Mºº ºf - , -, ----- - - - - --~~~~~~~~~< *, *.*.* -ºxº~~~~<&---, -: P : r *. * i *... - 4. : {`s, i. 3 A' & # ~zº ºf ſ? -- tº - 2", ...~~/ 2. ~ { } { \ *** .* {^ * : 3 | * § S * { } {^. ~~ t *... $/ & r^ ſº f } ; k At , , t → * *-. f § { } ~ 9, T. & > # # " #. = 3 2 :- # ~4. ; : 3. f ,” a", a. ** 'vº 7 () V. wº f } } t .#Aft f - s …” **. { g *- e. § ...& •. . . .” -ºš . . ...º.º. OPINIONS OF THE PRESS. – “This Essay, by Mr. Blackett, avoids the puerility and affected philosophy of the common writers of the day. It openly professes to be an Essay on the Spirit-level, and its ordinary applications and use, and to this it most strictly adheres. Hence it is one of the clearest books that we ever read : and one more useful to the Student or the ordinary ; ractice of the Surveyor could not have been written. The nstrument itself, and also the staves and other matters re- ; quired along with it, are so clearly explained, that nobody that reads the Essay can fail in understanding them. The A uses of the Instrument, and the various ways of using it, together with the best methods of recording the observa- t - tions and planning them, are given with equal clearness; nor have we ever seen a book in which the illustrative - | figures were more accurately and tastefully delineated. - We feel ourselves constrained to say, that upon a single subject this is a perfect model, and a model which cannot be too generally or too closely copied; such being the pro- perties of the book, we cordially recommend it to all those - for whose benefit it has been written.”—The Surveyor's, f Engineer's, and Architect's Journal. . “Several Years' practical experience in Engineering form - the ground-work of the Author's literary labours ; descriptions, rules, elementary and practical examples, the whole art of Levelling, and the principles upon which it is founded, make up an Essay which must afford valuable assistance to the Student, desirous of eminence in the emu- lative profession of Surveyor or Engineer.”—Literary Ga- gette. “We have had much pleasure in reading this work, which is one of the most useful, practical works that have ever been published. The necessity of Levelling, and, the re- quirement of the most extreme nicety on Railroads, we be- lieve, first brought Mr. B.'s attention to the utility of pub- lishing a treatise on the subject ; and a very valuable treatise he has here produced.—Recording levels, keeping field books, and such-like topics, are well discussed. The engravings of instruments, also of geometrical figures, plans, º sections, with the detailed description of the Spirit- level itself, render this one of the clearest and most inform- ing works, and also one of the least theoretical, on scientific subjects, with which we are acquainted. The examples, and a quantity of information to which we have not time to refer, add greatly to the importance of the work.”—Tyne Mercury. “An Essay on the use of the Spirit-level, seems a valua- * ble contribution to the scientific library. The tyro will find a master in this work, while the proficient in his art will find a valuable companion. The methods are briefly expounded, and the instructions are easy and readily un- derstood. It is illustrated with numerous geometrical figures, plans, and sections.”—Great Northern Advertiser. gº' - i. & - * T ~ * *** . . . . . . . . . . . . . , 3 *:: *, *, *... . . . . . . . . . . * , £, ºº, jºi i , ; ; ; ; J , , , - - º ** * * ... . . . . . %. 4.3, º **...* 2: . ^* °º º - § N&. * / * º, N. A Yx,'º'; \, 's .” */ at ". K. is, * §."; ty. ] ; j # *W** * > *º-º-º-º-º-º:lºg--" *** * *-* * *** - | ********************erºyºv, spiſy . .---- - -|-x ≡ ? * .· „º ae.' , ÎN* |-{� *• ș &* . . ^ ;· ſ. |-{.* AçºŁ - � +¿ #*ae- ș i •|-p. * x - |- ' i ,,-? piºſ,** 3● ----� _■ *** ș, º* . » | ---- …** # .----&* į. |-�ı § į“{\, }�? }• � , ， ,） $1 į. ;： ſºº-， ș\ } ·3. &. £ . ., , ， į.'.* №. ！ Ķ ſ.！ſ + + '.*¿? , * * í ģș* \, ae* |-\,}șº. : : º #. # E; =: º B. G E. -º E; : E; *-C Eº Eº E; É =: Eº E; Eº É º R É. ATI / º' ſ , ...T. . . . . ; ăl TRANsportation ºff LIBRARY, ſtrº [II] [it] [E]] frºm ºrſ cºſt º ºrt ſº I [º º ſº *· - ·\ ● 4 *� *-}-→ * ~*-|- · *~ -ſ ·（ - “, “ .‘… - - . ：:*...* --~~~~ ~~~~~|-; ; &' ~ .|-- （~~~~ ·* *,： --{ -r...“ > wș-**---- -*- ~~~.~ſºº <--！ ** *x → -+?**-* x_，_，，，，，-،*x_，→~*=~ ~--ș<！--º-º-º---º-：！：:: ~~~~, ，r.----*»---★ →āºr~ ~* ș•“ （, , ,· · ·-- ș* • *.！· * - s-» ' . -· ·� �: ） » wº|- * |-± }* #+- * , ， * ș«»<$ * -} * ?* %|- * & � zy- ſr* � •� ~-� -ž --* →� • și -• • • {� • —w- ------ - - -a, -º-º-º-º-º-º-º-º-º-º-º- - - - *- - ºr- - - -->s----.… -- ~~~~~~~~...~...~~~ :=-ºrtºn . . • - - - - - - . --, - - - gº - SPIRIT LEVEL. iſſi "ſiſſiſſiſſ | | | ſ | W § i. # | g | | || B ſ 8 | | ſ | . : : ſ: | | | |||| º º | | | * ! t ON THE USE OF THE SPIRIT LEVEL, AS A PPLIED TO ENGINEERING AND OTHER PURPOSES o/” º & IBY gºv . * OSWALD BLACKETT, SURVEYOR, &c. NEWCASTLE UPON TYNE: PRINTED BY T. AND J. HoDGSON, UNION STREET, - AND sold By ‘. E. CHARNLEY, BIGG MARKET ; AND SIMPKIN, MARSHAIPI, A ND CO., LONDON. : 1838. s#º .: PREFACE. lu. s ſº Nº * Vo ^ t! Q) THE great importance of the Art of Levelling, par- ticularly at the the present day when public en- terprize is leading to the accomplishment of the most stupendous undertakings in Railways, and other important works, will obviate the necessity of an apology for this attempt to facilitate the study of one of the most useful branches of sci- ence. - There has been little published on this subject, except detached fragments inconveniently ar- ranged, and so antiquated, as to be of no utility to those who seek for practical instruction. Of these truths every one acquainted with the subject must be convinced, and that a work systematically . . . . " ; ; . . .* - . . l ... 3 , sº arranged was required; I have, therefore, drawn up the present treatise, which I submit as likely to be useful to the civil and military Surveyor or Engineer, and of the greatest advantage to the ju- nior branches of society who may be designed for these professions. iv PREFACE. The present work comprehends, in addition to numerous practical examples, proper rules for re- cording levels; various methods of keeping field books, and necessary instructions in the several modes of operation now generally adopted in tak- ing levels; with such original matter as may lead to the better elucidation of this important subject, and in every part of the work I have used such modes of explanation as I thought would render the various subjects as plain and concise as pos- sible. The first part of this publication contains de- monstrations of all the principles immediately subservient to the art of levelling; the work is also illustrated with carefully executed engrav- ings of the various instruments used in this art, with numerous Geometrical Figures, Plans and Sections. I have also added a detailed description of the Spirit Level, and the mode of adjusting the various parts of which it is composed; also the true form or internal figure of the spirit tube; I hope therefore that this Essay will be found ac- ceptable to the practitioner, and useful to the stu- dent. It may here be necessary to remark that this work also embraces a few examples in the sim- plest form, for measuring inaccessible distances which may be met with in levelling, such as rivers, lakes, bogs, &c. * : *, **E=gssºrºrº , = , . . . " * ºr ºr º: , .” ". . . . . . . . PREFACE. - º The information contained in this compendium is deduced from Geometrical Principles, combined with several years' practical experience under one of the first civil Engineers in this kingdom; being thus arranged, I can with the greater confidence submit my labours to the candour of the public. This work has been a considerable time in the press, in consequence of the author's intention of publishing with it, Tables for the more readily finding by inspection the contents of earth-work; but as this would considerably increase the price of the work, it has been thought advisablé to pub- lish them separately. CONTENTS. PAGE Introduction, .......... 0 0 & 0 ° e º e º e º 'º e º 'º e s e º e º e s e e o e º e e s s e e s a e e e a • e l The Use of the Spirit Level, ... ........ . ................. 4 True Level—Elementary Example, ........................ 6 —--Practical Example,................ ~~~~ 8 Apparent Level—Elementary Example, ~~~~ 10 Reduction of the Apparent Levels, ... 11 •Practical Example, .................... H5 Simple Rules for determining the Depression or Differ- 'ences between the True and Apparent Level, ...... 17 Terrestrial Refraction, .......................................... 20 Description of the Spirit Level with its necessary Ad- justments, .................... .............................. 23 Graduated Station Staves, &c., ..................... 32 and 105 Simplest form of Spirit Level,.......................... ...... 35 Spirit Tubes, .................... ............................... . 39 Practical Levelling, ... .............. ........... ............... 42 Instructions or Rules for Recording Levels, ........ ..... 43 A new Method of Recording Levels with a Field Book, being a portion of the Stanhope and Tyne Railway, near South Shields, ...... ....... ........................ 45 Reduction of Distances, ............................. • * * * * * * e s s 52 A Table to reduce Dimensions taken in Links into Feet, and Inches, or vice versa, ...... • * * * * * * * * © g º º e º e º O s is e e º gº º 54 A Case of simple Levelling by the Back and Fore Ob- servations, ................. ........ .................. ..... 55 A Field Book of the above Levels, ....... .............. ..... 59 To Draw or Plot a Profile of the Ground from the above Levels, ..... “............ ........….......... 60 viii CONTENTS. PAGE. A Case of simple Levelling by the Fore Observations only, 61 Field Book to Ditto, and Method of Reducing the Ob- servations to the true Level,...................... .... .. 64 . Levels from Thornton Street to Parker's Quay, with a Field Book and Description, being a peculiar mode of recording Levels,..... ...................... .......... 66 Another copy and form of Field Book of the above Levels, but subsecutively arranged, ........................ ...... 78 - To change Depressions into Elevations,............ 74 and 75 t Description of Field Book, .................. ................. 75 . g How two or more Lines of Levels may be taken at one and the same time,...................................... .... 76 Reference to the Field Book, Plans, and Sections of the above Levels,........... .............. ...... ............. • 78 Levels taken from Scotswood to Crawcrook Mill Road, 81 Field Book of the above Levels, ......... ................... 88 To Measure inaccessible Distances such as Rivers, Lakes, Bogs, &c., ............ ............................. 99 To raise a Perpendicular on the Ground with the Chain onl 9 © tº e º 'º º 0 & 0 & 0 e º e º 'º e º sº e o 0 & e e o e s e e o O & © tº dº ſº tº e e • . . . . . . . . . . © & 105 E S S A Y ON THE USE OF - T H E SPIRIT LEVEL. INTRODUCTION. The Art of Levelling is that part of Mathema- tical Geography, aided by the sister sciences, Arithmetic, Geometry, and Trigonometry, which enables us to ascertain the height of any given point or place on the surface of the earth, above or below that of other given points or places on the same surface; and which also enables us to determine the difference in the distance of these points from the centre and circumference of the earth. 2 A surface may be said to be truly level, when all its parts are equally distant from the earth’s centre of attraction, similar to the smooth sur- face of lakes uninfluenced by tides, or unruffled by winds; for the surface of all fluids, when B 2 ESSAY ON THE unexposed to external agitation will become level, for the earth, being a sphere or globe (or nearly so), the surface of all waters are equally distant from its centre, which are kept, or sus- pended, in that state by the laws of gravitation. As the direction of gravity is in lines which meet near the centre of the earth; and as the surface of all fluids is perpendicular to that di- rection, their surfaces will be portions of a sphe- roid, similar to the earth ; and when these surfaces have no great extent, they may be . considered as planes, but when they have any magnitude, the curvature of the earth must be taken into account. The figure of the earth is now so well known as scarcely to require any comment; but as we shall have occasion to refer, for the purpose of elucidation to its form and dimensions in ano- ther part of the work, it may, therefore, be ne- cessary to state, that trigonometrical surveys, or geodoesic operations, have been undertaken for the purpose of measuring a degree of meridian circle in different latitudes, and also by the pendulum, and from thence determining the figure and magnitude of the earth, and which has been effected at several places on its surface by philosophers under the patronage of different governments; and I find, by taking a mean of ~~~~~~~~~rº-rº-º-º-º-º-º: USE OF THE SPIRIT LEVEL. 3 these results, that the equatorial diameter of the earth is 7919-75, say 7920 miles; and they have also discovered, that a degree at the poles is longer than a degree at the equator, so that the true figure of the earth would appear to be an oblate spheroid, the polar diameter being about 22 miles less than the equatorial; but this difference is so trivial, comparatively speaking, as to take little from its globular form, at least so small, as not to affect any of our operations in levelling; for the ratio of the polar diameter to that of the equatorial, as stated by that celebrated philosopher Huygens, is as 577 to 578, and by our equally celebrated countryman Newton, as 689 to 692. It is a fact, that the rotundity of the earth is not geometrically true; but the inequalities of its surface are so inconsiderable, that the high- est mountains bear no greater proportion to the bulk of the earth than a grain of sand does to a common globe. 4. ESSAY ON THE LEVELLING. THE USE OF THE SPIRIT LEVEL. VARIous are the methods used in marking level points, and numerous are the instruments employed on these occasions, viz. –the Plumb Level, Water Level (the Chorobates of the ancients), with various others; but such is the nature of these instruments, that they are not at all applicable to scientific purposes. I shall, therefore, confine my observations to that invaluable instrument, called the Spirit Level, by means of which a line may be drawn parallel to the horizon, describing a lesser circle of a sphere; for the bubble of air has that pecu- liar property of always forming a horizontal plane, and, according to the modern construc- tion of this instrument, the intersection of the cross wires of the telescope, which, forms the line of collimation, must be always parallel thereto; by this artificial horizon, we are ena- bled to find whether two or more points be in the same horizontal plane, or how much they may deviate therefrom : further particulars of this instrument I shall reserve for a subsequent part of the work. My immediate object shall USE OF THE SPIRIT LEVEL. 5 be to shew the principles upon which the most approved practical methods used in marking level points are founded; and, in order to ex- plain this subject more clearly, it will be neces- sary to give a few elementary examples. In the practice of levelling there are two methods adopted, the one of which gives the true level and the other only the apparent level. The first method, which is the most impor- tant, as being more simple and independent than any other, is, by the tangent of a circle, supposed to be applied to the middle point of the curve of the level, and carried to an equal distance on each and every side of the point of contact or instrument station, the extremities of which will be equally distant from the centre and circumference of the earth, for the real curve of the earth is the true level. The second method is, when the observations are only taken forward from the point of con- tact or instrument station, the tangent line will touch the circle or curve of the level at that point, and the other extremity will mark the apparent level; for one of the extremities of this tangential line will be further from the centre and circumference of the earth than the other. 6 ESSAY ON THE TRUE LEVEL. ELEMENTARY EXAMPLE. THE true method of levelling, or marking two or more level points, as I have already observed, is, by the tangent of a circle; that is, when the point of contact is exactly in the middle of the r tangent line, which is a straight line drawn, so as just to touch a circle without cutting it; and the point where it touches the circle is the point of contact, or true level point; and a tan- gent cannot touch a circle in more than one point.—See Prop. 16, 17, 18, 19, 3d Book Euclid. Thus supposing theannexed figure to represent a section of the earth, F = C. L. the centre, F C the ra- C S. dius, K L the tangent (perpendicular to the radius), C the point of contact; the two extre- mities of the tangent line KL are equally dis- tant from C (the point of contact), and also equally distant from the centre F; the angles at C are right angles, the angles at the centre USE OF THE SPIRIT LEVEL. 7 # are equal, the angles K and L are equal, and the triangles FK C and FLC are equal to one another, and the radius FC common to both triangles; therefore K and L are true level points.