A TREATISE 
 
 SUBTERRANEOUS SURVEYING 
 
 ETC. ETC. ETC. 
 
ELEMENTARY AND PRACTICAL TREATISE 
 
 ON 
 
 SUBTERRANEOUS SURVEYING, 
 
 AND THE 
 
 MAGNETIC VARIATION OF THE NEEDLE. 
 
 BY THOMAS FENWICK, 
 
 Colliery Viewer and Surveyor of Mln^. 
 
 ALSO 
 THE METHOD OF CONDUCTING 
 
 SUBTERRANEOUS SURVEYS WITHOUT THE 
 USE OF THE MAGNETIC NEEDLE, 
 
 other 
 
 BY THOMAS BAKER, C.E., 
 
 Author of "Railway Engineering," "Theodolite Surveying, Levelling," &c., in 
 Nesbit's " Surveying, Rudimentary, Land and Engineering Surveying, Statics 
 and Dynamics, Elements of Mechanism, Mensuration, Integi-ation," in Weale's 
 Series, &c, 
 
 THE THIRD EDITION. 
 
 LONDON: 
 JOHN WEALE, 59, HIGH HOLBORN. 
 
 1861. 
 
LONDON : 
 BRADBUEY AND EVANS, PRINTERS, "WHITEFRIAR3. 
 
 
PREFACE. 
 
 THE mineral wealth of this kingdom had become 
 of such great importance, ahout half a century ago, 
 as to induce Mr. T. Fenwick, of Dipton, in the 
 County of Durham, to compose a Treatise on Sub- 
 terraneous Surveying (which forms the basis of the 
 present Work) for the use and instruction of young 
 men designed for the profession of mining agents' 
 and surveyors, usually called colliery viewers : much 
 more, then, is such a treatise now necessary, as these 
 mineral productions have, up to the present time, 
 been more than quadrupled in value ; and by the more 
 general diffusion of mathematical, philosophical, and 
 mechanical science, the working of mines has been 
 conducted with greater skill and precision for the full 
 development of their vast wealth. 
 
 The general use of the magnetic needle in subter- 
 raneous surveys has been found to be a great source 
 of error, on account of ferruginous substances (which 
 exist in almost all mines) attracting the needle, and 
 causing it to give erroneous indications; whence, in 
 general, old surveys are found to be extremely defec- 
 tive. Indeed, Mr. Fenwick himself was so sensible 
 
 M 1635 
 
VI PEE FACE. 
 
 of this deficiency of the needle, that he proposed, in 
 the Second Edition of his Work, ahout forty years 
 ago, to dispense with its general use ; though he still 
 proposed to use it, at the first departure, or com- 
 mencement of the survey, from the top to the bottom 
 of the shaft of the mine. 
 
 This Edition of the Work contains, in a small 
 compass, the essentials of Subterraneous Surveying 
 in all its branches, both with and without the use of 
 the magnetic needle ; and to make it still more useful 
 to that class of men for whom it is chiefly intended 
 to convey information, there are added a great number 
 of explanatory figures and examples. 
 
 + 
 
 PART I. contains the method of surveying, with the 
 use of the magnetic needle, without attending to its 
 variation, as being more readily intelligible to begin- 
 ners; and the magnetic bearings being, at the same 
 time, at once adapted to the use of the Traverse 
 Tables. This part is arranged after Mr. Fenwick's 
 plan (whose method and examples are still retained), 
 in the following order : 
 
 1. Geometrical problems. 
 
 2. Theorems, and the methods of conducting sub- 
 terraneous surveys. 
 
 3.- Of determining the magnitude of angles. 
 
 4. Of determining bearings, and reducing angles 
 to the bearings which they form with the magnetic 
 meridian, with a rule and examples. 
 
PBEFACE. Vll 
 
 5. The method of reversing bearings. 
 
 G. Of reducing bearings to the angles they form 
 with the magnetic meridian, with rules and examples ; 
 and the manner of finding the magnitude of the angle 
 that two bearings form with each other. 
 
 7. The method of reducing bearings and distances 
 to the northing or southing, and easting or westing, 
 they contain, by the Traverse Table, with a rule and 
 examples. 
 
 8. The manner of surveying subterraneous exca- 
 vations with the form of the survey-book. 
 
 9. The method of taking back sights. 
 
 PART II. In this part, which treats extensively on 
 conducting subterraneous surveys, without the use of 
 the magnetic needle, Mr. Fenwick's examples are in 
 several cases retained, with full directions for adapting 
 them to the new method (they being already adapted 
 to the use of the Traverse Table), which will con- 
 stitute a useful exercise for the student in transferring 
 the angles from their magnetic bearings to the angles 
 which one line makes with the preceding one, as 
 taken by the theodolite. This part has the following 
 arrangement : 
 
 1. Mr. Fenwick's method of subterraneous sur- 
 veying, without the use of the needle, except at the 
 first departure or commencement of the survey. 
 
 2. Mr. Baker's method of commencing the survey by 
 suspending two weights down the shaft in the direction 
 
Vlll PREFACE. 
 
 
 of the first headway, and marking the same direction 
 on the surface ; and afterwards conducting the survey 
 with the theodolite, without the use of the needle. 
 
 3. Mr. Beauland's method of making the commence- 
 ment of the survey by the help of a transit instrument, 
 not using the needle, as in Baker's method. 
 
 4. Plotting and protracting surveys in various ways. 
 
 5. Of reducing the hearings and distances of a 
 survey into one common hearing and distance, or any 
 number of bearings and distances fewer than those 
 that compose the survey, whether the angles be taken- 
 with the needle, or the theodolite independent of the 
 needle. 
 
 6. The method of plotting on the surface in various 
 ways. 
 
 7. The method of making the survey where the 
 excavation inclines from the horizon. 
 
 8. A promiscuous collection of practical examples, 
 some of which relate to tunnelling. 
 
 PART III. contains subterraneous surveys, under the 
 necessary attention to the magnetic variation of the 
 needle. As the magnetic meridian has been found to 
 be in a state of variation from the true meridian for 
 upwards of 300 years, and still continues to vary, 
 therefore surveys made by the circumferentor, or any 
 other instrument under magnetic influence, must vary 
 accordingly as that meridian varies. For instance, 
 suppose the bearing of any one known object to have 
 
PREFACE. IX 
 
 been taken from a given point by the magnetic 
 meridian in the year 1700, and recorded; and if the 
 bearing of the same object be now retaken by the 
 magnetic meridian from the same given point, these 
 two bearings will be found, on comparison, to diifer 
 about 14, the magnetic meridian having in that time 
 changed thus far in its direction (see table, p. 96). It 
 is also well known to directors of mines that the plans 
 of their excavations, on examination, are always found 
 to be erroneous, some even to a great extent. This 
 frequently misleads the miner, adding expense to his 
 subterraneous pursuits, and the cause of such errors 
 originates through his inattention to the variation of 
 the needle in the plotting from time to time of his 
 surveys. 
 
 This part, therefore, shows the method of rectifying 
 the bearings of old surveys, in order to connect them 
 with those made by the scientifically correct method 
 laid down in the second part of this work. 
 
 The third part is thus arranged : 
 
 1. Axioms and observations. 
 
 2. The method of finding the true and invariable 
 meridian. 
 
 3. To determine the variation of the needle of the 
 circumferentor or other instrument used in sur- 
 veying. 
 
 4. To reduce bearings taken by an instrument, the 
 needle of which has any known variation, to bearings 
 
 with the true meridian, with rules and examples. 
 
 12 
 
X PBEFACE. 
 
 5. To reduce bearings from one magnetic meridian 
 to bearings with any other magnetic meridian, with 
 rules and examples. 
 
 6. To find the kind of meridian by which a plan 
 has been constructed, with rules and examples. 
 
 7. On planning surveys, and finding the magnitude 
 of an error in plotting, caused by inattention to the 
 magnetic variation, with examples. 
 
 8. On running bearings on the surface by the cir- 
 cumferentor or theodolite without error. 
 
 9. To determine the antiquity of a plan by its 
 delineated meridian. 
 
 10. On recording bearings. 
 
 11. The Traverse Tables, with examples of their use. 
 
 12. An expeditious method of calculating the pro- 
 duce of coal strata of any given thickness, with 
 examples. 
 
 13. Concluding examples in mining surveying. 
 Having now described the plan, and enumerated the 
 
 heads of this publication, I must leave it to practical 
 colliery viewers of scientific skill to judge of its merits 
 and utility, in its present improved form ; and I trust, 
 from my own practical experience in surveys of almost 
 every kind during the last forty years, that the diffi- 
 culties and intricacies of such a work will, to candid 
 and liberal minds, be sufficiently obviated. 
 
 T. BAKER. 
 
 
CONTENTS. 
 
 PART I. 
 
 PAGE 
 
 Geometrical Problems .,,.,...! 
 Theorems, and the method of conducting a subterraneous survey . . 4 
 
 To find the magnitude of angles 9 
 
 To determine bearings, and to reduce angles to bearings . , . 10 
 To reverse bearings . . . , . , , , .15 
 To reduce bearings to angles . . . ib. 
 
 To reduce bearings and distances to their northing and southing, and 
 
 casting or westing . . , 21 
 
 Surveying and recording bearings . . . . . . . 25 
 
 To survey subterraneous workings, and to prove the work, with 
 
 examples and form of survey-book 27 
 
 To take a back sight 39 
 
 PART II 
 
 Subterraneous surveying without the general use of the magnetic 
 needle (Mr. Fenwick's method) .41 
 
 Subterraneous surveying entirely without the use of the needle (Mr. 
 
 Baker's method) . . 43 
 
 The same by Mr. Beauland's method ...... 44 
 
Xll CONTENTS. 
 
 PAGE 
 
 To plot a survey on paper by the common method, with a description 
 
 of the protractor 48 
 
 To plot a survey on paper by the use of the ~["' s< l uare an ^ drawing- 
 board 51 
 
 To plot a survey, so that if an error be committed in any part of the 
 work, it will not affect the following part, with an illustrative 
 example 53 
 
 To reduce any number of bearings and distances to one bearing and 
 distance equal to the whole, with several examples both with 
 and without the use of the needle 63 
 
 To plot on the surface by the circumferentor or theodolite . . 70 
 
 To avoid an obstruction that interferes with the line of plotting on 
 
 the surface, with several examples . . . . . . 73 
 
 To make a survey when the subterraneous excavation inclines from 
 
 the horizon 82 
 
 The fallacy shown of putting two or more bearings into one, and thus 
 
 plotting them .......... 84 
 
 A promiscuous collection of practical questions in mining and 
 
 tunnelling . . . , . . . . . .85 
 
 PART III. 
 
 Axioms and observations . . . . . . . . . 92 
 
 On the variation of the magnetic needle . . . . . .93 
 
 A table showing the variation of the needle from the year 1576 to 
 
 the year 1858, both inclusive 94 
 
 A table showing the diurnal variation . . . . . .95 
 
 To find the true meridian . . . . . . . . 96 
 
 To find the true meridian astronomically . . . . .97 
 
 To determine the needle's magnetic variation in any instrument . . 98 
 To reduce bearings from a magnetic to the true meridian . . .99 
 To reduce bearings from one magnetic meridian to bearings with any 
 
 other magnetic meridian 103 
 
 To find the meridian by which a plan has been constructed . .109 
 

 CONTENTS. Xill 
 
 PAGE 
 
 To plan subterraneous surveys correctly, and to find the amount of 
 an error, arising in plotting, through inattention to the magnetic 
 variation of the needle . . . . . . . . 115 
 
 To run bearings on the surface by any eircumferentor or other 
 
 magnetic instrument without error . . . . . .124 
 
 To find the antiquity of a plan by its delineated meridian . . .127 
 To record the bearings of subterraneous surveys . . . .128 
 
 The use and application of the Traverse Tables 129 
 
 The use of the Table in reducing hypothenusal distances to horizontal 
 
 distances , . . . 131 
 
 A Traverse Table to every degree of the quadrant . ... 133 
 To calculate the produce of coal-strata of any given thickness in tons . 157 
 Concluding questions in mining surveying ....... 160 
 
EXPLANATION 
 
 TEEMS AND EXPRESSIONS IN THIS WORK. 
 
 Bearing to tJie right or left of a meridian. A. line is said to bear en 
 the right or left of the north or south meridian, when it is to the 
 right or left of a person, whose face is turned towards the north 
 or south. 
 
 Bearing on different sides of a meridian. Two lines are said to bear on 
 different sides of a meridian, when the one bears on the east side, and 
 the other on the west side thereof. 
 
 A Bord is an excavation in a seam of coal driven in a direction across its 
 fibres. 
 
 A Drift is a narrow excavation driven in any direction in coal or stone. 
 
 A Headway is an excavation in a seam of coal driven in the direction of 
 its fibres. 
 
 Different Meridians. When one line bears in a given direction with the 
 north meridian, and another bears in a given direction with the south 
 meridian, those lines are called bearing with different meridians. 
 Also, when one line bears on the east side of the north meridian, and 
 another on the west side of the south meridian, those lines are said 
 to bear on different sides of different meridians, and vice vend. 
 

TREATISE 
 
 ON 
 
 SUBTERRANEOUS SURVEYING, 
 
 ETC. 
 
 PART I. 
 
 1.- 
 
 GEOMETBICAL PROBLEMS. 
 
 -To divide a given line AB into equal parts. 
 
 WITH any distance greater 
 than half AB, and one foot of 
 the compasses on A and B, 
 describe two arches cutting 
 each other in C and D ; through 
 the intersecting points CD 
 draw a line CD, which will cut 
 AB in I into equal parts. 
 
 FIG-.!, 
 
 \ 
 / 
 
 2. To draw a line parallel to a given line CD, to pass 
 through any assigned point A. 
 
 From the given point A take the nearest distance to the 
 given line CD ; with that n$} . 
 
 distance, and one foot of E _* 
 
 the compasses, any where /''' "\. 
 
 towards C describe an / \ / 
 
 arch O ; through A draw ' 
 
 p . . _ .j_ , -_--_r.i '''^rai^i^'"''* Q 
 
 a line AB, just to touch 
 
 the arch O in O ; and the line AB will be the parallel 
 
 required. 
 
STJBTEEBANEOTTS SURVEYING, ETC. 
 
 3. To rtiise a perpendicular from a given point P in a given 
 line A3. 
 
 FIG. 3. 
 
 From the given point P describe the arch ED ; take PF, 
 
 and set from F to C, and from 
 C to D ; then with any con- 
 venient distance from C and 
 D describe the arches O, and 
 through their point of inter- 
 section from the point P draw 
 the line PO, the perpendi- 
 cular required. 
 
 4. To raise a perpendicular from a given point A, at the end 
 of a given line AB. 
 
 Set one foot of the compasses on A, and extend the 
 no, 4, other to any point C, above the 
 
 line AB ; on the centre C describe 
 the semicircle FAP, to cut AB 
 in F ; draw FC cutting the semi- 
 circle in P ; then draw AP, which 
 e perpendicular to AB. 
 
 5. From a given point P to let fall a perpendicular upon a 
 given line AB. 
 
 FIG 5 
 
 P 
 
 
 -._ i _. 
 
 ^r-- E 
 
 On the given point P as a 
 centre, describe the arch EF to 
 cut AB in E and F; with any 
 convenient distance, and one foofc 
 of the compasses on E and F, 
 describe two arches to cut each 
 other in I; through P and I 
 draw PI, which is perpendicular 
 
 to AB - 
 
GEOMETRICAL PROBLEMS. 
 
 Fl G . 6 . 
 
 
 6. To mnlce an angle ABC equal to a given angle ODE. 
 With any convenient extent of the compasses, and one 
 
 foot on D, draw the arch FGr ; 
 equal to the measure of the 
 given angle D draw a line BC, 
 and with the distance DF de- 
 scribe the arch HI ; then make 
 the arch HI equal to the arch 
 FGr, and through I draw the line 
 BA, forming the angle ; so the 
 angle ABC is equal to the angle 
 CDE. 
 
 7, To lay down an angle FDGr equal to any determined 
 
 number of degrees, which suppose 35 
 
 Draw the line D^ 1 at pleasure, and with 60 off the scale 
 of chords describe the arch 
 EH on the centre D ; from 
 the same chords take 35 
 (the quantity of the angle), 
 and lay upon the arch from E 
 to H, through which from D 
 draw the line DGr, and the 
 angle FDGr will contain just 
 35. 
 
 S. To determine the number of degrees contained in any 
 angle, suppose angle FDGr. 
 
 With 60, taken from the scale of chords, describe the 
 arch EH ; then extend the compasses from E to H, and 
 observe, on the same line of chords, what number of degrees 
 the extension measures, which will be the measure of the 
 angle EDH. 
 
 Or, apply the centre of the protractor to the angular 
 point D, and bring its straight edge upon the line DF, and 
 the degree the other line cuts on the divided arch is the 
 measure of the angle. 
 
 B 2 
 
SUBTEEEANEOUS SURVEYING, ETC. 
 
 FIG. 8. 
 
 A 
 
 
 THEOEEMS. 
 
 1. Every right angle, as ACB, contains 90 degrees or 
 
 equal parts. 
 
 2. Every circle ABDE, 
 is supposed to have its peri- 
 phery divided into, or to con- 
 tain, 360 equal parts, called 
 \ degrees, and those degrees 
 "-|B are divided into 60 equal parts, 
 / called minutes, and each mi- 
 nute is divided again into 60 
 equal parts, called seconds, &c. 
 3. Every circle AD, con- 
 tains four right angles, at 
 
 angles ACB, BCD, DCE, and EC A, which, from theorem 
 1, must contain 90 each. 
 
 4. Every semicircle EAB, contains two right angles, as 
 angles EGA and ACB, which, from theorem 1, must contain 
 90 each. 
 
 Draw the diameter AD, which will divide the circle 
 EABD into two equal parts EAB and EDB, each con- 
 taining a semicircle, or 180 ; 
 if, therefore, a line AC be 
 drawn perpendicular to EB 
 from the centre C, it will 
 k divide the semicircle EAB into 
 \ two equal parts, making two 
 -j z ' right angles EGA, ACB. 
 \ / 5. If any right line AY 
 
