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ROADS . ,fS I IN TWO PARTS. ^f-V^ PART FIRST. aj)sr gs^iE'^^?iis7. / . 1 ■ ■r •i '•J i^r-\ A o-mi. iiui'fO \W: S. f '.<'<{>{ ;;•','(• A « i!,.(! ■)]> iO "! ;JJ HUO; '(■' i-i'jf;>'l fr'jo :iii"?«>' it §^' -Ml' i\ »< ■iff: The suL all the niosi ns easy coir l)een estab] the people f peculiar im[ the legislatu selves in ih this matter i had not orig This defect ^"1 engineers One great of employini course rema laying out a Hot be afford and persons insignificant ihe irregular distant postei present genei ure seen on ii Much is sj the woods by in groping on in the woods after a plan o ire many circ ire to be we it the proper cor to be exercise should make . ' surface of the jit; and even extremely del [ •i, /-•. I'lH'i n'i'ir: ■ •'. '..hi .- PREFACE. ..(1 t'l .; ■;( ■\ The subject of Roads has of late years, occupied much attention in all the most enlightened nations : it has been found, that in proportion as easy communications between the diflferent parts of a country have been established, the wealth, comfort, intelligence, and moral worth of the people have advanced. In new countries, the subject possesses a | peculiar importance : without roads they are utterly worthless ; hence the legislatures of all the new countries of America, have exerted them- selves in the opening of roads. None have paid greater attention to this matter than that of Nova-Scotia ; but it is to be regretted that they had not originally been guided by a better system in laying them out. This defect has been attributed to the great expense of employing skil- ful engineers. ' ^''^• One great evil derived from this source is the idea, that as the expense of employing regularly educated engineers cannot be afforded, no middle course remains— that one person may nearly as well be employed in laying out a road as another — that because expensive instruments can- not be afforded, roads must be laid out without instruments, altogether ; and persons who would not be entrusted to lay the floor of the most insignificant building, are employed to construct a floor, for miles, upon the irreguliar surface of the country, and one which is to go down to distant posterity, as a monument of (he skill, or of the ignorance of the present generation. The consequences need not be pointed out ; they are seen on almost every road in the Province. Much is said oC the judgment of individual^' in laying out roads in the woods by the eye alone : there can be but little judgment exercised in groping ones way among hills in a thick fog ; and laying out roads in the woods without instruments is a somewhat similar operation. But after a plan of the country has been obtained, by proper surveys, there are many circumstances to be attended to ; inconveniences of one kind .»re to be weighed against inconveniences of another sort ; and it is in the proper comparison and adjustment of these matters^ that judgment is to be exercised, and not in attempting impossibilities. *' The engineer should make himself as well acquainted with the undulations, and the surface of the country, as if he had passed his iiand over every foot of it; and even supposing lie has a model of it before him, it becomes an extremely delicate and difficult problem to say what will be the best H IV PliEFACK. course to take for a line of road joining two points."^ This minute acquaintance with the undulations of the surface can on\y be obtained hy measuremeniSt and the person, whoever he may be, who undertakes to kiy out a road in a hilly country, without previously making the proper measurements, by that very act, proves that he is in that particular des- titute of the judgment necessary for conducting the work to a successful issue — that he has undertaken a most important duty, without the knowledge requisite for the proper performance of that duty. Xhe art of using instruments, and making up plans and sections of the ground, is much more easily learned than the use of the tools of any mechanical trade ; any person acquainted with the common rules of arith- roQti9, and possessed of ordinary ability, may acquire a sufficient know- ledge of such matters, and learn to draw plans equally useful for practical purposes, as the work of an accomplished artist, in less than a month. But the mental powernecesssiry to enable the engineer to make such arrange- ments ^nd combinations, as will procure all the conveniences, and avoid all the inconveniences possible, and to devise new plans adapted to new circumstances, cannot be communicated to him by others : it must bo acquired by steady habits of accurate thinking, on the subject, by the per- son himself; and the developemcnt of such powers, by observation, the perusal of books, and study, requires nothing more than the steady atten- tion of a sound and vigorous mind ; and is, in these days, not likely to be confined to any particular class of men, or mode of education. There are scores of young men in our back settlements, who have been schooled, by the circumstances of their situation, into the mechanical and mental halxits necessary to the engineer, and who, were they possessed of the means, of information, and their attention directed to the subject, would in a very short time become, so far as practical utility is concerned, as abje engineers of roads as any that could be imported; and were a considerable number of such persons instructed in the business of laying out and making roads, they might become as plentiful as workmen in other niechanical trades. But in order to be thus qualified, they must learn the method of taking measurements : these methods are entirely mechanical, ^nd very easily learned, but nevertheless cannot be dis- pensed vyith. It will be for the public to determine, whether, at a time every other art is rapidly progressing, that of road-nmking alone shall be permitted to remain in the present imperfect stat<', or whether a set of nun shall be called into operation, capable ol raising it to the station it occupies in other enlightened countries. The present treatise is an humble attempt to furnish some preliminary information on these sjjbjects. In the execution of this design, the author has endeavoured to adapt his instructions to the particular object . ' H ! , «■■ * Evidence ol' Dt I-ar^oer Ijefoie a I'arliamentarv Cctnaiittef, h^ ISItj. .:;(•' PREFACE ill view — the laying ont of roads by persons who do not possess the ad- vantage of a mathematical education. The chapter on Surveying is not designed to supersede the ordinary books on that art ; it may rather be considered as an introduction to them, but it is believed that it contaitiB all that is necessary to be known in laying out a road. The use of technical language is, as much as possible, avoided ; atid the subject treated as a mere mechanical art, to be learned in the same manner as others. The term science is in frequent use with respect to engineering, and its propriety cannot be questioned ; in itself, applied to that subject, it merely means the knowledge of a nuttiber of physical facts, arranged in regular order : but still, there is reason to think that it has rather an unhappy effect upon uneducated minds, Whd, when they hear of scientific road-makers and bridge builderi^, ar^ apt to consider this science as something beyond their reach->-something d6cult, or mysterious, and to be learned only of some Gamaliel of thft art, o( in some Greek or Latin school ; and no are deterred from attempting td obtain a knowledge of it. :>• ' v. , ; :u\ : hv.i if,r'ktnixyiUQmi mv visj This prejudice does not exist with respect to other trades : bous^, 6r shipbuilders draw their plans and carry their designs into execution; they are also acquainted with the properties of the various materials used in their structures, and put each to the proper use, and with Bi much accuracy as engineers do, without the term scientific being once thought of: such knowledge is, with respect to them, considered only that which Kvery such person ought ordinarily to possess, and within the reach of all who chose to pay proper attention to those subjects. Neither is it ever supposed, on the other hand, that mere labourers can direct the execution of their plans. This is because house and ship builders are so common : time was when it was otherwise, but those timei have passed away. Let road engineers become as plfn«y as builders, and the ideas of the occult and difficult nature of their orofesisibn will dis- appear. There is no attempt on the part of modern engineers ttj keep alive this feeling; on the contrary, they take every possible method to diffuse their knowledge as widely as possible, and it only remains for others to avail tbemselves of the information thus thrown in their i^ay. There has been a greater space devoted to the description and adjust- ment of instruments than is common in books of surveying, but it appeared to be a subject too important to be lightly passed over ; and i^ ol'ten not sufficiently understood even by professed surveyors. ' *' '^ ' '^ Connected with this is the plan of making cheap instruments, shown at page 200. Persons who art; only occasionally employed, cannot afford to purchase the expensive instruments used by civil engineers, and it i^ necessary that they be supplied with a cheaper kind. A cheap Woodeh •nmpasp and level, may be made to answer all the pur|K>ses of the mare VI FREFACC. i oxptMisive instruments, and, in the pecnliar ciicumstances of the country, will be found to be a necessary part of any improved system of laying out roads«i-);it |.»v>.rMjvi •»> ; ?t.i»t. J**,- ^Jiii,..<,r , - /". v The chapter on barometrical measurements, is new in hookn of sur- veying: the barometer is an invaluable instrument in the perambulations of extensive wilderness regions, and accordingly, such instructions and explanations are given, as it is presumed will enable any intelligent per- son, with ordinary attention, to make use of it. The chapters on elevations of hills, may appear tedious to some p(!r- sons, but it must be allowed, the subject is difficult to explain to the comprehension of the persons for whom the work is designed. The method employed — that of drawing inferences from examples — may be called unscientific, but it appeared to be tlie best way of establishing just principle in the minds of persons who could not folluw tlu; steps ol a mathematical demonstration, or read an al^^ebraic formula. Tht; sub- ject of these chapters cannot be too attentively considered ; tlio interest of every person is in some degree ;.irected by the state of tl)C roads with respect to hilly ness and len^tn ; and it may be hoped, that persons of influence will now and then Jt-voto a Itisurc hour to the; examination of this important subject. Want of attention to it has led to most o( the errors that have heretofore been committed iu planning the situations of roads. The mere laying out of a road, making up plans, Sic, is a simple routine of mechanical operations, more easily learned than any mechanical trade ; but to make arrangrnit iiis properly ndapied to tlu: surface of the country, and to collatt-ral circumstances, rcfjuires an inti- mate knowledge of the efiects of such arrangements. Of the last chapter, little need be said; it explains itself, but a perusal of it will show that laying out a road in the most proper manner, is not so trifling a matter as it has too often been supposed to be. , :. The manner in which this treatise is written, may require some obser- vations. The design in writing it is to inform the class of persons usually employed in making roads in this Province — persons that in general have devoted little or no time to mathematical or mechanical studies, and from the scarcity of books on those subjects, and the man- ner in which they are written, have but little opportunity of l)ecoming acquainted with them. It is a difHcuIt if not impracticable task so to adjust instructions of this nature to minds not previously exercised hi such studies, as to have just the proper degree of difiuseness. To some they may appear intolerably tedious, while to others they may not U: sufficiently explanatory. But it has been considered better rather to err on the side of tediousness than of obscurity to the unlearned reader. To the person who may chance to read it out of mere curiosity, it will doubtless appear tedious, while to the educated engineer it is unnecessary; PREFACE. VII but by the person of but moderate education, who is employed, or has a prospeet of employment in "uch works ; who bus never possosred the means of studying the subject, and wbo moreover feels, that for tlin proper performance of tho duties that may devolve upon him in that capacity, ho will bo morally accountable ; it may fairly ho presumed, that whether he derive pleasure from it or not, it will be rend and studied, and it may be confidently predicted, that such person will not find it too lengthy or minute in its descriptions. >^.rl!L^n^ mrf: ,\im ,;}.■ .. ;(|t V/lll)«.tI ''. iKl't h i U: ' • 'I ';- > • ♦ •I f «U I- 'f. » t* 'f.j%(^'iff *iJ'noit;;jh J];->iJXUKm ft. v: 1.%..,. .C!v,H a ?J.nQB;t'3q |f^o io './',.,' ^ .ii^'.'n.,. .■,,viJlj^^C*;''i')oi)8ni 'to >» ■ ' ^' ■ •■>!'l '}\\'i ■' ?4i|<0'l if r"-. ■.••..■ Acj • ( .wui ./jvJVf'-rUO JV-.uI :>dj f]lO ' i"^ I'. f ■' I i iiT'-'Tob :.«VGi(i ijvianog »;!> !Hi) io fituiiiGsriiHai )«ujbB ,;y o/' ..■f?:)t{'>:{«Iu' >'< •^V!:^i';i' i';;v' >iij .iiJ .'rUp; h<} o is:> ,:^-:i\t )VAy. ii':)m ,i:,x,'.' ;0i ' ■ ■:-''lH:. ;■ ifii'i ':>i'i.i(<^ itlji . 1. ; ■ ■'•■ A'.:'A :.*>Ui>.ui; :*;;!■«(>>£« '">i ■it! }' W^ :»■>•':; J ttJ'/.;^ '•i\v.h-y^yn^\ =*•';• 5i>i ■■un .•> H ii ^•yil^^A WiV:: Jii*..t' :!L:Kiih}* iiJ-H 'ii'/liiii.- ' ^■■y'^ 'ij-'iv:; •1'^.KI^ J ;• "•'..*!•. ^! :''.!•■'.' I ' '■ . « : . ; t . •! .. .1.... IMM) Hi .1)1 ■'f;(M ill,! ^ ••)ii.n it^it'i > /I' »i(!) ERRATA. r«g« 3. loth line, for " 10 inches," read " 80 inc/tti. " Pag« 16. 8th lint, for "formtd" read "found." Page 42. 12th line, for **them" read **it." Pagf 47, 22d line, for «• ;'^' ;l i>ivk, 4^,; ./I • 'Fr is also \ii iigurfis, aiid tc Tlie proof of t l)ut it docs no foie, to (Jcscri simple, and w in order to sarj/itogointo Plicae a ftiiblo i I considerable di the table, on tl from either of iMxi III >in I 'lio'i , /I' III!) i^r.li (») •/; lii» ;i.';.( I)) .)!!;'! ,, /',! ! (Ii*'|(> w.h » .nil V! !iii!f' !.■'■(•■•; • ' Ml, ■ '.ii: .i /d relations of triangles. The only one of these properties with which we have to do at present is, that similar I triangles have their like sides proporlional to each oilier. As an illustration, suppose the triangle A \\ C, to bo similar to the tri- angle D E Is that is, having its corresponding angles, or corners, the same, the sides of one triangle bear the same proportion to each Fig 1. other, as the sides of tlio other trian- gle, if, for example, A B in the larger triangle be (> feet, ACS feet, and 13 C 10 feet ; then, if D £ in the smaller triangle be 3 feet, it will follow that D F and K F will be 4 feet and 5 feet, respectively. Consequently, D F bears the same proportion to D E, that A C does to A B : also E F bears the same proportion to D E, that C B docs to A B. 'It is also proved thijt the same principle extends to all right lined Hgures, and to all lines similarly [)laced that may be drawn in them. The proof of these propositions may be found in any book of Geometry, but it docs not seem necessary to adduce it here ; we proceed, there- tore, to describe the method of making Plans, and begin with the most simple, and what has probably been the primitive mode. In order to become acquainted with this art, it is not absolutely neces- sary jto go into the field ; it may be learned nearly as well in a room. Plh^ actable near one side of a room, and make two dots upon it, at a considerable distance a[)art, and make a third mark about the height of the table^ on the op{K)site wall, and let it be required to find the distance from either of the marks on the table to that on the wall. 1 } ■if SURVEYING. V i •I .i: 1st. Lay your paper upon the table, so as to have a convenient pouit in it immediately over one of your dots. 2nd. From this point lay a ruler to range directly towards the mark upon the wall, and draw a line upon the paper by the edge of the ruler. 3rd. From the same point lay your ruler again to range directly to the other dot upon the table, and draw another line by it upon your paper. 4th. Lay your paper upon the table so that some convenient point in the line last drawn, shall be exactly over the second mark upon the table, and at ^e same' time^ the line last made upon the papier, ranging diroctly back-to the first mark. '■ i5th. From this last point lay your ruler to range directly towards the mark on the wall, and dra\V a line upon the paper intersecting the line first drawn. This point of intersection will be the corresponding post- ; .'' 1 1 1 ■•jOi'' liiiii !■)•( (.(. j j; ,», ,.;:!> AdavAArMu: The reasoh for this process is, that lines, real or imaginary, being drawn between the points A B and C, a triangle is formed thereby. By SURVfiVING. S the method described a similar triangle a b c is marked out on the paper, and whaterer ^proportion the line a b bears to A D, the same propoiition does the line be lie^r to B C, and a c to A C. Forexample^ if the line A B be three feet, and the line B € twelve feet, and we find a b to be nine inches, or one-fourth of A B, then the line be will be three feet, or one fourth of B C ; or, if the line a b be three inches, or one-twelfth of A i), the line be will be twelve inches, or one-twelfth of 3 C' Generally a b is to A B, as a c to AC. Hence, supposing ab to be 5 inches, and b c 20 inches, we will have : As 5 inches (a b), is ,to 36 inches (A B), so is 10 inches (b c) to 144 inches, the distance B Q* .Ji.!> Fig. 3* •i (i. lliere is another mode of performing this operation which might be more intelligible to some people — First, instead of making two dots, fasten the paper to the table with a pin at the point A, (Fig. 3) ; and jri set another pin at B. Then laying the ruler on the paper touching the ' pin at A, and ranging exactly toward the mark C on the wall, draw a line along its edge from the pin at A to the edge of the paper, (supposed to be included within the dotted line b c d e) ; also draw a line from the pin A across the paper towards the pin B, and, on the table, IVom the pin B towards the mark C. Then a line parrallel to the last may be drawn lipon the paper, as D E, and the triangle A D E will be truly similar to the larger triangle ABC; and the proportion will be as A D is to A B, so is D E to B C ; or as A D is to A E, so is A E to A C. For example, suppose A D 6 inches, and A B 4 feet ; also, upon measuring D E it is found to be 18 inches ; then we have, fi As 6 in. (A D) : 4 feet (A B) : : 18 in. (D E) : 12 feet (B C). Or, if A E measures 20 inches, we have, ' 'J.J *n; 5/ It As 6 iti. (A D) : 4 feet (A B) : ; 20 in. (A E) : 13.33 feet, (A C) 4 SUaVEYING. ' si" his particularly to be observed that if the lines in Figiires '2: and i3 be pot truly drawn, the point G will be shown out of the iproper position, and it will not give the true measuro,* corresponding to the distances A C and B C : also, the shorter the liiie A B, the more adute is tbd angle at C, and the greater the error from iiicorrectness in the work. Hence, when distances to inaccessible objects are measured in: this wayj.atteit- tioH is always paid to having the base, or measured ^ide^ of a considera- ble length. • . ! . Theoretically, indeed, the length of base, is of nd consequence/ but all the works of man are more or lessiimperfect, and the ablest operator is he who by his arrangements contrives to reduce the errors of his eye, and instruments, to the least possible amount. In the above example the side A B is taken for illustration, but it may be proper to observe, that any side of the triangle may be taken as a base from which to determine the other sides of the figure. The Student may conveniently exercise himself in plotting, by form- ing triangles with lines of chalk upon the floor, and laying down plans of these triangles, of different sizes. He may verify the correctness of his work, by making any given side of the triangle base, and noting the agreement of the other two sides with their representatives on tlie plan: the proportion being always — As the length of any given side of the plan, is to the side of the triangle it represents ; so is the length of any other side of the plan, to the side of the triangle it represents. It will be readily perceived, that by the same method which we have been describing, we can find the distance of an object in the Jiddf by merely operating upon a larger scale ; that is, by taking rods or clviiiis, instead of feet and inches. Also in determining great distances Jon the face of a Country; as, for instance, if A and l!5 be poirits in.'^iglit ol each other, on two mountains, and whose distance apart is knOVvn, and C be a point on a third mountain, visible from both A and B ; by tlie sahio method the distance of C is found, the base in this case instead of feet, being many miles. And by a like method, even the distances of the Heavenly bodies are found. , i, , . V The Astronomer has found the diameter of the earih, 'and"iippn tliis, as a base, contrives to get a triangle of the moon, or the sun, arid thus measures the distance. It is true that in these processes he uses instru- ments of an astonishing degree of exactness ; and instead of construct- ing a plan upon paper, and measuring it, he finds the distance of the point C by arithmetical calculation, but this is only for the purpose of greater exactness ; the operation, in its main features, is precisely the same. The principle of these processes, the proportionality of similar triangles, is not only the foundation of calculations, such as we have been describing, but of all the tables and rules of trigonometry ; the Student should therefore make himself thoroughly master of it by prac- SURVEYING. tising it (till it becomes familiar to his mind, and he will be rowafded for hiis pains^ by the ease and satisfaction with which he will proceed after- wards. |ffr i <, •,;->;. ■ ;* -"H •, ;.. ^his, {thus Itru- luct- the of the lilar iave the rac- iii 'i|i 3. if it were always necessary to find the lengths of lines upon our plan by a "Kule of Three" process, such as we have been describing, it would be veiy troublesome. To obviate this difficulty, certain mea- sures have been contrived, called Scales. These are merely the inch, whioh is the usual unit of measure for Plans, divided into a number of equalparts. By the help ofa^cale the Plan is constructed of a size bearing a determinate proportion to the original figure, and the length of the lines is found simply by measurement. !Fbr example, suppose in Fig. ^, that instead of laying down the line a b at random, and measuring if afterwards, we lay it down of a certain length, by a scale to suit our purpose, the same scale will necessarily be the proper measure for the other sides of the figure. That is, if we make a b an inch in length for every foot of A B, then it is evident that a c and b c must also be in the same proportion to A C and B C, that is, an inch for each foot, and that having only a measure of inches to apply to the lines, no calculation would be necessary. Where a very long line is to be represented on paper, it i^ often ne- cessary to use a scale upon which the inch is divided into a great num- ber of equal parts — thus in drawing the line a b, the tenth, or the for- tieth part of an inch in length might be taken for every foot in length of A B, and the work would still be correct, provided exactly the same uuniber of these small divisions were taken that there are of larger mea- sures m A B. ; . •; _ . ' . : ,. . •■. . ; , , For example, if A B were forty feet, and one-tenth of an inch were taken, to represent each foot on the Plan, a b must be laid down forty tenths, or four inches in length, and of consequence there will be the same number of tenths of an inch in a c and b c, that there are feet in ACandBC. Or, in drawing the ground plan of a house if a scale of ten to an inch were used, a room ten feet by fifteen, should bo laid down one inch and a half, or fifteen tenths long, and one inch and two tenths, or twelve tenths broad — but if a scale of twenty to the inch were employed, then the length must be three quarters of an inch, or fifteen twentieths, and the breadth twelve twentieths — yet both on the larger and the smaller scale, the length would bear the same proportion to the breadth, that the side and end of the room does to each other. .' , , » It will be perceived that these Scales are not absolutely necessary to the draughtsman ; their use is merely to abridge labor, by enabling him to find the length of any line represented upon the plan, at once, with- out the trouble of a calculation by the rule of three. They are named SURVEYING. from the numbers of equal divisions in the inch) as ten to an inch, thirty to an inch, &c., and arc made in many diflerent forms ; but essentiaHy, they are nothing more than certain known measures very truly divided into equal parts. ' • ' 4L The process which has l)een described for laying down one triangle, may be easily extended to the laying down of any given number of tri- angles, connected with each other ; or, with a slight modification, any zig-zag Hue. If the Survey be in the field, we cannot, for obvious reasons, lay the plan upon the ground ; we require a stool of a conve- nient height, and as the distances from point to point are considerable, there should be sights on the ruler to guide the eye. Small notches through the heads of pegs will answer the purpose tolerably well, but we must take care chat the line through them be perfectly parallel to, or which is better, that it coincides exactly with, the edge of the ruler. !•■!!! .1 i' ';.i I" "i *i i>ii E Ol ■>il n r\r,. ■J •> ) iD.ti six chains^ line G O b prototypn a the iliiie C J sonts, in the upon the p|j which havii twelve tenth the point E, % this m ground is tra smaller scale tlie same pro sent. It is obvioi arrangement and laying of upon the pap* %"fe at larg representation ^et it be r gioUnd. In SI upon the groui Suppose in point K is estj ijo paper, an inat the scale < ^^upon the '" Let it be required to lay down the plan of the line of which ABC D E, Fig. 4 is the representation, on a scale of ten chains to an inch.* ' First. Place the paper at B, and with the ruler directed to the points A and C, draw lines indefinitely in those directions. Then havuigB ^'"'® '^ff twelve measured the line AB upon the ground, and finding it, suppose teiiB'^''^"^ point 1 chains, I lay the distance answering on the scale to ten chains, whichB ^^^ *^'6 line I is one inch, from B towards A, and mark the point A. In like manner,! ^^'"''^^sponding having measured the distance B C on the ground, and found it cightl"P°" *^'c paper chains, lay off eight tenths of an inch towards C, and mark the point C. I ^"^^^^d* Layi The line A B C is now a correct miniature representation of the corres-l?'^^^.'?' vvhb pla ponding lines upon the ground. Having proceeded thus far, I removolj^^*'"*^ done so the paper to C, and place it in such a position that a ruler laid along the! '"®?sure offth. line B C will range back to B ; this brings the paper into the samJ^"" ^'^ *ui exact position, with respect to the line upon the ground, in which it lay whiiJj^* ' then proc at B. Then directing the ruler from the point C on the paper, towardJ'jV^^t'y towards D, I draw the line C D *. and having found the distance on the grounl ."^g to be p| I'avmg found th( * The chain is a measure of C6 feet, and it divided into 100 parts, caUed links. It is the measure conif y'^^SUj'c yg* ^ monlyused by Surveyors, pOint Ot In I'lk SURVEYING. six chains^ 1 lay off six tenths of an inch from C to D on that line. The line G D bv the plan corresponds therefore in length and position to its prototype on the ground. Lastly, 1 remove the paper to D, and bring the line C D upon the plan into the same position as the line it repre- sents, in the same manner as was done at C. Then laying the ruler upon the plan to range from D towards the poim E, I draw the line D E ; which having found to be twelve chains upon the ground, 1 set off twelve tenths of an inch^ or an inch and two tenths upon it, and mark the point E, and the Survey is completed. By this means an accurate representation of the real lines upon the ground is transferred to the paper, the lines upon which, though on a smaller scale, have the same position with respect to each other, and the same proportional lengths, with the corresponding lines they repre- sent. it is obvious that we can reverse this process; If we have a given arrangement of lines upon the paper, we can take it to the field, find laying oft' lines upon the ground in the relative positions of those upon the paper, and of the same proportional lengths, we construct the Bgure at large upon the ground of which that upon the paper is the representation. mi. *:) .l':> • •• '.ii, > : :!^;i.. • i • ■; ^ ;, .1; . ■ Let it be required to lay off the given figure A B C D E upon the groiind. In such cases as this, there is usually some line already known upon the ground to which the other lines are to be referred. Suppose in the ease before us, this bo the line D E, and that the point E is established. 1 first measure the length of the line D E upon liio paper, and finding it one inch and two tenths, and also observing that the scale of the plan is ten chains to an inch, 1 conclude the lino D E upon the ground is twelve chains in length, and accordingly I mea- sure off twelve chains along the line from E, and there set up a mark for the point D. Then at the point D I lay the plan in such a position that the line D E upon it, ranges exactly in the same direction as the corresponding fine D E upon the ground. It is evident, then, that D C upon the paper will also lie in its proper direction with respect to the ground. Laying the ruler therefore in the direction D C, I send an As- 'Isistant who plants a flag at a proper distance, exactly in that direction. „ jHaving done so, I measure the line DC, and finding it six tenths of an inch, the ^ '"'^^S""'*^ off the corrcspondirjg length 6 chains upon the ground, towards, ° and in an exact line with, the flag, and there set up a mark for the point C. 1 then proceed to C, and laying the plan with the line C D ranging dgrectly towards D, I lay the ruler along the lino B C, and having caused !■ I ivmg leiV MS Inner, 1 eight! lintC. same lwhil( Iward rouw ^'^^^'^g ^^ ^6 placed in the direction pointed out by the ruler, and also I liaving found the line B C upon the paper to be eight tenths of an inch, ^^ I measure off eight chains in the direction of the flag, and mark the Soint B. In like manner I place the plan at B, with the line B C di- I 8 SURVEYING. t\i ^'h ;»*■■. "■: I ■A ■ rcctod towards C, and having found the length of A B an inch, I set oA' ten chains in ithe range of the line A B, and the work is completed. This reverse method is seldom or never required in Road Surveying, as respects the original plan ; hut it would often have to be resorted to in laying down other lines in connection with those originally ^irveyed. Supjjbse, for instance, we want to run a straight line from A tp C, and by reason of obstructions to the view, those points cannot be seen from each other. In this case, a straight line could be carried through by means of stakes at small distances from each other, provided we could start in the proper direction. Here our plan comes in aid. Having placed it at A on the ground, with the line A B ranging towards B on the ground, the dotted line from A to C will be in the direction of the latter point, and the ruler laid along this line will give the direction to start the line of stakes upon. Or the plan may be placed at C, in its proper position by means of C B or C D, and the dotted hne A C, will give the direction towards A. By a similar process, any other line upon the plan may be laid upon the ground. i ;; . - ' • 5. The instrument with which these operations arc usually performed is called a Plane Table. It is a small plane board, mounted upon a stand, with ;a universal joint to level it by. A small Compass accompanies it, which can be attached to it, and by which a meridian line can he laid down upon the plan, as N S, Fig. 4 : the ruler is mounted with sights simi* lar to those of a Surveyor's Compass, for the more correcdy ranging it to objects, but the essentials are nothing more than a flat board and a ruler. It is fit to be used only in clear lands, and is by no means a con- venient instrument in Road Surveying ; but the Student would do well to practice with it for a short time^ because such practice is the best means of bringing him ac(](iainted with the nature of plans, and their connection with the ground they represent. When he is properly ac- quainted with the use of this instrument, he is sufficiently qualified for surveying Roads. He will find it proper to use other instriiments for comenience, but the principle is in all cases the srmo. / i • | »»: ? ; ,Jt is not necesary to go to much expense, he may merely prochre a small stool about four feet high, lay a piece of board eighteen inches square U|!ion it, to which his paper may be attach(;d with wafers, and a common ruler, with a peg standing in each end, will answer for him to range by with sufhcient exactness for his purpose. He may then set up stakes in a level field, lay down on the paper a plan of the ground marked ofi" by the stakes, by the method just pointed out, and verify the correctness Qf his w^rk by comparing the angles and the lengths of the lines upon the plan,'with the corresponding angles and lines upon the ground. For in- stance, in Fig. 4, he may lay his plan at A on the ground, and try whe- ther the line A B will range to the stake B, and at the same time the line A C A and C plan, an< parts of t A B and for that f of the op with those he may c( suitable tc It woul( an assistar to each otf consult on progress. acquainted stool to lay from a car| take a wax pair of cor simple instri off their grc and when instructions exercise the more real h ture or Schc 6- A ph representatii for supplying crooked roac the lengths and to other fection, or which the si glance, we i could we ov< for that purj posed insupc here those r seen fit to be reasoning po wake a repr SURVEYING. 9 Ismail ^uare imon re by LGS in iff by IgssqC |n the lor in- wbo- lUe Hne A C range to C ; he may also measure the distance between the stakes A and C and observe its agreement with the distance, as shewn by the plan, and in like manner he may verify the correctness of all the other parts of the figure. Or, he may set stakes at any distance apart, as at A 6 and C, Fig. 2, and make plans of them by the method pointed out for that figure, and on the different scales, and then try the correctness of the operations by comparing the measures and angles on the plans, with those represented by them on the ground ; and in a similar manner he may contrive figures to practise upon of any kind he may think most suitable to the object he has in view. It would be convenient for two Students to practise together, because an assistant is always required, and they would not only act as assistants to each other by turns, and become expert in all parts of the business, but consult on the methods to be taken, and by so doing faciUtate each other's progress. Let a couple of young men who wish to make themselves acquainted with matters of this nature, spend half an hour in making a stool to lay their board upon, procure a piece of planed board and a ruler, from a carpenter ; and if it is not convenient to get a Surveyor's chain, take a waxed cord for a measure, and with the addition of a scale and a pair of compasses, their apparatus is quite sufficient. If, with these simple instruments, they practice a few hours each day for a week, laying off their ground in different figures, and making plans on different scales, and when they find themselves puzzled, instead of looking for the instructions of a teacher, take a common sense view of the case, and exercise their own judgment, they will, by the end of the week, have more real knowledge of the subject than they would obtain in a Lec- ture or School Room in a month. 6. A plan may be compared to a miniature picture ; it gives a true representation of the ground on a very small scale ; and is an expedient for supplying the defects of our natural powers. Suppose we have a crooked road ten miles in length, and we wish to get acquainted with the lengths and positions of its several parts as related to each other, and to other objects in its vicinity. We cannot view it in a horizontal direction, on account of its great length and the numerous obstacles by which the sight is interrupted ; to get a bird's-eye view of it at one glance, we would need to be several miles high in the air ; and even could we overcome this difficulty, our powers of vision are insufficient for that purpose. It would seem at first view that nature had inter- posed insuperable barriers to the attainment of this knowledge ; but here those remarkable faculties that the Creator has in Eis wisdom seen fit to bestow upon us, come to our aid. By the direction of the reasoning power, we proceed slowly over the ground, and by degrees make a representation of it : this, though apparently an evasion of a 2 I 10 SURVEYING. restriction imposed upon us by nature, gives us a mucii greater advan- tage, than any natural power of seeing the whole at once, could ever give. Even could we obtain such a vit;vv, it would vanish when we turned away from it, or could we retain so vivid a recollection of the whole as to be able to act upon it, still we could not communicate the knowledge so obtained to others ; but by means of plans, and copies, it may be imparted to as many as we please, and may be transmitted to future generations. Nor do the advantages terminate here : our powers of correct vision are restricted within very narrow limits ; but we can, by using a proper scale, always make our plan of such a size as to be seen to the best advantage. If we have to make the plan of a country, we lay it down on a small scale, so as to comprehend its general form at a glance ; if of a piece of ground of only a few miles in extent, we use a larger scale ; and if of a very small lot, a still larger, so as to bring it to the size best adapted to our purpose. The instrument of which we have been treating, is probably one of the first which was used in Surveying, but it is attended with incon- veniences in the use : methods have therefore been invented for taking the measures of the angles in the field, and transferring them to paper afterwards. What these are, we proceed to show ; but first it will be necessary to define what is meant by the measure of an angle. ! ,;; 7. Whenever two lines, whether straight or curved, meet in a point, that point is called an angle^ and the angle is called small or great, according to the smaller or greater degree of divergence of the two lines from each other. 'I I i No. 1 A A Fi o. No 3 / / Thus No. 1, Fig. 5, is a small angle ; No. 2 is a greater, and No. 3 a greater still; the point A is called the angular point. Angles are divided into three classes ; the first class consists of those whose lines meet in a sharp point, and are named acuie^ (sharp or cutting) as No. 1 ; in the second class the lines form what in common language is called a square, In illustra and C A, Fia the obtuse an their angular of the circum lines, is, as CO ••espective ar SURVEYING. 11 as No. 2, and is named a right angle ; nnd in the third class the diver- «rL>nco is "till greater, as in No. 3, and the angle is called an obtuse, or blunt anj['i^.. The right angle, it will be perceived, occupies the middle ground between the acute and the obtuse, and this property is turned to good account in geometrical investigations, but in the present brief sketch we pass this over. 8. From the nature and formation of angles, it is evident that in finding a means of measuring them, we can have recourse to no measure of absolute length : the only means practicable is to compare them with the circumference of a circle ; in other words, if a circle be drawn, having its centre in the angular point, to measure the part of the cir- cumference contained between the angular lines, and note the proportion which that part bears to the whole circumference. This proportion is called the measure of the angle. Fig. 6. In illustration of this, let the acute angle formed by the two lines, B A iind C A, Fig. 6 ; the right angle formed by the lines B A and D A, and the obtuse angle formed by the lines B A and £ A, be all laid down with their angular points at A, the centre of the circle BCDEF; then the part of the circumference B C, or B D, or B £, contained between the angular lines, is, as compared with the whole circumference, the measure of these respective angles. The Student must here carefully observe that the 12 SURVEYINU. term measure is not used in its ordinary sense of an absolute quantity, such as the length of a house or of a field, in feet or in yards, but in the sense of proportionality. We cannot say that B C, the measure of the angle B AC,* is so many feet or yards, such a scale of measurement would not be applicable ; but we say it is such a proportional part, as one-tenth or one-twentieth of the circumference of n circle. This pro- portion will be always the same, whatever be the size of the circle : the line be, or bd, bears the same proportion to the circumference of the circle b c d e f, to which it belongs, as the corresponding line B C, or B D, bears to the circumference of the larger circle to which it belonjjs. In the case of the right angle, B A D, b A d, this is obvious ; the part B D or bd, of the circumference of either circle contained within the angular lines, being just one-fourth of the whole circumference to which they respectively belong. The same thing is not so obvious as regards the other angles, but it is proved to be a geometrical truth, and forms the basis of all our trigonometrical operations. 9. Suppose now, we wish to avoid the necessity of taking the plan into the field, we may, instead of laying it upon the plane table, take a piece of circular paper, and laying it upon the plane table at one of the angles of our line, as at B, (Fig. 4.) draw lines by the ruler from the centre to the circumference, in the directions B A and B C. The part of the circumference contained within these lines, will be the measure of the angle at B. In the same manner we may take off the angles at C and D, upon the same, or other pieces of circular paper, and at leisure lay the papers in their proper positions upon the plan, and transfer the angular lines marked upon them, to it. The length of the lines from angle to angle on the plan, must be laid down by a scale, as in the former case. The best practice for the Student, is, to make his plan upon the plane table in the manner formerly pointed out, and at the same time make his angular marks upon the circular papers, which may be afterwards used in constructing another plan. The agreement of the two plans will verify the correctness of the work. By these means we can make a survey upon the ground, and transfer it to a plan at our leisure, but if it were extensive, we would have a number of papers, troublesome to preserve ; or, if we took off several angles upon our paper, we would be very liable to mistakes in transferring them to the plan. We may obviate this inconvenience by dividing the periphery of our circular paper into a great number of equal parts, and merely noting the number of these parts intercepted between the situation of the two * Angles are designated by the three letter!) at the ends of the lines forming the angle, the middlemost letter always denoting the angular point. Thus, BAG denotes the angle formed by the lines B A and A C, and the ptsition of A, between B and C shows that A is at the point of meeting, or angular point. lines, as in ruler from periphery c parts betwe the paper v in two plac each other, at the ends ference, am means of oi in the field. This idea instead of n on metal, using in the number of p called a The fine brass ; si is of silver: 1 been describi much more c a strong ring arms for fixiii this circle we compass. A turn upon a c upon the end Thus there w the line of vis ring was the two distant p one of those fastened ; the through the periphery of the instrumen Thus in mc and directing pair to C, I n these lines of instrument at of parts contai out the Survey by means of tl SUnVEYINO. 13 we our )ers, our the y of )ting two lemost A ai>(i point. lines, as iiulicated hy the edge of the ruler. Thus, if by directing the ruler from the angular point, successively to where each line cuts the periphery of the circular paper, I find there is twenty of these equal parts between those ranges, 1 note it, and on making up the plan, lay the paper with its centre at the angular point, and mark upon the plan> in two places, at the edge of the paper, the same number of parts from each other. This is evidently the same as if the two marks were made at the ends of lines running from the centre' of the paper to its circum- ference, and avoids injuring it by drawing lines upon it. Thus, by means of one paper so marked, angles without number may be taken in the field, and transferred at leisure to a plan. This idea is generally acted upon in the making of Surveys, only that instead of marking the equal parts in question on paper, they are done on metal. One stout circular plate of metal is correctly divided for using in the field, and another thinner plate is divided into the same number of parts, for laying down the plan by. The former of these is called a Theodolite, the latter a Protractor ; they are generally made of fine brass ; sometimes the periphery on which the divisions are marked is of silver: they are merely substitutes for the circular paper we have been describing, but, owing to the material of which they are composed, much more correct. The form of the Theodilite formerly in use, was a strong ring of brass, about eight inches in diameter, with two cross arms for fixing it to a stand. Upon the extremities of a diameter ot* this circle were fixed two sights, similar to the sights of a Surveyor's compass. A flat brass ruler was also mounted upon this ring, so as to turn upon a centre, which coincided with the centre of the ring ; and upon the ends of this ruler were two other sights, similar to the former. Thus there were a pair of fixed sights, and a pair of moveable ones; the line of vision of both crossing the centre of the circle of which the ring was the circumference. In finding the angle contained by lines to two distant points by this instrument, it is placed upon the stand so that one of those points can be seen through the fixed sights, and it is there fastened ; the ruler is then turned round till the other point can be seen through the sights upon it ; the number of equal divisions upon the periphery of the circle between those lines of sight is registered, and the instrument set up at the next point of observatiofi, and so on. Thus in making the Survey, Fig. 4, I first set the instrument at B, and directing one pair of sights (it matters not which) to A, and the other pair to C, I note the number of the equal parts on the circle between these lines of sight, and then pass on to the point C. Then setting the instrument at C, with the sights to range to B and D, I note the number of parts contained in the angle, and so on at each angular point through- out the Survey. These angles can be afterwards transferred to the plan by means of the Protractor, which it is to be remembered is divided 14 SUUVEVINO. iiilo the same nutiiluT of equal parts as tlio circle of tlio 'llieodoliti', (iikI tticrefure the sainu number of parts luid oil' by it at tach angle upon tbc plan, as was foiuid upon the Theodolite between the ranges of vision, to the corresponding angular points upon the ground, will give tlie angles upon the plan the same as those upon the ground. There was formerly another instrument of the same kind, calculated to take vertical angles, such as the angle contained between the lines of vision from the eye of the spectator, to the bottom and top of a building, &c., the principle of which is the same as that of the Theodolite. 10. The modern Theodilite is a combination of these two instru- ments ; the place of the circular ring, and its cross arms, is supplied by a thick circular plate, and a thinner circular plate revolving upon it, supplies the place of the moveable ruler. Instead of the open sights, there is a telescope mounted upon the uppermost plate in such a manner that it can be elevated or depressed so as to bear upon high or low oh- jects. This instrument is so perfectly adapted to the use intended, as to leave little or no room for further improvement. Hitherto wo have considered the instrument as having its periphery merely divided into some convenient number of parts, but have men- tioned no particular number, because that is not a matter of consequence; all that is required in the protracting of plans being, that the Theodolite and Protractor be divided into the same number of parts. In practice, however, the number into which they are divided is always 360.* These divisions are called degrees, and each degree is divided into 60 parts, called minutes, which, for nice astronomical operations, are sub-divided into 60 other parts, called seconds ; but minutes and seconds are not marked upon the instrument ; there would not be room for so many distinct marks ; but by means of an ingenious appendage called a vernier, angles may be read off on most good instruments, to twenty seconds, or the third part of a minute. The Student must bear in mind that the number 360 is merely conventional. In the Theodolite, besides the parts already noticed, there is in the centre of the instrument a compass needle, with a graduated ring, similar to a Surveyor's compass. We have hitherto said nothing of the use of this appeildage, because it is not required for the purpose of measuring angles : its only use, as connected with a Survey by this instrument, line, so as t answers the to the j)Iune H. The I'V the j)lane (lie same ; ti •re laid direi mstru merit, i reasonably aj 1)6 at the cxf plane table a mswer is, tha exactness thf accordingly b ligations, by i 'h«i proper be t'le ground be 'ind capable oj at present con '"' angles, but *'z. : a Level, nmferentory o i'\ * The origin of this division is to be found in the ancient custom of carrying by twelve instead of ten, in all arithmetical calculations, and this number, it will be perceived, is a multiple of twelve, and, noU withataoding the superiority of the decimal arithmetic, it, as well as the duodecimal division of the day, hours, carpenters rule, &c. has continued principally in use since the time the latter was invented. The French Government during the Revolution, abolished these remains of the old duodecimal arithmetic, divided the circle decimally, and had all their nautical tables recalculated and accommodated to the deci- mal method. For this improvement, so important to the Navigator, as well as for a uniform system «t weiglitf and measures, the world is indebted to the genius of Talleyrand, 12. Hither plan made by common use, v convenient ; tl l/neridian, or N table, by drum land at every st Thus, in ma kt. 4, if the 11 m end N nort h all placed u pie S N, and >roper, we may ipon a separate ivith respect to Host convenien "»gles with an rom notes in tl nee being that MLItVEYIN(i. l.'l instrument, Ih to tiiid the dircciioii of a meridian, or Nortii and South lino, so as to enablo tiio Surveyor to lay it down upon liio plan ; and answers the sanio purpose as tin: small compass that is usuall)' attached to tin; plane table. > , , , 1 1. The reader will perceive that thn method of lading down a plan by the plane table, and by a Survey with the riu>odolite, are essentially the same ; the only dilK'renec ''oing, ih.a in the Iniiner case the angles are laid directly u|)on the paj)cr, and in the latter they are formed by the iiistrumefit, and alU-ruards •/7rt«.v/cm If:. of which are liable to minute errors. In the horizontal survey, imper- feciions of this kind are overlooked ; a few feet or yards of error is of no material consequence ; but in the levels a foot, or even a few inches, is often very important. Besides, if instead of six stations, we have, as is often the case, some hundreds, the uncertainty would, at length, be- come so great, that for a canal or rail-road, the survey could hardly be depended upon at all. To prevent this uncertainty, the expedient has been resorted to, of computing the height of each station from a sup- positious base hue, and entering it in a column of the notes. Column 7 contains these heights, calculated from a horizontal line drawn from A. They are found by adding those of column 5, or substracting those of column 6 for each station, and being merely additions and su^^stractions of numbers, no uncertainty can take place. This expedient also affords a great facility in laying down the section. It is only necessary to draw a horizontal base line, lay off the distances from station to station in succession along the line, from these points raise perpendiculars, and set off upon them the heights of the respective stations from the base line. Referring again to our example, from the point A, Fig. 8, we draw the indefinite line A G, as a base ; and upon this base set off 3 chains to s, 6.20 chains to z, 3.10 chains to y, 3.75 chains to x, and 4.46 chains to G. Then from these points we erect perpendiculars, and set off" as shewn in column 7, at s, 9 feet 3 inches ; at z, 20 feet ; at y, 29 feet; at X, 18 feet 6 inches ; and at G, 15 feet, which gives the points w n j r and m the same as before. Of these three methods of laying down the section the last is much the best, both as regards correctness, and saving of time. It may be proper for the beginner to practice a short time upon the two former, as by that means he will get acquainted with the connection between the section, and the ground it represents, but for general practice, (he last is that which is always employed. By filling up the 5th, 6th, and 7th columns at short intervals, the Surveyor can ascertain the comparative heights of different parts of the line as he proceeds. As a check upon the accuracy of the computation, it is necessary, from time to time, to add up the contents of the two columns containing the back and fore sights, and substracting the less from the greater, the difference shows the whole amount of the rise or fall of the ground ; which, if both com- putations have been correctly made, will be the same as the diffierence shown in the column of reduced levels. Thus in the field notes, the sum of the fore sights is 20, and the back sights 35 feet : the dif- ference, 15 feet, is the same as the height given in the column, (No. 7) of reduced levels. 16. Some Surveyors, as a means of facilitating their operations inj the field, carry a paper ruled into small squares, the lines being at equal interval field, su In th( sketch t vertical former, section t horizontj regularly he deterr purposes column ir place of Fig. 9 SI Page21,tr| by means between h\ without fui It will bl colours, ani line repres( pencil, and! ^vill supercj SURVEYING. 25 as intervals. By means of these lines, the section can be sketched in the field, suiTicieutly near the truth for ordinary purposes. In the example to which we have so often referred, if wc wish to sketch the section in this manner, wo rule a paper with parallel and vertical lines, at convenient distances apart, say half an inch for the former, and one tenth of an inch for the latter. Th ^ allowing our section to be the same as Fig. 8, each square on the paper represoijts horizontally two chains, and vertically two feet, and having the lines regularly numbered, the position of any point shewn by the notes, can be determined upon the plan sufficiently near the truth, for the general purposes required in the field. In this case, it is necessary to have a column in the notes showing the whole distance of each station from tlie place of beginning. Fig. 9. ! in , ^^ -~*\. / \ y »^^' ^«- --^-. n f^l- / '"*^,„^^ A ,„-^ • T-m -IHH *-^ ^^^^ . [ [ / 1 , , ' 1 A ly' \ ... .U_t-«»-u i 1 .10. .12. -14 .iCi. .IS. Fig. 9 shews the ruled paper, with the section taken from the notes page 21, traced upon it. The points w n j r and m are easily determined by means of the parallel rulings, and the line is afterwards traced in between by the judgment. The figure exhibits the method sufliciently, without further explanation. ■' ' ' ' ■ ^ . ■ . . It will be convenient to have the horizontal lines ruled in different colours, and at equal intervals a strong line, as a guide to the eye. The line representing the surface of the ground may be drawn in the field in pencil, and afterwards corrected by the scale, and done with ink, which will supercede the necessity of making up another section. 4 ,1- )j ■ 4,: ■t :-,i;, 26 SURVEYING. >:h I'M Ur- 17. These lines may be made further useful iu Road Surveying, hy drawing diagonals across them in proper situations, and at any required elevation ; which lines will at once snow the general range of the sur- face of the ground. These diagonals may be drawn just in the same way that any part of the section is drawn. For example, if m e wish to to draw a line representing one to thirty, from the point A, we take any convenient distance, as ten chains ; and calculate the height at that dis- tance, which is 22 feet. We then draw a line from A to the point of intersection of the parallels, of ten chains and twenty-two feet, which is the line required. 18. It may have been observed that the place where the measuring staff has been set up, and not the place of the level, is called the station. This is different from the practice in making the liorizontal survey. In that case the instrument is always set at the station ; but, in taking the level, the only condition is that the places of the staves be both seen from the instrument ; it matters not whether it be in the line between them, or in any other situation ; the object of the operation being merely to find a point at each of two contiguous stave stations, that shall be horizonf^l from each other. This will always be the case, if they be horizontal fiom any third point ; if, therefore, the instrument be so placed that both stations can be seen from it, their horizontal position can be readily determined. The same remark may be extended to the case of taking the height of several stations from the same point. For instance, from D, Fig. 8, we can direct the level to f, and to g, without the necessity of removing it to E ; merely noting the height of the line of sight above j. Or, we may enter the point j into the notes as a station, in tlie same manner as is done in the example; making the observed height the fore sight for one entry, and the same height the back sight for the next. It may be proper to explain here, that the terms back sight and forr sight are not taken as indicating the direction of the sight through the level. They merely mean the two ends of the space between two sta- tion staves, and are so named with reference to the direction with which the survey is proceeding. Back height and fore height would belter represent what is intended, but the other terms have, rather carelessly perhaps, got into general use, and all that can now be done, is to define their meaning. 19. It will have been''perceived by the reader, that in all the fore- going examples, the vertical scale of the section is different from that used in the horizontal direction. The reason of this is, that a rise of ground, if laid down in its true proportions, would not appear to the eye upon the paper as it does upon the ground. Fig. 10 shews the section of the ground on a line up the street from the Steam Boat wharf in Halifax, to the west side of the street below the Gran< the same scale. W they roprc It is an ( it to be so, A distort! medium, bi level ten or sometimes < entirely a n endeavour possible, tJ the case o the rises an tion, on a S( ^ew Bruns over ground feet to an ir idea of the the Koad b( length, wer on the line, inch would writers on the vertical expect the Another it affords a errors in pi occurring inl proportion SURVEYIWC. 27 the Grand Parade, laid down in its true proportions, ^^g. I shews the the sumo section so distorted that the vertical is six tin s tho hot /.ontal scale, if these sectfbns he compared with the appem ^ e ut tin , round they re[)re8ent, the latter seems to be the truest rcprcbciimtion. Fig. 10. Fig. 11. It is an optical deception which it is difficult to account for ; we know it to be so, and accommodate our sections to the circumstance. A distortion of six in the vortical to one horizontal, is found to be a good medium, but if the ground be very abrupt, four or five to one, or if very level ten or twelve to one, or in the case of a large extent of country, sometimes even twenty or thirty to one, will answer better. This is entirely a matter of taste and judgment with the Surveyor, who should endeavour to make his section to represent to the mind, as nearly as possible, the same appearance that is exhibited by the ground; or in the case of a section across the country, to give a definite idea of the rises and falls of its surface. For instance, in laying down the sec- tion, on a scale of one mile to an inch horiz^ jtal, of the Royal Road in New Brunswick, which was one hundred miles in length, and passed over ground sixteen hundred feet in height, above the sea, four hundred feet to an inch was found to be a good vertical scale for giving a proper idea of the heights of the country. On the contrary, if the section of the Road between Sackville and Windsor, which is thirty-five mdes in length, were laid down by the same scale, Ardoise Hill, the highest land on the line, would hardly be observed; probably, two hundred feet to an inch would make a better section. Hence we may perceive, that those writers on Engineering who recommend certain proportions between the vertical and horizontai scales, mean only a good medium, but do not expect the Surveyor to confine himself to any certain proportion. Another reason for enlarging the vertical scale of the section is, that it afibrds a greater exactness in the measurement of the heights ; small errors in plans are unavoidable, but they are of most consequence when occurring in the heights, and the effects of such errors are reduced in proportion as t' Juired for the purpose of explanation, is not laid own. 37 for the 3Q SURVEYING. I'- ll^ ;■.'■;:■ I .11 sight to 3. When this is done, he proceeds on, noting the distance as ho passes the chain-men, and takes another convenient station for a position'as at 4, leaving the chain-men with the vane at 3, for the next sight, the staff-man in'the mean time going forward with his vane to select a proper position for the next sight at 5. After he has taken the sight to 3, and while he is taking the sight to 5, the chain-men come up to him, give in the distances, and accompany him forward as before. Here it must be remembered that though he takes the sight ahernately backwards and forwards, this is only for the sake of compensating errors, the entries are all made in the notes as if they had been taken forwards. The reason of this is obvious ; it makes the notes read regularly forward, and prevents confusion in laying down the plan. The notes of the above are as follows, beginning at A. 1 9 3 4 5 6 7 8 -.— — ■, ,. J — '~SA, Course. Distance. No. Elevation. Depression. Perpendi- cular Height. Whole height Whole height from dntiim from A line C D 30.00 Rvnoarks. S 27 E. S. 30 E. S. 17 E. S. 22 E. S. 41 E. S. 24 E. 8.60 7.35 9,15 bAQ 10.27 15,10 1 2 3 4 5 6 4° 25' 6 20 2 40 0° 0' 4 6 5 15 2 10 43,64 54,02 28,08 — 26.00 — 62.30 37 80 43,04 97.66 125,74 99.74 37.44 75.24 73 64 127.66 1.55 74 129,74 67,44 105 24 In taking the observations. No. 2 appeared on the instrument, N. 30 W. depression six degrees twenty minutes, and No. 4 N. 22 W. elevation, four degrees six minutes, owing to the sights having been taken backwards from 2 to 1, and from 4 to 3; but they are noted just the reverse, which makes the notes read the same as if the instrument had been placed at 1 and 3, and the sights taken forward from 1 to 2, and from 2 to 4. It will be perceived by the above, that the instrument may not always happen to be set exactly at the same height as the vane. This is a matter of no consequence as to the general result ; the reversinj> of the direction of the sights will compensate any small error that might hap- pen in that way. This is the most expeditious way of making this kind of Survey, but one of the assistants should be capable of using the instrument, the conductor taking the staff, as he has then suflficient time for making observations upon the localities as the work proceeds. If he has not an assistant able to take the instrument, he M^ill hardly require the staff- man ; the hind chain-man measuring and holding the vane : the work will proceed more slowly, but there will be leisure afforded for making SURVEVING. 39 but the iking not staff- work iking tho necessary observations. If tlic assistants bo able to use the scab; and protractor, four miles a day may be surveyed, and the plan and section made up ; if they are not able to do this, about three miles will bo a good day's work. The most proper method of mana«j;inn; a survey of this kind, is to make a plan and section as the work proceeds, and on the return re-examine the ground, and fill up the plan with tho distant localities. This way of taking heights roughly, by means of elevations, is prac- tised in a great variety of ca^ .. If in making a purvey, a determinate point, as a building or other object, can be seen from two different sta- tions at a considerable distance from each other, the distance from the stations being determined by the bearings, the angular elevations or depressions will give the perpendicular height or depth from the levels of the station. Thus, suppose a building on a hill is ascertained to be half a mile distant, and the elevation two degrees, the height above the level of the station from which the elevation is taken is ninety-two feet. In this manner the heights of hills and depths of vallies within a reasonable distance on either side of the line of survey may often be determined with sufficient accuracy for practical purposes. If, in running a survey through a Country in which the sight near the ground is obstructed, but so open overhead that a tree can be seen at a dis- tance, the elevation to its top, or to some remarkable branch upon it, may be taken from different stations, and by this means tho position of the tree being determined, the relative height of the ground for half a mile, or a mile, may be found without the trouble of cutting out a line. Applications of this method will frequently suggest themselves to the mind of the Surveyor when making preliminary surveys, and by this means he may collect a great deal of information respecting the relative heights of the ground, with very little trouble. When levels are taken in this manner, the perpendicular heights must be computed from the angular elevations : this is done by finding the natural cotangents, (a term that will be explained further on} of the angles of elevation or depression, and dividing the distances by them. The following table gives the perpendicular heights for different dis- tances, at every 3 minutes of elevation, up to 12 degrees. Col. 1, is the angle of elevation or depression ; Col. 2, is the number of feet horizontal, to 1 foot perpendicular ; Col. 3, is the perpendicular ascent or descent at one chain ; Col. 4, the same at one chain and a half ; and Col. 5, the same at two chains. iC" 40 SIJKVEVING. •■'< ; t •l\ In' > ■ \a AiirIp. DIstaiiLM- for mil' fipiit in li)'tk'>it Hi>l)rlit ttt 1 chain. Ili-lKht ul l.:)U chain. ilpllthtot 'i clmlnN. Foft. Aii'g. niin. o 5 4 5 52 5 561 SIJRVEYINCJ. 41 I.--- r — Distnni'ii fur Dllt* font HclKlit at lli'lfiht D( llrlllht nt DiKtiiiice fur lli-lglit at lloiHhtnt lIcJKlitnt AnRic. ill IicIkIiI. 1 rliiklli. l.nuc'lmlii. 'icIllllllH. Ai'plo. III llplglll. 1 clioiii. i.muiiuiii. a cliuiilH. Ih'g, mill. Foil. 1-cft. Fuit. I'cut. Ui'K. mln. Foot. Feet. Feet. Foci. "4"0 14,30 4,61 6,92 "9;23~ 6 9,514 6,93 10,90 r37»7^ 4 4 14,06 4.69 7,01, 9,39 6 4 9,409 7,02 10,53 14,04 4 8 13,83 4,77 7,15 9,54 6 8 9,306 7,09 10,64 14,19 4 10 13,11 4,81 7,21 9,63 6 10 9,255 7,13 10,70 14,26 4 12 13,61 4,85 7,27 9,70 6 12 9,205 7,17 10,76 14,34 4 16 13,40 4,92 7,38 9,85 6 16 9,105 7,25 10,88 14,50 4 20 13,20 5,00 7,50 10,00 6 20 9,010 7,32 10,99 14,65 4 24 13,00 5,07 7,66 10,15 6 21 8,915 7,40 11,10 14,80 4 28 12,80 5,15 7,73 10,31 6 28 8,823 7,48 11,22 14,96 4 30 12,71 5,19 7,79 10,38 6 30 8,777 7,52 11,28 15,04 4 32 12,51 5,23 7,85 10,47 6 32 8,732 7,56 11,34 15,12 4 36 12,43 5,31 7,97 10,62 6 36 8,643 7,64 11,46 15,28 4 40 12,25 5,38 8,07 10,77 6 40 8,556 7,71 11,57 15,43 4 44 12,08 5,46 8,19 10,92 6 44 8,470 7,79 11,69 15,59 4 48 11,91 5,54 8,31 11,08 6 48 8,386 7,87 11,81 15,75 4 50 11,83 5,58 8,37 11,16 6 50 8,345 7,91 11,87 15,82 4 52 11,75 5,62 8,43 11,23 6 52 8,304 7,94 11,92 15,89 4 56 11,59 5,69 8,5't 1 1 ,39 6 56 8,223 8,02 12,03 16,05 5 11,43 5,77 8,66 11,55 7 8,144 8,10 12,16 16,21 5 4 1 1 ,28 5,85 8,78 11,70 7 4 8,067 8,18 12,27 16,36 5 8 11,13 5,93 8,90 11,86 7 8 7,990 8,26 12,39 16,52 5 10 11,05 5,97 8,96 11,95 7 10 7,953 8,30 12,4$ 16,60 5 12 10,99 6,00 9,00 12,01 7 12 7,9^6 8,31 12,51 16,68 5 16 10,85 6,08 9,12 12,17 7 16 7,842 8,42 12,63 16,84 5 20 10,71 6,16 9,25 12,33 7 20 7,770 8,49 12,74 16,99 5 24 10,58 6,24 9,36 12,48 7 24 7,700 8,57 12,86 17,14 5 28 10,45 6,32 9,48 12,64 7 23 7,630 8,65 12,98 17,30 5 30 10,39 6,36 9,54 12,72 7 30 7,596 8,69 13,04 17,38 5 32 10,32 6,39 9,59 12,79 7 32 7,562 8,72 13,09 17,45 5 36 10,20 6,47 9,70 12,94 7 36 7,495 8,80 13,20 17,60 5 40 10,08 6,55 9,83 13,10 7 40 7,429 8,88 13,32 17,76 5 24 9,961 6,62 9,94 13,25 7 44 7,364 8,96 13,44 17,92 5 48 9,845 6,70 10,05 13,41 7 48 7,300 9,04 13,56 18,08 5 50 9,797 6,74 10,12 13,49 7 50 7,269 9,08 13,62 18,16 5 52 9,732 6,78 10,17 13,56 7 52 7,238 9,12 13,68 18,24 5 56 9,622 1 6,86 10,29 13,72 7 56 7,176 9,20 1 13,80 18,40 if >• 6 I ' 42 SUUVKVfN(i. :'»■ J ►•J . I m >..{ i' ■' • 1 m Angle. nutanc* for one foot In holtflit. Height at 1 cliiiln. llelRht lit l.riOrlialn. lloliht at 'i ciiuliiii. AtiRlr. Dlitnnrfl for one fiiDt III lltMKllt. llelvht At 1 I'llUlll. HolRhtRt I.MI.'liulii. llel<|ht at 'i Clllllllj. Dfg. mlD. Feet. Foet. IVc't. loot. Dtg. mill, Fept. I'et.t. Feet. Fj-mI. 8 7,115 9,27 13,91 18,55 10 5,67 1 11,64 17,16 23,27 8 4 7,056 9,35 11,03 18,71 10 4 5,633 11,71 17,57 23,43 •8 8 6,997 9,^13 14,15 18,87 i 10 8 5,595 11,79 17,68 23,58 8 10 6,968 9,47 14,21 1 8,95 i 10 10 5,576 11,83 17,75 23,66 8 12 6,940 9,51 14,28 19,02 10 12 5,558 11,87 17,81 23,75 8 16 6,883 9,59 14,30 19,18 10 16 5,521 1 1 ,95 17,93 23,01 8 20 6,827 9,66 14,50 19,33 10 20 5,481. 12,03 18,05 24,07 8 24 6,772 '),74 14,61 19,49 10 24 5,449 12,11 18,17 24,23 8 28 6,718 9,82 14,73 19,65 10 28 5,413 12,19 18,29 24,39 8 30 6,691 9,86 14,79 19,72 10 30 5,395 12,23 18,35 24,47 8 32 6,665 9,90 14,85 19,80 10 32 5,378 12,27 18,41 24,51. 8 36 6,612 9,98 14,97 19,96 10 36 5,343 12,35 1 8,53 24,70 8 40 6,561 10,06 15,09 20,12 10 10 5,309 12,43 18,65 24,86 8 M 6,510 10,14 15,21 20,28 10 44 5,275 12,51 18,76 25,02 8 48 6,460 10,21 15,32 20,43 10 48 5,242 12,59 18,88 25,18 8 50 6,435 10,25 15,38 20,5 1 10 50 5,226 12,63 1 8,94 25,26 8 52 6,410 10,28 15,44 20,59 10 52 5,209 12,67 19,00 25,34 8 56 6,362 10,37 15,55 20,7i 10 56 5,177 12,74 19,11 25,49 9 6,314 10,45 15,67 20,90 11 5,145 12,82 1 9,23 25,65 9 4 6,267 10,.'^3 15,79 21,06 1 n 4 5,113 12,90 19,35 25,H1 9 8 6,220 10,60 15,90 21,21 11 8 5,082 12,98 19,47 25,97 9 10 ,6,197 10,64 15,96 121,29 11 10 5,066 13,02 19,53 26,01 9 12 6,174 10,68 16,02 121,37 11 12 5,050 13,07 19,60 26,14 9 16 6,129 10,76 16,14 2 1 ,53 11 16 5,020 1 o, 1 5 19,72 26,30 9 20 6,084 10,84 16,26 21,69 11 20 4,989 13,23 19,84 26,16 9 24 6,040 10,92 16,38 21,85 : 11 24 4,959 13,31 19,96 26,62 9 28 5,997 11,00 16,50 22,01 11 28 1,930 13,38 20,07 26,77 9 30 5,986 1 1 ,04 16,56 ,22,09 11 '30 4,915 13,42 20,13 26,85 9 32 5,954 11,08 16,62 22,17 11 32 4,901 13,46 20,20 26,93 9 36 5,912 11,16 16,74 22,32 11 36 4,872 13,54 20,31 27,09 9 40 5,871 11,24 16,86 22,48 11 40 4,843 13,62 20,43 27,25 9 44 5,830 1 1 ,32 16,98 22,64 11 44 4,815 13 JO 20,55 27,41 9 48 5,790 11,40 17,10 22,80 11 48 4,787 13,78 20,67 27,57 9 50 5,770 11,44 17,16 22,88 11 50 4,773 13,82 20,73 27,65 9 52 5,750 11,48 17,22 22,96 11 52 4,759 13,86 20,79 27,73 9 56 5,710 11,56 17,34 23,12 11 56 4,732 13,94 20,91 27,89 liy m can bo ii (nkcn to i'i'om eac multiplic ing to te merely s Thus, th( is. f)v th( i'or 10 lit If the c in the tab proportior tabic. T and tlie di for an an" ibct; the iSrnin. J 7.57 feet, vious as to By comj liiled up as The fir this eleva feet, consei feet. The gives S.05 feet, the pc The see Here we h feet, vvhici This distan shifting the stractiug th from No. 1 The thin 'leight at 1 place to the tance is 85 and conseqi 30.7, leaVcj The four the height SLRVEVI>(i 43 By means of tiiis table the alisoliitc height due to modcrnte distances can be found by inspection, or calculated mentally — especially if care be taken to have no fractions of half chains in the distances of the stations from each other. For distances within ten chains, one addition, or one multiplication by a low lij^urc, will generally sutHce. Heights correspond- ing to ten times, or to one-tenth, of the tabular distances, are found by merely shifting the decimal point one p ace to the right, or to the left. Thus, the height at two degrees of elev; tion and one chain in distance, is. by the table, 2..'Jfeet; therefore, for 10 chains it is 23. feet, and for 10 links, .23 of a foot. If the angle of elevation of the ground falls between the angles given in the table, the height due to thcnx can easily be found by taking a proportional average hetween the heights of the nearest angles m the table. Thus, suppose the givrn an£;le of elevation be 3deg. ]8min. and the distance 2 chains ; — The height given in the table at 2 chains for an angle of 3 deg. iGmin. is 7.53 feet; and for 3deg. 20min. 7.69 feet; the average of these is 7.61 feet, the height answering to 3 deg. I8min. If the given angle were 3 deg. 17 min. the heie;ht would be 7.57 feet, and if 3 deg. 19 min. it would be 7.65 feet. This is so ob- vious as to require no further explanation. By computations such as these, colunvi 6 in the notes, (page 38) is tilled up as follows : The first distance is 8.60 chains, and elevation 4 deg. 25 min. At this elevation the perpendicular height for 2 chains is, by th'^ table, 10.19 feet, consequently, the height at 8 chains is four times 10.19, or 40.76 feet. Then the height at 10 links is .509 feet, which multiplied by 6, gives 3.05 feet for 60 links, which being added to 40.76, makes 43.81 feet, the perpendicular height of No. 1 above A. The second distance is 7.35 chains, and elevation 6 deg. 20 min. Here we have by the table the height answering to 1.50 chains, 10.99 feet, which multiplied by 5, gives 54.95 feet, the height at 7.50 chains. This distance is 15 links too great, the height du;( to which is found, by shifting the decimal jjoint one place to i'* Itit, to be 1.09 feet; sub- siracting this from 54.95, leaves 53.86 feet for the perpendicular rise froni No. 1 to No. 2. The third distance is 9.15 chains, and elevation 2 deg. 40 min. The height at I chain is 3.07 feet, which, by shifting the decimal point one place to the right, becomes 30.7 feet, the height at 10 chains. This dis- tance is 85 links too great — the height at one chain is by the table 3.07, and consequently for 85 links, it is 2.59 feet ; which substracted from 30.7, leaves 28.11 feet, the perpendicular rise from No. 2 to No. 3. The fourth distance is 5.46 chains, and elevation 4 deg. 6 min. Here the height at 1.50 chains is 7.08 feet, which muliiphed by 3, gives '1 44 SURVEYING. V > in. 'ii il? [1 ;,.,; J- ' 21.24 feet in height for 4.50 chains; to which adding 4.73, the heij^ht answering to 1 chain, the sum 25.97 feet is the height at 5.50 chains, which is sufficiently near tlie truth. As the ground is descending, this height in cohimn 6 is marked with a — ^ the sign of substraction, to show that in making up column 7 it is to be substractcd. The fifth distance is 10.27 chains, and elevation 5 deg. 15 min. By shifting the decimal point of the height at 1 chain, one place to the right, we get the height at 10 chains 60.6 feet; and by shifting it one place to the left, we have the height at 10 links, 0.6 feet; hence the height at 27 links is 1.62 feet. This added to 60.6 gives 62.22 for the whole height, which, as the ground is descending, is also preceded by the sign of substraction. The sixth distance is 15.40 chains, and elevation 2 deg. 10 min. The height at this elevation, for 1.50 chains, is 3.75 feet; and by shifting the decimal point to the right we get the height for 15 chains, 37.5 feet. Also, the height for 1 chain being 2.5 feet, by shifting the decimal point to the left, we get the height for 10 links, 0.25 feel, which added to the former, gives 37.75 feet for the whole height. These heights it will be perceived, are not exactly the same as those in page 38 ; the diflerence is owing to the imperfection of the decimals, they having been calcu- lated by a different method. In these examples, the heights arc made up in such a manner as to exemplify the use of the table in facilitating mental computations of the heights. In lines through woods, the distances between the stations being short, the heights, (provided the distances contain no fractions of half-chains) may generally b(; found by ins[)ection alone, or in some cases, by adding two or three tabular heights together. Col. 7 contains the heights of the stations above a certain horizontal line, by means of which the heights of all the points on the line arc com- pared with each other. This is called the datum line, and may be placed at any height above or below the place of beginning. If, however, it be so chosen that the points of the section fail, some above, and others below it, the column of heights becomes in sonvp parts negative, and the computation can be managed only by persons who understand the Algebraic methods of adding. To avoid this difficulty, it should be assumed through either the highest or lowest points of the survey. As, however, in comparing the hei'j^hts of objects, the mind most readily refers the higher to the lower, it is considered prelerable to take the datum line through, or below, the lowest point. We say, for example, the summit of a hill is 100 feet above the level of the sea, or other cer- tain object, and not that the sea or other object, is 100 feet below the summit of the hill. This habit of mind, of referring the higher to the lower objects, suggests the propriety of taking the level or line of SURVEYING. 