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gives 4:08 nitrogen; 292 : 20 = 85 : x gives 5.82 hydrogen; and 292 : 48 = 85 : x gives 13.97 oxygen. The first formula also serves to find how much of

any

substance, simple or compound, is required to convert a given quantity of another substance into a given componnd, or to decompose a given quantity of any compound.- How much sulphur is required to convert 135 parts of copper into disulphuret of copper? In this compound, Cu? S, there are 2.31•8 = 63:6 copper combined with 16 sulphur: since then 63-6 copper require 16 sulphur, 135 parts of copper will require 33.96 parts of sulphur, for 63-6 : 16 = 135 : 33.96.—How much oil of vitriol is required for the decomposition of 79 pts. of nitrate of potash, so that bisulphate of potash may be formed while the nitric acid escapes? In nitrate of potash, 1 At. potash, (KO) = 39.2 + 8 = 47.2 is combined with 1 At. nitric acid (NO) = 14 + 40 = 54: the atomic weight of nitrate of potash is therefore 47.2 + 54 = 101.2. Oil of vitriol (SOHO) contains 1 At. sulphuric acid = 16 + 3.8 = 40, and 1 At. water = 1 + 8 = 9: therefore the atomic weight of oil of vitriol is 40 + 9 = 49. Since then 2 At. sulphuric acid are to combine with 1 At. potash, 1 At. or 101.2 parts of nitrate of potash (containing 47.2 potash) will require 2 At. or 2.49 = 98 parts of oil of vitriol (containing 80 sulphuric acid); now 101.2 : 98 :79: 76.5 the quantity of oil of vitriol required to decompose 79 parts of nitrate of potash.

By means of the second formula we may find the atomic weight of a substance when we know the relative quantity of it in a given compound, and also the number of its atoms which probably enter into the constitution of that compound. Suppose that in 100 parts of selenious acid we have found 71.43 parts of selenium and 28:57 parts of oxygen, and

as probable that it contains 1 At. selenium and 2 At. oxygen; we have then, in order to perform the operation indicated by the second formula, to divide the quantity of each element by the number of its atoms: thus

M
:2=

G
Se 71:43:1=71.43

0 28:57 : 2 = 14.285 According to this, the atomic weight of selenium would be 71.43 if that of oxygen were 14:285 ; but taking 8 for the atomic weight of oxygen, we have 14.285 : 71.43 = 8:40: if the atomic weight of oxygen be 100 we have 14.285 : 71.43 = 100 : 500. Hence the atomic weight of selenium is 40 when that of oxygen is 8, and 500 when that of

By the third formula we find in what numbers the atoms of the different constituents are united, when their relative quantities and atomic weights are known. If 100 parts of nitric acid contain 25.926 nitrogen, and 74:074 oxygen, and the atomic weights of nitrogen and oxygen are 14 and 8 respectively, what are the numbers of atoms of these two elements contained in nitric acid ? According to the formula, the relative quantity divided by the atomic weight gives the number of atoms; therefore

M : G= Z
N 25.926 : 14 = 1.852

0 74.074 ; 8 = 9.260 According to this, 1852 At. nitrogen are united with 9260 At. oxy

This complicated ratio may however (as in most other cases) be

oxygen is 100.

reduced by assuming the atomic number of the elements which gives the smallest quotient in the calculation = 1, and dividing the other quotients by this smallest quotient. Thus in the present example 1.852 : 9.260 = 1:5; consequently 1 At. nitrogen is combined with 5 At. oxygen.

Felspar contains in 100 parts, 16.65 potash, 18:14 alumina, and 65.21 silica: how many atoms of these three substances does it contain? Here we have to calculate the atomic weights of the three proximate elements: thus K 39.2 2Al 27.4

Si 14.8
08
30 24

20 16

:

Potash 47.2
Alumina 51.4

Silica 30.8
M G = Z
Potash ............. 16.65 : 47.2 = 0:3528
Alumina ........... 18:14 : 51.4 = 0:3528

Silica ...... 65.21 : 30.8 = 2:1172 Now 3528 : 3528 : 21172 =1:1:6. Consequently felspar contains 1 At. potash, 1 At. alumina, and 6 At. silica, probably combined as follows:

(K 0, 3Si 0?) + (Al2 O3 3Si 0). In many compounds, especially of the organic class, all the elements occur in more than 1 atom, and the division of the larger quotients by the smallest gives improper fractions, which must be got rid of by supposing the number of atoms of the element which gives the smallest quotient to be 2, 3, 4, &c. Dry benzoic acid, for example, contains in 100 parts, 74:34 carbon, 4:42 hydrogen, and 21•24 oxygen.

