RETAINING WALL! FOR FAPTH PvJi\ LLntfxJ I I E LIBRARY UNIVERSITY OF CALIFORNIA. Class WORKS OF PROF. M. A. HOWE PUBLISHED BY JOHN WILEY & SONS. The Design of Simple Roof-trusses in Wood and Steel. With an Introduction to the Elements of Graphic Statics. 8vo, vi -fi29 pages, 67 figures, and 3 folding plates. Cloth, $2.00. Retaining walls for Earth. Including the Theory of Earth-pressure as Developed from the Ellipse of Stress- With a Short Treatise on Foundations. Illustrated with Examples from Prac- tice. Third edition, revised and enlarged. izrno, cloth, $1.25. A Treatise on Arches. Designed for the use of Engineers and Students in Technical Schools. 8vo, xxv + 351 pages, 74 figures. Cloth, $4.00. RETAINING- WALLS FOR EARTH. INCLUDING THE THEORY OF EARTH-PRESSURE AS DEVELOPED FROM THE ELLIPSE OF STRESS. WITH A SHORT TREATISE ON FOUNDATIONS, ILLUSTRATED WITH EXAMPLES FROM PRACTICE. BY MALVERD A. HOWE, C.E., Professor of Civil Engineering, Pose Polytt clinic Institute f Member American Society of Civil Engineers. THIRD EDITION, REVISED AND ENLARGED. FIRST THOUSAND. NEW YORK: WILEY & SONS. LONDON : CHAPMAN & HALL, LIMITED. 1905. Copyright, 1896, BY MALVERD A. HOWE. ROBERT DRUMMOND, ELKCTROTYPKR AND PRINTER, NEW YORK. CONTENTS. THEORY OF EARTH-PRESSURE. PAGE Preliminary Principles 1 Resultant of Principal Stresses. Case 1 2 Case II 3 Caselll 3 Earth-pressure against a Vertical Plane 9 Direction of Resultant Earth-pressure against a Vertical Plane. . 11 Intensity of Earth-pressure against a Vertical Plane at any given Depth 12 Average Intensity of Earth-pressure against a Vertical Plane. ... 13 Graphical Construction for finding Thrust of Earth against any Plane 13-15 General Formula for the Thrust of Earth 15-17 " " " " Direction of the Resultant Earth-pressure 18 Plane of Rupture 18 Reliability of Theory 19 Earth Sloping Down and Away from Wall Special Method. . . 21 FORMULAS FOR EARTH-PRESSURE. Recapitulation. General Formula 23 Surface of the Earth inclined, a 24 Surface of the Earth Parallel to the Surface of Repose 24 Surface of the Earth Horizontal 25 ill \ IV CONTENTS. PAGE Fluid Pressure 25 Graphical Construction for determining the Thrust of Earth against any Plane 25 STABILITY OF TRAPEZOIDAL WALLS. Stability against Overturning 29 " Sliding 29 " " Crushing of Material 80 Determination of the Width of Base of a Trapezoidal Wall 33 FORMULAS FOR TRAPEZOIDAL AND TRIANGULAR WALLS. General Formula for Trapezoidal Walls 34 Formula for Vertical Wall 34 " "a Wall with a Vertical Back resisting a Normal Earth-pressure 35 General Formula for Tria'ngular Walls 36 Special Cases of Triangular Walls 36 FOUNDATIONS FOR WALLS RETAINING EARTH. General Discussion 37 Depth of Foundations 38 Depth of Foundation when the Intensity of the Pressure upon the Base is Uniform 39 Depth of Foundation when the Intensity of the Pressure upon the Base is Uniformly Varying 39-40 Depth of Foundation when the Earth has Different Depths on Opposite Sides of the Wall 41 Determination of the Breadth of the Base of a Trapezoidal Foundation 42 Abutting Power of Earth 43 Bearing Power of Earth 43 CONTENTS. T EXAMPLES. PAOE Examples illustrating the Application of Formulas for Earth- pressure, Depth of Foundations, etc 44-60 Examples of Retain ing- wall Profiles 61-65 FOUNDATIONS. Foundations upon Rock 66 Maximum Deviation of Resultant Pressure from the Centre of the Base of the Foundation 67 Ultimate Compressive Strengths of Stone 68 Foundations upon Earth 68 Firm Earth 68 Determination of the Breadth of a Symmetrical Trapezoidal Foundation 73 Examples 74 Unsymmetrical Distribution of Pressure upon the Base of the Foundation 75 Formula for Breadth of the Base 76 Projection of Foundation Courses, etc 77, 78 Table of Safe Projections of Courses 79 Foundations" upon Soft Earth 78 Projection of Steel or Iron Beams used in Foundations 80 Table of Safe Projections 81 Pile Foundations 81 Formula for Minimum Depth of Pile 83 Trautwine's Formula 85 Engineering News Formula 85 Screw Piles 85 Sheet Piles 86 FOUNDATIONS UNDER WATER AND DEEP FOUN- DATIONS. Coffer-dams 87 Timber Cribs 87 Open Caissons 88 VI CONTENTS. PAGE Gushing Cylinder Piers 89 Pneumatic Caissons ;,. . . 89 TYPES OP EXISTING FOUNDATIONS 90-97 REFERENCES, LIST OF 99-102 DIAGRAM I.... 103 TABLES. Weights of Materials 106 Angles and Coefficients of Friction 107 Values of Functions B, C, D, and E 108-110 Natural Sines, Cosines, Tangents, and Cotangents 111-132 PREFACE TO THE SECOND EDITION. THE first edition of this work was based upon the theory advanced by Prof. Weyraucb in 1878, but owing to the length of the demonstrations used by him,, it was thought advisable to present different and shorter demonstrations in this edition. To show that the new demonstrations give identical results with those obtained by Prof. Weyrauch, his demonstrations have been given in an appendix as they appeared in the first edition. The new demonstrations are based upon the theory first advanced by Prof. Rankine in 1858. Those readers who are familiar with Rankine's Ellipse of Stress can omit pages 1 to 9, inclusive, in following the demonstrations. An attempt has been made to present the theory in a shape easily followed by those who have only a knowledge of algebra, geometry, and trigonometry; whenever cal- culus has been resorted to, the work has been simplified as much as possible. For convenience in practice, the formu- las have been arranged in a condensed shape in Part I, and are followed by numerous examples illustrating their application. The values of various coefficients have been computed and tabulated and will be found to very materially decrease the labor of substitution in the formulas. vii vm PREFACE. It is hoped that the introduction of a brief treatment of the supporting power of earth in the case of foundations, as well as the formula for determining the breadth of the base of a retaining-wall, will prove acceptable. For valuable help in the verification of proofs of formu- las, and the critical reading of the whole text, I acknowl edge the kind assistance of Prof. Thos. Gray. M. A. H. PREFACE TO THE THIRD EDITION. IN this edition a large number of examples illustrating several profiles of retaining-walls and types of foundations selected from existing structures have been included. The Appendix of the second edition has been replaced by a treatise on Foundations sufficiently short and, the author believes, sufficiently complete for the use of technical schools, if judiciously supplemented by lectures or refer- ences to descriptions of existing structures. M. A. H. TERRE HAUTE, IND., Nov. 1896. NOMENCLATIVE. = the angle of repose, or the maximum angle which any force acting upon any plane within the mass of earth can make with the normal to the plane. e = the angle made by the surface of the earth with the horizontal; e is positive when measured above and negative when measured below the horizontal. a = the angle which the back of the wall makes with the vertical passing through the heel of the wall; a is positive when measured on the left and nega- tive when measured on the right of the vertical. 6 = the angle which the direction of the resultant earth- pressure makes with the horizontal. 0' = the angle of friction between the wall and its foun- dation. 0" = the angle of friction between the back of the wall and the earth. H = the vertical height of the wall in feet. h = the depth of earth in feet which is equivalent to a given load placed upon the surface of the earth. B' = the width in feet of the top of the wall. B = the width in feet of the base of the wall. Q the distance in feet from the toe of the wall to the point where R cuts the base. ix X NOMENCLATURE. P = the resultant earth-pressure in pounds against a ver- tical wall. E = the resultant earth-pressure in pounds against any wall. R = the resultant pressure in pounds on the base of the wall. G the total weight in pounds of material in the wall. y = the weight in pounds of a cubic foot of earth. W = the weight in pounds of a cubic foot of wall. p = the intensity of the pressure in pounds on the base of the wall at the toe. p' = the intensity of the pressure in pounds on the base of the wall at the heel. p o = the average intensity of the pressure in pounds on the base of the wall. x = H tan a. x" and x f = depth of the base of the foundation below the earth surface. B" = breadth of the base of the foundation. o = the oifset of a foundation course. G' = the total weight of the material above the base of the foundation. THEORY OF EARTH-PRESSURE. Preliminary Principles. Before demonstrating the gen eral formula for the thrust of earth against a wall, it will be necessary to establish the relations between the stresses in an unconfined and homogeneous granular mass. * In Fig. 1 let ABC be any small prism within a granu- H F Q .E Fio. 1. lar mass which is in equilibrium un^er the action of the three stresses P, Q, and R, having the intensities^, q, and r respectively. * In all the demonstrations which follow, the dimension perpen dicular to the page will be considered as unity. 1 2 THEORY OF EARTH-PRESSURE. Let represent the angle of inclination of the plane CB with AB, and the angle at A be a right angle. The planes AB and AC are called planes of principal stress, and P and Q are called principal stresses. CASE I. If tliQ principal stresses are of the same kind and their intensities the same, then will the resultant stress on any third plane he normal to that plane and its inten- sity be equal to that of either principal stress. In Fig. 1, for convenience, let AB = 1, then A C = tan 6, and CB -- -. Hence P = p, Q=:qtanO = p tan 6, since p = q, and R = -- fi . COS u Since P, Q, and R are in equilibrium, they will form a closed triangle, as shown on the right in Fig. 1. Hence or tan 8 e =/>'(! + tan 8 Also, Rco8FDE=P, or -7, cos FDE = p-, but r =p. cos u Hence cos 6 = cos FDE = cos HDG; .'. HDG = 6 and R is normal to CB. THEORY OF EARTH-PRESSURE. 3 CASE II. If the principal stresses are not of the same kind but their intensities the same, then will the resultant make the angle 6 witli the direction of the principal stress, but on the opposite side from that on which the resultant in Case I lies, and its intensity be equal to that of either prin- cipal stress. The demonstration of Case I proves this principle if Fig. 1 is replaced by Fig. 2. FIG. 2. CASE III. Given the principal stresses of the same kind but having unequal intensities, to determine the intensity and direction of the resultant stress on any third plane. Let P and Q be compressive and the intensity^ > the intensity q. The following identities can be written: and 4 THEORY OF EARTH-PRESSURE. or the resultant intensity on the plane CB may be con- sidered as being the resultant of two intensities, one being the intensity of the resultant stress caused by two like prin- cipal stresses having the same intensity \(p -j- q), and the other the intensity of the resultant stress caused by two unlike principal stresses having the same intensity %(p q)- FIG. 3. The intensity of the resultant stress caused by the first two principal stresses will be, by Case I, %(p + q), and the direction of the resultant will be normal to the plane CB. By Case II the resultant of the second pair of principal stresses will make the angle with the direction of P y and its intensity will be %(p q)', then the resultant intensity can be .found as follows: In Fig. 3 draw MD normal to EC, and make LD = J(j0 + 9 f )j with L as a centre and LD as radius, describe an arc cutting FD at F. Then the angle LFD = LDF = B. Lay off LG \(p q), and draw GD, which is the result- THEORY OF EARTH-PRESSURE. 5 iint intensity, and the intensity of the resultant stress on OD caused by the two principal stresses P and Q. GD ;;lso represents the direction of the resultant stress R. Since the intensities of the principal stresses remain con- stant, %(p -\- q) and \(p q) will remain the same for any inclination of the plane GB\ hence the intensity r of the resultant depends upon the angle when p and q are given. From Fig. 3, GL cos 20 = LM and GL sin 20 = GM, DM=DL + LM=$(p + q) + \(p - q) cos 20, or r = Vp* cos 3 + q* sin 2 0, .... (a) which is the general expression for the intensity of the resultant stress of a pair of principal stresses. As the angle changes, the angle ft will also change, and it will have its maximum value when the angle LGD = 90. This is easily proven as follows: With L as centre and GL as radius describe an arc; then ft will have its maximum value when the line DG is tangent to the arc; but when DG is tangent to the arc the angle LGD is a right angle, since LG is' the radius of the arc. sin max ft = - -- -, ..... (b) from which the following can be easily obtained: p 14- sin max ft -* - ' ___ J_ (Ct q 1 sin max ft' 6 THEORY OF which expresses the limiting ratio of the intensities of the principal stresses consistent with equilibrium, p being greater than q. CASE IV. Given the intensity and direction of the re- sultant stress on any plane, and the value of max (3, to determine the intensities and directions of the principal stresses. FIG. 4. Let ^4/) represent the given plane and GD the direction and intensity of the resultant stress at the point D. Draw DL normal to AD, and draw Dl, making the angle max ft with LD. At any point J in DL describe an arc tangent to DI, cutting GD in K and draw GL parallel to KJ\ with L as a centre and LG as radius describe THEORY OF EARTH-PRESSURE. 7 & circumference. This circumference will pass through G C* T and be tangent to DI\ hence -777 = sin max /?. L) j ffl _ Q Since sin max /3 = - -- - , and GL and LD are com- p + q ponents of r, GL = l(p-q) and DL = \(p + q); then ND = NL + LD = l(p-q)+i(p + q)=p, and MD = LD - LM = l(p + q) - l(p - q) = q, which completely determines the intensities of the principal stresses. According to Case III, the direction of the greater prin- cipal stress bisects the angle between the prolongation of LM and the line GL; hence RL represents the direction of the greater principal stress, and that of the other is at right angles to RL. The above intensities and directions being determined, the intensity of the resultant stress on any other plane passing through D is easily determined as follows: Let DY represent any plane passing through D, draw DL' normal to DY and equal to %(p -f q). Draw R'D parallel to RL, and with L' as a centre and L'D as radius describe an arc cutting R'D at 0, and make L' G' = i(jP~~~S r )5 then G'D = r' = the intensity of the resultant stress on DY. It is clear that if the value of max fi can be obtained for a mass of earth that the construction of Fig. 3 can be employed in determining the intensity of the earth-pressure at any point in any plane within the mass. R THEORY OF EARTH-PRfflSURfi. It has been established by experiment that if a body be placed upon a plane, that (as the plane is made to incline to the horizontal) at some angle of inclination the body will commence to slide down the plane, and that this angle depends largely upon the character of the surfaces in con- tact. E FIG. 5. In Fig. 5 let AB represent a plane inclined at the angle with the horizontal, and C any mass just on the point of sliding down the plane. Let EC represent the weight of the mass C, and ED and DC the components respectively parallel and normal to the plane AB. Then DE is the force required to just keep the mass C from sliding down the plane, assuming the plane to be perfectly smooth, or if the plane is rough this force represents the effect of fric- tion. DE or when the mass C is about to slide, the resultant pres- sure EC on AB makes the angle with the normal to the THEORY OF EARTH-PRESSURE. plane, the angle being the inclination of the plane A />, and is called the angle of friction. In the case of earth, considered as a dry granular mass, the inclination of the steepest plane upon which earth will not slide is called the angle of repose, and the plane the surface of repose. From the above, then, it follows that in a mass of earth the resultant pressure on any plane cannot make an angle with the normal to that plane which is greater than the angle of repose ; therefore the construction of Case IV applies to earth when max ft is replaced by > equals the triangle LYD and the angle G' DL' e; or tf/ae direction of the resultant earth-pressure against a vertical plane is parallel to the surface of the earth. From Fig. 6, i( P ~ 4) cos ^ = &X y> y cos e DY=DG' = DG- or /)#' ^ = Z>^- y (p 7) cos GO - \(P + Q) cos e - {(p - q) cos GO, i(p-\-q):sm&) :: $(p - q) : sin e, and P + 9 - sin to = - - sin e, P-0 or cos = - and since J(p + g') sin = J(^ g), GO = - - ^cos 2 e cos 2 0. cos sin 12 THEORY OF EARTH- PRESSURE. Substituting this value for cos GO in the equation for DO' . y, it becomes V) cos e - i(p-q) -- 1/cos 2 e - cos 2 0, or since sin ^ DG' - y J(p -j- 6r cos e -f- '/cos 2 e cos 2 cos e -f Vcos 2 e cos 2 Let x = the vertical distance between the two planes BQ and A D, then /)# = DQ = x cos e. / _\ r.^. / \ / cos e 4/cos 2 e cos 2 A . '. />' y = (x) y\cos e - ., A cos e -j- v cos 2 e cos 2 which is the expression for the intensity of the resultant earth-pressure on a vertical plane at any depth x below the surface. Let * A cos e Vcos 2 e cos 2 , n * ^4 = cos e - -= =. . . (d) cos e -j- '/cos 2 e cos 2 * See Rankine's Applied Mechanics ; Alexander's Applied Me- chanics j Theories of Winkler and Mohr. THEORY OF EARTH-PRESSURE. 