-See Prop. 12, 4th. Book Euclid. This method may, therefore, be practised without regarding the difference between the true and apparent level; because the line of vision is raised equally above the surface of the earth on the one side of the instrument as on the other; otherwise both sides may be con- sidered as apparent levels, and reduced accord- ingly, for this method rests solely on this circum- stance, that the Spirit Level is always placed precisely in the centre of any line, or at an equal distance from the station staves or gra- duated rods; for it is evident that if the instru- ment is set at a certain height, and remains at that height, a range of level points may be taken on each and every side of the instrument, which shall be within the circumference of a circle, whose centre shall be that of the pivot or cone on which the Spirit Level turns; consequently, equi-distant from the eye of the observer, and also equi-distant from the centre of the earth; the line of vision being on all sides raised equally above its centre, as shown in the fol- lowing figure. 8 ESSAY ON THE PRACTICAL EXAMPLE. s: zºº §§ º s -º-º: - º - º - º;'s gº. -.” º: :* * >3 - 5 º - " - *::::::::::: asº’ssº, ºcºs Yº - 㺠1 ºz ºr ** - - - - -º-ºººº...º.º.º.º. ...r.º.º. º •. - - 2-e-º: • ?: *, ºr 2: 2: $º $º. º ** ºf..., Svant sºrºr. - . --" :*** sº e s sº 4, sº •ºxy Let the instrument be placed at C, an equal distance from A and B, the two points of sight K and L, as shewn upon the station staves or graduated rods, set up at A and B, will be level points, and the difference between the two f heights, A K and BL, in feet or inches, will shew how much the one place is higher or lower USE OF THE SPIRIT LEVEL. 9 than the other; on inspection, it will clearly appear that the extremity of the line of colli- mation at L, is as much above F, the centre of the earth, as K, the other extremity, and are, therefore, both true level points. º: ºr . * 10 ESSAY ON THE APPARENT LEVEL. ELEMENTARY EXAMPLE. This method is also by the tangent of a cir- cle, but only carried in one direction from the point of contact, as the tangent is perpendicu- lar to the radius, one of the points must there- fore be further frem the centre and the circum- ference of the earth than the other, in propor- tion as it recedes from the point of contact, encreasing the length of the secant beyond that of the radius, which constitutes the difference between the true and apparent level. Thus in the opposite T} E. figure, E, on the extremity of the tangent line, shews the point of apparent level only, because the point of C contact D is not in the middle of the tangent line, but at one of its extreme- ties, and is nearer C, the centre of the earth, than’E, the other extremity of the tangent line, for every point of apparent level is higher than the true level, consequently the error will be the difference between the length of the radius USE OF THE SPIRIT LEVEL. I 1 gº CD, and the secant CE, or whatever E may be above the periphery of the circle. This method of taking levels will be found defective in point of accuracy, if the necessary allowance for the curvature of the earth is not made. . - - REDUCTION OF THE APPARENT Level. r The correction for the curvature of the earth may be found according to (Prop. 36, 8d. Book Euclid). “If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.” Let D be any point without the circle A B C, and D C A and D B two straight lines drawn from it, of which D C A cuts the circle, and D B touches the same ; the rectangle A D, D C is equal to the square of DB or (DC+2CE) x DC * * -- B D2 =B D", and 3CE-EDC =D C the apparent level, but D C being so indefinitely small compared to the semi-diameter of the earth, that for all 12 ESSAY ON THE ical º : , B D* — practical purposes we may assume it asgö E - DC. This expression which is simple, and without any sensible deviation from correctness, for the semi diameter of the earth being nearly 21 millions of feet, any difference there may be between the two modes of expression can never exceed the fraction rrrköz of an inch. There- fore, the difference between the true and appa. rent level will be equal to the square of the ... . distance between the two places, devided by the º . diameter of the earth. - … < *- Suppose we take it in numbers, and call the tangent or the observed level line B D, 5280 feet, equal to 1 mile, square this distance, and divide by the diameter of the earth A C, 41817600 feet, and the quotient will be the ap- parent level in feet or decimal parts; thus, *##### = 666666 decimal parts of a foot equal to 8 inches, the height of D above the true level, and this difference will be more or less in proportion to the length of the tangent; for this reason it will separate more from the circumference of a circle in proportion as it recedes from the point of contact, and the height of the apparent level will, in conse- quence, encrease in proportion as the square of the distance—that is to say, however much it USE OF THE SPIRIT LEVEL. 13 may rise above the earth’s surface at the dis- tance of one mile, it will rise four times as much at the distance of two miles, and nine times as much at the distance of three miles; thus, in the annexed figure. A is the point of contact or true level point, B the appa- rent level at a dis- tance of one mile, C at a distance of two miles, and D at a distance of three miles. *—#—2 A The difference between the true and appa- rent level may also be found according to the (Prop. 47, 1st. Book Euclid). In any right- angled triangle, the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle, or, in other words, in all right angled plain triangles, the sum of the “squares of the two short sides is equal to the square of the longest side, called the hypothenuse; and to find one of the shorter sides, we have only to subtract the one square from the other, and extract the square root of the remainder. Zº * : * 2% a tº ... . " . * / ...& 26. . A ~ *-*** - …?? - 1 - 14 ESSAY ON THE Suppose that the length of the tan- gent line B D is the same as in - C the preceding ex- ample, viz. 5280 feet, equal to one T E. mile, the radius, or semi-diameter of the earth, B E 20,- 908,800 feet; square these two numbers, that is, each number multiplied into itself, and add the sum of the squares together, extract the square root; then, from the root thus obtained, subtract the radius, or semi-diameter of the earth, which will leave the apparent level; thus, VB E*-ī-B D*=E 1)—E C=C D, and in numbers it will stand thus, The radius, or semi-diameter of the - earth.E B-20908800°=............ 437.177,91744,0000 Length of tangent line, B D-5280°= 27,878,400 The sum of the squares, V437.177,94531,8400– 20908800'666666, the root and length of the longest side, E D, from which subtract the semi-diameter B E, viz. 20908800 will leave 0.666666 for C D in decimal parts of a foot, equal to 8 inches, the height of D above the true USE OF THE SPIRIT LEVEL. 15 level I give this proposition a place here, as we shall have occasion to refer to it hereafter, in order to explain the method of reducing the distances measured upon ascending or descend- - ing planes, viz the hypothen usal to the true horizontal distance. PRACTICAL EXAMPLE. The following example will shew the method of reducing the apparent to the true level. / C Let the Spirit Level be placed at A, the point of contact, and over the centre of the 16 - ESSAY ON THE . . ~~~ . . . . iſ earth, C; at a distance of 1 mile from A, a gra- duated rod is set up at B; let the line of vision DE, mark upon the rod 10 feet, which will be the height of the apparent level, to be reduced to the true level for the curvature of the earth, &c. - Ft. In. The observed height on station staff,.............. ... 10 0 Ft. In. The height of instrument, ..... ............ 4 8 In. The correction for the curvature of the earth for 1 mile (see #! 8.00 page 22), ........ ....... ......... From which deduct terrestrial re- fraction (for 1 mile, see Table, X- 66 page 22), ..... - — 0 7.34 5° 3-34 The true difference of level between A and B (depression), ..... ............... .............. 4 8.66 It is evident on inspection of this figure, that one of the extremities of the visual line is fur- ther from the centre of the earth, C, than the other, and that the error in the level will be the difference between the length of the lines CE and CD, as already stated. When the observed height is less than the height of the instrument, take the difference be- tween the curvature of the earth and refraction from the observed height, and this last differ- ence deducted from the height of the instrument USE OF THE SPIRIT LEVEL. 17 fºr- -º-wºº. ". . . ºvir, will give the true difference of level, which will be elevation. To find the allowance for the curvature of the earth and refraction, look in the table (page 22) for the distance, whether in yards, chains, or miles ; then in the next column will be found the correction for the curvature, and in the third column the quantity of refraction corres- ponding to that distance. In the calculations hereafter described for de- termining the depression or difference between the true and apparent level; the distances in all cases are to be squared, whether taken in feet, yards, chains, or miles, and divided as shewn in the following simple rules and examples:— RULE 1. When the distance or length of any line is taken in feet, square that distance and divide by the diameter of the earth in feet, viz- 41817600, and the quotient will be feet or deci. mal parts; or should 3484800 be taken as a divisor, then the quotient will be inches and decimal parts. - EXAMPLE, Suppose the length of the line to be 5280 feet, equal to one mile ; 5280x5280=######3– 0.666666 decimal parts of a foot, equal to 8 18 ESSAY ON THE inches, for the first mile of apparent level, and to be deducted from it. RULE 2. If the distance should be taken in yards, the divisor in that case will be 4646400, and the quotient will be in feet or decimal parts of a foot; or take 387200 for a divisor, and the quotient will be inches and decimal parts. EXAMPLE. - Suppose the length of the line to be 1760 yards, equal to one mile; 1760×1760=######3– 0.666666, equal to 8 inches. RULE 3. If the distance should be taken in chains, the divisor will be 9600, and the quotient will be in feet and decimal parts; or take 800 for a divi- sor, the quotient will be inches and decimal parts. EXAMPLE. Suppose the length of the line to be 80 chains, equal to 1 mile; 80x80=#}}=0.666666 equal to 8 inches. RULE 4. If the distance should be taken in miles, di- vide by one and five-tenths, viz. 1-5, and the quotient will be in feet and decimal parts; or USE OF THE SPIRIT LEVEL. 19. multiply the number of miles by the number of chains in a mile (80), and divide as in the last example by 9600, the quotient will be in feet and decimal parts. EXAMPLE, Suppose the distance to be 1 mile ; 1x1=#3- 0.666666=8 inches, the height of the apparent above the true level, Upon these and the preceding geometrical principles I have constructed a table, shewing the quantity of curvature below the apparent level from 100 yards up to 20 miles; and in order to secure a greater degree of accuracy in these operations, I have given in another column of the table, the quantity of refraction corres- ponding to those distances. As the effect of re- fraction in incurvating the rays of light proceed- ing from objects near the horizon has been proved to be very considerable, it can by no means be neglected when the difference between the true and apparent level is estimated at con- siderable distances. 20 ESSAY ON THE TERRESTRIAL REFRACTION. TERRESTRIAL refraction is that by which ter- restrial objects appear to be raised higher than they really are, for the atmosphere being com- posed of vapours and other matter, which in- crease in density as they approach the surface of the earth, when a ray of light is passing from any object and enters this medium, it is turned from its rectilineal course into that of a curve, concave towards the earth, and meeting the eye in a different direction; thus it is that the ap- parent or observed elevations of objects are always greater than the true ones, and conse- quently must be subtracted from their apparent altitudes. In proof of these observations, I beg to men- tion a circumstance which is related to have occurred on the great trigonometrical survey of England. “In measuring the base on Houn- slow Heath, we had driven into the ground, at the distance of 100 feet from each other, about 30 pickets, so that their heads appeared through the boning telescope to be in a right line ; this was done in the afternoon. The following morning proved uncommonly dewy, and the USE OF THE SPIRIT LEVEL. 21 sun shone bright; when, having occasion to replace the telescope, we remarked that the heads of the pickets exhibited a curve, concave upwards, the farthermost pickets rising the highest; and we concluded they were not pro- perly driven, till in the afternoon, when we found that the curve appearance was lost, and the ebullition in the air had subsided.” The quantity of refraction contained in the following table is found by taken an average of the mean refractions given in the account of the operations of the great Trigonometrical Survey of England, and this I find to be equal to 1-12th of the contained arc. It also appears that the same average number was occasionally made use of by Col. Williams, Capt. Mudge, and others on that survey. But it has been very justly observed by Mr. Ivory, that it is fruitless to expect a near agreement in every instance between observations and any table of refrac- tions, because it is so affected by the different states of the atmosphere, and, therefore, can only be correctly ascertained by simultaneous observations. See Hutton’s Course of Mathe- matics, vol. 3, page 186, 7th edition. 22 ESSAY ON THE TABLE Shewing the difference between the true and apparent Levels, and also the quantity of Refraction for distances taken in yards, chains, or miles. The correction for the curvature of the earth and refrac- tion will be found in the columns under 1 and 2 in inches, and decis mal parts; and in the columns, under 3, in feet, inches and parts." I 2 3 Correction Terrestr. 3|Correction Terrestr. # Corºction|Terrestr. Hist Curvature, Refraction # cuºure Refraction s Curvature|Refraction Yds. §: | - — lit. in. dec. p. in.) dec. p. 5|inſ dec. p. lin.I dec. p. 61 ft. lin'ſ p. ſtin. p. 100 '02582 •02000 || 001 66|| || 0 800|| 0 0-666 | 200 - 10330 •08000| | |0ſ, 666|| 2 || 2 | O; 2.666 | 220 - 1 2500 • 12500 •0104.1 3| 6 || 0 |00|| 0 6|-000 300 -2324.4 • 18000|| || 0 1500|| 4 || 10| 800 0|10|-666 400 - 41322 •32000 ‘02661; 5 I 6, 800 I | 4-666 440 |"50000 •50000 •04,166; 6 24| 000] 2 U-000 500 64,566 ‘72000 •06000; 7: 32| 8||00] 2 S-666 600 92975. •98000 -08 1664, 8, 42| 800 3| 6|-666 700 1 26550 1 j 10666|| 9 54 000; 4, 6-000 | 800 1|-65289 | 62000 13500||10| 66 8|9|| 5|| 6-666 880; 2) •00000: 2|-00000| | 16666|| || 80ſ 800 6, 8-666 900] 2 09 194 2|-42000 20166||12| 96 OIO0 S. O.000 1000; 2 °58264 2| 88000 24000||13||12| 800 9| 4|-666 I 100 3 - 12500 3| 38000 •28 166||14|130| 8 § 10|-666 |200|| 3 | "71900 3} •92000 '32666||15||150 000|T2| 6-0 1320, 4 •50000 4|-50000 ‘87500||16|170; 8|0014, 2-666 1400, 5 -06190 5|- 12000 •42666||17|192| 8|00:16 O 666 1500 5|-81095 5. "Z8000 “48166||18|216 00018 0-000 1600 6, 6ll 57 6 : 48000 ‘54000||19|240 S100|20 O-666 | 700; 7: .46384 7|-22000 •60166||201266 800|22 2-666 1760. 8] -00000 8|-00000 '66666|2|{294 000/24 6-000 This Table may be applied to many other useful pnrposes, particularly to determine the extent of the visible horizon from any given point. By this important application we may determine the distance of one ship 'from another, or the distance of any vessel from land when just visible, the height of the eye of the observer above the level»of the sea or horizontal *ime being known ; and we may also determine the extent of vision on the rsurface of the earth, from the top of a mountain or tower. To find the distance of an object when it first comes in sight, the height •of the eye of the observer being 96 feet above the level of the sea. Thus, by inspection, look in the table in the column of correction for “difference of level, viz. –96 feet, and opposite, in the left hand column will be found 12 miles for the distance of the object, — Or thus, To the height of the eye of the observer add its half, extract the square root of this sum, and the root thus obtained will be the extent of the visible horizon in miles. The height of the eye, 96 feet. Add its half, ............ 48 A/− 144 = 12 miles. USE OF THE SPIRIT LEVEL. 23 & - SPIRIT LEVEL. SoME of these instruments have plain, or open sights; and others telescopic sights, constructed so as to remedy the defects arising from the re- frangibility of light, and are called Acromatic Telescopes. These are generally attached to the best kind of spirit levels, which enable the ope- rator to distinguish distant objects better, and obtain a more direct line of sight, affording a large field of view, and possessing a consi- derable degree of magnifying power; in the focus of the eye-glass are two very fine cross- wires, or hairs (I have generally made use of the fibres of cotton, which are extremely fine) fixed in a cylindrical ring at right angles to each other, connected to screws on the periphery of the tube, to move and adjust these cross wires to the axis of the telescope; at the object end of the telescope is an inner tube, which may be moved outwards, by turning a tangential screw on the side of the telescope, to such a distance as may suit the eye of the observer. The frontispiece of this work is a correct re- presentation of one of the best kind of instru- ments made use of in taking levels, and the fol- 24 ESSAY ON THE lowing is a detailed account of its parts, by letters of reference, &c. A, an acromatic Telescope, nearly 2 feet long; Fig. 2 is a cross section of the tube at f. showing the situation of the 4 screws, and the cross-wires to determine the axis of the telescope. 