45 reference through or below the lowest point, where there are no other circumstances to influence the selection. Suppose, in the progress of the survey some point beyond No. 6 should be found below the level of A, — say between twenty and thirty feet. Ail that is necessary is to assume the datum line at such a depth below A, as will keep every part of the section above that line. If the (latum be assumed a little lower than is necessary, no harm is done, but it should by no means be above the lowest point of the survey. In column 7 the datum line is assumed on the level of the point A, and is represented by the line A B, fig. 16. In filling up this column, we first transfer the height of No. I in column 6, 43.64* feet, to it. Then, by column 6, the height of No. 2 above No. 1, is 54.02 feet, which added to 43.64 gives 97.68 feet, the height of No. 2 above the datum line A B. Also, the height of No. 3 above No. 2, is 28.08 feet, which added to 97.68, gives 125.74 feet for the height of No. 3. Again; the depression of No. 4 below No. 5 is 26 feet, which, substracted from 12574, leaves 99.74 feet the height at No. 4. In the same manner, 62.30 is substracted from 99.74, leaving 37.44; and 37.80 is added to 37.44, making 75.24 feet, the height at Nos. 5 and 6. In column 8 the datum line is assumed 30 feet below A, and is repre- sented by the line C D. For filling up the column, 30 is taken for the commencement, and the additions and substractionsmade as before ; all the heights coming out 30 feet greater than in column 7. This will be better understood by reference to fig. 16. If, after column 7 is filled up, we take all the additive numbers in column 6 in one sum, and all the substractive ones in another, and sub- stract the latter from the former, the remainder will give the last height in No. 7. That is, adding together the first three and the last numbers in column 6, the sum is 163.54, and adding the fourth and fifth, their sum is 88.30 ; the difference, 75.24, is the same as the last number of column 7. This proof of the accuracy of the additions and substractions should never be neglected. In conducting a survey, a copy of the foregoing table should be car- ried in the field book, and the heights in columns 6 and 7 made up at short intervals, by which means a knowledge of the comparative heights of different parts of the line, and of the capabilities of the ground, will be obtained as the work proceeds. For instance, suppose that on ascending a rise of ground from one remarkable point to another, the distance be found 40 chains, and the height 74 feet ; — then dividing 2640, the feet in 40 chains, by 74, we get the quotient, 35.7. Or, which is more convenient, dividing the 74 feet by 40, the quotient 1.85 is the height in feet answering to 1 chain of distance ; and referring to the table, 1.84 feet of height at 1 chain, is found opposite to the angle 1 deg. 36 min. in the first column, and 35.8 in the second ; showing 46 SURVEYING. I*ii 1 B^W'i; < 1 ■t.-i •I pvi that a line having an ascent of 1 in 35.8 is practicable between those points, and that, provided this grade does not exceed the required maximum, it is unnecessary, so far as the level is concerned, to seek another line. The column of " remarks" in the notes should contain all such re- marks and observations as may be necessary to have kept in mind for future operations; and it should, espedially when the trace is near the proper site for the road, always contain the angle of slope of the ground transverse to the line. Mr. Tredgold, in his treatise on Railroads, shows an ingenious method of laying down sections transverse to the section of the principal line, which will be shown in another part of this work : but for common roads it will be sufficient merely to have the angles of the transverse slope noted, by which the height of the ground at any moderate distance from the line, or the effect that shifting the line will have upon the section, will be found by inspection of the table. Thus, if any particular point be 4 feet below the regular grade, and the ground rises to the left at an angle with the horizon of 5 degrees ; we find by the table that at that elevation the rise of ground is 1 foot in height, to 11.65 feet horizontal, and therefore 46.20 feet will be the proper distance to move to the left, to reach ground at the height of the grade. The note-book should have the regular notes of the survey on the left hand page when the book is open, and the right hand page devoted entirely to remarks and calculations. With respect to the manner of noting remarks generally, directions seem to be unnecessary ; each Sur- veyor adopts his own mode. But there is one method that it may not be improper to point out as very useful : in taking the elevations of a road with the Theodolite, there are often swells and depressions of surface between the stations, that it would be tedious to describe by words : tiie best method of describing these is to draw sections of them by the eye. These sections may be made very correct by taking a range near the sur- face, and observing the height at which the line of sight cuts persons walking over the ground. Thus, if there is a depression between two stations, and upon taking a range the line of sight cuts the chain men, or staff man about the middle when in the lowest part of it, it may be con- cluded to be about three feet deep, and may be entered in the remarks by a straight line representing the grade, and a crooked line below it representing the surface of the ground, with a small 3 between as de- noting the depth, and the same mode of measurement and notation may be resorted to if the ground contains a swell ; only in that case the range must be taken over the highest part of the ground, to persons. or other objects at the further station, keeping the eye as nearly as pos- sible at the same height from the ground as those objects. The method of noting is the same as before ; the,crooked line being above the straight one, and the number of feet of swell in the ground inserted in small %ures h when gn vane at below th 27. 1 can be ob ing the h< consequer ascertaine from the s ings from because th rectness. other in th culated fro would be a As an ei bears N. 8 1 of 10 minu and the an^ house bean same housv Here, ha\ I 38, we lay < from No. 2, point of inti lioiise. I'he I from No. 6, I plan, of the Mcasurinf 'louse 25.50 - ?ivcsfor this a is below N iVo. 4 being liierate ofdc Repression co Iperpendicular I not necessary leve^ fo calcu * The greater the I'urvejfing open field l^y which means, if t * fforizon, liere, si SURVEYING. 47 figures between. This is sufficiently exact for common purposes, but when greater exactness is required it will be necessary to set up the vane at short measured intervals, and note the depth of the surface below the grade line. 27. The foregoing method of making a survey, is, when long sights can be obtained, well calculated for surveying a road, and for ascertain- ing the heights of distant objects. The positions of such objects, and consequently their distances from certain points of the survey can be ascertained by protracting the bearings of them on the plan, (Art. 13.) from the several points at which these bearings were taken. Two bear- ings from different points are sufficient (Art. ],) but three are better, because the third affords a check upon the work with regard to its cor- rectness. If it be not correct, the three lines will not intersect each other in the same point.* In like manner, the heights should be cal- culated from each station of observation : the heights so brought out would be a check upon each other. As an example, — Suppose that from No. 2, (see notes p. 38) a house bears N. 81 E. and that it is at an angle of depression below the horizonf of 10 minutes. Also, that from No. 4, the same house bears N. 48 E. and the angle of depression is 13 minutes. Also, from No. 4 another house bear? S. 84 E., depression 1 deg. 10 min., and trom No. 6, the same house h :;■ N. 41 E. and depression 32 deg. Here, hav „v }:rst protracted the plan of the road from the notes, page 38, we lay down an indefinite line, (fig. 17,) in the direction-N. 81 E. from No. 2, as 2, a, and another line N. 48 E. from No. 4, as 4, a ; the point of intersection of these lines at a, gives the position of the first house. Then laying off a line S. 84 E. from No. 4, and another N. 41 E, from No. 6, the point of their intersection, b, is the position, upon the plan, of the second house. Measuring the distance from 2 to a, by the scale, we find the first house 25.50 chains from No. 2 ; and by the table, a depression of lOmin. itives for this distance, 4.83 feet in perpendicular depth, which the point a is below No. 2. In like manner, the distance of the point b from No. 4 being measured with the scale, is found to be 29.50 chains, and lilie rate of depression being, by the table, 1.34 feet per chain, the whole depression comes out 39.53 feet, which the point b is below No, 4. The perpendicular depressions of a, below No. 4, and of b below No. 6, are not necessary except for the purpose of verification. It is proper, how- |eve'', to calculate them, and if they do not nearly agree with the former, * The greater the number of bearings that arc taken to the same point, the more perfect the check. In Imrveying open fields, or lakes, &c. it is common to take a bearing to some central object at every station, jliy which means, if the survey does not close, the error can be easily discovered. ^ Horizon, here, signifies the level. h • ■ .1 1 'i •u J' ?f^ 4 k-1 ■ - H'. 48 SURVEYING. Fig. 17. 4i^'•'^: it is a proof that some error has been committed, aiul which can only be rectified by again going upon the ground. By means of observations such as the foregoing, tiie relative positions and heights of commanding points over aconsiderable tract of coun- try may be laid down upon a map from a single survey. To this end there must bo assumed, an horizontal plane of reference, similar to the datum line (Art. 26). la localities near the sea shore, the level of the sea is often taken for the plane of re- ference ; in other cases some fixed and permanent object should be selected, and, where practicable, a sheet of water, as a lake or river, should be preferred; these latter being permanent na- tural objects to which the mind naturally refers. But whatever object is selected for this purpose, it should, for the reasons adduced with respect to the datum line, be at least as low as ilio lowest part of the survey. In the present example we will suppose it to be on the level of the surface of a lake which is 20 feet below the commencement of the sur- vey at A. To find the heights of the various points of the plan, (Fig. 17) above the plane of reference,— as it passes 20 feet below the datum Ji the line , of a and were obs Thus, w< of the hi the vaile^ ' vey, 95.2 i\o. 2, wi the point 119.74 fi height of the map, By me£ topograph of the hot marked ut hill (Fig. reference hill, and ot should be proper sha as it is poa in a Treati fessor of JV the Siuden As an ej suppose th< at 3, and a through th( able with n the case by 15.73 chair distance by No. 5 to 1 sary to redi increase C: from b to a of height 3S ascent 1 in culty in obt The fore; liminary sur perience ant surveying; 49 rc- :U jie river, these nt na- the But icted lould, d with n line, as the survey. ^)le we on the a lake ow the he sur- nd the s points ) above ce, — ^^ I low the ' datum line A B, (Fig. 16), we must for the heights of the stations upon the line add 20 feet to their heights upon the section ; and for the heights of a and b, subtract from the heights of the stations from which they were observed,, the amount of their depression below those stations. Thus, we get the height at A, 20 feet ; at No. 2, 1 17.66 feet ; the top of the hill at No. 3, 145.75 feet; No. 4, 119.74 feet; the bottom of the valley at No. 5, ,57.44 feet ; and No. 6, the termination of the sur- vey, 95.24 foot. Then for the height of a, — it being 4.83 feet below No. 2, we subtract this from 117.66, which leaves 112.83 feet. Also, the point b, being 39.53 feet below No. 4, we subtract this height from 119.74 feet, (the height of No. 4) the remainder, 80.21 feet, is the height of b. These heights are marked in their proper positions upon the map, (Fig. 17). By mean« such as these a great deal of information respecting the topography of a country is communicated at a glance ; just as the form of the bottom of a harbour is readily comprehended by the soundings marked upon a chart. In the case of the horizontal lines around the hill (Fig. 13), they should have the heights above some place of reference marked upon them ; also the heights of the top of the hill, and other prominent points not particularly indicated by the lines, should be marked in the proper situations. This, combined with proper shading, will give, perhaps, as just an idea of the form of ground as it is possible to give by means of a map. This subject is ably treated in a Treatise on Surveying, published in 1836 by Charles Davies, Pro- fessor of Mathematics in the United States Military Academy, to which the Student is referred for further information. As an example of the use that may be made of surveys such as this : suppose the line from A to No. 6 be a road which passes over a high hill at 3, and a valley at 5, as shown by the section Fig. 16 ; and that a line through the points a and b, appears, as seen from the road, more favor- able with regard to levels, — we can make up a tolerable judgment on the case by the map. Thus, on the road, the distance from 3 to 5 is 15.73 chains, and difference of height 88.30 feet, and by dividing the distance by the height (both in feet), we get the average ascent from No. 5 to the top of the hill at No. 3, one in 11.76. Or, if it be neces- sary to reduce the grade to 1 in 30 by zig-zag line, we would have to increase the length of the road to half a mile. Aoain, the distance from b to a, is, as measured on the map, 22.50 chains, and the difference of height 32.62 feet ; whence, by dividing as before, we get the average ascent 1 in 44.5 — showing, that as regards the grade, there is no diffi- culty in obtaining a good line in that direction. The foregoing is the general method of proceeding in making pre- liminary surveys for Roads ; but as every thin^ depends upon the ex- perience and tact of the Surveyor, it is impossible to give more than a 7 I. If Jit, i '' h.«3R It:' 60 SURVEYING. general description : particular rules for such surveys are useless, as new cases, and sometimes difficult ones, are hourly occurring, which tha experience of the Surveyor alone will enable him to overcome, and suggest at the time a method of which no book, in all probability, could inform him. 28. With respect to the comparative merits of the two foregoing methods of levelling, that by the angular elevations, or that by the level, it may be laid down generally, that for all common Road Surveying, either in taking levels of the ground, or in running slopes upon sides of hills, and for all merely preliminary surveys of every kind, the Theodo- lite, as being the most expeditious, is the most proper instrument ; and as the errors in levelling by it are owing entirely to incorrect measure- ment of distances, they can be greatly reduced by a judicious and care- ful chain-man. But in all cases where great exactness is required, such as in finishing surveys for canals or rail-roads, the most proper instrument is the level. Fig. IK: t-i ■fii ■■■ , ''^ I- n 29. Having described the various modes of levelling, it now remains to offer a few remarks upon the instruments. The first thing we will notice is a very important appendage to the Theodolite for enabling the operator to read off angles with more ex- actness than could otherwise be done. This appendage is called a Vernier^ from the reputed inventor, a Frenchman, though the honor of the invention is claimed for a native of England, a Mr. Nonnius, by some Englishmen, who accordingly call it a Nonnius. When, therefore, we see in some books the term Vernier, and in others Nonnius, they mean the same thing; the former, however, is the more common name. Let the line A B, Fig. 18, be divided into any number of equal parts, each part of which it is proposed to subdivide into ten other equal parts by means of a vernier. Take the length of nine parts on the scale A B, as from A to 9, and transfer that distance to the vernier C D, as from to 10. Then that space divided into ten equal parts, becomes a vernier adapted for dividing the parts on the scale A B, into tenths. The line is the index, and is shown standing at the beginning of the scale. Suppose now, it were removed to a point between any two of the di- vision lines of the scale, as in Fig. 19, and we wish to know its exact position, we have only to look for a line on the vernier that coincides exactly with one on the scale; and the number of divisions from that line to the index, is the number of tenths which is to be added to the last division of the scale which the index has passed. For example, suppose the index to stand between 4 and 5, and that the fourth division of the vernier coincides exactly with a division of the 15 ..'■*«, I SURVEYING. 51 Fig. 18. Fig. 19. 10 10 15 20 A C — — D . — 4 s — . i i — B i -0 10 15 20 B D 10 scale, it Bhows that the index stands at four tenths from division 4 on the scale, and is read 4.4. To make this the more plain, sup> pose A B is a scale of inches which we wish to divide into ten equal parts hy means of a vernier ; we take the space of nine inches and divide it into ten equal parts for the vernier. Then if the index stands as above supposed, at between 4 and 5 inches on the scale, and the fourth division line of the vernier coincides with a division line on the scale, (which in this case will .o .t 8 inches) we ob- serve that from 8 back to 4 is four inches; but as each division of the vernier is only nine-tenths of an inch, four divisions on it, being the distance from the same plac<^ to the index, ia only ^& inches, which is four-tenths of an inch short of each division ; so far, therefore, is the index advanced beyond the fourth inch ; that is, it is 4.4 inches from the commencement of the scale. The same reasoning will hold good with regard to the coincidence of any other line of the vernier with a line of the scale ; that is, if line 5 coincides with a line of the scale, the index will be at 4.5 ; if 6, ut 4.6, and so on. In the foregoing illustration, we have, for the sake of simplicity, chosen the unit divided into ten parts ; but if we wish to divide it into any other given number of parts, we have only to take the length of the required number of divisions on the scale, less one, for the length of the vernier, and divide it by that number. Thus, sup- pose we wish to construct a vernier for sub-dividing the parts of the scale A B into twentieths, we take the 62 SURVEYING. 1^: ■'. length of 19 of those parts for the length of the ver- nier, and divide it into 20 parts. If we wish to subdivide into thirtieths, we take 29 parts for the length of the vernier, and divide it into 30 parts ; and so on for other subdivisions. When the divisions on a Sextant, or The- odolite, are ^hirds of a degree, or twenty minutes each, which is a common case, a vernier of twenty parts gives the reading to minutes, because a minute is the twentieth part of the third of a degree. When they are half degrees, a vernier of thirty parts gives the read- ing the same, because a minute is the thirtieth part of half a degree. As an example of the latter, let the length of 29 half degrees on the limb be divided into 30 parts for the vernier, and let the point be in on tlie right hand, — the reading of the limb being from the right towards the left.* " Let the point of the vernier coincide with the line marked 10 degrees on the limb. Now, since each space of the vernier is less by one minute than each space of the limb, the first line on the left of 0, will be one mi- nute to the right of the first line on the left of the 10 on the limb ; and if the vernier be moved one minute towards the left, these lines will coincide, and the se- cond line from will then be one minute to the right of the second line from 10 ; if the vernier be moved ano- ther minute these last lines will coincide. The vernier would then show 10 deg. 2 min. If the vernier plate be turned still further, till the third, fourth, fifth, &c. lines coincide, it is plain, that the point of the vernier will have passed the line 10 on the limb, by as many minutes as there are lines of the vernier which shall have coincided with lines of the limb. When the last line of the vernier coincides with a line of the limb^ the vernier will have been moved 30 minutes or half a degree, and the point will at the same time coincide with a line of the limb, and show 10 degrees, 30 minutes. ; The general rule for reading the angle for any posi- tion of the vernier, may now be stated. * Tb« readier is suppoied to have an instrument before him while pernsiog these inatruotioRS. I 5 A 20 C r i ; ; \ i 5 1 10 10 15 20 1 I 1 D 5 % i ( t SURVEYINC. 63 When the line of the vernier coincides with a line of the limb, the arc is easily read from the limb ; but when it falls between the two lines, note the degrees and half degrees up to the line on the right ; then pass along the vernier till a line is found coinciding with a line of the limb : the number of this line from the point, indicates the minutes which are to be added to the degrees and half degrees for the entire !> ' »»(!>• .■.iii;'i /•; ' ■ ii . ■ '1.1' i '!' angle."* In scales which are numbered both ways from a zero point, as the vertical arch of a Theodolite, a modification of the preceding plan of a vernier is necessary. The index, or point, instead of being at one end, as in Fig. 18 and 19, must be in the middle, as in Fig. 20, with the divisions numbere;d from it each way. That is, if the vernier con- tains ten divisions, there are five of these on each side of the point, and the reading is done upon one side of the point for one half of a division of the scale, and upon the other side, for the other half. In the figure, the point stands below division 9 on the scale, and the third division of the vernier below the point, coincides with a line on the scale ; consequently the vernier stands at 9.3 on the scale. If the movement be continued downward till its lowest division, numbered 5, coincides with a line of the scale, its upper end also numbered 6 will coincide with another line of the scale, and the point will obviously be half way between 9 and 10 ; that is, at 9.5. This is as far as the reading can proceed by the lower end of the vernier : if it is moved further downward, the additional readings will be from the upper end towards the middle. If it be moved till the first division from the upper end coincides, the point will be 9.6; if the second, 9.7, &c. as the Tcrnier is moved downwards. When the point coincides the reading will be 9 and ten-tenths, or 10, as indicated by the 10 at the middle. On the vertical arch of Theodolites, the divisions are usually half de- grees, which are subdivided by the vernier into minutes. This requires ;i vernier of the length of 29 half degrees on the arch divided into 30 parts. Such a vernier is numbered in two lines ; the inner lirte 5, 10, and 15 from the line outwards to each end, and the outer line con- taining 20 opposite to 10 on the inner, and 25 opposite to 5 on the same ; 30 being at the middle or point. In the use, the first 15 minutes are counted upon the end which is forward in the movement, and are shown by the inner line of numbers, and the remaining 15 are counted upon the other end, and from the outer end inwards, as shown by the outer line of numbers. This will appear plain by examination of the instru- ment. It may be proper to observe, that a vernier may be made by taking a space on the primary scale equal to one division more than the number m i ■ ■ 1 : J' tf:' ' ^11 I ft k Daylea' kirveying. 54 SVRVEYltiO, i' m 1^ir'« Ml f f IV ! I'H' K^'-l^' J of divisions corresponding to the intended 8ui)division, and dividing it into tile samo number of parts as tiic subdivision required. Thus, in the example of dividing lialf degrees into minutes, if, instead of dividing the space occupied by 29 half degrees by 30, as has l)een pointed out, we divide the space occupied by 31 half degrees by the same number, the result will produce the same effect : in either case there will be a difference between each division of the primary scale, and of the vernier, of one thirtieth part of the former. The only difference is, that in the former case the divisions on the vernier are less than those of the pri- mary scale, and in the latter greater. The former method is that which is in general use: a vernier upon the latter plan would be attend- ed with some inconveniences in the use which do not appertain to the former. It will be advisable for the student to make scales and verniers of pasteboard of different sizes and forms, and by slipping them along each other and observing the effect, he will be enabled to understand the Kuh- ject much better than by any thing that can be written. If we wish to ascertain the degree of minuteness to which an instru- ment is divided by means of its vernier, we must proceed as follows: — First. — Correct carefully the nmnber of spaces into which the ver- nier is divided. Secondly. — Turn the vernier till the line at one extremity coincides with a line of the graduated limb, when the line at the other extremity will also coincide with another line of the graduated limb, for the sum of the spaces on the limb; then count the number of spaces on the limb which the vernier covers. ' , s Thirdly. — Examine the limb of the instrument, and ascertain into what parts of a degree it is divided and express one of those equal parts in minutes. Fourthly. — Divide the number of minutes so found hy the number of equal parts in the vernier, the quotient is the excess of a space on the Jimb over a space on the vernier. Hence it appears that the power of the vernier is in the compound ratio of its. length and the smallness of the divisions. In the last exam- ple the spaces on the scale were each 30 minutes, — the number of divisions on the vernier was 30, and the quotient of 30 divided by 30 is 1 ; consequently the division by the vernier i&.' into minutes. If the divisions on the hmb were quarters of deojrees, or 15 minutes each, and the vernier of the same length, it would contain 60 divisions, and the quotient of fifteen divided by 60 is one fourth of a minute, or 15 seconds, which is the reading of each division of the vernier io this CiiSe* If the vernier contains 60 divisions, whatever number of minutes there may be in a division of the limb, each subdivision by the vernier SURVEYING. 65 it« will cojitain the same rumbor of seconds. Thus, in the last exnni)>1e the divisions on the lirnb were each 15 minutes, which were divided by the vernier to 15 seconds. \( the limb were divided into spaces of 10 minutes each, a vernier of 59 such spaces divided with 60, would give a reading to 10 seconds, and so on. The degree of minuteness to which divisions are made by this con- trivance is truly astonishing. There is a theodolite now before us, the diameter of whose horizontal limb is only four inches, on which the reading is to single minutes, and the vertical arch of the same is only 1 inch and S quarters radius, and reads to the same degree of minute- ness. The divisions on the former are about one 1700th, and on the latter one 1900th of an inch. On a good mountain barometer, the scale is divided directly into spaces of l-20th of an inch, which by means of a vernier containing 49 of such divisions divided into 50 parts, is sub-di- vided into thousandths of an inch ; and even this minute quantity can be sub-divided by the eye of an experienced observer into two or three parts. ^ • '■'■' h; •- .■•.' -, u - ., :.u\>):-. >■>,, This contrivance, it will be perceived gives us a power of taking mea- sures to a degree of exactness absolutely impossible by any other means,, and its importance in observations, relating to Navigation and Astronomy^ is such, that without it many operations in those departments of science could not be performed at all. For instance, t^e lunar observations for finding the longitude depend upon having the exact measure of the angle between the Moon and a Star; and so delicate is this operation that an error in the angle of one minute, will make an error of thirty miles in the result. The former methods of dividing could never ap- proach the accuracy necessary for this operation, so that if the know- ledge of the vernier were lost, observations for finding the longitude at sea must fail. 30. In using the theodolite it should be set level upon the stand: This is effected by two circular plates of. brass called psirallel plates^ the lower attached to the top of the stand, the upper about an inch and a half above it, and connected by a loose fastening in the centre. They are kept at a proper distance apart by four stout screws tapped into the upper plate near the edge. Some large theodolites have levels attach- ed to the plate for levelling by, but the smaller kind have only the level attached to the telescope. • • - ' - • > ' ■ To level the instrument, place the telescope at the zero of the arch at- tached to it, and ranging in the direction of one pair of the screws, bring it to a level by raising one edge of the plate and depressing the opposite. Then turn it round to a right angle and repeat the operation with the other pair of screws. If this is carefully done the instrument will be level in every direction. It will be found very convenient to set the stand so that one pair of screws will range in the direction of the sight, as any ...I 1.1 i ^1' B ^v i ft; I! .;". 56 SURVEYING. m ■ "I • •( minute alteration that may be required before taking the elevation will in that case be more easily made. One caution to the young practitioner respecting turning the sicrews may be proper : ifone pair is turned hard up and the plate requires moving witii the other pair, it is apt to operate upon the first as a lever and strain them. Persons unaccustomed to the instrument are very apt to beiid the screws : the rule to l)o ob- served is, whenever a screw begins to turn harder than usual to slacken those in the opposite direction. Parallel plates usually have the milled heads of the screws between the plates. If the heads wore above \\\o upper plate the plates might be within half an inch of each other, which, by shortening the screws would materially reduce the leverage by which they become strained. Observations may be taken without levelling the instrument very exactly upon its stand, provided the telescope be first levelled and the degree at which the index stands be noted, which is to be added to, or subtracted from the degrees of elevation or depression to the object, according as it is on one or other side of the zero. This method, how- ever, is liable to mistakes, and unless the surveyor is well practised the safer way is to proceed is in the ordinary manner. For trying the correctness of a theodolite, take the angle between two distant objects by a considerable number of difTerent parts of the circle, and if it shows the same angle in every case the instrument is correct ; trifling differences may be expected, but if they amount to a considerable quantity it is to be rejected. This method is applicable to both the horizontal and vertical arches. ,,i , , t- mm: -uh m vyw .< nu ;•■ 'f ■tK.)-; "'j;i!t>> /ill I "i V:;";w. .'^•<\ ;!i !K 31. It has been remarked in a former part of this Chapter, that where great exactness is required in finding distances and areas, measurements upon a plan are not sufHcicintly accurate. Instead of this tables have been constructed called Trigometrical Ta- bhsy from trigonometry, a word derived from the Greek denoting the measurement of triangles. These tables are, in fact nothing more than the lengths of certain straight lines connected with a circle of a certain diameter, and arranged in regular order for the sake of easy reference. Let D H L M, Fig. 21, be a circle whose radius is unity.* Divide it into four.equal parts by Jines from H to M, and from L to D, cutting each other at right angles in the centre of the circle A ; and from A draw the tine A K of an indefinite length, cutting the arch of the circle in C. Also7 let C B and D £ be drawn perpendicular to A D. Then, C 6, is called the sine» D£ the tangent, and A £ the secant of the angle B AC, in other words of the angle whose measure (art. 8) is the arch DC. I I ■ ■■ - » ■ * ■ ■■..I - a mm ■■■^1 ■■■■« ^ .^.i.« .■ ^» ■ ■ I I ■ . ■ ■■ ^.1 IK ■ - ■■ ■ .1. ■ ■ ■ 1,1 ■ »i i^a I I t>^ * Evny stiaight Uoe. from tbt tntu to tbt circuii>r«rMC» of • ciicU, u uUed a Raiiut. j j litl J C ' In li to A If angle ( It is liypothe is the si sine of t lengths I will be \ AC of 32. \ may be < exact for Icn;;tlis o similar ti sides by i in Art. 1. 'j<'ing, thi ineas{iriii« I'ouhd by tables, to such [\ raJ abri(Ii»in(l triangle has one of its an^sles a ri^jht. angl«, the othf is are acute (see art. 8) ; the . longest side of such a triitn^le is called the hyjiotheiiui'r. ; uf tho two sides which suhtend the right aiifjie, the shorter is called the j)erpendicular, and the longer, the base. Sumetiinea these two »ides are called le •' • . 35. In the application, it is only necessary to look in the table of sines for the length answering to these angles ; but the tables are gene- rally very extensive, being usually constructed for every degree and minute of the quadrant, making no less than 5400 different sines in the ninety degrees. If so extensive a table were arranged in the form given above, it would be necessary, after finding the sine of the given angle, to search for the sine of the corresponding angle at the distance of perhaps several pages. To obviate this inconvenience, the tables are so arranged that the corresponding sines always stand opposite to each other in the same line. This is eflected by arranging the sines in dou- ble columns, one containing the sines up to the half quadrant, or forty- five degrees, and the other the corresponding ones. These latter sines are designated in the tables by the name of co-sine, a word 'signifying sine of the complement or remainder. Under this arrangement, the foregoing tabic would stand as fol- lows : — I- im f I i '1 pi 62 SURVEYING. ' '' . i'l •■ !; ■ ' 1- i *;'''i„'f' i»: ■■ .V**' Deg. Sine. Cosine. Deg. .0000 1.0000 90 10 .1736 .9998 80 20 .3420 .9397 70 30 .5000 .8660 60 40 .6428 .7660 50 45 Deg. .7071 .7071 45 Cosine. Sine. Deg. f!i ;• ,i ; ' }' ' Wi-' i- ) .^i in this Table the degrees at each side, and the columns of sines are so disposed as to show that the cosine of any angle is the same as the sine of its complement, or remainder of ninety. Thus, the sine of twenty degrees appears to be .3420, and its cosine .9397 ; but at the bottom of the table the order of the terms is reversed, and taking these for the titles of the columns, the sine of seventy degrees appears to be, .9397, and its cosine .3420. The propriety of this arrrangement may be illustrated by Fig. 23. where the sines are exhibited by the lines k> ',:■ ' i;' : ■ : ill •. j.;i . ; V ;; ■.■ • i r HI • >\ •'»■ ■" {: nw'^ ! ' '.Ufit.' :' ;(•>!;•; t ) -/*!■;■ •. ^ • -"•!!'■: . ■< ■,. Fig. 23. Co«in«i ft; i:;i !■. , t '.i ! 'I ■ . : SURVEYING. 63 a 10, b 20, c 30, d 40, &c. from C to B ; and their corresponding co- sines by the lines i 10, k 20, 1 30, m 40, &c. from E to B, showing tl\^t the cosine of 30 degrees is •€ the same length as the sine for 60 I ' •; VI h- . 1 "I ',!;,, 1 iM . > f. g ' Fig. 24. ' K y < ' . ; • I ; "; ■ ■ • ' . '. Hi., ■\t' ; ., :.; J » ■ t ■ ' 1 1 . 1 1 1. " ^ i ■ 1 • ■ / i • ' 1 1 1 . .. * •'i 1 !■' ri' fif."' I ■, a' $. 1..'! 1^ ; I'- ) I >i1 I ! 64 SURVEYING. de|»rees, the cosine of 40 degrees the same as the sine of 50 degrees, and so on. The Tangents, and when they are introduced, the secants also, are arranged in the same manner ; .the tangent or secant of the complement of each angle, being arranged under the name o( co-tangent or co-secant, in the same line with the tangent or secant of the angle itself. Fig. 24 exhibits the tangents and secants to every ten degrees up to 70 degrees ; G a is the tangent of ten degrees, G b that of twen- ty degrees, &c., up to G g the tangeut of 70 degrees. F h is the co-tangent of 40, F i of 50, F k of 60, and F 1 of 70 degrees ; but these are of the same lengths as G e, G d, G c, and G b, the tangents of their respctive complemental angles, 50, 40, 30 and 20 degrees. Also, the lines A d, A e, A f, and A g, are the secants of 40, 50, 60, and 70 de- grees ; and the lines A h, A i, A k, and A I, are the cosecants of the same angles; but these cosecants are equal in length to A e, A d, A c, and A b, the secants of the corresponding complemental angles, 50, 40, 30, and 20 degrees. Thus, the terms cosine, cotangent, and cosecant of any angle, signify merely the sine^ tangent, pna secant of the angle contained in the remainder of the quadrant. If the tables were arranged in a natural order, beginning at zero, and proceeding regularly up to ninety degrees, the distinction of terms would not be required. It must not be forgotten that the common arrangement is in a mea- sure artificial, and has been adopted purely for the sake of easy re- ference. The pair of numbers, as sines, tangents, or secants, required in calculating upon a right-angled triangle, is brought into opposite co- lumns in the same page, and it is necessary to have terms for distinguish- ing the one from the other. The terms in use are admirably adapted to the purpose, indicating at the same time the distinction, and the affinity, of the lines they are applied to. In the tables at large, the number of degrees is written at the head of the page ; the sine and cosine, tangent and co-tangent, secant and co-secant, answering to the degrees and minutes, run in parallel columns down the page, the minutes being written in regular order dmvn the left hand side. At the bottom of the page, the titles of the columns are reversed, the number of degrees in the complemental angle is writ- ten across the bottom, and the odd minutes in regular order up the right hand side. The following is a specimen of such a table, calculated to every five minutes : u 20 25 30 35 40 45 50 55 60 M 36. degrees, left side ihe titles inore rha degrees, the sine, column. It has peat, tha perpendic Jng to on. that it is t t'jat each dicular an angles in »hat this '^e sines, radius of t 23, and 24 1 SURVEYING. 65 16 Degrees. M Sine. Cosine. Tangent, Cotangent. Secant. Cosecant. M .27563 .96126 .28674 3.4874 1.0403 3.6280 60 .27703 .96085 .28832 3.4687 1.0407 3.6093 55 10 .27843 .96045 .28990 3.4495 1.0411 3.59] b 50 15 .27982 .96005 .29147 3.4309 1.0416 3.5737 45 20 .28122 .95964 .29305 3.4124 1.0420 3.5559 40 25 .28262 .95923 .29463 3.3941 1.0425 3.5383 35 30 .28401 .95881 .29621 3.3760 1.0429 3.521 1 30 35 .28541 .95840 .29780 3.3580 1.0434 3.5038 25 40 .28680 .95798 .29938 3.3402 1.0438 3.4867 20 45 .28819 .95757 .30096 3.3227 1.0442 3.4700 15 50 .28958 .95715 .30255 3.3052 1.0447 3.4530 10 55 .29098 .95672 .30415 3.2880 1.0452 3.4360 5 60 .29237 .95630 .30573 3.2708 1.0457 3.4203 M Cosines. Sines. Cotangent Tangent. Cosecant. Secant. M 73 De grees. 36. In using the tables, when the given angle is less than forty-five degrees, we look at the top of the page for the degrees, and down the left side for the minutes, opposite to which we find the sine, cosine, &c., the titles being at the heads of the columns. When the given angle is more than forty-five des;rees, we look at the bottom of the page for the degrees, and up the right side for the minutes, opposite to which we find the sine, cosine, &c., the titles in this case being at the bottom of the column. It has been already'shown (Art. 31), but it may not be amiss to re- peat, that each corresponding sine and cosine, are, the actual base and perpendicular of a right-angled triangle , that all these triangles belong- ing to one set of tables are calculated to one certain hypothenuse ; and that it is this hypothenuse which is called the radius of the tables. Also, tiiat each tangent, and its corresponding secant are the actual perpen- dicular and hypothenuse of a right-angled triangle ; that all these tri- angles in the same set of tables are calculated to one certain base ; and that this base is of the same length as the hypothenuse in the case of the sines, and is also called the radius of the tables ; that is, it is the radius of the circle from which the tables are calculated. See Figs. 21, 23, and 24. 9 § f, ', '■ ^i| V? :■ i •13 Si.!>l,i t-''.1 i' !i ' ii' ■. > ■■■ t ■■ i it ■ i 66 SURVETINO. When we have ti certain given triangle to operate upon, we must seek out a similar triangle in the tables, and having found it, calculate the unknown sides of the given triangle from it b_y the rule of three (Art. 32). If the sides of the triangle be given to find the angles, we first find by the rule of three, the base or perpendicular of a similar tri- angle whose hypothenuse is unity ; we then seek in the tables for a sine, or its corresponding cosine, of the same lengths of the base or per- pendicular so brought out ; the angles of the table to which this sine and cosine belongs are the angles sought, This is evidently only a re- verse process to the former, in both cases the reasoning is from one triangle to another similar one ; the whole process being founded upon the principle of the proportionality of the sides of such triangle, (Art. 1). The tabular triangles are so nnmerous, that in practice we can always find one either exactly or so nearly similar to that which we have to calculate, that the error from the dis greemcnt will be quite insignifi- cant. In most books ot Surveying there are 5400 of tiitm in the quadrant, and any error in calculation arising from taking the nearest tabular triangle to the given one as a basis for calculating upon, could not exceed nine inches in a mile, and besides this there are easy methods by which even this slight error can be reduced almost to nothing. 37. Hitherto we have confined our attention to what are called the natural numbers ; that is the actual sides of right-angled triangles, and we have seen that trigonometrical operations are performed with them simply by the rule of three. Within the last 200 years, however, means have been discovered for materially abridging this labor. The most important of these is Loga- rithms.* In a table of Logarithms, each natural number is represented by an artificial number, which is called its logarithm. These logarithms possess several useful properties, but that which is the most important, and with which we have more particularly to do in the present case is, that multiplication or division of the natural numbers can be performed by means of addition or subtraction of their logarithms. In the common tables, the series of natural numbers runs from 1, to 1000, and there are rules given by which it may easily be extended. They are arranged in a column on the left of each page, and also across the head, by which contrivance the tabic is very much reduced in dimensions. The method of using them is pointed out in books of surveying or navigation. The following is a specimen of such a table : N. N. As an page 5£ the fourt by .5 in perform I answeri logarith of .5 w of the we fine as before The thus : * The Lpgarithtns were invented and given to the world by Lurd Napi«r, in the ytar ICU. By the SURVEYING. 67 N. 1 2 3 4 5 6 7 8 9 D. 300 4771217266 7411 7555 7700 7844 7989 8133 8278 8422 145 301 8566 8711 8855 8999 9143 9287 9431 9575 9719 9863 144 302 480007 0151 !0293 0438 0582 0725 0869 1012 1156 1299 144 303 1413,1586' 1729 1872 20162159 2302 2445 2588 2731 143 304 2874'3016!31593302 31453587 3730 2872 4015|4157 143 305 4300 4442 4585 4727 4869 501 1 5153 5295 5437 '5579 142 306 57215863 6005 6147 6289 6430 6572 6714 6855'rf997 142 307 71387280 7421:7563 77047845 7986 8127 8269 8410 141 1 308 8551 669218833,8974191 14 9255 9396,9537,9677;9818 141 809 9958 ..99 .239 .380 .520 .661 .801 .941 1081 1222 140 N. I 2 3 4 5 6 7 8 9 D. As an example of the use of logarithms, we will take example 4, page 59, where the proportion given is, as, .5 : 1.25 : : 866 : to find the fourth term. By multiplying .866 hy 1.25, and dividing the product by .5 in the common manner, we obtain the fourth term, 2.165. To perform the same operations by logarithms, we first find the logarithms answering to 1.25, and .836, and add them together; the sum is the logarithm of the product of those numbers. We then find the logarithm of .5 which we subtract from that sum, the remainder is the logarithm of the quotient. Then looking in the table for the logarithm last found, we find the natural number answering thereto, 2.165, the same result as before. ' The question worked out in full by the first method, will stand thus : As .5 : .866 1.25 1.25 4330 1732 866 .6)1.08250 ~2."l"65 By the Logarithme, the work is as follows : \ I il i V: f : t i ■'t\ 68 SURVEYING. II' . * :. IB I- P'' tit '- 'i> . H' • 1 1- ','1 , Logarithm of .866 is, Do. of 1.25 is Sum of Logarithms, Logaiithms of .5, .L937518 .096910 0.034428 -1.698970 0.335458 Which is the logarithm answering to the natural number, 2.165, the base required, as before. In this example we may perceive that the latter operation requires as many figures as the former, and also more time in the operation ; but this is accidental. In general, the logarithms savefc a great deal of time. It would be best, however, that in teaching trigonometry they bs not used until the pupil is well grounded in the method of calculation by the natural numbers : he would then under- stand the reasons for the process, whereas if he is taught only the logarithmic method he will be likely to follow it merely as an arbitrary rule, the reason of which he will be apt to consider as beyond his reach. 38. In working out an operation in trigonometry by the sines and logarithms as above, we have first to find the proper sines by the table, and then to find the logarithms answering to them in the table of logarithms. This is tedious, and is besides, from the necessity of keep- ing large numbers in mind while searching the logarithms, very liable to mistakes. To obviate these inconveniences, the logarithms of the sines and tangents have been calculated and arranged in tables. These logarithms are called artificial, or logarithmic sines and tangents^ to dis- tinguisli them from the proper sines and tangents, and which are de- signated by the term natural sines and tangents. Thus, in the last example, instead of first finding the natural sine of 60 degrees, and then finding its logarithm, we look in the first instance in the table of artificial sines, where we find the logarithmic sine and cosine of 30 degrees, 9,698970, and 9.937531, with which the operation is performed as follows : Logarithmic cosine ot 30 deg. Logarithm of 1.25, - - - Logarithm sine of 30 deg. Sum, 9.937531 .096910 10.034441 9.698970 0.335471 Which is the logarithm of 2.165065, the base required as before : the SURVEYING. 69 >>i tritling excess boing occasioned by tho greater exactness of tUe tabloa from which tliLso numbers are tukeii.^ ,i t V ..>«.' ,,; 39. Another table that is much used is the traverse table ; other- wise called, in books of Navigation, the table of difference of latitude ami departure. This, like the table of sines, is composed of the sides of a multitude of right-angled triangles. The only difference between them is that ill tlic table of sines tiic triangles are all calculated to one hypothenuse, which is always unity, leaving the lengths of the legs for any other hypothenusc to be calculated, whereas in the traverse table, this calcula- tion, for a great variety of hypothenuses, (called in that case distances,) is already made. , . . ; , . . ,, ;( In traverse tables for surveying, the hypothenuse generally increases from unity to 100, and the angles by quarters of degrees, from 1 to 45 degrees. This gives 100 different triangles for each angle., and as there iire 180 different angles, the whole number of triangles exhibited in the table is 180^100=18,000. But as in the angles above 45 degrees, the Icg^ are reversed in their characters, in the same manner as has been already explained with respect to the sines and tangents, the vir- tual number is 56,000. Besides, there are methods by which distances that are not in the table can generally be calculated for, by simple addition or subtraction of the tabular numbers. In Navigation, the operations to be performed by this table are less delicate than in surveying, and therefore in books of navigation it is com- monly less extensive. It usually runs from 1 to 100 in distance, and to angles for each degree only, giving 4500 different triangles. The traverse table is particularly adapted to casting up surveys made by the needle. In navigation it is necessary at proper times to find the ship's place upon the chart, but it is not necessary to lay down all the courses which she may have made in her progress : the table is adapted to these circumstances. The course the ship has run upon at each tack designates the angle of deviation from the north or south points. of the compass : if we look in the table, in the columns answering to the given angle, we will find opposite to the given distance in the column of distances, the two legs of the triangles under the titles of difference of latitude and departure ; the Southing or Northing gained, bein^ called difference of latitude, and the Easting or Westing, departure. For exam- pie, suppose the course be Norilv thirty degrees West, and distance.run ten miles; under the angle of thirty, and opposite 10 in the column, of distances, we find in the column of departure 5, and in that of difference o" !I !.'.'■ * 'I I ■: r * For a further account of Logarithms, ie« note A at the eild of the volume. '<» H 70 SURVEYING. 1 -I, of latitude 8.66 miles , showing that she has made 8.66 miles of North- ing, and 5 miles of Westing. In books of Land Surve^'ing there are certain rules laid down for the application of the traverse table, by which areas of irrc silarly shaped lots of ground may be determined with great facility . i ; uxyci- ness ; it is also very useful in determining the course and '^'rxtce between distant points of a field. In Road Surveying it is seldom or never required ; all the irregulari. ties in the line of road are to be laid down upon the map. The only use for it in that department is, for correcting the small errors that may accumulate in protracting a long line upon paper, and as a Check upon the protraction generally, by finding the position of certain point- by the table, and observing the agreement or disagreement with the same points of the line as protracted. As an example of the use of the traverse table, suppose the line, AB C D E, Fig. 26, to be a road which is surveyed, and we wish to find the course and distance from A to £ without the trouble of protracting; the courses and distances being as follows : ' .■ * ■.i.. i;l No. Courses. Dist. Ch. 1. AtoB N. 15E. 10.00 2. BtoC N. 25 E. 7.60 3. C toD N. 65 E. 7.50 4. D to E N. 45 E. 8.00 For the first course, A B, we look in the table in the column of 15 degrees, and opposite 10 in the column of distances, we find difference of latitude, 9.66, and departure, 2.59, and as the course is S. E., the dif- ference of latitude is Northing, and the departure is Easting.* These distances are shewn by aB, and a A. For the second course B C, we look under 25 degrees, and opposite 7.50 in the column of distances, we find difference of latitude, 6.79, and departure, 3.17, which is also Northing and Easting. These distances are shewn by C b, and B b. For the third course, C D, in the column of degrees, we find oppo- * Dtpmrture from any given point it a ttrm und to denote the distance direelly East or West of a n»- fidian,or North and South line drawn through that point. Difference of latitude i* the distance North or South of the £a8t and West line. site 7.60, i{ for departi the columni the bottom I For the find opposij and the sai The distan( No. 'II I • 8URVEYIM0. Fig. 26. 71 > . I I of 15 ference the dif- These C, we stances, is also Bb. oppo- ■nc« Noitb ■!.i 1( ■X , )-. \ o ' ; > site 7.50, in the column ot distances for difTerence oflatitude, 3.17, and for departure 6.79, which is also Northing and Easting ; but in this case the columns oflatitude and departure are reversed ; the title is found at the bottom of the page. The distances are C c and c D. For the fourth course, D £, looking in the column of 45 degrees, we find opposite 8 in the column of distances, 5.65 for difference oflatitude and the same for departure, which are shewn by the lines D d and £ d. The distances are arranged in a table as follows : I), '■->;! No. Course. Dist. Northing. Southing. Easting. Westing. 1. A toB. N. 15 E. 10.00 9.66 2.59 2. B to C. N.25.E. 7.50 6.79 . __ 3.17 3. C to D. N.65E. 7.50 3.17 6.79 4. DtoE. N.45E. 8.00 5.65 5.65 ■ W 3 r 1 .' i ■ ■ 25.27 18.20 I I I 4'' 72 SURVEYING. m ;■«: ;.>: t /'ii f^- ;. «' By reference to the figure, it will be perceived the sum of the North- ings is made up of the separate distances aB, bC, c D, andjd E ; and the whole is represented by the line E d ef k. In like manner, the sum of the Eastings is composad of the distances A a, B b, Cc, and Dd whose united length is A a g h k. The sum of the Northings therefore, 25.27, and of the Eastings, 18.20, are the lengths of E k and Ak, res- pectively. All this is preparatory to finding the cciirse and distance from A to E, To this end, if we join A E by the dotted line, we form a trianwio whose hypothenuse is A E, and whose base and perpendicular are A k, and E k. Thus, to find the course and distance from A to E, we look in the traverse table for the nearest co-relative numbers to 25.27, and 18.2u, and find under the angle of 35J degrees, and distance 31, difierence of latitude 25.16, and departure 18.11, being nearly the numbers sought. But as these numbers are a little pnder those required, though nearly in the same proportion to each other, the true distance is a little more than 31, and by making proper allowances we find it 31 chains 20 links, nearly. The line A N being a meridian, the course from A, is N. 35,5 E., and distance to E 31 chains 20 links. In this example all the courses are Northing, and of consequence, the columns of Southing and Westing are blank. If there should be South- ing or Westing alsO, in any such calculation, the difierence of latitude and departure must be entered into the proper columns, and the differ- ences of the sums of the Northings, and of thi^ Southings, of the East- ings and of the Westings taken, by which to find the general course and (distance. ^ 1 (i it m. t 40. These are all the tables that are usually employed for surveying l^^ ^rposes, and it will readily be perceived that their relative importance is very various. The natural sines are numbers that cannot be dispensed with ; they are the lines from which every other line connected with trigonometrical operations is, or may be calculated — the foundation of the whole superstructure. The tangents, secants, and traverse table are made up from the sines, and are merely contrivances for abridging labour. By the tangents, the calculator is enabled to have one of the terras of his proportion always unity, and so get rid of the labour of one miiltiplication or division in performing his operations. And by the traverse table he can combine a number of courses and distances into! one, besides performing other useful operations, by means of calcula- tions that have already been made by others. The Idgarithms are derived from a different source, from that of the | tables of sines and tangents, but their use, as has been already remark- ed, is oi tangents cany th no highe Tlie € ferehr. are perfi scale and is rather muliiplic; to a tool 1 than he o work moi 41. It of absolut by conseqi its circumt this reason gree of ca some book; use that is Navigation to an exten are sometin We now veying and ^vith the su And first, o 42. Pari they are sek lines is the of a right-j recommend making one own experie perpend icula thickness, mahogany is aboard cut PARALLEL RULER AND TRIANGLE AND RULER. 73 ridging of the of one by the es into mlcula- ed, is only to abridge labour. The logarithmic or artiificial sines and tangents, by obviating the necessity o^ a reference to diflferent tables, carry the abridgment still further, but it is to be observed, they possess no higher claim than that of a convenient instrument of calculation. The eftects of the different tables as regards accuracy, are also dif- ferelit. By the use of sines and tangents, trigonometrical operations are performed by the more exact calculation by numbers, instead of the scale and compasses. Logarithms abridge the labour, though the result is rather less exact than if the operations were performed by common multiplication and division. The sines and tangents may be compared to a tool that enables the artificer to perform much more accurate work than he could otherwise do ; the logarithms to a machine that does the work more speedily, but with rather less exactness. 41. It has been already remarked that the tables are not possessed of absolute exactness ; the exact length of the diameter of a circle, and by consequence of any straight line within the circle, as compared with its circumference, has never been discovered ; but the sineSi though for this reason, not absolutely perfect, may be brought to any assigned de- gree of exactness by increasing the number of decimals. Hence, in some books, the tables are more perfect than in others, according to the use that is to be made of them. Jn the common books of Surveying and Navigation they are carried to six places of decimals, and the logarithms to an extent to correspond thereto, but tables for astronomical purposes are sometimes computed as far as fourteen places of decimals. We now proceed to describe some of the instruments used in Sur- veying and making up plans, and as the latter is most in accordance with the subject which has just been discussed, we begin with them. — And first, of the f PARALLEL RTLICR AND TRIANGLE AND Rl LER. 42« Parallel rulers are too well known to require a description, but they are seldom very correct. A cheaper instrument for drawing parallel lines is the ruler and triangle. The triangle is a thin board of the form of a right-angled triangle : the exact form is not particular : some recommend it to be of about twice as much base as perpendicular, making one of its acute angles to be 60, and the other 30 degrees. My own experience has led me to prefer a nearer equality, say four inches perpendicular to six inches base, — about one-fifth of an inch is a good thickness. It ehould be made of wood which is not liable to warp : mahogany is the best wood for this purpose, and it should be taken from a board cut from the middle of the log ; th?: is, the laminae or grain of 10 I I 11 ii %4 t': A I i iii':**' 74 SURVEYING. Sim* c '4^ i It; i'l" the wood should run perpendicularly across the thickness, in the same manner as in split staves or shingles. Any open grained wood, whose laminae are in this direction, and well saturated with warm linseed oil, will hardly be much affected by atmospheric changes. This instrument is used by laying any one side of the triangle so as to coincide with the line to which the parallel is to be drawn, laying a straigiit edged ruler along one of the other sides, and then slipping it along the ruler till it comes to the proper place. Or, if the situation of the required line be such that it cannot be reached in this manner, the triangle can be slipped along the ruler in one direction, till it comes into a proper position for a movement in another direction, when by shifting the ruler the object is easily accomplished. For instance, suppose we have a line on the plan to which we wish to draw a parallel at a considerable distance ; we lay the hypothenuse of the triangle to coincide with the given line, but by placing the ruler along the base or perpendicular, we find it will not in either case come to the point intended, in such case we may first apply the ruler to the base, and then move the triangle along it to such a position that by shifting the ruler from the base to the perpendicular, it may be moved in a direction at a right angle to the first movement, and by this means reach the intended position. In lay- ing down the sections, the triangle is very convenient : by laying the ruler along the bfise line of the section, the right angle of the triangle may be applied as a square by which to draw the perpendiculars, it is not necessary to give examples of the use of this instrument, an hour's practice will give more information on the subject than any thing that can be written. This instrument is much superior to parallel rulers ; there are but few of them perfectly parallel, and their action is circumscribed ; whereas the triangle must of necessity, if the ruler be straight, be al- ways exactly in the same position with respect to the other lines upon the plan, and the scope of its action is only limited by the length of the ruler. THE DIAGONAL SCALK. 43. This Scale is always on one side of the small flat scales that are in the cases of pocket instruments, and on the large wooden scales used by Seamen. We will suppose the reader to have one of the latter be- fore him. There is at one end of the batten* a space about 1 1 inches long and near an inch wide appropriated to the Diagonal Scale. This * The ttrm bitten is UMd for the wholt piece of wood on which the scales are marked, to prevent confu* sion ia the BaoMf. space II number room fc Ther apart, v Now, the Dia^ the Sea dinal lin across fr the othe space on from the third line side, and direction, breadth o cross line at the upj down wan in additioi dinal divis or twelve of the scai just the s; of this arn equal part; the upper by means ( On the vided ifi tli inch. On the { diagonal sc of an inch and the oth and 400 to These sc veying chai fastened up links in the the inch oi •The render id THE DIAGONAL SCALE. 75 lat are used er be- inches This nt conftt. space in divided by longitudinal lines into 10 equal parts, which are numbered at one end, 2, 4, 6, 8, on every other line, there not being room for a figure al every line. There are also lines drawn across the space in question at one inch apart, which denote the inches and are regularly numbered. Now, it is the pecuuar manner of dividing the inch that constitutes it the Diagonal Scale, One of the inch divisions (that at the end of the Scale) is divided into ten parts on each of the outside longitu- dinal lines, and these points are connected by lines, not drawn square across from these divisions on one side to the corresponding divisions on the other, but the first cross line is drawn from the beginning of the space on the upper side to the 1st division on the lower;* the 2d line from the first division on the upper to the second on the lower; the third line from the 2d division on the upper, to the third on the lower side, and so on through the inch ; thus all the cross lines have a diagonal direction, or are out of square to the amount of one tenth of an inch, in the breadth of the scale. Hence, the distance from the beginning line to the cross line running from No. 1 on the upper, to No. 2 on the lower side, is at the upper side one tenth of an inch ; on the first longitudinal division downwards, it is one tenth of an inch, and one tenth of another tenth in addition, equal to 11 hundredths of an inch; on the second longitu- dinal division, it is one tenth of an inch, and two tenths of anot^r tenth or twelve hundredth of an inch, and so on till we come to the lower side of the scale, where the distance has increased to two tenths of an inch; just the same as to the second division on the upper side. The effect of this arrangement is, that the inch is virtually divided into one hundred equal parts; — that is, into 10 equal parts directly by the divisions along the upper side of the scale, and each of these into ten other equal parts, by means of the diagonal cross lines crossing the longitudinal lines. On the other end of the same scale there is a tk a)e of half an inch di- vided in the same manner, making a scale of t^vo hundred parts to an inch. On the small scales that are in most cases of pocket instruments, the diagonal scale is on one end, half an inch, luiu on the other one quarter of an inch divided in the same manner. The first of these is called 20, and the other 40 to an inch, but the real division is, as we have seen 200 and 400 to the inch. These scales are adapted to laying down plans by the common sur- veying chain, which is divided into ten parts by small pieces of brass fastened upon it, and each of these again into ten links, making 100 links in the chain of 66 feet, and corresponding to the 100 divisions of the inch on the scale. Hence in laying down a plan upon a scale of * Th« reader is supposed to have a scale before him, by the upper tide of which is meant that farthest off 76 SURVEYING. li'' '■ , ' if. Is ' f 1 , one inch to a chain, it is obvious that the inches represent chains, the tenths represent ten links each, and the hundredths represent single links ; if the plan be ten chains to an inch, the tenths of inches repre- sent chains, and the hundredths distances of ten links each. The half inch, and quarter inch scales are used in the same manner for making plans to one half and one quarter the size of the inch scale. On one side of the small pocket scales there are a number of dif- ferent scales, as 20, 25, 30, &.c. to the inch, which are convenient for laying down plans of sizes that are not adapted to the diagonal scale. The half inch diagonal scale, 20 to the inch, is very convenient for the working plan of a road : it answers for two chains to an inch hori- zontal, and 20 feet in the vertical of the section. THE LINE OF CHORDS. 44. This line is used as a substitute for the protractor, and is de- signated on scales by the letter C. It is formed from the protractor in the following manner : The chord of i: circle is a straight line from one part of its periphery to any other part, as D 10, D 20, D 30, &c. Fig. 26, and is designated by the number of degrees of the circum- ference included between its extremities : that is — the straight line D 10 is the chord of 10 degrees ; D 20, of 20 degrees; D 30, of 30 degrees; and so on, D G being the chord of 90 degrees. Now, if we take the lengths of a number of chords of the same circle, and lay them down on a straight line, that line is called a line of chords. Fig. 26. P 90 80 70 60 60 Thus, if we take the lengths of the chords '' 10, D 20, 1) 30, &c., and set them off from E to 10, £ to 20, £ to .' j, &c., on the straight line £ F, that line will be a line of chords adapted to the circle whose radius is the quad marked I In layj construct which th( chord of the same the comp circle it v was const line and s same ang] taken : th line of chi D A 50, 5 same as tl it need no of construi little upon «triJctin«T ?1 will give h cerning it. In the p line may be a semicircl upon the s( the semicir the paper i; at every an method is t proper ang angular line For insta we have dn inches from nient of the line ranging proper stati will run S. [ the range o upon the pr small mark circle, and 1 LINE OF CHORDS. 77 &c., raight ^hose radius is A D or A G, and containing the chords at each ten degrees of the quadrant. Lines such as these arc laid down on every scale, and marked to every degree of (he quadrant. In laying down a plan by the line of chords, the process required is to construct upon the plan, a quadrant or protractor similar to that from which the line was derived. This is easily done ; it is known that the chord of 60 degrees^ of any circle, is always just equal to the radius of the same ciicle. If, therefore, we take the distance from E to 60 in the compasses, and, with that as a radius, sweep a quadrant or semi- circle it will be of the same size as that from which the line of chords was constructed : Hence, if we take any given chord from the same line and set it off upon the periphery of the circle, it will subtend the same angle at the centre as that from which such chord was originally taken : that is, if we take the distances E 50, E 60, or E F from the line of chords, and set them off on the circle, they will give the angle D A 50, 50 degrees, D A 60, 60 degrees, and D A G 30 degrees, the same as those from which the chords were taken. This is so plain that it need not be -Iwelt upon ; it is merely the reverse operation to that of constructing the line of chords. The learner had better practise a little upon making up lines of chords from different circles, and recon- structino; rlie circles from the chords : a few hours practice of this kind will give him a better insight than any thing that can be written con- cernmg it. In the practice of laying down plans by the hne of chords, a meridian line may be drawn through each station, and from that point as a centre, a semicircle may be described. The proper angle may then be set off upon the semicircle by the same line of chords from which the radius of the semicircle was taken. This is, in fact, constructing a protractor upon the paper instead of laying down a metallic one. To repeat this process at every angle of the survey would be tedious : the most convenient method is to draw a potractor in some convenient situation, lay off the proper angles upon it, and draw the lines of the survey, parallel to these angular lines, by the ruler and triangle. For instance, suppose we have a line to lay down at S. 30 W., and we have drawn our protractor upon the paper at the distance of several inches from the point on the paper which we design for the commence- ment of the line, — we first lay off from the centre of the protractor a line ranging S. 30 VV., and then lay another line parallel to it from the proper station of the survey. It is manifest that this latter line, also, will run S. 30 W. as intended : and so on for any number of lines within the range of the parallel ruler. It is not necessary to draw actual Hnes upon the protractor at the respective angles ; it is sufficient to make a small mark at the proper number of degrees, on the periphery of the circle, and lay the parallel ruler in the range with that mark and the iii yUA ^ ti 78 SURVEYING. ii'f •(■•■! P^l |< I W M centre in the same manner as if a line had been drawn : There may also be several courses marked on the protractor at one time, and suc- cessively transferred to their proper places on the plan, by which means a map may be plotted with nearly as much expedition by the line of chords as by the protractor. THE SECTORAL SCALES. 45. The Sector is an instrument made of ivory, wood, or brass. It consists of two arms or sides, which open by turning round a joint at their common extremity in the manner of a Carpenter's rule. It is to be found in almost every case of pocket instruments. There are several scales laid down on the sector : those, however, which are chiefly used in making plans are, the scale of chords, and the scale of equ?.I parts. These scales run diagonally on each arm of the Sector and meet in the point about which the arms turn. SECTORAL SCALE OF CHORDS. 46. Tl : ii^erence between this scale and the line of chords just described is, laat the latter is confined to a certain radius, whereas the Sectoral Scale admits of a great number of radii : in the common six inch Sector the radius may be of any magnitude, from half an inch to near twelve inches. The arrangement by which this effect is produced is as follows : — On each arm of the Secior there is a line of chords, be- ginning at the joint and extending to 60 degrees at the other extremity of the arm — this line is designated by the letter C. In the application the Sector is opened till the points C, marked 60 on each arm, are at any convenient distance for a radius. With this radius in the compasses sweep the semicircle as in the former case ; and then, for laying down the angle, set one foot of the compasses at the degree denoting the given {ingle on one arm, and the other at the same degree on the correspond- ing line on the other arm ; this distanre is the chord of that angle to the ^iven radi'js. For example, to lay down ar; ingle of 35 v grees upon a radius of four i:, if ■ I fe arms of the sector arc the two equal sides of an isosceles triangle ; tho centre of the joint is the vertex, and the imaginary line joining their other extremities the hase. If any other imaginary line be dr«'vn across the arms parallel to such hase, the remaining part of the instrument above such line will be another triangle similar to the former, and of con- sequence its sides are in the same proportion to each other. Taking, for illustration, the scale or line of equal parts, — let the arms be opened to any convenient distance, — say four inches liotween the extremities of the lines. Let a small batten be laid across from one extremity to the other, of just four inches in length, and the triangle \h visibly completed. If we lay another small batten across the arms so as just to coincide with the point nimibered 60 on the same scale on each arm, then the parts of the scale between the points 50 and the vertex with the last mentioned batten as a base will be another triangle similar to the first. Now, on the scale of equal parts, from the vertex to the point 50 is manilestly just half the whole length of the lino, whence (art. 1) the last mentiom;d batten which forms the base of the smaller trian- gle is just half the length of that first mentioned, and which forms the base of the lander triangle : tiiat is, the bases of the two triangles are in the same proijortion as the sides. Hence if the base of the largtir tri- angle be (in the case supposed) 4 inches, that of the smaller will be two inches. The direct proportionality of the base to the sides of the triangle found by the instrument will hold while the two arms form an angle ;it the joint , and the same proportionality will also obtain when they are opened so as to form a st-.'ight line. In the latter case the scales will be directly end to cm], bu* it will still be just half the distance from 50 to 50, or one quarter from 25 to 25 on the scale of equal parts, that it is from 100 to 100. This is so plain to inspection that it requires no further illustration. These observations are, for the sake of simplicity, confined to the icale of equal parts, but they will equally apply to all the other scales on the instrument. We have been the more particular in the description of this little ne- glected but useful instrument, ( -ause it is not minutely described in books of Surveying, and its usefulness seems to be overlooked by the greater number of practical Surveyors. 50. The follovving are some practical examples of its use in making surveys. Let AC, (Fig. 27) be the width of a river which it is desirable to ob- tain, and there are no means at hcnd for plotting, or the weather will not admit of it. Let a stake be set on the bank at A, directly opposite to C, which is some fixed object on the further side. Then by means of the comp A as J C, w is tin 24). degHM distan( lines o of the A J3 is MNE9 OF SINES AND TANGENTS. 89 compass set a stake B. Mt a right angle to the lino AC, and as far from A as prncticnblc. Thtu set the compass at B, and take the bearing to C, which gives the angle A 13 C. Then taking A B as radius, A C is the tangent of the angle A B C, (Art. .'33 and 35, Fig. 21 and 'i4). Suppose now, the line A 13 is 400 feet, and tlio angle at B 25 degrees ; we open the sector to any convenient width, and taking the distance from 25 to 25 on the lines of tangents and applying it to the iinos of equal parts, find it reach from 4G.5 to 46.5. This is the length of the line A C corresponding to a base of 100 feet ; but as the base AB is 400 feet, the line AC is 4 times 46.5 or lb6 feet. '.