13 The average intensity of the resultant earth-pressure on a vertical plane of the length x will be ind hence the total pressure will be P = ~yA. . (e) Since the intensities of the pressures are uniformly varying from the surface, and increasing as x increases, the appli- cation of the resultant thrust will be at a depth of \x be- low the surface. Considering the earth as an unconfined mass, the above formula is perfectly general and can be applied under all conditions, including the case when e is negative. The resultant stress on any plane as AB, Fig. 6, can be found by applying the principles of Case IV. Draw PA parallel to RL, make AN = ZDand NO = LG\ then AO represents the direction of the resultant pressure on AB. Make A C = AO', then the area of the triangle ABC mul- tiplied by Y is the total pressure on the plane AB, and this pressure is applied at \AB below B. In unconfined earth this construction is perfectly gen- eral and applies to any plane. It also applies equally well to curved profiles. An example illustrating the applica- tion of the method will be given in the applications. See pages 22 and 23. The following graphical construction, Fig. 7, is more con- venient than that of Fig. 6. As before, let BE represent the surface of the earth, and 14: THEORY OF EARTH- PRESSURE. A D a plane parallel to the surface. At any point D in tliis plane, draw DE vertical and make DF = DE \ draw FG horizontal and make the angle HFD = 0. With L as a centre, describe an arc passing through G and tangent to MF' 9 then with L as a centre and LF as FIG. 7. radius, describe the circumference FON, cutting A D at N; through JV draw NO parallel to AB, then draw AC nor- mal to AB and equal to OG. The area of the triangle ABC multiplied by y will be the total earth-pressure on AB. To determine the direction of the thrust prolong OG to Q, then QN is the direction of the thrust. That this construction is equivalent to that of Fig. 6 is THEORY OF EARTH-PRESSURE. 15 proved as follows. The triangle GLF of Fig. 7 equals the triangle OLD of Fig. 6. q) and LF-y == LO-y == In Fig. 6, the angle JV^P = JVPJ. = 90- i(oj-e) - . In Fig. 7, the angle OLN=2e-2a. But GLN c^+e. .-. = w.e + Za, and of Fig. 7 equals AO of Fig. 6. In Fig. 7, the angle QNO = 90 - /?'. In Fig. 6, the angle OAB = 90 /?'. Therefore the direction of the thrust is the same in both constructions. The two constructions given above are all that is re- quired to determine the thrust of earth upon any plane within the mass of earth, as one can be used as a check upon the other; but as a formula is often very convenient, a general formula will now be deduced which will enable one to determine the values of E and d for any plane with- in a mass of earth. GENERAL FORMULA FOR THE THRUST OF EARTH. In Fig. 8, let BQ represent the surface of the earth and A B any plane upon which the earth-pressure is desired. Draw AD parallel to BQ and lot the vertical distance QD = FA = x. 16 THEORY OF EARTH- PRESSURE. From (e) the earth-pressure upon FA is parallel to the surface and equal to FIG. 8. But AF= x = H(l + tau a tan e) = // cos ( 6 ~ a l. cos a cos e cos e v ' cos cos e Now the thrust P combined with the weight of the prism ABF must produce the resultant pressure upon AB. THEORY OF EARTH-PRESSURE. 17 Then from Fig. 8, H*y V ^- tan a (1 -f tan a tan e) A H*y sin a cos (e a) ~T~ cos 2 a cos e ' * ^ ^ = |/( F+P sin e) 2 4-(P cos e) 2 = V F 2 +P a -j- 2 FP sin e. Substituting (/) and (#) in this it becomes cos (e - a) 2 cos 8 a cos e 4/ sin 2 a -4- 2 sin a sin e cos (e a) }- cos 2 (e cos e ' cos- e which becomes, by replacing A by its value from (d ), _ ~" 2 cos' 1 a cose + sin 2 a I cos e 4/cos* e cos 2 -j- 2 sm "

4 FORMULAS FOR EARTH-PRESSURE. where cos e Vcos? e cos 2 A = cos e . cos e -+- r cos 2 e cos 2 CASE II. Surface of earth inclined and a = 0. / cos e + r cos 8 e cos 2 (2) From Diagram I the values of A can be found for all values of from to 90 and of e from to 90, vary- ing by 5. 6 = e; ....... (2a) or for all vertical walls the direction of the earth-pressure is parallel to the surface of the earth. CASE III. The surface of the earth parallel to the surface of repose. 6=0. E _ Iy_ cos (0 a) ./sin 2 a + cos 2 (0 a) ,^\ 2 cos 2 a cos ^ + 2 sin or sin cos (0 oi)' t an rf = Bina + rin^B,^ -a) _ COS COS (0 ) CASE IV. T7ie surface of the earth parallel to the surface of repose and the back of the wall vertical. e = and a 0. ^=^ Z cos0 (4) d = . (4rt) FORMULAS FOR EARTH-PRESSURE. 25 CASE V. The surface of the earth horizontal. E = = y tan 2 a + tan 4 ^45 ^V . (5) tan a tan 6 = tan' (45- f) CASE VI. The surface of the earth horizontal and the back of the ivall vertical. e = and a = 0. (6) 6 = ........... (6a) CASE VII. Fluid pressure. e = = 0. $=a (7a) GRAPHICAL CONSTRUCTIONS FOR DETERMINING THE THRUST OF EARTH. The following constructions are perfectly general, and apply to any plane within a mass of earth. When applied 26 FORMULAS FOR EARTH-PRESSURE. for determining the thrust of earth against a retaining-wall, a and e are taken as positive. * Construction (a). Let BE represent the surface of the earth and BA the back of the wall. Draw AF parallel to BE; and at any point D in AF lay off DF equal to the vertical DE. Draw FIG. 10. FG horizontal, and FH, making the angle with DF. With any point J in DF describe the arc KI tangent to HF at / cutting FG at K, and draw GL parallel to KJ\ with L as a centre and LF as radius, describe the circum- ference FQON cutting AD at N. Through J^draw NO * See "Theorie desErddruckes auf Grund der neueren Anschau- ungen," by Prof. Weyrauch, 1881. FORMULAS FOR EARTH-PRESSURE. 27 parallel to AB cutting the circumference FQON at 0; at A draw A C equal to OG and normal to AB; the area of the triangle ABC multiplied by y will be the thrust of the earth on the wall. To determine the direction of the thrust E, prolong OG to (); then QN will be the direction of the thrust. This thrust acts on the wall at \AB below B. * Construction (b). Let BQ represent the surface of the earth, and BA the back of the wall. Draw AD parallel to BQ, and at any FIG. II. point D in AD draw the vertical DG equal to the normal DQ\ draw DM making the angle with the normal DQ. * This construction follows directly from Rankine's Ellipse of Stress. See Rankiue's Applied Mechanics. 28 FORMULAS FOR EARTH-PRESSURE. At any point J in DQ as a centre, describe the arc //T tan- gent to DM cutting DG at K, and draw GL parallel to JK. Bisect the angle gZ^/and at ^4 draw ^4P parallel to LR. At .4 draw ^A^ normal to AB and equal to DL\ with JV as a centre and ^lA^ as radius, describe an arc AP cutting AP at P- connect P and N, and make ^VO equal to LG\ with ^4 as a centre and A as a radius, de- scribe the arc OC cutting AN at C ; then the area of the triangle ABC multiplied by y will be the thrust against the wall. The direction of this thrust is parallel to A and it is applied at \AB below B. The constructions (a) and (b) give identical results in every case. STABILITY OF TKAPEZOIDAL WALLS As the majority of walls retaining earth are trapezoidal in section, the stability of such walls alone will be considered. If other forms occur in practice they can be divided into trapezoidal sections with horizontal beds, and the stability of each considered, commencing with the upper section. Walls having the rear faces in the form of steps can usually be considered as trapezoidal in section by re- placing the stepped portion by a straight line which approximately bisects each step. If the front faces are stepped they can be treated in a similar manner. In case the front face of the wall is curved in profile, the curve may be replaced by straight lines which are chords of the curve, thus binding the section into as many trapezoids as there are chords. It will be assumed that the direction and magnitude of the earth-pressure is known, that the position and extent of the back of the wall, and the width of the top are given, FORMULAS FOR EARTH-PRESSURE. 29 to determine the width of the base for stability against over- turning, sliding, and crushing of the material. Stability against Overturning. Let A BCD, Fig. 12, rep- resent a section of a trapezoidal wall, TR the direction of the earth-thrust, JG the vertical passing through the cen- tre of gravity of the wall, and JO the direction of the re- sultant pressure on the base AD caused by E and 6r. As long as R cuts the base AD, the wall will be stable against overturning. When R takes the direction JQ, the wall may be said to be on the point of overturning; then ON the factor of safety against overturning is ~^., where ON is the actual value of E, and QNi\\Q value of E required to make the resultant R pass through D. Stability against Sliding. Since the wall will not slide 30 FORMULAS FOR EARTH-PRESSURE. along the surface DA until the resultant R makes an angle with the normal to DA greater than the angle of friction 0', the factor of safety against sliding can be obtained iis follows: Draw JP making the angle JMU ' = 0'; then PN the factor of safety against sliding is --y^, where PJV is the force required in the direction of E to make R make the angle 0' with the normal to AD, and ON the actual value of K Stability against the Crushing of the Material In ordi- nary practice walls for retaining earth are not of sufficient height to cause very large pressures at their bases, but it is necessary to consider the subject on account of the ten- dency of the bed-joints to open under certain conditions. Let AB, Fig. 13, represent any bed- joint in the wall, /' the vertical resultant pressure upon the joint, and .r the distance of the point of application from the centre of the joint. The intensity of P at any point can be considered as com- p posed of a uniform intensity p Q = -^-,anda uniformly vary- ing intensity pj, so that p x = p Q -f- p '. Let a equal the tangent of the angle CDE, then p 9 ' = ax and p x =^> + ax. FORMULAS FOR EARTH-PRESSURE. 31 The pressure upon a surface (dx) the joint being con- sidered unity in the dimension normal to the page is p x dx = p dz 4- axdx, and the moment of this about DB is (p dx -f axdx)x. The algebraic sum of these moments for values of x be- T) tween the limits ~- must equal Fx , or a Integrating, l2x n P a - -r and or making x = -J5, / / \ ) ; ; ^ and if #, be replaced by \B #, where is the distance from A to the point where P cuts the base, (Fig. 13,) and = IB, p' = and jti = 2p,, 32 FORMULAS FOR EARTH-PRESSURE. from which it is seen that when R cuts the base outside the middle third, the joint will have a tendency to open at points which are at a maximum distance from R where it cuts the base. Therefore in no case should the resultant pressure be permitted to cut the base outside the middle third. This makes it unnecessary to consider the stability against over- Burning. FIG. 14. Then in designing a wall the following conditions must exist for stability : I. The resultant R must cut the base for stability against overturning. II. The resultant R must not make an angle vrith the normal to the base of the ivall greater than the angle of fric- tion 0'. FORMULAS FOR EARTH- PRESSURE. 33 III. The resultant R must not cut the base outside of the middle third, in order that there may be no tendency for the bed-joints to open. The above three conditions apply to any bed- joint of the wall; but if they are satisfied at the base and the wall has the section shown in Fig. 14, it will not be necessary to consider any joints above the base unless the character of the stone or the bonding is different. Determination of the width of the base of a retaining- wall under the condition that R cuts the base at a point rom the toe of the wall. Let H, B', x, d, and E be given to determine B. From Fig. 14, KF= f sin d + fcos 6 -^sin d, 666 rrn _ + %BB' - Bx - ZB'x - B' -6(B + B') For equilibrium E(KF) = G(HF) = B ^ B ' HW(ffF). A , Substituting the values of A^and HF'm the above uii. reducing, it becomes = %JL(H cos d + x sin 6) + ZB'x + B'\ . (8) 34 FORMULAS FOR EARTH-PRESSURE. which is the general equation for the width of the base of a trapezoidal wall. For a rectangular wall B' = B. For a triangular wall B' = 0. For a wall with a vertical front B' -f- x = B or B' = B - x. For a wall with a vertical back x = 0. Equation (8) is easily transformed to satisfy the require- ments of special cases. .The width of the base can be found graphically by as- suming a value for B and finding the value of Q-, if it is less than %B another value of B must be assumed, and so on until Q is equal to or greater than ^B. FOKMULAS FOR TRAPEZOIDAL AND TRIANGULAR WALLS. Formulas for the width of the base of trapezoidal walls under the condition that the resultant R cuts the base at a point distant from the toe of the wall equal to one third the width of the base, or Q %B. CASE I. Tlie general case in which the lack of the ivall is inclined, and E makes an angle with the horizontal. = 2*L (ff cos d + x sin 6\ + ZB'x +B'\ . (8) CASE II. The back of the wall vertical. = cos + (^sin must not have a greater value than that ob- tained from (15) = tan' sm y The value of x' as obtained from (16) is the least allow- able value consistent with equilibrium. Since x' is a func- tion of tan 4 (45 j, care must be taken that is assumed at its least value. As becomes smaller the value of x' increases rapidly. CASE II. When the intensity of the pressure on the base is uniformly varying. Let p represent the maximum intensity of the pressure on the earth and p' the minimum intensity; then for equilibrium p must not exceed the value obtained from the following equation (see 15) : sm For any assumed depth x' the maximum value of p can be 40 FOUNDATIONS FOR WALLS RETAINING EARTH. found from (17). For any assumed breadth B" of the foundation the value of p due to the resultant pressure upon the base of the foundation can be found from the formulas on page 31, when the value of x has been determined; this value must not be greater than the value of p found from (17), or the masonry will heave the earth. In order that the earth may not heave the masonry, p' must not be less than the value obtained from the following formula : -- sm Then ..... (18) _ p + _ ^ C /l + Bin0\ /I - sin 0y ) ~ a 2 Ul - sin 0/ U + sin 0/ J ' which expresses the maximum value p can have for the equilibrium of the earth and the masonry. In order that p' may never be less than the value obtained from (18), the resultant pressure upon the base of the foun- dation must cut the base within a certain distance of its centre. If x be this distance, then (page 31) Substituting the value of p from (19) and solving for # , - 6 ~' where A + riny ^ y= /l-8in0y \1 sm / \1 - sm / * Tabulated values of X and Fare given on page 72. FOUNDATIONS FOR WALLS RETAINING EARTH. 41 Depth of foundations when the surface of the earth has different elevations on opposite sides of the structure. WALL FOUNDATION \ P ,P xy FIG. 17. This case is illustrated in Fig. 17. From (17) and (18) for equilibrium ^ P < f ~ 1 -f sin ) a 1 sin i (22) and Combining (22) and (23) in the value of p^ sin 0V ' - sn , - ( Having assumed the values of y and for any particular case, the above formulas determine the permissible magni- 4:2 FOUNDATIONS FOR WALLS RETAINING EARTH. tudes of the intensities at the heel and toe of the founda- tion for any depth. The hreadth of the ba^e of the foundation may now be assumed, and the actual intensities compared with those permissible ; if p is too large or p' too small, another trial must be made. Usually one or two trials are sufficient. If one prefers to compute the width of the base of a trapezoidal foundation, the formula given below can be employed. Determination of the breadth B" of a trapezoidal foun- dation for a given loading and a maximum intensity p at the toe. (Back of foundation vertical. ) Fio. 18. Let G = total vertical weight supported by top of foun- dation ; E = thrust of earth ; p = maximum intensity of pressure at toe of foun- dation as found from (22) ; and B" = breadth of base of foundation. FOUNDATIONS FOR WALLS RETAINING EARTH. 43 Then - G tfMG x'B* W The foundation can nearly always be designed as a trape- zoid having a vertical back, and then if necessary the batter in front can be stepped. For walls under twenty feet in height, retaining material which will assume a slope of 1 to 1, the most economical foundation is rectangular in section if the base must be four feet deep to escape the action of frost. Where frost need not be considered, of course more shallow and broader foundations can be em- ployed. Abutting Power of Earth. Let the surface of the earth be horizontal and the body pushing the earth have a ver- tical face; then at the depth x' the maximum horizontal pressure per unit of area is (see Case I above) 1 -f- sin and since q varies directly as #', the total thrust P which the earth is capable of resisting is ._ (x'Yr 1 + sin 2 1 - sin 0* ' ' ' (26J Bearing Power of Earth. The bearing power or the in- tensity of the pressure which earth can resist depends not only upon the character of the earth, but upon the depth to which the foundation is extended, as shown by the formulas for p given above. For example, the foundation may be very broad and shallow or quite narrow and deep. The 4:4: FOUNDATIONS FOR WALLS RETAINING EARTH. intensity of the pressure in the first case being considerably smaller than in the second, and both conditions fulfilling the conditions of stability. It appears then that the bearing powers of earth given by various writers must be employed with caution, unless the conditions upon which the values were based are known. APPLICATIONS. The determination of the earth-pressure by the pre- ceding formulas and graphical constructions is a very simple operation when the angle has been determined or assumed. That care and judgment be used in assuming the value of is very important, since a change of a few degrees in the value of sometimes causes a large change in the value of E. An inspection of Diagram I shows that the value of the coefficient A increases very rapidly as decreases. When the earth to be retained contains springs, the bank must be thoroughly drained if it is to be retained by an economical tight wall; if it is not drained, the angle will be likely to become very small as the earth becomes wet. When the location of the earth to be retained is sub- jected to jars, the value of will be decreased. Hence, in assuming the value of 0, the engineer must be sure that the value assumed will be the least value which, in his judgment, it is likely to have. In constructing the wall the judgment and authority of the engineer must again be exercised in order that the wall be constructed as designed. In all cases, to insure perfect drainage between the back FOUNDATIONS FOR WALLS RETAINING EARTH. 