Copyright N°
COPYRIGHT DEPOSIT:
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FOREST MENSURATION
BY
HERMAN HAUPT CHAPMAN, M.F.
Harriman Professor of Forest Management,
Yale University
NEW YORK
JOHN WILEY & SONS, Inc.
Lonpon: CHAPMAN & HALL, LrmrtEep
ros T
Copyright, 1921
By HERMAN HAUPT CHAPMAN
BOT 2
BROOKLYN, N. Y.
7
PRESS OF "
5 . BRAUNWORTH & Co.
BOOK MANUFACTURERS
OCLA6 24703
TO
Bernhard Lduard Hernom
IN RECOGNITION OF HIS LIFELONG SERVICE
IN PROMOTING FOREST EDUCATION
AND IN DEVELOPING A HIGH STANDARD
OF PROFESSIONAL FORESTRY IN AMERICA
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PREFACE
Tuis text is intended as a thorough discussion of the measurement
of the volume of felled timber, in the form of logs or other products;
of the measurement of the volume of standing timber; and of the
growth of trees, stands of timber and forests. It is designed for the
information of students of forestry, owners or purchasers of timber-
lands, and timber operators. The subject matter so treated is funda-
mental to the purchase or exchange of forest property or of timber
stumpage, the valuation of damages, the planning of logging operations,
and the management of forest lands for the production of timber by
growth.
The publication is intended as the successor of Graves’ Forest Men-
suration, and was undertaken at the request of the author, H. 8S. Graves,
whose original text, Forest Mensuration, appearing in 1906, set a stand-
ard for text-books in forestry and has been of inestimable value to
foresters and timberland owners in America. The present text is not a
revision of the former publication, but an entirely new presentation,
both as to arrangement, methods of treatment and much of the subject
matter. The author has in some instances quoted or borrowed portions
of the former text and is indebted to it for many of the more fundamental
conceptions and descriptions of processes used in Forest Mensuration.
It is the purpose of Part I to bring out the relations of the cubic
contents of logs, and their measurement, to the contents as expressed in
terms of products, and to encourage the substitution of sound units of
measure and methods of measurement for defective standards and
methods as far as possible.
The application of these standards to the measurement of standing
timber is the subject of Part II. This part presents a complete analysis
of the art of timber estimating as practiced in every timber region of the
United States, the methods employed by skilled timber cruisers, the
principles upon which these methods are based, the relative accuracy
of the various systems used, the factors and averages which enter into
the use of these methods, and the application of these principles and
_ factors in practical work and in the training of men for timber cruising.
Wi
vi PREFACE
The object sought in Part III is to systematize the principles and
problems confronting the student in the, study of tree growth, and to so
correlate these problems that he is not diverted from the ultimate object
of suchsstudies, which is the determination of yields per acre, by details
of methods having to do with the measurement of growth of individual
trees. Research and field studies of growth per acre are rendered dif-
ficult not only by the lack of an accepted unit of measure, but by the
great variations in the character of the stands comprising our virgin
and second growth forests, yet it is just these stands, and not planta-
tions, whose growth will determine our yields of timber for the next
four or five decades.
Attention is called to the substitution of the International }-inch
kerf log rule in the present volume, for the j-inch kerf rule in
Graves’ Mensuration. It is hoped that this rule will be accepted as a
scientific standard for board feet since it is adapted to conditions of
second growth and is conservative in values.
Instead of attempting to include tables of volume or yield, a table
of references is printed to such tables as are of standard quality and
which are in possession of the U. 8. Forest Service, Washington, D. C.
The author wishes to acknowledge the many helpful criticisms
received from foresters in the preparation of this book.
TABLE OF CONTENTS
Part I
THE MEASUREMENT OF FELLED TIMBER AND ITS
PRODUCTS
CHAPTER I
INTRODUCTION TO FOREST MENSURATION
PAGE
Hee ennitionvand Purposeran.., ste a tute actin Pies ole Scie seek Bad awa ed 1
2. Relation between Lumbering and Timber Estimating................... 2
3. Relation between Forestry and Growth Measurements.................. 2
4. Relation between Forest Mensuration, Stumpage Values and the Valuation
Ciabionest we rOPERLVaace rite we ens PAS AA Ad ta tetoe odes shal Wize woe Schade soli 3°
5. Relation of Mensuration to other Forestry Subjects..................... 3
6. Absolute versus Relative Accuracy in Mensuration...................-. 3
PMP E CHE ILA WE Ngee tale tty acuatetes yeh Reswce sor ducea Rebates Ace vace AM aj Games siaieroteigabacs 12,8 6, niet 5
CHAPTER II
SYSTEMS AND UNITS OF MEASUREMENT
8. Systems of Measurement used in Forest Mensuration................... 6
EMEC EM NLCASUITG = 2 Vanes ace tices sores seh Me hic; cinas suave eles aks x aotisProng. he dice 7
Tid): WORST hI ENEWS ee nes cas Sad A nT a PA oH Rg i a
ee @UbICHVMCHSULGE Wan ara e Mere Um ee Rio rH se). nS citiath acess oot tes Se ee 8
Zee OardeNVlessunereeirs cc st pretreat Sake a, «, n0.s, crcncyes he tr eoamatte. 4) canoe 8
Free SO USED U Lees eee Mr cP Cr ere E Pas A. cS A CIE wy vs we nt HPht lees onewolsiel aie ete Sone 8
14. Measurement of Standing Timber Postponed till after Manufacture... .... 8
15. Measurement of Standing Timber Postponed till after Logging............ 9
16) Measurement of Standing Vimberim the Tree:.........0.....24-..5..0+4% 9
17. Need of Standardization for both Commercial and Scientific Measurements. 10
18. Forms of Products into which the Contents of Trees are Converted....... il
19P ihewvactoror Wastein Manufactures. .... s2s0..sacnedsacdeo cone cede: 13
20. Actual versus Superficial Contents of Sawed Lumber..................-. 13
Zoi heli ey pT e80 re6 F132G tbl D]vh0 1 OFS) Rea one eae aca ae 14
22, Lroducts made irom: Bolts-and Billets. 2). «ck «cid v eicrseotols ase Sieve wes 14
CHAPTER. Tr
THE MEASUREMENT OF LOGS. CUBIC CONTENTS
23) Total versus’ Merchantalble' Contents. 5 .co bela t sjecaiec elem aiele a0 swag eee 16
GUL, Moyer beraensl VG OE Geel o) a oe le Le Bae yi ae oe et a Ry a 16
25.
Diametersrand Areasvols CrossiSeCulonsesneycs a cicimcye s aeie ie cc oie Henvederncesc oc 17
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TABLE OF CONTENTS
PAGE
Mhesormyoh Woes e-s scecsctseerceiseiiaerselee Rcaeve streak Raieeave gee ee 18
Hormules tor solid’ Contents oflopgs-.. 0.20 ene ms «au oeerl wanes 19
Relative Accuracy of the Smalian and Huber Formule................... 21
Mhieshechnique ot Measunmn cslogsaermeeremeaciccorte cee ieee ee 22
Girth as a Substitute for Diameter in Log Measurements................ 24
CHAPTER IV
LOG RULES BASED ON CUBIC CONTENTS
. Comparison of Log Rules Based on Diameter at Middle and at Small End
OE MUO Bs cig cote eee eS LTE SE MSU hve ce is she rspenvar eet at aioie steel toi ene 26
* hog Rules/in( Use; Based onsGubie Volume... 12. 7) eee i 1- <0 sa ee 28
. The Blodgett/or New Hampshire Cubic Foot® ..2..52..00...... 5... uae 30
i Use'of Cubic: Bootunvlog Sealing... a. abate nck no ae tet hole 31
. Log Rules for Cubic Contents of Squared Timbers...................... 33
. Log Rules Expressed in Board-feet but Based Directly upon Cubic Contents 34
. Formula for Board-foot Rules Based on Cubic Contents. ................ 35
Comparison of Scaled Cubic Contents by Different Log Rules............ 36
Relation between Cubic Measure and True Board-foot Log Rules........ 39
CHAPTER V
THE MEASUREMENT OF LOGS. BOARD-FOOT CONTENTS
LW Necessity for Board=foot beg ilesincm gem atias sete yas be me eee 40
. Relation of Diameter of Log to per cent of Utilization inSawed Lumber... 40
. Errors in Use of Cubic Rules for Board-feet.... 2.20022. 5.65%0-2 02000 es 42
. Taper as a Factor in Limiting the Scaling Length of Logs for Board-foot
Contents. ho och sho eee ae icin ae eae 43
5 Able IaisuoxehbKentoyo Chi, ALyoverr suouroy Joye INNES che ano conbounconomudedsasc6: Ad
. Middle Diameter as a Basis for Board-foot Contents.................... 46
ee Detinitionsand) Sasis,ol Over=snuse merece ea ern ees. eee 46
. Influences Affecting Over-run. The Log Rule Itself..................... 47
. Influences Affecting Over-run. Methods of Manufacture................ 47
. Standardization of Variables in Construction of a Log Rule.............. 49
ERhe Need tor More AccunateIvocalvullesnm srs 1-0 «1 a1or oss a aie onion ee 50
a ubhe Waste trom slabsiancdel dommasteese) 4 sete eae eee naan 50
© The: Waste from: Crook Ommweepe-s .< si.-<t-!<!<,<\3-<iie 5 a chu eae eee ee ee 51
Luihe Wastertrom’ Saw Werlich er cc 0s sod oss amine cone een eres aeons 53
YT otal Per: Cent: of Waste ima wl. s... noe bc oe ee ere rei hase ane 55
CHAPTER VI
THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT
CONTENTS
Methods Used in Constructing Log Rules for Board-feet................. 58
The Construction of Rules Based on Mathematical Formule............. 59
Comparison of Log Rules Based on- Formule... ....: 2. 228.52 ee 61
MoKenzie Tog Title. ition Soe ac ee oak eee ei Se tana ar ete Sera 63
International Log Rule for $’”’ Kerf, Judson F. Clark, 1900,..,...,,...... 63
TABLE OF CONTENTS 1X
PAGE
60. International Log Rule for }” Kerf, Judson F. Clark, 1917............... 64
Slaebribishy Columbia loc Rule 19020) 2 ee ee eo saga sess ee st ee sce ees 64
62. Other Formula Rules, Approximately Accurate Both in Principles and
(QUI VONUTEEISA Botti 6 nt d Gio ci CERO RI OROU RaREICS CROAT Re ea RENE SIeT O 10 es 0 ea a 65
Sseeluicmann log ule sae Dy Miemann TOMO. je. he eens aces ye cones 67
64. Formula Rules Inaccurately Constructed. Baxter Log Rule............. 67
Buemibowle oe Houle toss sss sis< sees ye os “345 A Re OR AR ee 68
66. Effect of Errors in Doyle Rule upon Scaling and Over-run............... 70
67. The Construction of Log Rules Based on Diagrams..................... 2
GSMS Chi DuoreloCuEC Me mld Omran cree tmeeel twee Gta tea us» lege Gelert ratd aud) 8 oferos weal shale 73
Somspaulding WogehulesWSOSn = onda eee seit hoe ta hea de wane ewe aek ows to
TOM ViaineiordollandmhUle rl SG sae. aks cca ce «cia chalecncde are sons mvsve piers een 76
Tie, WOHva,. 1 Svat LZovrstl ge fers] ened een ac ie ely RT Ae i A 76
arley OTR ER LIRCS ps geet her cc crs Gite etic aa sce iateyaxe: is sia eielerw ie: rete Sierae ep 76
om Generalehormimllse tor alleboouulest oa: ace caries cs eee sss ae 26 seein vee 77
74. The Construction of Log Rules from Mill Tallies. Graded Log Rules..... 78
75. The Massachusetts Log Rule for Round-edged Lumber.................. 79
76. Conversion of Values of a Standard Rule to Apply to Different Widths of
Saws lenand suhnickmessestorlbumben. eee eicme scar se acimc ote e-
77. Limitations to Conversion of Board-foot Log Rules...................... 83
78. Choice of a Board-foot Log Rule for a Universal Standard............... 84
foeaUnusec and Obsolete Gor RUles 5... co.cc ce dete ke ence eat ebigetees 85
CHAPTER VII
LOG SCALING FOR BOARD MEASURE
Pe MUM IO ET SCE i ene Mae Pee aa soos Sodals alia apshetty Bays GA ARIA ES 88
81. The Cylinder as the Standard of Sealing..............: Rape ann Reg thf ea? 90
82. Deductions from Sound Scale, versus Over-run......................-.. 90
83. Scaling Practice Based on Measurement of Diameter at Small End of Log 91
84. Scaling Practice Based on Measurement of Diameter at Middle of Log, or
Wali erm caller keen es Re che, ES Ces mbes Hire tens aR ema 97
Gin}, SSR ECOnGS., 4 55565 saab a cole Gio DEeeeno Oe Renee nec enone ct eee aC 98
86. The Determination of What Constitutes a Merchantable Log............ 99
Sie Grades of mumberand yogi Gradesmanee ar cmiciec «6 hii eel eran ere 103
CHAPTER VIII
THE SCALING OF DEFECTIVE LOGS
88) Deductions from Scale for Unsound Defects... 04 02.02. e eee dees 105
oe Methods or MakingsDeductione i lite 2 os sae cca eats cn sed Beers sae 3 105
90. Effect of Minimum Dimensions of Merchantable Boards upon these Deduc-
CLOT SH rates Scene ee tear vy nema scoters Aah Sond ahh ofansns lidishan's tolls aM) iia! alesirsc 43 107
O api GerioruD elects: am mae tascam ices cen sea eek ete tar tterere ec Sess oiete's wtln hs sens 108
DAP XUeTIGKSELCC Ab cn eccyercte yap te olor eye choi ote Figrils scsitiays te sien ar uaye vie we ebe vies « 113
SC EOOKA OLS WEC IIs se irae tee tne ays ain var hatin ral NOs Want eis-s apete aia eevee lh oe 116
Beam eO HE CHaNS CH lin py atm aya ee ean men aPee re a anedasee cate doce one ei Gia yd aha bie Ute k's 117
Sout Scalinpifromybher stump aera ore cote eee cle etettnle care otis Halon 118
96, The Scalers. ......:.5+5; a meen iea Leet IEE S Mil ee hoe a 119
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TABLE OF CONTENTS
CHAPTER IX
STACKED OR CORD MEASURE
PAGE
Stacked Measure as a Substitute for Cubic Measure................... 121
The Standard Cord versus Short Cords and Long Cords................ PA
Measurement of Stacked Wood Cut for Special Purposes................ 122
Effect of Seasoning on Volume of Stacked Wood....................-.- 123
Methods of Measurement on Condwoodssen sca eee oii eiicee meer 123
Solid Cubie Contents ‘of Stacked Wioodisa-a- seas ants nee ele eee 124
Effect.of Irregular Piling on Solid Contents. 20. e005 os is) «eee ss = wi 124
Effect of Variation in Form of Sticks on Solid Contents................ 125
Effect of Dimensions of Stick on Solid Contents....................... 126
The Basis for. Cordwood ConvertinesHactors. »- os 2 snes oe eee oe eee 127
Standard Cordwood) Converting: Hactorss .4 ees -aeieie sete lee Bee As)
Converting Factors for Sticks of Different Lengths..................... 128
Converting Factors for Sticks of Different Diameters................... 129
The Measurement of Solid Contents of Stacked Cords. Xylometers..... 132
Cordwood Log Rules. The Humphrey Caliper Rule................... 132
Discounting for Defect im Cord Measure. oi 06.6) a). hs mies <i ee 133
The Measurement otebanksnn yerceeacierae orice aisranl uals sorete icile-kea eeeeee tee 134
Factors for Converting Stacked Cords to Board Feet................... 135
Weight as a, Messure of Cordwood @..)). 020... os. « je cack oe ei ee 137
Part II
THE MEASUREMENT OF STANDING TIMBER
CHAPTER X
UNITS OF MEASUREMENT FOR STANDING TIMBER
Board; Feet—Basis of Appliention: warace o.c.: os 2s sally cfeve occas ee 139
4D aYeWel Selec) RRL SE Ace Sear 22 5 d.o-a bitke clos haktieod aa Rdcncn aioe ga Gr So, c 140
Choiceiot Unitsanekistimatmnomlimbersneee eee ay eiatice eee a eae 140
The Log as the (Unit ime Bismimianias se oe ein ciate cect ate. ¢ efelalens el cys!s Shots eee 140
Teg Run, or, Average Log Methods tae) haa. am ak. 6. ua sls eee 143
The Tree as a Unit in Estimating. Volume Tables..................... 144
Volume Tables Based on Standard Taper per Log. ‘Universal’? Volume
TAD IGS oa oo in nic Se eas os SS ee 144
Substitution of Mill Factor for Log Rules in Universal Tables.......... 146
Volume Tables Based on Actual Volumes of Trees..................4.+ 147
The Point of Measurement of Diameters in Volume Tables............. 148
Bark as Affecting Diameter in Volume Tables......................0. 150
Classification of Trees by Diameters .\....) 05 thie cise - oe eine olen ee 151
Classification of Trees by Height................ PN ero. ers Nay Se era Til
Diameter Alone, versus Diameter and Height, as Basis of Volume Tables... 152
Standard’ versus wuocal: Volume: Tabla 2.5.0.5 oi sc eee cls cles cee erscins 153
CHAPTER XI
THE CONSTRUCTION OF STANDARD VOLUME TABLES
FOR TOTAL CUBIC CONTENTS
Steps in Construction of a Standard Volume Table..................... 154
Selection of \Treesor Wleastmemen te queries aiehati orien reieteteieie resi ae 154
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TABLE OF CONTENTS xi
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REMIT COME COL iss atin te corn ety hasnt seins low FNAL ive ent wed leeds 155
Measurements of the Tree Required for Classification.................. 156
Measurement Required to Obtain the Volume of the Tree. Systems'Used. 158
Computationvotmvolume: of the: Wneens i. 2... ee ee ace de es oie 161
Classification and Averaging of Tree Volumes According to Diameter and
eronity © la SSesrieas ricpaces oskadoteccicncssests eacielee ca suehsas cts ais sane avert MUR 163
The Graphic Plotting of Data—Its Advantages.....................0.5 166
Application of Graphic Method in Constructing Volume Tables. ........ 169
Harmonized Curves for Standard Volume Tables, Based on Diameter.... 169
Hanmonized unvessbasea on Eleiohitpmr sa cee. ser. aus s ee eens ee 170
Local Volume Tables, Their Construction and Use..................... 174
The Derivation of Local Volume Tables from Standard Tables. ......... 175
Volume Tables for Peeled or Solid Wood Contents..................... 176
CHAPTER XII
STANDARD VOLUME TABLES FOR MERCHANTABLE
CUBIC VOLUME AND CORDS
Purpose and Derivation of Tables for Cubic Volume of Trees........... 177
Branch woo dor sapwood Marc.) spe ae Sia ete Arete eevee nites co ae Wa
Merchantablepliamithiny ops and rat Dib vot nyonerecie snles 22 see 5 eee 177
SMM Cp Mh ee teed Prine Manet. ht Ae URNA 4. 5 SohaS tel aAMORTE c Soe ao 178
Mierchantablewjersus! Usedsenethe on 2 22s st cesemied ss Secs seceees 178
Waste, Definition and Measurement... 00.6565 5 Go. chic els soe clade ees 179
Wekee trom @ tills sh ok Ca gers hoe pe MRE ISR Ars SN USNs ae eae BRAN. Sis rs5 179
Conversion of Volume Tables for Cubic Feet to Cords.................. 180
CHAPTER XIII
VOLUME TABLES FOR BOARD FEET
The Standard or Basis for Board-foot Volume Tables................... 182
ACdopbionsolmansuandand Lope ihenothel ras s).)< «sie eieientere ice tinctonre 182
‘op, Diameters. ixed) or, Variable Limite (0... 0... bei eee PSO! 183
Welective UTreests WessunememGer cs icles, iicitsis, 0,0 eter ame 184
Total versus Merchantable Heights as a Basis for Tree Classes.......... 185
The Coérdination of Merchantable Heights with Top Diameters......... 185
Construction of Board-foot Volume Walbles .a\:)... 2.6 )sies aes edocs ecccen. 188
Data Which Should Accompany a Volume Table. ..................... 188
Checking thetAccuracy-of Volume Tables. of Ss. ee. ee 189
_CHAPTER XIV
VOLUME TABLES FOR PIECE PRODUCTS, COMBINATION
AND GRADED VOLUME TABLES
Volume.Vables for Piece Broducts:. p02). )ssics ow sche SS ee ly) 191
Volume Da blestoraiondiCross Mies ii. e000), eee Ben 191
Combination Volume Tables for Two or More Products. ............... 193
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TABLE OF CONTENTS
CHAPTER XV
THE FORM OF TREES AND TAPER TABLES
PAGE
Hormas a Lhird HactoreAttechne@Volumemon eos ececeie esse eects oe ane 196
®aner Tables, DefinitionjandsPurpose: «25 ec. a aeiwas « aiete aes he cele ssc s ws: = <0 197
Methods: of Constructing Maper Wables nae .- 2 on. ce semen s oe nitenin ss 197
[Mimitationsior laperslalblesemun erat cece eiceet a reciciec cio ice rela he ise 204
CHAPTER XVI
FORM CLASSES AND FORM FACTORS
The Need for Form’ Classes:in’ Volume Tables... ....-..25..0.----.2-- 205
Form Quotient’ as the Basis of Form Classes. ...............-.-.-0+00% 206
Resistance to Wind Pressure as the Determining Factor of Tree Form.... 208
AuGeneralitonnilla Torelnece sO lime i eeieice mratiitcas aici terrain ieieeciene 209
Applicability of Hoejer’s Formula in Determining Tree Forms.......... 210
Hormel vetOrs fda eet caksec Some oct eee Sis eve wiclelewa ata eat aA crepe tereneper areata 211
The Derivation of Standard Breast High Form Factors................. 213
MerchantableHormebactorse a -sreeeeiea: ea acc ee ieee ate ete 214
Blonmelei oh Genetic tecie, cee Roep eres ree ic oe tke itn eek ee eee 215
Form Classes and Universal Volume Tables as Applied to Conditions in
(Amaeric:,”, inet eke eee Re tee PER ITOREN eRe 215
CHAPTER XVII
FRUSTUM FORM FACTORS FOR MERCHANTABLE
CONTENTS IN BOARD FEET
The Principle:of the Prustum (Horm: Pactor = 2:5 26.225 esis Ge ee cis aoe oe 218
Basis of Determining Dimensions of the Frustum...................... 219
Character and Uiility, of Hrustum) Horm) Hactors\)--- sere... - +... aces 219
Caleulationiof thes Prue mrustumeHorm Hactorenrs. a. cic. oe oases 221
Calculation of the Volume of Frustums. Influence of Fixed Versus Variable
Top Diameters... ... 2 Gan Me yer moe tate SRE: Gees 2 ne ou ete eee 221
Construction of the Volume Table from Frustum Form Factors. A Short
Cuts Miethod!.ae) occa eee bra Oris cs ook Sens foo Ae eee 224
Other Merchantable Form Factors for Board Feet.................... 225
CHAPTER XVIII
THE MEASUREMENT OF STANDING TREES
The Problem of Measuring Standing Timber for Volume................ 226
The Measurement of Tree Diameters. Diameter Classes. Stand Tables.. 227
Instruments for Measuring Diameters. Calipers, Description and Method
OLFUSC8 ois cet ee ey Aen etc foetal noe tO ee 227,
ihe (iam eter Mapes aac m sete cies eters, check, Suatevntae Ayers owls conte lee 229
The =Biltm ore:Sticks We Wee Ok nee ne eras Seog Sacer p aaa 2 a 230
Ocular Mstimationsotelrees Dimensions sein eaeeeeeenic reas cee 234
ANita IM (args omy OT JEG, oa gcunde. seaueoeascuboaddundcoppeet ccc 235
Methods Based on the Similarity of Isosceles Triangles................. 235
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TABLE OF CONTENTS xiil
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The, Principle’ of the Klaussner Hypsometer.........5.............4. 00% 236
Methods Based on the Similarity of Right Triangles................... 238
Hypsometers Based on the Pendulum or Plumb-bob................... 239
‘whe Principle of the Christen Hypsometer.. ..:. 10.00.00... .a coe ke he 243
athe yechnique of: Measuring Heights .).0.22...... 0°44 225548 el ae 245
The Measurement of Upper Diameters. Dendrometers................. 247
Mnerlsiltmore: hacmymeters <);.o00 se the SALON ae a ee en ae 248
The d’Aboville Method for Determining Form Quotients............... 248
The Jonson Form Point Method of Determining Form Classes........... 249
Rules of Thumb for Estimating the Contents of Standing Trees......... 251
CHAPTER XIX
PRINCIPLES UNDERLYING THE ESTIMATION OF
STANDING TIMBER
Factors Determining the Methods used in Timber Estimating........... 255
Direct Ocular Estimate of Total Volume in Stand..................0.. 256
Actual Estimate or Measurement of the Dimensions of Every Tree of
MERCH Amba OLe OIZe Mn Meer SS yeyn bss 5 oly ays ae a lale ehare da aah Se Ne ves 257
Estimating a Part of the Timber as an Average of the Whole........... 257
The Six Classes of Averages Employed in Timber Estimating. .......... 258
The Choice of a System for Timber Estimating, with Relation to Accuracy
GUE LEE STUI NSH e Gs he RA oh Ge EN i gL er oa A 261
Relation between Size of Area Units and Per Cent of Area to be Estimated 262
Degree of Uniformity of Stand as Affecting Methods Employed.......... 265
CHAPTER XX
METHODS OF TIMBER ESTIMATING
The Importance of Area Determination in Timber Estimating.......... 267
The Forest Survey as Distinguished from Timber Estimating........... 268
Timber Appraisal as Distinguished from Forest Survey................. 269
Forest Surveying as a Part of the Forest Survey....................... 270
ithe Cull Factor,or: Deductions for Defects... .... 0. 608006. oe). 271
otal. or LOO Per Cent Hstimatess 20204 020.0... i See 271
Estimates Covering a Part of the Total Area. The Strip Method........ 273
BactorssDetermining the Widthvor strips se ee else. ia 274
Method of Running Strip Surveys. Record of Timber................. 276
ving inthe iscrips:, “The Basedianes) 60". Sos. Ni ade eh clin ot adele eh 281
Systems of ouip Hstimatng in Weert. oo. ent sv eects oe. hae one! 282
Methods Dependent on the Use of Plots, Systematically Spaced......... 285
CHAPTER XXI
METHODS OF IMPROVING THE ACCURACY OF TIMBER
ESTIMATES
Phe Use of “Morest: Lypes im Mstimating 60) .05. lak fe. lS 288
Method of Separating Areas of Different Types........................ 290
Site Classes and Average Heights of Timber...................000005- 291
XIV
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256.
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258.
259.
TABLE OF CONTENTS
PAGE
Methods of Estimating which Utilize Types and Site Classes. Corrections
TOT ATCS os isc 35 cea Bote tege Ue eR Mee neta A Seen oe fe ce Re 292
he Use of Correction|Kactorsiftor,Volumeyces Ay.)..~ 5 soe th ees oo oe 293
Methods Dependent on the Use of Plots Arbitrarily Located............ 297
Hstimatinge the Quality/of Sstandime, Mimbers asa. sc cienesee cleo ee 6 che 297
Methodof MillaRunvAppliedstosther stander seit ae 299
Method of Graded Volume Tables Applied to the Tree................. 299
Method of Graded Log Rules Applied to the Log...................... 299
Combination Method Based on Sample Strips and Log Tally............ 300
Limits: of Accuracy in ‘Timber Mstimating 020.0651 2.652 teens oe 301
The CostioMbstimatineaimbery-s reece eee oe eer ene 302
Methods of Training Required to Produce Efficient Timber Cruisers... . . 303
Gheckistimabin ery estes panessvects setae ont oreice tie chee ee eee eee ete 308
SuperticaliorsbixtensivesMmstimavesher crac eiehyae ees ieee sel bacteenels ie) lec 308
Estimating by Means of Felled Sample Trees......................... 310
Method of Determining the Dimensions of a Tree Containing the Average
Beard-toot, Volume.) ./) We Uckt setae «occ ae ems cee Fee ee 311
The Measurement of Permanent Sample Plots........................- 312
Part III
THE GROWTH OF TIMBER
CHAPTER XXII
PRINCIPLES UNDERLYING THE STUDY OF GROWTH
PAGE
Purpose and Character of ‘Growth Studies. 9.0.0.0... 022s ones bans 315
Relation between Current and Mean Annual Growth.................. 316
hetCharactemor Growea ber Gents ae ese. ou 8 Ac nts Doe oP cic wee 318
The Law of Diminishing Numbers as Affecting the Growth of Trees and
OUT AIS [Sh ay ONE TEtetth O's Gerad cain ta + ts a ee aoe or, 318
Yields: Definition and ‘Purpose of Study : 2.2.4 522. «5 cs cee oe oO 320
BAe) (GRA be oN ee teeetnalia de os aio oo ic OO eee eC occ oho 321
The Application of Yield Tables in Predicting Yields................... 322
Prediction of Growth by Projecting the Past Growth of Trees into the
HID bl hae Neen PePCIS hu. ol occ e ohn fa eee an OREO EAE ie Ss cr ols CRG Toro 323
The Effect of Losses versus Thinnings upon Yields..................... 324
The Factor of Age in Even-aged versus Many-aged Stands.............. 325
The Tree or Stem Analysis and the Limitations of its Use.............. 326
Relative Utility of Different Classes of Growth Data, and Chart of Growth
pobidies 517: ois ais ates areas eect oe ass helenae shite atu iiesteays 3-2 d uate 327
CHAPTER XXIII
DETERMINING THE AGE OF STANDS
Determining the Age of Trees from Annual Rings on the Stump......... 335
Correction for Age of Seedling below Stump Height.................... 336
Annual Whorls of Branches as an Indication of Age.................+-- 337
Definition of Even-aged versus Many-aged Stands...................-. 337
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285.
286.
287.
288.
289.
290.
291.
292.
TABLE OF CONTENTS XV
PAGE
Average Age, Definition and Determination............0cceceeeeeeeees 337
Determining the Volume and Diameter of Average Trees............... 338
Determining the Age of Average Trees and of the Stand................ 339
Age as Affected by Suppression. Economic Age...................205: 341
CHAPTER XXIV
GROWTH OF TREES IN DIAMETER
Purposes of Studying Diameter Growth, 2... 4......5. 52252 sdece cece. 342
The Basis for Determining Diameter Growth of Trees ................. 342
The Measurement of Diameter Growth on Sections.................... 342
The Determination of Average Diameter Growth from the Original Data. 346
Correction of Basis of Diameter Growth on Stump to Conform to Total
FANG CTO IMR CE epee penn raise. eee MET ve PE A acter heat Ave, din cics od evermore te 348
Correlation of Stump Growth with D.B.H. of Tree..................... 348
Factors Influencing the Diameter Growth of Trees Growing in Stands.... 351
Hitect of Species on Diameter Growth. .......05.0 00. ee kee ee ee cee 351
BitectrotOualitvicololterey are tire are cease ey ore tieie ke ores votete oeeree 352
Effect of Density of Stand................ be PONE eg Re mA A 352
Effect of Crown Class........: Ast RS hes Eh CER Ses etd MN ae Oat _. 353
Laws of Diameter Growth in Even-aged Stands, Based on Age........... 354
Laws of Diameter Growth in Many-aged Stands, Based on Diameter..... 357
Current Periodic Growth Based on Diameter Classes. The Increment
TS ORCL P eye cue Ree a Nee Ars Recess score heeueas ES cuepeh ere acai eaete hee eae 358
Method Based on Comparison of Growth for Diameter Classes.......... 360
Method Based on Projection of Growth by Diameter Classes............ 361
Increased Growth, Method of Determination......................... 363
CHAPTER XXV
GROWTH OF TREES IN HEIGHT
Purposefof onmpomiecmrht: Growthisd.. oe. s44 ale y Se Gets cad 365
influences sAtiectingubeight iGraybhe 92/58 h aide o).\./2 0 galve Sele cio ewre cee: 365
Relations of Height Growth and Diameter Growth..................... 367
Measurement of Height Growin oo «cs: oe sss soe odelagnanee seek clas 368
The Substitution of Curves of Average Height Based on Diameter for
Actual Measurement of Height Growth.......................-0c0ee 371
CHAPTER XXVI
GROWTH OF TREES IN VOLUME
Relation between Volume Growth, Form and Diameter Growth. ........ 374
Tree Analysis, its Purpose and Application..................60.2.0000. 374
Substitution of Volume Tables for Tree Analyses. ..................... 375
Measurements Required for Tree Analyses.................2.0.-eccees 376
Computation of Volume Growth for Single Trees. ...........5.......... 377
Method of Substituting Average Growth in Form, or Tapers for Volume.. 379
Substitution of Taper Tables for Tree Analyses........................ 382
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316.
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318.
319.
320.
321.
322.
323.
324.
325.
326.
TABLE OF CONTENTS
CHAPTER XXVII
FACTORS AFFECTING THE GROWTH OF STANDS
PAGE
Enumeration of Factors Affecting Growth of Stands.................. 384
Siteshactorsion Qualitviolasitesre eee eae ce oe aoe 384
Volume: Growthia Basisiorsine @ualitiessamer: ier rieeae ne ain 385
Height Growth/a, Basis for Site! Quallities.y.:..¢- 5.352): one te le 386
Other PossiblesBasesmonisine Qualitiesseseriet eee een ae ieee 387
The Form of Stands, Even-aged versus Many-aged.................... 388
Annual Ineremention Mamy-aredy Stands nels =e eee ie eerie 390
the tHitectiot) ireatmentionkGrowthlanasececr eters eo en eee 391
Density of Stocking as Affecting Growth and Yields................... 392
Composition, of Stands asito Species). . icc... .¢b es oes eee 393
CHAPTER XXVIII
NORMAL YIELD TABLES FOR EVEN-AGED STANDS
Definition,and urposerote wield Pables-ciss:.+ 2s eo eee eect 395
Standards for Vreld:ulables:: etre ian. voi stot be ee ee Cee 395
Construction of Yaeld- Tables; Baur’sMethod....). 2.5. o eee 396
Standard tors Normal 2 WensityaGi stockings cera: scene eee nee 397
A pevClASSes tiers cititha ne becsesoregae hs SMBS cece cao ate Shu bd ier ocean ee 397
Area ol) Plots ayia tin eis ac Aha ee este heeke psa eicts eatcase slaene Ie ene ee ee 397
Measurements) Requiredton Hacht Blot-s.5--- 2.) ee cee ee ae 398
Construction of Yield Table, with Site Classes Based on Height Growth.. 401
RejectionvorAbnormalselotssorpericcsy eee: coe cee oe OEE 404
Construction of Yield Table, with Site Classes Based Directly on Yields
DCEPACTIER Ha tctenesat erst shakes ia ce ebecere tate a ye aise reuietn Mestre tolls nee i ete 406
Yield Tables for Stands Grown under Management......,............. 407
Yield Tables for Stands of Mixed Species............... Klis ae 408
CHAPTER XXIX
THE USE OF YIELD TABLES IN THE PREDICTION OF
GROWTH IN EVEN-AGED STANDS, WITH APPLICA-
TION TO LARGE AGE GROUPS
Factors Affecting the Probable Accuracy of Yield Predictions........... 412
Methods of Determining Actual or Empirical Density of Stocking....... 413
Application of Density Factor, in Prediction of Growth from Yield Tables 414
Separation of the Factors of Volume, Age and Area.................... 416
Determination of Areas from Density Factor.......................00. 416
Application to Forest having a Group Form of Age Classes............. 418
Determination of Volume and Area for Two Age Groups on Basis of Average
BCC TOI 8 ene ARM nua ee RAN chy Fitch are ae AS RE EER bs Sc 419
Application of Results to Forest by Use of Stand Table and Per Cent.... 421
Determination of Volume and Area for Age Groups on Basis of Diameter
GLOWS Sie ne Oe RT aero ok i Sacco eae 422
The Construction of Yield Tables Based on Crown Space, for Many-aged
Sbarids, "2. eee Seen Meee wae poet amie ee eiccas tity dates Sie na os 422
Application of Method to Many-aged Stands.......................... 425
Yield Tables for Stands Grown under Management.................... 427
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TABLE OF CONTENTS XV1L
CHAPTER XXX
THE DETERMINATION OF GROWTH PER CENT
; PAGE
WetmitionvonGrowthewer Cente. 2s se aisg case +s corse Was ca sieta says. sco shops 429
Pressler’s Formula for Volume Growth Per Cent ...................... 429
Pressler’s Formula, Based on Relative Diameter...................... 430
Senneider/s Honmulastormstandinelbreesma\- secon see eae ee oe cle 431
Use of Growth Per Cent to Predict Growth of Stands.................. 432
Use of Growth Per Cent to Determine Growth of Stands by Comparison
Waihi Viea sured ela] OESiee cen esus teenie mem eno coats eis. Svcd MeTR ASRS ease 433
Use of Growth Per Cent in Forests Composed of All Age Classes......... 434
Growin ber Centiin, Oublity and’ Values; 5 fics. os cc ecsins cs Sere one e's 435
CHAPTER XXXI
METHODS OF MEASURING AND PREDICTING THE CUR-
RENT OR PERIODIC GROWTH OF STANDS
Use of Yield Tables, in Prediction of Current Growth.................. 436
Method of Prediction Based on Growth of Trees, with Corrections for
VOSS CS ae te Wet eae mR ne ce cei eos en RE RE | ten) SUS by SE a 436
inercased: Growth of stands after Cutting)... 62s.25 joe. ce ah syys's Smee g 438
Reduced Growth of Stands after Cutting... 25 ..02 5.00.2 e ee ec 438
Application of Yield Tables Based on Age, to Cut-over Areas............ 441
Permanent Sample Plots for Measurement of Current Growth........... 443
Measurement of Increment of Immature Stands as Part of the Total
igerement) ola Honest OT erlOd 4055. eo ones bigs ee Woes oul est es 448
Comparative Value of Current Growth versus Yield Tables and vies
PRTETUNT RG TOW ULM rs eerie ote tary Suni Ge asieteea ce MGs hes a he ee as 445
CHAPTER XXXII
COORDINATION OF FOREST SURVEY WITH GROWTH
DETERMINATION FOR THE FOREST
Factors Determining Total Growth on a Large Area.................4.. 447
Data; Required from the Worest Survey. <j .02.. <6 055.06 9. 2 aelee eee can 447
Site: Qualities; SeparatiominsWielWens ce...) 5a adatoms on ee eels 448
Relation between Volume and Age of Stands..................00000 eee 449
Averaging the Site Quality for the Entire Area....................000. 449
Growthron Areas of Immature Wimlbers. 262.2. <4 ase8. Wedel. bles 450
Effect of Separation of Areas of Immature Timber on the Density Factor
fOVANIS GmNe SGA GS). } Os Nese ie eats Sh. ee ees Pdkl asec ba Mawes. ws 453
Stand Table by Diameters for Poles and Saplings; When Required....... 454
APPENDIX A
LUMBER GRADES AND LOG GRADES
rrase aly Wor nGradest ewer certs niece Atte See savaisya kb ockis/aww nes cal ome date 455
Grades ofsliimmber st < itis store tins iis wes SOC SE OCORIes Soe r cre 455
[SVS TE! oy bitbael a) Gyro SS sey esnly f ea d e 455
XVIll TABLE OF CONTENTS
354.
355.
356.
357.
358.
359.
360.
361.
362.
363.
364.
365.
366.
367.
368.
369.
370.
PAGE
Grades for Remanufactured and Finished versus Rough Lumber........ 456
General Factors which Serve to Distinguish Lumber Grades............. 456
Grouping of: Grades of Rough bumber. 2.54 aas ee ns oe se es vee AO
ldprenyaayoyeroye Crepe lhayea lulls. ood ok oneasav ccc oo gaustaeneooodeadenod’ 457
Relation between Grades of Lumber and Cull in Log Sealing............ 458
oct Grades Determinationer ern Mor hyacr orci ater ert eran cee 459
xemples of og Grades se gots teen ie oor ase eet pape iii arc ne 460
Malll-oradevor:)Muill-scalers GUCICS een rrmret apes treats nee ene 461
Method of Conducting Mill-scale Studies.......................00c000- 462
APPENDIX B
THE MEASUREMENT OF PIECE PRODUCTS
Basia of Meashremonte 4) eche mrp Sea Wye erin Sit ee gee eed an ee 466
Round Products ss ia ever (ect ad oth ed ee Ne RE Dae eee ee ae 466
Roles. ace epee bas ea tc bee eee ee Lele re Eas ae ane 4 467
| ilar are emer era "EGE hae near @ ey RU MMENUDE eM TOR A) 470
Bostswltsrge Postssanc oma llWPolesn seis 2 eine pen cee ce eta 471
Winey mma ens ft oes eis ato ieee Ie eee one See ek oe eet ee 473
Cross Mies or Measles EAS awe he oh ee A at cS a eR 474
Inspection and Measurement of Piece Products.....................05- 477
APPENDIX C
TABLES USED IN FOREST MENSURATION (see Index of Tables) 479
APPENDIX D
BIBLIOGRAPHY ety suis nyse ox ce So erceme oie eeieiets Sfclavolajevels 6)6. s/s weve neat 521
ARTICLE
32
38
41
No.
i
Il
TABLES
TITLE PAGE
Comparison of Results Obtained by Scaling the Cubic Con-
tents of Logs, at Small End and at Middle of Log........
Comparison of Per Cents of Cubic Contents of Cylinders
Scaled by Various Log Rules, for Logs 18 Inches in Diam-
eter at Small End, with 2-inch Total Taper..............
Relation of Cubic and Board-foot Contents of 16-foot Logs
' with a Taper of 1 inch in 8 feet, Based on Tiemann’s Log
Rules eee Mn SAWN Cll mite met seycyld ne ee ph oie spvsirenn os Slane
Comparison of Blodgett and Tiemann Log Rules for Cer-
Effect of Different Methods of Scaling a Log...............
Gain in Output Secured by Sawing around Compared with
Slash Sawing in Per Cent of Latter Output...............
Distribution of Waste between Slabbing and Sawdust.......
Thickness of Plank to be Deducted for Slab Waste to Coin-
cide with a Collar 1.5 Inches Thick. Sawdust Allowance
PAD ARE OC CIS TG Geen cae knoe gee Re eo oe ae eee ee
Deductions for Slabbing and for Saw Kerf, for 12-inch Logs,
in Ten Log Rules Based on Formule.....................
OV errno mle sles CSAS. Nr tate cc tat qcletiy oes socks ae
Overs, Doyle ale, Ontario. iss sis uae. skalestaerce re
Decimal Values below 12 Inches, for Scribner Log Rule..... .
Conversion of International Rule 1-inch Saw Kerf for Other
NIAVLG UY TEMS) i ES SR Pe gh
Conversion of Log Rules with 4-inch Saw Kerf and No
Shrinkage Allowance to Other Widths of Saw Kerf........
Per Cent of Increase in Sawed Lumber Caused by Sawing
Lumber of Different Thicknesses. ..............2...02..0%
Correction in Per Cents for Contents of Logs in Superficial
Board Feet, for Lumber Sawed Less than 1 Inch in Thick-
Scaling Practice, or ‘Scale’ in Different Logging Regions. . .
Dedwetions for Crooks or Sweep. 2. ssyote ere ores gan “ers ow ak
polid: Contents of Stacked Wood! 5. cc ay.nisere s cto sain co.o oi
Standard Converting Factors for Cordwood................
Influence of Length of Stick upon the Solid Cubie Contents
Influence of Length of Stick on Solid Cubic Contents of a
StandardyCord. (balsam Wines oo. vids ec ui sinves Seu occ os oe
Interdependence of the Stick Length and the Volume of
Sold Woods per Cord) (Me oe ooc6.0 5.5 oss scene he cece es
XIX
27
37
41
XX
ARTICLE No.
109 XXIV
112 XXV
123 XXVI
137 XXVII
139 XXVIII
1440 XXIX
141 XXX
142 XXXI
152 XXXII
168 XXXIII
XXXIV
183 XXXV
184 XXXVI
XXXVIT
191 XXXVIII
XXXTX
203 XL
220 XLI
224 XLII
XLII
228 XLIV
238 XLV
240 XLVI
246 XLVII
249 XLVIII
250 XLIX
257 L
266 LI
269 LII
TABLES
TITLE PAGE
Solid Contents of a Standard Cord Based on Diameter of
Stick. ° ‘Average4-toot Woodica.25. OSGeo to. ones eee 131
Measurement of 4-foot Round Spruce Pulpwood, with Cull
Factors Based on Solid Cubic Contents................. 134
A Portion of a Volume Table Based on Mill Factors. ....... 147
Preliminary Averages for Pitch Pine. Volume Table Based
on Diameter and Total Height. 139 Trees............... 165
Comparison of Original and Harmonized Average Volumes.. 171
Volumes Read from Curves of Volume on Diameter for
Ditierent., Heiont Classes: . hua. aie ec dee oor eee 7%
Standard Volume Table Read from Curves of Volume on
Height for Different Diameter Classes................... 174
RocsliVolumie JE alale SRGOniua) sre ose cr tac bieue Brake eee ae 175
Conversion Factors for Second-growth Hardwoods by
D.B.H. Classes with Corresponding Diameters of the
Average 4-foot Stick in the Tree or in the Stack.......... 181
Form or Taper for White Ash Trees of Different Diameters
under 75 Years of Age, Giving Diameters Inside Bark at
Different Heights ab@ve Ground...:..............-..5) 198
Tapers*ot Loblolly Pine, Two Trees... 22... 2% occ eee 199
True Frustum Form Factors for Longleaf Pine, from Frus-
tums whose Top Diameter Coincides Exactly with the
Average Top Diameters of Trees of Each D.B.H. and
Hicighti Glassen Jonna ert tae tre us « oheeae athe seh eka 222
Frustum Form Factors for 555 Longleaf Pines, Coosa Co.,
Alabama. Based on Average Top Diameter of 13.2 Inches
for Hrustumis) 5) ies. cts odin Ris fot nis: <ysantesete eA Cte vee 223
Actual Average Top Diameters of Merchantable Lengths,
Longleaf Pine, Coosa Co., Ala. Basis 555 Trees. Average
of all “Kop Diameters: 43.2 )0NGhes, «S/o: ois 0s aoe ee 224
iDingovas) sua [Ufssveves 1Billnaaerrs Sins 4 ogovcodoes dodo aeobot soo 5< 232
Figures to be Used in Graduating a Biltmore Stick........ 233
Table for Determination of Form Class of Trees by Means
OMPositionvoleHormeeomtene: aoe ene ie ee eee 250
Relation of Width and Number of Strips to Area Covered. . 274
Sizes of@imenlartPlobse... oc: 2 cr. c-c\as so oaths moe eee 286
Relation between Plots and Area Covered................ 286
Per Cent of Total Area Required in Estimating........... 292
Comparative Estimates of a Tract of 40 Acres. Board Feet. 304
Estimate of Taylor’s Creek Logging Unit, Blooming Grove
‘Eract» Pikep@o.W ba NOU ce fe neta cs tte ads) 309
Growthot Jack Pie. sVimmesotay. . 050 ise. =. os aloe 318
Yield Dable for White "Pines: esc cee. we hes | oa 321
Yield Per Acre of Spruce, Cutting to Various Diameter
] Baba RS} ee eis. Aen Va APRA cli Rado EMRE a 322
Height of Seedlings at Different Ages, Western Yellow
Pine‘ColfaxiCo.; New sViexicoy 2d ita e os lanes s = Ae 336
Diameter Growth of Five Spruce Stumps................. 345
TET gr ER eee reper getiiesstsas meats Deena teen cece een e ness ence 350
ARTICLE No.
LIII
278 LIV
279 LV
LVI
284 LVII
288 LVIII
290 LIX
296 LX
298 LXI
314 BXII
LXIII
324 LXIV
LXV
337 LXVI
339 LXVII
Appendix.
365 LXVIII
LXIX
365 LXx
LXXI
LXXII
LX XIII
LXXIV
366 LXXV
Si) 1D Oar
LXXVII
LXXVIII
TESXOXGIEXE
LXXxXX
TEAXGXeXGT
TABLES XXxl
TITLE PAGE
Growth of Loblolly Pine, Old Field, in D.B.H. Based on
Age Giiirees WUraminnlua. 1... acme Aas eet: 2 a2 bs sis: 350
Current Growth of Spruce, Adirondacks Region, New York. 360
Shortleaf Pine, Louisiana. Growth by Diameter Classes.... 362
Current Growth, Loblolly Pine, by Diameters............. 363
Height Growth of Chestnut Oak, Milford, Pike Co., Pa.... 371
Growth of Chestnut Oak in Cubic Volume, from Diameter
and Height Growth and Use of a Standard Volume Table 376
StempAmalysis obra: ree. Fath atcra'd’, ad cimdevate s aus Paleicre 378
Standards of Site Classification Based on the Height of Tree
ea tema MRD ORITS ape evomeuei apse wee Neuere srao) sian she dayspakene apeve arena Cercle’ eee 387
Average Crown Spread of Loblolly Pine in the Forest at
WA 36 (S10 VU 4 HAAN i ea Alea or ae ee 389
Normal Yield per Acre in Cubic Feet and Cords of Better
Second-growth Hardwood Stands in Central New England 409
Percentage of the Various Species.in Mixture from Table
LXII Classified as to Type and Site Class............... 410
Trees per Acre Based on Crown Space................... 425
Yields of Cordwood, for Yellow Poplar in Tennessee—
Based on Crown Space and Volumes of Trees of Given
JANES) 82 No ld ae eee We ee io as ee ee er 426
Adirondack Spruce. Average Rate of Growth in Diameter
on the Stump of 1593 Trees on Cut-over Land at Santa
Gilet NG WHOLE 15) SoS ue cle ita eakaake a jays 6 het canoes 440
Areas Remaining Stocked on Cut-over Lands............. 443
Relation between Circumference and Diameter for White
(Cle vg va) sh, Bae ahs ah, ae ee ce eg neny m e 467
Minimum Dimensions of White Cedar Poles in Inches,
Grcumiberence sGIASSeS |, 6: ccwls-n x ss qade Pllc eae c Som we 468
Minimum Dimensions of Western Red Cedar Poles in Inches 470
Minimum Dimensions of Southern Yellow Pine Poles in
inches @inemmlerence sas! heats hid sae eho ene Pa 471
Minimum Circumference of Chestnut Poles in Inches....... 472
Minimum Sweep Poles, Standard........................ 472
Mini misweepreoless Country... =... sceseeessssess 5 sc 473
DIMENSIONS OLN | Los. oh. ee tees caer el an ss 473
Board-foot Converting Factors for Various Products, U. 8.
OTESLRS CEVA CCE See MoI CE Pacsk oe sick che SHAR aI os bated ine 9 Se 478
Cubic Contents of Cylinders and Multiple Table of Basal
JN evENS ch Bs ig RENIN, TOD eT Toe he ee ae aoe 480
Areas of Circles or Table of Basal Areas for Diameters to
INGARESE SUCH ta rts ae seimers SAMs Se eee coisas ec 490
Tables for the Conversion of the Metric to the English
Sysbemmands Vice: Versa ayy sha ome liens ote S's tice on ge ls 492
The International Log Rule for Saws Cutting a Linch
LEGG Oe 2S AIAN Bin eo Aa ee en 493
Tables for Values in Schiffel’s Formula for Cubic Volumes
OMPMNTIREHSLEMS eae ea ree ie ces Cae ee le
XXl1
ARTICLE No.
LXXXII
LXXXIII
LXXXIV
LXXXV
LXXXVI
LXXXVII
LXXXVIII
LXXXIX
TABLES
TITLE PAGE
Breast-nichYhonmattactOrsen ss eee meee aie tienen ee 497
Weights per Cord of Timber of Various Species, 7- to 8-inch
MVCoXar0 Gates =F ac tet catia TRAE Ay ct lnkey dio ats NEC ae aie tee 498
Tiemann Log Rule for Saws Cutting a 37-inch Kerf....... 500
Tiemann Log Rule Reduced to Small End Diameters...... 502
Seribner Wecimai© LocsRulestass see eee eens ae ae 503
Indexeto Standard Volume-Uables#2.-arsene. sees: 505
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FOREST MENSURATION
Aura all
THE MEASUREMENT OF FELLED TIMBER AND ITS
PRODUCTS
CHAPTER) 1
INTRODUCTION TO FOREST MENSURATION
1. Definition and Purpose. Forest Mensuration is that branch of
forestry which deals with the determination of the volume of the wood
material contained in logs or portions of felled trees, in standing trees,
in stands of timber and in forests, expressed in terms of cubic measure,
board measure, or any other unit. It also determines the growth and
future yields of trees, stands, and forests in any of the above units of
volume. The measurement of standing timber is termed T%mber
Estimating or Timber Cruising. The commercial measurement of the
contents of logs is called Scaling.
Forest property is land bearing forest trees as the principal vegeta-
tion. The trees may be valued for their appearance, as in parks, their
protective influences, as in forests at headwaters of streams, or their
wood, as in all forms of commercial use, including by-products such
as naval stores and bark. In past logging operations the land has not
always been regarded as true forest property, capable of growing other
crops of trees; but unless such land has a higher economic value for
agriculture, grazing, or other purposes than for any of the three forest
uses above mentioned, it is as truly forest property as the timber.
The measurement of the volume and growth of timber is an indispen-
sable factor in classifying lands for their highest use, whether for agri-
culture or forestry.
Forest Mensuration makes possible the systematic management
of forest property by ordinary business methods, which require, first,
a knowledge of quantities or amount of material, and its location and
2 INTRODUCTION TO FOREST MENSURATION
rate of production,! and second, information on which to base the value
of the property for the purpose of sale, exchange or the appraisal of
damages.
2. Relation between Lumbering and Timber Estimating. The
logging of timber is usually conducted as a business venture entirely
separate from the growing of trees or management of forest property,
but whether this is so, or the forest owner cuts and logs his own tim-
ber, the cost of the logging will depend in a great measure on the known
quantity of timber which can be brought out over a given route and by
a specific method of logging. The greater the volume of standing
timber, the greater the investment which is justified in roads, railroads,
chutes, or flumes to cut down the expense of hauling. Overestimates
cause losses through excessive investments; underestimates cause losses
through not investing enough money in these transportation systems.
The logger cannot wait until his timber is cut and scaled before planning
his operation. Accuracy in timber estimating is therefore an under-
lying factor in the successful conduct of the business of lumbering.
3. Relation between Forestry and Growth Measurements. Lum-
bering as a business begins at the stump, while forest production may
begin with the seedling, and may well be considered as a separate busi-
ness enterprise. The growth of trees is the basis of returns on this
business, no matter whether these returns are secured on the stump, or
by means of the additional operation of logging. The speculator in
standing timber hopes to realize a growth in unit prices such as was
experienced as a result of the war. But the business of forestry depends
for its profits on growth, first, in volume, and second, in quality, of the
product by reason of increased sizes and improved texture, increase in
prices being merely an additional guarantee of adequate returns. Since
growth determines the quantity of products to be expected, any expen-
diture in planting and care of the forest can be undertaken intelligently
only when the probable rate of growth per acre is known. The study
of growth is therefore a necessary part of the business of forestry and
unless growth data can be obtained, there is no possible method of
.1 A business is an undertaking which seeks to supply a public demand. The
most common form of business is that which produces raw materials and transforms
them into finished products delivered as such to the consumer. Any distinct step
in this process may and often does constitute a separate business. To accomplish
the purpose of its existence, a business deals with three factors, quantity, location,
and time. To supply forest products for the innumerable demands of modern
civilization, a well-conducted business operation requires full knowledge of the
quantity of raw material and finished products with which it deals, their location,
and the time or periods when these quantities will be available. Forest Mensura-
tion is as fundamental to forest production as is inventory and merchandise account
to a mercantile business.
RELATION OF MENSURATION TO FORESTRY SUBJECTS 3
determining either the proper investments and expenses, or the probable
returns and profits from such an enterprise.
4. Relation between Forest Mensuration, Stumpage Values and the
Valuation of Forest Property. In determining the value of forest
property for sale, exchange, or the appraisal of damages, it is necessary
first to know what the mature standing timber is worth on the stump
previous to cutting. This is known as stumpage value. The stumpage
value of standing timber is derived from the value of the finished prod-
ucts and is influenced by four factors, namely, the species of wood,
its quantity, its quality, and the unit price of the product. Forest
mensuration by means of a forest survey determines as accurately as
possible the first three factors. By determining through an appraisal
the price of stumpage for the different kinds and qualities of timber
found on the area, the value of the timber may be found.
The value of young timber and of forest soil can be calculated after
the possible yields at given ages have first been approximated and the
stumpage value has been appraised for this final yield.
5. Relation of Mensuration to Other Forestry Subjects. The rela-
tion of Forest Mensuration to other subjects in forestry is shown in
Fig. 1. In the threefold division of forestry indicated, mensuration
falls in the mathematical or business group, but is included in the phys-
ical branch of that group which deals directly with the forest.
Mathematics is the basis of Mensuration, since the latter subject
deals primarily with quantities. But as both timber estimating and
growth data must usually be expressed on terms of area or acreage,
Mensuration rests directly on Surveying.
Mensuration in turn furnishes the quantitative data required by
the science of Forest Finance as a basis on which to compute the cost of
production and the probable returns from forestry and to indicate the
choice of methods to use in forest production. Although it falls in the
business group, and is a basic subject underlying Forest Management,
Mensuration is a statistical science similar to Forest Finance. Neither
subject constitutes an applied science, which is the characteristic of
Forest Management. Mensuration is therefore not a direct subdivision
of Management, but a distinct subject preparatory to Management.
6. Absolute versus Relative Accuracy in Mensuration. Forest
Mensuration attempts to secure as close an approach to mathematical
accuracy as the conditions of the problem, the use to which the data are
put, and the cost of the work will permit. In scaling, the volumes of
logs are determined before sawing, and in timber estimating, the contents
of trees and stands are obtained before felling. But no log rule will
give the exact quantity of lumber which will be sawed from a given
log, and no tree volume table can predict the output in boards from a
INTRODUCTION TO FOREST MENSURATION
given tree, since these results will vary with the methods and conditions
of sawing and of utilization.
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For this reason,
Again, in estimating timber it is seldom possible to measure every
tree, on account of the time and expense involved.
FOREST SURVEY 5
only an average portion of the stand may be measured. The laws of
averages, or of sampling are applied to solve nearly every problem in
Forest Mensuration, in order to bring the cost of the field work within
practical limits.
When Mensuration deals with the growth of trees and stands, and
of whole forests, its purpose is to predict what will occur in the future.
It bases these predictions upon the results which have occurred in the
past, under conditions judged to be similar to those which will affect
these future stands. The laws of growth of trees, and especially, of
stands composed of great numbers of trees competing with each other
for existence and supremacy, can only be approximated on the basis of
probabilities and averages. The results of living forces cannot be
predicted with mathematical accuracy, and the study of growth par-
takes of the nature of research rather than of routine measurement of
definitely determinable quantities.
Neither Forest Mensuration nor Forest Surveying produces any
physical change or improvement in the forest, as does the application of
silviculture, protection, and lumbering. The achievements of forestry
depend upon the amount and character of the actual work done along
these latter lines. Misdirected work, done at the wrong time or place
and in the wrong quantity, or by too expensive a method when com-
pared with results, means waste, inefficiency, and ultimate ruin and
bankruptey of the enterprise. The data supplied by mensuration and
supplemented by forest finance are the balance wheel of forest industry.
But the necessity of restricting the funds expended upon the mere col-
lection of data to as small a per cent as possible of the total budget of
expenditures, reserving the greater portion for the operations which
effect actual change in the forest, is obvious and justifies the use of meth-
ods based on averages rather than extreme mathematical accuracy.
7. Forest Survey. Forest Survey is the general term applied
to the project of gathering all the quantitative data required regarding
a specific forest property. It includes a survey and maps of the area,
thus locating the property and its subdivisions, a measurement of the
volume and character of the timber, and it may cover other resources
such as land classification, waters, forage, game, and fish. Forest
Surveying and Forest Mensuration deal with the principles and methods
of accomplishing this work. The Survey itself is the enterprise or
project of securing the data. Accuracy in the results of a forest survey
is judged, not on an absolute standard, but in relation to the balance
between utility of the results and the cost of obtaining them, and is
therefore always a relative term.
CHAPTER II
SYSTEMS AND UNITS OF MEASUREMENT
8. Systems of Measurement Used in Forest Mensuration.
Throughout the United States and Canada the English system of
measure is used in all practical applications of Mensuration. In the
Philippines the metric system is the standard. (Appendix C, Table
LXXIX.) Efforts to substitute the metric system in the United States
for the units established by custom have so far failed, though its use
was sanctioned by Congress in 1866. Mensuration is applied more
generally to the solution of practical problems such as timber estimating
than to purely scientific research, and for the former, the results must
be expressed in the customary units to be intelligible. Scientific forest
measurements have also, except in a few instances, been expressed in
English units.
In measuring distances and areas, the chain of 66 feet, or 4 rods,
is a commonly used unit. Five chains constitute a tally, or 20 rods;
and 16 tallies, or 80 chains, equal 1 mile. One tally forms the side of a
square 2} acres in area. Distances are commonly measured by pacing,
or counting the number of paces, the average length of the individual
pace having been determined by previous tests. A true pace is the
swing of one foot, or twice the length of a step. In counting, the pace
rather than the step should be used, since it reduces the count by half.
The acre, containing 160 square rods or 43,560 square feet, is the
unit of area. In the rectangular system of survey adopted by the
United States the following definitions apply:
Township—a tract approximately 6 miles square containing
36 sections.
Section—a rectangular tract containing approximately 1 square
mile or 640 acres, but which may contain more or less
than this area in irregular surveys.
Quarter Section—a subdivision of a section containing approxi-
mately 160 acres.
“ Forty ”’—a colloquial term describing a ;'5th section or quarter
of a quarter section containing approximately 40 acres.
Lot—a tract ordinarily containing not less than 20 or more than
60 acres, but which may contain less area, of either
6
PIECE MEASURE 7)
rectangular or irregular shape, and which takes the place
of the “forty” in irregular surveys or bordering lakes
or streams.!
In measuring trees, the foot is the standard for height, and the
inch, divided into tenths of inches, for diameter. Basal area is the cross-
sectional area of a tree or stand, in square feet, measured at 44 feet from
the ground. This is obtained from area of circles whose diameters equal
those of the trees measured.
9. Piece Measure. Wood products which are used in the round, and
logs or bolts which are barked, shaped, and reduced to standard dimen-
sions where felled, are usually measured and sold by the piece. These
pieces are graded by size and by quality into accepted pieces and culls,
or rejects, whose defects render them unfit for the special purpose
required. The standard sizes are determined by specifications, which
also prescribe the species of tree and the required quality of the product.
The principal products purchased on this basis are cross ties, poles,
posts, piles, and mine timbers.
Where bolts of uniform size are sawed or split for manufacture
into special products, they may be counted and paid for by the piece.
Their average volume is determined beforehand. When the number
of pieces per cord, or per thousand board feet is agreed on, the payment
may be in terms of these latter units.
Linear measure is sometimes used for pieces of standard width and
thickness but of variable length. Such products are sold by the linear
foot. This standard is widely used for piling.
10. Cord Measure. When the pieces into which trees are sawed or
split are of lengths shorter than ordinary logs, and of irregular shape,
the expense of determining separately the contents of each piece is
avoided by stacking them in regular piles or cording them up, and
measuring only the exterior dimensions of the stack to get the total
stacked cubic space occupied. This stacked cubic measure does not
indicate the solid contents, which may vary widely. But if the average
per cent of solid contents per cubic foot of stacked measure is known for
sticks of given sizes and character, this stacked measurement becomes
a practical and serviceable standard, though not well suited to scientific
investigations.
The cord is the standard generally adopted for stacked wood.
1 References. Manual of Surveying Instruction for the Survey of the Public
Lands of the United States and Private Land Claims, Commissioner of the General
Land Office, Washington, D. C., Government Printing Office, 1902.
Manual for Northern Woodsmen, Austin Cary, Part I. Section VIII, 1918.
Harvard University Press, Cambridge, Mass.
8 SYSTEMS AND UNITS OF MEASUREMENT
The standard cord is 4 by 4 by 8 feet, containing 128 cubic feet. There
are, however, other cord units in use (Chapter IX).
11. Cubic Measure. The cubic volume of trees and logs affords
the only basis of accurate and permanent scientific records, and a uni-
form standard of measurement. For this purpose the cubic foot should
be used as the standard unit.
Where cubic volume was employed by lumbermen, other cubic
units, whose contents were based on cylinders of given sizes, have been
adopted arbitrarily. These units possess no advantages over the cubic
foot (Chapter IV).
In most regions, the desire to express the contents of logs in terms of
sawed lumber prevented the adoption of the cubic foot as the standard
of measurement for logs.
12. Board Measure. Board measure may be defined as a cubic
standard for measuring sawed lumber. A board foot is a board 1 foot
square and 1 inch thick. Twelve board feet: of sawed lumber equal 1
cubic foot. The board-foot contents of sawed lumber is found by
multiplying the product of the width and thickness in inches by the
length in feet.and dividing by 12.
13. Log rules. A log rule is a table giving the contents of logs of
different diameters and lengths. The unit of volume used may be
based on cubic measure, or board feet. The latter form of table differs
from that based on cubic contents since it indicates only the net volume
of the product in boards which result from sawing the log. The use of
such log rules is to measure the contents in the log before sawing, as
a basis of sale of logs or for other purposes requiring such measurement.
Fixed or arbitrary values are assigned or agreed upon for logs of each
diameter and length. The table thus becomes a standard of measure-
ment based upon a unit of volume.
This method of measuring logs has consequently led to the develop-
ment of numerous log rules whose construction is discussed in Chapters
IV, V and VI. These rules differ, some of them greatly, for logs of
the same dimensions.
To secure the universal adoption of a single log rule which is at once
accurate and acceptable is probably an impossible task, and several of
the more widely used ones will no doubt continue as standards.
14. Measurement of Standing Timber, Postponed till after Manu-
facture. This lack of standardization as to units for board-foot contents
of logs inevitably reacts upon the accuracy and consistency of measure-
ments of the board-foot contents of standing timber. The contents
of a given stand will vary widely with the log rule used in estimating.
The custom of estimating standing timber in terms of the product
is not confined to measurement by board-foot log rules. Hewn. ties,
MEASUREMENT OF STANDING TIMBER IN THE TREE 9
poles, staves and other piece products are customarily used as units for
timber estimating, when the timber is to be used for these purposes.
Thus the standard commonly sought in America for measuring stand-
ing timber is the net merchantable volume, which results from deducting
all forms of waste in manufacture from the total contents of the tree.
There is but one accurate method of measuring this net contents,
and that is to postpone the measurement until the timber is logged
and manufactured into boards or other products. Since a purchaser of
standing timber is always conservative wherever a doubt exists, it is to
the owner’s interest to sell on the basis of actual mill cut of boards or
output of other products, whenever this is possible. This basis is
often used in regions where the timber is cut by small portable mills,
located in or near the tract and where small amounts are purchased.
15. Measurement of Standing Timber Postponed till after Logging.
Where the logs must be driven down streams or hauled long distances
by the purchaser, this basis becomes impractical both because of the
delay in settlement of account and the difficulty of checking the output
of lumber. The timber owner is thus forced to substitute a log scale for
a mill tally of lumber. This scale is always based on some log rule agreed
upon beforehand, and may or may not give results coinciding with the
actual sawed output. If the log rule is known to be inaccurate, the
excess or deficiency of manufactured products can be ascertained only
by a comparison of the mill tally with the log scale. Such comparisons
will give an idea of over-run or under-run (§ 46). The owner can then
adjust the price in,subsequent sales of logs according to the difference
between the scaled contents of his logs and their probable output in
sawed lumber.
16. Measurement of Standing Timber in the Tree. But even the
log scale is inapplicable when standing timber is purchased in large
amounts and a long period is required for completion of logging. The
owner desires prompt payment even if based on a less accurate measure-
ment of volume. The volume of the standing timber must be measured
as well as possible, and since, at best, only the diameter of the trees
together with a few heights can be actually determined and the rest of
the work is done ocularly or by guess, the result is only a rough estimate.
This method has given rise to the term Timber Estimating. The prin-
cipal sources of error in timber estimating lie in the effort to arrive at the
net merchantable contents minus waste, in the use of inaccurate and
variable standards of log measure for this purpose, and in the difficulty
and cost of determining even the superficial dimensions of standing trees.
This leads to short-cut methods, approximations and guess work and
calls for the development of system and of personal skill. One improve-
ment in timber estimating widely used by foresters is the tree-volume
10 SYSTEMS AND UNITS OF MEASUREMENT
table, which gives the average contents of entire trees of different dimen-
sions, in terms of standard log rules or other units, thus eliminating a
certain amount of ocular work.
17. Need of Standardization for Both Commercial and Scientific
Measurements. The justification of the use of standards which give
the contents of standing timber in terms of products, rather than
actual cubic volume, lies in the fact that the value of the timber, standing
or cut, depends upon the volume and quality of these products and not
upon the cubic volume.
Had it been possible to secure the adoption of a uniform standard
of conversion into board feet, the use of this standard would be more
serviceable than the apparently simpler cubic standard. But in prac-
tice the same motives which here gave rise to standards based on products
have led the French to adopt, as substitutes for cubic measurement,
rules of thumb which are less accurate by far than many of our log
rules.!
The greatest drawback to the use of units intended to measure
the product directly lies not in their character but in their inaccuracy
and in the multiplicity of standards. It is easily seen that volume
tables and measurements of growth which are based on some widely
used commercial log rule may coincide with custom, but are incapable
of use or comparison with other log rules ($77) and are inaccurate as
a scientific basis of measuring growth or volume. This fact has led to
endless duplication of effort and has been the chief reason for the lack
of real progress in accumulating standard data on volume and growth
of American trees.
A continuance of such duplication of effort will hinder the progress
of forestry in America, which must depend in a large part upon the
accuracy of volume and growth data gathered by forest measurements.
While the local value of data based on log rules sanctioned by custom
will continue, these field data should be gathered in such form as to be
of permanent value independent of these variable local standards.
It is possible to convert all measurements to the common standard
of cubic feet, which gives a basis of scientific comparison between the
volumes of different trees and species, and a permanent basis for measure-
ment of growth for trees and stands. It is also possible to adopt, for
the purposes of permanent record, a log rule based on scientific principles
which will give an equally reliable comparison of the contents of trees in
board feet and the growth of stands expressed in this unit of product.
But for a permanent record from which the volumes of trees may be
derived in any unit of product, standard or local, the average form of the
1 Mensuration in France, Donald Bruce, Journal of Forestry, Vol. XVII, 1919,
p. 686.
FORMS OF PRODUCTS 11
tree is required, as expressed in diameters at different points on the
stem. Investigations of tree form are therefore at the root of all per-
manent progress in Mensuration (Chapter XVI).
18. Forms of Products into which the Contents of Trees are Converted. The
products manufactured from trees may be classed according to the following group-
ing:
Group I. Manufactured products of definite form, retaining the wood structure
and requiring waste in manufacture.
A. Manufactured from logs.
1. Lumber
a. For construction.
1’. Structural timbers.
2’. Dimension.
3’. Boards.
4’. Remanufactured or planing mill products.
5’. Special products.
6’. For export.
b. For remanufacture. Square edge or round edge.
1.’ For mill work, furniture, fixtures.
2.’ For utensils and supplies.
3.’ Boxes and containers.
2. Veneers.
3. Manufactured direct from log for finished articles.
B. Manufactured from bolts.
Billets, flitches, squares, blocks, shingles, spokes, staves, ete.
C. Manufactured from mill refuse, i.e., from slabs, trimmings and
edgings. Shingles, lath, boxboards, ete.
Group II. Bulk products in which the form or both form and structure are
destroyed.
1. Excelsior.
2. Wood pulp.
a. Mechanical.
b. Chemical.
3. Distillates.
. Extracts.
5. Fuel.
a. Charcoal,
b. Fuel wood.
6. Bark.
Group III. Piece products retaining in whole or in part the original form.
1. Round products,
Poles, piling, posts, ete.
2. Shaped products,
Hewn cross ties.
1’. Standard ties.
2’. Mine ties.
—
Group I. In converting round logs into lumber, there is unavoidable waste in
sawing due to the difference in shape between the products desired and the log,
and to the saw kerf. The per cent of waste depends upon the dimensions of the
12 t SYSTEMS AND UNITS OF MEASUREMENT
smallest board which is merchantable, and upon the thickness of saw used. Further
intensive utilization of slabs (pieces slabbed off from the round surface of logs in
sawing) and of edgings (pieces cut from the edges of boards to give parallel edges
and remove bark), by manufacture into sawed products depends upon finding a
market for pieces whose size is small enough to permit of their manufacture from
these otherwise waste products.
The waste in manufacturing articles direct from the log depends on the shape
of the manufactured article with reference to the bolts from which it is made. Unless
profitable use can be found for the portions so wasted, or unless antiquated methods
and machinery are in use, the portions of a tree or log lost in manufacture cannot
be regarded as wasted, any more than the loss in bulk of a rough block of stone in
process of transformation under a sculptor’s hand is considered waste. It is for
this group that log rules are required.
“Woods Waste Mill Waste Lumber
16.6% 44.3% 89.1%
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into lumber.
Group II. To this group belong also those waste products from Group I for
which use as bulk materials can be found. The characteristics of this group are
that the entire volume of the log, and a much larger per cent of the volume of the
tree is utilized than in Group I. Material may be taken to very small diameters,
since size is not a requisite of utility but merely a convenience in handling. For
this group, cubic volume is the required standard of measurement,-and the use of
stacked cubic measure is customary.
Group III. Nearly all the round or shaped products in this group may also be
obtained from larger logs by sawing as poles, ties, fence posts, in which case they
can be measured for their contents in sawed lumber. For round products, as poles,
piles or posts, or for hewn products, as hewn or “ pole ”’ ties, the number of pieces
of standard sizes and shapes is the simplest method of measurement. For this
group the important factor in measurement is the set of specifications which deter-
mine the grades of product. The waste to be expected in manufacture under Group I
is shown in Fig. 2.
THE FACTOR OF WASTE IN MANUFACTURE 13
19. The Factor of Waste in Manufacture. A waste product is one for which a
profitable use has not been found. It is not sufficient that the product could be used
for some purpose if it could be transported to some place other than the site of its
first appearance as waste. The value of the product must be such as to bear the
cost of manufacture and transportation plus a profit. Unless some portion of a
tree yields products which fulfill these conditions, the whole tree remains unutilized
to finally die and rot, a true waste product of nature. In inaccessible places, entire
stands go to waste.
Waste in tops and limbs represents those portions of the tree which under the
existing conditions do not yield profitable products. But little deliberate or inexcus-
able waste occurs over any long period without discovery and correction. The
per cent of waste for unprofitable portions of the trees is often as high as 50 per cent
for staves or other special products and 25 per cent or over for lumber. The average
of 16.6 per cent shown in Fig. 2 for lumber is far too high for bulk products such
as pulp wood or for trees with small limbs and boles of regular form.
Bark is a typical example of a ‘‘waste”’ product. As fuel, it is not wasted. When
tannin extract or cork is yielded it is carefully gathered. For lumber, it is entirely
wasted, except as incidental fuel. The waste in sawdust, slabs, edgings and factory
finishing, when reduced to the lowest possible terms by good machinery, can hardly
be regarded as avoidable waste, since the product which results from this apparent
waste has a value much higher and a utility much greater than before the “‘ loss ”’
of the extra bulk.
When this sawdust and refuse is used as fuel in the mill, as is now the common
practice, it replaces coal, thus not only effecting a great economy but performing an
important public function in saving transportation costs on coal. The only real
waste in manufacture is where methods are used which unduly increase sawdust
and slab waste at the expense of finished products. Waste caused by seasoning of
wood is not avoidable, and increases the value of the product in greater ratio than
its loss in bulk.
The per cent of actual avoidable waste in utilization of the tree is difficult to
determine or to prove. It constitutes the per cent of difference between what is
utilized in higher forms, and what could be utilized under the same economic condi-
tions, at a profit. It is a measure of the efficiency and alertness of the operator,
and will seldom exceed from 5 to 10 per cent even under exceptionally bad conditions;
while under good management this avoidable waste is probably not over from 2 to
5 per cent. .
The utilization of small-sized pieces and bulk products not only reduces the per
cent of waste in single trees, but brings entire trees of smaller dimensions into the
merchantable class, thus increasing the per cent of volume in a stand of timber
which is merchantable, and lowering the age at which trees can be marketed. Since
the number of trees per acre rapidly diminishes with increasing size, close utilization
of small diameters will very greatly increase the per cent of merchantable volume
in young stands and reduce the per cent of waste by natural losses of trees before
they reach the larger diameters.
20. Actual versus Superficial Contents of Sawed Lumber. ‘The variation
between actual cubic contents of sawed lumber, and the superficial contents as
expressed in board measure, must not be overlooked in Forest Mensuration. Log-
rules for board feet are uniformly based on the sawing of boards 1 inch thick. Mill
tallies of lumber which is sawed scant, such as 3-inch boxboard material, will con-
sequently greatly overrun the scale of the logs, in so-called superficial feet, which
is the number of square feet of surface measure regardless of thickness. On the
14 ‘SYSTEMS AND UNITS OF MEASUREMENT
other hand, hardwoods are customarily sawed to thicknesses slightly greater than
1 inch to allow surfacing down to full inch thickness, and this practice reduces the
superficial yield in board feet as compared to softwood species which are commonly
sawed scant. Either practice causes the actual output measured in board feet
(§ 12) to differ from the scaled contents of the logs. The actual dimensions of board
which are accepted as inch lumber and. other standard thicknesses, and the amount
of difference, scanting or extra thickness, permitted, is standardized by trade prac-
tice for each region and species.+
These differences in sawing affect the over-run of sawed lumber, which for the
same log rule would thus be greater for softwoods than for hardwoods.
21. Round-edged Lumber. Most lumber is square edged in sawing. Close
utilization by the box, match, sash and blind, woodenware, furniture and certain
other industries has led to the sawing of logs ‘‘ alive”’ or through and through into
boards from which the waney edges are not removed by squaring. These boards,
except when sawed from the middle of the log, have one face narrower than the other
and owing to the taper of the log, the faces are not of uniform width throughout
their length. As the lumber in such boards is closely utilized, its board-foot contents
is computed by measuring the average width of the narrow face. The thickness
is considered on the same basis as for square-edged lumber. Lumber of this char-
acter is usually cut by portable sawmills and sold direct to factories. The scale
at the factory is used to check that at the mill. This prevents taking advantage
of the uncertainties of the method. The logging and sawing are paid for on the
basis of the mill scale, which scale usually becomes the standard for measuring the
contents of the standing timber.
Round-edged lumber will yield from 10 to 20 per cent more scale than square-
edged, the excess being greater, the smaller the logs sawed. For plank 2 inches
or more in thickness, a loss is incurred both in utilization and in scaling by reason
of the wane, which causes an excessive difference in width of the two faces. This
loss is reduced by cutting 1-inch boards from the sides of the log (§ 51).
Closeness of utilization of the tree and stand is increased by this method of saw-
ing. Tops are sometimes taken down to 2 inches and never to greater than 4 inches.
Branches which crook only in one plane are used.
22. Products Made from Bolts and Billets. Bolts are sections of logs still in
the round, and less than 8 feet long, i.e., too short to be conveniently measured as
logs. Billets are obtained by halving, quartering, or otherwise splitting or sawing
bolts lengthwise. Bolts may be split into billets, each of which is intended to pro-
duce one finished article, such as a wagon spoke or stave. These are measured by
count. Billets of larger size may also be split from bolts. So-called shingle bolts
are billets split or sawed from large trees, or blocks from thick slabs.
Billets are also obtained by sawing bolts, and are then termed flitches, squares,
slats, or blocks. Squares are used in turning out round articles, such as shuttles,
spools and bobbins. On account of their regular form, squares are sold by count,
or by bulk, on standards agreed on, the price being based on either the number or
the board-foot contents. They may be sold by stacked cords. Bolts, and split
or sawed billets of irregular form, not yet manufactured into squares, are sold by
stacked cubic measure except in the case of bolts over 12 inches in diameter and over
4 feet long, which may be scaled by a log rule. The width of the stack is determined
by the length of the product and may range from 22 inches to 5 feet and over. In
1 Lumber and its Uses, by R. 8. Kellogg, 1914, Radford Architectural Company,
Chicago, Illinois.
: PRODUCTS MADE FROM BOLTS AND BILLETS 15
this case a cord is a stack 4 by 8 feet but whose width is that of the given product
(§ 99).
Different customs prevail in different industries. Shingle bolts (split or sawed
billets) are sold in lengths which allow three cuts. For 16-inch shingles, with 4
inches for trimming, the piece is 52 inches long. For 18-inch shingles, a length of
58 inches is required. The cord is 4 by 8 feet by the indicated width.
Spoke manufacturers dealing in standard 30-inch spoke billets compute a
cord as 4 by 8 by 23 feet, or 80 cubic feet. Others measure the cubic contents,
using 128 feet for a cord. In the stave industry a cord measuring 4 by 11 feet by
the length of the stave bolts is quite common. For 36-inch billets this gives 132
cubic stacked feet, but the rule is applied to billets of other lengths.
Billets and bolts for tool handles are always measured by the rank, in cords
measuring 4 by 8 feet by the required width.
REFERENCES
Measuring and Marketing Woodlot Products, Wilbur R. Mattoon and William B.
Barrows, Farmers Bulletin, 715, U. S. Forest Service, 1916.
Wood Using Industries of New York, John G. Harris, U. 8. Forest Service, New
York State College of Forestry, Series XIV, No. 2, 1917.
CHAPTER III
THE MEASUREMENT OF LOGS. CUBIC CONTENTS
23. Total versus Merchantable Contents. Logs are measured to
determine their total cubic contents with or without bark, or they
are scaled for merchantable contents only. The total cubic con-
tents is required in scientific studies of volume and growth and for
such commercial purposes as make use of the entire volume of the log.
The cubic contents is found by measuring the length and the diameter
at one or more cross sections and computing the volume of the log as a
whole, or by sections, from these measurements. Where the thickness
of bark is measured, the difference in volume of the log measured out-
side and inside the bark gives the volume of bark.
24. Log Lengths. Softwood or coniferous logs are usually cut into
even lengths, or multiples of 2 feet, and may be any length from 8 feet
to over 60 feet, being limited only by the height and upper merchant-
able diameter of the tree, the length of material demanded for manu-
facture, or the convenience of transporting long versus short logs.
Logs, especially hardwoods, are sometimes cut to odd lengths or multi-
ples of 1 foot. The standard commercial lengths for softwood logs
vary from 10 to 22 feet, and average 16 feet. In hardwoods, log lengths
average somewhat shorter, since utilization of shorter lengths is more
common. Log lengths are marked off on the felled tree by notching
with an axe. It is customary to use a wooden measuring stick 8 feet
long, and divided into 2-foot lengths.!
For exact measurement of length, the steel tape, graduated to feet,
and tenths instead of inches, is used. The log length is measured along
the surface, which is assumed to equal the length of the axis. For
commercial uses, an excess length of from 2 to 6 inches is required as a
margin for trimming. For total cubic contents the logs or sections are
measured to their actual lengths.
1 The accidental chopping off of the top of the measuring stick sometimes results
in short measurements. In some regions, notably in Southern pine, careless measure-
ment of log lengths resulting in excess trimming allowance and odd lengths causes a
waste in woods and mill, in trimming to standard sizes, of from 3 to 5 per cent of the
total cut. This statement is based on careful measurements covering 14 years’
experience in six states with eight different companies.
16
DIAMETERS AND AREAS OF CROSS SECTIONS 17
25. Diameters and Areas of Cross sections. Cross sectional areas
are assumed to be circular in form, and were this assumption correct
the measurement of any.average diameter would give the cross section.
If B =“‘basal’’ area, or area of circle,
D=Diameter of circle,
a = Ratio, or 3.1416.
Then
= .7854D".
But practically every cross section departs slightly from a true
circle, and a large proportion are very eccentric, some showing a dif-
ference of several inches between their longest and shortest diameters,
and having an elliptical or oval form.!
No attempt is ever made to compute the actual cross sectional area
of such eccentric sections. Instead, two diameter measurements are
taken at right angles and the average of these is assumed to be the
average diameter. A circle with corresponding diameter is assumed to
have the same cross sectional area as that of the actual section. Usually
the longest diameter is taken, and one at right angles to it, through the
geometric center of the section.”
Abnormal cross sections are occasionally encountered in which the average
diameter of the section and its area are either too large or too small to give the volume
accurately owing to some distortion in form of the log as a whole or of the portion
1 The area of an ellipse is
aDd
n= F
4
when D and d represent the long and short axes.
y D-+d
The area of a circle whose diameter is calculated as err ts.
_x(D+d)?
a 4)
Then
a(D+d)? «Dd_ (D—d)?
4(2) A EO
which is equal to the area of a circle whose diameter equals one-half the difference
between D and d. This correction which is always minus, is ignored in measuring
cross-sections.
*In determining the average diameter, no attention is paid to the growth rings
or the position of the pith or growth center of the section. In eccentric cross sections
the pith is always found some distance to one side of the geometric center, which is
the point through which the diameter measurement must fall,
18 THE MEASUREMENT OF LOGS. CUBIC CONTENTS
measured. Abnormally large sections are found at forks or at the base of limbs or
are caused by swellings. Stumps cut low give a section averaging much too large
to indicate the true volume of the log, due to the rapid flare of the butt.
Abnormally large diameters at the top end of logs should be measured by reduc-
ing the diameter to what the log would have if it held its regular form. Where
flaring butts are measured, the errors incurred may be serious. It is preferable to
adopt a method which does not require this butt measurement, or else to subdivide
the log by caliper measurements into shorter sections. Abnormal cross sections
caused by limb swellings, or knots, should be measured, if possible, by taking the
diameters at equal distances above and below the swelling. When logs are cut to
small diameters in the top, the log may taper rapidly in the last few feet, and the
disproportionally small diameter at the top will reduce the computed volume of the
log as a whole. This problem may be solved by measuring the tapering portion
separately as a short piece. In commercial scaling of logs which have abnormal
diameters, the scaler should apply a measurement which in his judgment will give
the correct contents of the log.
In ordinary scaling, the diameter of logs is expressed in the nearest
inch with fractions entirely dropped or rounded off ($83). For accu-
rate volume measurements, each diameter is secured to the nearest
tenth of an inch, for which purpose the rule or calipers used must be
graduated to tenths. In commercial practice, thickness of bark is never
included in measuring the diameter of a log except when the bark is to
be utilized, as for fuel or tannin,! in which case the diameter is measured
outside the bark.
When the diameter of the log is taken in the middle, the thickness
of bark must be ascertained and deducted. For accurate volume
measurements, thickness of bark on one side may be determined by
notching and measuring to the nearest tenth of an inch. Double this
thickness when deducted gives diameter inside bark. Or the bark may
be stripped from opposite faces in order to apply the calipers directly to
the wood. This latter method is laborious and is seldom used even
in scientific volume determination.
26. The Form of Logs. Logs diminish in diameter from butt to
top, corresponding to the form and growth of trees. This difference
or loss in diameter at successive distances from the butt, is termed taper.
The taper of logs gives them their characteristic forms. On account
of this taper, logs are never truly cylindrical no matter how closely
they may approach the cylinder in form.
The geometrical forms to which logs ean be compared must there-
fore be circular in cross section and tapering. The forms suitable for
this purpose are the paraboloid, cone, and neiloid.
1 Exceptions to this practice may be found in some regions, in scaling, when the
log rule in use gives a large over-run which is offset by including width of one bark
(§ 83).
FORMULA FOR SOLID CONTENTS OF LOGS 19
These three solids form a series of successively diminishing per-
centages of the volume of a cylinder of equal basal area and height.!
Each tapers to zero at the tip. But logs are cut with two parallel
_faces at the two ends. The corresponding solids are the truncated
forms of these bodies, termed frustums, as shown in Fig. 3.
y--------
my
= - - - Hy - -- - -
+
4
|
!
|
!
\
1
i
Fig. 3—Forms of the cylinder, paraboloid, cone and neiloid, and truncated forms
or frustums of the last three solids.
27. Formule for Solid Contents of Logs. The comparative vol-
umes of these four solids are stated by formule below; when
B= Area of base, square feet,
6b} = Area of cross-section, at 3 height,
b= Area of top,
h= Height or length, in feet.
1 Kach of these solids is formed by the revolution of a curve about a central axis.
A true Appolonian paraboloid is derived from that form of a conic section (a
symmetrical curve formed by the intersection of a plane with a cone) in which the
plane is parallel with the side of the cone. For the conoid formed by the revolution
of this curve about its axis, the ratio between a cross section taken at right angles
with the axis at any point, and the height above this point to the apex, is constant
Bh
for all points on the axis. This gives a volume equal to a Logs which taper
regularly will have straight sides, and resemble a truncated cone. Logs whose taper
is most rapid near the butt, diminishing towards the top, will have concave sides and
resemble a truncated neiloid. The form and volume of such logs will usually fall
somewhere between a neiloid and a cone. Most logs taper more rapidly at the top
than at the butt and will have convex sides, and resemble in form a truncated para-
boloid—their volume usually falls between that of a paraboloid and a cone. Where
most of the taper occurs close to the top, the log may exceed the paraboloid in volume,
falling between it and the volume of the cylinder.
20 THE MEASUREMENT OF LOGS. CUBIC CONTENTS
Form pein a Volume of Frustum
perfect solid
Cylinder Bh Bh
Bh (B+b h
Paraboloid = =e _ he or (B +0) 5 Smalian’s Formula
bth. Huber’s Formula
Bh ee
Cone = B+b4+V@-b)—
one z (B+b+V g ye
cally Bh h
Neiloid ru (B petal rt Newton’s Formula
Newton’s formula will also give the volume of the cone, paraboloid
and cylinder.
The per eent of the volume of the cylinder which is contained in the other three
forms, when of equal diameter at base and equal height, is
Parabaloudts toes desc. An Sie ae aes clei 50 per cent
COME sc etieys ort Rare tes chorea tnc tals eet Tels «kee COO DEINGeNE
INGUOIG: i fOON a Say Nts adie tee AE 25 per cent
But each of these three solids decreases in cross section from base to tip, while that
of a cylinder remains the same. The frustum of a cylinder is always a cylinder,
while the frustum of a paraboloid, cone or neiloid with equal basal area tends to
more nearly resemble a cylinder as the area of its top section approaches that of
its base, which results when the relative height of the frustum is shortened. The
per cent of the cubic contents of a cylinder of equal base and height, which is con-
tained in these frustums increases in the same manner, and the possible limits of
variation in form and volume between the cylinder and each of the other three
frustums correspondingly diminishes.
E.g., when the height of the frustum is one-fourth that of the perfect solid, the
per cent of cylindrical volume is, for
Hrustumd of paraboloid eect ios ee anit ae 87 per cent
Mrustumol cones sober aoe) Semis 77 per cent
drone MSOC eg hansodbeoedonn. obedo Ue 61 per cent
When the height is one-eighth of a perfect solid, these per cents are:
Brusthumlotiparaboloidecsere oe cise eiieteer 94 per cent
Prustums: of Cones aee 5. MANO k Pee es See 88 per cent
IdravisiApvany Cop novel, Me Ge sepa con ou omasloomh be 77.5 per cent
A rapidly tapering log forms a truncated section of a relatively shorter completed
paraboloid or cone than a log with gradual taper. The greater the height of a com-
plete paraboloid with a given basal area, the less it will taper for a given length, as
16 feet. Whether the taper is rapid or gradual, a log may exactly resemble the
frustum of a paraboloid, cone, or neiloid,
RELATIVE ACCURACY OF SMALIAN AND HUBER FORMULA 21
Provided it has the true form of one of these solids, its volume can be exactly
determined by employing the corresponding formula. But the true form of the
log may fall anywhere between the fixed points or forms in the series, which are
marked successively by paraboloid, cone and neiloid, and in this case the volume
even when calculated by the formula which corresponds most nearly to its crue
form, will still be in error by the amount of this divergence. This error may be
excessive for long logs.
But by taking advantage of the effect of reducing the proportional height of the
frustum, the probable error from this source may be reduced to any desired limit of
accuracy. This is done simply by shortening the length of the logs, or by dividing
each log into several shorter sections, measured separately. It is then no longer
necessary to employ two or more forms arbitrarily according to the variations in
the form of the logs, but a single standard geometric form may be chosen, which
most nearly resembles the average form of logs, and the same formule applied to all
logs measured.
The paraboloid comes nearest to answering this requirement, and for this reason
the Smalian formula and the Huber formula have been generally adopted for both
scientific and practical measurements of cubic volume of logs, to the exclusion of
the formule for cone and neiloid.
28. Relative Accuracy of the Smalian and the Huber Formule.
Logs having the form of a truncated paraboloid are measured with
absolute accuracy regardless of their taper by either Huber’s or Smalian’s
formula. But if the form of the log is more convex and lies between
that of the paraboloid and the cylinder, the Smalian formula, measur-
ing the two ends, gives too small a result, while the Huber formula will
give too large a volume. Nearly all logs lie between the frustum
of a paraboloid and the frustum of a cone in form, having slightly
convex sides, but not the full form of the paraboloid, so the end area
formula (Smalian’s) shows an excess, while the middle area measurement
(Huber’s) gives too small a result. In either of the above cases,
the error by Huber’s formula is one-half that of Smalian’s and opposite
in character.
Newton’s or Prismoidal Formula. To check the accuracy of measure-
ments made on sections of given length and to determine the maximum
length of section which will secure the desired degree of accuracy, the
prismoidal formula may be applied. This formula is correct for cylinder,
paraboloid, cone or neiloid, and consequently for logs of regular form
whose volume lies within these extremes. It will not measure accu-
rately eccentric or. distorted forms resembling none of the above solids.
The formula requires the measurement of both ends and the middle
section, and is known as Newton’s formula,
d | h
V=(B+4b} +b).
When the form of logs resembles more closely the cylinder, cone or
22 THE MEASUREMENT OF LOGS. CUBIC CONTENTS
neiloid than the paraboloid, the errors in the use of the Huber or the
Smalian formula may easily be checked by the above formula.!
29. The Technic of Measuring Logs. By either of the two para-
boloidal formule, Huber’s or Smalian’s, the area of a single average
cross-section is obtained which, multiplied by the length of log, gives
the cubic contents. By the Smalian method, this area is the average
of two cross-sections, while by the Huber method it is obtained directly.
The volume of the frustum, or log, is thus equal to that of a cylinder
of equal height, with a base equal in diameter to the average cross-
section.
Diameters Measured at Ends of Log. Diameter inside the bark is
usually required, and is best obtained at the exposed ends of the log.
But if only the small end is measured, the corresponding cylinder
does not give the cubic contents of the log on account of neglect of its
taper (§ 26). Although almost universally practiced in scaling for
board feet, this single measurement is never used to scale cubic contents.
The choice lies, therefore, between the single measurement at middle
of log, or the averaging of two end areas.
The volumes of cylinders vary directly as their basal areas, or as D2, and not as
their diameters. Hence an accurate procedure would require first, measurement
of each diameter; second, determination of each corresponding area; third, averag-
ing these areas; fourth, computing the corresponding diameter. The volume of a
cylinder of this diameter and length is required. Such a procedure is practical only
in scientific studies; in scaling, the two end-diameters are averaged directly. The
assumption is that,
D+d\?
v= 7854( +) ie
1The following formule are cited by Guttenberg, in Lorey’s Handbuch der
Forstwissenschaft, 3d Ed., Chapter XII, 1913.
h
Breymann, Va eae obs Ps)
h
Hossfeld, V7 803 +b).
: h
Simoney, V =, (20s +03) pty,
While the substitution of the Hossfeld formule for that of Smalian on butt logs
would give far more accurate results, and would be closer than the Huber formula,
the point one-third from butt is not ordinarily measured in the field and is trouble-
some to ascertain. Hence this formula is impractical. The same objection applies
to Breymann’s. Simoney’s formula has no advantage over either Huber’s or
Smalian’s, since by using the small lengths, one-fourth log, the latter formule will
secure results within 1 per cent of the true volume for the standard 16-feet length.
THE TECHNIC OF MEASURING LOGS 23
This gives a slightly smaller volume than by the correct method. The error increases
as the square of the difference between the top and the bottom diameters. !
This error, expressed in per cent of total contents, falls below 1 per cent for logs
not over 16 feet long with a taper of 2 inches or less. It also tends to offset the plus
error caused by the use of the Smalian method as a whole (§ 28). The error increases
with length of log scaled as one piece.
A far more serious source of error by this method is that due to the flare of butt
logs. Due to the excessively large cross-section thus obtained at the butt, this
error may give an excess cubic volume for the log of from 10 to 20 per cent. Chiefly
for this reason, the end area method is confined in practice to scientific studies of
volume, in which the length of the sections can be regulated to reduce this error,
and time is not the determining factor. For such studies, the computation of average
basal areas is no drawback. The volumes of the lengths into which the log is to be
divided are more conveniently computed by the Smalian formula than by the Huber
formula, which requires the middle diameter of each short section. Smalian’s
mean end formula is therefore universally adopted in these studies,
Diameter Measured at Middle of Log. Since it is impossible to
measure the diameter at the middle of a log unless the log is exposed,
logs cannot be scaled by this method if they lie in large rollways or
piled one on another. The scaling for cubic contents therefore requires
a time and place for the work where each log is exposed for its entire
length and is less convenient than scaling for board feet (§ 83).
By measuring the middle diameter, the error due to flaring butts
is avoided. But this practice requires, in addition to total length,
the determination of this middle point. The use of calipers is required,
since it is impossible to obtain consistent accuracy by placing a scale
stick across a log and judging the diameter; the error thus incurred
is always minus. This method is therefore termed a caliper scale.
In applying a caliper scale, the double width of bark is subtracted
either by taking off a fixed average thickness or by adjusting the calipers
1 The error in use of mean diameters is shown as follows:
Volume of truncated cone may be expressed as,
V = {D+ Data),
Volume of cylinder having a basal area equal to the mean diameter of the log is,
Te
4 2
Then,
ae ag, ee
= () :
t 2 12 2
Tv
= 2 2)\ ==
h(D?+Dd+a")
The minus error thus shown is equivalent to the volume of a cone having a basal
area equal to the difference between the mean end diameters of the log. For the
paraboloid, this error equals the contents of a cylinder with a basal area equal to
that of the above cone. The error thus increases with the total taper of the log.
24 THE MEASUREMENT OF LOGS. CUBIC CONTENTS
to read that much less in diameter for all logs alike. For more accurate
sealing the width of bark is deducted separately for each log.
The caliper scale is the more accurate of the two methods for
commercial use. The volumes by this formula, in average logs, are
slightly below the actual contents.!
Where the length of a log exceeds that which can be accurately
measured as one log by the above methods, the practice is to consider
it as composed of two or more shorter sections. By Smalian’s method,
the intermediate points measured are taken as the ends of these sec-
tions. By Huber’s method, the middle point of each section is found.
In either case, calipers should be used. The length of section which
can be measured without subdivision depends primarily on the rapidity
of taper. Logs or sections whose total taper does not exceed 2 inches
may be scaled or measured as one piece regardless of length. In com-
mercial scaling logs less than 18 feet long are seldom subdivided. In
scientific studies 8 feet is usually the maximum length between measure-
ments of diameter, and 4 feet is often required for the first or butt
sections.
30. Girth as a Substitute for Diameter in Log Measurements.
The circumference of the circle, corresponding to the girth of the log,
may be used to determine the area of the cross-section.” In this case.
if G=girth, and B=Basal or end area,
B patil .0796 G?.
Ar
A tape is used in which the results are read directly in inches of
diameter, each inch being equal to 3.1416 inches on the tape. A pin
in the end of the tape enables one man to encircle the log.
The ratio between diameter and circumference, 7, holds good only
for the circle. The more eccentric the cross-section, the greater this
ratio becomes, and the smaller the actual area in proportion to girth.
Hence, whatever error occurs by this method tends to give a cross-
sectional area greater than the actual area.?
1 Tests of 4398 spruce and fir logs measured in lengths up to 40 feet by this method
in Maine indicated that the scale required a correction factor of 1.049 or 4.9 per cent
over-run. The Measurement of Logs, Halbert 8S. Robinson, Bangor, Me., 1909.
2 Girth measurements are commonly used in India, and in commercial measure-
ment of imported logs in England. In the United States, the girth of large logs is
sometimes taken, when more convenient than the measurement of diameter, but
G
the result is reduced to diameter by the formula D =— = 3183.
Tv
3 Mensuration of Timber and Timber Crops, P. J. Carter, Office of Supt. of
Gov’t. Printing, Calcutta, 1893, p. 2.
GIRTH AS A SUBSTITUTE FOR DIAMETER 25
One advantage of girth measurements over diameter is that two
measurements taken at the same point give consistent results, while
in determining the average diameter of large and irregular or eccentric
logs, considerable differences may occur in two separate measurements.
Owing to the difficulty of measuring the girth of a log at its middle
point, the mean of the two ends may be taken. This incurs an error
identical with that by the mean diameter method (§ 29). This error
is offset by the tendency of girth measurement to over-run.
The volume of the cylinder whose basal area is obtained from girth
may be found by the method of the Fifth Girth in which
G\2
i (2) 2h’
G is here expressed in feet. If measured in inches, divide the result
by 144. Another method, known as the Quarter Girth, is expressed as
e ay :
v-(¢ h+113.
In this formula G is expressed in inches.!
1 The Fifth Girth method will give a result which is only approximately correct.
G=rD,
therefore,
on
D? D\?
ve should equal (2) 2h,
ya
.7854 should equal .6283? <2,
and
jr should equal (
ol a
.7854 should equal .7895,
an error of less than 1 per cent.
The Quarter Girth formula is of no particular value as it is merely a means of
correcting a commercial standard ($35 Hoppus or Quarter Girth Log Rule) to
obtain the full volume of the cylinder.
CHAPTER IV
LOG RULES BASED ON CUBIC CONTENTS
31. Comparison of Log Rules Based on Diameter at Middle and
at Small End of Log. Log rules giving the contents of logs in cubic
feet should be based on the diameter inside bark at middle of log. If,
instead, the diameter is measured at the small end of the log, the indi-
cated contents falls short of the true cubic volume (§ 29).
But the measurement of diameters at the small end of logs rather
than at the middle point is so great a convenience in log sealing (§ 83)
that efforts have been made to find a converting factor, or ratio, by
which the true contents of logs may be correlated with diameters at
the small end, and expressed directly in a log rule based on these diam-
eters. Since the true contents is assumed to be equal to the cylinder
whose diameter is that of the log at its middle point, the ratio or factor
desired is the multiple required for converting the volume of the smaller
cylinder whose diameter is measured at the small end of the log into
the true cubic volume of the log taken as equaling this large cylinder.
This ratio is influenced by three factors—namely, rate of taper, length,
and diameter of the log.
A log rule, if based on the same conversion factor for logs of all sizes and tapers,
will give correct volumes only for a log of a given diameter, length and taper and
will be in error for logs of all other dimensions.
A log rule based on separate conversion factors for logs of each diameter but
making no further distinction for different lengths or tapers will give correct volumes
only for logs of a specific length and rate of taper in each diameter class, and will
be in error for all other lengths and tapers.
A log rule based on separate conversion factors for each different diameter and
length, can be applied accurately to obtain the average scale of logs of all diameters
and lengths only in case the average taper of the logs scaled agrees with that of the
logs measured in determining the factor used, and is in error when the average
taper of the logs scaled is greater or less than this.
While these conditions apply to log rules based on measurement at the small end
of log, a log rule based on measurement at middle of log is correct for all the above
conditions, incurring only the errors due to divergence in shape of log from that of
a paraboloid. :
The ratio of volumes, and the loss in scaling Icgs by a rule based on the cylinder
measured at small end, are illustrated in Table I. The figures in the last column
represent the loss in scale expressed in per cent of the volume scaled, e.g., a 16-foot
log 6 inches at the small end with 2-inch taper contains 36 per cent greater volume
than shown by the scale.
26
27
COMPARISON OF LOG RULES BASED ON DIAMETER
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28 LOG RULES BASED ON CUBIC CONTENTS
Table I indicates that the per cent of error resulting from assuming that the total
contents of a log is equal to that of the cylinder measured at the small end decreases
with increased diameter, increases with the total number of inches of taper in the
log but for logs with a given diameter and the same number of inches of total taper,
the per cent of error is the same regardless of the rate of taper or length of log, and is
determined by the difference in volume of the cylinders based respectively on diameter
at small end and middle of log.
32. Log Rules in Use, Based on Cubic Volume. There are two
classes of log rules in use, based on cubic volume. The first class gives
the actual or total cubie contents of the log. The second class gives
the volume of sawed lumber expressed in board feet, but these rules
are based upon the use of a fixed ratio of conversion from cubic volume
and not upon the volume of sawed lumber which can actually be obtained
from logs of different sizes (§ 39).
Cubic measure was early adopted in log measurements, but owing
to the fact that logs are roughly cylindrical in shape, the custom grew
up of using the contents of a cylinder of standard dimensions instead
of the simpler standard of the cubic foot. There is no advantage in
this substitution of new arbitrary cubic standards for the cubic foot.+
The principle used in the application of such a standard ‘is that the
volumes of cylinders of different sizes will vary as the square of the
diameter multiplied by the length. The contents of all logs can then
be expressed in a log rule in terms of the number of standards they
contain.
The Adirondack Standard, or Market. In the Adirondack region
of New York several such standards have been used but the only one
of importance is the 19-inch or Glens Falls Standard, termed also the
Market.? This is a cylinder 19 inches in diameter and 13 feet long,
1'The cubic meter is the standard of volume used in the Philippine Islands.
Logs less than 8 meters (26} feet) long are measured as a cylinder whose diameter
is the small end. The average diameter in centimeters is taken, the end area is
obtained from tables and multiplied by the length of the log in meters to give the
volume in cubic meters. For logs over 8 meters in length, the diameter at the middle
is taken, or if this is impractical, the average of the diameters of the two ends is used.
2 It is assumed that one market equals 200 board feet which is 65.1 per cent of
its cubic contents regarding the log as a cylinder measured at the small end of log
and neglecting taper. This gives 7.8 board feet per cubic foot.
Tests of actual output in board feet per market, sawed from 600 logs of each sepa-
rate diameter, gave the results as shown in table on opposite page.
The saws used were a band and a band resaw, both cutting ;-inch kerf. The
lumber was 60 per cent 1-inch, the rest 11-inch and 2-inch thicknesses. These
ratios are therefore higher than for inch lumber sawed with 1-inch kerf. The ratio
is still further increased by the fact that the cubie contents measured does not include
the entire log but only the cylinder measured at small end while the sawed output
is from the entire log. H. L. Churchill, Finch, Pruyn Co., Glens Falls, N. Y.
Twenty-two-inch Standard, A different unit is in use to a slight extent
LOG RULES IN USE, BASED ON CUBIC VOLUME 29
equivalent to 25.6 cubic feet. In application the log is measured at
the small end and its contents are taken as that of the corresponding
small cylinder. The taper is disregarded.
When D=diameter of standard log in feet or in inches;
L=length of standard log in feet.
The volume of the standard is .7854 D?L.
Let d and / equal the diameter and length of any other log, whose
volume will be .7854 dl.
The volume of any log is found in terms of standard units by the
formula,
7854071 ~—s dl
.7854D2L D2L
-The market is still a common standard of log measure on the
Hudson River watershed in the Adirondack region.
Its neglect of the taper makes the Adirondack standard unsuitable
for measurement of pulp wood, but were it applied at middle of log
on the Saranac river drainage in New York, termed the Twenty-Two-Inch Standard.
The standard log is here 22 inches at small end, and 12 feet long, containing 31.68
cubic feet. It is assumed that one standard equals 250 board feet which equals
65.8 per cent of the cubic contents of the small cylinder. There have been still other
log standards, which are now obsolete.
|
Diameter at} Board feet | Board feet | Diameter at} Board feet | Board feet
small end per per | smallend | per per
inside bark.) market cubic foot | inside bark.| market cubic foot
Inches Inches
5 135 5.3 13 228 8.9
6 155 6.0 14 236 9.2
7 168 6.6 15 243 9.5
8 179 %.0 16 248 9.7
9 190 7.4 17 252 9.8
10 200 7.8 18 255 9.9
11 210 8.2 19 . 257 10.0
12 219 8.5 20 259 10.1
In principle and practice, these standards coincide closely with the use of the
cubic meter, the only difference being in the size or cubic contents of the unit. The
difference in shape, or use of a cylinder instead of a cubic foot, is of no significance.
Since the cubic meter contains 35.3156 cubic feet, the market is a smaller standard.
The cubic volumes are convertible from one of these standards to another by using
th ti efetnrcubie meters
e€ proper ratios; markets to Cubdic meters —
uae 35.31
=.725; markets to cubic feet 25.6.
30 LOG RULES BASED ON CUBIC CONTENTS
it would give accurate contents. This standard, in common with all
other cubic rules, is unsuited to the measurement of the board foot con-
tents of logs.
33. The Blodgett or New Hampshire Cubic Foot. A cylindrical
unit has been adopted as the legal standard of the state of New Hamp-
shire. The statute reads, ‘‘ All round timber shall be méasured accord-
ing to the following rule. A stick of timber 16 inches in diameter and
12 inches in length shall constitute 1 cubic foot; and in the same ratio
for any other size and quantity.” This arbitrary cubic foot contains
1.396 or approximately 1.4 cubic feet.
The contents of logs is computed in Blodgett feet by the formula,
2
D
———
Va7ax.
This log rule is based on the middle diameter, and is therefore more
accurate in application than the Adirondack stafdards. The diameter
is measured by calipers and double width of bark is deducted (§ 84).
This rule is a rough attempt to use the cubic foot, with an allowance for waste
in squaring round logs. But the per cent of waste by the rule is 28.4 per cent of the
cylinder, utilizing 71.6 per cent, while the area of an inscribed square is 63.6 per
cent of the circle with 36.4 per cent waste. The “‘squared”’ stick 1 foot long would
therefore have considerable wane. The Blodgett Rule was an attempt to secure a
standard which could be converted into board feet. The statute fixed the converting
factor as,
100 Blodgett feet =1000 board feet, or a ratio of 1 : 10.
But in scaling practice it was concluded that this ratio was unsatisfactory, and
gave too large a scale in board feet. So it was arbitrarily set in practice at
115 Blodgett feet =1000 board feet, or a ratio of 1 :8.7,
when the rule was applied, as intended, to the middle diameter inside bark. Though
the scale in Blodgett feet in either case was the same, the converted result gave for
the ratio of 1 : 10, 59.7 per cent of the contents of the log in board feet, and for the
ratio 1: 8.7, 51.9 per cent. Since 12 board feet =1 cubic foot,
10
E =833 per cent of 1 cubic foot,
and
Likewise,
8.7
DP =72.5 per cent,
and
725
——= = 019.
1.396
USE OF CUBIC FOOT IN LOG SCALING Sal
In order to permit measurement of diameter at the small end of log instead of
the middle (§ 31), a further modification of the rule more radical in its character
was now made. The loss in cubic contents by measuring the small cylinder was
offset by arbitrarily increasing the ratio of board feet to each Blodgett foot. This
new ratio was set for logs of all sizes at
106 Blodgett feet =1000 board feet.
When compared with the cubic contents of the small cylinder this makes the ratio
1:9.44. For the ratio of 1 : 9.44 the per cent of the small cylinder sealed as boards
is 56.2 per cent. But for the true cubic contents of the log the ratio would vary
with length and taper of log (§ 31).
9.44
ST On,
12
183
hr mae per cent.
From Table I, § 31, the following comparisons can be made between the volume
thus expressed and the true volume. Taking 16-foot logs with 2-inch taper,
Diameter | Per cent of total con- Per cent of total con-
: tents scaled as boards
of tents of log in small é
lo eyinden by above ratio of
g- 56.2 per cent.
Inches Per cent
6 73.4 Ale?
2 85.2 47.8
18 89.7 50.4
24. 92.2 51.8
30 93.7 200
The attempt to convert this rule to apply at small end gives values which agree
with the current ratio of 115 Blodgett feet to 1000 board feet in 16-foot only when
these logs are 24 inches in diameter and with 2-inch total taper, while for 6-inch logs,
51.9
of the true cubic scale measured at the middle point.
Thus the change in point of measurement destroys the consistency of this log
rule for cubic contents, while the conversion to board feet introduces still another
error, discussed in § 42. The rule should either be used for Blodgett feet only, as a
cubic measure, and applied only at middle diameter, or if the end diameter is used,
the conversion factor should have been separately computed for logs of different
diameters and lengths on basis of an average taper.
tapering 2 inches the scale is or 79.3 per cent, incurring a loss of 20.7 per cent
34. Use of Cubic Foot in Log Scaling. The cubic foot has been
substituted for the Blodgett foot as the basis for measuring logs, by
the U. 8. Forest Service on the National Forests in Maine and New
Hampshire.
32 LOG RULES BASED ON CUBIC CONTENTS
A caliper with a long arm to the end of which is attached a measuring wheel, is
used. The wheel consists of ten spokes, each tipped with a spike, and all painted
black except one, which is yellow. ‘The tips of the spokes are 6 inches apart. The
yellow spoke is weighted. When the wheel is run along a log, each revolution as
counted by the yellow spoke measures 5 feet, and the remaining spokes permit the
length of log to be measured to the nearest 6 inches. The measuring wheel is run
the length of the log, and then brought back to the center, at which point the caliper
measurement is taken. Allowance for bark is made by moving the caliper jaw
inward by a distance in inches equal to the estimated double width of bark on each
log separately.
The diameter in inches is stamped on one edge of the arm, and around the base
of the arm are placed standard lengths running from 8 to 34 feet. Opposite each
length, and below each diameter, on the arm, is stamped the cubic volume of a log
of these dimensions. The lengths are also stamped on the movable arm. When
the log is calipered, the scaler reads the volume which lies opposite the proper length,
Fra. 4—Caliper scale for measuring logs in middle, outside bark, with wheel for
determining length of log.
the diameter being indicated by the position of the movable arm after calipering the
log and taking off the bark correction. Defects are then deducted from the gross
volume, either by measuring the defective portion or by ocular estimate of the volume
of the defect. J. J. Fritz, Gorham, N. H., 1921.
Nore. In 1909 a commission of investigation recommended to the Maine
Legislature the adoption of the cubic foot as the statute rule of Maine. This was
not done. One lumber company, Hollingsworth & Whitney, Waterville, Maine,
has since 1904 used a cubic foot standard, measuring the middle diameter with cali-
pers, outside bark. The rule then allows 123 per cent deduction for volume of bark,
and gives the net cubic contents of solid wood. The per cent of volume of bark is
not constant but varies with the size of tree and its age and exposure. The arbitrary
figure chosen simply represented the approximate average volume for the species
and region in question, namely, spruce and balsam in Maine.
A converting factor for this rule has been suggested, of 185 cubic feet to 1000
feet B. M. This gives 5.4 board feet per cubic foot, or 45 per cent of the cubic con-
tents when measured at the middle. Reduced to diameter at small end, for a taper
of 1 inch in 8 feet, logs 18 inches in diameter would give 50 per cent of the small
LOG RULES FOR CUBIC CONTENTS OF SQUARED TIMBERS — 33
cylinder in board feet. This suggested ratio is therefore lower than those adopted
for the New Hampshire and most other converted cubic log rules.
Not. Weight as a Basis for Measuring Cubic Contents. Actual weight of logs
is seldom used as a basis of measurement, as the variation in moisture contents
caused by seasoning prevents standardization even for a given species. A few
valuable timbers are imported by weight. The long ton of 2240 pounds is used.
The ton as ordinarily used in measuring timber is a cubic measure equivalent to
either 40 or to 50 cubic feet and is usually applied to squared timbers. The unit of
50 cubic feet is also termed a ‘“‘load”’ and is used in measuring teak.
Red cedar logs are sometimes purchased by weight, on account of their extreme
irregularity and the difficulty of measuring them.
35. Log Rules for Cubic Contents of Squared Timbers. A definite
departure from the use of total cubic contents is found in log rules
giving the cubic contents of the squared timbers which may be hewn
or sawed from round logs. The waste constitutes the portion hewn
or slabbed off. A square inscribed in a circle occupies 63.6 per cent
of its area. Rules based on this principle would give a waste factor
of 36.4 per cent of the cylinder scaled.
Inscribed Square Rule. The width of a square inscribed in a 24-inch
circle is 17 inches.!. The width of any other inscribed square is seven-
teen twenty-fourths of the diameter of the log. The cubic contents
of the log is that of the square so determined, measured at the small
end of log.
The width of a square inscribed in a 17-inch circle is 12 inches, each
foot of log containing 1 cubic foot of squared timber. The cubic con-
D2
17?
Inscribed Square Rule is obtained. The latter method is termed the
Seventeen-Inch Rule. The rule gives 63.4 per cent of the cubic contents
of the small cylinder, and proportionately less of the entire log depend-
ing on taper, length and diameter (§ 31).
Big Sandy Cube Rule. Synonyms: Cube Rule, Goble Rule. This
Cube Rule, used on the Ohio River, assumes that it requires a log 18
inches in diameter at small end to give a timber 1 foot square. This
rule scales 56.6 per cent of the small cylinder. The volume of logs of
other sizes is found by the formula,
tents of any log is —>L. By either of these rules of thumb, the so-called
92
aig
VaoL.
This rule is sometimes expressed in board feet by multiplying the
cubic contents by 12.
‘The side of the inscribed square is found by squaring the diameter of the log,
dividing by 2 and extracting the square root,
34 LOG RULES BASED ON CUBIC CONTENTS
Two-thirds Rule. By this rule, the diameter of the log is reduced
one-third, the remainder squared, and multiplied by the length of the
log. As diameters are in inches the formula is V=(3D)? L+144.
This is a caliper rule applied to the middle area, and gives 56.5 per |
cent of the full cubic contents of the log. It is sometimes erroneously
applied to the small end.
Quarter Girth or Hoppus Rule. This rule depends upon the direct
use of the girth, rather than diameter. The average girth is taken
in inches at middle point, or by averaging both ends. Then V = Ces
This formula gives 78.5 per cent of the actual total cubic contents of
the log. It is a commonly used standard for measuring round logs in
England and India. To express the contents in cubic feet the result
is divided by 144. "
36. Log Rules Expressed in Board Feet but Based Directly upon
Cubic Contents. The Blodgett or New Hampshire rule is not the only
log rule based on cubic contents, which attempted to express the results
in terms of board feet. Any cubic rule can be converted into board-
foot form, in theory, by the use of a ratio similar to those used for the
Blodgett Rule. The ratio for board-foot contents of one cubic foot is 12.
Twelve l-inch boards cannot be sawed from 1 cubic foot, but a squared
timber 12 by 12 inches contains 12 board feet per linear foot. For con-
verting the entire log directly into board-foot contents of squared
timbers, it is evident that the ratio will be less than 12 board feet per
cubic foot, due to waste in squaring the log, while the conversion into
contents in inch lumber requires a still lower ratio.
The characteristic of all converted rules is that a fixed multiple
or converting factor is used, regardless of the diameter or taper of
the log. The rules differ only in the converting factor used, and in
the method of measuring the log, whether at middle, or end.
Constantine Log Rule. This rule is merely the expression of the cubic
contents of a log regarded as a cylinder, in terms of board feet, by
multiplying the cubic contents by 12. The diameter is measured at
the small end of log. The formula is
,_ 1D?
[ace
The rule is used to measure the contents of logs used for veneers.
Cuban One-fifth Rule. This Rule is based on the square of one-
fifth of the girth taken in middle of log. The formula when G is in
inches is
Ce
v= (912
FORMULA FOR BOARD-FOOT RULES 35
The rule gives just 50 per cent of the total cubic contents of logs
in board feet. This is equivalent to 6 board feet per cubic foot. This
rule is extensively used for imported hardwood logs. The contents
of logs in cubic feet is found by dividing by 144 instead of 12.
In practice, fractional inches resulting from the fifth girth are dropped as follows,
e.g.,
Girth, 50, 51 or 52 inches Square, 10 by 10 inches
53, 54 inches 11 by 10 inches
55, 56, 57 inches 11 by 11 inches
58, 59 inches 12 by 11 inches, ete.
Square of Two-thirds Rule. Synonyms: St. Louis Hardwood,
Two-Thirds, Tennessee River, Lehigh, Miner. This rule is derived from
the Two-thirds Rule by multiplying the cubie scale by 12. The rule
is used for hardwood logs in the Middle States, and for pine to some
‘extent in the South Atlantic States, and is frequently erroneously
applied to the small-end diameter of the log.
Cumberland River Rule. Synonyms: Evansville, Third and Fifth.
This rule resembles the Square of T'wo-Thirds Rule, in that one-third
of the diameter is deducted and the remainder squared. But it differs, in
that one-fifth of the volume of the squared stick is then subtracted for
saw kerf, and the remainder converted into board feet. The rule is
always applied to the small end of the log except for long logs, when
the diameter at middle point is taken. This rule is used on the Missis-
sippi Valley and its tributaries, for hardwood logs.
Square of Three-fourths Rule. Synonyms: Portland, Noble &
Cooley, Cook, Crooked River, Lumberman’s. In this rule, one-fourth
is deducted from the diameter at small end, and the squared timber
expressed in board feet. The rule was formerly used in New England
but is now obsolete.
Vermont Rule. This rule is derived from the Inscribed Square
Rule by multiplying the values by 12. It is the legal standard of the
State of Vermont. The contents of a 12-foot log may be calculated by
a rule of thumb, by multiplying the average diameter of the top of the
log inside bark, in inches, by half such diameter in inches. The rule is
not extensively used even in Vermont, being supplanted by others,
notably the New Hampshire or Blodgett Rule.
37. Formula for Board-foot Rules Based on Cubic Contents.
Any board-foot log rule the values for which are obtained by deducting
the same per cent from the cubic contents of logs of all sizes, may be
expressed by the formula
he
Board feet = (1— oes XTa4 poe bis
36 LOG RULES BASED ON CUBIC CONTENTS
in which C=total per cent of waste deducted from the cylinder,
1—C=per cent of cubie contents utilized,
1 .
144 reduces D? from inches to square feet, and
12 converts cubic feet to board measure.
The formula, simplified, becomes
Board feet = (1— OBL
But the important distinction remains, that some of these log rules
are meant to apply to the middle diameter and others to the small end,
and while the per cent subtracted from the cylinder measured is uniform
for the rule, the per cent actually subtragted from the log is uniform only
for those rules using middle diameter, and varies over a wide range for
rules based on diameter at small end of log.
Note. Obsolete Rules. The following log rules, obsolete or unused, are based
on the above formula and principles: Saco River (Maine), Derby (Mass.), Partridge
(Mass.), Stillwell’s Vade Mecum (Ga.), Ake (Pa.), Orange River or Ochultree
(Texas). A new rule, the Calcasieu (La.), deserves the same fate. The Tatarian
rule (Wis.), which is based on this principle, gives approximately correct board-
foot contents for a log of a given size, It has never been adopted in practice.
38. Comparison of Scaled Cubic Contents by Different Log Rules.
In Table II is shown the comparative volumes, in per cent of total cubic
contents, which are scaled by different log rules based upon cubic
volume. These per cents represent the converting factor used to obtain
the values given in the rule from the volumes of cylinders.
Note. The values in this table were obtained by applying the ratio between
the volume of two cylinders 16 feet long, 18 inches and 19 inches in diameter respect-
ively. This ratio is 28.27 : 31.50. Log rules based on cylinder at small end then
28.27
scale but Sen or 89.7 per cent of their volume, to which the reduction per cent for
5
waste is applied; e.g., the Vermont rule wastes 36.6 per cent by the inscribed square
method. Then, based on the small end, the per cent scaled is 63.4, but based on
middle diameter for the above size, it is 89.7 X63.4 =56.9 per cent. The table gives
a correct comparison of the different log rules which are constructed by using a
fixed per cent of cubic volume. The per cents given for the rule under the first
column, based on the point at which the rule is applied, are consistent for all logs.
But the equivalent per cents obtained by converting the scaled contents into terms
of the cylinder based on the other diameter—as middle, for logs measured at the end
and vice versa, will vary as the relative contents of these two cylinders varies (§ 31).
This will not change the rank or order in which the rules fall. The rules are tabulated
in order of the relative per cent of total contents which they scale.
There is no common standard for measuring the cubic contents of squared timbers.
The Quarter Girth method gives the fullest measurements, while the others more
closely approximate the net contents as given by board-foot rules,
COMPARISON OF SCALED CUBIC CONTENTS
TABLE II
Oo”
CoMPARISON OF PER Cents or Cusic CONTENTS OF CYLINDERS SCALED BY VARIOUS
Loa Russ, ror Locs 18 INcHEs IN DIAMETER AT SMALL END, WITH 2-INCH
ToraL TAPER
Cylindrical contents measured inside bark
Log rule
Cubic Standards
Market or Glens Falls standard
22-inch standard
Blodgett or New Hampshire.. .
Cubie foot—Maine
Cubic meter—Philippines: |
MprEEMO S40 is. an hi wes, Sd aye
Cubic Log Rules for Squared
Timbers '
Quarter girth or Hoppus
Inscribed square
Two-thirds
Cube rule, or Big Sandy......
Log Rules Expressed in Board
Feet but Based on Cubic
Contents
Constantine
Tatarian
Saco River
Derby
Square of Three-Fourths’.... .!
JEDIT Ts | Ae Se Oe
Blodgett, converted, ratio 100.
fo WOOOT6 1B: Mi 2 5s i.2.
Basis of measure-
ment of cylin-
der, in applica-
tion of rule
at at
small | middle.
end.
Per Per
cent cent
HOON, stiecrsche
HOON wines
Ait 0 100
ee | 100
100 mee |
Rie 100
a | vss |
GB.4) Tt oe ke
PS ee 56.5
SOOM et cas
OO al ease: |
S4s Ope |
EL le aie
otele ser ete.
CALLER) ee aA
Gar Gules cess:
tb Pas 59.7
* Added.
|
Per cent of scale Per cent deducted
if measured at|
other point
ate. (|| at
middle | small
end
BOUT | ote
ROU Ail nano
eee 111.4
nA" ea a ar
TO ten
Bok 1010-4
neo iat875
entOs | ale
ce may
BO Sy eee
BOP Tc ck:
TEE Aaa ied
Garni
64.7 | ‘Ae
Gael eo.
Gl Shia
1
bes EL | 66.5
from contents of
cylinder to ob-
tain contents
given in rule—
For rules applied
at at
small middle
end
0 10.
0 10.3
ia 0
14 0
0 10.3
Tal ete 0
125 PA ts:
36.6 | 43.1
3/all 43.4
43.4 | 49.2
0) 10.3
16.0 24.6
27.6 35.0
2429) SORE
28.3 Sone
olie2 38.2
a3). 40.3
38 LOG RULES BASED ON CUBIC CONTENTS
TABLE I1—Continued
| |
Basis of eneurelieey cent of Sealel Per cent deducted
ment of eylin- if measured at} from contents of
der, inapplica-| other point cylinder to ob-
tion of rule tain contents
given in rule—
For rules applied
Log rule a
| |
at at ate ie ad at at
small | middle.| middle | small | small | middle
end. end end
Per Per
cent cente
Log Rules.—Continued
22-inch standard, converted,
ration) porZoOMt wei. ee GILT I Gee SSnO Gl Aone 34.4 41.1
Market, or 19-inch standard,
converted, ratio 1 to 200 ft.
BIN CS ie ee eee a ae ee (CII, eo oe 5S x4 aie 34.9 41.6
WGI TAOS A Fe ees aos CRE ee eG OS oes ell ears Hos Owls 36.6 43.1
Vade Mecum (Stillwell’s)..... GS32% eer DOsdas lh eeste: 36.8 43.3
Square of Two-thirds........] ..... DORON bear | 16289) sia 43.5
AIK CR Res ties Ose eat eae G24 Pere 300) os oot 37.6 44.0
French’s (Los Angeles).......) ..... BOD Mi ihac. Fe BSODh VALS 47.8
Calcasicule: 4 o.:( wien ences DAS Te sete hs tog WEL Teele wae eae 42.2 48.1
Blodgett, converted, ratio 115
(HO) GOO) itis TBM Seo alse cll noaee OMEG | Buta Diesul 42.2) ied sen
Blodgett, converted, ratio 106
(Ho): IMO athy TEI ES Se oe oboe ao 155,08 Pg Beat 1910) 5¢: S| teens 43.8 49.6
CubaniOne-Wilth: 3. 5 455 cel eee FAO TIN fils pens te 55.9 44.1 49.9
Orxancenruivien: wus: epee nae HOMO!) ae: ANSE i ee eee 49.1 54.3
Maine cubic rule, converted)
1sseustit. per lOOO it. Beisel ee AD SOR ie. 50) 1 49.9 |) 55.0
CumberlandsRiverss. eee mea Deen |e oe AQ Gia laa se | 75428 59.4
Delaware or Eastern Shore...| 42.4 | ....: SOLS ee O70 61.9
Of the cubic log rules expressed in board feet, the Constantine is frankly a cubic
rule, converted from the cubic foot, but based on the small end of log. The rest
are suitable neither for cubic contents nor for board fect, since they do not express
the former nor do they measure the latter correctly (Chapter \).
These rules are all convertible into cubie units or from one to the other, when
based on cylinders measured at the same point.
D?
The formula, Board feet = (1 =O) ae can be used to obtain the values for any
of these rules, by substituting for C the per cent given in the last two columns of
Table II, e.g.
RELATION BETWEEN CUBIC MEASURE 39
To derive the Inscribed Square rule, the cubic contents of cylinders from Table IT
are multiplied by 1 —36.6, or 63.4 per cent.
To convert the Inscribed Square rule into terms of the Cumberland River rule;
since 1—54.8 =45.2 per cent, the volumes of the two rules are as 45.2 to 63.4. The
45.2 :
Cumberland River rule gives aa of the Inscribed Square rule, or 71.3 per cent.
But the Hoppus Rule cannot be converted into terms of either of the above rules,
since it is measured at the middle point, unless a log of a given diameter and average
taper is assumed.
39. Relation between Cubic Measure and True Board-foot Log
Rules. The conversion of these log rules from cubic to board feet is
based on the erroneous assumption that logs of all dimensions when
sawed into lumber will yield the same ratio of board-foot contents to
cubic contents. In practice, the larger the log, the greater will be the
ratio or per cent of its contents which makes lumber and the less the
per cent wasted. For this reason it is not possible to use the same
standard for scaling both the cubic- and board-foot contents of logs,
no matter what converting factor is chosen.
Cubic rules, converted to board-foot contents by a fixed ratio, tend
to scale small logs too high and large logs too low, as compared to the
actual sawed contents. The common mistake of the authors of these
rules is to assume that once the sawed contents of a log of given diameter
and length is found, the ratio obtained will apply unchanged to logs of
all other sizes. These rules have therefore fallen into disrepute in the
scaling of board feet, because of their inconsistencies for this purpose.
For products such as pulpwood, which utilizes the entire contents
of the log, these so-called board-foot rules give consistent results for
logs of all sizes, but do not possess any advantage over the direct use
of the cubic standard upon which they are based. On the other hand,
if log rules are intended for the measurement of the actual output of
1-inch lumber, they must be based on other principles (§ 54).
The two quantities of measurement, cubic volume, and squared
board feet obtainable, are incommensurable unless the diameter and
also the taper of each log is known. The lump sum of a lot of logs
measured in cubic volume therefore, cannot be converted into board-foot
measure except by readjusting each individual value by the diameter
of each individual log. The use of these hybrid rules should be discon-
tinued in favor of cubic standards on the one hand, and board-foot log
rules based on correct principles on the other.
CHAPTER V
THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
40. Necessity for Board-foot Log Rules. In other lines of industry
it is not customary to measure raw materials in terms of the quantity of
finished product contained therein. The volume or weight of the raw
product is the basis of sale. On this basis logs would be sold for their
cubic contents.
But the purchaser of raw material must know approximately the
quantity of finished product he can obtain from it before he can estimate
its value. If the product is to be lumber, the possible yield of boards
of certain qualities and grades determines for him the value of the logs.
If it had been found by experience that all logs regardless of size
would yield the same per cent of their contents in lumber, if sawed by the
same methods, the cubic standard might have been universally accepted,
as it was in the Adirondack region. But when it developed that there
was no consistent ratio of cubic to board feet the only alternative was
to measure the product directly as boards.
That the board-foot log rule was needed is shown by the fact that such
rules were originated independently in practically every lumbering
region. The contents of the log in sawed 1-inch boards was placed on
the seale stick, separately for each inch-class and each standard length.
These board-foot rules soon became practically the universal standard
of log measure, and are only recently being superseded where the logs
are used for other purposes than lumber; they will continue to be a
generally accepted commercial standard of log measure for the lumber
industry as a whole, until such time as the original stands of timber of
the country give way to smaller second-growth and closer utilization
and probably as long as a large percentage of logs are sawed into lumber.
41. Relation of Diameter of Log to Per Cent of Utilization in Sawed
Lumber. The sawed output from logs in board feet shows an increasing
per cent of utilization with increasing diameter of the logs. This result
may be expressed by the ratio of board feet produced from each cubic
foot of total volume. This tendency is illustrated in Table III.
The per cent of utilization in this table is based on the total cubic
contents of the log as measured by Huber’s formula at middle diameter
inside bark. But practically all log rules for board feet base the con-
tents upon the cylinder whose diameter is taken at the small end, in
40
RELATION OF DIAMETER OF LOG 41
which case the volume of the log lying outside the cylinder is neglected.
On this basis, the apparent per cent of utilization would be con-
siderably increased over the figures given in the table.!
TABLE III
RELATION OF CuBIc AND Boarp-roor ConTENTS OF 16-root Locs wiTH A TAPER
oF 1 IncH IN 8 FEET, BASED ON TIEMANN’S Loa RULE, 7-INCH SAW KeErRF,
(§ 63) :
Diameter : Sawed Ratio
Aube Cubic contents, Volume
inside bark at : feet B.M. to ae
: contents. Tiemann ; utilized
middle of log. 1 cubic foot
Log Rule.
Inches Cubic feet Feet B.M. Per cent
3 0.79 1 27, 10.5
4 1.40 4 2.85 23.8
5 2S 9 4.13 34.4
6 3.14 15 4.77 39.5
@ 4.28 23 ot 44.8
8 5.59 32 NATAL 47.7
9 7.07 43 6.08 50). 7
10 Seve 55 6.30 52n5
11 10.56 69 Oo 54.4
12 12.57 84 6.68 545) 1
13 14.75 101 6.85 57.0
14 17.10 119 6.96 57.9
15 19.63 139 7.08 59.0
16 22.34. 160 7.16 59.7
17 PAB ae 183 7.26 60.5
18 28.27 207 [BY 61.0
19 31.50 233 7.39 61.6
2 54.54 419 7.68 64.0
31 83.86 659 7.86 65.5
37 119.47 954 7.99 66.5
43 161.36 1301 8.06 67.2
49 209.52 1703 8.13 (ay/ 27
55 263 .98 2159 8.18 68.2
61 324.96 2669 8.22 68.5
1 For a 16-foot log 12 inches at middle, with 2-inch taper, and scaling diameter
at end of 11 inches, the cubic contents are 10.56 cubie feet, the ratio of board feet
to cubic feet is 7.95, and the apparent per cent of utilization is 664 per cent as against
an actual 55.7 per cent when the entire volume including taper is taken as the basis.
For logs with considerable taper, which permits more lumber to be cut from the slabs
lying outside the cylinder, the apparent per cent of utilization would be still greater,
while the actual per cent utilized would in reality be lower for such rapidly tapering
logs than for more cylindrical forms,
42 THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
It is practically impossible to secure closer utilization than 70 per
cent of actual total cubic contents of logs in the form of sawed inch
lumber exclusive of the utilization of slabs, edgings and sawdust when
circular saws whose kerf is } inch or more are used. By using band
saws which cut a §-inch kerf and by producing a large per cent of timbers
and boards thicker than 1 inch, thus reducing the waste from saw kerf,
the utilization may rise as high as 80 per cent for the larger logs.
42. Errors in Use of Cubic Rules for Board Feet. By comparing the
per cent of possible utilization in Table III (§ 41) with the per cents
given for cubic log rules in Table II (§ 38) the character and relative
accuracy of these log rules can be judged. For the Blodgett Rule, with
a ratio of 115 units to 1000 board feet measured at middle diameter,
the ratio or per cent scaled is 51.9 for all classes and sizes of logs. By
comparison with Tiemann’s Rule this*rule is shown to be correct for
logs between 9 and 10 inches in diameter, but over-scales smaller logs,
and under-scales larger logs. The original Blodgett ratio of 100 : 1000
gives a per cent of 59.7. This is correct for 16-inch logs, too high for
all logs of smaller diameter and too low for larger logs.
When the point of measurement is shifted to the small end of log, the
diameter measurement is correspondingly reduced. When the scale of
board-foot contents thus determined is compared with this smaller
cylinder, the per cent of utilization can be expressed for such log rules
and applies uniformly to logs of all sizes, but only to the small cylinder
thus measured (§ 81).
A comparison of the. Blodgett Rule applied at the small end of log,
with the Tiemann rule applied at the middle of log, is shown below. The
per cents will apply to logs of all lengths whose total taper is but 2 inches.
TABLE IV
CoMPARISON OF BLODGETT AND TIEMANN Loa RuLEs FoR CERTAIN Logs
Diam- Per cent of | Per cent of | Per cent of | Per cent of Error
Total : é
eter ieee small cylinder) total log total log total log in
log. scaled by in small scaled by scaled by Blodgett
Inches} Inches! Blodgett Rule) cylinder | Blodgett Rule/Tiemann Rule Rule
6 2 56.2 73.4 41.2 44.8 — 2.6
12 2 56.2 85.2 47.9 57.0 — 9.1
18 2 56.2 89.7 50.4 61.6 —11.2
24 2 56.2 92.2 51.8 64.0 —12.2
30 2 56.2 93.7 52.6 65.5 —12.9
Cubic rules, as a class, when converted to read in terms of board feet,
thus tend to over-scale small logs and under-scale large logs, whether
SCALING LENGTH OF LOGS FOR BOARD-FOOT CONTENTS 43
they are applied at the middle point, or at the small end. Of the two
methods the small end gives the mosi consistent results in board measure,
since both the actual per cent utilized and the per cent of total con-
tents scaled decrease with diameter of log. But the decrease in scaled
contents is always at a lesser rate than that of actual sawed contents,
hence the tendency to over-scale small logs remains though the size of
the error is reduced.
43. Taper as a Factor in Limiting the Scaling Length of Logs for
Board-foot Contents. Since board-foot contents of logs is equal to
cubic contents minus waste in sawing, the character and amount of this
waste determines the net scale of the log. This waste consists of saw-
dust, slabs and edgings. As lumber is commonly manufactured with
parallel edges, in even widths, the custom of sawing boards whose
- length equals that of the log and rejecting all shorter pieces would cause
a waste not only of the slabs sawed from the cross section at the small
end but of the entire taper of the log, which would be discarded as
edgings and slabs. When board-foot rules were first brought into use
close utilization of short lengths and of wedge-shaped pieces was not
practiced, and this total waste actually occurred. Under these con-
ditions the correct point of diameter measurement was not the middle,
but the small end of the log. Owing to their early origin, the com-
mercial board-foot log rules now in use are nearly all based on measure-
“ment at the latter point.