•« ^1 \:'\ Or, if vve take the distance in the compasses from the centre of the joint along the line of tangents on either of the arms to 25, and apply the same distance from the centre along the line of equal parts, it will reach to 46.5, which multiplied by 4, gives the distance AC 186 feet as before. Or, We may take 400 feet in the compasses from any convenient scale of equal parts, and open the sector till that distance just reaches from 45 to 45 on the line of tangents, then take the distance from 25 to 25 on the tangents, and apply it to the same scale of equal parts, and it will give 186 as before. As another example of the use of the sector, suppose wc have the distance upon several courses between two distant points, and wish to find the course and distance between those points, in a straight line. Let there be one line from A to B, N. 18 W. 20 chains ; thence another line N. 60 W. 15 chains from B to C, (Fig. 28,) and it is re- quired to find the conrse and distance direct from A to C. The course A B is N. 18 W. ; that is, the angle it makes with the meridian line A D is 18 degrees. Also the distance is 20 chains. First— Take 20 4n the compasses from any convenient scale of equal parts, and open the sector till that distance reachtts from 90 to 90 on the lines of sines. IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I If li^ IIIIIM ^ IM 1 2.2 If 1^ 12.0 1.8 1.25 1.4 1 1 h < 6" ► Photographic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. MS80 (716) •72-4503 k*^' •s? 4s y^ -^^rS 84 SURVCTING. It:" ! ! «f IP ill r t ■),-■; I" ttllt II '* .., Second — With the sector unmoved, take the distance from 18 to IB on the lines of sines, and apply the distance to the same scale of equal parts: it will give 6.2. This is the sine of 18 degrees answering to a radius of 20 ; and is the length of the line e B, which in the present instance is Westing. Third — Take the distance from 72 to 72 on the sines, and, applying it to the scale, it will give 19.0. This is the sine of 72 degrees, or cosine of 18 degrees (Art. 35) answering to the same radius, and is the length of the line Ae, which in this instance, is Northing. Thus, we get the Northing Ae, and Westing eB, of the first hue 19.0 and 6.2, respectively. Then, for the second line, N. 60 W. 15 chains, from B to C, — pro ceeding as before, we First, take 15 from the scale, in the compasses, and open the sector till that distance reaches from 90 to 90 on the sines. Then taking the distance from 60 to 60 on the sines and applying it to the scale, gives 13 chains for the distance f C. Also taking the distance from 30 to 30 (the difference between 60 and 90), on the sines and applying it in the same manner, gives 7.50 chains for the distance B f. That is, we have the Northing B f, 7.50, and the Westing f C 13 chains respectively, and by adding these to the former we get the whole Northing A D, 26.50, and the whole Westing D C, 19.20, (see Art. 39.) Now, to find the course and distance, we have A D, 26.50 chains, and D C, 19.20 chains ; and supposing the side AD to be radius (Art 33), the side D C will be the tangent of the angle D A C, (see Fig. 21 and 24.) To find the angle at A, take 26.50 in the compasses from any con- venient scale, and open the sector till they reach from 45 to 45 on the tangents. Then take 19.20, the distance DC in the compasses, and, apply- ing it to the sector, it will reach nearly from 36 to 36 on the tangents: The angle D A C is nearly 36 degrees, and the course from A to C nearly N. 36 W. Now, to find the distance from A to C, keep the compasses unmoved and open the sector till they reach from 36 to 36 on the lines of sines. Then take the distance from 90 to 90 on the sines and apply it to the scale ; it will give the distance A C 33 chains. The course is therefore N. 36 W. and distance 33 chains. It will be perceived that this process is very similar to finding the ge- neral course and distance by the traverse table : the difference in the first stages of the process being, that in the traverse table we have the sines of the angles of the different lines with the meridian, (under the names of difference of latitude and departure, 39), ready calculated, where sum, ( mann( betwe The planati angle J fig. 21, same a hy any iind the he requ is, in th would were 35 19.20 c chains ii from 36 distance It maj grees, tl equal to On the s have beei ^ this ir operation " Capta hardening needle thrc The greatL ■ .^ I ■ 1.11. ■ II ^ - ■ — * 1.3 to 1.5 ounce avoirdupoU. , OF l'U£ COMFASS. W gi(>a,tcst iliret^livo power. Various have been the forms given to com- pass needles ; the choice having been regulated more hy the whim and fancy of the maker, than by any reference to scientific principles. The lornis most frequently met with are the cylindric, the prismatic, that of a rhombus or parrallelogram, and that of the flat bar tapering like an arrow at the extremities. Coulpmb, who made many experiments on the subject, gave a decided preference to the last mentioned of these, as being that which, with a given weight of needle, retains the strongest directive force. On the other hand, he found that any expansion of (he needle at its extremities, a form which has sometimes been recom- mended, is attended with a sensible diminution of power. From the whole of his experiments, he was led to the general conclusion, that in needles of the same form, their directive forces are to each other as their masses. <«This inquiry has been still further pursued by Captain Kater, whose paper in the Philosophical Transactions contains an account of a series of experiments for determining the best kind of steel for a compass nee- dle, and the -best form that can be given to it. He found, on compara- tive trial, that the directive force is little, if at all influenced by the ex- tent of surface, but depends entirely upon the mass of the needle when magnetised to saturation. Two needles were prepared from that kind of steel which is called blistered steel, and two of spur steel, each weigh- ing 66 grains. They were in the form of a long ellipse, five inches in length and half an inch in width. One of each kind was pierced, as shown by Figs. 27 and 28 ; the weight so lost being made up by t^e Fig. 29. Fig. 30. '■:, \- ' I f i , ; 1 i I, :i additional thickness. It is evident that these pierced needles had, though of equal mass, much less extent of surface than those which re- mained solid. Having formerly had in his possession a compass of ex- traordinary power, the needle of which was composed of pieces of steel wire put together in the shape of a rhombus, he procured two needles of this form (Fig. 30) made from a piece of clock spring, which is 6f that kind of steel called shear steel. In one, the cross piece was brass ; in the other, formed of part of a clock spring. They weighed only 45 grains 12 ^J^'lf '» 90 SURVEYING. i^ " Ml'.'.' ■ '[. It' • <* The results of the enquiry were, that shear steel is capable df re- ceiving the greater magnetic force ; and that the pierced rhombus is the ^est for a compass needle. Needles of cast steel were also tried ; but were found so very inferior, as at once to be rejected. In the same plate of steel, of the size of a few square inches only, portions are found varying considerably in their capability of receiving magnetism, though not apparently differing in any other respect." *< When a compass needle is nicely balanced on a point, previous to its being magnetised, so as to traverse freely in a horizontal plane, it will no longer do sa after it has been rendered magnetic. One of its ends will preponderate, in consequence of the tendency of the needle to dip or place itself in a position parallel to the magnetic axis of the globe. In order to restore its equilibrium, therefore, it is necessary to add a small weight to one side of the needle. The weight requisite for this purpose will increase with the dip, so that it may be necessary to slide the weight farther from the centre in going towards the magnetic poles, and vice versa.^^* In explanation of the alwve it may be proper to remark that there are four different points, called magnetic poles, within the globe, to which the needle points ; two of them in the Northern, and two in the South- ern hemisphere. That which is the centre of attraction in North America, has been lately determined by Captain Ross to be in 78 de- grees of North latitude, and about 96 of West longitude from Lon- don. The direction of the needle is always towards this point, and the deviation from the true North is the variation, or declination of the needle. If a needle be freely suspended, it will not only point towards the magnetic pole, but its northernmost end will preponderate, or dip, as it is called, and after a certain number of oscillations, settle at a determinate point. The dip in London, in 1833, was about 69 degrees with the horizon. To counteract this tendency of the northern end ol the needle to preponderate after being magnetised, it is usual to make that end a little lighter than the southern ; any alteration of the mag- netism of the needle, or any considerable change in the place of obser- vation, towards the North or South, will render a readjustment necessary. A small brass ring bent round the needle, of such a size that it will just: Tiove freely along the bar, makes a very good bsjance weight for this purpose. I The position of thet point of support relative to its centre of gravity, is a material consideration in the construction of a needle. When the centre of -gravity coincides with the point of suppbrt the move- ment of the needle is perfectly steady; but unless the central pin is * Brewster on Magnetism, p, 323. " The CO tivo sides oi from the tri to point out of discoveri Irom this, ca that surface to balance i on which it suspension, hefore assut not its true arrange itse i"g the two modes of su " When ( bars slightly for a brass c pieces joine< combination For, unless i have been b ness, that sii plian the otli OF THE COMPASS. 91 very sharp, and the cap perfectly smooth and liard, it is liable to come to rest a little out of the proper magnetic direction. When the point of support is above the centre of gravity the needle acquires a very rapid vibratory or pendulum-like motion, which appears as a peculiar tremble. This trembling prevents it from sticking on its centre by means of any roughness of the point of suspension, but it at the same time increases the time of coming to rest, beyond what is necessary for bringing it truly into the magnetic meridian ; for it will sometimes con- tinue to tremble for a considerable time after it has ceased to oscillate horizontally. The best form upon the whole seems to be to have the centre of gravity about two tenths of an inch below the point of sus- pension, but the ends of the needle so raised as to be nearly on a line with it : with such a form the vibrations will disturb the ends but in a very small degree. A good profile for the needle is a segment of an ellipse, rising pretty quickly at the ends. ^ , ^ ^ Anpther matter to be taken into account in fornning a needle is its horizontal breadth : when this is great, there is danger that from ui^equal temper or density of the steel, or other causes, one side of the needle will be more intensely magnetised than the other. tMi '< The consequence of the unequal distribution of magnetism on the two sides of the needle, is evidently to produce a deviation of its axis from the true magnetic meridian ; and the instrument will therefore fail to point out the real direction of this meridian. There is only one way of discovering the existence and die amount of the deviation proceeding from this, cause ; it is to reverse the needle, that is, to turn upwards that surface which was before the under surface ; and when thus reversed to balance it as nearly as possible on the same point in its axis as that on which it was before supported. If the needle in this now stale of suspension, finally settles in a position somewhat different from that it before assumed, we may conclude that the axis indicated by its figure is not its true magnetic axis ; and that the latter, which alone tends to arrange itself in the magnetic meridian, lies in a situation* exactly bisect- |iiig the two positions assumed by the. needle in these two different modes of suspension. " When compasses are constructed of two separate pieces of steel [bars slightly bent at an obtuse angle in the middle, so as to allow a space for a brass cap on which it is to be suspended at the centre, and the two pieces joined by their extremities so as to compose a lozenge shaped combination, they are exceedingly liable to the imperfection just noticed. For, unless the ends of the separate pieces which compose sucli a needle have been brought, by tempering, to an exactly equal degree of hard- ness, that side which is the hardest will retain more magnetic power than the other side ; and will, consequently, have a stronger tendency %' m «*'4>« RURVEYINn. Il'i' ii- 1$ ;^, €■. to place itself in the magnetic meridian. The needle will accordingly, incline to the side which favours this tendency, and the line joining its extremities, and which must he regarded as the axis of its ^gure, will deviate from the magnetic meridian. This evil will have a tendency to increase by time : for the stronger magnetism on one side will tend first to impair, and at length to destroy, or even finally to reverse the polari- ties of the parts on the other side to which they arc adjacent.'' .'it Hence it appears that although the forms Fig. 29 and 30 give power- ful needles they are not to he depended on. The best form to avoid the imperfection just noticed is that of a parrallelogram in its cross section, with its broadest dimension vertical. Such needles are usually mado with the ends terminating in a sharp vertical ed^e, in the centre of the breadth. This form of the end is sometimes objected to as not afford- ing so correct a means of ol)serving the angle as could be wished, the objection may be met by making the ends square and drawing a longi- tudinal straight line along the middle of the upper side, passing exactly through the point of suspension ; either method will, however, answer sufficiently well for ordinary uses. A very thin piece of silver fastened upon the end of the needle with a central line upon it, forms a good mark to observe the angle by: and if the silver be just equal in width to a degree of the ring, and have a small mark on each side the central one, so as to divide the degree into four parts, it will be still better. The needle of Dolland's Diurnal variation instrument is made semi- circular at the ends, with a line along the middle. Coulomb found that when the end of a magnetic bar was sharpened to a point, the force diminished with its acuteness: hence it would seem that the very best form for the end is either square or semicircular ; but the difference in effect between these forms, and the common edged form of bar needles, is probably very small : and besides this we must not lose sight of the assertion of Dr. Brewster, that Coulomb himself gave the preference to the form of a " flat bar tapering at the extremities like, an arrow." Probably, the best inference we can draw from the whole is, that the form of the needle is not of much consequence as to its directive force. JVeight of a Compass Needle, ^ .,■■. 53. The. qualities required in the needle of the conipass, for thel perfect performance of its office, are these : — first, its directive force compared with its weight, or with the mass which that power has to set in motion, should be as great as possible ; while, secondly, the impedi- ments to the exertion of that force, and which consists principally in the friction between the cap and pivot, should be as small as possible.— * Treatise on OP THE COMPASS. 93 " Coulomb concluded from a set of experiments; that when the pivots terminate in a sharp point, and the caps are made of very hard materials, the friction is nearly proportional to the square root of the cube of the weights. Rut after long use, the point of the pivot becomes blunted, and the surface of contact with the bottom of the cap is considerably enlarged. In this state tho friction is found to bo proportional to the pressure. -w ,j <* Assuming this, then, to be the law of the friction, let us take a magnetised needle of any given size and shape, and support it upon a pivot in the usual manner. Let us next place upon it another nei^dle, precisely similar in all its dimensions, ana magnetised to the same de- gree. The pressure on the pivot will now be double what it was before : and therefore the friction, which is proportional to that pressure, will be double also. But the directive force, though increased, will not be twice as great as with the single needle ; because, as was formerly shown, the reaction of the similrr poles of the two magnets tends to diminish the power of each. Hence the ratio between the directive force and the resistance is diminished, and the compound needle is less sensible to the magnetic influence of the earth, and less fitted for indi- cating the magnetic points of the compass. The same mode of reason- ing applies to any increase of thickness that may be given to the needle. Hence it appears, that when all other conditions are the same, needles of very small thickness possess the greatest sensibility to terrestrial mag- netism. To this general proposition there is, however, a limit ; inas(- much as excessive thinness in the needle would endanger its bending by its own weight, which would be attended with a considerable loss of power V* . 1 ! , I . )'.u ,;il m: .!i,i.' M ■)|lt , ' . Length of (he Needle, 64. " It is very obvious, from preceding experiments, that in rcg;ular luagnets, with a uorth pole at one end, and a south pule at the other, the two kinds of magnetism, north polar and south polar, are > equaify and regularly distributed, the one occupying one half of tho magnet, and the other the other half. It is obvious also that each kind of magnetism has no intensity at the centre of the magnet, or its middle part, and that it increases, according to some regular law, from that point towards the two poles at the extremities of the magnet." " The first person who determined the law of distribution which we have now mentioned was M. Coulomb. The magnet which he employed fo( this purpose was a cylinder two lines in diameter, twenty-seven If * Treatise on Magnetism, Useful Knowledge Society. '*',' I h (I'll fV\- W t ., I ■ ^T''^ 94 SURVEYING. ,, inches long, and its woigiit 194(i 6;rain8."^ Ho also nsccrtaincd the intensity of magnetism at each point, from its middle to its extremity, by observing the number of oscillations ivhich a small magnetic needle performed in a minute, when it waa made to oscillate before different points of the wire. .!;|.. (,<,(.. ^ ,, ..hi..-, •».,., .,i„.^ .„!, ,, ** In this way Coulomb obtained the following results : ,,{ j .1/ »; >'\i 'I. J' ■■•".. (( -.;, ,'/ !' "'.! l.i/f Wiff .1. Ditl>neri in inohts from III* North Pal* of the Magnet. l" 3 4&6 " 6 I'lr..) i.;i( 1 r •)',\ .(1 • ' ■• It »/i i! li f') I ■-.(Oi 'ir ni: I \\l f{ JO / j "I •' il')iit ; OInvrvfld IntintUy of the MHsnctiim at these HintancGi. / . 166 '";.'. \: I.': din.'.!/ ■ !»•»•■' y J,,. - lift l^-h ^i1 mi ■.■,11 « 1 i.^i' y 96 SURVEYING. " TliQ disiiuctive peculiarity of Duliaiuel'H process consists in the cni- ployment of the small pieces of iron which form the ends of the parallelogram, and in the use of bundles of small bars, which are more efficacious than two single ones of the same size." It must be ol)served that the north end of ons bar will lie opposite to the south end of the other, and vice versa. The same method is applicable to curved bars, or those of the horse- shoe form, the top of the curve being taken for the middle of the bar. '' If a steel bar be heated, and placed in circumstances favourable to magnetic induction, if it be placed, for example, in the immediate vicinity of a magnet, and then suddenly cooled, it will be found on its removal from the magnet, to have become strongly and permanently magnetic. The greatest degree of magnetism is produced by heating the steel to redness, and while it is under the influence of a strong mag- net, quenching it suddenly with water." !,,| .,., Directive force of Needles. bQ, ** Captain Kater made a series of interesting experiments on the directive force of needles, produced by different methods of magnetising them. The needles which he used were right-angled parallelograms, five inches long, the one seven-tenths of an inch broad, and the other three and a half tenths. The broadest was made thinner till it had the same weight as the other, which was 142 grains. The following table contains the result of the experiments. ' lA. Directive Force. 1. The magnets placed perpendicularly on the centre of the needle, and the needle rubbed from end to end on both sides, 2. The same, but the magnets separated at top in I I the same way as at the bottom, - - _ 3. The same as number one, but the distance of the :- lower ends of the magnets two and a half inches, 4. The magnets joined on the centre of the needle, . < and each moved towards the nearest .pole, then lifted up and joined again, and so on, - 5. The magnets being joined on the centre of the needle, their lower end were made to move to u each pole, their upper ends remaining in con- tact, Small Netdle. Large Nfcdie. 655 674 595 580 760 780 993 1 155 n; - 1028 1160 6. By U 7. Thi 8. Th( 5. Ma^ thi 10. Sam th( n. Wire 12. Nee^ ene an ] nun Captain power of r plate of sti 13. Magm 14. Harde the I The met bv countinj greater the " The neec oscillating as the squal For instanc saturated w osciliations proportion ^00, or a bo j I'ength ; If Jsanie, the n| (square root p % and til m the form l''me, as the] fh or 4 to • Brewster on OF THE COMPASS. 97 Directive Force. Small Needle. Large Needle. 1070 1085 1160 1170 1195 1275 1158 1261 1145 1261 - 1260 1273 1815 1665 6. By Duliamel's method, the magnets inclined 45 ° to the needle, and moved from the centre to the poles - - 7. The same, but the inclination of the magnets 20 © 8. The same, but the inclination only 2 ® or 3 o d. Magnets laid flat on the needle, and drawn from the centre to the end, - - - - - 10. Same as number eight, but the separated ends of the magnets connected by an iron wire - 11. Wire removed, and experiment number eighf re- peated ------ 12. Needles hardened at a bright red, and then soft- ened from the centre to within three fourths of an inch of their extremities, and magnetised as number eight, Captain Kater next ascertained the effect of len<;th on the directive power of needles. He cut two needles of equal weight out of the same plate of steel, the one being jive, and the other eight inches long. 13. Magnetised to saturation as in number eight, - 1193 2275 14. Hardened and tempered beyond the blue, from the middle to within an inch of the poles, - - 1 805 2277 * The method of trying the intensity of the magnetism of a needle is by counting the number of oscillations it makes in a given time. The greater the magnetic force, the more quickly will the needle oscillate. "The needle is, in fact, in ihe same circumstances as a pendulum, oscillating by the action of gravity ; and, as in that case, the forces are as the squares of the number of oscillations made in the same time." For instance, if the needle oscillates 20 times in a minute when fully saturated with magnetism, and it is afterwards found to make only 14 oscillations in a minute, its magnetic power has been reduced in the proportion of the square of 14 to the square of 20 ; that is, as 196 to 400, or about one half. This remark applies only to needles of the same length: If the lengths are different, the force of magnetism being the same, the number of oscillations in a minute will be inversely as the square root of the length. Thus if we have two needles, one of which is 6J, and the other 4 inches in length, the number of oscillations made Iby the former should be to the number made by the latter in the same Itime, as the square root of 4 is to the square root of 6J, that is, as 2 to |2|, or 4 to 5. * Brewster on Magnetism, p. 320. ■il i: 13 98 SURVEYING. It-'- ' i rr 3l. M.I. i«; f« H. ;>-' i^!'^ Pi';-' i ft 1' Preservation of Magnets. bl. " If a single magnet be kept in an improper position, that is, one differing much from that which it would assume in consequence of the action of terrestrial magnetism, in process of time it becomes gra- dually weaker ; and this deterioration is most accelerated when its poles have a position the reverse of the natural one. Under these circum- stances, indeed, unless the magnet be made of the hardest steel, it will in no long time lose the whole of its magnetic power. Two magnets may also very much weaken each other if they be kept even for a short time, with their similar poles fronting each other. The polarity of the weaker magnet, especially, is rapidly impaired, and sometimes is found to be actually reversed. More frequently, however, there arises, from this ooposition of powers, considerable irregularity and confusion in the poles i' both magnets. Heat, as we have seen, impairs magnetism: care si ould therefore be taken to avoid exposing magnets to a high tempera- ture. We should likewise be very cautious to avoid all rough and violent treatment of a magnet ; for we see how quickly its virtue is lost by any concussion or vibration among its particles. A fall on the floor, especially if it strike against any hard substance, will materially weaken it : rubbing with coarse powders, for the purpose of polishing it, and grinding it to any required form, are equally injurious. A natural load- stone will, in like manner, suffer by such an operation ; hence we should attempt to alter its natural form as little as possible ; and when it is necessary to do so, it should be effected very rapidly by cutting it briskly in the thin disks of a lapidary's wheel." " Magnets should be polished, not indeed with a view to the increase of their magnetism, but because they are less liable to contract rust." When a compass is out of use, it should be laid by with the needle as nearly as possible in the direction of the dippping needle ; that is, in the direction of the magnetic meridian, with the north end pointing downward at about 70 degrees with the horison. Some Surveyors keep their compass with the needle playing freely upon its centre ; by this means it is sure to maintain the meridianai direction, but the centre is apt to wear and induce friction. The best method is to lift the needle off the point and lay it in the direction of the dipping needle. The needles of pocket compasses are particularly liable to become weakened by long keeping ; this is owing to the careless manner in which they are laid by : if care were taken to keep the needle in its proper position this would not happen. 58. the nee Mr. Ch it I. intensitj "2. 1 tensity i perature "3. I very rapl atui-e, th the diffoj "4. h of the m "On a effect on ing that t When 1 the intens "that an exhibited, increase o while ano strength n artificial (lays' exp( its exposuj gained m< north polej lens acquii On thesi "We attL ZantedescI their magi fays ; a rej increase o( Briwitcr oJ OF THE COMPASS. 99 Effect of heat upon the Needle. 58. *' Fi'om a number of experiments made with a balance of torsion, tiie needle being suspended by a brass wire jj-^ of an inch in diameter, Mr. Christie ascertained the following facts. " 1. Beginning with 3 degrees Fahrenheit, up to 127 degrees, the intensity of magnets decreased as their temperature increased. " 2. With a certain increment of temperature the decrement of in- tensity is not constant at all temperatures, but increases as the the tem- perature increases. " 3. From a temperature of about 80 degrees, the intensity decreases very rapidly as the temperature increases ; so that if, up to this temper- ature, the differences of the decrements are nearly constant, above it, the differences in the decrements also increase. "4. Beyond the temperature of 100 degrees a portion of the power of the magnet is permanently destroyed. " On a change of temperature, the most considerable portion of the effect on the intensity of the magnet is produced instantaneously, show- ing that the magnetic power resides on or very near the surface." When the heating power, however, proceeds from the rays of the sun the intensity is not diminished, but rather increased. Barlocci found "that an armed natural loadstone, which carried IJ Roman pound, exhibited, after three hours exposure to the strong light of the sun, an increase of energy equivalent to two ounces or one sixth of a pound, while another larger one, which carried 5 pounds 5 ounces, had its strength nearly doubled by two days' exposure. Zantedeschi tried an artificial horse-shoe magnet, which carried 13J ounces ; after three (lays' exposure to the sun it carried 3^ ounces more, and by continuing its exposure its power increased to 31 ounces. An oxidated magnet gained most power, and a polished one none. He found also that the north pole of a loadstone exposed to the sun's rays concentrated by a lens acquires strength, while its south pole, similarly exposed, loses it." On these experiments, Brewster, in another part of his work, remarks, "We attach some importance to the observations of Barlocci and Zantedeschi, who found that both natural and artificial magnets had their magnetism greatly increased by exposure to the common solar rays ; a result which could not arise from their heating power, as an increase of temperature invariably diminishes the power of magnets."^ .t" P * Brtwittr on Magnttism. 100 SURVETINO. l,l- m W lii ' i Variation of the Compass, 59. The variation of the compass, that is, the property by which it deviates from the [direction of the true meridian, is well known, and is supposed to have been discovered in Europe by Columbus on his first voyage to America. The variation of the needle experiences a progres- sive change in every part of the globe, and it is this variation only, that we shall at present notice. The following table shows the change which has taken place at Lon- don and Paris. Variation at London. Variation at Paris. Variation at London. Variation at Paris. Years, Deg. Min. De?. Min. Years. Deg. Min. JDeg. Min. 1541 7 Easterly. 1750 17 15 1550 8 1760 19 30 1576 11 15 Rasterly 1767 19 15 1580 11 17 maximnm. 1 1 oO niaxinium. 1774 22 20 1603 8 45 1778 22 11 1618 8 00 1780 20 35 1622 6 12 1785 22 00 1630 4 30 1800 24 36 22 12 1634 4 5 1806 24 8 1640 3 00 1807 22 34 1659 2 00 1813 24 20 1657 1814 22 54 1662 1815 24 27.3 srJ: 1664 40 1816 24 17 1666 34 Westerly. 00 1819 22 29 1667 15 Westerly. 1820 24 11 1670 2 6 1 30 1823 24 9.6 • 1672 2 30 1824 29. 23 1680 2 40 1899 • 22 12.5 1683 3 50 1831 24 00 1700 9 40 7 40 1840 23 23.5 1720 13 00 1841 23 17.6 174016 10 It is a matter of regret that I have not been able to find any record of the variation in Halifax ; such a record would be peculiarly valuable in Land Surveying, when, as is the case in this Province, it is mostl)? done by the needle. A very small annual sum appropriated by the Le- gislature, would probably induce the Professors of Natural Philosophy in our < who ar( 60, the neec the west then reti westerly morning, twenty -f( "The variation, 1787 and servations iJanu Febr |Mar( (April (May, Tunel (July (Augi (Sept* (Octol fov( iDecc Meai * The follow] and experiencec " Lines run , " About the " Near Yarm " Division lii^ , ,(N. B. Therl ihejr were run bf "AtAJeaghe/ OF THE COMPASS. 101 in our Colleges to keep a record of such matters for the benefit of those who are to succeed us.* Diurnal Variation of the Needle, 60. Besides this, there is a small daily change in the variation of the needle. At half-past seven, a. m. its north end begins to deviate to the west, and about two, p. m. reaches its most westerly deviation. It then returns to the eastward till the evening, when it has again a slight westerly motion ; and in the course of the night, or early the next morning, it moves easterly till it reaches the point from which it set out twenty -four hours before. "The following table contains the mean diurnal rlianges in the variation, according to the observations of Canton in 1759, of Gilpin in 1787 and 1793, and of Colonel Ceaufoy in 1818-19." The latter ob- servations are calhrl the most accurate. Months. Obstrviitions of Canton. 1759 Observatiuns of Gilpin. 1787. 1793. Colonel Beaufoy. 1817-18 19. January - - February March - - April - - - May - - - June - - - July August - - - - September - - - October r - - - November - - - December - - - Mean daily change. Min. Sec. 7 8 8 58 11 17 12 26 13 13 21 13 14 12 19 11 43 10 36 8 9 6 58 10 43 Min. Spc. 10 2 10 4 15 17 4 18 9 19 6 19 6 19 4 15 5 14 3 11 1 8 3 14 39 Min. Sec. 4 3 4 6 8 5 11 7 10 4 12 6 12 12 9 3 3 o 1 8 8 8 8 Min. Sec. 5 3 6 3 8 22 11 48 9 53 11 15 10 43 11 26 9 44 8 46 7 10 4 7 9 32 * The followini! information on this subject, was communicated to the author by Mr. Smith, an able and experienced Surveyor. " Lines run at Windsor in 1763 had in 1839 an increase of 4j to 5 decrees. " About the same time lines run in 1783 and '64 near flal)faz, bad an increase of 3 degrees. " Near Yarmouth, 2 degrees. " Division lines of Rawdon and DougUs, 4 degrees. (N. B. There are two of these, one run by Nugent, acd the other by Bond, so that it is not probabia they were run by the same compass ) "At Aieagher'g Grant Musquedoboit, the increase is greater than at Halifax," 102 SURVEYING. M ■■ U-. i-i.^'i': m:p I- ■ . * I.: Min. 10 Sec. 44 15 42 > 17 6> 15 43^ 12 19.9 12 10.1 10 53.4 70 36.5 The following Table shews the amount of the Daily Variations at other places compared with that of London. London, general mean - - - . Geneva ------ Chamouni - - - - - -176^ Saussure. Col du Geant Freiberg Petersburg JNicolajef Kasan " The very important discovery of the daily variation of the needle was made in 1772, by Mr.' Graham, a celebrated mathematical instru- ment maker in London. While the needle was advancing by an annual motion to the westward, Mr. Graham found that its north extremity movjed westward during the early part of the day, and returned again in the evening to the eastward, to the same position which it occupied in the morning, remaining nearly stationary during the night. Mr. Graham at first ascribed these changes to defects in the form of his needles ; but by numerous and careful observations, repeated under every variety of weather, and of heat and pressure of the atmosphere, he concluded that the daily variation was a regular phenomenon, of which he could not find the cause. It was generally a maximum between ten o'clock, a. m. and four o'clock, p. m. Between the 6tli February and the 12th May, 1722, he made a thousand observations in the same place, from which he found that the greatest westerly variation was 14 degrees 45 minutes, and the least 13 degrees 50 minutes ; but in general, it varied between 14 degrees 35 minutes, and 14 degrees, "iving 35 minutes for the amount of the daily variation." " When the diurnal variation of the needle was first discovered, it was supposed to have only two changes in its movements during the day. About seven, a. m. its north end began to deviate to the west, and about two p. m. it reached its maximum westerly deviation. It then returned to the eastward to its first position and remained station- ary till it again resumed its westerly course in the following morning. When magnetic observations became more accurate, it was found that the diurnal movements commences much earlier than seven, a. m. but its motion is to the east. At half past seven, a. m. it reaches its great- est easterly deviation, and then begins its movement to the west till two, r. M. It then returns to the eastward till evening, when it has again a slight westerly motion ; and in the course of the night, or early in the morning, it reaches the point from which it set out twenty-four hours before. The most accurate observations made in England were those of Cole solute 1 maxim "Tf] ring th( moves ( wards n maximu or eleve position daily va from 13 to 10 m does not " In tl the diurr stationar deviation 10, A. M.' In the sometime "In ad variation magnetic On thii to the Ui " It haj tlie magnl indicate " If th( again at continue time of tl at evening called dii4 fourth to The dii varying pi the phenol hypothesis • Brewiteri ^ Davit's SJ OF THE COMPASS. 103 of Colonel Beaufoy, when the variation was 24^ west. In these the ab- solute maxima were earlier than in Canton's observations, and the second maxima west about 1 1 , p. m. " The following were the diurnal changes observed at Paris. Du- ring the night it is nearly stationary. At sunrise its north extremity moves to the westward, as if it were avoiding the solar influence. To- wards noon, or more generally from noon to three o'clock, it attains its maximum westerly deviation, and then it returns eastward till nine, ten, or eleven o'clock in the evening; and then having reached its original position, it remains stationary during the night. The amount of this daily variation is, for April, May, June, July, August, and September, from 13 to 15 minutes, and for the other six months of the year from 8 to 10 minutes. On some days it rises to 25 minutes, and on others it does not exceed 5 or 6 minutes." *' In the northern regions, such as Denmark, Iceland, and Greenland, the diurnal variations are greater and less regular. The needle is not stationary during the night, and it does not reach its maximum westerly deviation till between 8 and 10, p. m., and its most easterly about 9 or )0, A. M." In the immediate vicinity of the magnetic pole, the diurnal variations sometimes amounted to 4 or 5 degrees. "In advancing from the north to the magnetic equator, the diurnal variation diminishes in amplitude, and it ceases to be perceptible in the magnetic equator."* On this subject Mr. Davies has the following remarks, as applicable to the United States. " It has been found by observation, that heat and cold sensibly aftect the magnetic needle, and that the same needle will, at the same place, indicate different lines at different hours of the day. " If the magnetic meridian be observed early in the morning, and again at different hours of the day, it will be found that the needle will continue to recede from the meridian as the dav advances, until about the time of the highest temperature when it will again begin to return, and at evening will make the same line as in the morning. This change is called diurnal variation, and varies during the summer season, from one fourth to one fifth of a degree."t The diurnal variation is " universally allowed " to be caused by the varying position of the sun with respect to the needle, though some of the phenomena do not seem to be capable of a full explanation on that hypothesis. * Brewster en MugnetittDi ^ , ^ D«vi«'e SuTTeying. r'l m I I- 104 SURVEYING. !■■■■ 11% I ■' h III ■ 1 ■ ' ■ I ■IM ' I" '■3' ' iu i ! Disturbing Influences. i Gl. The agents which produce disturbances in the direction of the needle, are principally electricity and the Aurora Borealis or Northern Lights.* It had long been suspected that there was some affinity be- tween electricity and magnetism; but within the last 30 years anew science has grown up called Electro Magnetism, by which the identity of these agents are all but proved. It is now known that the electrical state of the atmosphere greatly affects the action of the compass ; in some states of the atmosphere the intensity of directive force seems to be double what it is in other states. Serious errors may arise from the ignorance of surveyors of the existence of electrical disturbances. No- thing is more common than for such persons to carry their compass un- der the arm with the face inwards ; if there be no cover, by rubbing the glass against a woolen coat it becomes highly charged with electrici- ty, and will upon being set up for use exhibit signs of disturbance. On this subject Dr. Roget says, — " An electrical state of the glass cover, accidenlly excited by friction, has been known to occasion a sensible dis- turbance of the needle, by attracting its ends. This attraction, when it exists may be destroyed by moistening the surface of the glass." This is the best remedy, but sometimes it requires a little time to jiet rid of the electrical influence ; the eff'ect is by no means so instantaneous at one time as at another. The electrical disturbance can readily be distinguished from local at- traction: in the latter case the needle exhibits no unusual appearances; it is merely found, when placed in different situations within a short dis- tance of each other, to stand at different angles with the meridian, ac- cording to the position and varying intensity of the attracting matter. The electrical influence manifests itself in a different manner ; the needle appears agitated, its ends stick and cling to the glass, and sometimes to the bottom of the compass. * It will readily be perceived that it is pos- sible for a compass to become highly charged with electricity, especially in dry weather. Let it be carried several miles, as before, observed under the arm by a strap passing over the opposite shoulder, and the person dressed in woolen; electricity will be excited, and the instrument will be almost as well insulated as an electric machine in a lecture room. Then let this instrument be fastened upon a tripod of dry wood, the hands of the surveyor being covered with woollen gloves, and it will re- main insulated till the electricity is drawn off by the moisture of the air. But in running a line, whatever electricity may be lost in this way is re- stored by the mode of carrying, and the disturbing agent kept in a state * For local attraction of iron in the ground, and the methods of obviating its effects, see note B. at tlie end of the volume. OF THE COMPASS. 105 of activity. In a dry and highly electric state of the atmosphere these phenomena wi" bo more observable than at other times, but friction of the glass with Misulation will at all times produce some cfTect. The action of electricity, upon the needle is found to be at right angles to that of magnetism ; hence, whatever force is exerted upon it by this agent will tend to deflect it from its proper position ; and it is not improbable that a great many of the wrong courses found in land lines have been produced by this agency upon the needle. While the disturbance of the needle is unnoticed, its guidance is relied on, and when the aberation becomes so great as to force attention to it, it is supposed to be owing to iron in the ground, but electric action is rarely suspected. To avoid this, the compass should never be carried in such a manner as to produce friction on the glass cover, and if electricity should accidentally be excited, the best remedy is water, but it is not always sufficient to wet the glass only, the whole instrument should be wetted. *, Aiirora Borealis, 62. The disturbance created by local electricity may be prevented by prudent care, but that caused by the Aurora Borealis is beyond the control of man, and all that can be done is to observe the signs accom- panying it, and refrain from making important surveys while its influence lasts. The following quotations from Brewster's Treatise on Magnet- ism, contains some of the observations of the learned in Europe on th's subject. " The ' aurora borealis,' says Dr. Robison, * is observed in Europe to ilisturb the needle exceedingly, sometimes drawing it several degrees Irom its position. It is always observed to increase its deviation from the meridian, that is, an aurora borealis makes the needle point more wcstvvardly. This disturbance sometimes amounts to six or seven de- grees, and is. generally observed to be the greatest when the aurora l)orealis is most remarkable. " This is a very curious phenomenon, and we have not been able to find any connection between this meteor and the position of a mag- netic needle. It is to be observed, that a needle of copper or wood, or any substance besides iron, is not affected. We long thought it an electric phenomenon, and that the needle was aflected as any other body balanced in the same manner would be ; but a copper needle would then be affected. Indeed, it may still be doubted whether the aurora borealis be an electric phenomenon. They are very frequent and remarkable in Sweden, and yet Bergman says that he never observed any electric symptoms about them, though in the mean time the mag- netic needle was greatly affected. 14 m 106 SURVEYING. \ . I I' .1! I I.' tl i m t5i' 'I fed i " Wo sec the nccdio frequently disturbed, both from its general annual position, and from the change made on it by tlio diurnal variations. This is probably the cllect of aurora) boreales which arc invisible, eiiiicr on account of thick weather or daylight. Van Swinburn says he seldom or never failed to observe auroro) boreales immediately after any anoma- lous motion of the needle ; and concluded that thero had been one at the time, though he could not see it. Since no needle but a magnetic one is aflbctcd by the aurora borealis, we may conclude that there is some natural connection betvyeen the meteor and magnetism. This should further incite us to observe the circumstance formerly mentioned, viz. that the south end of the dipping needle points to that part of the heavens where the rays of the aurora appear to converge. VVc wish that this were diligently observed in places which have very different varia- tions and dips of the mariner's needle." " A valuable series of obseuvations on the influence of the aurora borealis on the magnetic needle was made by Dr. Dalton, at Kendal and Keswick, during seven years from May 178G to May 1793, and has been published in his Meteorological Observations and Essays, which appeared in 1793. During these observations he noticed the efTect which they produced on the magnetic needle, and he was thus led to study the phenomenon of the aurora, and to establish beyond a doubt the relation of all its phenomena to the magnetic poles and equator. His views and speculations on this subject we shall detail at some length in a future part of this article ; but we shall at present give our readers a specimen of the observations which he made on the magnetic needle during the cliange of an aurora. ^^ Feb. 12. The aurora appeared at Kendal after 6h. p. m. flaming over two thirds of the hemisphere. The beams converged to a point in the magnetic meridian, about 15 or 20 deg. to the south of the zenith. The following were the changes which he observed in the needle and Observations. west. altitude of the clear space south 35 dcg. altitude of ditto 20 deg. streamers bright, east. streamers bright and active all over the illuminated part. disappeared in the west, active east, active about the zenith, light faint, light faint, strong light northward. I mie, in the aurora • • li'. Time. Variation. /« m. Dejr. Mill. 5 p. M. 25 5 1, , . 6 35 24 49 6 42 24 55 6 50 25 OJ '•'1 \ ; 7 2 25 28 f 7 7 25 12^ >f- •• 7 10 24 40 ■ t : •: 7 20 24 35 7 35 24 45 lijilr ■ 8 2i 45 » 9 9 9 10 10 10 10 ^^5 15 20 30 15 35 " In t minutes, did not c " Prof dinary m slavering sition, ar borealis i operate a; tent of sij hours am the distur soon as tli the dij)pii several d " From Arago at effected b connectio aurora co number o hy M. Ar.-: losophers of above aurora too " Durini 1«34, and west longi I'he magnl on one oc( corruscati( through a I iuvariably OF TIIK COMPASS. 107 limu. a » 9 9 9 10 10 10 in. 10 1». M. 35 15 20 30 15 35 Variation. Observations. 21 2\ 21 2\ 21 24 24 24 Mill. 45 ) a largo uniform still light covering half the 47 ) • hemisphere, with (lashes now and then. 43 streamers north-west, bright east ; clouds. 43 the aurora bursting out openly. 50 > as fine and large a display of streamers as has 55 ) appeared this evening. 57 } ^Q > the light growing fainter and fainter. " In these observations, the deviation produced by the aurora was 53 minutes. In some cases during the prevalence of auroras Dr. Dalton did not observe any perceptible disturbance of the needle. " Professor Ilansteen" (of Denmark) observes, " that large extraor- dinary movements of the needle, in wiiich it traverses frequently with a shivering motion an arc of several degrees on both sides of its usual po- sition, are seldom, perhaps never, exhibited, unless when the aurora borcalis is visible ; and that the disturbance of the needle seems to operate at the same time in places the most widely separate. * The ex- tent of such extraordinary movements, ho adds, may in less than 24 hours amount to 5 degrees, or 5 degrees and a half. In most cases, the disturbance is also communicated to the dipping needle ; and so soon as the crown of the aurora fjuits the usual place (the points where the di])ping needle produced would meet the sky), the instrument moves several degrees forward and seems to follow it." " From an extensive series of accurate observations made by M. Arago at Paris since 1018, the needle was almost invariably found to bo clfected by aurora? that were seen in Scotland ; and so striking was the connection between the two classes of facts, that the existence of the aurora could be inferred from the derangement of the needle. From a number of corresponding observations on the hourly declination made by M. Arago," (in France) " and M. Kupll'er," (in Russia) " these phi- losophers were convinced that, notwithstanding a difference of longitude of above 47 dgrcees, the disturbance produced upon the needle by the aurora took place at the same instant. " During the journey of Captain Back to the polar regions in 1833, 1834, and 1835, at Fort Reliance, north 62 degrees 46 minutes, and west longitude 109 degrees, the aurora occurred almost every night. The magnetic needle seems to have been constantly affected by it, and on one occasion the effect exceeded eight degrees. * Brilliant and active corruscations of the aurora borcalis,' says Captain Back, * when seen through a hazy atmosphere, and exhibiting the prismatic colours, almost invariably affected the needle. On the contrary, a very bright aurora, h ^'- in fl 108 BURVEYINO. li^ Ij'." ti I * I, ) ^ 1 ^ - .!•! though attended by, and oven tinged vvitli a dullish red and yellow, in a clear blue sky, seldom produced any sensible change, bt^yond, at the most, a tremulous motion." *^ A dense haze or fog, in conjunction with an active aurora, seemed uniformly favourable to the disturbance of the ncedh; ; and a low tem- perature was favourable to brilliant and active corruscations. Clouds, also, were often perceived in the day time, in form and disposition very much resembling the aurora." " For nearly a month, howovcr, (previous to the 7th January, 1834,) he remarks, * the needle had not been perceived to bo ulfcctcd by the aurora, which, it may be proper to observe, was always very faint, apparently high, and generally confined to one part of the heavens: Captain Back repeatedly observed, that when the aurora was concen- trated in individual beams, the needle was powerfully aflected ; but it generally returned to its mean position when the aurora became gene- rally diflused. On several occasions the needle was restless, and exhi- bited the vibrating action produced by the aurora when this motion was not visible ; and Captain Back states that he could not account for this, except by supposing the invisible presence of the aurora in full day." " Notwithstanding the body of evidence which proves the connection between the aurora and the derangement of the needle, it is a very remarkable fact, that during the fretjuent occurrence of tliat meteor at at Port Bowen, Captain Foster did not observe any peculiar changes in the deviation of the needle, although, from his vicinity to the magnetic pole, the diurnal variation sometimes amounted to 4 or 5 degrees, and it was to be presumed that the slightest action of the aurora would, under such circumstances, have been visible. From these observations of Captain Foster and others, the natural conclusion is, that there are some aurora3 which do not disturb, while there are others which do disturb, the magnetic needle. " Dr. Dalton has shown, from numerous observations, that the aurora exercises an irregular action on the magnetic needle ; and he has ad- duced from these observations the following results : " 1. When the aurora appears to rise only about 5, 10, or 1/5 degrees above the horizon, the disturbance of the needle is very little and often insensible. " 2, When it rises up to the zenith, and passes it, there never fails to be a considerable disturbance. *' 3. This disturbance consists in an irregular oscillation of the hori- zontal needle, sometimes to the eastward and then to the westward of the mean daily position, in such sort that the greatest excursions on each side are nearly equal, and amount to about half a degree each at Kendal." (England.) "4. 1 former i In ad( and upoi vation, w uncomni in Marcl heat end cold fall three daj a very fc soon aft( In the . nomena, " The gre observed .' Good Ho[ The distu or less of hours evei towards t * Brewster i OF THE COMPASS. lO'J (« 4. VVlicn tho aurora ceases, or soon after, tho ncodlc returns to its former station."* In addition to this, Mr. Smifli, an experienced surveyor of this place, and upon whom every reliance niu) be placed for correctness of obser- vation, writes on this subject as follows: — ** The year 1831 was an uncommonly warm season, from Mar'b to August. — May flowers opened in March, — Garden vegetables ibrce weeks earlier than usual, — tho heat ended With a cold rain on th ■ 20th oi August, — thenceforward a cold fall followed by a very long winter. During tho fall there were three days in succession, clear and calm, but very chilly, — the sun gave a very feeble white light, although no proper lia/c could be seen, but soon after sunset tho sky became very clear, and the stars appeared bright in tho evening, while a larfjc black arch rose in the north l)efor(5 any aurora borealis appeared. The light increased so, that at half past nine, large print could be read by starlight ; at half ])ast ten, undulating flames appeared rising above the black arch, and continued till about three in the morning. At the end of the three days my compass needle had become useless, and I was obliged to come to town to apply tho magnet to it." The following is extracted from the London Mechanics' Magazine for January, 1842. " On the 25th September last a most extraordinary disturbance of the magnetic instruments was noticed at the magnetic observatory, at Green- wich. Within eight minutes of time the declination needle changed its position more than 2| degrees. During the appearance of an aurora in the morning the needles were in agitated state. At 2 p. m. all the needles were affected by some unusual cause of disturbance. The day (Sep. 25th) was cloudy throughout ; about 9 p. m. a few bright streams were seen through the clouds, then nothing more till 1 1 p. m. when an auroral arch, about 24 degrees high was visible for a short time." In the July number of the same work is a notice of the same phe- nomena, attributed to Sir John Herschell, in which the writer says, "The great disturbance of the 25th of September 1841, which was observed at Greenwich, was also observed at Toronto, the Cape of Good Hope, Cape Drummond, (St. Helena), and Travancore (India)." The disturbances were generally characterised by the diminution more or less of the horizontal intensity, prevailing more or less for several hours every where, and the movement of the north end of the needle towards the west. I I I h.\ f [ I •'ii * Brewster on Magnetlsn. no SURVEYING. r\ f:u: .4: 1 "V?' fe' 'V 1"' f. h -P ill Mi mi •^-? On the other hand the writer of the narrative of Captain Parrj^'s seeond voyage to the polar rcii;ions says : " At Winter Island in hit. GG and longitude 83 west, on the cvcninn- of the 24th November, 1821, and the morning and evening ot the 21th, the aurora was visible, and at times billliant, from N. W. round by the south to south east. The magnetic needle, which was attentively watched^ was not at all ajjectcd by any of these phcnomena.^^ On the 5th of December, " at 1 1 p. m. the aurora was seen formiti"^ an arch, about 5 degrees high in the centre, and extending from S. S. VV. to S. E. The magnetic needle of Alexander's compass ivas not percep- tibly qfl'ected during its continuance. On the 14tli of December the aurora was very brilliant and active in the S. E. and extended to the northward of the zenith. *' The elec- trometer was U'lci] several times, and two of Katcr's compasses exposed upon the ice, during the continuance of this aurora, but neither was perceptibly affected by ity . The aurora is often mentioned subsequently in the book, but there is no further observations respecting the compass ; from which it may be inferred that Captain Parry did not in any case find it affected by this phenomenon. Also, in the narrative of Captain Franklin's over land journey to the American polar sea in 1819, the following notice occurs of observations made at Cumberland House, near Lake Winnipeg, in latitude 54 North, longitude 102 West. Nov. 2bth. " Faint corruscations of the aurora borcalis appeared one evening, but their presence did not in the least aflcct the electrometer or the compass. Nov. 2^th. In the last week, the aurora borcalis was twice visible, but faint on both occasions. Its aj)pearance did not affect the elec- trometer, nor could we perceive the compass to be disturbed." It is but fair, however, to observe that in the volume in which the latter remarks arc found, the meteorological observations made bv the expedition are omitted, and it is ])osslble that there might have been other auroras observed that did disturb the compass. From all this it is evident that auroras do not always disturb the compass, and it is possible that the disturbances noticed above might be created by some other agent. The nature of the aurora is unknown, and of course its clfects can only be guessed at. On the other hand, it is known by experiments that electricity exerts a powerful iniluence on the needle, and that its' action is at right angles to that of magnetism,— tending powerfully to dellcct it from its proper direction ; and it is not impossible that the disturbance attributed to the aurora was caused, partly at least, by electricity. Mr. Smith, indeed, found the magnetism of his compass destroyed during the continuance of an aurora, but that does not has becri On th marks, electric £ this ques netic eft made son ticular mi I o by clcctrici forces are tion, subjcr action of s( I)y sudden I which exer( Itionof the jtrical equil [stones, the rvill render Imotcors, ari j«till feebler llieets of SI OF THE COMPASS. Ill does not fully prove that phenomenon lo bo the cause ; a similar effect lias been produced by a flash of lightninji:. On this part of the subject Sir David Brewster has the following re- marks. " It has become a question of some importance, whether the electric state of the clouds produces any effects upon the needle ; and this question has increased in interest since the discovery of the mag- netic eftects of galvanic and common electricity. Mr. Christie has made some valuable observations on this subject. Adjusting in a par- ticular manner a needle between two magnets, so that its directive force was considerably diminished, he found that changes in the position of electric clouds were accompanied by changes in the position of the needle. Captain Sir Everard Home also observed, that, in two in- stances, a vibrating needle came sooner to rest during a thunder storm than it did either before or after it. The number of vibrations was reduced in one case from 100 to 40, and in another from 200 to 120. " An analagous fiict was o[)servcd by Captain Back, in 18o3 at Fort Alexander, at the southern extremity of Lake Winnipeg, where * a con- siderable alteration appeared, both in the number of vibrations, and the point at which the needle finally rested. A second time shewed a similar discrepancy. The reason of this peculiarity I could not divine, until about an hour afterwards, when some gentlemen arrived from the westward, and acquainted me that they had just encountered a severe thunder-shower, though the sky over the fort underwent no visible change, and wore the same sultry aspect as it had done most of the fore- > jj iioon. The whole subject of magnetic attraction is involved in much ob- scurity, and no branch of it more so than that which we are at present discussing. The hypothesis of Sir David Brewster on this subject is, that the atmosphere contains ferruginous matter in a state of minute division ; that the matter is rendered magnetic, or rather, has its natural magnetism increased or diminished by the action of the sun's rays, and by electricity ; that under ordinary circumstances, "when the magnetic forces are in a state of equilibrium, the needle will take its mean posi- tion, subject cnly to those small diurnal changes which arise from the action of solar heat;" that this state of equilibrium "will be disturbed by sudden changes of temperature, and by the various electrical agencies which exercise so powerful an influence ever the meteorological condi- tion of the atmosphere ;" that " the more violent disturbances of elec- trical equilibrium will fuse, and throw down in the form of meteoric stones, the metallic vapour in their vicinity ; inferior electrical actions will render their progress visible in the form of lightning and fiery meteors, arising from the heated state of the metallic particles ; while Istill feebler electricities will, by their accompanying heat, produce the [sheets of summer lightning, and the more continued and shifting phc- M ■H: n 112 SURVEYING. K--I IJH?} I til IV \A-!i |v:. V IhI ' > .i nomena of the aurora ;" that by a local displacement of the magnetic matter, from the various causes which are constantly disturbing our atmosphere, or by local and limited electric action, the resultant of the forces which act upon the needle, and consequently its direction, may be changed ; but that those local and limited actions may be such as to balance each other, and not change the direction of the resultant force which acts either upon a horizontal or a dipping needle ; and of con- sequence, if the local situation of the disturbing cause be such that its action be in the direction of the needle, such needle will not be deflected though the intensity of magnetic action may be increased or diminished. " Hence, then," says Brewster, " it is easy to understand (nay, the fact is the necessary result of our hypothesis) why there arc auroras which disturb, and auroras which do not disturb the needle, why distant auroras aflfect it when nearer ones do not, and why the needle is in a shivering or constantly oscillating state during auroras in which the places where the magnetic atmosphere is disturbed are constantly changing. In the same manner we may account for the influence on the needle, observed by Sir Everard Home and Captain Back, during the preva- lence of a thunder storm ; the electricity of the atmosphere destroys by its action the magnetic equilibrium, when this action is not compen- sated by an equal one on the opposite side of the magnetic meridian. When such a conipensation takes place, the needle will not deviate from its mean position, though the number of its vibrations in a given time may be altered." " Among other causes which have a tendency to disturb the magnetic needle, we may enumerate earthquakes and volcanic eruptions, all of which are accompanied in general with electrical phenomena. In 1767, Daniel Bernoulli observed the dip of the needle to diminish half a degree during an earthquake ; and De la Torre observed changes of several degrees in the variation of the needle during an eruption of Vesuvius."* According to this hypothesis (which hypothesis is, in a greater or less degree, adopted by most of the philosophers of EuropeJ the great dis- turbing agent is electricity, the aurora being merely one of the external signs by which its action becomes visible ; and whether the needle is deflected from its proper position, or whether it is only rendered more sluggish or more active, having its direction unchanged, depends en- tirely upon the position of the disturbing force. The hypothesis, that there is " a uniform dissemination of ferruginous and other metallic matter in a state of vapour'' in the atmosphere, which may be heated by the electricity of the atmosphere so as to produce the phenomena of meteors, lightning, and aurora borcalis, with magnetic * BrcwBter on Magnetism. effects 1 varying day and the nee Others i though i plained certain, external periodic way ; w groundec at least v Blir w the needl great coi that at so; exhibits a cause is i rarely susj measures from the running ir Severa entirely ta first of th derangem County Si considcra he might them. Ar as shown stRte, will which mu ! deranged I number of the time w the magne [cover its pi cumstances I in this case jroade in th( I made of ar \h will be n OF THE COMPASS. 113 effects upon the needle ; and that it is besides, so acted upon by the varying heat communicated by the sun's rays at different times of the day and of the year, as to produce the annual and diurnal variations of the needle, is considered by Sir David Brewster, as "indubitable." Others may not consider the evidence of this to be so forcible as he does, though it must be confessed that the various phenomena are better ex- plained upon this hypothesis than upon any former one. We may be certain, however, that there are powerful causes of magnetic action external to the earth ; the progressive variation of the needle and slight periodic variations (Art. 60) can hardly be accounted for in any other way ; while the new science of electro-magnetism leads to a well- grounded suspicion that electricity and magnetism are, if not identical, at least very closely connected. But whatever may be the value of these speculations, the fact, that the needle is liable to be disturbed by external agencies, is a matter of great consequence to the Land Surveyor. It is known to surveyors that at some times the needle is sluggish and appears weak, and at others exhibits a peculiar shivering n^otion and is settled with difTiculty. The cause is not enquired into, and a deviation from its proper position is rarely suspected. Surveyors should be aware of those actions and take measures to ascertain, so far as may be practicable, whether ^ deviation from the meridian has taken place or not ; or otherwise abstain from running important lines while the unusual appearances continue. Several precautions may be taken by the surveyor, which, though not entirely taking away all uncertainty, will considerably lessen it. The first of these is to register the bearing of a distant object, and when derangement of the compass is suspected to again try its bearing. If a County Surveyor had a register of the bearings from each other of a considerable number of known objects in various parts of the county, he might often have the opportunity of trying his compass by some of them. Another test that might bo applied is, the magnetic intensity as shown by the oscillations of the needle. The needle, in a mean state, will vibrate a certain number oftimes in a given space of time, which must be found by trials, and registered. Then if at an^ time deranged action is suspected, it is only necessary to deflect it a certain number of degrees and let it vibrate freely till it comes to rest, taking the time with a stop watch and counting the vibrations. " The greater the magnetic force, the more quickly will the needle oscillate and re- I cover its primitive position. The needle is, in short, in the same cir- cumstances as a pendulum oscillating by the action of gravity, and, as in this case, the forces are as the squares of the number of oscillations made in the same time." If a stop watch is not at hand, a pendulum made of an ounce ball fastened to a silk string will answer equally well. It will be necessary to have an assistant to count the vibrations of the 15 H %)-^^ 114 SURVEYING. 1;..; mrir Ha .•■) , If-'*'- i ■'■' !':■■■: Si; '■■ I (1^ ": : ,1. ,. I ' ■ tl ' pendulum. A pendulum of the length of 9.8 inches from the centre of the ball to the end of the loop at the end of the string will beat half seconds, and such a pendulum might he kept in the compass case as a regular part of the apparatus. It is true, this will not detect an alteration in the position of the needle, but it will detect alterations in the magnetic intensity, and when that is the case in any considerable degree, change of direction may justly be suspected. This is a test that may be appiied at any time in a few minutes, and it will also be useful in ascertaining whether the needle has at any time suffered a permanent change of magnetic inten- sity by the mode of laying it by, or from other causes. Qualiiy of Materials of Compass. 63. The last thing we have to notice connected with the compass is the quality of the brass, and of the workmanship. On these subjects Sir David Brewster has the following observations : — " A series of careful experiments were made by M. Cavallo, on tliu magnetism of brass when hammered. He found that brass, whether old or new, British or Foreign, was made magnetic when placed between two pieces of card and hammered on an anvil with a common hammer; and that the magnetism thus imparted was always removed by heating the brass red hot, and could be again communicated to it. Lest it mijjin be supposed that ferruginous matter might pass to the brass through rents or openings in the card, he hardened a piece of brass by beating it between two large flints, using one piece as a hammer, and the other as an anvil. The hammered brass became magnetic, but not so strongly as before ; which arose probably from the rough and irregular surfaces of the flints, which prevented the brass from being hardened as uniformly as it was with the steel hammer. The flints, before and after the ex- periment, did not possess the slightest magnetism. " The degree of magnetism communicated to brass by hannnering is vaguely stated by Cavallo to have been such ' as to attract either pole of the needle from about a quarter of an inch distance.' The following are the conclusions which M. Cavallo has drawn from these and other experiments : *' ' 1st, That most brass becomes magnetic by hammering, and loses its magnetism by annealing or softening in the fire, or at least its mag- netism is so far weakened by it, as afterwards to be only discoverable when set to float on quicksilver. " 2d, The acquired magnetism is not owing to particles of iron or steel imparted to the brass by the tools employed, or naturally mixed with the brass. "3d, out any having "4th what str draws tl " 5th, that end " 6ih, a certair ing. Ti likewise " 7th, power oi magnetic affect the pieces of this case attract th the rest o senting ei one may " 8th, i-liave t\\ of brass and of los it was par becoming fused in viz. that ( " 9th, fire so str and some brass. At becoming the prope owing to of any irol plate bras( it in a strc possesses iiave that is to be u< needle is a OF THE COMPASS. 116 " 3d, Tliose pieces of brass which have that property, retain it with- out any diminution after a great number of repeated trials, viz. after having been repeatedly hardened and softened. " 4th, A large piece of brass has generally a magnetic power some- what stronger than a smaller piece, and the flat surface of the piece draws the needle more forcibly than the edge or corner of it. " 5th, If only one end of a large piece of brass be hammered, then that end alone will disturb the magnetic needle, and not the rest. " 6th, The magnetic power which brass acquires by hammering has a certain limit, beyond which it cannot be increased by farther hammer- ing. This limit is various in pieces of brass of different thicknesses, and likewise of different qualities. " 7th, Though there are some pieces of brass which have not the power of being rendered magnetic by hammering, yet all the pieces of magnetic brass that I have tried lose their magnetism, so as no longer to affect the needle, by being made red hot, excepting indeed when some pieces of iron are concealed in them, which sometimes occurs ; but in this case the piece of brass, aj'ter being made red hot and cooled, will attract the needle more forcibly with one part of its surface than with the rest of it ; and hence, by turning the piece of brass about, ai^d pre- senting every part of it successively to the suspended magnetic needle, one may easily discover in what part of it the iron is lodged. " 8th, In the course of my experiments on the magnetism of brass, Miave twice observed the following remarkable circumstance: A piece of brass which had the property of becoming magnetic by hammering, and of losing the magnetism by softening, having been left in the fire till it was partially melted, I found upon trial that it had lost the property of becoming magnetic by hammering ; but having been afterwards fairly fused in a crucible, it thereby acquired the property it had originally, viz. that of becoming magnetic by hammering. " 9th, I have likewise often observed, that a long continuance of a fire so strong as to be little short of melting hot, generally diminishes, and sometimes quite destroys, the property of becoming magnetic in brass. At the same time the texture of the metal is considerably altered, becoming what some workmen call rotten. From this it appears that the property of becoming magnetic in brass by hammering, is rather owing to some particular configuration of parts, than to the admixture of any iron ; which is confirmed still farther by observing that Dutch plate brass (which is made, not by melting the copper, but by keeping it in a strong degree of heat whilst surrounded by lapis calaminaris) also possesses that property, a^ least all the pieces of it which I hav^ tried liave that property. From these observations it follows, that when brass is to be used for the construction of instruments wherein a magnetic needle is concerned, as dipping needles, variation compasses, &c. &c. 'Al 116 SURVEYING. :i' ■ il^t]. 'I Mi H-..:' Hi : I 1^ tiMi ;1 If'- m<' l^ ^\ W- < the brass should be either left quite soft, or it should be chosen of such a sort as will not be made magnetic by hammering, which sort, however, does not occur very frequently.' " These judicious suggestions of M. Cavallo respecting the condition of the brass parts of azimuth compasses were not attended to as they ought, and we have no doubt that various grave errors have arisen from their neglect. Many examples have recently occurred, in which the errors were detected ; and it is now the invariable practice of well informed instrument-makers to reject hammered brass bowls for com- passes, and to use those which are cast and turned for the purpose." The above quotation requires no comment : it abundantly proves that the mode of working brass influences its magnetic properties, in- dependently of any ferruginous matter in the metal. But besides the creation of magnetism in brass by hammering, it is probable that a good deal of that metal contains a mixture of iron. I have often known new compasses affected by magnetism in parts which in all probabihty had not been hammered. Some years ago 1 saw one which had been pur- chased by a surveyor which attracted the needle so as to be quite use- less, and I now have a common compass lately imported from a very respectable maker, and which cost £5 sterling in London, which is, in certain parts, so affected by magnetism as to make it rather uncertain for running land lines, though it answers sufticiently for engineering pur- poses. Besides the induction of magnetism by hammering, and by the mix- ture of iron with the brass, it is not improbable that the brass of com- passes becomes magnetic by long use : in several instances I have attempted to make surveys with old compasses, and finding that the lines did not close, have upon examination found them affected with niaj^- netism. This, I think, could not have been the case when they were new : if so, the imperfection would probably at some period have been discovered by the owners. Another reason for this opinion is, that I have always found in such instruments the greatest degree of magnetism in the parts nearest to the needle. 1 once purchased an old theodolite, of the old fashioned kind with open cross sights, and found it so affected with magnetism that I could make no use of it as a compass. This instrument had belonged to a gentleman of high respectability, and with which some 30 or 40 years previous he had made extensive surveys; and I feel perfectly satisfied that had it been so magnetised at the tirr.c in which the surveys were made, he must have discovered it. Of the workmanship of the common cheap compasses, 1 can only say it is none of the best ; such as have been imported by the hardware merchants are very well polished and lacquered, but in many cases at least, that part of the workmanship upon which the correctness of the OF THE COMPASS. 117 [lition they I from h the well ■can only lardware cases ai IS of the instrument depends, is executed with extreme carelessness. Nor is this carelessness alwavs confined to the most inferior instruments. In 1827 I purchased one compass out of three that ha(d been specially imported for good instruments. That which I purchased was apparently of good workmanship, and t.wo levels attached to it. The price in HaUfax was eight pounds. Inferiority of the workmanship was not suspected, but when it came to be tried, the divisions of the ring were found to be so irregular as to be quite unfit for the guidance of a survey, and another ring had to be sent for to the maker, for which he charged twenty-five shillings sterling. Nothing is more common in instruments of a low grade, than to find the ring badly divided, the needle crooked, or the sights not fairly in the direction of the north and south line of the ring. This is the more pro- voking to a purchaser, as the qualification required in a workman for making a good compass instead of a bad one, is rather of a moral than of a physical nature ; and paying double or treble price fiar an instru- ment that is to be depended upon is, in a great measure, so much paid for the purchase - f a little common honesty in the workman. The differ- ence in instruments is almost wholly attributable to the attention, or otherwise, of the workman ; all the time that he can gain by making a bad compass instead of a good one does not exceed two hours. Being myself accustomed to mechanical pursuits, I can speak with some con- fidence ; and as this assertion may be a little startling to some, I will give my reasons. The essential parts of a compass are only four pieces of brass, besides the needle, — the plate, the ring, and the two sights. The first of these is worked off by a planing machine, and therefore must be straight and true without any care on the part of the workman ; the ring is turned with a lathe, and must also be truly formed ; the essential parts of the sights are the slits for looking through, and these are made with a small saw set in a gauge, in the same manner as a cabinet maker gauges a piece of wood, and requiring only one striight edge to the sight to guide the gauge. Also, the divisions on the ring arc made by a machine, and it is only required that it be placed truly concentric with the machine to ensure a perfect division. Lastly, in putting the work together the ring is sctrewed to the bottom of the plate, and then the sights are set to agree with it. In doing so one foot of a pair of compasses is set on the ring at its east and west points, and an isoscles triangle formed in the same manner as a perpendicular is raised geometrically upon a straight, line, except that no mark is left upon the plate, as such a mark, were it made, would be covered by the foot of the sight. The method follow- ed is to bend one foot of the' compasses outward, so that it will apply to an upright object, and then, placing the sight as nearly as possible in ts proper place, finding by trials the place at which the compasses will 4i *'\ ^^. r.'M 118 SURVEYING. I'll I '^^^ I m-f: show exactly equal distances from the centre of the eye-slits to the east nnd ^vcst |)oints of the ring. When the proper position is obtained, tlio sight is screwed fast with ti thumb vice, and two or three small holes and a large one drilled through the plate and foot of the sight. The small holes are to receive pins called steady pins, which sefve to keep it in its proper place, and the large hole is for the screw to fasten it with. Another way of setting the sights is to have a piece of wood or metal, with a perfectly true face, to fit down edgewise on the north and south line of the ring, and of the exact length between the sights : the block may be laid upon the instrument with its face coinciding with the north . and south line, and the sights set immediately by it. This method does If not appear quite so geometrical as the former, but it is more convenient, and fullv as exact. Now, let us see, in all these processes, how much time the workman can save by making bad work. In the first place, the ring must be placed truly concentric with the dividing machine ; this cannot require three minutes over what would be required to put it on in a careless manner ; probably one minute would be nearer the mark. Then an hour for careful measuring in placing the sights is certainly a very hberal allowance. The only other matter that requires a consumption of time is the cor- rection of the needle. This is done by first putting in the cap, then placing the needle, before being magnetised, on a centre point, and re- versing between two stationary points, till by grinding off the ends or bending it in the middle, or both, it is brought to reverse truly between the stationary points. This reversal of its ends between fixed points is ^ the most jigorous test of straightness that can be applied, and the work- man must be very unfortunate if he be required to spend more than an hour in the operation. If these matters are attended to the compass will be true whether it be rough or smooth ; and the extra time required to make it so is very trifling indeed. ■^■i' In choosing a compass it should be submitted to the following tests: 1. Fasten a strong sewing needle into a piece of wood, so as to be set-Upright upon the table, and put the compass needle upon it. Then hold the different parts of the compass to the ends of the needle, and observe if there be any attraction between them. If no attraction can be detected within a quarter of an inch of the needle, the instrument j may be considered sufficiently free from magnetism ; because in I using the compass, the attracting force would act upon the needle nearly in the direction of its axis, whereas in the trial it acts at right angles to the axis, and of consequence a force in the latter dirjction that would sensibly disturb it would be inappreciable in the former. In this process the pieces of brass must be moved slowly to avoid creating 40 degr dividers a Pi that the OF THE COMPASS. lit) the and mall [I its etal, outh (lock lorth does lient, knian ist be Bquire ire less len an I very le cor- L then iid re- nds or etween oints is work- han an ether it is very Lo- tests ; US to be Then lie, and ion can trument use ill needle at ri^ht irjction ler. In I creating currents of air, which would he apt to deceive the ohservcr. Care should also bo taken to prevent the creation of sucii currents hy tiic breath of the observer, or by persons moving about in the room. 2. Try the division of the ring with compasses, taking at first 30 or 40 degrees in tiie compasses, and then less distances. A pair of spring dividers is the best for this purpose. 