 \ /' stands upon another right line 
 
 X N. X ^/' DZ, it will make therewith 
 
 ~~~E ** kwo right angles, or two angles 
 
 whose sum is equal to two 
 
 right angles. (Euc. b. 1, p. 13.) If a line AY, be 
 drawn from any part Y of the circumference to A, it will 
 
 FIG. 9. 
 
THEOREMS. 
 
 divide the semicircle DXZ into two unequal parts, making 
 the angles DAY, YAZ, unequal ; but these two angles are 
 equal to a semicircle, or two right angle?. 
 
 6. If two right lines IL, KM, intersect each other, the 
 opposite angles A and C, as also B FIG.lo. 
 
 and D, are equal ; that is, the angle 
 A = the angle C, and the angle B 
 = the angle D. (Euc. b. 1, p. 
 15.) 
 
 7. If a right line OR, cuts two 
 parallel right lines NP and SQ, the 
 alternate angles KaE, QbO. are 
 equal, and consequently the lines 
 parallel. (Euc. b. 1, p. 29.) 
 
 8. If any side of a right-lined FIG u. 
 triangle be continued, see fig. 12, 
 
 the external angle is equal to 
 
 the sum of the two opposite in- n a . 
 
 ternal ones. (Euc. b. 1, p. 32.) f 
 
 Let UST be the given tri- 5 / 
 
 angle ; then the L STZ is = " A 
 
 L SUT -f L UST, = the sum / 
 
 of the opposite internal angles. /R 
 
 9. The three angles of 
 any triangle are together 
 equal to two right angles, 
 or 180. (Euc. b. 1, p. 32.) 
 See fig. 12. 
 
 In the triangle STU, the 
 L STU -*- L TSU + Z 
 SUT = 180, or two right angles. 
 
 10. The sides of similar triangles are proportional, and 
 the angles subtended by proportional or equal sides are 
 equal. (Euc. b. 6, p. 45.) 
 
 11. In any four-sided right-lined figure, called a square 
 parallelogram, rhombus, trapezium, &c., the sum of the 
 
 no. 
 
SUBTEEEAKEOUS SUEYEYING, ETC. 
 
 four angles is equal to four right angles, or 360. (Euc. 
 b. 1, p. 32.) 
 
 12. The sum of all the angles of any right-lined figure 
 (though it contain never so many sides) is equal to double 
 as many right angles, abating four, as there are sides in 
 the figure. (Euc. b. 1, p. 32.) 
 
 13. In right-lined triangles, equal sides subtend equal 
 angles (Euc. b. 1, p. 5). The greatest side subtends the 
 greatest angle (Euc. b. 1, p. 19), and the least side sub- 
 tends the least angle. 
 
 14. An angle in a semicircle is a right angle ; or if two 
 
 F i a ; i a , lines, as TE, SE, be drawn from T 
 
 and S (the ends of the diameter) 
 to E in the circumference, they 
 will form, a right angle TES. 
 (Euc. b. 3, p. 31.) 
 
 15. In any right-angled tri- 
 angle, the square of the hypo- 
 thenuse (or longest side) is 
 equal to the sum of the squares 
 of the other two sides or legs. 
 (Euc. b. 1, p. 47.) 
 
 16. The compass is divided into four cardinal points, 
 called nortb, south, east, and west ; the two first, north and 
 south, are formed where the meridian cuts the horizon, 
 and the other two, east and west, are 
 each 90 degrees distant from the 
 points north and south ; therefore 
 they divide a circle into four equal 
 
 w 1- E parts of 90 degrees each. 
 
 17. "When the face is turned to 
 the north N, the right hand is to- 
 wards the east E, and the left hand 
 towards the west "W ; and when the 
 
 face is turned towards the south S, the right hand is 
 towards the west W, and the left hand towards the east E. 
 
 N .F1C.I1-, 
 
THEOREMS. 
 
 18. The magnetic meridian is that line in which the 
 magnetic needle of the compass settles ; and every par- 
 ticular place on the earth has its respective magnetic 
 meridian. 
 
 19. The magnetic needle is here assumed to retain its 
 parallelism in every situation within the limits of a sub- 
 terraneous survey. 
 
 If in the situation A, a magnetic needle is placed, and 
 is found to settle in the direction of ab, if tty same 
 needle is removed to B or 0, it will settle 
 itself in the direction of cd and ef, both FIG, 15, 
 
 parallel to ab> But the magnetic meri- 
 dian of places very distant from each 
 other will not be parallel ; for the mag- 
 netic meridian of London will vary a 
 few degrees from its parallelism with that 
 of Edinburgh. The magnetic needle has a 
 small diurnal variation, being greatestabout 
 noon, also a small annual variation, which 
 seldom exceeds a few minutes of a degree. 
 
 Part Eirst of this work consists of the 
 manner of surveying under-ground, with- 
 out attending to the magnetic variation 
 of the needle, with several easy and ex- & el 
 peditious modes of plotting the same. 
 
 The instruments used in subterraneous surveying are 
 the circumferentor, the theodolite, Grunter's chain, in the 
 coal mines, which contains 100 links. In the lead mines, 
 a chain, divided into 100 feet, is now frequently used 
 instead of Grunter's chain. 
 
 The manner of conducting a subterraneous survey ~by tlie 
 magnetic needle. 
 
 (1.) Place the circumferentor, or instrument used, where 
 
8 SUBTERRANEOUS SURVEYING, ETC. 
 
 the survey is intended to commence ; then let a person 
 go forward in the direction of the line to be surveyed, 
 with a lighted candle in his hand, to tne utmost distance 
 his light can be seen through the sights of the instrument ; 
 its bearing then is taken by the circumferentor (the 
 manner of taking bearings will be shown hereafter), and 
 noted down in the survey book ; proceed then to take 
 the distance of the light or object from the instrument ; 
 remove the instrument, and let a person stand on the exact 
 spot where it stood, holding in his hand one end of the 
 chain, while another, going towards the object, holds the 
 other end, together with a lighted candle, in the same 
 hand ; then being directed by the former until that hand 
 which holds the candle and the chain is in a direct line 
 with the object or light whose bearing was taken, there 
 mark the first chain ; then he that stood where the instru- 
 ment was placed comes forward to the mark at the end of 
 tie first chain, the other advancing another chain forward, 
 with the candle and chain in the same hand, directed as 
 before, there mark the second chain, so proceeding in 
 the same kind of way until the distance of the object is 
 determined, which being noted down in chains and links 
 in the survey book, opposite to the bearing, then the first 
 bearing and distance is completed: Fix the instrument 
 again where the light, as an object, stood, or at the ter- 
 mination of the preceding bearing and distance, and take 
 the second bearing, by directing the person to go forward as 
 before, so far as his light can be seen, or at any shorter con- 
 venient distance, and proceed as before until the whole is 
 completed. 
 
 There should not be fewer than five people employed in 
 such surveys, to carry forward the work with expedition, 
 viz., one to carry forward the survey, and make the 
 necessary observations and remarks ; another to carry the 
 instruments ; another to direct the chain ; another to lead 
 it ; and another to go forward with a light, as an object, 
 
THEOREMS. 
 
 from station to station. During the time of making the 
 survey, be careful in not admitting any iron, steel, or other 
 ferruginous substance, within ten feet of the instrument, 
 for fear of attracting the needle ; I have seen the needle 
 affected at almost twice the above distance, by a very massy 
 piece of iron. Also if the glass of the instrument stand in 
 need of cleaning, it must be rubbed as gently as possible, 
 and not with any silken substance, for that will be apt 
 to excite electrical matter, which will prevent the needle 
 from traversing ; but if that matter should be excited, it 
 may be very easily discharged, by touching the surface of 
 the glass with the wet finger. 
 
 In order for familiarising the young miner with this 
 system of surveying, previous to his practising it in mines, 
 it would be necessary for him to fix up a number of marks 
 on the surface, and afterwards take their bearing and dis- 
 tance from each other, according to the method before 
 directed. But to approach nearer to the form of subter- 
 raneous surveying, it would be much better to do it at 
 night, by the assistance of candle-light ; many favourable 
 evenings might be found for this mode of practising. 
 Should the current of air be too strong for the naked flame 
 of the candle, lanterns may be used. 
 
 To find tlie magnitude of angles. 
 
 (2.) Every circle, ABCD, is supposed to contain 300 
 (see theorem 2) ; each semicircle DAB and DCB contains 
 180 ; and each quadrant AB, BC, CD, and DA, contains 
 90. Draw the line ab ; and if Z A.ab contains 50 L Dab 
 must contain 90 50 40, and L baC must contain 
 180 50 = 130 (see theorem 5). Also if ab makes 
 an angle of 50 with the line AC, and ad an angle of 30 
 with the same line, the semicircle ADC containing 180, 
 L A& = 50 + Z Cad = 30 = 80, then 180 - 80, 
 leaves 100 = /. bad. Or thus, L AD = 90; then 
 
 B3 
 
10 
 
 SUBTEEEANEOUS STJEVETINa, ETC. 
 
 90 - 50 / Aab = 40' 
 
 ' Z. baD ; also L DaC = 90 ; 
 then 90 - 30 L daC = 60 
 L Dad; consequently Z. ball 
 = 40 + L Dad = 60 = 
 100 L bad, as before. If al 
 make an angle of 50 with A, 
 and ac make another angle of 
 
 B 75 with the same line a A, 
 then the L cab 75 50= 
 = 25 ; and if ab make an an- 
 gle of 50 with #A, and ac an 
 angle of 25 with the line ab, 
 then 50 + 25 = 75 L 
 
 (Buc. b. 1, p. 15.) 
 
 The manner of determining bearings, and also reducing 
 angles into bearings. 
 
 (3.) The instrument used in subterraneous surveying is 
 the circumferentor, mentioned as before, whose effect 
 depends on the magnetic needle ; and the directions, 
 
 courses, or bearings, are 
 recorded according to 
 the angles these direc- 
 tions make with the 
 magnetic meridian. (The 
 magnetic meridian is the 
 north and south line, as 
 pointed out by the mag- 
 netic needle ; see theo- 
 rem 18.) 
 
 If we pass round from 
 the north N, to the east 
 E, and continue moving 
 from the east to the 
 south S, and from thence to the west "W, and lastly from 
 the west to the north N, from whence we first of all set out, 
 
THEOREMS. 11 
 
 we shall have made a circuit NESWJST of 60, which all 
 circles are upposed to contain (see theorem 2) ; and as there 
 are four cardinal points (see theorem 16) in that circle, 
 north, east, sonth, and west, dividing it into four equal parts, 
 consequently from north N to east E subtends an angle 
 of 90 ; from east E to south S subtends an angle of 90 ; 
 from south S to west "W subtends an angle of 90 ; and 
 from west W to north N subtends an angle of 90. Now 
 let NE, or the distance between north and east, also ES, 
 or the distance between east and south, also SW, or the 
 distance between south and west, and also "WN, or the 
 distance between west and north, be each divided into 90 
 equal parts or degrees, then a line in direction of CIST may 
 be called due north, and another in direction of CS may 
 be called due south, another in direction of CE may be 
 called due east, or north 90 east, or south 90 east, and 
 another in direction of CW may be called due west, or 
 north 90 west, or south 90 west ; likewise the line CD 
 passing between S and W, or between south and west, 
 is called south 50 west, being 50 towards the west from 
 south, or to the westward or right-hand (see theorem 17) 
 of the south meridian line. The line CE passing between 
 JST and W, or between north and west, is called north 20 
 west, being 20 towards the west from north ; the line CA 
 passing between N and E, or between north and east, 
 is called north 30 east ; and the line CB passing between 
 S and E, or between south and east, is called south 50 
 east ; for the bearing of any object from any point or place, 
 taken by the circumferentor, is only the angle that object 
 makes with the magnetic meridian of that point or place 
 from which the bearing is taken : Therefore, if the bearing 
 of B from C is required, it is nothing more than the 
 direction and angle that B makes with the magnetic 
 meridian of C ; CS is supposed the magnetic meridian 
 of C, and BCS is the angle the object makes with that 
 meridian. 
 
SUBTEEEANEOUS SUEYEYING, ETC. 
 
 Let WE, represent a circumferentor, and NS the magnetic 
 needle suspended on tbe pivot c as its centre of suspension 
 and centre of motion ; AB are two horizontal arras fixed 
 opposite to each other on the instrument; on the extremity 
 
 FJG.I8. 
 
 of each arm is the sight d and e perpendicular thereto, 
 through which is seen the object whose bearing is wanted : 
 The inner part of the circle to which the needle points is 
 divided into degrees, beginning at JN", and numbered to 90 
 each way to "W and E ; and also beginning at S, and 
 numbered to 90 each way to the same points "W and E. 
 The whole of the instrument is fixed on a stand, having 
 a ball and socket to allow of its being kept level and 
 turned freely round. This instrument is manufactured in 
 great perfection by Messrs. Elliott, Brothers, 30, Strand, 
 London. 
 
 To find the bearing of the line <?E, let the centre of the 
 instrument be fixed at c then turning it round so that the 
 eye of the observer may see F through the sights mn, the 
 
THEOREMS. lo 
 
 I 
 
 needle always continuing in the same position, or preserving 
 its parallelism, howsoever the instrument and sights are 
 turned, the end N of the needle, which, before the sights 
 were moved, pointed to north N, will, on the sight 
 being moved in direction of cF, point to li 30; for 7^ 
 will be brought to the situation of N ; then the angle 
 H$cg will be 30, which is the bearing of P with the north 
 magnetic meridian, and on being found to incline to the 
 right, therefore, from theorem 17, the bearing of F will 
 be north 30 east, which is usually written N 30 E. 
 
 Again, suppose the bearing of Gr from c is wanted, turn 
 the arms and sights ed in the situation of po, that is, in 
 direction of cGr, and the angle Ncf will be 50, for the 
 number of 50 at k will be opposite the end N of the needle ; 
 therefore, from theorem 17, the bearing will be found to 
 be N 50 E. 
 
 To find what point of the compass an object bears on, when its 
 direction, with respect to the magnetic meridian, is given. 
 
 (4.) RULE. If the given angle that the object makes 
 with the magnetic meridian is to the right of the north, the 
 object will bear to the east of that meridian ; if to the left 
 of that meridian, the object will bear to the west of it. 
 Also, if the given angle that the object makes with the 
 magnetic meridian is to the right of the south, the object 
 will bear to the west of that meridian ; if to the left, it will 
 bear to the east of it. See theorem 1.7. 
 
 EXAMPLE I. If I find an object makes an angle to the 
 right of 25 with the magnetic meridian, when I face the 
 north, what is the bearing of that object with that meridian ? 
 
 Prom the rule, the object will bear N 25 E, 
 
 EXAMPLE II. If I find an object makes an angle to the 
 left of 30 with the magnetic meridian, when I face the 
 north, what ia the bearing of that object with that meri- 
 dian? 
 
 The object will bo N 30 "W. 
 
14 STJBTEKEANEOUS SUBVEYING, ETC. 
 
 ' EXAMPLE III. If I find an object makes an angle 
 to the right of 30 with the magnetic meridian, when I face 
 the south, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear S 30 W. 
 
 EXAMPLE IV. If I find an object makes an angle to 
 the left of 25 with the magnetic meridian, when I face 
 the south, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear S 25 E. 
 
 EXAMPLE V. If I find an object makes an angle to 
 the right of 87 with the magnetic meridian, when I face 
 the south, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear S 87 W. 
 
 EXAMPLE VI. If I find an object makes an angle of 
 86 to the right with the magnetic meridian, when I face 
 the north, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear N 86 E. 
 
 EXAMPLE VII. If I find an object makes an angle of 
 89^ to the right with the magnetic meridian, when I face 
 the north, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear N 89^ E. 
 
 EXAMPLE VIII. If I find an object makes an angle 
 of 2 to the left with the magnetic meridian, when I face 
 the south, what is the bearing of that object with that 
 meridian ? 
 
 The object will bear S 2 E. 
 
 EXAMPLE IX. If I find an object makes no angle with 
 the magnetic meridian, when I face the north, what is the 
 bearing of that object with that meridian ? 
 
 The object will bear due north, or will be in the direction 
 of the magnetic meridian. 
 
 EXAMPLE X. If I find an object makes an angle of 
 
THEOEEMS. 
 
 15 
 
 20 to the right of another object which makes an angle 
 of 15 to the right with the magnetic meridian, when I face 
 the north, what is the bearing of the first object with that 
 meridian ? 
 
 The object will bear (20 -j- 15 = 35) N 35 E. 
 
 EXAMPLE XI. If I find a line makes an angle of 30 
 to the right of another line which forms an angle of 60 
 to the left with the magnetic meridian, when I face the 
 north, what is the bearing of that object with that 
 meridian ? 
 
 The line will bear (60 -30 = 30) N 30 \V. 
 
 The reversing of learinqs. 
 
 7 / U 
 
 (5.) If the bearing of N from S is found FFGI$ 
 to be due north, the bearing of S from N 
 will be due south, just the reverse of the 
 former; and if the bearing of B from S is 
 found to be N 20 E, the bearing of S 
 from B will be S 20 W, the reverse; and 
 so of any other. 
 
 To reduce bearings into angles. 
 
 (6.) Suppose the line CD to bear JS T 50 E with the 
 magnetic meridian NCS 
 (north being represented by 
 JN", and south by S), then 
 CD will make an angle of 50 
 NCD with the north magne- 
 tic meridian CN ; and with 
 the south magnetic meridian 
 CS it will make an angle of 
 180 - 50 NCD = 130 
 SCD (see theorem 5) : And if 
 the line OF bear S 30 E 
 with the magnetic meridian, 
 it will make an angle of 30 SCF with the south magnetic 
 
 F 10.20, 
 
16 SUBTERRANEOUS SURVEYING, ETC. 
 
 meridian CS ; and with the north magnetic meridian CN it 
 will make an angle of 180- 30 SCF = 150 NCF : Also if 
 the line CE bear due east with the magnetic meridian, it will 
 make an angle of 90 NCE, or SCE, with that meridian ; for 
 east or west always forms an angle of 90 with tbe meridian 
 (see theorem 16) : Or if the line CD bear N 50 E from the 
 point C, and that of CdN 80 E from the same point C, 
 then these two bearings being both of the same side of the 
 same meridian, will form an angle with each other of 80 
 50 = 30 /. DCW: Or if the line CD bear N 50 E from 
 the point C, and that of CFS 30 E from the same point 
 C, then these two bearings, being both of the same side of 
 different meridians, will form an angle with each other of 
 180 50^T30 = 100 L DCF : Or if CD bear N 50 E 
 from the point CaN 25 "W from the same point C, then 
 these two bearings, being of different sides of the same 
 meriftian, will form an angle with each other of 50 -f 25 
 = 75 L DC : Or if Ca bear N 25 W from the point C, 
 and CFS 30 E from the same point C, then these two 
 bearings, being of different sides of different meridians, will 
 form an angle with each other of 180 30 L SCF -f 25 
 NC0=175 Z. 0CF, or 30 25 = 5; which difterence 
 being taken from 180, leaves 175 L CF, as before : Or if 
 C<? bear N 30 "W" from the point C, and that of CFS 
 30 E from the same point C, then the one bearing as 
 much to the west side of the north meridian as the other 
 does to the east side of the south meridian, they will form 
 no angle at all, but a direct line, .with each other, or 30 
 30 = 0; which taken from 180, leaves 180, which, as 
 before, shows they form a direct line. (See theorems 4 
 and 5.) 
 
 (7.) If the magnitude of the angles B and C is required, 
 which is formed by the bearing AB taken from A to B, 
 S 50 E ; of the bearing BC taken from B to CS 45 W ; 
 and of the bearing CD taken from C to D, S 20 E ; now 
 to render the two bearings which form the L B to bearings 
 
THEOEEMS. 17 
 
 i 
 
 taken from that angular point, the bearing AB, which is the 
 
 bearing of B from A, must be made the bearing of A from B, 
 
 by reversing it (Art. 5) : Then the 
 
 L B is the angle formed by the 
 
 bearings N 50 W, and S 45 W; 
 
 which bearings, being on the same 
 
 side of different meridians, will form 
 
 an angle of 180 50 + 45 = 85 
 
 Z. B : And by reversing the bearing w c 
 
 BCS 45 W, the L C will be the 
 angle formed by the bearing N 45 
 ECB, and S 20 ECD; which 
 bearings, being on the same side of different meridians, will 
 form an angle of 180 45 + 20= 115 L C. In determin- 
 ing the magnitude of angles formed by bearings, those 
 bearings which compose the angles must be supposed to be 
 taken from the angular point. 
 
 To find the number of degrees contained in the angle that any 
 given bearing makes with the magnetic meridian. 
 
 (8.) BTJLE I. The number of degrees of the bearing will 
 be the magnitude of the angle that bearing forms with the 
 meridian it is taken from ; and the same number of degrees, 
 taken from 180, leaves the number of degrees contained 
 in the angle the same bearing makes with the contrary 
 meridian. 
 
 To find the number of degrees contained in an angle formed 
 by tii'O given bearings taken from the same point, wlien they 
 are both on the same side of the same meridian. 
 
 BULE II. From the number of degrees contained in the 
 one of the bearings, take the number of degrees contained 
 in the other, and the difference will be the number of degrees 
 contained in the angle formed by the two bearings. 
 
18 SUBTERRANEOUS SURVEYING, ETC. 
 
 To find the number of degrees contained in an angle formed by 
 two given bearings taken from the same point, when they 
 are both on the same side of different meridians. 
 
 EULE III.- Take the sura of the degrees contained in 
 the bearings from 180, and the remainder will be the num- 
 ber of degrees contained in the angle formed by the two 
 bearings. 
 
 To find the number of degrees contained in an angle formed 
 by two given bearings taken from the same point, when they 
 are on different sides of the same meridian. 
 
 EULE IV. The sum of the degrees contained in the 
 bearings is the number of degrees contained in the angle 
 formed by the two bearings. 
 
 To find the number of degrees contained in an angle formed by 
 two given bearings taken from the same point, when they 
 are on different sides of different meridians. 
 
 EULE V. Take the difference of the number of 
 degrees contained in the bearing from 180, and the re- 
 mainder will be the number of degrees contained in the 
 aogle formed by the two bearings. 
 
 To find the number of degrees contained in any angle which is 
 formed by given bearings not taken from the angular point. 
 
 EULE VI. Eeduce the bearings which compose the 
 angle required into bearings taken from that angular point 
 (which is done by reversing one of them ; Art. 5) then by 
 the preceding rules find the number of degrees contained 
 in the angle required. 
 
 EXAMPLE I. In the bearing N 5 "W, what is the mag- 
 nitude of the angle formed with that bearing and the north 
 magnetic meridian ? 
 
 Prom rule 1, Art. 8, the bearing will form an angle of 5 
 with the north magnetic meridian. 
 
 EXAMPLE II. In the bearing S 65 E, what is the 
 
THEOEEMS. 19 
 
 I 
 
 magnitude of the angle with that bearing and the south 
 magnetic meridian ? 
 
 The bearing will form an angle of 65 with the south 
 magnetic meridian. 
 
 EXAMPLE III. In the bearing S 20 W, what is the 
 magnitude of the angle with that bearing and the north 
 magnetic meridian? 
 
 From rule 1, Art. 8, from 180 -20 =160, the mag- 
 nitude of the angle formed with the north magnetic 
 meridian. 
 
 EXAMPLE IV. In the bearing N 80 E, what is the 
 magnitude of the angle with that bearing and the south 
 magnetic meridian ? 
 
 Prom 1 80 80 = 100, the magnitude of the angle 
 formed with the south magnetic meridian. 
 
 EXAMPLE V. In the bearing due east, what is the mag- 
 nitude of the angle with that bearing and the south, and 
 also north, magnetic meridian ? 
 
 The bearing will form an angle of 90 with both the south 
 and north magnetic meridians. (See theorem 16.) 
 
 EXAMPLE VI. In a bearing N 50 E, and another N 
 80 E, both taken from the same point, what is the mag- 
 nitude of the angle formed by the two bearings with each 
 other ? 
 
 Prom rule 2, Art. 8, the bearings being on the same side 
 of the same meridian 80 50 = 30, the magnitude of the 
 angle formed by the two bearings. 
 
 EXAMPLE VII. In a bearing S 60 E, and another S 10 
 E, both taken from the same point, what is the magnitude 
 of the angle formed by the two bearings with each other ? 
 
 60 10 = 50, the angle that the two bearings will form 
 with each other. 
 
 EXAMPLE VIII. In a bearing S 30 E, and another 
 N 50 E, what is the magnitude of the angle ' formed by 
 the two bearings with each other, when they are both taken 
 from the same point ? 
 
20 SUBTERRANEOUS SURVEYING, ETC. 
 
 Prom rule 3, Art. 8, the bearings being on the same side 
 of different meridians, then 180 30 + 50=z 100, the mag- 
 nitude of the angle formed by the two bearings. 
 
 EXAMPLE IX. In a bearing N 80 W,. and another 
 S 85 W, what is the magnitude of the angle formed by 
 the two bearings with each other, when they are both taken 
 from the samjp point ? 
 
 180 80^F85 = 15, the magnitude of the angle formed 
 by the two bearings. 
 
 EXAMPLE X. In a bearing N 50 E, and another N 
 40 "W, what is the magnitude of the angle formed by the 
 two bearings with each other, when both taken from the 
 same point ? 
 
 Prom rule 4, Art. 8, the bearings being on different sides 
 of the same meridian, then 50 4-40 = 90, the magnitude of 
 the angle formed by the two bearings. 
 
 EXAMPLE XI. In a bearing S 10 W, and another S 5 
 E, both taken from the same point, what is the magnitude 
 of the angle formed by the two bearings with each other ? 
 
 10 -j- 5 = 15, % the angle formed by the two bearings. 
 
 EXAMPLE XII. In a bearing N 50 E, and another 
 S 30 "W, both taken from the same point, what is the 
 magnitude of the angle formed by the two bearings with 
 each other ? 
 
 Prom rule 5, Art. 8, the bearing being on different sides 
 of different meridians, then 50 30= 20, which taken 
 from 180 = 160, the magnitude of the angle formed by the 
 two bearings. 
 
 EXAMPLE XIII. In a bearing S 60 W, and another 
 N 86 E, both taken from the same point, what is the 
 magnitude of the angle they form with each other ? 
 
 180 86 60 = 154, the magnitude of the angle formed 
 by the two bearings. 
 
 EXAMPLE XIY. In a bearing S 80 W, and another 
 N 5 W, both taken from the same point, what is the mag- 
 nitude of the angle formed with each other ? 
 
/ 
 
 THEOREMS. 21 
 
 180 80 -f 5= KJ8, the magnitude of the angle formed 
 by the two bearings.. 
 
 EXAMPLE XV. In a bearing N 20 W, and another 
 S 20 E, both taken from the same point, what is the mag- 
 nitude of the angle formed with each other ? 
 
 180 20 20= 180 ; therefore the two bearings form 
 no angle, but a direct line, with each other. 
 
 EXAMPLE XYI. Suppose the bearing ABS 50 E, fig. 
 Art. 7, taken from A to B, and BCS 45 W, taken from 
 B to C, required the magnitude of the angle B formed by 
 those two bearings ? 
 
 The two bearings which form the angle are not taken from 
 the angular point B, the leg AB being taken from the point 
 A : Therefore, from rule 6 3 Art. 8, by reversing the bearing 
 ABS 50 E, to BAN 50 W, the angle B will then be formed 
 of two bearings taken from the same angular point (viz.) 
 BAN 50 "W, and BCS 45 W; which bearing on the 
 same side of different meridians, from rule 3, Art. 8, will 
 be 180 50 ~+~45 = 85, the magnitude of the required 
 angle. 
 
 EXAMPLE XVII. In the bearing BCS 45 W, fig. 
 Art. 7, taken from B to C, and CDS 20 E taken from 
 C to D, required the magnitude of the angle C formed 
 thereby ? 
 
 The two bearings which form the angle are not taken, 
 from the angular point C ; Therefore, from rule 6, by 
 reversing BCS 45 W to N 45 E, the angle C will then 
 be composed of two bearings taken from that angular 
 point, N 45 E, and S 20 E ; which bearing on the same 
 side of different meridians, from rule 3, Art. 8, will be 
 180 45 + 20 =115, the magnitude of the required angle- 
 
 The reducing of hearings and distances to their northing 
 or southing, and easting or westing, from the point of 
 departure. 
 
 (9.) Suppose it is required to know how far B is north- 
 
22 
 
 SUBTERRANEOUS 
 
 ETC. 
 
 r/c. 2.2 
 
 F1C 23 
 
 ward of A. If SN represent the meridian, Aa will be the 
 northing of B from A, and B, or Ah, will be its easting, 
 or what B is eastward of the meridian of the 
 point A. 
 
 If we pass from any point A to B (lig. 23), 
 and from B to C, and from C to D, 'and 
 from thence return to the point A again, our 
 route will have as much southing as northing, 
 and easting as westing ; that is, the southing 
 will be equal to the northing, and the easting 
 will be equal to the westing. Let SN repre- 
 sent the meridian of A, the point of depar- 
 ture; the northing of AB from that point 
 will be represented by Aa, the northing of 
 ABC by Ab, that of ABCD by Ac ; and as the northing 
 of D from A is equal to Ac, the southing of A from D 
 
 will be equal to De = cA ; 
 therefore the southing will 
 be equal to the northing of 
 ABCD A: Also let the westing 
 of AB from the meridian of 
 A be represented by B, that 
 of ABC by 5C, that of ABCD 
 by cD ; then as the westing of 
 D from the meridian of A is 
 equal to cD, the easting of A 
 from D will be equal to eA 
 = c~D : Therefore the easting 
 will be equal to the westing 
 of ABCDA. 
 
 To find the northing or southing, and also the easting or 
 
 westing, of any given bearing and distance. 
 (10.) RULE. Look in the traverse tables, under the 
 degree answering to that of the bearing : and to the right, 
 opposite the length of that bearing (in the column of dig- 
 
THEOREMS. % 23 
 
 tances), will be tound the quantity of northing or southing, 
 according as the bearing is north or south, and also the 
 easting or westing, according as the bearing is east or west. 
 
 Note. When the given distance consists of chains and links, and the 
 angles of degrees and minutes, the method of finding the northing or 
 southing, and the easting or westing, is given in Art. 59. 
 
 EXAMPLE I. "What is the northing and easting of the 
 bearing and distance N 40 E 10 chains ? 
 
 Look in the traverse tables, under 40, and opposite 10 
 chains, in the column of lengths, is found 7 chains 60 links 
 of northing, and 6 chains 43 links of easting (the links are 
 usually written after the chains as decimals, see next 
 Example). 
 
 EXAMPLE II. "What is the northing and westing of !N" 
 10 W 6 - 50 chains from the point of commencement, or 
 point of departure ? 
 
 Its northing is 6*40 chains, and its westing is 1'13 chains. 
 
 EXAMPLE III. What is the southing and westing of 
 S 79 W 7-30 chains from the point of departure ? 
 
 Its southing is T39 chains, and its westing 7'16 chains. 
 
 EXAMPLE IY. What is the southing and westing of 
 S 80 W 6 chains ? 
 
 Its southing is 94 links, and its westing 5 36 chains. 
 
 EXAMPLE V. What is the northing and westing of 
 N 40 W 8-50 chains ? 
 
 Its northing is 6'50 chains, and its westing is 5-46 chains. 
 
 EXAMPLE VI. What is the southing and easting of 
 S 5 E 6-52 chains ? 
 
 Its southing is 6*49 chains, and its easting is 56 links. 
 
 EXAMPLE VII. In the following successive bearings and 
 distances taken from the pit A to the pit B, N 50 W 
 10 chains, N 20 E 5 chains, and S 40 W 7 chains, I 
 wish to "know what denomination of bearing the pit B 
 have from A ; also the length of each ? 
 
SUBTERRANEOUS SURVEYING, ETC. 
 PREPARATORY TABLE. 
 
 BEARINGS. 
 
 NORTHING 
 
 SOUTHING. 
 
 EASTING. 
 
 WESTING. ' 
 
 N 50 W 10 chains 
 N 20 E 5 
 S 40 W 7 ,, 
 
 Chains. 
 6-43 
 470 
 
 Chains. 
 5*36 
 
 Chains. 
 1-71 
 
 Chains. 1 
 7'66 
 
 4-50 
 
 11-13 
 5-36 
 
 12-16 
 1-71 
 
 5-77 
 
 10-45 
 
 Now, as the northing is greater than the southing by 
 577 chains, and the westing greater than the easting by 
 10'45 chains, the pit will have 577 chains of northing, and 
 10'45 chains of westing from A. 
 
 EXAMPLE VIII. What is the northing and westing of 
 the pit D from C, under the following bearings, N 20 E 
 10 chains, and S 60 W 6 chains ? 
 
 BEAPJNG6. 
 
 NORTHING. 
 
 SOTJTH Z NG. 
 
 EASTING. 
 
 WESTING. 
 
 N 20 E 10 chains 
 S60W6 
 
 Chains. 
 9-40 
 
 Chains. 
 3-00 
 
 Chains. 
 3-42 
 
 Chains. 
 
 5 V 20 
 3-42 
 
 9-40 
 3-00 
 
 1-78 
 
 6-40 
 
 The southing being taken from the northing, and the 
 easting from the westing, the pit D will have G'40 chains 
 of northing, and 1*78 chains of westing, from the pit C. 
 
 EXAMPLE IX. "What is the northing and easting of B 
 from A under the following successive bearings, S 20 W 
 10 chains, N 5 chains, N 30 E 20 chains, and N 5 E 
 8 chains ? 
 
 The pit B will have 20-89- chains of northing, and 7-28 
 chains of easting, from A. 
 
THEOREMS. % 25 
 
 Surveying and recording bearings. 
 
 (11.) Suppose the bearing of ABC to be required. Set 
 the circumferentor on A (the north being represented by 
 N and the south by S) : then turning that 24 
 
 part of the instrument having the fleur-de-lis \ 
 from you, or towards B, turn the instrument 
 until the object B is seen through, and cut by, 
 the hair in the sights ; and the angle NAB 
 being the angle that the sights and line AB 
 make with the magnetic meridian NS, will be 
 the bearing of B from A, suppose 30 ; which 
 also being to the right side of the north 
 meridian, will be N 30 E (see theorem 17): 
 Then bring the instrument forward to B, and 
 fix it there, directing the same sight at B 
 towards C as was directed at A towards B ; 
 then observe the angle that BC makes with the 
 magnetic meridian, which suppose 25 NBC ; 
 and being to the left of the meridian, will be N. 25 "W. 
 In order to prove the work, and try the accuracy of the 
 instrument when it is standing at B, apply the eye to that 
 sight which was next B when it stood at A; then take the 
 bearing of A from B, which, if found to be the reverse of 
 B from A, shows the work so far is true. The bearing 
 of B being taken, in like manner, from C, will prove the 
 truth of the survey. Observe always to take the degrees 
 of each bearing by the same end of the needle*. 
 
 (12.) Suppose the bearing of B from A, C from B, and 
 D from C, to be required : Fix the instrument at A, with 
 the fleur-de-lis towards B (the north being represented by 
 IS" and the south by S) ; then take the bearing of B, as 
 before-described, which suppose to make an angle of 30 
 NAB to the right with the magnetic meridian, or jfr 
 30 E ; remove the instrument to B, and take the bearing 
 of C, which suppose equal to 30 NBC to the loft, 
 
26 , 
 
 SUBTERRANEOUS SURVEYING, ETC, 
 
 or N 30 W; then remove the instrument to C, and 
 FIS,25t take the bearing of D, which sup- 
 pose equal to 65 SOD to the left, or 
 S 65 E: See below in the survey- 
 book. 
 
 From A to B, N. 30 E. 
 B to C, N. 30 W. 
 C to D, S. 65 E. 
 
 Note. This survey may be proved in the same 
 manner as the preceding ; and the methods of 
 plotting and protracting subterraneous surveys, 
 with the descriptions of the instruments used for 
 the purpose, are given in Arts. 23, 24, 25 and 
 26, to which the student is referred, as it would 
 greatly facilitate in these studies to lay down his 
 work on paper, as soon after he has finished it 
 as a proper opportunity presents itself ; all the 
 instruments required, in the first instance, being 
 of equal parts, a protractor, and a ~f"' S( l tiare ' 
 
 FIG 2 6 
 
 (13.) Suppose the subterraneous working ABCDA, to 
 be surveyed, beginning at the pit 
 A: Fix the instrument at the 
 centre of the pit A ; then let a 
 person hold a lighted candle at 
 B, being the utmost distance it 
 can be se'en through the sights 
 of the instrument, the bearing of 
 which being taken from A, sup- 
 pose due south, or in the direc- 
 tion of the magnetic meridian of 
 A, and its distance from A 
 suppose 6*57 chains ; which place 
 in the survey-book, as below: 
 Kemove the instrument to B, where the candle stood, 
 and direct the person to place the lighted candle at C ; 
 then take its bearing from B, which suppose to make 
 
THEOftEMS. 27 
 
 % 
 
 an angle CBS of 80 with the magnetic meridian, or to bear 
 S 80 "W; and its distance being found 7*10 chains, remove 
 the instrument to C, the lighted candle being removed to 
 D ; then take its bearing and distance as before, which 
 suppose N 10 "W 5 chains ; remove the instrument to 
 D, and direct the lighted candle to be placed at the centre 
 of the pit A, where the survey commenced ; then take its 
 bearing from D, which suppose 1ST 70 E 8*35 chains, 
 and the survey will be finished. 
 
 A survey of a subterraneous working, commencing at the 
 centre of the pit A. 
 
 AB, S. . . .6-57 chains. 
 EC, S. 80 W. ... 7-10 
 CD, N. 10 W. . 5-00 
 
 DA, N. 70 E 8-35 
 
 This survey, which is composed of four sides, may be 
 proved by adding together the degrees contained in the 
 interior angles, which, if they amount to 360, the work 
 will be right. (See theorem 11). 
 
 The proof. The magnitude of the angle DAB is 70 
 (see rule 1, art. 8) in the reducing of bearings into angles ; 
 angle ABC is 180 80 L. CBS = 100 ; angle BCD is 
 80 + 10 = 90 (see rule 4, art. 8) ; and angle CDA is 
 180 - 70 + 10 = 100 (see rule 3, art. 8). 
 
 Then /. DAB = 70 
 ABC = 100 
 /_ BCD = 90 
 CDA = 100 
 
 360 
 
 Also the proof may be made by finding the northing, 
 southing, easting, and westing of all bearings and distances. 
 If the southings are equal to the northings, and the west- 
 ings equal to the eastings, then the work will be right. 
 (See Art. 9.) 
 
 c 2 
 
28 
 
 SUBTERRANEOUS SURVEYING, ETC. 
 
 C. L. 
 
 Thus, S. . . 6 57 
 S. 80 W. 7 10 
 N. 10 W. 5 
 N. 70 E. 8 35 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 Chains. 
 
 4 : 93 
 2-87 
 
 Chains. 
 6-57 
 1-23 
 
 Chains. 
 7*85 
 
 Chains. 
 
 6 : 98 
 0-87 
 
 7 "SO 
 
 7'80 
 
 7'8o 
 
 7'85 
 
 ! 
 
 Therefore the northings and southings being equal, as 
 also the eastings and westings equal, the work is right. 
 
 (14.) Suppose the bearing and distance of B from A, C 
 from B, D from C, F from D, a from B, H from &, and I 
 from H, are required. Fix the instrument at A, and take 
 the bearing (as before described) of B from it, which sup- 
 pose to be N 30 "W", and the distance 5'50 chains; set 
 it down in the following survey-book ; also make a mark * 
 with chalk at B, which must likewise be noted down, to 
 return to. In order to take the bearings of C, D, and F, 
 remove the instrument to B, and take the bearing of C 
 from it, which suppose JS" 45 E, and distance 7 chains ; 
 the bearing of D from C suppose N 50 "W, and the 
 distance 5 chains ; the bearing of F from D suppose N 
 85 E, and distance 7 chains : Then bring the instrument 
 from D to the chalk mark at B, and take the bearing of 
 Gr from B, which suppose S 65 W, and distance 6 ! 50 
 chains ; the bearing of H from Gr suppose N 10 "W, and 
 distance 6 chains ; and lastly, the bearing of I from H 
 suppose IS". 60 E., and distance 4 chains. See them pro- 
 perly arranged in the following survey-book (p. 29). 
 
 Suppose the bearings and distances of B from the pit 
 A, C from B, D from C, F from D, Gr from F, H from 
 Gr, P from H, and A from P, also I from O, K from I, 
 L from I, and M from L, are required, together with any 
 remarkable circumstance that may be met with in the 
 survey: Fix the instrument at A, directing a person to 
 go with a lighted candle to B ; and take the bearing and 
 
THEOREMS. 
 
 SURVEY- BOOK. 
 
 FIG. 27, 
 
 Commencing at A. Chains. 
 
 X. 30 W. . .5-50 toB. 
 At B is a chalk i 
 
 mark * to re- 1 
 
 turn to. 
 N. 45 E. . .! 7-00 [to C. 
 N. 60 W. . .5-00 ,toD. 
 N. 85 E. . .: 7-00 rto F. 
 Returns to the 1 
 
 chalk mark * 
 
 at B, and pro-j 
 
 ceedstoGr, &c.| 
 
 S. 65 W. . J 6-50 :toGK 
 N. 10 W. . .i 6-00 toH. 
 N. 60 E. . 4-00 to I. 
 
 -IP E 
 
 FIG. 28. 
 
 distance of B from it, which suppose S 36 E 7 chains ; 
 which insert in the survey-book. Also at a, 3 chains from 
 A towards B, is the water- 
 course from the pit B, : Bring 
 the instrument to B, and take 
 the hearing and distance of 
 the lighted candle at C, 
 which suppose S 42 W 4 
 chain. At b, 3 chains from B 
 towards C, is the water-course 
 from the pit F : Remove the 
 instrument to C, and take 
 the bearing and distance of the 
 light at D, which suppose S. 
 75. W. 10 chains. At 4 
 chains from C towards D is a 
 chalk mark * at O, to return 
 to. Take the bearing and 
 distance of F from D, which 
 suppose N 42 AV 7-50 chains, 
 to a pit ; which note also down in the survey-book : Take 
 the bearing and distance of Gr from F, which suppose N 
 
30 
 
 SUBTERRANEOUS STJRYETIKG, ETC. 
 
 42 E 5 chains : Take the bearing and distance of H from 
 Gr, which suppose E 4 chains : Take the bearing and 
 distance of P from H, which suppose .N 9 E 4 chains. 
 At 2 chains from H, towards P, is the pit E- ; which note 
 down in the survey-book. Take the bearing and distance 
 of A from P, which suppose S. 69 E. 5'56 chains. Now 
 return to the * mark at O, and fix the instrument there : 
 Take the bearing and distance of the candle placed at I, 
 which suppose S 10 "W, 5 chains, and a chalk mark * 
 to return to : Take the bearing and distance of K from I. 
 which suppose S 80 E 6 chains. Eeturn to the mark at 
 I, and fix the instrument, and take the bearing and distance 
 of L from it, which suppose S 40 "W 4 chains: Take the 
 bearing and distance of M from L, which suppose S 45 E 
 4 chains, and the survey will be finished. 
 
 See the bearings and distances arranged inform of a Survey-book. 
 
 
 
 Chains.! 
 
 From A to B 
 
 S. 36 E. 
 
 7-00 
 
 
 At 
 
 3 '00 from A is a, the water-course 
 
 
 
 
 from the pit E. 
 
 BtoC 
 
 S. 42 W. 
 
 4-00 
 
 
 
 At 
 
 3-00 
 
 from B is 6, the water-course : 
 
 
 
 
 from the pit F. 
 
 CtoD 
 
 S. 75 W. 
 
 10-00 
 
 
 
 At 
 
 4-00 
 
 from C is 0, a chalk mark * 
 
 
 
 
 to return to. 
 
 D to F 
 
 N. 42 W. 
 
 7-50 
 
 and pit F. 
 
 F to G 
 
 N. 42 E. 
 
 5-00 
 
 
 GtoH 
 
 E. . . 
 
 4-00 
 
 
 HtoP 
 
 N. 9 E . 
 
 4-00 
 
 ,- 
 
 
 At 
 
 2-00 
 
 from H is the pit E. 
 
 Pto A 
 
 S. 69 E. 
 
 5-56 
 
 
 
 
 
 Eeturn to the chalk mark * 
 
 
 
 atO. 
 
 to I 
 
 S. 10 W. j 5-00 
 
 
 
 
 At I is a chalk mark * to 
 
 
 
 return to. 
 
 I to K ! S. 80 E. 
 
 6 -00 j 
 
 
 
 | Eeturned to the chalk mark * 
 
 
 
 
 
 at I. 
 
 I to L S. 40 W. 
 
 4-00 
 
 
 Lto M 
 
 S. 45 E. 
 
 4-00 
 
 
THEOREMS. 
 
 31 
 
 (15.) Suppose a survey of the subterraneous working 
 ABCDFGrHPA see last fig., is required, to commence at 
 the pit A : Proceed as in the last, recording each bearing' 
 and its respective distance in the following manner, as in 
 
 the survey-book : 
 
 THE SURVEY COMMENCING AT THE PIT A. 
 
 
 
 Chains. 
 
 From A to B 
 
 S. 36 E. 
 
 7-00 
 
 BtoG 
 
 S. 42 W. 
 
 4-00 
 
 CtoD 
 
 S. 75 W. 
 
 10-00 
 
 D to F 
 
 N. 42 W.' 
 
 7-50 
 
 F to Gr 
 
 N. 42 E. 
 
 5-00 
 
 GtoH 
 
 E. . . . 
 
 4-00 
 
 HtoP 
 
 N. 9E. 
 
 4-00 
 
 Pto A 
 
 S. 69 E. 
 
 5-56 
 
 To prove this survey by theorem 12 : The number of 
 sides which the survey contains is 8 ; then the amount of 
 all the angles contained in the figure is equal to 8 x 2 
 X~~90 5 4 x 90 = 1080. Now from the rules of 
 reducing bearings into angles (art. 8), L ~B = 102, L C 
 i= 147, L B 117, L F = 96, L G- 132, L H = 261, 
 Z. P = 78, and L A = 147 ; whose sum is equal to 
 1080, as before : Therefore the survey is right. 
 
 Also the same may be' proved by taking the northing, 
 southing, easting, and westing of the bearings (art. 9) ; 
 which, if the southings are found equal to the northings, 
 and the westings equal to the eastings, the survey will be 
 right. 
 
82 
 
 SUBTEREAKEOUS SURYEYINa, ETC. 
 
 Bearing and Distance. 
 
 Northing. Southing. 
 
 Easting. 
 
 Westing. 
 
 Chains. 
 
 Chains. 
 
 Chains. 
 
 Chains. 
 
 Chains. 
 
 S. 36 E. 7-00 
 
 
 5-66 
 
 4-21 
 
 
 S. 42 W. 4-00 
 
 ... 
 
 2-97 
 
 
 2-63 
 
 S. 75 W. 10-00 
 
 
 2-59 
 
 
 9-66 
 
 N. 42 W. 7-50 
 
 5-55 
 
 ... 
 
 
 4-97 
 
 N. 42 E. 5-00 
 
 372 
 
 
 3-35 
 
 
 E. . . . 
 
 
 
 4-00 
 
 
 N. 9 E. 4-00 
 
 3-95 
 
 
 0-63 
 
 
 S. 69 E. 5-56 
 
 
 2-00 
 
 5-21 
 
 ... 
 
 
 13-22 
 
 13-22 
 
 17-31 
 
 17-31 
 
 i 
 
 
 
 
 FIG 29 
 
 The northings and southings being equal, and the eastings 
 and westings being also equal, the survey must be right. 
 
 (16.) Suppose the subterraneous bearings and distances 
 of the workings ABCDF, are required, commencing at 
 
 the pit A ; and likewise 
 p JP^ the bearing and distance 
 
 on the surface of a sink- 
 ing pit Gr from the pit 
 / A : Fix the instrument 
 
 at the centre of the pit 
 A in the mine, and take 
 the bearing and distance 
 of B from it; also, of 
 C from B, D from C, 
 and F from D ; then the 
 survey under - ground 
 will be completed. As- 
 cend to the surface, and fix the instrument at the mouth 
 of the pit A ; and having previously placed a mark at 
 the pit Or, take its bearing and distance from A, which 
 insert in the survey-book. (Observe to take the bearing 
 of Gr from the same point of the pit A, on the surface, 
 that the subterraneous survey commenced under the sur- 
 face, so that the proper situation of F, or any other 
 part of the subterraneous working, may be shown with 
 
THEOREMS. 
 
 respect to the two pits.) If the bearing and distance of 
 the pit G- from that of A cannot be got at once, by the 
 interposition of any building or other obstruction, it must 
 be taken at two or three, or more, different' bearings. 
 
 THE SURVEY COMMENCING AT THE PIT A. 
 
 
 
 Chains. 
 
 From A to B 
 
 N. 30 W. 
 
 5-50 
 
 BtoC 
 
 N. 45 E. 
 
 7-00 
 
 C toD 
 
 N. 50 W. 
 
 5-00 
 
 DtoF 
 
 N. 85 E. 
 
 7-00 
 
 
 The bearing and dis- 
 
 
 
 tance of the sinking 
 
 
 
 pit G from the pit 
 
 
 
 A, taken on the 
 
 
 
 surface. 
 
 
 A to G- 
 
 N. 45 E. 
 
 18-00 
 
 (17.) Suppose the subterraneous workings CDFG-HI 
 KBLMOP are required to be surveyed, beginning at the 
 pit A : Fix the instrument at A, and take the bearing and 
 distance of the headways AC (as before shown), which 
 suppose S 10 E 3-10 chains. At 80 links is a bord 1 to 
 the right and left, holed into the headways each way ; at 
 1'GO chains is a bord 2 to the right and left, holed each 
 way ; at 2 40 chains is a bord 3 to the right, 1 chain to the 
 face, and to the left holed into the headways. Take the 
 bearing and distance of Aa, which suppose S 80 AY T60 
 chains : At 1 30 chains is a headways 11 to the right and 
 left, and a mark * to return to. Take the bearing and 
 distance of Gr, which suppose S. 70 "W. 1'SO chains : At 
 80 links is a headways I to the right, and a mark * to 
 return to; and at T20 chains is a headways Y to the left, 
 and a mark -f to return to. Take the bearing and distance 
 of the headways ED (by fixing the instrument at the mark 
 at 11), which suppose S 8 W 2'50 chains : At 70 links is a 
 bord 4 to the right and left, and holed each way ; at 1/50 
 chains is a bord 5 to the right and left, and holed each 
 
 c 3 
 
34 SUBTEBKAKEOUS SUBYEYItfa, ETC. 
 
 way. Take the bearing and distance of the headways VF 
 (by fixing the instrument at the mark at V), which suppose 
 
 S 10 "W 2-40 chains : At 80 links is a bord 6 to the right 
 1'30 chains to the face, and to the left holed into the head- 
 ways ; at 1'60 chains is a bord 7 to the right 1 chain to the 
 face, and to the left holed into the headways. Take the 
 bearing and distance of the headways AK (by fixing the 
 
THEOREMS, 35 
 
 instrument at A), which suppose N 10 W 4'20 chains : 
 At 80 links is a bord 8 to the right and left, and holed into 
 the headways each way ; at T70 chains is a bord 9 to the 
 right and left, and holed into the headways each way ; at 
 2-50 chains is a bord 10 to the right and left, and holed 
 into the headways each way ; at 3'30 chains is a bord 11 
 to the right, and holed into the headways, and none to 
 the left. Take the bearing and distance of the headways 
 El (by fixing the instrument at the mark at E), which 
 suppose N 2 "VY 3 chains : At 80 links is a bord 12 to the 
 right and left, and holed into the headways each way ; at 
 1-60 chains is a bord 13 to the right and left, and holed 
 into the headways each way ; at 2'40 chains is a bord 14 to 
 the right and left, and holed into the headways each way. 
 Take the bearing and distance of the headways Z>H (by 
 fixing the instrument at the mark at J), which suppose 
 N 1 W 5 chains : At 80 links is a bord 15 holed into 
 the headways to the right, and to the left 90 links to the 
 face; at 1'70 chains is a bord 16 holed into the headways 
 to the right, and to the left 60 links to the face ; at 2'55 
 chains is a bord 17 holed into the headways to the right, 
 and to the left 60 links to the face ; at 3'40 chains is a bord 
 18 to the right 50 links to the face, and to the left 55 links 
 to the face. Take the bearing and distance of AM (by 
 fixing the instrument at A), which suppose N 85 E 2'80 
 chains : At 1*30 chains is a headways X to the right and 
 to the left, and a mark + to return to ; at 2*50 chains is a 
 headways Q to the right and to the left, and a mark * to 
 return to. Take the bearing and distance of the head- 
 ways XP (by fixing the instrument at the mark X), which 
 suppose S 5 E 3 '10 chains : At 75 links is a bord 19 to 
 the right and left, and holed into the headways each way ; 
 at 1'60 chains is a bord 20 to the right and left, and holed 
 into the headways each way ; at 2'40 chains is a bord 21 
 to the right, and holed into the headways, and none to 
 the left. Take the bearing and distance of the headways 
 
SG STTBTEHEAXEOTJS SUEVEYIXG, ETC. 
 
 QO (by fixing the instrument at the mark Q), which suppose 
 S 4 E 2-30 chains: At 80 links is a bord 22 to the right, 
 and holed into the headways, and to the left 40 links to the 
 face ; at 1'GO chains is a bord 23 to the right, holed into the 
 headways, and none to the left. Take the bearing and 
 distance of the headways XYZB (by fixing the instrument 
 at the mark X), which suppose from X to Y N 2 W 2-80 
 chains : At 90 links is a bord 24 to the right and left, and 
 holed into the headways each way ; at 1*70 chains is a bord 
 25 to the right and left, and holed into the headways each 
 way ; at 2*60 chains is a bord 26 to the right and left, and 
 holed into the headways each. Take the bearing and dis- 
 tance of YZ (by fixing the instrument at Y), which suppose 
 N 5 W 2 chains : At GO links is a bord 27 to the left, 
 holed into the headways, and none to the right ; at 1*50 
 chains is a bord 28 to the left 30 links, and none to the 
 right. Take the bearing and distance of ZB (by fixing the 
 instrument at Z), which suppose N 3 "W" 2'30 chains, to 
 a pit B. Lastly, take the bearing and distance of the head- 
 ways QL (by fixing the instrument at the mark Q), which 
 suppose N 2W 3'60 chains: At 80 links is a bord 29 
 to the left, holed into the headways, and to the right 30 
 links to the face ; at 1 link is a bord 30 to the left, holed 
 into the headways, and to the right 20 links to the face ; at 
 2'60 chains is a bord 31 to the left, holed into the'head- 
 ways, and none to the right. See the survey-book, where 
 the whole is recorded ; 
 
THECEEMS. 
 
 37 
 
 SURVEY-BOOK. 
 
 A SURVEY OP A PIT'S WORKINGS, COMMENCING AT THE PIT A. 
 
 Bearings. 
 
 Remarks to Left. 
 
 Dist. 
 
 Remarks to Right. 
 
 
 
 
 Chains. 
 
 
 
 S. 10 E. 
 
 
 
 3-10 
 
 . 
 
 AC 
 
 
 Bord holed 
 
 0-80 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 1-60 
 
