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modifications of one and the same force; whilst others are inclined to believe that there is an essential difference between them, and that they are originally distinct from each other. It is almost unnecessary to observe, that these opinions are merely hypothetical, and that it is impossible (considering the present imperfect state of our knowledge upon this intricate and mysterious subject) to decide in favour either of the one or the other.

The attraction of gravitation is distinguished from the other species, by its operating upon large masses of matter at sensible distances: this power acts in a direct ratio to the quantity of matter, and inversely as the square of the distance. The magnetic and electric attractions act also upon masses of matter, placed at sensible distances, and in this respect they correspond with the attraction of gravitation.

By the attraction of cohesion is meant that force, or power, by means of which, particles of the same kind of matter are brought into more or less intimate union, and are retained in that state with different degrees of force. Thus, for instance, the particles of a piece of iron are united with greater force than the particles of a piece of wood; and the particles of the latter are far more closely united than those which constitute a fluid. It is obvious, therefore, that the density of any substance depends upon the degree of force which is exerted between its particles, and, in proportion to its density, will be the force required to overcome their cohesion.

2. If we mix together a quantity of sulphuric acid and a solution of pure potash, a compound is formed, very different in its properties from either of the substances which enters into its composition: the sulphuric acid and pure potash are powerful corrosives, whilst the sulphate of potash, which is the result of the affinity, is a mild, saline substance, not possessing, in the least degree, the acrimony or the deleterious properties of its constituent ingredients. All the physical and chemical qualities of the compound differ more or less from the substances, between which the affinity is exerted: the form, colour, taste, smell, specific gravity, fusibility, volatility, and disposition to combine, are sometimes so much altered, as to bear no resemblance to these properties in the original bodies.

In the first experiment, we have an example of chemical solution: this term is made use of to denote that action which takes place between a solid and a fluid, the result of which is a liquid compound. It has been supposed, that in this case the liquid is the active principle, and that the solid is dissolved by it, as if the solid possessed no power of attraction. There is, however, a reciprocal affinity exerted in producing the combination.

Berthollet has applied the term solution in a different sense, to denote that case of chemical action, in which there is the transition of a solid to the liquid state, in consequence of the action of a liquid upon it, without any important change of properties. He has even extended it so far as to apply Chemical attraction, or affinity, de- it to all cases of chemical union, whether notes that power, by means of which between a solid and a liquid, two particles of different bodies become liquids, two airs, or an aëriform subintimately united, and form new com- stance, and one either in the solid or binations, differing more or less from liquid form, which is not intimate, and the substances of which they are form- where the attraction is not sufficiently ed. After this affinity has been ex-powerful to produce a material change erted between two or more substan- in the properties of the substances ces, no spontaneous change takes entering into combination. place, nor can they be separated by Although, however, the change of any mechanical force; they may, how-properties after chemical action is ever, be disunited by chemical agency. often remarkable and important, it A few experiments will illustrate this will be premised, from what has been species of attraction. said, that it is not to be regarded as invariably so. In the combinations of saline and vegetable substances with water, and of animal and vegetable products with alcohol, in all the alloys that are formed by the union of different metals, some or other of the pro

1. If we pour water upon any soluble salt, the particles of the salt will enter into combination with the water, and be diffused through it, and it will be found impossible to separate them by any other than chemical means.

perties of the original ingredients are recognised in the compounds.

The older chemists supposed that the properties of the compound were intermediate between those of its constituent parts, or were derived from their elements; and it was from this, that the acute philosopher, Newton, conjectured the existence of an inflammable substance in water, founded upon its great refractive power. This opinion, however, is now rejected; for although some examples of combinations appear to favour the conjecture, others are quite opposed to it.

Besides a change of properties attending chemical combination, there occurs a change of temperature, that is, either heat or cold are produced. This is explained upon the principle, that different bodies possess different capacities for caloric: if, therefore, the compound resulting from chemical action possesses a capacity greater or less than the bodies which enter into its composition, there will be either an absorption or evolution of caloric.

