405 H11GASD I03MGB1BS, THE MINER'S GUIDE. SKW-STREET BQCAUE THE PRACTICAL MINER'S GUIDE: COMPRISING- A SET OF TRIGONOMETRICAL TABLES ADAPTED TO ALL PURPOSES OF OBLIQUE OR DIAGONAL, VERTICAL, HORIZONTAL, AND TRAVERSE DIALLING, WITH THEIB APPLICATION TO THE DIAL EXERCISE OF SHAFTS, ADITS, DRIFTS, LODES, SLIDES, LEVELLING, INACCESSIBLE DISTANCES, HEIGHTS, ETC. Also a Treatise on the Art and Practice of ASSAYING SILVER, COPPER, LEAD, AND TIN, WITH TABLES WHICH EXHIBIT AT ONE VIEW THE VALUE OF ASSAYED OEES, BULES FOB CALCULATING THE POWER OF STEAM AND WATEB ENGINES, A DISCOURSE ON THE QUALITY, MANUFACTURE, AND CHOICE OF CORDAGE FOB MINE SEBVICE ; Together with a Collection of Essential TABLES, KULES, AND ILLUSTEATIONS EXCLUSIVELY APPLICABLE TO MINING BUSINESS. The whole introduced and exemplified in the most plain and practicable manner. BY J. BUDGE. NEW EDITION. LONDON : LONGMANS, GREEN, AND CO. 1866. ivrary TO BENJAMIN TUCKER, ESQ. SURVEYOR-GENERAL OF THE DUCHY OF CORNWALL, AND JOHN TAYLOE, ESQ. DIRECTOR OF BRITISH AND FOREIGN MINING INSTITUTIONS. GENTLEMEN, THE propriety of composing an address under this head did not, until of late, occur to my imagination, and with much trepidity and circum- spection do I now attempt the difficult task. My apprehensions arise from a consciousness of the ex- treme delicacy of the undertaking, and the danger I have to encounter, arising from the probability of a misconstruction being put on the sentiments I may advance ; nevertheless I feel an enlivening hope, springing up as I proceed, that I shall not be unhappy enough to make an insertion of a single sentence but what you will either approve or pal- liate, and, this point secured, I shall be compara- tively indifferent of all other consequences. The succeeding remarks will prove explanatory of my motives, and I trust will be deemed a satis- VI DEDICATION. factory apology for my adventuring into the dedi- catory labyrinth, from whence but few escape without considerable loss in the estimation of the most discerning part of their readers. It is a prevalent opinion that gentlemen some- times allow authors to make an ostentatious display of their influential names in the front of their works, while at the same time they possess not the slightest knowledge of the composition, or of ever having seen a line thereof, until a finished copy has been formally presented them, adorned with their illustrious names and the writer's adulatory compliments ; but further, it is notorious that com- posers not unfrequently take the unwarrantable franchise of introducing the honourable names of eminent persons for this purpose without ever obtaining or even soliciting their permission for so doing. These considerations have induced me, with great diffidence, and contrary to my preconception of the matter, to frame this respectful address ; for, after mature deliberation, I have been led to con- clude that it would be doing an act of injustice to you, to myself, and to those who may be interested in the contents of this volume, were I to forbear giving publicity to the fact, that it was not until you had investigated the most essential parts of the manuscript, and felt assured that it was calculated to answer the end designed, and thereby prove DEDICATION. Vii advantageous to the mining interest, that you con- sented to honour it with your countenance, and allow your respected names to be introduced in a patronal capacity. Without fear of the imputation of flattery, I may with confidence remark, that your great expe- rience, knowledge, celebrity, and interest in mining affairs, are calculated to inspire a reasonable hope that, through your support and precedent, success will attend my humble efforts, and I shall ulti- mately obtain a fair pecuniary remuneration for my labours ; but, necessitous as I am, the animating thought of my exertions becoming instrumental in yielding an important benefit to a considerable and most useful class of my fellow-men, is by far the greatest cause of my exultation. It now only remains for me to acknowledge the obligations I feel, not for mere nominal patronage, but for the actual assistance I have received at your hands, whereby I have been enabled to over- come the formidable obstacles which presented themselves against the accomplishment of this dif- ficult and embarrassing enterprise. And at the same time I would not dare neglect to return my unfeigned thanks, in the most undisguised and so- lemn manner, to that supreme and gracious Power whose benign and omnipotent influence has been manifestly exercised in my behalf throughout the arduous undertaking. Vlll DEDICATION. Possibly this digression may be condemned as unseasonable, unsuitable, and unfashionable , by those who fancy themselves too wise and indepen- dent to allow it to be obligatory upon them openly to acknowledge the aid of Divine Providence in all their successful engagements ; but desirous as I am of giving universal satisfaction, far rather will I endure the scorn and sarcasms of such indi v duals, than avoid their contumely at the expense of an approving conscience, and the approbation of the truly wise and honourable. In conclusion, I sincerely beg excuse for the almost unprecedented latitude I have uninten- tionally taken for this subject, and allow me most cordially to congratulate you on the high degree of respectability as well as the national utility and importance the mining system of Great Britain has recently acquired, and to which, it is generally acknowledged, your example and instrumentality have materially contributed. That you may live long and prosperously, and that uninterrupted success may attend your every endeavour to promote your own and the public welfare, is the sincere and hearty desire of, Gentlemen, Your most grateful, most obedient, and very humble servant, THE AUTHOE. PREFACE. THROUGHOUT this volume the benefit of the Practical Miner has been constantly kept in view ; and al- though the Tables may be successfully used on other occasions, yet we have professedly the mining inte- rest solely for our object. It is hoped that the curious examiner will find no flagrant violation of the rules of composition or mathematical order ; but to any who may be dis- posed to search for defects we beg to state, that the work has been prosecuted and accomplished amidst numerous disadvantages, among which, the frequent interruptions arising from the almost in- cessant duties of a mining avocation have not been the least perplexing. But, notwithstanding all this, we feel it incumbent on us to state, in defence of the calculations, that, so far as Hutton's celebrated Logarithms, compared with those of other eminent authors, can be relied on as a foundation, together with the utmost care in, and repetition of, every single operation, supported by numerous subsequent proofs, both theoretical and practical, we are war- ranted in alleging our conviction, that the Tables may be received and applied to the most difficult and important operations in dialling, with the utmost confidence. X PREFACE. We now take a transient, but submissive leave of the Mine Agent, and respectfully address ourselves to persons in the capacity of Schoolmasters in min- ing districts. To that respectable class of men this work is also recommended, as a fit subject for the study of those youths committed to their instruction, who appear designed for a mining occupation ; and having our- selves had some years' experience in public teaching, we presume to declare our persuasion, that it is capable of being rendered extremely useful, by the prudent tuition of skilful preceptors. And why, we would inquire, should not the theory of the essential art of mining be taught in the seminaries of England, as weE. as in Mexico ? (where, we understand, the colleges or schools of mines are among the most noble establishments of the em- pire) ; but especially in Cornwall, where the prin- cipal support of the country depends on the prosperity of the mines, and where much of that prosperity depends on the judicious management of those persons to whom the superintendency there- of is committed. In conclusion, we beg to remark, that we have generally used such terms as are common, and in some cases almost peculiar, to mining business ; believing that this phraseology will render the work far more intelligible and acceptable to the majority of those for whose use it is designed, than if we had confined ourselves to a precise mathematical mode of expression. CONTENTS. PART I. PAGE INTRODUCTION 1 Explanation and Use of the Tables 6 Decimated Arithmetic Reduction 11 Addition 12 Subtraction 13 Multiplication . . . .13 ,, Division . . . . .14 Aliquot Parts of a Fathom 14 Preliminary Chapter . . . . . . .16 Definition of Right-angled Triangles 17 Introductory Examples 21 Plane Trigonometry ........ 23 CASE 1. Given the Angle and Hypothenuse to find the Base and Perpendicular by the First Table . . .23 by Construction 24 CASE 2. Given the Angle and Perpendicular to find the Base and Hypothenuse by the Second Table . . 24 by Construction 25 CASE 3. Given the Angle and Base to find the Hypo- thenuse and Perpendicular by the Third Table . . 25 by Construction . . . . . . .26 Diagonal Shafts 27 Xll CONTENTS. PAGE Perpendicular Shafts 28 Cross-cuts 29 When a Lode has changed the Underlay .... 30 When a Lode has reversed the Underlay .... 32 When a Shaft has been sunk in Error .... 35 To find the Junction of Lodes that underlie in the same Direction ........ 37 To find the Junction of Lodes that underlie toward each other 41 Shafts and Adits . . * . . . . . .44 Drifts . 47 Drifts and Intersections 48 Slide Lode thrown up 49 Lode thrown down 51 Horizontal Dialling . . . . . . .55 Vertical Dialling . . . - 58 Miscellaneous Examples 61 TABLE I. Hypothenuse Radius 67 TABLE II. Perpendicular ditto ..... 75 TABLE III. Base ditto 83 Levelling - . . .85 Traverse Dialling 87 PART II. Introduction 99 Assay of Silver Ore 101 Copper Ore ' . 104 Lead Ore 108 Tin Ore . 109 CONTENTS. Xlll PAGE Method of extracting Silver from Copper Ore . . .110 Smelting Silver Ore 110 Lead and Silver Ore 110 Silver Assay Table Ill Method of computing the Value of Lead and Silver Ore . 115 Copper Ore . . 116 Rule for discovering the Power of Steam Engines . . 117 Water Engines . . 119 Table of the Square Inches in a Cylinder .... 123 Table of the Weight of Water in a Pump, &c. . . . 125 Treatise on Cordage 126 Table showing the Number of Threads in a Rope . .135 Length of Rope to an Hundred- weight . 136 Weight of Ropes 100 Fathoms long . 137 Observations on Capstan Machinery .... 139 SUPPLEMENT, OR THIRD PART. Introduction . . 145 Traverse Dialling . ' . . . . ' . .149 Table for converting Angles into Bearings . . .165 Plans and Sections of Mines 190 Miscellaneous 203 Geology 206 EXPLANATION OF TEEMS . .217 EXPLANATION OF THE DIAGRAMS. TABLE I. Page 66. In this scheme the hypothenuse is made radius, consequently the other sides are the sine and cosine of the included angle. Corollary. Suppose one end of the line A B to remain at A while the other end B is moved round from e to /, then it is evident that the base C B will continue to increase, and the perpendicular B D to decrease, until the whole quadrant has been swept off. At 45, or the middle of the quadrant, the base and perpen- dicular are equal, and from that point to 90 the base will in- crease in the same ratio as the perpendicular decreased from 1 to 45 ; hence the propriety of the arrangement of this table in counting the degrees backward from 45 to 90. TABLE II. Page 74. Here the perpendicular is made radius; therefore the hypo- thenuse A C will be the secant, and the base B C the tangent, of the angle A. On this principle it is clear that as the angle increases, the base and hypothenuse will continue (throughout the whole quadrant) to increase in proportion. TABLE III. Page 82. In this diagram the base is made radius, therefore by mathe- matical demonstration the perpendicular A C is the co-tangent, and the hypothenuse B C the co-secant, of the angle C ; and here it Avill be plain, that as the angle C is increased, the hypothenuse and perpendicular will, proportionably, be dimi- nished. ILLUSTRATION OF THE CHARACTERS. -J- plus, or more, the sign of addition ; signifying that the num- bers or quantities between which it is placed are to be added together. minus, or less, the sign of subtraction ; denoting that the less of the two quantities between which it is placed is to be taken from the greater. x into, the sign of multiplication ; signifying that the quantities between which it is placed are to be multiplied together. -4- by, the sign of division ; signifying that the former of the two quantities between which it is placed is to be divided by the latter. : as, or to, '. I so is, the sign of an equality of ratios ; denoting that the quantities between which they are placed are pro- portional to each other. Thus, 2 : 3 : : 4 : 6, denotes that 2 is to 3 as 4 is to 6. = equal to, the sign of equality ; signifying that the quantities between which it is placed are equal to each other. Thus, 6 + 4 = 10, shows that 6 added to 4 is equal to 10. Z. Angle. Degrees. ' Minutes. A given line is represented by a stroke or dash ( i ), as the base A B in the triangle on page 26, and a required line by a cipher ( o ), as in the legs of the same triangle. ABBREVIATIONS. Deg. Degrees. E. East. Min. Minutes. W. West, Path. Fathoms. Prob. Problem. Ft. Feet. Ex. Example. In. Inches. Ansr. Answer. Hyp. Hypothenuse. Dia. Diameter. Perp. Perpendicular. Cwt. Hundred- weight. Comp. Complement. Qr. Quarter. Tab. Tabular. Lbs. Pounds. Dec. Decimals. Oz. Ounces. N. North. Dwt. Pennyweight. S. South. Grs. Grains. THE PRACTICAL MINER'S GUIDE. INTEODUCTION. IT is an acknowledged fact, that dialling, in all its varieties, is the most difficult and momentous part of the duty of practical mine agents : to assist them in that important operation, is the chief design in giving publicity to these Tables. Notwithstanding the great improvements which of late years have been made in the art of dialling, the most intelligent miners universally admit, that the practice is still very imperfect ; nay, so far are they from any determinate and general system, that two persons can scarcely be found who pre- cisely adopt the same method; consequently some plain scheme, founded on pure mathematical prin- ciples, is a great mining desideratum. Aware of the opposition which is so apt to arise against all attempts at innovation of an old and established habit (which, however faulty in itself, custom may have stamped with an imaginary per- fection), it may be necessary to make a few ob- servations in support of this work, and endeavour to prove its advantages over all the preceding B 1 INTRODUCTION. modes of performing a dialling operation in every respect. Not many years ago the customary way of as- certaining the perpendicular and horizontal lines corresponding with a diagonal shaft, was by the very uncertain, expensive, and tardy practice of dropping a plumb-line from the back to the bottom, there fixing a sollar or platform, and repeating the process from the brace to the foot of the shaft ; this usage is largely explained in ' Pryce's Treatise on Mines and Mining' (a celebrated work, published by subscription, about the year 1776), and therein described as the only system then known. It is true this most objectionable measure is now exploded, but not without great reluctance by many of its old practitioners, who were long before they could be prevailed on to abandon it, notwith- standing its glaring inconveniences, accompanied with the loss of time, waste of property, and hazard of their lives. By inserting this defectibility of our predecessors, we have no other design than of cautioning our mining countrymen to guard against the too pre- valent propensity of rejecting any new system, merely because it is new, or its utility not dis- cerned at first sight ; and to induce them to give the subject an impartial investigation, before they pass a conclusive judgment thereon. The use of mathematical instruments is how par- tially known in the mining world ; and, certainly, those agents who are well acquainted therewith, possess a decided advantage over others who are INTRODUCTION. 3 not ; for, doubtless, this science has the pre- eminence, in a high degree, over every other method heretofore employed in dialling. But without intending to undervalue instrumental operation, we appeal to the experience of our scientific readers for support, in avouching that the process is ever liable to errors of considerable extent, and which are prone to slide in unaccount- ably : but it is a palpable fact, that in pointing or sweeping off the angles, an almost imperceptible deviation will create a serious departure from truth ; and even in the course of bisecting, trisecting, in- scribing, describing, and circumscribing ; also in drawing parallels, raising or demitting perpen- diculars, the operation, even with the greatest care, is exposed to considerable mistakes : and so sensible are all professional men of this defect, that instru- mental operation is never resorted to, or relied on, in any case where great accuracy is required. But when we reflect on the laborious duties of the practical mine agent, and how much these duties are calculated to disqualify him for performing a geometrical plan with that delicacy and precision which the operation so indispensably demands, we then become established in our opinion of the ne- cessity of a work of this kind, and of its superiority over every other system hitherto introduced in dialling. Should any be yet disposed to advocate the existing practice, and to contend that it is fully adequate to the desired purpose, we beg permission to inquire of such persons, why it is that mistakes B 2 4 INTRODUCTION. so commonly occur in sinking shafts and driving levels in most of our mines? That irreparable errors do frequently happen, is a truth too notorious for contradiction or dispute, and sometimes even under the superintendence of men whose know- ledge, circumspection, and experience no one presumes to caU in question ; consequently a more convincing proof than this cannot be adduced of the fallibility of the best modern practice, and the necessity for the introduction of a more perfect system. Should it be inquired wherein the merit of this work is considered to consist, we answer, First Accuracy ; and it will be discovered at a glance, that every operation of the principal tables is wrought out to five places of decimals, or the ten thousandth part of an inch \ consequently we may affirm, without fear of confutation, that, in this property, we outvie every other system. Secondly Plainness. Of this quality our ex- pert readers will be convinced at first sight, and will need no instruction for enabling them to apply the numbers readily ; but we do not hesitate to say, that, by the help of the rules and examples, a common school-boy will find no insurmountable difficulty in solving the most abstruse problems relevant to dialling. Thirdly Despatch. To this desirable property no other system has an equal claim, or can, with any chance of success, enter into competition, with our method ; inasmuch as an answer, in most cases, may be obtained by the tables in less time than is INTRODUCTION. 5 necessary to make a preparation for performing the operation in any other way. And now, having briefly endeavoured to set forth the work in a true light, we commit it to the judgment of a liberal and discerning people; and should it be instrumental in happily preventing the grievous errors which are so prevalent in mining operations (and which, we are bold to say, must, in the nature of things, continue to take place by the present day practice) ; or should it only help to relieve the minds of faithful superintendents from that painful anxiety and suspense which never fail to harass them during the progress of any con- siderable work, whereby a heavy responsibility rests on them for the accuracy of their dialling ; or should it in any other way have the happy tendency of promoting the interest of mining, we shall not regret the labour, pain, expense, privation, trouble, and perplexity it has cost us, even though we should never receive any other compensation. EXPLANATION AND USE TABLES. AFTER so many preliminary observations, it will be necessary to say but little under this head, having already anticipated several things by way of intro- duction, which properly belong here. The reader will observe that the work is com- posed of three distinct tables, for the obvious rea- son of making each side of the triangle radius ; and certainly without such an arrangement it would have been incomplete. In each case the radius, or given side, is one fathom, being the most convenient and familiar proportion that could have been introduced. The principal calculations include every quarter, or fifteen minutes of a degree, and extend from 1 to 89 degrees, being sufficiently extensive and minute for mining purposes (the angle of any intermediate division not being distinguished or required) ; and here, it must be observed, that the divisions are expressed by 15, 30, and 45 minutes, which num- bers represent J, ^, and f of a degree. The first and most essential table is that wherein the hypothenuse, or longest side, is made radius, EXPLANATION OF THE TABLES. 7 extending nearly throughout the quadrant, and every calculation wrought out to five decimal places of an inch, hereby giving a direct answer, in exact ratio to six feet of the given side, to the ten thou- sandth part of an inch. Perhaps there may be a little difficulty at first, with persons unacquainted with mathematical order, in reading the first table. It must be remarked, that from 1 to 45, or the middle of the quadrant, the degrees and parts are all on the left-hand side descending, the base stands in the adjoining co- lumns, and the perpendicular on the same line to the right ; but beyond that point the degrees will be found on the right-hand side ascending, and then it must be specially noted that the perpendicular and base will have changed their positions, the base now standing on the right hand, and the perpen- dicular on the left hand side. In the second table the perpendicular is given and the angles extend to 60. One valuable min- ing property of this table is, that it gives at sight the underlay in a fathom of every angle within the range of 60 including the divisions : so that if it is required to know the underlay in a fathom on any degree, or quarter of a degree, between 1 and 60, it will He immediately discovered by an inspection of the base in the column adjoining the given angle in this table. In the third and last table the base is given, and as the application of this part of the work is not so general as the preceding, the angles have been given in degrees only : nevertheless this table is 8 EXPLANATION AND USE indispensable on some occasions, especially in level- ling or driving adits. It will be found, like the second table, to extend from 1 to 60 degrees. Having thus briefly stated the nature of the work under each separate head, it only remains for us, after a few general observations, to recom- mend the learner to the inspection of the following examples ; for we believe that one practical opera- tion will do more towards giving him a clear understanding or comprehension of the subject, than a volume written expressly thereon, confined to mere speculative description. It may be remarked that, in almost every instance, the geometrical construction of the figure is intro- duced, with the calculation, which will tend to the satisfaction of the practitioner and improvement of the beginner. In conclusion we would remark, that the same attention must be paid in taking the angle, and measuring the given line, when these tables are used, as if the operation were performed any other way. It is a common practice in mining to take the angle of underlaying shafts with the cover of the dial and a plumb-line ; and in short drafts, with great care, this method may answer well enough : but when any very important work is to be performed, we would strongly recommend the application of a more perfect instrument for ascertaining the angle ; for it is well known, that if this part of the process should not be correct, the result of the whole work must be erroneous as a matter of course; and in- OF THE TABLES. 9 deed it is next to impossible to distinguish the mi- nutia of an angle, with any tolerable degree of cer- tainty, by the foregoing method. There doubtless are instruments much better adapted to the work, both for speed and accuracy, than the dial ; and it is matter of surprise that they have not been more generally introduced in our mines : of these instru- ments the Theodolite certainly stands unrivalled for taking both horizontal and vertical angles. It is not our design to enter into controversy on this subject ; those who imagine the sextant or quadrant graduated on the cover of the dial well calculated for the purpose, let them continue to use it ; only we would especially note, that should an error ensue, it ought by all means to be attributed to the real cause, and to that only : for, as in all trigonometrical questions, the angle and side are always given to find the other parts of the triangle, consequently the sum of the one, and length of the other, are presupposed to have been correctly ascer- tained, previous to the commencement of any other operation. Finally, for the learner's sake, we observe, that as the tables exhibit only the relative proportions to the radius of one fathom, or six feet, and are wrought out to five places of decimals to an inch, it becomes necessary that every one who would use this work successfully should have some knowledge of deci- mated arithmetic ; because he will have, in most cases, to multiply for the whole numbers, and take parts for the fraction of the fathom. For example : suppose the given side to be the hypothenuse, mea- 10 EXPLANATION OF THE TABLES. suring 16 fathoms, 3 feet, and 6 inches, he will then have to take out the numbers opposite the given angle in the tables, and multiply them by 16, for the base and perpendicular respectively, then divide half the tabular measure for the 3 feet, and one sixth of the remainder for the 6 inches, and add them together for the sum of the required sides of the triangle. We have therefore introduced the following rules and examples in decimals, which are sufficient to enable any one hitherto unacquainted with this branch of arithmetic to use the tables with the greatest facility. 