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unequal numbers of atoms.-It sometimes happens that one atom of an element contained in a compound is replaced by two or more atoms of another element, or by two other elements without alteration of crystalline form. Hyperchlorate of potash (K O, Cl O1) has the same form as hypermanganate of potash (K O, Mn2 O'); here 1 At. chlorine is replaced by 2 At. manganese. Sal-ammoniac (NH Cl) crystallizes in the same form as chloride of potassium; hence K and N H are isomorphous. In such cases no such chemical resemblance exists between the interchangeable bodies as in cases A and B: thus manganese bears no resemblance to chlorine, nor does nitrogen to potassium.

The following is a general view of the several groups of simple and compound substances which exhibit the same crystalline form with or without slight differences of angular magnitude. Each group of isomorphous substances is distinguished by a number: if it contains bodies of different stoichiometrical nature it is further subdivided by means of letters. The same substance, if dimorphous or trimorphous, may be repeated in different groups. Mitscherlich's observations are denoted by Mt.

Regular System.

1. Homohedral. a. C (Diamond) P, K, Ti, Bi, Cd, Pb, Fe, Cu, Ag, Au.

b. Co As, Zn S, Pb S, Co S, Ag S, KI, Na I, K Br, Na Br, N H1 Cl, K Cl, Na Cl, L CI, Ag Cl, K F, Na F, Ca F.

c. Cu2 O, Cu S, Cu2 Cl, Hg Ag.

d. As O3, Sb O3, Wöhler.

e. Mg O, Al' 03, (Spinell),-Mg O, Fe 03, (Pleonast),—Zn O, Al3 O3, (Gahnite),-Zn O, Fe 0, (Franklinite), -Fe O, Fe2 O3, (Magnetic iron ore). Abich.

f. Ba O, NO,-Sr O, N 05,-Pb O, N O3, and according to Berzelius, Pb O, NO3.

g. N HCl, Pt C12,-N H' Cl, Ir Cl2,-K Cl, Pt C12,-K Cl, Ir Cl,2— K Cl, Os Cl2. Berzelius.

h. N HO, Al O3, 4S O3, 24Aq.-N H' O, Cr2 03, 4S 03, 24Aq.N HO, Mn 03, 4S O3, 24Aq.-N H' O, Fe 03, 4S O', 24Aq.KO, Al O, 4SO, 24Aq.-KO, Cr 03, 4SO', 24Aq.-KO, Mn2 O', 4S O', 24Aq.-KO, Fe2 O', 4S O3, 24Aq.-Na O, Al' 0", 4S O', 24Aq. Mt.

i. K O, Al2 03, 4Si O2, (Leucite).

k. Na O, Al' 03, 4Si O, 2Aq, (Analcime).

2. In pentagonal dodecahedrons: Fe S (Iron pyrites).-Co' As S (Cobalt-glance).

Four-membered or Square Prismatic System.

3. Ca O, W O',-Pb O, W O3,-Pb O, Mo 03, Levy (Pogg. 8, 513),Pb O, Cr O'. Johnston.

4. Ni O, SO3, 7Aq.-Ni O, Se O3, 7Aq.-Zn O, Se O', 7Aq. Mt. 5. N HO, 2H O, PO,-N H'O, 2HO, As 0,-K O, 2HO, PO,KO, 2H O, As O3.

Mt.

6. 3Cu O, 2Ur2 O3, 3P O3, 24Aq.-3Ca O, 2Ur 03, 3P O', 24Aq. 7. 2N H3, Ag O, S 03,-2N H3, Ag O Se 0,-2N H3, Ag 0, Cr 03.

8. a. Cu Fe S (Copper pyrites).-b. Mn2 O3 (Braunite). Kobell. 9. Ti O (Rutile),-Sn O (Tinstone).

Mt.

10. a. Ti O2 (Anatase).

b. KO, 8Ca O, 15Si O', 16Aq [?] (Apophyllite). Kobell. 11. a. 2Zr O, Si O2 (Zircon).

b. 3Ca O, 2A1' 03, 5Si Ó3 [?] (Wernerite). Breithaupt.

Two-and-two-membered or Right Prismatic System.

12. Sulphur.-Iodine.

13. As 03,-Sb O3. Wöhler.

14. a. Fe S (White iron pyrites).-b. Fe2 As S2 (Arsenical pyrites). 15. a. Mn2 O3, HO (Manganite).

b. 2Ca O, Al2 0, 3Si O2, Aq [?] (Prehnite). Kobell.

16. a. Ca O, CO (Arragonite),-Ba O, CO3,-Sr O, CO2,—Pb O, CO2. b. KO, NO3.