33, cylindrical rings or collarins on which the telescope turns: a the eye end, and b the ob- ject end of the telescope. B, a tangential screw on the side of the te- lescope, for moving outwards the inner tube to such a distance as may suit the eye of the ob- Serveſ. - C, the spirit tube, hung collateral to the tele- scope, containing the column of air, one end of which rests in a stirrup, with a small screw on either side to adjust the sydereal motion of the bubble, and the other is wrought up or down a male screw by the two capstan-headed female screws c c, for adjusting the bubble of air paral- lel to the axis of the telescope. D, the bar and compass-box. The compass- box is one piece with the bar, divided into four quadrants, subdivided into 90 degrees and also into 360 degrees, with a magnetic needle, trig- ger and spring to throw it off the centre when not in use, forming a perfect circumferentor. E, two supports or rests for the telescope, the lower ends of which are sunk perpendicularly * USE OF THE SPIRIT LEVEL. 25 into each end of the bar D, called wyes, from their resemblance to the letter Y; these are rais- ed or depressed by the vertical screws e,f, work- ing in the upright stem of the wyes, to bring the instrument to a level: 44, a bow, with a spring attached to the head of the wyes by a forked joint at one end and a pin hole at the other, to fasten down the telescope into its rest. - - - F, a conical brass ferule fixed to the under side of the compass-box (this constitutes the up- per portion of the instrument), which is fitted to the bell metal frustrum of a cone attached to the upper parallel plate. G, the upper parallel plate. .." & H, the under parallel plate, fixed to the upper plate by a strong central pin, ball, and socket. h h h h, four vertical screws for adjusting the parallel plates to the parallelism of the column of air and axis of the telescope, their heads resting on the under plate H, and working through and into cylindrical tubes fixed to the upper plate, G. - I, a clamping screw to fasten the brass ferule to the under portion of the instrument. K, a tangent screw which gives a horizontal motion to the telescope in order to bring it into a just line of collimation. - 26 . ESSAY ON THE L L L, three strong mahogany legs, fitted with joints, attached to the under side of the parallel plate H, and on which the whole rests when in use. - Telescopes have one defect, that is in short distances, when the sliding vane of the gra- duated staves come within 5 or 6 yards of the instrument, the centre of it cannot be distin- guished; many cases will occur in levelling through a country, where only very short dis- tances can be taken, in passing plantations, deep ravines, &c.; on these occasions I have gene- rally made use of a smaller kind of instrument, but it would be more advisable to have open sights (perforated pieces of brass) to attach oc- casionally to each end of the telescope, and to be placed parallel to its axis: the one at the eye end of the tube should be a round hole one- eighth of an inch in diameter, and the one at the object end a quarter of an inch in diameter, with a thread or hair across the centre, corresponding to the cross hairs of the telescope, by which means near objects would be seen distinctly. ADJUSTMENTs of THE INSTRUMENT. The necessary adjustments of this instrument are three. First—To fix the point of intersection of the cross wires in a line of collimation that USE OF THE SPIRIT LEVEL. 27 . shall exactly coincide with the axis of the tube of the telescope; but more particularly with the axis of the cylindrical rings on which the tele- scope turns. Second—To make the column of air or bubble parallel to the line of collimation, or the axis of the telescope. Third—To adjust the parallel plates for the horizontal motion to the parallelism of the column of air and teles- cope. - * … , * • ‘ 1st. To adjust the cross wires in order to obtain a just line of sight. Having set up the instrument and one of the graduated station staves, at a distance of 5 or 6 chains (or observe a horizontal line of any kind, the underside of a window head, or sill, the frame, &c.), or direct the sight to the brass wire, across the square hole in the centre of the slid- ing vane, and observe if the cross wire in the telescope, but more particularly the horizontal wire, coincide with it, turn the telescope in a la- teral direction half round on its axis, and if the intersection of the wires still corresponds with the object, they are in their right position, if not, adjustment is necessary, and which is ef- ected in the following manner: correct for half the différence, by moving the wire upwards or downwards, viz. by easing one of the capstan- headed screws and tightening the opposite one 28 ESSAY ON THE (this not being attended to will endanger the breaking of the threads of the screws, or the screws themselves), turn the telescope round into its natural position and adjust the wire with the object; again turn it half round on its axis, and continue repeating these opera- tions, until, in both positions of the telescope, the wire coincides with the same part of the ob- ject; the vertical screws 11, moving the hori- zontal wire; and the horizontal screws 22, the vertical wire.—See Figure 2, Plate 1. If the cross hairs or wires are next the eye glass of the telescope they will appear in a na- tural position, and will be readily adjusted; but if the hairs are without the eye-tube they will, in consequence, be inverted, and require to be moved in an opposite direction to that in which they may appear. Thus, for instance, if the horizontal wire has been adjusted with some distant object, and the telescope is turned, in a lateral direction, half round, the wire appears above the object, it is too low ; therefore, slacken the then under screw, and tighten the upper one; bring it again into a line with the distant, object, and if, on turning the telescope into its natural"position, the wire appears below the object, it is now too high; therefore slacken the upper screw, and USE OF THE SPIRIT LEVEL. 29 tighten the under one, and repeat these opera- tions untill you have proof of its adjustment. 2nd. To make the column of air parallel to the line of collimation or axis of the telescope. Bring the telescope, with the rims of the wyes open over a pair of the vertical screws h h, at- tached to the parallel plates; then, if necessary, raise one of these screws and depress the other until the bubble becomes stationary in the mid- dle of the tube; the telescope must now be taken out of its rest and laid the contrary way, if in this situation the bubble of air remains in the middle, the level has been properly adjusted; if not, the end to which the column of air runs will be too high ; therefore the position of the spirit tube must be so altered as to be equal to half the difference, by raising or depressing, as the case may require, the capstan-headed female screws c c, at one end of the spirit tube, and for the other half raise or depress the opposite ver- tical screw d or e in the bottom of the wyes or h h in the parallel plates; again reverse the te- lescope by bringing it to its former position, and if these adjustments have been accurately made the bubble of air will settle in the middle of the tube in both positions of the telescope; these operations must also be repeated until it bears this proof of accurate adjustment. 30 ESSAY ON THE 3d. To adjust the parallel plates for the ho- rizontal motion. - - Place again the telescope, &c., over a pair of the vertical screws, h h, which are attached to the parallel plates, and cause the column of air to become stationary in the middle of the spirit tube, by raising one of the screws and depressing the other; turn the telescope over the other two screws, raising one and depressing the other until the bubble of air rests in the middle ; the instrument will now become completely adjust- ed, and may be moved round on the cone at- tached to the parallel plates, without the column of air changing materially in its place, and the observer enabled to take a range of level points from any side he may judge necessary. TO PROVE THE ADJUSTMENTS OF THE SPIRIT LEVEL. Having chosen a level piece of ground, let each of your assistants, with their graduated staves, go off for a certain distance, say, 4 chains on either side of the instrument; and suppose you find the height on the front staff to be 5 feet 6 inches, and that of the rear staff 6 feet, making a difference of 6 inches; change the po- sition of the instrument within 2 or 3 chains of one of your assistants, and observe the same USE OF THE SPIRIT LEVEL. 31 points; if the difference should be the same the instrument has been properly adjusted: it is of the greatest importance that the instrument should adjust at an unequal distance in the manner I have just described, because parts of the instru- ment may be very far from the truth, and yet adjust when always placed at an equal distance from the station staves (situations will frequent- ly occur in a line of levels where this cannot be done). Let us suppose, for instance, that the cross hairs are not properly adjusted to the axes of the telescope, or the bubble not properly balanced in the case, then the line of collimation will be as much inclined on the one side as on the other, and therefore will give equal results; but there is another and greater defect than those now mentioned, and which is not so easily detected. The defect that I now speak of is in the mechanical construction of the instrument, the ends of the telescope not being correctly ba- lanced; if either end should have the preponder- ance of weight, it will have the same effect as that of the cross hairs of throwing the line of vision upwards or downwards, which would have a serious effect on a line of levels of 15 or 20 miles extent, where long and short distances are occasionally and unavoidably taken. Therefore whenever the telescope is suspected 3. ------~~~~ : - ~~~. . . . ---- ~--------~~~~~ ser---sºmºrrºr-rrºr . * # 32 ESSAY ON THE of not being properly balanced, procure a small ring of sheet lead, nearly the diameter of the tube of the telescope, to slide upon that end requiring such counter-balance; or it may be loaded with pieces of copper (pence or half. pence) until a proper balance is discovered, and the bubble turns in every direction without any material change of position. The operation of levelling being of a very ac- curate and important nature, and the best in- struments, when out of adjustment, being of little use, we would therefore recommend to every one, who wishes to rise in his profession, to make himself perfectly acquainted with, and skilful in adjusting, the various parts of which it is composed; without that he must not expect the instrument to answer the purposes for which it was intended, nor his observations have that degree of accuracy which is so requisite. THE GRADUATED STATION STAVES. The two Station Staves, or graduated rods, used in levelling; for the sake of portability, each rod is made up of two parts, of six feet each, tongued and grooved, the one made to slide upon the back of the other; two faces of the moveable portion of each of these laths are accurately divided; each face bearing - ºf º :… º.º.º. sº - ºr . . ; º . - r '#3. Yºgºr. *-ā- 3-ºxºº. . * * - ... º.º. ºw- º k º º g: º .. : 3 Fº .*.*. . **. ::... : . * '3 2. - # - _** … * w ** #: º - º x r:} { §º.", "c" . - , , ... … . . . . * : * > . . . * * * * *: *...*, *. * - . k: sº, . . . - , - - * : * , * - - º . *** - - *..., . . - - - - - --- - * - -*. - ; : + *..., - :- §§- - - - - $º e - # * , te -* * * * *** 5*…-- ze /øe33 7/3 WC2232/.2 g 2y IFrontView Cro.º.º. &cdon 3 ºf «.-----^} }ºÑ GNQ&3 |. $ ·！ 4} į.- *ſae |-§ }}}§»uva ſuae .*È ſ-����→ ||||||||||||||||||||||||||||||||||||||· ș ſë|||||||||||||||||||||||||||||||||||||||||||||–||–||–||–||–||–||–||–||–||–||–||–||–||–||–||–||–|—ť (I)Q și # Ē|o|---- §3� ſåN� wł. * *LÈ ！！ ！！ ！! ！！ Ț Ș -…“· . . . . . ., … , , ** ** USE OF THE SPIRIT LEVEL. 33 two sets of numbers, viz. feet, inches, and tenths, also feet and hundredth parts; the outer face numbered upwards to 5 ft. 9 in., and the inner face, taking up the divisions where the other left off, numbered consecutively downwards to 11 feet 6 inches, therefore, when the heights ex- ceed 5 feet 9 inches, the sliding vane must be fixed at that point, and all the heights above it will be shown on the inner face, beginning with 5 feet 9 inches, and its parts 5 feet 10 inches, 5 feet 11 in., 6 feet, &c. In Fig. 1 a, Plate 2, it is shown to stand at 6 feet 6 inches. * * SLIDING VANES. : . Each graduated rod has a sliding vane, which º is made with a groove in the back to slide steady #' up or down the staff, and to fasten with a spring; but this is apt to lose its power of action in dry weather from the pining of the wood, there- fore a screw is necessary, to work through a socket in one of the sides of the groove, into a clutch on the back of the spring, to ease or tighten, as occasion may require. See Fig. 1 a, Plate 2. The length of the vane is about 11 inches, breadth three and a quarter inches and thickness nearly half an inch, it has a square hole in the middle with a brass wire across its centre, to D vs. 34 ESSAY ON THE point out the precise divisions on the staff cor- responding to the visual line of the telescope. The face of each vane is veneered, and divided for the extent of the opening in the centre white, above and below it for half an inch in width black, the remainder white. See Fig. 1, Pl. 2. I have sometimes made use of a lath, 12 feet 8 inches long, dovetailed, with the divisions, feet, inches, and tenths on one side thereof, with a circular vane of 4 inches in diameter drawn up or down with a cord passing over a small sheave at the top, and another at the bottom. See Fig. 2, and 2 a, Plate 2. To fasten the vane a small eye'screw of iron or brass is fixed in the back of the lath at the height of 5 feet, through which the cord is drawn and pressed into the eye of the screw, is a circular wooden pin, slightly flattened on one side, to gripe the cord, which effectually pre- vents its slipping. USE OF THE SPIRIT LEVEL. 35 : … ºr *** - ---------. - - ------, - - - --—----------------------— $º. ------------sº **** * ! ----- SPIRIT L E V E L. SIMPLEST FORM. The simplest form of the Spirit Level, for fix- ing any plane horizontal, is represented in the following Figure 1. - It consists of a glass tube set in another one of brass, about # of an inch diameter, having an aperture in the middle whence the bubble of air may be observed; this tube is attached to a flat bar, 10 inches long, 4 broad, # thick, with two plain sights A D, B E, fixed at right angles thereto, of an equal height, and perpendicular to the tube: in the middle of the eye-end A is a drilled hole # of inch in diameter, and at the object end B is an opening of , inch in diameter, with a hair or wire across its centre to fix the point on a level with the instrument. ſ 36 ESSAY ON THE The glass tube is nearly filled with spirits of wine, turpentine, or ether; the remaining por- tion of the tube is occupied with air, which forms the bubble; it is either hermetically sealed, or plugged, to keep in the fluid. The glass tube is not strictly cylindrical, al- though it may have that appearance; it is slightly curved, the convex side being upwards. The method of fixing the glass tube into its brass case is this, the tube is first fitted into the case, and if it should be found too wide a few folds of fine paper are put under it; the tube is then placed on the forks or wyes of the instru- ment, called the bubble-trier, which is provided with a micrometer screw for raising or lowering the ends of the tube, to bring it into a proper ad- justment, the bubble C is made to stand between two marks or scratches on the glass tube at c c, the ends of the level are now reversed, that is, the end B is put where A was ; if in this position the bubble stands in the middle, it proves the le- vel to be correct and truly horizontal, but if it should run to either end, it will show the end to be too much elevated : suppose, for instance, it were to run to the end B, let a small wooden wedge be inserted between the upper side of the glass tube and the brass case, so as to press that end (B) downwards equal to half the error USE OF THE SPIRIT LEVEL, 37 or difference, let another small wedge be in- serted in the other end, between the under side of the glass tube and the brass case, so as to press this end (A) upwards equal to the other half of the error: the level must now be re- versed to verify these corrections; and when they are made, so that the bubble stands at the marks c c, in both positions, the level is correct If the bubble should have any sideral motion press a wedge in on that side to which it has a tendency to run. The tube is now made fast to the flat bar by the two screws a and b; at that part of each screw which will reach about the semi-diameter of the tube a groove is made to receive, on both sides and at right angles thereto, the ends of two very small screws or pins a ar, by which the tube is supported, and either end elevated or depress- ed, as the case may require. The screws a b, are for the purpose of adjust- ing the under surface of the bar or frame paral- lel to a tangent supposed to be applied to the middle point of the curve of the level. This adjustment is effected without much difficulty, by placing the level on an adjusting plane or bench, and then reversing it; if the bubble should stand exactly between the two marks on the tube in both situations of the level, it follows 38 Essay ON THE that neither end of the bubble tube, nor the un- der surface of the level is elevated ; but if it should run to one end, we shall suppose the end A, tighten the adjusting screw a, for one half the difference, and for the other half raise the tube by easing the opposite screw b, or raise the end B of the adjusting plane or bench ; continue these adjustments until, in both positions of the instrument, the bubble rests in the middle at the two marks c c, the level will then be correct, and may be applied to any surface. Now to render this simple instrument applica- ble to field purposes, I had attached, by means of the screws A B, as shown in figure 2, a ver- tical arch (milled only), of one and a halfinch in diameter, and three-eighths of an inch thick; this arch is wrought by the tangent screw c, by which means the bubble is accurately and expeditiously brought into proper adjustment, it is very port- able and may be used on the head of a walking- stick; or on the legs of a more perfect instrument, it will be foundextremely useful, not only in steep woody grounds, where short sights only can be obtained, but may be applied to general use, par- ticularly in draining of lands; its arrangements being so simple that any one may use it, and it possesses another important recommendation, viz., that it is not easily put out of order. USE OF THE SPIRIT LEVEL. 