11 EEDUCTION OF DECIMALS. EULE. Multiply the decimal by the number of parts in the next less denomination, and cut off as many places to the right hand as there are places in the given decimals. EXAMPLE. What is the value of 75014 of a fathom ? 6 4-50084 12 6-01008 ft. in. Answer 4 6-01008 What is the value of -93862 of a yard ? 2-81586 12 9-79032 ft. in. Answer 2 9-79032 What is the value of -27734 of a foot ? 12 3-32808 in. Answer 3-32808 fath. ft. in. Reduce 5 4 6-32 to feet, inches, and decimals. 6 in. Answer 34 6-32 12 ADDITION OF DECIMALS. EULE. Place the numbers so that the decimal points may stand directly under each other, add up as in Simple Addition, and cut off for decimals as many figures to the right as there are deci- mals in the greatest given number. EXAMPLE. What is the sum of 3-72 and 14-7368 and 146-2 and -728 and 5-034 ? 3-72 14-7368 146-2 728 5-034 170-4188 ft. in. ft. in. What is the sum of 2 11-9942 and 1 4-09658? 1 4-09658 4 4-09078 Add together the following measures ; viz. fath. 6 19 64 ft. 4 1 5 in. dec. 2-260 11-47298 3-087 9-9746 2-70643 91 5-50101 13 SUBTRACTION OF DECIMALS. EULE. Arrange and cut off the decimals as in Addition. From Take EXAMPLE, fath. ft. in. 4 2 9-7824 2 4 8-91773 1 4 0-86467 MULTIPLICATION OF DECIMALS. EULE. Multiply as in whole numbers, and cut off as many figures from the product as there are decimals in the multiplier and multiplicand. EXAMPLE, fath. ft. in. Multiply 2 4 7-92486 by 24 6 16 3 11-54916 4 6x4=24 66 3 10-19664 fath. ft. in. Multiply 9 3 1-4872 by 37 57 8-9232 6 342 9 5-5392 1-4872 352 1 7-0264 Here we multiply by 6 twice because 6 times 6 are 36, and add the given number, which makes it equal to 37, or 6x6 + 1=37. ft. in. Multiply 14 9-746 by 12 12 177 8*952 14 DIVISION OF DECIMALS. EULE. Divide as in whole numbers, and cut off as many figures in the quotient as the decimal places in the dividend exceed those of the divisor. EXAMPLE, fath. ft. in. Divide 2 4 3-7 by 6 6)2 4 3-7 fath. ft. 7)4 2 2 8-61 ft. 5 in. 0-3316 in. 10-30994 fath. 8)15 3 10-04427 1 5 10-5414 ALIQUOT PARTS OF A FATHOM. TABLE. Parts Feet Inches i of a fathom is 3 i ditto c\ i ditto 1 6 .1- ditto 1 i ditto ; 9 ditto 8 A ditto 6 TV ditto 44 TV ditto 4 A ditto 3 15 KEMAKKS. It has been observed that the radius in every case is 6 feet or 1 fathom ; consequently the num- ber of fathoms in the given side, whether that side be hypothenuse, perpendicular, or base, will be the multiplier of the tabular numbers, and should there be a fraction in the multiplier, the multiplicand must be divided by that fraction agreeably with the rule of practice. The table of aliquot parts of a fathom, in the adjoining page, will be found useful in facilitating this part of the process. In some of the following examples the product has been obtained in fathoms and parts, but we would recommend the learner to carry on the work in feet (except in cases where the answer is re- quired in fathoms), as he will find it more simple and expeditious ; we speak of the multiplicand or number multiplied : the multiplier must invariably be fathoms, and should the given side be nominated in feet, it must be divided by 6, to bring it into fathoms, before the operation is begun by the fore- going cases. It may be further noticed that when any of the given sides in the tables amount to 6 feet, they are expressed in fathoms, &c. : but whenever it may be required to produce the answer in feet, &c., the numbers should be reduced to that measure before they are multiplied, and this can be done by mere inspection; viz. fath. ft. in. ft. in. Table 2nd, f Base 1 1 8-1560 1 . . f Base 7 8-1560 L 52 \ Hyp. 1 3 9-6053 / sti ' e \ Hyp. 9 9-6053 16 PRELIMINARY CHAPTER TO THE PEACTICAL DIALLING EXAMPLES. IT must have been matter of regret to every re- flecting, well-informed, and interested person, that (previous to the present work) nothing has ever been published with a design to assist the British miner in his subterraneous operations ; and while the press has teemed with publications distinctly and exclusively adapted to benefit the navigator, the architect, the sculptor, the surveyor, and even the mechanic and artisan, not a single effort has ever been made to extricate the miner from the disadvantages under which he has ever laboured (solely for the want of a plain, concise, technical, and scientific treatise on dialling, accompanied with appropriate tables), although his profession yields to none in importance and utility : in fact, it may be said, in a certain sense, to be the parent of every art and science in the world ; the use of metallic substances, in some shape or other, being indis- pensable in every one of them : nevertheless this highly essential art has hitherto been totally dis- regarded by all classes of mathematicians, and while the famous invention of logarithms has caused the science of trigonometry to soar to the very skies, and traverse old ocean's vast and unfathomable expanse, the unsupported miner has PRELIMINARY CHAPTER. 17 been left to struggle under the greatest disad- vantages, with nearly as little obligation to geo- metrical science, as his antediluvian progenitors ; and although he has done everything that deep thought, strong natural understanding, unwearied perseverance, and inventive genius (unassisted by trigonometrical demonstration) could possibly ac- complish, yet, for the want of mathematical light, his exertions have been ineffectual and insufficient to disentangle him from the difficulties with which he has been encircled ; hence his avocation has, in general, been replete with toil, anxiety, apprehen- sion, dissatisfaction, and disappointment. How far the present work is adapted to answer the great end in contemplation, must be left for the judgment of the mining world to decide ; and we doubt not but the defects (real or imaginary) which may be considered to exist in the application, will be passed over and excused by every liberal man, on the grounds already stated in the preface, having an unshaken confidence that the fundamen- tals of the work, comprised in the trigonometrical tables, will be found plain, true, and unexceptiou-- able. DEFINITION OF RIGHT-ANGLED TRIANGLES. Iii order to .use the following tables with due effect, there is no necessity that the reader should understand anything of the science of trigono- metry, that part of the work having been accom- plished already to his hand ; so that, by the help 18 PRELIMINARY CHAPTER. of a few of the common rules of arithmetic, he may obtain, with the greatest ease and certainty, every- thing required to be known in the geometrical part of mining. Previous to an elucidation of the simple method of working by the tables, it may be satisfactory to introduce the operation by a few preliminary ob- servations and extracts on the nature and pro- perties of right-angled triangles. Plane trigonometry is the art of measuring the sides and angles of triangles described on a plane surface, or of such triangles as are composed of straight lines. The theory of triangles is the very foundation of all geometrical knowledge, for all straight-lined figures may be reduced to triangles. The angles of a triangle determine only its relative species, and are measured in degrees, minutes, and seconds ; but the sides determine its absolute magnitude, and may be expressed in fathoms, yards, feet, or any other lineal measure. THEOREMS. A right-angled triangle (the only kind generally necessary to be treated of for mining purposes) is that which has one right angle in it ; the longest side, or that opposite to the right angle, is called the hypothenuse, the other two are called the legs or sides, or the base and perpendicular : or, by Euclid's definition, 'In a right-angled triangle, the side opposite to the right angle is called the PRELIMINARY CHAPTER. 19 HYPOTHENUSE, and of the other sides, that upon which the figure is supposed to stand is called the BASE, and the remaining side the PERPENDICULAR.' The three angles of every triangle are together equal to two right angles, or 180 degrees. The greater side of every triangle has the greater angle opposite to it. The squares of two sides of a triangle are together double of the square of half the base, and of the square of a straight line drawn from the vertex to bisect the base. The sum of the three angles of every plane triangle being equal to half a circle, or 180 degrees, it therefore follows that if either acute angle, in such triangle, be taken from 90, the remainder will be the other acute angle, or the complement. The supplement of any angle is what that angle wants of 180 ; hence the supplement of any one angle is always equal to the sum of the other two. A few other properties of right-angled triangles may be worthy of notice, viz. : when the angle opposite the base is 30, the hypothenuse is exactly double the length of the base. When the angles are 45, the base and perpen- dicular are equal. When the angle opposite the base is 60, the hypothenuse is double the length of the perpen- dicular. APPLICATION. To show how a knowledge of the foregoing theorems may be rendered useful in mining prac- c 2 20 PRELIMINARY CHAPTER. tices, suppose in the triangle A B C, on page 24, the base BA represented a drift or cross-cut, and the side A C a lode, making an angle with the base of 66 30' ; consequently the angle A must be 23 30', because it requires that number of dgrees to con- stitute a right angle, the complement of the angle A, or 180, the supplement of the triangle ABC. Again, suppose the angle C of the diagonal shaft CA, page 25, were found to be 39 30', then the opposite angle A must contain 50 30'. We now approach towards the actual use of the tables, and have succeeded, we hope, in clearing all impediments out of the learner's way, so that he will find no difficulty in readily applying the numbers to dialling operations. We have previ- ously set a few examples of the mere act of taking out the primes, and have studiously endeavoured to render everything as perspicuous and compre- hensible as the nature of the work would possibly admit. But should anyone have gone thus far and still find an obscurity hang over him, so that he cannot penetrate into the nature of the subject as he would wish, or as he may have expected, yet let him not be discouraged ; this will always be the case with everyone who calculates on fully comprehending anything connected with the mathe- matics by definition or description only. Let him steadily, attentively, and perseveringly proceed with the examples, and if he is properly interested in the matter, he will soon find the subject open with per- spicuity and demonstration on his mind, and convey to him the incontrovertible assurance of the truth PRELIMINARY CHAPTER. 21 of the calculations, as well as the correctness of his own views, ideas, or conceptions of the subject. TABLE I. EXAMPLE. When the angle is 9 and the hypothenuse 1 fathom, what is the length of the other two sides of the triangle respectively ? (page 68.) Answer, Base 11-26328 Perp. 5 1111356 EXAMPLE. When the angle is 48 15', or 48J degrees*, and the hypothenuse 1 fathom, what are the lengths of the other sides ? (page 72.) ft. in. ft. in. Answer, Base 4 5-71613 Perp. 3 11-94348 TABLE H. EXAMPLE. When the angle is 35 45', or 35| degrees, and the perpendicular 1 fathom, what is the length of the hypothenuse and base respectively ? (page 78.) ft. in. fath ft. in. Answer, Base 4 3-8326 Hyp. 1 1 4-7165 * In this example, as the angle exceeds 45, it will be found standing on the right hand side of the page (as already explained), and the denomination of the required sides will be found at the bottom. A little attention to this order will prevent the mistake, which may otherwise take place, by an inversion of the base and perpendicular. 22 PRELIMINARY CHAPTER. EXAMPLE. Given the angle 59 30', perpendicular 1 fathom, the other sides are required. (page 81.) fath. ft. in. fath. ft. in. Answer, Basel 4 2-2317 Hyp. 1 5 9'8612 TABLE HI. EXAMPLE. Given the angle 5, base 1 fathom, the hypothenuse and perpendicular are required. *) fath. ft. in. " fath. ft. in. Answer, Hyp. 11 2 10-10734 Perp. 11 2 6-96374 EXAMPLE. Given the angle 30, base 1 fathom, the other sides are required. (page 83.) fath. ft. in. fath. ft. in. Answer, Hyp. 200 Perp. 1 4 4-70766 NOTE. The foregoing examples serve only to exemplify the manner of taking out the primes from the tables ; and as the given side is exactly one fathom, of course the tables give a direct answer. In the following examples the mode of taking out the tabular numbers is precisely as the foregoing, but the number of fathoms contained in the length of the given side, will be the multiplier of the other side of the triangle. 23 PLANE TRIGONOMETRY. BY THE TABLES. CASE I. WHEN THE HYPOTHENUSE IS GIVEN. EULE. Look in the first table, and against the given angle stands the base and perpendicular, answering to one fathom of the hypothenuse ; take out these numbers and multiply them re- spectively by the length of the hypothenuse. EXAMPLE. Given the angle 23 30', and hypothenuse 12 fa- thoms ; the base and perpendicular are required. OPEKATION. BASE. PERPENDICULAR. Feet 2 . 4-70993 Feet 5 . 6-02833 12 12 28 . 8-51916 66 . 0-33996 24 PLANE TRIGONOMETRY. BY CONSTRUCTION. PROCESS. SCALE 40 feet to an inch. Draw the line A B of any length, make the angle = 23 30' by a scale of chords, or with a pro- tractor; draw the hypothenuse A 0=72 feet from a scale of equal parts. From C let fall the perpendicular C B ; then ABC is the triangle required. A B, measured by the same scale of equal parts, will be 28 feet 8J inches, and B C will be 66 feet. CASE II. WHEN THE PERPENDICULAR IS GIVEN. RULE. Look in the second table, and opposite the given angle will be found the base and hypothenuse corresponding to one fathom of the perpendicular ; multiply these numbers sepa- rately by the length of the perpendicular. EXAMPLE. Given the angle 39 30', and perpendicular 9 fathoms 3 feet; the hypothenuse arid base are equired. OPERATION. fath. ft. in. fath. ft. in. 3 1 o 4 11-3522 3 i 1 1 9-3096 9 9 7 2 6-1698 11 3 11-7864 2 5-6761 3 10-6548 Base 7 4 11-8459* Hyp. 12 1 10-4412 * It has been before observed that it would be better to bring the answer out in feet than in fathoms, as in the last case. PLANE TRIGONOMETRY. 25 BY CONSTRUCTION. PROCESS. Draw the line A B of a suf- ficient length, at any point B erect the perpendicular B C, which make equal to 57 feet by a scale of equal parts. At C make the angle = 39 30', the com- plement of A. From C draw the hypothenuse, and it will cut the base A B in the point A ; then will A B A measure 47 feet, and A C 73 feet 10 inches. CASE HI. WHEN THE BASE IS GIVEN. EULE. Look in the third table, and opposite the given angle (as in the former cases) the corre- sponding numbers to one fathom of base will be seen, which, being multiplied by the given length of the base, produces the hypothenuse and per- pendicular. EXAMPLE. Given the angle 20 degrees, and base 28 feet 9 inches ; the hypothenuse and perpendicular are required. PLANE TRIGONOMETRY. i 1 yp- ft. 17 in. 6-51392* 4 i t ft. 16 ?81837* 4 70 8 2 2 2*05568 9-25696 11-08565 2-31424 65 8 2 2 11-27348 2-90918 8-96972 0-72729 84 0-71253 Perp. 78 11-87967 BY CONSTRUCTION. PROCESS. Draw the base A B, which make = 28 feet 9 inches, from a scale of equal parts, at B erect the perpendicular B C, make the angle A = 70 and draw the hypothenuse A C to cut the perpendicular B C in the point C ; then will A C measure 84 feet, and B C 78 feet llj inches. * These numbers stand in the tables in fathoms, &c. ; the hypothenuse will be found 2 fathoms 5 feet 6 inches, &c., and the perpendicular 2 fathoms 4 feet 5 inches, &c. 27 APPLICATION OF THE TABLES TO DIAGONAL SHAFTS. KEMAEKS. As in the foregoing cases each side of the triangle is distinctly made radius, it follows that every problem in oblique dialling, &c., can be solved by one or the other of these cases ; because, in every instance, a side and the angles are always given. GENERAL RULE. When the hypothenuse is given, work by case the first. When the perpendicular is given, work by case the second. When the base is given, work by case the third. EXAMPLE 1. A diagonal shaft A B was found to measure 84 feet,* and the angle of declination observed to * When the given line is denominated in feet, it must be brought into fathoms by dividing it by 6 (the number of feet in a fathom) ; thus in the above example the shaft being 84 feet is 14 fathoms, and therefore the numbers are multiplied by 7 and 2, -which are equal to 14. 28 DIAGONAL SHAFTS. be 48 degrees ; required the base B C, and per- pendicular A C. BY CASE I. L 48 4 5-50643 7 31 2-54501 2 Base 62 5-09002 ft. in. 4 0-17740 7 28 1-24180 2 Perp. 56 2-48360 EXAMPLE 2. A perpendicular shaft B C, measuring 57 feet, was found to intersect an underlaying shaft A C, whose angle of acclivity was observed to be 50 30'; required the length of the underlaying shaft A C, and the distance from the perpendicular at the sur- face A B. DIAGONAL SHAFTS. 29 Comp. ? 3930'J BY CASE H. in. 11-3522 9 44 2 6-1698 5-6761 AB 46 11-8459 Hyp- * ft. in. 7 9-3096 9 69 11-7864 3 10-6548 AC 73 10-4412 NOTE. In the above example, the angle having again been taken with the horizon, the operative angle will be 39 30', because 50 30' 90 = 39 30'. We may also observe that, the length of the shaft being 57 feet, the multiplier is 9-|, or 9 fathoms 3 feet. EXAMPLE 3. A horizontal cross-cut B C from the foot of a diagonal B A to a perpendicular shaft C A was found to measure 224 feet 8 inches, and the angle of acclivity (taken at B, the foot of the shaft) 40 degrees ; I require the respective lengths of the hypothenuse A B and perpendicular A C. 30 DIAGONAL SHAFTS. /_40 Comp. 50 1 B BY CASE III. ft. in. ft. in. i 7 9-98932* + 5 0-41517 12 12 93 11-87184 60 4-98204 3 3 281 11-61552 181 2-94612 7 9-98932 5 0-41517 4 2 7-32977 i 1 8-13889 10-44325 6-71279 B293 3-37786 AC 188 6-21247 EXAMPLE 4. When a lode has changed its underlay. EULE. Take out the numbers opposite the given angles, and work them by the former cases ; then add their sums together respectively for the answer. * It will be observed that this number stands in the table 1 fath. 1 ft. 9 98932 in., and the angle having been taken at the foot of the shaft, the complement of that angle (i.e., what it wants of 90) must be used ; therefore the above tabular numbers will be found in the column opposite 50, being the complement of 40. DIAGONAL SHAFTS. 31 PROBLEM. In dialling a shaft sunk on a lode, it was found that the first draft B D measured 71 feet, on an angle of 14 45', but from that depth to the foot of the shaft C the angle proved to be 40 15', and the length D C 54 feet ; required the distance from the brace of the diagonal B, where a perpendicular shaft ought to be sunk, in order to come down exactly at the foot of the underlay ; also the depth of the per- pendicular A C. DIAGONAL SHAFTS. Z1445' BASE. 1 OPERATION. fath. ft. in. 6-33134 12 3 3-97608 3-05522 3 0-92086 PERPENDICULAR. fath. ft. in. 5 9-6273 12 11 3 7-5276 11-6045 11 2 7-9231 BASE. fath. ft. in. Z4015'= 3 10-52093 9 5 4 10-68837 PERPENDICULAR. fath. ft. in. 4 6-95274 _ 9 6 5 2-57466 SUMMARY OF BASES. fath. ft. in. 3 0-92086 5 4 10-68837 4 11-60923 AB52 feet 11 in. SUMMARY OF PERPENDICULARS. fath. ft. in. 11 2 7-9231 6 5 2-57466 18 1 10-49776 _6 A C 109 feet 10 in. EXAMPLE 5. When a lode has changed or reversed its under- lay from north to south, or east to west. EULE. Add all the perpendiculars together, as in the last problem, but subtract the bases', made by the reverse or contrary shafts, one from the other ; the remainder will be the true length of the base. DIAGONAL SHAFTS. 33 PROBLEM. A diagonal shaft was found to incline and mea- sure as follows, viz. : AB BC CD 54 feet 18 45' 42 do. 12 15' 69 do. 25 0' throughout the above drafts, the declination or 34 DIAGONAL SHAFTS. underlay bore northerly, but from that depth D it made an angle of 7 30' in a southerly direction, and this last draft D E measured 96 feet. It is required to know the perpendiculars and bases of all the foregoing sides respectively and collectively. OPERATION. BASES NORTHERLY. fath. ft. in. Z1845'=0 1 11-14364 B a 2 5 4-29276 PERPENDICULARS. fath. ft. in. 5 8-17897 9 A a 8 3 1-61073 Z1215'=0 1 3-27680 7 C b 1 2 10-93760 5 10-36062 7 B b 6 5 0-52434 Z.25 O'=0 2 6-42852 11 4 3 10-71372 1 3-21426 D c 4 5 1-92798 5 5-25416 11 9 5 9-79576 2 8-62708 C c 10 2 6-42284 BASE SOUTHERLY. fath. ft. in. > 30'= 9-39789 8 1 3-18312 2 E d 2 6-36624 fath. ft. in. 5 11-38403 8 7 5 7-07224 2 D d 15 5 2-14448 DIAGOXAL SHAFTS. 35 SUMMARY. fath. ft. in. 2 5 4-29276 1 2 10-93760 4 5 1-92798 North 9 1 "5-15834 South 2 6-36624 7 10-79210 _6 F A 42 ft. 10 in. PERPENDICULARS. fath. ft. in. 8 3 1-61073 6 5 0-52434 10 2 6-42284 15 5 2-14448 41 6 3 10-70239 F E 249 ft. 10 in. EXAMPLE 6. When a shaft has been sunk in error/ exactly at right angles with the lode. or not RULE i. Work for the base and perpendicular as before, by Case I.; then find the deviation by- the following RULE II. Take out the base from the second table, standing opposite the angle of error, and multiply it by the length of the shaft. * Underlaying shafts are always intended to be sunk at right angles -with the lode ; that is, if the lode runs east and west, the horizontal bearing of the shaft will be either north or south, as the lode may happen to underlie. But it is sometimes the case, that through inattention of workmen or other causes, the shaft has declined from its true course and inclined toward the right or left ; and as this is neither a trivial nor uncommon occur- rence, and admits not of development by the ordinary mode of dialling, we have here introduced a rule which will hold good in all cases of the kind. 36 DIAGONAL SHAFTS. PROBLEM. An oblique shaft A B was found to measure 89 feet 6 inches, on an angle of 53 15', and it was also observed that the shaft had declined 3 45' west from the intended right angle of the east and west lode : required the base C D and perpendicular C A, and how far the shaft has departed from its true course AD. OPERATION. 15' \ ft. in. 4 9-69027 7 33 7-83189 ! 2 67 3-66378 2 4-84513 1 7-23009 4-80752 Base 71 8-54652 3 2 6 f ft. in. 3 7-07937 7 25 1-55559 2 50 3-11118 1 9-53968 1 2-35979 3-58994 Perp. 53 6-60059 DIAGONAL SHAFTS. 37 THEN FOE THE DEVIATION. Table 2nd. L 3 45' Base ft. in. 4-7189 7 9-0323 2 5 6-0646 2-3594 0-78 0-19 5 9-3940 Thus it is clear that if the above shaft were sunk on an east and west lode and the angle of error in- clined westerly, that the foot of the shaft B would be 5 feet 9J inches in that direction beyond its designed course A D. EXAMPLE 7. To find the perpendicular depth of the junction of lodes. CASE I. When two lodes underlay in the same direction. EULE. Subtract the tabular number of the base of the lesser angle from the greater ; then by direct proportion, say, As this difference Is to one fathom perpendicular, So is the distance of the lodes at surface To the junction of the lodes. 38 DIAGONAL SHAFTS. PKOBLEM. Two lodes were discovered at the surface, 12 fathoms apart from C to D, both underlaying north. The southernmost lode D B made an angle of 38 15': the other C B 23. Eequired the perpen- dicular depth A B where these lodes will unite, supposing they both regularly continue their re- spective angles of declination. OPERATION FromZ.38 15'=4 Take 23 Q'=2 65-622 2 2-1980 DIAGONAL SHAFTS. 39 ft. in. Then, As 2 2-198 12 fath. fath. : 1 :: 12 6 26-198 72 12 26198) 864-000 (32-9 78594 6 78060 5-4 52396 12 256640 4-8 235782 20858 fath. ft. in. Answer 32 5 4 AB 40 DIAGONAL LODES. IF it is required to find the respective lengths of the lodes C B and D B, and the horizontal line D A, work by Case II., where the perpendicular is given. TO FIND D B. ^38 15' fath. ft. in. 1 1 7-6831 11 14 0-5141 3 42 1-5423 10-1870 D B 41 5 3-3553 Here we multiply by 33 and subtract from the pro- duct what the hypothenuse is minus of that measure, which, being eight inches, is one-ninth of a fathom. This is the shortest method. TO FIND C B AND D A, OR C A. ^23 on fath. ft. in. 2 6-5622 11 4 4 0-1842 3 14 0-5526 3-3964 CA13 5 9-1580 HYPOTHENUSE. fath. ft. in. ||1 6-2179 | 11 11 5 8-3969 3 35 5 1-1907 8-6908 C B 35 4 4-4999 Then CA+CD=DA,or CA added to CD gives the line DA, 25 fathoms 5 feet 9 inches, &c. DIAGONAL LODES. 41 EXAMPLE 8. To find the perpendicular depth of the junction of lodes. CASE II. When two lodes, by their underlay, incline in- directly towards each other. EULE. Add the tabular bases together, then find the depth by direct proportion as in the last example. PKOBLEM. Two lodes were observed 36 fathoms apart at the surface from A to C, the northernmost lode A underlaying south 18 15', and the southernmost lode C underlaying north 31 45' ; required the \ 42 DIAGONAL LODES. depth B D at which these lodes will intersect each other. OPERATION. ft. To z!8 15'=1 Add ^31 45'= 3 in. 11-6220 8-5550 5 8177 ft. in. Then, As 5 8*177 : 12 foth. fath. 1 :: 36 6 216 12 68-177 68-177) 2592-0000 (38-0 204531 546690 545416 12740 Answer 38 fathoms. If required to find the length of the lodes A D and C D and the distance of the shaft B from the lodes C and A at the surface, work by Case II. thus: TO FIND A B AND A D. BASE. HYPOTHENUSE. fath. ft. in. fath. ft. in. LlS 15' = 1 11-622 1 3-8135 1 5 9-732 6 1 10-8810 6 6 11 4 10-392 37 5 5-2860 3 11-244 2 7-6270 A B 12 2 9-636 A D 40 0-9130 DIAGONAL LODES. 43 TO FIND BC AND CD. BASE. HYPOTHENUSE. fath. ft. in. fath. ft. in. L 31 45' = 3 8-555 1 1 0-7008 3 4 3-330 7 4-2048 6 6 22 1 7-980 42 2 1-2288 1 1 8-110 2 2 1-4016 BC*23 3 1-090 CD 44 4 2-6304 * It may be observed that A B and B C added together do not make 36 fathoms, by something more than an inch : now this does not happen through any defect in the tables, but be- cause the perpendicular has not been worked out for if the remainder (12740) were prosecuted, the perpendicular would prove to be 38 fath. ft. 1*3392 in., instead of 38 fathoms, which addition to multipliers would make up the exact defi- ciency. 