It will be seen that, although the quant.i.ty of silver lost increases with the silver present, the percentage loss is greater on the smaller b.u.t.tons.

The following results are often quoted:--Cupelling 1 grain of silver with 10 grains of lead, the loss was 1.22 per cent.; 10 grains of silver with 100 grains of lead, loss 1.13 per cent.; 25 grains of silver cupelled with 250 grains of lead, lost 1.07 per cent. The proportion of silver to lead was the same in the three experiments, and the largest b.u.t.ton gave the best result. Evidently, if the quant.i.ties of lead had been the same in the three experiments (say, 250 grains in each case), the loss on the smaller quant.i.ties of silver would appear worse in the comparison.

In judging these results, it must be borne in mind that it is difficult to regulate the temperature, &c., in consecutive experiments so as to get exactly similar results, so that the range in consecutive cupellations is greater than that in a batch cupelled side by side.

~Effect of Copper and Antimony.~--0.1 gram of silver was cupelled with 20 grams of lead, and to one batch 0.5 gram of antimony, and to another 0.5 gram of copper was added.

Loss in Silver Lost. Range. Percentage.

Without addition 2.9 0.3 2.9 With antimony 3.2 0.2 3.2 With copper 4.9 1.7 4.9

Perhaps the antimony has so small an effect because it is eliminated in the earlier part of the process, while the silver is still alloyed with, and protected by, a large proportion of lead; whilst the copper on the other hand makes its fiercest attack towards the close, when the silver is least capable of resisting it. The ill effects of copper are most strongly felt when the quant.i.ty of lead present is not sufficient to remove it: the coppery b.u.t.ton of silver got under these conditions is very considerably less than the weight of silver originally taken.

Although the above is a fair statement of the loss attending average work, it will not do in very important and exact work to place too much reliance on the figures given, or, indeed, on any other set of figures, with the object of correcting the result of an a.s.say. Each man must rely on his own work.

It is easy to determine what allowance must be made for the loss in cupellation by cupelling side by side with the a.s.say piece an alloy of similar and _known_ composition. For, if the two pieces are very nearly alike, we may justly conclude that the loss on each will be the same; and if, further, we take the average of three or four such determinations we shall get results accurate within 0.1 per cent. The method of getting such results may be best explained by one or two ill.u.s.trations. This method of working is termed "a.s.saying by checks."

Suppose we have an alloy of silver and lead in unknown proportions and that by cupelling two lots of 10 grams each there is got from I. 0.1226 gram of silver, and from II. 0.1229 gram. We should know from general experience that the actual quant.i.ty of silver present was from 2 to 4 milligrams more than this. To determine more exactly what the loss is, the following plan is recommended:--The two silver b.u.t.tons are wrapped up each in 10 grams of lead, and cupelled side by side with two other lots of 10 grams of the original alloy. If now the two b.u.t.tons I. and II. weigh 0.1202 and 0.1203, they will have suffered in this second cupellation an average loss of 2.5 milligrams. Suppose the two fresh lots of alloy gave 0.1233 and 0.1235 of silver, the average loss on these would also be 2.5 milligrams. Add this loss to each result, and take the mean; which is in this case 0.1259.

If copper is present in the alloy as well as silver, it is necessary to add about the same quant.i.ty of copper to the checks as is supposed, or known, to be present in the a.s.says. If the substance to be a.s.sayed is an alloy of silver and copper, first cupel 0.5 gram of it, with, say, 10 grams of lead, and weigh the resulting b.u.t.ton of silver, in order to get an approximate knowledge of its composition. Suppose the b.u.t.ton weighs 0.3935 gram. We know that this is below the truth: for the sake of round numbers take it as 0.4, and a.s.sume that the rest of the alloy (0.1 gram) was copper. Two check pieces are then weighed out, each containing 0.4 gram silver and 0.1 gram of copper wrapped in 5 grams of lead. Of course the silver must be pure. And there is also weighed out two (or better, four) a.s.say pieces each containing half a gram of the alloy wrapped in 5 grams of lead. The whole lot are then cupelled as nearly as possible under the same conditions. With four a.s.say pieces, the cupels should be placed close together in two rows of three across the m.u.f.fle; the two check pieces are put in the middle cupels. Suppose the b.u.t.tons of silver got weighed as follows:--

Check pieces I. 0.3940 II. 0.3945 a.s.say pieces I. 0.3905 II. 0.3912 III. 0.3910 IV. 0.3909

The average loss on the two check pieces is 5.7 milligrams, and the average result of the four a.s.say pieces is 0.3909. Add the average loss to the average result, and there is got the corrected result, 0.3966.