17. a. Ba O, S O3,—Sr O, S O3,-Pb O, S O3. Mt.

b. N HO, CI 0,-N H' O, Mn2 Ó',- K O, Cl 0,-K O, Mn2 O'.

Mt.

18. a. Na O, SO3,—Na O, Se O3,—Ag O, S O3,—Ag 0, Se O3 (fig. 59).

b. Ba O, Mn2 07.

Mt.

Mt.

19. a. KO, SO3,-K O, Se O3,-K O, Cr. 03,-KO, Mn 03 (fig. 76).

b. NHO, SO3, Aq. Mt.

Mt.

20. a. MgO, SO', 7Aq,-ZnO, SO', 7Aq,-Ni O, SO3, 7Aq,Mg O, Se 03, 7Aq,-Zn O, Se O', 7Aq (fig. 71, 72, 73). Mt.

b. Sb S3. Kobell.

21. Na O, PO3, 4Aq,-Na O, As 05, 4Aq (fig. 64). Mt. 22. 2Mn O, Si O (Chrysolite),-2Mn O, Si O. Berthier.

23. Na O, Al2O3, 3Sí 0, 2Aq (Natrolite),-Ca O, Al 03, 3Si O3, 3Aq (Skolezite).

24. Ba O, C H303, 3Aq (Acetate of baryta),-Pb O, CH 03, зAq (Acetate of lead), (fig. 60). ↑ Mt.

25. K3 Fe2 Cy,-K3 Co2 Cy

Two-and-one-membered or Oblique Prismatic System.

26. a. Sulphur.

b. K Ó, 2S 03, H 0,-K O, 2Se O3, HO. Mt.

27. Fe 0, Ta O3 (Tantalite),-Fe 0, W O3 (Wolfram). Breithaupt. 28. Ca O, SO3, 2Aq,-Ca O, Se O3, 2Aq. Mt.-Fe O, SO3, 2Aq. Graham.

29. Fe O, SO3, 6Aq,-Co O, SO3, 6Aq,-Mn O, SO3, 6Aq,-Co O, Se O3, 6Aq,-Mixtures of Fe O, S O3, with Cu O, SO3, or with ZnO, SO3; similarly of Cu O, SO3, with Zn O, SO3, or with Ni O, SO3, or with MgO, SO3; similarly of Mn O, SO3, with MgO, SO3, or with Zn O, SO3, always in combination with 6 At. water (fig. 111). Mt.

30. Mg O, SO3, 7Aq,-Zn O, SO3, 7Aq,-Co O, SO3, 7Aq,-Ni O, SO3, 7Aq,-Mg O, Se O3, 7Aq,-Co O, Se 03, 7Aq. Mt.

31. Na O, SO3, 10Aq,-Na O, Se O3, 10Aq,—Ña O, Cr 03, 10Aq (fig. 118, 119). Mt.

32. 2N HO, PO3, H 0,-2N HO, As 05, HO, (fig. 93, 94, 95). Mt. 33. 2Na O, PO', 25Aq,-2Na O, As 05, 25Aq, (fig. 96--100). Mt. 34. a. Na O, 2B O3, 10Aq, (Borax).

b. Ca O, Mg O, 2Si O, (Augite),—Na O, 2Fe O, 4Si O2 [?] (Achmite). Kobell.

35. 3Be O, 2A12 O3, 5Si O2 [?] (Euklase),—3Ca O, 2A12 03, 5Si O* [?] (Zoisite). Brooke.

One-and-one-membered or Doubly Oblique Prismatic System.

36. Mn O, S O', 4Aq,-Mn O, Se O3, 4Aq,-Zn O, Se O3, 4Aq,-Co 0, Se 0, 4 Aq. Mt.

37. CuO, SO, 5Aq,-Cu O, Se O, 5Aq,-Mn O, SO3, 5Aq. (fig. 121, 122, 123). Mt.

38. a. Na O, 3Ca O, 4A12 03, 12Si O2 (Labrador).

b. MgO, 3Ca O, 4A1 03, 8Si O2 (Anorthite).

Six-membered or Rhombohedral System.

39. 3Ag S, As S3 (Light red silver).-3Ag S, Sb S3 (Dark red silver). 40. a. CaO, CQ (Calespar),—MgO, CO,—CaO, CO + MgO, CO3,-Mn O, CO,-ZnO, CO',-Fe O, CO (fig. 141 and f.)

b. Na O, NO3,—KO, NO3. Frankenheim.