44 PEEPENDICULAE SHAFTS LEVELS, EULE. When the angle of acclivity is given, take the complement (or what it wants of 90) for the operative angle; in every other particular, work by the former cases. EXAMPLE 1. A perpendicular shaft having been sunk from the top of a hill at A, from whence the slope to C measured 330 feet : It is required to know the length an adit must be driven from the base of the hill at C to intersect the shaft at B, and what will be the depth of the shaft at that intersection, the angle of acclivity at C being 41 degrees. SHAFTS AND LEVELS. 45 BY CASE II. PERPENDICULAR, ft. Comp. of 1 3 41 is 49 J 35 212 3 in. 11-23625 5-12625 6 6-75750 11-23625 216 5-99375 BASE. ft. in. 4 6-33909 40 9-05181 6 244 6-31086 4 6-33909 249 0-64995 EXAMPLE 2. An adit having been driven 75 fathoms from A to B, required to know how far up the hill from A I ought to measure in order that a perpendicular may be sunk to intersect the adit at x, 58 fathoms from the tail at A ; also the depth of the shaft C x, the angle of acclivity from A towards C being 33 degrees. Or thus: Given the base 58 fathoms; angle of acclivity 33, of which the complement or angle of declivity is 57 ; required the hypothenuse and perpendicular. 46 SHAFTS AND LEVELS. BY CASE III. HYPOTHENUSE. ft. in. Comp. /_ 33 is 57= 7 1-85016 57 2-80128 7 400 7-60896 14 3-70032 A C 414 11-30928 PERPENDICULAR, ft. in. 3 10-75735 31 2-05880 7 218 2-41160 7 9-51470 Cx225 11-92630 EXAMPLE 3. From the foot of a perpendicular shaft AB, 70 36-1 .5 SHAFTS AND LEVELS. 47 fathoms in depth, a cross-cut was driven south 14 fathoms 3 feet in length (C), where a lode was discovered underlaying north, and the angle of as- cension or elevation 72 45' : required the length of this lode from the end of the drift C to the surface D : also the distance from the brace of the perpen- dicular shaft A to the back of the lode at grass (D), supposing the lode to have a regular underlay. BY CASE II. BASE. HTPOTHENDSE. fath. ft. in. fath. ft. in. Comp. of "1 1 10-3560 1 3-3911 L 72 45' is 17 15' / 7 7 2 1 0-4920 7 1 11-7377 10 10 21 4 4-9200 73 1 9-3770 Add length of drift 14 3 36 1 4-92 ANSWER. Length of lode Distance from shaft "I at the surface J fath. 73 36 1 5 48 SHAFTS AND LEVELS. EXAMPLE 4. From the depth of 36 fathoms 4 feet, in an engine shaft AB, a cross-cut was driven which pierced a lode C, 14 fathoms 2 feet from B. The lode was found to make an angle of 30 dgrees, inclining towards the shaft. Eequired the depth at which the shaft will intersect the lode, and the length of the lode from C to the point of intersection o. 30* BY CASE III. HTPOTHENUSE. fath. ft. in. i) 2 2 / PERPENDICULAR, fath. ft. in. i) 1 4 4-70766 2 4 3 2 28 24 9-41532 7 1 Ir9072 3 5-569 28 4 24 4 11-47624 ANSWER. Depth from A to B Depth from B to o Extreme depth fath. Length from C to o 28 fath. ft. in. 36 4 24 4 11-47624 61 2 11-47624 ft. 4 49 SLIDES. WHEN a lode has been thrown up by a slide, to find the base and perpendicular. EULE. Add the bases made by the segments of the lode together for the horizontal, and subtract the perpendicular made by the accession of the slide from the sum of the others for the perpen- dicular. EXAMPLE. A shaft having been sunk on a lode 114 feet from A to B, on an angle of 54 30', at this place the lode was separated and thrown up by a slide, from B to C, 32 feet, the angle of elevation at B being 47 : at C the lode was again cut and pro- secuted on an angle of 51, from C to D, 73 feet. Required to know the length from A to E at surface, where a perpendicular shaft should be put down, that would intercept the lode at the foot of the diagonal C D ; also the depth of the shaft E D. E 50 SLIDES. THE FOREGOING EXAMPLE BY THE TABLES. Z.A543(y= BASE. ft. in. 4 10-61632 6 PERPENDICULAR. ft. in. 3 5-81062 6 29 3-69792 3 20 10-86372 3 87 11-09376 4 10-61632 62 8-59116 3 5-81062 92 9-71008 66 2-40178 SLIDES. 51 L B Comp. 47 0' I 43 0' J ~ BASK. ft. in. 1 4 1-10388 I " 20 5-51940 1 4-36796 21 9-88736 PERPENDICULAR. in. 4-65747 5 21 11-28735 1 5-552 23 4-83935 lier\ ^5 feth~ 2 ftj L C .51 (X in. 7-95451 12 55 11-45412 9-32575 56 8-77987 ft. in. 3 9-31107 12 45 3-73284 /Multiplien U2 fa. 1 7-55184 45 11-28468 IftJ SUMMARY. BASES. ft. in. 92 9-71008 21 9-88736 56 8-77987 Answer E A = 171 4-37731 PERPENDICULARS. ft. in. A= 66 2-40178 C= 45 11-28468 112 B= 23 1-68646 4-83935 = 88 8-84711 NOTE. Perpendiculars to strike B or C and their respective horizontal distances from A are shown by the sums of the first and second operation in the above calculations. When a lode has been thrown down by a slide. EULE. Add the perpendiculars together for the depth, and subtract the base of the slide from the bases of the segments of the lode for the horizontal. E 2 52 SLIDES. EXAMPLE. A shaft A B having been sunk 77 feet on a lode, which made an angle of 34 45', it was there found that a slide had severed or disjointed the lode and carried it downward from B to C 40 feet, on an angle of depression or declivity 59. Here (at C) the lode was again discovered, and wrought 102 feet from C to D, on an angle of 42 15'; required the depth of the vertical line DE, and length of the horizontal A E. SLIDES. 53 NOTE. Should it be required to find the proper depth in the shaft D E from whence to drive a cross-cut to strike the end of the shaft A B (where the slide first appeared) the perpendicular of the first draft gives the depth, and the length of the cross-cut will be found by subtracting the base of the first draft from the horizontal line A E ; and should it be necessary to make a drift from the shaft D E to the angle C (where the lode was again discovered), the depth will be found by adding the perpendiculars of A and B together, and the bases of B and C will be the length of the drift. THE FOREGOING EXAMPLE BY THE TABLES. L A 34 45' BASE. ft. in. 3 5-03977 12 0-47724 8-51988 1-67992 43 10-67704 PERPENDICULAR. ft. in. i 4 11-15858 12 59 1-90296 2 5-57929 4 1 7-71952 63 3-20177 L B 59 ft. 1-71605 6 30 10-29630 2 6-85802 10-28600 34 3-44032 in. 1-08274 6 18 6-49644 1 6-54137 6-18045 20 7-21826 54 SLIDES. L ft. C 42 15' 4 in. 0-41041 4 16 1-64164 4 64 4 6-56656 0-41041 68 6-97697 PERPENDICULAR. ft. in. 4 5-2957 4 17 9-1828 4 71 0-7312 4 5-2957 75 6-0269 SUMMARY. PERPENDICULARS. L A. . L C . . B . . Ans. A E = ft. in. ft. in. . 43 10-67704 63 3-20177 . 68 6-97697 ^ ^^ Q 112 5-65401 . 34 3-44032 75 6-0269 78 2-21369 DE=159 4-44693 55 HOKIZONTAL DIALLING. EULE. Observe which side of the triangle is given, and work by the specified case. When there is more than one draft in the opera- tion, add the sums of the respective sides together for the answer. EXAMPLE 1. Being required to put down a shaft 618 feet due east of an engine shaft at A, I am prevented from measuring in a direct line by intervening hills and wood : I therefore find it necessary, in order to 56 HORIZONTAL DIALLING. avoid these obstructions, to go on an angle of 27 south of east from the shaft A. What distance must I proceed in this direction before I come at right angles with, or due south of, the eastern ex- tremity of the given line, and how far must I then measure in a northerly direction to come exactly on the required spot? Or the question may stand thus: Given the perpendicular 618 feet, angle 27 ; the hypothenuse and base are required. OPERATION. BASE. HYPOTHENUSE. ft. in. ft- in. 27= 3 0-6858 6 8-8075 10 10 30 6-8580 67 4-0750 10 10 /Multiplierx 305 8-5800 673 4-7500 V 103 fath. ; 9 2-0574 20 2-4225 314 10-6374 693 7-1425 EXAMPLE 2. It being required to find the distance between two shafts A and B, which are inaccessible to a direct measurement on account of a marsh or lake lying in the way : I consequently measure 352 feet on an angle of 63 south of west, from A to C ; at this station (C) I can see the shaft B, which I find by observation bears 29 north of west, and the line from C to B measures 615 feet : how far are these HORIZONTAL DIALLING. 57 shafts apart in a right line ? Or the question may stand simply thus : f Given angle 63, hypothenuse 352 feet. 1 I Given angle 29, hypothenuse 615 feet. J The sum of the perpendiculars* is required. OPEEATION. PERPENDICULAR, ft. in. 2 8-68732 L C29 C 11 29 11-56052 5 149 9-80260 8 2-06196 1 4-34366 5-44788 159 9-65610 ft. SUM. in. PERPENDICULAR. ft. in. 5 2-97262 10 52 5-72620 10 524 9-26200 10 5-94524 2 7-48631 537 10-69355 159 9-65610 537 10-69355 Ans. AB. 69r"8 T 34965 * As in this instance the perpendicular only is wanted, there is no necessity for taking out the other side. 58 VERTICAL DIALLING; OB THE MENSUEATION OF HEIGHTS. EULE. Observe the given side and angle,- and work by the respective cases as heretofore. EXAMPLE 1. From the bottom of a tower at B, I measured 200 feet in a direct line B A on an horizontal plane ; I then took the angle A 42 : required the height of the tower and staff B C. MENSURATION OP HEIGHTS. 59 OPERATION. Complement of L 42 is LC 48 / Multiplier \ V53 fath. 2 ftj ft. in. 5 4-82909 11 59 5-11999 3 178 3-35997 1 9-60969 Ans. BC 180 0-96966 In operations of this nature the hypothenuse need not be regarded. EXAMPLE 2. Wanting to ascertain the height of an irregular hill, I proceed, from the several stations A, B, and C, to take the angles and measure the distances as follows, viz. : From A to B L 41 0' length 210 feet. From B to 0^22 0' length 216 feet. From C to DZ. 37 30' length 247 feet. Required the altitude E D. 60 MENSURATION OF HEIGHTS. OPERATION. A 41 0' Comp. 49 0' 6)210 feet 35 Multiplier B 22 0' Comp. 68 0' 6)216 36 Multiplier l_ C 37 30' Comp. 52 30' 6)247 41 . 1 Multiplier ft. in. A 137 9-26875 B 80 10-98012 C 150 4-36875 Ans. height E D 369 Q-61762 PERPENDICULAR, ft. in. 3 11-23625 _7 27 6-65375 5 137 9-26875 2 2-97167 ^ 13 5-83002 6 80 10-98012 i 3 7-83082 10 36 6-30820 4 146 1-23280 3 7-83082 7-30513 150 4-36875 V 61 MISCELLANEOUS EXAMPLES IN THE FOREGOING RULES. Given the hypothenuse 14 feet 5 inches, angle 88' : required the base and perpendicular.* ft. in. A f Base = 14 4-89 AnSWer lPerp.= 6-03 Given the perpendicular 100 feet, angle 60 : re- quired the hypothenuse and base. ft. in. Given the base 118 feet, angle (Comp.) 23 : re- quired the hypothenuse and perpendicular. ft. in. Answer I H JP- = 301 U' 97 lPerp.= 278 0-02 Given the angle 53 : required the underlay in a fathom.f fath. ft. in. Answer 1 1 11-5472 Given the angle 36 45' : required the underlay in a fathom. ft. in. Answer 4 5-5650 * In single drafts, one or two figures of the decimal will be sufficient, the others may be rejected. f It has been before observed, that the underlay is given in the base of the second table. 62 MISCELLANEOUS EXAMPLES. Given the angle 4 15' : required the underlay in a fathom. in. Answer 5-3496 A diagonal shaft having been sunk 8 30' out of its true course ; what will be the extent of de- parture, supposing the length of the shaft 76 feet ? ft. in. Answer 11 4-9577 Suppose a diagonal shaft were sunk as follows, viz. : ft. in. L 87 0' = 14 5 Z.47 = 11 2 21 87 30 = 36 3 ^69 30 = 26 2 Z.77 30 = 23 2 30 = 9 2 Required the sum of the bases and perpendicu- lars. ^ (Perp. 52 8-45944 I Bases 169 6-90784 Wanting to know the distance between two shafts, inaccessible in a right line, I measured from the first shaft 126 feet, on an angle of 27 15' E. by N. ; from this station to the second shaft the line measured 91 feet, on an angle of 42 30' N. by W. : how far are the shafts apart ? ft. in. Answer 179 1-3 MISCELLANEOUS EXAMPLES. 63 Wanting to know the altitude of a precipice, I measured off from its base 66 feet, and from thence I take the angle to the summit, which I find to be 42 (and consequently the complement 48) : re- quired the height. ft. in. Answer 59 5-91999 At the foot of a hill the angle to the summit was 36, from this place an adit had been driven in a direct line 218 feet : how far must I measure up the hill to put down a perpendicular shaft on the end of the adit, and what will be the depth of the shaft? Answer j H ^ or sl P e 281 5>54804 1 Perp. or shaft 158 4-62816 At the foot of a diagonal shaft, 28 fathoms in length, sunk on a lode 27 45' underlaying north, another lode was cut making an angle 48 45' un- derlaying south : what is the distance from the brace of the shaft to the back of the north lode ? FIRST TABLE. BASE. PERPENDICULAR. ft. in. ft. in. /.2745' 2 9-5 5 3-7 7 7 19 6-5 37 1-9 4 4 78 2-0 148 7-6 Divide this by 6 for the multiplier of the 2nd angle, fath. ft. in. which will be 24 4 7'6 64 MISCELLANEOUS EXAMPLES. L 48 45' "I Comp. > 41 15' J THEN SECOND TABLE. BASE. ft. in. 5 3-14 6 81 6-84 4 126 3-36 2 7-57 10-52 5-26 0-65 ANSWER. ft. in. Base of north lode 78 2 Base of south lode 130 3 Required distance 208 5 130 3-36 A perpendicular shaft having been sunk 168 feet in the side of a mountain, the slope or declivity making an angle with the shaft of 54 15' : required to know how far I must measure down the hill to get at the right spot for driving an adit to come in the exact depth of the shaft, the length of the adit is also required. .. ' ft. in. A f Slope 287 8-58 AnSWer Udit 233 4-40 A lode underlaying south was observed to make an angle of 17 15' : required to know what dis- tance from the back of the lode will be proper for sinking a perpendicular shaft that shall intersect the lode at the depth of 45 fathoms. ft. Answer 83 in. 10-020 07 FIRST TABLE. HYPOTHENUSE RADIUS, ONE FATHOM. ANGLE BASE PERPENDICULAR Deg. Min. Feet Ins. Decimals Feet Ins. Decimals Deg. Min. 1 02094 6 89 59 2 04189 6 89 58 3 06283 6 89 57 4 08387 6 89 56 5 10482 6 89 55 6 12576 6 89 54 7 14670 6 89 53 8 16765 6 89 52 9 18859 6 89 51 10 20943 - 6 89 50 11 23038 6 89. 49 12 25132 6 89 48 13 27225 6 89 47 14 29319 6 89 46 15 31414 5 11 99932 89 45 30 62831 5 11 99726 89 30 45 94245 5 11 99381 89 15 PERPENDICULAR BASE ANGLE NOTE. This page had no place in the former edition, but will be found useful in particular cases for long lines where the angle is required to be very minute. It will be seen that as there is but the thousandth part of an inch difference in one fathom between the hypothenuse and perpendicular on the first 15' or first ^ of a degree, the introduction of the decimal at any less fraction would be useless. F 2 68 FIEST TABLE. ANGLE BASE PEEPENDICULAR Deg. Min. Feet Ins. Decimals Feet Ins. Decimals Deg. Min. 1 1 25657 5 11 98903 89 15 1 57067 5 11 98286 45 30 1 88474 5 11 97532 30 45 2 19877 5 11 96664 15 2 2 51276 5 11 95614 88 15 2 82666 5 11 94249 45 30 3 14060 5 11 93147 30 45 3 45442 5 11 91708 15 3 3 76819 5 11 90132 87 15 4 08188 5 11 88420 45 30 4 39549 5 11 86571 30 45 4 70902 5 11 84584 15 4 5 02246 5 11 82461 86 15 5 33581 5 11 80201 45 30 5 64905 5 11 77805 30 45 5 96219 5 11 75272 15 5 6 27521 5 11 72602 85 15 6 58811 5 11 69793 45 30 6 90090 5 11 66853 30 45 7 21354 5 11 63773 15 6 7 52605 ,5 11 60558 84 15 7 83842 5 11 57205 45 30 8 15063 5 11 53718 30 45 8 46269 5 11 50093 15 7 8 77459 5 11 46333 83 15 9 08633 5 11 42435 45 30 9 39789 5 11 38403 30 45 9 70926 5 11 34234 15 8 10 02046 5 11 29930 82 15' 10 33147 5 11 25490 45 30 10 64228 5 11 20914 30 45 10 95288 5 11 16203 15 9 11 26328 5 11 11356 81 15 11 57347 5 11 06374 45 30 11 88343 5 11 01256 30 45 1 19316 5 10 96004 15 10 1 50267 1 '5 10 90616 80 PERPENDICULAR BASE ANGLE HYPOTHENUSE RADIUS. 69 ANGLE BASE PERPENDICULAR Deg. Min. Feet Ins. Decimals Feet Ins. Decimals Deg. Min. 10 15 81193 5 10 85093 45 30 1 12096 5 10 79435 30 45 1 42973 5 10 73643 15 11 1 73825 5 10 67716 79 15 2 04650 5 10 61654 45 30 2 35449 5 10 55458 30 45 2 -66221 5 10 49128 15 12 1 2 -96964 5 10 42663 78 15 1 3 27680 5 10 36062 45 30 1 3 58365 5 10 29331 30 45 3 89021 5 10 22464 15 13 4 19648 1 5 10 15465 77 15 4 50243 5 10 08331 45 30 4 80807 5 10 01062 30 45 5 11338 5 9 93663 15 14 1 5 41838 5 9 86129 76 15 1 5 72204 5 9 72304 45 30 1 6 02736 5 9 70663 30 45 1 6 33134 5 9 62730 15 15 1 6 63497 5 9 54666 75 15 1 6 93825 5 9 46469 45 30 7 ;24116 5 9 38139 30 45 7 54371 5 9 29677 15 16 Z 84589 5 9 21084 74 15 8 14769 5 9 12359 45 30 8 44910 5 9 03502 30 45 8 75014 5 8 94514 15 17 9 05076 ! 5 8 85395 73 15 1 9 35099 5 8 76143 45 30 1 9 65082 j 5 8 66762 30 45 1 9 95023 ! 5 8 57250 15 18 1 10 24922 i 5 8 47607 72 15 10 54779 5 8 37833 45 30 10 84594 5 8 27931 30 45 11 14364 ! 5 8 17897 15 19 11 44091 5 8 07734 71 15 11 73772 i 5 7 97441 45 FEHPENDICULAB BASE ANGLE 70 FIRST TABLE. ANGLE BASE FEIiPENDICULAR Deg. Min. Feet Ins. Decimals Feet Ins. Decimals Deg. Min. 19 30 2 03409 5 7 87019 30 45 2 33000 5 7 76467 15 20 2 62545 5 7 65787 70 15 2 92043 5 7 54977 45 30 2 1 21493 5 7 44040 30 45 2 1 50895 5 7 32973 15 21 2 1 80249 5 7 21779 69 15 2 2 09554 5 7 10457 45 30 2 2 38809 5 6 99007 30 45 2 2 68013 5 6 87429 15 22 2 2 97167 5 6 75724 68 15 2 3 26270 5 6 63892 45 30 2 3 55320 5 6 51932 30 45 2 3 84320 5 6 39847 15 23 2 4 13264 5 6 27635 67 15 2 4 42156 5 6 15297 45 30 2 4 70993 6 6 02833 30 45 2 4 99776 5 5 90243 15 24 2 5 28503 5 5 77528 66 15 2 5 57176 5 5 64686 45 30 2 5 85791 5 5 51721 30 45 2 6 14350 5 5 38631 15 25 2 6 42852 5 5 25416 65 15 2 6 71295 5 5 .12077 45 30 ! 2 6 99680 5 4 98614 30 45 2 7 28006 5 4 85027 15 26 2 7 56272 5 4 71317 64 15 2 7 84479 5 4 57483 45 30 2 8 12622 5 4 43528 30 45 2 8 40708 5 4 29448 15 27 2 8 68732 5 4 15247 63 15 2 8 96692 5 4 00923 45 30 2 9 24590 5 3 86478 30 45 2 . 9 52424 5 3 71911 15 28 2 9 80195 5 3 57223 62 15 2 10 07902 5 3 42413 45 30 2 10 .35543 5 3 27483 30 PEEPBNDICTJIAH BASE ANGLE HYPOTHEXUSE RADIUS. 71 ANGLE BASE PEBPENDICULAB Deg. Min. Feet Ins. Decimals Feet Ins. Decimals Deg. Min. 28 45 2 10 63120 5 3 12433 15 29 2 10 90630 5 2 97262 61 15 2 11 18073 5 2 -81972 45 30 2 11 45450 5 2 66561 30 45 2 11 72759 5 2 51031 15 30 3 ooooo 5 2 35383 60 15 3 27173 5 2 19616 45 30 3 54276 5 2 03730 30 45 3 81310 5 $7726 15 31 3 1 08274 5 71605 59 15 3 1 35168 5 55366 45 30 3 1 61990 5, 39009 30 45 3 1 88740 5* 22536 15 32 3 2 15419 5 05946 58 15 3 2 42024 5 89240 45 30 3 2 68557 5 72418 30 45 3 2 95016 5 55481 15 33 3 3 21401 5 38428 57 15 3 3 47711 5 21261 45 30 3 3 73946 5 03978 30 45 3 4 00105 .4 11 86581 15 34 3 4 26189 4 11 69071 56 15 3 4" 52195 4 11 51446 45 30 3 4 78125 4 11 33709 30 45 3 5 03977 4 11 15858 15 35 3 5 29750 4 10 97894 55 15 3 5 55445 4 10 79819 45 30 3 5 81062 4 10 61632 30 45 3 . 6 06598' 4 10 43333 15 36 3 6 32054 4 10 24922 54 15 3 6 57429 4 10 06401 45 30 3 6 82724 4 9 87770 30 45 3 7 07937 4 9 69027 15 37 3 7 33068 4 9 50176 53 15 3 7 58117 4 9 31214 45 30 3 7 83082 4 9 12144 30 45 3 8 07965 4 8 92965 15 PERPENDICULAB ! BASE ! ANGLE 72 FIRST TABLE. BA8E PERPENDICULAR ANGLE Deg. if in. Feet Ins. Decimals I Feet Ins. Decimals Deg. ytin. 38 3 8 32763 4 8 73678 52 15 3 8 57476 4 8 54282 45 30 3 8 82105 4 8 34779 30 45 3 9 06649 4 8 15168 15 39 3 9 31107 4 7 95451 51 15 3 9 55478 4 7 75627 45 30 3 9 79763 4 7 55697 30 45 3 10 03961 4 7 35661 15 40 3 10 28071 4 7 15520 50 15 3 10 52093 4 6 95274 45 30 3 10 76026 4 6 74923 30 .45 3 10 998J1 4 6 54468 15 41 3 11 23625 4 6 33909 49 15 3 11 47290 4 6 13246 45 30 3 11 70864 4 5 92481 30 45 3 11 94348 4 5 71613 15 42 4 17740 4 5 50643 48 15 4 41041 4 5 29570 45 30 4 64250 4 5 08396 30 45 4 87365 4 4 87122 15 43 4 1 10388 4 4 65747 47 15 4 1 33318 4 .4 44271 45 30 4 1 56153 4 4 22696 30 45 4 1 78894 4 4 01021 15 44 4 2 01540 4 3 79247 46 15 4 2 24092 4 3 57374 45 30 4 2 46547 4 3 35403 30 45 4 2 68906 4 3 13335 15 45 4 2 91169 4 2 91169 45 PERPENDICULAR BASE ANGLE 75 SECOND TABLE. PEKPEKDICULAB EADIUS, ONE FATHOM. AN( JLE BASE HYJ OTHEN USE Deg. Min. Fath. Feet Ins. Decimals Fath. Feet Ins. Decimals 1 1 2568 1 0108 15 1 5710 1 0171 30 1 8854 0247 45 2 1998 0335 2 2 5143 0432 15 2 8289 0554 30 3 1435 0684 "45 3 4582 * 0828 3 3 7728 1 0986 15 4 0882 1 1159 30 4 4035 1 1346 45 4 7189 1 1544 4 5 0328 1 1757 15 5 3496 1 1980 30 5 6664 1 2171 45 5 9825 1 2484 5 6 2993 1 2736 15 6 6168 1 3024 30 6 9336 1 3312 45 7 2497 1 3636 6 7 5672 1 3960 15 7 8841 4298 30 8 2008 4658 45 8 5212 5026 7 8 8402 5400 15 9 1584 5803 30 9 4788 6192 45 9 7992 6624 8 10 1189 7056 15 10 4393 7531 30 10 7604 1 7992 45 I 11 0808 1 1 8474 76 SECOND TABLE. ANGLE BASE HYPOTHENUSE Deg. Min. Fath. Feet [us. Decimals Fath. Feet Ins. Decimals 9 15 o o 11 11 4034 7259 1 1 8971 9482 30 o 1 0485 1 1 0008 45 o 1 3696 1 1 0548 1 o 1 6936 1 1 1088 1U 15 o 1 1 0176 1 1 1664 30 o 1 1 3416 1 1 2262 45 o 1 1 6692 1 1 2859 11 o 1 1 9954 1 1 3476 15 o 1 2 3215 1 1 4106 30 o 1 2 6484 1 1 4750 45 o 1 2 9760 1 1 5410 12 o 1 3 3036 1 1 6085 15 o 1 3 6326 1 1 6775 30 o 3 9617 1 1 7481 45 o 4 2914 1 8202 13 o 4 6219 1 8939 15 o 4 9538 1 9691 30 5 2857 2 0459 45 5 6178 2 1242 14 5 9496 2 2042 15 6 2858 2 2857 30 6 6192 2 3688 15 6 9576 2 4535 15 7 2888 2 5399 15 1 7 6294 2 6338 30 1 7 9670 2 7174 45 1 8 3062 2 8087 16 1 8 6456 2 9015 15 1 8 9858 2 9961 30 1 9 3271 3 0443 45 9 6695 3 1902 17 10 0126 3 2898 15 10 3560 3 3911 30 10 7003 3 4941 45 11 0472 3 5988 18 11 3942 3 7053 15 11 6220 3 8135 30 2 0905 3 9234 45 2 4204 4 -0352 PERPENDICULAR RADIUS. 77 ANGLE BASE HYPOTHENUSE Deg Min. Fath Feet Ins. Decimals Fath Feet Ins. Decimals 19 2 7916 1 4 1487 15 2 1 1435 1 4 2640 30 2 1 4965 1 4 3811 45 2 1 8506 1 4 5000 20 2 2 2058 1 4 6208 15 2 2 5622 1 4 7434 30 2 2 9197 1 4 8679 45 2 3 2783 1 4 9942 21 2 3 6262 5 1224 15 2 3 9993 5 2526 30 2 4 3615 5 3846 , 45 2 4 7251 5 5186 22 2 5 0899 5 6545 15 2 5 4560 5 7924 30 2 5 8234 1 5 9323 45 2 6 1921 1 6 0741 23 2 6 5622 1 6 2179 15 2 6 9336 1 6 3638 30 2 7 3065 1 6 5117 45 2 7 6807 1 6 6617 24 2 8 0565 1 6 8138 15 2 8 4336 1 6 9679 30 2 8 8123 1 7 1242 45 2 9 1924 1 7 2826 25 2 9 5741 7 4432 15 2 9 9574 7 6059 30 2 10 3422 7 7708 45 2 10 7287 7 9380 26 2 11 1167 8 1073 15 2 11 5065 1 8 2789 30 2 11 8979 1 8 4528 45 3 2910 1 8 6290 27 3 6858 1 8 8075 15 3 1 0824 1 8 9883 30 3 1 4808 1 9 1714 45 3 1 8810 1 9 3571 28 3 2 2831 1 9 5450 15 3 2 -6870 1 9 7354 30 3 3 I -0928 1 9 9283 45 3 3 ! " -5005 1 10 -1232 SECOND TABLE. ANG LE BASE ___ HYP( )THENT J8E Deg. Min. ath. Feet Ins. Decimals Fath. Feet [us. Decimals 29 30 31 15 30 45 15 30 45 1FC o 3 3 3 3 3 3 3 3 3 3 3 4 4 5 5 5 6 6 7 7 9102 3219 7356 1514 5692 9892 4112 8355 2620 6907 1 10 10 10 10 11 11 11 11 11 3212 5220 7251 9303 1384 3494 5625 7788 9976 2192 Jn) 30 o 3 8 1216 1 4436 4.K o 3 8 5550 1 7008 oo ^rt) o 3 8 9906 1 9008 OS IK o 3 9 4286 1 1 1338 Xtl Of) 3 9 8691 1 1 1 3696 ou 45 3 10 3119 1 1 1 6084 33 15 3 3 10 11 7573 2053 1 1 1 1 2 8501 0949 30 o 3 11 6558 1 2 3427 45 o 4 1088 1 2 5937 34 4 5646 1 2 8477 15 o 4 9931 1 3 1049 30 o 4 1 4842 1 3 3653 45 o 4 1 9482 1 3 6289 35 o 4 2 4149 1 3 8958 15 4 2 8846 1 4 1660 30 4 3 3571 1 4 4395 45 o 4 3 8326 1 4 7165 36 4 4 3111 1 4 9969 15 4 4 7914 5 2808 30 4 5 2772 5 6819 45 4 5 5650 5 8591 37 4 6 2559 6 1538 15 4 6 7501 6 4520 30 4 7 2475 6 7540 45 4 7 7483 7 0597 38 4 8 2526 7 3693 15 4 8 7602 7 6831 30 4 9 2834 1 8 0000 45 4 9 7861 ' 1 1 1 8 3214 PERPENDICULAR RADIUS. 79 AN 3LE | BASE HYI OTHEJ, msE Deg. Min. Fath Feet Ins. Decimals Fath Feet Ins. Decimals 39 4 10 3044 1 1 8 .'6467 15 4 10 8265 1 1 i 8. 9761 30 4 11 3522 1 1 9 3096 45 4 11 8818 1 I 9 6473 40 5 4152 9 9893 15 5 9525 10 0956 30 5 . 1 4938 10 6863 45 5 2 0392 11 0413 41 5 2 5886 11 4009 15 5 3 1420 1 11 7651 e 30 5 3 7002 2 1338 45 5 4 2624 2 5049 42 5 4 8291 2 8855 15 5 5 4002 2 1 2686 30 5 5 9758 2 1 6566 45 5 6 5705 2 2 0496 43 5 7 1411 2 2 4476 15 5 7 7308 2 2 8507 30 5 8 3254 2 3 2591 45 5 8 9250 2 3 6727 44 5 9 5296 2 4 0918 15 5 10 1393 2 4 5163 30 5 10 7542 2 4 9463 45 5 11 3744 2 5 3820 45 1 0000 2 5 8234 15 1 6311 2 6 2706 30 1 1 2677 2 6 7237 45 1 9101 2 7 1828 46 2 5852 2 7 6481 15 3 2122 2 8 1195 30, 3 8722 2 8 5973 4o 4 5382 2 9 0814 47 5 2105 2 9 5721 15 5 8892 : 2 10 0694 30 6 5742 2 10 5735 45 7 2658 2 11 0844 48 7 9641 1 2 11 6023 15 8 6692 1 3 1273 30 1 9 3812 1 3 6596 45 1 1 10 1003 1 3 1 1991 SECOND TABLE. _ HYPOTHENUSE ANGLE Deg. Slin. Fath. Feet [ns. Decimals Fath. Feet Ins. Decimals 49 15 30 10 11 1 826o 5601 3012 0498 1 1 1 3 3 3 3 1 2 2 3 7462 3009 8634 4337 50 51 45 15 30 45 1 ^ 1 2 3 4 4 5 8062 5699 3430 1236 9126 7101 - 3 3 3 3 3 3 4 4 5 5 6 7 0122 5987 1936 7970 4091 0300 J.U 30 AX* 1 1 6 7 5164 3316 3 3 7 8 6599 2990 52 4:t) 1 ^ 1 1 8 8 1560 9893 1 1 3 3 8 9 9474 6053 53 J.U 30 45 15 30 45 1 1 1 2 2 2 9 10 11 1 2 8322 6848 5472 4197 3024 1956 1 3 3 3 4 4 4 10 10 11 1 1 2729 9505 6381 3360 0445 7636 54 IK 2 2 3 4 0995 0143 4 4 2 3 4937 2350 55 J.O 30 45 15 30 45 2 2 2 2 2 2 4 5 6 7 8 9 9403 8776 8267 7876 7606 7458 4 4 4 4 4 4 3 4 5 6 7 7 9876 7520 5282 3165 1172 9306 56 15 1 2 2 10 11 7444 7556 4 4 8 9 7570 6966 57 33 45 15 1 1 1 3 3 3 1 2 3 7801 8182 8703 9365 4 4 5 5 10 11 1 4497 3165 1976 0932 30 1 3 5 0174 5 2 0034 58 45 1 1 3 3 6 7 1131 2241 5 5 2 3 9287 8697 15 30 45 1 1 1 3 3 8 8 9 10 3507 4933 6523 5 5 5 4 5 6 8265 7994 7890 PERPENDICULAR RADIUS. 81 ANGLE BASE HYPOTHEJJX'SE Deg. Min. Fath. Feet Ins. Decimals Fath. Feet j Ins. Decimals 59 60 15 30 45 1 1 1 1 1 3 4 4 4 4 11 1 2 3 4 7281 0211 2317 4604 7077 1 1 I 1 2 5 5 5 5 7 8 9 10 7955 8194 8612 9212 0000 82 83 THIRD TABLE. BASE EADIUS, ONE FATHOM. ANGLE HYPOTHENUSE FEKPENDICITLAB Degrees Fath. Feet Ins. Decimals Fath. Feet Ins. Decimals 1 57 1 9 50554 57 1 8 87726 2 28 3 11 06698 28 3 9 81022 3 19 7 72726 19 5 84186 4 14 2 16226 14 1 9 64795 5 11 2 10 10734 11 2 6 96374 6 9 3 4 80760 9 3 1 03424 7 8 1 2 79665 8 10 39294 8 7 1 1 34135 7 8 30662 9 6 2 4 25663 6 1 10 59011 10 5 4 6 63148 5 4 33229 11 5 1 5 34070 5 10 40789 12 4 4 10 30087 4 4 2 73337 13 4 2 ' 8 06963 4 1 11 86626 14 4 9 61672 4 77622 15 3 5 2 18664 3 4 4 70766 16 3 3 9 21278 3 2 11 09384 17 3 2 6 26186 3 1 7 50139 18 3 1 4 99690 3 5 59321 19 3 5 15185 2 5 5 10318 20 , 2 5 6 51392 2 4 5 81837 21 2 4 8 91082 2 3 7 56641 22 2 4 20164 2 2 10 20626 23 2 3 4 26994 2 2 1 62137 24 2 2 9 01872 2 1 5 71465 25 2 2 2 36651 2 10 40450 26 2 1 8 24438 2 3 62187 27 2 1 2 59363 1 5 9 30796 28 2 9 36392 1 5 3 41231 29 2 4 51190 1 4 9 89144 30 2 ooooo 1 4 4 70766 31 1 5 7 79549 1 3 11 82812 32 1 5 3 86975 1 3 7 22408 o 2 84 THIRD TABLE. ANGLE HTPOTHENtTSB PEBPENDICtTLAB Degrees Fath Feet Ins. Decimals Fath, Feet Ins. Decimals 33 5 19765 3 2 87028 34 4 8 75699 2 10 74439 35 4 5 52817 2 6 82666 36 4 2 49371 2 3 09950 37 3 11 63809 1 11 54722 38 3 8 94738 1 8 15579 39 3 6 40913 1 4 91260 40 3 4 01211 1 1 80626 41 3 1 74622 1 10 82652 42 2 11 60231 1 7 96410 43 2 9 57201 1 5 21055 44 2 7 64807 1 2 55818 45 2 5 82338 1 00000 46 2 4 09178 5 9 52959 47 2 2 44758 5 7 14108 48 2 88555 5 4 82909 49 11 40094 5 2 58864 50 9 98932 5 41517 51 8 64669 4 10 30445 52 7 36931 4 8 25256 53 6 15377 4 6 25589 54 4 99689 4 4 31106 55 3 89577 4 2 41494 56 2 84768 4 56461 57 1 85016 3 10 75735 58 90084 3 8 99060 59 11 99760 3 7 26196 60 ! 