598 THE COLLIERY GUARDIAN September 20, 1918. THE VALUATION OF ORE RESERVES. By James Whitehouse, M.Sc. (Continued from page 546.J In our last issue we dealt with the methods adopted in taking samples of the ore deposit in different sec- tions of the reef. The figures shown on the assay plan, fig. 5 (see Colliery Guardian, p. 546), are here set out in tabular form (Tables A to D). Table A.—7th Drive West from Winze 1 to Winze 2. Reef Channel width. Reef Channel value. Inch dwts. Reef Channel width. Reef Channel value. Inch dwts. 24 .. 30’4 . . 730 984 19,019 21 . .. 45*5 . 9 5 29 .. . 11’2 ... 325 12 . .. 12*9 . 154 25 .. . 14’7 ... 368 16 . .. -8’5 . . 456 14 . . 13’2 ... 185 14 . .. 27*5 . 385 18 .. . 16’7 ... 301 9 . .. 17*0 .. 153 19 .. . 14’5 ... 276 12 . .. 15’0 .. 180 27 .. . 10’5 ... 284 15 . .. 40’0 . . 600 22 .. . 17’1 ... 376 10 . .. 330 ... . 330 15 .. . 26’4 ... 396 12 . .. 16’0 .. 192 12 .. . 21’5 ... 258 17 . .. 27’0 .. . 459 17 .. . 22T ... 376 16 . .. 24’4 .. . 390 19 .. . 36’3 ... 690 32 . .. 14’3 .. 458 23 .. . 26’5 ... 609 24 . .. 16’2 .. . 389 24 .. . 14’2 ... 340 25 . .. 18’5 .. . 463 26 .. . 20*1 ... 523 19 . .. 20’5 .. 390 24 .. . 16’4 ... 394 17 . .. 21’2 .. . 360 21 .. . 165 ... 347 16 . .. 16*6 .. . 266 19 19*7 ... 374 24 . . 23’3 .. 559 27 .. . 18*2 491 18 . .. 45*6 .. 821 24 .. , 16’6 ... 398 17 . .. 32’1 . 546 31 .. . 23*4 ... 725 19 . .. 16’5 .. . 314 14 .. . 343 ... 481 14 . .. 33*1 .. . 463 17 .. . 16*2 ... 275 22 . .. . 18’6 .. . 409 19 .. . 11’5 ... 219 26 . .. 12’4 .. . 322 29 .. . 24’2 ... 702 24 . .. 10’5 .. . - 252 27 .. . 19’6 ... 529 26 . .. 16’2 .. 421 30 .. . 18’5 ... 555 27 .. 14’3 .. 386 22 .. . 16’5 ... 363 29 .. .. 17’2 .. . 493 19 .. . 17*0 ... 323 31 .. ,. 14’5 .. . 450 21 .. . 23’2 ... 487 42 . .. 13’2 .. . 554 36 .. . 16*1 .;. 580 35 .. .. 15’6 .. 546 30 .. . 13’4 ... 402 36 .. .. 17’5 .. 630 57 .. . 14’6 ... 832 41 .. .. 18’6 .. 763 33 .. . 19’1 ... 630 32 . . 125 .. . 400 32 .. . 17*1 ... 547 29 . .. 18’7 .. 642 51 .. . 16’5 ... 841 31 .. .. 17’7 .. . 549 50 . 13’3 ... 665 37 .. .. 12’5 463 43 .. . 18’5 ... 796 39 .. .. 18’2 .. 710 i — 41 .. . 16’2 .. . 664 1,950 36,282 33 .. . 13’5 ... 446 18’6 dwts. 981 19,019 25’0". Table B.—8th Level. Drive West from Rise 1 to Rise 2. Reef Reef Reef Reef Inch Channel Channel men Channel Channel width. value. dwts. width. value. dwts. 19 . .. 35’0 .. 665 569 13,695 16 . ... 40’0 . 640 22 ... 16*1 .. 354 13 . ... 60’0 . 780 23 ... 12’4 .. . 285 12 . ... 33*0 . .. 396 25 ... 29’1 .. . 728 9 . .. 46’0 .. .. 414 30 ... 11’5 .. 345 11 . .. 11*4 . 125 27 ... 16’4 .. 442 • 12 . .. 17’1 . 205 26 ... 10’5 .. 273 17 . .. 16’2 . 275 24 ... 16’1 .. . 386 16 . .. 11*3 .. 181 22 ... 10’5 .. 231 14 . .. 12’4 .. ,. 174 23 ... 11’0 .. . 253 15 . .. 11*5 . 172 25 ... 24’3 .. . 608 18 . .. 16’2 .. . 292 27 ... 10’1 ... . 273 19 . .. 14’1 .. 268 23 ... 24’1 .. . 554 22 . .. 17’1 .. 376 21 ... 13’1 .. 275 13 . .. 18’7 .. 243 19 ... 23’2 .. . 441 16 . .. 16’4 .. 262 16 ... 14*6 .. 234 17 . .. 11’2 .. 190 17 ... 26*5 .. 451 15 . .. 16*5 .. 248 18 ... 11’5 .. 207 9 . .. 24’1 .. 217 16 ... 27’2 .. 435 13 . .. 18’5 .. 241 14 ... 18’8 .. . 263 12 . .. 46*5 .. 558 12 ... 19’6 .. . 235 9 . .. 34*1 .. 307 10 ... 31’4 .. 314 6 . .. 73’2 .. 439 7 ... 45’6 .. 319 4 . .. 62’6 .. 250 8 ... 39’9 .. . 319 3 . .. 71’4 .. 215 9 ... 27’7 .. 249 6 . .. 38’2 .. 229 12 ... 266 .. . 319 7 . .. 37’1 .. 260 11 ... 24’5 .. . 269 10 . .. 35’2 .. . 352 12 ... 24 5 ... 294 11 . .. 44’8 .. 493 13 ... 16’6 ... 216 12 . .. 34’6 .. 415 15 ... 18’5 .. 278 14 . .. 25’4 .. 356 16 ... 17’0 .. . 272 15 . .. 26 2 .. 393 12 ... 21’1 .. . 253 18 . .. 13’4 .. 241 15 ... 16’0 .. . 240 16 . .. 17’2 .. 275 16 ... 17’0 272 17 . .. 251 .. . 427 22 ... 24’5 .. . 539 22 . .. 16*2 .. . 356 24 ... 36*5 .. 876 18 . .. 24’0 .. 432 20 ... 43’0 ... 860 17 22 0 374 16 ‘ .. 