UC-NRLF SB EST Sfl3 REESE LIBRARY OF THK UNIVERSITY OF CALIFORNIA. Deceived MAS 33.1.894 \, 89 . ^Accessions No.* ^//2~ "NATIONAL." Patent Taper Protecting Sleeve- Couplings. Iron Fittings. Brass Goods. Ludlow Gate Valves for Gas f Stea in or Water. Ludlow's Improved Rubber- Faced Fire Hydrants. Steam and Gas Fitters' Supplies and Tools. All Genuine National Tube Works Co.s' Casing^ and Tubing Is fitted with perfect V Threads and Patent Taper Sleeve Couplings as shown in above cut. They are shipped with THREAD PROTECTORS insuring customers perfect goods when received Our Casing, Tubing and Drive Pipe have the Best Material and Workmanship, and are acknowledged to be THE STANDARD Our works are the largest in the world in our line, and the only one where pipes and tubes from I to 24 inches inclusive, are manufac- tured. NATIONAL TUBE WORKS GO,, Manufacturers of Special Lap-Welded Pipe Fitted with Converse Patent Lock Joint. TRADE MARK. This special pipe is well adapted for the conveyance of water, gas or air, under either light or heavy pressure; is tested and guaranteed to stand 300 pounds- per square inch, and is thoroughly protected against corrosion or the action of any acids or alkalies found in na- ture. It can be bent or roughly handled without cracks or injury and can be laid more RAPIDLY 'AND CHEAPLY than any other style of pipe; a great saving in FREIGHT being effected on account of its LIGHT WEIGHT. The great saving in FRICTION in this pipe enables SMALLER sizes to be used and equal results obtained, and a conse- quent saving in first cost. dL. The lengths average about 18 to 20 feet and require about one-half the quantity of lead per joint that cast iron does. The joint with the pipe has successfully stood an hydraulic pressure of over 1000 pounds per square inch in tests that have been made. Kalamein alloy imparts nothing inju- rious to water, and Kalamein pipe may be safely used to convey drinking water without any fear of contamination. This pipe recommends itself, through its many desirable features, to the consideration of all who con- template using pipe for water or gas wrks. Information and prices promptly furnished. A complete line of Fittings, Valves, Hydrants, Tools "tc.. etc.. are manufactured by us in connection with this pipe. This pipe lit! over 4(tO cities and villages in the United States ; nearly 2000 s having been laid in the pant eight years. W. P. BUTLER, GI1/IL i IRRIGflTION ENGINEER, Irrigation Water & Sswags plants AND DESIGNED AND SUPERINTENDED. Platting V Reservoirs ^aid Oaf. X^itehss & prains flames Designed & J^aid Oaf Estimates /Aade. and or Decorative. Roads Laid Oat, Farm Lines Run and Corners Relocated. COPIES OF THIS BOOK FOR SALE, 25 CENTS. W, P, BUTLER, ABERDEEN, SOUTH DAKOTA. IRRIGATION MANUAL, CONTAINING Hgsful Information and (Cables APPERTAINING TO I* IN THE STATES OF and South Bakota, TOGETHER WITH Many Tables, Rules, and Items of Miscellaneous Information, OF VALUE TO Farmer? and Bu?ine?s BY W. P. BUTLER, Civil and Irrigation Engineer, Aberdeen, S D. 1892. Let tldny* that llamm ve abfyfyl'teSrned by doing them. 1 HUKOX1TE PRINTING HURON, S. D. Entered) according to Act of Congress , in the year 1892, by W. P. BUTLER, in the office of the Librarian of Congress^ at Washington. PUBLISHERS' CERTIFICATE. HURON, S. D., June ist, 1892 The publishers of this book hereby certify that, in accordance with the orders of the author, they have printed and bound 3500 copies of the same. SHANNON & LONGSTAFF, Publishers. INDEX TO TABLE SUBJECT. PAGES NO. 1 Dimensions of Standard wrought iron pipe 16 2 Prices " " 17 3 Comparative prices of different pipes 18 4 Prices and sizes of x and xx strong pipes 19 " casing pipe 20 6 Comparative weights of different pipes 21 7 Dimensions of pipe couplings 22 and weights of Kalamein pipe 22 9 Relative area* of standard pipe. 23 10 Weights and sizes of cast iron pipe 23 11 sizes and prices of spiral riveted pipe 24 12 American and Birmingham wire gauges 25 13 List of Dakota artesian wells 39 14 Precipitation during irrigating season in Dakota 44 15 Water duty in Colorado 46 ) 16 ' " '' " Dakota 48 17 Weir measurement table k 56 18 Table of Miner's inches reduced to cu. ft. and gallons 58 19 4k " " inch measurements 59 20 " * ; Second feet reduced to gallons 60 ^" 21 Volume and Weight of water on one acre 61 2'1 Weight of water in pipes 62 23 a " " 63, 24 Pressureof " 64*"' 25 Volume and Wcght of water in 9oo feet of pipe 65 26 Diameters, areas, and contents of pipes in cu. ft. and gallons.. .. 66 27 Relative discharging capacities of pipes 67 28 Friction loss in j-ipes. velocity to 7 feet 68 29 " " "20 " 71 30 Tabular numbers for computation of flow of water in pipes 72 31 Horizontal and vertical distances reached by jets 63 32 Table for calculating the horse power of water 80 33 Volume per minute = to a given flow per day, and ) Volume per day = to a given flow per minute ) 83 34 Time required to flood different areas to different depths 84 f 35 Volumes thrown in different times by wells of different volumes per minute 86 36 Cubic feet reduced to gallons and gallons to cubic feet 87 'M V < >lumes from differen t >\/.ns per minute .' 89 39 Size and capacity of wind mills 90 40 Volume pumped per miuiite by wind mills 90 41 Velocity and force of wind 90 42 Wind in Dakota, for past 9 years 91 43 Rain ' " " " 10 " 91 44 ( 1 ross sections of reservoir banks 101 45 Reservoirs, areas, diameters, and circumferences . . 102 , loss by evaporation and filtration 103 , areas, diameters, circumf's and contents of banks.... 104 , '' , and volumes at different depths 105 49 " , cost 106 50 ', , flow of water from 107 51 Depths, sl<>],<-, areas, perimeters. &c. of ditches 113 52 Grades per jnile and per KX) feet 116 53 Irrigation statistics -from census reports 137 * B Index to Tables^Continued. NUNBER. SUBJECT. PAGES. 54 Table of time 154 55 ' wages 3 tables ... 155 56 Sizes of a one acre field 156 57 Square feet in different areas 156 58 Hills on one acre 157 58% Measurement of angles by a 2 ft. rule 158 59 Tables of nails and spikes 160 60 " ' wrought " 160 61 " " Manilla rope 160 62 " " well digging , 161 63 Capacity of cisterns for each 10 inches of depth 161 64 " " " in wine barrels 161 65 Lumber table joist 163 66 " boards 163 67 Decimals of a foot for each 1-32 inch 164 68 ." " an inch for each 1-64 inch 165 69 Square roots of 5th powers of numbers 166 70 lengths of circular arcs 167 71 Table of circles, areas and circmuf's, diameters in eights 169-171 72 " " " " " ' " tenths.... 172-171 73 " " " ' " " " "twelfths.. 178-184 74 Table of sq. and cu. roots 1 to 28, advancing by tenths 185 75 " " " " " " 1 to 1000 186-193 76 ' ' ' " " " 1000 to 10.000 194-197 77 ' ! Logarithms 198-200 78 " " Tangents and cotangents 148-149 INDEX TO FIGURES. FIG. 1 2 Section of lap-weld and butt-weld pipe " pipe couplings 14 20 3 Specials and pipe fittings 21 4 Section of a "telescope" well 27 5 Perforated pipe in well 28 6 Spill-box -52 7 Illustrating contraction on weirs 5;-i 8 Weir, and method of water measurement 54 9 Miners inch measurement 58 10 44 44 4. 59 11 Method of measuring the height of a stream 93 12 13 Rainfall and temperature map of Dakota 94 14 15 Slope diagram for reservoir banks Section of reservoir and bank 98 105 16 Form of gate in reservoir bank 108 17 Section of ditches Ill 18 " ditch 112 19 Pulsometer pump view 127 W 4; 44 <4 128 21 Simple form of level 130 ?,2 Leveling rods 131 23 Scales decimal and duodecimal 135 24 Measurements between inaccessible points 147 GENERAL INDEX. Aberdeen well .............. " sewer plant .............. 7>> Acre, size of circular ........... 157 4 foot .......................... 60 " defined .............. 51 61 " Hills on an- ............... 157 * A Size of one ................ 1 56 Acreage, to compute ........ 156 157 Angle. Complement and supple- ment of an ................... 152 Angles. Measurement of by a 2 ft. rule ........................ 15S Apparent level ................... 135 Apples in bin ..................... 162 Area of farms ............. 45 139 144 fields ................ 156 157 " Relative of pipes .... ....... 23 Arizona. Irrigation statistics of. 137 Artesian wells elewhere .......... 37 " in Dakota ....... 3s 41 B Barrel. Contents of a ......... 162 " Weight of a of water ..... 63 Board measure tables ........... 163 Brick ............................ 162 Butt welded pipe ................. 14 C Casing pipe. Prices and Sizes of. 20 Cast iron pipe. Sizes and weights of ............................. 23 Center of pressure . , .............. 42 Characters . Explanation of ... 203 Chimneys ...................... 162 Circles. Elements of ...... 152 153 " Explanation of tables of .168 " Tables of diam's in Sths, ............. . ...... 169 to 171 " Tables of diam's in lOths .................. .. 172 to 177 " Tables of diam's in 12ths .. ........................ 178 to 184 Circular arcs. Table of- ...... 167 Cisterns. Capacity of for each 10 inches ............... 161 '' Capacity of in wine barrels ......................... 161 Conclusion ....................... 204 Contents of pipes ................. 66 Corn and hogs ................... 154 *' in bin ........................ 162 Cost of ditching ................. 117 <; - wells. r . ................. 34 36 Couplings. Kinds of ........... 18 ' Tablesof .............. 22 Cubic ft. on one acre .............. 61 ' ' different areas ....... 84 " in pipes .................. 66 " '* reservoir ............. 105 " per sec. reduced to gals.. 60 '' reduced to Miners inches. 59 " ' gallons ........ 87 " thrown in 1 and 3 months.88 foot is equal to ............. 151 Cubes, squares and roots ____ l v :> 197 Dakota wells :;>> " Table of 39 Datum plane 129 Day. Astronomical 154 Siderial 154 ' Mean Solar 154 Decimals of a foot for each 1-32 inch 164 " an inch for each 1-61.165 Diameter. To find -to discharge given volume I'l Digging wells 160 Discharge from pipes 69 70 To find volume of of pipes 72 Discharging power of pipes. Rel- ative ... 67 Ditches 110 to 120 Area of section 112 113 " Contents of excavations of .119 Ditching machines for .. Ill 117 US Embankments and foot- ing of - UN " Excavation and cost of. 117 44 Flow of water in 113 " Form and size of 110 " Gates in 119 " Grades of 1 15 116 Location of- 120 *' Laying out 117 Length of wet perimeter of 112 " Maximum velocity of water in 114 " Mean velocity of water in 114 Small lateral Ill " Slopes of 113 " Table of areas of 113 " " grades of 116 44 Widths of Ill Division and measurement of water 49 Divisors for water 51 Drilling. Suggestions as to 33 Drive pipe 15 Duty of water 43 to 4;* " '* "' in Colorado 46 " " ' Dakota 47 " '" " " table 48 Embankments and footings. . . .11 s * Entry head 69 Excavation. Cost of 117 Excavations. Contents of 119 Extra and xx strong pipes 15 Evaporation and filtration 103 Farmer. The 8 Farms. Size of 45 137 1 42 Feet. Cubic see cubic feet " Second reduced to gallons. 60 D General Index Continued. Fields. Area of 156 157 " Laying out 120 Filtration from reservoirs 103 Flow of wells per day and per minute 83 Flumes 120 to 122 Formula for weir measurements.. 57 Foot. Acre denned 51 Cubic see cubic feet Decimals of a 164 4 ' Second denned 60 51 Footings for banks 118 Francis' formula for weirs 57 Friction head defined 67 70 " loss in pipes 68 to 72 Frosts in Dakota 92 Gage groupe of wells in Cal.. 3S i:{6 Gallons=to ...................... 151 in pipes .................. 66 ' reservoirs .......... 105 on different areas ....... 84 " one acre. . . ........... 61 per minute defined ...... 51 " day = to given gallons per minute ____ ...... 83 " per minute to given gal- lons per day .............. 83 reduced to cubic feet ____ 87 " <; second " ---- 60 thrown in different per- iods of time by wells of different volumes per min- ute ..................... ...86 ' thrown in 1 and 3 months . .88 " by jets ......... 89 Gates ............... ..... 41 107 119 Gauges. Water ............... 65 Wire ................. 25 Grades of ditches ............ 115 116 " Table of ................ 116 Grain in bin ...................... 162 162 69 69 69 69 Hay Head defined 44 Entry ' Friction " Velocity ' To find 72 Height of a stream. To meas- ure 93 Hills on an acre 1 57 Hitchcock mill 81 Hogs and corn . 154 Horse power defind 82 Horse power of water. To find the 80 | Hydrants 29 j Hydraulic mean depth 112 ! " radius 112 I ram 124 | Idaho. Irrigation statistics of 137 < Illustrations, see index to Figures page R . . I Inch, Decimals of an for each 1-64 165 Miner's 51 58 59 ' in California 59 60 " " Colorado 59 60 ' measurements 59 " reduced to gallons and cubic feet 58 " Statute defined 51 Irrigation. Early history of .6 76 in Dakota 7 statistics from census reports .137 J Jets. Discharge in gallons from . 89 " Distances reached by 73 ' To find altitude reached by 73 ' " " discharge of 73 K Kalameinpipe 23 Lap-welded pipe 14 Land. Value of 137139141 Lath 162 Level. The-- 129 " measurements. 135 " rod 131 ' Simple form of 130 " True and apparent 135 Leveling explained 132 " for a reservoir 133 134 " Form of note book 132 Location of ditches 120 "well 31 Log of well 31 32 Logarithms. Explanation as to table of- 201 " Table of 199200 Use of- 202 " " tables of . ..201 Longitude, length of degree 164 Lumber 162 " tables 163 M Machines. Cable 12 Ditching ....111 117 118 Hydraulic- 13 Jetting- 13 Kinds of- 11 " Pole- 11 Mean depth 112 " radius 112 Measure. To the height of a stream 93 Measurement of angles by a rule.158 " and division of water 49 of water by a weir. .53 Units of of water ... 51 Measures and weights 150 to 153 Melville law, 8 31 Mensuration 150 to 153 Mill sites 79 Mills at Hitchcock 77 78 81 E General Index Continued. Mill* at Springfield M " Woonsocket 7S si 41 " Yankton s l 11 mnbywella 77 TS si Miner's inch 31 :>s "inCal. andCol 5960 '' reduced to gals and cuft 58 Miner's inch measurements 59 Miscellaneous information 162 Module defined 31 Montana. Irrig'n statistics of 137 Mortar 162 Multipliers. Useful 153 N Nails. Tables of and spikes.. .160 Nettleton. Letter from Col. E. S..75 Nevada. Irrigation statistics of. 137 New era grader and ditcher 117 New Mexico. Irrigation statistics of- 137 Outlets and gates 41 107 Perforated pipe 2s Perimeter. Wet 112 113 Photographs of wells 143 146 Description for .. .144 List of and pho- tographers 146 Photographs. Where to buy. . 146 Pipe 14 to 28 ' Butt welded 14 ' Casing . prices and sizes. . .20 " Cast-iron 23 " Contents of 66 " Drive 15 '' Friction loss in >-S to 72 1 Kalamein 22 Lap-welded 1415 ' lines. Advantage of 123 ' for distribution... 122 123 Perforated 28 Prices. Comparative of .IS Prices of standard 17 Relative areas of 23 u discharging powers of 67 Spiral riveted 24 welded- 27 Standard- 16 Vertical opening to 30 ' weight of Comparative ..21 ' Weight of water in 62 ' x and xx 15 ' Prices and sizes of 19 Polygons 153 Power. Horse 82 of wells 77 to 82,204 ' To calcula te horse 80 Precipitation. Distribution of 44 in Colorado 44 " Dakota 91,92 ' " in April and May 44 Precipitation map of Dakota 94 Pressure and volume. Relation between 9 in 900 feet of pipe 65 " of wa ter, table 64 Static 9 To find of water 64 Prismoiclal formula 157 Pumps 125tol28 " Cost and duty of. . . .125 126 " Pulsometer 126 to 128 Rain making 26 " in Colorado 44 " " Dakota 4491 92 Ram. Hydraulic 124 Reaming 14 Relative areas of pipes 23 " discharging capacity of pipes 67 Relative weight of pipes 21 -Reservoirs .96 to 10$ 44 Areas, Diams, Circumfs of- 102 " Areas, Diam's, Circumfs and cubic capacity of banks of t . t 104 44 areas and capacities at different depths 105 " Banks of - 99 100 101 104 117 119 44 " Diagrams of 100 Sections of ..101 Washing of ..100 44 Capacity of at different depths 105 " Circumferences of ... 102 to 105 Cost of 106 117 " grading of banks of 117 Diameter? of .102 to 105 Evaporation from . . 103 Filtration " ....103 Flow - ....107 " Form of 97 Footings for bank of 119 Laying out ...9* 133 134 Location of 97 Outlets and gates from 41 107 108 Sections of banks of 101 41 Size of.. .97 102 104 105 " ' To calculate -.10:5 Slopes of banks of. .100 " Sub and storage ditches. 10S ' Washing of banks of . . . 100 Rod. Leveling 131 Rope. Manilla 160 Roots. Explanation as to tables of- 198 44 Sq & cube 1 to 28 by lOths 185 " " ' 1 to 1000.. 186 to 193 '.' 4i 1000 to 10000.194 to 197 I " To figure by logarithms.200 202 F General Index -Continued. Scales, decimal and dnodecimal.135 Second foot ............... 51.00 11 reduced to gallons.. .60 Sewer plant at Aberdeen.. . . 7^ Shingles ......................... 102 Size of farms, ................. 137.1-12 ' " pipe, see Pipe ............ .. " ik reservoirs, see Reservoirs . . Source and sni)j)ly of water ..... 74 Specials .......... ' .............. 29. 30 Illustrations of . ...21 Setting of 99 30 Spikes and nails ... '. '. V 160 Spillbox ........................ r,2 Spiral riveted ])ipe ........ 24 " welded *' 27 sprmgfieid mill. ..:::::::::::::::. si Square and cube roots .... 185 to 197 " roots of 5th powers .... 61 166 Squares ................... 150 to 1"2 and cubes ....... 185 to 193 Static pressure ................ 9, bo Statistics of irrig'n in 7 states.: 137 Statute inch ..................... ol Stonewall... .................... C2 Storage ditches ................. 108 Stream. To measure height of a-93 mbject, Ihe- .................. 6 Sub-rervoirs ................... ..108 hu b~surtace waters .............. 125 Suggestions as to drilling ........ 33 Supply of water .................. 74 T Tables -See index to tables page A Tangents and cotangents. .147 to 149 Telescope weU. . . .27 Temperature in Dakota ....... i 2 94 Theoretical velocity of water ____ 70 Threads of pipe .............. 18 Time Table of 154 " 'required for 'different ."sized' welfs to tlm.w given volumes of water ...... ..... S4 - Volumes thrown in differ- enf periods of by wells of given volumes per minute. S(> Ton. Weight of one-of water... .03 Tools. 14 Triangles'.'.'.''.'.'.'. '.' .'.'.'i"2 True and apparent level ........ 135 U Units of water measurement ..... 51 Useful multipliers .... . 153 Utah. Irrigation statistics of 137 Value of land ........... 139 to 141 "water ............. 136 to 139 Valves ............................ 29 V egeta tion and wa ter ........... 76 Velocity head ................... 09 Maximum surface in streams ................ 114 Velocity Menu of streams ....... Hi of sound in air ........... 90 -water ....... 90 rjieoretical ........... 70 of wind. . . ............ 90 '' m Dakota ....... 91 . '' ^S 8 ' To get the ~ ' ' 82 V olume of wells....... ... 50 ) )( ' r ( r tay * P er . mm ? " ! n ] &? months. ..88 - ' in diftprent pen- ^ . ...... of wells m different per- iotls of time ......... difterent areas ........ 84 Relation between and pressure. ..... 910 To compute discharged bv P^ 08 .............. 72 W Wages. Table of- ...... ..... 155 Water 4 to 76 u an d vegetation.'..'.''.'.'.".. ...76 u Annual cost of- ............ 138 < ("enter of pressure of- ...... 42 * Densitv of 63 Distribution of ' -.' .'..'. m to'm M by ditches. 110 to 120 " flumes. .123 to 122 "pipes 1 '>2 to 1 23 r . im _ ' 124 - . " pumps" &" wind mills ............. 124 tol2S ' Division and measurement 4 T 7' ' V ............... 'V; ' i < Duty of-. . . . 43 to 48 .. '', ~ k 1 1 or f lcl - '^'3 ., -Refereences to-4o Evaporation of ......... 103 g lo ^. of ~T t ? itc1 ^' 11 l t ? l l* riCt , 101 ; f ~ m P1P S ' ' M tO ^ Head of- ..... .............. 69 4 Horse power of- ........... 80 , Vi r Maximum surface velocity ^ , ^Velocity of-V '. ^ .T.m Measurement and division "' on one acre, vol. and weiglit.61 " different areas ......... .84 Phreatic ................ 125 ' Figure of - ............ 4264 (enter of ......... 42 4< to find- ............ 64 ' Properties of- ............. 42 ' Seepage of ................ 46 " Source and supply of ...... 74 " Sub-surface .............. 1 25 " Units of measurement of . 51 " Value of ........... 186 to 139 " Velocity of- ............... 114 General Index -Concluded. Water Volume of^-in pipes. ... ''> ' Wells Location of - ............... 31 --on 1 acre ........ lii ' Log of .................. 3132 on dinVn-nt " Number in Dakota ............ '.' arras .................. M " Photographs of ... 145 to 148 " Weight of- .................. W Whore to buy 14* 'in pipes ........ i-J Power of .......... ."> & 67 to 82 ' on an acre ...... <1 k Source A: supply of Wilted of. 74 u bbl., gaL, qt., pt, Telescope .................. 27 ic of" ..................... 63 : ' used for mill power ____ 77 to Nl Weather in Dakota table ....... 2 " Velocity of How of. .. ........ (M Weight of cuft of substances 159 ; " " ' ; ' To got. .82 different pipes. 16 to 24 j " Volume of not dependent i- water ........ 01 to 65 upon sizo .................. V Weights and measures. . . . 150 to 1T),3 ' Volume of per day and per Weir ............................ 51 minute ..................... s: ; ' Application of- table. .. 55 '* Volume of in 1 221 Harper & Brothers 240 Irrigation Age 239 Leffel, James, Co 229 Ludlow Valve Manfg ( 'o 224 National Tube Works Co., Front Cover and 1 Nye Steam Vacuum Pump Co... 247 Oil W r ell Supply Co 227 Pech Manfg. Co 223 Peltori Water Wheel Co 2?6 Pulsometor Pump Co 127 1* 244 Railway Chicago A: North \Vestern . 230 231 Railway Chicago, Milwaukee k St. Paul 232 233 Railway -Great Northern 235 Northern Pacific 286 Reading Iron Co. (Back Cover) Rife's Hydraulic Engine Co. . 214 Robinson & Cary Co 242 S wa n Broth ors 243 " A- Stacey ( W . E. Swan Co.) .228 Trautwine, J. C . . 215 Valley Land Jt Irrigation Co 250 Western Wlieeled Scraper Co.. .246 Williams Brothers 207 Well Machine A: Tool Co 212 Young A: Son '.'40 '241 See Index to articles advertised on next page. H INDEX TO ARTICLES ADVERTISED. Banks* First National, Huron, S. D. . . .250 Boilers. Oil Well Supply Co 227 Robinson & Cary Co 242 Books, This book, W. P. Butler 2 41 Engineering, J. C. Trautwine. ..215 Irrigation, Irrigation Age 209 Harper's Periodicals 249 Cameras. Blair Camera Co . . .222 Coffee Mills and Dynamos. Belknap Motor Co 237 Civil Engineer. W.P.Butler 2 Driller*. Swan Brothers 243 Swan & Stacy 228 Electrical Supplies. Belknap Motor Co 237 Engineering Publications. Engineering Magazine 234 News 208 J. C. Trautwine 215 Hydraulic Rom. Rife's Hydraulic Engine Co 214 Hydrants. See Valves Irrigation ('oinpnies. Consoldated Land fc Irrigation Co ." 251 Dakota Irrigation Co 245 Valley Land & Irrigation Co 250 Levels. Buff // /trilling. American Well Works 252 Austin, F. C., Mfg. Co 218 219 Brass & Iron Works ( V> 225 OH Well Supply Co 227 Pech Manfg. Co 228 W T ell Machine & Tool Co 212 Williams Brothers 207 Machines Roa < 1 . F. C. Austin Mfg. Co 218 219 Western Wheeled Scraper Co. ..246 Motors Electric <1 \ \ ' ter. Belknap Motor Co 237 Chicago Water Motor Co ..211 Jas. LeffelCo 229 Pel ton Water Wheel Co 226 Pipe Cast Jron. Addyston Pipe & Steel Co. ..... .216 Dennis Long & Co 217 Robinson & Cary Co 242 Pipe Wrought Iron. American Well Works 252 J. B. Clow & Son 206 G. \V. Crane & Co 213 National Tube Works Co., Front Cover and 1 Oil Well Supply Co 227 Reading Iron Co., Back Cover Robinson }} Mticln'neri/. See Machines well drilling \\'im? Mills. Pech Manfg. Co 223 PREFACE. The idea in presenting this little book to the public is to supply, in part, a demand for such tabulated and general in- formation as is needed by many, at the present time, who are becoming interested in the matter of irrigation. Few have access to books of tables and rules and fewer still are able, without them, to figure out the problems involved, and bence, many abandon the subject because unable to culti- vate an interest sufficiently satisfactory to themselves to warrant the taking of some definite step in the direction of a practical trial of that which, if properly managed, must open up the road to fortune to all who choose to enter. The idea is not to present an exhaustive treatise on irriga- tion, or to treat at length any of the matters presented, but simply to suggest them and, by giving many rules and tables, to supply the information needed, so that each may, for himself, make such estimates as the circumstances of his own case may require; and further, to put the investigator in the way of obtaining such desired information as cir- cumstances would not permit of being given here. In the selection of many rules and tables the following standard works have been freely consulted and properly credited : Haswell's Engineer's Pocket Book, (Harper i aad gpeaaqx ^^R 5 joaaqum* NMMMM " HMM .. a aad ?qSia^ Itmiraox | O id O 1-1 H d N ro in t> C3\ o' M" -nco* 0* It "jooj oiqno . o,^^S^JJ5 ) 8 < S,8.S^ < 8&5r Jj:9 uoo adi j jo mSaa^ N H* 05 0^ c c ** c/i rZZ, ^ ddddOHcJw -4-vd O\ N in CN "* 't- moo' ro 6 co tA i to 32 er proved fc w "eaJV | N H vo CO ro t^ t^-^-i-i T}-rOiNVOOO in v-ico f^ C\ O CN I s * ON roco si S S 0000 ^^M h? 2" % SlVO 1 ^. ON H? O fl Q bs aad adij jo q}8ua r j 1 cj, t^. in ^- ro N (N ON * N -4- in o\ N "Sco* M -4- tx M 1* 1-1 d d dodo d d o* d d d d o* d d d d d o* d d gallon of ) 300 Ihs. ;no reruov x 5 i! apis' ^ d O O O w w H ci cJ ro co ^- -4- in\o ti t^. o\ O N 11 apisnf XS3S ** X X X * .s ^ IT TABLE NO. 2. READING TROX COMPANY. ^STANDARD. WROUGHT IRON LAP-WELDED PIPE, FOR STEAM, GAS, AND WATER. MANUFACTURERS' PRICE LIST. REVISED AND ADOPTED SEPT. 18, 1889. To take the place of all previous lists and subject to change without notice. Nominal Inside Diameter. Price Price Nominal per Foot, per Foot, Weight Plain. Galvan'z'd per Foot. Thickness. No. of Thread pet- inch of screw. Inches. '# $ c. $ c. Pounds. .23 .26 2.68 Inches. H5 "X 2 30 -34 3-i .154 H/z */2 47 i -53 5-74 .204 8 3 .62 .68 7.54 .217 8 3$? OD cS II| ~ ^L ^S d * eS | a -i ||. 3 S 'E .12 .17 .21 .26 .30 36 .28 4 .39 4U .40 r> .44 .56 .72 .90 1 30 "".76"' 7 s 1.20 9 10 1 55 1.95 2.53 12 2.30 This table is arranged so as to show comparative prices of different grades of pipe. The prices for standard pipe being the net prices resulting from the discount and list prices given in table 2, for plain pipe. The prices here given will fully answer the purpose of es- timate. Exact prices can only be Lad by correspondence with the manufacturers, who will quote the latest lists and discounts. That feature of the pipe which is of the greatest eonsern to the well driller is the thread and it is chiefly on account of the thread that heavier pipe is needed. If the pipe is thin and light so much of the body of the metal is cut away in the operation of threading as to leave a thin shell not suffi- ciently strong to withstand the driving blows without dan- ger of stripping the thread. If the pipe is heavy the body of metal back of ^he threads is stronger and the pipe therefore more able to withstand heavy work. COUPLINGS. (See table No. 7.) The common form of coupling is straight threaded, that is, the line of the threads is parallel to the outer surface of the coupling. An improved form gives greater strength to both pipe and coupling and distributes the strain more even- ly over the line of the thread. This is known as the patent TAPEH COUPLING. From the illustrations of this form of coupling, shown in connection with the advertisements on the front and back covers and by Fig. 2 on page 20.. it will be seen that the inner face, or threaded surface of the coupling, has the form of a funnel to fit a corresponding conical taper on the pipe. In drive-pipe the ends of the pipe meet at the middle of the coupling. 19 TABLK NO. 4. READING 1RO\ T X STRONG AND XX STRONG WROUGHT IRON LAP-WELDED PIPE. X STRONG. Actual Nominal Nominal Size. rnce per Foot. Outside Inside Diameter. Diameter. Thickness. Weight per Foot. Inches. $ c. Inches. Inches. Inches. Pounds. 11 A .46 I.9O 1494 .203 3-63 2 .60 2-375 1-933 .221 5.02 2 X 94 2.875 2315 .280 7-67 3 1.24 3-5 2.892 .304 10.25 1.48 4.00 3-358 .321 12.47 4 1.76 4-5 3.818 .341 14-97 4^ 2.12 5- 4-25 -35 J 7-6o 5 2.56 5.563 4.813 .375 20-54 6 3-30 6.625 ! 5.750 437 28.58 7 4-20 7.625 6.62 .50 37 60 8 5-50 8.625 7.50 .56 47.85 XX STRONG. Actual Nominal Nominal Size. Price per Foot. Outside Diameter. Inside Diameter. Thickness. Weight per Foot. Inches. $ c. Inches. Inches. Inches. Pounds. 11 A .92 1.90 1.088 .406 6.40 2 1. 2O 2.375 I.49I .442 9.O2 2 l /2 1.88 2.875 1-755 .560 13.68 3 2.48 3-50 2.284 - .608 18.56 2.96 4.OO 2.716 .642 2275 4 4-50 3136 .682 2748 4^ 4.24 5- 3-56 .72 32.45 5 5.12 5-563 4.063 75 38.12 6 6.60 6.625 4.875 .875 53" 7 8.40 7.625 5.98 .82 60.34 8 11.00 8625 6.88 -87 71-52 Discount about 62 J^ per cent. Xot the most recent quotation. 20 TABLE NO 5. CASING, NET PRICES. Nominal Actual Nominal No. Threads Inside Price Outside Weight Per Inch Diameter. Per Foot. Diameter. Per Foot. of Screw. 3* 20 3i 4.27 14 3* 21 3f 4.6o 14 3? 24 4 5-47 14 4 25 4i 5-85 H 4T 27 4^ 6.00 H 4i 35 4! 9.00 H 4f 3 4 6. 50 14 4f 36 4^ 9.00 14 4 33 5 7-58 14 5 35 Si 8.00 J 4 5 41 Si 1000 14 5 48 si 13.00 iij 5^ 58 si 17.00 u| 5 16 39 si 8.50 H" Sfe 50 5l 13.00 n| 5f 45 6 10.00 14 51 5 6 12.00 n| 5l 55 6 I4.OO n| 1 59 64 6J 11.15 13.00 H" H 65 74 6f 17.00 III 6f 68 7 !3oo 14 6 f 78 7 17.00 ii| 83 8 I5.OO Il| 7l 95 20.00 Il| 84 95 8^ 16.15 III 8 1.05 8f 20.00 Il| i 15 8f 24.00 n| 8| . 1. 00 9 18.00 ni 9l 1.25 10 21.00 H^ 10 inch Light Pipe for Well Purposes .............................. Net, 1.50 As made by the Oil Well Supply Co., Pittsburg, Fig. 2 shows sections of pipe joints and the ferred to on P. 18. Fig. 2. , Penn. See advertisement patent taper coupling re- PATENT FLUSH JOINT. SLEEVE COUPLING. INSERTED JOINT. 21 EXPLANATION OF FH;. 3. A. Alain pipe of well. B. Gate valve. C. Hand wheel to valve. Cms*, the openings of which may all be of one size or may all be differ- ent. State sizes desired. Plugs, for closing dead openings. The tops may vary as shown. K. Bushing, for reducing size of openings. Nipples, for connecting specials, being short piece of pipe threaded part way or all the way and being of any length desired. Curved tee, just the form for top of pipe. Especial- for top of pipe. Especial- ly where well is used for power. I. Plug, plugged for gauge. J. Pressure gauge. L. Reducer. L. Elbow, can be had to any angle. M. Double elbow. N. Straight tee, can be had of any form or rize. O. Reducing tee. can be had of any form or size. Fig. 3. Specials and fittings for pipe TABLE TABLE OF COMPARATIVE WEIGHTS IRON (See page 21 . i NO. 6. OF DIFFERENT KIXUS OF WROUGHT PIPE. Size of pipe. Casing pipe. Standard j X. pipe. (Strong p ' Drive pipe. 2 2.23! 3.61J 3. 63 3 3.95 5.74 7. 67 3^ 4.27 7.54 10. 25 Drive mue is of standard 4 5.33 9.00 12. 47 weight and size but more expen- 4^ 5 6.00 7.25 10.66 12.34 14. 17. cj~ sive, stronger and better on ac- X,-. count of its being made of a bet- ter quality of iron. Then, too. 5M 7.66 the threads are cut longer to fit a 5J 6 ?>% 8.08 9.35 10.06 14.50 20. 54 longer and stronger coupling (see table 7) and of sufficient length to permit the ends of the pipe to butt together when coupled i8. 76 28. 58 12 45 this it not the case in standard f 13.50 15.10 23.27 37. 60 pipe thus very greatly adding to the strength of the pipe in the operation of heavy driving, the *% 9 16.15 17.25 28.18 47. Sg pipe being practically continous and not separated at each joint. 9% 33 70 ture of drive pipe 10 20 00 10% 40.06 Size outside diameter, weights pounds per foot. 2*2 TABLE NO. ". Dimensions of Wrought Iron Couplings. FOR STANDARD PIPE. Inside diam. of the pipe. 2 2 1 2 3U 4 11 ^ -j 1) 7 N 9 10 Outside dia . of coupling. 2 7 8; 3 a H 7 4 W 5A >i,\ 8*4 ^l 7 ,; 8 2 9 V lOH" UH Length of coupling. 2&j 3} a 3ft 3 5 S : 3?- 8 :; , i i 6ft 6ft FOR LINE PIPE, DRIVE PIPE AND TUBTM;. Inside diam. of pipe. Outside dia. of coupling. 23?, 3^ 4j g 4B ^!s : :, 615 Length of coupling. 6ft FOR CASING PIPE. Inside diam. of casing. 4 Ouiside dia . of coupling. 2 3 . Length of coupling. | 3 T ] 5 TABLE NO. 8. Dimensions, &c. of Special, Lap- Welded, KALAMEIN PIPE, for water and gas works, As made by the National Tube Works Co., Chicago. Outside diam . Weight of lock joint. Wf.io-hfr*f i Nominal le^e.X^ Aproximato price per foot. Inches. Pounds . 1 Pounds. Pounds. $ Cts. 2 4 1 1.80 .17 3 8 1% 3.35 .30 4 12 2^ 5.00 .42 5 17 3% " 15 .55 6 21 5 8.60 .67 7 30 6 11.25 .87 8 33 6^ 12.80 1.00 9 38 1U 15.10 1.25 10 40 8" 16.60 1.45 11 50 10^ 20. H5 1.70 12 56 11% 24.50 1.87 13 65 12K' 27.60 2.2^ 14 71 13M 30.00 2.50 15 100 15% 36.40 2.80 16 120 17 46.25 3.30 TABLE XO 1). TABLE SHOWING RELATIVE AREAS OK STANDARD PI ri:. Size .f =; Pipe. 1 1', - -'* :5 :{ '-: I 28.10 16.00 7.11 4.00 2.56 1.77 1.30 1.00 44.4 25.00 11.10 6.25 4.00 2.77 2.04 1.56 1.00 6 87.10 49.00 21.70 12.25 7 M 5.44 4.U; 3.08 1.96 1.81 1.00 > 113.70 64.00 28.40 16.00 10.21 7.11 4 '.00 2.56 1.77 1.30 1.00 ! ! 1.011 1 V- " :^ H'.> 1.774.00 1.00 2.25 ... UK) 7.11 11.10 16.0021.70 4.IM) 6.25 9.00 12.20 1.77 2.77 4.00 5.44 i.oo i.56 2.25 3. .... 1.00, 1.44 1.96 .... 1.00 l.Sl i 1.00 64.00 36.00 16.00 9.00 5.76 4.00 2 93 2.25 1.44 1.00 r> - s .... ! i 1 i From Win. J. Baldwin, M. E. in "Steam Heating for Buildings." Explanation of table: The relative areas of any two sizes of pipes given in the table will be found at the inter- section of the horizontal and vertical lines representing the given sizes. Thus, a 6-inch pipe 1.00 6-inch pipe, 1.44 5- inch pipes and 4 3-inch pipes; an 8-inch pipe 4 4-inch pipes, 16 2- inch pipes, 113.7 %-inch pipes, etc. Application It is desired to supply 50 three quarter inch pipes with a constant flow, what size of supply pipe should be used ? Take top horizontal line and run to the right, it will be seen that a 5 inch main will supply but 44.4 % inch pipes; but a 6 inch main will supply 64.00 % inch pipes, hence, a 6 inch pipe must be used. An 8 inch well is as large as 7.11 three inch wells, a 7 inch well as large as 3.06 .... 4 inch wells. As to Relative Dircharging Powers of Pipes, see Table No. 27. TABLE NO. 10. WEIGHT OF STANDARD CAST IRON PIPE. (Including Bowl and Spigot ends.) ( 'ast iron weighs 450 Ibs. per cubic ft. and .26041bs. per cubic inch. Diam. of Pipe. Weight per foot for following thicknesses. Length Feet. H H % '/2 % % % 1 . 2 3 4 5 6 8 10 12 3 4 5 6.5 8 10 14 15 6 9 11 13.5 16.5 21.5 27. 32 9.3 13 17 21 25. 32.5 40.5 48 14 18 23.5 29 34 44 55 65 19 23 30 36 43 56 69 82 29 37 45 53 68 84 100 44 53 63 81 99 117 52 62 73 93 114 135 8 12 12 12 12 12 12 12 As made by Addyston Pipe & Steel Co. (See adv't P. 216.) This table incudes all of the sizes and weights likely to find a place in water and gas works plants in Dakota, where the use of cast iron for water works is on the increase. * (See also the advertisement of Dennis Long & Co. P. 217.) 24 TABLE NO. 11. DIMENSIONS, PRICE, ETC., OF SPIRAL RIVETED PIPE. No. 18 Wire Guage. Thickness .049 inch. Diam. in inches. Price per ft. Black. Price, tar- red and asphalted. Price per ft. Galvan- ized. Approx. weight per 100 feet. Approx. bursting pressure NET. NET. NET. Ibs. Ibs per sq in. 3 !8 .17 8 .19 & 23 185 1300 4 .21 .23 .29 245 1000 5 .25 .28 .35 300 800 6 .29 .32 .43 360 700 7 .32 .35 .45 400 600 8 .37 .40 .52 460 500 9 .41 .45 .59 525 450 10 .45 .50 .65 575 400 11 .48 .53 .70 625 360 12 .58 .64 .82 750 330 13 .62 .69 .90 800 300 14 .67 .75 .98 900 280 15 .75 .83 1.05 950 260 16 .80 .88 1.13 1000 250 18 .88 .96 1.28 1125 220 20 1.00 1.10 1.45 1250 200 22 1.10 1.21 1.55 1350 180 24 1.20 1.32 1.67 1460 160 In lengths of 25 feet and less, with plain or crimped ends. As made by Abendroth & Root Mfg, Co. (See adv't P. 238.) The weights given are for the black pipe, other grades are from 10 to 20 per cent, heavier. This class of pipe is very extensively used in the west for conveying irrigation waters, and in many places for water works use. Its strength is very great while the weight is very light, and the cost low. On account of its strength, lightness and cheapness it will be especially adapted to use in Dakota, where water must be piped on or near the sur- face. The following table will show the comparative weight of the three classes of pipes Spiral, Standard wrought iron and Cast iron: WEIGHTS. Heaviest Spiral Standard Wrought Cast Iron Pipe. Iron Pipe. Pipe, % inch 4 * 6 ' 8 10 12 14 16 18 20 24 ...-2V 2 10^ " 17 18% ' 25 ....8 . ..10 ...13 ...15 ...18 ...20 )2 .'..'24 ...26 28 32 40 ' .. 40 49 < 48 58 c 56 64 ...72 79 ...95 " Pipes of this class in California have been in use since 1853 and hav given great satisfaction, many having done useful service for 25 and 3 years. 25 TABLE NO. 12 READING IRON COMPANY. "III "f w ^K H oo LJJ ^*J O D < ^.S^' C 3 'o if^yHisssssssHsf :: : wS,^ LU c |i| ^ i ^&l 00 n ! c 1? ^ rOONON^-cO^- ON NNON-N OS fO^O o 1=1 hSoo^o^oooooooooooooooo z QJ Q Z < Number of gauge. 00 ON O ** N fO Tt" vovO l>00 ON O "^ N fO Tt" ^OvO ^ OO \HRlCAFv ||| JO * < tu 111 TT vn O O O ^ <^OO O fO O "">OO "^ O ON vo to N voOO O w {kg 00 m N (75 I'll 1 i ^ Q a < 111 JivO O^O NOO voN OOOvO ^W *+ O ONOO t^vO *o ir> ^f z <&% < H C^ o v 5 O9O-Nro^- ^>vO t-^oo ON O N ro rj- r>vo r^ I 6 26 Inadvertently the text for this page was overlooked but two suggestions may be here inserted with profit, no doubt, to some. The first suggestion is prompted by the abundant rain-fail of the early months of 1892 which has been far greater than that of any former year within the history of the state. Some are heard to say that "irrigation will now be overlook- ed." Such will not and should not be the case, for, al- though 1892 may be a year of great productiveness without irrigation, it will still however good it may be fall far short of accomplishing what irrigation would accomplish. Through any given series of years Dakota's rain-fall can- not be relied upon to be sufficient for remunerative farm- ing; so irrigation must be resorted to by all who desire cer- tainty of return for each season's labors. If all who can will, during this favorable season, prepare for the unfavor- able seasons which are sure to come, they will exercise wise forethought by hastening to improve the opportunity so fortunately offered of preparing in advance. This promis- ing season will no doubt aid many financially to in whole or in part prepare for irrigation in the future. It is said of an Arkansas farmer that he refused to mend his leaky roof during fair weather because it was not neces- sary, and during foul weather he couldn't because it was wet. It is hoped that our farmers will not emulate such un- thrift by refusing to prepare for irrigation during wet sea- sons, because it is then unnecessary, and being compelled to put it off during dry seasons because too poor. A second suggestion will be risked, although somewhat outside of the scope of this work. It is: Do not be deceived by so-called Rain Makers ! Do not fol- low so intangible a will-o-the-wisp as this latest "fake" with which scheming sharpers are attempting to delude the peo- ple. The U. 8. government spent several thousand dollars in a vain attempt to produce rain; an attempt which was an acknowleded failure, except that it awakened in the breasts of certain shapers an idea which they have enshrouded in mystery, and on the strength of which they seek to extort money from a too credulous public. Bain-making has not been a success as yet we hope it may be in the future. Water we have below us. We know it is there, and that we can get it. Seek it, therefore, and do not delay in the vain hope that the secret of rain-making has been vouchsaf- ed to men of whom the world has never heard, men un- known in the sphere of science, men whose investigations were never heard of and whose successes are but hearsay or newspaper reports, men who want pay in advance and will not exhibit the powers which they claim thus suddenly to have acquired to the light of scientific investigation; men who work in the dark and who seek their own interests and not yours. Some wit has wisely said that, as yet, "the har- ness-maker is the only successful rein maker." SPIRAL WELDED PIPE. This pipe is very similar to the spiral riveted pipe, the joint being welded instead of riveted. The weights are about the same as the weights of riveted pipe, but, by reason of the welded joint, the pipe is claimed to be stronger, more durable, smoother internally. Both possess the same great advantages of lightness and cheapness and are equally well adapted to use in irrigation whenever a light, durable and inexpensive pipe can be used. (See distribution of water, P. 122.) From the foregoing tables it will be possible to select a quality or kind of pipe suited to the needs of the well, the water-Works plant, or the conveyance of water over the surf ace for irrigation . More detailed information maybe had by correspondence with the manufacturers or dealers in pipe whose advertisements appear herein. The proper grade of pipe having been selected, the plan of the well must be decided upon, for it may be on several plans. A large outer casing may be first used and sunk as deep as thought desirable, then a smaller size sunk inside of the first, and, possibly, still a smaller size within the second pipe; the latter being carried to the bot- tom. The two outer pipes may then be pulled up, leaving a continuous pipe from top to bot- torn. In some cases, as where the outer casing has become fast and cannot be lifted, the outer pipe is left in the well thus making a double string of pipe. In other cases, all the outer casing is removed, but 2 or 3 lengths, the space between the two casings being then calked. In some wells the telescope plan is used, In this case the well may start with an 8 inch pipe carried down say 300 feet; then a 6 inch pipe is carried down say 400 feet lower, or to a depth of 700 feet, and, by the use of a left-handed thread at the 300 foot level, the upper 300 feet of the 6 inch pipe is removed, leaving the lower 400 feet in the well as permanent casing. In like manner a 4J^ inch pipe may be sunk within the six inch pipe and carried to water; the upper 700 feet being then removed. Such a well, in section, would have the appearance shown in Fig. 4. Most of the earlier wells were of this class and many are still drilled on this plan, but the practice now appears to tend more in the direc- tion of wells with a continuous line of pipe from top to bottom, and such wells no doubt have many marked advantages over wells of other classes. Fig. 4. torn of the well. PERFORATED PIPE. Nearly all of the northern wells throw out more or less shlae mud, clean sand, or lumps of sand-rock or iron pyrites. These hard bodies have, in city water systems, caused much trouble by clogging the fire nozzles or water pipes. To pre- vent the throwing out of such masses many wells have been filled with lengths of perforated pipe dropped to the bot- .~ * <-!, ,n ' lengths of pipe thus inserted are per- forated with J or % inch holes which, while admitting the water or sand, prevent the admission of the larger solid bodies. The conse- quence of thus shutting off free access to the well is that large quan- tities of loose rock accumulate about the base of the pipe, as shown in Fig. 5, thus gradually shutting off : the water supply and diminishing : the volume and efficiency of the well; besides which, the effective erea of the base of the well pipe is reduced by the insertion of this smaller pipe thereby still further decreasing the capacity of the well. Additional disadvantages of this Fi 5 inserted pipe lie in the fact that it Showing a perforated pipe is out of reach and control, it be- in the bottom of a well, comes a loose and independent feat- ure of the well, not under control or subject to needed re- pairs, and it is apt to become out of line with the main pipe if not entirely disconnected from it thus forming a pos- sible and unmanageable obstruction at the base of the well. If the perforated pipe is left out, the well, at the bottom, will be clean and free to receive whatever comes to it. If rock is thrown, care for it at the sruface where it may be collected and disposed of. Put in a settling reservoir to re- ceive it, or, in case of water works, where the pressure must stand in the pipes, run the water through a large sand drum which will collect the heavy matter and permit only the water and lighter sediment to pass to the mains. It is, indeed, safer to collect the rock at the surface, where it may be cared for, than to permit it to accumulate at the base of the pipe where it cannot be cared for and may ruin the well. If the well becomes stopped up by an accumulation of sand or by other causes the pipe may be more easily cleaned put if it has a uniform diameter from top to bottom and it is unobstructed by the presence of a section of loose perfor- ated pipe. Usualiy the services of a well driller will be needed to open up a well which has become clogged. The objections urged against the use of perforated pipe in wells are not founded on theory alone but upon actual experience 29 (A. ^ in a number of the more important Sy ells of the state. VALVES, HYDRANTS AND SPECIADS^See Fig 3 p 21) Every well should have at le ist one gate valve in order that it may be shut off in whole or in part, for otherwise no control could be exercised over the flow by the person in charge. The kind of valve to buy is a matter of importance, for all are not equally good, either as to pattern, workmanship, or material. Of the many makes of valves the Ludlow and the Chapman are among the best and are the most used in the Dakotas. (See adv't Chapman Valve Co., P, 210; of the Ludlow Valve Co. P. 224; of the National Tube Works Co. front cover; of the Brass & Iron Works Co. P. 225; and of Kobinson & Cary Co. P. 242.) The greatest care is necessary in the selection of a hydiant for water works service. Almost any hydrant will work well in clear water but few, however, will prove satisfactory in case sand or gravel is held in suspension by the water. A hydrant haying a rubber or leather face or cone will need frequent repairs, owing to pieces of sand or gravel becom- ing imbedded in the soft surface. These, too, tend to wear the surface of the metal ring, and thus leaks are caused and the hydrant frequently freezes and becomes unserviceable. Where there is much grit in the water a metal faced hy- drant should be selected. Where the water is clear the others will prove as good. A gate valve should, be handled carefully. Do not close it suddenly for the "Water Ham- mer," due to the sudden checking of the velocity of a rapid- ly moving column of water, under heavy pressure, is very great and tends to injure the pipe and its connections. The arrangement of the valve, or valves, will depend upon the circumstances surrounding the well and its uses. Usually the main valve is placed horizontally on the main pipe and all connections are made above the valve. In this position the valve is usually put on before the main flow of water is struck, the drilling being continued through the opened gate care being taken to protect the face plates of the valves by a thin nipple set into the top of the well. If the valve is not set until after the flow is struck much loss of time and money may result before it is finally set to the pipe against the force of the flow. (A notable instance of this was that of the first "city well," at Aberdeen, where it was found to be impossible to set the valve because of the force of the water, and hundreds of dollars were wasted, and special tools finally constructed, before the water was finally shut off and the valve set.) This danger may not be ever present, especially in the smaller wells, but reference to it will call attention to its consideration. Sometimes a cross is set first, on top of the pipe, before the flow is struck. It is then an easy mat- ter to set the gate to the top or the side opening, the stream finding a partial outlet, meanwhile, through the other open- 30 ing. After the gate is set the other openings may be plug- ged or otherwise connected. If the main gate or any gate valve is set on any line of horizontal pipe, leading from a well throwing any sand or solid matter, the valve should be set vertically, that is, with the hand-wheel at the top. This will prevent sand or stone lodging in the working parts of the valve; a danger which is ever present if the hand-wheel is at the side of, or under- neath, the pipe. Whatever may be the location of the valves, or the use to which the well may be put, one thing should be observed, which is, so arrange the specials (which is understood to mean the crosses, tees, valves and such similar features of the pipe fittings) as to leave a vertical opening above the main pipe, which opening may be closed by a plug if not otherwise connected. By so doing ready access to the well is always possible, for the purpose of cleaning out, blowing off, or other pur- pose, without disturbing the other connections of the well. If the well is to be used for power, in the running of a mill or other heavy plant, much power may be saved by using long curved specials instead of the short, right-angled specials commonly used. Every well driller ought to have, as a part of his outfit, a full set of specials (crosses, tees, ys, nipples, bushing, plugs, elbows and a pressure guage) so that, on the completion of a well, a sufficient test of its pow- er and volume could be made to be of value as a matter of public record and also as a matter of value to the driller himself, who would, through the wide publicity given to all such systematic tests, derive a direct benefit, in the way of advertising sufficient to pay him for the expense and time invested. The more such matters are observed the more will public attention be called to our artesian wells and the more quick- ly will capital be attracted. Properly viewed, it would be a wise stroke of business policy for every well owner and con- tractor to interest himself in these features of a well and to be prepared to put them to efficient tests. Even the well owner cannot afford to be without the few specials necessary to a proper control over his well, or to its direction in such manner as may best suit his varied needs. Supposing the well to be 6 inches, what ought to be provided? 1 6-inch cross. 1 6-inch tee. 1 6-inch elbow. 2 6-inch plugs (one plugged for attachment of gauge.) 2 6-inch nipples. 2 4-inch " 2 2-inch " 1 nest of bushing for 4-inch and 2-inch connections. 1 pressure gauge. With these few specials the well, or any connection with 31 it may be reduced or directed as occasion may require. At least these specials should be obtained. LOCATION OF WELL. As a rule, a well for irrigation will be located on or near the highest point of land to be irrigated, but considerations of convenience or economy may, at times, suggest a location at a lower point or near one's buildings from which location the water may be piped to the higher ground. The reservoir will usually occupy the highest ground and the well may be placed at the most accessible point near it or at such a point as will best conserve the proper division of the fields or the location of the ditches. All of these things should be considered and mapped out before either the well or the reservoir is located; otherwise the location may, in the end, prove to have been badly chosen. At whatever point the well is located let that point be OUTSIDE OF THE RESERVOIR, Some wells have been located within the reservoir where they are not accessible because of either water or mud, where, in case of needed re- pairs, it would be difficult to convey the machinery and sup- plies, or to erect or handle the same, where the well cannot conveniently be used for anything else but to supply irri- gation waters and where its flow could not be easily regu- lated during the winter months. If located outside of the reservoir the well would be ac- cessible at all times and subject to control; it could be easily repaired or opened up if stopped up; its volume could be first used as power to run machinery, a revenue, possibly, being derived from the rental of the power, and the water then conveyed to the reservoir by a short pipe. It could be enclosed and protected from the weather as every well should be in order to protect and preserve the pipe and valves from rust, for the well is but a piece of machinery and should be cared for as such. It will wear out in time by rust and wear and will need recasing, but in order to pre- serve it as long as possible, its pipes should be painted and protected. If thus cared for it will last intact for mapy years and pay for itself many times. The cost for repairs being almost nothing. LOG OF WELL. Section 35 of the "Melville" law provides that the con- tractor of any township well shall keep a log of the well, or, in other words, a record of the successive strata through which the drill passes. From the very nature of the case this must be a dead-letter, for it cannot be enforced. The driller may report such a log as he chooses, and no one else be the wiser. The truth is, it is safe to say, that no properly recorded log has ever been made of a Dakota well. The author has seen many wells drilled, and has carefully noted the methods adopted, but in only one case, within his knowledge, was there any effort made to obtain an accurate log. 32 Dozens of records have been published in papers pam- phlets and reports, but all are subject to grave doubt, as to truth or accuracy. Some drillers will make no report pre- fering to keep, as a trade secret, whatever they may have discovered but most drillers pay no attention to the drill- ings, and, except for the fact that at one depth the drilling is hard and slow, and at another depth it is softer and more rapid, they know little or nothing about the character of the formations in which they have worked. The keeping of a log involves considerable extra labor, systematic watchfulness, a certain degree of knowledge of geology, and, above all, a certain amount of expense to which the contracting driller does not care to go. He agrees to drill a well, and not to instruct in geology, and, to him, the drillings discharged are all the same. It must be admitted that a carefully kept log, or rather series of logs, would be of much value, but how to secure them is a question each driller alone can decide. Certainly section 35, above referred to, can result in nothing more than a succession of false reports which will be worse than none at all. When the first well in the state was drilled, (the Ry. well at Aberdeen) by Mr. Swan, the author was present daily and assisted in keeping the log, preserved sam- ples of the drillings, dried and arranged them, and finally mounted them in 3-foot glass tubes secured for the purpose. If equal care was used with each well the logs would then approach the truth and possess some value. Each owner of a well should look to it that this is done. Equally important yes, far more important is the keep- ing of an accurate record of the performance of each well, and as to all its dimensions, thus depth and log, and length of each size ot casing in well. Size at top or bottom, or all the way. Pressure When closed, and when flowing from openings of different sizes. Volume When open full and when throwing streams of different sizes ; not guessed at but carefully measured with a weir. Discharge Exact height of stream thrown vertically when well is opened full, and from openings of 1, 2, 3, 4. 6 or 8 inches. Also, the ex- act distance these streams will be thrown horizontally, Temperature of the water. Whether hard or soft, clear or sandy or muddy. The exact time occupied in drilling the well, with dates. The quality of pipe used. The kind of machine used in drilling. The exact cost. There is nothing in the above form of record that cannot be kept by any farmer or driller and nothing that is not of importance or that cannot be determined if only a few spec- ials are at hand. The measurements of volume and height of streams are simple operations and are fully explained herein. (See measurements by weirs.) See how to meas- ure the height of a stream, page 93.) 33 A series of records kept as above suggested would have value, but the records as heretofore kept have but little. Even the published, official records, or reports, are far from accurate. A record, once carefully made, ought to be pre- served for future reference, for the memory alone cannot be relied upon. DEILLING. Little need be said under this head for it is assumed that an expert will be in charge of the work. If an inexperi- enced hand is in charge he has more to learn than a book of this size would hold. A few suggestions, however, will be in order. Do every part of the work thoroughly and with the greatest care. Tjse great care in handling tools about the pipe so as not to drop them in. Make every joint of the rod or the tools fast so they will not loosen, and cause the loss of a rod or tool. Keep the drills and reamers in proper cutting order, and inspect everything frequently to see that nothing is loose or defective. Do not work the drilling tools too long before pulling out, for it is better to pull out more frequently, and make sure that everything is safe and sound, than to attempt to work longer and lose a tool by reason of a loose joint. Above all, do the reaming well, so that the pipe will settle easily and not stick or require heavy driving. Keep the pipe pretty clos>e to the bottom, in order to avoid the caving in of the walls or the inrush of quick sands and the possible sticking of the tools. Many drillers will run from 20 to 100 feet without settling the pipe, and they usually have trouble in consequence. Only room enough is needed below the pipe to work the drill and the reamer and usually the length of a single section of pipe will be ample. Do not sink a smaller hole below the main hole, for it may endanger the latter work by causing the drill to stick or drill a sloping hole into which the pipe cannot be forced. Never leave a tool standing in the well, for a cave-in may bury it and render its extrication difficult if not im- possible If any accident happens do not cease labor until it is reme- died or until its remedy is seen to be impossible. Arrange in advance for all supplies, in order that no delay may endanger the continuation of the work. A "shut down" often sets the work back more, and causes greater expense, than though no work had been done. Always leave the work in a safe condition and protected from the depredations of the curious and thoughtless on- lookers. Cautions might thus be indefinitely extended each found- ed on some costly experience of the past but enough has been suggested to show the necessity of an exercise of such 34 a degree of care and watchfulness as is required in but few other callings. If no accident happens the driller de- serves much praise. If one does happen he usually has himself to blame. COST OF WELLS. Many thoughtless enthusiasts have raised the cry that wells ought to be drilled for from $1,200 to $2,000 but such persons are not authorities and do not know whereof they speak. The cost of a well depends not upon one thing, but upon many things. The size is, of course, the chief factor for the pipe for a large well will cost more than that for a small well; the rig used must, as a rule, be heavier; the tools heavier; the coal and water used will be much more; and the labor bill will be much greater because the drilling will take longer. The location of the well will effect its cost. If within the limits of a town, having a system of water works so that the water used in drilling may be readily secured (and under pressure), the otherwise large water-hauling bill will be saved. If the well is on a farm, or where no water is at hand, the hauling bill will mount to most respectable proportions. Add to these items the cost of moving the rig to its site, setting it up and taking it down, hauling the pipe and fuel, to say nothing of the many certain yet unforseen incidental expenses and you have the well driller's bill of expense, minus the ever-present chance of an accident which may cost hundreds of dollars or result even in his financial ruin. No man of good business judgment will assume these risks for the mere chance of earning dav's wages. He claims, and is fairly entitled to receive, a generous compen- sation for the risk he assumes, and, in addition to that, such wages as his skill as a driller entitles him to receive. For the purpose of illustration the following approximate cost is given of a 6 inch farm well 1,000 feet deep: 1000 feet of 6 inch pipe @ .62 per foot $ 620 Frieght at reduced rates about 50 Hauling pipe to the ground ' " casing pipe away , " " and transporting rig " 50 Setting up rig " 150 Taking down rig, and breakage " 100 Fuel, and hauling same " Hauling or obtaining water ' 100 Wear and tear on rig and tools 200 One gate valve 30 Couplings " 40 Interest on investment for 90 days " 75 Labor bills @ $10 per day for 60 days 600 Total " $2,315 In this estimate it is assumed that but 60 days are con- sumed in the work of moving, setting up, drilling and taking 35 down; that there are no accidents or unusual expenses and no delays. The incidental expenses could not safely be figured at less than $300, and most of the other items given are figured too law; so that, without any allowance for incidentals, accidents or profit, and allowing but three men on the work, and but 60 days of time, the expense still exceeds $2300 for a 6-inch well. It is not the intention to throw any unfavorable light on the matter of cost of wells, but rather to throw on the true light, and, by calling attention to the details, dispel some false light. A well is worth all it costs, and the driller must have some show as well as the owner. A 6-inch well costing from $3000 to $4000 is cheap, if prop- erly put down, and is a grand investment, and one which is better, at that price, for the farmer than for the driller, for where the driller may make $500 or $1000 profit on one well he may lose it all on the next; whereas, the farmer with the well has a sure thing and a competency. Any well will pay its cost in 5 years whatever the cost ma y be or at the rate of 20 per cent, on the investment. Some wells have paid for themselves in one year. If a farmer has a well which enables him to raise even 30 bushels of wheat to the acre, in a dry year when his neigh- bors fail to get back their seed, and he has but 140 acres un- der water, he receives 4,200 bushels, which, at but 50 cents per bushel, nets him $2,100, or sufficient to pay for a well large enough to thoroughly irrigate his 160 acres. This is not overdrawn but underdrawn as based upon actual expe- riences. One well, in 1891, more than paid its cost by garden irrigation, and, besides this, supplied water to the town. Many such examples could be given to show how service- able a well is and how short a time it takes to return its cost. Nor need one seek a dry year in order to show the contrast, for even in the best years the service of a well is so great as to make the increased yield pay very largely on its cost. It may be asked what do your Dakota wells cost ? The answer would be difficult to frame for lack of proper infor- mation and knowledge of all the facts entering into the matter of cost. Wells 4jor 4J^ inches have cost from $1,800 to $3,000. Wells of 6 inches from $3,000 to $7,000; although about $3,000 is the common price. Wells of 8 inches have cost about $4,000 or So, 000. The expensive wells have, in all cases, been expensive by reason of delays and accidents. As drillers have become more skilled in this field, and rigs have been adapted to its formations, the price of wells has been reduced, and a still further reduction may be expected as skill and competition increase. The cost of a Dakota well ought to be considered in connection with its volume. The mere hole has no value; it is the water which it supplies on which a value is placed. 