This waste, as measured in cubic volume, increases rapidly with
increasing length of log. The shorter the logs cut from a given tree,
the less will be the apparent waste from taper. Long logs, the scaled
contents of which are based on cylinders measured at their small end,
would give an entirely different and much smaller scale than if the same
logs were cut instead into two or more shorter sections and sawed into
correspondingly shorter lumber. Instead of sealing one log of a given
top diameter sometimes extending the entire length of the bole, we would
then have to scale a series of shorter logs, each of which has a top diam-
eter larger than the preceding one by the amount of the taper between
the points measured. The sum of volumes of these short logs would
always exceed that of the single log measured at small end. These long
logs are usually cut into two or more sections at the mill. For these
reasons, logs, if their length exceeds a definite maximum are scaled
as the sum of two or more shorter logs, by taking caliper measurements
at arbitrary points of division; e.g., a 26-foot log scaled as two pieces
would be measured at its small end, and at a point 12 feet from the end,
thus scaling as a 12-foot and a 14-foot log. The scaling diameter of the
larger or butt section exceeds that of the top end by the amount of the
taper between the points measured. Each section is thus scaled as a
44. THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
cylinder, and measured at its upper or small diameter, and the sum of
volumes of these cylinders gives the scale of the long log.
The shorter these scaling lengths are made, the larger the total scale
of the log, but the maximum scaling length must not be shorter than the
average length of the lumber sawed. In log rules, figures for lengths
up to 40 feet may be given, and scaling practice often corresponds, but
in selling logs the U. 8. Forest Service limits the scaling length to 16
feet, which is a standard commonly accepted by timber owners.
44. The Introduction of Taper into Log Rules. With the increase
in utilization, much of the lumber formerly wasted in slabs is now secured
as short lengths. All log rules in commercial use ignore this product
and treat the logs as if cylindrical, up to the maximum scaling length.
To overcome this drawback and include the products from slabs or taper
without requiring the measurement of logs in separate very short sec-
tions, the International log rule was constructed,! based on the principle
Taper, 2 inches in 16 feet. Vertical scale exaggerated.
Fia. 5.—Short versus long sections in measuring log contents and in constructing
a log rule.
of building up the scaled volume of a log from shorter cylindrical sec-
tions. These short cylinders are 4 feet long and each successive cylinder
is increased by }-inch in diameter. The scaled contents of each short
section is determined, and the sum of these sections gives the scale of
the log as given in the log rule. The soundness of this method depends
upon demonstrating that the average taper of most logs is not less
than that used in the rule, namely, 2 inches in 16 feet. This holds good
for most Northern and Western species, but for Southern pines the taper
does not always equal this figure. To guard against excessive error
from tapers differing from the rate used in the rule, the maximum
sealing length is limited to 20 feet.
If the log in Fig. 5 is regarded as a 64-foot log, scaled in four 16-foot lengths by
any commercial log rule, the scaling diameters are taken at A, B, C and D. The
gain in scale is caused by inclusion of the shaded portions.
1 The Measurement of Saw Logs, Judson F. Clark, Forestry Quarterly, Vol. IV,
1906, p. 79.
THE INTRODUCTION OF TAPER INTO LOG RULES 45
Regarded as a 64-foot log scaled by middle diameter the scaling diameter is C,
and the log content is that of a cylinder 64 feet long and of size indicated by C C’.
Regarded as a 64-foot log scaled by end diameter, the scaling diameter is A
and the log content is that of a cylinder 64 feet long and of size indicated by A A’.
Regarded as a 16-foot log scaled at small end, and not in middle, the loss in
scale is indicated by the shaded portions. This loss is common to all commercial
log scales based on small end of log.
But if the contents of the 16-foot log as given in the scale when measured at A
is built up by measuring the log as four 4-foot cylinders whose scaling diameters
are A, B, C and D, this loss from taper common to all the commercial log rules,
except when applied at middle diameter, is avoided and practically full scale secured.
A comparison of the results of these three methods of treating taper is brought
out in Table V.
TABLE V
Errect oF DIFFERENT METHODS OF SCALING A Loa
S ‘
Length : Scaled as Scaled as ees
‘ Scaling 16-foot logs
of Diameter 4 one log based} 16-foot logs ;
Oi diameter allowing
log. inside bark. on small each regarded} , °.
rounded off. : : 2-inch taper
diameter. jas a cylinder.
every 4 feet.
Feet Inches Inches Board feet | Board feet | Board feet
(1) (2) (3) (4) (5) (6)
0 24.5 Boe. LSE WS oes
16 20.6 21.0 328 328 355
32 19.6 20.0 590 623 675
48 17.3 17.0 618 829 900
64 14.0 14.0 531 962 1050
The final column in each of the above examples is the contents of a log 4 feet
long as sealed by the International log rule. The difference in scale by the other
methods is due entirely to the length of section scaled as one piece. In column 4,
this cylinder, with top diameter indicated, extends the full length of the log. In
column 5, a new diameter measurement is made every 16 feet, but the cylinder of
this diameter is 16 feet long. In column 6, the diameter is taken at 16-foot intervals,
but the cylinder from which this 16-foot log is scaled is built up from four cylinders
each 4 feet long, and each 3-inch greater in diameter than the one preceding it.
If the average taper of logs is }-inch for 4 feet, and pieces 4 feet long are mer-
chantable, then the scale in column 6 is correct. Based on this conclusion the loss
in scale through neglect of taper is as follows:
Length of Sealed as one | Scaled as 16-foot
log. log. logs.
Feet Per cent loss Per cent loss
16 8 8
32 13 8
48 31 | 8
64 ol 8
Thus the loss in scale is proportional to the length and total taper of the log.
46 THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
45. Middle Diameter as a Basis for Board-foot Contents. In some
regions no attempt is made to divide long logs in scaling. While short
logs are scaled at the end, logs over a given length are measured once at
the middle and the scale applied to the entire log. In cypress this
measurement is sometimes taken at a point distant from the small end
by one-third of the total length. This practice of substituting middle
for end diameters on long logs and scaling the log as one long cylinder
whose diameter is thus obtained assumes that the loss in sawing the
smaller top section will be offset by gain from taper in the butt portion.
The total scale by this method exceeds that obtained by scaling the log
as the sum of separate cylinders.
In theory this measurement of logs for board-f6ot contents at the middle diameter
should possess the same advantage over measurement at the small end as for cubic
contents. But for the former purpose, the factor of waste exercises a definite influ-
ence on the method of scaling adopted, where for cubic contents it does not.
With very close utilization of short lengths, it may be assumed that the sawed
output of two logs of the same middle diameter, one of which tapers rapidly, the
other gradually, would be nearly equal, since what is lost at the small end of the
rapidly tapering log would be saved at the larger end. That this is approximately
true is the premise on which Tiemann based his board-foot log rule (§ 63) on middle
diameter.
If, on the other hand, the minimum length of board corresponds with the ordinary
length of log sawed, the log with rapid taper loses a far greater percent than that
with small taper, and two logs whose diameters at their small end are the same
would give equal sawed contents regardless of differences in taper. Since the latter
condition held when the log rules in common use were invented, this fact, and not
the difficulty of scaling logs at the middle point, explains the general adoption of
the custom of basing the contents upon the diameter at the small end.
46. Definition and Basis of Over-run. The purpose of all log rules
is to furnish a standard of measurement for logs, fair alike to buyer and
seller. For board-foot log rules this is best accomplished when the
rule measures accurately the amount of lumber that may be sawed from
straight, sound logs. It was the intention and the claim that each of the
fifty or more log rules extant should perform this service under the con-
ditions for which it was made; yet in spite of this fact, the contents of
sound logs of the same dimensions, as measured by different rules, may
differ more than 100 per cent.
While some rules based on incorrect premises never were accurate, most of the
rules as checked by actual mill tests were probably satisfactory when first employed.
But these rules were not changed to keep pace with the closer utilization brought
about by the improvements in machinery, methods and markets. Although obso-
lete as a measure of actual product, they have been retained through custom. It is
difficult to supplant or alter a commonly accepted standard of measure, even if
grossly inconsistent and inaccurate.
Antiquated log rules thus cease to perform the true function for which they
INFLUENCES AFFECTING OVER-RUN 47
were intended, of measuring in the log the possible output of lumber. The sawed
product tends to over-run the scale of contents shown by the log rule.
An excess of sawed over scaled contents of logs is termed the over-run.
The over-run is always stated as a per cent of the log scale. The log
rule, whether accurate or defective, is accepted as the fixed standard,
giving the same contents for all straight and sound logs of the same
dimensions. Over-run, on the contrary, will vary with several factors.
A knowledge of the average per cent of over-run which may be expected
over the scale enables both buyer and seller of logs to gage their value
more accurately. As value is dependent on the price of lumber, the
dealer in logs must know whether for every 1000 board feet of lumber
scaled by the log rule, there will be obtained say 1250 board feet of
sawed lumber, or only the 1000 board feet scaled, for in the former
case the logs are worth 25 per cent more per 1000 board feet of scaled
contents than in the latter.
47. Influences Affecting Over-run. The Log Rule Itself. Two log
rules giving different scaled contents for logs of the same sizes will yield
correspondingly different per cents of over-run. Each rule is arbitrarily
assumed to represent a standard of 100 per cent, the over-run being
computed in terms of the rule employed.
For instance, a given quantity of logs when scaled by the Doyle rule may measure
67,000, and saw out 100,000 board feet. Instead of stating that the log scale gives
67 per cent of the actual product, with an “over-run”’ of 33 per cent, the scale is
taken as the standard or 100 per cent, and the correct over-run in this case is 49 per
cent. When scaled by the Scribner rule, these same logs may give 85,000 board
feet. In this case the over-run will be 17.6 per cent since 15,000 board feet is
17.6 per cent of 85,000 board feet scaled in the log.
Since the quantity of sound lumber contained in logs can be measured with
only approximate accuracy, due to hidden defects and other factors, the buyer
demands a certain margin of safety. A reasonable over-run of from 5 to 10 per
cent is usually expected. With a properly constructed log rule, the over-run should
be about the same for large as for small logs. The worst defect which a log rule
can possess is inconsistency in scale between logs of different sizes (§ 39). Slight
irregularities in scale of individual diameter classes may average out in the general
run of logs. But when the per cent of board-foot contents scaled by a log rule
increases or decreases in proportion to size of log, there is no way of adjusting it.
The over-run will then vary with the average size of the logs scaled. Such a rule
can never give permanent satisfaction to both the buyer and the seller of logs.
48. Influences Affecting Over-run. Methods of Manufacture.
With a fixed standard set by a log rule, the greater the economy of man-
ufacture, the greater will be the over-run. Any factor which reduces
the waste in manufacture increases the output. The waste in straight,
sound logs consists of slabs, edgings, trimmings and sawdust. In addi-
tion, there may be a loss or gain in the scale of lumber due to fractional
thicknesses not measured in board feet (§ 20).
48 THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
Saw Kerf. The fewer the number of saw cuts required, the less the
waste. Lumber sawed and measured to standard thicknesses greater
than 1 inch therefore increases the total output in board feet. A dimin-
ished thickness of the saw has a similar influence. Log rules, correct
when adapted to a }-inch saw kerf, give an over-run of more than 10
per cent when a $-inch saw kerf rs cut. The use of circular saws cutting
a ;-inch kerf partially accounts for the small scaled contents given
by some of the old log rules.
Slabs. Waste in slabs is reduced by sawing narrow and thin boards
and short lengths. The short lengths serve to fully utilize the taper in
long logs, increasing the over-run on this class of material. The method
of sawing a log also affects the per cert of utilization of slabs. Slash
sawing, or sawing alive, as practiced for round-edged boards (§ 21)
would result in waste where the boards are to be used in their full length,
and trimmed to square parallel edges. By this method, short boards
would be secured from but two sides of the log. The usual custom in
manufacturing lumber of standard lengths is to turn and square the log,
slabbing all four sides.
The gain in sawed product, by sawing around, in comparison with slash sawing,
for square-edged boards, was shown to equal the following per cents, as determined
by H. D. Tiemann.
TABLE VI
GaINn IN OuTpUT SECURED BY SAWING AROUND, COMPARED WITH SLASH SAWING,
IN Per Cent or Latrrer Output
Diameter
of log.
Inches
Length 10 feet. | Length 20 feet.
Per cent saved Per cent saved
Above 13 inches the difference is less perceptible. Where round-edged boards
are fully utilized and not reduced to square parallel edges, not only does sawing
around give place to slash sawing, but the per cent of utilization is much greater
than by either method of sawing for square-edged lumber, due to the shorter lengths
utilized in working up the round-edged lumber in the factory.
STANDARDIZATION OF VARIABLES IN LOG RULE 49
Full and Scant Thicknesses of Boards. Boards not cut to exact
dimensions, if cut full lose the excess when measured, and if too scant
are either rejected, or reduced in grade. If cut scant but within pre-
scribed limits, they are scaled by superficial measure, and increase the
over-run (§ 20).
In either case the sawyer to secure full scale of lumber must pro-
duce boards measuring within 35-inch of the required thickness. This
is impossible without good machinery. In local custom mills, much
lumber is manufactured in uneven thicknesses causing a loss in scale
and reducing the over-run.
49. Standardization of Variables in Construction of a Log Rule.
The over-run in sawing logs will depend for a given log rule upon thick-
ness of saw kerf, average dimensions of lumber, closeness of utilization
of slabs and of taper, and the exactness of manufactured dimensions.
All four of these factors are variables.
For a given mill, the saw kerf alone is constant and even then the waste will vary
if two or more saws of different kerfs are used. The other factors are variable.
For different mills, one or more conditions are certain to differ radically, giving a
corresponding increase or decrease in over-run. Standardization of output and
methods, possible in mills of the same class serving the same markets, may secure a
similar degree of slab utilization and of efficiency in sawing to exact dimensions,
but this still leaves the fourth variable, differences in thickness of lumber sawed, to
affect the over-run.
Where the sawed output is in thicknesses less than 1 inch, and expressed in
superficial feet, the product is not comparable with 1l-inch lumber and must be
reduced to terms of l-inch boards for a true comparison with the log scale.
Arbitrary Standards. The essentials of any standard of measure
are fixed qualities and common acceptance. Even a poor or faulty
standard which is universally used would be better than a number of
different rules, or a rule which may be changed to suit conditions or
the preference of the user. These four variables must therefore be
arbitrarily fixed in adopting values for a standard or common log rule,
and in the case of most rules which have found wide use this was done.
The thickness of lumber was fixed at 1 inch, permitting an over-run
whenever thicker dimensions are sawed. The width of saw kerf adopted
by the rule was that used at the time and place of constructing the
rule, and was usually j-inch or larger. Local custom determined the
width of the narrowest 1-inch board sawed and this fixed the amount
of waste allowed for slabbing and edging. Taper was disregarded.
Boards were usually measured only to the nearest full inch of width
and fractional inches disregarded. Skill in manufacture was considered
by checking the results of the rule with the actual sawed output, by
means of mill tallies.
50 THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
Variable Standards. As contrasted with these fixed standard rules,
comes the suggestion ! for a log rule in which average thickness of lumber,
saw kerf and degree of utilization of slabs and taper shall be represented
by variable quantities, and adjusted by each mill owner to suit the
conditions of manufacture prevailing at the time or for the past few
months. Such a rule, when adjusted, would eliminate over-run as
long as the variables in manufacture on which it was computed remained
unchanged. But as a standard of measurement it could never have
any general or legal status unless its values were fixed, when it would
at once be open to the same objections which by its flexibility it sought
to avoid.
50. The Need for More Accurate Log Rules. The great question
with log rules is whether conditions have changed so permanently that
new rules adjusted to these factors should replace those now in use.
The }{-inch circular saw is still retained in small custom mills, and there
is a tendency, in regions that have been cut over by big operators, to
revert to these primitive methods. The operator of a band saw mill
is probably entitled to the over-run resulting from the use of thinner
saws and closer utilization. A log rule made to scale closely the out-
put of such up-to-date plants would exceed the product of the small
mill. Provided the rule is consistent, a conservative log rule which
will give an over-run varying in per cent with closeness of utilization
is probably better for commercial uses than one which aims at securing
the maximum product from modern mills.
Log rules based on correct mathematical principles are the only
rules from which consistent and satisfactory results can be expected,
and this is a far more important factor than the elimination of over-
run. If, in addition, such log rules conform to the present conditions
of manufacture, they have a use in scientific measurements of logs and
standing timber, as a basis for estimates of volume and growth expressed
in the board-foot unit. This use of such a rule would justify its exist-
ence, entirely aside from the question of its possible universal adoption
as a legal standard of log measure.
51. The Waste from Slabs and Edgings. The total waste in sawing
straight sound logs is the sum of the two factors, sawdust, and slabs
plus edgings. For lumber of a given thickness, such as 1-inch boards,
the portion of the cross section of the log wasted in slabs and edgings
may be shown graphically by plotting on diagrams, allowing the proper
space between each board for saw kerf. From these diagrams it is
possible to compute the area of this waste, in square inches, and the
thickness of a ring or collar which will have the same area and thus
represent the waste from slabbing and edging.
1H, E. McKenzie, Bul. 5, California State Board of Forestry, 1915.
THE WASTE FROM CROOK OR SWEEP iil
When this is done for logs of all sizes it is found that except for the
* smaller logs the width of these collars is practically the same regardless
of diameter. This law does not hold for small logs, because the width
of the minimum boards remains the same for all logs and as the diameter
of the log approaches this minimum width of board, the proportional
waste in slabs and edgings rapidly increases until utilization becomes
zero and waste 100 per cent for a diameter of log just too small to saw
out the smallest board or piece that 1s merchantable.
The waste in slabbing and edging varies, for any log, with the aver-
age thickness of the lumber sawed. Logs sawed entirely into 24-inch
plank would show considerably
greater waste in edging than where
l-inch boards are sawed (§ 21).
The results shown by diagram are
confirmed by tests in the mill.
From these investigations it is
evident that the waste from slabs
and edgings is proportional, approx-
imately, to the surface of the log
inside the bark. The surface of a
log is equal to the circumference or
girth, multiplied by the length. As
circumference equals 7D for all
logs, the waste from slabs and edging
Fiag. 6.—Relative waste in slabs and
as then proportional to the diameter edgings from sawing 24-inch plank
of the log multiplied by its length. and 1-inch boards. If 1-inch boards
But the volume of the log in- are sawed, the waste is reduced by
the amount of the shaded portion.
creases as the cross sectional area, : :
The greater proportion of waste in
which is proportional to the square of sawing thick boards comes from the
the diameter (§ 27). The amount of side cuts, hence the practice is to
waste in slabs and edgings from a log cut 1-inch lumber from the sides.
20 inches in diameter is just twice
that for a 10-inch log, since the diameter and the surface are doubled.
But the 20-inch log contains four times the volume of the smaller piece,
and this reduces the per cent of waste from slabs and edgings based on
the volume of the larger log to one-half that for the 10-inch log.
52. The Waste from Crook or Sweep. Log rules apply only to
straight logs. But the standard as to what constitutes straight logs
requires definition. For all commercial log rules, this standard permits
of “normal” crook ($93). This is best defined as crook averaging
not over 13 inches in 12 feet, and including no log which crooks more
than 4 inches in 12 feet. Crook or sweep in long logs is reduced by
cutting them into two or more short sections before sawing. Where
52 . THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
very short material such as box boards is used, crook does not cause
abnormal waste in logs. Care in laying off log lengths in the woods
to secure the maximum length of straight sections by dividing the
tree at the points of greatest crook reduces this source of waste to small
proportions.
Waste from crook is deducted in scaling on the assumption that
the merchantable portion of the log must cut boards extending its
whole length. The influence of length of log upon the waste due to
crook is very pronounced, and where long logs are divided into shorter
lengths in the mill they should never be discounted for crook except
to the extent that this crook will affect the sawed contents of the shorter
pieces. For lumber longer than 12 feet the influence of crook rapidly
increases.
The relation of normal crook to taper is shown in Fig. 7 in which the
line DE is the axis of the cylinder corresponding to a straight log. The
line AB is parallel to this axis and tangent to the margin at the small
L
Fic. 7—Method of measuring amount of crook in a log, in inches. The line JM
represents the proper measurement, coinciding with the shaded portion JA or
waste in the circle representing small end of log.
end. The line AC isa straight line connecting the margins of both ends
of the log. Were the log cylindrical, the line HJ under these circum-
stances would represent the amount of crook. But the taper gives a
larger cross-section at JL than at AK. Unless crook exceeds the taper
for half the log, the cross-section JL when projected upon AK would,
completely cover it, permitting as much lumber to be sawed as if the log
were straight. In the diagram the crook exceeds this taper and the
upper shaded portion of the cross section which represents the small
end must be wasted in slabs, in addition to the normal slabbing of a
round log.
But this waste is incorrectly measured by any other method than
that shown by the line JM, which is the distance to the surface of the
log from a line parallel to the axis, and tangent to the margin of the small
end. This distance gives the crook in inches.
* For a 16-foot log tapering 2 inches, a crook of 1 to 15 inches at the
middle point has no appreciable effect on the output.
THE WASTE FROM SAW KERF 53
By slabbing in the direction of KN this waste may be still further
reduced, since the cylinder sawed is not parallel with the axis but follows
the crook at the small end, and takes maximum advantage of taper at
butt. Logs so crooked that their sawed contents is materially reduced
are not scaled ‘ straight and sound ” or full. Deductions for crook are
discussed in § 93. The waste from normal crook is included with that
for slabbing and edging and is in proportion to surface, and hence to
diameter.
53. The Waste from Saw Kerf. The total waste in sawdust, unlike
that in slabs and edgings, takes approximately the same per cent of the
cubic volume of all logs, regardless of their size. If a log is sawed by the
method called slash sawing, in parallel saw cuts without squaring it,
then, after the first slab is removed, there will be one saw kerf to each
CMLL
So
Fic. 8 —Waste incurred as slabs and sawdust in sawing round, straight logs.
board. The initial saw kerf, and the sawdust wasted in edging, and in
ripping wide boards into narrower boards, forms an additional percentage
of waste not exactly proportional to volume. Disregarding this: dis-
crepancy, the fixed per cent of waste from saw kerf for the log is the same
as the per cent wasted in sawing one board. If the thickness of board
plus that of the saw is taken as 100 per cent, this waste, for a 1-inch
board with }-inch saw kerf is as } to 14 or 20 per cent, while for a +-inch
saw kerf the proportion is § to 1$ or 11.1 per cent. A general formula
applicable to saws of all thicknesses is as follows:
Let K=width of saw kerf;
T =thickness of lumber.
Then
T+K=total volume of board plus kerf,
54 THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
K 2
TER Pe cent deduction for saw kerf,
T ee
ToK Pe cent of log utilized as lumber.
Efforts to account for the exact per cent of waste in sawdust have been made,
by including, first the saw kerf required for ripping or edging one edge, as shown
in Fig. 8,! and second, the additional saw kerf for the first slab. But neither method
is complete, since boards are edged when necessary on both edges. The best method
is probably to include this extra saw kerf, together with the edgings, in the waste
due to slabbing, leaving the sawdust as a straight per cent of volume.
Shrinkage. Where shrinkage is considered, or where lumber must be
sawed a trifle full, the extra thickness which is not measured in the
green lumber constitutes a waste exactly similar to saw kerf, and can be
added to the latter factor in the formula before calculating the per
cent of reduction.
For instance, if a log rule is intended to measure the output of 1-inch
lumber after seasoning, and the average shrinkage on inch boards is
j,-inch, and saw kerf {-inch, the per cent of waste in small logs is
tis _ .1875
1+44+ 3, 1.1875
=15.8 per cent.
1 By the inclusion of one edge, the formula for sawdust would be:
Volume of unit (W+K)(T+4),
Saw kerf K(W+T+4),
Pp pled (in NG KW Ee)
er cent of waste ——__——-
(W+K)(T+K)
H. E. McKenzie, Bul. 5, California State Board of Forestry, Sacramento, Cal.,
1915.
By inclusion of the extra saw kerf but not of the cut for edging.
Number of cuts =N,
ls
Average saw kerf per board =K +7)
K
Volume of unit =T+K +
eae
N
Per cent of waste — aera
T+kK+—
alsa N
C. M. Hilton, Bangor, Me., 1920.
TOTAL PER CENT OF WASTE IN LOG 55
Corrections for Saw Kerfs of Different Widths. Since the per cent of
waste caused by saw kerf applies directly to the residual volume of logs
after subtracting the waste for slabbing and edging, the effect of using
a saw of greater or lesser width than that used in constructing the rule
can be found in terms of a per cent of the values of the log rule. This
flat correction can then be applied if desired, to correct timber estimates,
convert the log rule into one which eliminates over-run from saw kerf,
or correct the scale of logs to coincide more closely with sawed output.
For instance, the above rule would utilize 1—.158 or 84.2 per cent of the net
cubic contents of the cylinder. A saw cutting a }-inch kerf, with the same allowance
for shrinkage, calls for the formula,
t+ds __.3125
(ee aoe.
=23.8 per cent,
giving 72.6 per cent utilized. The values expressed by the log rule made for the
3-inch kerf must now be taken as 100 per cent to which the correction will apply.
3 6.2 :
Then Se gives 90.5 per cent. The second rule requires values equaling 90.5 per
cent of the first, or a straight reduction of 9.5 per cent.
That this conversion can be accurately made was demonstrated on diagrams by
H. D. Tiemann, who found that the possible error was less than one-half of one
per cent.
54. Total Per Cent of Waste ina Log. The total per cent of waste in
a log is the sum of the waste from slabbing and edging, or surface waste,
and from saw kerf. The proportion of this total waste represented
respectively by slabbing and by sawdust will depend upon which of
these deductions is made first, and whether the sawdust made in slabbing
and edging is included as part of the waste in slabs and edgings, or is
counted as part of the waste in sawdust. If the deduction for sawdust
is made first, it will include a fixed per cent of the cubic volume of the
log. If on the other hand, the slab waste is first deducted as a ring or
collar of a given thickness, the subsequent deduction for saw kerf,
although the per cent is the same, applies only to the residual volume of
the log.
The total per cent of waste, and its distribution between these two factors is
illustrated in table VII. Let slab waste equal a ring ?-inch in thickness or a
reduction of 1.5 inches in diameter. Sawdust, for }-inch kerf, equals 20 per cent.
The per cent of waste will vary with diameter of logs, as shown:
In column 2 the per cent of waste is seen to be approximately one-half as great
for 20-inch logs as for 10-inch logs.
1 Proc. Soc. of Am. Foresters, Vol. V, 1909, p. 29.
56
TABLE VII
DISTRIBUTION OF WASTE BETWEEN SLABBING AND SAWDUST
THE MEASUREMENT OF LOGS—BOARD-FOOT CONTENTS
1 2 fb) 4 5 6 7 8
Diameter Lgsieue Total | Waste in
t sawdust Total Waste SE SE a a
e Waste in|20percent| waste | saw kerf Bee Pt Ulizae
small 3 | : saw kerf, | saw kerf 2
slabbing. of Columns in : tion.*
end of : Columns in
remainder} 2-+3. slabs.
log. 3-45. slabs.
of log.
Inches | Per cent | Per cent Per cent | Per cent | Per cent | Per cent } Per cent
10 thn UG: 14.45 42.20 5.55 20 22.20 57.80
20 14.44 ented: 31.55 2.89 20 11.55 68.45
40 If Parl 18.54 25.81 1545 20 5.82 74.19
* Of the small cylinder not including taper.
The waste in slabbing would be exactly proportional to diameter except for the
fact that the volume of the hollow cylinders representing the collar deducted for
slabs is not directly proportional to the outer surface of the respective cylinders in
logs of different sizes. The same relation is seen to hold whether or not the slab
waste is deducted before or after the sawdust. (Columns 2 and 7.)
Since the per cent of slab waste is roughly proportional to D, while that from
sawdust is as D2, the sum of these two factors causes the total per cent of waste to
decrease as shown in column 4, instead of remaining constant as in column 6. The
rate of decrease is less rapid than in columns 2 or 7 since only a portion of the waste
decreases in per cent with increasing diameter of log.
Were the total waste in logs proportional to D? as is the waste from
saw kerf, log rules could be converted from cubic to board feet by a
single ratio. But since the part of this waste due to slabbing is pro-
portional to D, the per cent of total waste decreases with increasing diameter
by a rate which is the sum of these two factors and is therefore directly
proportional to neither D nor D?. This explains the increasing per cent
of utilization secured in sawing larger logs and the need for log rules
based directly upon the board-foot unit and not derived by conversion
of cubic units.
To derive an accurate log rule, not only must the waste from slabs
and edgings be deducted separately from the waste from saw kerf, but
the correct amount must be deducted for each source of waste. A rule
which deducts too much for slabs and too little for saw kerf will deduct
TOTAL PER CENT OF WASTE IN LOG 57
too much on small logs, where the slab waste is normally high, and too
little on large logs, where the greater portion of the deduction is for saw
kerf. Such a rule can be correct only for a single diameter class where
the two errors happen to balance.
On the other hand, if too small a deduction is made for slabs, and
too large for sawdust, small logs may be overscaled, while the increasing
per cent of utilization possible in larger logs will not be shown in the
scale (Column 8), and the rule therefore tends to under-scale large sizes.
CHAPTER VI
THE CONSTRUCTION OF LOG RULES FOR BOARD-FOOT
CONTENTS
55. Methods Used in Constructing Log Rules for Board Feet. The
great variation in the contents of different log rules for board feet, and
the variation in accuracy and consistency of these rules is due to the
methods used in their construction as well as to the factor of over-run
resulting from closer utilization.
Four general methods have been used in constructing such rules.
These are:
1. By mathematical formule. A formula is used, which derives the
board-foot contents of the log directly from its diameter and length, by
allowing for reductions from D? XL for cubic volume, waste in saw
kerf, waste in slabs, and reduction of residual volume to board feet. If
the principles used in making these reductions (§ 54) are correct and the
amounts used are also correct, such log rules are superior to diagram
rules, but if errors in either principles or amounts of deduction are
introduced into the formula, the rule is worse than useless.
2. By diagrams. Full-sized circles of all diameters are drawn on
large sheets of paper, representing the top ends of the logs. On these
cross sections of the log the ends or cross sections of the boards which
could be sawed from these logs are drawn, leaving between each board a
space equal to the width of the saw kerf. The area of boards in square
inches is then reduced to board feet by the factor 7s length in feet, for
logs of a standard length, and from this, for logs of all lengths.
3. By tallying the actual sawed contents of logs at the mill for differ-
ent diameters and lengths. Owing to the variables introduced by the
thickness of lumber sawed, and by taper, this method has seldom been
accepted as the sole basis for a log rule, but has been extensively used
to check the accuracy of rules made by the preceding two methods.
4. By conversion of the cubic contents of logs into board feet, after
deducting a fixed per cent of this total cubic contents for waste in saw-
ing and slabbing. As shown in Chapter V, all board-foot log rules
constructed on this basis are fundamentally wrong.
A fifth method has been used, which is a combination of methods
1 and 2 or 3, namely, to alter or correct the values of an existing log rule,
by means of mill tallies obtained in sawing. The author of such cor-
58
THE CONSTRUCTION OF LOG RULES 59
rections may give a new name to such a rule, or may state that it is
an old rule corrected. Such corrected rules while undoubtedly better
than the originals have so far failed of adoption in place of the rules
from which they were made, owing to the force of custom in perpetuating
established standards even if in error.
56. The Construction of Rules Based on Mathematical Formule.
Many efforts have been made to evolve a formula which will give an
accurate basis for a board-foot log rule. Of these the erroneous formule,
or rules of thumb, based on a fixed conversion factor are most common.
Of those which recognize the fundamental difference between waste from
slabs, and waste from saw kerf, we have two groups, distinguished
not by principle, but by the method of procedure dependent on whether
the deduction for saw kerf is made first, from the total contents of the
log, or whether that for slabs and edgings is first deducted, and the
waste from saw kerf then taken from the residual volume.
Method of Deducting Slabs First. When the first plan is used, a constant, a,
representing in inches the double width or thickness of the hollow cylinder or sur-
face layer wasted in slabs, edgings and crook, is first deducted from the diameter of
the log at small end. From the area of the smaller circle thus obtained, the required
per cent is subtracted for saw kerf, shrinkage or surplus thickness of board required
in sawing.
The residual area of the circle in square inches is converted into board feet for
logs 1 foot long, by dividing by the factor 12. Disregarding the taper, the volume
of a log of any length is found by multiplying the contents by length in feet.
D=diameter of log in inches;
a=inches subtracted from diameter, a constant;
D—a=reduced diameter of log after subtracting waste from slabs and edgings;
m(D—a)?
4 =reduced area of small end of log in square inches;
b=per cent of volume deducted for saw kerf;
1—b=per cent remaining after deduction for saw kerf;
L=length of log in feet;
B.M.=volume of log in board feet;
then
Da)?
B.M. =(1 ae ea Le
4 12
A as
=(1—5) Ne
ILLUSTRATION
Let a=1.5 inches, representing a collar of .75 inch thickness deducted for
slabs, ete.
b=20 per cent representing a }-inch saw kerf.
60 THE CONSTRUCTION OF LOG RULES
Then for any log,
D—1.5)?
Bit ee) ee
48
For a 12-inch log 16 feet long,
3.1416(12—1.5)?
BM. = $0( sl A 6
=92 board feet.
Method of Deducting Sawdust First—By the second method, the per cent, of
waste in saw kerf is first deducted from the entire volume of the log. From the
residual volume the amount to be further subtracted for slabs, edging and crook is
taken. This is a smaller per cent than by the first method, as shown in Table VII,
column 7 since the sawdust used in slabbing is not included, and it is for convenience
computed in the form of a plank of width and length equal to the log, and whose
thickness is varied to give the required volume of waste.
Let A equal the width of this plank in inches. This is taken as a constant.
Then,
1D? L
B.M.=| (1—b)—— —AD ]—.
4 12
ILLUSTRATION
Let b=20 per cent —sawdust allowance, |
A =1.767 inches, the thickness of a plank whose width is equal to D, and
length to L—for slabbing allowance.
eee L
B.M.=] .80 pies —1.767D |—.
4 12
Then for any log,
For a 12-inch log 16 feet long,
B.M. =[.80(.7854 X12?) —1.767 X12]4
_
fe)
B.M. =92 board feet.
This result shows that for 12-inch logs, after subtracting 20 per cent from log for
sawdust, a plank 1.767 inches by 12 inches gives a deduction from the net volume,
equal to method 1 when a collar .75 inch thick is first deducted and 20 per cent for
sawdust taken from the remainder.
The two methods are not absolutely interchangeable. Their relation may be
shown by algebraical means.
Substitute C for (1—b).
Then C=per cent left after subtracting saw kerf.
Since D is in inches, and L exerts no influence on the relative values, the areas
of the small end of log, left after subtracting total waste, should be equal, and can
be expressed in square inches for each formula as:
Cx(D—a)?_CrD?
4 Re
AD.
Then,
4 Eh: 5T08aD =. 78540")
D
COMPARISON OF LOG RULES BASED ON FORMULA 61
The results, for certain diameters are shown below:
TABLE VIII
THICKNESS OF PLANK TO BE DEDUCTED FOR SLAB WASTE TO COINCIDE WITH A
; Couuar 1.5 Incues Tutck. Sawpust ALLOWANCE 20 PER CENT
Double thickness of col |Corresponding thick-|Ratio of thickness of
Diameter of | lar deducted for slab} ness of plank to be} of plank to collar
log. waste previous to de-| deducted after de-
ducting sawdust. ducting sawdust.
Inches Inches Inches
3 eS 1.414 0.940
6 1.5 1.649 1.099
9 1.5 1.728 1.152
12 153) 1.767 1.178
18 t5 1.800 1.200
40 1S 1.849 1.233
The use of these ratios would give identical results by both methods. But in
application the second method usually stipulates that the thickness of plank shall
be constant for all logs. This results in a greater proportionate deduction for slabs
on small logs than by the first method. This deduction is more in accordance with
the actual results of sawing, owing to the increasing effect of minimum widths of
board on per cent of loss in slabbing (§ 51). The best application is to adopt a
ratio which applies to medium-sized logs, and use this for all logs, large and small.
If a log rule is constructed to deduct the waste which actually occurs in sawing,
it must be based on one or the other of these two formule. If the waste allowances
are correct for the conditions assumed, there will still be over-run when other condi-
tions apply, but the per cent of over-run will be practically the same for all sizes,
the rule is consistent, and the results are subject to correction by a fixed ratio or
per cent.
If the waste allowance for either slabbing or sawing, or both, are incorrect for
the conditions assumed, the rule will not only give over- or under-run, but will also
be inconsistent, the per cent will differ with diameter, and the rule will not be subject
to correction by a fixed ratio, and will lack the basic requirements of a standard of
measure,
57. Comparison of Log Rules Based on Formule. In constructing
a formula log rule, the correct application of the deduction for saw kerf
presents no great difficulty. In the International rule, an extra deduc-
tion of ¢-inch was made for shrinkage. Other rules neglect all factors
but the actual width of saw kerf (§ 53).
The deduction for slabs, edging and normal crook requires determination not
only from diagrams but from practical tests. The following amounts are deducted
by the log rules given beluw, expressed both as a ‘“‘collar’’ deduction from diameter,
(a), and as a thickness of plank (A), to correspond with the two methods described
(§ 56),
62 THE CONSTRUCTION OF LOG RULES
TABLE IX
DEDUCTIONS FOR SLABBING AND FOR SAW Kerr, For 12-1ncH Logs, In TEN Loa
Ruues Basep on FormuLa&. THE Basis USED IN THE RULE IS SHOWN IN
Heavy Tyre.
| |
: Equivalent
pelnenes deduction in| Saw kerf Deduction
from diameter
. form of a plus for
Log Rule. for ;
SA plank shrinkage. saw kerf.
thickness.
Inches Inches Inches Per cent
internaionalae eee Ice 2.12 t+ 15.8
Umiv.ersalle yrs crore 1.66 2.00 + 20.0
Preston: Large logs....... 1.75 2.04 1 20.0
Small logs....... 1.50 INE TICE i 20.0
British Columbia......... 1.50 WEEE 3 20.3
GliGkoses ARRR IR oie Sa uvelavtionts 1.25 1.42 1 23.6
Clement Sy ee cctcrc ome. 1.18 132 t 25.0
WiallSOnieetsttc ecu a core 1.00 ile } 22.2
MhoOmastren cee eee 1.00 ijgaly/ } 22.0
Beedle “Senaboonaooce 0.87 1.05 1 20.0
Champlain ee ee 0.83 1.00 1 20.0
Ion Salecctiheted - Ayaeee Gierenty ats 4.00 5.00 ra 4.5
IBSXterersin aie ieee 1.00 1.00 1 33.8
* Diagram rule.
Of the rules above cited, the British Columbia and Doyle are the only ones used
extensively at present. The table is instructive as an indication of the proper allow-
ances to make for slabbing. The test of a formula is actual comparison with sawed
output. The deductions in the International rule were determined by careful
measurement on logs actually sawed. The Champlain rule is known to be too
close a rule, with too small an allowance for slabs. The British Columbia rule
neglects shrinkage and is a good standard. The Click rule was carefully checked
by sawed output. These results indicate that for 1-inch lumber sawed to exact
dimensions, an allowance for slabbing of 1.5 to 1.75 inches subtracted from diameter,
or one-half this deduction as the single thickness of the collar, is a fair allowance
for slabbing. This allowance would be too small for lumber of greater average
thickness than 1 inch or for very small logs.
When the deduction is made in the form of a plank whose width equals the
diameter, D, of the log, the thickness of plank required to make it equivalent to the
collar deduction is from 1.75 to 2 inches for 12-inch logs, slightly more for larger
logs, and decreasing in thickness for smaller logs. But where the deduction is made
in this form, as in the International and Champlain rules, it is used as a constant
for all dimensions (§ 59 and § 62) with results corresponding more closely to actual
waste than by the first method.
The allowance for saw kerf, on all log rules in commercial use, is }-inch or over.
The International rule in its original form gives values for a }-inch saw kerf, which,
with the other allowances, gives a rule intended to measure the output of modern
band mills.
McKENZIE LOG RULE, 1915 63
58. McKenzie Log Rule, 1915. This log rule is a universal formula
and’ not a commercial standard or true log rule. It is intended to
reduce all the variable factors in the production of sawed lumber to
elements in a formula, which will permit the determination of a local
rule that will accurately measure the sawed output in the log for any
condition, and eliminate over-run.
The factor of taper is treated by building up the log in 8-foot sections,
permitting the use of whatever actual average taper coincides with that
of the logs sawed. The allowance for slabs, edging and crook is made by
the first method, that of deduction from the diameter previous to sub-
tracting saw kerf. Shrinkage could be included with saw kerf, if neces-
sary, but the author does not mention it.
The formula is the one already shown to be correct and universal for board-foot
log rules,
L
B.M.=(1 oe) 85D 8)
The saw kerf allowance, b, is computed to include width as well as thickness of
lumber sawed ($53). To this general formula the author adds a constant, c, to
offset excessive taper on small logs.
The principal utility of this log rule will be found in determining, in advance of
sawing, the amount of over-run which may be obtained from logs scaled by a com-
mercial rule, or to test the results in over-run to be expected by the use of different
log rules and different methods of manufacture. The objections to adopting it as a
standard of measure are stated in § 49.
REFERENCE
Bul. 5, California State Board of Forestry, by H. E. McKenzie.
59. International Log Rule for {-inch Kerf, Judson F. Clark, 1900.
In constructing this rule, modern conditions of manufacture in large
mills were presupposed. The values of the rule as published are for a
band saw cutting a 34-inch kerf and are rounded off to 5 and 10 board
feet, thus approaching the principle of a decimal rule. Saw kerf is
first subtracted, allowing -inch for shrinkage, or a total of 33; inch.
The deduction for slabs and edging, including a normal crook of from
1 to 13 inches is then made in the form of a plank measuring 2.12D.
The formula reads:
L
B.M. tee ae
The rule was constructed as follows: Since the per cent of waste in saw kerf plus
od
+k
.158, and the factor for residual volume is .842. Then,
5 ; . ; 3 ; ;
shrinkage is i this becomes for inch boards 1663 or 3 parts in 19, which gives
.842(.7854D?) = .66D?.
64 THE CONSTRUCTION OF LOG RULES
The deduction 2.12D was determined from tests of sawed logs, including all crook
of 4 inches or less. .
Since the log is divided into 4-foot lengths, the sum of which gives the scale,
the formula reads for each length,
B.M. = (.66D?—2.12D)45
= 22D?—.71D.
A taper of 34-inch in 4 feet is allowed. D is thus increased by 3-inch for each sueces-
sive section and the sum of the scale of the separate 4-foot cylinders gives the scale
of the log ($43). On account of the allowance for shrinkage the rule is based in
reality on the production of 1,/s-inch boards measured as inch boards. A minimum
width of 3 inches, and a minimum length of 2 feet are adopted as standard, no piece
to contain less than 2 board feet. Standard values were published, it being the inten-
tion of the author to furnish a commercial log rule that could be accepted as a com-
mon standard for the measurement of logs as sawed in modern mills using a band
saw cutting a g-inch kerf.
60. International Log Rule for {-inch Kerf, Judson F. Clark, 1917.
For general adoption as a standard commercial log rule, the +-inch rule
is open to the objection that it over-scales the product of most small
mills, since it is seldom that such mills use saws cutting less than }-inch
kerf, or make close use of the taper of the log. - A log rule which gives
a safe margin, and which permits mills using thin band saws and up-to-
date equipment to secure an over-run of about 10 per cent is more
acceptable as a commercial standard than one which scales for the
closest possible standard of utilization. For this reason, Mr. Clark
has computed values for the International rule, for }-inch saw kerf.
This form of the rule is here published for the first time from values
furnished by its author (Appendix C, Table LX XX). To obtain this
rule, the original values for the {-inch rule were reduced by 9.5 per cent
and then rounded off to the nearest 5 or 10 board feet. The rule is
recommended as a standard for scientific measurements of volume and
growth in terms of board feet, for regions where the product is manufac-
tured by small mills using circular saws cutting a }-inch kerf.
61. British Columbia Log Rule, 1902. This is the only case of the
legal adoption and application in commercial scaling of a new log rule
based on sound scientific principles, as the direct result of a thorough’
investigation. In 1902 a commission of three men prepared from dia-
grams a rule to suceed the Doyle Rule for the province, which was
adopted in 1909 as the Statute rule.
Their results were embodied in a formula reading:
“For logs up to 40 feet in length deduct 13 inches from the diameter of the small
end inside the bark; square the result and multiply by the decimal .7854; from
OTHER FORMULA RULES : 65
the product deduct three-elevenths; multiply the remainder by the length of the
log and divide by twelve.”’ Or,
L
B.M. =(1—77)-7854(D —1.5)* 5
_m(D—1.5)? L
= PH :
12
The minimum width of board used was 3 inches.
For logs over 40 feet in length, an increase in diameter is allowed on half the
length of the log amounting to 1 inch on the diameter at the small end, for each
10 feet in length over 40 feet. Thus for logs from 41 to 50 feet long the contents
of the butt cylinder is scaled by a diameter 1 inch larger than the top end; for logs
from 51 to 60 feet long, the rise allowed is 2 inches, ete.
This allowance for taper is absurdly small and constitutes the only weak point
in the rule. It is a concession to the low standards of utilization practiced in the
province at the time.
62. Other Formula Rules, Approximately Accurate, Both in Princi-
ples and Quantities. When a log rule is constructed by using the prin-
ciples embodied in the standard formula, and when in addition, the
amount of deduction for both saw kerf and slabbing is approximately
correct, the resultant log rule will be far more accurate and consistent
than any of the commercial rules in common use except the last men-
tioned. Several rules have been constructed, whose values differ only
because of slightly different allowances for waste, as shown in Table IX.
Seven such rules are given below. This completes the list of log rules
known to the author, and based on diameter at small end of log, which
deserve to be classed as fundamentally correct standards for board-foot
contents of saw logs.
Champlain Log Rule, A. L. Daniels, 1902. This log rule, intended as a perfect
rule for 1-inch boards, is based on }-inch saw kerf and neglects taper. It is for
perfect logs. The deduction for slabs and edging, without normal crook, is made
equal to a 1-inch plank or 1D. No shrinkage is considered. The diameter is taken
at small end. Were it not for an over-run secured from taper or the methods of
sawing used, logs would never saw out what this rule calls for. The quantities
given are above normal in cylindrical contents for short logs. This error is offset
by neglect of taper, so that in long logs the rule falls below the International.
This rule has not been used commercially, except in a few instances in Vermont.
The formula is:
L
B.M.= (62832) — D)*
The author of the Champlain log rule realized that the slab allowance was too
small for actual conditions. By increasing the width of plank deducted for slabbing
to 2D, a modification, termed the Universal log rule was computed, using the formula,
L
B. M. =(.62832D? ego:
66 THE CONSTRUCTION OF LOG RULES
This rule compares favorably with other theoretically accurate rules except that
it shares the common fault of neglecting taper. Mr. Daniels states (1917), that he
favors the use of the Champlain rule as the more accurate of the two.
Wilson Log Rule, 1825.
m(D—1)2L
Bae 30
4 12
By Clark Wilson, Swanzey, N. H. Originated in 1825, and computed for 7-inch
boards. Now obsolete. This was unquestionably the first formula rule. The author
was a mathematician, and “estimated the difference in yield in gain of the large
logs over the small ones, and then calculated the intermediate spaces by nearly
regular integral differences as logs increase in size. The author intended it for
#-inch boards. It is recorded that E. A. Parks later used it for 1-inch boards, which
use resulted in a lawsuit.’ (John Humphrey, Keene, N. H.)
Preston Log Rule, An Old Rule.
a(D—1.75)? L
L l BM. = 30—————__—
arge logs, Ai G
a(D—1.5)? L
Small logs: B.M.=.80-———— —.
Small logs F 2
Still used in Florida. Known locally as a seller’s rule. Sold in Jacksonville, Fla.,
by H. & W. B. Drew Co.
Thomas’ Accurate Log Rule.
n(D—1)? L
BM. = i8-——— > =
+ 12
For }-inch saw kerf. Also computed for }-inch kerf.
Click’s.Log Rule, 1909.
m(D—1.25)? L
B.M.=.764 :
4 12
By A. C. Click, Elkin, N. C., 1909. This rule was based on 1-inch boards averaging
6 inches in width and makes reduction for saw kerf of }-inch as per the formula
(§ 58), used by McKenzie. Other rules for different widths of saw kerf were worked
out by the author. (Forestry Quarterly, Vol. VII, 1909, p. 145.)
Carey Rule, Date Unknown. This was a caliper rule to be applied to middle
diameter, and was used for round edge ane on thick. The values given are
almost identical with the Wilson rule. Formerl¥ used in Massachusetts.
Clement's Log Rule, 1904.
aD? L
B.M.= 75— } —1.18D |—.
4 12
This log rule illustrates the use of a rule of thumb, based on correct mathematics.
The above formula is expressed thus: Multiply half the diameter by half the cireum-
ference, then subtract half the circumference. The remainder will be the total
amount of feet board measure, in a 16-foot log.
This becomes:
L
B.M. =(.7854D?—1 STD)
from which the above formula is derived.
With the exception of the Preston, none of these rules is in commercial use.
TIEMANN LOG RULE 1910 67
63. Tiemann Log Rule, H. D. Tiemann, 1910. All of the com-
mercial log rules in use are open to the criticism that the taper is dis-
regarded, thus causing the over-run to vary according to the length
and amount of total taper of the log. The International rule, in which
taper is included, is not in commercial use to any extent. But one
attempt has been made to take proper cognizance of taper by the method
of applying a log rule for board feet to the middle diameter instead of the
small end. Most rules employing this method are cubic-foot rules or
based on cubic contents. The Tiemann log rule on the other hand is
a true board-foot rule based on a ;%;-inch saw kerf. The rule was made
from actual mill tallies accurately adjusted for saw kerf and for exact
thicknesses and the results worked out graphically by curves. Quite
remarkably the curves were found to correspond very closely to the
exceedingly simple formula
B.M.= (.75D?—2D)
which equals (7167) = 1.5D) 5
=
16’
12
_ The application of the rule is limited by its author to lengths not
exceeding 24 feet.
This log rule applies to logs scaled in the middle. When this is
possible, the rule is more accurate than any other board foot log rule,
since neither the variation in taper nor length of log affects it. It can
be adjusted to apply to the small end just as well as any other rule can,
but it is intended primarily for middle diameter as this largely elimi-
nates errors in estimates of taper. For scientific records it is of distinct
value. It is superior to the International rule as it eliminates taper
as a variable instead of averaging it. The obstacles to converting this
rule or any other rule into equivalent values at small end are discussed
in § 31. The rule is given in Appendix C, Table LXXXIV.
64. Formula Rules Inaccurately Constructed. Baxter Rule. If
the allowance for slabbing in a formula rule is excessive, and that for
sawdust too small, the resultant volumes will be too small for logs of
small diameters and too large for large logs, thus giving not only an
inaccurate but an inconsistent rule. If these errors in deducting waste
are reversed, slabbing allowance being too small, and that for sawdust
too large, the reverse is true, and the large logs will be under-scaled.
Baxter Log Rule. In adopting a rule of thumb for the construction of a log rule,
the author may have in mind a certain result, but the rule when expressed in a formula
may give quite a different result.
The Baxter Log Rule was constructed by the rule ‘‘Subtract 1 from the diameter
inside bark at the small end, square the remainder, and multiply by .52. The result
68 THE CONSTRUCTION OF LOG RULES
L
is the contents of a 12-foot log’’ (hence a gives the contents of any log). This squar-
ing and subsequent subtraction of one-half the square was intended to give suffi-
cient deduction for both slabs and saw kerf. But it actually gives,
BME cee
ye
The factor 1, for A, is insufficient for slabs and the factor .338 for C is far too great
for sawdust, corresponding in fact to a kerf of 3.inch. The rule therefore greatly
underscales large logs. Its inconsistency makes it worthless.
65. Doyle Log Rule. Synonyms: Connecticut River, St. Croix,
Thurber, Vannoy, Moore-Beeman (in part), Ontario, Scribner (erro-
neously).
This rule is used almost to the exclusion of all other rules for hard-
woods in parts of the Ohio Valley, and for Southern yellow pine. Its
use 1S extensive in every eastern state outside of New England and
Minnesota. In the West, it is not used to any extent.
The Doyle rule reverses the error of the Baxter rule by deducting
too large a per cent for slabbing and not.enough for sawdust. The wide
use of this rule has caused losses of millions of dollars to owners selling
logs and standing timber, by improper and defective measurement of
contents. The prevalence of its use is due first to the simplicity
of its application as a rule of thumb. The rule reads: Deduct 4 inches
from the diameter of the log as an allowance for slab. Square one-
quarter of the remainder and multiply the result by the length of the log
in feet. The result is the contents in board feet. Timber cruisers
estimate logs in 16-foot lengths. For this length of log the rule would
read: Deduct 4 inches from the diameter of the log inside bark, and
square the remainder. The result is the contents of the log in board
feet, by the Doyle rule. A rule as easily applied as this was sure to be
popular.
The second reason for its wide use was its substitution for the old
Scribner rule in Seribner’s Log and Lumber Book, after this publication
had already attained a large circulation. As this book was widely
accepted as a standard and almost the only publication on log rules,
the impetus given to the use of this inaccurate rule by this substitution
was tremendous.
The third reason for the continued use of the Doyle rule is the same
which operates to prevent reform in the use of log rules in general.
Custom, or habit of using it, is fixed. So far has this. gone that the
States of Arkansas, Florida and Mississippi prescribe its use by statute.
Added to this is the fact that a rule favoring the buyer will be advocated
by this class to its own advantage.
DOYLE LOG RULE 69
The seller can defend himself against the use of a short measure if
the latter is consistent and its per cent of error is known. “But with a
log rule like the Doyle, the per cent of error differs with every scale of
logs or stand of timber and it is practically impossible to determine the
actual loss without remeasuring the logs by a correct log rule or tally-
ing the sawed contents.
Since it will be impossible to displace this log rule by better standards unless
its vicious character is fully understood, the exact nature of the error should be made
clear. The original form of this rule read ‘Deduct 4 inches from the diameter
for slabs, then squaring the remainder, subtract one-fourth for saw kerf and the
balance will be the contents of a log 12 feet long.’ The sawdust allowance as
intended, would have corresponded to a 7-inch saw kerf. The author evidently
figured that 4 inches of slab would square the log sufficiently so that the sawdust
i Uae bal =r
Heal ted
| 1 |
el gl
hel A)
all iy
rege a 1 |
ee 1 |
no a
. 7
ane + |
Hl vel
| 1 |
1 Mie
eee ee one Ses
Fic. 9.—Actual deductions for slabs and for saw kerf made by the formula of the
Doyle rule, for logs 6 inches, and 28 inches in diameter respectively.
The square ABCD is the supposed residue after deduction for slabs, while the
outer inscribed circle represents the actual residue. The inner inscribed circle
represents the residual percentage shown as board feet by the rule. The sawdust
allowance is, therefore, the difference between the outer and inner inscribed circles,
whose area is but 4.5 per cent of the contents of the cylinder.
allowance could be applied in this manner to the squared or partially squared stick.
His fundamental error lay in his method of deducting for slabbing and edging. As
shown, the waste from slabs and edging does not amount to a reduction of 4 inches
in the diameter, but to about 1.75 inches, and instead of being slabbed from four
sides, it is distributed evenly over the entire surface as a collar. The assumption
made resulted in an actwal deduction for slab far in excess of what was intended,
this excess in turn reducing the sawdust allowance from an assumed 25 per cent to
negligible proportions.
The above diagrams (Fig. 9) will explain the reason for this inconsistency.
The diagram for the larger log shows that the squaring of the timber would not
require a 4-inch slab allowance. The standard formula Hoey gives the volume
.7854(D—4)? as the actual net result of deducting 4 inches from the diameter of the
70 THE CONSTRUCTION OF LOG RULES
log. This was the point overlooked in constructing the rule. The deduction so
made is in its effect a deduction for slabbing and edging although not so intended.
That it was not intended is shown by the instructions for next deducting one-
fourth of (D—4)? “for saw kerf.’ But this leaves .75(D—4)? for all logs, instead
of .7854(D—4)*, which is a further reduction of but .0354(D—4)?, the actual reduc-
03
tion for saw kerf
ion for saw kerf =|
= .045 or 4.5 per cent of the cylindrical contents for saw kerf
instead of the 20 per cent of the same cylinder required by a }-inch saw kerf. The
remaining 21.5 per cent of the supposed saw kerf is a true slab deduction of 4 inches
from diameter. Thus the amounts and proportions of slab deductions are grossly
out of balance and this ruins the rule.
This early form was not known as the Doyle rule. The present form, first
published in the decade 1870-80 was advertised as a new rule. The scale is identical
with the older form but the change in the wording of the rule to its present form
still further concealed the flaw in its construction. |
The formula for the Doyle rule is:
; D=4\3
B.M.= (P=) ite
4
corresponding to the standard formula:
Deh
B.m.= 955%2—* vs
way 2)
The true sawdust allowance can be shown by the following comparison:
D—A\?
(P=) L= .0625(D—4)2L.
The area contents of the cylinder D—4,
7 L
~(D—4)*— = .06547(D—4)?L.
ra age (D—4)
0625
Since the cylinder D—4 represents the log minus true slab deduction, aa 47"
95.5 per cent or the log minus both slabs and sawdust.!
66. Effect of Errors in Doyle Rule upon Scaling and Over-run.
The effect of this overbalancing of the respective allowances is to cause
this rule to give zero for the contents of logs 5 inches in diameter while
for logs above 47 inches, the scale yields more than 80 per cent of the
cubic contents, thus, for }-inch kerf, eliminating slab waste altogether.
The over-run would thus vary with increasing diameter, from infinity
to zero.
When the Doyle rule is applied to long logs, with a small top or scaling diameter,
the over-run becomes proportionally greater. A careful test, under direction of
the courts in Texas where logs of given sizes were actually sawed (Extending a
Log Rule, E. A. Braniff, Forestry Quarterly, Vol. VI, 1908, p. 47), showed that
for 24-foot logs sawed by circular saw, the Doyle rule gave an over-run for different
diameters, as shown in Table X.
1The author is indebted to material published by H. E. McKenzie in Bul. 5,
California State Board of Forestry, for this discussion of the error in the Doyle rule.
EFFECT OF ERRORS IN DOYLE RULE 71
TABLE X
OvER-RUN, Doyte Rute. Texas
Sawed product. |
Diameter at Scale Per cent of
small end. Doyle Rule over-run
Inches Board feet |
6— 64 35 6 483
7- 7 49 14 250
8- 83 61 24 150
g— 92 76 37 105
10-102 95 54 76
11-113 112 74 51
The over-run steadily diminishes with increasing diameter until at from 36 to 40
inches the rule gives practically full scale for {-inch kerf and normal allowance for
slab, disregarding taper.
An investigation made in 1904 for the Province of Ontario by Judson F. Clark,
showed that the volume of the average log cut in the Province had decreased in
25 years by 63 per cent and at that time averaged 61 board feet and 12 inches in
diameter. From mill tests of pine logs sawed with ;-inch kerf, the per cent of
over-run was as follows, for 12-foot logs:
TABLE XI
Over-RUN, DoyLe Rute. ONTARIO
Diameter of Per cent
Actual output of
log at small | Seale by Doyle rule. é of
inch lumber.
end. over-run
Inches Board feet Board feet
6 3 14 366
8 12 30 150
10 Par 50 85
12 48 76 58
14 UG 108 44
16 108 144 33
18 147 186 26
20 192 234 22
When the average log ran between 18 and 31 inches, the defects of this rule were
not so apparent, and the over-run was not excessive. But as the size of the logs
cut grows less with the advent of second-growth and closer utilization, the rule
becomes impossible. Its continued use in many regions is due largely to the fact
that logs are not often bought and sold, but the timber is purchased on the stump
and the owner is unaware of his losses. This rule must eventually be superseded
either by a more consistent standard or by the rejection of board-foot measure
72 THE CONSTRUCTION OF LOG, RULES
altogether. No owner of small logs or of young standing timber can afford to sell
on the basis of a scale or estimate made by the Doyle rule. As it stands, this rule
is a serious obstacle to the profitable marketing of second-growth timber, hence to
the practice of forestry.
67. The Construction of Log Rules Based on Diagrams. In con-
structing log rules based on diagrams (§ 55), the quantity of 1-inch
boards contained within a given diagram may vary, due to four different
factors. The first is whether a 1-inch board or a saw kerf is placed on
the center line. For some diameters the one method gives the most
lumber, for others the alternate plan, depending upon the relation of
the total diameter to the sum of the diameters of boards plus saw kerf.
The second factor is the minimum width of the boards to be sawed. The
narrower the board, the greater will be the product from circles of a
given diameter. The third source of variation lies in the choice of
plotting all boards as if slash sawed, or else arbitrarily choosing a given
method of sawing around or squaring the log on the diagram, with
boards taken from the slabs. The fourth factor is the acceptance or
rejection of fractional inches in the boards inscribed in the circle. When
all boards are read to the nearest full inch in width, dropping all frac-
tions, some diagrams will lose a much larger per cent than others—while
in actual sawing, these variations tend to even up.
For circles of the same diameter and with the same minimum width
of board and saw kerf, the board-foot contents will evidently vary con-
siderably according to the treatment of these four factors in construction
of the diagram. In a well-constructed consistent set of diagrams, the
values in board feet should increase by a regular progression. This
can be shown by plotting the original quantities on cross-section paper
and connecting the consecutive points by straight lines. Irregularities
are revealed by sharp angles in this continuous line. Most diagram
log rules show considerable irregularity, which the authors made no
attempt to smooth out, as could have been done by means of this graphic
plotting. A wholly inexcusable variation of such rules is caused by
increasing the average width of slab allowed on large logs. This increase
does not conform to the actual practice in sawing and results in a larger
over-run on large logs. It is the principal defect in both the Scribner
and the Spaulding diagram log rules. The Maine or Holland rule,
by avoiding this error, secured a more consistent result.
Diagram log rules tend to give the scale of perfect logs under a given standard
for saw kerf and width of slab. The waste for normal crook and irregular form
cannot be shown. Since the commercial rules have ordinarily allowed too thick a
slab or too wide a minimum board or have rejected fractions, this loss is compen-
sated, but formula rules if accurate are more practical and convenient.
Baughman Log Rules. As an example of a diagram rule which is too perfect
for commercial use, since it neglects shrinkage and normal crook and includes frac-
SCRIBNER LOG RULE, 1846 ae
tional inches, can be cited the Baughman log rules for }-inch and }-inch saw kerfs
respectively. The results obtained from these diagrams are so consistent that they
conform to the typical formula for a perfect log rule.
(D—.87)2 L
B.M.=.81— ve for 1-inch kerf,
4 12
and
' D—1)?L
Tete ee 1_inch kerf.
NTO
In practice the use of these rules would give an under-run: 1.e., the logs would not
saw out the scale.
In these diagrams the minimum board was 4 inches, the lumber exactly 1 inch.
The 1-inch board was always placed in middle of diagram. Taper was neglected.
H. R. A. Baughman, Indianapolis, Ind.
68. Scribner Log Rule, 1846. Synonym: Old Scribner. The
Scribner log rule is the oldest diagram rule now in general use. But for
the unfortunate substitution of the Doyle rule for this rule in Scribner’s
Log and Lumber Book, its use would now be practically universal.
The rule held its own in the North and West, and is the legal standard
for Minnesota, Wisconsin, West Virginia, Oregon, Idaho, and Nevada.
It is the standard prescribed in timber sales on National Forests through-
out the West and by the Dominion Forestry Branch of Canada.
The rule was published previous to 1846. The diagrams are for
1-inch lumber, and } inch saw kerf. The width of the minimum board
was not stated but the author modified an earlier edition of his rule by
increasing the allowance for slab on larger logs. As a result of this
unfortunate error, the rulegives a larger over-run on logs above 28 inches
than on smaller logs. The products of the diagrams were evidently
not evened off. The values, when plotted, show great irregularities,
but except for the factor just noted, the general tendency of the rule is
consistent.
The original values were for logs from 12 to 44 inches in diameter in
sections 15 feet long, ‘‘ the fractions of an inch inside the bark not
taken into the measurement.’”’ Taper is not considered on logs of the
lengths used. These factors the author intended to offset normal crook
and concealed defects. Values were then given for logs from 10 to 24
feet in length.
Modification to a Decimal Rule. Two important changes in this rule
have been made to meet the demands for a universal log rule. It has
been changed to a decimal rule, and values for logs below 12 inches,
and above 44 inches have been added. The practice of modifying a log
rule in sealing by reducing it to even tens, in order to eliminate the col-
umn of unit feet in adding, is found in connection with several rules.
With the Scribner, instead of dropping odd feet, thus reducing the scale,
74 THE CONSTRUCTION OF LOG RULES
the odd feet were rounded off to the nearest ten, values over 5 feet
being raised, while 5 feet and under are dropped. The average scale
of even a few logs by this method is practically identical with that
obtained by the original rule as the errors are compensating. This modi-
fied rule is known as the Scribner decimal rule.
Extension below 12 Inches. For values below 12 inches, the original rule pro-
vided no figures. The lack of a formula permitted individuals to supply their own
values for these sizes. As early as 1900, the Lufkin Rule Company tabulated the
decimal values then in use, under three schedules, termed A, B and C, shown below.
To read in board feet, add a cipher to each figure.
TABLE XII
DeEcIMAL VALUES BELOW 12 INCHES FOR SCRIBNER LoG RULE
Decirmat A | DEcIMAL B DecmmaL C
Diameter—inches
Length.
(Gy iMate 8)! 2 1K0) UE | Ct SOLO | etsy OO) iil
Feet ' Board feet, in tens
12 Le palit 2 oie ye PAR a3 A 4 lee ae By a!
14 eZee ee ‘aol) Ah 2 8h 8} AT OGs |e ear 2. 3 Ae
16 il De Se 4 5: Gy 2a. 3) 4b) elec ewe Omen
18 2s te 5 COM acer 2 alas Ome 18)" 2a ore: Ons
20 1 2268s) 16)! Slee aGa 7) 822) SSeS ie ee aS
22 to Qa Sribinh, (Ol SheAvieo. 0 38s. ONS) (4A eee)
24 1354) on i ON ae oetoe 7 9) LOS Ar Gemma)
Still other values resulted from the use of the full scale, rather than the decimal
form. In the Woodsman’s Handbook, (1910 Forest Service), values for 16-foot logs
used by a company in New York (Santa Clara Lumber Co.) were published. These
values were adopted by the Canadian Forestry Branch in 1914. The State of Minne-
sota adopted standard values differing slightly from these figures. Wisconsin
adopted definite values by law for these sizes, conforming exactly to the Decimal “C”
scale given above. Idaho prescribes that the Scribner Decimal Scale be used with-
out specifying values and both “A” and ‘‘C”’ scales are in use in the state. In
Oregon and West Virginia the “Scribner Scale” is called for by statute, leaving the
question open for values below 12 inches.
The weight of custom is at present in favor of the use of the Decimal ‘‘C”’ values
for this rule, and the utility of the Scribner Decimal Rule would be improved by a
universal adoption of this standard.
Extension above 44 Inches. With the adoption of the rule by the Forest Service,
its use on the Pacific coast required an extension from 44 to 120 inches. In this
SPAULDING LOG RULE, 1868 15
instance a similar but worse confusion might have resulted, but was avoided by the
adoption of a single standard of values prepared by the U.S. Forest Service about
1905, and published in the Woodsman’s Handbook, 1910 edition. The extension
(made by E. A. Ziegler) was based on a comparison of the curve formed by the
plotted values of the rule with similar curves for the formula rules such as the
- International, and for the Spaulding rule. Ziegler states, “It might be described
as an extension built on an old rule by graphic methods checked with the correct
mathematical formula in which the slab waste varies with D and the kerf with D2,
and compared with the accepted rules in the Northwest, notably the Spaulding.”
The extension was built up on a 12-foot log, and applied to lengths of from 8 to
16 feet. As a concession to logging methods in the Northwest, logs up to 32 feet
were scaled without taper by this rule.
No such difficulties in extension are encountered with rules constructed by the
use of correct formule, since the values of logs of all sizes are in this way determined.
Attempt to Improve the Rule. Further efforts to modify this log rule have been
made in order to even off the irregularities of value between contiguous sizes.
Examples of this are the Hanna log rule, 1885 (John 8. Hanna, Lock Haven, Pa.),
the White rule, 1898 (J. A. White, Augusta, Ment.) and a local rule used by M. E.
Ballou & Son, Becket, Mass., 1888, adopted from Scribner rule, for small logs. Such
modifications unquestionably improve the rule, but the minor irregularities do not
appreciably modify the scale of a large number of logs of different sizes. The con-
fusion which would result in attempting to secure universal agreement on any change
in accepted values for this rule has prevented their adoption, and the values still
stand as they were originally determined, subject only to the conversion to decimal
form.
The Scribner Decimal “‘C”’ log rule in spite of its imperfections
comes the nearest at present to fulfilling the demand for a universal
commercial log rule, because of its present wide acceptance and use
(§ 13), and reasonable consistency in over-run. The latter reason alone
makes it preferable to the Doyle rule. Not even this rule, however,
does justice to logs below 12 inches in diameter; and in regions of second
growth and small logs, a closer and more accurate rule is preferable.
69. Spaulding Log Rule, 1868. Synonym: California Rule. The
Spaulding Log Rule was adopted by statute in 1878 as the standard for
California, and the values were given. It was constructed by N. W.
Spaulding of San Francisco in.1868 from diagrams of logs from 10 to 96
inches in diameter, using an 33-inch saw kerf, and 1-inch lumber, and
afterwards tested by sawing logs of each size in two mills. The size of
the slab (width of minimum board) was varied according to the size of
the log. This error of construction tends to increase the over-run in
large logs. The values were given for lengths from 12 to 24 feet. The
author directed that longer logs be sealed by doubling the values in the
table, and this practice was incorporated in the statute. Thus the
rule neglects taper altogether. In scaling, this principle is not applied
to logs longer than 40 feet. It constitutes the most serious defect of the
cule at present. Owing to the large saw kerf considerable over-run is
76 THE CONSTRUCTION OF LOG RULES
secured by modern band saws but the rule is fairly consistent, as are
all well-constructed diagram rules.
70. Maine or Holland Rule, 1856. Synonym: Fabian’s. This
is the most accurate and consistent diagram rule in common use (§ 55).
It was constructed in 1856 by Chas. T. Holland for 1-inch boards,
allowing for a {-inch saw kerf and for a minimum width of board of 6
inches. Fractional parts of a foot amounting to over .5 are reckoned as
a whole foot, those less than’.5 are rejected. This resulted in a more
consistent rule from the diagrams. The rule is applied at the small
end of log and disregards taper, so cannot be applied to the scaling of
long logs without considering them as sections. The best practice now
limits the length of these sections to 16 feet (§ 48).
71. Canadian Log Rules. The practice of adopting standard log
rules by statute has been followed by New Brunswick, Quebec, Ontario
and British Columbia. Their use is practically universal in the pro-
vinces.
The New Brunswick Rule, 1854. This rule is the statute rule of
the Province and is probably based on diagrams. Values for from 5 to
10 inches were added by later regulations. Logs 26 feet and over are
measured in two lengths. The small end is used and the rule is based
on l-inch lumber.
Quebec Log Rule, 1889. To construct this rule, diagrams of logs
from 6 to 40 inches in diameter were divided into 1l-inch boards. A
second set was divided into 3-inch deals, using j-inch kerf. The mean
of the two resultant contents was taken, and from this an arbitrary
deduction was made, ranging from 0 to 17 feet. Taper was neglected.
This scale is applied at the small end for logs up to 18 feet in length,
above which the average diameter of the two ends istaken. The rule
is the statute rule of the Province.!
The British Columbia Rule is discussed in § 61.
72. Hybrid or Combination Log Rules. The inconsistency of the
Doyle rule by which small logs are under-scaled and large logs over-
scaled has led to its combination with the Scribner rule. The values
of the latter rule drop below the Doyle rule at 28 inches.
Low values in the log rule favor the buyer of logs. In purchasing
large logs, especially hardwoods, the Doyle rule was considered unsafe.
The combined rule, termed the Doyle-Scribner, retains the low values of
1The statute rule of the province of Ontario is the Doyle Rule which was
adopted in 1879. In spite of the facts brought out in an investigation in 1904,
that in that one year the Province lost 184 million board feet on the scale, equiv-
alent to 23 per cent of the contents of the logs cut, by reason of this rule, the
influences in favor of its retention were too strong to be overcome and it is still
the standard rule of the Province.
GENERAL FORMULA FOR ALL LOG RULES U6
the Doyle rule up to 28 inches, and substitutes the low values of the
Scribner rule above that point.
The reverse of this process was adopted by the State of Louisiana
in 1914. The values of the Scribner rule below 28 inches were combined
with those of the Doyle rule for 29 inches and over, and the resultant
hybrid rule, known as the Scribner-Doyle rule is the official rule of the
state.
The Doyle and Baxter rules were also combined, using the Doyle
values up to 19 inches, with those of the Baxter rule for the remaining
diameters. Both the Doyle-Scribner and the Doyle-Baxter are cut-
throat rules calculated to give the buyer the maximum advantage of
the -defeets of both rules. The Scribner-Doyle rule has no advantage
over the straight Scribner rule since most logs are below 28 inches in
diameter.
73. General Formule for All Log Rules. When log rules have not
been constructed by a formula, but from diagrams or mill tallies, no
formula can be found which will give the exact values of the rule. But,
consciously or not, the authors of log rules have attempted to deduct
the waste from saw kerf and from slabbing and edging and the average
results which they obtained, or the actual treatment of these two fac-
tors is revealed by reducing these rules to the nearest approximate
formula.
The general form of such a formula is:
eat L
Ravi (aD ep O)
in which aD? covers the per cent reduction of volume for sawdust after reducing the
square to a circle, bD gives the reduction of diameter or surface for slabbing and edg-
ing, while C is a constant added in an effort to correct irregularities in the rule itself.
L
The factor 1D reduces square inches to board feet.
Cubic rules converted to board feet correspond exactly to the formula,
L
B.M. = (aD?)—
1
or to
D2
[oR ag py) ea a
4X12
Perfect formula rules correspond to the formula,
L
.M.=(aD?2+bD)—
B (aD? + Ee
or to ;
™(D—a)?
B.M.=(1—)) L.
4X12
78 THE CONSTRUCTION OF LOG RULES
But imperfect or irregular diagram or formula rules require the formula,
L
Lee IDEs Oe
or
aD?
BM.=((- —b) -c)b.
4x12
The first of these sets of formule was originated by A. L. Daniels, the second by
H. E. McKenzie. By Daniels’ formula, the values of logs of three sizes will give
the formula. For the following rules, the formule read:
L
Doyle, B.M.=(.75D? —6D+12)-5
; L
Seribner, B.M.=(.555D?—.55D S24) ae
; L
Maine, Sn Oe eae
L
Champlain, B.M.=(.62832D2— D9)
L
Vermont, B.M.=(. Oa:
By the McKenzie formula, adding the constant C gives the following for:
aD?
Spaulding, B.M.=( (1—.266 —2)L;
cea kas ( risa )
D2
Scribner, B.M.=( (1—.266)————3 )L;
4x12
aD?
Maine, pa.=(a— 222) Ta or),
These formule permit of analysis and comparison of different log rules.
74. The Construction of Log Rules from Mill Tallies. Graded
Log Rules. A log rule based directly on mill tallies or the measured
product of sawing logs into lumber will have no over-run provided the
variable conditions of manufacture coincide with those which determined
the contents of the logs from which the rule was made. But this is
never the case. Standard log rules made for 1-inch boards do not con-
form to mill tally of lumber sawed partly into 2-inch plank, or even if
sawed full or 1,’g-inch in thickness. Standard rules for square-edged
lumber fall far aren) of measuring the product of small logs sawed and
tallied as round-edged boards. The board foot as a cubic measure will
not indicate the quantity of surface or superficial feet of lumber pro-
duced in sawing 3-inch boards.
Where it is desired to obtain, in the log, the probable actual contents
in boards, and existing rules are unsatisfactory, a new rule may be worked
THE MASSACHUSETTS LOG RULE 79
out based directly on mill tallies. Unfortunately, most of the rules so
obtained are not standardized for lumber of a given width, as 1-inch
boards, but include the mill run, with varying per cents of thicker plank.
This requires a statement as to the basis of the rule. Even when based
on arbitrary per cents of 1-inch and thicker lumber such a rule may be
superior, for local use, to one of the older commercial rules.
A mill tally, upon which a local log rule can be based, will also serve
two other purposes if rightly conducted, namely, a check on the amount
of. over-run to be obtained from logs of different sizes if scaled by an
existing log rule (Doyle rule, § 65), and an analysis of the product of
the log by grades of lumber, leading to the construction of graded log
rules.
For the single purpose of constructing a log rule for sound logs with
normal crook (§ 52) but two operations are required. Each log is meas-
ured, preferably at both the small end, inside bark, and the middle
diameter outside bark, and its length recorded. The contents of each
board sawed from the log is then tallied, and the total found, from which,
by averaging for logs of the same dimensions, and the use of graphic
plotting (§ 138) the log rule may be obtained.
When mill-scale studies are made to check a given log rule, and to determine
contents of logs by grades, from which a graded log rule is constructed (§ 87), the
work is planned as follows: Each log is given a number, and is scaled as it enters
the mill. A second man stationed at the edger places this number on the first and
last board sawed from the log. A lumber grader at the grading table indicates the
grade of each board, while a fourth man tallies the board-foot contents of the piece
on a ruled blank which contains columns for each standard grade, As the scaler
and grader are usually employees of the mill the work requires two extra men in
the mill.
The study is usually extended to include defective logs, which are kept separate
in the final averages, since the original scale of such logs is a matter of judgment
subject to wide errors. (Appendix A, § 361.)
By a proper system of numbering the logs in the woods, a mill scale study may
be applied to determine the graded contents of entire trees for the construction of
graded volume tables (§ 165).
REFERENCE
A Mill-scale Study of Western Yellow Pine, H. E. McKenzie, Bul. 6, Cali-
fornia State Board of Forestry, Sacramento, Cal., 1915.
75. The Massachusetts Log Rule for Round-edged Lumber. This
log rule is constructed for round-edged and square-edged boards as
sawed from small logs for close utilization of second-growth timber.
The per cent of square-edged lumber sawed varies from 0 to 50 per cent, increas-
ing with diameter of log. The rest of the cut was round-edged. The rule is for
#-inch saw kerf, varying in the per cent of round- or square-edged boards included.
It is based on mill tallies of 1200 logs down to 4 inches at small end. The rule is
80 THE CONSTRUCTION OF LOG RULES
expressed in two forms, one for application to diameter at small end, inside bark,
the other to diameter outside bark at middle of log. The latter form would apply
only to species with bark of similar average thickness to the second-growth white
pine on which the latter is based. The utility of this rule as a standard is inter-
fered with by the fact that a certain per cent, not stated, of 14-inch and 22-inch
lumber was included with 1-inch boards in its construction. The results are there-
fore somewhat too high for 1-inch lumber.
This log rule indicates that the contents of logs measuring from 4 to 10 inches
in diameter at small end are from 20 to 50 per cent greater when scaled by this rule
than by the International 4-inch rule. Above 12 inches, the excess is not over
10 per cent. Since these boards are measured at their average face, taper is fully
utilized, while waste from slabs and edging is reduced to a minimum. The result-
ant per cent of utilization is very consistent for logs of all sizes; hence it shows a
marked gain in the small sizes over the per cents utilized in square-edged boards as
shown in Table ITI.
The importance of a log rule of this character in scaling the board-foot contents
of second-growth timber in regions utilizing round-edged boards is obvious. Rules
of this character are nearly as satisfactory as the cubic foot in measuring small timber.
For complete accuracy in applying this rule to other species, the average taper
must be known, or the average thickness of bark. Similar local log rules have
been made for loblolly or old field pine in the Atlantic Coast States.
76. Conversion of Values of a Standard Rule to Apply to Different
Widths of Saw Kerf and Thickness of Lumber. Where over-run or
under-run is caused by a difference in the width of saw kerf used, or in
the thickness of lumber sawed, from the standards used in the log rule,
the per cent of this difference between scaled and sawed contents due to
these factors may be easily determined, and applied, if desired, to the
scale; or it may be incorporated in a new set of values or local log rule
similar to those made from mill tallies.
For saws of different widths.
Let AK =width of saw kerf in standard rule;
K’ =width of saw kerf used in sawing.
Then
isk =per cent of lumber, minus saw kerf by standard rule;
ae =per cent of lumber using different saw kerf.
The correction to apply to the standard rule in terms of per cent is:
yes
1+K’
Per cent correction = 100 ae
1+K
e.g., the International rule, }-inch kerf plus j;-inch shrinkage = #;-inch = 3125, .
1
100 x 13195) 76.3 per cent.
CONVERSION OF VALUES OF A STANDARD RULE
For a ;%-inch saw kerf plus jg-inch shrinkage = (4; = . 25,
1
100 XT 95 =80 per cent.
Then,
100 20 104.8=+4.8 t
—— =104.8=+4. cent.
Fe per cen
81
The following table will convert values for the International }-inch log rule to
products of saw kerfs of other widths, allowing jg-inch shrinkage in each case as
for the original rule.
TABLE XIII
CONVERSION OF INTERNATIONAL RULE }-INCH SAW KeErRF FOR OTHER
Wiptus or Krerr
i Per cent correc-
ieee re Per cent tion to obtain
eps utilized* product for
desired kerf
a B08 Beleieg
: 84.3 +10.5
- e050 + 4.8
4 76.3 0
16 72.7 = 1e7
3 69.6 Bers
is 66.7 —12.6
* This per cent applies only to the residual portion of the log after deducting the waste for
slabbing and edging. The ratio between the per cents utilized is the basis for correcting for saw
kerf.
Log rules which make no allowance for shrinkage may be adjusted in the same
manner by omitting this factor. Table XIV, Page 82.
Correction for lumber thicker than the standard. For this purpose the same
formula as for saw kerf is used, substituting the actual thickness of lumber (t) for
1 inch, and using K as a constant representing saw kerf.
Let 1=standard thickness of lumber;
t=actual thickness of lumber.
Then,
1
——=per cent of lumber, minus saw kerf by standard rule;
14+K
t
—— -=per cent of lumber, with thickness of ¢;
' t+K
and
eee.
1+K :
ag =per cent correction.
t+K
For {-inch saw kerf the results obtained are given in Table XV, Page 82 (§ 48):
82 THE CONSTRUCTION OF LOG RULES
TABLE XIV
CoNnvVERSION OF Loc RULES WITH }-INCH SAW KeErRF AND No SHRINKAGE
ALLOWANCE TO OTHER WIDTHS OF SAW KERF
i | Per cent correc-
y |
yeas! | Per cent tion to obtain
THehes* i Utilized | product for de-
| desired saw kerf
ea ale 12.7
$ 88.8 411.1
16 84.3 Bi
Z 80.0 0.
16 76.2 ALS
3 (at ot
i6 69.6 73°10
* Rules made by first subtracting slabbing and edging may evidently be altered for different
widths of saw kerf, as these deductions are directly proportional to volume, and are applied to the
reduced cylinder only. Where, as with the International rule, the deduction for saw kerf is made
before subtracting AD for slabs and edging, this rule still holds good, since the per cent of cor-
rection is not applied to the entire log, but to the values in the rule, which already exclude AD.
If worked out for the log, independent of the rule, the sawdust in the slabs is deducted before
the factor AD is found, and for larger saw kerfs this factor AD would be proportionally smaller,
so that the total net product in lumber is the same as if computed by the above correction.
TABLE XV
Per Cent oF INCREASE IN SAWED LuMBER CAUSED BY SAWING
LuMBER OF DIFFERENT THICKNESSES f
| Inerease in sawed
Thickness of lumber. | product over 1 inch
lumber.
Inches Per cent
et 4.1
13 Goll
13 9.4
2 Cel
21 12.5
3 13.6
+ In preparing tables of volume for Connecticut hardwoods (Bul. 96, Forest. Service), Frothing-
ham used the International rule, reduced for a }-inch saw kerf by subtracting the required 9.5
per cent of volume from-values for {-inch saw kerf. Complaint was later made that in applying
these tables to logs sawed in mills using }-inch saw kerf, the output over-ran the tables. This
was due not to error in the tables, but to the production of a large proportion of thick planks,
thus reducing the sawdust waste.
These per cents are applied to the scale of 1-inch lumber. When 50 per cent of
the output is in 2-inch plank, the correction would be 50 per cent of 11.1 per cent,
LIMITATIONS TO CONVERSION OF BOARD-FOOT LOG RULES 83
or 5.55 per cent. As the increase in per cent of correction in the total scale becomes
less with increasing thickness of boards sawed, this method is more accurate than
that of computing the average dimensions of the products sawed. In the above
case the latter would have been 13 inches, calling for a correction of 7.1 per cefit
instead of 5.55 per cent.
Correction for thin lumber based on superficial. contents. In a similar way,
log rules for 1-inch lumber may be corrected to give the product in superficial board
feet for lumber sawed to thicknesses less than 1 inch. Since the board, of whatever
: : 1 ;
thickness, measures 1 superficial foot, the ‘per cent of utilization”’ will be LE? t being
aie
thickness of board, K, saw kerf. For }-inch kerf and 1-inch lumber, the standard
1
Bs oe! : Be tat eae
per cent is i+ KO per cent. Then the correction per cent is
1+K
TABLE XVI
CorreEcTION PER CENTS FOR CONTENTS OF LOGS IN SUPERFICIAL BoARD FRET
FOR LUMBER SAWED Less THAN 1 INCH IN THICKNESS
Correction per
Thickness Bat cantar paraedias cent to add to
of Saw keri. utilization inch lumber log rule for
lumber. 1-inch boards
Inches Inches Per cent
3 i 11353533 80 66.6
5 1 114.3 80 42.9
3 1 100.0 80 25.0
z 1 88.8 80 Vata
77. Limitations to Conversion of Board-foot Log Rules. It is thus
seen that a correction of the total scale of logs regardless of diameter or
length can be made whenever this correction takes the form of a straight
per cent of the volume of the scale. In addition to the effect of saw kerf
and thickness of boards, this principle applies to cubic rules erroneously
used for board feet (§ 28). But no true board-foot log rule can be con-
verted by a constant or flat per cent into the values of any other log
rule, unless the deduction for waste from slabs and edgings is identical
for both rules, and the difference is wholly due to the use of different per
cents of waste for saw kerf. Otherwise, the conversion factor will vary
with diameter of log. Since tables of tree volumes and the scale of a
number of logs include logs of different sizes, such volume tables or
scale totals must be remeasured’ in the log in order to determine the
values for any other than the log rule originally used.
84 THE CONSTRUCTION OF LOG RULES
78. Choice of a Board-foot Log Rule for a Universal Standard. As
long as opinions and customs differ with regard to the measurement of
taper, scaling length, saw-kerf allowance and amount of waste in slabbing
which should be expressed in log rules, it will be impossible to reach
an agreement on a common standard. Meanwhile, custom is working
towards the elimination of rules which have not found favor and all but
about ten log rules in the United States can already be classed as obsolete.
A log rule becomes obsolete when it ccases to be used, regardless of
the reasons for its disuse. Poor rules should, and sometimes do, become
obsolete because they do not give satisfaction. But good and con-
sistent rules may also become obsolete or may never be taken up, because
the use of other and inferior rules is so firmly intrenched that a substitu-
tion is impractical. Rules which scale so closely as to permit no over-
run will be very difficult to bring into common use, owing to the opposi-
tion of buyers who prefer lower standards even if inaccurate.
The log rules whose use is sufficiently extensive to justify their con-
sideration, on this basis alone, for universal adoption include only the
foilowing:
Basis of Rule United States Canada
Formula Doyle Doyle
British Columbia
Diagram Scribner Quebec
Scribner DecimalC | New Brunswick
Spaulding
Maine
Hybrid Doyle-Scribner
Mill Tallies Massachusetts
Of these, the Doyle must be rejected because of its glaring inconsis-
tencies and the Doyle-Scribner because it combines the worst features
of both rules. The use of the Maine and the Spaulding rules is confined
to single states, and the Massachusetts rule is for a special form of
product; i.e., round-edged timber.
This leaves the Scribner, preferably in Decimal C form, as the only
logical rule now in wide use, which is applicable to the measurement of
square-edged lumber.
If the admitted irregularities of the Scribner rule are deemed so seri-
ous as to justify its rejection, its successor should not be chosen from
among the other rules in common use, but should rather be a rule based
on a formula and tested to conform to actual conditions of sawing. For
such a purpose, the International {-inch Rule is probably as perfect a
UNUSED AND OBSOLETE LOG RULES 85
rule as will ever be required in commerce. This rule is especially valu-
able for logs below 12 inches and above 28 inches, in which classes the
Scribner rule is defective. There is nothing to be gained by further
efforts to construct new “‘ perfect ”’ log rules.
79. Unused and Obsolete Log Rules. In addition to the rules described in
this chapter we may mention the following rules, all of which are now obsolete.
Bangor Rule. Synonyms: Miller, Penobscot. The Bangor Rule was constructed
from diagrams, and gives slightly higher and more consistent values than the Maine
rule. It shows more care in construction and is probably the best of the diagram
rules. Owing to the more extensive use of the Maine rule, this rule is almost obsolete.
Parson’s Rule. This rule is of similar construction to the Bangor and Maine
rules and its values are almost identical but a little below the Maine rule. The
difference is about 2 per cent. It is a local rule, still used to some extent.
Boynton Rule, 1899 (Vermont, local). Made up from values taken from Scrib-
ner and Vermont ruies.checked by mill tallies. A fair rule but of no general value.
D. J. Boynton, of Springfield, Vermont.
Brubaker Rule. No detailed knowledge.
Chapin Rule, 1883. The most erratic of all log rules, made up apparently by
selecting values from existing rules to suit the author.
Drew Rule, 1896. The Drew rule has been the statute log rule of the State of
Washington since 1898 but is used practically nowhere in the state. Instead, the
Scribner rule is universally used, except along the Columbia River, where the Spauld-
ing rule is in use.
This rule (by Fred Drew, Port Gamble, Wash.) was made from diagrams checked
by tallies of logs as sawed. The values are given for diameters from 12 to 60 inches
and lengths of from 20 to 48 feet. Taper is not considered. The values are said
to have been reduced to allow for hidden defects. The rule is inconsistent in scale,
resembling the Doyle in tendency on large logs. Its use is practically discontinued.
Dusenberry Rule, 1835. This rule was made in 1835 by a Mr. May, and adopted
by Dusenbe:ry-Wheeler Co., of Portville, N. Y. It was probably constructed
from mill tallies, and was intended to measure the output of pine sawed 1} inches
thick with some 13- and 2-inch pieces. The saw kerf was 7% inch. The rule is
very consistent and was generally adopted in the Alleghany Waters in Penne
sylvania. It is still used in that and adjoining states. Owing to the wide saw
kerf used, this rule under-scales Scribner from 15 to 20 per cent and is not suited
to present conditions.
Favorite Rule. Synonym: Lumberman’s Favorite. A diagram rule, made
by W. B. Judson in 1877 and published in Lumberman’s Handbook, 1880. The
values for small logs are lower by 15 per cent than Scribner’s. The rule is now
practically obsolete.
Finch and Apgar Rule. Date unknown. A diagram rule, erratic, for 3%;-inch
saw kerf. Gives low values.
Forty Five Rule. About 1870. Based on an inaccurate rule of thumb formula
which gives high values for small and large logs and low values petween these
extremes.
Herring Rule, 1871. Synonym: Beaumont. The values in the Herring rule
as originally made, to include from 12- to 44-inch logs, are practically identical
with the Dusenberry rule. The rule was applied at the small end to logs up to
20 feet in length. Above 20 feet a rise of 1 inch was added, and was applied at
middle point of logs up to 40 feet in length. Here another inch was added, and the
86 THE CONSTRUCTION OF LOG RULES
scale carried to 60-foot logs. The taper allowed in this was is about half of the
average taper.
The rule is used extensively in the pine regions of Texas and gives a large over-
run.
The same trouble was experienced with this rule as with the Scribner, in agreeing
upon an extension of values to cover logs less than 12 inches in diameter. The
values most commonly used are the so-called Devant extension, based upon the
Orange River rule, and agreeing closely with the Scribner extension.
Licking River Rule. No detailed knowledge.
Northwestern Rule. A diagram rule for 3-inch saw kerf. Erratic, and similar
to Seribner’s.
Ropp’s Rule. A rule published by C. Ropp & Sons, Chicago. Based originally
on diagrams of 1-inch lumber for a 4-inch saw kerf, it was reduced to a rule of
thumb which gives erroneous results especially for small logs, which are severely
under-sealed. The rule is therefore of no value.
Warner Rule. A diagram rule with excessive allowance of 3 inch for saw kerf.
Worthless.
Wheeler Rule. No detailed knowledge.
Wilcox Rule. A diagram rule for 3-inch saw kerf. Irregular. Low values.
Younglove Rule... Fitchburg, Mass., 1840. A caliper rule resembling the Baxter
in values.
REFERENCES
General Treatises on Log Rules
Relative Value of Round and Sawn Timber, James Rait, p. 114, Wm. Blackwood
Sons, London, 1862.
The Measurement of Saw Logs (Universal Rule), A. L. Daniels, Bul. 102 Vermont
Exp. Sta., 1903.
The Measurement of Saw Logs and Round Timber (Champlain Rule), A. L. Daniels,
Forestry Quarterly, Vol. ILI, 1905, p. 339.
The Measurement of Saw Logs (International Rule), Judson F. Clark, Forestry
Quarterly, Vol. IV, 1906, p. 79.
The Standardizing of Log Measures, E. A. Fics, Proc. Soc. Am. Foresters,
Vol. IV, 1909, p. 172.
The Log Scale in Theory and Practice (Tiemann Log Rule), H. D. Tiemann, Proc.
Soc. Am. Foresters, Vol. V, 1910, p. 18.
A Discussion of Log Rules, H. E. McKenzie, Bul. 5, California State Board of
Forestry, 1915.
Review of Bul. 5, California State Board of Forestry, by H. D. Tiemann. Proc.
; Soc. Am. Foresters, Vol. XI, 1916, p. 93.
Specific Log Rules
Scribner’s Log and Lumber Book (Cubic Measure, Two-thirds Rule, Doyle Rule),
S. E. Fisher, Rochester, N. Y., 1900.
Extending a Log Rule (Devant Extension of Herring Rule vs. Doyle Rule), E. A.
Braniff, Forestry Quarterly, Vol. VI, 1908, p. 47.
Report of Commission to Investigate Methods of Scaling Logs in Maine (Holland
Rule, Blodgett Rule, Hollingsworth & Whitney Rule), House Document No. 43,
74th Legislature, Maine, 1909.
1 Reference, Forestry Quarterly, Vol. XII, 1914, p. 395.
UNUSED AND OBSOLETE LOG RULES 87
A Comparison of the Maine and Blodgett Log Rules, Irving G. Stetson, Forestry
Quarterly, Vol. VIII, 1910, p. 427.
Woodsman’s Handbook, Henry S. Graves and E. A. Ziegler (Scribner Decimal C,
Doyle, Inscribed Square Log Rules, and Table of Comparisons of 44 log rules
for 16-foot logs), Bul. 36, U.S. Dept. Agr. Forest Service, 1910.
Comparative Study of Log Rules (Champlain, Vermont and Doyle Rules), Austin
F. Hawes, Bull. 161, Vermont Agr. Exp. Sta., Part I, 1912.
Log Rules Based on Mill Tallies
Log Rules for Second-growth Hardwood from Mill Tallies. {-inch Saw Kerf,
Round-edged Boards cut 13 inches thick. Based on Small End, Inside Bark,
and on Middle Diameter Outside Bark, C. A. Lyford, Reports of Forestry
Commission, N. H., 1905 and 1907.
Log Rule for White Pine, from Mill Tallies, {-inch Saw Kerf, for 60 per cent Round-
edged, 40 per cent Square-edged Boards, 70 per cent 1-inch Lumber, remainder
23-inch Plank, C. A. Lyford, Reports of Forestry Commission, New Hampshire,
1905 and 1907.
Log Rules for 12-ft. logs from Mill Tallies of Round and Square Edge Lumber,
separately for White Pine, and Hardwoods, L. Margolin, Proc. Soc. Am.
Foresters, Vol. IV, 1909, p. 182.
Comparison of Round-edged and Square-edged Sawing for 23-inch planks, H. O.
Cook, Forest Mensuration of White Pine in Mass., 1908, pp. 38-43.
Contrast of Output by Different Methods of Sawing, H. D. Tiemann, Proc. Soc.
Am. Foresters, Vol. IV, 1909, p. 173.
Log Rule for Hickories, in Cubic Feet, Bul. 80, Forest Service, 1910, p. 39.
Log Rule for Hardwood Logs from Mill Tally, Yellow Birch, Maple, Beech, I. W.
Bailey and P. C. Heald, Forestry Quarterly, Vol. XII, 1914, p. 17.
Log Rule for Loblolly Pine, based on Mill Tallies, Logs with less than 2-inch Crook,
1iinch Kerf. W. W. Ashe, Table 23a. Bul. 24, North Carolina Geological
Survey, 1915, p. 76.
CHAPTER VII
LOG SCALING FOR BOARD MEASURE
80. The Log Scale. The scale of a given quantity of logs is their
total contents expressed in the unit of measurement employed. The
term “scale” also refers to the general rules or customs of scaling
adopted in a given region or locality, upon which depend the liberality
or closeness of the measurement (§ 83). Differences in the method of
scaling may make from 5 to 50 per cent difference in the scaled contents
of the same logs (Table X VII).
To determine the contents of logs in board feet, the diameter of the
log is measured with a stick marked in inches, the length in feet is deter-
mined by measuring it with the above stick or by a tape or wheel
(§ 34), and the volume corresponding to these dimensions looked up in
the log rule.! This process is simplified by placing upon the sides and
edges of this stick, opposite each diameter, rows of figures giving the
values of the rule for each of several standard lengths. The volume in
board feet is then read directly from the stick, and recorded. A stick
so graduated is termed a scale stick or scale rule.
Seale sticks are made of hickory or maple about 1 by } inch in cross section,
graduated in inches, with the figures burnt into the wood (Fig. 10). Metal sticks
are also in use and in some regions caliper rules are used. The inch scale is on
one or both edges and the stick easily accommodates six or seven other rows of
figures corresponding to the contents in board feet of logs of as many different
standard 2-foot lengths. A metal tip aids in measuring the diameter inside the
bark. Other forms are made for scaling logs in water, or logs with ends rounded
or sniped. Lengths of scale sticks in inches correspond to the maximum diameters
of the logs to be sealed. Hexagonal scale sticks are sometimes used. Scale sticks
have been made,which are graduated at points giving volumes to exact tens or
hundreds of units, but these rules have never become popular as the basis of the
rule is not indicated (§ 111).
The purpose of a log scale depends upon the ownership of the timber
or logs. Where the logs are to be sold the scale is the basis of settle-
ment and must be far more carefully made than when the timber is
1 Experienced scalers sometimes substitute ocular or paced lengths on short
logs. The scale of logs shorter than the minimum length given in the rule is taken
as equaling one-half the scale of a log twice as long as the one in question, 7.¢.,
when the shortest length given on the scale is 10 feet, an 8-foot log is scaled as
one-half of a 16-foot log.
88
THE LOG SCALE 89
owned, logged and manufactured by the same firm. In the latter case,
the purpose of the scale is merely to provide a basis for the payment
of contractors for logging or sawyers for felling, or for checking the com-
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parative efficiency of crews or camps. Finally, the woods scale deter-
mines the quantity of timber felled, thus keeping track of the operation,
while a re-scale at the mill permits the keeping of costs and credits
separately, on the basis of the volume of logs delivered, between the
90 LOG SCALING FOR BOARD MEASURE
logging and milling ends of the business, as if they were under separate
management. Woods scaling also checks the accuracy of timber esti-
mates, whenever the timber from given areas is scaled separately in
logging.
When the purpose is to determine the basis for paying saw crews, logs are
scaled in the woods before skidding. When standing timber is sold on the basis
of the log scale, the scaling is done at the skidways or landings before removal
from the tract or vicinity. The mixing of logs cut from two or more tracts must
be avoided by any necessary measure such as sawyers’ marks, or scaling in the
woods. Where no question of sale is involved, the logs are scaled wherever it is
most convenient. Logs are usually re-scaled on the log ees Where logs are
rafted and sold, they usually are scaled in the water.
81. The Cylinder as the Standard of Scaling. A log rule does not
give an exact scale of lumber which will be or can be sawed from logs
(§ 46). The log rule is an arbitrary
standard fixing the quantity of 1-inch
lumber said to be contained in logs of given
diameters and lengths. When the top or
small end of the log inside the bark deter-
mines the diameter, as it does for all board-
foot log rules in common use, these rules do
not include any boards or pieces sawed
from the taper or swell of the log. The
scaler must therefore pay no attention to
Fic. 11—Projection of area that portion of the contents of the log
of top end of log on butt which lies outside of this cylinder, no
section, showing portion of matter whether this portion be sound or
buch towable’ Healt wens defective. On the butt end of a log, the
circle A represents the area : ar at
to be scaled. The presence Contents to be scaled lies within a smaller
of defect in area C doesnot circle representing the area of the top end
justify the shifting of this of the log, or the cross-section of the
circle to position B but de- Gyjinder whose diameter is this top end.
ductions for defect must be ; : are ; ae
a dis fete Te This cylinder must coincide in position
geometric center of the log With the axis of the log, so that the center
and of the scaled area A. of the cross-section or area to be scaled
coincides with the center of the butt or
larger end of the log. Common errors in scaling are the shifting of the
scaled cylinder towards one side to avoid defects, and the offsetting of
defects within the cylinder against sound short lumber which may be
scaled from the taper.
82. Deductions from Sound Scale versus Over-run. Log rules
give the scale of this cylinder in sound lumber and do not allow for
defects. The standard scaling practice is to make deductions from
SCALING PRACTICE 91
the scale for all visible defects which lie within the cylinder in each
log separately, of the amount of lumber which would be lost because of
the defect.
This rule is not always observed. In many species, certain defects may exist
without visible external indications either on the surface or at the exposed ends.
When the logs are in water it is difficult to detect defects. There has been a
tendency on the part of makers of log rules to reduce the standard volumes of the
log rule in order to offset these invisible defects (Scribner rule, § 68). Log rules,
like the Cumberland River rule which gives but 45 per cent of the cubic contents,
permit the buyer to ignore most defects with perfect safety.
The use of a log rule which is known to give a large over-run (§ 47) usually
gives rise to the practice of scaling “sound” and ignoring defects. The buyer
ean afford to be lenient, and the seller objects to any further discounts than those
inherent in the rule itself.
Except for a few species and regions, defects may usually be seen and
deducted. Where the opposite is true, custom sometimes permits a
reduction of the final scale by a straight per cent to allow for such
invisible defects.
Over-run (§ 46) is therefore an element which should not influence
in any way the practice of log scaling. Where an admittedly defective
rule is offset by lenient but inaccurate scaling practice, the entire
technique and standard of scaling suffers, and such conditions should
sooner or later yield to accurate standards, both in the rule used and
in its application.
83. Scaling Practice, Based on Measurement of Diameter at Small
End of Log. The advantages of measurement of the log at the small
end, which have made this custom practically universal in scaling, are
that the scaling diameter inside the bark can be directly measured
without guessing at bark thickness, and no matter how high a skidway
or rollway is piled, the ends of the logs are usually visible for scaling.
By contrast, logs to be calipered at the middle point can be measured
only when lying separately or before being placed on rollways, and the
bark thickness is usually guessed at.
The per cent of over-run on the log scale is affected by three main
factors. Two of these, namely, the elements affecting manufacture of
lumber and the character of the log rule itself, have been discussed in
Chapter V. The third is the practice of scaling, and the customs which
govern it, collectively termed the “ scale.” This practice affects, first,
the method of determining scaling diameters and lengths, for when
these are once ascertained the rule permits no variation in contents for
sound logs; and second, the deductions from this scale for defects, as
interpreted by the scaler.
Scaling Lengths. The total length of a log must be accurately deter-
mined. For log rules which are based on diameter at the small end,
92 LOG SCALING FOR BOARD MEASURE
logs whose length exceeds a given maximum are scaled as two or more
sections or shorter logs (§ 438). Custom or “scale ’’ determines the
maximum length to be scaled as one section and the method of deter-
mining the taper or diameter of the second or remaining sections to be
scaled. Short sections scaled to full or actual top diameter give the
maximum scale, while the loss from sealing long logs as one piece based
on diameter at top end may be very large, due to the increasing per cent
of volume in long logs which hes outside the cylinder and is thrown into
the over-run.
The standard lengths of softwood or coniferous logs are multiples of
2 feet, to which is added an allowance for trimming. Where long logs
are divided into two or more lengths for scaling, this rule is still adhered
to; e.g., a 26-foot log is scaled as a 14- and a 12-foot. Usually the
longer length is scaled as the butt log.
The tremendous variations in scale which may result from different
treatment of scaling lengths and taper in long logs is illustrated in Table
V (§ 44). In order to secure a consistent scale between long and short
logs, the scaling length should be limited to not over 16 feet, and the
actual diameter of each section taken as the scaling diameter.
Trimming Allewance. The trimming allowance varies according to the method
of transportation used. For logs hauled by rail or driven down sluggish streams,
from 2 to 3 inches is allowed for each 16 feet of length. Large logs require the
greater allowance, to guard against slanting cross cuts which might give a short
length on one side. Where logs are driven down swift rocky streams the trimming
length must be sufficient to allow for the brooming of the ends. In very bad waters,
the exact length of a log is immaterial and the loss from brooming a heavy item.
Odd lengths, 7.e., lengths measured in odd feet as 13 feet, are permitted in hard-
woods and to a limited extent in softwoods.
In ordinary scaling, trimming lengths in excess of standard 2-foot gradations
are not scaled. But sellers of logs, to reduce loss from careless cutting of log lengths,
may stipulate that when trimming lengths are in excess of the margin agreed
upon, the log shall be scaled as if cut from 1 to 2 feet longer. The U.S. Forest
Service adopts this practice as a penalty scale. }
Scaling Diameters. In the apparently simple process of measuring
the diameter inside the bark at the top end of the log, there are two ways
in which the buyer may be given the advantage of a smaller scale. Owing
to the irregular cross sections of logs, an average diameter should be
found by taking two measurements at right angles. Instead, the
practice of scaling the smallest diameter is common. The difference,
in large logs, sometimes amounts to 2 or 3 inches. The second choice
lies in the treatment of fractional inches. These fractions should be
rounded off to the nearest inch; e.g., the 18-inch log class should include
diameters from 17.6 inches to 18.5 inches. Instead, all fractions may
SCALING PRACTICE 93
be dropped, throwing logs from 17.6 inches to 17.9 inches into the 17-
inch instead of the 18-inch class.!
The variations in scaling practice or local “scale” for the different regions in
the United States and Canada are shown in Table XVII, p. 94.
It is seen that the standard set by the U. 8. Forest Service is almost nowhere
complied with in private operations, and that the departures from this standard
work uniformly in favor of the buyer. Except for hardwoods, there is no valid
reason for rejecting fractional inches, since these are in most instances already
rejected in the construction of the log rule itself (Scribner, § 68), and in any case,
the contents of logs of exact inch diameters represent a fair average for logs varying
up to } inch larger or smaller. In the same way, it is unfair to measure the
smallest diameter instead of the average, for the sawed contents of logs with
eccentric cross-sections is little if any less than for round logs, and certainly
does not diminish in proportion to the ratio between smallest and average diameter.?
1 ‘
<—___—_—_________-19 Feet >
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Fic. 12.—Effect of rapid taper at small end upon scaling diameter and
sealed contents of a log.
1 The adoption of these two buyers’ practices in the scale will result in a loss
to the seller which, by the Scribner log rule, amounts to from 5 to 15 per cent,
averaging 8 per cent for logs running 10 to the thousand board feet, and 13 per
cent for logs running 20 per thousand. The use of the average diameter, and the
rounding off of fractional inches are practices fair alike to buyer and seller, and
are required by the U. 8. Forest Service in selling public timber.
The practice of reducing unit feet in a log rule to tens, or converting the rule
into a “decimal’’ rule gives a third opportunity for discrimination in favor of
the buyer. The correct method is that employed in the Scribner Decimal rule where
all fractions above 5 feet are thrown to the 10-foot value above, while those less than
5 feet are dropped. But in one section of Maine it is the custom to drop all unit
feet scaled by the Maine rule. Thus a log scaling 19 feet would be entered as
10 feet. The effect of such a custom on the scale is self evident.
*In a contract for sale of logs, the log rule to be used must be mentioned.
The practice regarding scaling length, trimming allowance, method of measuring
taper or rise on logs of greater than scaling lengths, measurement of diameter and
treatment fractional inches should be specified. Otherwise, common custom or
scale in the locality will determine what constitutes a proper method. The method
of deducting for defects whether by each log separately or by a straight per cent
should be agreed upon, and if possible, standard instructions adopted for culling
defects. The minimum dimensions of a merchantable log should be defined, both
as to length and diameter, and as to per cent of total scale which must be obtained
after deducting for defects.
LOG SCALING FOR BOARD MEASURE
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SCALING PRACTICE BASED ON MEASUREMENT OF DIAMETER 97
Abnormal Diameters. The practice of basing the scaling diameter on that of
the small end of the log, with its consequent disregard of taper, gives rise to diffi-
culties on !ogs which taper rapidly at the small end, as for instance, rough or limby
logs on the basis of their top diameters may result in loss of scale when in reality
a greater volume of the tree has been utilized, Fig. 12, p. 93.
By the International {-inch rule this log would scale, in actual diameter
Length. | Scaling diameter. Scale.
Feet Inches | Feet B.M.
12 12 70
14 9 45
16 6 20
Rigid adherence to the scaling practice on such logs results in the refusal of
contractors to cut them. There are two possible modifications of the end diameter
rule which will meet this condition: First, to scale the log as a shorter log, at the
point which will give the largest total scale, in the above instance at 12 feet giving
a scale of 70 board feet; second, to scale it as two logs, including the short tapering
portion as a separate piece from the main portion. In the above case, the 6-inch
top, with a length of 4 feet would add one-fourth of the scale of a 16-foot log of
that diameter, or 5 board feet, giving a total scale of 75 board feet. The latter
method is the most equitable, otherwise there is no object to the contractor in
going into the top to secure closer utilization.
Abnormally large diameters, occurring at the small ends of logs are the result
of cross cutting through crotches or swellings caused by limbs, or by defects or
cankers. Such diameters must always be reduced to a size representing the normal
diameter of the cross section as determined by average taper. For slight swellings
this is judged by eye. For crotches, the diameter at butt end is sometimes taken
and average taper deducted.!
84. Scaling Practice Based on Measurement of Diameter at Middle.
of Log or Caliper Scale. None of the true board-foot log rules in common
use are applied at the middle of the log. By the Blodgett Rule, a cubic
rule expressed in board feet (§ 33) the log is usually measured in the
middle, outside the bark. When taper is taken on long logs by the ordi-
nary rules, the scaler depends upon his scale stick and ocular judgment
for the measurement of the upper diameters. But if logs are customarily
cut long, and must be scaled by getting actual taper rather than assumed
‘The following court decisions are important as defining the bearing of the
“scale”? on agreements:
“Tn the absence of any agreed standard of measure in a contract, that of the
place where a commodity is purchased will govern the contract.’’ Supreme Court
of New York, Dunberie vs. Spaubenberg, 121 N. Y. 299.
“Where a contract involves the measurement of logs by specified rule, but
does not indicate the manner of measuring whether by end, average or middle
diameter, local custom shall determine such manner.” Supreme Court of Louisiana,
13 So. 230.
98 LOG SCALING FOR BOARD MEASURE
standard tapers, calipers must be brought into use in scaling. The
calipers employed in scaling logs by the Blodgett rule are equipped with
a wheel of 10 spokes, one revolution measuring 5 feet in length (§ 34).
The greatest drawback to a caliper scale is the necessity of determin-
ing the width of bark, doubling this, and subtracting to get the scaling
diameter of the log. When all logs are calipered, it is a common prac-
tice to determine the average width of bark of the species and region,
and deduct twice this fixed amount on all logs regardless of variations
in actual bark thickness, relying on the law of averages to secure a true
scale. For the Blodgett rule, ?-inch for each bark is allowed and the
calipers are adjusted to read the diameter inside bark direct. On the
Big Sandy River in Kentucky (Big Sandy Cube Rule) the allowance is
1 inch for each bark.!
85. Scale Records. The tally is the record kept of the logs by the scaler or his
assistant, the tally man.2 The tally may consist merely of a record of diameter
and length of each log. From this the full scale is easily computed at camp. But
the system prevents deductions for defects from each log separately, and is used
only where such discounts are not made, or are made either as a per cent of total
scale, or by reducing the length or diameter of the log. This primitive method
of sealing has been largely replaced by the plan of recording the board-foot contents
of each log when scaled. From the full scale, deduction is made for defect, and the
net or sound scale recorded. For long logs scaled in two or more sections, only
the sum of these volumes is set down, giving the total scale for the log as one piece
and thus keeping the count intact. The purpose in this is to obtain a tally of
the exact number of pieces scaled as well as their total contents.
To still further insure an accurate record, logs are numbered serially, with
crayon, coinciding with printed numbers in the scale-book. This enables a check
scaler to re-scale and compare individual logs, or any number of logs, with the
original scale to determine the per cent of error and the specific faults in practice.
Without such enumeration, the entire number must be re-scaled to obtain a check,
and specific errors are not shown. The method of numbering is cumbersome where
large quantities of very small logs are handled, but it is the only plan by which a
uniform standard of scaling may be attained by a force of several scalers.
tA second method, employed in Maine in sealing cubic contents, is to assume
that the volume of bark is 123 per cent of the total volume of the tree with bark.
The diameter outside bark is measured direct, and the volumes given on the rule
are computed to express the contents of wood alone.
Bark is never removed, in scaling, to permit the calipering of the direct measure-
ment inside bark, as this process is too time consuming. The Tiemann log rule
(§ 63) which applies to middle diameter inside bark, if used commercially, would
probably be applied by the common method of deducting fixed widths of bark,
to be regulated by measurements taken of the species and locality. This practice
permits of an additional source of variation in measuring diameters (§ 29) through
the bark on individual logs being thicker or thinner than the arbitrary measure-
ment.
2 Scalers usually work alone, preferring the extra labor to the risk of errors
made in the record by incompetent tally men.
SCALE RECORDS 99
The scaler marks the logs with crayon as he scales them. If not numbered,
they are check marked.
Where logs are piled in rollways, unevenly, and cut different lengths, the count
must be checked carefully to see that none is missed. This is best done by making
a recount after scaling a rollway, and check marking the butts of the logs, the
tops having been marked in the scaling. Logs piled in high rollways can best be
scaled by two men, one working at each side of the rollway.
Cull logs which are not scaled are given a distinguishing mark. If already
skidded, they should be counted and recorded as culls. The scaling of logs in
the woods eliminates the culls from the scale altogether and saves the expense of
logging them.
Log Brands, Termed Stamps and Bark Marks. When the practice is necessary
the scaler must see that the logs have been properly stamped and bark marked.
A stamp is a pattern or die stamped into the end of a log with a marking hammer.
A bark mark is a pattern cut into the bark, usually near an end, with an axe.
Stamps and bark marks are used to distinguish logs when driven with those of
other owners down a common stream. These marks are recorded by scalers and
determine the ownership of the logs.
The Scale Book. A form of scale book is shown on p. 100 containing 100 printed
numbers on a page with spaces for entering the contents of logs, and for totaling
each column separately and adding these totals for the page.
The scale record shown in this sample page is for the Scribner Decimal C Scale.
The original records give the scale in tens of feet. At the foot of each column, the
total is entered parallel to the base, and the zero added to obtain full scale.
Logs whose scale has been culled show the net scale, and also the amount
culled enclosed in a circle as, (), which permits checking the cull.
Other forms of scale records are in use following these general principles.!
86. The Determination of What Constitutes a Merchantable Log.
A merchantable log is one which it is profitable to log. Logs whose con-
tents will not return the cost of logging and manufacture are unmer-
chantable. This may be due either to small size, to defects which
reduce the scaled contents of the log, or to high cost of logging.
Minimum Size. The costs of producing lumber are separated into
logging cost and milling cost. Both depend on the cubic volume of the
log. But both are modified by the time required in handling separate |
pieces. This causes the cost per cubic foot to increase for small logs.
In logging, and in small mills, the cost also increases per cubic foot when
logs reach large sizes difficult to handle.
The value of the product depends not upon the cubic contents of
the log, but on the quantity of sawed lumber which it contains, and
1 The following court decisions are of interest: ‘‘When record of scale is kept
on temporary paper and transferred every evening to permanent record, this
record holds in court as original evidence.” Court of Appeals, Alabama, 68 South.
698.
The U. 8. Forest Service instructs its sealers to make the original and final
record of scale in the field because of the liability of error in copying figures.
“Parties must abide by the official scaler’s report except that fraud or gross
mistake can be shown.’”’ Supreme Court, Michigan, Brook vs. Bellows, 146 N. W. 311.
LOG SCALING FOR BOARD MEASURE
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WHAT CONSTITUTES A MERCHANTABLE LOG 101
finally, upon the qualities or grades, and price of this lumber. The
ratio of board feet per cubic foot (§ 41), the quality and value, all
increase with increasing size of log. Due to these factors, logs below a
given diameter and length, or total scale, even if sound, become unprofit-
able or unmerchantable. This minimum diameter and length, when
specified, relieves the logger or purchaser of the requirement of remov-
ing such logs from the woods, cutting them from tops, or felling trees
which will not yield larger sizes. If he chooses to take these sizes,
especially from the tops, the logs are customarily scaled and paid for.
Defective Logs. Defective logs, which will produce only a portion of
the normal contents of sound logs of the same size, cost just as much to
log and saw as if sound. But the ratio of lumber secured per cubic
foot is reduced in proportion to the amount of cull, and the margin
between cost and value shrinks accordingly, until it disappears and the
log is classed as a culland not scaled even if taken by the logger. Defects
occur most frequently in large logs, whose quality and value are high.
A defective log which produces a small per cent of its contents but
of clear lumber or high grades may be merchantable, while a rough log
with a much smaller per cent of defect may not show a profit in handling.
Millmen who log their own timber can base their standard for culls
directly upon this margin of profit, and can afford to accept very defect-
ive logs for a few high-grade boards. Value or margin of profit, if
applied as a standard in selecting or rejecting logs, means an elastic
per cent of cull dependent on the character of the log itself. But the
logger or logging contractor is paid not by value or grade of sawed lum-
ber, but by the scale. Since his costs are determined by cubic volume
and size, he would prefer a cubic log scale, but in accepting payment on
the basis of board-foot contents, his profit in logging depends instead on
the ratio of board feet to cubic feet independent of quality, and is
diminished by reduction in scale caused by cull. On the other hand
the loggers’ costs vary with the distance which the log must be skidded
or hauled. A log with a given per cent of sound scale if near the point
of delivery will show a profit, while the same log is unmerchantable if
located at a greater distance from the track. For defective logs, then,
the merchantability is determined, for the millman, by comparing the
combined cost of logging and milling with the value of the product,
but for the logger it is determined by comparing the price per thou-
sand board feet secured for the scaled contents of the log with the cost
of delivering it to the point agreed upon.
Where firms are doing their own logging, sawyers and loggers are
frequently paid on basis of full scale disregarding cull. But in contract
logging, the scaler usually rejects cull, thus requiring an agreement on
the per cent of sound contents which constitutes a merchantable log.
102 LOG SCALING FOR BOARD MEASURE
This per cent cannot be varied from log to log according to value of
contents to favor the millman, or to location of log to favor the logger,
but is arbitrarily set at an average figure applicable to all logs of a given
species. Different per cents are permitted for species having different
average values, the greater the value the lower the per cent of sound
lumber accepted. As between the logger and the millman, the use of
the board-foot scale favors the latter, but its application regardless of
grades of lumber in the log is a concession to the logger. The rejection
of cull logs is a concession to the millman but the adoption of a fixed
percentage for each species simplifies administration and aids the logger,
who does not have to determine the profit in a log but only the cost of
logging. Contract loggers are favored, then, by a cubic basis, no
deductions for cull, and reduction of logging costs by leaving inaccess-
ible logs in the woods. The manufacturer considers the additional
factor of profit or value of the log, which the logger himself would
have to consider if he were selling his logs. Only by determining aver-
age total costs and average values for a given logging operation can
the actual specifications of a merchantable log be determined, and the
average agreed upon. In the U.S. Forest Service the custom is quite
widely adopted that logs of the more valuable species must scale 333
per cent of their sound contents, and those of inferior species, 50 per
cent to be merchantable.
The limits of merchantability will vary widely in every region, unless standard-
ized as is the case in the Pacific Northwest. The average conditions for different
regions for the year 1917 are indicated below:
; Smallest diameter. Per cent of sound
Region
Inches scale accepted
@entral hardwoods. ..0 22.6. ce 8 to 12 40 to 70, average 60
Dotitliers pines... i. OP Aree 7to 8 25 to 75, average 50
White pine, Lake States............. ANH)! fa) 10 to 25, average 20
MAG. Su. 05uhitah Sheets Hae: Get leet ee sire (2 20 to 33, average 25
Racifie. Northwest. 0. 5° ccs ok eke | 12 333
Southwestac. ate ea ee eee 6to 9 30 to 40, average 33
These limits apply to saw logs. For pulpwood, bolts are taken down to between
3 and 4 inches.
Tests on spruce logs in the Adirondacks showed that 5-inch logs had a relative
value per board foot of 56 per cent compared with 11-inch logs at 100 per cent,
while the relative value of 20-inch logs was 126 per cent.!
1 The following legal decision is interesting:
“A merchantable log is one that contains sufficient lumber to make it profitable
GRADES OF LUMBER AND LOG GRADES. 103
87. Grades of Lumber and Log Grades.! In the scaling of logs
the primary object is to determine the contents in board feet of sound
lumber as fixed by the arbitrary standard of the log rule, based solely
on dimensions of the log, and modified only by deductions for unsound
lumber (Chapter VIII).
But as shown in § 86, the purchaser of logs, or millman, is even
* more concerned with the value per 1000 board feet of the scaled contents.
This value will depend directly upon the amount, by per cent of the
total scale, of each of several standard or recognized grades of lumber
which the logs will yield when sawed, and the resultant weighted aver-
age value which this gives to the logs as a whole.
When the value of logs must be determined before sawing, as is
required when logs are purchased, and in the sale of standing timber,
the relative percentages of these standard grades which will probably be
produced from these logs or the stands in question must be estimated.
It is evident that this can only be done with approximate accuracy,
since a mere inspection of the surface and ends of logs will not reveal
exactly the condition of the interior as to texture, extent of defects
and per cent of better and poorer grades present.
In scaling, no attempt is ever made to divide or separate the total
scale of a log as indicated by the log rule, into the amounts or per cents
of different grades of lumber in the log. Not only would such a process
be too expensive and time consuming, but it would not be sufficiently
exact to pay for the effort of calculating the results separately log by
log to get the total scale for each grade of lumber.
Instead, a system has been substituted of establishing so-called log
grades, usually three in number, based on the average value of the con-
tents of logs as determined by the grades of lumber which they contain.
This classification permits of the fixing of separate prices for each log
grade. The total scale of each log is thrown to the log grade in which
it is classed.
Defects in lumber (§ 352-353) may be separated into two classes,
unsound defects which reduce the scale of the log as described above, and
sound defects which reduce the grades of sound lumber but do not reduce
the scale of the log. The effect of the first class is to render the log
unmerchantable if in excess of the determined limit; the effect of the
second class is to lower the value and consequently the grade of the
to take it to a mill and have it sawed.’’ Gordon vs. Cleveland Sawmill Co., 82
N. W. Rep. 230, Supreme Court, Michigan.
This ruling is based on the millman’s point of view, which, in the absence of
contract specifications protecting the logger, will always determine the standard of
merchantability. '
1 Ref. Appendix A,
104 LOG SCALING FOR BOARD MEASURE
log. The fact that, with increasing prices unsound lumber is sold and
is graded does not change the standard scaling practice, which takes
no account of these unsound grades and excludes them from the scale.
Such lumber merely increases the amount of the over-run.
The characteristic sound defects are tight or sound knots, pitch
and stain. Sound tight knots never reduce the scale unless present in
such size and quantity as to cause the lumber to fall apart or to be
rejected. Stained sap, which is still firm, or red heart, the precursor
of red rot, are scaled. Pitch is usually classed as a sound defect for
which no deduction in scale is made. But these defects, especially
knots, and others such as twisted grain and wide rings do serve to reduce
the grade of the log. The presence of unsound defects, such as rot,
shake and break, does not reduce the grade of a log, provided there is
sufficient sound lumber remaining to permit the log to meet the mini-
mum requirements of the grade. Since the purpose of log grades
is to establish value, log grading specifications are drawn so as to permit
logs of the same average value to be placed in the same grade, and too
detailed specifications are avoided.
By thus simplifying the classification of logs by grade, the total
log scale is easily separated into log grades, and any variation in the
average quality of logs within the grade can be adjusted in the price
of the grade (§ 359).
For any given region, and class of timber, the actual average per
cents of different standard grades of lumber contained in log grades
can then be determined by mill-grade or mill-scale studies (§ 361).
These per cents can then be applied to the total scale for each log grade
with far greater accuracy than could be attained by attempting to ana-
lyze the scale of each log.
Log grades, as analyzed by such mill-grade studies, have become the
basis of determining the stumpage value of standing timber in appraisals
as conducted by the U.S. Forest Service (§ 234),
REFERENCES
Cost of Logging Large and Small Timber, W. W. Ashe, Forestry Quarterly, Vol. XIV,
1916, p. 441.
Cost of Logging Small Timber, R. D. Forbes, American Lumberman, Nov. 15,
1919, p. 52.
Cost of Cutting Large and Small Timber, W. W. Ashe and R. C. Hall, Southern
Lumberman, Dec. 16, 1916.
Inland Empire Sawing and Skidding Studies, J. W. Girard, Timberman, September,
1920,
CHAPTER VIII
THE SCALING OF DEFECTIVE LOGS
88. Deductions from Scale for Unsound Defects. No deduction
will be made from the scale of a log unless there is some visible indica-
tion of unsound defect such as will reduce the quantity of sound lumber
that can be sawed from the log. The character and extent of the deduc-
tion to be made for the indicated defect is judged by the scaler based
on his knowledge of the given species and region and his experience in
observing the way such logs open up in sawing. Defects visible at the
ends of the log give a basis for judging the remaining contents. When
logs must be scaled as they lie after bucking, with ends still in contact,
as sometimes happens with overhead skidder operations, it is difficult
to make correct deductions for defects.
The surface of the log offers additional evidence of unsound defects,
especially -the character of the knots. Sound knots from live limbs
do not affect the scale, but the knots of dead stubs, if they show rot,
and especially the presence of rotten knot holes, with exudations of
pitch, indicate the presence of advanced stages of rot, which a little
experience in the mill will teach the sealer to allow for in full measure.
The mere suspicion that logs may be rotten does not justify deductions.
When timber is full of concealed defects with no surface indications,
the method of deducting a given per cent of the total scale may be
adopted instead of attempting to reduce the scale of each log separately.
89. Methods of Making Deductions. There are four methods of
reducing the scale of a log; by length, by diameter, by diagram or
specific quantity of lumber and by a per cent of the gross scale. The
reduction in either length or diameter enables the scaler to read the
reduced scale from his stick as for a log of smaller dimensions and is
the simplest form of discount, but least accurate except for certain
forms of defect.
Reduction in Length. <A reduction in length gives a proportionate
reduction in per cent of total contents. The per cent taken depends
on the relation between the lengths of the log before and after reduc-
tion. For a 16-foot log, 123 per cent of the total scale is deducted
for each 2-foot reduction. This deduction becomes 10 per cent for
a 20-foot log or 162 per cent for a 12-foot log.
Reduction in Diameter. Reduction in diameter is not a satisfactory
method of making deductions except for rotten sap found on logs cut
105
106 THE SCALING OF DEFECTIVE LOGS
from dead trees, or for surface checking. The per cent of the scale
thus deducted varies for every diameter of log, and for each difference
in the number of inches subtracted. This method of deduction should
not be used to offset some interior defect. By this method, a 20-inch
log by Scribner’s Rule would give the following deductions from scale
in per cents. For other diameters, the per cents would differ:
Reduction of | Per cent deduc- Per cent loss
diameter. tion in diameter in scale
Inches
1 5 142
2 10 Don
3 15 36.7
4 20 42.8
This method should usually be rejected in favor of one of the other
three, since it substitutes a guess for an accurate deduction.
Use of Diagrams. The diagram method is the most accurate way
of computing the actual number of board feet to deduct from a log
for a given defect. The cross section of the defective area is blocked
out as a square or rectangle, and its length decided upon, whether
running completely through the log or only part way through. For
rules based on 21-inch saw kerf, 20 per cent of the cross section of this
area must be deducted to get the net volume of 1-inch boards to be
deducted from the scale.
This is expressed by formula when
a-b=cross sectional area in inches,
1=length of defective section in feet,
y=cubic contents of the section in board feet,
x=volume of section, sawed into 1-in. boards, {-in. saw kerf.
La-b-l
le
Then
x=y— .20y= .80y,
or
wiarbel
15
In using a decimal rule, the resultant volume is rounded off to the
nearest 10 or “decimal value” before subtracting it from the log scale.
EFFECT OF MINIMUM DIMENSIONS 107
As a substitute for this calculation and to save time, scalers frequently
approximate the amount of deduction by guess, based on experience.
Deducting a Per Cent of Total Scale. The method of deducting a
per cent of the total scale, as distinguished from the above methods
is chiefly applied to logs containing defects within the log, evidenced
by rotten knots, punk, conks, or other indications and whose amount
can only be guessed at on the basis of experience obtained by observing
such logs as they are sawed in a mill.
Influence of Log Rule on Deductions for Defects. A log rule based either upon
diagrams of 1-inch boards and definite saw kerf, or upon a formula in which the
proper deductions are made both for saw kerf and slabbing, permits the scaler
to make deductions from the scale of each log separately on the basis of the actual
loss in l-inch boards from that portion of the log included in the scale or log rule.
But when a log rule is inaccurate, either because of excessively low valuations,
false basis as in converted cubic rules, or erroneous values in formule as in Doyle
or Baxter rules, such deductions when applied to logs already scaled too low would
take from the scale more than the proper per cent of defect, as the following com-
parison will show.
A log 10 inches in diameter and 16 feet long, which will saw out but one-half
of its scaled contents due to defect (and omitting boards sawed from outside the
cylinder), if scaled by the Scribner and Doyle rules respectively will give:
If actual loss in Net scale Gp sel
Sound 3 deducting 50 per
sawed content | deducting actual
Log rule scale. i vee | cent of sound
a scale.
Feet B.M. Feet B.M. i Feet B.M. Feet B.M.
Serlpner.:... 54 27 27 27
Doyle’. ... 24: 36 27 9 18
If the log is sawed by a mill whose output coincides with the Scribner rule,
the over-run on a sound log by the Doyle rule will be 50 per cent. The defective
log will give no over-run of sound lumber by Scribner. But if 27 feet, or one-half
of the actual sawed contents, is deducted from the scale by Doyle rule the over-run
will be 18 feet, which is 200 per cent of the residual scale of 9 feet, on this scale, or
four times as great on the defective as on the sound log. By deducting 50 per cent
of the Doyle scale for the log, the over-run remains at 50 per cent of the scale as
for sound logs.
Although the method last mentioned gives a consistent basis for making deduc-
tions in rules like the Doyle, while the deduction of actual loss in lumber gives
far too great an over-run, it is evident that when log rules are used capable of giv-
ing a scale equaling but two-thirds of the actual contents, the tendency will be to
overlook the defects in scaling unless very serious and numerous.
90. Effect of Minimum Dimensions of Merchantable Boards upon
these Deductions. Log rules made from diagrams, such as the Scrib-
Fia.
108
THE SCALING OF DEFECTIVE LOGS
ner and Spaulding Rules, were based on a minimum width of board of
not less than 6 inches.
In deducting for defects by diagram, the latter practice is
strips.
Present practice permits the sawing of 4-inch
used, and portions of the log which will yield 4-inch strips are scaled,
14.—The
lost are measured in-
side the smaller in-
scribed circle repre-
senting the top diam-
boards
eter. Three boards
are affected, 4 inches,
6 inches, and 8 inches.
The 6-inch board is
deducted. If the min-
imum width of board
utilized is 4 inches, a
4-inch strip is de-
ducted from the 8-inch
board. But the 4-inch
strip on the margin
was not scaled in the
original diagram and
should be omitted, as
constituting over-run
by this log rule. In
ordinary scaling prac-
tice this distinction
would probably be
overlooked as _ too
great a refinement,
waste in sawing straight lumber.
provided these dimensions lie within the cylin-
der and do not include taper. A rotten butt
with 6 inches of sound wood will be a total cull
unless the inscribed area of the top or small
end of the log contains within it at least 4 inches
of sound wood.
In theory, this rule must be modified for
deductions which take the form of slabs, since
the original diagram or scale rejected all boards
below 6 inches in width. This case is illustrated
in Fig. 14.
The minimum length of merchantable board
should first be standardized or agreed on in
scaling. Formerly a defect at one end of a
standard log, say 16 feet long, would cull the
boards affected for their whole length. But
where boards of 6- or 8-foot length are merchant-
able, defects which leave a sound length equal
to these minimum boards will be scaled only
for the actual length of the part affected. This
rule affects the results for nearly all forms of
defect. Standard minimum lengths are im-
portant in scaling crooked logs. The standards
now in use for saw timber vary from 6 to 10
feet with a tendency to become shorter.
91. Interior Defects. Unsound defects may
be classed as interior, causing waste in the interior
of log; side or exterior defects, causing waste
at the surface or outside; and defects in form,
i.e., crook, in otherwise sound logs, causing
Interior defects are due to rot,
shake, seams or checks, and worm-holes. The defect may extend
through the entire log, or be present only at one end. It may be cir-
cular, and regular in form, or irregular in form and extent.
Center Rot. Circular defects in the form of either rotten or hollow
logs, or ring shake, if they extend through the log, will be measured not
at the small but at the large end, provided the log is not over 16 feet
long. For longer logs the average of the dimensions at butt and top is
taken. If only one end is affected, the diameter of the defective portion
INTERIOR DEFECTS 109
is scaled at that point and its length judged by experience gained in
the locality by the butting off of defective logs; e.g., a log 20 inches in
diameter at the top end, 16 feet long, with a center rot measuring 3 inches
at top and 15 inches at butt, will lose the equivalent of a 15-inch butt rot,
and not a 3-inch piece. Should the log be 20 feet long, the average
ar eno ect >
|
|
———— eS b Feet —>
Fria. 15.—When the minimum length of board is 8 feet this log will seale one-
half of the contents of a 16-foot log. But with a minimum length board of
10 feet the log according to common practice will scale nothing and be culled.
dimension of this rot, or 9 inches, would be taken, according to the
above arbitrary rule of scaling. But if the rot is present only in the
butt, the 15-inch measurement would apply to that portion of the log
which was judged to be affected, provided the length of the remaining
sound portion equaled the minimum length of board prescribed.
Fic. 16.—Center rot extending through log. Effect of length of log in determining
the diameter of the portion to be culled.
The scale of this log, if sound, would be 280 board feet, Scribner Decimal C
rule. The deduction for a rotten butt 15 inches in diameter and 16 feet long
is 228 board feet, residue 52 board feet or 18.2 per cent of sound scale. The
log is a cull. The average wdth of rim left to be scaled after projecting the
area of the rotten butt upon the top end, is 24 inches, or less than minimum
width of board, and not the actual measurement of sound wood at either the top
or the butt.
If this log is 20 feet long, i.e., longer than a prescribed maximum length of
16 feet, the diameter of this rot is averaged at 9 inches. The 20-foot log, 20 inches
in diameter scales 350 board feet. The 9-inch measurement is applied to the
entire length of log, and the deduction is 111 board feet. The net scale is 240
board feet, or 68.6 per cent of total sound scale. Such a log is merchantable.
110 THE SCALING OF DEFECTIVE LOGS
It is evident that such rules for deductions are arbitrary. The 16-foot log
would yield considerable short lumber and is under-scaled by the rule. Where
short-length boards are commonly used, logs over 12 feet long might be scaled
on the basis of average diameter of rot, to correct this tendency. But it is better
to adopt arbitrary rules than to have no methodical plan for scaling defects.
The cull required by the presence of an unsound or hollow circular core is pro-
portional to the diameter of the core, and independent of that of the log. By the
diagram method, the deduction for center rot would be found by determining the
board-foot contents of a square with the diameter of the rotten core and of the
length indicated as above. This method when checked against actual sawed
contents gives too smal a deduction for cores up to 9 inches, and above that, too
large, the relation varying from 87 per cent for a 6-inch core to 110 per cent for
one 24 inches in width. The actual amounts of sawed lumber lost for cores of
each diameter are accurately expressed by a formula developed by H. D. Tiemann,
which reads,
L
Contents of core = s(D+1)* 5
i.e., add 1 inch to diameter of core, square and deduct 3, converting the remainder
into board feet by the factor
Length in feet
12
This formula calls for four-fifths of the sawed board-foot contents of a square
1 inch larger than the core (0.66D2=82.5 per cent or = of 0.80D2) instead of the
full sawed board-foot contents of a square of the same size as the core.
Several rules of thumb exist for determining the deduction for center rot, none
of which are absolutely correct, and some very inaccurate.
Example. In a 12-foot log 20 inches in diameter with a rotten center 6 inches
in diameter at large end and running through the log and a sound scale of 210
board feet, the correct deduction is 33 board feet which is 3(7?)}3. The following
rules of thumb can be cited, using Scribner Decimal C rule.
1. Deduct the diameter of core from that of log, and scale as a log. This
gives a cull of 90 board feet.
2 Deduct the scale of a log of same diameter as the core. This gives a cull
of 10 board feet.
3. Scale out a log with diameter 3 inches larger than the core. This would give
30 board feet, but the rule gives inconsistent results for larger and smaller cores.
4. Scale out the contents of a square timber whose side is the diagonal of the
square of the diameter of the core. This would be 1.4D? and gives 70 board feet.
If reduced by 20 per cent for saw kerf, and applied to small end of core, it would
come closer by balancing errors. None of these rules is accurate or consistent.
Butt Rot, Termed also Ground or Stump Rot. Butt rot enters the
butt log from the ground, and usually extends but a short distance into
the log. Its full diameter should seldom be applied to the entire log,
even if rot appears at the top end.
The diameter of the rotten butt must first be compared with the
scaling diameter as determined by the top end of log (§ 81). If the rim
of sound wood lying within this inscribed circle is wide enough for boards,
INTERIOR DEFECTS 111
or if the volume of the rotten core, shows a smaller cull than the
e
sound scale of that part of the log, deduction by diagram of the squared
core is made (preferably by Tiemann’s formula) to a length judged to
include the rotten portion.
Example. A log 12 feet long and 20 inches in diameter at top end has a rotten
butt 6 feet long, the rotten core measuring 17 inches across. Although the butt
measures 25 inches, leaving a 4-inch rim of sound wood, the inscribed circle repre-
senting the top of the log is only 20 inches, and the butt isa cull. This observation
is borne out by applying Tiemann’s formula:
Seale of 12-foot log, 210 board feet,
Seale of 6-foot length, 105 board feet,
Cull for butt rot, 3(18?)8; =108 board feet,
or more than the sound scale of butt. This deduction is not applied to the whole
log but only to the butt.
The scale of the log is then 105 board feet on the basis that the upper half is
sound,
If this core should measure 13 inches,
Cull for butt rot $(14?)8 =65 board feet.
The scale of the log is then 210 —65=145 board feet.
