LIBRARY UNIVERSITY OF CALIFORNIA. GIFT OK Class \ QUEEN & CO.'S MANUAL ...OF... Engineers and Surveyors INSTRUMENTS. Construction, Manipulation, Care, Theory and Adjustments. SECOND EDITION. Entered according to Act of Congress, in the year eighteen hundred and ninety-eight, by Queen & Co., in the office of the Librarian of Congress, at Washington. "cfo QUEEN & CO.'S MANUAL ...OF... Engineers and Surveyors INSTRUMENTS. Construction, flanipulation, Care, Theory and Adjustments. Published by QUEEN & CO.v Incorporated, Philadelphia, Pa. I' S. A. FIRST EDITION, CONTENTS. Page. Description of the Engineer's Transit 5 The Manipulation and Care of the Engineer's Transit 19 The Adjustments of the Engineer's Transit 25 The Mathematical Theory of the Errors of the Engineer's Transit . 37 The Graduated Circles of the Engineer's Transit 59 The Spirit Levels of Engineering Instruments 69 The Telescopes of Engineering Instruments 85 Description of the Engineer's Compass . 97 The Adjustments of the Engineer's Compass . . 100 Terrestrial Magnetism in its relation to Surveying Instruments . . . 105 Description of the Engineer's Level 119 The Adjustments of the Engineer's Level 123 Length Measurements in Engineering 131 Description of the Plane Table 133 The Adjustments of the Plane Table 135 The Solar Transit 139 The Adjustments of the Solar Transit 142 The Stadia and The Gradienter 147 The Sextant 159 The Barometer e 161 The Hand Level 171 The Tape and Chain . .....,,.,. 174 The Leveling Rod '177 The Tripod 184 VIEW OF TRANSIT PLATE. DESCRIPTION OF THli ENGINEER'S TRANSIT. GENERAL INTRODUCTION. THE uses of the Engineer's Transit are so varied and con- venient as to command for it the eminent interest of all called upon to do field work. Properly designated the " uni- versal instrument," the well-made transit is, above all others, the instrument suited to the general needs of the enginee: As combining portability with a high degree of accuracy, it is admirably adapted to the great majority of practical problem:: presented to the surveyor, the railroad engineer, the mining engineer, and the topographer. If of accurate, scientific con- struction, it may be relied on for good results in running straight lines, measuring horizontal or vertical angles, level- ing, and in telescopically measuring distances. The Quality of the Instrument being a most important factor in good field work, the purchaser should have clearly in mind the fact that the inferior instrument cannot always readily be distinguished from the superior, and that handsome finish, or even excellence in one particular, does not determine a good instrument. The general excellence of a transit instrument depends on scientific and practical knowledge, on the part of the maker, of every one of the many proper constructive features, and on a conscientious execution of the task in every detail. While a fine appearance and rich lacquering are by no means unbecoming a good instrument, there are in such an instrument hidden excellences of far greater importance. The kinds of metal used in the various parts of the instru- ment, the form of the <; centres,'* their truth, the accurate cen- tering of the graduated circles and verniers, the mechanical method of accomplishing this centering, the accuracy' and style of the graduations of circles and verniers, the mathe- matical relation of the planes of the graduated circles to the 5 6 DESCRIPTION OF THE axes, the sensitiveness and position of the level tubes, the form and position of the standards, the relation of the hori- zontal axis of the telescope to the axis of the instrument, the optical and mechanical construction of the telescope in gen- eral, the thorough testing and adjustment of every mathe- matical, mechanical, and optical characteristic of the instru- ment, and the numerous other details that cannot be enu- merated, are all, though often out of sight, of essential impor- tance to a first-class instrument. A fuller reference to details will be found in the following Description, and in the Special Articles of this Manual treating of the constructive features, and of the theory of the more important uses, of the engineer's transit and its accessories. A Special Test of Excellence of a transit instrument is equality in the grade of accuracy possessed by each essential feature. It is not unusual for makers to become hobbyists on some special feature of construction. Now, it is high magnifying power ; now, professed superiority of graduations ; and now, sensitiveness of levels ; and now, fine mechanical finish. But suppose, for example, a high magnification and inferior defini- tion and coarse levels and inaccurate divisions, and is not the grade of work determined by the most inaccurate feature ? The intelligent engineer well knows that the transit is a com- plex appliance for measurement, and that every feature of the instrument must be up to the standard of accuracy aimed at for the whole instrument, if it is to be, in any true sense, a measuring instrument. QUEEN & Co. suggest that the en- gineer will find no recreation more instructive than that of testing the various constructive features of transits, and then computing the errors which must, result under the various cop- ditions of use. The Final Test of Excellence of an instrument is its perform- ance in skilled hands. Unsatisfactory work and frequent and expensive repairs put a ban on any instrument. But aside from the test in the field, there are two points which determine the quality of the instrument . (i) the maker's reliability and (2) the maker's knowledge and skill. MESSRS. QUEEN & Co. wish it understood that they give conscientious attention to ENGINEKK S TRANSIT. 7 every detail of construction and adjustment, and that the best scientific talent co-operates with mechanical skill possessing years <>f experience. Their experts are not only generally familiar with the qualities that make the engineer's transit ef- ficient, but, from a study of the mathematical theory of the most accurate uses of the instrument in geodetic work, and from a broad study of the mathematical theory and refined uses of all sorts of instruments of precision, have attained a clear comprehension of the errors most to be feared, and hence, of the course of construction best suited to secure the highest efficiency of the instrument in the field. Description of the Instrument : The following description is intended to convey some idea of trie essential parts of the tran- sits of QUEEN & Co., and of the purpose of these parts. It is also intended to direct attention to the Special Articles, pre- sented in this Manual, on the theory, construction, and uses of various parts and accessories of the instrument. The Telescope of the engineer's transit, as distinguished from the theodolite proper, is made to turn over or transit at one or both ends, so as to reverse without horizontal motion. In the two ordinary sizes the telescopes are, respectively, eight and eleven inches in length, with apertures from one to one and one-fourth inches clear, and powers from eighteen to twenty-five, according to the requirements of the instrument. So much depending on the character of the telescope for de- finition, light and power, and alignment, QUEEN & Co. use all the resources of science and mechanical art to bring it to the highest perfection. For further indications of their attention to details, and for detailed description of parts, the reader is referred to the special article on " The Telescopes of Engineer- ing Instruments" The Object-Glass and Eye-Pieces require detailed description and explanation, and are referred to at length in the article just mentioned. A Diagonal Prism, placed immediately in front of the eye- piece, so as to reflect the rays at right angles to the eye, is used when it is desired to take vertical angles greater than it is possible to observe with the ordinary eye-piece. It is found 8 DESCRIPTION OF THE very convenient for observing the sun, on interposing dark glasses between it and the eye. The Eye-hole Slide is a little slide placed just inside the eye- hole, and movable by means of a little projecting pin. It ef- fectually excludes dust and rain from the instrument, and should always be used to close the eye-hole when instrument is not in use. The Sur.-Shade is an extra piece of brass tubing, fitted on the objective end of the telescope as an open cap. It excludes direct sunlight, dew, and dust. Its constant use in contin- uous work is insisted on by some supervising engineers, with great advantage to the quality of the work. The Slide-Protector is a tube screwed to the objective end of the telescope, and covering completely the delicately fitted slide upon which the object-glass is moved in and out for shorter or longer sights. It excludes dust and moisture from the slide and the inside of telescope. It is attached to all of QUEEN & Co.'s telescopes having the object-glass slide. The Cross-Hairs, placed in the common focus of the object- glass and eye-piece, are two fibres of the little black field spider. They are cemented in divisions of a metal ring ac- curately at 90 with respect to each other. Platinum wires are inserted only on special order. The Cross-Hair Ring, as figured in the accompanying Fig, i . can, upon release of its screws, be slightly turned for adjusting one hair to verticality. By re- moving the eye-piece and the screws of the ring, the ring itself may be taken out for the purpose of replacing broken wires. This is an operation, however, rarely necessary, and to be attempted only by one who can exercise the requisite care in replacing the spider-threads and the ring, and also in placing the eye-piece in its former centered position. ENGINEERS TRANSIT. 9 The Stadia Hairs, adjustable or fixed, are also attached to the cross-hair ring. The adjustable hairs are attached to movable pieces, a a, Fig. I, held in position by a spring, and can each be brought to equal distances on each side of the fixed thread for every desired scale of stadia reading. A dis, cussion of the important subject of stadia measurements is given in the special article entitled " Gradicntcr and Stadia Measurements" The Gradienter Screw is a specially cut screw, Fig. 2, with graduated head, acting upon an arm clamping to the horizontal axis, for turning off small ver- tical angles, and in the form furnished by QUEEN & Co. affords a ready means for run- ning grades and measuring dis- tances and differences of level. The screw-head reads directly to hundredths of a turn of the screw, and is so placed as to be easily read without change of position of the observer. One Fi s- 2 - revolution of the screw moves the telescopic sight-line so as to intercept one foot on a vertical rod at a distance of one hundred feet when the telescope is horizontal. For a com- plete indication of the advantages, theory, and use of this attachment, the reader is referred to the article on " Gradicntcr and Stadia Measurements." A Graduated Head for the Tangent Screw of the alidade is sometimes found a valuable addition, in the hands of the expert engineer, for measuring horizontal angles and deter- mining distances. Further details, concerning its use, are given in the article mentioned in the preceding paragraph. The Horizontal Axis of the telescope rests upon the carefully constructed V's of the standards, and is adjustable at one end, as described under the head of the standards. Plain cylindrical pivots are used where reversal of the telescope on the standards and the use of a striding level become nec- essary. 10 DESCRIPTION OF THE The Vertical Arc or Circle, attached to the horizontal axis for measuring angles of elevation or of depression, is graduated to read to minutes or less, according to requirement. The arc is sometimes made to clamp with respect to any position of the horizontal axis, so as to permit the measurement of an arc of greater extent than that of the instrument. The com- plete vertical circles are furnished either with one vernier or with two opposite verniers, according to the grade of work for which the instrument is intended. The Standards of the Transit are made shapely, light, and strong, and firmly attached to the upper or alidade plate. The bearing of the horizontal axis, at the upper portion of one Fig- 3- of the standards, is made vertically adjustable by means of a screw and jam nut. By moving this bearing up or down, as required, the horizontal axis of the telescope may be mao^ accurately perpendicular to the vertical axis of the instrument, as fully explained in the articles on the adjustments and errors of the transit. A Right-Angle Sight, formed by slits cut in the two clamping arms attached to the standards, and forming a means for quickly setting off lines at right angles to the telescopic sight- line, is found a desirable addition in some forms of the transit. The Clamp-and-Tangent Movement attached to the vertical KN;i\KKK S TRANSIT. II circle is a type of all clamp-and-tangent attachments used in the instrument, and may be readily understood from the figured instrument. The essentials are a clamp acting with certainty, a smoothly and easily moving tangent screw, and a stout and definitely acting spring. The spring adopted is a plain, stout strip of hammered German silver. QUEEN & Co. also furnish the usual enclosed spiral spring, if it is preferred. The clamp and tangent seen immediately above the upper plate of the leveling-head, when in use, enables the circle- plate to be slowly moved in its socket in the leveling-head. The clamp and tangent as seen near the edge of the alidade- plate, when in use, enables the whole alidade, with telescope, to be moved on its centre with respect to the graduated circle. The form preferred for this purpose clamps directly to the axis of the instrument, afid not to the plate. The clamp-bar fits snugly on the axis, and the clamp acts with the least mo- tion of the screw, and without strain upon the circle or the least disturbance of a pointing of the telescope. The Alidade, upper plate, or vernier plate, carries not only the verniers but the magnetic compass, standards, and tele- scope as well. It is shown in the accompanying diagram and vertical section of the instrument, Fig. 3, as attached to the inner axis or " centre." It fs made as light as possible, as is, indeed, every other portion of the instrument, consistent with the requisite strength and rigidity. The Verniers are two in number, lettered A and B, and placed inside the graduated circle, and, for convenience in use, at angles of about 30 with the line of sight. This position of the verniers enables a broad and firm base to be secured for the standards. The verniers are always double, having the requisite divisions on each side of the zero, and are num- bered so as to be counted in the same direction as the vernier is moved. The two opposite verniers furnish the means of using the well-known principle of reversion in order to determine and eliminate any outstanding error of eccentricity, to determine errors of graduation, and generally to eliminate errors by re version observations. 12 DESCRIPTION OF THE Reflectors, of celluloid or ground glass, are used to throw the requisite light on the divisions. The vernier glass covers are firmly cemented on the vernier openings, so as to exclude dust and moisture. For the theory of the vernier, and other points of interest relating to reading of circles, we refer the reader to the special article on " Tlic Graduated Circles of tJie Engineer's Transit'' Plain Reading Microscopes, for greater convenience and ac- curacy in reading the verniers, are attached to several of the larger special forms intended for city, tunnel, or triangulation work. Micrometer Reading Microscopes, instead of verniers, are applied to QUEEN & Co.'s largest and finest geodetic instru- ments. For description of this form of microscope, see article entitled " The Reading Microscope its Forms, Theory, and Ad- justrnents" Estimation or Scale Microscopes are coming into use where rapidity and a fair degree of accuracy are required in the read- ings. Consult the article referred to in preceding paragraph. The Compass-Box, though not an absolutely necessary feature of a transit, is for general work an important one. It is placed between the standards, directly on the upper plate. A glass cover protects the compass^circle, which is graduated to half degrees, and numbered both from the north point and the south point in each direction, from o to 90. The Magnetic Needle, four to five inches in length, accord- ing to the size of the transit, has at its centre a small brass cap, in which is inserted a little socket of hardened steel, or a highly polished jeweled centre, and by means of which the needle rests upon the hard, polished point of the centre-p^n. It can thus move freely in a horizontal direction, and take tfte direction of the magnetic meridian. It is somewhat weighted oniits south end by a small coil of fine brass wire, which can be easily moved along so as to adjust the needle to a truly horizontal position, or so as to prevent dipping. The north end is distinguished by a scallop. The needle is lifted from its pin, when not in use, by a lever actuated by a screw placed at the side of the compass-box. The same screw may be used ENGINEER S TRANSIT. 13 in checking vibrations of the needle. The form of needle pre- ferred is about six-hundredths of an inch deep and two- hundredths wide. The magnetization of the needle and other related matters, of interest to practical observers, are treated of in a special article of this Manual, entitled, " Terrestial Magnetism in its Relation to Surveying- Instruments." The Centre-Pin is a sharp-angled cone of hardened steel, the point being made glass hard and carefully ground. When the point is dull, or the pin bent, the pin is easily removed, ground, and replaced. On eccentricity of centre-pin, see article of this Manual on " The Adjustments of the Surveyor s Compass." The Circle-Plate, lower plate, or limb, as it is sometimes called, is made of the finest quality sheet brass, and in such manner as to obviate unequal expansion and contraction through temperature changes. The circle itself is either grad- uated directly on the brass, and then silvered, or upon a rim of silver securely set into the plate. In the production of an accurate graduated circle, there are two points of especial im- portance : First, the character of the graduation, and, secondly, the centering of the circle with respect to the axis of the in- strument. With the facilities possessed by QUEEN & Co. for producing finely graduated circles for astronomical and en- gineering instruments, no errors of graduation need be feared, but the graduation itself may be relied on with the utmost confidence. For a further description and discussion of the graduations, we refer the reader to a special article, entitled " The Graduated Circles of the Engineer s Transit." The cen- tering of the circle is provided for by special devices which not only allow it to be accomplished with certainty and ac- curacy, but also to be maintained after the adjustment has once been made. For a discussion of the subject of eccen- tricity, we refer the reader to a special article of this Manual, entitled : " The Errors of Eccentricity of the Engineer s Tran- sit:' The Graduations are made with fine, uniform, dark lines, so as at the same time to be read with ease and accuracy. The numbering is usually from o to 180, in two directions, with a second numbering on half of the circle, round to 360. 14 DESCRIPTION OF THE Thus angles may, with facility and certainty, be read in any manner desired. A very convenient set of inclined numbers has been adopted on the circle ; the inclination always indi- cating in what direction from the zero the reading is being made. Hence, with the kind of numbering adopted, and with the inclined figures, the engineer always has a sure method of remembering the direction of the angle measured. The sizes of the circles vary, usually, from five and one-half inches to six and one-half inches diameter. They are grad- uated, ordinarily, to half degrees, and read to minutes, or, in order to give wider space on the vernier, to twenty minutes and read to degrees, or to twenty minutes and read to thirty seconds, or, in the higher grades, to any required fineness of reading. Fig. 4. The Vertical Axis of the transit, as shown in section in the accompanying Fig. 4, is determined by two concentric conical " centres," as they are called. The vernier, or alidade- plate, is attached to the inner " centre," and the graduated circle is attached to the outer " centre," which, in turn, fits into the socket of the leveling-head. It is of the highest im- portance that these " centres " should be turned and fitted with mathematical accuracy, and to insure this QUEEN & Co. turn both " centres " finally on the lathe between dead centres. ENGINEERS TRANSIT. 15 The surfaces of the " centres " do not come in contact throughout their entire length, but are, for about one-third the distance, cut away, so as to insure a positive mathematical axis under all conditions of wear. Not only should the axis, when the instrument is sent out, be exactly concentric with the centre of the graduated circle,but it should have been so designed as not to introduce the error of eccentricity by wear. It has, however, been found that, in some patterns of " centres," wear not only produces the error of eccentricity, but introduces it in such form as to be irremediable without the construction of new centres. In order to prevent unnecessary wear, and lessen friction, the three metals of the inner " centre," the outer " centre," and the leveling-head socket are selected, not only with a view to the requisite rigidity, but with a view to a small rel- ative co-efficient of friction. Bell-metal, of the hardest quality, should be used for the inner " centre," a fine gun- metal for the outer " centre," and a superior quality of red metal for the socket of the leveling-head. MESSRS. QUEEN & Co. having in their own establishment superior facilities for making the necessary castings, are enabled to compound alloys of metals with a special view to the theoretical conditions in important pieces, such as the " centres " and their sockets. The Levels of the Transit are usually three in number. Two are attached at right angles to each other on the upper plate or alidade, one being parallel to the line of sight, the other transverse to it. Various positions are given to these levels on the alidade by makers, according to the different con- structive demands ; and the positions assigned are, indeed, quite indifferent, if the levels are in proper relation to the line of sight and easily adjustable. For adjustment of these plate levels, with respect to the vertical axis of the instrument, proper screws are provided, and care should always be taken to unloosen the little clamping screws at the ends of the bubble- cases before, and to tighten them after, moving the vertical adjusting-screws. The third level is the fine one attached to the telescope- tube, parallel to the line of sight. Sometimes a highly sensi- 1 6 DESCRIPTION OF THE tive striding-level is furnished, for leveling the horizontal axis, in the higher grades of instruments. And sometimes, also, a coarse circular level is attached to the alidade for quick level- ing. The solar and other attachments often have their own proper levels. The transits of QUEEN & Co. are furnished with accurately designed, carefully made levels, true and suitably sensitive, and each level, including the plate-levels, provided with di- visions throughout its entire length, so as to allow of accurate use under all conditions. The importance of the level as a constructive feature, and its general theory and use, are treated of in a special article of this Manual entitled: "The Spirit Levels of Engineering Instruments" The Leveling-Head is shown in the lower part of the ac- 'companying Fig. 3, giving a vertical section through the plates and centres. It consists, essentially, of the two leveling-plates and leveling-screws. In these long-centre transits, the level- ing-head is not, as in some inferior short-centre instruments, removable, but at all times forms an essential part of the in- strument. It need scarcely be remarked that in all high-grade long-centre instruments it is not removable, for the reason that only thus can the most accurate adjustments be attained and kept, at the same time that the centres are protected from irre- trievable injury. QUEEN & Co. have found that the short- centre instruments, with removable head, are those most fre- quently coming in for repairs. Leveling-heads with four leveling-screws are those usually preferred by American en- gineers ; bf v!., upon special order, heads with three leveling- screws arc also supplied. The screws are all covered with neat dust-caps, and provided with milled heads of moderate diameter, those of very large diameter having been found to give too much mechanical advantage to inexperienced and thoughtless users, and also to impede quick leveling. The leveling-head is attached to the tripod-plate, either by means of a neat and effective clamp, or by means of screw, as pre- ferred by the engineer. The clamping device saves a little time in setting up and dismounting the instrument. The Shifting-Centre, as now supplied with each of the QUEEN ENGINEER'S TRANSIT. 17- & Co. transits, allows the vertical axis, with its attached plumb-line and bob, to be accurately brought over a desired point, when once the instrument has been approximately set up over the point. With the leveling-screws somewhat loosened, the whole instrument may be freely moved on the lower level-plate to any required position. The great amount of time saved, and the accuracy attained in setting up by its means, makes the shifting-centre invaluable to the en- gineer. The Quick-Leveling Attachment consists of wedge-like rings, which, as a separate piece, is clamped or screwed directly on the tripod-plate. The instrument is then clamped or screwed upon the attachment, and, by an easy revolution of the rings, quickly brought to an approximately level position. The fine leveling is then accomplished by the leveling-screws. It is furnished only upon special order. The Tripod, furnished with QUEEN & Co.'s instruments, is designed to be rigid, of moderate weight, and adjustable to position with ease and certainty. Fine white ash-wood is used for the legs, as supplying the requisites of strength and lightness. The legs are furnished with a sharp steel shoe, well fitted to the wood. Winged clamping-screws are used to fasten the legs to the plate. The forms supplied are (i) the ordinary round leg of elegant pattern, (2) an improved " split- leg " tripod, and (3) an excellent extension tripod. The Plumb-Bob is accurately attached to the central axis of the instrument by means of a small hook and chain, and is in all cases made adjustable. It is supplied in any desired weight, from eight ounces up to the heavy ones of two and three pounds required for plumbing down deep shafts. They are usually made of brass, and steel pointed. The Plummet-Lamp, supplied for mining and other purposes, is so arranged that either the oil light or a small incandescent electric lamp can be used. The small incandescent lamp is attached centrally on the cap which covers the wick of the oil lamp when the latter is not in use. A small storage battery, or several cells of some suitable battery, will furnish the electrical energy required. The wires running to the 1 8 DESCRIPTION OF THE ENGINEER'S TRANSIT. incandescent lamp are perfectly flexible, and a key is inserted in the circuit, so as to enable the lamp to be lit and ex- tinguished rapidly for purposes of signaling. The entire steadiness, certainty, and safety of the electric lamp under all conditions in mining have induced QUEEN & Co. to fit the lamp also to targets of the leveling-rod, so as to permit the ready use of the gradienter-screw and stadia wires in under- ground or night work. The Solar Attachment, for determining the true meridian, is readily fitted to any form of transit, but for the most trust- worthy results requires to be fitted only to transits capable of meeting the mathematical requirements. For a full descrip- tion of the attachment, its theory, and use, the reader is re- ferred to the article of this Manual on " The Solar Transit, and Methods of Determining the Astronomical Meridian." The Forms of the Transit made by QUEEN & Co. range from the plain transit, without telescope, level, or vertical arc, to the large altazimuths of refined construction, intended for geodetic triangulation and astronomical field work. Some of these forms are more particularly described and figured in their Catalog-tee of Engineers' and Surveyors' 1 Instruments, and the reader is also referred to their Catalogue of Astronomical Instruments for information relative to in- struments made by them for astronomical observations. Popular forms of the transit are the complete engineer's tran- sit, with either six and a half-inch circle and five-inch needle, or with six-inch circle and four and a half-inch needle ; the light mountain transit, with five and a half-inch circle and four- inch needle ; and a cheaper grade of engineer's transit, with four and a half-inch circle and five-inch needle. In addition to instruments of the usual weight, QUEEN & Co. also make transits in which the metal used is, for the most part, alum- inum, and the weight reduced to a minimum. QUEEN" TRANSIT THEODOLITE. A 1470. Price, $850.00 THE MANIPULATION AND CARE OF THE ENGINEER'S TRANSIT. TO Set Up the Transit on nearly level ground, stretch out one leg of the instrument and set it loosely at a con- venient distance from the point over which the instru- ment is to be placed. This distance should be so taken that the legs of the transit will make angles of between 50 and 60 with the ground. Now spread out the other two legs and plant them in the ground so that the distances of each leg from the point will be nearly equal. Next, press on each of the three legs successively so as to drive them firmly into the ground. If the ground be hard very slight pressure will suffice. The distance to which each leg is driven into the ground should be so regulated as to bring the bob approxi- mately over the required point. The bob may now be brought accurately over the point by unloosening the plate-screws and sliding the shifting centre. Then level both ways, taking care to tighten fairly but not to strain the leveling screws, and the instrument is ready for work. A good surveyor will always endeavor to arrange his instru- ment in setting up so that the height of the eye-piece \vill nearly coincide with the height of his eye when standing erect. This will avoid a cramped position in taking sights. Judg- ment must be used in the case of a tall person, to prevent an insecure position of the instrument, such as would be caused by having the legs too close together. When setting up the instrument on ground of any slope whatever, one leg of the instrument should be placed on the slope above the point, the other two remaining below. A rough estimate should be made so that the upper leg may be brought further distant from the point than the other two, whose distances from the point should be nearly equal. The 19 20 MANIPULATION AND CARE OF THE excess of distance of the upper leg over that of the other two must be greater as the slope is more inclined. It is advisable first to push the upper leg into the embankment as far as pos- sible, and then to press in the other legs until a secure posi- tion is obtained. This method will bring the screw-plate more nearly level. In the case of setting up over a point on the edge of a per- pendicular cut, one leg should be driven into the side of the cut, the others being spread out over the top. Shouldering, carrying, and setting up an instrument requires practice and artistic method to avoid accidents and inconveni- ence. In taking the instrument up, first see that the lower clamp is loosened, and always leave it moderately loosened when the instrument is not in actual active use. Next bring one shoulder squarely against one leg near the tripod head, and rest the instrument against the shoulder while the instru- ment is turned upon this tripod leg as a pivot, and the other two are successively folded in toward it. Now take up the instrument and balance on the shoulder. In setting up, re- verse the process by first resting the instrument on one leg and turning the instrument upon its toe as a pivot, successively bring the other two legs into position, as indicated in the pre- ceding paragraph. Grasp the Instrument, in mounting and dismounting from tripod, always by the leveling head only. When the instru- ment is not in use, or not being carried, leave the leveling screws and the lower clamp only slightly clamped. The Tripod Legs should always have their shoes sharp and tightly screwed to the wood. The legs should also be snugly clamped to the tripod head. The Leveling Screws should all be fairly seated before af any time removing the instrument. If leveling screws or tan- gent screws work hard, clean the threads well by means of a small, stiff brush and a little oil, taking care finally to remove all oil. Overstraining of any and all screws should be avoided. The Magnetic Needle should always be very gently set free upon the centre pin, so as not to dull the pivot ; and the needle ENGINEER'S TRANSIT. 21 should also always be arrested and screwed fairly against the glass cover before moving, carrying, or dismounting the instru- ment. Wide vibrations of the needle may be gently checked by means of the needle-lifter. The glass cover of the com- pass-box should be wiped off only with linen, and then gently breathed on to relieve all electrification produced by rubbing. Iron, as disturbing the needle, should be carefully excluded from hat rims, buttons, watch chains, reading-glasses, specta- cles, and the like. On placing the instrument away after use, first release the needle, and then, after it has taken up the di- rection of the magnetic meridian, raise it against the glass. No false deflection, due to magnetization of the metals used in the instrument need be feared, since QUEEN & Co. take special precautions to carefully test all metals entering into the con- struction of the instrument, and reject any piece giving the slightest indication of magnetic properties. The Spirit Levels, in proportion to their sensitiveness, are liable to error from differences of temperature in their parts. They should not be touched, or exposed to any sudden changes of temperature. The bubble will invariably move toward the end having the higher temperature. Accuracy re- quires a carefully preserved, even temperature. For faults of levels, consult the article of this Manual on " The Spirit Levels of Engineering Instruments" The Focusing upon the hairs is accomplished by carefully turning the eye-piece like the nut of a screw, until the hairs appear most sharply defined. The focusing upon the object is accomplished by gently turning the milled head near the objective end, until the object appears most clearly defined in the telescope. Consult the paragraph under the same heading, in the article of this Manual on "The Telescopes of Engineering Instruments" The Sun Shade should be used as much as possible, as it is nearly always an advantage to good work, as well as to the protection of the instrument. The Cross-Hairs may be relieved of any annoying dust par- ticles that cling to them by removing the eye-piece and very gently blowing into the tube. Broken cross-wires may be re- 22 MANIPULATION AND CARE OF THE placed by an engineer accustomed to nice manipulation and patience, as follows : Provide a little shellac, dissolved in the best alcohol, a small, fine camel's-hair brush, and a U-shaped frame upon which has been previously spun off a continuous thread from a little black field spider, the thread best adapted to varying hygrometric conditions. Removing the cross-hair ring and carefully cleaning it with alcohol, place it on a table, with the graduated lines, intended to receive the threads, uppermost. Then carefully lay the U-frame on it, in such a manner as to bring one fibre approximately in coincidence with a division. Brush it gently into the division, and fasten at one end with a drop of shellac. Wait a minute for this to harden, and then stretch the fibre across and secure it in the division at the other end by means of a little shellac. After waiting, as before, for it to harden, remove all extraneous fibres, and proceed in like manner to insert the other thread at right angles to the thread already fastened. The Cleaning of the Lenses of a telescope should always be undertaken with caution. The fine polish of the lenses of first-class instruments, so necessary to the transmission of a high percentage of the light, is attained only by the use of the most delicate processes of the optician's art. And it would be most unfortunate if, from ignorance or carelessness, the highly transparent glasses should be dulled forever by a clumsy wip- ing. Therefore, as a precaution, do not unnecessarily attempt to clean them. Particularly do not add the insult of grease to the injury of dirt, by dabbing your fingers against the surfaces of the glasses. If dust is found upon the lenses, gently brush it off with a fine camel's-hair brush. If dirt still clings, slightly moisten the lens by breathing upon it ; then, take a piece of very old and very fine linen, and so wipe off the dirt as continually to push the dirt in front of the linen. Do not roll the dirt parti- cles under the linen, and then scratch the glass by pressure and rubbing. Silk and buckskin are objectionable ; the for- mer scratches, and the latter often contains gritty particles. Keep a piece of fine old linen in your box, and use that only. Moistening the lens with a little alcohol will sometimes be de- ENGINEERS TRANSIT. 23 sirable, in order to restore the original brilliancy of the sur- faces. Keep the outer surfaces of eye-piece and object-glass always free from dust, moisture, and grease by careful cleaning, as here indicated. Moisture penetrating between the crown and flint lenses of the objective, after exposure of the instrument in rain, will be- come visible there as a mist obscuring the view. ;. Since the lenses of the objective should never be separated, it is in such cases necessary to place the instrument in a warm room until the moisture has been thoroughly evaporated, or, if this does not prove successful, carefully unscrew the objective and ex- pose it to a gentle heat ; but do not, in any case, remove the lenses from their cell. If at any time it becomes necessary to dry out the interior of the tube, the eye-piece may be re- moved and the eye-end carefully covered with a fine clean piece of linen to exclude dust. The Object Slide, notwithstanding the nicely fitted slide- protector, may in time grind or work hard. The slide is ex- posed by unscrewing the protector, and, if necessary, also the pinion head which moves the objective. Careful cleaning is usually all that should be attempted. Oil gathers and holds dust. If the object-slide begins to fret, examine it instantly. The Centres and Graduation are exposed, and the main body of the instrument taken apart by unscrewing in turn the upper clamp, the dust-cover ring which embraces the lower plate, and, finally, the centre screw from which the plummet hangs. The graduations are first to be brushed with extreme care with a camel's-hair brush, and then, if necessary, wiped, but only at right angles to the divisions, and never rubbed, especially not on the edge. The centres, when clean, may be slightly lubricated with pure watch oil. It is to be clearK understood that only after years of use should it be necessary, and therefore desirable, to separate the centres for inspection and cleaning of the interior parts. QUEEN & Co. use every artifice and precaution which good design and fine workman- ship can provide for excluding dust and moisture from the instrument, and therefore only after long continued rough usage should an examination of the centres be necessary. If 24 MANIPULATION AND CARE OF THE, the centres fail to revolve with the usual freedom after expos- ure in extremely cold or hot weather, take an early oppor- tunity to inspect them. If the centres begin to fret, examine them instantly. The protection of the instrument from rain, dust, and con- tinued exposure to the direct rays of the sun are a constant 'duty and difficulty. The white, cashmere-lined gossamer rub- ber cover furnished by QUEEN & Co. with their transits, and always to be carried with the instrument, is, as a rain-proof, dust-proof, and heat-proof protector, of great practical advan- tage. Carelessness in exposing the instrument to the curiosity of cattle, or to other unnecessary risk, and in general, an un- couthness of usage, indicate such lack of respect for skilled and conscientious workmanship as to be quite unpardonable. The Instrument Box should always be used in transporting the instrument. QUEEN & Co.'s boxes are all provided with flexible rubber cushions for taking up the sudden jars or vio- lent vibrations incident to travel. The Manipulation in general should possess " an ease and smoothness " that makes it next to impossible on the one hand to give a good instrument a disposition to fret in any of its parts, or, on the other hand, to bring about serious injury in an instrument whose parts need careful cleaning or have been bent and strained by a fall. Repairs become necessary to the best instrument in time, and should not, when really needed, be unduly postponed. QUEEN & Co., from a long and varied experience in repairing all sorts and makes of engineering instruments, make it a dis- tinct aim so to construct their transits that (i) they may pass through a certain amount of rough usage without injury, and (2) may be repaired with success even after serious injury. QUEEN" ALT-AZIMUTH. A 1480, Price, S55O.OO THE ADJUSTMENTS OF THE ENGINEER'S TRANSIT. THE adjustments of an engineer's transit are of two kinds: (i) The maker's adjustments, or those which reliable scientific makers give the instrument while it is in process of construction ; and (2) The field adjustments, or those which occasionally have to be verified in the accurate field use of the instrument. The latter are, as a matter of course, included in the former, since scientific makers always find it necessary to verify all the adjustments, and deem it an essential requisite of a properly constructed and thoroughly tested instrument, to send it from their hands only when in every respect accurately adjusted for immediate use. THE MAKER'S ADJUSTMENTS. In order that the mathematical conditions of the practical problem of angular measurements in the field (see " Mathe- matical Theory of t/t: Errors of the Engineer s Transit" this Manual) may be realized in the instrument itself, it v is necessary that the following points of construction and adjustment be accurately attained. 1. The lenses of the objective and of the eye-piece of the telescope truly centered in their respective cells. 2. The optical axis of the system of lenses coinciding with the mechanical axis of the tube, in all the relative positions of the objective and eye- piece, the lenses remaining always at right angles to this axis. 3. The cross hairs, during each observation, in the common focus of the object-glass and eye-piece. 4. The vertical cross hair (all other adjustments made) at right angles to the horizontal axis of the instrument. 25 26 THE ADJUSTMENTS OF THE 5. The line of sight at right angles to the horizontal axis, or coinciding with the axis of collimation. 6. The axis of the telescope level lying in the 'same plane as the line of collimation, or not " crossed " with respect to the collimation plane. 7. The axis of the telescope level parallel with the line of sight. 8. The horizontal axis of the instrument at right angles to the axis of the alidade or to the axis of the upper plate ; and hence (all other adjustments made) the line of sight always lying in the plane which is at right angles to, and passes through the centre .of, the horizontal graduated circle. 9. The form of the pivots of the horizontal axis the equiva- lent of true cylinders. 10. The V's or bearings for these pivots of equal form. 1 1. The vertical graduated circle at right angles to the hori- zontal axis of the instrument. 12. The vertical graduated circle and its verniers truly centered with respect to the horizontal axis. 13. The alidade, or upper, plate at right angles to its axis. 14. The axis of the alidade, or upper, plate coinciding with the axis of the lower, or circle, plate. 