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THE QUARTERLY

ee Nae OE SCIENCE,

JANUARY, 1873.

i, ON THE PROBABILITY OF ERROR IN EXPERIMENTAL RESEARCH.

By WILLIAM CROOKES, F.R.S., &c.

CN SCIENTIFIC man engaged in any special pursuit a has much difficulty in making clear, to even the scientific public, the result of his experiments. The benefit of his research may be perfectly apparent; but if his experiments have been conducted with rigour there will be a certain individual departure from a general standard inthe results, which, if he merely state his conclusions, will confuse the attentive reader. Perhaps certain of the ex- periments were performed under better test conditions, and their numerical results are therefore more nearly correct than the results of another series of experiments. Should this be the case, to take an average of the results would yield an empirical result, deviating considerably from the truth. Yet many of our most eminent experimentalists are satisfied with recording their experiments, and leave the student of their labours in an uncomfortable uncertainty as to the exact value of the entire system of experiment.

In his ‘‘ Budget of Paradoxes,” Prof. De Morgan, in the consideration of the relation of facts to theory, asks the question—‘‘ What are large collections of facts for? To make theories from, says Bacon; to try ready-made theories by, says the history of discovery ; it’s all the same, says the idolater; nonsense, say we!” Whether, however, we take facts in subordination to theory, or the reverse, matters little for our present purpose; we have to regard the ob- servation of facts, ascertained experimentally or otherwise, as the test of theory. But a difficulty immediately occurs to the experimentalist, and may be framed in the question— ‘‘ Which, and how much, of these experimental facts am I to regard as correct, absolutely or approximately ?”

Absolute correctness evidently may not be expected of any of the human senses, since the absence of error would

VOL. Il: (N-S:) B

2 ) On the Probability of Error [January,

include perception and corre¢t estimation of the most minute deviation from the absolute standard. Between even this deviation and the absolute standard there are an infinite number of results that may be obtained. Approximate correctness is all, then, that the experimentalist has the probability of attaining. So that, given a series of experi- mental results, there remains the decision of two points— (1), the determination of the standard; and (2), the probable error of the assumed standard.

There are many engaged in experimental research, even in research of a relatively high order, to whom the methods of determining these two points are unknown. ‘To these I shall endeavour to explain the laws of probability as they have been laid down by eminent mathematicians. To those (and I am afraid their number is not legion) acquainted with these laws, I can offer illustrations only of the appli- cation of these laws. Without a due consideration of these principles astronomy could not claim its character of exactness; and there appears no reason why the physical and chemical sciences should not, as means of observa- tion increase in delicacy, attain to the rank and estimation of exact sciences. Our chronographs measure easily to the I-100,o0o0th of a second of time; our balances turn with a fragment of a hair weighing 1-10,oooth of a grain; the re- sults of electrical experiments have been obtained varying only 5 in the 1000. With this exactness, surely we may think it carelessness that does not ascertain the closest ap- proximation to accuracy, as well as the limit of error to be allowed this approximation.

The subject is a most subtle one. It may be defined as the best mode of combining observations so as to yield the most trustworthy mean; and in this light I am unable to mention any work affording so popular and so profound a discussion as the little volume, by Prof. De Morgan, entitled ‘An Essay on Probabilities.” The author shows how the observer may measure the degree of confidence to which the average of any series of observations is entitled. Thus, taking his own example,—that of fifteen observations giving the following results : 722, 933, 1033, 917, 1311, 1089, 972, 1294, 967, 1344, 1250, 744, 1309, 858, 1029,—if the average, or the arithmetic mean, of all the observations be T1051, the theory does not assist the observer in estimating the probability of this average being true. For true, in the absolute sense of the word, it, in all probability, is not, and therefore no theory is needed to assist in drawing that con- ciusion. But let any definite departure from truth be

1873.] in Experimental Research. 5

named, then the theory enables the observer to determine the degree of likelihood that his average is within such limit. Thus it is found that the probability of the average of 1051 being within 50 of the truth (whatever the truth may really be) is 0°66; and therefore the observer should contemplate the possibility of his average being within 50 of the truth, or, which is the same thing, that the truth lies - somewhere between the limits 1051 +50. ‘This he would assume with the same degree of confidence, neither more nor less, that he would yield to a witness who is known to speak truth 66 times and falsehood 34 times out of every hundred.