36 The hole costs so much, regardless of the volume of water thrown out, so that if two wells cost $2000 each, and one well throws out 1000 gallons per minute, while the other throws out but 500 gallons per minute, it may be fairly said that one well cost twice as much as the other, for the one supplies but half the service of the other, or has cost twice as much for a given return. 80, too, as between Dakota wells and those of other sections of the country. The Dakota artesian basin is the largest and the greatest in the world and the volumes and pressures of its wells greater than the volumes and pressures elsewhere. So it may be said that it costs far less here to get a given volume of water than it does any where else in the world. This ba- sin is the nearest to the manufacturers of well machinery, pipe, tools, and other supplies which therefore cost less. The depths are but moderate, and the volumes enormous, so that the duty or service received for the money expended is greater than in any other section or country. In Australia many wells are put down by the government at a cost of from $5,000 to $25,000, yet their best wells do not equal the average Dakota wells. Our farmers may therefore deem themselves most highly favored by nature and ought not to grumble at the expense of obtaining water, for, by no other system, and in no other section of the world, can an equal volume be obtained for the same amount of money. No reasonable man will complain of ex- pense when he pays far less than the balance of mankind and when all the conditions are so favorable for the speedy return of the money invested. Nor will any wise investor hesitate to put his money into Dakota wells or farm lands when the conditions, as they are here, are shown to him in comparison with the conditions elsewhere, under which conditions tens of millions have been invested to the great profit of the investor, prosperity of the settler, and glory of the state and nation. It must further be considered that the cost of the water is but a part of the cost of the land. The well is of no val- ue except as it supplies the water; the water is of little val- ue except as it feeds the ground and aids in producing a crop. The cost of land, well, ditches, reservoirs and other improvements could properly be "lumped," and the total value per acre found. In this, as in the cost of the water alone, Dakota will be shown to hold the palm as against the world. This matter will be more fully consider- ed under the head of land and water values. Some have asked how can I get a well the cheapest ? by contracting with a driller, or by buying a rig (either alone or by clubbing together with my neighbors) and doing my own work. Many reasons prevent a reply. Firstly, iusffici- ent data as to what has been done heretofore renders a reply impossible, or, at best, purely speculative. Secondly, the outcome will depend upon who you are, what your means 37 may be, what your general intelligence may be, and espec- ially as to the amount of natural mechanical ability you may possess. Many farmers could not drill a well with the best of tools. Some ingenuous farmers have actually drilled good wells with rigs and tools of their own make. Safety and economy would appear to lie in the selection of a con- tractor who has the tools, knows the business and is prepar- ed to assume all risks. It is to be hoped, however, that hundreds of rigs will be purchased by farmers, and that we may soon evolve a race of practical drillers from among our own people. AETESIAN WELLS, ELSEWHERE. It is within a comparatively short time that artesian well waters have been used for irrigation in this country, but their value is now being appreciated and thousands are be- ing sunk for this purpose. As above stated, there has not yet been discovered in the world another artesian basin of such extent as the Dakota basin nor one whose wells possess such great volume and pressure. Artesian wells are common to nearly all of our states and to most countries and some few wells have been drilled that compare very favorably with the better Dakota wells but they are few in number and widely separated, and the artesian basins thus far discovered are of but moderate area. The Dakota sand-rock formations extend far to the south so that Nebraska and Kansas have a few good wells but most of the southern wells are shallow and the flow but weak . A group of 5 wells at Coolidge, Kansas, cost an average of 8400 each and have an average flow of 25 gallons per min- ute. A like ratio between cost and volume would make a Dakota well of 1800 gallons cost $16.000, whereas there are several throwing a greater volume the cost of which has been from $3,000 to $4,000. The smaller wells of the Crook- ed Creek Valley, numbering about 100, and costing only about $20 each are used for irrigation and about 50 of these serve from 5 to 25 acres each. A new artesian basin has but recently been discovered in Washington, in the Yakima valley, where there is one well flowing 650,000 per day or 452 gallons per minute. This would rank among the smaller wells of Dakota. A com- pany has been organized to drill wells throughout this new field wherein hundreds of thousands of dollars have been expended in irrigation development by other systems and where, within a decade, a barren, sage-brush desert has been made the home of the peach and the prune, and the heart of a vast and prosperous agricultural interest. In Colorado several thousand wells have been drilled to depths ranging from 100 to 1800 feet, but in most cases to depths of from 300 to 700 feet . The water from many must be pumped but in most other cases the flow ranges from 10 to 75 gallons per minute. 38 The town well at Anamosa has a liow of 495 gallons per minute. This is the largest of over 2000 wells in the San Louis valley, Bucher's well, at the same place has a pres- sure of 25 pounds to the square inch. The Espinosa well, about 20 miles north of Monte Vista, according to the re- port of the state engineer, u throws a solid three-inch col- umn of water nearly 40 inches above the casing, and flows between 300 and 400 gallons per minute." Compare this pigmy, which thus deserves special notice in Colorado, with such Dakota gushers as the Aberdeen, Huron, Kedfield, Doland, Columbia, Woonsocket, Spring- field and Yankton wells not to mention a host of others each of which would be a marvel in any other land. In California there are 25 artesian basins of varying char- acter and pressure but that of Kern county is the most re- markable and more nearly resembles the Dakota basin than any other yet found. Its area is only about 18 by 14 miles and it has an elevation of about 300 feet above the sea. The average depth of the many wells in this area is about 500 feet. Ol these wells 54 range in flow from 150,000 to 4,000,000 gallons per day, or from 100 to 3,000 gallons per minute. One wells has a volume of 3,000 gallons per minute, two wells flow 2,100 and 2,400 gallons, nine wells flow from 1,400 to 2,000 gallons, and seventeen wells flow from 700 to 1,400 gallons per minute. The diameters range from 6 to 10 inches. The counties of Tulare, Los Angeles and San Bernardino have also remarkable artesian basins and hundreds of very fine wells from 150 to 500 feet in depth. About 4 miles south of San Bernardino is the Gage group of 29 wells, all within the radius of a mile, the average volume being about 389 gallons per minute, and the average depth but 150 feet. In other parts of the United States there are many nota- ble wells and artesian basins, as there are also in China, in the Sahara desert, and in nearly all of the countries of Europe, especially in Germany and in France. The scope of this little book will not, however, permit their considera- tion. It is sufficient to note that the artesian well is of world- w r ide interest to mankind but it is in Dakota that the great wells may be saidto be at home. DAKOTA WELLS. The pioneer well of Dakota was begun in the summer of 1881, at Aberdeen, by the Chicago, Milwaukee & St, Paul Ry., for the purpose of supplying water for its engines. The well was drilled by Mr. Swan, and, by reason of changes in the size of pipe, and unavoidable delays, the cost was far greater than it would otherwise have been. The flow was struck early in the spring of 1882, at a depth of 920 feet, The pipe was 6 inches at the top and 4^ at the bottom. The volume was not accurately measured at the time but a very close approximate measurement placed the volume at 39 1,200 gallons per minute and this increased later on to over 2,000. The pressure ranged from 150 to 180 pounds to the square inch. The 6 inch pipe was carried to a height of 70 feet and, from a 2-inch nozzle at the top of this pipe, a stream was thrown 60 or 70 feet into the air against a gentle breeze.* Encouraged by the success at Aberdeen, other wells soon followed throughout the length of the territory until, today, they stretch over an area of over 400 miles north and south by over a hundred miles east and west, and the limit of the field in any direction has yet to be found. A complete list of Dakota wells could not be given for lack of information, but a list is given below of a few typic- al wells which may be taken not as exceptional wells select- ed for the purpose of parade but as purely representative of the wells in all parts of the state such wells as any farmer in the state can get if he will but try, ajid wells which, when once obtained, will be to the owners a mine of wealth such as few at present dream of. TABLE NO. 13. KEPRESENTATIVE SOUTH DAKOTA WELLS. County. Town or Location. Depth in feet Bore in inches. Flow in gals, per min. Pressure in Bbsper sq. in. Aurora Plankinton . 750 6 1000 Beadle Huron well 862 5% 1668 120 Day" 840 4 476 120 *' Risdon" 960 5% 2250 175 4 Hitchcock 960 4&3 1240 155 Brown Aberdeen, Cy 908 5% 1800 180 4 ' Sewer 1000 6-41/2 1215 155 4 " Beard 1050 6&5 1000 138 Columbia 966 4 1 / 2 1399 160 Bon Homme Springfield 592. 8 3293 80 Tyndall 735 4H 552 45 Douglas Armour 725 4H 700 Hand Miller 1H5 3y 2 462 100 Hughes Harrold 1453 150 40 Marshall Britton 1004 4 1 / 2 601 120 Sanborn Woonsocket 725 5000 153 44 44 775 7 7000 150 Spink Ashton 900 4 750 100 44 Mellette 910 4H 1215 165 Redfield 964 A 1261 166 4< Doland 897 UA 710 112 44 Baker well 920 44 2000 165 Yankton Yankton 610 6 1800 56 " *' 610 6 2200 50 The author compiled the above table from previously published re- ports and has made such corrections as were possible. The figures given, are, in the main, correct. *This is the first accurate account published as to this first well. The record was made by myself at the time and has been carefully preserved. The record published by State 40 Engineer Coffin was erroneous, having been obtained, no doubt, from parties who were not properly informed. Sim- ilar errors appeared as to other wells, as to which 1 am ac- curately posted. The official reports ought to be as accur- ate as possible and none but the best authorities accepted. It is difficult, however, to attain to great accuracy in this matter. Maj. Coffin deserves praise for attaining so nearly to it. __ W. P. B. The Dakota artesian basin, as stated, is of unknown ex- tent. Wells are found throughout the length of the two Dakotas and far northward into the British possessions, as they are also to the south through Nebraska, Kansas and Texas. On the east the field appears to terminate within the borders of the state, where first appear the quartzite for- mations. Certain evidences are adduced by Maj. F. F. B. Coffin, ex-state engineer, to prove that even \vithin the quartzite area wells may be found, and that the true limit on the east is in Minnesota where the truearchaean formations appear. To the west is a domain as unknown as it is vast. If the supply of this basin, as supposed, comes from the mountains of Wyoming and Montana, then it would be possible to find wells at all points between the Missouri river and the mountains except within such areas as have been affected by igneous upheavals or other geologic dis- turbances. It is sufficient, however, to know that on any section with- in this broad basin, extending for over 400 miles north and south by about 100 miles east and west, a well may certainly be had. The water bearing formation is the Dakota sand- rock, a formation of unknown thickness in this field al- though of vast thickness in its far western out-croppings. The southern wells of the state penetrate this formation at a depth of about 600 feet. The formation dips thence to the northward until, at Jamestown, on the Northern Pacific it is over 1400 feet below the surface. The dip appears to be comparatively uniform so that it is possible to determine, within very close limits, at what depth water will be struck at any point. Overlying this soft, porous, water-bearing sand- rock there is usually a thin stratum, or cap-rock, of harder sandstone or limestone. Above this the formations are principally of blue and gray shale with occasional strata of sand or lime- stones. It is the drilling in these shale formations that is so difficult, for, as stated by some drillers, the shale seems to pack like putty or lead and does not mix readily with the water used in drilling. Much has yet to be learned as to Dakota wells, as to the formatioms to be penetrated, as to the relationship if any there be between volume and pressure and as to the source and the volume of supply, and, especially as to the best and cheapest way of drilling wells, the best machinery or process 41 to use arid, above all, the best use to be made of the water after it is obtained. The Dakota farmer has also to learn how to use the water so as to get out of it the highest duty, when to use it on different crops and in what quantity on different soils and durine: different seasons. A grand work is well begun, and our farmers have but to labor and gain dollars thereby, while the scientist speculates upon the mar- vels of nature as they develop and gains knowledge from his speculations. Under the head of Water, and of Reservoirs, will be found several tables relating to the duty of well waters. The vol- umes of wells, yol nines thrown per minute and per day and volumes per minute equal to given volumes per day, vol- umes thrown in one and three months by wells of different volumes per minute, volumes required to cover different areas to different depths and time required by different wells to do it, equivalence of cubic feet and gallons and of gallons and cubic feet, equivalence of other units of volume or measurement, and other tables of value relating to wells. The sequence of our subject requires that the Water fol- low the completion of the well, so that " Water, its pro- perties, measurement," tfec will next be briefly considered; after which will be a brief consideration of the matters of storage by reservoirs and its distribution by ditches, flumes and pipes. COPIES OF THIS BOOK FOR SALE BY Aberdeen, South Dakota, for 25 cents. Also sets of detailed drawings of gates, outlets, flumes, weirs, and similar constructive details of an irrigation plant. These drawings could not be inserted in this book. Price per set 25 cents . WATER. Its Properties, Duty and 3ieasurement, with tables of Weight, Pressure, Volume, Discharges, &c &c. Miscellaneous Notes. Pure water is composed of Hydrogen and Oxygen. By weight, ll.l 88.9 Parts. By measure , 2 1 " Its greatest desity is at a temperature of from 39.2 to 39.8 C from which point it expands by either heat or cold. It boils at a temperature of 212 , and freezes at 32 Fahr. Evaporates at all temperatures. Is but slightly compressible. Is not palatable when pure or distilled. Wieght See P. 62 & 63 Tables of weight, and notes appended. Weight See P. 61 " " " on one acre. Pressure See P. 64 " " pressure. of column per sq. in. = height of column X 4.331. " " " " circ. in. = height of column x .3369. Press, of 1 Ib per sq. in. is exerted by column 2.311 ft. high. Volumes See tables under head of Mensuration , and fol- lowing tables. A cu. ft. of saturated air at 50 contains 4.09 gr's. of water. A cu. ft. of saturated air at 55 contains 4.86 gr's. of water. A cu. ft. of saturated air at 60 contains 5.79 gr's. of water. A fall of snow of 11 inche^is equal to about one inch of rain, but this varies greatly. 11 inches being for a dry snow not drifted . Depth of water in in's. X 2,323, 200= cu. ft. per square mile. Depth of water in inches X 3,630= cubic ft. per acre. The "CENTER OF PRESSURE" is % of the depth from the surface- Thus, in a reservoir or tank 12 feet deep the average pressure on the sides will be found at a point 8 feet below the surface. The amount of this pressure is equal to the depth of this point X by 62% (the weight of 1 cu. ft. of water). In this case 8 ft., the depth, X 62%= 499 pounds = the average pressure per sq. ft. on the entire surface . To get the total pressure on the sides multiply the total area of the sides by the average pressure, as above found. The total pressure on sides and bottom = 3 times the weight of the fluid contained in the tank or reservoir. The pressure on a sluice gate, in the bank of a reservoir, 2x3 feet and the center 8 feet b low the surface of the wa- ter in the reservoir =8x62% =499 Bbs. per foot; 2x3=6 sq. ft. X499= 2994 pounds, or nearly 1% tons. The daily supply of water per capita in cities having water works systems ranges from 45 to 175 gallons, and averages about 75 gallons. In nearly all cases the per capita de- mand increases from year to year. Water presses towards an orifice from all directions and diminishes the velocity it the proportion of about 63 to 100; or the quantity delivered through the orifice will be less in this proportion than the calculated amount. 43 DUTY OF WATER. By the duty of water it is meant the amount of duty or service it will perform, or the extent of its usefulness in any given field. Considered as a power, it is so many horse power for a given volume under a given head. Considered as an irri- gating medium its duty is the number of acres a given vol- ume will adequately serve; or, as it is usually stated, the duty of a second foot is so many acres. That is to say, a volume of one cubic foot per second, fio\ying constantly during the irrigation season, will serve a given number of acres. This element of duty is not, of course, a subject of exact measurement for too many variable elements enter into its determination to render this possible; yet the duty may, in any particular section, be very clearly estimated. What the duty will be will depend altogether upon the crop to be served, and the nature of the sub-soil and surface soil on which the crop is grown. The duty in one state will differ from the duty in another state, as will the duty in one section of a state differ greatly from that in another section of the same state. One crop will require more water than another, or the same crop may require more water on one soil than on another. In Dakota little is known as to the duty of water for, as yet, no measurements have been made, no extended system of irrigation is in practice and little thought has yet been given to this matter; nor has any effort been made to arrive at the maximum duty of any one well. When the township well system becomes general, and the greatest service, or duty, is demanded of each well, then will carefully kept re- cords of duty be required, and such records will form the basis of estimates which will closely approximate to the duty of the well waters in the several sections of the state, and lead to a knowledge of better methods of application and conservation of the supply. Noi is duty a constant quality for it is constantly on the increase; that is, the duty increases from year to year oth- er things being equal the ratio of increase being very rap- id immediately after the installation of the system of irri- gation This is apparent on considering that when the water is first applied its volume is very largely absorbed in placing the soil in proper condition. This having been done, the same volume will, the next year, serve to supply the prepared area and still leave a surplus for the reclamation of a further area. So, each year, the field of duty is extended until the max- imum is finally reached. As stated, the duty in any locality will depend very largely on the nature of the soil, and it will depend still more upon the mean rain fall over that section. In a locality, or during a year, where the precipitation is small and nearly the full necessary supply must be artifici- ally supplied the duty will be low; but where the precipita- tion is nearly sufficient to supply the needs of agriculture, 44 and but a small portion need be artificially supplied, then the duty will be high. In considering, therfore. what the probable duty in Dako- ta will be, account must be taken of the character of the soil, the comparative precipitation and evaporation and the nature of the crop. Hon. J. S. Greene, state engineer of Colorado, in the 1888 report states, as an approximate estimate, that the precipi- tation on the mountain areas west of the great continental divide is 33 inches, and on the plains areas 10.7 inches; an average over the whole of that area of 25 inches. Also that on the mountain areas east of the divide the precipitation is 30 inches, and on the plains areas 15 inches; or a total average of 18.7 inches. He states further, and, in this, is in accord with other authorities, " that the limit of remunera- tive farming, without irrigation is drawn at an annual precipitation of twenty-two inches" that is, if the precipi- tation is less than 22 inches there cannot be certainty as to a remunerative return for agricultural labor. The matter of distribution of this precipitation enters here as a matter of the greatest importance as shown by the example cited on page 92. In this report it is further stated, with reference to the duty of water and the distribution of precipitation "as there is a demand for general results in this matter, it may be stated, relative to the duty of water on the plains of Col- orado, measured where distributed to the land, that one sec- ond foot, running throughout the irrigation season, in addi- tion to about 5 inches of lam-fall during April and May, and 4.5 during June, July and August, if distributed with fair care to diversified crops, on what might be called aver- age land, would irrigate from 60 to 70 acres. It is noticed that, to accomplish this duty, it must be measured where placed upon the land. This is not always considered when speaking of the duty of of water. " (P. 406.) Referring to table 14, below, it will be seen that the pre- cipitation during April and May, in Dakota, has equaled or exceeded 5 inches in past years, except daring 1890 and 1891; and that, in every year the precipitation during June. July and August has exceeded 5 inches, so that the conditions of distribution above quoted are much exceeded here, and hence the duty of our well waters would exceed the duty quoted (soil, average evaporation, and average humidity be- ing equal.) Year Pr. Apl & May Pr. June, July & Aug Total .1882 8.68 13.18 21.86 1883 6.59 11.30 17.89 1884 5.60 9.47 15.07 1885 6.26 13.84 20.10 1886 5.10 9.12 14.22 1887 5.11 15.07 20.18 1888 5.86 7.67 13.53 1889 6.45 5.21 11.66 1890 3.52 . 8.01 11.53 1891 3.89 10.52 14.41 TABLE NO. 14. Table of precipitation in Dakota during Apl. and May and during June, July and Aug. (From table No. 43.) Averages 5.70 10.34 16.04 45 Then, too, the average Colorado precipitation of 18 or 19 inches is less than the Dakota average of about 21 inches, so this operates still further to increase the probable duty of water here. In the recently published report of State Engineer J. P. Maxwell, of Colorado, (1890 report) are certain very perti- nent suggestions and estimates, relative to water duty which I cannot do better than to quote. "Water rights vested on the basis of the low duty assigned to water ten years ago, have, in instances, deteriorated lands and reduced their productiveness by as urfeit in application, while on adjoining lands through an enforced economy, a higher duty, better conditions of soil, and greater produc- tiveness have resulted." " Unskilled labor has a penalty of 25 to 50 per cent attach- ed to it in the application of water, and unfortunately this class is too prevalent in the irrigation fields, in many cases, no other being obtainable." "An abundant water supply tends to carlessness in its application and consequent waste. Where liberal and old water rights are provided, it is frequently the practice to turn the water upon the land and permit it to run without change or attention throughout the night ana sometimes during the day, a large volume of water soaking into the soil without benefit to the crop." "The duplication of ditches is another fruitful source of waste, reducing the duty of the volume of water." "Reference to some of the maps prepared by this depart- ment, will show, in different localities several ditches par- alleling each other at inconsiderable distances apart, the upper one of which could be made to answer the purposes of all with marked economy in water, as well as large sav- ing in capital." "Too little attention has been given to the proper prepara- tion of the surface to facilitate the rapid spreading of the water." "This is principally the result of too large individual own- ership f land, rendering it impracticable to give close sup- ervision and secure careful preparation of the land.'' "The best results will be obtained from small proprietary rights in land, and a consequent higher state of cultivation." The ownerships of the cultivated lands of the state should be multiplied by ten and the population increased to that extent." All that is here stated will apply with equal force to Da- kota, and he who would meet with the greatest measure of success will heed the cautions thus held out by so high an authority. Become an expert in irrigation by studying up from all available sources. Profit by the past experiences of others. Beware of attempting more than your means or experience will fully warrant and conserve well the supply of liquid wealth so freely granted you. The following table will serve to show the great range of duty in the same state, and as a very valuable basis of com- 46 parison with our own more favorable and less fluctuating climatic conditions. TABLE NO. 15. TABULATED STATEMENT OF WATER-DUTY ON STREAMS INDICATED FOR 1889 AND 1890. g A i .a 03 o o, . "-' It 09 ui 1 5C fe CK - r 03 O STREAMS GAUGED. jf.sl 2 si p | 03^ .sl ^*> 1 g 1? ' II *8 lallj gl | fi ; il 3 -l^S c o ^ w H fi Cache La Poudre j 1890 735.97 770.51 139,222 139,222 1.178 1.254 0.682 0.338 1.860 1.592 189.168 180.687 Big Thompson .. j jjgjj' 214.53 425.42 91,037 89,790 0.579 1.192 no data no data 424.35 211.06 St. Vrain j Jig- 215.46 284 238 94,013 q i qcjr; 0.563 739 0.532 i'.oiV, 436.33 33'^ 69 South. Boulder andj 1889! 461 ! 97 y-fc.o j. 77^682 l!406 168! 15 Boulder Creek. . . . I 1890. 419.33 76,682 1.34 1182.86 Bear Creek j J|' 60.40 33.98 10,173 8,112 1.4tJ 16v42 1.03 1 ; ^39.0-3 From 1890 Report of State Engineer of Colorado. It will be noted that, in all the above' cited estimates, the water is that of a natural stream the volume of which is largely augmented by seepage water. The water haying been used at a higher level, seeps through the soil and finds its way back into the stream at a lower level, there to be used again and again, thus raising the duty, over a given area, of a given original volume. In the level lands of the Dakotas, and on the purely in- dividual system of irrigation which will prevail here, no account need be taken of seepage waters as a source of secondary supply; although the presence of seepage water, and the power of the soil to retain it, will go far towards determining the ultimate duty of the original well-supply. Quoting, again, from the Colorado report of 1888, Engineer Greene says, "it is thought that when distributed with the greatest care, and in sufficient quantities to be handled without great waste, during seasons of average rainfall and to crops and soils fairly conditioned to its economical use, that the duty of water should approach 90 acres to the sec- ond foot." Also "Two cubic feet of water per second carried on to a field in one body, will, under conditions otherwise the same, irrigate more than twice the area that one cubic foot carried alone would irrigate. What will be the conditions of the duty of water under the Dakota well-system, and what the duty that may be 47 safely relied upon under average conditions y Note that the average rain-fall for 10 years has been 21.58 inches; the maximum 28.12 inches, and the minimum 14.68 inches. In this level country a rain-fall of 24 inches is sufficient to give abundant returns, and even less than that, with proper distribution and provided the soil could be maintained, year after year, up to a proper standard of saturation. For the sake of conservatism, reduce the average annual rain-fall to 18 inches, instead of 21 inches, then but 6 inches need be artificially supplied to give the maximum of 24 inches required ." Thus 6 inches may be taken to fairly represent the unit of duty required in Dakota. One cubic foot per second =448. 83 gallons per minute. This amount is equaled, or exceeded, by most of the small- er wells of the state . One second-foot =10,368,000 cubic feet in 4 months, (which may be said to cover the irrigation season, from April to J ulyj or a sufficient volume to cover 238 acres a foot deep, or 476 acres 6 inches deep. 476 acres may, therefore, be said to be the duty of a second-foot in that period of time. Allowing for deep seepage and evaporation, and call the actual duty 320 acres, instead of 476 acres (a loss of 156 acres), and it would appear that a second foot is amply sufficient to serve a half section of land during a poor year. Account is not here taken of the fact that during the months prior to the beginning of the irrigation season, the land may be prepared, by flooding, to such an extent as to render further service during the irrigation season almost unnecessary; and the further fact, that, by a system of res- ervoirs, an enormous volume may be stored to supplement the supply of the well itself during the 4 months of irriga- tion service. Thus the supply of the well during eight months of the year may be utilized to swell the duty of the well during the 4 months of service, to the extent of making the duty during that period extend over fully double the area above assumed to represent the estimated duty. The difference in the uniformity of supply of the Colora- do rivers and the Dakota wells is most marked. The 1890 gauging record of the Cache La Poudre river shows that the volume discharged during March varied from 50 to 150 cubic feet per second. During April, from 75 to 500 cubic feet; increasing thence rapidly to June 2d, when the dis- charge was 1825 cubic feet. The decrease was then quite rapid until the first of September, when it had fallen to less tf>an 100 cubic feet, and it so remained during the balance of the season of discharge. The same is true of all other western rivers whose waters are derived from the melting snows of the mountains. 48 There is therefore little chance to use the waters for pur- pose of irrigation except during the season of flood, or, in exceptional cases, where the waters are impounded in stor- age basins of great area. In Dakota, on the contrary, the supply is constant the year around. Winter and summer the flood pours forth with unabated energy, and the irrigat- or may as he actually does work in mid winter, with a hoe in his hand and a fur coat an his back. By reason of this periodicity the duty of the Colorado waters is limited to the actual duty during the irrigation season, and, contrariwise, the duty of the Dakota well should be measured by what might be fairly called its annu- al duty. I have little doubt but that the duty of the s< cond-foot in Dakota will be found, in the end, to be nearer 640 acres than 320 acres; but if, for the present, the lesser unite be adopted abundant alowance may be claimed and the claim be entitled to fair consideration by reason of .its actual conservatism . From table No. 20, of second feet reduced to gallons per minute, the following table may be constructed on the basis of a duty of but 320 acres per second-foot. TABLE NO. 16. DUTY OF WATER IX DAKOTA. Gallons per minute from well. Equivalent in second ft. Duty in acres. Gallons per minute from well. Equivalent in second ft. Duty in acres. 448 1 320 2692 6 1920 897 2 640 3141 7 2240 1346 3 960 3590 8 2560 1795 4 1280 4039 9 2880 2244 5 1600 4488 10 3200 i 49 THE DIVISION AND MEASUREMENT OF WATER. it has be^n stated by Prof. L. G. Carpenter, in his work on the above subject, that "one of the most important, as well as one of the most difficult problems of irrigation is that of making a just distribution of water." Reference being made to the distribution of irrigation waters in Col- orado and elsewhere where irrigation is carried on on a vast scale and by means of waters taken from large ditches or canals which serve a large area and are supplied from rivers or great storage reservoirs in the mountains. Every device which the ingenuity of the centuries could devise has been used to render this division more equitable, certain and economical and to prevent waste where, as is usually the case, the economy of water is of the first im- portance. The literature of the subject is voluminous, but the Da- kota farmer will look far, and in vain, for any information touching upon conditions similar to his own/ We have here no vast system of canals, nor will we have in the future; no vast storage basins and no need of the many devices used in other sections for the division and measurements of water. Our system is essentially individ- ual, but the day is at hand when certain simple devices will be required to divide the waters of our wells among the few consumers under service by each well operating under the township well law, or among those who rent water from the individual owners of a well. With us, too, it is not wholly a matter of device for the mere measurement of a given volume, or a question as to the unit of volume; but very largely a matter of legislation based upon our peculiar conditions and needs, which legis- lation has yet to be evolved and put to the test of practice. Contract, too, will enter largely into the matter of the division of water and, on the start, the terms will be more varied and uncertain than the devices necessary to carry them out. With the Dakota farmer, as with farmers else- where, the central idea will be to secure the greatest possi- ble service from the water at hand ; and the prevention of waste will soon demand attention. In the irrigation operations of the west all the elements are predetermined. The water supply is known, the ditches or canals are constructed of a certain size to perform a cer- tain service or serve a given area. This service cannot well be exceeded and great economy must be observed in order that the actual service may equal the calculated service. Here the main chanel or source of supply is the well, the volume of which is easily determined. The fountain head may be inexhaustible but only so much can be drawn off. The farmer may have a surplus which he may waste or 50 sell to his neighbor, in which case economy in his own use and in theirs will operate to increase his revenue from the sale of the surplus. So, too, in the operation of the township wells. The great- est service will be desired for each consumer and the well will be called upon to serve as many consumers as possible. In the latter case, as in the case of an individual owner, proper service to each consumer can only be had through the medium of a storage reservoir; for if a well will not on the instant serve one consumer fully it will certainly fail to serve several consumers. EACH MUST HAVE HIS OWN RESERVOIR. Herein will arise questions as to the manner of service, priority, etc. Suppose a well serves four quarter sections (say the E. J^ of Sec. 1 and the E. ^ of Sec. 12) and that by reason of the slope of the ground it is necessary to locate the well on the center of the N. E. JC of section 1. If the water is carried in a ditch to the other quarters, and the amount delivered is measured at the well, the owner of the S. E. J f ^ ec - 12 would receive far less water than the owner of the ]S\ E. J of Sec. 1 because of the far greater loss by evaporation and seepage. His loss, too, would be his neighbor's gain. If the water be distributed in a pipe line the loss of head due to friction in the longer pipe would operate to the same end but to a lesser extent. Again if each consumer measures his water at the point of delivery in his own reservoir a question will arise as to the priority of service. A may fill his reservoir first and D last, but meanwhile the water in A's reservoir has been low- ered a foot or two by evaparation and seepage and, at the period when greatest service is required, A may receive 20 per cent less service than D, yet each has received and paid for the same volume of water. If the service to the several reservoirs is by pipe line and is simultaneous the inequali- ties will be less and more easily subject to regulation. It is not the intention here to raise any question as to the details of distribution or the possibility of an equitable division of the water; nor the purpose to suggest remedies for anticipated controversies, but it must be known that questions of detail, such as those above suggested, will arise and demand a solution. When they do a solution will be found on lines of equity to all interests. Notwithstanding our conditions are so wholly different from those met elsewhere, the measurement of the volume of our wells must be treated the same, however much the final divisions of the waters may differ. Heretofore too little attention has been paid to the accu- rate determination of the volumes of our wells. Usually the volume has been guessed at or an approximate estimate has been made by timing the filling of a barrel, hogshead or 51 tank. In some cases the stream has been weired and an ac- curate estimate made as to the volume. In a few cases grossly exagerated reports have been cir- culated as to the volume of certain wells (notably the Risdon WP!! at Huron, which has been advertised as having a vol- ume of 10.000 gallons per minute, whereas its true volume is but 2,250 gallons per minute.) . Such exagerations can only result in harm and should be discouraged. The truth is sufficiently wonderful to satisfy the most exacting. UNITS OF MEASUREMENT. THE STATUTE INCH, is a unit of water measurement much used in the western states and territories. It varies in different states and even in different sections of the same state. It is equal to about 45 cubic inches per second. One second foot =38.4 statute inches in Colorado. This unit is practically the same as the miner's inch it being the miner's inch in the terms of a specific statutory specification. It varies in different states. THE MIXER'S INCH Is fully explained and illustrated in tables 18 and 19 and the accompanying notes and figures. When defined by state law it is known as the statute inch. THE ACRE FOOT is equal to 43,560 cubic feet or such an amount as will cover one acre to a depth of one foot (See table 21 and notes & P. 60). This unit is more largely one of service than of measurement. THE SECOND FOOT, or cubic foot per second, (See table 20 and note following.) is a unit definite as to both volume and time and is the one upon which all wier tables are constructed and is no doubt the coming unit in this and other countries. GALLONS PER MINUTE. Like the second foot this unit is definite as to both volume and time and is the one commonly used in Dakota. (See tables, 19 20, 36 and 37.) Two general methods have been adopted in the division and measurement of water. THE FIRST is known as the DIVISOR, the object of which is to divide the waters of the ditches or streams into certain proportionate parts among consumers. The idea is not to measure according to some fixed unit but simply to divide or proportion the water according to a certain ratio. J^ to each of two consumers; % to each of three, &c &c THE SECOND is known as the MODULE the purpose of which is not to divide but to measure according to some fixed unit. In Spain, Italy and India measuring devices or modules have been in use for centuries but of late years they have reached their greatest perfection in our western states Of all measuring devices the WEIR has proved to be the most acurate and satisfactory. (See the following table of weir measurements, table 17-) The rectangular weir wherein the crest is horizontal and the sides vertical is the common form and the one to which 52 the tables herein given apply. The trapezoidal weir has the crest horizontal and the sides sloping; this form possesses certain advantages which will not, however, be considered here. The triangular weir or notch is likewise claimed to possess certain advantages over other forms. THE SPILL BOX. Among the most satisfactory devices for the division and measurement of water is the excess weir or spill-box, myentf- ed by Mr. A. D . Fopte of Idaho and illustrated in Fig. 6, wherein A is the main ditch the now in which may be check- ed by gate B thus forcing a portion of the water into the spill-box D which has an opening F in the side, the discharge through which into the lateral ditch Gr is regulated by a slide and graduated scale as shown. The inner edge E E of the box is lower than the ends and outer side so that all water not passing through the opening F spills back into the main ditch. The head or height of the water above the opening being regulated by the height of the edge E E. By this means the head at the opening F is maintained constant at all stages of the water in the main ditch and the amoun of water discharged through an opening of any length is not subject to fluctuations due to change of head but remains constant. Not over a foot of fall need be lost to the main ditch by using this device. The spill edge E E should be beveled to give a sharp edge, on the box side, over which the water may flow without friction. This form of module will find a wide field of usefulness in Dakota as the practice of irrigqtion becomes more general and its details more closelv considered. Fig. 6. Spill Box. THE KECTANGULAK WEIR This form of module or measuring device haying been the subject of the most exhaustive investigation, is considered to be the best suited to the accurate measurement of water. The conditions of its proper operations are : 1st. That the crest shall be horizontal and the sides vertical. 2d. That the up-stream face be vertical. 3d. That both the crest and sides be sharp edges on the up-stream side. 4th. That the depth of water flowing over the weir be not less than 3 not- more than 25 inches 5th. That the depth of water flowing over the crest be not greater than 1 : i the length of the weir. 6th. That the weir opening be not over -'.-, the width of the stream ap- proaching it. 7th. That the discharge over the weir should be free and the approach of the water without velocity sufficient to produce eddies. 8th. That the distance from the crest to the bottom of the channel and from the ends of the weir to the sides of the channel, shall be at least twice as great as the depth of the water flowing over the weir. This is to secure complete contraction. Weirs may have either partial or complete contraction as illustrated by figures 1 to 5 of Fig. 7. Fig. 7. Illustrating Contraction on Weirs. In following over a weir water takes the form shown in Fig 1. The upward movement of the water toward the crest A of the weir A B causing the water to arch upward as shown. The true head, as shown at c, is reduced by the downward curve of the water, as shown at d e. This is called the con- traction. If the weir has the form shown in Fig. 2 the con- traction of the flow will be but partial; that is, there will be contraction at the crest a c but none at the sides a b and c d past which the water flows as shown in Fig. 4. If the weir has the form shown in Fig. 3 the contraction is said to be complete, for, in addition to the contraction at the crest, there is^also contraction at each side, a b and. where it is seen that the width of is less than the width of the illustrate not only the action of meaning of the term "Complete Contraction." which is a requisite to the proper application of the following table of weir measurements. TO CONSTRUCT A WEIR AND MEASURE THE VOL- UME OF A WELL. Select some convenient point where, by throwing up a low bank, a small pond may be formed by the stream from the well. Across the outlet set aboard or plank out of which has been cut a rectangular piece (say 12 inches deep by 4 feet long). Support the board by nailing to stakes driven into the ground taking care that the edge of the c d, as shown in Fig. 5 the outflowing stream a opening b. This will flowing water but the 54 opening is level or horizontal. Make the bank water-tight about the bottom and ends of the weir. Drive a stake sev- eral feet back of the weir and near the edge of the pond making the top of the stake level with the crest of the weir either by using a level < r by driving the stake to water level at the moment the water begins to spill over the weir. 55 Permit the water to rise to the full height at which it will stand while flowing over the weir. Then fueasure the depth of water over the stake. Enter the weir table w r ith this depth (as explained in ex- amples given) and get the quantity for one inch. Multiply this quantity by the length of the weir in inches to get the total volume flowing from the well, in cubic feet per minute. If possible have the up-stream edges of the weir lined with strips of tin or sheet iron to give a sharp edge for the water to flow over, if this is not at hand then bevel the crest and sides of the weir to a sharp edge on the up-stream side. See, in short, that ALL the conditions mentioned on page 52 have been complied with. The manner of con- structing and using a weir is illustrated on the opposite page, where A is the weir board with the beveled notch or opening B. E is the stake driven back to the side of the weir, out of the current, and from which the true depth is taken as shown. Application of Weir Table ]Vo. 17. This table gives the number of cubic feet of water passing per minute over each inch in width ot a weir, and lor depths from -jJg- inch to 25 inches. The top horizontal line of fractions are the fractions of an inch in depth, and the columns of figures at the rig-.t and left ends indicate the full inches of depth. The quan- tities inside the table are the cubic feet discharged. Thus / 5 inch of depth = .11 cu. ft. per inch width of weir, f See at "1 10 inches " " =12.71 " " . " " " '***** lOii \" ' " =13.19 " " " " " " } in the J 16H " " " =27.43 " " " ' " " L table J These examples will render clear the use of the table Examples of Use. How many cubic feet and gallons are discharged per minute by a well the water of which, in flow- ing over a weir 5 feet long, shows a depth of 7% inches? From table the quantity of water for one inch wide by 7% inches deep=8.05 cubic feet per minute; 5 feet wide=60 inches; therefore 8.05 multiplied by 60^483 cubic feet per minute. Referring to table No. 36 we find that 483 cubic feet=3612.8 gallons. Therefore by this simple process the volume of our well per minute has been found to be 483 cu- bic feet, or 3612.8 gallons per minute. The work involved in the construction of a weir is but slight, and the calculation of the flow, as above, is a mere matter of multiplication and addition. Every well owner should see that the volume of his well is accurately deter- mined in this way; and not once alone, but every few months, in order to know whether there is any increase or diminution in the flow. A series of suck systematic tests would no doubt result in furnishing valuable information leading up to a correct determination as to the source and supply of the artesian stream. TABLE NO. 17. AVIER MEASUREMENTS. ^ ft B 2 w 2 ? 1 S CM j IK 5 -* TH CO L CO C^ I X O ^ L , ?5 rc' **' tf? f* os o CM' -*" co' ! co" TH cc ic ' co THTHTHTHl-rHCMCMCMiCM GO CM * TH TH 1C C- ICC OS 1C < oc>TH-*ccroo5c~iciC] ic c^ 06 O CM * < ; CO CXI t CMCOiXOCOCO'OSOSCOQlTHOSCMT ICO icO|CO"*-<* | H j iicxo-'*ix)roo5coirooo5coc~ f -* ift c- co O i 2 S iS ^ r^ c? ^ 00 O M Of O CM 1C TH ?5 c 00 O CM -* CO "THCOgS^^lrtCOg rc ic co co O CM CC 1C > O CM ** It" OS CM TJH I C HJ* os ro ,ro t C- ft CO CO TH-M'rciccocoosTHroicic^ 1 1C: o CO 1C : i TH-MCClCCOGOOSTHrOlCjC-OS 1C CO 1C 1C .' CO O 9 fOO CM OO ** HH 'to OS TH HH CM -M CM ro ro r-j 00 CO 1C ro ro 4* * roncoooosTHCoi I -* CO CC-* i OS CM CO TH Tt* CO IT- * OS OS '. ITH -4* ro co f s -2: I tf5 t- 1 I 05 TH CO 13538 3 388 rc * to r- os TH ro TH3SS3 8 c8 5o r? fc- < ": t t- OS CO CO O < CO ^ D t TH TH S3 1.193629 7V2 19.09806 23 179.6067 68 1569.946 2 1.358084 7?4 20.39249 24 195.5642 70 1663.653 2^ 1.533150 8 21.72935 25 212.2007 72 1760.077 2 H 1.718826 8^ 23.10865 26 229.5163 74 1859.218 2p 1.915111 8l| 24.53040 27 247.5109 76 1961.074 2.122007 874 25.99458 28 266.1845 78 2065.646 2% 2.339512 9 27.50121 29 285.5372 80 2172.935 2% 2.567628 9% 30.64178 30 305.5690 82 2282.940 2/B 2.806354 10 33.95211 31 326.2798 84 2395.661 3 3.055690 10% 37.43220 32 347.6696 86 2511.098 3H 3.315636 11 41.08205 33 369.7385 88 2629.251 3*2 3.586191 11% 44.90166 34 392.4864 90 2750.121 3% 3.867357 12 48.89104 35 415.9133 92 2873.707 3% 4.159133 12% 53.05017 36 440.0193 94 3000.008 3% 4.461519 13 57.37906 37 464.8044 96 3129.026 3% 4.774515 13% 61.87772 38 490.2685 98 \ 3260.761 3J| 5.098121 14 66.54613 39 516.4116 100 3395.211 The weight of water in a given length (as one foot) of any pipe or other circular cylinder is in proportion to the square of the bore, or inner diameter. Hence the weight of water in 1 foot length of any cylinder of other diameter than those in the table can be found by multiplying that for a 1 inch pipe, 0.339521, by the square of the inner diameter of the given cylinder in inches. Thus, for a cylinder 120 inches diameter: diameter 2 = 120 2 = 14400 r and weight of water in 1 foot depth = 0.339521 X 14400 = 4889.10 Ibs. Similarly, (A) 2 = A 9 S = 0.191406, and 0.339521 X 0.191406 = 0.064986 Ib. = weight in 1 foot of T 7 ^ inch pipe. Here, also, r 7 ^ = half of J ; hence, weight for -^ inch = one- fourth of weight for | inch = one-fourth of 0.259946 = 0.064986. Weight of one square inch of water 1 foot high, at 62 J IDS. per cubic foot = 62.25 -j- 144 = 0.432292 Ib. For further information respecting weight of water, see page E 61 &^6& 63 TABLE NO. 23. TABLE OF WEIGHT OF WATER. Maximun density is at 39.8 Fahr. New. Cubic feet. = Pounds . Gallons. = Pounds. 1 62.425 1 8. 3216 2 124.850 2 16.6432 3 187.275 3 24.9648 4 249.700 4 33.2864 5 312.125 5 41.6080 6 374.550 6 X 49.9296 7 4:36.975 7 K- 58.2512 8 * 499.400 8 * 66.5728 9 40 561.825 9 H 74.8944 10 624.250 10 id 83.2160 20 .2 * 1248.50 20 a * 166.432 30 1872.75 30 249.648 40 Jj* 2497.00 40 332.864 50 3121.25 50 ' 416.080 60 & 3745.50 60 499.296 70 'G 4369.75 70 '3 582.512 80 "0 4994.00 80 O 665.728 90 M 5618.25 90 w 748.944 100 c 6242.50 100 832.160 200 ti c * 12485.0 200 g * 1664.32 300 18727.5 300 2496.48 400 "03 24970.0 400 03- 3328.64 500 J 31212.5 500 | 4160.80 600 J 37455.0 600 4992.96 700 43697.5 700 5825.12 800 s 49940.0 800 g. 6657.28 900 e 56182.5 900 Of fl 7489.44 1000 03 r| 62425.0 1000 rj 187 275. 3000 24964.8 4000 249700. 4000 33286.4 5000 1 312 125. 5000 0> 41608.0 6000 374 550. 6000 d o 49929.6 7000 ^ 436975. 7000 fe 58251.2 8000 499400. 8000 66572.8 9000 561825. 9000 74894.4 10000 624250. 10000 83216.0 100000 6242500. 100000 832160.0 1000000 62425000. 1000000 8 321 600.0 For ordinary purposes the weight of a cubic foot of water may be taken to be 62^ pounds. The weight varies with the temperature as shown in the following table. Temperature Fahrenheit. Lbs. per | cubic ft. | Temperature Fahrenheit. Lbs. per cubic ft. 32 freezing. 40 50 .62.417 | 70 62.302 .62.423 .62.409 .62.367 80 62.218 90 62.119 212 boiling 59.675 Cubic foot of ice = 57.2 Ibs. Cubic foot salt or sea water = 64.31 Ibs. 35.84 cubic feet of water weighs one ton. 39.13 " " ice " " " 2.311 feet of water = 1 lb. per square inch. 1 cubic inch of water = .036024 lb. approximately. 1 " " = .576384 ounce. 1 U. S. Pint = 1.0402 lb. of water 1 U. S. Quart = 2.0804 lb. of water. 1 U. S. Gallon = 8.3216 lb. of water. (8M) 1 U. S. Wine barrel 31 ^ GaL = 262.131 lb. of water. Trautwine and HaswelL TABLE NO. 24. PRESSURE OF WATER. T&e pressure of water in pounds per square inch for every foot in height to 500 feet; and then by intervals, to 1000 feet head. By this table, from the pounds pressure per square inch, the feet head is readily obtained; and vice versa. MIL Prvwure -or Pet Prewure Feet Hewl. PreMura Feet peT^u'are rt Preuure i 0-43 .65 28.15 12 9 5588 193 83.60 257 11.32 a ' 0.86 66 28.58 56.31 194 8403 258 11.76 3 1.30 67 29 O2 . 13* 56.74 84.47 259 12.19 4 i-73 68 2945 132 57.18 196 8490 200 12.62 i 2.J6 2 59 69 70 29.88 30.32 134 57-61 5804 |$ 85-33 85 76 26l 2O2 13.06 13-49 7 3-03 30.75 5848 199 86.20 263 13.92 8 3.46 72 136 58.91 200 86.63 264 M.36 9 3-89 73 3^62 137 5934 201 87.07 265 14.79 K? 11 4*76 74 75 3205 32.48 138 139 59-77 60.21 202 203 87.50 87.93 266 267 15 22 1566 12 520 76 3292 140 6064 204 88.36 268 16.09 13 14 13 i 3335 3378 1 4 I 142 61.07 61.51 SS.So 8923 269 270 16.52 16.96 11 ^l 6.49 6-93 7.36 g si 3465 3508 144 61.94 62.37 6281 207 208 209 8966 90 10 90.53 2 7 1 2 7 2 273 '7-39 17 82 1826 l8 7-79 82 3552 146 63.24 210 90.96 274 18.69 19 20 22 8.66 i, 3 35-95 36.39 H7 1 4 S 63.67 64.10 211 212 9 1 39 91.83 275 2 7 6 19 12 21 9.09 85 36.82 149 64.54 213 92.26 2/7 1999 22 953 86 37-25 64.97 2I 4 92.69 2 7 S 20 42 23 24 9.96 10-39 1 3768 3812 152 6540 65.84 215 2l6 93 13 93.56 279 2SO 20.85 21.29 25 10.82 89 38.55 153 66.27 217 9399 2Sl 21.72 36 3 11.26 11.69 90 9 1 3898 3942 154 66.70 67.14 218 21 9 94-43 94.86 2S2 -283. 22. IS 22.59 28 12.12 92 39.85 156 67.57 220 95 30 2S 4 23.02 29 13-55 93 40.28 157 68.00 221 95-73 2S S 2345 3 12.99 94 40.72 158 68.43 222 96 16 2S6 TI 3 13.42 1386 $ 4i.i5 41-58 !lo 6887 69-31 223 224 9660 97-03 287 2SS 24-75 33 14.29 97 42.01 161 69-74 225 97.46 289 25-18 34 14.72 98 4245 162 7017 226 97.90 290 25.62 35 15. 16 99 42.88 163 70.61 22 7 291 26.05 36 i v59 100 43 3 1 164 71-04 228 9876 292 26.48 37 It. 02 1OI 43-75 ig 71,47 229 9920 293 26 92 38 39 16-45 1689 102 103 44.18 44.61 166 167 71,91 72-34 230 99-63 100.06 294 295 27-35 27.78 40 104 45-05 168 72.77 232 loc 49 296 28.22 4 17-75 J05 4548 169 73.20 233 10093 297 2S6c 4* 18.19 106 459i 170 73-64 234 101 36 298 29.08 43 18.62 1O7 46.34 74-07 235 101.79 209 295' 44 1905 108 46.78 172 7450 2 3 6 102 23 300 2995 ^ 1949 109 4721 173 74-94 237 102,66 310 34-2* 46 1992 110 ?74 75-37 238 10309 320 3862 47 20.35 III 48 08 175 75.80 239 103 53 330 4 2 -95 48 20.79 112 48.51 176 76.23 2 4 103.96 340 47.23 49 21 22 113 48.94 766 7 2 4 I 104.39 51.61 5i 21.65 22.O9 "s 4938 4981 !?9 77 10 77-53 2 4 2 243 104.83 105.26 370 55-94 60.27 52 22.52 116 5024 180 77-97 2 44 105.69 380 64.61 53 22.95 117 5068 181 78.40 245 106.13 390 68.94 54 23-39 nS 5i ii 182- 78.84 2 4 6 106.56 400 73 27 P 23.82 24.26 119 12O 51-54 51-98 183 184 79.27 7970 2-J7 2 4 8 106.99 107.43 500 600 21658 259-90 57 2469 121 52.41 185 80.14 249 107.86 7ix> 30322 58 25.12 122 52.84 1 86 80.57 250 108.29 800 346. 54 59 25.55 | 123 53^28 187 81.00 25' 108.73 yoo 389.06 00 25-99 ; 124 53-71 iS>i S..43 252 109.16 10OO 433 8 61 62 2642 26.85 ! r* 54- '5 5458 189 190 81.87 82.36 253 254 1 1 o. 03 63 27.29 i 127 55-01 . x>r 8273 255 110.46 1 64 2772 i 128 55-44 192 83-7 256 no So From catalogue of Chapman Valve Mfg. Co. lo nnd the pressure per sq. in. of a column of water of any height multi- ply the height of the column by .43318 (or 434, as it is usually given.) See note on next page. Note, as to table on last page. Many suppose that a well having a static pressure of a certain number of pounds per sq. in. has the same service, duty and volume of delivery as would be obtained from a column of water falling through a pipe of same size and with a head corresponding to the pres- sure of the well. Such is not the case, however, there being no known relationship between the two so far as a well is concerned. To illustrate From table we see that a head of 231 feet will uive a pressure of 100.08 pounds per square inch and (although not given in the table) a certain volume will be delivered per minute. If either the head, pressure or vol- ume be known the other two may be accurately estimated. In case of a well, however, this is not true. A well having a pressure of 50 pounds per sq. in. may throw more water than another well having a pressure of 100 pounds per sq. inch and either one may throw either more or less than would be delivered from a pipe of the same size having a head of 116 feet, which corresponds nearly with a pressure of 50 pounds to the inch. In other words the volume of a well cannot be found by knowing its pressure; nor can the pres- sure be found by knowing its volume. The pressure must be measured with a gauge and the volume by weiring the stream or by some other accepted method. EVERY WELL SHOULD BE PBOVIDED WITH A GAUGE and a proper record preserved of the pressures during differ- ent seasons of the year, during different stages of the weather and directions of the wind and during the several stages of service of the well. Systematic records thus kept would no doubt go far toward settling the questions of source and supply. It has been claimed, and apparently on good grounds, that the standing of the barometer and the direction of the wind have a marked effect on both the volume and pressure of some wells. No systematic records having been kept of these observations it cannot be definitely stated that the fluctua- tions in volume and pressure of the wells were due to the changes in the weather,but the matter having been suggested is one well worthy of attention because of its scientific pos- sibilities. TABLE NO. 25. Diam. of pipe in inches. Area in square feet. Area in square inches. Gals, in 900 feet of pipe. Weight of water in 900 feet. 3 4 4.5 5 6 7 8 .0491 .0873 .1105 .1364 .1963 .2673 .3490 7.07 12.56 15.90 19.64 28.27 38.48 50.27 330 587 743 918 1322 1799 2350 2756 Ibs. 4897 * 6199 < 7656 * 11021 * 15011 ' 19598 An idea may be gained from this ta- ble as to the stupend- ous energy necessary to throw out this vol- ume of water at velo- cities ranging from 500 ft. to 2000 feet per minute as is done by Dakota's Artesian Wells. TABLE NO. 26. From Trautwine's "Civil Engineer** Pocket Book/' CONTENTS OF CYLINDERS, OR PIPES. Contents for one foot in length, in Cub Ft, and in U. S. Gallons of 231 cub ins, or 7.4805 Galls to a Cub Ft. A cub ft of water weighs about 62^ Ibs ; and a gallon about 8^ Ibs. Diams 2, 8, or 1O times as great, give 4, 9, or 100 t'~-~ v " Content. For the weight of water in pipes, see Table No. 22 For 1ft. in For 1 ft in For 1 ft. ia length. length. leu gth. Diam. Diam. Diam. Diam. Diam. in in deci- . a *-. CO in deci- ^ S fc. OS Diam. in deci- _^.o - CO IDS. mals of "S'JJ >9 IBB. mals of 'S'^ >2 in malsof IJ'ja . o a a foot. EC, la" a foot. fc * N Ins. a foot. ( &. } C a go g 1 !< lj* = ^ |o oq s 5* O i ^ i J 4 .0208 .0003 .0025 y .5625 .2485 1.859 19. 1.583 1.969 14.73 5-16 .0260 .0005 .0040 1. .5833 .2673 1.999 72 1.625 2.074 15.51 78 .0313 .0008 .0057 \/ .6042 .2867 2.145 20. 1.667 2.182 16.32 7-16 .0365 .0010 .0078 U .6250 .3068 2.295 K 1.708 2.292 17.15 \/ .0417 .0014 .0102 74 .6458 .3276 2.450 21 1.750 2.405 17.99 9-16 .0469 .0017 .0129 8. .6667 .3491 2.611 72 1.792 2.521 18.86 7ft .0521 .0021 .0159 i^ .6875 .3712 2.777 22. 1.833 2.640 19.75 11-16 .0573 .0026 .0193 i| .7083 .3941 2.948 72 1.875 2.761 20.66 3 .0625 .0031 .0230 % .7292 .4176 3.125 23. 1.917 2.885 21.58 13-16 .0677 .0036 .0269 9. .7500 .4418 3.305 Yz 1.958 3.012 22.53 is .0729 .0042 .0312 Til -7708 .4667 3.491 24. 2.000 3.142 23.50 15-16 .0781 .0048 .0359 i| .7917 .4922 3.682 25. 2.083 3.409 25.50 1. .0833 .0055 .0408 % .8125 .5185 3.879 26. 2.167 3.687 27.58 \/ .1042 .0085 .0638 10. .8333 .5454 4.080 27. 2.250 3.976 29.74 72 .1250 .0123 .0918 YA .8542 .5730 4.286 28. 2.333 4.276 31.99 74 .1458 .0167 .1249 i| .8750 .6013 4.498 29. 2.417 4.587 34.31 2. ' .1667 .0218 .1632 % .8958 .6303 4.715 30. 2.500 4.909 36.72 /4 .1875 .0276 .2066 11. .9167 .6600 4.937 31. 2.583 5.241 39.21 72 .2083 .0341 .2550 i^i .9375 .6903 5.164 32. 2.667 5585 41.78 74 .2292 .0412 .3085 i| .9583 .7213 5.S96 33. 2.750 5.940 44.43 3. .2500 .0491 .3672 % .9792 .7530 5.633 34. 2.833 i 6.305 47.13 /4 .2708 .0576 .4309 12. 1 Foot. .7854 5.875 35. 2.917 6.681 49.98 \/ .2917 I .0668 .4998 34L042 .8522 6.375 36. 3000 7.069 52.88 74 .3125 .0767 .5738 13. !l.083 .9218 6.895 37. 3.083 I 7.467 55.86 4. .3333 .0873 .6528 14L125 .9940 7.436 38. 3.167 7.876 58.92 74 .3542 .0985 .7369 14. 1.167 1.069 7.997 39. 3.250 8.296 62.06 72 .3750 .1104 .8263 1^1.208 1.147 8.578 40. 3.333 8.727 65.28 74 .3958 .1231 .9206 15. 1.250 1.227 9.180 41. 3.417 9.168 68.58 5. .4167 .1364 1.020 M1.292 i 1.310 9.801 42. 3.500 ! 9.621 71.97 /4 .4375 .1503 1.125 16. 1.333 1.396 10.44 43. 