silver is quite unaffected by hydrochloric acid. Again, 
when electric sparks are sent through a mixture of 2 
volumes of hvdroofen, with 2 volumes of chlorine and 
1 volume of oxygen, hydrochloric acid is exclusively 
formed, although the formation of water from the 
hydrogen and oxygen would be attended by a far 
greater production of heat. 

But the existence of chemical equilibria is, as we 
have already hinted, the most generalised argument 
that can be brought forward in opposition to the 
"law" of Berthelot. Let us suppose that the direct 
partial change of a particular case of equilibrium is 
attended by a heat evolution, then it follows from the 
well-established principle of the conservation of energy 
that the reverse partial change must involve a heat 
absorption. For the same reason, if the direct partial 
change is endothermic instead of exothermic, then the 
reverse partial change must be exothermic instead of 
endothermic. That is to say, an equilibrium demands 
the occurrence of two simultaneous chemical changes, 
one of which is associated with an evolution of heat, 
the other with an absorption of heat ; and when equili- 
brium is attained, these two changes are proceeding at 
exactly the same rates. If Berthelot's " law " were true, 


all reactions would belong to the complete type, and 
incomplete reactions, i.e., equilibria, would be impossible. 

If we interpret Thomsen and Berthelot's principle 
as merely asserting that every purely chemical change 
of a comjDlete type that takes place spontaneously must 
be accompanied by a loss of chemical energy which 
will finally appear as heat — the lowest form of energy 
— then we are bound to admit the truth of the prin- 
ciple at the same time as we deprive it of all practical 
import. For all the so-called chemical changes with 
which we have to do are not purely chemical changes, 
in this sense, that other forms of energy besides 
chemical energy undergo increase and decrease as the 
distribution of matter changes, and the heat evolved 
or absorbed by the reaction is a complex quantity, re- 
presenting not merely the changes of chemical energy, 
but the resultant of the sum total of energy changes 
of all kinds. A purely chemical change is a fiction of 
much the same order as an absolutely rigid bar, or a 
l^erfeetly frictionless constraint. 

Further, it can be shown that in incomplete re- 
actions {i.e., in cases of equilibrium) the chemical 
energy of the system suffers no decrease during the 
course of the reaction ; hence, if purely chemical energy 
were the only form of energy to be considered, it 
follows that all reactions leading to the establishment 
of an equilibrium ought to proceed without any heat 
absorption or evolution. But this is by no means 
the case, and so we are forced to the conclusion 
that in the so-called chemical changes other forms of 


energy besides chemical energy {e.g., volume energy, 
heat energy, surface energy, &c.) must undergo trans- 
formations in order that the actually observed thermal 
disturbances may be accounted for. 

But recognising the multiplicity of the specific energy 
changes which give rise to the thermal phenomena 
attendant on chemical change, the question may still 
be put, is there absolutely no connection under any 
conditions between the value and sign of the thermal 
changes and the necessity for the occurrence of 
chemical change ? Cannot we predict under any cir- 
cumstances which of two or more possible changes will 
occur ? 

It was a great advance that Horstmann made when 
he showed that the formulae of thermodynamics can be 
applied to problems in the domain of chemistry. The 
leading features of the dissociation of such a substance 
as chalk, in accordance with the symbolism 

CaCOy % CaO + CO^, 

are very similar to those of the evaporation of a homo- 
geneous liquid such as water. But the application of 
the second law of thermodynamics to the process of 
evaporation leads to the establishment of very im- 
portant relationships expressible in a simple formula, 
and Horstmann, on the strength of the strong analogy 
between the processes of evaporation and dissociation, 
applied this particular formula to certain cases of dis- 
sociation. The results to which the formula led were 
found to be in harmony with the facts ; and it was not 


long before Horstraann showed that the principles and 
formula3 of thermodynamics generally are applicable 
to all cases of chemical equilibrium. In other words, 
the relations of thermodynamics and chemistry are not 
limited to the application of one special thermodyna- 
mical formula to a certain circumscribed class of equi- 
libria distinguished as dissociations (see note 2, p. 199). 

The verdict passed on Berthelot's " law " by thermo- 
dynamics, is that only at absolute zero would such a 
law obtain — that only at the unattainably low tempera- 
ture of —273° 0. could prophecies founded on such a 
law be relied on. For, presupposing the possibility 
of chemical change at this temperature, it appears 
that at absolute zero all reactions would be com- 
plete ; all reactions would take place with an evolution 
of heat, and of two or more possible reactions that 
one would occur which is attended with the greatest 
heat evolution. The higher the temperature rises above 
the absolute zero, however, the more does Berthelot's 
law "deviate from the truth inclining towards it." 
With the rise of temperature above zero enters, 
according to thermodynamic deduction, the possibility 
of incomplete reactions — of mobile equilibria, and, 
moreover, the higher the temperature the more does 
a given equilibrium shift in favour of the endothermic 
partial change. 

Thus, the displacement of HNO3 from NaNOgAq 
by HgSO^Aq is endothermic ; the displacement of 
H2SO4 from NagSO^Aq by HNOgAq is exothermic. 
Hence it follows that a rise in temperature shifts 


the equilibrium of the system NaNOgAq, H^SO^Aq, 
HNOgAq, Na<,SO^Aq in favour of the darker arrow 
as shown in the following symbolism. 

NaoX.OgAq + H.SO^Aq ^ Xa^SO^Aq + H,N,O^Aq. 

Or, writing the reaction in equational form, 

NagK^OgAq + H^SO^Aq = a;Na^,SO^Aq + ^H.^NaOgAq + 
(l-x) Na^NoO^Aq + {1-x) H,S04Aq, 

we may state the same relation in another way by 
saying that x decreases in value as the temperature 

In cases where equilibrium is attained without 
thermal change, temperature is without influence 
thereon. Thus, nitric acid displaces hydrochloric 
acid from salt solution without evolution or absorp- 
tion of heat ; the same is true for the displacement 
of nitric acid from sodium nitrate solution by hydro- 
chloric acid, hence in the equation 

NaNOgAq + HClAq = arNaClAq + .«HNO.Aq + 
(l-x) XaXOgAq + (1 - x) HClAq 

the value of x' is independent of the temperature. 

The equilibria resulting from the etherification of 
alcohols by acids (see p. 202) are also attained with- 
out thermal disturbance, and are accordingly found 
to be independent of temperature changes. 

Having once and for all laid low the spectre of the 
" Law of maximum work," thermodynamics replaced 


it with a general law which, though of somewhat 
the same form as Berthelot's, differs from it in 
being universally true at all temperatures. This law, 
called the law of entropy, may be looked on as a 
particular form of statement of the Protean second 
law of thermodynamics. It states that a system is 
in stable equilibrium only when its entropy is a maxi- 
mum, and therefore that any change which entails an 
increase in the entropy of the system is not only cajjable 
of spontaneous occurrence, but will in fact actually 
proceed until the entropy of the system reaches the 
maximum value attainable under the conditions. 

Unfortunately this quantity or function entropy is 
a very difficult one to conceive, let alone measure, and 
the law concerning it is to chemists of more theo- 
retical interest than practical use. We can, however, 
arrive at some kind of a conception of entropy by 
the following considerations. 

The electrical energy of an isolated charged body 
is equal to the product |QV, where Q stands for the 
quantity of electricity with which the body is charged, 
and V is its potential. Suppose that for one body 
the electric energy is ^Q'V, and for another bod}^ 
|Q"V". What are the conditions that electric energy 
shall pass from one body to the other? Simply 
electric connection and the inequality of V'' and V". 
If V > V", then electric energy will pass from the 
first body to the second until the potentials of both 
bodies is the same, and this will happen even if the 
electric energy of the first body is greater in amount 


than that of the second body. The passage of electric 
energy from one system to another is independent of 
the quantities of energy possessed by the two systems, 
and depends solely on their potentials. Electric energy 
always flows from places of high, to places of low 

On this account V is regarded as the " intensity 
factor " of electrical energy, and Q as the " capacity 
factor," Energy of other forms can similarly be re- 
solved into capacity and intensity factors. For instance, 
the intensity factor of kinetic energy is velocity,^ 
the capacity factor is mass, and so on. 

What then are the factors of thermal energy ? The 
intensity factor is very familiar to us and easily 
capable of evaluation — it is temperature. The capacity 
factor does not appeal directly to our senses, nor can 
we easily form a clear conception of it. Yet this 
factor, which we are content to define rather than 
conceive, has received the name entropy. Hence we 
can restate the law of entropy in the following way : — 
Any change which can increase the value of the 
capacity factor of the heat energy of a system takes 
place with readiness, and the system only then attains 
a position of stability (of disinclination to undergo any 
further change) when the value of this capacity factor 
is at a maximum. 

In some forms of energy it is not possible to alter 
the capacity factor by adding energy to the system. 

^ Strictly speaking (velocity)-, the kinetic energy of a mass m moving 
with velocity v being h mv^. 


The addition of kinetic energy to a moving bullet, for 
instance, cannot alter the mass of the bullet, which here 
represents the capacity factor. But in the case of heat 
energy it is otherwise ; here it is possible, by adding 
thermal energy to a system, to alter thereby the thermal 
capacity factor of that system. 

Suppose we have a mass of a solid substance S at 
the absolute temperature T. Let us impart to S an 
additional quantity of heat energy q under conditions 
such that the intensity factor of the heat energy of the 
system is not thereby altered, i.e., such that T remains 
constant. This may be simply realised by supposing T 
to denote the melting point of S, and q to be the latent 
heat of fusion of S. Let us call the first state of the 
system A and the final state B. To bring the system 
to the state A from absolute zero requires an amount 
of heat energy, say Q ; to bring the system from zero to 
the state B requires Q + g- units of heat energy. There- 
fore in the passage from A to B the capacity of the system 
for heat energy has evidently increased, and the increase 
of heat capacity under the conditions named is called an 

increase of entropy, and is measured by the quotient ?. 

But thermodynamics has furnished us with tests of 
stability involving functions other than entropy ; and 
some of these tests possess the advantage of being more 
easily applied to actual cases than the entropy test.^ 

^ For details the reader is referred to Parker's Elementary Thermo- 
dynamics, also to Ostwald's Lehrhuch dcr allgemeincn Chemie, to which 
the author is indebted for the treatment of the subject of entropy given 
in the text. 