30 SPIRIT TUBES. To elucidate the nature and figure of the Spi- rit Tube more clearly, let the two following fi- gures represent longitudinal sections of two tubes, which I have now in my possession and in use; No. 1. is hermetically sealed, and the other, No. 2, PLUGGED : the manner in which this is effected is by corks made to fit the ends of the tube and covered with gut skin immersed in a compositon of gum arabic dissolved in wa- ter and plaster of paris ground together, which is the best cement for that purpose, and sets in the spirits of wine almost instantaneously, It is a fact not generally known that the hard- est gums, such as gum copal, &c., are soluble in spirits of wine, whilst the softest gums, which are readily dissolved in water, as gum arabic, are not soluble in that spirit. * Suppose the upper surface of these tubes to be segments of large circles A CB, then, according to the laws of hydrodynamics, the surface of any fluid, influenced by the laws of gravity and in equilibrium in any vessel, is horizontal, or at right angles to the direction of gravity; there- fore, it is plain that the bubble of air, being the lightest of the contents of the tube, will occupy the highest part of the circle C, and the two | | 40 ESSAY ON THE points A B, being equally distant from C, will be in the same horizontal line A D B. The larger the bubble C, and the radius of the circle A C B, the more sensible it will be to any deviation from the horizontal plane, because it will have to traverse a greater distance along the tube in proportion to any partial inclination of either end. Spirit Levels are too commonly made of the glass tube in the state in which it is obtained at the glass-house; but no one can form an idea of the defects and irregularities of the interior sur- face of these tubes, unless they are in the habit of grinding or seeing them ground. No tube ought to be attached to an astronomical or mathema- tical instrument unless it has been previously ground inside to a circle of 800 to 500 feet ra- dius, according to the length of the telescope to which it is attached. g The radius of the tube No. 1, whose bubble moves about six lines for a minute of inclina- tion, is 380 feet, and it would require a plumb line 1520 feet in length to give the same results with equal precision. tº In order to give that regular form to the up- per internal surface of the tube No. 2, I caused to be made two turned iron mandrils, twice the length of the glass tube and covered with lead USE OF THE SPIRIT LEVEL. 41 of the same length ; one of these covered rods was turned truly cylindrical, and the other rod to a spindle form, which was made to correspond with a portion of a circle of 2182 feet radius, and attached to a telescope 2 feet long. The cylindlical rod was fixed between the centres of a lathe, and the glass gently pressed and continued turning, with the hand, on the lead, during the operation of grinding with fine emery, sand, and water, which was fed in at that end of the tube of the smallest diameter, and ground until it became perfectly cylindrical, which was known by a guage made for that pur- pose: the other mandril or spindle was now ap- plied, and the glass tube kept in one position and ground with flour of emery and water; and it was thought sufficiently ground when every part of the upper circumference of the tube and spindle touched each other. - Spirit Tubes referred to in Page 39. 42 ESSAY ON THE PRACTICAL LEVELLING. The methods of Levelling may be divided in- to simple and compound; what is termed simple levelling is determining level points from one | 3. } station, or from one point direct to another, whether the Spirit Level be fixed at one of the points, or in the intermediate distance, is imma- terial; but it must be remembered that when the instrument is placed at one of the extremi- ties of a line, the result will be the apparent level only, which will require to be corrected or reduced to the true level. I would always re- commend placing the Spirit Level in the inter- vening space, whenever it can be effected at an equal distance from the graduated staves, where- by much time will be saved and unnecessary trouble avoided; and this reciprocal mode of levelling is undoubtedly the best and most ex- peditious, no reduction for the apparent level is necessary, neither have we occasion to regard the terrestrial refraction, for whatever be the quantity it will be equal, and the result of the practice will be as accurate as if there had been no refraction, because the density and constitu- USE OF THE SPIRIT LEVEL, 43 tion of the air and vapour at the same instant will be the same in each position of the instru- ment. However, an example in each case will render this part of the subject quite plain. INSTRUCTIONS FOR RECORDING LEVELS. RULE 1.-SIMPLE LEVELLING. The commencing station, or rear staff, may or may not have any determined height; but what- ever height may be shewn on the graduated rod +-we-ºr----- ~s or staff, must be entered in the field-book in the column marked rear heights, and the heights shewn on the front staff in the column marked Jront heights, and their difference (whatever it may be) in the columns of elevation or depres- sion; therefore the regular station heights from whence the levels are continued must progres- sively be added in each column, and deducted from each other to find the height of the last one in succession, by this means the Elevations and Depressions radiate from one general base line. If the sum of the rear heights exceed the front heights, the difference will be Elevation; but if the sum of the front heights exceed the rear heights, the difference will be depression. 44 ESSAY ON THE RULE 2.-compound LEVELLING. Offsets,” bench marks, intermediate and in- strument heights, are always to be treated as front heights (which in fact they are), from the number of the instrument station, or distance they may be taken from, because the are merely lines diverging, or let them be considered diverg- ing, from the rear staff, and they may or may not be carried to the columns of the general re- gistry; but when they are so entered, they must be carried to the column of front heights, and added to all the heights of that name above them, and deducted from all the rear heights as the case may require, by taking the less from the greater. When the offsets or intermediate levels are added to the last observed front heights, they must also be carried to the other column, be- cause in this case they become the rear heights to the next fore observation. * When these heights are numerous, when taking 3 or 4 lines of levels, to shorten the registry and prevent confusion, they are frequently recorded on the opposite sheet of the field-book, and entered in the column of front heights, and their relative heights are by this means calculated separately. USE OF THE SPIRIT LEVEL. 45 rºs-rr-, -r-z-ºr-º-º: RULE 3.—Recording Levels, &c. To the commencing station or rear height, if there is a probability of the general line of levels falling below the base line, add to the rear heights 100, 200, or 300 feet, by this means all the observed points become elevations in a greater or less degree, and the zero mark or starting point will be 100, 200, or 300 feet above the base line, consequently whatever sum be borrowed must be carried to the column of rise, and also to the column of total rise, as shewn in the following Field-book (page 48); and I may further observe that, if the falls are likely to exceed the rises at any point, any number of feet may be added to the rear heights during the progress of these operations, but care must be taken to carry the same number to the three columns already mentioned, for the pur- pose of proving the work in detail. . If the difference of the sums of the two first columns, that is the rear and front heights, and the difference of the sums of the two succeeding columns, rise and fall, are equal to the sum of the total rise, the operations have been correctly performed and afford so many proofs of the ac- curacy of the additions and subtractions, but if any of these suus should disagree, re-examine 46 ESSAY ON THE that column where such difference may arise. As this rule differs so materially from the preceding ones, and without arrogating to myself any merit or claim to this method I beg to say that this mode of recording the levels and form of computing was communicated to me by my friend Mr. T. E. Harrison, civil engineer, although it is not so simple in its operations as the two proceeding rules, yet for brevity it has the decided advantage, and I am so perfectly convinced of its general utility and efficiency, that I cannot but give it a place in this work. I shall now endeavour to explain this rule more fully, and I have to hope that my readers will find everything here which will enable them to undertake any part of the field practice, and that my detailed explanation will be found as simple as the nature of the subject will permit. In the first place then substract the rear heights from the front heights, which ever are greatest, and place that difference in its respec- tive column of elevation or depression, and proceed until one leaf side or half a page is completed; add up the sums in the column of rear heights including the sum borrowed, add up also the column of front heights, the column of elevations with the sum borrowed, and the column of depressions. Now if the difference USE OF THE SPIRIT LEVEL. 47 between the sums of the rear and front heights is the same as the difference between the sums of the elevations and depressions, this much of the work is correct, and this difference will be equal to the total rise at that particular point, but if they should not agree the whole should be re-examined. If the first difference be- tween the rear and front heights should be elevation it must be added to the sum borrowed in the column of total rise, whatever it may be, but if the difference should be depression it must be subtracted from that sum, and as these operations progress, add each individual rise to the sum of the total rise, but subtract each in dividual fall from the sum of the total rise. ~~~~~a a-- ~~~<=-------> --- - - - - - - .* i. 48 ESSAY ON THE I have in this field-book given a portion of the Stanhope and Tyne railway, near South Shields, with the levels taken at each chain length, and as there are certain parts of it steeply inclining ground, I shall take the oppor- tunity of explaining the mode of reducing the oblique measurements to the true horizontal distance, for when we actually measure up or down a slope of great steepness the line ought to be shortened in the proportion of radius to the Co sine of the angle of elevation. I commence the field-book from the bottom of each page and write upwards, and the calcu- lations are extended from left to right; the first difference that occurs between the rear and front heights is 0.94 decimal parts of a foot, for depression or fall, which will be found sub- tracted from the 100 feet borrowed, making 99ft. 06d. pts. for the total rise at the first chain distance; the next difference is also a fall of 1:00 one foot, and is also deducted from the total rise, leaving 98ft 06d. pts. for the second length, viz. 175; as the falls follow for some distance we shall pass over them and go to the approximate distance 3:43, where the first rise takes place and which is 4:15, viz.-four feet and fifteen decimal parts which is now added, making 66 feet 25 decimal parts for the total FIELD BOOK REFERRED TO. [To FACE PAGE 48. - -**- - i IDIST, R.E.A.R. FRONT TOTAL | RED, CH, I HEIGHT, HEIGHT, Rise. ****| Rise. Dist. LOCATIONS. | 350-13] 233-08|167-31 |50-26 26-00 Il-32 8-82. 2'50| – || 17-05|25-39|Mark near Quarry. 25 s 4°52′ 2:40 2-12) —H 14.55|24:39 24- 4°18 4-52 —| 34|| 12:43:23-39 B. M. 5-60 4-18] 1 '42| – || 12.77|B M - 23, 18 12-04, 5-60| 6’44 —ll 11.35|22:57|Surface of ground over - water-pipes next hedge. Offset 4-85 12-04| –| 7-19|104-91 offset jace of water in reser- 23. 5'08) 4-85| "13 – 112-1022.39 22 3:40, 5'08 — 1.68||111 -97.21-39 21 - 2-60. 3-40 —| -80 #: Cº. 20:00 2°58' 2-35 °23 —||114.45|l 9-39 J9- 3:40 2.58| -82 114, 22|18-39 18- 4-55 3.40 l’lā 113-40|17-39 17. 4:92] 4:55 37 112.25|16-39 16. 4'45| 4 -92 •37|111.88||5-39 A. 276.64. 16489.15218.898s 15 °45 7:53 4'45| 3:08 112.25||14-84 Y Surface of gr. over new water pipes. 15:00 10-95| 7-53| 3:42 109-17|14:39 14, 20 3.56 •47 3-09 105-75||13-59 14.00 12-08. 3-56: 8°52 102.66|13:40|r 13-27 4-80 •14|| 4 -66 94-14|12783 tº e 13:00 13.53| 1.80 8-72 s9.48|12-52.É Steeply declining * ground. 12:33, 7.07 I-52| 5-55 SO-75|| 1 '86 Occupation Road. 12:00 l l 50 7.07| 4:43 75 '20ſ II 54. I 1 -37 8-72 •31 || 8-4] 70.77|10-91 11-00 IO-25} 8-72; 1 -53 62-36|10-56 J 10-80 l l 50 10.25: 1-25 60-83|10 -36 On oppositeside of 10'75|| 10:25, 11.50 – 1 25, 59.58|10-31 Brook. - Into centre of brk. /d 24;" (10 im. water.) 1970 1000. 4325 — 25 60.83|1926., on side orbrook. 10°10| 6-77] 10:00 3.23| 61 08|966|. 10- 1-0|| 6-77 5-76, 64-3)] 9.57|3. 9 80 3:23| 13-60 10:37, 70.07| 9-39. 3 9°50' 4-35| 13-77 9.42| 80'44, 9:13 * * 9-17. 9-80 13.95 4.15 89-86 885 - Steeply declining gr 9. 6-90 9-80 2.90| 94 0 || 8 89 122-84. 25.93| 99.46|| 2:55, 96 9] 887 cross hedge into | * = **-* | *** *** T = e = | s= . East Dean. 8 ‘80 5-08, 6.9ſ, I 82 8.50; J 8 * 4, 55| 5 08 •53 ; 7-70 7. 4 -35 4. 55 •20 99.26 670 & 5 05 4-35 - 70 99.46|| 5 -70 5°50 1 1 00 5-05 || 5 95 98.76|| 5 20 5°23 6.24 4-52 l'72 – 92-8] 49s. .*::::::: º; into 5 • 1827. 624 7-08 — 91°09| 4:84 #steeply inclining gr. 4, 60] II '86 125 10-61 — 84.06| 4:45 # 4 • 10:45 325| 7:20 — 73°45' 3-88|J on oppo. side of brook 3.43 14'60 10.45| 4-15 – | 66°25' 3-32 Into centre of small] 3°35' 10-45 14-60 – 4-15 62°10' 3-24 brook (6 in. water.) On side of brook. 3:30 7.10| 10:45 – 3:35, 66:25; 3:19) 3- 1-52 7-10 — 5-58 69.60) 2-89 | ly declini 2-77 .io 1390 —13 so 75 is 2-63 K Steeply declining gr. - 2-37 5-68 13.96 gº 8-28 88 •98 2-34, | CroSS hedgeinto West 2" | . 4.-88 5-68 — ‘80ſ-97°26′ 2:003. Dean.” - I-75 3.88) 4-88 — 1.00. 93-06; "I “75 J - 2.94, 3-88 — , -94. 99-06 || -00- § 90 100.00 100.00 100 00 00. Borrowed 100 ft. i_flºan, South Shields, May 27, 1833. . . . . . . . . …" ;Stanhope and Tyne railway commenced Jewels from a mark in a field near Brewery * - , , , 3 : 3 / 3 2. 3 3 - d ? 7/7 of /4, 7 - 5 / %.'. : +. + f , A. : * º º * t : USE OF THE SPIRIT LEVEL. 49 rise at the distauce of 3:48 extending to the opposite side of the first brook. I think it would be quite unnecessary to enter further into this detail, because as the field- book now stands it is a mere matter of addition and subtraction, and a little attention to the preceding instructions will enable any one to manage the subsequent calculations. I shall just observe that instead of carrying forward at any succeeding page the gross numbers at the head of the four different columns, only carry forward the total rise and this sum must be placed at the bottom of the page mnder the head of rear heights, rise, and total rise, and whatever may follow must be conducted in the manner already described. - Let us now proceed to calculate for the true horizontal distance,—on examining the column of total rise and the column of approximating distances, we shall find four series of numbers requiring reductions, the 1st series commences at or between two chains and 2'37, conse- quently the difference in their distance is 37 links, and their difference of level 8 feet, 28 decimal parts, equal to 12.5 links, which may be found, according to instructions given in page 53, and by inspection of the table, page E 50 ESSAY ON THE 54, or say as 66 ft. : 100 links: 8 ft. 28 pts.= 12.5 links. - - - Then from the square of (37°)=3169 Subtract the square of (12.5°)= 156:28 Extract the square root of the re- mainder, ........................Y121275=34: links for the true horizontal distance, which added to the 2 chains will give 2:34, and that must be carried to the column of reduced dis- tances. The next reduction is between the 2.37 and 277, the difference in their distance is 40 links, and their difference of level 1380 links. Then from the square of... (40)=1600 Subtract the square of...... (21°)= 441 Extract the square root... v. 1159–84 links for the horizontal distance, which added to the last reduced distance 234 will make 268 for the true distance. The two succeeding distances of the first series, or declination, also require reduc- tion, viz. from 3 to 330; but having given two examples sufficiently explanatory, it would be superfluous to go further into detail of a sub- ject so simple. The second series commences at 8:43 and terminates at 5:23 inclination--the third ditto uSE OF THE SPIRIT LEVEL. 