If the calculation had been made for the limits 1051 + 10, the resulting probability would have been much less than 0°66; and if for 105% + 100, the resulting probability would have been much greater. This is in accordance with com- mon sense.

It must also be very important to the observer, when he has made different sets of observations, to know how best to combine their respeCtive averages. For both purposes the average of the set, or of each, may be “‘ weighted” by means of the formula— gee 1?

258”

where 2 = the number of observations and 3c? = the sum of the squares of the successive differences obtained by sub- tracting each observation from the arithmetic mean (average) of the whole.

The term weight is almost self-explanatory. Of a series of observations there may be one which the observer consi- ders to have been obtained under more favourable conditions than the others, and to which, in the balance of judgment, he should accord greater ‘‘ weight.” For if we suppose a _ satisfactory experiment to give 5, and one of unequal weight 6, it would be obviously unfair to take the average as 53; but it would be more reasonable to give the result 5 the ad- vantage of supposing it to have occurred, say, three times to the occurrence of the result of 6 once. This would be giving the observations 5 and 6 the weights of 3 and 1, and the average would be 54. Such a mode of reasoning gave rise, before mathematicians had constructed the theory of probabilities, to a rule for finding the average, which may be quoted as follows :—Weigh every observation, multiply it by its weight, take the sum of the produéts, and divide this sum by the sum of the weights. But it was found that the

4 On the Probability of Error (January,

theory of probabilities diated a variation of this rule, em- bodied in the formula previously stated. This formula may be understood in words as follows:—Square the number of _ observations, and divide this product by twice the sum of the squares of the errors.

Having now defined the term ‘‘ weight,” we have to trace the meaning of the terms mean risk and probable error.

If we consider positive and negative errors as equally probable, they will balance each other, so that the average of positive or of negative errors will be equal. We thus arrive at the meaning of the term average error, and can proceed easily to the determination of the mean risk ; and as the mean risk of positive error is the average positive error, the mean risk of negative error the average negative error, the mean risk may be taken as half the average error. Re- presenting the mean risk by m, and the weight byw, we have—

Mean risk = ek

709 Vw

or more nearly, = Bene Ww

Or, mean risk = prob. error X 0°591473.

The probable error is that error for which there are equal chances of exceeding or of not attaining. For instance, suppose the chances are equal that the error is included be- tween o and 2, or that it should exceed 2, assigning this as the limit of error, then, of course, for any number greater than (say) ro the chances are in favour of the error being in- cluded within the number. It has been calculated that—

g ‘ erat 67 The probable error = sa0te: or more nearly, = a ALIS

w Or, the probable error = m 1°690604. Calling the mean risk m, the probable error f, and the weight w, we have from the preceding reasoning the fol- lowing formule :—

ee is

~ 1420m?" "aed ol eh ead er nn ae rae

From the foregoing formule, when either the weight, probable error, or mean risk is given, the other two can be determined. As we are capable, in most scientific observa- tions, of so adjusting our instrumental means that the errors

1873.] in Experimental Research. 5

may have positive and negative signs, so are we nowina position to verify these observations, or select those most closely approximate to the truth.

But there have been tabulated the values of the celebrated i definite integral—

2 Ps 2 gs Mee vee ff : oO

and from these tabulated values (for the extension of which we are again indebted to Prof. De Morgan) we may, with much less trouble and more accuracy, arrive at the desired result. The values have been arranged in two tables: the columns of Table I. are headed thus :—

ip Ex. A. Ae. 0°50 0°52049 99 874 38 8 88 2°17 0°99785 II g 96 44 2°68 0°99984 94 84 5

¢ represents every hundredth of a unit from o to 2.

H represents the values of the area enclosed by an asymptote, this asymptote continually approaching but never reaching the abscissa, the whole of the enclosed area forming one square unit.

A represents the differences of these values.

A? represents the differences of these differences.