3.583 10.085 75.44 72 .4583 .1650 1.234 141.375 1.485 11.11 44. 3.667 10.559 78.99 74 .4792 .1803 1.349 17. 1.417 !l.576 11.79 45. 3.750 11.045 82.62 6. ' .5000 .1963 1.469 141.458 1.670 !l2.49 46. 3.833 ill. 541 86.33 & .5208 .2131 1.594 18. 1.500 1.767 13.22 47. 3.917 12.048 90.13 .5417 .2304 1.724 141.542 1.867 13.96 48. 4.000 12.566 94.00 \ Table continued, but with the diams in feet. Diam. Feet. Cub. Feet. U. s. Galls. Diam. Feet. Cub. Feet. U. S. Galls. Dia. \ Cub. Feet. 1 Feet. U. S. Galls. Dia. Feet. Cub. Feet. U.S. Galls. 4 12.57 94.0 7 38.49 287.9 12 ! 113.1 846.1 24 452.4 3384 1^ 14.19 106.1 ^ 41.28 308.8 13 132.7 992.8 25 490.9 3672 X^ 15.90 119.0 i^ 44.18 330.5 14 153.9 1152. 26 530.9 3971 74 17.72 132.5 74 47.17 352.9 15 176.7 1322. 27 572.6 4283 5 19.64 146.9 8 50.27 376.0 16 201.1 1504. 28 615.8 4606 \A 21.65 161.9 M 56.75 424.5 17 i 227.0 1698. 29 660.5 4941 / 23.76 177.7 9 63.62 475.9 18 254.5 1904. 30 706.9 5288 74 25.97 194.3 M 70.88 530.2 19 283.5 2121. 31 754.8 5646 6 28.27 211.5 10 78.54 587.6 20 314.2 2350. 32 804.3 0017 5* 30.68 229.5 J-2 86.59 647.7 21 346.4 j 2591. 33 855.3 6398 B 33.18 248.2 11 95.03 710.9 22 380.1 2844. o4 907.9 6792 i 35.79 267.7 Ji 103.90 777.0 2:-! 415.5 3108. 35 962.1 7197 67 fy^ TABLE NO. 27/ RELATIVE DISCHARGING CAPA^jfeK-O^ FULL SMOOTH PIPES. Dia. in Feet. Relative Discharg'g Power. 3 4 6 8 10 12 14 16 = - ** II Q~ 48 44 40 36 33 3 27 24 22 2C 18 16 M 12 10 8 6 4 3 d 4- 3.667 3-333 3- 2.750 2.500 2.250 48 1.667 1.500 1-333 1.167 \ 3 .667 .500 333 .250 31 32.0OO 25750 S 12.S4I 9.859 7-594 5- 6 57 2.756 2-052 1471 I. .6339 .3629 .1768 .0641 .0312 15-59 12.54 9.85 7-59 6.ii , 4-8o 3-70 2 -75 2.16 1.74 1-34 i 17-5 13-47 8.41 8.52 6-54 5.16 3-84 309 2-43 1.87 1-39 i 20.27 I5-58 12.54 9.85 7.59 5-65 4-5> 3.58 2-75 2.05 1.47 i 34-55 27.09 16.61 1558 12.53 9.88 7-J5 5.65 4.05 2.75 1-74 i 19.78 15-54 996 8.92 7-<7 5.66 4-34 3-23 2.32 1-57 I 42.95 32.00 25.73 20.29 15.58 1 1. So 8.52 s- 6 5 3-58 2.05 i 70.96 55.96 42.01 32.01 22.94 15.60 9.88 5-66 2-75 i 65-77 47.14 32-05 20.31 11.63 5-66 2.05 I* i From ]. T. FANNING^ "Water Supply Engineering. The foregoing table shows approximately the relative discharging pow- ers of pipes of different diameters. In the second colnmn the diameter 1 foot is assumed as a unit, and the figures show the relative discharging value of pipes whose diameter is given in the first column ; for example, a pipe four feet in diameter will discharge 32 times as much water as one which is one foot in diameter, other things being equal ; a pipe 3 feet in diameter 15.588 times as much, one 2 feet in diameter, 9.859 times as much and so on. * The numbers at the intersections of the horizontal and vertical columns from the diameters in inches give also approximate relative discharging capacities. For example, a 48-inch pipe is equal to 15.59, 16-inch pipes, or we find that a 24-inch pipe is equal to 32, 6-inch pipes or 15.58, 8-inch pipes, and that a 12-inch pipe is equal to 5.65, 6-inch pipes. 68 TABLE NO. 28. FRICTION HEADS AND DISCHARGES. For 100 feet of pipe. By Wiesbach's Formula. Trautwine. Diam. in Inches. Vel. in Vel- ( Feet head in o */2 4 4^ 5 trSec Feet. Frhead Ft per 100 ft. Cub ft per Mir Frhead Ft per 100 ft. Cub ft per Mir Frhead Ft per 100 ft. Cub ft per Min lOoTJ Per Mit Frhead Ft per 100ft. Cub ft per Mia 2.0 .062 .659 5.89 .565 8.02 .494 10.4 .439 13.2 .395 16.3 2.2 .075 .780 6.48 .669 8.82 .585 11.5 .520 14.6 .463 18.0 2.4 .090 .911 7.07 .781 9.62 .683 12.5 .607 15.9 .547 19.6 2.6 .105 1.05 7.65 .901 10.4 .788 13.6 .701 17.2 .631 21.3 2.8 .122 1.20 8.24 1.03 11.2 .900 14.6 .800 18.5 .720 22.9 3.0 .140 1.35 8.83 1.16 12.0 1.02 15.7 .905 19.8 .815 24.5 3.2 .160 1.52 9.42 1.31 12.8 1.14 16.7 1.02 21.2 .915 26.2 3.4 .180 1.70 10.0 1.46 13.6 1.27 178 1.13 22.5 1.02 27.8 3.6 .202 1.89 10.6 1.62 14.4 1.41 18.8 1.26 1.13 29.4 3.8 .225 2.08 11.2 1.78 15.2 1.56 19.9 1.39 25/2 1.25 31.0 4.0 .250 2.28 11.8 1.96 16.0 1.71 20.9 1 .52 20.5 1.37 32.7 4.2 .275 2.49 123 2.14 16.8 1.87 22.0 1.66 27.8 1.50 34.3 4.4 .302 2.71 12.9 2.33 176 2.03 23.0 1.81 29.1 1.63 36.0 4.6 .330 2.94 j 13.5 2.52 18.4 2.21 24.0 1.96 304 1.76 37.6 4.8 .360 3.18 ; 14.1 2.72 19.2 2.38 25.1 2.12 31.8 1.91 39.2 5.0 .390 3.43 14.7 2.94 20.0 2.57 26.2 2.28 33.1 2.05 40.9 5.2 .422 368 15.3 3.15 20.8 2.76 27.2 2.45 34.4 2.21 42.5 5.4 .455 3.94 15.9 3.38 21.6 2.96 28.2 2.63 35.8 2.37 44.2 5.6 .490 4.22 j 16.5 3.61 22.4 3.16 29.3 2.81 37.1 253 45.8 5.8 .525 4.50 17.1 3.85 23.2 3.37 30.3 3.00 38.4 2.70 47.4 6.0 .562 4.78 ! 17.7 4.10 24.0 3.59 31.4 3.19 39.7 2.87 49.1 6.2 .600 5.08 18.2 4.36 24.8 3.81 32.4 3.39 41.0 3.05 50.7 6.4 .640 5.39 18.8 4.62 25.6 4.04 33.5 3.59 42.4 3.23 52.3 6.6 .680 5.70 ; 19.4 4.89 26.4 4.28 34.5 3.80 43.7 .3.42 54.0 6.8 .722 0.02 20.0 5.16 i 27.3 4.52 35.6 4.01 45.0 3 61 55.6 7.0 .765 635 20.6 5.45 L8.0 4.77 36.6 4.24 464 3.81 | 57-2 Diam. in Inches. Vel. in Feet Vel- head in 6 7 8 9 10 per Sec. Feet. KSSortn KjperMin Frhead Ft per 100 ft. Cub ft per Min Frhead Ft per 100ft. Cub ft per Min F Fj r t h ,?^ i Cub ft i&fft. p er - Mi <> afteft 2.0 .062 .329 23.5 .282 32.0 .247 41.9 .220 53.0 .198 1 65.4 2.2 .075 .390 25.9 .334 35.3 .293 46.1 .260 58.3 .234 72.0 2.4 .090 .456 28.2 .390 38.5 .342 50.2 .304 63.6 .273 78.5 2.6 .105 .526 30.6 .450 41.7 .394 54.4 .350 68.9 .315 85.1 2.8 .122 .600 32.9 .514 449 .450 58.6 .400 74.2 .360 91.6 3.0 .140 .679 35.3 .582 48.1 .509 62.8 .453 79.5 .407 98.2 3.2 .160 .763 37.7 .054 51.3 .572 67.0 .508 84.8 .458 105 3.4 .180 .851 400 .729 54.5 .638 71.2 .567 90.1 .510 111 3.6 .202 .943 42.4 .808 57.7 .707 75.4 .629 95.4 .565 118 3.8 .225 1.04 44.7 .892 60.9 .780 79.0 '.693 101 .624 124 4.0 .250 1.14 47.1 .979 64.1 .856 83.7 .761 106 .685 131 4.2 .275 1.25 49.5 .07 67.3 .935 87.9 .832 111 .748 137 4.4 .302 1.35 51.8 1.10 70.5 1.02 92.1 .905 116 .814 144 4.6 .330 1.47 54.1 1.26 73.7 1.10 96.3 .981 122 .883 150 4.8 .360 1.59 56.5 1.36 76.9 1.19 100 1.06 127 .954 157 5.0 .390 1.71 58.9 1.47 80.2 1.28 105 1.14 132 1.03 163 5.2 .422 184 61.2 1.58 83.3 1.38 109 1.23 138 1.10 170 5.4 .455 1.97 63.6 1.69 86.6 1.48 113 1.31 143 1.18 177 5.6 .490 2.11 65.9 1.81 89.8 1.58 117 1.40 148 1.26 183 5.8 .525 2.25 68.3 1.93 93.0 1.68 121 150 154 1.35 190 6.0 .562 2.39 70.7 205 96.2 1.79 125 1.59 159 1.43 196 6.2 .600 2.54 73.0 2.18 99.4 1.90 130 1.69 164 1.52 203 6.4 .640 2.69 75.4 2.31 <- 102 2.02 134 1.79 169 1.61 209 6.6 .680 2.85 77.7 2.44 106 2.14 138 1.90 175 1.71 216 6.8 .722 3.01 80.1 2.58 109 2.26 142 2.01 180 1.81 222 7.0 .765 3.18 82.4 2.72 112 2.38 146 2.12 185 1.90 229 See exmaple of use on page 69. 69 Example of use of table No. 28. I have 150 Ibs. pressure at well; 2000 ft. of 3 inch pipe discharging 110 gallons per minute. What is the effective pressure at point of discharge ? From table 36 we find that 110 gals. = 14.7 cu, ft. From ta- ble 28, under head of 3 inch pipe, we find 14.7 cu. ft. discharge = 5 ft. velocity per sec. and a loss of 3.43 ft. head per 100 ft. 3.43 X 20 = 68.6 = ft. loss of head in 2000 ft. of pipe. From table 24 we find 68.6 ft. head to = 29.7 Ibs. of pressure. 150 Ibs. (given pressure) 29.7 Ibs. 120.3 lbs.= effective pressure at point of discharge. Further example of use of tarble 28. To get discharge from pipe of given size and length. From table 28 within certain limits may be found the volume discharged by a pipe of given size and length, under a given pressure. Example: A well has a pressure of 78 Ibs. per inch, and it is desired to convey water to a reservoir through 3000 ft. of 3 inch pipe; what will the pipe discharge per minute at the reservoir? From table 24 (P. 64.) we find that 78 Ibs. = head of 180 ft. which head is to be used to force the water through 30 hundred feet of pipe, therefore ^ of 180 = 6 ft. = the available head for 100 it. In table 28 we find, under 3 inch pipe, the nearest corresponding friction head which is 6 02 ft. which corresponds to a velocity of 6.8 ft. per sec. and a volume of 20 cubic ft. per minute, which, from table 36 = 149.6 gallons. (No account is here taken of the velocity head which is less than 1 ft. and remains the same for any length of pipe; being dependent only upon the velocity in the pipe.) Over column two of table No. 28 appears the heading " Vel. head in ft.", and over column three appears the head- ing " Fr. head ft. per 100 ft." The first is read as Velocity head and the second as Friction head. The distinction is here explained. By Head is meant the vertical distance in feet between the surface of the source of supply and the centre of the orifice through which the water flows. The total head is divided into 3 parts called, respectively, Entry Head- Velocity Head, and Friction Head ; the respective func- tions of which are as follows : Entry Head is that portion of the total head used in overcoming the resistance to the entry of the water into the pipe. The entry head is less as the edges at the point of entry are rounded. It is equal to about one- half the velocity head. Velocity Head is that portion of the total head used in maintaining a certain velocity within the pipe, assuming that there is no friction m the pipe. It is therefore equal to the height through which a body would fall in a vacuum to gain the same velocity as that of the water in the pipe. V 2 Expressed as a formula Vel. Hd. = -^- , in which V 2 the square of the velocity in ft. per sec. and g = the acceler- ation of gravity, or 32.2. The formula then becomes V 2 Velocity Head =-^j or, what is practically the same- Velocity or ) _ ( square of vel. > v m - ~ Theoretical Head J ~ { in ft. per sec. J * The velocity head rarely exceeds 1 ft. and is constant for all lengths of pipe. 70 Friction Head is the remainder of the total head; or such an amount as is just sufficient to overcome the friction in the pipe leaving the remaining head to cause the entry and velocity of the flow. The smoother and shorter the pipe is the less the friction head will be and the greater the velocity head will become. The Theoretical Velocity due to any given head is, if ex- pressed in a formula = \2gh = <64.4h, in which h = the gh head in feet. This is practically the same as Theor. Vel. = 8.03 times the sq. rt. of h. Example What is_the theoretical vel. under a head of 4 ft? v'64.4 X 4 = \25~T6 which, from table of roots, = 16.05 or by the second rule, the sq. rt. of h (4 ft.) = 2 which X 8.03 = 16.06. e The above explanation will not only explain clearly th e significance of the values in table 28 but will also be of us otherwise. Table 29 is similar to table 28, except that the velocities in the pipe are in single feet, and extend to 20 feet, instead of in feet and decimals, as in table 28. The values in table 29 differ slightly from those clue to corresponding sizes and vel- ocities given in table 28. This difference is due to calcula- tions having been made from different formulae, but they are too slight to be material since the variations in the pipes themselves will cause as great variations either more or less from the quantities given in either table. The limits of tables 28 and 29 are too narrow to suit all the conditions of our wells and practice, so a few simple rules are given to suit all conditions, these rules, and table 30 upon which they are based, being adapted from Haswell's Pocket Book. It may be added that by reason of varying conditions whatever rules or formulae are applied the result will be in a measure approximate. To find the Friction Head. Wiesbach's Formula. .01716 ) Length Vel 2 in Friction head ) ^144 _j_ i . : ( in feet ft per sec in feet = ) f X Diam > 64.4 >J per sec J j n f e et The use of this formula requires a knowledge of the velo- city in ft. per sec. which may be found by dividing the vol- ume in cubic ft. per second by the area of the pipe. (See page 82.) TABLE NO. 2>i). I*OSS OP HEAD BY FRICTION OF WATER IN CALCULATED FOR PIPES 1OO FEET LONG. Velocity of Water through Pipe in Feet per Second. INSIDE DIAMETER OF FIFE IN INCHES. 3 4 5 6 7 8 Discharge per Min. in Cubic Feet sf o-o o.-* c ^ k I'll Discharge per Min. in Cubic Feet No. of Ft. Loss, ofl head due to friction' i n n fa I 2 5' No. of Ft. Loss of head due to friction rtf ST cr SJ n' 1 * 1 51 i r ! 3 if eLo 0."** s? o ?8 I's, Discharge per Min. in Cubic Feet No. of Ft. Loss of head due to friction] Discharge per Min. in Cubic Feet No. of Ft. Loss ofl head due to friction] 1 2.95 .196 5.22 .147 8.17 .118 11.77 23.54 .098 16.03 .084 20.88 .074 2 5.89 659 1.35 10.44; -494 16.34 395 .329 32-05 .282 4X-76 .247 3 8.83 15-67 1.02 I.7I 24.51 .815 35.32 .679 48.08 .581 6264 509 4 11.80 2.28 20.89 32.69 1.37 47.09 58.87 1.14 64.11 977 83.52 .856 5 1 14.70 17.70 3-43 26 12 2.57 40.87 2.05 1.71 80.15 1-47 104.40 1.28 6 4.78 31-34 3-59 49-05 287 70.64 2.39 96.18 2.05 125.28 1.79 7 20.60 6.35 36.57 4-77 57.22 3-8. 82.41 3-18 112. 21 2.73 146.16 2.39 8 23.56 8.14 41-79 6.H 65.40 4.89 94.19 4.07 Jf? 6.16 128.24 3-49 167.04 3.06 9 26.51 10.12 12.32 47-02 7-59 73.57 6.07 739 10597 144.27 434 5.28 187.92 208.80 3-79 10 | J9-45 32.40 52.24 9-24 81-75 117.74 160.30 4.62 11 M.7, 57-47 11.03 89.92 98.10 8.82 12952 7-36 I7.34 6.31 229.68 5.52 12 35-34 17.31 62.70 12.98 15.08 10.38 141.30 8.65 *92 37 7-4J 250.56 6.49 13 38.33 20.10 23.12 67.92 106.27 12 06 153.07 10.05 208 40 8.61 9.91 271.44 7-54 14 4123 73-15 17.34 "4-45 13.87 164.85 11.56 224.43 292.32 8.67 15 44.20 47.12 26.32 78.38 19-74 122.62 1579 17663 13.16 240.46 11.28 313.20 9.87 16 29.7*, > 83.60 22 29 130.80 17.83 188.40 14.86 256.48 12.74 334.o8 11.15 17 50-05 33-33 88.8325.00 138.97 20.00 200.18 16.67 272.51 14.29 35496 12.50 18 53.00 37-14 94.05 27.86 147.15 22.29 211.96 18.57 288.54 5-92 375.84 3-93 19 5595 4M2 99.28 30.84 155.32*24.67 223.73 2056 304.57 7.62 396.73 5.43 20 58.89 45-32 104.50 33-99 3-5 *7 19 235.51 23.66 330.60 9.42 417.60117.00 72 TABLE SO. 30. TABLE AND RULES. From Ha. -*>'?! I. ter T tai - i Diameter inches. Tabular No. 1 4.71 7 612 32 1*4 S -^ 854 99 m ' 13.02 9 1147 61 i^it 19 i~> 10 1493 5 2 26 .'69 11 1894 9 2.', 4H.t)7 12 2356.0 3" 73. :> 13 2876 7 3i 108.14 14 3463 3 4 151.02 lo 4115 9 4J 194.84 16 4836 9 r> 263.87 17 562S 5 6 1 416.54 18 ! 6493 1 APPLICATION OF THE TABLE. I. To Compute Volume Discharged Length of Pipe, Diam- eter, and Fall or Head being; given. RULE Divide the tabular number, opposite to the diameter of the pipe. by the square root of the rate of inclination (head), and the quotient will give the volume required in cu. ft. per min. EXAMPLE A pipe has a diameter of 4 inches, a length of 2982 ft. and a head of 123 pounds pressure (284 ft.) What is the discharge per min.? = N 10.5=3. 24, and tabular number for 4 in. = 151.02. J?^? 284 then, !|!A-=46.6 cu. ft. per min.=(from table 36) 119 68 gals If head, as in above case, is iupoimds pressure reduce it to feet by reference to table 24; but if pipe is not connected with the well, and the pressure is due to gravity alone, then the head will be the vertical distance between the upper and the lower ends of the pipe. Keduce volume in cubic feet to volume in gallons by reference to table 36. II. To compute the Diameter necessary to discharge a given Volume the Head and Length being given. RULE Multiply the given volume by the square root of the ratio of the inclination head ; take the nearest corresponding number in the table, and opposite to it is the diameter required. EXAMPLE A pipe has a length of 2982 feet, the head is 123 Ibs., (284 ft.) What size of pipe will it require to discharge 46.6 cubic feet (119.68 gals.) per minute? _ /9QG9 46. 6x /^ 1 =46.6x3,24=150.98. The nearest tabular num- N/ y in 1 {Gallons discharged Horizontal distance of jet no 70 '34 90 '55 109 '73 126 189 1 4 2 205 '56 219 1 68 232 178 ft Vertical " 43 79 94 108 121 J 3' 140 '45 1* {Gallons discharged. .. . 7' 170 93 196 2 19 132 240 .48 259 '63 277 '75 $ ?W Hori/.ogtal distance of jet Vertical 43 63 I 8i 97 112 125 '37 148 S7 1* {Gallons discharged Horizontal distance of jet 171 73 210 96 242 i.8 271 J97 320 7 2 iS 363 198 207 Vertical 43 63 82 99 "S 129 142 '54 164 ^ ( Gallons discharged < Horizontal distance of jet 207 75 253 1DO 293 124 327 146 f 3S7 184 4'3 200 439 2l\ 462 224 ' Vertical '* " 44 6 5 85 102 1 18 I 4 6 '58 .69 FROM FAXNING'S "WATER SUPPLY". To calculate the altitude reached by jets. A=H /H a X.Q125 j ( in which A = altitude required, H = head on jet in * SXD / ( feet, and D = diameter of nozzle in inches, EXAMPLE What will be the altitude of a jet discharged from a IV Z inch nozzle under a head of 80 pounds pressure? (The head being given in Ibs. reduce it to feet by multiplying by 2.311 1 pound per sq. in. equalling 2.311 ft. of head.) 80 Ibs. X 2.311 = 184.88 = head in feet. Then A - 184.88- 1 =149.28 ft, altitude. To calculate discharge of jets in gallons per minute. <-8Tk\2 N, n oww < 0.288 i n which G=discharge in gals, per min. H = {head of jet in ft. D=diam. of nozzle in inches Using above example. What will be the discharge per min. from a inch nozzle under a head of 184.88 feet. (=80 Ibs. pressure) \'H =v'184.88=13.597 and (8 D) 2 = (8X1.5) 2 =144. Then formula becomes G=13,597X 144x0.288 which=563.89 gallons per minute. In this way the volume of a well may be calculated very closely. Table No. 38, page 89 gives the discharges from different nozzles, under different heads, as calculated by this formula. SOURCE AND SUPPLY. "Where does the artesian water come from?" has been asked a thousand times, but has, as yet, received no answer, other than a purely theoretical one. Nor can any answer be given until a careful geological survey has been made of this state and those adjoining it; and until some systematic investigations are made in the field of the wells themselves. When more wells have been drilled, so that the influence of one upon another may be ascertained, or when a series of purely experimental wells shall have been drilled by the U. S. government, we may then learn something as to the direc- tion of the flow and its source. A carefully prepared series of analyses, too, may aid in leading the way to the true source. There is infinite room for investigation, and noth- ing but room as yet provided for the investigator. The past season witnessed the taking of the first step leading to the determintion of the source of these subterranean waters. Considerable work in the way of geological study and sta- tistical investigation was done by the several members of the committee of Artesian Underflow, and Irrigation Inves- tigation, acting, by authority of Congress, under the De- partment of Agriculture. Without entering into any consideration of the many facts upon which this committee of experts based its opin- ion, as expressed in its reports to Congress, I state briefly the conclusion reached by them as to the probable source of this vast subterranean sea. As is well known, the water is, in all cases, found in the layers of more or less porous and soft sand-rock which underlies nearly the whole state and extends thence westward, finally to find an outcropping among the eastern foothills of the Rocky Mountains, and transverse to the courses of most of the large rivers which find a head in that vast drainage area. Many observed facts of great weight would tend to prove that the vast quantities of water known to be lost to the Missouri, the Yellowstone and other large rivers, while flowing over the upturned edges of this outcropping sand-rock, is carried through these porous sponge-like for- mations to find a lodgement beneath the broad acres of Da- kota, and an outlet, no one knows where. In the absence of any theory having the support of better evidence and a greater array of facts in its support this theory as to the source of the artesian waters will stand. There seems to be little doubt as to its correctness. Assuming it to be correct that the fountain head of our wells is in the vast water-shed of the Rockies and that the volume supplied to this great underground river is what it is calculated to be, the demon- stration is complete tnat the supply is absolutely inexhaus- tible for all time and under whatever tax it may serve this or future generations. In no ease has a well failed or shown any decrease in its volume, provided it has been kept clean and open. Some wells have become closed en- tirely but when cleaned out they have again flowed with their old time vigor. What the thickness or depth of the water-bearing sand- rock is, has not been determined for no drill has yet gone through it. Several wells have been sunk from 50 to 75 feet into this rock but the flow has then become so powerful as to prevent further drilling. It would be folly indeed to sup- pose that the feeble efforts of man to gain a little water for his use would have any effect upon the vast sea of water be- neath us the area of which is measured by hundreds of miles and the depth by hundreds of feet. ALL THE WATER THAT ALL THE WELLS IN DAKOTA CAN THROW FOR A HUNDRED YEARS WOULD, IF GATHERED TOGETHER, EQUAL A LESSER VOLUME THAN NOW UNDERLIES A SINGLE COUNTY BROWN. Figure it out. This is no guess. In conclusion I quote from a letter written by Col. E. S. Kettleton (The Chief Engineer of the Department of Irriga- tion Inquiry, of the U. S. Department of Agriculture.) to Mr. E. O. Richards of the Consolidated Land and Irrigation Co. of Huron, S. D. Col. Nettletori says: " In reply to your request for an expression of opinion con- cerning the extent and durability of the Dakota artesian water supply for irrigation purposes, I will state that after two seasons spent in^examining the artesian wells in South Dakota, and their probable source of supply, we have come to the conclusion that the supply comes from the elevated and mountainous country lying to the west (principally in Montana), where the rock strata are turned up so as to come to the surface. The water is transmitted through and is re- tained in the sand rock, which is estimated to be several hundred feet in thickness, and is made up of layers (more or less fractured) from one to fifteen feet in thickness, and of variable degrees of hardness and porosity. Below the strata are thin layers of impervious clay, shale, soft sand and lig- nite. This formation is exposed and is capable of imbibing a large amount of water from the unfailing supply from the mountains and the mountain streams and rivers, which have cut their way deeply into the artesian water bearing rock. I therefore conclude the supply will never fail. It is natural to suppose that the artesian supply can be found along the entire line between the source of supply and the present ba- sin, which has an extent, north and south, of about 425 miles. I am of the opinion that the deeper the water bear- ing strata are penetrated the greater will be the volume ob- tained." E. S. NETTLETON. Artesian. Water anxl Vegetation- Before irrigation was thought of in Dakota, and the water used upon grains, the opinion was frequently expressed that artesian water would injure house plants and trees and would kill grass. Experience has disproved all of these statements for the most delicate house-plants now thrive on this water, the finest lawns in our towns are sprinkled with it. Of field grains and garden truck the same is true. Where, without its use the plant would die, with its use and abund- ant use there is such an abundant growth as to astonish the grower. Plant growth is a chemical process and the plant itself a chemical creation brought about in the laboratory of the earth and through the agency of the air and water; the latter being nature's great solvent and reagent. From the air the plant derives its supply of nitrogen and oxygen, and from the water its supply of hydrogen, and, through the sol- vent action of water, its supply of lime, soda, potash, mag- nesia, iron, manganese, silica, chlorine and other chemicals all of which are indispensable to plant life. Different plants require different chemical ingredients in their food arid ab- sorb, of the same ingredient, different proport ons. Many analyses have been made of artesian waters and in no case has any showing been made of any chemical constit- uent of the waters that would be in any way injurious to plant life but, on the contrary, the result has shown that the artesian water was especially well adapted to the fertiliza- tion of our soil and the production of such plants and grains as are best suited to pur soil and climate. The analyses of this water show Silica 1 Alumina Sulphate of sodium " potassium " " calcium Carbonate of lime iron Chloride of sodium " magnesia Traces of organic matter " lime. " phosphates, which elements are in varying quantities according to the location of the well. The waters of the northern wells are very soft and this is true of some of the southern wells, but, as a rule, the south- ern well waters are harder and not so well adapted, on that account, to household uses. The taste varies greatly but in all cases the water is palatable when cold and it is used by thousands of families for drinking in preference to any other waters. When warm as when it flows from the well it, in some cases, has a brackish, saline, unpleasant taste; but on cooling this disappears. The temperature ranges from 55 to 68. In the winter it will run in ditches for several miles before freezing and ponds of it will remain open when the temperature ranges from 10 to 40 below zero for a week or two. This warmth imparted to the soil in the spring forms a valuable supplement to the warmth of the sun, quickens the act of germination and aids much in the early stages of growth. 77 THE POWER OF WELLS. It is not alone for irrigation and domestic use that the ar- tesian waters will be used but also for POWER. The first well at Aberdeen, in 1882, demonstrated the possibility of utilizing the pressure of the well for the purpose of forcing the water through water mains, thus furnishing a system of water supply and fire protection second to none in point of efficiency and equalled by none in economy of management and maintenance. No steam tire engine is necessary to force a stream through the mains and hose and over the highest buildings; nor is it necessary to provide for the care and maintenance of such an expensive plant as is necessary with a steam power plant. The first cost of the well was less than the cost of an engine, and it fills the double pur- pose of supplying the water and forcing it wherever it may be needed; and all this at no expense other than an occasion- al repair to pipe or valve. Few there are, no doubt, in the many towns of Dakota, where there are systems of artesian water works, who ever pause to consider what these towns would have been had it not been for these wells; or what they would have done for public fire protection or for domestic consumption, but for these wonderful "spouters." There is no other source adequate, other than to the Mis- souri river towns, except to an occassional town, where large surface wells, in sand formations, might have supplied a very limited public service. The wells have been a God- send indeed. The application of the well's pressure to fire- pressure service, led naturally to the idea of using it for power to run water motors. The first application of well power to the operation of machinery was by the Aberdeen Electric Light Co. They tapped the main pipe of the city's well with a % inch pipe and with this stream they ran the entire plant for some time. This power w T as, in the end, abandoned because the sand in the water cut out the buckets of the motor. At this time there was a move made to build a flour mill to be operated by artesian power, but the project was aban- doned upon the advice of several eastern hydraulic engineers to whom the matter was submitted by the author. Each declared it to be impracticable impossible to utilize the power of these wells, and such expressions of opinion are, even now, common among that class of experts; and little credence is given to what has since become a demonstrated fact. Soon the use of small motors became quite common, and to-day scores of motors of different makers are used to run coffee mills, feed mills, printing presses, elevators and simi- lar classes of machinery. The first application of well pow- er to the running of a flour mill was at Hitchcock, Beadle county, S. D., where, with a small well 3% inches at the bot- 78 torn, they run a mill grinding from 40 to 50 barrels of flour per day. The motor is a simple, home-made wheel and the efficiency fully up to what could be desired from an expens- ive steam plant. The saving in this instance is not alone the cost of fuel, oil, engineer's salary, expensive repairs to boiler and engine, etc., etc., but also the decreased' danger from fire and explosion and the consequent reduction in fire insurance rates. The saving in insurance alone will fully cover all the expense of operation by the well. power. This small well also supplies the domestic use and fire service of the town, and the exhaust water from the mill serves to irrigate a large farm. Where on earth, outside of this artesian valley, can an- other showing be made that will compare with this'? (See page 81.) A larger mill at Woonsocket, using a Pelton wheel, runs at a capacity of 100 barrels per day. (See page 81.) Other mills at Springfield, Yank ton and other points also use wells for their motive power. All the machinery in the "Huron- ite" publishing house, at Huron, S. D., is run by a Chicago Water Motor connected to the city water mains; and the electric light plant, operating both arc and incandescent lamps, is run by a 3 foot Pelton wheel connected directly to a 5% inch well, which also supplies water to the water works. A plant, unique in this field and having, to the engineer, a greater degree of interest than any other, because of the manner of applying the water and the results accomplished, is, the sewer plant at Aberdeen. This was the first applica- tion of a well to the performance of heavy duty and it is the only plant of its kind on the globe. The well is 4^ inches at the bottom and 6 inches at the top, and has a volume of about 1500 gallons per minute, under a pressure of from 140 to 160 pounds to the inch. The water is supplied through 3-inch pipes to two Worth- ington water motors and pumps. The application of the water to the pistons in the cylinders being the same as with steam in the cylinders of a steam engine the water operat- ing the same as the steam. When the two pumps are running at the rate of 60 strokes each per min- ute there is a reserve of pressure at the well of 40 pounds per inch. The pumps running at this rate have a capacity of 2,500.000 gallons per day of sewage pumped a vertical distance of 23 feet. When on their tour of in- spection the U. S. Senate committee on irrigation investigation pronounc- ed this plant to be the most wonderful adaptation of the power? of nature that had come under their observation. Any man who believes that a well cannot be successfully harnessed to a load needs but to witness the operation of this plant to be convinced that he is in error, for when a well, through the agency of proper machinery, will lift a load of twenty millions of pounds a day through 23 feet, or 479 millions of pounds one foot high in a day, that well may be fairly said to have performed a good day's WORK. Experts to the contrary, the artesian wells of Dakota supply the most wonderful power on the globe. The stupenduous unutilized, and to a great extent, unavailable power of mighty Niagara must pale in compari- son with the power of Dakota's artesian wells. 79 Here no special mill site must be chosen and then pur- chased of the owner at his own figures, for every inch of our broad domain is as good a mill site as there is on the earth. The ground here has but to be opened in order to pour forth the flood which will serve not one purpose alone but many. Power, domestic use, fire protection, irrigation, and even heat are but the chief among the many duties to which a well may be called. More there are which will soon find a place in the every day economy of Dakota life; and all com- bined will soon be the chief factors in making this the won- derland of America. Every well owner who can afford it should have a motor, for with it much labor of the farm may be performed. A very small expense, added to a little ingenuity and home la- bor, will harness the churn, the feed mill, the fanning-mill, the feed-cutter, the threshing machine, the grindstone and other farm machines to the motor and thus save a vast amount of labor, expense and even life itself. Any farmer will appreciate the great advantage of having his threshing done by water power instead of by steam power, in which latter case there is the constant danger from fire and explo- sion. All these things will come, in time, for Dakota's farmers are too enterprising to long delay the utilization of the forces thus gratuitously laid at their feet. Lack of means is the only obstacle to the proper utilization of that which, ere long, will transform Dakota into the most productive, prosperous, wealthy, and wonderful agricultural region in this or any other land. Nor will capital long hold back when it has been fully assured 01 the successes already achieved by the pioneers in the field of irrigation and the development of artesian pow- er. No more profitable investment can be found to-day than such as is made in Dakota lands on which wells are placed, or in the development of this inexhaustable power that flows not to wreck and to ruin but to fructify and enrich. It becomes, then, the duty of every lover of Dakota to her- ald the great truths (unembellished by any exaggerations) as to the wonderful possibilities that we ourselves have but just begun to appreciate. The ear of capital will be reached if we but call long and loudly, and when reached the means will cease to be the ob- stacle to success which now awaits us. On page 81 will be seen the reports of some of the millers of the state as to the service rendered them by artesian wells. In the face of such facts no argument need be given to prove the great value to Dakota of this great source of power. The reports are from points widely separated which shows the extent of the field. 80 TABLE FOR CALCULATING THE HORSE POWER OF WATER. The following table gives the horse power of one cubic foot of water per minute under different heads. TABLE NO. 32. Adapted from Peltou \Vatr \VlxM-l ( '<>, Heads in feet. Pressure per Horse Sq. inch, Ibs. Power. Heads in feet. Pressure pir sq. inch, Ibs. Horse Power. 1 .43 .001609S 310 134- .49903S 20 8.66 .032196 320 138 .515138 30 . 12.99 .048294 330 143 .531234 40 17.32 .064392 340 147 .547332 50 21.65 .080490 350 152 .563430 60 25.99 .096588 380 156 .579528 70 30.32 .112686 370 160 .595626 80 34.65 .128784 380 164 .611724 90 38.98 .144X92 390 169 .627X22 100 43.31 . 160980 400 173 .643920 110 47.64 . 177078 410 178 .660018 120 51.98 . 193176 420 \^2 .676116 130 56.31 .209274 430 186 .692214 140 60.64 .225372 440 191 .708312 150 64.97 .241470 450 195 .724410 160 69 31 .257568 460 199 .740508 170 73.64 .273666 470 204 .756606 180 77.97 . 289764 180 206 .772704 190 82.30 .305862 490 212 .788802 200 86.63 j .321960 500 216 .804900 210 90.96 .33,SO:> ( s 520 22r> .837096 220 95.30 .354156 540 231 869292 230 99.63 ; .370254 560 243 .901488 240 103.90 .3*6352 580 251 .9:53684 250 108.29 j .402450 600 200 .965880 260 112.62 ! .418548 650 282 1.046370 270 116.96 .434646 700 303 1 . 126S60 280 121.29 .450744 750 325 1.207350 290 125.62 .466842 800 346 1.287840 300 129.95 .482940 900 390 1.448820 When the Exact Head is found in the Table. EXAMPLE Have 100 foot head and 300 cubic feet of wa- ter. How many horse power have I ? From table H. P. for 100 ft. head =.160980 for 1 cu. ft. of water, hence .160980x300=48.294 the H. P. for 300 cu. ft. per minute. From table 3(5 we find that 300 cu. ft.=2244 gallons. If a well having a flow of 2244 gallons per minute will, while throwing that amount, show a pressure of 43 Ibs. per inch (=100 ft. head) then it will develop 48.29 effective horse power. When Exact Head is not found in the Table Take the H. P. of 1 cu. ft. under 1 foot head and multiply by the number of ft. head given, then by the number of cu. ft given. The product will be the required H. P. NOTE The table is based upon an efficiency of 85 percent. Note the fact that a well shows no pressure, or head, when discharging its full volume. Turn it off a little so as to get some pressure, then meas- ure volume and proceed according to above table to calculate the power. See page 82. 81 WOOXSOCKET MILL. Northy and Duncan of the Woonsocket mill report as fol- lows: Our well is 775 feet deep; 7 inches in diameter all the way; pressure 135 Ibs. when closed; 62 Ibs. with a 4-inch opening, 75 Ibs. with a 3-inch opening. We use a 3 foot PEL-TON wheel, Tunning at 275 revolutions per minute, the nozzle throwing a 1% inch stream. Wahave made 88 bar- rels of flour and 36 tons of good feed per day of 24 hours, and we figure on a saving of from $14 to $17 per day as com- pared with steam power of equal service. The element of safety being worth much that cannot be expressed in figures. SPRINGFIELD MILL. Mr. J. J. Kattleman of the Springfield mill reports as fol- lows: Our well is 593 feet deep, and 8 inches all the way. The pressure, when closed, is 80 Ibs., and when mill is run- ning it is 40 Ibs. We use a 16-inch turbine wheel, making about 800 revolutions per minute. The well cost $3,000, but could be drilled for less now. We put out about 60 barrels of flour per day, and figure on a saving of from $12 to $15 per day as against steam power. This item alone being a handsome profit or interest on the cost of the well. Repairs are very light and insurance much less than with steam. We get over 42 horse power from the well. YANKTOX-"FOUNTAIN" AND "EXCELSIOR" MILLS. Mr. E. Miner of the Fountain Roller Mills of Yankton says : Well is 600 feet deep, 6 inches in diameter, pressure from 48 to 56 pounds per inch, and flows from 1600 to 2000 gallons per minute. We use a Dubuque turbine wheel 12 inches in diameter and of guaranteed 27 horse power. The cost of the power plant, complete to run, was about $4,000. We pay 3 per cent insur- ance and would pay 4V or 5 if running by steam. I think we are paving over $8 per day as compared with an engine. Our mill is one of 40 barrel capacity. F. L. Van Tassell of the Excelsior Mill Co., says : Our well is 500 ft. deep, pipe 8 inches to the bottom; pressure when closed 52 Ibs., with 1 inch opening 48 Ibs., with 2 inch opening 42 Ibs., with 4 inch opening 20 Ibs. ; water clear and hard. We use a PELTON wheel 6 feet diameter with 23 inch nozzle, revolutions, 125 per minute. Power about 30 horse. We run our elevator and raise about 500 bushels of wheat per hour, shell 100 bush- els of corn and grind 4000 Ibs. of feed per hour. Will soon attach all the mill machinery to the well. The well flows 3000 gallons per minute, and, with wheel, power house, etc.. cost about $4,000. Cost of running it prac- tically nothing, so saving per year as compared with steam power is very great. HITCHCOCK MILL. Mr. M. B. Potter of the Hitchcock Milling Co., says : Size of well 4 inches at top. 3 inches at the bottom. Depth 960 feet. Volume 1240 gallons per minute. Pressure when closed 155 pounds. With 1 inch opening 140 pounds. With 2 inch opening 82 pounds. W T e get about 30 horse power from a wheel of our own design, it being 50 inches in diameter and runs at about 300 revolutions per minute. The well cost the town $4,500. We have had no expense for repairs since putting in the wheel in June, 1890 nearly 3 years. The mill has a capacity of 50 barrels in 24 hours. Be- sides running the -mill the well supplies water to the town, maintains water in an artificial lake, and waters an irrigated farm. The well has been running since 1886 and the volume is invariable and apparently inex- haustible and the pressure is uniform. 82 HOE8E POWER. A horse power issuch a power as will raise 83,000 pounds one foot high in one minute of time. The term is one of mechanics and does not fairly represent the power of the average horse which is only about two-thirds as much. To calculate the horse power of falling water multiply to- gether the number of cubic feet of water falling per minute, the vertical distance (head) through which it falls, and the number 62.3 (approximate weight of 1 cubic foot of water) and divide the product by 33000. EXAMPLE A well discharges 800 cubic feet per minute from a pipe 16 feet above the surface, what is the horse power of the well V 80Qcu.ft.Xl6ft.X62.31bs, 797440 *e, _ -24.17 H. P. This is the theoretical H. P. The actual H. P. as realized from machinery will be less because the wheel or motor does not realize the full efficiency of the water. The per- centage of efficiency realized will depend on the form of the wheel and the skill of the makers. It will range from 25 to 90 per cent, of the full power. Turbine wheels realize from 75 to 85 per cent, of the power and impact wheels about the same amount. The table on the next page will prove of value in this con- nection. TO GET THE VELOCITY OF THE FLOW OF A WELL. If the volume has been accurately measured. Divide the volume of the flow, in gallons, by the volume in gallons contained in one foot of the pipe of the well (the area of the cross section of the pipe). The answer will be the velocity in feet per minute. Thus Suppose a 6-inch well throws 1836 gallons per min- ute, what is its velocity of discharge in feet per minute ? From table No. 26 we see that 1 foot of 6-inch pipe con- tains 1.469 gallons. How many feet, therefore, will it take to hold 1836 gallons ? 1836-^1. 469 =1250= the number of feet necessary to hold 1836 gallons, or the length of the column of water thrown out each minute, or the velocity in feet per minute. 1250-^-60=20.8, the velocity in feet per second. This is the same as the rule for finding the velocity of any stream, viz: Divide volume per minute by area of section to get velocity per minute, and divide this quotient by 60 to get velocity per second. To Compute the Volume of Discharge per Minute. RULE Multiply the area of the wet section in sq. ft. by the velocity in feet per second to get volume in cubic ft, per sec. Multiply this product by 60 to get the volume per min. To Compute the Height of the Head in Feet. RULE Divide the volume in cu. ft. per second by the area, and the square of this quotient, divided by 64.33, will give the height of the head in feet. 83 TABLE NO. 33. TABLE SHOWING FLOW PER MINUTE EQUAL TO A GIVEN FLOW PER DAY AND TOTAL FLOW PER DAY FROM A GIVEN FLOW PER MINUTE. New. Total gallons perj Equal gallons ij Gallons per Equal gallons per (lay. per minute. minute. day. 100 .07 .1 144 200 .14 .2 288 300 .21 .3 432 400 .28 .4 576 500 .96 .5 720 600 .42 .6 864 700 .49 .7 1008 800 .56 .8 1152 900 .63 9 1296 1000 .7 1. 1440 2000 1.4 2. 2880 3000 2.1 3. 4320 4000 2.8 4. 5760 5000 3.5 5. 7200 6000 4.2 6. 8640 . 7000 4.9 7. 10080 I '' ; 8000 5.6 8. 11520 \ 9000 6.3 9. 12960 \ O 10000 25000 6.9 17.4 10 25 14400 36000 ^t 50000 34.8 50 72000 ^.N 75000 52.2 75 108000 100000 69.5 100 144000 200000 138.9 200 288000 300000 208.3 300 432000 400000 277.8 400 576000 500000 347.2 500 720000 600000 416.7 600 864000 700000 486.1 700 1008000 800000 555.6 800 1152000 900000 625.0 900 1296000 1000000 694.5 1000 1440000 2000000 1388.9 2000 2880000 3000000 2083.3 3000 4320000 4000000 2777.8 4000 5760000 5000000 4372.2 5000 7200000 6000000 4166.7 6000 8640000 7000000 4861.1 7000 10080000 8000000 5555.6 8000 11520000 9000000 6250.0 9000 12960000 10000000 6944.5 10000 14400000 This table will be most convenient in making quick com- parisons as between different wells in Dakota and those elsewhere where, as a rule, the flow is reported as so much per day while in.Dakota the flow is always so much per min- ute. The greatest wells outside of Dakota are those of Kern Co., California, which flow from 150,000 to 4,000,000 gallons per day or (see table) from 104.3 (69.5 + 34.8) to 2,777.8 gallons per minute. Of their 54 wells only 10 flow over 1,200,000 gal- lons per day or 833 4 gallons per minute. This table shows at a glance the superiority of the Dakota wells. Example of use of table. How many gallons per minute flow from a well throwing 5,359,800 gals, per day ? Add the quantities in 2d. column 3,472.2 + 208.3 + 34.8 + 6.3+ .56 3,722.16 gallons per minute. 84 85 By interpolation other quantities may be readily taken from the foregoing table ; thus To cover 10 acres 8% inches deep, Multiply 36,300 (amount for 1 inch) by 8 = 290,400 and add J of 36,300 " " " '" = 18,150 Total = 308,550 cu. ft. Where the required acres and the required depth are neither one in the table as Required the cu. ft. to cover 17 acres 7 inches, proceed thus Take out quantity for 1 acre and multiply by the given number of acres. Thus To cover 1 acre 6 inches 21,780 " 1 " 1 inch 3,63G " 1 ' 7 inches ,25,410 25,410 x 17, the given number of acres = 431,970 cubic feet, OB if the inches cannot be taken from the table as in above case multiply the amount for one inch by the given number of inches, Thus, amount for 11 inches = 3630 (amount for one inch) x 11 = 39,930 cu. ft. The volume in gallons may be found by multiplying the total cu. ft. by 7.48052, the number of gallons in one cu. ft. or by interpolation from Section B. How many gallons in 308,550 cu. ft. (amount to cover 10 acres 8J^ inches deep) ? From Section B. we find 3,258,500 as gals, to cover 10 acres 1 foot or 24 half inches; 8) inches = 17 half inches, therefore, divide 3,258,500 by 24, to get amount for one half inch, and multiply this quotient by 17 to get gals, for 17 half inches. OR see table No. 36 The time required for a well of given volume per minute to throw any given quantity of water is found by dividing the total volume by the volume of the well per minute and then reduce the number of minutes thus found to hours, days, weeks, &c. or If the quantity is given in the foregoing table take out the time from Section C. or, if the quantity is not given in the table proceed as in the following. Example: 9 inches deep on 100 acres from a 500 gal. well will take 2,178,000 cu. ft. = 6 inches. ) 1,089.000 " " = 3 " 3,267,000 cu. ft. = 9 inches. J .__ 32,585,000 = gals, on 100 Ac. 1 ft. deep A n (Sec. B.) divided by 12 = 2.715,417 X 9 A = 24,438,753 = gals, at 9 inches. From Section C we find it takes a 500 gal. well 1 mo., 15 ds., 6 hrs., to cover 100 acres 12 inches deep, or 1,086 hours. Since 9 = 3 of 12 take 2 of 1,086 hours = 813 hours or 33 days and 21 hours. Ans. From table 35 (next page) an approximation may be quickly taken. Thus, under head of 500 gal. well we see 21.600,000 = gals, thrown in 1 mo. and 720,000 = gals, in 1 day. 720.000 X 4 = 2,880,000 gals, which added to 21,600,000 gals. = 24,480,000 gals, in 34 days, or a little more than our esti- mated amount of 24,438,753 gals. From this it is shown that the amount will be thrown in a little less than 34 days (33 ds. 21 hours as above.) For exact amounts and times one should figure exactly which may be done from the tables by using a few more figures. 86 CM -M o o 5~ ct c . Bid > o o o Is -3,0 r ^ c3 O w S o g S 2 86619 10 432000 57748 1 s?96 000 173244 20 864000 115 497 2592000 346 491 25 1080000 144 373 3 240 000 433119 30 1 296000 173 247 3888000 519 741 40 1728000 230996 5184000 692988 50 2160000 6480000 866 235 60 2592000 346 495 7776000 1 039 485 70- 3024000 404244 9072000 1 212 732 80 3 456 000 461 993 10 868 000 1 385 979 90 3888000 519 743 11 664 000 1 559 229 100 4 320 000 577 492 12 960 000 1 732 476 200 8640000 1 154 986 25 920 000 3464958 300 12 960 000 1 732 479 38 880 000 5 197 437 400 17 280 000 2 309 972 51 840 000 6 929 916 500 21 600 000 2 887 466 64800000 8662398 600 25920000 ' 3464959 77 760 000 10 394 877 700 30 240 000 4 042 452 90720000 12 127 356 800 34560000 4619945 103 680 000 13859835 900 38880000 5 197 439 116 640 000 15 592 317 1 000 43200000 5 774 932 129 600 000 17 324 796 1100 47 520 000 6 352 425 142 560 000 19 057 275 1 200 51 840 000 6 929 919 155 5 000 20 789 757 1 300 56 160000 7507411 168480000 22 522 233 1400 60 480 000 8 084 905 181 440 000 24 254 715 1500 64800000 8 662 399 194 400 000 25 987 197 1600 69120000 9 239 891 207360000 27 719 673 1700 73440000 9 817 385 220 320 000 29 452 155 1800 77760000 10 394 878 233280000 31 184 634 1900 82080000 10 972 372 246 240 000 32 917 116 2000 86400000 11 549 865 259 200 000 34 649 595 2100 90720000 12 127 358 272 160 000 36 382 074 2200 . 95040000 12 704 852 285 120 00') 38 114 556 2300 99360000 13 282 344 298 080 000 39 847 032 2400 103680000 13 859 838 311 040 000 41 579 514 2500 108000000 14 437 332 324000000 43 311 996 3000 129600000 17 324 798 388800000 51 974 394 3500 151 200000 20 212 264 453600000 60 636 792 4000 172 800 000 23 099 731 518 400 000 69 299 193 4500 194400000 25987197 583200000 77 961 591 5000 216000000 28 874 664 648000000 86 623 992 5500 237600000 31 762 130 712 800 000 95 286 390 6000 259200000 34 649 596 777 600 000 103 948 788 7000 302400000 40 424 529 907200000 121 273 587 8000 345600000 46 199 562 1 036 800 000 138 598 686 9000 388800000 51 974 395 1 166 400 000 155 923 185 10000 432000000 57 749 328 1 296 000 000 173 247 984 See explanation on opposite page. 89 The table on opposite page is an extension of table on page 86, but changed to give two periods or* time and wells of a greater range of volume per minute; and giving the volumes in both gallons and cubic feet. The irrigation season lasts about three months and is preceded in the spring and fol- lowed in the f 11 by about equal periods of time, so that one month and three months are the periods assumed to be those upon which the greater number will desire to base estimates as to the volumes they can count on during these periods. By simple addition the volume of any well may be taken from the table. EXAMPLE What volume will a well with a volume of 3572 gals ; per min- ute throw in 3 months? 3000 gal. weU = 388,800,000 gals. 51,974,1394 cu. ft. 500 " " = 64,800,000 " - 8,662,398 " 70 " " = 9,072.000 " 1,212,732 2 " " = 259,200 " - 34,650 " 3572 " " 462,931,200 61,884,174 Having the amount for 3 months, the amount for any lesser or greater time may be found by division or addition. Thus: In above example the well, in 40 days, would throw +=(30 ds.+lO ds.) of the total amount or volume shown; or in 4J months a well would throw, total +-f-r=(3 Mo.+l Mo -\-% Mo) of the total volume shown. The table will be found useful for taking out rapid approximations as to volumes and in this will answer the purpose of the proceeding table table 37 thus, by inspection it is shown that a reservoir holding about 36,000,000 cu. ft. holds about 272,000,000 gals, and that a 2100 gal. well would be required in order to fill it in about 3 months. TABLE NO. 38. DISCHARGE OF JETS IN GALLONS PER MINUTE. Head on Jet in Pounds. Head on Jet in feet. Discharge from Jets of following diameters. X 1 inch. IK 1J4 1% Itt 20 46.16 70.4 125.2 158 196 237 282 25 57.70 78.7 140.0 177 219 265 315 30 69.24 86.3 153.4 194 240 290 345 40 92.32 99.6 177.1 224 277 335 398 50 115.40 111.4 198.0 251 309 374 445 60 138.48 121.9 216.8 274 339 410 488 70 161.56 131.8 234.3 297 366 443 527 80 184.64 140.8 250.3 317 391 473 563 90 207.72 149.4 265.6 336 415 502 598 100 230.80 157.5 280.0 354 437 529 630 110 253 88 293 6 372 459 555 661 120 276.96 306.7 388 479 580 690 130 300 04 319 2 404 499 604 718 140 323.12 1531.2 419 518 626 745 150 346 20 434 536 649 772 160 369 28 448 553 670 797 170 392.36 570 690 823 180 415.44 710 845 This table is calculated from the formula given on page 73 except that H. (head) in feet is taken at 2.308 ft. per pound of head instead of 2.311 as given. The difference is not material. 90 WIND MILLS. The following tables are from a circular issued by the U S. Department of Agriculture, office of Irrigation Inquiry. TABLE NO. 39. SIZE AND CAPACITY OF WIND MILLS AT VARIOUS DEPTHS. Diameter of wheel in feet 25 ft. Eelevation. 50 ft. Elevation. 100 ft. Elevation. Size of pump in in. Gallons per hour. Size of pump, ins. Gallons per hour- Size of pump,ins Gallons per hour. 10 12 14 16 3y 2 4 5 6 500 750 1150 1500 3 8H 300 500 800 1200 2 1 / 2 3 3K 200 350 550 800 This table is only intended as a general guide and is subject to modifi- cation by reason of some mills having greater capacity, for given size, than other mills ; and the same applies to the pump used and the manner of attachment. TABLE NO. 40. VOLUME OF WATER PUMPED PER MINUTE. From 10 to 100 Feet. Diameter of wheel Vertical distance from water to point of delivery, in feet. 10 15 25 50 75 100 Feet 8.5 10 12 14 16 18 20 25 30 Gallons 15.24 48.26 86.71 111.67 155.98 249.93 309.60 532.52 1080.11 Gallons 10.16 32.18 57.81 74.44 103.99 159.95 206.40 355.01 728.83 Gallons 6.16 19.18 33.94 45.14 64.60 97.68 124.95 212.38 430.85 Gallons 3.02 9.56 17.95 22.57 31.65 52.17 63.75 106.96 216.17 Gallons Gallons 6.64 11.85 15.30 19.54 32.51 40.80 71.60 146.61 4.25 8.49 11.25 16.15 24.42 31.25 49.73 107.71 VELOCITY OF WIND. - The average over the U. S., as determined by signal service examina- tions, is 5769 miles per month, or about 8 miles per hour. See page 91 ~table of wind velocity in Dakota . Experience has demonstrated that to operate a wind mill, there is required an average velocity of wind of 6 miles per hour. TABLE NO. 41. VELOCITY AND FORCE OF WIND.- Miles per hour. Feet per minute. Pressure per sq. ft. inlbs. Description of the wind. 1 to 3 6 88264 440 .005 .045 .125 Just perceptible Pleasant wind 10 880 .5 Fresh breeze 20 1760 2. Stiff breeze 30 2640 4.5 High wind 45 3960 10.125 Gale 60 5280 18. Great storm 80 7040 32. Hurricane 100 8800 50. 1 Tornado The mean weight of the air will support a column of water 33.95 ft. high, at sea level. The velocity of sound in air at 60 = 1107 ft. ,in water about 49,000 ft. per second. 91 TABLE NO. 42. WIND IN DAKOTA. Average daily and hourly Wind Velocity for 9 years from 1882 to 1891, inclusive, at Huron, S. D., by Sam. W. Glenn, U. S. Weather Bureau. Month. Average daily velocity, miles. Average hourly velocity, miles. January 232.5 9.7 February 242.6 10.1 March 239.9 1U.O April 274.8 13.1 May 265.7 11.1 June 238.6 9.9 July 220.2 9.2 August 217.5 9.0 September 254.0 10.6 October 244.7 10.0 November 227.0 9.5 December 224.2 9.3 Average hourly velocity for 9 years = 10.1 miles. TABLE NO. 43. KAIN IN DAKOTA. Total Rain Fall by months as recorded at Huron, S. D., from 1881 to 1*92 by S. \V. Glenn, L). S. Weather Bureau. Year. Jan Fob Mch Apr. May June | July I Aug. i Sep. Oct. Nov. Dec. Tot'l ISM 1 3.58 6.31 3.11 2.10i .45 .06 1882 .14 .25 .80 4.18 4.50 5.86 5.83 1.44 .86 3.:57 .61 .23 28.12 1883 .17 .47 .42 2.14 4.45 4.33 5.20 1.77 1.68 1.96 .05 .61 23.25 1884 .09; .581. 53 2.70 2.90 3.18 5.11 1.18 1.26 1.52 .17 .62 20. s4 1885 .15 .22 .12 1.06 5.20 5.43 4.52 3.M) 2.61 .98 1.50 .10 25.78 1888 .48 .16 .62 3.52 1.58 1.90 1.60 5.62! 1.59 1.26 1.18 .74 20.25 is>7 .: 1.11 .64 3.72 1.88 8:W 4.96 6.13 .15 .79 .25 2.09 25.54 1888 .78 .52 1.22 .88 4.98 1.10 3.11 3.46 .19 .29 .34 .18 17.05 1889 1.28 .93 .19 3.41 3.04 1.04 3.51 .68 3.89 .55 .16 1.53 20.17 1890 .66 .18 .32 .64 2.88 5.87 1.41 .73 .32 .61 .38 .68 14.68 1891 .07 1.32 1.64 3. 45 .44 8. OS 1.01 1.43 .47 .78 .94 .54 20.17 Mean .41 .57 .72 2.57 3.14 4.03 | 3.63 2.96 1.46 1.29 .55 .67 21.58 1892 | .28 .70 | 1.11 | 5.90 | 6,03 | 4.00 Total in 6 months=18.02 . Read carefully the note on the next page with reference to this table. Read it twice and don't forget it. PRECIPITATION FOR FIRST 6 MONTHS DURING THE FOLLOWING YEARS. I 1882 11883 1884 15.73 11.98 10.98 12.08 8.26 1887 11.16 9.48 9.87 1891 1892 Av'g 10.55 15.00 18.02 12.10 (See also table No. 14.) 92 NOTE As to precipitation table No. 43. This table of rain-fall has much interest as it shows the distribution and amount of our rains by months and years. 1882 was Dakota's "boom" year in rain-fall, as in other re- spects, and was the most bountiful on record in consequence. 1883 '85 and '87 were good years, while 1888 '89 and '90 were years of almost total failure. It will be of special in- terest to note that 1889 and 1891 have exactly the same total rain-fall; whereas 1889 was a year of drouth and failure, while 1891 was a year of phenominally good crops. Note further that the record of 1891 followed a record of but 14.68 in 1890; whereas the equal record of 1889 followed a record of 17.08 for 1838, so that, so far as the records for the two-year periods are concerned, the period of '89 and '90 ought to have shown better results than the period of '90 and 91. Note still further that the rain-fall of 1889 for the months from January to July was but 13.36 inches out of the total of 20.17; whereas in 1891 the rain-fall for these months was 16.01 out of the total of 20.17. Herein, then, lies the secret of the good year 1891 during the growing months of 1891 there was a rain fall of 2.65 inches greater than during these months of 1889 the totals for the two years being the same. In 1889 the rain came too late, while in 1891 it came in the proper season . A valuable lesson may therefore be drawn from the table it is, that the 2 or 3 inches of timely rain in 1891 saved Da- kota from a fourth year of failure, and enriched the people at the rate of OVER $5,000,000 PER INCH. There is the record! There is the lesson! From this draw the further lesson as to the true value of the water of a well the distribution of which you have in your absolute control both as to the quantity and the time when it shall be used. If this lesson alone is well learned by a few then will that one table have made this little book well worth the cost of publishing. First Last Temperature. Days Year Frost Frost Highest Lowest Clear. Fair Cloudy Rain *1881 Sept 15 95 6 6 62 81 41 66 1882 " 20 May 22 93.7 -20 113 171 i 81 96 1883 1884 1885 July 17 Sept 11 April 30 May 13 June 8 99.2 95.9 98.2 32 -38 33 110 139 129 168 155 164 87 72 72 115 111 95 1886 Aug. 31 May 6 103.6 33 121 180 64 118 1887 1888 Sept. 15 ' 3 < 18 99.2 101.7 43 -36 130 141 162 142 73 83 114 95 1889 " 5 ' 2 104.0 30 133 143 89 92 1890 Aug. 22 1 15 103.0 -28 151 150 64 90 1891 ' 23 ' 16 97.0 24 135 136 94 92 Records from Huron, S. D., Signal Station. *From July 1st 1881. 93 TO MEASURE THE HEIGHT OF A STREAM. The following method will enable any one to easily and quickly measure the exact height of the stream thrown out by a well, without the use or instruments or of tables of tangents. Referring to figure 11 let W be a well and EF the stream thrown. Carefully measure off a distance of say 100 feet and drive a stake 8, to the level of the pipe if possible. Drive another 3 or 4 feet nearer and across the top nail a piece of board B; which set level. Measure off AC = 5 feet (or any other amount) and nail the stick H to this mark, and at right angles to AC. Now look over the point of the board at A and have some one mark on the stick H a point D in line with E the top of the stream EF. Measure the length CD, then may the height EF be found by simple proportion. Example. AF = 100 ft. AC = 5 ft. CD = 4 ft. then, AC : AF : : CD : FE or 5 : 100 : : 4 : (required height) 100 x 4 = 400, 400 -s- 5 = 80 ft. = height of stream EF. If the horizontal line AF will not strike the top of the pipe, as at Y, measure the distance YZ and subtract it from the total height found. Although a rough method it is an easy one and sufficient accuracy may be obtained. If this is done by all wells, while throwing streams of different sizes, and a record made of the results it will be a vast improvement on the guess-work so freely indulged in heretofore. Fig. 11. Method of measuring height of a stream. e 4' & /op' (See also page 147.) 25 Xongitufle West 23 f- - From Harper's Magazine. Copyright, 1889, by Harper & Brothers. FIG, 12. WEATHER MAP OF NORTH AND SOUTH DAKOTA. By permission of Messrs. Harper & Brothers. Showing isothermal lines and areas of varying-rainfall. It will be seen that nearly all of the agricultural section of both states has a range of rainfall of from i$ 20 inches. This area should extend farther to the South than shown on the map. Harper's Magazine. Copyright, 1889, by Harper & Brother*. Fi g. 13- View of Brick- Yard Well at Yankton, S. D. From photograph by L. Janousek, Yankton. By permission of Harper and Brothers. Depth = 595 feet. Size of pipe = 6 inches. Pressure = 48 to 57 Ibs. per square inch. Volume = 1620 to 2000 gallons per minute. Location, on top of the Missouri river bluffs. Use, for power. Cost, about $3,000. The view as taken showed the well throwing a 6 inch stream about 6 feet above the top of a 20 foot stand-pipe. This well is one of a number of large wells in the southern portion of South Dakota having a compara- tively low pressure and very large volume. 96 RESERVOIRS. In the western states where irrigation by water taken from streams is the rule, and irrigation by well waters the excep- tion, the waters are, in most cases, impounded at some place near their head waters where the topography is such as to admit of the construction of a dam which will create a res- ervoir in the valley wherein are stored the waters of the freshet season for use, many miles away, during the season of drouth. {Such vast engineering works can only be entered upon by corporations possessing vast capital, for, in some cases, the dam, with flumes and ditches to convey the water to the irrigated districts, has cost over a million dollars. The general government has already provided for the lo- cation, survey and reservation of all sites on the public do- main where dams and reservoirs may, to advantage, be lo- cated in the future, and wise restrictions have been thrown around corporations securing such sites so as the best to pro- tect the individual comsumers from corporate exactions Vast tracts of the finest land in the world lie undeveloped and barren because the necessary capital has not yet been found to improve it by flrst constructing a dam and creat- ing a reservoir for the storage of the necessary water. IN DAKOTA how different is all this? There is not in the state a reservoir site worthy of the name and no money need be expended on great engineering works for the storage of water. Nor is there a stream that can, to advantage, be dammed. The Dakota reservoir will rarely if ever exceed 10 acres in area and in place of one cov- ering many miles there may be several small ones on one mile. When artesian irrigation was lirst agitated it was the popular belief that the well waters might be run directly into the ditches and thence distributed; but no thought was given to tlie fact that thereby the service of a well of but moderate volume would be very limited, for the water flow- ing within any given time would be insufficient, within that time, to cover any considerable area. If, however, the waters could be stored in a reservoir dur- ing such periods as it was unnecessary to apply any to the land then when water was needed over a broad area, and within a brief period of time, the accumulated store could be made to do service which the well alone could not do in the same time. The necessity for small storage reservoirs being thus apparent they become as much a part of every irriga- tion plant as the well itself. In fact if the land under ser- vice of any particular well is quite rolling it may, and in many cases will, be necessary to have two or more small res- ervoirs on the farm in order to secure the best service to the land and the most economical storage and distribution. Reservoirs being necessary, how and where shall thev be built? 