But if the minimum board length should be over 6 feet, the first log will be
culled entirely, and from the second log, a cull of $(14?)+3 or 131 board feet
Scribner Decimal C is deducted, leaving a scale of but 79 board feet, or 37.6 per
cent of the merchantable contents.
Shake. Shake is a mechanical defect caused by wind. The annual
rings have separated at one or more points, giving a circular or ring crack,
and the board falls to pieces when sawed. This flaw is found at the butts
of such species as hemlock, and is seldom more than a few feet in length
although entire logs may be shaky. Lumber sawed from shaky por-
tions of logs is often worthless.
A single circular shake is scaled out in the same manner as butt rot
except that the contents of a smaller sound core lying within the shake
may be added or restored to the scale. The diameter of this interior
core should be measured at the small end of the culled section if it extends
through the log, while the diameter of the culled portion is measured
at the butt or large end. In short sections whose length is guessed at,
a proportionate reduction from butt diameter is made in scaling the
sound core. This same method is used to scale out pitch rings, where
this is deemed necessary. In most cases pitch is considered a sound
defect (§ 82). Where shake shows in several rings, the entire shaky
portion of the log is butted, by shortening its length.
112 THE SCALING OF DEFECTIVE LOGS
Seams, Heart Checks, Frost Cracks or Pitch Seams. Seams are cracks
penetrating the log from the surface. They have the same effect as
shake, in causing boards to fall apart, and the deduction is made by
enclosing the seam in a timber of required dimensions to remove it.
Twisted grain, causing seams to take a
spiral form, results in ruining either the
entire log or a large per cent of its volume.
The deduction must include the entire
seam:in a squared timber. The width of
the plank deducted should not include the
portion which would be slabbed in sawing.
Method of deducting for a twisted seam
or check: The wedge enclosing the seam is
scaled as a per cent of total scale of cylinder
proportional to areas of cross sections.
But on long logs, of larger diameters, the
The aadth’ “of planks whould entire segment shown in Fig. 18 is not
exclude both the taper of log lost, if short boards of scaling length can
and the slab, on the small end. be sawed from the butt and top portions
of the segment respectively. This saving
will not amount to more than one-third of the total deduction.
Worm Holes. If the size and extent of worm holes is not sufficient to
cull the boards, their presence will not cause a loss in scaling. It is
difficult to judge the extent of damage from worm holes, except by local
experience in observing the sawing of logs.
Fria. 17.—Method of deduction
for a seam, or a heart check.
Fra. 18.—Position of twisted seam at butt, and at top of same log, and resultant
sector deducted in scaling.
Rot Entering from Knots. The most common forms of rot enter
the tree through dead limbs, stubs or knots, or through wounds or abra-
sions, which by penetrating or interrupting the layer of bark and live
sapwood, expose the heartwood to infection. From these points of
infection the fungus spreads through the heartwood both upwards and
EXTERIOR DEFECTS 113
downwards. The form which it takes depends upon the species of
fungus, and of trees attacked. The unsound portion is surrounded by
a stained portion which is yet sound. The area of the rot increases
with age of tree and time elapsing since the infection took place.
In deducting for rot, the amount of the loss depends upon the location
of the point of infection, usually a rotten knot. Stain which shows at
one end of a log requires no deduction if the rot of which it is an evidence
lies in the adjoining log as cut from the bole. On the other hand, two
or more rotten knots in a log, with stain showing, means a heavy dis-
count and a possible cull. Sawyers are accustomed to leave such logs
in the woods and even in the tree without sawing them. Rot from a
single point of infection will extend
from 2 feet to as much as 10 or 15
feet in either direction. It is deepest
and most complete at the point of entry,
tapering out with increasing distance
from this point. Rot of this character
is so irregular that experience is re-
quired in observing such logs sawed
before proper deductions can be made
by sealers.
In deducting for interior rot, the
probable extent and shape of the un- Fic. 19—Log A is infected at
sound portion therefore depends upon the point X and isacull. At
the appearance of the ends taken in the lower end no rot shows,
connection with unsound knots. The ae sae Files agent a
: ; nerefore shows at the upper
only portions of the log which can be end of log B, but causes no
scaled are those which will produce deduction for cull.
sound boards having the minimum
length and width prescribed in the rules for scaling. The deduction
will take the form of a per cent of the sound scale. Diagrams are some-
times of assistance, but in logs containing rotten knots the extent of
rot is usually greater than revealed at the cross section. The appa-
rent cull must ordinarily be increased, from 25 to 100 per cent. -
Since deduction of length is equivalent to a percentage reduction of
scale, this method is frequently used.
Peck in cypress, and the rot found in Incense cedar gives no
external indications, and is not always revealed on the cut ends of logs.
This condition tends to the substitution of a straight percentage deduc-
tion from the total scale instead of reducing the scale of individual
logs for defects.
92. Exterior Defects. Exterior defects, on the sides of logs, include
unsound sap, surface checks, cat faces, fire scars, and scars caused by
114 THE SCALING OF DEFECTIVE LOGS
mechanical injuries such as lightning or falling timber. Irregular
butt rot, appearing as a small patch on one side, or rot from knots
which is local in extent, can sometimes be scaled by the methods used
to scale side defects.
Exterior defects, especially at the butts of logs, may fall entirely
outside the inscribed circle representing the top or scaling diameter, in
which case they cause no deduction in scale. With defects which
penetrate deeper a further
portion is included in the
slab allowed in sawing,
within this circle.
Where the defect ex-
tends but a few feet in
length, as for instance a
fire scar at the butt of a
log, the deduction is con-
fined to that portion of the
length of the small cylinder
¢_——_Length of Cull ___s, whose contents is scaled,
which is affected by the
defect. The amount to
subtract may be found in
one of two ways; by dia-
gram of the slab affected by
the defect, or by culling a
per cent of the volume of
the log.
Deductions by Slabs.
The dimensions of the por-
Fic. 20.—Effect of fire scar at butt, on deduc- tion to be deducted as a
tions from scale. slab are not those of the
piece actually slabbed from
the butt, but only the depth of the portion lying within the inscribed
circle of the small end of log. From this again there is subtracted an
additional amount for slabbing, shown in Fig. 20. The remaining
depth, multiplied by the average width of the inscribed slab, gives
the area of the cross-section whose length will be that of the defect,
a-b-l
1 —
and volume, iB
Scaling Diamete
r
ee
In the above figure, the fire scar on the butt log is 8 inches deep, but only
5 inches of this is within the inscribed scaling dimensions. Of this 1} imches is
slab, giving 33 inches for lumber. The widths of the boards lost are 10 inches,
14 inches and 18 inches. The average width of the rectangle is 14 inches. A
EXTERIOR DEFECTS 115
diagram measuring 4 by 14 inches, whose length equals that of the fire sear lying
within the inscribed cylinder, gives the deductions. As the scar gets shallower,
the length lying within this cylinder is less than its total length. Tables could
be worked up by a scaler to express the board-foot contents that could be cut out
of slubs of given thickness on circles (inscribed) of given diameter for a standard
length of log, allowing a minimum width of board equivalent te that used by the
log rule (§ 67). But ocular methods are almost equally efficient after practice.
Deduction by Sectors. Side defects extending deeply into the log
(Fig. 21) cannot be slabbed off and are not easy to express by diagrams.
By enclosing them in V-shaped
areas representing sectors of a
circle, an idea may be obtained
of their extent. This method
may be used for any defect
occurring wholly on one side
of the geometric center of a wht Sz
log and which is more accu- Fra. 21—Method of deducting from scale
rately enclosed by a sector by means of sectors enclosing defective
than a slab. portion of log.
The cull per cent for the portion of the log affected is roughly equal to the
ratio between the area of the circle and of the sector. This rule is exact for the
ratio 4, and nearly so for smaller or larger sectors. The error in applying the rule
will average less than 3 per cent of the volume of the log, and if the defect is con-
fined to a short length, this error is proportionately less for the whole log (from inves-
tigations of H. D. Tiemann); e.g., a sector equaling one-fourth of a circle calls
for 25 per cent cull. Cull tables may be made for this deduction, but it is equally
convenient to apply the percentage directly to the scale. This latter method
adjusts the cull factor to any log rule (§ 89).
Other Surface Defects. Stained sap is scaled as sound. When
unsound or decayed, the scaling diameter is taken inside the sap.
Surface checks caused by prolonged weathering as in the case of dead
timber, or by neglect or exposure of logs, must be scaled out in the same
manner as sap. Cat faces, as defined for cedar poles in the Lake States,
are defects on the sides of logs caused by some mechanical injury to
the bark which has caused a wound. A cat face may be accompanied
by rot, or be merely a dry face, not healed over and forming an indenta-
tion in the bole. According to its shape and depth, a cat face is deducted
either as a slab or a segment, of proper length. The term cat face is
also applied to a fire scar at the butt of a tree, usually partly healed
over, which may be sound, rotten or wormy. Any surface defect partly
healed over, on the bole, caused by either fire or mechanical injury,
whether at the butt or on the bole, may properly be called a cat face.
Lightning scars, even when the tree is not shattered or killed, usually
116 THE SCALING OF DEFECTIVE LOGS
form a dead streak causing a surface defect, sometimes of considerable
proportions.
Breakage. The deduction for splits and breakage caused by felling
is made either by slabbing or by shortening the log length, to remove
the portion ruined by the breakage. Where this waste is avoidable,
owners stipulate that it shall be scaled as sound, but purchasers of logs
insist on the deduction. In the Pacific Coast States, breakage may
exceed 25 per cent of the scale.
93. Crook or Sweep. Crook may be defined as a rather abrupt
bend in the log at a given point, while sweep is a more gradual bend
extending over a considerable length. Crooks occurring near the ends
of a log may be allowed for in sealing by shortening the scaling length.
With gradual sweep affecting the form of the log as a whole, a different
deduction is necessary. The effect of sweep or crook upon the scaled
contents of the log (§ 52) depends directly upon the minimum length
of boards utilized and scaled, or upon the acceptance of fixed minimum
scaling lengths for the logs. If it is assumed that the minimum board
governs the scale, deductions for crook or sweep will seldom be made,
since almost complete utilization can be obtained of sound crooked
logs by the box factory. But if the scale of a log is based on the output
of boards of the standard sealing lengths into which the logs are cut,
and short lengths cannot be utilized, crook or sweep will cause deduc-
tions in scale when it exceeds the normal minimum permitted.
When logs crook in but one plane, the loss in sawed lumber is proportional
to the relation which the total deflection or crook bears to the diameter of the log,
and does not depend on the number of inches of crook independent of size of log;
e.g., for a 12-inch log a 6-inch crook is 50 per cent of the diameter but for a 24-inch
log, a 6-inch crook is but 25 per cent of the diameter, and a 50 per cent crook
indicates a crook of 12 inches.
By diagram checks, and sawing, the per cent of waste due to sweep for a given
total number of inches of crook per log is found to be independent of the length
of log, and to show the following results:
TABLE XVIII
DEDUCTIONS FOR CROOK AND SWEEP
Waste in terms of
scale of log.
Scribner rule
Sweep in terms of
diameter of log.
Per cent
83 (or +z)
163 (or ¢)
25 (or 3)
50 (or 4)
111
223
331
662
CHECK-SCALING Dy
From these results a rule of thumb may be suggested as follows: Add one-third
to the per cent of sweep as expressed in terms of diameter of log to obtain the
per cent of cull; e.g., a log 16 feet long and 16 inches in diameter scales 159 board
feet. With a sweep of 4 inches or 25 per cent, deduct 4X25=333 per cent or
53 board feet; scale, 106 board feet. With a sweep of 8 inches, deduct 450 =66}
per cent, or 106 board feet; scale 53 board feet. With a sweep of 2 inches no
deduction would be made, since this is merely the normal crook.
Logs which crook in two or more planes must be culled far more heavily than
when the axis lies in a single plane. For a given per cent of crook the scale is
roughly proportional to the square of the per cent scaled by the deductions set
forth above; e.g., a log which scales 50 per cent or one-half if crooked in one plane
will, if crooked in two planes, scale (4)? or 25 per cent of its contents.
94. Check-scaling. By check-scaling is meant the re-scaling of
selected logs or of a portion of a total run of logs, in order to determine
the relative accuracy of the original scale, check the methods used by
the scaler and detect and correct errors in these methods. A re-scale
requires the remeasurement of all of the logs. The necessity for a
re-scale is usually revealed by a check-scale.
Where a number of scalers are employed, check scaling becomes
necessary in order to maintain uniformity in scaling practice. No
matter how carefully the standard of scaling practice is set forth in
printed instructions which cover not only the “scale ”’ with respect
to diameters, length, taper and trimming allowance, but rules for deduc-
tions for defects, individual scalers tend to vary from this standard
through habit or carelessness and inexperienced men are slow to acquire
accuracy, especially in scaling defective logs.
A check scale should be made by the most experienced man available as fre-
quently as possible, but usually at from three to six months’ intervals. Where
logs are numbered, the original scale should show the deductions made from the
full scale of each log (§ 85). The check scale can be made at random on as many
logs as there is time for. The total scale for the logs checked is then compared
with the original scale of the identical logs, keeping separate the sound and the
defective logs. Using the check scale as 100 per cent, the per cent of error in
scaling is computed according to the following plan:
Sound logs Defective logs Total
Seale by |No. of logs |Scale per cent) No. of logs |Scale per cent) No. of|Scale per cent
+ or — + or — logs + or —
JAMES SMITH
Check scale by
Joun Kipp
The standard of accuracy in the U. S. Forest Service for check scaling requires
118 THE SCALING OF DEFECTIVE LOGS
that the scale should not vary from the check scale by more:than the following
per cents:
For sound logs, within 1 per cent;
For logs up to 10 per cent defective, within 2 per ¢ent;
On logs 11 to 20 per cent defective, within 3 per cent;
On logs over 20 per cent defective, within 5 per cent.
Check scales are made usually for the purpose of correcting the scaler, but not
as a basis of altering the scale. Only where the original scale is shown to be
decidedly in error so as to work an injustice on the purchaser (or seller) are logs
ever re-scaled.
Personnel. Scalers should never be reprimanded in general terms for scaling
too close or too high. The result is usually a worse error in the opposite direction.
Instead, the scale should be checked by individual logs to discover the sources of
error and the scaling practice corrected in detail. The fault may lie in some
specific practice such as an erroneous method of obtaining diameters or in allowing
for certain common defects.
Mill-seale studies do not furnish an adequate or satisfactory check
on scaling, but serve merely to determine ‘the over-run. The scale,
if in error, must be corrected by re-scaling the logs, not by measuring
the lumber (§ 74). Such studies do furnish an indication of the scale
of defective logs, where the scaler’s judgment may be in error, but an
exact check is impossible, as it would require the rejection of boards
sawed from the taper, which is not practicable.
95. Scaling from the Stump. Where timber has been cut in tres-
pass and the logs removed, the evidence remaining is the stump, the
indentation on the ground where the butt struck in falling, the sawdust
where the cuts were made in sawing into log lengths, and the top,
giving the upper diameter. The length of the tree can then be meas-
ured, and occasionally, that of each log sawed. The total difference
in diameter between top and butt is distributed according to the accepted
local customs for sealing long logs. This gives the scaling diameter
and length of each log in the tree. Specific deduction for defect can
be made only for stump rot, since this is revealed by the stump and
the average deduction for rot having the character and extent of that
shown can be made from the butt log. Further deductions if made
must be based on the average per cent of cull for timber of the given
species and character.
When tops are removed, burned or otherwise rendered indistinguish-
able, neither the top diameter nor the length of the tree can be judged.
Merchantable length must then be based upon the heights of trees in
the vicinity, and volumes taken from volume tables (§ 121) for trees
of given diameter and height. A table of stump tapers (§ 168) must
be used to express the diameter of the stump in terms of diameter 43
feet from ground (§ 134).
THE SCALER 119
96. The Scaler. A scaler with no other duties can number and scale 500 logs
per day, running 10 logs per 1000 board feet or 50,000 board feet at a cost of about
10 cents per 1000 board feet, based on wages and subsistence of $125.00 per month.
This average can be exceeded but is apt to be reduced in quantity by time lost in
travel to and from the logs, scaling in the woods, or an insufficient number of logs
on hand daily to occupy the full time of the scaler. Often these logs must be
scaled daily and cannot accumulate, because of insufficient room on the skids,
thus keeping a scaler in constant attendance. A scaler thus employed is often
given other duties such as inspecting the work of the saw crews. National Forest
Scalers supervise the disposal of brush, closeness of utilization and the marking
of timber for felling. This reduces the average cost of scaling to approximately
the basis mentioned.
Commercial scaling by private companies is done far more rapidly and cheaply
because of the elimination of numbering, and by careless or indifferent methods
of measuring lengths and deducting for defects. A scale of 1000 to 1500 pieces,
and 100,000 board feet per day and a cost of 5 cents per 1000 board feet or less
is not unusual on large operations.
So important is an accurate scale that the scaler must be given every facility
to obtain the measurement with the least trouble and greatest certainty. This
usually means providing a sufficient force of scalers so that they may be on hand
at the most favorable time, or constantly. When on account of small or scattered
operations the logs must accumulate the scaler is handicapped in various ways.
Large and high rollways require two men, one on each side, to get the length, even
approximately, and to distinguish top from butt, of each log. Logs landed on ice
will in time by their weight cause cracks and flooding, and small logs are frozen in.
Whole rollways may break through the ice and become partially submerged.
Snow covers and buries the piles, and logs are overlooked. Logs may be rolled
down steep banks and lie in such confusion that scaling is difficult and dangerous.
Steam skidders pile logs in huge heaps impossible to scale at all until loaded on
ears. The inability of the scaler to cover his route at frequent intervals encourages
careless sawing, timber stealing and poor scaling. Contracts should specify that
logs must be piled or skidded in such a manner that accurate scaling is possible.
Legal Status of Scaler. ‘A scaler whose services are agreed upon by both parties
to a contract or sale, is the sole arbiter between these parties in determining the
amount of the scale. But if one party furnishes the scaler without the expressed
consent or agreement of the other, his scale may be appealed from.” Frisco
Lumber Co. vs. Hodge, U. 8. Circuit Court of Appeals, 218 Fed. Rep. 778.
“A sealer furnished by the defendant and boarded by plaintiff would be one
mutually agreed upon, and they must abide by his decisions.”” Connecticut Valley
Lumber Co. vs. Stone, U. 8. Circuit Court of Appeals, 212 Fed. Rep. 713.
“Binding in the absence of fraud or mathematical mistakes.”” Hutchins vs.
Merrill, Supreme Court Maine, 84 Atlantic 412.
“Seale made by scaler appointed by defendant not binding in absence of some
stipulation to that effect in contract.” Owen vs. J. Neils Lumber Co., Supreme
Court of Minnesota, 145 Northwestern 402 (1914).
“Sealer who performed his duty fairly and honestly, though negligently, could-
not be held liable for discrepancy between the amount he scaled and the amount
of logs delivered, as permitting such action would destroy independence of arbitra-
tion.” Hutchins vs. Merrill, Supreme Court Maine, 84 Atlantic 412.
120 THE SCALING OF DEFECTIVE LOGS
REFERENCES
Instructions for the Scaling and Measurement of National Forest Timber, U. S.
Dept. Agr., Forest Service, 1916.
Checking Check Scalers, T. 8S. Woolsey, Jr., Proc. Soc. Am. Foresters, Vol. XI,
1916, p. 245.
Methods of Scaling Logs, Henry 8. Graves, Forestry Quarterly, Vol. III, 1905,
p. 245. Cull tables by Tiemann.
Methods of Making Discounts for Defects in Scaling Logs, H. D. Tiemann, Forestry
Quarterly, Vol. III, 1905, p. 354.
CHAPTER Ix
STACKED OR CORD MEASURE
97. Stacked Measure as a Substitute for Cubic Measure. Stacked
or cord measure is the cubic space occupied by stacked wood when
the exterior dimensions of the stacks are measured. This is expressed
in terms of standard units termed cords. Wood in the form of round
bolts or split bolts, which are termed billets ($9) is usually intended
either for use as bulk products such as firewood, pulpwood or acid wood,
or for manufactured articles whose dimensions conform to those of
the bolts or billets.
For the former uses, the total cubic contents of the wood, or of wood
and bark, is desired. This could be obtained as with logs, by measuring
the dimensions of each separate bolt and totaling their contents. On
account of the smaller sizes, greater number, and irregularity of form,
especially of billets, such a method would be time consuming, inaccu-
rate and impossible to check as to results without complete measure-
ment. Yet it is quite extensively employed to obtain actual cubic
contents of logs and bolts for commercial purposes, when the material
is fairly large and of regular shape (§ 29).
Where the pieces are short, small, split, or irregular in form, the
more convenient and simple method is to stack the wood in ranks and
measure the surface dimensions to get stacked cubic contents including
both solid wood and air space.
98. The Standard Cord versus Short Cords and Long Cords. A
standard stacked cord is a pile, 4 feet high, 8 feet long, of pieces 4
feet long, and contains 128 stacked cubic feet. For bulk products, the
net cubic contents of wood, either with or without bark is desired. The
use of wood with bark for fuel for domestic purposes utilizes by far the
greater portion of all wood sold in bulk. For this purpose the stand-
ard cord is the basis of delivery in the rough, to wood dealers.
But the domestic consumer seldom burns 4-foot wood, and usually
requires short wood of varying sizes commonly between 12 and 24
inches in length and making 4, 3 or 2 cuts to a 4-foot stick. Other
special lengths may be specified when the wood is cut direct from the
tree. This demand gives rise to the short cord. A short cord is a pile
measuring 4 by 8 feet on the side or face and one rank deep. The depth
and cubic contents depends on the length of the pieces. Since this
121
122 STACKED OR CORD MEASURE
substitution of surface measure reduces the cubic volume of short
cords, either the price must be reduced, or the full cubic contents of
a standard cord secured by requiring the cord to be two, three or four
ranks deep, or to have an additional length sufficient to make up 128
stacked cubic feet. A standard cord of 4-foot wood when cut into
stove lengths is considered a full cord, although in repiling it shrinks
from 8 to 13 per cent in stacked volume (§ 108). When the cord of
short wood is measured on this basis, the full dimensions of a standard
cord cannot be required on repiling.
Wood is also cut longer than 4 feet. The term long cord usually
refers to a cord 4 by 8 feet in surface by 5 feet in depth and containing
160 cubic feet. The standard length of stick for hardwoods for dis-
tillation or acid wood is 50 inches, giving a cubie contents of 1333
cubic feet. Unless long cords are accepted by custom, stacks measur-
ing more than 4 feet in length of stack are reduced to their equivalent
volume in standard cords. When pulp wood bolts, ordinarily cut 4
feet long, are cut 8, 12 or 16 feet long, they are measured as standard
cords, a stack 4 by 8 by 8 feet containing 2 cords.
99. Measurement of Stacked Wood Cut for Special Purposes. Stacked cubic
measure is commonly employed in measuring bolts or split billets intended for man-
ufacture into spokes, handles, staves for slack and tight cooperage, shingles and
similar piece products. Bolts measuring over 12 inches in diameter are usually
sealed in board feet. Billets, if split or rived into pieces each of which is to be
shaped into one finished article such a split staves, may be counted.
Bolts intended for sawing are usually measured by stacked contents. The
lengths of the bolts sawed from the tree must correspond to the required length
of the product plus a small margin for trimming, or must be a multiple of this
length, to avoid waste. For spokes, 30 inches is a common length. Handles
require lengths of from 12 to 60 inches. Common lengths for staves for tight
cooperage are 19 inches and 38 inches. The demands of the market or purchaser
determine the length in every case.
The measurement of shingle bolts is frequently by double cords, in lengths of
8 feet. On the West Coast, the bolts are cut in lengths equal to 3 shingles. For
16-inch shingles the cord is 4 feet 4 inches in depth, while for 18-inch shingles,
the length of bolt required is 4 feet 8 or 10 inches. Shingle bolts illustrate the
tendency to simplify and standardize measurements of products to save expense.
The bolts are not uniform in size, and one cord may contain from 16 to 40 bolts.
But it is common practice to first determine the average number of bolts in a cord,
and then measure the remainder by counting the bolts to avoid stacking. The
number agreed upon is used as a divisor to obtain the quantity in cords.
Stacks measuring more or less than 4 feet in length of stick can thus be measured
in either of the two ways described above (§98). Surface feet or 32 square feet
equivalent to 4 by 8 feet may be taken as a short cord. But stacked contents
based on the standard cord of 128 cubic feet is just as commonly employed. For
instance, in cooperage it is a common custom to measure 36-inch stave bolts in
ranks 4 by 11 feet for one cord, giving 132 cubic feet or approximately a standard
cord.
EFFECT OF SEASONING ON VOLUME OF STACKED WOOD 123
100. Effect of Seasoning on Volume of Stacked Wood. Green
hardwoods shrink on seasoning, decreasing from 9 to 14 per cent in
volume. Conifers shrink from 9 to 10 per cent. Contractors some-
times stipulate an extra height of 3 to 4 inches on the stack to offset
this loss. Where such extra allowance for shrinkage, or for any other
reason, 1S required, it must be specified by contract unless generally
accepted in the locality.
101. Methods of Measurement of Cordwood. Stacked cordwood
is measured by a stick usually 8 feet long, marked off in feet and tenths.
Choppers prefer to pile each cord separately, since the division into
a number of smaller piles reduces the cubic contents required for one
cord ($103). When surface measure, 32 square feet, is accepted for
short or long cords, their measurement is identical with that of standard
cords, the length of piece being measured only to insure conformity
with specifications. Stacks piled to more or less than standard height
and length are reduced to cords by dividing the surface feet by 32;
e.g., a Stack measuring 12.7 feet by 6.4 feet contains 81.28 surface feet,
or 2.54 cords.
When standard stacked contents is used as a basis, the length of
piece is also measured, the cubic contents of stacked wood obtained
and divided by 128; e.g., a stack of 30-inch bolts with the above surface
dimensions gives 81.28 by 2.5= 203.2 stacked cubic feet; — = 1.5875
standard cords, while a similar stack of 5-foot wood gives 81.28 by 5
=406.4 stacked cubic feet. eis standard cords, instead of
the 2.54 cords based on surface standard.
A cord foot is a pile measuring 1 by 4 by 4 feet or containing one-
eighth of a standard cord. It is also termed a foot of cordwood, being
equal to 1 foot in length in a stack of cordwood of standard dimensions.
The unit applies to short or long cords when surface only is measured
and not cubic contents.
The chopper is required to pile the rank to an even height, pref-
erably the standard of 4 feet. Unless otherwise specified, the height
of the pile is to be the average height of the tops of the sticks in the top
layer. With uneven, crooked or poorly piled stacks a point 1 or 2
inches below this is taken. From this height is subtracted whatever
allowance is required for shrinkage, when so specified.
If the ends of the stacks are not vertical the length is measured at
one-half the height of the pile. If wood is piled in irregular stacks
the average of both height and length is obtained, if necessary from
several equally spaced measurements.
Wood piled on inclined surfaces is measured incorrectly if the length
124
STACKED OR CORD MEASURE
of the pile is taken parallel with the surface of the ground or top of
stack, while height is taken vertically.
The true contents of a stack
with the dimensions shown in Fig. 22 is 87.5 per cent of a cord. The
f
|
>
See eo eae 2
i
|
Fic. 22.—In the example given, the ver-
tical height of the pile must be 4.57
feet to give 128 cubic feet. The actual
pile measures 112 cubic feet by either
method.
correct Measurement is secured if
length and height are taken at
right angles whether or not the
length is taken horizontally or
along the surface.
102. Solid Cubic Contents of
Stacked Wood. The stacked cord
is a measure purely of convenience.
The purchaser is interested not in
the cord, but in its solid cubic
contents of wood. Stacked round
bolts can never give 128 cubic feet
of wood to a cord. The highest
possible contents would be ob-
tained from bolts which were per-
fectly cylindrical and of uniform
diameter. These, if stacked in
hexagonal formation, or alternat-
ing, and with one end bolt in each
tier split in half to fill out the tier, would give 116.07 cubic feet, or
90.68 per cent of 128 cubic feet, which is the relation of the area of an
inscribed circle to that of a hexagon.
of any length or diameter.
A
/ _
YX v Vo \/ann AAW, V v |
L\ £\ AS £\ AS ras pas pAS pa
SBOCSCECCe
SAAS AS
This relation holds true for bolts
CVV NOY YY Oo
eeeceese
C9609 48%
Ps
SSSOSOSe
OOOO
Fic. 23.—Hexagonal piling—116.07 cubic feet per cord or 90.68 per cent solid wood.
Square piling—100.53 cubic feet per cord or 78.54 per cent solid wood. It
is evident that neither the diameter nor the length of sticks would in any
way influence the solid cubic contents of a cord unless taken in conjunction
with some other factor whose effect varies with the dimensions of the piece.
When these cylinders are piled directly above one another in square
formation, the cubic contents of a cord becomes 100.53 cubic feet, or
78.54 per cent of 128 cubic feet, which is the relation of the area of
an inscribed circle to that of square.
103. Effect of Irregular Piling on Solid Contents.
tice, the solid contents of a cord seldom exceeds 100 cubic feet.
In actual prac-
Straight
EFFECT OF IRREGULAR PILING ON SOLID CONTENTS 125
smooth sticks of uniform sizes, carefully piled, may yield from 105
to 107 cubic feet, but never as much as the 116 cubic feet theoretically
possible. This loss is due first to irregular piling, and second, to vari-
ation of the bolts or sticks from uniform cylindrical form.
Piling exercises an enormous influence, which increases in direct
proportion to the irregularities of form. When to extreme crooked-
ness and surface irregularities is added dishonest piling, including the
laying of sticks at angles with each other, or even piling over stumps
and other trade practices, the purchaser may incur a loss of from 20
to 30 per cent from piling alone. Choppers are always paid by stacked
‘measure and close supervision is required to secure a full cord. The
factor of piling may cause more variation in the solid contents of a cord
than that of form of sticks. Since this factor depends upon the laborer,
the contents of a cord of wood, as a commercial standard, is based on
what can be expected of. choppers rather than a theoretical maximum.
Conversion factors for obtaining cubic contents of wood are based on
average conditions of piling. The cord can never be satisfactorily used
as a basis of scientific measurements of volume produced by trees and
stands, or of growth, though for convenience, cubic contents is often
converted into cords to express the results of these investigations.
104. Effect of Variation in Form of Sticks on Solid Contents.
Variation in the form of sticks is caused by taper, eccentric cross sections,
crook, and irregularities or roughness of surface. All departures from
cylindrical form increase the air space in a stacked cord.
The effect of taper can be partially overcome by piling bolts with
large and small ends alternating. But this is never done in practice.
Sticks split from bolts which include stump taper are apt to be some-
what curved as well as tapering. Sticks with eccentric cross-sections
do not pack as closely as round sticks and give a smaller per cent of solid
contents.
Crook is one of the most important factors in reducing the cubic
contents of a cord. The slightest departure from a straight axis exerts
a corresponding influence in increasing the air space in stacking. Very
crooked sticks may reduce the contents of a cord by 50 per cent.
Irregularities of surface in round sticks are caused by bark, knots,
stubs and swellings. Every such protuberance, by contact with adjoin-
ing sticks, decreases the solid contents of the stack. Split sticks are
irregular in both form and surface and always take up more room than
the round bolts from which they were split or round bolts of equal
diameter and straightness.
Since sticks with the smoothest surface and least taper will pack
the closest, and the removal of bark affects both factors favorably, the
cubic contents of a cord of peeled wood is always greater than the cubic
126 STACKED OR CORD MEASURE
contents of a cord of wood with bark, for the same species and sizes of
sticks. The shrinkage in stacked contents after peeling exceeds that
caused by loss of bark because of this closer piling. Bark is a waste
product for pulpwood or excelsior and purchasers prefer to buy peeled
wood.
The thinner the bark on a tree the smoother it is apt to be. Species
with smooth bark yield appreciably more solid contents in stacks than
thick-barked trees, because in the latter case the bark is usually irregular
and fissured. Hence conifers such as spruce and balsam, and hard-
woods like white birch and poplar give the highest contents per cord,
while hardwoods such as oak and maple yield considerably less per
cord than conifers.
The same difference holds for branch wood as contrasted with body
wood, open-grown and limby trees compared with those grown free
from branches in close stands, and split wood with twisted grain com-
pared to straight grain.
While the splitting of sticks decreases the solid contents, by increasing
the irregularities of surface and the effect of crook through reduced
diameters, split cordwood is usually cut from much larger bolts than
round sticks, and hence a cord of split wood may contain a greater
solid content than one of round sticks, especially if the round pieces
are below 3 inches and cut from limbs.
105. Effect of Dimensions of Stick on Solid Contents. The effect
of a given amount or rate of crook, or of given irregularities of surface,
in diminishing the solid contents of a stack, increases with increased
length of stick, but this effect is more nearly proportional to the square
of the length than to the length. Hence the longer the sticks in a
stacked cord, the less its net cubic contents, other factors being equal.
This explains the shrinkage in cubic volume when 4-foot wood is
cut into shorter lengths and restacked. In sticks longer than 6 feet
this becomes a serious factor and pulpwood from fairly straight logs
when sold in from 8- to 12-foot lengths gives about 12 per cent less cubic
contents than for 4-foot bolts (Table X XI, p. 130).
Conversely, the cubic volume of sticks increases as their cross-
sectional area, which is as the square of the diameter, while the effect
of both crook and surface irregularities increases in porportion to the
surface of the stick, which is directly in proportion to diameter and
consequently less than cross-sectional area or volume. A crook of
2 inches in a stick with 3-inch diameter has twice the effect that a
2-inch crook would have on a 6-inch stick. Due to these relations, the
solid contents of a cord of wood always increases with the increased
average diameter of the sticks, but diminishes with increased
length. .
THE BASIS FOR CORDWOOD CONVERTING FACTORS 7,
106. The Basis for Cordwood Converting Factors. The value of
stacked wood depends upon the quantity of wood contained in the
stacked cord as well as upon its quality. It is just as consistent to
require a knowledge of the solid cubic contents of stacked cords as it
is to measure sawlogs for board-foot contents by a log rule. For this
purpose, converting factors are required, and these factors are deter-
mined by actual measurement of the solid wood in cords composed of
sticks of different diameters and degrees of straightness.
Since a cord contains 128 cubic feet of space, the solid contents in
cubic feet may be expressed in terms of per cent; e.g., a cord containing
90 cubic feet of wood gives 70 per cent of stacked contents in wood.
A cord of theoretically perfect cylindrical sticks piled square gives
100.5 cubic feet, or 79 per cent (§ 102). This in actual practice is about
the maximum contents of stacked cord, no matter how the piling is
done, for losses caused by taper, crook and surface compensate for any
gain by hexagonal over square arrangement of sticks. Smooth pine
or white birch may give 102 to 107 cubic feet for large sticks, but the
attainable maximum solid cubic contents of cords can for commercial
purposes be set at 100 cubic feet.
TABLE XIX
Soutp CONTENTS OF STACKED Woop *
Cubie feet solid wood
Per cent | inone cord or per
Class of product solid contents} cent of standard
in stack | contents of 100 cubic
feet per cord
Large smooth logs or bolts.................. | 75-80 96 .0-102.4
Averages pllininewOOGE sae aie aces ee a 60-75 76.8— 96.0
Mop and branch wood s0.0 5.06565. e094 as a3 50-65 64.0— 83.2
Fagot material (small branches and twigs) .... 30-45 38.4— 57.6
SEM AAO TOOUS: 5 a7. c les dort atae elas coos dc ba a ie 30—40 28 .4— 51.2
* Adolph R. von Guttenberg, in Lorey’s Handbuch der Forstwissenschaft, Vol. III, 1903,
Chap. XII, p. 179, Tiibingen.
There is thus a choice of two methods of expressing converting
factors for indicating the solid or cubic contents of wood in a cord;
first, the number of feet of solid wood in a cord of 128 stacked feet;
second, the per cent of a stacked cord which this cubie contents repre-
sents. Of the two, the former is preferable for two reasons; first, it
is directly applicable to cubic contents of trees as a divisor or con-
verting factor to obtain cords; second, it indicates the comparative
128 STACKED OR CORD MEASURE
solid volume in cords of different cubic contents on a basis which prac-
‘tically amounts to a 100 per cent commercial standard. For if 100
cubic feet, as indicated above, is the practical maximum solid cubic
contents of a cord of stacked wood, a cord containing 70 solid cubic
feet bears a 70 per cent relation to this maximum, regardless of the fact
that 70 feet is but 54 per cent of the space in a stacked cord of 128 feet.
This accidental relation holds good only for standard cords. To apply
this same basis of comparison, instead of the per cent of stacked con-
tents, to long or short cords, the solid contents would have to be com-
pared to 78.12 per cent or +$$ of the stacked contents. Average cord-
wood worked up from hardwoods, either split or round, is often reckoned
at 90 cubic feet or 90 per cent of a maximum cord, which is 70 per cent
of stacked contents.
107. Standard Cordwood Converting Factors. The cubic contents
of stacked wood has been thoroughly investigated by European author-
ities on the basis of the stacked cubic meter, of length equal to 39.37
inches or 8.63 inches short of a 4-foot standard. According to the per
cents given in Table X XI (p. 130) these results should give about 1 per
cent more than the contents of similar sticks 4 feet long.
The following Table XX is adopted from the results of an investi-
gation, conducted by Prof. F. Baur, and published in a pamphlet entitled
‘‘ Untersuchungen iiber die Festgeholt und das Gewicht des Schicht-
holzes und der Rinde,”’ Augsburg 1879, pp. 97-99. These factors
may be regarded as standard for 4-foot lengths, after subtracting 1 per
cent.
The difference in per cents between hardwoods and conifers in this
table is seen to fall largely in the smaller sizes. Where branch wood
is mixed in the cord the per cent of difference between hardwood and
conifers, usually about 6 per cent, may be increased to 12 or 15 per
cent, since many conifers lack merchantable branches, while hardwood
branches are usually crooked.
108. Converting Factors for Sticks of Different Lengths. The
influence of length on per cent of solid contents is fairly constant for
sticks of all diameters, but differs tremendously according to the amount
of crook in the average stick. Table XXII gives average results
for conifers, which as a rule are much straighter than hardwoods. It
is seen in the table that the per cents when standardized for sticks of
the same diameter do not differ much, whether the sticks average over
5.5 inches or are between 1 inch and 2.5 inches in diameter.
The differences in contents caused by crook and surface irregularities is well
shown in Table XXIII, prepared for hardwoods by Kénig, p. 131. In this table
the values for straight sticks 4 feet long slightly exceed the values in Table
XXI since these sticks are selected. But for other lengths even in this class the
CONVERTING FACTORS STICKS OF DIFFERENT LENGTHS 129
percentages increase more rapidly than for conifers; while for crooked and knotty
ia ye:
sticks the differences caused by length are excessive, when added to those caused
by diameter.
TABLE XX
STANDARD CONVERTING FacToRS FOR CoRDWOOD
Cubic feet
solid wood in
Per cent a cord or
, Diam- Class of Character of | solid wood | per cent of
Species : ’ : ‘
eter material piece ina standard
cord contents of
100 cubic feet
per cord
Conifers Large | Round logs Straight 80 | 102.4
Medium! Split firewood | Straight, smooth 75 96.0
Medium, Split firewood | Crooked, knotty 70 89.6
Small Firewood Round bolts 70 89.6
Small Firewood Top wood 60 76.8
Small | Strips Hewn from bole 50 64.0
Small | Chips Hewn from bole | 45 57.6
Hardwoods) Large | Sawlogs Straight 80 102.4
Medium] Split firewood | Straight, smooth 70 89.6
Large | Split firewood | Knotty, crooked 65 83.2
Small Firewood Round bolts 65 83.2
Small Firewood Knotty, crooked OD 70.4
Small Firewood Top wood 55 70.4
Small | Firewood Branch wood 45 57.6
Small | Strips Hewn from bole 35 44.8
Small | Chips Hewn from bole 25 32.0
Small Brush Long branches 15 19.2
109. Converting Factors for Sticks of Different Diameters. The
figures in table X XIV indicate the influence of diameter of stick upon
solid contents of stacked cords, for various species. The differences in
contents for species is due entirely to differences in form and smooth-
ness of sticks.
Second-growth white pine and Norway or red pine give results approximating
white birch. Old growth, knotty twisted grain and limby northern hardwoods
give 60 cubic feet per cord, as against 90 cubic feet for tall slender straight clear
second-growth. A cord of average hardwoods does not contain more than 70
cubic feet. A cord of second-growth hickory spoke bolts contains 95 cubic feet.
Chestnut acid wood on the Pisgah National Forest, N. C., is scaled as 110 cubic
feet of wood per cord of 160 stacked cubic feet, or 87 cubic feet per standard
cord. In California, a cord of red and white fir, averaging 60 sticks, contains 81
cubic feet. Western juniper in Arizona averages 62 cubic feet of solid wood
per cord,
TABLE XXI
ConiFErs *
STACKED OR CORD MEASURE
Influence of Length of Stick upon the Solid Cubic Contents of a Cord
130
|
Solid contents
per cord.
tee Sticks over
ds 5.5 inches in
: diameter at
small end.
Feet Cubic feet
1 91.80
2 90.90
3 89.98
4 88 .92
5 87.75
6 86.45
8 SB) 7/5)
10 81.00
12 78.05
14 74.85
Solid contents
per cord.
Per cent sticks from 2.5
to 5.5 inches in
of 4-foot :
coe diameter at
small end.
Cubic feet
58 ily ies
+ 2.2 84.35
+ 1.2 83.40
0 82.42
— 1.3 81.30
— 2.8 80.00
— 5.8 77.20
— 8.9 74.30
—12.2 (Mo20
—15.8 67.95
Solid contents
eee aoe {eee
in terms fie a eheaun in terms
of 4-foot| ,. of 4-foot
sticks BG sticks
small end.
Cubie feet
+ 3.4 65.69 + 3.2
+ 2.3 65.32 + 2.7
+ 1.6 64.60 + 1.5
0 63.62 0
— 1.3 62.60 — 1.6
— 3.0 61.60 — 3.2
— 6.3 59.40 — 6.6
= 989 56.90 —10.5
—13.6 54.25 —14.7
—17.5 51.50 —19.0
* Raphael Zon, Forestry Quarterly, Vol I, 1903, p. 132.
These results were verified by test on balsam fir in the Adirondack region of New
York
TABLE XO
INFLUENCE OF LENGTH OF STICK ON SoLip Cupic CONTENTS OF A STANDARD Corp,
BaLsaM Fir
Length. /|Diameter of sticks,
small end, 7 inches
and over.
Feet Cubic feet
4 96.7
8 91.6
2, 86.2
16 80.2
VOLUME
Loss in long |Diameterofsticks,| Loss in long
sticks. small end, 4 to 7 sticks.
inches.
Per cent Cubic feet Per cent
teak 92.4 :
— 5.3 87.4 — 5.4
—10.8 81.6 —11.6
—17.1 15.5 —18.3
This table was based on 56 cords by R. Zon, Bul. 55, U.S. Dept. of Agriculture,
p. 52.
CONVERTING FACTORS STICKS OF DIFFERENT DIAMETERS 131
A
TABLE XXIII
INTERDEPENDENCE OF THE Stick LENGTH AND THE VOLUME OF SOLID Woop PER
Length
of
stick.
Feet
aomnrwWhN Fe
Corp *
STRAIGHT STICKS
CROOKED STICKS
Kwnorry STicks
Volume.
Cubic feet
99.81
97 .28
94.72
92.16
89.60
87.04
Difference.
Per cent
Cubic feet
Volume.
Difference.
Per cent
Volume.
Cubic feet
93 .47
89.60
85.76
81.92
78.08
74.24
89.60
84.48
79.36
74.24
69.12
64.00
Difference.
Per cent
* Cited in Dr. Miiller’s Lehrbuch der Holzmesskunde, Graves Mensuration, p. 104.
TABLE XXIV
SoLtip CoNTENTS OF A STANDARD CorD BASED ON DIAMETER OF STICK
Average, 4-foot wood
Average Mixed
diameter at | Paper | Balsam Red hard-
middle bireh.* |). fir: ppricet/epeni§ | Beech § maple.|| | woods.§
of sticks.
Inches Cus ties |} Comrie | Cin, ey |) Cutis Wi Col ate, |) tists 1 Cus ite
3 64 76 75 49 67 60
4 72 82 80 57 see 69 65
5 82 86 84 64 54 70 69
6 87 88 86 71 62 (02 73
Ul 91 90 88 77 70 74 77
8 96 91 90 83 Wl 77 80
9 100 92 91 88 83 80 83
10 103 93 92 92 88 84 85
11 105 94 92 96 93 87 88
1 105 93 90 90
13 105 94 92 92
14 95 93 95
5 96 95 97
16 96 96 99
17 97 96
18 97
*§S. T. Dana. + R. Zon. ¢ H. L. Churchill. § E. H. Frothingham,
|| E. E. Carter.
132 STACKED OR CORD MEASURE
110. The Measurement of Solid Contents of Stacked Cords—
Xylometers. The solid or cubic contents of stacked cords must be
actually measured in order to determine the converting factors for
wood as influenced by any of the above conditions. The purpose may
be to obtain either an average factor for commercial use, or to further
test the effect of crook, diameter or length of sticks specially selected.
Two methods of measurement are available, actual calipering or
stereometric ! calculation, and xylometric? measurement. By the first
method, the diameter of each bolt is measured in the middle (Huber’s
method) taking two measurements at right angles to obtain the average.
The length is measured if necessary, but the sticks are usually cut to
a standard length. Split billets cannot be measured by this means,
and in this case, the round bolt must first be measured before splitting.
The measured wood is piled and the contents of the sticks required to
make a stacked cord are totaled for as many cords as possible, to obtain
average factors.
Wood after splitting, or very small crooked or irregular pieces such
as branches or root wood, is best measured by a xylometer.2 The dis-
placement of water when wood is submerged in a tank is: exactly equal
to the cubic volume of the wood. The only question is the fo m of the
tank and method of measuring the cubic volume of water displaced.
One plan (invented by Karl Heyer, Giessen, 1846) is to have an
overflow spout flush with the water level and to catch and measure
water which overflows.
But this is found to take seven times as long as Reisig’s method
(Darmstadt, 1837) which employes a tank about 53 feet high and about
twice as wide as the diameters of the largest sticks. The cross-section
must be uniform at all points. The scale is worked out for cubic feet
and decimals, corresponding to the inch scale in height of water in the
tank and is either marked on the inside of the tank, or better on a stand
pipe of glass outside the tank, with proper connection, and carefully
plumbed. This gives instant readings when a piece is submerged.
The endwise position favors complete submersion.
111. Cordwood Log Rules. The Humphrey Caliper Rule, 1882. Cord-
wood log rules are in use in Southern New Hampshire and in Massa-
chusetts for measuring the cubic contents of white pine logs in terms
of stacked cords and stacked cubic feet. These rules are based upon
the principle of the circle inscribed in a square (§ 102). It is assumed
that a cord, no matter what the diameter, length or character of the
timber, contains 100.5 cubic feet of solid wood. The diameter is cali-
pered in the middle of the log outside the bark, but the rule could be
1 Stereometry, the art of measuring solid bodies. Stereos (Gr.) =solid.
2 Xylos (Gr.) =water.
DISCOUNTING FOR DEFECT IN CORD MEASURE 133
applied to peeled wood by subtracting diameter of bark. The old
Partridge rule used at Winchendon, Mass., computes the stacked volume
of the log as (Dy with D=diameter in feet. Each ‘ cubic foot ”’
by this rule is 3s cord. The rule is thus based on stacked contents,
and fractional cords are reduced to decimals by the divisor 128; e.g.,
64 ‘feet ’’ would give .5 cord.
To simplify this process the cordwood caliper rule known as the
Humphrey Caliper! Rule, was divided into 74> of a cord; i.e., instead
of measuring a stacked cubic foot the unit or zj> cord equaled 1.28
stacked cubic feet. The scale stick for this rule was not marked off
in inches, but for each standard length of stick the graduations repre-
senting diameter were placed at the points which gave logs measuring
a certain even volume (§ 80). Hence no fractional stacked feet were
shown.
Since py either rule, the cubic contents of a cord is given as 100.5
cubie feet, the Humphrey Rule by using the decimal system expressed
cubic feet
the contents as — 100
of the rule thus correspond with those given for cubic contents of eylin-
ders, but pointed off for two decimals.
If we accept the standard of 100 solid cubic feet of wood as the
maximum contents of a cord, the Humphrey Caliper Rule measures
wood of any character or degree of straightness, surface, roughness,
length or diameter not only by a uniform standard of cubic contents
(as does the Partridge Rule) but directly in cubic feet, or in standard
cubic contents.
This rule therefore offers a double advantage. It is not only a cubic-
foot standard, which is desirable for all scientific measurements of volume
and growth, but it serves to standardize cord measure as well, on the
basis of solid rather than stacked contents. The limitations in the
use of the rule are the same as those of all caliper rules (§ 84). It can-
not be applied to wood in the stack but only to pieces measured singly.
Scale sticks made up for these values would enable measurements of
cubic contents to be made directly for logs or trees to be used for vol-
ume tables or other scientific purposes and would do away with cal-
culation of cubic contents. This rule is used as the principal com-
mercial standard in the vicinity of Keene, New Hampshire. It can be
made up by anyone on the basis of diameter by applying the cubic
contents of cylinders given in Table LX XVII, Appendix C.
within an error of but 0.5 per cent. The values
112. Discounting for Defect in Cord Measure. Pulpwood must be sound and
free from rot or defective knots. Where logs of 8, 12 or 16 feet are measured by
1 Invented by John Humphrey, Keene, N. H.
134 STACKED OR CORD MEASURE
the cord, defective portions may be culled by subtracting from the total stacked
volume, a piece whose volume is the square of the diameter in feet multiplied by
length in feet. This deduction coincides with the basis of a standard cord of
100.5 solid cubic feet and is based on ;3, cord for each cubic foot subtracted.
This method is the basis of the following table:
TABLE XXV*
MEASUREMENTS OF 4-FooT RouND SprucE PuLPwoop—wiTH CuLL Factors
BASED ON Sotip Cusic CONTENTS
PCS Solid contents of : Volume to be deducted
diameter of Sticks per cord. ;
aa cord. for each stick culled.
Inches Cubic feet Number Cubie feet
3 75.0 375 0.34
4 79.8 228 .56
5 83.6 152 . 84
6 86.1 109 1.16
a 87.7 82 1.56
8 89.6 64 2.00
9 90.3 51 2.51
10 91.6 42 3.08
11 92.4 35 3.66
1% 93.3 29.7 4.27
13 04.1 DED 5.02
14 95.0 22 5.87
15 95.8 19.6 6.67
16 96.5 iyfeal Catt
17 97.0 15.4 8.59
18 97.4 133-2 9.70
19 97.9 12.4 10.76
20 98.3 eS 12.06
* Prepared by H. L. Churchill for spruce in the Adirondack region, New York.
Where the contents of the cord are expressed directly in solid cubic
feet, special tables can be worked up for deducting the actual cubic
contents for sticks of given diameters.
The Humphrey Caliper Rule will serve to make deductions based
on solid measure, by sealing the contents of the defective portion as
a stick of a given length and diameter.
113. The Measurement of Bark. Bark, when used for tannin, is stripped off
in sheets and piled in cords. At the factory a cord is measured by weight. Eastern
hemlock bark must weigh 2240 pounds per cord, when dry.
The bark peelers are paid by the stacked cord measure, which is in some
localities 4 by 4 by 8 feet but more often is required to be full in one or more
dimensions, according to local specifications. In New York, the dimensions are
CONVERTING STACKED CORDS TO BOARD FEET 135
4 by 4 by 8 feet. In Upper Michigan, 43 by 43 by 8} feet is sometimes required,
in order that the cord shall check out in weight. Others stipulate 4} by 43 by 8
feet. In the West, hemlock bark is usually bought and sold by the standard cord,
although weight per cord (2240 pounds) is sometimes used. Tan-bark oak is sold
by weight.! ;
Bark forms the largest per cent of total volume in young, small and rapidly
growing trees, exposed to light and growing on dry exposed sites. It gives the
smallest per cent of total volume on old, large trees, grown in dense stands, and
on slow growing or suppressed trees.
Measurement of bark in per cent of total volume of tree with bark, for the
following species, show:
Species Character Per cent bark
Southern yellow pine species. ...... 2-inch trees 40
Diminishing with increased
diameter 30 to 15
Western yellow pine.............. 12-inch trees 24
Diminishing with increased
diameter 24 to 12
Yellow poplar, or tulip............ Diminishing with increased 15 to 12
diameter
PSH eres ME ays dat std ooh 3 Vay srera'eud ab Shae Diminishing with increased| 22.4 to 10.3
diameter
ARCO pee ys 755 doko ales aah slows wick owed Diminishing with increased 22 to 12
diameter
SUP ATMA DIONE a5 sure oc cesle Moone Seas All diameters Average 17
MOULOMWOOU HT .. cis .ic/tsi cists cciaa st All diameters Average 22
Spruce, balsam, white pine, white
DOIG Hey eyes eo oy sh cs ene sea a, hey ahs All diameters Average 11 to 12}
FRSA MOCKS cao PB cys 5 cts ay ayaa i SAS All diameters 15 to 19
iodgepolenpine secs eee ae ce All diameters Average 6
The manufacturers of pulp, excelsior and products requiring peeled wood,
when forced to purchase their raw material with bark on, soon determine the
reduction factor required for their species and locality. The large and variable
per cent of bark on loblolly pine in the South forces the purchaser of pulpwood
stock to insist on peeling.
114. Factors for Converting Stacked Cords to Board Feet. Where the output
of wood in a given region, or for a given tract or ownership is in the form of both
cordwood and sawlogs, it is often desirable to reduce cordwood to terms of its
equivalent in board feet, in order to express the total production in terms of a
single standard. Less often, this conversion is desired as the basis of sale or
contracts for logging. It is not the purpose of such conversion to determine the
actual quantity of lumber which can be sawed from sticks of cordwood sizes and
shapes.
1 The standard cord in Oregon is 2300 pounds, The standard cord in California
is 2400 pounds,
136 STACKED OR CORD MEASURE
The board-foot contents of a stacked cord depends first on the solid cubie con-
tents of the cord rather than its stacked measure, and second, on the diameter
of the sticks which it contains (§ 54). Since solid contents also depends on diam-
eter of stick, the ratio of board feet to stacked contents increases with diameter
from both sources, or much faster for stacked than for cubic volume.
The diameter of the average stick is the determining factor in this ratio. The
ratio itself will thus vary over a wide range depending on the class of wood handled.
Crook and other irregularities of form have the same double effect as diameter,
in reducing first the solid contents, and next, the board-foot contents per cubic
foot of wood. The latter ratio can be determined for straight sticks by Table III
(§ 41), Tiemann log rule, based on middle diameters, outside bark. For crooked
sticks, a further reduction in ratio is required.
To obtain the true ratio for a given cord of straight wood, it is necessary to
determine first, the converting factor for solid cubic contents, and second, the
average diameter of the sticks, at middle point outside bark. By use of Table II
the converting factor from cubic to board feet is found for logs or bolts of this
average size, and this multiplied by solid cubic contents gives contents of the
stacked cord in board feet.
But commercial log rules are based on diameter at small end and do not usually
give actual sawed contents. For such rules the ratio can be approximated directly
by determining the average diameter and number of sticks in a cord, and scaling
their contents with a log rule.
The ratio for actual board-foot contents of cordwood diminishes to zero for
sticks averaging from 3 to 4 inches in diameter, which is a common size for cord-
wood. If so determined, the converting factor is not an indication of the real
volume or utility of the contents of a cord of wood. For a given species and class
of cordwood an arbitrary converting factor can be obtained, based first on the
per cent of solid cubic contents of a cord of sticks of average diameter and second,
on an average or fair ratio between board feet and cubic feet, and not on the ratio
for the actual small or irregular sizes. For instance, western juniper cordwood
gives about 60 cubic feet per cord. Adopting a fairly low ratio of 46 per cent or
5.55 board feet per cubic foot of total solid contents, the board-foot converting factor
is 60 times 5.55 or 333 board feet per cord, or 3 cords per 1000 board feet. For
white pine, 100 cubic feet per cord, with nearly the same ratio, 5.5 board feet per
cubic foot, gives 550 board feet per cord. The ratio of 500 board feet per cord
adopted by the U. S. Forest Service for pulpwood gives 5.55 board feet per cubic
foot for wood yielding 90 cubic feet per cord, which is a fair average for well-shaped
sticks.
It would appear then that the factor 5.55 has some merits as a universal con-
verting factor and that the variation of board-foot converting factors for entire
cords should be based on the difference in cubic contents of the cord rather than by
the adoption of variable ratios between board feet and cubic feet. This practice
is sound. The factor 5.55 corresponds to the actual sawed contents of a log
between 7 and 8 inches in diameter at middle of stick inside bark. The basis
of this ratio is comparison between total cubic contents including taper, and actual
sawed contents. Commercial log rules deal with reduced values for both cubie and
sawed output, using the contents of the small cylinder for the one, and neglecting
over-run in the other. These two reductions may not be of equal weight, but tend
to give approximately equal ratios to those stated.
If the average diameter of logs exceed 7} inches at middle, inside bark, the actual
ratio is correspondingly larger. Only in this way can ratios as high as 575 board
WEIGHT AS A MEASURE OF CORDWOOD 137°
feet per cord, used on the Pacific Coast, be obtained. The ratio in New England
for pulp wood is 560 board feet.!
115. Weight as a Measure of Cordwood. For fuel, weight is a
better measure of the value of cordwood than solid cubic volume, and
of still greater utility for the measurement of stacked volume. Its
merits increase with the increasing irregularity of form in sticks which
render the determination of solid contents of stacks so uncertain. But
one factor operates against the substitution of weight for stacked
measure, for fuel wood, and that is the unfamiliarity of the public with
the proper standard weights which should constitute a cord. This
is due first to the great variation in weight between wood of different
species, a variation which would be equalized as to price if equal weights
regardless of bulk commanded approximately the same price, and second,
to the great difference in weight between green and air-dried wood.
If sold by weight, dealers would endeavor to sell the wood as green as
possible. Green wood has less net fuel value per pound, not only
because the purchaser pays for water instead of net dry weight, but also
because each pound of dry wood has to generate heat enough to vaporize
all the water in the wood and only the surplus heat is given off.
But for dead dry juniper or pinon or mesquite roots or for well-
seasoned woods difficult to measure in bulk, weight is practically the
universal standard. Dealers customarily deliver from 200 to 400
pounds less of weight per cord than the actual weight of an average
cord of such wood. For instance, pinon should weigh 3000 pounds
per cord, but it is often sold at 2000 pounds per cord. It would be
better to substitute weight altogether and not maintain the pretense
of delivering a cord by measure. This would place the dry wood
on the same basis as coal. .
Air-dried wood still contains from 15 to 20 per cent moisture. The
variation in per cent of water in green wood compared with dry wood
is extreme, as illustrated by Table LX XXIII (Appendix C).
REFERENCES
Factors Influencing the Volume of Solid Wood in the Cord, Raphael Zon, Forestry
Quarterly, Vol. I, 1903, p. 126.
Untersuchungen iiber die Festgehalt und das Gewicht des Schichtholzes und der
Rinde, F. Baur, Augsburg, 1879.
Mitteilungen aus dem Forstlichen Versuchswesen Oesterreiches, 1877-1881, Report
by Von Seckendorff.
Paper Birch in the Northeast, 8S. T. Dana, U. 8S. Forest Service Circular 163, 1909,
pp. 34-35.
‘In Forest Mensuration of White Pine in Massachusetts, p. 45, ratios for white
pine l-inch lumber are given, running from 488 board feet for 5-inch logs to 730
board feet for 24-inch logs, measured at middle of log outside bark.
138 STACKED OR CORD MEASURE
Second Growth Hardwoods in Connecticut; E. H. Frothingham, U. S. Forest
Service Bul. 96, 1912, pp. 63-64.
The Northern Hardwood Forest, E. H. Frothingham, Bul. 285, U. 8. Dept. Agr.,
1915, p. 62.
Balsam Fir, Bul. 55, U.S. Dept. Agr., 1914, p. 52.
Measuring Cordwood in Short Lengths, R. C. Hawley, Journal of Forestry, Vol.
XVII, 1919, p. 312.
A Practical Xylometer for Cross-ties, F. Dunlap, Forestry Quarterly, Vol. III, 1905,
p. 335.
A Practical Xylometer, J.S. lick, Journal of Forestry, Vol. XV, 1917, p. 859.
PART II
THE MEASUREMENT OF STANDING TIMBER
CHAPTER X
UNITS OF MEASUREMENT FOR STANDING TIMBER
116. Board Feet—Basis of Application. The value of standing
timber must be determined as a basis for sale either of the timber alone,
or of the land and the timber. This value depends upon the quantity
of wood which may be cut from the tract, but still more upon its value
per unit of volume. As set forth in Part I, the contents of logs and
trees in North America are expressed, whenever possible, in terms of
the final products instead of by cubic volume as in Europe. Standing
timber, therefore, is commonly measured in terms of board feet, cords,
or pieces such as poles, piles or railroad ties and is rarely expressed as
cubic feet, since it is seldom sold on that basis. If estimated by cubic
feet, the contents are usually converted into their equivalent in cords.
When the board-foot unit is used in timber estimating, the basis
of determining the contents of the standing timber must be identical
with that on which the timber is to be sold when cut.
If manufactured on the tract by small portable mills, the actual
sawed output in lumber, the mill cut, furnishes this basis. When
round-edged lumber is sawed and small trees utilized to a small top
diameter (§ 21) the yield in board measure may be 100 per cent greater
than when the “ sawlog”’-sized timber only is merchantable, as in
large logging operations.
When scaled and sold in the log, the estimated contents of the stand,
before cutting, should coincide, not with the sawed output, but with
the log scale. Since different log rules give different scaled contents
for the same logs, the estimate must be based upon the log rule which
will be used to scale the logs. Hence an estimate made on the basis
of the Doyle rule will differ from one based on the Scribner rule or the
International rule. In all large logging operations where the logs
are transported some distance to the mill, timber is estimated solely
on the basis of the standard log rule in use.
139
140 UNITS OF MEASUREMENT FOR STANDING TIMBER
Local log rules based on mill tallies may be substituted for the sawed
product as the basis of estimating timber on small tracts.
No such difficulties affect the estimating of timber in terms of cubic
units or cords, which include the entire contents of all trees within the
merchantable limits of size, up to the merchantable limit in the tops.
117. The Piece. Poles or piling usually comprise the entire mer-
chantable portion of the trees which produce them, but can only be
cut from trees having the specified dimensions. Familiarity with these
specifications enables the cruiser to count the number of pieces in the
stand, and to tally them in separate classes. The same method may
be used in estimating standard railroad ties, but in this case the number
of ties in each tree must be counted separately in accordance with the
five standard grades (Appendix B, § 369). Where the tree is large
enough to produce more than one standard tie from a single 8- or 83-
foot length, the cruiser must rely either on his knowledge of the contents
of the bolt in ties, or refer to a volume table for piece products (§ 162).
He gets the total tie count for the tree by adding the contents of each
separate bolt, up to a point where the diameter is too small to produce
another standard tie. Posts are counted in the same way but, owing
to their smaller value and greater number, the count is usually more
or less of an approximation. The same system may be used, if required,
in estimating the quantity of mine timbers and mine ties in a stand.
Products such as stave bolts, which demand a high quality of timber
practically free from knots and all forms of defect, and are of small
size, introduce two features common to estimating in board feet, namely,
a table of volumes, and discounts for cull. Stave timber for staves
of given sizes may be estimated by knowing how many staves may
be cut from bolts of given dimensions. The number and size of the
cuts in each tree will give their sound contents, from which are deducted
all visible defects. A liberal allowance is also made for invisible defects
in the interior of the tree.
Since only a portion of a stand is converted into these forms of
product, the estimating of piece products may be only a part of a
general estimate in which the remainder of the stand is measured
either for logs or for cordwood.
118. Choice of Units in Estimating Timber. Methods of timber
estimating are determined by the cruiser’s choice as to whether he will
deal directly with one of four units, namely, the stand as a whole, the
individual tree, the individual log, or the piece (§ 117). Any one of
the first three methods may be used when the volume of the stand
is expressed in terms of cubic units, or in board feet. If the tree or
log is not used, the stand is considered as a whole and a direct guess
or estimate is made of its total contents (§ 206). If the tree or the log
THE LOG AS THE UNIT IN ESTIMATING 141
is used, the method requires a count and tally by different sizes, and
gives rise to many systems of estimating, depending on whether the
entire area or only a portion of it 1s to be counted.
119. The Log as the Unit in Estimating. When the product to
be estimated in board feet is lumber, the log becomes a convenient
and much used unit for estimating. Lumber is measured or scaled
in the log by a given log rule. The contents is given for logs according
to their diameter inside bark at small end, and length. Hence a tally
of the top diameter inside bark and the length of each log in a tree,
and the use of a log rule, will give the board-foot contents of the tree.
If every log is so tallied the stand is measured by merely totaling the
contents of the logs, without computing the volume of separate trees.
No further volume basis is needed in this method than the log
rule or scale stick. But the cruiser must know the amount of taper
in each log, the thickness of bark to be deducted, and. the log length
to use in estimating.
Log lengths as actually cut are determined by the crooks and other
peculiarities of each tree. But in estimating timber, these variable
log lengths are disregarded and a uniform or standard length is adopted
which conforms within reasonable limits to the average log length most
frequently used. For eastern conifers this is 16 feet, while hardwoods
may require 12 feet. On the Pacific Coast, 32 feet is used by many
cruisers. If logs when cut average shorter than the standard, the
scaled contents of the logs will over-run the estimate, while if longer
logs are cut, the scale will fall short (§ 83).
The method of tallying the logs in a tree is as follows:
1. Estimate or measure the diameter of the butt log either at the
stump, at 45 feet from the ground, or at 1 foot above the butt swell,
choosing one of these methods to the exclusion of the others. Foresters
use 43 feet as the accepted standard.
2. Deduct the double thickness of bark to obtain the diameter,
inside bark, at this point.
3. Estimate the number of inches to deduct from this diameter for
taper, to obtain the diameter at the top of the first log of standard
length. This and all upper estimates of diameter are inside the bark.
4. Estimate by eye the number of standard logs in the tree, to the
limit of merchantable size. The top diameter at this point should
be known or estimated, inside bark.
5. From the diameter of the top of the first log, inside bark, deduct
successively the estimated taper, in inches, to obtain the diameter
of each remaining log.
An alternate plan frequently used is to measure the diameter out-
side bark at the butt, or at 43 feet, subtract the taper outside bark
142 UNITS OF MEASUREMENT FOR STANDING TIMBER
for the first log, and then subtract the estimated thickness of bark at
this point, or at the top of the first log instead of at the butt.
A third plan is to estimate directly the diameter, minus bark, at
the top of the first log, without measuring the butt. Or, a table may
be prepared showing diameter, inside bark, at the top of the first log,
for trees of different diameters at 43 feet.
Each of these plans aims to secure the diameter, inside bark, at
the top of the butt log as the basis from which to figure the top diam-
eters of the remaining logs.
The eye may be trained to estimate log lengths and taper by the use of a pole
with a cross-piece at the top, marked off in inches. The length of pole (about
12 feet) permits holding the cross-piece at the height of the top of the first log
plus an allowance for height of stump. By comparison with this measured length,
the number of logs in the upper bole may be estimated by eye. By measuring
the tree at 43 feet, and reading the cross-arm, the taper, in inches, for the butt
log is shown. Bark thickness is then subtracted as determined for the species
by observation on felled trees or logs. This varies for the top of the butt log,
from 2 inches to 1 inch for most species. The total number of logs, to the limit
of merchantable diameter, gives the total taper to that point. If 6 inches is the
merchantable limit, this diameter, subtracted from that of the top of the butt
log inside bark, indicates the taper to be distributed between the upper logs.
Bearing in mind the tendency to more rapid taper in the crown, the actual taper
of each log can be approximated with reasonable accuracy and its diameter inside
bark recorded. Two men usually work together in this practice, or in training.
One man may use the method if the pole is made long enough to be leaned against
the tree (17 to 18 feet), while he gets far enough off to judge its height.
This method assumes that the eye can be trained to judge diameters
to an inch, at varying distances and heights above ground. But in
timber estimating only the general character of the tree is noted, and
its total height, or the number of standard-length logs. The taper
of the successive logs is obtained from measuring the diameters of
felled or wind-thrown trees of the same character as the standing timber.
The taper for a 16-foot log may vary from 1 to 10 inches or even more,
depending on site, density of stand, butt diameter, and position of the
log in the tree.
Many cruisers assume that once the difference in diameter between
the top of the second and the first log is ascertained or assumed, each
successive upper log will have an equal taper, giving to the tree a uniform
taper per log of 2, 3 or more inches. They know that the butt log
will taper more rapidly than the second log, but the above practice
ignores the taper of the butt log.
They also know that as soon as the green crown is encountered,
the taper per log again increases. But in regions where rough logs
in the crown are seldom utilized, this assumption of a uniform taper
for the second and higher logs in the bole is approximately correct.
LOG RUN OR AVERAGE LOG METHOD 143
Where greater accuracy is sought, and especially, where the diameter
of the tree is measured at 43 feet rather than guessed at, tables may
be compiled from the actual measurement of the upper diameters of
felled trees which show the average taper for each log, for trees of given
diameter and height, and with the width of bark actually measured
and deducted for the top of the butt log. These tables will enable
the cruiser to tally the sizes of his logs without relying on his eye for
more than the determination of total height or number of logs.
Log grades (§ 87), when used in timber estimating, require the tally
of the top diameter of the logs, separated into grades. This permits
of the separate totaling of volume in each log grade on the tract.
120. Log Run or Average Log Method. The tallying of the actual
size of every log on a tract is so slow and expensive that it is possible
only when the timber is large and scattered. Woodsmen, who use the
log as the unit of estimating, do not usually tally any sizes but obtain
the total number of logs on the area by five steps, namely:
1. A count of the trees.
2. Decision as to the average number of logs per tree. This may
be in halves or even quarters, as 3+ logs per tree, referring of course
to the standard length adopted for estimating.
3. The board-foot contents of an average log.
The last point is based on familiarity with the results of scaling logs
cut from similar timber, and the cruiser expresses it in terms of “ log
run” or number of logs required to scale 1000 board-feet of lumber,
as illustrated by the following figures:
Log Run. Contents of Average Log.
2 per 1000 board feet. 500 board feet.
5 per 1000 board feet. 200 board feet.
10 per 1000 board feet. 100 board feet.
20 per 1000 board feet. 50 board feet.
40 per 1000 board feet. 25 board feet.
The ‘log run” increases as the average log content diminishes.
Knowing the log run, or guessing at it, the estimate in board feet is
obtained by:
4. Multiplying the total number of trees by the number of logs per
tree.
5. Dividing the total number of logs by the log run or number of
logs in 1000 board feet of lumber.
This method was used by many old-time cruisers in the Lake States
region to the exclusion of all others. When old and young, or large
and small timber is found on the same tract, separate classes are usually
made in the count.
144 UNITS OF MEASUREMENT FOR STANDING TIMBER
121. The Tree as a Unit in Estimating. Volume Tables. The
necessity for combined speed and accuracy to reduce the cost and
increase the reliability of timber estimates has led to the almost uni-
versal substitution of the tree unit for the log unit. Instead of entering
the size of each log separately, the dimensions of the entire tree are
noted.
This requires that the volume of entire trees of the sizes tallied be
previously known. ‘The sum of the volume of the logs which they con-
tain gives this information. A table, in which the average volume
of trees of given sizes is shown, is termed a volume table, in contrast
to a log rule or log table, which gives only the contents of single logs
and never that of entire trees.
To avoid confusion in these terms, it should be noted that the stand~
ard definitions are:
For a log-volume table—the term, Log Rule.
For a tree-volume table—the term, Volume Table.
The latter term should never be used by foresters to mean the
contents of logs, although the term log table may be used. The term
“volume table ”’ always refers to the volume of trees, being substituted
for the longer descriptive term, Tree-volume Table.
Timber cruisers were slow to see the advantage of thus tabulating
or summing up the total volumes of trees in systematic form. They
either adhered to the log basis, or in the instances when they used the
tree volume as a unit, merely calculated this for “ average ”’ trees by
mentally summing up the contents of the logs in individual trees, and
from the general knowledge thus obtained, assuming that trees in a
given stand averaged or “ ran ’”’ a certain volume per tree. This method
was universally used in the South, where the Doyle rule readily lent
itself to quick mental computations of the contents of 16-foot logs
(subtract 4 inches from the diameter inside bark, and square the
remainder for board-foot contents of log, §65). The total count of
trees, multiplied by the average contents per tree, gave the estimate.
122. Volume Tables Based on Standard Tapers per Log. ‘‘ Uni-
versal’? Volume Tables. In the Pacific Northwest, the great height
of the trees and consequent large number of logs in each tree, and
the relatively few trees per acre, each with a large volume, soon brought
a realization of the need for substituting the tree unit for the log. The
difficulty of mentally computing the contents of trees varying so widely
in volume forced the use of the volume table, in which was recorded
the total volumes of trees of all sizes. These cruisers’ volume tables,
of which several have been constructed, are, in most instances, based
on the principle of uniform taper per log, varying from 2 to 10 inches.
The contents of successive logs, as scaled by the accepted log rule,
VOLUME TABLES BASED ON STANDARD TAPERS PER LOG 145
diminishing in top diameter by the indicated taper, are totaled, and
the sum taken as the volume of the tree. These computations do not
require the measurement of the tree but are performed in the office
from the log rule.
The volumes in such a table are the scaled contents of logs by a given log rule,
and will apply only to regions where this same log rule is used. But it is a simple
matter to compute a new table for any other log rule, by the same method, since
no field work is required. Wherever the log rule is the standard, such a table is
applied to all species, types and character of trees, and in this sense is universal.
The assumption underlying such a table is that the merchantable portion of all
trees have the shape of the frustums of cones, hence the determination of the three
factors, average taper per log, diameter at top of first log, and number of logs in
the tree, determine the scaled contents of the tree as given in the table. As shown
below, the assumption is not correct.
In applying this table, these cruisers seldom attempt to tally the dimensions
of each tree. The trees are counted, separately by species, and also by classes,
as large, medium or small. Then the average diameter, average number of logs per
tree, and average taper per log is decided on usually by guess or by judgment.
The volume table merely serves to give the assumed volume of a tree of this
diameter, height and taper. The estimate or total for the species is obtained by
multiplying this volume by the tree count.
The advantages of obtaining a universal and elastic volume table, applicable to
any species, region and character of timbers are self-evident. The defects in
uniform or universal volume tables based on the frustums of cones are:
1. The form of the average tree of any species, when the merchantable portion
only is considered, resembles more nearly the frustum of a paraboloid than that of
a cone (§ 26). While the merchantable portion may be treated as the frustum of
a cone, yet investigation shows that the average volume of trees of different species
and diameters is usually either less or greater than that assumed by the table.
This possible error is consistently neglected.
2. For accurate application, the universal table requires the determination of
three dimensions for every tree whose volume is to be ascertained, namely, diam-
eter, height and taper. A tally of every tree by diameter and height is possible,
but the separation of a third factor, tree by tree, makes the tally too complicated,
and requires the substitution of average tapers for a species, or for groups of
diameters as indicated above. But the trees in any given stand or area never taper
uniformly. The larger trees have the greater taper. Those growing in dense
stands have the least. No average can be found which will apply even to the
trees of one diameter class, much less to trees of all classes. The assumption of a
definite taper for the trees on a plot will tend to over-estimate the volume of trees
larger than the selected average tree, and under-estimate those of small diameter.
Whether these errors balance depends more on luck than on skill.
3. The use of such a table presupposes the system of counting rather than of
tallying each tree, and assumes the risk of error in selecting, largely by eye, an
average tree which, when multiplied by the count, will give the approximate
estimate. It does not lend itself to an accurate inventory of the timber, tree
by tree, in which the diameter and merchantable length of each tree is
recorded.
4. Since such tables assume that upper diameters differ by gradations of 1 inch
per log, a 4-log tree will show top diameters in the table differing by 4-inch classes,
146 UNITS OF MEASUREMENT FOR STANDING TIMBER
while the average taper may be somewhere between these limits and the volume
be given incorrectly by either the upper or lower class. A tree 20 inches at the top
of the first log will be classed as having a taper per log of 1 inch, 2 inches or 3 inches.
At the top of the fourth log, the first tree will measure 17 inches, the second tree,
14 inches, and the third, 11 inches. The actual average top diameter may fall at
12 inches or at 15 inches.
123. Substitution of Mill Factor for Log Rules in Universal Tables. In the
above tables, the contents of the logs are determined by the standard log rule
used in sealing. Dr. C. A. Schenck substituted what is termed the mill factor
for the log rule, thus basing the volume of the tree upon the sawed output (§ 116).
Assuming, as a basis, that the cubic contents of the cylinder measured at the small
end of the log, when multiplied by 12, gives the maximum board-foot contents
(§ 12), the waste for slabbing, edging and saw kerf, independent of taper, which is
not considered, will reduce this output to from 8 to 5 board feet per cubic foot.
The per cents of cubie contents of the cylinder based on small end of log, which
these mill factors represent are;
Sealed contents of
Cubic | __ nearest equivalent
Mill factor contents. log rule
(Table II, § 38).
Per cent Per cent
8 663 Vermont (63.4)
i 584 Caleasieu (57.8)
6 50 Orange River (50.9)
5 412 Delaware (42.4)
An example of these mill-factor tables is given on page 147, for logs 16 feet long:
To determine these values the volume in cubic feet of the cylinder was mul-
tiplied by 5, 6, 7 and 8 respectively. These tables give the cruiser the oppor-
tunity to substitute a fixed per cent of utilization, as indicated above, for a log
rule. The other three variables remain the same, namely, diameter, number of
logs and rate of taper per log.
It is assumed that the mill factor can be chosen to suit the local conditions of
milling, the factor 8 or 663 per cent representing the use of band saws in large mills,
while the factor 5 approximates the conditions in small-local circular-saw hard-
wood mills, thus making the cruiser independent of log rules. This apparent
advantage is nullified by two serious defects: First, the taper of the log is neglected,
and this frequently produces a mill factor of 10 for large logs. Second, the board-
foot contents is assumed to vary directly as the cubic contents, so that the tables
force the use of log rules based on cubic rather than sawed products and introduce
the errors of this method. Mill factors inerease directly with the average diameter
of the log independent of mill practice. It is not sufficient merely to know the
general character of the milling, but the sizes of the timber must also be known.
An average mill factor based on both of these variables may be seriously in error
and the use of different mill factors for logs or trees of different sizes is apparently
necessary to secure accuracy. The use of these tables is therefore not as satis-
factory as their apparent simplicity seems to indicate.
VOLUME TABLES BASED ON ACTUAL VOLUMES OF TREES 147
TABLE XXVI
A PortTION oF A VOLUME TABLE Basep on Mini Factors
Trees measuring 9 inches at top of first 16-foot log, inside bark
TAPER PER Loa
16-foot Mill factor 1 inch | 2 inches | 3 inches | 4 inches
logs * HK |
Board feet
5 31 Sill 31 31
1 6 37 OM 3G oh
7 43 43 43 43
8 57 57 57 57
55 55 49 45 40
9 6 66 59 54 48
o od 69 62 57
8 89 79 7A 65
5 74 59
3 6 89 71
7 104. 83
8 118 95
124. Volume Tables Based on Actual Volumes of Trees. Volume
tables as used by foresters are based on the measurement of the actual
contents of entire trees, and not upon assumed regular taper or conical
form. The tree contents or volume table may give,
Entire cubic contents of stem, with bark, or without bark.
Merchantable cubic contents of stem, or of stem and larger
branches, with or without bark.
Merchantable contents of stem in terms of
Board feet
By a given log rule.
By mill tally, under given conditions of sawing.
Other units, such as
Standard cross ties.
Poles, or posts.
Staves or headings.
Cords, usually converted from cubic feet.
148 UNITS OF MEASUREMENT FOR STANDING TIMBER
Combination Volume Tables giving the merchantable volume in
Ties, and residual cords.
Board feet, and residual cords and other combinations.
Graded Volume Tables, giving the volume in
Board feet, by lumber grades.
Logs, by log grades.
The use of the last-named type has not yet been attempted.
Volume tables of this character make possible the tallying of every
tree, eliminate the risk of averaging the dimensions or volume of trees
counted, and require of the cruiser only the recording of diameters
and of heights, and discounts for defect.
Since trees vary so widely in form, height and taper, and the table
is implicitly relied on to give correctly the variable volumes caused
by these factors, without measuring the taper, the use of such tables
and their reliability or accuracy must be thoroughly understood, or
it may easily lead to errors of greater magnitude than those incurred
by an experienced cruiser using the universal ‘ taper ”’ table for volumes
(§ 149).
The greatest drawback in the use of specific volume tables is the
number of tables required, and the cost of their preparation. Species
may differ from each other in form or bark thickness, so as to require
separate volume tables. Substitution of a table made for one species
for use with a different species is justifiable only when research has
shown the two species to possess the same bark thickness and average
form. .
Tables made for one unit of measure, or even for a given log rule
are not serviceable for a different unit or log rule. Tables of merchant-
able volume, accurate for 4 given standard of tree utilization, become
obsolete when a closer standard is adopted. For these reasons, and
owing to the great number of species, range of conditions, difference in
log rules, and variety of products, the cruiser entering a new region
is usually confronted with a lack of tables, and is driven to adopt
either the universal taper system, or the log, as his means of estimating
volumes. The adoption of a universal cubic-foot basis for volume
would greatly simplify the problem of volume tables.
125. The Point of Measurement of Diameters in Volume Tables.
Either of the above types of volume table shows volumes for trees of
given diameters and heights. The diameter must be measured near
the base of the tree, where it can be reached with calipers or tape.
But there is no regularity about the flare of the butts of trees, for this
is determined by exposure to wind strain, by the size of the bole, the
site and the species. Butt swelling increases more rapidly with age
than does the diameter of the bole, so that the older and larger the tree,
DIAMETERS IN VOLUME TABLES 149
the more pronounced this swelling, and the further it extends up the
trunk. Tree volumes must be averaged on the basis of their diameter
in inches. If this diameter is taken at some point on the butt swelling,
a tree with a rapid butt swelling will have a far smaller volume than
one of the same stump diameter and a gradual swelling, as is illus-
trated in Fig. 24 by trees A and B. But if these diameters were taken
at a point above the butt swelling the two trees would properly fall
into different classes. Since it is necessary to put in a single class
trees whose volumes are as nearly similar as possible (trees A and ©),
the practice of classifying these trees by their diameter on the stump
is inaccurate. The height of stump itself is also a variable. Tables
A B C
Fic. 24—Comparison of stump height and breast height as points of measurement
to determine the diameter of standing trees.
based upon “ diameter at the stump,” which do not indicate at what
height this diameter is measured, are difficult to apply and unreliable.
For very large trees with excessive butt swelling such as cypress,
or many West Coast species, the diameter classes should be based
upon measurements takea above this swelling. A standard form of
universal table used on the Pacific Coast is based on a butt measure-
ment to be taken 1 foot above the point where the butt swelling ceases.
The disadvantage of measuring at a variable height is considered as
offset by the merit of avoiding this variable factor of butt swelling.
In cypress, one typical table was based on diameter at 20 feet from
the ground and cruisers customarily estimate cypress trees from the
diameter obtained above the butt swelling.
150 UNITS OF MEASUREMENT FOR STANDING TIMBER
For most species, the point 43 feet above ground has been accepted
by foresters for measurement of diameter as it falls above the swell-
ing and at a convenient height for use of calipers. This height is also
used in England and India. In Continental Europe, 1.3 meters, or
4.3 feet, is the standard height.
This measurement at 43 feet is termed diameter breast high, and
is abbreviated both in speech and record to D.B.H. Measurement
outside bark is always indicated by the abbreviation.
In the Philippines and other tropical countries it will be impossible
to use a similar height for many species owing to the development
of buttresses on the trunks. Such species will probably have to be
measured either above the flare, or at a height of 16 to 20 feet, by
eye, using the 43 foot standard point only for species and types which
permit it.
Where D.B.H. is adhered to for species like Western larch, red
cedar or Douglas fir.on the Pacific Coast, butt swelling greatly inter-
feres with the uniformity of the volumes for these species for trees of
given diameters when compared with other species like western yellow
pine whose swelling seldom reaches this height. This apparent dif-
ference in volume may be from 20 to 40 per cent in favor of the pine.
126. Bark as Affecting Diameter in Volume Tables. [or species
whose bark is of uniform thickness for trees of the same D.B.H., the
diameter taken outside the bark is preferable as a standard of classi-
fication to diameter inside the bark. The cruiser has no time to measure
bark thickness except on occasional test trees. The width of bark,
however, is seldom uniform. For trees of the same diameter, it is thick-
est on exposed and on rapidly growing trees, and thinnest on sheltered,
crowded and slow-growing or suppressed trees (§ 113). The larger
the trees, the greater the actual thickness of bark, and the wider the
possible variation in thickness. This thickness may range from 2
to 5 inches and over, on West Coast species. Volume tables based
on diameter inside bark, therefore, are more consistent and accurate
as tables, than those based on outside bark measurement.
But this would require the tallyman to throw off the double width
of bark from every tree tallied. The experienced cruiser, who deals
with single average trees only, can from his experience throw off the
proper average width of bark for the selected tree, increasing the deduc-
tion for open and exposed situations and vice versa. There is no
such choice in the tally of every tree. The mistakes made in mental
arithmetic and the errors in guessing the proper width of bark to allow
would be more serious than discrepancies in the table. In practice,
then, D.B.H. would have to be recorded and average bark thickness
afterwards deducted previous to computing the volume.
CLASSIFICATION OF TREES BY DIAMETER 151
Species with thick bark will show a smaller volume for the same
diameters than those with thin bark, because of taking the diameter
on the bark surface and not on the wood. Individual trees with thick
bark will give correspondingly less volume than the average for the
diameter class shown in the table. Timber on exposed sites will be
over-estimated by tables based on diameter outside bark unless con-
structed locally for the same sites. Width of bark, therefore, is a cause
of variation in the attempted standardization of volume by diameter
classes, which is eliminated in the universal tables when these are based
on diameter inside bark, at either top of log, D.B.H., or stump.
127. Classification of Trees by Diameter. Standard volume tables
are commonly based on D.B.H. outside bark. The actual diameter
of trees can be measured as closely as the nearest 75-inch. The aver-
age of two measurements taken at right angles is considered the diam-
eter of the tree.
For felled trees whose volume is to be measured in the construction
of volume tables, the diameters are recorded to the nearest actual
jo-inch. But these volumes are classified later by 1-inch, or 2-inch
classes. One-inch classes have been adopted as standard for Eastern
species, while in the West, owing to the greater range of diameters
encountered, 2-inch classes are deemed sufficient. Each 1-inch class
includes all trees whose average D.B.H. is above .5 in the inch below,
and .5 and under in the given inch class; e.g., the 9-inch class includes
trees measuring 8.6 to 9.5 inches. In 2-inch classes, the even inch is
used. A 10-inch class would include trees measuring 9.1 to 11.0
inches.
128. Classification of Trees by Height. Height is never used as
the sole basis of tree classes; diameter is the fundamental basis of
classification. But height exerts an enormous influence on the volumes
of trees of the same D.B.H., the extreme difference in volumes for dif-
ferent heights being more than 100 per cent. These differences in height
and volume for trees of the same diameters occur in stands of different
density, growing on different qualities of site, or at different altitudes.
They correspond with differences in the average taper per log, as dis-
tinguished in universal volume tables.
It follows that the separation of trees of a given diameter class into
several height classes previous to averaging their volumes is another
way of distinguishing between trees of gradual and of rapid taper,
and that if enough of these height classes are made, the differences in
volume due to more or less rapid taper are distinguished even more
accurately than by introducing taper as a factor in the table. The
height, rather than any arbitrary amount of taper, is the real basis of
classification, and the actual average volume, rather than an assumed
152 UNITS OF MEASUREMENT FOR STANDING TIMBER
volume, is then expressed in the table. The rate of taper for trees in
different height classes within any diameter class, as 20 inches D.B.H.,
need not be shown in such tables. If measured, it will be found to differ
by arbitrary fractions of inches instead of by exact 1l-inch classes per
standard log.
Height classes may be based on total height, or on the length of the
merchantable bole. In the former case, height classes are based on
either 5- or 10-foot gradations, using the same system of rounding
off as for diameters, e.g., the 70-foot height class with 10-foot gradations
includes all trees 66 to 75 feet in height. With 5-foot gradations, it
includes trees 68 to 72 feet in height. When merchantable heights
are used, these lengths are commonly standardized to conform to a
common log length such as 16 feet and expressed as 1, 2, 3 or more log
trees. The log length used is always stated. Half-log lengths may be
differentiated. With valuable hardwoods of variable merchantable
length, there is some need for closer classification of merchantable
lengths, but volume tables are seldom constructed for intervals of less
than 8 feet.
129. Diameter Alone, Versus Diameter and Height, as Basis of
Volume Tables. To separate or classify the volumes of trees of each
given diameter class into from 4 to 10 height classes requires the measure-
ment of from 250 to 1000 trees, in order that the average volume in
each of these numerous classes may be found with some accuracy
(§ 137). This makes it impossible to take the time to construct such
tables for local or immediate use. Hence many volume tables have
been based on diameter alone, averaging together trees of all heights.
Sometimes the average heights of the trees of each diameter class are
shown, often they are omitted.
For timber of uniform age and density of stand and growing on the
same quality of site, individual trees of the same diameter will still
differ considerably in height and volume; yet an average height for
each diameter may be found, which will indicate quite closely the
average volume for that particular stand or type and age class. But
such a volume table is quite worthless for application to any other
stand, age class or type, unless it can first be shown that the average
heights based on diameter are the same in both cases. Lacking,
first, the knowledge of the average heights used in the table, and second,
the demonstration that these coincide with those of the stand to be
estimated, the only possible procedure is the preparation of an entirely
new volume table.
But with a table based on a classification of heights and correspond-
ing volumes under each diameter class, stands of any degree of density
or age, and growing on any site, may be estimated by use of this table,
STANDARD VERSUS LOCAL VOLUME TABLES 153
if the volumes taken from the table are those for heights correspond-
ing to the trees in the stand.
130. Standard Versus Local Volume Tables. Volume Tables based
on both diameter and height classes, in whose construction from 500
to several thousand trees have been used, selected from as wide a range
of sites and locations as possible, are termed Standard Volume Tables,
while those based on diameter, either alone or with the average height
of trees of each diameter class stated, and applicable only to a given
stand or site, are known as Local Volume Tables.
It follows that local volume tables applicable to any stand, age
or site can be derived from the values given in a standard volume table
and can be expressed on the basis of diameter alone by first determin-
ing, for the stand, the average height to use for each diameter class.
Classification by both diameter and by height is not sufficient to
secure complete accuracy in volume tables because of differences in
average form (§ 166). But such tables, well constructed, are vastly
more accurate than any universal table based on uniform tapers, or
frustums of cones, and are known to apply with almost the same degree
of accuracy throughout the entire range of a species. Greater vari-
ation in form and volume of stand is caused by differences in soil, expo-
sure and density in a restricted locality than by a thousand miles dif-
ference in location.
CHAPTER: Xa
THE CONSTRUCTION OF STANDARD VOLUME TABLES FOR
TOTAL CUBIC CONTENTS
131. Steps in Construction of a Standard Volume Table. The
steps in the construction of a standard volume table, whether for total
cubie contents, or for any form of product, are practically the same.
They are:
1. Selection of felled trees in sufficient number, and representing
the complete range of diameter and height classes of the species or
locality.
2. Measurement of each tree to secure all the data needed for the
construction of the volume table.
3. Computation of volume of each tree.
4. Classification of tree volumes according to diameter and height
classes.
5. Averaging the volumes of trees of each separate diameter and
height class.
6. Elimination of irregularities in final table by graphic plotting
and curves.
132. Selection of Trees for Measurement. As only felled trees
can be measured with the accuracy needed for construction of volume
tables, the choice is presented of utilizing timber already felled, either
by wind, or by loggers, or of felling the trees for measurement. Wind-
fallen trees are usually of the larger sizes, and scattered individually
or in groups, and are measured more as a check on rough methods
of estimating than in the systematic construction of tables. A logging
job presents the opportunity to secure trees of all diameters except
those below merchantable size. The operation may be too local in
extent to embrace the extreme forms desired, and a standard table
covering the extremes of diameters and complete range of heights
should be based on trees cut from several different operations covering
the range of altitude and soil qualities for the species or type.
The influence of soil, altitude, age and other factors upon the form
of trees of the same diameter and height class is discussed in Chapter
XVI. When it can be shown that differences in volume can be cor-
related with age, or site, separate standard tables may be constructed
for trees of the specified classes or sites. In this case, the same principle
154
THE TREE RECORD 155
of securing as wide a range of diameter and height classes as possible,
by distributing the selection of the trees, applies within the limits of
the predetermined region, type or age class.
The number of trees necessary to secure a good basis for a volume
table increases with the range of diameter and height. Ten trees in
each separate diameter and height class will suffice, and only in a few
standard tables has this number been secured. This would call for a
total of 500 to 2500 trees. Ordinarily, a sufficient number of trees
is easily obtained for the smaller and more common diameter and height
groups, but the material becomes scarce as the larger sizes are reached.
The graphic methods of averaging are chiefly useful in overcoming this
deficiency ($138). The use of form factors also facilitates the con-
struction of tables from fewer trees (§ 175). Standard tables, com-
puted by averaging the volumes of trees by the method given in this
chapter should be based on at least 300 trees, and if used as a general
reference table should never have less than 500 and preferably over
1000 trees. Local tables based on diameter alone can be made from
10 to 50 trees. It is desirable to tabulate the number of trees measured
in each diameter and height class in the field as the work progresses,
and to make a special effort to find trees of the less numerous sizes to
fill out the table. On the other hand, the more common sizes should
be represented by somewhat greater numbers of trees in the table
than odd sizes, as errors in the table affect the results of estimating
in proportion to the per cent of volume of the stand which falls in
the specified classes.
To secure trees of smaller sizes than are considered merchantable
by loggers, in order to show total cubic contents for these classes, or
contents in terms of smaller products not being utilized in that locality,
the trees may be felled by the mensuration crew. This must be done
for all sizes in absence of logging, but it adds greatly to the time and
cost of the work.
133. The Tree Record. The data for each tree must be entered
on a separate blank, or printed form, and headed by the items,
Species,
Locality,
Date,
Name of investigator,
Number of analysis.
Records should be carefully filled in with legible figures, using a
4H or 6H pencil. They constitute permanent records of tree form
and may be available for use in compiling data many years afterward.
Description of site factors are useful in determining their influence,
if any, on the form and volume of trees of the same diameter and height.
156 CONSTRUCTION OF STANDARD VOLUME TABLES
These are,
Soil, origin, whether sedimentary or residual.
Depth, rock, physical character, sand, ete.
Exposure and slope.
Altitude.
Forest type.
Character and density of stand.
These items involve considerable repetition and are often omitted,
or may be written up for groups of trees. But if the material is to be
used for investigations, to determine the effect of site factors on form,
each tree analysis should be associated with a complete description
covering the points enumerated.
134. Measurements of the Tree Required for Classification. The
measurements of the felled tree must be taken before the logs are
removed by skidding. These may be divided according to their pur-
pose into those needed to
1. Classify the tree by dimensions and character.
2. Obtain the volume of the stem and branches.
The first class of measurements consists of D.B.H., height of stump,
total height, crown and bole. The D.B.H. (§ 125) is the most important
measurement taken. This point must be located on the butt log of
felled trees, unless the D.B.H. has been taken in advance of felling
the tree. To the stump height is added the additional height needed
to equal 44 feet, which is measured upon the butt log. If the butt cut
is slanting, care is taken to measure from the same point on the log as
on the stump, thus reproducing the measurement which would be taken
on the standing tree—otherwise a slight error is incurred. The D.B.H.
and all other measurements of diameter are taken in two directions,
at right angles. This is always possible on the felled trees as shown
in Fig. 25.
The average of these two diameters is obtained and recorded to
the nearest 75-inch, and is never rounded off to the nearest inch.
The height of stump is taken not only to obtain D.B.H. on felled
trees, but as a basis from which merchantable length and contents
is figured (Chapter XII). It is recorded in feet and tenths, or in feet
and inches. Stump height is measured vertically from the root collar
or point of contact with the ground, and at the average height of this
collar. On side hills, this point occurs half way between the upper
and lower sides of the stump.
The total height of every tree measured for volume should be recorded,
whether or not it is to be used as a basis of height classification (§ 137).
The most accurate method is to stretch a steel tape from the butt to
tip of crown, along the stem, although a pole graduated in feet is some-
MEASUREMENTS OF TREE REQUIRED FOR CLASSIFICATION 157
times substituted. To this height the stump height is added, and the
total recorded to the nearest foot. The height of a rounded or irregular
crown is measured to a line drawn at right angles to the bole, and tan-
gent to the highest point of crown. Height may also be obtained by
adding together the lengths of the separate sections of the bole, plus
the distance from the top of last section to tip of trees.
Character of crown may or may not be required. It is useful in
hardwoods where separate tree classes may be desired, and in any
-species where growth is being investigated and as the index of
form, as indicated -in Chapter XVI. On felled trees, two measure-
ments are taken. Width of crown is measured as the tree lies, at
widest point, at right angles to stem. Length of crown is the dis-
Fic. 25.—Method of measuring a log twice at right angles to obtain the average
diameter.
tance from tip to the point where the lowest vigorous and well-shaped
green branch joins the bole, or better still, at a point on the bole, oppo-
site the lower limit of the green crown or foliage. Some judgment is
required in excluding from crown-length small, feeble or straggling
single live branches which may have survived by accident on one side
but do not form part of the main crown of the tree. Dead branches
or knots form no part of the crown.
The position or class of the crown in the stand may also be described,
as open-grown, dominant, co-dominant, intermediate, or overtopped.
This is best judged before felling.
The following definitions have been adopted as standard by the Society of
American Foresters.
Crown Class. All trees in a stand occupying a similar position in the crown
cover. The crown classes usually distinguished are:
158 CONSTRUCTION OF STANDARD VOLUME TABLES
Dominant. Trees with crowns extending above the general level of the forest
canopy and receiving full light from above and partly from the side; larger than
the average trees in the stand, and with crowns well developed but possibly some-
what crowded on the sides.
Co-dominant. Trees with crowns forming the general level of the forest canopy
and receiving full light from above but comparatively little from the sides; usually
with medium-sized crowns more or less crowded on the sides.
Intermediate. Trees with crowns below, but still extending into the general
level of the forest canopy, receiving a little direct lght from above, but
none from the sides; usually with small crowns considerably crowded on the
sides.
Overtopped. Trees with crowns entirely below the general forest ‘canopy and
receiving no direct light either from above or from the sides. These may be
further divided into oppressed, usually with small, poorly developed crowns, still
alive, and possibly able to recover; and suppressed or dying and dead.
As currently used, overtopped trees are now classed as suppressed; and an
additional class, open-grown, is added, consisting of trees standing alone with
crown free on all sides.
The bole is not described unless there is some marked peculiarity
which may explain an abnormal shape or volume and enable the investi-
gator later to decide whether to use or reject it in his tables. Such
peculiarities include forks, dead tops, abnormal or swollen butts, especi-
ally if the D.B.H. is affected, or other deformities in shape. The pres-
ence of rot, shake, or other internal defects may be noted, but does
not influence the subsequent measurements (§ 156) or volume of the
tree, unless its form is affected abnormally, as sometimes happens
when rot at the butt causes abnormal butt swelling extending beyond
DB:
135. Measurements Required to Obtain the Volume of the Tree.
Systems Used. While the object of measurements of the stem is to
obtain its volume, these also serve to record the form of the bole. The
diameter is taken (§ 29) at definite points, dividing the bole into lengths
which are recorded consecutively. The cubic volume of round logs
of any length is easily computed from the end diameters (Smalian
formula) if the proper precautions are taken to guard against the influ-
ence of butt swelling (§ 29). But if the recorded diameters or form
of the trees are to be used to get average form or taper (§ 166) as well
as merely for volume, these measurements should be taken at the same
heights or intervals on all trees.
For cubic volume, the log lengths into which the bole is cut by the
loggers may be disregarded. This factor would exert no appreciable
influence on the tree contents when the full volume of each log is accu-
rately obtained.
There are three systems of taking these upper diameter or taper
measurements, as follows (Fig. 30, § 155):
VOLUME OF THE TREE. SYSTEMS USED 159
System A. Disregard stump height. Take diameter at every
10 feet from ground to tip. Record length of tip above last 10-foot
taper.
This method permits of accurate averaging of these diameters on
different trees to obtain average form, and also gives the total cubic
volume of the tree. But it is unsafe to rely solely upon these measure-
ments for the volume of the first 10-foot log, which should be supple-
mented by stump taper measurements, taken at 1, 2, 3, 4 and 43 feet
from the ground. This gives a complete record of form and an accu-
rate basis for total volume.
By means of form or taper tables (§ 167) based on these measure-
ments, the diameters at any other points may be obtained from dia-
grams, and the volume of the tree can then be calculated for any unit
of product.
System B. This method is a compromise between measurements
intended solely to secure form or total cubic volume, and those required
for merchantable volume (§ 145). The height of stump is first recorded
and the height of upper diameters is then taken from the stump as a
base. As stump height tends to increase with diameter of tree, the
upper measurements of larger trees fall at higher points on the bole,
by just the difference in stump heights. This inaccuracy is usually
accepted and the diameters which fall at equal height above the stump
are averaged together.
The length of log or interval adopted for upper diameter or taper
measurements by this method is a multiple of 4 feet. Four-foot inter-
vals give closest results, and correspond to cordwood lengths. A more
common interval is 8 feet, corresponding with the standard length of
cross-ties. Greater lengths give less accurate permanent data. If
only the 16-foot tapers are required for the immediate purpose of the
table, it is comparatively little extra work to take the 8-foot points
as well, for future use if needed.
System C. By this method the logs as cut by the sawyers are
measured as they le, for diameter and length. As these commercial
lengths vary, the taper measurements for different trees will fall at
several different points even for the first log, and require tabulation
at 2-foot intervals. Except when measured for total cubie feet, the
resultant, volumes will vary according to the lengths cut (§ 48), and
not solely according to the dimensions of the tree as by Systems A
and B. No advantage is gained by the securing of volume correspond-
ing to the used lengths of the tree measured, since in every logging
‘job, the average of lengths used will differ. This method is therefore
inadvisable. But a record can be made on the analysis blank of the
log lengths actually cut, and their scaled contents, to determine the
CONSTRUCTION OF STANDARD VOLUME TABLES
160
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COMPUTATION OF VOLUME OF THE TREE 161
difference between volumes as cut and sealed, and volumes from regular
tapers.
In case the study of the growth of trees at upper sections is required
(§ 289) either the trees will have to be felled and bucked into sections
of even lengths by System A or System B, or else the logs as cut by
System C must be accepted as the basis of this growth study.
For total cubic volume, the taper measurements are continued
to the tip in either system. With slight additional cost, these extra
measurements taken above the merchantable top diameter limit com-
plete a permanent record of tree form available for future computa-
tion of volume for any unit or limit of merchantable sizes.
A further modification is the addition of trimming lengths, usually
standardized as ;%o-feet in 16 feet, so that the points marked fall at
8.15 feet, 16.3 feet, 24.45 feet, ete. If this is done the fact should be
be noted on the analysis. Total cubic volume is obtained as accurately
by this method as by System A, and in addition, the data can be used
directly to determine the volume in board feet. It is therefore pref-
erable for most objects to System A.
The width, single, of bark is measured at each diameter (§ 29), and
recorded as read. This width is then doubled and subtracted to
obtain diameter inside bark.!
If the volume of sapwood is desired, this will require the sectioning
of the tree, and measurement of width of sap. Sapwood volume is
therefore most easily obtained by System C.
The measurements are entered on a blank, of which an example
is shown on p. 160.
This completes the field record. The remainder of the work is
performed at any time in the office.
The crew for field measurements of volume, when the trees are
already felled, should consist of two to three men, one of whom records
the data while the others measure the tree.
136. Computation of Volume of the Tree. For total cubic volume,
each section is usually computed by the Smalian or mean end formula
in which
B=area of large end of section in square feet;
b=area of small end of section in square feet;
l=length of section in feet;
V =cubic volume.
1 Abbreviations are used, as follows:
Diameter outside bark, D.O.B.
Diameter inside bark, D.I,B.
162 CONSTRUCTION OF STANDARD VOLUME TABLES
Then
_ (BH
laa (FP)
2 (B+b)5.
For the sum of the volumes of the sections each end area except
the first and last is evidently used twice. A series of three such sec-
tions would total
ye (FF) (> i+ (" yo
When, as in systems A and B, equal lengths of section (J) are used,
the formula can be expressed
= (B+2+20+0")5 = (FS +5+0')1,
i.e., average the first and last basal areas, and add the remaining areas.
Then multiply by length of one section to obtain the sum of volumes
of the sections.
The areas in square feet, corresponding to the diameters of each
section are found in Table LX XVIII, Appendix C, p. 490.
Sections different in length from the standard must be computed
separately.
The tip, beyond the last taper, is computed as a paraboloid, by the
same formula,
V= (CF )i=3t
The volume of stump, needed to complete the tree when system B
is used, is standardized by custom as a cylinder, whose diameter is that
of the stump section, thus neglecting the variable factor of stump
taper. Its volume is therefore
V=BIL
System A permits the volume of the section up to 4 or 43 feet to be
computed accurately if desired.
Owing to the serious error incurred by measuring the butt section
by the Smalian method, the use of Huber’s formula for the first 8- or
16-foot log may give more consistent results. In this case, for a 16-
foot log (l) the basal area at 8 feet (b’) gives the log volume, or
V=6'l.
A check should be made by this method against the Smalian method
for the butt section (§ 29).
The total cubic volume of branches and twigs is practically never
CLASSIFICATION AND AVERAGING OF TREE VOLUMES _ 163
computed. The measurement of merchantable volume of limbs and
branches is discussed in § 146.
For obtaining the total volume of the tree bole exclusive of branches
by regarding the bole as a complete paraboloid, the so-called Schiffel’s
Formula may be applied. For this purpose the area of the cross
section at D.B.H., and one at one-half height above stump is obtained
and applied, thus:
V =(.16 B+.66 63)h ($177).
Volume of Bark. The volume of the tree may be computed from
D.O.B. to give total cubic contents with bark. It is then computed,
if necessary, from the D.I.B., to give the peeled contents or wood
without bark. The volume of bark is obtained by subtraction of the
second from the first result.
Volume tables give the volume with bark, or without bark, accord-
ing to the use to which wood is put and the form in which it is sold.
When the peeled volumes are given, the per cent of bark in terms of
peeled volume may be shown for each diameter.
137. Classification and Averaging of Tree Volumes According to
Diameter and Height Classes. 1. The separate sheets are now sorted
first into diameter classes (§ 127).
2. The height classes, for tables giving total cubic volume, are based
on total height of tree. Whether 10-foot, or 5-foot classes are used
depends on the total height of the species. For second-growth hard-
woods or small timber, 5-foot classes are preferred, while in the extremely
tall timber of the West Coast, 20-foot classes are sometimes sufficient.
For either standard, trees are placed nearest their actual height. The
trees of each diameter class are now sorted into their respective height
classes. The trees in each separate diameter and height class are then
checked to see that no mistakes of classification have been made.
3. The average volume is found for the trees of each separate group
or class comprising all trees falling in the same diameter and height
class.
If trees having the same diameter and height had similar forms,
the volumes of all trees in any one diameter and height class would
be equal, except for the differences due to the fact that the actual
diameter, or height, though falling within the size limits required, may
be larger or smaller than the exact standard size of the class.
But variation in the form of the bole is a third factor which causes
considerable variation in volume for trees of the same total height
and diameter (§ 166). Trees whose form is full, lying between the
paraboloid and the cylinder, have a correspondingly greater volume
than trees with a form lying between the paraboloid and cone, or neiloid
164 CONSTRUCTION OF STANDARD VOLUME TABLES
(§ 26). The extreme range of volume caused by differences of form
alone for trees of the same height and D.B.H. is as much as 40 per cent.
Even the average volume of trees of the same ages or sites may differ
by more than 20 per cent.
The volume of single trees follow the general law of averages.
Those which depart most widely from this law are few in number,
while a range of 5 per cent above or below the average would probably
include by far the larger number of trees in fairly uniform stands.
When the exact volume of a specific tree is wanted it is unsafe to
assume that this tree is an average specimen. It must be measured
separately. But in estimating standing timber, the object sought is the
total volume of the stand, or the sum of all trees. If the average vol-
ume of trees of each size class is correctly given in a volume table,
the cruiser can assume that every tree tallied is an average tree, and
the result or total will be the same as if the true volume of each sepa-
rate tree were measured.
This averaging of the variable individual volumes of trees of each
class to obtain a reliable average volume is the principal service rendered
by volume tables. The timber cruiser stretches this same principle
much farther when he attempts to average the volumes of trees of totally
different diameters and heights, and the chances for error are much
greater, especially as this is usually a mental process or guess, while
the averaging of trees in a volume table is a calculation based on exact
measurements.
The method of obtaining the average volume of trees for a given
size is as follows. Enter ona sheet, labeled with the diameter and height
class, the data for each tree, according to the illustration given below
for four trees. Place at top of sheet the tree class, e.g.,
13 IncHEs—60 FEET
Diameter. Height. Volume with bark.
Inches Feet Cubic feet
12 56 59.0
il 58 63.2
13.4 61 66.0
68.2
256.4
CLASSIFICATION AND AVERAGING OF TREE VOLUMES
PRELIMINARY AVERAGES FOR PitcH PINE.
DIAMETER AND ToTaL HEIGHT.
D.B.H.
Inches
7
165
TABLE XXVII
VoLuME TABLE BASED ON
139 TREES
HeicuHt CLassEsS—FEET
50 55
7.5 1
6.96
52.6
8.0 1
8.73
52.0
60 65 | 70 75 80
1022) 1/9275: 4
14.88
53.4
11.5 110.9 6
17.67
55.6
12.3 112.3 6
17.93 24.18
52.0 55.1
4113.1 11
26.23
54.2
10.0
17.37
58.1
110.5 2
19.05
65.8
3) REDE
23.35
63.2
na bet
19.78
59.35
12.2 812.0 1
24.27 26.09
59.6 63.0
13.15 4/13.4 2
27.53 34.27
59.25 65.0
10
aii!
12
Legend 13
D.B.H. No. 14
Inches Trees
Cubic
feet 15
Total
Height
F
eet 16
17
18
19
20
139) 16
31.8
56.6
2)15:1 1
36.1
57.0
14.7
32.9
51.5
16.3 2
37.15
54.5
Nay 78)
44.67
54.8
1)14.3 2
46.1
78.0
14.0 914.1 514.1
31.61 34.05 42.32
60.3 64.1 68.5
2|13.6
38.92
73.4
2|15.0 1
43.55
77.0
3)15.2 4/15.1
39.96 45.3
64.2 68.8
15.1
39.44
60.2
LGR ad|honOs oGri peso
43.71 44.69 49.21
59.8 64.9 69.3
Ze Ooms
65.14
78.0
16.7 | 2/16..8
47.26 47.82
60.0 64.8
2)17.1
51.3
68.0
1)17.1
55.57
73.45
LEO LU TSAOy 4 Ss3 79 2
54.82 61.57 59.25
60.0 64.25 68.1
182659 TON 31920)" 2
60.45 65.27 71.82
66.0 70.2 74.0
166 CONSTRUCTION OF STANDARD VOLUME TABLES
The quotients represent respectively the actual average diameter,
height and volume for the class. These data, together with the number
of trees measured in each class, are entered on a large sheet in the form
shown in Table XX VII, p. 165, and constitute the basic or rough table
which is the first step in preparing a standard volume table. Thus
64.1 cubic feet is not the average volume for 13-inch trees 60 feet high
but for trees averaging 13.15 inches and 59.25 feet in height.
138. The Graphic Plotting of Data—Its Advantages. The volumes shown in
such a table should increase with both diameter and height. If sufficient basic
data has been obtained, this rate of increase in the values of the table, both verti-
cally and horizontally, will follow the law of averages which expresses the true
relation of the two variables; for the vertical columns, volume and diameter; for
the horizontal, volume and height. But where only a few trees are obtained in a
class, these trees may not only be larger or smaller in diameter and height than the
true average, but may have too full or too slender a form, and the average of their
volumes will be correspondingly higher or lower than the regular progression to be
expected. The form of this progression or increase will be determined by the
character of the two variables. For cubic volume based on diameter, with trees
of the same height and form, the increase in volume will be proportional to D?.
If these values are plotted on cross-section paper, the result will be a curve showing
graphically to the eye the law of increase in volume based on diameter.
The increase in volume based on height can be shown in a similar manner by
plotting the volumes and heights. This curve will differ in shape from the first,
since volume tends to increase directly as height for trees of the same diameter,
and the curve showing this approaches a straight line. When thus presented to
the eye, any irregularities or inconsistencies in the average volumes obtained in
Table X XVII become evident at once, while to detect them by mere examination
or checking of the arithmetical table would be far from satisfactory.
Since such irregular values do not conform to the general law of increase in
volume based on diameter and height, they cannot be depended upon to give the
true average volume of all the trees of a size class. One of two things must now
be done—either more data must be collected in the field in order to improve these
averages, or the averages obtained must be harmonized, and these irregular values
changed or corrected. The irregular volumes plotted would be based on sufficient
field data to bring out the real tendency or character of the law of the relations
sought. The minor irregularities in this case are not serious enough to prevent a
fairly accurate approximation of this law and a drawing of the curve as indicated
by the data.
The principles of graphic plotting are treated in analytical geometry, or graphic
algebra. The relation of the two variable quantities is shown by a series of plotted
points in which the horizontal and vertical lines each represent a scale of values
corresponding to one of the quantities or variables. Both being positive quantities,
the lower left-hand corner of the chart is taken as zero, or the origin. The hori-
zontal line passing through this point along the base of the sheet is the axis of
abscissee or horizontal scale, and the abscissa or value of each point is measured
parallel with this axis or along the scale thus indicated. The vertical line through
the origin, forming the left margin of sheet is the axis of ordinates or vertical scale.
The zero, or intersection of these two axes, is usually located to the right and above
the extreme lower corner of the sheet to give a margin for entering the scales. The
THE GRAPHIC PLOTTING OF DATA 167
scale of diameters, by inches, is then placed along the horizontal scale while the
volume scale is entered on the vertical scale. The whole forms a system of rectan-
gular co-ordinates. Each point on the paper represents two quantities, a diameter,
measured parallel with the base, and forming the abscissa of the point, and a
volume, measured vertically, and forming an ordinate. This is illustrated by
Fig. 26.
In this figure, the volumes of three average trees, or the averages volumes of
three groups of trees have been plotted, namely, 10-inch, 13.15-inch and 16.1-inch
trees. The horizontal and vertical values of each point are indicated by dotted
lines. If the theoretical
relation of volume, and
diameter for all points
is as y to px? we would
not only expect y (vol-
ume) to increase faster
than x (diameter), but
this increase would be
in the form of a regular
curve, and once the
position of this curve
is indicated by a suffi-
cient number of reli-
able points, all other
values for x and y,
representing the vol-
umes for all diameters,
would fall on the same
curve. False or ab-
normal average vol-
umes obtained from
too few trees will not
fall exactly on the
curve, but above or below it. The greater the number of trees used in obtain-
ing an average point, the more closely will the point representing this value approach
or coincide with the curve.
The actual shape of the curve will depend upon the relation arbitrarily estab-
lished between the two scales. Doubling the values on the ordinates, for instance,
reduces the ordinate distance one-half. The scale selected must bring all values
within the boundaries of the sheet, which is usually accomplished if the largest
ordinate is not less than one-half nor greater than one and one-half times the
greatest abscissa.
The value of using this method is that each separate point or average aids in
establishing the law, or fixing the values for all the others. If enough good or
well-weighted points are obtained, they correct the abnormality of other points
based on insufficient data and even show up arithmetical mistakes in obtaining
these averages. The curve makes possible the interpretation of missing data, but
it is considered unsafe to extend it to cover values beyond the limits of the original
data.
Although from the standpoint of mathematics it makes no difference which
variable is plotted on the horizontal and which on the vertical scale, yet as the
purpose of this plotting is to convey to the eye the tendency or law of increase in
EAS
——— EE —
&
>
Axis of Ordinates
Ae 43.71 Cu.Ft.
Ordinate 27.53 Cu.Ft.
=== == = — f= —
Ordinate 17.:
Ss SOs 9 10) iW 12 18) 14 15) “Aiinchesof p.B-H.
Axis of Abscissae
Fria. 26—Rectangular coordinates, showing position of
a curve of volume on diameter as determined by three
points whose ordinates and abscisse are known.
168. CONSTRUCTION OF STANDARD VOLUME TABLES
one variable when based upon another definite variable, as for instance, the increase
in volume due to increase in diameter by 1-inch classes, it is always preferable to
plot the independent variables on the horizontal scale and the dependent variables
on the vertical scale.
Neglect of this precaution not only conveys an ocular impression the reverse of
the actual law, but tends to create the false notion that the two variables are inter-
changeable, whereas one must always be an independent or fixed base, on which
Volume, Oubie Feet
D.B.H. Inches
Fria. 27.—Curve of volume based on D.B.H. for trees of a single height class.
the required data are collected, classified and arranged. For instance, in deter-
mining the relation between D.B.H. and age of trees, absolutely different results
are obtained if in the first instance,.the average D.B.H. is found for all trees of
given age classes, and in the second, the average age is determined for all trees of
given D.B.H. classes (§ 275). The values of these tables or curves are not inter-
changeable. The dependent variable can always be identified as the one whose
values are sought; the independent, the one whose values are already known.
The use of curves, or graphic plotting, enables the investigator to obtain a
given degree of accuracy with a greatly reduced number of field measurements.
APPLICATION OF GRAPHIC METHOD 169
This saving in field work is from 100 to 500 per cent; in fact it would be impractical,
though possible, to get the same degree of accuracy by the averaging of field data
as in Table X XVII without using the graphic method. The application of these
principles would have greatly improved the construction of certain log rules,
notably the Scribner rule (§ 68).
139. Application of Graphic Method in Constructing Volume Tables.—In
applying this method to the values in Table X XVII volume is evidently the variable
whose value is sought, while diameter and height are the two independent variables.
It is evident that not more than two values can be plotted in a single point,
nor more than two variables, as for instance, diameters and volumes in a single
curve. The volume of trees varies with both diameter and height, yet variations
due to height cannot be shown in the same curve with those due to diameter. But
if we select from the original table (X XVII) the volume of trees, all of which fall
in the same height class, the factor of height, for these volumes, becomes a constant,
except for deviations from the true average height of the class, which can be ignored
in plotting this curve. The curve formed by the volumes of this group of selected
trees will be designated as the volume curve based on diameters, for trees of the
specified height. Such a curve is shown in Fig. 27, with the original average volumes
plotted.
In determining just where the curve should fall, the weight of each point is
influenced by the number of trees included in the average column for that diameter;
the weight of a point varies with the square root of the number of entries and not
directly with the number of entries. Thus an average of a point representing one
tree and a point representing four trees would be on a straight line connecting them
and one-third of the way from the “4” point to the “1” point. The number of
trees in each class should therefore be entered on the sheets opposite the point
representing the volume.
The original-volume for the trees of a given diameter class may represent a
diameter slightly larger or smaller than the exact inch. For instance, in Table
X XVII, the average diameter for 17-inch trees, 55 feet high, was 16.7 inches. This
volume should not be entered above 17 inches, but above its true average diameter.
When the curve is completed, the values are read from it for each exact inch of
diameter.
A comparison of the original and harmonized values from the above curve is given
in Table XXVIII, p. 171.
The averages for 33 out of 38 trees and 6 out of 9 diameter classes fall within
2 per cent of the curve.
140. Harmonized Curves for Standard Volume Tables Based on
Diameter. So far, the volumes of trees of different diameters for but
one height class have been shown. By the same method, a curve is
constructed for each separate height class, based on the scale of diam-
eters. If, instead of making each of these curves on separate sheets,
they are all placed on the same sheet, their relation to each other is
shown.! All curves should show the same general trend, in harmony
with the law of variation between diameter and volume. The set
1 Where insufficient data are available and height divisions are small, the values
for different heights will frequently overlap. In such eases it is better to plot
every alternate height class first, and draw the respective curves before plotting the
intervening classes.
170 CONSTRUCTION OF STANDARD VOLUME TABLES
of harmonized curves of volume based on diameter is shown in Fig.
28 with height class of the trees in each curve indicated.
From this set of curves a table can be read, whose form is similar
to that of Table X XVII, but whose volumes increase regularly with
Volume, Cubic Feet
9 10 12 13 14 5S 16 17 18 19° p20
Diameter, Inches
Fia. 28.—Curves of volume based on diameter for separate height classes, plotted
from original averages in Table X XVII.
diameter, and whose values are interpolated to even inch classes from
the averages of the original table.
141. Harmonized Curves Based on Heights. But this table is
not necessarily in final form, for the variations caused by height must
also be harmonized. The first set of values has been made regular
HARMONIZED CURVES BASED ON HEIGHTS Wil
TABLE XXVIII
CoMPARISON OF ORIGINAL AND HARMONIZED AVERAGE VOLUMES
DPBoH.
Inches
9
10
11
12
13
14
15
16
17
18
19
Original Harmonized
volumes. volumes. Remarks
Cubic feet Cubic feet
Re co 14.0
17.38 16.5 One tree with full bole
19.78 19.75
24.27 23.4
27.53 27.4
31.61 32.1
39.44 37.3 Original volumes evidently too cylin-
drical for average
43.71 43.1
47 .26 49.5 Original diameter 16.7 inches, but aver-
age volume
54.82 56.2 One tree with poor form
eee 63.6
TABLE XXIX
VoLuMES READ FROM CURVES OF VOLUME ON DIAMETER FOR DIFFERENT HEIGHT
CLASSES
Inches
Hm COCO nN Nee
COO ON KF OK Wb
iS
Heicut Cuasses, FErr
0 14.0
5 17.6
9 21.3
2 25.1
zl 29.4
8 34.1 39.3 41.0 45.7
sll 39.0 44.0 46.0 51.4
0 44.7 49.0 51.5 57.2
2 51.3 54.4 57.4 63.6
5 2
Cusic FEET,
3
58.0 60.0 63.8 70.
65.0 66.0 70.2
172 CONSTRUCTION OF STANDARD VOLUME TABLES
within each height class separately, but this does not prevent the values
of all the trees of a given height class from being too low or too high.
In fact, if one of the volume curves representing a height class is incor-
rectly drawn lower or higher than it should be, this very result is pro-
duced.!
The law of variation of volume based on height may be expressed
by the equation y=pz, since volume (y) increases approximately in
direct proportion to height (a). For trees of the same diameter, whose
volumes lie on the same ordinate in Fig. 28, the curves of volumes for
regular gradations of height should be spaced at about equal distances.
This interval, of course, increases with each diameter class. Since this
is known, the first set of curves based on diameter may be harmonized,
not only in direction but in spacing, being placed at equal intervals
on each successive ordinate. The resultant table will then show volumes
increasing regularly by height.
A still better method of securing this regularity is to plot, from the
values obtained from the first set of curves, a second set in which
heights are the determinate variable, or basis plotted on the horizontal
scale, and volumes are plotted vertically as before. Diameter must
now be eliminated as a variable, by plotting all the volumes for trees
of a single diameter class in the same curve. Beginning with the first
diameter class in Fig. 28, which is intersected by two or more curves
of volume representing different height classes, these volumes at the
intersecting points are read, beginning with the lowest. The series
of values thus obtained represents the volumes of successive height
classes, and as such are plotted on the new sheet, and connected to
form a new curve, which represents only trees of the diameter class
so taken.
Each point so plotted should be placed above the actual average
height for the class, as found in the original averages shown in Table
XXVII, e.g., for the 15-inch curve, the 55-foot class must be plotted,
not above 55 feet, but above 57 feet, which is the actual average
height for this class.
Separate new curves are thus plotted for the trees in each diameter
class. Instead of plotting these values direct from the first set of
curves, a table may be made from the values read from these curves,
1The tendency to error may be greatly reduced in the original curves if the
the square of the diameter is made the basis of the table, or abscissee scale, in which
case the curves take the form of straight lines characteristic of those based on
height. The same result may be obtained by plotting on logarithmic cross-section
paper. (Logarithmic Cross-section Paper in Forest Mensuration, Donald Bruce,
Journal of Forestry, Vol. XV, 1917, p, 335.)
HARMONIZED CURVES BASED ON HEIGHTS 173
and the new values then replotted from this table.
In this case, the
values from each curve will be read horizontally from the table instead
of from the vertical
column as in the first
instance.
“Strip” Method of
Replotting. A rapid
method of replotting
direct from the curve is
by means of a strip of
paper. The zero or end
of strip is placed on the
base or abscissa, and
held in a vertical posi-
tion, so that the edge
lies on the ordinate re-
presenting the diameter
class to be transferred;
a mark is then made
where the curve of vol-
ume for each successive
height class intersects
the strip. These marks
may be numbered or
otherwise designated,
but their mere order is
a sufficient identifica-
tion. Transferring this
paper to the second
sheet, the vertical or
ordinate distance (which
represents volume in
each set of curves) for
the first height class,
is plotted on the ordi-
nate intersecting the
abscissa _—s representing
that height. The strip
is then moved to the
right, to intersect the
next height on the scale
and the corresponding
volume point transferred
to the sheet.
Volume, Cubic Feet
Fic. 29.—Curves of volume based on height.
Z|
; e
Z|
wea Lee eo
40 ae | a 1
sige 2288
25 ts Seale aA :
ees he dotted lines|show
ak file the orig ne veunyes,
he lack} of harmony in
| es
cane
15 aa transposed.
k On ne a
é 0 7. §
a, Gi
Height, Feet
Original
curves, dotted, from curves shown in Fig. 28, or
values from Table XXIX. Harmonized curves
drawn.
When plotted thus, these volumes indicate the position of the
curve of volume for different heights, for trees of the given diameter class.!
‘This method is described by W. B. Barrows, “Reading and Replotting Curves
by the Strip Method,” Proc. Soc. Am. Foresters, Vol. X, 1915, p. 65.
174 CONSTRUCTION OF STANDARD VOLUME TABLES
Irregularities in spacing the first set of curves are now shown by
this second set as similar distortions of each curve where they inter-
sect the same ordinate. This is shown in Fig. 29.1
Volumes read from this second and final set of curves increase with
both diameter and height according to the true laws of variation appli-
cable to each dimension. In this way Standard Volume Tables are
‘secured, which may be applied to a species throughout its range, unless
it is convincingly shown that there are consistent differences in form
and volume not due to either height or diameter, which can be cor-
related with age or site, and call for separate standard table.
TABLE XXX
STANDARD VOLUME TABLE READ FROM CURVES OF VOLUME ON HEIGHT FOR
DIFFERENT DIAMETER CLASSES
Heicut Ciasses, FEET
Be Ie 50 55 60 65 | 70 75 | 80
Inches Cusic FErr
9 10.3 11.8 13.2 14.6
10 13.6 153511 16.6 18.1
11 17.0 18.5 20.0 21.5
12 20:2 22.4 24.0 26.0
13 24.0 26.2 28.4 30.6
14 28.0 30.6 33.2 35.9 38.5 41.2 43.8
15 32.4 Bone 38.0 40.8 43.6 46.4 49.2
16 40.0 43.0 46.0 49.0 52.0 55.0
LZ whine ep ABrAlle ASAG. 1ANGlB |. AO. he or ate
18 sae Bane. 55.3 58.3 61.2 64.2 Gf
19 ee btn 61.2 64.4 67.6 70.8 74.0
142. Local Volume Tables—Their Construction and Use. In the
absence of a standard table, or when for any reason the available tables
are not reliable and there is no time to construct a table for all heights
1 Based on the law of variation between volume and height, this set of curves
(in rectangular co-ordinates the term “curve” applies to any line, curved or straight,
which follows a regular law and can be expressed by a formula) consists of lines which
are nearly straight, but not parallel, since the difference in volume increases with.
each diameter class representing a single curve.
LOCAL VOLUME TABLES 175
and diameters, a local table based on diameter alone may be made
directly, from whatever number of measurements can be secured. The
volumes of all trees of the same diameter are averaged regardless of
height. These averages must then be plotted, and a single curve drawn
similar to that shown in Fig. 27 but containing trees of all heights.
From this curve average volumes for each diameter class are read.
When diameter is shown in the table, such tables are useful only
within the same stand, age class or site class in which they are con-
structed. Timber whose average height is greater or smaller, for any
cause, for trees of the same diameter classes, cannot be measured by
this local table but require a new basis of volumes. If it is found that
the heights do average the same for each diameter the local table can
be used unless it is known that other factors influence form sufficiently
to require its correction. But where no record is made of heights of
the trees used in constructing the table, as frequently happens, the
cruiser has no way of knowing whether the table applies to any stand
but that in which it was made. - Where it is expected that such local
tables may be used again, heights should be measured as well as diam-
eter, and a curve of height on diameter drawn. The full data for such
a local table, which is to be saved for possible future use, are:
TABLE XXXI
Locat VotuME TABLE, Form
1D), 183, Jal: Volume. Height.
Inches Cubie feet Feet
12 20.2 50
13 PA 53
14 oom 58
15 39.1 62
16 46.0 65
ete.
143. The Derivation of Local Volume Tables from Standard Tables.
Where a reliable standard volume table is available, it is not necessary
to construct a local volume table based solely on diameter. If the
estimator does not need or desire to distinguish different heights in
tallying trees, he may select the volumes from the standard table which
represent trees of the average heights of the given stand, and tally
diameter only.
The first step is to determine the average height of trees of each
diameter class, by means of a few measurements, and the plotting of
176 CONSTRUCTION OF STANDARD VOLUME TABLES
a curve to show the average height of trees of each diameter (§ 209).
The volumes corresponding to these heights in the standard table are
taken. When the height for a diameter class falls between the fixed
heights given in the table, the volume for this class must be interpolated.
For instance, a height of 54 feet in a table showing volumes for 50-
and 60-foot trees, would require an addition to the 50-foot volume,
of four-tenths of the difference between those of the 50- and 60-foot
classes.
The standard volume table therefore permanently replaces all local
tables, provided the average form, the unit of volume, and the merchant-
able units used correspond to the conditions for the timber to be meas-
ured (§ 205).
144. Volume Tables for Peeled or Solid-Wood Contents. To
obtain volume tables for solid or peeled contents, the original tree
volumes are computed from D.I.B. measurements taken at stump and
at each section. The D.B.H. of each tree is based on the measurement
outside bark just as for volume tables with bark. This permits the
comparison of the volumes with and without bark for trees of the same
size class.
REFERENCES
Volume Tables and the Bases on Which They May Be Built, Judson F. Clark,
Forestry Quarterly, Vol. I, 1903, p. 6 (Schiffel’s formula).
Volume Tables, Henry 8. Graves, Forestry Quarterly, Vol. III, 1905, p. 227.
CHAPTER XII
STANDARD VOLUME TABLES FOR MERCHANTABLE CUBIC
VOLUME AND CORDS
145. Purpose and Derivation of Tables for Cubic Volume of Trees.
Volume tables for merchantable cubic volume are intended to measure
the merchantable portion of trees, thus excluding the stump, top and
branches too small for use. In America these tables are used for the
measurement of firewood, pulp or acid wood, or products to be totally
consumed or disintegrated (§ 18). The volumes in this class of tables
may be obtained from those for total cubic volume by subtracting
the waste or unused portion of the stem represented by stump and
top, or the merchantable portion of the bole may be computed directly.
For board contents or other units, different tables are employed.
146. Branch-wood or Lapwood. Where branch-wood is of sufficient
size for use, which occurs with many hardwoods used for firewood, its
volume is computed separately from the stem, usually in 4-foot lengths,
each of which is calipered at the center of the stick (by Huber’s formula).
The additional volume of branches is termed lapwood. The better
method is to keep this volume separate from that of the main bole
in the volume table, and express it by diameter classes as a per cent
to be added to the volumes in the table. Lapwood is an exceedingly
variable quantity, chiefly found in hardwoods, practically absent in
conifers, and dependent entirely upon the degree of density of the stand,
which also affects the form of the bole itself. Where lapwood is included
with the volume of the bole, the trees should be separated not only by
diameter but by crown classes, dependent on the degree of crowding
and the relative spread of crowns. No more than three such classes
would be practical, namely open-grown or large spreading crowns
containing a large per cent of merchantable lapwood, medium crowns
containing an appreciable quantity of lapwood, and trees without
lapwood in quantity sufficient to affect the estimates.
Standard volume tables (§140) will seldom include lapwood but will
be confined to the volume of the main stem. Where lapwood is included,
the tables will usually be local in character, and based solely on diam-
eter, with a separate table for each crown class.
147. Merchantable Limit in Tops and at D.B.H. Where cubic
volume is utilized, the limit of merchantable size in the tops lies between
177
178 STANDARD VOLUME TABLES
2 and 3 inches, outside bark. The same standard applies to branches.
The ‘‘ merchantable ” top diameter for European conifers is about 7
centimeters or 3 inches outside bark, but this applies to wood for manu-
facture, and practically the whole tree may be taken by the use of fagots;
i.e., brushwood, done up in bundles. There is considerable range in
top diameters even for these purposes, the top diameter limit, and
consequently the waste, increasing in regions of poor markets. The
top diameters used in constructing tables of merchantable volume
must be clearly stated. For peeled wood, diameter inside bark is given.
The minimum top diameter usually does not coincide with an
exact merchantable length, but when a length of 4 feet is used, the
practice may be adopted of accepting the last 4-foot stick which measures
the minimum diameter at the middle of piece. The average top diameter
will then coincide with the minimum established, half the sticks being
slightly below this limit at the top end.
The merchantable top diameter, combined with the minimum length
of a merchantable piece, indicates the smallest size of tree measured
at B.H. which can be shown in the volume table. Ordinarily, the mini-
mum commercial diameter limit will be somewhat larger than this,
based on the inclusion of cost of logging as a factor preventing the
marketing of trees with the minimum merchantable contents. Volumes
of trees of still smaller sizes can be shown only in tables for total cubic
volume. Since the merchantable limit of top diameters for cordwood
is small, in constructing standard volume tables for cubic feet or cords
the trees are classed by D.B.H. and total height, in 5- or 10-foot height
classes, as for tables giving total volume.
148. Stump Heights. Stump height varies with local custom and
with the scarcity and value of the wood. Stump heights, especially
for large trees, are not uniform but increase with the diameter of the
tree, and rules for cutting usually recognize this fact, specifying for
instance that the height of stump shall not exceed one-half its diameter.
For small timber, uniform stump heights may be specified, as low as
from 1 foot to 6 inches. If the stump heights used in constructing the
volume table are stated it enables the cruiser not only to know whether
the table conforms to local usage, but to correct it for difference in
practice.
The cutting of low stumps not only increases the merchantable
contents of the tree but will greatly increase the possibility of error
by use of Smalian formula for volume. This error is always plus and
will require special measurement of short lengths in butt log.
149. Merchantable versus Used Length. Where the portion of the
tree which is actually used falls short of the full possibility, due to eare-
less supervision or to failure to appreciate the economic conditions,
WASTE, DEFINITION AND MEASUREMENT 179
there arises a difference between the definition of merchantable length,
and used length. Merchantable length is the total length of a stem
which can be used under given conditions. Used length is the total
length of a stem actually utilized in commercial operations. There
is therefore no fixed or absolute merchantable length, since the very
definition of the term ‘‘ merchantable’ indicates that the product
must be salable. When an operator is actually utilizing all the material
that he can manufacture or market at a profit used length and merchant-
able length coincide.
150. Waste, Definition and Measurement. Waste is_ therefore
defined in two ways. First, there is the unavoidable waste in twigs,
branches, stump and top, that cannot be used under existing economic
conditions, logging costs, and markets. A better term for this material
is refuse. This waste was large in earlier periods and tends constantly
to diminish. Second, there is avoidable waste, caused by the fact
that the markets and logging possibilities have changed faster than
the logging practice. During the war this form of waste increased in
certain sections due to the inefficiency, indifference and independence
of woods labor. The amount of this avoidable waste is somewhat a
matter of judgment. When waste is demonstrated, practice tends
to take up the slack, and used lengths are readjusted to coincide with
merchantable lengths.
The unavoidable waste is usually taken as the difference between
the total and merchantable volumes of the bole, excluding branches.
For tops, the paraboloidal formula Vaz is used, while for stumps,
the cylindrical contents of the stump based on its upper area is usually
accepted in place of its actual total volume.
The avoidable waste represents the cubie volume of the top section
between the upper limit of used length and the merchantable diameter
limit, plus the cylinder representing the difference between actual
height of stump and height to which it should have been cut.
A more complicated method applied to board-foot contents is to
re-scale the contents of the tree, measuring the top diameter of each
log at a point lower than the existing point by the difference in stump
height. The difference in total tree scale so obtained is regarded as
indicating the waste.
151. Defects or Cull. For pulpwood, defective or rotten pieces are
not merchantable. This raises the question of cull or deductions from
the cubie volume table. The question is far more serious for board-
foot volume tables. No such deductions should be made for cull in
the volume tables themselves, especially in standard tables. The cull
per cent varies without any reference to tree form or total volume.
180 STANDARD VOLUME TABLES
The deduction of a given per cent for cull would ruin the table, making
of it a local table applicable only to timber which is assumed (one can
never know certainly) to show the given per cent of defect. Even if
the per cent of deduction is stated, the table would require complete
recalculation for stands varying from this per cent of cull. By contrast,
tables made for sound trees permit of the calculation of total volume
for trees or stand, after which the estimated per cent of cull may be
deducted from this total.
All volume tables should be constructed to show only the volume
of trees as if sound. They are based on exterior measurements or
form, without deduction for interior defects, which must always be made
by the cruiser from observation of the character of each separate tree
or stand.
152. Conversion of Volume Tables for Cubic Feet, to Cords. As
seen in Chapter LX the ratio of cubic to stacked volume increases with
the diameter, straightness and smoothness of the average stick and vice
versa. Tables of cubic volume may be converted into cords by the
use of ratios or converting factors, but if a constant ratio is used for
trees of all sizes, the corded or stacked contents of small trees will over-
run the values shown, while that of the larger trees will fall below it.
Fixed ratios, of which 90 cubic feet per cord, or 70 per cent is an example,
have the merit of standardizing the cubic or solid contents per stacked
foot for trees of all sizes, regardless of their actual stacked volume.
By mixing the cordwood from large and small trees, the average ratio
might be attained in practice. The best example of this principle is
the Humphrey caliper rule, which converts cubic to stacked measure
by the ratio of 100.5 cubic feet per cord or 78.5 per cent. If this principle
is adopted, the volume for each tree class is divided by the number of
cubic feet per cord, which converts the table to the form desired.
Where actual stacked volume is desired for trees of each size, the
ratio of conversion must be found separately for the different size
classes. The tree, and not the bolt of cordwood, is the unit to be meas-
ured, hence the average size of the cordwood from trees of different
sizes determines the converting factor. But few tables have been pre-
pared on this basis. The most satisfactory method is to stack the cord-
wood from trees of different diameters separately and determine the:
factors directly. A simpler method is to determine the diameter of the
average stick in the tree, and apply the ratio previously found to hold
good for cordwood of this average size.
The ratio or ratios used for conversion should always be shown
in connection with cordwood volume tables.
An example of the converting factors used in constructing cord wood volume
tables for second-growth hardwoods is given in Table XXXII.