In Table II. are three columns only, ¢, A, and K,—a mo-

dification of H,—headed thus :— t. K. pi 4°6 0°99808 40 Let us now take an illustration. There are ten observa- tions of which the arithmetic mean is— & =200°01577. The sum of the squares of the ten differences between a and each individual observation is— de? =0°00000007. Hence the weight of a is— (number of observations) _ I0o 227 ~ O°000000I4 The largeness of this figure indicates the high degree of probability that a is very near to the true value sought. But the query may be put—What is the true value? It will be seen that the question does not admit of absolute answer, and for the following reasons:—One of the observations

w= = 715000000.

6 On the Probability of Error |January,

was (say) as low as 200°0156; one was as high as (say) 200°0159. Further observations might have yielded results still more extreme. But assuming they would not, still the ‘number of possible values between 200°0156 and 200°0159 is infinite. The arithmetic mean a is but one of these, and although more likely than any other that could be named, it is not more likely than one or other of all the possible values. The odds are more than 1000 to 1 that a is not the truth ; but they are also more than Ioo0 to I that a is very near the truth. The question—How near ?—cannot be an- swered. Alter the question to—What is the probability that the truth is comprised within the limits a+ k ?—and the answer may easily be given, however small k may be. Thus, if k=o‘ooor. In other words, if the question be— What is the degree of likelihood that the truth lies between 200°0157 and 200°0159?—the answer is given by the formula— w= H.,, t=kVw,

where &, 0°0001,

»» W=715000000, and as log. w=8°854, log. Vw=4'427,

3 “w=26800. Then t=k Vw=2'68, and from Table I.—

7 =H 6g =0°99985.

The result, 0°99985, is so near to unity (the measure of cer- tainty) that for every practical purpose it may be considered certain that the truth is really comprehended within the limits named.

Take six other observations, the arithmetic mean of which is—

a=203°870;

and the sums of the squares of the six differences between a and each separate observation is—

Dy iat sy aia Oe Then the weight of a is— 36 0 2x67 De? O7FI515 The smallness of this figure, contrasted with the 715000000 of the preceding example, indicates a comparatively low degree of probability that the true number is comprised within the limits +, when & is very small. For instance, suppose the question to be—What is the likelihood that the true number is comprised between 203°77 and 203°97? As

= Bao.

1873.] in Experimental Research. 9

before, the probability will be determined by the given formula. Lick" 07100;

W =25°200, Vw= 5'020, t= 0°502,

pe Bede = aya: .

This result, 0°52, is just intermediate between unity or certainty and zero, the lowest degree of probability, other- wise denominated impossibility. Hence, that the true number is within the limits stated is just as likely as the throwing of Head with a single halfpenny, but not more likely.

I will now submit a practical application to the reader.

The value of the results obtained during any series of ex- periments must of course vary with the care taken in the performance of the individual experiments. In support of this view I have, in the practical application of the laws I here endeavour to simplify, taken the utmost pains to ensure accuracy. The application is the determination of the atomic weight of thallium; and I shall first enumerate the means (not usually employed) by which I deem accuracy to have been ensured, and then proceed to evolve the results.

With a metal of so high an atomic weight (203°642) as thallium, errors and inaccuracies comparatively trivial with elements of low atomic weight, are magnified into alarming prpportions. Impurity of the reagents employed, imperfect manipulation, but, more than any, the inaccuracies arising during the weighing from the omission of the cor- rections required by temperature, pressure, &c.,—all these influences must be eliminated in the determination of an atomic weight.

The atomic weight was derived by two methods :—First, by taking a known quantity of metallic thallium, dissolving it in nitric acid, and weighing the nitrate of thallium pro- duced. Secondly, in dissolving known quantities of sulphate of thallium in water, and ascertaining how much nitrate of barium is necessary to precipitate the sulphuric acid as sulphate of barium.