3. Put the needle upon the proper centre and place the coi-pass so that the needle will exactly coincide at its ends with two opposite di- visions on the ring : then turn the instrument gently round till it is re- versed, when if the needle again coincides with the same divisions, it is straight; if not, it is crooked. 4. The divisions being truly made, and the needle straight, try whe- ther the ends of the needle cut^iruly the north and south marks on the ring, and also the east and west marks: if it does so, the point of sup- port is exactly in the centre of the ring ; if not, the centre pin must be brought lo the proper centre by bending. This pin is, or ought to be, placed by a pair of spring dividers, on one foot of which is a ball with a small hole in it by which to steady it upon the point of the pin, while the other foot is swept round the ring. A trial of the needle however, at right angles is, provided it be straight, equally sure as a test of correctness in the centre. The needle nriay also be tried at other parts of the ring in the same manner. If on trial of a compass the needle does not cut the corresponding degrees at its ends iairly, it will bo uncertain whether the imperfection is owing to crookedness of the needle, to imperfect division of the ring, or to a wrong position of the point of support; and trial must be made on each of these points separately. Reversing the needle between fixed points should be resorted to, in the first place, because if it is not perfectly straight it can neither make correct wo'k nor be used as a test of the correctness of the other parts of the instrument. Being generally soft in the middle it can be correct- ed by bending. The division of the ring may be tried with spring dividers, but thounli it should not appear by this test to be very truly divided, it may often be made to answer tolerably w ell. If it has been divided by a correct machine, irregularity of division can only happen from its not bavin" been placed truly concentric on the machine, and there will be a point, though not exactly in the centre of the ring, from which, as a centre, the graduation will be correct. This point can only be found by re- Iversals of a straight needle. Try the needle between any two points, I and bend the centre pin, if need be, till it comes into the direct line between them ; then repeat the operation with the needle at right angles to its former direction, and continue making pairs of trials by different parts of the ring till the centre of graduation is found. If a straight 120 SURVEYING. l;i^. It ' 1:'1 I ? I. Kr 'i '•■| , u 4 ■ i- needle cannot by tlicsn means be made to cut tbc same degrees at caci end truly all round the ring, it is an evidence that the dividing macliiiK has been incorrect, in which case the fault is incurab'le. It may be oh served that the needle must he shorter than the diameter of the ring b\ twice the eccentricity, and may be found touching the ring at one ond, and perhaps a tenth of an inch of7 at the other. This is not desirable but it is the least of two evils. If the observer takes care to bring his eye into the direction of the needle, he can tell very nearly the part of the ring to which it points ; but if it be not on the centre of the gra- duation, he will have a different reading at each end without being able to give a preference to either. 5. Parallelism of the line of sight to the north and south line of the ring may be proved by the method already pointed out for setting on the sights; or a horse ha'*- may be stretched between the eye-slits in the sights, which hair, if the sights are properly set, will be exactly out of winding with the north and south line of the ring. If the eye is practised to ranging, this is a very good test, — probably the best that can be adopted. If the sights are not quite parallel no inconvenience will follow in making surveys, except that the lines run by the compacr will not agree with lines run by a true instrument. 6. Turn the com[)ass round on the table with a regular and easy mo- tion ; if the needle retains its position with respect to the meridian, we may conclude that the centre point is in order ; if on the other hand the needle moves with the compass a ^ew degrees, and then starts back to the meridian, there is friction in the centre which must be reduced by sharpening the point. Or, a better test of freedom fr(\*n friction at the centre, is to settle the needle as truly as possible by light tapping on the table, and then draw it about half a degree to one side with the point of a knife : if it returns again to its proper position the suspension may be considered sufficiently perfect. The best way of sharpening the point is to work it to a regular conical point with a slip of oil stone held at an angle of 15 or 20 degrees with the axis of the pin. Such a point is more durable than a sharper one, and equally free from friction. 7. Ascertain the stiite of magnetism of the needle: — First try whe- ther there be consecutive poles ; this may be done in two ways ; take a piece of hard steel wire about half an inch long and one twentieth of an inch thick and magnetise it. Suspend it by the middle with a small fil- ament of silk, and it becomes a very active needle. Move it gently along the needle to be tried, and it will show by its motions whether there are poles in other parts than the ends; the south of the small nee- dle being attracted by the north pole of the large one, and vice versa. Or, put some iron filings on a paper along a line the length of the nee- dle. Lay the paper upon the needle and tap gently upon it, so as to set the filings in motion ; they will gradually arrange themselves over the poles the enc 8. F balance lighter brass w lay the wire ; tl sistance The de longer a nient, at OF THE C0MPA9S. 121 sy mc- kan, we r hand ts back educed :tion at pension rpening )il stone Such a friction, ry whe- j take a ith of an mall fil- t gently whether nail nee- ;e versa. the nee- as to set over the poles of the needle, and if there be any poles between f)i liddi and the ends some of the AHngs will be clustered over them. 8. For trying the directive force of the needle a good tes» a toisio balance. This may easily be made. Take a small slip ol ood, th lighter the better, on which to lay the needle, and suspend it by a small brass wire. Set the piece of wood to range east and west, and then lay the needle upon it with its middle directly under the suspending wire ; the needle will move towards the meridional direction till the re- sistance of the wire to twisting is in equilibrio with the magnetic force. The degree of delicacy of the balance must be found by trials ; the longer and smaller the suspending wire the more delicate is the instru- ment, and vice versa. There should be a piece of paper graduated to degrees immediately below the balance, to read off the torsion by. The instrument used by philosophers is often expensive, but the above contains all the essential parts, and any ingenious person can make it in a few hours. In the application of this test regard must bo had to the weight of the needle ; a heavy needle may have a greater directive force, and still not be so efficient as a lighter one ; for as the friction is proportional to the weight (Art. 53) the light needle though abso- lutely weaker than the heavy one, may still possess a greater power of overcoming the resistance to friction at the centre. A torsion ba- lance would be very useful for trying the strength of the same needle at different times when there is a suspicion of its having lost a part of its magnetism ; some test of this nature should be applied to all com- pass needles, especially those of the common kind. There are great differences in the magnetic force of different needles ; Dr. Scoresby stated lately, at a meeting of the British Scientific Association, that he had found the needles of some ships compasses thr^e times as powerful as others, — some excellent, and others almost worthless. There is no doubt that a weakly magnetised needle is more susceptible of the in- fluence of disturbing agents than one in which the magnetism is very powerful ; and of course every possible attention should be paid to having the needle as powerful as possible. 9. Try whether the sights are out of winding with each other. The best way of doing this is to set the compass in the straight line between two distant objects, so that without moving: the instrument, the line of sight, when taken in opposite directions, will cut them both ; or if this be impracticable, set it to bear upon one distant object, the farther off the better, and direct an assistant to set a stake twenty or thirty rods off in an opposite direction, exactly in the line of sight, the compass conti- nuing unmoved. Then reverse the instrument, and if the line of sight again cuts the same objects, the sights are out of winding ; if it does not, they must be brought to the proper position by filing a little off the seat of one of them, and v^peating the operation till they range truly to both 16 n 122 SURVEYING. u i:t !'■ i > 1 » . ' objects with the compass in cither direction. It is necessary that the compass bo phiced quite level in the transverse direction, and the oh. jects to which the view is taken should be as nearly as possible on tho same level with it. If this is not attended to, a deviation of the sights from the perpendicular will give a false result. 10. Uun a line carefully, half a mih^ to n mile on level ground, mak- ing tho stations not more than ten rods apart. In running the line let an assistant set a flag exactlv in the line at each station, and then lot the compass be set by a pfumb line exactly over the spot where the flag stood ; and continue in this manner, paying no attention to the back I , sights, to the end of tho line. Then run the line back again to the place «t of beginning with the compass reversed, that is, the same end of the instrument forward, and the noodle road at the same part of the ring as before. If the second line coincides with the first the compass is correct ; if it diverges to a considerable degree, something is wrong ; but a trifling divergance of a foot or two may be expected in almost any compass. This is a very rigorous test, and the method is never adopted by sur- veyors in practice. When return parallel lines are run, the position of the compass with regard to the meridian is not changed, and the de- grees are always read ofT at the same end of the needle. Hence, if the test No. 9 has been properly attended to the lines must be par- allel. 11. Run out a regular polygon on level ground, and observe how near the last line will close to the place of beginning. Commence at some convenient station and run one side carefully to the length proposed for the side of the polygon ; change the course to the proper angle and run y another side ; and so on till it comes round to the place of beginning. Lines run round any figure will answer for a test of this nature, but regular polygons are to bo preferred as the most convenient on account of their angles being readily found. All that is necessary is to divide 360 by the number of sides in the proposed polygon, and change the course at each angle the number of degrees shown by the quotient. For example, if the polygon be eight sided, divide 360 by 8, the quotient is 45, which is the number of degrees which the course must be changed at each angle of the figure. Or, from the compass as a centre, set a number of stakes at an exactly equal distance, so as to form the angles of a square or regular polygon, ac- cording to their number. They must be set by the compass at the pro- per angles from each other 'according to the number of sides, and when so sot ought to bo exactly at equal distances from each other. If they are not, there is some imperfection in the instrument which must, if possi: 13, be discovered and corrected. In all these trials the distances must be carefully measured and the compass be set by a plumb-line exactly in its proper position. If proper attention be not be dete veyor. It i should be n With res opinions, possessing a be more like a six inch n According t< to bo 5 or 6 there is anot longer the n( more correct tho needles generally pre at Groenwic pended by a Colonel Beau and one live- five grains, £ pended in thel ping Needle < for Captain S and 1th of an the face of the pose of an ini is a very goot common survj equally well a| Some comi cross hairs in the level is su rods, they ans 64. Levek out the line of] shows it by th| level, which s( 'in a glass tub^ * London Mechao LEVET.S. 123 attention be not paid to correctness, and the figure docs not close, it can- not be determined whether the error is in the instrument or in the sur- veyor. It may hardly bo necessary to add tliat all trials of this nature should be made upon Icvol ground. With respect to the diameter of a compass, there are a variety of opinions. Dr. Hoget recommonds needles of 5 inches in length, as possessing as much directive power as larger ones, while they would be more likely to be free from consecuiive poles. Coulomb also found a six inch needle as powerfully magnetic as a larger one, (Art. 54..) According to these autlurities, it is advantageous lor a compass needle to be 5 or 6 inches in length, as regards its mechanical power. But there is another reason why tlie needle should be pretty lengthy. The longer the needle, the larger- are the degrees upon the ring, and the more correctly they can be read oiW In conformity with this view the needles for observing slight changes of magnetic direction are generally pretty lengthy. The needle of the Magnetic observatory at Greenwich is "2 feet long, 1| inch broad, and ^ inch thick, sus- pended by a skein of silk fibres nine feet long."* The needle of Colonel Beaufoy's Variation Compass " is a cylindar ten inches long and one five-hundredth part of an inch in diameter. It weighs sixty- five grains, and is terminated by two conical points." ft is sus- pended in the usual manner upon a point at its centre. Mitchell's Dip- ping Needle "was a foot long." Mayer's Dipping Needle, constructed for Captain Sabine was a "parallelepiped 11^ inches long, Iths broad, and ^th of an inch thick. The ends were rounded, and a line drawn on the face of the needle, through its centre to the extremities, for the pur- pose of an index.f" Upon the whole, it seems that from 5 to 6 inches is a very good length of needle for a compass for surveying land. For common surveys for engineering purposes, a smaller size will answer equally well and be more portable. Some compasses have a spirit level attached to them and holes with cross hairs in the sights, for the purpose of taking levels ; and provided the level is sufficiently sensible, and the distance does not exceed fifteen rods, they answer for common levelling sufficiently well. LEVELS. 64. Levels are of three kinds : — The plummet level, which pomts out the line of level by means of a plumb lino ; the water level, which shows it by the surfiice of water in a long trough or tube ; and the air level, which shows it by means of a bubble of air inclosed with a liquid in a glass tube. * London Mechanics' Magazine, for 1842. ^ Brewster oa Magnetism. 124 SURVEYING. Mt H 'H's ml ■ Ill'" '5 I [I..-.,, 1^ Of the first kind, as an instance, is the common carpenter's level. The instrument is too well known to require a description. 2dlj. The triangular level. This is composed of three rulers so joined as to form a triangle ABC (Fig. 31). At the vertex B, is fastened a plumb-line, which, when the piece A C is level, passes over a centre mark at D. As this level is very easily constructed and not liable to derangement, it may be proper to describe it more minutely. Let AC be a bar of wood about two feet and a half long, three inches deep, and an inch and a half thick ; and A B and C B be each an inch and a half wide and half an inch thick. These latter should be rivetted to the bar A C, and should be joined by a mortice and tenon, or by notching toge- ther, at B : also, they should be fastened together at B with a screw. From the point B, a plumb-line, or which is better, as not being so liable to oscillation, a brass rod may be let fall to D. The mode of ascertaining the place for the centre mark at D is very simple. Lay the piece A C, (both ends of which should be exactly of one depth) upon a straight piece of wood previously placed nearly level by the eye, and mark the place where the plumb-line crosses the bar at I) ; then reverse the ends of the level and repeat the process : if the piece of wood on which the trial is made be not level, the line on the last trial will cross the bar at a different place from the former, and the middle between the two marks will be the true place of the point D. This is all that is required for mere levelling, but for road purposes it is very convenient to have lines upon it for showing different elevations. This may be done either by drawing from B as a centre an arc of a circle at D and marking it off in degrees, or by drawing a line parallel to the base, and marking it so as to indicate the number of horizontal feet for one foot of rise. The latter mode is preferable to the former as being more easily compre- hended by persons unaccustomed to the measurement of angles. To this en( zontal require( we wisi tal, we D to a ; slopes o tieth, o should \ however at a cert ing, and Then mj the level distant o feet and so on ; th by the ru the line c cession, ( tant) and nil • I LEVELS. 125 this end, let the distance from the point of suspension at B to the hori- zontal line at D, be carefully measured, and the proportional measures required set off on each side of the centre line at D. For instance, if we wish a line indicating a slope of one foot rise in thirty feet horizon- tal, we may take one thirtieth part of the distance B D, and set it from D to a ; a line drawn from B through a, will be the line required. Or, for slopes one foot in twenty, or one in fifteen we may take D b one twen- tieth, or D c one fifteenth of B D, and so on. These measurements shoukl be very carefully made by a true scale. A more certain way, however, to obtain them correctly, is as follows : Let the level be set up at a certain distance from a perpendicular object, as the wall of a build- ing, and let a mark be placed upon it on the level from the instrument. Then make other marks upon the wall, upwards and downwards from the level, to indicate the required slopes.- As an example, if the wall be distant one hundred feet, two feet will give a slope of one in fifty ; two feet and a half, one in forty ; three feet four inches, one in thirty, and soon; the distance being always easily obtained by a single operation by the rule of three. Having made the proper marks upon the wall, let the line of sight of the instrument b'^. directed correctly to them in suc- cession, (which can be best done by means of a vane held by an assis- tant) and the place where the plumb line crosses A C carefully marked. This process is exactly the same in principle as the former, but the errors are diminished in proportion to the increase of the scale upon which the measurements are made ; and as the trouble is not great it seems the most proper to be adopted. This is a very convenient instru- ment ; it is not liable to derangement, and by only withdrawing the screw at B, the pieces A B and C B will fold down along side of the piece at A C, while the plumb line or brass rod B D, may be put into a groove cut out for it in the piece A C, and the whole rendered as por- table as can be desired. An ingenious cabinet-maker will make such an instrument in a day. By having this instrument so constructed that the edge of the ruler CB would be at an angle of 45 degrees with the horizontal piece CA, it is very useful in finding the height of timber, trees, or other inacces- sible objects. It might for this purpose be composed of three thin ru- lers, and fastened into a split in the head of a temporary stake. The range of the ruler C B would then strike the tree at the same height above the level line as the distance of the instrument from the tree. Thus, suppose the ruler B C to be directed to some branch or remark- able object near the top of a tree, and the level A C to strike it at the same time six feet from the bottom, the instrument being 60 feet from the tree, the height of the object would be 66 feet. A rough sort of level for temporary purposes, but equally correct, may be made upon the same plan, as follows : Take three strips of board I'M'/'; > V'\ v.. ¥ i ¥ M 1 ^ tv c i 1 i i : K ■ 1 ^ w ^1" • ii 1 : >- h . i 126 SURVEYING. of five or six feet in length, lay them together in the form of the letter A, but with the cross bar of the A within three or four inches of the bottom, and nail or pin them together at the angles. Then fasten a plumb-line at the vertex, in a cut made with a saw, and setting the feet of the level upon a piece of timber, or upon two blocks or stones, nearly level with each other, mark the place where the plumb-line cuts the cross bar. Reverse the level, taking care to set the feet exactly in the same places as before, and again mark the place where the plumb- line cuts the cross bar ; — the middle between these marks is the true plumb-line, which may be found with a pair of compasses. The cross bar is placed a few inches from the bottom, to allow the plummet to hang freely below it. A person having a board that he can split into three pieces, and three nails, can make such a level as this in ten minutes; it will be as correct as any, and perfectly safe with respect to getting out of order. Informing a road, three small laths about foiir feet in length may be fastened together for a level of this kind, and in general road forming, slopes of ground of moderate length may be graduated by it with sufficient accuracy ; but for this purpose it should spread to a width at the bottom of not less than ten feet, and be four or five feet high at the vertex. In building bridges, &c. in the woods, where boards are not at hand, three light poles fastened at the corners with nails or plus will answer sufficiently well. Fig. 32. B 65. Another level for road levelling may be made, as in figure 32. A B is a stout bar of wood for bearing the sights, and AC is n thin broad piece descending from it, and upon which the plumb-line is fast- ened. At C it is marked off on each side of the vertical line, to desig- nate slopes, in the same manner as Fig. 31. It is more easily made than the former, but not so portable, and more liable to derangement. f1 G6: tube th{ upright in a veri ture of LEVELS. 127 66. Another class of levels has been invented, in vthich the ruler, or tube that guides the sight, is fixed at right angles to the lower end of an upright bar ; vi'hich bar is suspended by its upper end, and keeps itself in a vertical position by its gravity. These levels are more of the na- ture of toys, than of useful instruments, and need not be described. gure oz. is ? thin e is faot- } fiesig- Iv made junent. Water Levels. 67. Levels of this kind show the horizontal line by .means of a sur- face of water or other liquid, and are founded on the principle that liquids always preserve a level surface. The most simple water level is a long wooden trough filled with wa- ter: its surface shows the line of level. In making this level nothing more is required than to take a piece of wood ten or twelve feet in length, make one edge straight, and cut a groove in it about one inch deep, and the same in width ; place this upon two stools and fill the groove with water. It will be a very perfect level. This level is easily made, and is very useful for finding the level for dams, or for drains in flat ground, but too unwieldly for common purposes. It was in com- mon use by the ancients ; it was also used in the first surveys for the Shubenacadie Canal. 68. An improvement of this instrument consists in covering the trough, and inserting small pipes of equal height into each end. When the water comes to the top of each pipe the instrument is level. An instrument of this kind was made in the following manner. A piece of wood about three feet in length, had a groove cut in its upper edge of about half an inch in depth, and the same in width ; a thin slip bedded in white lead was then laid upon the top, and a small copper tube was inserted vertically into each end, rising about a quarter of inch above the wood ; the covered groove furnishing a communication between them. In practice it was found to be troublesome to fill it with water : the tube being straight, air bubbles would often remain in it, and by coming I out unexpectedly, derange the operation. It, however, performed near- ly as true as the ordinary telescopic levels. Had the groove which formed the communication between the tubes been lowered about two inches in the middle of its length, the annoyance from the bubbles of I air would have been prevented. In England a level of this kind has been long in use : it is composed lof a copper, or brass tube, rising a little from the middle to the ends, and Iterminating in upright tubes. Cross sights are fixed upon its ends at lequal heights above the top of the tubes. It was cheap, and has been luch in use upon farms for directing lines of drainage. The wooden 128 SURVEYING. [)■:■■<:■■ ■ , ■■■■•'■ -i*', : ■1 Ml' -^ ■'< t'^ 'O Ir • '., f ■ i instrument described above is equally good. It may be made by a car- penter in about a day. Or, probably the best and cheapest method of making such an instrument would be laying a tin tube of about half an inch in diameter, bent to the proper form, between two pieces of wood. This level requires filling anew at each time of setting it up, and it is somewhat troublesome so to regulate the quantity of water as just to fill the two tubes. This can partly be remedied by substituting tubes of glass at the ends, of a height greater than the required height of the surface of the water. Small phials having their bottoms cut off, will answer very well. They may be marked with a scale upon the sides, and the water may be coloured. In removing from station to station the phials may be corked to protect the escape of the fluid ; but they should be open while taking the level, otherwise the elasticity of the confined air will cause an uncertain result. Floating Levels. 69. Si.5 : Another class of levels has been tried on the continent of Eu- rope, in which the sights were made to float on the surface of water or other fluid. The first of these we have an account of is De La Hire's level. It consists of two vessels filled with water, and communicating with each other by means of tubes. Small boxes float in these vessels, one of which carries the eye glass and cross hairs, and the other the object glass of a telescope. It was difficult to use this instrument, from the impracticability of keeping the glasses in their proper positions. These defects in De La Hire's level were partly removed by M. Couplet, by inserting the object glass and eye glass into the same tube, and by placing this telescope loosely on two boxes which floated on the fluid. The difficulty with respect to vision was overcome, but there still remained an uncertainty respecting the depth to which the boxes or floats would sink in the fluid,, and consequently of the correctness of the level. M. Deparcieux made a further improvement. It consisted in making the vessels, and the boxes which floated in them, of a large size. The former were 10 inches long, 7 inches wide, and 4J deep ; the latter about an inch smaller in their dimensions, so as to admit of free motion, The telescope was fastened upon the top of the floating boxes, which were also connnected together by a bar which carried a moveable leaden weight, that served to adjust the depth to which the boxes floated in I the water. A level was also constructed in which mercury, instead of water,! was employed for floating the sights. The principle is the same as in I Si the pr there 1 Tilt too un water Ano be put as ibllo Out screwei index w this latf trie wit J the indc The ind vernier of ciicd upol ^y a pin LEVELS. 129 the preceding, but Ihc mercury being a mucli heavier body than water, there is less danger of the floats sinking unequally below it. These levels do not appear to have come into general use : they were too unwieldly for convenience, and not more correct than the common water level. Another level that answers extremely well, is an appendage that may be put to a Surveyor's Compass. A level of this kind has been made as follows : On the middle of one of the upright sights of the compass, there was screwed a small knob, to serve for the centre of motion of an arm or index which reached across the compass to the opposite sight, and on this latter sight there was fastened vertically, a graduated arch concen- tric with the index. Tiiis arch was divided into thirds of a degree, and the index carried a vernier, by which the reading was brought to minutes. The index carried at each end a small horizontal sight similar to the up- right sights of the compass ; that on the end of the index which was the centre of its motion contained the narrow slit for the eye, and the other, the wider slii, with a horizontal hair in the middle, to be directed towards the object. The slits were about an inch in length. The index was retained in its proper place upon the arch by the friction of a spring fast- ened to it on the back side, and which, by means of a screw, could be increased or diminished. The zero of the graduation of the arch was in the middle of its height, — on a level with the centre upon which the index turned, and the zero of the index was in the middle of its length, so as to read upwards and downwards. The range was about fourteen degrees each way from the zero. The compass to which this apparatus was appended, had a spirit level with adjusting screws under the bottom. To enable the observer con- veniently to see the level, an oblong hole was cut through the bottom l)late immediately over it, into which a piece of plate glass was fitted, and cemented in with sealing wax dissolved in spirits of wine. The workman who constructed this instrument had not a dividing ma- chine, and the substitute he emi)loyed was a very large Nautical Quadrant. He took off the index and fastened the arch, for dividing, to the frame of the quadrant at the distance of its own radius from the centre, and in such position as to coincide truly with a circle of that radius drawn from that centre. He then took a piece of brass plate, fitted it to turn upon ;i pin which was fitted to the centre hole of the quadrant, and used it as a ruler by which to mark the graduation of the arch ; using the gra- duation of the quadrant for guiding the ruler. The vernier of the index was divided in the same manner by the vernier of the quadrant. The index plate of the instrument was fast- ened upon that of the quadrant, and retained in a concentric position by a pin which was fitted through the centre holes of the two indexes- 17 130 SURVEYING. By I |iJH f ; I It W^^M' m ■ i .1% I- J. V and of the ruler. The vernier was then marked by the vernier of the Quadrant, in the same manner as the arch was by the arch of the Quad- rant. It may be hardly necessary to remind the workman, that in both of these operations, the ruler must be so formed that its working edge will range directly to the centre of its motion. This instrument answers in surveys for common roads, all the pur- poses of the Theodolite, and is cheaper and more convenient. In the woods, we have the compass ready for running a line when required ; a thing that can hardly be done by a theodolite without having a flag-man forward; and with respect to correctness, lines of veritication have often been run by it in the woods, which agreed in the levels within six inches in the distance of a quarter of a mile, — a degree of correctness abun- dantly sufficient for any con^mon road. This level was executed by a watchmaker's apprentice under his mas- ter's direction, and took about a week's work ; an active workman would have done it in about four days. The price charged was twelve dollars. It has been 17 years in use and is now as good as ever. Upon the whole it may be considered one of the cheapest and most efficient instruments for laying out common roads in the woods that has yet been produced. If the graduation were done in silver riveted or soldered to the brass, it would be a great improvement, and the price would not be materially enhanced. 70. The common spirit level was invented by Dr. Hooke, it, as is well known, consists of a glass tube nearly filled with a liquid, leaving a bubble of air, which by its levity keeps in the highest part of the tube. This is properly the level; all the other parts of the most complicated instrument are only appendages for the purpose of guiding the sight parallel to the level.* The bubble tube and the bubble ought to be of considerable length ; the longer the more sensible : the greater proportion the capacity of the bubble bears to that of the tube the better, because when it is small in proportion to the quantity of spirit, the expansion of the latter by heat reduces the bubble to a very small size, and in that state it moves slug- gishly and is not to be depended on. Choosing a bubble tube should always be done in warm weather, or otherwise it should be warmed to blood heat. If the bubble is sensible at that heat we may be sure it will be equally or more sensible in cold weather ; but the bubble may act very well in cold and notwithstand- ing be very sluggish when warmed. If we take a spirit level and fasten it to a brass or wooden tube, cover * For an account of the theory of the spirit level, and of the allowance for the curvature of the earth and of refraction, see note C at the end of the volume. The or nion spyii of the ba formed, s< the object of the ob object anc are placet to it. The ha cobweb is These are wire is sor fine. Ind ^airs has LEVELS. 131 one end of the tube with a plate, leaving only a small hole in the centre to see through, and put a hair horizontally across the tube at the other end, it makes a level. If we put lenses into the tube in proper posi- tions we convert the tube into a spying glass or telescope, which gives a plainer view of distant objects, but possesses no other advantage over the open tube. In the telescopic level, there are generally but two lenses; one at each end : that at which the eye is placed is called the eye-glass, the other the object-glass. The image of a distant object is formed in the air, in the tube of the telescope, at the focus of the object-glass, is always in a position reverse to that of the object it represents, and it is this which we see in looking through a telescope. This image is view- ed with the eye-glass which magnifies it to the eye. The degree in which objects are magnified by these glasses is found by dividing the focal length of the object-glass by that of the eye-glass; the quotient gives the magnifying power, or apparent enlargement of the object. Thus if the focal length of the object be ten inches, and that of the eye glass an inch and a quarter, the magnifying power is 10 divided by Ij or 8 times : that is, an object will appear under an angle eight times as large through the glass as with the naked eye, or, in other words, appears at only one eighth the distance. It will not, how- ever, appear quite so plain, because the sight is in some measure ob- structed in looking through the glass. In many telescopes two, and in some instances four additional glasses are introduced near the eye end of the tube, but these serve merely to make objects appear in their natu- ral position, and do not increase their magnifying power. They always cause a diminution of brilliancy. The only difference between the telescope of the level and the com- mon spying glass is, that the former has hairs stretched across the inside of the barrel at the same place at which the image of the object is formed, so that they may appear to the observer as if they rested upon the object. In telescopes with but two glasses this place is at the focus of the object-glass ; or more correctly, in the common focus of the object and eye-glass. When there are more than two glasses, the hairs are placed in the common focus of the eye-glass and that which is next to it. The hairs are generally made of the strong spider line to which the cobweb is fastened ; the common threads of the cobweb being too weak. These are liable to stretch and become crooked in damp weather, and wire is sometimes substituted, but it is very difficult to get it sufficiently fine. India rubber dissolved in oil of turpentine and drawn out in fine hairs has been proposed with a probability of success ; it is said to be 132 SURVEYING. Ill > * l8''t'«(- I |ii,i t f\ ■■1 in »i. capable of being made as line as spider's lines, and is not liable lo hygromctic influences. In the best instruments the hairs arc fixed in a certain part of the tube, and the object and eye glasses in slides, so as to admit of being placed at different distances from them. The reason why these adjustments arc necessary is, that the images of objects which are remote are formed at a less distance from the object-glass than of those which are very near ; and with regard to the eye-glass, an object in its proper focus will not bo equally plain to all persons. A near sighted person would require a magnifier to be placed nearer to the object to be viewed than one whose eyes had become flattened by age ; and hence the con- venience of having means of adjustment. The moveable adjustment of the eye glass is, however, not absolutely necessary, and is often dis- pensed with ; any iittlc difficulty experienced by short sighted, or old persons, can be remedied by spectacles; — the adjustment of ihe object glass, when objects near at hand are to be viewed, cannot be dispensed with. In some instruments the object-glass is fixed, and the cross hnirs affixed to the tube which carries the eye-glass ; by wliich means they can be placed to meet the image formed by the object glass, by merely drawing out the tube. I'his arrangement does not admit of changing the distance of the eye glass to suit different eyes, but this, it appears, is not a very material defect. In very inferior instruments both glasses are fixed. In using the instrument in which the cross hairs are fixed, and the glasses moveable, — " the eyc-pirce must first be drawn out until tlio cross hairs are perfectly well defined, then the obj( ct-glass moved till distinct vision is obtained without parallax, which will be the case if, on looking through the telescope at some distant object, and moving the eyu sidewise before the eye-glass, the object and tlic hairs remain steadil)' in contact; but if the hairs have any parallax, the object will appear flitting to and from them." The reason why the eye-glass should be first drawn out is, that it is necessary that both the cross hairs and the imago be at the point which is the fi)cus of both glasses ; and by first placing the eye-glass in such a i)osition that the cross hairs will be in its focus, and then, by a movement of the object-glass, bringing the image to the same point, the intended effect is produced ; whereas were we to move the object-glass first, and then move the eye-glass to correspond to it, as the image is always at the common focus of the two glasses, that point would not, exce})t by accident fall exactly upon the cross hairs, and if not, these hairs would not be visible. 70. In the adjustment of this instrument, the object we have to at lend to is to get the line from the eye to the cross hairs, or line of col- limatioi must b( to a rin of the h by four I'wo of other; I the diap tically ai jiairs ha and arc There some ins copo, aiK coiinecti< capstan bring it j cope. One ki iiistrumer a strong I wbich to tills bar tl ending at cuinstanc( iinmoveal or lowerci angles, to tube, two wbich it the top o the other ^ which motion in V's, and u J)ass box lor throwii The adj " The fi make the i cylindrical * The line oi LEVELS. 133 to image 1 we to •espond glasses, c cioss to at of col- limation, exact))' parallel to the bubble tube. To lliis end one of these must be moveable. In some instruments the cross hairs are fastened to a ring of brass, called the diaphra^m^ a little smaller than the inside of the barrel of the telescope ; which ring is retained in its proper place by four small screws which pass vhrough the barrel, from the outside. Two of these screws are horizontal, and the other two vertical to each other ; hence, by slacking the one and tightening the other of any pair, the diaphragm, and with it the cross hairs, is moved horizontally or ver- tically as may be required. In soir . iiistruments, however, the cross liairs have been carefully placed in the line of collimation by the maker, and are immoveable.* There is the same variety in the fastening of the bubble tube ; in some instruments it is immoveably embedded in the barrel of the teles- cope, and in others it is so connected as to be capable of movement. The connection for this object generally consists of small vertical screws with capstan heads, by which the ends can be raised or lowered so as to bring it parallel to the optical axis, or line of collimation of the teles- cope. One kind of level very commonly used is called the Y level. In this instrument, the frame upon which the telescope is mounted consists of a strong bar of brass, having a socket screwed to its lowermost side by which to fasten it to the parallel plates of the tripod. At either end of tills bar there is a column of the same metal for supporting the telescope, ending at the top in a fork somewhat like the letter Y ; from, which cir- cumstance the instrument has received its name. One of these Y's is immoveably fixed ; the other is supported in a socket that can be raised or lowered by a screw, to adjust the telescope per|)endicular, or at right angles, to the vertical axis. The telescope has round the outside of the tube, two collars or rings, which are turned truly cylindrical, and on which it rests in these supports. It is kcj)t in its place by clips across the top of the Y's, which clips are fastened at one end by a joint, and at the other by a pin. The clips may be opened by withdrawing the pir, by which the telescope can be reversed, or turned round with a circular motion in its axis during the adjustment. Between the supports, or Y's, and upon the bar, or rather forming part of the bar itself, is a com- pass box for taking the magnetic bearings, and having a contrivance lor throwing the needle off its centre when not in use The adjustment of this level is performed as follows : " The first adjustment is that of the line of collimation ; that is, to make the intersection of the cross wires coincide with the axis of the cylindrical rings on which the telescope turns : it is known to be correct. n-m. * The line of collimation is the optical axis of the telescope. 134 SURVEYING. B 'ii III ¥:'■• |l|j J yi;- when an eye looking through tho telescope observes their intersection continue on the same jioint of a distant object during an entire revohi- tion of the telescope." The usual mode of making this adjustment is as follows : — First direct the telescope to a distant object and note the point covered by the horizontal hair. Having done this, revolve the telescope in the Y's half round, when the bubble tube will come to the side opposite to that at which it was before. See, if in this position, the horizontal hair appears above or below the same point ; and in either case, loosen one, and tighten the other of the two screws of the diaphragm that work the horizontal hair, till the horizontal hair has been carried over half the space between its last position and the observed point. Revolve the telescope back to its former place ; direct again the horizontal hair to the point, and repeat the operation till the horizontal hair covers exactly the same point in both positions of the telescope. A similar process will adjust the vertical hair. When the adjustment of both hairs is perfect the intersection of the hairs will cover the same distant point in every part of the revolution of the telescope. Second adjustment. To set the bubble tube parallel to the line of collimation. " Move the telescope till it lies in the direction of two of the parallel- plate screws, (the clips which confine the telescope in the Y's being laid open) and by giving motion to the screws, bring the air bubble to the middle of the tube, shown by the two scratches on the glass. Now re- verse the telescope carefully in its Y's, that is, turn it end for end ; and should the bubble not return to the centre of the level as before, it shows that it is not parallel to the optical axis, and requires correcting. The end to which the bubble retires must be noticed, and the bubble made to return one half of the distance by tiie parallel plate-scrinvs, and the other half by the capstan-headed screw at the end of the level, when, it the halves have been correctly estimated, the air bubble will settle in the middle in both positions of the telescope." Let the telescope be now revolved in the Y's one quarter of a revolu- tion, or till the bubble tube is on the side of the telescope, and by the parallel plate-screws bring the bubble to the middle of the tube. Then revolve the telescope one half of a revolution, or till the bubble tuhe comes to the opposite side of the telescope, and observe the bubble ; if it again stands in the middle of the tube the adjustment is perfect ; if not, move the tube by means of screws calculated to give it, when in its proper position, a horizontal motion ; and repeat this till the bubble stands at the middle of the tube in both positions of the telescope. It is difficult to make the first part of this adjustment, while the axis of the bubble tube is considerably inclined, horizontally, to the line of collima- tion; fi while ii axis of inclined making having i thus till colJimat This telescopi tube is n A thin upon whi line of CO First, t over two of the lev half roun( cope may in the mic corrected the paral turn the screws an examinati( level can at the cen revolves ai horizontal adjusted, or two, as erroneous LEVELS. 135 tion ; for, allowing that it is so inclined, — if it be placed truly horizontal while in its proper position, that is, perpendicularly above or below the axis of the telescope, it will not retain the horizontal position when inclined a little towards either side. This suggests the necessity of making the first part of the adjustment with tolerable accuracy ; then, Iiaving made the second with care, re-examine the first, and proceed thus till the bubble tube is brought to a perfect parallelism to the lino of colHmation both in the vertical and horizontal directions. This horizontal parallelism of the bubble tube to the axis of the telescope, is often attended to by the maker, and in that case the bubble tube is not furnished with a lateral movement. This account is extracted, in substance, from a Treatise of Surveying, by Mr. Davies, Professor of Mathematics in the United States Military Academy, and from a Treatise on Mathematical Instruments, by Mr. Simms of the Greenwich Observatory, London ; but notwithstanding these authorities I cannot feel a full reliance upon the second adjust- ment of the bubble tube. The perfection of the adjustment depends entirely upon the perfect equality of the diameters of the collars which he in the Y's ; and as these are often not more than four or five, and seldom above six to eight inches apart, a very minute difference in their diameters will create a considerable error in the results. A more certain mode of making this adjustment will be shown a little further on. A third adjustment is also necessary ; that is, to set the vertical axis upon which the instrument turns, at right angles to the bubble tube, and hne of coUimation. First, turn the instrument upon its stand, till the telescope is directly over two of the parallel-plate screws, and move them till the air-bubble of the level settles in the middle of its tube ; then turn the instrument half round upon the vertical axis, so that the contrary ends of the teles- cope may be over the same two screws, and if the bubble again settles in the middle all is right in that pos'tion ; if not, half the error must be corrected by raising or lowering the moveable Y, and the other half by the parallel plate screws over which the telescope is placed. Next, turn the telescope a quarter round, that it may lie over the other two screws and make it level by moving them. And thup proceed, making examinations by reversals of the instrument, and correcting, until the level can be turned entirely around without displacing the bubble at the centre of its tube. As this can only be the case when the level revolves around a vertical line, it follows that the telescope will then be horizontal, and the axis of the instrument vertical. The level is now adjusted. When used, however, it is best to re-examine it every day or two, as it is constantly liable to get out of adjustment, and so give erroneous measurements. • i Im-i K.it ib *i'^* i m ' I t 1 li''-. ijf; SURVEYINfJ. In somo instmrHoiits ilic tulcscopc instead of lujing laid in Y's, i*. uflixed to till) bar by a joint at one ond and a vertical screw at the other, lor raisin<5 and lowering it. Tiiis screw, which is rurnishcd with a capstan mil for Castoning it in any |)articular position, may be used li)r making the third adjustment and fixed by turning th(> capstan nut; um] should never afterwards bo touched, except lor the purpose of readjust- ment. 72. As levelling is often done with the Theodolite, it may not be im- proper to extend these directions so as to include that instrument. On the Theodolite the adjustment of the line of collmation, and of the bubble tube, is performed in the same manner as in the Y level. The adjustment of the vertical axis to the horizontal part of the instru- ment, or vernier plate, is carefully performed and permanently fixed by the maker. There arc, however, other adjustments required, which arc as follow : To make the axis of the vertical limb, or graduated arc, truly hori- zontal or perpendicular to the axis of the instrument. Bring the intersection of the cross hairs of the telescope upon a plumb line, or any well defined vertical object, and move the teles- cope with the rack and pinion in the vertical direction ; — if ihc in- tersection of the cross hairs continue on the vertical line, the axis is hor- rizontal. Or the adjustment may be effectc^d thus : — Direct the intersection of the cross hairs to a well defined point that is considerably elevated : then turn the vertical limb until the intersection of the cross hairs rests u[)on some other well defined point upon or near the ground: turn the telescope end for end in the Y's, and turn the vernier plate round 180 degrees, and observe if on elevating and depressing the telescope, tne intersection of the cross Iiairs passes through the two points before noted ; if so the axis is hori- zontal. If it be found, by either of the above methods, that the axis is not horizontal, it must be made so, by the screws which fasten the frame work to the vernier plate, where they are capable of adjustment ; or when they are not calculated for adjustment, by reducing the length ol the legs of the frame. This, however, may be generally presumed to have been attended to by the maker, though in inferior instruments it will be proper to make an examination of this matter. To ascertain whether the line of collimation of the telescope is fixed at right angles to the horizontal axis of the vertical limb. Dhect the intersection of the cross hairs to a well defined point ; then take the telescope out of the Y's, and turn the vertical arc quite upsidcdown : Then fasten the telescope into the Y's, vyhen it will be below the axis ; and when in this position direct the intersection of the cross hairs to the same point : if it covers it the telescope is at right LEVELS. 137 angles to the axis. It will bu necessary that the teleficopc be tho same side upwards in both observations, otherwise, nn error in the collimation might be taken for an error in the position of the axis of tho limb. If the theodolite bo so constructed that cither of the Y's admit of being moved laterally, so as to vary the angle between tho horizontal axis and the line of collimation, these 'ines may he adjusted at right angles to each other, if they have not been so placcc by the maker; if they do not admit of adjustment they may be presumed to be correct ; but in inferior instruments especially, the adjustment should always be ex- amined. The vernier of the vertical arc should be at zero when the telescope is horizontal. This is easily effected ; set the telescope truly horizontal by bring- ing the bubble into the middle of the tube, and observe whether the vernier points to the zero of the vertical arc : if it does not, and the vernier admits of a horizontal movement, it may be easily adjusted by moving it till the zero points coincide. If the vernier is fixed, the quan- tity of deviation must be noted as an index error, and added to, or sub- tracted from, the reading of the vertical angle observed. 73. When the cross hairs are connected with the tube that carries the eye-glass they arc sometimes affixed to a diaphragm that admits of adjustment, but they are often affixed to the tube itself, in *he line of collimation by the maker. In this last case the cross hairs being im- moveable, the bubble tube must be adjusted by them as shown in art. 71. This may be done as follows, viz. : 1. Set up two stakes, at A and B (Fig. 33) at about 20 rods apart, and on ground nearly level in the direction of the stakes. Fig. 33- e 2. Set up the level exactly in the middle between the stations ; or, at all events in such situation that the stakes will be at equal distances 18 1^ Km 138 SURVEYING. m '0 i from it. Then direct an assistant to hold a vane at either stake, sup- pose at A, and having levelled the telescope l)_y the bubble, cause hini to place the vane in the line of sight of the telescope and mark the point where the line of sight meets the stake, as at d. Repeat the operation with respect to the stake B, making the point of intersection of the line of sight with the stake at e. Now, whatever error there may be in the adjustment of the instrument, it is evident that the effect at the stakes A and B will be equal in every respect ; and of consequence the points d and e will be truly horizontal with each other. 3. Set the level at one of the stakes, as A, and mark the height of the telescope upon the stake ; which we will suppose to be at f ; and then make a mark, g, upon the stake B, at the same distance below e, that 1 is below d. 4. As the line d e is horizontal, the line f g being parallel, to it, is also horizontal : hence let the assistant hold the vane at g, and alter the po- sition of the bubble tube by the adjusting screws till the level cuts that point, and the instrument is adjusted. When the bubble tube is fixed by the maker, (Art. 70) the process is the same as before, with this difference only, that the level must be brought into adjustment by a movement of the cross lines by means of the screws of the diaphragm. Another method of trying the quantity of error of adjustment is as follows : 1. Let two stakes, as C and D (Fig. 34) be placed upon tolcrabl)- level ground, and at a sufficient distance, say 20 rods, assundcr. sight I K:' Fig. 34. 2. Set up the instrument at the stake C, and mark the height of the axis of the telescope upon the stake, at e ; and then causing an assistant to hold a vane at the st^ke D, mark the point f where it is cut by the cross hair, the bubble standing in the middle of tne tube. 3. Set up the instrument at the stake D, and in the same manner * For adju! "•.d of tht TO LEVELS. 139 mark the level of the telescope at g, and the point where the line of sight meets the stake C at h, the bubble being again in the middle of the tube. 4. Measure the distance f g on the stake D, and set it off from e to i on the stake C ; so will gi be parallel to f e, and the line g i will have the same angular deviation from- the true level downwards, as the line g h has upwards. 5. Hence mark the point k exactly in the middle between i and h ; so shall g k be the true level. 6. Cause an assistant to hold a vane at k, and alter the adjustment of the instrument till (the bubble being in the centre of the tube) the cross hairs will fairly cover the point k. Instead of placing the instrument against the nearest stake, it may be placed at one or two chains distance from it, and nearly in a line with them, and the apparent level marked upon each stake. Either method may be taken as is most convenient : there is little or no differ- ence in the correctness. The stakes ought to be squared and left in their places while the survey is going on in the neighbourhood, and the correctness of the level verified by the marks upon them every morning. A third method of adjustment is by means of a sheet of water, and when practicable is both convenient and accurate. At the edge of a smooth sheet of water, or of a ditch of which the water is stagnant and continuous for some distance, drive two pickets at a sufficient distance from each other with their heads just level with the water. Set up the level over one of the pickets, and screw the vane to the staff at the height of the centre of the telescope al)Ove the picket, then set the staff and vane upon the other picket and adjust to it by the bubble tube, or oollimation screws. The instrument will now be in complete practical adjustment for level, curvature of the earth, and horizontal refraction (Art. 24) for any distance not exceeding that of the stakes C and D from each other. These operations ought to be performed in a clear air : adjustments made in foggy weather, or when there is a haze over the ground, are not to be depended upon, on account of the unequal refraction that takes place in such states of the atmosphere. The author once tried his level by ranging to a fixed object across a sheet of ice of about a mile broad, iu the afternoon of a sunny day in April. It appeared to be out of ad- justment arid was corrected ; but it was afterwards found to have been put in error near three minutes of a degree. This was probably occasioned by the unequal refraction of a light vapour which was rising from the ice by the heat of the sun.* manner * For adjusting the eross hairs in the line of colUmation where the telescope ii fixed, see note C at the end of the rolume. w in. 140 im Iiti 1' h r k' ' •■ 1 1 " ; *■** 1 ■' ':'■ iih' ■'} ' r ; ■'^ ■''' ( ■ ii. '1 P i fir- f.- r " '' 1',' ■ - • '■. *. ! S ; SURVEYING. STATION STAVES. 74. . Station staves are made in various ways, but generally of tv/o pieces of wood, one stationary and the other moveable ; the moveable piece being, when the staff is in use, in front. It is about two inches wide and an inch thick, and is sunk in the middle about a quarter or three eighths of an inch in depth and an inch in width, forming a broad shal- low groove along one side of its whole length. The sides of this groove are also hollowed out so as to form a sort of counter check. The sta- tionary piece is of about the same size and made of a form to fit the former, by which means they are connected together. The lower ends are covered with brass plates to prevent wear. There is also a brass milled headed screw running through the stationary piece, and which serves by its friction against the moveable piece to fasten it at any required height. The divisions are marked on both the front and the backside of the moveable piece. Some staves are divided into feet, inches, and tenths of inches, and others into feet, tenths of feet, and hundredths of feet ; the later division is the most convenient. The divisions on the front read from the bottom upwards to six feet, and those on the back begin at six feet nine inches from the bottom, and read from the top downwards another six feet ; making in the whole twelve feet. By this arrangement, nine inches of the length of the staves remain in contact when the moveable one is at its full height. The vcme slides upon the front piece' and should be olackly fitted, so as to admit at one side, a spring to bear against the edge of the staff, which should be of such strength that, without rendering the movement of the vane difficult, it will have suflicient friction to retain it at any part required. It is also furnished with a milled headed screw to fasten it, when necessary, firmly to the staff. Fig. 35 is a cross section of the staff with the vane attached. A A shows the front part of the vane, B B the pieces across the back for connecting it to the staft', e the recess for holding the spring for steadying its n>otion, C the front part of the staff, and D the rear part. The reading on the backside is done by the top of the stationary staff, which, when both staves are on the ground, is just even with the six feet mark. The top of the staff being above the eye it is thinned off to an edge and plated with brass to take away the obstruction to the sight made by the square head of the staff, and to preserve a fine regular edge across the top to read by. Observations are made as follows : — the vane is moved by the hand upon the front staff for all distances below six feet. If the height re- quired is above six feet, it is screwed fast at the six feet mark of the front staff, and the staff with it attached raised to the proper height. The reading will be given by the top of the back staff. STATION STAVES. 141 Fig. 3d. B B These staves are usually made of very straight grained mahogany, inlaid with holly for marking; the divisions upon, and cost, in England, from one pound ten shillings to three pounds. They require careful usage, and on this account, are not so fit for rough and mountainous countries as st. ves of a more substantial kind. A good stu' T such situations may be made by taking two pieces of very toug» . aight grained wood, one of which should be about 2| inches wide by | inch thick ; the other 2 inches wide by 1 inch thick ; the broader piece in front, and the two pieces connected by clasps of sheet iron or brass, passing round the back piece and screwed to the edges of the front one. By this means both pieces retain their full strength, and if the clasps get injured they are easily repaired. The vane slides upon the front piece to the height of six feet, and then the front piece is, if necessary, lifted, with the vane attached, to any height between six and twelve feet. The graduation for the heights above six feet is on the edge of the back piece, its commencement about four inches from the bottom, at which height there must be an index or pointer attached to the front piece for pointing out the height. The numbering begins at six, at the bottom, and proceeds upwards to twelve feet. The graduation may be marked with paint. The wood should first be saturated with warm linseed oil, and then lightly primed with white lead paint. When this is dry the marking may be done with a black lead pencil, (the longitudinal lines being indented into the wood with a carpenter's guage), and the whole varnished with good copal varnish. The pieces should be about seven feet and a half long, so that when drawn out to the full height they will still be in contact for about a foot and a half. ]-l2 SURVEVlNCji. I 4 ■/'■'' i:T- . , \^y ;' T :ii it ■t 1, 1 m m i.!i-'i. If this siair is miido oHiglit tough wood it will be better for rough work than any imported one, and a workman can make it in about two days. Another staff' which is sometimes used is a single piece of light stion«r wood about two inches square, and twelve feet long, and graduated con- tinuously from the bottom to the top. The vane slides upon it and is moved by the hand the lowermost six feet, where it is connected to a small iron rod by a knob and spring, by which it is raised to the required height. The rod is kept steady by a knob at each end which run in a dovetail groove in the side of the stafl'. There is a pinching screw for holding the rod fast in any required position, and there are besides two small spirit levels set into the sides of the stafi'for setting it vertically by. This staff though not so portable as the last, is to be preferred for common use ; its weight has been objected to, but that is of little con- sequence when compared with the advantages. Another staff has been la.tely made, composed of three pieces sliding one into another and being only four feet and a half long when not drawn out. It costs in London about four pounds, but it possesses no advantage over other staves except in its greater portability. Fanes are made somewhat differently by different makers, but they may all be considered under two general forms, — where there is one horizontal line across the face, and where there are three. One of the best of the first kind has both a horizontal and a vertical line across its middle, dividing it into four quarters. Each of these quartt^rs is painted of a different colour, the colours as bright, and contrasting as strongly with each other, as possible. Another plan nearly the same, is for the horizontal line to be in the diagonal of a square, or of a diamond shape figure, the upper and lower portions being painted of different colours. The vane that appears to answer the best in most cases has three horizontal lines accross it, — black, upon a white ground, the middle line small, and the outside ones, each near a quarter of an inch broad, and about an inch and a half distant from the middle one. The vane is about ten inches long by six inches wide. The disadvantages attending the first mentioned 'kind, and the manner in which they are removed by the latter, may be pointed out as follows. The proper horizontal plane from which the measurement is taken passes through the centre of the horizontal hair of the level ; but this plane is not visible, and its exact place at the vane can only be estimated by the judgment of the observer. When the horizontal hair is very fine, the part of the vane which is invisible is so narrow as not to be worthy of much notice, but when it is large or when the levelling is done with open sights with horse-hair for a horizontal hair, the part of the vane hidden, especially if it be at a considerable distance from the instrument, is considerable ; and the line STATION STAVES. \^S upon the vane from which the measurement is taken may be in any part of this hidden space without the observer being able to tell exactly where. But by having another Hne on each side of the centre one, and at a proper distance, and making the stripe covered by the instrument to bisect the space, as nearly as can be judged by the eye, between the outside lines, the central position will be obtained extremely near the truth. The first of these plans is advantageous where the view is much ob- structed by bushes, &c. The large party-coloured face adds to its con- spicuousnessin such situations ; but the latter plan is most conducive to correctness of measurement, and should generally be preferred. Proba- bly, the two plans might be united to advantage ; the vane might in that case be about a foot wide, the central part done with the three horizontal lines, and the upper and lower parts painted of a bright red and yellow, and varnished. The vane must have a square hole through the middle to allow of reading the figures of the staff", it should come fully an inch and a quar- ter below the central line, so that the last inch can always be seen through it. If the vane be made of wood, the sides of the hole must be sloped down to an edge on the back side, and the central line carried quite down to the edge. Sometimes it is continued across the hole by a piece of wire let into the wood, but this is not necessary. Vanes are some- times-made of tin. For common road surveying with a theodolite, a single staff* about an inch and a half wide by an inch thick, with a vane to which a clasp of tin is fastened, for sliding upon the staff', is all that is required. There should bft a light spring in the clasp to create friction enough to hold the vane at its proper place. A piece of paper pasted to a thin board and ruled with ink, makes a very good temporary vane. A new kind of levelling slaves have lately been invented by Mr. Gra- vatt, the inventor of an excellent level, called GravatVs Level, They are described by Mr, Simms, in his Treatise on Instruments, as follows : " Several years ago, William Gravatt, Esq. had constructed for his own use a new kind of levelling-staff', which now appears hkely to come into general use. They have no vane to slide up and down, but the face of each staflf is made broad enough to contain sufficiently large graduations and figures, for the observer to read with certainty to the one hundredth part of a foot, at the distance of twelve chains or more, which is sufficient for most practical purposes, thus securing greater cer- tainty and expedition in the work; for it not unfrequently happened in I using the old staves, that when, by a succession of signals, the staff*- holder had nearly brought the wire of the vane to coincide with that of the telescope, he would, in his attempt to perfect it, remove the vane farther from coincidence than at first ; and we have been informed, that ,f «" if* I*. Fi hi M''^ ¥' I ' i* '; tit , ' } 144 SURVEYING. on one occasion the man held the staff upside down, which introduced cui error of several feet. To obviate these difficulties, Mr. Gravatt pro- posed that the observer should read the staff himself, which is now suc- cessfully practised. " The newly constructed staff consists of three parts, which pack to- gether for carriage in a neat manner, and when opened out for use, form a staff seventeen feet long, joined together, something after the fashion of a fishing rod : the whole length is divided into hundredths of a foot, alternately coloured black and white, and occupying half the breadth of the staff; but for distinctness, the lines denoting tenths of feet are con- tinued the whole breadth, every half foot or five tenths being dis- tinguished by a conspicuous black dot on each side. The whole con- trivance is very succecsful, and in some late levelling operations in which we were engaged, we were able perfectly to read the staff, with only a fourteen inch level, at the distance of twelve chains." These staves are made by Troughton and Simms, Instrument Makers, London, and sold at four guineas. The graduation is done with a cop- per plate on stout paper, which is pasted upon the staff. 1 have one of those papers now before me. The breadth of the part occupied by the lines of hundredths of feet is 0.6 of an inch, and the whole breadth of the engraved part 1.1 inch. The thickness of the lines is 0.08 of an inch, leaving the white parts half as w'ide again as the black. There are four of these broad black lines and five white spaces between each tenth of a foot. The figures which designate the feet, are about an inch, and those for the tenths of feet near three quarters of an inch in length, with broad strokes so as to be equally legible at a distance with the divisions of the staff. In using the staff a bisection of either a black or white line can be made with the cross hair of the telescope very easily, and which produces a virtual division into hundredths of leet. The staflf is constructed as follows : A square wooden tube is made of about three inches wide and two inches deep on the outside, and of such thickness of wood as will possess sufficient strength to bear rough usage, — say about three eighths of an inch. This leaves a square hol- low in the middle of 1 J by 2^ inches. Into this a second tube is fitted, made in the same manner, the wood of which may be about a quarter of an inch thick, except the front piece, which may be somewhat thicker to allow for a recess for the paper. The hollow in this tube is about five eighths of an inch by an inch and three quarters ; and into this is fitted a straight piece of wood. All the pieces are sunk a little in the parts covered with the paper to protect it from wear. On the lower end of the inside tube there is a broad brass spring, carrying a large thumb knob, which, when the lube is drawn up to the full height, drops into a hole in a brass plate fitted to receive it. The solid piece which slides v telescope distance aa open For ro is necess STATION STAVES. 145 U'itliin the tube is fitted with a spring in the same manner. The tube should be so much larger at the lower than at the upper end, that the sliding parts will move freely and fit well when fully drawn out. They should also be well fastened with brass rivets at the upper ends, to enable them to resist the stress they are subject to in windy weather. On the top of the outside tube there are two small spirit levels, at a right angle to each other, for setting it perpendicular by. They are embedded in the wood, and protected from injury by a brass plate. The length of the staff when shut up is about 4.5 feet, and the inner j)arts are drawn out about 3.5 feet ; making altogether 1 1.5 feet. This is a sufficient length for ordinary purposes, but if a longer stafT is re- (juired the tubes must be longer, in which case the levels will have to be let into the side and back at a proper height for the eye, and the wood stiffened behind them with a brass plate. The method of laying I* p ^ '-is to mark the "^ very exactly by a good two foot scale, at every .wot, and then wei, and if necessary, stretch the paper as evenly as possible till it comes to the same length, Avhen it may be fastened with warm paste in which a httle glue has been dissolved. The paper is made little short of the length to allow for this. That which has been described is 1 1| inches in length, which is to be tjtretclied to a foot. To guard against warping, the wood should be taken from a board cut out of the middle of the log ; that is, having the laminae of the wood running across the thickness, in the same manner as in split staves and shingles. The best wood is free straight grained mahogany, but old brutle oak or ash will answer nearly as well. Close grained or tough woods, and particularly such as have a cross or twisting grain, or are knotty, are to be avoided : they are very liable to warp. The wood should be saturated as much as possible throughout with warm linseed oil, and after the paper is laid on, the whole should be well coated with i'opal varnish. Such a staff may be made by a workman in about three (lays. It may be proper to observe that either of the staves heretofore de- scribed may be marked as above ; the only difference being that the front part of the staff must be stationary, and the back moveable ; and that there be means of fastening it at the full height. With common instruments the staff can be read at 5 or 6 chains. In cloudy weather, an eleven inch Gravatt level reads at 6^ chains by a young eye, and by an eye that requires spectacles at 5 chains ; a ten inch telescope of a theodolite, by Troughton and Simms, reads at the same distance ; a seven inch telescope of a small theodolite, at 2 J chains; and an open sight at 1 chain. For rough levelling by long sights, or when the view is obstructed, it is necessary to use the vane ; but wherever circumstances \yiU admit 19 14& 8URVEYIN0. kiti'^'!. r ^■\: ! vi iUiJ*'i m h'i^.i: * u i tl. the new staff should undoubtedly be preferred. If a staff were con- structed to combine the two plans it would be more generally useful than either. 