A momentary glance at the expression defining the 
function known as the free energy, or tlic tlicrmo- 
dynamic potential at constant volume, throws clear 
light on the question of Berthelot's " law." In the 

Fa denotes the free energy and Ua the total energy of 
a system in the state A. Its temperature in this state 
is Ta and its entropy Sa- 

Let us consider another state, B, of this system, for 
which the values are Fg, Ug, Ta, and Sp, the volume 
and temperature of the systems remaining the same in 
both states. 

From the two equations 

Fa = Ua - TaSa 

Fb = Ub - TaSb 

we get by subtraction — 

(Fa - F,) = (Ua - U,) - [Ta(Sa - S,)]. 

Now, it results from thermodynamic reasoning that 
the change from the state A to the state B can only 
proceed of itself when the free energy of the system is 
decreased by the passage, i.e., (Fa — F^) must be a 
positive quantity. 

Rearranging the equation we obtain 

(Ua - Up,) = positive quantity + Ta (Sa - S,.). 

The value of Sg being greater than that of Sa, the 
whole term Ta (Sa — Sg) must be negative. 


Suppose the absolute magnitude of this term to be 
less than the " positive quantity " term, then (Ua — Ug) 
must obviously have a positive value ; that is to say, 
the change of the system from the state A to the state 
B has been attended by a loss of energy to the system 
— has been an exothermic change. But this is not the 
only possible case. If the absolute magnitude of the 
term Ta(Sa — Sg) be greater than that of the positive 
quantity term, then (Ua — Ub) must necessarily have a 
negative value ; that is to say, the total energy of the 
system has been increased by its spontaneous passage 
from the state A to the state B — the change has been 
an endothermic one. 

It is clear that the importance of the term Ta(Sa — Sg) 
rises 'pari passu with the temperature at which the change 
proceeds. In other words, the higher the temperature 
the more likely are endothermic reactions to occur. 













Advanced Science Manuals - 


; Mechanics and Mechanism 

- 5 

Agriculture and Gardening - 



- 13 

Architecture - - . . 


Meteorology - 

- 18 

A.STRONO.MY . . - . 



- 13 




- 14 



Optics . . . . 

- 17 

Building Construction - 


Photography - 

- 17 

Chemistry . . . . 


Physics . . . . 

- 4 

Dynamics . . . . 


Physiography - 

- 16 

Electricity . . . . 



- 18 

Elementary Science Manuals 


Proctor's (R. A.) Works - 

- 15 

Engineering ... - 


Sound - . . . 

- 7 



Statics . . - . 

- 6 



Steam and the Steam Engine 8 

Health and Hygiene 


Strength of Materials - 

- 12 

Hydrostatics - - - - 



- 16 


7 , 


- 10 

London Science Class-Books - 



- 10 

Longmans' Civil Engineering 

Text-Books op Science - 

- 20 

Sehies .... 




Machine Drawing and Design 

14 j 

Tyndall's (John) Works 

- 11 

Magnetism .... 


Workshop Appliances - 

- 13 

Manufactures - - - - 


Scientific Works publislud by Longmans, Green, &= Co. 


ADD YMAN— Agricultural Analysis. A Manual of Quantitative 
Analysis for Students of A<j;riculture. By Frank T. Addyiian, B.Sc. 
(Lend.), F.l.C. With 49 Illustrations. Crown 8vo. 5s. net. 

ARMSTRONG— Organic Chemistry : the Chemistry of Carbon 
and its Comp(nintls. By H. E. Armstrong, Ph.D. With 8 Woodcuts. 
Fcp. 8vo. 3s. Qd. 

COLEMAN & ADD YMAN — Practical Agricultural 
Chemistry. For Elementary Students, adapted for use in Agri- 
cultural Classes and Colleges. . By J. Bernard Coleman, A.R.C.Sc, 
F.l.C, and Frank T. Addyman, B.Sc. (Lond.) F.l.C. With 24 
Illustrations. Crown 8vo. Is. Qd. net. 

CROOKES— Select Methods in Chemical Analysis, chiefly 
Inorganic. By William Crookes, F.R.S., &c. With 37 Woodcuts. 
8vo.' 24s. 

EARL— The Elements of Laboratory W"ork : a Course of Natural 
Science. By A. G. Earl, M.A., F.C.S., late Scholar of Christ's 
College, Cambridge. With 57 Diagrams and numerous Exercises and 
Questions. Crown 8vo. 4s. 6(/. 

PURNEAUX — Elementary Chemistry, Inorganic and Or- 
ganic. By W. FuRNEAUX, F.R.C.S., Lecturer on Chemistry, London 
School Board. With 65 Illustrations and 155 Experiments. Crown 
8vo. 2s. 6rf. 

HALL— First Exercises in Practical Chemistry. By A. I>. 
Hall, M.A., Senior Science Master at King Edward's School, Bir- 
mingham. Crown 8vo. Is. 6.'/. 

HJELT— Principles of General Organic Chemistry, By Pro- 
fessor E. Hjelt, of Helsingfors. Translated from the German by J. 
Bishop Tingle, Ph.D., Assistant in the Laboratory of the Heriot 
Watt College, Edinburgh. Crown 8vo. 6s. Qd. 

JAGO— W^orks by W. Jago, F.C.S., F.l.C. 

Inorganic Chemistry, Theoretical and Practical. W^ith 

an lntroductit)n to the Principles of Chemical Analysis Inorganic and 
Organic. With 196 Experiments, with 49 Woodcuts and numerous 
Questions and Exercises. Fcp. 8vo. 2s. 6d 

An Introduction to Practical Inorganic Chemistry. 

Crown 8vo. Is. 6(/. 

Inorganic Chemistry, Theoretical and Practical. A 

Manual for Students in Advanced Classes of the Science and Art 
Department. With Plate of Spectra and 78 Woodcuts. Cr. 8vo. 4s. Qd. 

KOLBE— A Short Text-Book of Inorganic Chemistry. By 

Dr. Hermann Kolbe. Translated and Edited bv T. S, Humpiuge, 
Ph.D. With 66 Illustrations. Crown 8vo. 8s. Qd. 

MENDELEEFP— The Principles of Chemistry. By D. Men- 

DEL^EFF, Professor of Chemistry in the University of St. Petersburg. 
Translated by George Kamensky, A.R.S.M., of the Imperial Mint, St. 
Petersburg, and edited by A. J. Green aw ay, F.l.C, Sub -Editor of 
the Journal of the Chemical Society. With 97 Illustrations. 2 vols. 
Svo. 36s. 

Scientific Works published by Longmans, Green, &> Co. 

MEYER— Outlines of Theoretical Chemistry, By Lothar 
Meyer, Professor of Chemistry in the University of Ttibingen. Trans- 
lated by Professors P. Phillips Bedson, D.Sc, and W. Carleton 
Williams, B.Sc. 8vo. 9s. 

MILLER— Introduction to the Study of Inorganic Chemis- 
try. By William Allen Miller, M.D., LL.D., F.R.S. With 71 
Woodcuts. Fcp. 8vo. 3s. 6rf. 

NE"WTH— Chemical Lecture Experiments. By G. S. Newth, 

Royal College of Science, South Kensington. With 224 Diagrams. 
Crown 8vo. " 10s. 6d. 

ODLING— A Course of Practical Chemistry, arranged for the 
Use of Medical Students, -with express reference to the Three Mouths 
Summer Practice. By William Odling, M.A. With 71 Woodcuts 
Crown 8vo. 6s. 

OSTWALD— Solutions. By W. Ostwald, Professor of Chemistry 
in the University of Leipzig. Being the Fourth Book, with some 
Additions, of the Second Edition of Ostwald's 'Lehrbuch der Allge- 
meinen Chemie'. Translated by M. M. Pattison Muir, Professor of 
Gonville and Cains College, Cambridge. 8vo. 10s. 6rf. 

PATEN — Industrial Chemistry. A Manual for use in Technical 
Colleges and Sdiools, based upon a Translation of Stohmann and 
Engler's German Edition of Payen's 'Precis de Chimie Industrielle '. 
Edited by B. H. Paul, Ph.D. With 698 Woodcuts. 8vo. 42s. 

REYNOLDS— Experimental Chemistry for Junior Students. 

By .J. Emerson Reynolds, M.D., F.R.S., Profe.ssor of Chemistry, 

University of Dublin ; Examiner in Chemistry, University of London. 

Fcp. 8\-o. with numerous Woodcuts. 
Part I. Introductory. Fcp. 8vo. Is. 6d. 
Part II. Non-Metals, with an Appendix on Systematic Testing for 

Acids. Fcp. 8vo. 2s. 6rf. 
Part 111. Metals and Allied Bodies. Fcp. 8vo. 3s. 6rf. 
Part IV. Carbon Compounds. Fcp. 8vo. 4s. 

SHENSTONE— AVorks by W. A. Shenstone, Lecturer on Chemistry 

in Clifton College. 
The Methods of Glass-Blowing. For the use of Physical 

and Cliemiral Students. Witli \i Illustrations. Crown 8vo. Is. 6'?. 

A Practical Introduction to Chemistry. Intended to 

give a Practical Ac(puuntance with the Elementary Fact-s and 
Principles of Chemistry. With 20 Illustrations. Crown 8vo. 2s. 

THORPE A Dictionary of Applied Chemistry. By T. E. Thorpe, 
B.Sc. (Vict.), Ph.D., F.R.S., Treas. C.S., Profes.sor of Chemistry in the 
Royal College of Science, South Kensington. Assisted by Eminent 
Contributors. Svol.s. 8vo. Vols. I. & II. 42s. each. Vol.111. 63s. 

Quantitative Chemical Analysis. By T. E. Thorpe, 

Ph.D., F.R.S. With SS WiKHlcuts. Fcp. 8vo. 4.s. 6(?. 

THORPE and MUIR -Manual of QuaUtative Analysis and 
Laboratory Practice. By T. E. Thorpk, Fh.D., F.R.S. E., and M. M. 
Pattison Muir. With 57 Woodcuts. Fcp. 8vo. 3s. 6rf. 