41. a. Si O (Quartz).-b. Ca O, Al2 03, 4Si O2, 6Aq. (Chabasite). 42. Al2O3 (Corundum),-Fe 0,-Cr2 0,-Fe Ti O3 (Ilmenite).

43. As,-Sb,-Te. Breithaupt. Tin also, according to Breithaupt, and zinc, according to Nöggerath, crystallize in regular six-sided prisms. 44. Sr O, S O3, 4Aq,-Ca O, SO3, 4Aq,-Pb O, S 05, 4Aq. Heeren. 45. Ca Cl, 9Ca O, 3PO (Apatite),—PbCl, 9PbO, 3PO3 (Grünbleierz), -Pb Cl, 9Pb O, 3As 05.

46. Mohsite and Eudialyte. Brooke.

47. a. Cd S,-Ni S,-Fe S.-b. Ni' As (Kupfernickel),-Ni2 Sb S2 (Nickeliferous grey antimony).

c. Ir Os. Breithaupt.

48. HO and Zn O, crystallize in regular six-sided prisms, but their isomorphism has not yet been established by the determination of their angular relations.

From these data the isomorphism of the following simple and compound bodies may be deduced:

Carbon, phosphorus, potassium, titanium, bismuth, cadmium, lead, iron, copper, silver and gold? (1,a)

The isomorphism of iron and titanium is more completely established by (42) inasmuch as Fe2O3 and Fe Ti O3 crystallize in the same form, and that of iron and cobalt by (25).

Potassium, sodium, lithium, calcium, zinc, lead, silver? (1,6)

Oxygen, sulphur, chlorine? (1, c)

Arsenic, antimony and tellurium (1, d, 13, 39, 43).

Platinum, iridium and osmium (1, g).

One atom of arsenic probably replaces two atoms of sulphur, inasmuch as Fe S and Co As S have the same form (2); so likewise Fe S* and Fe2 As S2 (14).

Potassium and ammonium, NH (1, b and g,-17, b).

KO and N HO; also under certain circumstances Na O (1, h,-5). On the other hand we might admit from (19) that N HO+ HÒ replaces

KO.

Na O and AgO (18, a). Just as KO in alum is isomorphous with Na O, so likewise in combination with N O5 it may under peculiar circumstances crystallize in obtuse rhombohedrons exactly like those of Na O, NO3 (41), so that N HO, KO, Na O, and Ag O, may be regarded as isomorphous in one or other of their states.

MgO, Mn O, Zn O, Fe 0, Co O, Ni O and Cu O, have been shown to

e isomorphous in their combinations with carbonic, sulphuric and selenic acids (1, e,-4,-20,-22,-29,-30,-36). Lime, Ca O, is also related to them in one of its dimorphous states.

(1,

Pb O, Ba O, Sr O, and Ca O (in one of its states) are isomorphous f-3,-16,-17,-24,-44,-45).

According to (35), if the formulæ are correct, Be O is isomorphous with Ca O. According to (23), we might suppose that Na O is interchangeable with Ca O, HO.

Al O3, Cr2 O3 and Fe2O3, are isomorphous in the separate state (42); Mn3 O3 is also isomorphous with them in combination (1, e,-1, h).

Ti O' and Sn O are isomorphous in the separate state, (9) although Ti and Sn crystallize in different forms.

WO3 in combination is isomorphous with Mo 03 and Cr 03 (3), also with Ta O3 (27).

S 03 in combination is isomorphous with Se O3, Cr O3, and Mn O3 (4,-7,-18, a,-19,-20,-26, b,-28,-29,-36,-37). Cr 03 seems also to form a connecting link of the series W O, Mo 03, Cr O3, Mn O3, Se O3, and S O3.

PO3 and As O3 are also isomorphous in combination (5,-21,-32,— 33,-35).

ClO in combination is isomorphous with Mn2 O (17, 6).

The following similarly formed compounds, however, differ so much in their chemical properties that their similarity of shape can scarcely be regarded as resulting from the substitution of one element for another:

Pb O, NO3 and Pb O NO, (1, f) have the same form though they differ in composition by 2 At. oxygen.

Leucite and Analcime have the same composition, (1, i) excepting that the latter contains 2 atoms of water.

Copper-pyrites Cu Fe S and Braunite Mn2O3 (8). Here it must be supposed that 3 atoms of oxygen may be substituted for 2 atoms of sulphur.

Anatase and Apophyllite (10).-Zircon and Wernerite (11).-Manganite and Prehnite (15);-all differing irreconcilably in their chemical composition.

Arragonite, Ca O, CO2 and nitre K O, N 05 (16)."

Ba O, SO3 on the one hand, and K O, C1 07 and K O, 2Mn O' on the other (17).

