THE COLLIERY GUARDIAN AND JOURNAL OF THE COAL AND IRON TRADES. Vol. CXVI. FRIDAY, SEPTEMBER 13, 1918 No. 3011. THE VALUATION OF ORE RESERVES. By JAMES WHITEHOUSE, M.Sc. It is proposed in these notes to give a brief outline of the methods used in the valuation of ore reserves on the Witwatersrand, and to describe in detail the method of sampling the gold-bearing reefs. The ore body is a sedimentary deposit conformable to the strata in which it lies. It is a siliceous con- glomerate, and is commonly known as “banket.” the Dutch word for almond rock, owing to its resemblance to this sweetmeat. It dips at various angles, from practically horizontal to vertical, and occurs in widths Fig. 1.—Section of Reef. DATE . DISTANCE FROM . SAMPLE N9 DIAGRAM. REEF. PARTINGS. REEF & PARTINGS . INGH DWH N°OF SECTIONS TO DATE. TOTAL REEF INCHES TO DATE. TOTAL INCH DWTS TO DATE . PEET ONLY. REEF PARTINGS. WIDTH VALUE WIDTH. VALUE AVERAGE WIDTH 10 DATE AVERAGE VALUE TO DATE TOTAL INCHES TO DATE AVERAGE WIDTH TO DATE AVERAGE VALUE IODATE I T + + I0-M7 50’ 1 ////a 19 10 1 20 39 3 9 1 9 1 10 1 7 4 2 1 8 0 17 4 12 5 2| 54 26 4 8 5 ■11 • • 4 1 c • 4 1 5 6 12 II 6 18 0 1 0 8 • IB * ° °o 6 5 0 3 0 0 *• FT * 6 78 0 4 6 8 • 1 5 i 3 4 0 1 2 a 17 1-17 55’ 6 1 25 25(0 15 40 15 6 6 2 4 II 1 9 9 2 8 0 4 18 1 14 1 3 pH 271 len j B 2 Fig. 3.—Sampling Sheet. varying from one inch to several feet in thickness. Generally, several layers separated by waste rock go to form the whole body, as shown in fig. 1. The whole section as shown in the above sketch would, for the purpose of valuation, be taken as the stope width, and would include the exterior waste of 10 in. and 12 in. above and below the reef. The width between A and B is known as the “ Reef Channel.” It will be observed that the actual 'reef width is only 25 in., made up of the three layers of 3 in., 18 in. and 4 in. respectively. In sampling the reef, sec- tions not exceeding 6 in. in width are taken, and hence the layer, which is 18 in. wide, would be split into three sec- tions of 6 in. each, the weight of each sample being the same —that is, equal weights from equal widths. The usual method adopted in sampling is to cut out a section of the ore body with a hammer and chisel, and the fragments of rock so cut out are caught in a pan .held under the sampling point by an assistant, as illustrated (fig- 2). When the required amount of sample has been obtained from the section which is being cut out, the fragments of ore are transferred from the pan to a sample sack, in which is put an identification card for reference in the assay office. On. reaching the sur- face the sampler delivers his sacks to the assay office, where the gold contained in each sample is accurately deter- mined. The results are then recorded by the sampler on sheets drawn up as shown in fig. 3. The usual practice in drives, raises and winzes, where driven on the reef, is to sample complete sections at 5 ft. intervals (see assay plan diagram, fig. 3). There are cases, however, where a mine is developed by drives which are. placed some little dis- tance under the reef, since the excessive earth pressure in mines of great depth makes it very difficult to maintain drives which have been driven on the reef, and in these cases the reef is exposed at 35 ft. intervals by means of crosscut raises, as illustrated in fig. 4. When working on this system samples are only obtainable in the crosscut raises, and in consequence it is not possible to obtain such a close valuation as where the drive is driven on the reef. Winzes are sunk to the level bottom at convenient intervals, and are started from the top of one of the crosscut raises which have been put up for valuation. The winze is, of course, sunk on the reef body, and is sampled at 5 ft. intervals, as in all cases where a heading is on the reef. The necessity of measuring the distances between the sampling points will be shown later. This system of driving under the reef proves very convenient during the development period, since the crosscut raise serves as a bin and affords temporary storage for the winze rock. In carrying out a valuation a block plan is prepared from the survey of the mine, drawn on the horizontal to a scale, usually, of 1 in 500, and on this all the blocks are laid out. The size and shape of each block 1 I 1 HF -4-?' ' -AAA”. .'F ■ • VT •-■V ~ • k --Hi™ I Fig. 2.