51 commences at 8:80 and terminates at 10:10 de- clination—the fourth ditto commences at 11:00 and terminates at 15:45 inclination. As the re- maining distances were measured over a surface nearly level, all that remains to be done is to find their difference in measurement as they ascend the column of approximate distance; thus having reached 15:45, the difference be- tween that and 16 chains is 55 links, which added to the last reduced distance leaves 15:39, and the difference between the two numbers at the top of the column, 25 and 26 chains, is 1:00 chains, which, added to the other column, leaves 25-39 for the true horizontal measure, making a difference in the whole distance of 61 links. As it is my intention to give every informa- tion I can upon this subject, I beg leave to state that in a clear open country these reductions might be avoided, by boning out the line and erecting poles over the sloping ground, at the distance of every 10 or 20 links, more or less, as the surface of the ground may require, and thereby measuring the distances correctly ; but in a thickly wooded country this could not be effected without considernble destruction of timber and underwood, besides many other dif. ficulties that we cannot here enumerate. 52 ESSAY ON THE REDUCTION OF DISTANCEs. In all operations in levelling we have always two sides of a right angled triangle given, viz. the oblique distance measured, or hypothenuse, and the elevations or depressions, which are perpendiculars to find the third side or base; therefore proceed according to the proposition given in page 18 of apparent level, by substract- ing the square of the difference of level between any two points from the square of the oblique distance, and extracting the square root of the remainder will give the true length of the horizontal or base line. - Suppose the difference of level between two points should be 100 feet equal to 151 links for the perpendicular B C, as shewn in the following figure, and the length of the measured line or hypothenuse, 6 chains, then VIA B*—B C*=A C. A. A B-................. = 6.00% chains =36.0000 B C= 100 feet ... = 1.51* (see table)= 2.2952 v337048–580 five chains and eighty links for the base A C being the true horizontal distance. USE OF THE SPIRIT LEVEL, 53 As we have just shewn, the difference between inclined and horizontal lines vary considerably, particularly when the inclined lines make large angles with the horizon, and if plotted to a large scale the oblique distance will greatly exceed the true measurement; it is the practice of most surveyors whenever the ground is slightly in- clined, to shorten each line a little, for it will be found next to impossible to measure so many different lines, and over surfaces of various in- clinations, with mathematical exactness, there- fore where great accuracy is required actual re- duction ought to be resorted to. - The following Table will materially assist in reducing dimensions, taken in links into feet, inches, and decimal parts, and, vice versa, to re- duce feet, &c., into links. Suppose I wish to know the number of feet and inches in 20 links—look in the table for the number of links and opposite, in the two right hand columns, will be found 13 ft. 2 inches and 40 decimal parts. 54 ESSAY ON THE A TABLE, TO REDUCE ANY DIM. ENSIONS TAKEN IN L, INKS 1&to FEET AND INCHEs of vicz versa. Links. | Feet. Inches.||Links. Feet. Inches. ||Links. Feet. Inches. l 0 || 7.92|| 34 22 5-28|| 67 || 44 || 2-64 2 1 3-84|| 35 || 23 1-20) 68 || 44 10-56 3 1 || 1-76|| 36 || 23 9-12|| 69 || 45 || 6-48 4 || 2 || 7-68|| 37 24 || 5-04|| 70 || 46 || 2:40 5 || 3 || 3-60|| 38 25 0-96|| 71 || 46 |10-32 6 || 3 |11-52|| 39 25 | 8-88|| 72 47 6-24 7 4 || 7-44|| 40 26 || 4-80|| 73 || 48 || 2-16 8 5 |3:336|| 41 || 27 0.72 74 || 48 || 10.08 9 || 5 |11-28 || 42 | 27 | 8.64|| 75 || 49 || 6-00 10 || 6 || 7-20|| 43 || 28 || 4-56|| 76 || 50 1-92 2. 11 || 7 ||3:312|| 44 29 || 0:48|| 77 50 | 9.84 * 12 || 7 || 1:04|| 45 29 || 8.40|| 78 || 51 | 5:76 . 13 8 || 6.96|| 46 || 30 || 4:32|| 79 || 52 | 1.68 14 9 2.88||47 ||31 || 0:24|| 80 52 9-60 15 | 9 ||10-80|| 48 || 31 8.16|| 81 53 5-52 16 || 10 || 6-72|| 49 || 32 || 4-08|| 82 || 54 1-44 i 17 | 11 || 2-64|| 50 || 33 || 0-00 || 83 || 54 9-36 º 18 11 ||10-56|| 51 || 33 || 7-92|| 84 || 55 5-28 19 || 12 || 6-48 || 52 | 34 || 3-84|| 85 56 1-20 20 | 13 || 2:40|| 53 ||34 |11.76|| 86 56 9:12 21 | 13 |10-32|| 54 35 | 7.68|| 87 57 5.04 22 || 14 || 6-24|| 55 || 36 || 3:60|| 88 || 58 || 0-96 * 23 15 2.16|| 56 || 36 |11-52|| 89 58 888 - 24 15 ||10-08|| 57 37 || 7-44|| 90 59 || 4-80 25 | 16 || 6-00 || 58 38 || 33-6|| 91 60 || 0-72 26 17 | 1-92 || 59 || 38 || 1-28 || 92 || 60 8-64, 27 | 17 | 9-84|| 60 || 39 || 7-20. 93 || 6 || || 4-56 28 18 5-76|| 61 | 40 || 3-12|| 94 | 62 || 0-48 29 || 19 || 1-68|| 62 | 40 |11-04|| 95 62 8-40 30 19 9-60|| 63 41 || 6.96|| 96 || 63 || 4:32 | 31 20 || 5.52|| 64 42 2.88|97 || 64 || 0-24 32 21 | 1.44|| 65 || 42 |10-80|| 98 || 64 8-16 - 33 21 |9-33 43 | 6′72| 99 || 65 | 408 ..-- + H. USE OF THE SPIRIT LEVEL. 55 A CASE OF SIMPLE LEVELLING BY THE BAck AND Fore observation. Suppose it were required to know the height of a lake of water at A, above the ground floor # of the bath-house at Z. At the lake of water A, drive down a stake (of due length and about 2in. square) until the . . . head be level with the surface of the water, upon … which let your first assistant set up one of the graduated staves,and cause your second assistant to set up another at a distance of 5 or 6 chains (each assistant ought to be provided with a small picket for the purpose of resting the bottom of the graduated rod, and marking out the precise point levelled to, the head of which ought to be pressed into the ground, level with the surface); 56 ESSAY ON THE place the instrument in the middle, about an equal distance from each of your assistants, and in a line with them and the building. Things being thus prepared, and the Spirit Level properly adjusted, look through your telescope to your first assistant or rear staff, and direct him to move the sliding vane upwards or downwards, as circumstances may require, until the cross wire of the vane corresponds with the horizontal wire in the telescope, and intimate to him, by some preconcerted sign, that the vane is in its true position; he must now make fast the slid- ing vane and observe the number of feet, inches, and tenths, viz.--2ft. 6in. 4tenths, shewn upon the graduated rod, which must be entered in the field-book in the column marked rear heights; turn the telescope round to your second assist- ant or front staff, at B, and cause the person there to move the sliding vane upwards or downwards, until the cross wire in the vane ap- pears in the line of collimation as before ; inti- mate to him that it is in its true position; let him make fast the sliding vane and observe the number of feet, &c. viz.-5ft. 3in. 4tenths, shewn upon the graduated rod, which must be entered in the field-book in the column marked front heights; deduct the one from the other, the less from the greater, and the remainder-will be USE OF THE SPIRIT LEVEL, 57 the difference of level between A and B, which is 2ft. 9in. 9tehth below A, and must therefore be entered in the column marked depression; the distance being now measured, and found to be 5'10 (5 chains 10 links); enter this also into your field-book in its proper column (distance in chains); this done, direct your first assistant to the station at C, and take up your position in the middle ground as before; the instrument being adjusted, look through the telescope to- wards your rear staff, and cause your assistant to raise or lower the vane until he has brought the centre into the visual line of the teles- cope; direct him to make it fast, and note what number of feet, &c., viz. –3ft. Oin. 9tenths are shewn upon the graduated rod, which enter into the field-book in the column of rear heights: turn the telescope round and observe the front staff, and desire your assistant there to raise or lower the vane until he has brought the centre also into the visual line of the telescope, desire him to make fast the vane, and observe the number offt. viz.-6ft. 6in.9tenths shewn upon his staff, which enter in your book in the column of front heights; add the rear heights together, add also the front heights together, subtract the less from the greater, and the difference will be fift. 3in. 40teaths, the ground at C being that much below 58 ESSAY ON THE A, which is entered in the column of depression; the distance measured up to C makes (11-10) 11 chains 10 links, to be entered in the column of distances: direct your second assistant to go forward to D; having taken up your position with the instrument half way between C and D, the Spirit Level being adjusted, look back to the rear staff, and, managing the vane as before, the visual line will shew the height of the vane on that staff, viz.-2ft. Oin.9tehths entered in the column of rear heights, turning the level to look at the front staff, the visual line will also give the height of the vane on that staff, viz.—6ft. 3in.0tenthsen- tered in the column of front heights; add the rear heights together, and add also the front heights together, deduct the one from the other, and the difference will be 10ft. 6in. 9x depression; the surface at D being that much below A; the distance measured up to D is 17-10 (17 chains 10 links). Proceed in the same manner with the remaining stations from D to E and from E to Z, entering their respective heights, distances, &c., in the manner shewn in the following field- book. Use of THE SPIRIT LEVEL. 59 * *-**** - - - wºº. . LEWELS - FROM THE RESERVOIR TO THE BATH HOUSE. ID F - i D LOCATIONS Fr ist º R t || -> €0teS- O - §. gºn Hits. Hº. Elevation. sio º eS - - July, 1882. Z || 32-00 || 14 || 3-1 || 30 || 3-1 || 16 — Level of floor wº of bath. 3 5-7 || 5 || 87| E 24-90 10 9°4 || 24 || 6-4 13 || 9-0 3 ||3-0|| 6 || 6-0 - D 17-10 7 || 6-4 #18 0.4 10 || 6-0 2 : 0-0 || 6 || 3-0 C I 1-10 5 || 6-4 || 1 || || 9°4 6 || 3-0 || 3 || 0-0 || 6 || 6-0 B 5-10 | 5 || 3-4 2 || 9-0 ; A 2 | 6’4 Water edge. I beg here to state, that on a measured dis- tance of 5 chains, or 110 yards, with an incli- nation or declination of 5 feet, the reduction will only be half an inch for the whole length; therefore, in the preceding example, we may let the measurements remain as they are, as only in one case, the declinations exceed 3 feet. Having now summed up all the columns se- parately and collectively, making the sum total of the rear heights 14ft. 3in. 1:enth, and the sum total of the front heights 30ft. Sin. Itenth; take the less from the greater, which will leave 16 ft. depression for the true difference of level be- tween A and Z, and the total distance 32 60 ESSAY ON THE -----ºr--" chains; making the proportional inclination or declination from A to Z as 1 to 132, that is for 1 foot altitudinal to 182 longitudinal. This system of taking and recording levels will be readily appreciated; for by progressively adding and subtracting, you have at any time , the height or depth below the original station, or zero mark, and it will be found equally ad- vantageous in making a profile or section of the ground, being at once easy and expeditious. Let it be required to draw a profile from the levels given in the field-book (see page 59.) Draw a base or horizontal line A Z, as in the following figure; on this line set off from the zero mark at A the different distances, viz.-for B 5:10, for C 11:10, for D 17-10, for E 24.90, and for Z 32.00 chains, let fall a perpendicular USE OF THE SPIRIT LEVEL. 61 from each of these distances. The base line being the level of A, or the water in the lake, set from B downwards 2ft. 9in.9tenth depression, from C 6ft. 3in., from D 10ft. 6in., from E 13ft. 9in., and from Z 16ft. Oin. ; connect all those points together, A and B, B with C, &c., and you have an exact profile of the ground over which the levels were taken. Having thus explained the mode of levelling by back and fore observations, we shall now proceed to shew the second method, which con. sists of levelling from one point direct to ano- ther by fore observations only, called the appa- rent level. - CASE OF SIMPLE LEVELLING BY THE FORE OBSERVATION, Let it be required to level from a point at B to another at X. Instead of placing the instru- ment between the two staves, as in the preced- ing example, fix it at one of the extremities of the line as at B, in the following figure, and 62 ESSAY ON THE | } ; ; t look forward to the staff at C; request your assistant then to raise or lower the vane until it corresponds with the line of vision of the telescope; enter in your field-book the height shown on the staff, viz., 10 feet 6 inches in the column of front height; take the height of spirit level, 4 feet 4 inches, that is to the intersection of the cross-hair in the telescope corresponding to the line of vision, which must be entered in the column of rear heights— deduct the one from the other and enter the dif- ference in its proper column, viz., 6 feet2 inches depression, because the front heights exceed the rear heights; measure the distance from B to C, 10 chains, which enter in the column of dis- tances; remove the instrument forward and place it over the mark at C, where your assistant had previously held his staff, send him forward to D; having adjusted the level, look towards the staff at D, the height of the vane above the surface at that point being 12 feet 4 inches which enter in the column of front heights as before, enter also the height of the spirit level, 4 feet 5 inches, in the column of rear heights, add the rear heights together, add also the front heights together, subtract the one from the other, and the difference will be 14 feet 1 inch depression, which enter in its proper column; USE OF THE SPIRIT LEVEL, 63 ... ------------------, -º-º-º-º-º-º-º-º----, - measure the distance up to D, which is 22 chains; the instrument is again broughtforward and placed at the mark D, having adjusted the spirit level, look forward to the front staff at E, the height of the vane above the surface is found to be 8 feet 6 inches, which is entered in the column of front heights. The height of the in- strument being 4 feet 3 inches entered in the column of rear heights, add the rear heights to- gether, add also the front heights together, de- duct the one from the other and the difference will be 13 feet 4 inches depression; measure the distance up to E, which is 40 chains, proceeding thus from one staff to another always taking fore-sights. Having gone through the whole of the operation, viz., from E to F, and from F to X, in a similar manner to that which has just been described and as explained in the following field-book. : § LEVELS FROM A POINT AT B TO ANOTHER AT X, BY FORE OBSERVATION ONLY. July, 1833. Commenced º levels from a mark at B. From Bear-Dist R Front D Correct for Reduced | Reduced gº ś|Hº Hºli, zººlºr| – TxTV 39 4 17 | 6 ||—| ‘970| 17 | 5-0 Surface at X below B 21, 10 ſºlo Ta Togo - 4 || 4 . . . . . . . . . F|—| 52.00 29 || 0 11 || 6 |-|-890 11| 5 || . . 17 | 6 || 2 || 8 | T80| | | | { 4 || 6 || - i & El— | 40-00 26 || 4 13 || 4 ||—| ‘710| 13 || 3-2 || | 13 || 0 ||—— —l –| 3 || 6 •405 4 || 3 . P- *|| || |* I tº 14 || 1 |-|-305] 14 || 0 6 -]—| 12 || 4 •180| || 4 || 5 —l C-| 10:00 10 || 6 6 || 2 ||—| 125| 6 || 1:8 B|—| -00 || 4 || 4 |. º Use of THE SPIRIT LVEL. 65 heights, 39 feet 4 inches—take the less from the greater and the difference will be 17 feet 6 inches depression—apparent level only to be re- duced to the true level. - - The distance between B and C on the first line being 10 chains, square this distance and divide by 800, the quotient will be inches or 10x10_100 decimal parts *...*=;=125 for the true dif. erence of level to be deducted from the appa- rent level, viz., 6 ft. 2 inches. 6 ft. 1 inch 8 tenths, the true level, which enter in the column of reduced levels; the next distance 22–10= #=;1803 édited from 14 feet 1 inch= 14 feet 0 inches 6 tenths for the true level at D; the distance to the third station 40–22=18 chains look in the table (page 22) for the num- ber and opposite to it, you will find '405(deci- mal of an inch for the correction)+(505-719 de- ducted from the next apparent level viz.: 13feet 4 inches, will leave 13 feet 3 inches 2 tenths for the true level at E, thus the whole may be reduc- ed by inspection or otherwise, making the true difference of level between B and X 17 feet 5 inches.and–9—tenths The advantage of taking the observations at a short distance from each other is here strik- ingly illustrated, for the difference between the F 66 ESSAY ON THE LEVELS from Nexbit's Cottage, near Thornton Street, to Parker's Quay, on the River Tyne, taken November 29, 1829, for a then true and apparent level is so trifling as only in one instance to exceed a quarter of an inch, but if the distance of 60 chains had been taken for- ward at a single observation, the difference or error would then have been 4 inches and a half. contemplated Branch of the Newcastle and Carlisle Railway. OFFSETS, BENCH MARKS AND INTERMEDIATE LEVELS. | - Offsets TSum of Sum of /ø-i-. A 3-& | From] Distance. I interm. front rear Eleva- |Depres- |Reduced Red. Locations. Stat. heights. heights. heights. tion. sion. I Levels. Dist. round. 