11 13844 3 5 56922 85 LEVELLING, EULE Add all the perpen- diculars together for the base line or horizontal distance, and subtract the bases made by the angles of elevation and depres- sion one from the other, for the perpendicular or difference of height.* EXAMPLE. Being required to level an ir- regular piece of ground, I mea- sured in a south-west direction 64 yards from A to B, on an angle of depression 9 45'; from this * The altitudes of irregular hills are generally ascertained by the assistance of a r* it level and perpendicular poles, and if ground rise and descend alternately, the differences between the heights of the poles are added when ascending, and sub- tracted when descending, in order to deter- mine the different elevations and depres- sions of the ground : the foregoing rule and method will be found far more correct and masterly, remembering always that the height of the instrument be accounted for, which may easily be done by taking the observation from a staff or target the height as the instrument. 86 LEVELLING. station I measured 120 yards from B to C, in the same cardinal direction, on an angle of elevation 16 30'; and from thence to the extent of the ground the line on the same course measured 44 yards from C to D, and the angle of depression 7 : required the base line or horizontal distance from the place where the levelling was begun, to the point where it was ended ; also, how much higher or lower the ground is at the place where the ope- ration terminated, than where it commenced. PERENDICULARS. ft. in. fath. ft. in. L 9 45' = 5 10 96004 x 32 = 189 2-72128 L 16 30' = 5 9-03502 x 60 = 345 2-10120 L 7 0' = 5 11 46333 x 22 = 131 0-19326 3)665 5-01574 AE 221 yds. 2ft. 5 in. BASES. ft. in. fath. ft. in. g f L .9 45'= 1 0-19316 x32 = 32 6-18112 1 \+ 17 O'=0 8-77459 x22 = 18 1-04098 r 50 7-22210 H d ^16 30'= 1 8-44910x60= 102 2-94600 I 3) 51 7-72390 ED 17 yds. Oft. 7j in. ANSWER. yds. ft. in. Horizontal distance A E 221 2 5 Elevation ED . . . 17 74 87 HORIZONTAL OB MAILING. PLANE sailing in navigation and horizontal dialling in mining, are nothing more than the practice of right-angled trigonometry, calling the hypothenuse the distance, the perpendicular the difference of latitude, the base the departure, and the angle opposite the base the course ; consequently any range of dialling, however complicated and exten- sive, may be reduced into a single triangle, the perpendicular of which will either be the east and west, or north and south line, according to the main direction or bearing of the work ; the hypo- thenuse will be the actual length of the dialling in a right line from the point of setting out to the termination ; the base wih 1 be the distance the ter- minating point will fall right or left of the perpen- dicular; and the angle made by the hypothenuse with the perpendicular will be the final course or direction of the work. It therefore follows, that the general practice of repeating or retracing a course of underground dialling on the surface may be avoided, and thereby the difficulties and dangers arising from obstruc- 88 TRAVERSE DIALLING. tions, irregular ground, and the attraction of the magnet by iron, which always abounds in the vici- nity of a mine, be done away. What is said of Mercator's sailing may, in the chief respect, be applied to horizontal dialling, viz. : 'It is the art of finding on a plane surface the motion of a ship upon any assigned course by the compass, which shall be true in latitude, longitude, and distance sailed ;' and certainly this includes the whole theory and practice of navigation ; and if any method could be devised for measuring a ship's course and distance truly, nothing would be want- ing: also in dialling, it is only required to find a method for reducing the various windings and angles of a level or adit into a right line, and discovering the real extent and direction of that line, to com- plete the art. But not to occupy the reader's time in telling him what he well knows already, we shall proceed to introduce the process for obtaining the length and bearing of a course of traverse dialling by the tri- gonometrical tables. The first thing to be attended to is the statement of the work, or so placing the drafts that there may be no confusion in the operation, and that the per- pendiculars and bases may fall on their proper sides. In order to succeed in this essential matter, which may be considered the foundation of the work, note on which cardinal point the main direction of your dialling runs, whether east, west, north, or south, and reckon off your degrees right or left from that TRAVERSE DIALLING. 89 line : thus if your dialling runs easterly or westerly, let the equator, or east and west line, be the point for numbering off your angles if northerly or southerly, the meridian or north and south line ; consequently this line will be the perpendicular of every triangle in the operation that comes within the sweep of half the circle, or 180 ; and should any of the drafts return beyond the north or south points, or exceed 90 right or left of the east point, then the angle must be counted from the west towards the north or south, as the draft may happen to incline. This being done it is evident that on a course of east and west dialling, the bases north and bases south must be subtracted one from the other, and the remainder will be the departure or base line north or south as the diaUing may have prevailed on this or that side, and if any of the drafts have gone westerly, then the perpendiculars west must be subtracted from the perpendiculars east, for the real length of the perpendiculars ; but if the dialling has prevailed most in a westerly direction, the per- pendicular will lie on that side : in short, as a matter of course, either for the difference of latitude, or rather difference of longitude in this case (the perpendicular), or for the departure (the base), the less number must be taken from the greater, and the differences will show the sides on which the opera- tion lies. This process must all be performed by the first table, where the hypothenuse is given, because in every case the actual measured line will be the 90 TRAVERSE DIALLING. longest side of the triangle, and after stating the work, as before directed, take out the numbers standing against the given angles in the table and multiply them respectively by the length of the hypothenuse, reduced into fathoms and parts (if any), and place them in their proper positions until the whole has been calculated ; then take the sum of the bases north and south one from the other, and the sum of the perpendiculars east and west one from the other ; the perpendicular remainders will show the east and west line, and the bases the distance the dialling has extended north or south of that line. The work is now brought to that case where the difference of latitude and departure is given to find the course and distance, and in order to avoid the necessity of introducing extensive and intricate tables, used by navigators for this purpose, we shah 1 have recourse to one simple act of instru- mental operation, and as two sides of the triangle are given, the thing may be quickly and safely performed ; thus draw the base the given length by a scale of equal parts, raise the perpendicular on one end of the base (and of course at right angles therewith), and mark off the given length, draw the hypothenuse, and the triangle wih 1 be complete: then, by the same scale, measure the hypothenuse, and it will be the actual length 'of the dialling in a right line, from beginning to end ; then, with a protractor or scale of chords, measure the angle opposite the departure or base, TRAVERSE DIALLING. 91 and it will be the true course, bearing, or direction of the extreme points. The degrees on the miner's compass are gene- rally graduated from 1 to 360, and are figured toward the left hand, consequently 90 stands at the west point, 180 at south, 270 at the east, and ends with 360 at the north ; and when the same course is to be pursued, that is, when the angles are to be taken and the drafts measured again, there will be no necessity for finding the real direction of the line, for as the sights are always fixed, the dialler need only be careful to observe that the needle stands at the same degree as in the original course : but when the operation is to be plotted or trigonometrically proved, there will be a necessity for ascertaining the actual bearing of every draft in the work, and this may be done by the following rule. BULB. (SIGHTS FIXED NORTH AND SOUTH.) I From 1 to 90 N. to W.i From 90 to 180 W. to S. From 180 to 270 S. to E. From 270 to 360 E. to N. S.3.S E. of N. Comp. N. of E. S. of E. Comp. E. of S. W.ofS.Comp.S.ofW. N.ofW.Comp.W.ofN. TRAVERSE DIALLING. 93 EXAMPLE 1. It is required to sink a perpendicular shaft on the end of a level whose angles and drafts measured as follows, viz. : ft. in. fath. ft. in. L 16 30' E. of S. 53 6 or 8 5 6 L 26 O'W. of S. 22 11 or 3 4 11 /L19 0' E. of S. 58 or 9 4 Z.34 30' W. of S. 21 6 or 3 3 6 L 57 30' W. of S. 53 8 or 8 5 8 ^39 30' E. of S. 29 10 or 4 5 10 What distance is the end C (in the annexed plate), where the dialling was finished, from the engine shaft A, where the dialling was begun, and what is the bearing of the line A C, or how many degrees are contained in the angle BAG? OPERATION. BASES. ft. in. fath. ft. in. ft. in. E. of S. 16i = 1 8-44910 x 8 5 6 = 15 2-33790 W.of S. 26 = 2 7-56272 x 3 4 11 = 10 0-53916 E. of S. 19 = 1 11-44091 x 9 4 = 18 10-58864 W. of S. 34 = 3 4-78125 x 3 3 6 = 12 2-13235 W. of S. 57| = 5 0-72418 x 8 5 8 = 45 3-18762 E. of S. 39| = 3 9-79763 x 4 5 10 = 18 11-55815 ft. in. Sum of bases W. of S. 67 5-85913 Sum of bases E. of S. 53 Q-48469 Base or departure Westerly B C=14 5-37444 94 TRAVERSE DIALLING. 95 PERPENDICULARS. in. fath. ft. in. ft. in. 9-03502x8 5 6 = 51 3-56228 4-71317 x 3 4 11 = 20 7*16851 8-07734 x 9 4 = 54 10-06606 11-33709 x 3 3 6 = 17 8-62417 2-68557 x 8 5 8 = 28 10-05018 7-55697 x 4 5 10 = 23 0-04485 Perpendicular or diff. of latitude, A B 196 3-51605 THEN BY CONSTRUCTION. Draw two lines at right angles, as A B and B C, and of an indefinite length, take 196 feet 3J inches in your compasses from a scale of equal parts, and with one foot in the right angle B, point off the distance B A for the perpendicular. Again take 14 feet 5 J inches from the same scale, and apply it to the other line B C for the base ; draw the hypo- thenuse to join A G, which by the same scale will be found to measure 197 feet. FOR THE ANGLE. With the chord of 60 in your compasses and centre A, describe an arc e d cutting A B and A C in d and e ; then take the distance e d in your com- passes, and setting one foot on the brass pin at the beginning of the chords on your scale, observe how many degrees the other foot reaches to, which will be 4 15' for the arc e d or angle BAG. ANSWER. 197 feet, on an angle of 4 15' west of south. TRAVERSE DIALLING. EXAMPLE 2. Given the following course of traverse dialling, viz. 162 143| 45 4 152] 87| 204| = L L L L L L L L 18 36 73 12 45 82 27 2 65 0' S. of E. 15' S. of E. 30' N. of E. 45' S. of E. 0' N. of E. 15'N.ofW. 30' S. of E. 30'N.of E. 30' S. of W. ft. 3G 44 30 28 17 15 72 16 73 in. fath. or 6 4 or 7 9 or 5 6 or 4 10 or 2 3 or 2 Oor 12 Oor 2 or 12 ft. 2 4 5 3 4 1 in. 4 9 6 10 3 Eequired the distance and bearing of the extreme points A C. OPERATION. BASES SOUTHERLY. ft. in. fath. ft. in. 18 0' == 1 10-24922 x 6 36 15' = 3 6-57429 x 7 2 4 12 45' = 1 3-89021 x 4 4 6 27 30' = 2 9-24590 x 12 65 30' = 5 5-51721 x 12 1 ft. in. 11 1-49522 26 2-57669 3-44849 2-95080 5-12605 6 33 66 143 3-59725 BASES NORTHERLY. ft. in. fath. ft. in. 30' = 5 9-03502 x 5 9 -. 0' = 4 2-91169 x 2 5 10 : 82 15' = 5 11-34234 x 2 2 30' = 3-14060 x 2 ft. 29 12 15 5-80448 7-14507 1-33685 8-37150 Subtract bases northerly 57 10-65790 ft. in. = 143 3-59725 = 57 10-65790 Departure B C 85 4-93935 TRAVERSE DIALLING. 97 PERPENDICULARS EASTERLY. 18 36 73 12 45 27 2 0' 15' 30' 45' 0' 30' 30' - ft. 5 4 1 5 4 5 5 in. 8-47607 10-06401 8-44910 10-22464 2-91169 3-86478 11-93147 fath. x 6 x 7 x 5 x 4 x 2 x!2 x 2 ft. 2 4 5 4 in. 4 9 6 10 = ft. 34 35 8 27 12 63 15 in. 2-85642 9-02851 10-80163 9-56704 7-14507 10-37736 11-81724 199 1-59327 PERPENDICULARS WESTERLY. ft. in. fath. ft. in. ft. in. 82 15' = 9-70926 x 2 3 3=2 0-67815 65 30 7 = 2 5-85791 x 12 1 = 30 3-27124 32 3-94939 ft. in. From perpendiculars east = 199 1*59327 Subtract perpendiculars west = 32 3-94939 AB 166 9-64388 ft. in. Perp. or east and west line. A B 166 9*64388 Base south of east C B 85 4*93935 Then by construction (as before) the hypothenuse A C will be found 187 feet 3 inches, and the angle pq27 degrees, south of east. 99 THE PEACTICAL MINER'S GUIDE, PART II. INTEODUCTION. THE qualifications necessary to constitute an ac- complished miner are more numerous and diffi- cult of attainment than is generally imagined, even by persons deeply interested in mining affairs ; and although it may not be expected that everyone who fills a mining situation should be an adept in all the various branches of the art, yet it is cer- tainly highly desirable that agents, who have the management of large adventures, should possess a general knowledge of everything connected with the profession of a miner. The following miscellaneous subjects are essen- tial to the practical miner, and require no comment to set forth their utility ; they may also be found useful and interesting to persons not immediately engaged in mining pursuits. The first article consists in a description of the art of assaying silver ; and as this has hitherto been a secret in the possession of but few persons, H2 100 INTRODUCTION. it is expected that it will form an acceptable part of the work, especially as it will come abroad at a time when foreign mining speculations (where the seat of action is principally among the precious metals) abound beyond all precedent. The next part of the work contains a plain statement of the method of assaying copper, includ- ing the established process of one of the most ex- perienced and respectable copper-assayers in the county of Cornwall. Eules for assaying lead and tin follow in succession, and this part of the trea- tise concludes with a description of the manner of extracting silver from copper ore, or of discovering the quantity of silver it contains ; and probably this article also may be productive of beneficial effects to the mining interest, as there is great reason to believe that a considerable proportion of silver is contained in the ores produced from many of our copper mines. The method is very simple, and the trial may be quickly and satisfactorily made. The subsequent part of the work is described in the table of contents. 101 ASSAY OF SILVEE OEE, Sample 1 ounce avoirdupois, pulverised and sifted through a fine hair sieve, then well mixed in the scoop with the following flux, viz. : Eed lead* . . . . 2 oz. Eed tartar .... 5 dwts. Nitre .... 9 dwts. Borax . . . .'4 dwts. Lime . . . . J oz. Salt .... 2 oz. Fluor spar (bruised) . . J oz. Smelt the ore in a wrought-iron crucible ; if this cannot be conveniently procured, and a stone pot used, add 1 ounce of iron. The sample will melt in a good heat in about 12 minutes, if the ore is tolerably free from sulphur and iron, otherwise it will require more time. When the sample has become quite fluid, take it out and pour it in a mould prepared to receive it, having been anointed on the inside with grease or * An ounce of red lead generally contains about l-32nd part of a grain of silver, or nearly 3 ounces of silver in a ton. Derby- shire lead ore is preferred, by some assayers, to red lead. The proportion of silver contained in the flux must first be known, and the regular deduction made from the produce, in order to obtain a true assay. 102 SILVER ASSAY. oil ; the process of taking out and pouring the sample must be done quickly, otherwise a degree of chill will take place, so that the metal will not run freely out of the crucible, and the assay will in consequence be imperfect. If the operation has been properly managed, the lump will separate clean from the slag or dross by a slight blow ; but if the metal and dross stick together, the assay is impure : it is probable a little more nitre would remedy this defect. Should the lump when broken display the metal disseminated throughout and uncombined among the slag, it is a proof the sample was not suffi- ciently flowed, or not kept time enough in the fur- nace. If the heat is too strong, or the sample left too long time in the fire, it will set, or become dry and callous, and this change will take place to all ap- pearance quite suddenly. Either the former cir- cumstance of too low a heat, or this of too high, renders the assay irremediable. Should the sample appear stubborn and refuse to melt in a brisk heat, add more nitre. TESTING OR REFINING PROCESS. The test or cupel should be composed of four fifths bone ashes to one fifth fern ashes, damped and well beat into an iron ring 2J inches deep, and 6 inches in circumference. The test should be put in the fire an hour or more before the refining process is begun, other- SILVER ASSAY. 103 wise the silver will be apt to be agitated by tlie unsettled test, spring over, and consequently the assay be destroyed. Should the assay set in refining before it has be- come pure, throw in about half an ounce of potter's lead.* If the fire is permitted to get low, or too much air admitted into the furnace, the assay will be apt to turn to litharge ; whenever this happens, in- crease the fire by putting in a few pieces of sea-coal instead of coke, at the same time sprinkle a little coal-dust on the test. When the assay is thoroughly pure or fine it will assume a globular shape, set, or become fixed, and in a few moments will throw up sprouts or branches from the top. Take out the test, weigh the prilhon, find in the table the produce or value per ton, and the work will be complete. * The fire should be gradually increased toward the close of the process. A muffle or arched cover to the test would pre- vent the air from taking an unfavourable effect on the assay, while the furnace is opened for the purpose of increasing the fire, by adding coal, wood, or coke. 104 ASSAY OF COPPEE GEE, Sample 400 grains pounded well in a mortar and sifted through a fine hair sieve, put in an earthen crucible, and frequently stirred while in the furnace with an iron rod or paddle. The sul- phur will be seen to go 'off in white fumes ; the process must be continued until this evaporation ceases, or nearly so, which will generally occupy from one to two hours. Great attention must be paid during this operation in order that a standard regal may be obtained, which being done, there will be no danger of producing a true assay. The ore, during the process, must be kept in a free, sandy state, which will be effected by stirring, and constant regulation of the degree of heat. If the ore becomes moist and begins to stick or adhere to the crucible, it must be immediately taken out of the fire and stirred a short time till this effect has ceased, and then returned. When it has become tolerably free of sulphur, it may be discovered by the evaporation having nearly ceased.* This be- ing observed, take it out of the fire, and let it gra- * It is only some very stubborn ores, containing a mixture of metals, or semi-metals, which require to be so effectually roasted or calcined. COPPER ASSAY. 105 dually cool in the crucible ; and if, when cold, the upper part appears red or brown, and the under part black, it is a proof of its having been well calcined. This being done, add standard flux ; viz. Borax . . . . . . 5 dwts. Lime 1J ladle.* Fluor spar (pulverised) . . 1 ladle. Mix these together with the calcined ore in the crucible, and cover the whole with salt, let it melt well, and a regal will be produced. MARKS AND REMARKS. A good or standard regal is brown, and full of cracks or fissures, and of a spherical shape. Should it come out flat, it is a mark of its not having been well calcined, and may be thrown back again with a small quantity of nitre. Should a regal come out too low or coarse (having, when broken, a cinder-like or cellular appearance), throw it back with additional nitre : if too high or line (having, when broken, a metallic appearance), return it to the crucible with a ladle of sulphur ; in either case let it work well together a short time, and in all probability a standard regal will be produced. A regal may be considered good, which will produce from 8 to 12 in 20, and this quality is * Common assaying ladle diameter ^ inch, depth ^ inch. 106 COPPEE ASSAY. easily known by inspection ; but if less than 8, or above 12, it would be better to reject it, and begin the process again with a new sample. Grey, black, and green ores, require a propor- tion of sulphur, in order to throw them back, as they contain too little of this mineral in their com- position to produce a good assay. Should a regal be too fine, put less nitre with it in refining; and therefore the coarser it is, the more nitre will be required. PINING PROCESS. Pound or pulverise the regal, put it in an earthen fining pot, and re-calcine it until perfectly sweet (i. e. free from sulphur), which may be discovered both by the appearance and fumigation. Then add Nitre ... . 3 dwts. i Eed tartar . 10 ditto I Covered or sprinkled Borax . . 5 ditto f over with salt. Salt . . 2 ladles J This brings down the assay into coarse copper. Should it come out having a transparent or horn- like appearance, add 4 dwts. of nitre and a ladle of salt, letting it work well in the fire. Should the assay come out black, plate it, and if the black flies off in flakes or scales, it is a proof of its not having been sufficiently calcined ; if not, its colour may be attributed to lead, or a mixture of metals ; the former defect renders the assay hopeless. COPPER ASSAY. 107 Should it come out clean, put the assay in the pot without flux, and when fluid, take out the pot and shake it gently until the surface assumes an azure or blue appearance ; then put Eefining flux* . . .5 dwts. (viz. 2 parts nitre, to 1 part white tartar) Salt . . . 1 ladle. Preparatory to pouring into the crucible, place the refining flux in the mouth or fore part of the scoop and the salt behind ; throw it in with the assay and let it melt until the flux settles well down, then pour the copper into one mould, and the slag or scoria into another; return the slag into the same pot with 2 ladles of red tartar, and let it melt well down ; take out the prillion and weigh it with the lump for the produce, and the work will be completed. * The refining flux should go through a calcining process before it is used ; it may be done by putting 2 parts nitre to one part white tartar in an iron mortar, to which apply a red-hot iron, and stir it therewith until the deflagration has ceased ; when cold, powder and sift it. This operation will prevent any commotion during the re- fining, which otherwise may be so violent as to cause some of the metal to spring out of the crucible, and thereby the assay be spoiled. 108 ASSAY OF LEAD ORE. Sample 1 oz. avoirdupois. FLUX. 1 common ladle red tartar. 1 ditto spar. 2 ditto salt. 7 \ ditto borax. | ditto nitre. J ditto lime. Mix the flux with the sample and put it in an iron crucible, stir it with an iron rod during the latter part of the process ; in about five minutes, in a brisk heat, the sample will be down, provided the crucible was red-hot when the assay was thrown in, which should always be the case. If the sample, to be tried, weighs four ounces, the proportionate quantity of flux must be added, agreeably to the above statement. It may be discovered when the sample is ready, by the grating of the rod against the bottom of the crucible in stirring it should then be immediately taken out and poured. The metal will separate clean from the slag in a good assay. To assay lead ore for discovering the quantity or proportion of silver it contains, the foregoing me- thod must first be used, and the assay then tested precisely the same way as described for refining a silver sample, page 101. The lead will go off in vapour, and the silver remain in the test. 109 ASSAY OF TIN OEE, Sample Two ounces black tin. FLUX. Culm . . . J weight of sample. Borax . . .4 dwts. PKOCESS. If the ore contains a large proportion of iron, add more culm ; * when the sample is properly down, or flowed, the surface of the assay in the crucible will be perfectly smooth and motionless ; in a strong heat this will occur in about twelve minutes. When taken out of the fire, stir it well with an iron rod before you pour it ; afterwards scrape the crucible, pulverise the scrapings in a mortar, and then van or wash them on a shovel. The prillion of a standard sample will not exceed 2 in 20. The criterion for the lump is its possessing a malleable quality, or bending to the hammer with- out breaking. Grain tin may be treated in every respect as the above, except in the subsequent addition of culm, which will not be required. * If the sample is very stubborn, add a small quantity of pulverised flour with the culm. 110 ASSAYING. METHOD OF DISCOVERING THE PROPORTION OF SILVER CONTAINED IN COPPER ORE. Sample One ounce. 1 ladle 1 ditto ^ ditto ^ ditto 1 ditto 1 ditto FLUX. red tartar, nitre, lime, borax. flour, red lead. Well mixed with the ore and melted in a wrought- iron crucible,* about eight minutes, in a brisk heat, will be sufficient ; the last five minutes the assay should be incessantly stirred with an iron rod ; pour the sample and cool it, then break out the lump, and test it in the usual way. REMARKS. Soon as the assay begins to flow, the lead, by the power of affinity, will presently attract the silver, or the silver, by the same law, will attach itself to the lead, and this being effected, it only requires the process of refining, or burning off the inferior metals, to find the produce. * If a stone crucible be used, one ounce of iron must be added to the flux. Ill A TABLE SHOWING THE NUMBER OF OUNCES AND PARTS OF AN OUNCE OF SILVER CONTAINED IN A TON OF ORE, BY ASSAY PRODUCED FROM ONE OUNCE AVOIR- DUPOIS. ASSAY PER TON ASSAY PEE TON ASSAY PER TON T oz. 2 dwts. 6 grs. 16 grs. 4 oz. 298 dwts. 13 grs. 8 8i oz. 606 dwts. 13 grs. 8 3 4 13 8 308 1 616 9 6 16 317 6 16 3. 