—Sampling. will be governed, of course, by faults, dykes, shaft pillars or boundaries, and where these are absent, by the winze of the adjoining block. The area of each block is measured with a plani- meter, with the arm set to read 10 sq. in. of area for one complete revolution of the roller. On a scale of 1-500, 1 sq. in. of area is thus equal to 1,736'11 sq. ft., and as a planimeter reads to l-100th of a sq. in., readings are taken with one l-100th as the unit, and hence unit reading is equal to 17'3611 sq. ft. The plan being drawn on the horizontal, to find the-in- clined area of a block it is necessary to apply the secant of the dip-angle to the planimeter factor, which, as stated above, is 17'3611. In a block where the reef body dips 30 degs., the area on the plane of the reef in sq. ft. = planimeter reading x secant of 30 degs. x factor. Thus, if the planimeter reading is 1,176, the area in sq. ft. will be— 1,176x 1'1547005x17-3611 = 23,575 sq. ft. To arrive at the tonnage contained in a block of 12 cu. ft. of rock are taken to be equivalent to 1 ton of 2,000 lb. This figure has been obtained from a number of determinations of the specific gravity of the banket. In calculating the tonnage in a block, the following formula is used : — Area in square feet x stope width in inches _ . a 144 ~ 8- The reason for dividing by 144 in the above formula is that stope widths are always expressed in inches and must be reduced to feet, and we must again divide by 12, since this number represents the cubic feet which are equivalent to 1 ton. Example.— For a stope with a width of 60 in., the above area will contain— -3'5'5 2L63 = 9,823 tons. 144 In practice, in dealing with the ore reserves of a large mine, tables of factors are prepared for the purpose of obtaining areas and tonnages direct, by applying them to the planimeter readings of the various blocks. Thus, in working out a factor of area for blocks dipping 30 degs. we have— 17'36 x sec. 30 degs. - 17'36 x 1 1547“05 = 20 (i46871. This figure represents the area on the plane of the reef for unit reading when th1' reef contained in a block is dipping 30 degs.. and the planimeter reading multiplied by this factor wil] give the area on the plane of the reef of any block dipping at that angle. In the same way in obtaining tonnages a factor is worked out for 1 in. of thickness per unit area, and this is multiplied by the stope width in inches and the units of area to obtain the tonnage contained in a block. Example.—Factor for tonnage for unit of reading on a dip of 30 degs. and for 1 in. of thickness: — 17'3611 x 1 in. x sec. 30 degs. 141 17'3611 X 1 X 1'1547005 nieooi) - - ----144’ --0139214 = tons for 1 in. of thickness per unit area of reading. Therefore the tonnage contained in a block dipping 30 degs. will be equal to : Units of reading, x stope width in inches x 0'139214. For the determination of value and stope width on which the gold contents of a block are to be estimated, it is necessary to proceed to the assay , plan, and it is in the use of the information which this presents that the experienced surveyor proves most valuable. No matter how unbiassed a surveyor may be, there is always an inclination on his part to return a block payable if possible, and. in consequence he must exer- cise the greatest care and adhere rigidly to the figures which the assay plan presents, and at the same time consider the methods. vvjhhh will be used for working the block concerned. For instance, it may prove a very dangerous practice in estimating ore reserves to say, in order to make it payable, that a stope should be worked in such and such a manner when it may be known that in practice it will not be possible to carry out this prograrnme. The averaging of sample sections necessarily differs from the averaging of arithmetical quantities, since in every section sampled there are two factors to be