15. The lower, or circle plate at right angles to the common axis of both alidade and circle plates. 1 6. The graduations of the horizontal circle and of its verniers, true and concentric with the common axis of the alidade and circle plates. 17. The zeros of each set of verniers or reading microscopes accurately 180 apart, as measured at the respective centres of the graduated circles. 1 8. The axis of each of the alidade levels at right angles to the vertical axis of the instrument. 19. The pivot of the compass needle coincident with the vertical axis. 20. The zeros of the compass graduations in the same plane as the line of collimation. 21. The magnetic needle perfectly straight. ENGINEER'S TRANSIT. 27 22. The magnetic axis of the needle coinciding with the axis of form. 23. The magnetic needle adjusted for the magnetic dip of the place of observation. 24. The axis of the suspended plumb-bob coinciding with the vertical axis of the instrument. While it would be difficult and unnecessarily tedious to set down every adjustment attended to by the skillful maker, the foregoing may be taken as a list of the more prominent ones. Other adjustments peculiar to the accessories of the transit and to special forms of the transit will be referred to in treat- ing of these elsewhere. THE FIELD ADJUSTMENTS. The following practical methods for detecting and correcting the errors of an Engineer's Transit are given for use in the field. A full explanation of the nature of each error is also made in order that the detection and correction may proceed intelligently. It is not to be inferred that QUEEN & Co., as scientific makers of Transits, pursue their tests of these field adjustments exactly as the practical engineer is here advised to do. Special appliances in the form of collimating telescopes and other delicate optical and mechanical devices, enable their adjuster to test and rectify the errors of a Transit by refined methods and consequently to secure a grade of accuracy in these adjustments which can scarcely be equaled in -the field, even by the accurate observer. First Adjustment: -To make the axes of the plate levels per- pendicular to the vertical axis of the instrument. DETECTION OF ERROR: Level the instrument carefully both ways, care being taken to make each bubble-tube parallel to a pair of plate-screws. Turn the telescope through 180 by measuring on the vernier plate. This measurement should be a direct angular measurement on the plate, and not a mere approximation. If the instrument is not in adjustment the 28 THE ADJUSTMENTS OF THE bubbles, after this revolution, will no longer remain in the centres of the tubes. This displacement of the bubbles is twice the true error of the instrument. For if aa f (Fig. 21) Fig. 21. represent the trace of the plane of the bubble-tubes, oo f the vertical axis of the instrument, the turning through 180 would bring a to a" and a' to a' n ', the angles a"o'o and a'"o f o being respectively equal to ao'o and a'o'o. The line KL re- presenting the proper position of the bubble-tube plane, the angle a'o'a" will therefore be the double error, and cause twice the displacement of the bubbles due to the true error. CORRECTION OF THE ERROR : To correct, bring the bubbles half-way back to the centres of the tubes by raising or lower-t ing either end of the tubes, screws being placed there for that purpose. Then level accurately by means of the plate- screws. This process should be repeated several times, as without extreme accuracy in this adjustment, any attempt to perform the other adjustments is valueless. Second Adjustment: To make the line of sight coincide with ENGINEER'S TRANSIT. 29 the line of collii nation, or to make the line of sight perpendicular to the horizontal axis of the telescope. DETECTION OF THE ERROR: The direction of the line of si^ht is determined by .two points, the optical centre of the object-glass, and the intersection of the cross-hairs. Of these the latter is movable and is the part whose position is to be corrected. Set up the instrument, level carefully, and sight, Fig. 22, to some well-defined point, A. Reverse the telescope (i. e., turn . C D B Fig. 22. it over) and sight to B. A and B should be as far distant as possible from the instrument, since the apparent deviation and consequently the accuracy of the subsequent correction in- creases as the distance. B H should be taken equal to A H. If the line of sight oo' be not perpendicular to the horizontal axis of the instrument EE ', A and B will not be on the same straight line with H. To determine whether this is so or not turn the telescope around on its vertical axis and sight to A. The horizontal axis of the instrument now occupies the posi- tion E" E'" , the angle OHE' of the old position correspond- in- to OHE" in the new, and the angle OHE to OHE'". \ w reverse the telescope (turn over on horizontal axis) ; its line of sight will strike this time as far to the left of the line Aoo' as it did before to the right, that is at C. The angle aHO' represents the doubled error, so also does E" HE, since these angles are equal. But the total angular movement from B to C represents the sum of these angles, and is consequently four times the true error. CORRECTION OF THE ERROR: To correct, with the telescope THE ADJUSTMENTS OF THE pointed at C, place a stake at D, the distance DC being made equal to one-fourth BC. Move the cross-hair ring by means of the capstan-headed screws placed on the side of the tele- scope, until the intersection of the hairs cuts the point D. This operation is accomplished by screwing both screws at the same time, the one in and the other out. It should be remembered that an inverting or astronomical telescope does not invert the motion of the cross-hair ring, and hence the screws must be turned so as to move the rino- in the same & direction as that apparently required to produce coincidence. With the usual terrestrial or erecting telescope the screws must be turned so as to move the ring in the opposite direction from that which the error apparently requires. Third Adjustment: To make the line of collimation revolve in a vertical plane, DETECTION OF THE ERROR : Set up the instrument, and , level carefully. Sight to. p \ i some high object. The ^ I top of a steeple is generally * /' most convenient. Depress the telescope and note care- fully where the intersection of the cross hairs cuts the ground. Turn the instru- ment through 1 80 (this time only approximately) and, reversing the telescope, sight to the same high point, depress the tube again, and again note where the line of collimation strikes the ground. The fault to be remedied is that the horizontal axis of the telescope is not parallel to Fig. 23. the plane of the plate bub _ bles. (Fig. 23.) Turning through 180 brings the support A to A' and inclines the axis as represented Fig. 24. ENGINEERS TRANSIT. 31 by the dotted line A' W , the angles BOA 9 or B'OA represent- ing the doubled error, since the line drawn through O parallel to the bubble-plane would bisect them both. The motion of the line of collimation is represented in Fig. 24. /'being the high point, K and L the two points on the ground ; M being the middle point which the cross hairs should cut if the instrument were in adjustment. CORRECTION OF THE ERROR : To correct, therefore, raise or lower one end of the axis AB by means of a screw placed in the standard for that purpose, until the line of sight revolves in the plane from P to M. The reflection in a basin of mer- cury of the high point will suffice to determine the point J/, and the consequent error KM or ML be determined without the reversal of the telescope. Instead of a very high terrestrial object a star may be advantageously used in this reflection- method. Fourth Adjustment: To make the axis of the telescope level parallel to the line of collimatioK. Fig. 25. DETECTION OF THE ERROR : Drive two stakes several hun- dred feet apart. Set up midway between them and, using the instrument as a level, bring the long bubble to the centre of its tube. Sight to a rod held on each stake. The difference of 32 THE ADJUSTMENTS OF THE these readings will be the true difference of height between the points, no matter what the error of the instrument may be. For if eOj Fig. 25, represent the position of the telescope, the line of sight will cut the rod at A. Turning the telescope around horizontally while the spirit level / 1' still indicates the same horizontal reading, the new position of the line of sight will be c f o' and will intersect the rod set over D at C. CD AJ5=truG difference of height of points D and B. For, since EF represents the proper position of the telescope, then FD /? true difference of height of points, and since 6* is midway between B and D, the angles which eo and e' o' , the two positions of the telescope, make with EF, being equal, must be subtended by equal distances on the rod, or EA=FC, hence adding to FDand EB, we have (7^9 +/^) (J5B+EA)= true difference of height of points (since this addition does not affect the balance of the equation), or true difference CDAB, as we stated at first. Now, clearly, having determined the true difference of height of the points, the instrument must be corrected so as to meas- ure this accurately. CORRECTION OF THE ERROR : Now set up the instrument over one of the stakes, measure the height of the cross hair above the top of the stake, either by direct reference to the horizontal set of screws of the cross-hair ring, or by looking through the objective toward a graduated rod held at a dis- tance of about a quarter of an inch from the eye-end, and with a neat lead-pencil point marking on the rod the centre of the small field of view. Set the target on the rod to this reading plus or minus the difference of height between the points, according as the point set up over is higher or lower than the second. Now sight to the rod thus adjusted and held on the second stake, and note if the cross hairs cut the target in the centre, when the long bubble is in the centre of its tube. If not, correct by lowering or raising one end of the level tube by means of nuts placed there for that purpose, until the desired intersection is obtained, the bubble still re- maining in the centre of the tube. Here the height of the cross hairs above the point over which the instrument is set ENGINEERS TRANSIT. 33 up 15 very approximately independent of any accuracy of adjustment. The entire error of the instrument is therefore shown by its deviation from the true reading as indicated on the rod, by the distance of the cross-hair intersection from the centre of the target. This adjustment will be further discussed in the article of this Manual on " The Adjustments of the Engineer's Level." Fifth Adjustment : To make the vertical circle read zero when the bubble of the telescope level is in the centre of its tube. DETECTION OF THE ERROR : This may be done in two ways. 1st. By simple inspection. 2d. By reversion. Bv REVERSION : Sight to some distinct point, note the read- ing on the vertical circle. Turn the instrument around hori- zontally half-way, reverse the telescope, and sight again to the same point. One-half the difference of the readings is the error, it having been doubled by reversion. CORRECTION OF THE ERROR : The correction is made by moving either the vernier or circle by loosening screws de- signed for the purpose of permitting circular motion. " The index error " may, however, be simply noted, and each obser- vation corrected by the required amount. Inspection is the readiest method by which to perform the above adjustment, but when the index error is small and difficult of detection, doubling it increases the accuracy of the correction. This error if it be small and the vertical circle have but one vernier, may also be corrected by first setting the circle so as to read zero altitude and bringing the bubble of the tele- scope level to a zero reading ; and then, by the method of the fourth adjustment, moving the cross-hair ring up or down so as to bring the line of sight parallel to the axis of the tele- scope level. Sixth Adjustment: To make the vertical cross hair truly ver- tical when the instrument is leveled. DETECTION OF THE ERROR : Set up the instrument and 34 THE ADJUSTMENTS OF THE Suspend a plumb line from some convenient Bring the vertical cross hair Fig. 26. level carefully, point. into coincidence with it, and note whether the line and hair cor- respond throughout their entire length. If they do not, the hair is out of adjustment, because, if the instrument be properly leveled the plumb line will be perpendicular to the plane of the bubble tubes. The same error may be detected by plunging the telescope and noting if the vertical hair passe's over some point sighted to, throughout its entire length. CORRECTION OF THE ERROR : To correct the error the cross-hair ring must be moved circularly. This is accom- plished by loosening the four screws of the cross-hair ring. These screws penetrate the ring a short distance, as shown in Fig. 26, and are allowed a certain amount of play sidewise by reason of the enlargement of the space through which the screw is inserted. When the screw is tightened the piece just below the head of the screw is clamped fast to the telescope tube. When all four screws are loosened, however, it permits the ring to be turned through a distance limited by the edges of the hole through which the screw is inserted. The verti- cal hair alters its direction with the turning of the ring. Relative Value of the Adjustments : For pure transit work, by which we mean the running of straight lines, the measur- ing of horizontal angles, and the like, the first three adjust- ments are the most important. The fourth and fifth refer to the instrument when used as an engineer's level, while the sixth, though classed with the first three, is by no means esien- tial. Indeed, this adjustment should be seldom made, inas- much as its performance is liable, by moving the cross-hair intersection eccentrically, to displace the second and third, which have already been performed. Should an adjustment of the vertical hair, however, become necessary, the second and third must be tested again so as to insure their non-dis- turbance. The verticality of the hair, though not absolutely ENGINEER'S TRANSIT. 35 necessary for accurate work, is exceptionally convenient for determining the true perpendicular, when only a small portion of a rod sighted to can be seen. Frequent tests of the vertical hair are useful, but its adjustment is unwise unless followed by a readjustment of the instrument in regard to the line of collimation. General Remarks on the Adjustments : It is well, to note that all of these adjustments, except the fourth, can be per- formed while the instrument still remains in one position. The fourth being entirely independent of the rest may be left until the last, and indeed is sometimes entirely omitted, as the use of the transit as a level is comparatively rare. The great fault of young surveyors is to blame inaccuracies in their work upon a faulty construction of the instrument For this there is no excuse. Errors may arise from three causes : (i) Errors in or damages to the parts of the instrument; (2) insufficient adjustment, and (3) carelessness in setting up or in sighting. The last are by far the most probable causes of inaccuracies in work, and, if the adjustment be unsatisfactory, the surveyor has no one to blame but himself, while errors in the instrument can always be detected by the refusal of the in- strument to respond to repeated tests while being adjusted. In the latter case, the only remedy beyond obtaining a new instrument is to note carefully what species of errors are likely to occur, and so to handle the instrument as to avoid them a~ far as possible. A wide and nearly level stretch of country is by all means preferable for the performance of the adjustments. The sights taken, except those in the fifth and sixth adjustments, should be as long as possible, so that the ensuing apparent error may be greater. After the surveyor has used his instrument for some time he may be sufficiently competent to judge of its accuracy. Until then the instrument should be tested at least once a week, if not more frequently. If he should find the instru- ment one of accuracy and great permanency of parts, less frequent adjustments may be made. Adjustments should al- ways be made if the instrument suffers a fall or if the surveyor has reason to believe that a severe jar has happened. 36 THE ADJUSTMENTS OF THE ENGINEER'S TRANSIT. The field adjustments of the compass as attached to the or- dinary form of the Engineer's Transit are essentially the same as those of the Surveyor's Compass. They will be found fully treated in the article of this Manual on " The Adjustments of the Engineer's Compass" THE FOREGOING METHODS, we would again remind engineers, while essential to the proper testing and use of a Transit, are intended only as instruction in practical field adjustments, and these do not take the place of the permanent adjustments given by scientific makers, although they are to some extent a test of the latter. THE ATTENTION OF ENGINEERS is particularly called to the methods of elimination of error and the methods of instru- mental manipulation suggested by the article of this Manual, entitled " The Mathematical Theory of the errors of the Engi- neers Transit" A summarized statement of the means for avoiding and eliminating the various forms of error is given at the close of the same article. QUEEN & Co. pay great attention to the theoretical accuracy and practical permanency of all the adjustments in order that the engineer receiving a perfectly adjusted and durable instru- ment may with reasonable use of it, for years secure a high degree of accuracy in his work with the minimum expenditure of'time and trouble. A SPECIAL CERTIFICATE, indicating all the instrumental con- stants and data required to be known by the engineer in the more scientific methods of manipulation, is furnished by QUEEN & Co. with each instrument. This certificate recites (1) The magnifying power of the telescope. (2) The angular value of the field of view of the telescope. (3) The angular value of one division of each of the pfote levels. (4) The angular value of one division of the telescope level. (5) The " least count " of each of the verniers, or the con- stants of each of the reading microscopes. (6) The constants peculiar to the accessory parts of the Transit, as, for example, the stadia hairs, the gradienter screw, the filar micrometer, and the solar attachment. QUEEN" CITY AND BRIDGE TRANSIT. A 1490. Price, $25O. The most accurate and best finished High Grade Transit made. THE MATHEMATICAL THEORY OF THE ERRORS OF THE ENGINEER'S TRANSIT, ALTHOUGH the practical treatment of the field adjust- ments has required some explanation of the nature of the errors to which the transit is liable, it is important that this matter be presented in a more mathematical and complete form. Alike the scientific construction and the intelligent use of a theodolite require as basis of such construction and. use a thorough discussion of the errors. For the maker, such a dis- cussion determines the elements to which special attention must be given in order to attain the highest constructive re- sult. For the user it suggests the methods of manipulation and schemes of observation necessary in order to eliminate the small outstanding errors of adjustment. It is found convenient to treat the subject under two general heads : I. Tlie Axial Errors, or errors due to the incorrect direction of the three principal axes of the instrument. II. The Errors of Eccentricity and of Graduation, or those pertaining to the reading of angles by means of the graduated circle. I. THE AXIAL ERRORS. In discussing the axial errors of an altitude-azimuth instru- ment we limit ourselves to a form of treatment best suited to an estimate of the effect of the given errors on the angular measurements. For the methods of determining by means of refined observation, the amount of the errors of an altazimuth we refer the reader to Chauvenet's Spherical and Practical As- tronomy, Vol. II, Chapter VII; to Briinnow's Traitt a" astron- omic sphsriqiic et d' astronomic pratique ', Edition Franqaise, par C. Andre, Vol. II, Chapter III, or other standard works on practical astronomy and geodesy. The following discussion is largely due to Dr. \V. Jordan's Handbuch der Vermessungs- 37 38 THEORY OK THE ERRORS kunde, dritte verbesserte und envsiterte Auflage, and to this work as well as to Bauernfeind's Vermessungskitnde we refer the reader for a treatment in some particulars more extended and detailed. There are three principal axes of the transit, and there is also one accessory axis, namely, the level axis. Let us desig- nate : I. The Sight axis, 5. II. The Horizontal axis, H. III. The Vertical axis, F, and IV. The Level axis, L. The following theoretical conditions are then to be fulfilled in the perfectly adjusted and accurately set-up instrument: (1) 5 -L //, or sight axis of telescope at right angles to horizontal axis of telescope. (2) //_L V, or horizontal axis of telescope at right angles to vertical axis of instrument. (3) L _L F, or level axis of (each) plate level, or of the strid- ing level, at right angles to vertical axis of instrument. The construction, final adjustment, and setting-up of the instrument should permit these conditions to be accurately attained. Yet, since all adjustments depending upon delicacy of manipulation are in the last analysis only approximations, it is highly important to know what the effect of any small outstanding errors of (i), (2), and (3) will be on the angular measurements made. The question plainly put is : Admitting a given error, what will be its effect on any proposed angular measurement ; and which of the three given conditions, SJL H, //J_ V, L J_ V, for a given error, produces the most serious effect on the angular measures ? Since there are two kinds (if angles measured by the transit, namely, horizontal and vertical, or angles of azimuth and angles of altitude, it becomes necessary to consider the effect of these errors, with respect to these classes of angles, separately. Investigation having, however, shown that the axial errors, though bearing important relations to the measurement of horizontal angles, have but a slight in- fluence on vertical angles, the major discussion will naturally concern the former. OF THE ENGINEER S TRANSIT. 39 I. EFFECT OF THE AXIAL ERRORS ON THE MEASUREMENT OF ANGLES OF AZIMUTH. (A.) ERROR IN THE CONDITION S _L H. If the line of sight is not at right angles to the horizontal axis but makes any angle, say 90 c, the quantity, c, is the error of the line of sight or the collimation error. The effect of such an error, r, on measurement of horizontal angles is best seen from Fig. 27. In this figure MN is the horizontal axis, OZ is the vertical axis, while OZ' , OP, and OS' are three po- sitions of the inaccurately adjusted sight axis or line of sight, which makes re- spectively the equal angles Fig. 27. Z'OZ, FOR, S'OT, or f , with the plane ZRT, so that Z'PS' is a parallel to the great circle ZRT. Let the sight axis be directed to a point P whose altitude is PS=h. Then, if the sight axis were accurately collimated, P would be projected on the horizon at S. But with the error r in collimation it is projected at S'. PR, as the arc of a parallel to MTV, very approximately equals c. For any alti- tude //, the error r, or PR, projected on the horizon, is S.T, or SS' in excess of the effect of the same error on a hori- zontal pointing. For varying altitudes, therefore, the given error consists of a constant part S'T and a variable part SS r . Denoting ST by Z, S'T by c, and 55' by (c), we evidently have from the figure and because PR may be assumed as approximately equal to c and is the arc of a parallel to ST. Z=e sec. // (i) and inserting this value in the previous equation, we have (c) =c sec. h c (2) which allows the variable collimation error to be computed as 40 THEORY OF THE ERRORS a simple function of the assumed constant error c and the altitude h. The following table, for various assumed altitudes and va- rious assumed values of becomes zero. Thirdly. The varying part, SS', of the projected collimation error is also for pointings of different altitudes eliminated, when the angle between the two points is determined by the principle of reversion, or when the angle is first measured in one position of telescope and then the telescope turned over OF THE ENGINEERS TRANSIT. 41 on its horizontal axis and round a vertical axis, the measure- ment again made, and the mean of the two measures taken. For, if Jc is considered positive in one position of the telescope it must be considered negative in the reverse posi- tion, and hence, entering with different signs, it is eliminated by taking the mean of the measures for the two positions of the telescope. Fourthly. From the table it is evident that the collimation error likely to exist, is, for low altitudes, negligible even in high-class work. Even for <: 10' and /i=io the table shows the error less than 10". The table also shows the necessity for painstaking collimation or for proper methods of elimina- tion of the error, when the pointings of the telescope are of any considerable altitude. (B.) ERROR IN THE CONDITION H _L V. If the horizontal axis of the telescope is not at right angles to the vertical axis of the instrument, but makes an angle 90 /, / is the error of the horizontal axis. In Fig. (28), OZ repre- sents the vertical axis, MN the horizontal axis at right angles to OZ, or in correct position, and M' N' the hori- zontal axis making an angle / with the correct position. The line of sight will there- fore move in the plane Z'PT instead of the plane ZRT, and if directed to P, the de- viation PR projected on the horizon will be ST. Let ZZ'= i, ST= (/), TR = //, and RZ=go h, then from the figure we have PR == (/) cos. // ; also PR = i cos. (90 h\ or, PR = i sin. 42 THEORY OF THE ERRORS and hence, (2) cos. // = / sin. /i, or finally, (/) = / tan. //, (3) from which formula the following table may be computed : TABLE SHOWING EFFECT OF AN ERROR i. OF HORIZONTAL Axis ON MEASUREMENT OF HORIZONTAL ANGLES. ALTITUDE h. 2 1 2 3 4 5 10 20 45 60 10" 0.17" o.35 /x 0.52" 0.70"! 0.87" 1.8" 3.6" C/IO" Q'I7" i' I.O5 i 2.IO 3- J 4 4.20 5- 2 5 10.6 21.8 I OO i 44 2' 2.09 i 4.19 6.29 8.39 10.50 21.2 43-7 2 OO 328 V 5.24 10.48 15.72 i 20.98 26.25 52.9 i'49" 500 8 40 10' 10.47 ! 20.95 31-44 41 96 52.49 I '46" 3 3 IO OO 17 19 '5' 15.71 '31-43 47-17 i' 3" i'i9" 239 528 15 oo 25 59 THE PRACTICAL DEDUCTIONS from this discussion are : First. The effect of the existence of an instrumental error /, or of the violation of the condition HA. V, may be elimi- nated by the method of reversion observation, already ex- plained in the practical deductions concerning the collimation error, c. Secondly. The effect of the error i is also eliminated by taking the difference of the readings for any two pointings of the same altitude. For, if we represent the effective errors for the two altitudes /^ and h 2 of an error i, by (i)^ and (z') 2 , and Ji (i )j (i ) 2 , we have evidently from equation (3), Ji-= i (tang. /^ tang. // 2 ), which for /^= h 2 becomes zero. Thirdly. This error, /, is of much more serious influence on horizontal angles than the collimation error. Fourthly. In a thoroughly tested and carefully adjusted, instrument, and with altitudes less than 5, this error need not be feared, but with an instrument having any considerable er r or 2, or with pointings of a considerable altitude, the result- ing error (i) on the horizontal angle is serious. Fifthly. It is to be borne in mind that in observations like those, for example, required in making the third adjustment, the effective error, (f , varies as the tangent of the angle of depression as well as of elevation. OF THE ENGINEERS TRANSIT. 43 Fig. 29. (C.) ERROR OF DEVIATION or THE VERTICAL Axis OF THE IN- I 'KfMENT FROM THE VERTICAL. This is due either (i) to error in the condition L J_ / ' that is, inaccurate adjustment of the level axis with respect to vertical axis, or (2) to untruthfulness and lack of sensitive- ness of the levels, or (3) to inaccuracy of use of the levels in setting up the instrument. In Fig. 29, OZ is the ver- tical, OZ' the vertical axis deviating from OZ by an angle ZOZ 1 ', which we de- signate i'. If the axis <>f sight is directed to P, this point will be projected to T instead of to ^ ; and if we designate AS by ;/ and A'T by //', their difference will be equal to the desired projection error, which we designate (?'), that is, ;/ //'= (V). The plane of the circle at right angles to the vertical axis will therefore take the position A M B' X' instead of AMBN, so that the angle BOB' between the planes is equal to v. The line of sight being directed to P % the horizontal axis must take the position of J/A r/ , at right angles to OT and approximately to OS, whence the inclina- tion to the true horizontal plane is JAJJ/", which we designate /'. \Ye have now a triangle LJDf right angled at J/, whose side LM= AS because AL and SM each equal 90. But the arc AS is the azimuth of the projected point P as meas- ured from the point of greatest inclination A, and this arc, or its equal LM, we designate //. In the right spherical triangle LMM' , LM= u, L = v, and MM' = /', and hence /'= i' sin. u. But an inclination i' of the horizontal a-xis produced a pro- jected error (/') in measurement of horizontal angles in which, according to the previous article, (B), (/') = /' tang, 44 THEORY OF THE ERRORS and therefore (/') = v sin. u tang. //, or (v) = v sin. u tang. //, (4) where (v) represents the effect of v, for any pointing, as pro- jected on the horizon. For the maximum value of sin. ti, or i, the formula takes the form (v) = v tang. //, and the table of the preceding section (B) gives the values of the effective error. THE PRACTICAL DEDUCTIONS from consideration of this error are : First. The error v made in adjusting and setting up the in- strument cannot be eliminated by reversion observations. Secondly. If we suppose an angle measured between two points of the same altitude we can find the expression for the maximum value of the error Av. Let // T and u v be respectively the altitude and azimuth (as measured from point of greatest inclination of horizontal circle) of the first point, and // 2 , 7/ 2 , the same of second point, and the difference between the effective errors (v^ and (z/ 2 ) be Av, that is, Av=(v^) (?/ 2 ) ; then from equation (4) we evidently have Av = v (tang. /^ sin. u^ tang. /i. 2 sin. ?/ 2 ). (5) This value attains, for h = // 2 , its maximum in relation to ! and u z when sin. u^= sin. ?/ 2 , or when u\ ?/ 2 = it 180. That is, the error becomes greatest for h v = // 2 when the angle measured n x 2 is 180. Under these conditions the above formula (5) becomes Maximum Av = 2 v tang. //, or the greatest error Av arising from the error v in vertically of axis will, for a straight angle between two points of the same altitude, be just double the values set down in the table as given in section (B). Thirdly. It is evident that for altitudes less than 5 and with good levels properly adjusted and care in setting up, no appreciable error need be feared, even in high-class work. OF THE ENGINEERS TRANSIT. 45 A FFW GENERAL INFERENCES to be drawn from the foregoing discussion of the axial errors c, i, and v, may be of practical use. First. If we measure horizontal angles with an Engineer's Transit whose collimation error is c, error of horizontal axis /, and whose vertical axis has a deviation of v from the ver- tical, the three effective errors (c), (z), (v), may combine in a total (s), so that for a single pointing and if Js represent the total error made in measuring an angle, or for t\vo pointings, Js = Jc+Jc+Jv, or reproducing their values from sections (A), (B), and (C), Js = c (sec. //! sec. // 2 ) + i (tang. /i { tang. /i 2 ) -f-i' (tang. //! sin. u^ tang. /i 2 sin. ?/ 2 ). (6) Secondly. From this equation (6) it becomes evident that it is of importance to choose points nearly of the same altitude if we would by reversion eliminate all instrumental errors eliminable. Thirdly. Only th? collimation error c and the error of the horizontal axis i can be eliminated by reversion. Fourthly. Since the error of verticality of axis v can be- come larger than any other of the errors and can also have a more serious result on the measurement of horizontal angles, it requires special attention. The error v, as already stated, depends not only on care in the use of the levels in setting up, but on their proper adjustment, and on their truthfulness and sensitiveness as well. And hence the careful attention (see the article on " The Spirit Levels of Engineering Instruments"} be- stowed by QUEEN & Co. on the plate levels, as well as on the telescope and striding levels, of the Engineer's Transit is fully justified. 46 THEORY OF THE ERRORS THE EFFECT OF THE AXIAL ERRORS ON THE MEASUREMENT OF ANGLES OF ALTITUDE. Having devoted considerable space to the consideration of the effect of small errors of direction of the. three principal axes apon the measurement of horizontal angles, we have now briefly to speak of their effect on measurement of angles of altitude. This subject has been rather carefully in- vestigated by Dr. W. Jordan in his inimitable Handbuch dcr Vermessungskunde, Vol. II, and we give here as a matter of considerable interest the general result of a cumbrous mathe- matical discussion. For a fairly adjusted altazimuth instrument and for vertical angles not exceeding 45, the effect of the usual small errors is altogether inappreciable. For angles of greater altitude than 45 and when extreme accuracy is required, greater care than usual must be taken with the adjustments. It is to be noted, however, that now we speak only of extreme accuracy and of instruments reading vertical angles to seconds of arc. For a total error of the axes of 10' the sum total of effective error on a vertical angle of 45 is only 0.87", of 60 only 1.51", and for a total error of 30' for vertical angle of 40 it is only 7.86", and for 60 only 13.60". Therefore, even in the use of a fine geodetic instrument, the three axial errors do not, with reasonable precautions, produce any error in measuring angles of altitude less than 60. Of course, in the use of the Engineer's Transit, these axial errors produce an entirely inappreciable effect on measures of mode- rate angles of altitude and are not in question. It would, however, be an entire misconception to suppose that, since the axial errors do not have an appreciable influence in the measurement of vertical angles, no errors are therefore to be feared in such measurement. The constant errors, such as the errors of graduation and of eccentricity of the circle, and particularly the index error and the error of the level lying in the same plane as the circle, are the ones requiring closest attention. Their elimination can be accomplished only by special methods of work and proper instrumental adjustment and design. QUEEN" FULL ENGINEERS' TRANSIT. A 1494, Price, $185.00 QUEEN" FULL SURVEYORS' TRANSIT. A 1502. Price, $140.00 OF THK ENGINEERS TRANSIT. 47 II. THE ERRORS OF ECCENTRICITY AND OF GRADUATION. Having treated the axial errors, we still have to consider those errors which are due to (i), the eccentricity of the tele- scope; (2), the eccentricity of the circle; (3), the eccentricity of the verniers, and (4) the inaccuracies of graduation. THE ECCENTRICITY OF THE TELESCOPE. Assuming, in the first place, that there is no eccentricity of the circle or of the vernier, there may still be an eccentricity of the telescope, on account of the line of sight not being mounted directly over the centre. In Fig. 29 the eccentricity of the line of sight of the telescope is represented by the ra- P, f. Fig. 29. dius of a circle conceived as described about the centre, C, of the circle. All lines of sighting will be tangent to this circle. P l and P 2 are two points to which the eccentrically placed telescope is in turn directed, and between which it is intended to measure the angle. The angle represents the true angle, while a! and a!' represent the angles measured with two posi- tions of the eccentric telescope. A simple inspection of the figure gives us the following relations : a -\- v = x = ' + n a-\-u y = a" 4- v 1< (l) a " = i* u (2) "-' = 2 (H r) (3) = 2 ' (4) If the respective distances of P l and P 2 , from the centre, are { and d 2 , and the eccentricity or radius of the small circle of 48 THEORY OF THE ERRORS the figure is represented by e y the angles of 11 and v may be expressed in seconds as follows : u = 206265 4r- v = 206265 -4- (S) ' and write ) (3) 7-"=/>'+y.sm. (+ff) (4) By taking the mean of these two readings as thus expressed, we get : = c s s' whence we see that the difference between the mean of the true readings and the mean of the vernier readings decreases as (A E) approaches 180, and when (A />) exactly equals 1 80, or when the verniers are rigorously 180 apart, this difference is nil. The mean of the readings of two verniers or microscopes which are 1 80 apart, therefore, completely elimi- nates the error of the eccentricity of the circle. In order to comprehend the effect of even a small displace- ment of the centre, let us from equation (2) take the maxi- mum value of s, or Maximum e =.- - - and assume c = 0.0003 m - an ^ r = 3-O in. Then we have : ,, . 2X0.0003X206265" // Maximum -s = =41.25' If c had been as great as 0.003 m - the maximum error of eccentricity would have been 6' $2.5." This fully illustrates the importance of three things: (i) Correct designs of the axes or " centres " of the instrument ; (2) care in adjusting circle for eccentricity; (3) the reading of both verniers or microscopes in the higher classes of work. The error of eccentricity of circles as here treated, is really made up of two mechanical errors, viz. : (i) Inaccurate cen- tering of the circle on its axis or " centre " and (2) ellipticity 52 THEORY OF THE ERRORS of the " centres " themselves. Moreover there arises in some designs of " centres," as elsewhere in this Manual already inti- mated, a wear of " centres " which produces a serious eccen- tricity, and which cannot be remedied mechanically except by furnishing the instrument with new "centres." QUEEN & Co. have selected a design of " centres " in which wear is not likely to introduce an appreciable error of eccen- tricity. The design is such also as to allow the nicest adjust- ment for eccentricity to be accomplished with mechanical certainty. It is therefore only incumbent on the engineer to read both verniers or microscopes in the finer classes of work. THE ERROR OF ECCENTRICITY OF THE VERNIERS. We have hitherto assumed that the zeros of the verniers or microscopes are exactly 1 80 apart. This may not be the case, and if it is not, we have what may be termed eccentricity of the verniers. The eccentricity of the verniers is the perpendicular distance between the centre of the alidade and the straight o line joining the zero of the verniers, and is in Fig. 31. repre- sented by C V. The effective error it produces is a constant 180 Fig. 3*. one, represented by the angle a. The effective error of eccen- tricity e, is, on the other hand, as already shown, a variable one. If then, the zero of the verniers or microscopes are not OF THK ENGINEERS TRANSIT. 53 accurately 1 80 apart, but make an angle of i8o-}-, so that, the eccentricity of the circle for the moment out of question, B' A'+ i8o + , and we may then find from equations (3) and (4) for the entire difference of reading between the two verniers, or B A 180= o. (5) Considering the alidade turned from its o position respect- ively through the angles 90, 180, and 270, we would have for these four respective values of A the following values of o : .E. (6) whence we find d l = a + 2C s cos. E. (;) N 2 S ' Z? /0\ o. 2 = o. - sin. h. (8) 2 e s r* / \ 3 = a - cos. h. (9) a = ^L+ '' i + ''- + f \ = the mean of all the 3's. ( i o) 4 4- I J /" > > 2: __ sin. h. =o o 2 r (12) which determine a and both c and E. We also see from equations (6) and (8) that r) = -|-, and o. 2 = a s o. t -\-o., o lt o., whence = " -I 2 and = - 2 2 The objection to the use of the last two formulae for deter- mining a and are that but two differences are employed, and hence errors of observation and of graduation may make the result uncertain. The only complete method for determining a and s, free from complication with errors of graduation and 54 THEORY OF THE ERRORS observation, is to determine a large number of d's for different direct and reversed positions of the alidade, and then treat the results of the observations according to the well-known method of Least Squares. For such treatment of the subject our readers are referred to standard treatises on Practical Astron- omy and Geodesy. Equations (10), (11), and (12), however, enable us for many practical purposes to derive fairly reliable values of a and e by simply making four sets of observations at intervals of 90 of the differences of the vernier or micro- scope readings. THE ERRORS OF GRADUATION. The errors of graduation, unless of the coarsest sort, can- not be investigated until the effect of eccentricity of the circle and of the vernier has been ascertained. After determining the value of the eccentricity of the circle and computing its effect on the division whose graduation error is to be found, the outstanding differences, allowing for the constant deviation of the verniers from the required 180, are to be attributed to graduation and observation errors. The errors of graduation are divided into two classes : (i) Those which are of a periodic character, and (2) those which are of an accidental character. The, former depend upon slow changes during graduation in the temperature of the engine, or in the condition of the cut- ting tool. The latter are not dependent on known conditions, and being as likely negative as positive, are classed as acci- dental. It is usually found in well-graduated circles that the major errors of graduation are of the first class and may be expressed as a periodic function of the varying angle. Instead of using the distance apart of the two vernier zeros as the standard angle, the length of the vernier may be used as a test when successively applied round the circle, and read by means of the excess graduations of the vernier. The ef- fect of the eccentricity of the circle on the length of the ver- nier, must, in this case, be computed and duly allowed for before errors of graduation as such can be noted. For a oi- Tin- ENGINEERS TRANSIT. 55 complete discussion of this subject we refer the reader to the / 'ermessungskuHtU of Jordan, and to the treatises on Practical Astronomy of Chauvenet, Briinnow, and Sawitsch. The errors of graduation, whether periodic or accidental,, when not known, are best eliminated by combining a number of readings at different parts of the circle by Bessel's method of Reiteration. This method is to be carefully distinguished from Borda's method of Repetition, whicn is no longer in favor among the most scientific observers, and therefore not here described. The method of reiteration consists in systematic- ally and by equal arcs displacing the zero of the circle with respect to the verniers or microscopes, so as to pass through an entire circumference, or, in the case of two verniers, simply through a semi-circumference. By thus giving the circle a number of equi-distant positions and taking the mean of all the observed readings, the periodic errors of graduation will be completely eliminated by compensation, and the accidental errors will, according to the method of Least Squares, be di- minished in the inverse ratio of the square root of the num- ber of reiterations. THE ERRORS IN PRACTICAL WORK. The foregoing discussion of the axial and circle errors, aside from its value in suggesting points of construction and adjustments of special importance to accuracy of work, should also afford many a hint to the practical engineer. The limited space does not permit us to state either the special features of instruments or the special programmes of work whirh are in the different cases required to avoid and eliminate .ill the errors. And yet we may not better close this review of the errors than by drawing attention to several points of caution to be exercised in the three most usual forms of work with the transit, viz. : the measurement of vertical angles, the laying out of straight lines, and the measurement of horiio/ital angles. 