75. We close this chapter with a short account of a sort of cheap wooden instruments that may be employed for laying out common roads. The wood of the bottom part of the compass is upwards of an inch thick, with a cell turned out of it for the needle similar to that in a brass compass ; and there is a brass socket screwed upon the bottom for at- taching it to the staff. The sights are of wood, and fit into mortices, through the ends of the bottom piece, about three quarters of an inch square ; they are about half an inch thick. The degrees are marked upon stout paper pasted upon the ring, or upon a thin plate of cop))er or brass. The needle is a thin light bar similar to the needle of a com- mon pocket compass. The wood should be cut out of the tree with the grain as directed in the last page, first steamed or boiled and then seasoned ; and after being roughly formed, well soaked with warm lin- seed oil as hot as the wood will bear. They should then be laid by till the oil and lithage becomes consolidated in the pores of the wood, after which ihey may be finished, ag£(in soaked with oil, and finally coated with good copal varnish. For dividing the ring ; — Rivet on a small piece of brass to the centre of the bottom, and drill an upright hole in it for the centre point of the compass. Also fit a pin into the centre hole of a nautical sextant, turn off the upper part of the pin to fit the hole in the bottom of the com- pass and place the compass upon this centre. Then fit a ruler to turn upon the same pin, and mark the ring by the degrees on the sextant, as shown in art. 69, shifting the compass at each 60 degrees round the circle. Or, the workman can in a day make the frame of a sextant of six or seven feet radius, and divide the arch with compasses in the same manner as a mill-wright divides for the cogs of a wheel. He must be careful to take the exact radius for the chord of 60 degrees of the arch. For marking the degrees on the compass, if the ring is paper, a drawing pen may be used with India ink ; if it is copper or brass, a steel cutter must be employed, and there should be attached to the ruler a small piece of metal with a slit in it for guiding the cutter. mj iy j^^if iiio The Tripod may be of wood ; the legs connected with a centre piece by mortices and tenons which form joints ; and parallel-plates of brass may be fastened upon the top of the centre piece. The level may be a wooden tube, covered at one end with a plate, having a hole in it for the eye, and having cross hairs at the other end: a bubble tube must be embedded in it, which must be longer and more correct than the small ones in common use by mechanics ; such as will answer the purpose may be bought for four or five shillings. The above instruments may be manufactured for about eight dollars, or ;] ; i ■; ■> >> \ I '\ ifri *^Vi J . \ ,'/ T •vs^. f('j iO I •!': .*! ' lo In'" * ' tn ».,?.. ■f ., y ' t . CHAPTER H. ' ■tiitl/.-: rw!!- /in»t ;-f? III!) » 1 i ^ / ' I • » * » nlllo Mbl/i 19d ^f" I-EVELLIN^ WITH THE BAROMETER. ,,, , : . /,,i- Vid 76. This method of finding the comparative heights of places, is founded upon that property of the atmosphere by which its pressure decreases as we ascend from the surface of the earth. Its introduction is quite modern, and a short account of the successive steps by which the theory on which it is founded, has been brought to its present state of perfection, may not be unacceptable to the reader. w, It is found that fluids press upon the surface that supports them in exact proportion to the area of that surface, — without reference to the area of surface of the fluid so supported. For example, if a vesrel of four feet in depth be filled with water, each square inch of the bottom supports a pressure equal to the weight of a column of water one inch square and four feet in height ; and this pressure is the same whether the surface of the vessel be wjde or narrow, or whatsoever may be its form or area, -w*-^- ••-i* -■-* -.■.■ '-^ r «■ — .;...s'i>.... . ' ■ ■! -■- The bottom of a pond or sea is pressed upon in the same manner ; each square foot of its area being loaded with the weight of a column of water a foot square, and reaching vertically to its surface : it is this cir- cumstance which makes it so very difficult to raise sunken vessels that are embedded under water in the mud. Now, the earth is surrounded with a deep sea (if we may be allowed the expression) of air ; and this fluid is found by experiment to be sub- ject in its pressure to the same rules that govern the pressure of water ; that is, each square foot of the surface of the earth is loaded with the weight of a column of air, a foot square and reaching vertically to the surface of the atmosphere. We cannot directly measure the height of the' atmosphere, so as to enable us to find the weight of this column, in the same manner as we could ascertain the weight of a column of water, but methods have been contrived to weigh it indirectly, without reference to its height* si''} i»ii f i.k, t i ,aj; ■ I'i..; uv^t oni|! 77. If we take a vessel having two branches, as the inverted syphon (Fig. 36), and put water into it, the surface of the water will stand in both branches upon the same level, as at a and b. The reason of this is that there is the same perpendicular depth from a to c, as from b to c ; and the section of the tube ^t c being virtually the bottom of the vessel, the pressur s at c in the opposite directions just balance each pther. I 148 LEVF.M.iNn wirri tfif. nAnoMF.TF.n. ilN,, !(1 r!ii< |..r' n >^l m I*. I ■ '(i li' V 1 i. Vi in 'cj; ;>7i e Fig. 36. K]i 10 I" {,) Superadded to the weight of tho water them is a*so the weight of n column of air, resting upon the surface of the water in each branch oi the syphon, of tlie height of the atmosphere, and of the area of the sec- tion of the tube at c. If the branches of the sypiion be different in size, these columns of air will indeed load the surfaces of the water at a and b with different weights, but, owing to the peculiar manner in which pressure is transmitted through fluids, the pressures on either side of the section at c will be equal to each other ; so that whatever be the area of the surfaces of the water at a and b, they will, notwithstanding an in- equality of pressure of the atmosphere, remain at the same level. ••;•. Here we must particularly notice that the point c is pressed on each side by two different weights; first, by that of a column of water of the size of tho tube at c, and of the perpendicular height from c to b or a ; and secondly, by a column of atmos- pheric air of the same size, and reaching to th^ top of the atmospheric ocean. If now, we can contrive to remove the atmospheric column from the water in one of the branches of the syphon, and can substitute for that column a known weight of some other substance, which will just keep up the equilibrium of the water the same as before, that weight will evidently be the same as the weight of the atmospheric column that has been removed. This can be effected. We can extract the air from one branch of the syphon, as from a to d, and cover it closely at d, so as to prevent the air from returning. 'Fhis takes off ihe weight of the column of atmosphere from that leg of the syphon, the opf}osite column still having its full effect at b upon the other leg. We can also put as much water into the leg d c as will make up by its pres- sure for the loss of the column of air which has been removed. If it is found, for example, that by increasing the height of water from a to e, an exact counterpoise is created at the point c, to the water from c to b with the addition of the atmospheric column, it is evident that the pressure at c, derived from that additional height of the water, is the true weight of the column of air which has been taken off from the branch of the syi)hon c e. This weight or pressure is easily known without having recourse to the mea- sure of the section of the tube at c, because, as already explained, it follows from the known laws of the pressure of fluids that whatever may be the form or area of that section, if a column of water of the perpen- dicular height from a to e does preserve the surface of the water in the ;l) -i' '.Ul fit -i^rrnuK I.r.VEM.INft WITH THE rlAROMCTRR. 149 other leg at b, on a level v/i(li a, tiicn the weight of a column of water of the length from a to e, and of the diameter of the section of the tube at c, is the true weight of a column of air of the same diameter, and of the iieight of the atmosphere ; and by parity of reasoning such an at- mospheric column of any size is always of the same weight as a column of water of the same size^ and of the height from a to e. i . '\i It . 1 1 i.i ''*4i I: external pressure of the atmosphorc. it occurred to him that if thr mercury in the Torricellian tube (ns the instrument was then called) was really supported by the counterpoising weight of the atmosphere, tlu: atmosphere must lie limited in its height, and of consequence the pies- sure would be less, and the mercury partially subside in the higher eleva- tions. To put this to the test he wrote to a friend who lived in another part of France, near a mountain, to make the experiment. He did so and found it as Pascal had conjectured : the mercury stood consideral)ly lower at the top of the mountain than at the foot. This was in 1G4(j. Shortly after this the air pump was invented in Germany, and this in- strument gave a still greater command of experimental means. It was found that by putting the Torricellian tube under the receiver, the mei- cury could be made to rise or fall at pleasure, by pumping out or Icttin^r in the air. All doubt of the correctness of the conjecture that the mercury was sustained by the atmosphere was now removed, and attention be- came directed to the use that might be made of the discovery in the measurement of the heights of mountains. It had been known for some time that the pressure of fluids was regu- lated entirely by the depths and it only remained to ascertain the relative specific gravities of air and mercury, to have the height of a column of air, — allowing the air to be of a uniform density, — that would balance a given height of mercury ; or in other words, the depth of the atmos- pheric ocean. It was thought that if this depth could once be ascer- tained, by simply observing the height of the mercury at the top and bottom, the altitude of a mountain could be found by a single proportion. With this view experiments we^e instituted, rude indeed at first, but Tii;tb /H .?^-'" 79. Little now seemed wanting to complete the practice of mea- MuVELLlNG UiTH IHK BAROIVILTRR. 161 suriiig liuil^hts b^ the huromoter ; but n new and lormidabln difllculty jippeured in the influenco o( variations of trm))er,Mtiire. If flu; lumpe- raturo were always equal, the calculation would be quite simple ; but heat afifects ihe obsorvatioiis in n variety of ways ; and the most diflicult part of the process, and that which has givci o j»reatcst exercise to the ingenuity of learned men, is the making oi proper allowances for the disturbances created by this agent. It was known that metals expanded by an increase of t(»mperaturp, and none more so than mercury. An increase of temperature woidd therefore, by increasing the volume of the mercury, diminiyh its specific gravity ; and of consequence, its height in the tube, under equal atmospheric pressures, would be increased, and vice versa. It was also found that the air was subject to tho same law. The same agent would therefore, by increasing or diminishing the volume of air, increase or diminish the length of the aerial column indicated by the range of the barometer. Investigations of these subjects could only bo cai kicd on by means of the thermometer, but that instrument was too imperfect to be relied upon. Here the subject was dropped for nearly seventy years, when in 1765 it was resumed by M. DeLuc, of Geneva. He commenced by m* king experiments upon the substances in use for filling thermometers tid at length fixed upon mercury as the best adapted for his pu»*nose. With the aid of this instrument he continued a series of experi uuiUs among the Alps for fifteen years, and published an account of tnem in 1772. This publication had the effect of bringing other accurate observers into the same field of enquiry, provided with superior instruments. In 1775, Sir George Shuckborough Evelyn made experiments by comparing trigonometrical with barometrical measurements among the Alps ; and General Roy pursued the same enquiries in Scotland. Since that time Professor Playfair, of Scotland, and LaPlace, of France, both Mathematicians of the first order, have investigated the subject, and probably have left little, if any room for improvement. Professor Leslie, irom whose work in theEncycIopoediaBritannir' ^ riiis account is in part abridged, says that they have examined all the circumstances that can I effect barometrical measurements, and that the great difficulty now to be overcome is to procure good observations, aiid to combine tolerable ac- curacy with expedition. " For this purpose," he says " a very portable barometer is still wanted, — an instrument light and commodious, exempt from injury or derangement, and yet sensible to minute changes of at- mospheric pressure. These properties, indeed, are seldom conjoined, and one advantage must generally be sacrificed to obtain another." We Imay add that this desideratum has lately been supplied; a barometer |has been invented at Paris, that leaves little more to hope for on this 152 LEVELLING WITH THE BAROMEIKII. m%:i !1i I . h ^Ult:-', fl't 1-' 1 li'. \ iH'; ■ 1' « ' 1 ' ■ '' '1 i,<: , ^ '■ < i''r 80. Ill selecting barometers for this service the main object to be kept in view is, that the scale of measurement be truly divided, and have a good vernier attached to it, and that the instrument be not liable to get out of order. Expensive workmanship is not required. One of the best barometers for this purpose is called the Mountain Barometer. It is composed of a common barometer tube standing in a glass cistern of mercury. The mercury is supported at the bottom by a leathern bag : the external atmosphere acts through the substance of the leather, but the mercury from the powerful cohesion of its own particles, cannot be squeezed through the pores of that casing without violent compression. The bag is enclosed within a cylindrical glass box, and on using the instrument th^j mercury is brought up to the same precisi? level by a screw which presses against the bottom of the bag. To enable the operator to observe the proper height to bring the surface of the mer- cury to, there are oblong horizontal apertures on the opposite sides of the outer case, through which light can be seen, and also the surface of the mercury in the basin. The mercury is adjusted for observation by raising it with the screw, till the light admitted through the aperture appears only a very thin line. The tube of the barometer is enclosed in a brass tube with slits longitudinally about two tenths of an inch in width, in front and rear, exhibiting between them the column of mercury. Along the edge of one of these slits are marked inches and parts for determining the height of the mercury. There is also another hollow tube that slides over that last mentioned, carrying a vernier which gives the height of the mercury to the thousandth part of an inch. It is moved by a rack and pinion, and is besides, sometimes furnished with a screw for making very delicate movements, somewhat after the manner of the tangent screw of a sextant. In taking an observation, the bottom ot the vernier tube is brought exactly into a horizontal line with the top of the mercury. A lens of about an inch and a (half focus is used for observing with, and which also serves for reading the vernier. A thermometer is attached to the instrument for the purpose of indica- ting the temperature of the mercury, which from the heat of the hand in carrying, or the influence of the solar beams, is commonly warmer than the external air. The barometer is suspended in a vertical direc- tion by jimbals from a tripod, which serves also for a case to put it in for carriage. In putting it up for carriage, the first thing to be done is to screw up the mercury from the bottom, so that it fills the tube to nearly the top ; taking special care to leave a vacancy of about a quar- ter of an inch, to allow room for the expansion of the mercury in case of an increase of the temperature ; as without such a precaution the tube would be liable to burst. It is then taken out of the jimbals and slowly inverted, and put into its case, which is formed by the legs of the tripod when shut together. The whole is then put into' a strong leathern case LEVELLING WITH THE BAROMETER. 163 with straps for carrying. It is carried diagonally across the breast of a man, with the cistern upwards. In setting it up for observation, — take it carefully out of its case, using care to preserve its diagonal position, with the top downwards. Then set up the tripod, and after turning up the instrument into its pro- per position with a moderate motion, put it carefully into the gimbals. After this, slack the screw at the bottom, and let down the mercury for the observation ; always observing before taking it out of the gimbals to screw it up again, so as to fill the tube, leaving a small vacuity at the top to provide for any accidental expansion as before observed. The rule to be observed is, never to allow it to be out of its perpendicular position, without having the mercury screwed up to fill the tube ; and in carrying never to permit it to be horizontal, or with its top end the highest. The reason of these precautions is, that the great evil to be guarded against is bubbles of air getting into the tube. Whenever ihis happens the barometer is useless until it is re-filled by the maker. While it is kept in an inverted position this cannot happen, because air bubbles will not make their way downwards ; but if it be inclined in the opposite direction, so that the mercury, by falling to one side of the cistern, lays bare the lower end of the tube, the air enters at once, and the instrument is spoiled. This is one of the best instruments, (i^ not the very best) for these purposes that has ever been invented ; the only ob- jectipa to it is its weight ; it weighs from ten to fifteen pounds. j? r •»»*; 81. A portable barometer has been invented in France, upon the principle of an inverted Syphon, or common wheel barometer. The shorter branch is sealed hermetically, leaving only a very fine capillary hole for the admission of air. The principal branch is contracted in its lower part, so as to let the mercury pass somewhat slowly, which is a guard against the passage unvvards of air bubbles. It also has a longer vacant space at the upper end thanis common, so that when the instru- ment is inverted, that branch holds all the mercury, leaving a very small space at its lower end to spare. It is therefore impossible that air can get into the tube while it is kept in this position. When it is turned up for observation, the short leg of the Syphon must be kept upwards ; the bend of the tube is soon filled with mercury, ancj the danger of air bubbles is past. It should also be turned steadily and pretty quickly ; as in that case the mercury descends in a compact body and expels the air before it. If it is turned timidly and slowly, or if in the act of turning it gets a shake, the mercury will incline to separate and run down the lower side of the tube, leaving a vacancy on the upper side by which the air will ascend and get mixed with the mercury. This will seldom happen under good management, but when it does happen, the air can, by a little shaking of the instrument, be worked out again 20 II'' !> : t f:1 ¥ m i-U< i4:-^r ; ;t- i' 154 LEVELLING WITH THE BAROMETER. when it is inverted. It must be extreme carelessness that allows it to get above the contracted part of the tube, but when such an occurrance takes place the instrument must be refilled by the maker. The two legs of the Syphon are close together, and the whole enclosed in a brass tube of about an inch in diameter, with slits in it for seeing the mercury through. The graduation is on the brass tube, which is numbered from a zero point in the middle both ways, and is furnished with verniers above and below for reading off minute divisions. The distances of the upper and lower surfaces of the mercury from the zero, are added together for the whole height of the column. This is as light and useful an instrument of the kind as we can per- haps hope for, its only disadvantage is in the smallness of the range of mercury, which is only half of that in the mountain barometer. It reads, however, to tenths of milimetres, which are about 4 one thousandths. of an inch, and an error of that extent would produce an error in height of only from three to four feet in a thousand.* Even this error may be much reduced by taking a mean of several observations. This is effected by throwing the barometer a little out of the perpendicular, and allow- ing the mercury to settle again, when it will take nearly the same position in the tube as before. This operation may be repeated as often as necessary, and the mean of all the observations taken for the true alti- tude. For carrying over rough or wooded countries, the Syphon Baro- meter is all that can reasonably be desired. It is kept in a stout leathern case, with a strap for slinging it across the breast, in the same manner as the mountain barometer ; but in rough ground or thickets, the best way of carrying it is to grasp it in the middle in one hand, — the other hand being at liberty to clear the way. It can be carried in this man- ner more safely, and with less fatigue than in any other. Its weight is from four to five pounds. S2. There is another barometer sometimes used for taking altitudes, which consists of a straight tube cemented at its lower end into a wooden cistern, sufficiently tight to hold the mercury without preventing the access of the external air. When inverted for carriage, the tube is filled with mercury, and is closed at the bottom with a piece of leather, which is pressed against it by a screw that goes through the bottom of the cistern. The parts are so arranged that when the instrument is held in an inverted position, about thirty degrees from the perpendicular, a very small part of the end of the tube is void of mercury. By this means room is left for an expansion of the mercury upon a rise of temperature; but unless great care is taken on turning up the instrument for observa- ' \ A Diilimetre is .039371 Engliih inehti. •>(;: 'a rifi, i,;i!i^ alini r, ^-i .fjfit; i]/; LEVELLING WITH THE BAROMETER. 155 us man- tion, a bubble of air will find its way up the tube. In using this instrument, the first operation is to place it inverted at about twenty or thirty degrees from a vertical position, while we withdraw the screw which closes the end of the tube. Then turn it over with a regular and moderately rapid motion and all will be right, in putting it up after an observation, the process must be reversed : it must be first inverted, and then stopped by the screw, taking care to l.j. As the constant number, 0144765, is to the difference betivten the loga- rithms of the barometic columns, at the two stations, so is 90O feet, to the elevation required. For example, suppose the barometer to stand at the bottom of a mountain at 29 inches, and at the top at 27 inches ; the difference of the logarithms of these two numbers is .031634, and the work stands thus: As .0144765 : 900ft. : : .031634 . 1966.68 Ajet, the height of atmosphere due to the difference of pressure between 29 and 27 inches. Now, the two first terms in our proportion being in every case the same, it is not necessary to be at the trouble of a formal operatioif of the rule of three ; it will answer equally well to divide the second term by the LEVELLING WITH THE BAROMETER. tirst, and use the quotient as a common niulti|)lit;r to the third, lo be appHed in all cases. 'Atv-v >^«,m «^ .. '. ..<., ,,,t .,. . , ; j.i.v.. > In the present instance the common multiplier is ^jj^Jc^ = 62170; *'a very tolerable approximation" says Professor Leslie, " at all seasons for a northern climate, and quite accurate indeed, if the mass of inter- vening air had a temperature of 46 Fahrenheit's scale." ->. In 1753, Boguer, a French Mathematician, deduced a rule from the comparison of more than thirty distinct observations on the Andes, in South America. "It is, that the difference between the logarithms of the mercurial columns at the two stations, being diminished by one thirtieth partf and the decimal point shifted four j^luces to the right, will express the required elevation in toises.^^ : ? « " Since the English is to the French foot, nearly as fifteen to sixteen, the rule would be accommodated to our mea- sures, and the result expressed in feet, if that logarithmic dift'erence v^'ere multiplied by 62000," agreeing very nearly with the rule of Dr. Halley. Fig. 37. i;!« C 86. These methods depend on the supposition of the relative density of air, and mercury being only affected by a change of pressure. The modifications induced by tem- . perature has not been taken into account ; but it is evident that the degree of heat of the atmosphere must materially ; influence the results. For illustration, let us suppose that the : whole height of the atmosphere is represented by the line . ac, fig. 37, and that a b represents the height of a moun- ' tain on the surface of the earth : also, suppose the baro- meter be observed at b to stand at 28 inches, and at a 29 inches. Now it is evident that the aerial column that produces the pressure of 28 inches at b, is that from b to c ; and that which produces the pressure of 29 inches at a, is the same column from b to c, with the addition of the co- lumn from a to b. The column from a to b is therefore that which by its weight causes the mercury to rise the additional inch in the barometer ; or in other words, the : column a b is equivalent in weight to a perpendicular inch • of mercury of the same diameter. But air is known to have its specific gravity materially reduced by increase of ; temperature. In such case, the height of the column a b, (the weight continuing the same) would be increased ; that is, the length of a column of air, a b, of a given diameter, aiid weight, must be greater when it is warm, and conse- ; quently light, than when it is colder and heavier. It follows, i therefore, that if on the elevation of a barometer from a to b ;•♦' '; : J v>i\ I -liJii Js i!i,ii' •■■t-^ i w . "'V 111: iiv t! : (' I * ' > ' 1 ; |-- ♦ • 1 , ':. t r ■ :')■• ' ■ '. ■ I 158 LEVELLING WITH THE BAROMETER. ' I in cold weather^ it suffers a depression of one inch, the point at which it would suffer the same depression in warm weather^ would be as much above b as would be necessary to make up the same weight under the circumstance of the diminished specific gravity of the air. If, for example, it has been found that at a certain temperature of the air, the height from a to b is 880 feet, but that the column of air has subse- quently expanded one twentieth part of its length, it will require 924 feet of the expanded column to produce the same effect upon the baro- meter. That is, if it required a rise of 880 feet to sink the mercury an inch in the former circumstance, it would require 924 feet in the latter. The same agent also produces changes in the specific gravity of the column of mercury in the barometer, and thus affects its height. For instance, if under a given pressure of the atmosphere it stands at 29 inches, and it be so expanded by increase of temperature as to require 29| inches in length, in the tube for the same mercury, it would, allow- ing the pressure to be unchanged, stand at 29^ inches, — the same atmos- pheric pressure supporting the same weight of mercury as before, though of a greater bulk. Changes such as these are constantly taking place, and though small in amount, would, unless properly allowed for, produce a great effect upon the result. Dr. Halley was acquainted with the general fact of these expansions, but as the expansion of the mercury, and of the air, affect tlie result in opposite directions, the one making it less, and the other greater than the truth, he was of opinion that these opposite errors would compensate each other. It was, however, soon discovered that a perfect compensation took place only in certain tem- ])eratures, and that general rules required to be framed with reference to the accidental variation of circumstances. When this came to be understood, it was found to be necessary that the expansions of air and of mercury, by increase of temperature, should 1)0 accurately known. It was also desirable that some certam tempera- ture should be assumed, at which to ascertain their respective gravities, which should serve as a standard of reference in all computations, and to which the general rule.s shoidd be adapted, — leaving the allowances for increase or diminution above or below the standard, to be added to, or subtracted from, the height as brought out by the logarithmic process. As the temperature of freezing water was made the zero of most ther- mometers, it seemed the most convenient for the purpose, and accor- dingly that temperature was fixed upon in the construction of rules. About the year 1775 General Roy instituted a series of experiments on these subjects, and found that " for each degree on Fahrenheit's scale, mercu'v expands the 9700th part, and air the 435th part of their respective baihS. It further appeared that the atmosphere has its tem- perature, almost uniformly, diminished at equal ascents; and that the logarithmic difference, reckoning as integers the first four digits, LEVELLING WITH THE BAROMETER. 159 expresses in English fathoms, the height of an aerial column as cold as the point of congelation." This is evidently the same as multiplying the logarithmic difference hy 60,000, for the height in feet. Subsequently to this, M. Biot, in France, in conjunction with M. Arago, instituted a series of careful experiments, and "thence infer, that in the latitude of Paris, at the point of congelation, air, under a pressure of 29,922 English inches, is 10463 times lighter than m*ircury at the temperature of water at its lowest contraction." As the tempe- rature of water at its lowest contraction is about 8 degrees of Fahrenheit above the freezing point, this mercury had about one 1212th part less specific gravity than if it had been at the freezing point ; hence the weight of air compared with that of mercury, both being at the freezing point of water, was as 1. to 10471.633; or 872,6359 feet in height, of air, was equivalent in weight to one inch of mercury. i *-.. ;;, ..,!, 87. Taking these data for our guide, the steps to be pursued in practice are as follows : — We must first make proper allowances for the effect of difference of temperature upon the lengths of the mercurial columns. It appears from General Roy's experiments that mercury at the temperature of 52 deg. of Fahrenheit expands one 9150th part for each degree ; but the cen- trigade thermometer being more convenient, is commonly used for these purposes; and this expansion will give one 5082nd part for each centri- grade degree. Hence the length of the column divided by 5083, and the quotient multiplied by the difference of temperature between the stations, in centrigrade degrees, gives the quantity which it has length- ened or shortened by increase or diminution of temperature. As the lower station is always made the point of reference for height, this operation is performed upon the column at the upper station. When its temperature is above that at the lower station, the allowance is to be subtracted ; or, which is the usual case, when below it must be added. By this means we obtain the length that the column of mercury ivould have^ if the temperatures at both stations were the same, a*. ^^\v\\ vv^v^\l\> The next operation is to find the height corresponding to the corrected difference of mercurial pressure between the stations. Referring to M. Biot's determination of the relative weights of mercury and air, and following the method of Halley,* we get for the logarithmic difference for the first term of the proportion .014514, answering to an inch of mercury ; both air and mercury being supposed at the freezing point of water. Whence, 872.6359 divided by .014514 gives 60123, the co- efficient adapted to common logarithms, and adjusted to the force of s ', * Mr. SomerTille gives the proportion between the density of air and mercury as I to 10477.9, cpn* stquently the co-efticicnt would, according to this proportion, be 60160. 160 LEVELLING WITH THE BAROMETER. h J' It tr i Ki attraction at the level of the sea ; differing only about one 400th from tlio coefficient determined by General Roy, and ''scarcely differing sensibly from tiie quantity which Raymond had deduced from very numerous sets of experiments made by him in the Pyrenees."* We then multiply the difference between the logarithm of the mercurial column (takin*' the corrected height of the column at the upper station) by the co- efficient, which gives the altitude in English feet, on the supposition that the temperature of the air is at the freezing point. The third operation is to correct this elevation for difference of tem- perature of the atmosphere. It has been determined by General Roy, (Art. 85) that air expands one 416th part for each degree from zero to 92 of Fahrenheit, which is equivalent to its 23 1st part for each centrigrade degree. It is therefore only necessary to add to the altitude already brought out, its 231st part for each centrigrade degree, or one 4*6tli part for each degree of Fahrenheit, th .t the mean temperature of the air is above the freezing point of water. The mean temperature is found by adding together the degrees at the upper and lower stations, and taking half the sum. If the mean temperature be below the freezing point the allowance must be subtracted from the approximate altitude brought out by the second operation. Professor Leslie, the writer of the article before alluded to in the Encylopoedia, gives a rule founded on the above reasoning, but with a slight alteration in the num- bers, to facilitate calculation. He says, *' it will be sufficiently accurate, tilt better data be obtained, to assume the expansion of mercury by heat as equal to the 6000th part of its bulk for every centisimal degree, while that of air is twenty times greater, being an expansion for each degree of the 250th part of the bulk of this fluid." He also uses for his con- stant multiplier 60000, the same used by General Roy. His rule is as follows '. ill-- - "v^M ■ ■' ' "" lUHijii '.tV'ii •'•Hi \ tr.i tf'riitii'K^' i ■". " 1st. Correct the length of the mercurial column at the upper station, adding to it the product of its multiplication into twice the difference be- tween the degrees on the attached thermometers, the decimal point being shifted four places to the left. 2nd. Subtract the logarithm of this corrected length, from that of the lower column, multiply by six, and move the detimal point four places to the right, the result is the approximate elevation expressed in English feet. 3rd. Correct this approximate elevation, by shifting the decimal pmt three places to the left, and multiplying by twice the sum of the degrees on the detached thermometers ; the product beiftg now added will give the true elevation*^^ '••■ '*-■ ^^ ........ ,^vv.^».*vt- tw»ioutf iw,. * Dr. Halley's method of finding; the first term of his proportion was by a compensation of errors »< expUincd Art. 85 ; but the proper method is to divide .4342945. the modulus 0f the system of logarithmi by the mercurial height. In this ease we divide .4342955 by 29.922 inches. ' "^ • ' ' - >•> 1 ' Th of the Th( Th< ing by sum ol adding The being i In \\ higher the cas cury wi the qua The peratun express( general! acquaini mean su The aut explanat 88. ing the loosely 50OOih, 9000th f heit; wl perature. The i subject : Thefij tile secoj one degrl • 1' . I • It must ii °««ree» betvJ ''7 niultii>lyii[ ^ Thi. Ta^ LEVELLING WITH THE BAROMETER. 161 n tho isibly eroiis iltiply aking e co- n that ' tem- l Roy, ero to igrade ilready 4 '6th of the iture is tations, 3VV the :)ximate ilie, the s a rule le nuir- cc urate, by heat ;e, while degree \\s con- ile is as station^ ince be- int being at of the places to iishfeet. nal j5oi«t £ degrees I give the m of errors a« of logarilhnu The first of tlieise operaiidHB is the same aB adding one 5000th part of the length of the column for each degree. The second is evidently multiplying by 60,000. The third is multiplying bv twice the sum of the degrees, and divid- ing by 1000, and produces the same result as multiplying by hnlf the sum of the degrees (the arithmetical mean) and dividing by 230, or adding one 250th part for each degree of mean temperature. The alterations in the multipliers are only to allow of the divisions being more conveniently performed than otherwise.* j In the first of the above operations, it is taken for granted that the higher station must always be colder than the lower. This is generally the case, but sometimes it is warmer, and when so, the column of mer- cury will be lengthened ; and the correction must bfe made by subtracting the quantity brought out by the rule. The correction brought out in the third operation, if the mean tem- perature is below the freezing point, must instead of being added, as expressed in the rule, be subtracted. The degrees below zero are generally written algebraically with the minus sign, and by persons acquainted with algebra the term adding, is understood in such cases to mean subtracting, but persons unacquainted with this might be misled. The auther has committed no mistake, he has oniy not been sufficiently explanatory for persons who do not understand algebra. ,, ,.» 88. The reader will have perceived that the foregoing rules for find- ing the corrections are, for convenience in the calculations, somewhat loosely constructed. The expansion of mercury is assumed at one 5000th, and of air at one 250th for each centrigrade degree, or one 9000th for mercury, and one 450th for air, for each degree of Fahren- heit ; whereas the expansions vary in a slight degree according to tem- perature. The following is the result of General Roy's experiments on this subject : The first column shows the temperature by Fahrenheit's thermometer ; the second, the expansion of mercury, and the third, that of air, for one degree of rise of temperature.f - . " > ' ^iii n w:! ; i .! h vi-iut Nior.fjf." ' > ti" h'^y •v':'j^. "■•',". I'll •iJi 8J.T mo I * It must not be forgotttn that the d*i;r«et of temperature are those of the centrigrad* $caU ; that is 100 degree* iMtweeo the freeiiDg and boiling points of water. Fahrenheit's degrees are turned into centrigrade by multiplying the degrees «6ott or btfow the fretting point b/ 10, and dividing the product liy 18, aind l'l«f eCTMi t Thii Table is computed from Tables 1 and 5, in Oregory's Mechanic;, Article 503, 1st Vol. ;>« r'{ J." X. \r. $ [■ li. > I l!|t n' M t\- :vi i 162 LEVELLING WITH THE BAROMETER. Temperature in Degrees. Expansion ot Mercury for 1 Degree. Expansion of Air. 2 1 649A 12 R610 1 469 1 447 22 H740 32 I M7a ' w '■" 42 1 62 I 9149 1 a9s 62 I 93»fi 1 384 72 82 1 9407 1 .^,,, ;, 359 ' 1 9MS 1 396 92 1 9764 1 413 Average I 90«a 1 416 1 ■'l:t *v, . *!«>! 'Ml" > 1, A,V[: "M f! ••1 I KV •'•Ml ii' ■*■ >v. 5i<- i'''ti, MI » f ■, :,>liK-:!' Again, 60,000, is on account of its convenience, a favorite multiplier for the logarithmic difference of the barometric heights ; it being only necessary to multiply by 6 for feet, or for fathoms, merely to shift the decimal point. But neither is this perfectly correct. The experi- ments of M. Biot gives it 60,123. Consequently the result will, by the rule, be rather too low. To remedy these trivial defects, the following table has been con- structed by Mr.jSimms, author of a treatise on Mathematical Instruments. In this table the multiplier of the barometic heights, is exhibited for each degree of Fahrenheit's scale, and adapted to the temperature of the atmosphere, so as to give a result requiring no correction on that account. The correction of the variations of the height of the mercurial column, caused by expansion or contraction, by change of temperature, is exhibited in another coulumn, and in a third, that owing to the cen- trifugal force from the rotation of the earth. The first column of the table, headed S, contains the sum of the heights of the detached thermometers by Fahrenheit's scale. The second, headed A, contains the logarithm of the multiplier adapted to the mean temperature exhibited in col. 1 ; that is to say, to one half of the given degrees. The sum of the heights instead of the mean, is given in the tablj for convenience. Sixty degrees for instance, is the sum of, perhaps, thirty-five at the lower, and twenty-five at the upper station ; the mean is thirty, and to that temperature the corresponding multiplier is adapted ; but the temperature is given in the column as sixty degrees (doub reason itself. iongin, her stc numbe The cols. 3 betwee latter b from thi produce subtract Thus a^ number logarithr of tempi Also, 1 rotation and col. ( produce latitudes not worti ' .- h,j *■ '-^ - WKWr^t; j -. i .' ■^■■TiXiM^rrs^iCrTr-^- ■' ■ V. rT.Trrr.=--fjx ' '•■■r'-rr.'j:^ •■■•,.»tt« ■-> y- . 1 — ■-— ! 1 -«. i * 1 cf-r.* {^.rf Oi '> ' ■^r^ VS ►'-' C ; ;■; ■*'• f,. !JI f%r O' ,'-'1 'ij* ""■ 1 1 ■ " ^ » • r *■ t .— l&l LEVELLING WITH THE BAROMETRR. ^fHa t •■ Plifli V .' i. ■ i I' ■ w *■ I ■ * ^4 I 2 QQ n: t2. be 52 o 3 a. E o U 0) u o o s .J o a, o «-> B o la U t^ O "Tf" •- 1^ »— »— ^ — o — ir: r* CO 05 o 05 CO I- :o — o o o oooo oooo o o o o o • vs r* «k •> o o o o o o o •■ A #« •% CO CO CO (SO -^f >o 00 ^ -f r^ ■ 2 . Im Cfl X CQ u S 2 2 O rt Scq L. (U o Q o -i* 05 CO r* o o o —< <-• o o O O O O O O O O o o o o o G^ CD O >0 05 5^) G^» GO CO GO o o o o o o o o o o o o o o o iGO CO G^) CO — Uf ^ ^ Uti CO '8SS8S o o o o o r« w «« «« r* o 1 . , ; . ^0 05 Tf CO CO CO r^ h- O O Q O C O O O O O O O O o o ^ •• »« •> ^ o SfO '-< G^ 00 ■'^ kO CO f^ 00 05 O^S*»G0-* ^COh»C005 r* F-« CO 00 05 05 o o o o o !?= C/J CO CO CO CO CO •rr* 05 CO CO c» O C — — G^) G^) r* G<» 1^ r-< |0 '— lO o »o (>* f— (;0 O O 05 -f* CO GO r- C) GO GO -?• -f* ^f '^3 ^ «5 CO COOOCOCOCOiCOODCOCOCO •s •% I c* CO CO CO CO CO v% «% «s r« 05 CO r- '— CO '-' CO O >0 05 i-^ t- CO CO or CO CO CO CO CO r« r> ro «<« «> I, .. 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J( MJ.-' ').|J t'' .\ ■ 1 ■' • orMDr T ■ iirtT • '.''.) '3H- >i.,-wl. s ;.^:'.^,,'. w it )''■•- M\: I: (lit ':! • **■ •^ ■ ■ ■ it it" -i N-i;! ^;l ■ vm '1 t . ' M ' i >.. , '.:- ni 166 LEVELLING WITH THE BAROMETER. The rules for computing by the foregoing Table, is given by Mr. Simms, as follows : — " Observe at the same time the height of the mercurial column at both the stations, whose difference of elevation is required, and also the temperature of the instrument by the thermometer attached thereto; ^nd that of the surrounding air by another, called the detached ther- mometer.* " The computations for deducing the difference of height from these observations, is rendered very easy by means of the foregoing Table, which is computed by the formula given by Mr. Baily, in his volume of Astronomical Tables and Formulae, and is similar to Table XXXVI. in the same volume, but more extended. " The following is the method of using the Table. "Find in the col. headed S the sum of the degrees read on the detached thermometers at the two stations, an«i take out the corresponding num- ber from the adjoining column, headed A ; next, in the c lumn D, find the difference of the degrees read on the attached thermometers, and tcike out the opposite number in the column 6 ; lastly, from the column C, take out the number opposite the latitude of the place of observation found in the column L ; then, " When the upper thermometer reads less than the Imver one, " To the number called B, add the log. of the height of the baro- meter at the upper station, and subtract their sum from the log. of the height of the barometer at the lower station, and call the remainder R ; then take out the log. of R and add it to the numbers A and C, and the sum, ^-ejecting the tens from the index, will be the log. of the difference of the altitudes of the two stations in feet. " fVhen the upper thermometer reads more than the lower one. *' From the log. of the height of the barometer at the upper station, subtract the number called B, and subtract the remainder from the log. of the height of the barometer at the lower station, and call the re- mainder R ; then take out the log. of R, add it to the numbers A and C, and the sum, rejecting the tens from the index, will be the log. of the difference of the altitudes of the two stations in feet. , r:-r~.^: ' •• EXAMPLE. ,^ ;.;. C ...- ' . :-> — . ■:■ -■• 3 'J _. " The following observations were made in the transit-room of the Royal Observatory, and at the base of the statue of George II. in Greenwich Hospital, latitude 51 dcg. 28 min. to determine the difference of altitude. , ,^ . , . ,. _ ,^ ,,, ,. ^^ * Thff mean result of seTer«I obscrrationi should b* Uken as that to b? used fur computation. , 90. Ai h^uced frof LEVELLING WITH THE BAROMETER. 167 Upper Station. lower Station. m of the e II. in lifference Detached thermometer - - - Attached ditto - - - Barometer, mean of 5 obs. - ■ A = 4.81719 B = C = 9.99976 log. of bar. upper station, 71deg. 5min. 71 deg. 5 min. 70 70 29.870 inches. 30.014 inche& .:> I'l log. of bar. lower station, 7.31806 log. O.OOOOO 1.47524 1.47524 1.47732 R = 0.00208 Sum 2.13501 log. of 136. 46 feet, the difference of altitude. " The difference of altitude, as obtained by levelling with the spirit- level, (Phil. Trans. 1831, Parti.) = 135.57 feet, differing only 0.89 feel from that obtained above. The observations should be made simul- taneously at both stations, but to do this, two observers and two baro- meters are required. When there is only one observer, he should, after making his first observations, lose no time in hastening to his second station, to make his observations there : which, if done quickly, and the atmosphere is undergoing no change at the time, will answer nearly as well as if simultaneous observations were made by a baro- meter at each station." 89. The foregoing rules require the help of logarithms. It is desir- able, however, to approximate at least to barometric measurements without such aid. A very simple rule for this object, has been given by Professor Leslie, in his Elements of Geometry. It is, ".^s the sum of the mercurial columns^ is to their difference, so is the constant number 52,000, to the approximate height in feet. This mode of calculation may be deemed sufficiently accurate for any altitude that exceeds 5000 ft. : but for greater altitudes the approximation may be carried further by adding lo the height brought out the cube of its two thousandth part." This rule is drawn from an algebraic formula, expressive of some of the properties of logarithms, and exhibits only the principal part of the formula, which causes the result to be a small matter under the truth. It is also to be observed that i is predicated upon the supposition of a temperature at I zero, and will require the same allowances for temperature as the other rules. , , ■ , ... 90. Another rule of this kind, is that of Dr. Robison. It was de- I duced from the tbllowing considerations. ' A'^^ >. *; 'fev- HJ ktion. 168 LEVELLING WITH THj: BAROMETER. ifi i I tit i -!" I I li'^-'l ;U "i: " 1. The height through which we must rise in order to produce anv fall' of the mercury, is inversely proportional to the density of the air that is, to the height of mercury in the barometer. 2. When the barometer stands at 30 inches, and the air and quick- silver are of the temperature of 32 degrees of Fahrenheit, we must rise through 87 feet to produce a depression of one tenth of an inch. 3. But if the air be of a different temperature, this 87 feet must be increased or diminished by about its 414th part, or 0.21 of a foot, for every degree of the difference of the temperature from 32 degrees. 4. Every degree of difference of the temperatures of the mercury at the two stations, makes a change of 2.833 feet, or 2 feet 10 inches in the elevation." ^ Hence the following rule: — 1st. Find the mean between the temperatures of the air at the upper and lower stations, and multiply the difference between it and 32, by 0.21 — the product is to be added to 87, if the temperature be above 32, or subtracted from it, if below: then this sum, or difference, is the cor- rected height through which we must rise to cause the barometer to fall from 30 to 29.9' inches. 2d. Multiply the corrected height by the difference of the barometric heights in tenths of an inch, and callthe product the first approximate height. ^ 3d. then we have the following proportions: — As the mean between the barometric heights, is to 30, so is the first approximate height, to the second approximate elevation, 4th. Multiply the difference of the mercurial temperatures by 2.833; and if the upper barometer has been the warmest^ add it to, or if the coldest, subtract it from the approximate elevation last brought out, aud the result will be the correct elevation. . ^ , . .i , 91. The last rule is founded on the supposition that the lower baro- meter stands arthe sea level. If it is at a higher level, the rise neces- sary to produce one tenth of an inch of depression of the mercury io the barometer, is^ increased proportionally to the^ logarithmic difference answering to a difierence of depression of one tenth of an inch at that higher level. < . " ' By means, however, of the following table, the rule may be accom- modated to varying circumstances. The table is formed by multiplying the logarithmic difierence answering to one tenth of an inch at the different heights laid down in it, by 60,346, which is the coefficient, or common multiplier used by Simms, and which I take for granted is more correct than 60,000, the number proposed by Leslie. ..; ., ,,:, By thi baromete inches) 8 inches, 9j lower bai that the c we use tl elevation 27 inches The ri founded elevations small to ties : it s| number, femembei 92. "I amples. baromete malthermi while on the attac 8-8 degre , •Itis8eld(L When the air il I and the detacti LEVELLING WITH THE BAROMETER. 169 .K ! ! •... V- .t ' ,11 MH! Height of lower Barometer. Rise for a de- presionofone tenth of an inch. 30 ^nches 87.30 feet. 29 do. 90.32 28 do. 93.55 27 do. 97.02 26 do. 100.74 : 25 do. 104.80 By this table, the height to be raised to depress the mercury in the barometer one tenth of an inch is, (when it is on the sea level or at 30 inches) 87.30 feet ; when at such height as to bring the mercury to 29 inches, 90.32 feet ; when to 28 inches 93.55 feet, Sic. Hence, if the lower barometric station be of such an elevation above the sea level that the ordinary height of the mercury is between 29 and 28 inches, we use the number 90.32 instead of 87 as given ia the rule ; or, if the elevation be such that the ordinary barometric height is between 28 and 27 inches, we may use the number 93.55, and so for other elevations. The rule of Leslie (Art. 89) is the most convenient, and being founded on the logarithmic principle it requires no alteration for varying elevations of country. The constant number 52j<^00, however, is too small to agree with the results of Biot's determinate ;n of specific gravi- ties : it should be 52,227. With this trifling ditTei<^nce in the constant nunnber, the rule will probably be more correct, and is very easily remembered. 92. " In illustration of these rules, we shall subjoin some real ex- andples. General Roy, in the month of August, 1775, observed the barometer on Caernarvon Quay, at 30.091 inches, the attached centesi- mal thermometer indicating 15.7 degrees, and the detached, 15.6 degrees ; while on the peak of Snowdon, the barometer fell to 26.409 inches, and the attached and detached thermometers marked respectively, 10 .0 and 8.8 degrees."* ■ J M * It is seldom that the attached and detached thermometers wiH stand exactly at the same height. When the air is getting warmer its temperature changes faster than that of the mercury in the barometer, and the detached will be higher than the attached thermometer, and vice versa 75 I: '■' ' ■!• jp,":| I* 170 LETELLINO WITH THE BAROMETER. *' Here^ twice the difference of the attached thermometers is 1 1.4 de- grees ; and 26.409 multipHed by 11.4 and the decimal point shifted four places to the left, gives for the correction of the mercurial column .031 inches ,; which added to 26.409 makes 26.440 for the corrected height. Then, we have, logarithm of 30.091 = 1.4784366 logarithm of 26.440 = 1.4222460 ?^l I 1 M J' ' i' 1 li I'i , ^ I; r !■ ' « DifTerence - - - Constant multiplier .0561416 , 60000 Approximate height 3368.496 " For the second correction ; twice the surti of the detached thermo- meters is 48.8 degrees, which multiplied by 3368.49 and divided by 1000, gives 164.38 feet, which added to the approximate height gives 3532.8 for the final result."* > The same calculated by Simm's method is as follows : Upper Station. Lower Station. Detached thermometer, Fahrenheit scale, 48 degrees 60 degrees. Attached do. . . - 50 do. 60 J do. Barometer, - - - - - 26.409 ins. 30.091 ins. A = 4.80137 ■'■' B = .000440 ' ■ log. of bar. upper station, 1.421772 Sum, log of bar. lower station. 1.422212 1.478436 Barometric difference, 0.066224 8.74991 logarithm of b^irometric difference. R Ul> 3.55128 = log. of 3559 feet, the height of the mountain. This is higher by 26 feet than the former determination, but the com- putation appears to be founded upon more exact data. If v/e follow the rule of Leslie, and take the expansions of air and mercury as deter- mined by Roy, (Art. 88) and the common multiplier 60123 as deduced from the relative specific gravities of air and mercury determined by Biot, (Art. 87^ the computation will be as follows : For the correction of the upper mercurial column, add to 26,409 inches its 1940th part for each degree of temp 'ature below the lower barometer: this gives the corrected height 26.408 inches. ' "* '^ . %, Enoyclopcedia Britsnnica. if.vv t^vjijjsr^n ■■ '■? hi LEVELLING WITH THE BAROMETER. 17,1 riien, log. of lower barometric height i30.09 1 log. of upper " " 26.438 ,*^u DifTerencc - - - - Constant multiplier Approximate height - - - - Correction for temperature of the air, 22 decrees above the freezing point, at one 400th of 3379. for each degree - - - ■■»■'.- ' . ■ • Final result - • - ■ - • - 1.478436 1.422228 .066208 60123 3379.4 185.9 3565.3 The computation by Mr. Leslie's rule, (Art. 89) is as follows : . Lower mercurial column - - - - 30.091 inches Upper ditto corrected for temperature, 26.458 " J^um 56.529 inches .■ Difference - - _ - - 3.653 inches Then as 56.529 : 3.653 : : 52227 : 3373.2 the approximate height. Add correction for temperature of the air, 22 degrees at one 400th part for each degree 185.5 3558.7 Add the cube of 1.78, the 2000th part of 3558.7 - . - - 5.6 Final result - - 3564.3 feet. By Dr. Robison's method, the computation is as follows : The mean temperature of the air is 22 degrees above the freezing point ; and 22 multiplied by .21 gives 4.62 which added to 87.3 gives 91.9, the corrected height in feet due to one 10th of an inch. Also the mean barometric height is 28.25 inches, and the difference of the barometric height is 3.68s inches. ^ • i Then, 91.9 multiplied by 3.68 =3381.9 = the first approximate height. Also, As 28.25 : 30 : : 3381.9 : 3591 feet =s the second approximate height. Again, 10.25 the diflference of the mercurial temperatures multiplied by 2.833 makes 29. which subtracted from 3593, leaveK 3562 feet for the final result. . :« n %> n.- . . :ir l^■! V ' *' Applying this correction to the height of Snowdon, in the first cxain< pie," (art. 92) " we have the latitude ahout 54 degrees, the natural cosine of which is .5878, and its square .3455. This multiplied by 29 gives the mean temperature for the latitude of 54 degrees 10.019 ; one iifth of this is 2. The sum of the detached thermometers is 48,8, to which the 2 being added, makes 50.8; and this sum being multiplied by 3368.496, (the approximate height) and divided by 1000, gives. 171.11 for the correction, instead of 165,34, being a difference of 6.77 feet, which is due to centrifugal force. ' 'f' r.;r \ " If we take Chimhoraoo for an example. The place being on the equator, the square of the cosine of the latitude is unity, and the mean temperature is one fifth of 29, or 5.8. This added to 53.8, gives 59.6, which multiplied by 18244.848 and divided by 1000, gives for the cor- rection 1087 feet, instead of 981 as before ; and giving 106 feet as duo to centrifugal force."* It must be remembered that when the mean of the upper and lower detached thermometers is Iteloiv zero the allowance for centrifugal force must be calculated separately and added to the height.f It i> always a quantity to be added, whereas we have seen that the correction for temperature of the air is, in temperatures below zero, to be subtracted. These are the allowances given by Professor Leslie ; but the former rule, given by Mr. Simms (Art. 88) taken from a formula by Mr. Bailly, being the latest, is probably the most correct. By this rule the allowance at the latitude of 45 degrees is nothing, and from this parallel it increases towards the equater, arid is to be added ; it also increases at the same rate towards the poles, but is to be subtracted. It is a correction, however, that is hardly worth attending to ; for Snowdon it is, by Leslie's rule, only one 522d part of the whole height, and for Chimboraco, an extremely high mountain, and under the equator; both circumstances calculated to increase centrifugal force to the' utmost; the correction is only one 180th ; but by Simms' rule it is not one half of these quantities. Of such small matters, the Professor very justly remarks : — " such an appearance of extreme accuracy, is perhaps to be regarded merely as a theoretical illusion, unsuited and inapplicable to any real state of practice." 94. We will now give another example taken from the notes of a survey made in New Brunswick in September, 1839, and which illus- trates the mode of dealing with some of the practical difficulties of such undertakings. ^ , 11 \. * Eoeyclopoedia Brittanica. t By Mro is meant the freezing point of water, that being the aero point of the eentrigrade thermome' ter. If Fahrenheit's thcrmooaiter be used, the degrees must be counted from the freezing point of thi scale. .iv-^ v I. «>«jii I«i»f» M"* Log, of I LEVELLING WITH THE BAROMETER. 175 At the foot of the Blue Mountain on the river Tobique, the barometer stood at 29.800 inches ; the attached thermometer at 33, and the de- tached at 36 degrees. On the top of the mountain, about a mile dis- tant from the place of the first observation, the barometer stood at 28.502 inches ; the attached thermometer at 57, and detached at 58 dejjrees. That is, ■■■•-- -'. .Wt - Lower Station. Upptfr Station. Barometer - - - 29.800 inclies. 28.502 inches. Attached thermometer - 33 degrees Detached " - 36 " 58 Then, following Simms' rule, the sum of the detached thermometers IS 94 degrees, consequently A is 4.714880 ' ' ; B - - - to be subtracted log. of bar. upper station. 57 degrees. .001040 1 .454875 Difference - - - 1.453835 log. of bar. lower station, 1.474216 8.309225 log. of R. R .020381 Sum 3.104105 = log of 1271 feet, the height of the mountain. Again, on returning to the foot of the mountain the barometer stood at 29.720 inches ; the attached thermometer at 58, and the detached at 59 degrees. Taking the observation in connection with that at the top of the mountain, we have — Lower Station. Upper Station. Barometer - - - - 29.720 inches. 28.502 inches. Attached thermometer - - 58 degrees 57 degrees. , Detached ditto - - 59 " 58 " ' Hence A== 4.805490 ' ' '. ' ' B= added, .000040 , ' lo.^ of bar. upper station, 1.454875 ■'■•li I, •• f/ Sum, - - - 1.454915 \'.' log. of bar. lower station, 1.473049 R— .018134 Log. of R— 8.258500 -.ifai'il^ v,'?t 3.063990 log. of 1159 feet the height of the mountain. 176 LEVELLING WITH THE BAROMETER. IJ'1 'A Ovy calculating by Leslie's rule (Art. 89) the computation is as fol- lows : — : -» fi: wr <..,., , . ,\f|.)j.^ inM,, By the first set of observations, the ' ■'■'"'' '*' '" " ' ■■ Lower mercuriiil column - - - 29.800 inches. Upper ditto corrected for temperature, 28.428 ** Sum 58.228 «« K Difference - 1.372 Then, As 58.228 : 1.372 : : 52227 : 1230 feet the approximate height. Add correction for temperature of the air 1 5J degrees above tho freezing .» . point at one 400th for each deg. 47 i , Final result - . - - 1277 s By the second set of observations we have, Lower mercurial column Upper ditto corrected « Sum 29.720 inches. 28.505 « 58.225 " (( Difference - 1.215 Then, As 58.225 : 1.215 :: 52227 : 1090 feet the approximate height. Add correction for (c.nperaturfi of air 26^ degrees above the freezing point - - - - - 72 ■ >f)h Final result - - 1162 ere is the practical difficulty alluded to. We have a difference of icsnlt between the two sets of observations of 112 or 115 feet. Let us now examine the case n little more minutely. The first of the above observations, was ii.ade at half-past 7 o'clock in the morning. The second at noon, and the third at 5 o'clock in the evening. The previous night there had been a slight frost, and in the morning the air was clear and becoming warm. At noon, when the observation was taken at the upper station, the temperature had risen to 58 degrees; and as the station had upwards of 1000 feet of elevation, it probably was at the same time 62 degrees at the lower station.* As it is the temperature of the atmospheric column between the stations * Tbetfaermonieter Mualiy moki about one d«/gree of Fahrtnlieit for eracj MO teet of the elevation. LEVELLING WITH THE RAROMETER. 177 thai exists at the instant of the upper obsermtion which determines the amount of correction (Art. 86), ilie true mean temperature from which to calculate is 60 degrees ; that is 28 degrees above the freezing point of water. This gives the correction for the first result 86 feet, and for «hc second 76 feet ; making the final result in the first case 1316, and ui the second 1166 feet. Here we have no less than 150 feet difierence in the results, owing to the change which had taken place between 7 o'clock in the morn- ning and 5 o'clock in the afternoon, in the atmospheric pressure. If this change were uniform we would only have to take the average between the two results ; but this is not- probable. On the preceding evening the weather was clear with the barometer at 29.690 : on the next morning it had risen to 29.800 ; at the f le time the temperature had fallen from 58 to 33 degrees. This, a' iri'r for the condensation of the mercury by the reduction of temj 29.872 at the temperature of the previous (. clear with easterly wind, but by noon it had become cloudy with a brisk wind at S. W. which continued till night. It is probable there- fore, that the greater part of the alteration took place in the forenoon, and accordingly, that if we allow two thirds of the change of pressure to have taken place in the forenoon, and one third in the afternoon, it will be near the truth. The difference of height brought out is 150 feet ; 100 feet of which deducted from 1316, or 50 feet added to 1166, makes 1216 feet for the corrected height. Or, we may take the station at the top of the mountain as the point of reference and adapt to it the correction of the mercurial columns for tem- perature, and then take such an average of the pressures at the lower station as from the observed rates of change may be most likely to give the true pressure at the time of the upper observation. Example as follows : ..... was equivalent to The morning was W- i'< Barometer Attached thermometer Detached ditto Corrected heights of bare meter, Upper Station. Lower Station. Lower Station. Morning;. Evening;. 28.502 ins. 29.800 ins. 29.720 ins. 57 degrees. 33 degrees. 58 degrees. 58 « 36 " - 59 » - 28.502 29.877 29.717 The difference between the corrected heights of mercury at the I bottom of the mountain is 0.160 inches, two thirds of which subtracted from the morning height, or one third added to the evening height,- gives the supposed height at noon, 29.771 inches. Hence we have — 23 J ■ M. IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I 1^126 |2.5 |5o "i^" mJ^M £ us 110 Photographic Sciences Corporation 1.25 u ijiA "< 6" ► 23 WIST MAIN STMIT WEBSTiR.N.Y. MSSO (716) •72-4503 17fl LEVELLING WITH THE BAROMETER. It *■'■■■■ m yl ■- Wi . liarometer at upper station, jI 'itiv/ 1. " at lower " ni\\ ,v. '. /it ' j'*t^' 28.502 inches, 29.771 •io! t>;;i;-.lM-/K* ■■(!(-•! -r., Sum, - - - 58.273'. .■';.T;^i,' l Difference, - - 1.269 n-^ftw -.^fj , And, as 58.273 : 1.269 : : 52227 : 1137 feet, tbe approximate height. To which adding 79 feet, correction for a temperature of the air, (28 degrees above the freezing point,) gives 1216 feet for the whole height, as before. ,^ ;., When the variation of the 4)ressure is uniform (a cirqumstance that must be determined by the judgment of the surveyor) the case is more easily managed : the corrections will be in proportion to the time elapsed between the observations. With reference to this ease Professor Phil- lips says: — " The fluctuations of the barometer are not necessarily productive of error in the use of the instrument. It is not requisite to have more than one barometer, provided the observer returns again, in the course of the day, to the point which he has chosen for his reference station, or verifies his results by including amongst his measures some point whose height, conspared to that reference station, is known, or in any other way can know the hourly rate of the rising or falling of the barometer. For Example, Sept. 22, 1832; . ,; r; Inn at Ilawcs Harontiptpr. 29.878 rime. 9h.40m. Att. and Dct. Therm. 60 deg. Correction for Temperature. .000 Corrected Pressure. 29.878 Gale- - - - 29.800 11 58 Add .006 29.806 Summit of a hill 28.735 12 b6 Add .015 28.750 Inn at Hawes 29.850 2 64 Subtract .012 29.838 *)■) Hence it is seen that in 4h.* 20m. the baromemeter fell .040 ; and by applying a correction, in this proportion, to all the observations, ' ' "' ' 29.878 add .000 =29.878 . ' , V29.8O6 add .012 =29.818 / , . wc have I .^3^.^ ^^^ ()22 = 28.772? ^^"^ "^^^^^^^^ ?'«*«'*'' - . '29.838 add .040 = 29.878 ^ V^ ' V/ ' The last is the readiest method of reducing the uncertainty in cases such as the above, but the most proper plan of management is to avoid as much as possible the occasion of it: there ought to be two observers, one at the upper, and the other at the lov\^r station, to take observation^ at the same instant of time. There should always be one or two men in a 54.42 fa la • i^hillip'8 Guide to Geology, p. 152. ' ' * •^■"" ^"'^'^^ ** ^»^^« »m^^«HW^ |»4iJ fc^)!" LEVELLING WITH THE BAROMETER. 179 surveying party, capable of using instruments, and who would require but very little extra wages ; and it is exceeding bad policy to make up a party without such persons, hhu h <; ^)a;!u . ^rifi 'Ui vkm !c^ v .l!^ 95. Notwithstanding the degree of perfection to which the art of measuring heights by the barometer has been brought by the labours of successive individuals, there are still some difficulties which have not yet been wholly overcome. On this part of the subject Professor Leslie has the following remarks : " We have," says he, already slated the principle on which the cal- culations of barometrical measurements proceed. But there are still some points, either assumed or overlooked, which may considerably affect the results. It is presumed that at equal successive heights the temperature ©f the atmosphere decreases uniformly. This jJroperty, however, does not hold strictly, and it may be shewn from a comparison of the best observations, that the decrements of heat follow a quicker progression in the higher regions. — The humidity of the air also nui- lerially affects its elasticity; and the hygrometer should therefore bo conjoined with the thermometer in correcting barometrical observations, but nothing satisfactory has yet been done with regard to that subject. The ordinary hygrometers, or rather hygroscopes are mere toys, and their application to science is merely hypothetical. — In the actual state of science it is preposterous, therefore, to affect any very high refinement in the formcla for computing barometrical measurements." /')!,! jk> Another difficulty connected with the subject is a slight uncertainty in obtaining the mercury of the barometer of a standard specific gravity. On this subject the author above quoted says : — " This article may not he improperly concluded by an observation of Mr. Magellan relative to a principal cause of error in barometrical measurements. This he states to be owing to the inattention of observers to the specific gravity I of the mercury with which their barometers were made. If two baro- meters were both at ^0 inches high, and equally circumstanced in every other respect, excepting only the specific gravity of the quicksilver, so that one be filled with the first kind I have tried, viz. whose specific gravity was = 13.62 and the other 13.45. In this case, and in all pro- bability many of this kind have often occurred, the error must have been unless than 327 feet; because 'the heights of the mercurial columns in each barometer must be in the inverse ratio of their specific gravities : viz. 13.45 : 13^32 : : 30 : 30.379 ; which difference shews thatdiere arc |54.42 fathoms between one place and another, or 327 feet ; although Iboth places are ia reality upon the«same level. But if the specific gra^ Ivity of the mercury in the two barometers were as in the two of Berg^" |nian and Fouroroy — viz. one ot 14.110, and the other of 13.000, which lay happen to be the case, as the heaviest is commonly reputed tl^e 180 LEVELLING WITH THE BAROMETER. ".■•V '»•■» t?7 111 (J m -i K:^!:i ■J it ; > !] purest mercury ; on this supposition the error must have amounted to 355.16 toises^ or above 21 34 J feet."* Another source of error connected with this, which it will not be improper to notice, is the inequality of the temperature of the air in a horizontal direction over large tracts of country. If the horizontal distance of two stations from each other is considerable, the slight vari- ations that iare constantly taking place in the atmosphere from local influences, and unsteady weather, may prevent complete uniformity. Professor Playfair remarks, — " equilibrium of the atmosphere, never takes place ; and therefore, it is necessary, in order that barometrical measurements be perfectly accurate, that the one barometer be imme- diately above the other, or, at least, that the horizontal distance between them be very small. If this be not the case, the unequal distribution of the heat through the different parts of the same"- (horizontal) ** stratum of air, will render it impossible to deduce the difference of the heights of the barometers from a comparison of the columns of mer- cury contained in them. It is evident, therefore, from barometrical measurements, there is always a degree of uncertainty introduced by the horizontal distance between the two stations, and that, besides those accidental errors, which are of less consequence, that, in a num- ber of observations, they may nearly compensate for one another. It must be confessed, too, that we have not at present the means of remov- ing this uncertainty, nor even of ascertaining its limits with tolerable exactness."! ^, ' •■ : ; i::u^'<: For example; let A B (Fig. 38) be the profile of a mountain, and let a barometer be placed at A, and another at B, — several miles Fig. 38. I : '.( . . from each other ; — and let C be a point in the air, on a level with B. The pressure of the atmosphere at B will be the same as at C ; but * Encyclopoedia Britanriici. t riayfair't Works, Vol. 8, p. 33. *- K>a4l5iJ * LEVELLING WITH THE BAROMETER. 181 unted to i not be \ air in a orizontal ight vari- om local niformity. re, never rometrical be imme- B between istribution jorizontal) jnce of the ns of mer- irometrical roduced by at, besides in a num- nother. It s ot remov- h tolerable and veral miles untain, B ..1 »vel withB. is atC; bull the allowance for the temperature of the air will not be correct, un- less the temperature at B be the same as that at C. This is some- what uncertain ; if the ground is rocky, and exposed to the rays of a hot siin, the air will be heated near the surface of the earth, by reflection from the rocks, beyond what it would be at C, which is supposed to be beyond the influence of these reflected rays ; or if it be covered with snow in a melting state, as olten happens in fine days in the spring, the air will be colder than on the same level beyond the frigorific influence of the melting snow. Besides this, gleams of sunshine, electric clouds, &;c. will sometimes irregularly affect the temperature over large tracts of country ; hence, the temperature at B may be higher or lower than at C, according to these several circum- stances. The same causes may also affect the temperature at A. For these reasons, if the barometers are at a considerable distance from each other, it will be proper to compute the decrease of temperature between the lower and upper barometer by the perpendicular height, which is about 250 feet for each degree of Fahrenheit.* With respect to the humidity of, the air ;-^the absolute weight of the atmosphere is certainly increased by the admixture of water, but it is not so certain that this increases the pressure upon the barometer. That it is the elasticity only that affects that instrument is proved by the fact that it will stand at an equal height in the open air, and in an air- tight box, cut ofl* from the surrounding atmosphere. The remarkable uniformity in the height of the barometer at the sea level all over the globe is a proof that it is not much, if at all afliscted by the humidity of the air. Atmospheric air, at the freezing temperature contains from a 200th to a 160th of its weight of water, and double at about every 24 degrees of Fahrenheit. At 32 degrees it contains 100th, at 74 degrees a 50th, and at 98 degrees a 25th ; and it is this variable capacity of taking up and retaining water according to temperature, that is one cause, at least, of the constant evaporation and condensation that goes on over the globe ; but the manner in which these processes are carried on, and the degree in which they aff*ect the elasticity of the air under different circumstances, are secrets not yet discovered. Playfair says : <' Moisture, when chemically united to air, or dissolved in it, so as to compose a part of the same honiogeneous and invisible fluid, appears to have a powerful effect to increase the elasticity of the air, and its ex- pansion for every additional degree of heat which it receives. In expe- riments with.the manometer, k has been observed, that till the moisture was dissolved in the air, it had no sensible effect on its elasticity ; but that as soon as it began to dissolve, the expansion for one degree of heat, was increased, and continued to be so, for every successive addi- ,-,O.Cln^S'it '*■ Some observers have made it 300 feet for eaeh degree. ■;.' J A 182 LEVELLING WITH THE BAROMETER. '^i '^' '4 • i ^ '■^^ , i. . ' ' ' ■ ,1, 1,1 ; . .. I'f' - ■ • ■ ' .> ' f ■ ii •>■ ,| ^ , 41 ,?i; i ' h^ f . . ■• .: : ■ I" yl - ■*;'! i« rt,,'- ■^i ", ; ■> '. . ■ !'■ tion of heat, from thence to the boiling point, where it became nine times that of dry air. Though the judicious and accurate experiments of General Roy have ascertained this effect of humidity, and have even gone far to determine the law of its operation, yet, for want of a mea- sure of the quantity of it contained at any given time in the air, it is impossible to make any application of this knowledge to the object under our consideration." The whole subject of the effect of humidity is obscure ; but enough has been discovered to prove that it amounts to very little indeed. It is not probable that it affects the general pressure further than in an ex- tremely slight degree ; and any alteration that it can make upon the correction for temperature of the air (art. 86) must be very minute. There are also other slight errors arising from the diminution of gra- vity of the quicksilver in the barometer, and of the air, as we ascend from the surface of the earth ; but they are too minute to be of any practical consequence , - •. - i .;,.,>, .; 96. The specific gravity of the mercury in the barometer is a matter of great consequence and should be especially attended to. Though wo cannot easily find a means of ascertaining this in any one barometer, we can easily find the difference of specific gravities in different baro- meters, and this is all that is required to be known. The specific gra- vity of the mercury is always inversely proportional to the height of the cohimn ; — because, being sustained by the weight of the atmosphere, 11 which is constant, the lighter a given bulk of mercury is, the longer p will be required the column requisite to make up the weight necessary y to counterpoise that of the atmosphere, and vice versa (Art. 77 ) Hence, i ■ the heights of the columns of two or more barometers are the proper measures of their respective specific gravities, and "from this datum proper corrections can easily be made. For example, suppose we have a barometer (which we will designate as No. 1) filled with mercury of such specific gravity that it stands, at the sea level, at 30 inches, while in another barometer (No. 2), the spe- cific gravity of the mercury is such that it stands, at the same place, at 31 inches. If these two barometers be used, one at the bottom and the other at the top of a mountain, a correction must be made upon one oi them sufficient to make it correspond in specific gravity to the other: and as the shorter column is the purer mercury, it is best to apply the correction to the ionger column. Suppose No. 2 is removed to the top of the mountain, where it stands at 27.9, while No. 1, at the foot of the mountain, stands at 30 inches ; — as the mercurial heights of the baro- meters are, under similar circumstances, 30 and 31 inches, and the spe- cific gravities are inversely as the heights, we have, — As 31 : 30 : : 27.9 : 27 inches, the height that No. 2 would have, provided the mer- f\ LEVELLING WITH THE BAROMETER. 