And if 0.5 gram of alloy contain 0.3966 of silver, 1000 will contain 793.2 of silver, and this is the degree of fineness.

A correction for the loss in cupellation is always made in this way when rich alloys are being a.s.sayed; and in the case of rich ores it may be done after the manner of the first of the above ill.u.s.trations. There is another method of working which relies more on experiment. This is to smelt the cupel as described further on (p. 114), and to again cupel the resulting b.u.t.ton of lead. The b.u.t.ton of silver got in this second cupellation is added to that first obtained. It will sometimes, but not often, happen that the two b.u.t.tons together will slightly exceed in weight the silver which was actually present. This is because of the retention in the b.u.t.tons of a small quant.i.ty of lead. It has been stated that the proportion of lead thus retained may be as much as 1% of the silver present; this, however, can only be under exceptional conditions.

A determination of the actual silver in the b.u.t.tons got in the series of cupellations quoted on pages 102, 103, gave an average percentage of 99.85, so that even with the larger b.u.t.tons the effect of the retained lead would be only to increase the weight by about 1 milligram. In the method of working with checks, the retained lead has no disturbing influence.

~The proportion of lead required~ for the cupellation of any particular alloy requires consideration. With too much lead the time occupied in the process is increased, and so is the loss of silver; on the other hand, too little lead is of greater disadvantage than too much. From 8 to 16 parts of lead are required for each part of silver alloy, or, if gold is present, about twice as much as this must be used. For the cupellation of 1 gram of a silver copper alloy containing different percentages of copper, the following quant.i.ties of lead should be used:--

Percentage of Copper in Alloy. Lead Required.

5 6 grams 10 8 "

20 10 "

30 12 "

40 14 "

50-100 16-18 "

The alloy, in not too large pieces, is wrapped in the required weight of lead foil and charged into the cupel at once; or the lead may be put in first, and, when the cupellation has fairly started, the alloy may be added wrapped in tissue paper; or a portion of the lead may be first started and the alloy wrapped in the remaining lead and subsequently added. The cupellation of large quant.i.ties of alloy or of alloys which contain tin, antimony, iron, or any substance which produces a scoria, or corrodes the cupel, must be preceded by a scorification. The advantages of this are that the slag is poorer in precious metal than that found on a cupel and is more easily collected and cleaned; that larger quant.i.ties of metal can be treated, and that, even if the substance is in part infusible, or produces at the start a clinkery ma.s.s or scoria, the oxide of lead gradually acc.u.mulates, fluxes the solid matters, and produces a good final result; but if the oxide of lead by itself is not sufficient for the purpose, borax or some other flux can be easily added.

If the b.u.t.ton of silver got is very small its weight may be estimated from its size; but it must be remembered that the weight varies as the cube of the diameter. If one b.u.t.ton has twice the diameter of another it is eight times as heavy and so on. Scales specially constructed for measuring silver and gold b.u.t.tons may be purchased; but it is much better to make the measurement with the help of a microscope provided with an eyepiece micrometer.

If the length of the long diameter of a silver b.u.t.ton be taken the following table will give the corresponding weight in milligrams:--

------------+-----------++------------+--------- Diameter. | Weight. || Diameter. | Weight.