56 THEORY OF THE ERRORS VERTICAL ANGLES have their zero in the horizon, and this zero must be physically determined by a level lying in a plane parallel to the graduated circle on which the measurements are to be made. This level, whether it be a plate level, the telescope level, or a special level attached to the vernier arm, should not only (/) lie in a plane parallel to the measuring circle, but (2) have a sensitiveness comparable to the fineness of the reading on the circle, and (j) always in an observation be adjusted to zero position of bubble or else be read for the :small deviation of the bubble. If the telescope level is used the vertical angle is simply the difference of readings on the circle for the zero position of the bubble and for the pointing. The error of vertical axis, or the deviation of this axis from the vertical, may affect the measurement to the whole amount. Both the error of adjustment of the plate level and the index error (see sixth adjustment in article on ''Adjustments ") can be eliminated by striking the mean of the measures of the angle taken with the telescope both in the direct and in the reverse or transited position, provided the alidade is carefully releveled after being revolved 180. The errors of eccentricity are eliminated by reading both verniers or microscopes, if there be two. Transiting and two verniers, however, require a com- plete circle. For an arc of a circle with one vernier, the ad- justments must be relied on. The eccentricity may, for small angles, be considered constant, and, if the " fourth adjustment " has been accurately made, it is eliminated by taking the differ- ence of the readings for bubble at zero and for the pointing. The graduation errors can only be eliminated by using an en- tire circle, capable of being shifted on its axis. The method of reiteration of the angle may then be employed. QUEEN & Co. desire engineers, when special accuracy is re-* quired in vertical angles, to indicate the grade of accuracy to be attained. They will then be able to recommend a design of instrument in every particular suitable to the kind of work. STRAIGHT LINES can be prolonged accurately only with good instruments and the most careful attention. Here the secret ; OF THE ENGINEER'S TRANSIT. 57 of the elimination of errors is so to arrange the programme of work as to distribute the errors symmetrically with respect to the proposed line. If a circumpolar star is observed for the direction of the meridian it is therefore important that the ob- servations both as to number and character, be arranged sym- metrically with regard to the time of transit, or the time of elongation, as the case may be. If the pointings for a line are all horizontal, and the line is to be prolonged by transiting the telescope, or turning it over on its horizontal axis, the constant collimation error will enter with double its value. If, secondly, one of the pointings is at an angle as in the case of determining the direction of a cir- cumpolar star, the errors of collimation, of the horizontal axis, and of verticality of the vertical axis, may all enter the result. Particularly would the error of verticality, due to the level at right angles to the line, be serious and necessitate at- tention to the sensitiveness, adjustment, and reading of the level lying in that direction. A line may be prolonged so as to eliminate all these errors by setting up over the forward point, leveling cross-level, bi- secting rear point, transiting telescope, and locating the re- quired point; and then revolving the alidade 180 and repeat- ing the operation and taking the mean position between the two located points as the true required point. QUEEN & Co. make instruments especially adapted for run- ning straight lines, including tunnel work. These are pro- vided with powerful telescopes, delicate striding levels, and are reversible on their horizontal axes. HORIZONTAL ANGLES, including the horizontal straight angles just referred to, are those most frequently measured in prac- tical work, and the errors to which they are liable have, there- fore, been fully discussed. The accurate measurement of a horizontal angle may pro- ceed as follows : Test the adjustments, particularly that of the levels. Level carefully. Set vernier A accurately to zero, and with clamped alidade turn the telescope upon the left-hand object. Clamp the circle and bisect by means of low%r, or 58 THEORY OF THE ERRORS OF THE ENGINEER S TRANSIT. circle, tangent screw. Vernier A still being at zero, read ver- nier B. Now unclamp alidade and turn telescope upon right- hand object. Clamp alidade and bisect by means of upper, or alidade, tangent screw. Read both verniers accurately. The difference between the means of the vernier readings is the measurement of the angle for the telescope in direct posi- tion. Now transiting the telescope, direct the telescope to left-hand object and shift the circle a fraction of 360 from its initial position and repeat the foregoing programme for this reversed position of the telescope. The mean of the results for direct and reversed telescope is the angle freed from the errors of collimation, horizontal axis, from error of verticality (as far as possible), and from eccentricities of telescope, verniers, and circle. Reiteration of this process by shifting th of n 360 if the angle is to be measured n times with each posi- tion of telescope, will give a mean result measurably free from graduation errors. A PRACTICAL INFERENCE of great importance alike to those who use, and to those who make engineering and geodetic in- struments follows from the foregoing Theory of the Errors of the Universal Altazimuth. It is that since in each of the three main classes of work adverted to, the errors to be feared and if possible, avoided or eliminated, are of a peculiar type, there- fore a peculiar type of instrument ought to be designed to meet the highest -demands in each class of work. An instru- ment maybe designed mainly for measuring horizontal angles or for prolonging straight lines, or for measuring vertical angles and the particular purpose, together with the degree of accuracy to be met in the special class of work, will, withjthe expert maker, determine every detail of the instrument. QUEEN & Co., accordingly, stand ready not only to meet the demands for good universal transits suited to all ordinary practical requirements, but also to furnish those special instru- ments required in the more difficult engineering and geodetic operations. QUEEN" LIGHT MOUNTAIN TRANSIT. A 1508. THE GRADUATED CIRCLES OF THE ENGINEER'S TRANSIT. THE GRADUATIONS. THE accurate graduation of circles is one of the most delicate operations in the mechanical arts. It requires not only machinery of unquestioned certainty of condition and of movement, but constancy of temperature during the entire process, and, even with purely automatic machines, the most alert and skillful attention. QUEEN & Co. have in their works two large dividing engines adapted to the graduation of the different classes of circles required for the astronomical and engineering instruments they make. Every attention is given not only to accurate centering, correct spacing, and to an even performance of the graduating engine, but to the final finish and numbering of the graduated circle, so as to secure ease and certainty, as well as accuracy, in the reading. Errors of graduation, though never so small, are to be found in every circle yet graduated by human skill. The problem is, then, one of degree of error. With QUEEN & Co. the aim is to furnish graduated circles whose error3 may safely be re- garded as infinitesimal, except in astronomical and geodetic work of the highest class. In this most refined class of work- there is, as the most noted observers have again and again demonstrated, absolutely no recourse excepting a complete examination of the graduation, and the preparation of a table of corrections. For a further reference to this subject consult "Errors of Graduation " in the article of this Manual entitled " The Mathematical Theory of the Errors of the Engineer's Transit? 59 60 THE GRADUATED CIRCLES MEANS FOR READING SUBDIVISIONS OF CIRCLES. The devices chiefly employed for reading the subdivisions of circles are the Vernier and the Micrometer Reading Micro- scope. Of these the former, on account of its simplicity, cheap- ness, and sufficient accuracy, is almost exclusively used in engineering instruments. It is only in high-class geodetic instruments that the use of the Micrometer Reading Micro- scope is at all warranted. The Estimation Microscope, referred to further on, is, however, coming into favor for the finer read- ings where rapidity of work is desirable. THE VERNIER ITS THEORY AND FORMS. The Vernier was first described in a work entitled La Con- struction, L usage et les Proprietes du Quadrant Nouveau dc MatJicmatiques, etc., du Pierre Vernier, Bruxelles, idji. The same appliance is by the Germans called a " Nonius" although the instrument described by the Portuguese " Nunnes," or " Nonius," in 1542, was in principle essentially different. The Vernier is an accessory divided scale placed alongside the main divided scale, and permits the subdivisions of the main scale to be read by noting the difference in length of the Vernier and the Scale divisions. In Circular Instruments the Vernier is, of course, an arc concentric with the main divided circle, and so graduated that the ratio of the divisions of the Vernier to those of the Circle may be the one required to give the reading to the subdivision intended. An easy mathe- matical discussion will make this clear in every detail. The general theory of the Vernier, forming the basis for the construction of all verniers may be stated, as follows : Let s = The value of a division of the main Scale or Circle. v = The value of a division of the Vernier. *- f '1 or >5= The " least count," or smallest subdivision of the v s ) Scale or Circle to be read by the Vernier. n = The number of divisions of the Vernier correspond- ing to (// /), or ( + /) divisions of the Scale or Circle. OF THE ENGINEER'S TRANSIT. 61 The Vernier is then always so graduated as to make ni' = (ni)s. (l) If the upper sign is used, then any single vernier division is smaller than a single scale or circle division, and the vernier is a direct reading vernier with divisions numbered in the same direction as the circle is read. If the lower sign is used a vernier division is larger than a scale or circle division, and the vernier is a retrograde vernier, reading and numbered in the direction opposite to the reading on the circle. From equation (i) we easily derive the following sets of equations for the two classes of verniers : FOR DIRECT VERNIERS. FOR RETROGRADE VERNIERS. = -*-. (2) = _-. (5) S V V S . H r / \ n-\-i tz\ v = ~s. ' (3) * = -X-A (6) s v=~s. (4) ,, s = -Ls. (7) The direct Reading- Vernier, being the one almost exclusively in use, we need illustrate only the first set of formulae by means of a few examples. Suppose a circle divided to 20', and that it is desired to read it to 30", then from equation (2) we see that n = = 40, or 40 vernier divisions must be 3 made equal to (40 i), or 39, scale divisions, in order to make 30" the least count. Also from (3), v= >X 1200" = 19' 30" 40 = value of one vernier division ; or, in other words, each vernier division will be 30" smaller than the scale division, and "hence if a given vernier division coincides, or forms the same straight line with a scale division, it shows how many times 30" the zero of the vernier has passed the scale division immediately preceding it. Also from (4), j v=~- 1200"= 30"= the 4. least count. The accompanying Fig. 33, represents a double 62 THE GRADUATED CIRCLES direct reading vernier, applied to a circle with 20' divisions, and reading to 30''. The reading of a circle by means of a vernier consists of two operations. First, to find beyond what graduation the zero of the vernier has passed ; second, to read the vernier itself for coincidence. We always read the vernier in the di- rection the numbering is inclined. If we read in the direction of the upper numbering, we use the right-hand vernier, as fol- lows : First, the zero of the vernier has passed I and 20' be- yond the 1 10 mark, and the first reading would therefore be iii 20'. Second, we find that the 25th division of the ver- nier is in coincidence with a division of the limb, and as the least count is 30", this would mean 12' 30"; adding this to ui 20', we have 1 1 1 32' 30" for the reading. Similarly, if we are reading in the direction of the lower numbering, first the rough reading is 248 20' ; second, the reading on the vernier is f 30" ; the sum of the two, 248 27' 3 o". Practically the reading of a vernier like the one here figured is made very quickly by first taking up the degrees, and while keeping in mind the minutes of the circle, adding to these the minutes and seconds of the vernier, the whole minutes being indicated by the alternate long lines of the vernier. Thus, reading to the right, the excess of 20' on the circle is mentally added to the reading of 1 2' 50" on the vernier, and the whole reading 1 1 1 32' 30" at once set down. A table illustrating the properties of the verniers employed with the usual graduations of QUEEN & Co.'s instruments is here appended. A study of it may prove useful to beginners, OF THE ENCINKKK S TRANSIT. 63 as familiarizing them with various kinds of graduations and verniers : Vernier. s n n / V j # f t ) 3' 30 29 29' oo" i ' (2) 20' 40 39 I 9 / 30" 30" (3) I 5 / 30 29 14' 30" 30" (4) 20' 60 59 19' 40" 20" (5) '5' 45 44 14' 40" 20" (6) 60 50 9' 50" 10" The Retrograde Vernier is sometimes used on the arc or circle of the Engineer's Compass. It is also used in connec- tion with barometer scales. Fig- 34- A retrograde double vernier of a compass is shown in Fig. 34, where 30 vernier divisions equal 3 1 of the limb and the limb is divided to half "Degrees. Consequently, according , to formula (/),?' s = - -s, or the least reading = X $o'=i'. This form of vernier is here only one-half as long as a double direct vernier. It extends to 15', and the upper figures on one-half are in a manner a continuation of the lower ones on the other half. Thus in the figure the zero of the vernier having been moved to the right, the lower figures of the left- hand vernier are read when the angle passed over is less than 15'; but as more have here been passed, the upper figures of the right hand are taken as a continuation, and the reading evidently is, i 30' (limb) 4- 23' (vernier),= i ( 53'. THE GRADUATED CIRCLES H THE READING MICROSCOPE ITS FORMS, THEORY, AND ADJUSTMENTS. The Micrometer Reading Microscope is esteemed an essential requisite for the highest class of circle readings. The accom- panying Fig. 35 shows a vertical section of the microscope as placed over the graduation. In the common focus of the objective and eye-piece at /MS formed an image of the division of the limb. The narrow lane formed by two parallel micrometer threads, as shown in Fig. 36, is then, by means of the micrometer screw, moved until it centrally includes the given division. The number of whole revolutions of the screw are counted by means of the notches seen in the field of view Fig. 36, and the fraction of a revo- lution is read off on the graduated head//. The notches used as counters are each a complete revolution distant from each other, and each fifth one is cut deeper v and specially marked. The graduated head //of the screw is usually divided into sixty divisions and reads directly to seconds, and by estimation to tenths of seconds. Figures 35 and 36 will, without much further assistance, indicate the construction of the micrometer microscope in suf- ficient detail. The eye-piece A B is a positive one, and (ex- cept in determining the requisite magnification and definition) does not enter into the optical theory of the reading micrl>- scope. The micrometer screw is opposed by springs, b b, which hold the slide a a, carrying the parallel threads, so that it always bears against one side of the screw threads c c, and there is no lost or dead motion. It is conducive to accuracy, nevertheless, always to turn the screw in only one predeter- mined direction before each bisection of a division of the limb. C Fig- 35- ol 11I1-. ENGINEERS TRANSIT. Fig. 3 6 - The optical theory of the Micrometer Microscope is put in sim- ple form as follows : Assuming that one revolution of the mi- crometer screw carries the set of parallel threads from one central position over a division to another, and letting : Sj= Linear movement of these threads due to one revolution of screw. s 2 = Length of one division of circle. d x = Distance of threads from the mi- croscope objective. (f. 2 = Distance of circle from the mi- croscope objective. We have, according to Fig. 37 : +=*i (0, and Sl = ( ' , whence by respectively eliminating and (f l by combining ( i) and (2) we hav =/+V. (3), df= The equations (3) and (4) give the distances respectively at which the threads and the limb must be placed from the microscope ob- jective, provided the eye-piece be a positive one, as shown in Fi *. 35. An eye-piece of the Huygenian sort, with its collec- tive lens, wou'd introduce other considerations. 66 THE GRADUATED CIRCLES The adjustments of the Micrometer Microscope may be stated as follows : 1. The threads of the microscope should be parallel to the circle divisions. This is accomplished by turning the entire microscope in its support 2. The optical axis of the microscope should be at right angles to the graduated limb. This condition may be tested .with sufficient accuracy by direct measurements. A good optical test is the precise equality of definition of a division of the limb as it passes across the field. 3. The distances d and d. 2 are to be so adjusted that a ^whole number of revolutions of the screw is equal to the dis- tance between two consecutive graduations of the limb. If the head of the screw indicates more than a whole number of revo- lutions for one division of the limb, d and d. 2 must be lessened, .i.-e., the objective brought nearer the threads, and the whole microscope nearer the limb. If the head of the screw indicate less than a whole number of revolutions for one division of the circle, d l and d. 2 must be increased. In each case d l is first lessened or increased, and then the microscope moved until the circle graduations again appear well defined. The changes in d l and d 2 for any given excess or deficit of the screw read- ing, are, however, most certainly and accurately made by first computing their value by formulae easily derived from equa- tions (3) and (4). 4. The micrometer screw should be as nearly as possible a perfect one, without inequalities or irregularities. The errors of the Reading Microscope are readily investigated. As in other features, so here, although a high grade of accuracy of adjustment is to be expected from competent and con- scientious makers, there will still be small errors of adju|t- merit as well as other errors arising from changes of tempera- ture and the like, which have to be determined and allowed for in the most refined classes of measurement. It is usually sufficient, even in the best work, to investigate the following- errors : I. The error of runs, or the excess of a circle division above a whole number of revolutions of the screw may be determined OF THK i;.v, INKER'S TRANSIT. 67 by measuring a number of divisions in different parts of the circle and taking the mean so as to eliminate graduation errors. A proportional part of this error must be allowed for in all readings. If one division, for example, measures 5-^- 60 revolutions, or equals 5'-|-i".8, each minute read off must be \" 8 corrected by = or o" '.36. Only for the highest ac- curacy need the error of runs be determined at different tem- peratures and corrected for inequalities of the screw. 2. The errors of inequality of the screw may be determined by measuring some small distance, as that between a circle graduation and a special graduation, or as that of the distance apart of the two micrometer hairs, if this is an aliquot part of a division. The mean of many such measures is then taken as the standard value for the preparation of a table of correc- tions for the inequality of the screw. These corrections should be allowed for before the error of runs is determined. But in well-made screws the errors of inequality are small enough to be entirely neglected. The Estimation Microscope, as recently applied to the reading of the circles of the theodolites, dispenses with the micrometer screw, and in its place has a fixed scale divided on glass. It is on this account sometimes called the Scale Microscope. The accompanying figure shows a circle divided to 10', as ap- pearing under an estimation micro- scope. The ten divisions marked o, 5, 10 belong to the microscope, and are together equal in length to 10'. The zero is 3', and, we esti- mate, o'./ more, beyond the 40 10' mark, and hence the reading is 40 1 3'7 = 40 13' 42". This method lacks the accuracy of the micrometer microscope, but has the advantage of rapidity. Single read- ings can be made by this means with a probable error of about =b 5". The ordinary graduation intended for vernier reading 68 THE GRADUATED CIRCLES OF THE ENGINEER'S TRANSIT. appears too heavy under the microscope for the most accurate reading by estimation, and hence, when desired, QUEEN & Co. make a specially delicate graduation, suited to the demands of the estimation method. THE ADJUSTMENTS of the Estimation Microscope are simi- lar to those of the Micrometer Microscope. The scale and the image of the graduation must both appear with good defi- nition. The divisions of the scale must be parallel to the di- visions of the graduation circle, and the whole microscope must have its axis at right angles to the plane of the circle. The interval of the scale must also correspond with that of the graduations, and there may hence also, from lack of ac- curate correspondence, be an error similar to the error of runs of the micrometer microscope. THE RELATIVE ACCURACY of verniers and micrometer read- ing microscopes has been investigated by Bauernfeind, who concludes that for circles of five inches and over the micro- scope is the more accurate, but that the time expended in adjusting and reading the microscope is very much greater than for the vernier. Well-made verniers, read with good illu- mination and with the axis of the eye in the same plane as the coinciding divisions, may produce results of a high order. But the highest accuracy with large circles can only be attained by means of the micrometer microscope. It is probable, how- ever, that taking both time and accuracy into consideration, the estimation or scale microscope is often to be preferred to either the vernier or micrometer microscope. A RECENT PLAN adopted to obviate the necessity for adjust- ing the microscope to correspondence with the graduations is, to carry the direct graduation of the circle down to such a degree of fineness that it is only necessary to use a single thread in the microscope as a means of estimating further sub- divisions. QUEEN & Co. believing that there is room for materially extending the accuracy of graduation and the convenience of circle reading as applied to engineering and geodetic instru- ments, make it their- constant aim to be abreast of the highest modern science and skill in this work. "QUEEN" RECONNOISSANCE TRANSIT. A 1518. Price, $125.00 THE SPIRIT LEVELS OF ENGINEERING INSTRUMENTS. AS an essential part of nearly every important engineering instrument, the spirit level deserves special considera- tion in respect of its theory, construction, and use. This the more on account of the apparent indifference among the engineering fraternity, and consequently among makers themselves, regard- ing the performance of the levels of instruments. Neglect of the subject is also shared by the standard American treatises on surveying. It is therefore deemed important to draw the special attention of the engineer to this essential part, in the hope that scientific makers may be fairly encouraged to fur- nish instruments suited, as well in this, as in other respects, to reliable work. Spirit Levels are the most sensitive, and therefore the most important, appliances for practically determining horizontal or vertical planes and for measuring small angles. They replace and far excel the plumb line as formerly used for the same pur- pose. They are of two kinds, cylindrical levels, and circular or box levels. The Cylindrical Level consists of a cylindrical glass tube, with the inner surface ground to circular curvature, and, being nearly filled with a very mobile liquid like alcohol or ether, sealed at both ends. The part of the tube not filled by the liquid is occupied by its vapor. A scale of equal divisions is usually either engraved on the outside of the glass tube or on a metallic strip placed near the level, and in the plane in which the level is to be used. The geometric features of the cylindrical level will be under- stood from Fig. 39. The curve in any plane, as that represented by this sectional 69 70 THE SPIRIT LEVELS OF view, is the arc of a circle whose chord is either AB, or CD. The "axis of the level " is a line parallel to the chord AB, as the medial axis MM, or it is the tangent, 7T, to the arc at the point 0. While the axis of the level may indeed be a line parallel to any tangent of the curve, the axis is by common consent taken as that line which is, or is parallel to, the tangent of the curve at trie marked zero. The " plane of the level " is the horizontal plane containing this axis. The central point, (9, of the arc which is occupied by the centre of the bubble when the axis is horizontal is called " the zero point " of the level. The grad- uated scale should read both ways from this zero. The prac- tice in vogue among some makers of leaving the central por- tions of the level without graduations is as unscientific and inconvenient as it is antiquated. The theory of the Spirit Level may be briefly stated as follows : Let, / = Amount of any given bubble displacement expressed in linear units. r = Radius of curvature of inner surface of the bubble tube, measured in the same linear unit. Tcr = Semi-circumference of this circle. ;/ = Number of scale divisions the bubble is displaced. d = Value in seconds of arc of each scale division. nd = The total displacement, expressed in seconds of arc. Then evidently we have the following relation i 80 That is, the linear displacement of the bubble is to the whole length of the semi-circumference, as the number of seconds of KN<;iNKKRIN<; 1 NSTIU'M KNTS. 71 arc of bubble displacement is t<> the total number of seconds in the semi-circumference. From equation (i)\ve derive: 9 / (->} r= 3 (i)- d D (A\ ~ 206265 ' Wl , and the lateral adjusting ones, cd. The cross-wise position of the level with respect to the axis of the instrument may, in the case of this striding level, be readily tested. Suppose, for example, that in Fig. 40 the end on the left projects forward, and the end on the right to the rear of the instrumental axis. Rotating the level on the in- strumental axis toward the rear, the bubble will move toward the left, because that end is thus raised. Moving the level forward, the bubble will be displaced toward the right. If, however, the level axis is parallel to the instrumental axis, there will be no movement whatever of the bubble upon rotat- ing the striding level upon the instrumental axis. This is the first adjustment to be made. It should also be tested after the second adjustment. The case of the cross-wise position of the level with respect to a line sight, as occurring in leveling instruments, is also of considerable importance and is fully discussed in the article of this Manual entitled "The Adjustments of the Engineer's Lev?/" The parallel position of the level axis with the physical line or physical plane forming the base of the level can be secured only after making a complete test, as now to be explained. The physical plane mentioned is here the plane joining the points of contact of the inverted V's of the striding level. The accurate use of a level always requires such a manipulation as shall eliminate any error due to lack of parallelism of its axis with the plane forming its base. It is not always necessary nor even desirable that the error shall be removed by adjustment, but it is essential that its value be known, and allowed for. Moreover, it ought to be distinctly understood that there is no form of level whatever not subject to this error. The follow- ing method of observation will be found to lead both to the ;lesired accuracy in observation and to the neatest means of determining the error and of accomplishing this adjustment of the level : 7 6 THE SPIRIT LEVELS OF Let AB in Fig. 41 represent a level tube applied in an east- west direction to a truly horizontal line E.W. ; e and w the end readings of the bubble. Let / equal the half-length of the bubble. The bubble readings, e and w, will be exactly the same, and each equal to /, pro- vided, First, the legs AE and BVV are equal and, Secondly, the zero point is in the middle of AB. If BW is the longer leg, the bubble will stand nearer B by, say, y divisions ; also, if the zero stands nearer A by, say, z divisions, the reading of w will be in- creased by that amount. Fig. 41. A E eO w \ B W f^^^^^ eO W B W Fig. 42. Letting e==y-\-s. The readings for the ends are then : w = I + e=l But if the end B be now raised, as shown in Fig.42, through an angle a which would of itself give, say, x divisions of dis- placement, the readings in this position of the level will then be And, if we now, in Fig. 42, reverse the position of the level, so that B stands over E and A over W, the errors j>-\-z=s, will change sign, and the readings of the bubble ends toward W and E will be respectively, \ IV. 2 / - -f- X = x (2) From these sets of equations, j(i) and (2), we have ENGINEERING INSTRUMENTS. 77 Hence x = X [ % ('i f ,) + X K '2)] (W* 4- If 2 ) - (^ 4- r 2 ) x v or finally x=\- (4) 4 The practical rule given by the last equation is : Place the level on the given inclined line. Read the divisions at the bubble-ends. Reverse and read again. Add together the two bubble-end readings of the one end, also the two bubble-end readings of the other end, and divide the difference of these sums by four. This result measures, in divisions of the level, the elevation of the end with the greater sum of readings. In order to find the angular elevation we must multiply the number of divisions, ;/, of bubble displacement, by the value of a division in arc, d, to obtain the angle a, or, a = nd. The errors y and 2 cannot be found separately, but their sum, e, is readily found from equations (3). If the level always remained in a constant condition, the errors y and z could be found and corrected, and their sum being then zero, either of the equations, (3), would give x without reversal of the level. In refined leveling this con- stancy should never be assumed. It is, however, always convenient to render as nearly as possible equal to zero. A practical example is furnished by the following readings of a level placed on the horizontal axis of an instrument : W. E. w e First position, 24.1 26.3 2.2 = Second position, 29.2 21.2 + 8.0 = Sums, 53.3 47-5 4) 10.2 47-5 2.55 = 4)5-8 1.45= X 78 THE SPIRIT LEVELS OF Assuming the value of a division, d, of this level as 1.8", the west end of the axis of the instrument inclines upward by 1.45 times this amount, or 2.6". The negative sign of s shows that in the first position of the level, the west end bubble reading is too small, or the west end of the tube is too low by that amount. The vertical adjusting screws must therefore be so turned that for this position the bubble is brought west 2.55 divisions. This being done, the reading for each position of the level, direct and reversed, will be 26.65 and 23.75 for the west and east end respectively; and in either position of the level, one-half the difference of the bubble-end readings will give the number, 1.45, of bubble-divi- sions of inclination of the axis of the instrument. Change of bubble length due to change of temperature dur- ing the reading of the level may introduce an error. It is eliminated by arranging the several readings in the two posi- tions of the level symmetrically with respect to the time. For reasons to be stated under the head of errors of the level, each set of readings should be made an independent one by lifting the level after each observation of both ends of the bubble. The rule would then be : Read the bubble-ends once in the first position of level, twice in the second position (taking care to lift level between these observations), and once again in the first position. The difference of the sums of readings on the same side, divided by the whole number of end readings, is, in bubble- j o * divisions, the inclination upward of the side having the greater sum of readings. METHODS OF FINDING THE VALUE OF A DIVISION OF A SPIRIT LEVEL. Taking great care to place the level tube while it is being tested under precisely the same conditions as when it is in use in connection with the instrument, a spirit level may have the value of a division determined by one or other of the fol- lowing methods : i. By the use of a Vertical Circle. If a finely divided verti- i-:.\( . i NKKRI N< ; 79 cal circle is at hand, the value of a division may be deter- mined by suitably attaching the level in the plane of the circle and simultaneously taking the readings of the circle and of the level with the bubble near one end, and then by a slight rotation bringing the bubble near the other end and taking the simul- taneous readings. The value of one division of the level will evidently result from a division of the number of seconds of an j^le measured on the circle, by the number of divisions of bubble displacement. By taking simultaneous readings with bubble in various positions of the tube, the equality of value of the divisions of the level may be tested. 2. By Means of Instrument and Rod. A convenient, practical method of finding the value of a division of the level of an engineer's transit, or of an engineer's level, consists in sighting the telescope to a leveling-rod set at a known distance from the instrument, and causing the bubble to run first toward the eye-end and then toward the object-end of the level tube, at the same time that the rod readings are taken for these different positions of the bubble. If D represents the distance of the rod from the instrument; r, the difference of the rod-readings for the two positions of the bubble; ?/, the number of divisions traversed by the centre of the bubble; d r ^ the value of one division of the level in units of the rod for the unit distance, and d s the value of one division of the level in seconds of arc, we have and d* = 206 265 -/" , (2). If we let E e equal the eye-end reading, and O e the object- end reading of bubble for the bubble run toward the eye-end of the tube ; E the eye-end reading, and the object-end reading of the bubble for bubble-run toward object-end of the tube ; R e the red reading for bubble run toward eye-end, and R the rod reading for bubble-run toward object-end, the bubble deviation being counted from the middle of the tube, and reckoned positive if toward the object-end, we may write equations (i) and (2) in the following suggestive forms : 8o THE SPIRIT LEVELS OF R. R, D " L-n \ And (R R e ) 206 265 O e E e D (3) (4) It is advantageous in practice to let each one of the let- ters representing readings in equations (3) and (4) stand for the mean of a number of readings. Equation (3) will be found useful in computing a table of corrections to the rod-readings, corresponding to various distances and bubble deviations, incident to the use of an Engineers' Transit or Engineers' Level. 3. By Means of a Level-Trier. The level-trier is an instru- ment specially designed for determining the value of a division of a level and investigating the uniformity of that Fig. 42. value in different parts of its scale; and under different con- ditions of temperature. Figure 42 gives a perspective view of a level-trier, or level-tester. This instrument consists of a main T-formed plate A mounted on three leveling-screw*; a second plate B hinged to the former at one end, by means of accurate pivots, and hence capable of having the height of the other end varied by means of a fine micrometer screw 5 placed there. This screw is provided with a graduated head, from which the seconds of arc may be directly read off Slides with suitable V's rest upon the movable plate, and serve to hold in place levels of various lengths. ENGINEERING INSTRUMENTS. 8l The theory of the level-trier is very simple. If the length, ( X accurately measured from the centre of the axis C to the axis of the micrometer screw, 6", be designated by /, one thread interval of the micrometer by /*, the total number of divisions on the graduated micrometer-head, A r , and ;/ the number of these corresponding to /divisions of the level, then the angular value, */, of one division of the level will be given by the equation , _ fi n 206 26 j /. A" / Here .'.- is evidently the tangent of the angle corresponding to a single turn of the micrometer screw, and since this angle is small, Jj- jo6 265 represents the value of the angle itself. The relations of , /, and N are so taken as to enable the micrometer-head to be read directly to seconds. THE FAULTS OF LEVELS. The faults to which levels are subject are the more worthy of remark, because so frequently overlooked, even by expert observers. Moreover, it sometimes happens that a whole series of very important measures is cast into doubt or alto- gether lost by a level which, from original faulty construction, suddenly shows seemingly inexplicable errors. Irregularities in the curve to which the level is intended to be ground, will, of course, produce irregular values for the different divisions. These values may, indeed, be investigated, and a table of them used for the various deviations of bubble ; but, practically, it is found best to reject all such levels or re-work their curves. Improper length of bubble may be due to original fault in filling, to leakage, to variations in the diameter of the level- tube, or finally to excessive temperature changes. Low tem- perature lengthens and a high temperature shortens the bubble. It is found that extreme shortness or length of the bubble somewhat influences the value of a division of bubble- 82 THE SPIRIT LEVELS OF displacement. The bubble should not much vary from one- fourth to one-half the whole length of the tube. A length of one-third that of the tube is a good average. Temperature variations not only affect the length of bubble, but may cause unequal stresses on the tube, owing to improper methods of securing it in its case. Particularly is unequal heating of the level to be carefully guarded against. The bubble always moves toward the point of higher temperature, and hence unequal temperature of tube may entirely destroy its value as a level. Levels should therefore be guarded from the direct rays of the sun, and from bodily heat. Particles of dust and glass in the sealed tube have been found to produce very serious and often mysterious errors in the in- dications of levels. Astronomers and others called upon to do delicate work with levels, have frequently verified the curious behavior of levels without quite comprehending the nature of the defect. QUEEN & Co. employ a kind of glass and a method of preparing the tubes, and of filling them, which effectively obviate this serious and unexpected class of errors. The elimination of errors, like those just mentioned, may perhaps best be accomplished by frequent disturbances and re- readings of the bubble during the progress of any work of special importance. Any tendency toward constancy of error may thus be translated into the province of accidental and .compensating errors. A level containing free solid particles or crystals formed by deterioration of the glass is, however, prone to systemattc error under all conditions of use. The deterioration of levels, although much discussed in tkc past, has only recently received a scientific explanation, and an adequate remedy through the elegant investigations of Prcfjs- sor R. Weber, of Berlin. This noted chemist has put it beyond question that the ordinary soft qualities of glass are dissc.Ved by water admitted with the ether, and that the quant--; / of crystalline matter developed inside of level tubes is propo f both to the impurity of the ether and the solubility of the ENGINEER I Xi ; INSTRUMENTS. 