Scientific Works published by Longmans, Green, cE- Co. 

TILDEN— Works by Wili iam A. Tilden, I>.Sc. (Lond.), F.C.S. 

Introduction to the Study of Chemical Philosophy. 

The Principles of Theoretical and Systematic Chemistry. With 5 
Woodcuts. With or without the Answers of Problems. Fcp. 8vo. 
4s. M. 
Practical Chemistry. The Principles of Qualitative 

Analysis. Fcp. 8vo. Ls. M. 

WATTS' Dictionary of Chemistry. Revised and entirely Re- 
written by H. FoRSTER MoRLEY, M.A., D.Sc, Fellow of, and lately 
Assistant- Professor of Chemistry in, University College, London ; and 
M. M. Patti.son Muir, M.A.', F.R.S.E., Fellow, and Praelector in 
Chemistry, of Gonville and Caius College, Cambridge. Assisted by 
Eminent Contributors. 4 vols. 8vo. Vols. I. & II. 42s. each (ready). 
Vol. III., 50s. (ready). Vol. IV., [In the p-ess. 

WHITELEY -Works by R. Lloyd Whiteley. F.I.C, Assistant 
Lecturer and Demonstrator in Chemistiy in the L^niversity College, 

— Chemical Calculations, witli E.xplanatory Note.s, Problems 

and Answers, specially mlapted for use in Colleges and Science 
Sc1io(j1s. With a Preiace Viv Professor F. Clowes, D.Sc. (Lond.). 
F.I.C. Crown 8vo. 2s. 

Organic Chemistry. [JSfearly ready. 


ARNOTT— The Elements of Physics or Natural Philosophy. 

By Neil Akxott, M.D. Edited by A. Baix, LL.D., and A. S. 

Taylor, M.D., F.R.S. With numerous Woodcuts. Cr. 8vo. 12s. 6d. 
COOK— Physics. (Specially adapted for Indian Schools and Students.) 

By J. Cook, M.A., Principal, Central College, Bangalore. With 

Examination Questions and 206 Illustrations. Crown 8vo. 2s. 6d. 

EARLi — The Elements of Laboratory Work : a Course of 
Natural Science. By A. G. Earl, M.A., F.C.S. With 57 Diagrams 
and numerous Exercises, etc. Crown 8vo. 4s. 6d. 

GANOT -Works bv Professor Gaxot. Translated and Edited by E. 
Atkinson, Ph.D.", F.C.S. 

Elementary Treatise on Physics, Experimental and Applied. 

With 9 Coloured Plates and 1028 Woodcuts. Crown 8\o. 15s. 

Natural Philosophy for General Readers and 

Young Persons ; a Course of Physics divested of Mathematical 
Formulge, expressed in the language of daily life. With 7 Plates, 
569 Woodcuts, and an Appendix of Questions. Crown Bvo. 7s. 6d. 

GLAZEBROOK and SHA^W— Practical Physics. By R. T. 
Glazebrook, M.A., F.R.S., and W. N. Shaw. M.A. 134 Woo.lcuts. 
Fcp. 8vo. 7s. Gd. 

GUTHRIE— A Class-Book of Practical Physics. Molecular 
Physics and S(jund. By F. Guthrie, Ph.D. With 91 Diagrams, 
Fcp. 8vo. Is. 6(f. 

Scientific Works published by Longmans, Green, <~ Co. 

HELMHOLTZ— Popular Lectures on Scientific Subjects. 
By Hermann L. F. Helmholtz. Translated by E. Atkinson, Ph.D., 
F.C.S., t'lirmerly Prut'essor of Experimental Science, Stalt' Collef;e. 
With 68 Illustrations. 2 vols., crown 8vo. 3s. 6(?. each. 

Contents — Vol. I.— The llelatiou of Natural Science to Science in 

General -Goethe's Scieutitic Researches — The Physiological of Har- 
mou3' in Music — Ice and Glaciers— The Inter-action of the Natural Forces — 
The Recent Progress of tlie Theory of Vision — The Conservation of Force — 
The Aim and Progress of Phj-sical Science. 

Vol. II. — Gustav Magnus. In Menioriani — The Origin and Significance 

of Geometrical Axioms — The Relations of Optics to Painting— The Origin 
of the Planetai-y System — Thought in Medicine— Academic Freedom in 
German Universities — Herman von Helmholtz. An Autobiographical 

WORTHINGTON— A First Course of Physical Laboratory 
Practice. Containin-,' 264 Experiments. By A. il. Worthington, 
F.R.S., M.A. Witli Illustrations. Crown 8vo. 4s. 6rf. 

WRIGHT— Elementary Physics. By :Mark. K. Wright., Prin- 
cipal of tlie Day Training' Colle,i,'e, Xewoa.-^tle-on-Tyne. With 242 
Illustration.-;. Crown 8vo. 2.s-. Qd. 


BALL— A Class-Book of Mechanics. Bv Sir B. S. Ball, LL.D. 
89 Diaffiams. Fcp. 8vo. Is. 6</. 

GOODBYE— Works by T. M. Goodeve, M. A., Professor of Mechanics at 

the Xonnal School of Science, and the B<iyal Scliool of Mine^i. 

Principles of Mechanics. With 253 Woodcuts and numerous 

Examj)les. Crown 8vo. (i.s. 

The Elements of Mechanism. With 342 Woodcuts. Crown 

8vo. 6.?. 

A Manual of Mechanics: an Elementary Te.\t-l)ook for 

Students uf Apjilied Mechanics. With 138 Illustrations and Diagrams, 
and 188 Examples taken from tlie Science Department Examination 
Papers, with Answer,-. Fc]). 8vo. 2.s. Gd. 

GOODMAN— Applied Mechanics. By John Goodman. 

[//( jirijinration. 

GRIEVE— Lessons in Elementary Mechanics. By W. H. 
Ukikve, I'.S.A., late Engineer R.N., Science Demonstiator for the 
London Schoi)l Board, &c. St.age 1. With 16o Illustrations and a lar^^e 
number of Examples. Fcp. 8vo. 1.5. Od. St^i.Lje 2. With 122 Illustra- 
tion.'!. Fcp. 8vo. Is. Gd. Stage 3. With 1('3 Illustratiims. Fcj). 8vo. 
Is. 6d. 

MAGNUS -Lessons in Elementary Mechanics. Introductory 
to the Study (jf i'hysical Science. Desi;;ned for the Use of Sclmol.s, and 
of Candidates for the London Matriculation and other Examinations. 
AVith numerous Exerci.^e.s, Exam])les, and Examination Questions. 
With Answeis, and 131 Woodcuts. 13y Sir Philip M.\(iNi s, B.Sc, 
B.A. Fcp. 8vo. 3s. 6d. Key for the u.'<e of Teachers only, i)rice 
5s. 3/t(/. net, post free, from the publish'Ts onhj. 

Scientific Works published by Longtnans, Green, &• Co. 

TAYLOR — Theoretical Mechanics, including Hydrostatics and 
Pneumatics. By J. E. Taylor, M.A., Hon. Inter., B.Sc, Central 
High Schools, Sheffield. With 175 Diagrams and Illustrations, and 
522 Examination Questions and Answers. Crown 8vo. 2s. 6ci. 

THORNTON— Theoretical Mechanics: Section 1. Solids; to 

cover the Advanced Course of Science and Art Department. By A. 
Thornton, M.A. [In -preparation. 

TWIS DEN— Works by the Rev. John F. Twisden, M.A. 

Practical Mechanics ; an Elementary Introduction to their 

Study. With 855 Exercises and 184 Figures and Diagrams. Crown 
8vo. "lOs. Qd. 

Theoretical Mechanics. With 172 Examples, numerous 

Exercises, and 154 Diagrams. Crown 8vo. 8s. Qd. 

WARREN— An Elementary Treatise on Mechanics ; for the 

use of Schools and Students in Universities. By the Rev. Isaac 

Part I. Statics. Crown Bvo. 3s. (Jc/. 
Part 11. Dynamics. Crown 8vo. 3s. 6rf. 


BURTON — An Introduction to Dynamics, including Kinematics, 
Kinetics, and Statics. With numerous Examples. By Charles V. 
Burton, D.Sc. Crown 8vo. 4s. 

GELDARD- Statics and Dynamics. By C. Geldard, M.A., 
formerly Scholar of Trinity College, Cambridge, Mathematical 
Lecturer under the Non-Collegiate Students' Board, Cambridge. 
Crown 8vo. 5s. 

GROSS — Elementary Dynamics (Kinematics and Kinetics). By E. 
J. Gross, M.A., Fellow of Gonville and Caius College, Cambridge. 
Crown 8vo. 5s. 6rf. 

MAGNUS -Hydrostatics and Pneumatics. By Sir Philip 

Magnus, B.Sc. Fcp. 8vo. Is. %d., or, with Answers, 2s. 
*:^* The Worked Solutions of the Prol)lems. 2s. 

ROBINSON— Elements of Dynamics (Kinetics and Statics). 
M'ith numerous Exercises. A Text-Book for Junior Students. By 
the Rev. J. L. Robinson, B.A. Chaplain and Naval Instructor at 
the Royal Naval College, Greenwich. Crown 8vo. 6s. 

SMITH — Works by J. Hamblin Smith, M.A., of Gonville and Caius 
College, Cambridge. 

Elementary Statics. Crown 8vo. 3s. 

Elementary Hydrostatics. Crown 8vo. 3s. 

Key to Statics and Hydrostatics. Crown 8vo. 6s. 

Scientific Works published by Longmans, Green, S' Co. 7 

WILLIAMSON and TARLETON— An Elementary Treatise 
on Dynamics. Containing Applications to Therniodynaniics, with 
numerous Examples. By Benjamin Williamson, D.Sc, F.R.S., and 
Francis A. Tarleton, LL.U. down 8vo. 10s. Qd. 

WORMELL — The Principles of Dynamics : an Elementary 
Text-Book for Science Students. By R. Wormell, D.Sc, M.A. 
Crown 8vo. 6s. 

WORTHINGTON— Dynamics of Rotation. : an Elementary 
Intioduction to Rigid Dyiuiniics. By A. M. WoRTHlNGTOX, M.A., 
F.R.S., Head Master and Professor of Physics at the Royal Naval 
Engineering C'lUege, Devonport. Ci-own 8vo. 3s. Qd. 