Na O, SO3 and Ba O, Mn2 O (18).

Sb S3 and MgO, SO3, 7Aq (20).-S and KO, 2S 03, HO (26).— Borax, Na O, 2B 03, 10Ag and Augite, Cu O, Mg O, 2Si O (34).-Labrador and Anorthite (38).

Lastly, of totally dissimilar composition are: Ca O, CO2 (Calcspar) and Na O, NO (40).-Quartz and Chabasite (41). Mohsite and Eudialyte.

Attempts have been made to bring some of these cases in accordance with the theory of isomorphism by altering the atomic weights of some of the substances concerned. The following is one of the most remarkable instances of this kind: Ca O, CO as arragonite is isomorphous with nitre (KO, NO3) in its usual form (16); CaO, CO, as calcspar, with KO NO as it is sometimes obtained, and with Na O, NO as it always crystallizes. Hence Ca O, CO2 in its two conditions is isomorphous with KO, NO in its two conditions. For this reason Count Schaffgotsch halves the atomic weights of potassium and nitrogen; nitre then becomes KO, NO4 = KNO3. This agrees with CaO, CO2 Ca CO3;

=

in both compounds 3 atoms of oxygen are combined with 1 atom of metal and 1 atom of either carbon or nitrogen. This halving of the atomic weight of potassium involves the halving of those of ammonium (N H'), sodium, silver and gold, because potash is isomorphous with oxide of ammonium (N H'O) and soda, and the last of these with oxide of silver; and because silver in combination with the most various quantities of gold always crystallizes in the same form, a circumstance which indicates the isomorphism of these two metals. The halving of the atomic weight of silver had before been proposed by H. Rose, because in grey copper ore 1 atom of silver takes the place of 2 atoms of copper, and the crystalline form of AgS as well as that of Cu S belongs to the regular system. According to this view the atomic weights of N, H, K, Na, Ag, and Au would be reduced to one-half of the values now assigned to them; potash would be K2 O, soda Na2O, oxide of silver Ag2 O, and suboxide of silver Ag O. By halving the atomic weights of potassium and chlorine the similar forms of K Ŏ, Cl O' and Ba O, S O3 would also be explained, (17) for the composition would then be K C1 O' and Ba S O'.

Clarke, on the contrary, doubles the atomic weights of sodium and silver in order to reconcile the composition of Na O, SO3 and Ag O, SO3 with that of Ba O, Mn2 O' (18). He thus obtains Na O, 2S 03 = Na S20 and Ag O2, 2S O3 Ag S O'; and this formula agrees with Ba O, Mn2 O' = Ba Mn O. But since the atomic weight of potassium must be doubled as well as that of sodium, the explanation of case (18) becomes by this alteration more difficult than before.

With regard to these attempts, we cannot but agree with the view recently adopted by Johnstone (who formerly made trial of the same hypothesis as Count Schaffgotsch), viz. that many of the formulæ of isomorphous bodies cannot be made to agree with one another in any way whatever others only by means of hypotheses which are either contradictory or greatly impair the simplicity of the chemical formula. Although similar formula often involve similarity of shape, it does not by any means follow that similar forms are inconsistent with dissimilar formulæ. There exists perhaps a higher law by which these cases might be explained: the discovery of such a law would give a new form to the theory of isomorphism.

Kopp and Schröder have remarked that isomorphous substances have equal atomic volumes (and therefore also equal atomic numbers). The simple substances (Table, page 55) exhibit approximations to this law, at least in some cases: e.g. Ni, Mn, Co and Fe; W and Mo; I, Br and Cl. But the atomic numbers of Sb and As, of Na and K, of Mn, Cr, S and Se, which at least are isomorphous in their acids, differ widely. According to table (page 68) equal atomic numbers are exhibited by Al O3, Cr2 03 and Fe2O3; by TiO2 and Sn O2; by W 03 and Mo 03; by As 03 and Sb 03; by several anhydrous carbonates, sulphates and nitrates (some too not isomorphous); and by several hydrated sulphates. Exceptions are however presented by K O, SO3 and K O, Cr O3; and by K Cl, Na Cl and Ag Cl; moreover the merely approximate agreement in the atomic numbers of the first named compounds may in a great measure be explained by the fact that similar formulæ give nearly equal atomic weights, and these being used as divisors of nearly equal specific gravities, the quotients cannot differ much from another. On the other hand, Kopp has shown that the small differences between the angles at the edges of the obtuse rhombohedron of calcspar and the corresponding angles in the other carbonates which are isomorphous with it, probably bear a simple relation to the different volumes of the atoms of which these crystals are composed.

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