83 This he has verified chemically In. several scientifically selected test cases, as well as by reference to some fifty different levels. The high importance of his investigations lies not only in having disclosed the true causes of the deterioration of levels but in having proposed and thoroughly tested a form of level whose permanence max* be guaranteed. Two points have to be attended to in making durable levels. First, the glass must be of a special chemical constitution, and secondly, the ether used for filling must be freshly rectified and freed from every trace of water. Deterioration is certain to follow the omission of either precaution. Levels filled for a long while should hence always be carefully examined for the characteristic clouding of the interior before being too confi- dently trusted in any delicate work. QUEEN & Co. now un- dertake to furnish fine levels with the special glass and filling. NEW FORMS OF LEVELS. Mr. H. H. Turner, of the Greenwich Observatory, suggests a form of level which is practically a combination of level and level-trier in one instrument. This is accomplished by the addition of a micrometer screw and system of levers for deli- cately moving the bubble and bringing it to the same mark in each position of the level. Inequalities of the scale do not affect the readings in this form. Dr. A. A. Common, of the Royal Astronomical Society, goes a step further and proposes, in refined work, to discard the filled level altogether, and in its place substitute a horizon- tal telescopic line of sight, whose direction, beyond the object- glass of the device, is rendered vertical by means of a right- angled prism, and then verified by reflexion' from mercury ac- cording to the familiar Bohnenberger method. THE LEVELS AS APPLIED TO INSTRUMENTS/ The Engineer's Transit of the ordinary form usually has three levels, two applied to the alidade and one of considerable sen- sitiveness attached to the telescope and enabling the instru- ment to be .used for leveling. If the instrument be designed 84 THE SPIRIT LEVELS OF ENGINEERING INSTRUMENTS. to measure vertical angles with accuracy, it may have a level attached to the vernier arm of the vertical circle. If de- signed for straight line work or for geodetic use, it may have a sensitive striding level. The solar attachment as applied to the transit also requires a small level to set the solar telescope to the required inclination. Instead of two cylindrical levels, one circular may be applied to the alidade. The axis of each plate-level is adjusted so as to be at right angles to the vertical axis of the instrument. The axis of the ^5 telescope level is adjusted parallel to the line of sight o*f the telescope. The bubble of the level of the vertical circle is ad- justed to read zero when the line of sight is horizontal and the vernier of the vertical circle reads zero. The axis of the strid- ing level is intended to be at right angles to the vertical axis of instrument, and its adjustment and use have already been fully explained. The axis of the level attached to the solar telescope is adjusted to be parallel to the line of sight of that telescope, when this line is parallel to the sight-axis of the main telescope. The Engineer's Level has ordinarily but one level attached parallel to the telescope. Sometimes, however, it is considered advantageous to have small cylindrical levels or a circular level attached to the leveling head of the instrument for use in rough adjustment of the instrument. The axis of the telescope level is, by adjustment, brought parallel to the sight-axis of the tele- scope, and must be of a sensitiveness proportional to the accuracy of which the instrument as a whole is to be capable. Other instruments, like the Engineer's Compass, and the Plane Table, as well as the usual Geodetic, and Astronomical instruments, have levels for similar purposes which will be readily understood from the discussions of this article. Queen & Co. take no little pains to make the levels of their instruments of reliable construction and of a sensitiveness suited to the purpose of the particular level and instrument. They also specially aim to so graduate all the levels as to facili- tate their convenient reading and proper use. The value, in angular measure, of a division of each level is furnished by th^ii in the certificate accompanying each instrument. QUEEN" BUILDERS' TRANSIT. A 1521. THE TELESCOPES OF ENGINEERING INSTRUMENTS. A GOOD telescope is generally admitted to be an essen- tial feature of an engineer's transit or of an engineer's level, and yet it is very doubtful whether the points necessary to excellence in the optical parts of the instrument are always fairly understood, since even direct misstatements of the scientific facts, such as that the excellence of a tele- scope is determined by its high magnifying power, are used as a means for exploiting inferior instruments. A detailed discussion of the construction of the telescope will best show in what points excellence consists. Every telescope consists of three essential parts : First, the image-forming apparatus ; second, the image-examining ap- paratus ; and third, the tube. If the telescope is to be used for measuring purposes a fourth essential is a set of cross wires in the common focus of the objective and eye-piece. In refract- ing telescopes, such as exclusively used in engineering instru- ments, the image is formed by an object-glass or objective through which the light is transmitted. By means of the object- glass, the rays are so bent as to unite in a certain plane behind the lens, called the focus, and there form a small image or picture of the objects toward which the telescope is directed. This imago, which may be readily seen by the unaided eye by placing a dull white surface in the focal plane, is then exam- ined by a set of lenses called the eye-piece or ocular, which acts like an ordinary hand magnifier or single short-focus lens, and causes the image to appear enlarged and clearly visible to the examining eye. The tube holds the object-glass and eye-piece in proper relation to one another. The Simple Astronomical Telescope of Kepler, Fig. 10, con- 85 86 THE TELESCOPES OF 'ENGINEERING INSTRUMENTS. sisting of two simple convex lenses, one of long focus, 0, the objective, and.the other of short focus, E, the ocular, is the best form to consider in a discussion of-the< general properties of the telescope. In the Kepler "teles cope the' 'distance apart of the two lenses when a distant object is viewed is equal to the sum of the focal lengths of the Senses. T-he'Compoimd/arhromatic objectives 'and oculars of other telescopes may be regarded as single lenses whose equivarenribcal lengths and positions are such as to produce a similar optical result. . Fig. 10. The magnifying power of any telescope is equal to the ratio of the angular size of the- object' ;as it appears in the telescope to that which it presents to' the naked eye, -or, in Fig. 10, the ratio of Mg=MENto bOa=.MO N, which, since .the angles are small, is equal to the ratio of Oi, the focal length, F, of the objective to Ei, the focal length,/, of; the eye-4ens. If M designates the magnifying power, It being difficult and inconvenient to measure the focal lengths of the lenses with accuracy, the magnifying power is practi- cally measured by other methods presently to be mentioned*. The Field of View is the angular space that can be viewed with the telescope at one and the same time. The angle formed, Fig. 10, .by the two .principal rays, a and b, passing through the centre, .0, of the objective and tangent to the diaphragm of the ocular, or the angle aQb=gOh, measures the field of view. The effective aperture of the ocular thus alone Determines the size of the field. THE TELESCOPES <>l KNt , I XEEK 1 N< , IXSTKOfEXTS 87 The field decreases with the increase of magnifying power. If we let a equal the aperture of.the eye-lens, J/the magnify- ing .power of telescope, / the focal length of objective, and/ focal length of eye-lens, then in minutes of arc, ; as isruspal, a == *^/,- the* following relations result ; Mag. power, \io 20 30 40 100 ... . Field, * 39' i 26' 56' 43':!;' . } '. ' , i ' . . The brightness of objects as seen through the telescope de- pends upon (l).the proportion of the Jight, L, transmitted through the lenses ;, (2) the clear aperture. of the objective, A ; - , / * (3) the aperture ofthe pupil of the observer's eye, e ; and (4) the magnifying power, M. The proportion of light trans- mitted through the best achromatic telescopes, taking the brightness as seen with^the unaided eye as I, is eighty-five per cent., though this proportion may in inferior instruments de- scend to seventy per cent. If B represents this brightness, the expression for it will 'be : 13 which indicates that the brightness of objects as seen through the telescope increases in proportion to the square of the in- strument's aperture and decreases as the square of its magni- fying power. It is thus seen that increase of magnifying power very rapidly decreases brightness. A limit of decrease of brightness beyond one-half that presented to the unaided eye should never be allowed. The maximum brightness of objects giving a sensible size of image is attained when the diameter of the cylinder of rays issuing from the telescope equals the aperture ofthe eye. The brightness is then equal to the natural one. Stars being, under all telescopic powers, mere points, increase in brightness 88 THE TELESCOPES OF ENGINEERING INSTRUMENTS. beyond the natural brightness in the ratio of the squares of the apertures of the objective and of the eye. The Simple Objective, formed of a single lens, has two serious defects. First, the image is fringed and rendered in- distinct by the spectral colors, and, secondly, the image is so curved that when projected on a plane it appears for the most part indistinct and hazy. The Achromatic Objective, formed by combining two lenses of different dispersive and refractive powers, usually of crown .and flint glass respectively, may be so constructed as almost wholly to avoid these two defects of chromatic and spherical aberration. The achromatism or colorlessness of the image will then depend on the ratio of the focal lengths of the two lenses, while the freedom from spherical aberration or from a nebulous, milky appearance of the image will be determined by the ratio of the curvatures of the lenses. The eye-pieces of a telescope may be of two kinds, astronomi- cal and terrestrial, the former usually comprising two lenses, and showing the image in the same inverted condition in which it is formed by the objective, and the latter usually com- prising four lenses and erecting the image. Although the terrestrial eye-piece is inferior in point of optical performance, it is still generally preferred by American engineers. The Astronomical Eye-pieces are either of the Huyghenian or of the Ramsden form. The former, or negative eye-piece, is used only for its qualities as a good seeing ocular, but cannot so well be used with cross- hairs, both because the focus lies be- tween the lenses and because the hairs can only be well de* fined in the centre of the field. It consists of two plano- convex lenses, with their convexities turned toward the object- glass. The Ramsden, or positive, consists of two plano-convex lenses, with their convexities, turned toward each other. The focus of this ocular lies in front of the field-lens, and it is for this reason, as well as on account of defining the threads well over the whole field, adopted for use with micrometer THK N-:i.i>0I'ES OF EXV.IXEKRIXr; TXSTRl'MKXTS. 89 threads. The purely optical defects of the positive for seeing purposes are greater than those of the negative eye-piece. The terrestrial eye-pieces are usually composed of four lenses, the first two, counting from the objective, being called the erectors. The focus of this lens, as shown in Fig. u, lies in front of the first lens, and it is at that point' that the cross- hairs are placed. The theory of this eye-piece is too compli- cated to be entered into here. Suffice it to say that, on account of the number of possible variables, the production of an excellent eye-piece involves science and art in combina- tion that is the exclusive property of the expert optician. The various forms known as the Fraunhofer, Kellner, Airy, Stein- heil, etc., are to be selected by the skilled optician with regard to the particular service to which the telescope is to be put. The clear aperture of a telescope is determined by the size of the pencil of light which passes through the entire instru- ment. The pencil entering the object-glass may be partly cut off by diaphragms, and thus the apparent aperture may not be the real one. Inferior telescopes not infrequently have a con- siderably less clear aperture than apparent. The following method is an easy test of the true aperture : First, having focused the telescope for distant objects, direct it to a bright cloud, or the well illumined sky, and bring the eye' to a posi- tion behind the eye-hole and at a distance from it equal to that of distinct vision, so as to permit the well-defined little " Ramsden's Circle," or image of the objective formed by the eye-piece, to be clearly seen. Then take a sharp pencil point and, placing it at the edge of the object-glass, move it across toward the centre and note the point where it first becomes visible in the little Ramsden disc. Subtract 9^ THE TELESCOPES OF ENGIXEERING "I^ 7 STRtfMENTS. double- this distance of tHe pencil point from tHe edge from the entire diameter of the object-glass, and the result is the clear aperture. A -.magnifier or low power microscope may be used for observing the little Ramsden circle and the ap- pearance of the pencil point in it. Diaphragms properly placed in the main tube are necessary for 'the exclusion of scattere'cfand injurious' fays. But through ignorance of the . optical theory determining their use, they are often so inserted as to vitiate this'purpose, and also reduce the effective aperture and the field of view. The eye-hole is such a diaphragm, and is intended to be so placed that the eye can easily be brought to that position be- hind the eye-piece where the 1 entire cone of rays may enter the eye. Its-,size arid^position can, -as in the case of the other diaphragms, be computed only from the course of two princi- pal rays, through the. system of lenses. The line of sight of a -telescope, if determined by two fixed points, namely, (i) the optical centre of the objective 'and (2) the centre of the cross-wires. The Image of a point of an object is brought centrally upon the crossing-point 'of the threads, and, since the rays of each point of the object must have passed through the optical centre of the objective, these two points " optical centre " and " crossing-point of the threads " fix the direction of the " line of sight," or " sight axis," or " sight line." If we speak according to the modern Gaussian theory of lenses, the first point is known as " the second principal. point " of the objective. It is also .seen that since this " second principal, point " is, for the objective and telescope, a fixed point, all adjustments of the line of sight * are made by moving the cross-hair ring, and, moreover, that any point on any thread may be selected as the second point determining the line of sight, but that for, convenience and definiteness the crossing-point of the two- middle threads is used. The line of collimation of a telescope is, strictly speaking, the mathematical line at right angles to a certain axis. In the THK ri:i.i>on:-' fi- K-M,INHKKL\<, INSTKTMENTS. 91 Engineers' Transit, and all oher"instrumeritS of that class, the line of collimation is the line at right angles to the horizontal axis of the telescope* 'An instrument is said to be collimated when the line of sight, is .brought' into coincidence with the line of collimation, or in. the -transit when the-line of sight is at right angles to the horizontal axis. '/The term, ' line of colli- mation," is often erroneously t and- loosely used by writers for " line of sight." ; ' . - . ; The centering of the telescope involves a number of delicate operations and adjustments implied in trie' processes (i) of centering each lens ; (2) of centering each combination of lenses (a) objective, (&) eye : piece; (3), of centering these combinations with respect to the tube ; and (4) "of centering the cross-hairs with respect to the optical and mechanical axis. - ' The centering of a lens must be performed in the grinding process. .A lens is truly centered when the' centre., of the eitcle determining its size lies, in the line joining the thickest or the thinnest part that is, in the axis of the lens. . ' ~ | - ; * The centering of the objective in its cell involves not only the primary centering of each of the two lenses, but their careful relative adjustment, so as to make the axis of each lie accu- rately in the same straight line. This common axis of the ob- jective lenses is thenceforth regarded as the optical axis of the telescope to which 1 all else must be centered. So important and delicate is this centering of -the objective in its cell that ho one except the skilled 6ptician shbuld attempt to disturb it by removal of the lenses. The centering of the ob- jective may be tested by setting the cross-hairs upon some point, and noting whether, upon unscrewing the objective through a complete turn, the point remains bisected. All telescopes have this error, ajt least to some small extent, and the object-glass should therefore be screwed in securely, and always remain in the same position. This proper position is always marked in QUEEN & Co.'s instruments. The centering of the lenses in the ocular tube is necessary to the proper optical performance of the eye-piece, and once ac- 92 THE TELESCOPES OF ENGINEERING INSTRUMENTS. complished by the maker, is not to be disturbed by unskilled hands. The centering of the objective slide is readily tested in the telescope applied to leveling instruments. For after having centered the cross-hairs, with the telescope focused for very distant objects, the slide is tested by focusing on a very near object, and noting whether, upon rotating the telescope about its mechanical axis, a point remains bisected. If there is a deviation, one-half its apparent value must be corrected by means of the slide-centering screws. In the telescope of the Engineers' Transit the following method is used : Sight to a distant point, note it, and, clamp- ing the horizontal circle, focus upon a near point. Now turn the instrument half-way round horizontally and transiting the telescope sight to the near point. Clamp horizontal circle and focus for the distant point. If the cross-hairs accurately bisect, it there is no error of the slide. Otherwise, one-half the apparent error is to be corrected by means of the slide- centering screws. This centering is important where both long and short sights enter into the work. Any error due to it is, of course, eliminated by keeping the focus and distances constant. The centering of the cross-hairs, assuming that the objective is correctly centered, may, in cases where the telescope can be rotated about its mechanical axis, as in the Engineers' Level, be accomplished as follows : Sight to a distant point, and note, upon rotating the telescope 180 in its wyes, whether the point remains bisected. One-half the apparent deviation is to be corrected by means of the cross-hair screws. In tele- scopes of the Engineers' Transit this centering is practically involved in bringing the line of sight into coincidence with the line of collimation as in the Second Adjustment of the Transit. The centering of the ocular-head slide in the case of tele- scopes having a fixed objective, as in the higher grades of in- struments, is accomplished in the same manner as in the case of the objective slide. The ocular-head slide carries both ocular and cross-wires. THE TELESCOPES OF ENGINEERING INSTRUMENTS. 93 The centering of the ocular in reference to the cross-wires is sometimes arranged for by means of a special set of screws. The ocular is then moved until the cross-hairs appear in the middle of the field of view. Focusing with accuracy is necessary not only for clear defi- nition, but also for the correct use of the telescope as a means of determining direction. In its completeness it involves two operations : First, it requires the cross-wires to be brought into the focus of the eye-piece. To accomplish this, direct the telescope to the sky, and then move the ocular in or out very carefully until the most distinct vision of the wires re- sults. A mean position between the points of equally fair vision of the wires for inward and for outward motion of the ocular will give the best focusing of the ocular. Secondly, it requires the cross-wires to be brought into the focus of the objective. To accomplish this, either move the objective with respect to the stationary ocular-head, which carries cross-threads and eye-piece, or move the whole ocular-head with respect to the stationary objective, until there is, with the same eye as em- ployed in focusing the ocular, the most distinct vision of dis- tant objects. Parallax of the wires, or an apparent displacement of the wires with respect to any visible object upon moving the eye in front of the ocular up and down or to the right and left, is due to the wires not being in the common focus of objective and eye-piece. If care has been taken to focus the ocular accurately on the threads, the parallactic displacement of the wires must entirely disappear in focusing the objective. In fact, this disappearance of parallax of the wires is the best test of accurate focusing. The measurement of the field of view is easily accomplished by either of the following methods: (Y) Select two distant points which appear at diametrically opposite edges of the field of view. Measure the actual distance, */, of these points 9^.. THE TELESCOPES OF ENGINEERING INSTRUMENTS. from each other, and also their distance, D, from the tele- scope ; then the field is expressed in minutes of arc thus : Field 3438' . The points required in this method are most conveniently furnished by a leveling rod placed at some distance. (2) Either the horizontal or vertical circle of the instrument may be used for directly measuring the angular distance apart of two points appearing at the diametrically opposite edges of the field, or for measuring the motion of a point throughout a diameter of the field. A knowledge of the angular value of the field may be .of assistance in roughly estimating angles and distances. The measurement of the magnifying power of a telescope may be performed in several ways. The ordinary two-eye method requires the telescope to be placed at a great distance, as compared with its length, before any object serving as a scale and distinctly visible, to the naked eye. As object, a distinctly visible measuring-rod, or even the regular pattern of a wall may answer. Looking through the telescope with one eye and viewing the scale directly with the other, two superimposed images are seen. If, now, n divisions, as seen with the telescope, appear to cor- respond with TV" divisions as seen with the. naked. eye, the mag- nifying power, M, is The inaccuracy of this method arises from the impossibility of securing distinct vision with the naked eye of an object at a sufficiently great distance. Jordan's method has the advantage over the usual two-eye methods, in that a horizontal axis of the telescope does not interfere, and- that both eyes are adjusted for distinct vision. Look through the telescope at a divided rod, or at some bright object of known size projected on a dark background, and hold up before the other eye, at the distance of distinct THE TELESCOPES OF KN< il \KKRI X(i INSTRUMENTS. 95 vision, an open pair of" compasses. Now bring the points of cue compasses, as clearly seen with one eye, into apparent co- incidence with the telescopic image of the rod as seen with the other eye, and measure off, as on a drawing, the apparent si/e of a portion, R, of the rod, and afterward find this distance apart, i\ of the compass points by means of a divided scale. The distance of the rod from the eye being /?, and the dis- tance of the compass from the eye, d, the magnifying power, J/. is evidently M- r -^*- rn ~ d ' D Rd Valz's method is both neat arid easily applied. It depends on the measurement of the angle which the rays, coming from an object of known angular diameter, form on issuing from the ocular of the telescope. The sun, on account of its bright- ness and well-known angular diameter, is for this purpose par- ticularly suitable. Place a screen at a distance, D, from the " eye-point," and there receive the solar image, whose linear diameter we shall call d. Let also s be the true angular diameter of the sun, and 5 the angular diameter of the image on the screen, subtended at the eye-point, then * ^ d dcot i * s ~tan. y 2 a 2D tan. l / 2 S~ 2.D And, finally, if we take 2 D equal to cot. y 2 S, M=d. That is, if the double distance, 2 D, of the image from the eye- point is taken equal to the cotangent of the semi-diameter of the sun, the number of parts of the scale comprised in the ex- tent of the image will express the magnification. Thus, in January, the image should be received and measured at 105 scale parts from the eye-point, in April and October at 107, and in July at 109 parts. The Gaussian method is, all considered, the most scientific, but requires for its use an additional instrument. The tele- scope whose magnifying power is to be determined is first 96 THE TELESCOPES OF ENGINEERING INSTRUMENTS. carefully focused on a distant object, and its eye-end is then directed' toward some well-illumined object of regular shape several hundred feet distant A second instrument is now set up, with its objective turned toward the objective of the tele- scope whose magnifying power is desired. The object will be seen through both instruments, but in reduced size, and its apparent angular size, a, is measured by means of the second instrument. Afterward the angular size, A, of the object is measured without the interposition of the first telescope. The magnifying power, M t of this telescope is then given by the expression M- tan ' ^ A tan. y 2 a Example: A piece of white card-board, placed at a distance of several hundred feet, subtends an angle, A, of i 30' 25", and on interposing a Wye Level, with its eye-end directed toward the object, the apparent angular size, a, of card, is found to be 2 r 30", hence, J/of the Wye Level ="-"-'- ^ ( ! 3 ,' ^U 36.27 diameters. tan. y 2 (2' 30") QUEEN & Co., possessing a wide experience in optical manufacture, keep pace with all the latest scientific improve- ments in optical glass making, and aim by combining the best optical theory and skill, to furnish their engineering instruments with telescopes of the highest excellence. They have no peculiarity of their telescopes to announce except it be the judiciously planned combination of aperture, focal length, power and qualities of glass best adapted to the uses of each kind of instrument. Good seeing capacity, and not the particularly high power with its concurrent disadvantag4s, is considered of the foremost consequence. It is greatly re- gretted that the necessary limits of the foregoing article have prevented a complete exposition of the theory of the telescope. A good-sized volume on the subject would, however, seem inadequate, and serve only to show more fully and clearly in how many essentials it is necessary to unite optical science with experienced skill in making telescopes that are adapted to satisfactory measurement in engineering. DESCRIPTION OF THE ENGINEER'S COMPASS. THE following description of the Engineer's Compass is intended to direct attention to its various parts and forms. The Tripod furnished with the engineer's compass is either of the ordinary round leg or split leg form. If desired a head and shoe to be used with an improvised Jacob's staff is also furnished. The Ball-spindle, on which the socket of the compass is fitted, is of conical shape, and at its lower end turned to a perfect sphere. This sphere is confined in a socket on the tripod head in such a manner as to enable the compass to be brought readily to an approximately level position. The Spring Catch, which engages in a groove of the spindle of the compass the moment ft is inserted in the socket, is attached at the side of the socket. It obviates the danger of the instrument slipping off the spindle when it is being carried. The Clamp Screw, by means of which the spindle of the instrument may be clamped in any position, is placed at the side of the socket of the compass. The Circle of the Compass is graduated to half degrees and the divisions so marked as to be read with the greatest ease. The figuring extends from o to 90, from the north and the south points in both directions. The line of zeros passes through the vertical axis of the compass and is also in line with the sights. The Tangent Screw attached to the circle enables the line of zeros to be set at an angle with the sight line equal to the variation of the magnetic needle. This angle is measured on 97 98 DESCRIPTION OF THE an accessory arc or circle, placed just outside the clamp and tangent movement. The Variation Arc or Circle is placed immediately on the main plate of the compass. Its centre is concentric with the vertical axis of the instrument. The vernier of the arc or circle is usually fastened to the main plate while the arc or circle plate forms one piece with the graduated compass circle. The arc or circle is used for setting off the magnetic declination of the place so as to enable the bearings to be taken with respect to the true astronomical meridian. When a complete circle is used, as in the railroad compass, horizontal angles may be measured with it for any purpose whatever. The Spirit Levels are placed directly upon the plate at right angles to each other and made adjustable. The Sights are vertical standards clamped to each end of the plate and at right angles to it. They have fine slits running through nearly their entire length. Large circular apertures are placed at intervals along the slits and allow a distant object to be the more readily seen. The north sight has graduated upon its lateral edges a scale of tangents corresponding to a circle whose centre is a small eye-hole placed upon the south sight The eye-hole at the lower end of the south sight is intended to be used in sighting for angles of elevation, the eye-hole at the top of the same sight being used for angles of depression. The Needle Lifter is actuated by a screw placed below the main plate. The needle should always be raised from its centre pin by means of the lifter before carrying the instrument. The Out Keeper is a small graduated dial turned by means of a milled head and used for the purpose of counting the number of chains measured. The Brass Cover fitting on the compass-box is intended to shield the glass cover from accidental injury during transportation. The Telescopic Sight is an appliance consisting substantially of a transit telescope with its fine level and a suitable clamp for attaching it at right angles to one of the sighting standards of the compass. It is supplied with any of jthe various forms of the compass. ENGINEER S COMPASS. 99 The Forms of the Compass made by QUEEN & Co. may be best understood in all their variety by reference to their Cata- logue of ^Engineering Instruments. The following are the chie f forms : The Plain Compass is furnished with needles of four, five, or six inches in length but has no variation plate. It is sometimes made with folding sights and may also be fitted with telescopic sights. The Vernier Compass is furnished with variation arc and has the tangent scales necessary for reading angles of elevation or depression. The Railroad Compass has the 'levels, sights, and needle of the ordinary Plain Compass, but has also underneath the main plate a graduated circle by means of which horizontal angles to single minutes may be taken independently of the needle. The Pocket Compass exists in a great variety of forms and is often valuable in preliminary rapid work. The prismatic com- pass of Schmallcalder deserves to be particularly mentioned among hand instruments. The graduated card of this com- pass is attached to the needle, and the prism permits the read- ing of the needle to be made simultaneously with taking the sight. The Solar Compass has, in addition to the features of a first- class surveyor's compass with full graduated circle and verniers, the characteristic devices whose chief use is to enable - the surveyor to take bearings with respect to the true or astronomical, meridian. These devices consist essentially of two arcs, one called the latitude arc, with a movable arm, and set at right angles to the horizontal plate of the compass ; and the other, a declination arc placed at right angles to an arm with an axis attached perpendicular to it and revolving in a socket carried by the latitude arm. This axis lying in, or parallel to, the planes of both arcs is called the polar axis, and also lies in or parallel to, the vertical plane containing the main line of sight of the compass. Its use and adjustment is referred to in the article of this Manual entitled. " The Solar Transit and other Methods of determining the Astronomical Meridian'' THE ADJUSTMEiMTS OF THE ENGINEER'S COMPASS. THE adjustments of an engineer's compass may be treated of as: (i) The maker's adjustment; and (2) The field adjustments. The latter are those which the surveyor finds it necessary and convenient to verify in practical work, and the former, in fact inclusive of the latter, are those to be accu- rately accomplished by the maker. THE MAKER'S ADJUSTMENTS. The following points of construction and adjustment of the Engineer's Compass must be accurately attained in order to realize the mathematical conditions of the problem. 1. The main plate accurately perpendicular to the spindle of the compass. 2. The variation arc or circle and its verniers truly gradu- ated and concentric with the spindle. 3. The sights and sighting-slits truly at right angles to the main plate. 4. The line joining the centre of the sighting-slits passing through the mathematical axis of the instrument. 5. The zeros of the verniers of the variation arc or circle in tfce same straight line with the sights and axis of the instrument. 6. The compass circle truly graduated, its centre concentric with the axis of the instrument, and its line of zeros coincident with the truly adjusted line of sights. 7. The axis of each of the plate levels at right angles to the axis of the instrument. 8. The pivot of the compass needle coincident with the ver- 100 ENGINEER'S COMPASS. 101 tical axis of the instrument, and sharp enough to obviate appreciable friction in the needle-cap. 9. The magnetic needle magnetically sensitive and perfectly straight. 10. The magnetic axis of the needle coincident with the axis of form. 1 1 . The magnetic needle adj usted for the magnetic dip of the place of observation. 12. The axis of the suspended plumb bob coincident with the vertical axis of the instrument. It is not intended that the foregoing shall represent an ex- haustive statement of the details requiring the attention of the skilled maker, but it is hoped that this statement may direct attention to essential features of construction otherwise likely to be overlooked by purchasers and users of the instrument. THE FIELD ADJUSTMENTS. The following methods for practically detecting and correct- ing the errors of adjustment of an Engineer's Compass are given for field use : First Adjustment : To make tJic axis of the plate levels pcr- pcudicular to tlic vertical axis of the instrument. DETECTION OF THE ERROR. Carefully level the instrument in the two directions parallel with the levels. Note some point seen through the sights, and turn the sights exactly through 1 80, or until the same point is 'again in line. Now examine each of the levels in turn, and see if there has been any dis- placement of the bubble. The amount of bubble displacement is in each case just double the error of the bubble-tubes, as already explained under " First Adjustment" of the Engineer's Transit. CORRECTION OF THE ERROR. By means of the screws near the ends of the level-tubes, carefully bring back the bub- ble through half the displacement, taking care to have the screws fairly tightened when done. The remaining half of the bubble displacement, being due to lack of horizontality of the plate, may now be corrected by leveling up the instrument. 102 THE ADJUSTMENTS OF THE Second Adjustment :-^- To bring the pivot of the magnetic needle into coincidence witk the axis of the instrument. DETECTION OF THE ERROR. Bring one end of the needle on a division of the circle, and note the deviation of the other end from the division making 180 with it. Then remember that this deviation from a true reading may be due to any one or all of the following defects : (i.) Errors of graduation in the circle. (2.) Eccentricity of the circle with respect to axis of instru- ment. (3.) Bent needle. (4.) Eccentricity of the pivot with respect to axis of instru- ment. The first two errors, if they exist, cannot be adjusted by the engineer, and they are here assumed as negligible errors. This reduces the causes of the deviation mentioned to the two last named. But in order to determine the nature of the errors fully, readings must be made round the circle at intervals, say, of 15, and the end deviations noted. Then, (i.) Constant difference between end readings of needle f Needle bent, and means < I Pivot centered. (2.) Variable difference between end readings of needle ( Pivot eccentric, and means < f straight, if difference is zero for any one (needle either J direction; or ( bent, if difference is never zero. This is made evident by (A), (B), and (C), of Fig. 49. Fig. (A) illustrates case (i) of pivot centered and needle bent, the differences S a, E b, etc., always remaining constant. Fig. (B) illustrates the case of straight needle and eccentric pivot, the difference of end readings becoming zero, say for the position WE, where the straight needle cuts both pivot, D, and centre of circle, C ; and the difference being at its maximum, vS" a, at 90 from the position of zero difference. Fig. (C) illustrates the case of eccentric pivot and bent needle; 5 a ENGINEERS COMPASS. 103 being the maximum ; and E b the minimum difference of the end readings. CORRECTION OF THE ERROR. Find the position of the maxi- mum difference of end readings, S a, Fig. 49, (C), and also the minimum, E b. Take one-half the difference of these differ- ences, and adjust the pivot through this amount at right angles to the position of maximum deviation. . Another method of correction proceeds as follows : (i.) Temporarily adjust pivot so as to allow needle in some position to cut diametrically opposite graduations. Reverse and thus double the error due to bent needle. Straighten needle by bending through one-half this difference. (2.) Adjust pivot till at all intervals, say, of 30, the needle points to opposite divisions. N (B.) (C.) Fig. 49- Third Adjustment: To straighten the magnetic needle. DETECTION OF THE EROR. This has already been for the most part explained under the head of the Second Adjustment. It is only necessary here to remark that the minimum devia- tion, E b, Fig. 49, (C), is altogether due to the bent needle. CORRECTION OF THE ERROR. Having found the position of the minimum deviation of end readings, Eb, Fig. 49, (C), bend the needle carefully near the centre to an amount equal to Eb- Fourth Adjustment: To make the plane of the sights per- pendicular to the plane of the levels. DETECTION OF THE ERROR. Carefully level the instrument and bring the plane of sights upon a plumb-line suspended at some convenient distance. Sight by looking through lower 104 THE ADJUSTMENTS OF THE ENGINEER'S COMPASS. part of one sight, and, running the eye along the other, note the latter's deviation from the vertical plumb-line. Similarly test the other sight. CORRECTION OF THE ERROR.- Any error of this sort can he corrected satisfactorily only by the maker. Temporary relief may be had by clamping under the sides of the sighting stand- ards thin bits of paper, so as to bring the sights truly vertical. Several other important points in the maker's work may also be easily tested : ( I .) To test whether the diameter passing through the zero graduations, or the " line of zeros," lies in the plane of the sights. Set the declination arc carefully to zero, and stretch two fine hairs vertically in the centre of the slits, and note if the zeros are in line. (2.) To test whether the line of sight passes through the centre, sight to a very near object, and read one end of needle. Reverse and read same end of needle. One-half the difference of the readings is the error due to the eccentricity of the line of sights. One-half the sum of the same readings is the true reading. Also, if both ends of needle are read, and one-half the sum taken, the eccentricity of the sight line is eliminated. (3.) The magnetic sensitiveness of the needle may be tested by setting the needle in vibration by approaching and remov- ing some iron piece, and then noting whether, upon repeated trials, the needle returns precisely to the same point. If not, the pivot is either dull or the needle lacks directive force, and must be remagnetized. (4.) The absence of metal in the compass capable of affect- ing the needle, may be verified by slowly turning the instru- ment about its axis and noting whether or no the needle is in any position slightly carried along. (5.) The horizontal swinging of the needle is affected by the Magnetic Dip, and is, with other matters pertaining to mag- netism, explained in the article of this Manual, entitled, " Ter- restrial Magnetism in its Relation to Surveying Instruments" QUEEN & Co. invariably test the mechanical perfection of their instruments by giving them, finally, a thoroughly com- plete adjustment. TERRESTRIAL MAGNETISM IN ITS RELATION TO SURVEYING INSTRUMENTS. THE earth acts , on magnetic substances placed on its surface very much as though it were itself a great magnet. One pole of this huge magnet is near the earth's North Pole, the other near its South Pole. If the magnetic condition of the earth were of an entirely constant nature, the surveyor should need nothing better than a freely-suspended magnetic needle directed by terrestrial magnetism, to give him a zero line, namely, the magnetic meridian, from which to measure his angles. But terrestrial magnetism is a very variable thing, and moreover bears peculiar relations to the needle of the surveying instrument. It is, therefore, desirable to give a brief explanation of these fundamental relations. Terrestrial magnetism may be studied by noting its action on a freely-suspended magnetic needle. The three factors usually measured are the Magnetic Intensity, the Dip of the needle, and the Declination of the needle. If a long steel knitting- needle of the old-fashioned type be suspended by a fine thread attached to its middle, it will when uifmagnctizcd, direct itself in some position in a horizontal plane determined by the slight torsion of the thread. On being magnetized, it will direct itself differently. In the first place, instead of being horizontal its north end will now incline downwards. The angle made by the north end of the needle with the horizon, is called the angle of Dip or of Inclination. In the second place, it will be noticed that this magnetized needle also directs itself in a plane which is nearly north and south. The angle which the north- south plane of the magnetic needle makes with the true north 7 south plane is called the Declination of the needle. This angle is also sometimes called the Variation of the needle, 105 106 TERRESTRIAL MAGNETISM IN ITS although this designation is both antiquated and misleading. Finally, the force with which the needle will direct itself in the magnetic meridian when disturbed from it is, other things being equal, determined by the Strength of the Earth's magnet- ism, or by the Magnetic Intensity. We shall now take up each of these terrestrial magnetic elements and show their practical relation to the surveyor's needle. I. The magnetic intensity or magnetic strength of any " field " is proportional to the square of the number of vibrations made in the unit of time, by any magnetic* needle placed in that " field." Vibrating the same magnetic needle at different places or in different " fields," the intensity of the earth's magnetism will vary as square of the number of vibrations made at each place in the unit of time. The Intensity, spoken of without qualification, is considered as taken in the direction of the earth's magnetic force, or in the line of dip. The earth's action on a horizontal needle is of course the horizontal com- ponent of the intensity. If, I, denote the Magnetic Intensity, H, its horizontal component, V, its vertical component, and D, the angle of Dip or Inclination . below the horizon, then evidently H= /cos D and V = /sin D. The magnetic moment of the needle combined with the strength of the earth's magnetic field determines the force with which the needle tends to direct itself in the magnetic meridian. The magnetic moment, M, of the needle is equal to the product of the " magnetic mass," ;;z, of one of its poles by the length, /, of the needle, or, M = ml. A magnetized needle movable about a vertical axis, as in the case of the surveyor's compass, obeys the horizontal component, H, of the earth's magnetic force, and directs itself so that its axis of magnetization is in the magnetic meridian. If the needle is turned out of the meridian through an angle d, the moment of the couple tending to bring it back is expressed by m I //sin d. The sensitiveness of the needle is measured by the accuracy RELATION TO SURVEYING INSTRUMENTS. 107 with which it returns to the same position after displacement from its natural direction in the meridian. From the foregoing expression it is seen that, so far as the needle is concerned, the amount of magnetization, ;;/, and the length, /, combine to make its magnetic moment effective in any given magnetic field. Acting against the moment tending to direct the needle, is the friction on the centre-pin or pivot. And, hence, with a needle lacking sensitiveness, it is a question either of sharpening the centre-pin and thus reducing the friction, or of increasing the magnetization, m, by remagnetizing the needle. When the needle is deflected, as by bringing near it a bit of iron, it should always return to the original position within a few minutes of arc. The magnetization of the needle, or the increase of the magnetic mass, m, is accomplished by stroking the needle with a good permanent magnet in the following manner : With the south pole of the magnet approach the middle of the needle in a direction at right angles to it, and then pass this south pole along the neeedle toward- the north pole of the needle and beyond it, returning by circular sweep to the mid- dle again. Repeat this, say, twenty times. Similarly stroke the south end of the needle with the north pole of the magnet. The needle may thus, in a few minutes, be magnetically saturated. The conservation of the needle's magnetism depends on its original proper tempering, its freedom from subsequent jars, and its remaining when unused in the normal position in the magnetic meridian. II. The Magnetic Inclination or Dip is, as already explained, the angle made with the horizon by the north end of the freely- suspended needle. The tendency of the north end of the needle to dip increases as we go north until the magnetic pole is reached, where the free needle occupies a vertical direction. It is on account of this variableness of the Dip that the surveyor's needles usually have wound round the south end a small bit of wire whose position may be varied so as to bring the needle into a horizontal position at the place the instrument is set up for use. It is for the same reason, therefore, to be borne in 108 TERRESTRIAL MAGNETISM IN ITS mind that however accurately the needle may be adjusted to a horizontal position by the maker in his locality, it will require careful adjustment by the surveyor for the Dip of the place of observation, if it be at any considerable distance from the place of original adjustment. The Dip may vary, also, at any given place, on account of the prevalence of some unusual magnetic disturbance. The dipping needle is a magnetic needle suspended on a horizontal axis, and free to move only in a vertical plane. If the plane of this needle be brought into the magnetic meridian its north end will incline downwards, and the angle of Dip may be read off on the circle. If, as the dipping needle is kept in the plane of the magnetic meridian the angle of Dip changes as the observer moves along, it is an indication of attractive force due to beds of iron ore. It is evident that the unwonted dipping of a previously well-adjusted surveyor's needle may be due to the same cause. III. The Magnetic Declination or Variation is the angle made by the free magnetic needle with the astronomical meridian, or true north-south plane. The term Variation, though almost out of use, still survives in the " variation plate " of the sur- veyor's compass. This magnetic element of the earth has by far the most important relation to the surveyor's work, and requires detailed explanation. The determination of the declination of the magnetic needle for a given place and time, has often to be undertaken by the surveyor. Since this requires a knowledge of the direction of the astronomical or true meridian, the subject is referred to in the article of this Manual, entitled, " The Solar Transit and Methods of Determining the Astronomical Meridian! The variations of the Declination are numerous and of a very* complicated nature. The direction of the needle changes from hour to hour through the day, from month to month through the year, and from year to year through the centuries. In addition, it is subject to extraordinary disturbances during magnetic storms. These special disturbances aside, the laws of the periodic changes in the declination have been fairly well established, and the surveyor is often obliged to have recourse RELATION TO SURVEYING INSTRUMENTS. 