ALEXANDER -Treatise on Thermodynamics. By Peter 
Ale-X'ander, M.A., Li^cturer nu .Matlieiaatics, Queen Margaret 
College, Glasgow. Crown Svo. 5s. 

DAY— Numerical Examples in Heat. By R. E. Day, M.A. Fcp. 
8vo. 3s. 6(i. 

HELMHOLTZ— On the Sensations of Tone as a Physiological 
Basis fur the Theory of Music. By Professor Helmholtz. Royal 
8vo. 28s. 

MADAN — An Elementary Text-Book on Heat. For the of 
Schools. By H. G. Madan, M.A., F.C.S., Fellow of Queen's College, 
Oxford ; late Assistant Master at Eton College. Crown 8vo. 9s. 

MAXWELL— Theory of Heat. By J. Clerk Maxwell, M.A., 

F.R.SS., L. & E. With Corrections and Additions by Lord Rayleigh. 
With 38 Illustrations. Fcp. 8vo. 4s. 6rf. 

SMITH (J. Hamblin)-The Study of Heat. By J. Hamblin 
Smith, M.A., of Gonville and Caius College, Cambridge. Cr. 8vo. 3s. 

TYNDALL-Works by John Tyndall, D.C.L., F.R.S. See page 11. 

WORMELL —A Class-Book of Thermodynamics. By Richard 
Woumell, B.Sc, M.A. Fcp. 8vo. Is. (id. 

WRIGHT— Works by Mark R. Wright (Hon. Inter., B.Sc, London). 

— Sound, Light and Heat. With 160 Diagrams and llhis- 
trations. Crown 8vo. 2s. 6d. 

— Advanced Heat. With 136 Diagrams and nunierous Examples 

and ExiiMiiuatiiiii Papers. Crown 8vo. 4s. 6(/. 

8 Scientific Works ptiblished by Long??ians, Green, & Co. 


BALE — A Handbook for Steam Users ; being Nutes on Steam 
Engine and Boiler Management and Steam Boiler Explosions. By 
M. Powis Bale, M.I.M.E., A.M.I.C.E. Fcp. 8vo. 2s. U. 

BOURNE— Works by John Bourne, C.E. 

A Catechism of the Steam Engine, in iia Variou.s Applica- 
tions in the Arts, to which is added a chapter on Air and Gas 
Engines, and another devoted to Useful Kules, Tables, and Memor- 
anda, illustrated by 212 Woodcuts. Crown 8vo. 7s. Qd. 

Recent Improvements in the Steam Engine. With 124 

Woodcuts. Fcp. 8vo. Qs. 

CLERK— The Gas Engine. By Dugald Clerk. With 101 Wood- 
cuts. Crown 8vo. 7s. 61:/. 

HOLMES— The Steam Engine. By George C. V. Holmes, 
(Whitworth Scholar) Secretary of the Institution of Naval. Architects. 
With 212 Woodcuts. Fcp. 'Svo. 6s. 

RANSOM— Steam and Gas Engine Governors. By H. B. 

Ransom. [/« ]}rej}aration. 

RIPPER— Works by William Ripper, Member of tlie Institution 
of Mechanical Engineers ; Professor of Mechanical Engineering in 
the Sheffield Technical School 

Steam. Witli 142 Illustrations. Crown 8vo. 2s. {3d. 

Steam and the] Steam Engine. An Advanced Course. 

SENNETT— The Marine Steam Engine. A Treatise for the Use 
of Em;ineering Students and Offi'ers of the Uoyal Navy. By Richard 
Sennett, R.N., Enyineer-in-Chief of the Royal Navy. With 261 
Illustrations. 8vo. 21s. 

STROMEYER— Marine Boiler Management and Construc- 
tion. Being a Treatise on Boiler Troubles and Re])airs, Corrosion, 
Fuels, and Heat, on the ])roperties of Iron and Steel, on Boiler 
Mechanics, Workshop Practices, and Boiler Design. By C E. 
Stromeyer, Graduate of the Royal Technical Colle<;e at Aix-la- 
Cliapelle, Member of the Institute of Naval Architects, etc. With 
452 Illustrations. 8vo. 18s. net. 

Scientific Works published by Lotigmafis, Green, S' Co. 


GWILT — An Encyclopaedia of Architecture. By Joseph Gwilt, 
F.S.A. Illustiated with innie tlian llUO Eu*^nivings on Wood. 
Revised (1888), with Alterations and Considerable Additions, by 
Wyatt Papworth. 8v(>. 52;;. 6c?. 

MITCHELL— The Stepping-Stone to Architecture : explaining 
in simple language the Principles and Progress of Architecture from 
the earliest times. By Thomas Mitchell. With 22 Plates and 49 
Woodcuts. 18nu). Is. sewed. 


Advanced Building Construction. By the Author of ' Riviugton'd 
Notes on Building Construction '. With 385 Illustrations. Crown 
8vo. 4s. 6(f. 

BURRELL —Building Construction. By Edward J. Burrell, 

Second Master of the People's Palace Technical School, London. 
With 303 Working Drawings. Crown 8vo. 2s. 6(/. 

SEDDON- Builder's 'Work and the Building Trade. By 
Colonel H. C. Seddon, R.E., Superintendinu Engineer H.M.'s Dock- 
yard, Portsmouth ; Examiner in Building Construction, Science and 
Art Department, South Kensington. With numerous Illustrations. 
Medium 8vo. 16s. 


Notes on Building Construction. Arranged to meet the require- 
ments of the Syllabus of the Science and Art Department of the 
Committee of Council on Education, South Kensington. Medium 8vo. 

Parti. First Stage, or Elementary Course. With 552 Woo<lcuts. 10s. 6rf. 

Part II. Commencement of Second Stage, or Advanced Course. With 
479 Woodcuts. 10s. 6rf. 

Part III. ^Materials. Advanced Course, and Course for Honours. With 
188 Woodcuts. 21s. 

Part IV. Calculations for Building Structures. Course for Honours. 
With 597 Woodcuts. 15s. 

lo Scientific Works published by Longmans, Green, &' Co. 


GUMMING— Electricity treated Experimentally. For the use 

of Schools and Students. By Linnaeus Gumming, M.A., Assistant 
Master in Rugby School. With 242 Illustrations. Crown 8vo. 4s. 6rf. 

DAY — Exercises in Electrical and Magnetic Measurements, 

with Answers. By R. E. Day. 12ino. 3s. 6rf. 

DE TUNZELMANN— A Treatise on Electricity and Mag- 
netism. By G. W. DE TuNZELMANN, B.Sc, M.I.E.E. [/?i Frefaration. 

GORE— The Art of Electro-Metallurgy, including all known 
Processes of Electro-Deposition. By G. Gore, LL.D., F.R.S. With 
56 Woodcuts. Fcp. 8vo. 6s. 

JENKIN— Electricity and Magnetism. By Fleeming Jenkin, 
F.R.S.S., L. & E., M.I.C.E. With 177 Illustrations. Fcp. 8vo. 3s. 6d 

LARDEN— Electricity for Public Schools and Colleges. By 
W. Larden, M.A. With 215 Illustrations and a Series of Examina- 
tion Papers with Answers. Crown 8vo. 6s. 

POYSER--W(uks by A. W. Poyser, B.A., Assistant Master at the 
Wyggeston Schools, Leicester. 

Magnetism and Electricity. With 235 Illustrations. Crown 

8vo. 2s. 6d. 

Advanced Electricity and Magnetism. With 317 Illus- 
trations. Crown Bvo. 4s. 6rf. 

SLINGO and BROOKER— Electrical Engineering for 

Electric Light Artisans and Students. By W. Slingo and A. Broker. 
With 307 Illustrations. Crown 8vo. 10s. %d. 

TYNDALL— Works bv John Tyndall, D.C.L., F.R.S. See j). 11. 


CULLEY— A Handbook of Practical Telegraphy. By R. S. 
CuLLEY, M.I.C.E., late Engineer-in-Chief of Telegraphs to the Post 
Office. With 135 Woodcuts and 17 Plates. 8vo. 16s. 

HOPKINS— Telephone Lines and their Properties. By William 
John Hopkins, Professor of Physics in the Drexel Institute of Art, 
Science and Industry, Philadelphia. Crown Bvo. 6s. 

PREECE and SI VE'WRIGHT— Telegraphy. By W. H. Preece, 
F.R.S., M.I.C.E., &c., Engineer-in-Chief and Electricuin to the 
Post Office ; and Sir J. Sivewright, K.C.M.G., General Manager, 
South African Telegraphs. With 255 Woodcuts. Fcp. 8vo. 6s. 

Scientific Works published by Longmans, Green, &= Co. 1 1 


D.C.Ii., LL.D., F.R.S. 

Fragments of Science : a Series of Detached Essays, Addresses aud 
Reviews. 2 vols. Crown 8vo. 16s. 

VOL. I. : — The Constitution of Nature— Radiation— On Radiant Heat in relation to the 
Colour and Chemical Constitution of Bodies — New Chemical Reactions produced by Light 
— On Dust and Disease — Voyage to Algeria to observe the Eclipse — Niagara — The Parallel 
Roads of Glen Ri>y— Alpine Sculpture— Recent Experiments on Fog-Signals— On the Study 
of Physics — On Crystalline and .Slaty Cleavage— On Paramagnetic and IJiamagnetic Forces 
— Physical Basis of Solar Chemistry — Elementary Magnetism— On Force -Contributions to 
Molecular Physics— Life and Letters of Fauaday— The Copley Medalist of 1870 — The 
Copley Medalist of 1871- Death by Lightning. — Science and the Spirits. 

VOL. II. :— Reflections on Prayer and Natural Law— Miracles and Special Providences — 
On Prayer as a Form of Physical Energy— Vitality— Matter and Force- .Scientific Materi- 
alism — An Address to Students— .Scientific Use of the luiagination— The Belfast Address — 
Apology for the Belfast Address— The Rev. .Jame.s Martineau and the Belfast Address — 
Fermentation, and its Bearings ou Surgery and Medicine— Spontaneous Generation — 
Science and Man— Professor Viiiciiow and Evolution— The Electric Light. 

