On the Specific Gravity of Alloys

XI. On the Specific Gravity of Alloys. By A. Matthiessen, Ph.D. Communicated by Professor Wheatstone. Received November 17,—Read December 22, 1859. Before commencing a research on the law of the conducting power for electricity of alloys, it was considered necessary to determine their specific gravities; to ascertain whether they expand or contract, so as to be able to account for differences which might be obtained in their conducting powers. The metals used for the alloys were those which were easily obtained in a pure state in large quantities, and were purified as follows: 1. Antimony.—By Liebig's process. 2. Tin.—Commercial metal dissolved in nitric acid, and the binoxide reduced by charcoal. 3. Cadmium.—Commercial metal dissolved in hydrochloric acid and precipitated by sulphuretted hydrogen; the sulphide dissolved in hydrochloric acid and precipitated by carbonate of soda; the carbonate heated, a part of the oxide reduced by hydrogen, and the rest distilled with charcoal. 4. Bismuth.—Commercial metal dissolved in nitric acid, precipitated by water and reduced by charcoal. 5. Silver.—Reduced from the pure chloride by fusion with carbonate of soda. The greater part of the silver used for making the alloys was procured in a state of purity from Messrs. Johnson and Matthey. 6. Lead.—Commercial acetate recrystallized three times and heated. 7. Mercury.—Commercial metal treated with nitric acid, and allowed to stand with it about a month, being at intervals well-shaken. 8. Gold.—Prepared by precipitating chloride of gold by algaroth powder, &c., and also by precipitation of the chloride of gold by protosulphate of iron*, &c. Some of the gold employed was procured pure from Messrs. Johnson and Matthey. The quantity of each alloy made was about 20 grms.; the two metals were weighed out accurately in proper proportions, and fused together in a porcelain crucible; a jet of gas being allowed to play in the same from above to prevent the oxidation of the metals. The alloys were cast in a wooden mould, a porcelain slab (previously blackened by holding it over a gas flame to prevent the adhering of the metal) forming the bottom. They were always re-fused and re-cast, at least three times, before the first determination was made, then re-fused before they were determined a second time, and again before * See Appendix at the end of my paper "On the Electric Conducting Power of Alloys," in this volume, p. 175. MDCCCLX. the third determination; often being re-cast several times, as the castings did not always succeed. To prevent as much as possible the formation of internal cavities from crystallization, the alloys were cast very thin, the thickness of the casting being in most cases about 3 to 4 millims. The method employed for taking the specific gravities, was that of hanging the alloys by a very fine platinum wire in distilled water, which had been boiled to free it from air, and allowed to cool \textit{in vacuo}. This