Artificial heat is produced by the

combustion of different substances from the three kingdoms of nature, by fermentation, and by the mixture of different chemical agents, the true source of which is chemical combi

nation.

In other combinations, cold is produced, (that is, heat is obstructed, for there is no such thing as positive cold,) as, for instance, by dissolving salts of different kinds in water and other fluids, or by permitting them to act upon ice and snow.

[To be continued.]

Answer to a Query inserted in Vol. I. col. 905.

MR. EDITOR, SIR,-In looking over your instructive Miscellany, I was highly delighted with the Mathematical Question proposed in the 10th No. for December, 1819. I hope, therefore, I shall not be thought intrusive, by sending a solution to the same. WILLIAM LAMB. Wigton, Cumberland, Dec. 17, 1819.

LETT the time in hours that each person travelled, when they were 12 miles asunder; then 18 — 4 T, and 5T will represent their respective distances No. 12.-VOL. II.

Conceive

from Wigan at the time T.
then they would form an oblique plane
triangle with Wigan. The angle at
Wigan being given 60° for an equila-
teral triangle, whose nat. co-sine is to
radius 1.

Then by plane Trigonometry ✔

234 T

4T+5T-2 × 18-4T X

(18
5T x ) = 12 by the question: this
equation involved, &c. becomes 61 T2
reduced, the two roots of T will be
180 a quadratic, which
found 1,06478, and 2,7718 hours; hence
the time they have travelled when they
53 sec. and again at 2 h. 46 min. 18 sec.
were 12 miles asunder, is 1 h. 3 min.

been on their journey, when they
Again; to find how long they have
were the nearest possible together;
change T into y, then the above equa-
tion becomes (18 4 y2 + 5 y 2

- 2 x 18

-

4 y 5y = a minifluxion of this being made equal to 0, mum, or 61 y' 234 ya min.; the and the equation reduced gives y=

1,918031 h. 55 min. 5 sec. the time

when they were the nearest possible

together.

[blocks in formation]

Wм. LAMB proposes the following question to be answered without the assistance of algebra.

SIX Gamesters, A, B, C, D, E, and F, each having these several sums before him, A £68, B £73, C £83, D 86, E £84, and F £61; a constable coming in, each man seized as much as he could. It now appears, if A laid down of what he got, B 2-3ds of what he got, Cof what he got, D 4-5ths of what he got, E 5-6ths of what he got, and F 6-7ths of what he got; and they divide that sum equally among them, each man would then have his own money again: how much did each man seize?

C

modifications of one and the same force; whilst others are inclined to believe that there is an essential difference between them, and that they are originally distinct from each other. It is almost unnecessary to observe, that these opinions are merely hypothetical, and that it is impossible (considering the present imperfect state of our knowledge upon this intricate and mysterious subject) to decide in favour either of the one or the other.

The attraction of gravitation is distinguished from the other species, by its operating upon large masses of matter at sensible distances: this power acts in a direct ratio to the quantity of matter, and inversely as the square of the distance. The magnetic and electric attractions act also upon masses of matter, placed at sensible distances, and in this respect they correspond with the attraction of gravitation.

2. If we mix together a quantity of sulphuric acid and a solution of pure potash, a compound is formed, very different in its properties from either of the substances which enters into its composition: the sulphuric acid and pure potash are powerful corrosives, whilst the sulphate of potash, which is the result of the affinity, is a mild, saline substance, not possessing, in the least degree, the acrimony or the deleterious properties of its constituent ingredients. All the physical and chemical qualities of the compound differ more or less from the substances, between which the affinity is exerted : the form, colour, taste, smell, specific gravity, fusibility, volatility, and disposition to combine, are sometimes so much altered, as to bear no resemblance to these properties in the original bodies.

In the first experiment, we have an example of chemical solution: this term is made use of to denote that action which takes place between a solid and a fluid, the result of which is a liquid compound. It has been supposed, that in this case the liquid is the active principle, and that the solid is dissolved by it, as if the solid possessed no power of attraction. There is, however, a reciprocal affinity exerted in producing the combination.