625 6 16 18 13 8 326 13 8 i 634 13 8 28 336 i 644 37 6 16 345 6 16 1 653 6 16 46 13 8 354 13 8 1 662 13 8 56 364 9 672 65 6 16 5 373 6 16 1 681 6 16 i ! 74 13 8 382 13 8 1 690 13 8 84 392 a 700 93 6 16 401 6 16 709 6 16 102 13 8 410 13 8 i 718 13 8 112 420 | 728 121 6 16 429 6 16 1 737 6 16 130 13 8 438 13 8 10 746 13 8 i 140 6 448 756 2 149 6 16 i 457 6 16 765 6 16 158 13 8 I 466 13 8 774 13 8 168 1 476 784 177 6 16 | 485 6 16 793 6 16 186 13 8 1 494 13 8 802 13 8 196 | 504 812 205 6 16 | 513 6 16 11 821 6 16 214 13 8 7 522 13 8 830 13 8 3 224 532 840 233 6 16 541 6 16 849 6 16 242 13 8 550 13 8 858 13 8 252 560 868 261 6 16 569 6 16 877 6 16 270 13 8 578 13 8 886 13 8 280 588 12 896 289 6 16 8^ 597 6 16 i 905 6 16 112 SILVER ASSAY TABLE. ASSAY PER TON ASSAY PER TON ASSAY PER TON if oz. 914 924 933 wts. 13 6 grs. 8 16 grs. OZ. 1390 1400 1409 Jwts. 13 6 grs. 8 16 $ oz. 1866 876 885 wts. 13 6 grs. 8 16 942 952 961 13 6 8 16 19 8 1418 1428 1437 13 6 8 16 \ 1894 904 1913 13 6 8 16 970 13 8 1446 13 8 - i 1922 13 8 980 o 1456 ! 1932 989 6 16 1465 6 16 26 1941 6 16 998 13 8 1474 13 8 1950 13 8 1008 ' 1484 1960 1017 6 16 20 1493 6 16 1969 6 16 1026 1036 13 8 1502 1512! 13 8 1978 1988 13 8 14 1045 6 16 1521 6 16 1997 6 16 1054 13 8 1530 13 8 2006 13 8 064 1540 27 2016 073 6 16 1549 6 16 5 2025 6 16 1082 13 8 1558 13 8 2034 13 8 1092 21 1568 2044 1101 6 16 1577 6 16 2053 6 16 1110 13 8 1586 13 8 2062 13 8 15 1120 1596 2072 1129 6 16 1605 6 16 2081 6 16 1138 13 8 1614 13 8 28 2090 13 8 1148 1624 2100 1157 6 16 1633 6 16 2109 6 16 1166 13 8 22 1642 13 8 2118 13 8 1176 1652 2128 1185 6 16 , 1661 6 16 2137 6 16 16 1194 13 8 1670 13 8 2146 13 8 1204 1680 2156 1213 6 16 1689 6 16 29 2165 6 16 1222 13 8 1698 13 8 2174 13 8 1232 1708 2184 1241 6 16 23 1717 6 16 2193 6 16 1250 13 8 1726 13 8 2202 13 8 1260 1736 2212 17 1269 6 16 1745 6 16 2221 6 16 1278 13 8 1754 13 8 2230 13 8 1288 1764 30 2240 1297 6 16 1773 6 16 2249 6 16 1306 13 8 1782 13 8 2258 13 8 1316 24 8 1792 2268 1325 6 16 1801 6 16 2277 6 16 1334 13 8 1810 13 8 2286 13 8 18 1344 1820 2296 1353 6 16 1829 6 16 2305 6 16 1362 13 8 1838 13 8 31" 2314 13 8 1372 1848 ft 2324 1381 6 16 1857 6 16 i! \ 2333 6 16 SILVER ASSAY TABLE. 113 ASSAY 1 PER TON i ASSAY 1! II PER TON ASSAY PER TON II gr 31 , oz. dwts. J2342 13 1 2352 t grs. oz. 371 1 2818 | 2828 dwts. 13 T gi 44- 3. oz. 3294 3304 dwts 13 T 2361 6 16 38 | 2837 6 16 3313 6 16 2370 13 2380 3 \ 2846 ! 2856 13 8 3322 3332 13 8 32 2389 6 16 ; 2865 6 16 3341 6 16 2398 13 8 2874 13 8 3350 13 8 i 2408 2884 45*" 3360 1 2417 6 16 ! 2893 6 16 3369 6 16 ; 2426 | 13 8 - 2902 13 8 3378 13 8 2436 39 2912 3388 2445 6 16 , 2921 6 16 i 3397 6 16 2454 13 8 2930 13 8 3406 13 8 33 2464 2940 3416 2473 6 16 2949 6 16 3425 6 16 2482 13 8 2958 13 8 46* 3434- 13 8 2492 . 2968 i 3444 2501 6 16 ', 2977 6 16 I 3453 6 16 2510 13 8 40 L 2986 13 8 3462 13 8 2520 2996 | 3472 if 2529 6 16 3005 6 16 4 3481 6 16 2538 13 8 3014 13 8 1 3490 13 8 i 2548 3024 | 3500 2557 6 16 3033 6 16 47 3509 6 16 2566 13 8 3042 13 8 3518 13 8 2576 3052 3528 2585 6 16 41*" 3061 6 16 3537 6 16 2594 13 8 I 3070 13 8 3546 13 8 | 2604 3080 3556 ! 35 |2613 6 16 3089 6 16 3565 6 16 2622 13 . 8 3098 13 8 i I2S74 13 8 2632 3108 48 ! 3584 2641 6 16 3117 6 16 . 3593 6 16 2650 13 8 3126 13 8 3002 13 8 2660 42^ 3136 8812 2669 6 16 3145 6 16 3621 6 16 2678 13 8 3154 13 8 . 3630 13 8 36* 2688 3164 j 3640 2697 6 16 3173 6 16 ; 3649 6 16 2706 13 8 3182 13 8 49 3658 13 8 2716 3192 3668 2725 6 16 3201 6 16 3677 6 16 2734 13 8 43 3210 13 8 3686 13 8 2744 3220 3696 2753 6 16 3229 6 16 3705 6 16 37 & 2762 13 8 3238 13 8 3714 13 8 i 2772 3248 ! 3724 1 2781 6 16 3257 6 16 50 3733 6 16 | 2790 13 8 3266 13 8 3742 13 8 i 2800 3276 I 3752 1 2809 6 16 44 3285 6 16 1 3761 6 16 114 SILVER ASSAY TABLE, ASSAY PER TON ASSAY PER TON ASSAY PER TON grs. OZ. 3770 3780 dwts. 13 g 16 OZ. 4013 4022 4032 wts. 6 13 grs. 16 8 grs. 57 OZ. 4256 4265 4274 wts. 6 13 grs. 16 8 1 I g 4041 6 16 4284 3808 3817 3826 6 13 16 8 o 4050 4060 4069 4078 13 6 13 8 16 8 4293 4302 4312 4321 6 13 6 16 8 16 3845 3854 3864 3873 6 13 g 16 8 16 55 , . 4088 4097 4106 4116 6 13 16 8 58 1 4330 4340 4?49 4358 13 6 13 8 16 8 52 i ' 3882 3892 3901 3910 3920 3929 3938 3948 3957 3966 3976 3985 3994 13 6 13 6 13 6 13 6 13 8 16 8 16 8 16 8 16 8 56 4125 4134 4144 4153 4162 4172 4181 4190 4200 4209 4218 4228 4237 6 13 6 13 6 13 6 13 6 16 8 16 8 16 8 16 8 16 59 60 , .. 4368 4377 4386 4397 4406 4415 4424 4433 4442 4452 4461 4470 4480 6 13 6 13 6 13 6 13 16 8 16 8 16 8 16 8 4004 4246 13 8 115 METHOD OP COMPUTING THE VALUE OF LEAD AND SILVER ORE. EXAMPLE. Required the value of 16 tons 10 cwt. 2 qrs. of lead and silver ore, the produce for lead being 8f in 20, and silver 3| grs. from a four-ounce sample. The price of lead 22/. per ton, and silver 5s. 3d. per oz. Returning charges 6/. 10s. per ton, and lord's dues one twelfth for lead, and one eighth for silver. OPERATION. i tons cwt. qrs. 16 10 2 132 4 851 211 *2Q) 142 10 2 7 2 2 at 15 10f per ton Deduct dues one twelfth s. d. 110 2 6 936 100 19 OPERATION. SILVER. oz. dwt. grs. By table (page 111) produce 3 is 72 6 16 per ton (3|-r- tons cwt. qrs. oz. dwt. grs. oz. s. d. s. d. and? 2 2x72 6 16=514 at 5 3 134 18 6 Deduct dues one eighth 1617 4 118 Answer 1 2 219 2 * It is not usual to make any allowance for waste on ores. f Returning charge deducted. i 2 rich 116 METHOD OF COMPUTING THE VALUE OF COPPER ORE. EXAMPLE. What is the value of 74 tons 13 cwt. 2 qrs. of copper ore, the produce, by assay, being 7, and standard 127/. 12*. 6 97 75 28 15 207-3 225 225 9)46642-5 112) 5182 (46 448 702 672 30 cwt. qr. Ibs. Answer 46 1 2 134 CORDAGE. TO FIND THE WEIGHT OF ROPES BEING 120 FATHOMS IN LENGTH. BULK Divide the circumference of the rope by 2, and square the remainder.* EXAMPLE. What is the weight of a 12-inch rope 120 fathoms long? 2)12 6 J5 Answer 36 cwt. EXAMPLE. What is the weight of a 144-inch rope 120 fathoms long ? 2) 14-5 7-25 7-25 52-5625 4 2-2500 200 50 7-0000 cwt. qrs. Ibs. Answer 52 2 7 * This rule is not perfectly accurate, but may be useful in affording a clue for finding the approximate weight of ropes, especially if the circumference is in even numbers ; it may then be used mentally, or by the mind only. CORDAGE. 135 TABLE I. SHOWING THE NUMBER OP THREADS IN THE STRAND OF A SHROUD-LAID ROPE. Size of Eope Size of Yarn Sixteens Size of Yarn Twenties Size of Eope Size of Yarn Sixteens Size of Yarn Twenties Inches Number Number Inches Number Number 2 7 9 gi 160 200 24 10 14 ib 2 177 222 3 16 20 104 196 245 34 21 27 11 215 268 4 28 35 n4 235 293 44 36 45 12 256 320 5 44 55 124 278 347 51 53 67 13 300 375 6 64 80 131 324 405 64 75 93 14 348 435 7 87 109 144 374 467 74 100 125 15 400 500 8 113 142 154 427 533 84 128 160 16 455 569 9 144 180 164 484 605 The difference of the number of threads in the whole rope will be found by subtracting the numbers standing under ' six- teens ' from those under ' twenties,' and multiplying the re- mainder by 3. (Thus 256 320 = 64 x 3 = 192.) Therefore it appears that a 12-inch rope made of 'twenties' contains 192 threads more than another, of the same circumference, made of ' sixteens.' 136 CORDAGE. TABLE II. SHOWING THE LENGTH OP SHROUD-LAID ROPES TO A CWT. FROM 1 TO 16 INCHES IN CIRCUMFERENCE. Size of Rope Fath. Feet Inches I Size of Rope Fath. Feet Inches Inches Inches 1 486 o-o 9 6 H 216 o-o 91 5 2 3-7 2 121 3 o-o 10 4 5 1-9 H 77 4 6-7 101 4 2 5-4 3 54 o-o 11 4 1-2 3i 39 4 o-o 111 3 4 0-9 4 30 2 3-0 12 3 2 3 4 24 o-o 121 3 7-9 5 19 2 7-7 13 2 5 3-1 51 16 4-3 131 2 3 11-5 6 13 3 o-o 14 2 2 10-4 6i 11 3 o-o 141 2 1 10-4 7 9 5 6-2 15 2 11-5 74 8 3 10-0 151 2 1-4 8 7 3 6-7 16 1 5 4-6 *i 6 4 4-3 161 1 4 8-5 The exact weight of a rope of any length may be found by the above table and the rule of proportion. EXAMPLE. Required the weight of 25 fathoms of 14-inch rope? fath. ft. in. cwt. fath. As 2 2 10-4 14 12 178-4 cwt. qrs. Ibs. Answer 10 10 i :: 25 6 150 12 178-4)1800(1 0-09 _4 Te 28 10-08 CORDAGE. 137 TABLE III. SHOWING THE WEIGHT OF SHROUD-LAID ROPES 100. FATHOMS IN LENGTH. Size of Rope Cwt. Qrs. Lbs. Inches 3 1 3 11-3 4 3 1 4 5 5 15 6 7 1 16 7 10 7 8 1>3 19 9 16 2 15 10 20 2 4 11 24 3 11 12 29 2 14 13 34 3 3 14 40 1 12 15 46 1 2 16 52 2 22 NOTE. The weight of any length of rope may be found by the above table and the rule of practice. EXAMPLE. What is the weight of 47 fathoms of 11-inch rope ? cwt. qrs. Ibs. 25 i 24 3 20 2 Answer 11 2 19 11 24 24 27 The weight and circumference of any rope being given, the length may be found by the foregoing table and the common rule of proportion, or by decimals. 128 CORDAGE. EXAMPLE. cwt. qrs. Ibs. What is the length of 7 3 14 of 7-inch rope ? cwt. qrs. Ibs. As 10 7 : fath. cwt. qrs. Ibs 100 :: 7 3 14 4 4 40 31 4 4 161 126 100 161)12600 78-26 cwt. As 10-0625 fath. ft. in. Answer 78 1 Or the length of any rope may be known by the 2nd table and the rule of practice. EXAMPLE. What is the length of 16 cwt. 2 qrs. 21 Ibs. of a 10^-inch rope? fath. ft. in. 4 2 5-4 to an cwt. by the table. 8 35 1 7-2 70 3 2-4 2 1 2-7 3 3-6 1 7-8 Answer 73 3 4-5 139 OBSERVATIONS ON THE CONSTRUCTION OP MINING CAPSTAN AND SHEARS. IT has been noted that there remains much room for improvement in the capstan machinery of our mines ; consequently it will not be irrelevant to the foregoing treatise briefly to submit our ideas on the subject in this place. By the present apparatus, a capstan rope of 14 or 16 inches in circumference is drawn over a single pulley, on the top of the shears, two feet in diame- ter, or thereabout, from whence it is brought down nearly to the foot, and then conducted under another pulley to the axle or barrel of the capstan ; a cylinder seldom exceeding 2J feet in 'diameter. The violence done to the rope in lifting great weights, as well as the augmentation of friction, in consequence of these sudden turns or incurvities, is certainly greater than has been generally under- stood ; but reflection and experience combine to teach us, that at all these bends or flexures a con- siderable proportion of the number of threads con- tained in the rope contribute nothing towards the support of the suspended weight; the outermost part of the cordage, from the grove of the pulley, necessarily bearing the whole strain. The excess of friction is chiefly produced by the 140 MINING CAPSTAN, ETC. lay or twist of the rope, it having thereby an in- . nate and unconquerable tendency to resist the constraint of being forced into a small curve ; con- sequently, the less scope it has the more power will be required. These arguments are self-evident, and no doubt but the inconveniences alluded to, and many more, are partially known and acknowledged; but the question is, How can they be remedied ? We respect- fully submit the following proposition : First, let the uprights of the shears stand farther apart on the top than usual, and the cap or head-piece of a ^convex shape, so that it may admit 3 pulleys in a triangular position,* the side pulleys horizontal, and the middle one standing higher than the others ; then let a sheave be introduced in a channel in the leg at the shears next the capstan, about one third down from the cap ; another in the stay of the span- beam, projecting 3 or 4 feet from the leg ; and the last pulley placed in a strong post fixed about 14 feet from the foot of the shears, in a direct line and parallel with the axle of the capstan, f By this simple contrivance it may be reasonably conjectured that one rope will endure as long as two, and a 14 be equal to a 16-inch on the old plan; and as the latter, 100 fathoms long, is above 12 cwt. heavier than the former, of course that superfluity * Or a straight piece may be used for the cap, letting the centre pulley be large and the side ones small ; but a semicir- cular cap with 5 small pulleys (one on the top and two on each side) will be still preferable. | The barrel of the capstan should be made proportionally larger, and the arms or bars of a corresponding length. MINING CAPSTAN, ETC. 141 will be avoided both in cost and gravity: * the shears will stand more erect than usual, where- by their height and strength will evidently be in- creased. We profess to know but little of the science of mechanics, nevertheless we feel confident that the foregoing proposition is quite practicable, and the subject is sufficiently important to demand con- sideration. We hope to see the hint improved and carried into effect by some of our ingenious engi- neers. * The safety, as well as convenience and economy, of this plan is too apparent to be overlooked. SUPPLEMENT, OB THIRD PART OF THE PRACTICAL MINER'S GUIDE. THE PRACTICAL MINER'S GUIDE. PART IIL INTEODUCTION. NEAELY twenty years have elapsed since ' The Practical Miner's Guide' was sent into the world, and the author is constrained to acknowledge that his extensive practice and experience in almost every branch of mining during that long period has not enabled him to discover where any im- portant improvement can be made in that work. The additions in the present volume are comprised in merely extending the principles originally laid down, and practically applying the mathematical tables and rules to more difficult, complicated, and momentous subterranean surveys; for it may be remarked, without subjecting ourselves to the charge of arrogancy, that the light thrown on the mining world by this publication has contributed towards expanding the minds of practical men generally, and qualifying them for pursuing and carrying out the scientific and demonstrative principles to the utmost extent of their difficult and highly important operations. L 146 INTRODUCTION. During the last five years the author com- menced a correspondence on mine surveying in the 1 Mining Journal,' with a view of rendering a last- ing benefit to the mining interest, by exposing the imperfection of the old method of dialling, by tracing, pegging^ or mechanical repetition, and showing the vast superiority of the trigonometrical system in every point of view. This attempt brought on a most extensive controversy, and many of ' the old school ' arose and came forward to advocate the old practice ; but, as if ashamed of the cause they had espoused, they were, almost to a man, anonymous writers. The unprejudiced and investigating part of the community honoured me, or rather the system I defended, with their able support, and rallied around my standard. The defeat of our opponents was complete, even before we attempted to apply the infallible test of experimental operation. Eea- son and historical proof had thrown them down; but when we brought forward problems, in the shape of actual surveys, and challenging them to furnish the true answers, they crept out of the field, and not one of them was heard of after that in- teresting, beneficial, and satisfactory investigation was introduced. Nearly all the problems that appear in this supplement were publicly brought forward by the author on this occasion, and of course un- derwent a rigid and extensive scrutiny ; and, so far from any error appearing, the truth of the calcula- tion and perfection of the system was demonstrated by exact corresponding solutions being publicly re- INTRODUCTION. 147 corded from persons residing in England, Ireland, and Wales. It will be seen, in the preface to the first edition of this work, that I called public attention to the great injury done to mining by the bad practice of surveying or dialling then in general use ; but as at that time there was no work written on the sub- ject, there was an excuse for the disastrous errors that took place then, that does not now exist ; and the mine agent who cannot now prove all his dialling operations, before a single stroke has been struck, ought not to presume to make the attempt ; and certainly it behoves directors, managers, and shareholders in mines, to test the abilities of those agents or captains who profess to be competent to undertake the momentous work of subterraneous surveying, by requiring them to give mathematical solutions to a series of practical questions on the subject ; and not, as is too often the case, proving their incapacity by some fearful error that they have committed, occasioning serious injury to the mine, great delay, and an extra cost of hundreds of pounds to the proprietors. And let it be under- stood that proof cannot be obtained by the old method of dialling ; that is, by tracing or repeating at the surface the drafts taken underground. This was fully demonstrated in the course of the late controversy, both argumentatively and practically. One convincing case was brought forward and confirmed, that occurred in Gwennap several years ago. It was required to find the point at surface for sinking a shaft to meet a rise that had been i, 2 148 INTRODUCTION. commenced at the adit level. This was certainly a very plain and easy job under a good system, but it presented insurmountable difficulties under the old practice. The shaft was set to a pair of eight men, and the captains proceeded to dial and peg to ascertain the true point. The first dialler fixed his terminating peg on a certain spot, and the next dialler's peg occupied another position ; and the history of the case is, that four agents were constantly occupied two or three weeks about this job, without being able to ascertain the true place for the shaft, which a competent man would have determined and proved in a few hours. At the close, they had a plantation of pegs occupying an area of several square fathoms ; and the manager, seeing it hopeless to expect certainty from such an uncertain practice, and tired of waiting and wasting any more time, proceeded to make the best of a bad matter, by lining out the shaft in the place where the pegs appeared to stand thickest I and the con- sequence was, a serious error of some feet in the holing. Now, by introducing this affair, our design is not to impeach men: it is the practice or usage that we condemn and expose, in order that it may be discountenanced and rejected, and thereby an incalculable benefit be conferred on metallic mining. 149 TRAVERSE DIALLING. IT is well known that our little army of mine agents or captains have almost to a man been se- lected from the ' ranks,' and have been brought up as working miners from their youth ; and the best judges admit the propriety and even necessity of this regulation, in order that they should be competent to fix the value or fair price for working a tut-work bargain, or tribute pitch, and possess a thorough knowledge of underground operations. This being admitted, we must conclude, that in. general their education has been much limited ; and, therefore, in writing for their assistance, although there may be some exceptions, we would accommodate ourselves to the lowest capacity, so that the young aspiring miner may not be discou- raged from prosecuting his incumbent and laudable studies, and qualifying himself for performing the high and paramount duties of a mine agent with credit to himself, and advantage to his employers and his country. Before this work was published, it is questionable whether a mining traverse had ever been trigono- metrically solved in this country ; and, consequently, in order to simplify the matter, the instructions given for finding the ultimatum of a course of 150 TRAVERSE DIALLING. dialling was by construction or instrumental opera- tion ; but as we believe our students are generally prepared to advance a step, we shall now recom- mend and show the more excellent way of perform- ing the whole by computation, or by figures. The trigonometrical method of working a course of dialling reduces the whole, however numerous and diversified, into two numbers ; for the four columns of easting, westing, northing, and south- ing being added up separately, and then the less deducted from the greater of the opposite cardinal points, reduces the whole into two numbers, forming the base and perpendicular of the great triangle, and are necessarily right angle cardinal bearings, such as easting and southing, or northing and west- ing, as the case may be ; and our next and last operation is to find the hypothenuse and angle corresponding with those two sides, which hypo- thenuse and angle is the final line, or course of the survey. EXAMPLE. A traverse has been worked, the columns added up, and the westing subtracted from the easting, showing the excess of easting to be 346 feet ; and the southing subtracted from the northing, the difference proved the excess of northing, 419 feet 5 inches. TRAVERSE DIALLING. 151 OPERATION. Find the hypothenuse by square root. EULE. Add the sum of the squares of the two sides together, and extract the square root of their sum. 346 419-4 346 419-4 2076 16776 1384 37746 1038 4194 119716 16776 175896-36 119716 295612-36(543-7 25 12 ..104)156 "81 416 1083) 4012 3249 10867) 76336 76069. 267 ft. in Answer Hyp. 543 8 152 TRAVERSE DIALLING. Find the angle by proportion. ft. in. ft- ft ' If 419 5 gives 346 what will 6 give? 12 _J12 ^ MJ33 "4152 72 72 8304 29064 in. ft. in. 5033)298944(59-39 or 4 11-39 25165 47294 45297 19970 15099 "48710 45297 4413 Then by inspection in the second table, page 79, this quotient of 4 feet 11'39 inches will be found standing opposite 39 30', which is the bearing, or sum of the angle opposite the shortest side of the great triangle. ANSWEE. Hypothenuse, or direct length from beginning to end, 543 feet 8 inches. Bearing, or direction from beginning to end, 39 30' east of north. TRAVERSE DIALLING. 153 EEMAEKS. In carrying out this system practically, after we have laid down this grand or final line at surface, and fixed a mark at the extreme end of the line which has been measured off from the starting point, 543 feet 8 inches on the bearing, 39 30' east of north (or 50 30' north of east, the com- plement), we are furnished with a double means of proving if this length and angle has been correctly laid down, by measuring off, due north, 419 feet 5 inches from the start, and then placing the theodolite, or dial, on the end of that line, and measuring off due east 346 feet ; consequently, if the whole has been well done, the last mark will exactly agree in both cases. Or should the ground be more favourable, we may avail ourselves of the convenience of laying off the east line first, and the north line last, which will bring us to the same point. One great advantage of these proof lines will appear, when we take into consideration that most of the instruments used in mines for taking hori- zontal angles have no vernier scale for reading off the fraction of the angle ; and, therefore, if the bearing falls between any quarter, or half of a degree, the surveyor must depend on the judgment of his eye for the division, and let it be known that an error of one quarter of a degree in 100 feet amounts to 5 inches and a decimal of -23596, or upwards of 2 feet 7 inches in a line of 100 fathoms ; hence the value of having this most satisfactory 154 TEAVERSE DIALLING. and convenient check for the laying down of the last grand line must be manifest to every observer, and should never be neglected. LOGARITHMS. Should the practitioner wish to prove the find- ing the angle and hypothenuse by logarithms, the following is the rule : From less side 346 and radius = 12-5390761 Subtract longest side, 419-4 = 2-6227140 Log. tangent of 39 30' . . 9-9163621 RULE FOR THE HYPOTHENUSE. From less side and radius (as before) 12-5390761 Subtract sine of 39 30' .' . . 9-8035105 Logarithm of 543-8 nearly . . 2-7355656 The rules expressed at length read thus : FOR THE ANGLE. Add the radius to the logarithm of the less side, and from the sum subtract the logarithm of the greatest side ; the remainder, or sum, will be the tangent of the angle opposed to the less side. FOR THE HYPOTHENUSE. Add the logarithm of the given side to the sine of the angle opposite to the side required, and from the sum subtract the sine of the angle opposed to the given side ; the remainder will be the loga- rithm of the side required. TRAVERSE DIALLING. 155 SYSTEM. There is much propriety in the remark, that ' system is the handmaid of science,' and the term may be considered as used in contradistinction to disorder, irregularity, or random. The man who would excel in the important work of mine sur- veying should have a system, and a good one. It is true, men are apt to be bigoted in this matter, and think so highly of their own system as to despise all others ; but certainly we must admit that a bad or an imperfect system is better than no system at all. He who has no fixed rule is liable to error every step he takes. We would recom- mend the young dialler to adopt a system in keep- ing his register or dialling book underground, so that his subterranean surveys may be perfectly clear and comprehensible, not only to himself, but to all practical men. Let us suppose we have to survey a level driven on the course of the lode, where there are several cross cuts driven off to the right and left. I would advise the student to keep the number of his drafts on the main line, or course of the lode, in regular numerical order ; and when he has to branch off on a cross cut, let him make the necessary mark, and call the first draft in that cross cut Number 1, and so on in succes- sion to the end of it. On his return to the mark where he departed from the main line, let the dialling on the cross cut stand in the book as a parenthesis, and let him resume his course on the lode, numbering his draft in order from where he 156 TRAVERSE DIALLING. branched off. By this system he will have no turning from one place to another in his book all will be regular ; and if the main course, or any other, should be required to be copied separately, in the fair dialling book, it can easily be done. Moreover, should a diagram or geometrical plan of the level and all its windings, and drifts or cross drivings, be required, by this mode of entry every- thing will appear in its proper place. Another part of the ' system ' is, to let the sight or vane fixed at 360 always take the lead, and the surveyor's eye placed at the opposite vane, except when taking back observations. This will be found under the head of 'Eernarks connected with the Converting Table ; ' and in horizontal dialling, let two drafts be made from every station, which will expedite the work, as the dialler will only have to wait for the settling of the needle once, instead of twice by the other method. SURVEYING WITHOUT THE MAGNETIC NEEDLE. This is a valuable modern discovery in mine surveying, and as ' necessity is the mother of in- vention,' the general introduction of railways and tramroads in mines drove the surveyor to seek some substitute for the needle, which the attrac- tion of iron rendered useless, and he has happily succeeded. This method of surveying cannot be performed with the common dial ; but the best circtim- ferenters are now made with an external gradua- TEAVERSE DIALLING. 