M :G= Z
C74.336 : 6 = 12:390
H 4.425 :1= 4.425

021.239 : 8 = 2.655 2.655 : 4:425 : 12.390 =1:1.66 ... : 4.66 ..., or multiplying by 3, = 3:5:14. Hence dry benzoic acid contains 3 At. oxygen, 5 At. hydrogen, and 14 At. carbon.

To save the trouble of making such calculations by the rule of three, Wollaston (Ann. Phil. 4, 176; comp. also Schw. 14, 126) introduced his Scale of Chemical Equivalents constructed on the principle of the ordinary Sliding Rule. A slide moveable up and down the middle of a narrow board is marked with the numbers 10 .... 500 placed at distances corresponding to their logarithms, so that, for example, the distance between 10 and 11 is as great as that between 100 and 110. On the right and left of the slide the names of the elementary substances and their more important compounds are marked on the board in places corresponding to their atomic weights. When the slide is set right in the board, that is to say, not drawn either up or down—the number 10 on the slide stands opposite 1 At. oxygen on the board; 11.25 on the slide opposite to 1 At. water on the board; so likewise 12.5 corresponds to 10 At. hydrogen; 20 to 2 At. oxygen, and 1 At. sulphur; 30 to 3 At. oxygen; 40 to 4 At. oxygen; 50 to 5 At. oxygen and 1 At. sulphuric acid; 130 to lead; 140 to oxide of lead; 190 to sulphate of lead, and so on. Consequently, in this position of the slide it may be seen that 190 parts of sulphate of lead contain 140 oxide of lead and 50 sulphuric acid; or 130 lead, 20 sulphur and 40 oxygen, it being supposed that the numbers of atoms of the con

stituents are previously known. If now it be required to find what quantities of these several elements are contained in 100 parts of sulphate of lead, the slide is to be so placed that the number 100 shall stand exactly opposite to sulphate of lead, when the required quantities will be found opposite the names of the several elements. In this and other ways the Equivalent-scale (which may also be made with a moveable circle instead of a slide) may be employed. However, the fractional parts of the numbers cannot be marked on the divisions of the slide with a degree of accuracy equal to that which may be obtained by calculation, and moreover the number of the elements and their compounds is so great that their names cannot all be marked on the board, so that searching for them in this manner often takes a longer time than calculation: hence the use of these Equivalent-scales has not become very general. D. Qualitative alterations of elements caused by chemical

combination. Since the chemical combination of heterogeneous substances produces a homogeneous mass, it must necessarily be accompanied by a change in the properties of the elements. In the less intimate combinations this change is very unimportant, no more in many cases than is necessary to cause the different properties of the elements to merge into one another. Thus common salt when dissolved in water loses its solid form and imparts its saline taste to the water, while the specific gravity of the solution is nearly a mean between that of the salt and that of the water. The properties of the more intimate compounds on the other hand are in almost all cases totally different from those of their elements. The two tasteless substances oxygen and sulphur produce by combination the intensely sour and corrosive sulphuric acid; the solid substances carbon and sulphur form when combined the volatile sulphuret of carbon: grey mercury and yellow sulphur form the bright red compound vermillion; &c. &c. Although all the elements of a compound body exert some influence in determining its properties, this influence is nevertheless exerted in very different degrees; it often bappens that one element is much more effective in determining the physical and chemical characters of a conpound than another; the former may be said to possess more formative power, while the latter serves either as a base or groundwork. Thus the metals

may

be said to act as bases, while the non-metallic elements, particularly oxygen, hydrogen, chlorine, fluorine, bromine, iodine, selenium and sulphur may be regarded rather as formative principles. The former, when they possess considerable specific gravity, impart this property more especially to the compounds, while the latter generally destroy the metallic lustre, opacity, and great conductive power of heat and electricity by which metals are distinguished, and impart to the compounds peculiar chemical characters, e.g., those of acids or salifiable bases. There is more resemblance between the compounds of oxygen with different metals, as also between the several metallic chlorides, sulphurets, &c. than betwern the compounds of one and the same metal with oxygen, chlorine, sulphur, &c.

a. Density. In most instances, the compound occupies a smaller space than its elements taken together before combination; condensation generally takes place, less frequently expansion, or neither.

a. Relation between the Density of Gaseous Compounds and that of their

Gaseous Elements. Most combinations of this class are attended with condensation, and always according to simple relations of volume; many however take place without alteration of bulk so that the compound takes up the same space as the sum of the elements before combination: we know of but one combination of gases which is accompanied by expansion.