1 09 to these observed laws. It is fortunate that in our own coun- try the study of terrestrial magnetism has been an important part of the work of the Coast and Geodetic Survey. Professor Charles A. Schott, the able scientist in charge of the discussion of the magnetic observations, has, in the Survey Reports, during many years, published comprehensive papers of the highest- value to the surveyor in the solution of problems involving changes in the declination of the needle. Irregular variations accompanying so-called " electric storms," are undoubtedly in close relation with changes in the sun, and its spots. Auroras frequently occur at the same time. Since these extraordinary deflections of the needle from the normal positions may either be limited to a few minutes of arc, or ampunt to several degrees, the careful observer must be con- tinually on the alert. The verification of a " magnetic storm " would be ample excuse to await its subsidence, before trusting the indications of the magnetic needle. The small periodic variations which require no attention on the part of the surveyor, are the annual variation of the decli- nation, its amplitude being at most one and a half minutes of arc ; the solar rotation variation having a period of about 26 days, and of very small amplitude ; and the lunar variations, the diurnal one exhibiting, like the tides, two maxima and minima each lunar day, and having a range at Philadelphia of about 27", the other lunar inequalities being of still smaller order. The Solar-diurnal variation is a systematic angular movement of the direction of the magnetic needle, having for its period the Solar day. The amount of this daily swing of the needle is on the average about 8', the north end having its extreme easterly position about 8 A. M., its extreme westerly, about 1.30 P. M., and its mean position about 10.30 A. M. and 8 p. M. This daily variation of the needle is not exactly the same for different places and seasons, but the following table, correct to the nearest tenth of a minute of arc for Philadelphia, presents a good average for the United States. It is derived from Appendix 8, of the Report of the United States Coast and Geodetic Survey of 1 88 1 . For the surveyor this diurnal variation, and the secular variation, presently to be described, are particularly important. no TERRESTRIAL MAGNETISM IN ITS ti K I ft) v d d -i d d d -f 4- + -h 4- + J d d o c + + + T -i d - * ON N VO 00 N VO "+ + + + + + n d d d c + + + 4- 4 o' g u-> r-. ro O irj \o ro O t^ >-" o ro ' + ' + 4- -f + + + + + H- -1 + ro 1 ir> TJ- cs ro o> oo "+ + + -? + + uf> oo q N c + + + + -1 ^ ro (S - -f s ro O ON N ON OO v + + T + + + TI- 10 10 q vc + + + + -4 q s ^- Q Q\ HH O "+ + + + + + rn co UT N OC u-) vd u-> ro C> 4- + + + H ) q 4- a i.. fO O t^ vO IH O v ri M' d fo rj- ^f + + + + + + ro o A r< r + + 4- + H ? Ch i >-i ro M vo - 0\ r^ 10 ON M 30 fO " < v O O O NH 1H M -f 4- + + + + *- CN PO O * + + + 4- H o o a \O "1 00 10 00 N t 7 t 7 f 7 VT) VO OO T 7 t t f 1 1 7 3 10 vo TJ- Tf o) oo . - - - - - - q t--. oo o^ i, TJ- ro N >-i H till r> vO T 00 >-< vr> r^ o r-~ >- . ^i ri to ^r 4- "~ ' 1 1 1 1 1 Th u-> u-> N c u-> vr> rj- M' * I I I T K CS Qs O 1 ^ ^O t^ O ^ M C^ CO r4- t/" ! 1 1 |;|;;:.y N. o T g vO M OO vO t~ O" f 7 7 f f f N t^ "-) CO C T T ? T ^ r^. d 1 . . . : : : : : * * : 1 i : i : : : : : : : : 1 1 1 1 * s & -2 a < s . 4 ' < ^ "1 1 , i ! 1 1 J December RELATION TO SURVEYING INSTRUMENTS, m The correction of observed bearings to the daily mean posi- tion of the needle is readily effected by adding or subtracting the 'numbers of this table, irrespective of the signs, according to the following rule: Before n a. m. subtract the tabular minutes from N. W. and S. E. bearings and add them to N. E. and S. W. bearings ; after n a. m. add the tabular minutes to N. W. and S. E. bearings and subtract them from the N. E. and S. W. bearings. The secular variation of the magnetic declination is probably of a periodic character, but requires several centuries for the completion of a cycle. During many years, therefore, the movement of the needle is progressively in one direction. The amount of the annual change of declination varies for different places and times, and it is on this account that over nearly the whole of the United States the effect of the secular variation is, at present, to increase the west declinations or decrease the east declinations ; that is, the needle is moving westward. On parts of the Pacific coast the effect is opposite, the needle there moving in an easterly direction. The annual change in declination, as already intimated, varies slightly from year to year. Its approximate value for any given locality may be taken from the accompanying map of Isogonic Lines, upon which also the amount of the annual change for the epoch and place have been noted. A plus sign in the annual change indicated increasing west declination or decreasing east declination, and a minus sign increasing east or decreasing west declination. The Isogonic Lines for any given epoch are imaginary lines on the surface of the earth joining points whose declination are at that time equal. An agonic line is one joining points of zero magnetic declination or points where the magnetic meridian coincides with the astronomical meridian. The Isogonic Chart which accompanies this article is a reduction of that of the United States Coast and Geodetic Sur- vey for 1890, the latest published. The approximate declina- tion for any place may either be directly taken from it or inferred by simple interpolation. The Table of Formulae which follows is the result of an ex- 112 TERRESTRIAL MAGNETISM IN ITS tended investigation by Professor Charles A. Schott and pub- lished in the United States Coast Survey Report for 1888. These formulae are the best known statement of the law of change of the declination for the given stations. The letter D in the last column stands for declination, a plus sign indicating west declination ; a minus sign, east declination. The letter ;// stands for the time, expressed in years and fraction of a year, which has elapsed since 1850; or, in other words, is equal to t 1850. Although the formulae are strictly only true for any time within the limits of observation, always, prior to 1888, they may also be used for estimations beyond these limits. As illustrative of the use of the expressions, the following steps in the computation of the declinations for Philadelphia and Denver for July 1st, 1893, are given. The only points that need to be specially noted are that care must be exercised in properly taking out the sines of angles greater than 180, and that the parts of a year are to be ex- pressed fractionally, as, for example, in our case, 1893.5. The value of m is then 1893.5 1850= 43.5. It will not harm again to remind the reader that values of the declination, whether taken from the map or derived from the formulae, are liable to considerable erfor, and that observation can alone yield accurate results. PHILADELPHIA : D=+'5. 3 6 + 3-17 sin (1.50 X 43-5 -26.1) +0.19 sin (4-0 X 43-5 + H6 ). D= + 5-36 + 3-17 sin 39.15 + 0.19 sin 320. D =-. -f- 5.36 + 3.17 sin 39 9' 0.19 sin 40. D = + 5.36 + 2.00 0.12. D = -f- 7.24, /. e., west declination. DENVER : D = - 15-30 + o.oi i X 43-5 + 0.0005 (43-S) 2 - D = 15.30 + 1.42. D 13.88, i. e., east declination. 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ON i ii i Q G Q O NNtotoroONrovotoNOroN ro 00 NO ^ ^ ON O E- < g -3 } o\*)o^ooao"oN < NOOoo-.io a ^ N 00 to 0* c" h. f ) "S "^ ^ S ^ * . ii':'' ;i|^ :fll jlfjlflf (Ijl Acapulco, Mexico, Vera Cruz, Mexico : .8 X U 8 X ^ A" I u u j a 5 1 2 * jfJi rt es ^ ill ^ u 2 118 TERRESTRIAL MAGNETISM. VO fOT^-iOOO M * O\ QQ \O N M M Qs^- 10 w^QO O^^O S 1 o _ COOOVO ^M 1-1 rotow O ONt^GO ro>H r-OO O\O O O N M -r-t--i--r-t--h-f + -f--h-f--h +..+ .4--+ .+ + 4- 4- 4- ^ rjC>Jtr>^-toQfOQCJ\Cy\'^-rovr>HHG\-icf5i-ioo a. TTTTTTTTTTTTiTTTTTTT i QQaQQQQQQQQQQQQQQQQQQ O ON t^ | ^j HHH^^HHHMHHhH^-(M^^l)-HMHH^^HHH4NHMH6) S ri J3 rOrOrOf^Tt-Tt-TtTj-Tj-T^-^Ttrj-iLOiOtouo^vO-. , 5 ^ 13 W ^ . . . . o . e te v 3 * * -2 -r . . -^ 3 ; ^1 1 - ! " ' ^ r ^ cf -73 0" 'o - - c -3 - : ' - c -3 - S T < ~ QUEEN" PRECISION LEVEL. A 1526. Price, $250.00 DESCRIPTION OF THE ENGINEERS' LEVEL. THE Engineers' Level consists essentially of a horizon- tally-directed telescope combined with a spirit-level parallel with it, and the whole suitably supported on, and capable of revolution about, a vertical axis. The telescope of the Engineers' Level is usually of a longer focus, of larger aperture, and of higher power than that of the transit. A full description of the optical characteristics of the telescope will be found in the article entitled " The Telescopes of Engineering Instruments" The cross hair-ring is usually provided with two threads, one horizontal and the other vertical, the ring being adjustable for the horizontality and verticality of these threads. Sometimes stadia wires are added for conveniently reading off distances on the rod. Fig. 50. The ocular slide, Fig. 50, is provided with a set of centering- screws accessible from the outside of the telescope. The process of centering the eye-piece can thus be accomplished with con- venience. The eye-tube is moved in and out by means of a smoothly-working screw adjustment, which obviates any dis- turbance of the telescope and permits the focusing on the hairs to be performed with great accuracy. 119 120 ENGINEERS LEVEL. The object slide is covered by a protector. The set of ad- justing screws at the middle of the telescope and accessible from the outside are intended for centering the object-glass . and its slide with respect to the mechanical axis of the tele- scope. A rack and pinion movement is attached to the object-slide Tind operated by a milled head placed near the middle qf the telescope. The sun-shade is an open brass cap supplied with every level and always to be used for the best results. The collars or rings fitting on the telescope-tube and sup- porting it when resting on the wyes, are usually about twelve inches apart. They are made of the hardest bell metal and very accurately turned to exactly the same diameter. The wyes upon which the collars rest are made of the best bell metal and shaped to precise similarity. They are each attached to the level-bar by means of two adjustable nuts. The telescope is held firmly in position by clips fastened by means of pins. In order to insure the correct position of the cross-wires a small projecting piece extends from the telescope and is brought in contact with a similar piece attached to one of the wyes. The level bar, made of the best bell metal, is usually of square cross-section, and has attached to its middle the inner axis or " centre " of the instrument. A vertical micrometer screw with graduated head is, in the finest grade of leveling instruments, attached to one end of the level-bar for the purpose of setting the bubble in refined work.* The centres, Fig. 51, are compound; the inner one attached to the level-bar is a long cone, of the hardest bell metal and held in place by means of the centre screw placed at its lowest ex- tremity ; the outer " centre " is made of hard red metal and fits into the socket of the leveling head. Both " centres " are accurately turned in the lathe between dead centres. The three metals used respectively for the inner centre, the outer centre, and the socket of the leveling head are selected so as DESCRIPTION OF THE 121 to secure the smallest coefficient of friction and great dura- bility. The clamp and tangent movement is attached to the inner 44 centre," and is of the same form as that supplied with QUEEN & Co.'s engineering transits. The leveling head has the usual plates and leveling screws, as shown in the foregoing section. It is usually clamped to the tripod head. The fine spirit-level, of about eight inches in length, is usually attached below the telescope, and furnished with adjusting screws which, at one end of the level tube, permit lateral or Fig- 51- horizontal motion, and, at the other end, vertical motion. In some forms of the leveling instrument it is found advantageous to place the spirit-level above the telescope. For a complete description of the spirit-level, its construction and theory, the reader is referred to the article of this Manual entitled " The Spirit-levels of Engineering Instruments" A reflector is sometimes attached for the purpose of allow- ing the position of the bubble to be read from the eye-end of the telescope, without change of position of the observer. If the spirit-level is below the telescope, the reflector is attached at the side ; if above the telescope, the reflector is mounted over it. 122 ENGINEERS LEVEL. The Forms of the Level range from the Simple Dumpy Level through various styles of the Engineers' Level to the higher types of the Precision Level. The following are taken as rep- resenting the chief classes : The Dumpy Level is a compact instrument possessing the smallest number of adjustments, and is hence least liable to derangement from rough usage. It is without wyes, and its telescope tube forms one rigid piece with the level-bar. Only the line of sight and the spirit-level are adjustable by the en- gineer. With intelligent usage, the- QUEEN & Co. Dumpy Level, made in a large and powerful form, is often capable of results equal to those secured by the more complicated wye level. The Architects' Level is a small "level of the wye form, fur- nished with a horizontal circle^ and hence adapted to many kinds of building and city work, One form of it, called the "Architect's Compass Level," i# fitted with a compass-box, in addition to the horizontal circle. The Engineers' Wye Level is the one we have taken as rep- resenting the general type in the foregoing description, and is made in several sizes and /orms. When furnished with a level mirror and a graduated mi- crometer screw for varying the inclination of the telescope with respect to the level axis, it is adapted to the higher methods of manipulation required in hydrographic and other precise work. The Precision Level, adapted to the highest grade of leveling, is furnished with the requisites for testing the performance of every feature, and for eliminating all forms of error, rt is provided with a finely-graduated horizontal circle, a vertical micrometer screw, having a graduated head ; a fine reversible spirit-level, and a telescope of the most accurate optical and mechanical construction. QUEEN" ENGINEERS' LEVEL. Price, $110.00. THE ADJUSTMENTS OF THE ENGINEERS' LEVEL. THE adjustments of an engineers' level may be conven- iently treated of under two heads: (i) The maker's adjustments, or those which the scientific maker gives the instrument in the course of its construction and testing ; and (2) The field adjustments, or those which require occasional verification by the engineer. THE SIAKER'S ADJUSTMENTS. It is necessary that the following conditions be realized in the construction and adjustment of a good level : (1) The lenses of the objective and of the eye-piece of the telescope truly centred in their respective cells. (2) The optical axis of the system of lenses coinciding with the mechanical axis of the tube, in all the relative positions of the objective and eye-piece, the lenses' remaining always at right angles to this axis. (3) The cross-hairs, during each observation in the common focus of the object-glass and eye-piece. (4) The cross- hairs truly centred with respect to the me- chanical axis of the telescope. (5) The collars truly circular and of exactly the same diameter. (6) The wyes of exactly equal shape. (7) The horizontal cross-hair (all other adjustments made) at right angles to the vertical axis of the instrument, and the vertical one vertical. (8) The line of sight at right angles to the vertical axis of the instrument, or coinciding with the axis of collimation. (9) The axis of the telescope level lying in the same plane as the line of collimation, or not " crossed " with respect to it. 123 124 ENGINEERS' LEVEL. (10) The axis of the telescope level parallel with the line of sight. (11) The telescope level of a sensitiveness corresponding to the magnifying power of the telescope. (12) The telescope level of equal sensitiveness throughout its entire scale. (13) The axis of the accessory levels, attached to the level- ing head, at right angles to the vertical axis of the instrument. This list is to be taken as but fairly representing the princi- pal adjustments to be accomplished by the maker. It is not intended to be absolutely exhaustive. THE FIELD ADJUSTMENTS. The following practical methods for detecting and correct- ing the errors of adjustment of the Engineers' Level are given for use in the field. An explanation of the nature of each error is incidentally embodied. There are but two principal adjustments to be verified by the engineer, viz. : that I. The sight-axis of the telescope and the axis of the tele- scope level parallel. II. The axis of the .telescope level at right angles to the vertical axis of the instrument. All other adjustments are subsidiary and accessory to these, and will be explained in their proper places. The sequence of these adjustments is, as here stated, in the case of any ad- justable wye level, like the Engineer's or Precision Level. The Dumpy Level, however, requires the converse order, as hereafter explained. First Adjustment : To make the line of sight parallel to the axis of the telescope level, This adjustment may be performed by two methods, each of which commends itself, under different circumstances. The first is called the Instrumental Method, because it depends only on manipulation of the instrument itself; the second, requiring also readings on the leveling rod, is called the Rod Method. THE Anjl'STMKNrs (>F TIIK 125 I. The Instrumental Method divides this adjustment into the two operations, (a) of bringing the line of sight into the geometri- cal axis of the rings or collars, and (/)) of making the axis of the telescope level parallel to the bottoms of the collars. As- suming that the rings are of exactly the same diameter, this indirect method of making the sight-axis and the level-axis parallel to the line joining the bottoms of the collars brings these axes parallel to each other. We may now briefly ana- lyze each of these sub-adjustments. (a) To bring the line of sight into tlie geometrical axis of tJic rings. DETECTION OF THE ERROR : Direct the telescope to as distant an object as may still be clearly defined. After loosen- ing the wye clips, carefully rotate the telescope upon the wyes and note whether the intersection of the cross-hairs remains on a given stationary point of the image. If the wires appear to move with respect to the image, the line of sight is not in the axis of the rings. The line of sight being determined by the optical centre of the objective and the point of intersection of the cross-hairs, both points should be brought into the axis of the rings, and in all conditions of use of the telescope re- main there. For a description of the centering of the tele- scope, the reader is referred to the article of this Manual entitled " The Telescopes of Engineering Instruments" It is now, in the first place, assumed that the optical centre of the objective is in the axis when the objective is in position for viewing a distant object. In the second place, the deviation of the line of sight during rotation of the telescope on the wyes is, therefore, due to the eccentric position of the intersec- tion of the cross-hairs. CORRECTION OF THE ERROR : Giving attention to each wire in turn, note the position of the rotated telescope, which gives the maximum deviation of the wire from the selected point of the image. Then by means of the proper set of capstan- headed screws of the cross-hair ring, bring each wire in turn half way back toward the point of .the image. Repeat until the centre of the cross-hairs remains accurately bisecting a 126 ENGINEERS' LEVEL. point of the image during a complete revolution of the tele- scope on the wyes. The centering of the objective slide is an accessory adjust- ment, and may be undertaken after the centering of the cross- hairs has been effected by the preceding method. It is only necessary to focus on a very near object by means of the slide, and then rotating the telescope in its wyes as before, correct half the deviation of each thread in turn by means of the slide- centering screws. See also the article on " The Telescopes of Engineering Instruments" already mentioned. (b) To make the axis of the telescope-level parallel to the bot- toms of the rings. DETECTION OF THE ERROR : Clamp the axis of the instru- ment, and carefully level, particularly with the pair of leveling screws lying parallel to the telescope. Now gently reverse the telescope end for end in the wyes, and note whether the bubble returns to the same central reading. If the bubble deviates from its original position, this deviation is double the error. CORRECTION OF THE ERROR : Correct one-half of the de- viation observed on reversal in the wyes by means of the ver- tical adjusting screws of the level-tube. Level again, and, as a check, repeat the operation. The crosswise position of the level, or the condition in which the level axis is not in the same vertical plane with the line of sight, is to be carefully avoided in connection with all adjust- ments and uses of the level. After every adjustment of the level-tube, careful examination should be made for the cross- ing. This condition is tested for by turning the telescope slightly on the wyes and noting whether the bubble still coA- tinues to remain central. If not, adjust by means of the lateral adjusting screws of the level-tube until, on rocking to and fro on the wyes, the bubble remains stationary. Compare the paragraph on " the crosswise position of the level " in the arti- cle of this Manual entitled " The Spirit-levels of Engineering Instruments." The importance of this adjustment lies in the fact that the error of crossing of the level may produce quite THE ADJl'STMKNTS OF THE 127 a material divergence of the line of sight from the horizontal direction, if the telescope happens to be turned slightly round in the wyes, oc if the instrument is not accurately leveled in the direction perpendicular to the line of sight. When, as in the Dumpy Level and in the Engineers' Transit, the telescope does not revolve in wyes about the line of sight, the following method, due to Helmert, may be used to detect and adjust for the crosswise position of the level axis. All other adjustments accurately made, set up the in- strument with the line of sight parallel to two leveling screws, and direct it to a rod placed at a distance of several hundred teet. Then, by means of the other set of leveling screws, slightly rotate the telescope about the line of the parallel set, at the same time that, by means of the parallel set, the level is kept to zero reading. The deviation of the line of sight thus caused and read off on the rod, will be a measure of the cross- ing error, provided allowance is made for the very small varia- tion in the height of the line of sight. The adjustment for the crossing is to be effected by means of the lateral adjusting screws of the level. The inequality in diameter of the rings may be found by means of a striding level which is read both in the direct and reversed positions on the rings, for each of the two positions of the telescope in the wyes, direct and reversed. The bubble movement, due alone to reversal of the telescope in the wyes, measures twice the inequality of the rings ; but the inequality, or angle at the apex of the arc formed, is also twice the angle made by the axis of the rings with the edge. Therefore, one- fourth of the bubble movement, due to reversal of telescope, equals the inequality of rings expressed in bubble divisions. This, multiplied by the angular value of a division of the level, gives the angular value of the inequality. If the instrument is properly made, the rings are so nearly of equal diameter that the assumption of equality required in the foregoing adjustment leads to errors quite inappreciable except in the highest class of work. II, The Rod Method requires the use both of the instrument' 128 ENGINEERS LEVEL. and of the leveling rod. and is frequently spoken of as the " peg adjustment." It has, in one form, been already described un- der the head of the " Fourth Adjustment" of the Engineers' Transit, and, as there given, is also applicable to the Engi- neers' Level. The rod method, being a direct one, and inde- pendent of the diameter of the rings, is of great practical im- portance, and is therefore here given in another form. DETECTION OF THE ERROR : Drive two stakes, several hun- dred feet apart, on nearly level ground. Set up the instrument successively in two symmetrical positions, as, Fig. 52, either in / and /, or in K and L, and near the rods. If we suppose the positions to be / and J y the eye-hole is to be brought very near the rod in setting up, and the height of the eye-end may then be found by looking through the objective, and with a sharp pencil point marking the centre of the small field upon the rod. If the positions used are K and Z, the readings on the rods near by are made through the telescope by moving out the focusing slide far enough to secure distinct vision. L BJ A Fig- 52. Letting e l equal the reading on the near rod for the instru- mental position either in /or in K, o^ the reading on the dis- tant rod for the sam position, c\ 2 the reading on the near r>d for the instrumental position either in /or in Z, o. 2 the reading on the distant rod for the same position, -|-/the elevation of A above B, and -\-d the upward deviations, as measured on the distant rod, of the line of sight from the axis of the level, we have the evident relations (2) THE ADJUSTMENTS OF THE 1 29 Whence, by simple elimination in (i) and (2), we easily find the following : % (*!+**) j('i + '2)=* (3) y 2 ( Oi _ ^ 2 )_ y 2 (V_ c , 2 )= / ( 4 ) Also from equation (2) we have o 2 d = e. 2 l (5) Equation (3) gives the upward deviation d, which, applied in (2), would give /. It is, however, convenient to use (4) to find /, and then use (5) as a check on the work. Example ^5.428 ft. ^=5.122 ft. ^2=5-175 " *2= Halfsums, 5.3015 5- 2 955 Half differences, 0.1265 0.1735 Whence d=o.oo6 and /=o.3OO Also, o 2 ^=5.169 and e 2 7=1:5.169 CORRECTION OF THE ERROR : With the instrument remain- ing in the last position namely, either in J or in L rset the target of the distant rod to the reading therefore equal to the arc PZ, or its equal, ME. ADJUSTMENT AND USE OF THE SOLAR TRANSIT. IT is, in the first place, implied that all the adjustments 01 the transit instrument heretofore described shall have been accurately made. In addition to these the two fol- lowing adjustments are to be accomplished. First Adjustment: To bring the "polar axis" at right angles to the line of sight and to the horizontal axis of the maiji telescope. This may be accomplished by leveling the whole instrument carefully, and after bringing the bubble of each telescope-level to its zero reading so adjust the screws at the base of the 44 polar axis " that a distant object may be simultaneously bisected in both telescopes. Another method for accomplishing the same adjustment is to bring the bubble of each telescope-level central as before and then by revolving the solar telescope around its polar axis, note whether its bubble remains central ; if so the polar axis is at right angles to the plane containing the line of sight and the horizontal axis of the main telescope. If the bubble of the solar telescope in revolving about the polar axis does not re- main central correct half the bubble displacement by means of the adjusting screws at the base of the polar axis, and the other half by revolving the solar telescope on its horizontal axis. Verify by repetition. The Second Adjustment : To bring the line of sight of the solar telescope parallel to the axis of its level. This may be effected by bringing both telescopes into the same vertical plane at the same time that ' oth telescopes are 143 !44 THE SOLAR TRANSIT. carefully made horizontal by means of their respective levels. Then measure the distance between the axes of the two tele- scopes and note whether the two lines of sight of the instru- ment include an equal space on a rod set at some distance from the instrument. If they do not, move the cross-hairs of the solar telescope until the space included between the lines of sight of the two telescopes as noted on the rod is the same as the dis- tance between the two axes of the telescopes as previously measured. METHOD OF USING THE SOLAR TRANSIT. The central principle to be applied in the use of the solar transit is the following : The attachment's axis, placed at right angles to the sight line of the larger telescope, can become a true polar axis only on two conditions : First, that the sight-line of the larger telescope lie in the plane of the celestial equator, and secondly, that this same sight-line and hence also the " polar axis " lie in the meri'dian. When the " polar axis " is a true one namely, lies in the me- ridian and is also at the elevation above the horizon equal to the latitude, the solar telescope may be revolved upon the polar axis in an east and west, or hour-angle direction and its line of sight thus, and thus only, brought upon the sun. Conversely, if the proper setting be made, first to the de- clination of the sun, and secondly to the co-latitude of the place, ME, Fig. 33, and the sun then brought into the centre of the field of the small solar telescope by simultaneously moving^the main instrument on its vertical axis and revolving the attachment on its " polar axis," this " polar axis," and hence also the l-ine of sight of the main telescope, must ha^e been brought into the meridian. I. DETERMINATION OF THE MERIDIAN. First, set the solar telescope to the declination of the sun by the following method. From the Nautical Almanac find the declination for the day and hour of the observation and apply the correction for refraction as explained later. Then incline the THE SOLAR TRANSIT. 145 main telescope downwards from a horizontal position through this corrected declination angle if the sun is nortJi of the equator, or incline it upwards if the sun has a south declination. Clamp the main telescope in this position and then make the solar telescope horizontal by means of its attached level. The solar telescope will thus have been elevated or depressed through an angle from its parallel position with the main tele- scope equal to the corrected declination angle. Clamp the solar telescope on its horizontal axis. Secondly, find the co-latitude of the place of observation, if it is not known, by the method given below, and then elevate the line of sight of the main telescope through this angle of the co-latitude by means of the vertical circle of the instru- ment. Thirdly, by simultaneously revolving the transit on its ver- tical axis, and the solar attachment on its polar axis, bring the sun accurately into the centre of the field of the solar tele- scope, and the line of sight of the main instrument must con- sequently lie in the plane of the meridian of the place. The direction of this meridian may then be readily staked off on the ground, or the declination of the magnetic needle may at once be read off. The time of day giving the best results in the use of the solar transit is from 7 to 10 A. M. and from 2 to 5 p. M. Earlier than 7 A. M. and later than 5 p. M. refraction introduces un- certain errors. Between 10 A. M. and 2 p. M. errors in declina- tion or in latitude greatly affect the azimuth. Since the hour angle has different signs before and after noon, the azimuth error also changes sign, and the azimuth error due to errors in declination and in latitude are best eliminated by taking the mean of two observations made at the same hour angle, one before and the other after noon. II. DETERMINATION OF THE LATITUDE. After carefully leveling bring the line of sight of the solar telescope into the same plane with that of the main telescope. Clamp the solar telescope upon its polar axis. Now set off the sun's declination for noon by the method 146 THE SOLAR TRANSIT. already described under " Determination of Meridian." Clamp the solar telescope upon its horizontal axis. Then, about ten minutes before the culmination of the sun, begin observation for latitude by elevating the main telescope and moving it in azimuth until the sun is seen 'in the solar. By means of the azimuthal tangent-screw and the vertical tangent-screw of the main telescope keep the sun in the centre of the field of the solar until the sun begins to lessen its altitude. Read off the altitude of the vertical circle of the instrument and this will be the co-latitude, excepting the correction for refraction and instrumental errors. The correction for refrac- 'tion for the given altitude may be taken from the " Table of Mean Refraction " at the end of this Manual. Since the effect of these instrumental errors on the " determination of the me- ridian " is eliminated by using the value of the co-latitude directly determined by means of the instrument, it is usually preferable to employ this value. III. DETERMINATION OF THE TIME. The solar attachment sometimes has a small hour-circle attached to the polar axis, in which case the apparent time may at once be read off as an hour angle of the sun from the meridian. This apparent time must then be corrected by ap- plying the equation of time as given in the Nautical Almanac. If no hour circle is attached the time may be found imme- diately upon getting the meridian by clamping both the verti- cal axis of the main telescope and the polar axis of the solar, and then turning each of the telescopes down on their horizon- tal axes until they are level and measuring the angle between the two directions. This angle converted into time will be the apparent time, which must, as before, be corrected for tfte equation of time in order to get the mean time. THE CORRECTIONS FOR HOURLY CHANGE AND REFRACTION. The hourly change of the declination is readily applied. The solar ephemeris of the" Nautical Almanac gives the declinations of the sun for Greenwich mean noon of the THK SOLAR TRANSIT. l ^j date. According as we use " Eastern," " Central," " Moun- tain," or " Western" time, we are approximately 5, 6, 7, or 8 hours west of Greenwich, and the declination of the sun for Greenwich mean noon as given by the ephemeris is therefore the declination at our station for the same date, but either for 7, 6, 5, or 4 o'clock A. M. Knowing then the declination for a given hour, we find the number of hours elapsing between that hour and the time of the observation, and multiplying the hourly change by this number, apply the result with proper sign to the tabular dec- lination. If the standard time differs considerably from the local time the known longitude of the place west from Green- wich may be used where extreme accuracy is required. The Refraction Correction, whenever the altitude of the sun is known, can easily be taken from the " Table of Mean Re- fraction" placed among the tables at the end of this Manual. When an observation is to be made out of the meridian, as is usually the case with the solar transit, the refraction correc- tion to the declination varies, not only with the declination but also with "the hour angle of the sun and with the latitude of the place. The correction may then readily be computed according to the following formula, whose equivalents are de- rived in cxtenso in works on practical astronomy. If we let A 7 be an auxiliary angle such that Tan. .V = Cot. cos. /, where $ is the latitude and / the hour angle, the refraction correction to the declination, C r is where o equals declination, and is plus or minus when the sun is respectively north or south of the equator, and A r is deter- mined by the preceding formula. Tables for a day's work at the given latitude of place and for given hour angles and dec- linations of the sun can be readily prepared in advance by means of the latter formula. THE STADIA AND THE GRADIENTER. A DISTANCE-MEASURER is an instrument furnished with devices for determining distance from a single point of observation. The Germans call such an instrument a distanzmesser, and the French designate it a telemeter. The term tachymeter has come to be used in Germany and else- where for an instrument which, in addition to the features of an engineer's transit, also possesses those of a distance- measurer or telemeter. Two kinds of distance-measurers are in use. The first class possesses in itself some line which is in fact the base of the triangulation. The military distance-measurers are of this class, and often consist of two telescopes mounted on the same base, and about a meter apart. The second class is charac- terized by measurements made upon a rod held at the point whose distance is to be determined. This is the only distance- measurer considered in engineering other than military, and we therefore limit ourselves to a review of this class, or to the distance-measurer proper. The simple basis of all distance measurements with the rod lies in the principle that the same object at a great distance subtends a less angle than when near at hand, or that the same angle intercepts more, say of a rod, in proportion as the dre- tance increases. The forms of distance-measurers are really quite numerous, if we would include all the European types. It is, however, here only necessary to speak of (i) The Vertical Circle as a distance-measurer ; (2) The Screw distance-measurer, or Gra- dienter. and (3) The Thread distance-measurer, or Stadia wires. I. The Vertical Circle of an engineer's transit or any other 148 THE STADIA AND THE GRADIENTER. 149 means for measuring vertical angles, can be used for deter- mining distance as follows : Fig. 34. Let PL represent a rod, to two points, P l and P 2 of which the line of sight is successively directed, and the altitudes a and 3, respectively, of the points measured. Let P 1 P 2 in Fig. 34 = a, and P 2 fi = b, and hence P^H = a -j- b, and let the dis- tance IH = D. Then we have : whence, a -f- b = D tan. a, and b = D tan. / /7 (I) tan. a tan. /? or, for logarithmic calculation, D=. a cos. a cos. /? (2) sin. (a ft) Formulae (i) and (2) permit the distance to be computed in terms of an intercepted length on the rod, and of two meas- ured angles. Incidentally it lies very near to call attention to the fact that if heights instead of distances are required, the following formulae result as convenient for logarithmic calculation : a cos. sin. 3 sin. ( ft) _ a sin. cos. sin. ( 3) (3) 150 THE STADIA AND THE GRADIENTER. These formulae possess, as suggested by Dr. Jordan, some decided advantages as a rapid means of leveling over a rough country, where the computations become a secondary matter. THE GRADIENTER. II. The Gradienter is next to be described as a means for distance-measuring. It consists of a finely-cut screw, which takes the place of the vertical tangent screw, and moves the clamping-arm attached to the horizontal axis. It acts against a strong spring, so as to produce positive motion of the arm in either direction. The screw has attached to it a graduated silvered head with fifty equal divisions. Parallel to the screw there is attached a graduated scale, which indicates the com- plete revolutions of the screw. The whole revolutions of the screw are thus read off on the parallel scale, and the parts of a turn on the graduated head. The distance between the threads of this screw is such that a single revolution causes the horizontal cross-hair of the telescope .to appear to move over .01 foot of the rod for one division, of the gradu- ated head when the rod is at'a distance of 100 feet from the instrument. This screw has two chief uses, namely: (i) that of establishing grades, and (2) that of measuring distances. Grades may be laid off by first taking the reading of the gradienter when the telescope is level, and then allowing I foot per loofor each division of the graduated head, set off to the desired grade. For instance, to set off a grade of 3.45 feet per 100 feet, it is necessary to move the gradienter 3.45 revolutions of the screw. A grade may be measured by finding the reading of the gradienter when the telescope is level, and then turning the graduated head until the line of sight points in the proper THE STADIA AND THE GR ADI ENTER. 151 direction, read the number of revolutions and fraction of a revolution, and this number will be the grade in feet per hun- dred. Distances may be measured either (i) by observing the dis- tance on the graduated rod passed over by one revolution of the screw, or (2) by taking an assumed length on the rod and finding the difference of readings for this length. In the latter method, IOO times the assumed length on the rod divided by the difference of readings equals the distance away of the rod, GRADIENTER WITH LINE OF SIGHT INCLINED. It is assumed that the rod is always to be held vertically. The use of the rod at right angles to the line of sight is con- sidered to introduce additional trouble and error. R Fig. 36. The theory of the use of the gradienter for inclined sighting may be readily inferred from Fig. 36 : Let IH ' = D = Horizontal distance of the point. IP = D x = Direct distance of the point. PO = r = Length of the vertical rod included by the angle /. PR = r t = Length of inclined rod included by the angle /. Then D tan. ( + >) = /? tan. a + r. (i) or D=- tan. (a tan. (2) 152 THE STADIA AND THE GRADIENTER. whence, by development and transformation, D = r (cot. 7 cos. 2 a sin. a cos. a) (3) and, finally, D = r (cot. y cos. 2 a ^ sin. 2 ) (4) Dividing (3) by cos. a we get i D l = r (cot. 7 cos. sin. a) (5) If, in the second terms of equations (4) and (5) we add and subtract r cot. 7, we get the following forms, which, involving only the sine, are adapted to accurate computation : I) = r cot. 7 r (cot. y sin. 2 a + ^ sin. 2 ) (6) Z?j = r cot. 7 r (cot. 7 2 sin. 2 ^ a + sin. a) (7) The latter formulae (6) and (7), although frequently used, do not give the tabular factors in quite as convenient a form as formulae (4) and (5). If we let cot.7 100, the value usually adopted in QUEEN & Co.'s gradienters, and also let 100 cos. 2 a. y^ sin. 2 a = F and 100 cos. a sin. a = F lt the formulae (4) and (5) assume the form D = rF' that is, simple multiplication of the difference of two readings on the rod, r, by the proper factor, gives either the horizontal distance, or the direct distance, as desired. The values of F and F l are given in Tlie Gradicnter Table at the end of this Manual. THE STADIA METHOD. III. The Stadia wires, so-called, are inserted in the common focus of the objective and eye-piece. The accompanying figure will show the arrangement of the wires, the three hori- zontal being used for stadia purposes. The distance between the central and lower or upper one may sometimes be con- THE STADIA AND THE GR ADI ENTER. 