157 tion and vernier scale, on the theodolite principle, on purpose for the performance of this work. Mr. W. Cox (from Arnold's, London), of Devon- port, makes these instruments in a superior style to any other in the west of England. The method of surveying, on this principle, differs from the magnetic method chiefly in one particular namely, that in every fresh draft the position of the bearing must be ascertained by the back observation, in the direction of the sights, and the angle made at the old station must be ob- tained and preserved at the new station ; and this is evident, because we have no magnet for our guide. For example : Suppose we are surveying over a railway in a level, and the last observation was 259 ; after measuring the length, the instru- ment is removed and carried forward to the place of the light where the angle was taken, and a mark and light left at the old station. Then, after the instrument has been adjusted in its true place, the next act of the surveyor is to place the centre of the vernier on 259, as it stood at the old station ; and if the instrument does not move by rack- work, he must keep all firm with his hands, and turn -the head toward the last station, until the candle is seen through the sights. He then removes behind the instrument, and moves the sights in the direc- tion for the next draft, where the assistant is hold- ing a light for the purpose (the graduation being fixed), and this new draft gives (say) 270 J, show- ing a difference between the two drafts of 11J. Although this process is somewhat tedious in de- 158 TKAVEESE DIALLING. scription, it is simple in practice, and the history of one draft is as well as a hundred ; and we may observe that, with proper care and judgment, this is the most perfect method of surveying, because there is no risk of attraction; and as the circle is much larger than the inside plate, and the divisions more distinct, together with the vernier scale being applied, the angle can be read off to one or two minutes, a nicety which cannot be attained by the needle in the common way. It is hardly necessary to state that, in order to obtain the bearing, there must be at least one draft in the traverse where the needle must be brought into play, and this draft will determine the polarity or direction of the whole. Further, let it be remarked, that a survey may be resolved into bearings, and worked trigonome- trically, when this method is used, as by the needle. Suppose a case that we are about to survey over a railway, but there is space enough clear of iron for the first draft ; and taking the observation with the needle, we find the north point (a right- hand dial) stand at 176^ ; we then fix the outer circle with the vernier precisely at the same point, and then, throwing off the needle, perform all the remainder of the traverse by means of the outer circle. Hence it will be evident, then, if the out- ward circle is also graduated toward the right hand, that the whole course will come under the imme- diate operation of the ' converting table,' as if the work had been performed with the needle ; and if TRAVERSE DIALLING. 159 the graduation should be reversed, the ' left-hand ' bearings will apply accordingly, regard being had to inversion in both cases. This instrument is also well adapted for taking the bearing of diagonal or underlaying shafts, having a lift of iron pumps a job that has often baffled the skill and ingenuity of diallers, and occasioned numerous and most serious errors. The operation may be performed thus : Sup- pose we are in the 60 fathom level, and from thence to the 100 the shaft was sunk on the course of the lode, on an underlay of 3 feet per fathom northerly. By applying the instrument at some point in the level near the shaft (but far enough away to be free from attraction by the pumps), we find the bearing by the needle, to a point opposite the shaft, to be due west, and the vernier on the outer rim standing at 90 ; we then remove the instrument to the shaft, where the light was held, and adjust the back observation as before directed, having 90 on the outer rim, and the needle thrown off as useless, because we are now close to the pumps. A light is to be carried down the shaft as far as it can be seen, and after the gradu- ated circle has been screwed fast, the rack is applied, and the sights turned until we cut the candle in the bottom of the shaft. This being done, we examine and read off the degree against the point of the vernier, which proves to be (say) 187f. Now, as when the instrument stood in a due west position the outer circle stood at 90, and in taking the bearing, it stood at 187J, therefore, by subtract- 160 TRAVERSE DIALLING. ing 90 from 187 J, we find the gain to the right hand of west is 97J, and, the underlay being northerly, the true bearing of the shaft is 7 J east of north. The imperative call for accuracy in cases of this kind will be seen when it is considered that the diagonal part of this shaft is upwards of 40 fathoms, and the underlay 3 feet in a fathom ; con- sequently, the whole base is more than 20 fathoms ; and an error in the bearing has the same effect on the survey as if it had been made in taking a hori- zontal draft of 20 fathoms long, and on which an error of 4 would throw the end of the line nearly 9 feet too far either to the right or left. Should a dialler be called to do a job of this kind in the absence of a suitable instrument, he may accomplish it in the following manner : Let him fix a cross-staff in such a position that, through one pair of sights, he can see the candle in the shaft, and in the line of the other parr he has the dial fixed in the level, out of the way of the attraction ; consequently, the light in the shaft, and the dial in the level, are two objects forming a right angle with his cross-staff. He then requests his assistant to look at a light held immediately over the head of his cross-staff, through the sights of the dial, and he finds this (say) 12 north of west : and as the bearing of the shaft is exactly at right angles with this line, if the underlay is northerly, the bearing of the shaft will be 12 east of north ; if southerly, 12 west of south. The best cross-staffs or instruments, for the express purpose of taking right angles, are now made of a hollow TRAVERSE DIALLING. 161 cylindrical shape, of brase, with cuts or apertures for taking the observation ; but a substitute may be used on a pinch, by drawing two lines at right angles on a board, about 6 inches square and an inch thick ; let these lines be cut half an inch deep with a fine saw, and then fix it on a three- feet stand ; if the lines are truly drawn and cut, this rough instrument will serve until a better one can be procured. CONSTRUCTION. The old method in laying down a traverse was by drawing a parallel line, and removing the pro- tractor at every draft. The evils of this practice are too glaring to require remark. Fix your protractor, and lay off as many drafts as will come within the convenient range of your parallel ruler ; number them in order as they stand in your dialling book ; remove the protractor, and lay off the first draft from the centre direct ; then apply the protractor to the centre and No. 2, and make the parallel movement until you touch the end of the last line, or No. 1, and then draw and point off the length of No. 2, and so on through all the drafts you have pointed off from the pro- tractor. The advantages of laying down or pointing off a number of drafts at one fixing of the protractor, and then applying them in their true length and position, is most conspicuous ; and the geometrician will testify of its superiority, both as it regards accuracy and expedition. M 162 TKAVERSE DIALLING. CONVERTING TABLE. Remarks on the following table for converting the de- grees recorded in the dialling book of an under- ground survey into the bearings. All practical men are aware of the difficulty, hazard, and delay that attend an attempt to obtain the bearing of every draft underground, in a long and complicated survey. The best process is to record the degree, or angle only, at which the needle settles, and after the work is finished under- ground, then convert the various angles into the real bearing or true direction of each draft, and we may remark, that the bearings must be obtained if the work is to be mathematically proved. But as it is not an easy matter to turn a long course of dialling into the bearings, with an assurance of being correct, this table has been constructed for that express purpose ; and its utility, simplicity, and perfection have been acknowledged by many prac- tical men. EXPLANATION. All circumferentors (dial or miner's compass) are not graduated alike. In all cases, 360 stands at the north point, and 180 at the south ; but some are figured toward the right hand, from the north point (which we call a 'right-hand dial'), and others toward the left hand ; so that a ' right- hand dial ' has 90 at the east point, and a ' left- hand dial ' has 90 at the west point. This diver- TRAVERSE DIALLING. 163 sity of graduation has often caused much perplexity and confusion among diallers. The following table is contrived to suit both sorts of instru- ments, and is so plainly arranged and marked as to require but little explanation. It must be specially regarded, that the table has been con- structed upon the consideration that the eye of the surveyor has been applied to the south sight or vane standing against 180; this must be inva- riably the case. Hence the north sight must always take the lead, and the young practitioner may here be told that in dialling a level and making double, or fore and back drafts, at every station, that although his eye must be placed at the north sight, necessarily, for the back observation, yet as the dial has not been turned, the needle will stand to the true degree for the record, and no confusion or liability to error can occur. In converting an underground survey, or any other, from angles into bearings, it is obviously our first object to know the graduation of the instru- ment by which the work has been performed ; and if it has been a 'right-hand dial,' and the first draft was 167, the bearing would be 13 west of south, but if it was done by a ' left-hand dial ' the bearing would be 13 east of south. The only thing where a liability to error at all exists in ob- taining the bearings by inspection from this table, and where caution is required, is in applying the fractions of degrees when they occur in the drafts. On these occasions, observe that when the angle and bearing progress alike, as in all the left-hand side M 2 164 TRAVEESE DIALLING. of the column, then the fraction must be added to the whole number of the bearing, but otherwise, as in the right-hand side, the fraction must be deducted from the whole number. Lastly, the following desirable proof may be resorted to : If the course has been correctly converted, the degree and bearing added together or subtracted from each other will make one of the following numbers : 0, 90, 180, 270, 360 ; and this may be done almost at a glance after the survey has been converted into bearings. TABLE FOR CONVERTING ANGLES INTO BEARINGS. Rt.Hd. Dial W. of N. Rt. Hd. Dial K ofW. Lt. Hd. DialE. of N. Lt. Hd. Dial N. of E. Rt. Hd. DialS. of W. Lt. Hd. DialS. of E. Rt.Hd.DialW.ofS. Lt. Hd. Dial E. of S. Angle Bearing Angle Bearing Angle Bearing Angle Bearing 1 is 1 46 is 44 91 is 1 136 is 44 2 2 47 43 92 2 137 43 3 3 48 42 93 3 138 42 4 4 49 41 94 4 139 41 5 5 50 40 95 5 140 40 6 6 51 39 96 6 141 39 7 7 52 38 97 7 142 38 8 8 53 37 98 8 143 37 9 9 54 36 99 9 144 36 10 10 55 35 100 10 145 35 11 11 56 34 101 11 146 34 12 12 57 33 102 12 147 33 13 13 58 32 103 13 148 32 14 14 59 31 104 14 149 31 15 15 60 30 105 15 150 30 16 16 61 29 106 16 151 29 17 17 62 28 107 17 152 28 18 18 63 27 108 18 153 27 19 19 64 26 109 19 154 26 20 20 65 25 110 20 155 25 21 21 66 24 111 21 156 24 22 22 67 23 112 22 157 23 23 23 68 22 113 23 158 22 24 24 69 21 114 24 159 21 25 25 70 20 115 25 160 20 26 26 71 19 116 26 161 19 27 27 72 18 117 27 162 18 28 28 73 17 118 28 163 17 29 29 74 16 119 29 164 16 30 30 75 15 120 30 165 15 31 31 76 14 121 31 166 14 32 32 77 13 122 32 167 13 33 33 78 12 123 33 168 12 34 34 79 11 124 34 169 11 35 35 80 10 125 35 170 10 36 36 81 9 126 36 171 9 37 37 82 8 127 37 172 8 38 38 83 7 128 38 173 7 39 39 84 6 129 39 174 6 40 40 85 5 130 40 175 5 41 41 86 4 131 41 176 4 42 42 87 3 132 42 177 3 43 43 88 2 133 43 178 2 44 44 89 1 134 44 179 1 45 45 rR.H.D.W. ^lLt.H.D.E. 1 135 45 180 South TABLE FOR CONVERTING ANGLES INTO BEARINGS. Rt. Hd. Dial E. of S.Rt, Hd. Dial S. of E. Lt. Hd. Dial W. of S. Lt. Hd. Dial S. of W. Rt.Hd.DialN.ofE. Lt.Hd.DialN.ofW. Rt.Hd.DialE.ofN. Lt.Hd.DialW.ofN. Angle Bearing Angle Bearing Angle Bearing Angle Bearing 181 is 1 226 is 44 271 is 1 316 is 44 182 2 227 43 272 2 317 43 183 3 228 42 273 3 318 42 184 4 229 41 274 4 319 41 185 5 230 40 275 5 320 40 186 6 231 39 276 6 321 39 187 7 232 38 277 7 322 38 188 8 233 37 278 8 323 37 189 9 234 36 279 9 324 36 190 10 235 35 280 10 325 35 191 11 236 34 281 11 326 34 192 12 237 33 282 12 327 33 193 13 238 32 283 13 328 32 194 14 239 31 284 14 329 31 195 15 240 30 285 15 330 30 196 16 241 29 286 16 331 29 197 17 242 28 287 17 332 28 198 18 243 27 288 18 333 27 199 19 244 26 289 19 334 26 200 20 245 25 290 20 335 25 201 21 246 24 291 21 236 24 202 22 247 23 292 22 337 23 203 23 248 22 293 23 338 22 204 24 249 21 294 24 339 21 205 25 250 20 295 25 340 20 206 26 251 19 296 26 341 19 207 27 252 18 297 27 342 18 208 28 253 17 298 28 343 17 209 29 254 16 299 29 344 16 210 30 255 15 300 30 345 15 211 31 256 14 301 31 346 14 212 32 257 13 302 32 347 13 213 33 258 12 303 33 348 12 214 34 259 11 304 34 349 11 215 35 260 10 305 35 350 10 216 36 261 9 306 36 351 9 217 37 262 8 307 37 352 8 218 38 263 7 308 38 353 7 219 39 264 6 309 39 354 6 220 40 265 5 310 40 355 5 221 41 266 4 311 41 356 4 222 42 267 3 312 42 357 3 223 43 268 2 313 43 358 2 224 44 269 i 314 44 359 1 225 45 27 {L.H.D.W. } 315 45 S60 North. TRAVERSE DIALLING. 167 APPLICATION OF THE CONVERTING TABLE. Suppose the needle stood at 2464 what is the bearing ? A f By a right-hand dial 231 South of E. ' r [ By a left-hand dial 23J South of W. It may be remarked that the table is equally applicable for changing bearings into angles if required. For example : An observation was made with a right-hand dial, and the bearing found to be 27 17' E. of N. : at what degree did the needle point ? Ans. 332 43', and if proof is required it will be seen that the sum of these degrees and minutes is 360. EXAMPLE. Convert the following angles taken with a left-hand dial into bearings : 305| 284 107 97J OPERATION. 210J is 30i W. of S. 210J-30i=180 176i 3J E. of S. 1764 + 34 =180 305J 35f N. of W. 305f -35| =270 281 284 E - of K 28 i ~ 28 i = 107| 174 S. of E. 107J -174 = 90 97 J 7| S. of E. 97| - 7 f = 90 348 12 W. ofN. 348 +12 =360 168 TRAVERSE DIALLING. EXAMPLE. Convert the following angles taken with a right- hand dial into bearings : 9 45' 239 25' 331 12' 160 58' 45 6' OPERATION. PROOF. 9 45' is 9 45'W.ofN. 9 45'- 9 45'= 239 25 30 35 S. of E. 239 25+30 35=270 331 12 28 48 E. of N. 331 12-1-28 48=360 160 58 19 2 W. ofS. 160 58+19 2=180 45 6 44 54 W. ofN. 44 54+45 6=90 N.B. In practice it would not be necessary or convenient to state proofs it is introduced here for the learner's sake, that he may be enabled to insure certainty in this essential matter. In pressing on our young mining friends the advantage of adopting a perfect system, we advise that in preparing a course of dialling for trigo- metrical solution, by changing the angles into bearings, care should be taken that all the drafts should be made either to exceed 45, or that they should all stand below, or at least not exceed that half quadrant. Our reason for being urgent on this matter is, that there may be a uniformity in placing the sides in the traverse table after the draft has been computed. And let it be par- ticularly noticed that, if the bearings are not suf- fered to exceed 45, that the last expression of the bearing will signify the longer of the two sides. That is, suppose a draft taken underground was 287 J, measuring 45 feet 8 inches; now looking at TKAVEKSE DIALLING. 169 the ' converting table ' we see that, if this draft was taken with a 'left-hand dial,' the bearing is 17 nor of west (or N. of W.), and the two sides will be found by computation to be 13 feet 7 inches, and 43 feet 7 inches. Query, into what columns respectively must these numbers be placed ? As the bearing was north of west, and our system states that ' the last expression of the bearing will signify the longer of the two sides,' consequently the longer side (43 feet 7 inches) must be placed in the ' west ' column, and 13 feet 7 inches in the north column. If this order is followed up, it will render the working of traverses (which is the most important operation in mine surveying) a plain, pleasing, and satisfactory exercise. In this edition we would needs bring forward everything likely to promote the advancement of the young mining officer in this paramount branch of his profession, and there- fore give him to understand that, in traversing, there must be a regular course from beginning to end. We shall make ourselves understood in this matter, by taking a case where a person makes a survey for the purpose of ascertaining the length and bearing of a level driven on an east and west lode ; and, for some convenient purpose, he begins his dialling at some point about the middle of the level, and dials from thence to the eastern end ; he then returns to the station or start at the middle of the level, and dials on to the western end, and thus completes the survey. 170 TKAVERSE DIALLING. Now if he were to proceed to work the traverse from his dialling book in this state, his results would appear as if his level were almost without length or bearing, as his eastings would be balanced by his westings, &c. In order to go systematically to work in this case, his first operation must be to reverse the order of one or the other of the diallings ; that is, if he pleases to let the first remain, which is the eastern dialling, and would accommodate the western part to suit the other, he must alter or reverse all the drafts by converting (say) 16 south of west into 16 north of east, and so of all the rest. In winding up this course of instruction, we will take a short survey, and go through with it at length, and the student may accompany us if he pleases ; for we are still of the same opinion as when we wrote the first volume, that practical teaching is the best. EXAMPLE. It is required to sink a vertical shaft on the end of a level, and the diallings from the bottom of an old downright shaft are as follows : Surveyed with a ' right-hand 1 dial. fath. ft. in. No. 1. 356$ Length 18 3 2. 84 12 i 6 3. 98 15 4 fath. ft. 4. A Winze 322 Underlay 25, Inclined Length 11 2 5. 107| Length. 25 5 6 End. This is the underground work, and our first TRAVERSE DIALLING. 171 operation is to find out the underlay of the winze, in order that it may stand as a common draft in the survey. OPERATION. The underlay, or angle made by the dip of the winze and a vertical line, being 25J degrees, we find it standing in the first table against 2 feet 7 inches, showing that every fathom of the winze gives a base of 2 feet 7 inches, and the length of the winze being 11 fathoms 2 feet, we multiply ft. in. i) 27 11-2 445 10 453 fath. ft. in. Here we find the base of the winze to be 4 5 3 The next thing is to refer to the converting table to reduce the drafts into bearings ; taking special notice that the work was done with a right- hand dial. We therefore find that No, 1. 356 J is 3|E. of N. 2. 841 _ 51 N. of E. 3. 98 - 8 S. ofW. Winze 4. 322 - 28 E. of N. 5. 107J - 17| S. of E. Our work is now prepared for entry in the traverse table as data for trigonometrical computa- tion. 172 TRAVERSE DIALLING. No. j ANGLES AND LINES TRIGONOMETRICAL RESULTS Draft Bearings Lengths East West North South fath. ft.in. 1 3fE.ofN. 18 3 2 5l N.ofE. 12 1 6 3 8 S. of W. 15 4 4 28 E.ofN. 453 5 17| S. ofE. 25 5 6 The above is the table with the bearings and lengths of the drafts entered in order for receiving the trigonometrical results in their proper and respective columns, and that everything may be clear to the learner we shall let this table remain as it is, and make a similar one, in which the computations are entered, and proceed to take out the tabular numbers from the first mathematical table, and multiply them by their respective lengths. FIRST DRAFT. ft. in. L 3 Tabular 4-7 ft. in. Tabular 5 11 -85 2 2-2 3 6 6-6 2-3 6 8-9 Easting. 35 11-10 3 107 9^30 2 11-92 110 9-2 Northing. Now the sides of the triangle formed by the first draft are ready to be transferred to the east and north columns of the traverse table. TRAVERSE DIALLING. 173 SECOND DRAFT. ft. in. ft. in. L 5 Tabular 6-9 Tabular 511-67 12* 6 10-8 1-7 7 0-5 Northing. 73 7'3 Easting. When the bearing does not diverge much from the cardinal point, there is but little difference between the length of the hypothenuse and the longest of the legs, as in the right-hand sides of the above two drafts. THIRD DRAFT. ft. in. ft. in. L 8 Tabular 10-02 Tabular 5 11-8 8 8 6 8-16 47 6-4 2 2 13 4-32 95 0-8 3-31 1 11-8 13 1-0 93 1-0 Westing. The length of the draft being 15 fathoms 4 feet, we have multiplied by 16, and deducted j as the shortest method. FOURTH DRAFT, OR BASE OF WINZE. ft. in. in. ft. in. in. / 28 Tabular 2 9-8 or 31-8 Tabular 5 3-6 or 63'6 5 5 169-0 318-0 4-2 7-9 12)164-8^ 12)310-1 "ifrfrS Easting, 25-1Q-1 Northing. 174 TRAVERSE DIALLING. In the above, it will be seen that we have thrown the tabular length into inches and parts, and the practitioner will find this, in general, the easiest way of calculating. FIFTH DRAFT. ft. in in. ft. in. in. Zl7f Tabular 1 1OO or 22'0 Tabular 5 8-6 or 68'6 26 26 132 411-6 44 1372 572-0 1-8 12)570-2 47-6-2 Southing. 1783-6 5-7 12)1777-9 148-1-9 Now the computations are ready for entry in the following table : No. ANGLES AND LINES TRIGONOMETRICAL RESULTS Draft Bearings Lengths East West North South 1 2 3 4 5 3| E. of N. 5} N.ofE. 8 S. of W. 28 E.ofN. 17| S. ofE. fath.ft.in. 18 3 12 1 6 15 4 453 25 5 6 ft. in. 6 8-9 73 7-3 - 13 8-8 148 1-9 ft. in. 93 1-0 ft. in. 110 9-2 7 0-5 25 10-1 ft. in. 13 1-0 47 6-2 242 2-9 93 1-0 93 1-0 Easting. 143 7-8 60 7.2 60 7-2 Northing 149 1-9 83 0-6 Now we might proceed to lay down the position or place of our new vertical shaft at the surface without any further operation. For by measuring off from the centre of the old shaft at surface 149 feet 2 inches, due east, and from the end of that line measuring 83 feet, due north, would bring us exactly over the end of the fifth or last draft, where TRAVERSE DIALLING. 175 the shaft is to come down, but we would work out the direct length and bearing also, as before de- scribed, and apply it. PROBLEM. At the celebrated South Caradon Copper Mine a new vertical shaft was commenced in the early part of 1842, which is intended to intersect the main lode at the depth of 100 fathoms below the adit level, which is about 40 fathoms from surface in the vicinity of the new shaft. From a point in this level, a drift or cross-cut has been begun, and designed to be driven in a direct line to the centre of the new shaft, and from thence to rise against it, if necessary : and the aim and object of the survey is to ascertain the exact length and bearing of the said cross-cut, as every proper means have been adopted to certify that it has been commenced at the nearest point to the shaft. The following is the whole course of dialling in its most simplified form, with the irregular surface lines reduced to horizontal measure, the angle of every draft converted into bearing, and the whole given in complete order for working the traverse without any preliminary preparation. The draft standing on the top of 934 feet is from the centre of the new shaft at surface to a line hung in the old engine shaft, which is also vertical to the adit, and the next draft is taken from that line in the adit and continued to the end of the 34th draft, 176 TRAVERSE DIALLING. through the same level, where the cross-cut com- mences. It is also required to furnish the bearing of the lode from the 3rd to the 34th draft inclusive. REMARKS. As this course of dialling has been rendered so plain, there appears to be no occasion to introduce a double entry of it, as the field and underground work is sufficiently manifest in the first three columns of the following table, in combination with the trigonometrical operation. It may be satisfac- tory to the student to be informed that this work has been accomplished and proved to be perfectly correct. The cross-cut was driven ah 1 the way (50 fathoms) through a hard granite country, at nearly 1000Z. cost, and occupied full two years of uninter- rupted labour. TRAVERSE DIALLING. 177 COMPUTATION. No. AXGLES AXD LINES TRIGONOMETRICAL EBSULTS Drafts Bearings Lengths | East West North South From new Shaft to Engine Shaft. ft. in. ft. in. ft. in. ft, in. ft. in. 14 18' S. of W. 934 . 905 0-7 . 230 8-3 1 13f S. ofE. 30 29 0-7 - - 7 1-6 2 4f E. ofS. 30 6 2 6-3 . - 30 4-8 On course of lode. 3 5 S. of E. 28 6 28 4-5 - - 2 8-8 4 4 N. ofE. 42 6' QA Q 42 4-7 - 2 11-6 8 5*4 5 6 16 S. of E. 2 do. oU o 32 31 11-7 . . 1 4-7 7 18i do. 29 2 10 f\ 27 8-9 - " - - 9 1-6 1 4'0 9 4-|- cio. 3 N. of E. lo U 36 35 10-2 . 2 2-4 10 13 S. ofE. 17 16 6-8 . . 3 9-9 11 19f do. 26 6 24 11-2 . . 8 11-4 12 14 do. 22 7 j 21 11-0 . . 5 5-6 13 15 do. 36 3 35 O'l - - 9 4-6 14 1 do. 46 6 46 5-9 - - 9-8 15 17 N. ofE. 41 3 39 5-4 - 12 0-7 16 4 do. 11 2 11 17 - 9-3 17 2U do. 12 8 11 9'4 - 4 7-7 18 1 do. 27 27 0-0 . 