14*2 ” 227 1,221 26,857 19 . .. 16’5 .. 314 22’0 dwts. 21 .. 19’9 .. 418 569 13,695 id y West from Rise 2 8th Drive Reef Reef Inch dwts. Channel Channel width. valued 18 .. . 41’2 ... 742 16 .. . 34’1 ... 546 14 .. . 21*4 ... 300 12 .. . 16’7 ... 200 16 .. . 18’5 ... 296 14 .. . 14*1 ... 197 19 .. . 13’1 ... 249 17 .. . 16’7 ... 284 16 .. . 11’2 ... 179 13 .. . 20’5 ... 267 15 .. . 21’2 ... 318 17 .. . 16’4 ... 279 14 .. . 24*7 ... 346 12 .. . 19’1 ... 229 9 .. . 36’5 ... 328 6 .. . 43’7 ... 262 4 .. . 54T ... 216 6 .. . 37*5 ... 225 238 5,463 to Dyke- Reef Channel width. Reef L Channel value. Inch dwts. 238 5,463 8 ... 29’6 ... 237 9 ... 41’5 ... 273 15 ... 40*6 ... 609 16 ... 21’5 ... 344 14 ... 12’7 ... 178 12 ... 11’6 ... 139 15 ... 12’5 ... 188 12 ... 37’3 ... 448 17 ... 36’5 ... 620 14 ... 38’2 ... 535 17 ... 41 ’5 ... 706 19 ... 272 ... 517 13 ... 23’6 ... 307 419 25’4 dwts. 13’5" 10,564 From Tables E and F it will be seen that Block 1 has an average reef channel of 18-8 in., with a value of 21*1 dwt., and Block 2 an average reef channel of 15*5 in., with a value of 23-8 dwt. As it is not possible to work a stope with a width of 18-8 or 15-5 in., allowance must be made for exterior waste—that is, the excavation in addition to the reef of a certain amount of country rock for the purpose of making the excavation large enough for the working and handling of the ore. In mines having a dip of less than 45 degs., stopes can seldom be worked at a width of less than 48 in., and applying this width to the above tables for the purpose of obtaining a stope value over the increased width, the length in the first column must be multiplied by 48. This will give “ stope-feet-inches ” as shown in column 3. The result divided into the “ feet-inch-dwt.” (column 5) will give the stope value. Applying this method to Block 1 with a stope width of 48 in., a value of 8-3 dwt. is obtained. Block 2 over the same width gives a value of 7-7 dwt. In the case of wide reef channels it is usual, when estimating the stope width, to add 20 to 24 in. in order to allow for exterior waste which may be mined during stoping operations. Thus if the reef channel were 50 in., which in itself would be sufficiently wide for stoping operations, when estimating the stope width 20 in. would be added, bringing the total width to 70 in. It is considered prudent to adopt this pro- cedure lest, when the reef is being mined, it is found that there is no bedding plane to which the miner Table C. 1 Winze West. Reef Reef Channel Channel Inch dwts. width. value. 332 6,875 11 ... 26*6 .. 293 9 ... 25’4 .. . 229 * 13 ... 43’1 .. 560 17 ... 41’3 .. 702 16 ... 16’4 .. 262 14 ... 17*9 .. 251 12 ... 21’4 .. . 257 11 ... 18 5 .. 203 - 10 ... 16*7 .. . 367 9 ... 33 5 . 301 6 ... 40 2 .. 241 10 ... 57*1 .. 571 13 ... 33*5 .. 435 16 ;.. 37’7 .. . 603 9 ... 29*9 .. 269 508 24T dwts. 12,219 14’5" 7th I jEvel, No. Reef Channel width. Reef Channel value. Inch dwts. 30 .. . 22*6 ... 678 25 .. . 33’7 ... 843 21 .. . 170 ... 357 22 .. . 16*5 ... 363 19 .. . 170 . . 323 16 .. . 16*5 ... 264 17 .. . 12*0 ... 204 19 .. . 33’0 ... 627 21 .. . 16*0 ... 336 14 .. . 17’0 238 17 . 18’5 ... 315 19 .. . 120 225 22 .. . 16’5 ... 363 18 .. . 13’7 ... 247 14 .. . 13’7 ... 192 10 .. . 36’5 . . 365 ' 7 .. . 31’6 ... 221 6 .. . 19’7 ... 118 3 ".. . 48’5 ... 145 12 .. . 37 6 ... 451 332 6,875 7th Level, No. 2 Winze West. Reef Channel width. Reef Channel value. Inch dwts. 16 .. . 15’0 ... 240 18 .. . 16’5 ... 297 24 .. . 33’5 ... 804 19 .. . 16’7 ... 317 16 .. . 12’5 ... 200 12 .. . 16’6 199 14 .. . 14’7 ... 206 9 .. . 23’6 ... 212 7 .. . 41’4 ... 290 8 .. . 46’5 ... 372 12 .. . 46’4 ... 557 11 .. . 46’7 ... 513 13 .. . 16’4 ... 213 > 12 .. . 48’3 ... 580 12 .. . 47’4 ... 569 14 .. . 33’0 ... 462 17 .. . 40’7 ... 692 21 .. . 60’1 ... 1,262 17 .. . 