Ne"W Fragments. Crown 8vo. 10s. 6d. 

CONTKNT.s : — The Sabbath— Goethe's ' Farbenlehre' — Atoms, M<ileculesand Ether Waves 
— Count Kuuiford— Louis Pasteur, his Life and L.abours— The Rainbow and its Congeners — 
Address delivered at the Birkbeck Institution ou 22nd October, 1884 — Thomas Young — Life 
in the Alps— About Common Water — Pei-sonal Recollections of Thomas Carlyle— On Un- 
veiling the Statue of Thomas ('arlyle — On the Origin, Propagation and Prevention of 
Phthisis — Old Alpine .lottings — A Moniiug on Alp Lusgen. 

Lectui-es on Sound. With Frontis- 
piece of F()g-8yreii, and 20-3 other 
Wooilcnts aii'l Di.igrains in the Te.\t. 
Crown 8vo. 10s. M. 

Heat, a Mode of Motion. With 

125 Woodcuts and Diagram.s. Cr. 
8v(.. l-2s. 

Lectures on Light delivered in 

the United States in 1^)72 and 1S73. 
Witli Portrait, Lithographic Plat^' | 
and .'iO Diagrams. Crown Svo. .''S. 

Essays on the Floating Matter of 

the Air in relation to l'utrciacti<jn 
and Infection. With 24 Woodcuts. 
Crown Svo. 7s. 6rf. 

Researches on Diamagnetism and 

Magnecrvstallio Action ; ini hiding 
the Question of Dianiagnetic Tcdarity. 
Crown Svo. l"2s. 

Notes of a Course of Nine Lectures 

on Liglit, delivered at the Royal 
Institution of Great Britain, 1869. 
Crown 8vo. Is. %d. 

Notes of a Course of Seven Lec- 
tures on Electrical Phcuonieua and 
Theories, delivered at the Royal In- 
stitution of Great Britain, 1870. Cr. 
Svo. l.s. ^d. 

Lessons in Electricity at the 

Royal Institution, 187:)-187ti. With 
58 Woodcuts and Diagrams. Crown 
Svo. 'Is. ^■(^. 

Address delivered before the 

ihitish Assmialion asscndiled at Bel- 
fast, 1874. With Additions. Svo. 
4.S'. y'd. 

Faraday as a Discoverer- Cro\Mi 

Svo. \')S. '(>d. 

1 2 Scientific Works published by Longmans, Green, &> Co. 

Edited by tlie Author of 'Notes on Building Consti'uction '. 

The following volumes of this new Series are in preparation, and other 
volumes will follow in due course : — 

Tidal Rivers : their Hydraulics, Improvement and Navigation. By 
W. H. Wheeler, M.Inst.C.E., Author of ' The Drainage of Fens 
and Low Lands by Gravitation and Steam Power'. With 75 Illustra- 
tions. Medium 8vo. 16s. net. [Ready. 

Notes on Dock Construction. By C. Colson, M.Inst.C.E. of H.M. 

Dockyard, Devonport. [In the press. 

Rail"way Construction. By W. H. Mills, M.Inst.C.E., Engineer- 
in-Chief, C4reat Northern Railway, Ireland. [In preparation. 

Calculations for Engineering Structures. By T. Claxton 
FiDLER, M.Inst.C.E., Professor of Engineering in the LTniversity of 
Dundee ; Author of ' A Practical Treatise on Bridge Construction '. 

[In pireparation. 

The Student's Course of Civil Engineering. By L. F. Vernon- 
H.\RCOURT, M.Inst.C.E., Professor of Civil Engineering at University 
College. [In preparation 


ANDERSON— The Strength of Materials and Structures : 

the Strength of Materials as depending on their Quality and as ascer- 
tained bv Testing Apparatus. Bv Sir J. Anderson, C.E., LL.D., 
F.R.S.E." With 66 Woodcuts. Fcp. 8vo. 3s. 6t/. 

BARRY— Railway Appliances : a Description of Details of Railway 
Construction subsequent to the Completion of the Earthworks and 
Structures. By John Wolfe Barry, M.I.C.E. With 218 Woodcuts. 
Fcp. 8vo. 4s.' Qd. 

DOWNING— Elements of Practical Construction, for the use 

of Students in Engineering and Architecture. By Samuel Downing, 
LL.D. Part I. Structure in direct Tension and Compression. With 
numerous Woodcuts in the Text, and a folio Atlas of 14 Plates of 
Figures and Sections in Lithography. 8vo. 14s. 

STONEY— The Theory of the Stresses on Girders and 

Similar Structures. With Practical Observations on the Strength and 
other Properties of Materials. Bv Bindox B. Stoney, LL.D., F.R.S., 
M.I.C.E. With 5 Plates and 143 Illustrations in the Te.xt. Royal 
8vo. 36s. 

UNWIN— The Testing of Ma,terials of Construction. Em- 
bracing the Desciiptiun of Testing Machinery and Apparatus Auxiliary 
to Mechanical Testing, and an Account of the most Important Re- 
searches on the Strength of Materials. Bv W. Cawthorne Unwin, 
B.Sc, Mem. Inst. Civil Engineers. With 141 Woodcuts and 5 
folding-out Plates. 8vo. 21s. 

Scientific Works published by Longmans, Green, ct^ Co. 13 


JAY and KIDSON Exercises for Technical Instruction in 

Wood- Work iiii;. DL'si<,nieil niid Drawn liy H. Jay, IVcliuical Instructor, 
Nottin^^liani School Board. Arranj^ed by E. R. Kidson, F.G.S., 
Science Demonstrator, Xottin,i,diani Scliool Board. 3 sets, price l.s'. 
each in cloth case. Set I. Plates 1-32. Set II. Plates 33-64. Set III. 
Plates 65-87. 

NORTHCOTT— Lathes and Turning, Simple, Mechanical and 
Ornamental. Bv W. H. Xorthcutt. With 338 Illustrations. 
8vo. 18.5. 

SHELLEY— "Workshop Appliances, includin<j; Descriptions of 
some of the (JauginLj and Measuring Instiuments, Hand-cutting Tools, 
Lathes, Drilling, Planing and other Machine Tcjols used by Engineers. 
By C. P. B. Shelley. 'M.I.C.E. AVith 292 Woodcuts. Fcp. 8vo. 
4s. M. 

UN"WIN— Exercises in "Wood-Working for Handicraft Classes in 
Elenieiitarv and Technical Schools. Bv William Cawthorne Unwin, 
F.R.S., M.I.C.E. 28 Plates. Fcp. fofio. 4.5. U. in case. 


BAUERMAN— Works by Hilary Bauerman, F Ci.S. 

Systematic Mineralogy. With 373 Woodcuts and Diagram.?. 

Fcp. 8vo. 6.5. 

Descriptive Mineralogy. With 236 Woodcuts and Diagrams. 

Fcp. 8vo. 6s. 

BLOXAM and HUNTINGTON— Metals : their Properties and 
Treatment. By C. L. Bloxam and A. K. Huntington, Professors 
in King's College, London. With 130 Woodcuts. Fcp. 8vo. 5s. 

GORE- The Art of Electro-Metallurgy, including all known 
Processes cjf Electro-Deposition. By (J. Gore, LL.D., F.R.S. AVitb 
56 Woodcuts. Fcp. 8vo. 6s. 

LUPTON— Mining. An Elementary Treatise on the Getting of 
Minerals, liy ARNOLD Lri'ToN, M.I.C.E., F.G.S., etc., Mining 
Ejigineer, Professor of Coal Mining at the Victoria University, York- 
shire College, Leeds. With 596 Illustration.s. Crown 8vo. 9.5. net. 

MITCHELL— A Manual of Practical Assaying. By John 
^IrrcHELL, F.C.S. Bcvised, with tlie Pii-cent Discoveries incorporated. 
By W . CrooivES, F.R.S. With 201 Illustrations. 8vo. 31s. 6rf. 

RUTLEY- The Study of Rocks; an Elementary 1Vxt-Book of 
Pelioldgy. By F. Bltley, F.G.S. With 6 Plates and «8 "Woodcuts. 
Fcp. 8vo. 4s. 6d. 

VON GOTTA- - Rocks Classified and Described : A Treatise 
on Litiiology. By Bkrnhard \'oN Coxta. ^^ith English, (Jei man, 
and French Svnonvnis. Tian.slated by Philip Henry Lawrence. 
F.G.S., F.R.G.S. Crown 8vo. 14s. 

14 Scientific Works published by Longmans, Green, 6^ Co. 


LOW AND BEVIS— A Manual of Machine Drawing and 
Design. By David Allan Low (Wliitwoith Scholar), M.I. Mecli. E., 
Head master of the Technical School, People',-, Palace, London ; and 
Alfred William Bevis (Whitworth Scholar), M.I. Mech.E., Director 
of Manual Training to tlie Birmingham School Board. With over 
700 Illustrations. 8vo. 7.s'. 6d. 

LOW— Improved Drawing Scales. By David Allan Low (Whit- 
worth Scholar), Headmaster ot the Technical School, People's Palace, 
London. 4rf. in case. 

LOW— An Introduction to Machine Drawing and Design, 
By David Allan Low, Headmaster of the Technical School, People's 
Palace, London. With 97 Illustrations antl Diagrams. Crown 8vo. 


UNWIN— The Elements of Machine Design. By W. Caw- 

THORNE Unwin, F.R.S., Professor (;f Engineering at the Central 
Institute of the City and Guilds of London Institute. Part I. General 
Principles, Fastenings and Transmissive Machinery. With 304 Dia- 
grams, &c. Crown 8vo. 6s. Part II. Chielly on Engine Details. 
With 174 Woodcuts. Crown Bvo. 4s. 6d. 


BALL— Works by Sir Robert S. Ball, LL.D., F.R.S. 

Elements of Astronomy. With 136 Figures and Diagrams, 

and 136 Woodcuts. Fcp. 8vo. 6s. 

A Class-Book of Astronomy. With 41 Diagrams. Fcp. 

8vo. Is. 6d 

BCEDDICKBR— The Milky Way. From the North Pole to 10° of 
South Declination. Drawn at the Earl of Rosse's Observatory at Birr 
Castle. By Otto Bceddicker. With Descriptive Letterpress. 4 
Plates, size 18 in. by 23 in. in portfolio. 30s. 