183 s cury were of the same specific gravity as that of No. 1 ; and accordingly we take for our data for calculating the height of the mountain, 30 inches of mercury at the bottom and 27 inches at the top. Suppose again, No. 2 he left at the bottom, and No. 1 be carried to the top, and that while the former stands at 30.4 the latter stands at 26.5 inches : — Here again we have, as 31 : 30 : : 30.4 : 29.42 inches, the height at which the lower barometer would stand if the mercury were of the same specific gravity as that of No. 1, and the heights of mer- cury to calculate by are 29.42 inches at the bottom and 23.5 at the top. As the first and second terms of the proportion are always the same for the same pair of barometers, the second may be divided by the first and the quotient used as a constant multiplier to the third, which is aU v;ays the height of the mercurial column which is to be corrected. Or, which is more convenient, the logarithm of this quotient may be noted and added to the logarithm of the height which is to be corrected. Thus, in the proportion of specific gravities assumed, the quotient of 30 divided by 31 is .96774. which, in the last example, multiplied by 30.4, gives 29.419 inches for the corrected height. Or, ihe log. of .96774 is — 1-985759, which added to 1.482874, the log. of 30.4 gives 1.468633, the log. 29.42, the corrected height as before. If the atmospheric pressure is taken at the top and bottom of a moun- tain with the same barometer, correction for,specific gravity need not be applied. In the above example, which may be considered an extreme case, barometer No. 1, stands at the foot of the mountain at 30, and at the top at 27 inches, and No. 2, at 31 at the foot, and 27.9 at the top; and the heights calculated by both measurements, come out within .06 of a foot oi each other. But when diflferent barometers are used, cor- rection for difierence of specific gravity, should any exist, is indispensa- ble ; hence, a survey should never be commenced without comparing the barometers. It would be very desirable that the mercury in each should be of the same specific gravity ; but should necessity oblige us to use such as differed a little in this respect, these differences may be allowed for by the above method. ■> ; ui •: For a ^milar reason, a small error in the position of the point at which the scale of inches commences, will not to a very great degree affect the result ; for that depends chiefly upon the difierence of the logarithms of the barometric heights, which will not be much affected by a sAiall and equal change of those heights. Suppose, for example, the lower baro- meter stood at 30 inches, and the upper at 27 inches, the height by the rule (Art. 87) would be 2745.42 feet ; but if the lower barometer were 29.9 inches, and the upper 26.9 inches, each less by one tenth of an inch, the height would come out 27.55.14 feet, — less than one two hundred and eightieth part in excess ; and an error of a tenth of an inch in the f ■■■■ T-M ffW) ■\-'. 1«4 I.EVELL!f:C WITH THE BAROMETER. W P : 'te P;'l, i«!, .!. I position of the zero is far greater than may reasonahly he expected to occur. The syphon barometer is quite free from an error of this nature; the sum of the distances to the surface of the mercury, "upwards and downwards from the zero, being in every case the height of the column, the position of that point is quite a matter of indifference. *", * .'. ^'V ■• .*'..-..■ .. . .f .. f ..•,.. , . ,, -; ■>ji:HH i..t». 97. Several sources of error being shown by scientific writers to exist, it would be improper to pass them by without notice. They may be distinguished into two classes, — those, the errors arising from which, do not, and those which do influence results sufficiently to render them proper objects of attention to the practical surveyor. Of the first kind Mr. Playfair enumerates — ' • -"'V' 1st. The decrease of density in the upper regions of the atmosphere, not being in the exact ratio of decrease of temperature, uyttx hi »; ,.i 2d. The departure of the law of the expansion of air by heat from uniformity, according to the pressure ; — that is, that the condensation or expansion by equal increments of heat |is not uniform ; "a given variation of temperature is accompanied with more or less variation of bulk, according as the air is compressed by a greater or less force." 3d. A slight departure of the law of the elasticity of the air from that of the direct ratio of the density. 4th. The diminution of the weight of (he quicksilvei' in the barometer according as it is removed further from the centre of the earth. lKMi»un: dth. Diminution of the weight of a given bulk of air from the same cause. »>.'''" -vin '^ (i'l;. >'ur>fti .V li; ijol ••■■: 6th. To which may be added the diminution of gravity arising from centrifugal force. The effects of these are extremely small, and as some give the result in excess and others in deficiency, they partly counterbalance each other, and at low altitudes are scarcely appreciable. Mr. Playfair says they are quite inconsiderable while the height is below five or six thousand feet ; and Mr. Leslie calls^such an appearance of accuracy a ** theoretical illusion, inapplicable to any real state of practice." ; '»?;} »t) a*) ir>7/. i;, The latter class comprises the difference of specific gravity of the mercury, and the uncertainty of the observed temperatures of the air, at the places of observation, being the true temperatures) from which the correction for the temperature of the air is to be made. The former is an imperfection in the instrument which must be sought out and ascertained, and when once well done need not be repeated : but if not strictly attended to may introduce great errors into the results. •'?r^'> ■ ■■■■'>'■:>!■■ ^:.^ The latter ought to be attended to, but if it is not, the error only ap- plies to the correction of the height for temperature of the air; an error LEVELLING WITH THG DAROMETfiR. 185 in the data, of one degree of Fahrenheit producing a corresponding error in the result of about three feet in each thousand feet of height. Tho sur^ ^yor, by attending to local circumstances of temperature, may re« duco this error very considerably, hv-sj , < j , ,i ^ w. > Notwithstanding these small difficulties, the degree of exactness with which altitudes are found by the barometer is not a little astonishing. As an intance of this, we may quote M. DeLuc's experiments on the Alps, before alluded to. This philosopher established 15 stations, at heights of as near 200 perpendicular feet above each other, as the nature of the ground would admit, on the mountain of Saleve, near Geneva. The heights of the^e stations from the base were carefully determined by levelling, and then by the barometer. The results are exhibited in the following table, where col. 1 shows the number of the experiment — col. 2, the heights found by the level — col. 3, the heights by the baro- meter, and col 4, the number of observations of which those latter aro (he mean. .ill -iKiJl (.•! til '[<■'■ < ai^iii)' in. .i*U}u->'»'i''^ ■iii . -nf y;.'! I! 'J 'i » '^jinj-SHi i) ^om\ hf .UH5 !!Q 1 11'; »•!• >.;'/•. ..(.), ';■!■ ^>'!;| 'r :. Another instance that may be quoted, took place in the autumn of 1839, in New Brunswick, where the author was employed on explora- tions connected wi^ the Boundary line of the United States. -*»^j* *M' 9/ 186 LEVELLING WITH THE BAROMETER. If; I'." i.'i I 'I.'. 1: iM § m ! U I) k A stationary barometer was established at the Grand Falls on the Rirer St. John, and thirteen observations were made with a portable baro- meter at the head of the Tobique, about fifty miles distant. The ob- servations were made at various times between the middle of Septem- ber, and first of ?'avember. The weather in some instances was stormy, which caused such discrepancies in the results that four of the observa- tions were rejected. The remaining nine produced results within a range of about nine feet only, h must be confessed that this does not afford conclusive evidence that the height of that station, as compared with the Grand Falls, was truly the same as that brought out by the barometric observations, but it proves the wonderful uniformity of the barometric pressure when not affected by storms; and coupled with the observations of DcLuc on the mountain of Saleve, is calculated to give us a great degree of confidence in such measurements. *l >f1! We quote the following remarks from Gregory's Treatise of Mecha- nics, vol. 1. page 490. " As to the advantages of the barometric compared with the geometri- cal method of measuring elevations, we shall state them chieny in the language of Mr. Nicholson, (Natural Philosophy, vol. 2.) First, the instruments are neither very expensive, nor even difficult for an ingenious philosopher to make in any country where he can procure quicksilver and glass tubes ; but the geometrical method requires instruments of considerable price, which cannot at all be accurately constructed by the most ingenious person who is destitute of the tools, and unacquainted with the artifices necessary to render them correct. Secondly, the barometers require no other adjustment than to observe previously whe- ther they agree, and, if they do not, to allow for their difference. The barometrical observations are likewise easily made ; whereas, on the contrary, the previous adjustment, and subsequent use of instruments for measuring angles, require a degree of precision and skill not usually obtained without practice. Thirdly, the error of observation in the barometrical method for all elevations is nearly a constant quantity, never amounting to so much as half a fathom for the mistake of the 500th of an inch ; but any error either in the measurement of lines or angles proportionally affects the result; so that the greater the eleva- tion required to be measured, the larger the quantity of error. " Fourthly, the barometrical observations require no particular cir- cumstances of advantages either in the figure or situation of the moun- tains, &^c. to be measured; nothing more being required than that both stations be accessible. These observations, and the computation, are performed after the same method in all cases ; but, in the geometrical method, if the horizontal distance of the two station^ be considerable, or if there be not a convenient plain for measuring a fundamental base, taken range unequ; equalit over : Upon settled, the atn the spi atmosp should 98. per pia main ui acquire! LETELLINO WITH THE BAROMETER. 187 icular cir- the moun- that both ation, are eonietrical 9iderab}e, ental base, the operation beoomes very complicated, and the probability of error is multiplied. ** After all, it must ROt be disguised that the principles of the geome- trical method are established and sure, and that an extreme degree of exactness may often be obtained in this way by good instruments in the hands of a skilfal observer : whereas the modifications of the atmos- phere with regard to the effect which exhalations of various kinds, and the greater or less abundance of the electric matter, may have in ex- panding the air without changing its temperature, are not yet sufficiently known to render the corrections altogether so perfect as might be wishedf. These remain to be ascertained more accurately by future observations : meanwhile it should be remembered, that the elevations determined by the barometer are most to be depended upon when the extreme tem- peratures of the column of air do not greatly differ, and when the air is cold and dry." Upon the foregoing extract we may remirk that though, as Mr. Ni- cholson observes, it is true that the principles of the geometrical method are sure, nevertheless its superior correctness in a practical point of view, is, in many instances at least, questionable. An elevation taken from a fundamental base on a plain, where such a convenience can 1)e obtained, to a distant point is not always so very perfect as might at first view be supposed. The distance can be obtained very exactly ; but the height depends upon the perfection of the spirit level of the instrument, and upon the absence of unequal refraction of the atmosphere. It requires a good instrument to give the true level within six inches in a mile, taken at one sight ; and the varying refraction of the atmosphere in a range nearly parallel to the earth's surface, sometimes creates much uncertainty in the result. The mirage seen on the deserts of the east, the appearance of ships in the air, while the real ships are below the horizon, and other phenomenon of the like nature, are all caused by unequal refraction. It is true, these are extreme cases, but small in- equalities often lake place, which tend to throw a degree of uncertainty over instrumental observations of level when the distance is great. Upon the whole, we may fairly conclude that when the weather is un- settled, the barometer is uncertain in its results from the uncertainty of the atmospheric pressure ; and the theodolite, from the imperfection of the spirit level, and of its adjustments, and from the uncertainty of the atmospheric refraction is also somewhat uncertain. Dry settled weather should be chosen for either operation. 98. In the practice of taking observations by the barometer, a pro- per place being chosen for setting up the instruments, they should re- main undisturbed a sufficient time for the detached thermometer to acquire the temperature of the air ; that is to say, till the contained yj 188 LEVEIJJNO WITH THE BAROMEYBR. % ''i m 4 ' U ■ ■( ■if ; ., .'I' •; ti :»■ II fluid is stationary. The observer must tlicn move llio slide (Art. 80) till its lower edge is just in a horizontal range with the top of the mcr* cury in the tube ; the observation being made with a convex lens of about 2 inches in focal length. If the barometer be thrown a little out of the perpendicular, so as to disturb the mercury, and tiien allowed to settle, several times in succession ; the height being taken at each time, and the mean of those heights taken as the true height, the minute errors of observation will bo much reduced ; or, what is better, if an observation be taken every hour through the day, at each station, the relative heights of the stations found for each pair of observations, and the mean of these be taken for the true relative height, the probability of error in the result will be considerably diminished. There is a slight attraction between the mercury and the sides of the tube, which prevents it from moving as freely at the sides as at the centre, and without proper precaution, if the tube be small, the error that may take place in a stationary barometer from this cause will be considerable. *'If the glass be small, shake the tube ; then if the air be grown heavier, the mercury will rise about half a tenth of an inch higher than it stood before ; but if it be grown lighter, it will siuk as much. And, it may be added, in the wheel or circular barometer, tap the instrument gently with the finger, and the index will visibly start forwards or backwards according to the tendency to vise or fall at that time. This proceeds from the mercury's sticking to the sides of ihu tube, which ])revents the free motion of it till it be disengaged by iho shock ; and therefore when an observation is to be made witli such a tube it should be first shaken."* Care must be taken that during these operations the instruments he well shaded from the sun and wind, and be also as much as possible out of the influence of local reflections of heat, and if at night, from direct exposure to a bright sky. If they be placed on a beach com- posed of stone or shingle which are exposed to sunshine, or in the neighbourhood of heated rocks, the detached thermometer, although shaded from the direct action of the sun, will give a temperature con- siderably above that of the air where no such influence exists, or if exposed to a clear sky at night it will be below, and so far will introduce error into the result. It is also necessary that the observations upon the stationary barome- ter, and upon the portable barometer, are made as nearly as possible at the same instant of time. One reason for this is, that there is a diurnal variation in the range of the barometer, which is independent of the accidental variations. "Between the tropics from 10 o'clock in the morning till 4 in the afternoon, it falls; it then rises till 10 at night; * London Eneyclopvdia. 'i,iij f im ,i^\U-'-i-j UWil^J^'^H^Ufi^),.^uJi'Ja^uih>^^ I.CVELUNO WITH THE BAROMETER. ]89 falls till 4 in tlio morning; and rises till 10 in the forenoon ; in all about one 500lh part of the entire elevation."* In the temperato regions these diurnal variations are not so perceptible, being masked by the greater accidental variations, but they nevertheless exist. ti;i>iLt> ..hi to Another reason is, that however the accidental variations of the pres- sure of the atmosphere may proceed, they, in ordinary weather, are very equal over large tracts of country. *' Considering the incessant currents which agitate its whole mai'A ....... u i<*"..',iui 99. With regord to the uses of the barometrical method of finding altitudes, it may be remarked, that for pA-curate levelling of largo tracts of country it is decidedly inferior in accuracy to tho ordinary method by the level ; that for measurinn; the heights of peaks of mountains, its inferiority to the method of finding such heights by observations taken at a distance by the theodolite is at least problematical ; but for ascer- taining the general features of a country in an easy and cheap manner, it has a decided superiority over all other methods. In taking'levels in the Northern parts of America, it is requisite in most cases to clear the line of brushwood before applying the instrument. This is tedious and expensive. A barometer can be carried along the line, and observa- tions made at intervals to approximate sufficiently near the truth for practical purposes, at a small comparative expense. In making surveys of large blocks of land, and in marking county and township lines, a course of barometrical measurements would be of great advantage. In conducting such surveys, the surveyor always directs the line by the compass, and thus is constantly occupied. There is no necessity for this, further than the saving of expense ; any careful person with a few days' training may perform that duty as well as the surveyor. The employment of such a person would leave the surveyor at liberty to pursue other objects. The employment most suitable for him is to carry a portable barometer with which to determine elevations and depres- sions; to climb trees at convenient points from which to take bearings of the ranges of hills and vallies, and sketches of distant hills ; to ex- amine the rocks and soils, and procure specimens of them ; and to make copious notes of whatever may seem worthy of notice. Observations by the barometer should be taken at the bottom of hol- lows and tops of hills, and also at the times at which the stationary barometer is observed ; which in this case, should for convenienee be at ^iiijAJ "•''!'*• * EM7«IopMli« BrilMBiM, Artielt Fbydeal Geography, t I^, ii TB!*-^ j'jjonfi m \y > "■)■ ! 1 i .' .( !; it, 190 LEVELLING WITH THE BAROMETER. morning, noon, and night. The latter stations, should, if practicable, be either at the bottoms of vallies or at the tops of hills. As the work proceeds th« section may be approximately made up by the indications of the barometer ; that is to say, the height of a hill from the adjoining hollow, or the depth of a hollow from the adjoining hill, calculated and laid down, and the intermediate space filled in by the judgment. Alon^r with this, the directions of vallies, and the bearings of remarkable objects should be taken by compass from the tops of trees, and laid down ap- proximately upon the map by light shading in pencil. As the survey proceeds, corrections on the positions of objects may be made from further observations, and sometimes comparative heights of distant ranges of ground may be approximated to, by observing their heights as compared with other ranges whose heights are known. The ap- proximate sections will be near the truth in their individual parts, though as a whole they may be enoneous. General corrections must be applied from a comparison of the regular barometrical observations compared with those made by the stationary barometer, which should be as near as practicable to the place of survey. If the country in the vicinity is settled, it may be placed in charge of some school teacher, or other suit' able person, who would attend to it for a moderate remuneration. It may here be noticed that in taking observations for the purpose of making up the section of the line, the second correction, that for the difference of temperature of the air, cannot be applied. It is only when observations are taken at the top and bottom of a hill simultane- ously, or at least while the air continues of the same temperature, that this correction is applicable. ..., i ; . ^ ji;!(4 i In the Geological department of his labours, the surveyor should obtain specimens of the rocks, and if they are stratified, measure the dip and strike of their beds.^ He should also note the height to which * Rocks are divided by Geologists into two principal classes,->i/ra<(/{M( and un$tratifitd. The former «1fiss comprises all those that lie in strata or layers, whether horizontal, perpendicular, or inclined; and their origin is commonly referred to the settlement of sand, mud, fee. to the bottom of water, where it tissbeen consolidated. They contain the reni»insof trees, shells, animals &c.; or, more properly speaking, the form» of those or{;anic matters io stone, hut it is not duabted that those forms fill the places furmerlj occupied hy the objects themselves, A fossil tree or shell is the form of the tree or shell in stone. Sir Charles Bel! says ;— '* The phosphate of lime " (the hard substance familiarly recognized us hone) " lu$«j its phosphoric acid, and the earth of bone remains incorruptible, while the softer animal matter undergoes the process of deeoniposition and is dissipated. The bone in this oondition may become fossilised ; silicious earth, or lime in composition with iron, or iron pyrites may pass by infiltration into the interstices of the original earthy matter, and in this state it is as permanent as the solid rock. It retains the form, though not the internal structure of bone.'t Dip, is the angular inclination of the strata to the horison. . Strike, .\% the direction by the connpass of a kvtl line, drawn along the strata. For taking the measure of the dip and strike, the surveyor should provide Himself with a sttai'ght walking staff of about thtee feet Add a half i« tengtbi with a small spirit level in its upper end, apfd marked with a scale of feet and inehes. This staff laid horiaontally alonfl the rock will give the strike, the difection pf which may be taken with a pocket cotnpaBb. For the dip, the staff xttny be held' horizontally- at ri^lit ' angles to the k'f t Bridgewater Treaiii*. •if Xri^^ LEVELLING WITH THE BAROMETER. 191 they rise,' the shape of the hills, visit conical peaks where they occur, observe whether the character of the rock changes in the ascent, and note every particular that may be thought necessary. These observations may be laid down on the plan in the following maner. If the rock be stratified, as slate, sandstone, &c., short, colored lines may be drawn up^n the plan showing the direction of tho strike, and corresponding marks should be made upon the section. If the rock^ be unstratified, as granite, basalt, &c. other characteristic marks may be made upon the plan and section in the proper positions. The specimens should be numbered, and the corresponding number put upon the plan and section ; also, the height at which they are found, computed from an imaginary horizontal plane, (as the level of some known point, or of the sea,) should be placed on the map in different coloured figures, and the same system of marking the heights above the fundamental or datum plane should be extended to every part of the map (such as the tops of hills, &.C.), where the information may be considered useful. If the surveyor has an assistant to run the line, he will have sufficient leisure for all these duties. The line will not generally be carried forward above two miles and a quarter per day ; which time he will have to make his observations, examine objects to right and left of his line, and lay down his work upon the plan. The morn- ing observation with the barometer may be made in the same place as that of the preceding evening ; thus giving two observations at each morning and evening station. These observations will not take up any . of the ordinary working hours : the observations made throughout the (lay will occupy about half an hour each, and each climb of a tree about an hour. The remaining time he will have for examination of rocks, '•: ••>#- III' 4'- ■ti'« "till U«i*-''^ »a)l!i strike, ifnd th« perpendiculat* distance from »ny convenient part of it to the face of the rook, measured by a |jlun)l) line*. Tliis will give ihe base und perpendicular of a right angled trianple, from which the angle of dtp may be found by a table of natural tanfients, ur by the sectof. If these are not at hand a tri»n^|tt may be drawn on papvr by the measures, and the angles measured by the protractor or line oJf churds. The unstrntifl^d rockf comprise all those which do not lie in beds or layers, such as Granite, Whin, Basalt, or Iron Stone &o. It i« supposed that they have been intlted masses ot nr.mera) matter, protruded upwards froni beneath at former penoa*, and that it is this action which has raised the hills and moun- tains, dislocated and lifted the previously Airmed stratified rocks, and thrown them into the variety of positions in which they arc found in mountainous regions. Besides tliese, there is another class, to which the name of Metamorphic has been given. These rocks are hard, but possess a laminated structure, and are supposed to have been originally the common stra> I tiSed rocks, and to have been indurated by heat. They are luund adjoining the la^t mentioned class, I and under circumstances that prove this opinion to be correct. On the Great Western Koad between Sickville and Ardoise Hill, nietamorp*iie slate is found in veins between whin dikes, and nearly as hard as the whin. Being very hard, and easily broken, it makes excellent metal for the road. Limestone, or marl, is always known by Us effervescence with the mineral acids, a phial of which I should be carried for making trials with. The muriatic aoid is the best^for this purpose, on account that it does not destroy the corks. Sulphuric acid, or aquafortis, will answer etjualiy well, but they mMt I be kept in bottles with glass stopples A surveyor may easily acquire so much knowledge of geology and mineralogy as will enable him to Idistinguish the general classes of rocks, and the more common kinds of ores and matals, and to judga of Itlie most likely places in which to look for organie remains. 192 LEVELLING WITH THE BAROMETER. 111'' i> -'I M w HI i ■ < m: !.5^ soils, timber, &ic. He should, in addition to his instrum'entsj carry a hatchet with a hardened steel poll, for breaking off specimens of rock, and a small tin flask of white lead paint to number them with, — paper labels being liable to get displaced in the carriage. The map should always be made upon the spot : no field-book how- ever fully written, can give the information that can be communicated by a map drawn while the country it represents is under the eye of the IHifJ I. M \i f ! i'i ^iii LEVELLING WITH THE BAROMETER. again at the top of the mountain, and observe with the thermometer the point at which it now boils ; the difference of temperature muhiplied by 630 foot, will give a close approximation to the height of the upper above the lower station. ' ■ •■ • "This will give an approximation, but if greater accuracy be requir- ed, it will further be necessary to correct for the difference of the tem- perature of the air at the two stations, in the following manner : — Add the temperatures of the air at the stations, and subtract 64 from their sum ; multiply the remainder by one thousandth part of the height found, this will be the correction to be added to the height formerly found. The result thus found will still require a slight correction for the figure of the earth, and latitude of the place: but this does not mount to more, in our latitude, than an addition of about two feet in a thousand, which forms a second correction. , " To illustrate the mode of deducing heights from the boiling-point, as we have given it, we take the following example : — Water boils on the top of Ben Nevis at 203.8 deg., while at the side of the Caledonian Canal it boils at 212 deg., the temperature being^^SO deg. on the summit of the mountain, and 35 deg. below. In order to determine the height. From Take 212 deg. 2U3.8 There remains Multiply by 8.2 dog. 530 • 4346 feet. First correction 4.346 2d approximation Second correction 4350.346 8.692 3d approximation 4359.038 To Add 30 deg. 35 ^ Sum Subtract 65 64 Remains Multiply 1 4.346 4.346 first correction. LEVRLLINQ WITH THE BAROMETER. 196 etev the iltiplied e upper ; requir- the tem- • :— Add )m thei| B height formerly iction for does not o feet in ng-point, t the side , being^^^SO i order to mat ion. eight. ,,.; , l^at. 56 nearly Multiply, By 4.346 2 'M I i M 8.692 second correctiou. D. " The true measured height is 4558 feet, the difference being only one fool. " This method, however, is seldom susceptible of so high a degree of accuracy, even with the most carefully conducted experiments." To carry out this plan, an apparatus should be provided containing a tin vessel for boiling th(^ water in, with a spirit lamp beneath. The thermometer should have a large bulb and a long stem ; and be so ndjiisted that the whole stem will bo occupied with 10 or 12 degrees of Fahrenheit. If the degrees be half an inch each, and a vernier applied to the scale, the height can be read to great exactness. The water should contain no mineral matter, as that would raise the boiling temperature; rain water is the best, but river water will generally answer sufficiently well. It has been found that when the bulb of iho thermometer, was imme/sed in the water, the effect was not so regular as when it was in the steam a little above the water ; and it is recom- mended to have a cover to the vessel with a hole in it through which to suspend the thermometer, with its bulb in the most proper situation ; which situation must be 'found by trials. The cover must have a vent hole, for the free escape of steam ; berause, if it is pent up, its pres- sure upon the water will raise the temperature of the boiling point. It must be remembered that this method, founded as it is upon the pressure of the atmosphere, is subject to all the uncertainty of the baro- meter ; and is besides, subject to a further uncertainty frbm the quality of the water. The rule is calculated for the computation of moderate alti- tudes, commencing at the sea level: for comparative heights at consi- derable elevations, it would require a modification similar to that at page 169 for computing heights by the barometer. The instrument is, as to correctness of results, inferior to the barometer; but it is cheap, port- able, and not liable to derangement. On these accounts it is very convenient for travellers; and is sufficiently correct to give a good general knowledge of the altitudes of a country. We will close this section of our work with the following directions of Mr. Babbage, relative to observing with instruments, and which will be well worth the attention of beginners. It is extracted from the London Mechanics' Magazine. . ' ' * ' " If the instrument is a divided one, the first thing is to learn to read the verniers. If the divisions are so fine that the coincidence is frc- (|uently doubtful, the best plan will be for the learner to get some acquaifi- % r: 19^ LEVELLING WITH IHE BAROMETER. ■i"-';,- tance who is skilled in the use of instruments, and having set the instru- ment at hazard, to write down the readings of the verniers, and then request his friend to do the same : whenever there is vny difference, he should: carefully examine the doubtful, and ask his friend to point out the minute peculiarities on which he founds his decision. This should be repeated frequently ; and, after some practice, he should note how many times in a hundred his reading differs from his friend's, and also how many divisions they usually differ. , * <' The next point is, to ascertain the precision with which the learner can] bisect an object with the wires of the telescope. This can be done without assistance. It is not necessary even to adjust the instrument, but merely to point it to a distant object. When it bisects any remark- able point, read off the verniers, and write down the results ; then dis- place the telescope a Httle and adjust it again. A series of such obser- vations will show the confidence which is due to the observer's eye in bisecting an object, and also in reading the verniers ; and as the first direction gave him some measure of the latter, he may, in a great mea- sure, appreciate his skill in the former. He should also, when he finds a deviation in the reading, return to the telescope and satisfy himself if he has made the bisection as complete as he can. In general, the stu- dent should practise each adjustment separately, and write down the result whenever he can measure its deviations. k|| ,? 'U a ** Having thus practised the adjustments, the next step is to make an observation ; but in order to try both himself and the instrument, let him take the altitude of some fixed object, (a ter^restrial one) and having registered the result, let him average the adjustment, and repeat the process fifty or a hundred times. This will not merely afford him ex- cellent practice, but enable him to judge of his own skill. ■J I' " The first step in the use of every instrument is to find the limits within which the observer can measure the same object under the same circumstances. It is only from a knowledge of this that he can have confidence in his measures of the same object under different circum- stances, and after that of different objects under different circumstances. *< These principles are applicable to almost all instruments. If a per- son be desirous of ascertaining heights by a mountain barometer, let him begin by adjusting his instrument in his own study ; and having made the upper contact, let him write down the reading of the vernier, and then let him derange the upper adjustment only; readjust, and repeat the reading. When he is satisfied about the limits within which he can make the adjustment let him do the game repeatedly with the lower, but let him not, until he knows his own errors in reading and adjusting, pronounce upon those of the instrument. In the cdse of a barometer, LEVELLING WITH VhE BAROMETER. 197 he must also be assured that the temperature of the mercury does not change during the interval. ** A frieiid once brought to me a beautifully constructed piece of mechanism for marking minute portions of time : the 300th part of a second was indicated by it. It was a kind of watch, with a pin for stopping one of the hands. I proposed that we should each endeavour to stop it 20 tinnes in succession at the same point. We were both equally unpractised, and our iirst endeavour showed that we could not be confident of the 20th part of a second. In fact, both the time oc- cupied in causing the extremities of the fingers to obey the volition, as well as the time employed in compressing the flesh before the fingers acted upon the stop, appeared to influence the accuracy of our obser- vations. 'From some few experiments I made, I thought I perceived that rapidity of the transmission of the effects of the will, depended on the state of fatigue or health of the body." , i,i ... ^ •(, i ( 1 .0 !'■ ( :hirf- ■■•■■■■ \h» ' •> .'•(■f •', .■^. ,.,. ■■;• ■,■'•! > ••► *i\ -•'h' ..i-r , ' /si ;r ;V ■ ;i 1 or M.i lt\'- .•S:''>t. '.. ■* . . ...;.■:.. .Uii .... . r 1 . ., ^ ■.'••! y-: ;•- -.;; I If'^' 'I, I I ||. ' ; fi.:l fii|r I?' I I- ! '■' r•'' ' '* .1 • *«" : tti 100. In laying out a line of road, the subject that is of the most essential importance to be attended to, is the angular elevations of the hills. If these be laid at grades above what circumstances will fairly warrant to expense nor skill in the making of the road can compensate for the error. But as levciness, though up to a certain pofnt, a pri- mary and indispensible condition, may, on the surface of a hilly country, be carried to an unnecessary, and possibly, injurious extreme, we shall treat this subject at some length. The advantage or disadvantage derived from the elevation of the slopes, always bears some proportion to the hardness and smoothness of the road. In drawing a load up a hill it is subject to resistance from two different sources, — Gravity and Friction, In reducing the elevations of hills, it is the first only of these elements that is affected. The re- sistance from gravity is always proportional to the sine of the angle of elevation of the hill, and will be reduced in the same proportion as the hill is reduced. On the other hand, the resistance from friction, is, under equal circumstances of hardness and smoothness of the road, on all elevations the same. Hence, the harder and smoother a road is, the greater the advantage in lowering the elevations of the hills: because, the constant resistance from friction being the less, that from gravity will he proportionally the greater, and a greater proportional advantage will be derived from the reduction of that resistance. When the resistance from friction is nearly reduced to nothing, as on a rail-road, it becomes a matter of primary importance to get rid of that arising from gravity: accordingly we find that rail-roads are made with the greatest possible attention to levelness. On this subject, the writer of the article Roadj in the Penny Maga- zine, says : " To be theoretically perfect, a road should combine the qualities of straightness and level, and its surface should be smooth and hard ; and the best road practically, will be that which makes the best compromise between unavoidable deviations from this theoretical perfection. It may be observed, however, that altho' some , writers speak of the absolute perfection of each of these qualities, as essential to a good road, it may be questionable whether it is desirable of any exceptNthe first. ANGULAR ELEVATIONS OF HILLS. 199 ■» t'.f. !■ ■ / •' ;■; itii- '■; • :-!»:.;•,-;■ , V • i .>.:■' the most ns of the ivill fairly mpensate int, a pri- >f a hilly extreme, ion of the jothness of tance from 1 elevations The re- B angle of :ion as the friction, is, \e road, on road is, the 5: because, gravity will antago will ) resistance it becomes )m gravity : est possible nny Maga- qualities of " hard ; and compromise on. It may the absolute road, it may " The qualities of strai?htncss and level, or the line of direction and line of draught should bu : try carefully adjusted to each other. » "It seems to be a prevailing opinion with modern engineers, that the line of direction has not generally been made as subordinate as it should be to the line of draught ; and it will bo well to remember, in laying out a new road, that while the effect of gravity must ever remain the same, the resistance occasioned by imperfections in the road and car- riages, will be reduced by every prospective improvemeni in their con- struction ; thereby increasing the proportionate effect of gravity, and making the line of direction still more subordinate to that of draught, or, in other words, increasing the length of level road that may be tra- versed, with the same expense of power as would raise the load up a given elevation." ^ The operation of the combined influence of gravity and friction, will be hetter understood from an examination of the following table, which exhibits the resistance to draught upon hills of different inclinations, from 1 in 10 to the level, and of different degrees of friction from ono 20th down to one 240th of the weight — the load being supposed 2400 lbs.: T|ie first column contains the different grades ; the second, the corres- ponding force of gravity for a load of 2400 lbs.; the third, the total resistance to draught in ascending the hill, under a friction of 120 lbs., or one twentieth of the assumed load ; and the fourth, the resistance to draught in descending the hill. The third column is computed by adding the resistance from gravity due to the grade, to the constant resistance from friction. On descending the hill, gravity assists the draught, and is to be subtracted from ths friction, and in this way the 4th column is com- puted. This, however, is only the case while the force of gravity is less than the friction ; when it is greater the 4th column is obtained by sub- tracting the friction from it. Thus, on an inclined plane of 1 in 30, the force of gravity tending to carry the load of 2400 pounds down the plane, is SOJpounds ; but the opposing resistance of friction is 120 pounds, and this must be wholly overcome before the load can move : there must therefore be, in addition to gravity, a force of 40 lbs. exerted by the cattle. But on an inclined plane of 1 in 12, the force of gravity is 20O pounds, and the friction being only 120 pounds, it is necessary for the cattle to /io/«i »r, 1 i r. nationSf and of different degrees of friction. AnsU of frietinn I in 40. FrictiunGOlb or oiitt 40lli o( the Wfiiglit. n«il«tanc« ReaUtance nptiitnncu Ascending. DMiccndlng. Aiocndinff. 60 60 48 80 40 €8 82 38 70 84 S6 72 86.66 33.33 74.33 90 30 78 92 28 80 94.3 25.7 82.33 97 23 85 100 20 88 103.66 16.4 91.66 108 12 96 113.33 6,66 101.33 120 00 108 128.66 - 8.66 116.66 140 -^20 128 166 - 36 144 180 - 60 168 220 -100 208 300 -180 288 160 - 40 148 200 - 80 188 240 -120 228 260 -140 248 Anirle of friction I in bO. Friction 49tt) or one &Otli of tliu weight. RpslUanco Deiccndlng. 48 28 26 24 21.33 18 16 13.7 11 8 4.4 00 5.33 12* 20.66 • 32 ■ 48 ■ 72 ■112 192 . 62 . 92* 132 ■162 Aiiiile of friotinn I in 340. Friction 10 lb or onu U40(U of tho weiKlit. Kt-iiiiitiinco Atcending, 10 30 32 34 36.66 40 42 44.3 47 60 63.66 58 68.33 70 78.66 90 106 130 170 250 110 150 190 210 ne^litiince Ucicendlug. 10 . 10 ■ 12 • 14 ■ 16.66 ■ 20 . 22 ■ 24.33 . 27 . 30 . 33.66 . 38 - 43.33 . 50 - 58.66 . 70 - 86 -110 -150 -230 - 90 -130 -170 -190 :) i-n i)'.)7;)iqa.! ■■■V''. pounds drawn up a hill of 1 in 15, 116| pounds, may, with the same exertion of the team, be drawn up a hill of 1 in 20 ; in other words, that ihe advantage in draught derived from a grade of 1 in 20 over that of 1 in 15 is 16| per cent. The same result may be more compendiously arrived at by finding in the table the force of draught required for each grade, and then saying : — As the less force, is to the greater, so is 100, to a fourth number; from which subtracting 100, the remainder shews the per- 26 202 ANGULAR i:li:vation» op IIIU.S. p ■ I ill.' •i! ^n ?■!• 4 '"■}... 1 cciitago by wliicli the easier grade exceeds the steeper in advantage of draught. To give another example; suppose the reduction is from 1 in 15 to I in 20, the friction i)ciiig one twentv-fifth of the load. Looking in tiio column headed friction one 26th, Fable 1 — the force answerable to a grade of 1 in 15 is found to be 26G pounds, and to a grade of 1 in 20, 21G pounds. ' "" • . f Then as 216: 256:: 100:nOJ; from which subtracting 100, there rcMiains Ul^, — the percentage required. Tiic abov(! examples are the first two in tal)Ie 2d, which table is con- structed to shew the comparative advantages of lowering the elevations of hills. It is limited in extent hut can easily be enlarged by the reader by the methods shewn above. For instance, if he wishes to know the advantage gained in draught by lowering a hill of 1 in 15 to 1 in G , the friction beinu in both cases one thirtieth of the load ; he must look in table J, and in the column headed friction one thirtieth, and opposite to 1 in 15, and to 1 in 35 ; ho will find the force of draught, on the ascent 240, and 148.6 pounds respectively. Then the proportion is^ As 148.6:240 :: 100: 161.5; from which subtracting 100, there re- mains 61.5, the gain per cent required. By this table we perceive that on a road on which the friction is one twentieth of the load, the advantage gained by reducing the angle of elevation from 1 in 1 "3 to 1 in 20 is only 16§ per cent, while the same reduction of elevation on a road, the friction of which is but one half of that amount — one fortieth- of the load, is 22.11 per cent; and when it is one two hundred and fortieth of the load, as on a railroad, it amounts to 30.7 per cent. And in every part of the table it is seen that as the friction decreases^ the gain per cent increases ; whence wc may infer as a general principle, that, as has been already observed, the harder and smoother a road is made, the greater is the avantage derived from a given reduction of the elevations, and vice versa, , From No. 10 to 16 the elevations increase by regular gradations of 1 degree each, and by the results it appears that the improvement of th« surface produces a less jjroportioHatc improvement in the draught, as the hill is steeper. Thus, in lowering the elevation of a hill from 1 in 57.3 (one degree) to the level, the gain, whore the friction is one 20th o( the load, is 35 per cent ; and where the surface is so improved as to reduce the friction to one 40th, the gain is increased to 70 per cent: but in lowering the elevation from 1 in 8 to 1 in 9.5 (from 7 to 6 de- grees), which is the same angular difference, the gain is, in the former case, 11.3, and in the latter only 13.5 per cent; and, even on a rail- road, no more than 16 per cent. Also, in lowering the elevations of hills, unless the situation be very peculiar, a half way alteration is less profitable than a more thorough one. This appears by the last three nlimbers, wher^ a reduction of ANGULAR ELEVATIONS OF HILLS 20J M.f v- ., „,,,,., ,., TAULK/II. . .. . 1 Of the gain per cent in draught up hills of difjerent degrees of steep- \ (1 i'»f( riiiivMf' ness J by reduction of the grades. •' ■ --— '.' ■! i 1 Gain perciiif. by a riduction of No. iloduction of Elevations. Elevations. Frlrtlnn Frlotlnn Frlrtldn Frli'tlon Frlrtlon Frf'-'ton ono 'JUtli. uiiu S.MIi. unu auili. oliu 4Uili. oiiv .'lUlli. UUtt 2-IUlil. 1 From lin l5tol ill 20 ~16.6 18.5 20 ~22rr 23.8 30.71 2 1 ill 20 to 1 in 25 11.1 12.5 13.6 15.4 16.6 22.6 3 — . 1 in 25 to 1 in 30 8 9.1 10. 1 1 .4 12.5 17.8 4 1 in 30 to 1 in 35 6 7. 7.7 8.8 9.8 14.2 5 _— . 1 ill 35 to 1 in 40 4.8 5.5 6.1 7.2 8.0 12.2 6 _— 1 in 40 to 1 in 45 3.8 4.4 5. 5.8 6.5 10.5 7 .^-. 1 in 45 to 1 in 50 3.2 3 7 4.1 5. 5.5 9.1 8 , — .' 1 ill 50 to 1 in 55 2.6 3.1 3.6 4.2 4.8 8.2 9 1 in 55 to I ill 60 2.25 2.6 3. 3.6 4.1 7.2 10 1 in 57.3 to Level 35 44 52 70 87.5 520 11 1 in 28.6 to 1 in 57.3 23 30 34.5 41 46.6 81 12 ^_ 1 in 19 to ) in 28.6 20.5 23 25.5 29 31.7 44.7 13 ____ 1 in 143 to 1 in 19 17. 19 20.4 22.5 24 31 14 1 in 11.4 to 1 in 14.3 14.6 16 17 18.4 19.5 23.6 15 ___ I in 9.5 to 1 in 11.4 12.7 13.7 14.5 1.5.5 16.3 19 16 _ 1 in 8 to 1 in 9.5 113 12 12.7 13.5 14 16 17 _:_ I in 8 to 1 in 14.3 44. 48 51. 56 59 71 18 1 in 8 to 1 in 19.0 69 76 82 91 97 124 19 — 1 in 6 to 1 in 28.6 103 117 129 146 ' 160 324 elevation from 1 in 8, which is about ilie jirade of our steep hills, to 1 in 14.3 (from 7 to 4 degrees) gives, at a friction of one 20th, 44, and of of one 40th, 56 per cent. But if wc lower he grade to 1 in 28.6 (from 7 to2 degrees) the gain is, in the former case 103, and in the latter, 146 per cent ; that is, as compared with tin; less improvement, as 2.3 to 1 when the friction is one 20th, and as 2.6 to 1 when the surface is so improved as to reduce it to one 40th. .... Whence we may learn that making a hard surface upon steep hills, or i partially lowering the grades, produces but little comparative benefit, either as to its present effect, or as a preparation for future improvement of the surHice; and that half measures in the reduction of hills, gene- rally involve a most preposterous expenditure of money. H >:i,']. ^' r-: ' 'i 'I' i 204 ANGULAR ELEVATIONS OF HILLS. m I- it ,i IT:! ': . .1 . ■! 102. From a consideration of the circumstances connected with the draught of heavy carriages, it appears at least probable, that no hill should be so steep as to cause a loaded carriage in its descent, to push the team ; and of consequence, that the steepest hills should not much exceed sjch an angle with the horizon, as that the friction would just be equivalent to the force of gravity which would produce motion down the hill. This, in the language of engineers, is called the angle of fric- tion, and is greater or less, according to the state of the road surface. The opinions of most writers on the subject are quite in accordance with this view of the case. Parnel says, — " An inclination of 1 in 35 is' found by experience to be just such an inclination as admits of horses being driven in a stage coach, wiih perfect safety, when descending in as fast a trot as they can go ; because, in such a case, the coachman can preserve his command over them, and guide and stop them as he pleases. — " For this reason it may be taken as a general rule in la)ing out a new line of road, never, if possible, to have a greater inclination than that of 1 in 35. Particular circumstances may no doubt occur to require a deviation from this rule, but nothing (except a clear case that the circuit to be made to give the prescribed rate, would be so great as to require more horse labour in drawing over it, than in ascending a greater inclination,) should be allowed to have any weight in favour of departing from this general rule." He also remarks that, — " a practical illustration that this rate of inclination is not loo great, may be seen on a part of the Holyhead road, lately made by the Parliamentary Coni- mission(3rs on the north of the City of Coventry, where the inclinations are at this rate, and are found to present no difficulty to fast driving, either in ascending or descending."* Evans says, — " According to the Road Act in England, the ascent or descent of roads, in passing through a hilly country, should not be more than one foot in height to 30 feet of the length thereof, if it should be practicable, without causing a great increase of distance." Mr. McNeil, the resident engineer on the H(flyhead Road says,— " No road should have a greater ascent than one in thirty or thirty-five feet." ^ ' ' ='•.■;; Mahan also says,— that " the principal point to be attended to " (in laying out a road) *' is to give it such a slope, that in the descent with the usual speed, there shall be no danger to the carriages from the accelerating force of gravity in the direction of the road ; and this will be accomplished by not making the fe'.ope greater than what is termed the angle of friction for the particular kind of road covering used, whe- ther it be pavement, a broken stone surface, or a gravel road: for when the slope of the road is equal to the angle of friction, the friction of the * Treatise un Roads by Sir Hi-nr}' Farnel, IS30. ANGULAR ELEVATIONS OF HILLS. 205 carriage wheels will be in equilibrium with the component of the force of gravity in the direction of the road, and this component will, ^here- forei have no tendency to increase the velocity of the carriage, which it would do, were it greater than tl^ force of friction, as the difference between the two forces would then act as an accelerating force on the carriage." He then goes on to remark that the angle of friction has been determined by experiments to be, on a " broken stone surface, laid on an old flint roadi 1 in 35 nearly ; on a broken stone surface, on a rough pavement bottom, 1 in 49; on a gravel road 1 in 15; and on a well made pavement, 1 in 68." It is to be remarked that the reason given by Parnel and Mahan, for preferring that particular slope on an ordinary road is, that coaches may descend hills at a rapid rate without danger, and so gain time. . . Parnel reasons as follows: — "When expeditious travelling is the object, the maximum rate of inclination that never should be exceed- ed in passing over hills, if it be practicable to avoid exceeding it, is that which will afford every advantage in descending hills, as well as in ascending them. For as carriages are necessarily retarded in ascend- ing hills, however moderate their inclinations may be, if horses cannot be driven at a fast pace in going.dovvn them, a great loss of time is the result. This circumstance is particularly deserving of attention, be- cause the present average fast rate of driving over any length of road, can be accomplished in no other way than by going very fast down the hills. But when the hills are very steep, and the coachman cannot keep his time except by driving very fast down them, he exposes the lives of his passengers to the greatest danger. How much time is lost in descending steep hills will appear from the following statement : — Suppose a hill to be so steep as not to admit of a stage coach going faster down a than at the rate of six miles an hour, five minutes will be required tor every half mile : but if the hill were of an inclination of 1 in 35, it might be driven down with perfect safety at the rate of twelve miles an hour ; at which rate the time for going half a mile would be two minutes and a half, so that there is a loss of half a mile in distance for every mile down a steep hill. ,, ;,. •. " Besides the loss arising from the additional horse-power required to draw over very steep hills, there are other circumstances which make it desirable to avoid them. *' in descending them, the drag becomes indispensibly necessary. In coach travelling, the stopping to put it on and take it off, will be the loss of at least one furlong to q. coach travelling at the rate of ten miles an hour ; for in slacking the pace of the horses and before they stop, nearly one minute will be occupied. " When coachmen, to save trouble, omit to put on the drag, or, as it sometimes happens, when it breaks, travellers are liable to the most 'i .»iis aoe ANGULAR ELEVATIONS OF HILLS. i> i, ^i m !, dangerous description of accidents, by the overturning of a coach, when going at a great velocity. Even with the drag, heavy Jpaded carts are always taken by their drivers into the side channels of the road to try to check their speed ; an(J thus the channels are cut into deep ruts or rather troughs, and the under-drains broken in, unless strong posts of wood or stone are set up, which are unsightly and dan- gerous to other carriages, when descending at a quick rate." if h ^ , This, fiowever proper as as a popular illustration, is not quite cor- rect ; the comparison, to be fair, should be of roads whose perpen- dicular elevations are the same. In such case, a descent of 1 in 17^ would be only one half the length of that of 1 in 35^ or one quarter of a mile ; and the latter would require the same lime in passing it at twelve miles an hour as the former at six miles; and supposing the re- maining quarter of a mile to be level, and the speed upon it nine miles an hour, we will have the whole time of passage over the half mile, four minutes and one sixth : still the difference is very considerable. In the foregoing quotations there is no reference to loaded teams ascending hiWs ; neither does it appear that any investigation with re- ference to this object has been made ;* but in this province facility for heavy traffic is of much greater consequence than for rapid conveyance by coaches ; we will therefore attempt to examine this branch of the subject somewhat at large, with such means of enquiry as can be ob- tained, leaving its more perfect investigation to future enquirers. 103. It has been already remarked, as a probability, that no should be so steep as to cause the load in its descent to push the team. The reason is, that in such a case the cattle have to exert a force in hoidinji; the load back, and on the ascent to exert a greater force in drawing it up than would be required on a lower angular elevation : thus a loss of effect as compared with the pow«r, takes place in both direc- tions. But when the hills are of so moderate an elevation that this effect does not follow, it is probable tliat the undulating road, provided the hills are not too lengthy, is equally advantageous for heavy traffic as a dead level. For, allowing the points of termination of any given imdulatory line to be horizontal with each other, the ascending and de- scending planes are of the same perpendicular height ; consequently the average increase of force on the ascents, compared with that re- quired on the level, will be just compensated by the average diminution on the descents, and the whole power exerted in drawing a load over the ascending and descending planes taken together will be just equal * The actual friction of very heavy waggons upon common road^ does not appear to hav« been experi« mentMllv determined. The heaviest load that we have an account of experiments upon, weighed one ton iocluding the wiftgon. The friction of this carriage on a broken stone road was 65tb , and it would be ovcrcoine by gravity on ■ slop? of one in thirty-four and a half. ANGULAR ELEVATIONS OF HILLS. 207 coach, loaded 3 of the fut into I, unless eind dan- [uite cor- 1 perpen- I in 17J uarter of ing it at jg the re- line miles mile, four ■ ed teams 1 with re- arility for anveyance ich of the an be ob- jrs. at no the team, a force in r force in ition : thus joth direc- thal this provided avy traffic any given ng and de- nsequently h that re- diminution load over J just equal mv b»en exp«n« on, weigbe** «"« b , and it would to that expended in drawing an equal load over the same distance upon the level. This appears by Table I. where on all the slopes beneath the angle of friction, the average of the ascending and descending force is shown to be just equal to the force upon the level. For example, in the 3rd and 4th columns, the force upon the level is pven at 120 pounds; at an elevation of 1 in 120 it is 140 pounds ascending, and 100 descending, — average 120 pounds; at 1 in 40 it is 180 and 60, — average 120 pounds ; and at 1 in 20, the angle of friction, it is 240 ascending, and nothing dscending, — average the same as before. * .iu\ !-• 'Iv/i it: Fig, 39. ■■!ii? ? ''orlfonfRl B tkHzjo d nooftO-'^-— 12UUieel. tii' ■ !* I. u!i;Kr To elucidate this subject still further by examples, suppose — 1st. We have a road of 2400 feet in length on the level (as A B, Fig. 39) the friction of which for a load of 2400 pounds is 80 pounds' The proper expression for the force employed on this road is 80 multi- plied by 2400 = 192000.* ; ', . ' • The term Meehanical power, is used by scientific men to designate the whole amount of force exerted inproducinjc a given motion in a (jiven amount of matter, and has reference, jointly, to the weight of the body moved, and to the distance through which it is moved in a given time. A very simple exemplifica- tion of this principle may be found in the commi-n steelyard. In this instrument, a small weight is made to balance a larger one, by means of the inei|uality of the length of the arms hy which they are sus- pended ; and in the case of anVfuilibrium between the two weights, the length of the longer arm will bear the same proportion to that of the shorter, as the greater weight bears to the less. For instance, if the small weight be 2 pounds, and the larger one 16 pounds, the length of the lespective arms of the steelyard must be in the same proportion, or as 2 to 16. If this machine be put in motion by depressing one end of the steelyard, the velocities of the respective weights will be obviously proportional to the lengths of tbe arms by which they are suspended ; and these we have seen, are inversely proportional to the weights by which they are loaded. Hence, allowing the shorter arm to be 3 inches, and the longer 24 inches in length, the greater weight will move perpendicularly a given distance, as 2 inches, in the same time that the lesser weight moves eight timea 2, ur 16 ii^fhes. The common expression for the mtchanieal power, asemployed in this case is, th« weights multiplied into the perpendicular space passed through by them respectively. That is to aay. 16>-the numbar of pounds in the greater weight, multiplied into 2, tbe inches of its descent gives • product of 32 ; and tbo number of pounds in tbe leuer weight multiplied by 16, the tnebei of its deieent in tbe Mm* time, gires • product of 32 «• before. % ; If , r • I •' 208 ANGULAR ELEVATIONS OF HILLS. 2d. Suppose we have a road of the same length, and friction, com- posed of two equal inclined planes, A d, and d B, one of which descends and the other ascends at elevations of 1 in 40. By the table we see that the force required in descending is 20 pounds, which continued for 1200 feet is expressed by 20 multiplied by 1200 = 24000. Also, that the force required in ascending the opposite plane is 140 pounds, which continued for "1200 feet, the expression for its amount is 140 multiplied by 1200 = 168000. These sums added together make 192000 as before. It is proper to observe that this is not strictly correct, but sufficiently so for our present purpose, — we should take the distance A d instead of A C, but the difference is less than half a foot. SI ':' * These examples, to-which several others drawn from the same column in Table 1. are added, are exhibited in the following Table, in which col. 1 shows the No. of the example, col. 2 the description of the plane as exhibited by the Figs. 39, 40, and 4 1 ; col. 3 shows the grade, &c. as explained by the heading of the table. ii n These numbers may signify either the number of inches through which one pound might be raised, or the number of pounds that might he laised one inch by the same power, in the same time; but in th«ir common use. they are considered merely us numbers serving tu compare the eRVcts of ditfvrent powerfi. In the instance under exemplification tliey are erjuul, — showing that the powers tbMt produced them are equal. * In sustaininjf weights upon inclined pl.ines. the same law holds. A part of the weight is sustained bj the plane ; and another part, which is proportional to the declivity nf the plane, is employed in producirg motion. This latter part multiplied by the length of the plane, designates the whole mechanical puwir generated in its descent, or that which would require to be exerted to raise the irce with which the body would tend to slide down theplane; or, abstracting friction, that which would be necessary to move it upwards along the plane. Here we see that it takes 100 pounds of force to balance 1000 poundl on the plane; but in case of motion taking place, that 100 would have to move through a space of 500 feet, the length of the plane, while the 1000 lbs. would be raised only 50 feet, the height of theplane. Also, if we have another plane 400 feet in length, and the same as the former in height, and a body of 1300 lbs. be laid upon it, the tendency of the body to slide down it will be 150 pounds. That is, it would require (allowing that there is no friction) in the first case, a force of 100 pounds, and in the second, of 150 pounds, to prevent the body from sliding down the plane. These forces, multiplied by the lengths of their respective planes, give numbers which designate the mechanical power of each. That is to say, for the first plane 100 m 600 the length of the plane, gives 50,000; and for the sec(«id, 150 m 400, gives 60,000; shewing that the mechanical power necessary to raise 100 pounds up a plane of 500 feet in length, and 50 feet in perpetidi- eular height, is to that required to raise 1200 pounds Up a platie of 400 feet in length, aild the same per- pendicular height as 50,000 to 60,000, or as 5 to 6. But the weights moved are iit tlietame piopdrtion;- hence it follows that the powifr reqalred to raise equal weight* up these planet it the tame. ' ANGULAR SLfiVATiaNS OF HILLS. fsm >ht be raised, or ne ; but in thtir itfvrent powers. >duc«(l them ate ( ; but in esse of jlh of the plane, we have another be laid upon it, ire (allowing that Dunds, to prevent respective planes, ,t plane 100 k 600 shewing that the ) feet in perpeiidi' aitd tbe same pef ime piopOttion;- me. ' 1 < S 6 Ji a o o 2 c •5; ec *=5 u p Q i t^ ^5 G^ C^) G^ G^ ^ OS 05 a a 05 ■"^ '"* ""• •^ l-N o o o G^ 05 § O G OP o o o o CO » nil CO 03 ^ J2 Si JZ 3 3 £ £ o o CO CO, 1-N CO P ^.S5 CO CO p f>o' 00 GO P P P P 5 GO G^ GO G^> CO CO CO CO GO i-^ 1—^ ^r^ ^M " p p p 000 CO G^) CO P O O O <# o P O o o o -^ P o o o o p o o CO CO '^ CO 6J5 . is bfi c ts (u a 03 fc- a C3 ce 5-^ GO GO 05 GO GO Oi >• V s a C 3 • p— •>-« 3 3 .£ .£ hJ p»< r-< 1-^ F-< f— < t— * f— < !-• Q O O :0-G0 c > c 'O >f? GO GO c c »0 10 GO GO a- c £3. C o o ^ ;:Q -OOQ « JQ bxy &d;:5 2 c 2 < ^-^ < Q bfi C33 bfil J3 WJ;;£ 00c k' «« •«-> c o -^ Pt. ^ O o o c o o o o o« = i '^ • mm 0\ Oi GO GO Oi CO >-0 p IT CO p ^:5 ^:5 p -• lUi m « u IJ ''■: i- 'Mi, 'S J), f I 210 ANGULAR ELEVAYiaNi OF HILLS. 'H. m I; ■ t 'Ml ' i!i: i l-i ;(.1 m Wi. I' f: In the first six examples of the foregoing table, the elevations are ar, or below the angle of friction, and the mechanical power consumed in passing over the assumed portion of the road, appears to be in every case the same. In the remaining four examples, in which one of the slopes is above the angle of friction, it is also the same in those cases in which the steeper slope is ascended ; but in^^hose cases of tiie direction of the motion in which it is descended, the power consumed increases rapidly as the angle of depression of that slope is increased. By reference to Table I. it will be perceived that the power required in the descent of the slopes which are above the angle of friction, is, in the language of algebra, n^a^ive ; that is, tne horse has to hold the load back ; but as that action requires as great if not greater exit^rtion than in drawing forward with the same force, there is no distinction made, on this account, in the examples. It may also be remarked that the foregoing examples are, for ease of calculation, taken from regular slopes, but the same principle extends 10* every variety of surface : there is no disadvantage- experienced from undulations, whatever may be their form, provided that in no part they exceed the angle of friction ; this may be proved by any person taking the trouble of making calculations sinnlal- to the preceding, for surfaces of different longitudinal forms. Also, if a comparison be made on a uniformly inclined plane, and on an undulatory road, between two points which are not horizontal with each other^ tl>e same result will follow. 104. The mechanical law that govet^ns the motion of bodies upon inclined planes is that (abstracting friction,) the velocity gained by de- scending any plane of a given perpendicular height will carry the body to an equal perpendicular height up an opposite plane; and this without any reference to the angles of ascent or descent, or to the path of the body in a vertical direction. A good practical proof of this law may be seen in the swinging of a pendulum, which being put in motion, continues it till the resistance of the air, which in this case is a retarding force equivalent to friction, brings it to a state of rest. If the carriage in passing over the road were void of friction, it would in descending one hill, like the pendulum, acquire a sufficient momentum to ,carry it up the next to the same perpendicular height from which it had previously descended. In the cases we have been considering, the horse is supposed to exert as much power upon the carriage as is equivalent to the friction : if he exerted this force constantly, the carriage would pass down and up the hills with accelerated and retarded motions, in the same manner as if friction did not exist. This is not practicable ; but the aggregate amount of force exerted by the horse, being equivalent to the aggregate amount ,*. 1 ANGULAR EtEVATIONS OP HILLS. 211 of friction, the result is that the effects of gravity on the ascending and descending grades neutralise each other, and that without reference to the regular or irregular ibrm of the surface. iT:; 'K»T 105. A theory has a few years since been proposed in England with respect to rail-roads, founded upon the same principle. Its advocates supposed that if a rail-road were formed in a series of undulations, the power of gravity would aid the engine in the descents, and the acquired momentum on the ascents; thus reducing the amount of artificial power required, and giving an advantage to the undulatory road over the level one. J-' It may be illustrated as follows. Suppose a rail-road were laid in an undulatory manner, as D h g £, Fig. 42, the inclined planes and the level between, being each, half a mile in length, and the perpendicular depth of h and g below D and E, 16 feet. Then allowing the friction to be just neutralised by the force of the ei^ne, the train starting from D, would descend with a uniformly accelerated motion to h, where it would attain a velocity of 32 feet per second. It would then pass with the same velocity over the level h g, and with a velocity uniformly retarded up the ascent g E, coming to a state of rest at E The time of pas- sage would be from.D to h, 165 seconds, from h to g 82| seconds, and from g to E 165 seconds ; making a total of 370 seconds, or six minutes and ten seconds ; being an average rate of upwards of fourteen and a half miles per hour, by a power just sufficient to balance the friction. This view of the case has been, at least partly, verified by running a model carriage moved by a spring upon an undulatory track, and by rolling smot^th balls along metal grooves. In this last experiment a straight luaden trough was laid at such a descent that a small ball would just descend along it with a slow motion. Another similar trough was bent into several undulations, and laid witli its ends coinciding with those of the straight trough. On allowing the ball to descend along the undu- lating trough, it moved with considerably greater rapidity than along the straight one. ''''' ■^*>>>^'iO\i'i>^-'\'^''^' ^^- ■ .;':u;:4. ,; ,i-.^hi^-i!u uh*. f^^-jv,:*, This theory excited Jmuch attention, but the general opinion of eri- iU m i '-I 212 ANGULAR ELEVATIONS OF HILL» ii'ii' rr^i. gineera was not favorable to it. Several scientific men in England are^ however, advocates of it, among whom is Dr. Lardner ; who has stated that on rail-roads, undulations of lower grades than at the rate of twenty feet to a mile is as efficient as a dead level. There is an obstacle to carrying the principle into effect in the peculiar action uf a steam en- gine, which does not give a steady and uniform force, at varying velo- cities, such as would be exerted by a spring or by gravity. It has, however, been experimentally provtici, that the theory is true, and that that within certain limits its application is practicable. ** In July, 1839, the Heda Engine with twelve carriages, making a gross weight, including the engine, of eighty tons, was run from Liver- pool to Birmingham and back in the same day ; by which means the same train, under as nearly ns possible the same circumstances, had to ascend and descend every plane on the line, a length of about ninety- five miles. The time of passing each quarter mile was carefully ob- served, so as to obtain the speed on every portion of the road. The following table, extracted from the seventh edition of Lardner on tho Steam-Engine, gives the results of observations on gradients varying from level to 1 in 177 or nearly thirty feet per mile. Gradient. .^PTli" .,! ,,i :■■ i'.^ One in 177 ,,265 400 632 .,r690 660 LeVel. Ascending. Miles per hour. . 22.25 24.87 25.2^ 26.8': 27.35 ! 27.37 :. 29.03 P Speed in Descending. Milvs per hour. . 41.32 ; 39.13 37.07 36.75 34.30 33.16 32.58 Mean Speed. .(m;; Iflilfiipcr hour. •m; 31.78 -/.i 32.00 ^ \s 31.16 31.81 , ' 30.82 : / /o 30.21 30.80 !o 30.93 i Mil .- r " From this table it appears that although the plane of 1 in 177 dimin- ished the speed from near thirty-one miles per hour, the velocity on a level, to little more than twenty-two miles in the ascent, the deficiency was fully compensated by the increased rapidity in the descent. The trifling difference in the mean speed on the different gradients, may probably be attributed to accidental circumstances, but, Sinall as it is, it is rather in favour of the steepest inclinations than otherwise. The result fairly indicates a most remarkable and valuable fact, that a liiie of rail- way with gradients of from twenty to thirty feet per milo may be worked in both directions by the same expenditure of power as a dead level; and this fact, if substantiated by more extended experiments, proves that many millions may be saved in the execution of future railways, ANGULAR ELEVATIONS OF HILLIS. 213 by being content with steeper inclinations than have hitherto been ad- mitted by most engineers to he advisable. The whole of the compen- sating effect here producd, is not to be attributed to the agency of gravity and momentum ; h part, and perhaps a very considerable part of it being due to the very diminished resistance of the air to the passing of the train on ascents, owing to its reduced velocity. The nature and extent of atmospheric resistiince to railway trains, is a point on which so little is known, and opinions are so conflicting, that the extent of its influence in the experiment alluded to cannot be stated with certainty, but it is probably considerable, as the result is very difl'erent from that which might by calculation have been expected from the mere effect of gravity and friction. The resistance of the air being almost impercep- tible in the case of common roads, owing to the great friction and mo- derate velocity, has frequently been considered too trifling to become an element in calculations on railway transit, and hence arises much of the error that has hitherto prevailed respecting inclined planes. ^^ Dr. Lardner thinks that his experiments indicate the gradient by which the gross resistance is doubled, to be nearer 1 in 195 than 1 in SOO, which he, in copnmon with many others, had formerly considered the limit, though 1 in 264 has been mentioned above ' as being a more moderate, and perhaps more usual calculation."^ In the foregoing illustrations, (Art. 103,) no account is made of the velocity of the carriage, because the proportion subsisting between the power, and the elevation and length of the hill, will be, provided the velocity be uniform, always the same. There is, however, one circum- stance connected with the subject of velocity that may properly be con- sidered in descending slopes, the depression of which is greater than the angle of friction, — the velocity of the carriage will, if not checked by the cattle, contihually increase till it comes to the bottom of the hill. If this velocity does not become so great as to be dangerous, there is but little inconvenience. Allowing the slope, for instance, to be 600 feet in length, the angle of friction 1 in 30, and the angle of descent 1 in 25, the velocity attained at the foot of the hill will be 16 feet per second, or near eleven miles per hour ; and at this velocity the horses can keep out of the way of the load. If the, descending plane were but 300 feet in length, the above velocity would not take place on a lower grade than 1 in :2l|, and the momentum acquired would carry the waggon near 120 feet upon the level at the foot of the hill. In rising in the opposite direction to these steep slopes, and to the same height, as from i to F, and from k to F, Fig. 41, (see examples 8 and 10,) the whole mechanical power necessary to raise the load to the height it had fallen from (the aggregate length of both slopes being m I •' >:,i: * Ptnny £n«7elopfl fUiVivyiht) i. . '.ent. 106. This property of slopes above the angle of friction may be turned to good account in cases where the traffic in the opposite direc- tions is unequal in weight. If the hills descending in the direction of the heavy traffic were made considerably steeper than the ascending grades, the expense of freightage would not be increased, and, very fre- quently, the cost of construction of the road, or the distance, be reduced. But this additional steepness, prc/^ably, should not be such as to make any hill, whatever may be its length, above four feet in perpendicular height above what it would be at the angle of friction that being a suf- ficient height, theoretically at least, to generate a velocity of eleven miles per hour. The shorter, therefore, these hills are, the steeper they may be without detriment to the traffic. This reasoning -does not properly apply to roads whose chief use is for stage coaches ; Parnel and Mahan lay it dowi^, that for these vehicles descending slopes should not exceed 1 in 35^ — fast driving would be unsafe for passengers unless the grades were such that the coachman could stop at any moment. But on roads for mere traffic, such pre- cautions are unnecessary : and as much the greater number of our roads are of the latter description, if any considerable distance, or »m- pense, can be saved by making them as here suggested, it seems to be not improper to do so. 107. It should be particularly remarked, that although in all cases of slopes below the angle of friction, the aggregate mechanical power required in drawing a load over a given portion of road, whatever may be the undulations of surface between the points of departure and arrival, is, as appears by table 3, the same, yet above that angle it in- creases rapidly. On this subject Parnel remarks, — *' On any rate of inclination greater than 1 in 35, the labour of horses, in ascending hills, is very much increased. The experiments detailed in the seventh re- port of the Parliamentary Commissioners of the Holyhead Road, made by a newly invented machine for measuring the force of traction or power to draw carriages over different roads, fully established this fact." In all the foregoing illustrations, 1 in 30 is assumed as the angle of friction, and upon common roads, this is nearly correct : but that angle is less as the road is more perfect in its surface. By experiments made by Mr. Telford on the Holyhead Road, the forces required to draw a ton upon the level on differently constructed roads were as follows. ANGULAR ELEVATIONS OF HILLS. Ist. On a well made paretncnt 2d. On a road made with 6 inches of brokoh stone of u-^r.t! .