97 LOCATION. The highest points will, of course, be the natural sites for reservoirs but the land may lay so as to make it not only better but cheaper not to locate the reservoir on the highest point. Such cases will be few and the conditions in mind will in all such cases be apparent to one on the ground. If a tract of land is divided into two or more parts by a gully or depression of any extent it may be. best in such case to have two or three smaller reservoirs, one on each tract or division of the land. If but one large reservoir were built the other tracts or elevations would have to be served from flumes which would be larger and more expensive than one sufficient to feed the reservoir alone, and they might, at the critical time, fail to do proper service by reason of adverse winds or other causes thereby causing more loss than a reservoir would cost. In ordinary cases the proper site for a reservoir may be se- lected by a farmer without the aid of an engineer but where any doubt exists as to the choice of locations then no chances should be taken and the services of one competent to judge should be secured. FORM. In most cases the circular form will be adopted because the greatest area is enclosed by a given amount of bank. Occasional departures from this form will be necessary by reason of the lay of the land. Only the cicular form will be considered in the tables. SIZE. The matter of size will, in a few cases, be governed by the land but, as a rule, the service to be rendered by the waters stored will govern. If a township well is to be provided with storage then the volume of the well should be deter- mined in order to know how small a reservoir would suffice not only to give service to the area to be irrigated but also to hold all the water the well will supply within the longest time it could be permitted to run without allowing the wa- ter in the reservoir to be drawn off. This would give all the necessary storage capacity without any waste of money in making it larger than needed. Since most wells throw over 500 gallons per minute the time of impounding could not be long except with a very large reservoir. Table No. 37 taken in connection with ta- bles 47 and 48 will quickly supply all needed information in this connection. From them it will be seen that a 500 gallon well will fill a 10-acre reservoir seven feet deep every 30 days, &c., &c. Where, as in case of a township well which will be used to serve several farmers, the volume used will be large the storage capacity should be as large as economy will war- rant and each consumer might to his own advantage be sup- plied with a sub-reservoir. In case of special-service or sub- reservoirs which are designed to serve only a limited area as for example, a knoll of 10 or 15 acres then the water to be 98 used on that area alone should be estimated and storage area provided only sufficient for that volume, allowance being made for seepage, evaporation and waste. Thus, assume a field of 10 acres to be supplied by a sub-reservoir and volume sufficient provided to flood the land 6 inches; what would be the size of reservoir required if the water be given a depth of 5 feet in the reservoir V Table 34 or table 21 gives the cu- bic feet of water required to flood 10 acres 6 inches deep as 217,800. Table 29, under head of water 5 feet deep, shows at a glance that a reservoir of 1^ acres will hold this volume and enough more to cover all waste. Table 45 gives the diameter, circumference and area of this reservoir. These suggestions will show the importance of duly con- sidering the elements of volume of well, time it may flow, area to be served, &c., in the laying out of a reservoir for either general or special service. The depth of water in the reservoir will always enter into the consideration. Where any considerable volume is required it will be best to have the depth in excess of 4 feet, first, because if the wa- ter is deeper the reservoir will occupy less ground for a given capacity; second, the evaporation will be less, the exposed area being less, and the waste from seepage will be less; third, the wash of the banks will be less because the wind will have less sweep over the surface. Table of sizes. Table No. 45 shows the diameters, circumferences, and areas in sq. ft. of reservoirs from % acre to 10 acres, for each % acre, and explanation follows as to calculating the elements for otht r sizes. LAYING OUT. The size haying been determined the staking out follows. If the reservoir is to cover a given area the whole bank will be within that area and the foot of the outer slope will bound the given area. If the area is to exclude the bank the foot of the inner slope will bound the area. If the water is to cover a given area then the high water line or the point half way down the bank therefrom will bound the given area. Or the area may be bounded by the center line either of the whole bank or of the top of the bank. Usually these considerations will not be of much import- ance, but in case of joint ownership or of contracting for the construction they may be important and should then be clearly understood and carefully specified . In staking out it will be best, for the convenience ot graders, to drive stakes on the outer and inner lines of the bank. The line of the top follows as a result of the slopes. The measurement may be made with a measured wire one end of which is fastened or held at the center while the outer end is carried around and stakes driven at convenient distances along the circle. If wire cannot be had then rope or even binding twine will answer the purpose. If the land is uneven or covered with stubble, corn stalks, growing grain or other obstructions which prevent swing- ing the wire or line around the center point then two per- sons may manage the wire or line as follows. A holds one end at the center while B drives stakes at the north points; (At both the inner and outer slopes of the banks.) both then walk south across the circle until B reaches the center when A drives the south stakes; they then walk back, B turning a little to the east or west, until A comes again to the center while B drives stakes at the outer end; A then, as before, walks straight across the circle and drives other stakes. Repeat this until the circuit of the circle has been made and all the stakes set . The result is the same but the walking a little more. Any farmer can thus lay put his own reservoir, if need be, in an hour's time and do it as well as it could be done by an engineer at an expense to the farmer of $5 to $10. The outlines having been staked out, and the stakes numbered, the levels should be taken to determine the height of the bank at each stake. If the ground is not fairly level the stakes will have to be set in or out to give the proper base line according to the length of the slope. Where the ground is comparatively level any farmer can do his own leveling not only for reservoirs but for ditches, but where it is rolling the services of an engineer should be secured as a measure of economy. Better to pay for having the work properly done by responsible parties than to do it wrong and then be obliged to have it done over again. See notes on leveling, page 128 and following pages. THE BANKS. The banks should be constructed of as firm earth as pos- sible in order to give strength and prevent percolation and washing, and they should be thrown up by drag scrapers which results in a more solid and firmly packed bank than can be made by the use of wheel scrapers or graders unless the work with the latter be properly done. (See embank- ments and footings under head of Ditches.) The outer slope may be one of 1^ horizontal to 1 vertical. The breadth of the top will depend upon the height and strength required. Most reservoirs will be 9 feet or less in height and for such heights a width of top of 5 feet will be suffic- ient. Where the bank exceeds 9 feet in height an additional foot in width may be added for each 2 feet of additional height, the slopes remaining the same. Fig. 14, on the next page shows in sectional diagram the inner slopes of banks from 1 ft. to 14 ft, high and with slopes of 2 to 1. The horizontal lines indicate the water levels and the diagonal lines the slopes of the banks. The upper horizontal line of figures indicate the distances of the foot of the banks from the top (measured horizontally ;) and the lower line of figures the amount the diameter of the reservoir is reduced by banks of the different heights. Thus, if the bank is 8 feet high and the water 4 ft. deep the shore line will be at A and the area of the water sur- face will have a diameter 21 feet less than that of the reservoir (measured 100 :> center line of top.) To get the volume, take the diameter half way own the bank, at C, which is 29 ft. less than the total diameter, and pro- sed as explained in the tables. The further use of the diagram will be Kla. 14. Slope Diagram for Banks of Reservoirs. 6 a TO is 14. FECT TO FOOT OF BANK . B 13 /? ai 25 29 3d 3? 41 45 0/AMTFt OF f?S. TO BE #eOUCD BY FT. Table No. 44 shows the cross sections of banks from 3 ft. to 10 ft. high ; with area of cross sections and cubic yards of earth per lineal foot and per 100 feet. This table will be of use to contractors and graders. To find the cubic contents of a bank X the area of the cross section by the length of the bank in feet and then divide by 27. Thus, in first exam- ple given in the table, the area of the cross section = 6 X 10 = 60 ) Total 20 X 5 = 100 \ = 235 15 X 5 = 75)sq. ft. this X 1656 (the circumference of a 6 acre reservoir) = 389,160 cubic feet which -!- 27 = 14,413 cu. yds. ; by table 870.37. the cu. yds. in 100 ft- X 16.56 = 14.413 the same as by the other and longer method. WASHING OF BANKS. The washing down of the banks by the waves in the reservoir is a mat- ter of much importance and yet little can be said as to the best means of preventing it. Where, as is the case in some sections, there are plenty of stone the water line may be partially protected by riprapping with them but this involves a large amount of labor. In most sections of the state there are no stone so other means must be used. In sections near the James, or other rivers, along which willows grow these willows may, at but little expense, be transplanted in the banks where they will form a self maintaining protection. Nor can this expedient be practiced by but few. The tough prairie sods taken from the surface of the ditch may be laid aside and" be afterward laid along the water line. This has been tried and has worked well and, although much labor is involved it probably re- mains the best for general use. Where gravel may be had a shore line may be covered with it thus forming a natural water break. In some cases it may be best to construct a break-water of plank sharpened and driven into the bank or laid to posts set in the bank. The steeper the bank the great- er of course will be the displacement of the earth by wave action. Outlets and Gates-See P. 107. 101 TABLE NO, lT 44. A CRO|S A |ECTION cSc OF RESERVOIR BANKS SECTIONS Area of cross section Sq. ft. 41* 47' 33' 2.35 189. CuYds erf t of bank Cu.Yds. perf t of per 100 ft. of bank. s. 70:57 7.0 870.37 700.0 122.5 93. 48. 31.5 44. 28.5 5.6296 562.96 4.5370 3.4444 2.5925 1.7777 1.6296 1.0505 453.70 344.44 259.25 177.77 116.66 162.96 105.05 102 TABLE NO. 45. RESERVOIR TABLE. Diameters, Circumferences and Areas in square ft. of reser- voirs from y% acre to 10 acres in area advancing by 3^ acre. New. Area in Acres. Diameter in feet. Circmuference in feet. Area in Square feet. Ys 83+ 261 5455 M 118 371 10890 n 167 525 21 780 M 204 641 32 670 235 738 43560 M 263+ 826 54450 1 288+ 905' 65340 M 312 980 76230 2 333+ 1046 87120 M 353+ 1109 98010 372+ 1169 108900 M 391 1228 119 790 3 408 1282 130680 M 425 1335 141 570 it 441 1385 152 460 M 456+ 1433 163 350 4 471+ 1480 174 240 M 486 1527 185 130 % 500 1571 196 020 M 513+ 1612 206 910 5 527 1656 217800 M 540 1696 228690 iz 552+ 1734 239 580 M 565 1775 250 470 6 577 1813 261 360 589 1850 272 250 M 601 1888 283 140 M 612 1923 294030 7 623+ 1957 304 920 M 634+ 1992 315810 }2 645 2026 326700 i 656 2061 337 590 8 666+ 2092 348 480 M 676+ 2124 359 370 i^ 687 2158 370 260 M 697 2189 381 150 9 707 2221 392 040 M 716+ 2249 402 930 M 726 2281 413 820 M 735+ 2309 424710 10 745 2340 435600 NOTE In the above table the diameters and circumferences are taken to the nearest foot. The area in square feet is correct for the given areas in acres. The signs of + and after the diameters indicate whether the di- ameters given are too large or too small. Thus, 83 + indicates that a fraction of a foot, less than l / 2 , must be added to 83 to give the true diam- eter ; and 118 indicates that a fraction less than % foot must be taken from 118 to give the true diaineter ; 83 is therefore a little too small and 118 a little too large less than V foot in each case. See explanation on next page. 103 Explanation as to table 45. Table No. 45 is constructed from table 72; the areas in square feet having first been cal- culated. The area in sq. ft. of a 5 acre res. being 217,800 enter table 72 in the column of areas and find 2181.28 as the area of a circle whose diameter is 52.7 and circumference 165.56. This tabular area agrees most nearly with the given area in sq. ft. Therefore, for a circle of 527 ft. diam. the circumference would be 1655.6 ft. (decimal point ONE place to the right.) and the area 218,128. (decimal point TWO places to the right.) This area corresponds most nearly to the given area and hence the diameter and circumference are the ones most nearly corresponding to the given area. If diameter is less than 100 the area and circumf. may be taken directly from the table. If diameter is more than 100 and less than 1000 enter the table 72 and from the first column take the whole number and decimal corresponding to the given diameter; then, for the area, move the decimal point TWO places, and for the circumference ONE place, to the right. Example, required the circumference and area of a circle or reservoir having a diameter of 472 ft. ? In table 72 opposite 47.2 (473) find circumf. = 1482.8 and area = 174 974.1 [The decimal point* having been moved as above described-^ The area in acres IS found by dividing the area in sq. ft. by 43560. If either the diameter, circumf. or area in sq. ft. or acres be given all the other elements may thus be found from table 72. EVAPORATION AND FILTRATION. Evaporation is the greatest during warm or windy weath- er; greater in shallow than in deep water and greater in run- ning than in still water. The evaporation from a ditch or reservoir during June, July and Aug. will rarely exceed .3 to ,4 inch per day. During the remaining months the aver- age will be about. I inch making for the year from 3 to 5 feet of loss by evaporation. To the loss by evaporation must be added the loss by seepage or filtration either into the earth or through the banks. The amount of seepage through the banks will depend not only upon the character of the soil of which they are made but also upon the solidity with which they have been thrown up. 80 with the seepage into the earth. If the soil is of soft loam, sand or gravel the per- centage of loss will be much greater than if the sub-soil is of clay or hard-pan. ed reservoir on average ground may be as after the reservoir has been in use for a s show the approximate volume of loss per different areas. TABLE NO. 46. Showing loss in Reservoirs from Evaporation and Filtration. Approximate only. >sumed to be about! inch per day eason. The following table will day in gallons from reservoirs oi Area acres i~ 2 3 4 5 Loss in j Area Gallons, 'acres ~~2710(r 1 6~~ 54300 7 81400 1 8 108600 i 9 135700 i 10 Loss in Gallons. 162000 190000 217000 244000 271000 104 $ %z %* Sw w s aS J OOO5 coo ^* ic 06 1 i so os co ** iC O5 C f] CO ^ 1 I<3 -* 1^5-a i lls .a SB- CO^Oi ^-c^C^ I CClCCD CXO5iH(M fHT-lTH iHiHS<15 s^ a>t g o 2 c g^3 e 5 g^^^ ^o^-g^'g.g ^If^lcf ^Its^fe f|^|a-*2 "at g S^~ i C i^gg"*! S-55' a o 2 -^ * o ^^.slt-s n e o a he t hi e c lj*SW S 2^lllil 1 Kl!i!i i PRlII l-^ol-^jS I^IPli S rtetH o o s^J^sg Biil! H*| tJD oOg^SooeS is-&*fee !1fls||| Hs^sii iiaii o^ ^^leg.S 1|8S_5: & |3 ^5 > S^H cc S o ^'slo fefg ^ o -"TwSj"- .d rt r> 4 5 O ^ - H hH CM CM CM CO CO CO C NOTE It is assumed that the price of moving earth will be from 6 to 8 cents per yard at which rate (8c) most of the subcontract work on Dakota Ry. grades has been let, the lesser rate of 6 cents has, in some cases, been paid. If the cost is desired for an embankment of any other size or cross section the length may be taken directly from table 45, the cross section from table 44 and the cubic yards then quickly calculated and multiplied by the price agreed upon, in order to get the total cost. This table will answer most purposes and will be of value for ready reference. 107 rmitimu'd from page 100. OUTLETS AND GATES. OUTLETS. The outlets or culverts through the banks to the main ditches should be set before the bank is built and with refeference to the location of the ditches. The size of the outlet will be governed by the amount of water to be de- livered to the ditch. If the ditch is small or short the size may be smaller than for a large or long ditch. In the latter case make the outlet large enough to deliver the requisite amount of water at a velocity not so great as to wash the banks of the ditch. The outlets may be made of plank or of sewer pipe, the latter being especially good, but, in most cases, not so readily obtainable. The earth should be well tamped about the box or pipe in order to make a water tight joint. By reason of the difference in sizes of the outlets, the dif- ference in length through banks of different breadths, and with the difference in the head due to constant lowering of the water in the reservoir, and the different methods of con- structing the outlets, no precise data can be given as to the relative discharging capacities of different sizes of outlets but the following table will give the approximate volumes in cubic feet per minute discharged. TABLE NO. 50. FLOW OF WATER FR OM RESERVOIRS. New. Head of water in feet. Outlet 12X12 inches Outlet 12X24 inches Outlet 12X36 inches Outlet 24X24 inches Outlet 24X36 inches 2 3 4 5 6 400 500 575 650 720 800 1000 1150 1300 1440 1200 1500 1725 1950 2160 1600 2000 2300 2600 2880 2400 3000 3450 3900 4320 Cubic ft. per min. GATES. The gates should be set at the the inner end of the outlets and a plank walk built from the top of the bank leading out over the water to a point over the gate in order that the gate may be lifted. In construction the gate is most simple; any farmer or carpenter being competent to make them. A tightly fitting slide over the end of the box or pipe outlet being all that is necessary to shut off the water. The gate may be raised or lowered by a stick of 2x4 bolted to the front of the gate and leading up through slides or guide holes in the end of the walk. Simple means too may be provided for fastening the gate either up or down. The pressure of the water against the gate will keep it in position and preserve a tight joint if the sliding surfaces have been properly dressed or surfaced. Guides should be provided in the sliding supports so as to make sure that the gate will return to its seat when it is desired to lower it. Modifications of detail are many and will suggest themselves 108 to any one as the conditions of the work or the setting may require. Fig. 16 shows a simple and common form of gate. Fig. 16. Simple form of gate. aa=side plank of outlet box. 66 and ((' top and bot- tom plank of outlet box. e upright plank supporting outer end of walk. ff = guides for gate. s = space in which * * gate slides, h = hoisting timber. Sub Reservoirs and Storage Ditches. As previously stated it may be best to have two or more reservoirs on the same farm or under service by the same well. These may be on different ridges or knolls and may be directly connected with the well or with each other by piping, flumes or ditches. A sub reservoir may be provided to receive the waters elevated from lower ditches or pools by wind mills or water rams. In many cases storage ditches will be necessary to give proper service to areas at a consid- erable distance from the well or reservoir. A storage ditch is merely a big ditch, or one made higher and wider than the ordinary main ditch so as to hold in store a large vol- ume of water ready for immediate service through lateral ditches to the adjacent lands. Such a ditch or canal along a quarter line might better serve adjacent farms than a res- ervoir of any other form, or if located along the top of a nar- row ridge where a large circular reservoir would be imprac- ticable or needlessly expensive. For the volume of water stored a storage ditch requires a greater cubic capacity of embankment and hence a greater proportionate cost than a circular reservoir; but the econ- omy of space, the lay of the land or the character of the ser- vice to be rendered may more than compensate for the in- creased proportionate cost. 109 DISTRIBUTION OF WATER BY DITCHES, FLUMES AND PIPES\^ C The water having been obtained and stored the next en- sideration is as to its conveyance from the well or reservoir to any desired place and then its distribution over the land to be irrigated. The distinctive feature of the great irrigation systems of the west, and of other countries, is the great length, size, and expense of the ditches and flumes necessary to convey the water from the storage reservoirs or rivers to the low- lying irrigated lands. These ditches are often of great size and extend for many miles; the cost reaching tens or hun- dreds of thousands of dollars. Great viaducts of masonry, or trestles of timber or iron, to carry the canal over rivers or valleys, deep cuts along the mountain sides, flumes sus- pended over or along precipitous canyons, tunnels through the rock hills, and enormous dams and head gates are feat- ures of great interest, as well as of expense, common to the distribution of irrigation waters in regions less favored than our own. How tame, in comparison, will be the means of distribu- tion on the Dakota prairies and under the individual sys- tem of irrigation by wells. Our people may well forego the glory of being the possessors of world renowned works of engineering skill, for the sake of the greater economy and the honorable distinction of being the possessors of the largest and most fertile valley in America, wherein irriga- tion may be more cheaply inaugurated and maintained than in any other state* All the leading features of other systems, such as dams, head-works, main canals, pipe lines, viaducts, &c., will not be known here. Probably few ditches will be larger than 10 feet at the bottom, and but few will be over 5 miles in length. Pipe lines will be small, and flumes will be low and short. In brief, there will be no heavy or expensive features at- tached to the distribution of Water in this prairie country, and hence the great economy of an irrigation system in Dakota. The result sought by all systems is the bringing of water to the land. While it may sound well, or arouse in one the spirit of pride, to say that we have the largest dam, the largest or the longest ditch, the longest tunnel, or the highest flume in the world, it is a distinction the wary capitalist will will- ingly forego for the more humble statement that, for a given outlay, we have under water a larger number of acres than can be shown any where else. This will be the pride of the Dakota irrigator. He will point not to his towering masonry, not to his navigable canal system, not to his sky- scraping trestle-work, nor to the dismal depths of a hole 110 through a nil], bat with pride to his perennial fountain, to his simple ditches and to his broad expanse of fertile fields, where more that is of profit may be seen, as the result of a dollar spent, than can be shown by any of his neighbors in other states. If this true picture does not soon attract the scrutinizing eye of capital, and Dakota ere long become their chosen pasture, then, indeed, will all signs fail. Water is conveyed from point of supply to place of distri- bution in ditches, flumes, or pipes, and is distributed over the land through smaller, lateral-ditches or by plow fur- rows, by the actual flooding of the surface, or by means of sub-irrigation through lines of tile pipes; the latter system however, being confined almost exclusively to the irrigation of garden and orchard lands. Volumes might be written on the subject of water distri- bution and allied subjects, but the limit of this little book will admit of but brief reference to some of the matters most likely to engage the attention of our farmers. 3DITOHIES. Form and Size. According to a classification adopted by the Census De- partment of Agriculture, irrigation ditches are divided into three classes. First, those under 5 feet in width, Second, those from 5 to 10 feet wide, and Third, those over 10 feet wide on the bottom, the depth in a general way corresponding with these widths being 1 foot, \y z feet, and 2^ feet and over. By reason of the com- paratively small volumes of water to be carried, and the re- stricted area to be served from* any one source, the Dakota irrigation ditches will be mostly small; few, it is safe to say, need be as large as 10 feet in width. A ditch need be only large enough to convey the water to the place whence it is to be distributed. By " large enough " is meant, of such a size as will deliver the volume of water needed, at a velocity not so great as to wash the banks of the ditch, and not so large as to present a needless excess of surface of bank, which will increase the percentage of seepage, or of surface to the air, which will increase the percentage of evaporation. In large ditches much depends upon the form or sectional outline of the excavation and banks. In smaller ditches this is of less importance so long as the flow is not impeded by the roughness of the sides or by the abrupt changes of direction. Ill The same degree of care in the original construction and future maintenance of ditches cannot be secured in a sec- tion where irrigation is first practiced, and where the new irrigator has yet to learn the importance of close attention to details, as in a section where irrigation has long been practiced and where each detail of the operation has been reduced to a system. The sooner attention is given to the careful and workman- like construction of ditches, the sooner will the labor devot- ed to irrigation return a satisfactory profit. A channel, roughly scratched in the ground is not a ditch, and, however much the owner may believe in its sufficiency to give proper service, the flowing water cannot be deceived and will not do its full service until given the opportunity which the laws of of hydraulics have decreed. The main distributing ditches should be built for perma- nent use. The smaller or distributing laterals may, in cer- tain cases, be cheaply built to serve the purpose for a season. They may be thrown out by a double-mould-board plow or as a single plow furrow. The larger sections can be most cheaply built with ditching machines. The section of the ditch may have the form shown in Fig. 17, where the slope of the bank in the cut or excavation is one foot horizontal to one foot vertical. The excavated earth may, and usually will, be put into the banks as shown at A, or it may be placed as shown at B, where a berm, or ledge, b is left at the sides of the ditch. The slope of the banks in the embank- ment being 1% to 1. Fig. 17 If excess earth is required to build the bank higher or wider either the ditch may be made wider and deeper or the extra eartn may be obtained from side ditches or borrow-pits D, or by both means. It is the province of the engineer to di- rect as to thse details of the work so we will here consider only such details as relate to the ordinary work which the farmer himself may be required to perform. For all ordi- nary purposes of distribution from the reservoirs to the more distant laterals, main ditches from 4 to 6 feet wide will suffice. (The width of ditch, as stated, is understdod to be the width at the bottom.) The construction should be workmanlike, the bottom even and free from sods, stones, lumps, of clay,or weeds; the sides smooth, even, and free from like obstructions to the even and free flow of the water. 112 Fig. 18 represents the cross section of a , - x , ditch 4 feet wide and **\ [5* ^v^ having water 3 feet vSEE S deep - The area of N ^l * Fig. 18 the wet section of the JD 4t C ditch is equal to the average width multiplied by the depth. In this case 10ft. + 4ft_ 14 2 = -g- =7, 7x3=21 sq. ft. = area of wet section The Wet Perimeter in the length of that portion of the surface of the cross-section which is covered by water, AB, BC, CD In order to determine this length, the length of the slopes A B and C D must be known. These may be found, for any depth of water or for any degree of slope as follows: The slope is the hypothenuse of the right-angled triangle ABE, and its length is therefore equal to the square root of the sum of the squares of the other two sides. In this case the sides A E and E B are each equal (the slope being 1 to 1) to 8 feet. The sum of the squares of A E & E B =9+9=18. The square root of 18 (see table of roots)=4.2, which is therefore the length of A B. If the slope had been 1J to 1, A E would = 4.5 feet which squared=20.25 which +9, the square of E B, = 29.25 the sq. rt. of which=5.4= length of A B. So with any other depth or degree of slope. In this case the wet perimeter 4.2+4+4.2=12.4 feet. The "mean radius" "hydraulic radius" "hydraulic mean depth" and "mean depth" are synonymous terms for the area of wet cross section area A B C D, Qf agin wet perimeter >r (AB+BC+CD) the above illustration, s ^t' = 1.69=mean radius. This term, "mean radius," is frequently used in the calcu- lation of volumes, grades, and velocities, by Kutter's and other formulae and it is is therefore explained, Since most slopes will be 1 to 1 or 1)^ to 1, and most depths from 1 to 5 feet, and most widths from 2 to 6 feet, the following table has been prepared to show at once the lengths of the slopes A B and C D for slopes of 1 to 1, and of 1J to 1, and for depths of 1 to 5 feet; also the wet areas of ditches, having bottom widths of 2 to 6 feet, and water from 2 to 2J feet deep; also the lengths of the wet perimeter, and the corresponding mean radii. Application The water in a ditch, having side slopes of 1 to 1, is 3% feet deep, what is the length of the wetted slope A B$ In second column, opposite depth of 3J, is 4.6= length in feet required. In third column is 5.8= correspond- ing length when slope=l^ to 1. A ditch has 2} feet of water and a bottom width of 5 feet, what is area of wet sec- 1.18 tion, length of wet perimeter and mean radius? Under head of depth of 2J feet take width of 5 feet; in succeeding columns find A+18.75 sq. ft, . P=\2 ft, and R = 1.56. The limits of the table will serve for the ordinary range of work and will no doubt save some time in making calculations. TABLE XO. 51. TABLE OF DEPTHS, SLOPES, WET AREAS, \VET PERIMETERS AND MEAN RADII OF SMALL DITCHES. X>'>r. Slope of bank j 1 hor. to 1 vert. Slope of bk 14 to 1 Deptli of water in ditches, 1'1. ~-~- -^ z c=~ 51 >'= Area of wet section, sq. feet. Length of wet- perime- ter in ft Mean Radius Depth of water in feet Length of slope (ab) in ft Length of slope (ab) in feet. 1 114 IH 1 3 4 2 m SK z% 3 tit 34 s* 4M 4u 4 3 4 5 1.4 1.8 2.1 2.5 2'.8 3.2 3.5 3.9 4.2 4.6 4.9 5.3 5.7 6.0 6.4 6.7 7.1 1.8 2.2 2.7 3.2 3.6 4.1 4.r> 1.9 5.4 :> N 6.3 6.7 7.2 7.6 8.1 8.5 9.0 D. w. A P. R I 1 1 1 2 3 4 5 I: 6. 5 . 25 6 . 75 S . 25 9.75 ' 478 5.8 6.8 7.8 .625 .690 .735 .76* m 1H 14 2 3 4 5 6.2 > > 9'. 2 .847 .937 1.01 1.06 2 2 2 2 2 2 3 4 5 6 8. 10. 12. 14. 16. 7.6 8.6 9.6 10.6 11.6 1.05 1.16 1.25 1.32 K3 2H 2 l /2 2V 2 2i/ 2 2V" 3 4 5 6 7 13.75 16.25 IS. 75 21.25 23.75 10. 1.37 11. 1.4S 12. 1.56 13. 1.63 14. 1.70 Flow of Water in Ditches. This complex branch of dydraulics is treated exhaustively in several large works on the subject, it being of prime im- portance in countries where water is taken from rivers, or from large storage basins, and carried for miles in large canals of ditches. Important, because upon its proper treat- ment rests the accurate gauging of rivers and canals, or the measurement of the volume of water flowing in them. On a knowledge of the exact volume of the supply rests the matter of the volume of apportionment to different districts or ditches. Many mechanical divices are used for measuring the vel- ocities of running streams, and many formulae and rules are given for the calculation of the velocity and volume. The Dakota system of irrigation being so entirely different, the necessi- ty for the accurate measurement of water in ditches is almost entirely done away with ; so but brief mention will be made of a few points in this connection. The measurement of most ditches and streams is in the unit of the cubic foot per second ; or the number of cubic feet of water the stream will discharge in one second. The discharge for a given depth of water in the ditch will depend upon the slope or grade of the ditch, the area of the section, the condition of the bottom and banks, and upon the direction and force of the wind, which exerts a considerable effect upon the exposed surface of the water. [One-tenth of the width of sur- face being allowed for wind resistance.] 114 As above explained, the sectional area of any ditch, or of the wet section thereof, is equal to the average width x by the depth. The velocity of a running stream is not the same at all points of the cross -section, it being least at the bottom and sides, where the friction is greatest, and less at the surface than at a point a short distance below it. The point of greatest velocity is therefore at the middle of the stream and just below the surface. To determine the velocity of any stream it becomes necessary, therefore, to determine the mean velocity, or such a velocity as would be common to all the threads of water of the stream if the discharge re- mained the same and all flowed at the same rate. Current meters and other mechanical devices are used to determine the velocity of the current at several points in the cross-section, and from a reduction of these observa- tions a mean is obtained for the whole section. Intricate formulae are likewise employed to determine the velocity and discharge, mathematically; but their ap- plication, involving a considerable knowledge of mathema- tics and hydraulics, they are not popular with the average irrigator. The simplest way to determine the approximate mean velocity of a stream is to take a certain percentage of the ascertained maximim surface velocity. By experi- ment the mean velocity has been found to be from 80 to 85 per cent of the maximum Mirface velocity. In this country 80 per cent is usually taken as the standard. To determine the maximum surface velocity, select a straight section of ditch, in good repair, and stake out a section of 100 feet. Place in the current at a short distance above the upper stake a small block of wood, so that when it passes the upper stake it will have acquired the velocity of the water. ]N ote carefully the exact time of its passage of both the up- per and the lower stakes, and record the interval. Repeat this, say four or five times, and take an average of the in- tervals to get the nearest true interval. Example, 1st. interval = 25 seconds. 2d. " 24 3d. " 25 4th. " 26 " 100 which H- 4 25 sec. = aver- age interval. If the current runs 100 feet in 25 seconds it runs J^ = 4 feet per second, maximun surface velocity. 80 per cent of 4 feet = 3.2 feet per second the mean velocity of the stream. The volume in cubic feet discharged will of course equal the wet area X by the mean velocity. Assume the ditch to be 5 feet wide and the water 2 feet deep. From table No. 51 we find the wet section to have an area of 14 square feet. Then 14 x 3.2 (area X mean vel.) = 44.8 = cubic feet per second discharged. Table 36 shows this to be equal to 335 115 gallons per second. The section of ditch should be in good condition and fairly uniform in section. The determination of the velocity and volume, as above described, necessitates the measurement of the surface velo- city. Where formulae are used this is not necessary. As above stated, the use of formulae not being convenient to the average irrigator, and the space within the limit of this little book being insufficient to properly explain even the simpler ones, the subject will not be considered. The reader being referred to such standard works as Trautwine's Engineer's Pocket Book where the formula of Kutter is fully explained and illustrated by examples and tables of coefficients (P. 571 to 2796, in editions of 1888 or 1891); Wies- bach's Mechanics, where is found a much simpler formula, and one more convenient, with table of coefficients; and to the recent exhaustive work of P. J. Flynn on Irrigation, and the Flow of Water in Open Canals. (See advertisement of Irrigation Age); as well as to any of the many standard works on hydraulics. Grades. A study of the details of the larger canals or ditches of the west shows a great variety of sizes and grades, yet more uniformity than some would expect. Ditches running from 20 to over 100 miles have widths from 20 to 80 feet, some be- ing built with, and some without, berms; the grades ranging from 1 foot to 7 feet per mile. The steeper grades are not common and are for short distances only. The average grades for main ditches, carrying from 2 to 6 feet of water, are from 1J^ to 2% feet per mile. Such low grades will an- swer only for the larger ditches carrying large volumes of water and where the ratio of volume to resistance, or friction on the sides, is large. In smaller distributing ditches, where the volume is small- er, and the resistance proportionately much greater, a steep- er grade must be allowed. It is frequently said by those who are not informed that this country is too level to irrigate to advantage. Such is far from being the case. The writter has yet to find a quarter section of land, in the most level portion of the James river valley, that is too level to irrigate. The gently rolling lands, or such as have a comparatively uni- form slope, are the best located for irrigation. The location of the well or reservoir, on or near the high- est point, fixes the point of radiation of the ditches, their lines being located according to the grades secured and the lay of the land to be served. The aim will always be to keep the water up as high as possible for it is useless to sac- rifice grade or make a ditch run at a greater grade than is necessary. It is an easy matter to let the water down but a difficult thing to raise it. By keeping the grades up, a broad- er area is kept within the range of service. 116 Grades of from 2 to 5 feet per mile will be ample to secure good delivery from the smaller main ditches, while the later- als will require steeper grades, which, in many cases, may be confined to the approximate level of the field, except on hill sides or quite abrupt slopes, in which case the grades will be carried around the slope as contours. The following table will show the grades per 100 feet corresponding to giv- en grades per mile. If the grade per rod is required it may be taken approximately from the table by taking | of the grade for 100 feet. If the grade is required exactly for any given distance, and corresponding to any given grade per mile, it may be found by simple proportion, thus: grade per mile : one mile : : required grade : given distance. Example, What is the grade for 3,500 feet, corresponding to a grade of 10 feet per mile ? 10 : 5280 ::(?): 3500 = 35000 4- 5280 = 6.62 = Ans. or 10 : 5280 : : 6.62 : 3500. That is, the given distance multiplied by the grade per mile and the product divided by 5280, the number of feet in a mile, equals the required grade. In this way any grades, other than those given in the table, may be found. In like manner the grade per mile, corresponding to the grade for any given distance, would be found, thus: grade per mile ( ?) : 5280 : : given grade : given distance. TABLE NO. 52. Table of Grades per Mile; or per 100 ft. measured horizontally . From Trautwine. Grade in ft. Grade in feet per 100 feet. NOTE. Grade in ft. Grade per 100 feet. per mi. per mi. 1 .01894 If the grade per mile con- .05 .00094 2 .03788 sists of feet and tenths add .1 .00189 3 .05682 to the grade per 100 ft. as .15 .00283 4 .07576 given in the first table , 2 .00379 5 .09470 the grade per loo feet for >25 .00473 6 .11364 the required tenths, as .3 .00568 7 . 13258 given in the second table. .35 .00662 8 .15152 Example, Grade per mile .4 .00758 9 . 17045 12.85 ft* what is grade .45 .00852 10 . 18939 per 100 feet and in 725 .5 .00947 11 .20833 ft.? .22727 + .01609 = .55 .01041 12 .22727 .24336 = grade in loo .6 .01136 13 .24621 ft. .24336 X 7 = i-735 2 .65 .01230 14 .26515 = grade in 700 ft. and .7 .01326 15 .28409 .24336 -*- 4 = .06084 = .75 .01420 16 .303 '3 grade in 25 ft. 1.70352 .8 .01515 17 .32197 + .06084 "= 1.76436 = .85 .01609 18 .34091 grade for 725 feet. OR .9 .01705 19 .35985 24336 x 7-25 = 1.76436 .95 .01799 20 .37879 1.0 .01894 117 Laying Out. The laying out of the ditches is the provience of the en- gineer or surveyor, although the more intelligent farmers may do much of their own work and thus save considerable expense. In the arrangement of fields it may become nec- essary to change the location of a ditch or to lay out a new one. This work the farmer may do with simple means, al- though, in many cases, it will pay an intelligent farmer to own a drainage "level. Its use on'his own, and on his neigh- bors' work, will soon pay for it. Simple devices for small jobs will be described later on. Something of a knowledge of leveling must be had in order to do the work, but sufficient may soon be acquired to per- mit of much home-work being done. If any doubt exists as to ones ability to lay out a piece of work it will be cheaper to hire some one to do it who knows how. The running of preliminary lines, making of profiles, cross sectioning, calculation of sizes, carrying capacities, and grades, and the final location and construction are details of the work, each the proper subject of a chapter. The limit of this little book will not permit, however, of any special consideration of these purely technical details of the work . (See remarks on leveling, P. 132 to 134.) Excavation and Cost. The smaller ditches may be constructed by hand-shovel- ing, by plowing and scraping, or by plowing with a large double-mould-board plow. The larger ditches by plowing and scraping, or by grading or ditching machines. Hand work is of course most expensive but it will be necessary in some places. Simple piowed ditches are of course the cheap- est, as they are also but temporary, and in the end the more expensive. Scraper woak will cover the greatest range of work and will fairly represent the average cost. Work done with a ditching machine is very satisfactory and far cheaper than other work. The New Era grader and ditcher (see advertisement) is the leading machine of its class. It will place in the bank from 1000 to 1400 cubic yards of earth per day at a cost of about 2 cents per yard; or it will load from 600 to 800 wagons per day. It has been used in all states, in all soils, and on all classes of work with full satisfaction and great economy. Its use on reservoirs is especially recommended. Done with a ditcher, the ditches on a section of average land need not cost to exceed $200, or $50 per quarter section. Under fav- orable circumstances the work has been done for half this sum. (See also page 246.) Dakota's soil and topography renders the operation of a grader easy, economical and altogether satisfactory. 118 No farmer can afford to buy a machine to do his own work alone, but when farmers become associated in the putting down of wells and construction of reservoirs and ditches, then it will pay to buy machines, for on a large job they will soon save their cost. The suggestion is made that town- ships or counties purchase not only drilling outfits but also ditching outfits. Each farmer could pay for its use on his work, at such a rate as would effect a great saving to him- self, and, at the same time, soon return to the township the cost of the machine. An additional advantage of such an arrangement would be in the use of the grader on the pub- lic roads where much cost to the tax-payers could be saved thereby. In this, as in all other fields, the machine has come to stay as against all other forms of labor. The suggestion here made will bear careful consideration by associations of farmers or by townships and counties. Most of the railway grading- in the state has been sub-let to f arme s and others at from 6 to 8 cents per yard, at w r hich rate and on large contracts, there is only fair wages. Table No. 49 shows the cost of grading reservoir embank- ments at the rate of 6 and 8 cents per yard . A reservoir of 5 acres, having an 8 foot bank, would cost $746 at 8 cents per yard. Four such reservoirs on adjacent farms would cost about $3,000. If done with a grading machine, at a cost of even 3 cents per yard, there would, on that small job, be a clear saying of $1,500 over other work Such conserva- tive illustrations show the value of properly considering the means of doing the work. What applies to reservoirs ap- plies likewise to ditches. Embankments and Footings. Under the head " Reservoirs, " on page 99, the qualified statement is made that the use of drag-scrapers will result in a more solid bank than when scrapers or graders are used. This is commonly so; but not necessarily so, for if the grad- er-work is properly followed up with a harrow the earth is torn, mixed, and more thoroughly compacted than in any other way and the resulting embankment is as good as if done by any other means. The object in any embankment is to have it sufficiently solid to hold water. Around gates and outlets the earth should be solidly tamped or puddled wetted down in order to make a tight joint. So, too, with the footings of high banks, they require special attention. If the dirt is thrown loosely on top ef the sod the water may percolate through the loose, filter-like footing of grass and weeds and cause a leak, and possibly a wash-out of the Dank. To insure against this there should be, along the middle- line of every heavy bank, several plow furrows turned and the sod cast aside* The fresh earth of the bank settles into 119 the trench and soon forms a tight joint with the solid sur- face. If the banks are but 6 or 8 feet high, this will suffice ; but if they are higher the trench may better be double- plowed and a bank of wet earth piled in and over it thus insuring a compact core for the bank . Reference has been made to the slope of the banks. The slope in the excavation need not usually be more that 1 to 1, but if the cut is of any considerable depth, and the soil sandy or loose, then a slope of 1% to 1 will be better. The slope in the fill or banks may usually be 1% to 1, but if they are high a slope of 2 to 1, on the wet side, will be safer. The slopes of the reservoir banks are thus given in the diagrams and tables under head of reservoirs. Cubic Contents of Excavations. Tables giving the cubic contents, per unit of length, for ditches of different depths, widths, and slopes, would be con- venient for reference, but they would necessarily be long in order to cover the whole ground. On this account they will be omitted and the simple rule given by which the calcina- tions may be made in any given case. RULE: Multiply the area of the section of the ditch, in square feet, by the length of the ditch, in feet, and divide the product by 27 to get the cubic yards of earth in the ditch. Determine the area of the section as explained in connec- tion with table 51. Example How many cubic yards in a ditch 4 feet wide, 2)4 feet deep, and 1835 feet long V . Bottom width 4 feet+top width 8^ feet 12}^ which H- 2 =Q%= average width. 6^ X2J^, the depth, =14.0625= area, and cubic yards in I ft. of ditch. 14.0625x1835, the length,=25,805 cu. ft. which-^27=: 956= cubic yards. To get the contents of the ditch in gallons, proceed as above, using the wet section and multiply the volume in cubic feet by 7.48052 to get volume in gallons. Gates. The gates or outlets from the main ditches to the laterals are too simple in construction to need illustra- tion or special consideration. They may be made with more or less complication, but a simple frame of plank with a board or plank slide or gate, fitted to slide vertically within cleats will answer every purpose. When the gate is down closed the mud in the ditch may be drawn about the base and sides to aid in keeping it water tight. In the working laterals, where it is desired either to cut off any further flow or to dam up the water for the flooding of a certain area, a small portable dam or stop of sheet iron or wood may be used. In case the water passing from the main ditch to the laterals is to be measured or gauged then the common gate will give place to the weir or to the spill- box shown in Fig. 6. 120 One matter will be mentioned as to the location of ditches the same applying to both flumes and pipe-lines which is to locate them, as nearly as circumstances of economy, grades, &c will permit, on such courses as will permit of the proper working of the land. Rectangular areas are the most convenient to cultivate, and sharp angular pieces the most difficult. So, in locating water-ways some considera- tion should be given to the after convenience of handling machinery in the cultivation of the land. A moderate in- crease of the first cost of the water-way would be justified in an effort to secure an area more favorable in form to convenient cultivation or access from other parts of the land. Flumes. Flumes are boxes or troughs used to convey water where ditches are impracticable or needlessly expensive either to construct or to maintain. Where a ravine, valley, or any considerable depression crosses the line of a ditch the water may be turned into a flume, carried over the depression, and then discharged into another ditch on the farther side. It may, too, be advisable to carry the water in a flume over loose, sandy soil, where the loss by percolation would be so excessive as to render a sufficient delivery from an open ditch either difficult or impossible. Many cases will therefore arise where the use of flumes will either save the farmer considerable expense or conserve his greater convenience. Special forms of sheet iron, or other sheet metal, flumes are much used in mountainous sections because of their lightness, tightness, and economy, and the facility of erecting them in difficult places. As usually constructed flumes are merely wooden boxes, open at the top, and of such size and strength as is neces- sary to carry and support the water supplied. Many in the west are of large size, great strength, and traverse long distances and at great height. Such as Dakota farmers will use will be small, short and low. The grades may, if neces- sary, be somewhat lighter, and the size smaller, than those of the ditches supplying them, because of the lesser friction and the greater facility of flow. The volume of water to be carried will regulate the size the same as in ditches and the rade will, in the same way, regulate the carrying capacity y increasing or decreasing the velocity of the current. The effect of friction of the water upon the sides of the flume, and of even a gentle wind upon the surface of the water, will be quite noticeable more so than in a ditch. An instance is cited. A flume 12 x 18 inches by 800 feet long, with a fall of 2 feet, ran to overflowing at the upper end while discharging but 3 inches at the lower end. Wind and friction prevented the water from running. 121 Since the delivery depends upon the vel ocity of flow, and since the velocity in an open water-way is due solely to gravity, and not to any confined head or pressure, the deliv- ering capacity of a flume will be governed by the size and grade not by the size of a pipe delivering water to it under high pressure. The volume and relative velocities must be considered. If the volume to be carried is that of the well alone, as where the flume is used to carry the water from the well to the ditches or the reservoir, the size may be mod- erate as compared with that of a flume farther away and- forming part of the waterway from a reservoir from which a much larger volume will flow at one time than would flow from the well alone. The flume box may be made of 2 inch plank, selected as free from loose knots or cracks, closely spiked with 5 or 6 penny wire spikes (wire spikes will hold better than others and are less apt to split the wood in driving.) If a small box is needed a single plank of 14 to 18 in. will do for the bottom, and similar ones for the sides. The addition of a second plank to the bottom, the sides remaining the same, will double the volume and a little more than double the carrying capacity of the flume,and at but slight increase of expense for the supports, braces, etc., may remain sub- stantially the same. The construction of a flume is but a simple matter. Any carpenter or intelligent farmer can ' build one. The supports may in many cases be a single line of heavy fence posts, which may be had in lengths as great as 12 or 14 feet. The buts set 2 or 3 feet in the ground, and well tamped, give a good foundation. The grade line for the tops is marked by leveling, and the tops then sawed to grade, the caps or cross bars spiked to the posts, and the flume then constructed on these. If of 6 feet or more in height the posts and cross bars had better be braced to pre- vent the rocking of the flume by heavy winds. Where greater heights than 10 or 12 feet are met a trestle of timber posts, properly footed, braced, and anchored, will be used. The rigidity of the supporting posts should be carefully looked to in this country of almost constant and heavy winds, for upon this will depend very largely the tightness of the flume and its freedom from leakage. The planks, before being spiked together, should be paint- ed along the edges in contact, with a coat of very thick paint. This will not only aid in making a water tight joint but will preserve the wood at the joint. The edges of the planks should be dressed true so as to fit properly. As rough sawed by the mill they are often wavy or uneven. Cut out all warped or crooked pieces for they cannot be worked in to advantage. If double widths of plank are used on the bottom or sides they should be tongued and grooved if possible, or at least 122 carefully matched and secured in close contact by cross pieces. The joints of the plank at the "bents" or supports, will be protected by side strips or braces and the box, at in- tervals between the bents, will be surrounded by strips or wooden braces to give rigidity to the flume and prevent loosening of the joints. The length of the space between the bents will depend somewhat on the style of the flume or upon the length of the lumber used. Where a single line of posts is used have the bents at the ends and middle of each length of 16 or 18 ft. plank (8 or 9 foot spaces.) If the flume is more solidly built 20 foot lumber may as well be used, leaving 10 foot spaces. If the ditch is large, and the flume correspondingly large, the trestles must be heavier and a line of stringers will sup- port the flume between the bents. The dressed surface of the lumber will be on the inside of the box to present as smooth a surface as possible to the running water. After the completion of the flume go over all the joints with a coat of thick paint applied with an old stiff brush. By so doing, and using care and plenty of nails, a box may be made that is perfectly watei tight. A small leak may often be stopped by filling the crack with stilt' clay or mud. The details of construction will depend somewhat upon the builder and his means, but they are so simple as to render further suggestion unnecessary. PIPES. The use of pipe-lines for conveying water, in the place of ditches or flumes, has increased much since the in- troduction of certain cheaper forms of pipe. In the west, pipes of wood, banded with iron, are extensively used as are pipes of spiral-riveted or welded iron or steel. These latter combining great strength with lightness and economy. Where waters can be forced under heavy pressure, as from our wells, the use of surface pipe-lines of light pipe will find a broad field of usefulness and should receive such consider- tion as its merits deserve; especially where the work of con- structing ditches or flumes is of any special magnitude. The pipe-line is intended to take the place of the main ditch or flume and not of the distributing laterals. The advant- age of a pipe-line over a ditch lies in this that the water supply is not reduced by seepage or evaporation and the duty of the well is thereby increased. The area of surface occupied by the pipe line is not nearly so great as the area occupied by the ditch and embankments and thus the area subject to cultivation in increased. The cost of mainte- nance is less, for a pipe-line will need but little attention, whereas, ditches, however well they may be made, will require .an annual overhauling; especially if made of loose or sandy soil which in a windy country soon blows 123 down. The matter of grade is of no importance for the wa- ter, being forced, will run up hill as well as down and the pipe may be laid to the grade of the surface and deliver water at a level higher than the well. The area under ser- vice from the well may thereby be increased by rendering it possible to reach areas to which gravity alone would not carry the water. In this way a well owner may be enabled to sell and deliver water to a neighbor whose land lies, or is controlled from a higher level. The advantage over a flume lies in the fact that evaporation and leakage are done- away with. The delivering capacity is greater because un- der pressure. The first cost may be less even than that of the flumes, and the cost of maintenance less. The matter of grade is eliminated and the line is on or near the surface where it may be more easily constructed or repaired and where less liable to damage from winds. The alignment, or location, too, may be accommodated to the circumstances of the surroundings more readily than that of either ditches or flumes. It is here assumed that the pipe line connects with the well; otherwise there could be no pressure upon the pipe and it would stand, in relation to delivery, on a plane with the ditch or flume. If the line is accommodated to the surface and there is any inverted or downward bend in the pipe there should be a valve set at the lowest point to permit of emptying or drain- ing the pipe during the cold weather or for repairs. The pipe may be laid on or near the surface on low supports of such form and material as circumstances may suggest. It should, at suitable intervals, be fastened or anchored down in some suitable way to prevent displacement by the wind or by other means, and it should be painted to preserve it from rust. The concluding remark as to location of ditches may be again referred to in this connection, and the suggestion made that the location of the lines of the water-ways be made as far as possible along the lines of the fields or along fences or roads. In the case of the smaller pipe-lines the fences themselves will often serve as sufficient and conven- ient supports for the pipe, intermediate supports being set if necessary. In view of the advantages possessed, under certain conditions, by pipe-lines over other forms of water- ways one should fully consider the advantages of each as well as the cost and maintenance before deciding which to adopt. On most lands there will be no use for either pipe- lines or flumes. Their service is justified only by the circum- stances of the topography and service. 