BRINKLEY— Astronomy. By F. Brinkley, formerly Astronomer 
Royal for Ireland. Re-edited and Revised by J. W. Stubbs, D.D., 
and F. Bronnow, Ph.D. With 49 Diagrams. Crown 8vo. Qs. 

CLERKB— The System of the Stars. By Agnes M. Clerke, 
With 6 Plates and numerous Illustrations. 8vo. 21s. 

HERSCHEL -Outlines of Astronomy. By Sir John F. W. 
Herschel, Bart., K.H., &c. With 9 Plates and numerous Diagrams. 
Crown Bvo. 12s. 

MARTIN— Navigation and Nautical Astronomy. Compiled 
by Staff-Commander W. R. Martin, R.N. Royal 8vo. IBs. 

MERRIPIELD— A Treatise on Navigation for the use of Students. 
By John Merrifield, LL.D., F.R.A.S., F.M.S. Crown Bvo. 5s. 

Scientific Works published by Longfnans, Green, &= Co. 15 
PROCTOR—Works by Richard A. Proctor. 

Old and New Astronomy. 12 Parts, Light Science for Leisure Hours : 

2s. 6(/. each. Suiniltini^itary Section, Faiiiili:ir Essays on Scientific Suhjects, 
Is. Coniiilete in 1 vol. •Ito. .36s. ! Natnral Pliciioniena, &c. 3 vols. Cr. 

8vo. f>s. each. 

Myths and Marvels of Astronomy. 

Crown 8vo. 5s. Silver Library 
Edition. Crown 8vo. 3s %d. 

The Moon : Her .Motions, Aspect, 
Scenery, and Physical Condition. 
With many Plates and Charts, Wood 
Engraving, and 2 Lunar Photograjjlis. 
Grown 8vo. 5s. 

The Universe of Stars : Researches 

into, and New \'i('ws respecting, the 
Constitution ot the Heavens. With 
22 Charts (4 coloured) and 22 Dia- 
grams. Svo. 10s. &d. 

Other Worlds than Ours: the 

Plurality of Worlds Studied under 
the Light of Recent Scientific Re- 
searches. With 1-1 Illustrations ; 
.Map, Charts, &c. Crown Svo. 5s. 
Silver Library Edition. Crown Svo. 
3s. M. 

Treatise on the Cycloid and all 

Forms of Cycloidal Curves, and on 
the Use of Cycloidal Curves in dealing 
with the Motions of Planets, Comets, 
&c. With 161 Dii'grams. Crown 
Svo. lOi-. M. 

The Orbs Around Us 

Moon and Planets, 
Comets, the Sun and 
of Suns. Crown Svo. 

; Essays on the 
Meteors and 

Coloured Pairs 

0\\i Place among Infinites : Essays 

contrasting our Little Abode in Space 
and Time with the Infinites around 
us. Crown Svo. fis. 

The Expanse of Heaven : Essays on 

the Wonders of ihc Firmament. Cr. 
Svo. 5s. 

New Star Atlas for the Library, 

the School, and the Observatory, in 
Twelve Circular Maps (with 2 Index- 
Plates). Witii an Intioduction on the 
Study of the Stars, Illustrated by 9 
Diagrams. Crown 8vo. 5s. 

Larger Star Atlas for Observers and 
Students. In Twelve Circular Maps, 
showing 6000 Stars, 1500 Double 
Stars, Nebuhe, &c. With 2 Index- 
Plates. Folio, 15s. ; or the Twelve 
Map.s only, 12s. &d. 

The Stars in their Seasons : an Easy 

Guide to a Knowledge of the Star 
Groups. In 12 Laige Maps. Im- 
perial Svo. 5s. 

The Star Primer: showing the Starry 
Sky, Week by Week. In 24 Hourly 
Maps. Crown 4 to. 2s. 6f^. 

Lessons in Elementary Astro- 
nomy ; with Hints lor Young Telc- 
sco})ists. With 47 Woodcuts. Fcj". 
Svo. Is. M. 

WEBB -Celestial Objects for Common Telescopes. By the 
Rev. T. \\. Wehb, M.A., F.R.A.S. Fifth Editiim, lU-viscl and grcatlv 
Enlarged, by the Rev. T. E. Espin, M.A., F.R.A.S. 2 vols. Vol. 1. 
now ready. With Portrait and a Reminiscence of the Author. 2 
Plates, and numerous Illustrations. Crown Svo. 6s. 

1 6 Scientific Works published by Longmans, Green, ^^ Co. 


ARNOLD— Steel Manufacture. By J. 0. Arnold, [hi prejjaration. 

MORRIS AND WILKINSON— Cotton Spinning. By John 
Morris and F. W. Wilkinson. [In yreparation, 

SHARP— The Manufacture of Bicycles and Tricycles. By 

Archibald Sharp. \In preparation. 

TAYLOR— Cotton "Weaving and Designing. By John J. 

Taylor, Lecturer on Cotton Weaving and Designing in the Preston, 
Asliton-under-Lyne, Chorley, and Todniorden Technical Schools, &c. 
With 373 DiagrcWs. Crown 8vo. 7s. Qd. net. 

"WATTS— An Introductory Manual for Sugar Growers. By 
Francis Watts, F.C.S., F.I.C., A.ssoc. Mason Coll., Birniinghani, 
and Government Chemist, Antigua, West Indies. Witli 20 Illustra- 
tions. Crown 8vo. 6s. 


BIRD — Works by Charles Bird, B.A., F.G.S., Headmaster of the 
Eoch ester Mathematical School. 

Elementary Geology. With Geological Map of the British 

Isles, and 247 Illustrations. Crown 8vo. 2s. Qd. 

Advanced Geology. \In j^reparation. 

GREEN — Physical Geology for Students and General 
Readers. With Illustrations. By A. H. Green, M.A., F.G.S., Pro- 
fessor of Geology in the University of Oxford. 8vo. 21s. 

LE"WIS— Papers and Notes on the Glacial Geology of 

Great Britain and Ireland. By the late Henry Carvill Lewis, M.A., 
F.G.S., Professor of Mineralogy in the Academy of Natural Sciences, 
Philadelphia, and Professor of Geology in Havei-ford College, U.S.A. 
Edited from his unpublished MSS. With an Introduction bv Henry 
W. Crosskey, LL.D., F.G.S. 

THORNTON— Work by John Thornton, M.A., Headmaster, Clarence 
Street Higher Grade School. 

Elementary Physiography: an Introduction to the Study 

of Nature. With 10 Maps and 173 Illustrations. New Edition, with 
Appendix on Astronomical Instruments and Measurements. Crown 
8vo. 2s. 6d. 

Advanced Physiography. With G Maps and 180 Illustra- 
tions. Crov.-n 8vo. 4s. 6'/. 

Scientific Works published by Longmans, Green, &= Co. 1 7 


BRODRIBB— Manual of Health and Temperance. liy T. Brod- 
RiBB. M.A. With Extracts from Gough'!? 'Temperance Orations'. 
Revised and Edited bv tlie Rev. W. Ruthven Pym, M.A. Crown 
8vo. !.>;. 6(/. 

BUCKTON -Health in the House; Twenty-five Lectures un Ele- 
mentary PhysioloLiy in its Application tu the Daily Wantt* of Man and 
Animals. By Catherine M. Buckton. With 41 Woodcuts and 
Diagrams. Crown 8vo. 2s. 

CORFIELD— The Laws of Health. Bv W. H. Corfield, M.A., 
M.D. Fcp. 8v<x l.s. U. 

FRANKLAND— Micro-Organisms in "Water, their Significance, 
Idenliticatiun, and Removal. Together with an Account of the 
Bacteriological Methods involved in their Investigation. Specially 
Designed for those connected with the Sanitary Aspects of Water 
Supply. By Professor Percy Fraxkland, PIi.D., B.Sc. (Lond.j, 
F.R.S', and Mrs. Percy Frankland. 

POORE— Essays on Rural Hygiene. Bv George 'S'ivian Poore, 
M.D. (Jrown 8vo. 6*-. 6(/. 

WILSON— A Manual of Health-Science : adapted for use in 
Schools and Colleges, and suited to the Requirements of Students pre- 
paring for the Examinations in Hvgiene of the Science and Art Depart- 
ment, &c. By Andrew Wilson, F.R.S.E., F.L.S., &c. With 74 
Illustrations. Crown 8vo. is. Gd. 


ABNEY— A Treatise on Photography. By Captain W. de Wive- 
LESLIE Abney, F. H.S., late Instructor in Cliemistry and Photography 
at the School of Military Engineering, Ciiatham. With Wood- 

cuts. Fcp. 8vo. 3s. 6rf. 

GLAZEBRO OK -Physical Optics. By R. T. Glazebrook, M.A., 
F.R.S., Fellow and Lecturer of Trin. Coll., Demonstrator of Physics 
at the Cavendi.sli Laboratory, Camhridge. With 183 Woodcuts of 
Apparatus, &c. Fc)). 8vo. Gs. 

WRIGHT— Optical Projection : a Treatise on the Use of the 
Lantern in Exliibition and Scientific Demonstration. By Lewis 
Wright, Author of 'Light: a Course of Experimental Optics'. 
With 232 Illustrations. Crown 8vo. 6s. 

1 8 Scientific Works published by Loni:^mans^ Green, &> Co. 


ASHBY^Notes on Physiology for the Use of Students 

prepaiing fur Exaniimition. By Henry Ashby, M.D. Witli 141 
Illustrations. Fcp. 8vo. 5s. 

BARNETT— The Making of the Body: a Reading Book for 
Children on Anatomy and Physiology With Illustrations and 
Examples. By Mrs. S. A. Barnett. [/;; the press. 

BIDGOOD— A Course of Practical Elementary Biology, 

By John Bidgood, B.Sc, F.L.S. With 226 Illustrations. Crown 
8vo. 4.S. 6d. 

BRAY -Physiology and the Laws of Health, in Easy Lessons 
for Schools. By Mrs. Charles Bray. Fcp. 8vo. Is. 