153 veniently used instead of the distance between the upper and lower. In many instances the wires are made adjustable so that they may be set for a distance of a hundred feet from the front focus of the objective. In QUEEN & Co.'s instruments the upper and lower wires are simultaneously adjustable from the central wire by means of the movable pieces Fi marked a a in the figure. THE OPTICAL THEORY OF THE STADIA. If a Ramsden's ocular or its equivalent is used, the rela- tions between the factors may be diagrammatically represented by the accompanying figure in which represents the objec- tive of the telescope, E the eye-piece, iv the interval between the wires, r the length intercepted on the rod by the wires,/ -D * d -t Fig. 38- the focal length of the object glass, D the distance of the rod from the objective, Df the distance of the rod from a point in front of the object glass equal to the focal length /, d the distance of the wires from the objective. Then from the prin- ciples of optics we have : - f D, and from the figure we have by similar triangles; 154 THE STA DIA AND THE .GRADIENTER. w r , s 7 = A < 2 > From the equations (i) and (2) we readily derive the follow- ing : *-/ = r (3) or D f =r-f- r w Accordingly D /y or the distance of the rod from the front focus is p/oportional to the length, r, intercepted on the rod. It is to be particularly noted that this distance D f and no other is the one to which the intercepted rod readings, 1-, are proportional. It is not worth while here to indicate the special modifica- tions of this simple theory, necessary to adapt it to the cases of the Huyghenian eye-piece, or that of the Porro eye-piece, the' 'latter having been specially designed to make the intercept on the rod proportional to the distance of the rod as measured from the centre of the instrument. If now we let D c equal the distance of the stadia rod from the centre of the instrument and d equal the distance of the objective from the centre of the instrument when the telescope is focused for the average of distances, we have : D c == D + 3, and inserting the value of D from equation (3), we have : D c =f+B + {-r (4) where/-f o is a constant peculiar to the particular instrument. Therefore, letting c f-\- d, D c = c+l-r (5) W Further -is the coefficient of the instrument depending THE STADIA AND THE GRAD1ENTER. 155 upon the focal length of the objective and the distance apart of the wires, and therefore letting K = equation (5) now becomes, whence DC = c 4- Kr D c= (6) (7) PRACTICAL DETERMINATION OF THE STADIA CO-EFFICIENT. As a practical illustration of the formulae last found, the following example is added : Determine c =/+ d by actual measurement of /and of d. Let, for example, c= 1.5 'feet. Then measure .1.5 feet from the plumb-line, depending from centre of instrument, and mark it by a stake. This stake will be f in front of the objective. Call this point so marked A. From A measure and stake off the 50 foot point, the 100 foot point, 150 foot point, 200, 250, etc., to 500 or 1,000. D c being the whole distance from centre of instrument, and c the distance of stake A, each of the measured distances 50 feet, 100 feet, etc., beyond A represents D c c in formula (5), while r represents the particular rod reading for each case. The following represents a number of rod readings at D c c distances. Five independent readings are taken for each point : Dc c Feet. (i) 50 0.501 IOO 150 I.OOO 1.501 Rod Readings. (2) (3)" (4) (5) 0.501 0.501 0502 0.500 I.OOO I.OOO 1. 001 1.002 1.503 1.501 1.500 1.502 Dcc Mean R. - Feet. 0.5010 99.804 1.0006 99.940 1.5014 99.907 200 2.005 2.007 2.002 2.005 2 .005 2.0048 99761 4)399-412 Practically, 99.85 = K. 99.853 = In the QUEEN & Co. instruments K is usually made equal to 100. Since this factor K, multiplied into r, gives the D } 156 THE STADIA AND THE GRADI ENTER. distance and not the D e distance desired, the following method of adjusting the wires may sometimes be advantageously adopted. The formula (6) may be written in the form : Now if h K be made equal to 100, the readings of the rod mentally multiplied by IOD, would give the distance from the centre of the instrument. Accordingly we must take, K= 100 For example let r= 1.5 feet corresponding to 1 50 feet as the average of distances it is desired to measure. Then K= 100 = 99, and D c loor, as desired. STADIA WITH INCLINED LINE OF SIGHT. The use of the stadia, as thus far explained, is adapted only to horizontal sighting. If the line of sight is inclined to the horizon, the rod-reading becomes greater, and varies with the inclination. The general formulae for any case may be derived from the accompanying figure, in which a represents the angle of elevation or depression, r the intercepted portion of the rod when held vertical ; and hence, r cos. a the intercepted portion Fig. 39- of the rod when held at right angles to the direction of the line of sight. IP or direct D c> equals the direct distance, arid THE STADIA AND THE GRADIENTS!*. 157 IQ, or horizontal D Ct equals the horizontal distance. But, evidently, for direct distance from the front focus we have: D/= Kr cos. a Whence, Direct Distance = IP = c + Kr cos. a (8) Horizontal Distance = IQ = c cos. + Kr cos. 2 # (9) and Difference of Level = PQ = c sin. -f- /4 Kr sin. 2 (10) These formulae very closely approximate to the strictly mathematical conditions. A very small error is committed in assuming that r cos. a represents the intercepted portion of the rod when the rod is held at right angles to the line of sight, since the rod is not within a few minutes of arc of 90 to PR and PS. Again, for 77) the horizontal distance to the foot of the rod, 7*5" sin. a would have to be added or subtracted, ac- cording to the inclination of the rod. But this also is small enough to be omitted in ordinary work. The formulae (9) and (10) are the practical general formulae for the stadia, giving respectively the horizontal distance and the difference of level. The most complete tables adapted to these formulae are the " Hulfstafeln fur Tachymetrie" by Dr. W. Jordan. The use of these tables obviates all inconvenient arithmetical operations or the study of complicated reduction diagrams ; and the heights and distances can, for ordinary accuracy, be directly taken from the tables, without interpolation. QUEEN & Co. furnish a special translation of the introduction to this work, and an adaptation of the tables to convenient use with any of their instruments. 158 TABLES. OR ADI ENTER TABLE. o w o c e y I * i s 1 ll .5 s i 2a I & g J) f u^- tT~ 2 1 ^ fa~Q 1 Ctf " o SO** o *j S e J3 | S fi *5b 8 O U u 8ti< VT u M ui o o o iJ 1 8 Q c o fc o ffi o ^Q o / \ o / OO OO IOO.OO IOO.OO 15 oo 93.05 96.33 o 30 99.98- 99.99 15 30 92.60 96.09 I 00 99-95 99-97 16 oo : 92 14 9585 I 30 99-90 99-94 16 30 91.66 0560 2 00 99-84 99.90 17 oo 91.17 95-34 2 30 99-76 99.86 17 30 90.67 95-7 3 99.67 99.81 18 oo 90.16 94.80 3 30 99-57 99-75 18 30 89.63 94-51 4 oo 99-44 9969 19 oo 89.09 9423 4 30 99.21 99.61 19 30 88.54 93-93 5 oo 99-15 99.53 20 00 87.98 93-63 5 30 98.98 99-44 2O 30 87.42 933 2 6 oo 98.80 99-35 21 00 86.82 93-0 6 30 98.60 99.24 21 30 86.22 92.67 7 oo 98.39 99.13 22 00 85.62 92-34 7 30 98.16 99.01 22 30 85.00 92.00 8 oo 97.93 98.89 23 oo 84.37 91.66 8 30 97.67 98.75 23 30 83-73 91.31 9 oo 97.40 98.61 24 oo 8308 90.95 9 30 97.11 98.46 24 30 82.43 90.58 IO OO 96.81 98-31 25 oo 81.76 90.21 10 30 96.50 98.14 25 3 8 1. 08 89-83 II 00 96.17 97-97 26 oo 80.39 89.44 II 30 95.83 97-79 26 30 79-69 89-05 12 OO 95-47 97.61 27 oo 78.98 88.65 12 30 95-10 97-41 27 30 78.27 88.24 13 oo 94.72 97-21 28 oo 77-54 87.82 13 30 94-32 97.00 28 30 76.81 87.40 14 oo 93-93 96.79 29 oo 7607 86.98 14 3 9349 96-56 29 30 75-32 86.54 15 oo 93-05 96.33 30 oo 74.56 86.10 NOTE. The difference of the rod-readings r, for loo divisions of the graduated head of the Gradienter screw, multiplied by f\ gives the horizontal distance of the rod from the horizontal axis of the telescope ; the same r, multiplied by F^ gives the direct distance. TABLES. 159 TABLE OF MEAN REFRACTION. Temperature, 50 F. Barometric Pressure Reduced to 50 /"., jo in. Apparent Altitude. I Mean Appirent \ Refraction. Altitude. I 1 Mean Refraction. Apparent Altitude. Mean Refraction. ooo" 33 / 47-9 // i6oo / 3' 20.8" 41 oo' i 7 07.0" I OO 24 22.3 17 oo 3 08.6 42 oo i 04.7 2 00 18 23.1 18 oo 2 57-7 43 oo j i 02.5 3 oo 14 28.7 19 oo 2 47-8 44 oo i 00.3 4 oo II 48.8^ 20 00 2 38.9 45 oo o 58-3 5 oo 9 54.8 21 oo 2 30.8 46 oo o 56.3 6 oo 8 30-3 22 OO 2 23.4 48 oo o 52.5 6 30 7 55-9 23 oo 2 16.6 50 oo o 48.9 7 oo 7 25.6 24 oo 2 IO.3 52 oo o 45-5 7 30 6 58.7 25 oo 2 04.5 54 oo o 42.3 8 oo 6 34-7 26 oo I 59-0 56 oo o 39-3 8 30 6 13.2 27 oo I 54.0 58 oo o 3 6 -4 9 oo 5 53.7 28 oo I 49-3 60 oo o 33 7 93 5 36.0 29 oo I 44-8 62 oo o 31.0 10 00 5 20.0 30 oo i 40.7 64 oo o 28.4 10 30 5 05.4 31 oo I 36.8 66 oo o 26.0 II 00 4 5i-9 32 oo i 33-1 69 oo o 22.4 ii 30 4 39-5 33 i 29.6 72 oo o 19.0 12 OO 4 28.1 34 oo i 26.2 75 oo o 15.6 12 30 4 17-5 35 oo i 23.1 78 oo o 12.4 13 oo 4 07.7 36 oo I 20.1 80 oo o 103 13 30 3 58.5 37 oo I 17.2 83 oo o 07.2 14 oo 3 So.o 38 oo I H5 86 oo O 04. T 14 3 3 42.o 39 oo i ii 9 89 oo O OI O 15 oo 3 34-4 40 oo i 09.4 90' oo o oo.o THE SEXTANT. THE Cut shows the details of construction of the Sextant. ABC is a light frame work of brass in the shape of a sector of 60 degrees, the limb AB having a graduated arc of silver (in some cases of gold) inlaid in the brass. It is held in the hand by a small handle at the back, either ver- tically to measure the altitude of an object, or in the plane passing through two objects, the angular distance of which is to be found. CD is a radius movable around C, where a small plain mirror of silvered plate glass. is fixed perpendic- ular to the plane of the sex- tant and in the line CD. At D is a vernier read through a small lense, also a clamp and a tangent screw which enable the observer to give the arm CD a very slow motion within certain limits. At E is another mirror " the horizon glass." Also, perpendicular to the plane of the sextant and parallel to CD, F is a small telescope fixed across CB, parallel to the plane CAB, and pointed to the mir- ror E. Dark glasses can be placed outside E and between E and C when observing the sun. As only the lower half of E is silvered, the observer can ^ee the horizon in the telescope through the unsilvered half, while the light from the sun on a start 6* may be reflected from the ' ' index glass " C to the silvered half of E and thence through .Fto the observer's eye, If CD has been moved so as to make the image of a star or of the limb of the sun coincide with that of the horizon, it is easy to see that the angle SCH (the alti- tude of the star or solar limb) is equal to twice the angle BCD. 1 60 THE SEXTANT. l6i The limb AB is graduated so as to avoid the necessity of doubling the measured angle, a space marked as a degree on the limb, being in reality only 30'. The vernier should point to o c' c ' when the two mirrors are parallel, or, in other words, when the direct and reflected images of a very distant object are seen to coincide. When the sextant is used on land an artificial horizon is re- quired. This is obtained by employing a basin of mercury protected by a roof of plate glass with perfectly parallel faces, which is levelled on three screws by spirit levels. The telescope being directed to the image, the celestial object reflected from the artificial horizon and this image is made to coincide with that reflected from the object glass. In this case the angle BCD will be double the altitude of the star. THE ANEROID BAROMETER. THE word Aneroid, from the Greek privative a y and neros wet, suggests the character of this instrument, whose indications are obtained by the pressure of the atmos- phere upon a delicate metal box, exhausted of air, instead of, as in the Mecurial Barom- eter, by the height of a fluid column. Invented about the be- ginning of the present cen- tury, it was not until about 1848 that the difficulties in- volved in the construction of such an instrument were overcome, and the present serviceable form devised by M. Vidie. Since that time, the Aneroid has continued substantially the same ; improvements being rather in the direction of more perfect workmanship in its parts, and in the more perfect adaptation of its metals, than in any change of form. As shown in the illustration, the Aneroid consists of a flat cylindrical vacuum box, the upper surface of which is cor- rugated, in order that it may yield more readily to external pressure. The lower surface of the vacuum chamber is firmly fixed at the center to a strong foundation plate, -whilst at the center of the upper surface is a metallic pillar C, which acts upon a powerful steel spring D. The varying atmospheric pressure causes the surface of the vacuum chamber to rise and fall ; these movements are trans- mitted to the spring, and thence by two levers, G and H, to a metallic axis /. From the latter rises a lever/, to whose ex- tremity a chain Q is attached, which turns a drum, the axis of which bears the index needle. A firm spiral spring keeps the chain constantly in proper tension. By this arrangement of 162 TIIK ANERIOD BAROMETER. 163 multiplying levers, a very small movement of the surface of the vacuum chamber causes a large deviation of the needle ; of an inch causing it to move through a space of 3 inches. Fig. A. Figure A shows a section of the vacuum box ; B being the pillar to which the main-spring is attached ; L the attachment to foundation plate ; D the tube through which the box is ex- hausted, and a, a, a, a, the overlapping thin German silver corrugated plates. Fig. B. In figure B, we have the chamber exhausted of air ; the dotted lines showing the tension to which the instrument is brought, and enabling it to be understood how readily the in- strument may respond to the varying atmospheric pressure. Compensation for temperature is effected, as in chronometers, by an adjustment of brass and steel in the main lever, by whose unequal expansion and contraction the liability to error from change of temperature is overcome. The dial is graduated arbitrarily to correspond with the mer- curial barometer, after the instrument is tested under the air- pump to find the range. It is apparent, therefore, that the Aneroid can never be used as an independent standard, but must be frequently compared with the mecurial barometer. 1 64 THE ANEROID BAROMETER. When so compared, however, and adjusted by a Mercurial Standard, the Aneroid possesses several advantages over the former. It is extremely portable and can be carried in any way, or subjected to any motion without danger of disturbance of its indications. It is not at all liable to get out of order is not easily broken, and lastly, it is very much more sensitive than the Mecurial Barometer. The late Admiral Fitzroy, Mr. Glaisher the aeronaut, and many other authorities, testify to the extreme sensibility of the Aneroid ; the former particularly noting ' ' its quickness in showing the variations of atmospheric pressure." Kven in observatories, therefore, where Mercurial Standards are in use, the Aneroid is most valuable in its capacity of giving earlier indications than can be obtained from the more sluggish mer- curial column. To the seaman, who has often extreme difficulty in using the barometer from the pumping of the mercury caused by the vessel's motion, the Aneroid is indispensable ; and from its greater delicacy, he can often prepare for a change in weather a considerable time before the Mercurial Barometer gives evi- dence of an impending storm. The value of the Aneroid in ascertaining differences of alti- tude, is obvious, and of this we speak more fully in the suc- ceeding pages. THE USE OF THE ANEROID FOR ALTITUDE. From its portability, sensitiveness, and the ease with which approximate altitudes may be ascertained, the Aneroid Barom- eter is very valuable to the engineer. In preliminary surveys and reconnoissances it has been found extremely useful, and for these purposes it is largely employed. Carrying one of these little instruments, the size of which need not exceed two or three inches in diameter, the engineer, riding rapidly over a country, can speedily and with ease procure the data for the determination of the line of a survey. Holding an Aneroid in his hand, the traveller seated in the railroad car, can mark the changes of elevation as his train moves ; the mountain climber can note, step by step, his gain in altitude ; and the miner, with the new mining Aneroid, can measure his descent in single feet. THE ANEROID BAROMETER. 165 We have elsewhere explained the principle of the Aneroid, and the manner in which its indications are obtained, and have referred to the necessity of accurate workmanship in its con- struction, and of intelligence and skill in its examination and adjustment. For hypsometrical work, it is especially im- portant that the Aneroid should be absolutely accurate ; that its compensation for effect of temperature on the metallic works be perfect, and that its indications should be identical with those of the mercurial column. The importance of compensa- tion, particularly for Pocket Aneroids, is evident when it is remembered that the change from a room to the external atmos- phere may frequently involve a difference in temperature of from 30 to 50 F., a difference, which, without proper com- pensation, may move the needle through a space equal to one hundred or more feet. It is also necessary that the Aneroid be tested for correspondence with the mercurial column. If the scale of the Aneroid be accurately divided and in accord with the instrument itself, the needle will move tenth by tenth, with the mercurial column, in perfect coincidence. There are many good-working Aneroids in use, which do not thus correspond with the Mercurial Barometer, and whose constants of error being unknown, give inaccurate results. Such barometers could be used with satisfaction if their correc- tions were known ; and all Aneroids require to be periodically tested adjusted to accord with the Standard Mercurial Barom- eter, and their corrections, if any are necessary, ascertained. CORRECTIONS DEPENDENT UPON PHYSICAL LAWS. In strictly accurate observations, it is necessary that the Aneroid, as well as the Mercurial Barometer, should be used with formulas for various corrections. The corrections, how- ever, for gravity, for temperature of the mercury, and for capillary attraction are of course unnecessary with the Aneroid; and. indeed, for all ordinary work, the only correction required is that for the temperature of the atmosphere, \vhich need only be considered when the temperature is above or below 50 F. It must of course be remembered, in using a barometer of any kind for the purpose of ascertaining the altitude of a place, that while the normal barometric pressure is assumed to be 1 66 THE ANEROID BAROMETER. represented by a mercurial column of about 30 inches at sea- level, it is but occasionally that this is actually attained. The variations of atmospheric pressure are continual, the periodic fluctuations being considerable, and the nonperiodic oscilla- tions so great and so irregular, that it is only by taking the mean of a long series of observations that the periodical varia- tions can be ascertained. It follows, therefore, that a single reading of the barometer can never, save by the rarest chance, indicate an absolute elevation. Aneroids for altitudes may be used with the ordinary scale of inches and tenths, or, as they are now more usually arranged, .with a graduated circle of feet in addition. TO MEASURE ALTITUDES WITH ANEROID BAROMETER, Without Altitude Scale. Roughly speaking, the barometer falls one inch for every 900 feet of ascent ; or at mean atmospheric pressure in this latitude. Above sea -level 917 feet, the barometer falls . . . . i inch. 1860 " " " .... 2 inches. 2830 " " 3 " 3830 " " " 4 " 4861 " " 5 " TO FIND THE RELATIVE HEIGHT OF TWO GIVEN PLACES. Take a reading of the Aneroid at first station ; subtract from this the reading at the second station. The product multiplied by 9 will give the difference of altitude in feet, thus ; First Station, . . . . . 30 20 Second Station, . . . . . 29 99 21 9 Difference of altitude, . . . 189 feet. THE ANEROID BAROMETER. This under ordinary pressures and with a temperature about 50 K. will give good results. If the temperature is over 70^ F., multiply by 10. The table prepared by Mr. Symons is more strictly accurate: Mean Temperature. 30 40 50 60 ?o 80 Mean pressure, 27 inches. 28 " 11 " 29 " 30 9-7 9-3 9.0 8.7 9.9 9-5 9.2 8.9 10. 1 9.8 9-4 9.1 10.3 10. 9.6 9-3 10.5 10.2 9 .8 9-5 10.8 10.4 10. 9-7 The best results may, however, be obtained by the use of the table prepared by Sir G. Airy, late Astronomer- Royal of England. TO USE AIRY'S TABLE, With mean temperature at 50. Take the reading in inches of the barometer scale, at the lower and upper stations. Find in the table the heights in feet, corresponding to the barometer readings. Subtract them and the remainder will be the height required. When the mean temperature is above or below 50 F., the following correction must be applied : add together the temp- erature of the upper and lower stations . If the sum is greater than 100 F., increase the height by yoW^ P art for ever 7 degree of the excess above 100 ; if the sum is less than 100, diminish the height by 1 ^ 6 th part for every degree less than. 1 00. The complete formula is : T and t are the observed temperatures ; H and h are the heights in feet taken from the table. 1 68 TABLES. AIRY'S TABLE. Arranged for temperature of 50 F. Height Aner id or Height Aneroid or Height Aneroid or Height Aneroid or i Corrected in Corrected in Corrected in Corrected feet feet. feet. feet. Barometer Barometer. Barometer. Barometer. ft. in. ft. in. ft. in. ft. in. o 31-000 1850 28-966 3700 27-065 15550 25-289 50 30-943 1900 28-913 3750 27-015 5600 25-242 100 30-886 1950 28-860 3800 26-966 5650 25-196 150 30-830 2000 28-807 3850 26-916 5700 25-I50 200 30-773 2050 28-754 3900 26-867 5750 25-I04 250 30-717 2IOO 28-701 3950 26-8I8 5800 25-058 300 30-66I 2150 28-649 4000 26-769 5850 25.012 350 30-604 22OO 28-596 4050 26-720 5900 24-966 400 30-548 2250 28-544 4100 26-671 5950 24-920 450 30-492 2300 28-491 4150 26-622 6OOO 24-875 500 30-436 2350 28-439 42OO 26-573 6050 24-829 550 30-38I 2400 28-387 I4250 26-524 6lOO 24-784 6OO 30-325 2450 28-335 J4300 26-476 6150 24-738 650 30-269 2500 28-283 I 4350 26-427 6200 24-693 7OO 30-2I4 2550 28-231 4400 26-379 6250 24-648 750 30-I59 26OO 28-180 4450 26-330 6300 24-602 800 30-I03 2650 28-128 45oo 26-282 6350 24-557 85-0 30-048 27OO 28-076 4550 26-234 6400 24-512 9OO 29-993 2750 28-025 4600 26-I86 6450 24-467 950 29-938 2800 27-973 14650 26-138 6500 24-423 IOOO 29-883 2850 27-922 47oo 26-090 6550 24-378 1050 29-828 29OO 27-871 4750 26-042 6600 24-333 1 100 29-774 2950 27-820 4800 25-994 6650 24-288 1150 29.719 3000 27-769 4850 25-947 6700 24-244 I2OO 29-665 3050 27-718 4900 25-899 6750 24-2OO 1250 29-610 3100 27-667 4950 25-852 6800 24-I55 1300 29-556 3150 27-616 5oo 25-804 6850 24-III I35C 29-502 3200 27-566 5050 25-757 6900 24-067 1400 29-448 3250 27-5I5 5100 25-710 6950 24-023 1450 29-394 3300 27-465 5150 25-663 7OOO 23-9791 1500 29-340 3350 27-4I5 5200 25-616 7050 23-935 1550 29-286 3400 27-364 5250 25-569 7100 23-891 1600 29-233 3450 27-3I4 5300 25-522 7150 23-847 1650 29-1/9 3500 27-264 5350 25-475 72OO 23-803 1700 29-I26 3550 27-214 5400 25-428 7250 23-760 1750 29-072 3600 27-164 5450 25-382 7300 23-716 I800 29-OI9 3650' 27.115 55oo 25-335 7350 23-673 1850 28-966 3700; 27'065 :555o 25-289 Ij 7400 23-629 TABLES. AIRY'S TABLE Continued. 169 Heigh in feet. Aneroid or Corrected Barometer. Height in feet. Aneroid or Corrected Barometer. Height in feet. Aneroid or Corrected Barometer. Height in feet. Aneroid or Corrected Barometer. ft. in. ft. in. ft. in. ft. 1 in. 7400 23-629 8550 22-653 9700 21-717 10850 20-820 7450 23-56 8600 22-611 9750 2I-677 10900 20-782 7500 23-543 8650 22-570 9800 21-638 10950 20-744 7550 23-500 87ooj 22-529 9850 21-598 1 1 oooi 20-706 7600 23-457 8750 22-487 9900 2I'558 11050 20-668 7650 23-4I4 8800 22-446 9950 21-519 IIIOO 20-630 7700 23'37I 8850 22-405 10000 21-479 11150 20-592 7750 23-328 8900 22-364 IOO5O 2I-440 I 1 200 20-554 7800 23-285 8950 22-3?3 IOIOO 21-401 II250| 20-5I7 7850 23-242 9000 22-282 10150 21-361 11300 20-479 7900 23-200 9050 22-241 10200 21-322 "350 20-441 7950 23-I57 9100 22-200 10250 21-283 11400 20-404 8OOO 23-II5 9150 22-160 i 10300 21.244 1 i 1450 20-367 8050 23.072 9200 22-119 !j 10350 21.205 11500 20-329 8lOO 23-030 9250 22-079 IO4OO 2 1 . 1 66 U550 20-292 8150 22-988 9300 22-038 ! 10450 21.128 11600 20-255 8200 22-946 9350 21-998 | 10500 21.089 11650! 20-218 8250 22-904 9400 21-957 10550 21.050 11700 20-181 8300 22-862 9450 21-917 10600 2I.OI2 11750 20-144 8350 22-820 9500 21-877 10650 20.973 11800 20-107 8400 22-778 9550 21-837 10700 20.935 11850 20-070 8450 22-736 9600 21-797 10750 20.896 11900 20-033 8500 22-695 9650 21-757 10800, 20.858 11950 19.996 8550 22-653 9700 21-717 10850 20.820 12000; 19.959 1 70 -THE ANEROID BAROMETER. MOUNTAIN ANEROIDS. The majority of Mountain Aneroids now have Airy's table engraved around the dial, the circle bearing the scale of feet being generally movable. This movable circle, as its zero can be turned to correspond with the barometer reading for the time, is convenient for approximate work, as the elevation can be read directly off. The barometer scale, however, being a diminishing one, this mode of use would lead to grave inac- curacies. It is better, therefore, that the zero point be set at 31 inches of pressure and the two readings of feet subtracted to get the difference in height. TO USE THE ANEROID, WITH ALTITUDE SCALE. Find the height in feet at first station and subtract this from the height in feet at second station. If the mean temperature is greater or less than 50 F., apply correction for temperature as before given. Example : Aneroid at Station A, 1,800 feet. Thermometer, 50. " B, 800 " " 70. The approximate height is 1,000 feet. The sum of the temperature is 120. A correction of -^20 is therefore applied. This is 20 feet. The difference of elevation is therefore i ,000+20=1 ,020 feet. SIZE OF THE ANEROID. Aneroids are graduated from 3,000 to 20,000 feet, from i^ inches diameter to 5 inches diameter. The larger sizes ^of course permit the use of more open scale, and are consequently more easily read. The smaller sizes are, however, extremely accurate, and their portability is a strong recommendation. POSITION .OF THE ANEROID IN USE. It should be borne in mind that all Aneroids vary in their readings with the position in which they are held, reading somewhat higher in a horizontal position with face up than THE ANEROID BAROMETER. 171 when vertical. As they are tested and adjusted in a horizontal position, it is better that they should be uniformly read from the horizontal dial. Before a reading is taken, the face should be tapped slightly with the finger to bring the needle fairly into equilibrium. ATMOSPHERIC DISTURBANCE. As there may be considerable atmospheric variation if any great interval of time elapses between two observations, engi- neers are now accustomed to use two matched barometers, one of which is kept in camp, where observations are taken at stated intervals, whilst the other is observed at corresponding times in the field. A correction can thus be applied for atmos- pheric oscillation. Where one barometer only is used, observa- tions may be made repeatedly and the mean taken, or where it is inconvenient to take the higher elevation more than once, the lower reading can be taken after as well as before the higher, by which method a partial correction may be obtained. LOCKE'S HAND LEVEL. THIS Instrument is made in three form, brass, nickel and German silver. The tube is 6 inches long, having, as shown in illustration, the small level on top and near the object end. There is an opening in the tube beneath, through which the bubble can be seen, and is reflected by a prism imme- diately under the level . Bothends are closed by disks of plain glass to exclude the dust. There is at the inner end of the sliding eye-tube a semi-circular convex lens which magnifies the level bubble and the cross wires beneath, and allows the object to be clearly seen through the open half of the tube. The cross wire is fastened to a small frame moving in the level tube and adjusted to its place by the small screw shown on the end of the level case. The level of any object in line with the eye of the observer is determined by sighting upon it through the tube, and bringing the bubble of the level into a position where it is bisected by the cross wire. The Abney Level and Clinometer, as show by the above illustration, combines the features of the Locke's Hand Level, with an excellent clinometer. The arc is divided to 90 degrees each side of zero. When the level bubble is brought to the 172 LOCKE'S HAND LEVEL. 173 middle, by setting the vernier arm to zero on the dividing scale, the bubble is seen through the eye piece and the level is ascer- tained the same as with the Locke's Level. As the main tube is square it can be applied to any surface, the inclination of which is ascertained by bringing the level bubble into the middle and reading off the angle to 5 minutes by the vernier and arc. The inner and shorter arc indicates the lines of different de- grees of slope, the left hand end of the vernier being applied to the lines and the bubble being brought into the middle as usual. THE ABNEY LEVEL WITH COMPASS. The attachment of bar needle compass to the regular Abney Level makes the instrument practically a Pocket Autometer. This instrument is sometimes made with Jacob Staff Mount- ings so that it can be used on a staff. Directions for use of Abney Level and Clinometer and Abney Level with Compass Attachment. When the height of any object is required to be taken, a distance should be correctly measured from the object, say 100 feet, this forms the base line, and at which point the observer would stand ; then, direct his vision through the tube of the level and elevate it until the highest point of the object is seen bisected by the horizontal edge of the reflector within the tube. While holding it steadily in this position, the spirit level which is attached to the axis of the arc should be turned upon its center until the bubble is seen reflected in the mirror, and also bisected by the horizontal edge of reflector, the alignment is then complete, and the height of object obtained by reading off the index of the arc. The arc has two graduated scales upon it, one giving the angular measurement by degrees, and subdivided by the vernier division on the index. The other scale is figured one to ten with their subdivisions, representing T ^ i> etc., of the length of the measured base, and is read off by the fiducial edge at the side of the index. If, therefore, the edge coin- cides with division 4, the height of the object would be ]^ of the base line, or 25 feet. 174 LOCKE'S HAND LEVEL. In using the Angle reading scale on arc the following tables may be referred to : Angle i gradient i in 57. Angle 12 gradient i in 4.7 i 30' " i " 38. " 14 " i " 4. " 2 i " 28.6 " 16 M i " 3-4 11 2 30' V I " 22.8 " 18 " I " 3. " 3 " i " 19. " 20 " i " 2.7 " 3 30' " I " 16.2 " 22 " I " 2.4 " 4 " I " 14.3 4< 24 " I " 2.2 ' 4 30' <( i " 12.6 " 26 " i " 2. (< 5 " i " 11.4 ; clamp and gradienter attachment to axle of telescope. Six -inch vertical arc graduated on solid silver to ]/? degrees with adjustable vernier reading to minutes. Figuring of gradu- ations on arc o to 90 each way from centre line. Vernier fitted with adjustable magnifier. Five-inch special magnet steel needle swung on sapphire centre, supported by hardened and well pointed centre pin. Variation plate with improved clamp and rack and pinion movement. Horizontal circle (graduated edge) 6^ inches in diameter, graduated on solid silver to }i degrees, with double verniers reading to 30 seconds. Figuring of graduations on circle in two rows from o to 360 degrees in opposite directions. Verniers fitted with patent adjustable magnifiers and ground glass reflectors ; clamp and opposing spring tangent to horizontal limb and centres. Two graduated right angle levels, one placed on horizontal circle and one on left-hand standard. Compound extra long centres of special formulae metal to reduce friction. Special skeleton leveling plate ; capped and packed leveling screws. Shifting centre tripod head ; split leg tripod. Hardwood box containing sunshade, plumb bob, screw driver and adjusting pins. Weight of transit, 17 Ibs.; weight of tripod, 7 Ibs. Price, $300 oo 22 QUEEN & CO., INC., PHILADELPHIA. "QUEEN" CITY AND BRIDGE COMBINED TRANSIT AND LEVELING INSTRUMENT. A 1487. QUEEN & CO., INC., PHILADELPHIA. 23 "QUEEN" CITY AND BRIDGE TRANSIT. A 1487. City and Bridge Transit (for repeating angles), with achromatic terrestrial telescope ii^ inches \ong, with dust cover to draw tube Object glass aperture, IT% inches; power of telescope about 24 diameters ; improved rack and pinion movement to object slide; semi-anastigmatic lens combination to eye-piece, giving high power without reducing the light or field. Patent spiral screw focussing arrangement to eye-piece. Special improved cross hairs. Ten -second ground glass level, 6 inches long, mounted under telescope. Six-inch vertical arc, graduated on solid silver to ^ degrees, with adjustable vernier reading to minutes. Figuring of graduations on arc, o to 90 each way from centre line. Clamp and gradienter attachment to axle of telescope. Five-inch special magnet steel needle, swung on a sapphire centre, supported by hardened and well- pointed centre pin. Variation plate, with improved clamp and i ack and pinion movement . Horizontal circle (graduated edge) , 6^ inches in diameter, graduated on solid silver to yi degrees, with double verniers reading to 30 seconds. Figuring of grad- uations on circle, in two rows, from o to 360 degrees in opposite directions. Verniers fitted with ground glass reflectors ; clamp and opposing spring tangent to horizontal limb and centres. Two graduated right angle levels, one placed on horizontal circle and one on left-hand standard. Compound extra long centres, of special formulae metal , to reduce friction. Special skeleton leveling plate ; capped and packed leveling screws. Shifting centre tripod head : split leg tripod. Hardwood box, containing sunshade, plumb bob, screw driver and adjusting pins. Weight of transit, 17 Ibs.; weight of tripod, 7 Ibs. For extras, see pages 63 to 69. Price, $250 oo A 1488. U. S. Ordnance Engineers' Transit, as made by Queen & Co. Horizontal circle, 6.65 inches in diameter, graduated on solid silver to 20 minutes, opposite verniers placed at angle of 30 degrees to telescope. Verniers, on solid silver, reading to 30 seconds. Ground glass reflectors over verniers. Five-inch needle, with variation plate. Telescope, 10^ inches long; rack and pinion movement to objective lens ; revolving rack movement to eye-piece. Special gradienter attachment to adjustable stadia wires. Drawn platinum cross wires. Special ground glass level under telescope. Vertical circle, 4^ inches in diameter, graduated on solid silver, reading by vernier to single minutes. German silver tangent screws, with deep-cut standard threads. Semi-anastigmatic lens combination eye- piece. All tangent screws fitted with spring-box opposing springs. Extra long compound centres. Clamp head, solid leg tripod. Hard wood, box, fitted with plumb bob, sunshade, 7ernier glass, adi*ting pins and screw driver. Price, $250 oo 24 QUEEN & CO., INC., PHILADELPHIA. "QUEEN" CITY AND BRIDGE TRANSITS. A 1489. City and Bridge Transit, same as A 1487, fitted with 5- inch Vertical Circle instead of Vertical Arc. Price, $250 o A 1490. City and Bridge Transit, same as A 1487 without Vertical Arc and Gradienter attachment. Price, $225 o A 1491. City and Bridge Transit, same as A 1487 without Vertical Arc, Telescope Level and Clamp and Gradienter attachment. Price, $200 o The level mounted under the telescope of the City and Bridge Transit is extra large and specially ground and the sensitiveness is equal to that of most Wye-levels. EXTRAS FOR CITY AND BRIDGE TRANSITS. Striding level 3^ inches long suspended from vertical axis . . . . $25 ex Adjustable Magnifiers fitted to all Verniers . . . 25 oo Graduations on Horizontal Circle reading to 30" t IO Graduations on Horizontal Circle reading to 20" 20 oo Graduations on Vertical Arc reading to 30" 5 oo Queen Solar Attachment 60 oo Sights on Telescope with Folding Joint 8 oo Sights on Standards at right angles to Telescope 5 oo Diagonal Prism for Eye Piece 8 oo Reflector for Objective Glass of Telescope . ... . . 4 oo Extension Tripod in place of Solid Leg 10 oo QUEEN & CO., INC., PHILADELPHIA. 25 "QUEEN " EXPLORERS' TRANSIT. The "Queen" Explorers' Transit is the smallest complete Transit made. It is 8 inches high, the outer diameter of the horizontal limb is 4^ inches. The Transit weighs 6 pounds, Tripod 5 pounds. The Explorers' Transit is of the same grade and quality as our City and Bridge Transit and of corresponding accuracy. A 1492. A 1492. -* Queen" Explorers' Transit, with achromatic telescope, 6> inches in diameter; graduated to. ^ degrees with double verniers reading to single minutes. Figuring of grad- uations on circle, in two rows, from o to 360 degrees in op- posite directions. Verniers fitted with ground glass reflectors. Clamp and opposing spring tangent to horizontal limb and centres. Two graduated right angle levels, one placed on horizontal circle and one on left hand standard. Compound extra long centres of special formulae metal to reduce friction. Four leveling screws ; shifting centre tripod head ; extension leg tripod. Hardwood box, containing sunshade, plumb bob, screw driver and adjusting pins. Weight of transit 6 pounds; weight of tripods pounds. Price, $220 oo Sole leather sling case for transit Price, $5 oo Sole leather sling case for tripod Price, $3 oo 26 QUEEN & CO., INC., PHILADELPHIA. QUEEN" TUNNEL TRANSIT. A 1493 QUEEN & CO., INC., PHILADELPHIA. 27 QUEEN" TUNNEL TRANSIT. The Tunnel Transit is designed especially for tunnel or other en- gineering work where the conditions are such that the ordinary Transit cannot be used on account of the reduced light. This Transit is the result of long experience in making tunnel transits, and meets the requirements of all work of this class. The formula of the Telescope Lenses is such that this instrument has an amount of light never before obtained in a transit telescope. The Telescope axis is hollow, and has a special reflector for il- luminating the Cross Wires. The Standards are very wide so as to secure greater steadiness. The Levels are long and of large diameter, accurately ground and graduated on the glass. The Verniers are directly in line with the Telescope, unusually large and fitted with ground glass reflectors and adjustable magnifying glass. A 1493. "Queen" Tunnel Transit, with achromatic telescope n/ 2 inches long. Object Glass aperture i ^ inch. Power of tele- scope from 20 to 30 diameters, as may be ordered. Dust f Cover to draw tube. Rack and pinion movement to ob- [' ject slide. Spiral screw focussing arrangement to eye- '< piece. Adjustable Stadia wires. Hollow telescope axle and reflector for illuminating cross wires. 20 second ground level, 6 inches long, mounted under telescope. Clamp and Tangent attachment to axis of telescope. 90 degrees vertical arc with vernier reading to single minutes. Right angle slotted sight mounted between standards. 5-inch needle with variation vernier. Horizontal circle, (graduated edge) 6^ inch in diameter, graduated on solid silver to YZ degrees, with double verniers reading to 30 seconds. Verniers in line with tele- scope, and fitted with adjustable magnifying glass. Extra long graduated levels mounted at right angles on the hor- izontal plate. Clamp and tangent attachment to horizontal plate and centers. Compound extra long centres. Capped and packed leveling screws. Shifting centre tripod head. Hardwood box containing sun shade, plumb bob, screw drivers and adjusting pins. Weight of transit 16 pounds, weight of tripod 7 pounds. Price, $250 oo QUEEN & CO., INC., PHILADELPHIA. QUEEN" FULL ENGINEERS' TRANSIT, A 1494, QUEEN & CO., INC., PHILADELPHIA. "QUEEN" FULL ENGINEERS 1 TRANSIT. The Full Engineers' Transit, as designed and improved by us, has A 1532 with tangent screw. Price, $55 oo QUEEN & CO., INC., PHILADELPHIA. 61 QUEEN " TILTING LEVEL. A 1532^. Architects' Tilting Level is the same as the Architects' Level A 1532, excepting that it has the addition of an attach- ment by which sights of 45 degrees above or below the hori- zontal can be taken. This attachment is a small set of standards screwed into the centre of the level bar, and when not in use can readily be removed. It has V-shap.ed grooves at the top to receive the telescope axle, also clamps to hold it in place. The small axle mounted on the telescope does not interfere when the instrument is used as an ordinary level. Price, $65 oo A 1532)^. Architects' Tilting Level with tangent screw. Price, $70 oo 62 QUEEN & CO., INC., PHILADELPHIA. QUEEN" ARCHITECTS' COMPASS LEVEL. A 1533- A 1533. Architects* Compass Level. This instrument is similar to the architects' level before described, but is fitted with com- pass with 2^ -inch needle. This is so arranged that it adds practically nothing to the weight or bulk, and does not inter* fere with the portability of the instrument, whilst its value in many kinds of work is obvious. The instrument is screwed on a tripod and packed in a box fitted with sunshade, plumb bob, screw drivers, adjusting pin and metal trivet. Price, $65 oo ~A I533>^. Architects' Compass Level, same as A 1533 but wit h tangent screw. Price, $70 oo QUEEN & CO., INC., PHILADELPHIA. 