method gave better results than that of weighing the metal or alloy in a bottle filled with water, on account of the difficulty of perfectly drying the bottle when full, and obtaining the same weight twice following. The amalgams which were liquid, and those not sufficiently hard to hang by the platinum wire, were weighed in a glass tube to which a platinum wire was soldered. The weight of the tube alone in air and water was determined at the temperature at which the experiments were made, and therefore, in calculating the specific gravities, these values had only to be subtracted from those found. The balance used was one of Liebiech's, which turns to the 0·1 mgr. when loaded with 100 grms. in each pan; and when the alloy was weighed in water, it turned to the 0·2 mgr. The air adhering to the alloy, when weighed in water, was removed by a soft brush, the alloy being brushed until its weight became constant. In calculating the specific gravities, the weight of the water displaced was corrected for the temperature, so that the unit is in all cases distilled water at 0° C. A similar correction could not be made for the temperature of the alloys, as their coefficients of expansion are not known. All the weighings were reduced to a vacuum, and a correction was made for that part of the platinum wire which dipped in the water. The length of wire dipping in was about 60 millims., which weighed 8 mgrs.; these would lose in water about 0·35 mgr. Supposing, as is really the case, that sometimes 10 millims. more or less dipped in, the error made would be about 0·06 mgr.; but as the 0·3 mgr. only make an error, if not brought into calculation, in most cases of about 0·001 per cent. of the specific gravity found, the error made in this way may be overlooked. The equivalents used for calculating the quantities of metal required for the alloys were— | Element | Equivalent | |-------------|------------| | Antimony | 122·3 | | Tin | 58 | | Cadmium | 56 | | Bismuth | 208 | | Silver | 108 | | Lead | 103·7 | | Mercury | 100 | | Gold | 197 | Table I. gives the specific gravities of the pure metals employed, and the temperature (T.) in the Centigrade scale: the values given are the results of three consecutive determinations. On account of the number of alloys experimented with, it was considered as well, in order to save space, only to give the mean of the three determinations; and * Dexter, Poggendorff's 'Annalen,' vol. c. p. 563. This is the latest determination, and the one adopted by Bunsen in his recent paper. Liebig's 'Annalen,' vol. cvi. p. 1. where they did not agree amongst themselves to 0·1 per cent. of the value, a + will be placed by the alloy, and the value there given is the mean of a number of experiments (generally six or more)*. Table I. | Metal | 1st Determination. | T. | 2nd Determination re-fused. | T. | 3rd Determination re-fused. | T. | Mean of Spec. grav. | T. | Determined by | |-------------|--------------------|----|----------------------------|----|----------------------------|----|---------------------|----|------------------------| | Antimony | 6·715 | 13·6| 6·713 | 14·4| 6·710 | 15·0| 6·713 | 14·3| A. Matthiessen | | Tin | 7·293 | 11·5| 7·295 | 12·8| 7·294 | 14·0| 7·294 | 12·8| A. Matthiessen | | Cadmium | 8·655 | 10·0| 8·657 | 10·2| 8·654 | 11·2| 8·655 | 10·5| A. Matthiessen | | Bismuth | 9·823 | 12·0| 9·824 | 12·4| 9·823 | 12·4| 9·823 | 12·3| Dr. M. Holzmann | | Silver† | | | | | | | 10·468 | 13·2| Dr. M. Holzmann | | Lead | 11·374 | 13·0| 11·380 | 16·5| 11·376 | 11·0| 11·376 | 13·5| Dr. M. Holzmann | | Mercury | 13·575 | 14·0| 13·569 | 14·7| 13·574 | 14·8| 13·573 | 14·5| Dr. M. Holzmann | | Gold | 19·261 | 10·0| 19·269 | 15·5| 19·264 | 12·8| 19·265 | 12·8| A. Matthiessen | Table II. gives the mean of the three determinations made with the alloys, the mean of the temperatures (T.), and the specific gravity calculated from the first of the following formulæ: \[ S = \frac{A + A_1}{V + V_1} = \left( \frac{V_s + V_{s_1}}{V + V_1} \right) \] \[ S = \frac{ns + n_s s_1}{n + n_s}, \] \[ S = \frac{As + A_1 s_1}{A + A_1}, \] where - \( S \) = the specific gravity of the alloy, - \( V \) and \( V_1 \) = the volumes of the metals, taking - \( n \) and \( n_s \) = the numbers of the equivalents of the metals, and - \( A \) and \( A_1 \) = their respective weights. - \( s \) and \( s_1 \) = their specific gravities. * Those alloys which are underlined have been made twice, as it was supposed these must have an error in the weighing out of the metals, as they do not agree with the calculated values. The values, however, were found to be correct. † No concordant results could be obtained with this metal. Experiments were made with it after having been fused under borax, chloride of sodium, charcoal, in hydrogen. The above value is the mean of a number of determinations which varied between 10·424 and 10·511. Some specimens of not quite pure silver were lent me by Mr. Ph. Worsley, who prepared them as follows: The silver was made as hot as possible, and well-stirred with a stick of charcoal before pouring. The mould was a steel one, forming a bar of about 25 millims. square and about 300 millims. high. The bar weighed about 2½ kilogrammes. The top of it, when cold, showed a funnel-shaped depression, and the soundest part of it was about two-thirds down, and from this different pieces were cut, which gave very good results. The values obtained were 10·504, 16°7; 10·505, 17°2; 10·502, 19°2. A second bar gave similar numbers; they were 10·500, 24°5; 10·496, 24°8; 10·492, 25°0. The specific gravity of an alloy is calculated from the above formulae, under the supposition that the specific gravity of the metals employed take part of that of the alloy in the ratio of their relative volumes (1.), equivalents (2.), or weights (3.). Of these formulae only the first is for all cases correct, supposing the alloy neither contracts nor expands; the second only when the volumes and equivalents of the metals employed are in the same ratio with each other, as in the case of gold, silver, &c.; and the third only when the specific gravities of the two metals are equal. The two last methods of calculation are here mentioned, as several chemists have calculated their results from these formulae. **Table II.