PURNEAUX— Human Physiology. By W. Fukneaux, F.R.G.S. 
With 218 Illustiations. Crown Svo. 2s. 6d. 

HUDSON and GOSSB— The Rotifera, or ' Wheel- Animal- 
cules'. By C. T. Hudson, LL.D., and P. H. Gosse, F.R.S. With 30 
Coloured and 4 Uncohnired Plates. In 6 Parts. 4to. 10s. 6d. each ; 
Supp)lement, 12s. 6d. Complete in 2 vols, with Supplement, 4to. £4 4s. 

MACALISTBR— Works by Alexander Macalister, M.D., Professor 
of Anatomy, University of Cambridge. 

Zoology and Morphology of Vertebrata. 8vo. 10s. 6d. 

Zoology of the Invertebrate Animals. With 59 Dia- 
grams. Fcp. 8vo. Is. 6(/. 

Zoology of the Vertebrate Animals. With 77 Diagramfi. 

Fcp. 8vo. Is. 6d. 

MORGAN -Animal Biology: an Elementary Te.xt-Book. By C. 
Lloyd Morgan, Professor of Animal Biology and Geology in Uui- 
versitj" College, Bristol. With numerous Illustrations. Cr. 8vo. 8s. Gd. 

THORNTON- Human Physiology. By John Thornton, 
M.A. W^ith 258 Illiisti'atiinis, sume ot wliich are coloured. Crown 


ABBOTT— Elementary Theory of the Tides : tlie Fundamental 
Theorems Demonstrated without ]\lathem<atics, and the Influence on 
the Length of the Day Discussed. By T. K. Abbott, B.D., Fellow 
and Tutoi', Trinity College, Dublin. Crown 8vo. 2s. 

JORDAN — The Ocean : a Treatise on Ocean Currents and Tines, and 
their Causes. By William Leighton Jordan, F.R.G.S. Svo. 21s. 

SCOTT — Weather Charts and Storm Warnings. By Robert 
H. Scott, M.A., F.R.S., Secretary to the Meteorological Council. 
With numerous Illustrations. Crown 8vo. 6s. 

Scientific JVorks published dy Longmans, Greeti, & Co. 19 


AITKEN- Elementary Text-Book of Botany. For the use of 

Schools. By Edith Aitken, late Scholar of Giitou College. With 
over 400 Diagrams. Crown 8vo. 4s. 6d. 

BENNETT and MURRAY — Handbook of Cryptogamic 
Botany. By Alfred W. Bennett, M.A., B.Sc, F.L.S., Lecturer on 
Botany at St. Thomas's Hospital ; and George Murray, F.L.S., 
Senior Assistant Department of Botany, British Museum. With 378 
Illustrations. Svo. 16s. 

EDMONDS— Elementary Botany. Theoretical and Practical. By 
Henry Edmonds, B.Sc, London. With 319 Diagrams and Woodcuts. 
Crown Svo. 2.«. <6d. 

KITCHENER— A Year's Botany. Adapted to Home and School 
Use. With Illustrations by the Author. By Frances Anna Kit- 
chener. Crown Svo. 5s. 

LINDLEY and MOORE— The Treasury of Botany ; or, Popular 
Dictionary nf tlie Vegetable Kingdom : with which is incorporated a 
Glossary of Botanical Terms. Edited hy J. Lindley, M.D., F.R.S., 
and T. Moore, F.L.S. With 20 Steel Plates and numerous Wood- 
cuts. 2 Parts. Fcp. Svo. 12s. 

McNAB -Class-Book of Botany. By W. R. McNab. 2 Parts. 
Morphology and Physiology. With 42 Diagrams. Fcp. Svo. Is. 6d. 
Classification of Plants. Witli 118 Diagrams. Fcp. 8vo. Is. 6rf. 

THOME and BENNETT— Structural and Physiological 
Botany. By Ur. (Jtto Wilhelm Thome and liy Alfred W. Ben- 
nett, M.A., B.Sc, F.L.S. With Coloured Map and 600 Woodcuts. 
Fcp. 8vo. %s. 

WATTS— A School Flora. For the use of Elementary Botanical 
Classes. ^\ W. Marshall Watts, D..Sc., Lond. Cr. 8vo. 2s. 6d. 


ADD YM AN— Agricultural Analysis. A Manual of Qnantitative 
Analysis for Students of Agriculture. By Frank T. Addyjlvn, B.Sc. 
(Limd.), F.I.C. With 49 Illustrations. Crown 8vo. 5s. net. 

COLEMAN a,nd ADDYMAN- Practical Agrictiltural Che- 
mistry. For Elementary Students, adapted for use in Agricultural 
Classes and Colleges. By J. Bernard, A.R.C.Sc, F.I.C, 
and Frank T. Ad'dyman, B.Sc (Lond.), F.I.C. Crown 8vo. Is. 6(f. 

LLOYD- The Science of Agrictilture. By F. J . Llovd. 8vo. 12«. 

20 Scientific Works published by Longmans, Green, & Co. 

LOUDON— Works by J. C. Loudon, F.L.S. 

— Encyclopaedia of Gardening ; the Theory and Practice of 

Horticulture, Floriculture, Arboriculture and Landscape Gardening. 
With 1000 Woodcuts. 8vo. 21s. 

— Encyclopsedia of Agriculture ; the Laying-out, Improvement 
and Management of Landed Property ; the Cultivation and Economy 
of the Productions of Agriculture. With 1100 Woodcuts. 8vo. 21s." 

Encyclopaedia of Plants ; the Specific Character, Description, 

Culture, History, &c., of all Plants found in Great Britain. With 
12,000 Woodcuts. 8vo. 42.s. 

RIVERS— The Miniature Fruit Garden ; or, The Culture of Pyra- 
midal and Bush Fruit Trees. By Thomas T. F. PavERS. With 32 
Illustrations. Crown Bvo. \s. 

VILLB— The Perplexed Farmer : How is he to meet Alien Com- 
petition ? By George Vjlle. Translated from the French by 
William Crookes, F.R.S., V.P.C.S., &c. Crown 8vo. 5s. 

WEBB-Works by Henry J. Webb, Ph.D., B.Sc. (Bond.) ; late Principal 
of the Agricultural College, AspaLria. 

— Elementary Agriculture. A Text-Book specially adapted 

to the requirements of the Science and Art Department, the Junior 
Examination of the Royal Agricultural Society and other Elementary 
Examinations. With 34 Illustrations. Crown 8vo. 2s. 6rf. 


{Adapted for the Use of Students in J'ahlic or Science Schools.) 

Photography. Bv Captain W. De Wiveleslie Abney C.B., F.R.S. 

105 Woodcuts. ' Fcp. 8vo. 3s. od. 

The Strength of Material and Structures : the Strength of 
Materials as depending on their Quality and as ascertained l)y Testing 
Apparatus ; the Strength of Structures, as depending on their form 
and arrangement, and on the materials (jf which they are composed. 
By Sir J. Anderson, C.E., &c. 66 Woodcuts. Fcp. 8Vo. 3s. 6d. 

Railway Appliances — A Description of Details of Railway Construction 
suhse(pient to the coujpletion of Earthworks and Structures, including 
a short Notice of Railwav Rolling Stock. By John AVolfe Barry, 
M.I.C.E. 218 Woodcuts." Fcp. 8vo. 4s. 6d. " 

Introduction to the Study of Inorganic Chemistry. By 
William Allen Miller, M.D., LL.D., F.R.S. 72 Woodcuts 3s. 9rf. 

Introduction to the Study of Organic Chemistry : the Chemis- 
try of Carbon and its Compounds. Bv Henry E. Armstrong, Ph.D., 
F.R.S. 8 Woodcuts. Fcp. 8vo. 3s. Gd 

Quantitative Chemical Analysis- By T. E. Thorpe, F.R.S., Ph.D. 
With 88 A^'oodcut^. Fcp, 8vc. 4s. 6d. 

Scientific Wo7-ks published by Longmans^ Green, & Co. 21 


Qualitative Analysis and Laboratory Practice. Bv T. E. 
Thorpe. Ph.D., F.R.S., uii.i M. M. Pattison Muik, M..\., F.KS.E. 

AVitli Plate of Spectra and 57 Woodcuts. Fcp. 8vo. 3.s-. (jtJ. 

Introduction to the Study of Chemical Philosophy. TLe 
Principles of Theoretical and Systematical Chenii-stry. By William 
A. TiLDEN, D.Sc. London, RR.S. With 5 Woodcuts.' With or 
without Answers to Problems. Fcp. 8vo. 4s. 6d. 

Elements of Astronomy. By Sir K S. Ball, LL.D., F.R.S. With 
136 Woodcuts. Fcp. 8vo. 6s. 

Systematic Mineralogy. By Hilary Baderman, F.G.S. With 
373 Woodcuts. Fcp. 8vo. 6s. 

Descriptive Mineralogy. By Hilary Bauerman, F.G.S. , &c. With 

236 Wooilcuts. Fcp. 8vo. 6.-;. 
Metals, their Properties and Treatment. By C L. Bloxam, 

and A. K. HuNTiNtiTOX, Professors in King's College, London. 130 

Woodcuts. Fcp. 8vo. 0.9. 

Theory of Heat. By J. Clerk ^Iaxwell, M.A., LL.L). Edin., L. and E. New Edition, with Corrections and Additions by 
Lord Rayleigh. With 38 Illustration.s. Fcp. 8vo. 4s. 6d. 

Practical Physics. Bv R. T. Glazebrook, M.A.. F.R.S., and W. N. 
Shaw, :\I.A. With 134 WcMjdcuts. Fcp. 8vo, 7s. M. 

Preliminary Survey. By Theodore Graham Griisble, Civil 
Engineer. Including Elementary Astronomy, Route Surveying, 
Tacneometry, Curve-ranging. Gray)hic Mensuration, Estimates, 
Hydrography, and Instruments. 130 Illustrations. Fcp. 8vo. 6s. 

Algebra and Trigonometry. By William Nathaniel Griffin, 
p.. I). 3s. 6'/. Niitfs on, with Solutions of the more ditticult Ques- 
ticnis. Fcj). 8vo. 3s. 6d. 

The Steam Engine. By George C. V. Holmes, Secretary of the 
Institution of Xaval Architects. 212 Woodcuts. Fcp. 8vo. 6s. 