124 HYDRAULIC RAM. The occasion will frequently arise where the area to be irrigated is divided by a water course, gully, or other depres- sion, the land on the side of the well and reservoir sloping gently toward the " draw, " the opposite side of which is high and comparatively level. The well and reservoir being at a distance from the draw it will hardly pay to lay a pipe line to serve the other side and the water cannot be carried across by ditch or flume. How then can it be delivered into a ditch on the opposite and higher ground? By elevating it only. This could be done from the end of an open ditch on the low side by means of a steam or wind pump. The for- mer way, by reason of fuel and attendance, would not prove profitable, and the latter way possibly ineffectual in spite of an abundant supply. A simple and inexpensive water elevator may be had in the hydraulic engine or ram which may be so set as to take the supply from the open ditch, with a fall of such an amount as the slope will permit, leav- ing drainage away from the ram. By this means the water may be forced across the draw in a constant stream, working night and day, rain or shine, and without fuel, attention, cost, or care. * The Rife's Hydraulic Engine (See advertisement, P. 214) is such a machine and one of high efficiency. The No. 40 ma- chine is fitted with a 4-inch supply pipe and a 2-inch dis- charge pipe, and, with a fall of from 4 to 6 feet, it will raise from 60 to 70 gallons per minute to a height of 20 feet or more, and lesser volumes to much greater heights. The machine will work under heads of but one or two feet and in such cases it could often be used to advantage along side slopes to raise a supply of water to a ditch at a higher level. Such appliances, together with wind mills and steam Simps, will, in the near future, find a welcome place among akota irrigators, for, although a well will do almost any- thing within its immediate reach, there will be duties to perform in connection with a properly managed irrigation system which are outside of the sphere of the well itself, yet properly within the sphere of other appliances, all of which must be considered if the greatest good is desired and secured. PUMPS. While this little book is devoted most especially to a con- sideration of artesian wells as a source of water supply for irrigation, it must not be forgotten that there are other sources of supply. Dakota has few lakes or rivers from which any supply could be drawn, except of course the Missouri, the supply from which is practically inexhaust ible. There are many sections all over the states where large, shallow wells may be sunk into the sand and gravel beds 125 from which an almost inexhaustible water supply may be obtained. It must of course be elevated by artificial means and the question will at once suggest itself as to whether it will pay to do this. Yes, It Will Pay! As to this there can be no question, and ere long this source of water supply will cut a very large figure in the ir- rigation of lands in Dakota. Certain very erroneous and misleading statements have been made by government specialists and agents as to the relative value of these phreatic or sub-surface waters, and the true artesian waters; they claiming that by far the larger supply was the sub-surface supply. These statements and reports were founded upon observations elsewhere than in Dakota, and upon a woeful lack of personal knowledge as to our true artesian supply. The sub-surface supply, while no doubt of vast extent and importance, cannot be compared with the artesian supply in its extent, universality, volume, or the ultimate economy of obtaining it. In other words a given volume, in a given time, may be obtained more cheap- ly from an artesian well than from any sub-surface source by whatever means it may be secured. Notwithstanding this great percentage in favor of the artesian supply the other sources should by no means be neglected or overlooked. The value to the state of the phre- atic supply will be beyond calculation if the people will but seek its development. As before stated it must be secured by mechanical means; either by wind or by steam power. Many farmers most of them cannot raise the means necessary to put down an artesian well, but there are few who cannot raise enough to put in a pumping plant at an expense of but a few hundred dollars. Reference must again be made to the west where the manufacture and use of water-elevating machinery is a very large and rapidly growing industry. Many sections of coun- try cannot be supplied by water taken from streams by dutches, so the water must be elevated. Thousands of wells have been put down in the several \vestern states and terri- tories from which the water will not fiow so it must be pumped. This industry is most fully developed in Califor- nia and in Colorado. The following illustration will show the comparative economy and great value of such means. A pumping plant, with a 50 horse-power engine, will raise 7,500,000 gallons of water to a height of 10 feet in 10 hours. This amount of water will cover 28 acres to a depth of one foot. The cost of the plant would be about $3000. One man can operate it with about one ton of coal per day. While so large a plant would not be in order except where the supply was very large, a plant of proportionately less 126 capacity and cost would accomplish proportionate results. Many places may be found from which enough water may be pumped to irrigate a quarter section of land. The question would follow as to the means to be used in raising the water to the surface in the greatest volume and at the least expense. The author knows of no better means than the use of the PULSOMETER or the N YE VACUUM steam pumps which possess features especially adapting them to such uses. They are both vacuum pumps, having no pistons or machinery to wear out or become deranged, are exceedingly simple, strong, and efficient, and, above all, are standard the world over; being used for irrigation purposes in many countries. All that is needed is the pump, a steam boiler, and a little pipe. There are hundreds of thresher engines in the state that could be used to supply steam, and straw being used as fuel the expense of running would be but nominal. A No. 6 Pulsometer pump throwing 300 gallons per min- ute (18,000 gallons per hour) would cost about $225; an en- gine to supply steam could be rented during its period of idleness and could be run at an expense of but $2 or $3 per day for fuel and attendance. Surely, then, here is a most valuable auxiliary supply in the irrigation field of Dakota, and a means of utilizing it not heretofore presented to our people. The cost of starting the plant buying the pump, pipe and fittings, digging and connecting 2 or 3 large wells and get- ting the boiler need not cost over $1000, yet on such an out- lay of capital enough may be easily made in any one year to pay the cost of installation and enough surplus very soon accumulated to warrant the sinking of an artesian well. The increased service rendered by a well, as the result of a given outlay or cost, renders that means, or source of sup- ply, cheaper in the long run, as it is otherwise the basis of more extensive operations; but if the greater source is be- yond one's financial reach then by all means grasp at the lesser and use a pump. WIND MILLS. In the utilization of this sub-surface supply the agency of wind mills may be made to play an important part and this is especially true in this country of almost constant winds. A wind mill may supply water for a very considerable area of garden and orchard, and, if reinforced by a proper water- elevating device, as to which there are several good ones in the market, and also a storage reservoir, the area of service could be very greatly extended and the profit of the farm greatly increased. This means, too, deserves the careful consideration of our farmers. Get the water from the most available source and by the most efficient means. Only get it! for to get it is to acquire a competency. 127 Wherever a deposit of sand or gravel is found, or where wells wherein there is a flow or current in and out are found, there is to be found, beyond much doubt, a supply which would abundantly serve the land upon which the supply is found. Every farmer should take some pains to investigate the extent and character of his sub -surf ace sup- ply with a view to its future utilization. Fig. 19. Showing the Pulsometer Pump as set for taking water from a stream for the use of irrigation. The view shows the extreme simplicity of the plant which renders it especially applicable to use where skilled labor or attendance is lacking. Any man can run it or set it up. [See next page and page 244.] 128 Fig. 20. Fig. 20. Shows a No. 6 Pulsometer [capacity 18,000 gallons per hour] throwing a stream 46 feet high through 160 feet of 3V inch pipe, into a flume on top of the bluff. The pump irrigates 1400 fruit trees, uses about Ys cord of soft wood per day and is operated by an Indain boy. The plant is in Idaho. A No. 9 pump, on a lift of 102 feet, used % cord of wood in 10 hours and delivered 60,000 gallons per hour. [See page 244.] 129 LEVELING. It would require more space, diagrams, and illustrations than can be here given to fully treat of the different kinds of levels, their adjustment, use, and care; and to describe and illustrate the many nice points in the art of leveling. Much of this techincal information may be had from the pamphlets issued by level manufacturers and supplied with the instruments. Enough will be given to convey to any person of average intelligence so much of a knowledge of the art as is neces- sary to aid in doing such work as may arise about the farm, and yet such as it would not pay to hire an engineer to do, even if one were to be had at call. The principle of level- ing is to reduce the inequalities of the surface to a uniform plane, or to determine the position of a succession of points with reference to a uniform plane. DATUM PLANE. It is apparent from this that some plane of reference must be chosen which shall be that to which all other points are referred Such an arbitrarily selected plane is called the Datum Plane, or plane of reference, and it is assumed to lie at a considerable distance below the surface in order that all points referred to it may have plus (+) elevations, instead of some plus (+) and some minus ( ) as would be the cas if some portion of the line to be run sank below the level of the datum plane. In a rough or mountainous country 500 or 1000 feet is taken as the depth of the plane of reference. In this level country 100 feet will be sufficient. That is, in starting any piece of level work assume that the starting point is 100 feet above this plane, or at an elevation of 100; then proceed to get the elevations of all other points, whether higher or lower than the starting point. Before describing the opera- tion of leveling let us very briefly consider the level or level- ing instrument. THE LEVEL. The engineer's level is a telescopic tube carried in Ys or collars, and having a long level-bubble tube attached, mounted on a horizontally revolving cross-head which is ad- justed and maintained in a level or horizontal position by four leveling-screws attached to the head of the tripod on which the instrument rests. Cross hairs in the tube give the exact center and the horizontal line of sight. Such are the main features of a level, and all are constructed on the same general plan. Some instruments are made with a less powerful and shorter telescope, with fewer parts, lighter weight, and cheaper in price. Levels of this class known as contractors, builders or architects levels are far cheaper than larg- 130 er engineer's levels but they are finely constructed and good for all classes of work. A still cheaper grade of level is the so called " drainage level " which is made for the express purpose of farm use inlaying out drains and ditches. In* this special class of instruments there is a wide range of design and price, the latter ranging from $10 to $30. (The manufacturers, Buff and Berger, W. and L. E. Gurley, and Young and Sons, whose advertisements appear herein, are leading makers of the finest instruments and will supply anything in the level line.) A $25 or $50 instrument will do good work and last a life- time, if properly cared for. One who can use a level will soon pay the cost of a good one by home-work. If no good level is at hand a simple one, for rough work, may be made out of three pieces of board as shown in Fig. 21. Take two pieces of nar- row board, AB and AC, of exactly equal length and form as shown, and hav- ing a span from B to C of 10 feet [one of 16^ foot span 1 rod may be more convenient.] At exactly equal distances from A, measured along the sides, attach the cross stick D. Fasten on the plumb line and bob P and then adjust the zero point O as follows : Drive two stakes in the ground, as supports for the level, having one of them 2 or 3 ins. higher than the other. Fig. 21. A simple form of level. Set the foot C on the higher stake and mark upon D the ex. act point where the line cuts the edge as at x. Then re- verse the level, end for end, so foot B is on the higher stake, and again mark the point where the line cuts D as at Y . Draw o just midway between these lines. Then whenever the plumb line cuts this o mark the feet B and C are <*n a level. In one foot a large screw may be set, as shown in the enlarged view at S. When screwed in flush the level is set for level work but when screwed out the level is set for run- ning grades. Thus if a ditch has a fall of 1 foot in 500 feet the screw would be turned out slightly over % inch. The level would be set 50 times in the 500 feet (it having 10 foot span.) so -fa of 1 foot would be the grade for each setting. Such a tool is of course crude but, if well made and skill- fully handled, it will yield quite good results. Other simple, home-made levels are frequently described but this is as good as any. Get a good level if possible and learn to do - good work with it. It will pay you if you do much irrigat- ing. THE HOD. 131 The level rod is a rod of dry wood from 8 to 12 feet long, marked into feet, and tenths and hundredths of feet, meas- uring upward from the bottom of the rod. The rod may have a target or be what is called a "self-reading" rod. The target rod has the graduations cut into the wood and the distances indicated by figures as at A, Fig. 22, the feet in large red figures and the tenths by smaller black figures. The Reveler views the cross lines on the target and the rod-man takes the reading as indi- cated by the target. (In the Fig. the target reads 4 feet) The self-reading rod needs no target, for the leveler takes the reading from sight at the instrument, the gradua- tions being made visible by painting as shown at B, Fig. 22. Here only the feet are numbered, the smaller gradu- ations not requiring it. Thus, if the horizontal hair of the level cuts at the following points on the rod the reading would be as follows. Kefer to B in the Fig. 1=1.0 feet. 4=1.5 feet. 2=1.05 " 5=1.75 " 3=1.3 " 6=1.85 " The reading to .05 feet being easily made, and, on short sights, a finer read- ing may be approximated although a reading of less than .05 is not necessary except in very fine work. Such rods can be easily and accurate- Fig. 22, Leveling Kods. ly made by any intelligent person, and at a cost of not over one dollar. The target may be made of sheet brass or of galvanized iron. LEVELING. Leveling is very simple work, and the keeping and reduction of level notes equally so. The first thing to do is to set up and level the instru- ment and to select the HUB or starting point. The form of note-keeping and the order of procedure is shown on the next page. In this sample page from a note-book the following is the significance of the letters head- ing the several columns. Stn. = Station Number ; B. S. = Back Sight [sometimes called + Sight] ; H. I. = Height of Instrument ; F. S. = Fore Sight [sometimes called Sight] ; Elev. or Ht. = Elevation or height of Station ; Rem. = Remarks. The hub, or starting point, which may be any permanent object, or a stake driven for the purpose, is assumed to have an elevation of 100 feet which fact is entered in the note-book as shown. The rod now being held on this hub the line of sight of the instrument, or the plane passing through its center, strikes the rod 4 feet from the bottom. Enter this un- der B. S. as shown. Now if the hub is 100 feet and the instrument reads 4 feet above it. the center of the instrument is evidently on a plane or level of 104 feet [so that Elev. added to B. S. = H. I. or 104 ft.] The H. I. being known the height of any other point is found thus. The rodman goes to station 1 and the leveler reads a F. S. of 5.20, which he enters as shown under F. S. 132 SAMPLE PAGE FROM LEVELER'S NOTE BOOK. Stn. B. S. H.I. F. S. Elev. Rem. Hub 4.00 104.00 100.00 Hub near well. 1 5.20 98.80 3 6.00 98. 3 - 7.35 103.80 7.55 8.80 96.45 95. T. P. [turning point.] Hub, at barn. 4 2.60 101.20 5 1.50 102.30 T. P. 6 1.20 103.50 8.60 94.90 7 2.10 101.40 1.70 101.80 If the instrument is on a level of 104 ft., and the reading on the rod at Stn. 1 is 5.20, it is evident that Stn. 1 is 5.20 ft. lower than the instrument. The level of Stn. 1 is therefore found by merely subtracting the F. S. reading on that Stn. (5.20) from the H. I. (104) = 98.80 which enter as shown. In like manner readings are taken at Stns. 2 and 3 which re- sult as shown in the notes. From where the instrument now stands stn. 4 cannot be seen so the level is moved to a new position from which stns. 4 and 5 may be seen. Set up and adjust as before. The rodman having staid at Stn . 3 the leveler now takes a B. S. reading on that point. The reading of 7.35 is entered as a B. S. Stn. 3 (T. P., or turning point) having an Elev. of 96.45 and the B. S. equaling 7.35 their sum, or 103.80, will give a new H. I. or plane of reference. Before proceeding to take the level ot Stn. 4 the leveler deems it best to take level on some new hub so that in case the original hub is moved or destroyed he can relocate his work from the new hub. The rodman sets up on the barn floor and the leveler reads 8.80 which substracted from 103.80 =95 as the Elev. of the barn floor. He then proceeds as before to take the elevations of other stations and to set such other hubs as he may desire. From this explanation may be drawn the whole secret of leveling and note keeping. The Elev. of any starting point added to the B. S. reading on that point give the H. I. and any F. S. reading subtracted from the H . I. gives the Elev. of the point on which the reading is taken. Any number of F. S. readings may be taken from one setting of the instrument so long as the range of sight is clear. Thus, the instrument may be set at or near the center of a reservoir and the levels taken at all points about the bank without moving. Aim, however, to have the lengths of B S and F S courses as nearly equal as possible in order not to magnify any slight error in the adjustment of the instrument. Note especially one fact as the grade or level runs doivn the target or reading runs up on the rod; that is, it takes a greatar length of rod to reach from the plane of the instru- 133 ment down to the surface. The reverse is also true as the surface rises the reading on the rod lowers. TO SET A LINE OF STAKES ON A LEVEL. Set one stake at the level desired, set the rod on this stake and clamp the target on the reading . Proceed then to set other stakes, tapping each one down until the target set on the stake comes into the plane of the instrument. TO SET A LINE OF STAKES ON ANY GRADE. Set and get level on first stake. Suppose now that the grade runs down at the fate of .1 ft. in 50 feet and that the stakes are 25 feet apart. Move the target up on the rod .05 ft., clamp it, and set the second stake by it. Move it up 05. again and set the third stake ; and so on to the end. Had the grade ran up then the target would have been set down at each setting. If, instead of setting long stakes to the line of the grade, short ones are set, the level of each short stake may be taken and then from the notes the height of the grade-line above or below each stake may be estimated and indicated. Many complications will arise in any extended practice but the principle is the same and the specimen notes given embrace the secrec of the whole operation. If care and judgment are exercised fairly good work may be done by one not skilled in the work. For still further illustration the notes are here given of the level-work in the laying out of a reservoir. A reservoir of but 1% acres will be taken for illustration. Stake out the circumference, on the center line of the top of the bank, into sections of 50 feet each (except where otherwise stated in the notes) circumference being 905 ft. LEVEL NOTES LAYING OUT A RESERVOIR- Stn. B. S. H.I. F. S. Elev. Height to Grade. Hub 1 5.2 105.2 5.0 100.0 100.2 106.0 5 8 2 5 5 99.7 6 3 3 6.2 99.0 7 3+30 7.6 97 6 8 4 +60 10.2 95.0 11 +90 7.5 97.7 8.3 4 6.6 98.6 7 4 5 4.2 101.0 5 o 6 o o 102.0 4 7 4 4 100 8 5 2 8 4.8 100.4 5 6 9 4 8 100 4 5 6 Stn = 105 ft 1 5.0 100.2 5.8 Set up near the center and proceed to take the level of e ach stake; first having set a reference hub at some conven- 134 lent place outside of the reservoir, the height of which call 100 ft., which, added to the B 8 of 5. 2 =105.2= the H I. The notes show a gradual descent from station 1 to a point 30 ft. beyond stn. 3 at which point there is a sudden descent into a shallow "draw", the bottom of which is at 3+60. Thence there is a sudden rise to 30+90 and then a gradual rise to stn. 6, where the highest point is reached, and thence a grad- ual fall to stn. 1 where, on a reading of 5.0, the level is found to check with the beginning of the work. In looking over either the F. 8. readings or the Elev. re- sults one may readily see, in the imagination, a profile of the work without platting it on paper.* Assume, now, that the top of the bank .will be 4 feet above the highest point, at stn. 6 the elev. of which is 102 ft., then the grade-line will be on a level of 106. Enter this in the last column as shown. It is apparent that the height of the bank at each stn. will be the difference between the level of that stn. and the level of the grade-line; therefore, sub- tract the height or elev. of each stn. from the grade-height (106) and the remainder will be the height of the bank at that stn., which enter as shown in the last column. The staking out of the toe or base of the bank on the in- side and outside may now be done since the height and slopes are known. The inner slope being 2 to 1 and the . outer slope l^to 1 measure off from each stake, toward and from the center of the reservoir the bottom widths occord- ing to the height of the bank at that point plus % the width of the top of the bank. Thus at stn. 4. the height being 7.4 ft., the distance to the inner toe would be 7.4x2=14.8+ 2.5 (J top)=17.3 ft. The distance to the outer toe would be 7.4x1.^=11.1+2.5=13.6 ft., a total width of 30.9 feet. The estimate of the number of cubic yds. of earth in the bank may be done with sufficient accuracy by assuming the cross-section to be level and the height of the bank in each section as a mean or average of the end heights. Thus, the height at stn. 6 is 4 feet; and at stn. 7 it is 5.2 ft. The aver- age height may be taken, therefore, as the height of the full stn., 4.0+5.2=9.2-^-2=4.6=average for 100 ft. Get area of section of this height, and compute cu. yds. for 100 feet as explained under head of " Keservoirs. " Do the same for each stn., add the sums to get the total cubic contents. This, it is believed, will make clear what is really a very simple operation and will enable any farmer to do, or to aid in doing, part or all of his own work. With three sticks, a ball of binding twine, a few stakes, and a hatchet, with a little good judgment and care thrown in, any farmer may do in two hours what it would cost him $5 to $10 to have done and still not be overcharged. Do seme level practice, if only for exercise. 1 1 2" _p ; o (* -3 jt 4 - 4t 6" . -6 _ __ . - - 9 : , 10 : ll 12 10 INCHES TENTHS 135 Fig.23. DECIMAL AND DUODECIMAL SCALES. TRUE AND APPARENT LEVEL. Brief mention only need be made of the difference between true and appar- ent level. In ordinary leveling opera- tions no account is taken of the curva- ture of the earth. True level is a water-level which is the true curvature of the earth. Apparent level is a horizontal plane tangent to the plane of true level at any point and extending indefinitely into space. In leveling the sights are short and constitute, therefore, a succession of tan- gent planes which closely approximate a curve of true level. The difference be- tween a curve of true level and a plane of apparent level is about 8 inches per mile [7.98 ins. or .667 ft.] and increases as the square of the distance; being 4 times 8 inches in 2 miles, 9 times 8 inches in 3 miles, etc. MEASUREMENTS. Nearly all measurements in engineer- ing work are made in feet and decimals tenths and hundredths instead of in feet and inches. This is especially nec- essary in leveling. Table Ko. 67, show- ing the decimals of a foot corresponding to each -fa of an inch will be of conven- ience in the conversion of measurements from one unit to the other. For ordin- ary work the decimal corresponding to the nearest half or quarter inch will be close enough. To aid in getting this at a glance Fig. 23 has been prepared show- ing (in > size) a foot measure divided into inches and eighths; and, on the op- posite side the divisions to tenths and hundredths. This will be of much use to the leveler in certain work . Examples. 6 inches = 5 tenths. 9 " =75 hundredths. 10 " =83 " and 7 tenths =8% inches. 25 hundredths = 3 inches, &c. The scale may be more readily used than a table. The unit of measurement used by the govern- ment in surveys of the public lands is the chain of 66 feet, 4 rods this being divided into 100 links of 7.92 inches each. For rules as to the conversion of chains and links to feet, yards, &c., see ''Mensuration" and table of multipliers. 13H VALUE OF WATER, VALUE OF LAND AND SIZE OF FARMS UNDER A SYSTEM OF IRRIGATION. VALUE OF WATER. Water for irrigation has a double value. First. The first cost of getting it upon the land, or the value of the Water right. Second. The annual rental value. Table No. 53, on the opposite page, shows statistics as to values, etc., which are official and as accurate as only the Government could secure. The table contains much of value and deserves careful study. The first cost of securing a water supply or right will de- pend upon the supply, the distance it must be brought, the manner of bringing, etc. All the expense of dams, head- gates, ditches, flumes, pipe-lines, or tunnels must be born-by the area served, so all these expenses enter into, and form a part or, the first cost per acre of a water right. The value of the right being such an amount as will pay all the ex- penses and leave a proper margin of profit. This value ranges from a mere nominal price to $30 or more per acre, but averages as shown in the table. The right attaches to the land and passes with the title thereto. Once paid for it is perpetual as a right, but the continued enjoyment of that right is contingent upon the performance of other conditions as the payment of an annual tax for the use of the water, or the performance of certain labors in maintaining the ditches. The amount of the value of the water right may usually be considered as the value of the land, for, as a rule, the land has little or no value without the right. As touching most directlv upon the value of well-waters reference may be made to the Gage group of 29 wells near San Bernardino, California. They are within a radius of 1 mile, are from 4 to 10 inches in diameter and have an aver- age daily flow of about 33 miner's inches, (about 300 gallons per minute) or a total of 954 inches, (about 8600 gallons per minute.) One inch is apportioned to 5 acres and is sold as high as $250 an acre, or $1250 an inch. The average price thereabouts being $1000 per inch. At this rate the total flow is worth $954,000 and it will water nearly 5000 acres. Four good Dakota wells will throw more water and will serve more land. Such being the case one Dakota well of 2200 gallons per minute would, according to this accepted California estimate, be worth $238,500. (Continued on P. 138.) 137 TABLE NO. 53. OS CO OS 30 00 "^ C- OS rH " lO lO OO IO - ' t-'d 6 183 S oa ^o TH CO t- 00 CO ^' d os I -i M rt s 8sf 5>- s CD 10 00* -H OO CO 00 *"'$:& CD 05 00 CO ^ TH " " -g -S So^ ^ ^ "C rt "^ ^ 0,0 -1-J ^ 2 0, a; N ^^ - s S)^ ^5 5 o o W3 O C 00 o ^ I o 138 It is not the intention to place such values on wells that can be sunk for $3000 or $4000 yet such is their legitimate value as compared with values elsewhere. Our wells possess values far in excess of their cost, and far greater than even their owners now dream of. A good well is really a fortune to its owner. In Oregon, on one large tract, the annual charge is $3.00 per acre for 1 foot depth of water (1 acre foot) to be used in 3 irrigations. At this rate a Dakota well would pay its cost in two years, if not in one. In other states the annual charge per acre foot is about the same, but, inasmuch as the crop is a certainty and abundant in amount, this apparently high tax is not felt as at all burdensome. The Dakota irrigator who would achieve success must abandon the false idea, which many farmers entertain, of getting someting for nothing. He must put in both money and labor, and considerable of each, in order to make a suc- cess of irrigation. Nor need he be discouraged ; for all the advantage is on his side. It will cost less here to secure a water right than in almost any other section because a given volume may be had for a lesser outlay. Again, the Dakota water-right is also a water-power which very largely increases its value. It is not subject to periodic fluctuations, prior rights of up-stream claimants, and such other uncertainties and annoyances as are experi- enced under other systems. It is perpetual, is under perfect control], may be put to many uses and in all respects has a value not possessed by water rights in other sections or un- der other systems The cost of reservoirs, ditches, gates, etc., is not a part of the water right, but a tax upon the land in its preparation for irrigation. In this respect also Dakota has a great ad- vantage, for her gently rolling or nearly level lands require but little preparation as compared with the heavy work of terracing, checking, diking, ditching, leveling and otherwise treating the land, as so often necessary elsewhere. Finally, as to the ANNUAL COST of water. Where, in other states, the annual cost is from 25 cents to $5 per acre averaging over $1 the Dakota average will be but a few cents, and in most cases nothing, for the flow of the well be- ing continuous, requires no attention or expense. Once ob- tained its volume comes free. In every essential particular wherein an irrigation system burdens the irrigator with expensefirst cost of water, an- nual cost of water, preparation of ground, future mainte- nance of plant he who irrigates in Dakota bears the least burden; has the greatest advantage; the most valuable, con- trollable, and diverse right; to say nothing of the proximity to the best and largest markets. 139 A consideration of many details only tends to strengthen and confirm this conclusion that Dakota's artesian irriga- tion system will be the cheapest and the best of the many systems developed" in this country. The experience of the failure years, 1888-1889-1890, taken in connection with the results obtained by the great crop of 1891 (See table No. 43 and remarks in connection therewith) prove not only the enormous value of water in Dakota but substantiate the estimate of duty of water given in table 16. If the estimate there given is approximately correct, and the annual value of water be taken to be but $2 per acre then from table 16 it will appear that a well of 1350 gallons per minute would be worth $1950 per year or fully 40 per cent on its cost. This is assumed to be a rental value. To the owner the actual value would be the net value of all crops raised in excess of the average yield of non-irriga- ted lands in his neighborhood. No reasonable person will estimate the probable average yield of irrigated wheat at less than 30 bushels per acre, which average would be fully 1 8 bushels more than the average without irrigation. As- suming a net return of but 50 cents per bushel, this would give to the water a value of $9 per acre to the owner; or an amount sufficient to pay the full cost of the well together with the cost of the land, in one year. This is not an exagerated estimated but rather an under- estimate as has been demonstrated by actual experience. A parallel cannot fairly be drawn between the values either of water or of land as between the fruit growing lands of California and the grain fields of Dakota; but mak- ing all needful allowances for the character of the crops raised, and their value per acre, the value of water to our grass and grain fields is still actually far beyond the amount which even sanguine estimate would give to it. A thousand gold mines would not be so valuable to our people as are these artesian waters. Hasten, therefore, to develope this pent-up wealth which awaits the opportunity to flow to the coffers of each enterprising claimant. VALUE OF LAND. One, in considering the relative values of irrigated and un- irrigated lands, may border closely upon the realm of the marvelous while yet not transgressing the bounds of cold facts, for it is truly marvelous that the worthless deserts of the arid west, have, within a few years, been clothed in semi- tropical luxuriance through the agency of irrigation, and have been raised in value from actual zero to as much as $2000 per acre. It is but a few years since California and Colorado were known only as great mining states. To-day, through the agency of the impounded waters of the moun- tain streams, they have been transformed into great agricul- 140 tural states; the harvest of the golden fruit and of golden grain having long since superseded in value the harvest of the golden metal. Where then there were mining camps now there are prosperous cities, and where then vice reigned supreme, now peace and plenty bless the community. Millions of acres of barren, sage-brush or of sand-flecked desert, of lava-beds and of sun-parched plains have been re- claimed arid are to-day the most valuable and productive lands on the continent. It is true that the high values of $1000 per acre and upward are usually fancy prices, but many thousands of acres have ready market values of from $50 to $500 per acre. Good lands, under water, the ditching and like preparation being done, are worth from $50 to $100 per acre, and find 'a ready market at these figures . Any piece of property is truly worth such an amount as will represent the principal upon which a fair rate of interest can be permanently earned. If land will produce annually a crop which will yiWd a net income of $10 per acre that land is worth $100 per acre to a man who demands a 10 per cent investment; or $200 per acre to a man who is content with 5 per cent. Such values, and only such, are legitimate. The remarkable development of Southern California has been due almost solely to irrigation . As an illustration of the increase in property values may be cited the statistics relative to San Diego Co., which may be taken to represent that section of the state. Real Estate. Improvements. 1880 1890 1880 1890 $1,307,302 $20,000,085 $341,948 $4,450,286 While no corresponding increase can be expected in any Dakota county there is still room for an increase in value far beyond the present values. Taking Brown Co., S. D., to fairly represent the two Dakotas, the average market value of the lands of the county would probably not exceed $6 per acre. An increase of $5 per acre would add over $6,000,000 to the valuation of the county and still leave the lands far below their actual value. Such a change in the ready market value of these lands may be brought about within two years if, within that time it can be shown that these lands can be made to produce from 25 to 50 bushels of wheat to the acre, no matter what the season may be. No doubt exists as to this being demonstrated it has been already in Brown Co. and in other counties within the arte- sian basin. As soon as the foreign land purchaser and investor learns of the wonderful possibilities of this artesian basin the pre- sent land owners will find a ready market for their surplus 141 holdings at prices now beyond their fairest fancies. What is it that can do this magic act the creation of millions of value where now little appears ? What is it that can and will do for Dakota what irrigation has done for our sister states ? What is it that can banish poverty, misfortune and ruin from our state and bring riches, prosperity and happi- ness in their place? That can quench the thirst of our once parched prairies with a perennial draught of nature's purest waters ? ARTESIAN WELLS! No agency is so pregnant of promise for the welfare of the Dakotas and none deserves the same attention as the de- velopment of this great industry artesian irrigation. It is not only a boon to him who puts it to practice but to the community in which he lives, for it shows to the world the possibilities awaiting all who choose to engage therein, and fixes to our lands a value because of their latent possibilities for successful agricultural development. The author has heard it remarked, but recently, by a wealthy eastern man who owns (perforce) several thousand acres of Dakota lands, but possesses no knowledge of irriga- tion, that if artesian irrigation proves to be what it is claim- ed to be he would sink several wells and thus trebble the value of the lands which today he would sell for what they cost. No doubt there are scores of such cases, and it is to prove to such men the true value of their lands, and to still further interest them and their monied friends in schemes of devel- opment that every effort should be put forth to demonstrate to the world the true extent and value of the latent possi- bilities we have within our reach and control . Every possible publicity should be given to every truth, to every demonstrated fact touching upon the well or irri- gation interests, and, by reason of the approaching World's Fair and its resultant era of prosperity and commercial activity every possible effort should be made to push the business of irrigation at home and a knowledge of its results abroad; for no better time will ever come for Dakota to enthrone herself in the good will of the capitalists of the world and regain her lost prestige, than the immediate future. The farmers and the business men of the state should organize and prepare- in every legitimate way to promote this all important industry, for the success or failure of the state depends upon it, and all other interests pale before it in importance and the effect upon the general prosperity of all classes. If this appeal to the patriotic home enterprise of Dakotans shall result in creating any .of that interest which the subject warrants, then will this little volume riot have been issued in vain. 142 SIZES OF FARMS. A word of caution as to over-irrigation, in point of area, will well-nigh be wasted inasmuch as the invariable tendency is to attempt to irrigate too large an area. A few unsuccess- ful attempts to irrigate too broad an area will convince the farmer that a lesser area, better served and cultivated, will yield better results. In a fruit-growing country an area of 5 or 10 acres is enough for a single holding. As the crop is changed to vegetables, grass, or cereals the area which may be advan- tageously cultivated increases. It is assumed that the hold- ing is worked on the plan of the average farm by the farmer and his family, with the assistance of the average amount of hired help. As the number of hands, actively engaged in the farm labor, increases, so may the area treated be increased. The character of the land to be cultivated whether it be easily managed or the reverse will likewise determine the area which a given service of labor can prop- erly manage; as will also, the character of the crops raised. It will be well in starting out to thoroughly treat such an area as the supply of water,as well as of labor, can treat to the best advantage. In short, go only so far as you can go with thoroughness. The following year this area will require far less attention so the surplus of water and of labor may be expended in an extension of the area served, until the max- imum shall have been reached. No other method of pro- ceedure will prove satisfactory unless " bonanza " methods are adopted. Table No. 53, of statistics, in the 3d, 4th, 5th and 6th lines, shows at a glance the results reached in 7 other states as to areas under irrigation. What there is shown is true of all other states and coun- tries, except that, as the country becomes older, and irriga- tion methods are improved, the duty of water increased, and more care and labor is given to a given area, the product of that area increases and a lesser holding is relied upon. So it will be in Dakota after the irrigation system is more general; the farms, instead of becoming larger will become smaller, and better and more thorough methods of cultivation will be practiced. From these smaller areas will be returned a larger yield and one as certain as the order of the seasons and as bounteous as the prosperity which will attend them. " Bonanza " farms may be, and no doubt are, fine things for their owners, but they are of little use to any community. A community of small farms, all of which are prosperous and each of which supports in plenty a family, is the most truly a model in all the elements which enter into the gen- eral prosperity, wellf are and happiness of the people. So each farmer will do better by his own interests, and those of his neighbors, if he seeks to place his present holding under more thorough cultivation rather than to extend his holding and neglect the proper cultivation of the whole. 143 PHOTOGRAPHS. Any good engraver can engrave a picture of an artesian well, and so to speak can doctor it up to show according to his own ideas of magnitude, or those of the person for whom he works, which ideas may far exceed the facts . Not so, however, with a photograph or any picture having a photograph as iis base such as photo-engravings. The camera, with the quickness of light, makes a record true to nature, and of the smallest details; a record with which the enthusiast cannot tamper; which none can question. The importance of photographing the wells of the state has but recently impressed itself upon the leading photog- raphers. Already several of them have quite fine collections of views of the wells in their neighborhood and take pains to secure views of each new well. Some have made a con- siderable profit out of their views, for a fine view finds a ready sale at home and abroad. Ere long the sale of well views will form an important item in the income of Dakota artists. A photograph of a well needs no argument back of it; it tells its own story; is its own best witness as to its truthfulness to nature, and convices the skeptic who would not otherwise accept the facts, as shown, on the affidavit of a friend, without some misgivings. Hence the importance of taking photographs and giving them a wide circulation. They are unimpeachable witnesses as to the volume and power of our wells and will command respectful attention where the most glowing verbal descrip- tion will be wasted on skeptical ears. The eastern man who has never seen a flowing well cannot comprehend the nature of one from a mere verbal descrip- tion; and even an old well driller, unacquainted with such great wells, will laugh in his sleeve at the narrator or will, with his friend the capitalist, say "that is the biggest Dakota lie I have heard yet." Show him a photograph, however, and his skepticism turns to wonder and amazement. No argument will prevail against the evidence of the light, and the capitalist whose interest, perchance, has been solicited will turn to investi- gate or to invest instead of turning away in disgust or in wonder at the stupendous lying abilities of the Dakota man. Enthusiasm on the well subject is ligitmate and laudable and increases as one sees and learns more of this wonderful power and supply. Enthusiasm is still further heightened by a comparison of the Dakota wells with those of other sections of the country. Not a comparison of reports, set in cold type, but a comparison of lifelike photographs. It is this enthusiasm that should be fostered by every resi- dent of Dakota, and especially by every photographer. 144 Every person and corporation should lend every possible aid to the photographer in his effort to secure good views; and the photographer in his turn should improve every oppor- tunity to secure views, and then place them at a price such as will enable every one to secure a supply to send away. There is no telling what one will find its way into the hands of some man who will invest thousands of dollars in wells and irrigation projects as the direct result of having seen, and been impressed with, a photograph of a well. Every person engaged in placing irrigation bonds, or the stocks of irrigation companies, should have a collection of the best views in the state and every eastern bond-negotia- ting agent should be similarly supplied. Collections of well views could, to excellent advantage, be handsomely framed and placed in the lobbies of the leading eastern hotels and in other places of popular resort. Such exhibitions would be seen by thousands of wondering and admiring spectators. Thus would a knowledge of the vast possibilities of Dakota's great wells be spread among a class of people who could not be reached by other means. Thousands of views could in this, and in other ways, be placed where they would be a greater advertisement to the state at large than any other that could be made. A lithograph of a goddess, of an eagle, of a gapping crowd of emigrants, or of a chariot procession may be a work of art but it can be of little value to the people; but if an equal number of views of our great artesian wells were scattered over the land the result would be a large influx of people, seeking to share the undoubted benefits the artesian waters will confer, and of money to develop an industry upon which the agricultural success of this agricultural state depends. Every view sent out should have attached a full and ACCURATE description covering as many as possible of the following points: Name, or location of the well. When drilled, and by whom. Depth, in feet. Pipe, size in inches all the way, or at top and at bottom. Volume, discharge in gallons per minute when opened and full size, and if possible, when discharging through smaller sized openings. Pressure, in pounds per sq. inch, when closed, and, if possible, when streams of different sizes are being discharged. Discharge, height of throw or discharge of streams of different sizes, or the horizontal distance to which the streams are thrown. Temperature, Character of water, hard, soft, clear, muddy, palatable, &o. Use to which the supply is put. 145 If several views are had of one well note which view is shown and what it is whether it is the 4 inch stream or the 6 inch stream, &c. Without this description the view has little value, and the value even then rests largely on the exact TRUTHFUL- NESS of the description given. It is poor policy, to say the least, to exaggerate as to^the volume, pressure, discharge, or the size or height of the stream shown. If an exceptionally fine negative is secured a duplicate should be made, for some accident may befall the first one or it may become gradually worn out through use. The author was desirous of having, as a prominent feat- ure of this little volume, a series of photogravure views of the leading wells of the state but the expense would have been greater than the circumstances of its issue would per- mit, so the idea was abandoned for the present edition. Should the book meet with such favor as to warrant another edition this feature will be added thereto. Through the courtesy of the leading photographers of the state the author has secured a collection of all the views of the wells thus far photographed. A list is added(on the next page)of the photographers hav- ing views, their addresses, and a list of the views they have for sale. This will be a great boon to the general public who will thus be informed as to what views may be had, and where to secure them. By this means it is to be hoped a large trade in views may be worked up and the photograph- ers thereby stimulated to the work of taking all such views as may be possible within their territory. The importance of cultivating this mutual interest is far reaching and it is hoped that added interest will be taken in well photography because of the great good that may flow therefrom to the people of all parts or the state. The author with pleasure acknowledges the courtesy of views received from the following: S. W. Fergusson, Bakersfield, Cal. 5 Kern Co. wells. Wm. Kennish, Wilmington, N. C. Ponce de Leon well, Fla. H. C. Humphrey, North Yakima, Wash. Yakima wells. And from all the photographers listed on page 146. 146 WHERE TO BUY WELL PHOTOGRAPHS. Photographs of Dakota's famous artesian wells may be secured by writing to the following Photographers. Photographer. Address. List of Views. Grade. B. W. Burnett. These views are among the best in the state. Tyndall, S. D. Springfield well, 6 inch stream. 4* 4 " " " and mill. Niobrara, Neb. well, 8 in. stream " " 2 derrick v'ws Zinnert well 3 in. stream. " Shadeland farm A A A A B A A D. O. Root. City well views are the best i n the state. Woonsocket, S. D. Large, of City well, 4 in. stream. 2 small " " Hinds well, vertical stream, horizontal & vert. s. A A B B L. Janousek. Yankton, S. D. Brick yard well, stand-pipe view. " boiler view. A A P. C. Anderson Redfield, S. D. Water works display view. B Quiggle & Johnson . Rapid City, S. D. Doland well 6 inch stream. 44 g U A A J. Q. Miller. Aberdeen, S. D. Railway well. Beard " 6 inch stream. " 4 " Williams " 4 " B . A A B Chas. H. Newcombe. These views Huron, S. D. Day well, vertical stream. " " double Dity " water works display. 10 views of irrigated farm. Jlisdon well, 8 in. derrick view. A A A B A are also very nice. 2 " 6 " clear 5 " 4 2i' 4 Kerr 3 views. A A A A A A A Note: In the above list ative values of the views, ceilence or interest and B A and B refer to the grade or rel- A indicates a view of special ex- a view of lesser value. 147 EXPLANATION OFTABLE OF TANGENTS & COTANG'S-P-l* 8 I. Required the tangent of the angle 65 20' 1 In the first column of degrees find 65, then pass horizont- ally across to the column headed 20' where find 2.17749 as the tang, required. If the number of minutes in the given angle is not found in the head of the table proceed as follows: II. Required the tangent of the angle 65 26 ' f Proceed as before to get the tangent for 65 20', which is the next lowest number of minutes given at the head of the table. This leaves an excess of 6 minutes. At the right hand of the table under the head of k< Prop . (Proportional) parts to 1 " find 169 in the same line with 65 at the left side. 169 x 6=1014 which added to 2.17749, the tang, for 65 20', equals 2.18763 as the required tangent. (This gives a suffi- ciently approximate Tangent for ordinary use. Exact Tangent =2. 187 55 .) COT A N G E N TS are taken from the table by taking the degrees from the column of degrees at the right side and the minutes from those indi- cated at the foot of the table, thus III. Required the cotangent of the angle 24 40 ? In the right hand column of degrees find 24, then pass horizontally across the table to the left to column haying 40 at the foot, and find 2.17749 as the cotang. required. From this it is seen that the tang, of any angle is the cotang. of the complement of that angle, for 65 20 '+24 40' =90. Proceeding as at II IV. Required the cotangent of angle 24 34'$ (The complement of 65 26'.) Obtain cotangt. for 24 30' which=2.19430 and from col- umn of prop, parts find 169, which multiplied by 4, for the 4' we have in excess of 30 ',=676. \Vhere, in finding the tangent, this correction was added it is now subtracted, in finding the cotangent. 2.19430 minus 676=2.18754 The exact cotangent = 2.18755. USE OFTABLE OF TANGENTS- Tangents are used principally in determining heights and distances by means of angles. Refering to Fig. 11, page 93, suppose a surveyor's tran- sit to be set at A, so the angle FAE can be measured, and suppose that angle to be 38 40 . The line EF is the tangent of the angle FAE. From the table we find the tangent of the angle 38 40' to be .80020 which mul- tiplied by 100, the distance from A to F,=80.02 or 80 ft. as the height of the stream. Proceed in like manner, for any other angle, to multiply the horizontal distance by the tabular tangent to get the length of the tangent. Suppose a 2 ft. rule is used to measure the angle, as described on page 158, and that the opening of the rule is 8 inches which cor- responds to an angle of 38 57' and that the joint is 100 feet from the well. We find from the follow- ing table that the tang, for 38 57 =.80855 whichXlOO =80.85. In this simple way the height of a stream may be determined within a foot or less. So, too, in measuring horizontal distances to in- accessible points, as across a stream. Suppose it is desired to measure the distance A B, Fig. 24, be- tween points on opposite sides of a river, across which measurements cannot be carried. From A lay off a right angle BAC and measure A C any suitable length, say 350 feet. From C measure an- gle A C B which=60 5 then tang, of 60 5'= Fig. 24. 1.73805which X 350=608.3 ft , the distance from A to B 148 TABLE NO. 78. See explanation of table on page 147. NATURAL, TANGENTS. Prop Deg. 0' NX 2W 30' 40' 50' Deg. parts tor o 00000 00291 00582 00873 01164 01455 01746 89 29 1 01746 02036 02328 02619 02910 03201 03492 88 29 2 03492 03783 04075 04366 04658 04949 05241 87 29 3 05241 05533 05824 06116 06408 06700 06993 86 29 4 06993 07285 07578 07870 08163 08456 08749 85 29 5 08749 09042 09335 09629 09923 10216 10510 84 29 6 10510 10805 ! 11099 11394 11688 11983 12278 83 29 7 12278 12574 12869 13165 13461 13758 14054 82 30 8 14054 14351 14648 14945 15243 15540 15838 81 30 9 15838 16137 16435 16734 17033 17333 17633 80 30 10 17633 17933 18233 18534 18835 19136 19438 79 30 11 19438 19740 20042 20345 20648 20952 21256 78 30 12 21256 21560 21864 22169 22475 22781 23087 77 31 13 23087 23393 23700 24008 24316 24624 24933 76 31 14 24933 25242 25552 25862 26172 26483 26795 75 31 15 26795 27107 27419 27732 28046 28360 28675 74 31 16 28675 28990 29305 29621 29938 3025-5 30573 73 32 JI 30573 30891 31210 31530 31850 32171 32492 72 32 18 32492 32814 33136 33460 33783 34108 34433 71 32 19 34433 34758 35085 35412 35740 36068 36397 70 3;} 20 36397 36727 37057 37388 37720 38053 38386 69 33 21 38386 38721 39055 39391 39727 40065 40403 68 34 22 40403 40741 41081 41421 41763 42105 42447 67 34 23 42447 42791 43136 43481 43828 44175 44523 66 34 24 44523 44872 45222 45573 45924 46277 46631 65 35 25 46631 46985 47341 47698 48055 48414 48773 64 36 26 48773 49134 49495 49858 50222 50587 50953 63 36 27 509.53 51319 51688 52057 52427 52798 53171 62 37 28 53171 53545 53920 54296 54673 55051 55431 61 38 29 55431 55812 56194 56577 56962 57348 57735 60 38 30 57735 58124 58513 58905 59297 59691 60086 59 39 31 60086 60483 60881 61280 61681 62C83 62487 58 40 32 62187 62892 63299 63707 64117 64528 64941 57 41 33 64941 65355 65771 66189 66608 67028 6745! 56 42 34 67451 67875 68301 68728 69157 69588 70021 55 43 35 70021 70455 70891 71329 71769 72211 72654 54 44 36 72654 73100 73547 73996 74447 74900 7535-5 53 45 37 75355 75812 76272 76733 77196 77661 78129 52 46 38 78129 78598 79070 79544 80020 8049X 80978 51 47 39 80978 81461 81946 82434 82923 83415 83910 50 49 40 83910 84407 84906 85408 &5912 86419 86929 49 50 52 41 86929 87441 87955 88473 88992 89515 90040 4* CO 42 90040 90569 91099 91633 92170 92709 93252 47 Do 43 93252 93797 94345 94896 95451 96008 96569 i 46 55 44 96569 97133 97700 98270 98843 99420 1.00000 45 57 Deg. X 40' 3W 20 7 10' 0' Deg. NATURAL COTANGENTS. 149 TABLE NO. 79 Continued. NATURAL TANGENTS. Prop Deg. 0' 10' 20' 30' 4(y 50> Ucg. parts tol* 45 1,00000 1.00583 1.01170 1.01761 1.02355 1.02952 1.03553 44 59 46 1.03553 J. 04158 1.04766 1.05378 1.05994 1.06613 1.07-237 43 61 47 1.07237 1.07864 ] .08496 1.09131 1.09770 1.10-414 1.11061 42 63 48 1.11061 .11713 1.12369 1.13029 1.1*694 1.14363 1.15037 41 66 49 1.15037 .15715 1.16398 1.17085 1.17777 1.18474 1.19175 40 69 50 1.19175 .19882 1.20593 1.21310 1.22031 1.22758 1.23490 38 72 51 1.2*190 .24227 1.24969 1.25717 1.26471 1.27230 1.27994 as 75 52 1.27994 .28764 1.29541 1.30323 1.3U10 1 31904 1.3.704 37 78 W 132704 .33511 1.34323 1.35142 135968 136800 1.37608 36 82 54 1.37638 1.38484 1.39336 1.40195 1.41061 1.41934 1.42815 35 86 5-5 1.42815 1.43703 1.44598 1.45501 1.46411 1.47330 1.48256 34 90 56 1.482-56 1.491JH) 1.50133 1.510*4 1.52043 1.53010 1.53987 33 95 57 1.539H7 1.54972 1.55966 1.56969 1.579H1 1 59002 1.60033 32 100 58 160033 1.61074 1.62125 1.63185 1.64256 1.65337 1.66428 31 107 59 1.66428 1.67530 1.68643 1.69766 1.70901 1.72047 1.73205 30 113 60 1.73205 1.74375 1.75556 1.76749 1.77955 1.79174 1.80405 29 120 61 1.80405 1.81649 1.82906 1.84177 1.85462 1.86760 1.88073 ft 128 62 1.88073 1.89400 1.90741 1.92098 1.93470 194858 1.96261 2i 136 68 1.96261 1.97680 1.99116 2.00569 2.02039 2.03526 2.05030 6 146 M 2.05030 2.06553 2.08094 2.09654 2.11233 2.12832 2.14451 25 157 65 2.14451 2.16090 2.17749 2.19430 2.21132 2.22857 2.24604 24 169 66 2.24004 2.26374 2.28167 2.29984 2 31826 2.33693 2.35585 23 183 S7 2.35585 2.37504 2.39449 2.41421 2.434.'2 2.45451 2.47509 22 199 68 2.47509 2.49597 2,51715 2.53865 2.56046 2.58261 2.60509 21 217 69 2.60509 2.62791 2.65109 2.67462 2.69853 2.72281 2.74748 20 235 70 2.74748 2.77254 2.79802 2.82391 2.85023 2.87700 2.90421 19 261 71 2.90421 2.93189 2.96004 2.98868 3.01783 3.04749 3.07768 18 289 72 3.07768 3.10842 3.13972 3.17159 3.20406 3.23714 3.27085 17 322 73 3.27085 3.30521 3.34023 3.37594 3.41236 3.44951 3.48741 16 360 74 3.48741 3.52609 3.56557 3.60588 3.64705 3.68909 3.73205 15 407 75 3.73205 3.77595 3.820a3 3.86671 3.91364 3.96165 4.01078 14 464 76 4.01078 4.06107 4.11256 4.16530 4.21933 4.27471 4.33148 13 534 77 4.33148 4.38969 4.44942 4.51071 4.57363 4.63825 4.70463 12 621 78 4.70463 4.77286 4.84300 4.91516 4.98940 5.06584 5.14455 11 732 79 5.14455 5.22566 5.30928 5.39552 5.48451 5.57638 6.67128 10 876 80 5.67128 5.76937 5.87080 5.97576 6.08444 6.19703 6.31375 9 1068 81 631375 6.43484 6.56055 6.69116 6.82694 6.96823 7.11537 8 1331 82 7.11537 7.26873 7.42871 7.59575 7.77035 795302 8.14435 7 1708 83 8.14435 8.34496 8.55555 8.77689 9.009R3 9.25530 9.51436 6 2270 81 9.51436 9.78817 10.0780 10.3854 10.7119 11.0594 11.4301 5 3168 85 11.4301 11.8262 12.2505 12.7062 13.1969 13.7267 14.3007 4 4728 86 14.3007 14.9&4 15.6048 16.3499 17.1693 18.0750 19.0bli 3 7806 87 19.0811 20.2056 21.4704 22.9038 24.5418 26.4316 28 6363 2 88 28.6363 31.2416 34.3678 38.1885 42.9641 49.1039 57.2900 89 57.2900 68.7501 85.9398 114.589 171.885 343774 cc Deg. SO" 40' 30' 20' 10' 0' DCS NATURAL COTANGENTS. 150 MENSURATION. WEIGHTS, MEASURES AXD USEFUL NUMBERS. AVOIRDUPOIS OR COMMERCIAL WEIGHT. 16 drachms = 1 ounce = 437.5 grains. 16 ounces = 1 pound = 256 drachms = 7000 grains. 28 pounds = 1 quarter = 448 ounces. 4 quarters = 1 cwt. = 112 pounds. 20 cwts. = 1 ton = 2240 pounds (long ton.) 2000 pounds = 1 short or commercial ton. APOTHECARIES WEIGHT. 20 grains = 1 scruple. 3 scruples = 1 drachm = 60 grains. 8 drachms = 1 ounce = 480 ' = 24 scru. 12 ounces = 1 pound = 5760 ' = 288 " = 96 drms. LONG MEASURE. 12 inches = 1 foot. 3 feet = 1 yard = 36 inches. 16H " =1 rod = 198 " 160 rods = % mile = 31680 " = 2640 feet. 320 " =lmile =63360 " =5280 " 3 miles = 1 league. A palm = 3 ins. A hand = 4 ins. A span = 9 ins. A fathom = 6 ft. GUIMTER'S CHAIN. 7. 92 inches = 1 link. 100 links = 1 chain = 4 rods = 22 yards = 66 feet. 80 chains - 1 mile =320 " =1760 " =5280 " SQUARE MEASURE. 144 sqi 9 100 30.25 160 16 10 640 lare inches feet yards rods chains acres _ -t = 1 square foot. = 1 yard. = 1 " (architects = 1 *' rod. = 1 " acre. = 1 u chain. = 1 " acre. = 1 " mile. measure.) i ,-, 43,560 sq. ft. = 1 acre = 208.71 ft. on each side. A circular acre is 235.504 ft. in diameter. MEASURES OF VOLUMES. LIQUID MEASURE. (See also Page 151.} 4 gills = 1 pint = 16 ounces. 2 pints = 1 quart = 8 gills = 32 ounces. 4 quarts = 1 gallon = 32 k ' =8 quarts. 31 gallons = 1 wine barrel. 63 ' =1 hogshead. DRY MEASURE. 2 pints = 1 quart. 4 quarts = 1 gallon = 8 pints . 2 gallons = 1 peck =16 " =8 quarts. 4 pecks = 1 bushel = 64 " =32 " =8 gallons 151 MENSUKATIOX, continued. CUBIC MEASURE. 172 s cubic iuches = 1 cubic foot. 27 " feet = 1 " yard = 46,656 cu, in. Note A cubic foot contains 2200 cylindrical ins., 33)0 spherical ins., or 6600 conical inches. LIQUID MEASURES. Giving approximate sizes of measures to contain given quantities of liquid. em Half pint Pint Quart Diam. ins. Height. 1% 3 2^4 3% 3 l / 2 3 Gallon 2 gallons 8 10 Diam. ins. Height. 7 t> 12 14 14 12 15 A cylinder 1 ft. in diameter and 1 ft. high contains .02909 cubic yards. .7854 " feet. 1357.1712 " inches. .6311U. S. dry bushels. 5.876 U. S. gallons - 48.96 Ibs. 2.524U. S. dry pecks. 20. 196 U. S. dry quarts. 40. 392 U. S. dry pints. 23.50 U, S. liquid quarts. A box 24 " 24 " 16 " 12 SQUARE BOX MEASURE. X 16 inches square and 23 inches deep contains a barrel. y 2 " 1 bushel. y t " Ipeck. .1 gaUon. i/ 2 " 1 quart. X 16 X 16% x 11*4 X 8H X 8*4 X 4% X 4& 14 8 8 8 4 4 4 MISCELLANEOUS A CUBIC FOOT is Equal to 1728 cubic inches. .037037 cubic yard. 7.48052 liquid gallons (of 231 cu. ins.) 6. 42851 U. S. dry gallons. .803564 U. S. bushels (of 3150.42 cu. in.) 3.31426 U. S. pecks. 3300.23 spherical inches. .23748 U. S. liquid barrel of 3iy 2 gals. 62.425 pounds of pure water (approximately 62 V Ibs.) A CUBIC YARD is Equal to 27 cubic feet . 46,656 cubic inches. 21.69623 U. S. bushels (struck.) 201.974 U. S. gallons. A GALLON is Equal to 231 cubic inches. 8.3216 pounds of water (by some authorities 8.3383) 8^ Ibs. .1:3368 cubic foot. A cylinder 7 inches in diam. and 6 inches high. A cube 6.1358 inches on a side. 152 MENSURATION, continued. OF SQUARES, RECTANGLES AND CUBES. The area of any parallelogram = length X width. Area of square = square of one side. The side of a square equal ) ( diameter X .88623, or in area to a given circle ) ( circumference X .2821. To find side of inscribed square X diameter by . 7071 . Area of inscribed square = square of radius X 2. The side of a square X 1.128 = diameter of an equal circle. Side of square = square root of its area. Side of square = square root of Yz the square of the diagonal. The side of a square =the diagonal X .707107 or + 1.41421 Side of square X 1.51967=side of equilateral triangle of equal area. The diagonal = the sq. root of twice the square of a side. The diagonal = side X 1.41421 The length of a rectangle = area -4- breadth. The 4 angles of any quadrilateral = 4 right angles. Any two adjacent angles of any parallelogram 2 right angles. The contents of a cube = length X breadth X height. The length of the side of a cube = the cube root of its contents. OF TRIANGLES AND POLYGONS. The area of any triangle = j %$*% Ste'. OT rpk u t t4 _ f half the product of the 2 sides and i the natural sine of the contained angle. The complement of an angle = its defect from a right angle (90) ' supplement " " " " " two right angles (180) The 3 angles of any triangle 2 right angles. Area of trapszoid = altitude X Y* the sum of the parallel sides. Area of trapezium = divide into 2 triangles and and find their area. Area of equilateral triangle = square of a side X .433. ( sum of its sides X perpendicular Area of any regular polygon K from center to one side and product ( divided by 2, OF CIRCLES. DIAMETER X 3.14159 = circumference. (commonly, 3.1416) X .88623 = side of equal square. X .7071 = " inscribed square, squared X .7854 = area of circle . = circumference -t- 3.14159 (3.1416). = side of equal square -*- .8862. " inscribed square + .7071. = v'area -*- .7854. = circumference X 0.3183. X 7 and product -*- 22. =1.12837 X square root of the area. = as 355 is to 113 so is circumference to diameter. CIRCUMFERENCE -+- 3.1416 = diameter. = diameter X 3.1416. = 3.5446 X square root of area. .