 Bord holed 
 
 
 
 Bord holed 
 
 2-40 
 
 Bord 1 chain from the 
 
 
 
 
 
 headways 
 
 
 S. 80 W. 
 
 . .... 
 
 1-60 
 
 . . 
 
 Act 
 
 
 Headways 
 
 1-30 
 
 Headways 
 
 
 
 And a chalk mark * 
 
 
 
 
 
 at R to return to 
 
 
 
 
 S. 70 W. 
 
 . . . . 
 
 1-80 
 
 . 
 
 aG 
 
 
 
 0-80 
 
 A headways b, and a 
 
 
 
 
 
 chalk mark * to 
 
 
 
 
 
 return to 
 
 
 
 Headways V, and a 
 
 1-20 
 
 
 
 
 chalk mark * to 
 
 
 
 
 
 return to 
 
 
 
 
 S. 8 W. 
 
 . . . 
 
 2-50 
 
 . . 
 
 RD 
 
 
 Bord holed 
 
 0-70 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 0-50 
 
 Bord holed 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * atV 
 
 
 
 
 S. 10 W. 
 
 . . 
 
 2-40 
 
 .... 
 
 VF 
 
 
 Bord holed . . . 
 
 0-80 
 
 Bord 1-30 chain from 
 
 
 
 
 
 the headways 
 
 
 
 Bord holed 
 
 1-60 
 
 Bord 1 chain from the 
 
 
 
 
 
 headways 
 
 
 
 Returned to the pit A 
 
 
 
 
 N. 10 W. 
 
 . 
 
 4-20 
 
 . 
 
 AK 
 
 
 Bord holed 
 
 0-80 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 1-70 
 
 Bord holed 
 
 
 
 Bord holed . 
 
 2-50 
 
 Bord holed 
 
 
 
 None . . . . 
 
 3-30 
 
 Bord holed 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * atll 
 
 
 
 
 N. 2 W. 
 
 
 3-00 
 
 
 RI 
 
 
 Bord holed . . . 
 
 0-80 
 
 Bord holed 
 
 
 
 Bord holed 
 
 1-60 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 2-40 
 
 Bord holed 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * at b 
 
 
 
 
 N. 1 W. 
 
 
 
 5-00 
 
 . 
 
 m 
 
 
 
 Bord 90 links from 
 
 0'80 
 
 Bord holed 
 
 
 
 the headways 
 
 
 
 
 
 Bord 60 links from 
 
 1-70 
 
 Bord holed 
 
 
 
 the headways 
 
 
 
 
SUBTERRANEOUS SURVEYING, ETC. 
 
 Bearings. 
 
 Remarks to Left. 
 
 Dist. 
 
 Remarks to Right. 
 
 
 
 
 Chains. 
 
 
 
 
 Bord 60 links from 
 
 2-55 
 
 Bord holed 
 
 
 
 the headways 
 
 
 
 
 
 Bord 55 links from 
 
 3-40 
 
 Bord 50 links from 
 
 
 
 the headways 
 
 
 the headways 
 
 
 
 Returned to the pit A 
 
 
 
 
 N. 85 E. 
 
 . . . 
 
 2-80 
 
 
 
 AM 
 
 
 Headways 
 
 1-30 
 
 Headways 
 
 
 
 And a chalk mark * 
 
 
 
 
 
 at X to return to 
 
 
 
 
 
 Headways 
 
 2-50 
 
 Headways 
 
 
 
 And a chalk mark * 
 
 
 
 
 
 at Q to return to 
 
 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * atX 
 
 
 
 
 S. 5 E. 
 
 . 
 
 3-10 
 
 . 4 
 
 XP 
 
 
 Bord holed 
 
 0-75 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 1-60 
 
 Bord holed 
 
 
 
 None 
 
 2-40 
 
 Bord holed 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * atQ 
 
 
 
 
 S. 4 E. 
 
 
 2-30 
 
 . . . 
 
 QO 
 
 
 Bord 40 links from 
 
 0-80 
 
 Bord holed 
 
 
 
 the headways 
 
 
 
 
 
 None 
 
 1-60 
 
 Bord holed 
 
 
 
 Returned to the mark 
 
 
 
 
 
 * atX 
 
 
 
 
 N. 2 W. 
 
 
 2-80 
 
 . 
 
 XY 
 
 
 Bord holed 
 
 0-90 
 
 Bord holed 
 
 
 
 Bord holed . . . 
 
 1-70 
 
 Bord holed 
 
 
 
 Bord holed 
 
 2-b'O 
 
 Bord holed 
 
 
 N. 5 W. 
 
 
 2-00 
 
 . . . 
 
 YZ 
 
 
 Bord holed 
 
 0-60 
 
 None 
 
 
 
 Bord 30 links from 
 
 1-50 
 
 None 
 
 
 
 the headways 
 
 
 
 
 N. 3 C W. 
 
 . 
 
 2-30 
 
 To pit B 
 
 ZB 
 
 
 Returned to the mai'k 
 
 
 
 
 
 * atQ 
 
 
 
 
 K. 2 W 
 
 
 3-60 
 
 
 QL 
 
 
 Bord holed 
 
 0-80 
 
 Bord 30 links from 
 
 
 
 
 
 the headways 
 
 
 
 Bord holed . . . 
 
 1-70 
 
 Bord 20 links from 
 
 
 
 
 
 the headways 
 
 
 
 Bord holed 
 
 2-60 
 
 None 
 
 
 Note. When marks are made to be returned to in the survey* observe 
 that they are returned to, otherwise the survey will be defective ; and 
 when the new method of taking the angles, given in Arts. 20 and 21, is 
 adopted, the angles, thus taken, must be inserted instead of the bearings, 
 the column being headed "angles" instead of "bearings." 
 
THEOREMS. 
 
 FIG 3! 
 
 The Back-Sight. 
 
 (18.) Suppose the bearing and distance of B from the 
 pit A is required : Eix the instrument at B, instead of A 
 (keeping the same sight foremost, 
 and pointing towards b, when it is 
 placed in the situation of B, as if 
 it had been placed in the situation 
 of A, for the purpose of taking the 
 bearing of B) ; then apply the eye 
 at the sight furthest distant from A, 
 turning the same until the light at 
 the pit A is cut by the perpendi- 
 cular hair in the other ; observe 
 then the bearing of A from B, 
 which, suppose S 30 E, on being 
 reversed (see p. 17), will become JST 30 W, for the bear- 
 ing of B from A, the distance, 
 being measured, is found to be 3 
 chains; making the bearing and 
 distance of B from A X 30 ~\V 
 3 chains. 
 
 Bearings taken in this way are 
 taken in a direction contrary to 
 the order of the survey, and the 
 eye is applied at the contrary 
 sight to that which it would be 
 applied when direct bearings are 
 taken. 
 
 (19.) Suppose the bearing of 
 ABCDFGr and H is required, c 
 making use of the back-sight 
 throughout the survey : Fix the 
 instrument at B, instead of A, 
 directing that sight towards A 
 which, in the situation of A, would have been hindmost, 
 
 FJC 32 
 
40 SUBTEREANEOUS SURVEYING, ETC. 
 
 in the manner before directed ; then the bearing A 
 from B being found to be 1ST 45 E, on being reversed 
 makes S 45 W, the bearing of B from A, which enter 
 into the survey^book. The instrument standing at B, turn 
 that sight towards C which pointed to a, and take the bear- 
 ing of C from B, which being found N 75 "W, enter the 
 same into the survey-book, without reversing, as it is not a 
 backsight. Remove the instrument from B to D, and direct 
 the sight back to C from D, in the same manner as from B 
 to A : The bearing then of C from D being found S 10 W, 
 which, being reversed, will be N 10 E, the bearing of D 
 from C, which enter into the survey-book. Then take the 
 bearing of E from D, which being found N 80 E, enter 
 the same into the survey-book, without reversing. Lastly, 
 remove the instrument to Gr ; then take the back-sight 
 from G- to E, which being found S 15 E, on being re- 
 versed will be N 15 W, the bearing of G- from E, which 
 being entered into the survey-book, then take the bearing 
 of H from G- ; which suppose N 30 E, which enter also 
 into the survey-book, without reversing, and the survey is 
 finished. By this mode of taking bearings, the instrument- 
 is on]j removed half the number of times it would otherwise 
 be, were the back-sights not taken. 
 
 SURVEY-BOOK. 
 
 The bearing of B from A, S. 45 W. 
 C from B, N. 75 W. 
 D from C, N. 10 E. 
 F from D, N. 80 E. 
 Gfrom F, N. 15 W. 
 II from G, N. 30" E. 
 
PART II. 
 
 ON SURVEYING SUBTERRANEOUS EXCAVA- 
 TIONS WITHOUT THE GENERAL USE OF 
 THE NEEDLE. 
 
 IT has long been found that the conducting of subter- 
 raneous surveys requires strict attention in guarding against 
 the presence of ferruginous substances, which exist in almost 
 all mines, and which, it is well known, affect the magnetic 
 needle, so as to cause it to give erroneous indications. On 
 this account Mr. Fenwick was induced, as long ago as 1822 
 (when the second edition of his work was published), to 
 suggest to the surveyor of mines the following new method, 
 in which the needle has no control except in the first 
 departure. 
 
 The use of the instrument.* 
 
 Suppose the subterraneous excavation ABCDEF to be 
 surveyed beginning at the pit A, and terminating at the 
 pit F. 
 
 (20.) Place the instrument at B, and turning it until the 
 vanes at zero cut the lighted candle at the centre of the 
 pit A, which suppose N 65 E ; and suppose AB to be 
 3 chains, the fixed sight at 0^ still remaining as ' before ; 
 screw the instrument fast, and turn the moveable sights so 
 as to cut a candle placed at C, taking care that the instru- 
 
 * The improved Circurafereutor, by Elliott Brothers, 30, Strand, London, 
 which is still much used, especially in secondary mining surveys ; but 
 the modern improved theodolite is much to be preferred. See 
 ff-.i Mathematical Instruments, Wealds Series. 
 
42 SUBVEYING SUBTEBBANEOUS EXCAVATIONS 
 
 ment has remained immovable. If so, read off the angle, 
 which the index makes with the moveable circle, which sup- 
 
 FIG. 33. 
 
 pose .120 ; then the angle ABC is 120, that is, the excava- 
 tions BC and AB make an angle of 120. Removing the 
 instrument to C, turn the sights and index so as to cut 
 the candle at B, keeping the instrument immovable ; then 
 turn the sights to the candle at D, reading off the angle 
 BCD, which suppose 80; and measure CB, which call 
 5 chains. Remove the instrument next to D, measuring 
 the distance CD, which call 3 chains ; and turn the sights 
 and index to the candle at C, the instrument, as before, 
 being kept immovable ; turn the sights to the candle E, 
 observe the angle CDE ? which suppose 70, and let the 
 distance DE be 4 chains. Remove the instrument to E, 
 and turn the sight and index to the candle at D, keeping 
 the instrument immovable; turn the sight to the candle 
 at E, and observing the angle DEF = 160 ; lastly, measure 
 the distance EF, which call 6 chains, and the survey is 
 completed. 
 
 The following method of conducting subterraneous survey 
 entirely without the use of the magnetic needle, was sug- 
 gested by Mr. T. Baker (who has now made the present 
 
WITHOUT THE TJSE OF THE NEEDLE. 43 
 
 additions and improvements to the new edition of Mr. 
 Fenwick's "Subterraneous Surveying"), at least 35 years 
 ago ; but it was ridiculed by the then colliery surveyors ; 
 yet is now recommended and adopted by several scientific 
 mining surveyors ; among whom I may name Mr. H. 
 Mackworth ; who has given more elaborate details for con- 
 ducting these surveys than those in the preceding article : 
 Mr. M.'s improvements on Mr. Baker's suggestion are 
 given in the following article. 
 
 (21.) To commence a survey without the magnetic needle, 
 where there is only one shaft to the mine, the following 
 plan should be adopted. Two thin copper wires, carrying 
 heavy weights, must be suspended from a strong straight 
 edge, at the surface of the shaft, and as near the edges of 
 the shaft as not to touch them, the weights reaching nearly 
 to the bottom of the shaft; while the weights must be 
 immersed in buckets of water, or what would be still better, 
 in vessels filled with mercury, to diminish oscillation, which 
 will still continue, if the shaft is deep ; but in the latter 
 case, for only a very short time. The observer standing 
 behind the wires must next send a candle along the head- 
 ing, as far as it can be seen, and have it fixed in a line with 
 the wires. He should repeat the operation in the opposite 
 direction, by placing a candle against one of the wires, 
 that the whole may be checked by seeing that the three 
 candles are exactly in a line. This line being the basis 
 of the whole underground survey, must be permanently 
 marked by four or more pegs driven into the roof, with 
 nails in them, or by marks on cross timbers or masonry. 
 Eeturning to the surface, permanent pegs should be placed 
 at some chains' distance, on each side of the shaft, in a line 
 with the wires, as G- and H (see last fig). "We then obtain 
 a line on the surface exactly corresponding with the base 
 line of our operation underground. The same process may 
 be adopted, if there is more than one shaft to a mine ; but 
 it is not generally desirable to repeat it at more than one 
 
44 SURVEYING SUBTERRANEOUS EXCAVATIONS 
 
 shaft. A few hours' labour in getting the fundamental 
 lines permanently fixed and connected, before commencing 
 the survey, is afterwards well repaid. 
 
 The angular instrument used for this purpose ought to 
 be the modern improved theodolite (see the foot-note to 
 last article). Three tripods should be provided, and two 
 lamps on stands, fitting on the tripod, of such a height that, 
 when the lamp is replaced by the theodolite, the fulcrum 
 of the axis of the telescope must be of the same height a& 
 the top of the wick in the lamp, a tripod with a lamp being 
 placed under the centre of the shaft, at some well-marked 
 station ; the second tripod is fixed with the theodolite upon 
 it, as far along the base-line as the light at the bottom oi % 
 the shaft can be seen. The theodolite is clamped to zero. 
 The third tripod with the other lamp on it, is sent as far 
 forward as the light can be seen from the theodolite. The 
 depth of the top of the wick in the first lamp below the top 
 of the shaft having been ascertained, we carry on a series 
 of levelling with the vertical arc of the theodolite all 
 through the mine, at the same time as the horizontal 
 angles and the measurement of the lines are taken. The 
 telescope of the theodolite being directed to the top of the 
 wick of the first lamp, the angle of elevation or depression 
 is read. The lower limb being then clamped, and the upper 
 relaxed, the horizontal angle is then read to the second 
 lamp, and at the same time its angle of elevation or depres- 
 sion is read. The distance having been carefully measured, 
 the first tripod is taken up, and carried forward beyond the 
 third tripod, a lamp is placed on the second tripod, and the 
 theodolite on the third tripod, when the observation of 
 the angles are repeated as before. 
 
 (22.) The leading feature of Mr. A. Beauland's plan 
 (see "Mining Surveys, Institute of Mining Engineers, 
 ]S~ewcastle-upon-Tyne ") consists in a method of fixing a 
 bearing, or meridian line at the bottom of the pit, the 
 direction of which is determined, either with reference to 
 
WITHOUT THE USE OF THE NEEDLE. 45 
 
 Hie true meridian, or with respect to some line arbitrarily 
 iixed on the surface, as PQ, fig. to Art. 20. By this means 
 the underground survey can be commenced, and carried 
 forward to any extent, by means of the theodolite/ and is 
 properly connected with the surface, the whole process 
 being effected without the aid of the magnetic compass. 
 
 This method is Mr. B.'s own invention, or, at least, he is 
 not aware that the idea has ever been carried out before, or 
 has ever occurred to any one else, though of course it is 
 quite possible that he may not be the first person who has 
 thought of such a plan. 
 
 The process is effected by means of a powerful transit 
 instrument, mounted in the line of the shaft, either at the 
 top or bottom as may be most convenient. For simplicity, 
 suppose the instrument to be at the top of the shaft. It 
 is -fixed and properly adjusted on a very firm support, 
 which must be so arranged as not to interrupt the view 
 of the telescope, when pointed vertically down the shaft. 
 
 Two marks are then fixed at the bottom of the pit, as 
 nearly as may be in the same vertical plane as the transit, 
 so that each of them can be seen through the telescope, 
 and appear in the centre of the field of view. These marks 
 are rendered visible by the light of a strong lamp reflected 
 upwards, and are likewise so arranged that both can be 
 seen by a theodolite placed at the bottom in a horizontal 
 line with them. They are made as small as will allow of 
 their being observed by the transit at the top, and are of 
 such form that they can be bisected by the wires with 
 great precision, the marks being as far apart as possible. 
 
 If now, on pointing the instrument downwards, each of 
 the marks be exactly bisected by the middle wire, it is 
 evident that the horizontal line, in which the marks are 
 placed, coincides with the vertical plane of the instrument, 
 and is, therefore, parallel to the position of the telescope 
 when pointed horizontally. In this case, therefore, we 
 have two lines, one at the top of the shaft, represented by 
 
46 SURVEYING SUBTERRANEOUS EXCAVATIONS. 
 
 the optical axis of the telescope when pointed horizontally 
 the other the line joining the centres of the two illuminated 
 marks at the bottom, and the bearing of the instrument 
 being determined, either with respect to the meridian, or 
 to some determinate line, which can be connected with the 
 surface survey, that of the line of direction of the marks 
 below is ascertained at the same time. 
 
 This, however, is on the supposition, that each of the 
 marks is seen precisely in the centre of the telescope.- If 
 this condition is not exactly fulfilled, the marks being a 
 little out of the centre of the field of view, the apparent 
 distance of each mark from the middle wire is accurately 
 measured by a micrometer, or some other means, and from 
 these distances, the angular deviation of the line of the 
 marks from the plane of the instrument is determined by 
 calculation. Having found the amount of this deviation, 
 the bearing of the line of marks is at once deduced from that 
 of the instrument, and the connection between the surface 
 and underground survey, made as in the former case. 
 
 It is necessary, in order to complete the process, that 
 permanent marks should be fixed above and below, the 
 marks above ground being set out in some given direction, 
 with respect to the plane of the telescope; those below, 
 with respect to the illuminated marks, which, as well as 
 the instrument, must be removed from their places in the 
 line of the shaft, before the colliery can resume working. 
 
 "Wherever the nature of the ground, or erections on the 
 surface, admit of it, marks may be placed at once in the 
 direction of the instrument above being set out in any 
 convenient positions, coinciding with the middle wire of 
 the telescope. These permanent marks should of course be 
 placed so that one of them can be seen from the other, it 
 is also desirable to have them conveniently placed for the 
 commencement of the surface survey. 
 
 Where, however, it is not practicable to set out a line in 
 the direction of the transit, owing to obstructions, some 
 
PLOTTING STTEYETS. 47 
 
 other direction must be taken, one mark being fixed in the 
 line of the instrument, and the other at any point at a con- 
 venient distance, and visible from the first. The direction 
 of the permanent line will, of course, be determined with 
 respect to that of the transit, by setting up the theodolite 
 at the nearer station, and measuring the angle between the 
 direction of the transit and that of the further station. 
 
 The permanent marks fixed at the bottom of the pit are 
 fixed in like manner, and their direction determined from 
 that of the illuminated marks, by the aid of the theodolite, 
 which is placed at some point near the shaft, in the line of 
 the illuminated marks, and from which a more distant point 
 can be seen. A permanent mark is then fixed at the place 
 occupied by the theodolite, and another at the more distant 
 point referred to, which may be chosen convenient for the 
 commencement of the underground survey. 
 
 Mr. A. B. has thus endeavoured to explain, somewhat 
 briefly, but he trusts with sufficient distinctness, the method 
 by which the underground survey may be connected with 
 the surface. It will scarcely be necessary for him to 
 observe, that the whole process is one requiring great care, 
 and an intimate acquaintance with the use and manipula- 
 tion of the instruments, such as can scarcely be acquired 
 without considerable expense. With proper management, 
 however, and a transit of sufficient size and power, he believes 
 the bearing may generally be fixed at the bottom of the pit 
 without any error exceeding one minute of an arc, a degree 
 of precision amply sufficient for all practical purposes. 
 
 On plotting subterraneous surveys. 
 
 (23.) Plotting may be divided into two kinds : The first 
 kind, the communicating of bearings and distances of a 
 subterraneous survey to paper, for the purpose of planning 
 the same ; the second kind, the manner of running on the 
 surface of the earth the different bearings or angles and 
 distances, in the same order as they were taken under- 
 
 
STJEYEYIKG SUBTEEEANEOUS EXCAVATIONS 
 
 ground in the survey. In the first mode, the protractor, 
 for setting off the angles contained in each beariDg, and 
 a scale of chains and links, for transferring the distances, 
 are requisite ; and in the second mode, the circumferentor 
 or theodolite, and Gunter's chain. Observe, in running off 
 the bearings on the surface, that the same instrument be 
 made use of as in the subterraneous survey ; and also let 
 the same end of the needle, when used, determine the 
 angles of the bearings as determined them under- ground. 
 This last precaution is not necessary when the magnetic 
 needle is not used. 
 
 (24.) Let ABCD represent a protractor, which is a cir- 
 cular rim of brass, and E its centre, of about 9 inches 
 
 diameter, divided into 
 degrees, and each de- 
 gree in quarters of a 
 degree, commencing 
 from the north and 
 south points A and B 
 and numbered up to 
 90 atC and D. Also 
 abc represents a semi- 
 circular protractor, 
 which for many pur- 
 poses, is more com- 
 modious than the 
 circular one, ab re- 
 presenting the meri- 
 dian, and e its centre. 
 These instruments 
 are manufactured by 
 Messrs. Elliott Bro- 
 thers, 30, Strand, 
 London. 
 
 In using this in- 
 strument in plotting bearings, the meridian line AB or ab, 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 
 
 must be applied to the assumed meridian line drawn on 
 paper; and if a line Ee is drawn from the centre E, through 
 the 50fch degree or division from B to C, supposing AB 
 the meridian, A the north, and B the south ; then Ee will 
 be N 50 ~W (see theorem 17), and the line E/ 1 passing 
 through the 20th degree or division, will be N 20 E. 
 
 (25.) Suppose the following bearings and distances 
 to be plotted on paper 
 
 10 chains. 
 
 7 
 6 
 
 FIC.35. 
 
 AB, N. 45 W. . 
 BC, N. 10 E. 
 CD, S. 50 E. . 
 
 Proceed thus : 
 
 Draw the meridian line NS on the paper where the work 
 has to be plotted, N for north, and S for south ; then fix on 
 any place on that meridian line for the commencement of 
 the work, as at the pit A; apply the meridian line 
 AB of the protractor on the as- 
 sumed meridian, with its centre 
 E on A ; let nesw represent the 
 protractor, n corresponding with 
 N the north, and s with S the 
 south, e will represent the east, 
 and w the west; then draw the 
 line AB from the centre of the 
 protractor at A through the 45th 
 degree from n towards w, or west, 
 and it will represent N 45 "W" : 
 Also from the scale of chains 
 take 10 with the compasses, 
 and setting the same from A 
 to B, and AB will represent 
 the first bearing and distance N 
 45 W, 10 chains : by the assist' 
 ance of a parallel ruler, or any 
 other method, draw the second meridian line ns, through 
 B, parallel to that drawn through A ; apply the protractor 
 
50 SURVEYING SUBTERRANEOUS EXCAVATIONS 
 
 as before directed, with its centre on the point B ; draw 
 the line BO from the centre of the protractor at B, 
 through the 10th degree from n towards e, and it will 
 represent N 10 E : Then from the scale of chains take 7 
 with the compasses, setting the same from B to C, and BC 
 will represent the second bearing and distance ; then draw 
 the third parallel line ns through C ; apply the protractor 
 as before, with its centre on C ; draw the line CD through 
 the 50th degree from s towards e, and it will represent 
 S 50 E : Then take 6 chains from the scale, setting the 
 same from C to D, and CD will represent the third bearing 
 and distance ; and the whole will be plotted. 
 
 Note. The student ought now to lay down on paper the several surveys, 
 commencing at Art. 12, not only by the old method of bearings, taken by 
 the magnetic needle, but also by the modern and more accurate methods, 
 given in Arts. 20, 21, and 22 (the methods given in the several articles 
 not differing materially except at the commencement of the surveys), that 
 he may thus acquire a skilful and ready method of performing this impor- 
 tant part of his profession. See the following article. 
 
 (250.) Let the following angles and distances, taken in a 
 coal-mine, be laid down on paper (see fig. to Art. 20). 
 
 Let NS be the true meridian, obtained by making proper 
 allowance for the magnetic variation ; and let the following 
 distances be measured, and angles be taken in a coal-mine 
 as below : 
 
 DISTANCES. 
 
 AB = 3 -.12 chains. 
 BC = 4-96 ,, 
 CD = 2-89 
 DE = 4-17 
 EF 6-02 
 
 ANGLES. 
 
 NAB = 64 39' 
 ABC 118 19' 
 BCD = 79 15' 
 CDE = 61 5' 
 DBF = 158 57' 
 
 Draw the meridian line NS, N representing the north 
 point, and let A in the line NS be the pit where the work 
 is to commence ; lay off from the meridian line NS by the 
 protractor, the angle NAB=64 39 r , in the manner already 
 directed; and from a scale of equal parts, lay off the dis- 
 
WITH OK WITHOUT THE USE OF THE NEEDLE. 51 
 
 tance AB = 3'12 chains, and extend the line, if necessary ; 
 next apply the line AB of the protractor on the line AB 
 on the plan, the centre E of the protractor being applied to 
 the angular point B : then lay off the angle ABC=118 19' ; 
 and the distance BC = 4'96 chains ; apply the protractor to 
 the line BC, as before directed, lay off the angle BCD=r 
 79 15', and the distance CD=2'89 chains : lay off succes- 
 sively the angles ODE = 61 5' and DEE = 158 57', and the 
 distances DE=4-17 and EE = 6'02 chains; and the work 
 will be completed, being a correct representation of the 
 survey made in the mine. 
 
 Next plot the surveys, given in Arts. 17, 18, and 19, by 
 laying off the successive angles, as directed in Arts. 20 and 
 21, the bearings being previously reduced to the angles, 
 which every two successive distances make with one another 
 by Art. 6. 
 
 Note. In the second column of the survey-book to Art. 17, the angles 
 NAB, ABC, &c., must be entered, as shown in this article. 
 
 Suppose the following subterraneous survey is to be 
 plotted by the application of the T square : 
 
 N. 54 W. . . .10 chains. 
 S. 42 W. . . . 7 
 N. 30 W. . . .6 
 
 (26.) On the drawing-board, or table ABCD, fix the 
 paper abed, on which the survey is to be plotted, and let 
 SN represent the T square applied thereon, which also 
 represents the magnetic meridian (N the north and S the 
 south). Eix upon the point /for the commencement of the 
 work ; apply the straight edge of the semicircular, pro- 
 tractor sn against the arm of the T square NS, with its 
 centre on the pointy/ then draw the line fg through the 
 54th degree of the protractor from north to west, setting 
 off the distance 10 chains from / to g : Then fg is the first 
 
 D 2 
 
52 
 
 STJIIVEYINQ SUBTEHEAITEOUS EXCAVATIONS 
 
 FIG 36 
 
 bearing and distance N 54 W 10 chains. Kemove the T 
 square along the line AC until its arm SN meets the point 
 y, where it represents the magnetic meridian ; then apply 
 
 the protractor as before- 
 directed, with its centre 
 011 g ; draw the line gli 
 through the 42nd degree 
 from south to west, setting 
 off the distance 7 chains 
 from g to h : and gli is the 
 second bearing and distance 
 S 42 W, 7 chains. Ke- 
 move again the T square 
 until its arm SN meets 
 the point h, representing 
 there the magnetic meridian; then apply the protractor 
 with its centre on Ji; draw the line Tik through the 
 30th degree from north to west, setting off the distance 
 6 chains from Ji to Tc : And Jik is the third and last bearing 
 and distance N 30 W, 6 chains. The work being finished, 
 take the paper off the board. 
 
 (27.) In the following subterraneous survey fgJik (see 
 Pig. to last Article), I wish to know, by one single bearing 
 and distance, the situation of k from f? 
 
 V 
 
 fg, N. 54 W. 
 gh, S. 42 W. 
 M, N. 30 W. 
 
 10 chains. 
 
 7 ,, 
 6 
 
 Protract the survey on the paper fixed to the drawing- 
 board, as before-directed; then draw a line from f to Jc ; 
 move the arm of the T square until it touches /, forming 
 therewith the magnetic meridian ; then apply the protractor 
 with its centre at f, observing what division or degree the 
 line fh cuts which will be found to be the 71st nearly, 
 which is the magnitude of the angle N/& : Measure the 
 distance to 7c from / by the same scale as the work was 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 53 
 
 plotted from, which distance is found to be 16*70 chains ; 
 then from rule, Art. 4, the bearing of k from / will be found 
 to be N 71 "W, and its distance 16'70 chains. 
 
 (28.) In the following survey of the subterraneous work- 
 ing ABCDF (see Fig. to Art. 16), driven from the pit A 
 towards Gr, I wish to know the bearing that the workmen 
 must proceed in from F to hit the pit Gr, and likewise the 
 distance between F. and Gr ? 
 
 Plot the survey from the given data in Art. 16, by the 
 use of the T square ; also by laying off the several angles, 
 as directed in Arts. 20 and 21, which will verify the survey. 
 
 Then the bearing of the pit Gc from F, from rule, Art. 4, 
 will be S 65 30' E. Measure the length of the line FG by 
 the same scale of equal parts as the work was protracted 
 from which is found to be 8*60 chains ; hence the bearing 
 and distance of the subterraneous working from F, to hit 
 the pit G-, must be S 65 30' E 8*60 chains. 
 
 ANOTHER METHOD. 
 
 Which may le thought more eligible than the preceding \for if 
 any error is made in this method of 'plotting, it only affects 
 the particular part where it occurs, and is not carried 
 throughout the remaining part of the work, as in the otner 
 methods already described. 
 
 (29.) Suppose the following survey to be plotted accord- 
 ing to this method : 
 
 Chains. 
 
 AB, S. 36 E. . . .7-00 
 EC, S. 42 W. . . . 4-00 
 CD, S. 75 W. . . . 10-00 
 DF, N. 42 W. . . . 7-50 
 
 Prepare the survey by taking the northing, southing, 
 easting and westing of all the bearings therein (see Art 10, 
 ex. vii.), placing each separately in its respective column, 
 in the following preparatory table : Thus the bearing and 
 
54 
 
 SURVEYING SUBTEBEANEOUS EXCAYATIONS 
 
 distance AB, S 36 E, 7 chains, will, from the traverse 
 tables, contain 5-66 chains of southing, and 4'12 chains of 
 easting ; and so of all the rest. 
 
 The next thing is to determine the northing and south- 
 ing of the bearings conjointly, from A the point of com- 
 mencement of the survey : Thus let NS represent the 
 magnetic meridian of A, the southing of the bearing AB 
 S 36 E, 7 chains is 5-66 chains A ; which place in the 6th 
 column of the preparatory table. The southing of the bear- 
 ing BC, S 42 W, 4 chains is 2-97 chains al, which, being- 
 added to 5'66 chains, makes 8'63 chains A.I for the south- 
 ing of the bearings ABC ; which place in the 6th column : 
 The southing of the bearing CD S 75 W, 10 chains is 2'59 
 
 FIG 37 
 
 chains lc, which, being added to 8'63 chains, makes 11-22 
 chains Ac for the southing of the bearings ABCD ; which 
 place in the 6th column : The next, DF, N 42 W 7'50 
 chains, will produce 5'55 chains of northing ce from D, which, 
 being subtracted from 11*22 chains, leaves 5 '67 chains Ae, 
 the southing of the bearings ABCDF from the commence- 
 ment A : Then determine the easting and westing distance of 
 
WITH OR "WITHOUT THE TTSE OF THE NEEDLE. 55 
 
 the end of each bearing from the assumed meridian of the 
 point A, or point of commencement. The easting of the 
 bearing AB, which is S 36 E, 7 chains from NS, the assumed 
 meridian, will be found by the traverse tables to be 4'12 
 chains &B ; which place in the 7th column of the following 
 table : The westing of the bearing S 42 W, 4 chains from 
 B will be found to be 2' 68 chains /C, which, taken from the 
 easting aB or &/4-12 chains, leaves 1'44 chains, 1C for the 
 easting of the bearings ABC from NS, the assumed meri- 
 dian of A : The westing of the bearing S 75 "W, 10 chains 
 from C will be found to be 9 -66 chains C^, from which take 
 1-44 chains of easting 5C, leaves Ig or e?D 8'22 chains for 
 the westing of the bearings ABCD from NS : The westing 
 of the bearing N 42 W, 7*50 chains from D will be 
 found to be 4*97 chains Dl, which, being added to 8'22 
 chains cD, makes d or eF 13 '19 chains for the westing of the 
 bearings ABODE from NS. Now, to prepare the survey for 
 plotting, the next thing is to assume another meridian, which 
 shall be to the west of the westmost bearing of the survey 
 from NS ; and from this second meridian find the easting 
 of the end of each bearing from it (see the 8th column of 
 the table). The greatest westing of the bearing from NS 
 is eF, or cl 13-19 chains : Suppose, then, this second assumed 
 meridian line to be ns 14 chains AO west of the first meri- 
 dian line NS, place the 14 chains at the top of the 8th 
 column of the following table, which is the distance that 
 the point A is eastward of ns : Then 14 chains ha + 4' 12 
 chains B = 18-12 chains TiB, the distance that B is east of 
 ns ; which place in the 8th column : Then 14 chains + 
 1'44 chains 5C = 15'44 chains 7cC, the easting of C from 
 ns : Then 14 chains 8'22 chains cD = 5'78 chains 0D, 
 the easting of D from ns : Lastly, 14 chains 13 f 19 chains 
 cF = 81 links m~F, the easting of F from ns; which, being 
 all entered in the 8th column of the following table, the 
 survey will be prepared for plotting. 
 
56 
 
 SURVEYING SUBTEEBAFEOUS EXCAVATIONS 
 
 
 
 ||S* 
 
 .W W pq H pq 
 
 
 
 
 *i? i5 *J 
 
 fl O (N --fi CO > 1 
 
 
 
 
 IH "^ 
 
 rH O T-l -^ t>. OO 
 
 
 
 06 
 
 f 111 
 
 J^J CO JO ^ b 
 
 
 
 
 illjr 
 
 <1 PQ P PS 
 
 
 
 
 llfd 
 
 J W C^ ^H (M Ci 
 
 
 
 
 o 
 
 7^ -* CM T-I 
 
 
 
 ~ 
 
 &> &> .2 
 
 -^ A^ co co 
 
 
 
 
 ^'3^3 
 
 O r-t 
 
 
 
 
 r O 5> 
 
 
 
 
 
 
 w^^a 
 
 *Q o o & 
 *w ^ 
 
 *-M 
 
 
 
 
 
 -= 
 
 
 
 * A . 
 
 CO OQ CO OJ 
 
 _U) 
 
 *s 
 
 
 CO 
 
 Il 
 
 g 'O CO <N h- 
 
 Jq o oo i^ b 
 
 6 ^ 
 
 <u 
 M 
 
 % 
 
 
 
 H S -* 
 
 ^ -<3 -<^ <j 
 
 48 
 
 
 
 
 
 <s 
 
 M 
 
 PQ 
 
 xd 
 
 1 
 
 S CO <> t- 
 
 .9 ^o to cs 
 
 e ?* * * 
 
 1 
 
 < 
 
 
 
 o ^ " 
 
 73 
 
 H 
 
 
 
 S-^ O R 
 
 
 
 J^ 
 
 
 
 m 
 
 .2 
 
 EATOR 
 
 * 
 
 be 
 
 g 
 
 1 
 
 pj C 1 ! 
 
 6 "* : : i 
 
 PQ 
 
 0> 
 
 1 
 
 1 
 
 2 
 
 
 
 e 
 
 g 
 
 H 
 
 
 
 OS 
 
 
 3 
 PH 
 
 
 fcb 
 .3 
 
 CO t^ O 
 
 .a co o o 
 
 p 
 
 s 
 
 
 CO 
 
 S 
 
 u : 
 
 i 
 
 
 
 
 
 -3 ^ 
 
 r5 
 a 
 
 
 
 
 m 
 
 1 
 
 
 
 1 
 
 '3 V 5 
 
 S 
 
 
 c* 
 
 f 
 
 Q xo 
 
 O : : : 
 8 
 
 J5 
 
 EH 
 
 
 
 
 
 PQ 
 
 
 
 
 
 & 
 
 
 
 00 
 
 p 
 
 | ? o f g 
 
 
 
 
 
 'S i>- ^ o t> 
 
 
 
 , 
 
 If 
 
 8 ^ p ^ 
 
 
 
 
 II 
 
 ?o c^ 2rs c< 
 
 
 
 
 '1 
 
 CO <**** 
 
 
 
 
 1 
 
 CO CO CO {25 
 
 
 
 
 
 PQ P fe 
 <1 PQ P 
 
 
WITH OR WITHOUT THE USE OF THE NEEDLE. 57 
 
 In order to plot the survey, fix the paper on the drawing- 
 board or table G-HIK ; then draw the meridian line ns by 
 the application of the T square, n representing the north 
 and s the south ; let O be the point for the commencement 
 of the work, and from the 6th column of the table set off the 
 different southings ; 1st, 5'GG chains Aa from O to k, being 
 the southing of the bearing AB ; 2dly, 8*63 chains Ab from 
 O to &, the southing of the bearings and distances AB and 
 BC ; 3rdly, 1T22 chains Ac from O to 0, the southing of the 
 bearings and distances AB, BC, and CD; and 4thly, 5'67 
 chains Ae from O to m, the southing of the bearing and 
 distances AB, BC, CD, and DF. This being done, apply the 
 T square to the side G-K, its arm crossing the meridian line 
 ns at right angles ; then from the 8th column of the table 
 set off 14 chains of easting from O to A, and A denotes the 
 place of commencement of the survey, or point of departure : 
 Move the T square down the side GrK until its arm comes 
 to Ti ; then set off 18*12 chains of easting from Ji to B, draw 
 the line AB, and it represents the first bearing and dis- 
 tance ; move the T square until the arm comes to &, then 
 setting off 15*44 chains of easting from Tc to C, draw the 
 line BC, and it represents the second bearing and distance ; 
 move the T square to 0, then setting off 5*78 chains of east- 
 ing from to D, draw the line CD, and it represents the 
 third bearing and distance ; move the T square to m, then 
 setting off 81 links of easting from m to F, draw the line 
 DP, and it represents the fourth and last bearing and dis- 
 tance. Then the whole survey will be plotted. 
 
 Next plot this survey from the given data by laying off the 
 several angles as directed in Arts. 20 and 21, the bearings 
 being previously reduced to the angles which the successive 
 distances make with one another by Art. 6 ; also plot the 
 surveys, given in Arts. 30 and 31, in the same manner. 
 
 (30.) Suppose the following subterraneous survey to be 
 plotted, beginning at the pit A : 
 
58 
 
 SUBYEYING SUBTEEBANEOUS EXCAVATIONS 
 
 FIG, 3 8, 
 
 Chains. 
 
 AB, N. 42 E. 5-00 
 BC, E. 4-00 
 
 CD, N. 9 E. 4-00 
 At 4 chains is a mark 
 * to return to. 
 
 DF, S. 69 E. 5-66 
 Returned to mark *. 
 
 DG, S. 36 E. 7-00 
 GH, S. 42 W. 4-00 
 
 TA 
 
 Prepare the survey for plotting, by taking the northing, 
 southing, easting, and westing of each bearing from the 
 traverse tables. 
 
 The northing and easting of the first bearing and distance 
 N 42 E, 5 chains, will be northing 3*72 chains, and easting 
 3-35 chains (which see in the following preparatory table, 
 together with the northing, southing, easting, and westing 
 of all the others) . Then find the northing and southing of 
 the bearings conjointly from the commencement of the sur- 
 vey at the pit A* which is had from the 2nd and 3rd 
 column of the table : The northing of the first bearing and 
 distance will be found to be 3'72 chains ; which place in the 
 6th column of the table : That of the second bearing and dis- 
 tance will be also 3'72 chains ; that of the third, 3'72 chains 
 + 3*95 = 7*67 chains ; and so of all the rest. Also take 
 the easting and westing of each bearing and distance from 
 the meridian of the pit A, which is had from the 4th and 
 5th column of the table : The easting of the first bear- 
 ing and distance will be found 3 -35 chains ; which place 
 in the 7th column of the table : That of the second will be 
 3-35 + 4 chains z= 7'35 chains of easting ; and so of all the 
 
WITH OB WITHOUT THE USE OF THE NEEDLE. 
 
 GO 
 
 fl, 
 
 H 
 
 CO O> rH 
 
 
 g 
 
 *irl 
 
 ** 
 
 a <M 
 
 g jo o co 
 
 *H CO O CO 
 
 -iq co _*^ o 
 
 I 
 
 CQ 
 
 00 
 
 1? 
 
 O -*( 
 
 6 
 
 II 
 
 02 
 
 od 
 
 G5 W 
 
 P Ci5 
 
60 STJRYEYINQ STJBTERBANEOTTS EXCAYATIONS 
 
 rest : As from the 8th column of the table the end of each 
 bearing in the survey will be east of the meridian NS of A ; 
 therefore no other need be assumed. 
 
 "Fix the paper abed on the drawing-board or table IKLM ; 
 draw a meridian line NS by the application of the T square, 
 and mark A for the pit, and commencement of the work ; 
 then make a mark with the compasses at e, on the meridian 
 line NS, 3*72 chains to the north of A (from the 6th column 
 of the table), which is the northing of the first and second 
 bearing and distance : Make another at/, 7'67 chains from 
 A to the north; another at g t 5-67 chains ; another at h, 1 
 link to the north of A ; and another at Jc, 2'96 chains to the 
 south of A : This being done, apply the T square to the 
 side LI, its arm crossing the meridian NS at right angles, 
 and corresponding with e ; then set off from e to B, 3*35 
 chains of easting to the right (from the 8th column of the 
 table), which is the easting of the first bearing and distance : 
 Draw a line from A to B, and AB represents the first bearing 
 and distance: Also set off from e to C, 7*35 chains to the right, 
 and draw the line BC : Eemove the arm of the T square to 
 /, and set off from /to D 7'98 chains to the right, and draw 
 the line CD ; there make a mark * to return to : Eemove 
 the T square to y, and set off from g to F 13*19 chains to 
 the right, and draw the line DF : Eemove the T square to 
 h, and set off from Ji to G 17'31 chains to the right, and 
 flraw the line DGr from the mark at D : Eemove the T 
 square to k, and set off from k to H 14-63 chains to the 
 right, and draw the line GH ; and ABCDFGH will repre- 
 sent the survey protracted. 
 
 (31.) An example showing that an error, committed 
 during the time of plotting the survey after this method, 
 is not communicated to the following part of the work : 
 
 Suppose the subterraneous survey ABCDF is required 
 to be plotted. 
 
WITH OK WITHOUT THE USE OF THE NEEDLE. 61 
 
 FIG 39 
 
 AB, S. 36 E. 
 BC, S. 42 W. . 
 CD, S. 75 W. 
 DP, N. 42 W. . 
 
 Chains. 
 7-00 
 
 4'00 
 10-00 
 , 7-50 
 
 (For Preparatory Table see next page.) 
 
 Fix the paper on the drawing-board GHIK, and draw the 
 assumed meridian NS 14 chains west of the meridian of A, 
 which exceeds the greatest westing in the 6th column ; let 
 O be the point thereon for the commencement of the work: 
 Set off, from the 6th column of the table, the different 
 southings from O to a b c, and d respectively ; and from the 
 8th column of the same table set off the different eastings 
 from to A, from a to B, from b to C, from c to D, and 
 from d to F ; and ABCDF will represent the survey truly 
 plotted. Now, suppose the plotter, in laying down the 
 eastings in the 8th column of the table, commits an error, 
 by setting off from the assumed meridian 25'44 chains be, 
 instead of 15*44 chains 5C, then the point C will be 
 removed to e, and BC will be represented by Be, and CD 
 by eD; therefore it appears, from inspecting the figure, 
 that the error will cease at D, and the following bearings, 
 be there ever so many, will be each in the same situation as 
 if no such error had ever existed; which is a peculiar advan- 
 tage in this mode of plotting. 
 
62 STJEYEYINa SUBTEEEANEOUS EXCAVATIONS 
 
 00* 
 
 CO 
 
 CO 
 
 et 
 
 a -203 
 
 Hi! 
 
 111! 
 
 a< 
 
 H* W 
 
 OQ CO 02 CQ 
 
 g 
 
 "I ^ 
 
 I 
 
 DQ OQ OQ 
 
 S 8 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 63 
 
 The manner of reducing any number of bearings and distances 
 into one bearing and distance. 
 
 (32.) The practical miner will frequently find it neces- 
 sary to have recourse to this mode of reduction in the 
 plotting of subterraneous surveys on the surface, for the 
 purpose of determining their extent. As when the circum- 
 ferentor is the only instrument used in such works, which 
 in windy weather is both troublesome and fallacious, there- 
 fore, if the whole survey can be reduced to one bearing and 
 distance, or to such a number as may be thought necessary, 
 the labour of protracting will be proportionally reduced, 
 and the work more to be depended on. 
 
 Suppose the following subterraneous survey ABODE, to 
 be reduced to one single bearing and distance from A 
 toF: 
 
 AB, S. 36 E. . 
 
 BC, S. 42 W. 
 
 CD, S. 75 W. . 
 
 DF, N. 42 W. 
 
 THE PREPARATORY TABLE. 
 
 Chains. 
 AB, S. 36 E. 7-00 
 
 r.c, s. 42 w. 4-00 
 
 CD, S. 75 W. 10-00 
 DF, N. 42 W. 7-50 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 Chains. 
 
 5-55 
 5-55 
 
 NFor 
 Aa 
 
 Chains. 
 5-66 
 2-97 
 2-59 
 
 11-22 
 5-55 
 
 Chains. 
 4-12 
 
 Chains. 
 
 2-68 
 9-66 
 4-97 
 
 4'12 
 
 NA or 
 Fa 
 
 17-31 
 4-12 
 
 5-67 
 
 13-19 
 
64 SURVEYING SUBTERRANEOUS EXCAVATIONS 
 
 By taking the northings from the southings, leaves 5*67 
 chains of southing of F from A; and by taking the eastings 
 from the westings, leaves 13 '19 chains of westing of F from 
 the meridian of A, which form the triangle NAF ; of which 
 NA 13-19 chains, NF 5 '67 chains, and the right L N, are 
 given, to find the side AF and Z NAF, which is done by 
 trigonometry, as follows : 
 
 As NA 13-19 1-120245 
 
 Is to radius 10 -000000 
 
 So is NP 5-67 -753583 
 
 To tang. Z NAP 23 15' . . . 9-633338 
 
 And as sine Z A 23 15' . . 9 '596315 
 
 Is to NF 5 -67 -753583 
 
 So is radius . 10-000000 
 
 To AF 14-36 1-157268 
 
 Or AF may be found thus : Euclid, b. 1, p. 47, 
 
 </ 13-19 + 5-67 = 14-3G chains = AF. 
 
 Then 90 - 23 15' = 66 45' L FA*. Therefore the 
 bearing and distance of F from A is S 66 45' W, 14'36 
 chains. 
 
 Or the bearing and distance may be found instrumentally, 
 if protracted on paper, by applying the protractor to the 
 meridian line ns, with its centre on the angular point A, 
 observing the magnitude of the /. FAs, which will be found 
 66 45' ; and, from theorem 17, the line AF will bear S 
 66 45' W. The distance may be measured by the scale 
 and compasses. 
 
 (33.) In a subterraneous survey ABCDF, commencing 
 at the pit A, I wish to have the direct bearing and distance 
 on the surface of F from A ? 
 
WITH OB WITHOUT THE USE OF THE NEEDLE. 65 
 
 FIG.4L 
 N 
 
 Chains. Q- 
 AB, N. 42 E. . .5-00 
 
 
 -~-~-^ 
 y~~^ 
 
 BC, E 
 
 4-00 
 
 
 CD, N. 9 E. . 
 
 4-00 
 
 k 
 
 DF, S. 69 E. . . 
 
 5-56 
 
 
 PREPARATORY TABLE. 
 
 Chains. 
 N. 42 E. 5-00 
 E. . . 4-00 
 N. 9 E. 4-00 
 S. 69 E. 5-56 
 
 Northing. 
 
 Chains. 
 3-72 
 
 3-95 
 
 Southing. 
 Chains. 
 
 2 V 00 
 
 Easting. 
 
 Westing. 
 
 Chains. 1 
 3-35 
 4-00 
 0-63 
 5-21 
 
 Chains. 
 
 7-67 
 2-00 
 
 2-00 
 
 13-19 
 
 
 5-67 
 
 
 
 
 Now the point F contains 5 chains 67 links of northing 
 AGr, and 13*19 chains of easting GIF, from the commence- 
 ment A of the survey: Therefore construct the triangle 
 A GrF, the line NS representing the meridian, N the north, 
 and S the south ; AGr being given 5-67, and also GrF 13'19, 
 and the right L Gr, to determine AF and the L NAF. 
 
 2 2 
 
 >/ 13-19 + 5-67 = 14-36 AF,or the distance of F from A. 
 
 As AG 5-67 . . . . -753583 
 Is to radius . . . . 10 '000000 
 So is GF 13-19 1-120245 
 
 To tang. Z A GG 45' . 
 
 IQ'366662 
 
 Therefore the bearing and distance of F from A is N 
 06 45' E, 14-36 chains ; and if that bearing and distance is 
 
66 
 
 SUBVEYING STJBTERB.O'EOTJS EXCAVATIONS 
 
 run off by a circumferentor and chain, on the surface from 
 A, it will determine the point thereon immediately vertical 
 to the point F in the subterraneous excavation. 
 
 Also, if the different bearings and distances ABCDF are 
 protracted on paper, on which the triangle AGrF is con- 
 structed, beginning at the point A, and making the side AGr 
 the meridian, the end of the last bearing and distance DF 
 will coincide with the angular point F of the triangle, if the 
 survey is rightly protracted. 
 
 (34.) In the subterraneous survey ABCDFG-H, com- 
 mencing at the pit A, I wish to know the direct bearing and 
 distance of the point D from A, and also the direct bearing 
 and distance of the point H from A, so that a pit may be 
 put down from the surface on each of those points ? 
 
 AB, N. 42 E. 
 
 BC, E. . 
 
 CD, N. 9E. 
 
 DF, S. 69 E. 
 
 FG, S. 36 E. 
 
 GH, S. 42 W. 
 
 Chains. 
 
 . 5-00 
 
 . 4-00 
 
 . 4-00 
 
 . 5-56 
 
 . 7'00 
 
 , 4-00 
 
 (See Preparatory Table opposite.) 
 
 The point D has from A 7'67 chains of northing A.a, and 
 7*98 .chains of easting aD ; and the point H has from 
 A 2-96 chains of southing A5 ; and 14*63 chains of easting 
 
 Construct the triangle AD, and let Aa represent 7'67 
 chains of northing, and aD 7'98 chains of easting ; also 
 construct the triangle AZH, and let A.b represent 2'96 chains 
 of southing, and 6H 14'63 chains of easting : The side AD 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 67 
 
 PREPARATORY TABLE. 
 
 Chains. 
 N. 42 E. 5-00 
 E. . . 4-00 
 N. 9 E. 4-00 
 
 S. 69 E. 5-56 
 S. 36 E. 7-00 
 S. 42 W. 4-00 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 Chains. 
 3-72 
 
 3-95 
 
 Chains. 
 
 2-00 
 5-66 
 2-97 
 
 Chains. 
 3-35 
 4-00 
 0-63 
 
 7-98 
 5-21 
 4-12 
 
 Chains. 
 2-68 
 
 7-67 
 
 7-67 
 
 10-63 
 7'67 
 
 17-31 
 2-68 
 
 2-68 
 
 2-96 
 
 14-63 
 
 and /. NAD is required in the former triangle, and the side 
 AH and L SAH in the latter. 
 
 Then, as A 7 '67. 
 Is to radius . . . . 
 So is D 7-98 
 
 884795 
 10-000000 
 902003 
 
 To tang. A 46 8' 
 
 10-017208 
 
 And V 7'67 + 7'98 = 11-06 AD. 
 
 Therefore the bearing and distance of a pit from A on 
 the surface, to hit the point D under-ground, will be N 
 46 8' E, 11-06 chains. 
 
 Also, as A6 2-96 . 
 
 Is to radius 
 
 So is 6H 14-63 . 
 
 To tang. A 78 33' 
 
 471292 
 
 10-000000 
 
 1-165244 
 
 10-693952 
 
 And V 14-63 + 2 '96 = 14-92 AH. 
 Consequently the bearing and distance of a pit from A 
 
68 STTBVEYING SUBTEREANEOUS EXCAVATIONS 
 
 on the surface, to hit the point H under-ground, will be 
 S 78 33' E, 14-92 chains. 
 
 (34#.) In the subterraneous survey ABCDEF, com- 
 mencing at the pit A, it is required to find the direct 
 bearing and distance of the point E from A, so that a pit 
 may be sunk from the surface to the point E (see Eig. to 
 Art. 20), the required bearing being taken both from the 
 meridian NS, and also from a well defined line GH, passing 
 through the fixed marks G- and H and the shaft A, and 
 corresponding to a line in the headway AB, determined in 
 the manner pointed out in Articles 21 and 22. 
 
 Let the distances be measured, and the angles be taken 
 by the theodolite as below : 
 
 Distances. 
 
 AB = 3-12 chains. 
 BC = 4-96 
 CD = 2-89 
 DE = 4-17 
 EF = 6-02 
 
 Angles. 
 
 ABC = 118 34' 
 
 BCD = 79 15' 
 
 CDE = 61 5' 
 
 DEF = 158 57' 
 
 Eeduce the angles at B, C, D and E to their bearings from 
 GH by Art. 3 ; then find the northing or southing and 
 the easting or westing from the Traverse Table by Art. 59 ; 
 then proceed as in Art. 34 to find Kg and Ey ; whence by 
 trigonometry, as shown in the last-named Article, the 
 bearing of E from the fixed line GH, and the distance AF, 
 will be readily found. 
 
 Next reduce the angles A, B, C, D and E to their bearing 
 from NS, then find the northing or southing and easting 
 or westing from the Traverse Table, and proceed as in 
 Art. 34 to find Am and Fwi ; whence by trigonometry, as 
 already shown, the bearing of E from the meridian NS 
 and the distance AE will be found. 
 
 Or the bearings and distance in both cases may be found 
 from the plan by measuring the angles GAF and NAF 
 with the protractor, and the distance AE by the same scale 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 
 
 of equal parts as that with which the plan was laid down. 
 By doing the work by all these methods its accuracy may 
 be further verified. 
 
 It would conduce much to the improvement of the 
 student to plot the surveys in the following Articles 35 and 
 36, by reducing the given bearings to the angles made by 
 every two successive lines in each example, as practice of 
 this kind will impart great facility in the exercise of his 
 profession; and besides, enable him to reason for himself 
 and not on every slight occasion to have recourse to 
 authors. 
 
 (35.) In the following subterraneous working ABCDF, 
 beginning at the pit A, I wish to know the bearing and 
 distance of the pit G from E, the bearing and distance of 
 Gr from A being given : 
 
 N 
 FIG, 43. 
 
 AB, S. 30' W. . 
 BC, N. 50 W. 
 CD, N. 50 E. . 
 DF, N. 53 W. 
 AG, N. 20 E. . 
 
70 STJBYEYINa STJBTEBBANEOTTS EXCAYATIO^S 
 
 PREPARATORY TABLE. 
 
 Chains. 
 S. 30 W. 4-00 
 N. 50 W. 8-00 
 N. 50 E. 9-00 
 N. 53 W. 8-00 
 
 N. 20 E. 24-00 
 
 Northing. 
 
 Southing. 
 
 Chains. 
 3-46 
 
 Easting. 
 
 Westing. 
 
 6F 
 
 Chains. 
 
 514 
 5-79 
 4-81 
 
 Chains. 
 6-89 
 
 Chains. 
 2-00 
 6-13 
 
 6-39 
 
 15-74 
 3-46 
 
 3-46 
 
 AZ> 
 Ka 
 
 6-89 
 8-21 
 
 14-52 
 .6-89 
 
 12-28 
 22-55 
 
 7-63 
 aG or 
 be 
 
 10-27 
 
 Then A.a 22-55 chains A5 12-28 chains = 10-27 chains 
 5or cGr, and P5 7*63 chains + aQr or Ic 8-21 chains = 15'84 
 chains ~Fc. 
 
 The L nFGr, or bearing of the line FG from the mag- 
 netic meridian ns, and the length of FG are both wanted ; 
 and the sides J?c, cQ-, and the right L c are given to nnd 
 
 them. 
 
 As Fc 15-84 .... 1-1997552 
 
 Is to radius . . . 10 '0000000 
 
 So is Gc 10 -27 . . . 1-0115704 
 
 To co-tang. F 57 3' . . 9-8118152 
 "Which will be JS" 57 3' E with the magnetic meridian ns. 
 
 Also v/ 15-84 + 10-27 = 18-87 EG. 