DEFECTS OR CULL 181
TABLE XXXII
CoNVERSION FACTORS FOR SECOND-GROWTH HaArDWwoops By D.B.H. Cuasses wItH
CORRESPONDING LEE OF THE AVERAGE 4-FOOT STICK IN THE TREE OR
IN THE STACK *
CHESTNUT BuLaAck Oaks Waite Oaks
Tree
diameter
breast-high.; Diameter |Conversion| Diameter leet Diameter | Conversion
average factor average factor average factor
stick. per cord. | — stick. per cord. stick. per cord.
Inches Inches | Cubic feet; Inches | Cubic feet | Inches | Cubic feet
1 0.9
2 1.8 63 1.8 63 1.8 63
3 2.6 70 2.5 69 2.5 69
4 3.3 75 3.1 74 3.1 74
5 4.0 79 3.6 77 3.5 76
6 4.7 83 4.1 80 3.9 79
7- 5.2 85 4.5 82 4.2 81
8 5.8 88 4.8 84 4.5 82
9 6.2 89 5.0 85 4.7 83
10 OFZ 91 5.3 86 4.9 84
11 a0 92 5.4 86 5.0 85
12 7.4 93 5.6 87 lst | 85
13 Ts 94 5.7 88 5.2 85
14 7.9 4 Sav 88 5.2 85
15 8.2 95 5.8 88 5.3 86
16 8.4 95 5.9 88 5.4 86
17 8.5 95 5.9 88
18 8.7 95 6.0 89
19 8.9 96 6.0 89
20 9.0 96
* Second-Growth Hardwoods in Connecticut, E. H. Frothingham, U. S. Forest Service, Bul. 96,
1912, p. 64.
From a table showing the contents in cords, by either of the above
standards, for trees of each size class, a second table can be constructed,
giving the number of trees of each class required to produce one cord
of wood. The cubic contents of a cord, according to the ratio adopted,
is divided by that of the tree as shown in a volume table. This gives
the number of trees required. These tables may be of value in estimat-
ing cordwood, by making rough counts. The principle involved is
the same as that used in estimating board feet by log run (§ 120).
CHAPTER XIII
VOLUME TABLES FOR BOARD FEET
153. The Standard or Basis for Board-Foot Volume Tables. In
Chapter X it was shown that the basis of measurement for standing
timber intended for sale is either the possible sawed output for tracts
that are cut by local mills, or the log scale for timber to be transported
to mills at some distance from the area. Even in the first imstance
the measurement of tree volumes requires a local log rule based on
mill tallies.
Volume tables for board feet must be based upon the contents of
the logs which can be cut from sound trees, as measured by the stand-
ard or log rule which forms the basis of sale of the timber. For the
purpose of timber estimating for which these tables are required, it
is not permissible to substitute volumes representing a different stand-
ard even if a more accurate one. -
But it is recognized that existing conditions requiring the scaling
of logs by defective log rules may change and for purposes of stock
taking or inventory of standing timber required by an owner for the
management of forest property which he intends to retain, and for the
prediction of growth, volumes of standing timber are preferably meas-
ured by tables based on log rules which give an accurate measurement
of the board-foot contents of the trees.
This conflict between a temporary economic condition and a per-
manent basis of management may require a double standard of measure-
ment, and two separate volume tables. The first step in the con-
struction of volume tables for board feet is to decide upon the log rule
to be used in obtaining the tree volumes.
For second-growth timber, and for the purpose of inventory and
basis of growth studies, this should if possible be a rule such as the
International, or one based on mill tallies of lumber such as the Massa-
chusetts log rule.
For commercial timber estimating it must of necessity at present
be the log rule in common use in the locality.
154. Adoption of a Standard Log Length. The standard practice,
in measuring the contents of entire trees for the construction of board-
foot volume tables is to disregard the actual log lengths as sawed, and
to measure the diameter on the bole at fixed points corresponding to
182
TOP DIAMETERS, FIXED OR VARIABLE LIMITS 183
logs of a standard length, since this basis coincides with the application
of the table by timber cruisers (§ 119). Sixteen feet is the standard
most commonly adopted, to which is added a trimming allowance of
.3 foot. Volume tables for hardwoods may, if advisable, be based on
logs 12 feet long but this is the exception. The objections to the alter-
native method of scaling the contents of the logs as sawed are summed
up in § 135, but this latter method has been extensively used in the past
in volume-table construction. The base from which log lengths are
measured is usually the actual height of the stump, as sawed. This
introduces a variable factor dependent upon the standard of heights
secured in felling.
155. Top Diameters, Fixed or Variable Limits. ‘The field measure-
ments of tree volumes are the same as for cubic contents of logs (§ 135).
If 16 feet is the standard log length, the taper measurements are com-
monly recorded for each 8-foot point as well. The purpose of the work
is to determine the merchantable contents. This evidently calls for
the omission of the volume of the top portion of the bole, which is not
merchantable. But shall the length of the rejected top be based upon
the actual utilization of the specific tree? If so, the last saw cut will
indicate the limit of merchantability, beyond which the contents of
the top is classed as waste. By the method of measuring the volume
of the logs as sawed, this top is rejected as it lies, regardless of whether
the utilization of the tree has been close or wasteful. If on the other
hand diameters are taken at fixed intervals, the point of measurement
will seldom coincide with that of the last cut, but will fall above or
below it.
If actual utilization practice is to be adopted as the basis of the
table, while at the same time the fixed length of section is to be retained,
the top diameter of the last “‘ merchantable ”’ log for the volume table
should be taken at the point which falls the nearest to the last saw cut,
whether this point is above or below the cut. When the saw cut is
midway between two points, the lower measurement may be taken,
or else the character of the bole may be made the basis of choice (p. 184,
Fig. 30).
When, by method B, only the merchantable volume is desired, if last cut is
at (1), the volume will be taken to the nearest 8-foot point Bs. If cut at (2), Be
is still the nearest point. But if cut at (3) equidistant from Bg and B7, either the
upper point Bz would be chosen on alternate trees or the point best representing
merchantable volume, in this case Be.
Utilization, especially where sawlogs are cut from trees with limby
tops, is seldom to a uniform diameter. The actual top diameter varies
widely but the average increases with the D.B.H. of the tree. By the
method outlined above, the contents of the volume table are made to
184 VOLUME TABLES FOR BOARD FEET
coincide with the portion of the tree which is actually used, and the
average top diameter with that which is actually cut.
But the variable practice of sawing and the arbitrary standards
set by saw crews as to waste in the tops, differing with different crews,
logging jobs, regions and seasons, is a strong
8 a a argument for adopting a fixed standard for
: 20 top diameters for saw timber. This stand-
Ong ard may either conform to the average
aa teers i
S »,= 2 diameter utilized, or may depart from it
cas and be smaller; e.g., as at Bz.
ae Where a fixed top diameter is chosen,
instead of the variable one coinciding with
utilization practice, the last taper measure-
ment will usually fall above or below this
diameter, as before. Here the same rule
of give and take can be applied; but if the
diameter limit is small the top tapers rap-
idly and it may be preferable to take no
measurement of less than the minimum top
diameter. The last top measurements will
then fall always either at or below the
point.
Where 16-foot measurements only are
made, it is necessary to take an 8-foot
length at the top whenever the last cut
falls more than 4 feet distant from the last
16-foot taper. This is another reason for
taking 8-foot tapers throughout.
156. Defective Trees, Measurement.
Frequently one or two top logs in certain
trees will not be utilized because of defects
in the upper portion of the bole. Where
the table is based on actual utilization,
such trees should be rejected for measure-
ment or else the defective logs should be
measured, since the cull is not due to form
but to defect. Where the top diameter is
fixed independent of the last cut, these defective trees should be
measured. All trees are suitable for volume measurements except
forked-topped trees, those with abnormal D.B.H. dimensions due
to butt swelling and frequently caused by fire scars, and _ trees
deformed in such a manner that a series of normal taper measure-
ments cannot be obtained. Abnormalities at a given taper point
———
/
D.B.H. is recorded for all methods.
ee a Ge a
A 0- * 10- * 40
A the diameters are taken at every 10-foot distance from ground to tip.
the diameters are taken at every 8-foot distance from stump to tip.
Fia. 30.—Three methods, A, B and C, for taking taper measurements of a felled tree.
diameters are taken at the top of each log as actually cut.
BASIS FOR TREE CLASSES 185
can be overcome by proper methods of measurement (§ 25). It
is the purpose of volume tables to show average volumes for sound
trees. Since defective logs or trees will be scaled as if sound in volume
table construction, they are suitable for this purpose.
157. Total versus Merchantable Heights as a Basis for Tree Classes.
Where cubic contents, either total or merchantable, are the basis of
tree volumes, the total height of the tree to tip of crown is the only
serviceable basis of classification by height ($137). Where the volume
of the tree is desired in merchantable units of product, such as board
feet, the height desired in practice is the merchantable length of the
bole or height of the top of the last log. Timber cruisers commonly
use the number of logs of given length in a tree, and not the total height
in feet, to obtain the contents. The practice of basing height on the
merchantable length of bole is most useful where the proportion of total
length used is most variable, as in large hardwoods or heavy-limbed
conifers, and where there is an evident variation between actual top
diameters utilized. Total heights in dense stands of tall old trees are
hard to see and measure while the top diameter limit is usually visible.
This basis is used almost universally in the estimation of old-growth
timber of all species.
The same height basis must be used in timber estimating as is used
in the tables, if volume tables are to be employed. Hence the method
of measuring heights in cruising will be either determined by the existing
tables, or else the tables must be constructed on the basis desired for
the estimating. The measurement of trees for the construction of vol-
ume tables should therefore include both the total and merchantable
height, to permit of constructing tables on each basis for use as desired.
158. The Coordination of Merchantable Heights with Top Diam-
eters. The use of volume tables to determine contents of standing
trees requires the determination in the field of but two dimensions,
namely D.B.H. and height, and is based on the assumption that the
volume of an average tree of these dimensions gives the average volume
of the trees of the same sizes in the stand to be estimated. Where
total height is used as the basis, there is little opportunity for error in
applying the volumes in the table, since but one point on the tree can
be measured for height, namely the tip. But where merchantable
height is the basis, a second variable is introduced, the top diameter.
The volume now depends, not on one definite factor of height as before,
but on securing coérdination between these two variables, i.e., height
of merchantable top, and diameter of merchantable top, in the applica-
tion of the volume table.
The choice of top diameter limits has been discussed. But the
effect of this choice upon the merchantable length (the height), in
186 VOLUME TABLES FOR BOARD FEET
such tables, needs special emphasis. If a large top diameter is adopted,
the merchantable height is correspondingly less for trees of the same
total height and form. A tree 100 feet high may have five logs, 16
feet long, if cut to 10 inches, but if cut to 16 inches instead, it may be
only a four-log tree. A 6-inch top may in turn
give 88 feet or 55 logs from the same tree. Thus
top diameter increases as merchantable length
diminishes. Whatever codérdination between
these two variables is adopted in constructing
the volume table will have to be used in applying
it; i.e., the same top diameters used for the
table must be used as the basis of merchant-
able heights in timber estimating. Failure to
observe this rule may result in serious errors
and has sometimes brought the use of such
volume tables into disfavor among _ practical
cruisers.
The results of such lack of coérdination are easily
illustrated, by comparing the volumes of trees, when
divided into 16-foot cylinders and scaled as __ logs.
Since the frustum of a cone is a regular solid resembling
the merchantable portion of the bole, it serves to illus-
Fic. 31—Cause of ‘tate the principle in question. Assume that a 6-inch
top has been adopted as a standard, and all trees meas-
ured to that point.
A four-log tree, 15 inches at the top of the first log,
inside bark, is assumed to have 3 inches taper per log.
The volume of this tree, by the International log rule,
will then be
errors in use of vol-
ume tables, when
based on merchant-
able heights and
fixed top diameters.
Total for
Logs First Second Third Fourth four logs
Diameter, inches. ..... 15 12 9 6
Volume, board feet... . 175 105 55 20 355
In estimating, if this table is to be used, the only 15-inch four-log tree whose
volume can be correctly measured is one which tapers 3 inches per log, and hence
has a 6-inch top diameter. But the cruiser may fail to observe the same coérdi-
nation between merchantable length and top diameter, and may tally a 15-inch tree
which tapers 2 inches per log, as a four-log tree. The dimensions of this tree up to
the top of the fourth log are
Total for
Logs First Second Third Fourth four logs
Diameter, inches...... 15 13 Wil | 9
Volume, board feet....] 175 130.2 418), OMe ess 450
MERCHANTABLE HEIGHTS WITH TOP DIAMETERS 187
This tree, if measured to 6 inches, has the additional length of 14 logs, whose
volume is
: Half of Total Total for
Tete seis sixth additional 53 logs
Diameter, inches......... a 6 Be
Volume, board feet....... 30 10 40 490
The recording of this tree as a four-log tree was probably based on the fact
that it would actually be cut at 9 inches in the top instead of at 6 inches. But
the cruiser, if he uses this volume table, does not obtain from it the volume of a
tree with a 9-inch top, but of one with a 6-inch top. The initial error for this tree
consists in not tallying it as a 5}-log tree with a 6-inch top. If the full contents
of the four actual logs which it contains could be obtained from the table, the
error would be the loss of 40 feet in the 13 logs not measured. This is 8 per cent
of the total tree volume. But instead, a much greater additional error is incurred.
The volume given in the table is for a four-log tree with a 6-inch top containing
355 board feet instead of one measuring 9 inches at top. This error, due to differ-
ence in top diameter not only of the last log but of the remaining logs, is 95 board
feet (450 —355) or 21 per cent.’
If the purpose of the estimate is to obtain, not the volume of all trees to 6 inches,
but the volume actually to be cut, the attempt to obtain this by dropping the
merchantable length of this tree to the 9-inch point, 1} logs below the 6-inch point,
has made the use of the above volume table impossible, for in place of a correct
deduction of 8 per cent from the true volume of a 5}-log tree, which would give
the true volume merchantable, the use of the table has lowered the estimate by
27 per cent, which is #23 of the desired estimate or 21 per cent too low. Errors
of this magnitude and even greater may and have been made in use of volume tables,
solely from this source.
The coordination evidently demands:
The estimation of height to the same point which has been used
in constructing such a table.
The deduction of the requisite per cent, representing the small
top log or logs, to obtain net merchantable volume, in case
utilization falls short of this point.
Errors in estimating merchantable heights, if consistently too great
or too small, incur both the above errors when the tally is applied to
the volume table. Other methods of avoiding these errors are:
To use total height as a basis.
To measure a few heights carefully instead of guessing at many
or all heights.
To construct the table so as to coincide with used top diameters,
and then exercise care in employing this same standard in
estimating!
1 The writer’s initial experience in timber cruising was with W. R. Dedon, in
Minnesota. Mr. Dedon did not believe in the use of volume tables, claiming that
188 VOLUME TABLES FOR BOARD FEET
159. Construction of Board-foot Volume Tables. The basis agreed
upon as to the top diameter to use, if merchantable heights are utilized,
will determine the height class into which each tree falls. The steps
in construction are the same as for tables of total cubic volume (§ 131)
with the following exceptions.
Compute the volume of each tree by means of the log rule chosen,
by scaling each 16-foot log. In volume table work, this scale per log
should preferably be interpolated to 75-inch values, for which purpose
the values of the log rule can be tabulated for the given interpolations.
The last or top log if 8 feet long is scaled as one-half the volume of a
16-foot log of equal diameter. If the logs are not scaled to 79-inch
they are rounded off to nearest inch above or below (§ 137) but where
but a few trees are measured in each size class, this incurs the risk of
unnecessary variations in volume of the tree classes.
When merchantable heights are taken to fixed lengths, the variable
at this point will be the top diameter. Therefore, the average top
diameters should be shown for each diameter and height class. These
tops may later be averaged solely on the basis of diameter at breast
height.
160. Data Which Should Accompany a Volume Table. Because
of the errors possible in misapplying tables for merchantable volumes,
as set forth, the use of such volume tables presupposes knowledge of
their reliability and applicability. For this purpose the following data
should always accompany the tables:
Species.
Region or locality where measurements were taken.
Age of trees to which values apply, when distinguished.
Sites or quality to which values apply, when distinguished.
Unit of volume used.
Log rule if in board feet, or mill tallies specifying character and
thickness of lumber included.
Specifications, if for piece products.
Number of trees measured as basis, by diameter classes.
Height of stumps.
on the only occasion on which he had attempted it, the table gave just half of the
true estimate. This was unquestionably due to the cause explained above, that is,
trying to coérdinate large top diameters with a table made to smaller tops. The
first impression, in using a table constructed to a small top diameter is that it
“secures a greater volume per tree.’ The error is just the reverse of this—it
under-estimates the timber. If, on the other hand, the top diameters in the table
are larger than those applied in the field and the per cent of total contents less,
the error in applying the table is an over-estimate equally great. These possi-
bilities of error in the use of volume tables based on merchantable length have
been commonly overlooked in practice.
CHECKING THE ACCURACY OF VOLUME TABLES 189
Top diameters used—by diameter classes if variable.
Method used in constructing table,
a. Based on measurements at fixed intervals.
b. Based on measurements of logs as cut.
c. From tables of taper or form (Chapter XV).
d. From form factors (Chapter XVI)
Author, and year of preparation.
The basis of classification of volumes, as to height and diameter,
is shown in the table itself. But tables based solely on diameter will
have their value increased if the average heights used in constructing
the table are also shown (§ 162).
161. Checking the Accuracy of Volume Tables. Volume tables
make no pretense of giving accurately the volume of single trees (§ 121).
If the average values given coincide with the average of the volumes
of the trees to be measured, the table is accurate for the purpose in hand.
But, although applied correctly ($158) volume tables will give
inaccurate results, first, if the table itself is inaccurately made and does
not give correctly the volumes of the trees from which it was constructed,
second, if the trees to be measured average greater or smaller volumes
for given diameters and heights than those given in the table, on account
of fuller form or vice versa.
Volume tables made in one locality may be serviceable in other
regions, covering the entire range of a species. If the estimates are
made to conform with the top diameters and log rules used in the table
the only possible variation in volume from such tables is that of average
form, and variations due to this factor can be determined without
constructing an entirely new table (§ 171).
To check the accuracy of construction of a table, the basis in trees
is first considered. Tables based on from 500 to 1000 trees or more
are regarded as fairly reliable, while if fewer trees have been used the
table is open to question. The total actual volume of the trees used
in constructing the table can be checked against the total volume of
the same trees figured from the table. This gives a basic check which
may, however, conceal compensating errors. The average volume of
the trees in each diameter and height group may then be checked
against the tabular values in the same way, and the errors recorded
in terms of per cent. These errors should compensate. A still more
accurate check is to record the divergence in volume of each tree from
the tabular volume and total the per cents of error plus and minus,
which should compensate. Or, the plus and minus errors may be
plotted to detect any trend towards high or low values at one end or
the other of the curves.
190 VOLUME TABLES FOR BOARD FEET
To test the accuracy of a table of proved value, when applied to
a specific stand or region, the volume of as many trees as convenient,
preferably about 100 trees, is determined by the same standards as used
in the table. The per cent of divergence of the actual volumes, one
by one, from those of the table, is computed. These per cents
may be tabulated and averaged by diameter and by height; if they
reveal a consistent difference in volume, the values of the table can be
raised or lowered by the average per cent indicated.
REFERENCES
The Problem of Making Volume Tables for Use on National Forests, T. T. Munger,
Journal of Forestry, XV, 1917, p. 574.
The Height and Diameter Basis for Volume Tables, Donald Bruce, Journal of
Forestry, Vol. XVIII, 1920, p. 549.
A Proposed Standardization of the Checking of Volume Tables, Donald Bruce,
Journal of Forestry, Vol. XVIII, 1920, p. 544.
Top Diameter in Construction and Application of Volume Tables Based on Log
Lengths, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 221.
CHAPTER XIV
VOLUME TABLES FOR PIECE PRODUCTS, COMBINATION
AND GRADED VOLUME TABLES
162. Volume Tables for Piece Products. The purpose of volume
tables for piece products is identical with that for board feet—to enable
the timber estimator to dispense with the necessity of judging by eye
the contents of separate trees, and substituting therefor merely the
record of diameters and heights.
Volume tables for piece products are limited in scope. The speci-
fications as to size of the product are the governing factor. For poles,
no volume table is needed. For small products such as staves, it is
almost impossible to make volume tables, on account of the effect of
cull in reducing the output and the difficulty of judging this in the
standing timber. Even here, tables showing the number of staves
of given dimensions in perfect trees of different diameters, or in sections
or bolts of different diameters may be of help in estimating. Here,
as elsewhere, the cull factor cannot be introduced into volume tables
but must be applied as a reduction factor to their contents.
To construct a volume table for any specific product, the same
methods used in constructing log rules can be applied; first, the number
of pieces of certain dimensions which can be cut from logs or bolts of
given diameters can be found by plotting with cross-section of the
standard piece upon the areas of circles. Second, these theoretical
results can be checked against the actual number of pieces hewn or
sawed from logs or bolts of the same diameter. The second check
is to ascertain the effect of irregular shapes, and of methods of cutting
or manufacture, as affected by the grain of the wood and tools used.
In such a check, only sound logs are taken, but the factor of cull may
be studied at the same time. The contents of these logs can then be
combined into volume tables by the methods outlined in Chapter XI.
163. Volume Tables for Railroad Cross Ties. The most useful
volume tables for such products are those for railroad cross ties. Just
as for poles, the length of the ties, usually standardized at 8 feet, is
a partial indication of the number of ties which can be cut from trees
of given sizes. Hewn or pole ties, flattened on the faces only, are cut
only from trees or the upper portion of boles which are too small to
produce two or more ties from one bolt. Volume tables are needed:
191
192 VOLUME TABLES FOR PIECE PRODUCTS
1. For trees of larger diameter, to show the number of ties which
can be obtained from each bolt, hence from the tree.
2. To show the number of ties of different grades as determined
by size, which ean be obtained from each bolt, and from the tree.
This latter requisite also applies to bolts from which but one tie
can be cut.
A good example of a tie-volume table is that prepared! for western larch and
Douglas fir, Kootenai National Forest, Idaho, in 1919, for the five standard grades
of hewn railroad ties specified by the U.S. R. R. Administration. The dimensions
called for are:
No. 1. 6 inches by 6 inches by 8 feet.
No. 2. 6 inches by 7 inches by 8 feet.
No. 3. 7 inches by 7 inches by 8 feet.
No. 4. 7 inches by 8 inches by 8 feet.
No. 5. 7 inches by 9 inches by 8 feet.
Each tree was measured at 8-foot intervals for diameter inside bark. The
method was to construct a taper table (§ 167) from which the sizes of pole ties
which could be cut from each bolt were determined. The steps were:
1. Determine the average top diameter inside bark required to produce a tie
for each standard size. These were:
For No. 1. 8.5 inches.
No. 2. 9.2 inches.
No. 3. 9.9 inches.
No. 4. 10.6 inches.
No. 5. 11.4 inches.
2. Separate the trees measured into D.B.H. and height classes. The height
classes used were the number of 8-foot lengths in the merchantable bole, to a top
diameter of 8.5 inches.
3. Determine the average diameter at each 8-foot point, for the trees in each
of these separate groups. ‘This gives a series of taper measurements and an average
form for the tree.
4. With distance above stump as the independent variable, on the horizontal
scale, and top diameter of each tie (each 8-fooé point) as the dependent variable
on vertical scale, plot the average diameter at each 8-foot point. By connecting
these points the form of the tree is shown. ‘These curves are used to smooth out
irregularities in values.
5. From the average upper diameter of each 8-foot bolt, for trees of each D.B.H.
class, and separate height classes, as 5-tie trees, 6-tie trees, etc., the class of tie
which can be cut from each bolt is indicated, and the number of ties of each grade
in the tree is shown. This constitutes the tie-volume table. Instead of recording
merely the total number of ties, regardless of grade, which could be done without
the table, the estimator now has his products classified.
The same method can be used for trees whose dimensions permit of sawing or
splitting two or more ties from one bolt, but usually trees of this diameter will
be measured in part as sawlogs in board feet rather than as sawed or split ties.
1 James W. Girard and W.S. Schwartz.
COMBINATION VOLUME TABLES 193
164. Combination Volume Tables for Two or More Products.
Close utilization of tree volumes requires the measurement of two or
more classes of products, such as saw timber and residual cordwood,
saw timber and residual mine props, railroad ties and residual mine
props.
In all tables of this class, the method of construction is to determine
the diameter which limits the sizes used for the higher purpose, and then
to measure the contents of the remainder of the bole to the smaller
diameter which limits the sizes used for the residual product. The
measurements must be taken on the felled tree before any portion is
skidded off.
For example, in constructing a sawlog, tie, prop table for lodgepole
pine, on the Arapahoe National Forest, Colorado, 6 inches was used
as the top diameter for sawlogs, to be scaled by Scribner Decimal C
log rule. Five inches was the top diameter for mine props. The
number of feet remaining in the top, between 6 and 5 inches, was
recorded as linear feet. In the same manner, 10 inches was fixed as
the top diameter for the production of hewn ties (this has now been
lowered to 8.5 inches by new specifications), and the number of ties
in each tree, to this point, recorded. Above 10 inches, the 8-foot
lengths are entered as prop material.!
The residual cordwood in the tops of trees cut for sawlogs or ties
is measured as for cubic feet. Where the volumes for the more valu-
able product are measured to a fixed top diameter, the problem of resid-
ual volume is easily solved. Where top diameter varies with other
factors, the amount of cordwood in the tops varies accordingly. This
variation is further increased when branch-wood or lapwood is included.
Tables usually express the volume of residual.cordwood in terms of
decimal fractions of cords per tree, and the data are frequently simplified
by averaging the contents on basis of diameter.
165. Graded Volume Tables. A graded volume table is an attempt
to show the amount of different standard grades of lumber which may
be sawed from trees of different dimensions. Its purpose is to aid in
estimating the value of standing timber. The preparation of graded
volume tables is one of the objects of mill-scale studies (§ 74). The
basis of these tables is the sawed lumber produced from logs. To
codrdinate these data with the volume of standing trees, the following
points must be considered: i
1. The logs sawed are usually cut into variable log lengths and
cannot be standardized to a given length, such as 16 feet.
2. In sawing logs, especially hardwoods, the resultant output will
1 Ref. Volume Table for Lodgepole Pine, A. T. Upson, Forestry Quarterly,
Vol. XII, 1914, p. 319.
194 VOLUME TABLES FOR PIECE PRODUCTS
be determined by the amount of defect in the log as well as the grades
of lumber—the net, not the gross scale will be obtained.
But the same objections hold against introducing into graded tables
the variable factor of the cull due to a great range of defects as have
operated to exclude such deductions from all standard tables. Hence
the only safe standard on which to construct such tables is sound logs.
3. The grades of lumber are first determined in logs of given diam-
eters and lengths, from which graded log rules may be constructed.
Such rules are of course never used in sealing logs (§ 87) but solely to
aid in the determination of the average price to be paid for the contents
as scaled.
4. The grades of lumber in trees of different sizes must be obtained
by correlating the sizes of the logs graded with the logs contained in
the trees.
One standard method used in constructing such tables is to follow
the logs from different trees through the mill, by numbering the logs
in the woods, a process impossible without much delay except in small
jobs.
Separation of butt logs and top logs is a less detailed method of
classification of logs.
A third plan is to prepare separately the graded log table without
reference to the trees, and then determine the sizes of logs in trees of
different D.B.H. applying the grades to the given logs to get the grades
for the tree. Of the three methods, this is the most practical and use-
ful. In this the graded log table is the real basis, local graded volume
tables being constructed from this table for use in each different stand
of timber (§ 87).
5. To show the actual contents of trees of each separate diameter
and height class, expressed in from four to eight standard grades would
call for a table of considerable bulk, and when in addition to this draw-
back the actual volumes shown are based on an arbitrary net sawed
output minus whatever cull happens to have been present in the logs
measured, the advisability of using such a form of standard table is
questionable.
6. Where graded volume tables of greater permanent value are
desired the purpose of the tables will be accomplished by the following
simplification:
; a. Substitute per cents of sawed contents for actual sawed con-
tents for each grade of lumber scaled.
b. Substitute D.B.H. alone for D.B.H. and height, as the basis
of classification of the trees.
If these per cents apply to sound logs, they may require modifica-
tion in the case of defective timber. Where heart rot is prevalent
GRADED VOLUME TABLES 195
it causes a greater loss in the middle portions of logs which on account
of the presence of knots are of lower grade than the sound outer portion.
On the other hand, cat face and exterior defects reduce the amount
of clear lumber of upper grades. Unless such factors can be judged
correctly, the same per cents of grades must be accepted for defective
logs as are shown in the table for sound logs.
It has been the common practice, in preparing graded volume
tables for hardwoods, to base the table upon the net sound contents
after deducting cull. Where sufficient typical sound logs of the larger
sizes cannot be obtained, the drawbacks of a table based on a partial
scale, i.e., culled, can be in a measure overcome by reducing this table
to per cent form as indicated above. Such a table should include a
statement of the basis on which it was made, the average per cent
of cull deducted, and the general character of the defects and influence
on the different grades. On this basis, its application to other timber
is possible.!
Graded log tables are of permanent value, and the utility of these
tables, if expressed in per cent, may be greater than is now imagined.
The permanence of such a table depends entirely on the maintenance
of the standard of grading, or grades of lumber on which the graded
table is based, hence such tables cannot have the permanent scientific
value of tables giving volume in standard units for sound trees.
REFERENCES
A Volume Table for Hewed Railroad Ties, James W. Girard and W. S. Schwartz,
Journal of Forestry, Vol. XVII, 1919, p. 8389.
Graded Volume Tables for Vermont Hardwoods, Irving W. Bailey and Philip ©.
Heald, Forestry Quarterly, Vol. XII, 1914, p. 5.
The Ashes, Their Characteristics and Management, W. D. Sterrett, Bul. 299,
U.S. Dept. Agr., 1915, p. 35. (Table based on per cents.)
Grades and Amounts of Lumber Sawed from Yellow Poplar, Yellow Birch, Sugar
Maple, and Beech, E. A. Braniff, Bul. 73, Forest Service, 1906. (Table by
per cents for Yellow Poplar.)
Assortment Tables, Mitteilungen der Schwarzerischen Centralanstalt fiir das forst-
liche Versuchswesen, Vol. XI, 2 Heft, pp. 153-272. Review in Forestry
Quarterly, Vol. XIV, p. 752.
Graded Log Tables for Loblolly Pine, W. W. Ashe, Bul. 24, North Carolina Geolog-
ical Survey, 1915.
1 European investigations have shown that the per cent of total volumes which
is obtained in the different grades of product varies with the diameter but does
not differ appreciably with height. “In proportion as the shorter stem is less
in volume than the longer, the assortment contents decreases but the per cent
relation remains the same.” Ref. Forestry Quarterly, Vol. XIV, 1916, p. 752.
CHAPTER XV
THE FORM OF TREES AND TAPER TABLES
166. Form as a Third Factor Affecting Volume. While standard
volume tables (Chapter XI) differentiate the volumes of trees of dif-
ferent D.B.H. and heights, they make no distinction between trees
having paraboloidal forms and those approaching the cone or neiloid
(§ 26) in form, but seek to average the differences in volume caused by
these variations. Occasionally two separate tables are made for a
species, one for old trees, the other for young second-growth, since
it has been found that the average volume of trees of these two age
classes differed considerably. Any such difference, whatever its cause,
is due to difference in form as indicated above, for trees which have the
same D.B.H. and height.
Volume tables have come to stay, since they substitute accurate measurements
of D.B.H. and of height, which may be checked by calipers or hypsometers (§ 193),
for too exclusive a use of the eye, and for the very uncertain method of guessing
at or figuring out the volume of an average tree whose dimensions are in turn
arrived at by guess or judgment.
The difficulty of having to depend solely on volume tables of this character lies
not in the tables themselves but,
(1) in their incorrect application (§ 124);
. (2) in their not being based on the same factors of volume determination as are
desired for the estimate;
(3) in the possibility of not having any tables and being forced to construct them.
To summarize here the factors in which the tables must agree with the basis of
estimating we find: (a) Choice of unit of measurement as board feet, specific log
rules, cross-ties, cords. (b) Closeness of utilization in tops and stump. (c) Point
of diameter and height measurement. (d) Thickness of bark. (e) Variations
caused by form independent of diameter and height. 5
For these reasons the demand for some form of universal volume table in esti-
mating is very strong.
The substitution of a fixed taper per log, and the use of tables showing volumes
for trees of the same diameter and height but with different rates of taper (§ 122)
is an attempt to differentiate between trees with different form, but, in effect,
this plan assumes that all trees have the same form, that of the frustum of a cone
and differ only in being tall or short, or tapering slowly or rapidly up to the top
diameter.
The only satisfactory basis of a universal volume table is one in
which all three of the variables, namely diameter, height, and form
196
TAPER TABLES, DEFINITION AND PURPOSE 197
classes are distinguished. In tables based upon diameter and height
only, no record of form is shown. The volumes as given in the table
do not indicate whether the tree is full-boled or conical. This draw-
back is further aggravated by the use of board-foot log rules whose
values are not interchangeable.
167. Taper Tables, Definition and Purpose. There are two methods
for recording differences in the form of trees, form tables or taper tables,
and form classes or form factors.
A table which does not show the volume of the tree, but shows
the actual form by diameters at fixed points from base to tip, 1s com-
monly termed a taper table. From such a table, the volume of the aver-
age tree for each diameter and height class can be measured as readily
in the office as from the felled tree. Tables of volume can thus be
constructed from a taper table, using any desired unit of product,
such as cubic feet, board feet or piece products. They therefore form
the basis for any required future volume table. For this reason, if
taper measurements are taken at regular intervals, preferably 8.15 feet,
from stump to top of tree, they constitute a permanent scientific record
of tree form which will make it unnecessary to measure felled trees
again for new volume tables.
168. Methods of Constructing Taper Tables. Taper tables are
based on total height-and hence they should record the form of the
entire bole.
A separate table is required for each height class showing the taper
of trees of each diameter in this class; e.g., for white ash! tapers are
shown for trees of 10-foot height classes from 30 to 120 feet.
For each height class, and D.B.H. class, the diameter of the tree
inside bark must be given at each fixed point, 8.15 feet or multiples
thereof above the stump.
The bole, below D.B.H., tapers much less regularly than above
that point, but a complete taper table should give the average diam-
eter inside bark preferably at 1, 2, 3 and 4 feet from the ground.
In Table XXXIII, p. 198, stump tapers are given, the diameter inside bark
at B.H. and the upper diameters at 8.15-foot intervals from stumps taken as
uniformly 1 foot high. But one class is shown, namely, 90-foot trees. A similar
table is constructed for trees of each separate height class, such as 80-foot or 70-foot
trees.
When the taper measurements have been taken at fixed points
on all trees, the average diameters at these points may be obtained
directly from the original data. The process is shown in Table XXXIV.
1 Bul. 299 U.S. Dept. Agr., The Ashes, W. D. Sterrett.
198 THE FORM OF TREES AND TAPER TABLES
TABLE XXXIII
ForM or Taper For Wuitr AsH TREES OF DIFFERENT DIAMETERS UNDER 75
Years or Aqae, Grvinc DIAMETERS INSIDE Bark AT DIFFERENT HEIGHTS
ABOVE THE GROUND
90-foot Trees
Hriagut ABoveE GROUND—FEET
Diam-
eter ee sls i lea tye a gl ag mee
breast-| 1 2 3. «| 4.519 Paha eSeco 97 Gan fBiey aioe, 05) GG a eee vend
high. ma haat l
£
Inches DIAMETER INSIDE BARK—INCHES
8 9218.5) 729i 7.3) 6281 76-4) “GF! S75) 4.9) 1422) 3.3") 223i" 14
9) 104/905) (8.982215 726) ae) (GVSIN622)" Sed 428) SES Qari) War
LOPEZ 1ON6) S29 Oe) Ses SeO 715) "6e9l 672) 544) 4230 Sel eie9 1
11 |12.9)11.7/10.9/10.1) 9 Sai mee Go|. Oxell ©. 0) ON ees nome 1
12 4S TA SO MISO MORAG Oe Ses, 726) G26 5.4) | 38-9 e2no 3
13 Porshe OWS Oe SIONS “Os8\" 920 Se2\ 73) Ono Wales 6
14 |16.5)15.1)14.0)/12.8)12.0)11.2) 10.5) 9:8) 9.0) 7.9) 6.5 | 4.9) 3.2 7
LS UT OMLGs215 OMS 2S 2 57) TS ST 2 OFA O26 8.5/5 720N tonalnoco 4
IGS HIST SiL7 SiO UA STL SOA a7) Tao OKs OFZ 9746) soe sng 2
17 |20.0)18.4/17.1]/15.6)14.5)13.4) 12.6/11.8) 11.0) 9.8) 8.1 | 6.2) 4.2
18 |21.2)19.7)18.2/16.5)15.3)14.2) 13.3)12.5) 11.7/10.4) 8.6 | 6.2) 4.6 1
19 |22.3/20.6)19.2)17.4/16.1)14.8) 14.0)18.2) 12.3]11.0) 9.2 | 6.7| 4.9 1
20) |23.5/21.7/20.2)18.4)17.0)15.7) 14.7/138.9] 13.0)11.5) 9.7 | 7.2) 5.3
21 |24.6/22.8/21.3/19.3)17.7/16.3) 15.3/14.5| 18.7/12.2/10.4 | 8.2) 5.8
22 |25.8/23.9/22.3/20.2/18.6/17.1) 16.1|15.3] 14.5|12.9110.9 | 8.6] 6.1
26
Original Curves, Tapers Based on Heights above Stump. In the
form shown, these average tapers or upper diameters may he insufficient
to bring out the true average form for large numbers of trees. The
irregularities of form, occasioned by the variation in form of individual
trees and lack of sufficient number of trees to secure a true average by
arithmetical means, are best shown by plotting the forms of the result-
ant average trees. For this operation, height above stump is taken
as the independent variable plotted on the horizontal scale while upper
diameter is the dependent variable plotted on the vertical scale. A
separate curve is required for trees in each D.B.H. class.
1 The details of constructing taper curves are fully discussed by W. B. Barrows,
Proc. Soc. Am. Foresters, Vol. X, 1915, p. 32.
METHODS OF CONSTRUCTING TAPER TABLES 199
TABLE XXXIV
Tapers or LosBLouiy Pring, Two Trees *
Tree Class, 15-inch, 80-foot
Srumpe HercuT ABove Stump—FrEer |
| Total
DB HE: 2 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 height.
RAAT), |
DIAMETER INSIDE BARK—INCHES Feet
15.4 NG eee else ee emlele Silesia ONO Sis onolesnO 76
ileal CeO.) a3. 3) taco) 12-5 11.9) 1028) 9-6) 8:0). 6.3; 3.8 84
30.5 Shel | 26.88 25.6) 23..9|° 23" 6) 21/9) 19.61- 16.8) 1222) 6.8 160
Avera,e
152 TORO LOR See Ol tes OO OL Sh kag MG dies 80
* Data taken from loblolly pine tapers at 8-foot intervals, without stump tapers. Two trees.
f
Efi
PANY.
aa
|S
SS
eS
eae
Sal
baa.
ae
ena
Soe
ered
lise
ae
a
ead |
Perea
ail
TTT]
Height above Stump, Feet
Fia. 32.—Actual upper diameters or tapers of four loblolly pine trees, inside bark,
based on height above stump, plotted to show form of trees. 90-foot trees.
200 THE FORM OF TREES AND TAPER TABLES
From these plotted forms of trees the diameters at any desired point or height
on the boles can be read.
The nature of these original averages is shown in Fig. 32 in which four single
trees of different D.B.H., 14.4 inches, 17.7 inches, 19.4 inches, and 21 inches, but
falling in the same height class, 90 feet, are plotted. The eccentricities of form
in this table are partly due to branches, partly to failure to obtain the true average
diameter at each point, and partly to the natural variations in form for individual
trees.
As in the preparation of volume tables, the averages obtained from a number
of trees are more consistent than the forms of single trees. A graph plotted in
this manner from averaged upper diameters instead of single trees, will be fairly
regular in the relation of the curves for successive D.B.H. classes and will resemble
Fig. 35, p. 204.
When, as is sometimes the case, the upper diameters are measured
on logs as cut by the saw crews, in irregular lengths, and hence fall at
different heights above the stump, only the measurements falling at
the same height can be averaged, as at 12, 14, 16, 18 and 20 feet. This
will be done, and all of the resultant upper diameters for trees of a given
D.B.H. and height class will be plotted, to obtain the curve of average
form. From this curve, the desired upper diameters at regular inter-
vals of 8 or 10 feet can be read.
These curves of form are not in final shape for a standard table of form. Although
the averages are improved by the use of larger numbers of trees, the values will
be slightly irregular for two reasons. The average D.B.H. may be larger or
smaller than the exact inch class desired, and the forms of the average trees of the
consecutive D.B.H. classes may vary in fullness. These two sources of variation
are well shown in Fig. 32. There is no reason why average 21-inch and 18-inch
trees should have a fuller form than 19-inch trees.
Values required are based on exact D.B.H. classes, and vary regularly with
D.B.H., as would be the case were sufficient trees included in the mechanical
average.
Second Set of Curves, Tapers Based on D.B.H. For trees of each
successive D.B.H. class which have the same total height and the same
general form, the diameters at each given height on the boles will
diminish in direct proportion with diminishing D.B.H. If D.B.H. is
then taken as the independent variable in a second set of curves, and
upper diameters plotted on D.B.H. as the dependent.variable, the
form of these new curves approaches straight lines as did those of volume
based on height (§ 141), and the irregularities between the forms or
upper diameters of different average trees are easily reduced. In this
second operation as in the first, the trees of a given height class form
the basis for a set of curves; e.g., 90-foot trees only are included in the
one set of taper curves, separate sets being required for 70-foot or 80-foot
trees. For this set of curves the same scale can be used for both vari-
ables, e.g., 2 inches= 1 inch.
METHODS OF CONSTRUCTING TAPER TABLES 201
To plot this second set of curves the values for a given tree, or set of tapers,
are transferred to this new sheet, in which process the strip method described in
§ 141 is most convenient.
The diameter of upper
tapers diminishes with in-
creasing height; each tree
is plotted in a single
vertical column, with
the D.B.H. at the top.
The D.B.H. column
must be that of the
actual average D.B.H.,
e.g., 14.4 inches, not 14
inches. When each set
of values has been
transferred and plotted
above its respective
D.B.H., the points rep-
resenting equal heights
above stump are con-
nected by lines. The
guide line for this set
of curves is a line drawn
at 45° angle whose value
would be DIB.=
D.B.H. For any tree,
the D.I.B. at D.B.H.
is less than the D.O.B.,
and at upper points,
D‘L.B. is still less; hence
all points above D.B.H.
will fall below this line.
Regular forms such
as are shown in Fig. 35
could be drawn directly
on Fig. 32 guided by
the original averages,
which will usually be
far more regular in
themselves than those
shown in the diagram.
But the desired shifting
of the basis to exact
D.B.H., e.g., 14 inches
instead of 14.4 inches,
Upper Diameter, Inches
and the far greater ac- m2e pals} 14 sh, al) 0 aly/ 18 UW 4 PADS Pal gp
curacy in harmonizing D.B.H., Inches
tapers secured by plot- Fic. 33.—Tapers of the four trees shown in Fig. 32, plot-
ting (Fig. 33) makes the ted on basis of D.B.H. for each 8-foot point, and
method of plotting a results evened off by curves. Separate curves are
second set of curves made for each height above stump. Effect is to
almost obligatory. reduce the irregularities of form in Fig. 32.
202 THE FORM OF TREES AND TAPER TABLES
With more regular original averages, the curves will coincide very closely with
the original data, instead of showing the wide variations indicated in this figure,
caused by the great irregularity of the original unharmonized values of Fig. 32.
The effect of this second plotting upon the irregular forms shown in Fig. 32 is
illustrated in Fig. 35, in which the curved or harmonized tapers from Fig. 33 are
replotted in the original form.!
The values when read from the curves are taken from the ordinates repre-
senting exact diameter classes. This set of curves therefore is evened off for values
of the diameter classes, and progresses regularly by 1-inch or 2-inch diameters.
Third Set of Curves, Tapers Based on Total Heights of Trees. We
now have, first, true averages of the original form of each separate
class, second, true averages for exact diameter classes instead of for
average diameters larger or smaller than these exact classes. Both
_
o
Upper diameters, inches
enwnwre am) Oo ©
ze
50
60 70 80 90
Total height of Tree, feet
Fic. 34.—Tapers based on total heights of trees. For trees of the same
D.B.H. class. 14-inch trees.
sets of curves deal, however, only with one separate height class. It
may happen that the trees of the 80-foot class are all slender, tapering
trees, while those of the 70-foot or 90-foot class are more cylindrical.
There is no reason why in a general table which seeks average form,
the accidental departure of form from the average, by a set of trees
in one height class, should be accepted if this deviation can be easily
shown and corrected.
To do this, it is necessary to compare the upper diameters of the
trees of different height classes, at the same points on the stem. D.B.H.
must therefore be eliminated as a variable and height substituted.
1Since height above stump is the basis of curves in Figs. 32 and 35, the tree
form is shown as if lying on its side. The diameter, instead of being plotted sym-
metrically on both sides of an axis, is plotted on the vertical scale above the base
of the figure. But by holding this figure at right angles, the form of the bole is
suggested.
METHODS OF CONSTRUCTING TAPER TABLES 203
A set of curves (the third) will therefore be made from all trees of
the same D.B.H., such as the 14-inch class. In this set the independent
variable which is plotted on the horizontal scale is the total height of
the tree in feet. The dependent variable is diameter or taper at upper
points, as in all the graphs used in this method.
The set of points, which is transferred from curves in Fig. 33 and falls in the
vertical column above the height of the tree, is the diameter of a 14-inch tree,
- 90 feet high, at each taper measurement, the larger diameters, beginning with
D.B.H., falling highest in the column.
After each series of points for 14-inch trees, representing trees of different total
heights as 80, 70, 60 and 50 feet, has been taken from the separate sets of curves
prepared in step 2, for each of these height classes, and plotted successively on
Fig. 34, the points representing diameters at the same height, e.g., at 8 feet from
stump, are connected.
Irregularities in the resultant curves show departure in form for one height
class as compared with others. By smoothing out these curves, the tapers of trees
of different height classes are harmonized. The scale used in this set is 5 feet
per inch for the horizontal scale, 2 inches per inch for the vertical scale. In Fig. 34
only the resultant harmonized values are shown
Fourth Set of Curves, Tapers Replotted on Basis of D.B.H. To utilize
the data from Fig. 34 the values may be read off direct, forming tables,
but it is customary to have these tables classified by height classes,
as in Fig. 33 instead of by diameter classes. To bring together these
values, the curved values for the separate diameters may again be assem-
bled on one sheet as in Fig. 33 with a separate sheet for each height,
diameters on the horizontal scale, upper diameters on the vertical scale,
and a curve for each fixed height above the stump. This replotting
should still further iron out any irregularities in taper values. The
taper table can be read from this set direct, but only for the fixed heights
given in the table, e.g., for 8, 16, 24 feet, ete.
Final Set of Curves, Tapers Replotted on Basis of Height above Stump.
One further step completes the curves of form, by restoring them to
the shape of the separate trees as shown in Fig. 32. In this final step the
values are plotted as for Fig. 35, with separate graphs for height classes,
height above ground on the horizontal scale, upper diameter or tapers
on the vertical scale and a curve for each diameter class.
The form of such a set of tapers for universal use should be graphic,
thus showing the upper diameter at every point on the stem. From
this set of graphs, board-foot volume tables for any log rule, length of
log, upper diameter limit or stump height, cubic volume, number and
dimensions of ties, poles or other piece products, can be determined.
It is apparently a universal basis for the construction of volume tables,
and while the number and diversity of such tables would remain as
great as ever, the field work of gathering data on form or volume would
204 THE FORM OF TREES AND TAPER TABLES
be obviated by the printing and general distribution of the graphs
giving the average form, from which tables could be prepared in the
office for whatever use was desired.
169. Limitations of Taper Tables. The real weakness in this
apparently sound method of preparing the basis for volume tables lies
in the fact that the result obtained does not differentiate form classes
of trees, but averages them on exactly the same basis as do the standard
volume tables. Its only merit therefore is in the transferring of records
Upper Diam
8 16 24 32 40 48 56 64 12 80 83 96
Height above Stump, Feet
Fic. 35.—Tapers read from Fig. 33 for four diameter classes, showing effect of har-
monized curves in smoothing out the irregularities of form shown in Fig. 32.
Similar curves are obtained from tapers replotted inform of Fig. 33 from curves
shown in Fig. 34. Such tapers will be harmonized by diameter and height classes.
of average tree forms to the office as a basis for future volume tables.
The form of the tables is bulky and does not lend itself to the further
extension necessary to show the form of trees of several different form
classes for each diameter and height class, though in the preparation
of standard volume tables by the U. 8. Forest Service, such taper tables
have been extensively employed. The use of taper tables in connec-
tion with standard form classes as a basis for universal volume tables
is discussed in Chapter XVI.
By preparing separate sets of taper tables for each form class based
on absolute or normal form of trees (§ 174) a permanent basic standard
of tree form is obtained which will fill all possible future requirements.
CHAPTER XVI
FORM CLASSES AND FORM FACTORS
170. The Need for Form Classes in Volume Tables. Trees which
have the same D.B.H. and total height may vary in form, as shown,
according as the tree is full boled, with “good” form, or concave
boled, with “bad” form. These gradations of form correspond with
differences in cubic volume. In order to further classify the volumes
of trees of the same D.B.H. and height, this range of volume due
solely to form must be separated into arbitrary classes or divisions.
Such a series is based on measurable differences in form, and the
classes thus established are termed form classes. The adoption of
form classes as a third variable in constructing volume tables has
been retarded in this country by the necessity for expressing volumes
in terms of board feet, by the labor of constructing even the simpler
tables based on diameter and height, and by the belief that the vari-
ations due to form could be more simply overcome by averaging them.
A second difficulty lay in the application of such form-class tables
in timber estimating, since cruisers were unaccustomed to judging
upper diameters by eye with the accuracy needed to distinguish between
the form classes. Differences in taper were readily recognized, but
differences in form were further obscured by the method of using
merchantable top diameter limits instead of total height. Practical
cruising did not seem to require such tables. But with the increasing
use of the cubic foot and the cord for pulpwood and in second-growth
timber, and the need for closer estimating, the desirability of distinguish-
ing form classes in volume tables is increasing. Such efforts as have
been made so far in this country follow standards prevailing in Europe,
where the universal use of the cubic unit, close utilization and high
values have made it necessary and possible to obtain more accurate
measurements of the standing timber.
One great possibility in this field is the demonstration that when
form classes are distinguished and the true form of the tree inside the
bark is made the basis, all species of trees will be shown to have practi-
cally the same forms and total volumes for the same form classes; hence
a single general table so classified would suffice for all field work. Were
this fact established, a basic table might then be constructed for each
205
206 FORM CLASSES AND FORM FACTORS
of various units of measure in addition to cubic feet. Once the average
form class of the trees or stand were determined, then volumes could
be obtained from these basic tables. Recent research in Sweden tends
to show that this generalization holds true for certain species already
investigated, namely spruce, fir, larch and Scotch pine.
171. Form Quotient as the Basis of Form Classes. The first real
step towards a solution of this problem was made by Schiffel in 1899,
who developed a method of expressing differences in form, previously
used (Schuberg, 1891) and known as the form quotient, which is the
percentage relation that the diameter at one-half the height bears to
the D.B.H.
The differences in form of the entire boles of trees (Chapter ITI)
are expressed by their divergence from a cylindrical form through a
series marked at definite stages by the complete paraboloid, cone, and
neiloid. Each of these solids can be measured by Newton’s formula:
V=(B+4,+0)e.
The middle point on the stem of a tree, regarding the entire bole as a
single complete solid, is evidently the point of greatest weight in deter-
mining its form and volume with respect to the cylinder whose base is
B and height h.
By a complicated calewation,- Schiffer: derives tne formua for
obtaining at one operation the true cubic contents of an entire stem as,
V =(.16B+.66b,)h.
This is known as Schiffel’s formula.
Newton’s formula, regarding the tree as a perfect, 1.e., compuete
conoid, and the diameter at top as zero would be,
V =(.162B+.662b,)h.
The ‘ universal’ character of Schiffel’s formula failed to make the
headway expected when it was first introduced in the United States
for the reasons that, to apply it, one must measure the diameters of
trees at one-half the stem height, and that the cubic unit of volume
was little in demand.
The really valuable part of Schiffel’s work was not the formula,
which was nothing new, but the form quotient. This was his demon-
stration that the true form, and consequently the variation in form of
1“New Method of Measuring Conifers,’ Review by B. E. Fernow of Article
by Schiffel, “Uber die Kubirung und Sortierung Stehender Nadelholz Schafter,”
Centralblatt fiir das gesammte Forstwesen, Dec., 1906, pp. 493-505, Forestry Quar-
terly, Vol. V, 1907, p. 29.
FORM QUOTIENT AS THE BASIS OF FORM CLASSES 207
different trees, could be indicated by the relation between diameter at
one-half height and D.B.H. (not diameter at stump).
In its standard form of expression:
‘ d
Form quotient = —.
4 D
In 1908 Tor Jonson corrected a slight inconsistency in Schiffel’s
method by insisting that the middle diameter be taken not at the middle
point of the stem but at the middle point measuring from B.H. This he
termed the absolute form quotient. This improvement finally secured a
consistent basis for expressing tree forms, eliminated height as a varia-
ble, and got rid of the great drawback of butt swelling. The absolute
form quotients of trees were now found to vary between .575 and
.825, i.e., the diameter at the middle point above B.H. bore this
relation to the D.B.H., whether both measurements were taken out-
side or inside the bark.
It was also discovered that in most cases the form quotient if reduced by a
constant would give the form factor for cubic contents of the tree. For instance,
J. F. Clark found that the reduction factor for the form quotients for balsam in the
Adirondacks was 0.21. This fact is of minor importance since it aids only in
obtaining the cubic contents of trees.
This standard of measuring form permitted the classification or
differentiation of the third variable of volume, namely, form independ-
ent of diameter or of height. Trees could be grouped into form classes
expressed by form quotients. Seven main form classes were formed,
namely, .50, .55, .60, .65, .70, .75, .80. Five sub-classes were also inter-
polated as .575, 625, .675, .725, .775. The extreme lower and upper
classes shown will be found only in individual trees. The average
form class for a given stand will fall usually between .575 and .75 and
may be correlated with the density of the stand as shown below.
|
Form class,
Character of stand based on
form quotient *
Poor density >... 2). ..6... 20 0.575-0.625
Fairly good density........ 65
Good'density= —s9: 5.2..." .675— .70
Overcrowdedins seas. oe 725— .75
* Tor Jonson, 1918.
But most important of all, the question as to whether the form of
trees was independent of species, site and region and dependent on gen-
eral laws, could now be determined.
208 FORM CLASSES AND FORM FACTORS
172. Resistance to Wind Pressure as the Determining Factor of
Tree Form. The theory explaining the form of the boles of trees,
which is now generally accepted, was first advanced by Prof. C.
Metzger, a German. This was, that the stem or bole is constructed
as a girder to withstand the pressure of wind. Based on this theory,
A. G. Hoejer, a civil engineer of Stockholm, devised the general formula
for tree form discussed in § 173. Prof. Tor Jonson applied this
formula first to spruce and then to Scotch pine, and demonstrated its
correctness; as a consequence, developing the basis for tables of abso-
lute form and volume for trees, and a new method of estimating
timber (§ 203).
Jonson’s conclusions, based on these investigations, are that tree
form depends entirely on the mechanical stresses to which the tree is
exposed, and is therefore independent of diameter, and height, and also
of species, age, site or any other factor, except as these factors in-
fluence the form of the crown. The force of the wind operates on
the crown of the tree and is focused or centered on a point representing
the geometric center of the crown. The pressure of the wind on the
tree crown constitutes a force which compels the tree to construct its
stem in such a manner that the same relative resistance to strain is
found at all points, the smallest possible amount of material being
used. As the concentrated force of the wind strikes a point situated
lower or higher on the tree, dependent on the crown area presented,
we get larger or smaller taper respectively, which means bad or
good form class. As the location of the point of attack of the bend-
ing force is determinative of form, this point is called the form point,
and can be expressed as a per cent of total height.
Here is a natural law, to which growth of trees, as mechanical struec-
tures designed to stand up against wind, corresponds. The full bole
of the forest-grown tree in a erowded stand, coinciding with a small
crown and high form point, meant that this location of the strain
required nearly equal strength along the total length of bole, which
could be attained by rapid growth of the upper bole. If the tree
were open-grown with a consequent long crown and a low form point,
this would permit of smaller upper diameters and require greater
strength lower down on the bole.
Since the form of the crown, especially its length, with relation
to the length of bole, determines this form point, this relation of crown
to bole, expressed by form point serves as an index to classify trees as
to their relative form classes or form quotients.
Any variation in average form, such as the admitted fact that the
average form quotient increases with age, is explained by a coincident
change in this crown and form point relationship. Open-grown trees
A GENERAL FORMULA FOR TREE FORM 209
possess a low form quotient, not because they are open-grown but
because the crowns of such trees are long and the form point low. Trees
with long clear length and high crowns possess a high form quotient,
whether they stand alone or in a crowded stand. Short trees may be
full-boled or the reverse—the rapidity of taper as a whole has no effect,
but the distribution of the taper, which alone affects the form quotient,
will vary with short trees as much as with tall, and on poor soils equally
with good.
173. A General Formula for Tree Form. On this basis, if the actual
form of trees with the same form quotient is similar, it would be possible
to construct taper tables based on each of the three variables, diameter,
height and form class, which would apply to all species of trees. To
apply this principle there was required a general formula which would
give the drameter of a tree of given form quotient, at any point on the
stem, and second, a demonstration that the actual measurements taken
on trees of this form quotient coincided with the results of the formula.
Once this was shown, the formula would permit of the construction
of a set of taper tables of universal application from which in turn any
manner of volume table could be derived. This is a more ambitious
program than the mere determination of form factors for cubic con-
tents, and promises permanent results.
The formula devised by A. G. Hoejer is based on the portion of the tree
above B.H.:
D=D.B.H. inside bark;
1=distance from top of tree to section;
d=diameter of section.
Then
d , ctl
—=( | y 5 ‘
D us c
C and ¢ are constants whose value depends upon the form quotient of the tree;
d ; = Eee :
1.€., upon D when d is measured at one-half height above D. Their value must be
found separately for each form class, and will then hold good for diameters at any
point on the bole of trees within this class, independent of total height of tree.
Absolute heights are not used in the formula, but percentage or relative heights,
regarding the height of any tree above B.H. as 100, and the distance below the
tip, of any other section as its per cent of this length, including sections below
B.H., whose per cent of height would exceed 100.
In the same way, absolute diameters are not used, but the D.B.H. is taken as
d i :
100, and the relative diameter D expressed as its proportion of 100.
These upper diameters are then measured at distances equaling tenths of this
total height above D,B.H.—thus falling at the same proportional height on each
210 FORM CLASSES AND FORM FACTORS
tree; e.g., for the form class 0.70 with diameter at 0.5 of height above B.H., as
0.7 of D.B.H., the values in the formula are:
For upper section,
70 c+50
= (7 | =. 1
Tee (1)
For D.B.H. section,
100 c+100
—=('] ft a ter et a ee
100 /— 7 me @)
If equation (2) is divided into equation (1), then
0.70 log (ce +100) =log (e+50) +(0.70—1) log C.
The value of this constant c is then found by trial. Inserting this value in equa-
tion (2) the value for constant C is found for the form class. Values for the remain-
ing form classes are found in a similar manner.
With the numerical value of the constants C and c determined, the normal diam-
eter of a perfectly formed tree can be found by this formula at any point on the
stem above B.H., and this normal diameter can also be calculated for stump height,
thus disregarding the stump taper.
By determining these normal diameters for trees of each D.B.H. and height
class, at intervals of one-tenth of the total height, and plotting these diameters
graphically, a set of taper curves is constructed (§ 167), for normal tree forms,
from which volume tables or form factors can be constructed which will have
universal application.
174. Applicability of Hoejer’s Formula in Determining Tree Forms. There
remained to test accuracy of these results by comparing them with measurements
on felled trees. The tests showed that for the conifers measured, spruce, fir, larch
and pine, the formula expressed the form of the living tree, when applied inside
the bark at all points including D.B.H., and that for species with thin bark such
as spruce, the same relations applied when measured outside bark. For Norway
Spruce the volumes of individual trees fall within + 3 per cent of those derived
by the formula. But for thick-barked species such as Scotch pine, a poorer form,
less cylindrical, was obtained outside bark, which changed the form class, but
did not seriously interfere with the application of the method. Claughton-
Wallin has since shown that this formula holds good for Norway or red pine
(Pinus resinosa) and white pine (Pinus strobus).
As with all attempts to study the laws of tree form, this formula depends on
measuring a diameter which is not affected by the abnormal flare at the butt;
hence any tree or species whose butt swelling extends above B.H. will not corre-
spond in form to the diameters in the formula based on this abnormal D.B.H.
It was found impossible to use the formula for western conifers since the form
d
quotient D was too low for this reason.
For general application, the second difficulty is the factor of bark thickness,
whose effect upon the form quotient and form class must be worked out for different
species with variable thicknesses of bark, so as to correlate the method with D.B.H.
measurements outside the bark, which must continue to be used in practical
estimating.
FORM FACTORS 211
Can these two variables be eliminated for American trees, and taper and volume
tables constructed for trees of each form class, thus attaining the goal of universal
volume tables?
For second-growth, or young timber, in which the factor of butt swelling will
not affect D.B.H., thiscan be done. Taper tables should be constructed from this
normal formula based on diameter inside bark at B.H. The average thickness of
bark at B.H. must be determined for the species, and by graphic interpolation
these D.I.B.“taper tables can be drawn for trees of each D.B.H. outside bark, from
which volume tables can be constructed in any desired unit.
For the larger trees or species with butt swelling extending above B.H., as for
instance, virgin stands of timber on the Pacific Coast, or Southern cypress, the
present practice of adhering to D.B.H. will probably be continued, and trees with
variable amounts of stump taper averaged together in volume tables regardless of
true form. The only alternative is to attempt a standard measurement of diameter
at a higher point on the bole, which will be difficult to adhere to in practice. Approx-
imate rather than absolute accuracy will continue in the preparation and use of
these tables for such timber.
When the variable influence of butt swelling is further aggravated by the
obsolete practice of basing volume tables on diameter at the stump, no consistent
volumes can be obtained to serve as standards for estimating.
175. Form Factors. The form of a tree is a variable independent
of diameter or height, while the form of a cylinder does not vary at all.
That of a cone is a constant, equal to one-third of the volume of a
cylinder of similar height. Taking the volume of a cylinder as the
unit of comparison, and dividing the volume of a cone by that of the
cylinder of equal diameter and height, the quotient is always .333 or
one-third. This can be termed the form factor of this cone, i.e., the
factor by which the volume of the cone is derived from that of the cylin-
der. It expresses the volume of the cone, but not itsform. In the same
way the form factor of the paraboloid is .5.
Form factors of trees can thus be found by dividing their cubic
volume by that of a cylinder of equal diameter and height.
B=Basal area of cylinder equivalent to that of tree;
h=height of cylinder and of tree;
Bh=volume of cylinder;
f=form factor or multiple expressing the relative volume of the
tree;
V =volume of tree.
Then
and
212 FORM CLASSES AND FORM FACTORS
Volumes of trees can thus be obtained from the volumes of cylinders,
when once the average form factor is known.
The form factor is therefore, in theory, a direct expression of the
relative volume of a tree compared with a standard or constant volume,
and tables of such factors were expected to give the key to universal
volume tables showing form classes. But the diameter of the cylinder
which is to serve as the unit or basic volume must first be obtained and
must equal that of the tree. If this diameter is taken at the stump or
at ground, the butt swelling gives an abnormally large irregular vari-
ation in the cylindrical volume. This method is known as the Absolute
Form Factor.
But the diameter can be shifted to B. H. with the cylinder equaling
the total height of tree as before. Form factors so calculated give uniform
or consistent results from which cubic volumes can be calculated,
and are termed Breast-high Form Factors. These form factors in turn
vary not only with the form of the tree, but with the total height as
well, hence could not be used to indicate absolute form. The reason
is that the diameter of the basic cylinder is taken, not at a height pro-
portional to the total height of the tree, but at the fixed height of 45
feet. For short trees this point falls proportionally nearer the tip,
with relatively smaller cylinder, than for tall trees of identical form.
The breast-high form factor therefore decreases as height of tree
increases.
In an effort to overcome this drawback and express form directly
by means of form factors, the so-called Normal Form Factor was devised,
in which the basal area is measured at a point on each tree represent-
ing a fixed ratio to the height of the tree. This plan has not proved
practical, owing to the difficulty of determining this point rapidly and
accurately. .
By comparing only the portion of the tree above B.H. with the
volume of a cylinder of equal height, the form factor for this portion
alone corresponds directly with variations in form for the tree. This
is known as Riniker’s Absolute Form Factor.
The Riniker form factor of trees of each form class was calculated by Jonson
from the normal form or tapers of trees of each D.B.H. and height class, taking
the diameters at points representing one-tenth of the stem above B.H. Then
yr
J
f ~ Bh
for the bole above B.H. only.
Since form quotients indicate correctly the relative forms of trees, absolute
form factors of trees whose form quotients are equal should also be equal. That
this is true is indicated by the following test, e.g., from investigations of Claughton-
Wallin and F, McVicker;:
STANDARD BREAST-HIGH FORM FACTORS 213
a Form Cubie Basis
rie quotient | form factor | trees
|
Reampime, Ontario; Came... 026 2.5.08. : 65 0.489 11
Scotch pine Sweden. 6..0:.0.00....0.. 65 441
Red pine, Ontario, Can......... GaN 70.3 480 30
peouch pine, Sweden... 2.2:.........- 70.3 484
Redsomes Ontario: Cani.....2........ 74.4 515 40
mpeotch maine, Sweden... ise... 0.2. cee as 74.4 . 524
White pine, Ontario, Can............. 70.8 482 9
HcoueaypmMe Sweden. os... ss. 4.3 0: - 70.8 489
White spruce, Ontario, Can............ 65.2 441 6
Scotch pine, Sweden)... 2 ......¢4-.4.. 0. 65.2 .444
176. The Derivation of Standard Breast-high Form Factors. The
two possible uses for form factors are seen to be, first, an expression of
relative forms of trees, second, a means of computing their total vol-
umes from that of cylinders.
It is not possible to combine these two functions in the same table
of form factors. The absolute form factors for total tree volume can-
not be correlated with D.B.H. nor with any other point on the bole,
while the form factors which are based upon D.B.H. and total volume
are not absolute but vary with height. But these Riniker’s absolute
form factors can be used to obtain a set of breast-high form factors
which represent the relative volumes of normally formed trees of all
diameters and heights when compared with the corresponding cylinders.
The steps in this calculation are:
1. Compute the Riniker form factor for trees of each form class.
2. Obtain the normal stump diameter from Hoejer’s formula. Stumps were
taken as 1 per cent of the height of the tree. The actual stump diameter is always
too large, due to butt swelling. The conception of a normal stump diameter is
the diameter which the stump would have if the normal curve of the stem from
top to D.B.H. were prolonged downward to stump height.
3. Find the diameter at one-half the distance from stump to top, by Hoejer’s
formula.
4. Express both the stump diameter and the diameter at one-half height in
per cent of D.B.H. and compute the new form quotient, this time based on height
above stump.
If diameter at 3h =67.7 per cent of D.B.H.
Stump diameter =103.0 per cent of D.B.H.
67.7
F fhenti: = —|Gbve
orm quotien 108 0 5
214 FORM CLASSES AND FORM FACTORS
5. From the table of absolute form factors interpolate for the form factor required
to coincide with this form quotient.!
6. The basal area corresponding to the normal diameter at the stump is found
as follows:
Do =normal stump diameter;
D=D:Beik:
o=normal basal area at stump;
B=basal area at D.B.H.
If o=1.0pD,
De? =) Op?D?,
iB _7Do
4
aD?
12092
4
=. 0p2B.
7. Total volume of the stem is then
V =Buhfo
=B1.0phfo.
8. Breast-high form factor is
— lé
Bh
=1.0p"fo.
f
This series of breast-high form factors shows the diminution with increased
height, the cause of which is set forth in §175. These form factors are given in
Table LX XXII, Appendix C, p. 497.
Since form is best shown by taper tables, and volume is best obtained
directly from volume tables, the use of form factors in America has
but little practical application and has been adopted to a very limited
extent. Were the breast-high form factors more regular they would
serve as a means of constructing volume tables by graphic methods
(§ 188) in which the curves being comparatively straight could be
extended and interpolated with less chance for error than by the ordi-
nary methods.
177. Merchantable Form Factors. Form factors based on the
merchantable contents of the tree in cubie feet, or upon the net cubic
1 These absolute form factors are for the entire tree, but are based on the
theoretical stump diameter, hence are inapplicable for practical use.
FORM CLASSES AND UNIVERSAL VOLUME TABLES 215
volume utilized as board feet or in any other unit, can be computed
by first ascertaining this net volume. The form factor is
Bh
far.
These form factors serve no useful purpose.
178. Form Height. Form height is the product of form times
height.
Since V=Bhf, tables of form height simply eliminate one of the
two multiplications necessary in deriving cubic volumes.
‘orm Class
0.710
0.690
eal =
i
|
HE
ee eee
350 ———
20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 195 100105110 115120
< Heightiin Feet
Fia. 36.—Curves of breast-high form factors for form classes from .50 to .80 inclu-
sive, showing effect of height upon the form factor. From Tor Jonson.
179. Form Classes and Universal Volume Tables as Applied to
Conditions in America. The standard form classes, when applied to
trees of different diameter and height, thus distinguish three variables
just as did the universal volume tables based on diameter, merchant-
able length and rate of taper. Universal volume tables if based on
total heights would show volumes for the given unit in three instead
of two dimensions; D.B.H., Height, Form Class.
But to derive universal volume tables by form classes to be based
on merchantable length instead of total height would not be so simple,
for the following reasons:
216 FORM CLASSES AND FORM FACTORS
If taken to a uniform or fixed top diameter, trees with a high form
quotient would be cut higher in the top and fall into a different merchant-
able height class than trees with a low form quotient. Therefore, for
trees of different form quotients, to attain the same merchantable top
diameter, trees with the lower quotients must be taller than those whose
form quotient is high. Hence total and merchantable heights are
not interchangeable for trees whose form quotients differ.
If taken to variable top diameters, this second variable will make
it practically impossible to distinguish form classes based on total
height in the volumes
72 ft.
64 ft. AD
given, for these tops
4 logs
80 ft.
would not vary in any
definite relation to
total height or form.
As long as mer-
chantable rather than
total heights are used
in volume tables and
timber estimating,
form classes based on
actual form of the
tree cannot be used
to construct volume
tables in which trees
of different form are
20” 20” 20”
Fic. 37.—Effect of cutting to a fixed top diameter, upon
merchantable height of trees having different form
quotients. A form quotient of .60 requires either a
shorter merchantable length or a taller tree than one separated, and _ the
of .80. principle of averaging
the differences in vol-
ume due to form must continue to be used for such tables.
But for cubic feet, basic volume tables may be made up giving the
volume of each diameter, height and form class. Similar tables can be
constructed in any unit of volume, or for any log rule, from tables of
normal taper. In applying these tables, the method would be not to
attempt to tally each tree in its proper form class, but to determine
average form classes ($171) for stands or other subdivisions of the
forest, the volumes for which can be taken from this basic table to form
a standard volume table for the trees to which it applies. Not over
three such tables would be apt to be needed for any tract, however
large and varied.
Methods of rapidly determining the form class of sample trees, in
order to apply such a system, are given in § 201,§ 202 and § 203.
REFERENCES 217
REFERENCES
New Method of Measuring Volumes of Conifers, Review of Schiffel’s method by
B. E. Fernow, Forestry Quarterly, Vol. V, 1907, p. 29.
Das Gesetz des Inholts der Baum Stiimme. Forstwissenschaftliches Centralblatt,
Aug., 1912, pp. 397-419.
Massatabellar fiir Triduppskattnung, Tor Jonson, Stockholm, Sweden, 1918.
Review, Forestry Quarterly, Vol. XI, 1913, p. 399.
Article by L. Mattson-Marne, Skogsverdsféreningens Tidskirft, Feb., 1917, pp. 201-36.
Form Variations of Larch, L. Mattson-Marne, Meddelanden frau Statens Skogsfor-
soksanstalt, 1917, pp. 843-922; Review, Journal of Forestry, Vol. XVI, 1918,
p. 725.
The Absolute Form Quotient, H. Claughton-Wallin, Journal of Forestry, Vol. XVI,
1918, p. 523.
Tor Jonson, “Absolute Form Quotient” as an Expression of Taper, H. Claughton-
‘ Wallin and F. MeVicker, Journal of Forestry, Vol. XVIII, 1920, p. 346.
Die Formausbildung der Baumstiimme, Von Guttenberg, Oecesterreichische Viertel-
jahrschrift fiir Forstwesen, 1915, p. 217; Review, Forestry Quarterly, Vol.
XIV, 1916, p. 114.
CHAPTER XVII
FRUSTUM FORM FACTORS FOR MERCHANTABLE CONTENTS
IN BOARD FEET
180. The Principle of the Frustum Form Factor. In an effort to
simplify the construction and improve the accuracy of volume tables
for board feet based upon merchantable heights and top diameters,
a merchantable form factor has been devised by Donald Bruce.
Timber cruisers in the Pacific Northwest had already made use
of the similarity in form of the merchantable portion of the tree to that
of the frustum of a cone, but had neglected the possible differences in
form and volume between the cone and the merchantable bole. The new
method adopts the frustum of the cone as the basic volume, instead of
the cylinder as for the form factors discussed in Chapter XVI, and then
compares this volume with that of the tree, to determine their true
relation. This relation is expressed as a form factor in the usual manner.
V =volume in tree;
V’=volume in frustum of cone;
f=form factor.
Then
V
f=
and
V=V*f.
The contents of this frustum were measured as the scaled board-
foot contents of cylinders representing the logs into which the bole
would be cut. The length of these sections was fixed at 16 feet, and
their upper diameters were determined by the diameter of the frustum
at the required point. The form factor obtained by comparing the
total scaled volume of the merchantable bole with that of the frustum
so measured is termed the Frustwm Form Factor and is a merchantable
form factor having values close to 1, since the deductions from full
cubic contents of bole have been made both in the frustum and in the
tree.
The merits of the frustum form factor method for constructing
volume tables are that it applies directly to the merchantable portion
218
BASIS OF DETERMINING DIMENSIONS OF THE FRUSTUM 219
of the tree, on the same basis as used in timber estimating to top
diameters, and that the values of the form factors tend to vary but little
from a straight line, thus permitting the construction of curves of board-
foot volume with greater accuracy than when volumes are plotted
directly (§ 138). This advantage permits of constructing such tables
on the basis of fewer measurements of felled trees.
181. Basis of Determining Dimensions of the Frustum. The top
diameter of the frustum is supposed to coincide with the top diameter
inside bark of the merchantable length of each tree class. The diam-
eter at its base, which is at stump height is arbitrarily fixed as equal
to D.B.H. outside bark. No pretense is made that this form factor
is a scientific basis for studying tree form. Actual D.I.B. at stump
may or may not coincide with D.B.H. outside bark. The base of the
cone must be correlated with D.B.H. rather than with stump diam-
eters (§ 175) and this assumption is satisfactory.
Since the sides of a cone are straight, the upper diameters of each
“log,” or standard length into which this frustum is divided, are
determined by proportion, to the nearest 75 inch.
In calculating the volumes of the frustums of cones the determination of the
diameter at the top of each successive 16-foot log for cones of different top and
base dimensions is best per-
formed by plotting the form
of the cone on cross-section
paper, on which the vertical
scale shows diameters and the
horizontal scale shows heights
in feet. Plot, first, D.I.B.
equals D.B.H. at zero or
stump height; next, top diam-
eter inside bark at the mer-
chantable height. | Connect SIG mn 2s o2n wed Nees) we bGlnnGd
these two points by a straight eae
line representing the side of Fic. 38.—Method of plotting a frustum from
the frustum. The diameters Which to determine the top diameters of the
inside bark at top of each log logs which it contains.
are then read at 16 feet, 32
feet, etc., to the nearest ;’5 inch. The log rule should be tabulated to show the
values for each 7o inch.
182. Character and Utility of Frustum Form Factors. That the frustum form
factor is a practical rather than a scientific basis of measurement is shown by the
following facts: The absolute form factor of the total contents of the bole (§ 175)
would be 0.5 when the tree has the form of a paraboloid. A truncated portion of
the bole, with the rapidly tapering top eliminated, when compared with a trun-
cated cone having the same top diameter, represents the lower portion of a cone
of considerably greater height than that of the tree or paraboloid.
For cone and paraboloid (or tree) of equal total height, the form factor of the
0.5
tree, compared with the cone is 033 or 1.50, since 0.5 and 0.33 are the respective
220 FRUSTUM FORM FACTORS
volume form factors of the paraboloid and cone when compared with a cylinder of
equal dimensions.
The nearer the top of the tree this upper diameter falls, or the closer the degree
of utilization, the shorter will the completed cone become, until it coincides with
the paraboloid in height. In the same manner the frustum form factor will increase,
until it reaches a maximum of 1.50 for the completed cone.
Chandler,! in an extensive investigation of the frustum form factor of northern
hardwoods, birch, beech and maple, determined that this factor was independent of
species, site or other influences, and independent of diameter and height, but was
dependent on the two factors, form quotient, and taper ratio. The form quotient
agrees in principle with that of Tor Jonson. Based on D.B.H., instead of stump,
it was computed for merchantable rather than total height, by first subtracting
diameter at top or d from both diameter at B.H. and at middle of merchantable
length. Then
d,—d
nasties Pere
The taper ratio is the ratio between top diameter of merchantable bole, and
DBsH:
Merchantable cubic frustum form factors were found to diminish as form
quotient diminished and as taper ratio increased. The first result is obvious.
The second confirms the conclusions set forth above as to the effect of close utiliza-
tion in increasing the frustum form factor.
These researches have definitely proved, on an empirical basis, the fact that,
other things being equal, frustum form factors based on a fixed top diameter do
not express a scientific relation between the form and volume, but will vary with
the relation between cone and paraboloid. In its final analysis, the frustum form
factor is an endeavor to express the paraboloidal forms of trees by the use of frustums
of cones and the application of a correction or form factor. Although a great
improvement over older methods if intelligently applied, it is not a universal
method, since its results vary with taper ratio, butt swelling, bark thickness, and the
top diameter utilized.
On the other hand, the natural divergence in the total form and cubic volume
of trees which gives rise to the variation in form quotients of from 0.575 to 0.8 is
overcome in a marked degree by the substitution of the merchantable frustum
form factor since, first, trees with a high-form quotient and of the same total height
will be cut higher in the tops than those with a low-form quotient (§ 179). The
merchantable form factor in itself coincides with this greater utilization and there-
fore approaches closer to unity, for both forms. If all trees are utilized to a fixed
top diameter, a cylindrical tree, being cut nearer to its tip than a conical tree,
would have fallen into a larger total height class than the conical tree, hence its
per cent of cylindrical contents would have been much greater for merchantable
form factor than that of the conical tree—a difference not appearing in the frustum
form factor. Second, where the actual top diameter is made to coincide with the
point at which the tree is commonly utilized instead of with a fixed top, there is apt
to be still closer approach to unity in the form factors. The length and character
of the crown usually determines the amount of taper from the base of the crown
to the tip of the tree and consequently its distribution on the stem (§ 172). In
rough utilization, the last saw cut tends to bear a direct relation to the length of
crown and to fall nearer to the base of the crown than to its tip. This is especially
1 Bul. 210, Vermont Agr. Exp. Sta. 1918.
CALCULATION OF THE FRUSTUM FORM FACTOR 221
true of hardwoods with branching crowns. Measured from this point, the frustum
of the tree will not differ greatly from that of either a cone or a paraboloid.
A great source of irregularity in frustum form factors, as in absolute form factors
for cubic contents, is found to be the influence of butt swelling extending above
B.H. and second, the influence of thickness of bark. Both of these factors reduce
the proportion of woody contents to the dimensions and consequently reduce the
form factor.
183. Calculation of the True Frustum Form Factor. A far more
serious difficulty in the use of the frustum form factor lies in securing
the exact coincidence of the top diameters of the frustums, used as the
unit or standard for volume, and the average top diameters of the trees
whose volumes are to be compared for the determination of the form
factors. There is but one exact method, namely to compute the form
factors of a given height separately for each tree whose D.B.H. and
top diameter differ even by ;5-inch, by using a frustum whose three
dimensions exactly coincide with those of the tree frustum. This
method gives the most consistent form factors. The results for long-
leaf pine given in the table on p. 222 were obtained by this method.
This method can be simplified by first averaging together for all
the trees in a diameter and height class the four factors, volume, D.B.H.,
height, and top diameter. The frustum of a cone having these aver-
age dimensions is then used to determine the frustum form factor of
the class, by comparing its volume with that of the average tree of
the class. While less accurate, this method reduces the computations
considerably and is within the required limits of accuracy of the method.
By this method, the computation of the frustum form factors is
the first step in the construction of the volume table for which they
are intended.
184. Calculation of the Volumes of Frustums. Influence of Fixed
versus Variable Top Diameters. The purpose of the frustum form
factors thus obtained is to make possible the construction of a volume
table in board feet, by applying these factors to the volumes of frustums
of cones. This may be done in the office, once the factors are known
and the dimensions of the frustums determined.
The second step is therefore to determine these dimensions of frus-
tums of cones. The base is fixed, being equal to D.B.H., in 1- or 2-inch
classes. But the top diameter of these cones is a source of trouble.
As seen in the construction of volume tables (§§ 157-158) the top diam-
eters to which trees are actually utilized tends to decrease as height
increases, and to increase with D.B.H. The table will be based on
one of two plans, a fixed top diameter, or variable top diameters coin-
ciding with actual utilization.
Whichever basis is adopted, the top diameters of the frustums
must coincide with the average top diameter of the merchantable boles,
222 FRUSTUM FORM FACTORS
whose volume is sought. If frustums having a fixed top diameter
limit are used, the form factors should have been computed from trees
measured to this same top diameter. If on the other hand, an attempt
is made to base the table on variable or actual used top diameters, then
the average actual top diameter for each diameter and height class
should first be found and the frustum having the requisite top dimen-
sion for each class computed.
TABLE XXXV
True FrustumM Form Factors ror LONGLEAF PINE, FROM FrRustuMs WHosE Top
DIAMETERS CoIncIpE EXACTLY WITH THE AVERAGE Top DIAMETER OF TREES
or Eacu D.B.H. anp Hetcaut Crass
Merchantable Length in 16-foot Logs
|
D.B-H: 2 2% | 3 | 32 4 | 42 Averaged by
| —- diameter,
Inches Frustum Form Factors Weighted
12 OPOSM FOROS ire ctw | teste alt Cexereran [eccrine 0.980
13 Oa 2184 ORGOM ar AOS eters 2 .992
14 .96 87 EOS /g LOS Rec wleeiee .952
15 SOD Mel sOie | OSs el OD mie) peared eles .958
16 IO2 ET e- .94°) 1.04 | 0.94 | 1.10 .953
17 .89 .95 91 .99 OOM eee .932
18 .89 .98 .90 5965) als 00 .9384
19 .96 .90 .94 .98 ROOT Re eee 954
20 1.05 .95 .88 97 94 .99 .937
21 S00) Whasreuee seta | eeeto es 94 .92 .902
22 Sor fie .92 .89 .94 .96 .99 .938
23 .93 .97 94 .88 | 1.00 91 .926
24 .93 94 87 A 9 fag tied leet ae .921
25 ee .96 .94 SOS = AOA. ee 1.000
26 SOF Aye ace .90 | 1.07 .90 .934
27 AORTA aya .96 .95 .93 .95 .941
28 Gute Store ll clout .93 .80 | .101 .913
~ 29 Deets diay plleKonl 2 Ub ee hoods .970
30 eye setae .98 .85 S908) oe .948
31 94 .80 who lien seeders a Ll bes ha se .927
32 nent Bree AN pasate SSO Mle .915
33
34 ee {O20 es .85 el || sess 817
Av’g’d by height, | Weighted
weighted. ..... 0.939) 0.961) 0.932) 0.958, 0.966) 0.962; average 0.9468
1
It is possible, of course, to prepare a table of frustum volumes using
fixed top diameters, and compute the form factors of trees for those
classes whose top diameters are larger or smaller, but in this case the.
CALCULATION OF THE VOLUMES OF FRUSTUMS 223
form factors vary not with form alone but also with difference in volume
due to difference in top diameter independent of form. The results
are shown in Table XXXVI where an average top of 13.2 inches was
used on all frustums,
TABLE XXXVI
Frustum Form Factors ror 555 LonGLteaF Pines, Coosa County, ALABAMA,
BASED ON AVERAGE Top DIAMETER OF 13.2 INCHES FoR FRUSTUMS
Merchantable Length in 16-foot Logs
; | 21 | alk se! hey | “
D.B.H.
Inches Frustum Form Factors
14 0.53 | 0.53 0.54
15 57 | 59 50 55
16 a pee 51 56 j| 0.53 0.57
17 67 | Cs aes 69 60
18 88 5D, | | 72 Tae | Hes 69
19 1.03 81 84 81 78
20 ots 1.00 | ee 96 87 86
21 Mey ily IQSt Ht ee 85 79
22 Pa 1.39 1300) - 7 OORT? STV OILE Vl 88
23 1.54 1.39 1.19 98 1.09
24 1.40 1.40 bale: 1.26
25 fe ie 1). 37; 1.34 1333) ol, licO6
26 2.60 95 1.85 1-21 1.47 97
27 1.97 1.52 1.22 123 1.14
28 te? 1.26 97 27
29 1.67 1.35
30 ia Dea 1.98 {237 17
31 2.36 1.04 1.18 GSP coher MeSetry
32 Oa 1.76 are: 1.43
|
Such a table serves no useful purpose.
The variation of top diameters actually utilized is shown in Table
XXXVII.
The values in this table, evened off by curves, would give proper
dimensions for frustums for the volume table desired.
The two steps described mean a double calculation of frustum
volumes, first, as a basis of regular form factors, second as a basis of
regular volumes. The second set of frustums also serves the purpose
of obtaining the volumes for exact diameter and height classes, instead
of for the actual average diameters and heights of the trees measured
(§ 187).
224 FRUSTUM FORM FACTORS
TABLE XXXVII
ActuAL AVERAGE Top DIAMETERS OF MERCHANTABLE LENGTHS, LONGLEAF PINE,
Coosa Co., Auta. Basis 555 Trees; AveRAGE oF ALL Top DIAMETERS 13.2
INCHES
Merchantable Length in 16-foot Logs
2 21 | 3 34 | 4 | 43 5
D.B.H. |
Inches Top Diameters, Instp— BAaRK—INCHES
10
11
12 9.5 8.5
13 9.7 1.5 8.8
14 9.9 9.2 9.3 8.7
15 10.4 10.3 8.9 9.1
16 1D 10.4 9.3 8.6 7.8
17 13 155 10.4 10.2 9.1
18 13.1 ART ie IKON O72 Gl -2E6
19 13.8 PAG} 1271 11.3 10.9 9.2
20 S35 7/ 130. a tant 13.1 12.3 11.6
21 16.7 erase 14.1 13.2 eel 11.4
22 rane 176d Oe dae 2 VAT Nae eld 7 a
23 18.0 LO eons 14.2 14.1 13.8
24 17.4 et 16.2 15.9 14.1
25 ae 17.2 IEF 5 16.7 13.3
26 21.3 15.4 19.7 16.9 N70 14.1
27 21.6 a ANG 19°42 4) dos efit 16.0
28 Me Pore aerate are 17.4 16.2 16.6
29 eee seks 20.5 18.8
30 Waksoee sae 24.0 20.8 16.2 NZ)
31 25.3 16.4 18.3 14.6 17.8
32 eos Sore 23.2 21.2
33
34 see 26.8 hie, 21.0 22.4
Of the two methods, the use of a fixed top diameter is preferable
wherever utilization does not depart too far from this standard. If
necessary, such a table of volumes could be corrected for actual utili-
zation, by subtracting the per cent of volume lost by cutting to a lower
point and larger diameter. In this case the same method must be used
in estimating the standing timber, namely, to tally the heights of the
trees to the fixed top diameter used, and then discount for waste.
185. Construction of the Volume Table from Frustum Form Factors.
A Short Method. The third and final step is to construct the volume
table by multiplying the volumes of the frustums by the form factors
for each class,
FORM FACTORS FOR BOARD FEET 225
Frustum form factors can be computed if desired, in cubic feet.
For board feet, any log rule may be used as desired.
A shorter but less satisfactory method is to first determine the top
diameters of the frustums to be used in the base table and prepare the
table of frustum volumes; second, to compute the arbitrary form
factors which are obtained by dividing the average volumes of the trees
in each class by the volume of the proper frustum, disregarding the
possible difference in top diameter and average height for the class;
and from these factors, to construct the volume table. This method
works best when fixed top diameters are used in logging and the dif-
ferences in top diameters between frustums and trees is small.
The method of frustum form factors has resulted in such a marked
increase In accuracy and economy in preparation of standard volume
tables based on merchantable board-foot contents that it has practically
superseded the standard methods of preparing these volume tables,
and until total height and tables based on form classes supersede the
use of merchantable heights in timber estimating, this method will
continue to be used extensively.
186. Other Merchantable Form Factors for Board Feet. Merchant-
able form factors based on the volume of a cylinder whose height equals
the merchantable length in the tree have been proposed by E. I. Terry.
Merchantable volume tables based on the contents of frustums of
paraboloids whose top diameters equal one-half D.B.H., scaled in 16-
foot logs, have been computed by the Forest Service. These correspond
in principle to the basic volumes of frustums of cones, and can be used
for calculating form factors in the same manner, but offer no special
advantage over the frustums of cones for the purpose required.
REFERENCES
A New Method of Constructing Volume Tables, Donald Bruce, Forestry Quarterly,
“Vol. 2X 1912) px 2s.
The Use of Frustum Form Factors in Constructing Volume Tables, Donald Bruce,
Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 278.
Further Notes on Frustum Form Factor Volume Tables, Donald Bruce, Proc. Soc.
Am. Foresters, Vol. X, 1915, p. 315.
The Use of Frustum Form Factors in Constructing Volume Tables for Western
Yellow Pine in the Southwest, Clarence F. Korstian, Proc. Soc. Am. Foresters,
Vol. X, 1915, p. 301.
Top Diameters as Affecting the Frustum Form Factor for Longleaf Pine, H. H.
Chapman, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 185.
Frustum Form Factors of Hard Maple and Yellow Birch, B. A. Chandler, Bul. 210,
Vermont Agr. Exp. Sta., May, 1918.
A Formula Method for Estimating Timber, E. I. Terry, Journal of Forestry,
Vol. XVII, 1919, p. 413.
Comment on Above, Donald Bruce, Journal, Vol. XVII, 1919, p. 691.
Further Comment, E. I. Terry, Journal, Vol. XVIII, 1920, p. 160.
CHAPTER XVIII
THE MEASUREMENT OF STANDING TREES
187. The Problem of Measuring Standing Timber for Volume.
Standing trees are measured to determine their contents in cubic feet
or in terms of manufactured products such as board feet or cross-ties.
Trees are measured as a means of determining the contents of entire
stands. These may be either average or sample trees, of which only
afew are measured, or all of the trees in a stand or part of a stand may
be tallied.
Thevolumescontained in standing trees cannot be measured directly.
Even the volume of the logs in the felled tree is computed from the
measurement of their diameters and lengths. These computations,
tabulated as log rules and as volume tables reduce the problem of esti-
mating the volume of standing trees to that of measuring their merchant-
able lengths and diameters.
The cruiser must determine the height of trees either by instruments
based on geometric principles of similar triangles, at considerable
expenditure of time or by the eye, which is the only practical method
where all or a large portion of the stand is to be so measured.
Still more difficult is the actual measurement of diameters at the
top of each log in the standing tree, which must be known when log
rules are substituted for volume tables in timber estimating. Instead,
the cruiser measures the diameter within reach, that at B.H. or stump,
and judges the rate of taper as well as height, by eye, thus arriving at
these upper diameters by calculation from a known measurement.
Diameter breast high (D.B.H) is the only actual and accurate
measurement which it is practicable to take upon all or a large per cent
of the timber. All upper points are either measured on a few trees
only, to obtain averages, or else are judged solely by eye; and since
such ocular measurements are confined to dimensions, heights or log
lengths, and diameters at upper points on the bole, the cruiser is depend-
ent entirely on the computed volumes for these dimensions shown in
log rules or volume tables. He may by experience correlate these
volumes with their respective dimensions, just as stock buyers learn
to guess the weights of animals, and may arrive directly at the volume
226
THE MEASUREMENT OF TREE DIAMETERS 227
of the tree or stand, but the method is far more uncertain than if depend-
ence is placed on the computed volumes of the logs or trees as shown
in tables.
In the use of volume tables, then, the accepted standards of volumes
set by these tables are substituted for guessing as to the contents.
The measurements required may be :
1. Diameter at base.
a. Standardized at D.B.H., outside bark.
b. Stump diameter inside bark, still in use by old time
cruisers.
2. Height of tree.
a. Total height to tip.
b. Merchantable height.
1’. To a fixed top diameter.
2’. To a variable top diameter.
3. Actual measurement of an upper diameter to determine
form (when form classes are distinguished).
a. At middle of stem above D.B.H. (Jonson).
b. At middle of stem above stump (Schiffel).
c. At top of last log.
188. The Measurement of Tree Diameters—Diameter Classes.
Stand Tables. Diameters will be averaged in either 1-inch or 2-inch
classes. In the East and with species of a small total range of diameters,
l-inch classes are preferable. Especially with such species as spruce
and white pine, l-inch diameter classes are necessary to give a proper
basis for determination of the rate of growth, and the number of such
classes is not great enough to act as a drawback in estimating.
A stand table is a tabular statement of the number of trees, in
each diameter class standing on a given area. By dividing the total
stand table by the area in acres, the stand per acre is shown, in which
case the trees in each diameter class are usually expressed in decimals
to two places, e.g., 12-inch class, 4.63 trees, ete.
On the Pacific Coast, with a wide range of diameters running up
to 60 inches or over, it is unnecessary and inadvisable to make smaller
than 2-inch diameter classes.!
189. Instruments for Measuring Diameter. Calipers, Description
and Method of Use. Calipers have been the standard instrument
1JTn French forest practice, 5 centimeters is the division used. This corresponds
to 1.97 inches.
The centimeter divisions were evidently too small and the next convenient
division point was 5 centimeters. This is not an argument against the use of
1-inch diameter classes for Eastern species.
228 THE MEASUREMENT OF STANDING TREES
for measuring the diameter of standing trees and their use is necessary
in taking taper measurements on down timber which cannot be meas-
ured with diameter tape. The standard type of calipers for eastern
Fic. 39—Calipers used in measuring the diameters of standing trees.
hardwoods has a beam 36 inches long with arms one-half that length.
A smaller type may be used for trees whose diameter does not exceed
2 feet as in spruce or second-growth timber. The standard calipers
have a beam graduated on both sides to inches and tenths, and two
arms, one of which is bolted to the end of the beam, the other a sliding
arm, the beam
| passing through a
slot.
a Ite z © Fig. 40 indicates
the construction
of thisarm. The
i essential feature
‘e im i Cher
a pressed against
the tree, the arm
Fic. 40.—Construction of calipers, to secure adjustment of jg easily moved
movable arm at right angles to bar. along the beam—
but when in use
it takes a position at right angles with the beam and parallel to the
other arm. The position of this arm is adjustable by the movement of
the screw (a) which sets a movable plate.
In use the arms must be at right angles to the beam. If warped or
out of adjustment, corresponding errors in measuring diameters will
occur. The correct diameter can be obtained only by holding the cali-
THE DIAMETER TAPE 229
pers horizontally, with the beam in contact with the tree at the point
desired, usually at B.H. If measured with the tips of the calipers,
the errors resulting from false adjustment or warping are exaggerated.
If measured with the calipers held at an angle, the point measured is
probably above D.B.H. and correspondingly too small. If measured
below D.B.H., a large error results from the rapidly increasing diameter
of the tree due to stump taper. An average measurement 6 inches
below the desired point or at 4 feet will incur from 5 to 8 per cent excess
volume, depending upon the rapidity of the taper.
Where the exact average diameter of a tree is desired, two measure-
ments must be taken at right angles and the mean recorded to 75 inch.
In timber estimating, where large numbers of trees are measured, but
one diameter is taken, with no efforts made to determine the average
even on trees of eccentric cross sections since it is assumed that errors
incurred in this way are compensating. A precaution sometimes used
is to measure half of the trees in one cardinal direction, and the remainder
in the other (French).
190. The Diameter Tape. The irregularity in the form of trees,
both as to cross section and bark, makes it practically impossible to
obtain consistent results in two successive measurements of diameter
of the same tree
with calipers even
when the mean
diameter is taken
as above indicated. °
For permanent
records on_ plots
to be subsequently
measured for deter-
mination of growth,
consistency in
diameter measure-
ment is absolutely Fic. 41—Tape for measuring girths and diameters.
required.
For this purpose it has been found that the diameter tape must be
substituted for calipers. The graduations on the diameter tape are in
inches of diameter, each inch equal to 3.1416 inches in girth. In theory,
the measurement of the circumference of a tree gives a plus error when
compared with the actual mean diameter. Actual tests at the Fort
Valley Experiment Station by Scherer on one hundred trees showed
that the excess in diameter from tape over caliper measurement was
2 per cent, but the consistency of two successive tape measurements
as compared with successive caliper measurements showed that the
230 THE MEASUREMENT OF STANDING TREES
total error of calipers over tape was in the proportion of 21 to 1. The
diameter tape should therefore be adopted for all measurements of
permanent sample plots.
191. The Biltmore Stick. Although calipers can be taken apart
for travel and packing, they are cumbersome to carry in timber esti-
mating especially through brush and over rough ground. When in
addition a beam of 60 inches in length is required, their use becomes
extremely burdensome.
The Biltmore Stick, devised by Dr. C. A. Schenck, substitutes a
straight stick for calipers and has been widely adopted by foresters
for practical timber cruising.
The principle of the Biltmore Stick is as follows: A straight stick,
if held horizontally, tangent to or in contact with the bole of the tree,
and at arm’s length from the eye, forms the far side of a triangle whose
other two sides are lines of sight from eye to each side of the tree, and
which intersect the stick at definite points. When the stick is held
; so that one of
C A these lines of
sight intersects
one end, a scale
A can be placed
upon the stick
starting at zero
at this end, and
the point of in-
Fic. 42.—Principle upon which the Biltmore stick is tersection of the
constructed. other line of
sight, if the eye
is held in its original position without turning the head, will indicate
on the scale the diameter of the tree at this point.
Since this intercepted distance on the stick is evidently less than the diameter
of the tree, which is at a greater distance and cannot even be seen correctly, the
distances corresponding to the diameters wanted will be less than these diameters
and this difference increases with diameter of tree, so that the graduations on the
stick for successive diameters fall closer together for the larger diameters. The
values of the graduations on the stick are directly dependent on the dimensions
of the triangle which is determined by the length of the arm or reach. This ranges
from 23 to 27 inches with an average of 25 inches.
The formula for computing the values of this scale is
a=length of reach in inches;
D=D.B.H.
THE BILTMORE STICK 231
aD
V a(a+D)
- | aD?
si a+D
The derivation of this formula is as follows:
Scale =
AB AB’
BC BC’
D
AB=a inches, and BC
Substituting these values,
a AB’
BC D’
2
D
= = AB'XBC.
aD
4/2
~ AB?
(AB’)2=(AC’)?—(B'C’)?.
(I) BC
By substitution,
DNA LDN
(AB’)?= («+5) ~ (5) =(a)?+aD=a(a+D).
2 2
(II) AB'=V/a(a+D).
Substituting this value for AB’ in equation (1),
aD
BC peal
V ala +D)
Since BC is the scale for 4} of the diameter of the circle, the formula for the scale
for the whole circle is !
aD a aD?
V a(a +D) at)!
Scale =
The Biltmore stick is less accurate than the calipers or diameter
tape and should therefore never be used for scientific measurements or
permanent records. To insure complete accuracy in the use of a prop-
erly graduated stick, the following conditions are necessary:
The tree must be circular in cross-section.
The stick must be held against the tree at a point 43 feet from the
ground.
: aD a VaV aD 2. V aD ae
Va(a+D) VaVatD Va+D a+D
282 THE MEASUREMENT OF STANDING TREES
The eye must be on a level with the stick (assuming that the tree
is erect).
The eye must be at the proper distance from the tree.
The stick must be held horizontal (assuming again that the tree
is erect).
The stick must be held perpendicular to the line of sight from the
eye to the center of the tree at the point of measurement.
Errors of 1 per cent in the measurement of diameter are incurred
under the following conditions:
The figures given represent the distances by which the position
of stick or eye departs from the above conditions.
TABLE XXXVIII
Errors in Ustne BILTMoreE STIcK *
RESULTING IN ERROR OF
1 Per Cent IN DIAMETER
Sign Cause D.B.H. of trees
10 30 60
Inches | Inches | Inches
— Eye above or below stick by.............. 9.2 7.3 rp
+ © | Stick not horizontal—one end higher than
ObnerDy.. Jae. Seek ees te aee kh. Has 4.6 4.2 4.1
+ Stick not perpendicular to line of sight—one
end nearer the eye than the other by...... 4.9 4.9 Seal
= Eye too near to or too far from tree by...... 1.4 0.65 0.45
Usually
a Measurement at wrong height............. (Variable)
+ Treeirregular in shape. oe 2s doce c a ees (Very variable—consider-
ably greater than with
calipers)
* Donald Bruce, Proc. Soc. Am. Foresters, Vol. IX, 1914, p. 46.
A still more serious error is incurred through the inevitable tendency of the
cruiser to raise the stick to the level of the eye, rather than lower the eye to the
level’of the stick. If the stick is held at 43 feet and the eye remains at 5 feet
3 inches, with a difference of 7 inches in height, the error is but 1 per cent of the
diameter, but if the stick is raised to the level of the eye, the diameter at the point
measured is appreciably less than D.B.H. The resultant average error varies from
3 to 6 per cent, dependent upon the rapidity of taper, and increases consequently with
the diameter of the tree.
The following table gives the graduations which should be placed upon Biltmore
sticks for a reach of from 23 to 27 inches respectively:
THE BILTMORE STICK 233
TABLE XXXIX
Ficgures TO BE USED IN GRADUATING A BILTMORE STICK *
DIsTANCE FROM EXYE TO TREE—INCHES
Diameter
of 23 | 24 | 25 | 26 | 27
tree.
Inches Distance to be marked on stick—Inches
3 2.82 2.83 ZS 2.84 2.85
5 ADS 4.55 4.56 4.58 4.59
Z 6.13 6.16 6.19 6.21 6.24
9 7.63 7.68 12? Calo 7.79
11 9.05 9.11 9.17 Q 22 9.27
13 10.39 10.47 10.54 10.61 10.68
15 11.67 al ee 11.86 11.94 T2803
ile 12.89 13.01 133. 112, S274 Beer
19 14.06 14.19 14.32 14.44 14.56
21 15.18 15.34 15.48 15.62 15 ac5
23 16.26 16.44 16.60 16.75 16.90
25 Wass 17.50 17.68 17.85 18.01
ii 18.31 18.52 18.72 18.91 19.09
29 19.29 19.51 19.73 19.94 20.14
31 20.23 20.48 20.71 20.94 PAL NE
33 PA U5 21.41 21.67 21.91 22.14
35 22.04 22732, 22.59 22.85 P33 MO)
Sie 22.91 23.21 23.50 PRCT. 24.03
39 PB UE 24.07 DASSIE 24 67 24 94
41 24.58 24.91 Dae2o 25.54 25.84
43 25ESS le 25.74 26.07 26.40 26.71
45 26.17 26 . 54. 26.89 Qie23 27.56
47 26 . 94 2HEOS Daf TY) 28.05 28.39
49 27.69 28.10 28.48 28.85 29.21
51 28.43 28.85 29 .25 29.64 30.01
53 29.16 29.59 30.01 30.41 30.79
55 29.87 30.31 30.75 31.16 31.56
57 30.56 31.03 31.47 31.90 32.32
59 3125 31.73 32.19 32.63 33.06
61 31.92 Soe 32.89 331.05 33.79
63 32.58 33.09 33.58 34.05 3451
65 334128 SB (5. 34.26 34.74 SAP Al
*W. B. Barrows, Journal of Forestry, Vol. XVI, 1918, p. 747
In this table, the graduations are given for odd diameters instead of even ones.
For instance, when diameters are tallied in 2-inch classes, every tree larger than
13 inches and smaller than 15 inches in diameter is tallied as a 14-inch tree.
These graduations thus mark the upper and lower limits of size of each 2-inch
234 THE MEASUREMENT OF STANDING TREES
D.B.H. class, instead of the average size, as 14 inches, enabling the cruiser to
classify accurately all trees on the border line between two diameter classes.
In measuring trees of eccentric or irregular cross section, the errors incident to
caliper measurement are exaggerated by the use of the Biltmore stick, but as before,
these errors tend to compensate and can be neglected.
Bruce has suggested that the volume tables standardized at D.B.H. should be
converted to values for diameter at the height of the eye, or D.E.H., standardized
at 5 feet 3 inches. To do this, taper measurements are taken to establish the
D.E.H. of trees of given D.B.H. By interpolation, the volumes corresponding to
given even D.E.H. inches can easily be obtained.
In the ordinary use of the Biltmore stick, it is necessary to bevel the edge
opposite the figures so that the measurement may be taken in contact with the bole.
Otherwise the thickness of the stick reduces the distance from the eye and incurs
an error whose magnitude is determined by this thickness. By deducting this
thickness (¢) from the distance (a) in the formula, so that this formula reads,
(a—)D
V a(a+D)
Seale =
the resulting values are correct for the face of the stick.
192. Ocular Estimation of Tree Dimensions. Where the diameter
of every tree on a given area must be recorded, the time consumed in
actually measuring the diameters is a considerable item of expense.
Except when scientific measurements or permanent plot records are
required, estimators plan to educate the eye to read as large a percent-
age as possible of the diameters directly without measurement, using
the calipers, diameter tape or Biltmore stick merely as a check. This
is especially desirable when the cruiser is doing his own tallying.
While the eye can be trained with considerable rapidity to a sufficient
degree of accuracy for estimating, it is constantly liable to error and
must never be relied upon for even a single day without instrumental
checks. These should be made on starting work and at intervals during
the day. The eye may be trained to judge diameters at different
distances equally well. Some men develop this faculty more rapidly
and to greater degree than others. It is the general tendency in ocular
estimation to favor a tree of a given size, diameters of trees of lesser
size being over-estimated while larger diameters are under-estimated.
The use of 2-inch diameter classes greatly facilitates ocular estimating.
In training the eye to estimate diameters, the greatest progress is
made by repeated guesses followed immediately by the measurement
of the tree which is then closely observed to fix the known diameter and
correct the faulty observation. Since ocular estimating is not a matter
of reasoning but of impression, the decision as to the dimensions of the
tree should be made instantly. Otherwise fatigue and consequent
inaccuracy ensue.
THE MEASUREMENT OF HEIGHTS 235
193. The Measurement of Heights. While in measuring diameters
it is possible to use the instrument upon every tree as a practical measure
when necessary, the greater difficulty and time required in measuring
heights makes the general use of an instrument for even a large per
cent of the trees impossible. Only on small, permanent sample plots
will the height of each tree be actually measured. Height measures,
or so-called hypsometers, are commonly used to obtain the height
of average trees from which the average height of the remaining trees
is determined, or to check the eye when the merchantable heights of
all trees are recorded.
In the latter case, ocular estimation of the number of merchantable
logs in each tree, or total merchantable height, is the only practical
means possible. It takes no longer to estimate the height of a tree
by eye than its diameter, but the measurement of height by hypsometer
takes about ten times as long as to caliper the tree.
The eye is slightly more unreliable in measuring heights than diam-
eters. The height scale is more difficult to fix in the mind. Con-
sequently the tendency is to arrive at the height of trees by comparison
with other trees. The result is that the standard of height for all trees
tends to shift from day to day unless heights are carefully checked at
the beginning of each day’s work in order to maintain this mental
basis or standard. In no other feature of ocular timber estimating
are such serious errors made even by experienced cruisers as in estimat-
ing heights, and the novice should never trust his judgment over-
night.
194. Methods Based on the Similarity of Isoceles Triangles.
Measurement of heights is based on the principles of similar triangles.
From the observer’s eye, the tree forms one side of a large triangle,
the other two sides of which are the lines of sight to the top and base
of the tree. The base of this triangle can be measured. The length
of the vertical side which is the height of the tree is the dimension
sought. To determine this inaccessible dimension, a smaller, measure-
able, similar triangle is used.
Similar triangles must have their three sides proportional and the
three angles equal. This is secured when either two sides are propor-
tional and one angle equal, or one side is proportional and two angles
equal.
The isosceles triangle with two sides of equal length forms the
simplest method of measuring the height of a standing tree. In this
triangle the base from the eye to the foot of the tree is equal to the
height of the tree and may be directly measured. The small triangle
in this case is used to find the point on the ground at which this base
will be equal to tree height. A triangle which has its own base and
236 THE MEASUREMENT OF STANDING TREES
height equal and whose line of sight from eye to top coincides with that
from eye to tip of tree gives this result.
A straight stick or short pole may be grasped by the thumb and first
finger at a distance from its top exactly equal to the distance from the
‘eye to the point thus marked. Holding this stick vertically, which
is best accomplished by having the greatest weight below the hand
to act as a pendulum, the observer moves backward or forward until
the line of sight Ab in Fig. 43 cuts the desired upper point on the tree,
and at the same time the line of sight Ac cuts the tree at its base. At
this point the triangle Abc has become similar to the triangle ABC,
and AC is equal to BC. The measured distance from eye to base of
tree is then equal to the
height of the tree. This
distance can be measured
along the ground to the
point below the eye with
sufficient accuracy, pro-
vided the slope is even.
Thismeasurementof height
can be taken from any
point of elevation, either
on a level with, above,
or below the base of the
tree without affecting its
accuracy.
195. The Principle of
Fig. 43.—Similar isosceles triangles formed by use the Klaussner Hypsom-
of pole, for measuring height of trees. eter.
For height meas-
urements which require
greater accuracy than is obtainable by such ocular methods as the
one just described, the small triangle is constructed in the form
of an instrument called a hypsometer, on which two of the sides
corresponding respectively to the lines AC and BC, or distance
to tree and height of tree, are graduated to units of distance. This
enables the observer to first adjust the scale AC for distance,
to equal in feet the known distance from the tree, hence to determine
what this distance shall be. The line of sight from the eye, beginning
_ at the zero point of this scale or apex of the small triangle is now brought
into line with the point on the tree whose height is to be measured,
which makes the small and large triangles similar. The point at which
this line of sight cuts the scale BC, whose graduations are equal to those
on the scale AC indicates the height of the tree. These graduations
may be of any size so long as both scales are graduated equally. They
THE PRINCIPLE OF THE KLAUSSNER HYPSOMETER 237
will serve to read height in feet, or in any other -unit of distance, as
meters, since whatever unit is used
to measure the distance from the
tree applies as well to its height.
The Klaussner Hypsometer. In
hypsometers based upon similar
triangles as shown in Fig. 43 the
vertical scale represents tree height,
the scale at base, distance to the
tree. Ii the scale bc is on a movable
arm, it may be set on the scale Ac
at any required distance. By sight-
ing along Ac towards C and by rais-
ing the sight or bar Ab to intersect
the line of sight AB, the total
height of tree is read directly from
the scale be. The standard hyp-
sométer of this make is known as
the Klaussner, Fig. 44. The verti-
eal scale is weighted to insure its
vertical position.
As is seen, two lines of sight
Fic. 44.—The Klaussner hypsometer.
must be adjusted for this reading. The instrument is therefore used
with a tripod and is rather slow in execution.!
‘In Forestry Quarterly, Vol. XIII, 1915, p. 442, S. B. Detwiler has suggested a
simple hypsometer based upon this principle, which for practical work does away
with the tripod apparently without sacrificing accuracy.
238 THE MEASUREMENT OF STANDING TREES
The Klaussner principle differs from that shown in Fig. 438 only
in that the height is measured on the vertical scale bc, the measure-
ment may be taken at any point from the tree by adjusting the scale
Ac to correspond with this distance, and the triangles may be of any
form, provided one side is vertical.
Merritt Hypsometer. The Merritt hypsometer is a scale placed on
the reverse side of the Biltmore stick (§ 191) and is read by holding the
stick in a vertical position at arm’s length, when standing at a given dis-
tance from the tree.
Six inches on the stick will give the height of a 16.3-foot log under
the following conditions:
Armylensthy imches te seer er aa 23 24 25 26 27
Distance from eye to tree, feet....... 6285) 16582 O72 9 ea ONOwiione
The similar triangles used here correspond in principle with those
of the Klaussner hypsometer.
For accurate results the stick must be held vertically and not raised
or lowered during the reading. Only approximate accuracy can be
secured, but the method serves as a ready check on ocular measure-
ments of log lengths.
196. Methods Based on the Similarity of Right Triangles. The
second general method for measuring heights is the use of the right
triangle. This method is based on securing a horizontal line of sight
from the eye to a point on the bole of the tree, and requires two
readings, one above, the other below this point of intersection, the sum
of which gives the height of the tree. This disadvantage is offset by the
fact that these instruments may be held in the hand, thus eliminating
the tripod, and making them compact and portable.
The horizontal line of sight may be secured by using either a bubble
or a plumb-bob. The simplest application of this method is that of a
right isosceles triangle, for which purpose a clinometer is used. This
is an instrument with bubble mounted on a graduated are reading in
per cents, or in degrees. In the latter case the graduations must be
reduced to per cents.
When the are on this clinometer is set at an angle of 45°, the line
of sight Ab coincides with the line AB at a definite distance from the
tree, from which a horizontal line of sight, which can then be taken by
setting the are at zero, gives a distance to the tree equal to the height
of the tree above the intersection of this line with the bole. If used
on fairly level ground, the distance below this point is within reach and
can be measured on the tree and added to the distance to the tree to
get its total height.
This instrument can also be used to measure heights from any dis-
tance from the bole, by taking two readings or angles, one to the upper
HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB 239
point, and one to the base. In this case the actual angle from station
to point on tree is read, and indicates the height in per cent of the hori-
zontal distance. At 100 feet distance, an 80 per cent angle to tip
equals a height of 80 feet above the eye. If the lower angle to base is
Fig. 45.—The Abney hand level and clinometer.
now 5 per cent, the additional height is 5 feet, total height 85 feet.
At 50-foot distance these per cents applied to 50 feet give a total height
of 423 feet. It is convenient therefore to read heights by this method
from distances easily converted into equivalent heights.
Fic. 46.—Goulier’s Clinometer.
197. Hypsometers Based on the Pendulum or Plumb-bob. These
angles can be read as easily from a pendulum, with graduated arc placed
below. <A clinometer constructed on this principle, and used as a
hypsometer, is illustrated in Fig. 46.
240 THE MEASUREMENT OF STANDING TREES
The Faustmann Hypsometer. Instead of graduating a circular are
in per cents, which requires a decreasing scale with increasing per cent
(since the tangents of the angles increase faster than the angle), the
height scale corresponding with this are may be placed on a straight
arm as in other hypsometers (§ 195) and graduated evenly.
The Faustmann hypsometer employs this principle of the pendulum,
using a plumb-bob to determine the angles BAD and CAD, and indicat-
ing the height of the tree above and below the point D by the intersec-
tion of this plumb-bob string with the “ height ’’scale on the base of the
hypsometer. This instrument is illustrated in Fig. 47. Its method
of use is shown in Fig. 48.
Fic. 47.—The Faustmann hypsometer.
The slide is first moved upwards until the number of units on the
vertical scale, from zero, thus set off, equals the distance to the tree
in feet (or in yards). When sighted at the upper point on the tree,
the plumb-bob falls to the near side towards the eye, and the number of
units or height is read in the mirror. The second reading is shown in
Fig. 48, the plumb-bob falling to the far side. The horizontal scale thus
extends in both directions from zero. On fairly level ground, this
second reading is sometimes omitted, providing the height of the eye
above the base of tree is regarded as a constant and added for total
height. For accurate measurements both readings must be taken.
Practice has demonstrated that the use of a plumb-bob and weight
reduces the serviceable character of the instrument, since the seweights
are easily lost and the strings broken. The mirrors also are easily
damaged.
Weise Hypsometer. The Weise hypsometer (Fig. 49) is the same
in principle as the Faustmann but substitutes a metal pendulum for
HYPSOMETERS BASED ON PENDULUM OR PLUMB-BOB- 241
the string and plumb-bob. The two arms when not in use can be placed
within the cylinder. The instrument is more durable than the Faust-
mann but slightly less accurate.
Forest Service Hypsometer. A more durable type of hypsometer
based upon this principle is known as the Forest Service hypsometer.
The distance at which this instrument reads the heights BD and DC
is fixed at 100 feet. The scale showing these heights is computed from
the tangents of the angles read at this distance and expressed in terms
of feet in height. This scale is placed on a circular pendulum which
Fic. 48 —Method of application of the Faustmann hypsometer.
is released by pressing a small knob with the thumb while sighting
through a peep-hole along the line of sight AB or AC. This scale is
enclosed in a metal frame in the form of a disk, and the instrument is
practically indestructible and can be operated with one hand. If read
at 50 feet, the readings shown must be divided by two. If at 200 feet,
they must be multiplied by two, and proportionately for other distances.
As in the case of other clinometers this hypsometer may be used to read
per cents of grade.
The Winkler Hypsometer. The same principle may be used in
constructing a hypsometer in the form of a square or rectangular
board or cardboard. In this instrument the line of sight, AB, coin-
cides with the top edge of the board.
A board whose top and bottom edges are parallei is laid off with a
242 THE MEASUREMENT OF STANDING TREES
horizontal scale at base and a vertical scale ad intersecting the scale
at base at right angles, at a point to permit this horizontal scale to extend
in both directions as in the Faustmann Hypsometer. Both scales are
marked off in the number of equal units or graduations desired, to cor-
respond with the distance from the tree at which the hypsometer is to
be used. A plumb-bob is suspended from point a, and the heights above
and below the eye read as usual. If but one fixed distance is desired
this is represented by a scale reproduced on the line at base of card.
p
5)
TITELETTLITSTILITTETTITETELIITE
4h
wg
a
il
Fia. 49—The Weise hypsometer.
This board may be graduated to read at lesser distances from the
tree, by placing other horizontal scales upon the board intersecting
the vertical or ‘‘ distance’ scale ad at the point below the apex a,
representing the distances desired, and graduating these horizontal
lines to the same scale as the base. This home-made hypsometer is
described in Farmers’ Bulletin 715, U. 8. Dept. of Agriculture, 1916,
DAlS:
The original instrument from which this type of hypsometer was
derived is known as the Winkler hypsometer, shown in Fig. 50. This
instrument is also used as a dendrometer (§ 200).
THE PRINCIPLE OF THE CHRISTEN HYPSOMETER 243
198. The Principle of the Christen Hypsometer. Many hypsom-
eters have been invented, principally by Continental foresters, using
one or the other of these general principles. The Christen hypsometer
introduces a different principle but has no special merit except the
simplicity of its operation. Description of this instrument, taken
from Graves’ Mensuration is as follows:
This instrument consists of a metal strip 16 inches long, of the shape shown in
Fig. 51. The instrument is made of two pieces hinged together, which are folded
@ GEBR. FROMME
Fic. 50.—Winkler Hypsometer.
when it is not in use. A hole is pierced in the upper end, from which it is suspended
between the fingers. Along the inner edge is a notched scale which gives directly the
readings for heights. The instrument is used as follows: A 10-foot pole is set against
the tree. The observer stands at a convenient station whence he can see the tip and
base of the tree and also the top of the 10-foot pole. The instrument is suspended
before the eye and moved back and forth until the edge b is in line of vision to the
top of the tree and the edge c in line of vision with the base. The point where the
line of vision from the eye to the top of the 10-foot pole intersects the inner edge
of the instrument indicates on the scale the height of the tree.
244 THE MEASUREMENT OF STANDING TREES
Each instrument is constructed for use with a specified length of pole. The
Fie. 51.—The
Christen hyp-
someter.
instrument described above is one designed by the author for
convenience with the use of English units. It was constructed
in the following way: The distance be on the instrument was
chosen arbitrarily as 15 inches and the length of the pole as 10
feet. It would, of course, be possible to construct an instrument
for a pole 12 feet or any other length and on a basis of any
desired length of instrument. The theory of the construction of
Christen’s instrument may be shown by Fig. 52. When used as
above described, two pairs of similar triangles are formed: ABC,
and Abc; ADC, and Adc, in which pos a and dc eee
de BC
With a known value of DC and bc, dec may be determined for all
different heights which are likely to be required. Thus it may be
assumed that it would not be necessary to measure trees less than
20 feet high, so that the lowest graduation on the instrument is
made for that height. To find the proper point for the 20-foot
graduation on the scale, the following formula was used:
BC. ‘be 20-15 150
DC de Tree dc = 30 =5.7 inches.
or
Fic, 52.—Method of application of the Christen hypsometer.
THE TECHNIQUE OF MEASURING HEIGHTS 245
This same method was used to determine the value of de for a 25-, 30-, 35-,
40-foot tree, ete., up to 150 feet, and the proper graduations made on the scale.
The scale is somewhat more easily read when a notch is made at each graduation.
The instrument is light and compact, and with practice can be used very rapidly,
provided one has an assistant to manage the 10-foot pole. It requires no measure-
ment of distance from the tree, and the height is obtained by one observation.
It is more rapid than either the Faustmann or Weise instrument.
Its disadvantages are that it requires a very steady and practiced hand to secure
accuracy, that it cannot be used accurately for tall trees, and that it is not adapted
for steady work because it is extremely tiresome to hold the arm in the position
required. This last objection may be overcome by using a staff to support the
hand.
199. The Technique of Measuring Heights. In rough checks for
timber cruising, the distances used in obtaining heights are usually
paced. Care must of course be taken to carefully check the paced
distance desired to avoid incurring a cumulative error. For the measure-
ment of average trees, depended upon to secure the heights of stands,
the distance should, if possible, be measured with the tape. This
latter method is the only one permissible in measuring the heights
of trees on permanent sample plots. .
By the method illustrated by the Klaussner hypsometer, this dis-
tance is measured along the ground whether the slope be level, gradual
or steep. By the method of right triangles the distance must be meas-
ured horizontally to the bole of the tree, and a considerable error would
be incurred in measuring it along the surface on very sloping ground.
Since the entire basis of the similar triangles used assumes that the
tree which forms one side of the larger triangle stands in a vertical
position, the consequences of measuring a tree which leans either towards
or away from the observer are very serious (Fig. 53).
From the position A, the distance to the base of the tree is AC.
But if the observer sights at the tip of the tree B; which leans towards
him, its height, when compared to the distance AC will be read as B’\C,
an error of +16 per cent. If the distance is measured instead to the
point directly below the tip B; the height is read as B,C, with an error
of —2 per cent. Again, if the tree Bz leans away from the observer,
and its distance is measured as AC, its height will be read as B’sC with
an error of —16 per cent, but if this distance is measured to the point
Co, the height will be read as B2C2 with an error of —2 per cent as
before.!
If it is necessary to measure leaning trees, this can be done by taking
a position at right angles with the line AC in Fig. 53, or at right angles
with the vertical plane in which the tree lies. The ocular measure-
1Some New Aspects Regarding the Use of the Forest Service Standard Hyp-
someter, Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772.
246 THE MEASUREMENT OF STANDING TREES
ment of heights largely avoids this specific error since the eye
allows for the leaning position of the tree while the instrument
does not.
Where total heights are measured to the tip of the crown, the
greatest accuracy is obtained in the measurement of conical-crowned
conifers. Broad- or deliquescent-crowned trees are difficult to measure
accurately. The source of error is the same as that which applies to
leaning trees. A line of sight AB, in order to be directed at the tip
B, must penetrate the foliage of the crown while if directed tangential-
ly to the edge
of this crown,
it ‘will ~ “take
the position of
AB,. The error
from the meas-
urementofbroad-
crowned trees,
unless this pre-
caution is ob-
served, is cumu-
lative and. tends
to over-estimate
their heights.
C; C Ce Merchantable
heights are meas-
Fic. 53.—Errors which may be incurred in measuring the
height of a leaning tree. To avoid error the measurement Ured by exactly
should be taken at right angles to the plane in which the the same princi-
tree falls. ples as are ap-
plied to total
heights, and upon broad-crowned trees may be obtained more
exactly. The element of uncertainty in the measurement of mer-
chantable bole is not height, but the determination of the point
on the bole at which the used length will terminate, that is, the
merchantable top diameter of the bole. Merchantable heights may be
measured in 16-foot log lengths by the use of the principle in Fig. 43.
(Merritt hypsometer, § 195.) This same principle may be more accu-
rately applied by leaning a pole of known length against the tree and
then noting the length of a pencil required to take up this given length at
the distance of the observer. This pencil length may then be measured
off by eye on the remainder of the tree to divide it up into logs.
It is common practice amongst timber cruisers to measure the
total or merchantable height of windfalls as a check on ocular timber
estimating. .
MEASUREMENT OF UPPER DIAMETERS.'‘DENDROMETERS 247
200. The Measurement of Upper Diameters. Dendrometers.
Upper diameters of standing trees must be measured, first, in estimating
timber to a merchantable top diameter; second, to determine the form
quotient of the tree, where form classes are to be distinguished.
In timber estimating, ocular methods are used entirely, and the
probable upper diameters approximated by knowledge of rates of taper
checked by the measurement of diameters on the boles of down trees.
But for the measurements required to determine form quotients, it is not
safe to depend altogether on chance windfalls, nor can cutting sample
trees be resorted to on account of the time and expense involved. The
eye is not sufficiently accurate to gage diameters at upper points, hence
these measurements for form quotient must be taken on standing trees
by instrumental means.
An instrument intended to measure the upper diameters of stand-
ing trees is termed a dendrometer.
The principle of the dendrometer is that of similar triangles; but in this case
two sets of triangles are used, first, those required in determining the height to the
point to be measured,
and second, those
used to measure the
diameter at this point
by comparison with
the side of a smaller
triangle on the
dendrometer. These
principles are _ illus-
trated in Fig. 54.
In determining the
* form quotient for
standing timber,
either according to
Jonson’s or Schiffel’s
methods, the diam-
eter at the middle
point, either above
D.B.H. or above the
stump respectively,
is sought. As point-
ed out, the absolute
form quotient cannot
be determined with scientific accuracy from measurements taken outside the bark
or on standing timber, but approximate results can be obtained.
The triangles whose bases are respectively B, b; and b. are similar, and the
relation between B and either 6; or b, determines the diameter at B. But the
points b; and b. are not the same, and this difference distinguishes two different
principles used in constructing dendrometers.
When the distance Ac to the horizontal scale on which will be read the upper
diameter B, is fixed, so that on sighting at point B this distance coincides with bn,
Fic. 54.—Principles underlying construction of dendrom-
eters, as illustrated by the Biltmore pachymeter.
248 THE MEASUREMENT OF STANDING TREES
as it does on most dendrometers, the proportion between the upper diameter B and
its equivalent C, corresponding to c on the instrument, is altered since the side Ab
remains of the same length and coincides with Ab, in the figure. This discrepancy
increases in proportion to the cotangent of the angle A and the distance read on the
dendrometer scale at b:, which is graduated for inches, will be less than the true
diameter B by just the amount of this error. The use of all dendrometers built
on these principles requires correction by a table, to obtain true upper diameter.
This difficulty is illustrated by a dendrometer attached to the Barbow cruising
compass, used to some extent on the Pacific Coast. The dendrometer on this
compass was a brass scale 1 inch long, finely graduated to read the apparent diameter
in inches at the upper end of the desired log, when held exactly 1 foot from the
eye by means of a string. But the true diameter had then to be looked up in a
table furnished with the compass. The correction varied with the angle of sight;
that is, with the number of log lengths in the tree. All readings were made at
100 feet from base of tree.
On the Pacific Coast a second plan has been adopted, that of making the length
of the scale b; equal to the diameter B, thus substituting two parallel lines of sight
for the horizontal triangles shown, and reading the diameter of the lower side of a
parallelogram directly in terms of inches of diameter at B. In an instrument
invented by Judson F. Clark and C. A. Lyford, a telescopic sight moves on a bar.
In one invented by Donald Bruce, both lines of sight are brought into the same
plane by means of two reflecting mirrors, set at exact angles of 45 degrees.
201. The Biltmore Pachymeter.!' By employing the second principle, in which
the side of the small triangle b:\C remains vertical, the diameter indicated at by
on the hypsometer remains in the same proportion to that desired at B, as when
the reading is taken at position C. Since the point opposite c may be taken at
the base of the tree, regardless of whether this point is horizontally opposite the
eye or above or below it, a projection of the diameter B upon the base of the tree
enables it to be directly measured on the tree, or on a scale c upon the instru-
ment, graduated for the distanee Ac. This principle is employed by an instrument
termed the “Biltmore Pachymeter.”’ (Ref. Forestry Quarterly, Vol. IV, 1906,
p. 8.) A slot, the two edges of which are absolutely parallel, or a stick or cane
of which the same is true is suspended in a vertical position in front of the eye.
A scale marked in inches is held by an assistant tangentially to the tree trunk at
D.B.H. The diameter at any desired point on the stem is obtained by finding the
distance from the tree at which the diameter of the slot or stick exactly obscures
that of the tree at the desired point, when the width corresponding to this diam-
eter will be indicated by the intersections of these edges on the scale below. The
instrument and its projection upon the tree trunk are shown in Fig. 54.
202. The d’Aboville Method for Determining Form Quotients. This method
depends on the measurement at’ bo, but is simplified by using a horizontal line of
sight from eye to tree, and an angle of 45 degrees at point A, in which case the
proportion between the lines AC and AB in Fig. 54 becomes 1.4, and the diameter at
B becomes 1.4b.. To make this measurement, a distance is found which is just
equal to the length of the bole between the point horizontally opposite the eye, as
in Fig. 54, and the upper point to be measured.
Substituting d and D for diameter at } height and D.B.H. respectively, the
form quotient of a tree, as read on the dendrometer, is
af yi 4
=p x14.
1 Pachymeter—an instrument for measuring small thicknesses —Century Dic-
tionary. :
J ‘
THE JONSON FORM POINT METHOD 249
The instrument consists of a graduated scale or straight-edge. For determining
merely the form quotient the actual diameters need not be asegrtained but only
their proportion or relation. The two measurements are taken by eye, holding the
horizontal scale at arm’s length (Ac and Ab,) for each reading. The principal
error to be guarded against is failure to secure the horizontal line of sight and the
corresponding distance, which will result in correspondingly large errors in reading
the proportional diameters. Failure to select the right point on the tree, provided
a definite point is selected and the method otherwise properly applied, incurs only
the error due to difference in taper between the point measured and the point
desired, which depends on rapidity of taper.
This simple method should be of great assistance both to practical woodsmen
in determining upper diameters, and to foresters desirous of testing the form quotient
of trees in order to ascertain the applicability of volume tables based upon principle
of form factors.
203. The Jonson Form Point Method of Determining Form Classes. In con-
nection with his studies of the form of trees and form quotients, Tor Jonson has
evolved a method for determining the form class of standing trees without the
necessity of measuring the upper diameter or the form quotient.
This method consists in locating a point on the stem of the tree, which he terms
the form point. The percentage relation which the height of this point from the
stump bears to the total height of the tree, he claims, bears a consistent relation
to the form quotient, and by means of a table showing these relations the form
quotient and form class of the tree may be determined.
Mr. Jonson describes the method as follows:
The shape and position of the crown has been found to be the most dependable
and useful indication of different tapers and form classes. This is connected with
the bole’s function to carry and steady the crown, especially against the breaking
forces of the wind, and it has been found that in the building of the bole only
enough material is used to make it equal in strength to the force of the winds. It
may therefore be said that it is the strength of the winds that determines the
necessary dimensions of the trunk, and as the force of the wind is generally applied
to the crown of the tree, it will be found that its weight, shape and position indirectly
influence the size and taper of the trunk.
While estimating, the D.B.H. is measured with caliper and the taper is then
determined through finding by ocular means the form point, i.e., the point where
the pressure of the wind is apparently concentrated which is usually the geomet-
rical center of the crown. By sighting at this point and at the same time at the
base and tip of the tree over a stick, approximately 30 cm. long, divided into 10
equal parts (Christen’s hypsometer), the height of the form point can be easily
found expressed in per cent of the total height. This form point can then be
looked up in the table giving the form point heights which are characteristic for
each form class. The higher the crown is placed, the less the taper and the more
cylindrical the form, and conversely, the lower the crown extends, the more rapid
will be the taper and the poorer the form.
When, as is often the case, the estimating is based on diameter outside bark,
the difference which is caused by variable thickness of the bark must be taken
into consideration. The spruce, fir and other species with thin even bark show
no difference in form when measured inside or outside bark, for which reason the
given normal form point heights give the form with, as well as without, the bark
for these trees.
White birch, larch and others, but especially the pine, show great reduction in
form when measured with bark, for which reason the form quotient outside bark
250 THE MEASUREMENT OF STANDING TREES
is different from what the crown normally signifies. On this account special tables
have been made up for use with outside bark measurements, but, as the Scotch pine
shows many different types of bark, four tables have been compiled for trees whose
bark is thin, medium, thick and very thick.
When judging the location of the form point, it should be remembered that it
is at the base of the branches where the acting forces of the wind are transferred
to the bole, for which reason deciduous trees with branches pointing up will have
the form point not in the center of the crown contour but as much lower as the
bases of the branches lie lower than the foliage on which the wind is acting. In
estimating trees which have quickly cleared themselves of branches, a better result
will be obtained, if the newly shed crown be imagined reconstructed before the
position of the form point is determined.
Finally, should the butt swelling extend so high as to influence the D.B.H.,
and consequently make the final result inaccurate, it will be satisfactory for prac-
tical work either to round the diameter off downward or measure the diameter
above the swelling; for scientific work, however, the form class should be lowered
as much as is made necessary by the butt swelling, which can be easily found through
a number of measurements taken above and below B.H.
In extensive timber estimating the density is a good indication of the general
form which the trees ought to possess, as the tree grown up in dense stands will
have a clean bole and high crown, while on the contrary the tree grown in the open
wi'l have a heavy, low crown and consequently a poor bole form,
TABLE XL
TABLE FOR DETERMINATION OF Form C.iaAss ofr TREES BY MEANS OF POSITION OF
Form Point!
: Form C.iass
Height
of == Pn tI hee ian ae LL ALLL a
tree 0. 500 5250. 550 : 5150 4 s00 : 6250 . 650 : era) : 700 ; 7250 ’ 750 5 775) .80
in
feet
Form point height in per cent of height of tree
10 37.5) 43.5|47 | 52 [57 62. 69 T3980 92998
20 |35.5) 40 |44 | 49 [54 59 ‘65 | 70.5/76.5} 82.5) 89 | 95.5)]....
30 34.5] 88 |43.5] 47.5/52.5) 58 (63.5) 69 |75 | 81 87 | 94
40 34 | 88 |43 | 47 |52 57 (62 | 68 |74.5) 80 | 86 | 93
50 3=6|34 | 388 |42.5) 47 [52 57 |62 | 68 |74 | 80 | 86 | 93
60 (34 | 38 [42 | 47 |52 57) 62) Wr G8. 917325) 80% |) 86" | S225) eee
70 34 | 38 + |42 | 47 |52 57 (62 | 68 (73.5) 79.5) 86 | 92
80 34 | 88 (42 | 47 |52 5f |62 9 68. \73 | 79 | 86 ),92
|
1 For spruce and fir in Norway, either inside or outside bark. Adapted from
Massatabeller for Triduppskatnung. Tor Jonson, Stockholm, 1918.
The prevailing density of a stand causes the greater number of the trees to acquire
a certain similarity as to form, and only a very small number, usually the smallest
and largest trees, differ from this average form class, Accordingly it is often
RULES OF THUMB 251
204. Rules of Thumb for Estimating the Contents of Standing Trees.
A rule of thumb represents an attempt to formulate a simple rule which
can be memorized and by the use of which the contents of trees of any
diameter and height may be found. Such a rule would enable the
cruiser mentally to compute the volume of average trees without looking
them up in a table. It is also desired as a substitute for a universal
volume table because of the difficulty: of finding volume tables for the
different species.
The factors of variation in tree form are exaggerated by application
of units of product and the variation in board-foot log rules, and the
further differences in the per cent of total contents utilized in trees of
different sizes make it impossible to devise rules of thumb which are
as accurate as good volume tables; but since their use in ocular timber
estimating frequently accompanies methods of cruising by which a
close degree of accuracy is not attained, a slight possibility of error
in application is not considered a sufficient drawback to offset the
advantage of simplicity. They are especially desired in judging by
eye the contents of single trees.
Rules of thumb must be based upon either the cubic or board-foot unit. The
simplest forms ignore the influence of height and are therefore inaccurate except
when applied to trees within a given range of heights.
The effort is always made to devise rules which may be applied to the dimensions
measured by the eye; that is, to diameter and height. Rules which require the
use of basal area call for tables.
For cubic contents, the following rules of thumb will serve as illustrations:
1. To obtain cubic feet multiply the basal area in square feet by the height
and divide by 2. This is based on the theory that the cubic form factor of trees
will average 0.5 which is the form factor for a paraboloid.
2. For trees averaging 80 to 100 feet in height, with a form factor of 0.49, the
contents in cubic feet equals the radius in inches squared (B. E. Fernow). For
“average” trees, volume in cubic feet equals one-fifth of the diameter squared
(C. A. Schenck).
Both of these rules of thumb are good only for trees of a given height and form
factor. They are similar to the European rule of thumb—volume in cubic meters
equals the diameter squared divided by 1000. In this rule, D is measured breast-
high in centimeters. This rule applies to pine 30 meters high, beech, oak and
spruce, 26 meters high, and correction factors are indicated as follows: for
each additional meter of length above or below these heights, for pine, a 3 per cent
correction; for beech, 5 per cent; for spruce and fir, 33 per cent. Hersche’s rule
of thumb reads, cubic meters =D? (5+), using meters. This applies to trees
50 to 115 feet in height.
possible to estimate the whole stand in the same form class, the smaller dimensions
a little higher and the larger dimensions somewhat lower than the average, e.g.,
.0.70 for over topped trees, 0.675 for intermediate and co-dominant trees, and 0.65
for dominant trees (§ 171). The highest and lowest form classes will never occur
as an average, but only for single trees.
252 THE MEASUREMENT OF STANDING TREES
Graves gives the following cubic rule of thumb for white pine:
Square the breast-high diameter in feet and multiply by 30. The rule gives
approximately correct results for trees 10 to 14 inches in diameter and 80 feet
high, 16 to 20 inches by 85 feet, 22 to 28 inches by 90 feet, and 30 to 36 inches by
95 feet. Other heights require a correction varying between 5 and 6 per cent,
for each 5 feet of length. It can thus be seen that both simplicity and accuracy in
these rules of thumb are seldom obtained in the same formula without considerable
cumbersome modification and it would seem that a volume table could be referred
to almost as easily and give as accurate results.