45 of the wall and the earth, numerous " weep-holes" should Be provided in the body of the wall, or proper arrange- ments made to carry away the water at the base of the wall. To facilitate drainage, the backing resting against the wall should be sand or gravel. In no case should water be permitted to get under the foundation of the wall, neither should the earth in front of the wall be allowed to become wet. In cold localities the back of the wall near the top should have a large batter to prevent the frost from moving the top courses of stone. As a guard against sliding, the courses of the wall should have very rough beds. The strength of a wall is increased the nearer it approaches a monolith. Care should be taken to have the foundation broad and deep enough to prevent sliding and upheaving of the earth in front. In clay the foundation should be deep, while in sand or gravel it may be broad and shallow. The following examples illustrate the application of the formulas : Ex. 1. Design a trapezoidal wall of sandstone, weighing 150 Ibs. per cubic foot, having a width of 3 ft. on top, a height of 30 ft., and the back inclining forward 5, to re- tain a bank of sand sloping upward at an angle of 20. Data. y - 100 Ibs., W= 150 Ibs.; e = 20, = 39, a = 5; H = 30 ft., B' = 3 ft., x = 2.63 ft. 1. Graphical determination of the values of E and 6. The graphical solution of the problem is shown in Fig. 19, where E is found to equal 15,000 pounds. $ lies between. 35 and 36. 46 FOUNDATIONS FOR WALLS RETAINING EARTH. 2. Algebraic determination of E and . E = Fia.19. Substituting the values of B, C, D, and E as given in the tables, and that of A as given by Diagram I, this becomes V(0.008)+(1.057)(0264) a +(0.061)0.264, tan 6 = ~ : ^ ; + tan e, . . (I' a) - 45,000 (1.036) V0.098 = 14,500 Ibs. sin a cos (e a) A FOUNDATIONS FOR WALLS RETAINING EARTH. 47 tan $ = 0.705 = tan 35 11', about. 3. Algebraic determination of the value of under the assumption that Q = %B. | Hcos S + a-sin o j + ZS'x + ". . (8) X 0.817 + 2.63 X 0.576J + 6 X 2.63 + 9, oU X loU B* + 7.795 = 172.53, B = - 3.89 A/172.53 .*. B = 13.69 - 3.89 = 9.80 ft.; or, practically, 10 feet is the required width of the base. 4. To determine if the wall will slide on a foundation of sandstone. From (14), . E cos 8 Taking B = 10 ft., G = -- 3 X 150 = 29250 llis. 4:8 FOUNDATIONS FOR WALLS RETAINING EARTH. ti = 35 11', cos 6 = 0.817, and sin 6 = 0.576, then 14500 X 0.817 G -f E sin tf ~~ 29250 + 14500 X 0.576 " From Table II, the value of tan 0' for masonry is 0.6 to 0.7; hence there is no danger of the wall sliding on the foundation. According to the Engineering News formula the base of this wall would be fZT"plus a few inches for good luck," or about 13 feet, and by the old rule of one third the height 10 feet. Ex. 2. Design a trapezoidal wall of sandstone weighing 150 Ibs. per cubic foot, having a width of 3 ft. on top, a height of 30 ft., and the back inclining backward 15, to retain a bank of sand sloping upward at an angle of 30. Data. y = 100 Ibs., W= 150 Ibs. ; e = 30, = 33, a =- 15; H = 30 ft., B' = 3 ft., x = 8 ft. 1. Graphical determination of the values of E and 3. In Fig. 19, let B 6r rep-resent the surface of the earth, and AB the back of the wall. Draw AF parallel to BG, and from any point D' in AF lay off D' F equal to the vertical D'G, and draw FL horizontal; lay off the angle IFD' =

9 and e being given. Graphical solution of the problem. Let BCDEA repre- sent the given profile, and let the surface of the earth be horizontal. Prolong BC until it intersects 8 A in 1 8; draw SR normal to BCS and equal to the intensity of the earth-pressure at S; connect B and R. Then from the middle point of B C draw GF parallel to SR; the distance GF multiplied by y will be the average intensity of the earth-pressure on BC. In a similar manner the average intensities on CD, DE, and EA can be found, and hence the total pressures on each determined. The points of ap- plication of these resultant pressures, E l z , and FOUNDATIONS FOR WALLS RETAINING EARTH. 55 can be found by the method used in Ex. 6 for finding the centre of gravity of a trapezoid. The directions of B FIG. 23. j?, , EI , E^ , and E t are found from the construction on the right. Ex. 9. Determine the thrust of the earth against a ver- tical wall when e is negative. For the explanation of this construction, see page 21, Fig. 9. Ex. 10. From the following data determine E, d, and Q- e = 0, = 38, a = 10 23'; y = 90 Ibs., W = 170 Ibs.j H = 15 ft., B = 6 ft., B' = 2 ft. Ans. E - 3037 Ibs., 6 = 37 37', Q = 2.2 ft. Ex. 11. Determine the dimensions of a trapezoidal wal] built of dry, rough granite, having a vertical back and being 20 feet high, to safely retain the side of a sand cut, 50 FOUNDATIONS FOR WALLS RETAINING EARTH. the surface of the sand being level with the top of the wall. jr=lG5.1bs., y=lOO Ibs., 0=:33 40', H = 20 ft., B' = 2 ft. .4w*. ^ =5734 Ibs., tf = 0, 5 = 8 ft., and Q = 2.8 ft., about. Ex. 12. The same as Ex. 11, with a 8 instead of = 0. ' Ans. E 6330 Ibs., B = 9.98 ft., and Q = 2.7 ft. FIG. 34. Ex. 13. What must be the dimensions of a rubble wall of large blocks of limestone, laid dry, to retain a sand filling which supports two lines of standard-gauge railroad track ? (Assume the depth of sand to produce a pressure on the earth equal to that produced by the railroad and trains as 4 feet.) FOUNDATIONS FOR WALLS RETAINING EARTH. 57 H = 15 ft., a = 8, = 33 40', y = 100 Ibs., W = 170 Ibs., B' = 3.5 ft. ^?w. ,#=5760 Ibs., tf = 26 7', 5 = 8 ft, = 2.7ft. Ex. 14. Determine E, d, B, and ft when W = 170 Ibs., y = 100 Ibs., or = 8, e = = 33 40', H = 20 ft., B'= 2ft. .4 //\ 2 /I - sin FOUNDATIONS UPON EARTH. 81 TABLE GIVING SAFE LENGTHS OP PROJECTIONS " O " IN FEET (SEE ILLUSTRATION), FOR "" = 1 FOOT AND VALUES OF " O" RANGING FROM 1 TO 5 TONS. Depth of Beam, in. Weight per Foot, Ibs. 6 (Tons per Square Foot.) 1 H u 2 at 21 3 3* 4 4i 6 20 80 14.0 12.5 11.5 10.0 9.0 9.0 8.0 7.5 7.0 6.5 6.0 20 64 12.5 11.0 10.0 8.5 8.0 8.0 7.0 6.5 6.0 6-0 5.5 15 80 12.0 10.5 9.5 8.5 8.0 7.5 7.0 6.5 6.0 5.5 5.0 15 60 10.5 9.5 8.5 7.5 7.0 6.5 6.0 5.5 5.5 5.0 5.0 15 50 9.5 8.5 8.0 7.0 6.5 6.0 5.5 5.0 5.0 4.5 4.5 15 41 8.5 8.0 7.0 6.0 6.0 5.5 5.0 4.5 4.5 4.0 4.0 12 40 8.0 7.0 6.5 5.5 5.5 5.0 4.5 4.0 4.0 3.5 3.5 12 32 7.0 6.5 5.5 5.0 4.5 4.5 4.0 4.0 3.5 3.5 3.0 10 33 6.5 6.0 5.5 4.5 4.5 4.0 4.0 3.5 3.5 3.0 3 10 25.5 5.5 5.0 4.5 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 9 27 5.5 5.0 4.5 4.0 4.0 3.5 3.5 3.0 3.0 2.5 2.5 9 21 5.0 4.5 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2.5 2.0 8 22 5.0 4.5 4.0 3.5 3.5 3.0 3.0 2.5 2.5 2 5 2.0 8 18 4.5 4.0 3.5 3.0 3.0 3.0 2.5 2.5 2.0 2.0 2.0 7 20 4.5 4.0 3.5 3.0 3.0 3.0 2.5 2.5 2.0 2.0 2.0 7 15.5 4.0 3.5 3.0 2.5 2.5 2.5 2.0 2.0 2.0 2.0! 1.5 6 16 3.5 3.0 3.0 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 6 13 3.0 3.0 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.5 5 13 3.0 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.5 1.5 5 10 2.5 2.5 2.0 2.0 1.5 1.5 1.5 1.5 1.5 4 10 2.5 2.0 2.0 1.5 1.5 1.5 1 5 4 7.5 2.0 2.0 1.5 1.5 1.5 1 5 Above table applies to steel beams. Values given based on ex- treme fibre stresses of 16,000 pounds per square inch. Pile Foundation. Pile foundations are employed in all kinds of earth, sometimes to save expense and sometimes because nothing else appears to be as good. In localities where the earth is uncertain in its character the use of 82 FOUNDATIONS UPON EAUTII. piles enables the engineer to put in a foundation which he foels sure is safe, as a single pile thirty feet long will sup- port several tons even when driven into mud, the load in this case being carried almost entirely by the friction of the BASEMENT in ~ 3 vtiwsmxmsnm s '3//=fff \ + J MASONRY MASONRY | I BEAMS IN CONCRETE CONCRETE] ^\ FIG. 37. mud upon the surface of the pile. If the pile is driven through the mud to a solid stratum below, then the pile acts as a column more or less supported its entire length, and consequently able to carry a very great load. Piles are usually spaced about three feet on centres, and the tops firmly bedded in a layer of concrete or stayed by a grillage of timber or by a combination of these methods, the object being to thoroughly and evenly distribute the load to be supported. The supporting power of a pile in a given earth can be found in the following manner: Let G' = the total load to be supported by the pile, in- cluding the weight of the pile; p = the intensity of the pressure upon the bottom of the pile; A = the superficial area of the pile in contact with the earth; FOUNDATIONS UPON AKTI1. S3 and f = a factor depending upon the friction resistance of a unit area of the surface of the pile. Then for a pile having a diameter of d But -f- sin * 2 G' and sn sm < For practical purposes this may be written jliBin|,' ' ( 1 sin ) For convenience this may be further simplified for special cases. The following values of f have recently been given by W. M. Patton, based upon his own and the experience of others : In very soft silt or liquid mud, / = 150 pounds per sq. ft. In ordinary clay or earth (dry), / = 300 " " " " " " (wet), /= 150 " " " In compact hard clay, / = 300 " " " " In sand, or sand and gravel, / = 500 " " " " * This formula was suggested by reading W. M. Pattern's article on piles in his " Practical Foundations." 84 FOUNDATIONS UPON KARTH. For the silt of swamps, muds, etc.,

t . 46. Sketch showing Cross-section of Coffer-dam, J L FIG. 47. Sketch showing Essential Features of Open Caisson. TYPMti OF EXISTING FOUNDATIONS. 97 r. - -54-6 12'x 12" \ 12"x 12" I 1 1 K 12x12 1 ' i 12" x 12" 1 1= IF" TARRED PAPER n* BRACES ABOUT 1C/APART _ f OAK Section of One of the Caissons employed in the Foundations of the Piers for the Washington Bridge. REFERENCES. EAETH-PEBSSUBB AND EETAINING-WALLS. A brief outline of the theories advanced by the follow- ing writers can be found in " Neiie Theorie des Erd- druckes," Dr. E. Winkler, Wien, 1872: D' Antony, Hoffmann, Poncelet, Ande, Holzhey, Prony, Andoy, de Lafont, Eankine, Belidor, Levi, Rebhann, Blaveau, de Koszegh Martony, Rondelet, Bullet, Maschek, Saint-Guilhem, Considere, Mayniel, Saint- Venant, Coulomb, Mohr, Sallonnier, Couplet, Montlong, SchefHer, Culmann, Moseley, Trincaux, Fran^ais, Navier, Vauban, Gadroy, Ortmann, Winkler, Gauthey, v. Ott, Woltmann. Hagen, Persy, AUDE. Poussee des Terres. Nouvelles experiences sur la poussee des terres. Paris, 1849. BAKER-CURIE. Note sur la brochure de M. B. Baker theorie. Annales des Ponts et Chaussees, pp. 558-592, 1882. The actual lateral pressure of earthwork. Van Nos- trand's Magazine, xxv, 1881; also Van Nostrand's Science Series, No. 56. 99 100 REFERENCES. BOUSSIN^ESQ. Complement a de precedentes notes sur la poussee des terres. *Annales P. et C., 1884. BOUSIN. Equilibrium of pulverulent bodies. The equilib- rium of earth when confined by a wail. fVan N., 188 1. CAIN. Modification of Weyrauch's Theory. VanN., 1880. - Earth-pressure. Modification of Weyrauch's Theory. Criticism of Baker's articles. Van N., 1882. Uniform cross-section, and T abutments : their proper proportions and sizes, deduced from Rankine's general formulas. Van N., 1872. - Practical designing of retaining-walls. Van N. Science Series, No. 3, 1888. CHAPERON. Observations sur le rnemoire de M. de Sazilly (1851). Stabilite et consolidation des talus. Annales P. et C., 1853. CONSIDERE. Note sur la poussee des terres. Annales P. et C., 1870. COUSINERY. Determination graph ique de Tepaisseur des inurs de soutenement. Annales P. et C., 1841. DE LAFONT. Sur la poussee des terres et sur les dimensions a donner, suivant leurs profils, aux murs de soutene- ment et de reservoirs d'eau. Annales P. et C., 1866. DE SAZILLY. Sur les conditions d'equilibre des massifs de terre, et sur les revetements des talus. Annales P. et C., 1851. EDDY. Retaining-walls treated graphically. VanN., 1877. FLAMANT. Note sur la poussee des terres. Annales P. et C., 1882. Resume d'articles publics par la Societe des Inge- nieures Civils de Londres sur la poussee des terres. An- nales P. et C., 1883. * Annales des Ponts et Chaussees. f Van Nostrand's Magazine, REFERENCES. 101 FLAMANT. Note sur la poussee des terres. Annales P. et C., 1872. - Memoire sur la stabilite de la terre sans cohesion par W. J. Macquorm Rankine (Extrait 1856-57). An- nales P. et C., 1874. GOBIN. Determination precis de la stabilite des murs de soutenement et de la poussee des terres. Annales P. et C., 1883. GOULD. Theory of J. Dubosque. Van N., 1883. - Designing. Van N., 1877. JACOB. Practical designing of retaining-walls. Van N., 1873; also Van N. Science 'Series, No. 3. JACQUIEE. Note sur la determination graphique de la poussee des terres. Annales P. et C., 1882. KLEITZ. Determination de la poussee des terres et eta- blissement des murs de soutenement. Annales P. et C., 1844. LAGKEUE. Note sur la poussee des terres avec ou sans sur- charges. Annales P. et C.. 1881. L'EVEILLE. De 1'emploi des contre-forts. Annales P. et C. 1844. LEYGUE. Sur les grands murs de soutenement de la ligne de Mezamet a Bedarieux. Annales P. et C., 1887. - Nouvelle recherche sur la poussee des terres et le profil de revetement le plus economique. Annales P. et C., 1885. MEBEIMAN. On the theories of the lateral pressure of sand against retaining walls. (School of Mines Quarterly.) Engineering News, 1888. - The theory and calculation of earthwork. Engineer- ing News, 1885. REBHANX. Theorie des Erddruckes und der Futtermauern. Wien, 1870 and 1871. 102 REFERENCES. SAINT-GTJILHEM. Sur la poussee des terres avec ou sans surcharge. Annales P. et C., 1858. ScHEFFLER-FouRNiE. Traite de la stabilite des construc- tions. Paris, 1864. TATE. Surcharged and different forms of retaining walls. Van N., 1873; also Van N. Science Series, No. '; Also published by E. & F. N. Spon. THORNTON. Theory. Van N., 1879. FOUNDATIONS. BAKER. A treatise on masonry construction. John Wiley & Sons, N. Y. PATTON. A practical treatise on foundations. John Wiley & Sons, N. Y. A treatise on civil engineering. John Wiley & Sons, N. Y. For articles in engineering periodicals the reader is re- ferred to a " Descriptive Index of Current Engineering Literature" (1884-1891), published by the Board of Managers of the Association of Engineering Societies. 'Engineering Index/' Vols. II and III, published by the Engineering Magazine. TABLES. Table I contains the crushing-strengths and the average weights of stone likely to be used in the construction of retaining- walls and foundations; also the average weights of different earths. Table II contains the coefficients of friction, limiting angles of friction, and the reciprocals of the coefficients of friction for various substances. Tables III, I V, and V contain the values of the coeffi- cients [see equation (!')] (B), (C), (D) and (E), where ' t cos 2 a: cos e' ( cos e cos (e a) and ( EI ) = 2 sin a sin e - - --- -. cos e The tables were computed with a Thacher calculating in- strument and checked by means of diagrams. It is believed that they are correct to the second place of decimals; an error in the third place of decimals does not affect the re- sults for practical purposes. Table VI contains the natural sines, cosines and tan- gents. 105 106 TABLES. TABLE I. VALUES OP W Name of Substance. Crushing Lds. in tons per sq. ft. Average weight in Ibs. per cu. ft. Alabaster 144 Brick best pressed 40 to 300 150 " common hard 125 soft inferior 100 Chalk 20 to 30 150 49.6 to 102 Flint 162 Feldspar 166 Granite . 300 to 1200 170 Gneiss ... ... 168 Greenstone trap . 187 Hornblende, black 203 Limestones and Marbles, ordinary 250 to 1000 J164.4 Mortar hardened ( 168 103 Quartz common 165 Sandstone 150 to 550 151 Shales 162 Slate .... 400 to 800 175 Soapstone 170 VALUES OP y. Name of Substance. Earth common loam loose . . . 72 to 80 shaken 82 9 'I <. rammed moderately 90 100 Gravel 90 106 S;ind 90 106 Soft flowing mud. . . . 104 120 Sand perfectly wet 118 129 Average weight in Ibs. per cu. ft. TABLES. TABLE II. * ANGLES AND COEFFICIENTS OF FRICTION. 107 tan . *> 1 tan $ Dry masonry and brickwork Masonry and brickwork with damp mortar .... 0.6to 0.7 0.74 31 to 35 364 1.67 to 1.43 1 35 Timber on stone Iron on stone Timber on timber Timber on metals about 0.4 0.7 to 0.3 0.5 "0.2 06" 0.2 22 35 to!6| 31 " 1H 2.5 1.43 to 3. 33 2 "5 1.67 " 5 Metals on metals Masonry on dry clay .... 0.25 " 0.15 51 14 " 8| 27 4 "6.67 1 96 " " moist clay Earth on earth 0.33 25 to 1 18* 14 to 45 3. 4 to 1 Earth on earth, dry sand, clay, and mixed earth. . . . Earth on earth, damp clay . Earth on earth, wet clay. Earth on earth, shingle and gravel .... ... 0.38 "0.75 1.0 0.31 81 21 " 37 45 17 39 to 48 2.63" 1.33 3.23 1 23 to 9 * From Raukiue's Applied Mechanics. 108 TABLES. TABLE III. a = 5 a = 6 a =7 a = 8 a = y (B) (B) (B) (B) (B) 1.004 1.005 1.007 1.010 1.012 5 1.012 1.015 1.018 1.022 1.026 10 1.019 1.024 1.029 1.035 1.040 15 1.027 1.034 1.041 1.048 1.055 20 1.036 1.044 1.052 1.062 1.071 25 1.045 1.055 1.065 1.076 1.088 30 1.055 1.066 1.079 1.092 1.105 35 1.065 1.079 1.094 1.109 1.124 40 1.078 1.094 1.111 1.129 1.147 45 1.093 1.111 1.181 1.152 1.173 1 (C) (C) (C) (C) (C) \ 0.008 0.011 0.015 0.019 0.024 TABLE IV. e a = 5 a = 6 a = 7 a = 8 a = 9 (D) CD) (D) (D) (D) 0.992 0.989 0.985 0.981 0.976 5 1.008 1.008 1.006 1.005 1.003 10 1.023 1.026 1.028 1.030 1.031 15 1.040 1.046 1.051 1.056 1.060 20 1.057 1.066 1.075 1.084 1.092 25 1.0,5 1 089 1.102 1.114 1.125 30 1.096 1.113 1.180 1.147 1 . 163 35 1.118 1 140 1 . 1 64 1.183 1.204 40 1.144 1.172 1.199 1 226 1.253 45 1.174 1.208 1.242 1.276 | 1.309 TABLE V. 6 a = 5 a = 6 a = 7 a = 8" a = 9 (E) OB) (E) (E) (E) 5 0.015 0.018 0.021 0.024 0.027 10 0.031 0.037 0.043 0.049 0.055 15 0.046 0.055 0.065 0.074 0.083 20 0.061 0.074 0.086 0.099 0.112 25 0.076 0.092 0.108 0.124 0.140 30 0.091 0.110 0.130 0.149 0.169 35 0.106 0.128 0.151 0.174 0.197 40 0.120 0.145 0.172 0.198 0.225 45 0.134 0.162 0.192 0.222 0.25:3 i TABLES. 