40’1 ... 682 21 .. . 21’2 ... 445 24 .. . 19’3 ... 463 27 .. . 21’4 ... 578 29 .. . 203 ... 589 31 .. . 16’4 ... 508 18 .. . 16’6 ... 299 322 11,549 7th Drive 1AI West fb Reef Reef Channel Channel Inch width. value. dwts. 24 ... 16*6 . 398 16 ... 25*0 . 400 19 ... 16*5 . 314 2. ... 13*7 . 274 23 ... 18’5 . 426 21 ... • 16’6 . 349 22 ... 15*2 . 334 17 .. 12’6 . 214 162 2,709 Reef Channe width. Reef 1 Channel value. Inch dwts. 322 11,549 21 ... 19’9 418 27 ... 17*7 . 478 30 ... 166 498 26 ... 18*4 478 14 ... 16’7 . 234 17 18’4 313 15 ... 19 7 296 12 ... 18’9 227 11 ... 19’7 . 217 16 ... 19’5 312 15 ... 21’2 318 6 . ... 42’4 254 5 . ... 40’0 200 14 ... 26’2 367 11 ... 27*4 301 13 . ... 18’3 . 238 15 ... 17*4 261 17 . ... 19*3 328 19 . ... 16*5 314 16 . .. 18*5 296 642 17,897 2 IT dwts. 16’5" D. Winze 2 to Dyke. Reef Reef Channel Channel Inch width. . value. dwts. 162 2,709 16 . .. 27’2 ... 435 6 . .. 44’6 ... 268 3 . .. 52’5 ... 157 —1 I - 187 . 3,569 191 dwts. 17*0" A summary of these details will be as follows: — Table E.—Block 1. Locality. 1 fl CD Hl Reef Channel. fl CH t> ® A 5 Sg be fl S fl A c5 Hlo<^ 7th No. 2 Winze West 225 .. . 16’5 . ... 3,713 . .. 24*1 . ... 89,4?3 7th Drive West 55 .. .. 17’0 ... 935 . .. 19’1 . ... 17,859 8th Drive West 155 .. . 13’5 . ... 2,093 . .. 25’4 . ... 53,162 ■ ■ —— ■ 1 -Illi 1 ■ ■ Totals & averages... 435 . .. 15’5. ... 6,741 . .. 23’8 . ..160,501 Average stope width and value — . .. 48" . ..20,880 . ..77. — can break, and it becomes necessary to carry a band of country rock either on the foot or hanging, or possibly on both. In actual practice this is invariably the case, and such a procedure ensures the total reef being mined. It must also be remembered that, in deep mines particularly, it is in many instances impossible to extract only the reef channel, owing to false hanging which, due to pressure, will fall during stoping opera- tions. Whatever the reef channel may be, in calculating the probable stope width no figure below that obtained in actual practice must be used, since the excavation must always be large enough for the working and handling of the broken rock. The minimum stope with which can be taken in any mine will depend very considerably on the dip of the reef. In steep mines much lower widths can be maintained than in flat ones, owing to the difficulty in the latter case, particularly where hand drilling is used, of swinging the hammer. This will be seen in fig. 8, which shows a narrow stope worked by hand labour. In calculating the tonnages contained in the blocks already referred to, the tabulation shown in Table G would be used. To obtain the average stope width of the two blocks, or of any number of blocks which may be contained in the summary (Table G), the following formula is used : Average stope width = tonsx 144 incline area For the purpose of comparison it will be interesting to take the same blocks and assume that the drives were not driven on the reef, but that the valuing was done from samples obtained in crosscut raises, which method of development has already been explained earlier in the paper. These conditions are illustrated in fig. 9. Tables H, I and J show the figures obtained when using this method of valuation. In order to obtain the average value of the ore contained in all the blocks of a mine, the total tons would be divided into the total “ton dwt.,” which figure is shown in column 10 (Table J). It will be ob- served that there is a slight difference in the final value obtained by this method, owing to the sampling points along the drive being 35 ft. apart instead of at 5 ft. intervals, as in the case where drives are driven on the reef. It will be seen that the points where the crosscut raises intersect the reef are a little lower in value than the average, but on the other hand they might have struck