By the attraction of cohesion is meant that force, or power, by means of which, particles of the same kind of matter are brought into more or less intimate union, and are retained in that state with different degrees of force. Thus, for instance, the particles of a piece of iron are united with greater force than the particles of a piece of wood; and the particles of the latter are far more closely united than those which constitute a fluid. It is obvious, therefore, that the den-case of chemical action, in which there sity of any substance depends upon the degree of force which is exerted between its particles, and, in proportion to its density, will be the force required to overcome their cohesion.

Berthollet has applied the term solution in a different sense, to denote that

is the transition of a solid to the liquid state, in consequence of the action of a liquid upon it, without any important change of properties. He has even extended it so far as to apply it to all cases of chemical union, whether between a solid and a liquid, two liquids, two airs, or an aëriform substance, and one either in the solid or liquid form, which is not intimate, and where the attraction is not sufficiently powerful to produce a material change in the properties of the substances entering into combination.

Chemical attraction, or affinity, denotes that power, by means of which particles of different bodies become intimately united, and form new combinations, differing more or less from the substances of which they are formed. After this affinity has been exerted between two or more substances, no spontaneous change takes place, nor can they be separated by Although, however, the change of any mechanical force; they may, how-properties after chemical action is ever, be disunited by chemical agency. A few experiments will illustrate this species of attraction.

1. If we pour water upon any soluble salt, the particles of the salt will enter into combination with the water, and be diffused through it, and it will be found impossible to separate them by any other than chemical means.

often remarkable and important, it will be premised, from what has been said, that it is not to be regarded as invariably so. In the combinations of saline and vegetable substances with water, and of animal and vegetable products with alcohol, in all the alloys that are formed by the union of different metals, some or other of the pro

perties of the original ingredients are recognised in the compounds.

The older chemists supposed that the properties of the compound were intermediate between those of its constituent parts, or were derived from their elements; and it was from this, that the acute philosopher, Newton, conjectured the existence of an inflammable substance in water, founded upon its great refractive power. This opinion, however, is now rejected; for although some examples of combinations appear to favour the conjecture, others are quite opposed to it.

[blocks in formation]

(184 T|2 +5T|2
Then by plane Trigonometry √
- 2 x 18-4T X
5T x ) = 12 by the question: this
equation involved, &c. becomes 61 T2

reduced, the two roots of T will be
234T-180 a quadratic, which
found 1,06478, and 2,7718 hours; hence
the time they have travelled when they
53 sec. and again at 2 h. 46 min. 18 sec.
were 12 miles asunder, is 1 h. 3 min.

Besides a change of properties attending chemical combination, there occurs a change of temperature, that been on their journey, when they Again; to find how long they have is, either heat or cold are produced. were the nearest possible together; This is explained upon the principle, change T into y, then the above equathat different bodies possess different capacities for caloric: if, therefore, the 2 x 18tion becomes (18 4 y2 + 5 y2 compound resulting from chemical action possesses a capacity greater or less than the bodies which enter into its composition, there will be either an absorption or evolution of caloric. Artificial heat is produced by the

combustion of different substances from the three kingdoms of nature, by fermentation, and by the mixture of different chemical agents, the true source of which is chemical combi

nation.

[blocks in formation]

4 y × 5y × 1) = a minifluxion of this being made equal to 0, mum, or 61 y3 234 ya min.; the and the equation reduced gives y

1,918031 h. 55 min. 5 sec. the time

when they were the nearest possible

together.

traveller's distance from Wigan on the Again, 18-4y=10,20788 miles, the Warrington road; and 5 y = 9,59015, the traveller's distance from Wigan on the Liverpool road.

By the same case as before in Trigonometry, (10,207882 +9,59015o 2 × 10,20788 × 9,59015 × 9,44864

9 miles, 789 yards, the nearest possible distance between them.

Two additional answers, which we have received to the above question, are not uniformly correct.

Wм. LAMB proposes the following
question to be answered without the
assistance of algebra.