------------------------------------------------ 0.04 inch | 3.6 || 0.015 inch | 0.19 0.035 " | 2.4 || 0.014 " | 0.15 0.03 " | 1.5 || 0.013 " | 0.12 0.025 " | 0.9 || 0.012 " | 0.097 0.02 " | 0.45 || 0.011 " | 0.075 0.019 " | 0.4 || 0.010 " | 0.056 0.018 " | 0.33 || 0.008 " | 0.028 0.017 " | 0.27 || 0.006 " | 0.012 0.016 " | 0.23 || 0.004 " | 0.004 ------------+-----------++------------+---------

The weight of a corresponding b.u.t.ton of gold is got by multiplying by 2.25. These figures are based on those given by Plattner, and apply only to b.u.t.tons of such shape as those left after cupellation. A sphere of silver 0.01 inch in diameter would weigh 0.09 milligram, and a similar sphere of gold weighs 0.167 milligram.

It is safer, however, to compare with a micrometer the diameter of the b.u.t.ton whose weight has to be determined with that of a standard b.u.t.ton of nearly equal size whose weight is known. The weights of the two b.u.t.tons are proportional to the cubes of their diameters. This plan of working is described more fully in Appendix B., page 440.

~Calculation of the Results.~--After deducting for the silver added, and correcting for the cupellation loss, the calculation is made in the usual way; reporting as so many parts per thousand in the case of rich alloys and as so many ounces and pennyweights, or better as ounces and decimals of an ounce, in the case of poor alloys and ores.

In this last case, however, it is less fatiguing to refer to a set of tables which give, either directly or by means of simple addition, the produce corresponding to any weight obtained from certain given weights of the substance. The following table gives the produce in ounces and decimals of an ounce per ton of 2240 pounds:--

------------+---------------------------------------------------------- | Weight of Ore taken.

Weight of |----------+----------+-----------+-----------+------------ Metal got. | 3 grams. | 5 grams. | 20 grams. | 50 grams. | 100 grams.

------------+----------+----------+-----------+-----------+------------ 0.0001 | 1.09 | 0.65 | 0.16 | 0.06 | 0.03 0.0002 | 2.18 | 1.31 | 0.33 | 0.13 | 0.06 0.0003 | 3.27 | 1.96 | 0.49 | 0.20 | 0.10 0.0004 | 4.36 | 2.61 | 0.65 | 0.26 | 0.13 0.0005 | 5.44 | 3.27 | 0.82 | 0.33 | 0.16 0.0006 | 6.53 | 3.92 | 0.98 | 0.39 | 0.19 0.0007 | 7.62 | 4.57 | 1.14 | 0.46 | 0.23 0.0008 | 8.71 | 5.23 | 1.31 | 0.52 | 0.26 0.0009 | 9.80 | 5.88 | 1.47 | 0.59 | 0.29 0.001 | 10.89 | 6.53 | 1.63 | 0.65 | 0.33 0.002 | 21.78 | 13.07 | 3.27 | 1.31 | 0.65 0.003 | 32.67 | 19.60 | 4.90 | 1.96 | 0.98 0.004 | 43.56 | 26.13 | 6.53 | 2.61 | 1.31 0.005 | 54.44 | 32.67 | 8.17 | 3.27 | 1.63 0.006 | 65.33 | 39.20 | 9.80 | 3.92 | 1.96 0.007 | 76.22 | 45.73 | 11.43 | 4.57 | 2.29 0.008 | 87.11 | 52.27 | 13.07 | 5.23 | 2.61 0.009 | 98.00 | 58.80 | 14.70 | 5.88 | 2.94 0.01 | 108.89 | 65.33 | 16.33 | 6.53 | 3.27 0.02 | 217.78 | 130.67 | 32.67 | 13.07 | 6.53 0.03 | 326.67 | 196.00 | 49.00 | 19.60 | 9.80 0.04 | 435.56 | 261.33 | 65.33 | 26.13 | 13.07 0.05 | 544.44 | 326.67 | 81.67 | 32.67 | 16.33 0.06 | 653.33 | 392.00 | 98.00 | 39.20 | 19.60 0.07 | 762.22 | 457.33 | 114.33 | 45.73 | 22.87 0.08 | 871.11 | 522.67 | 130.67 | 52.27 | 26.13 0.09 | 980.00 | 588.00 | 147.00 | 58.80 | 29.40 0.1 | 1088.89 | 653.33 | 163.33 | 65.33 | 32.67 0.2 | 2177.78 | 1306.67 | 326.67 | 130.67 | 65.33 0.3 | 3266.67 | 1960.00 | 490.00 | 196.00 | 98.00 0.4 | 4355.56 | 2613.33 | 653.33 | 261.33 | 130.67 0.5 | 5444.44 | 3266.67 | 816.67 | 326.67 | 163.33 0.6 | 6533.33 | 3920.00 | 980.00 | 392.00 | 196.00 0.7 | 7622.22 | 4573.33 | 1143.33 | 457.33 | 228.67 0.8 | 8711.11 | 5226.67 | 1306.67 | 522.67 | 261.33 0.9 | 9800.00 | 5880.00 | 1470.00 | 588.00 | 294.00 1.0 | 10888.89 | 6533.33 | 1633.33 | 653.33 | 326.67 ------------+----------+----------+-----------+-----------+------------