109 TABLE IllContinued. e ) (-D) 0.970 0.964 0.957 0.950 0.942 5 1.000 0.997 0.993 0.988 0.983 10 1.031 1.031 1.030 1.028 1.026 15 1.064 1.067 1.069 1.061 1.072 20 1.099 1.105 1.110 1.116 1.121 25 1 . 1 36 1.147 1.156 1.165 1.173 30 1.178 1.194 1.204 1.220 1.232 35 1.224 1.244 1.262 1.281 1.300 40 1.291 1.304 1.328 1.353 1.377 45 1.342 1.375 1.407 1.438 1.469 TABLE V Continued. e a= 10 a 11 a= 12 a= 13 a= 14 C0) (Jg?) CE) CE) CE) ^ 5 0.030 0.032 0.036 0.039 0.042 10 0.061 0.067 0.073 0.079 0.085 15 0.093 0.102 0.111 0.119 0.130 20 0.124 0.137 0.150 0.163 0.175 25 0.156 0.173 0.189 0.205 0.221 30 0.188 0.208 0.216 0.248 0.269 35 0.220 0.244 268 0.292 0.316 40 0.252 0.280 0.308 0.336 0.365 45 0.284 0.316 0.349 0.382 0.415 110 TABLES. TABLE HI Continued. a a = 15 a= 16 a = 17 a= 18 a= 20 (#) (fi) . f#) (B) go n 1.035 1.040 1.048 1.051 1.062 5 1.059 1.066 1.076 1.081 1.098 10 1.084 1.093 1.104 1.112 1.132 15 1.110 1.120 1.134 1.138 1.168 20 1.135 1.149 1.165 1.177 1.218 25 1.165 1.179 1.197 1.211 1.245 30 1.195 1.212 1.233 1 . 248 1.288 35 1.229 1.249 1.272 1.291 1.339 40 1.268 1.291 1.317 1.340 1.389 45 1.313 1.338 1.369 1.393 1.451 (CO CO) (C) (C) (CO 0.067 0.076 086 0.095 0.117 TABLE IN Continued. 1-0 a 18 6 a t (i (D) cz>) (D) (0) f\ 0.933 0.924 0.915 0.905 0.883 5 0.977 0.971 0.964 957 0.940 10 1.023 1.018 1.016 1.011 1.000 15 1.072 1.073 1.071 1 069 1.068 20 1.124 1.127 1.129 1.131 1.132 25 1.181 1.188 1.194 1.200 1.208 30 1.244 1.256 1.266 1.276 1.293 35 1.316 1.332 1.348 1.363 1.390 40 1.400 1.422 1.444 1.465 1.505 45 1.500 1.530 1.559 1.588 1.643 TABLE N Continued. e a= 15 a = 16 a= 17 a= 18 a= 20 CE) (#) CE) (#) (#) 5 0.045 0.047 0.050 0.053 0.058 10 0.091 0.097 0.102 0.108 0.119 15 0.139 0.148 0.157 0.165 0.183 20 0.188 0.200 0.213 0.225 249 25 0.238 254 0.270 0.177 . 31 S 30 . 289 0.309 . 3~>9 0.349 0.389 35 341 0.365 0.390 0.414 0.463 40 0.394 0.42:5 0.452 0.481 0.539 45 0.448 0.482 0.516 0.551 0.620 TABLE "VI. NATURAL SINES, COSINES, TANGENTS AND COTANGENTS. 112 NATDKAL SINES AND COSINES. / 1 2 3 40 Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin $ ~o .00000 One. .01745 .99985 .03490 .99939 .05234 T99863 .06976 .99756 60 1 .00029 One. .01774 .99984 .03519 .99938 .05263 .99861 .07005 .99754 59 2 .00058 One. .01803 .99984 .03548 .99937 .05292 .99860 .07034 .99752 58 3 .00087 One. .01832 .99983 .03577 .99936 .05321 .99858 .07063 .99750 57 4 .00116 One. i .01862 .99983 .03606 .99935 .05350 .99857 .07092 .99748 56 5 .00145 One. .01891 .99982 .03635 .99934 .05379 .99855 .07121 .99746 55 6 .00175 One. .01920 .99982 .03C64 .99933 .05408 .99854 .07150 .99744 54 7 .00204 One. .01949 .99981 .03693 .99932 .05437 .99852 .07179 .99742 53 8 .00233 One. .01978 .99980 .03723 .99931 .05466 .99851 .07208 .99740 52 9 .00262 One. .02007 .99980 .03752 .99900 .05495 .99849 .07237 .99738 51 10 .00291 One. .02036 .99979 .03781 .99929 .05524 .99847 .07266 .99786 50 11 .00320 .99999 .02065 .99979 .03810 .99927 .05553 .99846 .07295 .99734 49 12 .00349 .99999 .02094 .90978 .03839 .99926 .05582 .99844 .07324 .99731 48 13 .00378 .99999 .02123 .99077 .03808 .99925 .05611 .99842 .07353 .99729 47 14 .00407 .99999 .02152 .99977 .03897 .99924 .05640 .99841 .07382 .99727 46 15 .00436 .99999 .02181 .99976 .03926 .99923 .05669 .90839 .07411 .99725 45 16 .00465 .99999 .02211 .90976 .03955 .99922 .05698 .90838 .07440 .99723 44 17 .00495 .99999 .02240 .99975 .03984 .99921 .05727 .90836 .07469 .99721 43 18 .00524 .99999 .02209 .99974 .04013 .99919 .05756 .90834 .07498 .9P719 42 19 .00553 .99998 .02298 .90974 .04042 .99918 .05785 .90833 .07527 .99716 41 20 .00582 .99998 .02327 .99973 .04071 .99917 .05814 .99831 .07556 .99714 40 21 .00611 .99998 .02356 .99972 .04100 .99916 .05844 .99829 .07585 .99712 39 22 .00640 .99998 .02385 .99972 .04129 .99915 .C5873 .99827 .07614 .99710 38 23 .00669 .99998 .02414 .99971 .04159 .99913 .C5902 .99826 .07643 .99708 37 24 .00698 .99998 .02443 .99970 .04188 .99912 .05931 .99824 .07672 .99705 86 25 .00727 .99997 .02472 .99969 .04217 .99911 .05960 .99822 .07701 .99703 35 26 .00756 .99997 .02501 .99969 .04246 .99910 .05989 .99821 .07730 .99701 34 27 .00785 .99997 .02530 .99968 .04275 .99909 .06018 .90819 .07759 .99699 33 28 .00814 .99997 .02560 .99967 .04304 .99907 .06047 .99817 .07788 .99696 32 29 .00844 .99996 .02589 .99966 .04333 .92906 .06076 .99815 .07817 .99G94 31 30 .00873 .99996 .02618 .99966 .04362 .99905 .06105 .99813 .07846 .99692 30 31 .00902 .99996 .02647 .99965 .04391 .99904 .06134 .99812 .07875 .99689 29 32 .00931 .99996 .02676 .99964 .04420 .99002 .06163 .99810 .07904 .99G87 28 33 .00960 .99275 .02705 .99963 .04449 .99901 .06192 .99808 .07933 .99085 27 34 .00989 .99995 .02734 .99963 .04478 .99900 .06221 .99806 .07962 .99G83 26 35 .01018 .99995 .02763 .99962 .04507 .99898 .06250 .99804 .07991 .99080 25 36 .01047 .99995 .02792 .99961 .04536 .99897 .06279 .99803 .08020 .99078 24 37 .01076 .99994 .02821 .99960 .04565 .99896 .06308 .99801 .08049 .99676 23 38 .01105 .99994 .02850 .99959 .04594 .99894 .06337 .99709 .08078 .99673 22 39 .01134 .99994 .02879 .99959 .04G23 .90893 .06360 .99797 .08107 .99071 21 40 .01164 .99993 .02908 .99958 .04653 .99892 .06395 .99795 .08136 .99668 20 41 .01193 .99993 .02938 .99957 .04682 .99890 .06424 .99793 .08165 .99666 19 42 .01222 .99993 .02967 .99956 .04711 .99889 .06453 .99702 .08194 .99664 18 43 .01251 .99992 .02996 .99955 .04740 .99888 .06482 .99790 .08223 .99661 17 44 .01280 .99992 .03025 .99954 .04769 .99886 .06511 .99788 .08252 .99659 16 45 .01309 .99991 .03054 .90953 .04798 .99885 .06540 .99786 .08281 .99657 15 46 .013381.99991 .03083 .99952 .04827 .99883 .06569 .99784 .08310 .99654 14 47 .01367 .99991 .03112 .99952 .04856 .99882 .06598 .99782 .08339 .99652 13 48 .01396 .99990 .03141 .99951 .04885 .99881 .06627 .99780 .083G8 .99649 12 49 .01425 .99990 .03170 .99950 .04914 .99879 .06656 .99778 .08397 .99647 11 50 .01454 .99989 .03199 .99949 .04943 .99878 .06685 .99776 .08426 .99644 10 51 .01483 .99989 .03228 .99948 .04979 .99876 .06714 .99774 .08455 .99642 9 52 .01513 .99989 .03257 .99947 =05001 .99875 .06743 .99772 .08484 .99639 8 53 .01542 .99988 .03286 .99946 .05030 .99873 .06773 .99770 .08513 .99637 7 54 .015711.99988 .03316 .99945 .05059 .99872 .06802 .99768 .08542 .99035 6 55 .016001.99987 .03345 .99944 .05088 .99870 .06831 .99766 .08571 .99632 5 56 .016291.99987 .03374 .99943 .05117 .99869 .06860 .99764 .08600 99030 4 57 .01658 .99986 .03403 .99942 .05146 .99867 .06889 .99762 .08629 .99627 3 58 .01687 .99986 .03432 .99941 .05175 .99866 .06918 .99760 .08658 99025 2 59 .01716 .99985 .03461 .99940 .05205 .99864 .06947 99758 .08687 99022 1 GO .01745 .99985 .03490 .99939 .05234 .99863 .06976 99756 .08716 99619 _0 / Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine t - 89 * 88 87 . 86* - ' 85 NATURAL SINES AND COSINES, 113 6 1 6 70 8- 9 Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin U .08716 .99619 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 60 l .08745 .99617 .10482 .99449 .12216 .99251 .13946 .99023 .15672 .98764 59 2 .08774 .99614 .10511 .99446 .12245 .99248 .13975 .99019 .15701 .98760 5L ! : 3 .08803 .99612 .10540 .99443 .12274 .99244 .14004 .99015 .15730 .98755 5; 4 .08831 .99609 .10569 .99440 .12302 .99240 .14033 .99011 .15758 .98751 5C 5 .08860 .99607 .10597 .99437 .12331 .99237 .14061 .99006 .15787 .98746 55 6 .08889 .99604 .10626 .99434 .12360 .99233 .14090 .99002 .15816 .98741 54 7 .08918 .99602 .10655 .99431 .12389 .99230 .14119 .98998 .15845 .98737 53 8 .08947 .99599 .10684 .99428 .12418 .99226 .14148 .98994 .15873 .98732 52 9 .08976 .99596 .10713 .99424 .12447 .99222 .14177 .98990 .15902 .98728 51 10 .09005 .99594 .10742 .99421 .12476 .99219 .14205 .98986 .15931 .98723 50 11 .09034 .99591 .10771 .99418 .12504 .99215 .14234 .98982 .15959 .98718 49 12 .09003 .90588 .10800 .99415 .12533 .99211 .14263 .98978 .15988 .98714 48 13 .09092 .99586 .10829 .99412 .12562 .99208 .14292 .98973 .16017 .98709 47 14 .09121 .99583 .10858 .99409 .12591 .99204 .14320 .98969 .16046 .98704 46 15 .09150 .90580 .10887 .99406 .12620 .99200 .14349 .989G5 .16074 .98700 45 16 .09179 .99578 .10916 .99402 .12649 .99197 .14378 ,98961 .16103 .98695 44 ir .09208 .99575 .10945 .99399 .12678 .99193 .14407 .98957 .16132 .98690 43 18 .09237 .99572 .10973 .99396 .12706 .99189 .14436 .98953 .16160 .98686 42 19 .09266 .99570 .11002 .99393 .12735 .99186 .14464 .98948 .16189 .98681 41 20 .09295 .99567 .11031 .99390 .12764 .99182 .14493 .98944 .16218 .98676 40 21 .09324 .99564 .11060 .99386 .12793 .99178 .14522 .98940 .16246 .98671 39 22 .09353 .995G2 .11089 .99383 .12822 .99175 .14551 .98936 .16275 .98667 33 23 .09382 .99559 .11118 .99380 .12851 .99171 .14580 .98931 .16304 .98662 37 24 .09411 .99556 .11147 .99377 .12380 .99167 .14GC8 .98927 .16333 .98657 86 25 .09440 .99553 .11176 .99374 .12908 .99163 .14637 .98923 .16361 .98652 35 26 .09469 .99551 .11205 .99370 .12937 .99160 .14666 .98919 .16390 .98648 84 27 .09498 .995-18 .11234 .99367 .12966 .99156 .14695 .98914 .16419 .98643 83 28 .09527 .99545 .11263 .99364 .12995 .99152 .14723 .98910 .16447 .98638 82 29 .09556 .99542 .11291 .99380 .13024 .99143 .14752 .98906 .16476 .98633 81 30 .09585 .99540 .11320 .99357 .13053 .99144 .14781 .98902 .16505 .98629 80 31 .09614 .99537 .11349 .99354 .13081 .99141 .14810 .98897 .16533 .98624 29 32 .09642 .99534 .11378 .99351 .13110 .99137 .146C8 .98893 .16562 .98619 23 33 .09671 .99531 .11407 .99347 .13139 .99133 .14867 .98889 .16591 .98614 27 34 .09700 .99528 .11436 .99344 .13163 .99129 .14896 .98884 .16620 .98609 26 35 .09729 .99526 .11465 .99341 .13197 .99125 .14925 .98880 .16648 .98604 25 36 .09758 .99523 .11494 .99337 .13226 .99122 .14954 .98876 .16677 .98600 24 37 .09787 .99520 .11523 .99334 .13254 .99118 .14982 .98871 .16706 .98595 23 38 .09816 .99517 .11552 .99331 .13283 .99114 .15011 .98867 .16734 .98590 22 39 .09845 .99514 .11580 .99327 .13312 .99110 .15040 .98863 .16763 .98585 21 40 .09874 .99511 1 .11609 .99324 .13341 .99106 .15069 .98858 .16792 .98580 20 41 .09903 .99508 1 .11638 .99320 .13370 .99102 .15097 .98854 .16820 .98575 19 42 .09932 .99506 .11667 .99317 .13390 .99098 .15126 .98849 .16849 .98570 18 43 .00961 .90503 | .11696 .99314 .13427 .99094 .15155 .98845 .16878 .98565 17 44 .00990 .90500 .11725 .99310 .13450 .99091 .15184 .98841 .16906 .98561 16 45 .10019 .99497 .11754 99307 .13485 .99087 .15212 .98836 .16935 .98556 15 46 .10048 .99494 .11783 .99303 .13514 .99083 .15241 .98832 .16964 .98551 14 47 .10077 .99491 .11812 .99300 .13543 .99079 .15270 .98827 .16992 .98546 13 48 .10106 .99488 .11840 .99297 .13572 .99075 .15299 .98823 .17021 .98541 12 49 .10135 .99485 .11869 .99293 .13600 .99071 .15327 .98818 .17050 .98536 11 50 .10164 .89482 .11898 .99290 .13629 .99067 .15356 .98814 .17078 .98531 10 51 .10192 .99479 .11927 .99286 .13658 .99063 .15385 .98809 .17107 .98526 9 52 .10221 .99476 .11956 .99283 .13637 .99059 .15414 .98805 .17136 .98521 8 53 .10250 .99473 .1x985 .99279 .13716 .99055 .15442 .98800 .17164 .98516 7 54 .10279 .99470 .12014 .99276 .13744 .99051 .15471 .98796 .17193 .98511 6 55 .10308 .99467 .12043 .99272 .13773 .99047 .15500 .98791 .17222 .98506 5 56 .10337 .99464 .12071 .99269 .13802 .99043 .15529 .98787 .17250 .98501 4 57 10366 .99461 .12100 .99265 .13831 .990,9 .15557 .98782 .17279 .98496 3 58 .10395 .99458 .12129 .99262 .13860 .99035 .15586 .98778 .17308 .98491 2 59 .10424 .99455 .12158 .99258 .13889 .99031 .1*615 .98773 .17336 .98486 1 60 .10453 .99452 .12187 .99255 .13917 .99027 .15643 .98769 .17365 .98481 J) Cosin Sine Cosin Sine" Cosin Sine Cosin j Sine Cosin Sine t 84* 83' 83 81 80 114 NATURAL SINES AND COSINES. 10 11 12 13 14 / Sine Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin i "o .17365"!. 98481 .19081 .98163 .20791 .97815 .22495 797437 .24192 .97030 60 I .17393 '.98476 .19109 .98157 .20820 .97809 .22523 .97430 .24220 .97023 59 2 .17422 .98471 .19138 .98152 .20848 .97803 .22552 .97424 .24249 .97015 58 3 .17451 ..98466 .19167 .98146 .20877 .97797 .22580 .97417 .24277 .97008 57 1 .17479 .93461 .19195 .98140 .20905 .97791 .22608 .97411 .24305 .97001 56 5 .17508 .98455 .19224 .98135 .20933 .97784 .22637 .97404 .24333 .96994 55 6 .17537 .98450 .19252 .98129 .23962 .97778 .22665 X)7398 .24362 .96987 54 7 17565 .98445 .19281 .98124 .20990 .97772 .22693 .97391 .24390 .96980 53 8 .17594 .93440 .19309 .98118 .21019 .97766 .22722 .97384 .24418 .96973 52 9 .17623 .93435 .19338 .98112 .21047 .97760 .22750 .97378 .24446 .96966 51 10 .17651 .98430 .19366 .98107 .21076 .97754 .22778 .97371 .24474 .96959 50 11 .17680 .98425 .19395 .98101 .21104 .97748 .22807 .97365 .24503 .96952 49 12 .17708 .CJ1CO .19423 .93336 .21132 .97742 .223.35 .97358 .24531 .96945 48 13 .17737 .98414 .19452 .93C90 .21101 .97735! .22363 .97351 .24559 .96937 47 14 .17768 .93409 .19481 .93384 .21189 .97729 .22892 .97345 .24587 .96930 46 15 .17794 .93404 .19509 .98379 .21218 .97723! .22920 .97338 .24615 .96923 45 15 .17823 .93339 .19538 .93373 .2124G .97717 .22948 .97331 .24644 .96916 44 1? .17852 .98394 .19503 .93087 .21275 .97711 .22977 .97325 .24672 .96909 43 IS .17880 .98389 .19595 .93361 .21303 .97705 .23005 .97318 .24700 .96902 42 13 .17909 .98333 .19623 .98356 .21331 .97698 .23033 .97311 .24728 .96894 41 20 .17937 .98378 .19652 .98050 .21360 .97692 .23062 .97304 .24756 .96887 40 21 .17966 .98373 .19680 .98044 .21388 .97686 .23090 .97298 .24784 .96880 39 22 17995 .93368 .19703 .93339 .21417 .97680! .23118 .97291 .24813 .96873 38 2i .18023 .93302 .19737 .93333 .214 13 .97673 .23146 .97284 .24841 .96866 37 1 18052 .98357 .19766 93327 .21474 .97667 .23175 .97278 .24869 .96858 36 23 18081 .98352 .19794 .93321 .21502 .97661 .23203 .97271 .24897 .96851 35 23 18109 .93347 .19323 93316 .21533 .97655 .23231 .97264 1.24925 .96844 34 27 10138 .98341 .19851 98310 .21559 .97648 .23200 .97257 .24954 .96837 33 23 18166 .98336 .18880 93004 .21537 .97642 .23283 .97251 .24982 .96829 32 23 10195 .93331 .19903 97938 .21C1G .97030! .23316 .97244 .25010 .96822 31 30 18224 .98325 .19937 97992 .21644 .97630 .23345 .97237 .25038 .96815 30 31 18252 .98320 .19965 97987 .21072 97623 ' .23373 .97230 .25066 .96807 29 18281 .93315 .19394 97331 .21701 .97017 .23401 .97223 .25094 .96800 28 33 18309 .93310 .20022 97975 .21723 97G11 .23423 .97217 .25122 .96793 27 34 18338 .93304 .20051 97969 .21753 97G34 .23453 .97210 .25151 .96786 26 35 18367 .98299 .20379 97963 .21733 3^533 .23483 .97203 .25179 .96778 25 30 18395 .93294 .23108 97958 .21014 97592 .23514 .97196 .25207 .96771 24 37 18424 .98288 .20136 97952 .21043 97585 .23542 .97189 .25235 .96764 23 38 18452 .98283 .20165 97946 .21871 97579 .23571 .97182 .25263 .96756 22 39 18481 .93277 .20193 97940 .21899 97573 .23593 .97176 .25291 .96749 21 40 18509 .98272 .20222 97934 .21928 97566 .23627 .97169 .25320 .96742 20 41 18538 .98267 .20250 97928 .21956 97560 .23656 .97162 .25348 .96734 19 42 18567 .93201 .20279 97922 .21985 97553 .23684 .97155 .25376 .96727 18 43 18595 .93256 23307 97916 .22013 97547 .23712 .97148 .25404 .96719 17 44 18624 .93250 .'20336 97910 .22041 .97541 .23740 .97141 .25432 .96712 16 45 18052 .93245 .20364 97905 .22070 .97534 .23769 .97134 .25460 .96705 15 4G 1GG81 .93240 .20393 97899 .22098 .97528 .23797 .97127 .25488 .96697 14 47 1G710 .93234 .20421 97893 .22126 .97521 .23825 .97120 .25516 .96690 13 43 .10738 .93229 .20450 97887 .22155 .97515 .23853 .97113 .25545 .96682 12 49 .1G7G7 .93223 .20478 97881 .22183 .97508 .23882 .97106 .25573 .96675 11 50 .10795 .93218 .20507 97875 .22212,. 97502 .23910 .97100 .25601 .96667 10 51 .10824 .93212 .23535 97869 .22240 '.97490 .23938 .97093 .25629 .96660 9 52 .18852 .93207 .20563 97863 . 22268 |. 97489 .23966 .97086 .25657 .96653 8 53 .18881 .93201 .20592 .97857 .22297 .97483 .23995 .97079 .25685 .96645 7 54 .10910 .98190 .20620 .97851 .22325 .97476 .24023 .97072 .25713 .96638 6 55 .18938 .98190 .2C349 .97845 .22353 .97470 .24051 .97065 .25741 .96630 5 56 18967 .98185 .20677 .97839 .22382 .97463 .24079 .97058 .25769 .96623 4 57 18995 .98179 .20706 .97833 .22410 : 97457 .24108 .97051 .25798 .96615 3 58 .19024 .98174 -.20734 .97827 .22438 .97450 .24136 .97044 .25826 .96608 2 59 .19052 .98168 .20763 .97821 .22467 .97444 .24164 .97037 .25854 .96600 1 GO .19081 .98163 .20791 .97815 .22495 .97437 .24192 .97030 .258821.96593 l, Cosin Sine Cosin Sine Cosin Sine Cosin Sine Cosin I Sine / 79 78 ' 77 ' 76 75" NATURAL SINES AND COSINE'S. 115 21 31 15 Sine .25882 .25910 .25938 .25966 .25994 .26022 .26050 .26079 .26107 .26135 ,26191 .26247 .26275 Cosin .96593 .96585 .98678 .96570 .96562 .96555 .96547 .96540 .96517 .26331 ,26359 .96494 .96486 .96479 .96471 .96463 .96456 .96448 .96440 .26471 .96433 26500 .96425 26528 .96417 26556 .96410 ,26415 .96612 .26640 .26696 .26724 .26752 .26780 .26948 .26976 .27004 .27032 .27060 .27088 .27116 .27144 .27172 .27200 .27228 .27256 .96386 .96379 .96371 .96355 .96347 .96340 .96332 .96324 .96316 .96308 .96301 .96293 .96277 .96261 .96253 .96246 .27312 .27340 .27368 .27396, .27424 .27452 .27480! .275081 .275361 .27564 .96230 .96222 .96214 .96206 .96198 .96190 .96182 .96174 .96158 .96150 .96142 .96134 Cosin Sine 74 16' Sine Cosin .27564 .96126 .27592 .96118 .27620 .96110 .27648 .96102 .276761.96094 .27704 !. 