 Therefore the bearing of the pit G from E will be 
 N 57 3' E, and the distance 18-87 chains. 
 
 Plotting on the surface ly the circumferentor, or theodolite. 
 (36.) In this mode of plotting the bearings and distances 
 are run off on the surface of the earth in the same order as 
 taken in the subterraneous survey. Great care must be 
 taken in running the length of each bearing as nearly hori- 
 zontal as can be, where the surface is uneven and declining. 
 
WITH OB WITHOUT THE USE OF THE NEEDLE. 71 
 
 The first two examples show the different modes of 
 commencing the plotting of a survey on the surface, by 
 assuming a point to begin at ; and the others following 
 show the manner of avoiding an obstacle, as a house, a lake, 
 or any other thing that interferes with the line of survey. 
 
 Let the following subterraneous survey be plotted on the 
 surface, commencing at the centre of the pit A : 
 
 FIG.44. 
 
 Chains. 
 
 S. 45 W. . 6-00 
 
 S. 80 W. . . . 6-00 
 
 N. ..... 5-00 
 
 N. 70 E. ... 4-00 
 
 N. 20 E. . 10-00 
 
 Fix the instrument as near the pit A as convenience will 
 allow ; (observe to keep the same end of the instrument 
 first in the plotting of the survey as was first in making it 
 under-ground ; likewise the same end of the needle must 
 determine the bearings in the plotting as determined them 
 under-ground). Suppose a the place where the instrument 
 is fixed, which is such a situation that, when the fore-sight 
 is put in the direction of the first bearing, S 45 W, you 
 may, by looking backward from a, cut exactly the centre of 
 the pit A, the commencement of the survey, otherwise the 
 instrument is not placed in a proper situation. (This first 
 point A is obtained by shifting the instrument either to the 
 right or left, until it is in the situation before-mentioned.) 
 After the proper situation, of the commencement of the 
 survey is found, let the assistant take the chain, and 
 running 6 chains from the centre of the pit A, which 
 
STJRYEYINQ SUBTEBEANEOTJS EXCAVATIONS 
 
 suppose to extend to B, then AB is the first bearing and 
 distance plotted. Eemove the instrument to B, and put 
 the fore-sight in direction of S 80 W, measuring the dis- 
 tance from B to C 6 chains ; then BC is the second bearing 
 and distance. Remove again the instrument to C, and 
 put the foresight in direction of due north, measuring the 
 distance from C to D 5 chains; then CD is the third bearing 
 and distance. E/emove again the instrument to D, and put 
 the fore-sight in direction of N 70 E, measuring from D 
 to P 4 chains ; then DE is the fourth bearing and distance. 
 Lastly, remove the instrument to I\ and putting the fore- 
 sight in direction of N 20 E, measure 10 chains from 
 F to Gr ; then FG is the fifth and last bearing and distance. 
 If marks are made at B, C, D, F and G-, they will represent 
 on the surface the excavation with all its windings. 
 
 (37.) Suppose the following subterraneous survey 
 ABCDF, to be plotted on the surface, commencing at the 
 centre of the pit A : 
 
 FIG-,45, 
 
 S. 30' W. 
 N. 50* W. 
 N. 50 E. 
 N. 53 W. 
 
 Chains. 
 4-00 
 3-00 
 9-00 
 8-00 
 
 Instead of following the same mode of commencement, 
 as shown in the former example, make any place on the 
 surface the point of commencement, as a (the same not 
 being far distant from the pit A), and run off from that 
 assumed point a the first bearing and distance, in the same 
 
WITH OB, WITHOUT THE USE OF THE NEEDLE. 73 
 
 manner as if a was the centre of the pit A ; which first 
 bearing and distance S 30 W 4 chains suppose to be 
 represented by db. Before the instrument is removed, 
 from a take the bearing and distance of the centre of the 
 pit A from a, which suppose S 30 E 3 chains a A, and 
 insert it in the column of remarks in the survey-book (for 
 fear it should be forgot), as a deflection from the line 
 of the subterraneous survey; which deflection must be 
 accounted for before the whole of the survey is plotted. 
 Now remove the instrument to b, and there turn the sights 
 in the direction of S 30 E, running off 3 chains, which let 
 #B represent ; then the line AB represents the first bearing 
 and distance as if taken from the centre of the pit A (the 
 line of deflection A is now repaid). Remove the instru- 
 ment from b to B, and proceed to run off the second bearing 
 and distance N 50 W 8 chains BC, according to the 
 method described in the last example. Remove the instru- 
 ment to C, and run off the third bearing and distance 
 N 50 E 9 chains CD. Lastly remove the instrument to 
 D, and run off the fourth bearing and distance N 53 W 
 8 chains DF. And if marks are put up at BCD and E, 
 they will represent the course of the subterraneous excava- 
 tion on the surface. 
 
 Note. This survey ought also to be plotted by the new methods, given 
 in Arts 20 and 21, in the manner directed in Art. 34a. 
 
 To show the manner how to avoid an obstacle that interferes 
 with the line of survey when plotting it on the surface of 
 the earth. 
 
 (38.) Suppose the following survey ABCD is to be 
 plotted on the surface, commencing at the centre of the 
 pit A : 
 
SUBTEEEANEOUS EXCAVATIONS 
 
 S. 30 W. 
 N. 5.0 W. 
 
 A N. 50 E. 
 
 Chains. 
 4-00 
 
 8-00 
 9'00 
 
 Fix ib/: instrument at the point #, as the assumed centre 
 of the pit A, and run off the first bearing and distance from 
 thence, which suppose to extend to I ; then take the bearing 
 and distance of A from a for the deflection, which note 
 down in the column of remarks in the survey-book: suppose 
 it to be S 30 B 3 chains : Then remove the instrument 
 to 5, and from thence run off S 30 E 3 chains SB, and the 
 line AB will be the first bearing and distance as run off 
 from A. Eemove the instrument to B, and proceed to plot 
 the remaining part of the survey, Now the next bearing, 
 N 50 W, will be found to run over the lake e ; therefore, 
 to avoid this obstruction, let the plotter extend the line Be 
 to such a distance that, in running the second bearing 
 from e, he may avoid the obstruction. Suppose this line 
 Be to be due west 6 chains, which being noted down in the 
 survey-book, remove the instrument to c, and from thence 
 let the bearing N 50 -W 8 chains be run, which suppose 
 it to extend to d; then from d run off due east 6 chains 
 (being the reverse of Be), which suppose to extend to C ; 
 then BC will be the second bearing and distance. Remove 
 the instrument to C, and run off the third bearing and 
 distance, which suppose to extend to D ; then CD will 
 represent N 50 E 9 chains, and the whole is plotted. 
 
 The obstruction at e may be more easily avoided by 
 
WITH OR WITHOUT THE TTSE OF THE NEEDLE. 75 
 
 laying down the survey on paper, and drawing on it the 
 lines AC AD, which must be measured, and their bearings 
 from NS found ; thus the position of the points C and D 
 may be determined ; also various other similar methods will 
 readily suggest themselves to the student when the obstruc- 
 tions are even more formidable than that at e. 
 
 In plotting a survey, either on paper or on the surface of the 
 earth, it matters not whether we "begin with the first or 
 last bearing, the ending will le the same. 
 
 (39.) Thus, suppose the subterraneous bearings and 
 distances are required to be plotted, in order to determine 
 on the surface the situation of the end D from the com- 
 mencement A : 
 
 FIG. 47. 
 
 1st, N. 10 W. 
 2nd, N. 40 E. 
 3rd, N, 45 W. 
 
 Suppose A the point or place of commencement, and run 
 off from thence the first bearing and distance to B, then 
 AB will represent N 10 W 5 chains ; and from B run off 
 the second bearing and distance to C, then BC will repre- 
 sent N 40 E 7 chains ; and from C run off the third 
 bearing and distance to D, then CD will represent N 45 W 
 6 chains, and the whole is plotted in the order of the 
 survey. Now, to plot the same in a manner contrary to 
 the order of the survey, begin at the point A, and run off 
 
 E 2 
 
76 SURVEYING STJBTERKANEOUS EXCAVATIONS 
 
 the third bearing and distance N 45 W 6 chains, which 
 let AJ) represent ; run off from & the second bearing and 
 distance N 40 E 7 chains Ic ; also run off from c the first 
 bearing and distance N 10 "W 5 chains cD ; which termi- 
 nation will correspond with the point D in the former 
 method, if the work be right. 
 
 (40.) In the following subterraneous survey ABCDF; 
 beginning at the pit A, I wish to have the same plotted on 
 the surface, in order to determine the bearing and distance 
 of E from A : 
 
 FIC 48 
 
 
 Chains. 
 
 AB, N. 42 E. . 
 
 . 5-00 
 
 BC, E. . 
 
 . 4-00 
 
 CD, N. 9 E. . 
 
 . 4-00 
 
 DF, S. 69 E. 
 
 . 5-56 
 
 Commence the plotting on the surface according as 
 directed in the former examples; and running off the 
 bearing and distance AB N 42 E 5 chains, remove the 
 instrument to B, and run off the bearing and distance BC 
 due east 4 chains ; remove the instrument to C, and run 
 off the bearing and distance CD N 9 E 4 chains ; lastly, 
 remove the instrument to D, and run off the bearing and 
 distance DE S G9 E 5'56 chains, and there make a mark ; 
 then return with the instrument to the pit A, and take the 
 bearing of the mark at E, which suppose N 64 44' E j then 
 measure the distance, which suppose 14*40 chains, which 
 are the bearing and distance required. Or the circum- 
 ferentor may be fixed at E instead of A, and the bearing 
 of A taken from it ; which being reversed (see Art. 5), will 
 become the bearing of E from A, the same as before. 
 
 Note. In many cases, where the surveyor is desirous of plotting the 
 subterraneous survey on the surface, it will be best to make choice of a 
 
WITH OR WITHOUT THE USE OP THE NEEDLE. 77 
 
 level piece of ground, sufficiently large to contain the whole, and plot the 
 same thereon, assuming a point of commencement in the most advantage- 
 ous place. 
 
 (41.) In the following survey of the subterraneous 
 working ABCDF, driven from the pit A, I wish to know 
 by what bearing the miner must be conducted from F, the 
 extreme point of the excavation, just to hit the centre of 
 the pit G- ; and also what is the distance of G- from F ? 
 
 FIG. 49 
 
 AB, N. 30 W. . 
 
 Chains. 
 . 5-50 
 
 BC, N. 45 E. 
 
 . 7-00 
 
 CD, N. 50 W. . 
 
 . 5-00 
 
 DF, N. 65 E. 
 
 . 7-00 
 
 Commence the plotting at the pit A on the surface, as 
 before directed, running off the distances in direction of 
 their respective bearings: When the whole is run off to 
 F, fix the instrument there, and take the bearing of the 
 pit Gr from it, which suppose S 68 30' E ; then measure, 
 by the chain, the distance of G- from F, which suppose 
 8*60 chains, the direction and distance required to hit the 
 pit Gr. 
 
 In the foregoing subterraneous survey, commencing at 
 the pit A, I wish to know the bearing and distance on the 
 surface of F from A, without plotting the same ? 
 
 (42.) Reduce the bearings and distances of the survey to 
 their northing or southing, and easting or westing (see 
 Art. 10, Ex. VII.), in order to obtain the denomination of 
 bearing of F from the pit A. Thus : 
 
78 
 
 STJEVEYINa SUBTEEEANEOUS EXCAVATIONS 
 
 PREPARATORY TABLE. 
 
 Chains. 
 N. 30 W. 5-50 
 N. 45 E. 7-00 
 N. 50 W. 5-00 
 N. 65 E. 7-00 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 Chains. 
 4-76 
 4-95 
 3-21 
 2-96 
 
 Chains. 
 Aa 
 
 Chains. 
 4-95 
 6-34 
 
 Chains. 
 2-75 
 
 8*81 
 
 6-56 
 
 15-88 
 
 11-29 
 6-56 
 
 
 
 
 4-73 
 
 aF 
 
 The denomination of bearing of the extreme part of the 
 excavation E from the pit A is 15 '88 chains of northing, and 
 473 chains of easting. Therefore, 
 
 As Aa 15-88 . 
 Is to radius 
 So is aF 4-73 
 
 To tang. Z AF 16 35' 
 
 1-2008505 
 
 10-0000000 
 
 6748611 
 
 9-4740106 
 
 And V 15-88 + 4-73 = 16-56 = AF. 
 
 Now fix the instrument at the pit A, and run off from 
 thence the bearing and distance JST 16 35' E 16*56 chains, 
 and the situation of E, with respect to the pit A, will be 
 had on the surface. 
 
 (43.) In the workings of the pit A, see fig. 30 to 
 Art. 17, 1 wish to know how far each bord or excavation 
 opQqrst is distant from the boundary cdfgmn ? 
 
 To obtain what is required, fix the circumferentor at the 
 pit A, and survey in direction of AGr, YE, and 5H, which 
 are the excavations next the boundary, measuring the 
 distance that each bord opQqrst is driven towards the 
 boundary from the headways YE and H, entering them, 
 according to the following form, in the survey-book. 
 
WITH OB, WITHOUT THE USE OF THE NEEDLE. 79 
 
 SURVEY-BOOK. 
 
 Bearings. 
 
 Remarks to Left. 
 
 Distance. 
 
 Remarks to Right. 
 
 
 
 
 Chains. 
 
 
 
 S. 80 W. 
 
 . 
 
 1-60 
 
 . 
 
 Aa 
 
 S. 70 W. 
 
 t 
 
 1-80 
 
 
 
 aG 
 
 
 
 0-80 
 
 A headways 6, and 
 
 
 
 
 
 a chalk mark + to 
 
 
 
 
 
 return to. 
 
 
 
 A headways V, and a 
 
 1-20 
 
 
 
 
 chalk mark + to 
 
 
 
 
 
 return to. 
 
 
 
 
 
 Returned to . 
 
 
 mark + at V. 
 
 
 S. 10 W. 
 
 
 2-40 
 
 . 
 
 VF 
 
 
 
 0-80 
 
 Bordj), 1'30 chains 
 
 
 
 
 
 towards the boun- 
 
 
 
 
 
 dary. 
 
 
 
 
 1-60 
 
 Bord o, 1 chain to- 
 
 
 
 
 
 wards ditto. 
 
 
 
 Returned to . 
 
 
 mark + at b. 
 
 
 N. 1 W. 
 
 . 5-00 
 
 . . . . 
 
 6H 
 
 
 Bord q, 90 links to- 
 
 0-80 
 
 
 
 
 wards the boundary 
 
 
 
 
 Bord r, 60 links to- 
 
 170 
 
 
 
 
 wards the boundary 
 
 
 
 
 
 Bord s, 60 links to- 
 
 2-55 
 
 
 
 
 wards the boundary 
 
 
 
 
 Bord t, 55 links to- 3 '40 
 
 
 
 
 wards the boundary 
 
 
 
 
 Note. The student must recollect to enter in this and all other survey- 
 books in the first column the angles which every t\v^ successive lines in 
 the survey make with one another when the new methou% given in Arts. 
 20 and 21, are used ; besides, not only this survey, but also *he following 
 one, ought to be done without the use of the magnet. 
 
 Now the survey underground being finished, fix the 
 instrument at the pit A, on the surface, and run off the 
 bearing and distance therefrom, in the order ac taken 
 underground, the first S 80 "W. T60 chains A.a : Remove 
 the instrument to , and run off the next bearing and 
 distance S 70 W 1'80 chains Q- ; at 80 links make a mark 
 on the surface, as represented by I ; also at I 1 20 chains 
 make another, as represented by V; and at Gr make another: 
 Then with the chain measure the distance G/, which sup- 
 pose 1'30 chains, which is the distance the excavation Q- is 
 
80 SUKVEIING SUBTEBBANEOTTS EXCAVATION'S 
 
 short of the boundary, which must be recorded in the 
 miner's book of memorandums. Return with the instru- 
 ment to the mark made on the surface at V, and run off 
 S 10 W 2-40 chains YF ; at 80 links, in direction from 
 V to F, run off the bord p 1*30 chains to the right, per- 
 pendicular to the headways YF, and there make a mark 
 at p : Then measure the distance pe, which suppose 1 chain, 
 which is the distance of the bord p from the boundary, 
 which must be recorded. Also at 1/60 chains run off the 
 bord o 1 chain to the right, similar to the former, and make 
 a mark at o : Then measure the distance od, which suppose 
 70 links, which is the distance of the bord o from the 
 boundary, which must also be recorded. Return with the 
 instrument to the mark made on the surface at 5, and run 
 off N 1 W 5 chains 5H, and there make a mark : Then mea- 
 sure the distance Jin, which suppose 80 links, which is the 
 distance of the headways- 5H from the boundary. At 80 
 links, in the direction from 1) to H , run off the bord q 90 
 links to the left, perpendicular to the headways 6H, and 
 there make a mark at q : Then measure the distance qg, 
 which suppose 70 links, which is the distance of the bord q 
 from the boundary. From T70 chains run off the bord r 
 60 links to the left, and make a mark at r : Then measure the 
 distance r7i, which suppose 1-10 chains, which will be the 
 distance of the bord r from the boundary. From 2*55 
 chains run off the bord s 60 links to the left, and make a 
 mark at s : Then measure the distance sk, which suppose 
 1-50 chains, which will be the distance of the bord s from 
 the boundary. From 3'40 chains run off the bord t'55 links 
 to the left, and make a mark at t: Then measure the 
 distance tm, which suppose 1-80 chains, which will be the 
 distance of the bord t from the boundary, and the whole 
 will be finished. 
 
 (44.) In the following subterraneous survey ABCDF, 
 commencing at the pit A, I wish to know the bearing and 
 distance of F from A : 
 
WITH OB WITHOUT THE USE OF THE NEEDLE, 
 
 81 
 
 FIG 50 
 
 N. 30 W. 
 N. 45 E. 
 N. 50 W. 
 N. 65 E. 
 
 Chains. 
 5-50 
 
 7*00 
 5-00 
 7-00 
 
 H 
 
 Easting and 
 westing dist- 
 ance from the 
 meridian of A. 
 
 tfi ^" 
 
 Is 
 
 2-20E. 
 
 r-l 
 i 1 
 
 CO 
 
 CD 
 
 III 
 
 5 
 
 T 1 
 
 J25 
 OS 
 
 te 
 
 CO 
 
 oo 
 
 
 111 
 
 6^ 
 
 C5 
 
 
 I 1 
 
 5 
 
 p 
 
 > 
 
 Ji w 
 
 
 
 ; 
 
 II 
 
 00 
 CO 
 
 : 
 
 
 , 
 
 rf 
 
 10 
 
 
 _ 
 
 tf 
 
 il 
 
 i ; 
 
 OS 
 
 : 
 
 CO 
 
 
 
 
 
 
 
 
 CO 
 
 ii 
 
 1 ; 
 
 : 
 
 
 
 
 00 6 
 
 
 
 
 . 
 
 -C3 . 
 
 .1 
 
 10 
 
 rH 
 
 (0 
 
 c* 
 
 S c 
 
 "* 
 
 s 
 
 CO 
 
 s 
 
 
 1 
 
 1? 
 
 o 
 o 
 
 o 
 o 
 
 
 
 . 
 
 S) S 
 
 . 
 
 
 ^ 
 
 
 
 p 
 
 o 
 
 CO 
 
 j 
 
 
 
 Is 
 
 
 
 125 
 
 ^ 
 
 5 
 
 rf 
 
 E 3 
 
82 STJBYEYING SUBTEBBANEOT7S EXCAVATIONS 
 
 Fix the instrument at A, and run off the line Kd 15 
 chains 88 links on the magnetic meridian of A (from the 
 6th column of the table), for the northing of F from A ; 
 and also 4 chains 73 links d~F (from the 7th column of the 
 table), for the casting of F from the magnetic meridian of 
 A : Then at F fix up a mark, and take its bearing and dis- 
 tance from A, which suppose IN" 16 35' E 16'56 chains, 
 which is the bearing and distance required. 
 
 This mode of plotting will be tedious, and liable to error, 
 particularly where the surface is uneven. 
 
 The manner of making a survey wliere tlie subterraneous 
 excavation declines from the horizon. 
 
 (45.) In making surveys where the distances measured 
 are not horizontal, but rising or falling, or both, it will be 
 necessary for the surveyor to reduce all his measurements 
 to horizontal distances, which may be obtained by taking 
 the angle that each separate distance makes with the 
 horizon, noting the same down opposite its respective bear- 
 ing, in a column made for that purpose in the survey-book. 
 
 FIG 5! 
 
 *. - -^- :r f 
 
 i 
 
 
 Suppose Ae and ad to be lines parallel to the horizon, 
 and AS CD is the undulating excavation which is to be 
 surveyed, commencing at A ; let the bearing and distance 
 taken in such a situation as that of AZ> to be N 10 "W" 
 5 chains, and the angle fKb which such excavation makes 
 with the horizon to be 30 ; and another in such a situation 
 as that of 60 JST 20 W 6 chains, and the angle Cbc which 
 it makes with the horizon to be 20 ; also another in the 
 situation of CD JN" 20 E 12 chains, and the angle DCe 
 which it makes with the horizon to be 10 ; which bearings, 
 
WITH OR WITHOUT THE USE OF THE NEEDLE. 
 
 83 
 
 distances, &c., must be inserted in the following survey 
 book : Thus, the first column containing the bearings and 
 declining distances, the second column the magnitude of 
 the angle that each bearing forms with the horizon, and 
 the third the declining distance of each bearing reduced by 
 the traverse tables to horizontal distance. This third 
 column may be made at the surveyor's leisure, but previous 
 to its being plotted. 
 
 SUKVET-BOOK. 
 
 1. 
 
 2. 
 
 | 
 
 3. 
 
 Rising and falling 
 distances. 
 
 Angle that 
 each bearing 
 forms with, the 
 horizon. 
 
 The horizontal distance 
 of each bearing. 
 
 i 
 
 Chains. 
 N. 10 W. 5-00 
 N. 20 W. 6-00 
 N. 20 E. 12-00 
 
 30 
 20 
 10 
 
 Chains. 
 4-33 A/ or a& 
 5-64 be '* Gf 
 11-82 C .or cd 
 
 I shall protract the survey first without reducing the 
 declining measurements to horizontal 
 distances, from the first column of the 
 foregoing survey-book ; and, secondly, 
 by the same, reduced to horizontal 
 distances, taken from the third column, 
 in order to show the error arising 
 from the protracting of declining or 
 hypothenusal distances. 
 
 Without reducing the declining dis m 
 tances.~Let A.b represent N 10 W 5 
 chains, 1C N 20 W 6 chains, and CD 1ST 
 20 E 12 chains ; then A&CD will re- 
 present the survey protracted according 
 to the first column of the survey- 
 book. 
 
 Where the declining lengths of each 
 learing are reduced to horizontal dis- 
 
84 
 
 STTEYEYING SUBTEEEANEOUS EXCAVATIONS 
 
 tance Let AM represent N 10 W 4'33 chains (from 
 the 3rd column of the survey-book), Vc N 20 W 5 -64 chains, 
 and cd N 20 E 11-82 chains ; then Mod will represent 
 the true protraction, and A5CD the false one, and dD 
 will be the amount of the error. 
 
 As it is common among practical miners, when plotting- 
 their surveys, to add a number of bearings and distances 
 together, taking the mean sum of the degrees contained in 
 the bearings so added for the common bearing of the whole, 
 when they are all on the same side of the same meridian, 
 and the sum of the lengths of all the bearings for the 
 length of the whole, I shall therefore show the errors 
 which result from such practices. 
 
 (46.) Suppose AB N 30 W 10 chains, and BC N 50 W 
 20 chains to be plotted. 
 
 FIG. 53, 
 
 Hy the false method. 
 N. 30 W. . .10 chains. 
 N. 50 W. . 20 
 
 2)80 
 
 N. 40 W. , 
 
 . 30 chains. 
 
 Now it appears that N 40 "W 30 chains will be the bear- 
 ing and distance equal to both, by this method. 
 
WITH OB WITHOUT THE USE OF THE NEEDLE. 85 
 
 By the true method. 
 
 N. 30 W. 
 N. 50 W. 
 
 Chains. 
 
 . 10-00 
 
 . . 20-00 
 Aa 
 
 Northing. 
 
 Westing. 
 
 Chains. 
 8-66 
 12-86 
 
 Chains. 
 5-00 
 15-32 
 
 21-52 
 
 20-32 I aC 
 
 As 21 -52 
 Is to radius 
 So is 20 -32 . 
 
 To tang. L AC 43 21' 
 
 1-3328420 
 
 10.0000000 
 
 1-3079240 
 
 9-9750820 
 
 FIG. 54. 
 
 And V 21 '52 + 20 -32 = 29 -59 chains = AC. 
 
 Then N 43 21' W 29-59 chains is the true bearing and 
 distance of C from A, instead of N 40 W 30 chains ; 
 and the magnitude of the error will be their difference, i. e. 
 30 2959=41 links; it is hence presumed that no sur- 
 veyor will use the false method. 
 
 A promiscuous collection of practical questions. 
 
 (47.) EXAMPLE I. I wish to drive a drift or subter- 
 raneous excavation from 
 the point A to hit the 
 pit C, which is on the 
 other side of a river; 
 now I run a line AB 
 by the river side, N 85 
 E 20 chains long, which 
 from the point A, I 
 found C to bear N 42 
 E, and also from the 
 point B, I found C to 
 bear N 30 W ; I therefore desire to know what will be the 
 length of the excavation or drift AC ? 
 
86 /SURVEYING. SUBTERRANEOUS EXCAVATIONS 
 
 From the rules for reducing bearings into angles, Z.A 
 = 43, /. B = 65, and L C = 72 ; therefore, by trigonometry, 
 the excavation AC will be 19*05 chains in length. 
 
 EXAMPLE II. There is a pit C (see last fig.), on the 
 other side of a river, to which I wish to drive a drift from 
 a given point ; I took the bearing of the pit C from A, 
 which was N 42 E, and after running a line AB by the 
 river side in direction of N 85 E 20 chains, I also took its 
 bearing again from B, which I found to be N 30 "W"; now I 
 demand to know under what bearing I must set off a drift 
 from a point D, 8 chains from A, along the line AB, so that 
 I may hit C, and also what will be the length of the drift 
 DC? 
 
 L A = 43, L B = 65. The line D C, which is the direction 
 of the drift or excavation, will be found to form an angle 
 with the line DB of 65 33', and the line DB forms an 
 angle of 85 to the left of the north magnetic meridian ; 
 therefore, from the rule for reducing angles into bearings 
 (Art. 3), the drift DC will bear N 19 27' E, and its length 
 will be 14-29 chains. 
 
 EXAMPLE III. There is an inaccessible point C (see fig. 
 to Ex. I.), to which a drift is to be driven underground ; 
 now the angle A is found to be 43, the angle B = 65, and 
 the length of the drift AB = 20 chains: how far from A 
 must a drift be set off to arrive at C by the shortest dis- 
 tance possible ? 
 
 The shortest distance between AB and the point C is a 
 line perpendicular to AB, let fall from the point C. 
 
 The point, from which the drift DC must be driven, by 
 the shortest distance possible, will be 13'94 chains from A, 
 as required. 
 
 EXAMPLE IV. I made a survey along the side of a hill 
 from A to B, under the following bearings and distances 
 viz., A.a N 75 E 20 chains, ab S 80 E 19 chains, Ic N 73 E 
 15-60 chains, and cE S 71 E 18 '65 chains ; now I wish to 
 make a straight tunnel from A to B ; therefore I demand to 
 
WITH OB WITHOUT THE USE OF THE NEEDLE, 
 
 87 
 
 know under what bearing it must be conducted, and what 
 will be its length ? 
 
 FI&.53. 
 
 FIG. 5G. 
 
 From the traverse tables, the point B will have 7'63 
 chains of southing Ad, and 65'17 chains of easting dE from 
 A; and the angle SAB = 83 43', which is the angle that 
 the line AB makes with the south meridian, and AB being 
 the direction of the tunnel, therefore it must be conducted 
 from A to B under the bearing of S 83 43' E, and its length 
 will be 65-61 chains. 
 
 EXAMPLE V. There is a vein of lead ore AB, which I 
 find forms an angle CAB of 
 82 with the horizon ; now I 
 wish to know how deep my 
 shaft DB must be sunk before 
 I cut the vein, if I set it off 
 at the distance of 30 yards 
 from A to D at the surface ? 
 
 Ans. DB = 213-4 yds. 
 
 EXAMPLE VI. There is a 
 vein of lead ore AB (see last 
 fig.), which forms an angle 
 CAB of 70 with the horizon, 
 on which I wish to sink a shaft 
 DB ; I demand to know what 
 distance AD the shaft must be set off from the vein at the 
 surface, just to cut it at the depth of 141 yards ? 
 w .The distance AD that the shaft must be set off at the 
 surface from the vein AB, just to cut it at the depth of 141 
 yards, will be 51'3 yards. 
 
88 
 
 SURVEYING SUBTERRANEOUS EXCAVATIONS 
 
 FIG. 59 
 
 EXAMPLE VII. I have to set a drift BC from the bottom 
 
 of a pit AB, which is to be driven truly level ; now I wish 
 
 r . _ D to know at what 
 
 F I W.JO. ,. . ,, ,T 
 
 A. distance irom the 
 
 pit B it will cut 
 the stratum of coal 
 DE, which dips so 
 as to form an an- 
 gle dDE of 20 C 
 with the horizon, 
 the drift BC being 
 set from the bot- 
 tom of the pit at B, 40 yards perpendicularly below the 
 seam D, and driven in direction of the dip of the stratum ? 
 Ans. BC = 109-9 yds. 
 
 EXAMPLE VIII. I set off a drift at the side of a hill A, 
 which was driven truly level, and 
 cut a vein of lead ore at B, 100 
 yards distant from A, which vein 
 I found to make an angle of 65 
 ABC with the horizon'; now I 
 wish to know what depth a shaft 
 at A must be sunk just to cut 
 the vein at C ? 
 
 Ans. AC = 214-4 #<&. 
 EXAMPLE IX. In the sub- 
 terraneous survey ABCD, in 
 the form of a trapezium, are 
 two shafts F and |E, joined by 
 a fifth straight drift FE. Now 
 this survey was made with 
 a magnetic needle, which was 
 afterwards found to be de- 
 fective in its indications, on account of the presence of 
 ferruginous substances both in the mine and on the surface ; 
 therefore, how is the work to be plotted, since the angles 
 
WITH OR WITHOUT THE USE OF THE NEEDLE, 
 
 89 
 
 57. 
 
 cannot be relied upon ; and only the lengths of five drifts, 
 
 and the segments of the drifts 
 
 AB and CD made by the drift 
 
 EF, are given; moreover, the 
 
 tops of the shafts F and E 
 
 range with the sun at 1^ P.M. 
 
 on the 18th of October, 1860 ? 
 
 Note. The solution of this question will require a knowledge of the 
 application of algebra to geometry and of spherical trigonometry to 
 astronomy. 
 
 EXAMPLE X. There is a vein of lead ore AC, which 
 forms an angle aK.e of 80 
 with the horizon Ac ; now A EIG.GO. 
 
 I have sunk a shaft AB on 
 the vein at the surface, to 
 the depth of 120 yards 
 perpendicular; I desire to 
 know what distance the 
 bottom of the shaft B will 
 be from the vein ? 
 
 An*. BC=2M yds. 
 
 EXAMPLE XI. I made 
 a survey of a subterraneous 
 excavation ABCDFG- (see 
 the following bearings and 
 distances), commencing at the pit A ; now I wish to know, on 
 the surface, by one single bearing and distance, to be taken 
 from the pit A, where I must sink a pit perpendicularly 
 upon G-, the extreme end of the excavation ? 
 
90 
 
 SUETEYIITG SUBTEKBAKEOUS EXCAVATIONS 
 
 
 Chains. 
 
 AB, N. 20 W. . 
 
 . 15-50 
 
 BC, N. 60 E. 
 
 . 12-00 
 
 CD, N. 15 E. . 
 
 . 10-50 
 
 DF, N. 85 E. 
 
 . 15-00 
 
 EG, s. 25 B. . 
 
 . 16-60 
 
 The extreme point Gr of the excavation will have 16-98 
 chains of northing A#, and 29 '76 chains of easting Gr, from 
 A ; therefore the line Ad will be found to bear N 60 IT E 
 with SJX", the magnetic meridian of A, and its length will 
 be 34-26 chains, the bearing and distance required. 
 
 Note.' This Example ought also to be solved by taking the angles from 
 the direction of the drift AB (the position of which is assumed to be fixed 
 on the surface), by the method given in Art. 21. 
 
 EXAMPLE XII. I have to drive an excavation from B 
 towards A, which is to rise 1 inch in every 60 feet of its 
 
 length; now I wish 
 to put down an air- 
 shaft P thereon, just 
 1600 yards from its 
 mouth B ; what will 
 be the depth of the 
 ~- e shaft from the sur- 
 face to the sole of the 
 
 drift or excavation, when the surface at P, the place where 
 it has to be sunk, is 350 feet above the level of B, the mouth 
 of the excavation ? 
 Anns. 343gjfe<?. 
 EXAMPLE XIII. A head way is driven into a coal-stratum 
 
 Fid. 
 
WITH OE WITHOUT THE USE OF THE NEEDLE. 91 
 
 from the foot of a hill ; the straight portions of the headway, 
 commencing at A, are AB = 5*63 chains, BO :n 5*18, CD = 
 3-80, DE = 4-71, and EF = 7'02; the angles are ABC = 
 121 16', BCD = 228 5', CDE = 16452', and DEF = 168 
 29', all the angles being taken by the theodolite on the 
 right side of the lines in the headway. A shaft is required 
 to be sunk on the hill to the coal-stratum, at the levelled or 
 horizontal distance of 37'50 chains from the entrance of the 
 headway, from which the top of the proposed shaft bears 
 3742' to the right of the direction of the first straight por- 
 tion of the headway AB. Now the coal-stratum v rises 
 uniformly at the rate of If inches in a chain ; it is required 
 to find the direction and length of the additional headway 
 from F to the bottom of the proposed shaft, also its depth, 
 the angle of elevation of the top of the shaft from the 
 entrance A of the headway being 12 8'. 
 
PART III. 
 
 THIS part of the work treats of those subjects which are 
 particularly necessary to be attended to, because of the 
 great number of existing surveys, which have been made by 
 the help of the magnetic needle ; and the consequent neces- 
 sity of attending to the magnetic variation at the different 
 periods of time, at which those surveys were made ; of show- 
 ing the method of finding the true meridian, and of deter- 
 mining the variation of different magnetic needles at 
 different times, and of the manner of reducing bearings 
 taken with the magnetic meridian to those formed with the 
 true meridian. Yarious other subjects interesting to miners 
 are here discussed, concluding with a Traverse Table, and 
 the method of estimating the produce of seams of coal. 
 
 AXIOMS AND OBSERVATIONS. 
 
 (48.) 1. Two magnetic needles seldom have exactly the 
 same variation. 
 
 2. The magnetic variation not being stationary, the 
 variation of the needle of all instruments depending thereon 
 will change accordingly. 
 
 3. If a subterraneous survey is made by one instru- 
 ment, and plotted on the surface by another, the needles of 
 each having different magnetic variation, the plotting will 
 be erroneous if the bearings to be plotted are not pre- 
 viously reduced to bearings with that magnetic needle by 
 which it is to be plotted. 
 
 4. If a subterraneous survey is made by one instru- 
 
MAGNETIC VARIATION. 93 
 
 ment, and plotted on the surface by another, the needles of 
 both having the same magnetic variation, the survey will be 
 truly plotted. 
 
 5. If a survey is plotted on the surface immediately 
 after it has been taken under ground (by the same instru- 
 ment), no material error can result. 
 
 6. If a survey is plotted on the surface by the same 
 instrument it was made with, but at some distant time after, 
 the plotting will be erroneous, inasmuch as the magnetic 
 variation has changed in the time between the survey being 
 taken underground and its being plotted on the surface. 
 
 7. All bearings of subterraneous excavations which 
 are added, from time to time, on any plan kept for that 
 purpose, must be reduced to bearings with the delineated 
 meridian of that plan, previous to their being plotted 
 thereon, otherwise the plotting will be erroneous. 
 
 8. All surveys of subterraneous excavations which 
 are recorded for future purposes must be recorded with the 
 variation of the needle by which they have been taken, or 
 otherwise they must be reduced to bearings with the true 
 meridian, and so recorded, notifying the same. 
 
 9. All the preceding axioms and observations will be 
 unnecessary in new surveys, which are made without the 
 use of the needle, and which are unconnected with old 
 surveys. 
 
 Of the magnetic variation of the needle. 
 
 (49.) Since nearly all subterraneous surveys have been 
 made by, or have reference to, the magnetic needle, each 
 bearing (as shown in the first part of this work) is taken 
 by the angle it makes with the magnetic meridian ; and that 
 magnetic meridian has been continually changing at the 
 rate of about 9 minutes annually, for 230 years, from north 
 towards the west, up to 1793 ; but its annual declination was 
 afterwards not so great, for the north end of the needle was 
 little more than 24 degrees westward of the true meridian 
 
 
94 MAGNETIC VAEIATION. 
 
 of London in 1803 : At Paris it was somewhat less, still 
 continuing to increase or decrease at a slow rate ; while in 
 some parts of the world the north end of the needle was 
 even eastward of the true meridian at the last-named date. . 
 As the magnetic meridian is always changing, it must neces- 
 sarily follow, that the same line which formed an angle with 
 it, of a certain magnitude, on any particular day, will not 
 (we have strong reasons to suppose) form the same angle 
 that day twelve months with the then magnetic meridian : 
 Hence follows the great necessity of reducing every bear- 
 ing to the angle it will form with the true or invariable 
 meridian ; the manner of doing it will be shown hereafter : 
 Also the records of subterraneous surveys noted down for 
 future purposes, where the surveyor has neglected to insert 
 from what kind of meridian the bearings thereof are formed ; 
 by such neglect those records will not only cease to be of 
 use, but will tend to mislead. 
 
 I shall insert a table, showing the different degrees of 
 magnetic variation at different times from the year 1575 to 
 1858, which is nearly to the present time : 
 
 VARIATION AT LONDON. 
 
 Year. 
 
 Variation. 
 
 Year. 
 
 Variation. 
 
 1576 
 
 11 15' x 
 
 1745 
 
 16 53' > 
 
 
 1580 
 
 11 11 
 
 1750 
 
 17 54' 
 
 
 1612 
 
 6 10' U 
 
 1760 
 
 19 12' 
 
 
 1622 
 
 6 0' ( H< 
 
 1765 
 
 20 0' 
 
 
 1633 
 
 4 5' 
 
 1770 
 
 20 35' 
 
 
 1657 
 
 0' ) 
 
 1775 
 
 21 28' 
 
 
 1666 
 
 1 35' S 
 
 
 1777 
 
 21 57' 
 
 
 1672 
 
 2 30' 
 
 
 1779 
 
 22 4' 
 
 
 1683 
 
 4 30' 
 
 
 1780 
 
 22 26' 
 
 . 
 
 1692 
 
 6 0' 
 
 
 1786 
 
 23 19' 
 
 
 1700 
 
 8 0' 
 
 
 1789 
 
 23 36' 
 
 
 1717 
 
 10 42' 
 
 . 
 
 1793 
 
 23 51' 
 
 
 1724 
 
 11 45' 
 
 
 1797 
 
 24 2' 
 
 
 1730 
 
 13 0' 
 
 
 1800 
 
 24 6' 
 
 
 1735 
 
 14 16' 
 
 
 1803 
 
 24 9' 
 
 
 1740 
 
 15 40' j 
 
 
 1806 
 
 24 15' 
 
 
MAGNETIC VABIATION. 
 
 VARIATION AT LONDON. Continued. 
 
 95 
 
 Year. 
 
 Variation. 
 
 Year. 
 
 Variation. 
 
 1809 
 
 24 22' N 
 
 
 1835 
 
 23 32' 
 
 
 1812 
 
 24 28' 
 
 
 1838 
 
 23 19' 
 
 
 1815 
 
 24 35' 
 
 
 1841 
 
 23 6' 
 
 
 1818 
 
 24 41' 
 
 
 1844 
 
 22 52' 
 
 
 1820 
 
 24 32' 
 
 k w. 
 
 1847 
 
 22 41' 
 
 > W. 
 
 1823 
 
 24 20' f 
 
 1850 
 
 22 30' 
 
 
 1826 
 
 24 8' 
 
 1853 
 
 22 19' 
 
 
 1829 
 
 23 56' 
 
 1856 
 
 22 8' 
 
 
 1832 
 
 23 44' J 
 
 1858 
 
 22 2' 
 
 
 Note. By the variation being east or west, is meant that the north end 
 of the magnetic needle is on the east or west side of the true meridian ; 
 and where the variation is called east or west in the following part of this 
 work, it is to be understood that the north end of the magnet' c needle has 
 east or west variation accordingly, except it is particularly mentioned to 
 the contrary. 
 
 From the table it appears the magnetic needle had east variation in the 
 year 1576 ; that is, its north end was 11 15' on the east side of the true 
 meridian of London ; and in 1657 the needle was in direction of the true 
 meridian ; and since that time it has been veering about to the west, 
 'until it has got upwards of 24 to the westward thereof. Besides this 
 annual variation just mentioned, it has a daily variation. 
 
 I shall insert a table, showing the diurnal variation taken at different 
 hours of the 27th day of June, 1759, by Mr. Canton. (Phil. Trans., 
 vol. 51.) 
 
 
 Hrs. Min. 
 
 Declination 
 
 west. 
 
 Degrees of 
 Fahrenheit's 
 therm om. 
 
 
 ' 18 
 
 18 2' 
 
 62 
 
 
 6 4 
 
 18 58' 
 
 62 
 
 Morning . 
 
 8 30 
 9 2 
 
 18 55' 
 18 54' 
 
 65 
 67 
 
 
 10 20 
 
 18 57' 
 
 69 
 
 
 I 11 40 
 
 19 4' 
 
 684 
 
 
 50 
 
 19 9' 
 
 70 
 
 
 1 38 
 
 19 8' 
 
 70 
 
 Afternoon . 
 
 3 10 
 
 7 20 
 
 19 8' 
 18 59' 
 
 68 
 61 
 
 
 9 12 
 
 19 6' 
 
 59 
 
 
 t 11 40 
 
 18 51' 
 
 574 
 
96 TO FIND THE TEUE MEBIDIA.N. 
 
 The mean variation of each month of the year . 
 
 January . . 7' 8" 
 
 February . . 8' 58' 
 
 March . 11' 17' 
 
 April . . . 12' 26 " 
 
 May . . . 13' 0" 
 
 June 13' 21" 
 
 July . . .13' 14" 
 
 August . . . 12' 19" 
 
 September . . 11' 43" 
 
 October. . . 10' 36" 
 
 November . . 8' 9" 
 
 December 6' 58" 
 
 To find the true meridian. 
 
 (50.) I shall lay down an easy and comprehensive rule to 
 find the true meridian, which is preparatory to the deter- 
 mining of the magnetic variation of the needle. It is well 
 known that the sun, at 12 o'clock at noon, is due south in 
 all northern latitudes ; and if a pole is set up perpendicular 
 to the horizon, its shadow at that hour will bear exactly 
 north, or in direction of the true meridian ; also the shadow 
 of the pole will be shortest at that precise time. 
 
 Let ABC be a board perfectly plain and clear of twist- 
 ings, and of a triangular form, each side about 30 inches 
 long, having a number of concentric circles cde about 1J 
 inch asunder, drawn on its surface from a centre a. Now 
 let this board be placed horizontal by means of a spirit level, 
 with its angular point C towards the south ; and at a, the 
 centre of the concentric circles, let there be fixed an upright 
 pin about 10 inches long, exactly perpendicular to the 
 board, and also perpendicular to the horizon. All this being 
 done on a clear day, and before the sun arrives on the 
 meridian of the place of observation, which I shall say about 
 11 o'clock, then observe carefully the first concentric circle 
 that the end of the shadow of the pin fixed at a touches, 
 which suppose to be at/, and there make a mark : Then ob- 
 serve again carefully when the end of the same shadow 
 touches on the same concentric circle, which will be about 
 1 o'clock, suppose it to be at g ; there make another mark : 
 Then with a pair of compasses divide the distance fg, and 
 
TO FIND THE TRUE MERIDIAN. 
 
 97 
 
 FIG.: S3. 
 
 the point in tlie middle between which, suppose h, will bo 
 the direction of the shadow of the pin at 12 o'clock : Con- 
 sequently ah is the 
 direction of the true 
 meridian. Then by 
 placing an upright 
 sight E, with a slit 
 Tck in it, on the 
 table, the centre of 
 which coinciding with 
 the point A, the pin 
 at a paving an open- 
 ing in it similar to 
 Ib, with a perpen- 
 dicular hair in direc- 
 tion of the opening ; 
 and by looking 
 through the sight E, 
 together with the 
 hair in the centre of 
 the opening in the 
 pin placed at , the 
 meridian may be ex- 
 tended to any distance S on the surface ; in the direction of 
 which line it will be proper to place two permanent marks, 
 as represented by NS, whose distance may be from 100 to 
 300 yards, for the purpose of determining at all times the 
 magnetic variation of the needle of the different instruments, 
 made use of in surveying : Such a line every director of 
 mines ought to have marked out in the situation of the mine 
 he directs. 
 
 (50a.) If the student be acquainted with the application 
 of spherical trigonometry to astronomy, he will find the 
 following method of finding the true meridian to be greatly 
 preferable to that just given. Let S represent the place of 
 the sun's centre, P the north pole, and Z the zenith ; these 
 
98 TO FIND THE MAGNETIC VABIATION. 
 
 three points being the angles of a spherical triangle SPZ 
 (the student can readily draw the figure for himself), in 
 which SZ represents the co-altitude of the sun, when he 
 comes into the direction of the required bearing of the drift 
 in the mine ; SP the sun's co-declination on the day of 
 observation (which will be found in the Nautical Almanack 
 for the year in which the observation is made) ; and PZ the 
 co-latitude of the place of the mine (which is usually well 
 known). Prom the given spherical triangle SPZ the angle 
 Z may be readily found, which is the azimuth or bearing of 
 the sun from the north at the time of observation, and also 
 the bearing of the drift ; whence also the true meridian may 
 be readily deduced for the following purpose. 
 
 To determine the magnetic variation of the needle of any 
 
 instrument. 
 
 (51.) Suppose N and S to be marks representing the 
 true meridian, S the south and N the north : place the in- 
 strument (whose magnetic variation you would 
 wish to know) at S, and turn the sights in 
 N direction of SN until N is seen through them ; 
 
 at the same time observe the bearing of the 
 needle of the instrument, and whatever JS" 
 is found to bear from due north, as much will 
 the magnetic meridian differ from the true 
 c meridian. Suppose the north end of the 
 / needle to stand* in direction of Sc?, then the 
 / true meridian SN will be to the east of the 
 / magnetic as much as the angle dSN, which 
 / suppose 23; then SN will bear JST 23 E with 
 / the magnetic meridian : Consequently the 
 / needle of the instrument may be said to have 
 
 23 of west variation, as the north end 
 thereof is 23 to the west or left of the 
 S true meridian SN. Or if the north end 
 
 of the needle stand in direction of S0, then the true meri- 
 
SEDUCING BEAEINGS, ETC, 
 
 99 
 
 FIG. 
 
 dian SX will be to the west of the magnetic as much as 
 the angle eSX, which, if equal to 23, then SX will bear 
 N 23 W : Then the needle may be said to have 23 of east 
 variation, the north end thereof being' 23 to the east or 
 right of the true meridian SX. 
 
 The manner of reducing bearings from a magnetic to a true 
 
 meridian. 
 
 (52.) Let XS represent the true meridian, X the north 
 and S the south, and ns a magnetic needle suspended on a 
 centre c, representing the magnetic meridian, n the north 
 and s the south ; then the arch na will be the variation of 
 the magnetic meridian from the true meridian, which may 
 be called west va- 
 riation, the north 
 end of the needle 
 being to the west 
 side of the true 
 meridian : And if 
 the angle nca is 
 equal to 23, then 
 the needle will 
 have 23 of west 
 variation, and the 
 south end s will 
 have 23 of east 
 variation ; for 5 
 will be to the east 
 of the true south 
 meridian line as 
 much as the north 
 end n is to the west of the true north meridian line. 
 (See theorem 3.) 
 
 1st. Suppose the circle WE to represent a circuin- 
 ferentor, and that the bearing of the object O with the true 
 meridian is required ; if ns is the needle representing the 
 
100 EEDTTCING BEARINGS, ETC. 
 
 magnetic meridian, and the object O is found to form an angle 
 nca with it of 23, which (from the manner of determining 
 bearings, Art. 2) may be called N 23 E, and, as before, the 
 magnetic variation of the needle being 23 to the west of the 
 true meridian, then 23 23 = ; therefore the bearing 
 of O with the true meridian SdN" will be due north, for the 
 needle ought to have stood in direction db. 
 
 2d. Suppose again the bearing of the object A with the 
 true meridian is required ; the bearing of A with the mag- 
 netic meridian will be equal to the angle ncA., which call N 
 10' "W; but as the magnetic meridian has 23 of west varia- 
 tion, the bearing of A with the true meridian will be N 
 23 + 10 =33 W ; for angle acA. is equal to 33, which is 
 the angle that cA. makes with the true meridian ScN. 
 
 3d. Suppose again the bearing of the object C with the 
 true meridian is required ; the bearing of C with the 
 magnetic meridian will be equal to the angle ncC, which 
 call N 53 E ; but the variation of the needle being 23 to 
 the west of true north, and ought to have stood in the 
 direction of ab, consequently the bearing of C from c with 
 the true meridian will be N 53 23 = 30 E ; for angle 
 acC is equal to 30, which is the angle that the line cC makes 
 with the true meridian line ScN. 
 
 4th. Suppose the bearing of the object D with the true 
 meridian is required ; the bearing of D with the south mag- 
 netic meridian will be equal to the angle scD, which call 
 S 56 W ; but the south end of the needle having 23 of 
 east variation, and ought to have stood in direction of ab 
 the true meridian, consequently the bearing of D from c 
 with the true meridian will be S 56 - 23 = 33 W; for 
 angle foD is equal to 33, which is the angle that the line 
 cD makes with the true meridian line NcS. 
 
 5th. Suppose again the bearing of the object B with the 
 true meridian is required ; the bearing of B with the mag- 
 netic meridian will be equal to the angle scB, which call S 
 15 E ; but the south end of the needle having 23 of east 
 
EEDUCING BEABINGS, ETC. 101 
 
 variation, consequently the true bearing of B will be S 
 15 + 23 = 38 E ; for angle bcE is equti 1 to 38, which, is> 
 the angle that the line cQ makes with the true meridian 
 HneNcS. 
 
 Gth. Suppose again the bearing of the cbjeco F with the 
 true meridian is required ; the bearing of F with the mag- 
 netic meridian will be equal to the angle cF, which call N 
 13 E ; but the magnetic meridian has 28 of west variation, 
 consequently the bearing of F with the true meridian, will 
 be N 23 - 13 - 10 W ; for angle cF is equal to 10, 
 which is the angle that the line cF makes to the left with 
 the true meridian Sc~N. 
 
 7th. Suppose again the bearing of the object Gr with 
 the true meridian is required ; the bearing of Gr with the 
 magnetic meridian will be equal to the angle sc&, which 
 call S 13 "W ; but the south magnetic meridian has 23 of 
 east variation, consequently the bearing of Gr with the true 
 meridian will be S 23 - 13 = 10 E ; for angle IcQr is equal 
 to 10, which is the angle that the line cQt makes to the 
 right with the true meridian NcS. 
 
 8th. Suppose again the bearing of the object K with 
 the true meridian is required ; the bearing of K with the 
 magnetic meridian will be equal to the angle ?zcK, which 
 call N 80 W ; the magnetic meridian having 23 of west 
 variation, the angle that cK will make with the true north 
 meridian cN will be 80 + 23 = 103, acK; but as it exceeds 
 90, therefore 180 - 103 = 77, angle 5cK; then the bear- 
 ing of K with the true meridian will be S 77 "W ; for angle 
 ScK is equal to 77, which is the angle that the line cK 
 makes with the true south meridian line NcS. 
 
 N.B. The true bearing of any object is nothing more 
 than the angle that the object makes with the true meridian, 
 instead of the angle it forms with the magnetic meridian ; 
 therefore, by the several cases of Art. 52, the method of 
 solving the following examples will be readily seen : 
 
 EXAMPLE I. If the following bearings, N 20 W, N 60 
 
102 
 
 t BEABLNGS, ETC. 
 
 E, N 70 "W, and N 13 E are taken by an instrument whose 
 magnetic needle has 23 west variation, what will be their 
 bearings 'with ihe -true meridian ? 
 
 The '.first- bearing *!N" 20 "W will -form a bearing of N 
 20-*+ '-28' - 4SP-W- with the true meridian. 
 
 The second bearing, N 60 E, will form a bearing of IN" 
 60 - 23 = 37 E with the true meridian. 
 
 The third bearing, N 70 W, will form a bearing of 
 180 - 70 + 23 = 87, which will be S 87 W with the 
 true meridian. 
 
 The fourth bearing, N 13 E, will form a bearing of N 
 23 - 13 = 10 W with the true meridian. 
 
 With the magnetic meridian. 
 Thus, N. 20 W. 
 N. 60 E. 
 N. 70 W. 
 N. 13 E. 
 
 With the true meridian. 
 N. 43 W. 
 N. 37 E. 
 S. 87 W. 
 N. 10 W. 
 
 EXAMPLE II. If the following bearings are taken by a 
 meridian having 23 of west variation S 10 "W, N 10 E, 
 JS" 50 E, and JST 20 W what will be their bearings with 
 the true meridian ? 
 
 With the magnetic meridian. 
 S. 10 W. 
 N. 10 E. 
 N. 50 E. 
 N. 20 W. 
 
 With the true meridian. 
 S. 13 E. 
 N. 13 W. 
 N. 27 E. 
 N. 43 W. 
 
 EXAMPLE III. If the following bearings are taken by a 
 meridian having 10 of west variation N 50 "W, N 70 E, 
 S 5 E 3 and S 60 W what will be their bearings with 
 the true meridian ? 
 
 With the magnetic meridian. 
 N. 50 W. 
 N. 70 E. 
 S. 5" E. 
 S. 60 W. 
 
 With the true meridian. 
 N. 60 W. 
 N. 60 E. 
 S. 15 E. 
 S. 50 W. 
 
KEDTJCIKG BEABINGS, ETC. 
 
 103 
 
 EXAMPLE IV. If the bearings in the last example be 
 taken by a meridian having 6 of east variation, what will be 
 their bearings with the true meridian ? 
 
 With the magnetic meridian. 
 N. 50 W. 
 N. 70 E. 
 S. 5 E. 
 S. 60 W. 
 
 With the true meridian. 
 N. 44 W. 
 N. 76 E. 
 S. 1 W. 
 S. 66 W. 
 
 The manner of reducing a /bearing from one magnetic meridian 
 
 to its bearing with any other magnetic meridian 
 
 of different variation. 
 
 (53.) 1st. Suppose the bearing of the object P from C is 
 taken by a circumferentor whose needle has 10 of west 
 variation n's' y which bearing is to be reduced to the 
 bearing it will form with another magnetic meridian ns, 
 having 23 of west variation : Let NS represent the true 
 
 p - 
 
 meridian, and the bearing of CP therewith (from the man- 
 
104 BEDTJCING BEAEINGS, ETC. 
 
 ner of reducing bearings, &c., Art. 52) equal to the angle 
 PCN 45, or N 45 W ; also the magnetic meridian to which 
 the bearing PC is to be reduced equal to the angle ;iCN 
 23, or having 23 of west variation ; the object P and the 
 magnetic variation of the meridian to which its bearing is 
 to be reduced are both on the west side of the true meridian 
 NS ; therefore L PCN 45 Z. CN 23 = Z. PCw 22; 
 and as the angle PCN exceeds the angle nCN, the object P 
 from C must bear N 22 W with the magnetic meridian ns. 
 
 2d. Suppose the bearing of the object from C is 
 taken by an instrument whose needle has 10 of west 
 variation n's', which is to be reduced to the bearing it 
 will form with another magnetic meridian ns, having 23 of 
 west variation: Let the bearing of CO with the true meridian 
 be found equal to the angle OCN 8, or N 8 "W ; and the 
 magnetic meridian to which the bearing CO is to be re- 
 duced equal to the angle wCN 23, or having 23 of west 
 variation ; the object arid the magnetic variation of the 
 meridian to which its bearing is to be reduced are both on 