There were also two methods of weighing: one in air, at ordinary pressure and temperature, and one in a highly rarefied atmosphere. For the first method a balance was employed, made expressly for the work by Messrs. Keissler and Neu, which will indicate clearly a difference of o’o0or of a grain when loaded with 1000 grains in each pan. For the second method of weighing a balance was employed

which I term a vacuum balance. It was made by Oertling, and is-a duplicate of the first, but it is enclosed in a cast- iron case, connected with an air-pump, and arranged for the weighing to take place in air of any desired density. The best manner in which to use such a balance as this is to in- troduce a certain approximate weight, and then to alter the pressure of the air until the balance shows equilibrium. Two weighings, at different degrees of atmospheric pressure, varying by a considerable interval, give data upon which to calculate what the weight would be in a perfect vacuum. For the full elucidation of the formulz employed, for the method of adjusting the standard grain-weights according to their value 77 vacuo, and for the preparation of the glass apparatus and the pure reagents, I must refer the reader to my paper im extenso, contributed to the Royal Society.* But I may, from the abstract of that paper, collect the results of a series of the weighings. They were as follows:—

The weight of the glass + thallium. The weight of the glass + nitrate of thallium.

The weight of the glass alone. Grs.

True weight of thallium 7 vacuo . ~=183°790232 True weight of nitrate of thaliium imvacuo. . meat aA = 239°646066 True weight of class ae ade 5 = FOG sana (a) W eight of ‘thallium according to true value of weightsin air =183°783921 (6) Weight of nitrate of thallium in air (1005°425937—765°814578) =239°611359 (c) Weight of glass, &c., in air . =765°814578 Weights employed to balance (a) ~« =183°8099 Weights employed to balance (0) (1005°4364—765°8081) . . =239°6283 Weights employed to balance (c) . =765°8081

From these data the atomic weight can be deduced by simple proportion, but the results of the statements of the proportion are absolute only if the atomic weights of nitro- gen and oxygen are correct. The determinations of Prof. Stas show that the atomic w eights of nitrogen and oxygen should be represented by N=14‘009, and ©, =47°880, in- stead of N=14 and O=106, as hitherto more generally held. The equivalent of nitric acid thus becomes NO,=61°889, instead of the old equivalent NO,;=62. Taking as data Prof. Stas’s determination of the atemic weights of nitrogen

* June, 1872.

1873.] in Experimental Research. — of

and oxygen, and the weights zm vacuo, the quantity of nitric acid required to convert the thallium into nitrate is—

(239°646066 — 183°790232 = )55°855534 srs. We have then the proportion— iene of Wicicht of Atomic Weight stomlc Nitric Acid. Thallium. OP Nittie Acide <r Fac: Berea ses4 0) fy bes"790234 98: \'6E°SSg 2 2. x; .. = 203°642. _ Substituting the old equivalents we obtain—

Becegs 34) |) FO3°700232 28) 62 ) 2: :) 2047007 as the atomic weight; but I cannot admit this number to be so nearly correct as 203°642.

If we take the corrected weighings in air of ordinary density, we have, with NO,=61°889,

203°738. With NO,;=62, 204°103.

Accepting the uncorrected weights, observed in air, we have, with NO, = 61°889,

203162. With NO,=62, 204°1605.

The error of the last deduction is +0°523, a sufficiently large number to show the inutility of the application of the theory of probability until every care has been taken to eliminate the errors arising from inaccuracies. As I have stated, in the paper to which I have referred, the largeness of these errors has an immediate bearing upon quantitative analysis, for it is shown that, from data ordinarily given, very varying results may be obtained. Chemists have to deal with much smaller quantities than a quarter per cent, particularly in organic analysis, where so wide a difference from the truth may lead to very erroneous reasoning.

Pass we now to the application of the theory of proba- bilities to ten results of the most trustworthy weighings. These, with NO, =61°889, are as in Table I.—

Tabulating the results of the determinations, with the view to ascertain severally their degree of approximation to the arithmetic mean (Table II.)—

The arithmetic mean of the ten observations is—

_ 2036°424 _ 6 Oo wear

VOL. Its (N.S.) c

Io

- Deter- mination.

Ao MOM OO b>

On the Probability of Error

‘TABLE

True Weights im vacuo.

Weight of Thallium taken. Grs. 497°972995 293°193507 288°562777 324°903740 183°790232 190°842532 195°544324 201°856345 295°683523 2.99°203036

ieee eee oe

Weight of Nitrate of Thallium + Glass.

