Cupellation is well known to be one of the most effective methods of separating silver and gold from base metals and other impurities, as well as one of the most accurate means for their estimation. In the latter application it consists in absorbing in some porous medium the fused lead, oxide formed by the oxidation of the lead “bath,” which carries with it the oxides of other base metals present.

It has long been recognized that small amounts of both-silver and gold were removed and absorbed together with the base metals, as well as being to some slight extent volatilized, and in work of the highest accuracy a correction is made for the “cupellation loss.”

Thus in the assay of bullion this is done by means of “proofs” of like composition, which are manipulated throughout in precisely the same manner as the assay pieces, and are assumed to lose or gain like amounts. In the case of certain very rich ores and commercial products the loss is adjusted by assaying the cupel itself and recovering the precious metal absorbed, but this doubles the labor and does not remedy the loss by volatilization. Arbitrary tables have been drawn up by various authorities with the object of enabling a correction to be applied without the use of a check. These have been of very limited practical use owing to the fact that a number of factors affect the losses sustained.

For a fixed amount of precious metal the loss varies with the amount of lead used, with the nature and amount of the impurities, with the porosity of the cupel, with the air supply, and above all with the temperature at which cupellation is carried on. Pure silver loses relatively much more than gold, but the loss in either is diminished by an addition of the other metal. The concentration of precious metal in the litharge increases as the concentration in the lead increases, but little work has been published connecting the two. If all other conditions remain the same the actual total loss increases, but the percentage loss diminishes, with an increase in the weight of precious metal treated.

The results of an immense number of experiments have been published at various times during the past hundred years giving the actual or the percentage losses suffered under various conditions of cupellation, but the data are widely scattered and few attempts have been made to correlate them, so that no definite law has heretofore been shown to exist governing the relation of weight and loss, although Fulton has published curves covering certain conditions. If such a law were known it would enable a correction to be applied to a button of any weight, by a calculation applied to the loss observed in a proof of an entirely different weight, but cupelled at the same time under the same conditions. It is believed that such a rule is now available.

This empiric rule may be thus enunciated: When a Given Amount of Silver (or of Gold) is Cupelled with a Given Amount of Lead, under a Fixed Set of Conditions as to Temperature, etc., the Apparent Loss of Weight Sustained by the Precious Metal is Directly Proportional to the Surface of the Button of Fine Metal Remaining.

Probably the calculation should be based on the original weight of precious metal taken, but in practice we have to depend on the weight remaining. Variations in the amount of lead have comparatively little influence, and temperature conditions in a given row across a muffle are nearly uniform, so that for practical purposes the proportionality holds good for any one row in a cupellation run, provided the amounts of lead do not differ extremely. Most other variations have smaller effects. If the above is true the following must also be true.

The Loss of Weight Varies as the 2/3 Power of the Weight, or as the Square of the Diameter of the Button.

The Percentage Loss Varies Inversely as the Diameter of the Button, or Inversely as the Cube Root of the Weight.

Examination of a large number of experimental results, as well as the published data of others, proves that the last proposition is a close approximation to the truth, and therefore proves the others. The readiest proof of the rule, which avoids all calculation, is by the aid of logarithmic paper—that is, paper on which the co-ordinates are plotted on a scale like that of a slide rule. In place of using the ruled paper the distances may be actually laid off by means of a slide-rule scale. When plotted in this way the graph of any equation of the character y = Cxn appears as a straight line, and all such lines for a given value of the power n are parallel. If the horizontal and vertical scales are equal (as in Figs. 1 and 2) the tangent made by the line with the x axis is the exponent n.

If therefore we plot on the x axis the weights of a series of silver buttons cupelled under precisely similar conditions, and the corresponding losses on the y axis, and the corresponding points fall approximately on a straight line, then we know that y varies as some power of x. Drawing a line parallel to the general run of these points from the point whose co-ordinates are y = 1, x = 1 to x = 10 or 100, will indicate at once what the value of n actually is.

If any one will take the trouble to average and plot a series of cupel losses on buttons of various sizes carefully cupelled in the same row, he will, I think, find that they will fall nearly on lines parallel to

y1 (weight lost) = x2/3

and y2 (percentage lost) = x-1/3

The distances between the parallel lines obtained in various series simply correspond to the values of the constant C for different conditions of temperature, muffle draft, etc.

A few results are shown thus plotted in Fig. 1.

I have found that such series as those published by Klasek, Godshall, Beringer, and Kauffman (omitting certain erratic ones), and a transcription of the curves plotted by Fulton, all give points falling nearly into general parallelism with the lines indicated, and my own values for silver alone and gold alone agree well except for the smaller values, where irregularity naturally occurs. This rule is the dominant factor in cupellation loss, temperature alone excepted.

As to the possible application of this rule: An approximate correction may be obtained for an ore or the like, if one proof, as near the expected weight as possible, is cupelled in each row, and its exact loss noted. The corresponding point is plotted on the diagram (a in Fig. 2, A representing the final weight), and a straightedge is placed on the diagram, or a line drawn through a, parallel to the guide line, y = x2/3. Noting the points on the line or straightedge corresponding to the weights B, C, D, of other buttons weighed, the correction for each is read at once from the scale. In the example plotted in Fig. 2 a button of 140 mg. weight has lost 1.8 mg.; from this it appears that other buttons of 250, 35, and 15 mg. will respectively have lost about 2.85, 0.72, and 0.40 mg.

In a future paper I hope to present some further data on the cupellation of mixed metals, their relative rates of removal, and their concentration in various portions of the cupel.

Even if the data given should be considered sufficient to support properly the empirical rule as stated, this rule would be of extremely limited application in miscellaneous assaying. The fixed conditions must include equality of gold and silver where mixed beads are concerned, owing to the wide variation in the specific gravity of gold and silver. Also, the fixed conditions must include the presence of the same amounts of other base metals besides lead. Such an agreement is often lacking even in the beads from two fusions of the same ore. In practical work it is sufficiently general to be called universal that cupellation beads are not pure precious metal. An apparent loss in cupellation is an algebraic sum and in many cupellations the gains exceed the losses, especially with large beads where the, gains lie so completely in the judgment of the cupeller.

For several years I have been engaged in an investigation into the conditions affecting the accuracy of gold-bullion assaying, and have just completed an examination of cupels which included the assaying of 10,000 used cupels. The grand result of the cupel work is an emphatic warning against drawing rigid conclusions regarding cupellation. It is so easy to say “If all other conditions remain the same,” but it is extremely difficult, and in practical work impossible, to maintain equal conditions. Cupel absorptions, which constitute such a large proportion of cupellation losses, and in many cases the only loss, may vary considerably in different parts of the same row of cupels, even in carefully regulated work.