 the west side of the true meridian NS ; therefore Z. wCN 
 23 - Z. OCN 8 = L OCn 15 ; and as the angle OCN is 
 less than the anlge ?zCN, the bearing of O from C will be N 
 15 E with the magnetic meridian ns. 
 
 3d. Suppose the bearing of the object T from C is 
 taken by a magnetic needle having 10 of west variation 
 n's' 9 which bearing is to be reduced to the bearing it will 
 form with another magnetic meridian ns, having 23 of west 
 variation : Let the bearing of TC with the true meridian 
 be found equal to the angle TCN 23, or N 23 W ; and the 
 magnetic meridian to which the bearing TC is to be reduced 
 equal to the angle rcCN 23, or having 23 of west variation ; 
 then Z. TCN 23 Z. wCN 23 = ; therefore the bearing 
 of T from C will be in the direction of the magnetic meridian 
 ns, or due north. 
 
 4th. Suppose the bearing of the object Q from C is 
 taken by a magnetic needle having 10 of west variation V, 
 
BEDUCIffG- BEARINGS, ETC. 105 
 
 which bearing is to be reduced to the bearing it will form 
 with another magnetic meridian, ns, having 23 of west 
 variation : Let the bearing QC with the true meridian NS 
 be found equal to the angle QCN 15, or N 15 E ; and the 
 magnetic meridian to which the bearing QC is to be reduced 
 equal to the angle nCN 23, or having 23 of west variation ; 
 now the object Q and the magnetic variation of the meri- 
 dian to which its bearing is to be reduced are on contrary 
 sides of the true meridian NS ; therefore Z. QGN 15 + Z. 
 nCN 23 = / QCw 38 ; and also the bearing of Q will be 
 on the contrary side of that magnetic meridian ns that its 
 variation is on ; and as ns has west variation, therefore the 
 bearing of Q from C will be N38 E with the meridian ns. 
 
 5th. Suppose the bearing of the object A from C is 
 taken by the meridian n's', having 10 of west variation, 
 which is to be reduced to the bearing it will form with 
 another magnetic meridian ns, having 23 of west variation : 
 Let the bearing of CA with the true meridian NS be found 
 equal to the angle ACS 45, or S 45 E ; and the south 
 magnetic meridian to which the bearing AC is to be re- 
 duced equal to the angle sCS 23, or having 23 of east 
 variation (see theorem 3, Art. 48) ; the bearing of the 
 object A and the magnetic variation of the meridian to 
 which its bearing is to be reduced are both on the east side 
 of the true meridian ; therefore Z. ACS45 3 Z. sCS 23 = 
 L ACs 22 ; the angle ACS exceeding the angle sCS, the 
 bearing of A with the magnetic meridian ns will be S 
 22 E. 
 
 6th. Suppose the bearing of the object B from C is 
 taken by a needle n V, having 10 of west variation, which 
 is to be reduced to its bearing with another magnetic me- 
 ridian ns, having 23 of west variation : Let the bearing of 
 CB with the true meridian NS be found equal to the angle 
 BCS 8, or S 8 E ; and the south magnetic meridian to 
 which the bearing BC is to be reduced equal to the angle 
 sCS 23, or having 23 of east variation (see theorem 3, 
 
106 REDUCING- BEAEINGS, ETC. 
 
 Art. 48) ; the bearing of the object B and the magnetic 
 variation of the meridian to which its bearing is to be 
 reduced are both on the east side of the true meridian ; 
 therefore L CS 23 ^BCS 8 = Z. BCs 15 ; and as the 
 angle BCS is less than the angle sCS, the bearing of B from 
 C will be S 15 "W with the magnetic meridian ns. 
 
 7th. Suppose the bearing of the object D from C is 
 taken by a needle n's', having 10 of west variation, which 
 is to be reduced to its bearing with another magnetic me- 
 ridian ns, having 23 of west variation : Let the bearing of 
 CD with the true meridian NS be found equal to the angle 
 DCS 15, or S 15 W ; and also the south magnetic meridian 
 to which the bearing DC is to be reduced equal to the 
 angle sCS 23, or having 23 of east variation (see theorem 
 3, Art. 48) ; and as the bearing of the object D and the 
 magnetic variation of the meridian to which its bearing is 
 to be reduced are on contrary sides of the true meridian NS, 
 therefore ^DCS 15+sCS 23= Z DCs 38 ; and also the 
 bearing of D will be on the contrary side of the magnetic 
 meridian ns that its variation is on ; and as the south me- 
 ridian ns has east variation, therefore the bearing of D from 
 C will be S 38 W. 
 
 8th. Suppose the bearing of the object E from C is 
 taken by the meridian n's', having 10 of west variation? 
 which is to be reduced to the bearing it will form with 
 another magnetic meridian ns, having 23 of west variation : 
 Let the bearing EC with the*true meridian be found equal 
 to the angle ECN 77, or N 77 E ; and the magnetic 
 meridian to which the bearing EC is to be reduced equal 
 to the angle raCN 23, or having 23 of west variation ; the 
 bearing of the object E and the magnetic variation of the 
 meridian to which it is to be reduced are on contrary sides 
 of the true meridian NS ; therefore Z. ECN 77 + L wCN 
 23 = L ECra 100 ; but as the angle that the object E 
 makes with the north magnetic meridian ns exceeds 90, its 
 bearing in that case must be with the south or contrary 
 
REDUCING BEARINGS, ETC. 
 
 107 
 
 meridian ; then 180 100 = 80 / EC* ; consequently 
 the bearing of the object E with the magnetic meridian ns 
 wiU be S SO C E. 
 
 . From the several cases of Art. 53, the student will have no dif- 
 ficulty in solving the following examples, with respect to two different 
 magnetic variations. 
 
 EXAMPLE I. If the following bearings are taken by a 
 meridian having 10 of west variation, N 50 W, N 70 E, 
 S 5 E, and S 80 E ; what will be the bearing of each with 
 a meridian having 23 of west variation ? 
 
 With a meridian of 10 of 
 variation. 
 
 N. 50 W. 
 N. 70 E. 
 S. 5 E. 
 S. 80 E. 
 
 With a meridian of 23 of 
 variation. 
 N. 37 W. 
 N. 83 E. 
 S. 8W. 
 S. 67 E. 
 
 EXAMPLE II. If the following bearings are taken by 
 a meridian having 10 of east variation, S 60 W, S 10 E, 
 N 80 E, and N 10 W ; what will be the bearing of each 
 with a meridian having 20 of west variation ? 
 
 With a mwidian of 10 of east 
 variation. 
 S. 60 W. 
 S. 10 E. 
 N. 80 E. 
 N. 10 W. 
 
 With a meridian of 20 of ivest 
 variation. 
 Due west. 
 S. 20 3 W. 
 S. 70 E. 
 N. 20 E. 
 
 EXAMPLE III. The following bearings are taken by a 
 meridian having 20 of west variation, S 60 W, N 5 W, 
 N 30 W, and N 50 E ; what bearing wiU each form with 
 a meridian having 10 of east variation ? 
 With a meridian of 20 of west \ With a meridian of 10 of east 
 
 variation. 
 S. 60 W. 
 N. 5W. 
 N. 30 W. 
 N. 50 E. 
 
 variation. 
 S. 30 W. 
 N. 35 W. 
 N. 60 W. 
 
 N. 20 E. 
 
108 
 
 REDUCING BEAKINGS, ETC. 
 
 EXAMPLE IV. If the following bearings are taken by 
 the true meridian, S 60 W, N 5 W, N 30 W, and 
 N 50 E ; what bearing will each form with a meridian 
 having 23 of west variation ? 
 
 With the true meridian. 
 
 S. 60 W. 
 N. 5 W. 
 N. 30 W. 
 N. 50 E. 
 
 With a meridian of 23 of 
 variation. 
 S. 83 W. 
 N. 18 E. 
 N. 7W. 
 N. 73 E. 
 
 EXAMPLE Y. I have to plot a survey on the surface of 
 the following bearings and distances, N 25 "W 5 chains, 
 N 63 W 10 chains, N 20 E 3 chains, N 70 E 6 chains, 
 and S 84 E 9 chains, which has been taken by a eircum- 
 ferentor having 20 of west variation ; now 1 find the 
 circumferentor by which I have to plot the same has 23 
 of west variation, I demand to know the bearings under 
 which the survey must be plotted, so that the same may 
 be accurately clone ? 
 
 With a meridian of 20 of west 
 variation,. 
 
 N. 25 W. 
 N. 63 W. 
 N. 20 E. 
 N. 70 E. 
 S. 84 E. 
 
 Chains. 
 . 5 
 . 10 
 
 3 
 , 6 
 
 9 
 
 The bearings under which the sur- 
 vey must be plotted to be accu- 
 rately done, ly a needle having 
 23 of west variation. 
 
 Chains. 
 N. 22 W. . 
 N. 60 W. 
 N. 23 E. 
 
 N. 73 E. 
 S. 81 E. 
 
 5 
 
 10 
 3 
 6 
 
 
 
 EXAMPLE VI. In a subterraneous survey of the fol- 
 lowing bearings and distances, viz. N 20 W 10 chains, 
 N 60 W 3 chains, S 12 W 5 chains, IS" 87 W 4 chains, 
 and S 15 E 7 chains, surveyed by an instrument having 
 22 of west variation, which is to be plotted on a plan 
 whose meridian has 12 of west variation, I wish to know 
 
EEDTJCTNG BEARINGS, ETC. 
 
 109 
 
 under what bearing each must be plotted on the plan, so 
 that it may be accurately done ? 
 
 The bearings by a 
 
 meridian hav- The bearings with the plan's me- 
 
 ing 22 of west 
 
 variation. 
 
 ridian having 
 
 12 of west va- 
 
 
 
 riation. 
 
 
 
 Chains. 
 
 
 Chains. 
 
 N. 20 W. 
 
 . . 10 
 
 N. 30 W. 
 
 . 10 
 
 N. 60 W. . 
 
 . 3 
 
 N. 70 W. 
 
 . . 3 
 
 S. 12W. 
 
 . . 5 
 
 S. 2 W. 
 
 . 5 
 
 N. 87 W. . 
 
 . 4 
 
 S. 83 W. 
 
 . . 4 
 
 S. 15 E. 
 
 . . 7 
 
 S. 25 E. 
 
 . 7 
 
 FIG 67 
 
 ,V 
 
 To find what kind of a meridian a plan has leen 
 constructed ~by. 
 
 (54.) Where subterraneous excavations are to be added 
 to some previously delineated on a plan, it will be neces- 
 sary, first of all, to find what kind of meridian the plan 
 has been constructed by, in order that the bearings to be 
 plotted may previously be reduced thereto (see theorem 4, 
 Art. 48). 
 
 1. Suppose N'S' to be the meri- 
 dian of a plan whose magnetic varia- 
 tion is required to be known ; let the 
 bearing of the pit B from the pit A 
 be taken on the plan with the meri- 
 dian thereon', equal to the angle 
 BA^40, or N 40 W; and let the 
 bearing of the same two pits be 
 taken on the surface by a circum- 
 ferentor placed ab A, whose needle 
 is known to have 23 of west varia- 
 tion ns, and found to form an angle 
 BA = 27, or N 27 W; then, if 
 N'S' represent the true meridian, 
 the line AB will form an angle therewith of 27 
 = 50 BAN, or N 50 W : From L BAN 50 
 
110 
 
 BEDUCING BEABINGS, ETC. 
 
 ' 40, leaves L WAN = 10, which is the angle 
 that the plan's meridian makes with the true meridian; 
 and as the angle ~BA.W, which is the bearing of the 
 object with the plan's meridian, is to the left thereof, and 
 less than the L BAN, which is the bearing of the same 
 object, as taken by the circumferentor on the surface, with 
 the true meridian, and to the left thereof also, it follows 
 that L WAN, the variation of the plan's meridian, must 
 be to the left of the true meridian ; therefore S'W must have 
 10 of west variation. 
 
 2. Suppose WS' to be the meridian of a plan whose 
 magnetic variation is required to be known ; let the bearing 
 of the pit B from A be taken on the plan with the meridian 
 thereon, equal to the angle BA.ZV' 60, or N 60 W ; and 
 let the bearing of the same two pits be taken on the surface 
 by a circumferentor placed at A, whose needle is known 
 to have 23 of west variation ns, and found to form an 
 
 angle BArc = 27, or N 27 W ; then if 
 NS represent the true meridian, the 
 line AB will form an angle therewith 
 of 27 + 23 = 50 BAN, or N 50 
 W: Then from L BA^ 60 - L 
 BAN 50, leaves L WAN = 10, the 
 variation of the plan's meridian; but 
 as the L BA.ZV", which the bearing of 
 the object makes to the left with the 
 plan's meridian, is greater than the /. 
 BAN, which is the angle that the same 
 object, as taken by the circumferentor 
 on the surface, makes to the left with 
 the true meridian, the L -ZV'AN must be 
 to the right of the true meridian ; there- 
 fore jSWmust have 10 of west variation. 
 
 3. Suppose WS' to be the meridian of a plan whose 
 magnetic variation is required to be known ; let the bearing 
 of the pit B from the pit A be taken on the plan with the 
 
 & 
 
BEDTJCING BEARINGS, ETC. 
 
 Ill 
 
 FI&.69. 
 
 Bt 
 
 rj 
 
 meridian thereon, equal to the angle BAjY' 5, or N 5 E ; 
 and let the bearing of the same two pits be taken on the 
 surface by a circumferentor placed at A, whose needle 
 has 23 of west variation ns, be 
 found to form an angle BA?z = 
 18, or N 18 E ; then if NS 
 represent the true meridian, the 
 line AB will form an angle there- 
 with of 23 - 18 = 5 L BAN, 
 or N 5 W : Then L BA^' 5 + 
 L BAN 5 = Z JV'AN 10, the 
 variation of the plan's meridian ; 
 and as AB bears on different sides 
 of the two meridians N'S' and 
 NS, and L BAN being to the 
 left of the true meridian NS, L 
 NAJV' must be to the left thereof 
 also ; consequently the plan's me- 
 ridian N'S' must have 10 of west 
 variation. 
 
 4. Suppose N'S' (see last fig.), is the meridian of a plan 
 whose magnetic variation is required to be known ; let the 
 bearing of the pit B' from the pit A be taken on the plan 
 with its meridian, equal to the angle N'A.'B' 83, or 
 N 83 W ; and let the bearing of the same two pits be 
 taken on the surface by a circumferentor placed at A, 
 whose needle has 23 of w r est variation ns, be found to 
 form an angle wAB' = 70, or N 70 W ; then if NS repre- 
 sent the true meridian, the line AB' will form an angle 
 therewith of 87 L B'AS S 87 W (see Art. 52) : Now 
 L -Y'AB' 83 + L B'AS 87 = /. JV"AS 170, then 180 
 - 170 = 10 L NAJV', the variation of the plan's meri- 
 dian ; and as L NAN' 10 is what L SA^ r falls short of 
 180, reckoning from the south meridian S, therefore it must 
 be to the left or west of the north meridian N ; consequently 
 the plan's meridian N'S' must have 10 of west variation. 
 
112 
 
 EEDTJCING BEARINGS, ETC. 
 
 F I C 70 
 
 N 
 
 5. Suppose N'S' to be the meridian of a plan whose 
 magnetic variation is required ; let the bearing of the pit B 
 from the pit A be taken on the plan with its meridian 
 
 thereon, equal to the angle N'A^B 
 45, or N 45 W ; and let the 
 bearing of the same two objects, 
 taken on the surface by an instru- 
 ment placed at A, whose needle 
 has 23 of west variation ns, be 
 found to be equal to the same 
 angle *AB 45, or N 45 W, as 
 before ; then if NS represent the 
 true meridian," the line AB will 
 form an angle therewith of 45 + 
 23 = 68 NAB, or N 68 W: 
 Then L NAB 68 - L JVAB 
 45 = L NAJV' 23, the varia- 
 tion of the plan's meridian; but 
 as L -ZV'AB is to tlie left of the 
 plan's meridian, and is less than 
 L NAB, the L NAJV' must be to 
 
 the left of the true meridian SN ; therefore the plan's 
 meridian, will have 23 of west variation. When the 
 bearing of two objects, taken on a plan by its delineated 
 meridian, agrees with the bearing of the same two objects 
 taken on the surface by an instrument, the variation of the 
 plan's meridian will be the same as the magnetic variation 
 of the needle of that instrument. 
 
 6. Suppose N'S' to be the meridian of a plan whose 
 magnetic variation is required to be known ; let the bearing 
 of the pit B from that of A be taken on the plan by its 
 meridian thereon, equal to the angle NAB 68, or N 68 W: 
 and let the bearing of the same two objects be taken by an 
 instrument on the surface placed at A, whose needle has 
 23 of west variation ns, equal to the angle nKB 45, or 
 N 45 W ; then the object will form an angle with the true 
 
REDUCING BEABISTGS, ETC. 113 
 
 meridian of 45 + 23 = 68, or N 68 W: Now, as the 
 bearing of the two objects on the plan with its meridian, 
 agrees with the bearing of the same two objects taken on 
 the surface when reduced to the true meridian, therefore 
 the plan's meridian must be the true meridian. 
 
 From, the several cases in the last Article, where six 
 examples are solved, the method of solving the following 
 unsolved examples will be readily seen. 
 
 EXAMPLE I. I wish to know the variation of a plan's 
 meridian, when the bearing of two objects thereon with its 
 meridian is N 30 W, and the bearing of the same two 
 objects with each other on the surface is found, by an 
 instrument whose needle has 20 of west variation, to be 
 N19W? 
 
 The objects on the surface will form a bearing with each 
 other of N 39 "W by the true meridian. 
 
 Then 39 30 = 9 ; therefore the plan's meridian has 
 9 of west variation. 
 
 EXAMPLE II. I wish to know the variation of a plan's 
 meridian, when the bearing of two objects thereon with 
 its meridian is N 16 E, and the bearing of the same two 
 objects with each other on the surface is found, by an 
 instrument whose needle has 23 of west variation, to be 
 N 10 E ? 
 
 The objects on the surface will form, a bearing with each 
 other of N 13 W by the true meridian. 
 
 The 16 + 13 = 29 ; therefore the plan's meridian has 
 29 of west variation. 
 
 EXAMPLE III. I have a plan which I wish to know by 
 what kind of meridian it has been delineated : Now the 
 bearing of two objects thereon with each other by its meri- 
 dian is found to be N 80 "W, and the bearing of the same 
 two objects, taken on the surface by an instrument whose 
 needle has 21 of west variation, is N 74 W ? 
 
 The bearing of the two objects on the surface with the 
 true meridian will be S 85 W. 
 
114 BEDUCiya BEARINGS, ETC. 
 
 Then 180 80 + 85 = 15 ; therefore the plan has 
 been delineated by a meridian having 15 of west variation. 
 
 EXAMPLE IV. I wish to know the variation of a plan's 
 meridian, when the bearing of two objects taken thereon 
 by its meridian is found to be JST 40 E, and the bearing of 
 the same two objects, taken on the surface by an instru- 
 ment whose needle has 20 of west variation, is also 
 N40E? 
 
 Then the meridian of the plan will have the same 
 magnetic variation as the needle by which the bearing of 
 the objects was taken on the surface ; therefore the plan's 
 meridian will have 20 of west variation. 
 
 EXAMPLE V. I wish to know by what kind of meridian 
 a plan has been constructed, when two objects thereon by 
 its meridian form a bearing with each other of N 32 "W, 
 and the bearing of the same two objects, as taken on the 
 surface by an instrument whose needle has 22 of west 
 variation, forms a bearing with each other of N 10 "W ? 
 
 The two objects on the surface will form a bearing with 
 each other of N 32 "W by the true meridian. 
 
 Then the meridian of the plan will be the true meridian. 
 
 EXAMPLE VI. I wish to know the variation of a plan's 
 meridian, when the bearing of two objects thereon with 
 its meridian is S 16 W, and the bearing of the same two 
 objects with each other on the surface, taken by an instru- 
 ment whose needle has 23 of west variation, is found to 
 be S 10 W ? 
 
 The plan's meridian will have 29 of west variation. 
 
 EXAMPLE VII. I wish to know the variation of a plan's 
 meridian, when the bearing of two objects thereon with its 
 meridian is S 40 W, and the bearing of the same two objects 
 with each other on the surface, taken by an instrument whose 
 needle has 20 of west variation, is found to be S 23 "W? 
 
 The plan's meridian will have 6 of east variation. 
 
 EXAMPLE VIII. I wish to know the variation of a 
 plan's meridian, when the bearing of two objects thereon 
 
REDUCING EEARI^GS, ETC. 115 
 
 with its meridian is N 65 W, and the bearing of the same 
 two objects with each other on the surface, taken by an 
 instrument whose needle has 23 of west variation is found 
 to be N 20 W ? 
 
 The plan's meridian will have 22 of east variation. 
 
 EXAMPLE IX. I have a plan of a colliery workings, on 
 which I took the bearing of two pits with each other by 
 its meridian, which was N 5 W ; I also took the bearing 
 of the same two pits on the surface by an instrument whose 
 needle had 23 of west variation, which was N 5 E ; now 
 I wish to know the variation of the plan's meridian by 
 which it has been delineated ? 
 
 The plan's meridian will have 13 of west variation. 
 
 EXAMPLE X. I wish to know by what kind of meridian 
 a plan of a colliery working has been constructed, when 
 the bearing of two pits thereon with each other by its 
 delineated meridian is found to be JST 5 E, and the bearing 
 of the same two pits on the surface with the true meridiaji 
 is found to be N 14 W ? 
 
 The plan has been constructed by a meridian having 19 
 of west variation. 
 
 How to plan surveys, and also the manner of determining an 
 error arising in plotting, through inattention to the magnetic 
 variation of the needle. 
 
 (55.) It has been shown, in Art. 49, that the magnetic 
 meridian is always changing ; therefore the bearings of the 
 same objects, taken by such a meridian at [different times, 
 must also vary from each other, except reduced to bearings 
 with the true meridian. 
 
 Let Ts"S represent the meridian of a plan, which is also 
 supposed to be the true meridian ; and if a subterraneous 
 excavation is to be plotted thereon from the pit A, which 
 excavation is found to form a bearing of N 10 W 10 chains 
 by an instrument whose needle had 20 of west variation ; 
 
116 
 
 BEDTJCING BEAEINGS, ETC. 
 
 now if the excavation N 10 W 10 chains is plotted on the 
 plan by its meridian NS, which is the true meridian, it will 
 FIG- 71 ^ e re P resen ted by -AB ; but the bearing 
 being taken by a needle having 20 of 
 west variation, therefore (according to 
 the manner of reducing bearings from 
 one magnetic meridian to their bearings 
 with any other, Art. 53) it should form 
 a bearing of N 30 W with the meridian 
 NS, as represented by A5 ; then A.I will 
 be the true direction of the excavation 
 from the pit A, and b~B will be the magni- 
 tude of the error (see theorem 8, Art. 48): 
 \ Or, instead of reducing the excavation to 
 s its bearing with the true meridian NS, 
 it will be equally as true if ns is drawn 
 on the plan, and made to represent the magnetic meridian 
 of the needle by which the bearing was taken, with which 
 AS will form a bearing of N 10 AV. 
 
 I shall insert a few examples, illustrative of the error 
 arising from plotting a subterranous survey on a plan 
 without attending to the variation of the magnetic meri- 
 dian, and also how its magnitude can be ascertained. 
 
 EXAMPLE I. The following is a subterraneous survey, 
 commencing at a pit called the B pit, N 30 W 6 chains, 
 N 70 E 10 chains, N 30 E 5 chains, and N 25 W 
 8 chains, which was surveyed by an instrument whose 
 needle had 24 of west variation ; under what bearings must 
 the survey be plotted on a plan whose delineated meridian 
 has 15 of west variation ? 
 
 Eeduce the bearings, as taken by a meridian having 24 
 of west variation ; to bearings with a meridian having 15 of 
 west variation : Thus, 
 
REDUCING BEAEINGS, ETC. 
 
 117 
 
 Bearings with a meridian of 24 
 of west variation. 
 
 Chains. 
 
 N. 30 W. 6 
 
 N. 70 E. . 10 
 
 N. 30 E. . . 5 
 N. 25 W. 8 
 
 Bearings with a meridian of 15 
 of west variation. 
 
 Chains. 
 
 N. 39 W. . . 6 
 N. 61 E. . .10 
 K 21 E. . . 5 
 N. 34 W. 8 
 
 FIG. 
 
 The survey must be plotted under bearings with a 
 magnetic meridian having 15 of west variation, as above, 
 commencing at the B pit. 
 
 EXAMPLE II. If the following subterraneous survey, 
 N 9 W 8 chains, N. 30 E 7 chains, and N 21 W 8 chains, 
 is made by an instrument whose needle has 23 of west 
 variation, and plotted on a plan by a meridian having 5 
 of west magnetic variation, without 
 being reduced thereto, what will 
 be the magnitude of the error re- 
 sulting by such neglect ? 
 
 Suppose A, the point of com- 
 mencement of the survey on the 
 plan, and let the meridian of the 
 plan here presented be N'"S"', hav- 
 ing 5 of west variation with the true 
 meridian NS; then the first bear- 
 ing, IN" 9 "W 8 chains, will be re- 
 presented by AB, the second, 
 N 30 E 7 chains, by BC, and the 
 third bearing, N 21 W 8 chains, 
 by CD ; then ABCD will represent 
 the survey plotted without attend- 
 ing to the magnetic variation : But 
 as the survey was made by an in- 
 strument whose needle- had 23 of 
 west variation, therefore each bear- 
 ing, when truly plotted, must be set 
 off from a meridian of that variation, which let ns represent ; 
 
118 
 
 BEABINGS, ETC. 
 
 then N 9 W 8 chains will be represented by A5, N 30 E 
 7 chains by lc } and N 21 "W 8 chains by cd ; then Abed 
 will represent the survey truly plotted, and dD will be the 
 magnitude of the error. 
 
 Or the survey may be plotted by reducing the bearings, 
 as taken by a meridian of 23 of west variation, to bearings, 
 with a meridian of 5 of variation, as represented by N'S', 
 and plotted from it accordingly, which will exactly 
 coincide with A.bcd, as before. 
 
 To discover, by calculation, the magnitude of the error 
 reduce the bearings of the survey, as taken by a magnetic- 
 meridian having 23 of west variation, to bearings with the 
 true meridian, and also the same bearings, as if taken by 
 a meridian having 5 of west variation, to bearings with the 
 true meridian ; then determine the northing and easting of 
 D from^: Thus, 
 
 With a meridian 
 of 23 of west 
 variation. 
 
 With the true 
 meridian. 
 
 With a meridian 
 ' of 5 of west 
 variation. 
 
 With the true 
 meridian. 
 
 Chns. 
 N. 9W. 8 
 N. 30 E. 7 
 N. 21 W. 8 
 
 Chns. 
 N. 32 W. 8 
 N. 7E. 7 
 N. 44 W. 8 
 
 Chns. 
 
 N. 9 W. 8 ' 
 N. 30 E. 7 
 N. 21 W. 8 
 
 Chns. 
 N. 14 W. 8 
 N. 25 E. 7 
 N. 26 W. 8 
 
 Chns. 
 N. 32 W. 8 
 
 N. 7 E. 7 
 N. 44 W. 8 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 
 Chains. 
 678 
 6-94 
 5-75 
 
 Chains. 
 
 Chains. 
 0-85 
 
 Chains. 
 4-23 
 
 5-55 
 
 
 19-47 
 
 Aa 
 
 
 9-78 
 0-85 
 
 ad 
 
 8-93 
 
KEDTJCIIS'G 
 
 , ETC. 
 
 119 
 
 Chns. 
 N. 14 W. 8 
 N. 25 E. 7 
 N. 26 W. 8 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 Chains. 
 2-9*5 
 
 Westing. 
 
 Chains. 
 1-93 
 
 3-50 
 
 
 Chains. 
 7-76 ' 
 6-34 
 7-19 
 
 Chains. 
 
 
 21-29 
 
 Ae 
 
 
 5-43 
 2-95 
 
 
 
 
 
 
 2-48 
 
 cD or af 
 
 ad 8'93 chains af 2 '48 chains = fd 6'45 chains. 
 
 Ae 21'29 chains A 19 '47 chains = ae or/D 1'82 chains. 
 
 Then, as fd 6 -45 . . . -8095595 
 Is to radius. . . . 10 '0000000 
 
 Sois/D 1-82 . . . -2600714 
 
 To tang. /_ d 15 45' . . 9'4505117 
 From 90 15 45' = 74- 15', Z cidV. 
 
 And V 6-45 + 1'82 = 67 c?D, or 6 '70 chains. 
 
 Therefore the magnitude of the error, or the bearing and 
 distance of D from d t will (from Art. 3) be N 74 15' E 
 670 chains with the true meridian. 
 
 EXAMPLE III. If the following subterraneous survey 
 S 30 "W" 4 chains, N 50 W 8 chains, N 50 E 9 chains, 
 and IX" 53 W 8 chains, is surveyed by an instrument having 
 23 of west variation, and plotted on a .plan by the true 
 meridian, without being reduced thereto, what will be 
 magnitude of the error thereby ? 
 
 Suppose A to be the point of commencement on the 
 plan, and NS the true meridian thereon ; then ABCDF 
 will be the erroneous representation of the bearings and 
 distances, as plotted from that meridian, AB forming an 
 angle of 30 therewith, BC an angle of 50 therewith, 
 CD an angle of 50 therewith, and DF an angle of 53 
 therewith. 
 
120 
 
 HEDUCING BEABINGS, ETC. 
 
 To 
 
 plot the survey accurately, draw on the plan a meri- 
 dian line ns, having 23 of west 
 variation ; each bearing and dis- 
 tance being then plotted from it, 
 and Abcdfwill represent the sur- 
 vey accurately done, and/'F will 
 be the magnitude of the error: 
 Or, otherwise, if each bearing in 
 the survey is reduced from the 
 angle it formed with the mag- 
 netic meridian it was taken by, 
 to the angle of bearing it will 
 form with the plan's meridian, 
 which is the true meridian, and 
 plotted accordingly, the result 
 will be the same : Thus, 
 
 With a meridian having 23 of 
 west variation. 
 
 Chains, 
 
 S. 30 W. . . 4 
 N. 50 W. . 8 
 N. 50 E. . . 9 
 N. 53 W. , 8 
 
 With the true meridian. 
 
 Chains. 
 
 S. 7W. . . 4 
 N. 73 W. . 8 
 N. 27 E. . . 9 
 N. 76 W. , 8 
 
 Then A will represent S 7 W 4 chains, bo N 73 W 
 8 chains, cd N 27 E 9 chains, and cff, N 76 W 8 chains,, 
 the same as before. 
 
EEDUCINQ BEAKINGS, ETC. 
 
 121 
 
 Chns. 
 S. 30 W. 4 
 N. 50 W. 8 
 N. 50 E. 9 
 N. 53 W. 8 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 AF or ah 
 
 Chains. 
 
 5 V 14 
 579 
 4-81 
 
 1574 
 3-46 
 
 Chains. 
 3-46 
 
 Ah 
 
 Chains. 
 6-89 
 
 Chains. 
 2-00 
 6-13 
 
 6-39 
 
 14-52 
 6-89 
 
 7'63 
 
 12-28 
 
 Chns. 
 S. 7 W. 4 
 N. 73 W. 8 
 N. 27 E. 9 
 N. 76 W. 8 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 
 Chains. 
 
 2'-33 
 8-01 
 1-93 
 
 12-27 
 3-97 
 
 Chains. 
 3-97 
 
 Chains. 
 4-08 
 
 Chains. 
 0-48 
 7-65 
 
 7-76 
 
 15-89 
 4-08 
 
 
 8-30 
 
 Aa 
 
 
 11-81 
 
 / 
 
 From af ll'Sl ale 7'63 = fc/4'18. 
 
 AA 12-28 Aa 8 -30 = ah or &F 3 -98. 
 
 6211763 
 
 10-0000000 
 
 5998831 
 
 9-9787068 
 
 Then, as kf 4 18 
 
 Is to radius 
 So is JfcF 3-98 
 
 To tang. ^ / 43 35' . 
 From 90 43 35' = 46 25' ^ nfF. 
 And V418 + 3-98 = 5'77/F chains. 
 
 Therefore the bearing of F from /with the true meri- 
 dian will be N 46 25' E, and the distance will be 577 
 chains ; which is the magnitude of the error. 
 
 EXAMPLE IV. If the following subterraneous survey, 
 
122 
 
 EEDTJCING BEABINGS, ETC. 
 
 FF&.74-. 
 
 commencing at the pit A, S 30 ~W 4 chains, S 70 "W 
 10 chains, and S 50 E 5 chains, was surveyed by an instru- 
 ment whose needle had 
 23 of west variation, 
 and is plotted on a plan 
 by a meridian having 
 only 10 of variation to 
 the west, without reduc- 
 ing the bearings there- 
 to ; what will be magni- 
 tude of the error ? 
 
 If NS represent the 
 true meridian, ns the 
 meridian, having 23 of 
 west variation, by which 
 the survey was taken, 
 \ and IPS' the meridian 
 \ of the plan, having 10 
 ^ of variation, by which 
 the survey is to be plot- 
 ted ; the ABCD will be 
 the erroneous representation of the survey, as plotted by 
 the meridian N'lS' without reducing tne bearings thereto. 
 To plot the same truly, 
 
 With a meridiem of 23 of west 
 variation. 
 
 Chains. 
 
 S. 30 W, . .4 
 S. 70 W. . . 10 
 S. 50 E. . 5 
 
 With a meridian o/10 of west 
 variation. 
 
 Chains. 
 
 S. 17 W. . .4 
 S. 57 W. . . 10 
 S. 63 E. , 5 
 
 Now make AJb form an angle to the west with the meri- 
 dian -ZV'/S' of 17, lc an angle to the west of 57, and cd an 
 angle to the east of 63 ; then Ated will represent the 
 survey truly plotted, and the distance between D and d 
 will be the magnitude of the error. 
 
EEDTJCIKG BEABIKGS, ETC. 
 
 TO FIND THE MAGNITUDE OP THE ERROR. 
 
 123 
 
 With a meridian 
 of 23 of west 
 variation. 
 
 With the true 
 meridian. 
 
 With a meridian 
 of 10 of west 
 variation. 
 
 With the true 
 meridian. 
 
 Chns. 
 S. 30 W. 4 
 S. 70 W. 10 
 S. 50 E. 5 
 
 Chns. 
 S. 7 W. 4 
 S. 47 W. 10 
 S. 73 E. 5 
 
 Chns. 
 S. 30 W. 4 
 S. 70 W. 10 
 S. 50 E. 5 
 
 Chns. 
 S. 20 W. 4 
 S. 60 W. 10 
 S. 60 E. 5 
 
 Chns. 
 S. 7 W. 4 
 S. 47 W. 10 
 S. 73 E. 5 
 
 Northing. 
 
 Southing. 
 
 Easting. 
 
 Westing. 
 
 ad 
 
 Chains. 
 
 Chains. 
 3-79 
 6-82 
 1-46 
 
 12-25 
 
 Chains. 
 
 4'- 7 8 
 Aa 
 
 Chains. 
 0-49 
 7-31 
 
 7-80 
 4-78 
 
 3-02 
 
 Chns. 
 S. 20 W. 4 
 S. 60 W. 10 
 S. 60 E. 5 
 
 Northing. 
 Chains. 
 
 Southing. 
 
 Easting. 
 Chains. 
 
 4-33 
 
 Ae 
 
 Westing. 
 
 eD 
 
 Chains. 
 3-75 
 5-00 
 2-50 
 
 Chains. 
 1-37 
 8-66 
 
 10-03 
 4-33 
 
 11-25 
 
 5-70 
 
 Then Aa 12-25 Ae 11-25 = ae or fd 1. 
 
 And eD 570 ad 3 '02 = /D 2'68. 
 
 As/D 2-68 .... -4281348 
 Is to radius . . . . 10 '0000000 
 Sois/dl .... 
 
 To tang. /_ D. 20 27' . . 9-5718652 
 From 90 20 27' = 69 83', _ fdV. 
 
 And V 2-68 + 1 = 2'86 = Dd. 
 
124 HOW TO RUN BEARINGS, ETC. 
 
 Therefore the bearing of D from d with the true meridian 
 will be N 69 33' W, and the distance will be 2-86 chains ; 
 which is the magnitude of the error. 
 
 EXAMPLE V. The following subterraneous survey, 
 S 20 W 5 chains, S 70 W 10 chains, N 50 W 5 chains, 
 and N 3 "W 8 chains, was taken by an instrument having 
 23 of west variation, which I have to plot on a plan, the 
 magnetic variation of the meridian by which it has been 
 constructed is unknown ; I therefore wish to know how the 
 survey must be plotted, so that it may be accurately done? 
 
 In order to find by what kind of meridian the plan has 
 been constructed, I took the bearing of two pits thereon 
 by the delineated meridian, which I found to bear with 
 each other ]N T 25 W, and the same two pits on the sur- 
 face I found to bear N 22 W by an instrument whose 
 needle had 23 of west variation ; therefore the plan's 
 meridian will have 20 of west variation, and the bearings 
 of the survey must be reduced from a meridian of 23 of 
 west variation to bearings with a meridian of 20 of the 
 same variation, and plotted on the plan accordingly ; 
 Thus, 
 
 Searings with a meridian of 23 
 of west variation. 
 
 Chains. 
 
 S. 20 W. . .5 
 S. 70 W. . . 10 
 N. 50 W. . .5 
 N. 3 W. 8 
 
 Searings with the plains meridian 
 of 20 of west variation. 
 Chains. 
 
 S. 17 W. . . 5 
 S. 67 W. . . 10 
 N. 53 W. . .5 
 N. 6 W. 8 
 
 Sow to run bearings on the surface l>y a circumferentor, 
 without error. 
 
 (56.) It frequently happens that the practical miner has 
 to re-traverse on the surface the survey of a subterraneous 
 excavation from bearings taken at some former time : Now, 
 when that is the case, if the miner does it without attending 
 to the change that has taken place with the magnetic 
 meridian, between the taking of the survey and the re- 
 
HOW TO RUN BEARINGS, ETC. 
 
 125 
 
 traversing it, an error must inevitably be the result ; but 
 where surveys are recorded without mentioning by what 
 kind of meridian they were originally made, such surveys 
 cannot be re-traversed with any degree of accuracy. 
 
 Suppose the bearing of a subterraneous excavation AB, 
 is found to be N 20 W, which is taken by the needle 
 of an instrument placed at the pit A, whose magnetic 
 meridian is represented by NS ; now, if the 
 bearing of this excavation is run off on the 
 surface from the pit A, immediately after it 
 has been surveyed under-ground, and by the 
 same instrument also, the excavation AB 
 will be truly represented on the surface (see 
 theorem 6, Art. 48) ; but if it should be ne- 
 cessary, at any future time, to have the same 
 excavation represented on the surface by the 
 same survey already made, and in that in- 
 terval of time between the survey being made 
 and its second plotting on the surface, the 
 magnetic meridian NS has changed its situa- 
 tion to ns, the same excavation, IN" 20 "W, 
 run off from the then magnetic meridian ns, will be 
 represented by A&, which will be erroneous : Therefore, to 
 do the work truly, the bearing of AB, as originally taken 
 by the meridian NS, must be reduced to its bearing with 
 the meridian ns, and plotted on the surface from it accord- 
 ingly (see theorem 7, Art. 48). 
 
 I shall insert a few examples relative to plotting bearings 
 on the surface by different meridians. 
 
 EXAMPLE I. The subterraneous excavation commencing 
 at the pit A, N 20 W 5 chains AB, N 20 E 8 chains BC, 
 N 70 E 5 chains CD, and S 70 E 5 chains DF, was 
 surveyed by an instrument whose needle had 10 of west 
 variation ns, and is to be plotted on the surface by another 
 instrument whose needle has a different magnetic variation ; 
 how must it be plotted with accuracy ? 
 
126 HOW TO BUK" BEABINGS, ETC. 
 
 First, find the magnetic variation of the needle of the 
 instrument by which the survey is to be plotted (see 
 Art. 51), which suppose it to have 23 of west variation 
 N S ; then reduce the bearings, as taken by a meridian of 
 10 of west variation ns, to bearings with a meridian of 23 
 of west variation !N" S. 
 
 EXAMPLE II. If the following survey of a subterraneous 
 excavation, commencing at the pit A (see Eig. to Ex. IV. 
 Art. 55), S 30 W 4 chains, S 70 W 10 chains, and S 50 
 E 5 chains, was surveyed by an instrument which had 10 of 
 west variation ; what will be the magnitude of the error, if 
 the survey is plotted on the surface by another instrument 
 having 23 of west variation ? 
 
 Let N'S' represent the magnetic meridian of the needle 
 of the instrument by which the survey was made, having 
 10 of west variation, and let ABCD represent the survey 
 as plotted on the surface thereby, also let ns represent the 
 meridian of the instrument whose needle has 23 of west 
 variation, and AJbcd the excavation as plotted according to 
 that meridian; then AEOD will be the survey plotted 
 truly, and A.lcd the same plotted erroneously : Therefore, 
 from the manner of determining the magnitude of an error, 
 arising from plotting a survey by a different meridian than 
 that by which it was made (Art. 55), the error will be 
 2*86 chains, which is the distance of d from D. 
 
 EXAMPLE III. I have the survey of a subterraneous 
 excavation, commencing at a pit called the A pit; the 
 bearings are recorded to be taken by the true meridian, 
 viz., N SO W 5 chains, due north 8 chains, IN" 80 E 5 
 chains, JS T 45^ W 10 chains, and JS" 23J W 4 chains ; how 
 is the survey to be truly delineated by an instrument on the 
 surface, so that a pit may be sunk on the extreme point of 
 the last bearing ? 
 
 The first thing to be done, the surveyor must ascertain 
 the magnetic variation of the needle of the instrument by 
 which he intends delineating the survey (see Art. 49) 
 
TO FIND THE ANTIQUITY OF A PLAN, ETC. 127 
 
 which suppose to be 23 30' to the west, and reduce the 
 bearings of the survey thereto : Thus, 
 
 Bearings with the true meridian. Bearings with a meridian of 25 
 
 30' of west variation. 
 
 Chains. 
 N. 30 W. . .5 
 
 N 8 
 
 N. 80 E. . .5 
 N. 45f W. . . 10 
 
 Chains. 
 
 N. 6|W. . . 5 
 N. 23f E. . . 8 
 N. 76| E. . . 9 
 N. 22 W. 10 
 
 N. 23| W. . . 4 N. ... 4 
 
 Then fix the instrument at the A pit, and run off the first 
 bearing and distance N 6J W 5 chains, and the other 
 following ones in regular order, and the end of the last N 4 
 chains, will be the place on the surface where the pit must 
 be sunk, to hit the extreme point of the excavation. 
 
 To find the antiquity of a plan ly its delineated meridian. 
 
 (57.) As the magnetic meridian has, for a great number 
 of years past, been veering about to the west, hence plans 
 constructed at different times must have their magnetic 
 meridians of different variation ; those that are of the most 
 ancient construction will have their meridians more easterly 
 than those of a more modern date. Should a plan be found 
 to have been constructed by a meridian having 11 15' of 
 east variation, it will be reasonable to suppose it has been 
 made about the year 1576 ; for at that time the magnetic 
 meridian had 11 15' of east variation (see Table, Art. 49) : 
 Or, if its meridian is found to have 20 of west variation, 
 from the same principle it may be supposed to have been 
 made about the year 1765. 
 
 EXAMPLE I. If a plan is found to have a magnetic 
 meridian of 18 of west variation, in what year has it been 
 constructed ? 
 
 By looking in the table, Art. 49, it will appear to have 
 been made about the year 1750. 
 
128 MANNER OF BECOBDING STJBTEBEANEOFS SUBVEYS. 
 
 EXAMPLE II. I have a plan on which is a delineated 
 meridian ; I therefore wish to know iu what year it has 
 been made ? 
 
 First find the magnetic variation of the meridian on the 
 plan according to the rules for finding the same, Art. 54, 
 which suppose to be 6 of east variation; then, by the 
 table, Art. 49, it will appear to have been made about the 
 year 1^22. 
 
 The manner of recording subterraneous surveys. 
 
 (58.) As the necessity of recording surveys of subterra- 
 neous workings frequently occurs, I shall therefore show 
 how the same ought to be recorded, so that they may answer 
 the intended design : Thus, 
 
 A recorded survey of a subterraneous excavation, taken 
 June lOfch, 1800, beginning at the centre of the A pit, in 
 Blackburn colliery. 
 
 Each bearing "being reduced to the true meridian. 
 
 Chains. 
 
 N. 10 W 5-50 
 
 N. 20 E 4-20 
 
 N. 75 E 10-10 
 
 E 4-40 
 
 S. 71 E 6-30 
 
 N. 50 E 5-90 
 
 A recorded survey of a subterraneous working, taken 
 November 21st, 1801, beginning at the centre of the 
 Venture Pit, in Tanfield colliery. 
 
 Each bearing was taken by a needle having 23 of ivest variation, 
 and recorded accordingly. 
 
 Chains. 
 
 S. 50 W 5-24 
 
 S. 30 W 2-20 
 
 S. 86 W 5-70 
 
 N. 40 W 12-60 
 
 Now, either of these recorded surveys may be truly 
 re-traversed on the surface of the earth; at any future time 
 
NATURE AND USE OF TBAYEESE TABLES. 129 
 
 with accuracy, by an instrument whose magnetic needle 
 may have any known variation whatever, by referring to 
 Art. 56. 
 
 The nature and use of the Traverse Tables. 
 
 (59.) Thus, if it is required to know the northing and 
 easting of IS" 18 E 56 links, look in the tables under the 
 degree answering to the bearing, and to the right, opposite 
 56 in the column of bearing lengths, will be found 53 links 
 and 26 hundred parts of a link of northing, and 17 links 
 and 30 hundred parts of a link of easting. As the bearing 
 length is links, the northing and easting must be links and 
 parts of a link ; for in whatever denomination the bearing 
 length is, in the same denomination must the integral part 
 of the northing or southing and easting or westing be. 
 
 Also, if it is required to know the northing and easting 
 of N 18 E 5'65 chains, look in the table under the degree 
 answering to the bearing, and opposite 5 chains in the 
 bearing lengths will be found 4 - 76 chains of northing and 
 1*55 chains of easting ; then, for the remaining 65 links, 
 look opposite 65 in the same column of bearing lengths, 
 and there will be found 61' 82 links of northing, and 20*09 
 links of easting, which, added to the former northing and 
 easting, will make 5*3782, or nearly 5-38 chains of northing, 
 for the whole northing, and 1*7509 chains, or 1*75 chains 
 nearly, for the whole easting. 
 
 Suppose, again, the southing and westing of S 86 
 "W 98*20 chains is required, look in the tables under the 
 degree of the bearing, and the southing and westing will be 
 thus : 
 
 Chains. Chains. Chains. 
 
 For &8 '00 there is 6 '84 of southing and 97 '76 of westing. 
 For 00-20 1 -40 of ditto 01 9 '95 of ditto. 
 
 98-20 6-85-40 of southing and 97 '95 '95 of westing. 
 
 or, 6-85 of southing and 97 '96 of westing nearly. 
 
 a 3 
 
130 NA.TTJBE AND USE OF TEAVEESE TABLES. 
 
 If the southing and easting of S 18J E 20 chains is 
 required, take the southing and easting of the bearing 
 length under 18, and also under 19, in manner before 
 shewn, and half their sum will be the southing and easting 
 required ; thus : 
 
 Chains'. Chains. Chains. 
 
 S. 18 E. 20 will have 19-02 of southing 6'18 of easting. 
 S. 19 E. 20 will have 18 '91 of ditto. 6'51 of ditto. 
 
 2)37-93 12-69 
 
 18-96 of southing 6 '34 of easting. 
 
 Therefore S 18J E 20 chains will have 18'96 chains of 
 southing and 6'34 chains of easting. 
 
 Again, if the northing and westing of N 75 1 W 10'35 
 chains is required, 
 
 Chains. Chains. Chains. 
 
 ; N. 75 W. 10-35 will have 2 '68 '06 of northing 9 -99 '81 westing. 
 N. 76 W. 10-35 will have 2'50'47 of ditto. lQ-08'96 ditto. 
 
 2)5-18-53 20-08-77 
 
 N. 75|W. 10-35 will have 2-59-26 of nortiiing 10-04-38 westing, 
 or nearly 2-59 of northing 10'04| westing. 
 
 If the northing and easting of N 14 37' E 18 chains be 
 required, take the northing and easting of the bearing 
 length under 14 and the same under 15 ; take the 
 difference of each, multiply the respective differences by 
 the number of minutes, *. e. 37', and divide the products by 
 60 (the number of minutes in a degree), subtract the first 
 quotient from the northing, and add the second to the 
 easting ; and the sum and difference will be the northing 
 and easting required ; thus 
 
NATURE AND USE OF TRAVERSE TABLES. 131 
 
 N. 14 E. 18 chains will have 17 "47 of northing, and 4 '35 of easting. 
 N. 15 E. 17-39 of ditto, 4-66 of ditto. 
 
 08 diff. -31 diff. 
 
 37 37 
 
 60) 29-6 60)114-7 
 
 5 nearly. 19 nearly. 
 
 14-47 4-35 
 
 N. 14 37' E. 18 ch. will have 14'42 of northing, and 4-54 of easting. 
 
 The use of the Traverse Tables in reducing hypothenusal or 
 inclined distances to horizontal distances. (See Art. 45.) 
 
 (60.) When the table is used for the before-mentioned 
 PIC 75 purpose, the column called 
 
 a bearing lengths represents 
 the hypothenusal distance or 
 longest side of a right-angled 
 triangle, as CB ; the column 
 called N or S distance repre- 
 sents the horizontal distance AB ; and the column called E 
 or "VV distance represents the perpendicular AC. 
 
 If the horizontal distance AB or C# is required, when the 
 hypothenusal distance CB is 10 chains, and the angle CB 
 or CBA is 20, look in the table under 20, and Opposite 
 10, in the column of bearing lengths, will be found in the 
 column of N or S distance 9-40, which will be 9'40 chains, 
 equal to the horizontal distance AB or C. 
 
 If the horizontal distance AB or C is required, when the 
 hypothenusal distance CB is 8 chains, and the angle aCB or 
 CBA is 50, look in the tables under 50, and opposite 8, 
 in the column of bearing lengths, will be found 5'14 chains, 
 in the column of N or S distance, which is equal to AB or 
 Ca, the horizontal distance. 
 
 The horizontal distance of a line 20'50 chains, run under 
 an angle of 15 of elevation, is required ? 
 
 Look in the tables under 15, and in the column of 
 
132 NATURE AND USE OP TRAVEBSE TABLES. 
 
 bearing lengths for 2O50 chains, the horizontal distance 
 will be thus : 
 
 Chains. Chains. 
 
 For 20*00 of hyp. distance 19 '32 of horizontal distance. 
 For 0*50 of hyp. distance '4 8 of horizontal distance. 
 
 For 20'50 of hyp. distance 19 '80 the whole horizontal distance. 
 
 Therefore, 2O50 chains of hypothenusal or inclining 
 length will be equal to 19 chains 80 links, or 19'80 chains 
 of horizontal distance. 
 
TRAVERSE TABLES; 
 
 OR, 
 
 TABLES OF THE NORTHING OR SOUTHING, 
 
 AND 
 
 
 
 EASTING OR WESTING ; 
 
 WHEREIN THE DISTANCE IS EXTENDED TO ONE HUNDRED, 
 FOR EVERY DEGREE OP THE QUADRANT. 
 
TBAVERSE TABLES. 
 
 135 
 
 r 
 
 1 
 
 *>." 
 
 oof 
 
 S 
 
 *>J 
 
 i 
 
 *i 
 
 sj 
 
 ajf 
 
 *l 
 
 j 
 
 si 
 
 M 
 
 if 
 
 3 C 
 
 BJ 
 
 g| 
 
 si 
 
 1 C 
 
 o| 
 
 "s| 
 
 C 5C 
 si 2 
 
 t-. rj 
 
 Q *- 
 
 ;- c4 
 
 5| 
 
 I! 
 
 B| 
 
 s| 
 
 IJ 
 
 ^a 
 
 wS 
 
 3J 
 
 3 
 
 s'3 
 
 Sj 
 
 &3 
 
 wS 
 
 S5 
 
 i3 
 
 s'S 
 
 i 
 
 1-00 
 
 001 
 
 51 
 
 51-CO 
 
 045 
 
 1 
 
 1-00 
 
 0-02 
 
 51 
 
 50-99 
 
 0-89 
 
 2 
 
 2-00 
 
 0-02 
 
 52 
 
 52-00 
 
 0-45 
 
 2 
 
 2-00 
 
 0-03 
 
 52 
 
 51-99 
 
 C-91 
 
 3 
 
 3-00 
 
 0-03 
 
 53 
 
 53-00 
 
 0-43 
 
 3 
 
 3-00 
 
 0-05 
 
 53 
 
 52-99 
 
 0-92 
 
 4 
 
 4-00 
 
 0-03 
 
 54 
 
 54-00 
 
 046 
 
 4 
 
 4'00 
 
 0-07 
 
 54 
 
 53-99 
 
 094 
 
 5 
 
 5-00 
 
 0-04 
 
 55 
 
 55-00 
 
 0-48 
 
 5 
 
 5-00 
 
 0-09 
 
 53 
 
 54-99 
 
 0-96 
 
 6 
 
 6-00 
 
 005 
 
 56 
 
 56-00 
 
 0-49 
 
 6 
 
 6-00 
 
 o-io 
 
 56 
 
 55-99 
 
 098 
 
 7 
 
 7-00 
 
 0-06 
 
 57 
 
 57-00 
 
 0-50 
 
 7 
 
 700 
 
 0-12 
 
 57 
 
 5699 
 
 0-99 
 
 8 
 
 800 
 
 007 
 
 58 
 
 58-00 
 
 0-51 
 
 8 
 
 8-00 
 
 0-14 
 
 58 
 
 57-99 
 
 1-01 
 
 9 
 
 900 
 
 0-08 
 
 59 
 
 59-00 
 
 0-52 
 
 9 
 
 900 
 
 0-16 
 
 59 
 
 58-99 
 
 1-03 
 
 10 
 
 10-00 
 
 0-09 
 
 60 
 
 6000 
 
 0-52 
 
 10 
 
 10-00 
 
 0-17 
 
 60 
 
 59-99 
 
 1-05 
 
 11 
 
 11-00 
 
 0-10 
 
 61 
 
 61-00 
 
 0-53 
 
 11 
 
 11-00 
 
 0-19 
 
 61 
 
 60-99 
 
 1-07 
 
 12 
 
 12-00 
 
 0-10 
 
 62 
 
 62-00 
 
 0-54 
 
 12 
 
 12-00 
 
 021 
 
 62 
 
 61-99 
 
 1109 
 
 13 
 
 13-00 
 
 0-11 
 
 63 
 
 63-00 
 
 0-54 
 
 13 
 
 13-00 
 
 0-22 
 
 63 
 
 62-99 
 
 1-10 
 
 14 
 
 14-00 
 
 0-12 
 
 64 
 
 64-00 
 
 0-55 
 
 14 
 
 14-00 
 
 0-24 
 
 64 
 
 6399 
 
 1-12 
 
 15 
 
 15-00 
 
 013 
 
 65 
 
 65-00 
 
 0-56 
 
 15 
 
 15-00 
 
 026 
 
 65 
 
 64-93 
 
 1-14 
 
 16 
 
 16-00 
 
 0-13 
 
 66 
 
 66-00 
 
 0-57 
 
 16 
 
 1600 
 
 0-28 
 
 66 
 
 65-99 
 
 1-16 
 
 17 
 
 1700 
 
 0-14 
 
 67 
 
 67-00 
 
 0-58 
 
 17 
 
 17-00 
 
 0-29 
 
 67 
 
 6699 
 
 1-17 
 
 18 
 
 18-00 
 
 0-15 
 
 68 
 
 6S-00 
 
 059 
 
 18 
 
 18-00 
 
 0-31 
 
 68 
 
 67-99 
 
 1-19 
 
 19 
 
 19100 
 
 0-16 
 
 69 
 
 69-00 
 
 0-60 
 
 19 
 
 19-00 
 
 033 
 
 69 
 
 68-99 
 
 121 
 
 20 
 
 20-00 
 
 0-17 
 
 70 
 
 70-00 
 
 0-61 
 
 20 
 
 20-00 
 
 035 
 
 70 
 
 69-99 
 
 122 
 
 21 
 
 2100 
 
 0-18 
 
 71 
 
 71-00 
 
 0-62 
 
 21 
 
 21-00 
 
 0-37 
 
 71 
 
 70-99 
 
 1-24 
 
 22 
 
 22-00 
 
 0-18 
 
 72 
 
 72-00 
 
 0-63 
 
 22 
 
 22-00 
 
 0-38 
 
 72 
 
 7199 
 
 1-26 
 
 23 
 
 23-00 
 
 0-19 
 
 73 
 
 73-00 
 
 0-63 
 
 23 
 
 23-00 
 
 0-40 
 
 73 
 
 7299 
 
 1-28 
 
 24 
 
 2400 
 
 0-20 
 
 74 
 
 74-00 
 
 0-64 
 
 24 
 
 24-0") 
 
 0-42 
 
 74 
 
 7399 
 
 1-29 
 
 25 
 
 2500 
 
 0-21 
 
 75 
 
 75-00 
 
 0-65 
 
 25 
 
 25-00 
 
 0-44 
 
 75 
 
 74-99 
 
 1-31 
 
 26 
 
 26-00 
 
 022 
 
 76 
 
 76-00 
 
 066 
 
 26 
 
 26-00 
 
 0-45 
 
 76 
 
 75-P9 
 
 1-33 
 
 27 
 
 27-00 
 
 023 
 
 77 
 
 77-00 
 
 0-67 
 
 27 
 
 27-00 
 
 0-47 
 
 77 
 
 76-99 
 
 1-35 
 
 28 
 
 28-00 
 
 0-24 
 
 78 
 
 78-00 
 
 0-fiS 
 
 28 
 
 28-00 
 
 0-49 
 
 78 
 
 77-99 
 
 1-36 
 
 29 
 
 29-00 
 
 0-25 
 
 79 
 
 79-00 
 
 069 
 
 29 
 
 29-00 
 
 051 
 
 79 
 
 7899 
 
 1-38 
 
 30 
 
 30-00 
 
 0-26 
 
 80 
 
 80-00 
 
 0-70 
 
 30 
 
 30-00 
 
 0-52 
 
 80 
 
 7999 
 
 1-40 
 
 31 
 
 31-00 
 
 0-26 
 
 81 
 
 81-00 
 
 0-71 
 
 31 
 
 31-00 
 
 054 
 
 81 
 
 80-99 
 
 1-42 
 
 32 
 
 32-00 
 
 0-27 
 
 82 
 
 82-00 
 
 072 
 
 32 
 
 32-flO 
 
 0-56 
 
 82 
 
 81-99 
 
 1-44 
 
 33 
 
 33-00 
 
 0-28 
 
 83 
 
 83-00 
 
 0-73 
 
 33 
 
 33-00 
 
 0-58 
 
 83 
 
 82-99 
 
 1-45 
 
 3t 
 
 34-00 
 
 C-29 
 
 84 
 
 84-00 
 
 0-74 
 
 34 
 
 3399 
 
 0-60 
 
 84 
 
 83-99 
 
 147 
 
 35 
 
 35-00 
 
 030 
 
 85 
 
 85-00 
 
 0-74 
 
 35 
 
 34-99 
 
 0-61 
 
 85 
 
 84-99 
 
 1-49 
 
 36 
 
 36-00 
 
 031 
 
 86 
 
 86-00 
 
 0-75 
 
 36 
 
 3599 
 
 0-63 
 
 86 
 
 8599 
 
 1-51 
 
 37 
 
 37-00 
 
 032 
 
 87 
 
 87-00 
 
 0-76 
 
 37 
 
 36-99 
 
 065 
 
 87 
 
 86-99 
 
 1-53 
 
 38 
 
 38-00 
 
 0-33 
 
 88 
 
 83-00 
 
 0-77 
 
 38 
 
 37-99 
 
 0-67 
 
 88 
 
 87-99 
 
 1-54 
 
 39 
 
 3900 
 
 0-34 
 
 89 
 
 89-00 
 
 0-78 
 
 39 
 
 3899 
 
 0-69 
 
 89 
 
 8899 
 
 1-56 
 
 40 
 
 40-00 
 
 0-35 
 
 90 
 
 90-00 
 
 0-79 
 
 40 
 
 39-99 
 
 0-70 
 
 90 
 
 89-99 
 
 1-57 
 
 41 
 
 4100 
 
 0-36 
 
 91 
 
 91-00 
 
 0-80 
 
 41 
 
 40-99 
 
 0-72 
 
 91 
 
 90-99 
 
 1-59 
 
 42 
 
 42-f-O 
 
 036 
 
 92 
 
 9200 
 
 081 
 
 42 
 
 41-99 
 
 0-74 
 
 92 
 
 9199 
 
 1-61 
 
 43 
 
 4300 
 
 0-37 
 
 93 
 
 93-00 
 
 0-81 
 
 43 
 
 4299 
 
 076 
 
 93 
 
 92-99 
 
 1-62 
 
 44 
 
 44-00 
 
 0-38 
 
 94 
 
 94-00 
 
 0-82 
 
 44 
 
 43-99 
 
 0-78 
 
 94 
 
 9399 
 
 1-64 
 
 45 
 
 45-00 
 
 039 
 
 95 
 
 95-00 
 
 0-83 
 
 45 
 
 4499 
 
 0-79 
 
 95 
 
 9499 
 
 1-66 
 
 46 
 
 46-00 
 
 040 
 
 96 
 
 96-00 
 
 0-84 
 
 46 
 
 45-99 
 
 0-81 
 
 96 
 
 95-99 
 
 1-C8 
 
 47 
 
 47-00 
 
 0-41 
 
 97 
 
 9700 
 
 0-85 
 
 47 
 
 4609 
 
 0-83 
 
 97 
 
 .96-99 
 
 1-69 
 
 48 
 
 48-00 
 
 0-42 
 
 98 
 
 98-00 
 
 0-85 
 
 48 
 
 47-99 
 
 0-84 
 
 98 
 
 97-99 
 
 1-71 
 
 49 
 
 4900 
 
 0-43 
 
 99 
 
 99-00 
 
 0-86 
 
 49 
 
 48-99 
 
 0-S6 
 
 99 
 
 98-99 
 
 173 
 
 50 
 
 50-00 
 
 0-44 
 
 100 
 
 10000 
 
 087 
 
 50 
 
 4999 
 
 087 
 
 ICO 
 
 9999 
 
 1-75 
 
 
 E.orW 
 
 N.orS. 
 
 
 E.orW 
 
 N. or S. 
 
 
 E. or VV 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS. 
 
 89^ 
 
 89 
 
136 
 
 TRAVERSE TABLES. 
 
 2 
 
 3 
 
 'E 5o 
 
 II 
 
 l\ 
 
 E. or W. 
 
 Distance. 
 
 E &c 
 * p 
 
 j 
 
 HQ 
 
 Bearing 
 Lengths. 
 
 1 
 
 H'Q 
 
 Bearing 
 Lengths. 
 
 ll 
 
 E. or W. 
 Distance. 
 
 1 
 
 1-00 
 
 0-03 
 
 51 
 
 50-97 
 
 1-78 
 
 1 
 
 1-00 
 
 0-05 
 
 51 
 
 50-93 
 
 2-67 
 
 2 
 
 2-00 
 
 0-07 
 
 52 
 
 5197 
 
 181 
 
 2 
 
 2-00 
 
 0-1 1 
 
 52 
 
 5193 
 
 2-72 
 
 3 
 
 3-00 
 
 0-10 
 
 53 
 
 52'97 
 
 1-85 
 
 3* 
 
 S'OO 
 
 0-16 
 
 53 
 
 52-93 
 
 2-77 
 
 4 
 
 4-00 
 
 0-14 
 
 54 
 
 53-97 
 
 1-88 
 
 4 
 
 399 
 
 0-21 
 
 54 
 
 53-93 
 
 283 
 
 5 
 
 5-00 
 
 0-17 
 
 55 
 
 54-97 
 
 192 
 
 5 
 
 4-99 
 
 0-26 
 
 55 
 
 54-93 
 
 288 
 
 6 
 
 6-00 
 
 0-21 
 
 56 
 