** Antimony-Tin Series (determined by Mr. C. Long). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|-------------------------------------| | Sb\(_8\)Sn | 6·739 | 16·2 | 6·752 | 1·0019 | | Sb\(_4\)Sn | 6·747 | 13·4 | 6·770 | 1·0034 | | Sb\(_2\)Sn | 6·781 | 13·5 | 6·817 | 1·0052 | | Sb Sn | 6·844 | 13·8 | 6·889 | 1·0066 | | Sb Sn\(_2\) | 6·929 | 15·8 | 6·984 | 1·0079 | | Sb Sn\(_4\) | 7·023 | 15·8 | 7·082 | 1·0084 | | Sb Sn\(_6\) | 7·100 | 10·6 | 7·133 | 1·0046 | | Sb Sn\(_{10}\)\(^+\) | 7·140 | 19·0 | 7·186 | 1·0065 | | Sb Sn\(_{20}\) | 7·208 | 18·5 | 7·234 | 1·0036 | | Sb Sn\(_{40}\) | 7·276 | 19·4 | 7·262 | 0·9981 | | Sb Sn\(_{100}\) | 7·279 | 20·0 | 7·281 | 1·0003 | | Sb Sn\(_{200}\) | 7·284 | 20·2 | 7·287 | 1·0004 | Antimony-Bismuth Series (determined by Dr. M. Holzmann). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|-------------------------------------| | Sb\(_2\)Bi | 7·864 | 9·4 | 7·856 | 0·9989 | | Sb Bi | 8·392 | 11·0 | 8·355 | 0·9991 | | Sb Bi\(_2\) | 8·886 | 14·0 | 8·888 | 1·0002 | | Sb Bi\(_4\) | 9·277 | 12·1 | 9·272 | 0·9995 | | Sb Bi\(_6\) | 9·435 | 9·4 | 9·433 | 0·9998 | Antimony-Lead Series (determined by A. Matthiessen). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|-------------------------------------| | Sb Pb | 8·201 | 13·7 | 8·268 | 1·0082 | | Sb Pb\(_2\) | 8·989 | 11·7 | 9·945 | 1·0062 | | Sb Pb\(_4\) | 9·811 | 14·3 | 9·822 | 1·0011 | | Sb Pb\(_6\) | 10·144 | 15·4 | 10·211 | 1·0066 | | Sb Pb\(_{10}\) | 10·586 | 19·3 | 10·599 | 1·0012 | | Sb Pb\(_{20}\)\(^+\) | 10·930 | 19·9 | 10·952 | 1·0020 | | Sb Pb\(_{50}\) | 11·194 | 20·5 | 11·196 | 1·0002 | * Where \( v \) = volume of the alloy found, and \( V + V_1 \) = volumes of the metals composing it. ### Table II. (continued.) #### Tin-Cadmium Series (determined by A. Matthiessen). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Sn\(_6\) Cd | 7·434 | 12·7 | 7·456 | 1·0029 | | Sn\(_4\) Cd | 7·489 | 15·0 | 7·524 | 1·0047 | | Sn\(_2\) Cd | 7·690 | 12·9 | 7·687 | 0·9996 | | Sn Cd | 7·904 | 13·2 | 7·905 | 0·9999 | | Sn Cd\(_2\) | 8·139 | 11·1 | 8·137 | 0·9998 | | Sn Cd\(_4\) | 8·336 | 14·5 | 8·335 | 0·9999 | | Sn Cd\(_6\) | 8·432 | 15·0 | 8·424 | 0·9990 | #### Tin-Bismuth Series (determined by Mr. M. Cartey). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Sn\(_{44}\) Bi | 7·438 | 19·9 | 7·438 | 1·0000 | | Sn\(_8\) Bi | 7·943 | 20·0 | 7·925 | 0·9977 | | Sn\(_6\) Bi | 8·112 | 14·2 | 8·071 | 0·9949 | | Sn\(_4\) Bi | 8·339 | 13·9 | 8·305 | 0·9959 | | Sn\(_2\) Bi | 8·772 | 12·6 | 8·738 | 0·9961 | | Sn Bi | 9·178 | 15·9 | 9·132 | 0·9950 | | Sn Bi\(_2\) | 9·435 | 15·0 | 9·423 | 0·9987 | | Sn Bi\(_4\) | 9·614 | 12·7 | 9·606 | 0·9991 | | Sn Bi\(_6\) | 9·675 | 15·2 | 9·674 | 0·9999 | | Sn Bi\(_{10}\) | 9·737 | 19·8 | 9·731 | 0·9994 | | Sn Bi\(_{20}\) | 9·774 | 23·0 | 9·792 | 1·0019 | | Sn Bi\(_{44}\) | 9·803 | 22·8 | 9·801 | 0·9998 | | Sn Bi\(_{80}\) | 9·811 | 19·0 | 9·807 | 0·9996 | | Sn Bi\(_{90}\) | 9·814 | 19·5 | 9·812 | 0·9998 | | Sn Bi\(_{200}\) | 9·815 | 18·1 | 9·818 | 1·0003 | #### Tin-Silver Series (determined by Dr. M. Holzmann). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Sn\(_{36}\) Ag+ | 7·421 | 18·6 | 7·404 | 0·9977 | | Sn\(_{10}\) Ag+ | 7·551 | 18·8 | 7·507 | 0·9941 | | Sn\(_{12}\) Ag+ | 7·666 | 18·4 | 7·603 | 0·9918 | | Sn\(_6\) Ag+ | 7·963 | 19·3 | 7·858 | 0·9868 | | Sn\(_4\) Ag+ | 8·223 | 16·3 | 8·071 | 0·9815 | | Sn\(_2\) Ag | 8·828 | 13·8 | 8·543 | 0·9677 | | Sn Ag | 9·507 | 12·9 | 9·086 | 0·9558 | | Sn Ag\(_2\) | 9·953 | 14·8 | 9·585 | 0·9630 | #### Tin-Lead Series (determined by Mr. C. Long). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Sn\(_6\) Pb | 7·927 | 15·2 | 7·948 | 1·0027 | | Sn\(_4\) Pb | 8·188 | 16·0 | 8·203 | 1·0018 | | Sn\(_2\) Pb | 8·779 | 17·2 | 8·781 | 1·0002 | | Sn Pb | 9·460 | 15·5 | 9·474 | 1·0015 | | Sn Pb\(_2\) | 10·080 | 14·8 | 10·136 | 1·0055 | | Sn Pb\(_4\) | 10·590 | 14·3 | 10·645 | 1·0052 | | Sn Pb\(_6\) | 10·815 | 15·6 | 10·857 | 1·0039 | #### Tin-Mercury Series (determined by Dr. M. Holzmann). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Sn\(_2\) Hg | 9·362 | 9·9 | 9·282 | 0·9914 | | Sn Hg | 10·369 | 14·2 | 10·313 | 0·9946 | | Sn Hg\(_2\) | 11·456 | 11·3 | 11·373 | 0·9927 | ### Table II. (continued.) **Tin-Gold Series (determined by Dr. M. Holzmann).** | Alloy | Mean of Specific gravity found | Calculated specific gravity, from volume | Ratio of volumes, \( \frac{V + V_i}{v} \) | |-------|--------------------------------|------------------------------------------|----------------------------------------| | Sn\(_{100}\) Au | 7·441 | 22·9 | 7·446 | 1·0007 | | Sn\(_{30}\) Au | 7·801 | 22·8 | 7·786 | 0·9981 | | Sn\(_{18}\) Au | 8·118 | 22·4 | 8·092 | 0·9968 | | Sn\(_{12}\) Au | 8·470 | 23·1 | 8·452 | 0·9979 | | Sn\(_{8}\) Au | 8·931 | 25·6 | 8·951 | 1·0002 | | Sn\(_{6}\) Au | 9·405 | 23·7 | 9·407 | 1·0002 | | Sn\(_{5}\) Au | 9·715 | 22·4 | 9·743 | 1·0029 | | Sn\(_{4}\) Au | 10·168 | 23·7 | 10·206 | 1·0037 | | Sn\(_{3}\) Au | 10·794 | 23·6 | 10·885 | 1·0084 | | Sn\(_{2}\) Au | 11·833 | 14·6 | 11·978 | 1·0022 | | Sn Au | 14·244 | 14·2 | 14·028 | 0·9848 | | Sn Au\(_2\) | 16·367 | 15·4 | 15·913 | 0·9722 | **Cadmium-Bismuth Series (determined by A. Matthiesen).** | Cd\(_6\) Bi | 9·079 | 13·1 | 9·067 | 0·9987 | | Cd\(_4\) Bi | 9·195 | 15·5 | 9·181 | 0·9985 | | Cd\(_2\) Bi | 9·388 | 15·0 | 9·380 | 0·9991 | | Cd Bi | 9·554 | 13·4 | 9·550 | 0·9996 | | Cd Bi\(_2\) | 9·669 | 14·8 | 9·668 | 0·9999 | | Cd Bi\(_4\) | 9·737 | 14·7 | 9·740 | 1·0003 | | Cd Bi\(_6\) | 9·766 | 15·4 | 9·766 | 1·0000 | **Cadmium-Lead Series (determined by Dr. M. Holzmann).