The use of rules of thumb based on board feet is primarily caused by lack of
suitable volume tables. This is illustrated by the development of rules of thumb
based upon the Doyle log rule. These board-foot rules are efforts to obtain the
total board-foot contents of the trees from the sum of the contents of the logs which
they contain and were usually formulated before volume tables had come into use.
The simplicity of the formula for obtaining the contents of a given log in the
Doyle rule, namely, “subtract 4 inches from the upper diameter inside bark, square
the remainder, and the result is the scaled contents of a log 16 feet long”’ (the length
used in estimating), was an inducement to supplement this rule so as to obtain
the contents of the average log in a given tree. There are two rules for this.
1. Take the average diameter of the top and stump inside the bark for the
diameter of the average log. Secale this and multiply by the number of 16-foot
logs in the tree.
2. Multiply the diameter at breast-height inside the bark by the same diameter
minus 12. Multiply by the number of logs in the tree. This gives the scale of
the tree (C. A. Schenck).
Schenck also gives a rule which ignores height, as follows: For “tall” trees,
volume =3 diameter squared, measured at breast-height.
Efforts to formulate general rules of thumb, not based on the Doyle rule are
illustrated by the following examples:
1. Subtract 60 from the square of the estimated diameter at the middle of the
merchantable length of the tree. Multiply by 0.8 and the result is the contents
in board feet of the average log in the tree. Multiply by the number of 16-foot
logs for the total seale. (Graves’ Mensuration, p. 153.)
2. Average the base diameter of the tree and the top diameter of its merchant-
able timber. Get the scale of a log of that diameter, 32 feet long. Multiply by
the number of 32-foot logs less } log. (Cary’s Manual of Northern Woodsmen.)
D?XL
3. Board feet eas -,
60
when D=inches and L =feet.
(A formula method of estimating timber, E. I. Terry, Journal of Forestry,
Vol. XVII, No. 4, p. 413.) This formula, according to author, requires modification
by substitution of a divisor of
70 for trees from 12 to 19 inches D.B.H.
60 for trees from 20 to 29 inches D.B.H.
55 for trees from 30 to 35 inches D.B.H.
50 for all trees above 35 inches.
4. To base diameter, add one-half of base diameter and divide by 2; multiply
by 0.8, square and divide by 12. The result is the number of feet in the stick per ;
foot of its length. Three to 5 per cent may sometimes be added for contents above
the point stated.
RULES OF THUMB 253
There are two steps involved in these rules of thumb for board feet:
First, a rule or formula is required, which gives an approximation of actual
board-foot contents of logs of different sizes. This can only be obtained by rules
based on cubic instead of board-foot contents (§ 39). Taking a fixed per cent of
~~
12
The second step is to get the dimensions of an average log in a tree, thus averaging
large and small, or top, butt and middle logs together. Empirical results rather
than mathematical soundness has usually been the basis of all such rules of thumb.
Practically all these rules of thumb for board feet are based upon the log unit,
as might be expected. A more scientific application of a universal rule of thumb
is that devised by F. R. Mason (Ref. Rules of Thumb for Volume Determination,
Forestry Quarterly, Vol. XIII, 1915, p. 333). This rule is as follows:
5. The volume of a tree of each diameter and height class will correspond
closely with the volume as obtained by averaging the scale of the butt and top
logs and multiplying by the number of logs, using 16 feet as the standard log length.
Mason states that this rule has been in use by Minnesota cruisers. Its superior
accuracy is based upon the fact that it conforms to the form quotient of the tree
as well as to its diameter and height, by introducing upper diameters at two points.
For Douglas fir this rule was 3 per cent below actual scale; for cedar, above 24 inches,
10 to 15 per cent high. For white pine, spruce, yellow pine, larch, lodgepole pine
and fir, average results were within 5 or 6 per cent of actual volume for individual
trees of all sizes, a result which is closer than may be expected in the use of average
volume tables for single trees. The only difference between this rule and the tally
and computation of each log in the tree is elimination of the need for tallying logs
lying between butt and top. The size of the top log is constant where.a fixed top
diameter is used. Mason states that 3R? is the approximate board-foot contents
for 16-foot logs over 24 inches in diameter.
6. A rule given by J. W. Girard is, “add 6 inches to the D.B.H., divided by 2
and use this result as the diameter for the average login the tree. Multiply the
scaled volume of this log by number of logs for the tree volume.’ This rule holds
good for white pine and spruce cut to 6-inch top and for larch cut to 8-inch top.
For Douglas fir cut to 8-inch top, add 4 instead of 6 inches. For lodgepole cut to
6-inch top, add 5 inches. For yellow pine under 20 inches, add 6 inches; 20 to 25
inches, add 8 inches; 26 inches and over, add 10 inches.
Any rule of thumb should be based upon the log rule and standard of utilization
in use. Such rules are largely worked out as a matter of personal efficiency by
individuals and should be tested carefully before placing too much reliance upon
them.
the contents of all logs, the last rule above quoted reduces to (
REFERENCES
The Biltmore Stick and Its Use on National Forests, A. G. Jackson, Forestry
Quarterly, Vol. IX, 1911, p. 406.
Notes on the Biltmore Stick, Donald Bruce, Proc. Soc. Am. Foresters, Vol. LX,
1914, p. 46.
The Biltmore Stick and the Point of Diameter Measurements, Donald Bruce, Proc.
Soc. Am. Foresters, Vol. XI, 1916, p. 226.
A Folding Biltmore Stick, W. B. Barrows, Journal of Forestry, Vol. XVI, 1918,
p. 747.
Relative Accuracy of Calipers and Steel Tape, Normal W. Sherer, Proc. Soc. Am.
Foresters, Vol. IX, 1914, p, 102,
254 THE MEASUREMENT OF STANDING TREES
Another Caliper (Swedish pole and hook for measuring diameters at considerable
height). S.T. Dana, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 337.
Saving Labor in Measuring Heights, 8. B. Detwiler, Forestry Quarterly, Vol. XIII,
1915, p. 442.
A New Hypsometer, H. D. Tiemann, Forestry Quarterly, Vol. II, 1904, p. 145.
Comparative Test of the Klaussner and Forest Service Standard Hypsometers,
Douglas K. Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417.
Some New Aspects Regarding the Use of the Forest Service Standard Hypsometer,
Hermann Krauch, Journal of Forestry, Vol. XVI, 1918, p. 772.
A Simple Hypsometer, Vorkampff Laue, Forestry Quarterly, Vol. III, 1905, p. 195.
A New Dendrometer, Donald Bruce, University of California Publications, Vol. ITI,
No. 4, Nov., 1917, pp. 55-61. Review, Journal of Forestry, Vol. XVI, 1918,
p. 724.
A New Dendrometer or Timber Scale, Judson F. Clark, Forestry Quarterly, Vol. XI,
1913, p. 467.
The Biltmore Pachymeter, Ralph G. Burton, Forestry Quarterly, Vol. IV, 1906, p. 8.
Determination of the Middle Diameter of Standing Trees, P. d’Aboville. Trans-
lation, Journal of Forestry, Vol. XVII, 1919, p. 802.
Rules of Thumb for Volume Determination, F. R. Mason, Forestry Quarterly,
Vol. XIII, 1915, p. 333.
A Home Made Hypsometer (Winkler type). Construction described in Farmers
Bulletin 715, 1916, p. 18.
CHAPTER XIX
PRINCIPLES UNDERLYING THE ESTIMATION OF STANDING
TIMBER
205. Factors Determining the Methods Used in Timber Estimating.
There are five basic considerations which determine the conditions
and methods to be used in estimating timber. These are:
1. The form of product in which the volume of the timber is to
be estimated. This determines the unit of volume to be used, as the
piece (poles, railroad ties), the board foot for saw timber, and the cord
for bulk products ($§ 9-12).
2. The economic conditions, customs and usages governing thy
business of logging and lumbering. These determine the basis on
which standing timber is to be sold and the place and form in which
it is to be measured. The three considerations which affect the work
are, whether the basis of volume measurements is to be the contents
of logs or the sawed output in the form of lumber, what log rule is to
be used in scaling the logs, and the practice of scaling as to log lengths,
diameters and cull as affecting the scaled contents of the timber
($§ 81-83).
3. The character of the demand for timber products and the result-
ant closeness of utilization of the trees in the stand. This will determine
the top diameters and stump heights to which the timber must be esti-
mated, and the minimum D.B.H. (diameter limit) of trees to be esti-
mated as part of the merchantable stand, and consequently the per cent
of the total cubic volume of the stand which is estimated as merchant-
able (§ 23).
4. The available volume tables, their reliability and basis of numbers,
their method of construction, their basis of diameter, height and mer-
chantable top diameters (§ 124). This will determine,
(a) Whether to dispense with a volume table and substitute a
log rule, tallying the contents of the trees in the form of
separate logs or to depend upon a volume table for entire
trees.
(b) The point at which diameter must be measured in timber
estimated, as stump, D.B.H., or top of first log inside
bark.
255
256 ESTIMATION OF STANDING TIMBER
(c) The point at which heights are taken—total height or
merchantable log length.
(d) The top diameters to which tree must be estimated. Diver-
gence in these conditions from those used in the volume
table will make it impossible to apply the same.
5. The local characteristics of the timber to be estimated as to full-
ness of form or “ form quotient,’ quality and defects. This determines,
(a) For sound trees, the applicability of existing volume tables
without modification or their need of local percentage
corrections.
(b) For the defective trees, the amount of deduction for defects
and losses in scale to be made from the standard volume
table.
The object of any estimate of standing timber is to obtain the total
volume as indicated by the above five conditions upon the entire area
of a specific tract of land. This may be done in one of three ways:
By direct ocular guess or appraisal.
By actual estimate or measurement of the volume of every tree
of merchantable size.
By measuring or estimating a part of the timber as an average
_of the whole.
206. Direct Ocular Estimate of Total Volume in Stand. The direct
estimation or guess of the total volume of a tract of timber can have
but one basis, that of experience in cutting tracts of similar character.
This eliminates all doubtful factors, and the experience thus gained
is invaluable as a standard of estimating.
Skill and accuracy in this method depend upon the uniformity of
the stand, and the ability of the estimator to compare this uniform
stand with those of similar character whose yield he has ascertained.
As the area of timber so estimated iner ases, its variability of
stand becomes greater; yet the necessity for obtaining a true average
of these variable conditions pers'sts. Even in stands as large as 40
acres it becomes very difficult'even with the closest inspection to arrive
at the average stand on the tract, no matter how skillful the cruiser is
for smaller and more uniform areas. With increasing size of area,
accuracy soon becomes utterly impossible. For this reason, in spite
of the simplicity of the plan in theory, in practice cruisers who depend
solely upon this principle are apt to be unreliable and inaccurate.
Under no circumstances can this method be applied to timber with
which the cruiser is unfamiliar. It therefore limits his field of activity
to a narrow basis.
ESTIMATING A PART OF THE TIMBER 207
207. Actual Estimate or Measurement of the Dimensions of Every
Tree of Merchantable Size. This is known as a 100 per cent estimate
and differs radically from the total ocular estimate of stand just
described. It consists of recording the dimensions of each log on the
tract in case no volume table is used, or with a volume table, the dimen-
sions of every tree of merchantable size. The total volume is then
simply a matter of computation.
The trees are tallied by dots and lines, in blocks of ten, as indicated
in the following table, which shows the marks corresponding to dif-
ferent numbers:
1 2. 8 4. 5 6 q 8 9 10
e ee ee ee o—e
ee ee ae eet]
When diameter alone is being tallied, a single column giving diameter
classes suffices for each species. Where the height, either total or
merchantable is also recorded for each tree tallied, each species will
require a tally similar to
that shown below.
Where several species
are tallied by both diameter
and height, it is not cus-
tomary to make _half-log
divisions, since too many
columns would be involved.
Where the top diameter of
logs, instead of D.B.H., is Fic. 55—Method of tallying trees by diameters
the point tallied, the same and log lengths.
system of diameter classes
or tallies is used. It is possible to combine this tally of D.B.H. for
one species with top diameter of logs inside the bark for others, using
the same horizontal columns for diameter in each case.
208. Estimating a Part of the Timber as an Average of the Whole.
Where the greatest possible accuracy is demanded, it is obvious that
100 per cent of the trees should be measured. Only in extreme cases
can this be done, owing to the excessive cost. The process of measure-
ment accomplishes no constructive change in the form of the forest
(§ 6) as does logging or silviculture, but is of use merely in the orderly
management of the business of regulating these operations as to location,
quantity and time. Efficiency then demands the reduction of the cost
of obtaining these statistics to the lowest figure which will suffice for
the proper conduct of the business and avoid loss through errors in
appraisals of quantities and values.
With timber whose average value per tree is small, the cost of meas-
Species - Pine
258 ESTIMATION OF STANDING TIMBER
uring each tree is far too great to be undertaken. It is often physically
impossible to obtain the necessary force and personnel to perform the
work on this scale. Finally, the time required is too long since the
results of estimates, especially for the purpose of sale are usually required
within a limited period. For these reasons, the third of the above
methods, by which the principle of averages is utilized as a means of
reducing expense, diminishing the number of persons required and
shortening the time demanded for completing the work, is almost
universally used in estimating timber.
The use of this principle in timber estimating does not differ from
that applied in the commercial process of sampling employed in mines
or in grad‘ng wheat. If the product is uniform, a single sample suffices,
as in wheat, but if variable, as in ore, far greater care is required in
order that the samples may represent the average value for the entire
body to be tested. The advantage in timber estimating is that all
of the timber is actually visible and only the handicap of costs and
time prevent it from being seen and measured.
209. The Six Classes of Averages Employed in Timber Estimating.
There are six classes of averages employed in estimating timber. The
first three differ in regard to the methods of recording the dimensions
of trees. These methods are as follows:
1. The average height of the trees of each separate diameter class
is obtained. For this purpose, only a few sample heights for each
separate diameter are measured. The heights so measured are plotted
on cross-section paper on which diameter is the determinate variable
plotted on the horizontal scale, while height is the indeterminate vari-
able plotted on the vertical scale.
An illustration of a curve to obtain average heights based on diameter is shown
in Fig. 56. The trees to be measured for height must be selected in such a manner
that the resultant curve will give the true average heights for each diameter class
for the entire area to which it is to be applied. When a very few trees are taken,
these must be carefully chosen from those whose crowns are of average height
compared with the remaining stand. This is best accomplished in even-aged stands.
On large areas and in many-aged stands, a mechanical distribution of trees measured
for height is best, in order to secure a weighted average of differences caused by
variation of site and of growth.
In plotting the data, two methods are shown. By the first, all heights are
plotted above their respective diameters. A height curve may thus be sketched
by eye through the band of points shown. ‘This eliminates mechanical averaging.
By the second method, the average height is calculated for the trees in each diameter
class, and this point is plotted @. The points are then connected by straight
lines, their weight in numbers shown, and the curve drawn, as before, guided by
the original data.’
1—In the first system, when two heights fall on the same point, the number is
indicated as ?,
AVERAGES EMPLOYED IN TIMBER ESTIMATING 259
A combination of these two systems may be used as follows: First plot the
points, then compute the mechanical averages from the plotted data by using the
scale as follows: For the 9-inch trees, assume the 40-foot point as 0. The
trees are then entered as having the weights 0, 3, 8, 8; total 19; average 4.8 plotted
as 5 above the 40-foot point, or an average height of 45 feet. This method com-
bines the advantage of visualizing the data to indicate abnormally high or low
trees, with a slight reduction in the work of mechanical averages.
2. Instead of tallying the diameters of all the trees, they are merely
counted, but a certain fixed percentage of the total number is tallied
for diameter (the heights are either tallied individually or the method
70
Das Ge mei 8 PO i Pe ey a ay Pg Ew)
7 D.B.H., Inches
Fic. 56.—Method of constructing a curve of height based on diameter at B.H.
White Pine, Milford, Pike Co., Pa.
of averages described above is applied). The volume of the average
tree of the per cent tallied is used to find the average volume cf the
numbers counted but not measured.
In Southern longleaf pine, it is possible to count all of the trees on a tract,
and to tally the diameter and merchantable height of one tree in every three in
such a way that the trees tallied represent the mechanical average of those counted.
When the volume of the tallied trees is computed, it represents one-third of the
volume of the stand. The work of tallying has been reduced one-third and the
accuracy greatly increased, when considered with reference to the time required to
complete the work.
3. None of the trees in the stand is tallied for either diameter or
height. The trees are merely counted and the cruiser then decides
upon the volume which will be contained in the average tree of the stand.
He may obtain this either through a direct guess as to volume or through
260 ESTIMATION OF STANDING TIMBER
the selection of what he believes to be a tree of average diameter and
height whose volume he then ascertains. There are two modifications
of this system, dependent upon whether the unit used is the log or
the tree. When the log unit is used, the cruiser estimates the number
of logs in the average tree and the contents of the average log or log
run (§ 120).
In the above three methods of averaging, nothing has been said
about the question of area covered. The averages apply to that portion
of the area on which the timber is either counted or in addition is tallied
for dimensions. This may be 100 per cent or the total area. Although
it may not be possible to measure, by diameter and total height, each
tree on the entire area, yet by the employment of one of these three
methods of averaging the contents, all of the trees may actually be
accounted for.
The remaining three of the six methods of employing averages
apply to tracts whose area is too large to permit of 100 per cent esti-
mates, even by the simplest plan of counting and obtaining the average
tree. The principle here is to estimate the stand on a portion of the
area in an effort to derive the volume of the stand upon the remainder.
The systems used are as follows:
4. The stand per acre is guessed at or estimated es eye. This stand
multiplied by the area in acres presumably gives the total stand on the
tract. This is merely a modification of the method of total ocular
estimate, in which the problem of arriving at the average is approached
in a different manner. It is possible for a skilled estimator to guess
closely the stand on a given acre, but the difficulty les in either finding
a specific stand whose volume per acre happens to agree with the aver-
age on the entire tract or else to decide from the inspection of given
stands how much the actual stand per acre observed on specific plots
must be modified in order to obtain the true average for the entire
tract estimated. The probabilities of error in estimates made on this
basis increase with the size and diversity of the stand to be estimated.
5. The dimensions and volume of the trees on a given per cent of
the total area are obtained by one of the first three methods and the
stand thus found is assumed to represent the average stand per acre
for the entire tract. This requires, first, the accurate determination
of the area of the tract and of the area covered by the estimate, and
second, the location of this latter area in such a way that the assumption
that it represents the average of the remainder can be accepted as
approximately correct.
6. The same principle is employed as described under 5, but the
assumption that the per cent of area so measured will give an accurate
mechanical average applicable to the remaining tract is not accepted.
Instead, the remainder of the area is inspected by the method of ocular
THE CHOICE OF A SYSTEM FOR TIMBER ESTIMATING 261
comparison. None of the trees is actually measured except on the
per cent estimated. Using this estimated strip as a standard, the
estimate upon the remainder is taken as equaling, exceeding or falling
short of the stand per acre upon the estimated strip, and its volume
is obtained by applying a correction to this estimated stand per acre.
210. The Choice of a System for Timber Estimating, with Relation
to Accuracy of Results. All systems of timber estimating involve the
choice, first, of one of the three methods for determining the contents
of the trees and second, of one of the three methods of covering the area.
There are many different systems of timber cruising, involving the
possibility of an endless combination of these six elements Each of
these systems represents a decision as to the per cent of area required
to get the average stand per acre for the total area, the method of cover-
ing the area to obtain this per cent, and the question as to acceptance
or modification of the stand per acre as applicable to the whole tract;
it also involves the further reduction in the work of measuring dimen-
sions to get the volume of trees by substituting averages for height,
a per cent of total tallies for total tallies and average volumes for
individual volumes. These two groups of factors are closely inter-
related. For instance, where the per cent of area covered is reduced
to a low figure, the area which is actually estimated must be covered
thoroughly by careful measurement of distances and widths of strips,
the diameter of every tree should be measured or tallied, and each tree
may be tallied for height, especially if merchantable heights are used.
Where, on the other hand, all of the area is covered, it may be sufficient
merely to count the trees, substituting the method of an average tree
or log for the more detailed and time-consuming method of measuring
each diameter. The gain in accuracy in one of these factors may be
offset against possible inaccuracy in another, the sum of the factors
being determined by the total cost of the method. These points may
be briefly summed up as follows:
Area—
Full estimate, 100 per cent.
As modified by averages.
Sample plots taken as the average.
A given per cent accepted as the average.
A given per cent estimated as a basis for obtaining the remainder by compari-
son and correction.
Trees—
Full estimate, 100 per cent tallied for both diameters and height.
As modified by averages.
Average height obtained from sample measurements.
Volume of average tree obtained from tally of dimensions of a fixed per cent
of the total stand.
Volume of average tree obtained by inspection, from sample tree, or average
tree on sample plots,
262 ESTIMATION OF STANDING TIMBER
Both the degree of accuracy obtained and the expense of estimating
the timber are reduced:
By the reduction of the per cent of area covered.
By substituting tree counts for measurements of dimensions and
averages for totals.
By substituting ocular measurements of dimensions for instru-
mental measurements.
By substituting pacing for chained or measured distances.
As an offset to the loss of absolute accuracy by the substitution of
these laws of averages and reduction of detail, the relative accuracy
or efficiency of the application of the cheaper methods can be enormously
increased by the development of technical skill, experience and judg-
ment, so much so that the old-time timber cruiser depended upon these
factors both for his reputation and the reliability of his estimates.
This relative accuracy is increased:
By the choice of methods and care in location by which partial
areas are secured in such a manner as to insure the highest probability
of average volumes. This is similar to the methods used in sampling
ore.
By the development of skill and accuracy in the use of pacing
and in the use of the eye for measuring diameters, heights and width
of strips or plots.
By the ability to apply the methods of tallying a fixed per cent of
the stands or selecting average trees in such a manner that the true
average volume of the total number or count is obtained.
By painstaking observance of obtainable standards of accuracy in
the use of instruments for measuring distances, diameters and heights,
and in proper record or tally.
By individual training and ability to make the proper discounts
for defects.
By the careful checking of the reliability of volume tables used,
and the correlation of field methods with the conditions for which they
were constructed.
Finally, by correlating all of the above factors with the actual con-
ditions of the tract or stand to be estimated, which in themselves will
determined the degree of accuracy required in each step as above
outlined.
211. Relation between Size of Area Units and Per Cent of Area to
be Estimated. There are two elements to be considered in arriving
at accurate averages in estimating a given tract. First, the problem
of distributing the samples throughout the area in order to obtain the
greatest probability of true average; second, the uniformity of the stand
SIZE OF AREA AND PER CENT OF AREA ESTIMATED 263
itself as increasing or decreasing the probability of accuracy for a given
method of sampling.
The first of these problems is influenced by the size of the tract.
In any method of estimating based upon measuring a part of the area,
the system employed must be that of strips or plots spaced at regular
intervals. Otherwise the element of judgment in selection introduces
a difficult factor which will improve the average obtained only when
accompanied by considerable individual skill. With plots or strips
at fixed intervals, the number of such strips depends upon the dimensions
of the tract.
The choice between plots and strips does not affect this principle.
Plots, when substituted for strips and taken along compass courses at
regular mechanical intervals, serve to reduce the per cent of total
area covered. Since the distribution of the sample areas is more evenly
diffused on the basis of the per cent covered, by plots, than it is by
strips, the loss in accuracy by substituting plots for strips is not in
proportion to the reduction in per cent of area covered, but is consider-
ably less, thus resulting in a material saving where the use of plots
permits of the reduction in size of crew (§ 224).
The size of the separate units of area on which accurate estimates
are desired—as for instance, when owners require the estimates sepa-
rately by “ forties ”’ (§ 8), is the basis for determining the effect of the
spacing of these strips. If the estimate must be accurate only for the
entire tract, a quite different problem is presented from that when the
same degree of accuracy is required for smaller subdivisions. Assuming
that the tract is in the form of a square, the coefficient of accuracy bears
a close relation to the number of strips run across this area, rather
than to the distance between these strips. This may be expressed as
follows:
The per cent covered by strips will be the product of the number
of strips and width of each strip, divided by width of the area. With
strips of a uniform width, e.g., 8 rods or 132 feet, run at intervals of
x mile, the per cent of area covered is <5 or 10 per cent, whether the tract
be 40 acres, 1 square mile or 25 square miles. But the probability of
accuracy in securing an average stand is not in the same proportion
for each tract, but increases with the size of the tract. The reason is
that, regarded as a unit, the larger tract is more uniformly sampled,
and with reference to its total area, the strips or plots are more
thoroughly distributed than on the smaller areas. The relative accu-
racy is in proportion to the distribution of the sampled or estimated
strips with respect to this total unit, which for large tracts tends to
reduce the per cent of area required to obtain a given standard of accu-
racy.
264 ESTIMATION OF STANDING TIMBER
Standard distances between strips or plots are 80 rods, or once
across a forty for very extensive work of low accuracy; 40 rods, or
twice across a forty for work of average accuracy; 20 rods, or four
times across a forty for work approaching a 50 per .cent estimate;
10 rods, or eight times across a forty, which with a 10-rod_ strip
permits 100 per cent of the timber is to be measured.
The first problem then, in estimating a tract, is to decide upon the
proper per cent of the area which must be covered to secure the desired
standard of accuracy, and this per cent will be a direct function of the
size of the smallest unit of area upon which a separate estimate is
required (Fig. 57).
1 Square Mile
\% Sq.Mile
40 Acres 40 Acres 40
Acres
0 KW%Mile 0 YY % x 1 Mile 0 1 2 3 4 5 Miles
ee SS ee
Fic. 57.—Influence of size of tract upon probable error in obtaining average volume
per acre, by running strips 40 rods apart in each instance. Dotted lines
indicate location of strips.
Narrow strips spaced at one of these standard intervals are commonly
used for large tracts. Upon small tracts, the necessity for increasing
the per cent of area covered, as a substitute for increasing the number
of strips run, takes the form of widening the strip. This is usually
accompanied by a modification of the method of tallying the trees
and the substitution of a count for the measurement of every diameter.
For small areas as low as 40 acres, this frequently takes the form of a
100 per cent estimate, the strips being so arranged that they cover the
entire area, and where the value of the timber and its size is such that
accuracy is desired for each forty, 100 per cent of the entire tract is
covered, no matter what its total size.
The relations between the distance apart of strips or plots, width
or size of these strips or plots, and resultant per cent of area covered,
to the size of the unit of area to be estimated, is the most practical
UNIFORMITY OF STAND AS AFFECTING METHODS 265
problem of timber cruising upon whose solution depends the attain-
ment of the desired standard of efficiency secured by properly relating
costs to accuracy of results.
212. Degree of Uniformity of Stand as Affecting Methods Employed.
The second factor affecting the probability of accuracy in obtaining
the average stand per acre is the character of the stand as affecting its
uniformity. Uniformity depends, first, upon the range of sizes both.
as to diameter and height of the trees which compose the stand; second,
on the regularity or evenness of their distribution or the variation in
the density of the stand over the area. The greater the extremes,
both in sizes and density, the more difficult the attainment of a correct
average stand by a measurement of a part of the area, and the greater
the necessity of increasing either the number of strips or the per cent
of area covered in each strip to get a larger total per cent of area in
obtaining the average.
Age of timber increases both the range of sizes and the variation
in density. Old timber is never as evenly distributed as a young stand,
owing to the progressive losses from natural causes. Mixed forests,
composed of several species, are more difficult to average than pure
forests of a single or of two or three similar species. There is greater
irregularity both in size and distribution in the mixed forest. The
greatest irregularities for a given tract are caused by differences in
topography and soil, or site conditions, which are reflected in the char-
acter of the stand. In mountainous topography, the entire forest
changes from bottom to lower slope and from lower slope to upper slope.
In more level topography, the type changes as abruptly and completely
on the basis of the moisture content of the soil from swamp to drained
bottom, from drained bottom to dry upland. Any system of timber
estimating must be planned to secure:
1. The separation of areas which differ radically from each other,
but which within themselves are fairly uniform. These areas conform
with the types of forest cover.
2. An arrangement of the strips such as to secure the greatest pos-
sible accuracy in sampling, which is done by crossing these variations
of density, type and form, at right angles with their longest dimen-
sions of area, as far as possible (§$§ 219 and 228)
The degree of detail and cost of the work as reflected either in an
increased per cent of area or number of strips or an increased per cent
of trees tallied for dimensions, either diameter or height, will thus be
increased in proportion as
The size of the unit diminishes.
The size of the timber increases.
266 ESTIMATION OF STANDING TIMBER
The variety of the timber increases.
The topography is more mountainous or varied, resulting in a
greater diversity of types.
The number of products required increases.
Finally the degree of accuracy required, other things being equal,
will depend upon the stumpage value of the products to be estimated,
as influenced, first, by the character of the timber itself, and second,
by the unit price of the product. In the earlier days crude and inaccu-
rate methods of timber estimating were justified by the low price
per acre and per thousand feet at which stumpage changed hands.
With record stumpage prices running up to $27 per thousand feet for
white pine in state auctions in Minnesota, in 1920, a degree of accuracy
is justified which would not be thought of by old-time timber cruisers.
CHAPTER XX
METHODS OF TIMBER ESTIMATING
213. The Importance of Area Determination in Timber Estimating.
Except in a few instances where every tree on a tract is separately
measured, all methods of timber estimating depend upon the principle
of applying the results obtained on part of an area to the entire area,
or on small portions of an area to larger subdivisions. Any error in
determining the total area included within the boundaries of a tract,
or the correct area of any subdivision made within it, will incur a cor-
responding error in applying the results of the estimated portion to the
whole. The separation of timbered from non-timbered areas is an
example. If the average stand of the timbered portion is correctly
found, but its area is estimated to be 10 per cent greater than it actually
is, an error of plus 10 per cent is incurred in the estimate. Correct
determination of areas of the tract and its timbered subdivisions is
the first consideration in the field work of timber estimating and counts
for fully half in the total scale of accuracy.
The first essential is to locate and determine definitely the boundaries
of the area to be estimated. Where the tract lies in regions subdivided
by a rectangular system of government surveys this is not ordinarily
difficult. The area may be approximately located with sufficient
exactness for the work. Even here it is necessary to identify the
section corners and sometimes to re-run the lines if time permits. In
other regions where the land surveys follow an irregular pattern, the
identification of the corners and lines is best accomplished by the aid
of some local resident who is familiar with these bounds. The retrac-
ing and mapping of the boundaries of a property is an essential step
in management, but its cost is not properly chargeable against the item
of timber estimating alone.
If methods are used by which 100 per cent of the timber is estimated,
the total stand can be obtained independent of the actual area or shape
of the tract provided only that all of the trees upon it are counted and
their contents determined. When for a 100 per cent estimate is sub-
stituted an estimate covering only a part of the tract, the cruiser requires
a knowledge of its shape and size. In the rectangular system of surveys
most of the subdivisions are square and the smallest unit commonly
267
268 METHODS OF TIMBER ESTIMATING
used contains 40 acres. Even here fractional lots lying along the north
and west boundaries of a township or adjoining meandered streams
and lakes call for a plot which shows their dimensions. With these
rectangular areas it is a simple matter to obtain a definite per cent of
the total by running strips of a given width.
On irregular tracts, a map showing the boundaries and area is
required to enable the cruiser to determine, first, in what direction and
relation to lay out his lines or strips, and second, to compute the exact
per cent of the total. This desired per cent is approximated and the
exact relation secured is determined after the lines are run.
214. The Forest Survey as Distinguished from Timber Estimating.
Timber estimating may be undertaken for the sole purpose of determin-
ing the volume of timber on a tract, but as commonly carried out, this
requires the running of numerous definitely located compass courses,
gridironing the area, which gives an opportunity for the collection
of a large amount of additional data required in its permanent manage-
ment and in the logging of the area. The collection of this additional
data, together with the timber estimate, constitute what is termed a
forest survey. Even the crudest work of timber cruisers embraces
some elements of a forest survey. The features of such a survey are:
1. A map showing the topography of the area either by hachures
or contours, giving streams and ridges and other important features
which influence logging and management.
2. A map showing the character of the forest cover, classified as to
(a) Timber types, corresponding with divisions made in the
stand in timber estimating and showing blank areas, such
as water, barren, cultivated or grass-land.
(b) Divisions due to age of the timber such as burns, re-stocked
or barren, reproduction or immature timber, older age
classes.
3. Soil maps, locating land of agricultural value and land fit only
for forest purposes.
Under timber estimating proper, the forest survey makes an inven-
tory showing both the quantity and quality of timber by different
products, grades and sizes as required for the purpose of valuing the
tract as follows:
1. Quantity or volume.
(a) Separately by species.
(b) Separately by units of merchantable volume, as board feet,
poles, cords.
(c) Separately by character, as live or dead timber, sound or
cull, and giving the net volume after deductions for cull.
TIMBER APPRAISAL 269
2. A statement of amount and character of damage present due
to rot and other defects such as shake, fire damage to standing timber,
the presence of insect damage, windfall.
3. The quality and sizes of the timber under the items; average
diameters, average merchantable length in logs, form of bole as to
straightness, taper and clearness and finally the grades present, classi-
fied either as log grades or as grades of lumber.
The third class of data is that needed for permanent forest manage-
ment for the production of timber by growth. These data are fre-
quently omitted or overlooked in a timber survey, first, by old cruisers
who have not been trained to collect them; second, by foresters who
have failed to formulate a definite plan for their proper collection in
anticipation of the need for its use. These data fall under:
1. Age classes in the merchantable timber, either by area (maps),
or by size or diameter (stand tables of diameter classes), or both.
2. Age classes in immature timber either by areas as mapped, by
per cent of area occupied or by tree counts; the ages and sizes of these
age classes, their condition, thrift and the chances of survival.
In addition, a forest survey may include data on all other resources
of the forest such as forage for grazing, while under timber it should
determine the areas included within different site classes (§ 227).
Forest surveys include all data of every kind necessary for the making
of a working plan for the management of the area for permanent forest
production.
215. Timber Appraisal as Distinguished from Forest Survey. The
forest survey as described above is the preliminary step in the appraisal
of the value of timber stumpage. This appraisal constitutes a separate
operation, although the survey and the appraisal are so closely bound
together that they are frequently performed by the same man. They
must not be confused, however, for a timber appraisal is not a part of
Forest Mensuration, but belongs under the separate subject, Forest
Valuation (§ 5). It may begin where the timber survey leaves off,
using the data acquired by this survey. Separate parties may conduct
the timber survey and the timber appraisal with satisfactory results.
A timber appraisal covers the following points:
1. Logging conditions summarized for each logging unit, under
topogiaphy, slopes, surface, rock, brush and character of bottom as
affecting logging. Transportation possibilities, availability of streams
for log driving, routes for roads, flume or railroads, methods best adapted
for skidding and hauling the timber and the costs of these processes.
2. Costs of forestry such as the per cent of the stand to leave for
seed or second cut. the cost of brush disposal and other protective
measures.
270 METHODS OF TIMBER ESTIMATING
3. Economic conditions, markets and prices for lumber.
4. General appraisal, cost of milling, cost of logging, cost of trans-
portation, profits required.
5. Specific appraisal, the direct cost of logging the specific body
of timber and the resultant stumpage value of this unit.
A clear-cut distinction between the work of timber estimating and
of timber appraisal will prevent the mistake so often made of burden-
ing the timber estimating crew with the work of recording in great
detail items of cover, surface, brush, ete., which instead should be sum-
marized for an entire unit by the person who appraises the value of the
timber and sizes up logging conditions. It is seldom that the two jobs
can be effectively combined in the same party or individual. The
work of timber estimating requires routine and concentration on the
details of the job. The actual appraisal, even if the same party makes
it, should follow rather than accompany the estimate and should be
based first, upon the data on topography as shown by the map and
second, upon the data on volumes as shown in the estimate.
216. Forest Surveying as a Part of the Forest Survey. A forest
survey as above outlined includes the work of forest surveying or the
determination of the boundaries and area and the mapping of the topog-
raphy of a forest tract. This subject is not a part of Forest Mensu-
ration, but must be treated separately. Since the gridironing of the
tract requires the measurement of distance and direction and the plotting
of these lines will give the framework of a map, it follows that the work
of making a topographic map which may employ the same general
methods of examination for the area, can be advantageously combincd
with the work of timber estimating. Timber cruisers usually prepare
a crude map showing the intersection of streams and the position of
ridges and other topographic features of importance. The prepara-
tion of a map based upon basal elevations and giving contours is a
development of the timber survey introduced by foresters and adds
greatly to the efficiency of the survey. By combining this map-making
with the entirely separate operation of estimating, a crew of two men
can complete both operations with a very slight increase in expense,
not comparable with the cost of doing each piece of work separately.
At the same time the preparation of the type or timber-cover map
can proceed, and upon this in many instances depends the accuracy
of the timber estimate itself (§ 225).!
1The detailed methods of Forest Surveying employed in a forest survey cannot
be discussed in a text on Forest Mensuration without exceeding the limits of the
volume. Any summary of a system of forest survey must include a description
of the methods of surveying and topographic mapping which are to be used. The
various methods of survey must be co-ordinated with the methods of cruising and
with the cost and relative accuracy of the work desired, both for the survey and
the estimate.
THE CULL FACTOR, OR DEDUCTIONS FOR DEFECTS 271
217. The Cull Factor, or Deductions for Defects. Most timber
estimating for board-foot contents of stands is based on the amount
which the logs will scale (§ 116). Since a sound scale of logs requires
deductions for defects which will not make sound boards, the timber
estimator must make the same deductions in the standing trees. This
deduction from total sound scale is independent of any separation
of the timber into grades or quality, which calls for additional special
attention. Deductions from full sound scale of standing timber are
made either by the log unit or by the tree unit on the basis of the judg-
ment and experience of the cruiser. Where the estimate is made by
logs, only sound logs are tallied. Culled logs are dropped from the
tally altogether and trees which contain defective portions are scaled
by shortening the length or decreasing the size of the logs tallied so
as to represent only their net sound volume. Where it is impossible
or inaccurate to use this method of omission, a straight percentage
deduction for cull is either substituted for the method of dropping
or reducing logs or is subtracted after all of the clearly visible defect
has been deducted.
Tree units are handled in the same manner. Trees so defective
that they are practically cull are not tallied at all, but in species where
few, if any, trees are cull and the defect constitutes a portion of a large
per cent of the logs and is not easily deducted, cruisers deduct a straight
per cent from the total sound scale of the trees tallied. Usually a com-
bination of these methods is necessary since the per cent deducted
represents more accurately the loss in the sound scale of logs actually
sawed and taken to the mill, while a considerable additional cull is
found in logs and trees not utilized at all.
Foresters, in making a tally of diameters and heights, customarily
tally all trees, regardless of their condition, omitting only dead timber
which is unmerchantable, and then apply to the total volume a per-
centage deduction for total cull, which will cover both that portion
left in the woods and that lost in sawing.
218. Total, or 100 Per Cent Estimates. To completely cover a
small area, it is only necessary to avoid duplicating the count or measure-
ment of the individual trees. This may be done by the use of a bark
blazer or scratcher, or by tagging the trees, a method employed in India
where labor is cheap.
Trees may be given a light bark blaze. In working over a tract
in this manner, the blaze is placed upon the same side of all trees, facing
the direction towards which the measurement is proceeding. Where
topographic features are present on small areas, duplication may be
avoided by covering sections bounded by these natural features without
the necessity of spotting the trees.
272 METHODS OF TIMBER ESTIMATING
On larger areas, where it would be impossible to keep track of the
individual trees, parallel strips may be run. The trees on the outer
edge of a strip “can be blazed facing the strip which has not yet been
measured, and in this way the entire tract covered with a minimum
of effort. In dense swamps men may be employed to hew parallel
lanes through the underbrush; the cruiser then estimates all trees
between these lanes.
It is possible to dispense with all methods of marking the trees
provided sufficient care is taken, first, in running the strips accurately
as to direction so that they lie parallel and at fixed distances apart,
and second, by estimating or measuring the trees on strips so placed
that they cover the entire area; 1.e., strips whose borders are contiguous.
There is danger of overlapping or duplication by this method, and if
it is the intention to run a 100 per cent estimate, a slightly greater
accuracy can be insured by blazing. This ocular method, however,
is commonly employed as a substitute for blazing.
A modification of this method of completely covering the area by
strips, is the laying out of rectangular plots whose dimensions are such
as to cover the area without overlapping. These plots are estimated
consecutively and may be of any convenient width and length. As
an example, a method given in Graves’ Mensuration, page 196, consists
in laying out two tiers of plots, each 40 rods wide and 16 rods across.
Ten of these plots give the area of 40 acres. The cruiser proceeds 20
rods from the corner of the forty, and then crosses the center of the
first tier of five plots, returning through the center of the second tier.
To get the contents of the trees on areas 100 per cent of which is
estimated, the following systems may be used:
1. Tally the merchantable contents of each tree directly. This
is estimated by eye, or from a universal volume table which may be
printed on a Biltmore stick, or any other convenient form.
2. Tally the upper diameter, inside bark, of each log in the tree,
or tally the upper diameter of the butt log and top log (see Rule of
Thumb by F. R. Mason, § 204). The contents are then computed
from a log rule. .
3. Tally the diameter and merchantable height in 16- or 32-foot
logs or half-logs of every tree. The contents are then computed from
a volume table based on similar dimensions.
4. Tally the diameter only, of every tree, either by eye or by the
use of calipers. Measure, by a hypsometer, several sample trees of
each diameter to give a curve of average height on diameter. The
contents of the trees are then computed from a volume table based
on diameter and height. The heights measured may be either merchant-
able or total, but are usually the latter. In this method, types or areas
ESTIMATES COVERING PART OF TOTAL AREA 273
which differ in average height and diameter must be estimated sepa-
rately.
5. Count all the trees on the area and tally a fixed percentage such
as 1 in either 3, 4 or 5, whose volumes are found as by method 4 above.
6. Count all the trees on the area and determine their volume by
arriving at the contents of an average tree. This may be done:
By guessing at the average contents.
By selecting a tree of average diameter and height and determin-
ing its contents by the use of volume table.
By determining the number of logs per tree or average mer-
chantable height expressed in logs, thus getting the total
number of logs on the area and then guessing at the con-
tents of the average log or number of logs per thousand.
Method 6 may be applied to all of the timber considered as one
class, or the timber may be separated into two or possibly three dif-
ferent classes, corresponding with marked differences in size and char-
acter.
219. Estimates Covering a Part of the Total Area. The Strip
Method. There are two methods generally employed to estimate a
portion of the area, the strip method and the plot method. The strip
method adopts the principle of endeavoring to obtain the average
stand per acre for the whole area, from the portion estimated by the
running of strips parallel or in a given direction and spaced at mechanic-
ally regular intervals. By this means it is sought to eliminate judg-
ment or choice in the obtaining of the required average.
This average is still further improved by the choice of direction of
running these strips. The effect of differences in elevation and in drain-
age or soil moisture is to produce differences in the density and character
of the forest corresponding with these changes. The belts of forest
which have comparatively uniform stands usually run parallel with
contour lines and at right angles to the direction of slope. A basic
principle of strip estimating is therefore to cross these belts at right
angles or proceed directly up and down slopes or directly across the
larger stream or drainage bottoms as far as possible, and to avoid
traveling along contour lines or bottoms and in general along the long
axis of belts of timber. If this fundamental principle is neglected,
very large errors may be incurred in applying the average estimate
so obtained to the larger area.
In rectangular surveys, it is customary -to run the strips in one of
two cardinal directions, and the choice is therefore narrowed down to
either north and south, or east and west. In irregular surveys, or
where the topography is so mountainous that the estimate will be made
274 METHODS OF TIMBER ESTIMATING
by topographic blocks and units, rather than by forties or legal sub-
divisions, the system of strips will be planned with reference to base
lines run along the main bottoms and streams, from which, at regular
intervals, the strips will be run directly up the slopes and as nearly
parallel to each other as possible. The strips in each separate unit
may, therefore, have a different direction.
220. Factors Determining the Width of Strips. The standard widths
of strips used in timber estimating are six in number and their dimen-
sions are given in the following table:
TABLE XLI
RELATION OF WiptH AND NUMBER OF Strips TO AREA COVERED
A red by : ; °
WiptTH oF Strips NEM ae Strips per 4 mile
one strip per forty :
; to cover er.tire
acres or four per
area.
mile.
Feet | Rods | Chains Per cent Number
33 2s 2 23 40
66 Arvnlh| 1 5 20
110 63 12 84 12
132 Sail 2 10 10
165 10 2 123 8
330 20. | 5 25 4
On rectangular surveys, to compute this per cent of total area
covered by the strips, multiply the number of strips run per forty
or one-fourth mile square, by the width of the strip in rods, and divide
by 80 rods. These two factors, number and width of strips, are not
reciprocals since each has a distinct function to perform. The number
of strips per forty increases directly the probability of accuracy
in securing an average stand or proper sampling of the timber on the
area (§ 211). The width of the strip affects this average to a lesser
degree. Its principal function is to enable the cruiser to determine
accurately the dimensions and volume of the trees which stand upon
the strip estimated, and the factors which affect his ability to obtain
this accuracy will determine the width of strip without respect to its
effect upon the total area covered. If narrow strips must be run in
order to get accurate estimates of timber on the strip, and it is necessary
to increase the per cent of area, the number of strips will have to be
increased rather than the width of the strip.
An example of the relations between these two factors is cited by Austin Cary,
Manual for Northern Woodsmen, where a system on the Pacific Coast of using two
FACTORS DETERMINING WIDTH OF STRIPS 275
strips per forty, each 10 rods wide, covering 25 per cent of the area was abandoned
in favor of the use of a narrower strip 63 rods wide to increase the accuracy of the
estimate on the strip. The number of strips was then doubled, or four strips run
per forty, and the total per cent of the area estimated was thus increased from
25 per cent to 3334 per cent. If, instead, the number of strips had been kept the
same, but the width of each strip increased to 20 rods, a lesser degree of accuracy
would have been attained in spite of an increase to 50 per cent of the area covered.
In determining the number of strips required for a forest survey,
the character of the topographic map desired must be considered with
reference to the topography. Lines run 3-mile apart will give only a
rough scale map in bold mountainous topography. Lines placed at
t-mile intervals in mountainous slopes with large features, are sufficient
for an accurate topographic map with a large contour interval of from
50 to 100 feet. On all flat or gently rolling forested slopes with no
outlook, cut up by drainage or interspersed with swamps, it is Impos-
sible to make an accurate topographic map with proper contour interval
of from 10 to 20 feet and show all details of drainage and slope, unless
lines are run at }-mile intervals, but this interval is sufficient for all
maps on the ordinary scale of from 2 to 4 inches per mile. Only for
a much greater detail will lines be required at less than this interval.
The influence of the forest cover upon the number of strips required
for accuracy increases with the two factors, density of the forest cover
and variation of the timber, whether caused either by age, size or diver-
sity of species. Finally, the increasing value of the timber from any
cause, whether through quality or unit price, will require an increase
in the per cent of area covered, which means a greater number and
more closely spaced strips.
These conditions frequently require a full or 100 per cent estimate
by forties, the best examples of which are the heavy stands of rapidly
increasing value in the Pacific Coast States, or stands of large mature
hardwoods with great variety in size and value.
The width of strips is determined by the accuracy with which this
width can be measured by the eye and the dimensions of all the trees
standing thereon ascertained, or the timber upon it measured and
counted. This width is diminished directly by the amount of brush
and undergrowth which obstructs the vision. In brushy country, strips
seldom exceed from 4 to 63 rods. The width of a strip is also diminished
by decreasing size and increasing number of trees on the strip. In
young timber, with many stems per acre, a greater degree of accuracy
is obtained on a 4-rod strip accurately measured and counted than
upon a strip of twice the width. Conversely, open and large timber
with fewer and more scattered trees and an unobstructed view not
only permits a wider strip to be measured accurately, but requires an
276 METHODS OF TIMBER ESTIMATING
increase in the per cent of area, which is easily obtained by increasing
the width of the strip without an appreciable increase in the cost. This
is independent of the need for running more strips per acre, by which
the per cent is still further increased. With unobstructed vision, a
wide strip may be estimated with almost as great accuracy as a narrow
strip, since the error may be in proportion to the total width without
affecting the percentage of error in the estimate.
With increasing openness and irregularity of timber, strips may
give way altogether to a total count of timber on an entire forty,
since no system of partial or sample estimates can be depended upon to
secure an average or a correct total.
The method of determining the volume of the trees on the strip
affects the width of strip which can be used accurately. Where trees
are counted, without measuring the diameter of each tree, nearly
double the width of strip can be used because trees can be seen for
this additional distance while it is less possible to judge their diameters
accurately. Upon a calipered strip, the additional width sometimes
slows up the work and introduces a greater per cent of error.
The counting of trees in open country is so simple a matter that
cruisers accustomed to estimating such species as longleaf pine in the
South have usually abandoned the strip method altogether. Guided
by the compassman, they cross a forty about twice, pursuing a
snake’s course back and forth, and attempting to see and roughly to
count all of the trees on the forty.
221. Method of Running Strip Surveys. Record of Timber.
Strips are universally run with the compass. A hand compass is com-
monly used by cruisers working in dense, swampy or brushy country,
as it is more quickly read and increases the number of sights possible
without delaying the work. For ordinary accurate surveying, in which
a topographic map is made, the use of a staff compass adds to the accu-
racy of the direction of the strips, and is commonly employed (Fig.
58). In the use of either hand or staff compasses, it is a great advan-
tage to be able to turn off the declination of the needle on a movable
arc with a vernier so that a cardinal direction is indicated by the sights.
This is especially true in the Pacific Northwest, where variations up to
25 degrees are encountered.
The size of the field party for strip estimating depends upon the
methods used in measuring and recording the timber. Where the
diameters of each tree are measured either with the calipers or Bilt-
more stick, the party will consist of three or four men to best advantage.
One man runs the compass and makes the topographic and type maps.
A second man tallies the diameters; the third and fourth work, one
on each side, calipering trees. Heights are usually taken at regular
METHOD OF RUNNING STRIP SURVEYS 277
intervals so as to be distributed uniformly over the area. Consider-
able errors may be incurred in bunching sample heights in timber which
may be too tall or too short
for the average of the stand.
Where diameters and mer-
chantable heights are meas-
ured by the eye, the party is
usually reduced to two men,
one for the compass and map,
the other to record the dimen-
sions of the trees which he
estimates. It was a common
practice in the Lake States
in earlier days, for timber
cruisers to work alone without
the assistance of a compass-
man. The system of counting
timber and recording merely
the average dimensions and
volume enabled a man to run
his Own compass, keep track
of his paces, and at the same
time count the trees.
The record kept by cruis-
ers on strip estimating con- Fra. 58.—Staff compass.
sists primarily of a tally of
the trees by diameter, height, or volumes direct; second, of the
cull, per cent; third, notes on damage to the stand; fourth,
quality of timber and grades; fifth, young timber and reproduction;
sixth, soil and ground cover. A report or summary sheet for each sepa-
rate unit, usually by forties, is worked out. The following headings
are submitted as samples (p. 278):
f
is
a
I
l
In the Appalachian region upwards of twenty species and a variety of products
may be estimated. For the hardwoods, volume tables based upon diameter and
merchantable log lengths are used. It has been found necessary to have available
a table for one- and two-log trees to avoid errors in inaccurately applying small top
diameters for these trees rather than the actual merchantable top. Cull is deducted
from each tree by reducing the D.B.H. or number of logs. An additional per cent
is deducted for unseen defects. The tally is coordinated with existing volume
tables to secure a record of lumber, cordwood (principally acid wood), poles, ties,
posts, or other products. An example of the tally form used is shown on p. 279.
METHODS OF TIMBER ESTIMATING
278
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Seeds ly 4O
279
METHOD OF RUNNING STRIP SURVEYS
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TOOT M10
280 METHODS OF TIMBER ESTIMATING
REVERSE SIDE OF BLANK
Forest types, Lower slope
Age classes, 1-60
Condition of timber, Immature
{UE het 8 aes RELA Ohare Seo. apc 95 per cent
MOLUTEIS eon he oe Lee Ee 2 per cent
Decaderit's 4 05 A ivan tei ey eis 3. per cent
Binenicilled Maene Griese tote teeters ete .. per cent; damaged, 5 per cent
Mrisectrieulled ee oasis ceva ee eae sotto .. per cent; damaged, -— per cent
Giherkilled acer oes epee eke .. per cent; damaged, 2 per cent
Name of disease, Bark disease
Species affected, Chestnut
Quality of timber (give by log grade; percentage of tall, medium or short clear boles;
or number of clear logs of stated minimum length and diameter):
80% tall; 15% medium; 5% short
sevice atiny cls. ouleL ie: ele aef oieiie\ ah we, “eke. pine syie, > a) (s/s) (s) is) m /eumiel nl s)s0 \ele is \eye'(e eis! shel @ le (¢|\») 6, .0/s s,0) 8.0) eKe) pl lekeLoteiamwas lene
Logging factors:
Undergrowth; light-medium-dense, Light
Windfall; light-medium-dense, None
Bowlders and broken rock; numerous; occasional; absent, Absent
Other factors, Easy gradient. Logging conditions ideal as skid and wagon
roads can be constructed anywhere
Replacement: Species - Per cent
IN Ore placement, “Le sib 5 ve) wars sim Blaekats foe ness s 512s pres Goes sina ee
Ground one-third: stocked). eo Nek cee Pn rere Os bi ocsits tes ehs |B eeae
Ground twozthimds! Sto, kc-teveyene gene vthe bovteseel en ocd hhiexe te tome l<tee meter ene
Ground fully slocked, Chestnut, 50%; white, 5%, red, 5%, ;
black, 20%, and chestnut oaks, 10%; white, 1%,
pitch, 2%, and scrub pines, 2%; gum, 2%; sourwood,
19G> andeminplen2 Ossie eta cts eee ees . 100%
The stand shows an absence of poplar due to grazing
Additional Notes: This is a stand which was cut over for charcoal during the war
and since then was culled for chestnut ties and poles. Bark infested chestnuts
should be cut as well as suppressed chestnut for extractwood. The few mature
“Wolf” trees left from former cuttings should be removed as well as some of
the scarlet and black oaks where the stand is too dense. Removal of the
latter can be made for ties. The dead and down timber from the laps in the
tie and pole cuttings should be removed for extractwood
TYING IN THE STRIPS. THE BASE LINE 281
Explanation of Blank, by Supervisor J. H.Fahrenbach.
All saw timber is tallied by the number of 16-foot logs in each tree. If a tree
happens to have odd lengths “ we give and take.”’
Under chestnut all trees to be removed for extract wood are tallied in the ‘0 ”
column. All trees to be left are tallied in the one-log column, even though they
are not large enough to make one 16-foot log as is the case in trees under 10 inches
D.B.H. Street railway ties (6 by 6 inches by 8 feet) are tallied in trees which
have reached their maximum value for hewn ties. Standard gage ties are usually
sawed in saw timber operations, and are tallied as saw timber. Poles are tallied
by diameter class. In this way we are able to approximate the number of 25-foot,
30-foot, 35-foot, ete., poles.
Chestnut oak and hemlock trees, suitable for bark alone, are tallied in the “0”
column. In figuring the estimate for bark the number of trees tallied as saw timber
must also be included. It sometimes happens that we also have a market for black
oak bark, and in this event a “0” column must be entered under mixed oak.
Poplar and scrub pine pulp wood are entered in the ‘0 ’”’ column.
We class black, scarlet, pin and Spanish oak under mixed oak. If a ‘“‘0”’ column
is added, it is understood that black-oak bark is to be entered. Under mixed-oak
ties red-oak ties are included.
Pitch, short-leaf and table-mountain pine are tallied under yellow pine.
If there is a market for locust-tree nails they are tallied in the one- and two-log
columns for the larger locust trees and the smaller trees are tallied as posts, using
as a basis a post 4 inches in diameter and 73 feet long.
Under others are tallied beech, birch, gum, maple, sourwood and sycamore.
If there should be other valuable species for which provision has not been made
in the headings the diameter and number of logs in each tree are given at the bottom
of the Form. This includes walnut, ash and wild cherry.
If there is a market for fuel wood, provision must be made for a ‘‘ 0” column for
all those species which cannot be utilized for either bark, pulp or extract wood.
All the oaks can be thrown together in one heading, the pine in one heading and the
remainder of the species, except hickory, in another heading.
222. Tying in the Strips. The Base Line. In laying out and
recording the strips run in estimating, independent of the question |
of topographic mapping, it is necessary to tie in each strip to a known
point at each end, so that its position and the error incurred in running
it in both distance and direction may be determined. For this
purpose, and also to form the basis of a map when one is constructed,
a base line is first surveyed along the route from which the strip will
be later laid out. The strip, whether rectangular or irregular areas
are being estimated, will start as nearly at right angles as possible from
points on this base line, and will either be tied in to a second base line
approximately parallel to the first, or by offsets will be run back at the
proper interval and tied in to the original base line.
In laying out this base line, therefore, stations or measurements
are established at the exact points and intervals from which these strips
must later be initiated and tied in. Methods of survey and establish-
ment of base lines fall under the subject of Forest Surveying. The
282 METHODS OF TIMBER ESTIMATING
base line is a primary feature of the forest survey. Where a land survey
exists which is accurate and easily traced, or where such a survey is
retraced, it may serve as a base line.
Where the area is small, and a survey and map exists, the corners
and known or located points on the boundaries of the tract are sub-
stituted for a base line as points from which to initiate strip surveys.
The same rules apply as to the necessity of tying in each strip on its
completion to some known point on the map, in order to check errors
in the survey which would affect the areas determined.
In running the strip, the estimator is dependent upon the compass-
man for the distances from which the areas are determined and the
estimate separated by 40-acre tracts. Errors in measuring this dis-
tance will cause the cruiser to misplace timber, thus altering the accuracy
of the individual estimates per forty. Where types or differences in
stand are separated in estimating, the distance across each separate
type, as kept by the compassman, will determine the area and con-
sequently the accuracy of the estimate within the type. If errors are
incurred, their character and extent is revealed by tying in to known
points, which enables the construction of a correct map and the correc-
tion of the estimates.
In running estimates over separate forties, it is customary to run
strips 1 mile in length, cruising a tier of 4 forties before returning.
Where one strip per forty is run, the estimate for the forty is completed
at the end of 80 rods. Where two or more strips are run per forty,
the tally of the timber on each forty is separated for each strip as indi-
cated to the cruiser by the compassman, and is not completed until
the last strip on each forty is run. The results for each strip on the
same forty are usually tallied together on the same sheet, and care
must be exercised not to misplace or mix up these tallies. 5
223. Systems of Strip Estimating in Use. Examples of systems of
estimating in which the various factors itemized above are harmonized
to meet a given set of conditions, are given below:
Forest Service Standard Valuation Survey. This system was used almost uni-
versally by the Forest Service and with minor modifications is still a standard method
used on national forests. Its characteristics are:
Width ofisttip) ain aatue ieee ie 4 rods or 1 chain
Number of strips per forty.:......... 1 to 2
Per cent of area estimated........... 5 to 10
Measurement of distances........... By chain or tape
Measurement of trees, diameters...... By calipers or Biltmore stick or ocular
Heights aaa eens sos eee bet ee Sample heights by hypsometer
Forest, types 5th ou drei Separated and coordinated with avelage
heights
Cull factoryees eo ahead oe eee Estimated by a total per cent
Corrections from strip estimate for
SIVETAPE Sted Clee unn eae ee None
SYSTEMS OF STRIP ESTIMATING IN USE 283
In this system, as indicated in the last item, no effort was made to modify the
average stand per acre obtained from the strip in order to get a more correct total for
the area. The employment of inexperienced men made necessary the use of instru-
ments for diameter and height measurement, and the rigid elimination of the element
of judgment on every point possible. Where the unit of area was large, from 1
square mile up, this method gave excellent results, since the mechanical average for
areas of this size is quite dependable on the basis of a 5 to 10 per cent estimate.
The errors possible could be easily avoided by conscientious effort. These errors
consisted of too wide or narrow a strip, diameters measured too low, average heights
measured too high, dead trees calipered for live ones. When applied to large timber
in units of 40 acres or less, these mechanical results cannot be depended upon,
Lake States Cruisers’ Method
WURGLRAEOR SURG tins oars leat tee ee 8 to 10 rods—2 to 23 chains
Number of strips per forty......+....1 to 2
Per cent of area estimated........... 10 to 25
Measurement of distances...........By pacing
Measurement of trees............... Counted
LE Sra Fit erces ge ROR eS eae cee Average number of 16-foot logs per tree
NiGIMIAC aie cyt ise es oe dee eek Me From number of logs on tract and log run, or
contents of average log
MOneStPbyIDeSi. cha sinels <i sc eteue os eo: Timber of different age classes and quality
separated
Cullbiactoreecr reece oe Usually by per cent deduction from total esti-
mate
Corrections from strip estimate for
SVETAEE Stale. fs oe at cia Mee eee Close inspection of remaining area and modifi-
cation of average whenever necessary to
obtain correct total
Of late, timber cruisers in these states have been adopting the use of volume
tables, but in many instances these tables are based upon stump diameter inside
the bark which makes them less consistent and accurate than if based on D.B.H.
The more modern cruisers are adopting the use of standard volume tables constructed
by regular methods and differentiated by D.B.H..and height.
Southern Timber Cruisers’ Methods
VOL HEOTAStIT Ds ool hia sect eon eee ete A strong tendency to substitute ocular esti-
mate, based on the stand per acre, for the
running of strips. Great carelessness in
methods until recently
Measurement of distamces........... Paced by a compassman, the cruiser usually
riding a horse. Consequently estimates fre-
quently stopped at the edges of swamps
Measurement of trees............... Cruiser gets located by compassman, but does
not follow the strip. Trees are counted on
acre plots
Volume of average tree.............. Guessed at, using rule of thumb based on
Doyle rule. Trees on entire forty may be
counted to check results of plots and get
reduction factor
284 METHODS OF TIMBER ESTIMATING
Rorest types a) J NuneRe seas Accuracy of the better class of cruisers greatly
increased by careful elimination of blank
areas and containing net area of timber to
which reduction factor from stand per acre
is applied for total
Cullfactor: Curae ail ee neine coat Usually neglected on account of deficiencies in
Doyle scale
Corrections from strip estimate for
AVETAPEISbAIG!.vo eee ciate. teen eee This is based on general inspection and count-
ing since no systematic strips are run
Many Southern cruisers have adopted more systematic methods of late.
Yale Forest School Method in Southern Pine.
Width of stripina-3.2 5 sect ada ee 10 rods—2}4 chains
Number of strips per forty...........2
Per cent of area estimated........... 25
Measurement of distances........... By pacing
Measurement of trees............... Count of the trees on the strip, tally of one-
third to one-fifth of the timber by mechan-
ical selection to avoid choice.
IDIAMELETS oes Ses tee ee euune Lo ee Tallied by eye
Merchantable height................ Tallied by eye in 16-foot logs and mie of
all trees whose diameters are tallied
Volume onisanip ieee cae ae From anaes table for trees tallied multiplied
by 3, 4 or 5, according to per cent tallied
Horest types & < des Ret aes ape ee Areas not ee with merchantable timber
eliminated by mapping. Net area of timber
obtained. Types not usually separate
within a forty except on the map
Gullitactors:h yen et a oeetiee By per cent of total estimate
Correction from strip estimate for aver-
COZENS TOC Sn ee On ai Seen Oe FS Careful inspection at stated intervals of stand
on remainder of forty. Comparison by
weighted volumes with stand estimated.
Weighted correction factor applied to area
estimated to obtain proper stand per
forty
Horseshoe Method. This is a modification of the strip method, by which two
strips are practically combined in one by running a horseshoe or angular course
through the forty as shown in Fig. 59. This results, first, in a saving of time, cut-
ting down a certain amount of travel from one strip to another; second, in a better
inspection of the timber and, it is thought, in a better average, since the strips run’
in both cardinal directions. This method was employed extensively by a firm of
Southern timber cruisers, who used a 10-rod strip, thus running 25 per cent of the
area.
Pacific Coast Method.
Width ob siripwits Fie ee eee 10 rods, or 2} chains
Number of strips per forty........... 4
Per cent of area estimated........... 50
Measurement of distances........... By pacing
METHODS DEPENDENT ON THE USE OF PLOTS 285
Measurement of trees....:.......... The volume of each tree recorded directly,
based upon the universal volume tabies
HOES UBL VCS acer. eyete acer sieler over s,0/0c5-55 Not necessary to regard them
BOMUISERELOLS 2 chs ccs ode te se eee ce Se Deductions made for each tree when its
volume is ascertained
Correction from strip estimate for aver-
ACE IStAMGG ire hdn pel acre sears «hak eines By running 50 per cent, corrections are usually
avoided. Where inspection reveals the
necessity, modifications are made in the
total estimate
Separate record under this system may be made of the board-foot
contents and of other products, such as poles. The estimate is fre-
quently increased
to 100 per cent.
These examples
are cited merely to
show the various
combinations of ele-
ments which go to
make up a system
of timber estimat-
ing. The securing
of accuracy consists
in adapting the Fie. 59—Horseshoe method of strip estimating. Route
number and width of compassman shown by dotted line.
of strips to the
local conditions described as, first, character of timber to be
estimated and, second, size of the smallest unit of area to be
estimated. The details of measurement, whether by eye or instru-
ment, for distance or for tree dimensions, must be coordinated with
the volume table and with the skill and personal ability of the individ-
uals employed in the work. The saving in time by the substitution
of the eye and of ocular judgment requires dependence upon personal
skill. Where cruisers with sufficient experience are unobtainable,
accurate results may still be obtained by mechanical measurements,
carefully supervised and conscientiously applied.
224. Methods Dependent on the Use of Plots Systematically
Spaced. In the use of plots in timber estimating, the method employed
depends upon whether the principle of mechanical arrangement or
spacing is to be observed, in order to obtain an average stand, free
from the element of personal judgment, or whether instead, plots are
to be selected by the use of judgment in an effort to obtain thereby
an average stand which will apply to the area as a whole. By the
first principle, the plot method, so-called, is merely a modification of
% Mile
286 METHODS OF TIMBER ESTIMATING
the strip method. Compass strips are run at the usual intervals,
but instead of a continuous belt or ribbon of area being covered, this is
broken or separated into plots at fixed or stated intervals along the line.
These plots may be rectangular, but the use of such plots is not
common. In the measurement of rectangular plots, a crew is usually
employed, and this same crew can probably run out the entire strip
with better results. Rectangular plots for the measurement of young
growth and reproduction, which is desired only on a small per cent
of the area, are frequently used in conjunction with a strip for the
merchantable timber.
The common form of plots is circular to enable one man to work
to advantage without the assistance of a compassman. By dividing
the functions of pacing and compass work from those of estimating
and recording the diameters and heights of timber, the mind is kept
free for concentration on each task in turn. A crew of two men is
sometimes used for circular plot estimating with the same advantage
to the timber cruiser, who can inspect the stand for defect and quality
between the estimation of the volumes of his plots. The common
size of plots is as follows:
TABLE XLII
Sizes or CirrcuLar PLots
Size of DIAMETER
plot. Radius.
Acres Feet Feet Rods
4 59 118 The llss
4 83 166 10.0
1 118 236 14.3
The relation of these plots to the per cent of area covered is given
below.
TABLE XLIII
RELATION BETWEEN PLotTs AND AREA COVERED
SOE | Plots for 4 | Total area Per Cent oF 40 AcrES
distance : :
Size of plot. Betaee mile of included in | IncLUDED In RUNNING
ter strip plots.
Acres Rods Acres 1 strip 2 strips
m 8 10 23 64 123
3 10 8 4 10 20
1 16 5 5 123 25
METHODS DEPENDENT ON THE USE OF PLOTS 287
Great care must be taken in the use of circular plots to obtain the
width of the plot correctly. An error in this factor is more serious than
that on a strip, since it affects the entire boundary. The same principle
as to size and number of plots and per cent of area covered applies
to these methods as to strip estimating. In dense brush and with small
timber, the common size is one-fourth acre, while plots 1 acre in size
are required for old and large trees. The amount of timber on each
plot is obtained by the use of the same variety of methods as for strips.
Examples. Spruce in the Northeast on large tracts.
SEA EEG ION soos eos Fats ais assaf’ + acre
Number of strips per forty........... 1
Distance between plots on strip. ..... 20 rods—5 chains
Per cent of area covered............. 3
Measurement of distances........... By pacing
Measurement of trees............... D.B.H., calipered or tallied by eye
15 CeCe TES ROME ar etm A few sample heights taken on each plot for
curve of height on diameter
AV DES Creare cele res be ae Separated in mapping
COUNTRY EN ay ct Sed ts SAP SS hd By per cent applied to total estimate
Correction of estimates to get average. None
Large Timber on the Pacific Coast.
Number of strips per forty...........1 to 2
SIZE OlmplO taints ie thet Ge oar eb. 6s 1 acre
Number of plots per strip........... 5
IRencentsoleaneay a genie ee) ae aie 122 to 25
Measurement of distance............ By pacing
Measurement of trees on plot......../ Average tree selected for each species. Diam-
eter at stump inside bark and at top
measured. Average of these diameters
taken as diameter of the average log
AVOID CAVNG 8 SRR oie ee ota eas one Ee ee Obtained by rule of thumb (§ 214). (Any
of the three standard methods for obtaining
the contents of trees on a plot or area apply
to this method.)
NN] 01S skooe Mea RETO Ie 2a REG AES Seer a Blank areas eliminated and stand obtained for
average acre
(Oot Se tae Sree Cie eens Sereno pie By a per cent of the total estimate
Correction factor to the estimate..... Obtained by general observation and com-
parison with stands on the plots
CHAPTER XXI
METHODS OF IMPROVING THE ACCURACY OF TIMBER
ESTIMATES
225. The Use of Forest Types in Estimating. When only a part
of the area of a tract is covered in estimating, the accuracy of the
resultant estimate depends upon the success with which the actual
average stand per acre has been obtained. Although the per cent of
area taken has been properly chosen to fit the topographic conditions
and character of the timber and although the measurement of the timber
upon this area and the width of the strips has been accurately carried
out, so that no avoidable error remains in the work done, yet the esti-
mate may still be in error by the failure to secure the same proportion
of the different types and variations of stand on the strips as exist on_
the area as a whole. On account of the prohibitive expense of running
a sufficient per cent of the area to get this average mechanically, a
margin of error in timber estimating is permitted, and is gaged by the
value of the timber and the purpose of the estimate. Any modification
which will secure the required degree of accuracy and at the same time
avoid incurring an unreasonable expense will necessarily become a
part.of the system employed.
The more uniform the stand as to sizes and density of stocking, the
better the averages. This applies to the use of all six of the classes of
averages cited in § 209.
For the purpose of securing a greater degree of uniformity in the
stand on those subdivisions of total area to which the estimates obtained
on strips or plots are applied, the distinction of forest cover types is
indispensable. A forest type includes all stands of similar character
as regards composition and development due to given physical and
biological factors, by which they may be differentiated from other
groups of stands. A cover type is the forest type now occupying the
ground, whether this be temporary or permanent. Timber estimating
concerns itself only with the existing forest cover.
The factors which are reduced to greater uniformity by the sepa-
ration of forest types in estimating are composition of stand as to species,
and consequent relative per cent of total volume of stand represented
by the different species, a vital consideration in timber estimating. This
288
THE USE OF FOREST TYPES IN ESTIMATING 289
factor has an influence upon the total volume of the stand, as well as
its average height, though both of these are influenced even more pro-
foundly by differences in quality of site within the same cover type.
These differences in type may be caused by altitude, slope, moist-
ure and depth of soil. By separating the total into sub-areas, a far
greater uniformity of size and density of the timber in these sub-
divisions may be obtained, first by securing a more uniform mixture
of species in the per cents of the different species represented in the
- stand; second, by reducing differences in the density of stocking per
acre; third, by securing more uniform sizes both in height and diameter,
and a smaller range. The subdivision of an area into a number of
smaller units is a means of avoiding the necessity for securing a weighted
average of these factors in order to get the average acre. Doubling the
number of strips would probably secure the same result, but the expense
of separation of the estimate into two or more types is much less than
this increase in field work.
The only increased expense of separating types consists of the
increase in computations required by separating the areas and the
precaution required in changing the tally sheet on entering the type.
Proper coordination between the compassman who maps the area
and the estimator who records the timber is necessary.
Where areas as small as 40 acres are mapped and a large per cent
taken, distinctions between the two types of timber are not often made
by old woodsmen. The total volume of each species is obtained with-
out separate computations of area.
But the principle of type separations is universally applied in sepa-
rating areas which do not contain merchantable timber from those which
do. Blank areas caused by cultivation, burns, swamps, or unmerchant-
able reproduction must be subtracted from the total timbered area
under any system which permits the completion of a cover map. The
arbitrary inclusion of these unstocked areas makes it practically impos-
sible to obtain an average stand on the remainder. In theory the same
law of averages applies even in this case and with a sufficient number
of strips which cross blank areas in such a way that a per cent of the
blanks is taken as the merchantable stand, no error would be incurred
in the average. But the extreme danger of obtaining a different per
cent from that on the whole tract, and the comparative simplicity
of mapping out these blanks to obtain net timbered area, makes this
method universal wherever the number of strips per forty or 4-mile
amounts to at least two, and possible even when but one strip is run.
This correction requires, first, the area of the type whether timbered
or blank, from a map; second, the area covered by the strip in esti-
mating. The latter expressed in acres is computed by multiplying
290 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
length of strip by its width. The most convenient units are rods,
since 160 square rods equals 1 acre, or chains, 10 square chains to 1
acre. Distance in chains on strip required for 1 acre may be computed
for each width of strip. and the area of the strip obtained by dividing
its length by this factor.
226. Method of Separating Areas of Different Types. To determine
the total area of
the type accurately
fromamap, a plan-
7imeter may be used.
By the use of
this instrument a
direct reading on
the map is obtained
in square inches
Fig. 60.—Polar planimeter. of the area whose
boundary is traced
by the needle, moving clockwise. The stationary pin is placed outside
of the area to.be traced. When placed within the area so that the
movable pin finally encircles the pivot before returning to its point of
origin, a deduction or correction must be made in the indicated area, the
size of which depends upon the make of instrument used.
The equivalent in acres for square inches, as determined by scale
of the map, gives the acreage. Lacking a planimeter, the area of types
can be computed by the method of approximation through triangles
or the sum of small squares. For the latter purpose a map should be
plotted on fine cross-section paper.
The area of these types is required
only to a reasonable degree of
accuracy since the determination
of their field boundaries is a
matter of inspection and sketching
and the total area of the tract is
not involved.
As an illustration of the effect of
using type areas in estimating, the follow-
ing example may be cited: Area of
tract, 200 acres, divided into two types
containing 100 acres each. The stand
on the first type is 30,000 board feet per
acre, and on the second 10,000 board feet.
The total stand is therefore 4 million
board feet. Twenty-five per cent of this area or 50 acres is to be covered ‘by
strips. The result of the cruise is shown in Fig. 61.
Fic. 61.—Relation of areas of types to
strips in timber estimating.
SITE CLASSES AND AVERAGE HEIGHTS OF TIMBER 291
The result of running the five strips at regular intervals is to include within
type I, 30 acres, which at 30,000 board feet per acre would give 900,000 board feet.
In type II, 20 acres was included which at 10,000 board feet gives 200,000 board
feet, a total for the 50 acres run, of 1,100,000 board feet. As this is 25 per cent of
the area, the required factor for the tract without subdivision into types would
be a multiple of 4, giving an estimate of 4,400,000 board feet, an error of +10 per
cent caused not by errors in the strip but by failure to get the weighted average
stand from the strips run.
But if while running these same strips the tally sheet had been changed wherever
the strip passed from one of these types to the other, and both the map of the area
and the corresponding estimate of the timber, or tally, had thus been separated
into two areas, corresponding with each of the two types, the computed estimate
would show that while on 30 acres 900,000 board feet was tallied the average acre
for type I is 30,000 board feet, but instead of this applying to three-fifths of the total
area, it applies only to the actual area shown to be in the type, or one-half of the total,
which is 100 acres, totaling 3,000,000 board feet. The less fully-stocked type in
the same way is shown to contain 1,000,000 board feet or a correct total for the tract
of 4,000,000 board feet. The 10 per cent error incurred in the first method is elimi-
nated. The accuracy of this area correction obviously depends first upon ability
to obtain by sketch a correct map of the actual areas of the different types, and
second, to convert this area from the map into acres by use of the proper methods
of map reading as explained in this paragraph.
This system of type divisions is of especial value in mountainous regions where
sharp distinctions can be drawn between types coinciding with great differences
in the average density, volume, size and value of the timber. Under such circum-
stances the more valuable types would require a greater per cent of the total area
to be estimated, to obtain the same basis of accuracy as could be secured for the
less densely stocked and less valuable tracts with a smaller per cent. The type’
divisions also are more conveniently made in large or irregular areas than where
estimates are separated by rectangular tracts of 40 acres.
227. Site Classes and Average Heights of Timber. Liifferences
in the quality of the site on which timber is growing cause very great
differences in total volume per acre, and in the total heights of the
trees and stands. To quite an extent these differences are closely
correlated with changes in cover types, different types being found
on wet soils, fresh well-drained soils, and dry, shallow soils. But it
often happens that the same type of forest cover will extend without
appreciable changes in composition over a range of site quality so great
that it becomes necessary to subdivide the area within the type into
from two to three site classes, ranging from good to poor. This is
made necessary by the effect of site upon the height of the trees in the
stand, on account of the methods usually required, of selecting sample
trees to measure for height.
Heights constitute an extremely variable factor in timber estimating.
Not only do total heights range through limits of at least 100 per cent
for the same diameter, but merchantable heights, especially in old hard-
woods, vary still more widely. Just as, in a 100 per cent estimate,
the necessity for averages is eliminated, so when the height of every
292 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
tree in a stand is tallied there is no necessity for average heights. Only
when merchantable log lengths are used as the basis for height will the
height of every tree measured for diameter be tallied. Where total
height is used, far greater accuracy can be obtained by the measure-
ment of a few trees with a hypsometer than by attempting to guess
by eye the height of each tree.
In a large tract with varying site qualities, the securing of the average
height for each diameter class from a range of heights of 100 per cent
would require the selection of heights on the basis of the principle of °
a weighted average. If exactly the same proportion, as for instance,
1 per cent, of the heights for each diameter were obtained from large,
medium and short trees as existed in the original stand on the entire
tract, the height curve could then be applied to the tract as a whole.
Any failure to secure this weighted average would result in a curve
giving too high or too low an average for the timber as a whole.
The difficulty of securing a weighted average is eliminated if the
tract can be divided into two or three site qualities, separated as dis-
tinct units in the field in estimating. On each of these separate sites
the heights conform to a much closer range for the same diameter than
for the entire area, and a few selected trees for each class will give a
dependable height curve (§ 209) from which the volumes in each
diameter class may be accurately computed.
228. Methods of Estimating which Utilize Types and Site Classes;
Corrections for Area. An example of the application of these principles
is found in the standard methods of timber cruising adopted by the
Forest Service in the Appalachian region. Four types are used, termed
cove, lower slope, upper slope and ridge. The variations in the per
cent of estimate required are shown in the following table:
TABLE XLIV
Per Cent or ToraLu AREA REQUIRED IN ESTIMATING
]
TotaL AREA ESTIMATED
Area
of
estimate Average Heavily Lightly
unit. of all types.| timbered | timbered
types. types.
Acres. Per cent Per cent Per cent
0-100 | 50-100 50-100 | 50 -100
100— 500 25-— 50 25-100 10 — 25
500-1000 10— 15 20— 50 5 — 10
1000-5000 5- 10 15— 25 i 5
5000 + 38- 5 10— 25 B- 24
THE USE OF CORRECTION FACTORS FOR VOLUME 293
The problem of combining a large per cent of area on a heavily
timbered type, as the cove type, with a small per cent elsewhere, has
been solved here by running strips across the entire area, embracing
the minimum per cent. Where these strips cross the cove types, points
are marked on the ground which serve to tie in the strips run through
the coves. Where 100 per cent is not estimated, a plan of running
strips in a zigzag course from one boundary to the others of the type
through these goves has been adopted. The more acute the angle
between two courses and the
more nearly parallel the result-
ant strips, the greater the per
cent of the type included.
229. The Use of Correction
Factors for Volume. The pur-
pose of all estimates is to secure
the actual volume of timber on
the entire tract as accurately
and inexpensively as_ possible.
In systems of covering partial
areas, even after the probable ;
Fic. 62.—Method of running strips to cover
aa has been reduced by adopt- an additional 20 per cent of area in heavily
ing subdivisions based on type timbered type, on basis of original 5 per
or forest cover and site, there cent estimate for entire area. Strips 8 rods
remains a final possibility that — wide.
the average stand per acre within
the type differs from that secured by the methods employed.! The older
and more diversified a stand, the greater will be its irregularity of stocking,
and the greater the necessity for accuracy. Can this accuracy be still
further improved? A correction of an average, mechanically obtained,
rests upon the assumption of definite knowledge that this average is
wrong, and the ability to determine approximately how much it is in
error. Since the timber on the area lying outside the measured and
estimated strips is neither counted nor measured, the impression that
the average is wrong depends upon the ability of the cruiser to estimate
or size up timber by the eye and to compare it ocularly as a whole with
the stand upon the strip which he has measured. This comparison
is useless unless enough of the remaining timber can be seen so that
it is practically certain that the average stand on the whole remaining
area 1s greater or less than that measured on the strips. Where strips
are narrow and run at wide intervals, it is impossible to arrive at this
judgment and no reliable correction can be made by eye.
1 Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII,
1914, p. 167.
294 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
But where strips are run at intervals of { mile and the timber is
open and large, and especially in coniferous stands which have a fair
degree of uniformity of sizes, although varying materially in density,
it is possible to view the remaining timber without counting it or caliper-
ing. If there were time for additional measurements, these would be
made. The application of a correction factor is based on the assumption
that the per cent actually measured is the maximum possible under
the limiting conditions. Where an error would evidently be incurred
unless the mechanical average is corrected, this correction should alway s
be made.
The method of applying this sort of a correction in the past has
been as unsystematic as the ocular estimation of timber itself. The
estimate from sample plots or strips was arbitrarily raised or lowered
according to impressions obtained by the cruiser. This system may
be greatly improved and a much higher per cent of accuracy obtained
by observing the following principles:
1. The comparison sought is not an absolute estimate of the volume
per acre on the remaining area, but a percentage relation between this
stand and the strip which is measured, by which the estimate on this
remaining area may be obtained by increasing or diminishing that on the
strip.
2. The correction is an average for the whole area to be corrected,
in the form of a per cent of total volume. Single observations must
therefore be carefully weighted to obtain average results.
3. The correction actually applies only to the area lying outside
the strip and not measured. If applied to the entire area of the unit,
the estimate on the strip itself is arbitarily raised by the same per-
centage as applied to the residual area and this factor cannot be neglected
in arriving at the proper per cent.
To illustrate the last point, assume that 50 per cent of a tract has
been estimated. By observation, the correction factor on the remainder
is assumed as +10 per cent. The estimate is 100,000 board feet on the
strip. The correct estimate on the remaining area is therefore 110,000
board feet and the total, 210,000 board feet. If 10 per cent is applied
to the results obtained for the forty, the process would be, 100,000
times 2 gives the uncorrected estimate for the area, or 200,000 board
feet. A correction of 10 per cent gives 220,000 board feet, which is
an error of 4.8 per cent in the estimate.!
1 This multiple, which in this illustration is 2, is sometimes termed the correction
factor, but assumes no correction. It is merely the extension of the mechanical
average over the entire area. For a 25 per cent estimate, the multiple is 4; for
20 per cent, it is 5, ete. A method of applying the correction factor is in use, by which
this multiple is raised or lowered. Where the multiple is 4, a +25 per cent correc-
tion calls for 5; +123 per cent requires 43, ete.
THE USE OF CORRECTION FACTORS FOR VOLUME 295
Since this error consists in applying the per cent erroneously to the
area estimated within the strip, it diminishes with the per cent covered
by the strip; e.g., should 25 per cent of the above tract be estimated
and found to contain 50,000 board feet, and the correction factor be
actually 10 per cent, the remaining area, which if uncorrected would
have a stand of 150,000 board feet, has actually 10 per cent more than
this or 165,000 board feet or a total for the tract, of 215,000 board feet.
But applying 10 per cent to the entire tract indicates a total stand of
220,000 board feet or an error of +2.4 per cent. But with the decrease
in the per cent tallied, the probability of obtaining a close observation
of the remainder and applying a correct per cent also diminishes so
that if a correction factor is used at all, there is less need for modifying
the per cent. The conclusion is that when, on account of measuring
a large per cent of the area, it is possible successfully to use a correction
factor as applied to the remainder, there is all the greater necessity
for making a correct application of this factor.
To determine the actual correction from a per cent obtained by
weighted observations, two methods may be used. The first of these
methods applies to irregular areas where the per cent estimated is not
uniform, that is, in areas estimated by the separation of types. The
steps are as follows:
1. Reduce the stand on strip to stand per acre.
2. Apply the per cent correction to this stand per acre.
3. Calculate the stand separately for the area not estimated, using
the corrected average stand.
4. Add together the estimates on and off the strip for the total;
e.g., on 100 acres, 17 per cent is estimated and the remaining 83 acres
is judged to run 10 per cent heavier than the strip. The tally on the
strip is 170,000 board feet, averaging 10,000 board feet per acre. The
10 per cent correction gives 11,000 board feet per acre off the strip, or
a total estimate off strip of 913,000 board feet. The total, both on
and off strip is 1,083,000 board feet.
The second procedure may be applied when the per cent estimated
is uniform and type or area correction seldom applied. The rule is,
reduce the correction per cent by the proportion which the area estimated
in the strip bears to the total area. E.g., where the strips cover one-half
the area or 50 per cent, a correction factor of 10 per cent applies to the
other 50 per cent or one-half. Then, .50*.10=.05. <A 5 per cent cor-
rection can be applied to the total normal estimate. Where 25 per cent
is estimated and a 10 per cent correction is found, this applies only
to three-quarters of the area; .75X.10 is .075. The correction factor
of 74 per cent may then be applied to the total area. It makes no dif-
ference whether a correction of 10 per cent is applied to 75 per cent
296 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
of the area or 75 per cent of a correction of 10 per cent is applied to the
whole area.
Since the greatest danger in applying corrections to mechanical
averages lies in failure to obtain a proper weighted average, and since
it is better to let these mechanical averages stand rather than to intro-
duce an unknown factor, dependent merely upon a guess, observations
intended to demonstrate the need for a correction factor must be made
as systematically as the strips themselves arerun. Fixed points should
be chosen at definite intervals along the strips at which to take these
observations. These may be taken for instance at points 20 rods apart
on the strip. At these points, the areas on either side of the strip
should be compared with the stand upon the strip.
The final result is expressed in terms of a per cent, but if each sepa-
rate observation of a series is so expressed, the resultant per cent will
not be weighted by the volumes to which its components apply; e.g.,
two successive observations may give the following result:
;
Bierhion stra Correction per | Weighted volume
cent correction
10,000 +10 +1000
5,000 —10 — 500
Average of 2 plots 0 + 250
The actual correction factor is +23 per cent instead of zero.
This principle of weighting the observations by volume is very
simply applied. It consists of entering for each observation, not the
per cent of comparison, but a comparison based on an ocular estimate
of the stand per acre. The estimator puts down in two parallel columns,
first the stand per acre estimated to be on the strip at that point, second,
the stand per acre estimated to be on the remaining area. In arriving
at this he includes as large an area as comes under his observation
both on and off the strip. For double observations, 1.e., taken on both
sides of the strip, it is necessary to record the stand on the strip twice,
once for each observation off strip.
On the completion of the unit, these stands on and off strip are
totaled. By dividing the total off strip by the total on strip, the true
weighted volume correction factor is obtained.
This factor is a percentage relation and therefore does not require
that the ocular estimates per acre on which it is based be correct, pro-
vided they are in the proper proportion. Each ocular guess may be 25
per cent too low, yet the resultant correction factor will be identical
METHODS DEPENDENT ON USE OF PLOTS 297
with that obtained if the ocular guess in each case were correct. This
increases the probability of accuracy in applying the method. Actual
tests of this principle have shown that where the average stand per acre
off the strip differs as much as from 10 to 15 per cent from that on the
the strip, under conditions permitting the inspection or actual seeing
of the greater part of the timber, it is possible to reduce the error incurred
by the mechanical average by at least one-half, provided the cruisers
have some training and skill in application of the principle of ocular
' estimating.
230. Methods Dependent on the Use of Plots Arbitrarily Located.
In discussing the methods of estimating by means of sample plots,
only the systematic or strip method of arrangement has been described.
A second plan is to locate these plots arbitrarily by selection based upon
individual judgment, the purpose being to get the total estimate by
means of a few typical plots and greatly cut down the work required
in systematic measurements. As in the strip systems, one of two things
is done; either the plots which are measured are taken to represent
the average stand per acre for the larger area of which they are a sample,
or these plots are merely the basis of arriving at the stand by sub-
sequent application of a correction factor.
The first plan can be used only in conjunction with the area or type
method in order to eliminate, as far as possible, variations in the stand
by separating uniform and comparatively small areas. In this case,
sample plots selected with care after a thorough inspection may be
relied upon within reasonable limits of accuracy. By the second method,
the plots chosen are seldom relied upon without further close inspec-
tion of the stand. Cruisers using this method employ these plot
measurements in order to establish in their minds the volume of typical
stands having a definite density and appearance. Once fixed, this
standard is used as a basis with which to compare the average stand
on the area by exactly the same methods as were described under the
correction factor in the strip method. The plots are merely much
smaller and have more definite standards than the strips, and their
application to the larger area is more difficult. The use of these plots is
still further restricted, with improved accuracy, when they are intended
merely to determine the volume of the average tree of certain classes
of timber, and the estimate on the remaining area is determined by a
tree count covering practically 100 per cent.
Various combinations of the above plans are used, especially in the
South, by cruisers working in pine in an effort to cover the ground
accurately with a minimum of time and expense.
231. Estimating the Quality of Standing Timber. An estimate of
standing timber is in effect an inventory of raw materials intended
298 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
to establish the total value of the stock on hand. It is not sufficient
to know the quantity of wood in the forest in terms of board feet or
cubic feet. The estimation of poles, ties and other piece products
by sizes and grades illustrates this need. An inventory requires a
statement of the total quantity of each class of product, and of each
grade or quality within that class, which has a different unit price or
value.
Lumber grades differ enormously in value (§ 352), and the quantity
of separate grades of lumber which may be sawed from trees of different
ages and sizes differs as widely as their values. The estimation of the
amount of the different standard grades of lumber in standing timber
is as essential in determining its value as the measurement of the total
quantity in board feet. The neglect or inability of many foresters,
whose training was along lines of mechanical estimating (§ 223) to
determine the amount of the product by grades has done much to
withhold a recognition among practical cruisers of the great services
rendered the profession of cruising by foresters in contributing volume
tables and in systematizing the making of topographic maps.
What is wanted is the estimation of the total quantity of timber
ona tract, separated into the amount of each of several standard grades,
covering the range of the products and sufficient to include practically
the entire cut and to determine its average value on the stump. This
problem is closely related to that of discounting for defects in that both
require a close observation of the character of the standing timber
rather than its mere dimensions.
All defects which reduce the value of sawed lumber reduce its grade.
When these defects are of a character to reduce the grade below a certain
standard (§ 358, Appendix A), the material is no longer scaled under
the rule of sound scale. It may still be sawed and sold as lumber.
But when it ceases to hold together as boards it is cull.
The deduction of a per cent of the total estimate for defects brings
the estimate into conformity with the quantitative ‘‘ sound ”’ scale.
The further separation into grades of the sound portion of the timber
which will be scaled and estimated, recognizes the influence of defects,
chiefly knots, but including other classes, such as wormholes, sound
stain, and twisted grain, which lower the grades and nature of the
log contents (§ 352, Appendix A).
To determine grades, a knowledge of the results of sawing and the
study of logs as they are opened up and graded into products on the
sorting table is far more valuable than the experience gained in studying
the apparent defects of standing timber. This knowledge must then
be supplemented by a knowledge of the growth of trees in stands.
Open-grown trees, although large, are of low quality due to the presence
METHOD OF MILL RUN APPLIED TO THE STAND 299
of knots, while trees grown in dense stands have a higher per cent of
upper grades due to the history of their development. The skill required
in judging the per cent of grades in standing timber is based directly
on these two sources of information and is not a matter of guess work.
232. Method of Mill Run Applied to the Stand. Data on grades
produced in sawing takes two forms; the total output by grades for
mills sawing in a given region and character of timber, and the specific
contents of logs of different sizes and quality, as determined by mill-
scale studies (§ 361, Appendix A). This corresponds with two dif-
ferent methods of applying the information on grades to the standing
timber, namely, application to the stand as a unit, and application
to the tree or log units.
In applying mill-run grade per cents to the stand, the total estimate
in board feet is arbitrarily divided into the different grades which it
will probably yield, by per cents of this total. This method corresponds
with that of ocular estimate of a stand (§ 206) and its results are about
equally unreliable. The basis is the sawed output by grades from mills
in the vicinity. These per cents so obtained will apply to the timber
in question, only if it happens to average the same in quality as that
sawed, which assumption, considering the great variation in standing
timber, is wholly untrustworthy. This means that the per cents of
grade must be modified as the timber is better or poorer than that
sawed, which requires a knowledge of the standing timber previous
to sawing.
233. Method of Graded Volume Tables Applied to the Tree. Evi-
dently, a better basis is required and, just as in timber estimating for
volume, this must be found in the use of the tree unit or the log unit,
by which the varying quality of the timber can be standardized.
The tree unit has not proved a satisfactory basis for grading, though
it is possible to use it. The basis is graded volume tables (§ 165) which
show the per cent of standard grades in trees of different diameters,
preferably in the form of per cents of contents.
These per cents could be applied to the trees in each diameter class
and the total estimate divided in this way into the component grades.
The objection to this method is that it is not sufficiently elastic
to take care of the great range of quality in trees of the same diameters.
A given graded table will hold good only for timber of a certain character;
if more open-grown, shorter bolled or limbier, or otherwise different,
the volume table is not applicable. The method is probably better
than the ocular guess, but is equally subject to large corrections in the
field.
234. Method of Graded Log Rules Applied to the Log. The third
method employs the log as the basis of grades, and applies this basis
300 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
to the standing timber. The graded log table ($74) appears to
satisfy the requirements of the problem. Log grades are such as can
be recognized in standing trees, on the basis of diameter, surface appear-.
ance, presence of knots or limbs, and character of the tree and the stand
in which it is growing. In turn, these log grades can be analyzed by
mill-scale studies, so that the average per cent of grades of timber in
each log grade is known. Since three grades are usually made in valu-
able species, and at least two for the less valuable, trees of the same
D.B.H. can easily be thrown into the lumber grades corresponding
with differences in their character, by recording the logs which they
contain as grades No. 1, 2 or 3. By contrast, if graded volume tables
are used, ordinarily only one classification is available for the tree—
that corresponding with the table.
The final problem is the application of these graded log tables to
the standing timber, in a manner to conform to the methods used in
timber estimating. Cruisers who use the method of selecting an aver-
age tree (§ 209) usually analyze this tree by the use of the log grades,
or directly by per cents, into the grades of lumber which they believe
it will cut, and apply these per cents to the remainder of the stand.
This is a crude method.
Where the method of tallying the diameter of every log (§ 119) is
used, each log can be tallied under its proper log grade. The total
volume in each log grade is thus obtained directly. Where timber
is sold as logs, it is unnecessary to go beyond this point.
But where the sawed product determines stumpage value, these
log grades are merely the basis of application to the standing trees of
the grades of lumber which they probably contain, and the contents
of the log grades, in lumber of each grade, will be computed for the
estimate.
235. Combination Method Based on Sample Plots and Log Tally.
Where the tree tally and volume tables are used in estimating (§ 121),
the application of the log-grade unit to each tree is not possible, since
it would mean a shift to the tally of logs and not trees. Here a com-
bination method is necessitated, based on the principle that grades
or quality of timber can be determined by the measurement of a much
smaller per cent of the total volume than is required for volume estimate.
The method is to lay out sample or representative areas in the form
of strips crossing the types as for timber estimating (§ 209) and com-
prising a per cent of the area estimated, sufficient in the Judgment of
the cruiser to obtain the average quality sought. On these areas,
every log in each tree is totaled by upper diameter, in the log grade
in which it belongs. Instead of guessing at these upper diameters,
taper tables based on D.B.H. (§ 167) and total, or merchantable, heights,
LIMITS OF ACCURACY IN TIMBER ESTIMATING 301
possible if the latter are cut to a fixed diameter, or if made to conform
to average utilization, are used to get these diameters; e.g., for a tree
38 inches D.B.H. containing eight logs, the upper diameters are
respectively, from the table, 32, 30, 28, 25, 22, 18, 14, and 10 inches,
and are so recorded, each log under its proper log grade. (See § 207
for form of tally.)
The determination of the number of board feet of each standard
grade in logs of each diameter and grade, and the total scale for each
lumber grade, is based on the contents given for these log grades from
mill-seale studies of log contents. The purpose is to obtain the per
cent of each grade, regarding the total contents of the logs tallied as
100 per cent, and then to apply these per cents to the volume estimated
for the tract. These per cents can be obtained more accurately if over-
run is included in logs of each separate size (§ 46). The mill-scale
study will show the amount of over-run in logs of different diameters
and standard lengths. The scaled volume of these logs should then be
increased by this per cent of over-run, before the division into lumber
grades is made. On the total sawed contents thus obtained, the per
cent of each grade is based.!
Even if considerably in error, the value of an estimate expressed
by grades of lumber is much greater than one which entirely ignores
the quality and consequently the relative stumpage value of the tract.
In the absence of specific information on grades, a record of the sizes
of the trees, their clearness of bole, and the density of the stand may
furnish a basis for approximating the probable grades.
236. Limits of Accuracy in Timber Estimating. Purely ocular
estimates vary in accuracy up to errors of 100 per cent, dependent
upon how far the method is stretched from its original limitations.
This does not include errors due to inexperience, inefficiency or careless-
ness.
In mechanical methods of measurements, serious errors May occur
in computations. Such errors, of course, are inexcusable, but their
avoidance requires careful checking. The mechanical errors due to
the operation of the law of averages have been pointed out as a function
of the factors influencing these averages, the chief of which is the size
of the area unit.
The degree of accuracy must be based upon the standard of utiliz-
ation. It is entirely unfair to judge the accuracy of estimates based
upon one standard against the results of sawing attained by the appli-
cation of an entirely different standard. Where the standard is the
same in both cases, the present demands of timber estimating require
1 The details of this method are taken from the article by Swift Berry, Journal
of Forestry, Vol. XV, 1917, p. 438.
302 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
an accuracy of within 10 per cent. The error should be conservative
rather than an over-estimate if possible. Greater errors than 10 per
cent may be caused by differences in scaling practice alone, or in the
length of logs cut, or the thickness of lumber sawed.
237. The Cost of Estimating Timber. No figures will be given for
the costs of various methods of timber estimating. These must be
determined locally. The elements of cost are:
1. The size of the crew and the wages paid each member; the
character of supervision, such as the combining of several crews under
one supervisor; and the employment of a cook.
2. Accessibility of the tract as affecting transportation of men and
of supplies, especially of food. The means of transportation, such as
pack versus wagon haul.
3. Cost of location of boundaries and surveys and cost of establish-
ment of base lines from which strip surveys are to be run. This is a
function of the size of the tract and the character of the boundary survey
and monuments already established.
4. The number of strips or miles of line to be run per unit of area.
The cost is not exactly proportional to the miles run since certain
items such as travel to and from work and from one strip to another,
cost of computing the estimate, and cost of mapping in the office, increase
in a lesser ratio. Doubling the number of strips increases the cost from
50 to 80 per cent, dependent upon the saving in these items.
5. The rapidity of traverse or number of miles of line which may be
run per day. A standard day’s work varies directly with topography
and brush, and with the amount of detailed work required in the actual
estimate along the strip, as determined by the number of products,
the number of species, the number of trees and the details of record
required. In very brushy and mountainous or precipitous country
with a variety of species, 1 mile per day may be all that is possible,
varying up to 2 miles. An average day’s work in fairly open country
varies from 2 to 4 miles; on level open land with sparse timber and no
brush, 4 to 8 miles may be made.
6. The character of the topographic map required. To a certain
extent, a detailed topographic map appreciably slows up the work.
It is the object of a forest survey to require only that degree of accuracy
and detail which will not add appreciably to the cost by delaying the
party.
7. Computation or office work required. By practical cruisers, this
is almost eliminated through the methods employed. Methods of
tallying dimensions and the use of volume tables increase this addi-
tional expense.
8. Holidays, sickness and lost time. Only the number of hours
TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 303
on the actual work of running lines and estimating can be considered
as the basis of costs. All lost time for any other cause adds to the
costs per hour of work.
9. Personal efficiency. The training and personal efficiency of the
men employed may make from 25 to 50 per cent difference in the actual
cost of the work, but its principal effect is in greatly increasing the
relative accuracy of the estimate.
Cost of estimating should be computed as follows:
Total cost itemized under salaries, and cost of supplies, transporta-
tion and subsistence.
Cost reduced to the cost per hour of actual work by dividing this
total by the number of hours employed in estimating. These costs
can be separated into field work and office work, including mapping.
The costs can then be expressed as cost per unit of area or per acre
and finally as cost per unit of product, as per thousand feet or per
cord. This is the final test of cost. The cost should then be compared
with the stumpage value per unit. If possible it should not exceed
1 per cent of this value.
238. Methods of Training Required to Produce Efficient Timber
Cruisers. Mechanical methods of timber estimating, dependent upon
the measurement of diameters and heights with instruments, and secur-
ing the mechanical average stand per acre by strips, do not require
anything more than conscientious work and care in details. Skill and
training enter with the application of the laws of averages, even for the
construction of height curves. The demand for training is increased
by the use of ocular methods of measurement and reaches its maximum
in the application of cull for defects and in judging the quality of timber.
Aside from ‘amiliarity with cull and grades, there are no principles of
timber estimating that cannot be learned in a month’s intensive train-
ing. The common impression that it takes several years to develop
ability as a timber cruiser is based upon the unscientific methods
employed in training these men. They usually acquire their skill by
a maximum of hard work in the woods, with a minimum of accurate
comparisons of the estimated volumes with an actual cut. Even in
the matter of Judging defect, the basic training should not be in the
woods, but in the mill and in sealing. It is comparatively easy to recog-
nize the signs of defect in standing timber, but much more difficult to
judge of the amount of cull which it causes. In actual training of
timber cruisers it has been found that ability to secure accurate esti-
mates is greatest in men who have best developed their mental faculties
by education, close observation, memory and systematic coordination.
This same combination of qualities is desirable for success in any line.
Many cruisers lack this ability and remain permanently inefficient to
304 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
a marked degree. The only reason that such individuals have in the
past continued to practice timber cruising as a profession is the almost
complete absence of a reliable check on their results for years at a
stretch, and the comparative indifference of purchasers to the accuracy
of estimates due to a rising market and a plentiful lumber supply.
Standing timber cannot be “ measured.” There is always a residual
error in the closest work. Hence the use of the term ‘“ estimates.”
Although the only basic check on estimates is the measurement of the
timber after it is cut, yet it is possible, by the use of intensive methods,
to measure plots of standing timber so closely that they will serve as
checks on individual estimators.
An example of this check is cited below in the case of a Minnesota lumber com-
pany, which in 1907 required each of its timber cruisers to estimate an area which
had previously been carefully calipered and measured with a volume table and was
afterwards cut and checked out with these measurements. The results speak for
themselves. These men were given all the time they desired to make this estimate.
TABLE XLV
CoMPARATIVE ESTIMATES ON A TRAcT oF 40 ACRES
Board Feet
Calipered, Estimators, By InpivipuAL Mretuops
and
measured
by volume |
tables Uh Fave. a ll) we: Sim ige) Be peieeans
Dsisots oO. oO. 0.
deducted
White pines 2 5se. e 250,800 220,000 300,000 400,000 130,000
Norway pine......... 4,120
DEUCE A. eee 28 lee OES 7O Nine are ctey Me INE on Seas oo et oe. 10,000
PSMA TACK | 7, Aeene tates 35,480 23,000 45,000 35,000 10,000
Nacke pInere ser eisere GOO Me Sohn Vom caee caeee 3,000 15,000
Balsam. -eeee ta cesses 2,220
Hardwoodsseme aan 9,910
otal Sern 313,130 243,000 345,000 438,000 165,000
W hike wpine fete sis-ira any pe otraerenee No. 5 No. 6 No. 7 No. 8
199,000 175,000 125,000 115,000
* Number of cruiser. + No other species estimated by these four cruisers.
TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS 305
The tract, when cut, scaled by Scribner Decimal C log rule 314,350 board feet,
an error of yo of 1 per cent.
The best system of training men for timber estimating is by the use of sample
plots on which the diameter and merchantable heights in log lengths of each tree
are estimated by the eye and checked against the records. On these same plots,
each of the six classes of averages (§ 209) can then be tested and their application
mastered. Each day’s training can be checked against the measured volume of
the plot that night and not only the total error in per cent but the exact cause of
this error ascertained. On this basis, the progress of training is rapid and the
cruiser is advanced in a short time more than would be possible in several years of
estimating without these checks. The following outline will illustrate the possi-
bilities:
1. Plots of 20 acres, 40 by 80 rods, are laid out with compass. The boundaries
are marked by blazing the trees facing each of the four sides on the face towards the
plot. Stakes are set on all four sides at distances of 20 rods apart. Two plots are
laid out adjoining each other, together comprising 40 acres.
2. Every tree on the plot is calipered at B.H. in two directions, the average
being taken to the nearest even inch and the bark blazed to prevent duplication.
The blazes are made facing the portion or strip not yet measured. A crew of one
tally man and two caliper men are used and all trees above a fixed diameter are taken,
corresponding with the minimum exploitable diameter class.
3. The merchantable heights to the nearest 8-foot length or half-log are measured
by two or three additional men with Faustmann hypsometers. From 30 to 40 per
cent of all heights can be measured during calipering in this way. Height men
work with the diameter crew taking the diameter as measured, pacing for distance
from the tree and recording heights based on diameter. Forty to sixty heights
per hour can be recorded by each man. Upper diameters or merchantable lengths
are based upon the practice of sawing as applied to the species measured, provided
this is the basis on which the volume table was constructed.
4. The determination of the merchantable height of every tree from that of 30 to
40 per cent of the trees is made separately for each diameter class. The heights
tallied within the diameter class are taken to indicate the percentage or proportion
of the different height classes existing in this diameter class and the total number
of trees are then distributed according to the same proportion. As the result required
is a proper distribution for the plot as a whole, and not for each diameter separately,
this method gives a sufficient degree of accuracy.
5. The record for the plot will show the following data: total estimate in board
feet, total number of trees, average stand per acre, volume of average tree, volume
of average log or log run per thousand board feet, exact number of trees in each
diameter class, exact number of trees in each log and half-log height class independent
of diameter.
The exact number of trees in each separate diameter and height class is the
basis for the last two summaries; but the summaries rather than the detailed class-
ification are made the basis of the estimating, i.e., the tally is totaled for each
diameter class, and in turn, is totaled for each height class irrespective of diameter.
For each day’s work the cruiser hands in a report on the first five of the above
seven items and brings in his notebook in which he has totaled the number of trees
for each diameter class and each height class separately. His accuracy is computed
as a per cent of the total stand on the plot. The error in per cent is recorded. The
sources of error are then examined. These are four in number.
1. The width of the strip may be too great or too small. This is shown by an
error in the number of trees tallied.
306 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
2. The trees may not be counted accurately. This error is identical with the
first, but usually shows up as a deficiency of small timber near the minimum diameter
tallied.
3. The diameter of the trees may be over- or under-estimated either as a whole,
or in certain classes. There is a strong tendency to bunch diameters towards a tree
whose size seems to be the standard in the cruiser’s mind. This results in over-
estimate of small trees and under-estimate of trees of larger diameters.
4. The heights may be over- or under-estimated. When this happens it shows
up consistently for the whole tract, the standard of height apparently being tem-
porarily distorted in the mind of the cruiser.
A fifth source of error, the volume table and the failure to coordinate upper
diameters and merchantable lengths with the standard used in this table, serves
to exaggerate the per cent of error in the judgment of heights, but is always indi-
cated when the average heights are too high or too low to agree with the measure-
ments. When the volume of the average tree is high or low, it usually means an
over- or under-estimate of diameters or heights. The exact character of the error
in diameter and height is ascertained by a simple check as follows: the cruiser com-
pares the number of trees in each diameter class with that of the standard record and
sets down his difference plus or minus. If he is over-estimating, but has the right
number of trees, the minus sign will appear opposite the smaller diameters and the
larger diameters will show excess numbers. If under-estimating, the plus signs
will appear opposite the small diameters. The same rule applies to heights. An
over-estimate causes minus signs to appear opposite the lower height classes and
corresponding plus numbers in those of greater log lengths. The size of these dis-
crepancies shows the degree to which the error has been carried.
It is the tendency in cruising as in scaling logs, in an effort to correct a known
error, to incur immediately a still greater error in the opposite direction; but when it
is possible to check against a measurement which the cruiser admits is infallible and
in which he has confidence, this tendency to fluctuation is soon overcome and rapid
improvement is noted, not only in the total per cent of accuracy which is sometimes
merely the result of large compensating plus or minus errors, but in each of the four
elements of accuracy, thus insuring a consistent degree of accuracy from day to day.
The cruiser is expected to master but one detail at a time, and the schedule
is as follows:
1. During the calipering of the standard plots, the eye is trained in estimating
diameters which are then promptly checked by the measurements. The same is
true of heights.
2. The second period is devoted to a total or 100 per cent tree by tree estimate
with a tally of each diameter and merchantable length. The total area of the
plot is covered by eight strips, 5 rods wide, the cruiser working not in the center, but
on one side of this strip with compassman marking the opposite border. Width of
strip and success in getting 100 per cent of the area is dependent absolutely upon
use of eye, checked by pacing and judging distance, and the men are not permitted
to mark the boundaries of these strips to prevent overlapping. ‘Twenty acres per
day are covered by this method.
_ 3. The third step is to increase the area covered per day to 30 acres by doubling
the width of the strip to 10 rods, the cruiser taking the middle of the strip and judging
5-rod distance on each side. In all of this work, the cruiser tallies his own dimen-
sions of the trees. In these preliminary 100 per cent estimates, constant repeated
checks are made of the diameters and heights to continue the improvement of the
eye.
4, The 100 per cent estimate is continued, but the tally of every diameter is
TRAINING REQUIRED TO PRODUCE TIMBER CRUISERS — 307
discontinued and a total count substituted with a tally of one tree in three. The
area is increased to 60 acres per day. It is the universal testimony of cruisers
that this simplification of the tally relieves the mind of a strain and improves the
accuracy of the dimensions tallied and consequently of the total estimate. It has
been found that an average volume is obtained through a tally of one-third of the
stand under the following conditions:
When there are at least 500 trees per 40 acres of the species tallied and preferably
1000.
When the judgment or process of selection is entirely eliminated in favor of
mechanical selection of the trees to be tallied. This may be done by taking every
third tree in succession or by taking the nearest tree in each case. Where there are
insufficient trees to insure the mechanical average, or where the range of size is large,
the count may be separated into two groups, segregating the large from the small
trees, one tree in three tallied separately in each group. This adds very little to
the detail required when working with a single species.
5. Only 50 per cent of the area is estimated by the above method. The area per
day is nominally 120 acres. The remaining area is inspected by eye at distance of
20, 40 and 60 rods in order to apply a weighted
volume correction factor as described in § 229.
In this method, four strips are run, each 10 rods
wide, as before, starting from points, 5, 25, 45,
and 65 rods from the corner and alternating
with strips not estimated as per Fig. 63.
In order to check the correction factor, the
alternate strips not previously estimated are now
in turn estimated, keeping the record separate
from the original four strips. The correction
factor derived from observation is first com-
puted and the corrected estimate is then com
pared with the tally of the strips estimated. as
6. Up to this time no effort has been made Fic. 63.—Method of estimating a
to deduct for cull which would introduce an forty by use of the correction
arbitrary factor interfering with the comparison factor. Points at which obser-
of the work of the cruiser with the measurement vations are taken shown by
of the plot, both of which have been on basis dots.
of sound contents, disregarding possible cull.
The cull factor is now tested by close examination of 10 acres in which every tree
is individually estimated and the per cent of probable cull recorded and subtracted
from the estimate. Per cent figures also are obtained from the scale of logs of
similar timber in the vicinity and these per cents are used as a basis of cruising.
7. In actual cruising, the per cent of area covered is reduced to 25. The area
is increased to 320 acres per day, and 4 miles of line run. A cull factor is used and
hardwoods are added to the estimate by tallying the top diameter of each mer-
chantable log, inside the bark.
8. The cruiser is then brought back to the sample plots to receive training in
individual estimating. This consists of:
The use of circular plots covering different per cents of the area by a systematic
plot method and finally by the selection of a sample plot by eye. On these plots,
he first arrives at the volume of the average tree either by direct approximation or
by selection of a typical tree whose volume is ascertained from a volume table;
A tally of the diameter and height of each tree on the plot and the immediate:
computation of the volume to ascertain the true average tree for comparison with
308 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
the ocular guess. Two days of this work will greatly improve the ability of the cruiser
to substitute ocular methods for measurements.
An opportunity to run out strip estimates in which he does his own compass work,
counting the trees ahead of him in . rectangular blocks. The volume of these trees
is obtained:
By the log-run method of estimating the number of logs in the average tree
and the average contents of the log or log run per thousand;
By selecting an average tree in volume for each of eight separate strips, the
total tally of which is kept separate. This principle could, after practice, be applied
to the entire forty, or to separate groups.
The exact details of this system as to size of sample plots, widths of strip and
methods of tallying heights were worked out for Southern yellow pine, and several
of these points would need modification if applied to timber of radically different
type and conditions. But the general method of careful, original measurement
of the control plots and of proceeding from a 100 per cent intensive estimate
through various stages of less intensive work in which the six classes of averages
are employed as substitutes for the full tally, can be worked out for any forest
type and form the basis of rapid and practical training in the art of timber
cruising.
239. Check Estimating. Just as in the training of a cruiser his
greatest drawback is lack of any check on his estimates, so check esti-
- mating does not benefit the cruiser unless he can be told, not only what
the extent of his error is, but just how he made it. Check estimating
must depend either upon the infallibility of the check estimator, which
may be questioned in the mind of the person checked, or by the sub-
stitution of actual measurements on a basis which removes all source
of doubt, leaving only cull and quality to be judged. Check estimates
should therefore be made on definite areas or strips, prevously or sub-
sequently estimated by the cruiser and on which a record has been kept
similar to that indicated in the description of the methods of training
timber cruisers. The tree count, the total volume, the average volume
per tree, but most important, the tendency to over-estimate heights
and diameters should all be checked separately. When this is done,
one of two things will happen. Either the cruiser will rapidly acquire
a much greater accuracy or he will demonstrate his complete unfitness
for the job of timber cruising and can be put on other work.
240. Superficial or Extensive Estimates. The preliminary examina-
tion of a tract of land for the purpose of determining roughly whether
it has timber of value and approximately how much, calls for the exercise
of the maximum of skill and experience in order to attain a reasonable
degree of accuracy in the minimum of time allowed.
A description of the estimation of a tract of 2300 acres for the Blouming Grove
Hunting and Fishing Club, located in Pike County, Pennsylvania, will serve as an
illustration of methods possible in such an examination. The field work on Taylor’s
Creek logging ‘unit occupied two days including travel to and from the unit. Not
much over one day was put on the estimate itself. The fundamental basis of the
CHECK ESTIMATING 309
methods employed was the location of corners with the aid of a guide, the use of a
map and the sketching of the boundaries of areas of different types by intersection,
aided by rough triangulation from known points. Cardinal directions for strips were
not attempted in any instance. This tract was afterwards estimated by the strip
method, running 5 per cent of the area. The comparison of the two methods and
TABLE XLVI
Estimate orf Taytor’s CrEEK Loaaina Unit, BLoomina Grove Tract, PIKE
County, Pa., 1911
A. By extensive methods, in two days’ time, one man with guide.
B. By 4-rod strip, 5 per cent of area, diameters calipered, average heights.
Error By First
MerrHop
bes Method of cruising |Estimate.
Type ‘| Species employed under
A Amount.
M feet | M feet | Per cent
Acres B.M. B.M.
ee —————
Pitch pine, 375 |Pitch pine|j-acre circular plots} A 2178 | — 36 = eee
pure stands for sizes
8-rodrectangularplots| B 2214
counted, when con-
venient
scattered on| 1275 |Pitch pine/16-rod strip counted,
burns when convenient
White oak and} 200 |White oak!Total count of large) A 248 | —197 — 47
hardwoods trees B 445
Average trees guessed
at
Swamps with) 450 |Spruce_ /t-acre circular plots,), A 750 | +353 + 88
hardwood selected by guess for] B 397
and conifers average stand per
acre
WElemlocke |v eeenc sone eee A 750 | +223 + 42
B 527
Yellow |Some poplar counted | A 250 | +161 +181
poplar B_ 89
PN) 0a Js se ee A 100} — 25 | — 20
B 125
White Treetops counted) A 250 | — 382 — 11.3
pine from hill. Average] B 282
tree guessed at
Uniform old growth |
otal). > SUSUR SAM in 8! ic A A 4526 | +526 | + 10.9
| B 4079 |
310 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
their results is made on the basis of the assumption that accurate results on this
area were obtained by the strip method. The cost of the original estimate was $60.00
or 2.6¢ per acre, 1.3¢ per thousand. The cost of the subsequent strip estimate
was 8¢ per acre or 4¢ per thousand. The results clearly show that the average stand
per acre was successfully obtained for the pitch pine types in which the timber could
be seen, and where the area was carefully mapped in two degrees of density of stock-
ing and checked by strips and plots carefully selected there was no need of a subse-
quent estimate.
The method of counting every tree was successful for white pine since all of the
tree tops were seen and the average tree was correctly guessed at, but for white oak,
the total count apparently failed. This was due not to a defect in the method or
its application, but to the fact that 123,000 feet of white oak was found later con-
cealed in the swamps. This reduced the error to 23 per cent for the portion seen
and counted.
The estimate of spruce, hemlock and poplar broke down because of the funda-
mental difficulty of applying the sample plot method when based upon selection
and not on systematic arrangement. The swamp should have been crossed and all
parts examined. As it was, the sample plots were selected near the boundary where
the timber was one-half to two-thirds again as heavy a stand per acre as in the wetter
portions. This resulted in over-estimating spruce, hemlock and poplar. An
area or density correction here, or another day spent on that portion of the tract
would have greatly reduced this error.
In extensive mapping and estimating of large areas for purposes
of classification as in the preliminary examinations for the establish-
ment of national forests, rough sketch maps of the areas of timber
types are made on the above principles by location of the cruiser on
a map and by triangulation. The estimate must depend upon the
location of occasional sample plots chosen with the best skill possible
to get average stands.
In State work the construction of maps showing the timber resources
of the State or of various counties is usually carried on by similar
methods of mapping, using roads and the principle of the wheel or
odometer for distances and sample plots for average stands. In Massa-
chusetts a different principle is employed. Strips 4 rods wide are run
at 4-mile intervals on which detailed measurements are taken of the
stand. No attempt is made to complete the map of timber in the inter-
vening areas, but the data are assumed to show the average for an entire
town, an assumption which is probably correct owing to the large
area involved.
241. Estimating by Means of Felled Sample Trees. In the absence
of volume tables in earlier European practice, it was found that volume
of stands could be determined by calculating the diameter of the aver-
age tree, felling it and determining the cubic volume. This volume
multiplied by the number of trees in the stand was supposed to give
the number of cubic feet in the entire stand. Since height and form
factor of individual trees both varied over a wide range, it was quite
METHOD OF DETERMINING THE DIMENSIONS OF A TREE 311
difficult to get a tree which was actually an average for the stand, but
when the stand was divided into diameter groups, any required degree
of accuracy could be obtained, according to the number of groups made.
In determining the diameter of the average tree, the arithmetical
mean of diameters gave too small a result since the volumes of trees
of uniform height are in proportion to D’. With a table of the areas of
circles, the total basal area or sum of the areas of the cross sections at
D.B.H. for all the trees on the plot was obtained and divided by the
number to obtain the average basal area. The diameter correspond-
ing to this basal area was that of the tree sought. Where a tree of this
exact diameter to 75-inch could not be found, a larger or smaller tree
was selected and the difference found by the proportion existing between
the basal areas of the tree measured and the tree desired. This method
is termed the Mean Sample Tree Method.
In this country the application of these methods has been confined
to a few early investigations into the cubic volume of cordwood in second-
growth hardwoods. ‘The difficulty of selecting a tree of average height
and form as well as basal area and the expense of felling and measuring
a tree makes the use of volume tables far preferable whenever these
are dependable, and their substitution is practically universal.
242. Method of Determining the Dimensions of a Tree Contain-
ing the Average Board-foot Volume. Another use of sample trees is
in connection with the determination of the age and growth of stands
rather than to determine their volume. For this purpose, the volume
of the stand is first found from volume tables and the average tree then
determined. The volume sought is that of a tree which when multi-
plied by the number of trees on the plot, will give the total volume of
the plot in the unit of volume which was used in estimating.
1A recent test, 1920, by J. Nelson Spaeth, Harvard Forest School, in second-
growth hardwoods, in which mean sample trees for each 3-inch diameter group
were measured, gave the following comparison of accuracy with the use of a standard
volume table, although the latter was for but one species, red maple, comprising but
15 per cent of the stand:
Yields per 4 acre. Error.
Method Cords Per cent
D\onvenlsnoltione Obits soca Gee oe ble noes dames P45)
Stanaarcdevolume tables. ceo ee Fy Ae +1.70
Mean sample tree method.................. 5.935 +3.84
The refinements of these methods, known as Draught’s, Urich’s and Hartig’s
Methods, are set forth in Graves’ Mensuration, pp. 224-242. For application to
American problems that of the Mean Sample Tree is probably sufficient.
312 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
When cubic volume is used the average tree will not be the same
in diameter as when the board-foot unit is employed. The explanation
for this difference is that the volume sought is a weighted average of
the merchantable contents of all of the trees on the plot. Trees of
different diameters do not have the same weight in this average when
measured for board feet as when measured for cubic contents. The
tree containing the average board-foot volume will be larger than the
other. The smaller trees in the stand when measured in board feet
are more immature than they are for cubic feet and the merchantable
portion of the stand actually includes a lesser proportion of the whole.
In stands which are not of even age, this merchantable portion wouid
exclude many of the younger trees as being unmerchantable although
they would be included in the cubic volume, and the average age as
well as size of the portion merchantable for board feet is greater than
that included in the cubic volume. (The increase in average age of
stands due solely to the exclusion of a portion of the stand is a recog-
nized fact in European practice.)
To determine the size as well as volume of the average tree of a
stand, we have two variables, height and diameter, one of which must
be fixed or eliminated before the other can be determined. ‘The first
step is, therefore, to determine the average height of trees of each diam-
eter by a height curve (§ 209). The average tree can then have but a
single height and diameter and these dimensions may be found from
a curve of volume based on diameter for the plot.
This curve may be taken from a standard volume based on diam-
eter and height (§ 1483) by selecting the volumes corresponding to the
average heights for each diameter interpolated if necessary to the
nearest foot. At only one point on this curve will the average volume
coincide with the diameter.
243. The Measurement of Permanent Sample Plots. The purpose
of locating and measuring permanent sample plots is to determine the
growth of stands. Their original measurement therefore must be made
by methods which will permit of an exact scientific comparison of these
with subsequent measurements. In this way, not only can the growth
of individual trees be determined, but all changes which take place in
the forest by decadence and by the operation of natural forces, insects,
fungi and cutting and thinning, or other silvicultural measures may be
noted.
Permanent sample plots should be located on land under perma-
nent and stable ownership and should be accessible and easily found for
subsequent inspection and for a maximum of protection. The plot
should be square or rectangular and marked by permanent corners,
plainly labeled. Sample plots should be located in stands having
THE MEASUREMENT OF PERMANENT SAMPLE PLOTS 313
uniform conditions and their size should be governed, first, by the
possibility of securing this uniformity and second, by the expense of
measurement which limits the size of the plot. Third, wherever
possible, there should be a control strip of exactly similar timber sur-
rounding the plot on all four sides in order to eliminate the influence
of different conditions of density or site around the borders of the plot.
The merchantable timber on these plots is measured as follows:
Tree Number. Each tree should be permanently numbered either
by white paint or by attaching a metal tag to the tree with a copper
nail.
D.B.H. The point at D.B.H. is measured and spotted with white
paint or by the position of the tag. The D.B.H. is measured with a
diameter tape.
Crown Class. 'The crown class is one of the following:
x=trees standing alone;
d= dominant;
c=co-dominant;
7= intermediate;
s=over-topped, suppressed.
Height. The height is measured to the nearest even foot with a
standard hypsometer. The Klaussner principle, which gives one
measurement, is preferred.!
Forms are used which provide, for each tree, five vertical columns
in which to record the original and four subsequent measurements
which are taken at either 5- or 10-year intervals.
The trees on such plots are usually numbered and measured indi-
vidually down to 4 inches, although in some instances 2 inches is
adopted as the basis for individual tree records.
Immature timber below these sizes usually calls for smaller plots
which are sometimes laid out as subdivisions of a larger permanent
plot. The sizes of these plots are in proportion to the intensiveness of
the problem and the age of the timber. For determining the conditions
which affect germination, plots from 10 to 20 feet square are large
enough. On these plots every seedling is counted and sometimes each
is marked by inserting a pin on which a tag can be attached. In this
way the mortality and survival of the seedlings can be later ascertained.
For the study of the development of reproduction, larger plots, up to
1 acre in size, are required. On such plots there is no effort to keep
1Some New Aspects Respecting the Use of the Forest Service Hypsometer,
Herman Krauch. Journal of Forestry, Vol. XVI, No. 7, p. 772.
Comparative Tests of the Klaussner and Forest Service Hypsometer, D. K.
Noyes, Proc. Soc. Am. Foresters, Vol. XI, 1916, p. 417.
314 IMPROVING THE ACCURACY OF TIMBER ESTIMATES
a history of each individual tree, but the total number of trees in each
class is recorded in height classes as follows:
Overtopped 0 =3’ in height;
So = 9) j in height;
5 =4’ in height;
4’= 1" in diameter.
Free, same classes.
By inch classes, 1,2 and 3 inches. In these inch classes
the trees are recorded in five crown classes: 2, d, ¢, 2,
and s previously indicated.
REFERENCES
“« Average Log ”’ Cruise, W. J. Ward, Forestry Quarterly, Vol. V, 1907, p. 268.
Errors in Estimating Timber, Louis Margolin, Forestry Quarterly, Vol. XII, 1914,
p: 167.
A Method of Timber Estimating, Clyde Leavitt, Forestry Quarterly, Vol. II, 1904,
p. 161.
Forest Mapping and Timber Estimating as Developed in Mae land, F. W. Besley,
Proce. Soc. Am. Foresters, Vol. IV, 1909, p. 196.
An Efficient System for Computing Timber Bisgrenntes) C. E. Dunstan, C. R. Gaffey,
Forestry Quarterly, Vol. XIV, 1916, p. 1.
Timber Estimating in the Southern Appalachians, R. C. Hall, Journal of Foret:
Vol. XV, 1917, p. Sit:
Some Problems in Appalachian Timber Appraisal, W. W. Ashe, Journal of Forestry,
Vol. XV, 1917, p. 322.
Determining the Quality of Standing Timber, Swift Berry, Journal of Forestry,
Vol. XV, 1917, p. 488.
REVIEWS
Error of Strip Survey (Sweden), Journal of Forestry, Vol. XVI, 1918, p. 938.
Estimating for Yield Regulation, Schubert, Forestry Quarterly, Vol. XIII, 1915,
p. 399.
European Methods of Estimating Compared for Accuracy, Forestry Quarterly,
Vol. XIV, 1916, p. 521.
Volume Tables and Felling Results, Forestry Quarterly, Vol. IX, 1911, p. 632.
Results of Errors in Measuring, Schiffel, Forestry Quarterly, Vol. IX, 1911, p. 628.
Methods of Estimating Compared, Prof. Zoltan Fekete (Hungary), Forestry Quar-
terly, Vol. XIV, 1916, p. 521.
A New Method of Cubing Standing Timber (Hungary), Forestry Quarterly, Vol.
XII, 1914, p. 474.
JegaWans UGE
THE GROWTH OF TIMBER
CHAPTER XXII
PRINCIPLES UNDERLYING THE STUDY OF GROWTH
244. Purpose and Character of Growth Studies. The growth of
timber is studied in order to determine the rate of annual production
of wood as a crop on forest land. The yield of farm products is annual
and is measured at harvest. The essential difference between farm
and wood crops is that the period required to produce the latter is many
years in extent, and due to this fact forest land is not the only capital
involved in crop production. The growth which the trees lay on
annually becomes in turn part of the capital to which future growth
is added in the same manner as interest which is added to a savings
account.
This increase in total volume of a stand of timber does not continue
indefinitely, but only up to a certain age, which marks the culmination
of growth of the stand, from which time the losses occurring in the stand
more than counterbalance growth, and its volume and value diminish.
Forest crops therefore mature as do annual crops and one of the pur-
poses of growth study is to determine the period required for maturity.
The basic facts to be determined in the study of growth are, first,
the total yield of stands in terms of quantity of products, quality, and
money value, for the period required to grow a crop of timber from
origin to maturity; second, the average annual rate of growth to which
this final yield is equivalent, which is termed the mean annual growth
and is comparable to simple interest on land as capital or to annual
crops; third, the actual growth or increase in volume, quality, or value,
laid on during definite periods in the growth of the stand. The growth
for these short periods is expressed either as current annual growth which
is the growth for a single year, periodic annual growth which is the aver-
age annual growth for a short period, or periodic growth which is the
315
316 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
total growth for the short period. The length of these periods is com-
monly a decade, but may be from 5 to 40 years. The term current
annual growth is commonly used in place of the term periodic annual
growth, as indicating the average annual growth for a short period
instead of the separate growth for a single year, though this use of the
term is technically incorrect.
Finally, the relation which the increase in volume or growth bears
to the volume of the tree or stand on which it is produced may be
expressed as growth per cent, and indicates the rate of increase with
relation to the wood capital required for its production. This growth
per cent may be computed for volume alone, for growth in quality of
wood, or for growth in the unit price of the product (§ 334). A growth
per cent figure is not an index of absolute increase in either volume,
quality or price, since it is merely the expression of a relation between
capital and increment existing at a given time. Growth per cent is
usually based upon a single year’s growth, either current or average
for a period. One year’s growth is seldom measured, since a decade,
or at a minimum, a five-year period is required to eliminate variable
factors affecting a single season’s growth caused by climatic conditions.
Hence periodic annual growth is commonly substituted for current
annual growth as a basis for computing growth per cent.
245. Relation between Current and Mean Annual Growth. Growth
may be studied either for an individual tree or for a stand, expressed in
terms of growth per acre. In either case, the current annual growth
in volume increases at first slowly and then more rapidly to a maximum,
after which it begins to decline and finally ceases with the death of the
tree or the beginning of actual decadence of the stand. The sum of the
current annual growths laid on for the entire period gives the total
growth. The total growth or volume divided by the age in years
gives the mean annual growth (Fig. 64).
The mean annual growth is an average rate of growth representing
the total growth or yield at a given age, distributed or spread over this
period. The actual productiveness of the forest is in this way compared
with annual crops, which basis is otherwise obscured by the varying
rate or curve of growth in volume of the trees from decade to
decade.
The mean annual growth at any given year is this average of past
production. Current growth for the year or decade tends to increase
constantly up to a given maximum. During this period the volume
added each year to the total volume of the stand is greater than the
average or mean annual growth up to that year. Hence this average
is raised and the curve of mean annual growth increases. But it can-
not increase at as rapid a rate as the current growth curve, since the
CURRENT AND MEAN ANNUAL GROWTH 317
effect of this increase for the year upon the average increase is spread
over all previous years. -
When the current annual growth curve reaches its culmination and
begins to decline, the successive average or mean annual growth figures
for each year still continue to increase in spite of this fact, since the
amount of growth added to the stand during the year although less
than formerly is still greater than the average or mean.
When the current growth for the year finally falls to an amount
equal to the average or mean for the entire crop period, the curve of
mean annual growth has reached its highest point. During the follow-
|
Year lof Culmination of
Mean Annual ee
—
bo
o
lee)
o
Yield in Cubic Feet
fz)
Oo
0
0 5 10 1 20 25 30 35 40 45 50 55 60 65 70
Age in Years
Fic. 64—Current and mean annual growth of a normal stand.
Jack Pine Minnesota.
ing and subsequent years’ the current growth laid on is less than this
mean, hence this average or mean begins to drop, but only to the extent
that it is pulled down by the effect of this lesser current annual growth
total volume
age in years
this mean growth curve falls more slowly than the current growth
curve. Unless these stands are cut, losses in the stand will finally
exceed the growth, and the current growth curve would then become
negative. But until the entire stand is destroyed, the curve of mean
annual growth will still be positive. When properly computed on the
basis not merely of volume, but of quality and price increment as well,
the year of culmination of mean annual growth, rather than the current
growth data, indicates the maturity of a stand and the age at which,
if cut, it will produce the greatest average yields, when the period of
production is taken into account.
for single years upon the fraction,
Hence as before,
318 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
246. The Character of Growth Per Cent. The growth per cent of
a tree or stand cannot be compared with the per cent of interest earned
annually on a fixed capital, since this growth is not separable from
the wood capital on which it is laid, and thus causes this capital or base
volume to increase annually. To maintain the same rate of growth
per cent on this increasing volume, the amount of the annual growth
must continue to increase at a geometric rate. Although the increase
in volume of a stand during the period of most rapid current growth
for a time does approach a geometric rate when compared to a given
or fixed initial volume, yet even here the effect of the constantly and rapidly
increasing volume of accumulated wood capital upon the current annual
rate of increase will cause this rate of growth per cent to drop consistently
throughout the entire life of a tree or stand. The actual behavior of
the growth per cent of a stand is shown by the following table:
TABLE XLVII
GrowTH or JAcK Pine, MINNEsora *
Age. Yield per acre. Periodic Mean Periodic
annual growth. | annual growth. | annual growth.
Years Cubic feet Cubic feet Cubic feet Per cent
20 160 Bree 8
25 650 98 26 Mae:
30 1360 142 45 9 52
35 2210 170 63 4 68
40 2800 118 70 2 40
45 3160 72 70 1 56
50 3420 52 68 1.24
55 3640 At 66 1.08
60 3840 40 ' 64 0.88
65 4010 34 62 0. 80
70 4180 34 60 i
*From Bul. 820, U. S. Dep. Agr., 1920, Table 10, p. 14.
247. The Law of Diminishing Numbers as Affecting the Growth
of Trees and Stands. The growth in volume of individual trees tends
at first to follow a rate of geometric increase. Were the diameter growth
of trees to remain uniform for a long period, a condition characteristic
of many species, notably white and sugar pine, the resultant area and
volume growth would increase at a ratio similar to that of D?, rather
than D (§ 270). This rate of volume growth is strengthened by height
growth. With maturity, the height growth of trees falls to insignificant
proportions and the diameter growth of many species falls off to a marked
extent. The result is a flattening out of the curve of volume growth,
LAW OF DIMINISHING NUMBERS 319
which would otherwise continue to ascend sharply. This influence
of age and maturity upon individual trees which survive is due to loss
of vitality, but the same effect is observed in all the remaining trees
which are suppressed during the growth of the stand and ultimately
die because the space needed for their normal expansion is appropriated
by more vigorous trees.
A forest or stand represents an area of land stocked with trees.
The number of trees which can grow and thrive upon the acre is in
inverse ratio to the size of crown spread:and space required by the
individual tree. As trees increase in size their numbers will be reduced.
The enormous number of seedlings which may spring up on an acre
is merely a guarantee that a few will survive to maturity. The curve
of diminishing numbers which
is characteristic of all species
and classes of timber, drops
very rapidly in the first few
years, and more gradually later aay
on. Numbers diminish most sees
rapidly during the period of 3°
rapid height growth and crown $1
expansion. When trees have <= 1000
reached their mature heights, 8 750
their numbers have been re- E500
duced to a point where the — 250
further diminution is a much
10 20 30 40 50 60 70 80 90 100
slower process. Age, years
The cause of reduction is py. 65—Number of trees per acre at dif-
at first failure to survive the ferent ages in fully stocked stands of
juvenile period because of un- white pine. From Table XLVIII.
favorable climatic or soil factors
and competition with other vegetation, followed by suppression due
to the competition of older trees or of trees of the same age which have
attained dominance by some advantage at the start. The crown is
restricted in size and spread, is finally overtopped, and the tree dies.
This process is accompanied by a change in the rate of diameter
growth for the trees whose crowns and growing space are restricted
in the struggle. Consequently the dominant trees maintain at all
times the most rapid rate of diameter and volume growth, while others
which at a given period have not yet lost their dominance and still
show a rapid rate of growth, will later on, with the closing of the crowns
and crowding of the tree, show a falling off in growth, sometimes quite
sudden in character.. The prediction of the future growth of any single
tree is therefore impossible without knowing whether the tree will main-
320 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
tain its position in the stand and subdue its competitors. The net
growth on an acre is the sum of the growth of the surviving trees.
At any given period or year in the life of a stand, the number of
trees is considerably less than were present and living at any previous
period or decade, and is considerably greater than the number which
will be alive at any given period or decade in the future. This loss in
numbers, accompanied by rapidly lessening rates of growth of a portion
of the surviving trees, plus the normal growth of the remainder, produces
the net result or increase in the stand for the period, and any method
of study of growth which does not, take this natural loss and change
into account will be ineffectual in predicting or measuring the growth
of forests or stands.
248. Yields, Definition and Purpose of Study. The past growth
of the surviving portion of stands is represented by their present volume,
the measurement of which is dealt with in Part II. This present
volume represents the yield of the area, provided nothing has pre-
viously been removed as thinnings or otherwise. But without a knowl-
edge of the period required to produce this volume, the word yield is
meaningless as it cannot be expressed in terms of the rate of produc-
tion per year or mean annual growth. An estimate of standing timber
is merely a statement of the volume at present found on the area. A
yield, on the other hand, is a statement of the volumes produced on
the area within a definite period of time. the total volume is to be
expressed as a yield, then the total age of the stand must also be known.
If the yield for a shorter period, such as a decade, is to be stated, then
only that portion of the volume of the standing timber must be shown
as was laid on during this period. Otherwise, the rate of growth per
year is not indicated.
The growth of forests is studied primarily for the purpose of pre-
dicting future growth on forest land. On the basis of past records of
growth of trees and stands as shown by measurements of present
attained volumes and of age, predictions can be made as to the future
growth of these and of similar stands.
This application or prediction may be made in one of two ways:
1. By projecting the rate of growth of an existing stand into the
future. This is done either by assuming that the rate shown in the
immediate past will continue unchanged in the immediate future, or
else that this rate will change and that this tendency of future growth
may be predicted by the shape of the past growth curve. Of these
two assumptions the second is apparently the more accurate, but in
neither case is it possible to predict the growth for more than a short
period.
2. Some better method of prediction is required to cover longer
YIELD TABLES 321
periods and to determine the probable yield of crops of timber, the
production of which is the purpose of forestry. This is accomplished
by the second general method of prediction which rests on the principle
of comparison. The past growth of existing stands is taken as an indi-
cation of the expected future growth of other younger stands whose
prediction is desired for a similar period. It is assumed that similar
stands will grow in a similar manner. The task consists of demon-
strating the relation between the stands whose past growth is measured
and those whose future growth is sought.