*«< great hardness, laid on a foundation of largo stones set in the form of a pavement 3d. On a road made with a thick coating of broken stone laid on earth ------ 4th. On a road made with a thick coating of gravel laid on earth - - The angle of friction on each of these roads was — On the first, 1 in 68. On the second, 1 in 48|. On the third, 1 in 34|. On the fourth, 1 in 15. Pounds. 33 46 65 147 Respecting the last road, there has been probably some mistake in ring the account of tlu posribly, been made uporr loose gravel, and if so is not a fair test of the drawing up, or in printing the account of the experiment : or it has, caj)ability of a gravelled road. The former case is the most likely. It may be presumed that on our principal lines of trafHc, a bottom- ing of rQugh stones, with a covering of broken stone or gravel, will eventually be resorted to on all the hills ascending in the direction of the heavy traffic ; the angle of friction will in that case be near 1 in 40 ; and to that angle should these hills be brought, if circumstances will per- mit. On roads of less consequence 1 in 30 or 1 in 35 will answer sufficiently. 108. The foregoing reasoning on the effects of hills of low elevation is predicated on the as^sumption, that the powers of animals in drawing loads suffer ro more exhaustion by pulling sometimes harder and at others easie', the speed and distance being the same, than they would suffer by pulling with an average uniform force. It must, how- ever, be admitted, that our knowledge of the laws of animal action is not sufficiently perfect to enable us to come to a satisfactory conclu- sion on the subject by any a priori reasoning ; and it does not appear that regular and systematic experiments have been made. We have, however, what is nearly as satisfactory, — the opinions of drivers of teams and stages of all grades; and upon few subjects, the knowledge of which has been gained only by the experience of workmen, does such unanimity of opinion prevail. They nearly without exception say, not only that a slightly hilly road is as advantageous in this respect as a level I one, but that it is more so ; — that a team will draw as great a load in as " A^eiirdine to the new road act" (ia England) << the ascent or descent fihould not exceed tbe^rate I or proportion of one foot in height to tliirt^-five fevt in the length thereof, if the same be practicable* I vithdut causing a great ihorcase of distance. *'■**- Loudun^a Enc of AgricuHwt. "^'^ - ' ( ;: VW( t.; ^!- 216 ANGULAR ELEVATIONS OV HILLS. m H i> ,t ' •' »' .'. I 111 i ' I :;•' ( 1 short a time, and with less fatigue, and that a stage coach will puss a given distance in less time, and without extra fatigue to the horses, on the former kind of road than on the latter. Observations have often been made upon the diHen^nt states of the same team in drawing loads, partly over ice, and partly on an undulating roudj and tlio rosull has always been to the advantage of the latter. ii / m ii i'n •. hk) W we turn our attention to England, we find the same opinions, pre- vail : Edgeworlh says, — :ni.. • /♦ /tn; ». m...^ .mi i " In all cases where animal power is employed, this alternation of work and rest is, upon the whole, highly advantageous. Many years ago, when posting was carried on with uncommon spirit, Shrubby of Bin- son, who was considered as the most knowing horse-master on the Oxford Road, asserted that more of his horses were spoiled on the level stages, than on those where there were hills." Loudon says, — . , '. " ' .1 .' "A perfectly level road is not always the best for any species of draught. Slight and short alternations of rising and falling ground are serviceable to horses moving swiftly ; the horses have time to rest their lungs, and different muscles: and of this experienced drivers know well how to take advantage. Marshall concurs in this opinion, and also Walker, Telford, and most engineers; and Paterson considers that it miUld not be proper to line a road upon a perfect level, even to the length of one mile together, although it could be quite easily obtained. It is n fact, he says, well known to most people, at least every driver of loaded car- riages knows by experience, that where a horse dragging a load over a long stretch of road, quite level, will be exhausted with fatigue, the same length of a road having here a gentle acclivity, and there a decli- vity, will not fatigue the animal so much. This is easily accounted for. On a road quite level, the draught is always the same, without any relaxation: but on a gentle ascent, one of his powers is called into ex- ercise ; on the descent, another of his powers is called into action, and he rests from the exercise of the former. Thus are his different mus- cular powers moderately exercised, one after another, and this variety has not the same tendency to f&th^ue.^^ (Encyclopedia of Agriculture.) " Slight undulations are considered by most authors to be desirable in all cases where animal power is employed ; frequent changes in the amount of exertion being considered favourable to the horse. On this principle, it is recommended that where an undulating road is reduced to a uniform gradient, occasional levels should be introduced to ease the draught. Any inclination exceeding the angle of repose, or that beyond which a carriage would roll down by its own gravity, occasions a loss of power ; but all below it are attended with a compensating effect when the traffic in both directions is taken into account ; the advantage gained by descending carriages being equal to the additional labout re- AiNUULAR ELEVATIONS Of IIILL8. 217 quired ill the ascent. This angle has been stated by Lardner to bo about 1 in 40, with a good carriage, on a broken stone road of the l)C8t quaHty ; but the inclination allowed on the Holyhead road is 1 in 36^ a slope which may be ascended at a good rate of speed, and descended at twelve miles an hour without rink. A greater slope not only occa- sions much additional resistance in the ascent, but, by rendering it unsafe to drive down at full speed, causes a loss of time in the descent also. Modern Engineers consider it unudvisablo in any case to exceed an in- clination of 1 in 24, though there are hills at least twice as steep on some turnpike roads."* * , ^. . On an (>xauiiiiatioti of Dr. Lardner before a committee of the House of Commons in 1836, he stated his views on this subject as follows: <* There is a distinct mechanical character which attaches itself to acclivities " (of a road) *' depending on their steepness. One acclivity is not more injurious than another in the mere ratio in which it is more steep than another. There are some acclivities that aflbrd a certain com- pensating effect in the descent ; there are others that never compensate tor the power lost in their ascent. There is an acclivity, or an inclina- tion, which we designate in the department of mechanical science that relates fb these things, by the term of the angle of repose ; it is the steepest acclivity down which the carriage will not roll of its own accord — down which it will not roll by its own gravity. On more steep acclivities the carriage will roll down without any tractive power ; every acclivity under that limit will require more or less tractive force down- ward. Now, acclivities which are less steep than the angle of repose, give a compensation in descending for the excessive tractive force they require in ascending, — that is the case with acclivities between the per- fect level and the angle of repose ; and 1 take it that that inclination should be the major limit which ought to be imposed to hills, as they are called, upon the first class of turnpike roads ; the more they are under that inclination of course the better, but certainly they should never exceed it." **** " That acclivity will depend upon several circumstances ; it will depend in some measure on the carriage ; because a carriage of one structure will roll down a hill, when a carriage of another structure would not; Then it will depend upon the surface of the road; but if we take the very best class of broken-stone surface, constructed in the best manner, so as to be as hard as can be, and h good class of car- riage rolling upon it, I suppose, at a rough estimate, ono in forty would be the angle of repose. I should advise the great roads not to bo more steep than one in forty." To the same Committee, Mr. McNeil, in answer to a question, said : — 1 * Vnttvj Eucjrclopcdia. ^ «: 28 K"" n:;i I- -J 11 218 ANGULAR ELEVATIONS OF HILLS. m 1 . Mi) My PI ;^i- r » ' I !- i'- vS Vt '■ '■ :i ! .1* i|i! 'r« :. ]:•■. I' , " No road is perfect, unless it has rates of acclivity, equal or less than 1 in 40. ; .■,ir.^;< i; !}<■' ••';'■•'■' :■ ^'V ji i ■* /jr } y.^ These opinions are highly reasonable, and show that the engineer need not be extremely sensitive on the subject of levelness for turnpiko roads; and that by availing himself of the principle of undulations, he may sometimes improve the site of his road. He need not keep upon perfectly flat ground^ if he can obtain any advantage in distance, ma- terials, or expense by rising on the undulatory ground at a moderate height above it. >/.' or;. :i vk >.Ui-\ -.ir. •*•?'. 4» ^i'ArifM^t !'■' mi f 'ff» Hati.-...'i. It has been seen (ex. 7 and 9, Table 3) that when the load is drawn in the direction of ascent of the hills which are steeper than the angle of friction, the expense of mechanical power is not increased, and of consequence, theoretically at least, the angular elevation of such hills may, provided the perpendicular height be the same, be unlimited, if the power were inanimate^ this, in point of fact, would be the case : but it is limited by the capability of the animal, and of this, aa already observed, we are in a measure ignorant. The limit of draught we liavt assumed at double the ordinary draught, because at such elevations as will require this force, there is no increase of mechanical power required in drawing a load over the road in either direction (Art. 103») But it is very possible that a horse may occassionally, and for a short time, be capable of exerting a force much greater than double his ordinary draught, without impairing his general powers, provided this exertion is suc- ceeded by a corresponding relaxation. On several roads that. have been pointed out by drivers of teams, as being in their opinion equally or more advantageous than a level, many of the undulations were much above the angle of friction ; but whether the advantage was derived altogether from the undulations, from a harder and smoother surface, or from both combined ; or, whether the steeper undulations were not, in reality, attended with disadvantages, which were compensated by those that were more moderate, are questions which we have no means of answering. 109. There is Jittle doubt that hills may exceed the angle of fric- tion without any disadvantage in the descent. At that angle, the force of gravity urging the carriage to descend is barely in equilibrio with the friction, but it will require an increase of the angle to produce motion ; and on an ordinary road, and for such a velocity as may safely take place in going down a hill, this increase will be considerable, it has been remarked (Art. 106), that, theoretically, a hill may safely descend at such a rate as to fall four feet at the bottom below the angle of fric- tion. But it is found that the friction increases with the velocity : by Mr, McNeill's experiments (Art. IH, Tab. II.), the increase of friction, by an increase of velocity from 6 to 10 miles per hour, was from one 38th to one 31st of the load: hence, allowing the friction at the ANGULAR ELEVATIONS OF HILLS. 219 slower velocity to be one 30th of tijo load, (Art. 113) the elevation maj safely be raised to 1 in 25 for any length of hill, because at that grade, when the velocity is 10 miles per hour, the increased inclination to descend will be counterbalanced by the augmented friction, and con- sequently the celerity of motion will have no tendency to increase. These remarks, it must be borne in mind, relate only to the safetv of descent, and are offered rather as probable opinions than as demonstra- tions. The whole subject is involved in obscurity, and it is only by a proper course of experimental investigation, that principles to be fully relied upon can be discovered. ; .i. :iij. , i,; .. <,.,.. ..^ There is, however, one authority on the other side of this questfon, which it would be unfair not to present to the reader. It is that of Mr. Stevenson, author of the article "Road," in the Edinburgh Encyclopedia. He says, — " In an uphill draught, a carriage my be conceived as in a state of being continually lifted by increments proportional to its rise or progress upon the road. Every one knows that on a stage of twelve miles, the post-boy generally saves, as it is ternted, at least half an hour upon the level road, because on it he never requires to slacken his pace as in going uphill. Now, if he, or his company, would agree to take the same time to the level road that they are obliged to do upon the undulating onoy the po^t^master would find no difhculty' in determining which side of the argument Was in favour of his cattlfev'^ *' With regard to the fatigue or ease of the horse, Mr. Stevenson, on one occasion, submitted the subject to the consideration of a medi- cal friend (Dr. John Barclay of Edinburgh, no less eminent for his know- ledge^ than sucCfiSsful as a teacher of 'comparative anatomy '), when the Doctor made the following answer : — 'My acquaintance with the muscles by no means enables me to explain how a horse should be more fatigued by travelling on a road uniformly level, than by travelling over alike space upon one that crosses heights and hollows; but it is de- monstrably a false idea, that muscles can alternately rest and come into motion in cases of this kind. The daily practice of ascending ^heights, it has been said, gives the animal wind and enlarges his chest* It may also, with equal truth, be affirmed, that many horses lose their wind under this sort of trainings and irrecoverably suffer from such imprudent attempts to induce stich a habit.' In short, the Doctor ascribes ' much to prejudice originating with the man, continually in quest of variety, rather than the horse, who consulting only his awn ease, seems quite upcon%ious of Hogarth's line of beauty.' " — (Loudon's Encyclopedia of Agriculture,) Here we perceive that Mr. Stevenson attributes the greater stress upon the horses that is observed on a level road to fast driving ; and he quoted the authority of Dr. Barclay to prove that the muscles of the animal cannot be relieved by changes of elevation in the road. But, !'• I ' ' I ' I t I n !' C; }'■■ I, I I m 220 ANGULAR ELEVATIONS OF HILLS. If', \,' 'i> A •}%i ^M m- : i' witli all deference to the skill of the Doctor, I should think it safer to trust to the observations of a number of intelligent drivers of teams for the solution of the problem than to the dissecting knife. Besides, allow- ing the Doctor's opinion to be correct, it does not affect our main posi- tion ; namely, that the mechanical power expended on a slightly undu- lating road is no greater than on a level one. This is matter of demonstration. The question respecting the dynamical ability of the horse on different grades, must be solved as almost all physical problems are ; that is, not by abstract reasoning from doubtful premises, but b) direct observations of facts ; and though there does not appear to have been any regular series of experiments upon the subject, we have seen that the weight of opinion of observers is against Mr. Stevenson. But we have another authority to add to the list, which is well worth attend- ing to, — that of Mr. McNeill, the resident engineer of the Holyhead Road. He has, as himself informs us, deduced from practice, and with- out having recourse to theoretical investigations, pr abstruse calculations, a formula for computing the expense of draught upon different grades, and from which table 4, art. 117, of this work is calculated. From this table it appears that the expense of working grades of 1 in 40, ascend- ing and descending equal distances, is just equal to that of the whole distance upon the level ; and that where the grades are 1 in 56, the ex- pense is a minimum, and ahQut4 per cent less than upon the level. 110. The principle of undulations in a road may often be applied to good advantage in ascending mountains. In such localities, it is re- commended by writers to continue rising, or at least not, after rising, to fall again so as to lose a part of the-lieight that has been already gained. This is not always practicable, and it is satisfactory to find that shallow vallies, such as Figs. 39 and 40, may be crossed, on the ascent of the mountain, without disadvantage. It is held by most writers that in ascending a mountain, it is better, where the locality admits, to break the ascent into several slopes of the maximum elevation, with levels between them, than to make the whole of a uniform grade ; and the reason given is, that though the horses labour harder upon the ascents than would be necessary upon the uniform grade, yet, by resting upon the levels, they perform the journey, upon the whole, with less fatigue. This arrangement is supported by the same considerations as that of undulations in a generally level country : the horse is at times partially relieved, while the aggregate power ex- pended is not increased. , , .:.u 111. The comparative lengths of slopes in a given aggregate height, is also a subject requiring consideration. Sganzin says :— <* In all cases of a road in a mountainous country, it is a general principle not to em- ANGULAR ELEVATIONS OF HILLS. 221 ploy ramps (slopes) of a uniform length throughout tlie whole road, but to place the longest at the commenceaient of the ascent, diminishing as we approach the summit. This distribution of ramps between the points of departure and arrival, is intended to diminish the labour of the horses in proportion as their strength diminishes. This principle is not rigorous, and may be departed from when it will diminish the ex- pense."* The lengths of such slopes must depend in a great measure upon the formation of the ground ; but it is desirable that they do not exceed 50 to 100 rods in length; a horse will be 5 to 10 minutes in drawing a load up such slopes, and this is a sufficient length of time for great exertion without relaxation. If the situation does not admit of lengthy levels between the slopes, short flats for resting upon at the above distances would be advantageous. In accordance with this view of the subject. Marshal says : — " Ac- cording to theory, an inclined plane of easy ascent is proper ; but as the moving power on this plane is neither purely mechanical, nor in a sufficient degree rational, but an irregular compound of these two qualities, the nature and habits of this power require a varied inclined plane, or one not of a uniform descent, but with levels or other proper places for rest8."1^„. . , f; :.;..,.) * Sg«aiin*t Civil Engineering. * Loudon's Encyclopedia. ■^■ M . ;(--:!?' .>i' ■V'r Vij ^-xi'", ii '.UM :i .14 1// : ' :-. 'ifiii' H,\i-> >•'!■! -fo inotn • i t,in!r»7; • >• !M m; >i i I » i.i i ],>. '.:l 111,' iv! I'i: Kii ♦ )).> ■:r«v»ij.:;! ".JiL i!-^:* ••-j >u\[ !imi.{ Bii! r^ -/■' *iij] ikiiii nil' Hi Hjof''.^' Mil I ( J Oi.i.-. . v»i ;.,"■.,;..: ASCENTS AND DESCENTS OF HILLS. «"' ';-'li f ■'.<)■!!(; )Mi ri .•• iu.l\ 'k> juMJWfriui onj tUn;}- 112. The subject of the following chapter is an attempt to answer the question, How far is it proper, in a hilly country, to increase the length of a road for the purpose of reducing the angle of elevations of the hills? This is a most important problem in road engineering, and its complete solution seems to be, in the present state of our knowledge, impracticable. We may, however, attempt an approximation, with some hope of success. If a mountain be ascended by a road, the steeper the ascent is, the less will be the load that can be drawn up it. If we reduce the angle of ascent by increasing distance, as by a zig-zag line, the load may be increased, but the time of transit will be also increased. Allowing the road to be void of friction, these quantities of increase would exactly balance each other. For example, if it were improved from 1 in Id to 1 in 30 of elevation, the points of departure and arrival on the hill being th3 same, the distance between those points must be doubled. Hence, even though the load on the improved road might be doubled in weight, the length of the road being also doubled, a double time would be occupied in its conveyance between the ex- treme points, so that what would be gained in power would be lost in time. We have therefore, in the case supposed, a double length of road to make and keep in repair, without any benefit whatever from the additional expense. This is the theoretical state of the question abstracted from all other circumstances ; but in practice it is subject to some important modifi- cations. These are, — 1st. Friction. 2d. The gravity of the horse's body. 3d. The muscular strain arising^ from his structure. The^r«/ of these subjects has already been fliscussed, and the efTecl pointed out. The second, — the efifect of the gravity of the body of the horse, is as yet undetermined. When a horse steps]from a lower to a higher level, we do not know whether the muscular exertion required to raise his own weight is more or less than that which would be required to raise the same weight, to the same height, in the form of an additional load in a waggon, in the absence, however, of all experiments we may suppose it the same. ASCENTS AND DESCENTS OF HILLS. 223 The third is also undetsrmined, but of the existence of such a source of resistance there is no doubt. From the conformation of the animal, as well as from his actions when standing with his head up or down hill, it is evident that he is obliged to exert force in order to keep himself from falling, and that a strain takes place similar to that induced in draw- ing a load. It is, perhaps, impossible to ascertain the amount of these strains ; but if we attend to the effect upon the animal, we shall be con- vinced, that when the ground is steep they are considerable, and that they are moreover, so far as they go, a direct drawback upon his ' ffective power. It must also be observed that they exist quite independently of any movement, and arise entirely from his form. Somewhat similar views of this subject have been taken by engineers in England. Mr. Hughes says, — ♦' the horse, in ascending an inclina- lion, has to raise his own weight in addition to the load, and the power thus expended must, of course, be added to the load. **** In fact, the pdwer required for this purpose, is in no respect different, except in amount, from tfiat required to raise the load drawn by the horse. Hence, it will be proper, in determining the resistance of a load to be drawn up any inclination, to consider the weight of the horse itself as a part of the load. Vv ,,,..!■>, :( /n^u!- i hi j And agaioi:*^** Experience very plainly teaches^ that a horse cannot, with the same ease, or with only the same exertion of foTce, draw a load first up and then down any inclination whatever, as he could On a level of the same length. One reason why a greater exertion is required on the sloping plane, we have already assigned— namely, because his own weight has then to be raised as well as the load ; but it is also certain that there are some other considerations connected with the physical structure of the horse, which increase yet more the exertion required on sloping planes. Here, then, is the necessity for experiment: — It is re- quired to know what is the effective performance of a horse on different inclinations, as compared with that on a level. The determination of this problem certainly presents some difficulty, and yet in no other way can we strictly pronounce on the merit of a road with reference to the actual kind of power which is to be used upon it." There is certainly a great want of information on this subject. Road engineering can hardly yet be ranked as a science ; the study of its nature and adaptations has been much neglected ; the subject is difficult, and experience has shown that mathematical reasoning alone is not to be tr^tsted. The laws of motion as produced by gravity or by the ele- ments, have proved sufficiently difficult of investigation ; but when we come to consider the production of motion by the muscular power of animals the difficulty is immeasurably increased. In this, as in every other department of physical science, experiments appear to form the only proper basis for a correct theory ; and as* these have not yet been \\ ^ 224 ASCENT3 AND DESCENTS OF HILLS. siifficientl)' multiplied, any reasoning that can at present be offered upon the subject, must necessarily partake of the uncertainty of the data on which it is founded. ; " ! < . if ♦ / Iiil }r I'- I:: il W'.t . i i- i„- I ; l:^ lib »<■:.. r i- ^ m'' 'H^^ ,',.)'> 113. It has been proved (Art. 103) that when the ground is not steeper than the angle of friction, the mechanical power required to overcome the gravity and friction of the load, in the ascent and descent of a hill, is no greater than it would bo for the same distance upon the level, and it is at least probable that the same rule will hold as regards the gravity of the horse, and the disadvantage of his form. Mr. Hughs thinks otherwise. He says: — v v. • . v;; irv . i?^{-; voiji / '* It is probable that it requires just as much exertion to transport his weight in descending an inclined plane as on a level." This, however, does not seem quite correct : a horse, when travelling under the saddle, always inclines to go faster down a moderate slope than upon a level,— a proof that he derives some assistance from the descent — that he goes down hill more easily than on the level. This may be easily accounted for : the same conformation that obliges him to exert force to prevent himself from falling, when standing with his head down hill, will, within certain limits, assist in producing motion. Gravity inclines to pitch hitn forward ; when under the saddle, he counteracts the tendency to fall by quickening his pace ; when in harness, he rests upon the collar, and thus, when in the position of greatest ease, exerts some force upon the load. Hence the grade at which he will pass with a load downwards, with' the least effort, will be below the angle of friction. Mr. Tredgold takes the same view of the subject. He gives the rate of travelling which a horse can endure, on the level, aAswering to the different lengths of the working day ; and he observes : — " If the road be inclined, the velocity of ascent will be decreased in proportion to the sine of the inclination, and increased in descent in the same propor- tion."* »h;v: ^' ■ • -M ■ .')/i ' ii(^ • ;' ifiiv/ ». I. •::■:!•' >:■; --aoiu.nu 'JinO'KJ > 1 14. We may now perceive that the angle of friction is a very im- portant element in any investigation of this nature, and it is necessary, before proceeding further, to ascertain this as far as our limited means will admit. The only information of this nature that I have been able to obtain, is an account of a series of experiments made in 1829, by Mr. McNeill, the resident Engineer on the Flolyhea'd road, to ascertain the resistance to draught upon portions of that road, and which are detailed in Sir Henry FarnePs work on Roads. . foi n -i -ni: > oi ** The part of the road selected for these trials was of a uniform U-:.L .1 • i"i..^ ASC£NT3 AKD DESCENTS OF UILLS. 226 surface, the resistance of which was previously ascertained, by drawing a waggon over it, to be an average between the worst and most im- proved parts of the Holyhead Road ; and although the velocities are iot so varied, or so high as might be wished, yet several conclusions may be drawn from these experiments of considerable importance in road engineering ; one of which is, that the draught of a stage coach on a common turnpike road increases in a less ratio than the velocity increases, and not as the square of the velocity, which many persons have supposed." ^ ■ " For the purpose of ascertaining the draught up different hills, with different velocities, the instrument," (a dynamometer) " was attached to a common stage coach, which weighed 18 cwt., exclusive of seven pas- sengers. Stations were marked out on the different parts of thr road, of which the inclinations and the lengths were accurately determined, and the time of passing over each was ascertained by means of a stop watch." The results are detailed in table I. The first column contains the number of each experiment ; the second, the rate of inchnation of the hill ; the third, the number of observations of the index of the dynamo*^ meter made in the ascent, the mean of which is taken for the resistance ; the fourth, the length of the hill or inclined plane, in rods ; the fifth, the velocity in miles per hour ; the sixth, the corresponding draughts or force applied, in pounds ; the seventh, the resistance of the load from gravity ; the eighth, the resistance from friction ; the ninth, the angle of friction, and the tenth the percentage of the whole load due to the friction. Thus, in the first line of the first experiment, when the inclination was one in fifteen and a half, the number of observations of the instrument was 32, the length of the hill 35 rods, the velocity 3.41 miles per hour, the force of draught (being the average of the 32 observa- tions) 271 pounds, the gravity of the load due to the elevation of the hill 213 pounds, the friction of the road and axletrees (being the re- mainder of the whole draught) 58 pounds, the angle of friction of the road 1 in 57, and the proportion which the resistance from friction bears to the whole load 1.76 per cent, or 176 parts in ten thousand. The first six columns are copied from Parnel's Treatise ; the remain- iog four are computed from them. It is to be regretted that the weight of the load is rather vaguely given : it is here assumed to be 3300 pounds, which is, probably, not far from the truth. - i ; i^^^x i\. hi \ ;;■; . .i[ I \)i:' ii:\:<, ■. . . m %.^.. iiH m !. Ill , ;V1 l^.[: ' '{'.: ■mM 1,1 .It 29 n- i Pv I , 1 ! 1 1 i'" ill iil '0\ ■Id f- y ; '^1 \w\ mt ' r 226 A9CENT3 AND DESCCNTS OF HILLS. !;■ 2S o «* M <• 3. 3 n 3 2 4 TABLE 1. ic ')■ '^' .t.,>''v I 'rtnreji 2 3 4 o 8 10 Rates of io«liD*tion. 9 3 § a A O r a ;i* 8 Drauffht in tb. Gravity in lbs. Friction in lbs. Angle of Friction oj Uoad. 1 in 15A 32 22 13 13 SS 3.41 3.J4 8.32 11.87 271 276 298 326 213 213 213 213 68 85 112 lin 19 48 17 24 32 45 2.79 6.14 6.35 7.64 252 290 293 303 174 174 174 174 78 116 119 129 1 in 20 35 34 16 22 45^ 3.75 4.02 6.27 6.68 253 263 272 280 165 165 165 165 88 98 107 115 1 in21i 16 16 7 8 18 3.48 4.02 6.07 6.68 lin 23 29 23 13 13 31i 3.61 4.57 6.48 7.30 237 245 258 264 154 83 154 91 154 104 154 110 226 233 243 250 144 82 144 89 144 99 144 106 6 lin^3| J., 45 22 18 62| 3.75 5.52 7.55 8.46 230 240 248 253 140 140 140 140 90 100 108 113 16 3.82 200 127 73 lin 26 20 23| 3.88 202 127 75 Pared BMtom, Rartshil stone. 13 6.27 215 127 88 12 9.41 \^ 223 127 96 8 27 3.75 221 124 97 1 in 26J 19 34| 3.82 220 124 96 Net Paved, Limcttone 14 6.96 230 124 106 surface. 12 8.25 236 124 112 p n 57 n 52i n 39 n 29i n 42 a 28J n 28 n 25J 1.76 1.91 2.68 3.40 2^36 3.52 3.60 3.90 n 37i n 33| n 31 n 29 2.66 2.97 3,24 3.49 n 40 n SQ n 32 n 30 2.61 2.76 3.15 3.03 n 40 n36| n SS n 31 2.49 2.70 3.00 3.21 n SS n30J n 29 2.73 3.30 3.27 3.42 n 45 n 44 n37i n34i n 34. n 34 n 31 n 29 2.21 2.27 2.66 2.91 2.94 3.21 3.39 'M* ASCENTS AND DESCENTS OF HILLS. 227 ..»..vr^^ n * 1 52J 39 29i[3.40 42 2^36 28J3.52 28 13.60 26i|3.90l i 33|2.97 31 29 3.24 3.49 2.51 2.76i 3.1.5 ,3.03 r4l) 2.4i] ;i 12.70 n 33 I3.0q n 31 13.211 n 36i 12.73 n 33 3.30 n 30i 3.27 n 29 13.4^ 40 36 32 b 30 li36* .n 45 12.21 ;n 44 2.27 in37i2.66 in 34J 12.91 1 10 11 12 13 14 i}^- M TABLE I.— Continued. 2 3 4 5 6 7 8 10 Rate of inclination. 9 o a a n n o Cm (t 2. §3- ^3 Draught in lbs. Grav^' I Frietion in lbs. in lbs. - I '. 26 3.55 197 118 79 1 in 28 28 13 40 4.02 6.55 204 211 118 118 86 93 M 12 8.11 218 118 100 1 in 30^ >i •■■■ 16 12 9 6 18 3.54 3.95 6.82 8.86 161 174 187 210 108 108 108 108 53 66 79 102 38 3.95 153 100 53 1 in 33 15 17 43 5.39 6.07 175 182 100 100 75 82 15 8.80 198 100 98 1 in 341 Palchf t of new (tone uot work- ed in or oonto ' I i dated. 30 11 10 13 3.82 5.59 6.61 8.25 186 196 200 214 96 a6 96 96 90 100 104 118 iin'kl Snb-parotnent, surface, quartz StOPff. 19 18 13 10 24 3.62 4.02 6.40 8.73 146 150 167 170 \'\. I'm 39 Ko sub-pave- mgn't 9 taches onlmestone. 16 17 16 13 33 4.43 4.63 6.86 6.20 180 183 212 215 86 86 86 86 60 64 81 84 85 85 85 85 95 98 127 130 iiin 57 Ho sub-phve- mftit. quartt itoil'6 sUrrace. 21 12 la 10 33i 3.88 4.43 5.66 9.61 150 153 ^160 168 58 58 58 58 92 95 102 no 'A.<',i U> ill. I ,3n65A Nliv^ nAlit,si«4nA- eViiriiiACitoAe 21 24 IS 32 4.02 4.08 7.64 8.73 147 147 i il82 ~!202 52 52 52 ^■-i52 95 95 130 150 Angle uf Friction of load. 3. T ... II rl in 42 in38i in 35| in 33 2.39 2.60 2.82I 3.03 in 62 in 50 in 42 in 32 1.61 2.00 2.39 3.23 in 62 in 44 in 40 in 34 1.61 2.27 2.48 3.00 in 37 in 33 in 32 in 28 in 55 in 51 in 41 in 39 '2.70 3.03 3.15 3.58 1.82 1.94 2.45 2.55 in 34^ in 33 in 26 in25i 2.88 3.00 3.85 3.94 in 36 in 34} in 32 in 30 2.7 2.88 3.09 3.33 in 341 in 34| in25| in 22 2.88 2.88 3.94 4.54 /' '^1 228 ASCENTS AND DEBCEiNTS OV H1LL3. TABLE I. — Continued. rMii KLW I'lr '1 .■I i t' ■'T. 1 2 ■', ■ — ■• 3 gr-.- ■ ■ '.- 4 5 6 7 — ■— ■ - 8 9 10 25 o < p o M Rates of incination. 9 -1 < S. d n 3' ft 2. -t — g s- Drnusht in lbs. Gravity in Ibi. Friction in lbs. Angle of Friction of Ruad. 5? as n g 1 ^_ c' HI ■ -'• 11 .. , . 18 3.82 134 28 106 1 in 31 3.21 17 Iinll8 26 11 36^^ 4.50 6.82 140 146 28 28 112 118 I in 29i 3.39| 1 in 28 3.571 17 8.25 153 28 125 f 1 in 24i 3.79 35 4.16 133 24 109 1 in 30 3.30 18 1 in 137i 18 18 45 5.32 6.85 136 140 24 24 112 116 1 in 29i 1 in 28i 3.39 3.51 18 8.18 150 24 126 1 in 26 3.82 44 3.68 128 21 107 1 in 31 3.24 19 1 in 156 25 20 52, 4.50 6.89 133 J 39 21 21 112 118 1 in 29J3.39 1 in 28 3.6? 22 9.61 145 21 124 1 in 26| 3.77 41 2.86 82 21 103 1 in 32 »3.1i>| 20 1 in 156 15 52 . 6.95 95 21 176 1 in 28i 3.52 fall. 13 10.30 100 21 121 1 in 26i 3.66 16 10.84 105 21 126 1 in 26 8.82 28 4.23 125 13 112 1 in I9i 3.40 21 1 in 245 16 38i 6.27 128 13 115 1 in 29 3.48 rise. 15 9.30 131 13 118 1 in 28 3.58 12 9.82 138 15 125 1 in 26} 3.79 39 3.89 J 96 13 109 1 in 30 3.30 22 1 in 245 22 38i 4.30 100 13 113 lin 29 3.42 fall. 23 5.90 107 13 120 1 in 27A 3.64 11 9.41 117 13 130 1 in 25 3.94 42 6.27 112 5 107 1 in 31 3.24 23 1 in 600 25 60 6.61 114 5 109 lin 30 3.30 rise. 20 9.41 122 5 117 lin 28 3.64 23 10.43 130 6 125 1 in 26i 3.79 3.82 100 6 105 1 in 31 3.H .24 1 in 600 60 4.64 110 5 115 lin 29 3M fall, i 6.82 115 5 120 I in 211 3.64 ■ ( 10.67 127 5 132 lin 25 4.oq ASCENTS AND DESCENTS OF HILLS. 229 Table II. is computed from table I.; the first three columns are copied from Parnel, the remaining four are computed from them. , , , i.n < I .,., . , ,. TABLE 11. 1 2 3 4 6 6 7 Rale of inclinttion. Uate of Travelling in miles per hour. Foroe re- quired in Iba. Gravity in iba. Friction in Iba. Angle of Friction of load. Per centBge o( Friction to Load. Iin20 6 8 10 268 296 318 165 165 165 103 131 153 1 in 32 1 in 25 1 in 22 3.12 3.97 4.63 1 in 26 6 8 10 214 219 225 127 127 127 86 92 98 1 in 38 1 in 36 1 in 33 2.61 2.79 3.00 1 in 30 ? 6 8 10 165 196 200 110 110 110 55 86 90 1 in 60 1 in 38 1 in 3b 1.66 2.61 2.72 1 in 40 6 8 10 160 166 172 82 82 82 78 84 90 1 in 41 1 in 39 1 in 36 2.36 2.54 2.72 1 in 600 1 6 8 10 111 120 128 5 5 5 106 115 123 1 in 31 1 in 29 1 in 27 3.21 3.49 3.73 By the above table the general angle of friction of the road, i IS — At 6 miles per hour, about do. do. » < At 8 do. - At 10 do. 1 in 3P 1 in 33| 1 in 31 Table lUl is a " Table of Experiments made on the 28th of January, 1829, immediately after a rapid thaw; the mud was full one and a half or two inches thick on the road at the time." It was handed in to a Parliamentary Committee in 1831 by Mr. McNeil.* i I itt it * London Mechanic's Ma(;azine for March, 1842. 30 All' Vh h i'l.'. iiH m^ w m ^ V m fl: '■■ft: J- 230 ASCENTS AND DESCENTS OF IIIM.S. Col. 1 bhons ilii! weight experimented upon, including the vvnggon which weighed a ton ; col. 2 is the number of the plane on whicii ihi; experiments were mude; ccl. 3 shows the draught lUxvn^ and cci 6 the draught w/> the same piano; col. 4 is the average draught or that which would bo required on the same road surface, upon the leu'l ; and ccl. G shows the angle of friction, com])Utcd from col. 4. .. r TABLE III. i«- •,iit.ii 1 2 — -^■- - ^^- • •• ■ — — 3 4 5 — 1 -, — —VI 6 Weiiilit of load No. of Drdiigli t Drnti^lit on Draught up Angltf of Friction including the wagon riano. riane. tbu Ivvvi. the |>Une. of Uoad. - 1 30 64A 99 1 in 35 , 2 64 76^ 88 1 in 29A 2240 lbs. 3 4 75 75 80 80 85 85 1 in 28^ 1 in 28 -— ••• 5 80 84 88 1 in 27 6 8.3 89 93 1 in 25 Mean, - - - - - 1 in 28i 1 45 "^ 95 145 1 in 35i ■ ■ • - 2 105 ll2i 120 1 in 30 3360 lbs. 3 4 115 105 117i 110^ 120 115 1 in 28.V 1 in 30| 5 105 115 125 1 in 29 6 105 120 135 1 in 28 Mean - - - - - - - 1 in 304 1 58 134 210 1 in 35 2 125 I37i 150 1 in 34 4704 lbs. n O 4 135 135 145 145 155 155 1 in 32| 1 in 32A 5 135 150 165 1 in 3U 6 135 152 A 170 1 in 3\^ Mean - - - - - - 1 in 32^ i' ' if •. 1 15. It appears b_y these tables that the average angle of friction for slow velocities is from 1 in 25 to 1 in 50 ; averaging about 1 in 40. This, however, is on one of the best roads in England : on the same road, when covered with mud, the angle, as shewn by Table 3, is about 1 in 30 ; and as this comes near to the state of the best roads which we arc to expect in this country for a century to come, we may safely found our calculations tipon that grade. ;^ -^ ASC£MT8 AiND DfiSL'fiMTS OF HILLS. 23 i JUW 1 t '^riotion ad. 1 1 1 35 • 29A 28^ 28 27 25 28i 35h 30' 28.V 30| 29 28 304 I 35 34 I 32A 1 32JI I 3U i3r i32| frictio n for i40. This, ame road, about 1 in lich we arc fely f ound As an example, suppose wo liavo a waggon witli its load, weighing 3000 pounds, and that the friction is one thirtieth of that weight, or 100 pounds ;--then, on a slope of 1 in 30, it would just move downwards by its gravity. Suppose now the waggon to be phiccd on a slope of one in thirty-eighty with a horso of 800 pounds in weight attached to it ; then if he stands in the position natural to him on a level, his gravitv will throw him forward upon the collar with a forct; of one thirty-eighth of his weight, and in estimating the force tending to produce motion wo should add the weight of the horse to that r,, the load. This makes 3800 pounds, and on a slope of 1 in 38 the tendency to desecmd will be one thirty-eighth of the whole weight, or 100 lb., which is just equiva- lent to the friction. Tho slope may therefore be reduced from 1 in 30, the angle of friction of the load lUone, to I in 38, before any real exer- tion of the horso is required in the descent. This, it must be observed, relates only to slow motions ; but for quick motioTis, it appears by Table 1, that tiie reduction need not be carried helovv 1 in 35. This is the grade fjxcd upon in England by act of Par- liament, and recommended generally by Jiritisii Engineers : they say that OR a hill steeper than 1 in 3^^ a heavy carriage attains a dangerous velocity in the descent and is not within the full command of the horses. We may now perceive the reason : the weight of the horse is virtually added to that of the load ; but not being subject to friction, its propor- tioi\ of gravity due to the descent is wholly an addition of motive power applied to the carriage ; hence, the angle of descent may be so far re- duced, below tho angle of friction as will make proper allowance for that addition. ijr,, 1 16. Fixing upon 1 in 35 as the maximum elevation, we will now see what would be the effect upon the transportation arising from a re- duction of tho ascending grades of a hill ; there being a pioportional increase in tho length of the road. Let us take, for example, a road running up a hill at a grade of 1 in 15, the line of which is so altered as to reduce the grade to I in 35, but at the same time to increase the length in the same proportion. If, on the steeper grade we allow the weight of a waggon with its load to be 1500 lb., and that it is drawn by a horse weighing 800 lb. the whole weight of the horse and his load is 2300 lb. Then, allowing the friction of the road to be one 30th of the load, the whole resistance to the muscular force of the horse in the ascent of the hill is, — jn- r.i .; , , ,, ■ r„ \')'j\'^u ■■i)i: Ui. Friction one 30th of 1500 lb. Gravity one 15th of 2300 1b. 30 lbs. 153 (( •11 1 ;:.f •Mi:>ol':)/ ^o .r-'fvjrvni to •:)ju'a\ T'otal xWi - 203'>f-, >.h 232 ASCENTS AND DESCENTS OF HILLS. m ill m '•I .1 M: If i 1' ' > ■ !'' hi'- . ' ■ ■ ■ 1 ,i in r. f. ■' ;", if' * : «-"■ [-.^'1::, ill,,!- (If .Vri ■ 11 .'•■ • On the Tmproveii road, the friction being the same as before, we have for the resistance of the same load ; — .. .w ... ; . ,;,i4i,v, uj^, Friction one 30th of 1500 lb. Gravity one 3.5th of 2300 lb. - 50 lbs. 66 " 1.5 Total 116 " I'.'r -' .^ ■ i ■'.V- '■ •r i ■ !■ )/i . - i ti ^ » ' i' "'"5 1 i > ' '1" |L i being 87 lb. less than the former. But the load may be so augmented as to produce the same resistance as before. This, at one 35th for gra- vity and one 30th for friction, will require 1409 pounds ; making the equivalent weight to be drawn up the improved hill 2909 pounds—- nearly double the load on the former. Tills is the effect upon the amount of load ; but to obtain this advan> tage the road has been lengthened in the proportion of 35 to 15, or 7 to 3, while the increase of power effected by the improvement is less than 6 to 3. - ^ ' - ;- This example shews that it can never be profitable to run up a hill in a zig-zag line, or greatly to increase the distance by passing round it, for the mere purpose of reducing or avoiding the eleva- tions of that particular hill. It is only when taken in its connection with the rest of the line, of which it makes a part, — when, in fact, the hill constitutes a barrier to the general traffic, that it is justifiable to get rid of it in this manner. Even in such a case it is not proper to go below the general elevations of the rest of the line ; or in any case below 1 in 35, or at most 1 in 40. Distance is an element that can never be left out in the comparison of different lines of road : we may have, in most localities, nearly a perfect level if we choose to make great deviations from straightness, or we may have a straight line if we chose to en- counter the evil of very steep ascents : neither of these principles are admissable; the proper medium is to make the road as short as possible consistently with some regular principle with respect to hills. ;.;;/.;„., 117. It has been seen that grades of 1 in 35 to 1 in 40 are as low as are necessary for the economical transport of goods, and it might in most cases suflfice to rest upon that determination : but we wish to know the actual effect of different grades upon the cost of transport, as a datum upon which to found an estimate of the comparative advantage of different lines. t. i .m' ' '.fi; J j, On this subject Mr. McNeill says, — " In order to solve this important problem, and to arrive at an accurate result in this and similar inves- tigations, it is necessary to know correctly the expense of horse labour under the varying circumstances of velocity and force of traction on different inclined planes, and also the draught of carriages, and the ratio of the increase of^ draught in consequence of increase of velocity. ASCENtS AND DESCENTS OF HlLLS; 233 '• By the experiments lately made on the Holyhead Road by order of the Parliamentary Commissioners, these circumstances have been ac- curately ascertained from practical experience, which has enabled me to deduce the necessary formulae from actual practice, without having recourse to theoretical investigations or abstruse calculations. " To go into the detail by which these formulae were deduced would in this place be unnecessary ; it is sufficient to state that correct tables have been calculated from these formulae, which show the expense of drawing a given weight with a given velocity over every rate of acclivity atid declivity, and length of inclined plane. ! *' By means of these tables the expense of drawing a ton weight ove^ any line of road may be determined with great accuracy."* . j Unfortunately, I have not been able to procure the formulse or tables above referred to, but there is a table of results given by Parnel, which has been calculated by Mr. McNeill, from those formulae, with reference to a certain project for improving a part of the Holyhead road ; from his report respecting which improvement, the above quotation is extracted. I have also obtained some other tables of the same author drawn from the same formulae, from which the following table is computed, shewing the expense of drawing one ton over a distance of 100 feet by a stage coach, at an average velocity of ten miles per hour. The numbers distinguished in the table by apostrophes ('), are not deduced immediately from the tabic referred to, but interpolated by an empirical process. Col. 1 gives the rate of acclivity or declivity of the road ; col. 2 the expense, in pence, per 100 feet in length ascending, and col. 3 the expense, in pence, for the same distance descending. i.Uu: I .< .( .1 . 4 , , - • f ■ (.f ■•' .. 'It);)?-;. ' f I Bi . ( < .' . ■' , : • !■; '■ \ii * Pamel on Ron(1«, p. 406, I, • V «»v' \ < { ■ ^ . ■ ■_ ; • V ■'■■ . < I. .Jr.. \''U.. (Mil '" » ■ ■ h; . • .' ■ ■ I ■ r ; v't.U-J . ki \rf;f. .;i ?v<^/. 'I I''^ I- It 111- ':]'■; i r ^■.?i. ';; .:4,,j;;V. m^- I.,. ;; fl 234 ASCENTS AMD DESCENTS OF HILLS. inrofi !.:/»,! /Id; I TABLE IV. :Aivf ^Tn-?fi5:i ;nz'i Oilt tffl 1 2 3 1 2 3 1 in 10 .9656 .3085 1 in 50 .4942 .3085 11 .8926 .3085 51 .4927 .3085 !iM 3 12 .8336 .3085 52 .4912 .3085 ossf'.> 13 .7876 .3085 53 .4898 .3085 ;/ib:)::14 .7513 .3085 54 .4884 .3085 15 .7223 .3085 55 .4870 .3085 . r 16 .6980 .3085 56 .4857 .3085 17 .6774 .3085 57 .4844 .3138' 18 .6597 .3085 58 .4831 .3183' ^5-' i' 19 .6444 .3085 59 .4819 .3221' 20 .6309 .3085 60 .4808 .3253' 21 .6190 .3085 61 .4797 .3280' 22 .6083 .3085 62 .4786 .3303' 23 .5989 .3085 63 .4775 .3323' 24 .5901 .3085 64 .4765 .3341 25 ' .5819 .3085 65 .4755 .3358' 25 .5733 .3085 66 .4745 .3376 27 .5663 .3085 67 .4734 .3392' 28 .5626 .3085 68 .4724 .3407' 29 .5593 .3085 69 .4715 .3421' 30 .5518 .3085 70 .4707 .3434' 31 .5470 .3085 71 .4701 ,3U1 32 .5425 .3085 72 .4692 .3459 33 .5385 .3085 73 .4684 .3471' 34 .5346 .3085 74 .4676 .3482' 35 .5309 .3085 75 .4669 .3493' 36 .5275 .3085 76 .4662 .3503' 37 .5242 .3085 77 .4656 .3513' 38 .5213 .3085 78 .4650 .3523 39 .5186 .3085 79 .4642 3533' 40 .5157 .3085 80 .4635 .3542' 41 .5122 .3085 81 .4629 .3550' 42 .5100 .3085 82 .4624 .3558 43 .5082 .3085 83 .4618' .3566' 44 .5059 .3085 84 .4412' .3574' 45 .5037 .3085 85 .4406' .3582' 46 .5016 .3085 86 .4600' .3590' 47 .4996 .3085 87 .4595' .3597' 48 .4977 .3085 88 .4590' .3604' 49 .4959 .3085 89 .4585' .3611' ASCENT3 AND DESCENTS OF HILLS. 235 s y.\ixhjA xiwn f.rMr;7. iTABLE IV.— Continued. ; '^>.i;oi!M^fi.'. .■•'>'>nKtp 1 2 3 1 2 3 I in 90 .4580 .3618' 1 in 115 .4481' .3739' 91 .4575' .3624' 116 .4478' .3742' 92 .4570' .3630' 117 .4475' .3745' 93 .4565' .3636' 118 .4472' .3748' 94 .4560' .3642' 119 .4469 .3761 95 .4555' .3647' 120 .4467' .3754' 96 .4551' .3652' 130 .4444' .3777' 97 .4547 .3657 140 .4421' , .3799' 98 .4543' .3662' 150. .4399 .3820' 99 .4539' .3667' 160 .4383' .3839' 100 .4535 .3672' 170 .4368' .3858' 101 .4531' .3677' 173 .4362 .3872 102 .4527' .3682' 180 .4354' .3876' 103 .4523' .3687' 190 .4341' .3893' 104 .4519' .3692' 197 .4333 .3904 105 .4515' .3697' 200 .4330- .3908' 106 .4511' 5?702' 300 .4261 .3978' 107 .4507' i 07' 400 .4233' .4007' 108 .4503' .,1711' 500 .4206 .4035' 109 .4499' .3715' 600 .4296' .4046' 110 .4496' .3719' 700 .4187' .4056' 111 .4493' .3723' 800 .4179' .4065' 112 .4490' .3727' 900 .4171' .4074' 113 .4487' .3733' 1000 .4165 .4081' 114 .4484' .3735' Horizontal .4123 .4123 118. This table is probably the best guide we can at present obtain. The common mechanical theories do not appear to meet the case : nearly every book which treats of mechanics, makes some mention of horse-power ; but as far as I have had opportunity of observing, they all treat it in the same manner as gravity, pointing out its effects by the same theorems that are applicable to falling bodies. But the cases are not at all similar ; gravity is a constant power operating upon any given weight of matt».r with a certain force, under all circumstances, whether at rest or in motion, by a regular rule, or as it is termed, law : horse power, on the contrary, is under the control of a will ; sometimes he exerts himself to the utmost limit of his stren^ith, amounting to three or four times his ordinary draught, and then relaxes, so as to recover from the exhaustion. In fact he accomodates himself to a wide range of circum- V V/ il 536 ASCEIf TS AND OE8GEKT8 OF HILLS. I'hI iifi pi t.ii; 4 ^ .i I. ■,-i . *-; \ ■ .». . f- I ■'. Stances, and though the theories of mathematical writers may exhibit the average of his exertions under particular circumstances wiih tolera- ble correctness, they are not to be depended upon in making a com- parison of different roads. , » • . ■ 119. . It is evident that any investigation of this nature must be - Founded, upon the different rates of travelling upon the several grades; because, the load cannot be varied to suit the varying resistances of the road ; it is the rate of travelling that must vary ; and as the cost of a given time on the road is the same at all velocities, the expense and rate of travelling will always be inversely proportional to each other. Pro- bably, the best way to improve our knowledge of this subject will be to travel with teams and stages, and note the rates at which they move on the different grades, throughout a considerable length of road : the mean of a great number of observations of this nature would give an average rate very near the truth. It is probable that the formula of Mr. McNeill, from which the above table was computed, has been obtained in some such way as this ; at least he does not appear to have relied so much upon abstract reasoning as on experiment. He tells us his formulae are deduced from '' actual practice," and so far as that practice goes, his rules must be superior to those which have been deduced from reasoning alone. Table 4 appears to be founded upon this principle ; that is to say, upon the time spent in passing over a given distance on the several grades, or in other words, the effect which the grades have upon the rates of travelling as compared with a given rate upon the level. Hence we can easily turn the expense given in the table into time, and by this means enable ourselves to form a judgment of the truth of the table. For instance, supposing the velocity on the level to be at any given rate, and we wish to know the corresponding velocity for any given ascent, as one foot in 30 ; we find in the table the expense answering to 100 feet, upon the level .4123 pence ; for a grade of 1 in 30, ascending .5518 pence, and for the same grade descending, .3085 pence. The time of travelling over 1 00 feet will therefore be proportional to these num- bers, and the rate of travelling inversely proportional thereto. Allowing, therefore, the velocity on the level to be 10 miles per hour, we have, as .6518 : 10 : : .4123 : 7.47 miles per hour on the ascent ; and as, .3085 : 10 : : 4123 ; 13.36 miles per hour on the descent^ of the plane of 1 in 30. Tabje 5 is computed in this manner, where col. 1 contains the grades, col. 2 the corresponding rates of travelling of a stage coach ascending, and col. 3 the rate of descent ; — the rate. upon the level being 10 miles per hour. Columns 4 and 5 give the same calculation for teams, allowing the rate on the level to be 3 miles per hour, and columns 6 and 7 give the ASCENTS AND DESCENTS OF HILLS. 237 same, answermgto a rate upon the level of two miles and a half per hour. The computation of the last four columns is from a source different from that of col. 2 and 3, which relate to stage travelling. 120. Table 6 is derived from Table 5 ; it shews the length of time in minutes, consumed in passing over one chain in distance. Col. 1 gives the grades ; col. 2 the time per chain, ascending, and col. 3 the same on the descent^ allowing the wehc'ny on the level to be 10 miles per hour. Columns 4 and 5, show the same answering to a velocity of three miles on the level; and columns 6 and 7, tha same answering to two miles and a half per hour upon the level. The method of computation of this table is as follows. We first find the time of passing over one chain, at the given rate per hour, on the level ; then the time of passing over any other distance being inversely as the velocity, it is obtained by an operation of the Rule of Three. For example, suppose we wish to find the time of transit over one chain in length, ascending on the grade of 1 in 40, and with a team which moves three miles per hour on the level : — We first find the time of transit of one chain at three miles per houv, by dividing 60 minutes by 240, the number of chains in three miles, — the quotient is one fourth of a minute, or, expressed decimally, .25 minutes for the time of transit over one chain. Then, in the 4th co- lumn of Table 5, opposite the grade of 1 in 40, we find 2.21 miles an hour for the rate of travelling up that ascent ; and the times being in- versely as the rates, we have by the Rule of Three inverse, as 3 miles : .25 minutes : : 2.21 miles : .339 minutes the time required. Ilk practice, a formal operation by the Rule of Three is not necessary, because the first and second terms of the proportion being always the same, we may take their product as a constant number and divide it by thediff*erent rates. In the present case we may multiply 3 by .25, which gives the constant number .75, and this divided by 2.21 gives .339 minutes, as in the example. If the constant number be divided by 2, the rate answering to a grade of 1 in 30, the quotient, 3.75 is the time in minutes, of transit over one chain at two miles per hour, and so on for other rates. This rule has been derived from a particular case, by the Rule of Three, for the sake of greater clearness to persons who understand only arithmetic, but it is in reality applicable to all cases. The rule derived from the algebraic process is, — Divide 60, the minutes in an hour, by 80, the chains in a mile, and divide the quotient by the rate per mile, the result is the time of transit over one chain, in minutes. This quotient, or constant, as such numbers are called, is j, o). 75, and is always to be divided by the rate per mile. 31 'isi ta m] ^lil fm lit ■• vl-i ,1 ,. U-, f ■' ■'h-- 'i- lly - ■* iil ^8 ASCENTS AND DESCENTS OF HILLS. We have been the more particalar in describing this process, because it gives the means of correcting the table.. If it is found by observa- tion that the usual rates of travelHng upon any certain grade is different from that assumed in Table 5, it is only necessary to substitute the more correct rate per mile in that table, and divide .75 by the corrected number, for the corresponding correction in Table 6. >,? > Table 5 is not required in computations of the comparative power of roads, it is only introduced for the purpose of showing the grounds of the other tables, and of furnishing the means of improving them by making corrections upon it. . r< ; '■rf i:?'^fl i- '\\{u:nc^j iUOil • I » f , J! (/ ^A} tro r. r'trr en: ^ :.,.,,. , TABLE V. ,:>;j;;.. i- . J ..- .-■.■ .. - ■ 1 2 3 4 5 6 7 Rate W hour Rate ^ hour Rate ^ hour Rate ^ hour Rate V^ hour Rate ^ hour Elevations. ascending: Deitcending. scending. Descending. Ascending. " Descending. 1 in 10 4.27 0.71 4.00' 0.60 4.00' 16 6.70 1.29 4.00' 1.08 4.00' 20 6.54 * 1 1.62 4.00' 1.35 4.00' 30 7.47 2.00 4.00' 1.67 4.00' 40 7.99 13.36 2.21 3.90' 1.84 3.60' 60 8.34 13.36 2.34 3.75 1.96 3.34 60 8.57 12.67 2.44 3.61 2.03 3.17 70 8.75 12.00 2.61 3.66 2.09 3.00 80 8.89 11.64 2.56 3.46 2.13 2.S0 90 9.00 11 .39 2.61 3.31 2.17 2.85 100 9.09 11.23 2.64 3.26 2.20 2.80 150 9.37 10.99 2.75 3.23 2.29 2.70 200 9.52 10.56 2.81 3.11 2.34 2.63 300 9.67 10.36 2.87 3.06 2.39 2.59 600 9.80 10.22 2.92 3.04 2.43 2.65 1000 9.90 10.10 2.96 3.02 ' 2.47 2.52 Level 10.00 10.00 3.00 3.00 2.50 2.60 ■'.■ * ii;- ■ 11.. ASCENTS AND DESCENTS OF HILLS. ^39 because observa- dififerent the more corrected power of ounds of them by TABLE VI. ' •• 7 Rate V hour ' Descending. 4.00' 4.00' 4.00' 4.00' 3.60' 3.34 3.17 3.00 2S0 2.86 2.80 2.70 2.63 2.59 2.55 2.52 2.50 t''Ofljv ^'iilT I 2 3 4 5 6 7 Grades. Time ucendiiig at 10 inilps per hour. Time descend- in? at 10 miles per hour Time ascending at 3 miles < per hour. Time descend' ing at 3 milei per hour. Time ascending Time descend- at 2.^ miles ing at 2| miles per hour per hour. Minutes. Minutes, Minutes. Minutes Minutes. Minutes. 1 in 10 .1755 .0561 L056 .187' 1.250 .187' 15 .1311 .0561 .657' .187' .693 .187' 20 .1147 .0561 .463 .187' .555 .187' 25 .1056 .0561 .411' .187' .480' .187' 30 .1000 .0561 .r^^5 .187' .449 ,187' 35 .0964 .0561 .0:4' .190' .422' .200' 40 .09,34 .0561 .339 .192' .408 .209' 45 .0915 .0561 .329' .196' .394' 218' 50 .0900 .0561 .320 .200 .335 .225 55 .0885 .0561 .313' .204' .378' .23 r 60 .0874 .0591 .307 .207 .374 .236 65 .0864 .0611 .303' .209' .363' .244' 70 .0856 .0624 .300 .211 .357 .250 75 .0850 .0634 .2966 .214' .355' .255' 80 .0843 .0644 .293 .217 .353 .258 85 .0837 .0651 .2897 .220' .349' .261' 90 .0833 .0658 .287 .223 .347 .263 9p .0828 .0663 .2853 .226' .344' .265' 100 .0824 .0668 .284 .230 .341 .267 J 50 .0800 .0695 .272 .232 .335 .277 200 .0787 .0710 .267 .241 .320 .285 300 ' .0774 .0723 .261 .243 .314 .290 400 .0770 .0728 .258' .244' .311' .292' 500 .0765 .0731 .256 .246 .309 .294 600 .0763 .0734 .256' .246' .308' .295' 700 .0761 .0737 .255' .247' .307' .296' 800 .0759 .0739 .255' .247' .306' .296' 900 .0758 .0741 .254' .248' .305' .297' 1000 .0757 .0743 .254 .248 .304 .297 Level .0750 .0750 .250 .250 .300 .300 1! .^/t-V/'t. 121. In making use of the foregoing tables for comparing different roads, we may take either Table 4 or Table 6. . The latter is the most simple : it merely gives the time of passage over the roads to be com- pared, and in most cases of laying out new roads this is quite sufficient; but in alteHn^ old roads, and in some cases, in laying out new ones, the 240 ASCENTS AND DESCENTS OF HILLS. t", ■.. effects upon draught and expense of construction must be jointly consider- ed. Table 4 is calculated to meet this case ; instead of the time, the ex- pense of drawing a stage coach at the rare of ten miles per hour is taken as the basis of the table ; but as the expense is proportional to the time, both tables will give the same comparative result. It was on occasion of projecting an alteration of an old road, that Mr. McNeill gave the calculations of expense from which Table 4 is deduced. After describing his method, he says, — ** All that is necessary in the present investigation is, to calculate by the tables the expense of transporting a ton weight over the existing line of road, and also over the proposed improvements. The difference will be the Piiving in ex- pense of drawing one ton with the given velocity over the proposed improvement. This, multiplied by the number of tons that pass over the road each day, and by the number of days in the year, will give the annual saving, which, compared with the interest of the money neces- sary to be expended in making the improvement, will clearly show whether the saving in horse labour is commensurate with the proposed expense. By applying the same criterion to each of the proposed plans, it will at once be made evident which of them should be adopted, as that which would produce the most beneficial result at the smallest expense." . . He then describes one of his plans of improvement, on the merits of which he goes on to remark ; — • " For the purpose of ascertaining the comparative merit of this plan, the following calculation, as above described, has been made : " Pages 411 and 412 contain the calculation of the expense of draw- ing one ton over the present line of road between the given points, in both directions ; which amounts to 82.0647 pence. ( * " Page 413, contains the calculation of expense of drawing one ton over the proposed improved road, as above described, between the same points; which amounts to 76.1724 pence. By this it appears that the saving in horse labour on each ton will be 5.8923 pence; and for 170 tons the daily saving will be £4 3s. 6d., which, at 5 per cent, is interest for £30,310 lOs. The estimate for making this improvement is £23,757. ^. ^- •■ -•• ^■-- " The difference between tlie amount of the estimate and this savinf> to the public by the proposed improvement is, therefore, £6^653^ which is the actual sum the public would gain by this improvement, supposing the present trafific to continue ; if the traffic increased, the saving would be still more."* • Tarnel on Uoail», p, 408. ji > i ( ■•■.r"i 1- (■'»)"• ;!f iu'tfi .iin;- ASCfiNTS AND DESCENTS OF HILLS. 241 He then gdos on in his report to describe other plans, and calculates their effects in the same manner ; but they need not be adduced ; enough has been quoted to give a clear view of his method. It is possible that his assumption of the expense per mile is not suit- able to the scale of prices in this province, but if so ii will not afii ci the accuracy of the result as to the comparative draught on any two lines : it will only affect it as to the pecuniary benefit to be derived from an alteration. .jioiT,, iM':>."rv i , 'i;. ,., ,,,i •,, ,. 1.1' I 'i 122. There is one important circumstance connected with altera- tions of roads, which he has omitted to notice, — probably hccause it was not necessary in that particular case. The road upon which the calcu- lations were made runs across a valley about a mile and a half wide, and two hundred feet deep, and was in some places as steep as one in 15. The length of the alteration proposed was about two miles, and upon the expense of drawing a load over this part only, was the calcu- lation made. Now, if other parts of the same line of road were more level, these high and steep hills must have constituted a barrier to tiie traffic, and the benefit derivable from the improvement would consist, not merely in a reduction of the expense of haulage on that particular section, but in the increase of load that a team would, in consequence, take on other parts of the road. Mr. McNeill makes no observations oa this subject, he confines himself to the effect upon fast going stages ; but in this province, this is a secondary object. In stages, the team is always sufficiently powerful to take the load up hills; it is the speed only that is affected by them ; and in making arrangement for stage travel, each small section of the road may be considered independently of its relation to other parts. In heavy teaming the case is otherwise ; the time of transit is nearly fixed ; it is the quantity of goods carried at a given expense, that is affected by hills in the road, and a steep hill in one part, unlike its effect upon a stage, will cause a lower state than otherwise of the effective power of the road throughout its whole length. This must not be lost sight of in projecting improvements: in every district of country there is a certain grade of hills that is naturally adapted to that particular region, and which can by proper management be easily obtained. This grade should be ascertained for the whole line, and'when determined upon, should not on any account be exceeded ; neither need there be much solicitude as to obtaining grades very much beneath it ; because, partial levels in the road will cause little or no difference in the weight of load taken generally upon the line. In the application of rules, therefore, to this subject, a proper subordination must always be maintained, to these leading principles. 123. The followiijg example of the comparison of different lines of il :, fi I 1 Wr I- i |;>; 4-^ $42 ASCENTS AND DESCENTS OF HILLS. road is drawn from a real case on the Great Eastern Road, between Stewiacke and Truro. A E B (Fig. 43) is a portion of the road as now travelled, and it is proposed to snorten it by going upon the dotted line ACB. The formation of the ground is as follows. The point B is 63 feet above A, and the road rises from A with a gentle acclivity, in no case exceeding 1 in 32 ; but, generally, much below that angle. There is a swell of ground running in the direction F C £, and terminating at K ; tq avoid which swell was the object in view in carrying the road by E. The summit of ground on the road is at D, and of the ridge over which the line ACB runs, it is at C. The height of the point C is 14 feet above D, and 16 J feet above B. The distance from A to B is, by the road, 7,370 feet, and by the line ACB, 4,970 feet, being a difference of distance of 2,400 feet. Now, the problem to be determined is, whether will teams and stagps pass from A to B, and from B to A with the greatest economy of time and labour; on the longer line with its easy grades, or on the shorter, with its steeper gradients and higher summit ? ... ; 'i In making this comparison we first calculate the expense of each line by Table 4. This calculation is contained in Table 7, which gives the lengths of the planes in feet, the rates of inclination, and the expense. The result is, that in going from A to B it is, on the road, 32.7737 pence, and on the proposed line 23.0776 pence ; also, from B to A, on the road, it is 27.9215, and on the line, 18.1343 pence: consequently, the excess of expense of transit on the road exceeds that on the line ACB, in passing from A to B, 42, and from B to A 54 per cent. i I ( t ' ' t ' r '. '■ ii'isi •; ;)'vj')M'[;t', <,! null ,:.tbiiiu'}iv.> u')vi{ .1 ' ' •u i; ; ) f '■ . '!.^!L;-j'-:i : ): r •...•■ ;i'J7/ Ur- Hi ,' 'I!',, ' I !Ui\UK -^aJ r J 1 1 ASCENTS AND DESCENTP Of HILLS. 243 ;' / 244 ASCENTS AND UESCF.NTS OF HlttS. ii" flM.' ill, ;. . ' i •f . fe. I' TABLE VII. Expanse of drawi)iii' one Ton in a Coackj from B to \j and from A to B, by the Road. ( > " ■-'— .. ,...-> — From B to A Jt- ■ — rr*ii — 1 =3--- • ' From A to I II Len^tli in Rates of Exrenoe in Length in RdiM of Expvnco in feit, inolinitioni. I'enco fvvt. inclinatiuns. Penct. 460 r 1 in J 97 1.9932 165 r 1 in 32 .8951 600 f 125 1.8825 420 r 210 1.8170 460 f 300 1.8298 230 r 116 1.0300 165 f 105 .6105 230 r 125 1.0244 330 f 220 1.2916 400 r 147 1.7624 190 f 61 .5861 430 r ■\ 42 2.1930 300 f 32 .9255 594 r 88 2.7264 275 f 110 1.0230 360 r / 94 1.6416 264 f 130 .9970 550 r . / 132 2.4442 660 r 373 2.3744 600 f 250 1 .9760 600 r 250 2.1450 660 f 373 2.2400 550 f 132 2.0801 264 r 130 1.1732 360 f 94 1.3111 275 r 110 1 .2364 694 f 88 2.1407 300 r 32 1.6276 430 f 42 1 .3265 190 r 51 .9361 400 f 147 1.5248 330 r 220 1.4223 230 f 125 .8657 165 r 105 .7450 230 f 116 .8606 460 r 300 1 .9600 420 f 210 1 .6444 500 r 125 2.2275 165 f 32 .5090 460 f 197 1.7968 7383 27.9215 7383 32.7739 i I * a ! i ( ■, I' > A ill "is, "■ ABC&NTS AND OESCENTfl OF HILLS, 245 TABLE VII— Continued. Expense of drawing one Ton, in a Coach., from B /o A, and from A to B, by the line A C B. From B to A. From A to B. Ltngth in ft«t. Rttc* of inolinnUon. EspenM in Panot. I^sngth in fc«t. lU'tfli of inclination. Eipen*« in i'enoei 445 level 660 r 363 f 627 level 264 f 165 level 960 f 726 f 760 f 1 in 33 1 in 33 1 in 33 1 in 33 1 in 46 1 in 50 1.8347 3.5541 1.1198 2.5851 .8144 .6803 2.9616 2.2897 2.3446 760 r 726 r 960 r 165 level 264 r 627 level 363 r 660 f 445 level 1 in 50 lin46 1 in 33 1 in 33 1 in 33 1 in 33 3.7559 3.6416 5.1696 .6803 1.4217 f;.5851 1.9547 2.03C1 1.6347 i970 18.1343 4970 23.0796 Note:.— In the first column of this and the following tables, r, signiiios rise, and, f, fall. 124. The foregoing calculations relate to the transit of a stage coach, at the rate of 10 miles per hour on the level ; we will how cai- culate the time of transit of a loaded team^ allowing the rate of travel- ling on the level at three miles per hour. Table 8 contains this calculation founded upon Table 6, columns 4 and 5 ; by which it appears that the time of transit from A to B, is, by the road, 39.907 minutes, and by the proposed line 22.3 «"> ninutes : also, from B to A, by the road, it is 25.436, and by the lino, 17.392 minutes. Consequently, the time of transit on the road is greater than ihat on tlie proposed line, in going from A to B, by 39, aad from B to A by 46 per cent. The reason of the difference of per centage brought out by these two methods is that the team is assumed tc) move upon the steeper grades slower, in proportion to its speed upon the level, than the stage I coach does, which tends to reduce the advantage of diuiinution of dis- tance on the steeper elevations. 32 i;;» mm' H;!- ,tv- •*■<- 1-* '*? 246 ASCBNl'S AND DESCENTS OF HTLLS. TABLE VIIL a/ r T'imc employed by a Team in passing Jrom A to By^md from B to A, % the Road, From A to B From B to A. Length ia Rates of Time in Length in Rates of Time in chains. inclinations. iVIinutes. chains. inclinations. iVIinutes. 2.60 r 1 in 32 .915 7.00 r 1 in 197 1.865 6.30 r 210 1.644' 7.50 f 125 1.732 3.50 r 116 .980 7.00 f 300 1.701 3.50 r 125 .973 2.50 f 105 .575 6.00 r 147 1.632 5.00 f 220 1.205 6.50 r 42 2.177 3.00 f . 51 .600 9.00 r 88 2.583 4.50 f < 32 .846 5.50 r 94 1.573 4.20 f 110 .966 8.30 r 132 2.307 4.00 f • 130 .924 7.50 f 250 1.732 8.50 r 273 2.235 8.50 f 273 2.057 7.50 r 250 1.780 4.00 r 130 1.112 8.30 f 132 1.917 4.20 r 110 1.184 5.50 f r 94 1.248 4.50 r 32 1.642 9.00 f 88 2.007 3.00 r 51 .957 6.50 f 42 1.254 5.00 r 220 1.330 6.00 f -.:.-147 1.392 2.50 r* 105 .710 3.50 f il25 .808 7.00 r 300 1 .627 3.50 f 116 .805 7.50 r 125 2:085 6.30 f 210 1.106 7.00 f 197 1.687 2.50 f ■;.'> 32.. .470 111.80 30.907 111.80 25.456 ('•»•' •' /' luir' _ ■'■'I' It. • I'i i)'f---.";U;', '.MJ? I. 'J ■.. I .\ , : In ■ 'Ill ■' 'ii!'*! ('? '.i ;t'J il ill! ,,• , ;;o' iiHi. ASCEITTS AND DESCENTS OF HILLS. 247 TABLE VIII— Continued. M. Time employed by a Team- in passing from A to B, and from B io A, by ilie line A C B. From A to B. From B to A. Length in chains. Hates of inclination. Time in Minutes. Length in chains. Rates of inclination. Time in Minutes. 11.50 r 11.00 r 14.50 r 2.50 level 4.00 r 9.50 level 5.50 r 10.00 f 6.75 level 1 in 50 1 in 46 1 in 33 1 in 33 1 in 33 1 in 33 3.473 3.608 5.220 0.625 1.440 2.375 1.980 1.900 1.667 6.65 level 10.00 r 5.50 f 9.50 level 4.00 f 2.50 level 14.50 f ll.OOf 11.50 f 1 in 33 1 in 33 1 in 33 1 in 33 1 in 46 1 in 50 1.687 3.700 1.045 2.375 .760 .625 2.755 2.145 • 2.300 75.25 22.308 75.25 17.392 125. Another example may be taken from a part of the same road, about a mile northward of the place of the preceding, at Policy's Farm. The line ABC D, fig. 44, shows the road, which was carried by C to avoid alow swell of ground, whose summit is shewn by the dotted hne E C. The point B is the highest on the road, and is 23 feet above A. A level line carried along the surface of the ground from the point B, is shewn by the dotted line F B G. Between E and G, there is a swell of ground, whose summit is at E, which summit is 14 feet above this level line ; the whole height above A being 37 feet. Also» the distance from A to D, is, by the road, 3551 feet, and by the more direct line A F E G D, 2656 feet, there being a difference of 895 feet. Here again the question to be determined is, which of these two lines will be travelled with the least expense, the present road, or the shorter line with its higher summit. Following the same method as before, we calculate the expense of a coach on each line by Table 4, and the time of a team at three miles per hour upon the level, by Table 6. The results are contained in Table 9. w u m ■ \ • 248 ASCEWTS D]\\ ' '' ■ .... ' ■ % ! ■ i /• ?;, ].. ■■►* . Uf^ AND DESCENTS OF HILLS. '. , -t i . ' nv :>\AHr ,1.. 1 1 IWI: ASCENTS AND DESCENTS OF HILLS. 249 I '•>; TABLE IX. 'V;^'; ;;'. 1 Expense of drawing one Ton in a Coacky from A, by the Road, r A to D, and ' from D to ^1 From A to D . From D to A . ff ^H Length in feet. Rates of . inolinatiom. Ez pence in Pence. Length in feet. Rates of inclinations. Expence in Pence. I 150 r Iin70 .7060 198 f 1 in 30 .6109 317 r 63 1.5123 430 f 98 1.5746 '■^B^B ^H 363 r 31 1.9856 231 f 50 .7095 'Wk 442 r 96 2.0115 430 r 450 1.8146 1 I SOS lev. 1.4966 231 r 41 1.1780 198 f . 32 .6170 198 r 58 .9565 1 'I { V . t . ^H 198 f ^ ,, 56 .6302 198 r 32 1.0850 t\ blfl^DM 231 f 41 .6787 363 lev. 1.4966 IIHUi 430 f 450 1.7522 442 f 96 1.6140 ft 'jffifllnti 231 r 50 1.1366 363 f 31 1.1198 iWh^^ H 430 r 98 1.9535 317 f 63 1.0565 JaKWlM ^^H 198 r 30 1 1.0926 150 f 70 .5151 ■ii 3551 15.5928 3551 13.7313 1 Expense of drawing om ? Ton in a Coach from A to D, and from D to A, hy the line A E D. , , . ■i 1 ■i '■1 :l i'aj|H|ljpl . . From A to I ). . From D to A. Length in feet. Rates of inelination. Expense in Pence. Length in feet. Rates of inclination. Expense in Pence. ,1H 'IffimM 433r 1 in 60 2.0818 320 lev. 1.3093 ) " 't *'' 1 1023 r .. 38 5.3329 230 r Iin33 1.7770 .1 IflH 1 260 r • 94 1.1400 300 r 94 IMQO ;■ ^H 300 f 94 1.0926 250 f 94 .9105 } fin^Hl ^1 330 f 33 1.0180 1023 f 38 3.1560 it: 1 320 lev. 1.3093 433 f 60 1.4085 2656 11.9746 2656 9.9273 250 ASCENTS AND DESCElVTd OF IIlLLSi m H:. ft:- »••■ Pi 11''' ^■'' i: 1 ■ic ... Here we find the expense of a ^o'ach from A to D, by the road, 15.5928 pence, and by the line A ED, 11.9746 pence. Also, by the road, Irom D to A 13.7313, and by the line A ED 9.9273 pence.' The cost of transit, therefore, on the road exceeds that upon the line A E B, from A to D by 30, and from D to A, by 38 per cent. / ? n;— '.f 126. The time of transit of a tea?nf between the above points is shown by Table 10. From A to D, by by the road, is 14.86, and by the line 11.596 minutes. Also from D to A, by the road is 13.478, and by the line 9.561 minutes ; showing an excess of time in passing: between A and B, on the road, in the former case of 28, and in the latter of 41 per cent, — nearly the same as in the passage of the coach. 'M-i '' i i»i .' ., •I U •!■ ru: TABLE X. I 4ir; 3.00 r 58 3.00 r 32 5.60 level ■.■? I'll .■■ 6.75 f . 96 6:50 f 31 4;2p;r 63 2.;^bf: 70 < .i > )^M : .561 1.495 1.100 1.670 1.179 .927 1.095 1.375 1.525 1.0^4 .f33, 13. [\(-\)\ ^''i'MI ik-itV 1 t '» ,r ASCENTS AND DESCENTS OF HILLS* 251 e road, by the ;e.' The AEB, points is and by 478, and between ter of 41 t I . .1 . I ' I D to A, I \h Time employed by a Team in passing from A to D, and from D to A, by the line A E D. T4mein Minutes. 1.495 1.100 1.670 1.179 .927 1.095 1.375 1.525 1.0^4 tho'. From A to C • From D to i^ L« Length in chains. Rates of incHnatiun. Time in Minutes. Length in chains. Kates of inclination. Time in Minutus. .- 6.50 r 15.50 r 3.75 r 4.50 f 5.00 f 5.00 lev. 1 in 60 38 94 94 30 1.995 5.332 1.072 1.012 .935 1.250 5.00 lev. 5.00 r 4.50 r 3.75 f 15.50 f 6.50 f lin 30 94 94 38 60 1.250 1.875 1.287 .844 2.960 1.345 40.25 11.596 40.25 9.561 127. We will adduce one other exan>ple, and then conclude the subject. It is on the Great Western road, in the Township of Falmouth. A road had to be carried from the point D to the point E, fig. 45. The direct line D C E crossed a ridge whose crest is shown by the dotted line B C G. This ridge terminates at G in a point which juts out into flat ground. There is also a lesser ridge, or rather low swell of ground, whose top is represented by the line A I FT, and which terminates at H ; there being a continuous valley between the two ridges. This formation of the ground, admitted of three different hnes of road ; — The first following the dotted line frdm D, round the point of high ground at H, thence round the other point at G, and thence along the flat ground adjoining the base of the hill to E ; the second, crossing |[3 the low ridge at I, and falling into the former line near F ; and the third t|J proceeding on the dotted line D C E. The first of these lines follows the hollow ground between the ridges, and is uniformly level ; the only objection to it is its length. The second, is forty rods shorter than the first, and is that which has been adopted for the road ; where \t crosses the ridge, at I, it is 20 feet above the flat ground at G. The third, is 100 rods .shorter than the second, but possesses the disadvantage of crossing the high ground at C, which is 63 feet above the flat which ranges from G to E. The road, except the rise over the low ridge at I, is entirely level, and the comparison we have to institute, is between the circuitous, but level road, and the shorter, but more hilly line, D C E. Following the same method as before, the time of transit between the extreme points, is, as appears by the following table (No. 11) from D to E, by the road 28.827, and by the line D C E 23.687 minutes,— DESCENTS OF HILLS. 42. 10. 31. 83. \2i to the of the elevat ASCENTS AND DESCENTS OF HILLS. 253 .\ - '. .n'v.l ■ ' ^ H ' • ,,..-},, ■ Mil r excess of time upon the road 22 per cent. Also, from E to D the time upon the road is 27.159, and upon the line D C E 212.73 minutes, excess of time again by the road, 28 per cent. The expense as found by Table 4 is not introduced here, bein^ con- sidered unnecessary : the reader, if he chooses may make tlie calcula- tion for himself: enough has been written to show the method of pro- ceeding. ..I TABLE XI. Time employed by a Team in passing from D (o E^ and from E to D, by the Road, From Dto E 1 i. From E toD. I^ength in chains. Kates of inclination. 'I'iine in Minutes. Lenpth in chains. Rat3S of inclination. Time in Minutes. 5.00 r 1 in 57 1.550 75.50 level 18.875 8.50 r 72 2.540 10.00 r 1 in 44 3.310 6.00 r 20 2.778 3.50 f 46 0.689 3.50 r 46 1.144 6.00 f 20 1.548 10.00 f 44 1.940 8.50 f 72 1.802 75.50 level .; ' • ■ 18.875 5.00 f 57 1.025 108.50 28.827 108.50 27.159 ^ ''\io i28^i' On the above examples it may be remarked, tha'« with respect to the first and second, there cannot be a doubt of faulty arrangement of the road : all the hills of the shorter lines are within the general elevations of the hills on the other parts of the same line of road, and are, 33 A 254 ASCENTS AND DESCENTS OF HILLS. :'»!, •f ,1 ;f^ I'' .V .