When, as in this table, the fraction of an ounce is expressed by two places of decimals, it may be reduced to pennyweights (dwts.) by dividing by 5. For example, 0.40 of an ounce is 8 dwts. The fraction of a dwt. similarly expressed may be converted into grains with sufficient exactness by dividing by 4. Thus, 1.63 ozs. equal 1 oz. 12.60 dwts., or 1 oz. 12 dwts. 15 grains. In England it is usual to report in ounces and decimals of an ounce.

The way to use the table is best shown by an example. Suppose a b.u.t.ton of silver weighing 0.0435 gram was obtained from 20 grams of ore. Look down the 20-gram column of the table, and select the values corresponding to each figure of the weight, thus:--

0.04 = 65.33 ozs. to the ton 0.003 = 4.90 "

0.0005 = 0.82 "

------ ----- 0.0435 = 71.05 "

Add these together. The produce is 71.05 ozs., or 71 ozs. 1 dwt. to the ton.

Or, suppose an ore is known to contain 1.24 per cent. of silver. Look down the 100-gram column, select the values, and add them together as before.

1.0 = 326.67 ozs. per ton 0.2 = 65.33 "

0.04 = 13.07 "

---- ------ 1.24 = 405.07 "

This gives 405 ozs. 1 dwt. 10 grains to the ton.

The calculation becomes more complicated when, as is frequently the case, the ore contains metallic particles. These show themselves by refusing to pa.s.s through the sieve when the ore is powdered. When they are present, a large portion, or if feasible the whole, of the sample is powdered and sifted. The weights of the sifted portion and of the "metallics," or prills, are taken; the sum of these weights gives that of the whole of the sample taken. It is very important that nothing be lost during the operation of powdering.

Each portion has to be a.s.sayed separately. It is usual to a.s.say a portion of the sifted sample, say, 20 or 50 grams, and to add to the produce of this its share of the "metallics." This way of calculating, which is more convenient than correct, is ill.u.s.trated by the following example:--

Weight of whole sample 400 grams Made up of sifted portions 399 "

" "Metallics" 1 "

--- 400 "

Twenty grams of the sifted portion, when a.s.sayed, gave 0.1050 gram of silver. The whole of the "metallics" scorified and cupelled gave 0.842 gram of silver. Since the 20 grams a.s.sayed was 1-20th of the whole, 1-20th part of the 0.842 gram of silver (from the metallics) must be added to its produce. We thus get 0.1471 gram (0.1050 + 0.0421).

Referring to the 20 gram column, we get--

0.1 = 163.33 0.04 = 65.33 0.007 = 11.43 0.0001 = 0.16 ------ ------ 0.1471 = 240.25 ounces per ton.

A more legitimate method of calculation is as follows:--Calculate separately the produce of each fraction as if they were from different ores. Multiply each produce (best stated in per cents.) by the weight of the corresponding fraction. Add together the products, and divide by the weight of the whole sample. Taking the same example for ill.u.s.tration, we have:--

_Metallics._--Weight 1 gram.

1 gram of it yielded 0.842 grams of silver.

.". Produce = 84.2 per cent.

Produce multiplied by the weight is still ~84.2~.