** | Cd\(_8\) Pb | 9·160 | 13·7 | 9·173 | 1·0014 | | Cd\(_4\) Pb | 9·353 | 12·0 | 9·364 | 1·0012 | | Cd\(_2\) Pb | 9·755 | 14·7 | 9·780 | 1·0026 | | Cd Pb | 10·246 | 11·7 | 10·246 | 1·0000 | | Cd Pb\(_2\) | 10·656 | 13·4 | 10·663 | 1·0006 | | Cd Pb\(_4\) | 10·950 | 9·2 | 10·966 | 1·0015 | | Cd Pb\(_6\) | 11·044 | 14·8 | 11·088 | 1·0039 | **Bismuth-Silver Series (determined by Dr. M. Holzmann).** | Bi\(_{200}\) Ag | 9·802 | 23·5 | 9·825 | 1·0023 | | Bi\(_{50}\) Ag | 9·813 | 23·6 | 9·829 | 1·0016 | | Bi\(_{24}\) Ag | 9·820 | 23·3 | 9·836 | 1·0016 | | Bi\(_{12}\) Ag | 9·836 | 21·8 | 9·848 | 1·0012 | | Bi\(_5\) Ag | 9·859 | 21·0 | 9·871 | 1·0012 | | Bi\(_4\) Ag | 9·899 | 15·2 | 9·893 | 0·9994 | | Bi\(_2\) Ag | 9·966 | 14·9 | 9·949 | 0·9983 | | Bi Ag | 10·068 | 15·6 | 10·034 | 0·9966 | | Bi Ag\(_2\) | 10·197 | 13·2 | 10·141 | 0·9945 | | Bi Ag\(_4\) | 10·323 | 15·1 | 10·249 | 0·9928 | ### Table II. (continued.) **Bismuth-Lead Series (determined by Mr. M. Carty).** | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Bi\(_{30}\) Pb | 9·844 | 21·7 | 9·845 | 1·0001 | | Bi\(_{24}\) Pb | 9·845 | 21·6 | 9·850 | 1·0005 | | Bi\(_{20}\) Pb | 9·850 | 21·3 | 9·856 | 1·0006 | | Bi\(_{12}\) Pb | 9·887 | 20·6 | 9·877 | 0·9990 | | Bi\(_{10}\) Pb | 9·893 | 19·5 | 9·887 | 0·9994 | | Bi\(_{8}\) Pb | 9·934 | 21·1 | 9·902 | 0·9968 | | Bi\(_{6}\) Pb | 9·973 | 15·0 | 9·927 | 0·9953 | | Bi\(_{4}\) Pb | 10·048 | 10·7 | 9·974 | 0·9927 | | Bi\(_{2}\) Pb | 10·235 | 12·5 | 10·098 | 0·9866 | | Bi Pb | 10·538 | 14·0 | 10·290 | 0·9765 | | Bi Pb\(_2\) | 10·956 | 14·9 | 10·541 | 0·9621 | | Bi Pb\(_4\) | 11·141 | 12·7 | 10·805 | 0·9698 | | Bi Pb\(_6\) | 11·161 | 14·8 | 10·942 | 0·9803 | | Bi Pb\(_8\) | 11·188 | 20·8 | 11·026 | 0·9855 | | Bi Pb\(_{10}\) | 11·196 | 20·2 | 11·083 | 0·9899 | | Bi Pb\(_{24}\) | 11·280 | 22·5 | 11·238 | 0·9963 | | Bi Pb\(_{100}\) | 11·331 | 23·0 | 11·340 | 1·0008 | **Bismuth-Gold Series (determined by Dr. M. Holzmann).** | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Bi\(_{90}\) Au | 9·872 | 21·0 | 9·873 | 1·0001 | | Bi\(_{40}\) Au | 9·942 | 21·2 | 9·935 | 0·9993 | | Bi\(_{20}\) Au | 10·076 | 18·7 | 10·046 | 0·9970 | | Bi\(_{8}\) Au | 10·452 | 21·4 | 10·360 | 0·9912 | | Bi\(_{4}\) Au | 11·025 | 23·0 | 10·840 | 0·9833 | | Bi\(_{2}\) Au | 12·067 | 16·0 | 11·659 | 0·9662 | | Bi Au | 13·403 | 16·5 | 12·898 | 0·9631 | | Bi Au\(_2\) | 14·844 | 16·0 | 14·462 | 0·9743 | **Silver-Lead Series (determined by A. Matthiessen).** | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Ag\(_2\) Pb | 10·800 | 13·5 | 10·746 | 0·9950 | | Ag Pb | 10·925 | 13·8 | 10·894 | 0·9971 | | Ag Pb\(_2\) | 11·054 | 12·5 | 11·048 | 0·9995 | | Ag Pb\(_4\) | 11·144 | 18·2 | 11·175 | 1·0028 | | Ag Pb\(_6\) | 11·196 | 21·0 | 11·263 | 1·0060 | | Ag Pb\(_{20}\) | 11·285 | 22·2 | 11·327 | 1·0037 | | Ag Pb\(_{50}\) | 11·334 | 20·6 | 11·355 | 1·0018 | **Silver-Gold Series (determined by A. Matthiessen).** | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V + V_1}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Ag\(_5\) Au | 11·760 | 13·1 | 11·715 | 0·9961 | | Ag\(_4\) Au | 12·257 | 14·7 | 12·215 | 0·9965 | | Ag\(_2\) Au | 13·432 | 14·3 | 13·383 | 0·9963 | | Ag Au | 14·870 | 13·0 | 14·847 | 0·9984 | | Ag Au\(_2\) | 16·354 | 13·0 | 16·315 | 0·9976 | | Ag Au\(_4\) | 17·540 | 12·3 | 17·498 | 0·9973 | | Ag Au\(_5\) | 18·041 | 13·1 | 17·998 | 0·9976 | TABLE II. (continued.) Lead-Mercury Series (determined by A. Matthiessen). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V_1 + V_2}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Pb₂ Hg | 11·979 | 15·9 | 12·008 | 1·0024 | | Pb Hg | 12·484 | 15·7 | 12·358 | 0·9899 | | Pb Hg₂ | 12·815 | 15·5 | 12·734 | 0·9937 | Lead-Gold Series (determined by A. Matthiessen). | Alloy | Mean of Specific gravity found. | Calculated specific gravity, from volume. | Ratio of volumes, \( \frac{V_1 + V_2}{v} \) | |-------|---------------------------------|------------------------------------------|----------------------------------------| | Pb₂₀ Au | 11·841 | 23·3 | 11·794 | 0·9961 | | Pb₁₀ Au | 12·274 | 19·4 | 12·171 | 0·9916 | | Pb₈ Au | 12·445 | 21·6 | 12·346 | 0·9920 | | Pb₆ Au | 12·737 | 21·3 | 12·618 | 0·9906 | | Pb₄ Au | 13·306 | 22·1 | 13·103 | 0·9840 | | Pb₂ Au | 14·466 | 14·3 | 14·210 | 0·9823 | | Pb Au | 15·603 | 14·5 | 15·546 | 0·9963 | | Pb Au₂ | 17·013 | 14·3 | 16·832 | 0·9894 | From Table II., which gives in the fourth column the ratio of the sum of the volumes of the two metals to the volume of the alloy, it appears that the alloys of antimony are generally greater in volume than the aggregate of the constituent metals (expand), while those of bismuth, silver, gold, and mercury, generally are less (contract); and we find that the maximum expansion or contraction generally takes place about that point when the alloy contains equal volumes of each metal. The gold-tin and gold-lead alloys are all very brittle, except those very rich in lead or tin:—Sn Au₂ to Sn₃ Au are not at all crystalline, and have a glassy fracture; Sn₄ Au begins to show a crystalline structure, and has a crystalline fracture; Sn₅ Au to Sn₁₀₀ Au are exceedingly crystalline; and Sn₅ Au to Sn₁₂ Au all show a fracture like the cleavage plane of a crystal. The gold-lead alloys appear all to be crystalline, that is, their surface is very much so, but their fracture is glassy. The following alloys expand greatly on cooling, so much so, that the liquid metal breaks through the crust, forming large or small globules, viz. all those of bismuth-antimony, bismuth-gold, and bismuth-lead, which were experimented on; those of bismuth-tin, from Bi₂₀ Sn to Bi₉ Sn, the rest of the series very slightly; and bismuth-lead, viz. Bi₃₀ Pb to Bi₄ Pb (Bi₂ Pb slightly), the rest apparently not at all. Of the bismuth-cadmium series, Bi Cd₆ and Bi Cd₄ expand very slightly, the rest not at all. No concordant results could be obtained with any zinc-tin or zinc-cadmium alloys, on account of their very crystalline structure. In conclusion, my best thanks are due to Dr. M. Holzmann, Mr. C. Long, and Mr. M. Cartt for their assistance in carrying out the foregoing determinations.