Grs. I121°851852 IIII'387014

Q7I'214142 1142°569408 1005°306796

997°334615 1022°176679 1013°480135 1153°947672 1159°870052 TABLE II. 203°666 203°628 203°632 203°649 203°642 203°636 203°639 203°650 203°044 203°638

—_——,

Weight of Glass.

Grs. 472°557319 72.9°082713 994°949719 718°849078 706°133831 748°491271 707°203451 759°332401 768°403621 769°734201

+0°024 —O°OoI4 —o°o1o -++0°007 -++ 0000 —0'006 —0°003 +0'008 +0°002 — 0°004

' The sum of the squares of the differences is—

0°000576 0°000064 0'000049 0°000004 0°000000 0°000009 0°000016 0°000036 0°000I00 0°000196

Se? = 0'00I050

Calculated

Atomic

Weight from these Data.

Grs. 203°666 203°628 203°632 203°649 203°642 2.03°636 203°639 203°650 203°644 203°638

Therefore 25¢? =o°0021; and the weight (w) of a is—

I0o

= = 476109.

0°O002T

* Fully illustrated in the Paper.

1873.] in Experimental Research. LS

We have then, from the formula,—

The probable error a5 Tat

62 Seara cis log. 62 — (log. 130+log. 218) log. 0°0022,

the number 0’0022 as the probable error. Or by means of the tables calculated from the definite integral we can arrive at a similar result. Thus—‘‘ What is the probability that the truth is comprised within the limits atk?” If k=oror; and 7=H

t=kvw; then w=47619, Vy =218,

t=kvV¥w=2'18, and w = H,.13=0°99795, so near to unity, the measure of certainty, that the number 203°642 may, for all practical purposes, be regarded as the absolute truth. From the second table we can also obtain like results by entering with ¢% We obtain the argument from the formula— :

probable error : Therefore? °* 0°0022 There can remain no reasonable doubt, then, that the atomic weight of thallium is =203°642.

As simply as I am able, I have endeavoured to show the application of the theory of probabilities to the judgment of error, and the evaluation of the amount of accuracy in experi- mental research. The subject has, I think, been involved with undue difficulty. Perhaps it has hitherto been gene- rally held that the results of experimental research have not been sufficiently accurate to permit the refinement; but I must express an opinion quite opposed. Yet I would suggest that, in all kinds of delicate weighings, the effects of tem- perature and pressure of the atmosphere be taken into consideration. Let me make my meaning clear by an ex- ample. There are given to be weighed, let us say, 800 grains of water in 200 grains of glass. First arises the question, —Shall we employ brass or platinum weights for our deter- mination? We shall presently see the difference that would result, in the determination of the absolute weight of the glass and water, from the result of our choice. A brass

= 4°6=1, to which corresponds k =0°g99808.

a

weight of 1000 grains will displace 0°1462 grain of air; an equivalent platinum weight 0°058271 grain of air. The 1000 grains of glass and water displace 1°9736 grains of air, so that their absolute weight is 1001°9736 grains. Now the glass and water balanced by the brass weight would give, less the air displaced by the weight, 1001°8274 grains as the true value of the water and glass; while 1001°9736 grains, less 0°058271 grain, give 1001I°915329 grains as the value to be ascertained. So, supposing the barometrical pressure to remain constantly at 760 m.m., we have an error of 1°8276 grains per 1000 in weighing with brass weights uncorrected in air, and 1I°915329 grains per 1000 with platinum weights at the same barometric pressure. But we know that the barometer does not always record the same pressure. What, then, will be the result of its variation ?—the variation, of course, of the weight of air displaced. Now a litre of dry air (at Greenwich), at 760 m.m. pressure and o C., weighs 1°293561 grms., and its weight will be proportionately lower at lower pressures. At 740 m.m. the weight of air displaced by water and apparatus will be 1°g216 grains, and at 715 m.m. 1°8890 grains. The weight of air displaced by the brass and by the platinum weight also decreases propor- tionately. So that, weighing with the brass weight, we have, at 740 m.m., an error of 1°7792 grains on the Iooo, and at 715 m.m. an error of 1°7505 grains. With platinum weights we have, at 740 m.m., 1°864863 grains error, and 1°834334 grains at 715 m.m. ‘These discrepancies are too important to be disregarded. For suppose our weighings to have taken place on different days, at different pressures which were not noted, we should have serious error; and the error would be increased with a S ance lighter fluid than water.