65 "QUEEN" LAND LEVEL. The Queen Land Level, as recently intro- duced by us, is the only low-priced instrument on the market that combines all the working features of the finer engineering transits and levels. This complete little instru- ment, as shown in the above illustration, is practically indispensable to engineers, county sur- veyors; farmers, land- scape gardeners and planters. It is a great labor saver to the wheel- A 1535. wright in lining and set- ting up shafting ; to the builder and bricklayer a valuable substitute for the primitive level board formerly used in setting up foundations, floors, sills and running grades. It is also an excellent instrument for the scholar, illustrating the elementary principles of engineering and surveying. It can be used for angulation, level lines, grading streets, sewers and drains. The construction is extremely simple, having as few parts as possible, and combines compactness and efficiency so that anybody can at once w r ork it successfully and without special explanations. The telescope is 8^ inches long, having achromatic objectives, with magnifying power 10 times. The eye-piece has four (4) lenses, showing objects in their natural position. The cross wires are fixed in the telescope so that there is no danger of their losing the adjustment. The level is mounted on top of the telescope and is pro- vided with adjusting screws. The telescope and level are securely mounted on a swivel bearing which permits of an elevation or inclination of the tele- scope 25 degrees from the level line, and can be clamped in any position. The leveling frame is provided with four (4) leveling screws whose lower ends are ball jointed. The centre is cast of one piece with the leveling plate, and its outer edge bevelled and graduated into degrees. The socket is carefully fitted to the centre of the leveling frame, and is also provided with a clamp screw. The arc is cast on this socket and graduated into degrees. The lower end of the leveling plate has a half ball which connects the tripod plate to the upper part, like in the case of the regular transits and levels. The instrument is screwed to a substantial tripod and is packed in a wooden carrying case, making it exceedingly portable. A 1534. Queen Land Level, for h or izontar angles. Price, $20 oo A 1535. Queen Land Level, for horizontal and vertical angles. Price, $25 oo 6 4 QUEEN & CO., INC., PHILADELPHIA. ATTACHMENTS AND PARTS. A 1536. The Solar Attachment, as shown in the following cut, consists of a small telescope mounted on a horizontal axis, which rests upon two standards connected to a circular base. . This base is the socket of the so-called polar axis, and is attachable at its lower extremity to the horizontal axis of the telescope. The solar telescope is thus capable of being turned on its own horizontal axis and on its polar axis. A small level is applied parallel to the solar telescope. Two pointers are also attached for use as a specie of finder, the sun appearing the field of view of the telescope when the shadow of one of these pointers is thrown on the other. The solar tele- scope is provided with a right angle prism for conveniently observing the sun when it is at a considerable altitude. It is, of course, provided with shade glasses for the purpose of reducing the intensity of the solar rays transmitted. The small graduated circle sometimes attached to the polar axis enables the hour angle to be read off. Clamp and tangent are provided both for the vertical and for the hour angle movement. For instructions as to how the solar is used, we refer you to our Engineers' Manual. Price, $60 oo A 1537. Qradienter. This attachment consists mainly of a screw attached to the semi-circular expanded arm of the ordinary clamp of the telescope axis ; the screw is accurately cut to a given number of threads, and pas- sing through a nut in one side of the arm presses against a little stud, A, fixed to the in- side surface of the right-hand standard. As the value of the screw thread is such that a complete revolution will move the horizontal cross- wire of the telescope over a space of one foot on a rod at a distance of one hundred feet, it is cl ear that when the screw is turned through fifty spaces on the graduated head, the wire will pass over fifty one- hundred ths, or one-half a fc T 537- In this way the gradienter Grades can also be estab- on the rod, and so on in the same proportion. can be used in the measurement pf distances. lished with great facility, as follows : ist, level the instrument; bring the telescope level to its centre by the clamp of the gradienter screw ; move the graduated head until its zero is brought to the edge of the scale, and then turn off as many spaces on tha head as there are hundredths of feet to the hundrel in ths^ri'le t > be established. Price, $18 oo QUEEN & CO., INC., PHILADELPHIA. A 1538- A 1538. Queen's Opposite Vernier Attachment is of great value in cases where it may be desirable to eliminate errors and eccen- tricities in the graduation and veroiiers of the vertical circle in the same manner as in the horizontal graduation by reading two opposite, verniers. As the vertical circle is permanently attached to the telescope axle and cannot be turned independ- ently, as in repeating circles, the telescope must be reversed when a repetition of the angle is desired. The mean of the two readings is then accepted as the true result. In the above illustration the vertical circle is enclosed in an outside shield, fastened to which are two opposite double verniers reading to single minutes. Two opposing capstan head screws, working against a projecting stud on the standard, are provided to ad- just the zero point on the verniers to coincide with those of the vertical circle after the instrument has been leveled up and the telescope placed in a truly horizontal position. This at- tachment can be put on a 5 -inch full vertical circle in new instruments only. Price, extra, $20 oo The above illustration of the Opposite Vernier Attachment shows the Vertical Circle covered with an illuminum dust cover or guard, this can be put on the vertical circle of any new Queen transit. Price, extra, $5 oo 66 QUEEN & CO., INC., PHILADELPHIA. A 1539. A 1539- The Telescope Attachment for Survey- ors' Compass is attached in the same manner and takes the place of the regular standard, and can be furnished as an extra for new in- struments or independently be used on any surveyors' compass made. The telescope is 9 inches long, fine optical quality, with magnifying power of 20 diameters. Has regular -focussing and slide tube for eye-piece ; ground level tube on top of telescope; 3^ -inch vertical circle, graduated in ^ degrees and reading by vernier to 3 minutes. The telescope revolves for back sighting, and has clamp and tangent attachment. Complete, in- cluding counterpoise. Price, $30 . Pocket Compass, nickel plated, hunting case, stem stop, Singer's pearl dial. i^4 i^i $3.50 $4.00 each. 8o QUEEN & CO., INC., PHILADELPHIA. SIGHT COMPASSES. A r 593- A 1594. A 1593- Pocket Compass, bronzed, ring divided in single degrees, agate centre, bar needle, folding sights, mahogany case. 2 2}^ 3 $5-50 $6.00 $6. 50 each. A 1594. Pocket Compass, nickel plated, with cover, agate centre, bar needle, folding sights. i^ 2 2^3 $4-50 $5-50 $6.50 A 1595- Pocket Compass, brass, with cover, agate centre, bar needle, fold- ing sights. I>2 2 2> ..oo J.s.oo $6.00 A 1596. A 1596- Pocket Surveying Compass, brass, octagonal, agate centre, bar needle, folding sights, Jacob staff mounting, mahogany case. 2^ 3 $7-00 >.oo 1.00 QUEEN & CO., INC., PHILADELPHIA. Si GEOLOGISTS 1 AND MINERS' COMPASSES. GEOLOGISTS' COMPASSES. These compasses are applied to ascertain the angles of ' ' dip ' ' and ' ' strike ' ' in the strata of rock formations. Each instrument is furnished with a clinometer attachment, which consists of a pendulum with index traversing divisions upon the inner compass face, and an armature sliding from within the casing for establishing the base to clinometer. Geologists' Compass, open glass face, metal casing, silvered dial with clinometer de grees, and raised compass ring divided from o to 360 degrees, agate centre an& stop to needle. 2^ 2^ 3 in. A 1597. Nickel-plated, $5.00 $6.00 $7.00 A 1597. A 1598. Brass, 4.50 5.50 6.50 MINERS' COMPASSES. In the hands of the prospector the miners' compass or dipping needle proves a serviceable guide to the discovery and location of magnetic iron ore. In this instrument the magnetic needle is care- fully balanced upon a horizontal axis within a graduated circle, and in which the needle will be found to assume a position inclined to the horizon. This angle of deviation is called the inclination or dip, and varies in different latitudes, and even at different times in the same place. Hence, in reading the dip for the suspected presence of magnetic iron ore the observer must not only be governed by his instrument, but must also draw into requisition his knowledge of the general geological formation of the place of his survey ; and dependent on his experience, he will be enabled to approximate as to the probable mass and depth of the ore from the surface. When in use, the instrument should be held suspended by the ring, and the needle permitted to swing north and south, by placing the plane of the circle in that of the magnetic meridian. The inclination of the needle, as read off on the graduated circle, will show the dip. A 1599. Miners* Compass or Dipping Needle, 2^ -inch magnetic needle delicately balanced on adjustable agate centres, and traversing graduated 3 -inch silvered arc of 1 80 degrees, with improved stop to needle, and suspensory ring, highly sensitive ; in case. Price, $12 oo This instrument is warranted to be the best of its kind 'in the market, being unexcelled in point of delicacy, finish and efficiency. A 1599- 82 QUEEN & CO., INC., PHILADELPHIA. PRISMATIC COMPASSES. The advantage of the prismatic compass is that the distant point and the graduation of the compass are visible at the same time, the graduations being upon a ring attached to the compass needle and move with it ; thus one of the divisions will always appear directly continuous with vertical hair of the sight vane. The prismatic compass is used in preliminary recon- noissances, in clearing out lines, in filling in, in topographical surveying, etc. A 1600. A 1600. Combined Prismatic Compass, Clinometer and Altimeter, bronzed, pocket size, 2^ inches, floating card compass dial upon agate centre, with automatic stop and spring check ; mounted beneath 2^ -inch pendulum dial C, graduated for* altitude o to 1 80 degrees ; also divided o to 90 degrees both ways as clinometer, and bearing scale of rise or fall in inches per yard. Folding prism and sight vane with vertical wire. Bronze metal case, with cover and also leather sling case. Pric4 $27 oo This instrument when used as a prismatic compass is placed in a horizontal position, the altitude and clinometer dial C being fixed by stop D so that the compass divisions are rendered visible through the opening at C, thus rendering the instrument operative in the usual manner. As altitude instrument, it is placed in a vertical position, the stop D being released, thus causing the divisions of the altitude arc G to swing in view of and in line of the prism and hair sight ; when applied as horizontal clinometer, the readings are observed through opening E, which corresponds to the position of the clinometer base. QUEEN & CO., INC., PHILADELPHIA. A i6o[. A 1603. A 1601. Hutchinson's Prismatic Compass, bronzed, nearly en- closed top, floating card dial, 2 inches in diameter, graduated to ^ degrees, agate centre, improved stop and spring check, sight vane with vertical wire ; morocco case $i i oo A 1602. Same as A 1601, 3 inches in diameter, leather sling case . 16 oo A 1603. Prismatic Compass, floating metal dial, 3 inches in diam- eter, graduated to ^ degrees, agate centre, improved stop, folding prism and sight vane ; leather sling case 12 oo A 1604. A 1605. A 1604. Prismatic Compass, Barker's patent, bronzed hunting case , can be used as an ordinary compass without opening the cover, and as a prismatic compass by raising the cover ; glazed at S with plate glass, on which is etched a line, answering for the sight; with Singer's patent card dial, 2 inches 15 oo A 1605. Prismatic Compass, 3-inch floating silver compass ring* divided into ^ degrees, folding prism and hair sight, stop to compass effected by folding the hair sight, with socket for Jacob staff; leather sling case 14 oo QUEEN & CO., INC., PHILADELPHIA. PRISMATIC COMPASSES. A 1606. A 1606. Prismatic Compass, 3 inches in diameter, floating alumin- ium dial, automatic stop and spring check, graduated to ^ degrees, agate centre, folding prism with shades ; sight vane, with vertical wire and mirrors ; leather sling case . . ... . $20 oo A 1606^. Same as above, Jacob staff mounting 22 50 SIGHT COMPASS AND CLINOMETER. A 1607. A 1607. Bronzed Sight Compass and Clinometer, 2^ inches in diameter, engraved metal dial, graduated to 2 degrees, bar needle, with stop; agate centre. The sights are connected by a bar across the top, which, when turned down serves as the fiduciary edge in using the instrument as a clinometer. The clinometer is graduated to give slopes in inches per yard and in degrees ; in mahogany box 7 A 160$. Same as above, 3 inches in diameter 8 25 75 A i 609. Same as above, 4 inches in diameter 10 50 QUEEN & CO., INC., PHILADELPHIA. POCKET SURVEYORS' COMPASS A 1 6 ro. A 1610. Surveying Compass, with folding sights, needle 3^ inches long, nonius on side of compass, box for adding and subtract- ing magnetic variations, two straight levels, Jacob staff mountings , ...... $i 6 oo A 1611. Same as above but with \y 2 -inch needle ........ 18 oc A* 1612. Surveying Compass, same as A 1610, but without nonius, needle 3^ inches long 13 50 A 1613. Surveying Compass, same as A 1612, without levels and nonius, needle 3^ inches long 1200 A 1614. Surveying Compass, same as A 1613, but needle 2^/2 inches long 10 o Tripod, with cherry legs, for any of aboye compasses . , 700 86 QUEEN CO., INC., PHILADELPHIA. VERNIER SURVEYORS' COMPASS WITH TELESCOPE. QUEEN & CO., INC., PHILADELPHIA. 87 VERNIER SURVEYORS' COMPASS WITH TELESCOPE. The Variation Compass with Telescope is a valuable combination for surverors, as it is not only a surveyors' compass, but combines the practical working features of the transit. The needle is four inches long, and the graduated compass ring is slightly inclined to facilitate the reading of the needle. A variation plate is attached and is operated by loosening the clamp screw so that the compass ring can be moved in Azimuth to set off the mag- netic variation of the needles. It also has a circle for reading horizontal angles, graduated into ^ degrees, under the glass cover of the telescope box; the vernier of which reads to one minute, and is fastened to the centre, becoming part of the main socket. A clamp and tangent screw with opposing spring is attached to facilitate the reading of the vernier. Two ground glass levels are placed at right angles on top plate. The telescope is 9 inches long, of fine optical quality, with magnifying power of about 20 diameters. It has rack focussing and sliding tube for eye-piece. A truly ground level is attached on top of telescope. The vertical circle is gradu- ated in Y^. degrees and reads by vernier to three minutes. The telescope revolves for back sighting and has clamp and tangent attachment. The telescope supports are screwed in same place as the sights and are balanced on opposite sides by a counterpoise. The sights are also furnished, and are graduated into ^ degrees on the edge for angles of elevation or depression. The lower part has four leveling screws and clamp and tangent movement. The instrument is readily attached to the tripod by a screw fastened on head of tripod. The telescope and sights are detachable and packed in case with the compass. The box is fitted with plumb bob, screw drivers, wrench, etc. A 1615. Vernier Compass, with telescope and tripod and leveling screws complete, as above. Price, $75 oo 88 QUEEN & CO., INC., PHILADELPHIA. THE PLAIN COMPASS, A 1610. QUEEN & CO., INC., PHILADELPHIA. 89 THE PLAIN COMPASS. The Plain Compass as now made with all our extra attachments and furnished at a very slightly increased price, can be highly recommended, as it enables the surveyor to accomplish twice the amount of work that can be done by the old form. The needle is made in three different lengths, four, five and six inches, and the plates are thirteen, fourteen and fifteen inches long respectively. The compass rim is sligtly inclined to facilitate the reading of the needle, and is graduated into ^ degrees, figured in quadrants. Two ground glass levels are placed at right angles on top plate. The sights are graduated into *4 degrees on the edges for angles of elevation or depression. The lower part has four leveling screws and centre clamp screw. The instrument is readily attached to the tripod by a screw fastened on the head of tripod. The sights are detachable and are packed in case with the instrument. The case is fitted with plumb bob, screw driver, wrench, etc. A 1616. Plain Surveying Compass, 4-inch needle, 13-inch plate, as above, with tripod and leveling screws, complete $3C oo \ 1617. Plain Surveyors* Compass, 5-inch needle, i4-incli plate, as above, with tripod and leveling screws, complete ... ... 35 oo A 1618. Plain Surveyors' Compass, 6-inch needle, 1 5-inch plate, as above, with tripod and leveling screws, complete 40 oo THE VARIATION COMPASS. The Variation Compass is constructed on the same model as the Plain Compass, but has in addition a variation plate which is placed on com- pass plate and is operated by loosening the clamp screw so that the compasss rim can be moved in azimuth to set off the magnetic variation of the needle. A 1619. Variation Compass, 4-inch needle, 13-inch plate, as above, with tripod and leveling screws, complete $35 oo A 1620. Variation Compass, 5-inch needle, 14-inch plate, as above, with tripod and leveling screws, complete 40 oo A 1621. Variation Compass, 6-inch needle, 15-inch plate, as above, with tripod and leveling screws, complete 45 oo Any of these compasses can be furnished with ball and socket joint and Jacob staff mounting, instead of leveling screws and tripod without extra cost. QUEEN & CO., INC., PHILADELPHIA. THE VERNIER RAILROAD COMPASS, A 1622 QUEEN & CO., INC., PHILADELPHIA. 91 THE VERNIER RAILROAD COMPASS. The Vernier Railroad Compass is constructed on the same model as A 1615. The needle is made in three different lengths, four, five and six inches, and the plates are thirteen, fourteen and fifteen inches long respec- tively. The compass rim is slightly inclined to facilitate the reading of the needle and is graduated in half degrees figured in quadrants. A variation plate is attached and is operated by unloosening the clamp screw so that the compass rim can be moved in azimuth to set off the magnetic variations of the needle. It also has a circle for reading horizontal angles, graduated into half degrees, under the glass cover of the compass box, the vernier of which reads to one minute and is fastened to the centre, becoming part of the main socket. A clamp and tangent screw with opposing spring is attached to facilitate the reading of the vernier. The sights are graduated into half de- grees on the edge for angles of elevation or depression. The lower part has four leveling screws and clamp and tangent movement. The instrument is readily attached to the tripod by a screw fastened on head of tripod. The sights are detachable and are packed in case with the compass. The box is fitted with plumb bob, screw drivers, wrench, etc. A 1622. Vernier Railroad Compass, 4-inch needle, 1 3-inch plate, as above, with tripod and leveling screws, complete ... ... $45 oo A 1623. Vernier Railroad Compass, 5-inch needle, 14-inch plate, as above, with tripod and leveling screws, complete 55 oo A 1624. Vernier Railroad Compass, 6-inch needle, i6-inch plate, as above, with tripod and leveling screws, complete 65 oo QUEEN & co., INC., PHILADELPHIA. HAND LEVELS. A 1638. A 1638. Locke Hand Level, 5-inch, brass ,...., $6 oo A 1639 Do. do. 5-inch, German silver 8 oo A 1640. Do. do. 5-inch, nickel plated ... t ... 8 oo A 1641. A 1641, Queen Hand Level, square tube, 5-inch, nickel plated . . 4 50 In the Queen Hand Level the reflector is an oval-polished plate t crossing the centre of the field of view, so that the field appears on all iout Sides of the reflected bubble. A 1642. A 1642. Abney Level and Clinometer, a combination of the "Locke Hand Level," with the Clinometer, giving angles of elevation and slopes; in wood box $13 50 QUEEN & CO., INC., PHILADELPHIA. 93 A 1643. A 1643. Aoney's New Model Reflecting Level or Pocket 'Alti- meter, improved, with compass; in box $18 oo DIRECTIONS FOR USE. When the height of any object is required to be taken, a distance should be correctly measured from the object, say 100 feet. This forms the base line, and at which point the observer would stand; then direct his vision through the tube of the level, and elevate it until the highest point of the object is seen bisected by the horizontal edge of the reflector within the tube. While holding it steadily in this position, the spirit level, which is attached to the axis of the arc, should be turned upon its centre until the bubble is seen reflected in the mirror, and also bisected by the horizontal edge of reflector, the alignment is then complete, and the height of object obtained by reading off the index of the arc. The arc has two graduated scales upon it, one giving the angular measurement by degrees, and subdivided by the vernier divisions on the index. The other scale is figured i to 10 with their subdivisions, represent- ing iV, i, YZ, etc., of the length of the measured base^ and is read off by the fiducial edge at the side of index. If, therefore, the edge coincides with division 4, the height of object would be V of the base line, or 25 feet. In using the angle reading scale on arc the following tables may be referred to : Angle gradient . 33o'. 4' 43o'. 5 6 8 10 12 i in 57. in 38. in 28.6 Angle 14 " 16 18 in 22.8 11 20 in 19. in 16.2 in 14.3 in 12.6 " 22 " 24 11 26 " 23 in 1 1.4 in 9.5 in 7.1 in 5.6 " 30 " 35 " 40 11 45 in 4.7 gradient in 4. in 3.4 in 3. in 2.7 in 2.4 in 2.2 in 2. 88 73 40 20 When a slope or gradient is required to be set out to any given angle, the index of the arc should be set by reference to the above tables, and the instrument placed upon the object to be inclined ; this should then be raised or lowered until the bubble is seen in the centre of spirit level, the required gradient being thus given. QUEEN & CO., INC., PHILADELPHIA. CLINOMETERS. A 1644. A 1644. Boxwood Clinometer, T2 inches folding to 6 inches, brass mountings, 2 levels, compass and inclination scale, in leather case ... $8 50 -^64414. Boxwood Clinometer, with sights as illustrated, in leather case ii 50 A 1645. A 1645^. \ 1645. Clinometer or Slope Level, small, In morocco box . ... $800 ^ | ^45/^ Do. do. large, in morocco box .... 12 oo \ 1646. Do. do. large, with perpendicular sight 15 oo A 1647. A 1648. A 1647. Clinometer, of square frame, with arc running diagonally across; in box $12 oo A 1648. Linton's Hand-Level and Clinometer $20 oo QUEEN & CO., INC., PHILADELPHIA. 95 THE "QUEEN" MACHINISTS 1 LEVELS OF PRECISION. A 1649. Spirit Levels are the most sensitive, and therefore most important, appliances for practically determining horizontal or vertical planes, and for measuring small angles. They replace and far excel the plumb line as for- merly used for the same purpose. The production of an accurate spirit level is a work requiring much skill and patience and knowledge of the scientific principles involved . It includes principally the grinding of the curve and the sealing of the tube. The sensitiveness of a level depends upon the radius of curvature, which in ground levels is mainly obtained by the grinding of the inner sur- face to the requisite curve, which practically is a difficult operation, requiring special skill in its manipulation. The sensitiveness of a level varying directly as the radius of curvature ; levels ground to a short radius give scarcely any displacement of the bubble for a small variation of the angle, while those of sufficiently long radius may be made to show an appreciable displacement of a bubble for an angular value of but a fraction of second of arc. The sensitiveness of levels is usually stated as so much deviation of the bubble per single division of one French ligne of 2.26 mm. in length. In furnishing our Machinists' Levels of Precision, we are prepared to supply a level of any requisite degree of curvature and, consequently, any required degree of sensitiveness. Our Machinists' Levels of Precision are carefully mounted in iron case, with brass top and accurately planed sur- faces ; also are adjustable laterally and vertically. They are supplied with short cross level carefully ground, and the main bulb is graduated in inches and tenths. This form of Spirit Level has long been recognized as the best con- structed and most suitable form for setting up locomotives, stationary engines, boilers, planers, lathes and all fine machinery, and is guaranteed to give satisfaction. A 1649. Machinists' Level, 8 inches long $800 A 1650. Do. 10 do. . 10 oo A 1651. Do. 12 do. 12 oo A 1652. Do. 15 do. 15 oo A 1652^. Do. 18 do. 18 oo A 1652^. Do. 24 do. 24 oo QUEEN & CO., INC., PHILADELPHIA A 1653. A 1657. A 1653. High Grade Sextant. As made for the U. S. Navy, of hard bronze, finished smooth in a lustreless, durable dark color. The sextant capable of measuring an angle of 130 degrees. The radius of the instrument measures from centre of pivot to out- side edge of limb 7 inches. Graduated arc, upon silver, divided to 10 minutes, vernier reading to 10 seconds. One plain tube for sighting. One astronomical telescope. One terrestrial telescope. Two mirrors. Four colored shade glasses. One neutral glass to each telescope. Weight of instrument without telescope, 3^/2 pounds. Instrument complete with two screw drivers ; two neutral tinted sunshades ; one extra index mirror ; one extra horizon mirror, and the necessary tools for adjust- ment. Polished mahogany box with lock and key. Price, $130 oo A 1654. High Grade Sextant, as used in English Navy. Price, $95 oo A 1655. High Grade Surveyors' Sextant. As made for the U. S. Navy of hard bronze, finished smooth in a lustreless, durable, dark color. The sextant capable of measuring an angle of 130 degrees. The radius of the instrument measures from centre of pivot to outside of limb 5.72 inches. Graduated arc, upon sil- ver, divided to 20 minutes, vernier reading to 30 seconds. One plain tube for sighting ; one astronomical telescope ; one terres- trial telescope . Two mirrors, four colored shade glasses. One neutral glass to each telescope. Weight of instrument without telescope, 2.^/2, pounds. Instrument complete with two screw drivers : two neutral tinted sunshades ; one extra index mirror ; one extra horizon mirror, and the necessary tools for adjust- ment. Polished mahogany box with lock and key. Pric4 $no oo A 1656. Surveyors' Sextant, as used in English Navy. . Price, $62 oo A 1657. high Grade Octant. As made for the U. S. Navy, of hard bronze, finished smooth in a lustreless, durable dark color. The octant capable of measuring an angle of 100 degrees. The radius of the instrument measures from centre of pivot to out- side edge of limb 7 inches. Graduated arc, upon silver, divided to 20 minutes, vernier reading to 30 seconds. One plain tube for sighting; one terrestrial telescope. Two mirrors; four col- ored shade glasses. One neutral glass to telescope. Weight of octant without telescope, 2^ pounds. Instrument complete with two screw drivers ; two neutral tinted sunshades ; one extra index mirror ; one extra horizon mirror, and the necessary tools for adjustment. Polished mahogany box with lock and key. Price, $90 oo A 1658. Octant, as used in English Navy. Price, $32 oo QUEEN & CO., INC., PHILADELPHIA. POCKET SEXTANT. A 1659. A 1 659. Pocket Sextant, divided on silver to 30 minutes, vernier reading to i minute, with telescope, 2 neutral glasses, reading lens, and micrometer tangent screw. Metal box 3 inches in diameter by i^ inches high, in leather sling case. Price, $42 oo POCKET ALT-AZIMUTH. A 1660. A 1660. Pocket Alt-Azimuth, for travelers and military surveyors, 6^ inches long, 2J2 inches diameter, iyb inches thick, weight, 13 ounces ; in morocco case. Price, $47 oo Altitudes, azimuths, compass bearings, clinometer degrees and levels are all available by this convenient and highly reliable little instrument. The advantages of its use have been so increased by the recent addition of an excellent telescope as to make it perfect for the various purposes to which it can be applied. QUEEN & CO., INC., PHILADELPHIA. ARTIFICIAL HORIZON. A 1661. A 1661. Mercurial Horizon, of boxwood, with silver-plated copper bowl ; bottle of boxwood for mercury, brass rectangular roof with glass covers made of parallel glass. Complete, in case. Price, $45 oo AMSLER PLAN I METER. A 1663. 1663. Amsfcer Planimeter, for engineers. In morocco case, with instructions. Price, $30 oo QUEEN & CO., INC., PHILADELPHIA. HELIOGRAPHS. A 1665. A 1665. Heliograph. The above illustration shows the improved Heliograph as used by the U.S. Army for military signaling purposes. The heliograph equipment consists of i sun mirror, i station mirror, i screen, i sighting rod, i screw driver, all enclosed and packed in leather case. One minor bar in leather pouch attached to above case. Two tripod stands in skeleton leather case. One copy " Military Signal- ing," by Capt. Albert Gallup. Price, $60 oo 100 QUEEN & CO., INC., PHILADELPHIA. . A 1668. A 1672. A 1673. A 1668. Cross Staff Head, for turning right angles, in case, 2^ inches . . ... $3 oo A 1669. Cross Staff Head, for turning right angles, in case, 3 inches 3 50 A 1670. Cross Staff Head, with magnetic compass, 3 inches, needle 1 24 inches 4 75 A 1671. Cross Staff Head, with vertical axis and divided circle, o take angles 3^ inches .*........... 12 oo A 1672. Reflecting Hand Mirror, for turning right angles .... 5 oo A 1673. Rectangular Prism, for right angles, 2>^xi^(xi^ inches, in morocco case .' 5 oo A 1674. Surveyors' Angle Mirror, for right angles, with a small plumb bob. Size of instrument when packed, 3^x2x1^ inches . . . * V ...... . . . . 7 50 A 1675. Double Prism, to take angles of 90 and 45 degrees, in morocco ca"se . 10 oo QUEEN & CO., INC., PHILADELPHIA. 101 PEDOMETERS AND ODOMETERS* A 1688. A 1686. Pedometers ate pocket instruments for measuring distance traversed in walking the number of miles being registered by a mechanism, enclosed in a nickel plated watch casing, and operated by the motion of the body. Directions accompany each instrument. The following are of the best make only. A 1678. Pedometer, with dial divided to 12 miles and reading to quarters ..... $4 50 A 1679. Pedometer, as above, with mechanism rendered visible through' glass back 5 oo A 1680. Pedometer, dial divided to 10 miles and reading to quar- ters, with inner dial recording 100 miles 6 oo A 1681. Pedometer, as above, with mechanism rendered visible through glass back 6 50 A 1682. Pedometer, dial divided to 1,760 j^ards and reading to halves, with inner dial recording 50 miles, mechanism rendered visible through glass back . . 6 oo QUEEN & CO., INC., PHILADELPHIA. A 1683. Passometer, designated to record the number of steps, dial divided to 100, with two inner dials, registering respectively, 1,000 and 25,000 steps, mechanism rendered visible through glass back ; highly commendable $6 oo A 1684. Pedometer, similar to A 1679, with crown for instantly setting hand back to o 6 oo A 1685. Pedometer, similar to A 1681, with crown for instantly setting hand back to o 7 50 A 1686. Passometer, similar to A 1683, with crown for instantly setting hand back to o . 7 oo A 1687. Passometer, 100,000 steps, with crown for instantly setting hand back to o . . , 8 oo A 1688. A 1689. A 1688. The Queen Odometer is an instrument for ascertaining the number of miles traversed by a carriage or wagon, the revoVii tions of the wheel being registered, and the miles computed by an accompanying table. Odometer, recording 100,000 revolu- tions, in sole leather case, with strap for securing it to the wheel $15 oo A 1689. The Bell Odometer is designed to register, record and announce distances traveled by buggies or other wheeled vehicles. Attached to the axle, it is operated by a steel pin driven into the hub. and is automatic, neat and reliable. Price, complete 5 QUEEN & CO., INC., PHILADELPHIA. 103 CHESTERMAIM'S TAPES, CHESTERMAIM'S METALLIC TAPE MEASURES. These tapes are made of linen thread, in- terwoven with fine brass w r ire, not so liable to stretch as the usual linen tape and better cal- culated to withstand the effect of moisture. They are in substantial leather cases. A 1690. Metallic Tapes, 24 feet long, in icths or i2ths, each . . . $i 80 A 1691. Do. 33 do. do. ... 2 10 A 1692. Do. 40 do. do. ... 2 30 A 1693. Do. 50 do. do. ... 2 60 A 1694. Do. 66 do. do. . . . 3 oo A 1695. Do. 70 do. do. ... 3 20 A 1696. Do. 75 do. do. ... 3 30 A 1697. Do. 80 do. do. ... 3 70 A 1698. Do. 100 do. do. ... 4 20 CHESTERMAN'S METALLIC TAPES WITHOUT BOXES. A 1699. Metallic Tape, 50 feet long, in loths or i2ths, each . . . $i 50 A 1700. Do. 100 do. do. ... 2 90 CHESTERMAN'S STEEL TAPE MEASURES. Steel tape measures ; all steel, to wind up in a box, same as linen measures ; the most accurate, durable and portable measures. A 1701. Steel Tape, 25 feet long, in loths or i2ths, each $4 50 A 1702. Do. 33 do. A 1703. Do. 40 do. A 1704. Do. 50 do. A 1705. Do. 66 do. A 1706. Do. 75 do. A 1707- Do. 100 do. do. do. do. do. do. do. 5 20 6 oo 7 20 9 20 10 40 12 80 104 QUEEN & CO., INC., PHILADELPHIA. EDDY'S TAPES. Eddy's Improved Standard Steel Tapes, ^ inch wide, in leather -covered cases, flush handle, metal lined. A 1708. Steel Tape, 25 ft. long, in zoths, i2ths or metric measure, each $5 oo A 1709. Do. 33 A 1710. Do. 40 A 1711. Do. 50 A 1712. Do. 66 A 1713. Do. 75 A 1714. Do. IOO do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. do. 5 50 7 oo 8 oo 10 oo 12 00 15 oo Paine 's Patent Standard Steel Tapes, in iron cases, brass bound, mo- rocco covered, improved handles, and are detachable from case, and are furnished with detachable rings to avoid breakage. A 1715. .Steel Tape, 25 ft. long, in ioth A 1716. Do. 33 do. A 1717- Do. 50 do. A 1718. Do. 66 do. A 1719, Do. 75 do. A 1720. Do. 100 do. is or i2t]is, each . . $t 5O do. 4 SO do. v3 oo do. . .... 6 oo do. 8 oo do. . 12 OO QUEEN & CO., INC., PHILADELPHIA. 105 RELIABLE" STEEL TAPES. "Reliable" Patented Steel Tapes, 2/8 inch wide, in hard leather cases, nickel-plated trimmings, with double fold- ing flush handle, opened by pressing small pin or button on opposite side, graduated on the back with links and poles. Extra graduations of feet on one side, meters on the other or feet and i2th on one side and loths on other at 2)4c. per foot to list price. A 1721. Steel Tape, 25 feet long, in loth or i2th, each $4 50 5 20 6 oo 7 20 9 20 10 40 12 80 A 1722. Do. 33 do. do. A 1723. Do. 40 do. do. A 1724. Do. 50 do. do. A 1725. Do. 60 do. do. A 1726. Do. 75 do. do. A 1727. Do. 100 do. do. " Reliable" Frame Steel Tapes, ^ inch wide, nickel-plated frames and trimmings, with double folding flush handle, opened by pressing small pin or button on opposite side, graduated on the back with links. A 1728. Steel Tape, 50 feet long, in loth or i2th, each $7 50 A 1729. Do. 66 do. do. 9 50 A 1730., Do. 75 do. do. n 50 A 1731. Do. loo do. do. 13 50 io6 QUEEN & CO., INC., PHILADELPHIA. STEEL TAPES. " Rival" Steel Tapes, inch wide, nickel-plated steel case, flush handle, graduated one side only. A 1732. Steel Tapes, 25 feet long, in loths or i2ths, each $3 25 A 1733- Do. 50 do. do. 4 oo A 1734- Do. 75 do. do. ..... 5 25 A 1735- Do. 100 do. do. 6 75 Metallic Tapes, fyi inch wide, hard leather cases, with patent double folding flush handle, made of best woven linen, with metallic warp, graduated on back in links. ^^ A 1736. Metallic Tapes, 25 feet long, in roths or i2ths, each A 1737- Do. 33 do. do. A 1738. Do. 40 do. do. A 1739. Do. 50 do. do. A 1740. Do. 66 do. do. A 1741. Do. 75 do. do. A 1742. Do. IOO do. do. t>2 10 2 40 2 60 2 90 3 30 3 60 4 50 QUEEN & CO., INC., PHILADELPHIA. POCKET STEEL TAPES. GERMAN SILVER CASES, SPRING WIND, WITH STOP. 107 A 1 743 A. Pocket Tape, ^ in. wide , 36 in. long, in 1 6ths, each . . . $i 25 A 17436. Do. % do. 48 in. do. do. ... i 40 A I743C- Do. % do. 60 in. do. do. . . . i 50 A I743D. Do. # do. 72 in. do. do. ... i 75 A I743E. Do. ^ do. 7 ft. do. do. ... 2 OO A I743F. Do. T V do. 9 ft. do. do. ... 2 25 A 17430. Do. A do. 1 2 ft. do. do. . . , 3 oo A I744A. Do. ^ do. 36 in. long, in i6ths and meter, i 50 A I744B. Do. # do. 48 in. do. do. i 75 A 17440. Do. # do. 60 in. do. do. 2 00 A I744D. Do. % do. 72 in. do. do. 2 25 A I744E. Do. X do. 7 ft. do. do. 2 50 A I744F. Do. ^ do. 9 ft. do. do. 2 75 A I744G. Do. # do. I 2 ft. do. do. 3 50 RELIABLE JUNIOR POCKET STEEL TAPE. Reliable Junior Steel Tape, ^ inch wide, hard leather cases, with patent double folding flush handle, gradu- ated one side only. A I745R. Steel Tape, 25 feet long, in icths or i2ths, each A I745R- Do. 50 do. do. 4 oo 5 oo io8 QUEEN & CO., INC., PHILADELPHIA. QUEEN STEEL TAPE CHAINS ON PATENT REEL. NICKEL-PLATED. Queen Steel Tape Chains on Patent Reel. It allows the entire tape open to dry, and with it the tape can be reeled or unreeled as easily and readily as the linen or metallic tapes in cases. Also the tape can be easily detached and used without the reel. When in use, in mines or crowded thoroughfares, it is used the same as tapes in cases. All sizes except 200 and 300 feet can easily be carried in any average pocket. A i 74 6A. IOO feet long, every foot. End feet in tenths, Plain. $500 Nickel Plated. $600 Alumi- nium Plated. $ 7 00 A 17468. IOO do. do do. inches, 5 00 600 7 oo A I746C. IOO do. every 5 feet. do. tenths, 4 OO 5 00 6 oo A I746D. IOO do. every 5 feet. do. inches, 4 oo 5 oo 6 oo A 1 747 A. 66 do. every link - oo 6 oo 6 50 A I747B. 66 do. in Rods and tenths of a Rod . 5 6 00 650 A I747C. 66 do. every 5 links . Ea. end every link 4 oo 5 00 550 A I748A. 50 do. every foot. End feet in tenths, 4 00 5 oo 550 A 17488. 50 do. every foot. do. inches, 5 00 5 oo 550 A 17480. 60 do. every 5 feet. do. tenths, 3 00 4 00 450 A i 74 8D. 50 do. every 5 feet. do. inches, 3 00 4 oo 450 A I749A. 33 do. every link . , . 3 00 4 00 450 A 17498. 33 do. every 5 links . Ea. end every link 2 50 3 oo 350 A I750A. 200 do. every foot. End feet in tenths, 7 50 9 oo 1050 A 17508. 200 do. every foot. do. inches, 7 50 9 00 1050 A 17500. 200 do. every 5 feet. do. tenths, 6 GO 7 50 9 oo A I750D. 200 do. every 5 feet. do. inches, 6 oo 7 50 9 oo A i75iA. 300 do. every ft. End ft. in loths or ins. 1000 12 00 14 oo A 17518. 300 do. every 5ft. do. 8 00 10 00 12 00 A I752A. 400 do. every foot. do. 12 50 15 oo 1750 A 17528. 4OO do. every 5 feet. do. 10 00 12 50 1500 A I753A. 500 do. every foot. do. 15 00 18 00 21 00 A I753B. 500 do. every 5 feet. do. 12 00 15 oo 1800 A I7S4A. IOO feet, Electric Reel, without Tape I 50 A y *7" 17548. 2OO do. do. 2 OO A . *zc>rt do. do 2 50 Detachable Handles, per pair ^0 QUEEN & CO., INC., PHILADELPHIA. ENGINEERS' AND SURVEYORS' CHAINS. 109 A 1761. A 1760. Surveyors* Iron Chain, W. G. 9, 33 feet, 2 poles, oval rings $2 OO A 1761. Do. do. 8, 33 feet, 2 do. 2 50 A 1762. Do. do. 7, 33 feet, 2 do. 3 oo A 1763. Do. do. 9, 66 feet, 4 do. 3 50 A 1764. Do. do. 8, 66 feet, 4 do. 4 50 A 1765. Do. do. 7, 66 feet, 4 do. 5 50 A 1766. Surveyors* Steel Chain, W. G. 12, 33 feet, brazed links and rings 5 50 A 1767. Surveyors* Steel Chain, W. G. 12, 66 feet, brazed links and rings - IO OO A 1768. Engineers* Iron Chain, W. G. 7, 50 feet, oval rings . . . 4 oo A 1769. " " " 7, 100 " " ... 6 oo A 1770. Engineers* Steel Chain, W. G. 12, 50 feet, brazed links and rings 6 oo A 1771. Engineers* Steel Chain, W. G. 12, 100 feet, brazed links II OO METER AND VARA CHAINS. A 177*. Steel Chain, \V. G. 10, 10 meter, oval rings $T> so / / O * A 1774. Do do 10 15 do do *r O J 5 i i / /*! A 1775. Do do. 10, 20 do. do. 6 2<> 1 / jj* A 1776. Do. do. 10, 10 do. brazed links and rings . v/ 5 50 A 1777- 'Do. do. 10, 15 do. do. do. 7 50 A 1778. Do. do. 10, 20 do. do. do. 10 00 A I77O. Do do. 10, 10 varas, oval rings 7 SO k / / V B A 1780. Do do 10 20 do do O J 6 50 A 1781. Do. do. 10, 10 do. brazed links and rings . 5 50 A 1782. Do. do. 10, 20 do. do. do. 10 00 no QUEEN & CO., INC., PHILADELPHIA. MARKING PINS. A 1793- A 1791, A 1795- A 1790. A 1791. A 1792. A 1793- A 1794- A 1795- Marking Pins, No, 4 iron wire, ii in. set $i 25 2 oo 3 6 oo Do. Do. Do. Canvas Case, Stake Tacks, No. 6 steel wire, n in. set No. 6 steel wire, n in. set, weighted point, tempered steel, n in. set, ^ n - wide . . with shoulder straps, for pins 2 oo sralvanized, VA ib. boxes . 30 PLUMB BOBS. A 1800. A 1808. A 1806. A A A A A A A 1800. 1801. 1802. 1803. 1804. 1805. 1806. Brass Plumb Bob, 6 ounces, steel point, Do. do. 9 do. do. Do. do. 12 do. do. Do. do. 18 do. do. Do. do. 24 do. do. Do. do. 36 do. do. Patent Adjustable Plumb Bob, 8 ounces screw cap. . . . do. ... do. . . . do. . . . do. ... do. . . % $i 2 2 2 3 4 T 50 00 25 50 OO 75 A 1807. Do do 1 2 do o OC 5 A A 1808. 1809. Do. do. 12 do. Plumb Bob Cord, best linen, per yard concealed reel . . 2 50 re? A 1810. Do. do. braided silk, per vard . OS Nos. A 1806 and A 1807 are constructed with a reel at the upper end, upon which the line may be kept, and by dropping the bob with a slight jerk, while the ring is held in the hand, any length of line may be reeled off. A spring, which has a bearing on the reel, will check and hold the bob firmly at any desired point of the line. No. A 1808. Patent Adjustable Plumb Bob, with concealed reel, around which the string is wound by turning the milled head on top. The friction upon the reel within will hold the bob at any desired point of the line. QUEEN & CO., INC., PHILADELPHIA. in VERY ACCURATE POCKET ANEROID BAROMETERS. COMPENSATED AND SPECIALLY TESTED AND ADJUSTED FOR ENGINEERS' USE. These Aneroids have movable altitude scales, with silver enameled dials, and are in morocco cases. 13500. 13505. Plain Pocket Aneroid, iV 4 in. diameter $15 oo Do. do. 2}^ in. do 17 oo Do. do. i^ in. do. with thermometer . 2000 Do. do. $ l /> in. do. 21 oo Pocket Mountain Aneroid, compensated for temperature, i^ in. diameter, with altitude scale to 3000 feet. .... 20 oo Do. do. 5000 feet 20 oo Do. do. 10,000 feet 21 oo Do. do. 15,000 feet. . *. . . 24 oo Do. do. 20,000 feet 27 oo Pocket Mountain Aneroid, compensated for temperature, same as 13,505, 2% inches diameter, with altitude scale to 3000 feet 20 oo Do. do. 5000 feet 20 60 Do. do. 10,000 feet. . . , . 21 oo Do. do. 15,000 feet 24 oo Do. do. 20,000 feet 27 oo 112 QUEEN & CO., INC., PHILADELPHIA. GEOLOGICAL ANEROIDS, 13515- Front. !35'5' Geological Aneroid, compensated for temperature, silvered metal dial, with needle compass at back, 2^ inches diameter, in leather sling case, with altitude scale to 5000 feet .... $30 oo 13516, Do. do. 10,000 feet .... 31 oo 135*7* Do. do. 15,000 feet .... 33 50 13520. 13520. Geological Aneroid, compensated for temperature, with sil- vered metal dial, 5 in. diameter, in mahogany open face case, with leather strap, with altitude scale to 3,000 feet . . ... . . $33 oo I352J. Do. do. 5,ooo feet ..... 33 oo 13522. Do. do. io,oco feet 35 oo 3523- Do. do. 15,000 feet 37 oo 13524- Do. do. with thermometer, altitude scale to 3000 feet . , 35 oo 13525- Do. do. 5,ooo feet . . . . . 35 oo 13526. Do. do. 10,000 feet 37 oo 13527. Do. do. 15,000 feet 39 oo QUEEN & CO., INC., PHILADELPHIA. 113 SURVEYING AND MINING ANEROIDS. 13530- 1353' Surveying Aneroid, 5 in. diameter, compensated for tem- perature, silvered metal dial, graduated to hundredths, and reading by vernier to single feet, with magnifier, in leather sling case, with altitude scale to 5000 feet .... $50 oo 1353'- Do. do. 10,000 feet ... 55 oo 13532. Do. do. 15,000 feet .... 60 oo '3534- Mining Aneroid, same as 13,530, but arranged to register 2000 feet below sea level to 4000 above . . 50 oo The Surveying and Mining Aneroid has been designed and con- structed specially for the use of surveyors and engineers, for the purpose of readily ascertaining slight variations in gradients, levels, etc., and from its extreme sensitiveness will be found of considerable utility in mining and surveying work generally. Besides extreme sensitiveness, the specialty claimed for this instru- ment is an arrangement of the scale of altitudes which admits 'of subdivis- ion by a vernier, hitherto impracticable, owing to the altitude scale in or- dinary use being a gradually diminishing one, to which a Vernier cannot be applied. In the present instrument the action has been so adjusted as to give accurate readings upon a regular scale of altitudes, the barometrical scale of inches having been made progressive so as to afford the correct relative readings with the scale of altitudes. For mining purposes the entire circle of the dial is graduated to rep- resent 6 inches of the mercurial column, i. e., from 27 inches to 33. This scale will register about 2000 feet below sea-level to 4000 feet above ; the finest divisions, hundredths of the altitude scale, represent 10 feet measure- ments, which can be again subdivided by the vernier scale to single feet. The vernier scale is moved by a rack- work adjustment, and a magnifying lens which rotates on the outer circumference of the instrument facilitates the reading of minute quantities. For surface surveying purposes, where it is not required to be used below sea-level, the instrument is made with the scale divided from 25 to 31 inches, thus giving an altitude scale of 5000 feet above sea -level only, and with this open scale and the assistance of the vernier, the same minnte readings can be easily taken. H4 QUEEN & CO., INC., PHILADELPHIA. ANEMOMETERS. FOR MEASURING THE VELOCITY OF CURRENTS OF AIR IN COAL MINES, AND VENTILATORS, FLUES, ETC., OF PUCLIC BUILDINGS. The Anemometer, an instrument invented for the purpose of measur- ing the rate at which air moves in mines and ventilation passages, is now an indispensable adjunct of the former, the mining laws of most States requir- ing that a certain number of cubic feet of air shall be passed to the air- ways, and the anemometer furnishing the most convenient and satisfactory mode by which tne amount of air passing can be determined. No. 14,500. No. 14,505. 14,500. Bi rain's Anemometer, 6 inches diameter, reading to ten million feet, with disconnector, Fig. i $40 oo 14,561. Biram's Anemometer, 5 inches diameter, same as 14,500 . 39 oo 14,502. Biram's Anemometer, 3 inches diameter, same as 14,500 . 37 oo I4505- Biram's Anemometer, 12 inches diameter, reading to ten million feet, with disconnector 45 14,506.- Biram's Anemometer, 6 inches diameter, same as i4>55> 4 o 14,507. Biram's Anemometer, 4 inches diameter, same as 14,505, 37 50 QUEEN & CO., INC., PHILADELPHIA. 