249. Yield Tables. The most practical and useful expression of
growth is a yield table which shows the yields per acre for even-aged
stands at different ages by five- or ten-year periods separated into
different qualities of site. An example of such a yield table is shown
below:
TABLE XLVIII
YrrELp TABLE FOR WHITE PINE *
Quality IL +
Average | Diameter | Number | _ Basal ToraL YIELD
height | breast- | of | area sie
Age. of high of | trees | pers |
dominant | average | per "acre
trees. tree. | acre Cubic feet Board feet
Years Feet . Inches Square feet
10 6.0 1.4 2015 20 650 |
15 12.0 AD, 1834 50 1,150
20 19.5 3.2 1626 90 1,750
25 28.0 4.1 1420 131 2,420 5,400
30 36.5 at 1192 169 3,250 9,600
35 44.5 G-1 950 193 4,180 15,900
40 51.5 7.1 760 209 5,130 | 23,500
45 58.0 8.0 633 221 6,100 30,600
50 64.0 8.9 537 232 7,000 | 36,600
55 69.5 9.8 460 241 7,800 42,000
60 74.5 1050 397 248 8,500 46,900
65 79.0 11.6 348 255 9,200 51,600
70 83.0 12.4 311 261 9,840 56,100
75 86.5 13.3 277 267 10,400 60,200
80 90.0 14.1 251 272 10,930 64,000
85 93 .0 14.9 229 277 11,400 67,500
90 95.5 15.7 210 282 11,850 70,900
95 98 .0 16.4 195 286 12,250 74,000
100 100.0 ILrfsal 182 290 12,630 77,000
* Taken from Tables 4 and 6 in “‘ White Pine under Forest Management,” U. S. Dept. Agr.,
’ Bul. 18, Washington, 1914, pp. 22 and 23.
+ Similar tables are prepared for Qualities I and III.
322 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
From the above table, the periodic growth for separate five-year
periods may easily be obtained by subtracting the volume at one age
from that of the succeeding period.
250. The Application of Yield Tables in Predicting Yields. An
example of the prediction of volume growth in existing stands of timber,
on the basis of periodic growth by decades is given in the following
table which shows the present yield of timber over 10 inches and the
future yield which may be realized upon the timber left standing below
this diameter limit, and not shown in the table.
TABLE XLIX
YIELD PER ACRE OF SPRUCE CUTTING TO VARIOUS DIAMETER Limits *
Based on stands containing approximately 5000 feet B.M. of timber 10 inches
and over in D.B.H. per acre
Am’t | Seconp Cut | S—econpD Cut | Srconp Cur
of first} AFTER TEN |AFTER TWEN-| AFTER THIR-
cut. YEARS ty YEARS Ty Years |Interval
required
between
Num- Num- Num- equal
ber of ber of ber of cuts
Board | mer- | Board} mer- | Board) mer- Board) in
feet | chant-| feet |chant-| feet | chant-| feet | years
| able able able
| trees trees trees
Cutting to a 10-inch limit; 5213 | 7.
Cutting to a 12-inch limit} 4341 14.
Cutting to a 14-inch limit) 3382 | 10.
365 | 16.2 | 1087 | 26.8 | 2483] 438
1208 | 21.6 | 2325 | 30.5 | 4109} 32
1470 | 16.8 | 3044 | 40.8 | 6351 21
Ww w
* Compiled from Yield Tables in “ Practical Forestry in the Adirondacks,” Bul. 26, Division
of Forestry, U. 8S. Dept. Agr., 1899, pp. 83 and 84.
To understand the use or application of a yield table in predicting
growth, it must be realized that the stand or rate of growth upon a
given acre or tract will seldom if ever exactly agree with that shown in
a yield table even when these yields are separated by qualities into
3, 4 or 5 classes of site. In the case of bare land or very young timber,
this probable difference may be ignored, the site regarded as equivalent
to one of the site classes given and the yield predicted as if it would
coincide with that of the table. But for most stands which have already
reached a considerable age and the prediction of whose further growth
is desired, a comparison with the yield table should give a more exact
prediction of the growth of the stand in question. The yield table in
PREDICTION OF GROWTH 323
this case, instead of predicting exact future growth, is used as a standard
to express the relative increase or decrease in the yield or stand per acre.
The yields may be plotted and will form curves of growth in volume
per acre. The yield of any stand whose present volume and age are
known represents a definite per cent of some existing yield from this
table. The growth of this stand may be predicted by using the same
per cent of the values in the table for the future.
In Fig. 66 the present yield of a plot of white pine of fifty years is
indicated and the basis of prediction for its future yield is shown.
This percentage relation based upon standard yield tables is exten-
sively applied in forestry to obtain the actual yields of large forest
10,000
Quality I
9,000 —
uality IT
8,000 sect
<j
Quality III
a
a
2 4,000 poet x at 50 years yields
= reat 83 I standard.
ie yiel at! 65 years is
3,000 predicted ag 92% of the
pean at that aie
or Plot o the relation is
P 2,000 108% of Quality II at
40 years |
1,000 7
0
25 oOMmeon 400 45) 950) db) 60) 65
Age in Years
Fic. 66.—Method of predicting yields of specific stands by comparison with standard
curves of yield for different qualities of site. White Pine, Mass.
areas. It is the basic idea underlying the prediction of growth by
the method of comparison.
251. Prediction of Growth by Projecting the Past Growth of Trees
into the Future. By either of these methods, comparison or projec-
tion, it is assumed that no records exist of the past condition of the
stands whose growth is to befound. Their present volume, and the
age and past growth in diameter, height and volume of the trees now
standing can be studied, but there is no reliable indication of the
number of trees lost during the past period, though evidences remain
for a time in the form of dead and down trees.!
1 The writer once noticed in a densely stocked stand, the stems of hundreds of
small lodgepole pine which had fallen across a tamarack log and been preserved from
decay, when all trace of similar dead trees on the forest floor had disappeared.
324 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
In using the past growth of a stand on which to base the prediction
of its future growth, these records of past growth of the living trees
in diameter, height and volume are the only data available. This
prediction is based on one of two assumptions, either that the growth
for a future period will continue at the same rate as shown for a past
period, or that this future growth will be at a different rate, either increas-
ing or decreasing, and that the amount of this change may be deter-
mined by a study of past growth.
In the use of either of these methods to predict the growth of trees,
the method may be applied either to the volume of the tree or to its
diameter and height instead. If a volume analysis is made for two
or more past decades, it may be assumed either that this rate of volume
growth will continue unchanged, an assumption which is practically
never correct, or that the curve of volume growth which may be plotted
from past volumes can be prolonged to indicate the growth of the next
decade.
But the method more commonly employed is to substitute a study
of diameter and height growth for volume analysis. If future diameter
growth is assumed to be at the rate shown in the past decade, future
volume growth will increase (§ 270). If the past growth in diameter
is plotted, and a curve projected, the future diameter so obtained is
the basis of the predicted growth in volume.
252. The Effect of Losses versus Thinnings upon Yields. The
first conception in the study of growth is apt to be that it consists chiefly
of measuring the growth in diameter, height and volume of individual
trees. Although it is true that growth per acre is based primarily upon
the rate of growth of the individual trees which make up the stand
and that according as this rate of tree growth is rapid or slow, the yield
per acre will be large or small, yet the total growth per acre, which is
the result desired in all growth studies, is the product ot the growth
of individual trees and the number of trees surviving to the end of a
future period plus such growth as may take place on trees which die
and are removed during the period. The death of a certain number of
trees in the stand during the period will have this effect, that if these
trees can be removed as thinnings, their volume at the beginning of the
period, augmented slightly by growth which takes place in them before
they die, is part of the yield for the period, but does not appear in the
volume of the standing timber alive at its end. If these trees cannot
be harvested, their total volume as originally measured will disappear
from the live stand, and constitute a negative growth or loss which
must be deducted from the growth on the surviving trees before the actual
volume of the stand at the end of the period can be correctly ascertained
from its volume at the beginning.
AGE IN EVEN-AGED VERSUS MANY-AGED STANDS 325
This problem may be illustrated as follows:
A stand of pine has now 10,000 board feet per acre. The growth for ten years
upon the trees which will survive will be 4000 board feet. The trees which will die
in ten years have now a volume of 1500 board feet. This means, first, that the
growth of 4000 board feet is actually put upon a present volume of 8500 board feet;
second, that the remaining 1500 board feet must either be included in or deducted
from the final yield, on the basis of whether it is actually salvaged or not. There
may have been some growth on these trees, but this can be neglected. On the assump-
tion that no cutting of thinnings is possible, the net yield on this acre at the end of
the decade is 12,500 board feet. If thinnings are harvested, the yield is 14,000 board
feet. Had the growth prediction been attempted by measuring the growth of indi-
vidual trees, those representing the 1500 board feet would have to be excluded from
the calculation of total growth in either case. Unless salvaged, they represent an
actual negative growth reducing the net gain by 1500 board feet.
Unless it is possible to guess just how many and which trees are
going to die, not only the volume, but the growth for ten years on some
of these trees will probably be erroneously. included, instead of being
subtracted from the predicted total yield in ten years. The possible
error in subtracting either too few or too many trees is very large
since the size of the error is doubled for stands when thinnings are
impractical. It is obvious that a method depending instead on direct
measurement of the result at the end of the period on older stands
and the comparison of such measurements with similar younger stands
furnishes a safer basis of growth predictions on these younger stands
for any considerable period than efforts to project into the next period
the rate of growth of the trees now standing.
Where stands are under intensive management, the trees which
will die are thinned out, probably at the beginning of the period, and
utilized. The loss for the succeeding ten-year period is then exceedingly
small unless accidental inroads occur from wind, insects or other destruc-
tive agencies not anticipated. It is therefore safer to predict growth
for short periods on stands which have been under management and
have been thinned than it is on stands where thinnings and utilization
of the dying material is impossible.
253. The Factor of Age in Even-aged versus Many-aged Stands.
Where stands are measured as a unit to determine the production per
acre, three factors are needed: first, the present volume of the stand;
second, its average age or the time which it took to produce this volume;
third, the area which it occupies. The age of the stand as a whole
is desired. If the stand is even-aged it is sufficient to determine merely
the age of one of the trees adequately to measure the period of pro-
duction and the rate per year. This can be done by counting the annual
rings of growth without any measurement whatever, on the assumption
that the species has formed but one annual ring per year. This premise
does not always hold good, since with certain species in certain localities,
326 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
false rings may be formed, giving two rings per season (§ 256). Pro-
vided age can be determined, the study of diameter, height and volume
growth of individual trees is entirely unnecessary for even-aged stands,
as a means of determining the yields per acre.
But where stands are composed of trees of different ages on the
same area, it becomes practically impossible to determine the average
age of the stand by any such direct method. Within certain limits,
that is, if the ages of the trees composing the stand do not vary too
greatly, it is possible to determine an age which may be accepted as
the average period required to produce the present volume. Where
the diversity of age is so great that this is impossible, it is necessary
to shift the basis of age determination from the mere counting of the
rings to a determination of the age of trees of a given size or diameter.
To determine ages, trees must be cut down or the center reached by
borings or choppings. While possible on one or two trees, it becomes
out of the question to test every tree in this manner without cutting
down the stand. Diameter, on the other hand, can be readily measured.
For stands of mixed ages, therefore, two methods are possible. By
the first, the average diameter of the trees in the stand is found, and the
age of a tree of this size is determined and is assumed to indicate the
average age of the stand. By the second, no attempt is made to
determine the age of the stand, but instead the growth may be studied
for trees of given diameters, and for a short current period, past and
future. Either method requires the measurement of the diameter
growth of trees to determine the number of years or period which is
required to produce trees of given sizes or to grow 1 inch in diameter.
254. The Tree or Stem Analysis and the Limitations of its Use.
The volume growth of an individual tree may be analyzed with almost
absolute accuracy by cross-sectioning the bole and measuring the width
of the annual rings at different sections by decades. This is termed
stem analysis, or tree analysis. ‘The accuracy of these results for a single
tree is apt to create a false impression in the minds of investigators
as to the value of the figures thus obtained. To what use will volume
or total tree analyses of growth of trees be put? What question will
they answer? Will they predict the growth per acre of stands or the
rate of growth per year on an acre of land? The cost of a tree analysis
is excessive compared with the direct measurements of yields and
total age or even the measurement of diameter growth on the stump.
The number of trees ‘which may be analyzed is therefore limited. How
shall these trees be selected? It has been seen in the study of volume
tables that trees vary quite extensively in form. To get average
growth we must be sure of obtaining average form. Average form is
best obtained by averaging hundreds of trees as is done in the prepa-
CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 327
ration of volume tables, but the few trees analyzed for growth may
be either cylindrical or neiloidal in form. We therefore may have a
perfect record of the past growth of certain selected trees which vary
in form and volume at least 10 per cent from the average desired.
Even if this difficulty can be overcome by careful selection of trees
of average form quotient, and a few of these average trees analyzed
for past growth, how are these past results to be applied in predicting
future growth? It is evident that the growth of individual trees is
only a part of the problem, for the average tree in a well-stocked stand
at a given age does not remain the average tree for future periods and
was not the average tree at any period in the past. The trees which
dae in a stand are naturally the smaller, more suppressed specimens
with the smallest diameters. In the lapse of a ten-year period, the
loss of a number of trees from the lower diameter classes will raise the
average diameter and volume of the remaining trees so that the tree
which is now the average is in ten years dropped into a class below the
average.
There is but one way of even approximating the growth of a stand
in the future by means of the analysis of volume growth of individual
trees. If the number of trees which will probably survive to a given
age can be predicted (which can best be ascertained by the method
of comparison and yield tables), the selection of this number from a
younger stand, taking trees wholly in the dominant class, will indicate
the character of tree which must be cut and measured to determine
the growth for the future. Yet even here it is better to take a tree
which is fully mature and shows the growth for the entire period, in
which case the stand, rather than the tree, is the better unit.
255. Relative Utility of Different Classes of Growth Data, and
Chart of Growth Studies. To sum up these principles: past growth
is measured in order to predict future growth. Growth on an area
and not the growth of single trees is wanted. The three essentials
of growth are volume, time and area. For even-aged stands the time
element is the total age and may be determined by counting rings on
one or two sample trees. This requires a minimum of investigation
in addition to volume measurements.
Diameter growth of trees comes next in importance and is used
when size must be depended upon to determine age either for the total
period or for shorter current periods of growth when diameter is sub-
stituted for age.
Height growth of trees comes third in importance since it is used
to indicate site quality (§ 296). It may also be used together with
diameter growth, to predict the volume growth of trees by a method
much shorter than volume analysis (§ 288).
328 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
Volume-growth analysis of individual trees, although apparently
the most accurate and scientific basis of growth, is in reality the least
important and most inefficient when expense is compared with results.
It is invaluable to determine the laws of tree growth and the changes
which may take place in the form of individual trees as the result
of changed conditions, as for instance, on cutover lands, and as a pre-
caution against accepting general figures based on volume tables and
other short methods of growth study. But ordinarily, even where
volume of trees is desired, it will be obtained from diameter and height
growth supplemented by use of the form quotient rather than from
the stem analyses of trees. Many thousands of stem analyses have
been made in the past whose results were either not worked up at all
or since compilation have reposed in the archives of Government and
States while investigators vainly sought an answer to the pressing
problems as to what was the actual rate of growth per year on national,
state and private forests.
The best possible basis for growth predictions is the actual records
of the growth in successive periods of specific forest stands whose
history is known and whose conditions of management are fixed. The
establishment of sample areas which are measured successively by
ten-year periods will give a firm basis for growth predictions superior
either to the method of comparison, based on past growth of older
Purpose of growth study § 244
Productive capacity of different qualities of forest
land—§ 303
CHART OF
|
I |
Basis
Normal or index yields
per acre for even-aged
stands
1. Pure stands—§ 304
2. Mixed stands—S 314
Comparison of stands
1.
2.
Field measurements
Diameters B.H.—
§ 309
Heights, total
. Count of annual rings
on average trees—
§ 262
II 1. Timber estimate sepa-
Prediction of For even-aged stands! with normal yields at) rated by age classes—
fet ouerne —S8§ 256-262 same age—S 301 § 344
growth and
yields on
natural
For total age
. Counts of annual rings
on average trees—
forest areas; or long per- § 262
—§§ 247- iods—
248 §§ 249-250
CLASSES OF GROWTH DATA, CHART GRQWTH STUDIES 329
stands, or to the effort to predict the growth of stands from that of
the trees which they contain. As a result of similar actual records
of production the working plans for some European forests dispose of
the subject of growth quickly, stating substantially that the growth
in this class of forest is known, from past records covering (perhaps)
200 years, to be about so much.
In the chart, on pages 328-333, eleven main lines of investigation
of growth are listed, as a guide to the discussions in the following chap-
ters. The object of a study should first be understood, and the con-
dition of the stands to which it is to be applied, as indicated in the
three columns under “ Purpose of Growth Study.” In the column
under “ Basis”? the principles on which the solution of the problem
depends are outlined.
The remaining columns are self-explanatory. Column 6 shows the steps
by which the study can be applied to large areas of forest land, thus secur-
ing the data for which the preceding steps are merely preliminary.
By using this chart as a guide, and consulting the references to
discussions of principles and methods, under each step, one may hold
the purpose of growth studies clearly in mind and choose the best
method of accomplishing the desired object.
importance and reliability of the methods given are
The relative
indicated by the quality of type used in the table.
‘YROWTH STUDIES
Office records
Final data obtained |
|
Application to forest
areas
| Data derived from the
investigation
. Area of sample plots—
§ 308
. Volumes of trees (vol-
ume tables)—§ 131
. Age of sample trees—
§ 256, § 257
. Height of dominant
trees—§ 310, § 311,
§ 312
. Area of stand or age
class
. Volumes of trees (vol-
ume tables)§ 131
_ Age of sample trees—
§ 256, § 257
. Average volume per
acre for age class
is)
. Volume per acre—
. Age of stands—S 256
. Height of stands
. Reduction per cent or
. Empirical yield table
§ 306
relative volume de-
rived from this com-
parison—S 317
based on this reduc-
tion—§§ 304-316
Classification of site qual-
2.
1.
2.
- On basis of height
ities—§ 294, § 345
growth—S§ 296-310
On basis of volume
growth—S 295, § 312
Empirical yield tabie to
predict future growth
on each age class
Correction for in-
fluence of number of
trees per acre at differ-
ent ages—S§ 301-317
2.
ile
2.
- Mean annual growth
—§ 245
Number of trees per
acre
. Basal area per acre
. Maturity of stands—
§ 244 (rotation)
- Maximum yields
Future yields based on
actual stocking—
§ 301, § 343
Losses due to natural
agencies—4 293
. Gains possible from
protection and silvi-
culture
330
PRINCIPLES UNDERLYING THE STUDY OF GROWTH
Purpose of growth study
Prediction
of future
growth and
yields on
natural for-
est areas—
§§ 247-248
Prediction
of
growth and
yields on
natural for-
est areas—
§§ 247-248
iods—
§§ 249-250
future/For short
periods or
current
growth—
§§ 251-252
For total age
or long per-
| III 1
For large age groups—
§ 318, § 321
P,
LV,
For many-aged stands—
—§ 323
1.
§ 298, by dlameter groups) 2.
Basis
. Segregation of large
age groups—S 320
. Comparison of group
with normal yields at
average age— 301
Diameter groups. substl-
tuted for age classes—§ 276
Comparison of diameter
group with normal yields at):
indicated age—§ 301
CuHarT OF GROWTH
Field measurements
1. Diameters B.H.
2.Heights, average
based on diameter
3. Growth in diameter at
stump, based on age of
trees—$§ 265-269,
§ 320
1. Diameters B.H.
. Helghts
3. Counts of annual rings on
trees of each dlameter class—
§ 276
wr
For many-aged stands based
on crown space—§ 298
y)
Vb
On thinned areas—§ 326
{
VI
For even-aged stands
—§ 335
VII
For many-aged stands
§ 253, § 299
Va Li
Space requlred for develop-
ment of individual trees—
§ 300
Normal number of trees per
acre at different ages—§ 247
Same as Va
Same as II
Past growth of existing
trees—§ 336
=
. Diameters of crowns based
on D.B.H.—§ 324
. Growth In diameter at stump
based on age of trees—
§§ 275-279
. Growth In helght based on
age—§ 284
Same as Va
Measure only dominant trees—
§ 263
Same as II
1. Diameters B.H. by
crown classes
2. Heights, average
based on diameter
3. Growth in diameter at
B.H. or stump
—for given period of
years—S 278
—separated into 2 or 3
periods of five to
ten years—§ 279
CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 331
STuDIES—Continued
Office records
Total number of mer-}1.
Final data obtained
Data derived from the
Application to forest
| investigation
areas
Empirical yield table|Same as for II—§ 301
applied to area and
age of each group—
§ 322 and § 346
. Correction by segrega-
tion of areas occu-
pied by immature age
classes—§§$ 341-348,
§ 349
1.
Results only approximate due
to substitution of dlameter
for age
=
. Empirical yleld table ap-
plied to area of each diam-
eter group
. Correction by segregation of
areas occupied by immature
age classes—§ 341, § 348,
§ 350
if Areas occupied by
chantable trees each of two age groups
$ 319
2. Volumes of trees (vol-|2. Volumes in each age
ume tables) (average,) group—§ 321
on diameter)
3. Age as basis of each|3. Reduction per cent—
group, from normal § 317
yield table
4. Diameter of tree of in-/4. Empirical yield table
dicated age—§ 275 —§ 316
5. Volume of tree of indi-
cated diameter—$ 278
6. Number of trees in
each age group—S 321
1. Stand table by dlameter/1. Areas .occupled by each
classes—§ 188 diameter group—§ 319
2. Volumes of trees 2. Volumes in each group
3. Average age of trees of given|3. Reduction per cent—§ 317
diameters—§ 276, § 323 4. Empirical yleld table—§ 316
1. Space occupied by circular) Artificial normal yield table
crowns and resulting num-| based on number and size of
ber per acre—§ 324 trees at each age—§ 324
2. Relation between crown
spread and dilameter—
§ 324
3. Helght and volume of trees
of each diameter—§ 288
4. Average diameter of trees at
each age—§ 275
Same as Va
Same as II
1. Stand table by diam-
eter classes—§ 188
Growth in diameter
and height of trees by
diameter classes for
past period—§ 277
Volumes of trees now
and at end of period.
From volume tables—
$288. (Stem analyses
only as a check on
accuracy of 2 and 3)—
§ 254
Same as Va
Same as II
1. Growth in volume of
trees for future period
. Number and character
of trees which will die
during period—§ 257
. Net volume growth for
stand—§ 252
Reduction per cent for applica-
tion of yield table deter-
mined by comparison of
numbers of trees of each
diameter on area with num-
ber per acre In table—§ 325
Substitute for ylelds based on
even-aged stands when latter
cannot be obtained
Same as Va Means of predicting ylelds of
thinned stands
Most accurate basis for
current growth for
short periods, on even-
aged stands—S 327
Growth per cent
Same as II
As applied to trees and
stands
Future growth of trees
by comparison with
growth attained by
other larger trees for-
merly of same diame-
ter—§ 278
By extending into fu-
ture the past growth in
(UG General method for cur-
rent growth of stands
of any character of
stocking, form or ages,
and mixture of species
—§§ 245-342
Growth per cent (§ 246)
for trees or stands—
to
diameter on trees} This cannot in turn
whose future growthis| be substituted for
sought growth measurements
—by assuming it to} except on similar
equal past growth}
—hby prolonging curve
based on past peri-
odic diameter
growth—S 279
stands—8§ 331-333
‘For stands whose age
classes cannot be deter-
mined
332
PRINCIPLES UNDERLYING THE STUDY OF GROWTH
.
Purpose of growth study
Prediction
of future
growth and
yields on
natural for-
est areas
$$ 247-248
Prediction of
future
growth and
yields on
cutover
areas on
residual
stands—
§ 280
For short
periods or
current
growth—
§§ 251-252
For short
periods—
§ 336
For long periods
—§ 338
x
}
|
|
For many-aged stands
§ 253, § 299
VIII
For many-aged stands
—§ 254
Nib. ¢
For even-aged, or
large age groups or
diameter groups
—§ 339
Past growth of existing
trees—§ 336
Past growth of trees for
to
period since cutting, on}:
formerly cut-over areas
—§ 286, § 336
- Proportion of total area re-
maining stocked after cut-
ting, based on density equal
to emptrical yleld tables for
forest previous to cutting
. Residual area assumed to be
clear cut
. Growth predicted for stocked
area by empirical yield table
—see II—$ 316
Historical record of growth per acre—S 326
XI
Effect of numerical density of stocking, and of thin-
nings on growth of individual trees and on stand—
§ 270, § 273, § 274
Relation between diam-}1.
crown|2.
classes and number of]3.
Permanent sample plots
remeasured at stated
intervals—S§ 243
eter growth,
trees per acre, from
sample plots—§ 300
CuHart OF GROWTH
Field measurements
—for last inch or half-
inch of radius—
§ 278
. Growth in height
—by cutting back tip
for required pe-
riod—§ 294
—by substitution of
relation of height
to diameter—
§ 285
1, 2 and 4 same as VII
Growth in diameter
preferably at B.H.; for
period since previous
cutting. May be sepa-
rated into five- or ten-
year periods—8§ 278-
280
We
Same as III or [LV—§ 320
1. Diameters B.H. with
diameter tape—§ 190
Total heights, from
fixed stations—§ 199
Crown classes and
condition
Plot ‘escription
Tree ¢eags and perma-
nent boundary monu-
ments
Diameters B.H.
Heights
Growth in diameter
based on age, but rings
counted inward, per-
mitting study of cur-
rent growth on same
trees—$§ 265-269
CLASSES OF GROWTH DATA, CHART GROWTH STUDIES 333
Srupies—Continwed
Office records
4. Tally of trees with
suppressed crowns or
those apt to die
1, 2, 3 and 4 same as VII)
5. Partial stem analyses
for current growth in;
volume on sample
trees as check on effect
of increased growth at
stump—S$ 290
Same as III or IV—$§ 321
1. Individual record of
each tree on plot by
number, compared for
successive measure-
ments at five- or ten-
year intervals
. Record of conditions
and of external in-
fluences ]
Diameter growth for trees
of separate classes, by
diameters, and crowns
—§ 275, § 276, § 277
Final data obtained
1. Probable growth in
volume of trees left on)
cut-over areas
. Proportion of stand
showing _ increased)
growth—S 337
. Loss in numbers and
net growth in volume
2
Application to forest
areas
Data derived from the
investigation
As applied to forest areas
1. Stand table by diam-
eter classes
Growth from diam-|
eter and height
growth and volume
tables
Correction for loss in
numbers of trees
9
as
Future growth of trees
by comparison with
growth attained by
trees on areas after cut-
ting
Growth on forest areas
1, 2 and 3 same as VII
4. Per cent of stand
showing increased
growth—S 337
|
Areas in each age class for
timber left on cut-over area |
in)
. Volumes in each age class—
§ 339
Same as III or IV—§ 322
Permanent record of
changes in volume,
number of trees, and
dimensions for plot
2. Causes and extent of
damage
Effect of spacing or thin-
ning upon volume
growth and upon aver-|:
age sizes and quality of
individual trees—§ 301
. Location of plots with-
in control strips on
areas showing typical
conditions to be
studied
. Stand tables by diam-
1
eter classes
2. Ages of stands. The
data are applied inten-
sively to individual
stands in silviculture
Source of inaccuracy is in
determining mortality
per cent, hence cannot
be applied to long
periods
Effects of
—expansion of areas
of crowns and in-
creased growing
space
—competition of
species left after cut-
ting
—degree of severity of
cutting on remaining
stand
Minimum or conservative
ylelds on cut-over areas
No Increased growth assumed
Conditions would coincide
with cutting of even-aged
stands
Results contrasted with VIII
as check on that method of
prediction
Safe for application to long
periods
Current growth, measure-
ment of all factors of
change in stands under
conditions selected—
§ 340
Yield tables for stands
grown under manage-
ment. Ultimate solu-
tion of all growth prob-
lems—S 313
Proper spacing for plan-
tations
Character, and frequency
of thinnings
Class of material to grow
Character of initial natu-
ral stocking desired
Growth per cent on stand-
ing trees—§ 330
334 PRINCIPLES UNDERLYING THE STUDY OF GROWTH
REFERENCES
Climatie Cycles and Tree Growth, A. E. Douglass, Carnegie Institute Pub. No. 289.
Tree Growth and Climate in the United States. K. W. Woodward. Journal of
Forestry, Vol. XV, 1917, p. 520.
The Climatic Factor as Illustrated in Arid America, Ellsworth Huntington, Carnegie
Institution of Washington, D. C., 1914, Chapter XII.
Density of Stand and Rate of Growth of Arizona Yellow Pine as Influenced by
Climatic Conditions, Forrest Shreve, Journal of Forestry, Vol. XV., 1917, p.
695.
CHAPTER XXIII
DETERMINING THE AGE OF STANDS
256. Determining the Age of Trees from Annual Rings on the Stump.
The age of standing timber can only be determined from the ages of
the trees which compose the stands. The age of a tree is the period
elapsing from the germination of the seed or origin of the sprout to the
present year. A record of the number of years of growth in a tree is
made by the formation of the annual rings in which the light spring
wood is sharply differentiated in color and texture from the heavier
and darker band of summer wood of the year preceding. The count-
ing of these annual rings determines the age of the tree.
It is not always possible or easy to make this determination. Unless
the growth of a tree is marked by annual seasonal changes, there are
no annual rings to distinguish. This is true of most species of tropical
woods, except those growing in regions marked by an annual cessation
of growth due to annual recurrence of dry seasons. In some species
of hardwoods there is such a slight difference between the texture of
the spring and summer wood that the annual rings can be detected
only with difficulty and by the aid of coloring matter and magnifying
glass. This is true of such trees as basswood, hard maple and sweet
gum. Many trees on dry sites grow so slowly that the annual rings
are almost impossible to distinguish except by a glass. In counting
rings it is usually necessary to smooth off the surface with a sharp knife
or chisel in order to bring out the contrast.
Where growth is affected by severe droughts, and sometimes where
the trees are defoliated by insect attacks and later acquire new foliage,
a false ring may be formed, giving two rings in a single year which
would lead to an exaggeration in the age of the tree. This was found
to be the case with Rocky Mountain juniper on dry sites. False
rings may be detected if sufficient care is used, since they seldom form
a complete circle, but are present on only a portion of the circum-
ference and are therefore imperfect.
The last annual ring of wood is not completed until after the growth
for the year is finished. It must be distinguished from the ring of
new bark laid down in the same season. The first two or three rings
on some seedlings are difficult to distinguish.
335
336 DETERMINING THE AGE OF STANDS
The increment borer (§ 277) may be used to determine the age
of standing trees at breast height or at any section accessible, provided
the diameter is not too great and the position of the core of the tree
can be found by the instrument. This method is used with such
species as spruce.
257. Correction for Age of Seedling below Stump Height. The
number of rings in any cross section of a tree will indicate only the age
of the tree at that cross section and not the total age. No rings can
be formed at a given height above the ground until the tree reaches
that height. The age of each cross section made in sectioning a tree
will be less than that of the section below by just the number of years
occupied in height growth between the two points. Although the
total age of a tree can be determined theoretically by taking a section
even with the surface of the ground, this is seldom if ever done. The
rings are counted at the stump, which gives the age of the tree minus
the time which it took the seedling to reach this height. To get the
true age of any tree, seedling ages based on height must be added to
ring counts taken at stump heights. By cutting at the ground and
counting the rings on a sufficient number of dominant seedlings which
are sure to survive and therefore represent the average height growth
of mature timber when at this age, a table is constructed showing the
relation between the age of seedlings and different stump heights. In
rapidly growing trees this makes from one to five years’ difference
in the total age, but with some species which have a long juvenile period,
as much as twenty years may be required for a seedling to grow 2 feet
in height. This is true of certain Western conifers. Hardwood sprouts
on the other hand attain stump height in the first year.
TABLE L
HEIGHT OF SEEDLINGS AT DIFFERENT AGES, WESTERN YELLOW PINE, CoLrax Co.,
New Mexico
Age. Height. Age. Height.
Years Feet Years Feet
1 sh f ified
2 0.5 8 1.9
3 ON 9 PAP?
4 0.9 10 2.4
5 ied 11 Pn Uf
6 194 12 3.0
* Forest Tables—Western Yellow Pine, Circular 127, U. S. Forest Service, 1908.
ANNUAL WHORLS OF BRANCHES AS AN INDICATION OF AGE 337
The juvenile period for conifer seedlings is, as a rule, longer than
that for hardwoods, though there are exceptions. Stump height may
be separated into 6-inch height classes for determining the number of
years to add for seedling heights to get total age of tree.
258. Annual Whorls of Branches as an Indication of Age. There
is another method, of very limited application, for determining the age
of standing trees. This is applied to conifers and is confined to those
species which form but one whorl of branches per year. Species like
jack pine or loblolly pine, which form two or more whorls per year,
cannot be judged in this manner. The approximate age of the tree
and stand is obtained by counting the number of whorls. This record
holds good only when the branches or dead stubs remain visible and
when the height growth continues normal. The record is lost if all
traces of the lower whorls are obliterated. If this is only for a height
of from 5 to 10 feet, the average age of trees of this height may be
obtuined from a study of seedling heights and used to supplement
the remaining count. When the height growth of the tree has reached
its maximum, a new whorl of branches is no longer formed annually,
but the leader, as well as the branches, extends its growth by prolonging
a single shoot.
The ages of seedlings of many species may be determined by count-
ing whorls of branches, or terminal bud scars if the whorls are not all
there. In such eases it is not necessary to cut the seedlings and count
rings. The bud scars are distinct for many years on species such as
Douglas fir, Alpine fir, and others.
259. Definition of Even-aged versus Many-aged Stands. The age
of trees determines the age of stands. But unless it is known that
the entire stand originated in a single year, as is the case with sprouts
or with some species of conifers, such as jack pine or loblolly pine
on burns, there will be a variation in age due to natural seeding for
a period of reproduction which may extend to fifteen or twenty years.
Stands are termed even-aged if their crowns form practically a single
canopy or one-storied forest, which is true when the period of repro-
duction does not exceed approximately one-fifth of the rotation or
period required to reach full maturity. Where the crown cover of
stands of mixed ages varies so greatly that it is composed of different
stories, and must be separated into component age classes whose aver-
age age is separately distinguished, the stand is termed many-aged
or in some cases all-aged. The separation of such stand may be either
directly into age groups, or into groups based on size or diameter with
a limited range of age, whose average age is sought.
260. Average Age. Definition and Determination. The average
age of a group of trees showing a range of ages must be that age which
338 DETERMINING THE AGE OF STANDS
indicates or determines the rate of volume production per year at
which the stand has grown; therefore, the average age must be a
weighted age based on volume. The determination of average age
applies only to those stands which fall under the definition of even-aged
stands, yet have within the limits of the group a sufficient range of ages
so as to require a further investigation in order to fix the weighted or
average age of the group. For many-aged stands, the average age of
each age class must be determined separately.
For a given age class or even-aged stand as thus defined, the average
age is the age which would be required to produce an even-aged stand
containing the same volume as that of the uneven-aged stand in ques-
tion.
The methods possible for determining the weighted average age
of the trees comprising the age class usually involve the choice of
1. Treating the entire age class as a single group, or subdividing
it into from two to three, usually not over two, sub-
groups.
2. Determining the average tree, for the entire class, or sepa-
rately for each sub-group.
3. Ascertaining the age of these average trees.
4. Weighting the resultant ages of average trees of sub-groups,
to determine the weighted average age of the age class.
261. Determining the Volume and Diameter of Average Trees.
Subdivision of a group into two or more sub-groups will be made, if at
all, on the basis of diameters, by the diameter group method (§ 251).
In determining the average tree for the age class, or for a sub-
group, there are two reasons for basing this selection on average volume.
In the first place, if these selected trees are to be felled, and their ages
taken as indicating that of the stand, the larger trees must be avoided,
for in all probability they are advance growth, several years older
than the rest or possibly belonging to an entirely different age class.
The smaller trees would also be rejected since they may be late seedlings
some years younger than the average, or in extreme cases, so badly
suppressed that a certain number of rings may be lacking and the
growth aifficult to determine. Trees of about average size for the group
or stand must then be chosen. Where two or more groups are made,
an average tree for each group is separately selected.
Volume is the determining factor upon which the weighted average
age is to be based, hence the tree whose age is taken to indicate that of
the stand must be a tree whose volume is an average of the stand.
This principle applies not merely to cubic volume, but to the merchant-
able volumes expressed in units of product, such as board feet. Since
DETERMINING AGE OF AVERAGE TREES AND STAND 339
the purpose of the investigation is to determine the period which will
produce an equal volume of material in an even-aged stand, the product
in terms of which this volume is measured actually affects the average
age (§ 260). For board-foot contents which increases more slowly at
first and more rapidly later in the life of an individual tree, the average
tree will be larger and older than for cubic contents, since a portion of
the stand will be rejected altogether and fall in a younger age group
or else will logically receive a smaller weight in the average for determin-
ing the equivalent age of an even-aged stand.
The first step is therefore to determine the volume of the average
tree of the stand or sub-group. It is evident that the inclusion of a
large number of trees of the smaller diameters in a large group will
pull down the volume of the average tree and tend to unduly lower its
age. The plan of subdividing age classes into smaller diameter groups
is chiefly useful in avoiding this tendency to error, and is accomplished
by throwing together trees varying but little in size, to obtain the
average. It is of advantage therefore to make two or more of these
sub-groups where possible.
When volume is measured in cubic feet, basal area may be sub-
stituted for volume and the diameter of a tree of average basal area
determined. To obtain this, the sum of the basal areas of the trees
in the group is divided by the number of trees to obtain average basal
area. The diameter of a tree of this area is found in Table LXX VIII,
Appendix C, p. 490.
When measured in board feet, the volume of the average tree is
found directly by dividing the total volume of the stand or of the sub-
group in board feet by the number of trees. As in case of basal area,
the diameter of a tree of this volume is now required if sample trees
are to be felled to determine age. For this purpose a local volume
table based on diameter is used (§ 142) from which the D.B.H. of
a tree of the given volume can be determined to within 35-inch.
262. Determining the Age of Average Trees and of the Stand. The
age of these selected trees can then be obtained by felling trees of this
diameter. In stands of variable age from two to three trees are pref-
erable to one. As a substitute for this method, where it is extremely
uncertain that the tree selected will have the average age, a table of
diameter growth showing the ages of trees of different diameters may
be prepared from similar stands in the vicinity. If the average rate
ot growth thus obtained applies to the stand in question, the age of a
tree of the given diameter may be taken from this curve instead of
from felled timber. On account of the uncertainty of the correlation
between the growth figures obtained in this way and of the age of the
stand in question, the method has not been widely used and the felling
340 DETERMINING THE AGE OF STANDS
of the test trees or their age determination by borings or choppings
is the standard practice in determining the age of stands. When the
stand is treated as a single group, the average of the ages of the test
trees, all of which will be of the same average diameter, is taken as the
age of the stand. When two or more sub-groups have been separated,
the age of the entire stand must be calculated by weighting the pre-
determined ages of the sub-groups, in the proper proportions.
The following illustration will bring out the different methods possible in doing
this. An ‘ even-aged’’ stand composed of 30 trees is divided into two groups as
follows:
Average volume. Total volume of group.| Average age of trees in
Trees group.
Board feet Board feet Years
10 500 5000 100
20 125 . 2500 70
1. If each of these groups occupies an equal area and is given equal weight, the
average age may be found by adding the ages of the sample trees and dividing by 2.
This gives eighty-five years, and is known as the arithmetical mean sample tree
method. This method does not conform to the basic principle of weighted ages
sought.
2. When the trees are weighted by number the result is :
10 x 100 = 1000
20 70=1400
Total, 2400 +30 =80 years
This overemphasizes the number of trees rather than their volume, hence is unsat-
isfactory.
3. Trees are weighted by volume on the principle by which weighted volume
averages are always obtained:
100 years X 5000 = 500,000
70 years X 2500 = 175,000
Total, 675,000 +7500 =90 years. This method is acceptable.
4. The sum of the mean annual growth for the groups is obtained. The total
volume divided by this sum gives the average age. This method is considered
by European investigators to be more accurate than the others. As applied:
5000 + 100 = 50
2500+ 70=35.7
Total mean annual growth for stand, 85.7
7500 +85.7 =87 years.
By either method 8 or 4, it is seen that the average age is influenced by volume
rather than by area or number of trees.
AGE AS AFFECTED BY SUPPRESSION. ECONOMIC AGE 341
263. Age as Affected by Suppression. Economic Age. When stands
are comparatively even-aged and the trees composing them have grown
up as dominant individuals, free from suppression, the actual age of
such trees is a fair indication of the age which an even-aged stand would
require to produce an equal volume. But under this same definition,
the age of a tree which has been suppressed in the early period of its
life does not indicate the required age but one considerably greater.
The correction of the actual ages of suppressed trees to determine the
age desired is known as the determination of economic age. What is
wanted is the rate of growth of an average dominant tree on the same
site as that occupied by the suppressed trees. Where reproduction
takes place under a stand either of the same or of a different species,
the problem of growth is one of having two crops of timber on the same
land at the same time, and the rate of production per acre is the sum
of these two successive crops divided by the total period required to
produce them both. To isolate the period required for a single crop,
we must determine the rate of growth of the crop as if it were in sole
possession of the area.
A composite growth curve may be built up for average trees by
measuring the growth on these trees only down to the point at which
they were evidently freed from suppression and substituting from this
point on the average growth of seedlings and saplings measured on
dominant specimens. For instance, if the first 2 inches of an average
tree shows suppression, the average rate up to 2 inches must be taken
from other dominant, younger trees, and added to the remaining years
to get the total economic age of the tree in question. This factor has
been neglected in American growth studies, for the reason that with
such species but few attempts have been made to determine total
age, investigators being content with ascertaining growth for short
period based upon the diameter of the trees.
CHAPTER XXIV
GROWTH OF TREES IN DIAMETER
264. Purposes of Studying Diameter Growth. One purpose of
studying the growth of trees in diameter is to determine the total volume
of trees of given ages, or the growth in volume of trees for a short period.
The volume of trees is based on D.B.H. and height. The diameter
growth must always be correlated with D.B.H. for the trees measured,
and height growth is usually required. A second purpose is to determine
the dimensions or sizes reached by trees in a given period.
265. The Basis for Determining Diameter Growth for Trees. It
is impractical to cut sections at B.H. for growth measurements. Not
only is there a needless waste of timber, but the labor of felling and sec-
tioning the tree may also be avoided if the measurements are taken
at the stump following logging operations. Where current growth for
short periods is tested with an increment borer (§ 277) the measure-
ment is taken at D.B.H. The growth measurements on stumps require
three steps to determine the ages of trees of given D.B.H. outside the
bark; namely,
1. Diameter growth on the stump.
2. Correction for age of the seedling.
3. Correlation between stump diameter inside bark and D.B.H.
outside bark.
As diameter increases rapidly at the stump, the lower a stump is
cut the greater will be the apparent rate of growth for the tree. Stump
height classes differing by 6 inches may be made in growth studies,
but this is not often done. Stump heights usually vary with stump
diameters in a ratio of from one-third to two-thirds of the diameter,
depending on the closeness of utilization. For a given region and
standard, the stump heights for given diameters are fairly constant
and the average rate of growth is found for stumps of each diameter
with all stump heights averaged together.
266. The Measurement of Diameter Growth on Sections. The
section measured must be at right angles with the axis of the bole.
In stumps this means a horizontal cross cut. Slanting cross cuts exag-
gerate the length of the radius and result in a slight plus error in growth
measurements. The procedure is as follows:
342
MEASUREMENT OF DIAMETER GROWTH ON SECTIONS 348
An average radius is located. Its length must equal just one-half
of the average diameter inside bark (§ 25). To determine the -average
diameter, calipers graduated to 75-inch may be used (§ 189). In all
cross sections which are not perfect circles, the
lengths of the radi from the pith or center of
growth vary more widely than the diameters owing
to the fact that the pith is always located at one
side of the geometric center of the cross section.
Leaning trees grow largely on the under side and
this general law accounts for the position of the
pith.» On an eccentric cross section there are but Fig: 67—Stump _ see-
, ; tion fifty years old
two radii which are average in length and canbe 4... Nae
showing eccentric
measured for growth. It often happens that one growth, position of
or both of these radii (Fig. 67) are interfered with the two average
either by the undercut or by the presence of rot radii AB and AC
or derects which prevent growth measurement. ®@4 Tot on radius
. : . AB. Decades of
If either one is clear, the section may be meas- Ryd tee
k : : growth are shown.
ured. Otherwise, if measurement is absolutely — The growth must be
necessary, a longer or shorter radius can be taken measured on radius
and the measurements reduced by proportion to AC.
the required length.!
Method of Counting Decades. The next step is to count the number
of annual rings and indicate with a pencil the points at which the decades
fall. Except in scientific investigations where each year’s growth may
be separately measured to determine the influence of climate on annual
growth, the decade is ordinarily the smallest interval used in measure-
ment of diameter growth. For current periodic growth a five-year
period is sometimes used in order to get points for a curve in predicting
the growth (§ 279).
Unless the total age of the stump falls on a decade, as thirty, or
forty years, there will be one fractional decade laid off, representing
from one to nine years, depending on this total age. The dzameter
growth is always measured outward beginning with the pith or center
of growth. But in counting the annual rings to lay off these decades
of growth, two distinct methods of procedure are followed. In one,
the count begins at the center, laying off ten years from the pith, and
throwing the fractional decade to the outside as on the right side of
Fig. 68. By the other, the count begins at the cambium layer or
outer ring, and this throws the fractional decade to the center as on
the left side of the figure. .
Purpose of Counting Inward from Outer Ring to Center. The choice
1.g., if the average radius is 9 inches, and a radius of 10 inches is measured,
each measurement must be reduced by the factor 8; or .9
344 GROWTH OF TREES IN DIAMETER
of these methods is based on the purpose of the study. In all measure-
ments of diameter growth, an average rate is to be found by combining
the growth of a large number of trees. This means averaging together
the growth by decades. The trees so averaged usually differ in age,
sometimes over a wide range. The growth of the last decade, or current
periodic growth on all trees, regardless of their total age, is represented
by the outside or last ten rings. Any influence, such as cutting, fire or
climate, which affects diameter growth, must be studied on the basis
of current growth. In making a tree analysis, which requires the growth
Connie Counting
rom. from
oa s, Center,
Years
Fic. 68.—Alternate methods of counting and measuring annual rings on a cross
section 36 years old. On left, rings are counted in decades beginning with
outer ring. On right, count begins with center and odd rings fall on outside.
in diameter of upper sections (§ 289) the separation of the growth in
volume for each past decade requires the measurement of the same
ten rings on each of the sections analyzed. This is secured by counting
back from the outer ring. When growth is studied for these purposes,
rings must always be counted from the outside inward. In this case
the first measurement from the pith outward will be the fractional
decade. The average growth for this period represents the average
number of years less than 10 which were measured. This may vary
from 1 to 9 years but tends to average 5 years. The second decade
will include, on different trees, the years 2 to 19, the third, 12 to 29;
345
MEASUREMENT OF DIAMETER GROWTH ON SECTIONS
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346 GROWTH OF TREES IN DIAMETER
e.g., on a tree 21 years old, the decades are 1, 2-11, 12-21 years. On
a tree 29 years old the decades are 9, 10-19, 20-29 years.
Purpose of Counting Outward from Center to Outer Ring. In tracing the growth
of trees in diameter, based on their age, to determine the average sizes reached at
each decade, the above averages might tend to conceal or flatten out any changes
characteristic of the juvenile period. In this case a more clear-cut definition of
growth may be obtained if age is actually made the basis, and the same decades
averaged for each stump, e.g., 1-10, 11-20 years.
For this purpose the count would be made outward from the pith, coinciding in
direction with the measurement of growth, throwing the fraction to the outside.
But this causes the fractional decades to fall in as many different columns as there
are trees of different ages by decades. In tree analyses it would result in measur-
ing different fractions at each upper section instead of the same rings. It does
not give current diameter growth for a stand. The age of the seedling, which is
usually a fractional decade, must still be added. For these reasons the first method
is considered standard. But for the purpose indicated, diameter growth based on
age, the last fractional decade on the outside although recorded could be dropped
in obtaining average growth of several trees; e.g., a 43-year stump can be computed
for its first four decades only. By this plan, the averaging is simplified.
Method of Measurement. The measurement of diameter growth is
usually made with a steel rule graduated to inches and twentieths, or
05 inch, which is the smallest graduation commonly employed.
When the radius has been laid off and each decade marked, the zero
of the rule is placed at the center and the distance read to each decade
point. The measurements are cumulative, that is, the rule remains
in the same position until the complete radius is read. This avoids
errors which are sure to occur in moving the zero from one decade
to another to separate the decade measurements. The form of record
is shown on p. 345. The accuracy of the reading should be checked
by noting that twice the total radius should equal the average diameter.
267. The Determination of Average Diameter Growth from the
Original Data. The average diameter growth for the trees measured
may be obtained by arithmetical means, and by the aid of graphic
methods.
Table LI shows the method of computing the average growth.
When the decades have been counted from the pith with the final
fraction rejected, each decade is full and the averages fall at 10, 20,
30 years, etc. This completes the table in the form desired. But
when the rings are counted from the outside, the first decade being —
fractional, the growth is not shown for full decades, but for odd years
as 7, 17, 27 years, etc.
To obtain the growth at the required decades, a curve of radius
growth based on age is plotted as shown in Fig. 69, each point being
plotted above its proper age. The radius scale is then doubled to
AVERAGE DIAMETER GROWTH FROM ORIGINAL DATA 347
read directly in diameter growth. From this curve, the growth at
10, 20, 30 years, etc., is then read for the table.
Radius, Inches
(Double to read Diameter)
Fic. 69.—Growth in radius of 5 spruce trees plotted separately, and curve of average
growth. The average number of years in first fractional decade is 7. The
successive decade averages are plotted on 17, 27, etc. The last three points
represent averages based on less than five trees and should not be plotted on
the same curve.
The growth of each tree is shown by curves. In plotting data for a
growth curve the points plotted for single trees would not ordinarily be con-
nected. The average would either be sketched by eye, or plotted from the
position of the average points as indicated.
Substitution of Graphic for Arithmetical Method. For this computation
graphic plotting of the original data is sometimes substituted. This method is also
348 GROWTH OF TREES IN DIAMETER
illustrated in Fig. 69, in which the growth of five spruce trees is plotted, their rings
being counted from the outside inward. Each tree is plotted on the exact years on
which its measurements fall as determined by its total. age. Where a large number
of trees are plotted, the points are not connected but form a band, on which the
curve of average growth is sketched by eye. This method is intended to save the
labor of calculating the averages arithmetically.
Where trees of different ages are included in the average, the upper extremity of
the growth curve will represent a smaller number of trees, whose growth, if dominant,
will exceed the average rate, but if suppressed, will fall below it, causing the curve
to depart from a true growth curve, as illustrated in this Figure.
268. Correction of Basis of Diameter Growth on Stump to Conform
to Total Age of Tree. The next step is to correlate this curve of growth
with the total age of the tree. The average age of seedlings must be
determined for the given average stump height (§257). The number
of years thus indicated is added to the scale by moving the zero the
required number of points to the left. This new zero causes a shift
in the age of each section to correspond. The curve now shows, not
the diameter of stwmp secticns of various ages, but the diameter of
trees of various ages when measured at the height of the stump.
269. Correlation of Stump Growth with D.B.H. of Tree. The third
step is to determine the D.B.H. for these same trees in order to correlate
this with age. What is desired is not the age of the section at B.H.
but the D.B.H. of the tree, whose total age and growth at stump are now
known.
A tree of a given stump diameter, whose total age has been found,
has a set of upper diameters or tapers representing its form, as expressed
in a taper table (§ 167). Of these the most important is D.B.H. This
third step then consists simply of determining the average taper of the
butt, from stump height to B.H. so as to find the D.B.H. corresponding
to each inch stump-diameter class.
Standard stump tapers show the D.I.B. ($135) of stumps at heights
of 1, 2, 3, 4, and 43 feet, corresponding to each D.B.H. class. But
to determine growth of trees at B.H. corresponding to growth on the
stump inside the bark, heights of stumps are usually averaged, and a
direct comparison is made of average D.B.H. outside bark with average
D.1.B. on the stump for all trees falling in the given stump-diameter
class.
Stump tapers may be taken on the butt logs of felled trees in the
measurement of volumes ($168). The number of measurements so
obtained is often insufficient and may be supplemented by measuring
the diameter at stump height and width of bark to get D.I.B., on stand-
ing trees, together with D.B.H. Owing to the great variation in diam-
eters at the stump compared with D.B.H., a large number of stump
tapers are required to produce a curve free from irregularities, as illus-
CORRELATION OF STUMP GROWTH WITH D.B.H. OF TREE 349
trated in Fig. 70 for loblolly pine. These data can be obtained very
rapidly and without much extra cost.
These stump tapers are then classified on the basis of stump diam-
eter inside bark and not on D.B.H. since they are to be plotted on the
curve of stump diameter. An arithmetical average of these relations
is obtained, and expressed in the form of Table LII (p. 3£0).
2
18
16
yt-—--L__Stump D.uB. 14 inches |
Correspondin
=o espone™
Oe
Yh —-— — + — — ty = 9
Age of Tree of These Dimensions
Diameter—Inches
#2
a
Age of Stump Sectio
0 20 30
34 8 10 20 30 40 50
Age of Tree including Seedling
‘Fa. 70.—Diameters, inside bark at stump, outside bark at B.H., and inside bark
at 16 feet above stump, for trees at different ages. Loblolly pine, old fields,
Urania, La.
The D.B.H. outside bark for each stump-diameter class is now
plotted on the curve of D.I.B. on the stump as shown in Fig. 70. Since
this curve is based on age of tree, the diameter at any point on the
bole of a tree of a given age will fall on the indicated vertical line cor-
responding to this age. Thus, a tree measuring 14 inches on the stump
in Table LII is 30 years old at the stump, and 33 years old when
corrected for age of seedling which is 8 years. The D.B.H. far a 14-
inch stump is 13.2 inches, which is plotted above 33 years. In the
same way, D.I.B. at the top of the first 16-foot log, which is 10.8 inches,
would fall above the same 33-year point on the scale. In this manner
the stump tapers are each plotted by first finding the corresponding
3509 GROWTH OF TREES IN DIAMETER
D.I.B. at stump, on the curve of growth, which indicates the required
age of the tree above which the remaining dimensions are to be plotted.
TABLE LII
Stump TApERS—BASED ON Stump DI.B. ror Stumps 1 Foor HicH
Loblolly Pine, Urania, La.
|
Stump diameter | Average D.I.B. Avemige Dv
class. stump.
Inches Inches Inches
5 5.1 4.5
6 6.0 6.1
i! 6.8 6.8
8 8.2 (GX)
9 9.1 8.3
10 10.0 9.6
11 ih 10.4
12 11.9 11.0
13 13.2 12.3
14 14.1 12.7
15 15e 12:9
16 16.0 15.6
Ly 1752 15.8
18 igs! 16.7
19 18.7 18.2
The D.B.H.’s for different stump diameters are now connected by
a curve, which shows D.B.H. for trees of intervening ages, and for
all stump diameters. From this curve the D.B.H. corresponding to
each decade in the lie of the tree can be read, in the form of Table
LITI.
TABLE LIII
GrowtH oF LoBLOLLY PINE, OLD FreLp, iv D.B.H., Basep on AGE or TREE,
Urania, La.
Diameter at top
Age. DBs: of first 16-foot
log inside bark.
Years Inches Inches
10 BE 1)
20 9.8 7.0
30 12.5 9.9
40 14 ag 740)
50 17.0 13.8
DIAMETER GROWTH OF TREES GROWING IN STANDS _ 351
Since there can be no D.I.B. at 16 feet until the tree has reached
this point in height, the curve of these points would terminate at zero
diameter at an age equal to that required for the tree to grow 16 feet
in height, above the stump, which is 8 years in Fig. 70. In the same
manner the D.B.H. curve would terminate at a point representing the
year in which the tree reached 43 feet in height, which is 4 years. The
stump curve has already been shown to terminate at an age repre-
senting the growth of the seedling to stump height at 3 years. This
principle is later explained more fully in connection with a method
of plotting the volume growth of different trees (§ 291).
270. Factors Influencing the Diameter Growth of Trees Growing
in Stands. Diameter is the most variable factor of tree growth, dif-
fering with a wider range of conditions and showing greater diversity
between trees in the same stand than height growth. Growth in diam-
eter influences growth in volume of the tree to 4 much greater extent
than does height growth, the relation being that of d? or area. Since
the growth in area bears this fixed relation a the area growth of indi-
vidual trees is never studied, as all problems for which it is desired
are solved by the study of diameter growth. The rate of diameter
growth is determined by four factors: species, quality of site, density
of stand, and crown class.
Secondary factors modifying diameter growth are the amount of
shade endured by the specific trees studied, and the treatment of
the stand.
271. Effect of Species on Diameter Growth. Different species
have developed specific differences in average rate of diameter growth.
Those accustomed to growing on soil of good quality as dominant
species have acquired the fastest growth rate. Intolerant trees usually
grow faster than tolerant since they must maintain their dominance.
Of this, the cottonwood is an example. Trees which have the power
of enduring shade usually grow, even in the open, at a somewhat slower
rate than intolerant trees.
Trees do not indefinitely maintain a given rate of diameter growth.
Until a tree actually dies, it continues to increase in diameter, but there
comes a period when, in spite of the dominant position of the tree,
its rate of diameter growth diminishes. The period at which this
diminution sets in marks the maturity and the beginning of decadence
of the tree. The life cycle of different species of trees is as distinct
as that of different animals. Short-lived trees, like jack pine and
tamarack, show this falling off at 70 or 80 years or sooner, and disappear
within 30 or 40 years thereafter. The same is true of aspen. The life
cycle of conifers is apparently affected by general climatic conditions.
302 GROWTH OF TREES IN DIAMETER
That of western conifers is double the cycle characteristic of those
in the East, while that for redwoods and Sequoia is fully five times
as great as for most of the remaining western conifers.
The life cycle of any individual tree is governed by the average for
the species but appears to depend on size and not age. A tree is mature
when it has reached the maximum size permitted by its site and vigor
of crown, whether this is secured by continuous rapid growth as a
dominant tree or is delayed by a period of suppression. Trees character-
istically intolerant and dominant, and accidentally suppressed in youth,
if they recover from this suppression, will add the period of suppression
to the average age which they attain and continue to grow until they
reach the usual size. Trees naturally undergoing and recovering from
a period of suppression, such as spruce and balsam, may attain maturity
under these conditions 100 years later than trees of the same species
growing in the open, and their life cycle will be that much longer. This
law was also found to hold true for the Sequoia gigantea.!
272. Effect of Quality of Site. The greater productive capacity
of better sites is reflected in the increased rate of growth in diameter
of the species on these sites. Either deficiency or continuous excess
of moisture greatly reduces the site quality and slows down diameter
growth. The final expression of site quality is found in terms of total
volume or rate of growth per year, of which this average diameter
growth is one of the best indications.
273. Effect of Density of Stand. The rate of growth of the individ-
ual or average tree is profoundly influenced by the number of trees
in the stand. The original number of trees germinating and becoming
established on a site bears no relation to the number which may grow
to maturity. The reduction of numbers with increased size and crown
spread is accomplished by competition between individuals, resulting
in the death of the weaker trees. With species which become estab-
lished in dense stands in a single year and maintain an even height
growth, the inability of the stand to differentiate itself and destroy
the necessary proportion of the weaker trees is reflected in a great
reduction in diameter growth on all of the trees. Of this tendency,
lodgepole pine gives the best examples. In almost all species of conifers
and many hardwoods, dense, even stocking, unless artificially corrected
by thinning, gives a much lower rate of diameter growth than the aver-
age which may and should be secured by the species. Diameter growth
is therefore apt to be greatly reduced by increased number of trees
per acre in the stand, or overstocking,
: Ellsworth Huntingdon, The Climatic Factor, as Illustrated in Arid America,
Carnegie Institution of Wash., D. C., 1914, Chap. XII.
EFFECT OF CROWN CLASS 353
274. Effect of Crown Class. The individual rate of diameter
growth varies over a wide range with the same species, site and stand.
The rate of growth is coordinated directly with the crown spread of
the tree. There exists a relation between width of crown and diameter
which is found to hold good under almost every condition and for every
species, although varying with the species and its habit of growth.
This law, which might be of great use in determining the number of
trees which should exist per acre for a given species in mixed stands,
is somewhat interfered with by the fact that the volume of the crown,
rather than its mere diameter, is the factor affecting diameter growth,
and with western conifers, with very tall and slender crowns, width
alone does not properly express this value. As crowns receive more
growing space and expand, diameter growth correspondingly increases.
This elasticity of diameter growth correlated with crown spread is the
principal means of adjustment which a stand of trees possesses, by
which it constantly tends to fill in blanks and form a complete crown
canopy provided only that the distribution of the trees is such as to bring
these blanks within the possible maximum spread of individual crowns.
Effect of Shade. Diameter growth during the life of a tree de-
pends upon its history with respect to the remaining trees in the stand.
A tree which has remained dominant since germination maintains a
maximum rate of diameter growth. The crown spread at successive
decades is a maximum. ‘Trees which are at first dominant and later
suppressed, cease to grow in diameter because their crowns cease to
expand. The relation between diameter and crown is maintained,
but neither continues to increase. Trees which were originally sup-
pressed and later freed may show a marked increase in diameter growth
coinciding with an increased spread of crown, thus maintaining the
proportion under the changed conditions. But if their crowns have
lost the power to recuperate, which depends upon both the specific
character and the age of the tree, no increase is made in diameter
growth by reason of this liberation.
Effect of Treatment. The growth in diameter of trees can be pro-
foundly influenced by the artificial treatment of a stand. Since for
the individual tree it is a function of crown spread and its rate is governed
by the ability of the crown to expand, diameter growth is the most
easily governed and most adaptable function of tree growth. The
stand per acre or rate of growth for a period measured in cubic contents
may not be subject to great modification, but the sizes of the stock
produced and consequently the value per acre can be greatly influ-
enced by management. The behavior of trees in thinned stands and
on cutover lands must be studied separately from those subjected to
the natural laws of survival in original unthinned forests.
304 GROWTH OF TREES IN DIAMETER
275. Laws of Diameter Growth in Even-aged Stands, Based on
Age. The struggle of the individual trees for space produces different
results in even-aged and in many-aged stands, although the general
effect is a final reduction in numbers in either case. In the even-aged
stand the area occupied by an age class is definitely fixed. Expansion
of the crowns of individual trees can occur only by the prevention of
corresponding expansion of other crowns and by securing of additional
space through the actual death of the weaker trees. This process
results in a continuous differentiation of diameter classes in an even-
aged stand with advancing age. As the trees become fewer in number,
the difference in size of the survivors increases. These relations are
shown in Fig. 71, in which the number of diameter classes existing at
different ages in an even-aged stand is indicated.
The growth in diameter of the trees which compose this even-aged
stand is shown in Fig. 72. The diminution in diameter growth due
to suppression of crowns affects successive trees of larger and larger
diameter. The average tree at a given decade is seen to fall into the
lower half of the stand in the succeeding decade and at some future
period will become suppressed and finally die.
In Fig. 71 is shown the difference in basis and composition of the curves based
respectively on age and on diameter. The curve based on age in this figure is
composed of averages of all the diameter classes in successive even-aged stands, as
shown in the vertical columns. The curve based on diameter takes all trees of a
given diameter for each successive average, thus including trees from a number
of different age classes or stands as read horizontally in the diagram. This curve as
plotted in Fig. 71 is reversed, with the basis, diameter, plotted on the vertical scale.
The proper form of such a curve is shown in Fig. 73. The wide divergence possible
in the two bases, for dominant larger trees, is indicated in Fig. 71.
It is evident that growth measurements of diameter based on age, which include
trees whose total age varies from 20 to 50 years, corresponding with the diameter
classes A to L in Fig. 72, will not be correct for any single tree in the stand D. The
portion of this curve representing the earlier decades is depressed or lowered by the
inclusion of the slower growing trees F to L which afterwards die. With the suc-
cessive dropping out of these trees from the average, the latter portion of the
curve shows a more rapid growth than that of the trees which compose it.
To get the actual past growth of an average tree for a stand of a given age, C, it
is evident that only trees which have reached this age must be measured, A to E.
To secure average diameter growth for mature timber which in the future will be
grown to the given sizes and numbers per acre characteristic of this class of timber, it
is incorrect to include measurements of average trees for stands which have not yet
reached this age, F to L. By confining the selection of trees to timber of the desired
age and by taking the growth of all of the trees found on an area of sufficient size,
we obtain an average rate, showing the past growth of these trees, which is a true
growth curve, C. If it is desired to predict the rate of growth for the average tree of
a given age and character of mature stand, dominant trees must be selected from
younger stands rather than the average tree. The fewer of these trees, and the
greater their relative crown spread or dominance compared to the remaining stand,
LAWS OF DIAMETER GROWTH IN EVEN-AGED STANDS — 355
the greater the age with which the resulting growth curve will coincide as an expres-
sion of yield per acre and average tree; e.g., for predicting the growth to 35 years of
stands now 20 years old, the group of trees, A to H, whose average tree is D, must be
included, omitting classes J to L which would lower the average tree at 20 years
to F,
Diameter classes
entering average
when._based on|age
oN
S
Age vlasses
entering
average
when based
on diameter
(ae
peeupare
‘et beas|
ay
Total Trees =
5 45 ~ 65
Age, Years
Fic. 71—Number of trees in each diameter class in normal stands at four successive
ages, and resulting curves, when averaged respectively on basis of age and of
diameter.
The composite curve of average growth in which each successive decade is based
on a lesser number of trees than the preceding period, is a useful tabulation to show
the average diameter of surviving trees at given ages, but as shown does not correctly
indicate the progress of growth for any of the trees on which it is based, unless it is
confined to a given number of trees throughout.
356 GROWTH OF TREES IN DIAMETER
Diameter growth based upon age is used, in practical studies, princi-
pally as an aid in indicating the difference in rate of growth of species,
sites, and different methods of treatment and as an aid in determining
the average age of stands in the forest under different conditions.
This application is much more limited than is commonly supposed
sll ie fsa
24
22
20
18
—
oS
Diameter, Inches
oo
ae
_
bo
—
o
Age, Years
Fic. 72.—Differentiation of diameter growth as result of different rates of develop-
ment of crowns, in normal stands, even-aged.
since for many problems the substitution of yields per acre based directly
on total age answers the questions more directly and accurately, while
for forests in which the average age for stands cannot be ascertained,
diameter growth is not based on total age, but on diameter classes
(§ 336).
LAWS OF DIAMETER GROWTH IN MANY-AGED STANDS 357
276. Laws of Diameter Growth in Many-aged Stands, Based on
Diameter. When diameter growth is studied in order to determine
the age of trees of given diameters, the basis of the average is éntirely
different from that required when the diameter or size of trees of given
ages is required. By the inspection of Fig. 71, it will be seen that
when based on age for each decade, several different diameter classes
are averaged together. The average diameter even for the oldest
age class is several inches less than the maximum diameters reached
by the dominant trees. To prolong a curve of growth based on age
until the diameter of the maximum tree is reached, would add several
decades to the apparent age of a tree of this diameter.
On the other hand, if diameter is actually the basis and the average
age is sought, the classes included to obtain these averages are read
horizontally in Fig. 71 and include under the same diameter several
different age classes. The principal effect of this difference in the basis
of averaging is found when the larger diameters are reached. In
stands composed wholly of intolerant trees, where suppression and
prolonging of the life cycle is not a factor, the difference between the
age of the larger, dominant diameter classes which exceed the average
and the average age of smaller diameter classes, which include many
trees fully as old as the dominant classes, is much less than would be
indicated by a curve based on age. A curve showing the average age
of trees of given diameter is not expected to show the progress of trees
in diameter from dec-
ade to decade, but
expresses directly the
result of the total
growth or period for the
specific class of trees §
concerned. :
&
There is but one
way to determine ac-
curately the average
age of trees of separate
diameter classes and
that is by a total count
of rings for several trees Fyq.73.—Ages of trees of different diameters, shown
in each diameter class for two groups of longleaf pine, the first com-
to obtain the average posed of second-growth stands, the second of
age directly on this veteran or old-growth timber.
diameter basis. When
these points or averages are plotted, they will show a relation about
as indicated in Fig. 73.
1G 7 IBID) 20> ZAG 2823) (24125) 26" 27) 28
Diameter at Stump, Inches
358 GROWTH OF TREES IN DIAMETER
The application of such a growth study is to determine correctly
the average age of trees of given diameter classes and diameter groups
in a forest or stand when the basis of age for the stand cannot be directly
determined (§ 320). This presupposes that the stands are not even-
aged, but many-aged in character. In mixed many-aged stands or
groups, suppression usually plays a large role and again interferes with
this determination by requiring the substitution of the economic age
for the actual age (§ 263). But for the species such as the Southern
pines, which are fireproof to a certain extent, and the Western yellow
pine, for the same reason, the age groups may be intermingled and yet
the dominant character of growth maintained. Under these cireum-
stances, the direct determination of age based on diameter may be
used for determining the average age of diameter groups, especially
for the upper or dominant classes.
277. Current Periodic Growth Based on Diameter Classes. The
Increment Borer. A more common application of growth based on
diameter classes is for the prediction of current periodic growth in specific
stands, for short periods, by predicting the growth of each tree in the
stand in diameter and correlating this data with volume growth. The
drawbacks to this method have been discussed in § 251. Dealing,
as it does, with the specific stand and actual number of trees, it
is directly applicable to stands of all degrees of density and to
the actual stocking found on the ground, and to this extent is
applicable directly to the existing forest without the necessity
for a yield table. Tables showing the growth in diameter which
may be expected of trees of given diameters may be applied directly
to stand tables showing the number of trees of these diameters on
the average acre.
The current growth of trees of given diameter is measured either
on the stump or directly at B.LH. Growth measurements taken on the
stump must be laid out on an average radius (§ 25). As the growth
in D.B.H. outside bark is frequently less than that on the stump inside
bark (§ 269) correct results would require the reduction of the radial
growth on the stump to its equivalent at D.B.H. This is not usually
done, first because for trees of the smaller diameters D.O.B. at B.H.
tends to coincide with D.I.B. on the stump; second, because the total
error thus incurred in measuring the growth based on age is proportion-
ately reduced in measuring current growth, although the percentage
of error remains the same. This may be considered too small to require
correction. When measured directly at B.H., it is important to secure
an average radius if possible. The only method by which this can be
done is to take two readings on opposite sides of the tree, and determine
the mean.
CURRENT PERIODIC GROWTH BASED ON DIAMETER CLASSES 359
The increment borer (Fig. 74) can be used for measuring radial
growth at B.H. This instrument consists of three parts:
(a) A hollow auger, A, from 4 to 10 inches long, tapering and
threaded at one end, and square in cross section at the other end.
(6) A hollow metal handle, B, with a square opening in the center
into which the auger fits when in use. At the ends of this handle are
detachable caps.
(c) A narrow wedge, C, furnished at one end with a flat head, and
incised on one side at the other end.
Fic. 74.—Increment borer, showing construction.
The wedge and the auger are carried inside the hollow handle when
the instrument is not in use.
To use the instrument one bores into a tree to the desired depth,
then inserts the wedge through the auger with the incised «‘de turned
inward. The wedge is jammed down, thus holding tightly in place
the core of wood within the auger. The handle is then turned sharply
to the left, severing the core from the wood. The cylinder of wood is
then drawn out, and the rings counted or measured.
The best type of instrument is made in Sweden, and cores of from
6 to 8 inches may be secured by the larger sizes. The instrument is
easily taken apart and is convenient to carry. When taken at B.H.
360 GROWTH OF TREES IN DIAMETER
these measurements require no correction. Care must be taken if
but a single measurement is made on standing trees, to select the point
for testing on neither the lower nor the upper side of a leaning tree,
the growth of which is very eccentric, coinciding with its position.
278. Method Based on Comparison of Growth for Diameter Classes.
In Chapter XXII it was shown that growth is measured in order that
future growth may be predicted. This may be done ‘either by pro-
jecting the growth of a past period into the future on the specific trees
or stands measured, or by the method of comparing the growth on
trees or stands which have reached a certain size or age, with younger °
or smaller trees which are assumed to grow at a like rate. These
principles must be applied in utilizing the growth of trees for determin-
ing that of stands.
Since diameter, not age, is now the basis of the growth study, trees
are classified for growth on the basis of their present diameters at
B.H. and an average rate is determined for each class. The result of
such a study is applied to trees of given diameter classes in the stand
or forest. By the method of comparison, a tree now 15 inches in
diameter which has grown 1 inch in the last 8 years, was 14 inches
D.B.H. 8 years ago, and trees now 14 inches D.B.H. if compared with
this growth, will presumably grow at like rate for 8 years.
This requires current growth to be measured by inches of diameter,
or half-inches of radius, and not by decades or periods, in order that
the basis of comparison, D.B.H. classes in the past, may be obtained.
The rings in successive half-inches of radius are counted and averaged,
by diameter classes, in the following form:
TABLE LIV
CurRENT GROWTH OF SprucE, ADIRONDACKS REGION, NEw YORK
Present Number of rings! Diameter to
diameter. in last inch cf | which applied.
Inches diameter Inches
5 6.5 4
6 5.0 5
Uf 5.3 6
8 6.6 7
9 5.4 8
10 5. 1 9
PROJECTION OF GROWTH BY DIAMETER CLASSES 361
By plotting the values in column 2 on the basis of diameter, a curve
may be drawn to even out the irregularities shown. To apply such
a table in predicting growth for a period of 20 years, for 4-inch trees,
the growth of successive inch classes is used; e.g., the 4-inch tree takes
6.5 years to reach 5 inches, 5 years to reach 6 inches, and 5.3 years to
reach 7 inches, or a total of 16.8 years. The next inch requires 6.6
years, 3.2 of which lie in the 20-year period, equivalent to about 4-inch.
The tree will grow to be 73 inches in diameter in 20 years. In this
way the growth for each D.B.H. class can be predicted for any given
period on the assumption that the basis of comparison is trustworthy.
This is the simplest method of growth prediction for trees in many-
aged forests. In obtaining the average number of years in the last
inch, all trees included in the table must be measured for the same
period, i.e., the baszs must be $-inch of radius. If instead the last
20 years is measured, divided into half-inches of radius, and a fast-
growing tree used in the table as the equivalent of several smaller inch
classes, its influence on the average will be increased in like proportion
and too rapid an average rate obtained.
Where trees are measured for a past decade or fixed period of years,
the results are expressed as growth in inches for the period. This rate
of growth may then be reduced to mean periodic growth (average
growth per year for the period). Dividing 1 inch by this annual
growth gives the number of years required to grow an inch
in diameter for each inch class. This method is equally reliable, and
most tables of current diameter growth have been derived in this
manner.
The assumption underlying the basis of comparison, namely, that
the rate of diameter growth is a function of diameter, is most nearly
approximated in many-aged forests of tolerant species such as spruce
and for averages which include a wide range of ages and condi-
tions.
279. Method Based on Projection of Growth by Diameter Classes.
For single stands or specific conditions, growth for trees of the same
diameter varies tremendously (§ 274 and § 275) and shows its greatest
diversity, first in even-aged stands, second, between open-grown and
shaded trees. For such problems, prediction based on past growth
of the present trees, rather than comparison, is a more reliable
method.
For this purpose, past current growth is measured for the last 5- or
10-year period, or for two to four such periods, as required. If it is
assumed that future diameter growth will equal past growth, the growth
is tabulated as follows;
362 GROWTH OF TREES IN DIAMETER
TABLE LV
SHORT-LEAF PINE, LOUISIANA
Growth by Diameter Classes
Growth in ||
Be basl 10 Years.
Inches Inches
10 1.03
ib 1.60
12 1.36
13 1.44
14 1.67
15 152
| Growth in
Ph eal 10 Years.
Inches Inches
16 1.76
17 Ree aly
18 1.84
19 1.78
20 2.05
|
vt
Diameter, Inches
nae
Wa
Past Period
0 10
Fic. 75.— Method of predicting
future growth of trees of differ-
ent diameter classes based on past
growth in diameter and harmon-
ized curves. Loblolly pine, La.
20
0
Years
These values can be evened off
as described for Table LIV (p. 360).
This assumption of unchanging
future diameter growth is a make-
shift, inaccurate under most con-
ditions and not as reliable as the
method of comparison. But by
measuring the growth for two or
three periods, which for the pur-
pose are preferably shortened to
5 years so as to bring out any
recent tendencies of current growth,
the past growth of trees of each
diameter class may be used to pre-
dict future growth by means of a
curve drawn through these past
points (Fig. 75).
The original data, and the re-
sultant prediction of growth are
shown in Table LVI.
The advantages of this method
show most distinctly with even-
aged stands, in which case the
flattening out or termination of
the curve of the lowest diameter
classes occurs successively, and in-
dicates the death of these smaller
trees by suppression.
INCREASED GROWTH. METHOD OF DETERMINATION 363
TABLE LVI
CurrENT GrowtTH, LospLoLtty Prine, BY DIAMETERS
GROWTH IN Past GROWTH IN Furure
D.B.H.
10 Years. 20 Years. 10 Years. 20 Years.
Inches Inches Inches Inches Inches
10 0.76 2.26 Ors
11 .76 224 eo
12 Bh 2.19 A 0.6
13 1.00 2.50 35 8
14 .82 2.40 6 1.0
15 .80 2.90 5U 1.0
16 .76 1 aes Hi itl
17/ 122; Bay nll iL
18 aa MPR sf 1
19 1.88 Pe Cl 6 teal
20 adits 1.83 6 1.0
280. Increased Growth. Method of Determination. The effect on
diameter growth of trees of releasing their crowns by removal of a portion
of the stand in logging cannot be predicted accurately on stands pre-
vious to cutting. The release of additional supplies of soil moisture
and fertility, increased light and other favorable influences, is not deter-
minative. The ability of the tree to take advantage of these favorable
circumstances varies with the age and vigor of the individual crown.
When trees have passed a certain relative age and have become over-
mature, they no longer respond as vigorously, and some species make
no response at all, while others, such as lodgepole pine, seem to retain
the power of increasing their growth throughout their life. Some trees
are not released in partial cuttings; hence increased growth cannot
be expected except on those trees which are benefited and have the
power of response.
The factor of increased growth after cutting must therefore be meas-
ured by studying trees growing on tracts which have been cut over at
some previous period coinciding in length with the period for which
the prediction of growth is desired. This may be 10, 20 or 30 years.
Increase in growth due to cutting tends to disappear as the stand
adjusts itself to the new conditions and closes its crown canopy. The
competition of different species in a mixed stand and their ability to
occupy space released by cutting, determines which of these species
will benefit in form of increased growth.
364 GROWTH OF TREES IN DIAMETER
In order to predict growth of trees for any given set of conditions
from a study of diameter growth of existing trees, it is necessary to select
trees whose conditions of growth, for the past period measured, coincide
as closely as possible with the conditions of site, density of stand and
crown spread of the trees whose growth is to be predicted. Only in
this way can the excessive variability of diameter growth be averaged
on a useful and accurate basis.
Probably the greatest utility of the study of diameter growth is as
an indication of the possibilities of management. Its direct relation
to the crown, and its dependence on growing space make it an index
of the results of thinning, spacing in plantations, and selection of trees
for removal in mature stands. Maintenance of diameter growth
throughout the life of a stand is the proof of successful intensive manage-
ment. Since the rotation, or period requ-red to grow timber, is indi-
cated in part by the sizes or diameters of the trees which permits of
their use for given products, the rate of diameter growth in unthinned
versus thinned stands gives a direct indication of this rotation period,
and is so used.
REFERENCES
Some Suggestions for Predicting Growth for Short Periods, J. C. Stetson, Forestry
Quarterly, Vol. VIII, 1910, p. 326.
Accelerated Growth of Balsam Fir in the Adirondacks, E. E. McCarthy, Journal of
Forestry, Vol. XVI, 1918, p. 304.
Method of Taking Impressions of. Year Rings in Conifers, L. S. Higgs, Forestry
Quarterly, Vol. X, 1912, p. 1.
Notes on Balsam Fir, Barrington Moore and R. L. Rogers, Forestry Quarterly, Vol.
V, 1907, p. 41.
Accelerated Growth of Spruce after Cutting, in the Adirondacks, John Bentley Jr.,
A. B. Recknagel, Journal of Forestry, Vol. XV, 1917, p. 896.
Notes on a Method of Studying Current Growth Percent, B. A. Chandler, Forestry
Quarterly, Vol. XIV, 1916, p. 458.
CHAPTER’ XXV
GROWTH OF TREES IN HEIGHT
281. Purposes of Study of Height Growth. The rate of height
growth in trees is desired in order to determine the relative ability of
different species in a mixed stand to survive and dominate their com-
petitors. Height growth is the factor which largely determines the
future composition of mixed even-aged stands. A condition of sup-
pression is indicated by the diminution of height growth. Trees capable
of living under suppression have the power of maintaining a much
reduced height growth for a long period and of afterwards recovering
and increasing this rate. In the second place, data on height growth
are desired to determine the quality of site as a basis for classifying plots
in the study of yields per acre for yield tables. The relative heights
based on age which are attained by trees and stands are a close indica-
tion of the site quality, even superior to volume production as a reliable
index of site. Finally, height growth is desired as a step in the deter-
mination of the growth of trees in volume whenever the latter data are
required.
282. Influences Affecting Height Growth. Species. The juvenile
period following germination (§ 257) is followed by a period of rapid
height growth which is maintained until the tree has reached from
two-thirds to three-fourths of its total maximum height. This period
is coincident with the rapid reduction of numbers in an age class and
with the expansion of the crowns and the elimination by suppression
of those trees which are unable to maintain their position and crown
spread in the stand through being overtopped.
_ The third period is marked by increasing slowness and finally by
practical cessation of height growth and a marked change in form of
crown. In some hardwoods this is the result of division of the main
stem into several branches, and in conifers it is characterized by the loss
of the habit of producing annual whorls of branches. This habit,
however, is retained by many species such as spruce and fir. When
the power to produce annual whorls is lost, the growth in height becomes
similar to that of branches. The power of recovery of height growth,
which has been retarded or suppressed, is lost at an early age in intoler-
ant species, but with tolerant species may be retained for a long period.
365
366 GROWTH OF TREES IN HEIGHT
Unless trees can maintain a satisfactory continuous rate of height
growth individuals so stunted never attain the full height and form
of an average mature tree.
The rapidity of height growth and the total heights ultimately
attained are a specific characteristic which is retained whether the
species is growing in mixture with other species having different rates
of height growth, or in pure stands. Competition of faster growing
species does not serve to stimulate the rate of height growth of a species
to an appreciable extent. Height growth plays an important réle in
the survival, dominance and suppression of competing species.
Quality of Site. The height growth of trees and stands is directly
affected by the quality of the site, to such an extent that the rate of
growth of trees in height, and the total heights attained serve as the
most reliable index for determining differences in site qualities and
formulating a basis of classification for sites. This relation between
height growth and site quality is largely independent of one of the factors
which influence diameter growth of trees (§ 270) namely, density of
stand. Although in some species, especially hardwoods with deliques-
cent stems, total height attained is less for open-grown trees than for
crowded trees, this is not always the case and the rate of height growth
is usually retained. On the other hand, stands, especially of conifers,
which are so densely stocked as to lead to stunting and starvation,
will show a decided loss of height growth. One instance is recorded
in which a stand of lodgepole pine 70 years old containing 70,000 trees
per acre, had attained a height of but 10 feet.
The law of height growth of trees in a stand is to maintain as far
as possible an even rate of growth for all the trees in an age class or crown
canopy. There is considerable differentiation between trees with
dominant, intermediate and overtopped crowns, the individual rate
of height growth decreasing progressively with the loss of vigor and
dominance of the crown; but this differentiation is constantly dimin-
ished for the surviving trees in an age class by the death of the over-
topped trees whose rate of height growth has slowed down.
When the growth in height for stands is measured, it is gaged by
the growth of dominant or sub-dominant trees, which gives very con-
sistent results. By thus eliminating the effect of crown class, height
growth of stands becomes almost directly an expression of species and
of site quality.
Crown Class ana Suppression. The influence of shading, which
kills overtopped trees in an even-aged stand, also has a very marked
influence on height growth of trees of an age class growing under sup-
pression or in the shade of older trees. The normal rate of height
growth is checked by shade, and if it does not result in death the tree
RELATIONS OF HEIGHT GROWTH AND DIAMETER GROWTH 367
survives with so greatly reduced a rate of growth in height that this
rate is no indication of the capacity of the species nor of the quality
of the site. Normal heights, both as to growth for a current period
and total height attained at a given age, can be determined only for
trees which have grown throughout their life cycle free from suppression
or overtopping.
283. Relations of Height Growth and Diameter Growth. Although
both growth in height, and growth in diameter, are responsive to site .
quality, they follow different laws in response to density of stand and
crown class. As the result of the tendency for all trees in even-aged
stands of intolerant species either to maintain the average height growth
of the stand or to die, the relation between diameters and heights for
individual trees is not consistent. The diameter growth of dominant
trees is relatively faster than the height growth, while the height growth
of the trees in danger of being overtopped, although a little slower than
that of these dominant trees, is still relatively faster than their diam-
eter growth which falls off in proportion not to height but to spread
of crown. For this reason a dominant tree of a given height will be a
stout tree with low form quotient (§ 171) while a suppressed tree in
the same stand will be slender and cylindrical.
These relations are emphasized when trees of different stands are
compared on the basis of diameter. Dominant trees of a given
diameter will be comparatively short, while suppressed trees of this
diameter will be
tall and slender
of these trees are He one
When the ages
compared, the pee
short dominant
tree is found to
be a young tree,
compared with
the suppressed
tall tree, which is
much older.
These rela-
tions between
height and diam-
eter of stands
Height. Feet
1 Z 3
Diameter B.ff. Inches
Fra. 76.—Heights of trees based on diameter in three even-aged
and trees are stands compared with heights of dominant, intermediate and
shown in Fig. 76. suppressed trees of different diameters.
Within a given
age class, the curves indicate the somewhat slower growth in height
368 GROWTH OF TREES IN HEIGHT
of the suppressed trees, but the maintenance of nearly the average
rate for all surviving trees. But the dotted lines indicate the greater
height of suppressed trees having a given diameter, when compared
with dominant trees.
284. Measurement of Height Growth. For the juvenile period of
height growth of seedlings and saplings a practical method of measure-
ment is to determine the total
(1) Oy (GS) (A). (BY =
Rings Height Length Years to Years to age and the total height of
i f f L G yin G@ —to 7 y
SEU Aas rel SLL aN a Ee dominant trees (§ 256 and § 257).
= forilag-Beotion Trees which will not survive
70 should not be measured for
| height. For young conifers show-
ing annual whorls, the exact
height growth for each year may
be determined by measuring the
length of the whorl. This method
is used in measuring the annual
height growth of coniferous plan-
tations (§ 258).
—+ On older trees height growth
should be measured by analyzing
F
44
aa the growth of individual trees.
Total height growth for a given
= tree is obtained when its height
and total age are known, and a
composite growth curve may be
built up as suggested for seed-
lings, by obtaining these data for
a number of trees of different
ages on the same site quality,
plotting the heights on the basis
of age and drawing an average
curve of height on age. Buta
more accurate method is possible
Fia. 77.—Method of determining the when each tree has been cut into
growth in height of a tree from the :
ages of upper sections, or ring counts. several sections, the age of which
The difference in age between consecu- C40 be determined from ring
tive sections indicates the period re- counts. In this case as many
quired to grow in height from the lower points for a curve of height
to the upper section. growth are found as there are
sections cut, and these points
form a true growth curve for the tree. Diameter growth begins, at
a given section, in the year in which the tree reaches the height of this
of Seedling, 3 Years
of Tree; 70 Years
MEASUREMENT OF HEIGHT GROWTH 369
section. The number of rings shown by the section, when subtracted
from the total age of the tree (age of stump plus seedling age) gives
the years required to grow to this height. The process as shown in
Fig. 77 consists of the following steps:
1. Determine age of tree from stump plus seedling age (§ 257).
2. Count the rings at each successive upper section, and measure
length of section to get height from ground. Include
height of stump.
56
48
»
i—)
Ge
to
Height, Feet.
bo
>
16 }-
Trees averaged at fixed heights ®
40 b 70
Age, Years
Fia. 78.—Alternate methods of averaging the heights of trees, for a curve of height
based on age. Original data plotted. For curve - — -@-—- average age
at fixed heights is found. For curve — —@— — average height for each decade.
The prolonged curve is made necessary by dropping out of fast-growing
trees from the average by decades.
3. Subtract these counts successively from total age of tree, to
obtain total height growth at each section and age.
4. Subtract the age of any section from that of the one below,
to find the period required for the current growth in
height for the length of section.
This method may be simplified by first computing the height growth
curve for the portion above the stump, on all trees, and afterwards
making the average correction required for stump height and correspond-
ing age of seedling, on the final curve or table.
370 GROWTH OF TREES IN HEIGHT
Graphic Method. In averaging together the data for height growth on the basis
of age, it is evident that few if any points will fall at the same age, even if taken
at the same height above ground. For this reason, the most convenient method of
determining an average rate of height growth based on age is to plot the original
data for each tree, and draw a curve based on ocular inspection of the result assisted
by weighting the points or calculating the position of the average point if the data
are not sufficiently abundant to dispense with this step. In this graph, age is placed
on the horizontal scale and height in feet on the vertical scale.
It is not practicable to determine the arithmetical average height at each separate
age previous to plotting the data. This is best done from the graph. The height
growth of ten trees, which were sectioned at 8-foot intervals above the stump
is shown in Fig. 78. Stump height is omitted. The heights at each 8-foot section
fall on the same horizontal line, i.e., have the same ordinate. The total or final
heights represent the height of the tree.
Two methods of averaging the data are shown. By the first, all points falling
in the same decade are averaged for the points marked ©. The number of points
used is indicated at base of Fig. 78. This method is based on age, but in some decades
the same tree enters twice while in others it does not appear. The depression of the
Seca aa aeiciaig aloes ‘ curve at final decade is caused by
Ee GEES IGlscessesoeees the dropping out of eight of the ten
Sago Sao ES oes Peer oes trees from the average.
fe aoe Ievevonaae 2 Im be The second method is to aver-
L716 3th zeal 2OROOEr ct age the age at each 8-foot point.
oA t+ HE PEE EEE This average, marked @, is then
SHH Cee Ac qniaicicte based not on age but on height, but
an IGG Ree .agee is plotted on age. Since all ten trees
8-94-88 Te ieee) AH i enter this average at each of three
en ay a ne4neece aleislel points, the curve is more regular
Ae as HEE Fath cstanb—— eeeeae than the first. There is not the
Hetebt et A ip To tT same objection to interchanging the
Trpot aa ——— ST EEE basis of this curve between age and
eB ge of (Tree Baceee height as outlined above, as there
SEs is in studying diameter growth,
since the rate of height growth
has been shown to be more con-
sistently a function of age and vice
versa, for the same quality of site,
while for diameter growth two or
more additional variables influence the rate of growth (§ 296 and § 270).
The height growth, as read from the above curve, may be shown in a table based
on total age and height of tree, by adding average stump height (of 1 foot), and seed-
ling age (of 2 years) to the curve, and reading the corrected values from the pro-
longed curve, as shown in Fig. 79.
The values, read for even decades are given in Table LVII:?
Fic. 79.—Method of correcting curve of height
growth based on stump, by adding height
and age of seedling, thus giving height
growth of tree based on its total age.
1 The averaging of the above data to obtain the weighted average points may be
simplified, after the points are plotted, by the following method. For the first
decade, average heights include 7 trees, each 8 feet or points above the base of the
graph, or “up” and 1 tree 16 feet “ up” or a total of 72 points “up”; average for
8 trees, 9 points “up.” Average age includes 3 trees 4 years or points to right of
the left margin of the graph, or “over,” 2 trees 5 years “ over,” 1 tree 6 years, 1
tree 7 years and 1 tree 8 years, a total of 43 years, average 5.4 points “ over,” These
MEASUREMENT OF HEIGHT GROWTH 371
TABLE LVII
Hereut Growrs or Cuestnut Oak, Mitrorp, PrKE Co., Pa.
Basis, Ten Trees
| |
Age. Height. % Height.
Years Feet Ss Feet
2 1 40 35
10 10 50 41
20 19 60 46
30 28 70 50
|
The total height, based on total age, of these ten trees is shown by the last ten
points. It is evident that with a sufficient number of trees of all ages, a height curve
based on age could be constructed without analyzing the trees above the stump sec-
tion, but it is equally evident that such analyses, as shown in the figure, not only
multiply the weight of each tree by the number of sections taken but substitute
actual growth of given trees for composite growth by comparison of different trees.
Such a history or record of growth, whether it is of diameter, height or yields per acre,
(§ 266 and § 326), is the most reliable basis of growth data.
Current Height Growth. The current or periodic height growth
for the last decade or two may be required to complete the data for
determining the current volume growth of trees. This should be meas-
ured on felled trees by cutting back the tip until a section is found
containing the required number of rings. For determining growth
for short periods this is a simple process. Only on young trees should
the last period of growth be determined by counting back the number
of whorls from the tip In older timber and especially on pene
trees, it is impossible to secure accuracy by this method.
285. The Substitution of Curves of Average Height Based on
Diameter for Actual Measurement of Height Growth. In studies
intended to determine the volume growth of trees, especially of seed
trees and young timber left on cut-over lands, a method has been sought
data are identical with the original figures, the advantage lying in the graphic classi-
fication of the data for averaging. But for the next and subsequent decades the base,
for age, can be shifted to the right by one decade, so that the points ‘‘ over ’’ include
only the fractional decade, while for height the base can be raised to exclude that
portion of the graph which includes no points. Thus, for the third decade there are
9 points, whose weights vary from 1 to 10 years or points. For age, the basis or
zero is 20 years and the points “‘ over” are 1, 2, 3, 6, 6, 7, 8, 9 and 10, or a total of
52, average 5.8 points “ over” or 25.8 years. For height the base may be taken at
10 feet and the points “ up ” are then 6, 14, 14, 14, 22, 22, 22, 22, 30, a total of 166
points “ up,’”’ average 18.4 points up, or 28.4 feet. In plotting, where two or more
dots fall on the same point, a numeral must be written in, as indicated, to show the
weight of the point,
372 GROWTH OF TREES IN HEIGHT
by which this volume growth can be predicted by a study of diameter
growth and by the determination of the resultant volume of the tree
from its average height and volume as shown in a volume table. In
order to save the expense of determining the actual growth in height
of these trees, recourse is had to the relation between height and diam-
eter as expressed by a curve of heights based on diameter such as is
illustrated in Fig. 76. The process is as fo lows:
1. The increase in diameter for a given period for a tree of a certain
diameter is predicted or determined; e.g., the tree may grow from a
10-inch to a 12-inch diameter.
2. The average curve of height on diameter shows the heights of
a 10-inch and 12-inch tree respectively.
3. It is then erroneously assumed that the 10-inch tree will grow
in height by the amount of this difference, that is, that it will have,
when 12 inches in diameter, the height of a 12-inch tree. The fallacy
of this reasoning is clearly evident when applied to any single tree or
to any stand of a given age. If the tree or stand is young and the curve
of height on diameter has been prepared for trees of this class or age
in the vicinity, the tree will grow much faster than the difference in
height indicated by this curve, and the same is true of the trees in an
even-aged stand. But for old or mature even-aged stands, the reverse
may be true and the trees may grow more slowly than the difference
shown. Such a curve is not a growth curve at all, but a curve showing
the average heights attained by trees which may be all of the same
age. Only when the curve of height based on diameter includes trees
of all ages as well as diameters, does it approach the form of a true
growth curve, as shown by the dotted curves in Fig. 76. To do this
it must harmonize two variables, namely, diameter and age. In general,
small trees are young trees and large trees are old trees. If sufficient
data have been included, covering wide enough ranges both of diameter
and of age, and the measurements are taken on the same site quality,
a rough average is obtained in which the height of a tree of given diam-
eter is correlated with the age of tree of the same diameter. The more
nearly this general result is obtained, the more reliable will be the aver-
age results of applying this curve in predicting the growth in height
through the medium of the growth in diameter to trees or stands of all
ages, and thus avoiding a direct study of height growth. It is obvious
that for special! problems on specific classes, ages and stands of trees,
no such generalized curve should be depended upon, but a few measure-
ments of height growth on the trees in question will give results whose
accuracy justifies the expense.
The height curve of even-aged stands is determined either from the
height growth of the maximum or dominant trees in the stand, or from
REFERENCES 373
that of trees containing the average volume of the stand. It has been
found that the relation between dominant and average trees in height
growth is very consistent, and either basis furnishes an index to the
growth rate, which may be used later in classifying the plots on a basis
of site for the construction of yield tables.
On account of its uniformity for a given site qualitv, average height
growth may be determined from the analysis of from five to twenty-
five average or dominant trees with very satisfactory results.
REFERENCES
Relation between Spring Precipitation and Height Growth of Western Yellow Pine,
G. A. Pearson, Journal of Forestry, Vol. XVI, 1918, p. 677.
Relation between Height Growth of Larch Seedlings and Weather Conditions,
D. R. Brewster, Journal of Forestry, Vol. XVI, 1918, p. 861.
CHAPTER XXVI
GROWTH OF TREES IN VOLUME
286. Relation between Volume Growth, Form and Diameter Growth.
The growth of trees in volume is the product of the growth in height
and the growth in area at different portions of the stem, which is
expressed in diameter growth. The exact form of the tree and the rela-
tion between diameter and resulting area and volume growth at dif-
ferent heights from the ground are the result of mechanical laws of
resistance to stresses. The form of the tree is intended to resist wind
pressure in order to maintain its upright position and not be snapped
off or blown over. As was shown in Chapter XVI this pressure is
directly caused by the force of the winds acting on the crown and
focused in the center of area of the crown exposure ($172). Growth
in diameter will be distributed in response to this strain to give the
maximum resistance with the minimum of material.
As the form of crown and its position with respect to the bole changes,
the point of average pressure shifts and the form of the tree will be
modified by a more rapid diameter growth at the points requiring
strengthening. An increase in the stress to which the tree is exposed
will also cause changes in the distribution of growth. Trees which
have grown in a protected stand and are exposed by cutting will either
blow over or will rapidly strengthen their resistance by laying on
increased growth at the base or stump where the effect of this change
in exposure is most evident. The upper form of the tree, being influ-
enced by crown, does not change appreciably. Trees in a leaning ~
position centinually add most of the diameter growth on the under side.
Where the growth in volume of a tree on cut-over areas is Judged
from the growth in diameter on the stump, without correction, a rate
of from 50 to 100 per cent in excess of the true volume growth may be
obtained. Such measurements should therefore be taken at B.H.
where the effect of this increase is not felt, or else growth measurements
taken on the stump must be carefully compared with measurements
at upper points on the tree.
287. Tree Analysis, its Purpose and Application. The analysis of
an individual tree by the measurement of diameter growth at upper
sections, in order to determine its volume growth, is termed tree analysis,
(synonym, stem analysis, § 254). This process enables one to determine
374
SUBSTITUTION OF VOLUME TABLES FOR TREE ANALYSIS 375
the upper dimensions and volume of trees of a smaller size than those
which exist in a given stand. This is an advantage in case such
smaller sizes are lacking, but where present they may be directly meas-
ured. The volume which trees produce at given ages can thus be
obtained in one of two ways, either by measuring trees of different
ages directly for volume or by analyzing a single tree or a number of
trees in order to determine the past growth in volume. The latter
method alone will bring out the changes which take place in form, as
described above, due to altered conditions. In applying such growth
figures to answer the fundamental question of growth studies, namely,
what is the rate of growth in volume per acre, annually or for a given
period, not only must the growth of average rather than individual
trees be determined, but the relations of these average trees to the
number of trees which will survive on an acre at different ages must
also be known (§ 275). Since the recording and working up of growth
measurements to determine total volume growth is slow and expensive,
only a few trees may be taken. It is necessary that these trees have
the average form quotient for the stand to which their results will be
applied. This means either a careful selection or a chance of incurring
an error of from 10 to 15 per cent by the accidental selection of trees
which depart from this average in form.
288. Substitution of Volume Tables for Tree Analysis. The growth
of an average tree is determined by the average growth in D.B.H.,
the average height growth and the average growth in diameter at
upper sections, of which the most important is the diameter growth
at one-half of the height. The growth of upper diameters is usually
accompanied by a change in form, caused by a change in the length and
position of the crown. This is illustrated in Fig. 80 (§ 290) for
which tree both butt swelling and upper diameters increased faster
than growth at 8 feet.
Relying upon the maintenance of a consistent tree form for average
trees, a method is in common use as a substitute for the analysis of
trees to determine their volume growth. This method depends upon
the use of volume tables to determine the volume of trees whose height
and diameter are known. Since a standard volume table expresses
the actual volume of average trees much more accurately than it can
be obtained by the analysis of a few sample trees, the substitution
of a volume for the average tree taken from this table enables the investi-
gator to concentrate his effort on determining average growth in D.B.H.
and in height. The actual measurement of height growth involves
the counting of rings for determination of age of upper sections on at
least a few trees (§ 284), but dispenses with the measurement of diameter
growth on these upper sections, and requires from one-fifth to one-tenth
376 GROWTH OF TREES IN VOLUME
as many trees as are required for the study of average diameter growth
on account of the greater consistency of height growth based on age.
From a curve of growth in diameter, based on age (§ 267 and § 268),
the diameters of the average trees at different ages are determined.
From a second curve of height based on age (§284), the heights of the
same average trees for different ages are found. Since diameter and
height determine the volume as classified in these standard volume
tables, the requisite volume is interpolated from the values in the table
for the nearest 75-inch in diameter and foot in height. The successive
volumes found in this way indicate the growth laid on by the average
tree. This may be expressed in whatever unit of volume is represented
by the volume table employed. This method is almost universally
substituted for volume growth analysis wherever figures on average
volume growth of trees are desired. This method is illustrated by
Table LVII.
1The method of interpolation is illustrated as follows. The 60-year-old tree is
6.6 inches in D.B.H. and 46 feet high. The values in the standard table from
which to interpolate are, in cubic feet.
HEIGHTS
D.B.H. |
40 Feet | 50 Feet
Inches Cubic Feet
The difference for 1 inch is 1.5 cubie feet for 40-foot trees, and for .6 inch, is
.9 cubic foot, giving for 6.6 inches, 5.1 cubic feet. The average difference between
40- and 50-foot trees is .85 cubic foot. For 46-foot trees it is .6 times .85=.51 cubic
foot. Then 5.1-+.51=5.61 rounded off to 5.6 cubic feet as the interpolated volume
sought. These interpolations are more expeditiously made from graphic plotting
of the values in the volume table.
One drawback to the use of volume tables as a substitute for actual growth analy-
sis is illustrated in the attempt to measure growth at successive decades on sample
plots for scientific purposes. Even here, if a single volume table is carefully pre-
pared, combining all age classes, the transition in form from young to old trees is
blended with the volumes shown in the table for small and large trees, but where, as
for instance with Western yellow pine, separate volume tables were made for black
jack or young trees and for yellow pine or old trees which differed by about 10 per
cent in the average volume due to difference in form, the application of a different
volume table to trees passing from one age class to the other caused a jump of 10
per cent in the volume due apparently to growth, but in reality due to the irregular
distribution of this growth by separation of form classes in these tables.
MEASUREMENTS REQUIRED FOR TREE ANALYSES 377
TABLE LVIII
GrRowTH OF CHESTNUT OAK
In Cubic Volume, from Diameter and Height Growth and Use of a Standard
Age. DBH.
Years Inches
Volume Table .
Corresponding *
; volume from Periodic
ee table by growth.
interpolation.
Feet Cubic feet Cubic feet
10
19
28 it 3}
35 2.65 ee
\ 1.55
Al Ay?
} 1.40
46 5.6 | bac
50 7.0 ;
* Cubic volumes taken from Frothingham’s table for chestnut oak in Bul. 96 Forest Service,
“Second Growth Hardwoods in Connecticut.’”’ Height from Table LVII, § 284. Diameter from
growth of the same ten trees used in this table.
10 years
~
Height, feet
Le cates | Ave nOLnG
Diameter, inches
Fig. 80.—Stem analysis of a
tree 36 years old, by dec-
ades, counting in from
outer ring, based on stump.
Stump is shown below
point marked 0.
289. Measurements Required for Tree
Analyses. The data required in a tree
analysis, in addition to those taken for
volume and itemized in § 134 and § 135,
are, :
1. Age of each section (height above
stump and length given).
2. Growth on average radius from center
to outer ring, by decades.
3. Where needed, width of sap and
number of rings in sapwood.
290. Computation of Volume Growth for
Single Trees. The method of computing
the growth in volume for a given tree is
best shown by graphic illustration. Fig.
80 shows the dimensions of a chestnut oak
36 years old at the stump, and the size
which this tree had when 26, 16 and 6
years old.
To correlate the growth of upper section
for the same decades, these decades are
counted from the circumference inward, as
shown, with the odd rings at the center.
Diameter growth for each decade is then
378
GROWTH OF TREES IN VOLUME
measured from center outward. The full data for this tree analysis
are given in the following table:
TABLE LIX
Stem ANALYSIS OF A TREE
Species, Chestnut Oak.
Date, 1912.
Total Height, 40 feet.
Width Crown, 14 feet.
Tree Class, Suppressed.
Locality, Milford, Pike Co., Pa.
D.B.H., 4 inches.
Merch. Length, 20 feet.
Length Crown, 17 feet.
Height Stump, 1 foot.
Height Length | Diameter,| Width | Diameter,
above of outside bark, inside Age.
stump. section. bark. single. bark.
Feet Feet Inches Inches Inches Years
Stump 0 1 6.05 0.5 5.05 36
1 8 8 3.95 3 3.35 31
2 16 8 3.5 2 Sol 24
3 24 8 2.3 15 2.0 17
4 32 8 1.0 05 9 10
Tip, 39 7
The
Distance in inches on average radius from center to ring, by decades.
first column shows the number of years in the first fractional decade.
(1) (2) (3) (4)
(6) 0.5 1.3 2.1 2.5
(1) 0.05 0.65 1.25 Ney A
(4) 0.25 1.05 1.55
(7) 0.55 1.0
(10) 0.45
In addition, for a group of trees analyzed, the site, density of stand,
character of trees shown, conditions of cutting or other factors whose
influence on growth is to be determined, are recorded. With diameter
at each decade for each section recorded, the total volume of the tree
and its volume at each decade in the past, e.g., for 36, 26, 16 and 6
years, is obtained by methods indicated in Chapter III, using the
Smalian or the Huber formula for cubic contents.
But one detail is lacking—the actual height which the tree had
at the above decades, in case the former tip falls between two of the
sections counted. This tip contains a very small per cent of total
volume, and for merchantable contents would be ignored. But for
accurate studies of total cubic contents the height is obtained by assum-
ing that the height growth maintained the same rate per year as shown
SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS 379
for the entire section concealing the tip; e.g., in Fig. 80 the third sec-
tion took 24—17=7 years to grow 8 feet. The tip contains 4 rings,
or 4 years’ growth. Hence its height is + of 8 feet=4.5 feet. For the
second section the period required was 31—24=7 years. The tip
has 1 ring, hence its height is 7 of 8 ft. or 1.1 ft. or
Age of tip
Length of tip= = eo anit Gace —| Length of section.
The age of any one tree will probably fall at an odd year instead
of an even decade and the age of the average tree whose volume is
calculated will fall on one of these odd years; e.g., for the chestnut
oak above analyzed which took 2 years to grow to stump height, the
table and figures above will show the age of a tree 8, 18, 28 and 38 years
in age. To find the volume of the tree at even decades, as 10, 20, 30
years instead of odd years, the volumes as determined are now plotted
on cross-section paper on which age is placed on the horizontal scale
and volume on the vertical scale. From these curves the volumes
for even decades can be read. By averaging these volumes on the
basis of age the average growth in volume is obtained for all the trees
analyzed.
291. Method of Substituting Average Growth in Form or Tapers,
for Volume. The taper measurements or diameters determined from
Fig. 80 thus enable one to ascertain the volume of the tree at different
ages expressed in any unit. In this it does not differ from taper tables
discussed in § 167 except that age is now the basis of the dimen-
sions shown.
The advantage of recording the tapers for the individual tree rather
than its separate volumes at different ages applies equally to the average
of a number of trees analyzed for volume growth. For this reason
the method of computing volumes directly for each tree has given way
entirely to the method described below by which the average tapers
or dimensions of all of the trees studied are first determined. From
the average tree thus plotted, the volumes can then be found for any
of the desired units, such as cubic feet, board feet in any given log
rule, standard ties or poles, for each age or decade. This method
reduces the work of computing volumes to a single average tree for
each tree class.
The first requirement of this method is a curve of average growth
in height based on age (§ 284). This establishes the year or age in the
life of the tree at which the diameter growth of each upper section
at a given height originates and marks the zero or origin of the curve
for this section when plotted on the age of the tree (§ 269). Second,
a separate curve of diameter growth based on age is constructed for
380 GROWTH OF TREES IN VOLUME
all sections which fall at the same height above the ground. The sum
of the age or period required for the average tree to reach this height,
plus the age or period represented by the growth of the section equals
the age of the tree regardless of the height of section. It is evident
then that the average curve of growth in diameter for any of these
sections can be plotted on a single sheet of cross section paper whose
horizontal scale represents the age of the tree and whose vertical scale
represents the diameter of any cross section. A cross section which
does not begin to grow in diameter for 17 years will diminish to zero
and the curve representing its growth will intersect the base or zero
diameter at 17 on the horizontal scale representing age of tree.
In Fig. 70 (§ 269) a curve of stump diameter based on the age of the
tree was shown as intersecting this base at the age represented by the
seedling. On this same sheet a curve representing the D.B.H. and one
showing the diameter at the top of the first 16-foot log were indicated
with their points of intersection. On a single vertical line the points
shown were the diameters of a tree of a given age and indicated the
D.B.H., D.I.B. at stump and D.I.B. at top diameter of first log for
this age. But to get a curve showing these three dimensions for trees
of different ages in the illustration given, the points were not taken
from the growth of one tree, but by the measurement of several trees
differing in age, stump diameter and corresponding D.B.H. and upper
tapers. The connection of the points for these separate trees which
differ on the basis of age, gives the curves showing the increase in the
upper diameters or tapers for trees of different ages.
The method of plotting the upper diameters showing the growth
of an average tree at the different ages of its life is identical with this
previous method, with the exception that instead of these ages being
represented by the final, present or outer dimensions of separate trees,
they include the past, interior dimensions as well, by the measurement
of past growth. Even though the growth is an average of many trees,
the method still remains the same since each decade’s growth is a com-
posite of the actual growth or internal dimensions of a number of trees.
The method of plotting the data is as follows:
1. Prepare and plot a curve of average height based on age on a
separate sheet.
2. Prepare on separate sheets, curves of average diameter growth
for all cross sections falling at each separate height, as for instance a
curve for sections falling at 8 feet, 16 feet, etc., including one for the
stump section. It is assumed that the height of seedlings based on
age has been determined and that D.B.H. has been correlated with
stump D.I.B.
3. After determining the initial or zero year for each of the curves
SUBSTITUTING AVERAGE GROWTH IN FORM OR TAPERS d81
of diameter growth, including the stump section, transfer or assemble
each of these curves on a single sheet whose zero represents the zero
year of the tree’s age.
In Fig. 81 the curve of stump growth from Table LIX is plotted
with the zero at 2
years, age of seed-
ling of stump height.
This is usually as-
sumed to be also
the origin of the
D.B-H. curve. For
the curve of diam-
eter growth at 8 feet,
the period required
to.grow) to this
height by Fig. 81,
or by interpolation
in Table LIX is 7
years plus 2 years
for seedling. The
zero is placed at 9
years. Since the eevee
first fractional dec- Fic. 81.—Diameters at 8-foot points, for an average tree
ade averaged 6 years at, different ages, or growth analysis. Chestnut Oak,
on these sections, the = Milford, Pike Co., Pa.
first diameter is plot-
ted above 9+6=15 years, and subsequent decades at 25, 35 years,
etc., as indicated by the points.
The height growth for section 3 at 16 feet took 15+2=17 years.
The first fractional decade was 6 years. The points are plotted above
23, 33, 43 vears. In this way each upper section is plotted on the sheet
representing the age of the average tree.!
To read this record for the purpose of determining the volume in
any given unit for a tree of a given age, the dimensions of a tree of the
required age fall in the vertical line intersecting this age. For instance,
a tree 40 years old will have its diameter inside bark at the 16-foot
cross section indicated in Fig. 81 as 2.4 inches. Reading upwards
as the diameter increases, the next lower cross section has a diameter
of 3.4 inches and D.B.H. is 4.8 inches. Since the height or distance
between these cross sections cannot be shown on this diagram, but
Diameter, inches
1JTn the above figure, D. B. H. outside bark exceeds D. I. B. at stump up to
about 7 inches. This frequently occurs on small thick-barked trees.
382 GROWTH OF TREES IN VOLUME
only diameter based on age, it is necessary to indicate upon the curves
the height which each curve represents.
This series of curves can be used only to determine the diameters
at the definite points, as 8, 16, 24 feet, ete., for which curves have been
drawn. It corresponds with Fig. 32 (§ 168) for taper curves. To
obtain the growth in form for the tree at intervening points, these
curves should be replotted in the form shown for a single tree, in Fig. 80.
From the average tree thus shown, the growth by decades in any
form or length of product can be directly computed, to any required
diameter limit.!
292. Substitution of Taper Tables for Tree Analyses. Just as the
above method: substitutes the form of the average tree at different
ages for the direct ealculation of the volume at these ages, so it is pos-
sible to go one step further and to substitute the entire form or taper
of trees of different diameters, heights and ages, just as was done in
Fig. 70 on the curve of stump diameter growth, for D.B.H. and top
of first log. To make this substitution, the diameter and height of
average trees are first determined for each decade in age. Second,
from a table of average tapers, the form or taper of trees of the cor-
responding diameters and heights are taken. This may be done by
interpolation in case the required diameter or height falls between
inch diameter classes or 5- to 10-foot height divisions expressed in taper
table. The tapers thus borrowed are assumed to be those of the tree
at the different ages.
This method has the same advantages and drawbacks as the sub-
stitution of the volumes from a volume table for the actual volume
of sample trees as described in § 242. The average tapers are taken
in.most instances from a much larger number of trees than could be
analyzed for form at the different decades of their growth. These
tapers therefore probably represent quite closely the average form of
the tree of these sizes and ages. On the other hand, this average, just
as for volumes, may depart from the actual average of the trees to be
measured in case the data do not coincide in origin and the trees differ
in average form quotient.
The best check upon the accuracy of substitution of taper tables
for tree analyses is to test the form quotient both of the taper tables
and of the trees desired. A considerable departure in this form quotient
indicates that the tapers do not represent the average sought.
1This method of graphic plotting of average growth in diameter at each upper
section was devised by A. J. Mlodjiansky (Measuring the Forest Crop, Bul.
No. 20, Division of Forestry, U. S. Dept. Agr., 1898). The method of assembling
all the curves on the same sheet was devised by H, 8, Graves (Forest Mensura-
tion, 1906, p. 295).
REFERENCES 383
REFERENCES
Difficulties and Errors in Stem Analysis, A. S. Williams, Forestry Quarterly, Vol. I,
1908, p. 12.
Pitch Pine in Pike Co., Pa., John Bentley, Jr., Forestry Quarterly, Vol. III, 1905,
p. 14.
Stem Analyses, John Bentley, Jr., Forestry Quarterly, Vol. XII, 1914, p. 158.
A Simplified Method of Stem Analysis, T. W. Dwight, Journal of Forestry, Vol. XV,
1917, p. 864.
Mechanical Aids in Stem Analyses, E. C. Pegg, Journal of Forestry, Vol. XVII,
1919, p. 682.
CHAPTER XXVII
FACTORS AFFECTING THE GROWTH OF STANDS
293. Enumeration of Factors Affecting Growth of Stands. The
rate of growth per acre or total volume production of stands is the result
of five classes of factors, namely, site, form, treatment, density, and
composition.
Under site are included all factors of local environment such as soil,
exposure and altitude, which influence growth (§ 294).
The term form alludes to age, and the forms of stands distinguished
in yield studies are even-aged and many-aged (§ 259).
Treatment refers to the silvicultural management of the stand,
in the form of thinnings, and protection; untreated stands are those
grown under natural conditions (§ 300).
Density means primarily the completeness of crown cover, but this
factor is also influenced by the number of trees per acre (§ 301).
Under composition, pure and mixed stands are distinguished. Pure
stands are those in which a single species comprises 80 per cent or more
of the volume. Mixed stands are those made up of two or more species,
none of which amounts to 80 per cent of the volume. Stands may be
alluded to as pure if 80 per cent or more is composed of trees of the
same genus, such as pure pine or pure oak stands.
Natural enemies such as insects and fungi, and climatic factors
such as tornadoes and ice storms reduce the density of stocking and
lower the rate of growth, thereby widening the gap between average
and fully stocked stands.
294. Site Factors, or Quality of Site. In estimating the volume
of stands, the forest type is made a distinct unit of area for the purpose
of increasing the probability of accuracy in obtaining an average stand
per acre, or in securing a curve of average height on diameter (§ 225
and § 227). In the measurement of growth and yields, not only is
the forest type also a fundamental factor, since it determines the
species and composition of the stand, whose capacity for growth under-
lies the results obtained, but these types must be further subdivided
into site classes.
The rate of growth per year or total yield for a given period for
different species depends directly upon the combination of factors
384
VOLUME GROWTH A BASIS FOR SITE QUALITIES 385
which influence this growth, chief among which are quality and depth
of soil, average moisture contents, slope and exposure, altitude and
climate. Site factors cause a variation in total possible yields of from
200 to 300 per cent. Hence for a given stand or area the yield cannot
be predicted within a reasonable degree of accuracy unless the quality
of site is taken intoaccount. This difference in yieldon good and on poor
sites is caused by the more rapid growth in height, diameter, and volume,
of the trees in the stand, when growing on more favorable sites. Fewer
trees may mature on good sites than on poor, because of the larger
sizes and crown spread attained, but the sum of their volumes will
exceed those of the trees maturing on the poorer sites. When the
period of years required to produce these yields is considered, and the
mean annual growth is computed (§ 245) it will be seen that the more
rapid growth on good sites produces éven more striking differences in
the annual rate of growth between poorer and better sites. These
differences are further increased when the value of the yield is compared
with the cost of production, so that it becomes of utmost importance
in forestry to determine, for any large area of forest land, the acreage
embraced in each of several grades or qualities of site.
295. Volume Growth a Basis for Site Qualities. Forest types some-
times show abrupt transition from one to another, corresponding to
sharp differences in soil moisture; but more often the change is gradual
and the separation of areas in each type, as made in the field, is arbitrary.
The differences in site quality within a type form an unbroken series
of gradations, which must be separated, on a purely arbitrary basis,
into a convenient number of site classes, whose average yields may
be expressed in tables. In European practice five qualities are recog-
nized when a few species occupy a wide range of conditions. In America
three qualities have so far sufficed to cover the range of a single species.
The problem of classifying site qualities is two-fold. First, the
plots whose yields are measured to determine the average rates of
growth for different sites must be separated into the predetermined
site classes. Second, some convenient means must be found to apply
this site classification to forest lands during a forest survey in order
that the total area may be subdivided on this basis for the prediction
of growth on the forest.
The most direct method of classifying plots measured for yield is
by the rate of growth per year actually produced, i.e., the total yield
based on age of the stand. This has been the basis of most of the yield
tables constructed in America, and might suffice were it not for the
four other factors which modify the yields per acre independent of site;
namely, form of stand, treatment, degree of stocking, and composition
of stand.
386 FACTORS AFFECTING THE GROWTH OF STANDS
The influence of these variable factors is tremendous, and it has
usually been considered necessary to eliminate them by constructing
yield tables for given fixed conditions only, such as for even-aged
stands, artificially grown and thinned, of normal or full stocking, and
of pure species. Where these conditions do not apply, as for instance
in mixed stands of broken density in forests of all ages, it has often
been considered impossible to determine the rate of growth per acre.
296. Height Growth a Basis for Site Qualities. A'though it may
be possible, by rigid selection, to eliminate these four variables and thus
base the site qualities upon the rate of growth or the total yield per acre
based on age, yet when it comes to reversing the process and applying
this standard of site classes to the classification of lands on a larger
area, the remaining variables are present and must be dealt with.
This problem may be summed up as follows:
1. The factors of site, such as climate, and soil, are too complicated
to be directly measured in the field as a means of site classification.
Results expressed in forest growth, rather than causes, must be used
as the indicator of site.
2. Volume as a.site indicator is incomplete without the determina-
tion of age. For most conditions the relative volume based on age
is too variable and difficult of determination to serve as a field basis
of classification of large areas.
3. Dimensions of typical dominant trees in a stand may serve as
the required indicator, since the tree unit is independent of the variables
of age, form, composition and density which affect the stand.
4. The dimensions which may serve for this purpose are diameter
and height. Of these, height alone is a reliable index of site quality
since it is affected but little by varying density or degree of stocking,
or by the treatment of the stand. Height based on age is: a more
reliable basis than volume on age for stands of varying degrees of stock-
ing, and for both wild or unmanaged forests and thinned or managed
stands. This reduces or eliminates two of the five variables, namely,
treatment, and density of stand. Height growth is retarded by shade
to a marked degree; hence in forests of all ages, and in mixed stands
of several species, height based on total age ceases to be a reliable
index, since the factor of economic age is introduced.
Total height or height at maturity remains, even in mixed stands,
a distinguishing characteristic of different site qualities. The growth
of dominant, unsuppressed trees, a few of which may be found in almost
every stand, may be ascertained in a very few tests and will hold good
for the stand or site. Thus the remaining two variables, form and
composition, may be eliminated by selection of dominant trees or fully
mature trees.
OTHER POSSIBLE BASES FOR SITE QUALITIES 387
Site qualities, whether three or five in number, must be adapted
to the range of actual yields of the species to be measured. Different
species require a different range of site factors. The conifers thrive
in soils too poor for hardwoods; hence quality I for pines may be quality
II for oaks.
The adoption of a common standard of site index for species with the
same range of soil requirements is desirable. One suggestion is to
classify the trees of the country into groups, based on their total growth
in height at a definite age. This principle is illustrated by the follow-
ing table, in which four site classes are made for each group, based
on even gradations of total height for dominant trees of the same age.
TABLE LX
STANDARDS OF SITE CLASSIFICATION BASED ON THE HEIGHT OF TREE AT 100 YEARS
Site Standard a. | Standard b. | Standard c.
Feet Feet Feet
I 110 90 70
II 90 75 60
Ill 70 60 50
IV 50 45 40
A standardization of this character serves the double purpose of
coordinating the yield tables for species of similar growth habits, and
furnishing the simplest basis for site classification during forest survey.
297. Other Possible Bases for Site Qualities. Medwiedew’s Method. A
method of site classification suggested by Medwiedew, a Russian, and applied by
Hanzlik to Douglas fir is as follows:
A site factor is calculated by the formula,
: cx
Site factor = ‘
n
when c=basal area on the average acre;
h=average height of stand;
n=age of stand.
These so-called site factors may then be grouped to represent different site
qualities, all factors falling between certain limits indicating quality I, ete. This
basis is not consistent as an indication of site, since it is nothing but the mean annual
growth of the stand in a different form. If f=form factor, then, chf=total cubic
chf s
volume, and —-=mean annual growth of stand. As mean annual growth varies
n
with age as well as site, it cannot be substituted for either volume or height as an
absolute basis of classification.
388 FACTORS AFFECTING THE GROWTH OF STANDS
A still more impracticable plan is to base site factors on the current annual
growth of a stand.
298. The Form of Stands. Even-aged versus Many-aged. There
is an essential difference in the character of even-aged stands and those
composed of all ages on the same area, and this difference constitutes
one of the greatest difficulties in determining the rate of growth or yields.
It has been shown (§ 274) that the competition between individual trees
made necessary by the expansion of their crowns and growing space
occurs In an even-aged stand between trees of the same age class. Except
around the borders of this age class there can be no expansion of the
areas occupied by the total stand belonging to this age class. The
factor of area can therefore be standardized in yield tables. Since
the yield of even-aged stands is composed of the volumes of trees which
have remained dominant throughout the life of the stand, the rate of
growth of the individual trees is a maximum both in height and diameter
and the mean annual growth resulting on an acre is the maximum for
the site when measured for the period required for the growth of the
average tree from seedling to maturity.
The conditions are entirely different in many-aged stands, the dif-
ference being greatest for species which may be subjected to a long
period of suppression and yet retain the power to survive and recover.
In these stands several different age classes are brought into competi-
tion not merely with trees of their own age, but with older and younger
trees. The older trees have the advantage of the younger in appropriat-
ing space vacated by the death of veterans or by the removal of trees
for any cause. The young trees growing under partial shade are held
back in height growth, diameter growth and consequent volume growth.
The economic space occupied by the younger age classes growing under
partial shade may be defined as the actual percentage of the total grow-
ing space as represented by the available light, moisture and soil fer-
tility which is appropriated by these young trees to the exclusion of
its use by other age classes. This proportion of space so used is exceed-
ingly small and may be negligible, yet the reproduction may survive
as scattered individuals for many years. When old trees die, the space
released is not, as in the case of even-aged stands, occupied entirely
by reproduction, but is distributed among all of the trees so placed
that they may avail themselves of it by expanding their crowns. A
portion only of released space is taken by additional reproduction.
1“ Concerning Site,’’ Carlos G. Bates, Journal of Forestry, XVI, 1918, p. 383.
Not only is this basis impractical of measurement and classification in the field, but
it varies with age of the stand to a much greater degree than does mean annual
growth, hence is not trustworthy as a means of separating sites, though the postulate
that the best sites are capable of yielding the largest current annual growth is per-
fectly true.
oe
THE FORM OF STANDS. EVEN-AGED VERSUS MANY-AGED 389
The result of these two factors is that the area of an age class is at first
small, its growth retarded and mortality heavy, but with advancing
age, the area or per cent of total area occupied by this class increases
until it reaches a maximum at a period when the stand is at maturity
and before the loss of veterans begins to leave holes in the canopy.
TABLE LXI
AVERAGE CROWN SPREAD OF LOBLOLLY PINE IN THE ForREST, AT VREDENBURGH,
ALA.
aye - Be MPS : tea ik ic eee
N | Diameter of Per cent of Per cent of
iat crown. mecrease in | increase in Trees per acre
Years Feet diameter | area |
oS ———— | PEE ee) | Ro ee 8
30 13.0 |
40 15.5 19 42 140
50 19.0 46 | 113 116
60 | 22.0 69 186 88
7 | 24.5 88 255 70
80 27.0 108 332 59
[_] Area occupied by Crowns
ISG Area not occupied by Crowns
Even-aged Single age-class in
stand. . Many-aged forest.
Fic. 82.—Possible expansion of area occupied by crowns of trees of a given age
class in a many-aged forest, contrasted with limited expansion possible in
crown area in an even-aged stand. Loblolly Pine, Ala. Dotted lines show
possible expansion of 7 per cent in even-aged stand. Shaded area shows pos-
sible expansion of stand of 332 per cent in many-aged forest.
On the left, in Vig. 82 an even-aged stand occupies a square area of 4 acres, 417
feet square. During its growth, crown expansion is effected by a reduction in the
number of trees from 140 at 40 years, to 59 at 80 years, with much more rapid reduc-
tion previous to 40 years. The only expansion of area possible for the age class is
around the edges of the square. The trees can extend their crowns an average of
14 feet, or 7 feet on one side, in the 50-year period (27-13 feet). This gives a final
area in square feet of 4312 or an expansion of 7 per cent.
390 FACTORS AFFECTING THE GROWTH OF STANDS
By increasing the area of the stand, this possible expansion of area becomes less.
By reducing the area, the per cent of expansion possible becomes greater, since a
greater per cent of the total number of crowns are so placed as to be able to utilize
the increased space. The maximum possible expansion occurs when there are but
59 trees per acre at 30 years, equally spaced, and unobstructed by older age classes,
in which case the area actually utilized by this age class expands 332 per cent or is
432 per cent of its original area, and the stand becomes fully stocked at 80 years.
This expansion of actual are is shown on the right, in Fig. 82.
This second process is what takes place in a forest composed of stands of many
different ages. In the case of even-aged stands, thinning or removal of trees simply
permits the remainder to grow, with no change in area for the class, and the removal
of the final crop is followed by reproduction which in turn occupies the entire original
area. But with many-aged stands, when the final crop is removed, which takes place
on any acre in several different cuttings, the area so released is reproduced only in
part. The remainder is absorbed by the crown spread of the intermediate age
classes which thus increase their total area in the manner shown by Fig. 82.
In the illustration, this stand at 30 years occupies but one-fourth of the total
area of the 4 acres. The remainder can be occupied by older timber, which in the
50-year period is removed as it matures. By assuming this 4 acres to be but a part
of a larger area, and to be distributed over the area coinciding with the distribution
of the single age class in question, the conditions of a many-aged forest are visualized.
This factor of crown expansion and competition between different age classes is the
basis of the differences between the increment of many-aged and even-aged stands.
It explains suppression, economic age, and increased growth after cutting. The
actual amount of expansion and rate of increase due to this factor will be consider-
ably less in all instances than the per cents given in table LXI since only a portion
of the maximum space required by each tree of the class for expansion is available
at all, and but a part of this can be taken from other age classes. Summed up,
this factor represents an additional rate of increment to be added to that which an
even-aged stand of like volume would show, and caused by the fact that the volume
of the age class in the many-aged forest, while occupying only a certain per cent of
the area of the forest, is thereby distributed over a much larger area into which its
crowns can expand.
299. Annual Increment of Many-aged Stands. The rate of growth
per year based on a unit of area for many-aged forests does not repre-
sent production of a single age class, but of the sum of all the age classes
on the area, averaged for a long period. If desired for a single age
class, this rate or yield per acre should not be based on the area occupied
by the timber at maturity divided by the total ages of the trees com-
posing this stand, for this would greatly under-estimate the rate of
mean annual growth. The error can be expressed and corrected in
one of three ways: (1) either the age used as a divisor must be shortened
to represent the economic age of dominant trees growing in even-aged
stands, or (2) the area occupied by the mature crop must be reduced
to represent the average area for the stand during its life, which is
practically impossible, or (3) to the yield for the period represented
by the total life of the trees in the stand as actually shown by ring
counts, must be added the additional yields from other crops of timber
THE EFFECT OF TREATMENT ON GROWTH 391
which this same area produced during the period when the final crop
was only occupying a portion of it. The latter problem may be illus-
trated best by the yield or rate of growth per year of stands which
have come up to spruce following poplar or white birch on a_ burn.
In the period required to produce a mature crop of spruce, a crop
of poplar and birch has also been produced. The mean annual growth
for the whole period must include the total yield of both species.
Owing to the difficulty of adjusting these yields on one of these
three bases, it is customary to employ a substitute method of determin-
ing the rate of growth, not for the total period by any of these adjust-
ments, but for a partial period, measuring the current periodic growth
based upon trees or stands which have already reached a given diameter
or average age. This will be discussed in Chapter XXXI._ Its effect.
is to eliminate most of the uncertainty attending the adjustment of
the factor of competition in many-aged stands, but it introduces the
question as to whether the current growth measured represents the
true mean or average for the site over a complete period of crop pro-
duction.
300. The Effect of Treatment on Growth. The fact that the growth
of individual trees demands expansion of their crowns influences
not merely the yield per acre which may be attained, but more especi-
ally the dimensions of the individual trees in the stand. Since the
production of lumber and of certain piece products and the value of
products grown on a given acre depend much more largely upon dimen-
sions and sizes and upon quality than upon total cubic volume, yields
attained in board feet are profoundly influenced by the number of trees
brought to maturity in stands of equal degrees of crown density or
stocking. It has been commonly assumed that a normal or fully
stocked stand simply meant one which showed a complete crown density
throughout its life regardless or independent of the number of trees
which composed it. This conception neglects the fundamental idea
of the tree as an individual. Stands which are fully stocked when
young, so that crown density is early established, usually become over-
stocked almost immediately. The normal number of trees, to attain
best results or highest yields, is least on good sites with strong growing
species, rapid height growth and correspondingly rapid diameter growth,
and increases as the sites become poorer. The danger of over-stocking
and stagnation of both height and diameter growth increases with
poor sites, even-aged stands, and tendency to abundant reproduction.
These natural tendencies are affected tremendously by artificial control.
All operations such as planting, in which the initial spacing is fixed,
and subsequent thinning by which the resultant number of trees per
acre at each decade is determined, have a direct effect upon the diam-
392 FACTORS AFFECTING THE GROWTH OF STANDS
eter growth of the remaining stand, which in stands continually under
management may be maintained at an almost constant rate until
the maturity of the stand.
It has been found that in stands originally stocked with only part
of the normal number of trees for smaller ages, as the age of such stands
advances and the number of trees required in a stand of maximum or
normal density decreases, the poorly stocked stand tends to approach
and to equal the yield per acre of the stand which has been normally
stocked throughout its life. There is therefore a universal tendency
under natural conditions for stands to approach a full crown cover as
well as for the more densely stocked stands to become over-stocked.
This tendency must be recognized in dealing with density factors or
per cents in prediction of yield and forms a conservative factor in the
prediction of growth for partly stocked empirical or average stands.
Ideal conditions for growth are found in stands which have been main-
tained at a normal number of trees per acre as well as a normal crown
density through repeated thinnings. Not only is the total volume
produced per acre and the rate of growth greatly increased by a proper
balance between thinnings and the remaining stand, but the maturity
of the stand is hastened and its rotation may be reduced if desired.
301. Density of Stocking as Affecting Growth and Yields. In
spite of the tendency of natural stands to approach normal density of
stocking through the expansion of their crowns, the attamment of
normality or full stocking under natural conditions of growth is seriously
interfered with by many agencies. Natural spacing or stocking is
largely. a matter of chance and fails over extensive areas. Much of
the reproduction may be destroyed during these early years by grazing,
fires, frost or drought. Saplings and poles may be further destroyed
by fire, insects and disease. Later on, insects, disease, fire and wind
continue to make gaps in the age class and crown density. Most of
these detrimental factors are reduced under protection and the average
density greatly improved, yet forests covering wide areas ordinarily
can not be brought to a perfect or full condition of crown cover or stock-
ing, no matter how intensive the care which is bestowed upon them.
The yields of forests are desired on the basis of their actual average
production and not upon the small per cent of stands showing maximum
or perfect conditions of density and numbers per acre. This gives
rise to the problem of applying tables of yield to these conditions, first
as to the selection of areas or plots for the measurement of yields, and
second, as to whether the area so selected shall be an average of all
conditions of stocking within the site class or shall make no attempt
to attain this empirical average.
It has been generally accepted that the best method of obtaining
COMPOSITION OF STANDS AS TO SPECIES 393
yields is to select plots which show a fairly complete crown density,
not seriously reduced by avoidable factors of damage, and to con-
struct the table of yields entirely from such plots. This is supposed
to give the normal relation between yields at different ages for well-
stocked stands. There remain many variable factors, the chief of
which is the number of trees per acre in the plots measured. It has
been suggested that the age or ages at which the final yield is to be
harvested shall be taken to indicate the normal number of trees per
acre and that stands of lesser age having this number or more trees,
while not showing the full yield for these ages may be regarded as fully
stocked, if not to be cut until the final age. The only difference between
such stands and stands which remain fully stocked would be found in
the thinnings in the interval and in the quality and limbiness of the
timber.!
Yield tables based on a given standard such as described may be
discounted to predict the average degree of stocking for average areas,
which are known as empirical yields. In some instances efforts have
been made, by collecting data on large areas, to obtain these empirical
yields or averages directly in the field instead of by discount from
yield tables. In either one or the other of these forms, the empirical
or actual average is the final result desired, and the normal or standard
yield table is but the means to this end. The arguments in favor of
obtaining a normal or standard yield table by the selection of plots
are that the variables represented in the average or empirical stocking
by differences in form or mixed ages, differences in density and dif-
ferences in composition of the forest, are eliminated from the table,
which is confined to showing differences in yield based on site qualities
and age. The relations of more than two variables can not be accu-
rately set forth in a single table.
302. Composition of Stands as to Species. Stands composed of
a mixture of species may vary in yield from pure stands. Species may
differ considerably in their capacity for growth and yields even on the
same site. They vary in height growth and consequently are affected
differently by the factor of suppression when in mixed stands. The
rate of survival and the dimensions vary so that the composition of
the stand changes with its growth. Finally, the original composition,
independent of these later changes, varies greatly. For these reasons the
prediction of yields in stands of mixed species has always been regarded
as extremely difficult. Approximate rather.than accurate results must
be accepted. Recent investigations indicate that for certain character-
istic types and mixtures of species naturally growing together, yields
1The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am.
Foresters, Vol. IX, No. 2, p. 177.
394 FACTORS AFFECTING THE GROWTH OF STANDS
determined for the mixed stands do not differ very widely from those
of pure stands (§ 314).
REFERENCES
Universal Yield Tables, Fricke (Based on height classes); Review Forestry
Quarterly, Vol. XII, 1914, p. 629.
Classifying Forest Sites by Height Growth, E. H. Frothingham; Journal of Forestry,
Vol. XTX, 1921, p. 374.
A Generalized Yield Table for Even-aged Well-stocked Stands of Southern Upland
Hardwoods, W. D. Sterrett, Journal of Forestry, Vol. XIX, 1921, p. 382.
Concerning Site, F. Roth, Forestry Quarterly, Vol. XIV, 1916, p. 3.
Site Determination and Yield Forecasts in the Southern Appalachians, E. H. Froth-
ingham, Journal of Forestry, Vol. XIX, 1921, p. 14.
CHAPTER XXVIII
NORMAL YIELD TABLES FOR EVEN-AGED STANDS
303. Definition and Purposes of Yield Tables. A yield table is
intended to show the yields per acre which can be expected from stands
of timber at given ages or for given periods, in terms of a given unit
of volume or of product.
A complete yield table will show yields for successive decades
or five-year periods covering the range of age of a species. Ordinarily,
yield tables do not show the loss in yields per acre during the decadent
period in over-mature stands, but they can be constructed so as to do
so. In forests under management, the maximum ages shown are those
of the oldest stands before cutting.
Yield tables are used primarily to predict the yield of existing
stands, hence they are assumed to represent the actual development
of individual or typical stands throughout their life cycle. This they
do not always do, since naturally stocked areas tend constantly to pass
from a condition of under-stocking to one of over-stocking. It follows
that the most reliable yield tables are those constructed for stands
grown under management, where thinnings have controlled the incre-
ment.
Yield tables are the fundamental data required for the determination
of the value of forest lands and the profits of forestry, the appraisal
of damages to forest property, the choice of a rotation or average age
at which timber should be cut, the advisability of thinnings, the choice
of species, and the relative profit from expenditures for all forestry
operations on different sites. An accurate or even an approximate
knowledge of yields per acre and the average rate of growth per year
tends to place forestry on a business basis rather than one of blind
speculation.
304. Standards for Yield Tables. Yield tables undertake to set
standards in which the variables affecting yield are eliminated. The
basis of all yield tables is a separation into site qualities, with separate
average yields for each quality, since the fundamental variable is site
quality.
Form of stand requires separate yield tables for even-aged stands,
and many-aged stands (§ 252).
395
396 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
The factor of density of stocking (§ 273) separates yield tables into
Normal or Index tables which are based on an average full or maximum
stocking, and Empirical tables, which represent the actual average
density of stocking on a given area including partially stocked and
unstocked portions.
Composition of the forest is distinguished by constructing tables
for pure stands (§ 314) separately from mixed stands.