the richer area, in which case the latter valuation would have proved somewhat higher than the former. The closer the sampling, the more accurate will be the valuation. Each block in the mine is treated in the manner described above, and the tonnage and value thereby obtained. Some of the blocks will be payable and others unpayable, and as a dividing line a “ pay limit ” is fixed. The “ pay limit” is the amount which it is estimated it will cost to extract the ore from the mine and treat it, and includes all expenses inci- dental to running the mine. When this figure has been determined, it is converted into the equivalent pennyweights, and all blocks which fall below this value are considered unpayable. If, for instance, the “ pay limit” has been fixed at 4-3 dwt., which would be equivalent to costs of 18s. Id., all blocks having this or a greater value would be included in the payable ore reserves, and anything below this value would be considered unpayable. There are conditions, however, where the working of ore which is slightly below the pay limit value may be justified. It will be obvious that when a block of ore has been fully developed all expense in this con- nection has already been incurred, and the money spent on this work cannot be recovered if the ore contained in the block is allowed to remain intact. In these circumstances the cost of development may be excluded from the amount representing the pay limit, when deciding whether a doubtful block can be worked or not. Again, the actual working conditions of* a block bordering on the pay limit must be seriously con- sidered before deciding definitely to leave it in the mine. Easy breaking and large widths may so reduce the cost of mining that a figure considerably below the general pay limit adopted for the mine may be used when considering a particular block, which should be considered on its own merits, since ore which can be mined cheaply may be more profitable at 4-1 dwt. than that obtained from a narrow block going 5 dwt. where mining is difficult and expensive. Conditions may prevail which prevent a mine which is equipped with a mill capable of crushing, say 50,000 tons per month from feeding the latter to its full capacity with ore taken entirely from reserves having a value above the pay limit fixed for the mine. The question then arises as to whether the spare capacity can be used to treat ore slightly below the pay limit. In deciding this question it must be pointed out that there are many charges which go to make up the working costs of a mine—which are, say, 18s. Id. per ton—which will not be reduced during a month’s opera- tions, whether the maximum tonnage is crushed or not. These include such items as the following: Supervision ; pumping; ventilation; fixed charges ;* head office charges. It will therefore be seen that, provided there is a large enough proportion of the required tonnage avail- able from blocks of good value, it is possible to supply the remaining portion from reserves which fall slightly below the pay limit, and that this tonnage may actually provide extra profit to that which would have been earned if only ore from payable ore reserves had been milled. When a mine is so developed that its full milling capacity can be supplied from reserves having a value above the pay limit, the working of lower grade ore would not be justified. Having outlined the methods used for the valuation of the reserves of a mine, it may be of interest to work out the life of a mine and the present value of its shares. The capital of a company may be assumed to be £1,000,000, and the payable ore reserves at the moment * Note.—Fixed charges cover all expenditure which must be continued irrespective of the tonnage crushed, and.include certain charges for white wages, native wages, and stores and maintenance.