SIX Gamesters, A, B, C, D, E, and F,
each having these several sums before
him, A £68, B £73, C £83, D 86, E £84,
and F £61; a constable coming in,
each man seized as much
as he
could. It now appears, if A laid down
of what he got, B 2-3ds of what he
got, C of what he got, D 4-5ths of
what he got, E 5-6ths of what he got,
and F 6-7ths of what he got; and they
divide that sum equally among them,
each man would then have his own
money again: how much did each man
seize?

C

Critical Remarks on Participles, &c.

TO THE EDITOR OF THE IMPERIAL
MAGAZINE.

SIR,

(Notes & Observations under Rule 10.) Why should the pronoun their in this sentence, 'Ye shall know them by their fruits,' be denied the honour of the same rank?

Being of opinion with Gamma Delta, that there are several other points in which Murray is either erroneous or defective, I should be glad to draw the attention of some of your enlightened correspondents to the following in particular.

"A substantive without any article to limit it, is generally taken in its widest sense: as, A candid temper is proper for man;' that is, for all mankind." The noun man seems to be the only word to which this observation will apply; for "The article is omitted before nouns that imply the different virtues, vices, passions, qua

I am not a little surprised that a man of learning, as your correspondent M. S. appears to be, should not be aware of the imprudence of writing in haste on any science. But, I suppose, if he has allowed himself time to peruse your less hasty correspondent Gamma Delta, he will have discovered the error into which his haste has led him, respecting my observations on "The cause of my not receiving it." I shall not, therefore, waste your valuable time in pointing it out; but proceed to my next objection, which M. S. considers as unworthy of his notice. When I said that "Prudence pre-lities, sciences, arts, metals, herbs, &c." vents our speaking or acting impro- and in all other cases this sense is experly," was a sentence authorized by pressed by the singular noun with an Mr. Murray himself, I only meant that article before it: as, Ye generous Mr. M. had made use of this form of Britons, venerate the plough;" "The expression; not that it was authorized ox knoweth his owner, and the ass his by any rule or observation in his Gram- master's crib; but Israel doth not know, mar: on the contrary, I believe I shall my people doth not consider.” prove, by references to that grammarian, that it is not. M. S. allows that "the present participle, with the definite article the before it, becomes a substantive;" and, if he had read a little further, Mr. Murray would have told him, that "the same observations which have been made respecting the effect of the article and participle, appear to be applicable to Critical Observations on Participles, &c.

the pronoun and participle when they are similarly associated." This being the case, the words speaking and acting are substantives, because they have the pronoun our immediately before them. What then shall we make of the word improperly? It ought not to be an adverb; for "An adverb is a part of speech joined to a verb, an adjective, and sometimes to another adverb, to express some quality or circumstance respecting it;" whereas improperly is here" added to a substantive, to express its quality," answering to the definition of the adjective; therefore, according to Murray, it ought to be Prudence prevents our improper speaking or acting."

66

Without combating M. S.'s last argument, I shall merely observe, that "Substantives govern pronouns as well as nouns, in the genitive case: as, 'Every tree is known by its fruit.""

66

I intended to make a few observations on some other parts of this celebrated author, particularly Rule 7. Syntax; but I am afraid I have already been too prolix; so, for the present, I remain, Sir,

Painshaw, Nov. 17, 1819.

Yours,

A. B.

TO THE EDITOR OF THE IMPERIAL
MAGAZINE.

SIR,
I have perused with interest, the cri-
ticisms of your correspondents A. B.
Gamma Delta, and J. Ŵ. in cols. 419,
420, 636, 732, and 733, of your valuable
work, and beg leave to say, with them,
that though I cheerfully subscribe to
the general merits of J. Murray's Eng-
lish Grammar, I must dissent from it
in certain particulars.

Mr. Murray says, participles are sometimes governed by the articles, for the present participle (ending in ing,) with the definite article before it, becomes a noun; and must have of after it." But I think the following rules prove, that the participle is not governed by the article the, but by the prepositions, which are often written before participles ending in ing: as,

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