Chemists are aware how greatly an error of similar character would influence the determination of the amount of carbonic acid and of- water yielded by an organic body under combustion. Suppose the potash bulbs em- ployed in the analysis to weigh 600 grains, there would be displaced 0°366 of a grain of air at 760 m.m. pressure, 0°327 grain at 740 m.m., and 0°316 grain at 715 m.m. Thus if weighings were made at 715 m.m. and at 760 m.m., there would be an increase of weight of 0°02 grain; and this, if 3°5 grains of the organic compound were under analysis, would give an error of 0°6 per cent. Similarly with a chloride of calcium tube, weighing, with its contents, 350 grains, there would be an error which—with the error in the estimation of the carbonic acid—would give a total error of

1873.] Colorado Gold Mines. 13

nearly I percent. Of the effect and importance of such an error it is unnecessary to speak; to all in the least acquainted with analytical research there will appear full reason for the more careful study of the subject.*

These facts clearly show the necessity,—first, of great care and great delicacy in all manipulation connected with experimental research; secondly, of carefully ‘‘ weighing” the individual merit of each result, and its relative merit in the series of results. How this may he effected I have en- deavoured to explain ; and I think that there would be no series of observations (to which this or an analogous method has not been applied) but would benefit by the application. The application should of course proceed from the experi- mentalist himself, but there are many series of results, the members of which have been obtained by different processes, that would be rendered still more practically useful by an evaluation according to some one of the principles of the theory of probabilities. - Perhaps in future years the theory may be universally understood, and it will not be required to revert to the elements of the Science.

II. GOLD-MINES AND MILLING OF GILPIN COUNTY, COLOKADO, UNITED STATES.

By JAMES DouGLas, Quebec. £5 WEF in Dry Gr years ago a party of miners detected gold | in Dry Creek and other spots near the present town of Denver. The news spread; a rush ensued, and exploration was rapidly carried from the plains up the gorges of the Rocky Mountains. Before 1859 had closed, the gulches round Central City, 40 miles distant from Den- ver, were swarming with gold-diggers ; and mining had also commenced on the rich surface quartz of the lodes, whose disintegrated débris had supplied the gold that enriched the neighbouring valleys.

In what is now Gilpin County, and within an area whose centre is Central City, and radius about 14 miles, was dis- covered, before 1863, a gold-bearing lode at almost every hundred feet ; and many of these lodes were yielding gold

* In the course of my experiments with the delicate apparatus employed in this research, I have noticed some curious effects of the action of heat upon gravitating bodies. Led to pursue the investigation with specially constructed apparatus, in air and in vacuo, I hope, at no distant date, to bring forward some results.

and matter for exaggeration so abundantly that American brokers were enabled to form, in the cities of the east, no less than 186 public gold-mining companies. The com- panies generally possessed capital enough to build a mill, but before the mill was running it in many cases happened that the surface rock, which yielded its gold to mercury, was exhausted, and after a few experiments the mill was _ stopped; and mill and mine have remained closed ever since. A few mines, however, rich enough to bear the loss of from three-fourths to two-fifths of their produce in the mill, have remained open, to testify to the extraordinary richness of the district. As the mills existed they have continued to be used, despite the defects of their work ; but unless some better system be introduced mining must lan- guish, for no mines can long sustain such waste.

The present article is a contribution towards the solution of the question, which, as it involves the saving or loss of several million dollars’ worth annually of gold, silver, and copper, is well worthy the attention of metallurgists. So abundant is the ore that were mining conducted systematic- ally, and the product of the mines utilised, Gilpin County would probably yield more value in mineral than any district of equal size in the world.