 5597 
 
 1-95 
 
 6 
 
 5-99 
 
 0-31 
 
 56 
 
 55-92 
 
 293 
 
 7 
 
 7-00 
 
 0-24 
 
 57 
 
 5697 
 
 1-99 
 
 7 
 
 6-99 
 
 0-37 
 
 57 
 
 5692 
 
 2-98 
 
 8 
 
 800 
 
 0-28 
 
 58 
 
 57-97 
 
 2-02 
 
 8 
 
 7-99 
 
 042 
 
 58 
 
 57-92 
 
 3-04 
 
 9 
 
 8-99 
 
 031 
 
 59 
 
 58-96 
 
 206 
 
 9 
 
 8-99 
 
 047 
 
 59 
 
 58-92 
 
 3-09 
 
 10 
 
 9-99 
 
 0-35 
 
 60 
 
 59-96 
 
 209 
 
 10 
 
 9-99 
 
 0-52 
 
 60 
 
 59-92 
 
 3-14 
 
 11 
 
 10-99 
 
 0-38 
 
 61 
 
 60-96 
 
 2-13 
 
 11 
 
 10-98 
 
 0-58 
 
 61 
 
 60-92 
 
 3-19 
 
 12 
 
 1199 
 
 0-42 
 
 62 
 
 61-96 
 
 2-16 
 
 12 
 
 11 -93 
 
 063 
 
 62 
 
 61 '92 
 
 3-25 
 
 13 
 
 1299 
 
 0-45 
 
 63 
 
 62-96 
 
 2-20 
 
 13 
 
 1298 
 
 0-68 
 
 63 
 
 62-92 
 
 3-30 
 
 14 
 
 13-99 
 
 0-49 
 
 64 
 
 6396 
 
 2-23 
 
 14 
 
 13-98 
 
 0-73 
 
 64 
 
 63-91 
 
 3-35 
 
 15 
 
 14-99 
 
 0-52 
 
 65 
 
 6496 
 
 2-27 
 
 15 
 
 1493 
 
 079 
 
 65 
 
 64-91 
 
 3-4) 
 
 16 
 
 1599 
 
 056 
 
 66 
 
 65-96 
 
 2-30 
 
 16 
 
 1598 
 
 0-84 
 
 66 
 
 65-91 
 
 3-46 
 
 17 
 
 16-99 
 
 059 
 
 67 
 
 66-96 
 
 2-34 
 
 17 
 
 1698 
 
 0-89 
 
 67 
 
 66-91 
 
 3-51 
 
 18 
 
 17-99 
 
 063 
 
 68 
 
 67-96 
 
 2-37 
 
 18 
 
 1798 
 
 0-94 
 
 68 
 
 6791 
 
 3-56 
 
 19 
 
 18-99 
 
 0-66 
 
 69 
 
 68-96 
 
 2-40 
 
 19 
 
 18-97 
 
 1-00 
 
 69 
 
 6891 
 
 361 
 
 20 
 
 19-99 
 
 0-70 
 
 70 
 
 6996 
 
 3-44 
 
 20 
 
 19-97 
 
 1-05 
 
 70 
 
 6990 
 
 366 
 
 21 
 
 20-99 
 
 0-73 
 
 71 
 
 70-96 
 
 2-47 
 
 21 
 
 2097 
 
 1-10 
 
 71 
 
 70-90 
 
 372 
 
 22 
 
 21-99 
 
 0-77 
 
 72 
 
 71-96 
 
 2-51 
 
 22 
 
 2197 
 
 115 
 
 72 
 
 71-90 
 
 3-77 
 
 23 
 
 22-98 
 
 0-80 
 
 73 
 
 72-96 
 
 2-54 
 
 23 
 
 22-97 
 
 1-20 
 
 73 
 
 72-90 
 
 3-82 
 
 24 
 
 23-98 
 
 0-84 
 
 74 
 
 73-95 
 
 258 
 
 24 
 
 23-97 
 
 1-26 
 
 74 
 
 73-90 
 
 3-88 
 
 25 
 
 24-98 
 
 0-67 
 
 75 
 
 74-95 
 
 2-61 
 
 25 
 
 24-97 
 
 1-31 
 
 75 
 
 74-90 
 
 3-93 
 
 26 
 
 25-98 
 
 091 
 
 76 
 
 7595 
 
 2-65 
 
 26 
 
 25-96 
 
 1-33 
 
 76 
 
 75-90 
 
 3-98 
 
 27 
 
 26-98 
 
 0-94 
 
 77 
 
 76-95 
 
 268 
 
 27 
 
 26-96 
 
 1-42 
 
 77 
 
 76-90 
 
 404 
 
 28 
 
 27-98 
 
 0-98 
 
 78 
 
 7795 
 
 2-72 
 
 28 
 
 2796 
 
 1-47 
 
 78 
 
 77-89 
 
 4-09 
 
 29 
 
 28-98 
 
 1-01 
 
 79 
 
 78-95 
 
 2-75 
 
 29 
 
 28-96 
 
 1-52 
 
 79 
 
 78-89 
 
 4-14 
 
 30 
 
 2998 
 
 1-05 
 
 80 
 
 7993 
 
 2-79 
 
 30 
 
 2996 
 
 1-57 
 
 80 
 
 7989 
 
 4-19 
 
 31 
 
 30-98 
 
 1-08 
 
 81 
 
 80-95 
 
 2-82 
 
 31 
 
 30-96 
 
 1-62 
 
 81 
 
 80-39 
 
 4-24 
 
 32 
 
 3193 
 
 1-12 
 
 82 
 
 81-95 
 
 286 
 
 32 
 
 31-98 
 
 1-68 
 
 82 
 
 81-89 
 
 4-29 
 
 33 
 
 32-98 
 
 1-15 
 
 83 
 
 8-295 
 
 289 
 
 33 
 
 32-95 
 
 1-73 
 
 83 
 
 82-89 
 
 4-35 
 
 34 
 
 33-98 
 
 1-19 
 
 84 
 
 8395 
 
 293 
 
 34 
 
 33-95 
 
 1-78 
 
 84 
 
 83-89 
 
 4-40 
 
 35 
 
 34-98 
 
 122 
 
 85 
 
 84-95 
 
 296 
 
 35 
 
 3495 
 
 183 
 
 85 
 
 8488 
 
 4-45 
 
 36 
 
 3598 
 
 1-26 
 
 86 
 
 8595 
 
 30) 
 
 36 
 
 3595 
 
 1-88 
 
 86 
 
 8588 
 
 4-50 
 
 37 
 
 36-98 
 
 1-29 
 
 87 
 
 86-95 
 
 3-03 
 
 37 
 
 3*595 
 
 1-94 
 
 87 
 
 86-88 
 
 4-56 
 
 38 
 
 37-98 
 
 1-33 
 
 88 
 
 87-95 
 
 307 
 
 38 
 
 3795 
 
 199 
 
 88 
 
 87-88 
 
 4-61 
 
 39 
 
 3898 
 
 1-36 
 
 89 
 
 8895 
 
 310 
 
 39 
 
 38-95 
 
 2-04 
 
 89 
 
 88-88 
 
 4-65 
 
 40 
 
 39-98 
 
 1-40 
 
 90 
 
 89-95 
 
 3-14 
 
 40 
 
 3995 
 
 2-09 
 
 90 
 
 89-88 
 
 4-71 
 
 41 
 
 40-98 
 
 1-43 
 
 91 
 
 90-94 
 
 3'17 
 
 41 
 
 40-94 
 
 2-15 
 
 91 
 
 90-88 
 
 4-76 
 
 42 
 
 4198 
 
 1-47 
 
 92 
 
 91-94 
 
 3-21 
 
 42 
 
 4194 
 
 220 
 
 92 
 
 91-87 
 
 4-82 
 
 43 
 
 42-98 
 
 1-50 
 
 93 
 
 9294 
 
 3-24 
 
 43 
 
 42-94 
 
 225 
 
 93 
 
 92-87 
 
 4-87 
 
 44 
 
 4397 
 
 1-53 
 
 94 
 
 93-94 
 
 3-28 
 
 44 
 
 4394 
 
 2-30 
 
 94 
 
 93-87 
 
 4-92 
 
 45 
 
 4497 
 
 1-57 
 
 95 
 
 94-94 
 
 331 
 
 45 
 
 41-94 
 
 236 
 
 95 
 
 94-87 
 
 4-97 
 
 46 
 
 45-97 
 
 1-60 
 
 96 
 
 9594 
 
 3-35 
 
 46 
 
 45'94 
 
 2-41 
 
 96 
 
 95-87 
 
 5-02 
 
 47 
 
 46-97 
 
 1-64 * 
 
 97 
 
 96-94 
 
 338 
 
 47 
 
 4694 
 
 2-46 
 
 97 
 
 9687 
 
 5-08 
 
 48 
 
 47-97 
 
 '1-67 
 
 98 
 
 9794 
 
 342 
 
 48 
 
 47-94 
 
 2-51 
 
 98 
 
 9787 
 
 5-13 
 
 49 
 
 4897 
 
 1-71 
 
 99 
 
 9894 
 
 345 
 
 49 
 
 48-93 
 
 2-57 
 
 99 
 
 9887 
 
 5-18 
 
 50 
 
 49-97 
 
 174 
 
 100 
 
 99-94 
 
 3-49 
 
 50 
 
 4993 
 
 2-62 
 
 100 
 
 99-86 
 
 6-23 
 
 
 E. orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. N.orS. 
 
 
 E. or W. 
 
 N.orS. 
 
 88 
 
 87 
 
TRAVERSE TABLES. 
 
 137 
 
 4 
 
 5 
 
 sc - 
 
 -S 8 
 
 >8 
 
 - S 
 
 fe-4 
 
 MS 
 
 02 *' 
 
 fc* 
 
 iJD^ 
 
 . 
 
 j 
 
 1} 
 
 |g 
 
 M 
 
 11 
 
 i .S 
 
 aa 
 
 "^ a 
 
 'E S 
 
 S l 
 
 s| 
 
 If 
 
 EC 3 
 
 5 3 
 
 g| 
 
 xu3 
 
 55 Q 
 
 wS 
 
 *! 
 
 
 K"5 
 
 1,2 
 
 fc'S 
 
 WQ 
 
 3^ 
 
 fcS 
 
 KG 
 
 i 
 
 i-oo 
 
 0-07 
 
 51 
 
 50-88 
 
 3-56 
 
 i 
 
 i-oo 
 
 0-09 
 
 51 
 
 50-81 
 
 4-45 
 
 2 
 
 2-00 
 
 0-14 
 
 52 
 
 51-87 
 
 3-63 
 
 2 
 
 1-99 
 
 0-17 
 
 52 
 
 1-80 
 
 4-53 
 
 3 
 
 2-99 
 
 0-21 
 
 53 
 
 52-87 
 
 3-70 
 
 3 
 
 2-99 
 
 0-26 
 
 53 
 
 52-80 
 
 4-62 
 
 4 
 
 3-99 
 
 0-28 
 
 54 
 
 53-87 
 
 3-77 
 
 4 
 
 3-98 
 
 0-35 
 
 54 
 
 53-79 
 
 4-71 
 
 5 
 
 4-99 
 
 0-35 
 
 55 
 
 54-87 
 
 3-84 
 
 5 
 
 4-98 
 
 0-44 
 
 55 
 
 54-79 
 
 4-79 
 
 6 
 
 6-99 
 
 0-42 
 
 56 
 
 55-86 
 
 3-91 
 
 6 
 
 5-93 
 
 0-52 
 
 56 
 
 55-79 
 
 4-88 
 
 7 
 
 6-98 
 
 0-49 
 
 57 
 
 56-S6 
 
 3-98 
 
 7 
 
 6-97 
 
 0-61 
 
 57 
 
 56-78 
 
 4-97 
 
 8 
 
 7-98 
 
 0-56 
 
 58 
 
 57-86 
 
 4-05 
 
 8 
 
 7-97 
 
 0-70 
 
 58 
 
 57-78 
 
 5-06 
 
 9 
 
 8-98 
 
 0-63 
 
 69 
 
 58-86 
 
 4-12 
 
 9 
 
 8-97 
 
 0-78 
 
 59 
 
 58-78 
 
 5-14 
 
 10 
 
 9-98 
 
 0-70 
 
 60 
 
 59-85 
 
 4-19 
 
 10 
 
 9-96 
 
 0-87 
 
 60 
 
 59-77 
 
 5-23 
 
 11 
 
 10-97 
 
 0-77 
 
 61 
 
 60-85 
 
 4-26 
 
 11 
 
 10-96 
 
 0-96 
 
 61 
 
 60-77 
 
 5-32 
 
 12 
 
 11-97 
 
 0-84 
 
 62 
 
 61-85 
 
 4-32 
 
 12 
 
 11-95 
 
 1-05 
 
 Qs 61-76 
 
 5-41 
 
 13 
 
 12-97 
 
 0-91 
 
 63 
 
 62-85 
 
 4-39 
 
 13 
 
 12-95 
 
 1-13 
 
 63 
 
 62-76 
 
 5-49 
 
 14 
 
 13-97 
 
 0-98 
 
 64 
 
 63-84 
 
 4-46 
 
 14 
 
 1395 
 
 1-22 
 
 64 
 
 63-76 
 
 5-58 
 
 15 
 
 14-96 
 
 1-05 
 
 65 
 
 64-84 
 
 4-53 
 
 15 
 
 14-94 
 
 1-31 
 
 65 
 
 64-75 
 
 5-67 
 
 16 
 
 15'96 
 
 1-12 
 
 66 
 
 65-84 
 
 4-60 
 
 16 
 
 15-94 
 
 1-39 
 
 66 
 
 65-75 
 
 5-75 
 
 17 
 
 16-96 
 
 1-19 
 
 67 
 
 66-84 
 
 4-67 
 
 17 
 
 16-94 
 
 1-48 
 
 67 
 
 68-75 
 
 5-84 
 
 18 
 
 17-96 
 
 1-26 
 
 68 
 
 67-83 
 
 4-74 
 
 18 
 
 17-93 
 
 1-57 
 
 68 
 
 67-74 
 
 5-93 
 
 19 
 
 18-95 
 
 1-33 
 
 69 
 
 68-83 
 
 4-81 
 
 19 
 
 18-93 
 
 1-66 
 
 69 
 
 68-74 
 
 6-02 
 
 20 
 
 19-95 
 
 1-40 
 
 70 
 
 69-83 
 
 4-88 
 
 20 
 
 19-92 
 
 1-74 
 
 70 
 
 69-73 
 
 6-10 
 
 21 
 
 20-95 
 
 1-47 
 
 71 
 
 7 '83 
 
 4-95 
 
 21 
 
 20-92 
 
 1-83 
 
 71 
 
 70-73 
 
 6-19 
 
 22 
 
 21-95 
 
 1-54 
 
 72 
 
 71-82 
 
 5-02 
 
 22 
 
 21-92 
 
 1-92 
 
 72 
 
 71-73 
 
 6-28 
 
 23 
 
 22-94 
 
 1-61 
 
 73 
 
 72-82 
 
 5-09 
 
 23 
 
 22-91 
 
 2-00 
 
 73 
 
 72-72 
 
 6-36 
 
 24 
 
 23-94 
 
 1-68 
 
 74 
 
 73-82 
 
 5-16 
 
 24 
 
 23-91 
 
 2-09 
 
 74 
 
 73-72 
 
 6-45 
 
 25 
 
 24-94 
 
 175 
 
 75 
 
 74'82 
 
 5-23 
 
 25 
 
 24-91 
 
 2-18 
 
 75 
 
 74-72 
 
 6-54 
 
 26 
 
 25-94 
 
 1-82 
 
 76 
 
 75-81 
 
 5'3) 
 
 26 
 
 25-90 
 
 2-27 
 
 76 
 
 75-71 
 
 6-63 
 
 27 
 
 26-93 
 
 1-89 
 
 77 
 
 76-81 
 
 5-37 
 
 27 
 
 26-90 
 
 2-35 
 
 77 
 
 76-71 
 
 6-71 
 
 28 
 
 27-93 
 
 1-96 
 
 78 
 
 77-81 
 
 5-44 
 
 28 
 
 27-89 
 
 2-44 
 
 78 
 
 77-70 
 
 6-80 
 
 29 
 
 28-93 
 
 2-03 
 
 79 
 
 78-81 
 
 5-51 
 
 29 
 
 28-89 
 
 2-53 
 
 79 
 
 78-70 
 
 6-89 
 
 30 
 
 29-93 
 
 2-09 
 
 80 
 
 79-81 
 
 5-58 
 
 30 
 
 2^-89 
 
 2-61 
 
 80 
 
 79-70 
 
 6-97 
 
 31 
 
 30-92 
 
 2-16 
 
 81 
 
 80-80 
 
 5-65 
 
 31 
 
 30-83 
 
 2-70 
 
 81 
 
 80-69 
 
 7-06 
 
 32 
 
 31-92 
 
 2-23 
 
 82 
 
 81-60 
 
 5-72 
 
 32 
 
 31-88 
 
 2-79 
 
 82 
 
 81-69 
 
 7-15 
 
 33 
 
 32-92 
 
 2-30 
 
 83 
 
 82-80 
 
 5-79 
 
 33 
 
 32-88 
 
 2-88 
 
 83 
 
 82-68 
 
 7-24 
 
 34 
 
 33-92 
 
 2-37 
 
 84 
 
 83-80 
 
 5-86 
 
 34 
 
 33-87 
 
 3-96 
 
 84 
 
 83-68 
 
 7-32 
 
 35 
 
 34-91 
 
 2-44 
 
 85 
 
 84-79 
 
 5-93 
 
 35 
 
 34-87 
 
 3-05 
 
 85 
 
 84-68 
 
 7-41 
 
 36 
 
 35-91 
 
 2-51 
 
 86 
 
 65-79 
 
 6-00 
 
 36 
 
 35-86 
 
 3-14 
 
 86 
 
 85-67 
 
 7-50 
 
 37 
 
 36-91 
 
 2-58 
 
 87 
 
 86-79 
 
 6-07 
 
 37 
 
 36-86 
 
 3-22 
 
 87 
 
 86-67 
 
 7-58 
 
 38 
 
 37-91 
 
 2-65 
 
 88 
 
 87-79 
 
 6-14 
 
 38 
 
 37-83 
 
 3-31 
 
 88 
 
 87-67 
 
 7-67 
 
 39 
 
 38-90 
 
 2-72 
 
 89 
 
 88-78 
 
 6-21 
 
 39 
 
 38-85 
 
 3-40 
 
 89 
 
 88-66 
 
 7-76 
 
 40 
 
 39-90 
 
 2-79 
 
 90 
 
 89-78 
 
 -28 
 
 40 
 
 39-85 
 
 3-49 
 
 90 
 
 89-66 
 
 7-84 
 
 41 
 
 40-90 
 
 2-86 
 
 91 
 
 90-78 
 
 6-35 
 
 41 
 
 40-84 
 
 3-57 
 
 91 
 
 90-65 
 
 7-93 
 
 42 
 
 41-90 
 
 2-93 
 
 92 
 
 91-78 
 
 6-42 
 
 42 
 
 41-84 
 
 3-66 
 
 92 
 
 91-65 
 
 8-02 
 
 43 
 
 42-90 
 
 3-00 
 
 93 
 
 92-77 
 
 6-49 
 
 43 
 
 42-84 
 
 3-75 
 
 93 
 
 92-65 
 
 8-11 
 
 44 
 
 43-89 
 
 3-07 
 
 94 
 
 93-77 
 
 6-56 
 
 44 
 
 43-83 
 
 3-84 
 
 94 
 
 93-64 
 
 3-19 
 
 45 
 
 44-89 
 
 3-14 
 
 95 
 
 94-77 
 
 6-63 
 
 45 
 
 44-83 
 
 3-92 
 
 95 
 
 94-64 
 
 8-28 
 
 46 
 
 45 -S9 
 
 3-21 
 
 96 
 
 95-77 
 
 6-70 
 
 46 
 
 45-83 
 
 4-01 
 
 96 
 
 95-64 
 
 8-37 
 
 47 
 
 46-69 
 
 3-28 
 
 97 
 
 96-76 
 
 6-77 
 
 47 
 
 46-82 
 
 4-10 
 
 97 
 
 96-63 
 
 8-45 
 
 48 
 
 47-88 
 
 3-35 
 
 98 
 
 97-76 
 
 6-84 
 
 48 
 
 47-82 
 
 4-18 
 
 98 
 
 97-63 
 
 8-54 
 
 49 
 
 48-88 
 
 3-42 
 
 99 
 
 98-76 
 
 6-91 
 
 49 
 
 48-81 
 
 4-27 
 
 99 
 
 98-62 
 
 8-63 
 
 50 
 
 49-88 
 
 8-49 
 
 00 
 
 99-76 
 
 6-98 
 
 50 
 
 49-81 
 
 4-36 
 
 00 
 
 99-62 
 
 8-72 
 
 
 E.orW 
 
 N.orS. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E. or W. 
 
 N.orS. 
 
 
 E. or W. 
 
 N. or S. 
 
 86 
 
 85 
 
138 
 
 TEAVEESE TABLES. 
 
 6 
 
 7 
 
 e.3 
 
 <s 
 
 0*3 
 
 i 
 
 cl 
 
 ^s 
 
 s*i 
 
 *rjs 
 
 s| 
 
 i 
 
 *3 
 
 | 
 
 fcl 
 
 I-IP 
 
 s| 
 
 *-* _s 
 
 to 
 
 tc 
 
 4 
 
 4 
 
 11 
 
 4 
 
 B .S 
 
 JS = 
 
 n 
 
 "So 
 
 ol 
 
 a j 
 
 Q 
 
 w'S 
 
 i3 
 
 *G 
 
 HO 
 
 
 
 Q 
 
 HQ 
 
 tt^ 
 
 fc'S 
 
 KQ 
 
 l 
 
 0-99 
 
 o-io 
 
 51 
 
 50-72 
 
 5-33 
 
 i 
 
 0-99 
 
 0-12 
 
 51 
 
 50-62 
 
 6-22 
 
 2 
 
 1-99 
 
 9-21 
 
 52 
 
 51-72 
 
 5-44 
 
 2 
 
 1-99 
 
 0-24 
 
 52 
 
 51-61 
 
 6-34 
 
 3 
 
 2-98 
 
 0-31 
 
 53 
 
 52-71 
 
 5-54 
 
 3 
 
 2-98 
 
 0-37 
 
 53 
 
 52-60 
 
 6-46 
 
 4 
 
 3-98 
 
 0-42 
 
 54 
 
 53-70 
 
 5'64 
 
 4 
 
 3-97 
 
 0-49 
 
 54 
 
 53-60 
 
 6-58 
 
 5 
 
 4-97 
 
 0-52 
 
 55 
 
 54-70 
 
 5-75 
 
 5 
 
 4-96 
 
 0-61 
 
 55 
 
 54-59 
 
 6-70 
 
 6 
 
 5-97 
 
 0-63 
 
 56 
 
 55-69 
 
 5-85 
 
 6 
 
 5-96 
 
 0-73 
 
 56 
 
 55-58 
 
 6-82 
 
 7 
 
 6-96 
 
 0-73 
 
 57 
 
 56'69 
 
 5-96 
 
 7 
 
 6-94 
 
 0-85 
 
 57 
 
 56-57 
 
 6-95 
 
 8 
 
 7-96 
 
 0-84 
 
 58 
 
 57-68 
 
 6-C6 
 
 8 
 
 7-94 
 
 0-97 
 
 58 
 
 57-57 
 
 7-07 
 
 9 
 
 8-95 
 
 0-94 ' 
 
 59 
 
 58-68 
 
 6-17 
 
 9 
 
 8-93 
 
 1-10 
 
 59 
 
 58-56 
 
 7-19 
 
 10 
 
 9-95 
 
 1-05 
 
 60 
 
 59-67 
 
 6'27 
 
 10 
 
 9-93 
 
 1-22 
 
 60 
 
 59-55 
 
 7-31 
 
 11 
 
 10-94 
 
 1-15 
 
 61 
 
 60-67 
 
 6-38 
 
 11 
 
 10-92 
 
 1-34 
 
 61 
 
 60-54 
 
 7-43 
 
 12 
 
 11-93 
 
 1-25 
 
 62 
 
 61-66 
 
 6-48 
 
 12 
 
 11-91 
 
 1-46 
 
 62 
 
 61-54 
 
 7-56 
 
 13 
 
 12-93 
 
 1-36 
 
 63 
 
 62'65 
 
 6-59 
 
 13 
 
 12-90 
 
 1-58 
 
 63 
 
 62-53 
 
 7'68 
 
 14 
 
 13-92 
 
 1-46 
 
 64 
 
 63-65 
 
 6-69 
 
 14 
 
 13-90 
 
 1-71 
 
 64 
 
 63-52 
 
 7-80 
 
 15 
 
 14-92 
 
 1-57 
 
 65 
 
 64-64 
 
 6-79 
 
 15 
 
 14-69 
 
 1-83 
 
 65 
 
 64-51 
 
 7-92 
 
 16 
 
 15-91 
 
 1-67 
 
 66 
 
 65-64 
 
 6-90 
 
 16 
 
 15-88 
 
 .1-95 
 
 66 
 
 65-51 
 
 8-04 
 
 17 
 
 16-91 
 
 1-78 
 
 67 
 
 66-63 
 
 7-00 
 
 17 
 
 16-87 
 
 2-07 
 
 67 
 
 66-50 
 
 8-17 
 
 18 
 
 17-90 
 
 1-88 
 
 68 
 
 67-63 
 
 7-11 
 
 18 
 
 17-87 
 
 2-19 
 
 68 
 
 67-49 
 
 8-29 
 
 19 
 
 18-90 
 
 1-99 
 
 69 
 
 68-62 
 
 7'21 
 
 19 
 
 18-86 
 
 2-32 
 
 69 
 
 68-48 
 
 8-41 
 
 20 
 
 19-89 
 
 2-09 
 
 70 
 
 
 7-32 
 
 20 
 
 19-85 
 
 2-44 
 
 70 
 
 69-48 
 
 8-53 
 
 21 
 
 20-88 
 
 2-20 
 
 71 
 
 70'61 
 
 7-42 
 
 21 
 
 20-84 
 
 2'56 
 
 71 
 
 70-47 
 
 8'6 
 
 22 
 
 21-88 
 
 2-30 
 
 72 
 
 71-61 
 
 7-53 
 
 22 
 
 21-84 
 
 2-68 
 
 72 
 
 71-46 
 
 8-77 
 
 23 
 
 2-87 
 
 2-41 
 
 73 
 
 72-60 
 
 7-63 
 
 23 
 
 22-83 
 
 2-80 
 
 73 
 
 72-45 
 
 8-90 
 
 24 
 
 23-87 
 
 2-51 
 
 74 
 
 73-59 
 
 7-74 
 
 24 
 
 23-82 
 
 2-92 
 
 74 
 
 73-45 
 
 9-02 
 
 25 
 
 24-86 
 
 2-61 
 
 75 
 
 74-59 
 
 7-84 
 
 25 
 
 24-81 
 
 3-05 
 
 75 
 
 74-44 
 
 9-14 
 
 26 
 
 25-66 
 
 2-72 
 
 76 
 
 75-58 
 
 7-94 
 
 26 
 
 25-81 
 
 3-17 
 
 76 
 
 75-43 
 
 9-26 
 
 27 
 
 26-85 
 
 2-82 
 
 77 
 
 76-58 
 
 8-05 
 
 27 
 
 26-80 
 
 3-29 
 
 77 
 
 76-42 
 
 9-38 
 
 28 
 
 27-85 
 
 2-93 
 
 78 
 
 77-57 
 
 8-15 
 
 28 
 
 27'79 
 
 3-41 
 
 78 
 
 77-42 
 
 9-51 
 
 29 
 
 28-84 
 
 3-08 
 
 79 
 
 78-57 
 
 8'26 
 
 29 
 
 28-78 
 
 3-53 
 
 79 
 
 78-41 
 
 9-63 
 
 30 
 
 29-84 
 
 3-14 
 
 80 
 
 79-56 
 
 8-36 
 
 30 
 
 29-78 
 
 3-66 
 
 80 
 
 79-40 
 
 9-75 
 
 31 
 
 30-83 
 
 3-24 
 
 81 
 
 80-55 
 
 8'47 
 
 31 
 
 30-77 
 
 3-78 
 
 81 
 
 80-39 
 
 9-87 
 
 32 
 
 31-82 
 
 3-34 
 
 82 
 
 81-55 
 
 8-57 
 
 32 
 
 31-76 
 
 3-90 
 
 82 
 
 81-39 
 
 9-99 
 
 33 
 
 32-82 
 
 3-45 
 
 83 
 
 82-55. 
 
 8-68 
 
 33 
 
 32-75 
 
 4-02 
 
 83 
 
 82-38 
 
 10-12 
 
 34 
 
 33-81 
 
 3-55 
 
 84 
 
 83-54 
 
 8-78 
 
 34 
 
 3375 
 
 4-14 
 
 84 
 
 83-37 
 
 10-24 
 
 35 
 
 34-81 
 
 3-66 
 
 85 
 
 84-53 
 
 8-89 
 
 35 
 
 34-74 
 
 4-27 
 
 85 
 
 84-36 
 
 10-36 
 
 36 
 
 35-80 
 
 3-76 
 
 88 
 
 85-53 
 
 8-99 
 
 36 
 
 35-73 
 
 4-39 
 
 86 
 
 85-36 
 
 10-48 
 
 37 
 
 36-80 
 
 3-87 
 
 87 
 
 86-52 
 
 9-10 
 
 37 
 
 36-72 
 
 4-51 
 
 87 
 
 86-35 
 
 10-60 
 
 38 
 
 37-79 
 
 3-97 
 
 88 
 
 87-52 
 
 9-20 
 
 38 
 
 37-72 
 
 4-63 
 
 88 
 
 87-34 
 
 10-72 
 
 39 
 
 38-79 
 
 4-08 
 
 89 
 
 88-51 
 
 9-31 
 
 39 
 
 38-71 
 
 4-75 
 
 89 
 
 88-33 
 
 10-85 
 
 40 
 
 39-78 
 
 4-18 
 
 90 
 
 89-51 
 
 9-41 
 
 40 
 
 S9-70 
 
 4-87 
 
 90 
 
 89-33 
 
 10-97 
 
 41 
 
 40-77 
 
 4- 9 
 
 91 
 
 90-50 
 
 9-52 
 
 41 
 
 40-69 
 
 5-00 
 
 91 
 
 90-32 
 
 11-09 
 
 42 
 
 41-77 
 
 4-39 
 
 92 
 
 91-50 
 
 9-62 
 
 42 
 
 41-69 
 
 5-12 
 
 92 
 
 91-31 
 
 11-21 
 
 43 
 
 42-76 
 
 4-49 
 
 93 
 
 92-49 
 
 9-72 
 
 43 
 
 42-68 
 
 5-24 
 
 93 
 
 92-31 
 
 11-33 
 
 44 
 
 43-76 
 
 4-60 
 
 94 
 
 93-48 
 
 9-83 
 
 44 
 
 43-67 
 
 5-36 
 
 94 
 
 93-30 
 
 11-46 
 
 45 
 
 44-75 
 
 4-70 
 
 95 
 
 94-43 
 
 9-93 
 
 45 
 
 44-66 
 
 5-48 
 
 95 
 
 94-29 
 
 11-58 
 
 46 
 
 45-75 
 
 4-81 
 
 96 
 
 95-47 
 
 10-04 
 
 46 
 
 45-66 
 
 5-61 
 
 96 
 
 95-28 
 
 11-70 
 
 47 
 
 46-74 
 
 4-91 , 
 
 97 
 
 96-47 
 
 10-14 
 
 47 
 
 46-65 
 
 5-73 
 
 97 
 
 96-28 
 
 11-82 
 
 48 
 
 47-74 
 
 5-02 
 
 98 
 
 97-46 
 
 10-25 
 
 48 
 
 47-64 
 
 5-85 
 
 98 
 
 97-27 
 
 11-94 
 
 49 
 
 48-73 
 
 5-12 
 
 99 
 
 98-46 
 
 10-35 
 
 49 
 
 48-63 
 
 5-97 
 
 99 
 
 98-26 
 
 12-07 
 
 50 
 
 49-73 
 
 5-23 
 
 00 
 
 99-45 
 
 10-45 
 
 50 
 
 49-63 
 
 6-09 
 
 00 
 
 99-26 
 
 12-19 
 
 
 E. or W.| N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E.or W. 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 84 
 
 83 
 
TEAVEESE TABLES. 
 
 139 
 
 8 
 
 9 
 
 J 
 
 i 
 
 jj 
 
 *- 
 
 no* I 
 
 'I 
 
 6D 
 
 C "* 
 
 02 | 
 
 tel 
 
 ri 
 
 *i 
 
 l 
 
 c "S 
 
 (H OS 
 
 'r+ ^ 
 
 '3 t 
 
 - * 
 
 b 
 
 
 5-i 33 
 
 jj 
 
 P "ic 
 
 SH c3 
 
 I* o3 
 
 cs S 
 
 C ..2 
 
 ! 
 
 3 P 
 
 o -g 
 55 3 
 
 c *- 
 
 II 
 
 *!5 
 
 a5 
 
 HP 
 
 I s 
 
 *rl 
 
 a 
 
 1 
 
 0-99 
 
 0-14 
 
 51 
 
 50-50 
 
 7-10 
 
 i 
 
 0-99 
 
 0-16 
 
 51 
 
 50-37 
 
 7-98 
 
 2 
 
 1-98 
 
 0-27 
 
 52 
 
 51-49 
 
 7-24 
 
 2 
 
 1-98 
 
 0-31 
 
 52 
 
 51-36 
 
 8-13 
 
 3 
 
 2-97 
 
 0-42 
 
 53 
 
 52-48 
 
 7-38 
 
 3 
 
 2-96 
 
 0-47 
 
 53 
 
 52-35 
 
 8-29 
 
 4 
 
 3-96 
 
 0-56 
 
 54 
 
 53-47 
 
 7'52 
 
 4 
 
 3-95 
 
 0-63 
 
 54 
 
 53-34 
 
 8-45 
 
 5 
 
 4-95 
 
 0-70 
 
 55 
 
 54-46 
 
 7-65 
 
 5 
 
 4-94 
 
 0-78 
 
 55 
 
 54-32 
 
 8-60 
 
 6 
 
 5-94 
 
 0-84 
 
 56 
 
 55-46 
 
 7-79 
 
 6 
 
 5-93 
 
 0-94 
 
 56 
 
 55-31 
 
 8-76 
 
 7 
 
 6-93 
 
 0-97 
 
 57 
 
 56-45 
 
 7-93 
 
 7 
 
 6-91 
 
 1-10 
 
 57 
 
 56-30 
 
 8-92 
 
 8 
 
 7-92 
 
 1-11 
 
 58 
 
 57-44 
 
 S-07 
 
 8 
 
 7-90 
 
 1-25 
 
 58 
 
 5F-29 
 
 9-07 
 
 9 
 
 8-91 
 
 1-25 
 
 59 
 
 58-43 
 
 8-21 
 
 9 
 
 8-89 
 
 1-41 
 
 59 
 
 58-27 
 
 9-23 
 
 10 
 
 9-90 
 
 1-39 
 
 60 
 
 59-42 
 
 8-35 
 
 10 
 
 9-68 
 
 1-56 
 
 60 
 
 59"26 
 
 9-39 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 11 
 
 10-89 
 
 1-53 
 
 61 
 
 60-41 
 
 8-49 
 
 11 
 
 10-86 - 
 
 1-72 
 
 61 
 
 60-25 
 
 9-54 
 
 12 
 
 11-88 
 
 1-67 
 
 62 
 
 61-40 
 
 8-63 
 
 12 
 
 11-85 
 
 1-88 
 
 62 
 
 61-24 
 
 9-70 
 
 13 
 
 12-87 
 
 1-81 
 
 63 
 
 62-39 
 
 8-77 
 
 13 
 
 12-84 
 
 2-03 
 
 63 
 
 62-22 
 
 9-86 
 
 14 
 
 13-86 
 
 1-95 
 
 64 
 
 63-38 
 
 8-91 
 
 14 
 
 13 S3 
 
 2-19 
 
 64 
 
 63-21 
 
 10-01 
 
 15 
 
 14-85 
 
 2-09 
 
 65 
 
 64-37 
 
 9-05 
 
 15 
 
 14-82 
 
 2-35 
 
 65 
 
 64-20 
 
 10-17 
 
 16 
 
 15-84 
 
 2-23 
 
 66 
 
 65-36 
 
 9-19 
 
 16 
 
 15-80 
 
 2-50 
 
 66 
 
 65-19 
 
 10-32 
 
 17 
 
 16-83 
 
 2-37 
 
 67 
 
 66-25 
 
 9-32 
 
 17 
 
 16-79 
 
 2-66 
 
 67 
 
 66-18 
 
 10-48 
 
 18 
 
 17-82 
 
 2-51 
 
 68 
 
 67-34 
 
 9-46 
 
 18 
 
 17-78 
 
 2-82 
 
 68 
 
 67-16 
 
 10-64 
 
 19 
 
 18-82 
 
 2-64 
 
 69 
 
 68-33 
 
 9-60 
 
 19 
 
 18-77 
 
 2-97 
 
 69 
 
 68-15 
 
 10-79 
 
 20 
 
 19-81 
 
 2-78 
 
 70 
 
 69-32 
 
 9-74 
 
 20 
 
 19-75 
 
 3-13 
 
 70 
 
 69-14 
 
 10-95 
 
 21 
 
 20-80 
 
 2-92 
 
 71 
 
 70-31 
 
 9 -S3 
 
 21 
 
 20-74 
 
 3-29 
 
 71 
 
 70-13 
 
 11-11 
 
 22 
 
 21-79 
 
 3-06 
 
 72 
 
 71-30 
 
 10-02 
 
 22 
 
 21-73 
 
 3-44 
 
 72 
 
 71-11 
 
 11-26 
 
 23 
 
 22-78 
 
 3-20 
 
 73 
 
 72-29 
 
 10-16 
 
 23 
 
 22-72 
 
 3-60 
 
 73 
 
 72-10 
 
 11-42 
 
 24 
 
 23-77 
 
 3-34 
 
 74 
 
 73-28 
 
 10-30 
 
 24 
 
 23-70 
 
 3-75 
 
 74 
 
 73-09 
 
 11-58 
 
 25 
 
 24-76 
 
 3-48 
 
 75 
 
 74-27 
 
 10-44 
 
 25 
 
 24-C9 
 
 3-91 
 
 75 
 
 74-08 
 
 11-73 
 
 26 
 
 25-75 
 
 3-62 
 
 76 
 
 75-26 
 
 10-58 
 
 26 
 
 25-68 
 
 4-07 
 
 76 
 
 75-06 
 
 11-89 
 
 27 
 
 26-74 
 
 3-76 
 
 77 
 
 76-25 
 
 10-72 
 
 27 
 
 26-67 
 
 4-22 
 
 77 
 
 76-05 
 
 12-05 
 
 28 
 
 27-73 
 
 3-90 
 
 78 
 
 77-24 
 
 10-88 
 
 28 
 
 27-66 
 
 4-38 
 
 78 
 
 77-C4 
 
 12-20 
 
 '29 
 
 28-72 
 
 4-04 
 
 79 
 
 78-23 
 
 10-99 
 
 29 
 
 28-64 
 
 4-54 
 
 79 
 
 78-03 
 
 12-36 
 
 30 
 
 29-71 
 
 4-18 
 
 80 
 
 79-22 
 
 11-13 
 
 30 
 
 29-63 
 
 4-G9 
 
 80 
 
 79-02 
 
 12-52 
 
 31 
 
 30-70 
 
 4-31 
 
 81 
 
 80-21 
 
 11-27 
 
 31 
 
 30-62 
 
 4-86 
 
 81 
 
 80-00 
 
 12-67 
 
 32 
 
 31-69 
 
 4-45 
 
 82 
 
 81-20 
 
 11-41 
 
 82 
 
 31-61 
 
 5-01 
 
 82 
 
 SO'99 
 
 12-83 
 
 33 
 
 32-68 
 
 4-59 
 
 83 
 
 82-19 
 
 11-55 
 
 33 
 
 32-59 
 
 5-16 
 
 83 
 
 81-98 
 
 12-93 
 
 34 
 
 33-67 
 
 4-73 
 
 84 
 
 83-18 
 
 11-69 
 
 34 
 
 33-58 
 
 5-32 
 
 84 
 
 82-97 
 
 13-14 
 
 35 
 
 34-66 
 
 4-87 
 
 85 
 
 84-17 
 
 11-83 
 
 35 
 
 34-57 
 
 5-48 
 
 85 
 
 83-95 
 
 13-30 
 
 36 
 
 35-65 
 
 5-01 
 
 86 
 
 85-16 
 
 11-97 
 
 36 
 
 35-56 
 
 5-63 
 
 86 
 
 84-94 
 
 13-45 
 
 37 
 
 36-64 
 
 5-15 
 
 87 
 
 86-15 
 
 12-11 
 
 37 
 
 36-54 
 
 5-79 
 
 87 
 
 85-93 
 
 13-61 
 
 38 
 
 37-63 
 
 5-29 
 
 88 
 
 87-14 
 
 12-25 
 
 38 
 
 37*53 
 
 5-94 
 
 88 
 
 86-92 
 
 13-77 
 
 39 
 
 38-62 
 
 5-43 
 
 89 
 
 88-13 
 
 12-39 
 
 39 
 
 38-52 
 
 6-10 
 
 89 
 
 87-90 
 
 13-92 
 
 40 
 
 39-61 
 
 5-57 
 
 90 
 
 89-12 
 
 12-53 
 
 40 
 
 39-51 
 
 6-26 
 
 9J 
 
 88-89 
 
 14-08 
 
 41 
 
 40-60 
 
 5-71 
 
 91 
 
 90-11 
 
 12-66 
 
 41 
 
 40-50 
 
 6-41 
 
 91 
 
 89-88 
 
 14-24 
 
 42 
 
 41-59 
 
 5-85 
 
 92 
 
 91-10 
 
 12-80 
 
 42 
 
 41-48 
 
 6-57 
 
 92 
 
 90-87 
 
 14-39 
 
 43 
 
 42-58 
 
 5-98 
 
 93 
 
 92-09 
 
 12-94 
 
 43 
 
 42-47 
 
 6-73 
 
 93 
 
 91-86 
 
 14-55 
 
 44 
 
 43-57 
 
 6-12 
 
 94 
 
 93-09 
 
 13-08 
 
 44 
 
 43-46 
 
 6-88 
 
 94 
 
 92-84 
 
 14-70 
 
 45 
 
 44-56 
 
 6-27 
 
 95 
 
 94-08 
 
 13-22 
 
 45 
 
 44-45 
 
 7-04 
 
 95 
 
 93-83 
 
 14-86 
 
 46 
 
 45-55 
 
 6-40 
 
 96 
 
 95-07 
 
 13-36 
 
 46 
 
 45-43 
 
 7-20 
 
 96 
 
 94-82 
 
 15-02 
 
 47 
 
 46-54 
 
 6-54 
 
 97 
 
 96-06 
 
 13-50 
 
 47 
 
 46-42 
 
 7-35 
 
 97 
 
 95-81 
 
 15-17 
 
 48 
 
 47-53 
 
 6-68 
 
 98 
 
 97-05 
 
 13-64 
 
 48 
 
 47-41 
 
 7-51 
 
 98 
 
 96-79 
 
 15-33 
 
 49 
 
 48-52 
 
 6-82 
 
 99 
 
 98-04 
 
 13-78 
 
 49 
 
 48-40 
 
 7-C7 
 
 99 
 
 97-78 
 
 15-49 
 
 50 
 
 49-51 
 
 6-96 
 
 100 
 
 99-03 
 
 13-92 
 
 50 
 
 49-38 
 
 7-82 
 
 100 
 
 98-77 
 
 15-64 
 
 
 E.orW 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N.orS. 
 
 E. or W.j N. or S. 
 
 82 
 
 81 
 
140 
 
 TRAVERSE TABLES. 
 
 10 
 
 11 
 
 3 
 
 ill 
 
 *l 
 
 5*3 
 
 5 | 
 
 i 
 
 || 
 
 02 a 
 
 ^ 
 
 hcj 
 
 i 
 
 *i 
 
 II 
 
 o~ 
 
 s| 
 
 II? 
 
 Hj 
 
 B] 
 
 i a 
 
 sj 
 
 sl 
 
 ' ti 
 
 c3 z. 
 
 c| 
 
 ol 
 
 33 
 
 fc'S 
 
 w'5 
 
 33 
 
 55 S 
 
 Kfi 
 
 
 
 fc'5 
 
 . .= 
 
 PSQ 
 
 OJ 0; 
 
 p 
 
 KQ 
 
 1 
 
 0-99 
 
 0-17 
 
 51 
 
 50-23 
 
 8-86 
 
 i 
 
 0-98 
 
 0-19 
 
 51 
 
 50-06 
 
 9-73 
 
 2 
 
 1-97 
 
 0-35 
 
 52 
 
 51-21 
 
 9-03 
 
 2 
 
 1-96 
 
 0-38 
 
 52 
 
 51-04 
 
 9'92 
 
 3 
 
 2-95 
 
 0-52 
 
 53 
 
 52-19 
 
 9-20 
 
 3 
 
 2-94 
 
 0-57 
 
 53 
 
 52-03 
 
 10-11 
 
 4 
 
 3-94 
 
 0-70 
 
 54 
 
 53-18 
 
 9-38 
 
 4 
 
 3-93 
 
 0-76 
 
 54 
 
 53-01 
 
 10-3 ) 
 
 5 
 
 4-92 
 
 0-87 
 
 55 
 
 54-16 
 
 9-55 
 
 5 
 
 4-91 
 
 0-95 
 
 55 
 
 53-99 
 
 10-49 
 
 6 
 
 5-91 
 
 1-04 
 
 56 
 
 55-15 
 
 9-72 
 
 6 
 
 5-89 
 
 1-14 
 
 56 
 
 54-97 
 
 10-69 
 
 7 
 
 6'89 
 
 1-22 
 
 57 
 
 5*5-13 
 
 9-90 
 
 7 
 
 6-87 
 
 1-34 
 
 57 
 
 55-95 
 
 10-88 
 
 8 
 
 7-88 
 
 1-39 
 
 55 
 
 57-12 
 
 10-07 
 
 8 
 
 7-85 
 
 1-53 
 
 58 
 
 56-93 
 
 11-07 
 
 9 
 
 8-86 
 
 l-o6 
 
 59 
 
 58-10 
 
 10-25 
 
 9 
 
 8-83 
 
 1-72 
 
 59 
 
 57-92 
 
 11-26 
 
 10 
 
 9-85 
 
 1-74 
 
 60 
 
 59-09 
 
 10-42 
 
 10 
 
 9-82 
 
 1-91 
 
 60 
 
 58-90 
 
 11-45 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 11 
 
 10-83 
 
 1-91 
 
 61 
 
 60-07 
 
 10-59 
 
 11 
 
 10-80 
 
 2-10 
 
 61 
 
 59-88 
 
 11-64 
 
 12 
 
 11-82 
 
 2-08 
 
 62 
 
 61-06 
 
 10-77 
 
 12 
 
 11-78 
 
 2-29 
 
 62 
 
 60-86 
 
 11-83 
 
 13 
 
 12-80 
 
 2-26 
 
 63 
 
 62-04 
 
 10-94 
 
 13 
 
 12-76 
 
 2-48 
 
 63 
 
 61-84 
 
 12-02 
 
 14 
 
 13-79 
 
 2-43 
 
 64 
 
 63-03 
 
 11-11 
 
 14 
 
 13-74 
 
 2-67 
 
 64 
 
 62-82 
 
 12-21 
 
 15 
 
 14-77 
 
 2-60 
 
 65 
 
 64-01 
 
 11-29 
 
 15 
 
 14-72 
 
 2-86 
 
 65 
 
 63-80 
 
 12-40 
 
 16 
 
 15-76 
 
 2-78 
 
 66 
 
 65-00 
 
 11-46 
 
 16 
 
 15-71 
 
 3-05 
 
 66 
 
 64-79 
 
 12-59 
 
 17 
 
 16-74 
 
 2-95 
 
 67 
 
 65-98 
 
 11-63 
 
 17 
 
 16-69 
 
 3-24 
 
 67 
 
 65-77 
 
 12-78 
 
 18 
 
 17-73 
 
 3-12 
 
 68 
 
 66-97 
 
 11-81 
 
 18 
 
 17-67 
 
 3-43 
 
 68 
 
 66-75 
 
 12-98 
 
 19 
 
 18-71 
 
 3-30 
 
 69 
 
 67-95 
 
 11-98 
 
 19 
 
 18-65 
 
 3-63 
 
 69 
 
 67-73 
 
 13-17 
 
 20 
 
 19-70 
 
 3-47 
 
 70 
 
 68-94 
 
 12-16 
 
 20 
 
 19-63 
 
 3-82 
 
 70 
 
 68-71 
 
 13-36 
 
 21 
 
 20-68 
 
 3'65 
 
 71 
 
 69-92 
 
 12-33 
 
 21 
 
 20-61 
 
 4-01 
 
 71 
 
 69-69 
 
 13-55 
 
 22 
 
 21-67 
 
 3-82 
 
 72 
 
 70-91 
 
 12-50 
 
 22 
 
 21-60 
 
 4-20 
 
 72 
 
 70-68 
 
 13-74 
 
 23 
 
 22-65 
 
 3-99 
 
 73 
 
 71-89 
 
 12-68 
 
 23 
 
 22-58 
 
 4-39 
 
 73 
 
 71-66 
 
 13-93 
 
 24 
 
 23-64 
 
 4-17 
 
 74 
 
 72-88 
 
 12-85 
 
 24 
 
 23-56 
 
 4-58 
 
 74 
 
 72-64 
 
 14-12 
 
 25 
 
 24-62 
 
 4-34 
 
 75 
 
 73-86 
 
 13-02 
 
 25 
 
 24-54 
 
 4-77 
 
 75 
 
 73-62 
 
 14-31 
 
 26 
 
 25-60 
 
 4-51 
 
 76 
 
 74-85 
 
 1S-20 
 
 26 
 
 25-52 
 
 4-96 
 
 76 
 
 74-60 
 
 14-50 
 
 27 
 
 26-59 
 
 4-69 
 
 77 
 
 75-83 
 
 13-37 
 
 27 
 
 26-50 
 
 5-15 
 
 77 
 
 75-58 
 
 14-69 
 
 28 
 
 27-57 
 
 4-8S 
 
 78 
 
 76-82 
 
 13-54 
 
 28 
 
 27-49 
 
 5-34 
 
 78 
 
 76-57 
 
 14-88 
 
 29 
 
 28-56 
 
 5-04 
 
 79 
 
 77-80 
 
 13-7-2 
 
 29 
 
 28-47 
 
 5-53 
 
 79 
 
 77-55 
 
 15-07 
 
 30 
 
 29'54 
 
 5-21 
 
 80 
 
 78-78 
 
 13-89 
 
 30 
 
 29-45 
 
 5-72 
 
 80 
 
 78-53 
 
 15-26 
 
 31 
 
 30-53 
 
 6'38 
 
 81 
 
 79-77 
 
 14-07 
 
 31 
 
 30-43 
 
 5-92 
 
 81 
 
 79-51 
 
 15-46 
 
 32 
 
 31-51 
 
 6-56 
 
 82 
 
 80-75 
 
 14-24 
 
 32 
 
 31-41 
 
 6-11 
 
 82 
 
 80-49 
 
 15-65 
 
 33 
 
 32-50 
 
 5-73 
 
 83 
 
 81-74 
 
 14-41 
 
 33 
 
 32-39 
 
 6-30 
 
 83 
 
 81-47 
 
 15-84 
 
 34 
 
 33-48 
 
 5-90 
 
 84 
 
 82-72 
 
 14-59 
 
 34 
 
 33-37 
 
 6-49 
 
 84 
 
 82-46 
 
 16-03 
 
 35 
 
 34-47 
 
 6-08 
 
 85 
 
 83-71 
 
 14-76 
 
 35 
 
 34-36 
 
 6-68 
 
 85 
 
 83-44 
 
 16-22 
 
 36 
 
 35-45 
 
 6-25 
 
 86 
 
 84-69 
 
 14-93 
 
 36 
 
 35-34 
 
 6-87 
 
 86 
 
 84-42 
 
 16-41 
 
 37 
 
 36-44 
 
 6-43 
 
 87 
 
 85-68 
 
 15-11 
 
 37 
 
 36-32 
 
 7-06 
 
 87 
 
 85-40 
 
 16-60 
 
 38 
 
 37-42 
 
 6-60 
 
 88 
 
 86-66 
 
 15-28 
 
 38 
 
 37-30 
 
 7-25 
 
 88 
 
 86-38 
 
 16-79 
 
 39 
 
 38-41 
 
 6-77 
 
 89 
 
 87-65 
 
 15-45 
 
 39 
 
 38-28 
 
 7-44 
 
 89 
 
 87-36 
 
 16-98 
 
 40 
 
 39-39 
 
 6-95 
 
 90 
 
 88-63 
 
 15-63 
 
 40 
 
 39-26 
 
 7-63 
 
 90 
 
 88-35 
 
 17-17 
 
 41 
 
 40-38 
 
 7-12 
 
 91 
 
 89-62 
 
 15-80 
 
 41 
 
 40-25 
 
 7-82 
 
 91 
 
 89-33 
 
 17-36 
 
 42 
 
 41-36 
 
 7-29 
 
 92 
 
 90-60 
 
 15-93 
 
 42 
 
 41-23 
 
 8-01 
 
 92 
 
 90-31 
 
 17-55 
 
 43 
 
 42-35 
 
 7-47 
 
 93 
 
 91-59 
 
 16-15 
 
 43 
 
 42-21 
 
 8-20 
 
 93 
 
 91-29 
 
 17-75 
 
 44 
 
 43-33 
 
 7-64 
 
 94 
 
 92-57 
 
 16-32 
 
 44 
 
 43-19 
 
 8-40 
 
 94 
 
 9'-i-27 
 
 17-94 
 
 45 
 
 44-32 
 
 7-81 
 
 95 
 
 93-56 
 
 16-50 
 
 45 
 
 44-17 
 
 8-59 
 
 95 
 
 93-25 
 
 18-13 
 
 46 
 
 45-30 
 
 7-99 
 
 96 
 
 94-54 
 
 16-67 
 
 46 
 
 45-15 
 
 8-78 
 
 96 
 
 94-24 
 
 18-32 
 
 47 
 
 46-29 
 
 8-16 
 
 97 
 
 95-53 
 
 16-84 
 
 47 
 
 46-14 
 
 8-97 
 
 97 
 
 95"22 
 
 18-51 
 
 48 
 
 47-27 
 
 8-34 
 
 98 
 
 96-51 
 
 17-02 
 
 48 
 
 47-12 
 
 9-16 
 
 98 
 
 96-20 
 
 18-70 
 
 49 
 
 48-26 
 
 8-51 
 
 99 
 
 97-50 
 
 17-19 
 
 49 
 
 48-10 
 
 9-35 
 
 99 
 
 97-18 
 
 18-89 
 
 50 
 
 49-24 
 
 8-68 
 
 00 
 
 98-48 
 
 17-37 
 
 50 
 
 49-08 
 
 9-54 
 
 00 
 
 98-16 
 
 19-08 
 
 
 E. or W. 
 
 N.orS. 
 
 
 E.or W. 
 
 N. or S. 
 
 
 E.or W. 
 
 N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 80 
 
 79 
 
TBAVEI1SE TABLES. 
 
 141 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 i 
 
 
 
 1 
 
 2 
 
 
 
 1 
 
 
 1 
 
 3 
 
 
 
 sJ 
 
 u t 
 
 *i 
 
 t< <a 
 
 ^ a 
 o * 
 
 y>j 
 'S *i 
 
 *| 
 
 if 
 
 w>2 
 
 s -z 
 
 d 
 
 ft 
 
 ITJ 
 
 CO 
 
 *J 
 
 II 
 
 ej 
 
 ^3 
 
 y 3 
 
 s c 
 
 V O> 
 
 3 i-3 
 
 Q 
 
 a 5 
 
 2 
 
 fc3 
 
 11 
 WQ 
 
 3_5 
 
 Q 
 
 KQ 
 
 j 
 
 0-98 
 
 0-21 
 
 51 
 
 4989 
 
 10-60 
 
 1 
 
 0-97 
 
 0-22 
 
 51 
 
 4969 
 
 11-47 
 
 2 
 
 1-96 
 
 0-42 
 
 52 
 
 5086 
 
 10-81 
 
 2 
 
 1-95 
 
 0-45 
 
 62 
 
 50-67 
 
 11-70 
 
 3 
 
 2-93 
 
 0'62 
 
 53 
 
 51-84 
 
 11-02 
 
 3 
 
 2-92 
 
 0-67 
 
 53 
 
 51-64 
 
 11-92 
 
 4 
 
 3-91 
 
 0-83 
 
 54 
 
 52-82 
 
 11-23 
 
 4 
 
 3-90 
 
 0-90 
 
 54 
 
 52-62 
 
 12-15 
 
 5 
 
 4-89 
 
 1-04 
 
 55 
 
 53-80 
 
 11-44 
 
 5 
 
 4-87 
 
 1-12 
 
 55 
 
 53-59 
 
 12-37 
 
 6 
 
 5-87 
 
 1-25 
 
 56 
 
 54-78 
 
 11-64 
 
 6 
 
 5-75 
 
 1-35 
 
 56 
 
 54-57 
 
 12-60 
 
 7 
 
 6-85 
 
 1-46 
 
 57 
 
 55-75 
 
 11-85 
 
 7 
 
 6-82 
 
 157 
 
 57 
 
 55-54 
 
 12-82 
 
 8 
 
 7-83 
 
 1-66 
 
 58 
 
 56-73 
 
 12-06 
 
 8 
 
 7-79 
 
 1-80 
 
 58 
 
 56-51 
 
 13-05 
 
 9 
 
 880 
 
 1-87 
 
 59 
 
 57-71 
 
 12-27 
 
 9 
 
 8-77 
 
 2-02 
 
 59 
 
 57-49 
 
 13-27 
 
 10 
 
 978 
 
 2-08 
 
 60 
 
 58-69 
 
 12-47 
 
 10 
 
 9-74 
 
 225 
 
 60 
 
 58-46 
 
 13-50 
 
 11 
 
 10-76 
 
 2-29 
 
 61 
 
 59-67 
 
 12-68 
 
 11 
 
 10-72 
 
 2-47 
 
 61 
 
 59-44 
 
 13-72 
 
 12 
 
 lt-74 
 
 2-49 
 
 62 
 
 6065 
 
 12-89 
 
 12 
 
 11-69 
 
 2-70 
 
 62 
 
 60-41 
 
 13-95 
 
 13 
 
 12-72 
 
 2-70 
 
 63 
 
 61-62 
 
 13-10 
 
 13 
 
 12-67 
 
 2-92 
 
 63 
 
 61-39 
 
 14-17 
 
 14 
 
 13-89 
 
 2-91 
 
 64 
 
 6260 
 
 13-31 
 
 14 
 
 13-64 
 
 315 
 
 64 
 
 62-36 
 
 14-40 
 
 15 
 
 14-67 
 
 312 
 
 65 
 
 63-58 
 
 13-51 
 
 15 
 
 14-62 
 
 337 
 
 65 
 
 6333 
 
 14-62 
 
 16 
 
 15-65 
 
 3-33 
 
 66 
 
 6i-5ti 
 
 1372 
 
 16 
 
 15-59 
 
 360 
 
 66 
 
 64-31 
 
 14-85 
 
 17 
 
 10-63 
 
 353 
 
 67 
 
 6554 
 
 13-93 
 
 17 
 
 1656 
 
 3-82 
 
 67 
 
 65-28 
 
 1507 
 
 IS 
 
 1761 
 
 3-74 
 
 68 
 
 66-51 
 
 14-14 
 
 18 
 
 17-54 
 
 4-05 
 
 68 
 
 6626 
 
 15-30 
 
 19 
 
 18-58 
 
 3-95 
 
 69 
 
 67-49 
 
 14-35 
 
 19 
 
 18-51 
 
 4-27 
 
 69 
 
 67-23 
 
 1552 
 
 20 
 
 19-56 
 
 4-16 
 
 70 
 
 63-47 
 
 14-55 
 
 20 
 
 1949 
 
 450 
 
 70 
 
 68-21 
 
 15-75 
 
 21 
 
 20-54 
 
 4-37 
 
 71 
 
 69-45 
 
 14-76 
 
 21 
 
 20-46 
 
 4-72 
 
 71 
 
 69-18 
 
 15-97 
 
 22 
 
 21-52 
 
 4-57 
 
 72 
 
 70-43 
 
 1497 
 
 22 
 
 21-44 
 
 4-95 
 
 72 
 
 70'16 
 
 16-20 
 
 23 
 
 22-50 
 
 4-78 
 
 73 
 
 71-40 
 
 15-18 
 
 23 
 
 22-41 
 
 5-17 
 
 73 
 
 71-13 
 
 1642 
 
 21 
 
 23-48 
 
 4-99 
 
 74 
 
 72-38 
 
 15-39 
 
 24 
 
 23-38 
 
 5-40 
 
 74 
 
 7210 
 
 1665 
 
 25 
 
 24-45 
 
 5-20 
 
 75 
 
 73-36 
 
 15-59 
 
 25 
 
 24-36 
 
 5-62 
 
 75 
 
 73-08 
 
 1687 
 
 26 
 
 2543 
 
 5-41 
 
 76 
 
 74-34 
 
 1580 
 
 26 
 
 25-33 
 
 5-85 
 
 76 
 
 74-05 
 
 17-10 
 
 27 
 
 26-41 
 
 5-61 
 
 77 
 
 75-32 
 
 16-01 
 
 27 
 
 2631 
 
 6-07 
 
 77 
 
 75-03 
 
 17-32 
 
 28 
 
 27-39 
 
 5-82 
 
 78 
 
 76-30 
 
 16-22 
 
 28 
 
 27-28 
 
 6-30 
 
 78 
 
 76-00 
 
 17-55 
 
 29 
 
 28-37 
 
 6-03 
 
 79 
 
 77-27 
 
 16-43 
 
 29 
 
 28-26 
 
 6-52 
 
 79 
 
 76-98 
 
 17-77 
 
 30 
 
 29-34 
 
 6-24 
 
 80 
 
 78-25 
 
 1663 
 
 30 
 
 29-23 
 
 6'75 
 
 80 
 
 77-95 
 
 18-00 
 
 31 
 
 30-32 
 
 6-45 
 
 81 
 
 79-23 
 
 16-84 
 
 31 
 
 30-21 
 
 6-97 
 
 81 
 
 78-92 
 
 1822 
 
 32 
 
 31-30 
 
 6-65 
 
 82 
 
 80-21 
 
 17-05 
 
 32 
 
 31-18 
 
 7-20 
 
 82 
 
 7990 
 
 18-45 
 
 33 
 
 32-28 
 
 6-86 
 
 83 
 
 81-19 
 
 17-26 
 
 33 
 
 3215 
 
 7-42 
 
 83 
 
 80-87 
 
 18-67 
 
 34 
 
 33-26 
 
 7-07 
 
 84 
 
 82-16 
 
 17-46 
 
 34 
 
 33-13 
 
 765 
 
 84 
 
 81-85 
 
 18-90 
 
 35 
 
 34-24 
 
 728 
 
 85 
 
 83-14 
 
 17-67 
 
 35 
 
 34-10 
 
 7-87 
 
 85 
 
 82-82 
 
 1912 
 
 36 
 
 35-21 
 
 7-48 
 
 86 
 
 84-12 
 
 17-88 
 
 36 
 
 35-08 
 
 8-10 
 
 86 
 
 83-80 
 
 19-35 
 
 37 
 
 36-19 
 
 769 
 
 87 
 
 85-10 
 
 18-09 
 
 37 
 
 36-05 
 
 8-32 
 
 87 
 
 84-77 
 
 19-57 
 
 33 
 
 37-17 
 
 7-90 
 
 88 
 
 86-08 
 
 18-30 
 
 38 
 
 37-03 
 
 8-55 
 
 88 
 
 85-74 
 
 1980 
 
 39 
 
 38-15 
 
 8-11 
 
 89 
 
 87-06 
 
 18-50 
 
 39 
 
 3800 
 
 8-77 
 
 89 
 
 86-72 
 
 20-02 
 
 10 
 
 39-13 
 
 8-32 
 
 90 
 
 88-03 
 
 1871 
 
 40 
 
 3397 
 
 9-00 
 
 90 
 
 87-69 
 
 20-25 
 
 41 
 
 40-10 
 
 8-52 
 
 91 
 
 89-01 
 
 19-92 
 
 41 
 
 3995 
 
 922 
 
 91 
 
 88-67 
 
 20-47 
 
 42 
 
 4108 
 
 873 
 
 92 
 
 89-99 
 
 1913 
 
 42 
 
 40-92 
 
 9-45 
 
 92 
 
 89-64 
 
 20-70 
 
 43 
 
 42-06 
 
 8-94 
 
 93 
 
 90-97 
 
 19-34 
 
 43 
 
 41-90 
 
 9-67 
 
 93 
 
 90-62 
 
 2092 
 
 44 
 
 43-04 
 
 9-15 
 
 91 
 
 91-95 
 
 19-54 
 
 44 
 
 42-87 
 
 9-90 
 
 94 
 
 91-59 
 
 21-15 
 
 45 
 
 44-02 
 
 936 
 
 95 
 
 9292 
 
 19-75 
 
 45 
 
 43-85 
 
 10-12 
 
 95 
 
 92-57 
 
 21-37 
 
 46 
 
 4499 
 
 956 
 
 96 
 
 9390 
 
 19-96 
 
 46 
 
 4482 
 
 10-35 
 
 96 
 
 93-54 
 
 21-60 
 
 47 
 
 45-97 
 
 9-77 
 
 97 
 
 94-88 
 
 20-17 
 
 47 
 
 45-80 
 
 1057 
 
 97 
 
 9451 
 
 21-82 
 
 48 
 
 46-95 
 
 9-98 
 
 98 
 
 95-86 
 
 20-38 
 
 48 
 
 46-77 
 
 10-80 
 
 98 
 
 95-49 
 
 22-05 
 
 49 
 
 47-93 
 
 10-19 
 
 99 
 
 96-84 
 
 20-68 
 
 49 
 
 47-74 
 
 11-02 
 
 99 
 
 96-46 
 
 2227 
 
 50 
 
 48-91 
 
 10-40 
 
 100 
 
 97-81 
 
 2079 
 
 50 
 
 48-72 
 
 11-25 
 
 ICO 
 
 97-44 
 
 22-50 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 
 71 
 
 i 
 
 
 
 
 
 7' 
 
 r* 
 
 
 
142 
 
 TRAYERSE- TABLES. 
 
 14 
 
 15 
 
 irl 
 
 I 
 
 *t 
 
 el 
 
 rfl 
 
 *f 
 
 hcj 
 
 an I 
 
 ^i 
 
 *>2 
 
 o> 
 OJ 2 
 
 1 
 
 "si? 
 
 SI 
 
 !-> 8 
 
 ..S 
 
 3 c 
 
 Si 
 
 *] 
 
 Si 
 
 1 
 
 si 
 
 = 
 
 n} c 
 
 S~ 
 
 g| 
 
 3 
 
 so 
 
 WQ 
 
 33 
 
 fc5 
 
 HQ 
 
 S3 
 
 53 S 
 
 w'S 
 
 [5 
 
 fc'3 
 
 K"3 
 
 i 
 
 097 
 
 024 
 
 51 
 
 4949 
 
 1231 
 
 1 
 
 097 
 
 0-26 
 
 51 
 
 49-26 
 
 13-20 
 
 2 
 
 1-94 
 
 0-48 
 
 52 
 
 50-46 
 
 1258 
 
 2 
 
 193 
 
 0-52 
 
 52 
 
 5023 
 
 13-46 
 
 3 
 
 2-91 
 
 0-72 
 
 53 
 
 51-43 
 
 1282 
 
 3 
 
 2-90 
 
 0-78 
 
 53 
 
 51-19 
 
 13-72 
 
 4 
 
 3-88 
 
 0-97 
 
 54 
 
 5240 
 
 1306 
 
 4 
 
 8-86 
 
 1-04 
 
 54 
 
 52-16 
 
 13-98 
 
 5 
 
 4-85 
 
 1-21 
 
 55 
 
 53-37 
 
 1331 
 
 5 
 
 4-83 
 
 1-29 
 
 55 
 
 53-13 
 
 11-24 
 
 6 
 
 5-82 
 
 1-45 
 
 56 
 
 54-34 
 
 13-55 
 
 6 
 
 5-80 
 
 1-55 
 
 56 
 
 54-09 
 
 14-49 
 
 7 
 
 6-79 
 
 1-69 
 
 57 
 
 5531 
 
 13-79 
 
 7 
 
 6-76 
 
 181 
 
 57 
 
 55-06 
 
 14-75 
 
 8 
 
 7-76 
 
 1-93 
 
 58 
 
 56"28 
 
 14-03 
 
 8 
 
 7-73 
 
 2-07 
 
 58 
 
 56-02 
 
 15-01 
 
 9 
 
 8-73 
 
 218 
 
 59 
 
 57-25 
 
 14-27 
 
 9 
 
 8-69 
 
 2-33 
 
 59 
 
 56-99 
 
 15-27 
 
 10 
 
 9-70 
 
 2-42 
 
 60 
 
 58-22 
 
 1452 
 
 10 
 
 9'66 
 
 2'59 
 
 60 
 
 57-96 
 
 15-53 
 
 11 
 
 10-67 
 
 266 
 
 61 
 
 59-19 
 
 1476 
 
 11 
 
 10-63 
 
 2-85 
 
 61 
 
 58-92 
 
 1579 
 
 12 
 
 1164 
 
 290 
 
 62 
 
 60-16 
 
 15-00 
 
 12 
 
 11-59 
 
 311 
 
 62 
 
 5989 
 
 16", 5 
 
 13 
 
 12-61 
 
 3-14 
 
 63 
 
 61-13 
 
 15-24 
 
 13 
 
 12-56 
 
 336 
 
 63 
 
 60-85 
 
 16-31 
 
 14 
 
 13-58 
 
 3-39 
 
 64 
 
 62-10 
 
 15-48 
 
 14 
 
 13'5 i 
 
 3-62 
 
 64 
 
 61-82 
 
 16-56 
 
 15 
 
 14-55 
 
 3-63 
 
 65 
 
 6307 
 
 15-72 
 
 15 
 
 14-49 
 
 3-88 
 
 65 
 
 6279 
 
 16-82 
 
 16 
 
 15-52 
 
 387 
 
 
 64-04 
 
 15-97 
 
 16 
 
 15-45 
 
 4-14 
 
 66 
 
 63-75 
 
 17-08 
 
 17 
 
 16-50 
 
 411 
 
 67 
 
 65-01 
 
 16-21 
 
 17 
 
 16-42 
 
 4-40 
 
 67 
 
 64-72 
 
 17-34 
 
 18 
 
 17-47 
 
 435 
 
 63 
 
 6598 
 
 16-45 
 
 18 
 
 17-39 
 
 4-66 
 
 68 
 
 65 H8 
 
 17-60 
 
 19 
 
 18-44 
 
 4'60 
 
 69 
 
 66-95 
 
 16-B9 
 
 19 
 
 18-35 
 
 492 
 
 69 
 
 6665 
 
 17-86 
 
 20 
 
 19-41 
 
 4'84 
 
 70 
 
 67'92 
 
 16-94 
 
 20 
 
 19-32 
 
 518 
 
 70 
 
 67-61 
 
 1812 
 
 21 
 
 20-38 
 
 5-08 
 
 71 
 
 63-S9 
 
 17-18 
 
 21 
 
 20-28 
 
 5-44 
 
 71 
 
 6858 
 
 18-38 
 
 22 
 
 21-35 
 
 5-32 
 
 72 
 
 69-86 
 
 17-42 
 
 22 
 
 21-25 
 
 569 
 
 72 
 
 69-55 
 
 18-o3 
 
 23 
 
 22'32 
 
 5-56 
 
 73 
 
 70-83 
 
 17-66 
 
 23 
 
 22-22 
 
 5-95 
 
 73 
 
 70-51 
 
 18-89 
 
 24 
 
 23-29 
 
 5-81 
 
 74 
 
 7rso 
 
 17-90 
 
 24 
 
 23-18 
 
 6-21 
 
 74 
 
 71-18 
 
 19-15 
 
 25 
 
 24-26 
 
 6-05 
 
 75 
 
 72-77 
 
 18-14 
 
 25 
 
 24-15 
 
 6-47 
 
 75 
 
 72-44 
 
 19-41 
 
 26 
 
 25-23 
 
 6-29 
 
 76 
 
 73-74 
 
 18-39 
 
 26 
 
 2511 
 
 6-73 
 
 76 
 
 73-41 
 
 19-67 
 
 27 
 
 26-20 
 
 653 
 
 77 
 
 74-71 
 
 18-63 
 
 27 
 
 26-08 
 
 699 
 
 77 
 
 74-38 
 
 1993 
 
 28 
 
 27-17 
 
 6-77 
 
 78 
 
 7568 
 
 18-87 
 
 28 
 
 27-05 
 
 7-25 
 
 78 
 
 75-34 
 
 20-19 
 
 29 
 
 28-14 
 
 7-02 
 
 79 
 
 76-65 
 
 19-11 
 
 29 
 
 28-01 
 
 7-51 
 
 79 
 
 76-31 
 
 20-45 
 
 30 
 
 29-11 
 
 7-26 
 
 80 
 
 77-62 
 
 19-35 
 
 30 
 
 28-98 
 
 7-76 
 
 80 
 
 7727 
 
 20-71 
 
 31 
 
 30-08 
 
 7-50 
 
 81 
 
 78-59 
 
 19-60 
 
 31 
 
 2994 
 
 802 
 
 81 
 
 78-24 
 
 20-96 
 
 32 
 
 31-05 
 
 774 
 
 82 
 
 79-o6 
 
 1984 
 
 32 
 
 30-91 
 
 8-28 
 
 82 
 
 79-21 
 
 21-22 
 
 33 
 
 32-02 
 
 7-98 
 
 83 
 
 80-53 
 
 2008 
 
 33 
 
 31-88 
 
 8-54 
 
 83 
 
 80-17 
 
 21-48 
 
 34 
 
 32-99 
 
 8-23 
 
 84 
 
 81-50 
 
 20-32- 
 
 34 
 
 32-84 
 
 8-80 
 
 84 
 
 81-14 
 
 21-74 
 
 35 
 
 33-96 
 
 847 
 
 85 
 
 82-48 
 
 2056 
 
 85 
 
 33-81 
 
 906 
 
 85 
 
 8210 
 
 2200 
 
 36 
 
 34-93 
 
 8'71 
 
 86 
 
 8345 
 
 2081 
 
 36 
 
 3477 
 
 9-32 
 
 86 
 
 83-07 
 
 22-26 
 
 37 
 
 3590 
 
 895 
 
 87 
 
 8442 
 
 21-05 
 
 37 
 
 3574 
 
 9-58 
 
 87 
 
 84-04 
 
 22-52 
 
 38 
 
 33-87 
 
 9-19 
 
 88 
 
 8539 
 
 21-29 
 
 38 
 
 3671 
 
 984 
 
 88 
 
 851)0 
 
 22-78 
 
 39 
 
 37'84 
 
 943 
 
 89 
 
 86-36 
 
 21-53 
 
 39 
 
 3767 
 
 10-09 
 
 89 
 
 85-97 
 
 23-03 
 
 40 
 
 38'81 
 
 9-68 
 
 90 
 
 8733 
 
 21-77 
 
 49 
 
 88-64 
 
 10-35 
 
 90 
 
 8693 
 
 23-29 
 
 41 
 
 39-78 
 
 9-92 
 
 91 
 
 88-30 
 
 22-01 
 
 41 
 
 3960 
 
 10-61 
 
 91 
 
 87-90 
 
 23-55 
 
 42 
 
 40-75 
 
 1016 
 
 92 
 
 89-27 
 
 22-26 
 
 42 
 
 40-57 
 
 1087 
 
 92 
 
 88-87 
 
 23-81 
 
 43 
 
 41-72 
 
 10-40 
 
 93 
 
 90-24 
 
 22-50 
 
 43 
 
 41-53 
 
 11-13 
 
 93 
 
 89-83 
 
 24-07 
 
 44 
 
 42-69 
 
 1064 
 
 94 
 
 91-21 
 
 22-74 
 
 44 
 
 42-50 
 
 11-39 
 
 94 
 
 90-80 
 
 21-33 
 
 45 
 
 43-6 
 
 1069 
 
 95 
 
 92-18 
 
 2298 
 
 45 
 
 43-47 
 
 1165 
 
 95 
 
 91-76 
 
 24-59 
 
 48 
 
 4163 
 
 11-13 
 
 96 
 
 93-15 
 
 2122 
 
 46 
 
 4 1-43 
 
 11-91 
 
 96 
 
 92-73 
 
 2485 
 
 47 
 
 4560 
 
 11-37 
 
 97 
 
 94-12 
 
 2347 
 
 47 
 
 45-40 
 
 12-16 
 
 97 
 
 9369 
 
 25-11 
 
 43 
 
 46-57 
 
 11-61 
 
 98 
 
 95-09 
 
 23-71 
 
 48 
 
 4636 
 
 12-42 
 
 98 
 
 9466 
 
 25-36 
 
 49 
 
 47-54 
 
 11-85 
 
 99 
 
 9606 
 
 2395 
 
 49 
 
 47-33 
 
 12-68 
 
 99 
 
 95-63 
 
 2562 
 
 50 
 
 4851 
 
 12 10 
 
 100 
 
 9703 
 
 24-19 
 
 50 
 
 48-30 
 
 12-94 
 
 100 
 
 96-60 
 
 25-88 
 
 
 E. orW 
 
 N.orS. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS 
 
 76 
 
 76 
 
TBAYEESE TABLES. 
 
 143 
 
 
 
 1 
 
 3 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 g 
 
 i\ 
 
 S'l 
 
 If 
 
 ui 
 
 Si 
 
 | c | 
 
 5- C3 
 
 SI 
 
 -1 
 
 jf 
 
 Si 
 
 
 sjj 
 
 o *-* 
 
 5 
 
 c -g 
 
 o 
 
 5 c 
 
 ?! 
 
 K 
 
 5 c 
 
 1e 
 
 c ~ 
 
 'ea,3 
 
 5 
 
 wa 
 
 
 
 3 
 
 KQ 
 
 s3 
 
 
 w"5 
 
 % 
 
 Q 
 
 a-S 
 
 j 
 
 o-DT- 
 
 0-28 
 
 51 
 
 4902 
 
 14-06 
 
 1 
 
 0-96 
 
 0-29 
 
 51 
 
 48-77 
 
 14'91 
 
 2 
 
 1-92 
 
 0-55 
 
 52 
 
 4999 
 
 14-33 
 
 2 
 
 1-91 
 
 0-58 
 
 52 
 
 4973 
 
 15-20 
 
 3 
 
 2-88 
 
 0-83 
 
 53 
 
 50-95 
 
 14-61 
 
 3 
 
 2-87 
 
 o-ss 
 
 53 
 
 50-68 
 
 15-50 
 
 4 
 
 3-85 
 
 1-10 
 
 51 
 
 51-91 
 
 1488 
 
 4 
 
 3-83 
 
 1-17 
 
 54 
 
 51-64 
 
 1579 
 
 5 
 
 4-Sl 
 
 1-38 
 
 55 
 
 52-87 
 
 15-16 
 
 5 
 
 4"78 
 
 1-46 
 
 SS 
 
 52-60 
 
 16-08 
 
 6 
 
 5-77 
 
 1-65 
 
 56 
 
 53-83 
 
 15-44 
 
 6 
 
 5-74 
 
 175 
 
 56 
 
 53-55 
 
 16-37 
 
 7 
 
 6-73 
 
 1-93 
 
 57 
 
 54-79 
 
 15-71 
 
 7 
 
 6-69 
 
 2-05 
 
 57 
 
 54-51 
 
 16-67 
 
 8 
 
 7-69 
 
 2-21 
 
 58 
 
 55-75 
 
 15-99 
 
 8 
 
 7-65 
 
 2-33 
 
 58 
 
 55-47 
 
 10-90 
 
 9 
 
 865 
 
 2-48 
 
 59 
 
 56-71 
 
 16-26 
 
 9 
 
 8-61 
 
 2-63 
 
 59 
 
 5642 
 
 17-25 
 
 10 
 
 961 
 
 2-76 
 
 60 
 
 57-68 
 
 16-54 
 
 10 
 
 956 
 
 292 
 
 6) 
 
 57-38 
 
 17-54 
 
 11 
 
 10-57 
 
 3-03 
 
 61 
 
 58-64 
 
 16-81 
 
 11 
 
 10-52 
 
 3-22 
 
 61 
 
 53-33 
 
 17-83 
 
 12 
 
 11-54 
 
 3-31 
 
 62 
 
 59-60 
 
 17-09 
 
 12 
 
 11-48 
 
 3-51 
 
 62 
 
 59-29 
 
 18-13 
 
 13 
 
 12-50 
 
 3-58 
 
 63 
 
 6056 
 
 17-37 
 
 13 
 
 12-43 
 
 3-80 
 
 63 
 
 60-25 
 
 18-42 
 
 14 
 
 13-45 
 
 3-86 
 
 64 
 
 61-52 
 
 17-04 
 
 14 
 
 13-39 
 
 409 
 
 64 
 
 61-20 
 
 1871 
 
 15 
 
 14-42 
 
 413 
 
 65 
 
 62-48 
 
 17-92 
 
 15 
 
 14-34 
 
 439 
 
 65 
 
 62-16 
 
 19-00 
 
 16 
 
 15-38 
 
 4-41 
 
 66 
 
 63-44 
 
 1819 
 
 16 
 
 1530 
 
 4-68 
 
 66 
 
 6212 
 
 19-30 
 
 17 
 
 16-34 
 
 469 
 
 67 
 
 64-40 
 
 18-47 
 
 17 
 
 1626 
 
 4-97 
 
 67 
 
 64-07 
 
 1959 
 
 IS 
 
 17-30 
 
 4-96 
 
 68 
 
 6537 
 
 18-74 
 
 18 
 
 17-21 
 
 526 
 
 68 
 
 65-03 
 
 19-88 
 
 19 
 
 18-26 
 
 5-24 
 
 69 
 
 66-33 
 
 19-02 
 
 19 
 
 18-17 
 
 553 
 
 63 
 
 65-98 
 
 2017 
 
 20 
 
 19-23 
 
 5-51 
 
 70 
 
 67-29 
 
 19-29 
 
 20 
 
 1913 
 
 5-85 
 
 70 
 
 6694 
 
 2047 
 
 21 
 
 20-19 
 
 5-79 
 
 71 
 
 65-25 
 
 1957 
 
 21 
 
 20-08 
 
 6-14 
 
 71 
 
 67-90 
 
 20-76 
 
 22 
 
 21-15 
 
 6-06 
 
 72 
 
 69-21 
 
 1985 
 
 22 
 
 21-Ot 
 
 6-43 
 
 72 
 
 68-85 
 
 21-05 
 
 23 
 
 22-11 
 
 634 
 
 73 
 
 70-17 
 
 20-12 
 
 23 
 
 2199 
 
 6-72 
 
 73 
 
 69-81 
 
 21-34 
 
 24 
 
 23-07 
 
 6-62 
 
 74 
 
 71-13 
 
 20-40 
 
 24 
 
 22-95 
 
 7-02 
 
 74 
 
 70-77 
 
 21*64 
 
 25 
 
 24-03 
 
 6-89 
 
 75 
 
 72-09 
 
 20-67 
 
 25 
 
 23-91 
 
 7-31 
 
 75 
 
 7172 
 
 2193 
 
 26 
 
 2499 
 
 7-17 
 
 76 
 
 73-06 
 
 20-95 
 
 26 
 
 24-86 
 
 7-60 
 
 76 
 
 7268 
 
 22-22 
 
 27 
 
 2595 
 
 7-44 
 
 77 
 
 74-02 
 
 21-22 
 
 27 
 
 25-82 
 
 7-89 
 
 77 
 
 7364 
 
 22-51 
 
 28 
 
 26-92 
 
 7-72 
 
 78 
 
 74-98 
 
 21-50 
 
 28 
 
 26-78 
 
 8-19 
 
 78 
 
 7459 
 
 22-80 
 
 29 
 
 27-88 
 
 7-99 
 
 79 
 
 7594 
 
 21-78 
 
 29 
 
 27-73 
 
 8-48 
 
 79 
 
 75-55 
 
 23-10 
 
 30 
 
 28-84 
 
 8-27 
 
 80 
 
 76-90 
 
 22-05 
 
 30 
 
 28-69 
 
 8-77 
 
 80- 
 
 76-50 
 
 23-39 
 
 81 
 
 29-80 
 
 8-54 
 
 81 
 
 77-86 
 
 22-33 
 
 31 
 
 29-65 
 
 906 
 
 81 
 
 77-46 
 
 2368 
 
 32 
 
 30-76 
 
 8-82 
 
 82 
 
 78-82 
 
 22-60 
 
 32 
 
 30-60 
 
 9-36 
 
 82 
 
 7842 
 
 23-97 
 
 33 
 
 31-72 
 
 910 
 
 83 
 
 7978 
 
 22-88 
 
 33 
 
 31-56 
 
 9-65 
 
 83 
 
 79-37 
 
 24-27 
 
 34 
 
 32-68 
 
 9-37 
 
 84 
 
 80-75 
 
 23-15 
 
 34 
 
 3251 
 
 994 
 
 84 
 
 80-33 
 
 24-56 
 
 35 
 
 33-64 
 
 965 
 
 85 
 
 81-71 
 
 23-43 
 
 35 
 
 3.3-47 
 
 10-23 
 
 85 
 
 81-29 
 
 24-85 
 
 36 
 
 34-61 
 
 992 
 
 86 
 
 82-67 
 
 2370 
 
 36 
 
 34-43 
 
 10-53 
 
 80 
 
 82-24 
 
 25-14 
 
 37 
 
 35-57 
 
 1020 
 
 87 
 
 83-63 
 
 2398 
 
 37 
 
 35-38 
 
 10-82 
 
 87 
 
 8320 
 
 25-44 
 
 38 
 
 36-53 
 
 10-47 
 
 88 
 
 84-59 
 
 24-26 
 
 38 
 
 36-34 
 
 11-11 
 
 83 
 
 84-15 
 
 2573 
 
 39 
 
 37-49 
 
 10-75 
 
 89 
 
 85-55 
 
 24-53 
 
 39 
 
 37-30 
 
 11-40 
 
 89 
 
 8511 
 
 26-02 
 
 40 
 
 38-45 
 
 11-03 
 
 90 
 
 86-51 
 
 24-81 
 
 40 
 
 33-25 
 
 11-69 
 
 90 
 
 88-07 
 
 26-31 
 
 41 
 
 39-41 
 
 11-30 
 
 91 
 
 87-47 
 
 25-08 
 
 41 
 
 3921 
 
 11-99 
 
 91 
 
 87-02 
 
 26-61 
 
 42 
 
 40-37 
 
 1158 
 
 92 
 
 88-44 
 
 25-36 
 
 42 
 
 40-16 
 
 1228 
 
 92 
 
 87-98 
 
 26-90 
 
 43 
 
 4133 
 
 11 '&> 
 
 93 
 
 89-40 
 
 25-63 
 
 43 
 
 41-12 
 
 1257 
 
 93 
 
 8894 
 
 27-19 
 
 44 
 
 42-30 
 
 12-13 
 
 9t 
 
 90-36 
 
 25-91 
 
 44 
 
 4208 
 
 12-83 
 
 94 
 
 89-89 
 
 2748 
 
 45 
 
 4326 
 
 1240 
 
 95 
 
 91-32 
 
 26-19 
 
 45 
 
 43-03 
 
 13-16 
 
 90 
 
 90-85 
 
 27-78 
 
 46 
 
 44-22 
 
 12 GS 
 
 96 
 
 9228 
 
 26-46 
 
 46 
 
 43-99 
 
 13-45 
 
 o; 
 
 91-81 
 
 28-07 
 
 47 
 
 45-18 
 
 12-95 
 
 97 
 
 93-24 
 
 26-74 
 
 47 
 
 4495 
 
 1374 
 
 97 
 
 92-76 
 
 28-36 
 
 48 
 
 46-14 
 
 1323 
 
 98 
 
 94-20 
 
 27-01 
 
 48 
 
 45-90 
 
 1403 
 
 98 
 
 93-72 
 
 28-65 
 
 49 
 
 47-10 
 
 13-51 
 
 99 
 
 95-K3 
 
 27-29 
 
 49 
 
 4686 
 
 14-33 
 
 99 
 
 9467 
 
 28-94 
 
 50 
 
 48-06 
 
 13-78 
 
 100 
 
 93-13 
 
 2756 
 
 50 
 
 47-82 
 
 1462 
 
 100 
 
 95-63 
 
 29-24 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N.orS. 
 
 
 E. or W. 
 
 N.orS. 
 
 
 
 7 
 
 r 
 
 
 
 
 
 7 
 
 3 
 
 
 1 
 
144 
 
 TEAVEBSE TABLES. 
 
 18 
 
 19 
 
 9 
 
 S 
 
 1 
 
 %z 
 
 tn 
 
 | 
 
 J 
 
 on I 
 
 8 
 
 S 
 
 00 I 
 
 3 
 
 II 
 
 of 
 
 1 
 
 3 a 
 
 S .l 
 
 sj 
 
 Iti 
 
 aj C 
 
 *j 
 
 t-f 00 
 
 11 
 
 J 
 
 ?! 
 
 ttJ 
 
 fc'S 
 
 WQ 
 
 OtS 
 
 53Q 
 
 HP 
 
 MJ 
 
 fc'S 
 
 WQ 
 
 33 
 
 
 w"3 
 
 j 
 
 095 
 
 031 
 
 51 
 
 4850 
 
 15-76 
 
 1 
 
 0-95 
 
 0-33 
 
 51 
 
 48-22 
 
 16-60 . 
 
 2 
 
 1-90 
 
 0-62 
 
 52 
 
 49-45 
 
 16-07 
 
 2 
 
 1-89 
 
 0-65 
 
 52 
 
 49-17 
 
 16-93 ' 
 
 3 
 
 2-85 
 
 0-93 
 
 53 
 
 50-41 
 
 16-38 
 
 3 
 
 2-84 
 
 0-98 
 
 53 
 
 50-11 
 
 17-26 
 
 4 
 
 3-80 
 
 1-24 
 
 54 
 
 51-36 
 
 16-69 
 
 4 
 
 378 
 
 1-30 
 
 54 
 
 51-06 
 
 17-58 
 
 5 
 
 4-76 
 
 1-55 
 
 55 
 
 52-31 
 
 1700 
 
 5 
 
 4-73 
 
 163 
 
 55 
 
 52-00 
 
 17-91 
 
 6 
 
 5-71 
 
 1-85 
 
 56 
 
 53-26 
 
 17-30 
 
 6 
 
 5-67 
 
 195 
 
 56 
 
 52-95 
 
 18-23 
 
 7 
 
 6-66 
 
 2-16 
 
 57 
 
 54-21 
 
 17-61 
 
 7 
 
 6-62 
 
 2-28 
 
 57 
 
 53-89 
 
 18-56 
 
 8 
 
 7-61 
 
 2-47 
 
 58 
 
 55-16 
 
 17-92 
 
 8 
 
 7-56 
 
 2-60 
 
 58 
 
 54-84 
 
 18-88 
 
 9 
 
 8-56 
 
 278 
 
 59 
 
 56-11 
 
 18-23 
 
 9 
 
 8-51 
 
 293 
 
 59 
 
 55-79 
 
 19-21 
 
 10 
 
 9-51 
 
 3-09 
 
 60 
 
 57-06 
 
 1854 
 
 10 
 
 9-46 
 
 3-26 
 
 60 
 
 56-73 
 
 19-53 
 
 11 
 
 10-46 
 
 3-40 
 
 61 
 
 58-01 
 
 1883 
 
 11 
 
 10-40 
 
 3-58 
 
 61 
 
 57-68 
 
 19-86 
 
 12 
 
 11-41 
 
 371 
 
 62 
 
 5897 
 
 19-16 
 
 12 
 
 11-35 
 
 3-91 
 
 62 
 
 58-62 
 
 20-19 
 
 13 
 
 12-36 
 
 4-02 
 
 63 
 
 59-92 
 
 19-47 
 
 13 
 
 12-29 
 
 423 
 
 63 
 
 5957 
 
 20-51 
 
 14 
 
 13-31 
 
 4-33 
 
 64 
 
 60-87 
 
 19-78 
 
 14 
 
 13-24 
 
 4-56 
 
 64 
 
 60-51 
 
 20-84 
 
 15 
 
 14-27 
 
 4-64 
 
 65 
 
 61-82 
 
 20-09 
 
 15 
 
 14-18 
 
 4-88 
 
 65 
 
 61-46 
 
 21-16 
 
 16 
 
 15-22 
 
 494 
 
 66 
 
 62-77 
 
 20-40 
 
 16 
 
 15-13 
 
 5-21 
 
 66 
 
 62-40 
 
 21-49 
 
 17 
 
 16-17 
 
 525 
 
 67 
 
 6372 
 
 20-70 
 
 17 
 
 1607 
 
 553 
 
 67 
 
 63-35 
 
 21-81 
 
 18 
 
 17-12 
 
 5-56 
 
 68 
 
 6467 
 
 21-01 
 
 18 
 
 17-02 
 
 5-86 
 
 68 
 
 64-30 
 
 22-14 
 
 19 
 
 18-07 
 
 5-87 
 
 69 
 
 65-62 
 
 21-32 
 
 19 
 
 17-96 
 
 6-19 
 
 69 
 
 6524 
 
 22-46 
 
 20 
 
 1902 
 
 6-18 
 
 70 
 
 66-57 
 
 21-63 
 
 20 
 
 18-91 
 
 6-51 
 
 70 
 
 66-19 
 
 2279 
 
 21 
 
 19-97 
 
 6-49 
 
 71 
 
 67-53 
 
 21-94 
 
 21 
 
 19-86 
 
 6-84 
 
 71 
 
 67-13 
 
 23-12 
 
 22 
 
 20-92 
 
 6-80 
 
 72 
 
 68-48 
 
 22-25 
 
 22 
 
 20-80 
 
 716 
 
 72 
 
 68-08 
 
 23-44 
 
 23 
 
 21-87 
 
 7-11 
 
 73 
 
 6943 
 
 22-56 
 
 23 
 
 21-75 
 
 7-49 
 
 73 
 
 69-02 
 
 23-77 
 
 24 
 
 22-83 
 
 7-42 
 
 74 
 
 70-38 
 
 22-87 
 
 24 
 
 22-69 
 
 7-81 
 
 74 
 
 69-97 
 
 24-09 
 
 25 
 
 23-78 
 
 7-73 
 
 75 
 
 71-33 
 
 23-18 
 
 25 
 
 23-64 
 
 8-14 
 
 75 
 
 70-91 
 
 24-42 
 
 26 
 
 24-73 
 
 8-03 
 
 76 
 
 72-28 
 
 23-49 
 
 26 
 
 24-58 
 
 8-46 
 
 76 
 
 71-86 
 
 24-74 
 
 27 
 
 25-68 
 
 8-34 
 
 77 
 
 73-23 
 
 23-79 
 
 27 
 
 25-53 
 
 8-79 
 
 77 
 
 72-81 
 
 25-07 
 
 28 
 
 26-63 
 
 8-65 
 
 78 
 
 74-18 
 
 24-10 
 
 28 
 
 26-47 
 
 9-12 
 
 78 
 
 73-75 
 
 25-39 
 
 29 
 
 2758 
 
 896 
 
 79 
 
 75-13 
 
 24-41 
 
 29 
 
 27-42 
 
 9-44 
 
 79 
 
 74-70 
 
 25-72 
 
 30 
 
 28-53 
 
 9-27 
 
 80 
 
 76-08 
 
 24-72 
 
 30 
 
 28-37 
 
 9-77 
 
 80 
 
 75-64 
 
 26-C5 
 
 31 
 
 29-48 
 
 9-58 
 
 81 
 
 77-04 
 
 25-03 
 
 31 
 
 29-31 
 
 1009 
 
 81 
 
 76-59 
 
 26-37 
 
 32 
 
 30-43 
 
 9-89 
 
 82 
 
 77-99 
 
 2534 
 
 32 
 
 30-26 
 
 10-42 
 
 82 
 
 77-53 
 
 26-70 
 
 33 
 
 31-38 
 
 10-20 
 
 83 
 
 78-94 
 
 2565 
 
 33 
 
 31-20 
 
 10-74 
 
 83 
 
 78-48 
 
 27-02 
 
 34 
 
 32-34 
 
 10-51 
 
 84 
 
 79-89 
 
 2596 
 
 34 
 
 32-15 
 
 11-07 
 
 84 
 
 79-42 
 
 27-35 
 
 35 
 
 33-29 
 
 10-82 
 
 85 
 
 80-84 
 
 2627 
 
 35 
 
 33-09 
 
 11-39 
 
 85 
 
 80-37 
 
 27-67 
 
 36 
 
 34-24 
 
 11-12 
 
 86 
 
 81-79 
 
 2658 
 
 36 
 
 3404 
 
 11-72 
 
 86 
 
 81-31 
 
 28-00 
 
 37 
 
 35-19 
 
 11-43 
 
 87 
 
 82-74 
 
 26-88 
 
 37 
 
 34-98 
 
 12-05 
 
 87 
 
 82-26 
 
 28-32 
 
 38 
 
 36-14 
 
 11-74 
 
 88 
 
 8369 
 
 27-19 
 
 38 
 
 3593 
 
 12-37 
 
 88 
 
 83-21 
 
 28-65 
 
 39 
 
 37-09 
 
 1205 
 
 89 
 
 84-64 
 
 27-50 
 
 39 
 
 3687 
 
 12-70 
 
 89 
 
 84-15 
 
 28-98 
 
 40 
 
 3804 
 
 12-36 
 
 90 
 
 85-60 
 
 27-81 
 
 40 
 
 37-82 
 
 13-02 
 
 90 
 
 85-10 
 
 29-30 
 
 41 
 
 3899 
 
 12-67 
 
 91 
 
 86-55 
 
 2812 
 
 41 
 
 38-77 
 
 13-35 
 
 91 
 
 86-04 
 
 29-63 
 
 42 
 
 39-94 
 
 1298 
 
 92 
 
 87-50 
 
 28-43 
 
 42 
 
 39-71 
 
 1367 
 
 92 
 
 8699 
 
 29-95 
 
 43 
 
 40-90 
 
 13-29 
 
 93 
 
 88-45 
 
 28-74 
 
 43 
 
 40-66 
 
 14-00 
 
 93 
 
 87-93 
 
 30-28 
 
 44 
 
 41-85 
 
 1360 
 
 94 
 
 89-40 
 
 29-05 
 
 44 
 
 41-60 
 
 14-32 
 
 94 
 
 88-88 
 
 30-60 
 
 45 
 
 42-80 
 
 1391 
 
 95 
 
 90-35 
 
 29-36 
 
 45 
 
 42-55 
 
 1465 
 
 95 
 
 89-82 
 
 30-93 
 
 46 
 
 4375 
 
 1421 
 
 96 
 
 91-30 
 
 2967 
 
 46 
 
 43-49 
 
 14-98 
 
 96 
 
 90-77 
 
 31-25 
 
 47 
 
 4470 
 
 14-52 
 
 97 
 
 92-25 
 
 29-97 
 
 47 
 
 44-44 
 
 1530 
 
 97 
 
 91-72 
 
 31-58 
 
 48 
 
 45-65 
 
 14-83 
 
 98 
 
 93-20 
 
 30-28 
 
 48 
 
 4538 
 
 15-63 
 
 98 
 
 92-66 
 
 31-91 
 
 49 
 
 46-60 
 
 15-14 
 
 99 
 
 94-15 
 
 30-59 
 
 49 
 
 46-33 
 
 15-95 
 
 99 
 
 9361 
 
 32-23 
 
 50 
 
 47-55 
 
 1545 
 
 100 
 
 95-11 
 
 30-90 
 
 50 
 
 47-28 
 
 16-28 
 
 100 
 
 9455 
 
 32-56 
 
 
 E. orW. 
 
 N. orS. 
 
 
 E.orW. 
 
 N. orS. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E. or W. 
 
 N.orS. 
 
 72 
 
 71 
 
 1 
 
TliAVEKSE TABLES. 
 
 145 
 
 20 
 
 21 
 
 >* 
 
 ril 
 
 *1 
 
 sa 
 
 | 
 
 | 
 
 go 
 
 *i 
 
 i 
 
 g>! 
 
 ! 
 
 $i 
 
 E "tc s- 5 
 
 II sM 
 
 A 
 
 5 So 
 
 ci 8 
 
 <a j 
 
 30 
 
 ril 
 
 3 s 
 
 *l 
 
 cdS 
 
 1! 
 
 J 
 
 o| 
 HQ 
 
 i 
 
 0-94 
 
 0-.34 
 
 51 
 
 47'92 
 
 17-44 
 
 1 
 
 0-93 
 
 0-36 
 
 51 
 
 47-61 
 
 18-28 
 
 2 
 
 1-88 
 
 0-68 
 
 52 
 
 48-86 
 
 17-79 
 
 2 
 
 1-87 
 
 0-72 
 
 52 
 
 48-55 
 
 18-63 
 
 3 
 
 2-82 
 
 1'03 
 
 53 
 
 49-80 
 
 18-13 
 
 3 
 
 2-80 
 
 1-08 
 
 53 
 
 49-48 
 
 18-99 
 
 4 3-76 
 
 1-37 
 
 54 
 
 50-74 
 
 18-47 
 
 4 
 
 3-73 
 
 1-43 
 
 54 
 
 50-41 
 
 19-35 
 
 5 
 
 4-70 
 
 1'71 
 
 55 
 
 51-68 
 
 18-81 
 
 5 
 
 4-67 
 
 1-79 
 
 55 
 
 51-35 
 
 19-71 
 
 6 
 
 5-64 
 
 2-05 
 
 56 
 
 52-62 
 
 19-15 
 
 6 
 
 5-60 
 
 2-15 
 
 56 
 
 52-08 
 
 20-07 
 
 7 
 
 6'58 
 
 2-39 
 
 57 
 
 53-56 
 
 19-50 
 
 7 
 
 6-54 
 
 2-51 
 
 57 
 
 53-21 
 
 20-43 
 
 8 
 
 7-52 
 
 2-74 
 
 58 
 
 54-50 
 
 19-84 
 
 8 
 
 7-47 
 
 2-87 
 
 58 
 
 54-15 
 
 20-78 
 
 9 
 
 8-46 
 
 3-08 
 
 59 
 
 55-44 
 
 20-18 
 
 9 
 
 8-40 
 
 3-23 
 
 59 
 
 55-08 
 
 21-14 
 
 10 
 
 9-40 
 
 3-42 
 
 60 
 
 56-38 
 
 20-52 
 
 10 
 
 9-34 
 
 3-58 
 
 60 
 
 56-01 
 
 21-50 
 
 11. 
 
 10-34 
 
 3'76 
 
 61 
 
 57-32 
 
 20-86 
 
 11 
 
 10-27 
 
 3-94 
 
 61 
 
 56-95 
 
 21-86 
 
 12 
 
 11-28 
 
 4-10 
 
 62 
 
 58-26 
 
 21-21 
 
 12 
 
 11-20 
 
 4-30 
 
 62 
 
 57-88 
 
 22-22 
 
 13 
 
 12-22 
 
 4-45 
 
 63 
 
 59-20 
 
 21-55 
 
 13 
 
 12-14 
 
 4-66 
 
 63 
 
 58-82 
 
 22-58 
 
 14 
 
 13-16 
 
 4-79 
 
 64 
 
 60-14 
 
 21-89 
 
 14 
 
 13'07 
 
 5-02 
 
 64 
 
 59-75 
 
 22-93 
 
 15 
 
 14-10 
 
 5'13 
 
 65 
 
 61-08 
 
 22-23 
 
 15 
 
 14-00 
 
 5-38 
 
 65 
 
 60-68 
 
 23-29 
 
 16 
 
 15'04 
 
 5-47 
 
 66 
 
 62-02 
 
 22-57 
 
 16 
 
 14-94 
 
 5-73 
 
 66 
 
 61-62 
 
 23-65 
 
 17 
 
 15'97 
 
 5'81 
 
 67 
 
 62-96 
 
 22-92 
 
 17 
 
 15-87 
 
 6-09 
 
 67 
 
 62-55 
 
 24-01 
 
 18 
 
 16-91 
 
 6-16 
 
 68 
 
 63-90 
 
 23-26 
 
 18 
 
 16-80 
 
 6-45 
 
 68 
 
 63-48 
 
 24-37 
 
 19 
 
 17'85 
 
 6-50 
 
 69 
 
 64-84 
 
 23-60 
 
 19 
 
 17-74 
 
 6-81 
 
 69 
 
 64-42 
 
 24-73 
 
 20 
 
 18-79 
 