34°54 6-8-7-1-114 6-9 |–46 7.2 74| 84 erge of steeply declining] .. O {; 38.5]+114] 6-9 |—46 || 7-2 71| 8-2 Garden fence. BM [ . I-6-0|+114|| 6-9 |—46 || 7-2 69 5-7 On Upper-gate Crook. Il 22-36 || 3:9-0|-|-102|11-9 |—45 || 4-3 61 4-6 m| 30-00 || 3:9.3 + 96, 4-6 ||—44 3.9 55|10-0 28-88 15-1-0|+ 86 6-8 –43 9-6 57|10-2 Bottom of clay-hole. 28.48 || 13.1.0+ 86 6.8 —43 9:6 55|10-2 Surface of water in clay-hole. 27-88 15-1-0|+ 86 6-8 —43 9-6 57|10-2 Bottom of clay-hole 2 feet. l 27.75 8-7-5]+ 86|| 6-8 —43 9-6 51| 4-7 - 27-43 || 3:9-0|+ 86| 6-8 |—43 9-6 46|| 6-2 26.96 || 2-3-4|+ 86 6-8 |—43 9.6 45' 0.6 Fence. BM [ 1-6-0+ 86| 6-8 —43 9:6 |44; 3:2 Top of a stake in Fence. k 25.70 || 3-8-4|+ 82 0.8 –39 2-8 46| 6’4 j || 21:37 || 3-10-0|+ 57|10.1 –32 || 5.6 29, 2-5 i 20-26 3.9-0|+ 50 4-5 –30 5-9: 23| 7.6 h 18-85 || 3-8-3]+ 43 7-3 ||—28 11.4 18| 4-2 g § §: ; § Tº }} º § On a large flat stone in field. f {; 3-9.9}-H 24, 5-3 —22 || 1:7 6|| 1.5 º 14.88 || 3-9.5|-|- 24 5-3 –22 || 1:7 6|| 1 || Verge of high ground. e 13:00 || 3:9-04- 2311-0 –15 1-2 12|| 6-8 IBM 5.0-0 + 20, 6-9 – 7 || 5-3 18| 1-6 On stone wall. 11:00 || 7-3-1|+ 20, 6-9 – 7 || 5-3 20|| 4-7 Into gardens. d { 10-16 || 3:10.6+ 20, 6-9 – 7 || 5-3 17| 0:2 occupation road. 10-06 || 5-0-1|+ 20, 6-9 – 7 || 5-3 18 1-7 C 7-50 || 3-9-5]+ 14 37 – 6 5-1 11| 8-1 b 4-00 || 3-9:54- 610-0 |- 3 || 7-1 7| 0-4 à, 1-00 || 3-8-2}+ 0| 0-0 – 2 | 6-8, || 1-6 Offsets and intermediate levels on line to Thornton Street. §*. - i g : LEVELS FROM THORNTON STREET TO PARKER'S QUAY. ,--Dist. in R Front | El Depres- I Reduce Reduced! — jbearing...]."|h;,] ... ." |*.* |*::::::::::::: Locations. º 37-4672 9-8 who, 126| 2-1 Base of Quay. T5] 0-0|| 15 00 tide. - 37-43|67 9-8 183|10-9 116| 2-1 High water mark, spring - r 3 0-9 5| 0-0 on the River Tyne. 24 37-42|64, 8-9 || 178|10-9 114| 2-0 To edge of Parker's Quay, 5|| 0:2 3| 0-9 Lead Factory to Newcastle. 23 36-50 59 8-7 || 175|10-0 116, 1-3 Occupation Road, from 3-3-5 1030 22 36.00|56, 5-2 | 165| 7-0 109 1-8 : 3| 37|12|66 2I 35-60|53. I-5 || 153| 0-4 99|10-9 * e 3|0|5||11 6.2 | 20 - 35-16|50 l’0 || 141| 6-2 91| 5-2 Tal B-8'ſ 15|3.3 19 (34.70|46 7-2 || 127 9.9 81| 2-7 O { Tl29ſ. 13| 3:0 18 34°00'45| 4:3 || 114 6-9 69| 2.6 Il T] 0.4T III 7.0 17 31-38|44; 3.9 || 102.11-9 58| 8-0 In | 6′3| 67.3 *... 16 28-92 43 9-6 || 96|| 4-6 52| 7-0 Edge of Clay-hole } I { Al 68 g|9-3 # 15 26-7239| 2:8 || 86 6.8 47| 4:0 ! k 3|8-6-4 6-0 - § 14 24-25|35, 6-2 || 82 0-8 46|| 6-6 TIB-0|7| 95 #3 23-003310-2 || 74 3-3 40|| 5-1 j T 4-6 8| 44 12 22.0022. 5-6 || 65||109 33, 5-3 i j 1|11-7 || 8 0-8 H 11 21:0030) 5-9 || 57|10-1 27| 4-2 - i 1| 6′5 || 7| 5-6 10 19:62|28||114 || 50|| 4-5 21| 5-1 3 h 1| 9°5 || 6 9-2 9 18-39|27| 1.9 || 43| 7-3 16| 5-4 A cross mark in the field. : 8. 3| 6-7 6||11-8 i 8 17.4333| 7-2 || 36|| 7-5 13| 0-3 º | 5.5 || 7 | 6-2 : 7 16.0022. 1:7 29| 1.3 6||11-6 South Verge of high ground. &- f { 7| 0.5 ! 4 8:0 6 13-82|15; 1-2 || 24, 5-3 9| 4-1 H € 7| 7-9 6-3 - 5 12:00, 7] 5:3] 2311-0 16| 5-7 II •60 Cross fence. d { | I] 02 || 3| 4:1 - - 4 8-75. 6. 5*I 20 6-9 14| 1-8 Face of stone wall. O c 2|10-0 || 6 || 3-2 . . . * ~ * 3 6:00 3, 7-1 || 14 37 10| 8-6 * b | 1, 0-5 || 7 5-7 2 2-00 6|10-0 4, 3-4 . * - 2– s • 4. 1 | " I 00 26.6 ſ ] - . ... Commmenced at a mark near to Nesbit's Cottage, Thornton-street, Newcastle. —— * – --> * > . .” -- ~~~~. = a-, -º-º------ * - - - - - -, * * *-* -- *-ºs-----º-º-º-º-º-º-º-º-º-º-º-º-º-º-º-º:* -- . . . . . . . . -, -, -i-. … . . . . . . . . . - - . . . . . 72 g ESSAY ON THE #-- added to the sum of the front heights, namely, 20 ft. 6 inches and 9 tenths, is equal to 25 feet, 7 inches, from this subtract the sum of the rear heights, 7 feet, 5 inches, 3 tenths, and the re- mainder will be 18 feet, 1 inch, and 7 tenths, depression. Now the sum of the rear heights and the sum of the front heights are the same as in the last case, up to the 5th station; the second inter- mediate height 3 feet, 10 inches, and 6 tenths, taken at the distance of 10:15, a few links fur- ther than the last, in an occupation road (now known by the name of the Scotswood Road), which added to the sum of the front heights, 20 ft. 6 inches, and 9 tenths, is equal to 24 feet, 5 inches, and 5 tenths, from which deduct the sum of the rear heights, 7 feet, 5 inches, and 3 tenths, the difference will be 17 feet, 0 inches, 2 tenths, depression. The third intermediate height was 7 feet, 8 inches, and 1 tenth, taken at the distance of 11:00 (in the garden ground), to this add the sum of the front heights, 20 feet, 6inches, and 9 tenths, will give 27 feet, 10 inches, from which subtract the sum of the rear heights, 7 feet, 5 inches, 3 tenths, as before, their dif. ference will be 20 feet, 4 inches, and 7 tenths, depression. - The last height of this series is the bench- mark, 5 feet, 0 inches, 0 tenths, taken upon a ~, | º, Zº . . . , 's # w \ \,”, cº- 31 ºf LEVELS from Thornton Street to Parker's Quay collec- tively, as a proof to former Field Book. From Distances Rear Front Eleva- || Depres- e Stat. in Chains. Heights. Heights. tion. sion, Locations. #jº T Qſ 37-48] 2 0-0 2 +. 126) fl:1 Base of Quay. 3 *, *, *| 5 || 0-0|| 15| 0:0 37:44, 211| 0-0|| 327 I •l 116 'll |High water mark spring tides. 3| 0-9| 5 || 0-0 e G ſº * > the River Tyne. 24, 37-42 sº 11 *l 322] I'l 114 2-0 |Tö edge jºrs quay on 5| 0 |2| 3| 0-9 23 36-50; 202 10-9) 319|| 0 |2| 116 l'8 |Occupation road from factory. 3| 3•5| 10 3-0 22 36:00 199| 7-4, 308| 9-2 109|| 1:8 3| 3-7| 12 6-6 21 35,60|| 196|| 3-7| 296 2.6 99||10.9 3| 0-5 11| 6′2 20 35° 16, 193 3-2 284 8-4, 91 5-2 3| 5-8| 13 8-3 19 34-70, 189| 9.4| 271 (). 1 81| 2-7 ſ *- : 6|| 8-7| 13| 3:0 round 34:54, 183 0.7| 257 9.1 '74, 8.4 vš. of steeply declining e 3| 8-5, 6, 8 ~7 o - 34.25 179| 4,2| 251 0°4. 71 | 8°2 learden fence. | * 1 6-0|| 3| 8-5 BMſ 177|10-2 247 3-9 69| 5’7 ||On upper gate crook. U 1| 2.9ſ 1 || 6-0 - 176|| 7-3] 245| 9.9 69| 2.6 l8 34 00 sº 3| 9-0|| 1 || 7-0 172 10-3] 234 2-9 6|| 4-6 Il 32°36|—||—|-|-- 1 || 0 °4. 3| 9-0 17 31 38 171 || 9.9| 230 5-9 58| 8-0 3| 93 67.3 Ill 30.00) 168|| 0 6 223| 10:6 55|10-0 ... 6'3| 3| 9-3 16 ſ 28:92] 167| 6′3 220 1 3 52| 7-0 |Edge of clay-hole. 15| || 0 | {}| 9.8 28:88) 152| 5'3| 210 3-5 57|10-2 |Bottom of clay-hole. 13| 1.0l 15, 10 28° 48' 139|| 4°3| 195| 2-5 55|10-2 |Surface of water., c. h. 15| | |0|| 13 1.0 - 27-88 124|| 3:3| 182 1 -5 57|10-2 |Bottom of clay-hole. 8| 7.5 J5|| 1:0 27.75] 1 15| 7-8| 167| 0:5 5]| 4-7 3| 9-0|| 8 || 7-5 l 27-43| 1 || || 10°8| 158 5-0 46|| 6’2 2 3'4| 3| 9 0 26.96] 109|| 7-4 154 8-0 45| 0:6 || 6-0 2| 3-4 * * U BMI 108 l'4, 152 4-6 44|| 3:2 |Top of stake in fence. 4, 6-8 || 6-0 15 26-72; 103 6'6|| 150| 10.6 47| 4:0 3| 8°4| 4 || 6-0 k 25.70| 99| 10:2| 146|| 4-6 46|| 6’4 3| 8-6 3| 8 °4, l 4. 24, 25 96 l'6|| 142| 8-2 46; 6.6 iſ so 79.5 13 23 00. 94, 5-6|| 134 10-7 40|| 5 || 1| 4'6|| 8 || 4-4. 12| 22:00. 93 1-0 126|| 6′3 33| 5'3 3|10-0 8|| 0-8 j 21:37: 89) 3-0|| | 18| 5-5 29| 2'5 | | | 1.7 3 l ():0 | | 21:00 87| 3'3| || 14, 7-5 27| 4-2 3| 9:0| 7| 5-6 i 20°26′ 83| 6′3| 107 1-9 23| 7:6 || 6-5 3| 9 () I () 19.62| 8 || 11.8| 103| 4-9 2|| 5 “I 3| 8°3| 6 || 9 °2 h 18-S5, 78; 3-5] 96 7.7 18| 4-2 ||| 9-5 3| 8 3 Q 18-39, 76, 6-0 || 92] 1 1-4 16| 5'4 |A cross mark in the field. 3| 6-7| 6 || II •8 § 17.70 72|ll 3| 85| 11-6 13| 0-3 3| 67 3| 6.7 8 17:43| 69| 4'6| 82| 4'9 13| 0-3 I 5'5| 7| 6-2 t 7 16:00 67 l l ‘l 74 10-7 6|ll'6 To Verge of high ground. 2| 0:0 4| 8-0 ſ BMT 65||11.1| 70 2-7 4|| 3:6 |Cross on large flat stone in field. - 3| 9°9| 2 0-0 - \ f 15:41, 62. 1 °2| 68| 2-7 6| l'5 | 3| 9°5 || 3 9-9 U 1488, 58] 3-7, 64 4-8 6| l'I 7| 0'5| 3 9 5 6 13.82 5 l 3'2' 60 7.3 9| 4 •l a 9-ol. 63 e 13.00. 47| 6’2 60 1 0 12| 6-8 7| 7-9| 3| 9-0 5 12:00 39| 10:3| 56 4'0 16| 5-7 5|| 0-0|| 3| 4, 1 * ſ IBM 34|10:3| 52 11-9 18| l'6 |Cross mark on stone wall. - 7| 3•l 5|| 0-0 II .00) 27| 7-2 47 11.9 20|| 4-7 |Cross into garden ground. d sº 8 10.6 7 3.1 Scot d d. 10-15, 23| 8-6, 40 8.8 17| 0:2 Iº *:::::::: road, now 5|| 0:1 3| 10:6 10-06| 18 8-5 36|| 10-2 18| 1.7 U 1 || 0:2 5|| 0-1 4. , 8.75] 17 8°3| 3 || 10:1 14|18 ||Face of stone wall. 3.95 6' 3-2 C 7.50; 18|10-8|| 25 6-9 II. 8-1 2| 10-0|| 3| 9.5 3 6:00 l l () 8 21 || 9'4. 10| 8*6 -- ~. 3| 9-5 7| 5-7 b 4.00| 7| 3:3| 14 37 7| 0 °4. 1| 0 °5| 8 9-5 2 2°00' 6' 2-8 10| 6-2 4| 3:4 || – 3. 8-2 6|| 10:0 à, 1.00; 2 6-6 3| 8-2 I | 1.6 ...] ...| 3| 8:8 I •00] 2 6-6 Commenced levels from a mark near Nesbitt's Cottage, Thornton Street, ewcastle. -----|-†****-· · ·,≤)---- ------>| +--~~~~:：~~=>*-~~~~）;*zą*- -±- -�±•ø -� *-�? } «»} � ** *-*-------> ...& , *, *. # * : *. º, º - PROFILE OF GROUND BETWEEN THORN TON st'REET & PARKERs or AY. | | 2× | Lºzzo Š§ § N № ſae/?zaeae º#???!—ł#### -ºzº ae //www.º/º//*/：/：.：º ¿ $ſ=####| Main Line of Railway Zºzzazzº LſzºwczyźZº ººººº| 110，1€.|| ：：：-：109.18// no-ebol ∞, 10.0 50-16L_91.5.2 ： +70ſºlº.7 7+）, ± oſ718.1 54-001_69.20 1.olae |- 51-58 | 58:8 o · · nn，.10.0 hl- …laeae /ºe/?18-39L | . . . . . . . 2：3-9） /zz7zzºwe 25. o.o. 22-001 lº es： +0.6,2 g 17.45 16.00 13-8，2 12.00 d Zºzzzzzzºzwe /ø/， Jaewoo， Zzzzz， Lae az， „ſzowe/， // ans 6-o-o º-o-o 20…+ | 17.0.0} Z/www.zºº.ºº^ laelº | | | | -·-00110.8.0 7.0. |-ſae llº ſºzºeazzae， ºzaye a Zºzzzzzzzz Jazze 2 zºzzzzzy a zºzzzzº /2/?ºw.yºzze zºzºa azz /zºº/ & sº. § *...*. • cºr--ºrrº- | } } } { . . . .-sarvºº-º-º-º-º-º-e-r-., - ~~~~~~~~ ºr ºr ºr șºzā sºr-strº-- į } .*.*, * ~~ ---------~~~~~~ USE OF THE SPIRIT LEVEL. 73 f t;. projection of a thorough-stone in a wall, on the left hand side of the line (as a point to return to upon any occasion), this also add to the sum of the front heights, viz., 20 feet, 6 inches, 9 tenths, equal to 25 feet, 6 inches, and 9 tenths, from this also deduct the sum of the rear heights, 7 feet, 5 inches, and 3 tenths (it being the least number), and the difference will be 18 feet, 1 inch, and 6 tenths for depressions (see profile plate 8). The method of performing the remaining ex- amples is precisely the same as those just detailed, and is the most advantageous manner in which they may be performed, and I hope will be found sufficiently comprehensive : but to render the subject more easy and intelligible I have given in the annexed Table, another copy and form of Field Book, the same levels, but subsecutively ar- ranged, which will serve as a sort of connecting chain, and will enable the learner more readily to understand and review the whole of these cases, and the results will be found the same in every particular; therefore I conceive that further explanation would be unnecessary. It would certainly have given me great satisfaction if I could have curtailed this matter, or made use of language less tautologous, but in describing a subject of this kind it is quite unavoidable. Having in a former part of this work explained 74 ESSAY - ON THE the method of plotting, I shall only now, there- fore, refer to the profile of the ground between Thornton Street and Parker's Quay, for the purpose of stating that the whole of the cases are depressions, which was intentional : now in practice it is preferable to have them elevations, that the figures shewing the heights should be sufficiently below the surface line so as to leave it, and the space above it, clear for further ope- rations, such as describing the line of road with its inclinations (per mile, yard, or proportion- ate), also the depths of cuts and heights of em- bankments, &c. Now to reverse these depressions, and suppose I borrow, subsequent to my calculations, the sum of 200 feet, then my starting point or first station is that much above an assumed base line ; then proceeding up the columns of the field book I deduct each individual depression from this sum and their difference will be elevation, thus:– DEPRES-1 SUM | ELEWATIONS, STAT, - SIONS, BOR, ft. in. x| feet. 3d or at 6:00 10 8 6, 200 | 189 3 4, b or at 4:00 intermediate point. 7 0 4 200 | 192 11 6 2d or at 2:00 4, 8 4, 200 | 195 8 6 a or at l’00 intermediate point. I l 6, 200 198 10 4 |lst for starting point. - 0 0 0| 200 | 200 feet. So proceed in a similar manner to the end, entering these elevations in the column of re- duced levels opposite their respective counter USE OF THE SPIRIT LEVEL. 75 º i. parts; and they may also be reversed by start- ing from the opposite end of the line or termini, as at Parker's Quay, and returning down the co- lumn of depression to Thornton Street; now, the fall at the former place is the greatest at the base of the Quay, 126 feet, 1 inch, 1 tenth, there- fore deduct each individual fall from this sum and their difference will be elevation, thus:– |-------------------rz--—-----------— ----------------------, the end. DEPRES-ITOTAL FALL. ELEVA- DIST. So continue to l SIons. BASE of PAR-1 Tions. KER’s QUAY. 36-00 109 1 1 126 1 1 16 11 3 &c. &c. 36-50 tº-rººmsº 116 I 8: 126 l l 9 11 8|Occupation Road. 37-42 114 2 0 126 l l 11 11 1 Edge of Parker's Q. 37°44'. ' 116 1 1 126 l l 10 0 0|Level of high water. 37-48||New Zero mark. 126 l l 126 l l | 0 0 0|Base of Parker's Q, DESCRIPTION OF FIELD BOOK. The pages of the Field Book are divided into ten columns, or may be less than that number as may suit the taste of individuals. The first column is for the number of the station from which the operations may com- mence, the second is for the bearings of one station from another, the third is for the pro- gressive distance or surface measure, the fourth for the heights observed on the rear staff, the fifth for the heights observed on the front staff, the sixth for the elevations, the seventh for the depressions, the eighth for the reduced levels, -------- 76 ESSAY ON THE - | (that is when the difference of the observed heights requires to be reduced to the curvature of the earth by allowing for the curvation and refraction,) the ninth reduced distances, (as the surface measure is generally oblique, it is abso- lutely necessary for the accuracy of the work to reduce them either in the field or in doors to the true horizontal distances), the tenth loca- tions; this column is for noting down such re- marks and observations as may be requisite for the better explaining the progress of the work and the crossing of fences, roads, rivers, &c., and may be entered from top or bottom of each page as may be found most convenient. The characters used to denote observations, taken on the right or left to the main line, thus:— T to the right hand, and right angled thereto; } oblique, on the right; T to the left hand and right-angled thereto; # oblique to the left being to some particular mark. HOW TWO OR MORE LINES OF LEVELS MAY BE TAKEN AT ONE AND THE SAME TIME. In describing the method of taking several lines of levels, at one and the same time, and to convey a correct idea of the operations, I have *... . i PLATE II: ZZZZ. 6/roſſ MD P/AM of 3 lines of Zevels, ºwing the mode aſ operation with the heights on the stares at the various points of the surface. -- - - - Z - - A. % See * o/recordºy the Zevels in Pºeza Book payezs. - -- - --- - - --- *7%. 2. Zowc/7/72/MAZ SEC 770V sheriny Zºe Alerations of 3 lines of Zevels taken collectively AT. To prevent confuszon Zºe Aegyhts on the nameº.ca/Zºzze orzine-AB are on/y skewn see &oana Pan/and Aze/ZAook 24/e 73/ - s s § § S. § s S. s s s s - s * º s s * § s s § § s !----------------------------------------- ----------------------------------------- --- ----------- ----------------- 3 3. 3. s º: = : : : 3. $: 3. - - - - c - c - 2 c 3. - - ~ 3. - - - Fºy, 3. */4. - cross section of the grow wid Cross SECTION of the 6RotºWD aſ a al-b b az +500 s.t. - - - - - - - - - - - * s & - - - - s s - - - - - º º - - - . -º-º-º: - - - ~ - - - - - º ~ 3. : 2 º - = -----！\， ， ,· ·. USE OF THE SPIRIT LEVEL. 77 introduced an appropriate example with a field book, a plan, and longitudinal and transverse sections. (See plate, No. 4.) - I am not aware that such a method has been practised by any surveyor or engineer; how- ever it will be found to possess peculiar advan- tages, particularly when the operations are ex- tended to the exploring of a country intended for Public Works; it offers a choice of so many different lines either for canals, railways, turn- pike roads, or for draining extensive tracts of boggy or marshy lands. - In detailing these operations I beg to observe that I have shewn the levels to have been takens. only on one side, viz., on the left hand of the line A B, which I shall in this instance call the main line, and on which the distances appear to be taken, although they were actually carried forward on the operative line A Y; my object in this arrangement was to make the subject more explicit, and to destroy the appearance of confusion which the frequent crossing and re- crossing of the centre line might create; when a method is properly understood, any alteration may be made according as the necessities of the case may require, for practice in all cases will suggest improvements. The longitudinal line of levels is taken at 78. ESSAY ON THE :----, six---> . ;- -,-,-,-,-,-,-,-,- -- " " - - - - a five chains, and the transverse levels at ten chains apart, making the total distance in the lateral direction a quarter of a mile; but in operations of this kind the transverse distances may be assumed. When the distance of these level points exceeds ten or fifteen chains it will be found advisable to place staff holders on each line, as so much time is occupied in travelling backward and forward. In reference to the field book, plan and sec- tion—to commence with I borrow 20 feet, which is entered in the column of rear heights, conse- quently the base line will be that much below the starting point; the instrument stations on the central line are marked thus o on the plan ; each station on the main line is marked by numbers with a x, and the transverse level points by letters of reference with a x, and their distance from the line A B.