The most important distinction is probably that made between
natural stands and those grown under management. Owing to the
great influence of treatment upon growth and yields, the standard
of normality (see above) is entirely different for natural and for arti-
ficially grown stands, and yield tables based on the yields of planted,
thinned and managed forests must be made to replace the present
normal yield tables, when the material for such measurements becomes
available in sufficient quantity to furnish a proper basis.
Normal or index yield tables serve their chief purpose as a standard
of comparison, since most stands will produce either larger or smaller
yields than those shown (§ 250). This function is better served if
the standard of normality set by the table is not abnormally high,
but is made to conform to the results possible of attainment on the
average acre of the site class, with reasonably thorough protection from
destructive agencies and reasonably full stocking.
305. Construction of Yield Tables, Baur’s Method. There are two
methods possible in the preparation of yield tables. The first, known
as Baur’s method ! is based on the measurement of the present volume
and age of numerous plots which are then classified as to site and age
and form the basis of curves of average yields based on age for from
three to four site classes. This method corresponds with the defini-
tion of a yield table cited in § 249 since it does not pretend to trace
the past history of these individual stands; yet the use to which such
a table is put is to predict from these average curves the growth of a
given stand by decades. For original stands under natural conditions,
this method is universally used. The second method is to re-measure
established plots at stated intervals to determine the volume of growth,
diminution in number of trees per acre and other changes in the stand.
While more accurate, the collection of such data must await the growth
of the timber and the method is best applied to stands under manage-
ment.
Yield tables can be constructed by Baur’s method on the basis of
from 50 to 200 plots dependent on the range of site qualities and condi-
tions of growth. The aim is usually to get at least 100 plots.
1 Die Holzmesskunde, Franz Baur, Professor of Forestry, University of Munich,
Bavaria, 1891.
STANDARD FOR “NORMAL” DENSITY OF STOCKING 397
306. Standard for ‘‘ Normal’? Density of Stocking. In selecting
plots for a yield table, in natural stands, it is neither possible nor advis-
able to seek areas which show the maximum theoretical density of
stocking, either as to crown canopy or number of stems per acre. Nor
should any effort be made to select plots which represent the empirical
average of stocking. The standard should be to exclude from the plots
all larger blanks caused by destructive agencies or failure of stocking
and to select areas reasonably well stocked, with comparatively complete
crown canopy. ‘This standard of selection should be such that a suf-
ficient number of plots can be readily obtained from the larger areas,
without refinements either in size or in location. If too high a standard
is set, the plots conforming to this standard will be found to be either
located exclusively on the better portions of each site, or the area of
the plots'will be too small for safe results. In natural stands this ten-
dency will lead to the selection of plots containing too great a number
of trees, which will result later in over-stocking.
The average yield obtained from plots selected on this basis is
termed the normal yield, though it may be exceeded by the best plots,
or by stands grown under management.
307. Age Classes. ‘The area of a plot should include but one age
class. Where stands are actually even-aged over considerable areas,
plots are easily and rapidly located. Where there is difficulty in dis-
tinguishing the age classes, and in locating areas which exclude all
trees but those belonging to the class desired, it may be necessary to
include a few scattered trees of a different age class in order to obtain
plots of a suitable size. The net area of the plot can then be found
by deducting the space occupied by these trees, which can be based
on the area covered by their crown spread, modified in open stands
to include a proper proportion of the gaps in the crown cover.
Stands whose period of reproduction is from ten to thirty years,
depending on site and climatic factors, but which may still be classed
as.even-aged stands (§ 259) will be measured as such and their average
age determined.
308. Area of Plots. The value of a single plot in indicating normal
yield increases with its size, within the limit which permits of securing
a uniform stocking and crown cover conforming with the standard
sought. Since one plot represents but a single age and one shade of
site quality, and the cost of measurement increases with size, it is better
to limit the size of plots for a yield table and obtain a greater number
more widely distributed.
The size of plots should increase with the size and age of the trees
to be measured. The greatest danger in measuring small plots is
failure to coordinate the quantitative site factors utilized in producing
398 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
the yield with the area measured. This error is best illustrated by the
measurement of an isolated clump of trees with wide crown and root
spread. <A plot laid out to include their boles will have too small
an area, and an excessive yield (Fig. 83).
In dry regions especially, root spread exceeds that of crowns and
cannot be determined accurately. The effect of these errors is especially
noticeable when the size of the plots is small, the yield per acre varying
inversely with area of plots. By increasing the size of the plot, the
proportional influence of a faulty location of its boundaries is lessened,
and when coupled with care in making these boundaries inclusive of
crown space and probable root space of the trees measured, the error
is negligible. Just as for other sample plots (§ 243), it is better to
have a smaller plot surrounded by a control strip of similar timber than
to extend the
boundaries to in-
clude the whole
of a stand to be
measured, and it
is usually possi-
ble, in regions of
Lt fine pele Taree Al average rainfall,
to have such a
Fia. 83.—Relation between growing space occupied by crowns :
control strip.
or roots of. trees and size of plot measured to secure
yield per acre. The size of plots
A—Too small an area. under the above
B—Correct for humid region or site. principles will
C—Approximately correct for arid region. vary from -
acre, for dense
young stands, to 5 acres for veteran scattered timber in dry regions.
Ordinary sizes run from }$ to 2 acres. Since these boundaries
should be accurately run, plots should be square or rectangular,
and since the area contributing to the growth of single trees is
in theory a circle, rectangular plots should not be too narrow: their
short dimension should be at least four times the average width of
crowns of the trees measured. For the same reason plots should never
be triangular or have sharp angles. Unless intended for permanent
location and re-measurement, the corners of plots are marked tempora-
rily by any convenient means, and their side lines blazed or marked
so as to exclude all trees falling outside of the boundary.
309. Measurements Required on Each Plot. Dimensions of Trees.
A diameter limit is determined, dependent on minimum merchantable
sizes. All trees above this are measured at B.H. and recorded in diam-
eter classes of 1 inch or 2 inches. Since these plots are for the purpose
MEASUREMENTS REQUIRED ON EACH PLOT 399
of measuring yields they are selected in stands which have reached
merchantable sizes. Plots on which a portion only of the trees are
merchantable may require the counting of the remaining stand and its
classification as to size. Dead trees are recorded by diameter. Species
are separately tallied.
The height of trees for a yield table should be taken separately
on each plot. Several trees of different diameters, whose heights are
average for the stand should be measured and recorded together with
their diameters, the number varying with the stand, from 5 to 15.
Where merchantable and not total height is desired, the satisfactory
determination of heights for the plot is made much more difficult by
the variation in top diameters and the danger of error in judging heights.
Such a yield table, while practical, is less reliable than one based on
total heights. Total height should always be recorded regardless of
whether merchantable height is used, since it is required for a permanent
standard of site quality.
Where the merchantable height unit is used it may be better to tally
the merchantable length of every tree on the plot than to rely on a few
trees measured by the hypsometer. This introduces the element of
ocular guess.
Age and Volume of Stand. The age of each plot is separately
determined by methods discussed in Chapter XXIII. The common
method of determining the volume on the plot is by standard volume
tables, based on diameter and height. This assumes that the variation
of the trees on each plot as to shape or form quotients from the average
form for this species or region, is not sufficient to require separate
determination. Since trees must either be felled or cut into, to deter-
mine age, except when the increment borer will suffice, and since the
trees selected for this purpose would be average in volume for the stand .
or for diameter groups within it, these sample trees are sometimes used
to determine the volume of the stand. This method is useful when no
reliable volume table exists, and when cubic volume is sought. The
additional accuracy attained in measuring the volume of the sample
trees for the plot itself is offset by the possibility that the trees cut
may vary from the true average of the stand. The methods of deter-
mining the size of such sample trees for felling are described in § 241.
Crown Classes. Each tree on the plot is usually tallied in the crown
class in which it falls, as classified in § 274.
Description of Plot or Site. Since in the preparation of a yield no
effort is made to classify the plots into site qualities by inspection of
the site factors in the field, the description of the plot should be brief,
and serve merely to explain the results obtained and check their value..
The points to be covered are the following:
400 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
1. Location of plot. Region, watershed or block, section or forty.
Relocation is not contemplated from this description.
2. Density of crown cover. This has in some studies been used
in an attempt to reduce the area to a fixed standard of density; e.g.,
a stand showing .9 crown density would be considered as the equivalent
of but .9 of a full yield on the plot. The element of judgment thus
introduced is dangerous and had best be omitted.
3. Altitude:
Absolute—approximate.
Relative—with respect to nearest stream, when it affects the
quality of site.
Aspect—as affecting exposure.
Degree of slope.
Geological formation.
Soil, kind, depth, consistency and degree of moisture.
Origin of stand, whether from sprouts or from seed.
9. History of stand.
10. Condition of stand with respect to evidence of damage caused
by fire, insects, wind or other agencies should be especially noted.
11. Exposure to winds, degree and character.
12. Amount and character of tree reproduction on the ground.
13. Herbaceous and shrubby vegetation under the timber.
DO'S ee Stine
Record of Data for each plot. The data of permanent value for each
plot are,
1. ‘Area, in acres.
2. Age.
3. Total number of living trees, by species.
4. Number of living trees above merchantable diameter limit, by
species. (This may be shown for two diameter limits, as for
cordwood and saw timber units.)
5. Average diameter (from diameter of tree of average basal area,
or volume) (§ 242).
6. Height of dominant trees, or dominant height of stand; total;
merchantable.
7. Total basal area at B. H. of trees per acre, in square feet.
This is a valuable index to density of stocking.
8. Yield per acre, in cubic feet, total.
9. Yield per acre, in merchantable units, to given top diameters
and stump heights.
10. Dead standing trees, number or per cent.
- 11. Density of crown cover.
12. Description of plot.
TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 401
310. Construction of Yield Table with Site Classes Based on Height
Growth. There are two possible bases on which to separate site quality,
namely yields or rate of growth, and total height or height growth.
In choosing between these as the basis of site quality, not only must
the construction of the table be considered but also its later application
in the field. Whichever basis is used, the range of growth for a species
or region must be divided arbitrarily into site classes, once its maximum
and minimum limits are determined. When volume or yield is chosen
as the direct basis of site classes, regular and consistent results may be
obtained by eliminating most of the variables in the choice of plots.
But when these results are later used as a means of determining site
qualities in the field on the basis of mean annual rate of growth per year
or total yield based on age, the system breaks down.
On the other hand, if the division of plots into site qualities is based
on height growth as indicated in § 296 not only are the original plots
apt to be separated more accurately into their true site classes since
variations in volume due to over- or under-stocking as reflected in the
board foot or other unit are minimized, but the division of a large
area in the field into site classes for the application of the growth data
in predicting yields is made possible in striet conformity with the
standard used in the table itself (§ 345).
While volume has been made the direct basis of many European
yield tables, yet in these regulated and fully stocked stands most of
the variables are reduced to reasonable proportions. Under our con-
ditions of abnormal and accidental stocking, with the maximum of
damage to the stands during growth, the variations from the factor
of density of stocking due to variable number of trees per acre, even
in stands of full crown cover, is so great as to discourage most investi-
gators on first attempt.
The steps in the construction of a yield table based on height are
as follows:
1. On cross-section paper on which age is plotted on the horizontal
scale, and height on the vertical scale, place the average height for each
plot above the age of the stand. These heights may be the heights of
the dominant trees (§ 296). These points will fall in a comet-shaped
band increasing with age.
2. Draw a curve indicating the maximum height growth, and one
for minimum height growth as in Fig. 84.
3. Decide upon the number of site classes to use. These will depend
largely on the total range of heights found for trees of a given age, and
the possibility of convenient subdivisions not too small to be serviceable,
ie., large enough to overcome the slight variations in height based on
age which may be due to density of stand instead of site.
402 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
4. Divide the space between the maximum and minimum curves, on
each ordinate, into arbitrary spaces of equal magnitude, corresponding
to the number of site classes established, and connect the points so found
by curves.
5. The numbered plots whose height falls in each division of the
chart are assigned to the indicated site quality. Owing to variables
affecting yield, some of the plots in a lower site class may exceed the
growth of plots whose site class is better.
100
80
70
for)
o
Height, feet
3
~
o
Average height at
100 years, feet
30
20
10
10 20 30 40 50 60 70 80 90 100
Age, years
Fic. 84.—Method of separating plots into three site qualities based on the height
attained by dominant trees in the stand, plotted on age of stand. Jack Pine,
Minnesota.
The height of dominant trees on 131 plots of jack pine, plotted on
the basis of age, is shown in Fig. 84. By this method (Baur’s), the
positions of the maximum and minimum curves determine that of the
curves separating the site qualities. One or two plots with abnormally
rapid or slow growth must not be permitted to influence unduly the
position of these outer curves. With height, the true position of the
boundary curves can be found with greater certainty than if volume is
used originally as the basis of classification. In this figure, the average
heights of qualities I, Il and III at 100 years were taken as 90, 75 and
TABLE WITH SITE CLASSES BASED ON HEIGHT GROWTH 403
60 feet, following the suggestion of Roth as an example of class C in
height classification (Table LV, § 296), and with these guiding
points the curves limiting the three classes were drawn by Baur’s
method.
6. The yield of all plots in a single site class are then plotted on
cross-section paper whose base or horizontal scale is age, and whose
vertical scale is volume. From these data, a curve of average yield
Cubic Feet
Gon 80 90 100 110 120 130 140 150 160 170 180 190
Age. Years
Fic. 85—Curves of yield obtained by averaging the yields of plots whose height
growth has placed them in the same site class. The final curves smooth off
irregularities in these averages. Second growth Western Yellow Pine, California.
S. B. Show.
based on age may be drawn from which the yields for the site class
for each decade or five-year period are read. A separate curve is plotted
for each site class. The yield table finally shows the average yields
based on age for each separate site class.
404 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
When constructed on this basis, yields for different site classes
increase at a greater ratio than do the indicating heights.
In drawing the curve of yield based on age for a single site class,
it is best to first obtain the average yield for a given decade by arith-
metical means and connect these averages by straight lines. Even if
-each plot were normal, the averages at different points might fall above
or below the mean for the site as the plots happened to be on the better
or poorer portions of this site class—and to this factor, the natural vari-
ation in density or yield is added.
7. For this reason, the average curves so constructed, for each
site class, should now be assembled on a single sheet, as shown in Fig.
85. The curves of yield based on age can then be harmonized for all
site classes by the same principle as used for volume tables (§ 140).1
311. Rejection of Abnormal Plots. As shown in § 304, the intent
of this table is to establish a standard of yield, termed normal or index,
with which the yields of any existing stand may be compared. After
the separation based on height growth is effected, the yields of plots
in the same site class will show great variation, due to the
Natural range of site quality within the arbitrary boundaries
established;
Number of trees per acre in the natural stocking;
Completeness of the crown canopy.
The eccentric behavior of the averages plotted in Fig. 85 indicates the
effect of these variations in yield. The question arises as to whether
all of the plots should be included in these averages or certain plots
rejected as abnormally stocked. A method of correcting the yields
by a factor of density of crown has been generally rejected as unsatis-
factory (§ 309). The area of plots is accepted as measured. There
are, then, two possibilities of rejection; first, by ocular selection in the
field, which eliminates those plots which are incompletely stocked;
second, by further inspection of the plotted volumes based on age.
Baur’s rule for rejection of plots is quoted by Graves as follows:
“Stands which have the same age and average height are compared,
and all are considered normal whose basal area lies within a range of
15 per cent; that is, the basal area of the best and poorest stocked stands
must not differ more than 15 per cent.”’? The application of this rule
rests upon the interpretation of the term “average height.’? Where
from three to five site classes are made as in Fig. 85, and a curve of
average height is found for each site class, which would fall midway of
‘The yields shown in Fig. 85 are from an unpublished manuscript by S. B.
Show, U.S. Forest Service, California, for second growth Western yellow pine,
' ® Graves’ Forest Mensuration, p. 319,
REJECTION OF ABNORMAL PLOTS 405
the limits shown in the figure, the rule has been applied in this country
to all plots whose heights classify them with a given site. The natural
variation in volume for plots within one site class is greater than 15 per
cent, zndependent of abnormalities—hence if all plots which vary 73
per cent above or below the average volume for the site at that age are
rejected, about half of the plots, although normal, may be thrown out.
If this rule is to be correctly applied as a test of normality, the arbitrary
permitted variation of 15 per cent, 2f used at all, should first be corrected
by finding what the normal yield of the particular plot should be, based
on its actual height. If height for the plot is midway between quality
I and II, normal yield is also midway between the averages for these
qualities. The steps necessary would be as follows:
1. Draw curves of average height as shown in Fig. 84, and curves
of average volume as shown in Fig. 85.
2. Determine the per cent of variation above or below average height,
for each plot, and subtract oradd the same per cent from the volume of
the plot. This gives the corrected volume of the plot based on
average height for the site.
3. Compare the corrected volume of the plot with the average volume
for the site. If it falls above or below the calculated normal by more
than the desired per cent of error the plot can be thrown out.
4. After testing the normality of all piots, re-compute the average,
using only those plots accepted as conforming to the standard.
If 15 per cent is a proper standard of variation for forests under
management, it is probable that even with the above method this per
cent is too small as a criterion of normality for natural stands. It
should be possible, by eye, to select plots of which at least 95 per cent
will be suitable for inclusion in obtaining the average results for a stand-
ard yield table. With a range of basal area increased to 25 per cent
for plots of the same height based on age as indicated, it is probable that
only distinctly abnormal plots will be rejected.
In constructing volume tables it is not customary to reject trees
after they have been measured for volume, since rejection can take
place in the selection of the tree. With plots for yield tables, the desire
to secure a theoretically normal or uniform standard may easily lead
to too rigid a rejection of plots which are entirely suitable for the aver-
age sought. Maximum yields, on the basis of site alone, should never
be sought by these average curves of yield, since the best portions of
the site will exceed the average. Again, such tables, if made for natural
stands, should show what can reasonably be expected in stands repro-
duced naturally and not thinned, on the average acre for site. A con-
sistent average showing the probable progress of a fully or normally
stocked acre by decades, and not an abnormal maximum yield, is the
406 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
object sought both in field selection of plots and in their further sifting
in the office for the preparation of normal yield tables for natural
growth.
312. Construction of Yield Table with Site Classes Based Directly
on Yields per Acre. The main objection to the direct classification
of site on the basis of yield or volume on age by Baur’s method is the
impossibility of using this basis later as a means of classifying forest
lands into site qualities from field examination. Furthermore, yield
alone gives an unsatisfactory basis for correlating yield tables for given
species when made for different regions, or for correlating the yields
of different though similar species. It is this need of standardization
that has led to the adoption of height growth rather than volume as
the basic standard.
A further objection to the direct use of yields lies in the method of
plotting, and the testing of plots for normal density. By this method,
the volumes of all plots, based on age, are entered on the same sheet as
shown in Fig. 86. The drawing of the maximum and minimum curves
is the next step. There is no way by which the abnormality of the plots
can be first tested as with heights. So the elimination consists wholly
of drawing these boundary lines to exclude certain plots whose yield
is so much greater or smaller than the remainder that their inclusion
would unduly influence the position of these limiting curves.
The third step is to divide the space thus blocked off into equal
bands by the method used for height, i.e., by dividing the distance
on each ordinate into equal parts, and connecting the points so estab-
lished.
Finally, a curve is drawn exactly midway of each space as described
for height (§ 310), and the values are read from this curve at each decade
to form the table of yield based on age.
By this method yields increase with site quality by exact intervals.
No averages are attempted, and the result is entirely independent of
height and is influenced principally by the maximum and minimum
yields rather than the general weight of the plots studied.
Using as the basis the plots which have been classed as belonging
to each separate site by either of the above methods, curves showing
the average at different ages can also be prepared for the following
additional data:
Number of trees per acre;
Total,
Above a minimum diameter.
Average diameter.
Average height of dominant trees.
Total basal area.
YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 407
313. Yield Tables for Stands Grown under Management. Normal
yield tables for stands grown under management may be constructed
by the above methods, whenever plots are available which have been
under proper management, but may in the course of time be checked
and finally supplemented entirely if desirable by the yields of plots
which have been measured at intervals of from five to ten years.
3000
bo
ou
S
(=)
Cubic Feet
bo
(=)
So
S
H
oa
S
(=)
1000
500
10 20 30 40 50 60 70 80
Age, Ycars
Fie. 86—Curves of yield based directly on cubic volume plotted on age. Jack
Pine, Minnesota.
Where a series of plots, differing in age by ten years, is available,
the measurement a decade later on these plots will give fragments of
a curve of growth which may be pieced together. The greater the
period over which these re-measurements extend, the more nearly do
these fragmentary curves form a complete series. ,
It may be expected that yields on areas under treatment will exceed
the so-called normal yields used as a standard for natural growth.
408 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
The latter tables thus become the basis or minimum from which such
increased yields may be computed for fully stocked areas.
314. Yield Tables for Stands of Mixed Species. Practically all
stands are composed of more than one species, though some conifers
as Western yellow pine and lodgepole pine grow in practically pure
stands. So prevalent is the mixture that a stand which is composed
of 80 per cent and over in volume for the given age class of a single
species is termed a pure stand of that species. There may exist a large
number of trees in an under-story of different species, and yet the volume
of the trees of other species in the main stand may not exceed 20 per
cent.
In even-aged stands composed of two or more species in mixture,
two methods have been proposed for the determination of yields. One
is to prepare yield tables for pure stands of each species, and then to
determine the per cent of these species in the mixed stand. The further
yield of such a stand is predicted by applying the per cent thus indicated,
to each yield table, and taking the sum of the two partial yields as the
yield of the mixed stand.
In applying these tables on this basis to get yields for the future
from young stands, the question of survival may affect the result, in
“ease one species tends to crowd out another. But when stands are
even-aged, the association is apt to be of species which customarily
grow in mixture and maintain their places in the stand. The yields,
however, will be for the per cent of future, not of present mixture.
Where species differ radically in their characters, and grow in a
mixed stand, such as a hardwood species with conifers, there is apt to
be greater variation in yields, but with trees of similar habits, such
as mixed sprout hardwoods or mixtures of two or more conifers, the
stand behaves much as it would for pure stands.
For all such even-aged mixed stands, it is possible to prepare yield
tables by disregarding the per cent of mixture, or recording it merely
as a descriptive item, and proceeding as if the stand were pure.
An example! of a yield table for mixed stands of second-growth hardwoods in
New England is given below. The conclusions based on this study were, first, that
in spite of wide variation in percentages of species in mixture, for a given age, site,
and density, the volumes in board feet, cubic feet and cords were constant, and,
second, that the volumes of trees of given height and diameter in cords and cubic
feet were the same, regardless of species.
1 Bulletin of the Harvard Forest No. 1. Growth Study and Normal Yield Tables
for Second-Growth Hardwood Stands in Central New England. By J. Nelson
Spaeth, Cambridge, Mass., 1921,
YIELD TABLES FOR STANDS OF MIXED SPECIES
TABLE LXII
409
NorMau YIELD PER ACRE IN CuBic Frvt anpD Corps or BETTER SECOND-GROWTH
Harpwoop STANDS IN CenTRAL NEw ENGLAND
(All trees 2 inches in diameter and over)
SITE CLASS I
Forest
form
factor
0.582
542
.501
.503
.520
.520
.520
.520
.520
.520
.§22
.521
. 520
|
Trees Basal Height | D.B.H. | Volume | Vc!ume
per area in in | per acre. | per acre.
acre | Sq. ft. Feet | Inches Cu. ft. Cords
1250 6610.) 27.1 Sh iian os 15.80
1120 | 90.8 33.0 3.86 1625 23.71
LOMO Ma LOE: Bil) 4.41 2150 29.75
900 119.9 41.5 4.94 2628 34.96
800 130.2 45.0 5.46 3058 39.63
700 139.7 48.2 6.05 3495 44.03
610 148.0 50.7 | 6.69 3898 48.00 |
525 ISIS) 7 53.1 7 BU 4298 51.84
450 162.5 55.4 8.14 | 4677 55.50
390 169.0 57.8 8.91 , 5068 | 59.25
340 175.1 59.8 Ous2 eu 5462 62.75
300 180.9 61.9 10.51 5833 66.18
270 186.3 64.0 11.25 6200 69.50
SITE CLASS II
(All trees 2 inches in diameter and over)
Trees Basal Height | D.B.H. | Volume | Volume
per area. in in per acre. | per acre.
acre Sq. ft. Feet Inches Cue ft: | “Cords
1360 59.8 27.8 2.84 982 | 14.65
1235 77.9 31.8 3.40 1380 20.40
1125 91.1 34.8 3.86 1798 25.48
1030 101.6 37.4 4.25 2180 29 .53
940 110.3 39.8 4.66 _ 2534 33.04
855 117.9 41.5 4.94 | 2828 35.98 |
775 124.6 42.8 5.43 3118 38.55 |
700 130.7 44.2 5.85 3375 41.08 |
630 136.6 45.3 6.31 3638 43 .42
565 142.2 46.3 6.79 3895 45.61
500 147.7 47.0 7.36 4146 47.75
440 153.0 47.6 7.78 4390 49.80 |
i
Forest
The percentage of species in mixture in the stands comprising the above tables is
shown in Table LXIII,
410 NORMAL YIELD TABLES FOR EVEN-AGED STANDS
TABLE LXIII
PERCENTAGE OF THE VARIOUS SPECIES IN MIxTURE FROM TABLE LXII CLassIFIED
AS TO TYPE AND SITE CLAss
MAPLE Bircu
Better Beale Beechion EES ECs cs. Mise.*
Red nut / wood! lar | white
Red) Hard, Gray|Paper) Yel.
Qual. I 2 5 3 0 2 8 2 6 9 a 15 6
Qual. II YAO) |) Ai 6 0 8 10 7 5 3 8 14 7
Inf. Hwd. DAs |) O24 2 38 3 4 0 1 0 1 1 10
* Under miscellaneous are included all species whose combined representation in the plots of
any one type or site class is less than 5 per cent of the total number of trees. These species
are: white oak, black cherry, pignut hickory, white pine, hemlock, elm, butternut, hop horn-
beam, black birch, flowering dogwood, and shad bush.
By either of the above two methods of constructing yield tables for
mixed stands, the yield of the entire stand is taken as the standard of
yields.!
The classification of mixed stand may be greatly simplified by group-
ing together all plots in which 80 per cent or over of the merchantable
volume is made up of certain species. In a study of the mixed conifer
type on the Plumas National Forest in California, containing Western
yellow pine, sugar pine, Douglas fir, white fir, and incense cedar,
75 per cent of 156 plots were found to contain but two principal species
whose combined volume was over 80 per cent of the plot. The yields
could be grouped as
1. Yellow pine—Douglas fir.
2. Yellow pine—Fir (Douglas or white).
3. Douglas fir—white fir.
As indicating the possibilities of simplifying the problem of yields of
mixed stands, it was found in this study that the average basal areas, for
plots showing the same standard of height growth (§ 296) was as follows:
Per cents of yellow
Type : Basic plots pine—Douglas fir
type
Yellow pine—Douglas fir........... 43 100.0
Douglas fir—white fir../........... 65 97.0
Yellow pine—ir: 2h . (5 Ret 21 105.1
1A method by which the per cent of yields in plots of mixed species is recorded
on the cross section paper, and the yield per acre expressed for different species
which constitute different per cents of the total stand, is described in Graves’
Forest Mensuration, Chapter XVII, p. 332.
REFERENCES 411
This result strengths the conclusion that for species which form
part of the same crown canopy, differences in total yield, of plots with
different per cents of mixture, may not constitute a serious obstacle
to the construction of yield tables based on age.!
REFERENCES
Rate of Growth of Conifers in the British Isles. Bul. 3, Forestry Commission,
1920.
Comparison of Yields in the White Mountains and Southern Appalachians, K. W.
Woodward, Forestry Quarterly, Vol. XI, 1913, p. 503.
Hinheitliche Schatzungstafel fir Kiefer, Zeitschrift fir Forest- und Jagdwesen, June,
1914, p. 325. Review, Forestry Quarterly, Vol. XII, 1914, p. 629.
The Use of Yield Tables in Predicting Growth, E. E. Carter, Proc. Soc. Am. Foresters,
Vol. IX, 1914, p. 177.
Yields of Mixed Stands, Schwappach, Untersuchungen in Mischbestanden, Zeit-
schrift fiir Forest- und Jagdwesen, Aug., 1914, p. 472. Review, Forestry
Quarterly, Vol. XIII, 1915, p. 98.
1A Preliminary Study of Growth and Yield of Mixed Stands, 8. B. Show and
Duncan Dunning, U. S. Forest Service, San Francisco, Cal., 1921. Unpublished
manuscript.
CHAPTER XXIX
THE USE OF YIELD TABLES IN THE PREDICTION OF GROWTH
IN EVEN-AGED STANDS, WITH APPLICATION TO LARGE
AGE GROUPS
315. Factors Affecting the Probable Accuracy of Yield Predictions.
If the average yield on Quality I site for a species is taken as 100 per
cent, and but three qualities are distinguished, the relative yields shown
for Qualities IT and III may be as low as 72 and 45 per cent of that on
Quality I, respectively.!. This means gaps of 28 and 27 per cent in the
series between the points arbitrarily marked by the average curves
expressed in the yield table. The use of five qualities of site reduce
these intervals to about 15 per cent. For young stands, or areas just
growing up to timber, this is as close a prediction as can be expected.
If the site is properly classified, its future yield if normally stocked will
differ by an extreme of one-half of the above interval, either above
or below the standard. Once the site is identified by the use of average
height based on age, the future yields can be predicted by use of the
yield table, either for bare land or for partly grown young stands,
provided the degree of stocking agrees with that incorporated in the
table.
The larger part of the area of any natural forest is not comparable
with these conditions. The variables of density of stocking, form of
age classes, and composition of species must all be dealt with before
yields on any considerable area can be predicted within the desired mar-
gin of accuracy. The degree of accuracy attainable in prediction of
yields in our wild forests is not yet known even approximately since
for many-aged forests and mixed stands, yield tables based on age
have not been attempted until recently (§ 314). This much can be
said—the degree of accuracy attainable, and hence required, is greatest
for short periods, i.e., for the current growth of a decade or two, and
diminishes as the length of the period increases. But the relative
importance of accuracy also diminishes with the length of the period,
thus permitting the use of yield tables based on averages.
1 Norway Pine in the Lake States, U. 8S. Dept. Agr., 1914, Bul. 139, p. 15. ©
412
ACTUAL OR EMPIRICAL DENSITY OF STOCKING 413
316. Methods of Determining Actual or Empirical Density of
Stocking. For even-aged, pure stands, but one variable is present
in addition to site quality, that of the density of stocking. As this
variable is the result, first, of the intrusion of small areas of unstocked
land into the timbered area, which it may not pay to exclude in mapping
(§ 306) and second, of the uninterrupted play of natural agencies of
destruction operating on stands which are themselves originally the
result of chance at the time of reproduction, the problem is to arrive
at an average yield per acre which expresses not so much the capacity
of the site as the accidental product of these various conditions. This
average will in all cases be less than the standard or normal yields for
the same area, sometimes by as much as 50 per cent. Evidently the
determination of site quality is but the first step in predicting the yields
of existing stands from such a standard table, and without correction
these predictions may range from 50 to 100 per cent too high except
on small tracts, such as plantations or managed forests, whose density
factor is known to coincide closely with the yield table.
Use of Empirical Yield Tables. There are two methods of over-
coming this difficulty. The first is an attempt to arrive directly at
the average yields based on age for the larger area, or to make an empir-
ical yield table (§ 303) which will reflect the degree of stocking present.
This applies the principle used in timber estimating in determining the
volume of the average acre (§ 209). But the operation is more dif-
ficult, as it involves the separation of the entire area into stands based
on age, whose area is known, and the combining of these data into a
yield table subnormal in character and representing a purely arbitrary
percentage of standard yields. In the preparation of such a table, the
curves of yield are affected by the varying per cents of stocking of dif-
ferent age classes and areas so that practically the entire area must be
analyzed to obtain the true average, and then the table will be incorrect
in its prediction of yield for any specific age class or stand which differs
from this arbitrary average stocking. The table will be correct only
for the tract on which it is made since empirical density varies with
every forest and block. Empirical yield tables on this basis have the
same drawbacks as volume tables for defective trees which express
the net contents only (§ 151).
Use of Normal Yield Tables by Reduction. The better plan, and
the one which will probably be universally used, is to depend upon a
standard normal yield table (just as-upon a volume table for sound
trees only) and to ascertain the relation or percentage of deduction from
this table, which applies to the specific stand or larger area for which
yield is desired. For even-aged stands, the application of the yield
414 THE USE OF YIELD TABLES
table to the larger area involves the same steps for this area as are
required in the construction of the normal yield table itself, or for the
preparation of an average empirical yield table. These are as
follows:
1. Determine the volume, the area occupied, and the age of each
separate age class.
2. From these data in turn compute the volume per acre for the given
age.
3. Determine the relative density by dividing this unit volume by
the yield of an acre of the same age from the yield table; this is expressed
as a per cent of the standard yield for that age. Per cent density can
thus be found separately for each age class, or for each separate stand
if desired.
317. Application of Density Factor in Prediction of Growth from
Yield Tables. Future yield can now be predicted for all stands from
the same yield table,- by applying the reduction per cent to this table
which is required by the stand or age class in question.
Influence of Number of Trees per Acre. There is one valid objec-
tion to this assumption that relative density as expressed at a given
age in terms of volume will remain constant for future yields and that
is that under the laws of growth of stands partially stocked this stand
will tend to become fully stocked (§ 301). A knowledge of the number
of trees per acre required for full stocking at the age of cutting is also
obtained from a normal yield table, and this knowledge may be directly
applied in determining the per cent of density in immature stands,
not on the basis of crown cover existent but of the ultimate yield to
be expected from the trees which will probably survive. In the same
way, for older stands, when volume per acre is less than that in a nor-
mal stand, but the number of trees per acre is sufficient, the reduction
can be lessened as applied to these partially stocked stands as long as
the trees are so distributed as to utilize the area; e.g., in one case,
a 50 per cent average stocking may represent 100 per cent stocking on
50 per cent of the area, with the rest blank. No correction should
be made. In another case the entire area is covered with a stand whose
volume is 50 per cent of normal, but trees are well placed. In this case
the yield will probably be normal at the age at which the normal num-
ber of trees per acre drops to about the average number now present in
the natural stand.
The former or simpler method is of course extremely conservative
and allows a margin for the continuance of natural losses by fire, wind,
insects and diseases, while the latter may be applied to more intensively
managed and better protected forests.
PREDICTION OF GROWTH FROM YIELD TABLES 415
This method is illustrated below based on a standard yield table, § 314.
SECOND-GROWTH HARDWOODS IN CENTRAL NEW ENGLAND
Site Class I
PREDICTION OF
Actual | Standard YIELD 63 Per Cent
Mea lps) evita | SCE eauetion.| OY STANDARD IN
per per
acre. | acre.
10 Years. | 20 Years.
Acres | Years Cords | Cords Cords Per cent Cords Cords
1D ax|) 225 150 15 23.71 63 22 27.7
This assumes no increase in the density factor with age and is the most conserva-
tive method.
Assuming that future yield will be influenced by the number of trees and their
distribution, the future yields as shown may be increased as follows:
Number of | Normal | Reduction | Yield in Normal | Reduction | Yield in
trees | number in : per cent in|} 10 years. | number in | per cent in| 20 years.
per acre now! 10 years | 10 years Cords 20 years | 20 years Cords
eee
3 a ao 663 23.3 700 86 37.8
This basis gives the maximum possible yields to be expected by contrast to the
first method, since it does not contemplate the loss of any of the original six hundred
trees, and assumes that these trees are distributed at equally spaced intervals over
the area.
Somewhere between these two predictions the actual future yield will be found.
Use of Basal Areas. Basal area may be substituted for yields in
determining the percentage relations, and as a basis for predicting
yields in cubic feet. If in the above example the basal area at twenty-
five years is 57.2 square feet per acre, the reduction per cent is 63 and
the same prediction of future yield is obtained, which can be modified
by comparing the number of trees per acre in the same way.
These illustrations bring out the function of a yield table as dis-
tinguished from that of merely stating the yields of stands. When the
total age of any given stand is determined in addition to its volume,
the rate of growth per year for that stand can then be found, or its past
yield. But the whole purpose of a yield table is to predict the future
yields of stands. A standard yield table gives a means of predicting
this future yield, by indicating first the yield relation as to density of
416 THE USE OF YIELD TABLES
the stand in question with the standard yields, the second, the rate of
growth for future decades, which can be reduced to fit the existing
stand.
318. Separation of the Factors of Volume, Age and Area. The
difficulties surrounding the prediction of yields lie in the fact that this
requires for any stand the determination of three factors: volume, which
can always be measured; age, which can be determined for a given tree
but is difficult to find for an entire stand of mixed ages; and area, which
can be measured, provided the boundaries of the age class are known
or defined. The trouble arises entirely from the mixture of trees of dif-
ferent age classes on the same area, the overlapping of crowns and root
spread, and the shifting of total areas occupied by each separate age
class in successive periods (§ 298 and § 299). Thus two of the essential
factors, age and area lose their clear definition. These two factors
are interdependent in such forests. Age classes cannot be confined
to stands of a single age but must include an age group. The area
occupied by such a group will be influenced by the number of separate
ages included in the group.
It has been shown previously in this chapter that the area occupied
by a given age class, when determined by mapping, determines the
relative density of stands whose age is known. The yield table expresses
an arbitrary standard yield on 1 acre at a given age, representing
100 per cent density at each age. (This means that the table is accepted
as standard, but does not necessarily represent the maximum yields
possible on any acre, which may exceed this standard, by from 15 to
20 per cent.) When both area and age are determinable for a stand,
the exact relation as to density or yield when compared with the standard
can be found for each stand separately. When neither can be found
with accuracy, they must be found by such means as is possible, and the
results, while not as accurate, will be serviceable and worth attaining.
The general method of solving this problem is to work from the known
to the unknown, accepting averages and approximations when exact
determination is impossible.
319. Determination of Areas from Density Factor. One of the
simplest and most useful applications of this principle is in the deter-
mination of the area occupied by each of several age classes, whose
age and volume are known but which have not been or cannot be mapped
separately.
The total area of the tract can always be determined. If for any
reason it is impossible to map the area of each age class, these areas may
still be found by proportion if we are willing to assume that the average
density of the entire stand can be applied separately to each age class.
While admittedly less accurate than the separate determination of
DETERMINATION OF AREAS FROM DENSITY FACTOR A417
density by classes, yet the total error is probably very small. The
method is as follows:
The standard density, or 100 per cent, as expressed in the yield
table, calls for a definite volume per acre, differing with each age.
The total volume and age of each age class in the forest are known.
By dividing this volume by the standard volume on 1 acre of the
required age from the yield table, the area which would be required by
the age class if stocked at 100 per cent density is found. ‘
The sum of the areas found in this manner for all the age classes
would be the total area of the forest if the density of stocking were
100 per cent.
Since the total area actually stocked is known for this sum or total
of age classes, but not for each age class separately, it follows that,
Actual per cent of density for total area
— 100 per cent stocked
100,
Total area
and, assuming this per cent for each class,
Area 100 per cent ) 100
Hg ode fais 2
Area in each age class stocked in age class/ per cent of density
ILLUSTRATION
SECOND-GROWTH HaArRDWoops IN CENTRAL NEw ENGLAND
Yield of 1 acre from | Area of 100 per cent
Age. Volume. table. stocked.
Cords Cords Acres
20 1738 15.80 110
30 5593 29.75 188
40 3854 39.63 97
50 1008 48 .00 21
4
otal ver aie o s¥ 416 acres
Actual area 624 acres.
416 ;
Density per cent aoe which will be assumed to apply to each of the four
age classes represented.
To determine the area in each age class;
100
Ratio to fully stocked area 6627 1.5.
Do
418 THE USE OF YIELD TABLES
Age class. Area 100 per cent Actual area in age
stocked. class.
Years Acres Acres
20 110 | 165
30 188 282
40 97 145.5
50. 21 31.5
Mota ernes eo tee 416 624
This method of obtaining the area of separate age classes makes
possible the prediction of yields from yield tables based on age for
long periods with considerable accuracy, where without such separation
this would not be possible and yields could be predicted only for the
current decade or two.
320. Application to Forests Having a Group Form of Age Classes.
Forests composed of species which are intolerant and _ fire-resistant
tend to form groups of approximately even age. A yield table based
on age can be obtained for such species, which will serve as a 100 per
cent standard. But it is very difficult to separate the forest itself into
its component age classes by mapping the areas which they occupy,
and equally difficult to determine in a practical manner the average
actual age of the stand on such areas even if mapped. But the forest
can still be separated into these age classes based on area and age,
permitting the application of this yield table to predict its growth,
provided proper use is made of the laws of averages. (In timber estimat-
ing, it is permissible to employ averages known to be subject to error
because itis not practicable to attain mathematical accuracy on account
of expense.)
The problem here is,
1. To determine the trees which belong to each age class so that the
volume of the class may be found.
2. To determine the age of the age class.
3. To find its area. Given the first two of these elements, the
method of finding the third has already been shown (§ 319).
By reference to § 275 it is seen that diameter is an indicator of the
age of trees, but that a given age class will include a wide range of diam-
eters. Where stands are composed of trees of many different ages so
that it is not possible to ascertain the age of a given stand by felling
one or two trees, nor to map the separate areas in the forest which are
occupied by these age classes, the only alternative in obtaining age
is through the use of average diameters. The diameters can be meas-
VOLUME AND AREA FOR TWO AGE GROUPS 419
ured. In timber estimating, a stand table can be made giving the range
and distribution of diameters in the stand. The substitution of diam-
eters for ages thus furnishes a means of separating age classes in forests
of mixed ages.
Choice of Methods. There are tnree gradations in the possible
applications of this method.
1. Diameter is used merely to determine the age of an average tree,
but the forest is separated into actual age classes as nearly as possible,
rather than diameter classes (§321).
2. Diameter is used as the basis of separation into classes, whose
average age is then determined on the basis of these diameters (§ 323).
These, as shown (§275), are not true age classes since they do not
include all the trees of a given age.
3. Diameter is substituted altogether for age, and the total age of
trees is not determined for these classes, but current growth is predicted
merely for trees of given diameters for short periods. This method is
discussed in Chapter X XXII.
The use of diameter to indicate total age is most reliable when applied
to large areas and numbers and to forests of many age classes, for species
and stands whose actual and economic age agree, 1.e., which usually
do not show a period of suppression.
321. Determination of Volume and Area for Two Age Groups on
Basis of Average Age. While the method to be described is limited
in its application to two age groups, yet even this subdivision will be
found of great value in Mensuration and Regulation. In the French
many-aged forests, but two groups are made in timber above exploit-
able size. In our forests, when under management, the subdivision
into two groups will be equally effective.
In natural stands containing decadent timber, three groups are
needed instead of two, for timber above the minimum diameter. These
may be termed “‘ young merchantable,” ‘‘ mature ”’ and “‘ veteran.”
In the Western yellow pine stands for which this method was
developed, it was possible to separate the young merchantable timber
by the appearance of bark into a class termed “ Blackjack,” leaving
the remaining yellow pine timber for separation into mature and
veterans. In forests where this cannot be done, it is possible to first
separate the young merchantable timber on a diameter class basis,
leaving the larger mature and veteran timber for division by this method.
Where the forest is cut over, and but two age classes are required,
the method will separate the young merchantable from the mature
timber. The three steps in this method are as follows:
1. A standard yield table based on age for even-aged stands can
be made the basis of separation of the forest into two age groups. This
420 THE USE OF YIELD TABLES
yield table can be constructed by standard methods from selected plots
in the groups of which the forest is composed. From this yield table
two ages are chosen, representing respectively the younger and the
older age class. The development of the normal stand as indicated
by its current and its mean annual growth is the basis for this choice
of ages.
2. The ages thus chosen from the yield table must then be correlated
with a given diameter since it is impossible, in the forest, to determine
either the age or area of age classes directly. '
This requires a table of diameter growth on the basis of age, for the
species and site (§ 267 to § 269) based on a sufficient number of trees
to insure a reliable average. Age is the direct basis of this curve, and
not diameter (§ 275). From this table, the diameter sought is indicated,
for each of the two age classes.
3. The total volume on the area contained in the two age classes
can be separated into the volume in each age class, by means of these
two trees of average diameter, representing average age of each class.
This requires:
(a) That the average volume contained in a tree of this average
diameter be found. For this purpose, a curve of average height based on
diameter is constructed for the site (§ 209). With the height of a tree
of the required diameter thus indicated, its volume is found from the
standard volume table for the species and region.
(b) That the number of trees with this average volume be found
for each age class, which is required to make up the total volume of the
combined group. This number, multiplied by the average volume
will give the volume of each age class.
This solution is simple, when the total number of trees and their total volume
are known. Deducting a given number of trees of a given average volume from the
group leaves a residual volume, which is equivalent to a fixed number of trees of the
average volume for the remaining group; i.e., with total number, total volume, and
the average volume of each tree of two groups fixed, there can be but one solution by
which the number in each group, and consequently the sum of their volumes equals
the required or existing estimate or total in the stand.
If «=number of trees in younger group;
y =number of trees in older group;
a=volume of average younger tree;
b=volume of average older tree.
Then
x+y =total number of trees in stand, c
and
ax+by =total volume of stand, d.
If all the trees c had the volume a then instead of a total volume d,
ax-+ay =ac,
APPLICATION OF RESULTS TO FOREST 421
The difference between this volume and the total actual stand is d—ac and repre-
sents the surplus volume in the older trees, of which there are y. The difference
in volume for each tree is b —a, and for all of the older trees is (b—a)y.
Then
(b—a)y=d—ac;
and
d—ac
Yy fan b—a ’
while
r=c—y
Having the values, or number, of each group x and y, the total volume is obtained
by multiplying this number by the volume of the average tree for the group.
Illustration, Western Yellow Pine.
Total volume in group (d) =27,042,800 feet B.M.
Total number of trees (c) =44,4238.
Age of older trees, veterans, chosen as 300 years.
Age of younger trees, mature, chosen as 200 years.
Diameter, from curve of growth, veterans, 27 inches.
mature, 20.7 inches.
Volume of average tree of this size, veterans 805 feet B.M.
mature, 340 feet B.M.
Then
(1) 340xz+805y = 27,042,800 feet B.M.
(2) 3402+340y =340 c.
= 15,103,820 feet B.M.
Subtracting (2) from (1)
465y = 11,938,980 feet B.M.
y = 25,675 trees;
x=18,748 trees.
Volume of younger class = 6,374,320 feet B.M.
Volume of older class =20,668,375 feet B.M.
322. Application of Results to Forest by Use of Stand Table and
Per Cent. It is not necessary that a 100 per cent tally of the number
of trees, and total volume for the site be obtained, but only that the
stand table (§ 188) from which the determination is made be representa-
tive of the total area.
If in the timber survey, 5 per cent of the area is covered and assumed
to represent the average stand, the total count of trees on this 5 per
cent and the total estimate on the strip, give the data needed. UH,
in turn, but 10 per cent of the strip itself or 75 of 1 per cent of the total
area is tallied, and this per cent gives the run of sizes of the timber
without reference to its density of stocking, the data are still sufficient.
To obtain the separation of the total stand by means of the data
from the smaller area counted, the volume of each age class is first
expressed as a per cent of the total. These per cents are then applied
to the total estimated volume on the entire area.
422 THE USE OF YIELD TABLES
In the above case, the per cents are:
Veterans 76.4
Mature 23.6
The total stand is 2,583,940,000 feet B.M.
The stand of veterans is then 1,974,130,000 feet B.M.
and of mature is 609,810,000 feet. B.M.
To secure this division, a little over 1 per cent of the total stand was tallied and
estimated for the basic data, while the total estimate was secured by ocular means
(§ 206) (Coconino National Forest).
323. Determination of Volume and Area for Age Groups on Basis
of Diameter Groups. Where the second alternative is chosen (Method 2,
§ 320) to obtain the separation of age classes, namely, diameter rather
than age, the following changes in procedure are necessary.
1. The volume of the so-called age classes is directly obtained from
a stand table, in which the number of trees of each diameter class must
be shown.
2. The diameter of the average tree is obtained by first finding the
average volume for the group, and second, the tree of this volume
from a local volume table based solely on diameter, which is obtained
from a curve of average heights and a standard volume table. |
3. The age of a tree of this average diameter is then found, not
from the yield table as before, but from the curve of growth based on
diameter, which gives directly the ages of trees of given diameters.
The ages indicated will be those of the respective age groups into which
the forest has been separated. As indicated, this method works back
from diameters to age, while the first is based on age directly.
By either of these methods, the area in each age class may now be
found by following the precedure described in $319. The age, and
consequent normal yields for 1 acre at these ages, have been determined
for each age class. The total normally or 100 per cent stocked area
can be found, and from this the reduction per cent and the area in each
age class. From the reduction per cent an empirical yield table can
be computed, which will be used as the basis for predicting the yields
of the forest or site class as a whole (§ 250).
Since the above-described methods of determining areas of age
groups are based primarily on the factor of relative density of the stands
as determined by volume, they apply only to the age groups which
have already grown to merchantable sizes. The problem of determin-
ing the area of immature age classes is treated in § 348, and must be
considered in working out a plan for growth predictions for any large
area, in connection with the above methods.
324. The Construction of Yield Tables Based on Crown Space, for
Many-aged Stands. The above methods depend upon the construc-
tion of yield tables from plots whose average age is determined, so that
THE CONSTRUCTION OF YIELD TABLES 423
the yields are given as for even-aged stands. Since it is seldom that
any species is so distributed in age classes and so free from major sources
of damage as never to be found in stands of even age, plots based on
age can be obtained under a greater range of conditions than is commonly
admitted.
But when this method is apparently impracticable, there remains
one possibility for constructing a yield table based on age, which although
far from being accurate, is based on a fundamental law of growth of
stands. It was shown in § 274 that as trees develop, they require
increased crown space, and that this expansion of crown can be attained
only by the reduction of numbers of trees per acre.
The diameters of crowns of trees is an index of the growing space
which they require though it seldom exactly measures this space. But
if it can be shown that the space occupied by trees of different diameters
is proportional to the diameter of their crowns, the relative number
of trees per acre of different diameters which can stand on an acre
can be determined.
To obtain such data, crowns can be assumed as circular in shape,
(though the actual shape varies according to the light and growing
space available, especially in hardwoods), and that the space occupied
by each crown is in proportion to the square of its diameter or width
in feet.
Measurement of Width of Crowns. To determine the average width
of crown for trees of different diameters, two men may work together.
One stations himself behind a plumb-bob suspended from a pole so to
hang clear from a height of about 8 feet. He lines in the second man
at a point below the outer edge of the crown of the tree, whose width is
then measured on the ground to the point intersecting the opposite
edge of crown. For this purpose a pole, marked in feet, can be used.
The distance measured must be at right angles to the lines of sight. A
record is made of the D.B.H. and crown width."
Areas of Crowns. To obtain a true average of crown area, each
crown width must be squared. The sum of the areas so obtained for
each diameter class is divided by the number of trees in the class, to
get the average area of the square for that class. The square root,
or side of this square is the average width of the crown for the class.
Now, if it be assumed that the space occupied by this diameter squared
represents the actual growing space required by the tree, the number
of trees per acre for the diameter class is found by dividing the area
1 No effort need be made to obtain the area of each crown by two or more measure-
ments or by plotting the projected area of the crown. Reliance is placed on a large
number of measurements of one diameter, rapidly and accurately taken, to obtain
the true average diameter of crowns for each D.B.H. class.
424 THE USE OF YIELD TABLES
of one acre, 43,560 square feet, by this area. This method is employed
in finding the number of trees per acre required to plant an acre, if
spacing is 4, 6, 8 or 10 feet apart in both directions.
Density of Crown Cover. In actual stocking, the absolute number
of trees cannot be so simply determined. As crowns tend to adjust _
themselves to light, they depart from a circular form, and the circular
spacing itself may permit of more trees per acre than the square. The
relation of the area of an inscribed circle to a square is .7854. That
of an inscribed circle to a hexagon is .9018.
If either of these relations is consistently maintained, the total
number of trees per acre for full crown cover may differ, but the relative
number, for trees of different diameters will remain constant. From
the number so found, a curve of number of trees per acre based on diam-
eter can be plotted. This is a standard, intended to show relative,
not absolute, numbers. For instance, if the number per acre from
such a table for a given diameter is 400 trees, a stand of 200 trees per
acre of this average diameter would be 50 per cent of the standard.
Two factors interfere to prevent the satisfactory application of such
a table in predicting yields. First, the number of trees in fully stocked
stands does not always decrease in direct proportion to their increase
in crown space. In tolerant species, a great over-lapping and suppres-
sion of crowns occurs, doubling the number of trees per acre over the
theoretical number indicated by the spread of crown, while in over-
mature stands, the increasing demand for light and moisture reduces
the stand per acre below that indicated by the crowns. The relation
is therefore not consistent except within rather narrow limits of age
and species; and yields based on this assumption will be excessively
large for over-mature age classes.
The second factor tends to offset the first in stands not fully stocked—
this is the tendency (§ 301 and § 316) to improve the degree of stocking
with age. When a stand of a given age has only the number of trees
required for one twice this age, its rate of mortality will be very much
less since each tree has more than enough room to survive. Hence
the assumption, in stands not fully stocked, that the growth of a stand
can be predicted by determining the per cent which the number of
trees now in the age class bears to the normal number, will not be
borne out, but better results will be obtained.
Method of Construction of the Yield Table. In stands which
possess a full crown cover, but whose age classes are distributed in
many-aged form, the rate of mortality may be assumed to hold for
all classes. An illustration of the above method of constructing a
yield table for yellow poplar in Tennessee is given below.!
1 Based on data collected by W. W. Ashe.
METHOD OF CONSTRUCTION OF THE YIELD TABLE 425
TABLE LXIV
TREES PER ACRE BASED ON CROWN SPACE
D.B.H. Diameter of crown. |Area of crown based on Trees per acre.
1 D?.
Inches Feet Square feet Number
7 11.0 121 360
8 11.6 134 325 .
9 12.4 154 283
10 13:3 177 246
11 ee 187 233
12 14.4 207 210
13 Leal 228 191
14 15.8 249 175
15 16.5 272 160
16 Wr’ 295 148
rh 17.9 320 136
18 18.6 346 126
19 19.4 376 116
20 20.0 400 109
21 20.7 428 102
22 21.3 453 96
{
The above data must now be correlated with age. The steps are
as follows:
1. From a curve of age based on diameter, the diameters at each
five-year period are found, and the number of trees per acre, formerly
based on diameter, are then interpolated for the fractional diameters
corresponding to these exact ages.
2. From a curve of height growth based on age the height of the
average tree is found.
3. From diameter and height, the volume of each tree is taken
from a standard volume table (§ 288).
4. The yield per acre at each age is the product of the number of
trees per acre and this average volume.
The application of this method is shown in Table LXV, p. 426.
325. Application of Method to Many-aged Stands. To apply this
standard table to the many-aged forest for the prediction of yield,
the same principles are used as were described in § 316. But in this
case, the number of trees in given diameter classes is the basis of comparison
to determine the reduction per cent or density factor.
It makes no material difference whether the standard table above
illustrated exactly represents the true or actually possible normal yield
of a pure, even-aged fully stocked stand, provided it approximately
426 THE USE OF YIELD TABLES
indicates the proportional yields at different ages, correlated with the
proportional falling off in numbers of trees per acre at these ages, both
factors correlated with diameter of the average trees, for it is evident
that in such a forest no stands will be found which are pure, even-aged
or fully stocked over any large area; hence the use to which the table
is put must be solely as a standard to be discounted by a reduction per
cent.
TABLE LXV
YIELDS oF CorDWooD, FOR YELLOW PopLAR IN TENNESSEE—BASED ON CROWN
Space AND VOLUMES OF TREES OF GIVEN AGES
6 *
Age. D.B.H. Average f elms Trees Yield
| Height. | see per acre
Years Inches Feet . 160 cord feet. er acre ie d
€ eet | Cords p ong cords
40 10.5 78 0.148 237 Son
45 11.8 83 .198 214 42.6
50 13.0 87 254 191 48.5
55 14.2 91 Jaily 172 54.5
60 15.4 94 .38l 155 . 69.0
65 16.5 97 445 141 62.7
70 MZ 5 101 “lil 130 66.4
75 18.4 104 .569 121 68.8
80 19.3 107 .630 114 71.8
85 7.04 110 .693 108 74.8
90 PALO) 113 (RS 102 Te 0)
95 21.8 115 .825 97 80.0
100 22.5 17 .880 94 82.7
* From volume table 5, p. 22, Bulletin 106, Yellow Poplar in Tennessee, W. W. Ashe, State
Geological Survey of Tennessee, 1913.
The age of stands, by this method, is assumed as the age of trees
of given diameters. To determine this age, for each diameter class,
a curve of growth is required in which ages are averaged on the basis
of diameter (§ 276). Otherwise the ages of trees of the larger classes
will be over-estimated.
To apply this yield table for the prediction of yield in the forest,
a large area must be considered; otherwise the assumed correlation
between age and diameter will not hold good. The stand table (§ 188)
for this area must show the number of trees of each diameter class in
the forest.
One of the principal services rendered by such a table is its indication
of the probable rate of loss of numbers, which is a most difficult problem
to solve by any other method.
YIELD TABLES FOR STANDS GROWN UNDER MANAGEMENT 427
In applying such a table, it can be assumed that the mortality mn
the forest will be at the proportional rate indicated by the table. The
prediction of yields will then be based on a stand table giving the number
of trees in each diameter class. Several methods of applying the
standard table are possible, as
1. Base the prediction upon the total number of trees in each diam-
eter class or group. The per cent of reduction in numbers is obtained
from the table. This per cent is applied to the stand in the forest,
and the future growth obtained by computing the future volume of
the remaining trees, as shown in the illustration.
2. Base the prediction upon yields. The number of trees in each
diameter class is divided by the number per acre in the standard table.
This gives the area normally stocked by that class, from which its future
yield is taken directly from the standard yield table. This area forms,
of course, but a small per cent of the forest, and is the total area occupied
by trees of the diameter class.
The forest can be divided into age classes, based on diameter, and
the area occupied by each of these age classes obtained as described
in § 316.
At best, it can be seen that this substitution of standard yields
based on growing space per tree is a makeshift compared with determin-
ing these relations from even-aged plots in which the factors of site,
tolerance and soil at different ages are directly measured.
326. Yield Tables for Stands Grown under Management. European,
experience with stands grown under management has shown, first,
that the best results and heaviest total yields per acre are obtained
by several thinnings at frequent intervals, in which not only the trees
which would otherwise die before the next cutting are removed, but the
remaining crowns are freed from competition.
Second, that the proportion of the total yield removed as thinnings
under this system may equal one-third or more of the total yield.
Third, that the diameter growth of the surviving trees can by proper
thinnings be sustained at a uniform rate until the final crop is cut.
The development of each tree in the stand proceeds actually at the rate
of growth of a dominant tree which maintains its crown spread through-
out its life.
Even where second-growth stands have sprung up, in this country,
and reached sizes suitable for logging, they have usually received no
care in the form of thinnings. Stagnation sets in on many of these
stands, especially with conifers on old fields, and the diameter
growth of the whole stand suffers. This occurs even in plantations
on which thinnings have been neglected.
The actual yields and sizes which may be grown on such stands
428 THE USE OF YIELD TABLES
under sustained management and thinnings may be roughly approxi-
mated by measurements taken on natural stands not under management,
by the method just discussed, of computing the number of trees per acre
for given diameters. The rate of diameter growth should be that of
trees now dominant in the stand. This gives the age of the diameter
classes. The approximate amount of material yielded by thinnings in
such a forest may also be roughly predicted by noting the number of
trees which drop out of the stand at each decade, and computing their
average diameter and volume.
By establishing permanent plots, re-measured at intervals of 5
or 10 years, and properly thinned, data will finally become available
showing not merely the yield of stands grown under management, at
final cutting, but the total yield including thinnings. The absence
of such stands precludes the construction of yield tables on this basis
at present and justifies efforts to predict such yields by means of crown
spread and number of trees per acre in normal stands. The nearest
approach to such yield tables is found in tables constructed from second-
growth stands, or plantations, but it is seldom that these stands have
been repeatedly and properly thinned, hence the yields shown merely
indicate a normal possibility for fully stocked, wild stands.
REFERENCES
The Measurement of Increment on All-aged Stands, H. H. Chapman, Proce. Soc.
Am. Foresters, Vol. IX, 1914, p. 189.
Yield Table Methods of Arizona and New Mexico, T. S. Woolsey, Jr., Proc. Soc. Am.
Foresters, Vol. IX, 1914, p. 207.
Yield in Uneven-aged Stands, Barrington Moore, Proc. Soc. Am. Foresters, Vol.
IX, 1914, p, 216,
CHAPTER XXX
THE DETERMINATION OF GROWTH PER CENT
327. Definition of Growth per Cent. Growth per cent is an expres-
sion of the relation between growth and volume.
Current growth per cent is the relation of growth during a given
year to the volume at the beginning of the year.
Periodic growth per cent is the relation of the growth during a period,
to a basic volume, which may be taken as the mean or average volume
for the period (§ 328), but is usually that at the beginning of the period.
Mean annual growth per cent is the per cent which the mean annual
growth (§ 245) for a given age bears to the total volume at that age,
and represents the average rate of growth per year, at which this volume
has been produced. Growth per cent requires for its determination
a knowledge of two factors, the growth for a period and the volume
upon which this growth was laid. The primary purpose for which
growth per cent is utilized is to test the maturity or ripeness of individual
trees and of stands of timber. Those trees or stands which show the
lowest per cent of increment on their present volume compared with
other trees or stands, should be selected for cutting. The object of
such selection is to withdraw from the forest the greatest possible volume
of wood capital, while at the same time reducing the volume of expected
growth by the smallest possible amount. If carried out, the effect is
to transform the forest capital from a condition in which the ratio of
growth to volume is low, to one in which this ratio is materially increased
for the forest as a whole.
On individual trees the difference in volume or growth for the decade
may be found by analysis (§ 287 and § 288). For stands, the difference
is taken from yield tables for the decade. In each case one year’s
growth is one-tenth of the growth for a decade. The growth per cent
of average test trees is frequently assumed to be that of the stand.
328. Pressler’s Formula for Volume Growth Per Cent. To deter-
mine growth per cent as a means of judging the ripeness or maturity
of stands or trees, the same methods apply whether the unit is the tree
or the stand. Since volume growth is measured for periods of a decade,
the growth for one year is found by division. Let n equal the period
representing a decade. This may be a longer or shorter period if neces-
429
430 THE DETERMINATION OF GROWTH PER CENT
sary. Let V equal volume at present, and v equal volume n years ago.
Then growth for one year equals If it is assumed that this
growth for n years is laid on in equal annual installments, then the growth
so obtained is considered that of the current year or for any year during
the period.
If the growth per cent is obtained on this basis, the result will vary
according to the year in which the volume of the stand is taken as the
basis. If for ten years ago, then the formula is,
V-—v
) 100.
nm;
Growth per cent = (
But if the per cent is desired for the last or present year,
V-—v
Vn
For an average year midway of the period, the capital or volume is
Growth per cent = ( ) 100.
and growth per cent is
Va
ive
V+o
2
This is known as Pressler’s formula.
329. Pressler’s Formula Based on Relative Diameter. Further modifications
of this formula by Pressler are intended to reduce it to terms of diameter so that it
may be applied to measurements on standing trees taken at B.H. If height and form
factor do not change, then
( 7) 200
n= —.,
D?+d?/ n
‘In this formula D is the present D.B.H. and d is the diameter n years ago. D—d
; D D
is then designated as a and — is called the relative diameter. By making —=q,
a a
and substituting ag for D, and a(q—1) for d, he reduced the formula thus to
f= @=D?\200
~ \@+q-1?/ x
for which expressions values are computed in a table.
To use this table the present diameter D is divided by twice the width of the
rings in the period n, thus indicating the relative diameter. The values in the table
give the per cent of volume growth for the period. This is then divided by the num-
ber of years in the period to get the current annual growth per cent.
’
1 This table is given in Principles of American Forestry, Samuel B, Green, John
Wiley & Sons, N. Y., 1903, p. 178,
SCHNEIDER’S FORMULA FOR STANDING TREES 431
Further modifications of this formula are discussed in Graves’ Mensuration, pp.
306-7.
330. Schneider’s Formula for Standing Trees.. The most con-
venient formula for testing the growth per cent of standing trees is
known as Schneider’s formula, developed in 1853 by Professor Schneider,
Eberswalde. This formula is applied at B.H. and requires the deter-
mination of diameter, D, at that point, and the number of rings in the
last inch of radius, n. Then
The following description of the derivation of the formula is taken from Graves’
Mensuration, p. 308.
If n represents the number of rings in the last inch of radius at breast-height,
: eee :
then the periodic annual growth during n years is — inches. Let the present diameter
n
4 2 ;
be represented by D, then the diameter last year was D—— and the diameter at the
n
2
’ end of one year from now will be D+—.
n
2h,
f that of one year ago was
“(p ys
re ae a
The growth for the last year is then
tD*hf (v-2) iy E( 4).
4 4 n A\n yn
D
The present volume of the tree is é
The growth per cent is:
went ful 2 _*) =100: p.
4 4 nm. n*
400 400
nD n2D?
2 2
If the growth be calculated on the basis of d+ — instead of d—-, then the follow-
n n
ing formula will result:
_ 400 400
nD n2D=
The average between the two formule is taken, namely,
Inasmuch as Schneider’s formula assumes that there is no change
in height and nor change in form factor, the results are very conservative.
432 THE DETERMINATION OF GROWTH PER CENT
An attempt has been made to adapt the formula to rapid-growing
trees by substituting other values for 400, but the resulting formule
have little practical value.
331. Use of Growth Per Cent to Predict Growth of Stands. Growth
per cent is sometimes used to determine the growth of trees or stands,
by both the standard methods, that of prediction, and of comparison.
It is not well adapted to secure accurate results by either method.
Owing principally to the variability of the per cent relation, and its
direct dependence on and derivation from the two factors, volume and
increment, the problem of reversing this process and deriving increment
from growth per cent is apt to lead to error through a mistake either in
choosing the basis of volume for deriving the per cent figure, or in
applying this figure in turn to the wrong volume basis.
The method of prediction of growth by means of growth per cent
consists of determining this per cent for a stand, either from sample
trees ($ 241) or by direct use of yield tables or other methods of measur-
ing the past growth for a decade.
Schiffel states, “If in any period of life the current annual incre-
ment per cent of a tree is to be calculated, it would be contrary to nature
and incorrect to relate the increment to any former dimensions or
volume, but it must be related to the dimensions or volume of the previ-
ous year.”
The formula, growth per cent= (Tz) a0
Tree when n=10 years,
bases growth per cent on volume five years ago, and is correct as an
average per cent of the past ten-year period. If applied to the next
decade, and based on V, or present volume, it assumes an increase in
growth for this period. When this per cent is applied only to the current
year, and is based on V the per cent is more conservative.
While individual trees are growing rapidly in diameter, as dominant
trees, their growth per cent for a time falls less rapidly than that of
slower-growing trees. In even-aged stands, growth on individual trees
is proportional to their diameters. Growth per cent in area is about
twice the per cent of diameter growth. If determined for the trees
which will be retained under management, this relation of growth to
volume may be fairly consistent in such even-aged, thinned stands.
Hence sample or average trees may give a close indication of the growth
per cent or present status of the stand. But the assumption that this
growth per cent will continue to be laid on annually breaks down at
once; hence the real assumption and the only one possible, if growth
per cent is to be applied for predictions, is that the volume indicated
by this per cent will continue to be laid on annually. And this in turn
is inaccurate.
GROWTH PER CENT TO DETERMINE GROWTH OF STANDS 483
The sources of inaccuracy in this method are:
1. Predicting the volume growth of a stand from that of one or two
selected or average trees. The growth per cent of a stand is practically
always less than that of the average trees which survive, due to loss
of numbers and falling growth rate of the suppressed class.
2. Applying a growth per cent obtained from a past period on a
smaller volume, to the present volume of tree or stand, under the assump-
tion that not only will the rate of growth in volume continue the same
but the per cent will remain unchanged, when, as shown, growth per
cents always fall as wood capital increases.
3. Assuming that the growth per cent as derived from average
trees, or even from sample plots, will apply to larger areas and to dif-
ferent proportions of age classes in mixture, when in fact, so doubly
sensitive is this per cent relation, that any difference in average age
and volume between the forest and the sample areas will result in a
large error in determining the true weighted per cent by this means.
The possible errors may be illustrated as follows:
From a yield table for White Pine ! the actual known yields are,
Ait, SO AV CATS cps eene sp eteickths, ahemepa nahh b auaie toyed Bye 3750 cubic feet
AQAYGR hss Base Ob AA AO nai aotere 6590 cubic feet
HOGVCATS Emit agree iett ier Nctele a eras sheers sic1ss 8035 cubic feet
GORVEATS cei sietaete ts a wie wieis a Miahele ote si vee 9075 cubic feet
By Pressler’s formula, the current annual growth per cent for these decades is,
SO Oaths oo SS Sh cin ana ae adgioe mos abean oleate me
AD COPOO VCaTS rac ets ics arose cise akenai srs ans) istsl oe = 2.0 per cent
HOSCOLOULV CATS aint cs he sara crests: ws io) psieeciche-ale ors 1.2 per cent
If the growth for the decade from thirty to forty years be taken to indicate the
current growth in the fortieth year, of 284 board feet, this gives a current growth per
cent for that year on 6590 board feet, of 4.3 per cent. Assuming that this growth
per cent will continue for the next decade, we have a total increase of 43 per cent or
2834 board feet. The actual growth is 1445 board feet. The error is 96 per cent
excess.
Such errors are the result of use of the growth per cent, even when the basic
data are correct. The errors may be greatly increased when growth per cent is
obtained from single trees and the losses in the stand are ignored, since too high a
current growth per cent will be obtained.
332. Use of Growth Per Cent to Determine Growth of Stands by
Comparison with Measured Plots. The only merit which growth per
cent has as a method of determining growth lies in the possibility of
using it as a means of comparison. Since per cent does not express
1 Forest Mensuration of the White Pine in Mass., H. O. Cook, Office of State
Forester, 1908, p. 21.
434 THE DETERMINATION OF GROWTH PER CENT
absolute quantity but a relation, the assumption is that this relation
once established for a given stand will apply to other stands of a similar
character but differing in area and total volume. Growth per cent
on sample plots could for instance be applied to determine the annual
growth on the stand within which they are located.
In so far as it can be known that the relation between the volume
of the larger area and the growth on this area is the same as on the stand
sampled, the method is obviously correct. The error lies in applying
such growth per cent figures to stands or areas on which this relation
is not the same, because the average age, thrift, or other conditions,
differ from the sample area. The simplicity of assuming that growth
per cent for a sample tree, or for a sample plot, can be applied to large
areas has led to its use as a substitute for sound growth data in many
instances. No such short cut will actually measure the growth on a
forest comprising many stands of different ages, site qualities, and
densities of stocking.
333. Use of Growth Per Cent in Forests Composed of All Age
Classes. Growth per cent is a direct expression of current growth in
its relation to past or total volume. Hence it varies with the current
growth curve. Current growth per cent is equal to mean annual
growth per cent in the year in which the mean annual growth culmi-
nates (§ 245).
In a forest composed of stands of all ages, or in a stand composed
of trees of all ages, equally proportioned as to area or ultimate yield,
and under management, the current growth per cent for the whole ©
forest or the whole stand, when weighted by volume of each age or tree
class, will be equal to the mean annual growth per cent for every year,
since there is no change from year to year in either of the two factors,
total volume or increment, which determine it.
For such a forest the average growth per cent can be found separately
for each diameter class. By weighting each per cent according to the
volume of the trees in this class for the stand, a composite per cent is
obtained which shows the present status of the forest, and is applicable
in predicting its growth. But accurately to determine this per cent,
the growth itself must first be found on the trees or plots measured.
If in determining this growth, the future factors are really considered,
the numbers reduced, and the rate of diameter growth and probable
suppression taken into account, the result is a quantitative statement
of growth for the next decade or two instead of for the past decade.
This prediction of growth, on a few acres or a small per cent of the stand,
can then be reduced to the form of a per cent of present volume, and
applied, in this form, to the remaining stand as a convenient means of
computing growth on the total area.
GROWTH PER CENT IN QUALITY AND VALUE 435
334. Growth Per Cent in Quality and Value. Growth in money
value of a stand is treated in Forest Valuation.! This depends upon
the three factors mentioned in § 244, namely, increase in volume, in
quality, and in unit price independent of the other two factors. The
growth in quality differs from that in volume, since it tends in a measure
to raise the value of the previous growth, especially when this increased
quality is due to increased dimensions. Per cent increase in value is
usually computed as an annual per cent found by dividing the periodic
per cent by the years in the period, and is applied to the volume at
the beginning of the period, thus showing simple interest on the initial
value. When thus expressed, the per cent of increase is made up of
the sum of the per cents due to each of the three separate factors.
For young and immature timber, growth per cent in volume forms the
chief element of increase, but as the trees reach maturity this diminishes,
and is greatly exceeded by per cent increase in price due to quality, and
to unit prices—so that the per cent of increment in value may con-
tinue for a much longer time than that of volume.
The growth in quality of a stand can be measured by the use of
graded log tables (§74) or graded volume tables ($165) provided it
is carefully ascertained that these tables apply to the trees in the stands
to be measured, at the successive ages,
REFERENCES
A Practical Application of Pressler’s Formula, A. B. Recknagel, Forestry Quarterly,
Vol. XIV, 1916, p. 260.
Table for Determining Financial Increment Per Cent for Trees Based on their
Market Values, Erling Overland, Translated by Nils B. Eckbo, Forestry Quar-
terly, Vol. V, 1907, p. 36.
Increment Per Cent, Schiffel, Centralblatt f. g. d. Forstwesen, Jan., 1910, p. 6.
Review, Forestry Quarterly, Vol. VIII, 1910, p. 377.
Hilfstafel zur Zuwachserhebung, Forstwissenschaftliches Centralblatt, Apr., 1911,
p. 200. Review, Forestry Quarterly, Vol. IX, 1911, p. 321.
Relative Increment of Tree Classes, Review, Forestry Quarterly, Vol. IX, 1911, p.
633.
Zuwachsuntersuchungen an Tannen, Allgemeine Forst- und Jagdzeitung, Sept.
1907, p. 305. Review, Forestry Quarterly, Vol. V, 1907, p. 431.
Ueber Zuwachsprocent, Centralblatt f. d. g. Forstwesen, Jan., 1910, p. 6. Review,
Forestry Quarterly, Vol. VIII, 1910, p. 377.
1 Forest Valuation, H. H. Chapman. John Wiley & Sons, N. Y., 1915.
CHAPTER XXXI
METHODS OF MEASURING AND PREDICTING THE
CURRENT OR PERIODIC GROWTH OF STANDS
335. Use of Yield Tables in Prediction of Current Growth. The
current growth of stands for short periods can always be predicted
with greater accuracy than for long periods. Not only can the present
condition of the stand be gaged, as to species, numbers, crown density,
form, thrift and rate of growth in immediate past, and this information
applied in predicting the rate at which growth will continue, but the
inevitable changes, some of them unforeseen, which will occur in the
future to modify this rate of growth, take place at a rate which bears
a close relation to the length of the period of prediction.
Only when the net results of all the various factors which produce
yields have been measured on stands after they have passed through
the period is an approximate degree of accuracy obtained for long periods,
hence the use of yield tables based on age. It follows that for the pre-
diction of current growth for short periods on existing stands, the net
current growth shown by the above yield tables, reduced on the basis
of age and relative density to apply to the stand in question, is the
best basis of growth prediction even for these short periods.
336. Method of Prediction Based on Growth of Trees, with Cor-
rections for Losses. In endeavoring to use these yield tables for
stands which differ greatly from the normal in number of trees per acre,
density of crown cover, form or distribution of age classes, and com-
position of species, it is often difficult to find or make a table which will
apply to the stand even when corrected for density. In such cases,
a direct measurement of the stand may be resorted to instead of a com-
parison with a standard yield. The growth of any stand of whatever
character, for the next decade, will be the sum of the growth in volume
of the trees which survive till the end of this period minus the loss of
the total volume of the trees which do not survive (§ 252). The elements
which give stability to this method are a knowledge of the exact pres-
ent number and diameter of the trees in the stand, which may be
supplemented by a classification of crowns to indicate those now domi-
nant, intermediate or already suppressed, and by a tabulation of past
growth in diameter, by diameter classes (§ 278). The elements of
436
PREDICTION BASED ON GROWTH OF TREES 437
uncertainty are probable loss of numbers in the next period, and future
rate of diameter, height and volume growth of the survivors. At best,
owing to the great difficulty of predicting for a given stand the loss in
numbers and the rate at which diameter growth will be maintained,
for long future periods, the method can be used only for periods of
ten to twenty years, except for slow-growing or long-lived species where
the factors of change are slowed down correspondingly.
To apply this method of predicting tree growth to obtain current
growth of stands, the steps are,
1. Prepare a stand table of the forest or area (§ 188).
2. As an aid in determining mortality, tally or estimate the number
or per cent of each diameter class which is suppressed or will probably
die within ten or twenty years.
3. Decide upon the method to be applied in predicting diameter
growth (§ 278 and § 279) and prepare table of growth by diameter
classes to conform to the requirements of the method.
4. Obtain data and construct a curve of average height growth
(§ 248), which will probably be best expressed as current height growth
based on height, for the last decade or two.
5. Obtain volume tables giving the volume of trees of each diameter
and average height. A standard volume table classified by heights is
needed for best results.
6. From present number of trees in each diameter class, deduct
the per cent or number which will probably die within the period.
7. Compute the average diameter which surviving trees of each
diameter class will attain at end of period.
8. Compute the increase in height for each diameter class. (The
false method described in § 285 is frequently used as a substitute for
a curve of height growth.) .
9. The volume of the present stand is calculated from the stand
table and volume table.
10. The volume of the surviving stand at end of period is obtained
from the future diameter and height of the surviving trees of each diam-
eter class, and volumes taken from the standard volume table.
11. The difference in volume thus found is the net growth for
the period, in stands which have not been thinned and in which no
salvage of dying or dead timber is possible. The volume of the trees
which die is thus deducted from the growth on the survivors, and
only the net growth is represented in increased volume of the stand.
In stands which are thinned, this prospective loss in numbers is
not lost nor deducted, but is expressed in the form of thinnings. Where
thinnings are marked and will be made in such stands, they will com-
monly include more trees than will actually die during the period,
438 CURRENT OR PERIODIC GROWTH OF STANDS
since the suppression of diameter growth is to be avoided, and this begins
considerably in advance of the death of the tree and may affect the
entire stand if too crowded.
By this method, neither a full volume analysis of current growth
of trees is needed on the one hand, nor a yield table based on area and
age on the other. Nor is it necessary to compute the average tree of
the stand, and by predicting the growth of this tree for the next decade,
seek to determine that of the stand (§ 275) since all the trees in the stand
are given their proper weight in predicting growth. Only for very
regular stands can average trees be used safely, and for such stands
yield tables are better.
337. Increased Growth of Stands after Cutting. The method of
predicting diameter and volume growth of trees after release by cutting
is shown in § 280. The problem of predicting growth of stands left
on cut-over lands is one of properly combining the growth data for the
different classes of trees left on the area.
That diameter growth of individual trees should increase when
their crowns and roots are given increased growing space is a natural
law of growth of stands. The question is, ‘‘ What is the total net
current growth per acre on such lands? ”
The first result of cutting should be to tremendously increase the
growth per cent on the remaining stand, or change its status, by removing
large, old and slow-growing trees with a low growth per cent, and leaving
small, young and more vigorous trees with a larger growth .per cent.
This change would occur even if no increased growth followed the cutting.
The total growth per acre laid on after cutting is the sum of the
current increments on the residual trees. In spite of change in growth
per cent or status, and of possible increased growth on the trees left,
the total net volume increase may be less than on the original stand.
If the number of trees is greatly reduced this is usually the case. But
if the stand cut over is many-aged, and only the decadent and sup-
pressed trees are taken, the combination of a large number of trees
left on the area, an increased rate of growth on these trees, and especially
the prevention, by cutting, of a loss of volume by death of trees which
would otherwise have to be deducted from current growth, may result
in a larger actual net increase per acre from the cut-over stand than
before it was cut, as well as a greater growth per cent.
This expansion of diameter and volume growth of the residual
stand after cutting, is, for even-aged stands, a response to increased
light, soil, moisture and space in which to expand. In many-aged
stands it may mean, as well, an expansion of the total area of the age
class (§ 253).
The method of determining the growth of individual trees in the
REDUCED GROWTH OF STANDS AFTER CUTTING 439
stand to obtain the growth of the stand (§ 277), is favored in studies
of cut-over lands, first, because such studies are usually made in many-
aged stands of mixed species, second, because the difficulty of sepa-
rating the age classes by area and age is even greater than on stands
before cutting; hence the application to these stands of yield tables
based on age is very difficult.
The stimulation of growth on the trees left after logging is similar
in character to the beneficial effects of repeated thinnings on stands
under management. It undoubtedly increases the rate of yield per
acre over that realized if the natural processes of selection are not
interfered with.
Two factors must be considered in analyzing this growth; first,
to what extent have the trees left on the area been liberated or given
increased growing space?—second, to what extent can they utilize or
monopolize the area released by cutting? The maximum of increased
growth would be found in a stand, either even- or many-aged, in which
the cutting was so evenly distributed as to affect all of the remaining
trees, and so light that the space released could all be absorbed by these
trees.
When cutting is either too light or too poorly distributed to affect
all trees, the trees showing increased growth will be only a certain per
cent of the total number. This per cent of each diameter class which
will be released, as affected by the increased rate, will give the net
actual increase over the previous rate of growth.
Table LXVI illustrates the data required in a study of increased
growth after cutting (p. 440).
From a table of this character the average increase in growth may
be computed by weighting the rate of increase by the per cent of trees
affected; e.g., since 18 per cent of the trees are affected, an average
increase of 18 per cent of the difference between the two classes of trees,
those not affected and thus growing faster, can be added to the slower
or original rate to get the new average for the forest.
338. Reduced Growth of Stands after Cutting. In heavier cuttings,
even on parts of the same cut-over area, openings may easily occur
from cutting even-aged or mature groups, which affect but few of the
remaining trees. These clear-cut spots will result in a net reduction
of current increment per acre for the forest, just as would the clear
cutting of a larger area. There is no possibility of increased growth
because there is no timber left on which to lay this growth. In even-
aged stands cut clear, the growth for the forest occurs on separate areas
of maturing timber, not on the areas cut over; the growth on cut-over
areas must result from reproduction of a new crop and come along in
time. Thus on heavily cut-over areas, in mixed age classes, a heavy
440
CURRENT OR PERIODIC GROWTH OF STANDS
reduction of growth per acre will occur for the present regardless of in-
crease on the residual trees or stand.
TABLE LXVI
ADIRONDACK SPRUCE
Average Rate of Growth in Diameter on the Stump of 1593 Trees on Cut-over Land
at Santa Clara, New York
Current
annual
Current cee ™! No. of
ee Current diameter vee No. of Current
5 sey annual | since first cape pects annual
Diam- | No. of ee growth in) cutting. eae eae growth in
eter. trees |. ee diameter | Values te Brow || S20WINE | diameter
just before ame Ae) ate 1 inch |! increased neers
ise cutting. regular by) ,. eyemte cutting.
cutting. ee A diameter
Inches Inches Inches Inches Inches
5 8 0.095 0.095 | 0.09 11 1 0.100
6 158 080 100 10 10 16 .180
7 329 .090 110 109 9 63 185
8 350 105 125 .125 8 77 205
9 277 -120 140 .140 7 59 .205
10 226 e135 150 APSO 7 50 215
11 135 130 145 160 ii 18 210
12 64 .165 vb .170 6 7 240
13 30 .165 .170 .178 6 2 .170
14 tt . 150 150 .185 6 1 .200
15 1 080 080 .192 6
16 4 . 200 200 200 5
AV CrA@ en ieee | 0. 112 Que STA ln geheets at lth hte caualllWnaree Chae 0.20
No. years to grow |
tinehy < t | QAR hal ARSE Sod TaD TDP Mau ese 8 | 5
Total number of trees, 1593.
Number of trees showing increased growth, 294, or 18 per cent.
The condition of such cut-over areas would be more accurately gaged
if it were possible to separate the age classes in the cut-over stand on
the basis of the actual area which they occupy. Thus, in a stand on
which the timber cut formerly occupied 90 per cent of the growing
space, it is not reasonable to expect that the trees which occupy the
remaining 10 per cent of space will be able to expand sufficiently to
absorb nine times their former crown space, even if properly distributed
YIELD TABLES BASED ON AGE, TO CUT-OVER AREAS 44]
so as to make this possible. The increment on this area for any con-
siderable period into the future depends on securing reproduction
to fill the gaps.
The method of measuring increment on cut-over lands solely by the
growth expected on the trees left after cutting is best adapted to typical
many-aged or “‘selection’”’! forests, and the more closely the conditions
both as to distribution of cutting and of the residual stand resemble
a many-aged forest, the better the results obtained. This method
gives best results also on areas under intensive management, where if
trees die or are blown over, their volume is not lost, and when the danger
of reduction or loss in numbers is at a minimum.
The necessity for reducing the number of trees for loss during the
period remains, and applies to all stands on cut-over lands as well as
elsewhere. Neglect of this factor means over-estimation of probable
net growth.
339. Application of Yield Tables Based on Age, to Cut-over Areas.
Where stands in the original forest can be or have been separated
by area and age by any method, and a yield table based on age exists,
a more conservative method of calculating growth on cut-over lands
can be used, which bases this growth not on the theory of the many-
aged forest and crown expansion of the age class, but on that of even-
aged stands (§ 298). If age classes are on separate areas and cut clean,
the cutting of one stand has no effect on the growth of another. — If
the forest is divided into age classes, and part is cut over, it can be
assumed that this cutting removes an age class without stimulating
the growth on the remainder, and that this area cut over is to be repro-
duced to young timber rather than absorbed by existing age classes.
To determine the area which is cut over, and that which remains
stocked, the density or reduction per cent already determined for the
original forest (§ 317) is assumed to apply to the residual stand. The
area stocked to this degree of density can be found by dividing the
volume in each age class left on the cut-over area, by that of the empirical
yield table for the given age which has been prepared for the original
forest previous to cutting (§ 304). The sum of these areas, including
that stocked already by young or immature age classes, subtracted
from the total area, gives the area actually cut over. The actual yields
of the age classes left on the cutover area will be in proportion to the
per cent of the total area which they occupy, plus the degree of expansion
or increased growth which they put on. The growth to be expected
in the absence of any such expansion will be predicted by the empirical
yield table from the net area or per cent of area stocked. This fixes
1 Selection—A term applied to forests in which the entire series of age classes is
intermingled over the whole area and not separated by areas.
442 CURRENT OR PERIODIC GROWTH OF STANDS
the minimum expectancy and is safe for a long future period (§ 248).
Studies of growth on the individual trees and on permanent sample
plots as stimulated by release will in time indicate the maximum growth
possible on the same area. The actual growth will be somewhere
between these two extremes, dependent on the balance between the
forces tending to expand the crown
area, and the destructive agencies
tending to reduce the numbers in the
stand, as shown in Fig. 87 by the lines;
A. Based on average growth per
acre in original stand, with normal
Joss of numbers.
B. Based on increased growth after
eutting and no loss of numbers.
C. Probable rate somewhere between
A and B, based on increased growth
of a part of the stand and a reduced
rate of loss in numbers.
Probably the safest basis for growth
prediction for long periods on cut-
over lands is not the current growth
0 10 20 30, study based on diameters, but, where
. oars u possible, yields based on age, at the
Fic. 87.—Possibilities of Growth rate produced in the past on virgin
on Cut-over Areas. forests, and figured for the net areas
stocked, to which a percentage of in-
crease may be added to represent expansion of crowns due to release
and stimulus following cutting.
Vield per Acre
An illustration of this principle of growth prediction is as follows:
The empirical yield table for Western yellow pine, Coconino National Forest,
Arizona, gives 66.2 per cent of the normal or index yield.
The stand of timber left on the cut-over areas, separated into three age classes
by the method given in § 321 is found.
By dividing the stand for each age class by the yield per acre from the empirical
yield table, the area which is stocked with timber, for each age class, is determined.
The area reproduced to poles and saplings is estimated. The total area of cut-
over land is known. The remaining area, not shown as stocked either with mature
timber or young timber is the area cut clean and awaiting restocking. The results
are given in Table LX VII.
The prediction of growth is now made by applying the empirical
yield table to the areas and ages represented in the table.
With the area and age of each age class indicated, the future yields
on cut-over lands may be predicted by applying the empirical yield
table, increased by the per cent of expansion agreed upon.
PLOTS FOR MEASUREMENT OF CURRENT GROWTH 443
TABLE LXVII
AREAS REMAINING STOCKED ON CutT-over LANDS
Vield’por Stand Empirical Per cent of
Age. area 70,654 acres;
Class acre. | total M. aE
| equivalent | also per cent
Years | Board feet | Board feet acres | of 1 acre
Veteran’: 2!..).0% 300 | 12,050 27,900 2,315 one
Matures. 4..4.| 200 16,750 | 9,702 579 0.8
Blackjack. ..... ; 100 7,480 | 70,908 9,493 13.4
Bolesme ieee. fer: SOME Mere cae all bo ee re. 6,006 8.5
Saplingsues a. - DOME ye ethos 17,663 25.0
Not restocked.. . OM aageit rade ON. Ley. | - 34,598 49.1
Totals....] 108,510 ,; 70,654 | 100.0
| |
340. Permanent Sample Plots for Measurement of Current Growth.
The best method of measuring the current growth of a stand is by means
of permanent sample plots, established in stands which are typical of
the conditions to be studied, and re-measured at intervals of from five
to ten years. Methods of establishing and measuring such plots are
described in § 248. In this way, just as for yield tables the actual net
results of all factors which affect the current growth of the stand as a
whole, such as wind, insects, disease, suppression, or increased growth,
are measured, rather than either compared or predicted. The only
precautions to observe on re-measurement of plots are that the diameters
and heights of the trees must be taken in successive measurements in
such a way as to give exact comparisons, whose difference indicates
growth rather than discrepancies in re-measurements.
Krauch has pointed out that the height of trees should be measured
on such plots from the same position or point at each measurement,
to avoid discrepancy due to the departure of the tree from the per-
pendicular (§ 199). The diameter tape insures consistency in re-measure-
ment of diameters (§ 190). The same volume table should be used in
calculating successive volumes for trees of each size class. These pre-
cautions insure the isolation of the current growth in successive measure-
ments.
341. Measurement of Increment of Immature Stands as Part of
the Total Increment of a Forest or Period. The increment of a forest
or large area, just as in the case of a single stand, may be expressed as
the total growth over a definite period, or yield, the average annual
growth or mean for this period, or the actual volume laid on each year
dt CURRENT OR PERIODIC GROWTH OF STANDS
or current annual growth. A forest resembles more closely a many-
aged stand than one composed of a single age class. In such a stand
or forest, it is not possible to separate one period which coincides with
the complete cycle of production for a crop of timber, as can be cone
in the even-aged stand. The total production of the many-aged area
or of the forest, for a period equal to that required to grow one crop
from seed to maturity, may equal that of the even-aged stand, but it
is laid on in many stands.
In a regular many-aged forest the current growth for one year is
the growth in volume of each stand, including those which are as yet
unmerchantable. This is true of the forest, whatever its form. The
current growth on the mature timber is but part of the total; that which
represents the younger stands is equally important. Growth is not
usually measured, on either trees or stands, until a size is attained which
is merchantable for some form of product. Another reason for post-
poning the measurement of young stands is that a very large per cent
of the existing trees in such stands will never reach maturity, and the
total volume at any period previous to an age at which it can be used
is misleading and serves no useful purpose, while by contrast the natural
selection of surviving trees in stands measured at merchantable age
has already occurred and the results are accurately gaged.
When the volume is finally measured on a young stand for the first
time, it represents the growth for the entire preceding period. Perhaps
but 10 per cent of the trees are large enough to measure at this time.
After another decade, the stand is again measured. By this time
50 per cent of the trees may be merchantable. The growth for this
decade now includes the current growth, for ten years, on the original
10 per cent, plus the growth since germination on the remaining 40
per cent. At the third measurement, ali trees which survive may be
merchantable and are measured, but a portion of them have entered
the merchantable class after being missed for the two previous decades.
What happens is that although current increment by decades is sought,
yet for trees which mature and are measured for the first time, total
growth is substituted for current growth since there is no other way
to handle it.
If this example is now applied to a forest composed of a series of
even-aged stands, the same thing is seen to occur. For the forest,
the current increment is the increase in merchantable cubic volume
of stands already partly merchantable; but to this is added, in each
decade, stands measured for the first time, whose volume though added
as current increment is in reality the total growth of several periods
instead of one. It follows that for a stand just becoming merchantable,
the apparent current growth will be very rapid during this process
VALUE OF CURRENT GROWTH VERSUS YIELD TABLES 4465
while its actual average or mean annual growth, which takes in the true
period required, is much less.
But in a many-aged stand, or on a forest composed of stands of all
ages, these elements counterbalance each other. As growth cannot
be measured on stands below merchantable age or size, it is not meas-
ured on ‘the areas covered by such young stands, or on the portion
occupied by immature trees in mixed stands. But as soon as these
stands or trees mature, the growth is measured all at once and greatly
exceeds the actual current rate on the areas measured or for the trees
in these age classes. Whenever the age classes are distributed evenly,
the excess of current growth so caused is balanced for the area or forest
by the neglect of the current growth on the younger stands. It follows,
first, that in forests with well distributed age classes, the total current
annual growth actually laid on in stands of all ages should be about
equal to the current growth obtained by measuring only the merchant-
able stands, provided the maturing volumes of young timber are included
as current growth. For a single even-aged stand, or a forest devoid
of younger age classes, this premise does not hold good, and the current
growth for the period of early maturity will greatly exceed the real
rate for the area or total period. On such stands or forests this rate
‘will not be maintained, and the true yield must be found by dividing
by age, in the form of mean annual growth.
342. Comparative Value of Current Growth versus Yield Tables
and Mean Annual Growth. The relative value and utility of the
methods of studying the increment on forests or large areas may be
summed up as follows:
Increment or growth is always desired for areas of land rather than
individual trees.
The rate of growth per year on an average acre is the object sought.
Where forestry is a permanent land policy, the rate of growth desired
is that which represents the average for the life of a crop of timber,
and which can be maintained, in consequence, indefinitely.
This rate can be found most accurately whenever growth can be
measured directly on the basis of area and total age, as in yield tables
for even-aged stands, and applied to the forest by the necessary reduc-
tion per cents.
-The current growth on stands or forests is best obtained from these
same yield tables.
But where it is not possible or practicable to construct such yield
tables, current growth for short periods only can be measured directly
on merchantable trees, and applied in predicting growth of the stand
and forest.
This method gains in accuracy over yield tables, by measuring
446 CURRENT OR PERIODIC GROWTH OF STANDS
directly the density of the stand, and by predicting growth on basis
of actual volume and,conditions. It loses in comparison, because it
measures only one current section of the growth curve for the stand or
forest, which may be above or below the mean, and because the basis,
the individual tree, while accurate to start with, rapidly loses its reli-
ability, while by contrast, yield tables retain a fair degree of reliability
over long future periods.
Current growth, if it is actually measured in terms of volume, and
the errors of using growth per cent are avoided, is well adapted to answer
questions regarding the immediate future growth of specific stands,
but is poorly adapted to growth predictions covering long periods.
REFERENCES
Growth Rate in Selection Forest. Der Gemischte Buchen Plenterwald auf Muschel-
kalk in. Thiiringen, Mathes, Allgemeine Forst- u. Jagdzeitung, May 1910, p.
149. Review, Forestry Quarterly, Vol. IX, 1911, p. 129.
Increment in Selection Forests. Zur Ermittlung des laufenden Zuwachses speziell
im Plenterwalde, Christen, Schweizerische Zeitschrift fur Forstwesen, Feb.
1909, p. 37. Review, Forestry Quarterly, Vol. VII, 1909, p. 206.
A Method of Investigating Yields per Acre in Many-aged Stands, H. H. Chapman,
Forestry Quarterly, Vol. X, 1912, p. 458.
Accelerated Growth of Spruce after Cutting, in the Adirondacks, John Bentley,
Jr., Journal of Forestry, Vol. XV, 1917, p. 896.
Method of Regulating the Yield in Selection Forests, Walter J. Morrill, Forestry
Quarterly, Vol. XI, 1913, p. 21.
Determination of Stocking in Uneven-aged Stands, W. W. Ashe, Proc. Soc. Am.
Foresters, Vol. IX, 1914, p. 204.
The Relation of Crown Space to the Volume of Present and Future Stands of Western
Yellow Pine, George A. Bright, Forestry Quarterly, Vol. XII, 1914, p. 330.
Remeasurement of Permanent Sample Plots, G. A. Pearson, Forestry Quarterly,
Vol. XIII, 1915, p. 60.
Observations in Connection with Annual Increment of Growing Crops of Timber,
Transactions of Royal Scottish Arboricultural Society, July, 1918, p. 164.
CHAPTER XXXII
COORDINATION OF FOREST SURVEY WITH GROWTH DETER-
MINATION FOR THE FOREST
343. Factors Determining Total Growth on a Large Area. The
solution of the problem of determining the amount or volume of wood
which will be grown on a forest or area of forest land in a given period
depends upon six factors:
1. An analysis or classification of the forest into the areas included
in each of the site qualities present.
2. The areas occupied by stands of given type and mixture of species.
3. The actual present density of stocking, volume and number of
trees. per acre, and size of diameters of the present stand on the forest.
4. The actual age classes present, and the area which each occupies.
5. The length of the period for which growth is desired, whether
for a short current period, or for permanent management and a rotation.
6. The rate of growth, to be determined by whatever method can
best be applied to the forest as a whole by obtaining the actual growth
on the stands which compose it.
344. Data Required from the Forest Survey. The first four of
these elements require the collection of data in connection with the
forest survey. Studies of the rate of growth (6) for the period deter-
mined (5) will not solve this problem in the absence of quantitative
data to tie this growth study to the tract in question.
Unless a forest is to be cleared for farms, the prediction of future
growth is a basic consideration of its future management. A forest
survey that is so conducted as to fail to obtain the necessary data on
which growth for the forest can be determined must later be repeated
to obtain this data, or supplemented in some way, while if the need
were recognized at the start, the information could be obtained in final
form with trivial extra cost.
The character of this data depends upon the form of the forest as
to its age classes. It may be itemized as,
1. Site classification.
2. Age of stands.
3. Area of stands.
4. Volume of stands.
447
448 COORDINATION OF FOREST SURVEY
When these factors cannot be directly ascertained, the requisite basis
must be obtained for calculating them. The most fundamental and
useful basis is,
5. Diameter of trees in stand by species, or a stand table.
Finally, because of its inadequate handling, special emphasis must
be placed on obtaining
6. The area stocked by immature age classes.
345. Site Qualities—Separation in Field. Site qualities in the
forest should be separated by area. Where several types exist, such
as cove, lower slope, upper slope and ridge, which correspond closely
with difference in site, the division by types goes a ee way toward
separating the site qualities (§ 228).
Where site qualities must be determined directly, there are but two
methods possible of which the first is direct judgment based on obser-
vation of site factors, such as soil, altitude, slope, rock, moisture (as
swamps) and general character of the timber growth. This method
is subject to serious errors (§ 226). The second method! is based on
the height growth of dominant trees (§ 227). But to determine directly
the site class indicated by trees of different heights, their age must be
known. When the forest is composed of a few large age classes of even
age, direct determination of a few ages may give this basis.
But where the age classes are mixed, the age of individual dominant
trees, rather than age of stand, must be relied on to indicate site quality.
If we could assume that diameter growth did not decrease for the average
tree, on poor sites, and that average trees of a given diameter were
as old on Quality I site as on Quality III, diameter could be substituted
for age; but average diameter growth varies with the site quality itself,
which prevents this substitution.
To obtain the basis of field classification of site, the heights of dif-
ferent trees based on age are plotted and divided into site qualities
based on the standard chosen, as illustrated in Fig. 84 (§ 310) except
that in this case the data are obtained by plotting individual trees,
and by analysis of the height growth of trees, rather than from plots.
To apply this table or set of curves, in determining the quality of
a given site, a selected tree or two is measured for height. If fully
matured, total height may indicate directly the site quality. If the
stand is young, age must always be ascertained. The average height
for the given age is then looked up on the chart. The trees chosen
should preferably be dominant and must never be suppressed. The
position of the height with reference to the curves or table indicates
the site quality.
The unit of area on which sites are separated should be that used
1 Journal of Forestry, Vol. XV, 1917, p. 552.
RELATION BETWEEN VOLUME AND AGE OF STANDS 449
in separating stands or units of volume estimating, such as small legal
subdivisions, e.g., 10 acres, except where, by the aid of topography,
the site qualities can be mapped to conform more closely with natural
boundaries. Types are commonly separated in the forest survey by
mapping the areas, and the estimate is usually separated to coincide
with the divisions thus made (§ 221) though on forties this is not always
done.
346. Relation between Volume and Age of Stands. Density of
stocking, as shown, is not determined by the total merchantable volume
of a stand, but by a comparison of the existing volume with the index
volume which stands should have at given ages. Density when deter-
mined by comparison of volumes, is therefore a function not solely of
area but also of age. To determine density for large areas, therefore,
a basis of separation of the volume into age classes is required. This
means either the direct mapping of areas of separate age classes, or a
tally of diameters and a stand table for diameter classes in the stand.
Methods of forest survey which utilize diameter tallies to obtain volumes
(§ 207 and § 209) naturally lend themselves to the securing of such
a stand table. The use of such tallies for determining age groups and
average ages are shown in § 320 and § 323. In general, density of stock-
ing for mature age classes will be found not in the field, but after the
volumes have been computed or stand tables prepared, and by means
of a comparison of volumes with the yield table, on the basis of similar
ages.
Age classes and their actual ages may be determined directly during
timber survey only when the areas which they occupy are separate, large
and easily distinguished, and when time permits of the testing of trees
forage. In intensive management, this method will be followed on small
areas; but for large areas of mixed ages, the general method of depending
upon diameters to indicate age should be relied on; hence the stand
table is the basis of this age class division, both for age and area (§ 318
to § 323.)
347. Averaging the Site Quality for the Entire Area. Site qualities,
when not correlated with type, present difficulties in classification,
so much so that on large extensive projects site qualities may for the
time have to be waived and an average yield table obtained for all
sites. (This method was adopted in the preliminary working plan
for the Coconino Nationa! Forest, Arizona.) A composite stand table,
including stands on all sites, is best for this purpose. Its application
to the average site will depend on the average density or reduction
per cent found for the area. Only when the divisions of the total area
into site qualities can be coordinated with similar divisions of the esti-
mate and stand can these divisions be made the basis of separate growth
450 COORDINATION OF FOREST SURVEY
predictions for the forest. Wherever possible, this division must be
made.
348. Growth on Areas of Immature Timber. The growth on any
large area, whether the form of forest is even-aged in pure stands, or
many-aged in mixed stands (§ 314) must include that of the young,
unmerchantable stands. This growth is a prediction of future volume,
and as such, may be obtained, not by measuring the present volume
of the stand, nor by counting the number of trees in very young stands,
but by the method of comparison with older stands. The yield table
based on area and age gives this comparison. But to utilize the table,
the one thing necessary to determine is the area which is stocked with
the immature timber. Its age is more easily determined than for old
timber, either by cutting or by counting whorls. Based on area and
age, the future yield is a matter of density of stocking. The rate of
growth per year may be taken as the mean annual growth, shown
by the reduced or empirical yield table, for the age at which the stand
will be cut.
The density per cent for young stands is practically independent
of the density of crown cover, and depends instead upon the number
of trees per acre as compared with the normal number required at
maturity, the distribution of these trees over the area, and the chance
of survival (§ 316). Mortality in scattered stands where each tree
has room to grow is much less than in crowded stands; and if the
spacing of the reproduction is such that, allowing for a reasonable
rate of loss from insects and causes other than suppression, the stand
will reach full stocking at least a decade before maturity, it can be
considered as fully stocked now.
If a large area is being measured and an average density per cent
is found for this area, resulting in an empirical yield table somewhat
lower in values than the normal table, a conservative plan is to assume
that the ultimate yield of young stands will not exceed this density,
and to use the empirical yield table as the basis for calculating their
future yields.
That area and yield per acre is the only possible basis of prediction
of yield for immature stands must become evident by considering the
difficulties of the opposite plan, that of counting numbers of trees on
snall plots. In tallying or counting reproduction or immature sizes,
it is customary to lay off the plots at fixed intervals, comprising from
one-tenth of the estimated strip, down to less than 1 per cent of the
strip, and to count the seedlings and saplings upon these plots. The
only way in which these data can be used to predict growth on such
small timber is by predicting the percentage of this count which will
survive. The method of comparison by numbers of trees is useless,
GROWTH ON AREAS OF IMMATURE TIMBER 451
first, because number of trees per acre at these ages does not in any way
indicate the future yield, since this is determined by the number that
survive; second, because the area rather than the number will determine
the future yield. Ona plot of 100 square feet there may be one hundred
seedlings; yet if fully stocked at maturity not more than one tree would
be able to survive from this number. Such counts on plots serve only
to determine the extent to which reproduction is becoming established
and do not give the data needed for growth predictions.
Age Classes Based on Size. Immature timber may be divided into
at least three classes for purposes of growth study; seedlings, saplings
and poles. Seedlings are trees under 3 feet high.! Saplings include
trees from 3 feet high to 4 inches D.B.H. Poles are trees from 4 to 12
inches D.B.H.
Saplings may be divided into
Small—from 3 to 10 feet high.
Large—from 10 feet high to 4 inches D.B.H.
Poles may be divided into
Small—from 4 to 8 inches D.B.H.
Large—from 8 to 12 inches D.B.H.
Methods for Seedlings and Saplings. In determining the quantity
of reproduction and immature timber present on an area, in order to
predict its growth by comparison with a yield table, the procedure
will depend upon the form of the forest. In even-aged stands, areas
stocked with seedlings in sufficient numbers can be entered by mapping
them as fully stocked. Danger of destruction is chiefly by fire, and for
this, correction can be made when fires occur. But in many-aged
stands, suppression must be considered. Depending upon the silvical
characteristics of the species and the behavior of the seedlings, the object
should be to record only the area of mature forest which will result from
the present stocking. Seedlings which are suppressed will be ignored.
Those which grow in openings and are thrifty will be regarded as prob-
able survivors. In rather open, group-selection ? forests like yellow
pine, the areas stocked in this manner are easily distinguished. With
species such as spruce, seedlings starting under shade and not in open-
ings should be disregarded altogether, both because of suppression,
and because their age will be prolonged by this cause and they will
not become an economic factor in the stand till a later period (§ 263).
With saplings, the establishment of the stand in many-aged forests
1 Standard definitions, Society of American Foresters.
* Group-selection, a forest composed of trees of all ages intermingled in small
fairly even-aged groups,
452 COORDINATION OF FOREST SURVEY
is more certain, and the area so stocked with trees which will probably
survive can be better determined.
For both these classes of timber, the best method of determining the
area, and consequent future growth, during the forest survey, is to record
on each strip the per cent of total area on the strip which is stocked
with young timber, on the basis of probable survival to maturity.
This per cent is then reduced to acres for the strip. The average size
and age can also be noted. Seedlings and saplings can be separately
noted, or thrown together, depending on the intensiveness of the work
and size of area.
A second method of record on the basis of area, formerly used in the
Southwest, was to note the reproduction in general terms, based on
whether the stocking was sufficient to replace the present stand. If so
it was termed excellent. Different per cents less than this were termed
good, fair, poor, and none. This system does not distinguish between
the areas of mature and young timber or consider the relation which
one bears to the other.
To supplement the per cent method of ocular guessing at areas
restocked, plots may be laid out at given intervals, on which the areas
stocked can be mapped, and computed in terms of acres. The per cent
of the plot thus shown as reproduced serves to correct the ocular work
and to check the results.
Methods for Poles. With poles, the area method can still be applied
directly in even-aged stands, by mapping. In many-aged stands, a
choice of two methods is offered. Either the area per cent can be used
as for saplings, but separately, and the number of trees in this class
ignored as before, in which case merely the average size and age of the
poles on each strip is recorded with the per cent of area occupied, or
instead, the poles may be counted.
The purpose of the count is to obtain a second basis of comparison
with the empirical yield table. The latter should show the number
of trees per acre required at different ages. The yield table data may
be made to include pole sizes, by including plots of this age in construct-
ing the normal tables of yield. In case this has been done, the area
occupied by poles can be very roughly determined by means of the
numerical comparison with the empirical table. For instance, if poles,
averaging sixty years old and 7 inches in diameter run 120 per acre
in the normal table, and the reduction per cent is 663, the empirical
stocking is 80 poles per acre. A count of 8000 poles on the area indicates
an area of 100 acres stocked with pole sizes.
A definite plan for the determination of the stocking with poles must
be made preliminary to undertaking the timber survey. Trees which
are part of an even-aged mature stand, but which are not yet merchant-
SEPARATION OF AREAS OF IMMATURE TIMBER 453
able or are suppressed, are not considered, since the yield table for the
stand takes care of them. Only in many-aged stands must poles be
counted, or their area determined by per cent of the total, the former
method to be used if the yield table permits of direct comparison of
numbers, the later, if only the mature classes are shown in the table.
349. Effect of Separation of Areas of Immature Timber on the
Density Factor for Mature Stands. The separation by area of the
immature age classes accomplishes more than the determination of
future yield for these age classes. In the many-aged forest, the mature
timber is not segregated as it is in even-aged stands, but is intermingled
with areas of reproduction, saplings, and poles. In the attempt to
separate this mature timber into two or more age classes, either based
on diameter classes, or by age groups (§ 320 and § 323) it is necessary to
begin with a knowledge of the total area occupied by all the mature
age classes. If the area actually stocked with seedlings, saplings and
poles to the exclusion of mature timber is neglected, then the area appar-
ently required by the mature timber is greater than that actually
required, by just the amount of this error. In the even-aged forest
no such mistake is possible, and by analogy, its correction for the many-
aged forest must be undertaken.
The effect of not separating the area of immature stands is to lower
the reduction per cent or apparent density factor for the mature age
class. E.g., a reduction per cent of 40 is found for mature timber when
it is assumed to occupy the entire area. Segregation of young timber
shows that one-half or 50 per cent of the area is occupied by these age
classes. The total area is 10,000 acres. The actual area occupied by
mature timber is now 5000 acres, which doubles its density, and gives
a density per cent of 80 instead of 40.
At first glance it would appear that no difference is made in the cal-
culation of yield of these mature age classes by either assumption since
reduced area and increased density are reciprocal and refer to the same
actual stocking and volume and presumably the same future yield.
The benefit lies in the fact that the corrected density factor more nearly
indicates the rate of growth per year for the forest or on the average acre,
which is the information most needed in permanent management.
By separating the yield and area of the young timber, it is possible
to predict the total actual yield of the forest over a long period, instead
of for the shorter period required to harvest timber now mature. Instead
of an extremely low per cent of density for mature timber and for the
forest, which would indicate the need of considerable reduction in yields
from the standard table (§ 316), the true conditions are revealed.
Finally, it gives the same data as to age classes for the many-aged
forests as are obtained by mapping for even-aged stands.
454 COORDINATION OF FOREST SURVEY
350. Stand Table by Diameters for Poles and Saplings: When
Required. When diameter is definitely substituted for age and area,
the growth of the forest for a period of from ten to twenty years into
the future will include not only the increase on existing merchantable
trees, but the volume of all young trees which grow during the period
to a size which brings them into the merchantable class (§ 277).
The number of diameter classes which will become merchantable
will be determined by the length of the period and the rate of growth
in diameter. At a rate of 1 inch in five years, trees now 4 inches below
the minimum diameter will reach the required size in 20 years.
In order to predict the growth of the stand for this period, the number
of trees of each diameter class included in the group which will mature
within the period must be recorded during the forest survey. Either
all of the trees of these sizes must be calipered or counted, and the
average diameter approximated, or these sizes may be calipered on a
part of the area, distributed mechanically to obtain an average for the
whole. This again indicates the need for correlation of the method
to be used in predicting growth with the timber survey, before the latter
is undertaken.
REFERENCES
Coordination of Growth Studies, Reconnaissance and Regulation of Yield on National
Forests, H. H. Chapman, Proc. Soc. Am. Foresters, Vol. VIII, 1913, p. 317.
APPENDIX A
A. LUMBER GRADES AND LOG GRADES
351. Purpose of Log Grades. The most useful purpose of timber estimating
and log scaling is to determine the value of the logs and standing timber. This
value depends upon the amount or per cent of lumber of different qualities which
can be obtained from the logs or timber to be valued. In § 87 it was shown that for
this purpose logs are separated into grades, usually three in number, but that the
specifications for and value of each log grade depend upon the contents of logs as
expressed in grades of lumber, and in resultant average value or price per 1000 board
feet.
352. Grades of Lumber. Wood varies in texture or closeness of grain, difference
between heart- and sapwood, uniformity of texture and freedom from knots, number,
size, placement and character of knots, and presence of or freedom from various
defects which lower the value of the piece by altering its appearance, strength,
surface or suitability for the purposes for which it may be used. Pieces which are
entirely free from all defects are suitable for the highest uses and possess the greatest
value. At the opposite extreme are found pieces with defects so numerous or serious
that they are unfitted for any useful purpose, hence possess no market value and are
disposed of as refuse to the burner or as fuel. Certain “cull” grades, formerly
refuse, are now generally handled as merchantable, but the practice of scaling has
not been altered and such grades are still excluded from the scale as unsound.
The output of a mill in lumber, if separated according to the quality and value
of each board, would form an unbroken series from the most perfect pieces descend-
ing through an increasing per cent of more and more serious defects until the poorest
merchantable boards are passed, and refuse only is left.
For practical purposes, this series must be separated by arbitrary standards
into groups termed lumber grades, so defined that any piece may be assigned by its
appearance to its proper classification or grade. These grades are then made the
basis of lumber prices and lumber trade.
The specifications for a grade are intended to define the poorest piece which will
be accepted in the grade, thus excluding all lumber whose quality and defects are
such as to unfit it for this grade. The average quality of lumber in any grade will
therefore be better than the minimum specifications. Lumber which would qualify
for a given grade is sometimes included in a lower grade, but this is not in the interest
of the seller and tends to destroy the standards of grading.
353. Basis of Lumber Grades. The requirements of a lumber grade are, that it
be generally adopted in a region or for the trade which handles the lumber from this
species or region; that it be consistently applied throughout this region; that it be
capable of definition and application in grading; and that it conform to the require-
ments for certain definite uses of lumber. To use lumber for a given purpose, when
it is better than is necessary and is suitable for a higher use, is wasteful, but to admit
455
456 APPENDIX A
lumber to a grade intended for a given use, when it possesses defects which unfit it
for this use, destroys the basis of sound business.
Again, a grade, as applied to the lumber of a given species or region, must be so
defined as to permit of securing a sufficient volume of output qualifying for the
grade to make it a commercial or market product. No purpose is served in making
grades for clear lumber, to apply to second-growth stands which produce little if any
lumber of this grade.
Defects characteristic of one species but absent or rare in others call for modi-
fications of grading rules to suit the species in order to prevent the rejection of too
large a percentage of the output for grades for which it is otherwise suited.
To secure uniformity in both definition and application, grades of lumber are
established by regional associations of lumber manufacturers and dealers, which
frequently employ a corps of grading inspectors acting under a central head. These
grading rules are modified from time to time as market conditions change. The
latest specifications for any region or species should be obtained from the local
associations. Not only do specifications change, but there is considerable fluctua-
tion in their application as a whole, and in individual mills, which it is the purpose
of inspection and standardization to avoid as far as possible. .
354. Grades for Remanufactured and Finished versus Rough Lumber. For
the purpose of valuing logs and standing timber, only those grades of lumber are
serviceable which can be applied with some degree of accuracy directly to the log.
Lumber is finally sold on the basis of its grade when finished or remanufactured.
But these final grades are made the basis of the grading of the rough boards on the
sorting table, with the modification that the better grades of rough lumber may be
split up into several special grades, including lumber intended for specific uses. In
all such cases, the general grade of the rough lumber is the basis of log grading.
Structural and dimension lumber calls for a different basis of grading, as do
sawed cross ties. Where a considerable proportion of the output is in these forms,
the basis of log grading is affected. While a system based on this form of products
could be worked out for logs, it has not been attempted, but the basis of log grades
has been confined to 1-inch rough lumber. The average value of each standard grade
of lumber may be obtained from that of the grades of remanufactured lumber which
it produces.
It is always possible to recognize and estimate separately the quantity and value
of trees containing unusual or special dimensions, in the nature of piece products.
355. General Factors which Serve to Distinguish Lumber Grades. Face. Lum-
ber is graded on the appearance of the poorest face for certain uses and in certain
regions. For other uses and in other regions, the appearance of the best face deter-
mines the grade. The specific practice is in each case determined by the local grad-
ing rules.
Defects. With respect to perfect pieces, all departures from standard as defined
in § 352 constitute defects. With regard to each specific grade, the defects which
disqualify the piece and throw it into lower grade are defined. Defects which dis-
qualify in one grade may be accepted in the grade below.
The principal defects are caused by,
. Knots, sound or unsound, encased, firm or loose, and knot holes.
Rot.
Shake, season checks, seams and cracks.
Pitch.
Worm holes.
. Stain, either as blue sap or red heart.
NO ne) ND Te
LUMBER GRADES AND LOG GRADES 457
7. Mechanical defects, as splits, torn grain.
8. Wane, or round edges.
These defects or any combination of them may reduce grade by affecting the
utility and value of the piece through its appearance, surface, texture, or strength.
356. Grouping of Grades of Rough Lumber. Even when standard grades of rough
lumber only are considered, it is best not to attempt to base log grades or quality of
standing timber on the determination of given per cents of each of these standard
grades supposed to be contained in the logs. Instead, these grades should be com-
bined into a few groups with similar characteristics conforming to the grading rules
for the species ‘and region. Three such groups may be distinguished in softwoods,
namely, finishing grades, factory or shop grades, and common grades. Based on the
practice of “sound ”’ sealing, a fourth group may be made to include grades which
contain rot or other defects in sufficient quantity to cause their rejection in scaling
logs.
Finishing grades include all of the so-called upper grades of lumber, characterized
by freedom from all but a few small defects. These grades are suitable for use with-
out being cut up, for purposes requiring appearance as the prime factor, combined
with definite and sometimes considerable width and length.
These grades are used for outside and inside finish and for many purposes of
manufacture. The entire piece is graded as a unit, any defect serving to reduce its
grade as a whole.
Factory or Shop Grades. Boards suitable for factory or shop grades are such as
will yield smaller pieces of upper grade material when ripped or cut up as to exclude
or cull out disqualifying defects. In these grades, therefore, the piece is not graded as
a unit but on the basis of the per cent of its volume that can be utilized. The
remainder is rejected as refuse and may therefore contain defects of any character
without affecting the grade of the piece.
Common Grades. As applied to lumber cut from conifers or “ softwoods,’’ com-
mon lumber is distinguished from the other two groups by a general coarseness of
appearance caused by various defects or combinations of defects, such as nu-
merous large or small knots, which not only render it unsuitable for the upper grades
but prevent cuttings being made from it which would qualify it for factory grades.
Common lumber. of this class is graded for the entire piece and finds its principal
use in construction. Owing to the large volume of common lumber, in conifers,
which constitutes from 60 to 95 per cent of the total output, this group may be
subdivided in each given region. These specific common grades are not always
given identical names any more than are the grades in the other two groups. The
most widely accepted nomenclature is,
No. 1 Common,
No. 2 Common,
No. 3 Common.
357. Example of Grading Rules. Southern Yellow Pine—Finishing, or Upper
Grades. ‘‘ A”’ Finishing, inch, 14, 14 and 2-inch, dressed one or two sides, up to
and including 12 inches in width, must show one face practically clear of all defects,
except that it may have such wane as would dress off if surfaced four sides.
13-inch and wider “ A ”’ finishing will admit two small defects or their equivalent.
“B” Finishing, inch, 14, 14 and 2-inch, dressed one or two sides, up to and
including 10 inches in width, in addition to the equivalent of one split in end which
should not exceed in length the width of the piece, will admit any two of the following
or their equivalent of combined defects: slight torn grain, three pin knots, one
standard knot, three small pitch pockets, one standard pitch pocket, one standard
‘
458 APPENDIX A
pitch streak, 5 per cent of sap stain, or firm red heart; wane not to exceed 1 inch in
width, 1-inch in depth and } the length of the piece; small seasoning checks.
11-inch and wider ‘‘ B”’ Finishing will admit three of the above defects or their
equivalent, but sap stain or firm red heart shall not exceed 10 per cent.
Select Common Finishing, up to and including 10-inch in width will admit, in
addition to the equivalent of one split in end which should not exceed in length the
width of the piece, any two of the following, or their equivalent of combined defects:
25 per cent of sap stain, 25 per cent firm red heart, two standard pitch streaks,
medium torn grain in three places, slight shake, seasoning checks that do not show
an opening through, two standard pitch pockets, six small pitch pockets, two stand-
ard knots, six pin knots, wane 1 inch in width, 3 inch in depth and one-third the
length of the piece. Defective dressing or slight skips in dressing will also be allowed
that do not prevent its use as finish without waste.
11 and 12-inch ‘“‘ C ” Finishing will admit one additional defect or its equivalent.
Pieces wider than 12 inches will admit two additional defects to those admitted in
10-inch or their equivalent, except sap stain, which shall not be increased.
Pieces otherwise as good as “‘ B”’ will admit of twenty pin-worm holes.
Common Grades. No. 1 Common boards, dressed one or two sides, will admit
any number of sound knots. The mean or average diameter of any one knot should
not be more than 2 inches in stock 8 inches wide, nor more than 23 inches in stock
10 and 12 inches wide; two pith knots; the equivalent of one split, not to exceed in
length the width of the piece; torn grain, pitch, pitch pockets, slight shake, sap stain,
seasoning checks, firm redheart; wane } inch deep on the edge not exceeding 1 inch
in width and one-third the length of the piece, or its equivalent; and a limited num-
ber of pin-worm holes well scattered; or defects equivalent to the above.
No. 2 Common boards, dressed one or two sides; No. 2 Shiplap, Grooved Roof-
ing, D. & M. and Barn Siding will admit knots not necessarily sound; but the mean
or average diameter of any one knot shall not be more than one-third of the cross
section if located on the edge, and shall not be more than one-half of the cross section
if located away from the edge; if sound may extend one-half the cross section if
located on the edge, except that no knot, the mean or average diameter of which
exceeds 4 inches should be admitted; worm holes, splits one-fourth the length of
the piece, wane 2 inches wide or through heart shakes, one-half the length of the
piece; through rotten streaks } inch wide one-fourth the length of the piece, or its
equivalent of unsound red heart; or defects equivalent to the above.
A knot hole 2 inches in diameter will be admitted, provided the piece is otherwise
as good as No. 1 Common.
Miseut 1-inch common boards which do not fall below $-inch in thickness shall
be admitted in No. 2 Common, provided the grade of such thin stock is otherwise
as good as No. 1 Common.
No. 3 Common boards, No. 3 Common Shiplap, D. & M. and Barn Siding is defect-
ive lumber, and will admit of coarse knots, knot holes, very wormy pieces, red rot,
and other defects that will not prevent its use as a whole for cheap sheathing, or
which will cut 75 per cent of lumber as good as No. 2 Common.
358. Relation between Grades of Lumber and Cull in Log Scaling. From the
standpoint of the lumber trade, lumber which is merchantable, no matter what the
extent and character of defects it contains, is placed in a recognized grade, while
cull lumber is lumber which is not merchantable. Grades of common lumber below
No. 3 are sawed from unsound or defective portions of logs, which would be culled
in scaling. In mill-scale studies and in determining log grades, it is proper, there-
fore, to throw all grades under No. 3 Common into the group termed cull. In addi-
LUMBER GRADES AND LOG GRADES 459
tion, the grade designated as No. 3 Common may in certain regions contain unsound
material which would not be sealed on the basis of sound scale. Hence a portion of
the No. 3 grade, if so constituted, plus all of the cull grades of lumber, when utilized,
go to increase the amount of over-run secured in manufacture.
From one to three grades of lumber below No. 8 Common may be recognized,
according to the species and region.
Common Grades Culled in Sound Scale of Logs. Southern Yellow Pine. No. 4
Common boards shall include all pieces that fall below the grade of No. 3 Common,
excluding such pieces as will not be held in place by nailing, after wasting one-fourth
the length of the piece by cutting into two or three pieces; mill inspection to be
final.
359. Log Grades. Determination. The purpose of defining log grades is to
furnish a basis for separating the logs into groups whose average value or price per
1000 board feet can be determined, instead of attempting to arrive at an average
price for the entire run of logs. Three such groups permit of a sufficient differentia-
tion for this purpose.
Where logs are not bought or sold, but standing timber is manufactured by the
purchaser, log grades (§ 87) form the best basis for appraising the value of this timber.
The specification for determining the grade of logs must apply to the external
appearance and dimensions of the log. In application, logs on the border line between
two grades are usually thrown to the grade below, since a part of the surface is invis-
ible. Log grades are based on
1. Minimum diameters and lengths.
2. Surface appearance, and presence of knots or visible defects.
3. Judgment of scaler, based on 1 and 2 as to the minimum per cent of upper
or better grades of lumber contained therein.
The specifications for log grades are more elastic than for lumber grades, since
the presence of a smali per cent of high grade lumber may serve to offset serious
defects and give the log the value of a grade from which it would be excluded if based
solely on quantity or scale. These specifications should be drawn in such a manner
as to furnish the most serviceable basis of subdivision of the existing range of quality
found for the species and region, which object may be secured by modifying the
requirements as to size and per cent of upper grades required for logs of first and
second grades. _
Log grades should be established only after thorough mill-scale studies, and by
some agency similar to that of the United States Forest Service or a Lumber Manu-
facturers’ Association, so as to secure uniformity over as wide an area as possible.
Within the limits of a log grade a certain variation in average quality will oecur
in different quantities of logs, owing to the preponderance of higher or lower grades
of lumber within the limits set. The quality of the logs which form the basis of the
mill-seale study may be better or poorer than the average, even after classification
into grades. But as logs and timber stumpage are worth considerably less than
lumber, it is unnecessary to attempt a greater refinement, nor could it be practically
applied.
Diameter. Yor logs of the best grade, diameter is a reliable guide. Up to a
certain size, trees retain the branches, either alive or dead, and the central bole of
the tree is filled with these knots. Stunted, slow-growing, and consequently small
trees still have these knots, and during their growth, have made very little clear
lumber. Large trees, on the other hand, even if no older, have laid on much clear
wood outside of the knots.
The minimum diameter for the highest grade can be fixed to include practically
460 APPENDIX A
all logs of this class, not barred by knots or defects. This diameter will vary with
the same species in different regions, and for different species.
Effect of Defect upon Grades of Logs. The defect most easily seen, both in logs
and standing timber, is a knot. In grading hardwood logs, one sound, bright knot,
with a maximum diameter of 4 inches is taken as a standard defect. Other defects
are compared with this knot, on the basis of an equal amount of damage to quality.
These may be worm holes, smaller or larger knots, shake, rot, cat faces or fire scars.
The maximum number of standard defects, or their equivalent, is prescribed for each
grade of logs.
For conifers, a different system is employed, and the specifications lay stress on
the possible percentage of yield of certain grades, with indication as to the general
appearance and character of defect in logs which will yield this ratio.
Defects are of two classes, those which cause loss of grade, but no discount in
total scale, i.e., sound defects, and those which require elimination from the scale
of the defective part. To the first class belong sound knots, stain, firm red heart
and pitch. In the second class fall rot, shake, fire scars, cat faces, and crook or
sweep. Worm holes may be in either class, according to size and frequency.
In the grading of hardwood logs, no distinction is made, and the presence of more
than two “ standard” defects serves to throw the log into the lowest class, or No.
2, except when over 24 inches in diameter, when it must cut at least 75 per cent of
No. 1 common and better lumber.
With conifers, the presence of either class of defect will not reduce the grade of
a log as long as the minimum percentage of upper grades can still be secured. But
in reality, the value of the log is greatly lessened by such defects. With increasing
amounts of defect, the log is de-graded either to second or third grade, and finally
is rejected as cull.
360. Examples of Log Grades. Hardwoods—National Hardwood Lumber
Association, 1916 Oak, White and Red.
No. 1 logs. 2 inches of bright sap is no defect. Sap in excess of 2 inches is one
standard defect.
No. 1 logs must be 24 inches and over in diameter.
24 to 29 inches inclusive will admit of one standard defect or its equivalent.
30 inch and over will admit of two standard defects or their equivalent.
Select. Select logs must be 18 inches and over in diameter.
2 inches of bright sap is no defect. Sap in excess of 2 inches is one standard defect.
18 to 21 inches wide inclusive must have ends and surface clear.
22 and 23 inches will admit of one standard defect or its equivalent.
24 inches and over will admit of one more standard defect than is admitted in No.
1 logs of same size.
No. 2 logs. No. 2 logs must be 16 inches and over in diameter.
Bright sap is not a defect in this grade.
16- and 17-inch will admit of one standard defect or its equivalent.
18 to 23 inches inclusive will admit of two standard defects or their equivalent.
24 inches and over must cut 75 per cent or more into No. 1 common and better
lumber.
The grades for other species are similar.
Softwoods—Columbia River Log Scaling and Grading Bureau, Washington
and Oregon, 1920.
No.1 Logs. No. 1 logs shall be logs which, in the judgment of the scaler, will be
suitable for the manufacture of lumber in the grades of No. 2 ciear or better to an
amount of not less than 50 per cent of the scaied contents.
LUMBER GRADES AND LOG GRADES 461
No. 1 logs shall contain not less than six annual rings to the inch in the outer
portion of the log equal to one-half of the log content; and No. 1 logs shall be straight
grained to the extent of a variation of not more than 2 inches to the lineal foot for a
space of 2 lineal feet equidistant from each end of the log.
Rings, rot, or any defect that may be eliminated in the scale, are permitted in a
No. 1 log, providing their size and location do not prevent the log producing the
required amount of No. 2 clear or better lumber.
A No. 1 log may contain a few small knots or well scattered pitch pockets as per-
mitted in grades of No. 2 clear or better lumber; or may contain a very few grade
defects so located that they do not prevent the production of the required amount of
clear lumber.
No. 2 Logs. No. 2 logs shall be not less than 12 feet in length, having defects
which prevent their grading No. 1, but which, in the judgment of the scaler, will
be suitable for the manufacture of lumber, principally in the grades of No. 1 common
or better.
No. 3 Logs. No. 3 logs shall be not less than 12 feet in length, having defects
which prevent their grading No. 2 but which, in the judgment of the scaler, will be
suitable for the manufacture of inferior grades of lumber.
Cull Logs. Cull logs shall be any logs which do not contain 334 per cent of sound
lumber.
Logs which contain considerable clear lumber but not sufficient to grade No. 1,
and contain also large coarse knots or other grade defects of No. 3 quality, will be
classed as No. 2 if the average value of the lumber falls in this class, regardless of its
actual grade. Logs which are on the border line between two grades should be graded
alternately or in equal amount in the upper and the lower grade.
361. Mill-Grade or Mill-scale Studies. In §81 and § 82 it was shown that the
log scale should make no attempt to measure the actual sawed contents, which is
the sum of the scale, plus this over-run. It is equally impossible for the scaler to
separate his scale into grades, for in doing so he would be compelled to substitute
judgment for facts; vet the actual value of logs can be determined only by a knowl-
edge of both of these factors.
When the sawed output of a run of logs has been tallied and totaled separately
by grades, its comparison with the log scale shows for the entire quantity scaled, the
average over-run per thousand board feet of scale, and the per cent represented by
each grade produced. The value of the product of an average thousand feet B. M.
log scale in terms of sawed lumber is determined by first multiplying the price of
each grade of lumber sawed by the per cent of the grade in one thousand board feet,
adding the by-products, and multiplying by the total per cent of over-run.
This general check, applied to an average run of logs, and termed the mill run,
will serve to determine the value of similar average sizes and quality. But for
timber averaging larger or better, or smaller, knottier and poorer, the true value can
be obtained, by this method, only after sawing.
But individual logs of similar sizes possessing certain distinctive features, as
shown by surface indications such as clearness, knots and other defects, will cut out
about the same per cent of grades and values wherever found.
By using the log as the standard, it is possible to apply the results of mill-scale
studies of separate logs to stands whose average quality may be entirely different
from that which is being sawed, provided only that some logs of all qualities are
analyzed. For this reason, mill-scale studies should be based on the separate analy-
sis of the product of individual logs, by grades of lumber. Such studies determine,
for logs of each diameter, length and grade, first, the over-run in sound lumber, and
462 APPENDIX A
in all merchantable grades; second, the amount of each standard grade of rough
boards, expressed in per cent of the total scale of the log, net and gross.
362. Method of Conducting Mill-scale Studies. A tabulation, classification
and summary of the logs so analyzed permits, first, a correlation between logs of given
sizes, appearance and defects, and the actual sawed contents in grades which these
logs will produce, hence their actual value; second, the adoption of arbitrary
specifications for separating the logs themselves into log classes or grades; third, a
comparison of the value of logs of each size and grade with the cost of logging them,
enabling both owner of stumpage and operator to determine both the lower limits of
merchantability as to minimum size and per cent of sound lumber in a log which
warrants its removal and manufacture, and in case only a portion of the merchant-
able stand is removed, to know the relative value and profit of removing certain
definite classes and sizes of material and leaving others (§ 96).
The steps in a mill-scale study are:
1. Decision as to the exact number and designation of the grades of rough lumber
to be tallied.
2. Seale and record of each log, on the deck. If log grades have already been
adopted, the sealer assigns each log to its apparent grade. A full record would
embrace the following items: number of log (serial); length, in feet and inches;
position in tree, as butt, middle, top; species; average diameter inside bark at small
end; at large end; width of sapwood; thickness of bark; scale, by standard log rule,
full and net after deductions for cull defects; estimated log grade; description of
defects, preferably graphic, on a diagram showing large and small ends, and both
sides of logs. This record requires one man, an experienced log scaler, who will
place a number on each log to coincide with his record. Logs sealed sound are given
a special mark, and separated in the final tables.
3. Identification of this product of separate logs. A marker standing behind the
head saw marks with crayon each piece sawed from a log. The number of the log is
placed on the first few pieces. Different-colored crayons are used for alternate logs.
A count may be made of the total number of pieces from a log, as a check on the tally.
This work is made quite difficult by a resaw, which tends to mix the products of con-
secutive logs on the chains and requires the marking of both sides of the piece. Gang
saws further complicate the study. The marker can also check logs scaled as sound
for unseen defects appearing in sawing, and make final record of the logs which saw
up sound.
4. Record of grades and sizes. An expert grader, familiar with the standard for
the species and locality, will grade each piece. The record, kept on a separate sheet
for each log, and given the log number, will show length, width, and grade, by pieces,
and a recapitulation or summary for the log, giving in addition to the data copied
from the scales, the total board-foot contents in each grade, and the per cent of the
sound seale which this equals. This tally requires the services of a tallyman, mak-
ing a crew of four men.
5. Additional data needed. (a) Data on per cent of total contents utilized
embrace the measurement of the cubic contents of a log, and the analysis of the
volume which goes into slabs, edgings, and sawdust.
(b) Data on sawing practice include gage of saws, actual widths and lengths of
lumber sawed, efficiency of sawyers, methods of sawing, and the output or per-
formance of mill.
(c) Data. on the character of the timber and logs measured, to indicate the
comparison with other tracts, whether of higher or lower quality.
6. Tables or compilation of results. The logs can be classified, first, into sound
LUMBER GRADES AND LOG GRADES 463
and defective. Where log grades are used, these grades are also separated.
Next, the logs in each separate class are sorted into diameter classes, 1-inch or 2-
inch (volume based on differences of 100 board feet was used in the studies conducted
in District 1, Missoula, Montana). Asa result of this tabulation, the logs when orig-
inally classed by the scaler into grades by judgment, can be re-graded in accordance
with actual specifications for the grades. A sample form of tabulation would be,
by columns:
Diameter class.
Number of logs as a basis.
Average lengths of logs.
Per cent and value per 1000 board feet of each grade, represented in the prod-
uct obtained.
Total lumber tally, excluding cull lumber-sawed.
Over-run, excluding cull lumber sawed.
Tally of cull lumber sawed.
Over-run, including cull lumber sawed.
Net scale.
Per cent of total net scale in each class of logs.
Value per 1000 board feet, based on net tally.
Value per 1000 board feet, based on net scale.
Gross scale.
Per cent deducted for defect.
These data, shown thus for each class of logs, can be totaled for all logs, and
averaged.
7. Deductions or summaries. Irregularities are sure to occur in the final sum-
maries. These can frequently be evened off by means of curves. The final curves
and tables should show, for each separate log grade, the per cent of each grade of
lumber obtained for logs of each diameter class, and the value of the average log for
the class.
Effect of Waste or Cull. Such studies indicate the effect of increasing amounts
of waste or cull upon the value of the gross scale or log. Cull lumber may not
reduce the sale value of the residual lumber cut from the log, but the cost of log-
ging is based upon the actual size of the log, which is best measured by its gross
scale. The value of the product divided by this total scale gives a more correct
gage of the value of the whole log in terms of price per 1000 board feet, for the
purpose of determining whether the log is merchantable.
A crew of five men can usually tally two hundred logs per day of average
sizes. A single mill-scale study requires from one thousand to two thousand logs
for best results.
Instructions for Recording Data, U. S. Forest Service. Logs should be lettered
A, B, C, ete., A being the butt log. The species may be written out or the atlas
number may be used, thus: “ Loblolly pine”’ or “ P76.” The log length should
be measured to the nearest tenth of a foot. The crook may be measured by noting
the distance in inches between a straight line connecting the ends of the log on the
concave side and the log itself. If relative terms such as “ V”’ (very crooked),
“MM” (moderately crooked), and ‘‘S”’ (slightly crooked) are used, they should be
carefully defined. Thus, if the crook is more than one-half the diameter of the log
the term “ V”’ might be applied; if one-quarter to one-half the diameter it would
be “M’’; while less than one-quarter it would be “8.” If practically straight
indicate this by “O” after heading ‘‘ Crook.”
ry
464 ‘ APPENDIX A
Form of Record for Mill-scale Studies, U. S. Forest Service
Form 234 | Larce | Smann
Revised July 1, 1912 END. | END.
df If) Rae BRAC RS EST SECRET EA Ue Puma TG0G ee Bes tk
(Number.) (Letter.) Disb
SPECIES VE: Bin Wks TEARS WE SIs SORE eee eee wees
Width of bark,
ognlengineenaeee net COO ose KOs eee
| | Ditowb:.
1 2 3
Width of sap,
Rings,
Cubic ) Peeled,
feeti.<\eus 7
With bark,
Full scale,
_Net scale,
Sawed out,
4 5 6 if
OlOIN | |or | [Oo |e
LUMBER GRADES AND LOG GRADES 465
Knottiness may not always be of importance, but if it is recorded letters may
be used, as for crook. Two diameters inside bark at right angles should be measured
and the average recorded to the nearest tenth inch. The average width ‘of bark,
measured on a radius, should be recorded, care being taken to make the measurements
where bark is not partly worn off. The width of sap, in case desired, should be
measured along an average radius. In case the age at either end of the log is found
it can be inserted opposite ‘‘ Rings.” If the cubic content of a log is found in the
office it may be entered opposite ‘‘ Cubic feet.”” ‘‘ Full scale’? means the number of
board feet that would be tallied by the log sealer if the log were straight and sound.