96086 .277311.96078 17" Sine .29237 .27759 .27787 .27815 .27843 .27871 .27927 .27955 .27983 .28011 .28067 .28095 .28123 .28150 .28178 .28206 .28262 .28290 .28318 .28374 .2845^ .28513 .28541 .28569 .28597 .28708 .28736 .28764 .28792 .28875 96070 .96054 .96037 .96013 .96005 .95997 .95981 .95972 .95964 .95956 .95940 .95931 .95923 .95915 .95907 .95898 .95890 .95874 .95865 .95857 .95841 .95832 .95824 .95816 .95807 .95791 .95782 .95774 .95766 .95757 .95749 .95740 .95732 .95724 .95715 .95707 .95698 .95681 ,95673 ,95664 ,95656 ,95647 .29237 Cosin .95630 Sine .29321 .29348 .29376 .29404 .29432 .29460 .29487 .29515 .29543 .29571 .29599 .29626 .29654 tB9682 .29710 .2973' .29765 .29793 .29821 .29849 .29876 .29960 .29987 .30015 .30043 .30071 .30126 .30154 .30209 .30237 .30320 .30348 .30376 .30431 .30459 .30486 .30514 .30542 .30570 .30597 .30708 .30763 .30791 .30819 .30846 .30874 .30902 Osin Cosin .95630 95613 95605 18 Sine 95588 95579 95571 95562 95554 ,95545 95536 95528 95519 95511 95502 95493 95485 95476 95467 95459 95450 ,95441 95433 ,95424 ,95415 ,95407 .95380 ,95372 .95354 .95345 .95337 .95319 .95310 .95301 .95203 .95275 .95266 .95257 .95248 .95231 .95222 .95213 .95204 .95195 .95186 .95177 .95168 .95159 .95150 .95142 .95133 .95124 .95115 .95106 Sine .30957 .30985 .31012 .31040 .31068 .31095 .31123 .31151 .31178 .31206 .31233 .31261 .31289 .31316 .31344 .31372 .31399 .31427 .31454 .31482 .31510 .31537 .31565 .31593 .31620 .31648 .31675 .31703 .31730 .31758 .31786 .31813 .31841 .31868 .31896 .31923 .31951 .31979 .82006 .32034 .32061 .32089 .32116 .32144 .32171 .32199 .32227 .32254 .32419 .32447 .32474 72' .32529 .32557 Cosin Cosin .95106 .95097 .95088 .95079 .95070 .95061 .95052 .95043 .95033 .95015 ,95006 ,94997 .94979 .94970 .94961 .94952 .94943 .94933 .94915 .94906 .94897 .94888 .94878 .94869 .94860 .94851 .94842 .94832 .94814 .94805 .94795 .94786 .94777 .94768 .94758 .94749 .94740 .94730 .94721 .94712 .94702 .94684 ,94674 ,94665 ,94656 ,94646 94637 94627 94618 .94590 94571 94561 94552 Bind 71 19 Sine .32557 .32584 .32612 .32667 .32694 .32722 .32749 .32777 .82804 .32859 .32914 .32942 .32969 .32997 .33024 .33051 .83079 .83106 .83134 .33161 .83189 .33216 .83244 .83271 .83298 .83353 .33408 .83436 .33463 .33490 .33518 .33545 .835 .83600 .33627 .83655 .33710 .33737 .33764 .83792 .83819 .83846 .83874 8392Q .84011 .84065 .84120 .84147 .84175 .34202 Cosin Cosin 194552 .94542 .94533 .94523 .94514 .94504 .94495 .94485 .94476 .94466 .94457 .94447 .94438 .94428 .94418 .94409 .94399 .94390 .94380 .9437( .94361 .94351 .94342 .94332 .94322 .94313 .94303 .94293 .94284 .94274 .94264 .94254 .94245 .94235 .94225 .94215 .9420( .9419( .9418( .94176 .94167 .94157 .94147 .94137 .94127 .94118 .94108 .94098 .94088 .94078 .94068 .94058 .94049 .94039 ,94029 94019 93979 93969 Sine 70 e 60 116 NATURAL SINES AND COSINES. 20 Cosin 34257 34284 34311 34339 34393 34421 34448 34475 34503 .34530 34557 34584 34612 34639 34694 .34721 34748 34775 .34803 34830 .34857 34S12 34966 .35048 .35075 .35102 .35130 .35157 .35184 .93929 .93919 .93909 .93879 93829 93819 93799 93779 93759 93748 93738 ,93728 93718 93708 936^ .9365? .93647 93637 21 Sine 135837 ,35864 Cosin .93348 ,35918!. 93327 .93316 ,35973 ,36000 ,36054 ,36135 ,36162 ,36190 ,36217 ,36244 36298 36325 36352 36379 ,36434 ,36515 ,36542 ,36569 ,36596 .36677 .36704 .36731 ,36758 ,36812 .93295 .93274 93243 93211 ,93201 ,93190 ,93180 ,93169 ,93159 ,93148 .93137 .93127 .93116 .93106 .93095 .93084 .93074 .93063 .93043 .93020 .93010 .92978 22 24 .40806 .40833 .40860 .37757 .37784 .37811 .37838 .37865 .37892 .37919 .37946 .37973 .37999 .93488 .92477 .92466 .92455 .92444 .92432 .92421 .92410 .92399 <;<> .38322 .38349 .38376 .38403 .38430 or 38 .OOZ.ll .35239 . yaoyo .93585 . ooooy .36867 tweaot .92956 .oo OOG-10 156.259 .C2386 41.9158 .04133 24.1957 .05G33 16.9990 38 23 OOCC3 119.405 .C2415 41.4106 .04162 24.02G3 .05012 16.9150 37 24 OOGC3 113.237 .02444 40.9174 .04191 23.8593 .05041 16.8319 36 25 .00727 137.507 .02473 40.4358 .04220 23.6945 .05970 16.7496 35 ,-:;; .00756 132.219 .02503 39.9655 .04250 23.5321 .05999 16.6G81 34 27 .007G5 327.321 .02531 39.5059 .04279 23.3718 .06029 16.5874 33 2S .CC315 122.774 .02560 39.0568 .04308 23.2137 .OGC58 16.5075 32 39 .CC344 118.540 .02589 38.6177 .04337 23.0577 .06087 16.4283 31 SO .00873 114.689 .02619 38.1885 .04366 22.9038 .06116 16.3499 30 31 .00902 110.892 .02648 37.7686 .04395 22.7519 .06145 16.2722 29 .00931 107.426 .02077 37.3579 .04424 22.6020 .06175 16.1952 28 33 .009CO 104.171 .02706 36.9560 .04454 22.4541 .06204 16.1190 27 84 .009G9 101.107 .02735 36.5627 .04483 22.3081 .06233 16.0435 2G 35 .01018 3.2179 .02764 36.1776 .04512 22.1640 .062C2 15.9687 25 36 .01047 95.4895 .02793 35.8006 .04541 22.0217 .06291 15.8945 21 ::7 .01076 92.9085 .02822 35.4313 .04570 21.8813 .06321 15.8211 23 38 .01105 90.4633 .02851 35.0695 .04599 21.7426 .06350 15.7483 22 39 .01135 88.1436 .02881 34.7151 .04G28 21.6056 .06379 15.6762 21 40 .01164 85.9398 .02910 34.3678 .04658 21.4704 .06408 15.6048 2;) U .01193 83.8435 .02939 34.0273 .04687 21.3369 .06437 15.5340 19 \-l .01222 81.8470 .02968 33.6935 .04716 21.2049 .06467 15.4638 18 13 .01251 79.9434 .02997 33.3662 .04745 21.0747 .064C3 15.3943 17 11 .01280 78.1263 .03026 33.0452 .04774 20.9460 .06525 15.3254 16 45 .01309 76.3900 .03055 32.7303 .04803 20.8188 .06554 15.2571 15 13 .C1338 74.7292 .03084 32.4213 .04833 20.6932 .06504 15.1893 It 17 .01367 73.1390 .03114 32.1181 .048G2 20.5691 .06G13 15.1222 18 18 .01396 71.6151 .03143 31.8205 .04891 20.4465 .06642 15.0557 12 :') .01425 7'0.1533 .03172 31.5284 .04920 20.3253 .OGG71 14.9898 11 CO .01455 68.7501 .03201 31.2416 .04949 20.2056 .06700 14.9244 1C 51 .01484 67.4019 .03230 30.9599 .04978 20.0872 .06730 14.8596 9 :,2 .01513 66.1055 .03259 30.6833 .05007 19.9702 .06759 14.7954 8 5.3 .01542 64.8580 .03288 30.4116 .05037 19.8546 .06788 14.7317 7 54 .01571 63.6567 .03317 30.1446 .05066 19.7403 .06817 14.6685 6 55 .01600 62.4992 .03346 29.8823 .05095 19.6273 .06847 14.6059 5 56 .01629 61.3829 .oa376 29.6245 .05124 19.5156 .06876 14.5438 4 57 .01658 60.3058 .03405 29.3711 .05153 19.4051 .06905 14.4823 58 01687 59.2659 .03434 29.1820 .05182 19.2959 .06934 14.4212 c 59 .01716 58.2612 .03463 28.8771 .05212 19.1879 .06963 14.3607 1 60 .01746 57.2900 .03492 28.6363 .05241 19.0811 .06993 14.3007 / Cotang Tang Cotang Tang Cotang Tang Cotang j Tang / 89 a 88" li 87* 06 122 NATURAL TANGENTS AND COTANGENTS 4 5 1 1 6 : [ 7 Tang Cotang Tang Cotang _Tang_ Cotang Tang Cotang "6 .06993 14.3007 .08749 11.4301 .10510 9.51436 .12278 8.14435 (50 1 .07022 14.2411 .08778 11.3919 .10540 9.48781 .12308 8.12481 59 2 .07051 14.1821 .08807 11.3540 .10569 9.46141 .12338 8.195SG T;S 8| .07080 14.1235 .08837 11.3163 .10599 9.43515 .12367 8.C8600 .07110 14.0655 .08866 11.2789 .10628 9.40904 .12397 8.C6C74 6G g .07139 14.0079 .08895 11.2417 .10657 9.38307 .12426 8.04756 65 <; .07168 13.9507 .08925 11 .2048 .10687 9.35724 .12456 8.C204S 54 7 .07197 13.8940 .08954 11.1681 .10716 9.33155 .12485 8.00948 63 8 .07227 13.8378 .08983 11.1316 .10746 9.30599 .12515 7.9C058 62 9j .07256 13.7821 .09013 11.0954 .10775 9.28058 .12544 7.97176 61 10 .07285 13.7267 .09042 11.0594 .10805 9.25530 .12574 7.95302 50 11 .07314 13.6719 .09071 11.0237 .10834 9.23016 .12603 7.93438 40 12 .07344 13.6174 .09101 10.9882 .10863 9.20516 .12633 7.91582 13 .07373 13.5634 .09130 10.9529 .1C893 9.18028 .12662 7.89734 4"! 14 .07402 13.5098 .09159 10.9178 .1C922 9.15554 .12692 7.87895 4!) 15 .07431 13.4566 .09189 10.8829 .10952 9.13093 .12722 7.86064 45 16 .07461 13.4039 .09218 10.8483 .10981 9.10646 .12751 7.84242 41 17 .07490 13.3515 .09247 10.8139 .11011 9.08211 .12781 7.82428 43 18 .07519 13.2996 .09277 10.7797 .11040 9.057C9 .12810 7.80622 4-2 10 .07548 13.2480 .09306 10.7457 .11070 9.03379 .12840 7.78825 20 .07578 13.1969 .09335 10.7119 .11099 9.00983 .12869 7.77035 40 21 .07607 13.1461 .09365 10.6783 .11128 8.98598 .12899 7.75254 80 22 .07636 13.0958 .09394 10.6450 .11158 8.96227 .12929 7.72480 .v ; 23 .07665 13.0458 .09423 10.6118 .11187 8.93867 .12958 7.71715 87 24 .07695 12.9962 .09453 10.5789 .11217 8.91520 .12988 7.69C57 ', > 25 .07724 12.9469 .09482 10.5462 .11246 8.89185 .13017 7.68208 35 26 .07753 12.8981 .09511 10.5136 .11276 8.86862 .13047 7.66466 34 27 .07782 12.8496 .09541 10.4813 .11305 8.84551 .13076 7.64732 33 28 .07812 12.8014 .09570 10.4491 .11335 8.82252 ) .13106 7.63005 39 29 .07841 12.7536 .09600 10.4172 .11364 8.79964 .13136 7.61287 31 30 .07870 12.7062 .09629 10.3854 .11394 8.77689 .13165 7.59575 30 31 .07899 12.6591 .09658 10.3538 .11423 8.75425 .13195 7.57872 29 32 .07929 12.6124 .09688 10.3224 .11452 8.73172 .13224 7.56176 28 33 .07958 12.5660 .09717 10.2913 .11482 8.70931 .13254 7.54487 27 34 .07987 12.5199 .09746 10.2602 .11511 8.68701 .13284 7.52806 26 35 .08017 12.4742 .09776 10.2294 .11541 8.66482 .13313 7.51132 95 36 .08046 12.4288 .09805 10.1988 .11570 8.64275 .13343 7.49465 24 37 .08075 12.3838 .09334 10.1683 .11600 8.62078 .13372 7.47806 '23 38 .08104 12.3390 .09864 10.1381 .11629 8.59893 .13402 7.46154 :2:2 39 .08134 12.2946 .09893 10.1080 .11659 8.57718 .13432 7.44509 81 40 .08163 12.2505 .09923 10.0780 .11688 8.55555 .13461 7.42871 20 41 .08192 12.2067 .09952 10.0483 .11718 8.53402 .13491 7.41240 19 42 .08221 12.1632 .09981 10.0187 .11747 8.51259 .13521 7.39616 18 43 .08251 12.1201 .10011 9.98931 .11777 8.49128 .13550 7.37999 17 44 .08280 12.0772 .10040 9.96007 i .11806 8.47007 .13580 7.3G889 16 45 .08309 12.0346 .10069 9.93101 .11836 8.44896 .13609 7.34786 IS 46 .08339 11.9923 .10099 9.90211 1 .11865 8.42795 .13639 7.33190 14 47 .08368 11.9504 .10128 9.87338 | .11895 8.40705 .13669 7.31600 13 48 .08397 11.9087 .10158 9.84482 .11924 8.38625 1 .13698 7.20018 12 49 .08427 11.8673 .10187 9.81641 .11954 8.36555 .13728 7. 8442 11 50 .08456 11.8262 .10216 9.78817 .11983 8.34496 .13758 7.26873 10 61 .08485 11.7853 .10246 8.76009 1 .12013 8.32446 i .13787 7.25310 9 52 .08514 11.7448 .10275 9.73217 .12042 8.30406 .13817 7.23754 8 53 .08544 11.7045 .10305 9.70441 .12072 8.28276 .13846 7.22204 7 54 .08573 11.6645 .10334 9.67680 8.26355 .13876 7.20661 6 55 .08602 11.6248 .10263 9.64935 .'12131 8.24345 .13906 7.19125 6 56 .08032 11.5853 .1CCC3 9.G2205 .12160 8.22344 .13935 7.17594 4 "7 .08661 11.5461 .10422 9.59490 .12190 8.20G52 .13965 7.16071 3 ?I3 .08690 11.5072 .10452 9.56791 .12219 8.18370 .13995 7.14553 g 3 .08720 11.4685 .10481 9.54106 .12249 8.16398 .14024 7.13042 i 60 .08749 11.4301 .10510 9.51436 .12278 8.14435 .14054 7.11537 t Cotang Tang Cotang Tang Cotang Tang Cotang Tang 9 85' : 84 83* 82* NATURAL TANGENTS AND COTANGENTS. 123 8 I! 9 10 IP Tang Cotang Tang Cotang Tang Cotang Tang Cotang .14054 7.11537 .15838 6.31375 .17633 5.67128 .19438 5.14455 80 ] .14084 7.10038 .15868 6.30189 .17663 5.66165 .19468 5.13658 59 o .53246 1.87809 .55507 1.80158 .57813 1.72973 .60165 1.66209 58 3 .53283 1.87677 .55545 1.80034 .57851 1.72857 .60205 1.66099 57 4 .53320 1.87546 .55583 1.79911 ; .57890 1.72741 .60245 1.65990 50 g .53358 1.87415 .55621 1.79788 1 .57929 1.72625 .60284 1.65881 55 e .53395 1.87283 .55659 1.79665 .57968 1.72509 .60324 1.65772 54 7 .53432 1.87152 .55697 1.79542 .58007 1.72393 .60364 1.65663 53 8 .53470 1.87021 .55736 1.79419 ;i .58046 1.72278 .60403 1.65554 52 9 .53507 1.86891 .55774 1.79296 .58085 1.72163 .60443 1.65445 51 10 .53545 1.86760 .55813 1.79174 .58124 1.72047 .60483 1.65337 50 11 .53582 1.86630 .55850 1.79051 .58162 1.71932 .60522 1.65228 49 12 .53620 1.86499 .55888 1.78929 .58201 1.71817 .60562 1.65120 48 13 .53657 1.86369 .55926 1.78807 .58240 1.71702 .60602 1.65011 47 14 .53694 1.86239 .55964 1,78685 .58279 1.71588 .60642 1.64903 46 15 .53732 1.86109 .56003 1.78563 .58318 1.71473 .60681 1.64795 45 16 .53769 1.85979 .56041 1.78441 .58357 1.71358 .60721 1.64687 44 17 .53807 1.85850 .56079 1.78319 .58396 1.71244 .60761 1.64579 43 18 .53844 1.85720 .56117 1.78198 .58435 1.71129 .60801 1.64471 42 19 .53882 1.85591 .56156 1.78077 .58474 1.71015 .60841 1.64363 41 20 .53920 1.85462 .56194 1.77955 .58513 1.70901 .60881 1.64256 40 21 .53957 1.85333 .56232 1.77834 .58552 1.70787 .60921 1.64148 39 J-.' .53995 1.85204 .56270 1.77713 .58591 1.70073 .60960 1.64041 38 -,>:; .54032 1.85075 .56309 -1.77592 i .58631 1.70560 .61000 1.63934 37 24 .54070 1.84946 .56347 1.77471 .58670 1.70446 .61040 1.63826 36 25 .54107 1.84818 .56385 1.77351 .58709 1.70332 .61080 1.63719 35 36 .54145 1.84689 .56424 1.77230 ' .58748 1.70219 .61120 1.63612 34 27 .54183 1.84561 .56463 1.77110 .58787 1.70106 .61160 1.63505 33 28 .54220 1.84433 .56501 1.76990 .58826 1.69992 .61200 1.63398 32 ',",) .54258 1.84305 .5C539 1.7G869 .58865 1.69879 .61240 1.63292 31 30 .54296 1.84177 .56577 1.76749 .58905 1.69766 .61280 1.63185 30 31 .54333 1.84049 .56616 1.76629 .58944 1.69653 .61320 1.63079 29 32 .54371 1.83922 .50654 1.70510 .58983 1.69541 .61360 1.62972 28 83 .54409 1.83794 .56693 1.76390 .59022 1.69428 .61400 1.62866 27 Ml .54446 1.83667 .56731 1.70271 .59061 1.69316 .61440 1.62760 26 -55 .54484 1.83540 .56769 1.70151 .59101 1.69203 .61480 1.62654 25 36 .54528 1.83413 .56808 1.76032 : .59140 1.69091 .61520 1.62548 24 37 .54560 1.83286 .56846 1.75913 ! .59179 1.68979 .61561 1.62442 23 38 .54597 1. 83159 .56885 1.75794 ] .59218 1.68866 .61601 1.C2336 22 39 .54635 1.83033 .56923 1.75675 .59258 1.68754 .61641 1.62230 21 -10 .54673 1.62906 .50962 1.75556 .59297 1.68643 .61681 1.02125 20 41 .54711 1.82780 .57000 1.75437 .59336 1.68531 .61721 1.62019 19 !3 .54748 1.82654 .57039 1.75319 .59376 1.68419 .61761 1.61914 18 43 .54786 1.82528 .57078 1.75200 .59415 1.68308 .61801 1.61808 17 44 .5^S24 1.82402 .57116 1.75082 .59454 1.68196 .61842 1.61703 16 15 .54862 1.82276 .57155 1.74964 .59494 1.68085 .61882 1.61598 15 16 .54900 1.82150 .57193 1.74846 .59533 1.67974 .61922 1.61493 14 47 .54938 1.82025 .57232 1.74728 .59573 1.67863 .61962 1.61388 13 48 .54975 1.81899 .57271 1.74610 .59612 1.67752 .62003 1.61283 12 19 .55013 1.81774 .57309 1.74492 .59651 1.67641 .62043 1.61179 11 50 .55051 1.81649 .57348 1.74375 .59691 1.67530 .62083 1.61074 10 51 .55089 1.81524 .57386 1.74257 .59730 1.67419 .62124 1.60970 9 52 .55127 1.81399 .57425 1.74140 .59770 1.67309 .62164 1.60865 8 53 .55165 1.81274 .57464 1.74022 .59809 1.67198 .62204 1.60761 7 54 .55203 1.81150 .57503 1.73905 .59849 1.67088 .62245 1.60657 6 55 .55241 1.81025 .57541 1.73788 .59888 1.66978 .62285 1.60553 5 56 .55279 1.80901 .57580 1.73671 .59928 1.66867 .62325 1.60449 4 57 .55317 1.80777 .57619 1.73555 .59967 1.66757 .62366 1.60345 3 58 .55355 1.80653 .57657 1.73438 .60007 1.66647 .62406 1.60241 2 59 .55393 1.80529 .57696 1.73321 .60046 1.66538 .62446 1.60137 1 no .554'il 1.80405 .57735 1.73505 .60086 I.fifi428 .02487 1.60038 / Cotang Tang Cotang Tang Cotang Tang Cotaug Tang 9 61 60 59' 58 NATURAL TANGENTS AND COTANGENTS. 129 32 o 33 34 35 o Tang otang Tang otang Tang Cotang Tang Cotang 8 .62487 .000*5 .64941 .53986 67451 .48256 70021 .42815 jO 62527 .59930 .64982 .53888 67493 .48163 70064 1.42720 9 2 .62568 .59826 .65024 .53791 67536 .48070 1 70107 .42638 8 3 .62608 .59723 .65065 .53693 67578 .47977 70151 1.42550 7 4 .62649 .59620 65106 .53595 67620 .47885 70194 1.42462 5 5 .62689 .59517 65148 .53497 67663 .47792 70238 ..42374 3 6 62730 .59414 65189 .53400 67705 1.47699 ' 70281 [.42286 4 7 .62770 .59311 .65231 .53302 67748 .47607 j 70325 1.42198 3 8 .62811 .59208 .65272 .53205 67790 1.47514 .70368 1.42110 2 9 .62852 .59105 .65314 .53107 67832 ..47422 70412 1.42022 1 10 .62893 .59002 .65355 .53010 67875 1.47330 70455 1.41934 50 11 .62933 .58900 .65397 .52913 67917 1.47238 .70499 1.41847 9 12 .62973 .53797 .65438 .52816 67960 ..47146 .70542 1.41759 8 13 .63014 .58695 .65480 .52719 68002 [.47053 .70586 1.41672 7 14 .63055 .58593 .65521 .52622 68045 1.46962 .70629 1.41584 6 15 .63095 .58490 .65563 .52525 68088 1.46870 .70673 1.41497 5 16 .63136 .58388 .65604 .52429 .68130 [.46778 .70717 1.41409 44 17 .63177 .58286 .65646 .52332 .68173 [.46686 .70760 1.41322 3 18 .63217 .58184 .65688 1.52235 .68215 1.46595 .70804 1.41235 42 19 63258 .58083 .65729 1.52139 .68258 1.46503 .70848 1.41148 1 20 .63299 1.57981 .65771 1.53043 .68301 1.46411 .70891 1.41061 40 21 .63340 1.57879 .65813 1.51946 .68343 1.46320 .70935 1.40974 39 22 .63380 1.57773 .65854 :. 51850 .68386 1.46229 .70979 1.40887 38 23 .63421 1.57G76 .65896 1.51754 .68429 1.46137 .71023 1.40800 17 24 .63462 1.57575 .65938 [.51658 .68471 1.46046 .71066 1.40714 IG 25 .63503 1.57474 .65980 [.515G2 .68514 1.45955 .71110 1.40627 IE 26 .63544 1.57372 .66021 1.51466 .68557 1.45864 .71154 1.40540 34 27 .63584 1.57271 .66063 1.51370 .68600 1.45773 .71198 1.40454 J 28 .63625 1.57170 .66105 1.51275 .68642 1.45682 .71242 1.40367 32 29 .63666 1.57069 .66147 1.51179 .68685 1.45592 .71285 1.40281 31 30 .63707 1.56969 .66189 1.51084 .68728 1.45501 .71329 1.40195 30 31 .63748 1.56868 .66230 1.50988 .68771 1.45410 .71373 1.40109 Of 33 .63789 1.56767 .66272 1.50893 .68814 1.45320 .71417 1.40022 28 33 .63830 1.56667 .66314 1.50797 .68857 1.45229 .71461 1.39936 2' 34 .63871 1.56566 .66356 1.50702 .68900 1.45139 .71505 1.39850 26 35 .63912 1.56466 .66398 1.50607 .68942 1.45049 .71549 1.39764 25 33 .63953 1.56366 .66440 1.50512 .68985 1.44958 .71593 1.39679 24 37 .63994 1.56265 .66482 1.50417 .69028 1.44868 .71637 1.39593 2< 38 .64035 1.56165 .66524 1.50322 .69071 1.44778 .71681 1.39507 3$ 39 .64076 1.56065 .66566 1.50228 .69114 1.44688 .71725 1.39421 21 40 .64117 1.55966 .66608 1.50133 .69157 1.44598 .71769 1.39336 20 41 .64158 1.55866 .66650 1.50038 .69200 1.44508 .71813 1.39250 10 42 .64199 1.55766 .66692 1.49944 .6924S 1.44418 .71857 1.89165 1C 43 .64240 1.575666 .66734 1.49849 .69286 1.44329 .71901 1.39079 44 .64281 1.55567 .66776 1.49755 .69329 1.4*239 .71946 1.38994 45 .64322 1.55467 .66818 1.49661 .69372 1.44149 .71990 1.38909 46 .64363 1.55368 .66860 1.49566 .694N 1.44060 .72034 1.38824 47 .64404 1.55269 .66902 1.49472 .69459 1.43970 .72078 1.38738 48 .64446 1.55170 .66944 1.49378 .69502 1.43881 .72122 1.38G53 49 .64487 1.55071 .66986 1.49284 .69545 1.43792 .72167 1.38568 50 .64528 1.54972 .67028 1.49190 .69588 1.43703 .72211 1.38484 51 .64569 1.54873 .67071 1.49097 .69631 1.43614 .72255 1.38399 52 .6461 1.54774 .67113 1.49003 .69675 1.43525 .72299 1.38314 53 .6465 1 .54675 .67155 1.48909 .69718 1.43436 .72344 1.38229 54 .6469 1.5457 .67197 1.48816 .69761 1.43347 .72388 1.38145 55* .64734 1.5447 .67239 1.48722 .69804 1.43258 .72432 1.380GO 56 .6477 1.5437 .67282 1.48629 .69847 1.43169 .72477 1.37976 57 .6481 1.5428: .6732^ 1.48536 .69891 1.43080 .7252: 1.37891 58 .6485 1.54183 .6736 1.48442 .69934 1.42992 .72565 1.37807 9 .6489 1.5408 .6740 1.4834J .6997 1.42905 .72610 1.37722 60 .6494 1.53986 .6745 1.48256 .7002 1.42815 .72654 1.37638 Cotan Tang Cotan Tang Cotan Tang j Cotan Tang 57 56 53 1 540 2 130 NATUtlAL TANGENTS ANT) COTANGENTS. ; 3 B 3 7 I 3 5 $ 9 Tang Cotang Tang Cotang Tang Cotang Tang Cotang .72654 1.37638 .75355 1.32704 .78129 1.27994 .80978 1.23490 GO 1 .72699 1.37554 .75401 1.32624 .78175 1.27917 .81027 1.23416 59 2 .72743 1.37470 .75447 1.32544 .78222 1.27841 .81075 1.23343 58 3 .72788 1.37386 .75492 1.32464 .78269 1.27764 .81123 1.23270 57 4 .72832 1.37302 .75538 1.32384 .78316 1.27688 .81171 1.23196 5C 5 .72877 1.37218 .75584 1.32304 .78363 1.27611 .81220 1.23123 55 6 .72921 1.37134 .75629 1.32224 .78410 1.27535 .81268 1.23050 54 7 .72966 1.37050 .75675 1.32144 .78457 1.27458 .81316 1.22977 53 8 .73010 1.36967 .75721 1.32064 .78504 1.27382 .81364 1.22904 52 9 .73055 1.36883 .75767 1.31984 .78551 1.27306 .81413 1.22*31 51 10 .73100 1.36800 .75812 1.31904 .78598 1.27230 .81461 1.22758 50 11 .73144 1.36716 .75858 1.31825 .78645 1.27153 .81510 1.22685 40 13 .73189 1.36633 .75904 1.31745 .78692 1.27077 .81558 1.22612 48 13 .73234 1.36549 .75950 1.31666 .78739 1.27001 .81606 1.22539 47 14 .73278 1.36466 .75996 1.31586 .78786 1.26925 .81655 1.22467 4G 15 .73323 1.36383 .76042 1.31507 .78834 1.26849 .81703 1.22394 45 16 .73368 1.36300 .76088 1.31427 .78881 1.26774 .81752 1.22321 44 1? .73413 1.36217 .76134 1.31348 .78928 1.26698 .81800 1.22249 43 18 .73457 1.36134 .76180 1.31269 .78975 1.26622 .81849 1.22176 42 19 .73502 1.36051 .76226 1.31190 .79022 1.26546 .81898 1.22104 41 SO .73547 1.35968 .76273 1.31110 .79070 1.26471 .81946 1.22031 40 81 .73592 1.35885 .76318 1.31031 .79117 1.26395 .81995 1.21959 39 J2 .73637 1.35802 .76364 1.30952 .79164 1.26319 .82044 1.21886 38 .'3 .73681 1.35719 .76410 1.30873 .79212 1.26244 .82092 1.21814 37 24 .73726 1.35637 .76456 1.30795 .79259 1.26169 .82141 1.21742 3C 25 .73771 1.35554 .76502 1.30716 .79306 1.26093 .82190 1.21670 35 86 .73816 1.35472 .76548 1.30637 .79354 1.26018 .82238 1.21598 34 87 .73861 1.35389 .76594 1.30558 .79401 1.25943 .82287 1.21526 33 88 .73906 1.35307 .76640 1.30480 .79449 1.25867 .82336 1.21454 go X!!) .73951 1.35224 .76686 1.30401 .79496 1.25792 .82385 1.21382 81 30 .73996 1.35142 .76733 1.30323 .79544 1.25717 .82434 1.21310 30 31 .74041 1.35060 .76779 1.30244 .79591 1.25642 .82483 1.21238 20 32 .74086 1.34978 .76825 1.30166 .79639 1.25567 .82531 1.21166 28 88 .74131 1.34896 .76871 1.30087 .79680 1.25492 .82580 1.21094 27 34 .7417S 1.34814 .76918 1.30009 .79734 1.25417 .82629 1.21023 26 35 .74221 1.34732 .76964 1.29931 .79781 1.25343 .82678 1.20951 25 36 .74267 1.34650 .77010 1.29853 .79829 1.25268 .82727 1.20879 24 87 .74312 1.34568 .77057 1.29775 .79877 1.25193 .82776 1.20808 23 38 .74357 1.34487 .77103 1.29696 .79924 1.25118 .82825 1.20736 22 39 .74402 1.34405 .77149 1.29618 .79972 1.25044 .82874 1.20665 21 40 .74447 1.343S3 .77196 1.29541 .80020 1.24969 .82923 1.20593 20 41 .74492 1.34242 .77243 1.29463 .80067 1.24895 .82972 1.20522 19 43 .74538 1.34160 .77289 1.29385 .80115 1.24820 .83022 1.20451 IB 13 .74583 1.34079 .77385 1.29307 .80163 1.24746 .83071 1.20379 17 44 .74628 1.33998 .77382 1.29229 .80211 1.24672 .831CO 1.20308 16 45 .74674 1.33916 .77428 1.29152 .80258 1.24597 .83169 1.20237 15 46 .74719 1.33835 .77475 1.29074 .80306 1.24523 .83218 1.20166 14 47 .74764 1.33754 .77521 1.28997 .80354 1.24449 .83268 1.20095 13 48 .74810 1.33673 .77568 1.28919 .80402 1.24375 .83317 1.20024 12 49 .74855 1.33592 .77615 1.28842 1 .80450 1.24301 .83366 1.19953 11 no .74900 1.33511 .77661 1.28764 .80498 1.24227 .83415 1.19882 10 51 .74946 1.33430 .77708 1.28687 .80546 1.24153 .83465 1.19811 9 52 .74991 1.33349 .77754 1.28610 .80594 1.24079 .83514 1.19740 8 53 .75037 1.33268 .77801 1.28533 .80642 1.24005 .85564 1.19669 7 54 .75082 1.33187 .77848 1.28456 .80690 1.23931 .83613 1.19599 6 55 .75128 1.33107 .77895 1.28379 .80738 1.23858 .83662 1.19528 5 50 .75173 1.33026 .77941 1.28302 .80786 1.23784 .83712 1.19457 4 57 .75219 1.32946 .77988 1.28225 .80834 1.23710 .83761 1.19387 3 58 .75204 1.32865 .78035 1.28148 .80882 1.23637 .83811 1.19316 2 59 .75310 1.32785 .78082 1.28071 ,80930 1.23563 .83860 1.19246 1 00 .75355 1.32704 .78129 1.27994 .80978 1.23490 .83910 1.19175 t Cotang Tang Cotang Tang Cotang Tang Cotang Tang / ( )3 i (2 6 1 | NATURAL TANGENTS AND COTANGENTS. 131 40 41 o 42" 43 Tang Cotang Tang Cotang Tang Cotang Tang Cotang 1 (' .83910 1.19175 .86929 1.15037 .90040 1.11061 .93252 1.07237 60 .83960 1.19105 .86980 1.14969 .90093 1 10996 .93306 1.07174 59 .84009 1.19035 .87031 1.14902 .90146 1.10931 .93360 1.07112 58 8 .84059 1.18964 .87082 1.148S* .90199 1.10867 .93415 1.07049 57 4 .84108 1.18894 .87133 1.14767 .90251 1.10802 .93469 1.06987 56 i 5 .84158 1.18824 .87184 1.14699 .90304 1.10737 .93524 1.06925 55 6 .84208 1.18754 .87236 1.14632 .90357 1.10672 .93578 1.06862 54! 7 .84258 1.18684 .87287 1.14565 .90410 1.10607 .93633 1.06800 53 1 H .84307 1.18614 .87338 1.14498 .90463 1.10543 .93688 1.06738 52! 9 .84357 1.18544 .87389 1.14430 .90516 1.10478 .93742 1.06676 51 JO .84407 1.18474 .87441 1.14363 .90569 1.10414 .93797 1.06613 50 11 .84457 1.18404 .87492 1.14296 .00621 1.10349 .93852 1.06551 49 19 .84507 1.18334 .87543 1.14229 .90674 1.10285 .93906 1.06489 48 18 .84556 1.18264 .87595 1.14162 .90727 1.10220 .93961 1.06427 47 14 .84606 1.18194 .87646 1.14095 .90781 1.10156 .94016 1.06365 46 15 .84656 1.18125 .87698 1.14028 .90834 1.10091 .94071 1.06303 45 16 .84706 1.18055 .87749 1.13961 .90887 1.10027 .94125 1.06241 44 17 .84756 1.17986 .87801 1.13894 .90940 1.09963 .94180 1.06179 43 18 .84306 1.17916 .87852 1.13828 .90993 1.09899 .94235 1.06117 42 19 .84856 1.17846 .87904 1.13761 .91046 1 .09&34 .94290 1.06056 41 80 .84906 1.17777 .87955 1.13694 .91099 1.09770 .94345 1.05994 40 81 .84956 1.17708 .88007 1.13627 .91153 1.09706 .94400 1.05932 39 23 .85006 1.17638 .88059 1.13561 .91206 1.09642 .94455 1.05870 38 88 .85057 1.17569 .88110 1.13494 .91259 1.09578 .94510 1.05809 37 24 .85107 1.17500 .88162 1.13428 .91313 1.09514 .94565 1.05747 36 85 .85157 1.17430 .88214 1.13361 .91366 1.09450 .94620 1.05685 35 26 .85207 1.17361 .88265 1.13295 .91419 1.09386 .94676 1.05624 34 87 .85257 1.17292 .88317 1.13228 .91473 1.09322 .94731 1.05562 33 88 .85308 1.17223 .88369 1.13162 .91526 1.09258 .94786 1.05501 32 89 .85358 1.17154 .88421 1.13096 .91580 1.09195 .94841 1.05439 31 30 .85408 1.17085 .88473 1.13029 .91633 1.09131 .94896 1.05378 30 81 .85458 1.17016 .88524 1.12963 .91687 1.09067 .94952 1.05317 29 :w .85509 1.16947 .88576 1.12897 .91740 1.C9003 .95007 1.05255 28 :::: .85559 1.16878 .88628 1.12831 .91794 1.CG940 .95062 1.05194 27 84 .85609 1.16809 .88680 1.12765 .91847 1.08876 .95118 1.05133 26 86 .85660 1.16741 .88732 1.12699 .91901 1.08813 .95173 1.05072 25 86 .85710 1.16672 .88784 1.12633 .91955 1.C8749 .95229 1.05010 24 87 .85761 1.16603 .88836 1.12567 .92008 1.08686 .95284 1.04949 23 88 .85811 1.16535 .88888 1.12501 .92062 1.08622 .95340 1.04888 22 ::<) .85862 1.16466 .88940 1.12435 .92116 1.03559 .95395 1.04827 21 40 .85912 1.16398 .88992 1.13369 .92170 1.08496 .95451 1.04766 20 41 .85963 1.16329 .89045 1.12303 .92224 1.08432 .95506 1.04705 19 i;3 .86014 1.16261 .89097 1.12238 .92277 1.C33G9 .95562 1.04644 18 (3 .86064 1.16192 .89149 1.12172 .92331 1.03306 .95618 1.04583 17 44 .86115 1.16124 .89201 1.12106 .92385 1.08243 .95673 1.04522 16 45 .86166 1.16056 .89253 1.12041 .92439 1.08179 .95729 1.04461 15 46 .86216 1.15987 .89306 1.11975 .92493 1.08116 .95785 1.04401 14 47 .66267 1.15919 .89358 1.11909 .92547 1.08053 .95841 1.04340 13 48 .86318 1.15851 .89410 1.11844 .92601 1-07990 .95897 1.04279 12 49 .863G8 1.15783 .89463 1 11778 .92655 1.07927 .95S52 1.04218 11 60 .86419 1.15715 .89515 1.11713 .92709 1.07864 .96008 1.04158 10 61 .86470 1.15647 .89567 1.11648 .92763 1.07801 .96064 1.04097 9 68 .86521 1.15579 .89620 1.11582 .92817 1.07738 .96120 1.04036 8 68 .86572 1.15511 .89672 1.11517 .92872 1.07676 .96176 1.03976 7 54 .86623 1.15443 .89725 1.11452 .92926 1.07613 .96232 1.03915 6 65 .86674 1.15375 .89777 1.11387 .92980 1.07550 .96288 1.03855 5 66 .86725 1.15308 .89830 1.11321 .93034 1.07487 .96344 1.03794 4 57 .86776 1.15240 .89883 1.11256 .93088 1.07425 .96400 1.03734 3 68 .86827 1.15172 .89935 1.11191 .93143 1.07362 .96457 1.03674 2 69 .86878 1.15104 .89988 1.11126 .93197 1.07299 .96513 1.03613 1 (K .86929 1.15037 .90040 1.11061 .93252 1.07237 .96569 1.03553 t Cotang Tang Cotang Tang Cotang Tang Cotang Tang 49 48 47 46 132 NATURAL TANGENTS AND COTANGENTS. i 4 40 4 4 4 40 t t Tang Cotang Tang Cotang Tang Cotang .96569 1.03553 60 20 .97700 1.02355 40 i40 .98843 .01170 20 1 .96625 1.03493 59 21 .97756 .02295 39 41 .98901 .01112 19 2 .96681 .03433 58 22 .97813 .02236 as 42 .98958 .01053 18 8 .96738 .03372 57 23 .97870 .02176 37 43 .99016 .00994 17 4 .96794 .03312 56 24 .97927 .02117 86 44 .99073 .00935 16 5 .96850 .03252 55 25 .97984 .02057 35 45 .99131 .00876 15 6 .96907 .03192 54 26 .98041 .01998 34 46 .99189 .00818 14 7 .96963 .0313* 53 27 .98098 .01939 33 47 .99247 .00759 IS 8 .97020 .03072 52 28 .98155 .01879 : 48 .99304 .00701 12 9 .97076 .03012 51 , 29 .98213 .01820 31 49 .99362 .00642 11 10 .97133 .02952 50 30 .98270 .01761 30 50 .99420 .00583 10 11 .97189 .02892 49 31 .98327 .01702 29 51 .99478 .00525 9 12 .97246 .02832 48 32 .98384 .01642 28 I 52 .99536 .00467 8 13 .97302 .02772 47 83 .98441 .01583 27 53 .99594 .00408 7 14 .97359 .02713 46 34 .98499 .01524 2 54 .99652 .00350 6 15 .97416 .02653 45 35 .98556 .01465 25 55 .99710 .00291 5 1fi .97472 .02593 44 36 .98613 .01406 24 56 .99768 : .00233 4 17 .97529 .02533 43 37 .98671 .01347 23 57 .99826 .00175 3 18 .97586 : .02474 42 38 .98728 : .01288 22 58 .99884 .00116 2 19 .97643 .02414 41 39 ,98786 .01229 21 159 .99942 .00058 1 90 .97700 .02355 40 40 .96843 .01170 90 60 1.00000 .00000 Cotang Tang f 1 Cotang Tang , 1 , Cotang Tang / 4 5 4 V i I 4 5 SHORT-TITLE CATALOGUE OP THE PUBLICATIONS OF JOHN WILEY & SONS, NEW YORK. LONDON: CHAPMAN & HALL, LIMITED. ARRANGED UNDER SUBJECTS Descriptive circulars sent on application. Books marked with an asterisk (*) are sold at net prices only, a double asterisk (**) books sold under the rules of the American Publishers' Association at net prices subject to an extra charge for postage. All books are bound in cloth unless otherwise stated. AGRICULTURE. Armsby's Manual of Cattle-feeding lanao, $i 75 Principles of Animal Nutrition 8vo, 4 oo Budd and Hansen's American Horticultural Manual: Part I. Propagation, Culture, and Improvement i2mo, i 50 Part II. Systematic Pomology i2mo, i 50 Downing's Fruits and Fruit-trees of America 8vo, 5 oo Elliott's Engineering for Land Drainage i2mo, i 50 Practical Farm Drainage i2mo, i oo Green's Principles of American Forestry i2mo, i 50 Grotenfelt's Principles of Modern Dairy Practice. (Woll.) i2mo, 2 oo Kemp's Landscape Gardening i2mo, 2 50 Maynard's Landscape Gardening as Applied to Home Decoration i2mo, i *o Sanderson's Insects Injurious to Staple Crops i2mo, i 50 Insects Injurious to Garden Crops. (In preparation.) Insects Injuring Fruits. (In preparation.) Stockbridge's Rocks and Soils 8vo, 2 50 Woll's Handbook for Farmers and Dairymen i6mo, i 50 ARCHITECTURE. Baldwin's Steam Heating for Buildings i2mo, 2 50 Berg's Buildings and Structures of American Railroads 4to, 5 oo Birkmire's Planning and Construction of American Theatres 8vo, 3 oo Architectural Iron and Steel 8vo, 3 50 Compound Riveted Girders as Applied in Buildings 8vo, 2 oo Planning and Construction of High Office Buildings. 8vo, 3 50 Skeleton Construction in Buildings 8vo, 3 oo Brigg's Modern American School Buildings 8vo, 4 oo Carpenter's Heating and Ventilating of Buildings 8vo, 4 oo Freitag's Architectural Engineering 8vo, 3 50 Fireproofing of Steel Buildings 8vo, 2 50 French and Ives's Stereotomy. , 8vo, 2 50 Gerhard's Guide to Sanitary House-inspection i6mo, i oo Theatre Fires and Panics i2mo, i 50 Holly's Carpenters' and Joiners' Handbook i8mo, 75 Johnson's Statics by Algebraic and Graphic Methods 8vo, 2 oo 1 Kidder's Architects' and Builders' Pocket-book. Rewritten Edition. i6mo,mor,, 5 oo Merrill's Stones for Building and Decoration 8vo, 5 oo Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 oo Monckton's Stair-building 4 to, 4 oo Patton's Practical Treatise on Foundations 8vo, 5 oo Peabody's Naval Architecture Svo, 7 50 Richey's Handbook for Superintendents of Construction i6mo, rnor., 4 oo Sabin's Industrial and Artistic Technology of Paints and Varnish Svo, 3 oo Siebert and Biggin's Modern Stone-cutting and Masonry Svo, i SG Snow's Principal Species of Wood Svo, 3 50 Sondericker's Graphic Statics with Applications to Trusses, Beams, and Arches. Svo, 2 oo Towne's Locks and Builders' Hardware iSmo, morocco, 3 oo Wait's Engineering and Architectural Jurisprudence Svo, 6 oo Sheep, 6 50 Law of Operations Preliminary to Construction in Engineering and Archi- tecture Svo, 5 co Sheep, 5 50 Law of Contracts Svo, 3 oo Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. .Svo, 4 oa Woodbury's Fire Protection of Mills Svo, 2 50 Worcester and Atkinson's Small Hospitals, Establishment and Maintenance, Suggestions for Hospital Architecture, with Plans for a Small Hospital. i2mo, i 25 The World's Columbian Exposition of 1893 Large 4to, i oo ARMY AND NAVY. Bernadou's Smokeless Powder, Nitro-cellulose, and the Theory of the Cellulose Molecule i2mo, 2 50 * Bruff 's Text-book Ordnance and Gunnery Svo, 6 oo Chase's Screw Propellers and Marine Propulsion Svo, 3 oo Cloke's Gunner's Examiner. (In press.) Craig's Azimuth 4to, 3 50 Crehore and Squier's Polarizing Photo-chronograph Svo, 3 oo Cronkhite's Gunnery for Non-commissioned Officers 24tno, morocco, 2 co * Davis's Elements of Law 8vo r 2 50 * Treatise on the Military Law of United States Svo, 7 oo Sheep, 7 50 De Brack's Cavalry Outposts Duties. (Carr.) 24010, morocco, 2 oo Dietz's Soldier's First Aid Handbook i6mo, morocco, i 25 * Dredge's Modern French Artillery 4to, half morocco, 15 oo Durand's Resistance and Propulsion of Ships 8vo, 5 co * Dyer's Handbook of Light Artillery i2mo, 3 oo Eissler's Modern High Explosives 8vo, 4 oo * Fiebeger's Text-book on Field Fortification Small Svo, 2 co Hamilton's The Gunner's Catechism iSmo, i oo * Hoff's Elementary Naval Tactics Svo, i 50 Ingalls's Handbook of Problems in Direct Fire Svo, 4 oo * Ballistic Tables Svo, i 50 * Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and II. . Svo, each, 6 oo * Mahan's Permanent Fortifications. (Mercur.) Svo, half morocco, 7 50 Manual for Courts-martial i6mo, morocco, i 50 * Mercur's Attack of Fortified Places i2mo, 2 oo * Elements of the Art of War Svo, 4 oo Metcalf's Cost of Manufactures And the Administration of Workshops. .Svo, 5 oo * Ordnance and Gunnery. 2 vols i2mo, 5 oo Murray's Infantry Drill Regulations iSmo, paper, 10 Nixon's Adjutants' Manual 24010, i oo Peabody's Naval Architecture Svo, 7 $o> 2 * Phelps's Practical Marine Surveying 8vo, 2 50 Powell's Army Officer's Examiner I2mo, 4 oo Sharpe's Art of Subsisting Armies in War i8mo, morocco, i 50 * Walke's Lectures on Explosives 8vo, 4 oo * Wheeler's Siege Operations and Military Mining 8vo, 2 oo Winthrop's Abridgment of Military Law i2mo, 2 50 Woodhull's Notes on Military Hygiene \. i6mo, i 50 Young's Simple Elements of Navigation i6mo, morocco, i oo Second Edition, Enlarged and Revised i6mo, morocco, 2 oo. ASSAYING. Fletcher's Practical Instructions in Quantitative Assaying with the Blowpipe. i2mo, morocco, i 50* Furman's Manual of Practical Assaying 8vo, 3 oo Lodge's Notes on Assaying and Metallurgical Laboratory Experiments. . . .8vo, 3 oo Miller's Manual of Assaying I2mo, i oo O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 2 oo Ricketts and Miller's Notes on Assaying 8vo, 3 oo Ulke's Modern Electrolytic Copper Refining ? 8vo, 3 oo Wilson's Cyanide Processes i2mo, i 50 Chlorination Process i2mo, i 50 ASTRONOMY. Comstock's Field Astronomy for Engineers 8vo, 2 50- Craig's Azimuth 4to, 3 50 Doolittle's Treatise on Practical Astronomy 8vo, 4 oo Gore's Elements of Geodesy 8vo, 2 50 Hayford's Text-book of Geodetic Astronomy 8vo, 3 oo- Merriman's Elements of Precise Surveying and Geodesy 8vo, 2 '50 * Michie and Harlow's Practical Astronomy 8vo, 3 oo * White's Elements of Theoretical and Descriptive Astronomy i2mo, 2 oa BOTANY. Davenport's Statistical Methods, with Special Reference to Biological Variation. i6mo, morocco, i 25 Thome' and Bennett's Structural and Physiological Botany i6mo, 2 25 Westermaier's Compendium of General Botany. (Schneider.) 8vo, 2 oo CHEMISTRY. Adriance's Laboratory Calculations and Specific Gravity Tables I2mo, I 25 Allen's Tables for Iron Analysis 8vo, 3 oo Arnold's Compendium of Chemistry. (Mandel.) Small 8vo, 3 50 Austen's Notes for Chemical Students 12010, I 50 Bernadou's Smokeless Powder. Nitro-cellulose, and Theory of the Cellulose Molecule 12010, 2 50 Bolton's Quantitative Analysis 8vo , i 50- * Browning's Introduction to the Rarer Elements 8vo, i 50- Brush and Penfield's Manual of Determinative Mineralogy 8vo, 4 oo Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood. ). .8vo, 3 oo Cohn's Indicators and Test-papers i2mo, 2 oo- Tests and Reagents 8vo, 3 oo Crafts's Short Course in Qualitative Chemical Analysis. (Schaeffer.). . .12010, i sa Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von Ende.) i2mo, 2 50 Drechsel's Chemical Reactions. (Merrill.) i2mo, i 25 Duhem's Thermodynamics and Chemistry. (Burgess.) , .8vo, 4 oo Eissler's Modern High Explosives 8vo, 4 oo Effront's Enzymes and their Applications. (Prescott.) 8vo, 3 oo Erdmann's Introduction to Chemical Preparations. (Dunlap.) i2mo, i 25". 3 Fletcher's Practical Instructions in Quantitative Assay irg with the Blowpipe. i2mo, morocco, i 50 Fowler's Sewage Works Analyses i2mo, 2 oo Fresenius's Manual of Qualitative Chemical Analysis. (Wells.) 8vo, 5 oo Manual of Qualitative Chemical Analysis. Part I. Descriptive. (Weils.) 8vo, 3 oo System of Instruction in Quantitative Chemical Analysis. (Coin.) 2 vols 8vo, 12 50 Fuertes's Water and Public Health 12010, i 50 Furman's Manual of Practical Assaying 8vo, 3 oo * Getman's Exercises in Physical Chemistry i2mo, 2 oo Gill's Gas and Fuel Analysis for Engineers i2mo, i 25 Groten/eit's Principles of Modern Dairy Practice. (Woll.) i2mo, 2 oo Hammarsten's Text-book of Physiological Chemistry. (Mandel.) 8vo, 4 oo Helm's Principles of Mathematical Chemistry. (Morgan.) i2iro, i 50 Hering's Ready Reference Tables (Conversion Factors) i6rr.o, rr.orocco, 2 50 Hind's Inorganic Chemistry 8vo, 3 oo Laboratory Manual for Students i2mo, 75 Holleman's Text-book of Inorganic Chemistry. (Cooper.) 