The country rock is granitic, with some gneissic varieties. The lodes have a general E. and W. course, and dip almost vertically. They are very free from faults, and many of them can be traced, running with remarkable regularity, for long distances; but the productive portion rarely exceeds 4000 feet. The deepest shaft in any of them is only 700 feet, and there are few others deeper than 500 feet: it is therefore impossible to predict what their character will continue to be, and whether the gold yield will be perma- nent; and the changes which have taken place in certain of the lodes, at different depths, are too inconsistent with one another to allow of any deductions being drawn from them. The structure of the lodes is very chara¢teristic of fissure- veins. The walls are usually distinct, and marked often with well-polished schlicken sides. A clay sewage, then a band of almost pure iron and copper pyrites, intermixed with small quantities of blende and galena, or of blende and galena alone, or of all these sulphurets mixed in almost - equal proportions, occurs on one or both sides, while the centre of the lode is composed—where the lode is rich—of a gangue of decomposed quartz or felspar, carrying more or less of the same sulphurets. The solid sulphurets of iron and copper, known as No. I., or smelting ore, usually yield

1873.] Colorado Gold Mines. ies

to the miner from 60 to 80 dollarsaton. The copper pyrites carries most gold, and the fine-grained iron pyrites more than the coarse, distin€tly cubical, variety. The blende is also associated with gold, and in some mines isthe principal vehicle of it, and the galena is invariably argentiferous. This rich ore is always sold to the smelter, as it refuses to . give even as large a percentage of its gold to mercury as the less concentrated ores of the body of the lode, where the gold seems to be in a freer form. ‘The second class ore, in first class mines, will usually carry—

I°4 ozs. of gold,

5°6 ozs. of silver,

2°8 per cent of copper.

It is always treated in stamp-mills where battery amal- gamation is employed, and not over 33 per cent of the above-named valuable constituents of the ore recovered.*

The proportion of No. I. ore to No. II. ore rarely exceeds one-tenth, and in most mines the quantity is too small to make it worth while effecting any separation.

The width of the lodes runs from 18 inches to Io to 12 feet. An average width of the really productive lodes may be set down at 3 feet, but they are all subject to contractions and expansions, sometimes pinching to a mere thread, at other times bulging into enormous bunches. Nor are any of the lodes consistently productive. The mineralogical portions are said to run in chimneys, which are interrupted by streaks of poor or altogether barren rock. The term ‘*chimney” has been borrowed from California, but is not applicable in Colorado, as the rich ground does not form continuous vertical streaks, alternating with vertical streaks of barren rock, but irregular regions of rich ore, merging vertically and horizontally into poorer ground. The term *‘cap” is applied indiscriminately to merely lean and alto- gether barren ground. Of the latter there is comparatively little ; and as the former includes all ore that will not yield 20 dollars of gold to the ton, much that is now left standing in the mines, it is to be hoped, will some day or other be removed with advantage.

Unfortunately the mining in Gilpin County has been as faulty as the milling, owing chiefly to two causes :—

I. The subdivision of the lodes into very small claims.

II. The failure of the companies very generally to work their claims,—which has led to the mines being either let or

* Mr. ALBERT REICHENECKER, in the Berg-Hiittenmannische Zeitung, re- produced in RAYMOND’s Report on Mines and Mining for 1870, p. 360.

worked on tribute. In either case the miner, having no in- terest in the property, aims only at extracting as much ore as he can during the term of his lease, without regard to the future of the mine.

I. To what a degree the subdivision of the lodes has been carried may be judged from the following enumeration of the claims on some of the principal lodes in the district. The list is taken from Mr. G. W. Baker’s pamphlet on the treatment of gold ores in Gilpin County, Colorado.

On the Gregory Lode—

Feet.

The Black-Hawk Coe. owns:.) 005." =" t.3500 », Consolidated Gregory Co.owns. . 500 »» Marragansett Co: owns)\:> "=: .. 2 ¢@e » Rocky Mountain Co.owns . . . 200

i». Dette Ce Owns. os oa » Russell (Extension) Co.owns . . 360 > biiges Co. owes.) 25 te PAO

» ~omith and Parmlee Co.owns . . I100 » New York (Extension) Co. owns . 250 », United States Co.owns . . . . 250 . po.) AMES IEEE EGEA ha Sg saga shah a owe? ee

4750 On the Bobtail Lode— Feet.

The Bobtail Coowns . 3) 3%." 7) ae 5 usu ime ‘Co. owas) i502 oo ,, “dorastow Co. owns 2 kh Sie a ie », sensenderter Co. owns: <2 2) 5 Eas

Private owners in small claims own from

700 to 800

1483

Feet.