5-7 19 2 do. 38 8 38 7-7 . 1 4-2 20 1 S. ofE. 18 18 0-0 . . 3-8 21 20 do. 12 6 11 8-9 . . 4 3-4 22 7 do. 11 6 11 5-0 - - I 4-8 23 1 do. 25 8 25 8-0 - - 5-3 24 4 N. ofE. 31 6 31 6-1 - 2 2-3 25 13 S. of E. 34 6 33 7-4 - - 7 9-1 26 1 N. ofE. 18 8 18 8-0 - 3-9 27 5 do. 28 27 10-7 . 2 5-3 28 8 S. ofE. 65 64 4-4 . . 9 0-6 29 2 do. 36 6 36 0-4 - - 1 3-3 30 5 do. 18 17 H-2 - - 1 6-8 31 6A N. of E. 24 8 24 6-0 - 2 9-5 32 1 do. 12 3 12 3-0 . 2-6 33 18 do. 29 6 28 0-7 . 9 1-4 34 12 do. 20 1 19 7'8 - - 4 2-1 899 6-1 905 0-7 45 8-7 345 9-6 899 6-1 45 87 Westing 5 4-6 Southing 300 1-9 178 TRAVERSE DIALLING. Then by the foregoing method of proceeding, the required answers will be found as follows : Length of cross-cut from adit to centre of shaft, 300 feet 2 inches. Bearing of cross-cut 1 2' west of north. Bearing of lode from 3rd to 34th draft, inclu- sive, 2J south of east. PROBLEM. A lode was opened on the back by costeening in several places, and its course, by compass, found to be 10J south of east ; but this was on the ascent of a steep hill whose angle of elevation was 16J, and the lode underlaying northerly three feet in a perpendicular fathom. Query. What is the true bearing or course of the lode? and what would be the amount of error in carrying on the line 600 fathoms (horizontal measure), supposing the run of the back of the lode on the ascent had been taken, by mistake, instead of the true horizontal course ? OPERATION. We find in the first table that 16J of elevation gives 1 ft. 845 in. perpendicular, and 5 ft. 9*04 in. base for the corresponding sides of the triangle. ft. ft. ft. in. Hence If 6 perp. gives 3 underlay, what will 1 8*45 give ? _12 _12 12 _ 72 36 20-45 36 72)736-20(10-2 TRAVERSE DIALLING. 179 Showing that the underlay of the lode carries the line 101 inches further north than the line taken at the surface (or bearing) on every horizontal line of 5 ft. 9-04 in. Therefore we have the two sides of a right-angled triangle 5 ft. 9-04 in. and 10-2 in., and the angle opposite the shortest side will be the amount of the angle of error. ft. in. in. ft. As 5 9-04 : 10-2 :: 6 12 12 69-04 72 10-2 in. 69-04)7 34-4(10-63 By inspection of the 2nd table we find the nearest next less angle standing opposite this number (10-63 in.) is 8 15', giving 10-44 in. ; and as the difference between this and the next greater (8^) is '32, and the difference between 10-63 in. and 10 -44 in. is -19, we say, As -32 is to -19, so is 15' = 9'. And 9 added to 8 15' gives 8 24' for the angle of error ; and by deducting this angle of error (if it may be so called) from the course of the lode on the inclined surface (10J south of east), we have 2 6' south of east for the true bearing of the lode ; and as the error is 10*64 in. in a horizontal fathom, this number multiplied by 600 gives 6384-00 inches, or 88f fathoms, too far south, on a line of 600 fathoms. N 2 180 TRAVERSE DIALLING. REMARKS. We beg to call the particular attention of our young mine agents to this case. The vast sums of money expended every year in this country in costeening or right-angle open cuttings at the surface in searching for lodes, is well known to practical men ; and probably there is no branch of mining in which there is a greater waste of time and money. Workmen are often put to co- steen at random, when a scientific survey might have put them in a position for opening the lode in a few hours which has occupied them for weeks or months, and at the last all their labours fraught with doubt and uncertainty ; but these are not the worst consequences arising from ignorance or in- attention to this subject. I know a rich mine in this county, where the angle of ascent was made in error, and carried on to find the lode in the ad- joining set, and the effect was, that they pitched to cut the lode in a new set nearly 200 fathoms out of the line ; and they have been driving now nearly five years through a hard country at a cost of some thousands of pounds, and have not yet cut the lode ! Volumes might- be written on the errors that have taken place from this source ; and probably there is not a man of experience to be found but what can confirm the report with his testimony. PROBLEM. In a 20 fathom level driving on an east and west lode, underlaying north, a winze has been TRAVERSE DIALLING. 181 commenced bearing due north, and it is determined to pitch a rise against it in the 40 fathom level (the 30 fathom level not having been driven far enough east to rise from). The following is a state- ment of the dialling from the middle of the above winze, in the 20, through the level west towards another winze sunk to the 30 fathom level : No. ft. in. 1 2824 59 10 2 286* 61 8 No. ft. in. 3 264J 33 4 4 2604- 77 3 This brings us to the brace of the winze com- municating with the 30 fathom level, which we may call No. 5, its diagonal length, 65 feet ; under- lay, 22| degrees ; bearing, 9 east of north. From the foot of this winze in the 30, the dialling is con- tinued westerly to another winze communicating with the 40 fathom level ; viz. : No. ft. in. 6 272i 60 9 7 256~ 52 8 287J 45 8 We now arrive at the brace of the winze to the 40, which we call No. 9, length, 70 ft. 6 in. ; under- lay, 314 ; bearing, 4 west of north. From the bot- tom of this winze in the 40, the course turns easterly, and is continued in that direction ; viz. : No. ft. in. No. ft. in. 10 83 85 4 13 90 77 6 11 77 28 5 14 924 23 8 12 1 O/l 1 76 15 99 107 2 182 TRAVERSE DIALLING. At the end of this 15th draft we place an assumed mark in the back of the 40 fathom level. Question. It is requested to know how far we must measure east or west from this mark in order to arrive at the exact point for rising against the winze sinking from the 20 fathom level ? also what will be the average underlay at that place, and what will be the length of the winze from the 20 to the 40 fathom level ? COMPUTATION. (SURVEYED WITH A LEFT-HAND DIAL.) No. ANGLES AND LINES TRIGONOMETRICAL RESULTS Draft Degree Bearing Length East West North South ft. in. ft. in. ft. in. ft. in ft. in. 1 282^ 12^ N. of W. 59 10 - 58 6 12 8 2 286 16 N. ofW. 61 8 . 59 3 17 3 264 5* S. of W. 33 4 . 33 2 3 2 4 "2604 9| S. of W. 77 3 . 76 2 . 13 1 5 Winze 9 E. ofN. 24 10 4 . 24 6 6 272 2 N. of W. 60 9 . 60 8 2 8 7 256 14 S. of W. 52 . 50 6 . 12 7 8 287 17i N. ofW. 45 8 . 43 7 13 7 9 Winze 4 W. of N. 36 10 . 2 7 36 9 10 83 7 N. of E. 85 4 84 8 10 4 11 77 13 N. ofE. 28- 5 27 8 _ 6 5 12 104 14 S. of E. 76 73 8 . 18 9 13 90 East 77 6 77 6 14 924 2 S. ofE. 23 8 23 8 . . 1 15 99' 9 S. of E. 107 2 10510 - - - 16 9 397 384 5 12311 65 4 384 5 65 4 Easting 12 7 Northing 58 7 Now, we discover by the foregoing calculation that our assumed mark in the 40 fathom level is 12 feet 7 inches too far east for the central point of TRAVERSE DIALLING. 183 the rise against the winze sinking from the 20, and which was the paramount object required. NOTE. As the last draft (reversed) is 9 N. of W., in order to be quite accurate it will require us to measure 12 feet 9 inches back through the level to make good 12 feet 7 inches westing, and this will give 1 foot 10 inches more of base or northing, which added to 58 feet 7 inches, the underlay shown by the column of northing, will give the answer to the question, 60 feet 5 inches for the whole underlay. The first operation in working this problem is to find the base and perpendicular of the two winzes numbers 5 and 9, and their respective bases form the operative lines in the above traverse. ft. in. ft. in. Winze No, 5 gave 24 10 base, and 60 1 perpendicular. Winze No. 9 gave 36 10 base, and 60 1 perpendicular. Now the vertical depth being 120 2, and the base or northing 60 feet 5 inches, we have thus the two sides of a right-angled triangle to find the hypothenuse and dip or angle of declination, which on trial will be found Hypothenuse, or length of winze, 134 feet. Angle, or underlay of winze, 26 degrees. PROBLEM. A tunnel has been commenced at the foot of a hill, and is intended to be driven through it. The bearing from the above point, or the course of the tunnel, is to be due east, and it is required to know the exact corresponding point on the other side of the hill, in order to set another company of men to drive a dead level to meet the drivings that are progressing from the west side. The length of the tunnel is also required. 184 TRAVERSE DIALLING. The following is the survey from the first point : ft. No. 1 Elevation 14 Length 26 2 12J 26 3 11 17 4 _ 18J 90 5 10 60 6 74 119 7 Horizontal 29 8 Depression 5| 28 16 230 Judging that we have now arrived somewhere near the level or horizontal plane of the start, or that our ' depressions ' have made good our * ele- vations,' we place an assumed mark at the end of the last or 9th draft, and retire to work out our lines and angles by trigonometry. OPERATION. PERP. BASE. fath. ft. ft. in. ft in. No. 1 Elevation 14 Length 4 2 Tabulars 1 5-4 5 9'9 5 9-6 23 3-6 5-8 1 11-3 6 3-4' 25 2 : 9 Thus we find the 1st draft gives a rise or eleva- tion of 6 feet 3*4 inches, and base or horizontal length 25 feet 2' 9 inches ; and proceeding in the same manner with all the drafts, and finding the difference between the elevations and depressions, TRAVERSE DIALLING. 185 we shall obtain true data for correcting our assumed mark, and replacing it in its proper position. Elevation Horizontal ft. in. ft. in. No. 1 gives 6 34 and 25 2'9 2 5 6-2 25 4-9 3 3 2-9 16 8-3 4 28 6-0 85 4-0 5 10 5-0 59 0-1 6 14 8-5 118 1-0 68 8-0 7 29 0-0 Depression gives 2 8-2 27 10'5 9 63 3-8 220 3-0 66 00 606 10-7 Now as the depressions are 2 feet 8 inches less than the elevations, it demonstrates that our as- sumed mark is 2 feet 8 inches too high, and as the declination of the ground from the last draft east- ward continues on the same angle of depression of 16 degrees, we have perpendicular 2 feet 8 inches and angle 16 to find the corresponding hypothe- nuse and base ; and by inspection of the 2nd table we see that the 4 tabulars ' opposite 16 are 1 foot 8-6 inches, and 6 feet 2-9 inches hypothenuse Therefore, if 1 foot 8'6 inches give 6 feet 2*9 inches, what will 2 feet 8 inches give ? Which will be found to give 9 feet 8 inches of hypothenuse. And by the 1st table it will be found that 9 feet 186 TRAVEBSE DIALLING. 8 inches of hypothenuse on an angle of 16 will give for the longest side, or base, 9 feet 4 inches. ADJUSTMENT. By removing the assumed mark 9 feet 8 inches, due east on the slope, we fix on the exact spot for commencing the eastern end of the tunnel, and we need hardly observe, that the two extreme marks mean the bottom or floor of the tunnel. Then by adding the base, 9 feet 4 inches, made by the corrections, to the sum of the horizontals, 606 feet 10-7 inches, we have just 616 feet 3 inches for the length of the tunnel. NOTE. Should it be required to put down vertical shafts on the tunnel, the foregoing computations reveal what their depths would be respectively at all parts of the tunnel, and the deepest shaft would be 1 1 fathoms 2 feet 8 inches at the end of the 6th draft, and 55 fathoms from the western mouth of the tunnel. PEOBLEM. It is intended to sink a shaft on the end of a level driven from Pendarves' shaft, and the follow- ing is the survey from the centre of Pendarves' shaft to the end of the level, viz : No. 1 3 2 71 3 8j 4 5 12 W. of K N. of E. N. of E. East S. of E. ft. 45 24 18 49 30 in. 6 1 No 6 7 8 9 10 15 5 S. S. N. N. W of E. of E. of E. of E. . of N. ft. 27 16 21 14 28 in. 5 7 As profound accuracy is required in this case (it being intended to facilitate the work by rising TRAVERSE DIALLING. 187 against the new shaft from the end of the level), a reverse or proof course of dialling -has been made from the end back to the centre of Pendarves' shaft ; viz. : ft. in. No. ft. in. 26 10 6 li S. of W. 44 7 7 S. of W. 26 8 9| S. of W. 22 8 9 24- E. of S. 43 10 No. 1 84 2 11 3 4| 4 13 5 E. of S. S. of W. S. of W. K of W. 15 19 20 JST. of W. 52 It is now required to know if there is an exact agreement between these two surveys, or fore and back diallings (or what is the difference between them), and if so, what is the length and bearing from the centre of Pendarves' shaft, at the* surface, to the point exactly over the end of the level where the centre of the new shaft must be fixed ? OPERATION. FROM PENDARVES' SHAFT TO EASTERN END. No. ANGLES AND LINES TRIGONOMETRICAL RESULTS Drafts Bearings Lengths East West North South ft. in. ft. in. ft. in. ft. in. ft. in. 1 3 W. ofN. 45 - 2 4-2 44 11-2 2 7i N. of E. 24 6 24 3-7 . 3 1-1 3 8 N. of E. 18 17 9-6 . 2 7-9 4 East 49 1 49 1-0 5 12 S. ofE. 30 29 4-1 - . 6 2-8 6 6| S. of E. 27 26 9-8 - . 3 2-1 7 15 S. of E. 16 5 15 10-3 - - 4 3-0 8 5 N. of E. 21 20 11-0 - 1 10-0 9 10 12|N. ofE. 9 W. of N. 14 7 28 14 3-0 4 4-6 3 1-1 27 7-9 198 4-5 6 8-8 83 3-2 13 7-9 6 8-8 13 7'9 Easting 191 7'7 Northing 69 7'3 188 TRAVERSE DIALLING. PROM EASTERN END TO PENDARVES' SHAFT. No. ANGLES AND LINES TRIGONOMETRICAL RESULTS Drafts Bearings Lengths Bast West North South ft. in. ft. in. ft. in. ft. in. ft. in. 1 2 8 S. of E. 11 S. ofW. 26 10 15 3 11 6 14 8-7 ; 26 6-5 2 10-3 3 4$ S. ofW. 19 6 19 5-2 . 1 7'4 4 131 N.ofW. 20 19 5-6 4 70 5 9} N.ofW. 52 3 51 6-5 8 75 6 1} S. of W. 44 43 11-9 . 11-5 7 7 S. of W. 26 25 9-7 . 3 2-0 8 9 9J S. ofW. 2} KofS. 22 8 43 10 1 8-6 22 4-1 . 3 10-1 43 9-6 5 8-2 197 3-7 13 2-5 82 9-4 5 8-2 13 2-5 Westing 191 7-5 Southing 69 6-9 Now we find that as the westing and southing of the back dialling corresponds with the easting and northing of the direct dialling to the fraction of an inch, it amounts to a mathematical demonstration of the perfection of the underground survey. It now only remains for us to obtain the hypothenuse and angle opposite the base of the two given sides of the triangle formed by the easting 191 feet 7J inches, and northing 69 feet 7 inches, which will be found to give Length (from centre of Pendarves' shaft to point over end), 203 feet 11J inches. Bearing 20 degrees north of east. N.B. After this length and bearing has been applied at the surface, and the point fixed for the centre of the new shaft, an infallible and desirable proof that this last and important work has been TRAVERSE DIALLING. 189 done correctly may be obtained by availing our- selves of the ready means placed within our reach by the cardinal points or sides of the great triangle. Thus, by measuring off from the centre of Pen- darves' shaft 191 feet 7f inches due east, and then from the end of that line 69 feet 7 inches due north, the end will fall exactly on the point fixed at the end of the line 203 feet 11 J inches on the bearing of 20 degrees north of east, if the whole has been done correctly. 190 PLANS AND SECTIONS OF MINES. PERSONS who have not had practical experience in mining often acknowledge that they find great diffi- culty in comprehending the plans and sections of a mine, or of having a true idea of the workings from an inspection of the drawings. This obscurity may be occasioned from an imperfection in the plans ; for if they have been executed under a good system, it can hardly fail to exhibit clearly every part of the workings, and, indeed, if the diagrams have not been executed perfectly, and according to rule and order, even miners themselves cannot comprehend them. It requires four distinct ma- thematical or geometrical drawings to represent a mine, which we will briefly notice under each head ; and we may observe, as we pass on, that the common cause of people in general not understand- ing the plans is because they expect to know too much from one single drawing. Every separate plan exhibits both a true and false view of some parts of the mine ; and the knowledge necessary for the observer is, what parts of the workings it is that each drawing furnishes a true delineation of. jWith this introduction we proceed to state that the set of drawings may be described thus : PLANS AND SECTIONS OP MINES. 191 1. Ground plan. 2. Horizontal or working plan. 3. Longitudinal section. 4. Transverse section. And taking them in the order in which they have been placed, we begin with (1.) THE GROUND PLAN. This is, in the main, a general survey of the whole set, or land granted to the adventurers for the purpose of mining. This plan may be on a scale of three or four chains to an inch ; and every lord or landowner's bounds should be distinctly marked on this map. All the lodes are laid down with their true position and course on this plan, as far as they can be ascertained; and we may remark, that this survey should be made at the outset or plant of a mine, and before anything has been determined as to the position of an engine shaft, or any other important work, so that the manager may have the benefit of this map, with the lodes, cross courses, and every necessary thing faithfully de- lineated thereon, to assist his judgment in forming the most judicious arrangement for future opera- tions. For want of this precaution, how often is it that shafts have been sunk in improper places, to the endless disadvantage of the company; and sometimes they have been abandoned and new shafts sunk, at a fearful loss of time and money! In fact, we believe there are but few mines where the conductors have not had cause to regret," 192 PLANS AND SECTIONS OP MINES. ultimately, that they had not taken another po- sition for sinking the principal shafts, and which might have been known, at the outset, if the necessary steps had been pursued. On this map it should be particularly pointed out if there is any intervening ground on the course of the lodes that has not been legally granted, so that proper applications may be made in due time, and not leave it until the workings have been commenced, and good discoveries made, and then this landowner, taking advantage of the neglect or oversight, demanding an unreasonable premium and dues for his land, or prohibiting us from driving an inch under it, on pain of knocking us to pieces with the powerful arm of the lord warden of the stanneries. Among the many inconveniences that have arisen from this cause, I select one that occurred in this neighbourhood some eight or nine years ago. A silver mine called Wheal Sisters, in the parish of Calstock, was in full work, and just at the zenith of her glory. Everybody concerned with the mine, in the shape of London directors, local directors, managers, secretaries, agents, shareholders, &c., thought assuredly (if they ever thought at all) that all the land in the set belonged to the duchy of Cornwall, for no survey such as we have been speaking of had ever been made. But it so turned out, that a field under which the levels had just been driven was freehold ! And what was the consequence ? Why, forth came the proprietor in the person of Michael Williams, PLANS AND SECTIONS OF MINES. 193 Esq., of Scorrier House, and says, ' Stop ! ' Well, but she did not stop then ; no, she went on faintly, but in an expiring state, after exhausting her resources in paying the peremptory demand of Mr. Williams. How much was that? Exactly 5000/. ! Yes, and that gentleman was paid every shilling of it ; and I believe not 10/. of silver ore was broken in his ground afterward. And let it be known, this enormous sum was for the dues only ; the little field is still the property of its original owner. This affair is well known, and is calculated to put parties on their guard respecting their mining rights and liabilities. So much for the map of the set or ground plan. (2.) HORIZONTAL OR WORKING PLAN. This is the miner's plan, his chart, his guide, his right hand. Whoever attempts to conduct the operations of a mine without a perfect working plan, is unfit for his office. The very circumstance of his supposing himself capable of doing so is a certain proof of his ignorance. This plan gives what surveyors call ' a bird's eye view ' of the mine ; or let us suppose that the ground was transparent, and by walking over every part at the surface we could look down and distinctly see all the workings. A person who never saw a mine will understand from this view that he could distinguish the course of the levels in all their turns and windings, and, 194 PLANS AND SECTIONS OF MINES. as respects all the ' horizontal ' drivings, he would have a true view of them; but these drivings are the only thing that he would obtain a true view of in this plan. Keeping his position in view, he hardly requires to be told, that he can only see the brace or mouth or base of all the vertical or downright shafts, even if they were 200 fathoms deep. As for the diagonal shafts or winzes (which are small ventilating shafts sunk on the declination of the lode from level to level), he would only see the 'underlay' of them, or the distance that they diverge from a perpendicular line. As lodes, almost if not altogether without an exception, have a dip or declination, called by miners ' underlay/ it follows that the levels are generally removed away from the vertical line, and not concealed one by another, although this is sometimes partially the case when there is a reverse or change of underlay. In addressing myself to the miner, in reply to his question or inquiry respecting the best method of constructing and keeping up a working plan, I will endeavour to explain the system I always adopt, and which I believe is the best, at least I have found it so, after thirty years' ex- perience. Let the scale be five fathoms to an inch. Before you begin to lay down any part of the workings, draw faint lines throughout the whole length and breadth of your sheet of drawing paper at right angles, forming two-inch squares ; these lines will be your cardinal points. If your lode bears east and west, the longest way of the paper PLANS AND SECTIONS OP MINES. 195 will of course be appropriated for that bearing. These lines are always to remain ; and as they are to be single, and fine, and the course of your levels drawn with double lines, they will not in the least confuse, especially as your levels must be distinctly and variously coloured between the double lines (which represent the breadth of the level), so that every level, with ah 1 its drifts and connections, may be distinguished in a moment or two, however numerous or complicated your levels and drivings may be. One grand advantage of these cardinal cross lines is, that every intersection forms a proper and suitable point for laying on the centre of the double-limb protractor or any other, on all oc- casions, so that in keeping up the plan or laying down any additional drafts, there is always a point close at hand for the protractor, without the inconvenience and risk of bringing on a north and south line, for the purpose, from a distant part of the paper. Another convenience of these lines is, that the bearing of the lode, or any part of it, may, by their help, be obtained in a few seconds ; for instance, as every side of one of the squares gives 10 fathoms, when a level has been laid down, we can, by inspection, see very nearly (and by the application of a scale exactly) what it has diverged to the right or left from the main course, and if we find it to be (say) 125 fathoms east, and 19^ fathoms north, the tables will tell us that the bearing is 8 50' north of east ; and, by the same means, we may always check or prove the truth of the plan or the construction by trigonometrical o 2 196 PLANS AND SECTIONS OP MINES. computation, and which should always be done before the plan is relied on, or pronounced perfect. This plan, proved and well kept up, becomes in- valuable to the mine agent. Does he want to sink a winze in one level and rise against it in another ? Everything he can wish for is before his eyes. The two corresponding points for the sink and rise, the amount of underlay, the bearing, the length of the winze and its vertical depth, are all embodied in the plan. Has the lode split, and have the workmen driven on the wrong branch ? look at the plan, and compare notes with the general bearings, and the course to be adopted will be apparent. I have known a case where the plan betokened that a mis- driving had taken place in a level, but the agent persisted that the driving was right in spite of the plan ; however, the manager, having more confidence in computation than in conceit, was convinced by the indications of the plan that they were gone off the main branch, and ordered them immediately to ' turn house,' or cut north at right angles : this was done, and in driving two fathoms, the main lode was discovered with a large and rich course of copper ore. (3.) LONGITUDINAL SECTION. This drawing supposes that a section of the ground has been cut away, and that a side view of the mine is exposed. If it is an east and west run, the observer is placed at the south of the mine, and taking a panoramic north view of all the exca- vations. PLANS AND SECTIONS OF MINES. 