= as 113 is to 355 so is diameter to circumference. AREA = square of diameter X . 7854. " circumference X .07958. ' = y z diameter X Yz circumference. * = square of radius X 3.1416. " = ^ areas of circles are to each other as the squares of their ~ ( diameters. Continued on next page. 153 MERSURATION, continued. Doubling the diameter of a circle increases the area 4 times. X side of iTO Diameter of circle of equal priphery as square = side X 1.2732. Side of square of equal periphery as circle = diameter X .7854. Diameter X 1.3468 = side of an equilateral triangle of equal area. Length of arc = number of degrees X .017453 X radius. f From area of outer circle take the area of 1 inner cicle, remainder = area. Area of circular ring = '-{ OR I Sum of diameter X difference of diameters Land product X .7854. Area of sector of circle = length of arc X V& radius. Surface of cylinder equals circumf . X length + area of two ends. Contents Surface of sphere Contents " " of widge pyramid or cone The square of the diam. of a sphere X 3.1416 = its surface. The product of the two axes of an eclipse X .7854 = its area. The sq. rt. of V& the sum of the squares of the two diameters of an elipse X 3.1416 = its circumference. area of end X length . diameter X circumf. cube of diam. X .5236. area of base X Vz altitude. [area of base X 34 altitude. USEFUL MULTIPLIERS. Note : The converse is obtained by dividing instead of by multiplying. Lineal feet X .00019 miles. yards X .000568 Square inches X .00695 -2 square feet. feet X .111 : " yards. ;< yards X .0002067 -s acres. Acres X .4840 square yards. Cubic inches X .00058 = cubic feet. " feet X .03704 S3 yards. Circular inches X .00546 = square feet. Cylindrical inches X .0004546 = cubic '* feet X .02909 se- ' ; yards. Links X .22 ts yards. ' X .66 feet. Feet X 1.5151 = links. Square feet X 2.2957 square links. Width in chains Cubic feet X 8. X 7.48052 = acres per mile. U.S. gallons. inches X .004329 = Ct t, and place marks. Measure the distance in feet between the marks. Then Sine of half _ the angle half the distance between the marks the distance measured toward one of the objects *From a table of sines tind this angle and multiply it by 2- 159 WEIGHT OF A CUBIC FOOT OF SUBSTANCES. Trautwine. Name of substances. Average weight, Ibs. Aluminum, 162 Brick, best pressed " common, hard 125 soft 100 Coal, Pennsylvania anthracite, solid 93 broken, loose 54 moderately shaken 58 heaped bushel. . . . (77 to 83) Bituminous, solid 84 broken, loose 49 heaped, loose bushel (74) Coke, loose 23 to 32 heaped bushel 35 to 42 Cement, Amei ican Hydraulic, Rosendale 56 " Louisville 50 English " Portland 90 Clay, loose 63 Earth, common loam, dry, loose 76 ' moderately rammed 95 " as soft mud 108 Flint 162 Glass 157 Gneiss 168 Granite 170 Gravel 90 to 106 Ice :. 58.7 Iron, cast 450 " wrought 480 Lead 711 Lime, loose or in small lumps 53 S" struck bushel. . . . [66] imestone and marble 168 loose, in fragments Masonry of Granite or limestone, well dressed " mortar rubble 154 " sandstone, well dressed 144 Mortar, hardened 103 Quartz 165 Salt, coarse 45 " fine 49 Sand, pure quartz, dry. loose 90 to 106 " well Shaken 99 to 117 " wet 118 to 130 Sandstone 151 Shales 162 Silver 655 Snow, freshly fallen 5 to 12 " moistened and compacted 15 to 50 Steel 490 Water, pure. 62.425 [Fuller], 62. 37925 [HaswellJ approximately 62^ sea 64.3 WOODS Ash 47 Boxwood 60 Cherry 42 Cork 16 Elm 35 Hemlock .* 25 Hickory 53 Maple 35 Oak, live .... 59, white .... 48, red or black .... 32 to 45 Pine, white 2o yellow 35, southern 45 Green timber usually weighs from to more than dry. 160 TABLE NO. 59. NAILS AND SPIKES. Carnegie, Phipps & Co. Standard Steel Wire Nails. | Steel wire spikes. |Com'n. iron na'ls Size. Long Common. Finishing. Long Diam ins. No. perlb Size. Long No. perlb Diam ins. No . perlb Diam ins. No. perlb 2 d 1 in. .0524 1060 .0453 1558 3 in. .1620 41 2 d 1 in. 800 3 d u .0588 640 .0508 913 3A " .1819 30 8 d U 400 4 d 14 ' .0720 380 ,0508 761 4 " .2043 23 4 d 14 300 5 d If ' .0764 275 .0571 500 44 " .2294 17 5 d U 200 6 d 2 * .0808 210 .0641 350 - 5 " .2576 13 6 d 2 150 7 d 2i * .0858 160 .0641! 315 5* " .2893 11 7 d 2i 120 8 d 24 ' .0935 115 .0720 214 6 " .2893 10 8 d & 85 9 d 2f ' .0963 93 .0720 195 64 " .2249 7| 9' d 21 75 10 d 3 ' .1082 77 .0808 137 7 " .2249 7 10 d 3 60 12 d 3i ' .1144 60 .0808 127 8 " .3648 5 12 d 3J 50 16 d 34 ' .1285 48 '.0907 90 9 " .3648 44 16 d 34 40 20 d 4 ' .1620 31 .1019 62 20 d 4 20 30 d 4} .1819 22 30 d 44 16 40 d 5 * .2043 17 =0 d 5 14 50 d 5* * .2294 13 50 d 54 11 60 d 6 ' .2576 11 60 d 6 8 TABLE NO. 60. WEOUGHT SPIKES. Number to a keg of 150 pounds. Carnegie, Phipps & Co. Length Ins. iin. No. A in. No. fin. No. Length Ins. i in. No. * in< No. fin. No. A in. No. 4 in. No. 3 2250 7 1161 622 482 445 306 34 44 1890 1650 1464 i208 1135 1064 8 9 10 635 573 455 424 391 384 300 270 256 240 222 5 1380 930 742 11 249 203 6 1292 868 570 12 236 180 TABLE NO. 61. TABLE OF MANILLA KOPE. Trautwine. Diam- eter Ins. Circum- ference Inches. Wt. per ft Ibs. Breaking load. Diam- eter [nches . Cir- cumf. Ins. Wt. per ft Ibs. Breaking load. Tons. Lbs. Tons. Lbs. .239 .318 .477 .636 .795 .955 1.11 ? f 34 .019 .033 .074 .132 .206 .297 .404 .25 .35 .70 1.21 1.91 2.73 3.81 560 784 1 568 2 733 4 278 6 115 8 534 1.27 1.43 1.59 1.75 1.91 2.07 2.23 4 g f 64 .528 .668 .825 .998 1.19 1.39 1.62 5.16 6.60 8.20 9.80 11.4 13.0 14.6 11 558 14 784 18 368 21 952 25 536 29 120 32 704 TABLE NO. 62. 1 cubic yard = 201.95 gallons. 161 WELL DIGGING. Adapted from Trautwine. Diameter Cubic yds. for each Diameter Cu. yds. for each Diameter Cubic yards for each in feet. foot of in feet. foot of in feet. foot in depth. depth . depth. 1 .0291 3* .3563 6 1.047 | .0455 .4091 i 1.136 .0654 4* .4654 i 1.229 3 .0891 i .5254 1.325 2 .1164 .5890 7 1.425 i .1473 I .6563 i 1.636 I .1818 5 .7272 8 1.862 .2200 i .8018 i 2.102 3* .2618 .8799 9 2.356 i .3073 1 .9617 * 2.625 For diameters twice as great as those given in the table, for the cu. yds . of digging, take out those opposite % of the greater diam., and X by 4. Thus, for the cu. yds. in each foot of a well 12 ft. in diam., take out the yds. for a well of 6 ft. diam. andxby 4....1.074x4=4.188=cu. yds, for a well of 12 feet diameter. TABLE NO. 63. CAPACITY OF CISTERNS IN GALLONS. For each 10 niches in depth. Haswell. Diam. Gallons . Diam. Gallons . Diam. Gallons. Diam. Gallons. Feet. 2. 2.5 3. 3.5 4. 4.5 19.50 30.60 44.60 59.97 78.33 99.14 Feet. 5. 5.5 6. 6.5 7. 7.5 122.40 148.10 176.25 206.85 239.88 275.40 Feet. 8. 8.5 9. 9.5 10. 11. 313.33 353.72 396.56 461.40 . 489.60 592.40 Feet. 12 13 14 15 20 25 705.0 827.4 959.6 1101.6 1958.4 3059.9 In this table the capacity being given for 10 inches it is but necessary to divide by 10 by moving the decimal point one place to the left, in order to get the capacity for 1 inch . Thus, the capacity for 6 ft. diam and 10 inches deep =176.25 gals., and for 1 inch deep it =17. 625 gals. The capacity for any depths may be found by multiplying the capacity for 1 inch by the depths in inches. Example. How many gals, in a cistern 12 feet in diam. and 9 feet deep? 9 ft. =108 m. 70.5, gals, in one inch, x 108= 7614 gals. Ans. TABLE NO. 64. CAPACITY OF CISTERNS IN BARRELS. OF 31j GALLONS. Leffel. Depth Diameter in feet. in feet. 5 6 7- 8 9 10 11 12 13 14 5 23. 3 1 33. 6 45.7 59.7 75.5 93.2 112.8 134.3 157.6 182.8 6 28.0 40.3 54.8 71.7 90.6 111.9 135.4 161.1 189.1 219.3 7 32.747.0 64.0 83.6 105.7 130.6 158.0 188.0 220.6 255.9 8 37.3:53.7 73.1 95.5 120.9 149.2 180.5 214.8 252.1 292.4 9 42.060.4 82.2 107.4 136.0 167.9 203.1 241.7 283.7 329.0 10 46.7 67.1 91.4 119.4 151.1 186.5 225.7 268.6 315.2 365.5 11 51.373 9 100.5 131.3 166.2 205.1 243.2 295.4 346.7 402.1 12 56.0180.6 109.7 143.2 181.3 223.8 270.8 322.3 378.2 438.6 13 60.787.3 118.8 155.2 196.4 242.4 293.4 349.1 409.7 475.2 14 65.394.0 T27.9 167.1 211.5 2H1.1 315.9 376.0 441.3 511.8 162 A BAKREL. The standard wine barrel contains 31^ gals, of 231 cu. in. In Pennsylvania a wine bbl. =32 gals. The standard wine bbl. contains 4.211 cu. ft. A hogshead =63 gals. The aver- age size of the barrel used for oil or vinegar is about 19J^ ins. diam. of head, 22% ins. diam. of bung, and 29 to 30 ins. long and contains from 48 to 52 gals, the contents being usually marked on the head. In figuring on the barrel capacity of a cistern the size or volume of the barrel should be given or, in case of contract work, it should be specified. By reason of the size of the ordinary barrel being from 48 to 52 gals, it would, for con- venience, be best to figure on the basis of 50 gals, to the bbl. The bbl. of 31^ gals., however, is the one commonly used. MISCELLANEOUS. Shingles. 1000 laid 4 inches to the weather will cover one square of 100 sq. ft. and 5 Dbs of nails will lay them. Lath. 1000 will cover 70 sq. yds. of surface and 11 flbs. of nails will lay them. Mortar. 8 bushels of lime, 16 of sand and 1 of hair will make mortar for 100 sq. yds, of surface. Stone Wall. 1 cord of stone, 3 bushels of lime, and 1 cu. yd. of sand will lay 100 cu. ft. of wall. Brick. 5 courses of brick will lay 1 foot high. 6 brick in a course will lay a flue 4 by 12 inches. 7 9 10 Thickness of wall. 12 8 ' 16 ' 12 " 12 ' 12 ' 16 ' 12 " 20 No. to sq. ft. of wall. 8 inches = 1 brick 14 12 li ' 21 (No allowance being made for 16 " 2 4 28 < mortar or extra thickness of 20 " 2i 35 (brick. Brick 8 X 4 X 2 inches. 24 " 3 * 42 Flooring & Siding. Add to the area to be covered to allow for lap. This is the lumberman's rule in selling. Hay. Get the number of cubic feet in the mow or stack; then, for new hay, divide by about 270 to get tons; for old hay, divide by about 230 to get tons; and for dry clover divide by about 310 to get tons. The weights of different grasses, in the different stages of dryness or compression, vary so greatly that any rule for weight by volume must be so purely arbitrary as to be of but little value. Corn. Get the cubic feet and divide by 2J to get bushels. Apples, Potatoes, & Grain in Bin. Get cu. ft. and X by 8, then point off 1 place for decimals to get contents in bushels or from cubic ft. deduct and the remainder =bushels in bin. (bush. =1.24445 cu. ft.) Example. 100 cu. ftx8=800, pointed off=80 bush or 100 (20) =80 bushels. 163 LUMBER TABLES. TABLE NO. 65. FEET, BOARD MEASURE, IN JOIST, SCANTLING AND TIMBER. Length in feet. IO 12 14 16 18 20 22 24 26 28 30 Size in Inches. FEET, BOARD MEASURE. 2x4 HH s 9 : \ 101 12 13 14s 16 174 181 20 10 12 14 16 18 20 .22 24 26 28 30 2 x 8 134 16 193 214 24 261 294 32 34| 374 40 2x|Q 161 20 23^ 26g 30 334 361 40 434 46| 50 2x|2 20 24 28 32 36 40 44 48 52 56 60 2x|4 2N '28 32| 37i 42 461 514 56 631 654 70 3x4 10 12 14 16 18 20 22 24 26 28 30 3x6 15 18 21 24 27 30 33 36 39 42 45 x 8 20 24 28 32 36 40 44 48 52 56 60 1 O 25 30 35 40 45 50 55 60 65 70 75 3x|2 so 36 42 48 54 60 66 72 78 84 90 3x|4 :tt t2 49 56 63 70 77 84 91 98 105 4 4 in A IB 18| 214 24 261 294 32 341 374 40 4x6 3) 21 28 32 36 40 44 48 52 56 60 4x 26? 32 371 421 48 534 58 64 694 741 80 4 x IO 33| 40 46 53' 60 661 734 80 861 934 100 4 X I 2 40 48 56 64 72 80 88 96 104 112 120 6 x 6 30 36 42 48 54 60 66 72 78 84 90 6x8 40 48 56 64 72 80 88 96 104 112 120 6x|Q 60 60 70 80 90 100 110 120 130 140 150 6x12 HO 72 84 96 108 120 132 144 156 168 180 x 8 x IO 53} B6J 64 80 741 93i 85i 1061 96 120 106 1334 1174 146| 128 160 1381 1734 1494 186 160 200 8x12 80 96 112 128 144 160 176 192 20? 224 240 I Ox IO 8.34 100 117 133 150 167 183 200 217 233 250 IOx| 2 100 120 140 160 180 200 220 240 260 280 300 1 2x| 2 120 144 168 192 216 240 264 288 312 336 360 12x14 140 168 196 224 252 280 308 336 364 392 420 14x14 1634 196 228| 261i 294 3261 3594 392 424 4574 490 TABLE 1X0. 66. FEET BOARD MEASURE, IN 1 INCH BOARDS. New ' Width in inches. Length in feet. 8 10 12 14 16 18 20 22 24 4 6 8 10 12 14 16 18 20 2% 4 6% 8 12 /3 5 3 6% 10 3 11% 15 3 4 6 8 10 12 14 16 18 20 11>* 14 3 18% 21 23^ 8 3 13^ 16 3 21^ 24 26% 6 9 12 15 18 21 24 27 30 P 23^ s* 33^ I* 111 22 25% 29^ 33 36% 8 12 16 20 24 28 32 36 40 RULE for estimating ft. b. m. in any piece of board or timber. [A foot b. m. = 12 X 12 inches by 1 inch thick, = 144 cubic inches.] Multiply the width by the thickness + product by 12 and X quotient by length. Thus : A stick 8 by 10 inches by 10 feet equals 8 X 10 = 80 inches of sectional area which -*- 12 =6% ft. b. m. per foot of length ; this X 10 = 66% ft. 3" by 12" by 10 equals 3 X 12 = 36 , 36 -4- 12 = 3, 3 X 10 = 30 ft. B.M. 4" by 6' by 10' equals 4 X 6 = 24, 24 -H 12 = 2, 2 X 10 = 20 ft. B.M.&c. 164 From Trail ti TABLE NO. 67. ie's t'ivil Engineer's Pocket Book.-' of a Degree of I> .5026 .6693 .8359 1-16 .0052 .1719 .33*5 .5052 .6719 .8385 3-32 .0078 .1745 .3*11 .5078 .6745 .8411 % .0104 H .1771 X .8438 M .5104 h .6771 H .8438 5-33 .0130 .1797 .3164 .5130 .797 .8464 :-;-! .0156 .1823 .3 WO .5150 .6823 .8490 7-32 .0182 .1849 .3516 .5182 .6849 .8516 K .0208 % .1875 % .3542 y .5'208 y* .6875 % .8542 9-32 .0234 .1931 .3568 .5234 .6901 .8568 5-16 .0260 .1927 .3594 .5260 .6927 .8594 11-82 .0286 .1955 .3620 .52b6 , .6953 .8620 % .0313 % .197J 3 8 .364(5 % .5313 % .6979 % .8646 13-32 .0339 .2005 .3672 .5339 .7005 .8672 7-16 .0365 .2031 .3698 .5365 .7031 .8698 15-32 .0391 .2057 .3724 .5391 .7057 .8724 \i .0417 X .20t j 1;, .3750 .5417 y* .7083 y* .8750 17-32 .0443 .2109 .3776 .5443 .7109 .8776 9-16 .0469 .2135 .3802 .5469 .7135 .8802 19-32 .0495 .2161 .3828 .5495 .7161 .8828 K .0521 K .2188 H .3854 N .5521 % .7188 % .8854 21-32 .0547 .221 1 .3880 .5547 .7214 .8880 11-16 .0573 .2240 .3906 .5573 .7240 .8906 23-32 .059J .2263 .3932 .5599 .7266 .8932 K .0625 .2231 H .3958 3 4 .5625 *A .7292 N .8958 25-32 .0651 .2318 .3984 .5651 .7318 .8984 13-16 .0677 .2344 .4010 .5677 .7344 .9010 27-32 .070.5 .2370 .4036 .5703 .7370 .9036 % .0729 % .2396 H .4063 h .5729 % .73% X .9063 29:3 .0755 .2422 .4089 .5755 .7422 .9089 15 IB .0781 .2448 .4115 .5781 .744fc .9115 31-32 .0807 .2474 .4141 .5807 .7474 .9141 1 .0833 3 .2500 5 .4167 7 .5833 9 .7500 11 .9167 1-32 .0859 .252(5 .4193 .5859 .7526 .9193 1-16 .0885 .2552 .4219 .58*5 .7552 .9219 3-3U .0911 .2578 .4245 .5911 .7578 .9245 K .0938 % .2604 U .4271 h .59S8 M .7604 X .9271 5-32 .0964 .2630 .4297 .5964 .7630 .9297 3- 16 .0990 .2656 .4323 .5l$)0 .7656 .9323 7-32 .1016. .2882 .4349 .6016 .7682 .9349 y< .1042 tt .2708 X .4375 i/ .6042 y .7708 K .9375 9-32 .1068 .2734 .4401 ' .6068 .7734 .9401 5-16 .1094 .2760 .4427 .6094 .7760 .9427 11-32 .1120 .2786 .4453 .6120 .7786 .9453 h .1146 % .2813 % .4479 % .6146 % .7813 % .9479 l. l-32 .1172 .2&?9 .4505 .6172 .7839 .9505 1 -16 .1198 .2865 .4531 .6198 .7865 .9531 15-S2 .1224 .2891 .4557 .6224 .7891 .9557 H .1250 1 A i .2917 y* .4583 x. .6250 X .7917 M .9583 n-sz .1276 .2943 .4609 .6276 .7943 .9609 9-16 .1302 .2969 .4635 .6302 .7969 .9635 19-32 .1328 .2995 .4661 .6328 .7995 .9661 fc .1354 % .3021 % .4688 % .6354 % .8021 % .9688 21 -32 .1380 .3047 .4714 .6380 .8047 .9714 11-16 .1406 .3073 .4740 .6406 .8073 .9740 23-32 .1432 .3099 .4766 .6432 .8099 .9766 H .1458 H .3125 % .4792 H .6458 % .8125 H .9792 25-32 .1484 .3151 .4818 .6484 .8151 .9818 13-16 .1510 .3177 .4844 .6510 .8177 .9*44 27-32 .1536 .3203 .4870 .6536 .8203 .9870 H .1563 % .3229 % .4896 % .6563 % .8229 % .9HH5 W32 .1589 1 .3255 .4922 .6589 .8255 .9922 15-16 .1615 .3281 .4948 .6615 .8281 .9948 81-32 .1641 I .3307 .4974 .6641 .8307 .9974 165 TABLE NO. 68. DECIMALS OF AN INCH FOR EACH &th. INCH. ^ds. Aths. Decimal. Fraction. &ds. Aths. Decimal. Fraction. 1 2 1 2 3 4 .015625 .03125 .046875 .0625 1-16 17 18 33 34 35 36 .515625 .53125 .546875 .5625 9-16 3 5 6 .078125 09375 . 19 37 38 .578125 .59375 4 7 8 '.109375 .125 1-8 20 39 40 .609375 .625 5-8 9 . 140625 41 .640625 5 10 '. 15625 21 42 .65625 11 171875 43 .671875 6 12 .1875 3-16 22 44 .6875 11-16 13 203125 45 .703125 7 14 21875 23 46 .71875 15 .234375 47 .734375 8 16 .25 1-4 24 48 .75 3-4 17 . 265625 49 .765625 9 18 . 28125 25 50 .78120 19 296875 51 .796875 10 20 .3125 5-16 26 52 .8125 13-16 21 .328125 53 .828125 11 22 . 34375 27 54 .84375 23 .359375 55 .859375 12 24 .375 3-8 28 56 .875 7-8 25 .390625 57 .890625 13 26 .40625 29 58 .90625 27 .421875 59 .921875 14 28 .4375 7-16 30 60 .9375 15-16 29 .453125 61 .953125 15 30 .46875 31 62 .96875 31 .484375 63 .984375 16 32 .5 1-2 32 64 1 . 1 166 TABLE NO. 69. From Traiitwine's "Civil Engineer** Pocket Book/' HYDRAULICS. TABLE Of the hers. In this table the i mansions ; that is, both iu iuche: square roots of the fifth powers of iium- i umbers and the roots are supposed to be in the same di- j feet, 54 21428 81 59049 1.75 4.051 8.5 210.64 20.5 1902.8 34. 6741 55 22434 82 60888 2. 5.657 8.75 226.48 21. 2020.9 34.5 6991 58 28468 83 62762 2,25 7.594 9. 243. 21.5 2143.4 35. 7247 57 24529 84 64669 2.5 9.882 9.25 260.23 22. 2270.2 35.5 7509 58 25620 85* 66611 2.75 12.541 9.5 278.17 22.5 2401.4 36. 77*i 59 26738 86 63533 & 15.588 9.75 296.83 23. 2537. 36.5 8049 60 . 27886 87 70599 3.25 19.042 10. 316.23 23.5 2677.1 37. 8327 61 29062 88 72646 3.5 22.918 10.5 357.2 24. 2821.8 37.5 8611 62 30268 89 74727 3.75 27.232 11. 401.3 24.5 2971.1 38. 8901 63 31503 90 76843 4. 32. 11.5 448.5 3125. 38.5 9197 64 32768 91 78996 4.25 37.24 12. 498.8 2o!5 3283.6 39._ 9498 65 34063 92 81184 4.5 42.96 12.5 552.4 26. 3446.9 9806 66 35388 93 83408 4,75 49.17 13. 609.3 26.5 3615.1 40'. 10119 67 36744 94 85668 5. 55.90 13.5 669.6 27. 3788. 41. 10764 68 38131 95 87965 5.25 63.15 14. 733.4 27.5 3965.8 42. 11432 69 39548 96 90298 5.5 70.94 14.5 800.6 28. 4148.5 43. 12125 70 40996 97 92664 5.75 79.28 15. 871.4 28.5 4336.2 44. 12842 71 42476 98 95075 6. 88.18 15.5 945.9 29. 4528.9 45. 13584 72 43988 99 97519 6.25 97.66 16. 1024. 29.5 4726.7 46. 14351 73 45531 100 100000 6.5 107.72 16.5 1105.9 30. 4929.5 47. 15144 74 47106 6.75 118.38 17. 1191.6 30.5 5138. 48. 15%3 75 48714 Numbers, in inches. Square roots of fifth powers, in feet. Sq. Rt. of 5th Pow. Sq. Rt. of 5th Pow. Sq. Rt. of 5th Pow. Ins. Feet. Ins. Feet. Ins. Feet. i^ .00006 39* .0547 12. 1.000 H j -00017 4. .0641 % 1.108 M .00035 Lt .0731 13. 1.221 M .00062 % .0827 i^ 1.342 .00098 H .0971 14. 1.470 r/ .00144 5. .1120 y^ 1.605 j^ .0020 1^ .1271 15. 1.747 H .0027 Ht .1428 1.896 .0035 .1590 16. 2.053 u .0044 6. .1768 HI 2.217 1 .0055 /4 .2160 17. 2.389 N .0067 7. .2599 M 2.567 K .0081 .3088 18. 2.756 J^ .0096 8. .3628 2.950 2. .0113 .4228 19. 3.155 .0152 9. .4871 3.365 iz .0198 j^ .5577 20. 3.586 9 .0252 10. .6339 ^ 3.813 8. .0312 .7162 21. 4.051 .0383 11. .8043 H 4.297 H .8990 22. 4.551 Sq. Rt. of 5th Pow. Sq. Rt. of 5th Pow. Ins. Feet. Ins. Feet. 22 X 4.813 42 22.92 23 5.086 43 24.31 H 5.365 44 25.74 24 5.657 45 27.23 25 6.264 46 28.77 26 6.909 47 30.36 27 7.593 48 32.00 28 8.316 49 33.69 29 9.079 50 35.44 30 9.882 51 37.25 31 10.73 52 39.13 32 11.61 53 41.02 33 12.54 54 42.96 34 13.51 55 44.97 35 14.53 56 47.05 36 15.59 57 49.17 37 16.69 58 51.35 38 17.84 59 53.60 39 19.04 60 55.90 40 20.29 61 58.2T 41 21.58 TABLE NO. 70. 167 From Trautuiiie'K "Civil Eii-iiic>er's Pocket Book." MENSURATION. To find the length of a circular arc by tbe following 1 table* Knowing the rad of the circle, and the measure of the arc in deg, min, &c. RULE. Add together the lengths in the table found respectively opposite to the deg, min, &c, of tbe arc. Mult the sum by the rad of the circle. Ex. In a circle of 12.43 feet rad, is an arc of 13 deg, 27 min, 8 sec. How long is the arc? Here, opposite 13 deg in the table, we find, .2268928 27 min " " " .0078540 * sec " " Sum rr .2347856 And .2347856 X 12.43 or rad = 2.918385 feet, the reqd length of arc. LENGTHS OF CIRCULAR ARCS TO RAD 1. No errors. Deg. Length. Deg. Length. Deg. Length. m.. Length. Sec. Length. 1 .0174533 m 1.0646508 121 2.1118484 1 .0002909 1 .0000048 : .034906* 62 1.0821041 122 2.1293017 2 .0005818 2 .0000097 3 .0523599 63 1.0995574 123 2. 1407 550 3 .0008727 3 .0000145 4 .0698132 64 1.1170107 124 2.1642083 4 .0011636 4 .0000194 5 .0872665 65 1.1344640 125 2.1816616 5 .0014544 5 .0000242 6 .104719* 66 1.1519173 126 2.1991149 6 .0017453 6 .0000291 7 .1221730 67 1.1631)706 127 2.2165682 7 .0020362 7 .0000339 8 .1396263 68 1.1 868239 128 2.2340214 8 .0023271 8 .0000388 9 .1570796 69 1.2042772 129 2.2514747 9 . .0026180 9 .0000436 10 .1745329 70 1.2217305 130 2.2689280 10 .0029089 10 .0000485 11 .1919862 71 1.2391*3* 131 2.2863813 11 .0031998 11 .0000533 12 .2094395 72 1. 2566:571 132 2.303H346 12 .0034907 12 .0000582 13 .22O92* 73 1.2740904 133 2.3212879 13 .0037815 13 .0000630 14 .2443461 74 1.2915436 134 2.3387412 14 .0040724 14 .0000679 15 .261799+ 75 1.8089W9 135 2.3561945 15 .0043633 15 .0000727 16 .2792527 76 1.3264502 136 2.3736478 16 .0046542 16 .0000776 17 .2967060 77 1.3439035 137 2..:911011 17 .0049451 17 .0000824 18 .3141593 78 1.36135G8 138 2.40S3544 18 .0052360 18 .0000873 19 .3316126 79 1.37^101 139 2.42*10077 19 .0055269 19 .0000921 20 .3490659 SO 1.3952634 140 2.4434610 20 .0058178 20 .0000970 21 22 .3665191 .3839724 gj 1.4137167 1.43117D 142 2.47r3675 "2 !0063995 22 .0001018 .0001067 23 .40142.17 83 1.4483233 14:5 2.4958208 23 .0066904 23 .0001115 24 .4188791) 84 1.4660766 144 2.)132741 24 .0069813 24 .0001164 25 .43633 .'3 85 1.4835299 145 2.5307274 25 .0072722 25 .0001212 26 .4537856 86 1.5009832 146 2.5481807 26 .0075631 26 .0001261 27 .4712389 87 1.51 84 >ii 4 147 2.5656340 27 .0078540 27 .0001309 28 .4886922 88 1.5358 3:)7 148 2.5830873 28 .0081449 28 .0001357 29 .5061455 89 1.553343) 149 2.6005406 29 .0084358 29 .0001406 30 .52359*8 90 1.57)7975 150 2.6179:,9 30 .0087266 30 .0001454 31 .5410521 91 1.588219. 151 2.6354472 31 .0090175 31 .0001503 32 .55*5054 92 1. 6057*2 J 152 2.6529005 32 .009301-4 32 .0001551 33 .5759587 93 1.6231562 JM 2.6703538 33 .0095963 33 .0001600 34 .5934119 94 1.6406395 154 2.6878070 34 .0098902 34 .0001648 35 .6108652 95 1.65306'JS 155 2.705-J6C3 35 .0101811 35 .0001697 36 .6283185 96 1.6755161 156 2. 72271 M6 36 .0104720 36 .0001745 37 .6457718 97 1.69J5K594 157 2.7401f>(;9 37 .0107629 37 .0001794 38 .6632251 98 1.7104227 158 2.7576202 S8 .0110538 38 .0001842 39 .680678: 99 1.7278760 159 2.7750735 :^9 .0113446 39 .0001891 40 .6981317 100 1.7453293 Ifr) 2.7925268 40 .01163: 5 40 .0001939 41 .715585) 101 1.7827825 161 2.8099801 1 .0116264 1 .0001988 42 .7330383 102 1.7802358 162 2.P274334 2 .0122173 2 .0002036 43 .7504916 103 1.797999] 163 2.8448887 3 .0125082 3 .0002085 44 .7679449 114 1.8151424 164 2.SJVJ3IOO 4 .0127991 4 .0002133 45 .7853982 1)5 1.8:2.-)972ififi 6 .0133809 6 .0002230 47 .8293017 107 1 " ( 7V''j'> 167 2.5H 16999 47 .0136717 7 .0002279 48 .83775:) i08 l.-M'r- ; 168 2.^2:',3l 48 .n!T9fi26 8 .0002327 ^9 .8552113 109 1.9:)240S9 19 2.:-l4(>Of,4 49 .0142535 9 .0002376 50 .87268 46 no 1.919*622 170 2.W705!7 50 .0145444 50 .0002424 51 .8901179 111 1.93731:5 171 2.9*45130 :.l .014*353 51 .0002473 52 .90757-2 112 1.95476 fc 8 172 3.0019663 52 .0151262 52 .0002521 53 .9_>:W2t5 1!3 1.972*221 173 3.0194196 53 .0154171 53 .0002570 54 .912477^ 1 '4 1.9#K?-S 174 3.0368729 54 .01570*0 54 .0002618 55 .95991 M 115 2.017'1"^ 175 3.054326? 55 .0159989 55 .0002666 56 .5*77 '-H 1 '6 2. '"''2 1 5 s '9 176 3.07177H5 =>6 .0162897 56 .0002715 57 .994*377 117 2.0T2V-CV2 177 3.0Mt'_>2'.>s 57 Olfi5806 57 .0002763 58 1.0122910 i :s AO.VHS.--! 17 S.l'V.f.MU M .0168715 58 .0002812 59 1.0297443 119 , 2.079 .0171624 59 .0002860 60 1. U47 157; 120 1 2.0943951 80 .0174533 60 .0002909 168 EXPLANATION OF TABLES OF CIRCLES. It will be noticed that there are three tables of circles. FIRST Table giving diameters in units and EIGHTHS- SECOND - " " TENTHS THIRD ' TWELFTHS- The diameter in all cases extending to 100. The following rules with reference to the table giving the diameters in TENTHS will also be of value. To compute the area or circumference of a diameter great- er than 100 and less than 1001: Kule Take out the area or circumference from the table as though the number had one decimal, and move the deci- mal point two places to the right for area and one place for the circumference. Example Wanted the area and circumference of 567. The tabular area for 56.7 is 2524.9687, and circumference 178.1283. Therefore area for 567=252496.87 and circumf.= 1781. 283. To comptue the area or circumference of a diameter greater than 1000. Rule Divide by a factor 2, 3, 4, 5, etc . , if practicable, that will leave a quotient to be found in the table; then multi- ply the tabular area of the quotient by the square of the factor, to get required area; and the tabular circumference by the factor to get the required circumference. Example Wanted the area and circumference of 2109. Dividing by 3 the quotient is 703, for which the area is 388,150.84 and the circumference 2208.54. Therefore area of 2109 = 388150.84 X 9 ( 9 = square of 3 ) = 3493357.56, and the circumference = 22 08.54 X 3 = 6625.62. The following rules with reference to table giving the diameters in EIGHTHS will also be found of value. If the required diameter is not in the table, separate it and take the circumference of each and add them. Example Wanted the circumference of 25f inches. Circumference of 25 m.=78.5398 and of |J=2.06167; adding these we get 80.60147 the required circumference. This pro- cess will not answer for the area, however. In case the area is wanted, reduce the given diameter to a decimal and multiply this by itself and the product by .7854 (area=square of diameter x. 7854). Reduce to a decimal of a foot or of an inch by use of tables 67 and 68. See AKEA P. 152. Where the diameter contains more than one decimal, or where it contains fractions of an inch, see small tables following the tables giving diameters in TENTHS & TWELFTHS respectively, on pages 177 and 184. See rules on page 152 for calculating diameters, circum- ferences, or areas, or the sides of equal squares, without the use of tables. TABLE NO. 71. 169 From Trautwine*s fivii Engineer's Pocket BooR.'* CIRCLES. TABLE 1 OF CIRCLES. Diameters in units and eighths, &c. Circumferences or areas intermediate of those in this table, may be fonnd by sim- ple arithmetical proportion. No errors. Diam Circumf. Area. j Diam. Circumf. Area. Diam. Circumf. Area. ' Diam. Circumf. Area 1-64 .049087 .00019 3. H 10.9956 9.621 10* i 31.8086 i 80.516 19^4 60.4757 291.04 1-3-2 .098175 .00077 9-16 11.1919 9.9678 X 32.2013 82.516 % 60.8684 294.83 3-64 .147262 .00173 K 11.3883 10.321 K 32.5940 84.541 M 61.2611 298.65 1-16 .196350 .00.507 11-16 11.5846 j 10.680 M 32.9867 86.590 N 61.6538 302.49 3-32 .294524: .00690 h 11.7810 11.045 33.3794 88.664 % 62.0465 306.35 M .3926991 .01227 13-16 11.9773 11.410 H 33.7721 90.763 % 62.4392 310.24 5-32 .490874 .01917 X 12.1737 11.793 % 34.1648 92.886 20. 62.8319 314.16 3-16 589049 .0:1761 15-16 12.3700 12.177 11. 34.5575 95.033 H 63.2246 318.10 7-32 .687223 .0.-J75S 4. 12.56:; I 12. JIM! X 34.9502 97.205 VA. 63.6173 322.06 M .785398 .04 0) MS 12.7o27 12.90.' /4 35.3429 99.402 % 64.0100 326.05 9-32 .885573 .0.-5213 % 1295JI i r:.3<>4 H 35.7356 101.62 3 64.4026 330.06 5-16 .98(748 .071)70 3-lii 1.5.1554 13.772 H 30.1283 103.87 *A 64.7953 334.10 11-32 1.07992 j):i2^i 14 13.3518 14.186 % 36.5210 106.14 % 65.1880 338.16 M 1.17810 .11015 5-16 13.5481 14.607 H 36.9137 10*. 43 y 65.5807 342.25 13-32 1.27627 .12:*!-' :i 8 1.5.711.") 15.0 5.J. y 37.3064 110.75 21. 65.9734 346.36 7-16 1.37445 .150:5! 7-ltJ 1394H 15.46(5 12. 37.69'Jl 113.10 M 66.3661 350.50 15-32 1.47262 .17257 ?4. 14.1.572 15.904 H 38.0918 115.47 J4 66.7588 354.66 M 1.57080 .19835 9-16, 14.3.555 16.:H9 YA. 38.4*45 117.86 M 67.1515 358.84 17-32 1.66897 .2216. % 14.52 )J 16.800 % 3S.S772 120.28 % 67.5442 363.05 9- IB 1.76715 .2U-y) 11-16 14.7282 17 257 % :;: 2!)!! 1 ) 122.72 % 67.9369 367.28 19-32 1.S6532 .27')^ % 14.92215 17.721 % 39.15626 125.19 % 68.3296 371.54 % 1.9S35U .303-0 13- 1. i 15.1 IS.) 18.190 ?i 40.0553 127.68 % 68.7223 375.83 21-32 2.06167 .3!^2t y B 15. 51 5- J 18.665 % 40.4480 130.19 22. 69.1150 380.13 11-16 2.15984 .37122 15-16 15.5116 19.H7 13. 40.8407 132.73 % \ 69.5077 884.46 23-32 2.25802 .4U574 5. 15.703J 19.635 M 41.2334 135.30 V\ 69.9004 388.82 K 2.35619 .4U7:> 1-16 15.M45 20.12J W 41.6261 137.89 % 70.2931 393.20 25-32 2.45437 .479.57 X 16.101)7 20.629 % 42.0188 140.50 H 70.6858 397.61 13-16 2.55254 .51 8 W 3-16 16.2970 21.135 H 42.4115 143.14 % 71.0785 402.04 27-32 2.65072 .55911 Yi 16.49,54 : 21.648 K 42.8042 145.80 % 71.4712 406.49 J* 2.74889 .60132 5-16 16.fi897 22.166 % 43.1969 148.49 H 71.8639 410.97 29-32 2.84707 .64504 K 16.8861 22.691 % 43.5896 151.20 23 72.2566 415.48 15-16 2.94524 .6902:) 7-16 17.0324 23.221 14 43.9823 153.94 M 72.6493 420.00 31-32 3.04342 .73708 %\ 17.2788 28.758 X 44.3750 156.70 73.0420 424.56 1. 3.14159 .78540 9-16 17.4751 24.301 y 44.7677 159.48 H 73.4347 429.13 1-16 3.33794 .88664 % 17.6715 24.850 % 45.1604 162.30 ^ 73.8274 433.74 H 3.53429 .99402 11-16 17.8678 25.406 45.5531 165.13 % 74.2201 438.36 3-16 3.73064 1.1075 % 18.0642 25.967 45.9458 167.99 H 74.6128 443.01 Y< 3.92699 1.2272 13-16 18.2605 26.535 3^ 46.3385 170.87 y 75.0055 447.69 5-16 4.12334 1.3530 % 18.4569 27.109 H 46.7312 173.78 75.3982 452.39 % 431969 1.4849 15-16 18.6532 27.688 15. 47.1239 176.71 H 75.7909 457.11 7-16 4.51604 1.6230 6. 18.8496 28.274 M 47.5166 179.67 y\ 76.1836 461.86 ^ 4.71239 1.7671 X 19.2423 1 29.465 47.9093 182.65 H 76 5763 466.64 9-16 4.90874 1.9175 J4 j 19.6350 ; 30.680 % 48.3020 185.66 y* 76.9690 471.44 K 5.10509 2.0739 %! 20.0277 31.919 % 48.6947 188.69 % 77.3617 476.26 11-16 5.30144 2.2365 K 20.4204 33.183 % 49.0874 191.75 H 77.7544 481.11 % 5.49779 2.4053 H 20.8131 34.472 % 49.4801 194.83 X 78.1471 485.98 13-16 5.69414 2.5S02 % 21.2058 35.785 X 49.8728 197.93 25 78.5398 490.87 Jg 5.89049 2.7612 K 21.5984 37.122 16. 50.2655 201.06 M 78.9325 495.79 15-16 6.08684 2.9483 7. 21.9911 38.485 H 50.6582 204.22 y\ 79.3252 500.74 2. 6 28319 3.1416 H 22.3838 39.871 H 51.0509 207.39 % 79.7179 505.71 1-16 6.47953 3.3410 H 22.7765 41.282 % 51.4436 210.60 y* 80.1106 510.71 K 6.67588 3.5466 * 23.1692 42.718 K 51.8363 213.52 % 80.5033 515.72 3-16 687223 3.75S3 K 23.5619 44.179 % 52.2290 217 08 % 80.8960 520.77 H 7.06858 3.9761 % ! 23.9546 45664 H 52.6217 220.35 % 81.2887 525.84 516 7.26493 4.2000 %i 24.3473 47.173 % 53.0144 223.65 26 81.6814 530.93 % 7.46128 4.4301 X 24.7400 48.707 17. 53.4071 226.98 H 82.0741 536.05 7-16 7.65763 4.6664 8. 25.1327 50.265 M 53.7998 230.33 y*. 82.4668 541.19 K 7.85398 4.9087 X 25.5254 51.849 y 54.1925 233.71 X 82.8595 546.35 9-16 8.05033 [5.1572 y* 25 9181 53.456 % 54.5852 237.10 % 83.2522 551.55 ^ 8.24668 i 5.4119 H 26.3108 55.088 H 54.9779 240.53 K 83.6449 556.76 11-16 8.44303 5.6727 X 26.7035 56.745 % 55.3706 243.98 X 84.0376 562.00 V\ 8.63938 5.9396 % 27.0962 58.426 X 55.7633 247.45 % 84.4303 567.27 13-16 8.83573 6.2126 % 27.4889 60.132 % 56.1560 250.95 27 84.8230 572.56 X 9.03208 6.4918 % 27.8816 61.862 18. 56.5487 254.47 U 85.2157 577.87 15-16 9.22843 6.7771 9. 28.2743 63.617 Ml 56.9414 258.02 3 85.6084 583.21 . 9.42478 7.0686 M 28.6670 65.397 ^ 57.3341 261.59 % 86.0011 588.57 1-16 9.62113 7.3662 M 29.0597 67.201 N 57.7268 265.18 % 86.3938 593.96 J^ 9.81748 7.6699 % 29.4524 69.029 H 58.1195 268.80 N 86.7865 599.37 3-16 10.0138 7.9798 M 29.8451 70.882 N 58.5122 272.45 K 87.1792 604.81 % 10.2102 8.2958 N 30.2378 72.760 % 58.9049 276.12 % 87.5719 610.27 5-16 10.4065 8.6179 K 30.6305 74662 % 59.2976 279.81 28 87.9646 615.75 % 10.6029 8.9462 X 31.0232 76.589 19. 59.6903 283.53 H 88.3573 621.2S T- 16 10.7992 9.2806 10. 31.4159 78.540 60.0830 287.27 y* 88.7500 636.84 170 TABLE NO. 71 COST. From Trautwine's "Civil Engineer's Pocket Book." CIRCLES. TABLE 1 OF CIRCXES (Continued). Diameters in units anil eighths, Ac. . Area. Diam. Uiroami. Area. M& 89.1427 j 632.36 38. 119.381 : 134.1 47% ! 149.618 1781.4 O'xi 179.856 ! 2574.2 | 89.5354 637.94 X 119.773 141.6 150.011 1790.8 xi 180.249 2585-4 89.9281 643.55 120.166 149.1 y 150.404 1800.1 xi 180.642 2596.7 % 90.3208 649.18 % 120.559 156.6 48 150.796 1809.6 xi 181.034 2608.0 % 90.7135 654.84 120.951 164.2 xi 151.189 1819.0 3 4 181.427 2619.4 S9. 91.1062 660.52 % 21.344 171.7 i 1.51.582 1828.5 y 8 181.820 2630.7 H 91.4989 666.23 % 21.737 179.3 iL 151.975 1837.9 5S. 182.212 2642.1 91.8916 671.96 % 22.129 186.9 \o 152.367 1847.5 X 182.605 2653.5 H 92.2843 677.71 39. 22.522 194.6 % 152.760 1857.0 182.998 2664.9 i^ 92.6770 683.49 x 22.915 202.3 153.153 1866.5 % 183.390 2676.4 xii 93.0697 689.30 xi 23.308 210.0 y 153.545 1876.1 i^ 183.783 2687.8 x4 93.4624 695.13 % 23.700 217.7 49. 153.938 1885.7 RX 184.176 2699.3 % 93.8551 700.98 y* 24.093 ' 225.4 l /i 154.331 1895.4 8 4 184.569 2710.9 30. 94.2478 706.86 % 24.486 233.2 i^ 154.723 1W)5'.0 TX 184.961 2722.4 H 94.6405 712.76 % 24.878 241.0 N 155.116 1914.7 59. 185.354 2734.0 95.0332 718.69 % 25.271 248.8 x^ 155.509 1924.4 rx 185.747 2745.6 x'S 95.4259 724.64 40. 23.664 256.6 % 155.902 1934.2 Ji 186.139 2757.2 % 95.8186 730.62 y*, _r,.n5i 264.5 ?4 156.294 1943.9 N 1*6.532 2768.8 8* 96.2113 736.62 ' 4 26.449 272.4 % 156.687 1953.7 y* 186.925 2780.5 96.6040 742.64 3/8 26.842 280.3 50. 157.080 1963.5 187.317 2792.2 yt 96.9967 748.69 hi 27.235 288.2 i^j 157.472 1973.3 % 187.710 2803.9 81. 97.3894 754.77 % 27.627 296.2 i ' 157.865 1983.2 y 188.103 2815.7 i* 97.7821 760.87 ?i 28.020 304.2 ^8 158.258 1993.1 60. 188.496 2827.4 98.1748 766.99 % 128.413 312.2 LJ 158.650 2003-0 iz 188.888 2839.2 % 98.5675 773.14 41. 128.805 320.3 % 159.043 2012.9 y 189.281 2851.0 j^ 98.9602 779.31 129 198 328.3 H 159.436 2022.8 % 189.674 2862.9 % 99.3529 785.51 2 129.591 336.4 % 159.829 2032.8 / 190.066 2874.8 ^i 99.7456 791.73 % 129.983 344.5 51. 160.221 2042.8 BX 190.459 2886.6 W 100.138 797.98 % 130.376 352.7 \z 160.614 2052.8 % 190.852 2898.6 82. 100.531 804.25 % 130.769 1360.8 IX 161.007 2062.9 191.244 2910.5 /^ 100.924 810.54 H \ 131.161 369.0 x8 161.399 2073.0 61. 191.637 2922.5 i,' 101.316 816.86 K 131.554 377.2 161.792 2083.1 192.030 2934.5 y 101.709 823.21 42. 131.947 385.4 M 162.185 2093.2 M 192.423 2946.5 1 102.102 829.58 X I32.:uo 393.7 162.577 2103.3 H 192.815 2958.5 RZ 102.494 835.97 >4 \ 132.732 402.0 rx 162.970 2113.5 193.208 2970.6 $ 102.887 842.39 * g 133.125 410.3 52. 163.363 2123.7 RX 193.601 2982.7 rx 103.280 848.83 14 133.518 418.6 H 163.756 2133.9 xi 193.993 2994.8 33. 103.673 855.30 x g 133.910 427.0 164.148 2144.2 % 194.386 3006.9 H 104.065 861.79 34 | 134.303 435.4 % 164.541 2154.5 62. 194.779 3019.1 i^ 104.458 868.31 % ! 134.696 443.8 yd 164.934 2164.8 H 195.171 3031.3 % 104.851 874.85 43. ! 135.088 452.2 % 165.326 2175.1 y\ 195.564 3043.5 N 105.243 881.41 xi 135.481 460.7 % 165.719 2185.4 % 195.957 3055.7 105.636 888.00 M 135.874 469.1 % 166.112 2195.8 % 196.350 3068.0 9i 106.029 894.62 2 8 136.267 477.6 53. 166.504 2206.2 % 196.742 3080.3 V 106.421 901.26 % 136.659 1486.2 166.897 i 2216.6 % 197.135 3092.6 34. 106.814 | 907.92 K 137.052 1494.7 ^ 167.290 2227.0 % 197.528 3104.9 Ji 107.207 914.61 137.445 1503.3 167.683 i 2237.5 63. 197.920 3117.2 . i/ 107.600 921.32 xfc 137.837 1511.9 X 168.075 ! 2248.0 xfi 198.313 3129.6 % 107.992 928.06 44. 138.230 1520.5 % 168.468 2258.5 IX 198.706 3142.0 ^ 108.385 934.82 \z 138.623 1529.2 % 168.861 2269.1 x"8 199.098 3154.5 N 108.778 941.61 Y 139.015 1537.9 % 169.253 i 2279.6 V4 199.491 3166.9 109.170 948.42 % 139.408 1546.6 54. 169.646 2290.2 xi 199.884 3179.4 *x 109.563 955.25 ix 139.801 1555.3 % 170.039 2300.8 xi 200.277 3191.9 85. 109.956 9(52.11 xi 140.194 1564.0 IX 170.431 i 2311.5 % 200.669 3204.4 110.348 969.00 9i 140 586 1572.8 % 170.824 2322.1 64. 201.062 3217.0 34 110.741 I 975.91 TX 140.979 ! 1581.6 1^ 171.217 2332.8 xi 201.455 3229.6 ^/ 111.134 982.84 45. 141.372 1590.4 Y 171.609 2343.5 y\ 201.847 3242.2 s 111.527 989.80 N 141.764 1599.3 % 172.002 2354.3 % 202.240 3254.8 tx 111.919 996.78 42.157 1608.2 y 172.395 2365.0 x*> 202.633 3267.5 % 112.312 1003.8 az 42.550 1617.0 55. 172.788 2375.8 % 203.025 3280.1 TX 112.705 1010.x IX 42.942 1626.0 173.180 2386.6 H 203.418 3292.8 M. 113.097 1017.9 H 43.335 1634. xi 173.573 2397.5 203.811 3305.6 113.490 1025-0 43.728 1643. 173.966 2408.3 65. 204.204 3318.3 M 113.883 10321 K 44.121 1652. X 174.358 2419.2 % 204.596 3331.1 / 114.275 1039.2 46 44.513 1661. 174.751 2430.1 y\ 204.989 3343.9 i^ 114.668 1046.3 M 44.906 1670. H 175.144 2441.1 N 205.382 3356.7 RX 115.061 1053.5 45.299 1680. TX 175.536 2452.0 x^ 205.774 3369.6 5i 115.454 1060.7 % 45.691 1689. Mk 175.929 2463.0 N 206.167 3382.4 7X 115.846 1068.0 ix 46.084 1698. xf) 176.322 2474.0 206.560 3395.3 87. 116.239 1075.2 fcX 46.477 707. 1^ 176.715 2485.0 K 206.952 3408.2 116.632 1082.5 % 46.869 716. ^8 177.107 2496.1 66. 207.345 3421.2 M 117.024 1089.8 TX 47.2H2 725. ^ 177.500 2507.2 % 207.738 3434.2 N 117.417 1097.1 47. 47.655 734. N 177.893 2518.3 % 208.131 3447.2 117.810 1104.5 4,SO; > 744. * 178.285 2529.4 % 208.523 3460.2 118.202 ; 1111.* 48.440 753. 178.678 2540.6 y* 208.916 3473.2 / 118.596 1119.2 % 48.833 762. 57. * 179.071 2551.8 N 209.309 3486.3 K J. 18.988 i 1126.7 H 149.226 772. 179.463 2563.0 N 209.701 3499.4 TABLE NO. 71 CON. 171 From Trautwiue** -4Jivii Engineer'* iPoeket Book." CIBCLES. TABLE 1 OF CIRCI.ES-(Continued). Diameter** in units and eighths, Ac. Diam. Circumf. Area. Diam. Circumf. Area. Diam. Circumf. Area. Diam. Circumf. Area. ~% 210.094 i 3512.5 210.487 3525.7 75^; 236.405 4447.4 236.798 ! 4462.2 ^8jg! 262.716 263.108 5492.4 5508.8 92. 289.027 6647.6 289.419 6665.7 IX 210.879 3538.8 1^; 237.190 4477.0 v 263.501 5525.3 IX 289.812 6683.8 ^ 211.272 3552.0 xi 237.583 4491.8 84. 263.894 5541.8 xi 290.205 6701.9 xi 211.665 3565.2 H 237.976 4506.7 xi 264.286 5558.3 xi 290.597 6720.1 xi 212.058 3578.5 rx 838.368 4521.5 264.679 5574.8 xi 290.990 6738.2 xi 212.450 3591.7 76. 238.761 4536.5 xi 265.072 5591.4 H 291.383 6756.4 Ji 212.843 3605.0 239.154 4551.4 265.465 5607.9 291.775 6774.7 JX 213.236 3618.3 H 239.546 4566.4 xi 265.857 5624.5 93. ' 292.168 6792.9 68. 213.628 3631.7 % 239.939 4581.3 xi 266.250 5641.2 xi 292.561 6811.2 xi 214.021 3645.0 240.332 45%. 3 xi 266.643 5657.8 292.954 682V.5 214.414 3658.4 xi 240.725 4611.4 85. 267.035 5674.5 xi 293.346 6847.8 xi 214.806 3671.8 xi 241.117 4626.4 xi 267.428 5691.2 xi 293.739 j 6866.1 xi 215.199 3685.3 u 241.510 4641.5 k 267.821 5707.9 xi 294.132 6884.5 215.592 3698.7 77. 241.903 4656.6 xi 268.213 5724.7 H 294.524 6902.9 a// 215.984 3712.2 242.295 4671.8 xi 268.606 5741.5 294.917 6921.3 >i 216.377 3725.7 IX 242.688 4686.9 268.999 5758.3 94. 295.310 6939.8 69. 216.770 3739.3 xi 243.081 4702.1 x^ 269.392 5775.1 xi 295.702 ! 6958.2 xi 217.163 3752.8 }*> 243.473 4717.3 xi 269.784 5791.9 IX 296.095 6976.7 217.555 3766.4 xi 243.866 4732.5 86. 270.177 5808.8 xi 296.488 6995.3 9i 217.948 3780.0 H 244.259 4747.8 xi 270.570 5825.7 xi 2%.881 7013.8 218.341 3793.7 244.652 4763.1 x4 270.962 5842.6 % 297.273 7032.4 2i 218.733 3807.3 78. 245.044 4778.4 N 271.355 5859.6 * 297.666 7051.0 3 i 219.126 3821.0 ^ 245.437 4793.7 271.748 5876.5 298.059 7069.6 JX 219.519 3834.7 xi 245.830 4809.0 xi 272.140 5893.5 95. 298.451 7088.2 70. 219.911 3848.5 246.222 48'24.4 h 272.533 5910.6 xi 298.844 7106.9 220.304 3862.2 xi 246.615 4839.8 272.926 5927.6 x4 299.237 7125.6 IX 220.697 3876.0 xi 247.008 4855.2 87. 273.319 5944.7 N 299.629 7144.3 xi 221.090 3889.8 % 247.400 4870.7 273.711 5961.8 N 300.022 7163.0 xi 221.482 3903.6 247.793 4886.2 H 1274.104 5978.9 xi 300.415 7181.8 xi 221.875 3917.5 79. 248.186 4901.7 % 274.497 5996.0 8 300.807 7200.6 5 222.268 3931.4 % 248.579 4917.2 274.889 ! 6013.2 V 301.200 7219.4 H 222.660 3945.3 y* 248.971 4932.7 xi 275.282 6030.4 96. 301.593 1238.2 71. 223.053 3959.2 % 249.364 4948.3 9i 275.675 6047.6 IX 301.986 7257.1 xi 2-23.446 3973.1 249.757 4963.9 Ji 276.067 6064.9 H 302.378 72760 223.838 3987.1 Y 250.149 4979.5 88. 276.460 6082.1 % 302.771 7294.9 xi 224.231 4001.1 H 250.542 4995.2 276.853 6099.4 303.164 7313.8 3^ 224.624 4015.2 xi 250.935 5010.9 xi ! 277.246 6116.7 xi 303.556 7332.8 xi 225.017 4029.2 80. 251.327 5026.5 277.638 6134.1 H 303.949 7351.8 a^ 225.409 4043.3 xi 251.720 ! 5042.3 y 278.031 6151.4 304.342 7370.8 x 225.802 4057.4 252.113 ! 5058.0 xi 278.424 6168.8 97. * 304.734 7389.8 72. 226.195 4071.5 xi 252.506 5073.8 a/ 278.816 6186.2 xi 305.127 7408.9 226.587 4085.7 252.898 5089.6 xi i 279.209 | 6203.7 305.520 7428.0 M 226.980 4099.8 xi 253.291 5105.4 89. 279.602 6221.1 xi 305.913 7447.1 xi 227.373 4114.0 253.684 5121.2 , 279.994 6238.6 xi 306.305 7466.2 xi 227.765 4128.2 u 254.076 5137.1 y* 280.387 6256.1 xi 306.698 7485.3 N 228.158 4142.5 81. 254.469 5153.0 % 280.780 6273.7 307.091 7504.5 xj 228.551 4156.8 254.862 5168.9 xi ! 281.173 6291.2 V 307.483 7523.7 H 228.944 4171.1 M 255.254 5184.9 281.565 6308.8 98. 8 307.876 7543.0 73. 229.336 4185.4 255.647 5200.8 N 281.958 6326.4 xi 308.269 7562. J 229.729 4199.7 xi 256.040 5216.8 ?i 282.351 6344.1 N 308.661 7581.5 y* 230.122 4214.1 N 256.433 5232.8 90. 282.743 6361.7 s 309.054 7600.8 xi 230.514 4228.5 ji 256.825 5248.9 xi 283.136 6379.4 N 309.447 \ 7620.1 230.907 4242.9 Ji 257.218 5264.9 | 283.529 6397.1 % 309.840 7639.5 xi 231.300 4257.4 82. 257.611 5281.0 xi 283.921 6414.9 &i 310.232 i 7658.9 J^ 231.692 4271.8 xi 258.003 5297.1 X* 284.314 6432.6 xi 310.625 7678.3 xi 232.085 4286.3 >i 258.3% 5313.3 xi 284.707 6450.4 99. " 311.018 7697.7 74. 232.478 4300.8 xi 258.789 > 5329.4 x4 285.100 .6468.2 xi 311.410 7717.1 232.871 4315.4 259.181 5345.6 xi 285.492 6486.0 311.803 7736.6 14 233.263 4329.9 xi 259.574 5361.8 91. 285.885 6503.9 xi 312.1% 7756.1 ft 233.656 4344.5 xi 259.%7 5378.1 286.278 6521.8 IX 312.588 7775.6 % 234.049 4359.2 Ji 260.359 1 5394.3 j/ 286.670 6539.7 xi 312.981 7795.2 N 234.441 4373.8 83. 260.752 5410.6 xi 287.063 6557.6 II 313.374 7814.8 234.834 4388.5 ^i 261.145 5426.9 Ix. 287.456 6575.5 ?i 313.767 7834.4 235.227 4403.1 y* 261.538 5443.3 R/ ! 287.848 6593.5 100. 314.159 7854.0 75. 235.619 4417.9 xi 261.930 5459.6 a/ 288.241 6611.5 ft 236.012 4432.6 X 262.323 5476.0 * 288.634 6629.6 172 TABLE NO. 72. From Trantwine's "Civil Engineer's Pocket Book." CIRCLES. TABLE 2 OF CIRCLES. Diameters in units and tenths. Dia. Circumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. 0.1 .314159 .007854 6.3 19.79203 31.17245 12.5 39.26991 122.7185 .2 .628319 .031416 .4 20.10619 32.16991 .6 39.58407 124.6898 .3 .942478 .070686 .5 20.42035 33.18307 .7 39.89823 126.6769 .4 1.256637 .125664 .6 20.73451 34.21194 .8 40.21239 128.6796 .5 1.570796 .196350 .7 21.04867 35.25652 .9 40.52655 130.6981 .6 1.884956 .282743 .8 21.36283 36.31681 13.0 40.84070 132.7323 .7 2.199115 .384845 .9 21.67699 37.39281 .1 41.15486 134.7822 .8 2.513274 .502655 7.0 21.99115 38.48451 .2 41.46902 136.8478 .9 2.827433 .636173 .1 22.30531 39.59192 ;3 41.78318 138.9291 1.0 3.141593 .785398 .2 22.61947 40.71504 .4 42.09734 141.0261 .1 3.455752 .950332 .3 22.93363 41.85387 .5 42.41150 143.1388 .2 3.769911 1.13097 .4 23.24779 43.00840 .6 42.72566 145.2672 .3 4.084070 1.32732 .5 23.56194 44.17865 .7 43.03982 147.4114 .4 4.398230 1.53938 .6 23.87610 45.36460 .8 43.35398 149.5712 .5 4.712389 ! 1.76715 .7 24.19026 46.56626 .9 43.66814 151.7468 .6 5.026548 i 2.01062 .8 24.50442 47.78362 14.0 43.98230 153.9380 .7 5.340708 : 2.26980 .9 24.81858 49.01670 .1 44.29646 156.1450 .8 5.654867 2.54469 8.0 25.13274 50.26548 .2 44.61062 158.3677 .9 5.969026 2.83529 .1 25.44690 51.52997 .3 44.92477 160.6061 2.0 6.283185 3.14159 .2 25.76106 52.81017 .4 45.23893 162.8602 .1 6.597345 3.46361 .3 26.07522 54.10608 .5 45.55309 165.1300 .2 6.911504 ! 3.80133 .4 26.38938 55.41769 .6 45.86725 167.4155 .3 7.225663 4.15476 .5 26.70354 56.74502 .7 46.18141 169.7167 .4 7.539822 4.52389 .6 27.01770 58.08805 .8 46.49557 172.0336 .5 7.853982 4.90874 .7 27.33186 59.44679 .9 46.80973 174.3662 .6 8.168141 5.30929 .8 27.64602 60.82123 15.0 47.12389 176.7146 .7 8.482300 5.72555 .9 27.96017 62.21139 .1 47.43805 179.0786 .8 8.796459 j 6.15752 9.0 28.27433 63.61725 .2 47.75221 181.4584 .9 9.110619 , 6.60520 .1 28.58849 65.03882 .3 48.06637 183.8539 8.0 9.424778 7.06858 .2 28.90265 66.47610 .4 48.38053 186.2650 .1 9.738937 ! 7.54768 .3 29.21681 67.92909 .5 48.69469 188.6919 .2 10.05310 ! 8.04248 .4 29.53097 69.39778 .6 49.00885 191.1345 .3 10.36726 ; 8.55299 .5 29.84513 70.88218 .7 49.32300 193.5928 .4 10.68142 i 9.07920 .6 30.15929 72.38229 .8 49.63716 196.0668 .5 10.99557 9.62113 .7 30.47345 73.89811 .9 49.95132 198.5565 .6 11.3097^ 10.17876 .8 30.78761 75.42964 16.0 50.26548 201.0619 .7 11.62389 10.75210 .9 31.10177 76.97687 .1 50.57964 203.5831 .8 11.93805 11.34115 10.0 31.41593 78.53982 .2 50.89380 206.1199 .9 12.25221 11.94591 .1 31.73009 80.11847 .3 51.20796 208.6724 4.0 12.56637 12.56637 .2 32.04425 81.71282 .4 51.52212 211.2407 ^ 12.88053 13.20254 .3 32.35840 83.32289 .5 51.83628 213.8246 '.2 13.19469 13.85442 .4 32.67256 84.94867 .6 52.15044 216.4243 .3 1 13.50885 14.52201 .5 32.98672 86.59015 .7 52.46460 219.0397 .4 13.82301 15.20531 .6 33.30088 88.24734 .8 52.77876 221.6708 .5 14.13717 15.90431 .7 33.61504 89.92024 .9 53.09292 224.3176 .6 | 14.45133 16.61903 .8 33.92920 91.60884 17.0 53.40708 226.9801 .7 14.76549 17.34945 .9 34.24336 93.31316 .1 53.72123 229.6583 .8 15.07964 18.09557 11.0 34.55752 - 95.03318 .2 54.03539 232.3522 .9 15.39380 18.85741 .1 34.87168 96.76891 .3 54.34955 235.0618 5.0 15.70796 19.63495 .2 35.18584 98.52035 .4 54.66371 237.7871 .1 16.02212 20.42821 .3 35.50000 100.2875 .5 54.97787 240.5282 .2 16.33628 21.23717 .4 35.81416 102.0703 .6 55.29203 i 243.2849 .3 16.65044 22.06183 .5 36.12832 103.8689 .7 55.60619 ! 246.0574 .4 16.96460 22.90221 .6 36.44247 105.6832 .8 55.92035 248.8456 .5 17.27876. 23.75829 .7 36.75663 107.5132 .9 56.23451 251.6494 .6 17.59292 24.63009 .8 37.07079 109.3588 18.0 56.54867 254.4690 .7 17.90708 25.51759 .9 37.38495 111.2202 .1 56.86283 257.3043 .8 18.22124 26.42079 12.0 37.69911 113.0973 .2 57.17699 260.1553 .9 18.53540 27.33971 .1 38.01327 114.9901 .3 57.49115 263.0220 &o 18.84956 28.27433 .2 38.32743 116.8987 .4 57.80530 265.9044 .1 19.16372 29.22467 .3 38.64159 118.8229 .5 58.11946 268.8025 .2 19.47787 30.19071 .4 38.95575 120.7628 .6 58.43362 271.7163 TABLE NO. 72 CON. 173 From I i .mi \\ in< s < ivil Engineer's Pocket Book." CIRCLES. TABLE 2 OF CIRCLES (Continued). in uiiifs and tenths. Dia. Cireumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. 18.7 58.74778 274.6459 24.9 78.22566 486.9547 31.1 97.70353 759.6450 .8 59.ur>liq 277.5911 25.0 78.53982 490.8739 .2 98.01769 764.5380 .9 59.37610 280.5521 .1 1 78.85398 494.8087 .3 98.331 85 769.4467 19.0 59.69026 283.5287 .2 79.16813 498.7592 .4 98.64601 774.3712 .1 r,!25 .6 80.42477 514.7185 .8 99.90265 794.2260 .5 61.26106 298.6477 .7 80 73893 518.7476 .9 100.2168 799.2290 .6 61.57522 301.7186 .8 81 .05309 522.7924 32,0 100.5310 804.2477 .7 61.88938 304.8052 .9 81.36725 526.8529 .1 100.8451 809.2821 .8 62.20353 307.9075 26.0 81.68141 530.9292 .2 101.1593 814.3322 .9 62.51769 311.0255 .1 81.99557 535.0211 .3 101.4734 819.3980 20.0 62.83185 314.1593 .2 82.30973 539.1287 .4 101.7876 824.4796 .1 63.14001 317.3087 .3 82.62389 543.2521 .5 102.1018 829.5768 .'2 63.46017 3:20.4739 .4 82.93805 5473911 ' .6 102.4159 834.6898 .3 63.77433 323.6547 .5 83.25221 551.5459 .7 102.7301 839.8184 .4 ; 64.08849 , 326.8513 .6 83.56636 555.7163 .8 103.0442 844.9628 .5 64.40265 330.0636 .7 : 83.88052 559.9025 .9 103.3584 850.1228 .6 i 64.71681 333.2916 .8 84.19468 564.1044 33.0 103.6726 855.2986 .7 I 65.03097 336.5353 .9 84.50884 568.3220 .1 103.9867 860.4901 .8 65.34513 339.7947 27.0 I 84.82300 572.5553 .2 ! 104.3009 865.6973 .9 65.65929 343.0698 .1 85.13716 576.8043 .3 | 104.6150 870.9202 21.0 65.97345 346.3606 .2 ' 85.45132 581.0690 .4 104.9292 87S.1588 .1 66.28760 349.6671 .3 85.76548 585.3494 .5 105.2434 881.4131 .2 66.60176 352.9894 .4 86.07964 589.6455 .6 105.5575 886.6831 .3 66.91592 356.3273 .5 86.39380 593.9574 .7 105.8717 891 .9688 .4 67.23008 359.6809 .6 86.70796 598.2849 .8 i 106.1858 897.2703 .5 67.54424 363.0503 .7 87.02212 602.6282 .9 106.5000 902.5874 .6 67.85840 366.4354 .8 87.33628 606.9871 34.0 106.8142 907.9203 .7 68.17256 369.8361 .9 87.65044 611.3618 .1 107.1283 913.2688 .8 68.48672 373.2526 28.0 87.96459 615.7522 .2 107.4425 918.6331 .9 68,80088 376.6848 .1 88.27875 620.1582 .3 107.7566 924.0131 22.0 69.11504 380.1327 .2 88.59291 624.5800 .4 108.0708 929.4088 .1 69.42920 383.5963 .3 88.90707 629.0175 .5 108.3849 934.8202 .2 69.74336 387.0756 .4 89.22123 633.4707 .6 108.6991 940.2473 .3 70.05752 390.5707 .5 89.53539 637.9397 7 109.0133 945.6901 .4 70.37168 394.0814 .6 89.84955 642.4243 & } 109.3274 951.1486 .5 70.68583 397.6078 .7 | 90.16371 646.9246 .9 ; 109.6416 956.6228 .6 70.99999 401.1500 .8 90.47787 651.4407 35.0 109.9557 962.1128 .7 71.31415 404.7078 9 90.79203 655.9724 .1 110.2699 967.6184 .8 71.62831 408.2814 29.0 91.10619 660.5199 .2 110.5841 973.1397 .9 71.94247 411.8707 .1 91.42035 665.0830 .3 110.8982 j 978.6768 23.0 72.25663 415.4756 .2 91.73451 669.6619 .4 111.2124 984.22% .1 72.57079 419.0963 .3 92.04866 674.2565 .5 111.5265 989.7980 .2 72.88495 422.7327 .4 92.36282 1 678.8668 .6 111.8407 995.3822 .3 73.19911 426.3848 .5 92.67698 683.4928 .7 112.1549 1000.9821 .4 73.51327 i 430.0526 .6 92.99114 688.1345 .8 112.4690 1006.5977 .5 73.82743 433.7361 .7 93.30530 692.7919 .9 112.7832 1012.2290 .6 74.14159 i 437.4354 .8 93.61946 697.4650 36.0 113.0973 1017.8760 .7 74.45575 j 441.1503 .9 1 93.93362 702.1538 .1 113.4115 1023.5387 .8 74.76991 444.8809 30.0 94.24778 706.8583 .2 113.7257 1029.2172 .9 75.08406 448.6273 .1 94.56194 711.5786 .3 114.0398 1034.9113 24.0 75.39822 452.3893 .2 94.87610 716.3145 .4 114.3540 1040.6212 .1 75.71238 456.1671 .3 95.19026 721.0662 .5 114.6681 1046.3467 .2 76.02654 459.9606 .4 95.50442 725.8336 .6 114.9823 1052.0880 .3 76.34070 463.7698 .5 95.81858 730.6166 .7 115.2965 1057.8449 .4 76.65486 467.5947 .6 96.13274 735.4154 .8 115.6106 1063.6176 .5 76.96902 471.4352 .7 96.44689 740.2299 .9 115.9248 1069.4060 .6 77.28318 475.2916 .8 96.76105 745.0601 37.0 116.2389 1075.2101 .7 77.59734 479.1636 .9 97.07521 : 749.9060 .1 116.5531 1081.0299 .8 77.91150 483.0513 31.0 97.38937 754.7676 .2 116.8672 1086.8654 174 TABLE NO. 72 CON. From Trautwine's "Civil Engineer's Pocket Book." CIRCLES. TABLE 2 OF CIRCL,ES-(Continued). Diameters in units and tenths. Dia. Circumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. 37.3 117.1814 1092.7166 43.5 136.6593 1486.1697 49.7 156.1372 1940.0041 .4 117.4956 1098.5835 .6 136.9734 1493.0105 .8 156.4513 1947.8189 .5 117.8097 1104.4662 .7 137.2876 1499.8670 .9 156.7655 1955.6493 .6 118.1239 1110.3645 .8 137.6018 1506.7393 50.0 157.0796 1963.4954 .7 118.4380 1116.2786 .9 137.9159 1513.6272 .1 157.3938 1971.3572 .8 118.7522 1122.2083 44.0 138.2301 1520.5308 .2 157.7080 1979.2348 .9 119.0664 1128.1538 .1 138.5442 1527.4502 .3 158.0221 1987.1280 38.0 119.3805 1134.1149 .2 138.8584 1534.3853 .4 158.3363 1995.0370 .1 119.6947 1140.0918 .3 139.1726 1541.3360 .5 158.6504 2002.9617 .2 120.0088 1146.0'844 .4 139.4867 1548.3025 .6 158.9646 2010.9020 .3 120.3230 1152.0927 .5 139.8009 1555.2847 .7 159.2787 2018.8581 .4 120.6372 1158.1167 .6 140.1150 1562.2826 .8 159.5929 2026.8299 .5 120.9513 1164.1564 .7 140.4292 1569.2962 .9 159.9071 2034.8174 .6 121.2655 1170.2118 .8 140.7434 1576.3255 51.0 160.2212 2042.8206 .7 121.5796 1176.2830 .9 141.0575 1583.3706 .1 160.5354 2050.8395 .8 121.8938 1182.3698 45.0 141.3717 1590.4313 .2 160.8495 2058.8742 .9 122.2080 1188.4724 .1 141.6858 1597.5077 .3 161.1637 2066.9245 39.0 122.5221 1194.5906 .2 142.0000 1604.5999 .4 161.4779 2074.9905 .1 122.8363 1200.7246 .3 142.3141 1611.7077 .5 161.7920 2083.0723 .2 123.1504 1206.8742 .4 142.6283 1618.8313 .6 162.1062 2091.1697 .3 123.4646 1213.0396 .5 142.9425 1625.9705 .7 162.4203 2099.2829 .4 123.7788 1219.2207 .6 143.2566 1633.1255 .8 162.7345 2107.4118 .5. 124.0929 1225.4175 .7 143.5708 1640.2962 .9 163.0487 2115.5563 .6] 124.4071 1231.6300 g 143.8849 1647.4826 52.0 163.3628 2123.7166 .7 124.7212 1237.8582 !9 144.1991 1654.6847 .1 163.6770 2131.8926 .8 125.0354 1244.1021 46.0 144.5133 1661.9025 .2 163.9911 2140.0843 .9 125.3495 1250.3617 .1 144.8274 1669.1360 .3 164.3053 2148.2917 40.0 125.6637 1256.6371 .2 145.1416 1676.3853 .4 164.6195 i 2156.5149 .1 125.9779 1262.9281 .3 145.4557 1683.6502 .5 164.9336 2164.7537 .2 i 126.2920 1269.2348 .4 145.7699 1690.9308 .6 165.2478 2173.0082 .3 126.6062 1275.5573 .5 146.0841 1698.2272 .7 165.5619 1 2181.2785 .4 126.9203 1281.8955 .6 146.3982 1705.5392 .8 165.8761 1 2189.5644 .5 127.2345 1288.2493 .7 146.7124 1712.8670 .9 166.1903 ! 2197.8661 .6 127.5487 1294.6189 .8 147.0265 1720.2105 53.0 166.5044 2206.1834 .7 127.8628 1301.0042 .9 147.3407 1727.5697 .1 166.8186 2214.5165 .8 128.1770 1307.4052 47.0 147.6549 1734.9445 .2 167.1327 2222.8653 .9 128.4911 1313.8219 .1 147.9690 1742.3351 .3 167.4469 2231.2298 41.0 128.8053 1320.2543 2 148.2832 1749.7414 .4 167.7610 2239.6100 .1 129.1195 1326.7024 .3 148.5973 1757.1635 .5 168.0752 2248.0059 .2 129.4336 1333.1663 .4 148.9115 1764.6012 .6 168.3894 2256.4175 .3 129.7478 1339.6458 .5 149.2257 1772.0546 .7 168.7035 2264.8448 .4 130.0619 1346.1410 .6 149.5398 1779.5237 .8 169.0177 2273.2879 .5 130.3761 1352.6520 .7 149.8540 1787.0086 .9 169.3318 2281.7466 .6 130.6903 1359.1786 .8 150.1681 1794.5091 54.0 169.6460 2290.2210 .7 131.0044 1365.7210 .9 150.4823 1802.0254 .1 169.9602 2298.7112 .8 131.3186 1372.2791 48.0 150.7964 1809.5574 .2 ; 170.2743 2307.2171 .9 131.6327 1378.8529 .1 151.1106 1817.1050 .3 i 170.5885 2315.7386 42.0 131.9469 1385.4424 .2 151.4248 1824.6684 .4 ! 170.9026 2324.2759 .1 132.2611 1392.0476 .3 151.7389 1832.2475 .5 171.2168 2332.8289 .2 132.5752 1398.6685 .4 152.0531 1839.8423 .6 171.5310 2341.3976 .3 132.8894 1405.3051 .5 152.3672 1847.4528 .7 I 171.8451 2349.9820 .4 133.2035 1411.9574 .6 152.6814 1855.0790 .8 j 172.1593 2358.5821 .5 ! 133.5177 1418.6254 .7 152.9956 1862.7210 .9 1 172.4734 2367.1979 .6 133.8318 1425.3092 .8 153.3097 1870.3786 56.0 1 172.7876 2375.8294 .7 134.1460 1432.0086 .9 153.6239 1878.0519 .1 173.1018 2384.4767 .8 134.4602 1438.7238 49.0 153.9380 1885.7410 !2 173.4159 2393.13% .9 134.7743 1445.4546 .1 154.2522 1893.4457 .3 173.7301 2401.8183 43.0 135.0885 1452.2012 .2 154.5664 1901.1662 .4 174.0442 2410.5126 .1 135.4026 1458.9635 .3 154.8805 1908.9024 .5 174.3584 2419.2227 .2 135.7168 1465.7415 .4 155.1947 1916.6543 .6 174.6726 2427.9485 .3 136.0310 1472.5352 .5 155.5088 1924.4218 .7 174.9867 2436.6899 .4 136.3451 1479.3446 .6 155.8230 1932.2051 .8 175.3009 2445.4471 TABLE NO. 72 CON. 175 From Trautwi II<**M "Civil Engineer*** Poeket Book." CIRCLES. TABLE 2 OF CIRCLES (Continued). Diameters in units and tenths. Hia. I Hrcumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. 56.9 1 75.0150 2454.2200 6-2.1 195.0929 3028.8173 68.3 214.5708 3663.7960 66.0 175.9292 2403.0086 .2 195.4071 3038.5798 .4 214.8849 3674.5324 .1 1 76.2433 2471. MM .3 195.7212 3048.3580 .5 215.1991 3685.2845 .2 76.5575 2480.0330 .4 196.0354 3058.1520 .6 215.5133 3696.0523 .3 76.8717 2489.4687 .5 196.3495 3067.9616 .7 215.8274 3706.8359 A 77.1858 2498.3201 .6 196.6637 3077.7869 .8 216.1416 3717.6351 .5 77.5000 2507.1873 .7 190.9779 3087.6279 .9 216.4557 3728.4500 .6 77.8141 2516.0701 .8 197.2920 I 3097.4847 69.0 216.7699 3739.2807 .7 78.1283 2524.9687 .9 197.0062 3107.3571 .1 217.0841 3750.1270 .8 78.4425 2533.8830 63.0 197.9203 3117.2453 .2 217.3982 3760.9891 .9 78.7560 2542.8129 .1 198.2345 i 3127.1492 .3 217.7124 3771.8668 67.0 79.0708 2551.7586 .2 198.5487 3137.0688 .4 218.0265 3782.7603 .1 179.3849 2560.7200 .3 198.8628 3147.0040 .5 218.3407 3793.6695 .2 179.0991 2569.6971 .4 199.1770 3156.9550 .6 218.6548 3804.5944 .3 180.0133 2578.6899 .5 199.4911 3166.9217 .7 218.9690 3815.5350 .4 ' 180.3274 2587.6985 .6 199.8053 3176.9042 .8 219.2832 3826.4913 .5 180.6416 2596.7227 .7 200.1195 3186.9023 .9 219.5973 3837.4633 .6 180.9557 2605.7626 .8 200.4336 3196.9161 70.0 219.9115 3848.4510 .7 181.2699 2614.8183 .9 200.7478 3206.9456 .1 220.2256 3859.4544 .8 181.5841 2623.8896 64.0 201.0619 3216.9909 .2 220.5398 3870.4736 .9 181.8982 2632.9767 .1 201.3761 3227.0518 .3 220.8540 3881.5084 68.0 182.2124 2642.0794 .2 201.6902 3237.1285 .4 221.1681 3892.5590 .1 182.5265 2651.1979 .3 202.0044 3247.2209 .5 221.4823 i 3903.6252 .2 182.8407 ! 2660.3321 .4 202.3186 3257.3289 .6 221.7964 3914.7072 .3 183.1549 2669.4820 .5 202.6327 3267.4527 .7 222.1106 ; 3925.8049 .4 183.4690 2678.6476 .6 202.9469 3277.5922 .8 222.4248 3936.9182 .5 183.7832 2687.8289 .7 203.2610 3287.7474 .9 222.7389 i 3948.0473 .6 184.0973 2697.0259 .8 203.5752 3297.9183 71.0 223.0531 3959.1921 .7 184.4115 2706.2386 .9 203.8894 3308.1049 .1 223.3672 ; 3970.3526 .8 184.7256 2715.4670 66.0 204.2035 3318.3072 .2 223.6814 3981.5289 .9 185.0398 2724.7112 .1 204.5177 3328.5253 .3 223.9956 3992.7208 69.0 185.3540 2733.9710 .2 204.8318 3338.7590 .4 224.3097 4003.9284 .1 185.6681 2743.2466 .3 205.1460 3349.0085 .5 224.6239 4015.1518 .2 185.9823 2752.5378 .4 205.4602 3359.2736 .6 224.9380 4026.3908 .3 186.2964 2761.8448 .5 205.7743 3369.5545 .7 225.2522 4037.0456 .4 186.6106 2771.1675 .6 206.0885 3379.8510 .8 225.5664 ! 4048.9160 .5 I 186.9248 2780.5058 .7 206.4026 3390.1633 .9 225.8805 4060.2022 .6 187.2389 2789.8599 .8 2067168 3400.4913 72.0 226.1947 ! 4071.5041 .7 187.5531 2799.2297 .9 207.0310 3410.8350 .1 226.5088 4082.8217 .8 ' 187.8672 2808.6152 66.0 207.3451 3421.1944 .2 i 226.8230 ; 4094.1550 .9 188.1814 2818.0165 .1 207.6593 3431.5695 .3 1 227.1371 1 4105.5040 60.0 188.4956 2827.4334 .2 207.9734 3441. 9603 .4 227.4513 ' 4116.8687 .1 188.8097 2836.8660 .3 208.2876 3452.3669 .5 i 227.7655 ! 4128.2491 .2 189.1239 2846.3144 .4 208.6018 3462.7891 .6 , 228.07% i 4139.6452 .3 189.4380 2855.7784 .5 208.9159 3473.2270 .7 228.3938 i 4151.0571 .4 189.7522 2865.2582 .61 209.2301 3483.6807 .8 228.7079 j 4162.4846 .5 190.0664 , 2874.7536 .7 ! 209.5442 3494.1500 .9 229.0221 j 4173.9279 .6 , 190.3805 2884.2648 .8 209.8584 3504.6351 73.0 229.3363 > 4185.3868 .7 190.6947 2893.7917 .9 210.1725 3515.1359 .1 1 229.6504 i 4196.8615 .8 191.0088 2903.3343 67.0 210.4867 525.6524 .2 229.9046 i 4208.3519 .9 191.3230 2912.8926 .1 210.8009 3536.1845 .3 230.2787 i 4219.8579 61.0 191.6372 2922.4666 .2 211.1150 i 3546.7324 .4 230.5929 ! 4231.3797 .1 191.9513 2932.0563 .3 211.4292 3557.2960 .5 230.9071 4242.9172 .2 192.2655 2941.6617 .4 211.7433 3567.8754 .6 231.2212 j 4254.4704 .3 192.57% 2951.2828 .5 212.0575 3578.4704 .7 231.5354 1 4266.0394 .4 192.8938 2960.9197 .6 212.3717 3589.0811 .8 231.8495 ] 4277.6240 .5 193.2079 ' 2970.5722 .7 212.6858 3599.7075 .9 232.1637 4289.2243 .6 193.5221 2980.2405 .8 213.0000 3010.3497 74.0 232.4779 4300.8403 .7 193.8363 2989.9244 .9 213.3141 ! 3621.0075 .1 232.7920 i 4312.4721 .8 194.1504 2999.6241 68.0 213.6283 ' 3631.6811 233.1062 ' 4324.1195 .9 194.4646 3009.3395 .1 213.9425 3642.3704 i3 1 233.4203 1 4335.7827 fl?0 194.77*7 wn 9.0705 .2 214.2566 3653.0754 .4 i 233.7345 j 4347.4616 176 TABLE NO. 72 CON. From Traut wine's " Civil F,un inker's Pocket Hook CIRCLES. TABLE 2 OF CIRCLES (Continued). Diameters in units and tenths. Dia. Circumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. 74.5 234.0487 4359.1562 80.7 253.5265 5114.8977 86.9 273.0044 5931.0206 .6 234.3628 4370.8664 .8 253.8407 5127.5819 87.0 273.3186 5944.6787 7 234.6770 4382.5924 .9 254.1548 5140.2818 .1 273.6327 5958.3525 *8 284.9911 439-1.3341 81.0 254.4690 5152.9974 2 273.9469 5972.0420 .9 235.3053 4406.0916 .1 254.7832 5165.7287 .3 274.2610 5985.7472 75.0 235.6194 4417.8647 .2 255.0973 5178.4757 'A 274.5752 5999.4681 .1 235.9336 4429.6535 .3 255.4115 5191.2384 .5 274.8894 6013.2047 .2 236.2478 4441.4580 .4 255.7256 5204.0168 .6 275.2035 6026.9570 .3 236.5619 4453.2783 .5 256.0398 5216.8110 .7 275.5177 6040.7250 .4 236.8761 j 4465.1142 .6 256.3540 5229.6208 .8 275.8318 6054.5088 .5 237.1902 4476.9659 .7 256.6681 5242.4463 .9 276.1460 6068.3082 .6 237.5044 4488 8332 .8 256.9823 5255.2876 88.0 276.4602 6082.1234 .7 237.8186 4500.7163 .9 257.2964 5268.1446 .1 276.7743 6095.9542 .8 238.1327 4512.6151 82.0 257.6106 5281.0173 .2 277.0885 6109.8008 .9 238.4469 4524.5296 .1 257.9248 5293.9056 .3 277.4026 6123.6631 76.0 238.7610 4536.4598 o 258.2389 5306.8097 .4 277.7168 6137.5411 .1 I 239.0752 4548.4057 !a 258.5531 5319.7295 .5 278.0309 6151.4348 .2 ! 239.3894 J 560.3673 .4 258.8672 5332.6650 .6 278.3451 6165.3442 .3 239.7035 4572.3446 .5 259.1814 5345.6162 7 278.6593 6179.2693 .4 240.0177 4584.3377 .6 259.4956 5358.5832 '.% 278.9734 6193.2101 .5 240.3318 4596.3464 .7 259.8097 5371 .5658 9 279.2876 6207.1666 .6 240 6400 4608.3708 .8 260.1239 5384.5641 89.0 279.6017 6221.1389 .7 240.9602 4620.4110 .9 260.4380 5397.5782 .1 279.9159 6235.1268 .8 241.2743 4632.4669 830 260.7522 5410.6079 .2 280.2301 6249.1304 .9 , 241.5885 ; 4614 5384 .1 261.0663 5423.6534 .3 280.5442 6263.1498 77.0 241.9026 4656.6257 .2 261.3805 5436.7146 .4 280.8584 6277.1849 .1 242.2168 i 4668.7287 .3 261.6947 5449.7915 , 281.1725 6291 2356 .2 242.5310 4680.8474 .4 262.0088 5462.8840 ! 281.4867 6305.3021 .3 242.8451 4692.9818 .5 262.3230 5475.9923 .7 281.8009 6319.3843 .4 243.1593 4705.1319 .6 262.6371 5489.1163 .8 282.1150 6333.4822 .5 243.4734 4717.2977 .7 262.9513 5502.2561 .9 282.4292 6347.5958 .6 243.7876 4729.4792 .8 263.2655 5515.4115 90.0 282.7433 6361.7251 .7 244.1017 4741.6765 .9 263.5796 5528.5826 .1 283.0575 6375.8701 .8 244.4159 4753.8894 84.0 263.8938 5541.7694 .2 283.3717 6390.0309 .9 244.7301 4766.1181 .1 264.2079 5554.9720 .3 283.6858 ' 6404.2073 78.0 245.0442 4778.3624 .2 j 264.5221 5568.1902 .4 284.0000 6418.3995 .1 245.3584 4790.6225 .3 264.8363 5581.4242 .5 284.3141 6432.6073 .2 245.6725 4802.8983 .4 265.1504 594.6739 .6 284.6283 6446.8309 .3 245.9867 4815.1897 .5 265.4646 5607.9392 .7 284.9425 6461.0701 A 246.3009 4827.4969 .6 265.7787 5621.2203 .8 285.2566 6475.3251 .5 246.6150 4839.8198 .7 266.0929 5634.5171 .9 285.5708 6489.5958 .6 246.9292 4852.1584 .8 266.4071 5647.8296 91.0 285.8849 6503.8822 ,7 IJ47.243? 4864.5128 .9 ! 266.7212 5661.1578 .1 286.1991 6518.1843 .8 247.5575 | l8/tj.3828 85.0; 2670354 5674.5017 .2 286.5133 6532.5021 .9 247.8717 . 4889.2685 .1 ! 267 3495 5687.8614 .3 286.8274 6546.8356 79.0 248.185S 4901 .669 .2 267 6637 5701.2367 .4 287.1416 6561.1848 .1 248.5000 4914.087-.: .3 267 9779 5714.6277 .5 287.4557 ! 