8vo, 2 50 Text-book of Organic Chemistry. (Walker and Mott.) 8vo, 2 50 * Laboratory Manual of Organic Chemistry. (Walker.) i2mo, i oo Hopkins's Oil-chemists' Handbook 8vo, 3 oo Jackson's Directions for Laboratory Work in Physiological Chen.Isiry. .8vo, i 23 Keep's Cast Iron 8vo, 2 50 Ladd's Manual of Quantitative Chemical Analysis i2mo, i oo Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo * Langworthy and Austen. The Occurrence of Aluminium in Vege'able Products, Animal Products, and Natural Waters 8vo, 2 oo Lassar-Cohn's Practical Urinary Analysis. (Lorenz.) i2mo, i oo Application of Some General Reactions to Investigations in Organic Chemistry. (Tingle.) i2mo, i oo Leach's The Inspection and Analysis of Food with Special Reference to State Control. 8vo, 7 50 Lob's Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz. ).i2mo, i oo Lodge's Notes on Assaying and Metallurgical Laboratory Experiments. .. .8vo, 3 co Lunge's Techno-chemical Analysis. (Cohn.) i2mo, i oo Mandel's Handbook for Bio-chemical Laboratory i2mo, i 50 * Martin's Laboratory Guide to Qualitative Analysis with the Blowpipe . . i2mo, Co Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 3d Edition, Rewritten 8vo, 4 oo Examination of Water. (Chemical and Bacteriological.) i2rro, i 25 Matthew's The Textile Fibres 8vo, 3 50 Meyer's Determination of Radicles in Carbon Compounds. (Tingle.). .12010, i oo Miller's Manual of Assaying i2mo, i .00 Mixter's Elementary Text-book of Chemistry i2mo, i 51 Morgan's Outline of Theory of Solution and its Results i2iro, i oc Elements of Physical Chemistry i2mo, 2 oo Morse's Calculations used in Cane-sugar Factories i6mo, morocco, i 50 Mulliken's General Method for the Identification of Pure Organic Compounds. Vol. I ' Large 8vo, 5 oo O'Brine's Laboratory Guide in Chemical Analysis 8vo, 2 oo O'Driscoll's Notes on the Treatment of Gold Ores 8vo, 2 oo Ostwald's Conversations on Chemistry. Part One. (Ramsey.) 12010, i 50 Ostwald's Conversations on Chemistry. Part Two. (Turnbull.). (In Press.) * Penfield's Notes on Determinative Mineralogy and Record of Mireral Tests. 8vo, paper, 50 Pictet's The Alkaloids and their Chemical Constitution. (Biddle.) 8vo, 5 oo Pinner's Introduction to Organic Chemistry. (Austen.) i2mo, i 50 Poole's Calorific Power of Fuels 8vo, 3 oo Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- ence to Sanitary Water Analysis i2mo, i 25 4 * Relslg's Guide to Piece-dyeing 8vo, 25 oo Richards and Woodman's Air, Water, and Food from a Sanitary Standpoint 8vo, 2 oo Richards's Cost of Living as Modified by Sanitary Science i2mo, i oo Cost of Food, a Study in Dietaries i2mo, i oo * Richards and Williams's The Dietary Computer 8vo, i 50 Ricketts and Russell's Skeleton Notes upon Inorganic Chemistry. (Part I. Non-metallic Elements.) 8vo, morocco, 75 Ricketts and Miller's Notes on Assaying. . . . ' 8vo, 3 oo Rideal's Sewage and the Bacterial Purificat on of Sewage vo, 3 50 Disinfection and the Preservation of Food 8vo, 4 oo Rigg's Elementary Manual for the Chemical Laboratory 8vo, i 25 Rostoski's Serum Diagnosis. (Bolduan.) i2rno, i oo Ruddiman's Incompatibilities in Prescriptions . vo, 2 oo Sabin's Industrial and Artistic Technology of Paints and Varnish . .Svo, 3 oo Salkowski's Physiological and Pathological Chemistry. (Orndorff.) Svo, 2 50 Schimpf's Text-book of Volumetric Analysis i2mo, 2 50 Essentials of Volumetric Analysis i2mo, i 25 Spencer's Handbook for Chemists of Beet-sugar Houses i6mo, morocco, 3 oo Handbook for Sugar Manufacturers and their Chemists. . i6mo, morocco, 2 oo Stockbridge's Rocks and Soils Svo, 2 50 * Tillman's Elementary Lessons in Heat Svo, i 50 Descriptive General Chemistry Svo, 3 oo Treadwell's Qualitative Analysis. (Hall.) Svo, 3 oo Quantitative Analysis. (Hall.) Svo, 4 oo lurneaure and Russell's Public Water-supplies Svo, 5 oo Van Deventer's Physical Chemistry for Beginners. (Boltwood.) i2rno, i 50 * Walke's Lectures on Explosives Svo, 4 oo Washington's Manual of the Chemical Analysis of Rocks Svo, 2 oo Wassermann's Immune Sera : Haemolyslns, Cytotoxins, and Precipitir.s. (Bol- duan.) i2mo, i oo Well's Laboratory Guide in Qualitative Chemical Analysis Svo, i 50 Short Course in inorganic Qualitative Chemical Analysis for Engineering Students i2mo, i 50 Text-book of Chemical Arithmetic. (In press.). Whipple's Microscopy of Drinking-water Svo, 3 50 Wilson's Cyanide Processes i2mo, i 50 Chlorination Process i2mo, i 50 Wulling's Elementary Course in Inorganic, Pharmaceutical, and Medical Chemistry i2mo, 2 oo CIVIL ENGINEERING. BRIDGES AND ROOFS. HYDRAULICS. MATERIALS OF ENGINEERING. RAILWAY ENGINEERING. Baker's Engineers' Surveying Instruments 12 mo, 3 oo Bixby's Graphical Computing Table Paper 19^X24! inches. 25 ** Burr's Ancient and Modern Engineering and the Isthmian Canal. (Postage, 27 cents additional.) Svo, 3 50 Comstock's Field Astronomy for Engineers Svo, 2 50 Davis's Elevation and Stadia Tables Svo, i oo Elliott's Engineering for Land Drainage I2mo, i 50 Practical Farm Drainage i2mo, i oo Fiebeger's Treatise on Civil Engineering. (In press.) Folwell's Sewerage. (Designing and Maintenance.) Svo, 3 oo Freitag's Architectural Engineering. 2d Edition, Rewritten Svo, 3 50 French and Ives's Stereotomy Svo, 2 50 Goodhue's Municipal Improvements . . larno, i 75 Goodrich's Economic Disposal of Towns' Refuse Svo, 3 50 Gore's Elements of Geodesy Svo, 2 50 Hayford's Text-book of Geodetic Astronomy Svo, 3 oo Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50 5 "Howe's Retaining Walls for Earth i2mo, i 25 Johnson's (J. B.) Theory and Practice of Surveying Small 8vo, 4 oo Johnson's (L. J.) Statics by Algebraic and Graphic Methods 8vo, 2 oo Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.) . i2mo, 2 oo Mahan's Treatise on Civil Engineering. (1873.) (Wood.) 8vo, 5 oo * Descriptive Geometry 8vo, i 50 Merriman's Elements of Precise Surveying and Geodesy .8vo, 2 50 Elements of Sanitary Engineering 8vo, 2 oo Merriman and Brooks's Handbook for Surveyors i6mo, morocco, 2 oo Nugent's Plane Surveying 8vo, 3 50 Ogden's Sewer Design i2mo, 2 oo Patton's Treatise on Civil Engineering 8vo half leather, 7 50 Reed's Topographical Drawing and Sketching 4to, 5 oo Rideal's Sewage and the Bacterial Purification of Sewage 8vo, 3 50 Siebert and Biggin's Modern Stone-cutting and Masonry 8vo, i 50 Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 Sondericker's Graphic Statics, with Applications to Trusses, Beams, and Arches. 8vp, 2 oo Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo * Trautwine's Civil Engineer's Pocket-book i6mo, morocco, 5 oo Wait's Engineering and Archi'. ectural Jurisprudence 8vo, 6 oo Sheep, 6 50 Law of Operations Preliminary to Construction in Engineering and Archi- tecture 8vo, 5 oo Sheep, 5 50 Law of Contracts 8vo, 3 oo ^Warren's Stereotomy Problems in Stone-cutting 8vo, 2 50 Webb's Problems in the Use and Adjustment of Engineering Instruments. i6mo, morocco, i 25 * Wheeler's Elementary Course of Civil Engineering 8vo, 4 oo Wilson's Topographic Surveying 8vo, 3 50 BRIDGES ATO ROOFS. Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 2 oo * Thames River Bridge . . 4to, paper, 5 oo Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and Suspension Bridges 8vo, 3 50 Burr and Talk's Influence Lines for Bridge and Roof Computations. . . .8vo, 3 oo Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 oo Poster's Treatise on Wooden Trestle Bridges 4to, 5 oo Fowler's Ordinary Foundations 8vo, 3 50 Greene's Roof Trusses 8vo, i 25 Bridge Trusses 8vo, 2 50 Arches in Wood, Iron, and Stone 8vo, 2 50 JHowe's Treatise on Arches 8vo, 4 oo Design of Simple Roof-trusses in Wood and Steel 8vo, 2 oo Johnson, Bryan, and Turneaure's Theory and Practice in the Cesiprirg of Modern Framed Structures Small 4to, 10 oo Merriman and Jacoby's Text-book on Roofs and Bridges: Part I. Stresses in Simple Trusses ' 8vo, 2 50 Part II. Graphic Statics . 8vo, 2 50 Part III. Bridge Design - - 8vo, 2 50 Part IV. Higher Structures - 8vo, 2 50 Morison's Memphis Bridge % 4to, 10 oo Waddell's De Pontibus, a Pocket-book for Bridge Engineers. . i6mo, morocco, 3 oo Specifications for Steel Bridges i2mo, i 25 Wood's Treatise on the Theory of the Construction of Bridges and Roofs . . 8vo, 2 oo Wright's Designing of Draw-spans : Part I. Plate-girder Draws 8vo, 2 50 Part II. Riveted-truss and Pin-connected Long-span Draws 8vo, 2 50 Two parts in one volume 8vo, 3 5 HYDRAULICS. Bazin's Experiments upon the Contraction of the Liquid Vein Issuing from an Orifice. (Trautwine.) 8vo, 2 oo Bovey's Treatise on Hydraulics 8vo, 5 oo Church's Mechanics of Engineering 8vo, 6 oo Diagrams of Mean Velocity of Water in Open Channels payer, i 50 Coffin's Graphical Solution of Hydraulic Problems i6mo, morocco, 2 50 Flather's Dynamometers, and the Measurement of Power I2mo, 3 oo FolwelTs Water-supply Engineering 8vo, 4 oo Frizell's Water-power . . .8vo, 5 oo Fuertes's Water and Public Health . . i2mo, i 50 Water-filtration Works . . i2mo, 2 50 Ganguillet and Kutter's General Formula for the Uniform Flow of Water in Rivers and Other Channels. (Bering and Trautwine.) 8vo 4 oo Hazen's Filtration of Public Water-supply 8vo, 3 oo Hazlehurst's Towers and Tanks for Water-works 8vo, 2 50 Herschel's 115 Experiments on the Carrying Capacity of Large, Piveted, Metal Conduits . . . 8vo, 2 oo Mason's Water-supply. (Considered Principally from a Sanitary Standpoint.) 8vo, 4 oo Merriman's Treatise on Hydraulics 8vo, 5 oo * Michie's Elements of Analytical Mechanics . .8vo, 4 oo Schuyler's Reservoirs for Irrigation, Water-power, and Domestic Water- supply L&i.^e 8vo, 5 oo ** Thomas and Watt's Improvement of Rivers. (Post., 440. additional.) 4to, 6 oo Turneaure and Russell's Public Water-supplies ?vo, 5 oo Wegmann's Design and Construction of Dams 4to, 5 oo Water-supply of the City of New York from 1658 to 1895 4to, 10 oo Wilson's Irrigation Engineering . .Small 8vo, 4 oo Wolff's Windmill as a Prime Mover 8vo, 3 oo Wood's Turbines 8vo, 2 50 Elements of Analytical Mechanics 8vo, 3 oo MATERIALS OF ENGINEERING. Baker's Treatise on Masonry Construction . .8vo, 5 oo Roads and Pavements . 3vo, 5 oo Black's United States Public Works Ob?ong 4*0, 5 oo Bovey's Strength of Materials and Theory of Structures Svo. 7 50 Burr's Elasticity and Resistance of the Materials of Engineering 8vo. 7 50 Byrne's Highway Construction 8vo, 5 oo Inspection of the Materials and Workmanship Employed in Construction. i6mo, 3 oo Church's Mechanics of Engineering 8vo, 6 oo Du Bois's Mechanics of Engineering. Vol. I Small 4to, 7 50 Johnson's Materials of Construction Large 8vo, 6 oo Fowler's Ordinary Foundations 8vo, 3 50 Keep's Cast Iron 8vo, 2 50 Lanza's Applied Mechanics 8vo, 7 50 Marten's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 7 50 Merrill's Stones for Building and Decoration 8vo, 5 oo Merriman's Text-book on the Mechanics of Materials 8vo, 4 oo Strength of Materials i2mo, i oo Metcalf's Steel. A Manual for Steel-users ." . . i2mo, 2 oo Patton's Practical Treatise on Foundations 8vo, 5 oo Richardson's Modern Asphalt Pavements. (In press.) Richey's Handbook for Superintendents of Construction i6mo, mor., 4 oo Rockwell's Roads and Pavements in France i2mo, i 23 7 Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo Smith's Materials of Machines i2mo, i oo Snow's Principal Species of Wood 8vo, 3 50 Spalding's Hydraulic Cement . i2mo, 2 oo Text-book on Roads and Pavements i2mo, 2 oo Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo Thurston's Materials of Engineering. 3 Parts ' . ,8vo, 8 oo Part I. Non-metallic Materials of Engineering and Ivletailurcy 8\o, 2 oo Part II. Iron and Steel 8vo, 3 50 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their Constituents 8vo, 2 50 Thurston's Text-book of the Materials of Construction 8vo, 5 oo Tillson's Street Pavements and Paving Materials 8vo, 4 oo Waddell's De Pontibus. (A Pocket-book for Bridge Engineers.). . i6mo, mor., 3 oo Specifications for Steel Bridges i2mo, i 25 Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on the Preservation of Timber 8vo, 2 oo Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 oo Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and Steel . . 8vo, 4 oo RAILWAY ENGINEERING. Andrew's Handbook for Street Railway Engineers 3x5 inches, morocco, i 25 Berg's Buildings and Structures of American Railroads 4to, 5 oo Brook's Handbook of Street Railroad Location > . . . i6mo, morocco, i 50 Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 Crandall's Transition Curve i6mo, morocco, i 50 Railway and Other Earthwork Tables 8vo, i 50 Dawson's "Engineering" and Electric Traction Pocket-book . i6mo, morocco, 5 oo Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 oo * Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half mor., 25 oo Fisher's Table of Cubic Yards Cardboard, 25 Godwin's Railroad Engineers' Field-book and Explorers' Guide. i6mo, mor., 2 50 Howard's Transition Curve Field-book i6mo, morocco, i 50 Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- bankments 8vo, i oo Molitor and Beard's Manual for Resident Engineers i6mo, i oo Nagle's Field Manual for Railroad Engineers i6mo, morocco, 3 oo Philbrick's Field Manual for Engineers i6mo, morocco, 3 oo Searles's Field Engineering i6mo, morocco, 3 oo Railroad Spiral i6mo, morocco, i 50 Taylor's Prismoidal Formulae and Earthwork 8vo, i 50 * Trautwine's Method of Calculating the Cube Contents of Excavations and Embankments by the Aid of Diagrams 8vo, 2 oo The Field Practice of Laying Out Circular Curves for Railroads. i2mo, morocco, 2 50 Cross-section Sheet Paper, 25 Webb's Railroad Construction i6mo, morocco, 5 oo Wellington's Economic Theory of the Location of Railways Small 8vo, 5 oo. DRAWING. Barr's Kinematics of Machinery 8vo, 2 50 * Bartlett's Mechanical Drawing 8vo, 3 oo * " " " Abridged Ed 8vo, i 50 Coolidge's Manual of Drawing 8vo, paper i oo Coolidge and Freeman's Elements of General Drafting for Mechanical Engi- neers '. Oblong 4to, 2 50 Durley's Kinematics of Machines 8vo, 4 oo Emch's Introduction to Projective Geometry and its Applications 8vo. 2 50 8 Hill's Text-book on Shades and Shadows, and Perspective 8vo, 2 oo Jamison's Elements of Mechanical Drawing 8vo, 2 50 Jones's Machine Design: Part I. Kinematics of Machinery 8vo, i 50 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo MacCord's Elements of Descriptive Geometry 8vo, 3 oo Kinematics; or, Practical Mechanism 8vo, 5 oo Mechanical Drawing 4to, 4 oo Velocity Diagrams. 8vo, i 50 * Mahan's Descriptive Geometry and Stone-cutting 8vo, i 50 Industrial Drawing. (Thompson.) 8vo, 3 50 Moyer's Descriptive Geometry. (In press.) Reed's Topographical Drawing and Sketching 4to, 5 oo Reid's Course in Mechanical Drawing 8vo, 2 oo Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo Robinson's Principles of Mechanism 8vo, 3 oo Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo Smith's Manual of Topographical Drawing. (McMillan.) 8vo, 2 50 Warren's Elements of Plane and Solid Free-hand Geometrical Drawing. ?2mo, Drafting Instruments and Operations i2mo, Manual of Elementary Projection Drawing i2mo, Manual of Elementary Problems in the Linear Perspective of Form and Shadow i2mo, Plane Problems in Elementary Geometry i2mo, oo 25 Primary Geometry i2mo, 75 Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 General Problems of Shades and Shadows 8vo, 3 oo Elements of Machine Construction and Drawing 8vo, 7 50 Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 Weisbach's Kinematics and Powerof Transmission. (Hermann and Klein)8vo, 5 oo Whelpley's Practical Instruction in the Art of Letter Engraving i2mo, 2 oo Wilson's (H. M.) Topographic Surveying 8vo, 3 50 Wilson's (V. T.) Free-hand Perspective 8vo, 2 50 Wilson's (V. T.) Free-hand Lettering , 8vo, i oo Woolf's Elementary Course in Descriptive Geometry Large 8vo, 3 OQ ELECTRICITY AND PHYSICS. Anthony and Brackett's Text-book of Physics. (Magie.) Small 8vo, 3 oo Anthony's Lecture-notes on the Theory of Electrical Measurements. . . . i2mo, i oo Benjamin's History of Electricity , 8vo, 3 oo Voltaic Cell 8vo, 3 oo Classen's Quantitative Chemical Analysis by Electrolysis. (Boltwood.).8vo, 3 oo Crehore and Squier's Polarizing Photo-chronograph 8vo, 3 oo Dawson's "Engineering" and Electric Traction Pocket-book. i6mo, morocco, 5 oo Dolezalek's Theory of the Lead Accumulator (Storage Battery). (Von Ende.) i2mo, 50 Duhem's Thermodynamics and Chemistry. (Burgess.) 8vo, oo Flather's Dynamometers, and the Measurement of Power i2mo, oo Gilbert's De Magnete. (Mottelay.) 8vo, 50 Hanchett's Alternating Currents Explained i2mo, oo Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 50 Holman's Precision of Measurements 8vo, oo Telescopic Mirror-scale Method, Adjustments, and Tests. . . .Large 8vo, 75 Kinzbrunner's Testing of Continuous-Current Machines 8vo. 2 oo Landauer's Spectrum Analysis. (Tingle.) 8vo, 3 oo Le Chatelien's High-temperature Measurements. (Boudouard Burgess.) I2mo, 3 oo Lob's Electrolysis and Electrosynthesis of Organic Compounds. (Lorenz.) i2mo, i oo 9 * Lyons's Treatise on Electromagnetic Phenomena. Vols. I. and II. 8vo, each, 6 oo * Michie's Elements of Wave Motion Relating to Sound and Light 8vo, 4 oo Niaudet's Elementary Treatise on Electric Batteries. (Fishback.) i2mo 2 50 * Rosenberg's Electrical Engineering. (Haldane Gee Kinzbrunner.). . .8vo, i 50 Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 Thurston's Stationary Steam-engines 8vo, 2 50 * Tillman's Elementary Lessons in Heat . .8vo, i 50 Tory and Pitcher's Manual of Laboratory Physics Small 8vo, 2 oo Ulke's Modern Electrolytic Copper Refining 8vo, 3 oo LAW. * Davis's Elements of Law 8vo, 2 50 * Treatise on the Military Law of United States 8vo, 7 oo Sheep, 7 50 Manual for Courts-martial. . i6mo, morocco, i 50 Wait's Engineering and Architectural Jurisprudence 8vo, 6 oo Sheep, 6 50 Law of Operations Preliminary to Construction in Engineering and Archi- tecture 8vo, 5 oo Sheep, 5 50 Law of Contracts 8vo, 3 oo "Wlnthrop's Abridgment of Military Law i2mo, 2 50 MANUFACTURES. Bernadou's Smokeless Powder Nitro-cellulose and Theory of the Cellulose Molecule i2mo, 2 50 Bolland's Iron Founder i2mo, 2 50 " The Iron Founder," Supplement i2mo, 2 50 Encyclopedia of Founding and Dictionary of Foundry Terms Used in the Practice of Moulding i2mo, 3 oo Eissler's Modern High Explosives 8vo, 4 oo Eff rent's Enzymes and their Applications. (Prescott.) 