These relations are exhibited in the following table. The first division includes the cases in which no change of volume takes place; the second those attended with condensation; the third the single case accompanied by expansion. But few organic compounds are mentioned in this table, as their relations of volume will be fully treated of in another place.

Column A. Names of the compounds.
B. Their chemical formulæ.
C. The number of measures in which the bodies combine.

D. The sum of these measures or the volume of the elements before combination.

E. The number of measures occupied by these elements after combination.

F. The atomic weight of the compound.
G. Spec. grav. of the conipound, that of air being assumed = 1.

H. Quotient obtained by dividing the sp. gr. by the atomic weight, i.e. the atomic number.

I. Reduced atomic number, obtained on the supposition that 1 vol. hydrogen gas contains 1 . x atoms of hydrogen.

The columns F, G, H, I are comparable with columns B, C, D, E of the table, page 55.

Since the specific gravities of many simple substances occurring in the compounds here enumerated is not known from observation, we are obliged in regard to them to calculate the sp. gr. and thence the relation by volume hypothetically. Thus from analogy, the vapours of selenium and tellurium have been assumed to be 6-atomic, that of antimony 2-atomic, and fluorine gas together with the vapours of carbon, boron, silícium, titanium, tin and bismuth as 1-atomic. Since for example the atomic weight of tin is 59 times as great as that of hydrogen, and the sp. gr. of hydrogen gas = 0·0693, the hypothetical sp. gr. of vapour of tin = 59.0.0693. The atomic weight of antimony is 1.29, and its vapour is supposed to be 2-atomic, hence the hypothetical sp. gr. of its vapour 2.129.00693; to find that of selenium we multiply by 6.40, and so on. The hypothetical parts of the calculation are denoted in the table by notes of interrogation: in most cases the hypothetical element is the number of volumes ; in that of nitric acid it is the sp. gr of the vapour

VOL. I.

F

stituents are previously known. If now it be required to find what quantities of these several elements are contained in 100 parts of sulphate of lead, the slide is to be so placed that the number 100 shall stand exactly opposite to sulphate of lead, when the required quantities will be found opposite the names of the several elements. In this and other ways the Equivalent-scale (which may also be made with a moveable circle instead of a slide) may be employed. However, the fractional parts of the numbers cannot be marked on the divisions of the slide with a degree of accuracy equal to that which may be obtained by calculation, and moreover the number of the elements and their compounds is so great that their names cannot all be marked on the board, so that searching for them in this manner often takes a longer time than calculation: hence the use of these Equivalent-scales has not become very general. D. Qualitative alterations of elements caused by chemical

combination. Since the chemical combination of heterogeneous substances produces a homogeneous mass, it must necessarily be accompanied by a change in the properties of the elements. In the less intimate combinations this change is very unimportant, no more in many cases than is necessary to cause the different properties of the elements to merge into one another. Thus common salt when dissolved in water loses its solid form and imparts its saline taste to the water, while the specific gravity of the solution is nearly a mean between that of the salt and that of the water. The properties of the more intimate compounds on the other hand are in almost all cases totally different from those of their elements. The two tasteless substances oxygen and sulphur produce by combination the intensely sour and corrosive sulphuric acid; the solid substances carbon and sulphur form when combined the volatile sulphuret of carbon: grey mercury and yellow sulphur form the bright red compound vermillion; &c. &c. Although all the elements of a compound body exert some influence in determining its properties, this influence is nevertheless exerted in very different degrees; it often happens that one element is much more effective in determining the physical and chemical characters of a coinpound than another; the former may be said to possess more formative power, while the latter serves either as a base or groundwork. Thus the metals may be said to act as bases, while the non-metallic elements, particularly oxygen, hydrogen, chlorine, fluorine, bromine, iodine, selenium and sulphur may be regarded rather as formative principles. The former, when they possess considerable specific gravity, impart this property more especially to the compounds, while the latter generally destroy the metallic lustre, opacity, and great conductive power of heat and electricity by which metals are distinguished, and impart to the compounds peculiar chemical characters, e. g., those of acids or salifiable bases. There is more resemblance between the compounds of oxygen with different metals, as also between the several metallic chlorides, sulphurets, &c. than between the compounds of one and the same metal with oxygen, chlorine, sulphur, &c.

a. Density. In most instances, the compound occupies a smaller space than its elements taken together before combination; condensation generally takes place, less frequently expansion, or neither.

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