 6-84 
 
 70 
 
 65-78 
 
 23-94 
 
 20 
 
 18-67 
 
 7-17 
 
 70 
 
 65-35 
 
 25-08 
 
 21 
 
 19-73 
 
 7-18 
 
 71 
 
 66-72 
 
 24-28 
 
 21 
 
 19-61 
 
 7-53 
 
 71 
 
 66-28 
 
 25-44 
 
 22 
 
 20-67 
 
 7'52 
 
 72 
 
 67-66 
 
 24-63 
 
 22 
 
 20-54 
 
 7-83 
 
 72 
 
 67-22 
 
 25-80 
 
 23 
 
 21-61 
 
 7-87 
 
 73 
 
 68-60 
 
 24-97 
 
 23 
 
 21-47 
 
 8-24 
 
 73 
 
 68-15 
 
 26-16 
 
 24 
 
 22-55 
 
 8-21 
 
 74 
 
 69-54 
 
 25-31 
 
 24 
 
 22-41 
 
 8-60 
 
 74 
 
 69-09 
 
 26-52 
 
 25 
 
 23-49 
 
 S'55 
 
 75 
 
 70-48 
 
 25-65 
 
 25 
 
 23-34 
 
 8-96 
 
 75 
 
 70-02 
 
 26-88 
 
 26 
 
 24-43 
 
 8-89 
 
 76 
 
 71-42 
 
 25-99 
 
 26 
 
 24-27 
 
 9-32 
 
 76 
 
 70-95 
 
 27-23 
 
 27 
 
 25-37 
 
 9-28 
 
 77 
 
 72-36 
 
 26-34 
 
 27 
 
 25-21 
 
 9-68 
 
 77 
 
 71-89 
 
 27-59 
 
 28 
 
 26-31 
 
 9-58 
 
 78 
 
 73-30 
 
 26-68 
 
 28 
 
 26-14 
 
 10-03 
 
 78 
 
 72-82 
 
 27-95 
 
 29 
 
 27-25 
 
 9-92 
 
 79 
 
 74-24 
 
 27-02 
 
 29 
 
 27-07 
 
 10-39 
 
 79 
 
 73-75 
 
 28-31 
 
 30 
 
 28-19 
 
 10-26 
 
 80 
 
 75-18 
 
 27-36 
 
 30 
 
 28-01 
 
 10-75 
 
 80 
 
 74-68 
 
 28-67 
 
 31 
 
 29-13 
 
 10-60 
 
 81 
 
 76-12 
 
 27-70 
 
 31 
 
 28-94 
 
 11-11 
 
 81 
 
 75-62 
 
 29-03 
 
 32 
 
 30-07 
 
 10-94 
 
 82 
 
 77-06 
 
 28-05 
 
 32 
 
 29-87 
 
 11-47 
 
 82 
 
 76-55 
 
 29-39 
 
 33 
 
 31-01 
 
 11-29 
 
 83 
 
 77-99 
 
 28-39 
 
 33 
 
 30-81 
 
 11-83 
 
 83 
 
 77-49 
 
 29-74 
 
 34 
 
 31-95 
 
 11-63 
 
 84 
 
 78-93 
 
 28-73 
 
 34 
 
 31-74 
 
 12-18 
 
 84 
 
 78-42 
 
 30-10 
 
 35 
 
 32-89 
 
 11-97 
 
 85 
 
 79-87 
 
 29-07 
 
 35 
 
 32-68 
 
 12-54 
 
 85 
 
 79-35 
 
 30-46 
 
 36 
 
 33-83 
 
 12-31 
 
 86 
 
 80-81 
 
 29-41 
 
 36 
 
 33-61 
 
 12-90 
 
 86 
 
 80-29 
 
 30-82 
 
 37 
 
 34-77 
 
 12-65 
 
 87 
 
 81-75 
 
 29-76 
 
 37 
 
 34-54 
 
 13-26 
 
 87 
 
 81-22 
 
 31-18 
 
 38 
 
 35-71 
 
 13-00 
 
 88 
 
 82-69 
 
 30-10 
 
 38 
 
 35-48 
 
 13-62 
 
 88 
 
 82-16 
 
 31-54 
 
 39 
 
 36-65 
 
 13-34 
 
 89 
 
 83-63 
 
 30-44 
 
 39 
 
 36-41 
 
 13-98 
 
 89 
 
 83-09 
 
 31-89 
 
 40 
 
 37-59 
 
 13-68 
 
 90 
 
 84-57 
 
 30-78 
 
 40 
 
 37-34 
 
 14-33 
 
 90 
 
 84-02 
 
 32-25 
 
 41 
 
 38-53 
 
 14-02 
 
 91 
 
 85-51 
 
 31-12 
 
 41 
 
 38-28 
 
 14-69 
 
 91 
 
 84-96 
 
 32-61 
 
 42 
 
 39-47 
 
 14-36 
 
 92 
 
 86-45 
 
 31-47 
 
 42 
 
 39-21 
 
 15-05 
 
 92 
 
 85-89 
 
 82-97 
 
 43 
 
 40-41 
 
 14-71 
 
 93 
 
 87-39 
 
 31-81 
 
 43 
 
 40-14 
 
 15-41 
 
 93 
 
 86-82 
 
 33-33 
 
 44 
 
 41-35 
 
 15-05 
 
 94 
 
 88-33 
 
 32-15 
 
 44 
 
 41-03 
 
 15-77 
 
 94 
 
 87-76 
 
 33-69 
 
 45 
 
 42-29 
 
 15-39 
 
 95 
 
 89-27 
 
 32-49 
 
 45 
 
 42-01 
 
 16-13 
 
 95 
 
 88-69 
 
 34-04 
 
 46 
 
 43-23 
 
 15-73 
 
 96 
 
 90-21 
 
 32-83 
 
 46 
 
 42-94 
 
 16-48 
 
 96 
 
 89-62 
 
 34-40 
 
 47 
 
 44-17 
 
 16-07 
 
 97 
 
 91-15 
 
 33-18 
 
 47 
 
 43-88 
 
 16-84 
 
 97 
 
 90-56 
 
 34-76 
 
 48 
 
 45-11 
 
 16-42 
 
 98 
 
 92-09 
 
 33-52 
 
 48 
 
 4f8t 
 
 17-20 
 
 98 
 
 91-49 
 
 35-12 
 
 49 
 
 46-04 
 
 16-76 
 
 99 
 
 93-03 
 
 33-86 
 
 49 
 
 45-75 
 
 17-56 
 
 99 
 
 92-42 
 
 35-48 
 
 50 
 
 46-98 
 
 17-10 
 
 100 
 
 93-97 
 
 34-20 
 
 50 
 
 46-68 
 
 17-92 
 
 100 
 
 93-36 
 
 35-84 
 
 
 E.orW 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 70 
 
 69 
 
146 
 
 TEAVEESE TABLES. 
 
 22 
 
 23 
 
 M 
 
 J 
 
 ft 
 
 g 
 
 5l 
 
 ft 
 
 | 
 
 i 
 
 i 
 
 _d 
 
 02 
 
 $4 
 
 'if 
 
 g-| 
 
 o| 
 
 II 
 
 t! 
 
 o| 
 
 Stb 
 Ja 
 
 o-g 
 
 o-" 
 
 Etao 
 
 
 r~ jf 
 
 33 
 
 JziS 
 
 wS 
 
 O> 03 
 
 &Q 
 
 a S 
 
 | 
 
 
 wo 
 
 II 
 
 fci 
 
 HQ 
 
 i 
 
 0-93 
 
 0-37 
 
 61 
 
 47-29 
 
 19-10 
 
 1 
 
 0*92 
 
 0-39 
 
 51 
 
 46*95 
 
 19'93 
 
 2 
 
 1-85 
 
 0-75 
 
 52 
 
 48-21 
 
 19*48 
 
 2 
 
 1-84 
 
 0-78 
 
 52 
 
 47*87 
 
 20*32 
 
 3 
 
 2-78 
 
 1'12 
 
 53 
 
 49-14 
 
 19*85 
 
 3 
 
 2*76 
 
 1-17 
 
 53 
 
 48*79 
 
 20*17 
 
 4 
 
 3-71 
 
 1-50 
 
 54 
 
 50-07 
 
 20-23 
 
 4 
 
 3-68 
 
 1-56 
 
 54 
 
 49*71 
 
 21'10 
 
 5 
 
 4-64 
 
 1-87 
 
 55 
 
 51-00 
 
 20-60 
 
 5 
 
 4-60 
 
 1-95 
 
 55 
 
 50*63 
 
 21*49 
 
 6 
 
 5-56 
 
 2-25 
 
 56 
 
 51-92 
 
 20-98 
 
 6 
 
 5-52 
 
 2-34 
 
 56 
 
 51-55 
 
 21*88 
 
 7 
 
 6-49 
 
 2-62 
 
 57 
 
 52-85 
 
 21-35 
 
 7 
 
 6-44 
 
 2-74 
 
 57 
 
 52*47 
 
 22*27 
 
 8 
 
 7-42 
 
 3-00 
 
 58 
 
 53-78 
 
 21-73 
 
 8 
 
 7-36 
 
 3-13 
 
 58 
 
 53-39 
 
 22*66 
 
 9 
 
 8-34 
 
 3-37 
 
 59 
 
 54-70 
 
 22-10 
 
 9 
 
 8-28 
 
 3-52 
 
 59 
 
 54-31 
 
 23-05 
 
 10 
 
 9-27 
 
 3-75 
 
 60 
 
 55-63 
 
 22-48 
 
 10 
 
 9-21 
 
 3-91 
 
 60 
 
 55*23 
 
 23-44 
 
 11 
 
 10-20 
 
 4-12 
 
 61 
 
 56-56 
 
 22-85 
 
 11 
 
 10-13 
 
 4-30 
 
 61 
 
 56*15 
 
 23 '83 
 
 12 
 
 11-13 
 
 4-50 
 
 62 
 
 57-49 
 
 23-23 
 
 12 
 
 11-05 
 
 4-69 
 
 62 
 
 57*07 
 
 24-23 
 
 13 
 
 12-05 
 
 4-87 
 
 63 
 
 58-41 
 
 23-60 
 
 13 
 
 11-97 
 
 5-08 
 
 63 
 
 57*99 
 
 24-62 
 
 14 
 
 12-98 
 
 5-24 
 
 64 
 
 59-34 
 
 23-97 
 
 14 
 
 12-89 
 
 5-47 
 
 64 
 
 58-91 
 
 25'01 
 
 15 
 
 13-91 
 
 5-62 
 
 65 
 
 60-27 
 
 24-35 
 
 15 
 
 13-81 
 
 5-86 
 
 65 
 
 59-83 
 
 25-40 
 
 16 
 
 14*83 
 
 5-99 
 
 66 
 
 61-19 
 
 24-72 
 
 16 
 
 14-73 
 
 6-25 
 
 66 
 
 60-75 
 
 25-79 
 
 17 
 
 15-76 
 
 6-37 
 
 67 
 
 62-12 
 
 25-10 
 
 17 
 
 15-65 
 
 6-64 
 
 67 
 
 61-67 
 
 26-18 
 
 18 
 
 16-69 
 
 6-74 
 
 68 
 
 63-05 
 
 25-47 
 
 18 
 
 16-57 
 
 7-03 
 
 68 
 
 62-59 
 
 26-57 
 
 19 
 
 17-62 
 
 7-12 
 
 69 
 
 63-98 
 
 25-85 
 
 19 
 
 17-49 
 
 7-42 
 
 69 
 
 63-51 
 
 26-96 
 
 20 
 
 18-54 
 
 7-49 
 
 70 
 
 64-90 
 
 26-22 
 
 20 
 
 18-41 
 
 7-81 
 
 70 
 
 64-44 
 
 27-35 
 
 21 
 
 19-47 
 
 7'87 
 
 71 
 
 65-83 
 
 26-60 
 
 21 
 
 19-33 
 
 8'21 
 
 71 
 
 65-36 
 
 27-74 
 
 22 
 
 20-40 
 
 8-24 
 
 72 
 
 66-76 
 
 26-97 
 
 22 
 
 20-25 
 
 8-60 
 
 72 
 
 66-28 
 
 28-13 
 
 23 
 
 21-33 
 
 8-62 
 
 73 
 
 67-68 
 
 27-35 
 
 23 
 
 21-17 
 
 8-99 
 
 73 
 
 67-20 
 
 28-52 
 
 24 
 
 22-25 
 
 8-99 
 
 74 
 
 68-61 
 
 27-72 
 
 24 
 
 22-09 
 
 9-38 
 
 74 
 
 68-12 
 
 28'91 
 
 23 
 
 23-18 
 
 9-37 
 
 75 
 
 69-54 
 
 28-10 
 
 25 
 
 23-01 
 
 9-77 
 
 75 
 
 69-04 
 
 29-30 
 
 26 
 
 24-11 
 
 9-74 
 
 76 
 
 70-47 
 
 28-47 
 
 26 
 
 23-93 
 
 10-16 
 
 76 
 
 69-93 
 
 29-70 
 
 27 
 
 25-03 
 
 10-11 
 
 77 
 
 71-39 
 
 28-84 
 
 27 
 
 24-85 
 
 10-55 
 
 77 
 
 70-88 
 
 30-09 
 
 28 
 
 25-96 
 
 10-49 
 
 78 
 
 72-32 
 
 29-22 
 
 28 
 
 25-77 
 
 10-94 
 
 78 
 
 71-80 
 
 30-48 
 
 29 
 
 26-89 
 
 10-86 
 
 79 
 
 73-25 
 
 29-59 
 
 29 
 
 26-69 
 
 11-33 
 
 79 
 
 72-72 
 
 30-87 
 
 30 
 
 27-82 
 
 11-24 
 
 80 
 
 74-17 
 
 29-97 
 
 30 
 
 27-62 
 
 11-72 
 
 80 
 
 73-64 
 
 31-26 
 
 31 
 
 28-74 
 
 11-61 
 
 81 
 
 75-10 
 
 30-34 
 
 31 
 
 28-54 
 
 12-11 
 
 81 
 
 74-56 
 
 31-65 
 
 32 
 
 29-67 
 
 11-99 
 
 82 
 
 76-03 
 
 30-72 
 
 32 
 
 29-46 
 
 12-50 
 
 82 
 
 75-48 
 
 32-04 
 
 33 
 
 30-60 
 
 12-36 
 
 83 
 
 76-96 
 
 31-09 
 
 33 
 
 30-38 
 
 12-89 
 
 83 
 
 76-40 
 
 32-43 
 
 34 
 
 31-52 
 
 12*74 
 
 84 
 
 77-88 
 
 31-47 
 
 34 
 
 31-30 
 
 13-28 
 
 84 
 
 77-32 
 
 32-82 
 
 35 
 
 32-45 
 
 13-11 
 
 85 
 
 78-81 
 
 31-84 
 
 35 
 
 32-22 
 
 13-68 
 
 85 
 
 78-24 
 
 33-21 
 
 36 
 
 33-38 
 
 13-49 
 
 86 
 
 79-74 
 
 32-22 
 
 36 
 
 33-14 
 
 14-07 
 
 86 
 
 79-16 
 
 33-60 
 
 37 
 
 34-31 
 
 13-86 
 
 87 
 
 80-66 
 
 32*59 
 
 37 
 
 34-06 
 
 14-46 
 
 87 
 
 80-08 
 
 33-99 
 
 38 
 
 35-23 
 
 14-24 
 
 88 
 
 81-5) 
 
 32*97 
 
 38 
 
 34-98 
 
 14-85 
 
 88 
 
 81-00 
 
 34-38 
 
 89 
 
 36-16 
 
 14-61 
 
 89 
 
 82-52 
 
 33-34 
 
 39 
 
 35-90 
 
 15-24 
 
 89 
 
 81-92 
 
 34-78 
 
 40 
 
 37-09 
 
 14-98 
 
 90 
 
 83-45 
 
 33-71 
 
 40 
 
 36-82 
 
 15-63 
 
 90 
 
 82-85 
 
 35-17 
 
 41 
 
 38-01 
 
 15-36 
 
 91 
 
 84-37 
 
 34-09 
 
 41 
 
 37*74 
 
 16-02 
 
 91 
 
 83-77 
 
 35-56 
 
 42 
 
 38-94 
 
 15-73 
 
 92 
 
 85-30 
 
 34-46 
 
 42 
 
 38*66 
 
 16-41 
 
 92 
 
 84-69 
 
 35-95 
 
 43 
 
 39-87 
 
 
 93 
 
 86-23 
 
 34-84 
 
 43 
 
 39*58 
 
 16-80 
 
 93 
 
 85-61 
 
 36-34 
 
 44 
 
 40-80 
 
 16-48 
 
 94 
 
 87-16 
 
 35-21 
 
 44 
 
 40-50 
 
 17-19 
 
 94 
 
 86-53 
 
 36-73 
 
 45 
 
 41-72 
 
 16-86 , 
 
 95 
 
 88-03 
 
 35-59 
 
 45 
 
 41-42 
 
 17-58 
 
 95 
 
 87-45 
 
 37-12 
 
 46 
 
 42-65 
 
 17-23 
 
 96 
 
 89-01 
 
 35-96 
 
 46 
 
 42-34 
 
 17-97 
 
 96 
 
 88-37 
 
 37-51 
 
 47 
 
 43-58 
 
 17-61 
 
 97 
 
 89-94 
 
 36*84 
 
 47 
 
 43-26 
 
 18-36 
 
 97 
 
 89-29 
 
 37-90 
 
 48 
 
 44-50 
 
 17-98 
 
 98 
 
 90-83 
 
 36*71 
 
 48 
 
 44-18 
 
 18-76 
 
 98 
 
 90-21 
 
 38-29 
 
 49 
 
 45-43 
 
 18-36 
 
 99 
 
 91*79 
 
 37-09 
 
 49 
 
 45-10 
 
 19-15 
 
 99 
 
 91-13 
 
 38-68 
 
 50 
 
 46-36 
 
 18-73 
 
 100 
 
 92-72 
 
 37-46 
 
 50 
 
 46-03 
 
 19-54 
 
 100 
 
 9"-05 
 
 39-07 
 
 
 E. or W. 
 
 N.or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.or W. 
 
 N.orS. 
 
 iE.orW. 
 
 N. or S. 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 68 
 
 67 
 
TEAYEltSE TABLES. 
 
 147 
 
 24 
 
 25 
 
 vl 
 
 i 
 
 
 
 cj 
 
 1 
 
 jj 
 
 j 
 
 *s 
 
 t*J 
 
 ^P,3 
 
 | 
 
 ft 
 
 II 
 
 o 
 
 8* 
 
 3* p 
 
 oo 
 
 o ^ 
 
 -a a 
 
 o 5 
 
 si 
 
 it 
 
 *| 
 
 s| 
 
 
 fcS 
 
 K 
 
 
 s 
 
 . 
 
 II 
 
 fc5 
 
 3 
 
 JsS 
 
 
 WQ 
 
 1 
 
 0-91 
 
 0-41 
 
 51 
 
 46-59 
 
 20-74 
 
 i 
 
 0-91 
 
 0-42 
 
 51 
 
 46-22 
 
 21-55 
 
 2 
 
 1-83 
 
 0-81 
 
 52 
 
 47'50 
 
 21-15 
 
 2 
 
 1-81 
 
 0-85 
 
 52 
 
 47-13 
 
 21-98 
 
 3 
 
 2-74 
 
 1-22 
 
 53 
 
 48-42 
 
 21-56 
 
 3 
 
 2-72 
 
 1-27 
 
 53 
 
 48-04 
 
 22-40 
 
 4 
 
 3-65 
 
 1-63 
 
 54 
 
 49-33 
 
 21-96 
 
 4 
 
 3-63 
 
 1-69 
 
 54 
 
 48-94 
 
 22-82 
 
 5 
 
 4-57 
 
 2-03 
 
 55- 
 
 50-25 
 
 22-37 
 
 5 
 
 4-53 
 
 2-11 
 
 55 
 
 49-85 
 
 23-24 
 
 6 
 
 5-48 
 
 2-44 
 
 56 
 
 51-16 
 
 22-78 
 
 6 
 
 5-44 
 
 2-54 
 
 56 
 
 50-75 
 
 23-67 
 
 7 
 
 6-39 
 
 2-85 
 
 57 
 
 52-07 
 
 23-18 
 
 7 
 
 6-34 
 
 2-96 
 
 57 
 
 51-66 
 
 24-09 
 
 8. 
 
 7-31 
 
 3-25 
 
 58 
 
 52-99 
 
 23-59 
 
 8 
 
 7-25 
 
 3-38 
 
 58 
 
 52-57 
 
 24-51 
 
 9 
 
 8-22 
 
 3-66 
 
 59 
 
 53-90 
 
 24-00 
 
 9 
 
 8-16 
 
 3-80 
 
 59 
 
 53-47 
 
 24-93 
 
 10 
 
 9-14 
 
 4-07 
 
 60 
 
 54-81 
 
 24-40 
 
 10 
 
 9-06 
 
 4-23 
 
 60 
 
 54-38 
 
 25-36 
 
 11 
 
 10-05 
 
 4-47 
 
 61 
 
 55-73 
 
 24-81 
 
 11 
 
 9-97 
 
 4-65 
 
 61 
 
 55-28 
 
 25-78 
 
 12 
 
 10-96 
 
 4-88 
 
 62 
 
 56-64 
 
 25-22 
 
 12 
 
 10-88 
 
 5-07 
 
 62 
 
 56-19 
 
 26-20 
 
 13 
 
 11-88 
 
 5-29 
 
 63 
 
 57-55 
 
 25-62 
 
 13 
 
 11-78 
 
 5-49 
 
 63 
 
 57-10 
 
 26-62 
 
 14 
 
 12-79 
 
 5-69 
 
 64 
 
 58-47 
 
 26-03 
 
 14 
 
 12'69 
 
 5-92 
 
 64 
 
 58-00 
 
 27-05 
 
 15 
 
 13-70 
 
 6-10 
 
 65 
 
 59-38 
 
 26-44 
 
 15 
 
 13-59 
 
 6-34 
 
 65 
 
 58-91 
 
 27-47 
 
 16 
 
 14-62 
 
 6-51 
 
 66 
 
 60-29 
 
 26-84 
 
 16 
 
 14-50 
 
 6-76 
 
 66 
 
 59-82 
 
 27-89 
 
 17 
 
 15-53 
 
 6-91 
 
 67 
 
 61-21 
 
 27-25 
 
 17 
 
 15-41 
 
 7-18 
 
 67 
 
 60-72 
 
 28-32 
 
 18 
 
 16-44 
 
 7-32 
 
 68 
 
 62-12 
 
 27-66 
 
 18 
 
 16-31 
 
 7-61 
 
 68 
 
 61-63 
 
 28-74 
 
 19 
 
 17-36 
 
 7-73 
 
 69 
 
 63-03 
 
 28-06 
 
 19 
 
 17-22 
 
 8-03 
 
 69 
 
 62-54 
 
 29-16 
 
 20 
 
 18-27 
 
 8-13 
 
 70 
 
 63-95 
 
 28-47 
 
 20 
 
 18-13 
 
 8-45 
 
 70 
 
 63-44 
 
 29'60 
 
 21 
 
 19-18 
 
 8-54 
 
 71 
 
 64-86 
 
 28-88 
 
 21 
 
 19-03 
 
 8'87 
 
 71 
 
 64-35 
 
 30-01 
 
 22 
 
 20-10 
 
 8-95 
 
 72 
 
 65-78 
 
 29'28 
 
 22 
 
 19-94 
 
 9-30 
 
 72 
 
 65-25 
 
 30-43 
 
 23 
 
 21-01 
 
 9-35 
 
 73 
 
 66-69 
 
 29-69 
 
 23 
 
 20-85 
 
 9-72 
 
 73 
 
 66-16 
 
 30-85 
 
 24 
 
 21-93 
 
 9-76 
 
 74 
 
 67-60 
 
 30-10 
 
 24 
 
 21-75 
 
 10-14 
 
 74 
 
 67-07 
 
 31-27 
 
 25 
 
 22-84 
 
 10-17 
 
 75 
 
 68-52 
 
 30-50 
 
 25 
 
 22-66 
 
 10-57 
 
 75 
 
 67-97 
 
 31-70 
 
 26 
 
 23-75 
 
 10-58 
 
 76 
 
 69-43 
 
 30-91 
 
 26 
 
 23-56 
 
 10-99 
 
 76 
 
 68-88 
 
 32-12 
 
 .27 
 
 24-67 
 
 10-98 
 
 77 
 
 70-34 
 
 31-32 
 
 27 
 
 24-47 
 
 11-41 
 
 77 
 
 69-79 
 
 32-54 
 
 28 
 
 25-58 
 
 11-39 
 
 78 
 
 71-26 
 
 31-72 
 
 28 
 
 25-38 
 
 11-83 
 
 78 
 
 70-69 
 
 32-96 
 
 29 
 
 26-49 
 
 11-80 
 
 79 
 
 72-17 
 
 32-13 
 
 29 
 
 26-28 
 
 12-26 
 
 79 
 
 71-60 
 
 33-39 
 
 80 
 
 27-41 
 
 12-20 
 
 80 
 
 73-08 
 
 32-54 
 
 30 
 
 27-19 
 
 12-68 
 
 80 
 
 72-50 
 
 33-81 
 
 31 
 
 28-32 
 
 12-61 
 
 81 
 
 74-00 
 
 32-94 
 
 31 
 
 28-10 
 
 13-10 
 
 81 
 
 73-41 
 
 34-23 
 
 32 
 
 29-23 
 
 13-02 
 
 82 
 
 74-91 
 
 33-35 
 
 32 
 
 29-00 
 
 13-62 
 
 82 
 
 74-32 
 
 34-65 
 
 33 
 
 30-15 
 
 13-42 
 
 83 
 
 75-82 
 
 33-76 
 
 33 
 
 29-91 
 
 13-95 
 
 83 
 
 75-22 
 
 35-08 
 
 34 
 
 31-06 
 
 13-83 
 
 84 
 
 76-74 
 
 34-16 
 
 34 
 
 30-81 
 
 14-37 
 
 84 
 
 76-13 
 
 35-50 
 
 35 
 
 31-97 
 
 14-24 
 
 85 
 
 77-65 
 
 34-57 
 
 35 
 
 31-72 
 
 14-79 
 
 85 
 
 77-04 
 
 35-92 
 
 M 
 
 32-89 
 
 14-64 
 
 86 
 
 78-56 
 
 34-98 
 
 36 
 
 32-63 
 
 15-21 
 
 86 
 
 77-94 
 
 36-35 
 
 37 
 
 33-80 
 
 15-05 
 
 87 
 
 79-48 
 
 35-38 
 
 37 
 
 33-53 
 
 15-64 
 
 87 
 
 78-85 
 
 36-77 
 
 38 
 
 34-71 
 
 15-46 
 
 88 
 
 80-39 
 
 35-79 
 
 38 
 
 34-44 
 
 16-06 
 
 88 
 
 79-76 
 
 37-19 
 
 39 
 
 35-63 
 
 15-86 
 
 89 
 
 81-31 
 
 36-20 
 
 39 
 
 35-35 
 
 16-48 
 
 89 
 
 80-66 
 
 37-61 
 
 40 
 
 36'54 
 
 16-27 
 
 90 
 
 82-22 
 
 36-60 
 
 40 
 
 36-25 
 
 26-90 
 
 90 
 
 81-57 
 
 38-04 
 
 41 
 
 37-46 
 
 16-68 
 
 91 
 
 83-13 
 
 37-01 
 
 41 
 
 37-16 
 
 17-33 
 
 91 
 
 82-47 
 
 38-46 
 
 42 
 
 38-37 
 
 17-08 
 
 92 
 
 84-05 
 
 37-42 
 
 42 
 
 38-06 
 
 17-75 
 
 92 
 
 83-38 
 
 38-88 
 
 43 
 
 39-28 
 
 17-49 
 
 93 
 
 84-96 
 
 37-82 
 
 43 
 
 38-97 
 
 18-17 
 
 93 
 
 84-29 
 
 39-30 
 
 44 
 
 40-20 
 
 17-90 
 
 94 
 
 85-87 
 
 38-23 
 
 44 
 
 39-88 
 
 18-60 
 
 91 
 
 85-19 
 
 39-73 
 
 45 
 
 41-11 
 
 18-30 
 
 95 
 
 86-79 
 
 38-64 
 
 45 
 
 40-78 
 
 19-02 
 
 95 
 
 86-10 
 
 40-15 
 
 46 
 
 42-02 
 
 18-71 
 
 96 
 
 87 70 
 
 39-04 
 
 46 
 
 41-69 
 
 19-44 
 
 96 
 
 87-01 
 
 40-57 
 
 47 
 
 42-Q4 
 
 19-12 
 
 97 
 
 88-61 
 
 39-45 
 
 47 
 
 42-60 
 
 19-86 
 
 97 
 
 87-91 
 
 40-99 
 
 48 
 
 43-85 
 
 19-52 
 
 98 
 
 89-53 
 
 39-86 
 
 48 
 
 43-50 
 
 20-29 
 
 98 
 
 88-82 
 
 41-42 
 
 49 
 
 44-76 
 
 19-93 
 
 99 
 
 90-44 
 
 40-26 
 
 49 
 
 44-41 
 
 20-71 
 
 99 
 
 89-72 
 
 41-84 
 
 50 
 
 45-68 
 
 20-34 
 
 100 
 
 91-35 
 
 40-67 
 
 50 
 
 45-32 
 
 21-13 
 
 100 
 
 90-63 
 
 42-26 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW 
 
 N.or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 66 
 
 65 
 
 
148 
 
 TEAVEESE TABLES. 
 
 26 
 
 27 
 
 If 
 
 "1 
 
 isf 
 
 It 
 
 ti 
 
 l*| 
 
 *C "M 
 
 dj 
 
 is| 
 
 *' 
 
 ii 
 
 ?1 
 
 i 
 
 "to 
 
 ^ tfl 
 
 4 a 
 
 "M 
 
 ^ 03 
 
 3 s 
 
 tc 
 
 ^ "02 
 
 5 C 
 
 o ~ 
 
 C " 
 
 MJ 
 
 fc'S 
 
 WQ 
 
 MJ 
 
 Q 
 
 HQ 
 
 MJ 
 
 SZJQ 
 
 HQ 
 
 fflvJ 
 
 Q 
 
 HQ 
 
 i 
 
 0-90 
 
 0-44 
 
 51 
 
 45-84 
 
 22-36 
 
 1 
 
 0-89 
 
 0-45 
 
 51 
 
 45-44 
 
 23-15 
 
 2 
 
 1-80 
 
 0-88 
 
 52 
 
 46-74 
 
 22-80 
 
 2 
 
 1-78 
 
 0-91 
 
 52 
 
 46-33 
 
 23-61 
 
 3 
 
 2-70 
 
 1-32 
 
 53 
 
 47-64 
 
 23-23 
 
 3 
 
 2-67 
 
 1-36 
 
 53 
 
 47"22 
 
 24-06 
 
 4 
 
 3-60 
 
 1-75 
 
 54 
 
 48-53 
 
 23-67 
 
 4 
 
 3-56 
 
 1-82 
 
 54 
 
 48'U 
 
 24-52 
 
 5 
 
 4-49 
 
 2-19 
 
 55 
 
 49-43 
 
 24-11 
 
 5 
 
 4-46 
 
 ' 2"27 
 
 55 
 
 49-01 
 
 24-97 
 
 6 
 
 5-39 
 
 2-63 
 
 56 
 
 50-33 
 
 24-55 
 
 6 
 
 5-35 
 
 2-72 
 
 56 
 
 49-90 
 
 25-42 
 
 7 
 
 6-29 
 
 3'07 
 
 57 
 
 51-23 
 
 24-99 
 
 7 
 
 6-24 
 
 3-18 
 
 57 
 
 50-79 
 
 25-88 
 
 8 
 
 7-19 
 
 3-50 
 
 58 
 
 52-13 
 
 25-43 
 
 8 
 
 7-13 
 
 3-63 
 
 58 
 
 51-68 
 
 26-33 
 
 9 
 
 8-09 
 
 3-95 
 
 59 
 
 53-03 
 
 25-86 
 
 9 
 
 8-02 
 
 4-09 
 
 59 
 
 52-57 
 
 2679 
 
 10 
 
 8-99 
 
 4-38 
 
 60 
 
 5393 
 
 26-30 
 
 10 
 
 8-91 
 
 I 4-54 
 
 60 
 
 53-46 
 
 27-24 
 
 11 
 
 9-89 
 
 4-82 
 
 61 
 
 54-83 
 
 26-74 
 
 11 
 
 9-80 
 
 4-99 
 
 61 
 
 54-35 
 
 27-69 
 
 12 
 
 10-79 
 
 5-26 
 
 62 
 
 55-73 
 
 27-18 
 
 12 
 
 10-69 
 
 545 
 
 62 
 
 55-24 
 
 28-15 
 
 13 
 
 11-68 
 
 5-70 
 
 63 
 
 56-62 
 
 27-62 
 
 13 
 
 11-58 
 
 5-90 
 
 63 
 
 56-13 
 
 28-60 
 
 14 
 
 12-58 
 
 6-14 
 
 64 
 
 57-52 
 
 28-06 
 
 14 
 
 12-47 
 
 6-36 
 
 64 
 
 57-02 
 
 29-06 
 
 15 
 
 13-48 
 
 6-58 
 
 65 
 
 58-42 
 
 28-49 
 
 15 
 
 13-37 
 
 6-81 
 
 65 
 
 57-92 
 
 29-51 
 
 16 
 
 14-38 
 
 7-01 
 
 66 
 
 59-32 
 
 28-93 
 
 16 
 
 14-26 
 
 7-23 
 
 66 
 
 58-81 
 
 29-96 
 
 17 
 
 15-28 
 
 7-45 
 
 67 
 
 60-22 
 
 29-37 
 
 17 
 
 15-15 
 
 7-72 
 
 67 
 
 59-70 
 
 30-42 
 
 18 
 
 16-18 
 
 7-89 
 
 68 
 
 61-12 
 
 29-81 
 
 18 
 
 16-04 
 
 8-17 
 
 68 
 
 60-59 
 
 30-87 
 
 19 
 
 17-08 
 
 8-33 
 
 69 
 
 62-02 
 
 30-25 
 
 19 
 
 16-93 
 
 8-63 
 
 69 
 
 61-48 
 
 31-33 
 
 20 
 
 17-98 
 
 8-77 
 
 70 
 
 62-92 
 
 30-69 
 
 20 
 
 17-82 
 
 9-08 
 
 70 
 
 62-37 
 
 31-78 
 
 21 
 
 18-87 
 
 9-21 
 
 71 
 
 63-81 
 
 31-12 
 
 21 
 
 18-71 
 
 9-53 
 
 71 
 
 63-26 
 
 32-23 
 
 22 
 
 19-77 
 
 9-64 
 
 72 
 
 64-71 
 
 31-56 
 
 22 
 
 19-60 
 
 9-99 
 
 72 
 
 64-15 
 
 32-69 
 
 23 
 
 20-67 
 
 10-08 
 
 73 
 
 65-61 
 
 32-00 
 
 23 
 
 20'49 
 
 10-44 
 
 73 
 
 65-04 
 
 33-14 
 
 24 
 
 21-57 
 
 10-52 
 
 74 
 
 66-51 
 
 32-44 
 
 24 
 
 21-38 
 
 10-90 
 
 74 
 
 65-93 
 
 33-60 
 
 25 
 
 22-47 
 
 10-96 
 
 75 
 
 67-41 
 
 32-88 
 
 25 
 
 22-28 
 
 11-35 
 
 75 
 
 66-83 
 
 34-05 
 
 
 23-37 
 
 11-40 
 
 76 
 
 68-31 
 
 33-32 
 
 26 
 
 23-17 
 
 11-80 
 
 76 
 
 67-72 
 
 34-50 
 
 27 
 
 24-27 
 
 11-84 
 
 77 
 
 69-21 
 
 33-75 
 
 27 
 
 24-06 
 
 12-26 
 
 77 
 
 68-61 
 
 34-96 
 
 28 
 
 25-17 
 
 12-27 
 
 78 
 
 70-11 
 
 34-19 
 
 28 
 
 24-95 
 
 12-71 
 
 78 
 
 69-50 
 
 35-41 
 
 29 
 
 26-06 
 
 12-71 
 
 79 
 
 71-00 
 
 34-63 
 
 29 
 
 25'84 
 
 13-17 
 
 79 
 
 70-39 
 
 35-87 
 
 30 
 
 26-96 
 
 13-15 
 
 80 
 
 71-90 
 
 35-07 
 
 30 
 
 26-73 
 
 13-62 
 
 80 
 
 71-28 
 
 36-32 
 
 31 
 
 27-86 
 
 13-59 
 
 81 
 
 72-80 
 
 35-51 
 
 31 
 
 27-63 
 
 14-07 
 
 81 
 
 72-17 
 
 36-77 
 
 32 
 
 28-76 
 
 14-03 
 
 82 
 
 73-70 
 
 35-95 
 
 32 
 
 28-51 
 
 14-53 
 
 82 
 
 73-06 
 
 37-23 
 
 33 
 
 29-66 
 
 14-47 
 
 83 
 
 74-60 
 
 36-38 
 
 33 
 
 29-40 
 
 14-98 
 
 83 
 
 73-95 
 
 37-68 
 
 34 
 
 30-56 
 
 14-90 
 
 84 
 
 75-50 
 
 36-82 
 
 34 
 
 30-29 
 
 15-44 
 
 84 
 
 74-84 
 
 38-14 
 
 35 
 
 31-46 
 
 1634 
 
 85 
 
 76-40 
 
 37-26 
 
 35 
 
 31-19 
 
 15-89 
 
 85 
 
 75-74 
 
 38-59 
 
 36 
 
 32-36 
 
 15-78 
 
 86 
 
 77-30 
 
 37-70 
 
 36 
 
 32-03 
 
 16-34 
 
 86 
 
 7663 
 
 39-04 
 
 37 
 
 33-26 
 
 1622 
 
 87 
 
 78-19 
 
 38-14 
 
 37 
 
 3297 
 
 16-80 
 
 87 
 
 77-52 
 
 39-50 
 
 38 
 
 34-15 
 
 16-66 
 
 88 
 
 79-09 
 
 38-58 
 
 38 
 
 33-86 
 
 17-25 
 
 88 
 
 78-41 
 
 39-95 
 
 39 
 
 35-05 
 
 1710 
 
 89 
 
 79-99 
 
 39-02 
 
 39 
 
 3475 
 
 17-71 
 
 89 
 
 79-30 
 
 40-41 
 
 40 
 
 3595 
 
 17-53 
 
 90 
 
 80-89 
 
 39-45 
 
 40 
 
 35-64 
 
 18-16 
 
 90 
 
 80-19 
 
 40-86 
 
 41 
 
 36-85 
 
 17-97 
 
 91 
 
 81-79 
 
 39-89 
 
 41 
 
 36-53 
 
 18-61 
 
 91 
 
 81-08 
 
 41-31 
 
 42 
 
 37-75 
 
 18-41 
 
 92 
 
 82-69 
 
 40-33 
 
 42 
 
 37-42 
 
 19-07 
 
 92 
 
 81-97 
 
 41-77 
 
 43 
 
 38-65 
 
 18-85 
 
 93 
 
 63-59 
 
 40-77 
 
 43 
 
 38-31 
 
 19-52 
 
 93 
 
 82-86 
 
 42-22 
 
 44 
 
 3y-55 
 
 19-29 
 
 94 
 
 84-49 
 
 41-21 
 
 44 
 
 39-20 
 
 1998 
 
 94 
 
 83-75 
 
 42-68 
 
 45 
 
 40-45 
 
 19-73 
 
 95 
 
 85-39 
 
 41-65 
 
 45 
 
 40-10 
 
 2043 
 
 95 
 
 84-65 
 
 43-13 
 
 46 
 
 41-34 
 
 20-17 
 
 96 
 
 86-28 
 
 42-08 
 
 46 
 
 40-99 
 
 20-88 
 
 93 
 
 85-54 
 
 43-58 
 
 47 
 
 42-24 
 
 20-60 
 
 97 
 
 87-18 
 
 42-52 
 
 47 
 
 41-88 
 
 21-34 
 
 97 
 
 86-43 
 
 44-04 
 
 48 
 
 43-14 
 
 21-04 
 
 98 
 
 88-08 
 
 42-96 
 
 48 
 
 42-77 
 
 21-79 
 
 98 
 
 87-32 
 
 44-49 
 
 49 
 
 44-04 
 
 21-48 
 
 99 
 
 88-98 
 
 43-40 
 
 49 
 
 43-66 
 
 22-25 
 
 99 
 
 88-21 
 
 44-95 
 
 50 
 
 44-94 
 
 21-92 
 
 100 
 
 89-88 
 
 43-84 
 
 50 
 
 44-55 
 
 22-70 
 
 100 
 
 89-10 
 
 45-40 
 
 IE.OVW. 
 
 N. orS. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N. or S. 
 
 64 
 
 63 
 
 
TRAYERSE TABLES. 
 
 149 
 
 28 | 29 9 
 
 g>i 
 
 i 
 
 *| 
 
 aJ 
 
 02 | 
 
 ft 
 
 be? 
 
 c ~~ 
 
 0*1 
 
 ft 
 
 iC X 
 
 rfl 
 
 ft 
 
 fH 
 
 ci B 
 
 B] 
 
 f 
 
 If 
 
 fe-3 
 
 "5 
 
 *l 
 
 P 
 
 o 
 
 *J 
 
 "^ br, 
 
 ji s 
 
 ~ a 
 
 ts 
 
 *| 
 
 3 
 
 E'Q 
 
 w5 
 
 3 
 
 KiS 
 
 H*S 
 
 35^ 
 
 fc5 
 
 w"3 
 
 ^ * 
 
 a 
 
 HQ 
 
 1 
 
 0-88 
 
 0-47 
 
 51 
 
 45-03 
 
 23-94 
 
 1 
 
 0-87 
 
 0-48 
 
 51 
 
 44-G 1 
 
 24-73 
 
 2 
 
 1-77 
 
 0-94 
 
 52 
 
 45-91 
 
 24-41 
 
 2 
 
 1-75 
 
 0-97 
 
 52 
 
 45-48 
 
 25-21 
 
 3 
 
 2-65 
 
 1-41 
 
 53 
 
 46-80 
 
 24-88 
 
 3 
 
 2-62 
 
 1-45 
 
 53 
 
 46-35 
 
 25-69 
 
 4 
 
 3-53 
 
 1-88 
 
 54 
 
 47-68 
 
 2535 
 
 4 
 
 3-50 
 
 1-94 
 
 54 
 
 47-23 
 
 28-18 
 
 5 
 
 4-41 
 
 2-35 
 
 55 
 
 48-56 
 
 25-82 
 
 5 
 
 4-37 
 
 2-42 
 
 rt 
 
 48-10 
 
 26-66 
 
 6 
 
 5-30 
 
 2-82 
 
 56 
 
 49-45 
 
 28-29 
 
 6 
 
 5-25 
 
 291 
 
 56 
 
 48-98 
 
 27-15 
 
 7 
 
 6-18 
 
 3-29 
 
 57 
 
 50-33 
 
 26-76 
 
 7 
 
 6-12 
 
 3-39 
 
 57 
 
 49-85 
 
 27-63 
 
 8 
 
 7-06 
 
 3-76 
 
 58 
 
 51-21 
 
 27-23 
 
 8 
 
 7-00 
 
 3-88 
 
 58 
 
 50-73 
 
 28-12 
 
 9 
 
 7-95 
 
 4-23 
 
 59 
 
 52-09 
 
 27-70 
 
 9 
 
 7-87 
 
 4-36 
 
 59 
 
 51-60 
 
 28-60 
 
 10 
 
 8-83 
 
 4-69 
 
 60 
 
 52-98 
 
 28-17 
 
 10 
 
 8-75 
 
 485 
 
 60 
 
 52-48 
 
 29-09 
 
 11 
 
 9-71 
 
 5-16 
 
 61 
 
 53-86 
 
 28-64 
 
 11 
 
 9-62 
 
 5-33 
 
 61 
 
 53-35 
 
 29-57 
 
 12 
 
 1060 
 
 563 
 
 62 
 
 54-76 
 
 29-11 
 
 12 
 
 10-50 
 
 5-82 
 
 62 
 
 54-23 
 
 30-06 
 
 13 
 
 11-43 
 
 6-10 
 
 63 
 
 55-63 
 
 29-58 
 
 13 
 
 11-37 
 
 6-30 
 
 63 
 
 55-10 
 
 30-54 
 
 14 
 
 12-86 
 
 6-57 
 
 64 
 
 56-51 
 
 30-05 
 
 14 
 
 12-24 
 
 679 
 
 64 
 
 55-93 
 
 31-03 
 
 15 
 
 13-24 
 
 7 '04 
 
 65 
 
 57-39 
 
 30-52 
 
 15 
 
 13-12 
 
 7-27 
 
 65 
 
 56-85 
 
 31-51 
 
 16 
 
 14-13 
 
 7-51 
 
 66 
 
 58-27 
 
 30-99 
 
 16 
 
 13-99 
 
 7-76 
 
 6 ( 3 
 
 57-72 
 
 32-00 
 
 17 
 
 15-01 
 
 7-98 
 
 67 
 
 59-16 
 
 31 45 
 
 17 
 
 14-87 
 
 8-24 
 
 67 
 
 5860 
 
 32-48 
 
 18 
 
 15-89 
 
 8--15 
 
 68 
 
 60-04 
 
 31-92 
 
 18 
 
 15-74 
 
 873 
 
 68 
 
 59-47 
 
 32-97 
 
 19 
 
 16-78 
 
 8-92 
 
 69 
 
 60-92 
 
 3239 
 
 19 
 
 16-62 
 
 921 
 
 69 
 
 60-35 
 
 33-45 
 
 20 
 
 17-66 
 
 9-39 
 
 70 
 
 61-81 
 
 32-86 
 
 20 
 
 17'49 
 
 970 
 
 70 
 
 6122 
 
 3394 
 
 21 
 
 18-54 
 
 9-86 
 
 71 
 
 62-69 
 
 3333 
 
 21 
 
 18-37 
 
 10-13 
 
 71 
 
 62-10 
 
 34-42 
 
 22 
 
 19-42 
 
 10-33 
 
 72 
 
 63-57 
 
 33-80 
 
 22 
 
 19-24 
 
 10-67 
 
 72 
 
 62-97 
 
 34-91 
 
 23 
 
 20-31 
 
 10-80 
 
 73 
 
 6446 
 
 34-27 
 
 23 
 
 212 
 
 11-15 
 
 73 
 
 63-85 
 
 3539 
 
 24 
 
 21-19 
 
 11-27 
 
 74 
 
 65-34 
 
 34-74 
 
 24 
 
 20-99 
 
 11-64 
 
 74 
 
 6472 
 
 35-88 
 
 25 
 
 22-07 
 
 11-74 
 
 75 
 
 66-22 
 
 35-21 
 
 25 
 
 21-87 
 
 12-12 
 
 75 
 
 6560 
 
 36-36 
 
 2G 
 
 22-96 
 
 12-21 
 
 76 
 
 67-10 
 
 3568 
 
 26 
 
 22-74 
 
 12-61 
 
 76 
 
 66-47 
 
 36-85 
 
 27 
 
 23-84 
 
 12-68 
 
 77 
 
 67-93 
 
 36-15 
 
 27 
 
 23-61 
 
 13-09 
 
 77 
 
 67-35 
 
 37-33 
 
 28 
 
 24-72 
 
 1315 
 
 78 
 
 6887 
 
 3662 
 
 28 
 
 2449 
 
 13-57 
 
 78 
 
 68-22 
 
 37-82 
 
 29 
 
 25-61 
 
 1361 
 
 79 
 
 6975 
 
 37d9 
 
 29 
 
 25-36 
 
 14-06 
 
 79 
 
 69-09 
 
 38-30 
 
 30 
 
 26-49 
 
 14-08 
 
 80 
 
 70-64 
 
 37-56 
 
 30 
 
 26-^4 
 
 14-54 
 
 80 
 
 69-97 
 
 38-78 
 
 31 
 
 27-37 
 
 14-55 
 
 81 
 
 71-52 
 
 38-03 
 
 31 
 
 27-11 
 
 15-03 
 
 81 
 
 70-84 
 
 39-27 
 
 32 
 
 28-25 
 
 15-02 
 
 82 
 
 72-40 
 
 38-50 
 
 32 
 
 27-99 
 
 15-51 
 
 82 
 
 7172 
 
 39-75 
 
 33 
 
 29-14 
 
 15-49 
 
 83 
 
 73-28 
 
 38-97 
 
 33 
 
 28-86 
 
 1600 
 
 83 
 
 72-59 
 
 40-24 
 
 34 
 
 30-02 
 
 15-96 
 
 84 
 
 74-17 
 
 39-44 
 
 34 
 
 29-74 
 
 16-48 
 
 84 
 
 73-47 
 
 40-72 
 
 35 
 
 30-90 
 
 16-43 
 
 85 
 
 75-05 
 
 39-91 
 
 35 
 
 30-61 
 
 16-97 
 
 85 
 
 74-34 
 
 41-21 
 
 36 
 
 31-79 
 
 1690 
 
 86 
 
 75-93 
 
 4037 
 
 36 
 
 31-49 
 
 17-45 
 
 86 
 
 75-22 
 
 41-69 
 
 37 
 
 32-67 
 
 17-37 
 
 87 
 
 76-82 
 
 40-84 
 
 37 
 
 32-36 
 
 1794 
 
 87 
 
 76-09 
 
 42-18 
 
 38 
 
 33-55 
 
 17-84 
 
 88 
 
 77-70 
 
 41-31 
 
 38 
 
 33-23 
 
 18-42 
 
 88 
 
 76-97 
 
 4266 
 
 39 
 
 34-43 
 
 1831 
 
 89 
 
 78-58 
 
 41-78 
 
 39 
 
 34-11 
 
 1891 
 
 89 
 
 77-84 
 
 43-15 
 
 40 
 
 35-32 
 
 18-78 
 
 90 
 
 79-47 
 
 42-25 
 
 40 
 
 3498 
 
 19-39 
 
 90 
 
 . 78-72 
 
 43-63 
 
 41 
 
 36-20 
 
 19-25 
 
 91 
 
 RO-35 
 
 42-72 
 
 41 
 
 3586 
 
 19-88 
 
 91 
 
 79-59 
 
 44-12 
 
 42 
 
 37-08 
 
 1972 
 
 H2 
 
 81-23 
 
 4319 
 
 42 
 
 36-T3 
 
 20-36 
 
 92 
 
 80-47 
 
 44-60 
 
 43 
 
 3797 
 
 20-19 
 
 93 
 
 82-11 
 
 43-66 
 
 43 
 
 37-61 
 
 2085 
 
 93 
 
 81-34 
 
 45-02 
 
 44 
 
 3885 
 
 2o-66 
 
 91 
 
 83 CO 
 
 44-13 
 
 44 
 
 3S-48 
 
 21-33 
 
 94 
 
 82-21 
 
 45-57 
 
 45 
 
 3973 
 
 2113 
 
 95 
 
 83-88 
 
 44-60 
 
 45 
 
 39-36 
 
 21-82 
 
 95 
 
 83-09 
 
 46-06 
 
 46 
 
 40-62 
 
 21-60 
 
 96 
 
 84-76 
 
 45-07 
 
 46 
 
 40-24 
 
 22-30 
 
 9*5 
 
 83-96 
 
 46-54 
 
 47 
 
 41-50 
 
 22-i7 
 
 97 
 
 85-65 
 
 45-54 
 
 47 
 
 4111 
 
 2279 
 
 97 
 
 84-84 
 
 47-03 
 
 48 
 
 42-38 
 
 2253 
 
 98 
 
 8653 
 
 46-01 
 
 48 
 
 41-98 
 
 23-27 
 
 98 
 
 85-71 
 
 47-51 
 
 49 
 
 43-26 
 
 2:Kn 
 
 99 
 
 87-41 
 
 46-48 
 
 49 
 
 42-86 
 
 23-76 
 
 99 
 
 86-59 
 
 48-00 
 
 60 
 
 44-15 
 
 23-47 
 
 100 
 
 88-29 
 
 4695 
 
 50 
 
 43-73 
 
 2424 
 
 ICO 
 
 87-46 
 
 48-48 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E. or W.j N.orS. 
 
 62 
 
 61 
 
150 
 
 TEAVEESE TABLES, 
 
 30 
 
 31 
 
 CM 
 
 y 
 
 1 
 
 '1 
 
 c -5 
 
 fcQ 
 
 E. or W. 
 
 Distance. 
 
 gf 
 
 S3 
 
 ** .S 
 
 WQ 
 
 11 
 
 fcQ 
 
 WQ 
 
 ! 
 
 0-87 
 
 0-50 
 
 51 
 
 44-17 
 
 25-60 
 
 1 
 
 0-86 
 
 0-52 
 
 51 
 
 43-72 
 
 26-27 
 
 2 
 
 1-73 
 
 1-00 
 
 52 
 
 45-03 
 
 26-00 
 
 2 
 
 1-71 
 
 1-03 
 
 52 
 
 44-57 
 
 26-78 
 
 3 
 
 2-60 
 
 1'50 
 
 53 
 
 45-90 
 
 26-50 
 
 3 
 
 2-57 
 
 1-55 
 
 53 
 
 45-43 
 
 27-30 
 
 4 
 
 3-46 
 
 2-00 
 
 54 
 
 46-77 
 
 27-00 
 
 4 
 
 3-43 
 
 2-06 
 
 54 
 
 46-29 
 
 27-81 
 
 5 
 
 4-33 
 
 2-50 
 
 55 
 
 47-63 
 
 27-50 
 
 5 
 
 4-29 
 
 2-58 
 
 55 
 
 47-14 
 
 28-33 
 
 6 
 
 5-20 
 
 3-00 
 
 56 
 
 48-50 
 
 28-00 
 
 6 
 
 5-14 
 
 3-09 
 
 56 
 
 48-00 
 
 28-84 
 
 7 
 
 6-06 
 
 3-50 
 
 57 
 
 49-36 
 
 28-50 
 
 7 
 
 6-00 
 
 3-61 
 
 57 
 
 48-86 
 
 29-36 
 
 8 
 
 6-93 
 
 4-00 
 
 58 
 
 50-23 
 
 29-00 
 
 8 
 
 6-88 
 
 4-12 
 
 58 
 
 49-72 
 
 29-87 
 
 9 
 
 7-79 
 
 4-50 
 
 59 
 
 51-10 
 
 29-50 
 
 9 
 
 7-71 
 
 4-64 
 
 59 
 
 50-57 
 
 30-39 
 
 10 
 
 8-66 
 
 5-00 
 
 60 
 
 51-96 
 
 30-00 
 
 10 
 
 8-57 
 
 5-15 
 
 60 
 
 51-43 
 
 30-90 
 
 11 
 
 9-53 
 
 5-50 
 
 61 
 
 52-83 
 
 30-50 
 
 11 
 
 9-43 
 
 5-67 
 
 61 
 
 52-29 
 
 31-42 
 
 12 
 
 10-39 
 
 6-00 
 
 62 
 
 53-69 
 
 Sl'OO 
 
 12 
 
 10-29 
 
 6-18 
 
 62 
 
 53-14 
 
 31-93 
 
 13 
 
 11-26 
 
 6-50 
 
 63 
 
 54-56 
 
 31-50 
 
 13 
 
 11-14 
 
 6-70 
 
 63 
 
 54'CO 
 
 32-45 
 
 14 
 
 12-12 
 
 7-00 
 
 64 
 
 55-43 
 
 32-00 
 
 14 
 
 12-00 
 
 7-21 
 
 64 
 
 54-86 
 
 32-96 
 
 15 
 
 12-99 
 
 7-50 
 
 65 
 
 56-29 
 
 32-50 
 
 15 
 
 12-86 
 
 7-73 
 
 65 
 
 55-72 
 
 33-48 
 
 16 
 
 13-86 
 
 8-00 
 
 66 
 
 57-16 
 
 33-00 
 
 16 
 
 13-71 
 
 8-24 
 
 66 
 
 56-57 
 
 33-99 
 
 17 
 
 14-72 
 
 8-50 
 
 67 
 
 58-02 
 
 33-50 
 
 17 
 
 14-57 
 
 8-76 
 
 67 
 
 57-43 
 
 34-51 
 
 18 
 
 15-59 
 
 9-00 
 
 68 
 
 58-89 
 
 34-00 
 
 18 
 
 15-43 
 
 9-27 
 
 68 
 
 58-29 
 
 35-02 
 
 19 
 
 16-45 
 
 9-50 
 
 69 
 
 59-76 
 
 34-50 
 
 19 
 
 16-29 
 
 9-79 
 
 69 
 
 59-14 
 
 35-54 
 
 20 
 
 17-32 
 
 10-00 
 
 70 
 
 60-62 
 
 35-00 
 
 20 
 
 17-14 
 
 10-30 
 
 70 
 
 60-00 
 
 36-05 
 
 21 
 
 18-19 
 
 10-50 
 
 71 
 
 61-49 
 
 35-50 
 
 21 
 
 18-00 
 
 10-82 
 
 71 
 
 60-86 - 
 
 36-57 
 
 22 
 
 19-05 
 
 11-00 
 
 72 
 
 62-35 
 
 36-00 
 
 22 
 
 18-86 
 
 11-33 
 
 72 
 
 61-72 
 
 37-08 
 
 23 
 
 19-92 
 
 11-50 
 
 73 
 
 63-22 
 
 36-50 
 
 23 
 
 19-71 
 
 11-85 
 
 73 
 
 62-57 
 
 37-60 
 
 24 
 
 20-78 
 
 12-00 
 
 74 
 
 64-09 
 
 37-00 
 
 24 
 
 20-58 
 
 12-36 
 
 74 
 
 63-43 
 
 38-11 
 
 25 
 
 21-65 
 
 12-50 
 
 75 
 
 64-95 
 
 37-50 
 
 25 
 
 21-43 
 
 12-88 
 
 75 
 
 64-29 
 
 38-63 
 
 26 
 
 22-52 
 
 13-00 
 
 76 
 
 65-82 
 
 38-00 
 
 26 
 
 22-29 
 
 13-39 
 
 76 
 
 65-14 
 
 39-14 
 
 27 
 
 23-38 
 
 13-50 
 
 77 
 
 66-68 
 
 38-50 
 
 27 
 
 23-14 
 
 13-91 
 
 77 
 
 66-00 
 
 39-66 
 
 28 
 
 24-25 
 
 14-00 
 
 78 
 
 67-55 
 
 39-00 
 
 28 
 
 24-00 
 
 14-42 
 
 78 
 
 66-86 
 
 40-17 
 
 29 
 
 25-11 
 
 14-50 
 
 79 
 
 68-42 
 
 39-50 
 
 29 
 
 24-86 
 
 14-94 
 
 79 
 
 67-72 
 
 40-69 
 
 30 
 
 25-98 
 
 15-00 
 
 80 
 
 69-28 
 
 40-00 
 
 30 
 
 25-72 
 
 15-45 
 
 80 
 
 68-57 
 
 41-20 
 
 31 
 
 26-85 
 
 15-50 
 
 81 
 
 70-15 
 
 40-50 
 
 31 
 
 26-57 
 
 15-97 
 
 81 
 
 69-43 
 
 41-72 
 
 32 
 
 27-71 
 
 16-00 
 
 82 
 
 71-01 
 
 41-00 
 
 32 
 
 27-43 
 
 16-48 
 
 82 
 
 70-29 
 
 42-23 
 
 33 
 
 28-58 
 
 16-50 
 
 83 
 
 71-88 
 
 41-50 
 
 33 
 
 28-29 
 
 17-00 
 
 83 
 
 71-15 
 
 42-75 
 
 34 
 
 29-44 
 
 17-00 
 
 84 
 
 72-75 
 
 42-00 
 
 34 
 
 29-14 
 
 17-51 
 
 84 
 
 72-00 
 
 43-26 
 
 35 
 
 30-31 
 
 17-50 
 
 85 
 
 73-61 
 
 42-50 
 
 35 
 
 30-00 
 
 18-03 
 
 85 
 
 72-86 
 
 43-78 
 
 36 
 
 31-18 
 
 18-00 
 
 86 
 
 74-43 
 
 43-00 
 
 36 
 
 30-86 
 
 18-54 
 
 86 
 
 73-72 
 
 44-29 
 
 37 
 
 32-04 
 
 18-50 
 
 87 
 
 75-35 
 
 43-50 
 
 37 
 
 31-72 
 
 19-06 
 
 87 
 
 74*57 
 
 44-81 
 
 38 
 
 32-91 
 
 19-00 
 
 88 
 
 76-21 
 
 44-00 
 
 38 
 
 32-57 
 
 19-57 
 
 88 
 
 7543 
 
 45-32 
 
 39 
 
 33-78 
 
 19-50 
 
 89 
 
 77-08 
 
 44-50 
 
 39 
 
 33-43 
 
 20-09 
 
 89 
 
 76-29 
 
 45-84 
 
 40 
 
 34-61 
 
 20-00 
 
 90 
 
 77-94 
 
 45-00 
 
 40 
 
 34-29 
 
 20-60 
 
 90 
 
 77-15 
 
 46-35 
 
 41 
 
 35-51 
 
 20-50 
 
 91 
 
 78-81 
 
 45-50 
 
 41 
 
 35-14 
 
 21-12 
 
 91 
 
 78-00 
 
 46-87 
 
 42 
 
 36'37 
 
 21-00 
 
 92 
 
 79-68 
 
 46-00 
 
 42 
 
 36-00 
 
 2163 
 
 92 
 
 78-86 
 
 47-38 
 
 43 
 
 37-24 
 
 21-50 
 
 93 
 
 80-54 
 
 46-50 
 
 43 
 
 36-86 
 
 22-15 
 
 93 
 
 7972 
 
 47-90 
 
 44 
 
 38-11 
 
 22-00 
 
 94 
 
 81-41 
 
 47-00 
 
 44 
 
 37-72 
 
 2266 
 
 94 
 
 80-57 
 
 48-41 
 
 45 
 
 38-97 
 
 22-50 
 
 95 
 
 82-27 
 
 47-50 
 
 45 
 
 38-57 
 
 23-18 
 
 95 
 
 81-43 
 
 48-93 
 
 48 
 
 39-84 
 
 23-00 
 
 96 
 
 83-14 
 
 48-00 
 
 46 
 
 39-43 
 
 23-69 
 
 96 
 
 82-29 
 
 49-44 
 
 47 
 
 40-70 
 
 23-50 
 
 97 
 
 84-00 
 
 48-50 
 
 47 
 
 40-29 
 
 24-21 
 
 97 
 
 83-15 
 
 49-96 
 
 48 
 
 41-57 
 
 24-00 
 
 98 
 
 84-87 
 
 49-00 
 
 48 
 
 41 14 
 
 24-72 
 
 98 
 
 84-00 
 
 50-47 
 
 49 
 
 42-44 
 
 24-50 
 
 99 
 
 85-74 
 
 49-50 
 
 49 
 
 42-00 
 
 25-24 
 
 99 
 
 84-86 
 
 50-99 
 
 50 
 
 43-30 
 
 25-00 
 
 100 
 
 86-60 
 
 60-00 
 
 50 
 
 42-86 
 
 25-75 
 
 00 
 
 86-72 
 
 51-50 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.or W.I N.or S. 
 
 iE.orW. 
 
 N. or S. 
 
 60 
 
 59 
 
TBAYEKSE TABLES. 
 
 151 
 
 32 
 
 33 
 
 ri 
 
 02 | 
 
 *f 
 
 = J2 
 
 ail 
 
 *i 
 
 11 
 
 *l 
 
 *i 
 
 i?! 
 
 n| 
 
 f 
 
 i= r - 
 
 - 93 
 
 o -*- 1 
 
 si 
 
 Z t>D 
 
 ss a 
 
 sl 
 
 s| 
 
 
 s| 
 
 sf 
 
 C be 
 * c 
 
 g| 
 
 o| 
 
 33 
 
 fcS 
 
 piS 
 
 3 
 
 fcS 
 
 w*5 
 
 IJ 
 
 &3 
 
 W"Q 
 
 <S3 
 
 .-i 
 
 Q 
 
 KQ 
 
 i 
 
 0-85 
 
 0-53 
 
 51 
 
 43-25 
 
 27-03 
 
 1 
 
 0<84 
 
 0-54 
 
 51 
 
 42-77 
 
 27-78 
 
 2 
 
 1-70 
 
 1-06 
 
 52 
 
 44-10 
 
 27-56 
 
 2 
 
 1-68 
 
 1-09 
 
 52 
 
 43-61 
 
 28-32 
 
 3 
 
 2-54 
 
 1-59 
 
 53 
 
 44-59 
 
 28-09 
 
 3 
 
 2-52 
 
 1-63 
 
 53 
 
 44-45 
 
 28-87 
 
 4 
 
 3-39 
 
 2-12 
 
 54 
 
 45-79 
 
 28-62 
 
 4 
 
 3-35 
 
 2-18 
 
 54 
 
 45-29 
 
 29-41 
 
 5 
 
 4-24 
 
 2-65 
 
 55 
 
 46-64 
 
 29-15 
 
 5 
 
 4-19 
 
 2-79 
 
 55 
 
 46-13 
 
 29-96 
 
 6 
 
 5-09 
 
 3-18 
 
 56 
 
 47-49 
 
 29-68 
 
 6 
 
 5-03 
 
 3-27 
 
 56 
 
 46-97 
 
 30-50 
 
 7 
 
 5-94 
 
 3-71 
 
 57 
 
 48-34 
 
 30-21 
 
 7 
 
 5-87 
 
 3-81 
 
 57 
 
 47-80 
 
 31-05 
 
 8 
 
 6-78 
 
 4-23 
 
 58 
 
 49-19 
 
 30-74 
 
 8 
 
 6-71 
 
 4-36 
 
 58 
 
 48-64 
 
 31-59 
 
 9 
 
 7-63 
 
 4-77 
 
 59 
 
 50-03 
 
 31-27 
 
 9 
 
 7-55 
 
 4-90 
 
 59 
 
 49-48 
 
 32-15 
 
 10 
 
 8-48 
 
 5-30 
 
 60 
 
 50-88 
 
 31-80 
 
 10 
 
 8-39 
 
 5-45 
 
 60 
 
 60-32 
 
 32-68 
 
 11 
 
 9-33 
 
 5-83 
 
 61 
 
 51-73 
 
 32-33 
 
 11 
 
 9-23 
 
 5-99 
 
 61 
 
 51-16 
 
 33-22 
 
 12 
 
 10-18 
 
 6-36 
 
 62 
 
 52-58 
 
 32-86 
 
 12 
 
 10-06 
 
 6-64 
 
 62 
 
 52-00 
 
 33-77 
 
 13 
 
 11-02 
 
 6-89 
 
 63 
 
 53'43 
 
 33-38 
 
 13 
 
 10-90 
 
 7-08 
 
 63 
 
 52-84 
 
 34-31 
 
 14 
 
 11-87 
 
 7-42 
 
 64 
 
 54-28 
 
 33-91 
 
 14 
 
 1174 
 
 7-62 
 
 64 
 
 53-67 
 
 34-86 
 
 15 
 
 12-72 
 
 7-95 
 
 65 
 
 55-12 
 
 34-44 
 
 15 
 
 12-58 
 
 8-17 
 
 65 
 
 54-51 
 
 35-40 
 
 16 
 
 13-57 
 
 8-48 
 
 66 
 
 55-97 
 
 34-97 
 
 16 
 
 13-42 
 
 8-71 
 
 66 
 
 55-35 
 
 35-95 
 
 17 
 
 14-42 
 
 9-01 
 
 67 
 
 56-82 
 
 35-50 
 
 17 
 
 14-26 
 
 9-26 
 
 67 
 
 56-19 
 
 36-49 
 
 IS 
 
 15-26 
 
 9-54 
 
 68 
 
 57-67 
 
 36-03 
 
 18 
 
 15-10 
 
 9-80 
 
 68 
 
 57-03 
 
 37-04 
 
 19 
 
 16-11 
 
 10-07 
 
 69 
 
 58-57 
 
 36-56 
 
 19 
 
 15-93 
 
 ltf-35 
 
 69 
 
 57-87 
 
 37-58 
 
 20 
 
 16-96 
 
 10-60 
 
 70 
 
 59-36 
 
 37-09 
 
 20 
 
 16-77 
 
 10-89 
 
 70 
 
 58-71 
 
 38-13 
 
 21 
 
 17-81 
 
 11-13 
 
 71 
 
 60-21 
 
 37-62 
 
 21 
 
 17-61 
 
 11-44 
 
 71 
 
 59-55 
 
 38-67 
 
 22 
 
 18-66 
 
 11-66 
 
 72 
 
 61-06 
 
 38-15 
 
 22 
 
 18-45 
 
 11-98 
 
 72 
 
 60-38 
 
 39-21 
 
 23 
 
 19-51 
 
 12-19 
 
 73 
 
 61-91 
 
 38-68 
 
 23 
 
 19-29 
 
 12-53 
 
 73 
 
 61-22 
 
 39-76 
 
 24 
 
 20-35 
 
 12-72 
 
 74 
 
 62-76 
 
 39-21 
 
 24 
 
 20-13 
 
 13-07 
 
 74 
 
 62-06 
 
 40-30 
 
 25 
 
 21-20 
 
 13-25 
 
 75 
 
 63-60 
 
 39-74 
 
 25 
 
 20-97 
 
 13-62 
 
 75 
 
 62-90 
 
 40-85 
 
 26 
 
 22-05 
 
 13-78 
 
 76 
 
 64-45 
 
 40-27 
 
 26 
 
 21-81 
 
 14-16 
 
 76 
 
 63-74 
 
 41-39 
 
 27 
 
 22-90 
 
 14-31 
 
 77 
 
 65-30 
 
 40-80 
 
 27 
 
 22-64 
 
 14-71 
 
 77 
 
 64-58 
 
 41-94 
 
 28 
 
 23-75 
 
 14-84 
 
 78 
 
 66-15 
 
 41-33 
 
 28 
 
 23-48 
 
 15-25 
 
 78 
 
 65-42 
 
 42-48 
 
 29 
 
 24-59 
 
 15-37 
 
 79 
 
 67-00 
 
 41-86 
 
 29 
 
 24-32 
 
 15-79 
 
 79 
 
 66-25 
 
 43-03 
 
 30 
 
 25-44 
 
 15-90 
 
 80 
 
 67-84 
 
 42-39 
 
 30 
 
 25-16 
 
 16-34 
 
 80 
 
 67-09 
 
 43-57 
 
 31 
 
 26-29 
 
 16-43 
 
 81 
 
 68-69 
 
 42-92 
 
 31 
 
 26-00 
 
 16-88 
 
 81 
 
 67-93 
 
 44-12 
 
 32 
 
 27-14 
 
 16-96 
 
 82 
 
 69-54 
 
 43-45 
 
 32 
 
 26-84 
 
 17-43 
 
 82 
 
 68-77 
 
 44-66 
 
 33 
 
 27-99 
 
 17-49 
 
 83 
 
 70-39 
 
 43-98 
 
 33 
 
 27-68 
 
 17-97 
 
 83 
 
 69-61 
 
 45-21 
 
 34 
 
 28-83 
 
 18-02 
 
 84 
 
 71-24 
 
 44-51 
 
 34 
 
 28-51 
 
 18-62 
 
 84 
 
 70-45 
 
 45-75 
 
 35 
 
 29-68 
 
 18-55 
 
 85 
 
 72'08 
 
 45-04 
 
 35 
 
 2y-35 
 
 19-06 
 
 85 
 
 71-29 
 
 46-29 
 
 36 
 
 30-53 
 
 19-08 
 
 86 
 
 72-93 
 
 45-57- 
 
 36 
 
 30-19 
 
 19-61 
 
 86 
 
 72-13 
 
 46-84 
 
 37 
 
 31-38 
 
 19-61 
 
 87 
 
 73-78 
 
 46-10 
 
 37 
 
 31-03 
 
 20-15 
 
 87 
 
 72-96 
 
 47-38 
 
 38 
 
 32-23 
 
 20-14 
 
 88 
 
 74-63 
 
 46-63 
 
 38 
 
 31-87 
 
 20-70 
 
 88 
 
 73-80 
 
 47-93 
 
 39 
 
 33-07 
 
 20-67 
 
 89 
 
 75-48 
 
 47-16 
 
 39 
 
 32-71 
 
 21-24 
 
 89 
 
 74-64 
 
 48-47 
 
 40 
 
 33-92 
 
 21-20 
 
 90 
 
 76-32 
 
 47-69 
 
 40 
 
 33-55 
 
 21-79 
 
 90 
 
 75-48 
 
 49-02 
 
 41 
 
 84-77 
 
 21-73 
 
 91 
 
 77-17 
 
 48-22 
 
 41 
 
 34-39 
 
 22-33 
 
 91 
 
 76-32 
 
 49-56 
 
 42 
 
 35-62 
 
 22-26 
 
 92 
 
 78-02 
 
 48-75 
 
 42 
 
 35-22 
 
 22-88 
 
 92 
 
 77-16 
 
 50-11 
 
 43 
 
 36-47 
 
 22-79 
 
 93 
 
 78-87 
 
 49-28 
 
 43 
 
 36-06 
 
 23-42 
 
 93 
 
 78-00 
 
 50-65 
 
 44 
 
 37-31 
 
 23-32 
 
 94 
 
 79-72 
 
 49-81 
 
 44 
 
 36-90 
 
 23-97 
 
 94 
 
 78-83 
 
 51-20 
 
 45 
 
 38-16 
 
 23-85 
 
 95 
 
 80-56 
 
 50-34 
 
 45 
 
 37-74 
 
 24-51 
 
 95 
 
 79-67 
 
 51-74 
 
 46 
 
 39-01 
 
 24-38 
 
 96 
 
 81-41 
 
 50-87 
 
 46 
 
 38-58 
 
 25-05 
 
 96 
 
 80-51 
 
 52-29 
 
 47 
 
 39-86 
 
 24-91 
 
 97 
 
 82-26 
 
 51-40 
 
 47 
 
 39-42 
 
 25-60 
 
 97 
 
 81-35 
 
 52-83 
 
 48 
 
 40-71 
 
 25-44 
 
 98 
 
 83-11 
 
 51-93 
 
 48 
 
 40-26 
 
 26-14 
 
 98 
 
 82-19 
 
 53-37 
 
 49 
 
 41-55 
 
 25-97 
 
 99 
 
 83-96 
 
 52-46 
 
 49 
 
 41-09 
 
 26-69 
 
 99 
 
 83-03 
 
 53-92 
 
 50 
 
 42-40 
 
 26-50 
 
 100 
 
 84-81 
 
 52-99 
 
 50 
 
 41-93 
 
 27-23 
 
 100 
 
 83-87 
 
 54-46 
 
 
 E. orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E. or W. 
 
 N. or S. 
 
 58 
 
 57 
 
152 
 
 TEAYEESE TABLES. 
 
 34 
 
 35 ~x 
 
 |J 
 
 It 
 
 oaf 
 
 S .l 
 
 ll 
 
 38 P 
 
 Ij 
 
 "S 
 
 If 
 
 02 g 
 
 || 
 
 
 
 ft 
 
 s! 
 
 si 
 
 Si 
 
 fc 
 
 wo 
 
 CQ 5 
 
 
 w'S 
 
 
 fc'S 
 
 f45 
 
 II 
 
 fc'5 
 
 wS 
 
 ! 
 
 0-83 
 
 0-56 
 
 51 
 
 42-28 
 
 2852 
 
 i 
 
 . 082 
 
 0-57 
 
 51 
 
 41-78 
 
 29-25 
 
 2 
 
 1-66 
 
 1-12 
 
 52 
 
 43-11 
 
 29-08 
 
 2 
 
 164 
 
 1-15 
 
 52 
 
 42-50 
 
 29-83 
 
 3 
 
 2-49 
 
 1-68 
 
 53 
 
 4394 
 
 2964 
 
 3 
 
 2-46 
 
 1-72 
 
 53 
 
 43-41 
 
 30-40 
 
 4 
 
 332 
 
 2-24 
 
 54 
 
 44-77 
 
 30-20 
 
 4 
 
 8-28 
 
 2-29 
 
 54 
 
 44-23 
 
 30-97 
 
 5 
 
 4-15 
 
 2-80 
 
 55 
 
 45-60 
 
 3076 
 
 5 
 
 4-10 
 
 2-87 
 
 55 
 
 45-05 
 
 31-55 
 
 6 
 
 4-97 
 
 3-36 
 
 56 
 
 46-43 
 
 31-31 
 
 6 
 
 4-91 
 
 3-44 
 
 56 
 
 45-87 
 
 32-12 
 
 7 
 
 5-80 
 
 3-91 
 
 57 
 
 47-26 
 
 31-87 
 
 7 
 
 5-73 
 
 4-02 
 
 57 
 
 46-69 
 
 32-69 
 
 8 
 
 6-b3 
 
 4-47 
 
 58 
 
 48-08 
 
 32-43 
 
 8 
 
 6-55 
 
 4-59 
 
 58 
 
 47-51 
 
 33-27 
 
 9 
 
 7-46 
 
 5-03 
 
 59 
 
 48-91 
 
 32-99 
 
 9 
 
 7-37 
 
 5-16 
 
 59 
 
 48-33 
 
 33-84 
 
 10 
 
 8-29 
 
 5-59 
 
 60 
 
 49-74 
 
 33-55 
 
 10 
 
 8-19 
 
 5-74 
 
 60 
 
 49-15 
 
 34-41 
 
 11 
 
 9-12 
 
 6-15 
 
 61 
 
 50-57 
 
 34-11 
 
 11 
 
 9-01 
 
 6-31 
 
 61 
 
 49-97 
 
 34-99 
 
 12 
 
 9-95 
 
 6-71 
 
 62 
 
 51-40 
 
 34-67 
 
 12 
 
 9-83 
 
 688 
 
 62 
 
 50-79 
 
 35-56 
 
 13 
 
 10-78 
 
 7-27 
 
 63 
 
 52-23 
 
 35-23 
 
 13 
 
 10-65 
 
 7-46 
 
 63 
 
 51-61 
 
 36-14 
 
 14 
 
 11-61 
 
 7-83 
 
 64 
 
 53-06 
 
 35-79 
 
 14 
 
 11-47 
 
 8-03 
 
 64 
 
 52-43 
 
 36-71 
 
 15 
 
 12-44 
 
 8-39 
 
 65 
 
 53-89 
 
 36-35 
 
 15 
 
 12-29 
 
 860 
 
 65 
 
 53-24 
 
 37-28 
 
 16 
 
 13-26 
 
 895 
 
 66 
 
 54-72 
 
 36-91 
 
 16 
 
 13-11 
 
 9-18 
 
 66 
 
 54-06 
 
 37-86 
 
 17 
 
 14-09 
 
 9-51 
 
 67 
 
 55-55 
 
 37-47 
 
 17 
 
 13-93 
 
 9-75 
 
 67 
 
 54-88 
 
 38-43 
 
 18 
 
 14-92 
 
 10-07 
 
 68 
 
 .56-37 
 
 38-02 
 
 18 
 
 14-74 
 
 10-32 
 
 68 
 
 55-70 
 
 39-00 
 
 19 
 
 1575 
 
 10-62 
 
 69 
 
 57-20 
 
 38-58 
 
 19 
 
 15-56 
 
 10-90 
 
 69 
 
 56-52 
 
 39-58 
 
 20 
 
 16-58 
 
 11-18 
 
 70 
 
 58-03 
 
 39-14 
 
 20 
 
 16-38 
 
 11-47 
 
 70 
 
 57-34 
 
 4015 
 
 21 
 
 17-41 
 
 11-74 
 
 71 
 
 58-86 
 
 39-70 
 
 21 
 
 17-20 
 
 12-05 
 
 71 
 
 58-16 
 
 40-72 
 
 22 
 
 18-24 
 
 12-30 
 
 72 
 
 59:69 
 
 40-26 
 
 22 
 
 18-02 
 
 12-62 
 
 72 
 
 58-98 
 
 41-30 
 
 23 
 
 19-07 
 
 12-86 
 
 73 
 
 60-52 
 
 40-82 
 
 23 
 
 18-84 
 
 13-19 
 
 73 
 
 59-80 
 
 41-87 
 
 24 
 
 19-90 
 
 13-42 
 
 74 
 
 61-35 
 
 41-38 
 
 24 
 
 19-66 
 
 13-77 
 
 74 
 
 60-62 
 
 42-44 
 
 25 
 
 20-73 
 
 13-98 
 
 75 
 
 62-18 
 
 41-94 
 
 25 
 
 20-48 
 
 14-34 
 
 75 
 
 61-44 
 
 43-02 
 
 26 
 
 21-56 
 
 14-54 
 
 76 
 
 63-01 
 
 42-50 
 
 26 
 
 21-30 
 
 14-91 
 
 76 
 
 62-26 
 
 43-59 
 
 27 
 
 22-38 
 
 15-10 
 
 77 
 
 63-84 
 
 43-06 
 
 27 
 
 22-12 
 
 15-49 
 
 77 
 
 63-07 
 
 44-17 
 
 28 
 
 23-21 
 
 15-66 
 
 78 
 
 64-67 
 
 43-62 
 
 28 
 
 22-94 
 
 16-06 
 
 78 
 
 63-89 
 
 44-74 
 
 29 
 
 24-04 
 
 16-22 
 
 79 
 
 65-49 
 
 44-18 
 
 29 
 
 23-76 
 
 16-63 
 
 79 
 
 64-71 
 
 45-41 
 
 30 
 
 24-87 
 
 16-78 
 
 80 
 
 66-32 
 
 44-74 
 
 30 
 
 24-57 
 
 17-21 
 
 80 
 
 65-53 
 
 45-89 
 
 31 
 
 25-70 
 
 17-33 
 
 81 
 
 67-15 
 
 45-29 
 
 31 
 
 25-39 
 
 17-78 
 
 81 
 
 66-35 
 
 46-46 
 
 32 
 
 26-53 
 
 17-89 
 
 82 
 
 67-98 
 
 45-85 
 
 32 
 
 26-21 
 
 18-35 
 
 82 
 
 67-17 
 
 47-03 
 
 33 
 
 27-36 
 
 18-45 
 
 83 
 
 68-81 
 
 46-41 
 
 33 
 
 27-03 
 
 18-93 
 
 83 
 
 67-99 
 
 47-61 
 
 34 
 
 28-19 
 
 19-01 
 
 84 
 
 69-64 
 
 46-97 
 
 34 
 
 27-85 
 
 19-50 
 
 84 
 
 68-81 
 
 48-18 
 
 35 
 
 29-02 
 
 1957 
 
 85 
 
 70-47 
 
 47-53 
 
 35 
 
 28-67 
 
 20-08 
 
 85 
 
 69-63 
 
 48-75 
 
 36 
 
 29-85 
 
 20-13 
 
 86 
 
 71-30 
 
 48-09 
 
 36 
 
 29-49 
 
 20-65 
 
 86 
 
 70-45 
 
 49-33 
 
 37 
 
 30-67 
 
 20-69 
 
 87 
 
 72-13 
 
 48-65 
 
 37 
 
 30-31 
 
 21-22 
 
 87 
 
 71-27 
 
 49-90 
 
 38 
 
 31-50 
 
 21-25 
 
 88 
 
 72-96 
 
 49-21 
 
 38 
 
 31-13 
 
 21-80 
 
 88 
 
 72-09 
 
 50-48 
 
 39 
 
 32-33 
 
 21-81 
 
 89 
 
 73-78 
 
 49-77 
 
 39 
 
 31-95 
 
 22-37 
 
 89 
 
 72-90 
 
 51-05 
 
 40 
 
 33-16 
 
 22-37 
 
 90 
 
 74-61 
 
 50-33 
 
 40 
 
 32-77 
 
 22-94 
 
 90 
 
 73-72 
 
 51-62 
 
 41 
 
 33-99 
 
 22-93 
 
 91 
 
 75-44 
 
 50'89 
 
 41 
 
 33-59 
 
 2352 
 
 91 
 
 74-54 
 
 52-20 
 
 42 
 
 34-82 
 
 23-49 
 
 92 
 
 76-27 
 
 51-45 
 
 42 
 
 34-40 
 
 24-09 
 
 92 
 
 75-36 
 
 52-77 
 
 43 
 
 35-65 
 
 24-05 
 
 93 
 
 77-10 
 
 52-00 
 
 43 
 
 35-22 
 
 24-66 
 
 93 
 
 76-18 
 
 53-34 
 
 44 
 
 36-48 
 
 24-60 
 
 94 
 
 77-93 
 
 52-56 
 
 44 
 
 36-04 
 
 25-24 
 
 94 
 
 77-00 
 
 53-92 
 
 45 
 
 37-31 
 
 25-16 
 
 95 
 
 78-76 
 
 53-12 
 
 45 
 
 36-86 
 
 25-81 
 
 95 
 
 77-82 
 
 54-49 
 
 46 
 
 38-14 
 
 25-72 
 
 96 
 
 79-59 
 
 53-68 
 
 46 
 
 37-68 
 
 26-38 
 
 96 
 
 78-64 
 
 55-06 
 
 47 
 
 38-96 
 
 26-28 
 
 97 
 
 80-42 
 
 54-24 
 
 47 
 
 38-50 
 
 26-96 
 
 97 
 
 79-46 
 
 55-64 
 
 48 
 
 39-79 
 
 26-84 
 
 98 
 
 81-25 
 
 5480 
 
 48 
 
 39-32 
 
 27-53 
 
 98 
 
 80-28 
 
 56-21 
 
 49 
 
 40-62 
 
 27-40 
 
 99 
 
 82-07 
 
 55-36 
 
 49 
 
 40-14 
 
 28-11 
 
 99 
 
 81-10 
 
 56-78 
 
 50 
 
 41-45 
 
 27-96 
 
 100 
 
 82-90 
 
 5592 
 
 50 
 
 40-96 
 
 28-68 
 
 100 
 
 8192 
 
 57;36 ; 
 
 
 E. orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E. or W. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS. 
 
 56 
 
 55 
 
TEAVEESE TABLES. 
 
 153 
 
 36 
 
 37 
 
 . 
 
 d 
 
 
 
 a? 
 
 A 
 
 t: 
 
 5*" 
 
 . 
 
 
 
 . 
 
 . 
 
 
 
 jifl 
 
 02' a 
 
 r H 
 
 ; pC 
 
 O) p2 
 
 f g 
 
 = 5 
 
 QQ p3 
 
 P* 
 
 C ^ 
 
 CO p 
 
 r 2 
 
 - -~ 
 
 
 f-i 3 
 
 '. 5c 
 
 -- 56 
 
 1* a3 
 
 "S w> 
 
 ?-i 3 
 
 P * 
 
 """ ^ic 
 
 t-f flS 
 
 c3 
 
 3 P 
 
 o S 
 
 O 02 
 
 i 
 
 30 
 
 O "^ 
 
 5 s 
 
 O * 
 
 O "^ 
 
 g = .2 
 
 O "g^ 
 
 sj 
 
 
 WQ 
 
 3 
 
 S5Q 
 
 a 5 
 
 O; i, 
 
 zo 
 
 s 
 
 11 1 f4 M 
 
 F3Q 
 
 1 
 
 0-81 
 
 0'59 
 
 51 
 
 4T26 
 
 29-98 
 
 1 
 
 0-80 
 
 0-60 
 
 61 
 
 40-73 
 
 30-69 
 
 2 
 
 1-62 
 
 1-18 
 
 52 
 
 42-07 
 
 30-57 
 
 2 
 
 1-60 
 
 1-20 
 
 52 
 
 41-53 
 
 31-29 
 
 3 
 
 2-43 
 
 1-76 
 
 53 
 
 42-88 
 
 31-15 
 
 3 
 
 2-40 
 
 1-81 
 
 53 42-33 
 
 31-90 
 
 4 
 
 3-24 
 
 2-35 
 
 54 
 
 43-69 
 
 31-74 
 
 4 
 
 3-19 
 
 2-41 
 
 54 43-13 
 
 32-50 
 
 5 
 
 4-05 
 
 2-94 
 
 55 
 
 44-50 
 
 3-2-33 
 
 5 
 
 3-99 
 
 3-01 
 
 55 
 
 43-93 
 
 33-10 
 
 6 
 
 4-85 
 
 3-53 
 
 56 
 
 45-31 
 
 32-92 
 
 6 
 
 4-79 
 
 3-61 
 
 56 
 
 44-72 
 
 33-70 
 
 7 
 
 5-66 
 
 4-12 
 
 57 
 
 46-11 
 
 33-50 
 
 7 
 
 5-59 
 
 4-21 
 
 57 
 
 45-52 
 
 34-30 
 
 8 
 
 6-47 
 
 4-70 
 
 58 
 
 46-92 
 
 34-09 
 
 8 
 
 6-39 
 
 4-81 
 
 58 
 
 46-32 
 
 34-90 
 
 9 
 
 7-28 
 
 5"29 
 
 59 
 
 47-73 
 
 34-68 
 
 9 
 
 7-19 
 
 5-42 
 
 59 
 
 47-12 
 
 35-51 
 
 10 
 
 8-09 
 
 5-88 
 
 60 
 
 48-54 
 
 35-27 
 
 10 
 
 7-99 
 
 6-02 
 
 60 
 
 47-92 
 
 36-11 
 
 11 
 
 8-90 
 
 6-47 
 
 61 
 
 49-35 
 
 35-86 
 
 11 
 
 8-79 
 
 6-62 
 
 61 
 
 48-72 
 
 36-71 
 
 12 
 
 9-71 
 
 7-05 
 
 62 
 
 50-16 
 
 36-44 
 
 12 
 
 9-58 
 
 7-22 
 
 62 
 
 49-52 
 
 37-31 
 
 13 
 
 10-52 
 
 7-64 
 
 63 
 
 50-97 
 
 37-03 
 
 13 
 
 10-38 
 
 7-82 
 
 63 
 
 50-31 
 
 37-91 
 
 14 
 
 11-33 
 
 8-23 
 
 64 
 
 51-78 
 
 37-62 
 
 14 
 
 11-18 
 
 8-43 
 
 64 
 
 51-11 
 
 38-52 
 
 15 
 
 12-14 
 
 8-82 
 
 65 
 
 52-59 
 
 38-21 
 
 15 
 
 11-98 
 
 9-03 
 
 65 
 
 51-91 
 
 39-12 
 
 16 
 
 12-94 
 
 9-40 
 
 66 
 
 53-40 
 
 38-79 
 
 16 
 
 12-78 
 
 9-63 
 
 66 
 
 52-71 
 
 39-72 
 
 17 
 
 13-75 
 
 9-99 
 
 67 
 
 54-20 
 
 39-38 
 
 17 
 
 13-58 
 
 10-23 
 
 67 
 
 53-51 
 
 40-32" 
 
 18 
 
 14-56 
 
 10-58 
 
 68 
 
 55-01 
 
 39-97 
 
 18 
 
 14-38 
 
 10-83 
 
 68 
 
 54-31 
 
 40-92 
 
 19 
 
 15-37 
 
 11-17 
 
 69 
 
 55-82 
 
 40-56 
 
 19 
 
 15-17 
 
 11-43 
 
 69 
 
 55-11 
 
 4r52 
 
 20 
 
 16-18 
 
 11-76 
 
 70 
 
 5ti-63 
 
 41-14 
 
 20 
 
 15-97 
 
 12-04 
 
 70 
 
 55-90 
 
 42-13 
 
 21 
 
 16-99 
 
 12-34 
 
 71 
 
 57-44 
 
 41-73 
 
 21 
 
 16-77 
 
 12-64 
 
 71 
 
 56-70 
 
 42-73 
 
 22 
 
 17-80 
 
 12-93 
 
 72 
 
 58-25 
 
 42-32 
 
 22 
 
 17-57 
 
 13-24 
 
 72 
 
 57-50 
 
 43-33 
 
 23 
 
 18-61 
 
 13-62 
 
 73 
 
 59-06 
 
 42-91 
 
 23 
 
 18-37 
 
 13-84 
 
 73 
 
 58-30 
 
 43-93 
 
 24 
 
 19-42 
 
 14-11 
 
 74 
 
 59-87 
 
 43-50 
 
 24 
 
 19-17 
 
 14-44 
 
 74 
 
 69-10 
 
 44-53 
 
 25 
 
 20-23 
 
 14-69 
 
 75 
 
 
 44-08 
 
 25 
 
 19-97 
 
 15-05 
 
 75 
 
 59-90 
 
 45-14 
 
 26 
 
 21-03 
 
 15-28 
 
 76 
 
 61-49 
 
 44-67 
 
 26 
 
 20-76 
 
 15-65 
 
 76 
 
 60-70 
 
 45-74 
 
 27 
 
 21-84 
 
 15-87 
 
 77 
 
 62"29 
 
 45-26 
 
 27 
 
 21-56 
 
 16-25 
 
 77 
 
 61-50 
 
 46-34 
 
 28 
 
 22-65 
 
 16-46 
 
 78 
 
 63-10 
 
 45-85 
 
 28 
 
 22-36 
 
 16-85 
 
 78 
 
 62-29 
 
 46-94 
 
 29 
 
 23-4(3 
 
 17-05 
 
 79 
 
 63-91 
 
 46-44 
 
 29 
 
 23-16 
 
 17-45 
 
 79 
 
 63-09 
 
 47-54 
 
 30 
 
 24-27 
 
 17-63 
 
 80 
 
 64-72 
 
 47-02 
 
 30 
 
 23-96 
 
 18-05 
 
 80 
 
 63-89 
 
 48-14 
 
 31 
 
 25-08 
 
 18-22 
 
 81 
 
 65-53 
 
 47-61 
 
 31 
 
 24-76 
 
 18-66 
 
 81 
 
 64-69 
 
 48-75 
 
 32 
 
 25-89 
 
 18-81 
 
 82 
 
 66-34 
 
 48-20 
 
 32 
 
 25-56 
 
 19-26 
 
 82 
 
 65-49 
 
 49-35 
 
 33 
 
 26-70 
 
 19-40 
 
 83 
 
 67-15 
 
 48-79 
 
 33 
 
 26-36 
 
 19-86 
 
 83 
 
 66-29 
 
 49-95 
 
 34 
 
 27-51 
 
 19-98 
 
 84 
 
 67-96 
 
 49-37 
 
 34 
 
 27-15 
 
 20-46 
 
 81 
 
 67-09 
 
 60-55 
 
 35 
 
 28-32 
 
 20-57 
 
 85 
 
 68-77 
 
 49-96 
 
 35 
 
 27-95 
 
 21-06 
 
 85 
 
 67-83 
 
 51-15 
 
 36 
 
 29-12 
 
 21-16 
 
 86 
 
 69-58 
 
 50-55 
 
 36 
 
 28-75 
 
 21-67 
 
 86 
 
 68-68 
 
 51-76 
 
 37 
 
 29-93 
 
 21-75 
 
 87 
 
 70-38 
 
 51-14 
 
 37 
 
 29-55 
 
 22-27 
 
 87 
 
 69-48 
 
 52-36 
 
 38 
 
 30-74 
 
 22-34 
 
 88 
 
 71-19 
 
 51-73 
 
 38 
 
 30-35 
 
 22-87 
 
 88 
 
 70-28 
 
 52-96 
 
 89 
 
 31-55 
 
 22 -9 i 
 
 89 
 
 72-00 
 
 52-31 
 
 39 
 
 31-15 
 
 23-47 
 
 89 
 
 71-08 
 
 53-56 
 
 40 
 
 32-36 
 
 23-51 
 
 90 
 
 72-81 
 
 52-90 
 
 40 
 
 31-95 
 
 24-07 
 
 90 
 
 71-88 
 
 54-16 
 
 41 
 
 33-17 
 
 24-10 
 
 91 
 
 73-62 
 
 53-49 
 
 41 
 
 32-74 
 
 24-67 
 
 91 
 
 72-68 
 
 54-76 
 
 42 
 
 33-98 
 
 24-69 
 
 92 
 
 74-43 
 
 54-08 
 
 42 
 
 33-54 
 
 25-28 
 
 92 
 
 73-47 
 
 55-37 
 
 43 
 
 34-79 
 
 25-VJ7 
 
 93 
 
 75-24 
 
 64-66 
 
 43 
 
 34-34 
 
 25-88 
 
 93 
 
 74-27 
 
 55-97 
 
 44 
 
 35-HO 
 
 25-86 
 
 94 
 
 76-05 
 
 65-25 
 
 44 
 
 35-14 
 
 26-48 
 
 94 
 
 75-07 
 
 56-57 
 
 45 
 
 36-41 
 
 26-45 
 
 95 
 
 76-36 
 
 55-84 
 
 45 
 
 35-94 
 
 27-08 
 
 95 
 
 75-87 
 
 57-17 
 
 40 
 
 37-21 
 
 27-04 
 
 96 
 
 77-67 
 
 56-43 
 
 46 
 
 36-74 
 
 27-68 
 
 96 
 
 76-67 
 
 57-77 
 
 47 
 
 38-02 
 
 27-63 
 
 97 
 
 78-47 
 
 57-02 
 
 47 
 
 37-54 
 
 28-29 
 
 97 
 
 77-47 
 
 58-38 
 
 48 
 
 38-83 
 
 28-21 
 
 98 
 
 79"28 
 
 57-60 
 
 48 
 
 38-33 
 
 28-89 
 
 98 
 
 78-27 
 
 58-98 
 
 49 
 
 39-64 
 
 28-80 
 
 99 
 
 80M.9 
 
 58-19 
 
 49 
 
 39-13 
 
 29-49 
 
 99 
 
 79-07 
 
 59-58 
 
 60 
 
 40-45 
 
 29-39 
 
 100 
 
 80-90 
 
 68-78 
 
 50 
 
 39-93 
 
 30-09 
 
 100 
 
 79-86 
 
 60-18 
 
 
 E.or W 
 
 N.orS 
 
 
 E.or W 
 
 N.orS 
 
 
 E.or W 
 
 N.orS 
 
 
 E.orW 
 
 N. or S 
 
 54 
 
 53 
 
 H 3 
 
154 
 
 TBAYERSE TABLES. 
 
 38 
 
 39 
 
 hn 
 
 c ^ 
 
 02 
 
 H 
 
 ij 
 
 "I 
 
 1 
 
 il 
 
 05 
 
 f 
 
 rj 
 
 02 
 
 *l 
 
 * 5' 
 
 
 o *j 
 
 g 
 
 S| 
 
 H 
 
 Z 60 
 3! C 
 
 S J 
 
 ! 
 
 SJC 
 
 ~ 
 
 s| 
 
 J 
 
 fcS 
 
 wa 
 
 ^ 
 
 fc"3 
 
 wS 
 
 S 
 
 Q 
 
 HQ 
 
 j 
 
 5 
 
 mo 
 
 1 
 
 0-79 
 
 0-62 
 
 51 
 
 40-19 
 
 31-40 
 
 i 
 
 0-78 
 
 0-63 
 
 51 
 
 39-63 
 
 32-09 
 
 2 
 
 1-58 
 
 1-23 
 
 52 
 
 40-98 
 
 32-01 
 
 2 
 
 1-55 
 
 1-26 
 
 52 
 
 40-41 
 
 32-72 
 
 3 
 
 2-36 
 
 1-85 
 
 53 
 
 41-76 
 
 3263 
 
 3 
 
 2-33 
 
 1-89 
 
 53 
 
 41-19 
 
 33-35 
 
 4 
 
 3-15 
 
 2-46 
 
 54 
 
 42-55 
 
 S3 25 
 
 4 
 
 3-11 
 
 2-52 
 
 54 
 
 41-97 
 
 3398 
 
 5 
 
 394 
 
 3-08 
 
 55 
 
 43-34 
 
 33-86 
 
 5 
 
 3-89 
 
 3-15 
 
 55 
 
 42-74 
 
 34-61 
 
 6 
 
 4-73 
 
 3-69 
 
 56 
 
 44-13 
 
 34-48 
 
 6 
 
 4-66 
 
 3-78 
 
 56 
 
 43-52 
 
 35-24 
 
 7 
 
 5-52 
 
 4-31 
 
 57 
 
 44-92 
 
 35-09 
 
 7 
 
 5-44 
 
 4-41 
 
 67 
 
 44-30 
 
 35-87 
 
 8 
 
 6-30 
 
 4-93 
 
 58 
 
 4570 
 
 35-71 
 
 8 
 
 6-22 
 
 5-03 
 
 58 
 
 45-07 
 
 36-50 
 
 9 
 
 7-09 
 
 5-54 
 
 59 
 
 46-49 
 
 36-32 
 
 9 
 
 6-99 
 
 5-66 
 
 59 
 
 45-85 
 
 3713 
 
 10 
 
 7-88 
 
 6-16 
 
 60 
 
 47-28 
 
 36-94 
 
 10 
 
 7-77 
 
 629 
 
 60 
 
 46-63 
 
 37-76 
 
 11 
 
 8-67 
 
 6-77 
 
 61 
 
 48-07 
 
 37-56 
 
 11 
 
 8-55 
 
 6-92 
 
 61 
 
 47-41 
 
 38-39 
 
 12 
 
 9-46 
 
 7-39 
 
 62 
 
 48-86 
 
 38-17 
 
 12 
 
 9-33 
 
 7-55 
 
 62 
 
 48-18 
 
 39-02 
 
 13 
 
 10-24 
 
 8-00 
 
 63 
 
 49-64 
 
 38-79 
 
 13 
 
 10-10 
 
 8-18 
 
 63 
 
 48-96 
 
 3965 
 
 14 
 
 11-03 
 
 8-62 
 
 64 
 
 50-43 
 
 39-40 
 
 14 
 
 10-88 
 
 8-81 
 
 64 
 
 49-74 
 
 40-28 
 
 15 
 
 11-82 
 
 9-23 
 
 65 
 
 51-22 
 
 40-02 
 
 15 
 
 11-66 
 
 9-44 
 
 65 
 
 50-51 
 
 40-91 
 
 16 
 
 12-61 
 
 9-85 
 
 66 
 
 52-01 
 
 4063 
 
 16 
 
 12-43 
 
 1007 
 
 66 
 
 51-29 
 
 41-53 
 
 17 
 
 13-40 
 
 10-47 
 
 67 
 
 52-80 
 
 4125 
 
 17 
 
 13-21 
 
 10-70 
 
 67 
 
 5207 
 
 4216 
 
 18 
 
 14-18 
 
 11-08 
 
 68 
 
 53-68 
 
 41-86 
 
 18 
 
 13-99 
 
 1133 
 
 68 
 
 52-85 
 
 42-79 
 
 19 
 
 14-97 
 
 11-70 
 
 69 
 
 54-37 
 
 42-48 
 
 19 
 
 14-77 
 
 1196 
 
 69 
 
 53-62 
 
 43-42 
 
 20 
 
 15-76 
 
 12-31 
 
 70 
 
 5516 
 
 43-10 
 
 20 
 
 15-54 
 
 12-59 
 
 70 
 
 54-40 
 
 44-05 
 
 21 
 
 16-55 
 
 12-93 
 
 71 
 
 55-95 
 
 4371 
 
 21 
 
 16-32 
 
 13-22 
 
 71 
 
 55-18 
 
 44-68 
 
 22 
 
 17-34 
 
 1354 
 
 72 
 
 56-74 
 
 4433 
 
 22 
 
 17-10 
 
 13-84 
 
 72 
 
 55-95 
 
 45-31 
 
 23 
 
 18-12 
 
 14-16 
 
 73 
 
 57-52 
 
 44-94 
 
 23 
 
 1787 
 
 14-47 
 
 73 
 
 56-73 
 
 45-94 
 
 24 
 
 18-91 
 
 14-78 
 
 74 
 
 58-31 
 
 45-56 
 
 24 
 
 18-65 
 
 15-10 
 
 74 
 
 57-51 
 
 4657 
 
 25 
 
 1970 
 
 15-39 
 
 75 
 
 59-10 
 
 46-17 
 
 25 
 
 19-43 
 
 15-73 
 
 75 
 
 58 29 
 
 47-20 
 
 26 
 
 20-49 
 
 16-01 
 
 76 
 
 59-89 
 
 46-79 
 
 26 
 
 20-21 
 
 16-36 
 
 76 
 
 5906 
 
 47-83 
 
 27 
 