Şall the observed and-heights. The first observed which is a rear height is at a stake mark surface level near A= 7:50 viz, 7 feet and 50 decimal parts, which is entered in the column of rear heights, and ad- ded to the 20 feet borrowed, making 27°50 pro- ceeding from right to left. The next height is on the central line at a-5 feet, entered first in - the column of front heights, and added to all the heights of that name (if any), and it must FIELD BOOK, SHEWING THE ENTRY OF THREE LINES OF LEVELS, Rear (From Dist, Stat. ings. \ inch, Back Sights. Fore Sights. eTElevaſ tion. Depres- S1011, Reduced Levels. | Red. |Dist. Locations, 278|90 600 27290 12 260 25 65 254165 2100 25265 600 24665 75 259/90 4.175 255] 15 13 242 00 l6 1225 234|40 * 75 233.65 4|75 228|90 RH 50 65 4. 237 13 215 00 90 8 229 00 65 00 65 14 215 5 210 8 202 00 90 00 90 16 199 25 40 oo 90 14 188 75 65 4. 194 16 I'72 25 65 R.H 12|50 18215 4|75 16790 Tsº 179|15 12|50 155|40 00 15 7 172 11 160 O º 4. 156 25 90 00 90 75 15 2|50 15290 00 90 25 65 7 145 11 134, 00 O 134|65 00 is I0 146 RH 200 144|15 6100 138||15 11|25 12690 4. 129 75 90 1000 | 1990 2 117 25 65 00 65 6 I 11 —125 12665 1 1/25 100/40 4. 121 75 90 –25|| 100 15 10 80 12 109 R. H 2 107 00 80 4. 95 12 83 75 40 10 30 00 80 7 100 |50 SO 3 79 12:00 88.80 7 72 00 80 90 87.90 1200 6080 90 00 4. 83 0 59 90 90 12 70 75 25 90 00 RH 3|00 67|25 75 25 00 25 6 6] 50 75 13 47 50 75 00 75 00 75 50 25 50 25 00 25 25 00 50 75 50 8250 25 50 5 27 00 50 50 00 7 20 50 00 : 00 —l- 24 20 14 25 21 18 12 10 22 14 23 16 24. 20 15 26 21 14 24 21 27 28 15 2] 14 26 es 19 26 22 20 25 25 00 50 75 75 50 00 50 25 25 50 25 25 75 40 50 00 00 10 10 25 00 50 00 50 00 25 00 50 00 Z 60-00 45-00 Q 40’00 85 °00 25'00 10:00 C 5-00 Height of instrument. On Main line A B. 20" ch. T of Main line A B 10" ch. T of Main line A B House. mark at A, near Herd's Commenced at a stake. Borrowed 20 feet which added to the R.H., or rear heights, will make all the points elevations. ! USE OF THE SPIRIT LEVEL. 79 also be carried to the other column, because it becomes the rear height to the next fore obser- vation; deduct the one sum from the other and the difference will be 22:50 elevation, because the sum of the rear heights exceeds the front heights, therefore the mark at a will be that much above the base line. The next height is on the third line, at b-1'50, and is likewise car- ried to the columns just mentioned, making the sum of the rear heights at this point =32:50, and the sum of the front heights 6:50, leaving a difference of 26 feet for the elevation of b, which is 20 chains to the left of A. (See ground plan.) We now turn again to our assistants, on the main line, who have measured out a distance of 5 chains, the instrument remaining as before, the observed height which is the fourth 8:25. The fifth is the instrument height, at c=4'50; the sixth is at d=1-0; the seventh is at 10 chains on the main line = 13.50; the eighth is at e=6-0 feet, all of these are carried to the two columns in the manner already described; first to the front heights and then to the rear heights. The ninth is on the third line at ſ=#5 feet, and being the last observation of the first series this sum, therefore, is only carried to the co- lumns of front heights, and added to all the 80 ESSAY ON THE heights of that name : a picket must be put down here to rest the staff and mark the precise spot levelled to. As the instrument is to be removed from this position to another at g, the person carrying the staff must remain here un- til a height has been obtained for the next series of level points; that the whole may be consecu- tively arranged. The sum of the rear heights, up to this station, is 67°25, and the sum of the front heights 42:25, leaving a difference of 25 feet for the elevation of f. The instrument being now removed to g, point the telescope to the staff at ſ, and observe the height thereon, viz., 3 feet, which must be carried to the column of rear heights only (see R H on plan), and added to the heights of that name. The telescope is next directed to a point on the main line, at 15 chains, where the observed height is 1275, this is first added to the sum of the front heights and afterwards to the sum of the rear heights as before directed as the subsequent cases are all similar to those already enumerated, it would be quite superflu- ous to proceed further in the detail of this sub- ject, and I shall suppose that my readers have by this time, acquired some knowledge of the art, so as to understand these instructions; observe, however, to enter every thing in their USE OF THE SPIRIT LEVEL. 81 respective columns, particularly the heights which are to be added, alternately, to the one and then to the other, excepting the first and the last of each series. See Field Book, (Plan, and Section Plate 4.) LEVELS TAKEN FROM SCOTSWOOD TO CRAWCROOK MILL ROAD, BEING A PART of THE NEWCASTLE AND CARLISLE RAIL- WAY, a PORTION OF WHICH IS ALSO IN THE LINE. or THE ONCE PROJECTED CANAL BETWEEN THIS PLACE AND MARYPORT. - My object in giving the section (See Plate 5), is to shew, that, in the crossings of Rivers, Brooks, &c., the soundings or depths of water may be taken, and added to the general line of Levels, without any apparent break in the chain. - These Levels commence at a stake in an oc- cupation road leading from Scotswood to Ben- well, and to this add 100 feet, which is car- ried to the Field Book (page 88), and entered in the column of rear heights, also in the column of elevations, which is to raise that object 100 feet above the assumed base line. (See section). The first observation or rear height (is from the stake just mentioned), and is entered in that G 82 ESSAY ON THE ---,--- ~~~~~-ºr--- column 4 feet 6 inches and 1-tenth of an inch, (4, 6, 1) the next is an intermediate level (4,2,2) this is carried first to the column of front heights, and then again to the column of rear heights, the distance 40 links, the fore observation is a bench mark on a cantch cut in a tree, in the centre of a fence, and standing a little to the right of the line, at the head of Mold’s Meadow, and nearly its level, and corresponds with a dis- tance of 70 links on the main line, the height , of which is 9, 10, 8, entered in the column of front heights only. The instrument being re- moved to the next station, and as nothing parti- cular occurs until we reach the edge of the ri- ver, I shall just give the different heights as they were taken, without preface; and, there- fore, beg to refer my readers to the entries in the field book, wherein they will find the suc- ceeding observations to be, first, a rear height (2, 9, 7,) and its front height (4, 1,6,) distance 2:50. Rear height (7, 6,2,) and its front height (4, 7, 9,) distance 4.25. ; the next rear height is (1, 4,0,) and its front height (8, 3, 4,) distance 5:50; again, the rear height (1, 7, 5,) and its front height (6, 9, 0,.); distance, 7:50, to the low water line" on the North, or Scotswood * If the depth is taken at High Water Spring Tide, then deduct the full rise of ordinary Spring Tide from the Depth USE OF THE SPIRIT LEVEL. 83 side of the River Tyne, where a stake has been driven, or some other mark made, such as a large flat stone laid level with the water. Place the instrument at some convenient distance from this mark, and observe how far the opposite side of the stream agrees with that on the nor- thern shore (for in rivers of considerable width and where the current sets strong to one side, or a boisterous wind blowing athwart the chan- nel, the water will be raised on one side and de- pressed on the other); therefore, if any difference should be found, and the water higher on the north than on the south side, add one-half of the found, and the remainder will be the depth to be inserted in the Draught. (At low Water.) 3 ſ 1st Hour before and after high water, deduct #} \ ºf # 2d Hour before and after high water, deduct # # 3 J 3d Hour before and after high water, deduct # 5 * # 4th Hour before and after high water, deduct # ſº; # 5th Hour before and after high water, deduct tº ### # leth Hour before or about low water, deduct & J 5°º If the depth is taken at High Water Neap Tide, from each depth deduct # of the full rise of Spring Tide, or the whole rise except one-fifth part. ſ 1st Hour before and after high water, deduct # 2d Hour before and after high water, deduct # | 3d Hour before and after high water, deduct # |; Hour before and after high water, deduct # i : 5th Hour before and after high water, deduct # 6th Hour before or about low water, deduct # J 5 These allowances are not given as quite precise, for they will vary a little from several causes; but as a general rule, will be found sufficiently exact on most occasions. º Mackenzie's Maritime Surveying i 84 ESSAY ON THE difference to the first and subtract one-half of the difference from the last observed height, (viz. that at the edge of low water), and let a stake be driven to within low water mark on the opposite edge of the stream, equal to the other half of the difference; it will be necessary to observe, that in tidal rivers, when the wa- ter is ebbing or flowing, an assistant ought to be placed at one of the extremities of the low water line whilst the soundings are taken, to notice whether the water rises or fahls, above or below the stake head, which must be added or substracted to or from the soundings as the case may require, so as to reduce the whole to one horizontal plane; previous to taking the depths, let a strong line or cord be stretched across the stream, from one stake to the other, having small cork-floats attached to it at every 10 links, painted white on one side, and num- bered 10, 20, 30, 40, &c.; these, will keep the line on the surface of the water, and pre- vent its getting foul with any thing at the bot- tom, and being thus numbered, will answer every purpose of the chain, but the cord must be hauled perfectly tight, and in the direction of the intended line. A boat must be provided, and which will require to be pulled along the cord line, the principle surveyor will occupy USE OF THE SPIRIT LEVEL. 85 the head of the boat, to record the depths, and two assistants the stern, the one to take the numbers or distances, and the other the sound. ings, which are to be taken at 50 links apart, and the depths may be ascertained, either with the levelling staff, or a staff provided for that purpose, with a trencher foot, of three or four inches diameter, to prevent its sinking in the sand or silt (when they exceed two or three fa- thoms, a ship's line ought to be used); now as those soundingsprogress, they willalternately be- come rear and front heights to each other, with the exception of the first and last; at low water mark, the depth is nought, and is entered in the field-book accordingly (0.0.0.) in the column of rear heights; at 50 links from the shore, mak- ing 8 chains from the starting point, the sound- ing is found to be 5 feet, entered in the column of front heights, it is also carried to the opposite column, because, it becomes the rear height to the next sounding; particular attention should be paid to these operations, as an error may very easily be committed; the third sounding is 4 feet, entered in the column of front heights, and again, in the column of rear heights, dis- tance, 8'50; and the fourth sounding which is 2 feet, becomes its front height, distance, 9 chains; the fifth sounding is 1 foot, distance, 86 ESSAY ON THE 9:50 ; the sixth is 1 foot, distance, 10 chains; the seventh is 1 foot, distance, 10.50; the eighth is only 6 inches, distance, 11 chains, (these are to be recorded in the manner described above,) and the ninth or last, brings us up to the ter- mini or low water mark, on the south side (0, 0, 0,) entered in the column of front heights only, and the elevation of which, will be found to agree with the opposite extremity of the low water line, viz. 84, 0, 8, and the distance 11 chains, 50 links. Ordinary spring tides rise from 7 to 8 feet above this mark. The next series of levels are over a portion of the bed of the ri- ver, the rear height is 10, 10, 9, an interme- diate height 9, 9, 3, entered first as a front height (distance 14 chains); and, again, as a rear height 9, 9, 3, and its front height 2, 2, 0, distance 1460 upon the bank of the river or towing path. Nextin succession is, a rear height 5, 11, 0, and its front height 4, 8, 3, distance 18 chains. As the subsequent operations and process for determining the relative heights of the remaining portion of the line are similar to those already described, therefore, I con- ceive it would be unnecessary to go further with the detail, but at once refer my readers to the field book, commencing in page 88, in which they will find the whole entered according to USE OF THE SPIRIT LEVEL. 87 the observations taken in the field, and conform- able to the rule given in page 44. It is almost impossible to avoid the appearance of intricacy and labour in the construction of such exam- ples, however, the student will do well to con- sider attentively, so that he may perfectly com- prehend the principles on which these opera- tions are founded, and thereby be enabled to employ the leading lines when required, without regard to the minuter divisions of them, which may in some cases be omitted. 88 ESSAY ON THE LEVELS FROM ScotswooD TO CRAWCROOK MILL RoAD. From Bear- BET Rear Front Eleva- i Dep Red. * Stat. : chains. heights. lº. : * Levels. |# Locations. | | 18:00 16s, 0.969 orb 93 04 ſ Carried forward. - 5||11-0 || 4 || 8-3 * towing path. 14-60 157] I '9|64. 4-2 92 9.7 * Bºer, or º 9| 9-3 i & | | | 14:00 147 4-6 85 24 -- Bed of river. - 10110.9 - |. e pººr . e a.ol | South side of Twne. + 11 50 136 5-7 84 0-8 Edge of i. *:::: & ſº ſº 6-0|. 4 | 11-09) 135||11 7 83; 6 S # 1| 0-0 9 | 10-50) 13411"/ 83 0-8 § ºf . ºº rt; || 0-0 - # 10:00 133|II •7 83| 0-8 ## *= 'sº I | 0-0 || || 0-0 .# 9 •50 1821.7 49| 10-9. 83 0-8 §§ “º ſ = - -º Eg 2| 0-0 || 1 || 0-0 5: 9:00 130ill 7|48] 10-9 82 0-8 # 4|| 0-0 |2|| 0-0 * 8-50) 12611 -7|46 10-9 80 0-8 # gº ºn O 5|| 0-0 || 4 || 0-0 CD 8:00 121|II •7|42; 10-9 '79 0-8 0|| 0-0 || 5 || 0 (. Tyne. : 7-50. 121|11 -7|37| 10-9 84| 0-8 north side of river i. A Edge of low water, : iſ 7-5 6' 9-0 - 5-50l 120 4-glgil i-9 39| 2.8 : 4-0 || 8 || 3°4 4-25, 119 0-2 |22 10-5] 96 l'7 Road to Lemington. # *== gº t * 7| 6-2 || 4 7.9 p * 2-50 111 || 6-0 il8 i: 93 3-4 Mold's meadow. >- 2| 9-7 || 4 || 6 BM | 108 8-3 |14|| 1 |0| 94 7.3 F Cantch cut on tree. 4 2-2 3. 10-8 * •40 104 6-1 || 4 2-2 100 3-9 - - me ºn I - *:::::... ood t Onº SCOESW O º - º 6-1 || 4 22 * in the road leading *. Borrowed, 100]. ... [...] ... 100. From top of a stake Levels of a portion of the Newcastle and Carlisle rail-road. from Scotswood to Crawcrook: 1827. USE OF THE SPIRIT LEVEL. 89 | I,EWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. From | Bear-i Dist. º Rear. Front Eleva- |Pº. Red. I Red. L — Stat.I ings.] chains. I heights. I heights. tion. Sion. I levels, ſist. Locations. 48:00, 176 7-181| 92 94 9-9 Carried forward. - 3 : 46.00. I'72| 9 • 9| 45.75 16; 78 5-9 94 4-0 Verge of New cut. l 2 º •7| 88|Il 3 - Ditto opposite side. º 88! I 1-3 Bottom of Cut. ! 9 45 °15' 154. 8 ; : - 3. . 45:00 146 89| 10:6 * ment. 97 6-0 BM On side of embank- 44, 50l 145 ;#. : l 44'25] 143 99| 4, -9 Ditto opposite side. º i 2 i 43.00. 140 99 4-9 Surface of Turnpike. 2 4 3 - “$: 39| 2-5 94; 3-6 Bottom of slope. 7 42-4ſ) 133 7 To º 3 1 3. § 42:00 125 93| 10-3 —; º- ; : 2 7 39-00 | 121 94| 3:0 * == F * 4. 36:00 118 6.9l 95|10-4 0. tº 33-00 113 6-8|19|| 0-2 94 6-6 30.00. 109' 5'5|15. 6-3, 93 l 1-2 27:00 105|10:41, 8.8l. 94| 2:1 2-9 24-00 | 101 || 7-5, 7, 8.5 93 l l =0 I 21:00. 97 6 5) 3| 9-7 93 8.8 I º •4 Brought forward. 90 ESSAY ON THE LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. Stat. From [Bear-ll)ist. in Rear Front | Eleva- |* | 1.* | : Locations. ings. chains. heights. ſh; tion. sion. 84-00 186| 4-789) 5 0, 96 || 1 || 7 Carried forward. 5|| 1 °6|| 4 || 4-7 81 00 181| 3•185 $3. 96] 2-8 4, 10°5' 5|| 0-5 {80-001 mile. 7800. 176 4.67911 s 96 4.6 4 10-1| 7| 8-1 77.00 17]] 6-572, 3-7, 99 2-8 I •l || 4 || 10°] 5°467 B-6 95] 11 -8 8 75-00. 163 : 73°25 157 8 3•959 5-2| 97 10-7 Road to Beaumont’s 0-0 6, 1-5 72°50 149, 3.953 3-7 96|| 0:2 3| 8-7| 8 || 6-7 west side. 7200 145|| 7-2|44. 9-0|| 100 10-2 |siºsewoºd, 4| 0°2' 4 0°4. in centre. 69-00 | 14|| 7-0|40 so 100 10-4 Surface of New road, 3 37 # : 0°4. - Lead wharf. 7.2 l east side. I •4, 100 62] Surface of New-road, 3| II •4. 67.00. 137, 7-6 7| 3•5; 3 T 1-4 66:30 130 4-133 2-0. 97 2-1 6 II •9| 7| 3-5 66-00 128 4-2|25 | 10-5 97 5-7 4|| 1 */ 4| 0°2 68–00: 119| 2-521) 10-8 ####| 60-00 II5 0°5|18| 2-4. 96 10-1 6, 11-0|| 6 || 8 -- | 57:00 10s IB|12| 0-6 96 0-9 5||7.4|4| 6.5 - 54.00. IO2 6-1 || 7| 6-1. 95– 3| 6-4, 311-3 51*00. 98 11-7| 3| 6-8: 95) 4-9 3||s|3| 6′s 94. 9.9 Brought forward. |USE OF THE SPIRIT LEVEL. 91. LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. From] Bear-IDist. i R * leva- Red. | Red. - •, |º i. ği. hºis. #. º Pººl 1. |† Locations. 110°00| 195] 11 299||10-0 99|| 1 °2 - Carried forward. - - New Quay. 6|II •3| 7 8-7 bow, top of Stella BM. 188||11.9189 1-8 99||10–6] ſ Iro cramp in the El- 2 o'el 4 o'9 106:00 186||11785, 04 101|118 East end of cottage. | --|11-3 2 oz 104°00' 186|| 0:483| 0-2 103|| 0-2 - 5l 0-4 5 º - 101 00 l81| 0-0|77|| 6-2 lo& 5-8 lstella Old Quay. 10| 7-0, 6, 2-2 100.00. 170 5-0|7|| 4-0. 99 l =0 9 I •5 10 7-0 wharf. 99°50' iól 8:350 9-0 100. 6-5 West end of Lead 7| 1.7| 9| 3-5 º º 99°25' 154, 1-8||5|| 5-5 º 8-3 Highest ground in do 8 º: 7 1-7 wharf sº e ſº § - º 98-25 || 145|| 3-2|44, 3-8| 100 11-4 - London Company’ 6 5 °5 3| I •4 wharf. 