{^, i moreover, at such grades as reduces the mechanical power expended in passing over them to the same amount as it would be for an equal dis- tance upon the level. Besides, as the ascents in the direction of the heavy traffic are quite short, — one being only 20, and the other 40 rods in length, — a team can take no greater load upon the parts in question of tile present road, by reason of its levelness, than it could upon the shorter lines ; because there are many other parts of the road having hills equally high and steep. Also, this state of things must continue, be- cause a reduction of the grade of these hills can never be effected with> out incurring an expense that would be uncompensated by any con- ceivable benefit to be derived from it. For stage coaches the advantages of the shorter routes will be still greater than for teams, (Art. 122). The public have, therefore, in this instance, to travel five-eighths of a mile further than i necessary, without any countervailing advantage whatever. 129. With respect to the third example, the advantage from the shorter line is not so obvious. It has been selected as one of the large class of cases that puzzles the engineer, and requires the application of more correct rules than have, as yet, perhaps, been discovered. Our rules make no allowance for the length of hills, but this, we know, has an efi'ect upon a team. A road, for example, having four alternate ascents and d:^cents of a furlong each, contains in the aggregate, the same ascent and descent, as one continued ascent and one descent each of half a mile ; and the mechanical power required in the latter case would be only the same as in the former. Not so with the team : its power of action will decrease by the longer continued exertion on the long ascent. We do not know the law of this decrease, but we know that such effects take place, and that it is necessary in calculations of this kind to make some allowance for them. ^ It is probable, however, that in the peculiar circumstances of this case, an advantage would be obtained by going upon the shorter line. On the side C £, the disadvantage of one long ascent may be obviated : the point £, the beginning of the long ascent from the flat ground may be removed to three times its present distance from C, without increasing the perpendicular height, or lengthening the general line ; and conse- quently, the rise of 63 feet may be broken into several short ascents with levels of double their length between them. This, partly at least, ob- viates the objection from the length of the hill. The ascent from D to C admits of no modification ; but here it is not so much required as on the former : the heavy traffic passes up that ascent, and down this, and half a mile going at ease will be a pretty good compensation to the team for pulling the load up the other side of the ridge. On the return, this advantage is not attainable, but the necessity for it is less ; not only ASCENTS AND DESCENTS OF HILLS. 255 ended in iqual dis- ihe heavy ) rods in lestion of he shorter ving hills linue, be- ?\ed with- any con- ill be still re, in this •y, without I from the flhe large plication of jred. Our know, has r alternate regate, the Bscent each case would ts power of ong ascent, such effects [id to make af this case, line. On viated: the nd may be increasing and conse- iscents with it least, ob- t from D to uired as on m this, and tion to the the return, i; not only because the traffic in the ascending direction is less weighty, but also because there arc within a few miles distance on the same road, other hills much higher and steeper, of which the improvement appears im- practicable. Any load, therefore, that is reasonably adapted to those hills will be easily taken up the hill in question. For stage travelling, there is no question but it is best to go over the hill and save the 100 rods of distance. The rules of Mr. McNeill show this, and besides, it is quite in unison with the opinions of experienced drivers. 130. Before quitting this subject, there is one other test which it may not be improper to point out as being applicable to cases of this nature, and more within the comprehension of persons who are not practised in the application of tables. This is the usual and ordinary time taken by a team in passing over a road as observed by experienced drivers. Such persons distinguish the paces of a team horse as follows : A very slow Walk, A slow do. An ordinary do, A slow trot, 2 miles per hour, 2^ do. do. 3 do. do. 4 do. do. The first of these motions takes place on hills above 1 in 40 ; the second on rising ground below that elevation ; the third on the level ; and the fourth on descents so steep as that gravity will just overcome the friction. * ^ Applying this mode of calculation, to example 1st. we get the time of going from A to B, by the road, — 105 chains at 2J miles per hour, - - - 31.5 minutes. 7 do. at 3 do. do. - - 1.8 33.3 (( (( Between the same points by the shorter line, we get, — 50 chains at 2 miles per hour • . - 1 8.75 minutes. 15 do. 3 do. do. - - 3.75 10 do. , 4 do. do. - . - 1.90 u (( ) r 24.40 u On the return from B to A, we have, by the road, — 7 chains at 2J miles per hour - - -2.1 minutes. 105 do. at an average of 3^ miles per hour, 22.5 ' ' ■.- Is \iH-'i .i H 24.6 u 266 ASCENTS AND DESCENTS OF HILLS. Hi , ■■ .^1 . ;. './ 'i;'i:yi . i ! ' 1 i •.'■n ^k "'" ■'iif<.; ,■ And by the shorter line,— ' • "i* "f* 'jii - a. 'mIi ,.» iiuii r.ili i id 16 chains at 3 miles per hour - - - 3.76 minutes. 10 do. 2 do. do. - . ' 3.76 »* 60 do. 4 do. do. - - - 9.37 *' ' 16.87 (I Applying the same calculation to the second example, we have, from A to D,- by the road, — 20 chains at 2| miles per hour - 30 do. 3 do. do. 3 do. 2 do. do. By the shorter line, — 15 chains at 2 miles per hour 15 do. 3 do. do. 10 do. 3Jdo. do. Also, from D to A, by the road, — 3 chains at 4 miles per hour 15 do. 2 do. do. 16 do. 2 J do. do. 20 do. 3| do. do. . By the shorter hne, — 10 chains, average 2J miles per hour, 15 do. 3 do. do. 15 do. , , , 4 do. do. 23 chains at 2| miles an hour 10 do. 4 do. do. 75 do. 3 do. do. By the shorter line, — 52 chains at 2 miles per hour 31 do. 4 do. do. 6.0 minutes. ■ 7.6 " . I 1.1 ** 1 14.6 " , 1 ' 5.6 minutes. 1 - 3.7 " ■ 2.2 « 1 11.5 "' 1 0.6 minutes. 1 tal 3.7 " - . : ^H 5.5 " -i^ I ma 4.3 «,!';.■!■' 1 • /_.! ,ii ,1 ' ••:' • ffU'' I car . .lui^l ^^'^ " *'- 1 "^ ., '• t 1 diff 3.0 minutes. ver - 5.7 " ace 2.8 " , . 1 - ■ ' tot 11.6 " ' tob rom D to E, by the road,— side 6.'9 minutes. mak 1.96 " allt - 18.75 *• coui • it «)< disti a ,.;,.,, -v 27.51 ^^,,;^ pr6|: * hav< 19.5 minutes. five 6.8 " of h ness 26.3 « for s ASCENTS AND DESCENTS OF HILLS. 257 Also, from E to D, by the road, — 75 chains at 3 miles per hour 10 do. 2 do. do. 23 do. 4 do. do. By the shorter line, — 31 chains at 2 miles per hour 52 do. 4 do. do. 18.7 minutes. 3.7 '« 4.4 " 26.8 ({ 11.6 minutes. 9.2 " . 20.8 i( By these calculations we get the excess in time in passing over the road : — i i In the first example, From A to B 36^ and from B to A 46 per cent. In the second example, From A to D 20, and from D to A 21 per cent. ,. In the third example. From D to E 9, and from E to D 29 per cent. Differing not very materially from the results brought out by the tables. This method is less accurate than the former, but with judicious management it will probably be sufficiently near the truth. If the rates ot travelling assumed, be not deemed quite correct, each calculator can assume such rates as may appear consonant to experience, — keeping in mind, that the true practical proportions in the rates of travelling on different grades, must furnish the data required. This method will be very useful to the surveyor in the course of his work, when he has not access to tables, and but little time to go into details. 131. We have been the more full upon this subject, because it relates to the theory by which the practice of engineering of roads is, or ought to be guided, and because it does not appear to have been properly con- sidered in this Province. Fifteen years ago, the ideas of our road makers were all in favour of straight lines ; now, making roads level is all the rage ; and to obtain extreme levelness they are run along the courses of brooks, or other level grounds, without reference to either distance or curvatures. We have endeavoured to place the subject in a pr6per point of view by means of such lights as could be obtained, and have drawn examples from roads which have been made within the last live years, under what has been considered an improved system, — that of levelness. These examples have been adduced to show that level- ness may be carried to an injurious extreme, and that it is not sufficient for surveyors to merely follow level ground, without regard to distance. 'i ■4. 1' '■i ;» • I < ( »r CHAPTER V. !"• «t!. n, 5'.!., Ill h OF THE PRACTICE OF ROAD BNCINEERINO. 132. When a road is to be made through a tract of countrj, the general route, its points of departure and arrival, the intermediate points upon which it should touch, &c., must be determined by the Legislature. The filling up of this outhne must be in a great measure left to the skill and industry of the surveyor, it is proposed to point out first the methods of laying out a road in a cleared country, and then the further operations necessary in a country covered with woods and thickets. If the points between which the road is to be made are far distant from each other, it will first be necessary to survey the country between them, to ascertain its main features, such as hills, vallies, lakes, &,c. and lay them down on a working plan. This may often be done, sufficiently near for the purpose, by surveying the existing roads, and noting the bearings, and estimating the distances of all the remarkable objects on cither side. But, if there should be no roads in the proper situations, lines must be run through the country in their stead. This plan will give a tolerably correct idea of the tnain features of the country. The most difficult parts of the ground should then be examined, and the proper passes of rivers, ravines, and ridges, determined. These preliminaries being settled, a minute survey must be made of the whole line touching upon the fixed points ; in the progress of which, the situation and qualities of ground, the positions of bogs and other obstructions, and the relative heights of the different parts, approximately taken, should be ascertained and laid down upon the working plan. Sometimes it may happen that a road near the most direct line from one point to another, would not be the best, nor even the shortest that might be obtained : for when the points of departure are very dis- tant from each other, the general route may diverge to a considerable distance on either side of the straight line between those points, without making an increase to the length of the road so great as woukl arise from several short bends on the direct line. On this account it will often be found necessary to carry the survey over a con- siderable breadth of country. Parnell says,— "the surveyor should survey and take the level of all the various lines that on a perambula- tion of the country appear favourable. It is only by such means that the best line can be determined." Having determined these points, he may proceed to mark out the line for working upon, by the level, as directed in the chapter on surveying. .. . ; FRACTICi: OF ROAD ENUINECRINU. 269 ry, the i points slature. [he skill irst the further Lets. • distant between &,c. and fficiently )ting the bjects on ituations, jlan will ry. The and the In conducting the foregoing operations, in a clenr country, there i^ but littlo difficulty : the surveyor standing upon an eminence, can, «it a single glance, observe «ts principal features ; if the line is to m.j over a mountain ridge, he can at a distance sweep the horizon | S with his theodolite, and observe, very nearly, the lowest part of the sum- ] *^ mit, as well as the various ravines and other obstructions upon its sides ; if rising ground lies in his way, he can, by a single observation, ascer- tain its angular elevation ; or if its rise is too great for the road, ho can set his instrument to the given elevation and observe the features of the ground on the oblique line across the hill ; if swamps or bogs lie in the way, he can ascertain, almost at a glance, the best way of avoiding or crossing them ; — in fine he can have the full benefit of an unobstructed view of the country, in aid of his surveys and plans. 133. When the country is covered with woods the case is widely different ; and is beset with difficulties that can only be surmounted by the patient application of judicious methods of survey. Whoever will make the experiment of attempting to ascertain the true shape of the ground in thick woods, will be satisfied that he has undertaken a task of no ordinary difficulty. Looking around him, lie may at first suppose that the boundary of distinct vision is at a considerable distance ; but if he notes the objects upon this boundary and then measures their dis- tances from him, he will find it not to exceed, in full grown woods, eight to ten rods, and in bushy ground, four to six rods. Let him then go into a cleared field and measure off* the distances around him, and he will perceive that what appeared in the woods a large area, is in reality so very small as to be utterly unfit for a g;uide to the shape of the ground. This jsmallness of the field of view is the principal cause of the blunders that are committed in laying (mt roads without instru- ments. The art of judging, by the eye, of the shapes, magnitudes, dis- tances, and positions of objects, is gradually obtained by experience.^ This experience is the offspring of necessity, and is gained for the most part by viewing objects on clear ground. But very few persons are under any necessity of acquiring the habit of Judging accurately res- pecting the shape and position of ground in the woor^s ; hence, in the case of laying out roads in such situations, by the eye, there is the want of practice to be superadded to the natural difficulties of the subject. When a survey is to be made through a tract of country covered with woods, the first object of the surveyor is to obtain a knowledge of the general features of the country. Having the general course and dis- Itance previously determined, he commences his survey at some con- I \i\ * Se« Rvid on the Mind, where (his sul>ject it fuMy discusMd. !ir (t yfl< I f"i 260 PRACTICE OF ROAD ENGINEERING. m Lt ' ( i i i^: ^#=> ^1.', 1 ''i 1 ■■1.r < : j~ ,^!!i ~li: venient part, and proceeding cautiously, follows such ranges of ground as may appear the best adapted to the end in view. In the progress of the survey he should occasionally climb tall trees on commanding points of view ;* by this means he can observe the general shape of the hills and vallies around him, nearly as well as he could if the country were cleared, and the observations were made from the surface of the ground. He should be provided with a pocket com- pass with which to take the bearings of the different parts of the land- • The surveyor should himself climb; mere assistants cannot give him the information tliat he will obtain by his own view ; appearances that an unpractised person would hardly notice, may to him be very important. The best tree for climbing upon is the Spruce, it is tall, and the wood is tough to the vtry top : Pine and Juniper are very brittle towards the top, and should be climbed with caution. The host time of tie day is in the morning or evening; by reason of the position of the sun the form of the ground can be seen better at thiit time than at any other. A rough panoramic sketch of thu h lis and vales within vit W, shouiu be taken from the tree, as well as notes of whatev er may be considered worth retaining in mex mory. Tlie paper containing the sketch should have a ;. int marked upjn it to represent the point whence the view is taken, and from t'lis point lines should be drawn to each remarkahli> oi'jt^ct ; on these lines should be marked the bearings taken by a pocket compass, and the distances: or if great exactness is required, let an assistant set a stuke in the direction of the ol jVct, the bearing of which can be afterwards taken with the, large com- pass from the foot o( the tree. Distances can be estimated by the apparunt size of the tops of trees, which after a little practice be- comes a very good criterion. Colour, or brightness, cannot he depended upon ; they are too tTiucli influenced by the state of the atmosphere. Distances within 10 miles can generally be estimated within a fifth of the truth: for greatir distances the estimate is n;ore uncertain. Cliinbin^r trees may he facilitated by what tho woodsmen call an Indian ladder ; take a young tree that is fn'.l of branches, trim tiiem cfT, leaving about six inches of the inner ends, and set it nearly upright against the tree to be climled, so as to reoch tu the lowermost branches, and it will be almost as convenient as a comnioii ladder. Ir(m instruments for pnttin;; on the feet should nlwf.ys be car- ried fur climbing with, a b c d e, isa side view of such an instru- ment: it is a plate of iron made to fit upon the boot just fuiwaid of the heel : the part cd comes under the bottom of the foot, ta extendi up tiiu inside of the leg, neaily to the knee, and at li there is a liend outwards to prevent pressure upon the ancle: at c there is a spur of steel, tempered at the point, for strik- ing into the tree. The instrument is fastened tu the foot with a strap round the heel, and a strap and buckle across the instep, in the manner of a horseman's spur : at a, there is a broad piece of stiff leather fastened to it which is secured round the leg witii a strap and buckle. The c//m6er from which the figure is taken is from e to d, 2 inches, d to c, 3 inches; e to a, 13 inches; the iron is about 1^ inches broad, with a piece priji'cting forward at b 1^ inches, to fasten the instep strap to : there are also proper openings made for fastening the other straps. The spur at e, is an inch long, a quarter of an inch broad, stout at the inner end, and tapered off to a sharp lancet point. The iron ate is about a quarter of an inch thick, the other parts quite thin, particularly towards a ; the weight, with- out straps, is about a pound and a half. These instruments ate in common use in some parts of England, where they areas plentiful among the boys, as skates are in Nova Scotia. In the exploration of a wilderness country, observations from trees are indispensable : by climbing trees on cororoanding points of view, the surveyor obtains ali the Edvantages of view that be would have from the same points were the country cleared; without it he is perpetually groping his way and fallin; into mistaken . A surveyor who cannot of will not climb, may answer sufliciently to run land lines, but is verv inefficient iu making explorations in which the features of the country is, to be ascertained. PRACTICE OF ROAD ENGINEERING. 261 ground all trees ;rve the 11 as he ide from let com- hc land- tliat he will > him be very I) to the vtry ,n. The hest reason of the eeo better at ketch of thu tree, as well as lining in me« have a ; 'nt view is taken, 5h remarkable bearings taken it exactness is 1 of the olject, the. large com- itimated by the tie practice be less, cannot be the state of tlie lly be esiiniatiil the estimate is oodsmen cal' an branches, trim ■ nds, and set it as to reach to convenient as a nlwftys be car- such an irstru. oot just foiwaiil of the foot, ta . knee, and at b upon the anck: point, for sttik- to the foot witl> icross the instep, ^ is a broad piece lund the leg wiili etoa. 13 inches; tn the instep strap is BH inch long, I. The iron at c the weight, with- parts of England, tt ble: by climbing hat he would have in way and fallin,; un land lines, but ascertained. scape: if it be necessary to ascertain the direction of any particular place with a greater degree of exactness, he may cause an assistant to set a stake in the direction of the object, and afterwards take the bear- ing with the large compass on the ground. It is convenient to make particular marks at the angles, and at every ten chains in the intermediate parts of the line, to serve as points of reference in the future operations. A mark very proper for this purpose, and easily distinguished, is three blazes or chips taken from a tree or stake, in a line above each other. These marked points should be regularly numbered with red chalk or other durable figures. By proceeding in this manner on each apparently favorable line, and by making occasional examinations of the ground on either hand, he obtains a tolerably correct plan of the ground proper for a road. The next process is to examine all the difficult places; such as bogs, ravines, banks, hills, &c. ; ascertain by survey, and if necessary, rough levelling, the most practicable passes through them, and lay them down on the map. The different practicable road lines may then be drawn in pencil very nearly in their true positions, and their lengths ascertained with sufficient precision, by stepping them with a pair of compasses. The engineer is now, and not till now, prepared to exercise his judg- ment correctly as to the most proper line to be adopted : he has made what would in a clear country be called a perambulation, and but little if any thing more ; and he is now to determine upon the most proper line to proceed with. This is in some cases a tolerably easy task, but in many others a matter of great difficulty : there are often many degrees between a practicable route, and the very best that the face of a country admits of; and previous to a proper choice, a balance of con- ditions is required, which can only be adjusted by considering large por- tions of the line in its general connections, and by minute examinations; Without these previous surveys, he has no proper data on which to found an opinion. The following very judicious rules for tracing the line of a new road are copied from Sir Henry Parnel's Troaiise on Roads : — " This business of tracing the line of a road should never be under- taken without the assistance of instruments; and all local suggestions should be received with extreme caution. "To guard against errors in this important point, it is essentially necessary not to trust to the eye alone, but in every case to have a sur- vey made of the country lying between the extreme points of the in- tended new road. For this purpose an experienced surveyor should be employed to survey and take the levels of all the various lines that, on a perambulation of the country, appear favourable. It is only by such means that the best line can be determined. These surveys should be Ineatly and accurately protracted and laid down on good paper, on a 34 'I Jl w i 'ti I HGH PRACTICE or ROAD ENGINEERING. fii|r ,?i;^i>' i.f . ' y.v -;» ; ; 1 ' ,'i ; •*■; ' i i ( • ,1 i C I I scale of sixty-six yards to an inch, fertile ground plan, and of thirt}- feet to an inch for the vertical section.* " The map should be correctly shaded, so as to exhibit a true repre- sentation of the country, with all its undulations of high' grounds and vallies, streams and brooks, houses, orchards, churches, ponds of water adjacent to the line of road ; and all other conspicuous objects should 1)0 laid down in the map. A vertical section should be made, and the nature of the soil or different strata should be shown over which each apparently favourable line passes, to be ascertained by boring ; for it is by this means alone that the slopes at which the cuttings and em- bankments will stand can be determined and calculated, If it be neces- sary to cross rivers, the heights of the greatest floods should be marked on the sections ; and the velocity of the water, and the sectional area of the river, should be stated.f .■■ i i . -i . :' ;; " If bogs or morasses are to be passed over, the depth of the pent should be ascertained by boring ;t and the general inclination of the country for drainage should he marked. *' All the gravel pits or stone quarries contiguous to the line should be described on the map, with the various roads communicating with them; and the existing bridges over the streams or rivers which are immediately below the proposed point of crossing them, should be carefully measured, and the span or water-way stated on the section. t; , •> " These preliminary precautions are absolutely necessary, to enable an engineer to fix upon the best line of road, without respect to general direction, and longitudinal inclination. Without the unerring guide of actual measurement and calculation^ ail will be guess and uncertainty." • Two chains to an inch horizontal, and 20 feet to an inch vertical, is a better scale for working by, In some cases it may adviri in these noithcrn regions, by observing tba mirkt made upon tiiits by floating ice. These marks are usiMlly at the height of the highest fl.od*, and may be relied upon. Onco, upon examining the ice ma>ks upon the (wnks of a river, I fdiind some old scars upop the bark of some trees about three feit above the general level of the more recent rnark'^ ; and upon chopping into the trees, and counting the annual rings of woc>d, found them to be 43 years old, but coulii not tell whether the injury had been dotie to the tree by the ii-e, or in some other way. Upon enquirr, however, I learned that about 43 years before that time,, there had l)een a tvintcr freshet full three feet higher than any that had happened since; so correct is this method of ascertaining the height of floods. Where it is proposed to carry a rosd upon low ground near a stream, the ice morks, and lodgments of drift wo"(! should hu examined, and levels run from them to the proposed line. But if the stream be small, tiie etfect of ol'c useful to the young beginner : Uraw the princij)al lines stronger than the secondary, so as to make an obvious distinction to the eye. Put in lioet, a^ roads, sliort". of lakes, &c. which art* not surveyed, in dots only. Put in rivers and strtams which are not surveyed, on ■ coloured map, by spotting them with the colour of the water between dotted lints. Always mark the direction of the streams with arrows pointing in its direction. This is an eitentiai point to be attended to, it is a good guide 'to the na* .al features of the country. PRACTICE OF ROAD SnCINEERmG. 263 tiirt} feet lie repre- ' grounds ponds of IS objects be made, ver which iring ; for and em- be neces- ic marked iial area of f the pent ion of the 3 should bo with them ; iimediately ' measured, to enable to general ng guide of certainty." for working by. ervjng tbs mark? lods, and may be a some old wars ii!uk« ; and up"" s old, but coulii Upon enquiry. let full tliree feet e height of floods, ind lod;<«Tients d if the stream be lowed for. Such i, and at the same very irregular in idicutioni of ttiem i notion to tbo eye. •m with the colour This ,i8 »n eMontul f ; f > I i / 1 " 135. This last observation refers to a clear country, but as already observed, in a country covered with wood, it applies with much greater force. '•■ '' '•-;■■■! '! . ;' .'.i- ■:"■:'■ • • ■■' ■• .' The circumstances under whicl "oads are to be laid out are so various, that it is impossible to lay down rules that will be applicable to all cases: a few general principles may be pointed out, but the application must be left to the judgment of the engineer. The following may serve as a tolerable guide. 1st. The first matter to be determined is the most proper scale of elevation of hills that the country will admit of; which may be found by making trials of the most difficult parts of the route. This previous determination is indispensable to success in laying out a good line. In every district of country there is a certain medium elevation of hills that is adapted to that particular region, which can, by proper management, be easily obtained, and which cannot be materially reduced without running into unwarrantable expences. It may be difticult to ascertain this just medium upon any certain line, but when once fixed upon, it is useless to incur great expense in the construction, or to make a great increase of distance for the sake of greater levelqess in any particular part. On the other hand, it may be often worth while to submit to a very heavy expense in forcing a way through some barrier, or to increase distance in avoiding, it for the sake of bringing the whole line down to the grade determined on. This adaptation of the scale of grades to the nature of the surface of the country, and to the quantity of the traffic, as well as to the funds, is one of the most difficult parts of the business of an engineer, and unhappily, is that part of his duty for the duo performance of which he receives the least credit. It is shewn in the foregoing chapters, that moderate slopes may be introduced without injury, and that low points of ground may ia cio.ssed without inconvenience, and often with advantage to the d stance and curvatures. Even on ground of abrupt character, and paiticularly when a road runs horizontally along the side of a mountain rfuige, the iinro- duction of undulations will often enable the enj^incei to chose more convenient ranges of ground than would be practicable were he con- fined to the level. 136. 2d. The maximum elevation of hills should in no case exceed the angle of friction^ if it can be avoided ; and the line should be as short as is practicable in conformity with this condition. This proposition is investigated in chapter 4 ; whence it appears that m t m ' { 'i Never put in shading to represent a hill except just where it is known to exist: parts which are not seen had better be left blank. Always make a broad distinction between what is certainly known and what is only guessed at \ nevw leave it doubtful to which of these clastes things laid down on the map belong. 264 PRACTICE OF ROAD ENGINEERING. ni 'I'i it is quite possible that the reduction of the elevations may be carried so far as, by the increased length of the road, to create an incon- venience greater than the advantage derivable from lessening the power necessary for drawing a load upon it. The following quotations are corroborative of these views : ' ■ The writer of the article Road, in the Penny Cyclopaedia, says, — «' It should always be borne in mind thai the occurrence of one sleep hill on a line of road affects the working of the whole line, as the number of horses required for ascending it must be used, although a portion of their power may be unemployed on the greater part of the road." Mr. Mahan, Professor of Military and Civil Engineering in the Mili- tary Academy of the United States, also says, in relation to this subject: " In laying out a road, where one point is higher than another, or when it is necessary to pass a ridge at a point higher than either of the ex- treme points, the line followed should be direct between the two points, so long as the ascent is within the foregoing limits," (the angle of fric- tion) " according to the character of the road covering, and no other obstacles intervening which would render necessary a change of direc- tion. If owing to any of these causes, a change of direction should become necessary at any point, it will be made, and be continued, in the new direction until the direction towards the point of arrival can be resumed." Again : — " In all cases where it can be done with a due regard to economy in the outlay of construction, a uniform ascent should be ob- tained between the points of departure and arrival, to avoid useless ascents and descents, which occasion a loss of power. Cases of this character not unfrequently present themsdves : as for example, where the points of departure and arrival, lying on opposite sides of a hill, can be connected by a straight line by crossing the ridge at a level higher than either of the points ; or else by taking a circuitous direc- tion around the base, by which the ascent between the two would be made uniform. In such cases, the choice of the engineer must be governed by his judgmfint, founded on a comparison of' the expense of the two lines, and the advantages which they severally offer tvith respect to the tim§ and means of conveyance:''^ ., ; : — Marshall says, — " When the intervening country," (between two points) " is broken into hill and dale, or if one ridge of hill only inter- venes, a straight line of carriage road is seldom compatible with perfec- tion. In this case, which is nearly general, the best skill of the surveyor lies in tracing the midway between the straight and the leve! line. The line of perfection for agricultural purposes, is to be calcr iated by the time and exertion, jointly considered, which are required to convey a * Mahan** Civil Engineering, p. 67. 1-' h "lct> ^t ^ <^nd ^i a>°e derived. It'K l:u ■ mi ■ pi .. I I -'^ 266 FKACTICE or ROAD ENGINEERINO. If ♦be comparison be made between grades of 1 in 35 and I in 20, the friction being one-fortieth, the additional cost will be no less than 40 per cent. These are the theoretical effects of the hills in question ; in practice, by extraordinary exertion of the team on the steepest hills, the disadvan- tages may be somewhat reduced. Making, however, reasonable allow- ance for this, tlie loss occasioned by a few such hills must bo considerable, and every possible means ought to be employed to reduce them. Too much attention cannot be bestowed upon this object ; because, unless it is ctTectcd, the superior levelness of the other parts of the line cannot be fully available in reducing the cost of transportation. Twenty-five, or even fifteen per cent, in the carriage, is a heavy drawback upon the profit on an article whose chief marketable value consists in. the cost of its transportation. Suppose, as an exampl", tiiat there is a tract of country over which a tolerably direct line can be carried at elevations of 1 in 30, exceptin*^ some few hills, amounting. ; one-twentieth of the whole distance ; whicli hills, without very he^vy wc.rks, or an increase of distance, cannot be laid below 1 in 20 ; in* sn; pose this obstruction to be in the form of a vall?y, abed, Fhi. 46, lyi'-r directly across the general course of the road ; also, suppose this v H^^y to 1)C 66 feet deep, and the hills on earh side to be 60 rods in length, givin;^; an elevation of 1 in 15. Now these hills must either be reduced, or a loss of between twenty and thirty per Fig. 46 o ■ :i': 1 (. ■ • I e ;' .1 f-' . ; ; . I '.■ i;'>i,u; •n; •>f .b i\ i ; • Section. ■::\ !; :. I cent submitted to in carrying freight upon the road : to reduce th^m to a slope of 1 in 30, would require 16000 cubic yards of excavation) the PRACTICE OF ROAD ENGINEERING. 2G7 1 in 20, than 40 irac+ice, isadvan- e allow- iderable, n. loo ilcss it is an not be |r'-five, or upon the ic cost of 'er which 3xceptini-:cr m I*"* vo PRACTICR OF ROAD KNQINF.KRING. ) < i Fi' ■! 'I ■ fit ■ m in m m ! 1 'i i i , • i; ( ■ 1 i 1 ■1 J ■ ^ ■ ':''■ :h a proper adaptation to the traflic is very important, and rules arc given by which to make the necessary calculations ; but for common roadij such rules arc unnecessary. If the descents in the direction towards the t«wns be regulated by the hnavy traffic towards them, there will, in most cases, he (juite sufficient facility for the return freight. Suppose, for example, the steep- est hill allowed descending towards town be 1 in 20, and ascending, 1 in 30, which is also the angle of friction of the road ; — the forces re- quired to draw 2400 pounds up these slopes are (Art. 100) 200 pounds for the former, and 160 pounds for the latter. The loads that might he drawn up them by any certain force are inversely proportional to these numbers, and allowing the force, in boili directions, to he that which draws 2400 pounds up the former ascent, the load that the same force will draw up the steeper ascent is found by the following proportion. As 200 : 160 : : 2400 : 1920 pounds. A load, therefore, of 1920 pounds drawn up an ascent of 1 in 20, will require the satne force as 2400 pounds drawn up an ascent of 1 in 30 : that is, the hill of 1 in 20 will admit of four fifths, or 80 per cent of the load that might be taken with the same force of draught up a hill of 1 in 30. If we allow the weight of the waggon to be one third of the whole load towards town, or 800 pounds, and that the return freight is carried on the same waggon, the useful effects will be 2400 and 1920 pounds, less the weight of the wp'^gon, or IGOO and 1120 pounds ; the latter being 70 per cent of the former. If the waggon be one-fourth of the v. uij^ht of the greatest load, or 600 pounds, the useful effects will bo as 1800 to 1320 ; the latter being 73 1-3 per cent of the former. 'f ^^ "orle of friction were 1 in 40, and the steepest hill ascending t V .' , '1 I "m were at the same elevation; the descending grades being ^ / »e forces required to draw 2400 pounds uj) these slopes would be id 156 pounds respectively : and when the waggon is one third of tho weight of the greatest load, the useful effect on the latter elevation will be 6oh per cent of that upon the former. Also, if the weight of the waggon be one-fourth of tht; j^reatest load, the useful effect will be on the return, 69 1-3 per cent. Thus we see, that as it can in no case be advisable to make any hills steeper than 1 in 20 to 25, on account of the descent of loads upon them, on a suitable arrangement of the gradients to accommodate the direct traffic towards the town, nearly 70 per cent of that amount may be returned by the same teams ; and as this is a much greater quantity than will usually be required, all that is generally necessary in laying out a road for traffic is so to arrange the slopes as to give the greatest pos- sible facility for the movement of freight to the place of general market. iMtACirct; or road engi^iberimo. 271 given I roads ted by J quite 5 steep- ding, 1 ces re- pounds light be thesft t which le force •portion. 1 pounds as 2400 1 20 will ken with be whole is carried pounds, he latter load, or ter being iscending grades ese slopes iT(Ton is fct on the Also, if the useful B any hills )ads upon lodate the [lount may r quantity laying out eatest pos- )f general 138. 4ih. The ascents should not bo too lengthy. — It is true that the same constant I'orco is exerted in drawing a load up a given ascent, whatever may be its length ; but practically, a long hill of small elevation will, probably, cause more fatigue to the animal than a hill, of the same |)erpendi>*ular height, that is shorter and steeper. If a height of a hun- dred feet is to be overcome, and the ground admits of a uniform slope of 1 in 60, the best practice will be to break it into two or three slopes of 1 in 30, with levels between : all the coach drivers that have been consulted concur in this opinion. There are several parts of both the Eastern and Western main roads, in which there is a long easy ascent to the height of thegroundy which then falls rapidly to the same level from which it rose , and in all these cases, the coachmen observe that they can pass in the direction in wiiich they ascend the ?^' per and shorter hill, in considerably less time than the contrary wa and without any more fatigue to the horses. This seems to show tL l -i latler is more advantageous than the former. No ascent should, if it can be avoided, he of a greater length than a quarter of a mile ; and where there are several in succession, the longest should be at the bottom of the mountain. 139. r)th. Where the ground is nearly level, provision should be made for longitudinal drainage. — If the road be perfectly level the water cannot run off, except to the sides, i.\\(\ the smallest ruts prevents this. If, as is commonly the case, it be carelessly made, in small hollows, there will be, in wet weather, a puddle in each hollow ; and unless this is pre- vented, and the surface freed from water, it is almost useless to lay on gravel, or to attempt improvement. A very slight observation of the roads, in wet weather, will show that this a matter of some consequence. '* However desirable a perfect level may bo in theory, a road with moderate inclinations, as of 1 in 100, is found to be preferable in prac- tice, because without such a slope it is difficult to get rid of water fast enough, unless the road be raised to a few feet above the surrounding land and thereby exposed to the free action of sun and wind."* Ed<;worth says, — '' A perfectly level road both with respect to its direction and its breadth, is always dirty in wet weather; because the rain water can neither run off to the side of the road, nor along the ruts. Such roads therefore, as are level in their line of direction, should always have a fall from the middle to the sides, and should be kept as much as possible from ruts." Sganzin says, — " Perfect levels are to be avoided, particularly for stone causeways, because in establishing a level road the transversal — ■ ' — ■ — — .— — — • — ^— — — — — — — . — ' I .■-■■■, '* Fenny Cyclopedia, Art, Road. ■''»»■ J IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I If 1^ 1^ •^ 1^ ill 2.2 ■;£ 2.0 1.8 1.25 1.4 III 1-6 ^ 6" — ► <^ /M '/ Photographic Sciences Corporation ^ s. '<^ \ ^-v\ V '<<^j^ o^ 23 WiST MAIN STRUT WnSTH.N.Y. 14580 (716) 873-4903 '4^ m y.f':i I ^.'i I, I 1:*' 11 fill: 272 PRACTICE or ROAD ENGINEERING. slope must be increased, in order to carry off the water, which is inju- rious, and even dangerous for carriages." , * : if.. Mahan says, — " This convexity" (nine inches in a breadth of 30 feet) " which is as great as should be given, will not bo sufficient in a flat country to keep the road surface dry ; and in such localities, if a slight longitudinal slope cannot be given to the road, it should be raised, when practicable, three or four feet above the general level ; both on account of conveying off speedily the surface water, and to expose the surface better to the action of the wind." Parnel says, — " A perfectly flat road is to be avoided, if it is not to be raised by embanking at least three or four feet above the general level of the land on each side of it, so as to expose the surface of it fully to the sun and wind ; for if tiiere is not a longitudinal inclination of at least 1 in 100 on a road, water will not run off", in consequence of which, the surface, by being for a longer time wet and damp than it otherwise Vould be, will wear rapidly away, and the expense of keeping it in order by scraping it and laying on materials, will be very much increased." The following observations of Mr. Walker, President of the Society of Civil Engineers, are so judicious, that although containing some matter extraneous to this particular subject, we copy the whole : — " Attention in the forming and repairing of roads, will in all cases do much to compensate for the inferiority of thn material used for that pur- pose, of which the improvement in the general state of the highways within the last twenty years aflfords the best [)roof. To form the road upon a good foundation, and to keep the surface clear of \> uter after it is formed, are the two most essential points towards having the best roads possible, upon a given country, and with given materials. For obtaining the first of these objects, it is essential that the line for the road be taken so that the foundation can be ke])t dry either by avoiding low ground, by raising the surface of the road above the level of the ground on each side of it, or by drawing off the water by means of side drains. The other object, viz. that of clearing the road of water, is best secured by selecting a course for the road which is not horizon- tally level, so that the surface of the road may in its longitudinal sec- tion, form in some degree an inclined plane ; and wben this cannot be obtained, owing to the extreme flatness of the country, an artificial in- clination may generally be made. When a road is so formed, every wheel track that is made, being in the line of the inclination, becomes a channel for carrying off the water, much more effectually than can be done by a curvature in the cross section or rise in the middle of the road, without the danger, or other disadvantage which necessarily attend the rounding of a road much in the middle. 1 consider a fall of about one inch and a half in ten feet, to be a minimum in this case, if it is PRACTICE or ROAD EWGINEERINQ. 273 h is inju- )f 30 feet) in a flat if a slight sed, when HI account he surface : is not to le general rface of it inclination equence of mp than it of keeping very much the Society ining some ole : — • all cases do or that pur- e hidiwavs form the ar of w ater having the 1 materials, the line for y either by (ve the level by means of ad of water, not horizon- itudinal sec- lis cannot be artificial in- rmed, every 3n, becomes than can be liddle of the ssarily attend all of about lease, if it is attainable without a great deal of extra expense. It is in the knowledge of the above points, and of the application of them in practice that what may be called the science of road-making consists, as the observations apply in every case.' >j* 139. 6th. Facilities for surface drainage on hills. — When a hill is very lengthy, water accumulates in the ruts towards the bottom, and wears the road rapidly away ; and the steeper the hill the more violent is the action of the water. The remedy proposed by most writers, is to make hollows across the road at proper intervals, to catch the water and turn it ofi' to the sides, as described in the section on drainage. A bet- ter method, is for the engineer to provide a remedy in the laying out of the road. This may be done by leaving levels, or more properly planes, rising a i'ow inches in the direction opposite to the general rise of the ground, to intercept the water : they may be one or two rods in length, and fifteen to thirty rods apart, according as the hill is more or less steep ; the steeper elevations requiring the less distance asunder. Such an arrangernont may often be made to accord with the natural form of the ground, and will cause but a very slight addition to the general elevation. These levels, besides preserving the road from washing away, will afford convenient resting places for heavily loaded teams, in their passage up the hill, and render it unnecessary for drivers to put stones on the road for the purpose of blocking the wheels. A B (Fig. 47) represents a section of hill so laid out, showing the levels for drainage at c and d. CD represents the same section with hollows for drainage at e and f. Fig. 47. 141. 7th. Curvatures. — For the radii of the curvatures no rule ap- plicable to all cases can be given : they must be governed by the nature * Evidence before a Committee of Parliament, 1819. 274 PRACTICE OF ROAD £NCiI?l£ERING. in-- :|;--^ H-'V' of the surface. It h best to have them as easy as possible : when they al.-ince the ci-ntri* (ugal force ; as is done on railways. To hnd the transverse elevation of the road, — divide S2 limes the radius of l/ie curve, in feet, hy the S(jvure of the vtiociii/ of the carriage, in ftut per second ; the quotient u-ill be the number of feet horizontal for one foot rise. Thus, suppose the radius of th« curve to be 80 fee', and the velocity of the carriage 20 fiet perstCDnd ; 32 times bO is 25ti0, and t!ie square of 20 is 400; anil dividing 2560 by 400 we get 6.4 feet. The road would, therefore, rujuire a declivity inwards of J in 6.4, or about 3 feet in the width of a uumnion road. Unilcr these circu'UNtances the pressure upon tlie rond would be directed perpendicularly to the surface ; tlie same as if the road 'vere straight, and level in its cross section. In rail roads, the rule, with r.ome modifications to suit other circumstances, mu^t be strictly attended to, because it is necessary to prevent the Hange of the outer wheel from binding upon the rail; but in common roads the rise of the outer side need not be so irreat. It is not absolutely necessary for the centre of pressure to fall in the middle between the wheels : if an accidental rise of the inner whuci does not shift the centre of gravity so far ds to throw the centre of pressure, on the ground, beyond thu outer wheel, the carriage will not overturn. A rise of the outer side of the road, of less than half of that brought out by the rule, will probably ensure sufficient safety : but on no account should it fall nS beloff the level. The whole drainage trankversclj should be to the inuei side of the cuive. road V 111 lay equaf the ro I a dec 'than land w Ibutfo t A jpo Purw en pre of « ( PRACTICB or nOAD ENGINEERING. 275 vhen thev veil worso hundred [lort turns of a hill : jch cases, obliquely c unavoid- eral grade, e hill, the ground, so iage. This )y reducing ord greater are not so Oesides, the 3ye. le foot of a ler, so as io tendency to the general 11 each side vel ; and in an abruptly (opposite ex- levelness, is straightness, lercase, an lly obtained ;vcnte(lby makiii'; lalancc the ccntri- Ihide a2 limes ikt cond ; the quotitnt j iiirve to be 80 fee'. of 20 is 400; ai>'l nwurdsof 1 i»6.4T ^ure upon tlie tonA It, and level in its :es, must be strictly iing upon the rail ; iiely necessary lor of tlie inner wlio«l round, beyond thu •M than half of that .Id it fall off bel"* On this subject, Mr. Stevenson, author of the article Road in the new Edinburgh Encyclopedia, remarks : — *' Although in road-making the line of direction must always be subordinate to the line of draught,* yet the former is notwithstanding of importance, both as it regards the safety of the traveller, and the trackage of the load. Independently of the numerous accidents which occur from the sudden collision of carriages travelling at speed upon a tortuous line of road, it were even better to go up a moderate acclivity, than to introduce numerous turns, which io a certain extent, are not less detrimental to the effective power of the horse, than the uphill draught. Every turn in the road, which ultimately amounts to a right angle, does in effect, suppose the carriage to have been brought from a state of motion to a state of rest, and from rest to motion again. Turns in a road, where they are unavoidable, ought to be formed on curves of as large a radius as the situation will admit. There ought, in laying out a road, to he a kind of compensating balance between the lines of direction and draught." On the other hand, the ideal perfection of a perfectly straight road is condemned by Edgeworth. He says : — " It may, perhaps, appear sur- prising, that there is but little difference in the length between a road that has a gentle bend, and one that is in a perfectly straight line. A road ten miles long, and perfectly straight, can scarcely be found any where ; but if a road could be found, and if it were curved, so as to prevent the eye from seeing further than a quarter of a mile of it in any one place, the whole road would not be lengthened more than one hun- dred and fifty yards. It is not proposed to make serpentine roads merely for the entertainment of travellers ; but it is intended to point out, that a strict adherence to a straight line is of much less consequence than is usually supposed; and that it will be frequently advantageous to deviate from the direct line, to avoid inequalities of ground."t 142. 8th. The transversal slope of the ground and position of the road with respect to banks running longitudinally should be attended to. — In laying out a road, that ground should be preferred, (other things being equal) which is nearest to a level in the direction transverse to that of the road. The opinion entertained by some persons, that ground having a declivity in the transverse direction is more cheaply formed into a road than a horizontal surface, is a mistaken one. If a narrow track only, land without much drainage, is required, it is easily cut in such ground; but for a finished and well drained road, the less transversal declivity • The line of draught Is the longitudkial section of the surface. t A ifood method of getting acquainted with the proper curvatures, is to measure the radii of eurra- kurtsen different (urns on old roads. Let ABC, be a wheel track round a turn, and nearly in the lire of a circU : raensure a chord line of any certain length acrots from A to C, and from its middle point 1 ■■•! 276 PRACTICE OF ROAD ENGINEERIMG. li m 1' ^w^ 1; , -M !..''• ; ' • : J( .' ( •:•;',;.., <)-i :' c: ;; W. *'^!. ■. ' there is in the ground the better — more particularly if it bo of a clayey nature. Let A B (Fig. 48) represent the transierse section of a road of 24 feet in width, on ground having a transverse declivity of 1 foot in 8 ; and B D (Fig. 49) a section of the same road upon ground transversely level : it is plain that neither are the drains at C and D of the latter, equal in magnitude to the excavation at B, or embankment at A of the former, nor is the earth to be removed to so great a distance. In the Fig. 48. Su rs jj. Fig. 49. , >1 I .-lU' D «?"? '—' j:«* _!-'*i- *e* - * .sf.ifl ' U! '' iJ '* .B J^ supposed instance, the excavations of fig. 48 exceeds those of fig. 49, in the proportion of 3 to 2, and when the distance of removal is taken D, in the straight line hetwcc n A and C, measure the distance D Ti. Then C D or D A, is the sine, and D B the versed sine of the arch B C or H A ; an(i the square of the sine divided by the versed sine, gives the diameter of the whole circle of whieh the arch ABC is a part of the circumferenci>. Hence, stip- posinf; D C 66 feet, and D B 6 feet; — the sqmre of 66 is 4356, whicli divided by 6 pives 726, the remain- der of the diameter, and 6, (D B^, added to this number {{ives 732, tiie whole diameter of the circle, half of which is 366 feet the radius. i i 07? ; iTu'lT'" n ^/ -'^ ^'"X'?'^ ? ^.^ feet.-the squnro of 33 is 1089. which divided by 4 gives 272. to which 4 being added gives 276 for the diameter, and 138 for the radius. It is very coLenient curve can be taken in a kw mm^xU,. If the radius is small the lesser distance should be token, other. PRACTICE OF ROAD ENGINEERING. 277 a clayey d of 21. i 8 ; and isversely lie latter, \ of the 111 the I ;•,■(''■- of fig. 49, d is taken is the sine, and icrsed sine, gives Hence, sup- 726. the remain- of the circle, half !,i- divided by 4 gWcs is very convenient n rhe radius of any be Uken, other' into account, the expense is nearly as two to one. It is true, so great a differencti of expense is not often incurred in making new roads, but the reason is, that the drain at B is not made sufficiently large, nor is its land side sloped back sufficiently to insure permanent drainage. The consequence, is that it is soon filled by the sliding of the bank ffom above, and the road becomes flooded with water, or a greater expense is incurred in keeping open the drain than would have been necessary to create a proper drainage at the first. If cross sections of groundf, similar to fig. 48, of dififerent angles, be tried, it will be found that the expense will increase in a much higher ratio than the increase of the angle ; and that of all forms of cross sections, that which is level affords the greatest facility for the formation of a road. Sideling ground for the site of a road should therefore be considered as a matter to be submitted to, rather than sought, and, where there is a choice of ground, should be avoided. In gravelly or sandy ground, that does not require drainage, and of which the angle of repose is considerable, the difference in favour of level ground is not so great as in ground of a contrary character.* The greatest disadvantage from the above cause is experienced in carrying a road along the side of a steep bank. Such a bank usually stands at the natural angle of repose of the material, and when the road is cut into it the earth above gradually slides down, and must be from time to time removed, until the bank again comes to the angle of repose. If the road be near the top of the bank, the quantity of earth to be so removed will not be very great, and the road will be formed mostly in excavation ; if it be near the bottom, it will be formed principally in em- bankment, and in either case at a comparatively cheap rate : but when it is made near the middle of the height of the bank, there is a great quantity of earth above it that will require removal, and the depth below is so great that th/3 earth so nioved will make but a small breadth of embankment. In such situations the disadvantage is at th@ maximum. Side cuttings in steep banks are always expensive, and often incon- venient, and should never be carried to a greater distance than is abso- lutely necessary : they should therefore always be run at the maximum elevation of the line until they attain either the top or bottom of the bank as may be most advantageous to the general line. On the Truro Road there is a bank near the Stewiacke River, and another about four miles further towards Truro, where may be seen specimens of this error. On the first the greater part of the road might have been made at the bottom, and on the second, at the top of the bank, without any inconvenience to the grades, and with a saving of expense. Connected with this subject is that of carrying a road along the bot- * The angle of rtpote is that angle with the horizon at which banks naturally support theniK«Iv(a. ant) is from 25 to 35 degrees with the horizon. 36 278 PRACTICE OF ROAD ENGINEERING. iri'',.''' t^^'i"': '.:t ' torn of steep banks. U sometimes happens that for saving valuable ground, and for convenience in getting materials, the road is made partly jin excavation at the foot of the bank, which, thus losing its support, is liable to slide and fill the drain of the road ; and this more especially if it be composed of clay. In such cases the road, including the drain, should be laid entirely upon the flat ground, and where, as is often the case, there is a stripe of easy sloping ground at the foot of the bank, it should be at a sufficient distance from the steep part to admit of the side of the drain coming to its angle of repose without under- mining the bank above. The object to be aimed at in both cases, is to place the road beyond the reach of slips from above. If funds be low, the best way of proceeding is to make a cheap road in such situation as to admit of a drain six to seven feet in width between it and the bank ; being the least width that can be admitted in ordinary ground for a permanent open drain of two feet in depth. If the ground be gravelly, the distance from the root of the bank need not be so great. In carrying a road along a valley, the flat ground should, if convenient, be preferred ; but if not, that side should be chosen which will be least exposed to floods of water from the adjoining hills. Generally, it is improper to lay a road under a long range of descending ground if it can conveniently be avoided. 143. 9th. Facilities for getting materials should also be attended to. " It will sometimes happen that road materials can he better obtained by carrying a line of road in one direction than in another. This will be a good reason for making a road deviate from the direct line, liecause the expense of making and repairing it will much depend upon the dis- tance which materials have to be carried." This is a quotation from Parnel, and is very judicious, but requires some explanation. Materials, in his phraseology, is the stone or gravel surface of the road, and has no reference to the bottom or foundation upon which they are laid. In Europe they do not call the; mere foun- dation of earth, ^Ae road; itj^is called the road fornix and requires the crust or covering of stone or gravel to constitute it, in their estimation, a road. He would never advise a deviation of the line for the sake of a little advantage in the mere digging of the earth of which the road is formed, and for this simple reason, that the forming once done is never to be repeated ; whereas the crust requires constant renewal, and the materials for repairs constitute a large item of the annual expense. These remarks have been thought necessary, because there is a strong tendency in opening roads to deviate from the best line for the purpose of avoiding some swamp or other trifling obstacle, to the lasting injury, if not future lose of the road. The authority above quoted gives no countenance to this ; his reasoning in other parts of his work goes to PRACTICE OF ROAD £NGIN£ER1N0. 279 quite the reverse : but under the rapid wear of an immense traftic, sucli as passes over some of the roads in England, a saving in cartage of matejfials is a matter of consequence. After all, this is a subject that is confined within narrow limits : it is only when other circumstances are nearly equal th^t the materials can be much considered : the essential attribute of levelness must not be sacrificed on any account ; and even but little increase of distance can be afforded for such an object. The question is entirely one of expense : when it happens that of two given lines of nearly equal distances and levels, one requires a greater expense than the other in forming, but has better materials, it is a mere matter of calculation whether to expend the greater present sum for the sake of securing the future advantage, or the contrary. Such a calcula- tion would be very much affected by the character and design of the road : if it be mainly used for light travelling, and the traffic upon it small in amount, the principal expense is in the first making, 'and the saving to be effected in future repairs would bear but a small proportion to the first cost. On the other hand, if it is a great thoroughfare and under the wear of an immense traffic, as is the case vvith some roads in England, the first cost bears a less proportion to the future repairs, and a saving in the lattpr becomes a matter of more consequence. Parnel very Justly remarks as follows : — " There, is not to be found in any of the books on road-making a dis- tinction between roads for great and roads for little traffic. Each author has written as if there ought to be only one kind of road for every kind of use. Til lb is a great mistake, and has led to much confusion in forming opinions upon the proper construction of roads. A road of earth put into a regular form will answer for a park drive. The same with a coating of gravel will do for light carts and other carriages. So a road made with ten or twelve inches of broken stones laid on the na- tural soil, will be a sufficiently good roa • ''hen the traffic is not consider- able ; while very great traffic requires a read to be constructed in a dif- ferent manirer, that is with much greater solidity and hardness, so as to allow carriages to be drawn on it with the smallest possible quantity of tractive power, the object that all road-makers ought to have in view." Bogs ought to be sfvoided if it can be done conveniently ; but this rule does not extend to common swamps, with hard bottom within a reason- able distance of the surface, and which can be drained. " The elastic nature of all bogs and marshes, and of all boggy and bottom land, makes it impossible to form a road of perfect hardness over a soil of this kind, unless a great deal of expense is applied in draining the soil, and after- wards compressing it, by loading it with large quantities of earth em- banked upon it, in order to destroy the elasticity of the subsoil. For this reason it will giincrally be prudent to deviate from the direct line in ' 1 ;i •i !l i m ZBO PRACTICE OF ROAD EMGlNfiElUNG. I H n Pi "m *■■%■ :^i' frill •■■ ■: 'fjll ■'■■■' .*, hi l{ ,• ■.■• i *• ..*'*. if ';"■ ' * mM ':r laying out a new road, if by doing so this sort of subsoil can be uvoidud, without adding much to the length of it."^ The elasticity of such grounds will not much affect teams, provided the surface of the road is hard : because though a load ivill draw somewhat heavier, the road is level, and consequently the load will not be diminished on account of it. For fast going stages the case is otherwise ; (he rate of travelling would be reduced. Levels of bogs should be taken, and examinations made with reference to drainage : sometimes a drain properly situated will lay the bog dry, while a much greater expense laid out upon the road would uot be of much service. For raising the road, the best material is the soil of the bog itself; it is as light as wood, easily obtained, and if taken from side drains, will, in connection with proper outlet drains, at the same time drain the road. This substance is very durable, and will not sink into the bog fo such an extent as gravel and brush. The proper material to cover it with, previous to gravelling, is clay. 143. 9th. Exposure* — ** It is necessary in making a road through a hilly country to take particular care to give it a proper aspect. It is a great advantage to have a road on the north side of a valley fully ex- posed to the sun. For the same reason, all woods, high banks, high walls, and old fences ought to be avoided, in order that the united ac- tion of tlie sun and wind may have full power to produce the most rapid evaporation of all moisture. Too much attention cannot be bestowed on this object, in consequence of the effect of water in contributing to cut and wear down the hardest substances, It is for this reason that road materials, when they are wet or damp, wear rapidly away under the weight and pressure of heavy carriages. The hardest limestones wear away very quickly when wet, and all stones of an aluminous character, and also gravel, that consists of flint, sandstone, or other weak pebbles. "The great advantage of having a road perfectly exposed to the action of the sun and wind, will be more accurately conceived, by referring to writers of science on evaporation. Dr. Halley states, that one-tenth of an inch of the surface of the sea is raised per diem in vapour. He also says, that the winds lick up the water somewhat faster than it exhales by the heat of the sun. Other writers say the dissipa- tion of moisture is much accelerated by the agency of sweeping winds, the effects being sometimes augmented five to ten times. " Trees are particularly injurious by not allowing the sun and wind to have free action on the surface of roads, in producing evaporation." * * * " It is of the utmost importance that evaporation should have full • Pdrnell on Roads. IMlACllCi: OF UOAI) LMGINKElilNG. •^ai I'oidud, ided the mewhat finished ise ; \\ie efercncc bog dry, lot be of 3il of the ri'oiu side ime lime sink into lateiial to through a t. It is a f fully cx- uiks, high united ac- most rapid bestowed ibuting to eason that under the ones wear character, ak pebbles. sed to the iceived, by states, that er diem in what faster 10 dissipa- ping winds, and wind ^aporation." Id have full eil'ect in drying up the surface of a road, by iiliowing the sun and wind to act upon it ir tiic freest manner. *' If roads be kept dry, tlioy will be maintained in a good state with proportionally less expense. It has been well observed, that the sta- tuary cannot saw his marble, nor the lapidary cut his Jewels, without the assistance of the powder of the specific materials on which ho is acting; this, when combined with water, produces sufficient attrition to accomplish his purpose. A similar efl'ect is produced on roads, since the reduced particles of the material, when wet, assists the wheels in rapidly grinding down x\\e surface. '^ The superior condition of roads at all times crossing unenclosed land, shows how valuable a full exposure to the sun and wind is, in con- tributing to the preservation of roads."* , 144. lOih. Kxpcmc. — Where other circumstances are nearly equal, the engineer will naturally choose the least expensive route. In, how- ever, the iar greater number of instances, when a choice is to be made, it is between a great expense on the one line, and some other disadvan- tage on the other. If the difierence be considerable, the proper course is to survey both routes, and lay the matter before the proper authori- ties. On main roads, a greater expense may with propriety be incur- red than on cross roads, or than is warranted by the present amount of traffic. This Province is as yet only in its infancy; but population and traffic are rapidly increasing, and if the roads arc not now planned with reference to the future rather than the present, they >vill undergo alteru- lioiis, and their present expense will, eventually, be thrown away. 145. llth. Watering places^ when opportunities ofifer for making them, ought not to be neglected. If good springs be found in tk« vici- nity of the line, it should, if practicable, be brought within reach of them, even though some disadvantage should be submitted to in other respects. Public attention is now drawn to the more necessary objects of opening new roads and making them passable : there is neither time nor money to bestow upon mere conveniences ; but this state of things will have an end ; the mere track through the wilderness at present, will be the spacious and finished road of the next century; and then, next to the essential attributes of levelness and smoothness, good water will be prized as one of the most desirable objects. 146. 12th. Appearante. — Trivial as the mere appearance of a road may at first view seem, it should not be neglected. In fixing apon a design for a building, appearance is by common consent, allowed to have ,:? V * Parncl's Treatise on lluads. Jm I'RACTICE OF IIOAD £NG1>£ERING. i 1" ''. • it .it; ■ ^r inn ;tj.JI « ... considerablo w<;ight ; l)ut a road is entitled to not only as great, but ;ven greater attention as regards appearance. In a building, a regular a])pnaran('e gratifies tlie eye alone; whereas in a road, judicious mnnagc- inent produces not only a gratification to the eye, but by concealing the real difficulties of the way, creates a feeling of ease and comfort to the traveller. Nor are there any disadvantages connected with arrangcj- ments of this nature, sufficient to counterbalance the advantages. WhiMi the efl'ect of situation, upon the eye, is not sufficiently attended to, app«mrances will somotiines be exhibited quite different from what vvaH anticipated. As, when n road runs straight for a considerable dis- tance, there is generally a succession of hills and hollows, often oi trilling elevations, but that at a distance have a steep and disagreeable appearance ; when the road runs across a valley in a straight line, to a spectator on one side, the opposite rising ground appears to be much steeper than it is in reality — more especially if the ground be of a light co- lor ; and when, in any situation, there is a long straight line at a consider- able angular elevation, the appearance, when the view is taken down hill, is much steeper than the reality. These are all optical illusions, aided, perhaps, by the imagination, and by comparisons with more favoural)l« parts of the line. These disagreeable appearances may be prevented by making slight turns at the hollows, and in other proper situations, so as on the hilly parts, to present but a small part of the road to view at any one time;. 147. 13ih. Another matter to be attended to in laying out a road through a country not (ally settled, is the quality of the soil. In Ireland a project has lately been set on foot to intersect the country with rail- roads ; and it is judiciously proposed to carry the rail-roads and their branches, as much as possible, through those parts of the country, con- taining the densest population. Carrying roads, in an unsettled country, through veins of fertile land, would be similar conduct: wherever roads are made through good land there will in time be a dense population, and consequently the means of improving and keeping up the road, la great leading lines, this can only be attended to when distances are nearly equal, but in all roads of a lofcal nature, it is proper to carry them throush the best land, even should it be attended with some increase of distance or expense. 148. In the foregoing pages, no notice is taken of laying out rail- roads, because it is unnecessary. The engineering of a rail-road is governed by the same principles as that of a common road. Make a road of earth, lay a coat of broken stone upon it, and it becomes a macadamised road ; lay two stripes of stone, or of iron, or of wood faced with iron, longitudinally along it, for the wheels to run upon, and it is phactice of uoad knuinekhi.ng. 283 roat, but L rei^ulur iminage- aling the jrt to tho arrangtj- ' attended rem what jiablo dis- ofteii ol jagreeahln line, to a bo much a light co- i considor- down hill, )ns, aidiid, fav()urabl« rove n led by ions, so as i^ievv at any out a road In Ireland y with rail- and their mntry, con- ,ed country, jrever roads population, e road. In IS are nearly lem throusli of distance le ng out rail- rail-road is Make a becomes a wood faccil )n, and it is d. called a tram, or track-way ; lay bars of iron, or timbtu's faced with iron, iind adnpted to wheels of a peculiar form, and it is a rail-way. The angle ot friction of a common road is 1 in 30 to 1 in "35 ; of a tram, or track-way, about 1 in 160, and of a railway 1 in 250 : the railway, also, should, on account of the long train of connected carriages that is drawn upon it, be as straight as possible : but with these differences in tho details, the /)nVtc//;/6 on which the engineering operations are copductcd, is in all, the same, and there is equally as mucji skill and attention Re- quired in layin*:; out a common road as a rail road. There is, in many cases, greater difficulty in the former than in the latter: in a rail-road, if obstacles intervene, there is no room for much doubt upon the subject, because it is absolutely necessary that the road be brought to a cer- tain degree of perfection in its grades and curvatures, olherwis(? it will not answer the purpose intended ; but a common road will admit of a a great degree of imperfection, and the state of the funds, and tho amount ol traffic, often make it extremely difficult for the engineer to make such a disposition of his work as will produce the best effect with limited means. 149. At page 1.39 is a note referring to aii account, in " Note C," of adjusting the cross hairs of a telescopic level to the line of collima tion, where the instrument is immovably fixed in its frame. As that note may not be published, we give tho method below : — It may bo premised that in the telescope, the image of a distant ob- ject is formed in the air, in the dark tube, at the focus of the object glass; and that it is this imager and not the object itself, which wc see in looking into the telescope ; the eye glass being merely a magnifier to make the image appear larger than it otherwise would. This image is formed by the rays of light from the object, passing in a peculiar manner through the object-glass. By reason of the peculiar form of that glass tho ray which passes through its middle, continues straight onward as if no glass was interposed, but all the rays which pass through other parts of the glass are bent or deflected inwards towards the central ray, until they meet in a point at the focus, and there form the image of the object. This central ray, or rather, the line in which it lies, is called the optical axis, or line of collimation of the telescope : it may, or may not, be ex- actly in the centre of the tube, but in a well made instrument it is gene- rally near it. If the point at which the hairs cross each other is exactly in this line, every object, be it far oflf, or near at hand, which is really in the same straight line with the line of collimation, will appear in the same straight fine in the telescope : but if the hairs cross upon some other part of the image, a line really straight, will appear through the telescope, crooked, and the hairs must be moved by means of the screws of the diaphragm into their proper position. t 284 PRACTICE OF ROAD ENGINKERIIXG. :t».' M i' '1- ■^?* ¥■]■ In tlm Y level this adjustment is made by reversing the tel6sco|re, (Art. 70,) but when the tplescope is fixed, it can only be done by placing difierent objects in a straight line, and moving the hairs (if required) till the same objects appear in a straight line through the instrument. The most ready method of adjustment, is to set up the instrument so as to bear upon some well defined distant object, and direct an assistant to plant, a vane at the distance of one or two chains, and in a straight line from the centre of the barrel of the telescope to the distant object, by the eye. Then looking into the telescope, direct the hori- zontal hair to the vane, and observe whether it cuts above or below the distant object ; and move the diaphragm (if necessary) till it does so. The vertical hair must be adjusted in the same manner : place a vertical mark, as an ink line on a piece of paper, or a stake, to range by the eye, in a straight line from the centre of the barrel of the teles- cope to a distant object, and then adj ;st the vertical hair so that the same objects will appear in a straight line through the instrument. The adjustment of the bubble tube must be afterwards made, as shown in article 72. Or, the adjustments of both the collimation and bubble tube may be done at the same time, by the following, method : — set up three stakes in a' straight line which we will call A B and C. Let the distance i'rom A to B be about two, and from B to C, 6 or 8 chains ; and mark a level upoD each pair as shewn in fig. 33. Then set the instrument at A, and by measuring upwards or downwards, (as maybe required) from those marks, get a line on the level of the centre of the telescope, on each of the three stakes, in the manner shown with respect to the stakes C and D, fig. 34. Both the collimation and the bubble tube can then be adjusted by this straight and level line at the same time. If the marks on the stakes cannot be clearly seen, a vane may be held by an ^assistant on a level with them. The same thing may be done by measurements from the ground at the different points with the vane, but the process is more troublesome and liable to mistakes, than by the stakes. mimm wr ■"■..; . it- ■':.. ■4 ■ END OF THE FIRST PART. .4 ': * ' / t' (- ■ tel6sco|Te, by placing * required) unient. trument so in assistant I a siraight the distant X the hori- 3 or below till it does er : place a 3, to range f the teles- 80 that the iment. The as shown in tube nnay be three stakes the distance ; and mark nstrument at squired) from telescope, on to the stakes ube can then ime. If the B held by an Tround at the iiblcsonie and ■ill i % ■H m Dii : »,-'