6575.5498 .2 248.8141 4926.5199 .4 268.2920 5728.0345 .6 287.7699 6589.9304 .3 249.1283 4938.9685 .5 268.6062 5741.4569 .7 288.0840 6604.3268 .4 249.4425 4951.4328 .6 268.9203 5754.8951 .8 288.3982 6618.7388 .5 249.7566 4963.9127 .7 269.2345 5768.3490 .9 288.7124 6633.1666 .6 250.0738 4976.4084 .8 269.5486 5781.8185 92.0 289.0265 6647.6101 .7 250.3843 '; 4988.H9S .9 269.8628 5795.3038 .1 289.3407 6662.0692 .8 250.6991 50Ci/.-469 86.0 ! 279.1770 5808.8048 .2 289.6548 6676.5441 9 251.0133 5013.9897 .1 ! 2'* 0.4911 5822.3215 .3 289.9690 6691.0347 80.0 251.3274 026.5482 .2 ; 270.8053 5835.8539 * .4 290.2832 6705.5410 .1 251.6416 5039.1225 .3 271.1194 5849.4020 .5 290.5973 6720.0630 .2 251.9557 5051.7121 .4 271.43H6 5862.9659 .6 290.9115 i 6734.6008 .3 252.11699 5064.3180 .5 271.7478 5876.5454 .7 291.2256 6749.1542 .4 252.5840 i 5076.9894 .6 ' 272.0619 5890.1407 .8 291.5398 6763.7233 .5 252.8982 ; 5089.5764 .7 272.3761 5903.7516 9 291.8540 6778.3082 .6 253.2124 i 5102.2292 .8 '' 272.6902 5917.3783 9s!o 292.1681 ; 6792.9087 TABLE NO. 72 COX. 177 From Trautwine's * ivil i:n^iiio<>r*s Pocket Book." CIRCLES. TABLE 2 OF CIRCLES (Continued). Diameters in units and tenths. Dia. Circumf. Area. Dia. | Circumf. Area. Dia. Circumf. Area. 93.1 292.4823 6807.5250 955 300.0221 7163.0276 97.8 307.2478 7512.2078 .2 292.7964 6822.1569 .6 300.3363 7178.0366 .9 307.5619 7527.5780 .3 293.1106 6836.8046 .7 300.6504 7193.0612 98.0 307.8761 7542.9640 .4 293.4248 6851.4680 .8 300.9646 7208.1016 .1 308.1902 7558.3656 .5 293.7389 6866.1471 .9 301.2787 7223.1577 .2 308.5044 7573.7830 6 294.0-')31 6880.8419 96.0 301.5929 7238.2295 .3 308.8186 7589.2161 .7 294.3672 6895.5524 .1 301.9071 1 7253.3170 .4 309.1327 7604.6648 .8 294.6814 6910.2786 .2 302.2212 7268.4202 .5 309.4469 7620.1293 .9 ! 294.9956 6925.0205 .3 j 302.5354 7283.5391 .6 309.7610 7635.6095 94.0 295.3097 6939.7782 .4 302.8495 7298.6737 .7 310.0752 7651.1054 .1 295.6239 0954.5515 .5 303.1637 7313.8240 .8 310.3894 7666.6170 .2 295.9380 6969.3406 .6 303.4779 7328.9901 .9 310.7035 7682.1444 .3 296.2522 6984.1453 .7 303.7920 7344.1718 99.0 311.0177 7697.6874 .4 296.5663 6998.9658 . .8 304.1062 7359.3693 .1 311.3318 7713.2461 .5 29(5.8805 7013.8019 .9 304.4203 7374.5824 .2 311.6460 7728.8206 .6 297.1947 7028.6538 97.0 304.7345 7389.8113 .3 311.9602 7744.4107 .7 297.5088 7043.5214 .1 305.0486 7405.0559 .4 312.2743 7760.0166 .8 297.8230 7058.4047 .2 305.3628 7420.3162 .5 312.5885 7775.6382 .9 298.1371 7073.3037 .3 305.6770 7435.5922 .6 312.9026 7791.2754 95.0 298.4513 7088.2184 .4 305.9911 7450.8839 .7 313.2168 7806.9284 .1 298.7655 7103.1488 .5 306.3053 7466.1913 .8 313.5309 7822.5971 .2 299.0796 7118.0950 .6 306.6194 7481.5144 .9 313.8451 7838.2815 .3 299.3938 7133.0568 .7 306.9336 7496.8532 100.0 314.1593 7853.9816 .4 299.7079 7148.0343 Circumferences when the diameter has more than one place of decimals. Diam. Circ. Diam. Circ. Diam. Circ. Diam. Circ. Diam. Circ. .1 .314159 .01 .031416 .001 .003142 .0001 .000314 .00001 .000031 .2 .628319 .02 .062832 .002 .006283 .0002 .000628 .00002 .000063 ! .3 .942478 .03 .094248 .003 .009425 .0003 .000942 .00003 .000094 .1 1.256637 .04 .125664 .004 .012566 .0004 .001257 .00004 .000126 .5 1 570796. .05 .157080 .005 .015708 .0005 .001571 .00005 .000157 .6 1.884956 .06 .188496 .006 .018850 .0006 .001885 .00006 .000188 .7 2.199115 1 .07 .219911 .007 .021991 .0007 .002199 .00007 .000220 .8 2.513274 .08 .251327 .008 .025133 .0008 .002513 .00008 .000251 .9 2.827433 .09 .282743 .009 .028274 .0009 .002827 .00009 .000283 Examples. Diameter = 3.12699 Circumference = Circ for dia of 3.1 .02 " .006 " .0009 " .00009 Sum of = 9.738937 Circumfce = Diameter = Dia for circ of M 9.823729 9.738937 = Sum of 3.1 .02 .006 .0009 .00009 = .062832 = .018850 .084792 .062832 = = .000283 .021960 .018850 = 9.823729 .003110 .002827 = .000283 .000283 = 178 TABLE KG. 73. From Trawtwine*s "C'ivil Engineer** Pocket Book." CIRCLES. TABLE 3 OF CIRCLES. Dia ins in units and twelfths ; as in feet and inches. Dia. Circumf. Area. Dia. Circumf.j Area. Dia. C'ircumf. Area. Ft.In. Feet. Sq. ft. Ft.In. Feet. Sq. ft. Ft In. Feet. : Sq. ft. 5 15.70796 19.63495 10 31.41593 78.53982 1 .261799 .005454 1 15.96976 20.29491 1 31.67773 79.85427 2 .523599 .021817 2 16.23156 20.96577 2 31.93953 81.17963 3 .785398 .049087 3 16.49336 21.64754 3 32.20132 82.515-S'J 4 1.047198 i .087266 4 1(5.75516 22.34021 4 32.46312 : 83.86307 5 1.308997 .136354 5 17.01696 23.04380 5 | 32.72492 85.22115 6 1.570796 .196350 6 17.27876 23.75829 6 32.98672 86.59015 7 1.832596 .267254 7 17.54056 24.48370 7 33.24852 : 87.97005 8 2.094395 .349066 8 17.80236 25.22001 8 33.51032 89.36086 9 2.356195 441786 9 18.06416 25.96723 9 83.77212 90.76258 10 2.617994 .545415 10 18.32596 26.72535 10 34.03392 92.17520 11 2.879793 .659953 11 18.58776 27.49439- 11 34.29572 93.59874 1 3.14159 .785398 6 18.84956 28.27433 11 34.55752 ; 95.03318 1 3.40339 .921752 1 19.11136 29.06519 1 34.81932 i 96.47853 2 3.66519 1.06901 2 19.37315 29.86695 2 35.08112 ! 97.im7J 3 3.92699 1.22718 3 19.63495 30.67962 3 1 35.34292 ! 99.40196 4 4.18879 1.39626 4 19.89675 31.50319 4 35.60472 j 100.8800 5 4.45059 1.57625 5 20.15855 32.33768 5 35.86652 ' 102.3690 6 4.71239 1.76715 6 20.42035 33.18307 6 36.12832 ! 103.8689 7 4.97419 1.96895 7 20.68215 34.03937 7 36.39011 105.3797 8 5.23599 2.18166 8 20.94395 34.90659 8 36.65191 106.9014 9 5.49779 2.40528 9 21.20575 35.78470 9 36.91371 108.4340 10 5.75959 2.63981 10 21.46755 36.67373 10 1 37.17551 1(19.9776 11 6.02139 2.88525 11 21.72935 37.57367 11 | 37.43731 111.5320 9 6.28319 3.14159 7 21.99115 38.48451 12 37.69911 1 13.0973 1 6.54498 3.40885 1 22.25295 39.40626 1 : 57. 96091 114.6736 2 6.80678 3.68701 o 22.51475 40.33892 2 ' 3.S.22271 116.2607 3 7.06858 3.97608 3 22.77655 41.28249 3 ' 38.48451 117.8588 4 7.33038 4.27606 4 23.03835 42.23697 4 38.74631 119.467S 5 7.59218 4.58694 5 23.30015 \o 20235 5 :ri9.00811 121 0*77 6 7.85398 4.90874 6 23.56194 '.4, .7865 6 39.26991 122.71. S5 7 8.11578 5.24144 7 23.82374 45.16585 7 39.53171 124.3602 8 8.37758 5.58505 8 24.08554 46.16396 8 39.79351 126.0128 9 8.63938 5.93957 9 24.34734 47.17298 9 40.05531 127.6763 10 8.90118 6.30500 10 24.60914 48.19290 10 40.31711 129.3507 11 9.16298 6.68134 11 24.87094 49.22374 11 40.57891 131.0360 8 9.42478 7.06858 8 25.13274 50.26548 13 40.84070 132.7323 1 9.68658 7.46674 1 25.39454 51.31813 1 41.10250 134.4394 2 9.94838 7.87580 2 25.65634 52.38169 2 41.36480 136.1575 3 10.21018 8.29577 3 25.91814 53.45616 3 41.62610 137.8865 4 10.47198 8.72665 4 26.17994 54.54154 4 41.88790 139.6263 5 10.73377 9.16843 5 26.44174 55.63782 5 42.14970 141.3771 6 10.99557 9.62113 6 26.70354 56.74502 6 42.41150 143.1388 7 11.25737 10.08473 7 26.96534 57.86312 7 42.67330 144.9114 8 11.51917 10.55924 8 27.22714 58.99213 8 42.93510 146.6949 9 11.78097 11.04466 9 27.48894 60.13205 9 43.19690 148.4893 10 12.04277 11.54099 10 27.75074 61.28287 10 43.45870 150.2947 11 12.30457 12.04823 11 28.01253 62.44461 11 43.72050 152.1109 4 12.56637 12.56637 9 28.27433 63.61725 14 43.98230 153.9380 1 12.82817 13.09542 1 28.53613 64.80080 1 44.24410 155.7761 2 13.08997 13.63538 2 28.79793 65.99526 2 44.50590 157.6250 3 13.35177 14.18625 3 29.05973 67.20063 3 44.76770 159.48411 4 13.61357 14.74803 4 29.32153 68.41691 4 45.02949 161.3557 5 13.87537 15.32072 5 29.58333 69.64409 5 45.29129 163.2374 6 14.13717 15.90431 6 29.84513 70.88218 6 45.55309 165.1300 7 14.39897 16.49882 7 30.10693 72.13119 7 45.81489 167.0335 8 14.66077 17.10423 8 30.36873 73.39110 8 46.07669 168.9472 9 14.92257 17.72055 9 30.63053 74.66191 9 46.33849 170.8732 10 15.18436 18.34777 10 30.89233 75.94364 10 46.60029 172.8094 11 15.44616 18.98591 11 31.15413 77.23627 11 46.86209 174.7565 TABLE NO. 73 CON. From Traiitwine's "Civil Engineer's Pocket Book." CIRCLES. man TABLE 3 OF CIRCLES (Continued). in units and twelfths; as in feet and inches. Dia. Circumf. Area. Dia. Circumf. Area. Dia. Circumf. Area. Ft.In. Feet. Sq. ft. Ft.In. Feet. Sq. ft. Ft.In. Feet. Sq. ft. 15 47.12389 176.7146 20 62.83185 314.1593 25 78.53982 490.8739 1 47.38569 178.6835 1 63.09365 316.7827 1 78.80162 494.1518 2 47.64749 180.6634 2 63.35545 319.4171 2 79.06342 497.4407 3 47.90929 182.6542 3 ; 63.61725 322.0623 3 79.32521 500.7404 4 48.17109 184.6558 4 ! 63.87905 324.7185 4 79.58701 504.0511 5 48.43289 186.6684 5 64.14085 327.3856 5 79.84881 507.3727 <1 48.69469 188.6919 6 64.40265 330.0636 6 80.11061 510.7052 7 48.95649 190.7263 7 64.66445 | 332.7525 7 80.37241 514.0486 1 49.21828 192.7716 8 64.92625 335.4523 8 80.63421 517.4029 9 49.48008 194.8278 9 65.18805 338.1630 9 80.89601 520.7681 10 49.74188 196.8950 10 65.44985 340.8846 10 i 81.15781 524.1442 11 50.00368 198.9730 11 65.71165 343.6172 11 81.41961 527.5312 16 50.26548 201.0619 21 65.97345 346.3606 26 ! 81.68141 530.9292 1 50.52728 203.1618 1 66.23525 349.1149 1 81.94321 534.3380 2 50.78908 205.2725 2 66.49704 351.8802 2 82.20501 537.7578 3 51.05088 207.3942 3 66.75884 354.6564 82.46681 541.1884 4 51.31268 209.5268 4 67.02064 357.4434 4 82.72861 544.6300 5 51.57448 211.6703 5 67.28244 360.2414 5 ! 82.99041 548.0825 6 51.83628 213.8246 6 67.54424 363.0503 6 ! 83.25221 551.5459 7 52.09808 215.9899 7 67.80604 365.8701 7 83.51400 555.0202 8 52.35988 218.1662 8 68.06784 368.7008 8 83.77580 558.5054 9 52.62168 220.3533 9 68.32964 371.5424 9 84.03760 562.0015 10 52.88348 222.5513 10 68.59144 374.3949 10 84.29940 565.5085 11 53.14528 224.7602 11 68.85324 377.2584 11 84.56120 569.0264 17 53.40708 226.9801 22 69.11504. 380.1327 27 84.82300 572.5553 1 53.66887 229.2108 1 6937684 383.0180 1 85.08480 576.0950 2 53.93067 231.4525 2 69.63864 385.9141 2 85.34660 579.6457 3 54.19247 233.7050 3 69.90044 388.8212 3 85.60840 583.2072 4 54.45427 235.96&5 4 70.16224 391.7392 4 85.87020 586.7797 5 54.71607 238.2429 5 70.42404 394.6680 5 86.13200 590.3631 6 54.97787 240.5282 6 70.68583 397.6078 6 86.39380 593.9574 7 55.23967 242.8244 7 70.94763 400.5585 7 86.65560 597.5626 8 55.50147 245.1315 8 71.20943 403.5201 8 86.91740 601.1787 9 55.76327 247.4495 9 71.47123 406.4926 9 87.17920 604.8057 10 56.02507 249.7784 10 71.73303 409.4761 10 87.44100 608.4436 11 56.28687 252.1183 11 71.99483 412.4704 11 87.70279 612.0924 18 56.54867 254.4690 23 72.25663 415.4756 28 87.96459 615.7522 1 56.81047 256.8307 1 72.51843 418.4918 1 88.22639 619.4228 2 57.07227 259.2032 2 72.78023 421.5188 2 88.48819 623.1044 3 57.33407 261.5867 3 73.04203 424.5568 3 88.74999 626.7968 4 57.59587 263.9810 4 73.30383 427.6057 4 89.01179 630.5002 5 57.85766 266.3863 5 73.56563 4306654 5 89.27359 634.2145 6 58.11946 268.8025 6 73.82743 433.7361 6 89.53539 637.9397 7 58.38126 271.2296 7 74.08923 436.8177 7 89.79719 641.6758 8 58.64306 273.6676 8 74.35103 439.9102 8 90.05899 645.4228 9 58.90486 276.1165 9 74.61283 443.0137 9 90.32079 649.1807 10 59.16666 278.5764 10 74.87462 446.1280 10 90.58259 652.9495 11 59.42846 281.0471 11 75.13642 449.2532 11 , 90.84439 656.7292 19 59.69026 283.5287 24 75.39822 452.3893 29 91.10619 660.5199 1 59.95206 286.0213 1 75.66002 455.53^4 1 : 91.36799 664.3214 2 60.21386 288.5247 2 75.92182 458.6943 2 91.62979 668.1339 3 60.47566 291.0391 3 76.18362 461.8632 3 : 91.89159 671.9572 4 60.73746 293.5644 4 76.44542 465.0430 4 92.15338 675.7915 5 60.99926 296.1006 5 76.70722 468.2337 5 , 92.41518 679.6367 6 61.26106 298.6477 6 76.96902 471.4352 6 92.67698 683.492* 7 61.52286 301.2056 7 77.23082 474.6477 7 j 92.93878 687.3591 8 61.78466 303.7746 8 77.49262 477.8711 8 93.20058 691.2377 9 62.04645 306.3544 9 77.75442 481.1055 93.46238 695.1263 10 62.30825 308.9451 10 78.01622 484.3507 10 L 93.72418 699.026J 11 62.57005 311.5467 11 78.27802 487.6068 11 93.98598 702.9361 180 TABLE KO. 73-COSr. From Trautwine's "Civil Engineer's Pocket Book." CIRCLES. TABLE 3 OF CIRCIiES-(Continued). Dianm in units and twelfths; as in feet and inches. Dia. jcircumf. Area. Dia. .Circumf. Area. Dia. Circumf. Area. Ft. In. Feet. Sq. ft. Ft.In Feet. Sq. ft. Ft.In Feet. Sq. ft. 30 94.24778 706.8583 35 109.9557 962.1128 40 125.6637 1256.6371 1 94.50958 710.7908 1 110.2175 966.6997 1 125.9255 1261.8785 2 94.77138 714.7341 2 110.4793 971.2975 126.1873 1267.1309 3 95.03318 718.6884 3 110.7411 975.9063 B 126.4491 1272.3941 4 95.29498 722.6536 4 111.0029 980.5260 4 126.7109 1277.6683 5 95.55678 726.6297 5 111.2647 985.1566 i 126.9727 1282.9534 6 95.81858 730.6166 6 111.5265 989.7980 e 127.2345 1288.2493 7 96.08038 734.6145 7 111.7883 994.4504 7 127.4963 1293.5562 8 96.34217 738.6233 8 112.0501 999.1137 8 127.7561 I 1298.8740 9 96.60397 , 742.6431 9 112.3119 1003.7879 9 128.0199 1304.2027 10 96.86577 746 6737 10 112.5737 1008.4731 10 128.2817 1309.5424 11 97.12757 750.7152 11 112.8355 1013.1601 11 128.5435 1314.8929 31 97.38937 754.7676 36 113.0973 1017.8700 41 128.8053 1320.2543 1 97.65117 758.8310 1 113.3591 1022.5939 1 129.0671 1325.6267 2 97.91297 . 762.9052 2 113.6209 1027.3226 2 129.3289 1331.0099 3 98.17477 766.9904 3 113.8827 1032.0623 5 129,5907 1336.4041 4 98.43657 771.0865 4 114.1445 1036.8128 4 129.8525 1341.8091 5 98.69837 775.1934 5 114.4063 1041.5743 5 130.1143 1347.2251 6 98.96017 779.3113 6 114.6681 1046.3467 6 130.3761 1352.6520 7 99.22197 783.4401 7 114.9209 1051.1300 7 130.6379 1358.0898 8 99.48377 787.5798 8 115.1917 1055.9242 8 130.8997 1363.5385 9 99.74557 791.7304 9 115.4535 1060.7293 9 131.1615 1368.9981 10 100.0074 795.8920 10 115.7153 10G5.54-13 10 131.4233 1374.4686 11 i 100.2692 800.0644 11 115.9771 1070.3723 11 131.6851 1379.9500 82 100.5310 804.2477 37 116.2889 1075.2101 42 131.9469 1385.4424 1 100.7928 808.4420 1 116.5007 10S0.05S8 1 132.2087 1390.9456 2 101.0546 812.6471 2 116.7625 1084.9185 2 132.4705 1396.4598 3 1101.3164 816.8632 3 117.0243 1089.7800 3 132.7323 1401.9848 4 1 101.5782 821.0901 4 117.2861 1094.6705 4 132.9941 1407.5208 5 1101.8400 825.3280 5 117.5479 1099.5629 5 133.2559 1413.0676 6 102.1018 829 5768 6 117.8097 1104.4662 6 133.5177 1418.6254 7 102.3636 ; 833.8365 7 118.0715 1109.3804 7 133.7795 1424.1941 8 102.6254 838.1071 8 118.3333 1114.3055 8 134.0413 1429.7737 9 1102.8872 842.3886 9 118.5951 1119.2415 9 134.3031 1435.3642 10 1103.1490 846.6810 10 ] 18.8569' 1124.1884 10 134.5649 1440.9656 11 103.4108 850.9844 11 119.1187 1129.1462 11 134.8267 1446.5780 33 ; 103 .6726 855.2986 38 119.3805 1134.1149 43 135.0885 1452.2012 1 : 103.9344 859.6237 1 119.6423 1139.0946 1 335.3503 3457.8353 2 ; 104.1962 863.9598 2 li 9.9041 1144.0851 2 135.6121 1463.4804 3 104.4580 868.3068 3 r:0.1659 1149.08C6 3 135.8739 1469.1364 4 ;104.7198 872.6646 4 120.4277 1154.0990 4 136.1357 1474.8032 5 i 104.9816 877.0334 5 120.6895 1159.1222 5 136.3975 1480.4810 6 105.2434 881.4131 6 120.9513 1164.1564 6 136.6593 1486.1697 7 1105.5052 885.8037 7 121.213J 1169.2015 7 136.9211 1491.8693 8 1105.7670 9 1106.0288 890.2052 894.6176 8 9 121.4749 121.7367 1174.2575 1179.3244 8 9 137.1829 137.4447 1497.5798 1503.3012 10 106.2906 899 0409 10 121.9985 1184.4022 10 137.7065 1509.0335 11 106.5524 903.4751 11 122.2603 1189.4910 11 137.9683 1514.7767 34 106.8142 907.9203 39 122.5221 1194.5906 44 138.2301 1520.5308 1 107.0759 912.3763 *1 122.7839 1199.7011 1 138.4919 1526.2959 2 107.3377 916.8433 2 123.0457 1204.8226 2 138.7537 1532.0718 3 107.5995 921.3211 3 123.3075 1209.9550 3 139.0155 1537.8587 4 107.8613 925.8099 4 123.5693 1215.0982 4 139.2773 1543.6565 5 108.1231 930.3096 5 123.8311 1220.2524 5 139.5391 1549.4651 6 108.3849 934.8202 6 124.0929 1225.4175 6 139.8009 1555.2847 7 108.6467 939.3417 7 124.3547 1230.5935 7- 140.0627 1561.1152 8 108.9085 943.8741 8 124.6165 1235.7804 8 140.3245 1566.9566 9 109.1703 948.4174 9 124.8783 1240.9782 9 140.5863 1572.8089 10 109.4321 952.9716 10 125.1401 1246.1869 10 140.8481 1578.6721 11 109.6939 957.5367 11 j 125.4019 1251.4065 11 ! 141.1099 1584.5462 TABLE NO. 73 CON. 181 From I raul \\ in* x civil LH^HMMT s Pocket Book." CIRCLES. TABLE 3 OF C'lRCL-ES (Continued). Plain* in units and twelfths; as in feet and inches. Dia. Circumf. Area. Dia. Circumf, Area. Dia. Circumf Area. Ft.In. Feet. Sq. ft. Ft.In. Feet. Sq. ft. Ft.Ia. Feet. Sq. ft. 45 141.3717 1590.4313 50 157.0796 1963.4954 55 172.7876 2375.8294 1 141.6335 1596.3272 1 157.3414 1970.0458 1 173.0494 2383.0314 2 141.8953 1602.2341 2 157.6032 1976.6072 2 173.3112 2390.2502 3 142.1571 1608.1518 3 157.8650 1983.1794 3 173.5730 2397.4770 4 142.4189 1614.0805 4 158.1268 : 1989.7626 4 173.8348 2404.7146 5 142.6807 1620.0201 5 158.3886 1996 3567 5 174.0966 2411.9632 6 142.9425 1625.9705 6 158.6504 , 2002.9617 6 174.3584 2419.2227 7 143.2043 1631.9319 7 i 158.9122 2009.5776 7 174.6202 2426.4931 8 143.4661 1637.9042 8 159.1740 2016.2044 8 174.8820 2433.7744 9 143.7279 1643.8874 9 159.4358 2022.8421 9 175.1438 2441.0666 10 143.9897 1649.8816 10 i 159.6976 ! 2029.4907 10 175.4056 2448.3697 11 144.2515 1655.8866 11 159.9594 i 2036.1502 11 175.6674 ! 2455.6837 46 144.5133 1661.9025 51 160.2212 2042.8206 56 175.9292 ! 2463.0086 1 144.7751 1667.9294 1 160.4830 : 2049.5020 1 176.1910 2470.3445 2 145.0369 1673.9671 2 160.7448 2056.1942 2 176.4528 2477.6912 3 145.2987 1680.0158 3 161.0060 2062.8974 3 176.7146 2485.0489 4 145.5605 1686.0753 4 161.2684 2069.6114 4 176.9764 2492.4174 5 145.8223 1692.1458 5 161.5302 207*). 3364 5 177.2382 2499.7969 6 146.0841 1698.2272 6 i 161.7920 2083 0723 6 177.5000 2507.1873 7 146.3459 1704.3195 7 162.0538 2089.8191 7 177.7618 2514.5886 8 146.6077 1710.4227 8 162.3156 2096.5768 8 178.0236 2522.0008 9 146.8695 1716.5368 9 162.5774 I 2103.3454 9 178.2854 2529.4239 10 147.1313 1722.6618 10 162.8392 2110.1249 10 178.5472 2536.8579 11 147.3931 1728.7977 11 163.1010 2116.9153 11 178.8090 2544.3028 47 147.6549 1734.9445 52 163.3628 2123.7166 57 179.0708 2551.7586 1 147.9167 1741.1023 1 163.6246 2130.5289 1 179.3326 2559.2254 2 148.1785 1747.2709 2 163.8864 2137.3520 2 179.5944 2566.7030 3 148.4403 1753.4505 3 164.1482 2144.1861 3 179.8562 2574.1916 4 148.7021 1759.6410 4 164.4100 2151.0310 4 180.1180 2581.6910 5 148.9639 1765.8423 5 164.6718 2157.8869 5 180.3798 2589.2014 6 149.2257 1772.0546 6 164.9336 2164.7537 6 180.6416 2596.7227 7 149.4875 1778.2778 7 165.1954 2171.6314 7 180.9034 2604.2549 8 149.7492 1784.5119 8 165.4572 2178.5200 8 181.1652 2611.7980 ,9 150.0110 1790.7569 9 i 165.7190 2185.4195 9 181.4270 2619.3520 10 150.2728 1797.0128 10 165.9808 2192.3299 10 181.6888 2626.9169 11 150.5346 1803.2796 11 166.2426 2199.2512 11 181.9506 2634.4927 48 150.7964 1809.5574 >3 166.5044 2206.1834 58 182.2124 2642.0794 1 151.0582 1815.8460 1 166.7662 2213.1266 1 182.4742 2649.6771 2 151.3200 1822 1456 2 167.0280 2220.0806 2 182.7360 2657.2856 3 151.5818 1828.4560 3 167.2898 2227.0456 3 182.9978 2664.9051 4 151.8436 1834.7774 4 167.5516 2234.0214 4 183.2596 2672.5354 5 152.1054 1841.1096 5 167.8134 2241.0082 5 183.5214 2680.1767 6 152.3672 1847.4528 6 168.0752 2248.0059 6 183.7832 : 2687.8289 7 152.6290 1853.8069 7 168.3370 ' 2255.0145 7 184.0450 2695.4920 8 152.8908 1860.1719 8 168.5988 2262.0340 8 184.3068 2703.1659 9 153.1526 1866.5478 9 168.8606 2269.0644 9 184.5686 2710.8508 10 153.4144 1872.9346 10 169.1224 2276.1057 10 184.8:304 2718.5467 11 153.6762 1879.3324 11 169.3842 2283.1579 11 185.0922 2726.2534 49 153.9380 188-3.7410 54 169.6460 2290.2210 59 1 185.3540 , 2733.9710 1 | 154.1998 1892.1605 1 169.9078 2297.2951 1 185.6158 2741.6995 2 154.4616 1898.59,10 2 170.1696 2304.3800 2 185.8776 2749.4390 3 154.7234 1905.0323 3 170.4314 2311.4759 3 186.1394 2757.1893 4 154.9852 1911.4846 4 170.6932 2318.5826 4 186.4012 2764.9,506 5 155 2470 1917.9478 5 170.9550 2325.7003 5 186.6630 2772.7228 6 155.5088 1924.4218 6 171.2168 2332.8289 6 186.9248 2780.5058 7 155.7706 ! 1930.9068 7 171.4786 2339.9684 7 187.1866 2788.2998 8 156.0324 1937.4027 8 171.7404 2347.1188 8 187.4484 2796.1047 9 156.2942 i 1943.9095 9 172.0022 \ 2354.2801 9 187.7102 2803.9205 10 156.5560 i 1950.4273 10 172.2640 2361.4523 10 187.9720 2811.7472 11 156.8178 1956.9559 11 172.5258 j 2368.6354 11 188.2338 2819.5849 182 TABLE NO. 73-CON. From Traiitwine's "Civil Engineer's PoeKet Book. CIRCLES. TABLE 3 OF CIRCLES (Continued). Diams in units and twelfths; as in feet and inches. Dia. Circumf. Area. Dia. Circumf. Area. Dia. Cireumf. Area. Ft.In. Feet. Sq. ft. Ft.Iu. Feet. Sq. ft. Ft.In. Feet. Sq. ft. 60 188.4956 2827.4334 65 204.2035 3318.3072 70 219.9115 3848.4510 1 188.7574 2835.2928 1 204.4653 3326.8212 1 220.1733 3857.6194 2 189.0192 2843.1632 2 204.7271 3335.3460 o 220.4351 3866.7988 3 189.2810 2851.0444 3 204.9889 3343.8818 3 220.6969 3875.9890 4 189.5428 2858.9366 4 205.1*507 3352.4284 4 220.9587 3885.1902 5 189.8046 2866.8397 5 205.5125 3360.9860 5 221.2205 3894.4022 6 190.0664 2874.7536 6 205.7743 3369.5545 6 221.4823 3903.6252 7 190.3282 2882.6785 7 206.0361 3378.1339 7 221.7441 3912.8591 8 190.5900 2890.6143 8 206.2979 3386.7241 8 222.0059 3922.1039 9 190.8518 2898.5610 9 206.5597 3395.3253 9 222.2677 3931.3596 10 191.1136 2906.5186 10 206.8215 3403.9375 10 222.5295 3940.6262 11 191.3754 2914.4871 11 207.0833 3412.5605 11 222.7913 3949.9037 61 191.6372 2922.4666 66 207.3451 3421.1944 71 223.0531 3959.1921 1 191.8990 2930.4569 1 207.6069 3429.8392 1 223.3149 3968.4915 2 192.1608 2938.4581 2 207.8687 3438.4950 2 223.5767 3977.8017 3 192.4226 2946.4703 3 208.1305 3447.1616 3 223.8385 ' 3987.1229 4 192.6843 2954.4934 4 208.3923 3455.8392 4 224.1003 3996.4549 5 192.9461 2962.5273 5 208.6541 3464.5277 5 224.3621 4005.7979 6 193.2079 2970.5722 6 208.9159 3473.2270 6 224.6239 4015.1518 7 193.4697 2978.6280 7 209.1777 3481.9373 7 224.8857 4024 5165 8 193.7315 2986.6947 8 ! 209.4395 3490.6585 8 225.1475 4033.8922 9 193.9933 2994.7723 9 ! 209.7013 3499.3906 9 225.4093 4043.2788 10 194.2551 3002.8608 10 209.9631 3508.1336 10 225.6711 4052.6763 11 194.5169 3010.9602 11 210.2249 3516.8875 11 225.9329 4062.0848 62 194.7787 3019.0705 67 210.4867 3525.6524 72 226.1947 4071.5041 1 195.0405 3027.1918 1 210.74&5 3534.4281 1 226.4565 4080.9343 2 195.3023 3035.3239 2 211.0103 3543.2147 2 226.7183 4090.3755 3 195.5641 3043.4670 3 211.2721 3552.0123 3 226.9801 4099.8275 4 195.8259 3051 .6209 4 211.5339 3560.8207 4 227.2419 4109.2905 5 196.0877 3059.7858 5 211.7957 &569.6401 5 227.5037 4118.7643 6 196.3495 3067.9616 6 212.0575 3578.4704 6 227.7655 4128.2491 - 7 196.6113 3076.1483 7 212.3193 3587.3116 7 228.0273 4137.7448 8 196.8731 3084.3459 8 212.5811 3596.1637 8 228.2891 4147.2514 9 197.1349 3092.5544 9 212.8429 3605.0267 9 228.5509 4156.7689 10 197.3967 3100.7738 10 213.1047 3613.9006 10 228.8127 4166.2973 11 ! 197.6585 3109.0041 11 213.3665 3622.7854 11 229.0745 4175.8366 63 197.9203 3117.2453 68 213.6283 3631.6811 73 229.3363 4185.3868 198.1821 3125.4974 1 213.8901 3640.5877 1 229.5981 4194.9479 2 198.4439 3133.7605 2 214.1519 3649.5053 2 229 8599 4204.5200 3 198.7057 3142.0344 3 214.4137 3658.4337 3 230.1217 4214.1029 4 198.9675 3150.3193 4 214.6755 36673731 4 230.3835 4223.6968 5 199.2293 3158.6151 5 214.9373 | 3676.3234 5 230.6453 4233.3016 6 199.4911 3166.9217 6 215.1991 3685.2845 6 230.9071 4242.9172 7 199.7529 3175.2393 7 215.4609 3694.2566 7 231.1689 4252.5438 8 200.0147 3183.5678 8 215.7227 3703.2396 8 231.4307 4262.1813 9 200.2765 3191.9072 9 215.9845 3712.2335 9 231.6925 4271.8297 10 200.5383 3200.2575 10 216.2463 i 3721.2383 10 231.9543 4281.4890 11 200.8001 3208.6188 11 216.5081 3730.2540 11 232.2161 4291.1592 64 201.0619 3216.9909 69 216.7699 3739.2807 74 232.4779 4300.8403 1 201.3237 3225.3739 1 217.0317 3748.3182 1 232.7397- 4310.5324 2 201.5855 3233.7679 2 217.2935 3757.3666 2 233.0015 4320.2353 3 201.8473 3242.1727 3 217.5553 3766.4260 3 233.2633 4329.9492 4 202.1091 3250.5885 4 217.8171 3775 4962 4 233.5251 4339.6739 5 202.3709 3259.0151 5 218.0789 3784.5774 5 233.7869 4349.4096 6 202.6327 3267.4527 6 i 218.3407 3793.6695 6 234.0487 4359.1562 7 202.8945 3275.9012 7 218.6025 3802.7725 7 234.3105 4368.9136 8 203.1563 3284.3606 8 218.8643 3811.8864 8 234.5723 4378.6820 9 203.4181 3292.8309 9 219.1261 3821.0112 9 234.8341 438,8.4613 10 203.6799 3301.3121 10 219.3879 3830.1469 10 235.0959 4398.2515 11 203.9417 3309.8042 . 11 219.6497 3839.2935 11 285.8676 4408.0526 TABLE NO. 73 CON. 183 From Traiit wine's "Civil Engineer** Pocket Book." CIRCLE*. TABLE 3 OF CIRCLES (Continued). IManis in units and twelfths; as in feet ami indies. Dia. Circumf. Area. Dia. { Circumf. Area. Dia. Circumf. A rea. Ft.Iu. Feet. bq. ft. Ft.In. Feet. Sq. ft. Ft.lu. Feet. Sq. ft. 75 235.6194 4417.8647 80 251.3274 5026.5482 So 267.0354 5674.. ". -17 1 235.8812 4427.6676 1 251.5892 5037.0257 1 267.2972 5685.6K37 2 236.1430 4437.5214 2 251.8510 5047.5140 2 ! 267.5590 5696.7765 3 236.4048 4447.3662 3 252.1128 5058.0133 3 267.8208 5707.9302 4 236.6666 4457.2218 4 252.3746 5068.5234 4 268 0826 5719.0919 5 236.9284 4467.0884 5 252.6364 5079.0445 5 268 3444 5730.2705 6 237.1902 4476.9659 6 252.8982 5089.5764 6 268.6062 5741.4509 7 237.4520 4486.8543 7 253.1600 5100.1193 7 268.8080 5752.0543 8 237.7138 4496.7536 8 253.4218 5110.6731 8 269.1298 5763.86-.-6 9 237.9756 4506.6637 9 253.6836 5121.2378 9 209.3916 5775.08 IS 10 238.2374 4516.5849 10 253.9454 5131.8134 10 269.6534 5780.3119 11 238.4992 4526.5169 11 254.2072 5142.3999 11 269.9152 5797.5529 76 238.7610 4536.4598 81 254.4690 5152.9974 86 270.1770 f,8U8 ftO-18 1 239.0228 4546.4136 1 254.7308 5163.6057 1 270.4388 5820.0070 2 239.2846 4556.3784 2 254.9926 5174.2249 2 270.7006 5831 3414 3 239.5464 4566.3540 3 255.2544 5184.8551 3 270.9024 5842.6260 4 239.8082 4576.3406 4 255.5162 5195.4961 4 271 2242 5853.9210 5 240.0700 4586.3380 5 255.7780 5206.1481 5 271.4860 5805.2280 6 240.3318 4596.3464 6 256.0398 5216.8110 6 271.7478 5876.5454 7 240.5936 i 4606.3657 7 256.3016 5227.4847 7 272.0096 5887.8737 8 240.8554 4016.3959 8 256.5634 5238.1694 8 272.2714 5899.21 2 '3 9 241.1172 4626.4370 9 256.8252 5248.8650 9 272.5332 5910..' 630 10 241.3790 4636.4890 10 257.0870 5259.5715 10 272.7950 5921 l-24'> 11 241.6408 4646.5519 11 257.3488 5270.2889 11 273.0568 5933 1959 77 241.9026 4656.6257 82 1 257.6106 5281.0173 87 2733180 5944 i-7:>7 1 242.1644 4666.7104 1 257.8724 5291.7565 1 273.5804 5956.0724 2 242.4262 4676.8061 2 258.1342 5302.5066 2 i 273.8422 5967.4771 3 242.6880 4686.9126 3 258.3960 5313.2677 3 274.1040 5978.8926 4 242.9498 4697.0301 4 258.6578 5324.0396 4 274.3658 5990.3191 5 243.2116 i 4707.1584 5 258.9196 5334.8225 5 274.6270 6001.7504 6 243.4734 4717.2977 6 259.1814 5345.6162 6 274.8894 6013.2047 7 243.7352 4727.4479 7 259.4432 5356.4209 7 275.1512 6024.6039 8 243.9970 4737.6090 8 259.7050 5367.2365 8 275.4130 6036.134* 9 244.2588 4747.7810 9 259.9668 5378.0630 9 275.6748 6047.6149 10 244.5206 4757.9639 10 260.2286 5388.9004 10 i 275.9366 6059.106* 11 244.7824 ,4768.1577 11 260.4904 5399.7487 11 276.1984 6070.6091 78 245.0442 4778.3624 83 260.7522 5410.6079 88 276.4602 6082.1234 1 245.3060 4788.5781 1 261.0140 5421.4781 1 276.7220 6093.6480 2 245.5678 4798.8046 2 261.2758 5432.3591 2 276.9838 6105.1835 3 245.8296 , 4809.0420 3 261.5376 5443.2511 3 277.2456 6116.7300 4 246.0914 4819.2904 4 261.7994 5454.1539 4 277.5074 6128.2873 5 246.3532 4829.5497 5 262.0612 5465.0677 5 ! 277.7692 6139.8556 6 246.6150 4839.8198 6 262.3230 5475.9923 6 278.0309 6151.434& 7 246.8768 4850.1009 7 262.5848 5486.9279 7 278.2927 6163.0.48 8 247.1386 4860.3929 8 i 262.8466 5497.8744 8 278.5545 6174.6253 9 247.4004 4870 6958 9 263.1084 5508-8318 9 i 278.8163 6186.2377 10 247.6622 4881.0096 10 263.3702 5519.8001 10 i 279.0781 6197.8605 11 247.9240 4891.3343 11 263.6320 5530.7793 11 i 279.3399 6209.4942 T9 9 248.1858 i 4901.6699 84 263.8938 5541.7694 89 i 279.6017 6221.1389 1 248.4476 4912.0165 1 264.1556 5552.7705 1 279.863.') 6232.7944 2 248.7094 4922.3739 2 264.4174 5563.7824 2 280.1253 6244.460* 3 248.9712 i 4932.7423 3 264.6792 5574.8053 3 280.3871 6250.1:>si: 4 249.2330 4943.1215 4 264.9410 5585.8390 A 280.6489 6267.8264 5 249.4948 4953.5117 5 265.2028 5596.8837 5 280.9107 6279. 52-V, 6 249.7566 4963.9127 6 ! 265.4646 5607.9392 6 281.1725 6291.235> 7 250.0184 4974.3247 7 265.7264 5619.0057 7 281.4343 0:;i)2 95M 8 250.2802 4984.7476 8 265.9882 5630.0831 8 281.6961 6314.6885 9 250.5420 4995.1814 9 26*3.2500 5641.1714 9 281.9579 6326.4313 10 250.8038 5005.6261 10 266.5118 5652.2706 10 282.2197 6338.1850 11 251.0656 5016.0817 11 266.7736 5663.3807 11 282.4815 6349.9496 H TABLE NO. 73 COJS T CL. From Traiitwine's "Civil Fii$;-iiiccr*N Pocket Book.' CIRCLES. TABLE 3 OF CIRCLES (Continued). in units and twelfths; as in feet and inches. Dia. Circumf. ! Area. Dia. Circumf. Area. Dia. Circuraf. Area. Ft.In. ! Feet. Sq. ft. Ft.In. Feet. Sq. ft. Ft.In. Feet. Sq. ft. 90 282.7433 6361.7251 1)3 5 293.4771 6853.9134 96 9 303.9491 7351. 7C86 1 283.0051 6373.5116 6 293.7389 6866.1471 10 304.2109 7364.4386 2 283.2669 6385.3089 7 294.0007 ! 6878.3917 11 304.47L7 7377.1195 3 ! 283.5287 6397.1171 8 294.2625 6890.6472 97 304.7345 73C9.8113 4 ! 283.7905 6108.1)303 9 294.5243 6902.9135 1 304.9963 7402.5140 5 ! 284.0523 6420.7663 10 294.7861 ' 6915.1908 2 305.2581 7415.2277 6 i 284.3141 6432.6073 11 295.0479 6927.4791 3 305.5199 7427.9522 7 284.5759 6444.4592 94 295.3097 I 6939.7782 4 305.7817 7440.6877 8 : 284.8377 6156.3220 1 295.5715 ! 6952.0882 5 306.0435 7453.4340 9 i 28'). 0995 6168.1957 2 295.8333 < 6964.4091 6 306.3053 7466.1913 10 | 285.3613 6180.0803 3 296.0951 6976.7410 7 306.5671 7478.C595 11 ' 285.0231 6491.97o8 4 I 29*3569 6989.0837 8 306.8289 7491.7385 11 2858849 6503.882-J 5 296.6187 7001.4374 9 307.0907 7504.5285 1 286.1467 6515.7995 6 296.8805 7013.8019 10 307.3525 7517.32SJ 2 286-408-') 6527.7278 7 297.1423 7026.1774 11 307.6143 7530.141i 3 286.6703 6539.6669 8 297.4041 7038.5638 98 307.8761 7542.S640 4 286.9321 6551.6169 9 297.6059 7050.9611 1 308.1379 75C5.7976 5 287.1939 6563.5779 10 297.9277 7063.3693 2 308.3997 7568.0.421 6 1 287.4557 6575.5498 11 298.1895 7075.7884 3 308.6615 7581.4176 7 287.7175 6587.5325 95 298.4513 7088.2184 4 308.923 7594.SG39 8 ' 287.9793 6599.5262 1 298.7131 7100.6593 5 309.1851 7607.2H2 9 2882411 0611.5308 2 I 298.9749 7113.1112 6 309.4469 7620.1293 10 288.5029 6623.5463 3 | 299.2367 7125.5739 7 309.7087 7633.0284 11 2887647 6635.5727 4 299.4985 7138.0476 8 309.9705 764f.e884 92 i 289.0265 6647.6101 5 299.7003 7150.5321 9 310.2323 7658.8593 1 1 289.2883 (Kv'9.6583 6 300.0221 7163.0276 10 310.4941 7671.7911 2 289.5501 0671.7174 7 300.2839 7175.5340 11 310.7559 7684.7338 3 289.8119 6683.7875 8 300.5457 7188.0513 99 311.0177 7697.6874 4 290.0737 6695.8684 9 300.8075 7200.5794 1 311.2795 7710.6519 5 290.3355 6707.9603 10 301.0693 7213.1185 2 311.5413 7723.6274 6 290.5973 6720.0630 11 301.3311 7225.6686 3 311.8031 7736.6137 7 290.8591 0732.1767 96 301.5929 7238.2295 4 312.0649 7749.6109 8 291.1209 0744.3013 1 301.8547 7250.8013 5 312.3267 7762.6191 9 291.3827 6756 4368 2 302.1165 7263.3840 6 312.5885 7775.6382 10 291.6145 67(58.5832 3 302.3783 7275.9777 7 312.8503 7788.6681 11 291.9063 6780.7405 4 302.6401 7288.5822 8 313.1121 7801.7090 93 292.1681 6792.9087 5 302.9019 7301.1977 9 313.3739 7814.7608 1 292.4299 6805.0878 6 303.1637 7313.8240 10 313.6357 7827.8235 2 292.6917 68172779 7 303.4255 7326.4613 11 313.8975 7840.8i'71 3 292.9535 6829.4788 8 303.6873 7339.1095 100 314 J 593 7853.9816 4 293.2153 6841.6907 Circumferences in feet, when the diam contains fractions of ail inch. See similar process, p 177 Diam. Circumf. Diam, Circuraf, Diam, Circumf, Diam, Circumf, Diam, Circumf, Inch. foot inch foot Inch foot. inch. foot. inch. foot. 1-64 .004091 7-32 .057269 27-64 .110447 5-8 .163625 53-64 .216803 1-32 .008181 15-64 .061359 7-16 .114537 41-64 .167715 27-32 .220S93 3-64 .012272 & .065450 29-64 .1186-28 21-32 .171806 55-64 .2249S4 1-16 .016362 17-64 .069540 15-32 .122718 43-64 .175896 7-8 .229074 5-64 .020453 9-32 .0736M1 31-64 .126809 11-16 .179987 57-64 .233165 3-32 .024544 19-64 .077722 % .130900 45-64 .184078 29-32 .237256 7-64 .028634 5-16 .081812 aOi .134990 23-32 .188168 59-64 .241346 X .0327-25 21-64 .085903 17-32 .139081 47-64 .192259 15-16 .245437 9-64 .036S16 11-32 .089994 35-64 .143172 % .196350 61-64 .249528 5-32 .04090(5 23-64 .094084 9-16 .147262 49-64 .200440 31-32 1 .253618 11-64 .044997 % .098175 37-64 | .151353 25-32 .204531 63-64 | .257709 3-16 .049087 25-04 .102265 19-32 .155443 51-64 .208621 1 .261799 13-64 1 .< 153178 13-32 .106356 39-64 .159534 13-16 .212712 TABLE NO. 74. 185 From Trautwine's "Civil Engineer's Pocket Rook." SQUARE AND CUBE ROOTS. Square Roots and Cube Roots of X timbers from .1 to 28. No errors. No. Square. Cube. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. No. Sq. Rt. C. Rt. .1 .01 .001 .316 .464 .7 2.387 1.786 _4 3.661 2.375 .15 .0225 .0034 .387 .531 .8 2.408 1.797 .6 3.68K 2.387 .2 .04 .008 .447 .585 .9 2.429 1.807 .8 3.715 2.399 .25 .0625 .0156 .500 .630 6. 2.449 1.817 14. 3.742 2.410 .3 .09 .027 ' .548 .669 .1 2.470 1.827 .2 3.768 2.422 .35 .1225 .0429 .' .592 .705 ,| 2.490 1.837 .4 3.795 2.433 .4 .16 .064 .633 .737 .3 2.510 1.847 .6 3.821 2.444 .45 .2025 .0911 I .671 .766 .4 2.530 1.857 .8 3.847 2.455 .5 .25 .125 .707 .794 .5 2.550 1.866 15. 3.873 2.466 .55 .3025 .1664 1 .742 .819 .6 2.569 1.876 .2 3.899 2.477 .6 .36 .216 .775 .843 .7 2.588 1.885 .4 3.924 2.488 .65 .4225 .2746 .806 .866 .8 2.608 1.895 .6 3.950 2.499 .7 .49 .343 837 .888 .9 2.627 1.904 .8 3.975 2.509 .75 .5625 .4219 .866 .909 7. 2.646 1.913 16. 4. 2.520 .8 .64 .512 .894 .928 .1 2.665 1.922 .2 4.025 2.530 .85 .7225 .6141 1 .922 .947 .2 2.683 1 .931 .4 4.050 2.541 ,9 .81 .729 .949 .965 .3 2.702 1.940 .6 4.074 2.551 .95 .9025 .8574 .975 .983 .4 2.720 1.949 .8 4.099 2.561 1. 1.000 1.000 1.000 1.000 .5 2.739 1.957 17. 4.123 2.571 .05 1.103 1.158 1.025 1.016 .6 2.757 1.966 .2 4.147 2.581 1.1 1.210 1.331 1.049 1.032 .7 2.775 1 975 .4 4.171 2.591 .15 1.323 1.521 1.072 1.018 .8 2.793 1.983 .6 4.195 2.601 1.2 1.440 1.728 1.095 1.063 .9 2.811 1.91)2 .8 4.219 2.611 .25 1.563 1.963 1.118 1.077 8. 2.828 i 2.000 18. 4.243 2.621 1.3 1.690 2.197 1.140 1.091 .1 2.846 2.008 .2 4.266 2.630 .35 1.823 2.460 1.162 1.105 .2 2.864 2.017 .4 4.290 2640 1.4 1.960 2.744 1.183 1.119 J 2.881 2.025 6 4.313 2.650 .45 2.103 3.049 1.204 1.132 .4 2.898 2.033 . -8 4.336 2.659 1.5 2.250 3.375 1.225 1.145 2.915 2.041 19. 4.359 2.668 .55 2.403 3.724 1.245 1.157 Jt 2.933 2.0 19 .2 4.382 2.678 1.6 2.560 4.096 1.265 1.170 .7 2.950 ; 2.057 .4 4.405 2.687 .65 2.723 4.492 1.285 1.182 .8 2.966 j 2.065 .6 4.427 2.696 1.7 2.890 4.913 1.304 1.193 .9 2.983 2.072 .8 4.450 2.705 .75 3.063 5.359 1.323 1.205 9. 3. 2.080 20. 4.472 2.714 1.8 3.240 5.832 1.342 1.216 .1 3.017 2.088 .2 4.494 2.723 .85 3.423 6.332 1.360 1.228 .2 3.033 2.095 .4 4.517 2.732 1.9 3.610 6.859 1.378 1.239 .3 3.050 1 2.103 .6 4.539 2.741 .95 3.803 7.415 1.396 1.249 .4 3.066 ! 2.110 .8 4.561 2.750 . ! 4.000 8.000 1.414 1.260 .5 3.082 2.118 21. 4.583 2.759 .1 4.410 9.261 1.449 1.281 .6 3.098 2.125 .2 4.604 2.768 .2 4.840 10.65 1.483 1.301 .7 3.114 I 2.133 .4 4.626 2.776 .3 5.290 12.17 1.517 1.320 .8 3.130 ; 2.140 .6 4.648 2.785 .4 5.760 13.82 1.549 1.339 .9 3.146 2.147 .8 4.669 2J94 -5 6.250 15.63 1.581 1.357 10. ' 3.162 : 2.154 22. 4.690 2.802 .6 6.760 -47.58 1.612 1.375 .1 3.178 2.162 .2 4.712 2.810 .7 7.290 19.68 1.643 1.392 .2 3.194 2.169 .4 4.733 2.819 .8 7.840 21.95 1.673 1.409 .3 3.209 j 2.176 .6 4.754 2.827 .9 8.410 24.39 1.703 1.426 .4 3.225 2.183 .8 4.775 2.836 8. 9. 27. 1.732 1.442 .5 3.240 2.190 23. 4.76 2.844 .1 : %.61 29.79 1.761 1.458 .6 3.256 2.197 .2 4.817 2.852 .2 ! 10.24 32.77 1.789 1.474 .7 3.271 2.204 .4 4.837 2.860 . j 10.89 35.94 1.817 1.489 .8 3.286 2.210 .6 4.858 2.868 .4 11.56 39.30 I.b44 1.504 .9 3.302 2.217 .8 4.879 2.876 .5 12.25 42.88 1.871 1.518 11. 3.317 2.224 24. 4.899 2.884 .6 12.96 46.66 1.897 1.533 .1 3.332 2.2*1 .2 4.919 2.892 13.69 50.65 1 .924 1.547 .2 3.347 2. 287 .4 4.940 2.900 is 14.44 54.87 1.949 1.560 .3 3.362 2.244 .6 4.960 2.908 .9 15.21 59.32 1.975 1.574 .4 3 376 2.251 .8 4.980 2.916 4. 16. 64. 2. 1.587 .5 3.391 2.257 25. 5. 2.924 .1 16.81 68.92 2.025 1.601 . 3.406 2.264 .2 5020 2.932 .2 17.64 74.09 2.049 1 613 .7 3.421 2.270 .4 5.040 2.940 .3 18.49 79.51 2.074 1.626 .8 3.435 2.277 .6 5.060 2.947 .4 19.36 85.18 2.098 1 .6:59 .9 3.450 j 2.283 .8 5.079 2.955 .5 20.25 91.13 2.121 1.651 12. 3.464 2 2H9 26. 5099 2.962 .6 21.16 97.34 2.145 1.663 .1 3479 2.296 .2 5.119 2.970 .7 : 22.09 103.8 2.168 1.675 .2 3.493 2.302 4 5.138 2.978 .8 23.04 110.6 2.191 1.687 .3 3.507 2.308 .6 5.158 2.985 .9 24.01 117.6 2.214 1.69*- .4 3.521 2.315 .8 5.177 2.993 6. 25. 125. 2. 286 1.710 5 3.536 2.321 27. 5.196 3.000 1 26.01 182. 7 2.258 1.721 !6 3.550 2.327 .2 5.215 3.007 .2 27.04 140.6 2.280 1.732 .7 3.564 2.333 .4 5.235 3.015 .3 , 28.09 14K9 2.302 1.744 .8 j 3.578 2 339 .6 5.254 3.022 .4 29.16 ! 157.5 2.324 1.754 .9 3.592 2.345 .8 5.273 3.029 .5 i 3C.25 166.4 2.345 , 1.7T 13. 3.306 2.351 28. 5.292 3.037 .6 31.36 175.6 2.36.2743 183 33489 6128487 13.5277 5.6774 248 61504 5252992 15.7480 6.2828 184 33856 6229504 13.5647 5.6877 249 62001 5438249 ] 5. 7797 3.2912 185 34225 6331625 13.6015 5.6980 250 62500 15625000 15.8114 6.29M 188 TABLE NO. 75-CON. From Traut wine** Civil Engineer's Pocket Book.* 9 SQUARES, CUBES, AND ROOTS. TABLE of Squares, Cubes, Square Roots, and Cube Roots, of lumbers from 1 to 1OOO (CONTINUED.) No. Square. Cube. Sq. Rt, C. Rt. No. Square. Cube. Sq. Rt. C. Rt. 511 512 261121 262144 133432831 134217728 22.6053 22.6274 7.9948 8. 576 577 331776 332929 191102976 192100033 24. 24.0208 8.3203 8.3251 513 263169 135003697 22.6495 8.0052 578 334084 193100552 24.0416 8.3300 514 264196 135796744 22.6716 8.0104 579 335241 194104539 24.0624 8.3348 515 265225 136590875 22.6936 8.0156 580 336400 195112000 24.0832 S.3396 516 266256 137388096 22.7156 8.0208 581 337561 196122941 24.1039 8.3443 517 267289 138188413 22.7376 8.0260 588 338724 197137368 24.1247 8.3491 518 268324 138991832 22.7596 8.0311 583 339889 198155287 24.1454 8.3539 519 269361 139798359 22.7816 8.0363 584 341056 199176704 24.1661 8.3587 520 270400 140608000 22.8035 8.0415 585 342225 200201625 24.1868 8.3634 521 271441 41420761 22.8254 8.0466 586 34339B 201230056 24.2074 8.3682 522 272484 42236648 22.8473 8.0517 587 344369 202262003 24.2281 8.3730 523 273529 43055667 22.8692 8.0569 588 345744 203297472 24.2487 8.3777 524 274576 43877824 22.8910 8.0620 589 346921 204336469 24.2693 8.3*25 525 275625 44703125 22.9129 8.0671 590 348100 205379000 24.2899 8.3872 526 276676 45531576 22.9347 8.0723 591 349281 206423071 24.3105 8.3919 527 277729 4636318: 22.9565 8.0774 592 350464 207474688 24.3311 8.3967 528 278784 47197952 22.9783 8.0825 593 351649 208527857 24.3516 8.4014 529 279841 48035889 23. ' 8.0876 594 352836 209584584 24.3721 8.4061 330 280 WO 148877000 23.0217 8.0927 593 354023 210644875 24.892*i 8.4103 531 281961 * 149721291 23.0134 8.0978 596 355216 211708736 24.4131 8.4155 532 283024 150568768 23.0651 8.1028 597 356409 212776173 24.4336 8.4202 533 284089 151419437 23.0868 8.1079 598 857604 213847192 24.4540 8.4249" 534 285156 152273304 23.10X4 8.1130 599 358801 214921799 24.4745 8.4296 535 286225 153130375 23.1301 8.1180 600 360000 216000000 24.4949 8.4343 536 287296 153990656 23.1517 8.1231 601 361201 217081801 24.5153 8.4390 537 288369 154854153 23.1733 8.1281 602 362404 218167208 24.5357 . 4437 538 289444 155720872 23.1948 8.1332 603 363609 219256227 24.55bl 8.4484 539 290521 156590819 23.21(54 8.1382 604 364616 220348864 24.5764 8.4530 540 291600 157464000 23.2379 8.1433 4*40104 25. 1794 .51*07 570 324900 185193000 23.8747 8.2913 635 403225 256047.S75, 25.DWJ 8.5958 571 326041 186169411 23.8956 8.2962 (536 40 UM 257259456' 25.2190 : 8.5997 572 327184 187149248 23.9165 8.3010 ;{? 4()5761 258474853 25.23M9 8.6043 573 32aS29 188132517 23.9374 8.305M 63S 407014 2596:^4072 25.25X7 S.H3 574 675 329476 330625 189119224 iio 23.:>83 28.979-2 8.3107 . 8 ..'ll-vS 639 408321 4.n<*uxi 20i>l71l9 >' 1 i4-<3 260 67600 17576000 16.1245 6.3X25 325 105625 34328125 18.0278 6.8753 261 nan 177795*1 16.1555 6.3907 32(5 106276 34645976 18.0555 6.8824 262 6*6 i t I7:HH2> 16.1864 6.39x^ 327 10;>-'9 34965783 18.0831 6.8894 169 69169 18191447 it;. 21 7:1 6.4070 328 107584 35287552 18.1108 6.8964 264 9fi% 18399741 16.2481 6.4151 329 108241 35611289 18.1384 6.9034 265 70225 18609625 16.2788 6.4232 330 108900 35937000 18.1659 6.9104 166 70756 1XH21096 16.3095 6.4312 331 i 109561 36264691 18.1934 6.9174 267 71389 19034163 16.3401 6.43113 u:;_' 110224 36594368 18.2209 6.9244 m 19248832 16.3707 6.4473 333 | 110889 36926037 18.2483 6.9313 269 72361 19465109 16.4012 6.4553 334 ! 111556 37259704 18.2757 6.9382 270 72900 19683000 16.4317 6.4633 335 112225 37595375 18.3030 6.9451 271 734*1 19902511 16.4621 6.4713 336 112896 37933056 18.3303 6.9521 272 73984 2012364X 16.4924 6.4792 337 113569 38272753 18.3576 6.9589 MS 74529 20346417 16.5227 6.4872 338 i 114244 38614472 18.3848 6.9658 274 75076 20570824 16.5529 6.4951 339 114921 38958219 18.4120 6.9727 275 75625 20796875 16.5831 6.5030 340 115600 39304000 18.4391 6.9795 276 76176 21024576 16.6132 6.5108 341 116281 39651821 18.4662 6.9864 277 76729 21253933 16.6433 6.5187 342 116964 40001688 18.4932 6.9932 278 77384 21484952 16.6733 6.5265 343 117649 40353607 18.5203 7. 279 77841 21717639 16.7033 6.5343 344 118336 40707584 18.5472 7.0068 280 78400 21952000 16.7332 6.5421 345 119025 41063625 18.5742 7.0136 Ml 7X961 22188041 16.7631 6.5499 346 119716 41421736 18.6011 * 7.0203 282 79524 22425768 16.7929 6.5577 347 120409 41781923 18.6279 7.0271 H0089 22665187 6.8226 6.5654 348 121104 42144192 18.6548 7.0338 284 X0f>56 2290830* 6.8523 6.5731 349 121801 42508549 18.6815 7.0406 285 81225 23149125 6.8819 6.5808 350 122500 42875000 18.7083 7.0473 286 81796 23393656 6.9115 6.5885 351 123201 43243551 18.7350 7.0540 287 X2369 23639303 6.9411 6.5962 352 123904 43614208 18.7617 7.0607 288 82M4 23887872 6.9708 6.6039 353 124609 43986977 18.7883 7.0674 888 83521 24137569 6.6115 354 125316 44361864 18.8149 7.0740 xoo 84100 24389000 7^0294 6.6191 355 126025 44738875 18.8414 7.0807 291 84681 24642171 7.0587 6.6267 356 126736 45118016 18.8680 7.0873 292 85264 248970X8 7.0880 6.6343 357 127449 45499293 18.8944 7.0940 3M 85849 25153757 7.1172 6.6419 358 128164 45882712 18.9209 7.1006 294 66 25 U 21*4 7.1464 6.6494 359 128881 46268279 18.9473 7.1072 295 87025 25672375 7.1756 6.6569 360 129600 46656000 18.9737 7.1138 296 87616 2593433* 7.2047 6.6644 361 130321 47045881 19. 7.1204 297 88209 26198073 7.2337 6.6719 362 131044 47437928 19.0263 7.1269 398 88804 2646:1592 7.2627 6.6794 363 131769 47832147 19.0526 7.1335 299 89401 26730899 7.2i)16 6.6869 364 1324% 48228544 19.0788 7.1400 300 90000 27000000 7.3205 6*6943 365 133225 48627125 19.1050 7.1466 301 90601 27270901 7.3494 6.7018 366 133956 49027896 19.1311 7.1531 302 91204 27543608 7.3781 6.7092 367 134689 49430863 19.1572 7.1596 303 91X09 27818127 7.4069 6.7166 368 135424 ! 49836032 19.1833 7.1661 304 92416 2X094464 7.4356 6.7240 369 136161 50243409 19.2094 7.1726 305 93025 28372625 7.4642 6.7313 370 136900 50653000 19.2354 7.1791 306 93636 28652616 7.4929 6.7387 371 137641 51064811 19.2614 7.1855 307 94249 2X934443 7.5214 ! 6.7460 372 138384 51478848 19.2873 7.1920 308 94864 29218112 7.5499 6.7533 373 139129 51895117 19.3132 7.1984 30?) 95481 29503629 7.5784. 6.7606 374 139876 52313624 19.3391 7.2043 310 96100 29791000 7.6068 : 6.7K79 375 140625 52734375 19.3649 7.2112 311 96721 300X0231 7.IB52 6.7752 376 41376 53157376 19.3907 7.2177 312 97344 30371328 7.6635 6.7824 377 42129 535X2633 19.4165 7.2240 313 97969 30664297 7.6918 6.7897 378 42-W4 54010152 19.4422 7.2304 314 98596 30959144 7.7200 6.7'W>9 379 43641 54439939 19.4679 7.236* J15 992*3 31255875 7.74>V^ 6.8041 3*0 44400 54372000 19.4936 7.2431 190 TBALE NO. 75-CON. From Trautwine's "Civil Engineer's Pocket Book." SQUARES, CUBES, AND ROOTS. TABLE of Squares, Cubes, Square Roots, and Cube Roots, of Numbers from 1 to 1OOO (CONTINUED.) No. Square. Cube. Sq. Rt. C. Rt. No. Square. Cube. Sq. Rt. C. Rt. 381 382 145161 145924 55306341 55742968 19.5192 19.5448 7.2495 7.2558 446 447 198916 199809 88716536 89314623 21.1187 21.1424 7.6403 7.6460 383 146689 56181887 19.5704 7.2622 448 200704 89915392 21.1660 7.6517 384 147456 56623104 19.5959 7.2685 449 201601 90518849 21.1896 7.6574 385 148225 57066625 19.6214 7.2748 450 202500 91125000 21.2132 7.6631 386 148996 57512456 19.6469 7.2811 451 203401 91733851 21.2368 7.6688 387 149769 57960603 19.6723 7.2874 452 204304 92345408 21.2603 7.6744 388 150544 58411072 19.6977 7.2936 453 205209 92959677 21.2838 7.6801 389 151321 58863869 19.7231 7.2999 454 206116 93576664 21.3073 7.6857 390 152100 59319000 19.7484 7.3061 455 207025 94196375 21.3307 7.6914 391 152881 59776471 19.7737 7.3124 456 207936 94818816 21.3542 7.6970 392 153664 60236288 19.7990 7.3186 457 208849 95443993 21.3776 7.7026 393 154449 60698457 19.8242 7.3248 458 209764 96071912 21.4009 7.7082 394 155236 61162984 19.8494 7.3310 459 210681 96702579 21.4243 7.7138 395 156025 61629875 19.8746 7.3372 460 211600 97336000 21.4476 7.7194 396 156816 62099136 19.8997 7.3434 461 212521 97972181 21.4709 7.7250 397 157609 62570773 19.9249 7.3496 462 213444 98611128 21.4942 7.7306 398 158404 63044792 19.9499 7.3558 463 214369 99252847 21.5174 7.7362 399 159201 63521199 19.9750 7.3619 464 215296 99897344 21.5407 7.7418 400 160000 64000000 20. 7.3681 465 216225 100544625 21.5639 7.7473 401 160801 64481201 20.0250 7.3742 466 217156 101194696 21.5870 7.7529 402 161604 64964808 20.0499 7.3803 467 218089 101847563 21.6102 7.7584 403 162409 65450827 20.0749 7.3864 468 219024 102503232 21.6333 7.7639 404 163216 65939264 20.0998 7.3925 469 219961 103161709 21.6564 7.7695 405 164025 66430125 20.1246 7.3986 470 220900 103823000 21.6795 7.7750 406 164836 66923416 20.1494 7.4047 471 221841 104487111 21.7025 7.780S 407 165649 67419143 20.1742 7.4108 472 222784 105154048 21.7256 7.786d 408 166464 67917312 20.1990 7.4169 473 223729 105823817 21.7486 7.7915 409 167281 68417929 20.2237 7.4229 474 224676 1 06496 424 21.7715 7.7970 410 168100 68921000 20.2485 7.4290 475 225625 107171875 21.7945 7.8025 411 168921 69426531 20.2731 7.4350 476 226576 107850176 21.8174 7.8079 412 169744 69934528 20.2978 7.4410 477 227529 108531333 21.8403 7.8134 413 170569 70444997 20.3224 7.4470 478 228484 109215352 21.8632 7.8188 414 171396 70957944 20.3470 7.4530 479 229441 1 03902239 21.8861 7.8243 415 172225 71473375 20.3715 7.4590 480 230400 110592000 21.9089 7.8297 416 173056 71991296 20.3961 7.4650 481 231361 111284641 21.9317 7.8352 417 173889 72511713 20.4206 7.4710 482 232324 111980168 21.9545 7.8406 418 174724 73034632 20.4450 7.4770 483 233289 112678587 21.9773 7.8460 419 175561 73560059 20.4695 7.4829 484 234256 113379904 22. 7.8514 420 176400 74088000 20.4939 7.4889 485 235225 114084125 22.0227 7.8568 421 177241 74618461 20.5183 7.4948 486 2361% 114791256 22.0454 7.8622 422 178084 75151448 20.5426 7.5007 487 237169 115501303 22.0681 7.8676 423 178929 75686967 20.5670 7.5067 488 238144 116214272 22.0907 7.8730 424 179776 76225024 20.5913 7.5126 489 239121 116930169 22.1133 7.8784 425 180625 76765625 20.6155 7.5185 490 240100 117649000 22.1359 7.8837 426 181476 77308776 20.6398 7.5244 491 241081 118370771 22.1585 7.8891 427 182329 77854483 20.6640 7.5302 492 242064 119095488 22.1811 7.8944 428 183184 78402752 20.6882 7.5361 493 243049 119823157 22.2036 7.8998 429 184041 78953589 20.7123 7.5420 494 244036 120553784 22.2261 7.9051 430 184900 79507000 20.7364 7.5478 495 245025 121287375 22.2486 7.9105 431 185761 80062991 20.7605 7.5537 4% 246016 122023936 22.2711 7.9158 432 186624 80621568 20.7846 7.5595 497 247009 1227G3473 22.2935 7.9211 433 187489 81182737 20.8087 7.5654 498 248004 123505932 22.3159 7.9264 434 188356 81746504 20.8327 7.5712 499 249001 124251499 22.3383 7.9317 435 189225 82312875 20.8567 7.5770 500 250000 125000000 22.3607 7.9370 436 190096 82881856 20.8806 7.5828 501 251001 125751501 22.3830 7.942$ 437 190969 83453453 20.9045 7.5886 502 252004 126506008 22.4054 7.9476 438 191844 84027672 20.9284 7.5944 503 253009 127263527 22.4277 7.9528 439 192721 84604519 20.9523 7.6001 504 254016 128024064 22.4499 7.9581 440 193600 85184000 20.9762 7.6059 505 255025 128787625 22.4722 7.9634 441 194481 85766121 21. 7.6117 506 256036 129554216 22.4944 7.9686 442 195364 86350888 21.0238 7.6174 507 257049 130323843 22.5167 7.9739 443 196249 86938307 21.0476 7.6232 508 258064 131096512 22.5389 7.9791 444 197136 87528384 21.0713 7.6289 509 259081 131872229 22.5610 7.9843 445 196025 88121125 21.0950 7.6346 510 260100 132651000 22.5832 7.989* TABLE NO. 75-CON. 191 From Traut wine's "Civil Engineer** Pocket Book." SQUARES, CUBES, AND ROOTS. TABLE of Squares, Cubes, Square Roots, and Cube Roots, of X timbers from 1 to 10OO (CONTINUED.) Square. Cube. Sq. Rt. C. Rt. No. Square. Cube. Sq. Rt. C. Rt. 410881 263374721 25.3180 8.6222 706 498436 351895*16 26.5707 8.9043 412164 264609288 25.3377 8.6267 707 499849 353393243 26.5895 8.9085 41. 'ill') 265847707 25.3574 8.6312 708 501264 354894912 26.6083 8.9127 414736 2670*99*4 25.3772 8.6357 709 5026*1 3564008-29 26.6271 8.9169 416025 268336125 25.3969 8.6401 710 504100 357911000 26.6458 8.9211 41 73 16 269586136 25.4165 8.6446 711 505521 359425431 26.6646 8.9253 418609 270840023 25.4362 8.6490 712 506944 360944128 26.6833 8.9295 419304 272097792 25.4558 8.6535 713 508369 362467097 26.7021 8.9337 421201 27:W5:U49 25.4755 8.6579 714 509796 363994344 26.7208 8,9378 422500 274625000 25.4951 8.6624 715 511225 365525875 26.7395 8.942C 423801 275894451 25.5147 8.6668 716 512656 367061696 26.7582 8.9462 425104 277167808 25.5343 8.6713 717 514089 368601813 26.7769 8.9503 426409 278445077 25.5539 8.6757 718 515524 370146232 26.7955 8.9545 427716 27972IW64 25.5734 8.6801 719 516961 371694959 26.8142 8.9587 429025 281011375 25.5930 8.6845 720 518400 373248000 26.8328 8.9628 430336 282300416 25.6125 8.6890 721 519841 374805361 26.8514 8.%70 4;n35!U-593 25.6320 8.693-4 722 521284 376367048 26.8701 8.9711 4:i2yt>4 284890312 25.6515 8.6978 723 522729 377933067 26.8887 8.9752 434281 286191179 25.6710 8.7022 724 524176 379503424 26.9072 8.9794 435600 287496000 25.6905 8.7066 725 525625 381078125 26.9258 8.9835 436921 288804781 25.7099 8.7110 726 527076 382657176 26.9444 8.9876 4389*4 290117528 25.7294 8.7154 727 528529 384240583 26.9629 8.9918 439569 291434247 25.7488 8.7198 728 529984 385828352 26.9815 8.9959 440896 292754944 25.7682 8.7241 729 531441 387420489 27. 9. 442225 294079625 25.7876 8.7285 730 532900 389017000 27.0185 9.0041 443556 295408296 25.8070 8.7329 731 534361 390617891 27.0370 9.0082 444889 296740963 25.8263 8.7373 732 535824 392223168 27.0555 9.0123 446224 298077632 25.8457 8.7416 733 537289 393832837 27.0740 9.0164 447i61 299418309 25.8650 8.7460 734 538756 395446904 27.0924 9.0205 448900 300763000 25.8844 8.7503 735 540225 397065375 27.1109 9.0246 450241 302111711 25.9037 8.7547 736 541696 398688256 27.1293 9.02*7 45 1584 303464448 25.9230 8.7590 737 543169 400315553 27.1477 9.0328 452929 304821217 25.9422 8.7634 738 544644 401947272 27.1662 9.0369 454276 306182024 25.9615 8.7677 739 546121 403583419 27.18i6 9.0410 455625 307546875 25.9808 8.7721 740 547600 405224000 27.2029 9.0450 456976 308915776 26. 8.7764 741 5490S1 406869021 27.2213 D.0491 458329 31028*733 26.0192 8.7807 742 550564 408518488 27.2397 9.0532 459684 311665732 26.0384 8.7850 743 552049 410172407 27.2580 9.0572 461041 313046839 26.0576 8.7893 744 553536 > 411830784 27.2764 9.0613 462400 314432000 26.0768 8.7937 745 555025 413493625 27.2947 9.0654 463761 315821241 26.0960 8.7980 746 556516 415160936 27.3130 9.0694 465124 317214568 26.1151 8.8023 747 558009 416832723 27.3313 9.0735 466489 318611987 26.1343 8.8066 748 559504 418508992 27.3496 9.0775 467*56 320013504 26.1534 8.8109 749 561001 420189749 27.3679 9.0816 469225 321419125 26.1725 8.8152 750 562500 421875000 27.3861 9.0856 705% 322828856 26.1916 8.8194 751 564001 423564751 27.4044 9.08% 71969 324242703 26.2107 8.8237 752 565504 425259008 27.4226 9.0937 73344 325660672 26.2298 8.8280 753 567009 426957777 27.4408 9.0977 74721 327082769 26.2488 8.8323 754 568516 428661064 27.4591 9.1017 76100 328509000 26.2679 8.8366 755 570025 430368875 27.4773 9.1057 77481 329939371 26.2869 8.8408 756 571536 432081216 27.4955 9.1098 78864 331',73*88 26.3059 8.8451 757 573049 433798093 27 5136 9.1138 80249 33 f .812557 26.3249 8.8493 758 574564 435519512 27.5318 9.1178 481636 3:C4255384 26.3439 8.8536 759 576081 437245479 27.5500 9.1218 483025 ^35702375 26.3629 8.8578 760 577600 438976000 27.5681 9.1258 484416 337153536 26.o818 8.8621 761 579121 440711031 27.5862 9.1298 485809 338608873 26. 4008 8.8663 762 580644 442450728 27.6043 9.1338 4*7204 340068392 26.4197 8.8706 763 582169 444194947 27.6225 9.1378 4**01 341532099 26.43*6 8.8748 764 5836% 445943744 27.6405 9.1418 490000 343000000 26.4575 8.8790 765 585225 447697125 27.6586 9.1458 4B1401 344472101 26.47f ' 8.8833 766 586756 4494550% 27.6767 9.1498 492804 345948408 26.4953 8.8875 767 588289 451217663 27.6948 9.1537 49*203 3 4742*927 26.5141 88917 768 539824 45284832 27.7128 9.1577 4)5616 348913664 26.5330 8.8959 769 591361 454756609 27.7308 9.1617 497026 350402625 26.5518 8.9001 770 592900 456533008 27.7489 9.1657 192 TABLE NO. 75-CON. From Tra lit wine's " Civil Engineer's Pocket Hook." SQUARES, CUBES, AND ROOTS. TABLE of Squares, Cubes, Square Roots, and Cube Roots, of Numbers from 1 to 1OOO (CONTINUED.; 1 No. Square. Cube. Sq. Rt. C. Rt. No. Square. Cube. I Sq. Rt. C. Rt. 1 771 594441 458314011 27.7669 9.1696 836 698896 5842770561 28.9137 9.4204 772 595984 460099648 27.7849 9.1736 837 I 700569 586376253! 28.9310 9.4241 773 ! 597529 461889917 27.8029 9.1775 838 702244 588480472* 28.9482 9.4279 774 1 599076 463684824 27.N209 9.1815 839 703921 590589719 28.9655 9.4316 775 600625 465484375 27.8388 9.1855 840 705600 592704000 28.9828 9.4354 776 1 602176 467288576 27.8568 9.1894 841 707281 594823321 29. 9.4391 777 603729 469097433 27.8747 9.1933 842 708964 596947688 29.0172 9.442* 778 ; 605284 470910952 27.8927 9.1973 843 710649 599077107 29.0345 9.4466 779 606841 472729139 27.9106 9.2012 844 712336 601211584 29.051 7 9.4503 780 608400 474552000 27.9285 9.2052 845 714025 603%! 125 j 29.0689 9.4541 781 1 609961 476379541 27.9464 9.2091 846 715716 605495736 29.0861 9.4578 782 611524 478211 768 27.9643 9.2130 847 717409 607645423 1 29.1033 9.4615 783 613089 480048887 27.9821 9.2170 848 719104 609800192 29.1204 9.4652 784 614656 481830 W4 28. 9.2209 849 720801 611960049 29.1376 9.4690 785 , 616225 483736625 28.0179 9.2248 850 722500 614125000 29.1548 9.4727 786 6177% 485587656 28.0357 9.2287 851 724201 616295051 29.1719 9.4764 787 619369 487443403 28.0535 9.2326 852 725904 618470208 291890 9.4801 788 620944 483303*72 28.0713 9.2365 853 727609 620650477 29. 20(52 9.4838 789 622521 491169069 28.0891 9.2404 854 729316 622835864 29.2233 9.4875 790 624100 493039000 28.1069 9.2443 855 731025 625026375 29.2404 9.4912 791 625681 494913671 28.1247 9.2482 856 732736 627222016 29.2575 9.4949 792 627264 496793088 28.1425 9.2521 857 734449 629422793 29.2746 9.4986 793 628819 498677257 28.1603 9.2560 858 736164 631828712 29.2916 9.5023 794 630*36 500566184 28.1780 9.2599 859 737881 633839779 29.3087 9.5060 795 632025 502459875 28.1957 9.2638 860 739600 636056000 29.3258 9.5097 796 633616 504358336 28.2135 9.2677 861 741321 638277381 29.3428 9.5134 797 635209 506261573 28.2312 9.2716 862 743044 640503928 29.3598 9.5171 798 636804 508169592 28.2489 9.2754 863 744769 642735647 29.3769 9.5207 799 638401 510082399 28.2666 9.2793 864 7464% 644972544 29.3939 9.5244 800 640000 512000000 28.2843 9.2832 865 748225 647214625 29.4109 9.5281 801 641601 513922401 28.3019 9.2870 866 749956 6494618% 29.4279 9.5317 802 643204 515849608 28.3196 9.2909 867 751689 651714363 29.4449 9.5354 803 61480;) 517781627 28.3373 9.2948 868 753424 653972032 29.4618 9.5391 804 64H416 519718464 28.3549 9.2986 869 755161 656234909 29.4788 9.5427 805 648025 521660125 28.3725 9.3025 810 756900 658503000 29.4958 9.5464 806 649636 523606616 28.3901 9.3063 87,1 758641 660776311 29.5127 9.5501 807 651249 525557943 28.4077 9.3102 872 760384 663054848 29.5296 9.5537 808 652864 527514112 28.4253 9.3140 873 762129 665338617 29.5466 9.5574 809 654481 529475129J 28.4429 9.3179 874 763876 667627624 29.5635 9.5610 810 656100 531441000' 28.4605 9.3217 875 1 765625 669921875 29.5804 9.5647 811 6')7721 533411731: 28.4781 9.3255 876 767376 672221376 29.5973 9.5683 812 6VM41 535387328' 28.4956 9.3294 877 769129 674526133 29.6142 9.5719 813 f, ; ;0lii9 537367797 28.5132 9.3332 878 770884 676836152 29.6311 9.5756 8H 66>5:->6 :>39353144 : 28.5307 9.3370 879 772641 679151439 29.6479 9.5792 815 664225 541343375 28.5482 9.3408 880 774400 681472000 29.6648 9.5828 816 665856 543338496; 285657 9.3447 881 776161 6&3797841 29.6816 9.5865 817 667489 545: :>5 13 28.5832 9.3485 882 777924 686128968 29.6985 9.5901 818 669124 547343432' 28.6007 9.3523 883 77%89 688465387 29.7153 9.5937 819 670761 ,->i9;ry;jr>9 28.6182 9.3561 884 781456 690807104 29.7321 9.5973 820 672400 551368000 28.6356 9.3599 885 783225 693154125 29.7489 9.6010 821 674041 ' 553387661 28.6531 9.3637 886 7849% 695506456 29.7658 9.6046 822 675684 555412248 28.6705 9.3675 887 786769 697864103 29.7825 9.6082 823 677329 557441767 28.6880 9.3713 888 788544 700227072 29.7993 9.6118 824 678976 , 559476224 28.7054 9.3751 889 790321 702595369 29.8161 9.6154 825 680625 561515625 28.7228 9.3789 890 792100 704%9000 29.8329 9.6190 826 681276 563559976 28.7402 9.3827 891 793881 707347971 29.84% 9.6226 827 683929 5656092H3 28.7576 9.3865 892 795664 709732288 29.8664 9.6262 82H 685584 567663552 28.7750 9.3902 893 797449 712121957 29.8831 9.6298 829 687241 569722789 28.7924 9.3940 894 799236 7145169H4 29.8998 9.6334 830 688900 571787000 28.8097 9.3978 895 801025 716917375 29.9166 9.a-no 831 690561 573856191 28.8271 9.4016 896 802816 719323136 29.9333 9.6406 832 692224 575930368 28.8444 9.4053 897 804609 721734273 29.9500 9.6442 833 693889 578009587 28.8617 : 9.4091 898 806404 724150792 29.9666 .6477 834 695556 580093704 791 9.4129 899 808201 726572699 29.9833 9.6513 835 697225 582182875 28.8964 > 9.4166 900 810000 729000000 30. 9.654* TABLE NO. 75-CONCL. 193 From Trantwine's ' Civil FiiiiiM'r*s Pocket Book." SQUARES, CUBES, AND ROOTS. TABLE of Squares, Cubes, Square Roots, and Cube Roots, of Numbers from 1 to 1OOO (CONTINUED.) No. Square. Cube. Sq. Rt. C. Rt. No. Square. 1 Cube. Sq. Rt. C.Rt. 901 902 811801 i 731432701 30.0167 813604 i 733870808 30.0333 9.6585 9.6620 951 952 904401 906304 860085351 862801408 30.a383 30.8545 9.8339 9.8374 903 815409 73631432" 30.0500 9.6656 953 908209 865523177 30.8707 9.8403 904 817216 738763264 30.0666 9.6692 954 910116 868250664 30.8869 9.8443 905 819025 741217625 30.0832 9.6727 955 912025 870983875 30.9031 9.847T 906 820836 743677416 30.0998 9.6763 956 913936 873722816 30.9192 9.8511 907 822649 7t14-.'Ki: 30.1164 9.6799 957 915849 876467493 30.9354 9.8546 908 824464 7 48613:51 _ 30.1330 9.6834 958 917764 879217912 30.9516 9.8580 909 82M&J 7:>HKH2! 30.1496 9.6870 959 919681 881974079 30.9677 9.8614 910 828100 753571000 30.1662 9.6905 960 921600 884736000 30.9839 9.8648 911 829921 756058031 30.1828 9.6941 961 923521 887503681 31. 9.8683 912 831744 758.550528 30.1993 9.6976 962 925444 890277128 31.0161 9.871T 913 833569 761048497 30.2159 9.7012 963 927369 893056347 31.0322 9.8751 914 8353% 763551944 30.2324 9.7047 964 929296 895841344 31.0483 9.8785 915 837225 ! 766060875 30.2490 9.7082 965 931225 898632125 31.0644 9.8819 916 839056 768575296 30.2655 9.7118 966 933156 901428696 31.0805 9.8854 917 840889 771095213 30.2820 9.7153 967 935089 i 904231063 81.0966 9.8888 91* 4'-'724 773620632 30.2985 9.7188 968 937024 907039232 31.1127 9.8922 919 844561 776151559 30.3150 9.7224 969 938961 909853209 31.1288 9.8956 9'20 846400 778688000 30.3315 9,7259 970 940900 912673000 31.1448 9.8990 921 848241 781229961 30.3480 9.7294 971 942841 915498611 31.1609 9.9024 922 850084 783777448 30.3645 9.7329 972 944784 918330048 31.1769 9.9053 923 851929 786330467 30.3809 9.7364 973 946729 921167317 31.1929 9.9092 924 853776 788889024 30.3974 9.7400 974 948676 924010424 31.2090 9.9126 925 855625 791453125 30.4138 9.7435 975 950625 926859375 31.2250 9.9160 926 857476 794022776 30.4302 9.7470 976 952576 929714176 31.2410 9.9194 927 859329 796597983 30.4467 9.7505 977 954529 932574833 31.2570 9.9227 928 861184 799178752 30.4631 9.7540 978 956484 935441352 31.2730 9.9261 929 863041 801765089 30.4795 9.7575 979 958441 938313739 31.2890 9.9295 930 864900 804357000 30.4959 9.7610 980 960400 941192000 31.3050 9.9329 931 866T61 806954491 30.5123 9.7645 981 962361 944076141 31.3209 9.9363 932 868624 809557568 30.5287 9.7680 982 964324 946966168 31.3369 9.93% 933 870489 812166237 30.5450 9.7715 983 966289 949862087 31.3528 9.9430 934 872356 814780504 30.5614 9.7750 984 968256 952763904 31.3688 9.9464 935 874225 817400375 30.5778 9.7785 985 970225 955671625 31.3847 9.9497 936 876096 820025856 30.5941 9.7819 986 972196 958585256 31.4006 9.9531 937 877969 822656953 30.6105 9.7854 987 974169 961504803 31.4166 9.9565 938 879844 825293672 30.6268 9.7889 988 976144 964430272 31.4325 9.959$ 939 881721 827936019 30.6431 9.7924 989 978121 967361669 31.4484 9.9632 940 883600 830584000 30.6594 9.7959 990 980100 970299000 31.4643 9.9666 941 885481 833237621 30.6757 9.7993 991 982081 973242271 31.4802 9.9699 942 887364 8358968*8 30.6920 9.8028 992 984064 976191488 31.4960 9.9733 943 889249 838561807 30.7083 9.8063 993 986049 979146657 31.5119 9.9766 944 891136 841232384 30.7246 9.8097 994 988036 982107784 31.5278 9.9800 945 893025 843908625 30.7409 9.8132 995 990025 985074875 31.5436 9.9833 946 894916 846590536 30.7571 9.8167 996 992016 988047936 31.5595 99866 947 896809 849278123 30.7734 9.8201 997 994009 991026973 31.5753 9!9900 948 898704 851971392 30.7896 9.8236 998 996004 994011992 31.5911 9.9933 949 900601 854670349 30.8058 9.8270 999 998001 997002999 31.6070 9.996T 950 902500 857375000 30.8221 9.8305 1000 1000000 1000000000 31.6228 10, To find the square or cube of any whole number ending 1 Mil li ciphers. First, omit all the final ciphers. Take from the table the square or cube (as the case may be) of the rest of the number. To this square add twice as many ciphers as there were final ciphers in the original number. To the cube add three times as many as in the original number. Thus, for 905003; 9052 = 819025. Add twice 2 ciphers, obtaining 8190250000. For 905003, 9053 = 741217625. Add i times 2 ciphers, obtaining 741217625000000. 