96-40 138 9-7|4|| 2-4| 97, 7-3 BM and East end of Lead 7| 5-8| 1 || 6-7 95-00. 131 35;} 7-7 91} 8-2 7|10-5] 3| 7-1 • 94-36|| 123| 5-436|| 0 6| 87| 4-8 Into Blaydon Burn. 5 sºlºſio’s 9375] 117 sºft's 2-1 39 6-8 5 ; 5| 8-5 92.50|| 11 || 11 922. 5-6, 89. 6-3 4| 1-4 5| 9°4 - 89.25] 107|10-bilé 8.2 911 2-3 3 #-O 8: 8°5 88.25 104 5-5 7|11 7| 96 5-8 - 2 11-1] 3 5-0 86-50 101: 6-4, 4 6-7 96 11-7 | 6-7 4|| 6-7 96l 11-7 - JBrought forward. 92 ESSAY ON THE LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. from Bear Dist. in TR FTEITTEETRTRT — º #. ...' him. hiº. #. º Lº. º Locations. - 18600 1981-19s sº los 78 Carried forward. - 9| 0-3 || 5-5 - | | |13475, 187|10-891|10-0. 96 0.8 - iRoad to boatlanding. 9| 3-5] 2 2-0 || } 133-00 178| 7-389 8-0 88 11-3 i *- : + *m. 4 7|3's 7 5-3 I of river. . 129'50' 171| 3.5182] 2-7| 89 0.8 | |siºound, bank! * 7| 9-1 r 126'75, 163| 6-4. i 1 7-8 d 126'25] 161 || 10:6 t *– ! w 4ſ 2-6 § 125°00; IBW 8-0 - 5| 8-6 124°50' 15||11-4 | 3||12|3|8-6| 122:50, 148 0-241; 5-3. 106| 6.9 simpams sºme mm . * gate. 1 8-2 6 9-8 - depôt below On- 121 "W5| 146|| 4-0||34 7.5; Ill: 8°5 . Mark on Flag's coal 3| 5 6' 4 4-5 119.25 142|10-430 3-0. 112 74 9| 3-9| 3| 5-6 I 18.00. 133| 6′526 9-4 106, 9°l || 3:3| 9| 3-9] . | 16.70| 132: 3-2|17| 5-5] 114 9-7 4|10-2 6 11-5 Stella coal staith. 1 16-40 127| 5-0|10| 6-0|| 11 6 11-0 Mark on the Offgate, g|1-0|2| 2.2 I 15.25 i IS 4-0 8. 3-8 110 0°2 3| 7-1 2 4-8 | 14-50 l 14 8-9] 5| 11 0 108 9-9 tº dº | *-mº wºº ºh-ºº-º- º 10| 9 2 3 7-1 - | 13-00 || 103 l l 7|2| 3-9| 101 || 7-8 4|10 5|2| 3-9 99] I -2 JBrought forward. USE OF THE SPIRIT LEVEL. 98 LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. From! Bear-[Dist. in Stat.) ings.] chains. Rear Front heights. | heights. | Red. I Red. levels. J dist. 165 •00 160-00 158-00 157°00 155-00 BM. 17: āīā 3| II •3 3: 8°5 168 7.5||70 10.9 imºmº I ºmºmi º -ºms 6-0|| 4 || 5-8 I68] 1 °5|66|| 5-1 2 3•5 tº e - 165|10-0|65 6-0 11-1 s|10-0|3|113 162| 0-0||61||11-3 4|II 2 3|10-0 157 0-8||58] 1-3 153-00 5| 6:6; 4 15|| 6-253 11 2 2-l 151 °00 2.8 11.8 3| 8-0|| 5 I47 149-00 147-00 10-2|47 6|| 6 || 3 141| 4°ll44 8-0 •3 3 5°ll 4 II •0 3 137 3 9 ‘. 145.00 3 o } 4. 133 : 2 143'00 5 127 l I § : 141 00 140 00 189-00 BM. BM. 2 125 ; º : I l : l 6 | 2 : 1. Eleva- Depres- tion. S10Il. | Locations. 97| 11 °4. 97| 8-6 IOI 8-4, 99| 10-9 100 0-7 98 99| 10-9 0-8 4's 2-6 0.7 99 2-8 101| 9:6 101| 5-2 101| 1.6 11-5 Carried forward. miles. Post. Mark, bottom Gate Newburn. Road from Stella to Townley, Esq. |Inclosed Pºp. E. Kiln. Flagging, Stella Lime Stella. Level of quay, High Brought forward. 94 Essay on THE LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. From Bear-IDist. in | . Rear Front | Eleva-. Pºº- . Red. Stat. ings. chains. heights: ſh; tion. sion. evels. dist. Locations. - 20400. Its 10°3 78 4-0|| 99| 6′3| | - Carried forward. 3| 9 || 3 5.9 201-00 IT2| 1 2.72|10-1| 99 3•I 5 198°00' 166 2-1 || 5 || 4-2 11-167| 5-9 99 5-2 - 3| 8'1| 3| 4-1 195-00. I63 3-0|64. I-8| 99 I •2 4|| 3-8| 3 || 0-5 I92.00. I58||11 260 3-8 98 ºf -9 6||11-7 , - * 4. 53 3-6, 105] 0-6| | | | | | Into plantation. -- 158 7-8 7-8 IO5| 3-4 : : : 9 • 4. 3 I86-00 i. I 6. I 10°4 : 183.00. 148 t 102| 3-0 : 4. | 4. 180:00 143 98 6.5 7 - > 178°50′ 135 98 8-0|| | | | Grass land. ; : § ;%§ |2 6 | i. 178-80) 128 99|| 4-0|| | | ||Water course. ;º - mound. 102 4-4 Top of Caomb, hedge § ;% 17823, 125|| 2 & hedge. 99||10-3| 4. |Base of Caomb of 6 ; : 178°16' 118 I } 177:00 112 100 0°4 : i 2 174-00 º 100) 7.9 I : 171*00 105 99 º i : ; : 168-00) 102 º;:; | 97 3. 9. s |Brought forward. Use of THE SPIRIT LEVEL. 95 LEWELS FROM, SCOTSWOOD TO CRAWCROOK MILL ROAD. |Fºr Bear=|Dist. i R | | | Front Eleva-. ID Red. | Red. • º º: i. hºis. liš. . | * i. dist. | Locations. | | |2600||1857.781 tº 104 1-1 || |Carried forward. II 3-2 || 5-9 245:00 184. 4-580 0-7| 104.3-8. 8, 9.7| 4 4-6 243-00 180 6-8|75|| 8-1 104|10-7| 4. 9-6|| 8 9-7 . | | 240-00 17; 9:2|7|10-4 103|10-8| | | | | 3|Miles. 5| Bºls 92 . . . . " 237-00 I'70 4-068|| 1.2| 102 2-8 5 4-0|| 3: 6-8| i side of Gut. :- 234°00 165| 0-0|64 6-4 100 5-6 || ||Water edge, opposite| 9| 0-0 6||3.3 - 230-50, 156|| 0-0|58] 2-6 97 9.4| " - Centre of Gut. 6|| 3-8 f 0-0 Gut. 227-00) 149| 82.49 2.6] 100 5-6 water edge, Ryton | 4| 3•7| 4 || 4-2 223-00 || 145|| 4-5144|| 10-4 IOI 6-1 4| 9-3, 7, 2-3 21900 140 72.87 sq. 102nd 6|| 9 |3| 8 || 5-2 217.00, 188! 99|29| 2.9| 1041 7-0 2 #| 6| 9-3 | 214:00. 131|| 8-822. 5-6 109. 3-2 3| 9-0 || 5 || 1 °3| . BM. 127|11.8|17| 4-8 109] ".5| stake toporcsome to Newburn. • 7| 0-0 8 9-0 Road, from Ryton 218-75) 120 11-8|13| 7-3. 107 4-5|| Centre of Peth Lane 6| 7-4 7| 0-0 213:00 114|| 4-4 6|| 7-3. 1071. 9-1 6||77|| iſ 2-1 210.00. 107| 8-7| 5 || 5-2 102 3-5 4 5-0|2 ; . 207-00 IO3| 3-7 3| 0-0 100, 3.7 * 3| 9-4 3| 0-0 - 99. 6-3 . . . Brought forward. 96 - ESSAY ON THE | : * LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. |FromiRear-IDist. * Rear Front Eleva- * Red. |: Locatio Stat.) ings.] chains. heights. heights. tion. sion. Levels. dist. Catlong. 266°00| 217 || 4 || || 10 sºlos 7-8 - stake in Hall's field. 1|ss 611.9 265-00. 215| 7-3|103 8-4|11 || 10-9 8|| 6-0|| 1 §: 264.60. 207: 1-3|10||11 -6|105] 1 7 s|| 6-0 93 5-6||12| 1-0 7| 8-3| “.. 7-5 | 260-50, 197|10-3] 92|10-1|105] 0-2 ford and ferry boat. Water Lane Road to 1 || 6-7 264-25, 205] 6-6 * | 10-4 91 || 1 -7|102, 9-0 257-50, 194 |03|| 10-6) 254°00' 185 84| 0-0|101 || 8-9 21 255 00 isi 6|| 5-5 side of Creek. 77|| 6-5| 94| 9.4 Water edge, opposite 8 7 l 0 •8 §#.§ 253-50 IT2 Bottom of Creek. 252.75 15s 3-5 64 6-5 89| 9.4 l 9 0. 0 252°00' 140 94| 9.4| Water edge in Creek. 45 6 5 251-00 || 130 98|| 0-0 7 : : 249-50|| 127 102 8-0 : 96 - 9 249 •00| 117 4°l 2 4. 247°50' 114 I 7 : % 7 l i 246.75|| 106 .93| 3-6 Broken ground. : • - e.% : l 246-25 || 105 99|| 3-0 : ºe l Brought forward. i ar—---------- ---wº º USE OF THE SPIRIT LEVEL. 97 LEWELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. |From] Bear-| Dist. | Stat.], ings. chains. Front Rear heights. | heights. | SIOIA, Eleva: Depres: tion. | Red. levels. - |...} dist. Locations. 317-00 l9 | 4. 2 S4 48 106 314-0ſ) 31 1-00 5 185 I | - 5 • } 8 80 3, 10 181| 7 º 3 77 308-00 305-00 302-00 3|| 177 4. 172 6 166 *=mm- - I 0 °5 8-6 2 75 ; 6 69 §# º 3 65 5 °5 I 1 -3 3-0 8-3 5-6 •7 104 103 102 2 § § 103 10] 299-00 4. 16] I § 3. 4. 60 l 10] 296-00 5 156 5 54 i I 10] 293.00 290 00 287-00 15] 2 149 146 4. l : i. § I º : 5 49 I % 102 4. 45 9 103 4. 40 284.00 141 l : 3 37 3. ; 105 ; § 104. 283.00 131 : 10 26 280 00 130 I § : l l §. º 105 & 112 278-00 10 119 1 º : 110 274-00 6 I 13 . . 106 270-00 4. 109 : l 105 2 106 i ; : : 11 4 5-8 10-8 8.4 3. 1 2-6 6°) 0-8 II •] 7.7 I •6 2.7 10-9 2-8 5-8 I •6 Carried forward. Stanners. Stake, west end of the Stanners. * * • º * | i ! j w Stake, east end of the Brought forward. Essay on the LEVELS FROM SCOTSWOOD TO CRAWCROOK MILL ROAD. Stat. From º: Uist. in Rear Front | Eleva- |Depres- | Red. | Red. tº ings." chains. heights. h; tion. | | | | Locations. sion. evels. | dist. longs, 22 yds. ford, 4 miles, 3 fur- - Mill to Stanner’s 351-00 167| 6-660) 2-9. 107 3-7 _* To stakein road from 4, 7-6] 2 9 0 349.00 162] 1 1-0|57| 5'9| 105 5-1 3| 7-0 34700 155 tº 52] I l 5, 107 4-5 § º 4. 9 6 - 2 344-00| 1561 i 107| 4-8 ; ; 3 ; ‘5 341*00 152 46| 2-6' 106] 2-8 § : 2 I 388-00 | 1.48 (). 104.] I 18 (3 g § 3 9 l º 335°00|| 144, 104 6-4 —; ; ; g 5 332-00 || 40 104 || 6 7 i. ; : () BM. I.32): 3 0 || 101 || 10 “I ſ|Cantch on ash tree. ; 2 3 330-00. I29 106] 2-8 3 º:* ; 328°00| 125 2 | 8 - l "7| 105 || 4-6 * •{ ; l : 0 3.7| 107| 1 °3 ! 326 00 º 324°00' 119 5 5 10-2| 107| 9-7 9 I 322 00|| || 15 107| 6-5 i | 8 I 3 || 105 3-6 4|miles. : : r *~~rººmsº d ! : s |Brought forward. * - - - s. § Š Aae aerº/， //////√≠√∂ waeſzºwſz， ż， in ºymry | _ _---- ſºpravza sºuoſtae søſt， * / …，- .……！！！ -- …—łae ſaevae -lae ….…… … ···---··· -º-~~~~ -…-- ae wºrzº zozzzz，|-_ _ · -...……… - …-…-…--~~~~ - …………-- /…/…， º-º-ºor|- — º-º-ºor sºtſin { +-tr.º.º.， www.wwww *////www.aeºryzae| º-º-º-o? |- - º---º---…-..-…--~~~~ ！， --laeae º.rº/ae） low-wºº ···---··· · aerº oo-Zae º-º---， -l，~--~~~~ º aevº-100-tae …º.º.º. | | Lºzcº *-º-ººr- ººººº| |-| | -º-，ae º z-zoº-）ſloo-66， ºzºwww/%' *///zºzº zºzº ºyº/y-º-，ooºoºº º.º. º.or…）! ooºººº |- r. zraelºr-oo..oºº Z-Z-vor） laez |ſº-raeaeſae： Z. z.º.ºr.vº-ººz ſør-ærae， ， ºº º-º-ºz，Hwaeºº - - |- 8-º-º-ºrø， º ſº-vººrø， ſzawy，ºyº/， /， ±（− º.z.ºor.47：7-997 ywogae zºwo zawo yºy, og ø»） ou et rørew №ºſſºſ;ººººº … ºtvºſºſ， ~~~~--~~~~|…º…ººº — »-6 zvz.， ººr-ººr~~~~，~~~ \– % º.rºaerºº _*-º-º…º.º.º.º. xºº 10_^ ,-rºſſº,º.ſ.） -—~~'+6…！！！！！！！ / »…ºff， %， zvºyae// ±-zae，-- Zºſº zvºyº，TIaetaewae zaeøº-Złº _` |%%%%ſáſz- |~~~~，Zaeſſae º ae，wae （ ） - ~ ~ ~/aerorſººſ … ! syſ， wae|ſº wrºot s otſuſe hººae |º-º-º-º?--wo-Zºº |-ſº-º-，aerº | ynº troņael|-|* 646 –~~~~ ~~~~ | | ：-º-，» Zºº zrºzºz1，： |tºtt-æraeøø. 6： ø-/-ae azøv-Zta quae /4ſº z wg_ ael， ºor —##### gyºze »wº« ſae/º ž.，|z-6，aerº º. 9.66ſae --~~~~ z. 2.66ae-zºº. z-z-ºff|×»， ººr z-r-66ſø- ººr 6-Z-e6«»-z0z º aerººrooºººw ！ — ſº por|aerººr -ſ o aeror~~~~ ~~~~ - .– º 9 gº — ſoo-oºr zzzzzzz »， «www./6 ， ！=-%， -º， -+-0-001-− 00： | ） | – - - - - - -|- ----|-|- |- |-|- I 6 …’ a’r， , ， • • • • 6，5：： - zzz • • • • 8，…?，? - ººr |- |z. wz. 26— 1.， - ººr // ±º · 8 · 26– soluſ， z, ， ， ， \*-º- /17/… - aer |：：：:：：， , .ºz. | T， ， ， ， ，–， º vºi wzzsaz， «zuzºzwykº · ſ · 86 zzzzzzzzz， º zzzºzºzzzz/zzzzzy|i - t-ae· · ·：·º·：· {• • • • • • •…， - tºt |-º …» …，…， - ， * - t- → º，|-， ， ， ！ ！ …，…* --~~~~ ： ： ： …：） ----… - ººtae |-/..., . （~~~~ ſgwy yw， zºzº/ae/~w wz/ae.….….….º.º.|.…… ttt … º • • • • •… - … zºzy zzzz27 %/w/%// w8|ſºſºſ–……* - ººr Ažºvý zºzºwyyºyaeZºzº 7 w8§# {{##|o， ººr |Ne o øa -） ºz. *** | º ta ºſºſae - ººr •Zºzzy,//ſyzzzZzzzzzzzºZºzzº，|* … ：-… - 6，1 … a 68.ºz-ººr /• • º6| ， ، ، ، ، º · 2 · 66： ~~~~ |º · 6 · t，·******/ 6 - º -º，…ººº …：/ |º ae| 92 - zzz e* - Z - zaeºra estae |×z · 6 · 9ør–ſø， ºrt ！ Z - 6 - zzz-|， , or Zºzzzzyzwazº zº zºzzº， ºw, w rºzrzy~：： - zae ae|3# №ſí \a .o. aer==） ºra - wae \6 - 6 - 8，–， º aetae |º …， - ，， , ºw/ |-|a - 1 - 66… - .ae | -|- |- - | -· ſraena， maeu， w， ， ，º …?/. ：： hºmº nav ryſºry ſu， ú， ù，ſă._£ - vrae aer， ， ， ºr |- | | .· · · · ·：·º·：·|…， -ae， | ſør， ºmºgynºſ | |-|-- º - ， , ， ）， , ， ！− ， ！ſae;−√2 − √ -|-ſº: {{{}}{=1%;$$ /ae///pwºff /nuw/wa，zaºpaº/\ — t-ae， */wae º， \| /ae/prº/, /º/naestry////// ºtwaes'.ſº/ae/…//lae?Ź，º · Z.Zº –ør-øé dn |-|~§; %—, ， , ， uitnº uopſæº-tº-. aecae tº ---- 81Iſi№ſºſ— v^ . e6 £, º - ºº —， ， ， ：:： ~ ~ ~~ſvº - wae ** - º-º-º· · *** Z zzaehae - sºº ||- |Zºzzº： ）， - tºº ||- |- º ： · 96， - / º º[[JWI Llocº， o ſe /º • • • º6o， , º.ſ. 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To MEASURE INACCESSIBLE DISTANCEs, such AS RIVERS, LAKES, BOGS, &c. As a variety of obstacles of this "kind are frequently met with in surveying and levelling through a country, I purpose to give a few examples for the more readily surmounting these difficulties, and I shall confine my illustrations to problems or such examples as bear the simplest form ; but whose calculations depend upon pure geometrical principles, and particularly the si- milarity of triangles. - To FIND THE BREADTH OF A RIVER WITH THE. CHAIN ONLY. - } ID Having placed a staff at the point A as near the edge of the river as convenient, fix up ano- 4 --- i 100 ESSAY ON THE ther at C on the opposite shore to that on which you stand; then with the aid of a cross staff or chain at A, raise A B perpendicular to A C; make also A E equal to E B, erect the perpen- dicular Bf5, and produce that line until it meets at D, the direction of the line C E ; then the distance B D will be equal to A C the breath of the river. For the angle A E C=B E D and A E=E B (and A C = BD) the angles A and B are right angles; and the triangles A C E, E B D are therefore identical and equal in all respects. This problem may be applied to any inacces- sible distance, for example let EB=4, B D=8, and AE = 12, chains; then by similar triangles as E B : B D :: A E : A C. Thus, A C = ** =# = 24 chains, the width of the river. +i ~.* USE OF THE SPIRIT LEVEL. 101. ; : TO OBTAIN THE MEASUREMENT OF AN IN- * ACESSIBLE DISTANCE AS THE BREADTH OF THERIVER WITH THETHEODOLITE, SECTANT, CIRCUMFERENTOR, OR COMPASS. .”Wi ºt EXAMPLE II. Place your instrument near the edge of the Aº river at A, desire your assistant to plant a | staff at B, and direct the sights and the zero i. point of your instrument to that object, then, fix- * ing it tight, move the sights round until they form an angle of 45 degrees; now desire your assistant to draw the line B C (perpendicular to A B) and let him carry a staff along that line until he has brought it into your line of collima- tion at D, measure the distance from B to the point of intersection at D, and you will obtain the width of the river A B. For B D = A B. 102 ESSAY ON THE - TO MEASURE THE BREADTH OF A RIVER OBLIQUE TO ITS COURSE. EXAMPLE III. Suppose the line to be running in the direction of AB, them, as in the preceding example, plant the instrument near the edge of the water at A, set up a staff at B, on the *posite side of the river, having your theodolite properly fixed with the telescope direct upon B, turn the moveable in- dex round until it forms an angle of 26° 34, draw the line B C perpendicular to A B, and let your assistant move a staff along that line until he brings it to the line of collimation at D as before, then measure the distance from B to the point of intersection at D, which will be equal to one-half the length of the line A B. Therefore, 2 B D = A B the breadth of the river in that direction. USE OF THE SPIRIT LEVEL. 103 To MEASURE THE BREADTH OF A LAKE. zºº.” as ºr • 㺠= : º T. C D *=- Fº-T-S-Eºs::== --Sºrrºs \ | B S. NSS3 --> * * ſº- - ºn Nº. N Nº. EXAMPLE IV. Plant the theaolite at A, and direct your as- sistant to set up a pole or staff on the opposite side at B ; set the index to zero or 360 degrees on the limb, turn the theodolite round till through the telescope you observe the pole at B; screw the instrument fast in that position ; then turning the index round until it form an angle of fourteen degrees two minutes, your assistant in the mean time having raised B C (perpendicular to A B), let him now move along that line with a staff until that object ex- actly corresponds with the vertical wire of the telescope, and there let him plant the staff D; measure the distance B D, which, it must be ob. :* . ... *- - -º. --.- 104 ESSAY ON THE served, will be only equal to one fourth of the breadth of the lake A B. ºf . Therefore, 4 B D = A B. Now let us suppose the lake to be 100,Chains in breadth. Having two angles given, viz. A and B, the sum of which is 14:02 + 90–104-02 —180 will leave 75-58 for the angle D. • Then as radius is to the natural co-tangent of the Z. A so is B D to A B. The following table of angles and multipliers will greatly assist these operations. Supposing the instrument to be always placed in a similar situation to A, and the sights direct- ed to the object on the opposite side at B, move the index round to any of the angles in the table, and multiply the length of the line B D by the multiplier standing opposite to the angle applied to the observation, and the product will be equal to the breadth of the river or lake. ANGLES. MULTIPLRS. 459,00’ 269-34' 180.26% 149-02, 119-19ſ 99.287 7o-08. 59.437 l USE OF THE SPIRIT LEVEL. 105 } When the instrument or staff cannot be plant- ed near the edge of the water, deduct the dis- tance between these points from the total width, and the difference will be the true width of the TiVer. To RAISE A PERPENDICULAR ON THE GROUND WITH THE CHAIN ONLY. With the numbers 3, 4, and 5, or any multi- ple thereof. Set off from C to D on the line A B 40 links, and - planting a staff at }-Hz #– each of those places, fasten one end of the chain at C, and the other at D, stretch the chain tight, and with 30 links in one hand extending from the point C, and 50 links in the other extending from the point D ; set up a staff in the angle of meeting at E, then the line C E will be perpen- dictilar to A. B. In conclusion, I think it necessary to say that having in another part of this work given a plate and description of levelling staves, I omitted to notice the valuable invention of Mr. Gravatt as being the best adapted for expedition; the feet are divided into hundredth parts up the cen- L 106 Essay on THE USE of THE SPIRIT LEVEL. tre of the staff in the form of a scale in alternate black and white streaks, and the tenths in each foot are numbered alternately 1, 3, 5, 7, 9,-10 30, 50, 70, 90, the top of the figure completing the number, and the bottom of these figures are substituted for the intervening ones, viz., 20, 40, 60, 80, so that each figure is one-tenth of a foot in height; on the left hand side of the divi- sions is the number of each foot (from ſ to 14), the whole of those figures are of such a size as to be distinguished through the telescope at a considerable distance. By this arrangement, the whole responsibility rests with the person super- intending these operations; but where great accuracy is required, and where attentive and skilful assistants are employed, I certainly would prefer those with, sliding vanes, manufactured by Messrs. Troughton, W. and S. Jones, Elliott, and other eminent Mathematical Instrument Makers, in London. - - ERRATA. Page 24 line 17 for sydereal read lateral. – 30 – 14 after materially, dele in. — 37 — . 9 for syderal read lateral. – 44 – 5 for the read they. - — 50 – 12 for 1380 links read 13.80 feet. – 78 – 19 after A B insert and. In Field Book at page 48 on line 8-80 instead of 18'504 read Î 96-91 f8:50 . & * > # . . . NEWCASTLE: # PRINTED BY T. AND J. 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