115 14508. 14508. Bi ram's Anemometer, 6 inches diameter, reading to 1000 feet, with disconnector .....*,.... $25 oo 14509. Bi ram's Anemometer, 6 inches diameter, reading to 1000 feet, without disconnector 22 50 14510. Biram's Anemometer, 4 ins. diameter, reading to 100 feet, 20 oo 14511. Do. same as above, with disconnector, 22 50 14512. Do. 3 ins. diameter, reading to 1000 feet, 1500 14515- 14515. The Portable Air Meter, diameter of fan wheel 2^ inches, with disconnector, which is extensively used for testing the ventilation of hospitals, schools and public buildings ; forms also an admirable pocket anemometer for tourists. The indications are obtained by the revolution of a series of fans (similar to those of Biram's Anemometer) acting first upon a long hand capable of recording the velocity of fifty feet per minute on the large dial, divided to 100 feet, and then success- ively, by a train of wheels on the indices of five smaller dials, recording respectively 100, 1000, 10,000, 100,000 and 10,000,- ooo feet, or 1893 miles .......... $3 14516. Air Meter, some as preceding, but reading only to 1000 feet, 25 oo 14517. Watch Anemometer, very small and sensitive, outside dimensions 2^ ins., in white metal hunting case . ..... 4000 14518. Watch Anemometer, same as above, in silver hunting case, -45 oo QUEEN & CO., INC., PHILADELPHIA. POCKET MAGNIFIERS. A 205 i . A 20101. Magnifiers, folding, oval shape, in rubber case with i lens. A 2050. Magnifier, 24 -inch diameter ......... A 2056. A 2062. A 2068. A 2074. A 2078. Do. Do. Do. Do. Do. do. do. do. do. do. Magnifiers, folding, oval shape, in rubber case, with 2 lenses. A 2051. Magnifier, y and ^-inch diameter ...... A 2057. A 2063. A 2069. A 2075. A 2079. Do. Do. Do. Do. Do. and i and i and i and i and 2 do. do. do. do. do. Magnifiers, folding, bellows shape, in rubber case, with i lens. A 20101. Magnifier, fy-inch diameter A 20110. Do. fa do. A 20119. Do. i do. .Magnifiers, folding, bellows shape, in rubber case, with 2 lenses. A 20102. Magnifier, s/ 8 and 24 -inch diameter A 201 1 1. Do. Y^ and fa do. A 20121. Do. ?A and i do. .... 30 40 60 70 90 16 50 65 85 i 10 1 65 2 15 40 50 60 60 75 i oo QUEEN & CO., INC., PHILADELPHIA. 117 CLEVELAND CaseAve Wilson Ave. Willoughby.. .Reynolds... Meutor. HUSLEY The above cut represents Fig. i, the " Speed Protractor,'' as set at a speed angle of 25 miles per hour, and part of a Chart. Fig. 2 represents the lower head, C, with the speed scale, G, engraved on it. Fig. 3 is a cross section of the lower head, C. the upper and movable head, B, and part of the blade, A. The blade, A, is 42 inches long, made of hard rubber and backed with mahogany wood. The two heads, B and C, are made of steam- dried satin-wood and faced with ebony. Dimensions of lower head, C, 4x15 inches ; of upper head, B, 2^x14)^ inches. D, E, F, Fig. 3, represent the fixed brass pivot and thumb -screw, for setting the instrument at any required speed. Il8 QUEEN & CO., INC., PHILADELPHIA. 1135. Hill's Railroad Time Charts. The principal features of the charts are : 1. The positively mathematical correctness of the spacing. 2. The ease with which the five minutes, half hour, and hour lines can be distinguished, as well as their perfect clearness and cleanness. 3. Their enormous size (28x50), admitting of larger hour-spaces than any chart at present in use. 4. The excellence of the paper on which they are printed, as well as its peculiar tint, rendering it peculiarly fit for night work, while its cardboard- like texture obviates the necessity for dampening and stretching, and the consequent distortion of the diagram. 5. Their cheapness, which enables us to furnish them to railroads in smaller quantities and at lower price than they could be obtained by litho- graphic or any other process. The " Speed Protractor," which is generally used with the charts, needs hardly any recommendation. The simplicity of its construction, the care bestowed in its manufacture, its greater accuracy than that of the semi- circular angle protractor, and its low price, speak for themselves. The price of the Charts, without name of stations, station lines, and heading, is $12.00 per quire; complete and ready for train plotting, the scale of prices is as follows, viz.: 50 Sheets ,.;.,... . . $75 oo 100 do no oo 150 do 1 20 oo 200 do 1 60 oo Speed Protractor 10 oo In favoring us with an order for complete charts, please send list of stations with intermediate distances, and underscore such stations as you may desire to have printed in heavy type on account of their importance. The following is an extract from a letter of Mr. James Tillinghast, General Superintendent of the New York Central and Hudson River Rail- road, to whose judgment Mr. Hill submitted both charts and protractor: NEW YORK CENTRAL AND HUDSON RIVER RAILROAD, 1 Gen'l Supt Office, Albany, N. Y., Jan. I5th, 1876. ] "ALBERT HILL, ESQ.: " Dear Sir : I am in receipt of yours of the I4th inst., with sample of diagram of Chart sheets. * * * I have not found any better plan to secure accuracy in forming the basis or proof of time tables, for the reason that it presents to the eye in a clear, con- densed form, all the trains the schedule is to cover, and in such manner that the station figures are accurately indicated, and from which the figures for .the printed form can be readily copied. " Your plan of ' Speed Protractor ' is the best I have seen, and will be tery useful in connection with the Charts, and I have no doubt that, with the facilities you mention for the production of charts so accurately lined as your process will produce, you will be able to .secure orders. * * * Yours truly, "JAMES TILLINGHAST." The following is a list of some of the principal railroad companies by which these Charts have been so far adopted : Pennsylvania Railroad. Central Railroad of New Jersey. Lake Shore and Michigan Southern Railroad. Toledo, Wabash and Western Railway. Cleveland, Tuscarawas and Wheeling Railroad, etc., etc. If desired, we will send by mail, postage paid, a chart of any of the above-named roads, as a sample. QUKEN & CO., INC., PHILADELPHIA. Architecture, Carpentry and Building. Bell. Carpentry Made Easy. Or, the Science and Art of Framing on a New and Improved System. With Specific Instructions for Building Bal- loon Frames, Barn Frames, Mill Frames, Warehouses, Church Spires, etc. Comprising also a System of Bridge Building, with Bills, Estimates of Cost, and Valuable Tables. Illus- trated by fprty-four plates, comprising nearly 200 figures. Svo. $5.00. Birkmire. Architectural Iron and Steel, and its Application in the Con- struction of Buildings. Fully illustra- ted from original designs. 8vo. $3.00 Birkmire. Skeleton Construction in Buildings. Fully illustrated with engravings from Practical Examples of High Buildings. Svo. $3.00 Birkmire. Compound Riveted Girders as applied in Buildings. Svo. $2.00 Brooks. Rudimentary Treatise on the Erection of Dwelling Houses. 111., I2mo., boards. London. $1.00 Brunner. Cottages, or Hints on Economical Building, containing 24 plates of Medium and Low Cost Houses, and a Chapter on the Water Supply, Drainage, Sewerage, Heating and Ventilation, etc. Svo. N.Y. $1.00. Bryan. Architectural Proportion. A new system of proportion showing the relation between an order of archi- tecture and a building of any kind. 4to. San Francisco. $1.50. Bullock. The American Cottage Builder. A .Series of Designs, Plans and Specifications, from $200 to $20,- ooo, for Homes for the People; to- gether with Warming, Ventilation, Draining, Painting and Landscape Gardening. By John Bullock, Archi- tect, Civil Engineer, Mechanician. Illustrated by 75 engravings. 326 pp. , Svo. $3.00. Bullock. The Rudiments of Archi- tecture and Building. For the use of Architects, BuiJders, Draughtsmen, Machinists, Engineers and Mechanics. Edited by John Bullock. Illustrated by 250 Engravings. 468 pp. Svo. $3.00. Bury. Architecture. The Styles of Architecture of Various Countries from the earliest to the present period, 111., I2mo. boards. London. So cts. Clark. Building Superintendence. A Manual for young Architects, Stu- dents and others interested in Build- ing Operations as carried on at the present day. 111., I2mo. $3.00. Collins. A Practical Treatise on Handrailing. 111., I2mo. boards,, London. 60 cts. Creswell. Handrailing and Stair- casing ; a Complete Set of Lines for Handrails by "Square Cut "System, and full Practical Instructions for Making and Fixing Geometrical Stair- cases. 100 Working Drawings. I2mo. London. $1.50. Davis A Practical Treatise on the Manufacture of Bricks, Tiles, Terra- Cotta, etc.; including Hand-made, Dry Clay, Tempered Clay, Soft Mud, and Stiff Clay Bricks, also Front, Hand-Pressed, Steam-Pressed, Re- Pressed, Ornamentally Shaped and Enanimelled Bricks, Drain Tiles, Straight and Curved Sewer and Water- Pipes, Fire-Clays, Fire-Bricks, Glass Pots, Terra-Cotta, Roofing Tiles, Flooring Tiles, Art Tiles, Mosaic Plates and Imitation of Intarsia or In- laid Surfaces. Third edition. Thor- oughly revised. 261 engravings. Svo. $5-oo. Dobson. ATt of Building. 111., I2mo. boards. London. 80 cts. Dobson. Brick and Tile Making. I2mo. boards. London. $1.20. Dobson. Foundations and Concrete Works. I2mo. boards. London. So cts. Dobson. Masonry and Stone-Cut- ting. I2mo. boards. London. $1.00. Gould. Carpenters' and Builders Assistant and Wood-Workers' Guide Fourth edition. 111., Svo. N. Y. {2.50, Gould. Steel Square Problems, to- gether with a large number of Geo- metrical Demonstrations of Practical Value to Mechanics. 111. N. Y. $1.00. Gould. The American Stair-Build- era' Guide. Third edition, revised. 111., Svo. N.Y. $2.50. Gould. The Art and Science of Stair-Building. 111., I2mo. N.Y. |i.oo< QUEEN & CO., INC., PHILADELPHIA. Gwilt. An Encyclopaedia of Archi- tecture, Historical, Theoretical and Practical. Illustrated with more than 1,100 Engravings on Wood by R. Branston from drawings by John Se- bastian Gwilt, revised by Wyatt Pap- worth, and additionally Illustrated with nearly 400 Engravings on Wood by O. Jewett and nearly 200 other Engravings. 8vo. London. $17.50. Hallett. Hints on Architectural Draughtsmanship. iSnio. London. 60 cts. Hamilton. Architects' and Stair Builders' Tables of Treads and Risers. Small oblong. N. Y. 50 cts. Hammond. The Rudiments of Practical Bricklaying. Edition 111., I2ino., boards. London. 60 cts. Hatfield. The American House Carpenter. A Treatise on the Art of Building, comprising Styles of Archi- tecture, Strength of Materials, etc., a Manual for the Practical Use of Archi- tects, Carpenters, Stair-Builders and others. 8vo. N. Y. $5.00. Hatfield. The Theory of -Trans- Terse Strains and its Application to the Construction of Buildings, with Tables calculated expressly for the work, etc. Fully illustrated. Second edition, with additions. 8vo. N. Y. $5,00. Hodgson. Practical Carpentry, be- ing a guide to the Correct Working and Laying Out of all Kinds of Car- penters'' and Joiners' Work. Ill.,i2mo. N. Y. $1.00. Hodgson. The Builders' Guide and Estimators' Price Book. i2mo. N. Y. '$2.00. Hodgson. Treatise on the Carpen- ters' Steel Square and its Uses. Sec- ond edition, revised and enlarged. 111., I2tuo. N.Y. $1.00. Kent. Architectural Wrought Iron, Ancient and Modern. A Compilation of Examples from Various Sources from Mediaeval Times down to the Present Day. 4to. N.Y. $5.00. A7 Practical Directions to Assayers, Miners and Smelters, for the Testa and Assays, by Heat and by Wet Pro- cesses, for the Ores of all the Princi- pal Metals, of Gold and Silver Coins and Alloys, and of Coal, etc. A new Revised and Enlarged Edition. Illus- trated. I2mo. Philadelphia, 1893. $1.50. Lintern. The Mineral Surveyor and Valuers' Complete Guide, com- prising a Treatise on Improved Min- ing, Surveying and the Valuation of Mining Properties, etc. I2mo. Boards. London, 1887. $1.40. Lock. Practical Gold Mining. A Comprehenr^e Treatise on the Origin and Occurrence of Gold-Bearing Gra- vel, Rocks and Ores, and the method by which the Gold is extracted. Il- lustrated by 8 plates and 271 engrav ings. London, 1889. $15.00. Lock. Mining and Ore-Dressing Machinery. A Comprehensive Treat- ise dealing with the Modern Practice of winning both Metalliferous and Non-Metalliferous Minerals, including all the Operations Incidental Thereto, and Preparing the Product for the Market. 639 illustrations. 4to. Lon- don, 1890. 10.00. Lupton. Mining. An Elementary Treatise on the Getting of Minerals. Fully Illustrated. I2ino. London, 1893. $3.00. Lyell. Principles of Geology ; or, the Modern Changes of the Earth and its Inhabitants, Considered as Illus- trative of Geology. Revised edition. 2 vols. 8vo. N.'Y. $8.00. Macfarlane. An American Geo- logical Railway Guide, giving the Geological Formation at every Rail- way Station, with altitudes above mean tide- water, and a Description of each of the formations. Second edition, revised and enlarged. 8vo. N. Y., 1890. $2.00. Makins. A Manu&l of Metallurgy, Second edition. Illustrated. I2mo. London, 1873. $3-0"- McMillan. A Treatise on Electro- Metallurgy, Embracing the Applica- tion of Electrolysis to the Plating, Depositing, Smelting and Refining of Various Metals, and to the Reprodur- QUEEN & CO., INC., PHILADELPHIA. tlon of Printing Surfaces and Art Work, etc. With numerous illustra- tions. i2mo. London, 1891. $3.50. ' MichelL Mine Drainage, being a Complete and Practical Treatise on Direct-Acting, Underground Steam Pumping Machinery, etc. With 137 Illustrations. 8vo. London, 1881. $6.00. Mitchell. A Manual of Practical Assaying. Edited by William Crookes. Sixth edition. 201 Illustrations. 8vo. London. 1888. $10.00. Moses and Parsons. Elements of Mineralogy, Crystallography and Blow- pipe Analysis, from a Practical Stand- point. Illustrated. 8vo. N. Y., 1895. $2.00. Mott.The Chemists' Manual. A Practical Treatise on Chemistry, Quali- tative and Quantitative Analysis, Stoichiometry, Blowpipe Analysis, Mineralogy, Assaying, Toxicology, etc. Illustrated. 8vo-. N. Y., 1883. $4.00. Murphy. Practical Mining. A Field Manual for Mining Engineers, with Hints to Investors in Mining Properties. i6mo. Morocco tucks. N. Y., 1890. $1.50. O'Driscoll. Notes on the Treat- ment of Gold Ores. Illustrated. 8vo. London, 1889. $2.00. Orton. Underground Treasures, How and Where to Find Them. A Key for the Ready Determination of all the Useful Minerals within the United States. I2mo. Philadelphia, 1893. 1.50. Osborn. A Practical Manual of Minerals, Mines and Mining : Com- prising suggestions as to the Localities and Associations of all the Useful Minerals, Together with Analysis, Mining, etc. Second edition, revised. 171 Illustrations. 8vo. Philadelphia, 1895. $4-5. Osborn. The Prospectors' Field Book and Guide in the Search for and Easy Determination of Ores and Other Useful Minerals. Illustrated by 44 engravings. Philadelphia, 1892. $1.50. Percy. Metallurgy . The Art of Ex- tracting Metals from their Ores. In- troduction, Refactory, Materials and Fuel. Illustrated. 8vo. London, 1875. $12.00. Percy. Metallurgy of Lead, includ- ing Desilverization and Cupellation. Illustrated. 8vo. London, 1870. $12.00. Percy. Silver and Gold. Part I. Illustrated. 8vo. London, 1880. $12.00. Peters. Modern American Meth- ods of Copper Smelting. Sixth edi- tion, revised and enlarged. Il- lustrated. 8vo. New York, 1894. $4.00. Phillips. Elements of Metallurgy. A Practical Treatise on the Art of Ex- tracting Metals from their Ores. Third edition, revised and enlarged. Illus- trated. 8vo. London, 1891. $9.00. Pinner. An Introduction to the Study of Organic Chemistry. Trans- lated" and revised from the Fifth Ger- man edition. By Peter T. Austin. I2mo. New York, 1884. $1.50. Plattner. Manual of Qualitative and Quantitative Analysis, with the Blowpipe. From the last German edition, revised and enlarged. By Prof. Th. Richter. Translated by Henry B. Cornwall and John H. Cas- well. Seventh edition. Illustrated. 8vo. New York, 1892. $5.00. Plympton. The Blowpipe. 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LVI. THE ACTUAL LATERAL PRESSURE OF EARTHWORK. By Benjamin Baker, M. Inst. C. E. LVIT. INCANDESCENT ELECTRIC LIGHTS, WITH PARTICULAR REFERENCE TO THE EDISON LAMPS AT THE PARIS EXHIBITION. By Comte Th. du Moncel, William Henry Preece, J. W. Howell, and others. Third edition, in press. LVI 1 1. THE VENTILATION OF COAL-MINES. By W. Fairley, M. E., F. S. S. LIX. RAILROAD ECONOMICS; or, Notes, with Comments. By S. W. Robinson r C. E. LX. STRENGTH OF WROUGHT-!RON BRIDGE MEMBERS. By S. W. Robinson, C. E, LXI. POTABLE WATER AND THE DIFFERENT METHODS OF DETECTING IMPURITIES, By Charles W. Folkard. LXII. THE THEORY OF THE GAS-ENGINE. By Dugald Clerk. LXIil. HOUSE DRAINAGE AND SANITARY PLUMBING. By W. P. Gerhard. LXIV. ELECTRO-MAGNETS. By Th. du Moncel. Second revised edition. LXV. POCKET LOGARITHMS TO FOUR PLACES OF DECIMALS. LXVI. DYNAMO-ELECTRIC MACHINERY. By S. P. Thompson. With notes by F. L. Pope. Third edition. LXV 1 1. HYDRAULIC TABLES BASED ON " KUTTER'S FORMULA." By P. J. Flynn. LXVIII. STEAM-HEATING. By Robert Briggs. Second edition, icvised, with ad- ditions by A. R. Wolff. LXIX. CHEMICAL PROBLEMS. By Prof. J. C. Foye. Second edition, revised and enlarged. LXX. EXPLOSIVES AND EXPLOSIVE COMPOUNDS. By M. Bertholet. LXXI. DYNAMIC ELECTRICITY. By John Hopkinson, J. A. Schoolbred, and R. E, Day. LXXII. TOPOGRAPHICAL SURVEYING. By George J. Specht, Prof. A. S. ^lardy, John B. Me Master, and H. F. Walling. LXXIII. SYMBOLIC ALGEBRA; or, The Algebra of Algebraic Numbers- By Prof. W. Cain. LXXIV. TESTING MACHINES: Their History, Construction, and Use. By Arthur V. Abbott. LXXV. RECENT PROGRESS IN DYNAMO-ELECTRIC MACHINES. Being a Supplement to Dynamo-Electric Machinery. By Prof. Sylvanus P. Thompson. LXXVI. MODERN REPRODUCTIVE GRAPHIC PROCESSES. By Lieut. James S. Pettit. U. S. A. QEEEN & CO., INC., PHILADELPHIA. LXXVII. STADIA SURVEYING. The Theory of Stadia Measurements. By Ar- thur Winsio-s-. LXXVIII. THE STEAM-ENGINE INDICATOR, AND ITS USE. By W. B. Le Van. LXXIX. THE FIGURE OF THE EARTH. By Frank C. Roberts, C. E. LXXX. HEALTHY FOUNDATIONS FOR HOUSES. By Glenn Brown. LXXXI. WATER METERS. Comparative Tests of Accuracy, Delivery, Etc. Distinctive Features of the Worthington, Kennedy, Siemens and Hesse meters. By Ross F. Browne. LXXXII. THE PRESERVATION OF TIMBER BY THE USE OF ANTISEPTICS. By Samuel Bagster Boulton, C. E. LXXXIII. MECHANICAL INTEGRATORS. By Prof. Henry S. H. Shaw, C. E. LXXXIV. FLOW OF WATER IN OPEN CHANNELS, PIPES, CONDUITS, SEWERS, ETC. With Tables. By P. J. Flynn, C. E. LXXXV. LUMINIFEROUS ^THER. By Prof, de Volson Wood. LXXXVI. HAND-BOOK OF MINERALOGY ; Determination and Description of Minerals Found in the United States. By Prof. J. C. Foye. LXXXVII. TREATISE ON THE THEORY OF THE CONSTRUCTION OF HELICOIDAI, OBLIQUE ARCHES. By John L. Culley, C. E. LXXXVIII. BEAMS AND GIRDERS. Practical Formulae for their Resistance. By P. H. Philbrick. LXXXIX. MODERN GUN-COTTON ; Its Manufacture, Properties and Analysis. By Lieut. John P. Wisser, U. S. A. XC. ROTARY MOTION, AS APPLIED TO THE GYROSCOPE. By Gen. J. G. Bar- nard. XCI. LEVELING. Barometric, Trigonometric, and Spirit. By Prof. I. O. Baker. XCII. PETROLEUM : Its Production and Use. By Boverton Redwood, F. I. C., F. C. S. XCII I. NOTES EMBODYING THE RECENT PRACTICE IN THE SANITARY DRAIN- AGE OF BUILDINGS. With Memoranda on the Cost of Plumbing Work. By William Paul Gerhard, C. E. XCIV. THE TREATMENT OF SEWAGE. By Dr. C. Meymott Tidy. XCV. PLATE GIRDER CONSTRUCTION. By Isami Hiroi, C. E. XCVI. ALTERNATE CURRENT MACHINERY. By Gisdert Kapp, Assoc. M. Inst., C. E. XCVII. THE DISPOSAL OF HOUSEHOLD WASTE. By W. Paul Gerhard, Sanitary Engineer. XCVIII. PRACTICAL DYNAMO-BUILDING FOR AMATEURS. How To WIND FOR ANY OUTPUT. By Frederick Walker. Fully Illustrated. XCIX. TRIPPLE-EXPANSION ENGINES AND ENGINE TRIALS. By Prof. Osborne Reynolds. Edited with notes, etc., by F. E. Idell, M. E. C. How To BECOME AN ENGINEER, or the Theoretical and Practical Training necessary in fitting for the duties of the Civil Engineer. By Prof. Geo. W. Plympton. CI. THE SEXTANT, and other Reflecting Mathematical Instruments. With Practical Hints for their adjustment and use. By F. R. Brainard, U. S. Navy. CII. THE GALVANIC CIRCUIT INVESTIGATED MATHEMATICALLY. By. Dr. G. S. Oem, Berlin, 1827. Translated by William Francis. With Preface and Notes by the Editor, Thomas D. Lockwood. M. I. E. E. CHI. THE MICROSCOPICAL EXAMINATION OF PORTABLE WATER. With Dia- grams. By Geo. W. Rafter. QUEEN & CO., INC., PHILADELPHIA. CIV. VAN NOSTRAND'S TABLE BOOK FOR CIVIL AND MECHANICAL, ENGINEERS. Compiled by Prof. Geo. W. Plympton. CV. DETERMINANTS. An Introduction to the Study of, with Examples and Applications. By Prof. G. A. Miller. CVI. COMPRESSED AIR. Experiments upon the Transmission of Power by Compressed Air in Paris. (Popp's System.) By Prof. A. B. W. Kennedy. The Transmission and Distribution of Power from Central Stations by Com- pressed Air. By Prof. W. C. Unwin. CVII. A GRAPHICAL METHOD FOR SWING-BRIDGES. A Rational and Easy Graphical Analysis of the Stresses in Ordinary Swing-Bridges. With an Introduction on the General Theory of Graphical Statics. By Benjamin F. La Rue. 4 Plates. CVIH. SLIDE VALVE DIAGRAMS. A French Method of Obtaining Slide Valve Diagrams. By Lloyd Bankson, B. S., Assistant Naval Constructor, U. S. Navy. 8 Folding Plates. riX. THE MEASUREMENT OF ELECTRIC CURRENTS. Electrical Measuring Instruments. By James Swinburne. Meters for Electrical Energy. By C. H. Wordingham. Edited, with Preface, by T. Cornmerford Martin. Folding Plate and numerous illustrations. QUEEN & CO., INC., PHILADELPHIA. 143 ENGINEERS AND SURVEYORS SAY ...OF OUR... ENGINEERING INSTRUMENTS. (Copy.) GIRARD, O., March ist, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : About the ist of February, 1895, we purchased from you one Full Engineers' Transit, No. A 1494, and one Engineers' Level, No. A 1528, which we have had in use at our mine in Minnesota ever since, and we are ready to say that we have had the very best results, and they are pronounced by civil engineers to be standard instruments, and were we in need again of the same kind of instruments we would order them exactly like the ones you sent us. Yours truly, BIWABIK BESSEMER COMPANY, (Signed) HENRY B. SHIELDS, Secretary. (Copy.) NEW ORLEANS, LA., March 6th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : We are in receipt of yours of the 3d inst. in regard to the Reconnoissance Transit, No. A 1518, purchased from your company by our firm July 23d, 1895. In reply we would say that this instru- ment has given very good satisfaction. Yours very truly, (Signed) FORD, BACON & DAVIS. ^44 QUEEN & CO., INC., PHILADELPHIA. (Copy.) EBENSBURG, PA., March 5th, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS: The Full Engineers' Transit, No. A 1494, purchased from you in 1895 has given the most perfect satisfaction. I can truthfully say that without exception the graduations are the most accurate that I have ever seen, and the optical quality of the telescope without an equal. It is the only instrument I have been able to work with the entire day without the nerves of my eyes being greatly strained and tired. The power, being exceedingly high, does not reduce the amount of light or field in the least. Yours truly, (Signed) C. T. ROBERTS. (Copy,) COLUMBIA, PA., March i5th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : The Reconnoissance Transit, No. A 1518, that I purchased from you in 1894 has proven itself to be of very accurate construction and has served my purpose very satisfactorily.. I consider it equally as good as any builders' transit on the market, and am very much pleased to be in possession of so fine an instrument. Yours very respectfully, (Signed) JEREMIAH KOCH, Architect. (Copy.) LYLES, PA., March 3d, 1897. QUEEN & Co., INC., GENTLEMEN : ^ The Surveyors' Transit, No. A 1502, purchased from you in November, 1894, has been very satisfactory to me, and my work with it has always been received by my customers with apparently entire satisfaction. Yours truly, (Signed) ALFRED WOOD, Surveyor. QUEEN & CO., INC., PHILADELPHIA. 145- (Copy.) RUNGE, TEXAS, April 22d, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : Your favor of the 24th inst. came duly to hand", and through momentarily setting it aside for more pressing matter, it was over- looked. Apologizing for the neglect, I hasten to state that I have had the Surveyors' Transit, No. A 1502, purchased from you in use for a year now. In that time I have laid off one town site, Nord- heim, on the line of the San Antonio and Arkansas Pass Railway, and done a multiplicity of other work, in all of which I have been pleased with my instrument to an eminent degree. It has come fully up to my expectations. Yours truly, (Signed) WM. H. LECKIE, Eight years County Surveyor, Kansas County, Texas. (Copy.) Laurens Cotton Mills. LAURENS, S. C., March 6th, 1897. MES'SRS. QUEEN & Co., INC., GENTLEMEN : We are pleased to say that the Full Surveyors' Transit, No.. A 1502, purchased of you is entirely satisfactory. Yours truly, (Signed) W. E. LUCAS, President and Treasurer. (Copy.) TAMAQUA, PA., March 4, 1897. MESSRS. J^UEEN & Co., INC., DEAR SIRS : Your Surveyors' Transit, No. A 1502,, has been received and we find it first-class in every particular. Yours respectfully, (Signed) WEAVER, SON & HALDEMAN, Builders and Contractors. 146 QUEEN & CO., INC., PHILADELPHIA. (Copy.) Buffalo, Rochester and Pittsburg Railway Company. ROCHESTER, N. Y., March 4th, 1897. QUEEN & Co., INC., GENTLEMEN : The Reconnoissance Transit, No. A 1508, which I purchased oi you for the use of one of my relatives has given entire satisfaction. It seems .to have been very well and thoroughly made, and the graduations are very accurate. Yours very truly, (Signed) WM. E. HOYT, Chief Engineer B., R. & P. Rwy. (Copy.) 254.1 Third Avenue. NEW YORK, February 22d, 1897 MESSRS. QUEEN & Co., INC., GENTLEMEN : I have been constantly using the Engineers' Transit, No. A 1494, which I bought from you in 1895, and I can safely say, not- withstanding the very inclement weather it has been subjected to, it has proved entirely satisfactory and one of the best instruments I have used ; my experience having covered a period of twenty years Respectfully yours, (Signed) P. E. AMIOT, B. S. A., Civil Engineer and City Surveyor. (Copy.) Department of Public Works, Fifth Survey District, 521 West Venango St. PHILADELPHIA, June gth, 189^ QUEEN & Co., INC., GENTLEMEN : The City and Bridge Transit, A 1490, which you built for me about three years ago has given perfect satisfaction. Yours truly, (Signed) WALTER BRINTON, Sur. and Reg. Fifth Dist. QUEEN & CO., INC., PHILADELPHIA. 147 (Copy.) RosELLE, N. J., April 6th, 1897. QUEEN & Co., INC., GENTLEMEN : Referring to your Engineers' Transit, No. A 1494, will say that I have been much pleased with the work I have been able to do with the instrument. It has been tested where varying degrees of accuracy were required, and the results have always been satis- factory. I should be pleased to recommend it to any would-be pur- chasers. Yours truly, (Signed) J. WALLACE HIGGINS. (Copy.) Wellington & Powdlsville R. R. Co. EDENTON, N. C., March 8th, 1897. MESSRS. QUEEN & Co., DEAR SIRS: Replying to your favor of the 2d, would say that the Engineers* Transit, No. A 1494, we bought of you in 1895 our chief engineer says is one of the finest he ever used. We notice since he has had this instrument that he has been able to give us better curves and grades over our road than he formerly did with the old instrument. Therefore we think it far superior to anything that we have had. Yours truly, (Signed) J. W. BRANNING, President. (Copy.) DUSHORE, PA.J February, 4th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : The Surveyors' Transit, No. A 1502, which I bought of you in May, 1895, is an excellent instrument and has given the best ot satisfaction. I do not believe that it can be surpassed, and the engineer owning one, is well equipped to do accurate work. Respectfully yours, (Signed) NATHAN PERSUN, C. E. 148 QUEEN & CO., INC., PHILADELPHIA. (Copy.) PITTSTON, PA., March 6th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : In reply to yours of 24th of February, it gives us much pleasure to be able to truthfully say, that the Transit you shipped us on the i3th of June, 1895, is giving us entire satisfaction in every way. We have done some very nice work with it and in all cases have been able to verify our work. The instrument has never been out of adjustment since we had it. Yours truly, (Signed) C. R. PATTERSON & SON, Architects and Civil Engineers. (Copy.) The W. J. McCahan Sugar Refining Co. PHILADELPHIA, March 4th, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS : Replying to your inqury of the 2nd inst., we beg to advise that the new improved Architects' Level, No. A 1532, purchased from you in August, 1894, has, so far, given perfect satisfaction. Yours very truly, THE W. J. McCAHAN SUGAR REFINING CO., (Signed) JAS. M. McCAHAN, Manager. (Copy.) MOORESTOWN, N. J., Feb. 24th, 1897. MESSRS. QUEEN & Co., INC.,- ^ GENTLEMEN : The Surveyors' Transit, No. Ai5O2, I bought of you April 2d, 1896, I find to be a very fine and accurate instrument, and surely -ought to satisfy any surveyor. Yours truly, (Signed) URIAH BORTON, Surveyor, Conveyancer and Commissioner of Deeds. QUEEN & CO., INC., PHILADELPHIA. 149 (Copy.) / 018 Academy Street. PHILADELPHIA, March, nth, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS : In answer to your inqury, the Architects' Level, No. A 1532, which I purchased from you in October, 1894, is very satisfactory indeed. I have used it a great deal, not only saving time, but obtaining more accurate results. I take pleasure in recommending it. Yours respectfully, (Signed) CHARLES J. W. PLATT, Carpenter and Builder. (Copy.) W. H. Ashwell& Co. DETROIT, MICH., Feb. 26th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : In reply to yours of the 24th, regarding the Full Engineers' Transit, No. Ai494, and Engineers' Y Level, No. A 1528, pur- chased from you in July, 1894, I beg to say that the same have been almost constantly in the field since that time and to-day are .virtually as good as the day they were purchased. Yours very truly, (Signed) WM. H. ASH WELL. (Copy.) W ABASH, IND., March i2th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : In May 1895, I purchased one of your Full Surveyors' Tran- sits, No. 1502, it has been in constant use and has given perfect satisfaction. Your improvements and workmanship are excellent, it has proved to be valuable and reliable in all respects. Yours very truly, (Signed) EDWARD A. LOWER, County Surveyor and Civil Engineer. 150 QUEEN & CO.. INC., PHILADELPHIA. (Copy.) in W. Third Street. JAMESTOWN, N. Y., March ist, 1897. MESSRS. QUEEN & Co., INC., SIRS : I purchased one of your Engineers' Transits, No. Ai494, las Fall and have used it in all kinds of weather since, part of thp tirm the mercury close to zero and found it exactly as represented. Respectfully, (Signed) C. B. V&H&Y.. (Copy.) GRAHAM, N. C., Manv 'fi'a, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : The Engineers' Transit, No. A 1494, purchased f/oni you on July 25th, 1895, was for a builder doing contract work for us. The instrument seemed to please him very much, and so f ar as we observed his work was very accurate with your instrument. Yours truly, ONEIDA COTTON MILLS, (Signed) L. BANKS HOLT, Proprietor. (Copy.) 874 Broadway. NEW YORK, March i, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS : The Architects' Level, No. A 1532, which we purchased from you about a year ago, has proved satisfactory beyond our expecta- tions. While we have never used it for a longer run than about half a mile, within that distance, sometimes over rough country, the results have checked out within one or two hundredths, tfce rod being read only to hundreths. In other words, on all work for which we have used it, it has been as satisfactory and appeared as accurate as if we had used our regular Engineer's Level. It has been in nearly continuous use since we purchased it. Very truly yours, (Signed) WARING, CHAPMAN & FARQUHAR. QUEEN & CO., INC., PHILADELPHIA. 151 (Copy.) 233 W. Third Street. WILLIAMSPORT, PA., March 4th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : Referring to your communication of 2d inst., we are pleased to state that the Full Engineers' Transit, No. A 1494, we purchased of you Nov. 1 7th, 1894, has been in constant use up to date. It has been a profitable instrument and we appreciate its value, as a labor saving and accurate instrument. Most respectfully, (Signed) W. H. C. HUFFMAN & SONS, Architects and Builders. (Copy.) CANTON, PA., March 23d, 1897. QUEEN & Co., INC., GENTLEMEN : We have been using your Engineers ' Transit, No. A 1494, now for over eighteen months and have done some very accurate and satisfactory work. It is very light to carry, but at the same time very rigid and accurate. -We do not hesitate to say that it is, in our estimation, the height of perfection. Respectfully yours, (Signed) CLARK & JEWELL, Surveyors. (Copy.) Office of County Surveyor. WAVERLY, O., March 8th, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : Permit us to say that the 20 in. Improved Engineers' Y Level bought of you has, after two years' service, proved to be all that is claimed for it ; and I see no reason why it should not endure a life- time. Not a single adjustment has been required in the two years' service to which it has been subjected. Respectfully, (Signed) H. W. OVERMAN, County Surveyor and City Engineer. I 5 2 QUEEN & CO., INC., PHILADELPHIA. (Copy.) STEUBENVILLE, O. Feb. 26th, 1897. QUEEN & Co., INC., GENTLEMEN : The Complete Engineers' Transit, No. A 1494, which I bought of you May 5th, 1894, has been thoroughly tried in active service ever since, and I have found it the most accurate and convenient transit I ever used. Yours truly, (Signed) C. E. FLANAGAN, Civil Engineer, (Copy.) 211 South roth Street. PHILADELPHIA, Feb. i9th, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS : The Engineers' Transit, No. A 1494, purchased from you last March, has given perfect satisfaction. The operator is very much pleased with it. Two of our surveyors who furnish their own instruments also use those made by you and speak very highly of them. Yours truly, (Signed) D. L. RISLEY, Real Estate Operator. . (Copy.) ments, including Full Engineers' Transit, No. Ai5O2, and Engi- neers' Y Level, No. A 1528, for the past eighteen months, and it affords us pleasure to recommend them to any one desiring to use first-class engineering instruments. Very truly, (Signed) T. J. PHILLIPS & CO. QUEEN & CO., INC., PHILADELPHIA. 161 (Copy.) DAVIDSON COLLEGE, N. C., March gth, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : In reply to your recent letter it gives me pleasure to state that the econnoissance Transit, No. A 1518, which the college bought from you three years ago, has given entire satisfaction in every respect. Yours truly, (Signed) W. D. VINSON, M. A., LL. D. Professor Mathematics. (Copy.) No. 70 Kilby St. BOSTON, MASS., February 23d, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS : Replying to yours of the i9th requesting our opinion of the combined Transit and Level, No. A 1494, which you shipped us on January 28th, 1896, would say that we did not give this instrument any great amount of use, as it was destroyed in the fire which we had at our works last Fall, but from the use which we did give it, we found it to be a very satisfactory instrument, exceed- ingly light and portable. Yours truly, BOSTON BRIDGE WORKS, (Signed) R. N. BROWN, Chief Engineer. ARDMORE, PA., March loth, 1897. MESSRS. QUEEN & Co., INC., DEAR SIRS: The Architects' Level, No. A 1532, received from you a year ago has given me great satisfaction. It has never been out of order, or required adjustment so far, although we have done a great deal 01 with it. Yours truly, (Signed) EDWARD CAMPBELL, Landscape Architect. 162 QUEEN & CO., INC., PHILADELPHIA. (Copy.) The Pusey & Jones Co. WILMINGTON, DEL., February 24th, 1897. MESSRS. QUEEN & Co., INC., OENTLEMEN : I purchased one of your Improved i8-in. Engineers' Y Levels early in the year 1896 and have used it on many occasions. It affords me pleasure to state that this instrument has been very satisfactory in every respect. Yours truly, . (Signed) T. H. SAVKRY, V. P. (Copy.) SALEM, MASS., March 2d, 1897. MESSRS. QUEEN & Co., INC., GENTLEMEN : In reply to yours in regard to the i8-in. Engineers' Y Level, would say that I like it very much. It is neat, light, handy, and has excellent lenses. Anyone wanting such an instrument I should certainly recommend your make. Very truly, (Signed) JOS. C. FOSTER. (Copy.) Grandview Cemetery Co. WILLIAMSPORT, PA., March 5th, 1807. MESSRS. QUEEN & Co., INC., GENTLEMEN: The Architects' Level, No. A 1532, purchased of you has given entire satisfaction, the adjustment and finish being perfect and its work accurate. Yours truly, (Signed) J. W. MUSSINA. INDEX. PAGE. Alt-Azimuth 18, 19 Architects' Levels 60, 61, 62- Alt-Azimuth (Pocket 97 Artificial Horizon 98 Anisler Planimeter 98 Angle Mirrors IOI Aneroid Barometers in, 112, 113 Anemometers 114, 115 Builders' Transits 52, 53 City and Bridge Transits 20, 21, 22, 23, 24 Clinometers 94, 95 Cross Staff Heads . . . . * , . . . 100 Chains 109. Diagonal Prisms 67 Engineers' Transits 28,29,30,31,32,33,34,35 Engineers' Y Levels 58, 59 Explorers' Transit 25 Extras and Parts . . . . 63, 64, 65, 66, 67, 68, 69 Gradienter 64 Geologists' Compasses 81 Hand Levels 92, 93 Heliograph 97 Light Mountain Transits 42, 43, 44, 45, 46, 47, 48, 49 Land Levels 63 Machininists' Levels 95 Marking Pins no Magnifying Glasses . . . , '. 116 Odometers 102 Plane Tables 54,55 Precision Levels 56, 57 Plummet Lamps 67 Pocket Compasses 77, 78, 79 Prismatic Compasses 82, 83, 84 Pedometers IOI, 102 Plumb Bobs no Reconnoissance Transit 50, 51 Reflectors 67 Repair Work 71 Rods 72, 73, 74, 75 Reflecting Mirrors 100 Rectangular Prisms . . . 100 Surveyors' Transits . . * 36, 37, 38, 49, 40, 41 Solar Attachment 6tf Side Telescopes . . ;_ 66, 67f Spirit Levels . -. TO Sight Compasses 80 Surveyors' Pocket Compasses 85 Surveyors' Compasses 86, 87, 88, 89, 90, 91 Sextants 96, 97 Stake Tacks no Scientific Books 119 to 142 Transit Theodolite 16, 17 Tripods 76 Tapes 103, 104, 105, 106, 107, 108 Time Charts 117, "* Tilting Level 61 Tunnel Transits 26, 27 Vernier Attachment. 65 WE PUBLISH PRICED AND ILLUSTRATED CATALOGUES As follows, any or all of which will be mailed on receipt of price : Catalogue Mathematical. Containing Drawing Instruments, Protractors, Scales, Calculating Instruments, Planimeters, Tri- angles, T Squares, Curves, Rulers, Drawing Boards, Drawing, Tracing and Profile Papers, Erasers, Pens, Pencils, Ink, etc. Price, 20 cents. Catalogue Engineering. Containing Transits, levels, Compasses, Rods, Tapes, Scientific Books, etc. Price, 15 cents. Catalogue B. Microscopical Instruments, 108 pages. Contains list and prices of Reading-glasses, Simple Microscopes, Compound Microscopes, Microscopic Objectives and Accessories, Mounting Materials, Microscopic Objects (including Histological and * Pathological Specimens), Works upon Microscopy, Graphoscopes,, Stereoscope, etc., etc. Price, 35 cents. Catalogue C. Second-Hand Microscopes, Accessories, etc., 16 pages. Catalogue D. Ophthalmological Instruments, 125 pages. Contains description and prices of all good forms of Spectacles and Eye-glasses, with copious explana- tions, Models of the Eye, Artificial Eyes, Ophthalmoscopes, Phakometers, Optometers, Trial Sets, Trial Frames, Test Cards, Color Tests, Works upon the Eye, etc., etc. Price, 20 cents. Catalogue E. Spectacles and Eye-Glasses, 75 pages. Contains description and prices of all the latest styles of Spectacles and Eye-Glasses, Lorgnettes, Eye* Glass Chains, Hooks, Cases, etc. Price, 10 cents. How to Fit Glasses, 112 pages. A Manual for the use of Opticians, Jewelers, Druggists and others who sell Spectacles and Eye- Glasses. It is concisely and plainly written, with illustrated cases. A supplement contains list of such goods as dealers in glasses would require. The whole is indispensable to one who wishes to be- come an Optician, and is also replete with information of great value to one who is already familiar with the optical trade. Profusely illustrated. Price, 75 cents. Catalogue F. Opera-Glasses, Tourists^ Glasses, Race-Glasses. Field-Glasses and Spy- Glasses, 43 pages. Price, 10 cents. Catalogue G. Astronomical Telescopes and Appliances^ 36 pages. Price, 8 cents. Catalogue H. Projecting Lanterns and Views, 132 pages. Contains list and prices of Lanterns for Public and Private Exhibitions, Sciopticons, Stereopticons, Scientific Lanterns, and accessory apparatus to be used with them; Lantern Slides of all descrip- tions. Price, 15 cents. Catalogue I. Physical Instruments, 255 pages. Contains list and prices of instruments to illustrate lectures in every department of Physics and Chemical Science, Air Pumps, Electric Machines, Galvanic Batteries, Globes, Auzoux's Anatomical Models, and books relating to Scientific Subjects. Price, 40 cents. Catalogue I, No. 46. Physical Optics, 30 pages. Price, 6 cents. Catalogue K. Chemicals, 48 pages. Price, 6 cents. Catalogue N. Meteorological Instruments, 127 pages. Contains lists and prices of Thermometers, Mercurial and Aneroid Barometers, Hygrometers, Ane- mometers, Rain Gauges, Wind Gauges, Tide Gauges, Current Meters, Pyrometers, Hydrometer, Salinometers, Vacuumeters, Water Gauges, Miners' Safety Lamps, Pressure and Vaccuum Gauges, and all instruments for measuring Steam, Air, Gas or Water. Price, 12 cents. Catalogue O and P. Photographic Apparatus, 140 pages. Including Cameras, Lenses, Dry Plates and Photographic Supplies. Price, 12 cents. Catalogue S. Chemical Apparatus, 375 pages. Contains list and prices of Apparatus as used in every department of Chemistry. Price, 50 cents. Catalogue X. Electrical Test Instruments, 72 pages. Price, 10 cents. Catalogue 221. Anatomical Models, 24 pages. Price, 6 cents. The price of any of our single Catalogues will be deducted from the first order amounting to $10. We will bind all our Catalogues mentioned above in cloth with leather back, and mail the complete book to any address for $3.50. QUEEN & CO., Mathematical, Optical and Philosophical Instruments, 1010 Chestnut Street, Philadelphia. THE HOUSE ...OP... QUEEN & Co., inc. Was established in 1853 and REORGANIZED in 1896, and consists of the following Sales Departments : Optical Department, comprising Optical and Ophthalmological Instruments, and Field and Opera Glasses. Mathematical and Engineering Department, comprising Drawing Instruments and Materials, and Engineering and Surveying Instruments. Microscopical Department, comprising Microscopes ; Magnifiers, and Botanical and Bacteriological Supplies. Physical and Electrical Department, comprising Physical and Electrical Instruments and Apparatus, X-Ray Apparatus and Anatomical Models. Astronomical and Projection Department, comprising Projection Apparatus, Astronomical Telescopes and Polar- izing Apparatus. Meteorological Department, comprising Meteorological Instruments, Barometers and Thermometers and Pyrometers for physical and technical use. Photographic Department, comprising Cameras and Lenses, and Photographic Supplies in general. Chemical Department, comprising Chemicals and Chemical Apparatus and Fine Balances. These Sales Departments depend principally upon our WELL EQUIPPED FACTORIES, of which we maintain the following : Physical, Electrical and Engineering Instrument Factory, Optical Factory, Thermometer and Chemical Glassware Factory, Electrical Laboratory, Wood Working Factory. Each of our Sales and Manufacturing Departments is under a competent manager, with whom is associated an able corps of assistants, many of whom are recognized experts in their special lines. Jn addition to our own products, we represent a number of well-known foreign houses about whose apparatus, which we can supply, either from stock or import duty free for institutions, we are at all times prepared to give information. M.OGUE and CIRCULARS of any of the departments will be sent free by mail upon application. QUEEN & CO., Inc. ioio Chestnut Street NEW YORK BRANCH, 59 Fifth Avenue PHILADELPHIA saimiiiwwvFvvvf ,, .................>............................,.,.. ................................................................................ ,.... "QUEEN" FULL ENGINEERS' TRANSIT. ! 14 DAY USE RETURN TQ RROWED This book is due on the last date stamped below, or on the date to which renewed. Renewed books are subject to immediate recall. iMar'57PW : REC D LD f L ij or J^N- i t-tb 25 iybA ^'sn'lOUri 64 Uoiv^S^C^rnia Berkeley YC