8vo, 3 oo Fitzgerald's Boston Machinist i2mo, i oo Ford's Boiler Making for Boiler Makers i8mo, i oo Hopkin's Oil-chemists' Handbook 8vo, 3 oo Keep's Cast Iron 8vo, 2 50 Leach's The Inspection and Analysis of Food with Special Reference to State Control Large 8vo, 7 50 Matthews's The Textile Fibres 8vo, 3 50 Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo Metcalfe's Cost of Manufactures And the Administration of Workshops. 8vo, 5 oo Meyer's Modern Locomotive Construction 4to, 10 oo Morse's Calculations used in Cane-sugar Factories i6mo, morocco, i 50 * Reisig's Guide to Piece-dyeing 8vo, 25 oo Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo Smith's Press-working of Metals 8vo, 3 oo Spalding's Hydraulic Cement i2mo, 2 oo Spencer's Handbook for Chemists of Beet-sugar Houses. ... i6mo, morocco, 3 oo Handbook for Sugar Manufacturers and their Chemists . i6mo, morocco, 2 oo Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 oo Thurston's Manual of Steam-boilers, their Designs, Construction and Opera- tion 8vo, 5 oo * Walke's Lectures on Explosives 8vo, 4 oo Ware's Manufacture of Sugar. (In press.) West's American Foundry Practice i2mo, 2 50 Moulder's Text-book i2mo, 2 50 10 Wolff's Windmill as a Prime Mover 8vo, 3 oo Wood's Rustless Coatings: Corrosion and Electrolysis of Iron and Steel. .8vo, 4 o MATHEMATICS. Baker's Elliptic Functions 8vo, i 50 * Bass's Elements of Differential Calculus i2mo, 4 oo Briggs's Elements of Plane Analytic Geometry i2ino, oo Compton's Manual of Logarithmic Computations i2mo, 50 Davis's Introduction to the Logic of Algebra 8vo, 50 * Dickson's College Algebra Large i2mo, 50 * Introduction to the Theory of Algebraic Equations Large i2mo, 25 Emch's Introduction to Projective Geometry and its Applications 8vo, 50 Halsted's Elements of Geometry 8vo, 75 Elementary Synthetic Geometry 8vo, 50 Rational Geometry i2mo, 75 * Johnson's (J. B.) Three-place Logarithmic Tables: Vest-pocket size. paper, 15 100 copies for 5 oo * Mounted on heavy cardboard, 8 X TO inches, 25 10 copies for 2 oo Johnson's (W. W.) Elementary Treatise on Differential Calculus. . Small 8vo, 3 oo Johnson's (W. W.) Elementary Treatise on the Integral Calculus. Small 8vo, i 50 Johnson's (W. W.) Curve Tracing in Cartesian Co-ordinates I2mo, i oo Johnson's (W. W.) Treatise on Ordinary and Partial Differential Equations. Small 8vo, 3 50 Johnson's (W. W.) Theory of Errors and the Method of Least Squares. i2mo, i 50 * Johnson's (W. W.) Theoretical Mechanics i2mo, 3 oo Laplace's Philosophical Essay on Probabilities. (Truscott and Emory.). i2mo, 2 oo * Ludlow and Bass. Elements of Trigonometry and Logarithmic and Other Tables 8vo, 3 oo Trigonometry and Tables published separately Each, 2 oo * Ludlow's Logarithmic and Trigonometric Tables 8vo, i oo Maurer's Technical Mechanics fev , , 4 oo Merriman and Woodward's Higher Mathematics 8vo, 5 oo Merriman's Method of Least Squares 8vo, 2 oo Rice and Johnson's Elementary Treatise on the Differential Calculus. . Sm. 8vo, 3 oo Differential and Integral Calculus. 2 vols. in one Small 8vo, 2 50 Wood's Elements of Co-ordinate Geometry 8vo, 2 oo Trigonometry: Analytical, Plane, and Spherical i2mo, i oo MECHANICAL ENGINEERING. MATERIALS. OF ENGINEERING, STEAM-ENGINES AND BOILERS. Bacon's Forge Practice i2mo, i 50 Baldwin's Steam Heating for Buildings i2mo, 2 50 Barr's Kinematics of Machinery 8vo, 2 50 * Bartlett's Mechanical Drawing 8vo, 3 oo * " " " Abridged Ed 8vo, i 50 Benjamin's Wrinkles and Recipes i2mo, 2 oo Carpenter's Experimental Engineering 8vo, 6 oo Heating and Ventilating Buildings 8vo, 4 oo Cary's Smoke Suppression in Plants using Bituminous Coal. (In Prepara- tion.) Clerk's Gas and Oil Engine Small 8vo, 4 oo Coolidge's Manual of Drawing 8vo, paper, i oo Coolidge and Freeman's Elements of General Drafting for Mechanical En- gineers Oblong 4to, 2 50 11 Cromwell's Treatise on Toothed Gearing i2mo, i 50 Treatise on Belts and Pulleys i2mo, i 50 Durley's Kinematics of Machines 8vo, 4 oo Flather's Dynamometers and the Measurement of Power i2mo, 3 oo Rope Driving i2mo, 2 oo Gill's Gas and Fuel Analysis for Engineers i2mo, i 25 Hall's Car Lubrication i2mo, i oo Bering's Ready Reference Tables (Conversion Factors) i6mo, morocco, 2 50 Button's The Gas Engine 8vo, 5 oo Jamison's Mechanical Drawing 8vo, 2 50 Jones's Machine Design : Part I. Kinematics of Machinery 8vo, i 50 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo Kent's Mechanical Engineers' Pocket-book i6mo, morocco, 5 oo Kerr's Power and Power Transmission 8vo, 2 oo Leonard's Machine Shop, Tools, and Methods. (In press.) Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) (In press, i MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo Mechanical Drawing 4to, 4 oo Velocity Diagrams 8vo, i 50 Mahan's Industrial Drawing. (Thompson.) 8vo, 3 50 Poole's Calorific Power of Fuels 8vo, 3 oo Reid's Course in Mechanical Drawing 8vo, 2 oo Text-book of Mechanical Drawing and Elementary Machine Design. 8 vo, 3 oo Richard's Compressed Air ' i2mo, i 50 Robinson's Principles of Mechanism 8vo, 3 oo Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo Smith's Press-working of Metals ^ 8vo, 3 oo Thurston's Treatise on Friction and Lost Work in Machinery and Mill Work 8vo, 3 oo Animal as a Machine and Prime Motor, and the Laws of Energetics . i2n:o, i oo Warren's Elements of Machine Construction and Drawing 8vo, 7 50 Weisbach's Kinematics and the Power of Transmission. (Herrmann Klein.) 8vo, 5 oo Machinery of Transmission and Governors. (Herrmann Klein.). .8vo, 5 oo Wolff's Windmill as a Prime Mover 8vo, 3 oo Wood's Turbines 8vo, 2 50 MATERIALS OF ENGINEERING. Bovey's Strength of Materials and Theory of Structures 8vo, 7 50 Burr's Elasticity and Resistance of the Materials of Engineering. 6th Edition. Reset 8vo, 7 50 Church's Mechanics of Engineering 8vo, 6 oo Johnson's Materials of Construction 8vo, 6 oo Keep's Cast Iron 8vo, 2 50 Lanza's Applied Mechanics 8vo, 7 50 Martens's Handbook on Testing Materials. (Henning.) 8vo, 7 50 Merriman's Text-book on the Mechanics of Materials 8vo, 4 oo Strength of Materials I2mo, i oo Metcalf's Steel. A manual for Steel-users i2mo. 2 oo Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, 3 oo Smith's Materials of Machines . . I2mo, i oo Thurston's Materials of Engineering 3 vols., 8vo, 8 oo Part II. Iron and Steel 8vo, 3 50 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their Constituents 8vo > 2 5O Text-book of the Materials of Construction 8vo, 5 oo. 12 Wood's (De V.) Treatise on the Resistance of Materials au ." *-n Appendix on the Preseivation of Timber 8vo, 2 oo Wood's (De V.) Elements of Analytical Mechanics 8vo, 3 oo Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and Steel 8vo, 4 oo STEAM-ENGINES AND BOILERS. Berry's Temperature-entropy Diagram i2mo, i 25 Carnot's Reflections on the Motive Power of Heat. (Thurston.). .... i2mo, i 50 Dawson's "Engineering" and Electric Traction Pocket-book. . . .i6mo, mor., 5 oo Ford's Boiler Making for Boiler Makers i8mo, i oo Goss's Locomotive Sparks , . .8vo, 2 oo Hemenway's Indicator Practice and Steam-engine Economy i2mo, 2 oo Button's Mechanical Engineering of Power Plants 8vo, 5 oo Heat and Heat-engines 8vo, 5 oo Kent's Steam boiler Economy 8vo, 4 oo Kneass's Practice and Theory of the Injector 8vo, i 50 MacCord's Slide-valves 8vo, 2 oo Meyer's Modern Locomotive Construction 4to, 10 oo Peabody's Manual of the Steam-engine Indicator i2mo. i 50 Tables of the Properties of Saturated Steam and Other Vapors 8vo, i oo Thermodynamics of the Steam-engine and Other Heat-engines 8vo, 5 oo Valve-gears for Steam-engines 8vo, 2 50 Peabody and Miller's Steam-boilers 8vo, 4 oo Pray's Twenty Years with the Indicator Large Svo, 2 50 Pupin's Thermodynamics of Reversible Cycles in Gases and Saturated Vapors. (Osterberg.) i2mo, i 25 Reagan's Locomotives: Simple Compound, and Electric i2mo, 2 50 Rontgen's Principles of Thermodynamics. (Du Bois.) 8vo, 5 oo Sinclair's Locomotive Engine Running and Management i2mo, 2 oo Smart's Handbook of Engineering Laboratory Practice 12010, 2 50 Snow's Steam-boiler Practice. . 8vo, 3 oo Spangier's Valve-gears 8vo, 2 50 Notes on Thermodynamics i2mo, i oo Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo Thurston's Handy Tables 8vo. i 50 Manual of the Steam-engine 2 vols., 8vo, 10 oo Part I. History, Structure, and Theory 8vo, 6 oo Part II. Design, Construction, and Operation 8vo, 6 oo Handbook of Engine and Boiler Trials, and the Use of the Indicator and the Prony Brake 8vo, 5 oo Stationary Steam-engines Svo, 2 50 Steam-boiler Explosions in Theory and in Practice i2mo, i 50 Manual of Steam-boilers, their Designs, Construction, and Operation Svo, 5 oo Weisbach's Heat, Steam, and Steam-engines. (Du Bois.) Svo, 5 oo Whitham's Steam-engine Design Svo, 5 oo Wilson's Treatise on Steam-boilers. (Flather.) i6mo, 2 50 Wood's Thermodynamics, Heat Motors, and Refrigerating Machines. . .Svo, 4 oo MECHANICS AND MACHINERY. Barr's Kinematics of Machinery Svo, 2 50 Bovey's Strength of Materials and Theory of Structures Svo, 7 50 Chase's The Art of Pattern-making i2mo, 2 50 Church's Mechanics of Engineering Svo, 6 oo 13 Church's Notes and Examples in Mechanics 8vo, 2 oo Compton's First Lessons in Metal-working i2mo, i 50 Compton and De Groodt's The Speed Lathe i2mo, i 50 Cromwell's Treatise on Toothed Gearing i2mo, i 50 Treatise on Belts and Pulleys i2mo, i 50- Dana's Text-book of Elementary Mechanics for Colleges and Schools. . i2mo, i 50 Dingey's Machinery Pattern Making i2mo, 2 oo Dredge's Record of the Transportation Exhibits Building of the World's Columbian Exposition of 1893 4to half morocco, 5 oo Du Bois's Elementary Principles of Mechanics : Vol. I. Kinematics 8vo, 3 50 Vol. II. Statics 8vo, 4 oo Vol. III. Kinetics 8vo, 3 50 Mechanics of Engineering. Vol. I Small 4to, 7 50 Vol. II Small 4to, 10 oo Durley's Kinematics of Machines 8vo, 4 oo Fitzgerald's Boston Machinist i6mo, i oo Flather's Dynamometers, and the Measurement of Power i2mo, 3 oo Rope Driving i2mo, 2 oo Goss's Locomotive Sparks 8vo, 2 oo Hall's Car Lubrication i2mo, i oo Holly's Art of Saw Filing i8mo, 75 James's Kinematics of a Point and the Rational Mechanics of a Particle. (In press.) * Johnson's (W. W.) Theoretical Mechanics i2mo, 3 oo Johnson's (L. J.) Statics by Graphic and Algebraic Methods 8vo, 2 oo Jones's Machine Design: Part I. Kinematics of Machinery 8vo, i 50 Part II. Form, Strength, and Proportions of Parts 8vo, 3 oo Kerr's Power and Power Transmission 8vo, 2 oo Lanza's Applied Mechanics 8vo, 7 50 Leonard's Machine Shop, Tools, and Methods. (In press.) Lorenz's Modern Refrigerating Machinery. (Pope, Haven, and Dean.) (In press.) MacCord's Kinematics; or, Practical Mechanism 8vo, 5 oo Velocity Diagrams 8vo, i 50 Maurer's Technical Mechanics 8vo, 4 oo Merriman's Text-book on the Mechanics of Materials 8vo, 4 oo * Elements of Mechanics " i2mo, i oo * Michie's Elements of Analytical Mechanics 8vo, 4 oo Reagan's Locomotives: Simple, Compound, and Electric i2mo / 2 50 Reid's Course in Mechanical Drawing 8vo, 2 oo Text-book of Mechanical Drawing and Elementary Machine Design. 8vo, 3 oo Richards's Compressed Air i2mo, i 50 Robinson's Principles of Mechanism 8vo, 3 co Ryan, Norris, and Hoxie's Electrical Machinery. Vol. 1 8vo, 2 50 Schwamb and Merrill's Elements of Mechanism 8vo, 3 oo Sinclair's Locomotive-engine Running and Management 12 mo, 2 oo Smith's (O.) Press-working of Metals 8vo, 3 oo Smith's (A. W.) Materials of Machines i2mo, i oo Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 oo Thurston's Treatise on Friction and Lost Y/ork in Machinery and Mill Work 8vo, 3 oo Animal as a Machine and Prime Motor, and the Lawc of Energetics.. i2mo, i oo Warren's Elements of Machine Construction and Drawing 8vo, 7 50 Weisbach's Kinematics and Power of Transmission. (Herrmann Klein. ).8vo, 5 oo Machinery of Transmission and Governors. (Herrmann Klein. ).8vo, 5 oo Wood's Elements of Analytical Mechanics 8vo, 3 oo Principles of Elementary Mechanics i2mo, i 25 Turbines 8vo . 2 50 The World's Columbian Exposition of 1893 4to, i oo 14 METALLURGY. Egleston's Metallurgy of Silver, Gold, and Mercury: Vol. I. Silver 8vo, 7 50 Vol. II. Gold and Mercury 8vo, 7 50 ** Iles's Lead-smelting. (Postage 9 cents additional.) i2mo, 2 50 Keep's Cast Iron 8vo, z 50 Kunhardt's Practice of Ore Dressing in Europe 8vo, i 50 Le Chatelier's High-temperature Measurements. (Boudouard Burgess. )i2mo, 3 oo Metcalf's Steel. A Manual for Steel-users i2mo, 2 oo. Smith's Materials of Machines i2mo, i oo Thurston's Materials of Engineering. In Three Parts 8vo, 8 oa Part II. Iron and Steel 8vo, 3 50 Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their Constituents. 8vo, 2 50 Ulke's Modern Electrolytic Copper Refining 8vo, 3 oa MINERALOGY. Barringer's Description of Minerals of Commercial Value. Oblong, morocco, 2 50 Boyd's Resources of Southwest Virginia 8vo, 3 oo Map of Southwest Virignia Pocket-book form. 2 oo Brush's Manual of Determinative Mineralogy. (Penfield.) 8vo, 4 oo Chester's Catalogue of Minerals 8vo, paper, i oo Cloth, i 25 Dictionary of the Names of Minerals 8vo, 3 50 Dana's System of Mineralogy. . Large 8vo, half leather, 12 50 First Appendix to Dana's New " System of Mineralogy." Large 8vo, i oo Text-book of Mineralogy 8vo, 4 oo Minerals and How to Study Them I2mo, i 50 Catalogue of American Localities of Minerals Large 8vo, i oo Manual of Mineralogy and Petrography i2mo 2 oo Douglas's Untechnical Addresses on Technical Subjects. i2mo, i oo Eakle's Mineral Tables 8vo, i 25 Egleston's Catalogue of Minerals and Synonyms 8vo, 2 50 Hussak's The Determination of Rock-forming Minerals. ( Smith.). Small 8vo, 2 oo Merrill's Non-metallic Minerals: Their Occurrence and Uses 8vo, 4 oo * Penfieid's Notes on Determinative Mineralogy and Record of Mineral Tests. 8vo. paper, o 50 Rosenbusch's Microscopical Physiography ot the Rock-makimg Minerals (Iddings.) 8vo. 5 oo * Tillman s Text-book of Important Minerals and Rocks ... .8vo. 2 oo Williams's Manual of Lithology 8vo, 3 oo MINING. Beard's Ventilation of Mines I2mo. 2 50 Boyd's Resources of Southwest Virginia 8vo. 3 oo Map of Southwest Virginia Pocket book form. 2 oo Douglas's Untechnical Addresses on Technical Subjects i2mo. i oo * Drinker's Tunneling, Explosive Compounds, and Rock Drills. .4to,hf.mor 25 oo Eissler's Modern High Explosives 8vo 4 oo Fowler's Sewage Works Analyses i2tno 2 oo Goodyear's Coal-mines of the Western Coast of the United States . . i2mo. 2 50 Ihlseng's Manual of Mining 8vo. 5 oo ** Iles's Lead-smelting. (Postage QC. additional.) i2mo. 2 50 Kunhardt's Practice of Ore Dressing in Europe .8vo, i 50 O'DriscoU's Notes on the Treatment of Gold Ores 8vo, 2 oo * Walke's Lectures on Explosives . 8vo, 4 oo Wilson's Cyanide Processes i2mo, i 50 Chlorination Process i2mo, i 50 15 Wilson's Hydraulic and Placer Mining '..... i2mo, 2 oo Treatise on Practical and Theoretical Mine Ventilation T2mo. i 25 SANITARY SCIENCE. FolwelFs Sewerage. (Designing, Construction, and Maintenance.) 8vo, 3 oo Water-supply Engineering 8vo, 4 oo Fuertes's Water and Public Health I2mo, i 50 Water-filtration Works i2mo, 2 50 Gerhard's Guide to Sanitary House-inspection i6mo, i oo Goodrich's Economic Disposal of Town's Refuse DemySvo, 3 50 Hazen's Filtration of Public Water-supplies 8vo, 3 oo Leach's The Inspection and Analysis of Food with Special Reference to State Control 8vo, 7 50 Mason's Water-supply. (Considered principally from a Sanitary Standpoint) 8vo, 4 oo Examination of Water. (Chemical and Bacteriological.) I2mo, i 25 Merriman's Elements of Sanitary Engineering 8vo, 2 oo Ogden's Sewer Design i2mo, 2 oo Prescott and Winslow's Elements of Water Bacteriology, with Special Refer- ence to Sanitary Water Analysis I2mo, i 25 * Price's Handbook on Sanitation I2mo, i 50 Richards's Cost of Food. A Study in Dietaries I2mo, i oo Cost of Living as Modified by Sanitary Science i2mo, i oo Richards and Woodman's Air, Water, and Food from a Sanitary Stand- point 8vo, 2 oo * Richards and Williams's The Dietary Computer 8vo, i 50 Rideal's Sewage and Bacterial Purification of Sewage 8vo, 3 50 Turneaure and Russell's Public Water-supplies 8vo, 5 oo Von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, i oo Whipple's Microscopy of Drinking-water 8vo, 3 50 Woodhull's Notes on Military Hygiene i6mo, i 50 MISCELLANEOUS. De Fursac's Manual of Psychiatry. (Rosanoff and Collins.). . . .Large i2mo, 2 50 Emmons's Geological Guide-book of the Rocky Mountain Excursion of the International Congress of Geologists Large 8vo, i 50 Ferrel's Popular Treatise on the Winds 8vo. 4 oo Haines's American Railway Management i2mo, 2 50 ITott's Composition, Digestibility, and Nutritive Value of Food. Mounted chart, i 25 Fallacy of the Present Theory of Sound i6mo, i oo Ricketts's History of Rensselaer Polytechnic Institute, 1824-1894. .Small 8vo, 3 oo Rostoski's Serum Diagnosis. (Bolduan.). i2mo, i oo Rotherham's Emphasized New Testament Large 8vo, 2 oo Steel's Treatise on the Diseases of the Dog 8vo, 3 5 Totten's Important Question in Metrology 8vo, 2 50 The World's Columbian Exposition of 1893 4to, i oo Von Behring's Suppression of Tuberculosis. (Bolduan.) i2mo, i oo Winslow's Elements of Applied Microscopy i2mo, i 50 Worcester and Atkinson. Small Hospitals, Establishment and Maintenance; Suggestions for Hospital Architecture : Plans for Small Hospital . i2mo, i 25 HEBREW AND CHALDEE TEXT-BOOKS. Green's Elementary Hebrew Grammar i2mo, i 25 Hebrew Chrestomathy 8vo, 2 oo Gesenius's Hebrew and Chaldee Lexicon to^tb*OS3^8^ment Scriptures. (Tregelles.) ^&**~Ptfjp*liL 4*0. half morocco, 5 oo Lettems's Hebrew Bible ,/..:.. .P. F . 7"* .** ^1 8v ' 2 * 5 UNIVERSITY OF CALIFORNIA LIBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW OCT31 19 fEBttri* 2Jul'56RF IN 1 9 19. 30m-l,'15 VB 1106, TA770 -t^tx