194 TABLE NO. 76. From Tra lit wine's "Civil Engineer's Poeket Book. 9 SQUARE AND CUBE ROOTS. Square Roots and Cube Roots of Numbers from 1OOO to 1OOOO. No errors. Num. Sq. Rt. Cu. Rt Num. Sq. Rt. Cu. Rt. Num. Sq. Rt. Cu. Rt. Num. Sq. Rt. Cu. Rt. 1005 31.70 10.02 1405 37.48 11.20 1805 42.49 12.18 2205 46.96 13.02 1010 31.78 10.03 1410 37.55 11.21 1810 42.54 12.19 2210 47.01 13.03 1015 31.86 10.05 1415 37.62 11.23 1815 42.60 12.20 2215 47.06 13.04 1020 31.94 10.07 1420 37.68 11.24 1820 2.66 12.21 2220 47.12 13.05 1025 32.02 10.08 1425 37.75 11.25 1825 2.72 12.22 2225 47.17 13.05 1030 32.09 10.10 1430 37.82 11.27 1830 2.78 12.23 2230 47.22 13.06 1035 32.17 10.12 1435 37.88 11.28 1835 2.84 12.24 2235 47.28 13.07 1040 32.25 10.13 1440 37.95 11.29 1840 2.90 12.25 2240 47.33 13.08 1045 32.33 10.15 1445 38.01 11.31 1845 2.95 12.26 2245 47.38 13.09 1050 32.40 10.16 1450 38.08 11.32 1850 3.01 2.28 2250 47.43 13.10 1055 32.48 10.18 1455 38.14 11.33 1855 43.07 2.29 2255 47.49 13.11 1060 32.56 10.20 1460 38.21 11.34 1860 3.13 2.30 2260 47.54 13.12 1065 32.63 10.21 1465 38.28 11.36 1865 43.19 2.31 2265 47.59 13.13 1070 32.71 10.23 1470 38.34 11.37 1870 43.24 2.32 2270 47.64 13.14 1075 32.79 10.24 1475 38.41 11.38 1875 43.30 2.33 2275 47.70 13.15 1080 32.86 10.26 1480 38.47 11.40 1880 43.36 2.34 2280 47.75 13.16 1085 32.94 10.28 1485 38.54 11.41 1885 43.42 2.35 2285 47.80 13.17 1090 33.02 10.29 1490 38.60 1.42 1890 43.47 2.36 2290 47.85 13.18 1095 33.09 10.31 1495 38.67 1.43 1895 43.53 2.37 2295 47.91 13.19 1100 33.17 10.32 1500 38.73 1.45 1900 43.59 2.39 2300 47.% 13.20 1105 33.24 10.34 1505 38.79 1.46 1905 43.65 2.40 2305 48.01 13.21 1110 33.32 10.35 1510 38.86 1.47 1910 43.70 2.41 2310 48.06 13.22 1115 33.39 10.37 1515 38.92 1.49 1915 43.76 2.42 2315 48.11 13.23 1120 33.47 10.38 1520 38.99 1.50 1920 43.82 2.43 2320 48.17 13.24 1125 33.54 10.40 1525 39.05 1.51 1925 43.87 2.44 2325 48.22 13.25 1130 33.62 10.42 1530 39.12 1.52 1930 43.93 2.45 2330 48.27 13.26 1135 33.69 10.43 1535 39.18 1.54 1935 43.99 2.46 2335 48.32 13.27 1140 33.76 10.45 1540 39.24 1940 44.05 2.47 2340 48-37 13.28 1145 33.84 10.46 1545 39.31 l!56 1945 44.10 2.48 2345 48.43 13.29 1150 33.91 10.48 1550 39.37 1.57 1950 44.16 2.49 2350 48.48 13.80 1155 33.99 10.49 1555 39.43 1.59 1955 44.22 2.50 2355 48.53 13.30 1160 34.06 10.51 1560 39.50 1.60 1960 44.27 2.51 2360 48.58 13.31 1165 34.13 10.52 1565 39.56 1.61 J965 44.33 2.53 2365 48.63 13.32 1170 34.21 10.54 1570 39.62 1.62 1970 44.38 2.54 2370 48.68 13.33 1175 34.28 10.55 1575 39.69 1.63 1975 44.44 2.55 2375 48.73 13.34 1180 34.35 10.57 1580 39.75 1.65 1980 44.50 2.56 2380 48.79 13.35 1185 34.42 10.58 1585 39.81 1.66 1985 44.55 2.57 2385 48.84 13.36 1190 34.50 10.60 1590 39.87 1.67 1990 44.61 2.58 2390 48.89 13.37 1195 34.57 10.61 1595 39.94 1.68 1995 44.67 2.59 2395 48.94 13.38 1200 34.64 10.63 1600 40.00 1.70 2000 44.72 2.60 2400 48.99 13.39 1205 34.71 10.64 1605 40.06 1.71 2005 44.78 2.61 2405 49.04 13.40 1210 34.79 10.66 1610 40.12 1.72 2010 44.83 2.62 2410 49.09 13.41 1215 34.86 10.67 1615 40.19 1.73 2015 44.89 2.63 2415 49.14 13.42 1220 84.93 10.69 1620 40.25 1.74 2020 44.94 2.64 2420 49.19 13.43 1225 35.00 10.70 1625 40.31 1.76 2025 45.00 2.65 2425 49.24 13.43 1230 35.07 10.71 1630 40.37 1.77 2030 . 45.06 2.66 2430 49.30 13.44 1235 35.14 10.73 1635 40.44 1.78 2035 45.11 2; 67 2435 49.35 13.45 1240 35.21 10.74 1640 40.50 1.79 2040 45.17 2.68 2440 49.40 13.46 1245 35.28 10.76 1645 40.56 1.80 2045 45.22 2.69 2445 49.45 13.47 1250 35.36 10.77 1650 40.62 1.82 2050 45.28 2.70 2450 49.50 13.48 1255 35.43 10.79 1655 4d.68 1.83 2055 45.33 2.71 2460 49.60 13.50 1260 35.50 10.80 1660 40.74 1.84 2060 45.39 2.72 2470 49.70 13.52 1265 35.57 10.82 1665 40.80 1.85 2065 45.44 12.73 2480 49.80 13.54 1270 35.64 10.83 1670 40.87 1.8o 2070 45.50 12.74 2490 49.90 13.55 1275 35.71 10.84 1675 40.93 1.88 2075 45.55 12.75 2500 50.00 13.57 1280 35.78 10.86 1680 40.99 1.89 2080 4561 12.77 2510 50.10 13.59 1285 35.85 10.87 1685 41.05 1.90 2085 45.66 12.78 2520 50.20 13.61 1290 35.92 10.89 1690 41.11 1.91 2090 45.72 12.79 2530 50.30 13.63 1295 35.99 10.90 1695 41.17 1.92 2095 45.77 12.80 2540 50.40 13.64 1300 36.06 10.91 1700 41.23 11.93 2100 45.83 12.81 2550 5050 13.66 1305 36.12 10.93 1705 41.29 11.95 2105 45.88 12.82 2560 50.60 13.68 1310 36.19 10.94 1710 41.35 11.96 2110 45.93 12.83 2570 50.70 13.70 1315 86.26 10.96 1715 41.41 11.97 2115 45.99 12.84 2580 50.79 13.72 1320 86.33 10.97 1720 41.47 11.98 2120 46.04 12.85 2590 50.89 13.73 1325 36.40 10.98 1725 41.53 11.99 2125 46.10 2.86 2600 50.99 13.75 1330 36.47 11.00 1730 41.59 12.00 2130 46.15 12.87 2610 51.09 13.7T 1335 36.54 11.01 1735 41.65 12.02 2135 46.21 12.88 2620 51.19 13.79 1340 36.61 11.02 1740 41.71 12.03 2140 46.26 2.89 2630 51.28 13.80 1345 36.67 11.04 1745 41.77 12.04 2145 46.31 2.90 2640 51.38 13.82 1350 36.74 11.05 1750 41.83 12.05 2150 46.37 2.91 2650 51.48 13.84 1355 36.81 11.07 1755 41.89 12.06 2155 46.42 2.92 2660 51.58 13.86 1360 36.88 11.08 1760 41.95 12.07 2160 46.48 2.93 2670 51.67 13.8T 1365 36.95 11.09 1765 42.01 12.09 2 65 46.53 12.94 2680 51.77 13.89 1370 37.01 11.11 1770 42.07 12.10 2 70 46.58 12.95 2690 51.87 13.91 1375 37.08 11.12 1775 42.13 12.11 2 75 46.64 12.96 2700 51.96 13.92 1380 37.15 11.18 1780 42.19 12.12 2 80 46.69 12.97 2710 52.06 13.94 1385 37.22 11.15 1785 42.25 12.13 2 85 46.74 12.98 2720 52.15 13.96 1390 37.28 11.16 1790 42.31 12.14 2 90 46.80 12.99 2730 52.25 13.98 1395 37.35 11.17 1795 42.37 12.15 2195 46.85 13.00 2740 52.35 13.99 1400 37.42 11.19 1800 42.43 12.16 2200 46.80 13.01 2750 52.44 14.01 TABLE NO. 76 CON. 195 From Trautwine's "Civil Engineer's Pocket Book." SQUARE AND CUBE ROOTS. Kquare Roots and Cube Roots of Numbers from 1OOO tolOOOO (CONTINUED.) Num. Sq. Rt. Cu. Rt Num. Sq. Rt. Cu. Rt Num. Sq. Rt. Cu.Rt Num. Sq. Rt. Cu. Rt. 27(50 52.54 14.03 3550 59.58 15.25 4340 65.88 16.31 5130 71.62 17.25 2770 52.63 14.04 3560 59.67 15.27 4350 65.95 16.32 5140 71.69 17.26 2780 52.73 14.06 3570 59.75 15.28 4360 66.03 16.34 5150 71.76 17.27 2790 52.82 14.08 3580 59.83 15.30 4370 66.11 16.35 5160 71.83 17.28 2800 52.92 14.09 3590 59.92 15.31 4380 66.18 16.36 5170 71.90 17.29 2810 53.01 14.11 3600 60.00 15.33 4390 66.26 16.37 5180 71.97 17.30 2820 53.10 14.13 3610 60.08 15.34 4400 66.33 16.39 5190 72.04 17.31 2830 53.20 14.14 3620 60.17 15.35 4410 66.41 16.40 5200 72.11 17.32 2S40 53.29 14.16 3630 60.25 15.37 4420 66.48 16.41 5210 72.18 17.34 2850 53.39 14.18 3640 60.33 15.38 4430 66.56 1642 5220 72.25 7.35 2860 53.48 14.19 3650 60.42 15.40 4440 66.63 16.44 5230 72.32 7.36 2870 53.57 14.21 3660 60.50 15.41 4450 66.71 16.45 5240 72.39 7.37 2880 53.67 14.23 3670 60.58 15.42 4460 66.78 16.4 5250 72.46 7.38 2890 53.76 14.24 3680 60.66 15.44 4470 6686 16.47 5260 72.53 7.39 2900 53.85 14.26 3690 60.75 15.45 4480 66.93 16.49 5270 72.59 7.40 2910 53.94 14.28 3700 CO. 83 15.47 4490 67.01 1650 5280 72.66 7.41 2920 54.04 14.29 3710 60.91 15.48 4500 67.08 1651 5290 72.73 17.42 2930 54.13 14.31 3720 60.99 15.49 4510 67.16 16.52 5300 72.80 7.44 2940 54.22 14.33 3730 61.07 15.51 4520 67.23 16.53 5310 72.87 7.45 2950 54.31 14.34 3740 61.16 15.52 4530 67-31 16.55 5320 72.94 7.46 2960 54.41 14.36 3750 61.24 15.54 4540 67.38 16.56 5330 73.01 17.47 2970 54.50 14.37 3760 61.32 15.55 4550 67.45 16.57 5340 73.08 17.48 2980 54.59 14.39 3770 61.40 15.56 4560 67.53 16.58 5350 73.14 17.49 2990 54.68 14.41 3780 61.48 15.58 4570 67.60 16.59 5360 73.21 17.50 3000 54.77 14.42 3790 61.56 15.59 4580 67.68 16.61 5370 73.28 17.51 3010 54.86 14.44 3800 6164 15. (50 4590 67.75 16.62 5380 73.35 17.52 3020 54.95 14.45 3810 61.73 15.62 4600 67.82 16.63 5390 73.42 17.53 3030 55.05 14.47 3820 61.81 15.63 4610 67.1-0 1.>4 5400 73.48 17.54 3040 55.14 14.49 3830 61.89 15.65 46 i :o 67.97 16.C6 5410 73.55 7.55 3050 55.23 14.50 3840 61.97 15.66 4630 68.04 16.67 5420 73.62 7.57 3060 55. 32 14.52 3850 62.05 15.67 4640 68.12 16.68 5430 73.69 7.58 3070 55.41 14.53 3860 62.13 15.69 4650 68.19 18.C9 5440 73.76 7.59 3080 55.50 14.55 3870 62.21 15.70 4660 68.26 16.70 5450 73.82 7.60 3090 55.59 14.57 3880 62.29 15.71 4670 68.34 16.71 5460 73.89 7.61 3100 55.68 14.58 3890 62.37 15.73 4680 68.41 16.73 5470 73.96 7.62 3110 55.77 14.60 3900 62.45 15.74 4690 68.48 16.74 5480 74.03 7.63 3120 55.86 14.61 3910 62.53 15.75 4700 68 56 16.75 5490 74.09 7.64 3130 55.95 14.63 3920 62.61 15.77 4710 68.63 16.76 5500 74.16 17.65 3140 56.04 14.64 3930 62.69 15.78 4720 68.70 16.77 5510 74.23 17.66 3150 56.12 14.66 3940 62.77 15.79 4730 68.TT 16.79 5520 74.30 17.67 3160 56.21 14.67 3950 62.85 15.81 4740 68.85 16.80 .5530 74.36 17.68 3170 56.30 14.69 3960 62.93 15.82 4750 68.92 16.81 5540 74.43 17.69 3180 56.39 14.71 3970 63.01 15.83 4760 68.99 16.82 5550 74.50 17.71 3190 56.48 14.72 3980 63.09 15.85 4770 69.07 16.83 5560 74.57 17.72 3200 56.57 14.74 3990 63.17 15.86 4780 69.14 16.85 5570 74.63 17.73 3210 56,66 14.75 4000 63.25 15.87 4790 6921 16.86 5580 74.70 17.74 3220 56.75 14.77 4010 63.32 15.89 4800 69.28 16.87 5590 74.77 17.75 3230 56.83 14.78 4020 63.40 15.90 4810 69.35 16.88 5600 74.83 17.76 3240 56.92 14.80 4030 63.48 15.91 4820 69.43 1689 5610 74.90 17.77 3250 57.01 14.81 4040 63.56 15.93 4830 69.50 16.90 5620 74.97 17.78 3260 57.10 14.83 4050 63.64 15.94 4840 69.57 16.92 5630 75.03 17.79 3270 57.18 14.4 4060 63.72 15.95 4850 69.64 16.93 5640 75.10 17.80 3280 57.27 14.86 4070 63.80 15.97 4860 69.71 16.94 5650 75.17 17.81 3290 57.36 14.87 4080 63.87 15.98 4870 69.79 16.95 5660 75.23 17.82 3300 57.45 14.89 4090 63.95 15.99 4880 69.86 16.96 5670 75.30 7.83 3310 57.53 14.90 4100 64.03 16.01 4890 69.93 16.97 5680 75.37 7.84 3320 57.62 14.92 4110 64.11 16.02 4900 70.00 16.98 5690 75.43 7.85 3330 57.71 14.93 4120 64.19 16.03 4910 70.07 17.00 5700 75.50 7.86 3340 57.79 14.95 4130 64.27 16.04 4920 70.14 17.01 5710 75.56 7.87 3350 57.88 14.96 4140 64.34 16.06 4930 70.21 17.02 5720 75.63 7.88 3360 57.97 14.98 4150 64.42 16.07 4940 70.29 17.03 5730 75.70 7.89 3370 58.05 14.99 4160 64.50 16.08 4950 70.36 17.04 5740 75.76 17.90 3380 58.14 15,01 4170 64.58 16.10 4960 70.43 17.05 5750 75.83 17.92 3390 58.22 15.02 4180 64.65 16.11 4970 70.50 17.07 5760 75.89 17.93 3400 58.31 15.04 4190 64.73 16.12 4980 70.57 17.08 5770 75.96 17.94 3410 58.40 15.05 4200 64.81 16.13 4990 70.64 17.09 5780 76.03 17.95 3420 58.48 15.07 4210 64.88 16.15 5000 70.71 17.10 5790 76.09 17.96 3430 58.57 15.08 4220 64.96 16.16 5010 70.78 17.11 5800 76.16 17.97 3440 58.65 15.10 4230 65.04 16.17 5020 70.85 17.12 5810 76.22 17.98 3450 58.74 15.11 4240 65.12 16.19 5030 70.92 17.13 5820 76.29 17.99 3460 58.82 15.12 4250 65.19 16,20 5040 70.99 17.15 5830 76.35 18.00 3470 58.91 15.14 4260 65.27 16.21 5050 71.06 17.16 5840 76.42 18.01 3480 58.99 15.15 4270 65.35 16.22 5060 71.13 17.17 5850 76.49 18.02 3490 59.08 15.17 4280 65.42 16.24 5070 71.20 17.18 5860 76.55 18.03 3500 59.16 15.18 4290 65.50 16.25 5080 71.27 17.19 5870 76.62 18.04 3510 59.25 15.20 4300 6557 16.26 5090 71.34 17.20 5880 76.68 18.05 3520 59.33 15.21 4310 65.65 16.27 5100 71.41 17.21 5890 76.75 18.06 3530 59.41 15.23 4320 65.73 16.29 5110 71.48 17.22 5900 76.81 18.07 8640 59.50 15.24 4330 65.80 16.30 1 5120 71.55 17.24 5910 76.88 18.08 196 TABLE NO. 76 COX. From Train wine's ' Civil Engineer's Pocket Book.* SQUARE AND CUBE ROOTS. Bqiiare Roots and Cube Roots of Numbers from 1OOO to 1OOOO (CONTINUED.) Num. Sq. Rt. Cu. Rt. Num. Sq. Rt. Cu.Rt. Num. Sq. Rt. Cu. Rt. Num. |Sq. Rt. Cu.Rt 5920 76.94 18.09 6710 81.91 18.86 7500 86.60 19.57 8290 91.05 20.24 593C 77.01 18.10 6720 81.98 18.87 7510 86.66 19.58 8300 91.10 20.25 5940 77.07 18.11 6730 82.04 18.88 7520 86.72 19.59 8310 91.16 20.26 5950 77.14 18.12 6740 82.10 18.89 7530 86.78 19.60 8320 91.21 20.26 5960 77.20 18.13 6750 82.16 18.90 7540 86.83 19.61 8330 91.27 20.27 597G 77.27 18.14 6760 82.22 18.91 7550 86.89 19.62 8340 91.32 20.28 5980 77.33 18.15 6770 82.28 18.92 7560 86.95 19.63 8350 91.38 20.29 5990 77.40 18.16 6780 82.34 18.93 7570 87.01 19.64 8360 91.43 20.30 6000 77.46 18.17 6790 82.40 18.94 7580 87.06 19.64 8370 91.49 20.30 6010 77.52 18.18 6800 82.46 18.95 7590 87.12 19.65 8380 91.54 20.31 6020 77.59 18.19 6810 82.52 18.95 7600 87.18 19.66 8390 91.60 20.32 6030 77.65 18.20 6820 82.58 18.96 7610 87.24 19.67 8400 91.65 20.33 6040 77.72 18.21 6830 82.64 18.97 7620 87.29 19.68 8410 91.71 20.34 6050 77.78 18.22 6840 82.70 18.98 7630 87.35 19.69 8420 91.76 20.34 6060 77.85 18.23 6850 82.76 18.99 7640 87.41 19.70 8430 91.82 20.35 6070 77.91 18.24 6860 82.83 19.00 7650 87.46 19.70 8440 91.87 20.36 6080 77.97 8.25 6870 82.89 19.01 7660 87.52 19.71 8450 91.92 20.37 6090 78.04. 8.26 6880 82.95 19.02 7670 87.58 19.72 8460 91.98 20.38 6100 78.10 8.27 6890 83.01 19.03 7680 87.64 19.73 8470 92.03 20.38 6110 i 78.17 8.28 6900 83.07 19.04 7690 87.69 19.74 8480 92.09 20.39 6120 73.23 8.29 6910 83.13 19.05 7700 87.75 19.75 8490 92.14 20.40 6130 78.29 8.30 6920 83.19 19.06 7710 87.81 19.76 8500 92.20 20.41 6140 78.36 8.31 6930 83.25 19.07 7720 87.86 19.76 8510 92.25 20.42 6150 78.42 8.32 6940 83.31 19.07 7730 87.92 19.77 8520 92.30 20.42 160 78.49 8.33 6950 83.37 19.08 7740 87.98 19.78 8530 92.36 i 20.43 6170 78.55 8.34 6960 83.43 19.09 7750 88.03 19.79 8540 92.41 i 20.44 6180 78.61 8.35 6970 83.49 19.10 7760 88.09 9.80 8550 92.47 20.45 6190 78.68 8.36 6980 83.55 19.11 7770 88.15 9.81 8560 92.52 20.46 6200 18.74 8.37 6990 83.61 19.12 7780 88.20 9.81 8570 92.57 20.46 6210 78.80 8.38 7000 83.67 19.13 7790 88.26 9.82 8580 92.63 20.47 6220 78.87 8.39 7010 83.73 19.14 7800 88.32 9.83 8590 92.68 20.48 6230 78.93 8.40 7020 83.79 19.15 7810 88.37 9.84 8600 92.74 20.49 6240 78.99 8.41 7030 83.85 19.16 7820 88.43 9.85 8610 92.79 20.50 6250 79.06 8.42 7040 83.90 19.17 7830 88.49 9.86 8620 92.84 20.50 6260 79.12 8.43 7050 83.o 19.17 7840 88.54 9.87 8630 92.90 20.51 6270 79.18 8.44 7060 84.02 19.18 7850 88.60 9.87 8640 92.95 20,52 6280 79.25 8.45 7070 84.08 19.19 7860 88.66 9.88 8650 93.01 20.53 6290 7931 8.46 7080 84.14 19.20 7870 88.71 9.89 8660 93.06 20.54 6300 79.37 8.47 7090 84.20 19.21 7880 88.77 9.90 8670 93.11 20.54 6310 79.44 8.48 7100 84.26 19.22 7890 88.83 9.91 8680 93.17 20.55 6320 79.50 8.49 7110 84.32 19.23 7900 88.88 9.92 8690 93.22 20.56 6330 79.56 8.50 7120 84.38 19.24 7910 88.94 9.92 8700 9:5.27 20.57 6340 79.62 8.51 7130 84.44 19.25 7920 88.99 9.93 8710 93.33 20.57 6350 79.69 8.52 7140 84.50 19.26 7930 89.05 9.94 8 20 93.38 20.58 6360 79.75 8.53 7150 84.56 19.26 7940 89.11 9.95 8 30 93.43 20.59 6370 79.81 8.54 7160 84.62 19.27 7950 89.16 9.96 8 40 93.49 20.60 6380 79.87 8.55 7170 84.68 ! 19.28 7960 89.22 9.97 8 50 93.54 20.61 6390 79.94 sise 7180 84.73 : 19.29 7970 89.27 9.97 8 60 93.59 20.61 6400 80.00 8.57 7190 84.79 19.30 7980 89.33 9.98 8 70 93.65 20.6.2 6410 80.06 8.58 7200 84.85 19.31 7990 89.39 9.99 8 80 93.70 20.63 6420 80.12 8.59 7210 84.91 19.32 8000 89.44 20.00 8 90 93.75 '20.64 6430 80.19 8.60 7220 84.97 19.33 8010 89.50 20.01 8800 93.81 20.65 6440 80.25 8.60 7230 85.03 19.34 8020 89.55 20.02 8810 93.86 20.65 6450 80.31 8.61 7240 85.09 19.35 8030 89.61 20.02 8820 93.91 20.66 6460 80.37 8.62 7250 85.15 19.35 8040 89.67 20.03 8830 93. 97 20.t>7 6470 80.44 8.63 7260 85.21 ! 19.36 8050 89.72 20.04 8840 94.02 20.68 6480 ! 80.50 8.64 7270 85.26 j 19.37 8060 89.78 20.05 8850 94.07 20.68 6490 80.56 8.65 7280 85.32 19.38 8070 89.83 20.06 8860 94.13 20. 6 6500 80.62 8.66 7290 85.38 19.39 8080 89.89 20.07 8870 94.18 20.70 6510 80.68 8.67 7300 85.44 19.40 8090 89.94 20.07 8880 94.23 20.71 6520 80.75 8.68 7310 85.50 19.41 8100 90.00 20.08 8890 94.29 20.72 6530 80.81 8.69 7320 85.56 19.42 8110 90.06 20.09 8900 94.34 20.72 6540 80.87 8.70 7330 85.62 19.43 8120 90.11 20. 8910 94.39 20.73 6550 80.93 18.71 7340 85.67 19.43 8130 90.17 20. 1 8920 94.45 20.74 6560 80.99 18.72 7350 85.73 19.44 8140 90.22 20. 2 8930 94.50 20.75 6570 81.06 18.73 7360 85.79 19.45 8150 90.28 20. 2 8940 94.55 20.75 6580 , 81.12 18.74 7370 85.85 19.46 8160 90.33 20. 3 8950 94.60 20.76 6590 81.18 18.75 7380 85.91 19.47 8170 90.39 20. 4 8960 94.66 20.71 6606 81.24 18.76 7390 85.97 19.48 8180 90.44 20. 5 8970 94.71 20.78 6610 81.30 18.77 7400 86.02 19.49 8190 90.50 20. 6 8980 94.76 20.79 6620 81.36 18.78 7410 86.08 19.50 8200 90.55 1 20. 7 8990 94.82 20.79 6630 81.42 18.79 7420 86.14 19.50 8210 90.61 I 20. 7 9000 94.87 20. SO 6640 HI. 49 18.80 7430 86.20 19.51 8220 90.66 j 20. 8 9010 94.92 20.W 6650 81. 55 18.81 7440 86.26 19.52 8230 90. T2 \ 20. 9 9020 9.97 20.82 6660 81.61 18.81 7450 ! 86.31 19.53 8240 90.77 ; 20. 9030 95.03 20.82 6670 81.67 18.82 7460 i 86.37 19.54 8250 90.83 20. 1 9040 95.08 i 20.83 6680 , 81.73 18.83 7470 Mi. 43 19.55 8260 90. MS 20. 1 9050 95.13 20.84 6690 81.79 1K.K4 74X0 86 49 1956 8270 90.94 20. 2 9060 95.18 20.8& 6700 81.85 18.80 7490 86.54 19.57 6280 90.99 20.23 9070 95.24 j 20.B& TABLE NO. 72 CON. 1U7 From Trautwine's "Civil Kn^iiieer'N Pocket Book." SQUARE AND Cl'BE ROOTS, r Square Roots and Cube Roots ol > umbers fi (CONTINUED.) Num. Sq. Rt. Cu. Rt. Xum. Sq. Rt. Cu. Rt. Num. Sq. Rt. Cu. Rt. Num. Sq. Rt. <'u. Rt. 90H> 95.29 20.86 9320 96.54 21.04 9550 97.72 21.22 97M) 98.89 21.39 9090 95.34 20.87 9330 96.59 2 1 .0:1 9560 97.78 , 21.22 9790 9M.94 21.39 9100 95.39 20.88 9340 96.64 l.Oti 9.-.7U 97.83 21.23 9800 9K.99 21.40 9iio 95.45 20. h9 9350 96.70 1.07 9580 ;7 >-* 21.24 9810 99.115 21.41 9120 95.50 20.89 9360 96.75 1.07 9590 97.93 21.25 920 99.10 I 21.41 in 30 95.55 20.90 9370 W.sO l.i is 9600 97.98 21.2;> 9*30 99.15 21.42 9140 96.60 20.91 9380 9t;.>5 .09 9610 9K03 ' 21.26 9840 99.20 21.43 9150 95.66 20.92 9390 96.90 .10 9620 98.08 21.27 9850 99.25 21.44 9160 95.71 20.92 9400 96.95 | .10 9630 98.13 21.> 9860 99.30 21.44 9170 95.76 20.93 9410 97.01 .11 9640 98 18 i 21.28 9870 99.35 21.45 180 95.81 20.94 9420 97.06 .It 9650 98.23 I 21.29 9880 99.40 21.46 MHO 95.86 20.95 9430 97.11 .1.1 9660 96.29 21.30 9890 99.45 21.47 .9200 95.92 20.95 9440 97.16 M 9670 9h.:-!4 21.30 9900 99.50 21.47 9210 95.97 20.96 9450 97.21 .14 9K*0 98.39 21.31 9910 99.55 21.48 9220 96.02 20.97 9460 97.26 .18 9690 98.44 21.32 9920 99.60 21.49 9230 96.07 20.98 9470 97. 31 2 .if, 9700 9h.49 21.33 9930 99.65 21.49 9240 96.12 20.98 9480 9... a 2 .16 9710 9K54 21.33 9940 99.70 21.50 9250 96.18 20.99 9490 97.42 2 .17 9720 98.59 21.34 9950 99.75 21.51 9260 96.23 21.00 9500 97.47 2 .IS 9730 98.64 21.35 9960 99.80 21.52 9270 96.28 21.01 9510 97.52 2 .18 9740 98.69 21.36 9970 99.85 21.52 9280 96.33 21.01 9520 97.57 2 .19 9750 9S.74 21.36 9980 99.90 i 21.53 9290 96.38 21.02 9530 97.62 2 .20 9760 98.79 21.37 9990 99.95 21 .5i 9300 96.44 21.03 9540 97.67 ; 2 /.'I 9770 98.84 21.38 10006 100.00 21.54 9310 96.49 21.04 I To liiid Square or Cube Roots of large 11 umbers not con- tained in the column of numbers of the table. Such roots may sometimes be taken at once from the table, by merely regarding the columns of powers as being columns of numbers; and those of numbers as'being those of roots. Thus, if the sq rt of 25281 is reqd, first fled that number in the column of squares; and opposite to it, in the column of numbers, is its sq rt 159. For the cube rt of 857375, find that number in the column of cubes ; and opposite to it, in the col of numbers, is its cube rt 95. When the exact number is not con- tained in the column of squares, or cubes, as the case may be, we may use instead the number nearest to it, if no great accuracy is reqd. But when a considerable degree of accuracy is necessary, the following very correct methods may be used. For the square root. This rule applies both to whole numbers, and to those which are partly (not wholly) decimal. First, im the foregoing manner, take out the tabular number, which is nearest to the given one ; and also its tabular sq rt. Mult this tabular number by 3 ; to the prod add the given number. Call the sum A. Then mult the given number by 3 ; to the prod add the tabular number. Call the sum B. Then A : B : : Tabular root : Reqd root. Ex. Let the given pumber be 946.53. Here we find the nearest tabular number to be 947 ; and its tabular sq rt 30.7734. Hence, 947 = tab num 1 f 946.53 =: given num. 3 3 2841 946.53 = given num. and -i 2839.59 947 = tab num. Tab root. J0.7734 Reqd root. 30.7657 +. Then 3787*.53 The root as found by actual mathematical process is also 30.7657 -}-. For the cube root. This rule applies both to whole numbers, and to those whJch are partly decimal. First take out tTie tabular number which is nearest to the given one; and also its tabular cube rt. Mult this tabular number by 2 ; and to the prod add the given number. Call the sum A. Then mult the given number by 2; and to the prod add the tabular number. Call the sum B. Then A : B : : Tabular root : Reqd root. Ex. Let the given number be 7368. Here we fid thejjearest tabular number (in the column of tube*) to be 6859 ; and its tabular cube rt 19. Hence, 6859 = tab num. ^ r 73^ - gi v , n DHm . ! I f 13718 ', and \ 14736 7368 = given num. 6859 = tab num. 21086- A. [ 21595 -B. A. B. Tab Root. Reqd Rt. Then, as 21086 : 21595 : : 19 : 19.45*5 The root as found by correct mathematical process is 19.4588. The engineer rarelv rpniiires even 198 From Trautwine's Civil Engineer's Pocket Book. SQUARE AND CUBE ROOTS. this degree of accuracy ; for his purposes, therefore, this process is greatly preferable to the ordinary laborious one. To find the square root of a number which is wholly decimal. Very simple, and correct to the third numeral flgure inclusive. If the number does not contain at least five figures, counting from the first numeral, and including it, add one or more ciphers to make five. If, after that, the whole numher is not separable into twos, add another cipher to make it so. Then beginning at the first numeral figure, and including it, assume the number to be a whole one. In the table find the number nearest to this assumed one ; take out its tabular sq rt ; move the deci- mal poiut of this tabular root to the left, half as many places as the finally modified decimal number has figures. Ex. What is the aq rt of the decimal .002? Here, in order to have at least five decimal figures, counting from the first numeral (2). and including it, add ciphers thus, .00.20,00.0. But, as it is not now separable into twos, add another cipher, thus, .00,20,00.00. Then beginning at the first numeral (t), assume this decimal to be the whole number 200000. The nearest to this in the table is 199809; and the sq rt of this is 447. Now. the decimal number as finally modified, namely, .00.20,00,00, has eight figures ; one-half of which is 4; therefore, move the decimal point of the root 447, four places to the left; making it .0447. This is the reqd sq rt of .002, correct to the third numeral 7 included. To find the cube root of a number which is wholly decimal. Very simple, and correct to the third numeral inclusive. If the number does not contain at least five figures, counting from the first numeral, and including It, add one or more ciphers to make five. If, after that, the number is not separable into threes, add one or more ciphers to make it so. Then beginning at the first numeral, and including it, assume the number to be a whole one. In the table find the number nearest to this assumed one, and take out its tabular cub rt. Move the decimal point of this rt to the left, one-third as many places as the finally modified decimal number has figures. Ex. What is the cube rt of the decimal .002? Here, in order to have at least five figures, counting from the first numeral (2), and including it, add ciphers thus, .002,000,0. But as it is not now separ- able into threes, add two more ciphers to make it so ; thus, .002,000,000. Then beginning with the first numeral (2), assume the decimal to be the whole number 2000000. The nearest cube to this in the table in the column of cubes, is 2000376 ; and its tabular cube rt as found in the col of numbers, is 126. Now, the decimal number as finally modified, namely, .002 000 000, has nine figures ; one-third of which is 3; therefore, move the decimal point of the root 126, three places to the left, making it .126. Thia is the reqd cube rt of the decimal .002, correct to the third numeral 6 included. To flnd roots by logarithm* For tables of sq. rts. of 5th powers see table 69, page 166. To find the sq. or cu. rt. of a number consisting of intigers and decimals. Multiply the difference between the root of the intiger part of the given number, and the root of the next higher number, by the decimal part of the given number, and add the product to the root of the given intiger. The sum is the root required. Ex. Required the sq. rt. of 20.321 square root of 21 = 4.5825 " " 20 = 4.4721 Difference = .1104 .1104 X .321 = .354384, add to rt. of 20, 4.4721, and get 4.5075384=rt. required. Ex. Required the cu. rt. of 16.42 cube root of 17 = 2.5712 " " 16 = 2.5198 Difference = .0514 .0514 X .42 = .021588, add to rt. of 16, 2.5198, and get 2.541388 = rt. required. To find the sq. or cu. rt. of a higher number than is contain- ed in the table, when the number is divisib e by 4 or 8 with- out leaving a remainder. RULE. Divide the number by 4 or 8 respectively, as the sq. or cu. rt. is re- quired ; take the rt. of the quotient in the table, multiply it by 2, and the product will be the root required. Ex. What are the square and cube roots of 2400? 2400 -h 4 = 600 and 2400 -*- 8 = 300. Then thesq. rt. of 600, per table, = 24.4949, which, being X 2 = 48.9898 = sq. rt. required. Then the cu. rt. of 300, per table, = 6.6943, which, being X 2 = 13.3886 = cu. rt. required. To find the 4th root of any number. Take the square root of its square root. To find the 6th root of any number. Take the cube root of its square root. To flnd any root or any power by logarithms see pages 200 and 202. TABLE NO. 77. Logarithms of Numbers, from to 1OOO.* 199 Vo. O 1 2 3 4 5 6 7 8 9 Prop. 00000 30103 4771260206 6989" 77815 84510 90309 95424 10 00000 00432 00860 0128301703 02118 02530 02938 03342 03742 415 11 04139 04532 04921 05307 05690 06069 06445 06818 07188 07554 379 12 07918 08278 08636 0899009342 09691 10037 10380 10721 11059 349 13 11394 11727 12057 12385 12710 13033 13353 13672 13987 14301) 323 14 14613 14921 15228 15533J15836 16136 1C435 16731 1702f 173181 300 15 17609 17897 18184 18469 18752 19033 19312 19590 19sif> 20139) 281 16 20412 20682 20951 21218 21484 21748 2201U 22271 22530 22788 264 17 23045 23299 23552 23804 24054 24303 24551 24797 25042 25285 249 18 25527 25767 ! 26007 26245 26481 26717 2(5951 27184 27415 27646 236 19 27875 28103 j 28330 28555128780 29003 29225 29446 29666 29885 223 80 30103 30319 30535 30749:30963 31175 31386 31597 31806 32014 212 21 32222 32428 32633 32838 133041 33243 33445 33646 33845 34044 202 22 34242 34439 34635 3483035024 35218 35410 35602 35793 35983 194 23 36173 36361 36548 3673536921 37106 37291 37474 37657 37839 185 24 38021 38201 38381 38560 38739 38916 39093 39269 39445 39619 177 25 39794 39967 40140 40312 40483 40654 40824 40993 41162 41330 171 26 41497 41664} 41830 41995 42160 42324 42488 42651 42813 42975 164 27 43136! 43296 43456 43616 43775 43933 44090 44248 44404 44560 158 28 447161 44870 45024 45178 45331 45484 45636 45788 45939 46089 153 29 46240 46389 46538 46686 46834 46982 47129 47275 47421 47567 148 30 47712 47856 48000 48144 48287 48430 48572 48713 48855 48995 143 31 49136 49276 49415 49554 49693 49831 49968 50105 50242 50379 138 32 50515 50650 50785 50920 51054 51188 51321 51454 51587 51719 134 33 51851 51982 52113 52244 j 52374 52504 52633 52763 52891 53020 130 34 53148 53275 53402 53529 53655 53781 53907 54033 54157 54282 126 35 54407 1 54530 54654 54777 54900 55022 55145 55266 55388 55509 122 36 556301 55750 55870 55990 56110 56229 56348 56466 56584 56702 119 37 56S20J 56937: 57054 57170 57287 57403 57518 57634 57749 57863 116 38 57978 58092! 58206 58319 58433 58546 58658 58771 58883 58995 113 39 59106 592171 59328 59439 59549 59659 59769 59879 59988 60097 110 40 60206 1 603141 60422 60530 60638 60745 60852 60959 61066 61172 107 41 61278 1 61384 61489 61595 61700 61804 61909 62013 62118 62221 104 42 62325 62428 62531 6263462786 62838 62941 63042 63144 63245 102 43 63347 63447 63548 63648 63749 63848 63948 64048 64147 64246 99 44 64345 64443 64542 64640 64738 64836 64933 65030! 65127 65224 98 45 65321 654171 65513 65609 65705 65801 65896 65991 66086 66181 96 46 66276 66370 66464 66558166651 66745 66838 66931 67024 67117 94 47 67210 67302 67394 67486 67577 67669 67760 67851 67942 68033 92 48 68124 68214 68304 6839468484 68574 68663 68752 68842 68930 90 49 69020 69108 69196 69284 69372 69460 69548 69635 69722 69810 88 50 69897 69983 70070 70156 70243 70329 70415 70500 70586 70671 86 51 70757 70842 70927 71011 71096 71180 71265 71349 71433 71516 84 52 71600 71683 71767 71850 71933 72015 72098 72181 72263 72345 82 53 72428 72509 72591 72672 72754 72835 72916 72997 73078 73158 81 54 73239 73319 73399 73480 73559 73639 73719 73798 73878 73957 80 55 74036 74115 74193 74272 74351 74429 74507 74585 74663 74741 78 56 74818 74896 74973 75050 75127 75204 75281 75358 75434 75511 77 67 75587 75663 75739 75815 75891 75966 76042 76117 76192 76267 75 68 76342 76417 76492 76566 76641 76715 76789 76863 76937 77011 74 59 77085 77158 77232 77305 77378 77451 77524 77597 77670 77742 73 60 7T815 77887 77959 78031 78103 78175 78247 78318 78390 78461 72 61 78533 78604 78675 78746 78816 78887 78958 79028 79098 79169 71 62 79239 79309 79379 79448 79518 79588 79657 79726 79796 79865 70 63 79934 80002 80071 80140 80208 80277 80345 80413 80482 80550 69 64 80618 80685 80753 80821 80888 80956 81023 81090 81157 81224 68 66 81291 81358 81424 81491 81557 81624 81690 81766 81822 81888 67 * Each log is supposed to have the decimal sign before it. An error of less than 1 in the final decimal exists in a number of the logs of this table, it will not, however, be material in ordinary computations. 2UO TABLE NO. 78. Logarithms of Numbers, from O to 1OOO* (Continued.) No. 1 1 | 2 3 4 5 6 7 9 9 Prop. 66 81954 82020 82085 82151 82216 82282 82347 82412 82477 82542 66 67 82607 82672 82736 82801 82866 82930 82994 83058 83123 83187 65 68 83250 83314 83378 83442 83505 83569 83632 83695 83758 83821 64 69 83884 83947 84010 84073 84136 84198 84260 84323 84385 84447 63 70 84509 84571 84633 84695 84757 84818 84880 84941 85003 850f4 62 71 85125 85187 85248 85309 85369 85430 85491 85551 85612 85672 61 72 85733 85793 85853 85913 85973 86033 8093 86153 86213 86272 60 73 86332 86391 i 86451 86510 86569 86628 86687 86746 86805 86864 59 74 86923 86981 87040 87098 87157 87215 87273 87332 87390 87448 58 75 87506 87564' 87621 87679 87737 87794 87852 87909 87966 8S-024 57 76 88081 88138 88195! S8262 88309 88366 88422 88479 88536 88592 56 77 88649 88705 88761 88818 88874 88930! 88986 89042 89098 89153 56 78 89209 89265 89320 89376 89431 894871 89542 89597 89652 89707 55 79 89762 89817 89872 89927 89982 90036 90091 90145 90200 90254 54 80 90309 90363 90417 90471 90525 90579 90633 90687 90741 90794 54 81 90848 90902 90955 91009 91062 91115 91169 91222 91275 91328 53 82 91381 91434| 91487 91540 91592 91645 91698 91750 91803 91855 53 83 91907 91960 92012 92064 92116 92168 92220 92272 92324 92376 52 84 92427 92479 92531 92582 92634 92685 92737 92788 92839 92890 51 85 92941 92993 93044 93095 93146 93196 93247 93298 93348 93399 51 86 93449 93500 93550 93601 93651 93701 93751 93802 93852 93902 50 87 93951 94001 94051! 94101 94151 94200 94250 94300 94349 94398 49 88 94448 94497! 94546 i 94596 94645 94694 94743 94792 94841 94890 49 89 94939 94987 ! 95036 95085 95133 95182 95230 95279 95327 95376 48 90 95424 95472 95520; 95568 95616 95664 95712 95760 95808 95856 48 91 95904 95951 95999; 96047 96094 96142 96189 96236 96284 96331 48 92 96378 96426 96473: 96520 96567 96614 96661 96708 96754 96801 47 93 96848 96895 96941; 96988 97034 97081 97127 97174 97220 97266 47 94 97312 97359 i 97405 97451 97497 97543 97589 97635 97680 97726 46 95 97772 97818 97863 97909 97954 98000 98045 98091 98136 981 81' 46 96 98227 98272 98317 98362 98407 98452 98497 98542 98587 98632 45 97 98677 98721 98766 98811 98855 98900 98945 98989 99033 99078 45 98 99122 99166 99211 99255 99299 99343 99387 99431 99475 99519 44 99 99563 99607 99651 99694 99738 99782 99825 998691 999131 99956 44 * See foot note on paere 199. The log of 2870 is 3.45788 I The log of .287 is 1.45788 287 is 2.45788 " " " .028 is 2.44716 .002 is 3.30103 287 is 2.45788 28.7 is 1.45788 2.87 is 0.45788 .0002 is 4.30103 What is the log of 2873? Here, log of 2870 = 3.45788 And prop 153 X 3 = 459 3.458339 To find roots divide the log (with its index) of the given number, by that amber which expresses the kind of root. The quotient will be the log of the required root. Example. What is the cube root of 2870 ? Here, the log of 2870, with its index, is 3.*5788. And -- - - = 1.15263. Hence the cube root ia 14.2. The Hyperbolic, or Napierian logarithm is the common log of the table multiplied by 2.3025651. Sq. rt. 6925=Log 3.84042-*-2=log 1.92021, corresponding No. =83. 2138= sq. rt Cu-rt.6925= " 3.84042-*-3= " 1.28014, " =19.0669=cu. rt. 4th rt. 6925= " 3.84042+4= l< '96010, " = 9.1222 = 4th rt. Proceed in like manner for any other root required. This method of ex- tracting roots is more rapid and simple than any other. 201 EXPLANATION AS TO TABLES OF LOGARITHMS. LO G A R I T H M S are the exponents with which a fixed number must be affected in order to produce a given number. The fixed number is called the BASE. The base of the common system of logarithms is 10. Since 10 = 1 the logarithm of 1 is 0. " 10 1 = 10 " " 10 " 1. " 10 2 - 100 " " 100 " 2. Thus, the logarithms of all powers of the base are integral numbers, while the logarithms of numbers intervening between exact powers of the base are composed of an intiger and a fractional or decimal part called the MANTISSA. The integral part of the logarithm being called the liunrxor CHARACTERISTIC NOTE WELL THE FOLLOWING RULES. I. The log. of any exact power of 10 is a positive (+) intiger one less than the number of places in the number. Thus See figures at foot of table on page 200 Log of 2870 has 3 for its index, there being 4 figures in the number. 2S7 28 2 II. The characteristic of any decimal number is negative ( ) and numerically one more than the number of zeros immediately following the decimal point. Thus See figures on page 200 (2d column.) Log of. decimal .287 (being no zeros) = 1. ( Negative, and 1 in excess of .023 ( ' 1 zero ) = 2. < the number of zeros immedi- .002 ( ' 2 zeros] = 3. ( ately following deci'al point. j The minus sign^instead of being placed befori the index, as ) < here shown, is usually placed above thei ndex, thus, 3. USE OF TABLE. The logarithms of numbers from 1 to 9 are taken from the top horizontal line of the table, Log of 9 being .95424 ; and logs of numbers from 1L to 99 are taken from the first column, headed by O, the index 1 being added as above explained [IJ. Thus the log of 91 = 1.95904, Log of 80 = 1.90309. Logs of numbers from 100 to 1000 are taken from the table as follows required the log of 915 ; find 91 in first column and then run horizontally across the table to the column headed 5 where is found the log .96142 to which add an index of 2, as above explained, making 2.96142 the log required. Log of 800 would in like manner be 2.90309, log of 801 = 2.90363. Since the decimal part of the logarithm is not changed by multiplying or dividing the number by any power of 10 the logarithm of a number of 4 or 5 places may also be taken from the table as shown at the foot of the table. The log of 287 = 2.45788 and log of 2870 = 3.45788 the index only being changed. If, however, the 4th figure is other than O, as 2873, then proceed as follows : find the log of the 3 left hand figures and in the same horizontal line, at its intersection with the last vertical column, headed * Prop." [Proportionate parts] take the number indicated and multiply it by the last figure of the given number . Exclude one figure from the product and add the remainder to the log first found. In case as shown at foot of table log is taken for 2870 then in last column is found 153 which X 3, the last number of the given number 2873, exclude the right hand figure from the product of 459 and add the remainder, 45, to the log first found. What is the log of 28735? Here log of 28700 = 4.45788 And prop 153X35 = 53.55 Log of 28735 =4.45841 Here 2 figures are cast off because there are 2 figures in the multiplier [35] . With numbers of 5 figures this may be in error 1 in the last decimal. 202 In the use of logarithms it is not only necessary to find the log corres- ponding to a given number but also to find the number corresponding to any given log. III. Given any log to find the corresponding number. A. Where the mantissa is found in the table. Look in the table for the given log, take out the corresponding number and place the decimal point according to the given index. Example Given log 4.96142, what is the corresponding number? Look in table for log 96142 and find it corresponds to the number 915. The given index 4 indicates a number of 5 places therefore point off the number obtained to have 5 places and to read 91500. Log of 2.90309 corresponds to 800; Log .30103 to 2. &c. B. Where the mantissa is not found in the table. Take from the table the next lesser mantissa and its corresponding num- ber. Then subtract this mantissa from the given one and divide the re- mainder by the number opposite in the column " Prop." Annex the quo- tient so found to the tabular number taken out and then point off as indi- cated by the given index. Example Given the log 1.96166 to find the corresponding number . From table we find .96142 to be the nearest lesser mantissa and 915 to be the corresponding number. .96166, the given mantissa, minus .96142 the lesser one = difference of 24 which being divided by 48, the number found in column " Prop." = .5. This being annexed to the tabular number 915= 9155. The given index 1 indicates a number of 2 places, so 91.55 becomes the required number, THE USE OFLOGARITHMS. The ADDITION of logarithms corresponds to ordinary MULTIPLICA- TION and any number of given numbers either integral, decimal or mixed, may be multiplied togeth Thus : multiply togethe Log 166. = 2.22010 may be multiplied together by one operation Thus : multiply together 166, 71.5, 8.25 and .078 (=7637.7). 71.5 = 1.85430 8.25 = 0.91645 .078 = 2. Note. The index of the last log being minus it is subtracted from the sum of the -f- indices, 5, leaving 3 the index of the sum. " of product = 3.8 By method B, above given, the log 3.88294 is found to correspond to the number 7637. 7 which is the required product. The SUBTRACTION of logarithms corresponds to ordinary DIVISION. The log of the divisor being subtracted from the log of the dividend gives, as a remainder, the log of the quotient. Thus Divide 86.32 by 6.85 (=12.601) . Log 86. 32 = 1.93611 " 6.85 = 0.8 " quotient= 1.10042, which, by method " B," = 12.601 = quotient. TO RAISE A NUMBER TO A POWER. Rule. Multiply the log of the number by the exponent of the power and find the number corresponding to the product. Thus What is the 5th power of 7.65? Log of 7.65= .88366 which X 5 = 4.41830 the number corresponding to which is 26200. TO FIND ANY ROOT BY LOGARITHMS. See explanation at foot of table on page 200. The cube root 14.2 being the number corresponding to log 1.15263. Proceed in like manner for any other root required . 203 The foregoing explanations as to the use of logarithms are cheifly for the benefit of those who have, by disuse, become '"rusty" in the use of the tables ; although any one may in a day or two become f amilliar with them and may, by their use, greatly lessen the drudgery of mathematical calculations. Such uses only have been explained as pertain to the sim- pler mathematical operations. EXPLANATION OF CHARACTERS. The following brief explanation is given of a few of the more com- mon characters used in calculations, etc. and which are so frequently met with in mathematical and similar works. = Signifies Equality, as 2 + 2 = 4. -f- " Plus, as 2 + 2 = 4. " Multiplied by, as 2 X 4 = 8. " Minus, as 8 2 = 6. -f- Divided by, as 8 -*- 2 = 4. : & : : " Proportion, as 2 : 8 : : 4 : 16 reads .... as 2 is to 8 so is 4 to 16, or, 2 is to 8 as 4 is to 16. The Vinculum or Bar indicates that all the numbers over which it is placed are to be considered as one quantity, thus, 2 -(- 8 -*- 2 = 5 ; or 5X8 2 =30. ( ) [ ] Parenthesis or Brackets indicate, as in above, that all included figures are to be considered as one quan- tity, thus, ( 3 X 5 ) -f 10 = 25 ; or 3 X [ 5 + 10 ] = 45. Decimal Point. V The Radical or Root sign when placed before a num ber indicates that the square root of the number is required, \ 16 = 4; \15 -f- 10 = 5. The degree of the root, other than the square root, is indicated by a figure placed above the radical, which figure is called the Index. V = Cube root ; *y = 4th. root etc. Z Signifies Angle. J. " Perpendicular. A Triangle, or triangular as A iron or inches. Square, as n " " " O Circle or Circular, as O '* " ** Therefore or Hence. " Because. ft The Ratio of the circumference of a circle to its diam- eter, which = 3.1416 . > < Greater and Less, a> b reads - a greater than b. 00 Infinity. Degrees. Minutes, and Seconds of arc. " Feet and Inches. 1 I &c. ' when set superior to a number, that the square or cube root etc. is wanted, thus 25$ indicates the sq. rt.of 25. i f I . 9 Province Court, Boston, Mass. They aim to secure in their Instuments. Accuracy of division; Simplicity in manipulation; Lightness combined with strength; Achro- matic telescope, with high power; Steadiness of adjustments under vary- ing temperatures; Stiffness to avoid any tremor, even in a strong wind, and thorough workmanship in every part. Their instruments are in general use by the U. S. Government Engineers, Geologists and surveyors, and the range of instruments, as made by them for River, Harbor, City, Bridge, Tunnel, Railroad and Mining Engineering, as well as those made for Triangulation or Topographical Work and Land Surveying^ is larger than that of any other firm in the country. Ilhistrated Manual and Catalogue sent on application. TRAUTWINE'S Civil Engineer's Pocket Book. "If you can own but a single book let it be this, and by all means have this if you are but a rodman, if you intend to continue in the work." Railway Age, Oct. 9, 1884. "Without doubt it has proved itself to be the most useful hand- book in the language for the Engineering profession." Engineering and Mining Journal, ,Aug 25, 1 888. "The best general text-book on civil engineering in the English language. It is a whole library in itself." Engineering News, Jan. 27th, 1883. "It is a book for the civil, mechanical, hydraulic and mining en- gineer, and architect and builder. Its tables are invaluable, and al- most absolute reliance can be placed in them." Engineering and Building Record, Aug. nth, 1888. "It is, deservedly, one of the most popular of Pocket Books, be- cause the information it contains is presented in such plain terms as to be readily comprehended by those who have not had the advant- ages of a technical education. Every statement is in the fewest words that will clearly convey the meaning." American Machinist, May 9 th, 1885. For sale by John Wiley 2250 W. & L. E.GURLEY, TIEtOY, 1ST. IT. Largest manufacturers in America of Civil Engineers' and Sur- veyors' Instruments; our latest illustrated price list on application. THE ARCHITECT'S LEVEL. Price as shown, with tripod, $50.00. This figure represents the level introduced by us in 1874, and which has since been very largely used by architects, builders, en- gineer?, and surveyors, in the grading of streets, drives, sewers, etc., in all parts of the country. It has a telescope 12 inches long, furnished with rings, wyes, ere, precisely like our larger levels, and adjusts in the same way. The leveling head has the ordinary screws and a clamp to the spindle; it has also a horizontal circle 3 inches in diameter, fitted to the upper end of the socket, and turning readily upon it; the circle is graduated to degrees, figured from o to 90 each way, and is easily read to five minutes of a degree by a vernier which is fixed to the spindle. The adjustments are not liable to derangement, and ordinarily re- quire but little attention. A 221 TROY, N. Y. FARMER'S OR DRAINAGE LEVEL. Price, as shown, with tripod, $25.00. This Level combines the extremes of simplicity and compactness with real efficiency, and at moderate cost. The telescope, 9 inches long, is achromatic, and of sufficient power. The cross wires are not easily disturbed. The level and telescope are both inclosed in an outer bronze case. The instrument is approximately leveled by the ball spindle on the socket and then precisely so by the leveling screws. The advantage of this form of Level in the work of the farmer in laying out ditches and reservoirs will be apparent on in- spection. When desired we add to this level a 3-inch needle mag- netic compass at an extra cost of $5. This is fitted to the case as shown below and can be removed at pleasure. 222 223 WELL MACHINERY. gend for our (Catalogue DESCRIBING A FULL LINE OF ARTESIAN WELL OUTFITS, PORTABLE ROCK DRILLS, AND THE CELEBRATED Petzh Well /lugeF, WIND MILLS, GENERAL WELL SUPPLIES, &c.. &c. THE PECH MFE. CO., SIOUX CITY, IOWA. 224 Valve Manufacturing Co., MANUFACTURERS OF Valves ai?d F!FE Double and Single Gate VALVES, ALSO Check Valves, Foot Valves, and Vard and Wash HYDRANTS- FACTORY AND OFFICE. 938 to 954 River St., and 67 to 83 VaiJ Ave., TROY, N. Y.,U. S.A. IFOIR, 225 WELL DRILLING [ MACHINERY, AND TOOLS, ADAPTED TO ALL KINDS of work, and prospecting. Horse and Steam Power. They never fail. They are Sim- ple, Practical, and Thorough. We also make a full line of gas and Water Works Goods, Gate Valves, & Hydrants. Our open-way hydrants are the best in the market. Corporation Cocks, and the best Tapping Machine in the world. Write for Circalars, and let us talk it over with you. Address the Brass X Iron Works Go, FOSTORFA, OHIO. 226 THE PELTON WATER WHEEL. Affords the most efficient and reliable power for all purposes, be- ing especially adapted to utilize the power from ARTESIAN WELLS. They are warranted to give from 25 to 40 per cent better results than any other wheel. The Woonsocket and Yankton Mills and Huron Electric Lights are run with Pelton wheels. (See page 81.) PELTON WATER MOTORS, embrace the smaller wheels set in iron casings ready for pipe connections Made of capacities from a fraction of 1, up to 50 horse power. The cheap est and, most convenient power. Parties interested in the development of Dakotas great artesian power will be furnished with catalouge, circulars, and other information on demand to the 227 Oil Well Supply Co., PITTSBURGH, PENN. Manufacture every article, tool or appliance needed at ARTESIAN WELLS. ARTESIAN WELL MACHINERY. Boilers, Engines, Pxnrxps, Derricks, Cordage, "Filings, Drilling and Yislving Tools, Txitoing and Casing. and Iron Good? and Supplier For Steam, Gas, Petroleum or Water. Catalogues and Price Lists on application. 228 W. E. SWAN. P. J. STAGEY. W. E. SWAN CO., ANDOVER, S- D. Drilled the first well in Dakota, at Aberdeen. Have had TEN YEARS' experience IN DAKOTA. Being the oldest drillers in the state, and having the most experience in the hard Dako- ta formations, and the best rigs and most im- portant tools we are better equipped for rapid and successful work than any drillers in the Dakota basin. Our experience extends over 6 states and our record is as good as our experi- ence is broad and varied. We are prepared to drill to any depth and of any size. Among our wells are the following: WELLS IN N. AND S. DAKOTA. Aberdeen, Columbia, Groton " WOTS in Manitoba, \ndover Many in Minnesota. Ashton, ' Wisconsin. Huron Iowa - Mellette, Illinois. Devils Lake, Bismarck, Grafton, Correspondence solicit- Frankiort, ed. (ive us a chance Ipswich, to bid on your work if And many farm wells you want good work in both states. and promptly done. 230 The Great Northwest is traversed by the Chicago & Northwestern Railway. The finest cars in the land are run on its trains between Chicago and all the principal points in ILLINOIS, HRfQRffl NEBRASKA, WISCONSIN, IE9lfH|j| SOUTH DAK., MINNESOTA, !ffifffl H AND IOWA. Chicago, Milwaukee, Madison, St. Paul, Minneapolis, Duluth, Ashland, Superior, Winona, Council Bluffs, Omaha, Des Moines, Sioux City, Sioux Falls, Mitchell, Huron, Watertown, Pierre, Aberdeen, and Oakes, are all reached by our lines. Parties desiring to visit the great ARTESIAN BASIN of Dakota should take this line for all the great artesian wells are reached by our road. The best farming land in America is to be had in the Dakotas where IRRIGATION BY ARTE- SIAN WELLS will make every farmer rich. 231 Profitable Investments. THE CHICAGO AND No RTH WESTERN RAILWAY CO. Owns Lots in most of the Cities and Towns on its}lines in SOUTH DAKOTA. These Lots are For Sale at such prices and terms as to secure to purchasersjsafe and profitable investments. South Dakota is All Right, and those seeking locations for investments, or opportunities for the investment of capital, should give it an intelligent investigation. For particulars apply to CHAS, E, SIMMONS, Land Commissioner C* & N.-W. Ry. Company, CHICAGO, ILLINOIS. 232 A GREAT RAILWAY. The CHICAGO, MILWAUKEE & ST, PAUL RAIL- WAY COMPANY now operates over sixty-one hun- dred miles of thoroughly equipped road in ILLINOIS, WISCONSIN, NORTHERN MICHIGAN, MINNESOTA, IOWA, MISSOURI, SOUTH and NORTH DAKOTA. Each recurring year its lines are extended in all di- rections to meet the necessities of the rapidly popu- lating sections of country west, northwest and southwest of Chicago, and to furnish a market for the products of the greatest agricultural and stock raising districts of the world. In Illinois it operates 317 miles of track; in Wisconsin 1,636 miles; in Northern Michigan 96 miles; in Iowa 1,551 miles: in Minnesota 1,115 miles; in South Dakota 1,092; in North Dakota 118 miles; in Missouri 140 miles, and the end is not yet. It has terminals in such large cities as CHICAGO, MILWAUKEE, LA CROSSE, ST. PAUL, MINNEAPOLIS, FARGO, Soiux CITY, COUNCIL BLUFFS, OMAHA and KANSAS CITY and ST. JOSEPH, MISSOURI, and along its lines are hun- dreds of large and small thriving cities, towns and villages. Manufacturing interests are cultivated, and all branches of trade find encouragement. The Railway Company has a just appreciation of the value of its patrons, and its magnificent earnings are the result of the good business tact which char- acterizes the management of its affairs. 233 THE POPULARITY OF THE Chicago, Milwaukee and St. Paul Railway is attested by the fact that notwithstand- ing the strongest kind of competition of old and new lines, the Chicago, Milwaukee & St Paul Railway continues to carry the greater proportion of all the business be- tween Chicago, Milwaukee, St. Paul and Minneapolis. It is the best patronized route between Chicago, Council Bluffs and Omaha and to and from all points in Wisconsin, Minnesota, Dakota and Iowa, and its Kansas City and St. Joseph line has taken equal rank with the older lines leading to and from the Southwest. On all its THROUGH LINES of travel the CHICAGO, MILWAUKEE & ST. PAUL RAIL- WAY runs the most perfectly equipped trains of Sleeping, Parlor and Dining Cars. The through crains on all its lines are systematically HEATED BY STEAM. No effort is spared to furnish the best ac- commodations for the least money, and, in addition, patrons of the road are sure of courteous treatment from its employes. 234 THE Engineering Magazine A high-class, beautifully illustrated monthly magazine, like the Century and Harper's, but devoted exclusively to industrial affairs and engineering problems. It covers the entire field of industry, and besides nine special depart- ments, and a monthly index to all that is of value in tech- nical literature, each number contains ten leading articles by distinguished authorities upon topics that are uppermost in public interest. The following are among the leading articles published in recent numbers: Progress in Aerial Navigation, (Illustrated) O. Chanute, president American Society C. E. The Future of our Wagon Koads Wm. Claypoole, C. E. The Solution of the Block Signal Problem, (111.) H. Ward Leonard, E. E. Is the limit reached in armored Warships? Albert Williams, Jr., E. M. Pure Water and Public Health. Floyd Davis, Ph. D. Chemist, Iowa State Board of Health. The Canadian Pacific Bailroad T. K. Thomson, C. E. Worthless Government Engineering Geo. Y. Wisner,C. E. Followed by a criticism by Lieut. Col. W. B. King of the Engineer Corps, and a rejoinder by the author. The World's Store of Tin, (111.) E. W. Claypole, A. B., D. Sc. The Bights of the Lowest Bidder; What the Contractor Wants to Know, L. Allen, A. B., M. E. The Answer of the Law, C. E. Hellier, LL. B. The Decline in Bailroad Building, T. L. Greene. The Wind as a factor in Geology (111.), G. P. Merrill. The Manufacture of Ice, L. Allen, A. B., M. E. The Purification of Water, F. Davis, Ph. D. 'Edited with marked ability." Boston Herald. 'Readable from cover to cover." Indianapolis News. 'Studded with ideas of practical value." Norfolk Virginian. The contributors are men of the highest rank." St. Louis Eepublic. 'We heartily commend it to the general public." Post on Transcript. 'Unquestionably the most elaborately illustrated engineering journal that has yet appeared on either side of the Atlantic. "Mechanical World London. PRICE 25 cents a number; $3.00 a year. At all news stands, or by mail. Send 10 cts. for a sample copy, and men- tion this manual. THE ENGINEERING MAGAZINE CO., World Building, NEW YORK, U. S. A. 235 Great Northern Ry, Has 3 lines in South Dakota, connecting Sioux Falls, Huron, Watertown and Aberdeen WITH St, Paul, Minneapolis, Mutt, Superior AND THE EAST. Reaches more points in Minnesota, AND North Dakota than any other line. Has 2 Lines from St. Paul and Minneapolis to the It is the direct route to GREAT FALLS, HELENA and BUTTE. Gives choice of TWO ROUTES TO THE PA- CIFIC COAST. Round Trip Tourist Tickets to all the leading points in the west. For Maps, publications and in- formation apply to any agent of the Co., or address F. I. WHITNEY, G. P. & T. A., ST. PAUL, MINN. 236 * TAKE THE * Northern Pacific Railroad. A -H* Car Lin. TO ALL PRI NCI PALI POINTS IN The Greatjorthwest For Rates, Time-Tables and Illustrated Tourists' Publications, address J. N. HANNAFORD, CHAS. S. FEE, " ^Gen'l Traffic Manager, ^j :j Gen'l Pass. & Ticket Agent. St. Northern Pacific Railroad, 237 j [IMPROVED.! in the \V)orld. Specially adapted to high pressure service for running machinery of all kinds, from % to 15 horse-power. Manufacturer.-; of Little Giant Water Motors The B. C. Standard Electric Motors and Dynamos, the Combined Water Motor and Dynamo, Combined Engines and Dynamos, Water Motor Cyclone Coffee Mills, and Electric Motor Church Organ Piston Motors. Also all other Electrical Supplies. 238 ROOT'S Steel or Iron Spiral Riveted Pipe 3 to 24 inches diameter. 2 to 25 feet lengths. Connections and Fittings to suit service required. Unrivaled for Water Works, Hydraulic Mining AND IRRIGATION, AS HAS BEEN PROVED BY 14 2Jeap$ Practical (See pages 24, 122, 123 herein.) Facfory at Greenpoint, L. I. New York Office 28 Cliff Street. Pacific Coast Office, 23 Davis Street, San Francisco, Cat. A. L. ALDERSON, Representing GEO. F. EBERHARD, Mgr. ABENDROTH & ROOT MFG. CO. (See next page also.) 239 (See page 238.) o, i H OH U OJ "o3 CU -t > CJ Abendroth & Root S. Co.: Bolted Joint Section. 240 YOUNG 4 SONS, Manufacturers of Engineering, Mining, and Sur- veying Instruments. Established 1820. No. 43 North Seventh St., Philadelphia. 241 DRAINAGE LEVELS. 5ei?d IOF our Special Ligt oT e Bevels. Mailed to any address upon application TO YOUNG & SONS, NO. 43 NORTH 7TH ST., PHILADELPHIA. 242 FJobinson Gang Co., JOBBERS OF Wrought Iron PIPE Cast Iron FITTINGS, PUMPS, VALVES, x&C, ENGINES, BOILERS, MACHINERY, Railway, Miners' & Mill Supplies 4TH * WACOUTA STS., St. Paul, - Minnesota. 243 SWAN BROS., Well Drillers, ANDOVER, SOUTH DAKOTA. "BY THEIR DEEDS SHALL YE KNOW THEM." QQ OQ We have drilled wells in all parts of the Dakotas, in Wis- consin, Iowa, Minnesota and in the Canadian Northwest. We are always successful. We use the best rigs, tools, and machinery, and we are acknowledged to be the best drillers in this field. We let our work speak for us. Correspondence solicted. 244 Time Tested, Best and Cheapest Automatic Steam Vacuum Pump Known, for Irrigation, Mining and General Farm Purposes, Requires no Engine, Belt- ing, Housing, Oil, Packing, Attention or Expensive Over 21,i in use f Has no Piston Rods , Cranks, Eccen- trics, Levers, Beams, Jets, Weights or other Compli- cated Mechan- ism to get out of order and absorb power, * Requires Less Steam and Fuel than other Pumps. OPERATES HUNG UP OR STATIONERY. ANYBODY CAN OPERATE IT IT WILL NEVER WEAR OUT, Catalogues, Estimates and Particulars Furnished on Application TO THE PULSOMETER STEAM PUMP CO., Sole Owner and Manufacturer, NEW YORK. See also pages 126, 127, 128 . 245 ARTESIAN IRRIGATION IN ITS PERFECTION. Where power of well is used for Threshing and Grinding Feed. \ . We B\xy , Irrigate, and Sell l_iand-. 2. We Sink. Rrtesian Wells \>y Contract. 3. "We Bent l_iai\d and Pay Taxes lor ^cm-resi&en^s and Corpo- raUons. 4. We Sell \tae Best Paying and Salest Seoxxrities in tlie \3 . S. Dakota Irrigation ABERDEEN, S. D. S. W, Narregang, President, Excelsior Block- 246 The Western Wheeled Scraper Co,, AURORA, ILL. (Formerly oi Mount Pleasant, Iowa.) THE LEADING MANUFACTURERS OF GRADING IMPLEMENTS. Our celebrated Western Wheeled SCRAPERS are used in all parts of the world. Our Western Double- bottom Drag SCRAPERS are un equaled and are the favorite with all graders. We make the MOORE IRRIGATING DITCHER which is extensively used in all the Western States for making Irri- gating Ditches and laterals, and for leveling land. We also make the I^est Road TVlacbine on garth. Also Wheelbarrows, Dump-Carts and Farm Wagons. Send for Catalogues and Prices to the )beeled craj>er G.> AURORA, ILLS. 247 IsTSTIE'S STEAM VACUUM PUMPS FOR IRRIGATION, Etc. TYie Cheapest, TY\e Simplest, and. \,tie most, Pump m The pump works equally well if the water is loaded with sand or gravel . Ho Pistons, no parts to Wear or Break. Any man or boy can manage it. (See page 126.) Please write for Catalogue and full information, to the NYE STEAM VACUUM PUMP CO., 7 and 9 S. Jeffers >n St., Chicago, 111. 248 500FOOT MACHINE set up in 30 MINUTES. ANY ONE can RUN IT. later Your Farms and Irrigate Your Lands WITH THE VERY BEST AND CHEAPEST Artesian W)ell For wells 2.000 feet or less ten sizes set up and has the well half way down before an ordinary ^Derrick" couid be built. Drills 30 to 80 feet per 24 hours in hard rock. Manu- factured in the great oil fields of Pennsylvania. Ko extras needed with these machines. Made with or without "trac- tion attachment." Our 2,000 foot rig can be run by a thresher engine. Buy one and make money with your idle thresher engine the year round. A skilled operator sent free to set and start each machine and give full instructions in its use. Every machine guaranteed. Correspondence solicited from parties wanting artesian wells. SOLD DIRECT TO USERS AT MANUFACTURERS PRICES. Catalogue of Artesian Irrigating IPTJIMIIIPS for wind or steam pow- er. Can be run with a thresher engine. Will save 50 per cent, of power, and do more work than any other pump. KEYSTONE DRILLER CO., Beaver Falls, Penn. 249 Now is the Time to Subscribe. HARPER'S MAGAZINE, One Year $4.00 HARPER'S WEEKLY, One Year - - 4.00 HARPER'S BAZAR, One Year - 4.0o HARPER'S YOUNG PEOPLE, One Year, 2.0o ity Postage free to all subscribers in the United States, Canada, and Mexico. The Volumes of the WEEKLY and BAZAR begin with the first numbers for January, the Volumes of the YOUNG PEOPLE with the first number for Novem- ber, and the Volumes of the MAGAZINE with ths Numbers for June and Decem- ber of each year. Booksellers and Postmasters usually receive subscriptions. Subscriptions sent direct to the publishers should be accom- panied by Post-Office Money Order or Draft. When 110 time is specified, sub- scriptions will begin with the current Number. The MAGAZINE is an overflowing store of good literature and exquisite art a delightful production deserving all the fame and the material success which have been won by it. The WEEKLY is a rarely illustrated chronicle of the year's events; there is no end of pleasure and profit in its pages. The BAZAR is a repository of fashion, and a gallery of some of the finest engravings of the time. The YOUNG PEOPLE is a treasure-house fascinating to every boy and girl as well as to plenty of persons older. A remarkable and valu- able, an instructive and delightful line of publications, indeed. N. Y. Sun. Address: HARPER & BROTHERS, Franklin Square, New York City. 250 JOHN H. MILLER. PRES. JOHN L. PYLE, SEC. W. N. COLER, VICE PRES. ALVA E. TAYLOR, TREAS Valley Land and Irrigation Company, HURON, SOUTH DAKOTA. CAPITAL STOCK, $2,000,000. INCORPORATED 1891. 100,000 ACRES OF FARM LANDS IN THE ARTESIAN BELT FOR SALE ON EASY TERMS. Address: NORTH AMERICAN LOAN & TRUST CO., Agents, 190 and 192, Dearborn St., Chicago, 111. First National Bank UNITED STATES DEPOSITORY, HURON. SOUTH DAKOTA. , $7^,000. garplus, $1^,000. R (SerjEFal Banking BugirjEss THOS. H. CAMPBELL, President. J. W. MACKENZIE, Cashier. ED. J. MILLER, Assistant Cashier. 251 ARTESIAN IRRIGATION CONSOLIDATED LAND AND * IRRIGATION COMPANY, HURON, SOUTH DAKOTA. (, Reliable 7W edium for both J-Juj/ercind Seller of goutb JOHN E. DIAMOND, PRESIDENT. D. L. BUSH, VICE-PRESIDENT. M. H. PRICHARD, SEC. & TREAS. R. O. RICHARDS, MANAGER. Irrigated, Sought, Sold and Managed. 251 A See Advertisements OF Wra X* ON pages 2 and 41. 251 B Of Making Many Books There is no End. Remember \fQ Goiloty Records, Bank Books, and all Kinds of Blank Books, Send in your Magazines and have them Bound in Handsome Volumes, English Tree Calf, and Red Undergilt Edges down to the cheapest styles. Preserve your old Books and send them in. C' ne Send Your Orders to Us* Save Money and Time. Mail Orders Promptly Attended to. The Largest and Best Equipped Job Office in the State. Bend TOP Sample Gopieg of tlje Baily and SHANNON & LONGSTAFF, , S. 3D. UNIVERSITY OF CALIFORNIA LIBRARY This is the date on which this FEB 7 M (Or II an< H book was charged out. AIT orks, lias, Texas; and WAT] PR Operated b Interested .f| Elip Combi] ST Deep P IS, AND TERY, fijy SIZE HOLE, corn- illustrating and [30ra-6,'ll] , Rope or at- ..VES, I Valves, UtC. RETURN CIRCULATION DEPARTMENT TO*- 202 Main Library LOAN PERIOD 1 HOME USE 2 3 4 5 6 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 1 -month loans may be renewed by calling 642-3405 6-month loans may be recharged by bringing books to Circulation Desl Renewals and recharges may be made 4 days prior to due date DUE AS STAMPED BELOW JES. CUt KAY FORM NO. DD6, 60m, UNIVERSITY OF CALIFORN 1 778 BERKELEY, CA 94> J YA 01453 HADING IRON CO, Manufacturers of BROUGHT IRON PIPE DRIVE PIPE, tesian or Oil Well Tubinsj an^'Jasing, BOILER Basing, taper-tapped (See above cut.) or Deep Artesian Wells. Chicago Office, 22 W. Randolph Street, . SAMUEL CLIFFORD, Agtj . Communicate wlth us and Get Prlces - See pages 16, 17, 19, 25.