The Rocky Mountain Co.owns . . . 250 » Dates and, Baxters Co, owns 9.3 =, 300 » Unton Co. ownse. =... ee ee 3° Luoker Co-- Owns 2. 20 See oe ee

. 9 “Gregory Co. owns) Goose eee - ee Private persons .)2.45 0 2 eee eee

On the Bates Lode—

1550 These three lodes have been the most productive in the distriét, and the most diligently worked. The Bobtail has,

1873.] _ Colorado Gold Mines. 17

it is estimated, yielded about 3,000,000 dollars’ worth of bullion,—no insignificant yield, considering how short is the really metalliferous portion of the lode and shallow the Shalts,.yew ‘exceeding 400 feet. “These lodes carry less galena and blende than most others, and a larger percentage of copper. These three lodes run almost parallel, and so close together that the slight convergence in their course westward has given rise to the conjecture that they unite to ~ form the Mammoth Lode, which can be traced for about 3000 feet from a point a little west of the known westernly limits of the Bobtail. This lode is likewise divided intoa numbet of small claims, the longest of those owned by companies being 400 feet. The lode is wide, and the ore highly charged with iron pyrites; strange to say, almost free of gold. _But proceeding further west, and crossing a ravine known as Spring Gulch, we reach a group Of parallel lodes so similar in course and dip to the Gregory, Bobtail, and Bates, that, though undetected in Spring Gulch, one cannot but look upon them as a continuation of those three lodes, or, if they are really united in the Mammoth, of this lode again split up into several branches. The most notable of this group is the Burroughs Lode, on Quartz Hill, on which—

Feet.

shine Opn Oey owhisec” ve.) e182, So) ) Pa: « . 402

SCE UPL Os, OIG. wrk aaIMEL AW) hal ot, BOBS Bape OLGA A OnpOWhS:. ora? are wl s 6 a BOD MEO URS CO. OMTUS Klin .~ <5) wires BOG Pane: GOSE a CU cONTIIS yp. AT ods, b riven > yi, pT andesits: COtommSts “Ehigut oh. e. a, 200 2 Pactne. National Co.cowms: 5s. « «> 550 First) National Gos owns is. ss 00a

Cold -EallOos Owils Ai adie ie). t 3. FO wi Orneirta Mo Ol, Gate ei als a, Pedi

This group and the lodes of the neighbouring Nevada district are, as a rule, poorer in gold and copper, but richer in argentiferous galena, than the preceding.*

The ill effects of such a subdivision it is not difficult to conceive. As every proprietor sinks one or more shafts, a vast amount of unnecessarily expensive work is done. Moreover, the chances of individual failure are greatly in- creased ; for unless the owner be fortunate enough to hit a rich chimney of ore, which sinks vertically without inter-

* For a full and accurate description of the most important mines consult

vol. iii. of the United States Geological Exploration of the 4oth Parallel, On Mining Industry, by JAMes D. HaGueE.

VOls LET. (N.S.) D

ruption, when he runs out of good ground he is sure to be in unproductive ground from end to end of his claim, and therefore as sure to fail financially. The evil is now, how- ever, curing itself. As the mines have been sunk the water has become more and more troublesome, and combination has been forced upon the owners by the refusal of some to pay their share of the expense of pumping. A process of what is termed ‘’ freezing out” has been going on for some time on the principal lodes, which, by a method hardly jus- tifiable, is likely to lead to the desired union of interests, though at the expense of the shareholders of the companies. A mine fills with water; all returns cease; the company’s affairs are liquidated, at the suit of the superintendent or some privileged creditor, for perhaps a trifling sum. The property is sold by the sheriff, before perhaps any of the shareholders