197 In this position he will have a perfect sight of all the vertical shafts, and a general view of the stopes, or ore ground broken away between the levels, also the dip of the courses of ore may be portrayed and distinguished, and the surface line of the country, with a perspective view of the buildings and machinery, may be seen or exhibited fairly by this section. But the levels, diagonal shafts, cross- cuts, and winzes, will have a false or imperfect ap- pearance here. For instance, the levels will appear to be perfectly straight, however serpentine or crooked their course may be. The diagonal shafts and winzes will appear to be perpendicular, because their dip is in the line of the inspector's eye ; and as an end view will be taken of the north and south cross-cuts, the extent of these drivings will not be seen. The only real benefit of this section to the miner is, that it may be so contrived as to show the dip, or inclination, or declination, of the bunches or courses of ore, and this circumstance he may turn greatly to his advantage in working the mine. For ex- ample, suppose in driving the 50 fathom level, going east, we cut into a course of ore, and it lasted 25 fathoms in length ; let these two points of the ' coming in ' and ' going out ' of the course of ore be correctly marked in this 50 fathom level of this section. In the 60 fathom level, or next level below, the same course of ore was cut 4 fathoms farther west than it was in the 50, and the course of ore at this level proved to be 28 fathoms long. Let these 198 PLANS AND SECTIONS OF MINES. points also be marked on the section, and as there is a general regularity in the dip of ores, the agent is now in possession of a clue, whereby he may form a reasonable judgment at what place the course of ore will come in at the 70 fathom level, or levels still deeper, and also at what point it will fail in driving east, hence he will be better qualified for setting tribute with the help of this section than if he had no such guide. The longitudinal sketches that are usually shown in mines, with a pell-mell blotch of the stopes, and, as we have shown, the false view of the levels, diagonals, and winzes, are useless to the miner, and deceptive to the stranger. (4.) TRANSVERSE SECTION. Here the view is taken at one end of the workings. Suppose again the drivings to be east and west, and the dip of the lode northerly, the observer is placed at the west end, with his face easterly. Now, for the first time, he will have a fair view of the decli- nation of the shafts and winzes that have been sunk on the course of the lode, and thereby he will see all the dip and variations of the lode from the surface to the bottom of the mine. Here he will see the northing and southing made by the cross- cuts, and if a vertical shaft is in sinking to take the lode at a certain depth, the point of intersection will be apparent to his view. Eespecting the levels driven on the course of the lode, he will only see their western end. If there has been no diagonal shaft, but the mine has been worked by a downright PLANS AND SECTIONS OF MINES. 199 sump or engine-shaft, this section will exhibit a regular and correct view of all the drifts or cross- cuts, from the shaft to the lode, and from this data, or the extreme ends of the cross-cuts, the 'declina- tion of the lode will be conspicuous. The trans- verse view of the surface line will finish ah 1 that can be fairly seen by this drawing. OBSERVATIONS. After such a detail we think there will be no occasion for ' summing up,' or repeating to the inquisitive stranger, or adventurer, what may be seen, and what may not be seen, on each and every drawing. To the practical man, or with him, we may converse of the best and readiest means of making these drawings. Let us suppose the hori- zontal or working plan to be drawn and executed, and proved in a correct and masterly manner, and all the vertical shafts truly dropped or measured. We are then in possession of every thing necessary for drawing the two sections without going out of the office ; for by parallels, or a drawing board and slides, all the shafts, winzes, &c., may be transferred from the plan to the paper prepared for the sections, with despatch and accuracy. True, we may have recourse to the dialling book for the position, length, height, and depth of the stopes and sinks ; and if a perspective drawing of that part of the set where the buildings are placed should be required, a sketch must be made for that purpose. To the learner we would observe, that, if he is about to survey a mine and draw a working plan, 200 PLANS AND SECTIONS OF MINES. let him lay down his shallow adit, or the upper levels, first, and the others in succession ; because, wherever any crossings take place, or one level or draft passes immediately under another, the upper level must be entire or unbroken, and the under level will not be shown, as a matter of course, be- ing necessarily obscured or concealed by that part of the workings that passes immediately above it. One method of proving his work as he proceeds is as follows : Suppose he has surveyed the adit level, and there are four winzes communicating with the 10 fathom level, and he has taken the bearing, and depression, and length of those winzes, and plotted or laid down this level and the true base of those winzes on his working plan. He then proceeds to survey the 10 fathom level, making good every thing as he proceeds ; and of course when he arrives at the foot of those winzes which he surveyed in the adit, he minutely enters in his dialling book the mark at their foot, where he took his diagonal observation and measurement. Then in laying down his 10 fathom level, if all his work has been well done, the points in those winzes will exactly correspond" with his survey in the 10 fa- thom level and on the plan, and this desirable check he may and should pursue throughout the whole survey. It is too common in these cases, in order to avoid the time and labour in surveying the winzes, to ' let them take their chance,' by merely entering their ' brace ' in one level and 4 foot ' in another, and let the truth of their re- spective bearings and underlay depend on the PLANS AND SECTIONS OF MINES. 201 horizontal survey of the levels. This practice is reprehensible, and should never be tolerated. But with all this precaution, we advise, by all means, that every part of the plan be proved by trigonome- trical computation, and the surveys by fore and back diallings. Let us suppose we have surveyed a level by double diallings. How shall we ascer- tain if there is a perfect correspondence? We have introduced a problem on this subject, and it is plain that the final two sums of the traverse will demonstrate either the agreement of the difference. This being done, and the underground work proved correct, we proceed to construct or draw the level on the plan, and it is most desirable that we should know if this part of the work has been well exe- cuted ; and as we have computed the workings, we are furnished with a ready and certain test. Sup- pose we found, by computation, that the level gave, from beginning to end, 184 fathoms 3 feet of southing, and 34 fathoms 4 feet of westing. Now, applying these numbers to the plan, we shall, by the convenient help of the cardinal lines and instru- ments, presently prove if the latitude and longitude between the start and terminus of the level on the plan make good these lines. Lastly, I would re- commend that the instruments for drawing and keeping up the working plan should be a 6 or 7 inch circular protractor, on the best principle, with double limb and vernier scale for reading off the angle, so that there may be no guessing, or judging by the eye, merely, for the fractional part of the de- gree ; also, a parallel ruler of the best kind. I 202 PLANS AND SECTIONS OP MINES. prefer those rulers that travel on rollers, both for expedition and accuracy, but I admit it requires some practice to use them well. There is an ad- vantage in those rulers, in that they have an ivory edge and a graduated scale, so that the lengths may be pointed off at the same time that the line is drawn, without using a compass or dividers ; and these two instruments are all that are required for the drawing department. The parallel ruler should be a foot long, divided into thirty feet to an inch ; so that any line within the extent of 360 feet can be pointed off at once. 203 MISCELLANEOUS. THE following articles are extracts from some parts of my public correspondence during the controversy alluded to at the beginning of this Supplement, and I think will be found useful and satisfactory to many of my mining friends. LEVELLING. CUEVATUEE OF THE EABTH. In cutting long leats or watercourses for mining purposes, it is necessary that allowance should be made for the ' curvature of the earth.' RULE. Consider the radius of the earth and the length of the levelling, in a right line, as the two sides of a right-angled triangle ; add the sum of the squares of those sides together, and extract their square root for the hypothenuse. The difference between the length of the radius and the hypothenuse will be the ' curvature.' It will be found that the curvature on one mile will be 8 inches, and on two miles 2 feet 8 inches ; and although this rule will not answer for very long distances, yet it is sufficiently accurate for the first 204 STANDARD OF COPPER ORE. 5 or 6 miles, and consequently adapted for mining purposes. The diameter of the earth is 7963 miles, and the half of it, or radius (say) 3831 miles, which it will be convenient to reduce into inches, after it has been squared, and, of course, the line of levelling also. There is reason to believe that failure has taken place in bringing home long leats, where the fall has been limited from want of proper attention to this subject. N.B. An easy and expeditious rule of approxima- tion is to square the length of the line of levelling in miles and divide by 8. The answer will appear in inches. STANDARD OF COPPER ORE. Since my arrival in this city I have been requested to furnish a plain definition of the term l standard,' as applied to copper ore ; for I am told there still exists among persons not conversant with practical mining much mystery respecting its real meaning. The word ' standard,' divested of its disguise, as applied to mining, simply means ' the present value of a ton of fine copper,' and to be understood as to its practical effect, it must be associated with its two near kinsmen, ' price ' and k produce.' Standing se- parately, they may be thus defined ; viz. * standard,' the value of a ton of copper ; ' produce,' the number of tons of copper in 100 tons of ore ; ' price,' the value of a ton of copper ore. Now it will be STAND AKD OF COPPER ORE. 205 seen that any two of these terms being given, the third may be found by proportion. EXAMPLE. Given standard, 116/.,and produce 8|, the 'price' is required. s. d. As 116 : 8J : : 100 = 10 3 Deduct returning charge 2 15 per ton. Answer 780 per ton. s. d. Given ' price,' 103 Produce 8|, require the ' standard.' As 10 3 : 100 :: 8=Ans. 116. s. d. Given ' standard,' 116, 'price,' 10 3 require the ' produce.' s. d. As 10 3 : 100 : : 116= Ans. 8|. These operations mutually prove the rule, and I suppose will render the meaning and effect of the ' standard ' clear to all parties. 206 GEOLOGY. UNDER this head we shall confine ourselves to those mysterious phenomena in mines called heaves, slides, cross-courses, faults, up-throws, and by what- ever names miners or geologists may call that sudden dislocation of lodes, or separation of the vein, by the intersection of another vein crossing it, either obliquely or at right angles, and sometimes removing or severing (apparently) one part of the lode from the other, and carrying it away a great many fathoms. When a lode has been thus separated it is called by miners ' a heave.' A 'slide' is of another character, although they are sometimes confounded together. If a lode running east, and underlying north, is intersected by a parallel vein, or another vein whose course is nearly parallel, but underlying contrary to it or south, and it is found at the intersection that the lode has been severed by the flookany vein, it is called a ' slide ; ' and the technical expressions are, ' cut out by a slide,' or ' thrown up,' or ' thrown down,' by a slide. The doctrine of ' heaves ' and ' slides ' is of great consequence to the miner ; so that when one of those cross veins comes in, and ' the lode is lost,' as it is expressed, he may know in what direc- tion to drive to find it again. GEOLOGY. 207 There are indications known to practical men whereby they can generally give a fair guess whether it is a ' left hand ' or a ' right hand ' heave ; but sad experience tells us that they are sometimes mistaken in this important matter, and long and wrong drivings of discovery have been made on these occasions, at a great loss of time and money. Therefore we conclude that in this, as in all of nature's operations, although there is a general rule, yet there are exceptions, and the usual guides of the bending or inclining of the last few fathoms of the lode, towards the severed part, with the scroll and particles of ore, scattered in that direction, &c. sometimes prove fallacious. Now we are not going to step out of our place to presume to advise the miner respecting the best indications we submit to his judgment ; but I think I shall obtain his vote, when I recommend that if a lode has been ' hove,' and has not been found by driving a few fathoms right and left on the cross- course, that the most advisable plan is to ascertain the true bearing of the lode, and set to drive on this bearing, 'through the country,' at the point where the separation took place. I am borne out in giving this opinion, from the well-known facts that, although the course of a lode has been altered by a < heave,' yet there is generally an inclining to recover the original course ; but especially as sometimes it is so disordered or ' squeezed up ' close to the cross-course, that it cannot be identified ; but by driving out a few fathoms through the country, on the course of 208 GEOLOGY. the lode, and then l turning house,' or driving at right angles, we shall be sure to find the lode, and being in settled country, to know it when found. Of course we recommend this proceeding only in those vexatious cases where our efforts have been baffled in seeking for the lost lode by driving on the cross-course. We might bring forward some strong ' tried cases ' that would preponderate in favour of this ' dernier ressort ; ' but we will only select the well-known case in point at Holmbush Copper-mine, in this neighbourhood. Nearly three years ago, in driving west they found the lode was ' hove ' by a large cross-course ; and after driving some distance north and south on the cross-course, and being strongly prepossessed in favour of the doctrine of ' right-hand heaves,' they discontinued driving south, and concentrated their force in ex- ploring north in search of the ' lost lode ; ' and after a fruitless labour in driving some 50 or 60 fathoms on the cross-course, and west on some scattered branches, they remembered that they had cut a small vein in driving south about 6 or 7 fathoms south of the point of dislocation ; and in driving a few fathoms on this disowned and rejected branch, they found it to expand into a large and fine course of copper ore, and to be the very lode they had ex- pended so much time, labour, and money in search- ing for in the wrong direction. But we would now turn from the miner to the geologist : what strange, contradictory, and out- rageous things have been published respecting the GEOLOGY. 209 * formation of lodes and mineral veins,' and the causes of ' heaves ' and dislocations ! How amusing to the practical miner it is to read 1 The Transactions of the Boyal Geological Society,' and to see how wild, erroneous, and contradictory their notions are on those subjects ! There is cer- tainly one point in which they all seem to be unanimous, and that is, in 'rejecting the truth!' One grave professor will tell us, the lodes are 'secondary formations,' and have been subsequently filled from the surface; another says, the ore has been thrown up into them by ' volcanic action ; ' another, that it has been drawn into them sideways by 'electricity,' having been 'held in solution' in the adjoining rock ; but not one of them appears ' to be valiant for the truth,' by declaring that the whole is a contemporaneous creation ! No, they will leave the ' truth ' for unsophisticated men to deal with, while they seem to take pleasure only in endeavouring to reconcile impossibilities. I doubt not but a vast majority of my practical brethren are on my side in favour of the doctrine of 'contemporaneous formation.' As for the term ' heave, ' ' slide,' ' throw,' ' separated,' or any other word betokening subsequent disturbance, it is no- thing more than a name. These phenomena are the wise and admirable order of creation for the benefit of man. Miners know well (however ignorant geologists may be of the fact) how highly beneficial to mining operations this grand arrange- ment is ; how advantageous are cross-courses in a granite or any other hard country, where they can p 210 GEOLOGY. drive ten fathoms in about the same time and cost that they could drive one fathom through the rock ! Another incalculable advantage is, that these cross- courses, being generally composed of a stiff clay, impervious to water (called ' flookan ' by the miner), effectually dam back the stream ; and on some hollow or porous lodes, were it not for these cross- courses, the influx or drainage would be so extensive, that it would be impossible to work the mine with- out an immoderate expense of machinery. As to these ' heaves ' being secondary tilings, the doctrine is fraught with absurdity and impossi- bility. We find ' heaves ' of several fathoms, and all the ' country ' or rock in its vicinity, without a single fracture, and not the slightest sign that ever a hairbreadth movement or agitation had taken place since the six days of creation! but what must have been the mighty wreck and crash, if some supernatural power had caused our ponderous globe to shift some 10, 20, or, as in some cases, 80 fathoms, one part from another ? Moreover, those cross-courses, which are said by those 'secondary men ' to be either the cause or proofs of those dis- locations, we often find them serpentine or zigzag in their course, and that they are not interminable, but often fail, and discontinue, when a change of strata or country takes place. How can we reconcile this with the idea of dislo- cation? Surely if the cross-course hove the lode, before we receive the doctrine we must be assured that the cross-course extended throughout the globe, without interruption, and straight as a line! GEOLOGY. 211 In writing on this subject, during the controversy alluded to, I called the attention of the public to a notable circumstance that speaks loudly on the subject, and that can hardly fail to come under the notice of every observant man I mean the minia- ture display of all the phenomena of lodes, cross- courses, heaves, slides, splits, faults, and everything else of the kind that may be seen in some species of stone. what ' faithful witnesses ' are those little representations where everything is exactly por- trayed in perfect and exact harmony with the stupendous and magnificent order of the formations to be found in a mine of 20*0 fathoms ! If we look at the top of one of those stones, we are reminded of the working or horizontal plan of a mine, and the fractured end truly represents the transverse section. How deeply rooted must be the prejudices of men who will not receive this corroborating evidence ! I have before me the ' Mining Journal ' of February 4, 1843, wherein my arguments on this subject were followed up by a practical man, as follows : To the Editor. 'Sir, ' After reading Mr. Budge's statement of facts inserted in the Supplement to the " Mining Journal " of Saturday, 28th inst., I recollect, many years ago, being at a mine called Seal Hole, situated in the parish of Saint Agnes, in Cornwall, now called p 2 212 GEOLOGY. Polberou Consols, seeing there a flat blue killas or clay-slate stone, about four inches wide, five or six inches long, and half an inch thick ; on the surface of which we could distinctly trace several rich tin lodes in miniature, so very similar to the disposition of the great metallic lodes, that it might be thought an exact representation of what you might expect to see 'in the plan and section of a mine. The little representatives of lodes, the largest of them perhaps not much larger than a stout pack-thread, and others less, all intersected by a little diminutive cross-course, composed of what the miners term spar, which heaved the different veins as is done in a large champion lode. From the above and other alike corroborative evidence, I am led to believe, also, that the lodes, and the country about them, were formed at one and the same time. ' S. P.' If anything more is wanting to prove that those * heaves' are originals, we may bring forward the fact well known to miners, that oftentimes a cross- course intersecting several lodes, the ' heaves * are found to differ materially in their distance, and some not ' heaved ' at all, and there are known to be both right and left-hand heaves on the same cross- course. I shall close this subject with the extract of a letter I inserted in the ' Mining Journal,' December 3, 1842 : GEOLOGY. 213 To the Editor. 'Sir, ' At last I observe, with pleasure, that one of our practical miners has had the courage to come forward and openly throw down the gauntlet against the host of modern geologists. This champion for the truth is Mr. Thomas Deakin, of the Blaenavon Mines, whose letter appeared in last week's Journal. I hope his efforts will be seconded by abler hands than mine ; for surely it is high time that the per- nicious march of geological error should meet with a check from some quarter. ' Permit us to inquire what benefit mining has received from all the writings, lectures, societies, premiums, researches, and labours of our large body of theoretical geologists? If I am wrong, please to set me right ; but I declare, I know not a single instance where any good has emanated from their exertions, to the value of a swabbing-stick ! All the progress made in the discovery and working of mines has been without their help the ancient methods of detecting or identifying a metallic lode by shodes, gossans, mineral waters, gases, &c., have received no improvement from them, although we are persuaded that a fine field for art and science is still open here ; for as nature always works by general laws, we believe that if all the indications which attend a rich metallic lode could be detected, that mining would not be so much a speculation as it is at present. But what can be the cause that such a large body of talented men, devoted to the 214 GEOLOGY. subject, ambitious to excel, and " with all appli- ances and means to boot," should be thus noto- riously useless and unprofitable ? Your Blaenavon correspondent has revealed the secret. Now, Mr. Editor, allow me to observe that theology will never disgrace the columns of the " Mining Journal ;" and if we consult the best judges, I think they will admit that it should ever be the basis of geology. This, Sir, is the grand cause why the efforts of our geo- logical societies have utterly failed they have set themselves against the truth they have rejected the inspired history of the creation of the world ; hence their writings and sayings are replete with error, inconsistency, and contradiction. ' Let them begin again ; cancel what they have written, and lay their foundation on the sublime accounts so minutely given us in the Scriptures. Then let them follow nature in all her grand and stupendous subterranean operations, and they will discover a world of harmonious wonders, and will bring to light, to the admiration and benefit of mankind, the cause and effect of the magnificent order of every part of creation that is allowed to fall under the inspection of man. ' I shall be borne out in stating my firm con- viction that no sceptic ever made a good geologist ; and whatever those men may think of themselves who dare to write in contradiction to the Word which the Creator has graciously condescended to bestow on His creatures, they are no better than practical atheists in the judgment of all men " who believe and know the truth," and their writings are GEOLOGY. 215 calculated to inflict a serious injury on society. See, Sir, how these talented infidels try all they can to sap the foundation of the Christian's faith ! their first, second, and third formations. One thing pro- duced by another. Coal formed of vegetable matter ! and lately they have discovered that slate is a marine production I Oh, Sir, if you are not one of that school, let me entreat you to point your powerful pen against the doctrines of this geological demon, or, at least, give full introduction to those who feel themselves imperatively called on to come forward in defence of the truth. 'JOHN BUDGE.' EXPLANATION OF TERMS USED IN THE FORE- GOING- WORK. Acclivity, the rising steepness of a hill. Aliquot, such a part of a number or quantity as is contained in it so many times without a remainder. Angle, the space between two lines which cross each other. Base, the bottom, the foundation. Bisect, to divide into two parts. Complement, so much of an angle as is wanting to make a right angle. Construction, the contriving such lines and figures as will show the truth of a problem. Corollary, conclusion drawn from antecedent demonstration. Cosecant, the secant of the complement of an arch to 90 degrees. Cosine, the right sine of an arch which makes up another arch of 90 degrees. Cotangent, the tangent of an arch which is the complement of another arch to 90 degrees. Declination, the act of bending. Declivity, the steepness of a hill downwards, gradual descent. Definition, a clear and short description. Degree, the 360th part of the arc of a circle. Demonstrate, to prove with certainty. Denomination, a name given to any thing. Depression, the act of pressing down. Desideratum, a desirable improvement in a science yet unat- tained. Diagonal, a line drawn from one angle to another. Diagram, a scheme drawn for the explanation of any thing. Elevation, a raising or lifting up. Geometry, the science of extension. Horizon, the line that bounds the visible from the invisible part of the earth. Horizontal, level with the horizon. Hypotlienuse, the longest side of a right-angled triangle. Inaccessible, not to be approached. Q 218 EXPLANATION OF TERMS. Intersect, to cut each other. Intervene, to come between. Junction, the act of joining together. Mathematics, that science which contemplates whatever is capable of being numbered or measured. Oblique, not perpendicular, not parallel. Perpendicular, a line that stands upon or crosses another at right angles. Problem, that which proposes something to be done. Protractor, an instrument to lay down or measure angles. Quadrant, one fourth part of a circle containing 90 degrees. Radius, a right line drawn from the centre to the circumference of a circle, half the diameter. Bight Angle, an angle containing 90 degrees, made by the touch of two lines perpendicular to each other. Scale, a mathematical instrument containing lines divided into equal or unequal parts. Scheme, a plan, a mathematical diagram. Secant, a right line drawn from the centre of a circle that meets the tangent Segment, a part cut off. Sine, a right line drawn from one end of an arc perpendicular upon the diameter. Summary, compendium, abridgment. 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