 21-28 
 
 16-62 
 
 77 
 
 60-68 
 
 47-41 
 
 27 
 
 20-98 
 
 1699 
 
 77 
 
 5984 
 
 48-46 
 
 28 
 
 22-06 
 
 1724 
 
 78 
 
 61-46 
 
 48-02 
 
 28 
 
 2176 
 
 17-62 
 
 78 
 
 60-62 
 
 49-09 
 
 29 
 
 22-85 
 
 17-85 
 
 79 
 
 62-25 
 
 48-64 
 
 29 
 
 22-54 
 
 18-25 
 
 79 
 
 61-39 
 
 49-72 
 
 30 
 
 23-64 
 
 18-47 
 
 80 
 
 63-04 
 
 49-25 
 
 30 
 
 23-31 
 
 18-88 
 
 80 
 
 62-17 
 
 50-34 
 
 31 
 
 24-43 
 
 19-09 
 
 81 
 
 63-83 
 
 49-87 
 
 31 
 
 24-09 
 
 19-51 
 
 81 
 
 62-95 
 
 50-97 
 
 32 
 
 2522 
 
 19-70 
 
 82 
 
 64-62 
 
 50-48 
 
 32 
 
 24-87 
 
 20-14 
 
 82 
 
 63-73 
 
 51-60 
 
 33 
 
 2600 
 
 20-32 
 
 83 
 
 65-40 
 
 51-10 
 
 33 
 
 25-65 
 
 20-77 
 
 83 
 
 64-50 
 
 52-23 
 
 34 
 
 26-79 
 
 20-93 
 
 84 
 
 66-19 
 
 51-72 
 
 34 
 
 2642 
 
 21-40 
 
 84 
 
 65-28 
 
 52-86 
 
 35 
 
 27-58 
 
 21-55 
 
 85 
 
 66-98 
 
 52-33 
 
 35 
 
 27-20 
 
 22-03 
 
 85 
 
 66-06 
 
 5349 
 
 36 
 
 28-37 
 
 2216 
 
 86 
 
 67-77 
 
 52-95 
 
 36 
 
 27-93 
 
 22-66 
 
 86 
 
 66-83 
 
 54-12 
 
 37 
 
 29-13 
 
 22-78 
 
 87 
 
 6856 
 
 53-56 
 
 37 
 
 28-75 
 
 23-28 
 
 87 
 
 67-61 
 
 54-75 
 
 38 
 
 29-94 
 
 23-40 
 
 88 
 
 6934 
 
 54-18 
 
 38 
 
 29-53 
 
 23-91 
 
 88 
 
 68-39 
 
 55-38 
 
 39 
 
 30-73 
 
 2401 
 
 89 
 
 70-13 
 
 54-79 
 
 39 
 
 30-31 
 
 24-54 
 
 89 
 
 69-17 
 
 56-01 
 
 40 
 
 31-52 
 
 24-63 
 
 90 
 
 70-92 
 
 5541 
 
 40 
 
 31-09 
 
 25-17 
 
 90 
 
 69-94 
 
 56-64 
 
 41 
 
 32-31 
 
 25-24 
 
 91 
 
 71-71 
 
 56-03 
 
 41 
 
 3186 
 
 25-80 
 
 91 
 
 70-72 
 
 57-27 
 
 42 
 
 33-10 
 
 25-86 
 
 92 
 
 72-50 
 
 56-64 
 
 42 
 
 32-64 
 
 26-43 
 
 92 
 
 71'50 
 
 57-90 
 
 43 
 
 33-88 
 
 26-47 
 
 93 
 
 73-28 
 
 57-26 
 
 43 
 
 33-42 
 
 2706 
 
 93 
 
 72-27 
 
 58-53 
 
 44 
 
 34-67 
 
 27-09 
 
 94 
 
 74-07 
 
 57-87 
 
 44 
 
 34-19 
 
 27-69 
 
 94 
 
 73-05 
 
 5916 
 
 45 
 
 35-46 
 
 2770 
 
 95 
 
 74-86 
 
 58-49 
 
 45 
 
 34-97 
 
 28-32 
 
 95 
 
 73-83 
 
 59-78 
 
 46 
 
 36-25 
 
 28-32 
 
 96 
 
 75-65 
 
 59-10 
 
 46 
 
 35-75 
 
 28-95 
 
 96 
 
 74-61 
 
 60-41 
 
 47 
 
 37-04 
 
 28-94 
 
 97 
 
 76-44 
 
 59-72 
 
 47 
 
 3653 
 
 2958 
 
 97 
 
 75-38 
 
 61-04 
 
 48 
 
 3782 
 
 29-55 
 
 98 
 
 77-22 
 
 60-33 
 
 48 
 
 37-30 
 
 30-21 
 
 98 
 
 76-16 
 
 61-67 
 
 49 
 
 3861 
 
 30-17 
 
 99 
 
 78-01 
 
 60-95 
 
 49 
 
 33-08 
 
 30-84 
 
 99 
 
 76-94 
 
 62-30 
 
 50 
 
 39-40 
 
 30-78 
 
 100 
 
 78-80 
 
 61-57 
 
 50 
 
 38-86 
 
 31-47 
 
 ICO 
 
 77-72 
 
 62-93 
 
 
 E.orW 
 
 N.orS 
 
 
 E.orW 
 
 N. or S 
 
 
 E.orW 
 
 N.orS 
 
 |E. or W.j N.orS. 
 
 52 
 
 51 
 
TEAVEESE TABLES. 
 
 155 
 
 40 
 
 41 
 
 . 
 
 iJC ' 
 
 s 
 
 ft 
 
 rd 
 
 "I 
 
 ft 
 
 r| 
 
 oil 
 
 ft 
 
 d 
 
 ?i 
 
 ft 
 
 ' tc 
 
 Ti C 
 
 k, cs 
 o ** 
 
 3* 
 
 it 
 
 
 
 1 
 
 It 
 
 S* 
 
 8j 
 
 C M 
 o c 
 
 ij 
 
 i 
 
 St-S 
 
 aS 
 
 wa 
 
 | 
 
 Q 
 
 si 5 
 
 Z3 
 
 *3 
 
 w"5 
 
 z$ 
 
 fcS 
 
 s'S 
 
 1 
 
 0-77 
 
 0-64 
 
 51 39-07 
 
 32-78 
 
 i 
 
 0-75 
 
 0-66 
 
 51 
 
 38-49 
 
 33-46 
 
 2 
 
 1-33 
 
 1-29 
 
 52 
 
 39-83 
 
 33-43 
 
 2 
 
 1-51 
 
 1-31 
 
 52 
 
 39-24 
 
 34-12 
 
 3 
 
 2-30 
 
 1-93 
 
 53 
 
 40-60 
 
 34-07 
 
 3 
 
 2-26 
 
 1-97 
 
 53 
 
 40-00 
 
 34-77 
 
 4 
 
 3-06 
 
 2-57^ 
 
 54 
 
 41-37 
 
 34-71 
 
 4 
 
 3-02 
 
 2-62 
 
 54 
 
 40-75 
 
 35-43 
 
 5 
 
 3-81 
 
 3-21 
 
 55 
 
 42-13 
 
 35-35 
 
 5 
 
 3-77 
 
 3-28 
 
 55 
 
 41-51 
 
 36-08 
 
 6 
 
 4-60 
 
 3-86 
 
 56 
 
 42-90 
 
 36-00 
 
 6 
 
 4-53 
 
 3-94 
 
 56 
 
 42-26 
 
 36-74 
 
 7 
 
 5-36 
 
 4-50 
 
 57 
 
 43-66 
 
 36-64 
 
 7 
 
 5-28 
 
 4-59 
 
 57 
 
 43-02 
 
 37-40 
 
 8 
 
 6-13 
 
 5-14 
 
 58 
 
 44-43 
 
 37-28 
 
 8 
 
 6-04 
 
 5-25 
 
 58 
 
 43-77 
 
 38-05 
 
 9 
 
 6-89 
 
 5-79 
 
 59 
 
 45-20 
 
 37-93 
 
 9 
 
 6-79 
 
 5-90 
 
 59 
 
 44-53 
 
 38-71 
 
 10 
 
 7-66 
 
 6-43 
 
 60 
 
 45-96 
 
 38-57 
 
 10 
 
 7-55 
 
 6-56 
 
 60 
 
 45-28 
 
 39-36 
 
 11 
 
 8-43 
 
 7-07 
 
 61 
 
 46-73 
 
 39-21 
 
 11 
 
 8-30 
 
 7-22 
 
 61 
 
 46-04 
 
 40'02 
 
 12 
 
 9-19 
 
 7-71 
 
 62 
 
 47-49 
 
 39-85 
 
 12 
 
 9-06 
 
 7-37 
 
 62 
 
 46-79 
 
 40-68 
 
 13 
 
 9-96 
 
 8-36 
 
 63 
 
 48-26 
 
 40-50 
 
 13 
 
 9-81 
 
 8-53 
 
 63 
 
 47-55 
 
 41-33 
 
 14 
 
 10-72 
 
 9-00 
 
 64 
 
 49-03 
 
 41-14 
 
 14 
 
 10-57 
 
 9-18 
 
 64 
 
 48-30 
 
 41-99 
 
 15 
 
 11-49 
 
 9-64 
 
 65 
 
 49-79 
 
 41-78 
 
 15 
 
 11-32 
 
 9-84 
 
 65 
 
 49-06 
 
 42-64 
 
 16 
 
 12-26 
 
 10-28 
 
 66 
 
 50-56 
 
 42-43 
 
 16 
 
 12-08 
 
 10-50 
 
 66 
 
 49-81 
 
 43-30 
 
 17 
 
 13-02 
 
 10-93 
 
 67 
 
 51-32 
 
 43-07 
 
 17 
 
 12-83 
 
 11-15 
 
 67 
 
 50-57 
 
 43-96 
 
 18 
 
 13-79 
 
 11-57 
 
 63 
 
 52-09 
 
 43-71 
 
 18 13-58 
 
 11-81 
 
 68 
 
 51-32 
 
 44-61 
 
 19 
 
 14-55 
 
 12-21 
 
 69 
 
 52-86 
 
 44-35 
 
 19 ! 14-34 
 
 12-47 
 
 69 
 
 52-07 
 
 45-27 
 
 20 
 
 15-32 
 
 12-86 
 
 70 
 
 53-62 
 
 45-00 
 
 20 
 
 15-09 
 
 13-12 
 
 70 
 
 52-83 
 
 45-92 
 
 21 
 
 16-09 
 
 13-50 
 
 71 
 
 54-39 
 
 45-64 
 
 21 
 
 15-85 
 
 13-78 
 
 71 
 
 53-58 
 
 46-58 
 
 22 
 
 16-85 
 
 14-14 
 
 72 
 
 55'15 
 
 46"28 
 
 22 
 
 16-60 
 
 14-43 
 
 72 
 
 54-34 
 
 47-24 
 
 23 
 
 17-62 
 
 14-78 
 
 73 
 
 55-92 
 
 46-92 
 
 23 
 
 17-36 
 
 15-09 
 
 73 
 
 55-09 
 
 47-89 
 
 24 
 
 18-38 
 
 15-43 
 
 74 
 
 58-69 
 
 47-57 
 
 24 
 
 18-11 
 
 15-75 
 
 74 
 
 55-85 
 
 48-55 
 
 25 
 
 19-15 
 
 16-07 
 
 75 
 
 57-45 
 
 48-21 
 
 25 
 
 18-37 
 
 16-40 
 
 75 
 
 56-60 
 
 49-20 
 
 26 
 
 19-92 
 
 16-71 
 
 76 
 
 58-22 
 
 48-85 
 
 26 
 
 19-62 
 
 17-06 
 
 76 
 
 57-36 
 
 49-86 
 
 27 
 
 20-68 
 
 17-36 
 
 77 
 
 58-99 
 
 49-49 
 
 27 
 
 20-38 
 
 17-71 
 
 77 
 
 58-11 
 
 50-52 
 
 28 
 
 21-45 
 
 18-00 
 
 78 
 
 59-75 
 
 50-14 
 
 28 
 
 21-13 
 
 18-37 
 
 78 
 
 58-87 
 
 51-17 
 
 29 
 
 22-21 
 
 18-64 
 
 79 
 
 60-52 
 
 50-78 
 
 29 
 
 21-89 
 
 19-03 
 
 79 
 
 59-62 
 
 51-83 
 
 30 
 
 22-98 
 
 19-28 
 
 80 
 
 61-30 
 
 ,31-42 
 
 30 
 
 22-64 
 
 19-68 
 
 80 
 
 60-38 
 
 52-48 
 
 
 
 
 
 
 
 
 
 
 
 
 
 31 
 
 23-75 
 
 19-93 
 
 61 
 
 62-05 
 
 52-07 
 
 31 
 
 23-40 
 
 20-34 
 
 81 
 
 61-13 
 
 53-14 
 
 82 
 
 24-51 
 
 20-57 
 
 82 
 
 62-82 
 
 52-71 
 
 32 
 
 24-15 
 
 20-99 
 
 82 
 
 61-89 
 
 53-80 
 
 83 
 
 25-28 
 
 21-21 
 
 83 
 
 62-56 53-35 
 
 33 24-91 
 
 21-65 
 
 83 
 
 62-64 
 
 54-45 
 
 34 
 
 26-05 
 
 21-85 
 
 84 
 
 64 -35 
 
 53-99 
 
 34 25-66 
 
 22-31 
 
 84 
 
 63-40 
 
 55-11 
 
 35 
 
 26-81 
 
 22-50 
 
 85 
 
 65-11 
 
 51-64 
 
 35 26-41 
 
 22-96 
 
 85 
 
 64-15 
 
 56-77 
 
 36 
 
 27-58 
 
 23-14 
 
 86 
 
 65-88 
 
 55-28 
 
 36 
 
 27-17 
 
 23-62 
 
 86 
 
 64-91 
 
 56-42 
 
 37 
 
 28-34 
 
 23-78 
 
 87 
 
 66-65 
 
 55-92 
 
 37 
 
 27-92 
 
 24-27 
 
 87 
 
 65-66 
 
 57-08 
 
 38 
 
 29-11 
 
 24-43 
 
 88 
 
 67-41 
 
 56-57 
 
 38 28-68 
 
 24-93 
 
 88 
 
 66-41 
 
 57-73 
 
 39 
 
 29-88 
 
 25-07 
 
 89 
 
 68-18 
 
 57-21 
 
 39 
 
 29-43 
 
 25-59 
 
 89 
 
 67-17 
 
 56-39 
 
 40 
 
 30-64 
 
 25-71 
 
 90 
 
 68-94 
 
 57-85 
 
 40 
 
 30-19 
 
 26-24 
 
 90 
 
 67-92 
 
 59-05 
 
 41 
 
 31-41 
 
 26-35 
 
 91 
 
 69-71 
 
 58-49 
 
 41 30-94 
 
 26-90 
 
 91 
 
 68-66 
 
 59-70 
 
 42 
 
 32-17 
 
 27-00 
 
 92 
 
 70-48 
 
 59-14 
 
 42 
 
 31-70 
 
 27-55 
 
 92 69-43 
 
 60-36 
 
 43 
 
 32-94 
 
 27-64 
 
 93 
 
 71-24 
 
 59-78 
 
 43 
 
 32-45 
 
 28-21 
 
 93 70-19 
 
 61-01 
 
 44 
 
 33-71 
 
 28-28 
 
 94 
 
 72-01 
 
 60-42 
 
 44 
 
 33-21 
 
 28-87 
 
 94 70-94 
 
 61-67 
 
 45 
 
 34-47 
 
 28-93 
 
 95 
 
 72-77 
 
 61-07 
 
 45 33-96 
 
 29-52 
 
 93 71-70 
 
 62-33 
 
 4-; 
 
 35-24 
 
 29-57 
 
 96 
 
 73-54 
 
 61-71 
 
 46 34-72 
 
 30-18 
 
 96 i 72-45 
 
 62-98 
 
 47 
 
 36'CO 
 
 30-21 
 
 97 
 
 74-31 
 
 62-35 
 
 47 
 
 35-47 
 
 30-83 
 
 97 73-21 
 
 63-64 
 
 48 
 
 36-77 
 
 30-85 
 
 98 
 
 75-07 
 
 62-99 
 
 48 
 
 36-23 
 
 31-49 
 
 98 73-96 
 
 64-29 
 
 49 
 
 37-54 
 
 31-50 
 
 99 
 
 75-81 
 
 63-64 
 
 49 
 
 36-98 
 
 32-15 
 
 99 74-72 
 
 64-95 
 
 50 
 
 38-18 
 
 32-14 
 
 100 
 
 76-60 
 
 64-28 
 
 
 
 37-74 
 
 32-80 
 
 100 ! 75-47 
 
 65-61 
 
 
 E. or W 
 
 N.orS. 
 
 
 E.or W. 
 
 N. or S. 
 
 
 E.or W. 
 
 N.orS. 
 
 E.orW 
 
 N. or S. 
 
 50 
 
 1 
 
156 
 
 TKA.YEKSE TABLES. 
 
 42 
 
 43 
 
 M 
 
 ri| 
 
 *'! 
 
 5PJ 
 
 CO g 
 
 | 
 
 gJ 
 
 rf| 
 
 'I 
 
 spj 
 
 rf| 
 
 M 
 
 if 
 
 ol 
 
 o -g 
 
 i C 
 
 i* a 
 
 O '*-' 
 
 o| 
 
 It 
 
 s| 
 
 l 
 
 5 c 
 
 o +* 
 
 fcJ 
 
 33 
 
 fc5 
 
 wS 
 
 
 &5 
 
 HQ 
 
 33 
 
 fc 
 
 w3 
 
 
 SB a 
 
 w'S 
 
 j 
 
 0-74 
 
 0-67 
 
 51 
 
 37-90 
 
 34-13 
 
 i 
 
 0-73 
 
 0-68 
 
 51 
 
 37-30 
 
 34-78 
 
 2 
 
 1-49 
 
 1-34 
 
 52 
 
 38-64 
 
 34-79 
 
 2 
 
 1-46 
 
 1-36 
 
 52 
 
 38-03 
 
 
 3 
 
 2-23 
 
 2-01 
 
 53 
 
 39-39 
 
 35-46 
 
 3 
 
 2-19 
 
 2-05 
 
 53 
 
 38-76 
 
 36-15 
 
 4 
 
 2-97 
 
 2-68 
 
 54 
 
 40-13 
 
 36-13 
 
 4 
 
 2-93 
 
 2-73 
 
 54 
 
 39-49 
 
 36-83 
 
 5 
 
 372 
 
 3-35 
 
 55 
 
 40-87 
 
 3680 
 
 5 
 
 3-66 
 
 3-41 
 
 55 
 
 40-22 
 
 37-51 
 
 6 
 
 4-46 
 
 4-01 
 
 56 
 
 41-62 
 
 37-47 
 
 6 
 
 4-39 
 
 4-09 
 
 56 
 
 40-96 
 
 38-19 
 
 7 
 
 5-20 
 
 5-68 
 
 57 
 
 42-36 
 
 38-14 
 
 7 
 
 5-12 
 
 4-77 
 
 57 
 
 41-69 
 
 38-87 
 
 8 
 
 5-95 
 
 5-35 
 
 58 
 
 43-10 
 
 38-81 
 
 8 
 
 5-85 
 
 5-46 
 
 58 
 
 4242 
 
 39-56 
 
 9 
 
 6-69 
 
 6-02 
 
 59 
 
 43-85 
 
 39-48 
 
 9 
 
 658 
 
 6-14 
 
 59 
 
 43-15 
 
 40-24 
 
 10 
 
 7-43 
 
 6-69 
 
 60 
 
 44-59 
 
 40-15 
 
 10 
 
 7-31 
 
 6-82 
 
 60 
 
 43-88 
 
 40-92 
 
 11 
 
 8-17 
 
 7-36 
 
 61 
 
 45-33 
 
 40-82 
 
 11 
 
 804 
 
 7-50 
 
 61 
 
 44-61 
 
 41-60 
 
 12 
 
 9-92 
 
 8-03 
 
 62 
 
 46-07 
 
 41-49 
 
 12 
 
 8-78 
 
 8-18 
 
 62 
 
 45-34 
 
 42-28 
 
 13 
 
 9-66 
 
 8-70 
 
 63 
 
 46-82 
 
 42-16 
 
 13 
 
 9-51 
 
 8-87 
 
 63 
 
 46-08 
 
 42-97 
 
 14 
 
 10-40 
 
 9-37 
 
 64 
 
 47-56 
 
 42-82 
 
 14 
 
 10-24 
 
 9-55 
 
 64 
 
 46-81 
 
 43-65 
 
 15 
 
 11-15 
 
 10-04 
 
 65 
 
 48-30 
 
 43-49 
 
 15 
 
 10-97 
 
 10-23 
 
 65 
 
 47-54 
 
 44-33 
 
 16 
 
 11-89 
 
 10-71 
 
 66 
 
 49-05 
 
 44-16 
 
 16 
 
 11-70 
 
 10-91 
 
 66 
 
 48-27 
 
 45-01 
 
 17 
 
 12-63 
 
 11-38 
 
 67 
 
 49-79 
 
 4483 
 
 17 
 
 12-43 
 
 11-59 
 
 67 
 
 49-00 
 
 45-69 
 
 18 
 
 13-38 
 
 12-04 
 
 68 
 
 50-53 
 
 45-50 
 
 18 
 
 13-16 
 
 12-28 
 
 68 
 
 49-73 
 
 46-38 
 
 19 
 
 14-12 
 
 12-71 
 
 69 
 
 51-28 
 
 46-17 
 
 19 
 
 13-90 
 
 1296 
 
 69 
 
 50-46 
 
 47-06 
 
 20 
 
 14-86 
 
 13-38 
 
 70 
 
 52-02 
 
 46-84 
 
 20 
 
 14-63 
 
 1364 
 
 70 
 
 51-19 
 
 47-74 
 
 21 
 
 15-61 
 
 14-05 
 
 71 
 
 5276 
 
 47-51 
 
 21 
 
 15-36 
 
 14-32 
 
 71 
 
 51-93 
 
 48-42 
 
 22 
 
 16-35 
 
 14-72 
 
 72 
 
 53-51 
 
 48-18 
 
 22 
 
 16-09 
 
 15-00 
 
 72 
 
 52-66 
 
 49-10 
 
 23 
 
 17-09 
 
 15-39 
 
 73 
 
 54-25 
 
 48-85 
 
 23 
 
 1682 
 
 1569 
 
 73 
 
 53-39 
 
 49-79 
 
 24 
 
 17-84 
 
 16-06 
 
 74 
 
 54-99 
 
 49-52 
 
 24 
 
 17-55 
 
 16-37 
 
 74 
 
 54'12 
 
 50-47 
 
 25 
 
 18-58 
 
 16-73 
 
 75 
 
 55-59 
 
 49-79 
 
 25 
 
 18-28 
 
 17-05 
 
 75 
 
 5485 
 
 51-15 
 
 26 
 
 19-32 
 
 17-40 
 
 76 
 
 56-48 
 
 50-85 
 
 26 
 
 19-02 
 
 17-73 
 
 76 
 
 55-58 
 
 51-83 
 
 27 
 
 20-06 
 
 18-07 
 
 77 
 
 57-22 
 
 51-52 
 
 27 
 
 19-75 
 
 18-41 
 
 77 
 
 56-31 
 
 52-51 
 
 28 
 
 20-81 
 
 18-74 
 
 78 
 
 57-96 
 
 52-19 
 
 28 
 
 20-48 
 
 19-10 
 
 78 
 
 57-05 
 
 53-20 
 
 29 
 
 21-55 
 
 19-40 
 
 79 
 
 58-71 
 
 5286 
 
 29 
 
 21-21 
 
 19-78 
 
 79 
 
 57-78 
 
 53-88 
 
 30 
 
 22-29 
 
 20-07 
 
 80 
 
 59-45 
 
 53-53 
 
 30 
 
 21-94 
 
 20-46 
 
 80 
 
 58-51 
 
 54-56 
 
 31 
 
 23-04 
 
 20-74 
 
 81 
 
 60-19 
 
 54-20 
 
 31 
 
 22-67 
 
 21-14 
 
 81 
 
 59-24 
 
 55-24 
 
 32 
 
 23-78 
 
 21-41 
 
 82 
 
 60-94 
 
 51-87 
 
 32 
 
 23-40 
 
 21-82 
 
 82 
 
 59-97 
 
 56-92 
 
 33 
 
 24-52 
 
 22-08 
 
 83 
 
 61-68 
 
 55-54 
 
 33 
 
 24-13 
 
 2251 
 
 83 
 
 60-70 
 
 56-61 
 
 34 
 
 25-27 
 
 22-75 
 
 84 
 
 62-42 
 
 56-21 
 
 34 
 
 24-87 
 
 23-19 
 
 84 
 
 61-43 
 
 57-29 
 
 35 
 
 26-01 
 
 23-42 
 
 85 
 
 63-17 
 
 56-88 
 
 35 
 
 25-60 
 
 23-87 
 
 85 
 
 62-16 
 
 57-97 
 
 36 
 
 26-75 
 
 24-09 
 
 86 
 
 63-91 
 
 57-55 
 
 36 
 
 26-33 
 
 24-55 
 
 86 
 
 62-90 
 
 58-65 
 
 37 
 
 27-50 
 
 24-76 
 
 87 
 
 64-65 
 
 58-21 
 
 37 
 
 27-06 
 
 25-23 
 
 87 
 
 63-63 
 
 59-33 
 
 38 
 
 28-24 
 
 25-43 
 
 88 
 
 65-40 
 
 58-88 
 
 38 
 
 27-79 
 
 25-92 
 
 88 
 
 64-36 
 
 60-02 
 
 39 
 
 28-98 
 
 26-10 
 
 89 
 
 66-14 
 
 59-55 
 
 39 
 
 28-52 
 
 26-60 
 
 89 
 
 65-09 
 
 60-70 
 
 40 
 
 29-73 
 
 26-80 
 
 90 
 
 66-88 
 
 60-22 
 
 40 
 
 2925 
 
 27-28 
 
 90 
 
 65-82 
 
 61-38 
 
 41 
 
 30-47 
 
 27-43 
 
 91 
 
 67-63 
 
 60-89 
 
 41 
 
 2999 
 
 27-96 
 
 91 
 
 66-55 
 
 61-06 
 
 42 
 
 31-21 
 
 28-10 
 
 92 
 
 68-37 
 
 61-56 
 
 42 
 
 30-72 
 
 28-64 
 
 92 
 
 67-28 
 
 62-74 
 
 43 
 
 31-96 
 
 28-77 
 
 93 
 
 69-11 
 
 62-23 
 
 43 
 
 31-45 
 
 29-33 
 
 93 
 
 68-02 
 
 63-43 
 
 44 
 
 32-70 
 
 29-44 
 
 94 
 
 69-86 
 
 62-90 
 
 44 
 
 32-18 
 
 30-01 
 
 94 
 
 68-75 
 
 6411 
 
 45 
 
 33-44 
 
 30-11 
 
 95 
 
 70-60 
 
 63-57 
 
 45 
 
 32-91 
 
 30-69 
 
 95 
 
 69-48 
 
 64-79 
 
 46 
 
 34-18 
 
 30-78 
 
 96 
 
 71-34 
 
 64-24 
 
 46 
 
 33-64 
 
 31-37 
 
 96 
 
 70-21 
 
 65-47 
 
 47 
 
 34-93 
 
 31-45 
 
 97 
 
 72-08 
 
 64-91 
 
 47 
 
 34-37 
 
 32-05 
 
 97 
 
 70-94 
 
 66-15 
 
 48 
 
 35-67 
 
 32-12 
 
 98 
 
 72-83 
 
 65-57 
 
 48 
 
 35-10 
 
 32-74 
 
 98 
 
 71-67 
 
 66-84 
 
 49 
 
 36-41 
 
 3279 
 
 99 
 
 73-57 
 
 66-24 
 
 49 
 
 35-84 
 
 33-42 
 
 99 
 
 72-40 
 
 67-52 
 
 50 
 
 37-20 
 
 33-50 
 
 100 
 
 74-31 
 
 66-91 
 
 50 
 
 36-57 
 
 34-10 
 
 ICO 
 
 73-14 
 
 68-20 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.orS. 
 
 
 E.orW. 
 
 N. or S. 
 
 
 E.orW. 
 
 N.or S. 
 
 48 
 
 47 
 
TRAVERSE TABLES. 
 
 157 
 
 44 
 
 45 
 
 
 . 
 
 
 I " ' 
 
 
 
 
 
 
 . 
 
 2fjc! 
 
 rh * 
 
 M 
 
 SfjS 
 
 
 *J 
 
 60 JS 
 
 to | 
 
 fe S 
 
 ifi^- 
 
 to * 
 
 fe S 
 
 5 z 
 
 l 
 
 
 it 
 
 si 
 
 
 11 
 
 g| 
 
 c| 
 
 gte 
 
 c C 
 
 c *; 
 
 o| 
 
 
 ft A 
 
 H'S 
 
 
 .5 . .s 
 
 fcQ SO 
 
 (33 
 
 fc5 
 
 w5 
 
 83 
 
 fc'S 
 
 WQ 
 
 1 
 
 0-72 
 
 0-69 
 
 51 
 
 36-69 
 
 35-43 
 
 1 
 
 0-71 
 
 0-71 
 
 51 
 
 36-06 
 
 36-06 
 
 2 
 
 1-44 
 
 1-39 
 
 52 
 
 37-41 
 
 36-12 
 
 2 
 
 1-41 
 
 1-41 
 
 52 
 
 36-77 
 
 36-77 
 
 3 
 
 2-16 
 
 2-08 
 
 53 
 
 38-13 
 
 36-82 
 
 3 
 
 2-12 
 
 2-12 
 
 53 
 
 37-48 
 
 37-48 
 
 4 
 
 2-88 
 
 2-78 
 
 54 
 
 38-84 
 
 37-51 
 
 4 
 
 2-83 
 
 2-83 
 
 54 
 
 38-18 
 
 38-18 
 
 5 
 
 3-60 
 
 3-47 
 
 55 
 
 39-56 
 
 38-21 
 
 5 
 
 3-54 
 
 3-54 
 
 55 
 
 38-89 
 
 38-89 
 
 6 
 
 4-32 
 
 4-17 
 
 56 
 
 40-28 
 
 38-90 
 
 6 
 
 4-24 
 
 4-24 
 
 56 
 
 39-60 
 
 39-60 
 
 7 
 
 5-04 
 
 4-86 
 
 57 
 
 41-00 
 
 39-60 
 
 7 
 
 4-95 
 
 4-95 
 
 57 
 
 40-31 
 
 40-31 
 
 8 
 
 5-75 
 
 5-55 
 
 58 
 
 41-72 
 
 40-29 
 
 8 
 
 5-66 
 
 5-66 
 
 58 
 
 41-01 
 
 41-01 
 
 9 
 
 6'47 
 
 6-25 
 
 59 
 
 42-44 
 
 49-98 
 
 9 
 
 6-36 
 
 6-36 
 
 59 
 
 41-72 
 
 41-72 
 
 10 
 
 7-19 
 
 6-95 
 
 60 
 
 43-16 
 
 41-68 
 
 10 
 
 7-07 
 
 7-07 
 
 60 
 
 42-43 
 
 42-43 
 
 11 
 
 7-91 
 
 7-64 
 
 61 
 
 43-88 
 
 42-37 
 
 11 
 
 7-78 
 
 7-78 
 
 61 
 
 43-13 
 
 43-13 
 
 12 
 
 8-63 
 
 8-34 
 
 62 
 
 44-60 
 
 42-07 
 
 12 
 
 8-49 
 
 8-49 
 
 62 
 
 43-84 
 
 43-84 
 
 13 
 
 9-35 
 
 9-03 
 
 63 
 
 45-32 
 
 43-76 
 
 13 
 
 9-19 
 
 9-19 
 
 63 
 
 44-55 
 
 44-55 
 
 14 
 
 10-07 
 
 9-73 
 
 64 
 
 46-04 
 
 44-46 
 
 14 
 
 990 
 
 9-90 
 
 64 
 
 45-26 
 
 45-26 
 
 15 
 
 10-79 
 
 10-42 
 
 65 
 
 46-76 
 
 45-15 
 
 15 
 
 10-61 
 
 10-61 
 
 65 
 
 45-96 
 
 45-96 
 
 16 
 
 
 11-11 
 
 66 
 
 47-48 
 
 45-85 
 
 16 
 
 11-31 
 
 11-31 
 
 66 
 
 46-67 
 
 46-67 
 
 17 
 
 12-23 
 
 11-81 
 
 67 
 
 48-20 
 
 46-54 
 
 17 
 
 12-02 
 
 12-02 
 
 67 
 
 47-38 
 
 47-38 
 
 18 
 
 12-95 
 
 12-50 
 
 68 
 
 48-92 
 
 47-24 
 
 18 
 
 12-73 
 
 12-73 
 
 68 
 
 48-08 
 
 48-08 
 
 19 
 
 13-67 
 
 13-20 
 
 69 
 
 49-63 
 
 47-93 
 
 19 
 
 13-44 
 
 13-44 
 
 69 
 
 48-79 
 
 48-79 
 
 20 
 
 14-39 
 
 13-89 
 
 70 
 
 50-35 
 
 48-63 
 
 20 
 
 14-14 
 
 14-14 
 
 70 
 
 49-50 
 
 49-50 
 
 21 
 
 15-11 
 
 14-59 
 
 71 
 
 51-07 
 
 49-32 
 
 21 
 
 14-85 
 
 14-85 
 
 71 
 
 50-20 
 
 50-20 
 
 22 
 
 15-83 
 
 15-28 
 
 72 
 
 51-79 
 
 50-02 
 
 22 
 
 15-56 
 
 15-56 
 
 72 
 
 50-91 
 
 50-91 
 
 23 
 
 16-54 
 
 15-98 
 
 73 
 
 52-51 
 
 50-71 
 
 23 
 
 16-26 
 
 16-26 
 
 73 
 
 51-62 
 
 51-62 
 
 24 
 
 17-26 
 
 16-67 
 
 74 
 
 53-23 
 
 51-40 
 
 24 
 
 16-97 
 
 16-97 
 
 74 
 
 52-33 
 
 52-33 
 
 25 
 
 17-98 
 
 17-37 
 
 75 
 
 53-95 
 
 52-10 
 
 25 
 
 17-68 
 
 17-68 
 
 75 
 
 53-03 
 
 53-03 
 
 26 
 
 18-70 
 
 18-06 
 
 76 
 
 54-67 
 
 52-79 
 
 26 
 
 18-38 
 
 18-38 
 
 76 
 
 53-74 
 
 53-74 
 
 '27 
 
 19-42 
 
 18-76 
 
 77 
 
 55-39 
 
 53-49 
 
 27 
 
 19-09 
 
 19-09 
 
 77 
 
 54-45 
 
 54-45 
 
 28 
 
 20-14 
 
 19-45 
 
 78 
 
 56-11 
 
 54-18 
 
 28 
 
 19-80 
 
 19-80 
 
 78 
 
 55-15 
 
 55-15 
 
 29 
 
 20-86 
 
 20-15 
 
 79 
 
 56-83 
 
 54-88 
 
 29 
 
 20-51 
 
 20-51 
 
 79 
 
 55-86 
 
 55-86 
 
 30 
 
 21-58 
 
 20-84 
 
 80 
 
 57-55 
 
 55-57 
 
 30 
 
 21-21 
 
 21-21 
 
 80 
 
 56-57 
 
 56-57 
 
 31 
 
 22-30 
 
 21-53 
 
 81 
 
 58-27 
 
 56-27 
 
 31 
 
 21-92 
 
 21-92 
 
 81 
 
 57-28 
 
 57-28 
 
 32 
 
 23-02 
 
 22-23 
 
 82 
 
 58-99 
 
 56-96 
 
 82 
 
 22-63 
 
 22-63 
 
 82 
 
 57-98 
 
 57-98 
 
 33 
 
 23-74 
 
 22-92 
 
 83 
 
 59-71 
 
 57-66 
 
 33 
 
 23-33 
 
 23-33 
 
 83 
 
 58-69 
 
 58-69 
 
 34 
 
 24-46 
 
 23-62 
 
 84 
 
 60-42 
 
 58-35 
 
 34 
 
 24-04 
 
 24-04 
 
 84 
 
 59-40 
 
 59-40 
 
 35 
 
 25-18 
 
 24-31 
 
 85 
 
 61-14 
 
 59-05 
 
 35 
 
 24-75 
 
 24-75 
 
 85 
 
 60-10 
 
 60-10 
 
 36 
 
 25-90 
 
 25-01 
 
 86 
 
 61-86 
 
 59-74 
 
 36 
 
 25-46 
 
 25-46 
 
 86 
 
 60-81 
 
 60-81 
 
 37 
 
 26-62 
 
 
 87 
 
 62-58 
 
 60-44 
 
 37 
 
 26-16 
 
 26-16 
 
 87 
 
 61-52 
 
 61-52 
 
 38 
 
 27-33 
 
 26-40 
 
 88 
 
 63-30 
 
 61-13 
 
 38 
 
 26-87 
 
 26-87 
 
 88 
 
 62-23 
 
 62-23 
 
 39 
 
 28-05 
 
 27-09 
 
 89 
 
 64-02 
 
 01-82 
 
 39 
 
 27-58 
 
 27-58 
 
 89 
 
 62-93 
 
 62-93 
 
 40 
 
 28-77 
 
 27-79 
 
 90 
 
 64-74 
 
 62-52 
 
 40 
 
 28-28 
 
 28-28 
 
 90 
 
 63-64 
 
 63-64 j 
 
 41 
 
 29-49 
 
 28-48 
 
 91 
 
 65-46 
 
 63-21 
 
 41 
 
 28-99 
 
 28-99 
 
 91 
 
 64-33 
 
 64-33 
 
 42 
 
 30-21 
 
 29-18 
 
 92 
 
 66-18 
 
 63-91 
 
 42 
 
 29-70 
 
 29-70 
 
 92 
 
 65-05 
 
 65-05 
 
 43 
 
 30-93 
 
 29-87 
 
 93 
 
 66-90 
 
 64-60 
 
 43 
 
 30-41 
 
 30-41 
 
 93 
 
 65-76 
 
 65-76 
 
 44 
 
 31'fi5 
 
 30-57 
 
 94 
 
 67-62 
 
 65-30 
 
 44 
 
 31-11 
 
 31-11 
 
 94 
 
 66-47 
 
 66-47 
 
 45 
 
 32-37 
 
 31-26 
 
 95 
 
 68-34 
 
 65-99 
 
 45 
 
 31-82 
 
 31-82 
 
 95 
 
 67-18 
 
 67-18 
 
 46 
 
 33-09 
 
 31-95 
 
 96 
 
 69-06 
 
 66-69 
 
 46 
 
 32-53 
 
 32-53 
 
 96 
 
 67 -88 
 
 67-88 
 
 47 
 
 33-81 
 
 32-65 
 
 97 
 
 69-78 
 
 67-38 
 
 47 
 
 33-23 
 
 33-23 
 
 97 
 
 68-59 
 
 68-59 
 
 48 
 
 34-53 
 
 33-34 
 
 98 
 
 70-50 
 
 68-08 
 
 48 
 
 33-94 
 
 33-94 
 
 98 
 
 69-30 
 
 69-30 
 
 49 
 
 35-25 
 
 34-04 
 
 99 
 
 71-21 
 
 68-77 
 
 49 
 
 34-65 
 
 34-65 
 
 99 
 
 70-00 
 
 70-CO 
 
 50 
 
 35-97 
 
 34-73 
 
 100 
 
 71-93 
 
 69-47 
 
 50 
 
 35-35 
 
 35-35 
 
 100 
 
 70-71 
 
 70-71 
 
 IE. orW. 
 
 N. or S. 
 
 
 E. or W 
 
 N. or S. 
 
 
 E. or W. 
 
 N.or S. 
 
 
 E. or W 
 
 N. or S. 
 
 46 
 
 45 
 
158 
 
 OF THE PEODUCE OF SEAMS OF COAL. 
 
 (61.) From the various experiments which have been 
 made on the produce of tracts of coal mines, in the neigh- 
 bourhood of Newcastle-upon-Tyne, it has been found that 
 a cubic yard of coal weighs -936 of a ton ; therefore, an acre 
 of that stratum, 1 foot thick, will produce (if all wrought 
 out) 1510 tons; consequently an equal area of stratum, 
 2, 3, 4, &c., feet in thickness, will produce 2, 3, 4, &c., times 
 the quantity of tons of coal that a seam of 1 foot thick will 
 produce. 
 
 From this datum easy rules may be constructed for the 
 use of the practical miner, which with facility may be 
 retained for application in calculating the produce of seams 
 of any given thickness in tons. 
 
 To find the number of tons of coal contained per acre by 
 a seam of any given thickness. 
 
 EULE I. Multiply 1510 by the thickness or height of 
 the seam in feet, and the product will be the number of 
 tons of coal contained in an acre of that seam. 
 
 To find the number of tons of coal produced per acre by a 
 seam, where part thereof is only worlced or taken away, 
 the other part being left as a support to the roof. 
 
 EULE II. As the sum of the two parts, i.e., that left 
 and that taken away, is to the part excavated or taken away, 
 so is the whole number of tons contained in an acre of the 
 seam to the number of tons produced per acre by the ex- 
 cavated part. s 
 
 EXAMPLE I. What number of tons of coal is contained 
 in an acre of coal stratum 6 feet thick ? 
 
 From rule 1st, 1510 x 6 = 9060 tons, the content. 
 
 EXAMPLE IT. What number of tons of coal is contained 
 in an area of coal stratum of 100 acres, 5 feet thick ? 
 
ON THE PRODUCE OF SEAMS OF COAL. 159 
 
 1510 x 5 = 7550 tons contained in one acre. 
 Then 7550 x 100 = 755,000 tons contained in 100 acres. 
 EXAMPLE III. What number of tons of coal is con- 
 tained in 400 acres of coal stratum 5 feet 3 inches thick ? 
 
 First 5 ft. 3 in. = ft. 
 4 
 
 And 151 X21 X 4<30 = ^^ ^ 
 
 EXAMPLE IV. What number of tons of coal is contained 
 in 400 acres of coal stratum 8 feet 4 inches thick ? 
 
 OK 
 
 First 8 ft. 4 in. =~ft. 
 3 
 
 , 1510 x 25 x 400 r nyq r 
 
 And = 5,033,333 tons. 
 
 3 
 
 EXAMPLE V. What number of tons of coal is contained 
 in 500 acres of coal stratum 4 feet 9 inches thick, exclud- 
 ing a band of stone which lies therein 6 -inches thick ? 
 
 4-75 __ -50 = 4*25 feet, the thickness of the coal stratum, 
 exclusive of the band of stone. 
 
 Then 1510 x 4'25 x 500 = 3,208,750 tons contained in 
 500 acres. 
 
 EXAMPLE VI. In a seam of coal which is 7 feet 3 inches 
 thick ; that is to say, 6 feet of its thickness is marketable, 
 and 1 foot 3 inches inferior ; I wish to know the produce in 
 tons per acre, both of the marketable and the inferior parts 
 of the seam ? 
 
 1510 x 6 = 9060 tons per acre, the marketable produce 
 of the seam 
 
 First 1 ft. 3 in. = I ft, 
 
 1510 x 5 . . 
 
 And = 1887J tons of the inferior parts. 
 
 EXAMPLE VII. In a seam of coal 6 feet thick, I wish to 
 know what number of tons it produces per acre, when 1 part 
 is taken away, and 2 left for pillars or supports ? 
 
 1510 x 6 = 9060 tons, the whole content per acre. 
 
160 ON THE PBODUCE OF SEAMS OF COAL. 
 
 Prom rale 2nd, as 2 + 1 =3:1:: 9060 : 3020 tons, 
 the produce per acre of the part taken away. 
 
 EXAMPLE VIII. In a seam of coal 3 feet 6 inches thick, 
 
 1 wish to know what number of tons it will produce per 
 acre, when two parts are taken away and 1 left ? 
 
 1510 x 3-5 = 5285 tons, the content per acre. 
 As 2 + 1 = 3 : 2 : : 5285 : 3523'33 tons, the produce 
 per acre of the part taken away. 
 
 EXAMPLE IX. In 1000 acres of co'al5feetthick ; whereof 
 
 2 parts are worked and 1 left, I wish to know how many 
 years this stratum of coal will produce an annual quantity 
 of 50,000 tons ? 
 
 1510 x 5 = 7550 tons, the whole produce of the seam 
 per acre. 
 
 Then as 3 : 2 : : 7550 : 5033, the quantity got per 
 acre. 
 
 EXAMPLE X. I have a tract of 600 acres of coal stratum, 
 containing 2 seams, the first 5 feet 3 inches thick, and the 
 second 3 feet 6 inches thick : Out of the first seam 3 parts 
 are got and 1 left ; and out of the second 4 parts are got and 
 1 left. JSTow, if the annual vend of the two seams together 
 is 75,000 tons, what number must be wrought out of each 
 seam yearly, so that they may terminate together ; and how 
 many years will the colliery last ? 
 
 - = 7927J tons, the whole produce per acre of 
 
 the first seam. 
 
 And 4:3:: 7927 J : 5945 tons, the quantity wrought 
 per acre out of the first seam. 
 
 Then 5945 x 600 = 3,567,000 tons, total produce of the 
 first seam. 
 
 Again, - - 5285 tons, the whole produce per 
 acre of the second seam. 
 
 
ON THE PllODUCE OE SEAMS OF COAL. 161 
 
 Aiid 5:4:: 5285 : 4228 tons, the quantity wrought per 
 acre out of the second seam. 
 
 Then 4228 x 600 = 2,536,800 tons, total produce of the 
 second seam. 
 
 Now, to make the two seams terminate together, the 
 quantity wrought out of each seam annually must bear the 
 same proportion to each other as the quantity wrought out 
 of each acre of each seam. 
 
 Therefore 5945 + 4228 = 10,173 : 5945 : : 75,000 : 
 43,829 tons, the quantity to be wrought out of the first 
 seam annually. 
 
 And 75000 43829 ^ 31,171 tons, the quantity to be 
 wrought out of the second seam annually. 
 
 3567000 + 2536800 
 
 Whence = 80 years 18 days, 
 
 YoOOu 
 
 the duration of the colliery. 
 
 Note. Elaborate statistics and details of the extent, the probable pro- 
 duce and duration of all the coal-fields in the United Kingdom, also the 
 extent and thickness of the strata of those of the United States and the 
 British colonies, as far as they are known ; as well as those of Belgium, 
 France, Germany, and other foreign countries, are given in the Reports of 
 the Institution of Mining Engineers of Neivcastle-upon-Tyne, to which the 
 student is referred, who may be desirous to be acquainted with these 
 -subjects. 
 
 Questions in Mine Surveying. 
 
 Note. The solutions to the two following Questions in Mine Surveying 
 will require a knowledge of the application of Algebra to Geometry, and 
 the latter of the two will require a further knowledge of the application of 
 Spherical Trigonometry to Astronomy. See Question- XVII, page 211, 
 Baker's Land and Engineering Surveying. Wealds Series. The student 
 will have no difficulty in sketching the figures and assigning the dimensions 
 to the given parts in the two Questions. 
 
 Question 1. There are four drifts in a coal mine formiug 
 a trapezium, the given lengths of which are a, b, c, d, and 
 the sums of the opposite angles of the trapezium are known 
 to be equal to two right angles, none of the angles being 
 separately given. It is required to plot this subterraneous 
 survey by the help of the following formula. 
 
162 ON THE PRODUCE OF SEAMS OF COAL. 
 
 Let S - half the sum of the lengths of the four drifts 
 -J (a + b + c + d), and D the diameter of circle, which will 
 circumscribe the trapezium ; then 
 
 T) _ / ( (ac + ld) (al + cd) (ad+ Ic) 
 = V \ (S-o) (-&) (S-,) (S-dj 
 
 Note. This formula will divest the preceding Question of its chief diffi- 
 culty, while it will accustom the student to the application of this species 
 of mathematical analysis. 
 
 Question 2. There are five straight drifts, AB, EC, CD, 
 DE, EA, in a coal-mine, forming an irregular polygon ; now, 
 the several lengths of each of the five drifts are given, and 
 the angles at B, C, and D are known to be equal to one 
 another, but are not given : also at each of the angles B and 
 D is a shaft, and the tops of these two shafts range with 
 the sun at 3 h. 35' P.M. on the 22d of October, 1860. It is 
 required from these data to plot this subterraneous survey 
 in its true position with respect to the cardinal points. 
 
 NOTE. This question was proposed by B. Gksmpertz, Esq., F.R.S., in 
 the Gentleman's Mathematical Companion ; to which he gave a solution in 
 a concise, novel, and ingenious manner by his Principles of Imaginary 
 Quantities : other solutions by the ordinary methods were also given to the 
 same problem. 
 
 THE END. 
 
 BRADBTJET AND EVANS, PRINTERS, WHITE FRIARS. 
 
CATALOGUE 
 
 OF 
 
 RUDIMENTARY, SCIENTIFIC, EDUCATIONAL, AND 
 CLASSICAL WORKS, 
 
 FOR COLLEGES, HIGH AND ORDINARY SCHOOLS, 
 AND SELF-INSTRUCTION; 
 
 ALSO FOR 
 
 MECHANICS' INSTITUTIONS, FKEE LLBKAKIES, &c. &c., 
 
 PUBLISHED BY 
 
 VIRTUE BROTHERS & CO,, 1, AMEN CORNEE, 
 PATEKNOSTEE EOW, LONDON. 
 
 * THE ENTIRE SERIES IS FREELY ILLUSTRATED ON WOOD 
 AND STONE WHERE REQUISITE. 
 
 The Public are respectfully informed that the whole of the 
 laic MR. WE ALE'S Publications, contained in the followinff Cata- 
 logue, have been Purchased by VIRTUE BROTHERS & Co., and 
 that all future Orders will be supplied by them at the above address. 
 
 *** Several additional Volumes, by Papular Authors, are in 
 preparation, and will sJwrtly be ready for delivery. 
 
 RUDIMENTARY SERIES. 
 
 2. NATURAL PHILOSOPHY, by Charles Tomlinson . . 1*. 
 
 3. GEOLOGY, by Major-Gen. Portlock, F.E.S., &c. . Is. 6d. 
 G. MECHANICS, by Charles Tomlinson . . . . 1*. 
 
 12. PNEUMATICS, by Charles Tomlinson . . . .15. 
 
 20, 21. PEESPECTIVE, by George Pyne, 2 vols. in 1 . . 2*. 
 
 27, 28. PAINTING, The Art of ; or, A GEAMMAE OF 
 
 COLOUEING, by George Field, 2 vols. in 1 . 25. 
 
 3G, 37, 38, 39. DICTIONAEY of the TECHNICAL TEEMS 
 used by Architects, Builders, Engineers, Siureyors, &c., 
 
 4 vola. in 1 4s. 
 
 In cloth boards, 5.5. ; half morocco, 6?. 
 
 40. GLASS STAINING, by Dr. M. A. Gessert, With an 
 
 Appendix on the Art of Enamelling . . . .15. 
 
 41. PAINTING ON GLASS, from the^German of Emanuel 
 
 O. Fromberg Is. 
 
SCIENTIFIC AND MECHANICAL WORKS. 
 
 69, 70. MUSIC, a Practical Treatise, by C. C. Spencer, Doctor 
 
 of Music, 2 vols. in 1 2s. 
 
 71. THE PIANOFORTE, Instructions for Playing, by C. C. 
 
 Spencer, Doctor of Music Is. 
 
 72 to 75*. EECENT FOSSIL SHELLS (A Manual of the 
 Mollusca), by Samuel P. Woodward, 4 vols. in 1, and 
 
 Supplement 5s. Gd. 
 
 In cloth boards, 6s. 6d. ; half morocco, 7s. 6d. 
 
 83. BOOK-KEEPING, by James Haddon, M.A. . . . Is. 
 
 84. ARITHMETIC, with numerous Examples, by Professor 
 
 J. R. Young. ... . . . . . Is. Gd. 
 
 84*. KEY TO THE PRECEDING VOLUME, by Professor 
 
 J. R. Young . . Is.Gd. 
 
 96. ASTRONOMY, POPULAR, by the Rev. Robert Main, 
 
 M.R.A.S Is. 
 
 101*. WEIGHTS AND MEASURES OF ALL NATIONS ; 
 Weights of Coins, and Divisions of Time; with the 
 Principles which determine the Rate of Exchange, by 
 Mr. Woolhouse, F.R.A.S Is. Gd. 
 
 103. INTEGRAL CALCULUS, Examples of, by Prof. J. Hann 1*. 
 
 112. DOMESTIC MEDICINE, for the Preservation of Health, 
 
 by M. Raspail Is. Gd. 
 
 131. MILLER'S, FARMER'S, AND MERCHANT'S READY- 
 RECKONER, showing the Value of any Quantity of 
 Corn, with the Approximate Value of Mill-stones and 
 
 Mill Work Is. 
 
 (In Preparation.) 
 PHOTOGRAPHY. A New Manual. 
 
 PHYSICAL SCIENCE. 
 
 1. CHEMISTRY, by Professor Fownes, F.R.S., including 
 
 Agricultural Chemistry, for the use of Farmers . . Is. 
 4, 5. MINERALOGY, with a Treatise on Mineral Rocks or 
 
 -aggregates, by James Dana, A.M., 2 vols. in 1 . . 2s. 
 
 7. ELECTRICITY, an Exposition of the General Principles of 
 
 the Science, by Sir William Snow Harris, F.R.S. . Is. Gd. 
 7*. GALVANISM, ANIMAL AND VOLTAIC ELECTRI- 
 CITY; A Treatise on the General Principles of Gal- 
 vanic Science, by Sir William Snow Harris, F.R.S. Is. Gd. 
 
 8, 9, 10. MAGNETISM, Concise Exposition of the General 
 
 Principles of Magnetical Science and the Purposes to 
 which it has been Applied, by the same, 3 vols. in 1 3s. Qd. 
 11, 11*. ELECTRIC TELEGRAPH, History of, by E. High- 
 ton, C.E 2s. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
SCIENTIFIC AND MECHANICAL WORKS. 3 
 
 133. METALLURGY OF COPPER, by R. H. Lamborn . 2s. 
 
 134. METALLURGY OF SILVER AND LEAD, by Dr. 
 
 R. H. Lamborn 2s. 
 
 135. ELECTRO-METALLURGY, by Alex. Watt, F.R.S.S.A. Is. Gd. 
 138. HANDBOOK OF THE TELEGRAPH, by R. Bond . Is. 
 141. EXPERIMENTAL ESSAYS On the Motion of Cam- 
 phor, and Modern Theory of Dew, by C. Tomlinson . Is. 
 
 BUILDING AND ARCHITECTURE. 
 
 16. ORDERS OF ARCHITECTURE, and their Esthetic 
 
 Principles, by W. H. Leeds Is. 
 
 17. STYLES OF ARCHITECTURE, by T. Bury . . Is. Gd. 
 
 18. 19. ARCHITECTURE, Principles of Design in, by E. L. 
 
 Garbett, 2 vols in 1 2s. 
 
 22. BUILDING, the Art of, in Five Sections, by Edward 
 
 Dobson, C.E. ! Is. 
 
 23, 24. BRICK AND TILE MAKING, by E. Dobson, C.E., 
 
 2 vola. in 1 2s. 
 
 25, 26. MASONRY AND STONE-CUTTING, with the Prin- 
 ciples of Masonic Projection Concisely Explained, by 
 E. Dobson, C.E., 2 vols. in 1 2s. 
 
 30. DRAINING and SEWAGE OF TOWNS and BUILD- 
 INGS, Suggestive of Sanatory Regulations, by G. D. 
 
 Dempsey, C.E Is. Gd. 
 
 (With No. 29, DRAINAGE OP LAND, 2 vols. in 1, 2s. Gd.) 
 
 35. BLASTING ROCKS, QUARRYING, AND THE QUA- 
 LITIES OF STONE, by Lieut.-Gen. Sir J. Burgoyne, 
 Bart., G.C.B., R.E Is. Gd. 
 
 42. COTTAGE BUILDING, or Hints for Improving the 
 
 Dwellings of the Labouring Classes .... 1*. 
 
 44. FOUNDATIONS AND CONCRETE WORKS, A Treatise 
 
 on, by E. Dobson, C.E Is. 
 
 45. LIMES, CEMENTS, MORTARS, CONCRETE, MAS- 
 
 TICS, &c., by G. R. Burnell, C.E Is. 
 
 57, 58. WARMING AND VENTILATION, by Charles Tom- 
 linson, 2 vols. in 1 2s. 
 
 111*. ARCHES, PIERS, AND BUTTRESSES, the Principles 
 
 of their Construction, by William Bland . . Is. Gd. 
 
 116. ACOUSTICS; Distribution of Sound, by T. Roger Smith, 
 
 Architect Is. Gd. 
 
 123. CARPENTRY AND JOINERY, a Treatise founded on 
 
 Dr. Robison's Work Is. Gd. 
 
 123*. ILLUSTRATIVE PLATES to the preceding . . 4s. Gd. 
 
 VIRTUE BROTHERS & CO., ' 1, AMEN CORNER. 
 
4 SCIENTIFIC AND MECHANICAL WORKS. 
 
 124. KOOFS FOR PUBLIC AND PRIVATE BUILDINGS, 
 
 founded on Dr. Robison's Work > *.- , . Is. G<7. 
 124*. IRON ROOFS of Recent Construction a Series of 
 
 Descriptive Plates 4s. 6cL 
 
 127. ARCHITECTURAL MODELLING, Practical Instruc- 
 
 tions in the Art , . . 1$. &?. 
 
 128, 129. VITRUVIUS ON CIVIL, MILITARY, AND 
 
 NAVAL ARCHITECTURE, translated by Joseph Gwilt, 
 Architect, with Illustrative Plates, by the Author and 
 Joseph G-andy, 2 vols. in 1 .. '*. .* . '. . . 5s. 
 
 130. GRECIAN ARCHITECTURE, Principles of Beauty in, 
 
 by the Earl of Aberdeen 1*. 
 
 132. ERECTION OF DWELLING-HOUSES, with Specifica- 
 tions, Quantities of Materials, &c., by S. H. Brooks, 
 27 Plates : . . ;' ; 2s. Qd. 
 
 MACHINERY AND ENGINEERING. 
 
 33. CRANES and MACHINERY for LIFTING HEAVY 
 
 WEIGHTS, the Art of Constructing, by Joseph Glynn Is. 
 
 34. STEAM ENGINE, by Dr. Lardner Is. 
 
 43. TUBULAR AND OTHER IRON GIRDER BRIDGES, 
 
 including the Britannia and Conway Bridges, by G. D. 
 Dempsey Is. 
 
 47, 48, 49. LIGHTHOUSES, their Construction and Illumina- 
 tion, by Allan Stevenson, C.E., 3 vols. in 1 .'.. . 3s. 
 
 59. STEAM BOILERS, their Construction and Management, 
 
 by R.Armstrong, C.E Is. 
 
 62. RAILWAYS, Principles of Construction, by Sir E. Stephen- 
 son Is. Go?. 
 
 62*. RAILWAY WORKING IN GREAT BRITAIN AND 
 IRELAND, Statistics, Revenue, Accounts, &c., by E. D. 
 
 Chattaway Is. 
 
 (Vols. 62 and 62* bound in 1, 2s. Qd.) 
 
 67, 68. CLOCK AND WATCH MAKING, including Church 
 Clocks and Bells, by Edmund Beckett Denison, M.A., 
 with an Appendix, 2 vols. in 1 . . . .,.-, . 3s. Qd. 
 
 78, 79. STEAM AND LOCOMOTION, on the Principle of 
 connecting Science with Practice, by John Sewell, L.E., 
 2 vols. in 1 2s. 
 
 78*. LOCOMOTIVE ENGINES, a Treatise on, by G. Drysdale 
 
 Dempsey, C.E Is. Qd. 
 
 79*. ILLUSTRATIONS TO THE ABOVE . . . 4s. Qd. 
 
 98, 98* MECHANISM AND THE CONSTRUCTION OF 
 MACHINES, by Thomas Baker, C.E. ; and TOOLS AND 
 MACHINES, by J. Nasmyth, C.E., with 220 Woodcuts 2s. Qd. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER, 
 
SCIENTIFIC AND MECHANICAL WORKS. 5 
 
 114. MACHINERY, its Construction and Working, by C. D. 
 
 Abel,C.E Is. Gd. 
 
 115. ILLUSTRATIVE PLATES TO THE ABOVE, 4to. 7s. Qd. 
 139. THEORY OF THE STEAM ENGINE, by T. Baker, C.E. Is. 
 
 CIVIL ENGINEERING, &c. 
 
 13, 14, 15, 15*. CIVIL ENGINEERING-, by Henry Law, 
 
 3 vols. ; with Supplement by G. R. Burnell, 4 vols. in 1 4s. Qd. 
 
 29. DRAINING DISTRICTS AND LANDS, the Art of, by 
 
 G. D. Dempsey, C.E Is. 
 
 (With No. 30, DRAINAGE AND SEWAGE OP TOWNS, 2 vols. in 1, 25. Qd.) 
 
 31. WELL-SINKING AND BORING, by John G. Swindell, 
 
 revised by G. R. Burnell, C.E 1$. 
 
 46. ROAD-MAKING, the Construction and Repair, by S. C. 
 Hughes and H. Law, C.E., and Gen. Sir J. Burgoyne, 
 Bart,, G.C.B., R.E. Is. Qd. 
 
 60, 61. LAND AND ENGINEERING SURVEYING, by T. 
 
 Baker, C.E., 2 vols. in 1 2s. 
 
 63, 64, 65. AGRICULTURAL BUILDINGS, FIELD EN- 
 GINES, MACHINERY, and IMPLEMENTS, by G. H. 
 Andrews, 3 vols. in 1 3s. 
 
 66. CLAY LANDS AND LOAMY SOILS, by Professor Do- 
 naldson, A.E Is. 
 
 77*. ECONOMY OF FUEL, by T. S. Prideaux . . . Is. 
 
 80*, 81*. EMBANKING LANDS FROM THE SEA, with 
 Examples of actual Embankments and Sea Walls, by 
 John Wiggins, F.G.S., 2 vols. in 1 . , . .2*. 
 
 82, 82*. POWER OF WATER, as applied to the Driving of 
 Mills, and Giving Motion to Turbines, and other Hy- 
 drostatic Machines, by Joseph Glynn, F.R.S., C.E. . 2s. 
 
 82**, 83*, 83 bis. COAL GAS, its Manufacture and Distribu- 
 tion, by Samuel Hughes, C.E. 3s. 
 
 82***. WATER-WORKS FOR THE SUPPLY OF CITIES 
 
 A^D TOWNS, by Samuel Hughes, C.E. . . .3s. 
 
 117. SUBTERRANEOUS SURVEYING, & RANGING THE 
 
 LINE without the Magnet, by T. Fenwick, Coal Viewer, 
 with Improvements and Additions by T. Baker, C.E. 2s. Qd. 
 
 118, 119. CIVIL ENGINEERING IN NORTH AMERICA, 
 
 by D. Stevenson, C.E., 2 vols. in 1 . . . .3s. 
 
 120. HYDRAULIC ENGINEERING, by G. R. Burnoll, C.E., 
 
 2 vols. in 1 3s. 
 
 121, 122. RIVERS AND TORRENTS, from the Italian-of 
 
 Paul Frisi, and a Treatise on NAVIGABLE CANALS, 
 AN.D RIVERS THAT CARRY SAND AND MUD 2s. Qd. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
6 SCIENTIFIC AND MECHANICAL WORKS. 
 
 125, 126. COMBUSTION OF COAL, 'AND THE PREVEN- 
 
 TION OF SMOKE, by Charles Wye Williams, M.I.C.E. 3s. 
 
 140. OUTLINES OF. MODERN FARMING, by R, Scott Burn. 
 
 Vol. I. Soils, Manures, and Crops . . . .2s. 
 
 H2. Vol. II. Farming 
 
 Economy, Scientific and Practical . . . . 2-s. 
 
 SHIP-BUILDING AND NAVIGATION. 
 
 51, 52, 53. NAVAL ARCHITECTURE, Principles of the 
 
 Science, by J. Peake, N.A., 3 vols. in 1 . . . . 3s. 
 53*. SHIPS AND BOATS FOR OCEAN AND RIVER 
 
 SERVICE, the Principles of Construction, by Captain 
 
 H. A. Sommerfeldt . ... . . . 1*. 
 
 53**. ATLAS OF 14 PLATES TO THE PRECEDING, 
 
 Drawn to a Scale for Practice ' ' . ' . . '_ . 7s. Gd. 
 54. MASTING, MAST-MAKING, and RIGGING OF SHIPS, 
 
 by R. Kipping, N. A. . . . . ". '. Is. 6d. 
 54*. IRON SHIP-BUILDING, by John Grantham, C.E. 2*. Qd. 
 54**. ATLAS OF 24 PLATES to the preceding Volume 22s. Qd. 
 80, 81. MARINE ENGINES AND THE SCREW, by R, 
 
 Murray, C.E., 2 vols. in 1 2s. 6rf. 
 
 83 bis. SHIPS AND BOATS, the Principles of Construction, 
 
 by W. Bland, of Hartlip . . .. . , ; . . Is. 
 106. SHIPS' ANCHORS FOR ALL SERVICES, by George 
 
 Cotsell, N.A 1*. Qd. 
 
 ARITHMETIC AND MATHEMATICS. 
 
 32. MATHEMATICAL INSTRUMENTS, AND THEIR 
 
 USE, by J. F. Heather, M.A Is. 
 
 55, 56. NAVIGATION ; the Sailor's Sea Book : How to Keep 
 the Log and Work it off, &c. ; Law of Storms, and Expla- 
 nation of Terms 2s. 
 
 61*. BEADY RECKONER for the Measurement of Land, its 
 Valuation, and the Price of Labour, by A. Arman, 
 Schoolmaster . * - v . - ' v : . - . Is. Qd. 
 
 76, 77. GEOMETRY, DESCRIPTIVE, with a Theory of Sha- 
 dows and Perspective, and a Description of the Principles 
 and Practice of Isometrical Projection, by J. F. Heather, 
 M.A, 2 vols. in 1 2s. 
 
 85. EQUATIONAL ARITHMETIC: Questions of Interest, 
 
 Annuities, &c., by W. Hipsley Is. 
 
 85*. EQUATIONAL ARITHMETIC: Tables for the Calculation 
 of Simple Interest, with Logarithms for Compound Inte- 
 rest, and Annuities, by W. Hipsley .... Is. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
SCIENTIFIC AND MECHANICAL WORKS. 7 
 
 86, 87. ALGEBRA, by James Haddon, M.A., 2 vols. in 1 . 2s. 
 86*, 87*. ELEMENTS OF ALGEBEA, Key to the, by Prof. 
 
 Young Is. Qd. 
 
 88, 89. GEOMETRY, Principles of, by Henry Law, C.E., 
 
 2 vols. in 1 2s. 
 
 90. GEOMETRY, ANALYTICAL, by James Hann . . Is. 
 
 91, 92. PLANE AND SPHERICAL TRIGONOMETRY, by 
 
 Prof. James Hann, 2 vols. in 1 (The two divisions sepa- 
 rately, Is. each} 2s. 
 
 93. MENSURATION, by T. Baker, C.E Is. 
 
 94, 95. LOGARITHMS, Tables of ; with Tables of Natural 
 
 Sines, Co-sines, and Tangents, by H. Law, C.E., 2 vols. inl 25. 6d. 
 97. STATICS AND DYNAMICS, by T. Baker, C.E. . . Is. 
 99, 100. NAVIGATION AND NAUTICAL ASTRONOMY, 
 
 by Professor Young, 2 vols. in 1 2s. 
 
 100*. NAVIGATION TABLES, compiled for Practical Use 
 
 with the preceding volume Is. Qd. 
 
 101. DIFFERENTIAL CALCULUS, by Mr. Woolhouse, F.R.A.S. Is. 
 
 102. INTEGRAL CALCULUS, by H. Cox, M.A. . . . Is. 
 
 104. DIFFERENTIAL CALCULUS, Examples of, by J. 
 
 Haddon, M.A Is. 
 
 105. ALGEBRA, GEOMETRY, and TRIGONOMETRY, First 
 
 Mnemonical Lessons in, by the Rev. T. P. Kirkman, M.A. Is. Qd. 
 
 136. RUDIMENTARY ARITHMETIC, by James Haddon, 
 
 M.A., with Additions by A. Arman . . .15. Qd. 
 
 137. KEY TO THE ABOVE, containing Answers to all the 
 
 Questions in that Work, by A. Arman . . 15. Qd. 
 
 MISCELLANEOUS, 
 
 50. LAW OF CONTRACTS FOR WORKS AND SERVICES, 
 
 by David Gibbons, S.P Is. 
 
 107. METROPOLITAN BUILDINGS ACT, and THE ME- 
 
 TROPOLITAN ACT FOR REGULATING THE 
 SUPPLY OF GAS, with Notes .... 25. Qd. 
 
 108. METROPOLITAN LOCAL MANAGEMENT ACTS Is. Qd. 
 108*. METROPOLIS LOCAL MANAGEMENT AMEND- 
 MENT ACT, 1862 ; with Notes and Index . . .15. 
 
 110. RECENT LEGISLATIVE ACTS applying to Contractors, 
 
 Merchants, and Tradesmen 15. 
 
 111. NUISANCES REMOVAL AND DISEASE PREVEN- 
 
 TION ACT Is. 
 
 113. USE OF FIELD ARTILLERY ON SERVICE, by 
 
 Lieut.-Col. Hamilton Maxwell, B.A. . . . 15. Qd. 
 113*. MEMOIR ON SWORDS, by the same . . . 1,. 
 83**. CONSTRUCTION OF DOOR LOCKS . . 15. Qd. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
NEW SERIES OP EDUCATIONAL WORKS. 
 
 [This Series is kept in three styles of binding the prices of each 
 are given in columns at the end of the lines.'] 
 
 HISTORIES, GRAMMARS, AND DICTIONARIES. 
 
 d 
 
 
 13 
 
 || 
 
 Sj 
 
 3 
 
 1, 2, 3, 4. CONSTITUTIONAL HISTOEY OF 
 England, by W. D. Hamilton . 
 5, 6. OUTLINES OF THE HISTOEY OF 
 
 Greece, by E. Levien, M.A., 2 vols. in 1 . 
 7, 8. OUTLINES OF THE HISTOEY OF 
 Eome, by the same, 2 vols. in 1 . ,< ~- - 
 9, 10. CHEONOLOGY OF CIVIL AND 
 Ecclesiastical History, Literature, Art, and 
 Civilisation, from the earliest period to the 
 present, 2 vols. in 1 . . . . r. 
 11. GEAMMAE OF THE ENGLISH LAN- 
 GUAGE, by Hyde Clarke, D.C.L. 
 11*. HAND-BOOK OF COMPAEATIYE 
 Philologv, by the same .... 
 12, 13. DICTIONAEY OF THE ENGLISH 
 Language. A new Dictionary of the Eng- 
 lish Tongue, as spoken and written ; above 
 100,000 words, or 50,000 more than in any 
 existing work, by the same, 3 vols. in 1 
 
 s. d. 
 4 
 
 2 6 
 2 6 
 
 2 6 
 1 
 1 
 
 3 6 
 1 
 
 2 
 2 
 
 1 
 2 
 1 6 
 
 1 
 
 5. d. 
 5 
 3 6 
 3 6 
 
 3 6 
 
 4 6 
 5 6 
 
 5 
 (5 
 
 4 6 
 
 5 6 | 
 
 s.d. 
 5 6 
 4 
 4 
 
 4 
 
 5 
 6 
 
 5 6 
 6 6 
 
 5 
 6 
 
 14. GEAMMAE OF THE GEEEK LAN- 
 GUAGE, by H. C. Hamilton 
 15, 16. DICTIONAEY OF THE GEEEK AND 
 English Languages, by H. E. Hamilton, 
 2 vols. in 1 
 17, 18. DICTIONAEY OP THE ENGLISH AND 
 Greek Languages, by the same, 2 vols. in 1 
 GEEEK AND ENGLISH 
 
 and English and Greek, 4 vols. in 1 . 
 
 19. GEAMMAE OP THE LATIN LANGUAGE, 
 by the Eev. T. Goodwin, A.B. . 
 20, 21. DICTIONAEY OF THE LATIN AND 
 
 English Languages, by the same. Vol. I. 
 22, 23. DICTIONAEY OF THE ENGLISH 
 and Latin Languages, by the same. Vol. II. 
 
 
 24. GEAMMAE OF THE FEENCH LAN- 
 GUAGE, by the Lecturer at Besan9on . . 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
SEW SERIES OF EDUCATIONAL WORKS. 
 
 HISTORIES, GRAMMARS, AND DICTIONARIES. 
 
 a 
 
 M 
 
 || 
 
 "5 o 
 
 25. DICTIONARY OF THE FRENCH AND 
 
 English Languages, by A. Elwes. Vol. I. 
 26. DICTIONARY OF THE ENGLISH AND 
 French Languages, by the same. Vol. II. 
 
 S.d. 
 
 1 
 1 6 
 
 s.d. 
 3 6 
 
 s.d. 
 4 
 
 ,.,,..,. . , . "with, the French. Grammar 
 
 
 4 6 
 
 5 
 
 27. GRAMMAR OF THE ITALIAN LAN- 
 
 1 
 
 
 
 28, 29. DICTIONARY OF THE ITALIAN, 
 English, and French Languages, by the 
 same. Vol. I 
 30, 31. DICTIONARY OF THE ENGLISH, 
 Italian, and French Languages, by the 
 same. Vol. II 
 32, 33. DICTIONARY OF THE FRENCH, 
 Italian, and English Languages, by the 
 same. Vol. Ill 
 
 2 
 2 
 
 2 
 
 
 
 
 
 7 G 
 
 8 6 
 
 
 
 8 6 
 
 9 G 
 
 34. GRAMMAR OF THE SPANISH LAN- 
 GUAGE, by the same 
 35, 36, 37, 38. DICTIONARY OF THE 
 
 Spanish and English Languages, by the 
 same, 4 vols. in 1 
 
 1 
 40 
 
 5 
 o 
 
 5 6 
 fi A 
 
 39. GRAMMAR OF THE GERMAN LAN- 
 GUAGE, by the Lecturer at Besan^on . 
 40. CLASSICAL GERMAN READER, from 
 the best authors, by the same . 
 41,42,43. DICTIONARIES OF THE ENGLISH, 
 German, and French Languages, by N. E. 
 Hamilton, 3 vols., separately Is. each 
 
 1 
 1 
 
 3 
 
 4 
 5 
 
 4 6 
 K a 
 
 44, 45. DICTIONARY OF THE HEBREW 
 
 and English Languages, containing the 
 Biblical and Rabbinical words, 2 vols. 
 (together with the Grammar, which may 
 be had separately for Is.) by Dr. Bresslau, 
 Hebrew Professor 
 46. DICTIONARY OF THE ENGLISH AND 
 Hebrew Languages. Vol. III. to complete, 
 by the same 
 
 7 
 3 
 
 10 o 
 
 14 O 
 
 47. FRENCH AND ENGLISH PHRASE, 
 Book 
 
 1 
 
 1 6 
 
 
 
 
 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
10 GREEK AND LATIN CLASSICS. 
 
 Now in the course of Publication. 
 
 GREEK AND LATIN CLASSICS. 
 
 A Series of Volumes containing the principal Greek and Latin Authors, accom- 
 panied by Explanatory Notes in English, principally selected from the best and 
 most recent German Commentators, and comprising all those Works that are 
 essential for the Scholar and the Pupil, and applicable for the Universities of 
 Oxford, Cambridge, Edinburgh, Glasgow, Aberdeen, and Dublin ; the Colleges at 
 Belfast, Cork, Galway, Winchester, and Eton ; and the great Schools at Harrow, 
 Bugby, &c. also for Private Tuition and Instruction, and for the Library. 
 
 LATIN SERIES. 
 
 1. A New LATIN DELECTUS, Extracts from Classical 
 
 Authors, with Vocabularies and Explanatory Notes . Is. 
 
 2. CAESAR'S COMMENTARIES on the GALLIC WAR; 
 
 with Grammatical and Explanatory Notes in English, 
 and a Geographical Index . . ,. . . . 2s. 
 
 3. CORNELIUS NEPOS ; with English Notes, &c. . . 1*. 
 
 4. VIRGIL. The Georgics, Bucolics, and doubtful Works ; 
 
 with English Notes . . ; '*;.>.'. ; . Is. 
 
 5. VIRGIL'S ^ENEID (on the same plan as the preceding) . 2s. 
 
 6. HORACE. Odes and Epodes; with English Notes, and 
 
 Analysis and Explanation of the Metres . . . Is. 
 
 7. HORACE. Satires and Epistles ; with English Notes, &c. 1*. Qd. 
 
 8. SALLUST. Conspiracy of Catiline, Jugurthine War . Is. Qd. 
 
 9. TERENCE. Andrea and Heautontimorumenos . Is. Qd. 
 
 10. TERENCE. Phormio, Adelphi, and Hecyra . .2s. 
 
 14. CICERO. De Amicitia, de Senectute, and Brutus . . 2s. 
 
 16. LIVY. Books i. to v. in two parts 3s. 
 
 17. LIVY. Books xxi. and xxii Is. 
 
 19. Selections from TIBULLUS, OVID, and PROPERTIUS . 2s. 
 
 20. Selections from SUETONIUS and the later Latin Writers . 2?. 
 
 I 
 Preparing for Press. 
 
 11. CICERO. Orations against Catiline, for Sulk, for Archias, 
 
 and for the Manilian Law. 
 
 12. CICERO. First and Second Philippics ; Orations for Milo, 
 
 for Marcellus, &c. 
 
 13. CICERO. De Officiis. 
 
 15. JUVENAL and PERSIUS. (The indelicate passages ex- 
 
 punged.) 
 
 18. TACITUS. Agricola ; Germania ; and Annals, Book i. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
GREEK AND LATIN CLASSICS. 11 
 
 GREEK SERIES, 
 
 ON A SIMILAR PLAN TO THE LATIN SERIES. 
 
 1. INTEODUCTOEY GEEEK EEADEE. On the same 
 
 plan as the Latin Eeader 1.?. 
 
 2. XENOPHON. Anabasis, i. ii. iii 1*. 
 
 3. XENOPHON. Anabasis, iv. v. vi. vii. . . . .1*. 
 
 4. LTJCIAN. Select Dialogues Is. 
 
 5. HOMEE. Iliad, i. to vi Is. Qd. 
 
 6. HOMEE. Iliad, vii. to xii Is. Qd. 
 
 7. HOMEE. Iliad, xiii. to xviii Is. Qd. 
 
 8. HOMEE. Iliad, xix. to xxiv Is. Qd. 
 
 9. HOMEE. Odyssey, i. to vi Is. Qd. 
 
 10. HOMEE. Odyssey, vii. to xii .Is. Qd. 
 
 11. HOMEE. Odyssey, xiii. to xviii Is. Qd. 
 
 12. HOMEE. Odyssey, xix. to xxiv. ; and Hymns . . . 2s. 
 
 13. PLATO. Apology, Crito, and Phaedo . . . .2s. 
 
 14. HEEODOTUS, i. ii Is. Qd. 
 
 15. HEEODOTUS, iii. iv Is. 6d. 
 
 16. HEEODOTUS, v. vi. and part of vii. . . .Is. Qd. 
 
 17. HEEODOTUS. Eemainder of vii. viii. and ix. . . Is. Qd. 
 
 18. SOPHOCLES; CEdipus Eex Is. 
 
 20. SOPHOCLES; Antigone 2s. 
 
 23, 24. EUEIPIDES ; Hecuba and Medea ... Is. Qd. 
 
 26. EUEIPIDES; Alcestis Is. 
 
 30. JESCHYLUS; Prometheus Vinctus Is. 
 
 41. THUCYDIDES, i Is. 
 
 Preparing for Press. 
 
 19. SOPHOCLES; CEdipus Colonaeus. 
 
 21. SOPHOCLES ; Ajax. 
 
 22.* SOPHOCLES; Philoctetes. 
 25. EUEIPIDES; Hippolytus. 
 
 27. EUEIPIDES ; Orestes. 
 
 28. EUEIPIDES. Extracts from the remaining plays. 
 
 29. SOPHOCLES. Extracts from the remaining plays. 
 
 31. AESCHYLUS; Persa. 
 
 32. AESCHYLUS ; Septem contra Thebes. 
 
 33. JESCHYLUS; Choephoraj. 
 
 34. .3ESCHYLUS; Eumenides. 
 
 35. ^SCHYLUS; Agamemnon. 
 
 36. AESCHYLUS; Supplices. 
 
 37. PLUTAECH ; Select Lives. 
 
 38. AEISTOPHANES ; Clouds. 
 
 39. AEISTOPHANES ; Frogs. 
 
 40. AEISTOPHANES ; Selections from the remaining Comedies. 
 
 42. THUCYDIDES, ii. 
 
 43. THEOCEITUS ; Select Idvls. 
 
 44. PINDAE. 
 
 45. ISOCEATES. 
 
 46. HESIOD. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER. 
 
12 WOKKS ON MECHANICS AND THE ARTS. 
 
 In 2 vols. super-royal 8vo., price 2 5s., cloth gilt, 
 
 TOMLINSON'S CYCLOPEDIA OF USEFUL AETS, Mechani- 
 cal and Chemical, Manufactures, Mining, and Engineering ; 
 with 40 Engravings on Steel, and 2,477 Woodcuts. 
 
 In 3 vols. royal 4to., price .4 14s. 6d., 
 
 TREDGOLD ON THE STEAM ENGINE ; Its Principles, Prac- 
 tice, and Construction. Illustrated by upwards of 200 En- 
 gravings, and 160 Woodcuts and Diagrams. 
 
 In 1 vol. demy 4to., price 1 Us. Qd., 
 
 NICHOLSON'S CARPENTER'S GUIDE. Edited by JOHN HAY, 
 Esq., Architect, Liverpool. Illustrated by numerous Engravings. 
 
 In 1 vol. post 8vo., price lOs.'Gc?., cloth, 
 
 A DICTIONARY OF TERMS IN ART ; Edited and illustrated 
 by F. W. FAIRIIOLT, F.S.A., Author of " Costume in England," 
 &c. ; Honorary Member of the Society of Antiquaries of Nor- 
 mandy, Poitiers,. and Picardy; and Corresponding Member of 
 the Society of Antiquaries of Scotland. Illustrated by 500 
 Engravings. 
 
 In demy 4to., price 12s., cloth lettered, 
 
 PRACTICAL HINTS ON PORTRAIT PAINTING: Illustrated 
 by Examples from the Works of Vandyke and other Artists. 
 By JOHN BURNET, F.R.S., Author of "Letters on Landscape 
 Painting," "Rembrandt and his Works," &c. &c. With 12 
 Engravings on Steel. Re-edited, and with an Appendix, by 
 HENRY MURRAY, F.S.A. 
 
 In demy 4to., price 12s., cloth lettered, 
 
 LANDSCAPE PAINTING IN OIL COLOURS, Explained in 
 Letters on the Theory and Practice of the Art, and illustrated 
 by Examples from the several Schools. By JOHN BURNET, F.R.S., 
 Author of " Practical Hints on Painting," " Rembrandt and 
 his Works," &c. &c. Re-edited, with an Appendix, by HENRY 
 MURRAY, F.S.A. Illustrated with 11 Steel Engravings. 
 
 In 1 vol. demy 8vo., price 5s., 
 
 THE SCHOOL PERSPECTIVE: Being a Progressive Course of 
 Instruction in Linear Perspective, both Theoretical and Prac- 
 tical. Specially designed for the Use of Schools. By J. R. 
 DICKSEE, Principal Drawing Master to the City of London 
 School; to the Normal College for Training Teachers of the 
 British and Foreign School Society. Illustrated with many 
 Woodcuts and 40 Engraved Plates. 
 
 VIRTUE BROTHERS & CO., 1, AMEN CORNER.