Electricity and Magnetism. By Fleeming Jenkin, F.R.SS., L. 
and PI With 177 Wooilcuts. Fcp. 8vo. 3s. M. 

The Art of Electro-Metallurgy, including all known Processes of 
Electn)-l)e]H)siti(ui. By G. (4oRt:, LL.D., F.R.S. With 56 Wood- 
cuts. Fcp. 8vo. 6s. 

Telegraphy. Bv W. H. Preece, F.R.S., M.I.C.E., and Sir J. 
Sivewright, M.A., K.C.M.G. 255 Woodcuts. Fcp. 8vo. 6.5. 

Physical Optics. R. T. Glazebrook, M.A., F.R.S. With 183 

A^ oodruts. Fcp. 8vo. 6s. 

Technical Arithmetic and Mensuration. By Charle.s W. 
Merrifield, F.R.S. 3.s-. (id. Key, by the Rev. John Hunter, M.A. 

Fc].. Hvo. 3s. 0'/. 
The Study of Rocks, an Eleuientary Text-Book of Petrology. By 
Frank Rutley, F.G.S. With 6 Plates and 88 Woodcuts. Fcp. 
8vo. 4s. 6'/. 

2 2 Scientific Works published by Longmans, Green, &= Co. 

"Workshop Appliances, includiug Descriptions of some of the Gauging 
and Measuring Instruments — Hand-Cutting Tools, Lathes, Drilling, 
Planing, and other Machine Tools used by Engineers. By C. P. B. 
Shellky, M.I.C.E. With 291 Woodcuts. ' Fci>. 8vo. 4s. 6(^. 

Elements of Machine Design. Bv W. Cawthorne Unwin, F.R.S., 
B.Sc, M.I.C.E. 
Part I. General Principles, Fastenings, and Transmissive Machinery. 

304 Woodcuts. 6s. 
Part II. Chiefly on Engine Details. 174 Woodcuts. Fcp. 8vo. 

4s. m. 

Structural and Physiological Botany. By Dr. Otto Wilhelm 
ThomiS, and A. AV. Bennett, M.A., B.Sc, F.L.S. With 600 Wood- 
cuts. Fcp, 8vo. 6s. 

Plane and Solid Geometry. Bv H. W. Watson, M.A. Fcp. 8vo 
3s. 6(/. 


Written S'pecially to meet the requirements of the Elementary Stage of 
Science Subjects as laid down in the Syllabus of the Directory of the 
Science and Art Department. 

Practical Plane and Solid Geometry, including Graphic Arith- 
metic. By I. H. Morris. Fully Illustrated with Drawings prepared 
specially for the Book. Crown 8vo. 2s. 6d. 

Geometrical Drawing for Art Students. Embracing Plane Geo- 
metry and its Applications, the Use of Scales, and the Plans and 
Elevations of Solids, as required in Section I. of Science Subject I. 
By I. H. Morris. Crown 8vo. Is. 6d. 

Being the First Part of Morris's Practical Plane and Solid Geometry. 

Text-Book on Practical, Solid, or Descriptive Geometry. 

By David Allen Low (Whitworth Scholar). Part I. Crown 8vo. 2s. 
Part II. Crown 8vo. 3s. 

An Introduction to Machine Drawing and Design. By David 
Allen Low (Whitworth Scholar). With 97 Illustrations and Dia- 
grams. Crown 8vo. 2s. 

Building Construction. By Edward J. Burrell, Second Master at 
the Technical School of the People's Palace, London. With 308 
Illustrations and Working Drawings. Crown 8vo. 2s. 6d. 

An Elementary Course of Mathematics. Containing Arith- 
metic ; Euclid (Book I. with Deductions and Exercises) ; and Alo-ebra 
Crown 8vo. 2s. 6d. 

Theoretical Mechanics. Including Hydrostatics and Pneumatics. 
By J. E. Taylor, M.A., Hon. Inter. B.Sc. With numerous Examples 
and Answers, and 175 Diagrams and Illustrations. Crown 8vo. 2s. 6d. 

Scientific Works published by Lotigmans, Green, S^ Co. 23 


A Manual of Mechanics : un Elementary Text-Book for Students of 
Apjilied Mechanics. .With 138 Illustrations and Diagrsnns, and 188 
E.vainples taken from the Science Department E.\.amination Papers, 
witli An.swers. By T. M. Ooodevk, M.A. Fcp. 8vo. 2s. M. 

Sound, Light, and Heat. By Mark K. Wright (Hon. Inter. B.Sc. 
London). With 160 Diagrams and Illustrations. Crown 8vo. 2.^. Gd. 

Physics. Alternative By Mark E. Wright, Author of 'Sound, 
Light, and Heat'. With 242 Illustrations. Crown 8vo. 2s. Qd. 

Magnetism and Electricity. By A. W. Poyser, M.A. With 235 

Illustiations. Crown 8vi>. 2.5. 6(/. 

Inorganic Chemistry, Theoretical and Practical. With an 
Introductii n to the Principles of Chemical Analysis. By William 
Jago, F.C.S., F.I.C. With 49 Woodcuts and numerous Questions 
and Exercises. Fcp. 8vo. 2.5. 9f?. 

An Introduction to Practical Inorganic Chemistry. Bv 

William Jago, F.C.S.. F.I.C. Crown 8vo. l.s. 6(/. 

Practical Chemistry : the Principles of Qualitive Analysis. By 
William A. Tildkn', U. Sc. Fcp. 8vo. Is. Gc/. 

Elementary Inorganic Chemistry. By W. S. Furneaux, F.R.G.S., 
Crown 8vo. 2s. 6cf. 

Elementary Geology. By Charles Bird, B.A., E.G. 8. With 
Coloured Geological Map of the British Islands, an-1 247 lllustration.s. 
Crown 8vo. 2s. 6f/. 

Human Physiology. By William S. Furneaux, P'.R.G.S. With 
218 Illustrations. Crown 8vo. 2s. Qd. 

Elementary Botany, Theoretical and Practical. By Henry 
Edmonds, B.Sc, London. With 319 Woodcuts. Crown 8vo. 2s. 6rf. 

Steam. By William Ripper, Member of the Institution of Mechanical 
Engineers. With 142 Illustrations. Crown 8vo. 2s. Qd. 

Elementary Physiography. By .1. Thornton, M.A. With 10 
Ma]>s and 173 Illustrations. With A])pendix on Astronomical 
Instruments and Measurements. Crown 8vo. 2s. iid. 

Agriculture. By Hkxry J. Webu, Ph.D., Agricidtural College, 
Asjiatiia. \Vilh 34 Illustrations. Crown 8vo. 2.s-. ikl. 

A Course of Practical Elementary Biology. By J. Bipgoop, 
J5.Sc. With 22(; Illustrations. Crown 8vo. 4.s-. fu/. 

24 Scientific Works published by Longmans, Green, & Co. 


Written speciulhj to meet the requirements of the Advanced Stage of 
Science Subjects as laid down in the Syllabus of the Directory of the 
Science and Art Department. 

Magnetism and Electricity. By Arthur William Poyser, M.A., 
Trinity College, Dublin. With .'^7 Diagrams. Crown 8vo. 4.s. Qd. 

Inorganic Chemistry, Theoretical and Practical. A Manual 
for Student.s in Advanced Classes of the Science and Art Department. 
By William Jago, F.C.S., F.I.C. With Plate of Spectra, and 78 
Woodcuts. Crown 8vo. 4s. Qd. 

Physiography. By John Thornton, M.A. With 6 Maps, 180 Illus- 
trations, and Coloured Plate of Spectra. Crown 8vo. 4s. 6rf. 

Heat. By Mark R. Wright, Principal of the Normal Department, 
Durham College of Science, Hon. Inter. B.Sc. (Lond.). With 136 
Illustrations and numerous Examples and Examination Papers. Crown 
8vo. As. 6d. 

Building Construction. By the Author of ' Rivington's Notes on 
Building Construction '. With 385 Illustrations, and an Appendix, 
of Examination Questions. Crown 8vo. 4s. 6d. 

Geology. By Charles Bird, B.A. [In preparation. 

Human Physiology. By John Thornton, M.A. With 258 Illustra- 
tions, some di' which are coloured. Crown 8vo. 6s. 

Theoretical Mechanics : Section 1., Solids. By A. Thornton, M.A. 

[7?i preparation. 


Edited by G. Carey Foster, F.R.S., and by Sir Philip Magnus, B.Sc, 

B. A., of the City and Guilds of London Institute. 
Astronomy. By Sir Robert Stawell Ball, LL.D., F.R.S. With 41 

Diagrams. Is. Qd. 
Mechanics. By Sir Robert Stawell Ball, LL.D., F.R.S. With 89 

Diagrams. Is. Qd. 
The Laws of Health. By W. H. Corfield, M.A., M.D., F.R.C.P. 

With 22 Illustrations. Is. 6f?. 
Molecular Physics and Sound. By Frederick Guthrie, F.R.S. 

With 91 Diagrams. Is. 6^/. 
Geometry, Congruent Figures. Bv O. Henrici, Ph.D., F.R.S. 

With 141 Diagrams. Is. 6(/. 
Zoology of the invertebrate Animals. By Alexander McAlister, 

M.D. With 59 Diagrams. Is. 6rf. 
Zoology of the Vertebrate Animals. By Alexander McAlister, 

M.D. With 77 Diagrams. Is. 6(/. 
Hydrostatics and P'neumatics. By Sir Philip Magnus, B.Sc, 

B.A. With 79 Diagrams. Is. Gd. (To be had also vnth Answers, 2«.) 

The Worked Solution of the Problems, 2s. 
Botany. Outlines of the Chissification of Plants. By W. R. McNab, 

M.D. Witii 118 Diagrams. Is. 6(i 
Botany. Outlines of Morphology and Physiology. By W. R. McNab, 

M.D. With 42 Diagrams. \s". Qd. 
Thermodynamics. By Richard Wormell, M.A., D.Sc With 41 

Diagrams. Is. 6d. 

[5000.— 12/93.] 



}^hysical Ac 
-\ppliMl Sd. 

Carnegie, J^ouglas 

Law and theory in chemistry