“Net scale’ is the number of board feet tallied by the scaler after deducting for
defects of any kind. ‘‘ Sawed out ” is the number of board feet of lumber actually
sawed out.
The large spaces are for the dimensions of boards sawed out, each space being
for a separate grade. The name of the grade may be written or stamped in at the
head of the column. The total number of board feet of each grade sawed out should
be entered opposite the proper grade number in the small spaces under ‘‘ Sawed out,”
which is the grand total of these grade totals. The boards may be tallied thus:
“13X16,” meaning a board 1 inch thick, 3 inches wide, and 16 feet long. Frac-
tions may be indicated thus: 3!*3?12 (31/33 x12’). Asa rule the thickness
should be recorded to the nearest even quarter inch below, the width to the nearest
inch below, and the length to the neavest foot below the actual measurement. In
some cases it may be preferable to tally the number of board feet direct. This
means that the number of board feet in a board is read from a rule and entered at
once. Thus for a board 1’’ 3” X12’, the figure 3 would be tallied.
APPENDIX B
THE MEASUREMENT. OF PIECE PRODUCTS
363. Basis of Measurement. Any finished products of uniform or standard dimen-
sions, manufactured or cut from trees or logs may be measured by tallying or count-
ing the pieces. The size or contents of the standard piece determines its value,
either directly or by conversion to cubie or board-foot contents. The relative
value of pieces of different sizes is seldom directly proportional to their cubic volume,
though for such products as mining timbers this may be true. But for piling and
poles, value per cubic foot increases with increased length. The contents of sawed
or hewn pieces of rectangular shape is easily computed in board feet. Finished pieces
may be classed as round, hewn, or manufactured products. | Squares and bolts
intended for further manufacture may be sold by count (§ 9).
364. Round Products. Round products include poles, piling, posts, mine
timber, and certain lesser products such as hop poles and converter poles. Prac-
tically all round pieces are intended for uses requiring durability against atmospheric
and soil moisture, and strength to support weight or strains. Peeling reduces
weight for transportation.
Durability differs markedly with different species; hence whenever two or more
species are available, at least two classes of product are recognized, the first con-
taining the more durable or resistant species, the second, those which decay more
rapidly or require preservative treatment.
Round products are classed by length and diameter. Both minimum and maxi-
mum specifications are quoted for length. For diameter, the minimum is given
for each grade, since an excess adds to strength of piece. Prices are fixed by grades.
Straightness is a quality necessary to strength, in poles and especially in piling.
The degree of crook or sweep permitted in such products is always specified.
A minimum taper is desired in poles and piles, especially when long, in order to
diminish weight in handling. The diameter or circumference at both ends of poles
and piling is specified, and both minimum and maximum limits given, corresponding
to specified top diameters. Such limitations must ccirespond to the average shape
of the material available, both to insure strength and prevent rejection of too large’
a percentage of pieces.
Defects which will weaken the piece or decrease its durability serve to reject
products of this character. The specifications are remarkably similar whether for
poles, piles, mining timbers or cross ties. Such defects are shake, checks, splits,
large coarse or rotten knots which weaken the piece, and rot. When the qualities
of the piece for the use for which it is intended permit of knots, or of a certain amount
of center or pipe rot, these defects may be permitted, especially if their exclusion
would cause the rejection of a large percentage of the output. For poles, the presence
of center rot requires an increased diameter at the butt, for acceptance of piece.
Round products as a class give almost complete utilization of the bolt or log, and
of the tree. The ends of piling, cross ties, and butts of poles are cut square with a
saw, and the only waste is the bark. Where there is a market for posts or small
466
THE MEASUREMENT OF PIECE PRODUCTS 467
mine props, the tops are also utilized down to 3 or 4 inches. These small round prod-
ucts also permit the utilization of suppressed trees and small timber, thus reducing
total per cent of waste in a stand to a minimum.
365. Poles. Standard poles are 20 feet or more in length, and are used prin-
cipally for telegraph or telephone lines. Specifications are based usually on
circumference rat er than diameter. Since the ratio between the two measure-
ments for a circle is 3.1416 to 1, and this is exceeded for eccentric cross sections,
specifications, especially for large sizes, call for } to 1 inch greater circumference than
the proportion of 3 to 1 for dry poles and an extra } to ? inch for green or water-
soaked poles.
White cedar, which furnishes the larger part of the poles utilized, is measured
either by circumference or diameter. The specified relation of these measurements
for peeled poles is,
TABLE LXVIII
RELATION BETWEEN CIRCUMFERENCE AND DIAMETER FOR WHITE CEDAR POLES
Seasoned poles, Seasoned poles, Green or water-soaked poles,
Top diameter. Circumference at top. Circumference at top.
Inches Inches Inches
+ 12 123
5 15 16
6 183 193
7 22 228
An excess of 6 inches in length is permitted, or 1 half-inch secant for every 5 feet
in length.!
The standard specifications for Eastern white cedar poles, (American Telephone
and Telegraph Company), are given below:
All poles shall be reasonably straight, well proportioned from butt to top, shall
have both ends squared, the bark peeled, and all knots and limbs closely trimmed.
The dimensions of the poles shall be in accordance with the following table, the
“top”? measurement being the circumference at the top of the pole and the “ butt ”’
measurement the circumference, six (6) feet from the butt. The dimensions given
are the minimum allowable circumferences at the points specified for measurement
and are not intended to preclude the acceptance of poles of larger dimensions.
When the dimension at the butt is not given, the poles shall be reasonably well
proportioned throughout their entire length. No pole shall be over six (6) inches
longer or three (3) inches shorter than the length for which it is accepted. If any
pole is more than six (6) inches longer than is required, it shall be cut back.
Quality and Defects of Timber. The wood of a dead pole is grayish in color. The
presence of a black line cn the edge of the sapwood (as seen on the butt) also shows
that a pole is dead. No dead poles, and no poles having dead streaks covering more
than one-quarter of their surface, shall be accepted under these specifications. Poles
having dead streaks covering less than one-quarter of their surface shall have a cir-
cumference greater than otherwise required. The increase in the circumference
shall be sufficient to afford a cross-sectional area of sound wood equivalent to that of
svund pieces of the same class.
1 Northwestern Cedarmen’s Association.
468 APPENDIX B
TABLE LXIX
Minimum DIMENSIONS OF WHITE CEDAR POLES IN INCHES
CLASSES
A B C D E Pome
Length | 6 feet| 6 feet! '6 feet; 6 feet
of | Top from) Top from, Top from | Top ‘from Top | Top | Top
poles _ butt | butt | | butt | butt
(Feet) | | |
CIRCUMFERENCE, INCHES
20 234 | 33 | 214 | 380 | 182 | 28% | 18: | 26 17; 153.) 12%
22 231 | 34 | 214 | 31 | 182 | 293 | 18} | 27 17 | 163 | 125
25 2320 86rd 2th | “SselMessisiael Ter |-og4 | 17 | Lopes
30 23%.) 40 | 213 | "86 | 183; 344 183 | 312 | 17 | 154 | 122
35 931'|. 43 | 214 | 40 | 18% | 372 | 184 | 342 | 17° | 15%
40 232 | 47 | 214 | 43 182 | 40 ) 184-1) 3872 | 27~ |) 154
45 233 | 50° | 213 | 46 | 182°] 43 | 183 | 40
50 233 | 53 | 214 | 49 | 182 | 46 | 182 | 438
55 234 | 56 | 213 | 52 |
60 23% | 59 | 213 | 54
No dark red or copper-colored poles, which when scraped do not show good
live timber, shall be accepted under these specifications.
No poles having more than one complete twist for every twenty (20) feet in length,
no cracked poles and no poles containing large season checks shall be accepted under
these specifications.
No poles having “‘ cat faces,’’ unless they are small and perfectly sound and the
poles have an increased diameter at the ‘‘ cat face,”’ and no poles having ‘‘ cat faces ”’
near the six (6) foot mark or within ten (10) feet of their tops, shall be accepted under
these specifications.
No shaved poles shall be accepted under these specifications.
No poles containing sap rot, evidence of internal rot as disclosed by a careful
examination of all black knots, hollow knots, woodpeckers’ holes, or plugged holes;
and no poles showing evidences of having been eaten by ants, worms or grubs shall
be accepted under these specifications except that poles containing worm or grub
marks below the six (6) foot mark will be accepted.
No poles having a short crook or bend, a crook or bend in two planes or a reversed
curve shall be accepted under these specifications. The amount of sweep, measured
between the (6) foot mark and the top of the pole, that may be present in poles accept-
able under these specifications, is shown in the following tables:
35-foot poles shall not have a sweep of over 103 inches.
40-foot poles shall not have a sweep of over 12 inches.
45-foot poles shall not have a sweep of over 9 inches.
50-foot poles shall not have a sweep of over 10 inches.
55-foot poles shall not have a sweep of over 11 inches.
60-foot poles shall not have a sweep of over 12 inches.
THE MEASUREMENT OF PIECE PRODUCTS : 469
Poles having tops of the required dimensions must have sound tops. Poles
having tops one (1) inch or more above the requirements in circumference may have
one (1) pipe rot not more than one-half (3) inch in diameter. Poles with double
tops or double hearts shall be free from rot where the two parts or hearts join.
No poles containing ring rot (rot in the form of a complete or partial ring) shall
be accepted under these specifications. Poles having hollow hearts may be accepted
under the conditions shown in the following table:
App To Burr REQUIREMENTS
Average diameter ;
or rot = | c R
of 25 and 30-foot | of 35-, 40-and 45- | of 50-, 55-, 60- and
poles foot poles | 65-foot poles
2 inches Nothing Nothing Nothing
3 inches 1 inch Nothing Nothing
4 inches 2 inches Nothing Nothing
5 inches 3 inches 1 inch Nothing
6 inches 4 inches 2 inches 1 inch
7 inches Reject 4 inches 2 inches
8 inches Reject 6 inches 3 inches
9 inches Reject Reject 4 inches
10 inches Reject Reject 5 inches
11 inches Reject Reject 7 inches
12 inches Reject Reject 9 inches
13 inches Reject Reject Reject
Scattered rot, unless it is near the outside of the pole, may be estimated as being
the same as heart rot of equal area.
Poles with cup shakes (checks in the form of rings) which also have heart or star
checks may be considered as equal to poles having hollow hearts of the average
diameter of the cup shakes.
Western Red Cedar forms the main source of supply of poles in the West. The
specifications for these poles permit a much smaller taper than for Eastern timber
since the tree form is more cylindrical.
The specifications (American Telephone and Telegraph Company) are given
in Table LXX, p. 470.
For Southern Yellow Pine poles for creosoting, the required dimensions are
given in Table LXXI, p. 471.
Chestnut has been a standard pole timber but is rapidly disappearing in Eastern
states because of the ravages of the chestnut blight. The specifications differ only
slightly from those for white cedar, and are as follows:
Dimensions. Length. Poles shall not be over six (6) inches shorter or twenty-
four (24) inches longer than the length specified in the order.
Circumference. Poles shall be classified with respect to their circumferences at
six (6) feet above the butt and at their top in accordance with Table LXXII, p.
472. This table gives the minimum allowable circumference at six (6) feet above
the butt and at the top for poles of each class and length listed and shall not preclude
the acceptance of poles having greater circumferences at those points of measure-
ment than those given in the table.
470
APPENDIX B
TABLE LXX
(Mrintmum DiMENsIONS OF WESTERN RED CEDAR PoLEs IN INCHES)
CLASSES
A B Cc D E F
(Minimum) (Minimum) (Minimum) (Minimum
Tench i circum-|top cireum-)top circum-|top circum- (Minimum (Meuaene
of erence ference ference ference top circum: ton eee
oles =e ne): as ae ference ference
(Feet) | Circumfer-| Circumfer-| Circumfer-) Circumfer- 15) 12)
ence 6 feet | ence 6 feet | ence 6 feet | ence 6 feet
from butt | from butt | from butt | from butt
|
INCHES
20 30 28 26 24 | No butt | No butt
22 32 30 27 25 | require- | require-
25 34 31 28 26 ment | ment
30 37 34 30 28 |
35 40 36 32 30
40 43 38 34 32
45 45 40 36 34
50 47 42 38 36
55 49 44 40 38
60 52 46 4] 39
65 54 48 43
(Chestnut poles, continued) Shape. No poles shall contain short crooks.
With respect to other deviations from straightness, poles required in the order to be
of the ‘‘ town ”’ class shall be free from all deviations from straightness except sweep
in one plane only. The amount of sweep between the top and the butt of these poles
shall not be greater than that specified for their length in the Table LX XIII, p. 472.
Poles required by the order to be of “‘ country” class may have sweep in two
planes or sweep in two directions in one plane provided that a straight line con-
necting the center of the butt with the center of the top does not, at any intermediate
point, pass through the external surfaces of the pole. Where sweep is in one plane
and one direction only, the amount between the top and the butt shall not be greater
than that specified for the length of the pole in Table LX XIV, p. 473.
366. Piling. All piles are peeled before measuring. Piling should show close
grain or slow growth, and be straight, with a minimum taper. If a straight line
drawn between the centers of the butt and top falls outside the peeled pile at any
point the piece is usually rejected. Hence long piling brings a proportionally higher
Specifications for piling prescribe minimum and maximum diameters for
Examples of such specifications are shown
price.
the butt, and a minimum top diameter.
in Table LXXV, p. 473.
Piling is sold by the linear foot, but the price per foot increases with length of
stick. In Southern pine, piling is frequently measured by log scale, by taking the
diameter at the middle of the log.
THE MEASUREMENT OF PIECE PRODUCTS 471
TABLE LXXI
Minimum DIMENSIONS OF SOUTHERN YELLOW PINE POLEs In INCHES—
CLASSES
B C D KE
Length
of 6 feet 6 feet 6 feet 6 feet 6 feet
poles Top | from ; Top | from | Top | from | Top | from | Top | from
(Feet) butt butt butt butt butt
CIRCUMFERENCE, INCHES
20 22 293 20 27 18 26 16 24 14 21
22 22 303 20 28 18 2 16 25 14 22
25 22 324 20 29% 18 283 16 26 14 23
30 22 35 20 32 18 303 16 284 14 244
35 22 38 20 34 18 325 16 30 14 26
40 22 40 20 36 18 3435 16 32 14 275
45 24 424 DP} || BS 20 36 18 334
50 24 44} 22 40 20 38 18 35
55 24 47 22 421 | 20 40
60 24 49 22 443 20 42
65 24 51 22 47
70 24 53 22 49
75 24 55 22 51.
80 24 57
85 24 59
90 24 61
Defects. Defects in piling are rot, loose or rotten knots, wind shake, twisted
grain, checks or other defects which interfere with driving or durability.
367. Posts, Large Posts and Small Poles. Standard fence posts are cut, 7, 72
or 8 feet long. Dimensions up to 10 feet are termed large posts, while lengths of
12 to 18 feet inclusive are small poles; the distinction being based partly on the
uses to which they are put. Standard cedar posts may be 2 inches short, and {
inch scant in diameter when seasoned, but must be full if green or water-soaked.
Posts are graded by inch classes measured at top or small end. They will permit
knots and other defects which will not weaken the piece for the purpose of a post.
Cedar may contain a certain amount of center or pipe rot. White cedar posts may
have a sweep of 4 inches. Western juniper and red cedar posts may have much
greater sweep, provided it lies in one plane or “‘ crooks one way.”
Post material in round bolts whose diameter exceeds 6 to 7 inches, when not
needed for corner or gate posts, is usually split into two or more fence posts whose
cross-sectional area will equal or exceed that of round posts of the standard dimen-
sions.
Posts must be cut from live timber and, in white cedar, rot or other defects are
permitted which do not impair the strength of the post for uses of a fence post.
472
APPENDIX B
TABLE LXXII
Mrinimuw CrrcUMFERENCE!S OF CHEestNut Poues IN INCHES
CLASSES
|
A B C D EK F | G
Length |
(Feet) 6 feet 6 feet 6 feet 6 feet ‘ feet 6 feet
Top! from | Top) from | Top) from | Top} from | Top, from Top) from ; Top
butt butt butt butt | butt butt |
|
INCHES
| | | [eect
20 24 | 34 | 22| 31 | 20] 29 | 18 | 27 | 16) 24 | 22 | 15
25 DAs | AC NW 22 Ne SE Ne20 || e321). 1s) 29) 16 eee | 24 1915
30 24 | 40 | 22 | 37 | 20/ 35 | 18] 32 16 | 29) | 15 27s
35 D4) | «AS || 22") 40 a0 | 287 || 18! 85 | 16 | 382 29 | 15
40 24 | AG. | 22) | 43 20 |-40-'| 18>) Sia! 16 | 35 32) Seb
45 24 | 49 | 22 | 46°) 20 | 43 | 18 | ADM 16) e380
50 D4 | 2. || 22) 49. 0200) 46 || 18) 48
55 24° | 55 | 22.) 52 4/920) | 49
60 24 | 58 | 22) 55
65 26 | 60 | 22| 58
70 26 | 62 | 22 | 60
75 26 | 64 | 22 62
80 26 | 66 | 22 | 64
85 26 | 68 | 22 | 66
90 26 | 70 | 22 | 68
TABLE LXXIII
Maximum Sweep, PoLes, STANDARD
Length Maximum Length Maximum | Length Maximum
of pole. sweep. of pole. sweep. of pole. sweep.
Feet Inches Feet Inches Feet Inches
20 4 45 9 70 14
25 5 50 10 75 15
30 6 55 11 80 16
35 7 60 12 85 17
40 8 | 65 13 90 18
Small cedar poles up to and including 18 feet in length may have a sweep of
4 inches, which for lengths of 16 to 18 feet is measured from a poiht 4 feet from the
butt, in the manner prescribed for long poles.
Fire-killed lodgepole pine is accepted for poles and posts in the Rocky Mountains.
THE MEASUREMENT OF PIECE PRODUCTS 473
TABLE LXXIV
Maximum Sweep, Poites, Country
|
Length Maximum | Length | Maximum Length Maximum
of pole. sweep. | of pole. sweep. of pole. sweep.
Feet Inches Feet Inches Feet Inches
20 6 45 133 70 21
25 The 50 15 75 223
30 9 55 163 80 24
35 103 60 18 85 253
40 12 | 65 19} 90 27
TABLE LXXV
DIMENSIONS FOR PILING
Minimum top Diameter limits,
ee hength- diameter—Inches| butt
Not less than Inches
Hardwoods—Eastern......... 20-35 6 12 and over
40-50 6 14 and over
TPeyarnvaarey (Ceatls Ao Ab oo weet oe Under 30 6 12 to 16
30-50 6 12 to 18
W@aMlitOumiser. cove she casi eon © Under 60 9 13 to 17
Southern Pace Rin. os... ee Over 60 9 13 to 20
Te TOC ee Ben Bc BWis 2 seiie cts vonage Under 30 9 13 to 18
30-40 9 14 to 18
40-69 8 14 to 18
70 and over 8 16 to 18
All classes of poles and posts are usually seasoned to decrease weight for trans-
portation.
Fence stays are round or split pieces about 2 inches in diameter and 5 to 6 feet
long. They are used between posts for wire fences as upright pieces not set in the
ground, to which the wires are stapled to prevent their being spread apart by stock,
and to reduce the number of posts required.
Converter poles, called also furnace poles and brands, are consumed in the process
of refinmg copper. The Montana specifications call for poles with a top diameter of
3 to 4 inches and length of 24 feet. They should have as little taper as possible.
Eastern brass mills use poles 25 to 40 feet long, 2 inches and over at top, and 5 inches
and over at butt. The bark is not removed and poles must be green.
Standard California hop poles are made from split pieces 2 by 2 inches by 8 feet.
In the East hop poles are usually made from round pieces of approximately the same
dimensions.
368. Mine Timbers. Mine timber can be classed as stulls and props, lagging,
shaft timbers and lumber, and mine ties. Stulls include round props used as posts,
caps to connect pairs of opposite posts, and girts to connect posts lengthwise of the
A74 APPENDIX B
gallery. Their dimensions depend on size of galleries. Diameters vary from 53
to 24 inches. Square props are used for similar purposes. Small round props used
principally in coal mines are termed mine props and run from 4 inches up in diam-
eter and from 4 to 10 feet in length. These timbers are used to support the ground
and must be straight, sound and free from knots that will impair the strength of
the piece, or from defects affecting strength or durability.
Mine timber is bought by the linear foot, by classes based on top diameter.
Split props must have a cross-sectional area in square inches equal to that of a round
post of minimum specified diameter.
Pole lagging varies from 14 to 5 inches in diameter at small end and averages 16
feet in length. Four- to five-inch poles may be split. Lodgepole pine is the
principal species used. Lagging is bought by the piece.
Mine Ties. Cross ties for mine tramways are usually 5 to 53 feet long but may
be from 3 feet to 6 feet in length, and vary for individual mines, from 3 by 4 inches
to 5 by 6 inches in diameter. Their small size makes a market for very small timber,
which can be grown in 20 to 30 years. Ties are bought by count, and on basis of
specifications.
Round mine timber of these classes and mine ties not only utilize the entire stick,
but permit the almost complete utilization of the felled tree and of the stand. In
fact, the tendency is to exploit young second-growth stands while still too small to
bear seed, and under private management forests in mining regions are rapidly
destroyed. The same conditions permit of thinnings in dense stands, the removal
of small diseased trees and a short rotation, and under forest management offer
very favorable conditions for profitable production of timber.
369. Cross Ties. Standard railroad cross ties are either hewn, with two parallel
faces, or sawed to specified dimensions. Switch ties are sawed in sets of graduated
lengths. Hewn ties, termed also pole ties, are made from round bolts hewn on two
sides to produce parallel faces. Bolts 14 inches and over in diameter are usually
split into two or more ties, hewn on four sides. Hewn ties are preferred to sawed
ties as they are said to be more durable.
The standard specifications for cross ties of the U. S. Railroad Administration
have since March, 1920, been adopted with slight changes by over two-thirds of the
railroad mileage of the country. These specifications are shown graphically in Fig.
88. The specifications of the Pennsylvania Railroad System, based on the above,
are as follows:
All ties shall be free from any defects that may impair their strength or durability
as cross ties, such as decay,! splits, shakes, large or numerous holes ? or knots,* or
oblique fiber with slope greater than one in fifteen.
Ties from needle-leaved trees shall be of compact wood with not less than one-
1'Ties must be rejected when decayed in the slightest degree, except that the
following may be allowed: in cedar, “ pipe or stump rot ” up to 14 inches diameter
and 15 inches deep; in cypress, ‘‘ peck’ up to the limitations as to holes; and, in
pine, ‘ blue sap stain.”
2 A large hole in woods other than cedar is one more than 3 inch in diameter and
3 inches deep within, or one more than 1 inch in diameter and 3 inches deep outside
the sections of the tie between 20 and 40 inches from its middle. Numerous holes
are any number equaling a large hole in damaging effect.
3 A large knot is one exceeding in width more than } of the width of the surface
on which it appears; but such a knot may be allowed if it occurs outside the sections
of the tie between 20 and 40 inches from its middle. Numerous knots are any
number equaling a large knot in damaging effect.
THE MEASUREMENT OF PIECE PRODUCTS 475
third summerwood when averaging five or more rings of annual growth per inch, or
with not less than one-half summerwood in fewer rings, measured along any radius
from the pith to the top of the tie. Ties of coarse wood, with fewer rings or less
summerwood, will be accepted when specially ordered.
Acceptable Rejectable
Acceptable
aimee ual | near eh pa raeoata
Sm see Voetvaet eet (new (Ode
ae ‘ i 1
n= | Fa ee
al] | i
ee)
Acceptable
" > 1
|
Fic. 88.—Standard sizes for cross ties accepted under U.S. Railway administration specifications.
Grade
re nN (>) bow ”
Ties for use without preservative treatment shall not have sapwood wider than
one-fourth the width of the top of the tie between 20 and 40 inches from the middle,
and will be designated as ‘heart ” ties. Those with more sapwood will be desig-
nated as “‘ sap ’’ ties.
Manufacture. Ties should be made from trees which have been felled not longer
than one month.
476
All ties shall be straight, well manufactured,! cut square at the ends, have bottom
APPENDIX B
and top parallel, and have bark entirely removed.
Dimensions.
the following grades
will be accepted.
Before manufacturing ties, producers should ascertain which of
All ties shall be eight (8) feet six (6) inches long.
All ties shall measure as follows throughout both sections between 20 and 40
inches from the middle of the tie.
pee Sawed or hewn top, Sawed or hewn top
bottom and sides and bottom
1 None accepted 6” thick x6” wide on top
2 6” thick X7” wide on top | 6” thick x7” wide on top
7” thick <6” wide on top
3 6” thick <8” wide on top | 7’ thick x7’” wide on top
6” thick 8” wide on top
4 7” thick X8” wide on top | 7” thick X8’’ wide on top
5 7” thick X9” wide on top | 7” thick X9” wide on top
The above are minimum dimensions. Ties over one (1) inch more in thickness,
over three (3) inches more in width, or over two (2) inches more in length will be
degraded or rejected.
The top of the tie is the plane farthest from the pith of the tree, whether or not
the pith is present in the tie.
Ciass U—Ties wuich May Bre Usep UNTREATED
Group Ua Group Ub Group Uc Group Ud
“ Heart”’ Cedars
“ Heart’’ Cypress
“Heart’’ Redwood
“Heart’’ Black Locust
“ Heart’? White Oaks
“ Heart’? Black Walnut
“ Heart’? Douglas Fir
“ Heart’ Pines
““Heart’’ Catalpa
“Heart’’ Chestnut
‘“Heart’’ Red Mulberry
“Heart’”’ Sassafras
Ciass T—Ties wuHicH SHOULD Br TREATED
Group Ta Group Tb Group Tec Group Td
Ashes ““Sap’’ Cedars Beech “Sap” Catalpa
Hickories ““Sap’’ Cypress Birches “Sap”? Chestnut
““Sap”’ Black Locust “Sap’’ Douglas Fir |... Cherries Elms
Honey Locust Hemlock Gums Hackberry
Red Oaks Larches Hard Maples Soft Maples
“Sap’’ White Oaks “Sap” Pines “Sap’’ Mulberries
“Sap’’ Black Walnut “Sap’’ Redwood ““Sap”’ Sassafras
Spruces
Sycamore
White Walnut
1A tie is not well manufactured when its surfaces are cut into with score-marks
more than 3 inch deep or when its surfaces are not even.
THE MEASUREMENT OF PIECE PRODUCTS 477
370. Inspection and Measurement of Piece Products. Piece products, while
graded on basis of dimensions, may be rejected either because of scant length, thick-
ness or width, below requirements for lowest grade, or because of disqualifying
defects. As these products are usually hauled to track or landing before being
graded, considerable losses are occasioned by failure to conform to these specifi-
cations.
Although the character and amount of defect disqualifying a piece is usually pre-
scribed as exactly as possible in the specifications, yet there is always considerable
latitude exercised by the inspector, and the closeness or laxity of inspection may
vary under instructions according to the demand for the product. This method of
regulating supply supplements price adjustments and is open to serious objec-
tions. Good inspectors are thoroughly familiar with the qualities required of
product and display a certain leniency in judging pieces which almost conform to
specifications, provided the general run of the product is of good quality and work-
manship. An inspector must command respect for his integrity and reputation for
giving both parties a square deal.
The contents of various classes of piece products may be desired in terms of either
cubic feet or board feet, in order to reduce different kinds of products to terms of a
common standard or to simplify terms of payment or of record. Since most of these
products are exposed to decay, and their value is measured by their resistance to
fungus attacks, wood preservation is becoming more prevalent. Creosoting plants
base their charges upon the cubic contents of such pieces as are treated as a whole.
The volume in cubic feet of poles of different dimensions is obtained by the for-
mul given in § 27 by applying the values for cubic volumes of cylinders shown in
Table LXXVII, Appendix C. The middle diameter measurement is the most
accurate method for long poles, owing to the errors resulting from large butts.
For short poles, piling or mining stulls, the middle diameter measurement is
probably the most satisfactory, and the table of cylindrical contents, or Humphrey
caliper cordwood rule will suffice as a standard. Prices for mining stulls of different
lengths and diameters sold by the U. 8S. Forest Service in Montana, are based
upon the cubic contents of pieces of each standard size.
Smaller material such as fence posts or other round pieces may be converted to
cubic feet by the same means.
Cross ties, on account of uniformity of size, are converted into their equivalent
in board feet, and expressed either by average contents per tie, or by the number of
ties per 1000 feet B. M. The average contents of hewn ties may be obtained by
scaling a large number as logs 8 feet long. Or their cubic contents may be cal-
culated from the thickness and face and reduced to board feet. The first method
deducts for sawdust, and the second for squaring the tie. By either method a 6- by
8- inch tie scales about 32 board feet, or 30 ties per 1000 feet B.M. Ties 83 feet long,
7 inches thick by 9- inch face may average 40 to 44 board feet, or 25 to 23 per 1000
board feet.
Ratios are easily worked out on the basis of specifications and actual scale, and,
once determined, may be substituted for measurement and applied to the count of
ties, separately for each size class or grade of tie.
To reduce piling to board feet, pieces are sometimes scaled directly by a log rule.
For small poles, posts or mining timbers the best method of conversion is to apply
a converting factor to the cubic contents of pieces of given dimensions. Where
total or actual cubic contents is measured, the best ratio is probably 5.5 board feet
per cubic foot. If cubie contents includes only the cylinder measured at small end,
a larger ratio is required,
478
APPENDIX B
The following table gives converting factors adopted by the U. 8. Forest Service
for products of various classes and dimensions:
TABLE LXXVI
ConveRTING Factors, PimcE Propucts To Boarp FEET
Product
Long cord (acid wood,
pulpwood, and dis-
tillation wood).....
Cord (spruce pulp-
Cord (shingle bolts)...
Cord (fuel material
averaging 5 inches or
less in middle diame-
Cord (fuel material
averaging 6 inches or
more in middle diam-
Load (in the rough)*..
Pole (telephone)......
Pole (telephone)......
Tie (standard).......
Tie (2d\class)< ei
Tie (narrow gauge)...
Tie (narrow gauge)...
Tie (narrow gauge)...
Derrick pole. a... a5.
Derrick set (11 pieces)
Assumed
dimensions
4’ Ch? SARE
4’ «4! Se
4’ x4’ <8’
4’ x4’ X98’
4’ x4’ x8’
4’ x4’ x8’
1 cord
7” X30!
9” X30’
7” X30’
10” x 16’
6” x< Si x ey
6” x qe Sc gs’
BONS
7" > 8” < 61”
6” 4 et Ded 63’
7X8" 8!
7” x9" Xx 8!
7” X30’
Equiv-
Reuse Product
feet
Trestle timber......
: Trestle timber.......
625 Housellog-. ee ae
Housellogcenracctes wat
560 FLouBe Og ia. eins
600 Mining timber.......
333} Props ieee
Converter pole......
Pole (fence).........
500 iIRole*@ence) suse ee
Lagging (6 pieces)...
Cubie foot (round)...
Riatle(Split)iae csi
PIECES Ate ee bien ce
3333 Sticks.As sciatiieee
60 Slab.
100 IROStrmn ieee ie
60 Post (circumference,
60 UStinches):.kasee sac
30 Post): cette neva tater
20 Linear foot.....
15 IBTACES ar varayiysciecccire
25 Stay, (fence)... 5... 2...
15 Stay. ch See ee
30 Shake (roof)........
35 Shake (fruit tray)....
602 Wi Pieketoemnne. trowel
480 Stake (fence)........
Assumed
dimensions
10’ X 20’
” « 12’
8” x 16’
vied x 16/
qv x10’
6” x 10’
6” x 10’
4” < 20’
16’
4” x 20’
Bf >4 6’
6” we 4 td
2 X66?
6” < vite
st eS
5 «x7
10” x1’
4” x 6’
Q” x 6’
4” « 6’
a1) x6” «x o
ou «5K 32”
BY >< 5/
3" 5!
Equiv-
alent in
board
feet
70
20
30
30
15
10
10
10
* This refers to small irregular pieces of wood and not to material that can be ricked for
measurement.
APPENDIX C
TABLES USED IN FOREST MENSURATION
TABLE LXXVII
CuBIc CONTENTS OF CYLINDERS AND MULTIPLE TABLE OF
BasaL AREA
This table serves a double purpose. It shows, in the first place,
the contents of cylinders of different diameters and lengths. It may be
used to determine the contents of logs whose diameters are measured
at the middle. The table shows also the sums of the basal areas of
different numbers of trees. Thus the total basal area of fifty-one
trees 9 inches in diameter is 22.53 square feet. This table will be found
very useful in computing the total basal area of different diameter
classes in forest surveys.
The values given in this table are practically identical with those
of the Humphrey Caliper Cordwood Rule (§ 121) fer which it may be
substituted. By multiplying the values in the table by 1.28 the
contents of logs will be found in terms of stacked cubie feet of cord-
wood, p. 480.
TABLE LXXX
THe INTERNATIONAL Loa RULE FoR SAws CUTTING A } INCH
KERF
This log rule is derived from the values of the International log
rule for saws cutting a §-inch kerf, by applying the factor .904762 to
the values in the former rule, computing to the third decimal place,
and then rounding off the resultant values to the nearest 5 board feet.
The values were computed and checked by Judson F. Clark in 1917,
p. 493.
TABLE LXXXI!
Values in square feet for .16 and for .66 of the area of circles of dif-
ferent diameters, for computing the cubic volume of trees by the Schiffel
formula, V =(.16 B+.66b) h, p. 494.
1Computed by the U.S. Forest Service.
479
480
APPENDIX C
TABLE LXXVII
Cunic CONTENTS OF CYLINDERS AND MutripLE TABLE oF BasaL AREAS
Length,
Feet, or
Number
of Trees.
|
COO ONDA MNPWDH A
Diameter in Inches.
|
2 3 | 4 | 5 6 7 8
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
0.02 0.05 0.09 0.14 0.20 On 7/ 0.35
0.04 0.10 OL, 0.27 0.39 0.53 0.70
0.07 0.15 0.26 O.41 0.59 0.80 1.05
0.09 0.20 0.35 0.55 0.79 1.07 1.40
O.II 0.25 0.44 0.68 0 98 I. 34 6 7/5}
Ong 0.29 0.52 0.82 1.18 1.60 2.09
0.15 0.34 0.61 0.95 WISH 1.87 2.44
Only 0.39 0.70 -1.09 1.57 pig 249.9
0.20 0.44 On79 ae eg 2oAT Bye iyi
0.22 0.49 0.87 1.36 1.96 2.67 3.49
0.24 0.54 0.96 1.50 2.16 2.94 3.84
0.26 0.59 1.05 1.64 220 By. 4.19
0.28 0.64 L038 7, 2.55 BAT 4.54
0.31 0.69 i273 1.91 2.75 Bye'g fl 4.89
OF33 On7a: Teor 2.05 2.95 4.01 5:24
0.35 0.79 1.40 2.18 Zell 4.28 5-59
O.. 37 0.83 1.48 2.32 3-34 4.54 5-93
0.39 0.88 ei) 2.45 2G 4.81 6.28
0.4! 0.93 1.66 2.59 3.73 5.08 6.63
0.44 0.98 1.75 2.73 3-93 5-35 6.98
0.46 1.03 1.83 2.86 4.12 5.61 Taos
0.48 1.08 1.92 3.CcO0 Avg? 5.88 7.68
0.50 ih 0% 2.01 3.14 4.52 6.15 8.03
On52 1.18 2.09 RgAG] An7 6.47 8.38
0.55 T¥2 2.18 3.41 4.91 6.68 8.73
Ons 1.28 PAGS B55 Goat 6.95 9.08
0.59 1A 2} 2.36 3.68 50) Wee 9.42
0.61 Loy 2.44 2es 5.50 7.48 O77.
0.63 Ls A\2 253 3.95 5.69 Ted 10.12
0.65 1 A7, 262 4.09 5.89 8.02 10.47
‘0.68 Ta52 Zavjal Ano 6.09 8.28 10.82
0.70 1 allst7/ 2.79 4.36 6.28 8.55 Lleal7,
0.72 1.62 2.88 4.50 6.48 8.82 TS 2
0.74 i 0}7/ 2.97 4.64 6.68 9.09 iintsiy/
0.76 Le f2 3.05 Angi 6.87 9.35 12322
OL7 Wega 3.14 4-91 7. O77 9.62 25. 5K,
0.81 jt gol 2823 5.05 7.26 9.89 12.92
Length,
Feet, or
Number
of Trees.
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
Siz
58
59
60
TABLES USED IN FOREST MENSURATION
000
Fm belie ts o0000
el niin ila ln
OO ee
ee
2
TABLE LXXVII—Continued
Diameter in Inches.
ee ee ei ie
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
87
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.16
10.
.69
42
96
22
Tae20
TRO
13.96
TAaE
14.66
15.01
Wiss 5 B18)
Mesa 7p
16.06
16.41
16.76
WO
17.45
17.80
nts) a 1615
18.50
18.85
19.20
19.55
19.90
20.25
20.60
20.94
481
482
Length,
Feet, or
Number
of Trees.
CO ONDA NASHWDH Hw
_
APPENDIX C
TABLE LXXVII—Continued
Diameter in Inches.
9 | 10 | 11 | 12
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
44
88
+33
-77
eer
—~
we RO
OOMW0 CONNINAD NAL HWW
Anum Ww WNAHO
oOo ons
NU OAMS WWwWN HO
13 | 14 | 15
_
COO ONDA UAPWDN
.O7
Hoty
Oy
28
»35
.41
.48
739
62
.69
.76
.83
.90
-97
.O4
.10
oh 7)
.24
5 ay
a oke
45
52
59
66
-73
-79
. 86
-93
.0O
07
sil
52
.28
-35
.42
.48
-55
Length,
Feet, or
Number
of Trees.
38
39
40
41
42
43
++
45
46
47
48
49
50
51
52
53
54
55
56
57
58
TABLES USED IN FOREST MENSURATION
9
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
-79
23)
.67
salad
56
.0O
44
88
32
-76
a2mr
.65
.09
+53
-97
41
. 86
. 30
-74
.18
.62
.O7
.51
-95
-39
.83
127
“72
TABLE LXXVII—Continued
10
20.
2
21
2D\.
22
23.
24.
24.
25
25.
26.
26.
2G fe
Ath.
28.
28.
29.
30.
30.
ele
Bite
Bon
Bk
33-
33-
34-
34-
35:
36.
3605
37 -
37-
38.
38.
39.
39.
40.
40.
Diameter in Inches.
11
12 | 13
.85
63
.42
.20
-99
77
.56
-34
a1
JI
.70
.48
277
.06
.84
.63
a) ars
46.
47.
49.
50.
Gite
Ge
483
484 APPENDIX C
TABLE LXXVII—Continued
Diameter in Inches.
Length, ¥ ;
Feet, or 16 | 17 | 18 19 ~20 | 21 | 22
Number
of Trees. =
COONAN NLPWHNH
_
Contents of Cylinders in Cubic Feet, or Basal Areas in pau piContents) of Cylindi rsdn (Cab ieirctnc Deal ananareinect ae Feet.
.40
-79
.19
-59
.98
.38
hal
cet?
NNN N |
APN RO
to
Ss)
fe)
¢
at.
-77
53
.30
o7/
.84
.60
S30
.14
.9O
.67
44
21
-97
74
S51
41
.81
122
.62
.03
-43
.84
Length,
Feet, or
Number
of Trees.
38
39
40
TABLES USED IN FOREST MENSURATION
16
Contents of Cylinders in Cubic Feet, or Basal Area
oh OAN
HNN NW
No
_
a
3
TABLE LXXVII—Continued
17
18 | 19
Diameter in Inches.
20
21
485
22
s in Square Feet.
59.
Ol.
One
68
Ti Dye
74.
75-
15
.92
70.
69
g1.40
93.81
96.21
98.62
101.02
103.43
105.83
108.2
110.64
113.05
115.45
117.86
120.26
122.67
125.07
127.48
129.89
13 2i42C
134.70
1277.10
139.51
141.91
144.32
TA6.. 72
149.13
T§51.53
153-94
156.34
158.75
161.15
163.56
165.96
168.37
Li Oy,
173.18
175-59
177-99
180.40
100.
102.
105.
108.
110.
rye
116.
118.
CAN ie
124.
126.
129.
HBIt
134.
7)
139.
142.
145.
14/.
T5Or
Tee
155.
158.
161.
163.
166.
168.
171.
eae
176.
7Oe
182.
184.
187.
190.
192.
195.
197.
486
Length,
Feet, or
Number
of Trees.
OO ONDA MNPWDHNH
-_
23
APPENDIX C
TABLE LXXVII—Continued
24
Diameter in Inches.
25 | 26
27
28 | 29
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
.89
-77
.66
84.
103.
106.
109.
113%
116.
.69
-37
.06
-75
-44
A@)
. 81
.50
.18
.87
.56
.24
-93
.62
31
-99
.68
-37
.05
-74
-43
ati
.80
-49
.18
. 86
-55
.28
“55
.83
51
.38
.66
+93
ol
.48
io
.O4
231
-59
. 86
.14
.42
.69
-97
san
52
Length,
Feet, or
Number
of Trees.
38
39
40
TABLES USED IN FOREST MENSURATION
23
TABLE LXXVII—Continwed
24
Diameter in Inches.
25 | 26
27
28 | 29
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
64
.52
41
- 30
.18
.O7
“95
84
11)
122
125
128.
Tighe
1a 3
138.
I41.
144.
DAT
150.
153.
57h
160.
163.
166.
169.
W7 2).
WS
179.
182.
185.
188.
19l.
194.
197)
201"
204.
207.
210.
PIGS
216.
219.
222K
226.
229.
232,
225.
38
55)
.66
129)
132"
136.
139.
143.
146.
149.
Tye
156.
160.
163.
167.
17/6)
Wofeie
U7 Fc
180.
184.
187.
190.
194.
197.
201.
204.
207.
Divitee
Dif
218.
DP
224.
228.
Pat
235.
238.
242.
245.
248.
PSP)
255.
140.
143.
147
LS
154.
158.
162
165.
169.
7h
Lor
180.
184.
188.
TOE:
195.
199.
202.
206.
210.
2a
PUG
De te
224.
228.
222%
235.
239.
243.
247.
PIX) 5 7/
254.
258.
261.
265.
269.
DDK.
276.
ray
79
.48
17
85
54
23
92
151
155
159
163.
167).
WOE
7k
178.
182.
186.
190.
194.
198.
202.
206.
210.
214.
216.
22D e
226.
220);
234.
238.
242.
246.
250.
254.
258.
262.
266.
270}
2A
278.
.09
.O7
04
162.
166.7
Fae
fly
179.
183.
188.
192.
196.
200.
205.
209.
DUB
218.
222i.
226.
230.
2B Ss
239.6
DAB IT
248.
2B}
256.
260.
265.
269.
27a
Cafe 5
282.
286.
290.
295.
299.3
174.
178.
183.
188.
192.
197.
201.
206.
211.
PUG
220.
224.
229.
2337
238.
243.
247%
252.
487
488
Length,
Feet, or
Number
of Trees.
CO ONIA NPWHH
~
30
APPENDIX C
TABLE LXXVII—Continued
31 | 32 | 33
Diameter in Inches.
34
35 | 36
Contents of Cylinders in Cubic Feet, or Basal Areas in Square Feet.
.24
.48
-59
519)
-94
.88
. 82
. 30
61
TABLES USED IN FOREST MENSURATION
TABLE LXXVII—Continued
489
30
31
32 | 33
Diameter in, Inches.
34
35 | 36
Contents of Cylinders in Cubic Feet, or Basa! Areas in Square Feet.
186.
IQl.
196.
NN WN N
NR NN
RNNN N NNN NN
NN NN
212).
P39 3
D238
228.
234.
240.
245.
OOhrs
nN
Wwn
NON
ww NNN N
NHM
239.
245.
252.
268.
27 5c
Melee,
289.
296.
303.
gute
318.
325.
Gea).
339.
346.
303:
360.
367.
374.
381.
3288.
395.
402.
409.
Asta
Qui,
431.
438.
445.
452.
459.
466.
473.
480.
487.
494.
501.
508.
516.
522),
530.
"490 APPENDIX C
TABLE LXXVIII
AREAS oF CIRCLES OR TABLE OF BasAL AREAS FOR DIAMETERS TO NEAREST
zo INcH
vo o 1) v o +)
Fs ~ a fa w fe oT fe uw = ma -
Ou i) Ou Ow Ow © Ou v Ow o
S82. fea|| ae looaee ll Sed pee Mica, Secu ec) pxeeull ae liam
A < fa < fa < fa < ‘a <q fa <
T20) |) 2006) ||20 O227)||2 30 049 ||4.0 087 15.0 | .136 ||6.0 | .196
Tl =007 a0 024 I 052 at |. O92 Peper a0 203
2 | .008 2 026 2 056 .2 | .096 PLAN e A UA) 42 210
3m) 2009 3 029 3 059 He eLOr 3 153 +3 216
Ail Orr Bt O31 4 | .063 .4 106 4 | -~159 +4 223
1.5 | .O12 }/2.5 | -034 |[3.5 | -067 |]4-5 | -110 [15.5 | -165 |/6.5 | .230
6 O14 .6 037 6 o71 .6 115 6 Teal 56) e230
7 | -016 |] .7 | .040 7-975 I -7 120 7 Weckv 7) a7 ees
8 o18 .8 | .043 8 079 70 126 Sao .8 252
9 020 -9 | .046 9 083 SO) | beg 9 190 9 260
7.0} .267 |[8.0 | .349 |19.0 | .442 |]10.0} .545 |{11.0] .660 |/12.0] .785
Bit 275 I} .358 I | .452 I} .556 tl) 2072 -I] .799
.2 283 2) 2367 2 |. 462 2] .567 2] .684 2|(SSx2
Bay aczoh 3 | -376 3.] -472 3} -579 3} .696 .3| -825
-4 | -299 4 | -385 4 | .482 4] .590 4] -709 .4| .839
Fos 307 |18.5 | -394 lI9-.5 492 |{10.5] .601 }J11.5] .721 |j12.5]) .852
.6 315 6 | .403 Onl) 3503 "6|26r3 6) .734 6| .866
“7 |= 323 7 | -413 7 \ Shes .7| -624 iN 047 7\ -880
.8 332 8 422 8 524 .8] .636 8} .759 8} .894
-9 | -340 9 | -432 9] -535 .9| .648 9] .772 9} -908
13.0] .922 ||14.0]1.069 |}15.0]1.227 |]16.0]1. 396 }/17.0]1.576 |]/18.0]1. 767
sil) sou I]I.084 I]I.244 IjI.414 -1/1.595 1|1.787
2} .950 2}1. 100 2}1 . 260 2)1.431 2|1.614 2|1. 807
3) .965 BileLLs Blle2y 3|1.449 31 L032 3]1.827
4] -979 4|I. 131 4]. 294 4|1 . 467 .4{1.651 4|1.847
13.5] -994 ||t4.5]1.147 |]15.5]1.310 1/16. 511.485 |]17.5]1.670 ||18.5]1.867
.6]1 .009 6|1. 163 ROL nese 7 6]1. 503 6|1.689 6|1. 887
.7|1.024 711.179 -7|1.344 71.521 .7|1.709 7|1.907
. 8] 1.039 8]1.195 .8]1. 362 8}1. 539 .8}1.728 &]1.928
Q|1.054 Qi. 211 -9|1.379 g]t.558 .9/1.748 9|1.948
TABLES USED IN FOREST MENSURATION 491
TABLE LXXVIII—Continued
2 fy C fea © fy s (oa fe om i. fy
on o vu e ou ro) Ou 2 vy 2 On 2
o4 3 oe _@ | oe Ss |] os 8 og ms o8 _@
A Elbe ad a | 2 A | 2 a < A <
19.0} 1.969]/20.0] 2.182//21.0] 2.405]/22.0] 2.640]/23.0] 2.885]!24.0] 3.142
Ee OOO] eatie2 204i) eat 2aAeiy tl 22664]! a1) 2.970] 11! 3.168
220m p22. 2206 32) 2h4'51 .2| 2.688 72| 2.936 aj 2) 3.194
=|) 2-022 Not 2. 246 -3| 2-474] .3] 2.712 .3| 2.961 | Bowen
pA 2 OF =Ale22270|) .4) 2.408 a Aegletg) -4| 2.986 vAl 3.247,
19.5} 2.074||20. 5} 2.292//21.5] 2.521|/22.5| 2.7611123.5| 3.012]124.5] 3.275
.6] 2.095 .6] 2.315 .6] 2.545 .6| 2.786 AO EanOzo 36)| Bosrou
Sy) Bastia Ale2sou, ST 2563 57) AowKe) 27\| Bean S| Gauges
ate|| gp sees! .8] 2.360 .8] 2.592 Sts] Aarts .81 3.089 RO 3355
29) 2560] .coie2'2382)) | 0] 2.656), to) 2. 860i) of, 3.7'75|| 0] 3.382
= a a & Ks ey bi od a io
Br, 2 || 8¢ ge |) 3¢ ge || 84 oes 2
og .& od ~€ og aS OG 8 OG 8
A < A < A 4 A <4 a <
25 0nl 3409) 12620) | 93.687 ||27 208) 3.976 ||28.0 ff 4.276 ||20,0 4.587
Sit || Bacteta) ep esr Fes .I | 4.006 1) AsO7, 5 it 4.619
22) |) 32464! a2 AA, 2 ARORS aA || Zhe skey 2 4.650
Ss 4 OI Stale ears ae OOS, 23) | 42368 58 4.682
-4 | 3.519 -4 | 3-801 -4 | 4.095 -4 | 4.399 -4] 4.714
DSS esa S4gn i202 5 ees |27-5) lef ke 2555) 1) 4420 129.5 4.746
|) Bagel .6 | 3.859 A || A eS .6 | 4.461 6 4.779
Sap \ I Bel OOPs G7 || Sesteretes eA LSS 7 W444 Os ai 4.811
ats) || Sia(lgia set} Se@H7/ 508) || A BOP [e452 8 4.844
-9 | 3-659 -9 | 3-947 -9 | 4.246 On 4555 -9 | 4.876
30.0 | 4.909 |131.0 | 5.241 |/32.0 | 5.585 1133-0 | 5.940 [134.0 6.305
25.On | OLOst ||2GnOn a 71O608||e7 Onl e467) ||2SsOnle 7a o7 OM IGOKo© 8.296
AOLOn| eon] 2 41.0 | 9.168 |/42.0 | 9.621 |/43.0 [10.085 ||44.0 | 10.559
45.0 |11.045 146.0 |11.541 |]47.0 ]12.048 |/48.0 {12.566 |l49.0 | 13.095
50.0 {13.635 |{51.0 |14.186 |/52.0 ]14.748 |153.0 |15.321 |154.0 | 15.904
55.0 116.499 156.0 |17.104 |157.0 |17.721 {158.0 |18.348 [159 0 | 18.986
60.0 |19.635
492 APPENDIX C
TABLE LXXIX
TABLES FOR THE CONVERSION OF THE Metric To THE ENGLISH SYSTEM AND
Vice VERSA.
Hectares Acres to
to Acres. Hectares.
I 2.47109 I= .40467
2= 4.94213 = .80934
BG Lae 3=1.21401
4= 9.88436 4=1.61868
5= 12.35545 SF 2.02335
6=14.82654 6=2.42802
7 =17.29763 7 = 2.83269
8=19.76872 8 = 3.23736
Q= 22.23981 9= 3.64203
Cubic Meters
Kilos to Pounds. Ber eetere t
per Acre.
= 2.20462 I= 14.291
= 4.40924 2= 28.582
3= 6.61386 3= 42.873
4= 8.81848 4= 57.164
5 — O22 10 5= 71.455
6=13.22772 6= 85.746
7=15.43234 7 = 100.037
8= 17 .63696 8=114. 328
9=19.84158 9= 128.619
Centimeters to Kilometers to 5
Inches. Miles.
I= .39370423 I= .62137676
2= .78740846 2=1.24275352
3=1.18111269 3=1.86413028
4=1.57481692 4=2.48550704
5=1.96852115 5=3.10688380
6= 2. 36222538 6=3.72826056
7 = 2.75592961 7=4.- 34963732
8= 3.14963384 8=4.97101408
9=3- 54333807 9=5.59239084
Meters to Feet. Cubic Meters
to Cubic Feet.
I= 3.280869 I= 35.315617
2= 6.561738 2= 70.631234
3= 9.842607 3= 105.946851
4=13.123476 4=141. 262468
5=16.404345 5= 176. 578085
6=19.685214 6=211.893702
7 = 22.966083 7 = 247 . 209319
8= 26. 246952 8 = 282.524936
9= 29. 527821 9= 317 840553
THE INTERNATIONAL Loa RULE FoR Saws CurTtine A }-INcH KeERF.
TABLES USED IN FOREST MENSURATION
TABLE LXXX
493
Standard scale for seasoned lumber with 7s-inch shrinkage per 1-inch board, and saws cutting
a }-inch kerf, or for green lumber, for saws cutting a 37-inch kerf.
Diam 8
4 aise
5 5
6 10
rai 10
8 15
9 20
10 30
11 35
12 45
13 55
14 65
15 75
16 85
17 95
18 110
19 125
20 135
21 155
22 170
23 185
24 205
25 220
26 240
27 260
28 280
29 305
30 325
31 350
32 BY)
33 400
34 425
35 450
36 475
37 505
38 535
39 565
40 595
41 625
42 655
43 690
44 725
45 755
46 795
47 830
48 865
49 905
50 940
51 980
52 1020
53 1060
54 1100
55 1145
56 1190
57 1230
58 1275
59 1320
60 1370
LenetH or Loa In FEET
9 10 11 12 13 14 15 16 17 18 19 20 | Diam
5 5 5 5 5 5 5 5 5 10 10 4
5 5 5 10 10 10 10 10 15 15 15 15 5
10 10 10 15 15 15 20 20 20 25 25 25 6
15 15 15 20 20 25 25 30 30 35 35 40 7
20 20 25 25 30 35 35 40 40 45 50 50 8
25 30 30 35 40 45 45 50 55 60 65 70 9
35 35 40 45 50 55 60 65 70 75 80 85 10
40 45 50 55 65 70 75 80 85 95 | 100 | 105 11
50 55 65 70 75 85 90 95 } 105 |} 110 | 120 | 125 12
60 70 75 85 90 | 100 | 105 } 115 | 125 | 135 | 140 | 150 13
70 80 90 | 100} 105 | 115 | 125 | 135 | 145 | 155 | 165 | 175 14
85 95 | 105 | 115 | 125 | 135 | 145 | 160 | 170 } 180 | 195 | 205 15
95 | 110 | 120 | 130 | 145 | 155 | 170 | 180 | 195 | 205 | 220 | 285 16
110 | 125 | 135 | 150 | 165 | 180 | 190 | 205 | 220 | 235 | 250 | 265 17
125 | 140 | 155 | 170 | 185 | 200 | 215 | 230 | 250 | 265 | 280 | 300 18
140 | 155 | 175 | 190 | 205 | 225 | 245 | 260 | 280 | 300 | 315 | 335 19
155 | 175 | 195 | 210 | 230 | 250 | 270 | 290 | 310 | 330 | 350 | 370 20
175 | 195 | 215 | 235 | 255 | 280 | 300 | 320 | 345 | 365 | 390 | 410 21
190 | 215 | 235 | 260 | 285 | 305 | 330 55 | 380 | 405 | 430 | 455 22
210 | 235 | 260 | 285 | 310 | 335 | 360 90 | 415 | 445 | 470 | 495 23
230 | 255 | 285 | 310 | 340 | 370 | 395 | 425 | 455 | 485 | 515 | 545 24
250 | 280 | 310 | 340 | 370 | 400 | 430 | 460 | 495 | 525 | 560 | 590 25
275 | 305 | 335 | 370 | 400 | 435 | 470 | 500 | 535 | 570 | 605 | 640 26
295 | 330 | 365 | 400 | 435 | 470 | 505 | 540 | 580 | 615 | 655 | 690 27
320 | 355 | 395 | 430 | 470 | 510 | 545 | 585 | 625 | 665 | 705 | 745 28
345 | 385 | 425 | 465 | 505 | 545 | 590 | 630 | 670 | 715 | 755 | 800 29
370 | 410 | 455 | 495 | 540 | 585'| 630 | 675 | 720 | 765 | 810 | 860 30
395 | 440 | 485 | 530 | 580 | 625 | 675 | 720 |, 770 | 820 | 870 | 915 31.
420 | 470 | 520 | 570 | 620 | 670 | 720 | 770 | 825 | 875 | 925 | 980 32
450 | 500 | 555 | 605 | 660 | 715 | 765 | 820 | 875 | 930 | 985 |1045 33
480 | 535 | 590 | 645 | 700 | 760 | 815 | 875 | 930 | 990 |1050 |1110 34
510 | 565 | 625 | 685 | 745 | 805 | 865 | 925 | 990 |/1050 | 115 |1175 35
540 | 600 | 665 | 725 | 790 | 855 | 920 | 980 |1045 |1115 |1180 |1245 36
570 | 635 | 700 | 770 | 835 | 905 | 970 |1040 {1110 |1175 |1245 |1315 37
605 | 670 | 740 | 810 | 885 | 955 |1025 |1095 |1170 |1245 |1315 |1390 38
635 | 710 | 785 | 855 | 930 |1005 |1080 (1155 |1235 |1310 |1390 |1465 39
670 | 750 | 825 | 900 | 980 |1060 |1140 |1220 |1300 |1380 |1460 |1 40 40
705 | 785 | 870 | 950 |1030 |1115 |1200 |1280 |1365 |1450 |1535 |1620 41
740 | 825 | 910 | 995 |1085 |1170 |1260 |1345 |1485 |1525 |1615 |1705 42
780 | 870 | 955 |1045 |1140 |1230 |1320 |1410 |1505 |1600 |1695 |1785 43
815 | 910 |1005 |1095 {1195 |1290 |1385 |1480 |1580 |1675 |1775 |1870 44
855 | 955 |1050 |1150 |1250 |1350 |1450 |1550 |1650 |1755 |1855 |1960 45
895 | 995 |1100 /1200 |1305 |1410 |1515 |1620 |1730 |1835 |1940 |2050 46
935 |1040 |1150 |1255 |1365 |1475 |1585 |1695 |1805 |1915 |2030 |2140 47
975 |1090 /1200 |1310 |1425 |1540 |1655 |1770 |1885 |2000 |2115 |2235 48
1020 |1135 |1250 /1370 |/1485 |1605 |1725 |1845 |1965 |2085 |2205 |2330 49
1060 /1185 |1305 |1425 |1550 |1675 |1795 |1920 |2045 |2175 |2300 |2425 50
1105 |1235 |1360 |1485 |1615 |1745 |1870 |2000 |2130 |2265 |2395 |2525 51
1150 |1285 |1415 |1545 |1680 |1815 |1945 |2080 |2215 |2355 |2490 |2625 52
1195 |1335 |1470 |1605 |1745 |1885 |2025 |2165 |2305 |2445 |2590 |2730 53
1245 |1385 |1530 |1670 |1815 |1960 |2100 |2245 |2395 |2540 |2690 |2835 54
1290 |1440 |1585 |1735 |1885 |2035 |2185 |2330 |2485 |2640 |2790 |2945 55
1340 |1495 |1645 |1800 |1955 |2110 |2265 |2420 |2575 |2735 |2895 |3050 56
1390 |1550 |1705 |1865 |2025 |2185 |2345 |2510 |2670 |2835 |3000 |3165 57
1440 |1605 |1770 |1930 |2100 |2265 |2430 |2600 |2770 |2935 |3105 |3275 58
1490 |1660 |1830 |2000 |2170 |2345 |2515 |2690 |2865 |3040 |3215 /3390 59
2425 |2605 |/2785 '2965 |3145 13325 |3510 60
Formula: {(D?X0.22) —0.71D} X 0.904762 for 4-foot sections.
_ Taper allowance: 3 inch per 4 feet lineal.
494 APPENDIX C
TABLE LXXXI
TABLES FOR VALUES IN SCHIFFEL’S FoRMULA FOR CuBIC VOLUMES OF ENTIRE STEMS.
This table is for use in calculating the cubic contents of trees by a short method (Schiffel’s
formula):
V=H(0.16B+0.66b).
The field measurements necessary for this calculation are the diameter breast-high and the
diameter at the middle height of the tree. To find the volume look up 0.16 of the area corre-
sponding to the D.B.H. of the tree. Add to this 0.66 of the area corresponding to the diameter
at the middle height. The sum of the two multiplied by the height of the tree equals the total
volume of the tree in cubic feet. Thus, if the total height of the tree is 62.5 feet, the diameter
breast-high 10.4 inches, and the diameter at the middle 8.1 inches, from tables 0.16B and 0.666
it is found that the areas corresponding ot these diameters are 0.094 and 0.236, respectively.
Their sum, 0.330, multiplied by the height, 62.5, equals the volume, 20.6 cubic feet.
0.16 or THE AREA OF A CrircCLE AT Breast HetcutT (0.16B)
Diametersy| == == ese: {ae
i)
0.0 Or 0.2 0.3 0.4 O25) ||) 2OR6 0.7 0.8 0.9
Inches Sq. ft. | Sa. ft. | Sa. ft. | Sa. ft. | Sa. ft. | Sa. ft. | Sq. ft.) Sa. ft. | Sa. ft. | Sa. ft.
| |
1 0.001 | 0.001 | 0.001 | 0.001 | 0.002 | 0.002 | 0.002 | 0.003 | 0.003 | 0.003
2 .003 .004 .004 .005 .005 005 006 .006 .007 .007
3 008 .008 009 010 .010 O11 O11 .012 .013 .013
4 .014 015 015 .016 017 .018 .018 .019 .020 .021
5 022 023 024 025 025 .026 .027 .028 .029 .030
6 031 .032 .034 .035 036 .037 038 .039 .040 .042
of 043 044 045 047 .048 049 .050 052 053 054
8 .056 AUS .059 .060 . 062 .063 065 .066 .068 .069
9 O71 .072 074 Ono 077 .079 .080 . 082 .084 .086
10 087 089 091 093. .094 .096 .098 . 100 . 102 .104
11 .106 .108 . 109 eb Li 113 aka les) pea li liz 119 .122 .124
12 .126 .128 .130 .1'32 .134 .136 .139 -141 .143 .145
13 .147 zs iks4 0) .152 154 Balter) .159 161 . 164 . 166 .169
14 ed: sale! .176 178 .181 .183 .186 .189 -191 .194
15 .196 .199 . 202 . 204 . 207 .210 212 215 .218 .221
16 .223 . 226 .229 232 «200 .238 . 240 . 243 . 246 249
17 . 252 .255 . 258 .261 . 264 . 267 .270 273 .276 . 280
18 . 283 . 286 . 289 . 292 -295 . 299 . 302 . 305 . 308 .312
19 315 .318 -o22 02D 328 -332 -335 -339 342 346
20 . 349 003 . 356 . 360 - 363 . 367 .370 3874 .378 .381
21 . 385 . 389 .392 .396 -400 .403 -407 -411 -415 .419
22 -422 -426 .430 .434 438 442 446 .450 454 458
23 462 .466 .470 .474 .478 .482 486 -490 494 .498
24 . 503 . 507 oll OLD .520 .524 .528 532 .537 541
25 545 . 550 . 554 .559 . 563 . 567 .572 .576 .581 585
26 . 590 .594 .599 . 604 .608 -613 .617 622 627 631
27 . 636 .641 . 646 . 650 .655 . 660 665 .670 .674 .679
28 . 684 . 689 . 694 .699 . 704 .709 .714 .719 . 724 .729
29 . 734 . 739 . 744 . 749 . 754 .759 .765 .770 Atta . 780
30 . 785 791 .796 .801 . 806 .812 817 822 828 .833
31 . 839 . 844 . 849 855 . 860 . 866 .871 877 .882 .888
32 . 894 .899 905 .910 .916 .922 .927 .933 939 .945
33 950 .956 .962 .968 974 .979 .985 .991 -997 | 1.003
34 1.009 | 1.015 | 1.021 | 1.027} 1.033 | 1.039 | 1.045 | 1.051 | 1.057 | 1.063
35 1.069 | 1.075 | 1.081 | 1.087 | 1.094 | 1.100 | 1.106 1 Mpa ta Li fp a Bese br Ip he ga Uey L455
Diameter.
Inches
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
TABLES USED IN FOREST MENSURATION
TABLE LXXXI—Continued
0.16 or THE ARPA OF A CircLE aT Breast Hetent (0.16B)
0.0 0.1 0.2 0.3 0.4 0.5
Sq. ft. | Sa. ft. | Sq. ft. | Sq. ft. | Sq. fit. | Sq. ft
TSTMS 7a eleaAe e150) |) Leoenl) 163
JEKOSN IE ZON e208 | teeta. | toot eo,
1-260) | 122677) 1.273" | 1-280) | 1.287 1) 1-294
1327 I lessa| tesat | 1.848 (e355 |) dese2
1.396 | 1.403 | 1.410 | 1.417 | 1.424 ] 1.431
1.467 | 1.474 | 1.481 | 1.488 | 1.496 | 1.503
1.539 | 1.547 | 1.554 | 1.561 | 1.569 | 1.576
1.614 | 1.621 | 1.629 | 1.636 | 1.644 | 1.651
W689 Leo, L705. L713) fb L720) 0) 1728
IZB Tle Leo LTS sulelecOla|els 799) We le S07
1847 esas ele ses lesil il t.879) 1) 1. 887
1.928 | 1.936 | 1.944 | 1.952 | 1.961 | 1.969
2.011 | 2.019 | 2.027 | 2.037 | 2.044 | 2.053
De || oaks || Ysa) || Caen |) Were || eres
2.182 | 2.190 | 2.199 | 2.208 | 2.217 | 2.226
2.270 | 2.279 | 2.288 | 2.297 | 2.306 | 2.315
2.360 | 2.369 | 2.378 | 2.387 | 2.396 | 2.405
2.451 | 2.461 | 2.470 | 2.479 | 2.488 | 2.498
2.545 | 2.554 | 2.564 | 2.573 | 2.583 | 2.592
2.640 | 2.649 | 2.659 | 2.669 | 2.678 | 2.688
2.737 | 2.746 | 2.756 | 2.766 | 2.776 | 2.786
2.835 | 2.845 | 2.855 | 2.865 | 2.875 | 2.885
2.936 | 2.946 | 2.956 | 2.966 | 2.976 | 2.986
3.038 | 3.048 | 3.058 | 3.069 | 3.079 | 3.089
3.142 | 3.152 | 3.163 | 3.173 | 3.184 | 3.194
3.247 | 3.258 | 3.269 | 3.279 | 3.290 | 3.301
3.355 | 3.365 | 3.376 | 3.387 | 3.398 | 3.409
3.464 | 3.475 | 3.486 | 3.497 | 3.508 | 3.519
3.574 | 3.586 | 3.597 | 3.608 | 3.619 | 3.630
3.687 | 3.698 | 3.710 | 3.721 | 3.733 | 3.744
3.801 | 3.813 | 3.824 | 3.836 | 3.848 | 3.859
3.917 | 3.929 | 3.941 | 3.953 | 3.964 | 3.976
4.035 | 4.047 | 4.059 | 4.071 | 4.083 | 4.095
4.155 | 4.167 | 4.179 | 4.191 | 4.203 | 4.215
4.276 | 4.288 | 4.301 | 4.313 | 4.325 | 4.337
4.399 | 4.412 | 4.424 | 4.436 | 4.449 |] 4.461
4.524 | 4.536 | 4.549 | 4.562 | 4.574 | 4.587
4.650 | 4.663 | 4.676 | 4.689 | 4.702 | 4.714
4.779 | 4.792 | 4.805 | 4.818 | 4.831 | 4.844
4.909 | 4.922 ] 4.935 | 4.948 | 4.961 | 4.975
5.041 | 5.054 | 5.067 | 5.080 | 5.094 | 5.107
5.174 | 5.187.| 5.201 | 5.214 | 5.228 | 5.241
5.309 | 5.323 | 5.337 | 5.350 | 5.364 | 5.378
5.446 | 5.460 | 5.474 | 5.488 | 5.502 | 5.515
5.585 | 5.599 | 5.613 | 5.627 | 5.641 | 5.655
0.6
cs Getibe
. 169
.234
. 300
. 368
.438
es
.510
. 584
659
.736
815
os
.895
977
061
. 147
.234
NNwN ee
.324
.414
. 507
. 602
. 698
bo bo
Now bw
796
.895
BOO
. 100
. 205
bw bw to
ww
-311
. 420
- 5380
. 642
755
Wwwww
.871
-988
-107
-227
- 350
Pee PW Ww
-474
. 600
-127
857
-988
PPR
-120
.255
391
.529
. 669
or or or Or Or
or
or
oe ee Hm Hm He HR wWwwww wo wWwwwh wo Nonwmwnwb bw NNN ee etl eel eee el ool
or or or
bo bh
to be
PP PP OO
— i
NNN ee
to bw bh
ww w
wWwwwww
oe; PPP
or or or or or
oF; > Fk ee ee CO Wwwwww wowwnr do NnwNWwhb tb NWNN Ee Se et
or Or Or Or or
495
496
APPENDIX C
TABLE LXX<XI—Continued
0.66 or THE AREA OF A CIRCLE AT THE MIDDLE HEIGHT OF THE TREE (0.66B)
Diameter.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 ONT 0.8 0.9
Inches Sq. ft. | Sa. ft: | Sq: ft. | Sq. ft. | Sqatt: Sq. ft: | Sq. ft. | Sa: ft. Sq: ft. | Squat
1 0.004 | 0.004 | 0.005 | 0.006 | 0.007 | 0.008 | 0.009 | 0.010 | 0.012 | 0.013
2 014 016 O17 019 021 .023 .024 026 028 .030
3 .032 0385 .037 039 042 044 047 049 052 .055
4 058 206101. .064 067 .O70 .073 .076 O80 083 086
5 .090 094 097 .101 105 .109 113 milaly/ 121 125
6 .130 .134 .138 .143 .147 .152 ita / . 162 166 lyn!
7 .176 . 182 187 .192 .197 202 .208 .213 .219 225
8 .230 .236 . 242 . 248 254 . 260 266 APACE 279 285
9 . 292 .298 805 oul .318 325 332 .339 346 3853
10 . 360 . 367 ot . 382 . 389 .397 .405 412 420 428
ig .436 444 .452 .460 468 .476 .484 493 .501 .510
12 .518 527 586 545 .554 . 563 572 581 .590 .599
13 608 .618 627 . 637 646 . 656 666 .676 . 686 .696
14 .706 Gy .726 .736 . 746 Stay . 767 .778 .788 .799
15 810 .821 .832 . 843 854 865 .876 . 887 899 910
16 .922 933 .945 956 .968 -980 .992 | 1.004 } 1.016 | 1.028
17 1.040 1.053 | 1.065 | 1.077 | 1.090 | 1.102 1.105 } 1.228") 17140.) Lats
18 1.166 Limo} 2.192) 152054) L219 La2o2 1.245 | 1.259 | 1.272.,; 1.286
19 1.299 1.303 | Lesov | Desa els55) DS6en 1ss83e) Leso7 | 1244 eas
20 1.440 1.454 | 1.469 | 1.483 | 1.498 | 1.513 LO2Sa] knb42 ele 57 ahora
21 1.587 1.603 | 1.618 | 1.633 | 1.649 1.664 1.680 | 1.695 | 1.711 1.726
22 1.742 DS |) Levee | L790) 1.80601 2.822 15839) ll s8550) Lest 1.888
23 1.904 1) 17920) 1-987 ) 1954} 1.971 | 1.988 | 2.005 | 2:022 |) 2.089 | 27056
2 2.0%3 | 2.091 | 2.108 | 2.9296 | 2.143 | 2.161 | 2-178 | 2.196 | 2.214 | aga2
25 2.250 | 2.268 | 2.286 | 2.304 | 2.322 | 2.341 | 2.359 | 2.378 | 2.396 | 2.415
26 2.433 | 2.452 | 2.471 | 2.490 | 2.509 | 2.528 | 2.547 | 2.566 |} 2.585 | 2.605
Parl 2.624 | 2.644 | 2.663 | 2.683 | 2.703 | 2.722 | 2.742 | 2.762 | 2.782 | 2.802
28 2.822 | 2.842 | 2.863 | 2.883 | 2.903 }| 2.924 | 2.944 | 2.965 | 2.986 | 3.006
29 3.027 | 3.048 | 3.069 | 3.090 | 3.111 | 3.133 | 3.154 | 3.175 | 3.197 | 3.218
30 3.240 | 3.261 | 3.283 | 3.305 | 3.327 | 3.349 | 3.371 | 3.393 | 3.415 | 3.437
31 3.459 { 3.482 | 3.504 | 3.527 | 3.549 | 3.572 | 3.595 | 3.617 | 3.640 |] 3.663
32 3.686 | 3.709 | 3.732 | 3.756 | 3.779 | 3.802 | 3.826 | 3.849 | 3.873 | 3.896
33 3.920 | 3.944 | 3.968 | 3.992 | 4.016 | 4.040 | 4.064 | 4.088 |] 4.112 | 4.1387
34 4.161 | 4.186 | 4.210 | 4.235 | 4.260 | 4.285 | 4.309 | 4.334 | 4.359 | 4.385
35 4.410 | 4.435 | 4.460 | 4.486 | 4.511 | 4.537 | 4.562 | 4.588 | 4.614 | 4.639
36 4.665 | 4.691 | 4.717 | 4.743 | 4.769 | 4.796 | 4.822 | 4.848 | 4.875 | 4.901
37 4.928 | 4.955 | 4.981 | 5.008 | 5.035 | 5.062 | 5.089 | 5.116 | 5.148 | 5.171
38 5.198 | 5.225 | 5.253 | 5.280 ] 5.308 | 5.3386 | 5.363 | 5.391 | 5.419 | 5.447
39 5.475 | 5.503 | 5.532 | 5.560 | 5.588 | 5.616 | 5.645 | 5.673 | 5.702 | 5.731
40 5.760 | 5.788 | 5.817 | 5.846 | 5.875 | 5.904 | 5.934 |] 5.963 | 5.992 | 6.022
41 6.051 | 6.081 | 6.110 | 6.140 | 6.170 | 6.200 | 6.230 | 6.260 | 6.290 | 6.320
42 6.350 | 6.380 | 6.411 | 6.441 | 6.471 | 6.502 | 6.533 | 6.563 | 6.594 | 6.625
43 6.656 | 6.687 | 6.718 | 6.749 | 6.780 | 6.812 | 6.843 | 6.874 | 6.906 | 6.937
44 629695) 7001 1-7.038) 900641) 70960 7. Lassie GON 7a1980| weeeDnlew eon
45 7.290) 71822 | 7.354) 75387. | (7.420 |) 7.4520) 72485. 1 7b) | 7e5oL | 7684
46 COLT ST AESOM I) ZGSS taal ya OO CSE tl ud selva eS alle lent ase on doe hes
47 7.952 | 7.986 | 8.020 | 8.054 | 8.088 | 8.122 | 8.156 | 8.190 | 8.225 | 8.259
48 8.294 |] 8.328 | 8.363 | 8.404 | 8.433 | 8.467 | 8.502 | 8.537 | 8.573 | 8.608
49 8.643 | 8.678 | 8.714 | 8.749 | 8.785 | 8.820 | 8.856 | 8.892 | 8.927 | 8.963
50 8.999 | 9.035 ' 9.072 | 9.108 | 9.144 | 9.180 | 9.217 | 9.253 | 9.290 | 9.326
TABLES USED IN FOREST MENSURATION
0.525
TABLE LXXXII
BREAST-HIGH Form Factors
0.55 |0.575
ToraL Cusic VOLUME OF STEM
For Various Heights and Form Classes
Form Crass
0.60
0.625) 0
65
0.
675
0.70
0.725
0.75 |0.775
BreAsT-HIGH ForM Factor
20 |0.524)0.532/0.541/0.548)0. 559
Height
in
feet | 0.50
(5-foot
classes)
25 472
30 443
35 424
40 409
45 398
50 389
55 583
60 378
65 373
70 369
75 366
80 364
85 361
90 359
95 357
100 356
105 354
110 353
115 352
120 350
482
454
436
422
412
404
397
392
388
385
382
380
378
376
374
373
371
370
368
367
494
466
449
437
427
420
414
409
405
401
398
395
393
392
390
389
387
386
385
384
504
478
464
452
442
435
429
424
420
417
415
412
410
409
407
405
404
403
402
401
517
494
478
468
459
451
445
441
437
434
431
429
427
425
424
423
421
420
419
417
0.569
530
508
494
483
474
468
463
459
455
452
449
446
444
442
441
440
439
437
436
434
474
* From table, Massatabeller fiir Triduppskattning.
p. 66, by conversion of height in meters to height in feet.
0.607
577
559
547
537
530
524
519
515
512
509
507
505
503
501
500
499
498
497
495
494
/0.620
595
579
568
559
552
546
542
538
535
532
529
527
525
523
522
521
520
519
518
516
0.80
0.641/0.661\0. 683
614) 635
598} 621
588) 611
580) 603
574| 597
569} 592
565) 588
562} 584
559} 581
556} 579
553) 577
550) 575
548) 573
546) 571
545) 570
544) 569
543) 568
542) 567
541! 566}
540} 565
657
643
635
628
623
619
615
612
609
606
604
603
601
600
598
597
596
595
594
593
497
Height
in
feet
(5-foot
classes)
95
100
105
110
115
120
Tor Jonson, Stockholm, Sweden, 1918,
498 APPENDIX C
TABLE LXXXIII *
WEIGHTS PER CoRD oF TIMBER OF VARIOUS SPECIES—7- TO 8-INCH Woop
Harpwoops
Sie 3 Wate Se ee ee eee
, Pounds, | Pounds, ; Pounds, | Pounds
Species | Species :
green | seasoned, green | seasoned
Allders red™ Seeman | 4150 2600 Hackbermry.:..-..5...| 4500 3500
Ash, Biltmore....... 4050 365) Haw spears .F.toA. 5650 4550
Ash: blak. cutee | 4700 3300 Hickory, bigshellbark} 5650 4800
Ashblie, és cic 4.2 veie 4150 3800 Hickory, butternut...) 5750 4550
Ash ereenty seer 4300 3800 Hickory, mockernut..| 5750 4900
Ash; Oregon... 2. 4150 3600 Hickory, nutmeg....| 5500 4000
Ash, pumpkin.......| 4150 3450 Hickory, pig nut..... 5750 5050
Ash, white (forest Hickory, shagbark...| 5750 4850
growth). 42- .0r- 4150 3750 Hickory, water...... 6200 4300
Ash, white (second Holly, American.... . 5150 3750
growth) = 5 ehh ae 4600 4300 Hormbeam), 02% 5.6: 5400 4900
Aspen sce: nda ectine: 4250 2500 Laurel, California....) 4850 3650
Aspen, large tooth...} 3850 2500 Laurel, mountain....} 5600 4550
Basswood.......... | 3700 2450 || Locust, black....... 5200 4550
Beeclion <s. tre ater ns 4950 4050 Locust, honey.......| 5850 4750
Binchwipapemen. cia 4600 3550 Madrona Aarne orice 5400 4000
Birch, sweet........ 5300 4400 Magnolia, evergreen .| 5600 3250
Birch, yellow’...... 5200 4100 Maple, Oregon...... 4250 3200
Bird’s eye, yellow....| 4400 2350 Maple red). if... 4600 3450
Buckthorn, casecara..| 4500 3350 Maple, silver........| 4150 3200
Buttemut. saeecese 4150 2500 Maple, sugar....... 5050 4100
Cherry, black....... 4150 3350 Oaks soumb.-. Hr. ee: 5600 4200
Cherry, wild red.....| 2950 2600 Oak, California,
@hestniitne sey «eis: 4850 2850 DLAC Fey cle | 5900 3650
Chinquapin, Western.) 5500 3000 Oak, canyon live....| 6400 5200
Cottonwood, black...) 4150 2250 Oak, chestnut.......| 5600 4300
Cucumber tree...... 4500 3200 Oak NCOWi cc ceecue ce: 5850 4650
Dogwood, flowering..| 5850 5050 Oak, laurel......... 5850 4400
Dogwood, Western. .| 4950 4400 || Oak, Pacific post.....| 6100
Elder, pale. .2.... 5.5 5850 3450 Oak, post.i......-5..| , 9600 4500
Bm reork: eh. 68.3 4750 ADE, || Oalk, Ted =. apes. ss 5750 4100
Elm, slippery....... 5050 3500 Oak, Spanishhighland| 5600 3900
Mlmiawihitewers. oer: 4700 3250 Oak, Spanish lowland| 6050 4600
Gum, black.........)| 4050 3350 Oak, water. 5 och. 5650 4200
Gum blues 6300 4900 Oak, white. =. .<-.=.|) 5600 4500
Gum) cotton:-).-..- 5950 3450 Oak, willow.........| 6050 4300
Guim; rede ec kot 5 4150 3250 Oak, yellow.........| 5650 4100
ea
* From General Orders No. 63, War Department, p. 4.
TABLES USED IN FOREST MENSURATION 499
TABLE LXXXIII—Continued
Harpwoops—Continued
; Pounds, | Pounds, | ; | Pounds, | Pounds,
Species | Species
green | seasoned | | green | seasoned
Poplar, yellow.......| 3400 2600 | Sumach, staghorn. . .| 3700 3200
Rhododendron, great.| 5600 afo0 | Sycamores..-...:... 4700 3400
SCGSO i 3950 3000 || Umbrella, Fraser... .| 4250 2900
Service berry....... 5500 4900 Willow, black....... 4600 2400
Silver-bell tree...... 3950 3000 Willow, Western black} 4600 2900
‘S010 70010 Gel a0, oto. |) Watch hazeliien. 2... 53800 | 4300
|
CONIFERS
| |
Cedar, incense...... i AN50:) |) 2400) “|| Pine: jack...:...... 4500 2800
Cedar, Port Orford... | 3500 2900 Pine, Jeffrey........ 4250 2600
Cedar, Western red..| 2450 | 2100 || Pine, lobloily....... 4750 | 3600
Cedar, white........ 2500 1950 Pine, lodgepole......| 3500 2700
Cypress, bald....... 4300 3200 Pine, longleaf....... 4550 3950
‘Cypress, yellow. .... 3150 ' Pine, Norway....... 3800 3200
Douglas fir, Pacific Rinespiiche eee 4 S50 3200
Northwest........| 3400 3250 Bine sponds. es 22. 4400 3750
Douglas fir, mountain | Pine, shortleaf...... 4500 3500
VID ORE oie asics 5 3100 2900 Pines sugar. see: 4500 2500
Hine Allpines. 24.4. 2500 2050 Pine, Table Mountain} 4850 3450
(Burana pilise ey a. 4250 2700 || Pine, Western white..! 3500 2800
irssballsamas ses 4050 2350 Pine, Western yellow.) 4150 2650
BirNoble.. ..4..... 2800 2600 || Pine, white......... | 3500 2500
Bintawihiten cae a 5050 2400 Spruce, Englemann..} 3500 2200
Hemlock, black..... 4050 3000 |; Spruce, Sitka.......| 3250 2400
Hemlock, Eastern. ..| 4350 3100 || Spruce, white....... 3300 2650
Hemlock, Western...; 4200 2900 diamaaralckane eee eer 4250 3550
Larch, Western..... | 4300 3500 Yew, Western.......| 4850 4200
PinemC@ubane es aoe 4750 | 4200 |
| |
Two pounds of air-dried wood are equivalent to 1 pound of average hard coal.
The above table indicates the comparative fuel value of different species of wood
compared with coal. For anthracite, the equivalent is 2.5 pounds of dry wood
to 1 pound of coal, or 3} pounds green wood to 1 pound coal.
APPENDIX C
TABLE
Tue TreEMANN Loc RULE FOR Saws
This log rule is applied to the diameter inside bark at middle of
on mill tallies, for 1-inch boards, but conforms to the formula,
Middle
diameter,| 4 5 6 | a
Inches
3 + i igcteale!
4 1 1 2 2
5 2 3 4
6 4 5 6 H(
7 6 7 9 10
8 8 10 12 14
9 ii 13 16 19
10 14 17 21 24
11 17 21 26 30
12 21 26 32 37
13 25 31 38 44
14 30 37 45 52
15 35 43 52 61
16 40 50 60 70
17 46 57 69 80
18 52 65 78 91
19 58 73 87 | 102
20 65 81 98 |. 144
21 72 90 | 108 | 126
22 8021" A001 20) 40
23 88 1 PROM | aso aleahes
24 96 | 120 | 144 | 168
25 105. | ASi-e\e57 bss
26 114 | 142 | 171 | 199
27 123 | 154 | 185 | 216
28 133 | 166 | 200 | 233
29 143 | 179) |. 2i5r |) 2a
30 154 | 192 | 231 | 269
31 165 | 206 | 247 | 288
32 176 | 220 | 264 | 308
104
116
130
144
160
175
192
209
228
246
266
286
308
329
352
103
116
131
146
162
179
197
216
236
256
277
299
322
346
371
396
fen 1
2 3
5 6
9 10
14 16
20 22
27 29
34 38
43 47
52 58
63 69
74 82
87 95
100 110
114 126
129 142
145 160
162 179
180 , 199
199) eed
219 | 241
240 | 264
262 | 288
284 | 313
308 | 339
332 | 366
358 | 394
384 | 423
412 | 453
440 | 484
TABLE
TIEMANN
LENGTH or
12 | 13
ConTENTS—
1 1
3 3
a 7
11 12
17 18
24 26
32 35
41 45
52 56
63 68
76 82
89 97
104 113
120 130
137 148
155 168
175 189
195 211
217 2a
239 259
263 285
288 312
314 340
341 370
370 400
399 432
430 465
461 500
494 535
528 572
TABLES USED IN FOREST MENSURATION 501
LXXXIV
CurTTING A 33-INCH KERF
log, by caliper scale with deduction of widths of bark. It is based
B.M.=(0.75D? -2D)<+.
LXXXIV
Log RULE
Loc—FEEtT
14 | 15 | 16 | 17 18. 19 20 21 22 23 24
Boarp FEET
1 1 1 1 1 1 1 1 1 it 1
4 4 4 4 4 5 6 6 6
8 8 9 9 10 10 11 11 12 13 13
13 14 15 16 17 18 19 20 21 22 22
20 21 23 24 26 27 28 30 3l 33 34
28 30 32 34 36 38 40 42 44 46 48
37 40 43 45 48 51 53 56 59 61 64
48 52 55 58 62 65 69 72 76 79 82
60 64 69 73 77 82 86 90 95 99 103
74 79 84 89 94 | 100 | 105 110 116 121 126
88 94. 101 107 113 120 | 126 132 139 145 151
104 112 119 126 | 134 | 141 149 156 164 iL7/Ak 178
121 130 139 147 156 165 173 182 191 199 208
140 150 160 170 | 180 190 | 200 | 210 | 220 230 240
160 tel 183 194 | 206 | 217°) .228 | 240 | 251 263 274
181 194 | 207 | 220 | ‘233 | 246 | 259 | 272 | 285 298 310
2U\4 213) 233" || 247° 2625-2764) 291 | 305) |) 320 335 349
228 244 260 | 276 | 292 | 309 | 325 | 341 358 374 390
253 271 289 | 307 | 325 | 343 | 361 379 | 397 415 433
279 299 319 339 | 359 | 379 | 399 | 419 | 4389 459 478
307 329 dol 373 | 395 | 417 | 488 | 460 | 482 504 526
336 | 360 384 | 408 | 4382 | 456 | 480 | 504 | 528 552 576
366 | 393 419 | 445 | 471 | 497 | 523 | 550 | 576 602 628
398 | 427 455 | 4838 | 512 | 540 | 569 | 597 | 626 654 682
431 462 493 | 524 | 554 | 585 | 616 | 647 | 678 708 739
466 | 499 532 | 565 | 598 | 6382 | 665 | 698 | 732 765 798
501 537 573 | 609 | 644 | 680 | 716 | 752 | 788 823 859
538 | 577 | 615 | 653 | 692 | 730 | 769 | 807 | 846 884 922
576 | 618 | 659 | 700
616 ! 660 | 704 | 748
741 782 | 823 | 865 | 906 947 988
792 | 836 | 880 | 924 | 968 | 1012 1056
502 APPENDIX C
TABLE LXXXV
TrEMANN Loa RULE
Reduced to end measurement assuming a taper of 1 inch to 8 feet.
Lenctu or Loc—FErt
Small get ses v.:
end | | |
diameter, 6 | 8 10 | 12 14 | 16
Inches |-
ConTENTs oF Loc—Boarp FEET
4 2 3 4 6 7 9
5 4 6 8 10 12 15
6 7 9 12 16 19 23
if 10 14 18 22 27 32
8 13 19 24 30 36 43
9 18 24 3l 39 47 55
10 22 jl 40 49 59 69
11 28 38 49 60 72 84
12 34 46 59 72 86 101
13 40 55 70 86 102 119
14 47 64 82 100 119 139
15 55 75 95 116 138 160
16 63 86 109 133 157 183
17 72 98 124 151 178 207
18 81 110 139 170 201 233
19 91 123 156 190 224 260
20 101 137 174 211 249 289
21 112 152 192 233 276 319
22 124 167 212 257 303 351
23 136 184 232 282 332 384
24 149 201 253 307 363 419
25 162 218 276 334 394 455
26 176 237 299 362 427 493
27 190 256 323 392 461 532
28 205 276 348 422 497 573
29 221 297 374 453 533 615
30 237 318 401 486 572 659
3l 253 341 429 519 611 704
32 271 364 458 554 652 751
TABLES USED IN FOREST MENSURATION 503
TABLE LXXXVI
ScRIBNER DecimMAL C Loa RULE For Saws CuTTING A }-INCH KERF
This log rule disregards taper, and is applied at small end of log,
inside bark. It is based on diagrams of 1-inch boards, values not made
regular by curves, and deduction for slab too large above 28 inches.
The Decimal form is given, with values of the original rule rounded
off to the nearest 10 board feet and the cipher dropped. To read in
board feet, add the cipher. Decimal C values are eiven, as in
Table XII, § 68. Values above 44 inches adopted by the U. 8. Forest
Service.
504
APPENDIX C
TABLE LXXXVI
ScriBpnerR Decimat C Loa RULE
LENGTH—FEET
Diam-
eter >| 2G hey Biol (00 STO ithe este | ees |) pela
Inches CoNnTENTS—BOARD FEET
6 0. (Oa Wea (es 1 1 1 1 1 1 2
7 0. 1 1 1 1 2 2 » 2 2, 3
8 1 1 1 1 2 2 Dy, 2 2 2 3
9 1 2 2 2 3 3 3 3 3 3 4
10 2 2 3 3 3 3 3 4 4 5 6
11 2; 2 3 3 4 4 4 5 5 6 7
12 3 3 4 4 5 5 6 6 1 7 8
13 4 4 5 5 6 7 @ 8 8 9 10
14 4 5 Gr sen6 7 8 9 9 10 11 11
15 iF 6 7 8 9 10 11 12 12 13 14
16 6 i 8 9 10 11 12 13 14 15 16
17 7 8 9 10 12 13 14 15 16 17 18
18 8 9 11 12 13 15 16 lz 19 20 21
19 9 10 12 13 15 16 18 19 21 22 24
20 11 12 14 16 17 19 21 y) 24 26 28
21 12 13 15 iy 19 21 23 25 2 28 30
22 13 15 lz 19 21 23 25 27 29 31 33)
23 14 16 19 21 23 26 28 31 33 35 38
24 15 18 21 23 25 28 30 33 35 38 40
25 17 20 23 26 29 31 34 37 40 43 46
26 19 22 25 28 Silt 34 37 41 44 47 50
27 21 24 27 31 34 38 41 44 48 pile 55
28 22 DS 29 33 36 40 44 47 51 54 58
29 23 27 31 3D 38 42 46 49 53 57 61
30 25 29 33 37 41 45 49 53 57 62 66
31 Pel 31 36 40 44 49 53 58 62 67 71
32 28 32 37 4] 46 51 55 60 64 69 74
33 29 34 39 44 49 54 59 64 69 73 78
34 30 35 40 45 50 55 60 65 70 75 80
35 33 38 44 49 Do 60 66 71 Ue 82 88
36 35 40 46 52 58 63 69 75 81 86 92
37 39 45 51 58 64 71 We 84 90 96 | 103
38 40 47 54 60 67 73 80 87 93 | 100 | 107
39 42 49 | (56 63 70 TE 84 91 98 || 105.) 112
40 45 53 60 68 75 83 90 | 98] 105 | 113 } 120
41 48 56 64 72 79 87 ee | MOBI], wale || alas). |i aber
42 50 59 67 76 84 | 92.) 101 | 109 | 117 ; 126 | 134
43 52 61 70 79 87 96) 105) is) | 1225 (St 440
44 56 65 74 83 93 | 102 | 111 | 120 | 129 | 189 | 148
45 57 66 76 85 OF 104) 114s 1238 san 14s e52
46 59 69 79 89 99 | 109 ! 119 | 129 | 189 | 149 | 159
47 62 (2 83 93 104 | 114 | 124 | 1384 | 145 | 155 | 166
48 65 76 86 | 97 108 | 119 { 180 | 140 | 151 | 162 | 173
49 67 79 90 |101 112 || 1:24: | 135 | 146 | 157 | 168 | 180
50 70 82 94 |105 117 | 129 | 140 | 152 | 164 | 175-| 187
Diam-
eter,
Inches
TABLES USED IN FOREST MENSURATION 505
TABLE LXXXVII
INDEX TO STANDARD VOLUME TABLES
Standard volume tables (§ 140) have been constructed by the
U. 8. Forest Service, by state forestry departments, by forest schools,
and in some instances by private corporations, or individuals.
This index is intended to include such of these tables as are of
value for future timber estimating, and can be obtained in published
form, or from the U. 8. Forest Service. The index briefly describes
each table under the standard headings to enable the estimator to
decide whether or not it is suitable for his purposes. The final column
gives the Forest Service designation of such tables as have not so far
been published.
506
APPENDIX C
TABLE
Harpwoops
Species Locality Tree class aay ae ae ae Log rule
ASPEN fershoe citar New Hampshire 25-50 yrs. Cubiceits peeled) || 2ren. see
merch.
INSU sin OHO abo A Maine)! 7 W505 tl) Giokveneceretes Cubicift: peeled’ |. 3). eee
merch,
ANSE WR cer esters Maine 9 9) Sao saree Cords EN ee eee
AB DELIM Mera dcjaihesiee= UiGathy yc owl 2 ae owl ce eacioncenackcters Board ft. Scribner Dee C.
INsheblacks eacy.¢ 5 General Over 75 yrs. Cu. it?, peeled’ total 0.2... .2 eee
Ashe black 322.10: General Over 75 yrs. Cords)» \0 «| 2Gl) 23epse eee
Ash iblack) “~~. General Over 75 yrs. Board feet Scribner Dec. C.
Ashyigreen (2.5... - General Under 75 yrs. (Cu: ft7, peeled total) 225.. .. see
ASH GECOW. | jie ete at General Over 75 yrs. Cu. ft:, peeled total) 2... eee
ASH, Qreew Fs. :1 General Wnder'75*yrs;"|Cords! ~~ |W eee oe
Ashiereent oe ./es-2 General Over 75 yrs. Gordsia ss ee eee
‘Ash green! (sweet General Under 75 yrs. | Board feet Seribner Dec. C.
ASh /PTeCO i (ierceu +: General Over 75 yrs. Board feet Scribner Dec. C.
Ashe wihtte: (<i General Wnder 75 yrs. ||\Cu. ft:, peeled total! -2 2 eee
Ashtewihite 00.t sce General Over 75 yrs. Culit; peeled total". 5.5. 42
Ashe white, © eo cs General Under /5,yrss)|iCords)) 9) eee
WAshenwihtte) servis sc General Over 75 yrs. Cordsy - ) >" et 2 eee
Ashby white iis .5 <. General Under 75 yrs. | Board feet Scribner Dec. C.
Ash. whitem .. 6.0. General Over 75 yrs. Board feet Scribner Dec. C.
Asheewhite! 9) ene. astern U.S: 9 9 ee aes, sereeeveys Gu. ft; of. branch ||" 22. eece eee
wood
Ash white eo... . Vermont Second growth | Cu. ft., with limbs} ..............
Ashi white goo .c ce Vermont Second growth | Bd. ft. and cu. ft. in| ..............
tops
Basswood......... IhaketStates™ 4 t|aeascessistscs Board feet Seribner Dec. C.
Beech” 22 daa atnes WVERMOnG. (4 8) oo lon. scccee tec Cu ftz, with limbs ||). eee
Beech Aevcceterstsieret Vermont; ~\ |) menace en Bd itand cu; ft. in| >>... eee
tops
(Beech ere ees IMiaehican 9 SS a ckererre; ose tere Gubiefeét~ | 32222 eee
IBGE CHA yore ic iether cists Pennsylvaniay — 9 | eat ashes ae Cubie feet ~ = 1"... eee
Beech .iyscieta shearers INewallampsnine is) |leerjeiciseiestee Board feet Scribner Dec. C.
Beech jee teil Pennsylvaniay || -sieejee see we srs Board feet Scribner Dec. C.
Beech sac cucu seine IMichigania’ oo Fo di teas /awyeiceecer tects Board feet Scribner Dec. C.
Birch, paper....... New Hampshire 45-60 yrs. Cubic ft) merch; "7/5 4. eee
Birch, paper....... New Hampshire 45-60 yrs. Board feet Mill tally
(Birch, aperiei-r =e
Birch; paper... 1.
Birch, paper...
Birch, papers. el.
Birch; paper. ...). =.
Birch, yellow......
Birch, yellow......
Birch, yellow......
Birch, yellow......
Whestnut.- ice mer
Chestnut... es oom
G@hestnuten ees
Cottonwood.......
Cottonwood.......
Maine, N. Hamp.
Maine, N. Hamp.
Maine, N. Hamp.
Maine, N. Hamp.
Maine, N. Hamp.
Vermont
Vermont
New Hampshire
Lake States
Connecticut
Connecticut
Connecticut
Mississippi Valley
Mississippi Valley
Second growth
Second growth
Second growth
Second growth
Second growth
Second growth
Second growth
Cu. ft., total
Cubie ft., merch.
Board feet
Cubic ft., merch.
Board feet
Cu. ft., total with
limbs
Board feet
Board feet
Board feet
Cu. ft., merch. O.B.
Board feet
Cubic feet merch.
Cu. ft.,peeled total
Board feet
ee ee ee ey
a a eer a)
Scribner Dec. C.
Scribner Dec. C.
i” kerf
ee ar ae?
Scribner Dec. C.
TABLES USED IN FOREST MENSURATION
507
LXXXVII
HARDWOODS
D.B.H.| Height Pep. | waeis. U.S.F.8
ives : diameter. Date Publication 1 a ie
(Inches): (Feet) (nebo) iirees designation
5-13 OCU I) Somicice 289 | 1905 | Bul. 36, U. S. Forest Service
5-20 30-— 90 4 362 | 1911 | Bul. 93, U. S. Forest Service
5-20 30- 90 4 362 | 1911 ze
10-27 1-4 log 9 GiGi AS We Aincwoc.crsaioic.o Gicino. crowed Gra.o.0 COIIeCIGn W5-V10
6-30 GO=110) || Sens 116 | 1915 | Bul. 299, U. S. Dept. Agr.
6-30 GOS1lO Ds aeeiaeee 116 | 1915 ue
8-30 2-6 log 6-12 116 | 1915 ae
4-24 40-100) Jl oe 278 | 1915 pa)
8-44 GO=1S05 9 eae 918 | 1915 a
4-24 AQ=100, «| % 2s 278 | 1915 a
SA ale eOO—130) 5) 8 oe. 918 | 1915 SS
BRatastene 40-100 6-10 223 | 1915 i
8-44 60-130 6-10 918 | 1915 =
2-22 20= 900 FN) steed ys 806 | 1915 oS
6-36 OHIO) Sa acne 488 | 1915 5
4-22 Z2O=BO0) Naas 696 | 1915 4
6-32 50-120) |) sunk 487 | 1915 a
8-24 2 Sploge ||) occ 423 | 1915 Sr
Soleo ne |e r trae 6-18 475 | 1915 oe
Be ESA Wunrsslecc sees: 2 1915 “a
3-21 405590) 1) ccetuaeet 285 | 1914 | Bul. 176, Vt. Agr. Exp. Sta.
3-20 A0— 90) valli 285 | 1914
8-40 2-43 6-24 319 | 1915 | Bul. 285, U. S. Dept. Agr.
3-14 BOSON | 5 ic con 102 | 1914 | Bul. 176, Vt. Agr. Exp. Sta.
3-14 SOR 90), ln sels 102 | 1914 ae
4-26 40-100 6-15 289 | 1915 | Bul. 285, U. S. Dept. Agr.
8-30 70-110 6-21 120 | 1909 ns
7-24 3-33 log 6-17 376 | 1915 Mg
10-30 2-4 log 6-21 118 | 1915 ,
seen eas 1-4} log 6-15 285 | 1915
Beate. ahs 10-50 used 4-10 427 | 1905 | Bul. 36, U. S. Forest Service
6-16 |10—50 used 4-10 427 | 1905 pe
4-16 SOS 90) i eeeac 443 | 1909 | Circ. 163, U. S. Forest Service
5-14 |12-60used | ...... 396 | 1909 a7
5-14 |12-60 used | ...... 396 | 1909 a
5-18 50-- 90
5-18 50— 90 3.3-6.1| 396 | 1909 | Cire. 163, U. S. Forest Service
3-15 AQ=870) il yarns 1914 +0
3-14 AQ=eiQ) || = seis boca |) eh oN
7-32 3-33 log 6-21 651 | 1915 | Bul, 285, U. S. Dept. Agr.
8-30 3-33 log 6-17 237 | 1915 os
2-25 20-— 90 2 218 | 1912 | Bul. 96, U. S. Forest Service
9-25 50- 90 7-12 118 | 1912 a
7-20 5O="90F Sincere 517 | 1905 | N. H. Forestry Com. Report
5-30 5O=150) ihe ene e ee A108): || RIONIOs|| Seoocdadacodue canbe men oncrcmotond Ww94-V8
11-30 80-150 7-19 ON Mile: “Senoce pose UCC pOS oo maecamDOD Dic Ww94-V8
508
Species
Eucalyptus
(Blue gum)
Eucalyptus
(Blue gum)
Gum, red
Gum, red
Gum, red
Hickories
Hickories
Mianleyredicr «sis ss
Maple, red
Maple, sugar. .
Maple, sugar
Maple, sugar......
Maple, sugar
Maple, sugar
Maple, sugar
Maple, sugar ......
Maple, sugar.......
Maple, sugar
Oek, chestnut
Oak, chestnut
Oak redles. 3. ete. 21-12
Oak. redikran tices
@aletmedh: (Fava cae-<
Oakaredhe, 6. 4aau.s
Oalkineds A-arveried-«
Oak, red, scarlet and
black
Oak, red, scarlet and
black
@aky white... ....4--
Oaks white. ts on we cs
@aleiwihite ven ..e
@ak, whitest. .o...
Poplar, yellow.....
Poplar, yellow.....
Poplar,
Poplar, yellow.....
Poplar,
APPENDIX C
TABLE LXXXVII
Harpwoops—Continued
Locality
California
California
Southern States
Southern States
Southern States
Eastern States
Eastern States
Massachusetts
Massachusetts
Vermont
Vermont
Lake States
Pennsylvania
Pennsylvania
New Hampshire
Lake States
Lake States
Lake States
S. Appalachians
S. Appalachians
New Hampshire
New Hampshire
S. Appalachians
S. Appalachians
S. Appalachians
Connecticut
Connecticut
Connecticut
Connecticut
New York
S. Appalachians
S. Appalachians
S. Appalachians
S. Appalachians
S. Appalachians
Virginia
Virginia
Tree class
Plantations
Plantaticns
Under 75 yrs.
Over 75 yrs.
Over 75 yrs.
Second growth
Second growth
Second growth
Second growth
Over 75 yrs
Over 75 yrs.
Second growth
Second growth
Under 75 yrs.
Over 75 yis.
Over 75 yrs.
Second growth
Second growth
Second growth
Second growth
Second growth
1—50 yrs.
51-100 yrs.
Under 100 yrs.
Over 100 yrs.
Second growth
Second growth
Unit of measure-
ment
Cubic feet
Board feet
Board feet
Board feet
Board feet
Cubie ft., merch.
Cubic ft., total
Cubie ft., merch.
Cords
Cu. ft., with limbs
Bde tte wcus its ain.
tops
Cu. ft., merch. O.B.
Cu. ft., merch. O.B.,
cu. ft. in tops
Board feet
Board feet
Board feet
Board feet
Board feet *
Board feet
Board feet
Cubie ft., merch.
Board feet
Board feet
Board feet
Board feet
Cubie ft., merch.
Board feet
Cu. ft., merch. O.B.
Board feet
Cu. ft., merch. O.B.
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, total
Board feet
Log rule
Scribner Dec.
Cc
Scribner Dee. C.
Scribner Dec. C.
Scribner Dec. C
Scribner Dec. C
Seribner Dee. C
Seribner Dec. C.
Seribner Dee. C.
Seribner Dec. C
Seribner Dec. C
Scribner Dec. C
Mill tallies
Scribner Dec.
Scribner Dec.
Scribner Dec.
2”’ kerf
kerf
Seribner Dec. C.
Scribner Dee. C.
Scribner Dec. C
Mill tallies
Mill tallies
Scribner Dec. C.
TABLES USED IN FOREST MENSURATION
509
—Continued
Harpwoops—Continued
D.B.H Height ep Basis Uss rs
sex fae: * |diameter. ‘| Date Publication , ee aa
(Inches) (Feet) (Inches)| Trees Cesignation
2-23 SO=N60! leacc.<< 2611 GO Gis aperorss ever arekens ier evoke evesere aveestics Suess axe G93-V2-3
7-24 SO-AGOM ih Gerisscuses GS 5a LOGE he tr streets avarato avers oie esete: oak ot eee fon tins G93-Vl1
8-32 1-6 log 6-13 SHIP? || MANO OY Ugh Se ences ey caches Dealers co Gio OES Seas G71-V5
8-48 1-7 log 6-23 TAO Ma NOLO OAS iis eet arson once merce eaaratsrst oh sou eect sas she tars G71-V7
8-48 80-140 6-23 1740 MQ A 8 op cstctete tic. 4 te ASGTAL Stat shou anaee elalerelc G71-V8
5-28 5-65 used 4-20 630 | 1910 | Bul. 80, U. S. Forest Service
5-18 AQ OO Ss | |Meteetep ens c 365 | 1910 | Bul. 80
2-17 20- 80 Z 397 1915 | Bul. 285, U. S. Dept. Agr.
3-17 20— 80 2 397 | 1915 ba
2-15 Ap S80). | erate, ss 222 | 1914 | Bul. 176, Vt. Agr. Exp. Sta.
7-14 20-580), | ek ne 222 | 1914 a
6-30 50-100 6-17 305 | 1915 | Bul. 285, U. S. Dept. Agr.
*10—-28 70-110 6-16 41 1915 a
10-28 24-4 log 6-16 41 1915
7-32 4-4 log 6-21 360 | 1915 ey
8-30 4_4 log 6-17 278 | 1915 ae
8-30 2-5 log 6-13 278 | 1915 ay
8-30 1-14 log 7-22 278 | 1915 a
8-40 1-5 log 6-20 SOLO SiMe Cher stich steve eer teelciarstcrcysiveuesepat sy aisceushelisyc Q68-V19
8-40 40-110 6-20 2239 P1913) | Bule 285; US: Dept. Agranata-.- - Q68—-V20
5-20 10—50 used 5- 9 683 | 1905 | N.H. Forestry Com. Report
5-20 | 10-50 used 5- 9 683 | 1905 “and Bul. 36, U. 8. For. Serv
8-25 40-100 6-13 OSB PNOWAT terete ok chris a onscctieer rave sicace sont Rios Q61-V18
8-44 1-5 log 6-22 US OO MELOM Ae ere aewretett wera cies roles eaenohey cuevsQcla ei eteyls Q61-V15
8-44 40-130 6-22 SOOM PMO MART strobe o ctorittas see ueKa te eastexs, ouchs ice vterets —| Q61-V16
2-19 20— 80 2 441 | 1913 | Bul. 96, U. S. Forest Service
9-19 50— 80 7-10 175 | 1913 ."
2-16 20- 80 2 293 | 1913 s
9-16 50-— 70 6 26 | 1913 ns
2-13 20- 60 1 349 | 1905 | Bul. 36, U. S. Forest Service
10-40 1 Sylogy yal) asimye AS Gu leLOOSm mente a.scee tevrisiseseuls Ha cene ep heb onis ts Q82-V1
7-26 1-5 log 6- 8 ASO ROU Mil lee tees abel cvoysnay sboteces sparsiseee ences ake ate ote W82-V24
9- 30 1-6 log 6-14 HO 2a Pel tS ee liewew eee ae cole 2 altar Aka mractst ciate oie W82-V25
7-26 1-5 log 6- 8 ASQM MUON Wl |Mieestont ce votaier dso sc tvceee wees yereutissne ors W82-V26
10-40 2-6 log 6-17 AD Tani e eLO Msp We hc Aleting vio. suaster en eras Raroroat s Oebale W 82--V28
5-20 5O—N00) — Ail Braet. 491 | 1907 | Bul. 36, U. S. Forest Service
7-20 40-100 5.9-7.2| 480 | 1907 ae
510
Species
Cedar, incense.....
Cedar, incense.....
Cedar, incense... .
Cedar, western red. .
Cedar, western red. .
Cedar, western red..
Cy pressanicloseeses
GCypresst sche. chee
Douglastire ss. oe.e
IDYounPAI NTA Gy Ge ac
Douglas fry. - s+ =
Douglas fire =. as
Dourlas fin. ts es
Douglas fre scr
Douglastina.. cs l=
Douglasifire.s sas
Fir,
Fir,
Fir,
Amabilis......
balsam: Stoner
balsamigg.....-
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Fir, balsam, western.
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Fir,
Memloclko nwt
Hemlock. i.:-h0 se
Hemlock. si 6 ss
Hemloek.ces cites
Hemlockw nici s
Hemlocka.esuee sa:
iMemiloekiweesciee aes
ifiemloclee ae a cverelerer
Hemlock, western. .
Hemlock, western. .
MuBiperss.s ones
divisor eon cogocdoo
Larch, western.....
=|
APPENDIX C
TABLE LXXXVII
CONIFERS
Locality Tree class Unit of measure- Log rule
ment
California eee ee Cubie feet, total
Calhiforniay = ee eerie Board feet Scribner Dec.
Californias § oe | eee Board feet Scribner Dec.
Purei sce Weslo ee eee eee Board feet Scribner Dec.
Idaho
Idaho
South Carolina
South Carolina
Washington, Oregon
Washington, Oregon
Oregon
California
California
New Mexico
Montana, Idaho
Montana, Idaho
Washington, Oregon
New York, Maine
New York
Maine
New Hampshire
New York, Maine
New Hampshire
Northeast
Northeast
Quebec
Idaho, Montana
California
California
California
California
California
California
California
California
California
New Hampshire
Mich., Wis.
New Hampshire
Wis., Mich.
Wis., Mich.
Wis., Mich.
Wis., Mich.
Wis., Mich.
Washington
Washington
Utah, Arizona
Utah, Arizona
Montana
Board feet
Board feet
Board feet
Board feet
Cu. ft., peeled total
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, total
Cubic feet, peeled
merch.
Cubic feet, peeled
merch.
Cubic feet, peeled
merch.
Cords
Cords
Board feet
Board feet
Board feet
Board feet
Cubic feet,
Cubic feet,
Board feet
Board feet
Cubic feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, merch.
Cu. ft., merch. O.B.
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, total
Cubic feet, total
Cords with branches
Cubic feet, total
Seribner Dec.
Cc
Cc
Cc
Scribner Dee. C.
Cc
Scribner Dec. C
Cc
Scribner Dec.
Scribner Dec. C
Scribner Dec. C
Seribner Dec. C.
Seribner Dec. C.
Scribner Dec. C
Scribner Dec. C
Scribner Dec. C
Cc
Scribner Dec.
ae
Scribner Dee. C.
Maine
Quebec
Scribner Dec. C.
Scribner Dec. C.
Scribner Dec. C
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
ete) (e, 9 {e/\s! s/s! 's (e)¥ hn enie
Mill tally
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Vermont
Scribner Dec.
TABLES USED IN FOREST MENSURATION 511
—Continued
CONIFERS
D.BH.| Height. ||, 1°? | Basis. | U.S. F.S
diameter. | | Date Publication ae Eras
(Inches) (Feet) | (Inches) Trees | She
16-62 GO=M5O) WI wees cee 1054 | 1918 | Bul. 604, U. S. Dept. Agr.
14-60 2-9 log 1054 | 1918 oa
16-60 40-200 1084 | 1918 oe
10=50' ; Short, me- || ...... WZ Oi) aes ce ib museertceeec ier ckedewarene oie cie¥ePaierchehorere ensite!s T6-V3
dium, tall
8-31 1-6 log 6-7 LSOOE | UONON || A. raetorccdte cis wo asateiereteteucrscedere. srs mene T6-V3
10-42 NEC) cys WW soon bo 186 | 1914 | Manual for Timber Reconnaisance,
| Dist. 1, U. S. Forest Service
6-30 1-5log || 6 24 441 | 1915 | Bul. 272, U. S. Dept. Agr.
at 20 ft. |
8-30 1-6log || 6-25 437 | 1915 3
2-44 20220) ererenerenet= 1747 | 1911 | Cire. 175, U. S. Forest Service
12-46 2-10 log 8 967 | 1911 "
10-76 2-15 log 10 1394 UO OB Pe evecrors cheas tata nonemeteteteretaveigs) aera sre D1-V18
10-60 40- 200 7-11 SSO MOUS ees cu seckeis cc ceateworel meters a ob sete cathe rorin tate st D4-V32
10-60 1-10 log (Goll 880 | 1913 | Cire. 175, U. S. Forest Service D4-V31
10-60 1-9 log a OA SO GAA | acye capone cue aiet-vorrcvedeastonetetfetereascere sk eh.e D1-V35-36
7-37 1-7 log 6 YAR oe (ree A ene Renn eer’ 6.c Secure D1-V29
8-40 Ono gy alll) eae aie 1914 | Manual tor Timber Reconnaisance,
Dist. 1, U. S. Forest Service A8-—-V2
12-50 1-53 log 10 BON TOV ees hey Anas Gieio OOO 0 O.orn t. 410 cob ecko. oot A-35-V2
3-14 ZO=280) = ||lI) wxerdegets DSTA TOYS Nl) = ee sete rcioloresciain c.ticidt.o cai Pc onc choc
6-16 40— 80 4 947 | 1914 | Bul. 55, U. S. Dept. Agr.
8-15 50— 90 4 330 | 1914 ~
6-15 40— 60 6 100 1914 as
3-14 20— 80 4 2171 | 1914 is
6-15 40— 60 6 100 | 1914 .
7-16 40— 80 5.8-6.8 1914 Nt,
7-16 40— 90 D9 Oc4 i) coe = 1914 a
6- 22 39- 91 4 1866 | 1911 | For Quar., IX, 593
8-30 1-Onlog | sc skond 33 | 1914 | Manual for Timber Reconnaissance,
Dist. 1, U. S. Forest Service
10-40 40150 allie irre (77 all SION — en peibeor GacinomoecoDnoOOere rong Al-V4
10-50 ZO S150) Willie menses FPSO) UVTI ll 8S oe athe O Clo OO ROmoo.ocuS to.0.d otto A1l—-V6-7
10—50 40-150 7-10 7Pid| Vike op peOOn Od Choo es.c poo CO.uo iG Al-V2
10-50 1-8 log 7-10 UO) |) TIO Se gos eooodbn pose anounaDo OOob Al-V3
7-40 40-170 || ...... Oe) TCO a). otnaie dip hielo Gio be oro ocr Oe A2-V3
7-44 40-180 A EAl (St) apa eotee Ga ep Go cat occ rool host eDowkc A2-V2
18-60 3-10 logs ||8.7-14.5| 366 a, Wee ets Poe AD ADOC CLOW AO Ont RO CxO A2-V5
12-60 90-220 9-15 TATE 9] ARON ISIA ee a eee eioreio.o cep Diciteo 0 ceo cuo to. g Ga C000 A2-V15
11-40 2-8 logs 6— 9 322 | 1913 | For. Quar., XI, 362 A2-V17
6-17 30— 70 4.46.5] 317 | 1905 | For. Com. N. H., 1905; Bul. 152,
| U.S. Dept. Agr.
5-36 30-100 4 .... | 1915 | Bul. 152, U. S: Dept. Agr.
6-17 30— 70 4.4-6.5| 317 | 1905 HE
8-38 30-100 6-12 542 | 1915 ra
8-38 1-5 log 6-12 542 | 1915 ai H65-V20
10-50 50-120 7-26 1402 | 1915 at
8-50 1-7 log 6-17 1370 | 1915
8-30 ANON — WI ccicve thats 320 | 1910 | Bul. 161, Vt. Agr. Exp. Sta.
12-60 2-11 log 8 AAO I TIGCWIAA ||" Gea toncoee ou Oop oan Ucn OOo H6-V5
6-40 50=200) || ... 5. Sei Hh -TICYO0). || 2 a poopoiocO00.0.0.00.0.0.0 ohmic oe H6—-V4
3-23 1O=920) iliac fie 495 | 1900 | Cire. 197, U. S. Forest Service
3-23 HO=V2O) II wccdeatene 495 | 1900 ha
11-44 SO=160), oth... ep Ae Osa etal ehete cksis oleieteleleisletelel «isin ore Seeuepeusrere L7-V3
512
APPENDIX C
TABLE LXXXVII
Contrers—Continued
Tree class
Species Locality
Larch, western..... | Montana
Larch, western..... Montana
Larch, western..... Montana
Pine Jackie eee | Minnesota
Pine Jackin ce Minnesota
Pines ac kaceeery eine | Minnesota |
Pines Jackie oe ceee Minnesota |
Pine wehreyen sie California
Pine, loblolly
Pine, loblolly
Pine, loblolly
loblolly
loblolly
Pine, loblolly
Pine, loblolly
Pine, loblolly
Pine, loblolly
Pine, loblolly......
Pine, loblolly......
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole
Pine, lodgepole ..
Pine, longleaf... .
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
Pine,
shortleaf.....
shortleaf
shortleaf......
shortleaf
Maryland, Virginia
Maryland, Virginia
Maryland, Virginia
Maryland, Virginia
North Carolina
North Carolina
North Carolina
North Carolina
North Carolina
North Carolina
North Carolina
Montana
Montana
Montana
Montana *
Montana
Oregon
Oregon
Oregon
Oregon
Colorado, Wyoming
Alabama
Minnesota
Minnesota
Minnesota
Minnesota
Minnesota
Minnesota
Maryland
Maryland
Maryland
North Carolina
North Carolina
Arkansas
Arkansas
California
California
California
New Hampshire
Massachusetts
Massachusetts
New Hampshire
Massachusetts
Minnesota
Minnesota
Minnesota
New Hampshire
S. Appalachians
Under 75 yrs.
Over 75 yrs.
Under 75 yrs.
Over 75 yrs.
Under 75 yrs.
Over 75 yrs.
Under 130 yrs.
Over 200 yrs.
Second growth
Second growth
Second growth
Second growth
Second growth
Second growth
Second growth
Second growth
Original
Original
Original
Second growth
Under 75 yrs.
Unit of measure-
ment
| Board feet
Board feet
| Board feet
Cu. ft., peeled total
Cu. ft., merch. O.B.
Board feet
Board feet
Board feet
| Cu. ft., merch. O.B.
Peeled
Board feet
Board feet
Cu. ft., peeled merch.
Board feet
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet,
Board feet
Board feet
Cubie ft., total O.B.
Board feet’
Board feet
Poles
Ties
Board feet
Board feet
Board feet
Cu. ft., peeled total
Board feet
Board feet
Cubie feet, total
Board feet
Board feet
| Cords O.B.
Cords, peeled
Cu. ft., total O.B.
Cubie feet, merch.
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, merch.
Cu. ft., total O.B.
Cu. ft., merch O. B.
Cords
Board feet
Board feet
Board feet
Board feet
Board feet
Cubic feet, merch.
Board feet
merch.
Log rule
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Mill tallies
Mill tallies
Mill tallies
Scribner Dec.
Scribner Dec.
oe
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dee.
Scribner Dec.
Scribner
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner
Scribner
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Scribner Dec.
Mill tallies
Mill tallies
Scribner
Scribner Dec.
Scribner Dec.
TABLES USED IN FOREST MENSURATION 513
—Continued
Conrrers—Continued
: Top é :
TEEN en aiameter| | Date Publication ae ese
esignation
(Inches) (Feet) (Inches) | Trees
SS (8
12-42 80-160 7.3-10.8] 1388 | 1907 Bul. 36, U. S. Forest Service L7-V2
12-42 3-8 log 7.3-10.8] 1394 | 1907 - L7-V4
8-40 TOM OG IN tie tert 233 | 1914 | Manual for Timber Reconnaissance,
Dist. 1, U. S. Forest Service
2-20 20=—:80b) VG Sisco 658 | 1920 | Bul. 820, U. S. Dept. Agr.
4-20 20— 80 3 615 | 1920 he
8-20 20— 80 525 288 | 1920 -
8-20 1-4 log 525 288 | 1920 oe
14-54 40-130 6-16.4 AIS USOT mai ae eerie eee rotenone aieletetaitsts ets cayien er 8) s P7-Vl
3-20 15- 80 13 372 | 1914 | Bul. 11, U. S. Dept. Agr.
3-20 15- 80 14 372 | 1914 ns
7-20 40- 80 5.5 372 | 1914 re
4-8 30- 70 2.5 |Tapers} 1914 SF
6-30 20-120 3-5 1915 | Bul. 24, N. Car. Geol. Survey
7-22 40-120 5-11 1915 cS P76-V24
14-36 90-140 7-15 1915 7s P76-V28
8-22 40-120 5-11 1915 - P76- V23
14-36 90-140 7-15 1915 s P76-V27
7-22 40-120 5-11 1915 = P76-V21
14-36 90-140 7-15 1915 oo P76-V25
3-20 30-100 2 -3 .... | 1915 | Bul. 234, U.S. Dept. Agr.
7-24 1-5 log 6 555 1915 2
10+ 1-5 log 6.2-6.6] 1808 | 1915 oie
4-22 SOR GO) ji i SRE 644 | 1907 | Cire. 126, U.S. Forest Service
10-24 50-100 6 1817 | 1907 ;
7-22 4-4} log 6 AG MUGS MI eet aOR ah Go PO-V13
Bich archaea 30— 70 3-4 255 | 1913 Be Re EI RGR eC ris PO-V14
8-18 0-6 log 9 2000 SReNs ESN Hl ore Peter isy meats fore scuch cciete ne enere atone Joventas tests PO-V12
9-18 34-34 log 8 LS Ae AL OPES atte, pete ct RA See ep hpaee ate Write felis AansNoctn ones PO-V11
8-25 3-5 log 8 1971 LOE AN Maes eee isin cc serrate Pere tae th states Po he) cue 'sihe! cette te PO-V28
7-36 40-120 6-18 614 | 1904 | Bul. 36, U.S. Forest Service
5-20 AQ-NOO SFP kare 303 | 1914 | Bul. 139, U. S. Dept. Agr.
8-34 30-120 6 4282 1914 ime
8-34 1-7 log 6 4282 | 1914 a
7-30 AD=120)) ee GUS LOO DMMP eA. oazerclee. (sce eee ota et eronesanesenet nitane P31-V11
7-18 60-100 6 259 | 1909 | Bul. 36, U. S. Forest Service
10-27 AOS LOON, yi eee 964 1909 ri
2-12 LOZ MOP 1 t..4 es 228 | 1911 | Bul. 94, U. S. Forest Service
4-12 Ose Ow | een eae 228 | 1911 Si
2-12 20270 * esas 228 | 1905 | Bul. 36, U. S. Forest Service
6-20 40— 90 6-8 317 | 1915 | Bul. 308, U. S. Dept. Agr.
6-20 40— 90 6-8 317 1915 ns
8-34 40-120 6-13 3206 | 1915 ve
8-34 14-6 log 6-13 3206 | 1915 coe
10-80 40-220 8-16 | 910 | 1917 | Bul 426, U. S. Dept. Agr.
10-80 1-12 log 8-16 910 | 1917 aa
10-80 60—240 8-16 (UdiS a |LOSMMlinEete Weston ian eeelistem ain aa a eae P3-V13
5-26 30-120 5 1578 | 1905 | Bul. 13, U. S. Dept. Agr.
5-25 30— 90 4 2000 | 1908 Se
5-27 30— 90 4 2000 | 1908 re
5-26 30-120 5 1578 | 1905 “and Bul. 820, U. 8. Dept. Agr.
5-27 30— 90 4 2000 1908 | Bul. 13, U. S. Dept. Agr.
8-40 40-140 6-14 3899 | 1910 ay
8 42 40-110 6 SSA MOMS sanckbenotnts cteetnta tec tonie F lh rks eeer ae P32-V40
8-42 13-7 log 6 TT BUNT TO ily Zetec A Me P32-V39
5-26 30-120 5 WE HSp hl lOO DwNbenrtheecr totals aicccic sisters tir ete ce aaa P32-V25
8-20 40— 90 : 6 260 ' 1913 '
P32-V42
514
Species Locality Tree class Log rule
ment
Pine, white........ S. Appalachians Under 75 yrs. | Board feet Scribner Dec. C.
Pine, western white.| Idaho = | .........-.- Board feet Scribner Dee. C.
Pine, western white.| Idaho = | ...-.-seeeee Board feet Scribner Dee. C.
Pine, western white.| Idaho = = | ...-.+.eee-e Board feet Scribner Dec. C.
Pine, western white.| Idaho —|s- cc ee eevee Cubic feet J Tahousieievelereierereans
Pine, western yellow| Black Hills, S. Dak.| ............ Cubic feet, total
Pine, western yellow| California =|, ws ee eee eee @ubie feettotal) Gi" sees
Pine, western yellow| Black Hills, S. Dak.} ............ Board feet Scribner
Pine, western yellow| Klamath, Ore. | .........-.- Board feet Scribner Dec. C
Pine, western yellow] Blue Mts., Ore. | .........-.- Board feet Scribner Dec. C
Pine, western yellow] Arizona ~—||.— «eee eee ee es Board feet Scribner Dec. C
Pine, western yellow] Arizona =—=§ |, «eee eee eens Board feet Scribner Dec. C
Pine, western yellow] Arizona = | .-.-...---.- Board feet Scribner Dec. C.
Pine, western yellow] Arizona == ||: «eee eee eee Board feet Scribner Dec. C.
Pine, western yellow| California = | ...-...-.-.- Board feet Scribner Dec. C
Pine, western yellow| S. Dakota, Idaho | ............ Board feet Scribner Dec. C
Pine, western yellow] Montana | .........-.-- Board feet Scribner Dec. C
Pine, western yellow] Montana = | ..........--- Board feet Scribner Dec. C
Pine, western yellow| Montana i # || ........-.--- Board feet Scribner Dec. C
Pine, western yellow] Montana | .........--- Board feet Scribner Dec. C
Pine, western yellow| Colorado =| ......-.--e- Board feet Scribner
Redwoodiaee.. 6 oe California Sprouts Cuz tt totaliO.B:* |teaa- cease
Redwooduen s-irel California Sprouts Board feet Scribner Dee. C.
Redwood) 2.......- California Original Board feet Spaulding
Spruce, black...... Quebee? © 8) - lshie cine Settee Cubie-feet @ © pl) 2étduck eee
Spruce, black. ..... @tebecs Fy "ili seecc stn Board feet Quebec
Spruce, red........ Maine (6. Wi scucnseterklitsyeysiere Cubic feet; merebvy iii. eee
Spruce, red........ New Hampshire Old field Cubieftutotal'©:B. | tae asc eee
Spruce, red........ New Hampshire Old field Cu: ft., merch. ©:B5)|) Sj).0. eee
Spruce, red........ New Hampshire Original @ukft., merch: O2B> enon oe eee
Spruce, red........ New Hampshire Original @ubie feet, peeled’ |)" 32) ..cn eee -
Spruceyred.. 3... - New York Original @urtt: merch: O:BS|\ eee eee
Spruce; med’: 2.6 - West Virginia Original @u: ft.,.merch..O38)|Na. eee
Sprucepmed. <1. New York Original Standards Dimick
Spruce, red........ New York Original Standards Dimick
Spruce, red........ Mainee'* 5 Salaceiieereei Board feet Maine
Spruce, red........ Mainesg:i.6 9 ( ilieerese@ek - Board feet Maine
Sprucenredie. series Wier, VE Il Sere ua sodbe Board feet Scribner Dec. C.
Spruce, red........ Wier | Geo nooono oc Board feet Scribner Dec. C.
Spruce; red........ News Hampshire) eile ietct-etet Board feet New Hampshire
Spruce, red........ News Hampshire 9072. .-ac rile Board feet New Hampshire
SYoniteey axel Googane News Hamps hire sa|| sense Board feet Scribner Dec. C.
Spruce, red........ INewsblampshireren || cinic terre Board feet Scribner Dec. C
Sprucemredi cs oe News Wonk) 0. ea hee sense Board feet Scribner Dec. C.
Spruce; red.......- NewYork) |) Seb ladecReoeeeee Board feet Scribner Dec. C.
Spruce, red........ WrestpVirginiaie es silin. irs cin ekhetel Board feet Scribner Dec. C
Spruce, red........ Wiest Virginia «| ||) 2... oa ..%.- Board feet Scribner Dec. C
Spruce, Englemann.| Colorado, Utah | ............ Gubieifeet}imerch: 4) 2.450 p eee
; peeled
Spruce, Englemann.| Colorado, Utah | ............ Board feet Scribner Dec. C.
Spruce, Englemann.| Colorado, Utah | ............ Board feet Scribner Dec. C.
Spruce, Englemann.| Colorado, Utah | ............ Board feet Scribner
Spruce, Englemann.| Idaho, Montana | ............ Board feet Scribner Dec. C.
Spruce, white......
APPENDIX C
TABLE LXXXVII
Con1rers—Continued
ee a
Unit of measure-
Cubic feet, merch.
ey
Spruce, white......
Tamarack......... | Minnesota
—
Board feet
Cubic feet, total
TABLES USED IN FOREST MENSURATION
—Continued
Contrers—Continued
Diam- 4 Top Be|
eter. BINS diameter. ESS) Date Publication
(Inches) (Feet) (Inches)| Trees
8-20 1-31 log 6 ZGOM PLO US Were tare ee oo Ubi amry. 3, Bae cs
8-36 30-160 6-8 1791 | 1908 | Bul. 36, U. S. Forest Service
8-36 2-10 log 6-8 1791 1908 a
8-60 1=OMoe il) ieee ce 306 | 1914 | Manual of Timber Reconnaissance,
Dist. 1, U. S. Forest Service
8-44 SOSVOO™ We Spent 1790 | 1914 | Bul. 36, U.S. Forest Service
8-25 BO=9 GOW Fi eereconn 1004 | 1908 | Cire. 127, U.S. Forest Service
12-48 SO=160F lh 3ee.c. 710 | 1908 sy
8-25 40-100" |) steer 1419 UGINOM | aire tee onata eiobetete are chalel are) oretera tes cal'sue
12—50 2-81 log 6-14 823 1917 | Bul. 418, U. S. Dept. Agr.
10-42 2-83 log | 6-16 | 1536 | 1917 ax
10-50 30-150 8 GODOT ee rarcwreow in csicveversie ae Steel erate area rel cevie tel one etetee lores
10-50 1-8 log 8 6099 BO 1S A CR REE ROO ROCEEC DL ocOusterACaCh Cheese ETC
12—40 40-120 8.3-17 | 1822 | 1911 | Bul. 101, U.S. Forest Service
12-40 1-6 log 8.3-17 1822 1911 ot
12-70 60-220 8-14 2396 OMG L ta ey ae Se, «cca cave Gyeanayemeten teker aren acheroistals
12-50 2-10 log 8 1193 1) ej Sere ICReIaE osteo aca ciao Gat
10—40 1-8 log 6-10 AZM eel ORM ete wor 2 Stee, dearer ehcha aiteemer neencvtowens the
10-40 30-140 6- 10 427 OFS a nee Ga ceer coc. e. Sysccrehehe see ete etna rte hone
8-40 Pe Bilbma teenie DRO Om lieMO Gs lee eek ey | WN ee a eS
8-40 30-140 6-18 2438 OG als atte cc eee retrey Sek sv apit cLcheter avs = Wapedeitey evens
12-43 eto eu Gala LONG 2G Tal AMONG. Ie ce pas. = ats os aren anct eres ele
6-24 © 30-790) tyes. BSS LOO | Meewk see stv. cilecese aie eusie cleie ie sie chee oat
7-24 30— 90 6-7 CATES TOON | tes eons ence Renee Grate a cients ees Clor
20-112 HOS MUSON cI ts, sicp evere 503 | 1917 | Timberman, Dec., 1917, p. 38
7-20 46— 89 4 317 | 1911 | For. Quar., Vol. IX, p: 591
6-20 RS ee | 4 317 | 1911 a
6-25 A0—s90in |) 4a5 246 | 1920 | Bul. 544, U. S. Dept. Agr.
6-14 ANVEP7A 0S WIP aia oloreet 711 | 1920 rs
6-18 40— 80 5 711 | 1920 “s
5-28 40— 90 | 4 1226 | 1920 ta
6-14 40— 70 4-6 711 | 1920 ogi
6-26 30-100 4.5 1591 1920 ee
6-34 50-100 4.5 417 |. 1920 ae
8-26 1-5 log 6 1507 1920 or
8-26 30-100 6 1507 | 1920 ir
7-25 40— 90 6 241 1920 a
7-25 1-41 log 6 241 | 1920 ts
7-25 40— 90 6-9 241 1920 Ny
7-25 1-5 log 6-9 241 1920 28
8-26 30-— 80 6 668 | 1920 ais
8-26 1-4 log 6 668 | 1920 os
8-26 30— 80 6 668 | 1920 ie
8-26 1-4 log 6 668 | 1920 -
8-26 30-100 6 1507 | 1920 oh
8-26 1-5 log 6 1507 | 1929 +4
8-34 50-110 6 416 | 1920 a
8-34 13-6 log 6 416 | 1920 us
7-36 40-120 | 68 676 | 1910 | Cire. 170, U.S. Forest Service
8-30 40-120 6-8 676 | 1910 “3
8-30 1-6 log 6-8 671 1910 ue
7-26 35-115 6 PB ESTO) || MAU ES «| Ri eo Glctosttone Ge OrKGICTOlo, OR iC Semon
8-40 1=9:log | sesnes 189 | 1914 | Manual for Timber Reconnaissance,
Dist. 1, U. S. Forest Service
7-25 51-100 4 441 | 1911 | For. Quart., Vol. IX, p. 590
6-25 44-112 4 1351 | 1911 one p. 592
(15) 60100) 5 8S. aa DYN UNG IGT OS Il Srareeare custo Ge enaione ko CIOISIO TG DOI RRC RPE RE eT
515
Wiis: HS
designation
P32-V41
P2-V3
P2-V4
P2-V5
P4-V39
P4- V42
P4 V5
P4-V36
P4-V37
P4- V38
P4-V61
R1-V3
R1-V2
S$2-V4
$2-V1
S2-V5
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APPENDIX D
BIBLIOGRAPHY
List of the most important works dealing with Forest Mensuration, in English:
Carter, P. J. Mensuration of Timber and Timber Crops. Calcutta, Ind., 1893.
Cary, A. Manual for Northern Woodsmen. Harvard University, Cambridge,
1918.
Cook, H. O. Forest Mensuration of the White Pine in Massachusetts. Bostoa,
1908. Office of State Forester.
D’Arcy, W. E. Preparation of Forest Working Plans in India. Calcutta, 1898.
Graves, H.S. Forest Mensuration, John Wiley & Sons. New York, 1906.
Graves, H.S. - Woodsman’s Handbook. Bul. 36, U.S. Forest Service, 1910.
Martroon, W. R., and Barrows, W. B. Measuring and Marketing Woodlot
Products. Farmers’ Bul. 715, U.S. Dept. Agr., 1916.
McGreeor, J. L. L. Organization and Valuation of Forests. London, 1883.
Muopzransky, A. K. Measuring the Forest Crop. Bul. No. 20, Div. of Forestry,
U.S. Dept. Agr., 1898.
Prncuot, Girrorp. The Adirondack Spruce. New York, 1898.
Prncuot, G., and Graves, H.S. The White Pine. New York, 1896.
Scuenck, C. A. Forest Mensuration. Sewanee, Tenn., 1905.
ScuticH, WM. Manual of Forestry, Vol. III. London, 1911.
WINKENWERDER, H. Manual of Exercises in Forest Mensuration. John Wiley
& Sons. New York, 1921.
List of the most important works dealing with Forest Mensuration, in German.
Selected from bibliography published in “Forest Mensuration,”’ by H. 8. Graves,
with some additions:
SpeEcIAL WorkKS ON ForEsST MENSURATION
Baur, Franz. Die Holzmesskunde. Berlin, 4th ed., 1891.
BREHMANN, Karu. Anleitung zur Aufnahme der Holzmasse. Berlin, 1857.
Anleitung zur Holzmesskunst. Berlin, 1868.
FankuHaAuser, F. Praktische Anleitung zur Holzmassen-Aufnahme, 3d edition,
Bern, 1909.
Heyer, Gust. Ueber die Ermittelungen der Masse, des Alters und des Zuwachses
der Holzbestiinde. Dessau, 1852.
Heyer, Karu. Anleitung zu forststatischen Untersuchungen. Giessen, 1846.
Kuauprecut. Die Holzmesskunst. Karlsruhe, 1842 and 1846.
Konia, G. Die Forst-Mathematik mit Anweisung zur Forstvermessung. Gotha,
1835. Revised by Dr. Grebe, 1864.
Kunze, M. F. Lehrbuch der Holzmesskunst. Berlin, 1873.
LANGENBACHER, FerRD. Forstmathematik, Berlin, 1875.
LAMGENBACHER, F. L., und Nossex, E. A. Lehr- und Handbuch der Holzmess-
kunde. Leipzig, 1889.
Miiititer, Upo. Lehrbuch der Holzmesskunde. Leipzig, 2d edition, 1915.
Scuwappacu, ApaM. Leitfaden der Holzmesskunde. Berlin, 1903.
521
522 : APPENDIX D
SMALIAN, L. Beitrag zur Holzmesskunst. Stralsund, 1837.
Anleitung zur Untersuchung des Waldzustandes. Berlin, 1840.
Sratz, Paut. Die Abstandszahl, ihre Bedeutung fur die Forsttaxation, Bestandes-
erziehung und Bestandespflege, Freiburg, 1909.
TKaAcHENKO, M. Das Gesetz des Inhalts der Baumstimme und seine Bedeutung
fiir die Massen- und Sortimentstafeln. Berlin, 1912.
Works on Forest MANAGEMENT CONTAINING CHAPTERS ON FOREST
MENSURATION
BoraereEve, B. Die Forstabschitzung. Berlin, 1888.
von Fiscupacu, C. Lehrbuch der Forstwissenschaft. Berlin, 1886.
GRANER, F. Die Forstbetriebseinrichtung. Tiibingen, 1889.
VON GuTTENBERG, A. F. Forstbetriebsienrichtung. Wien and Leipzig, 1903.
Hess, R. Encyclopedie und Methodologie der Forstwissenschaft. N6rdlingen,
1885.
Heyer, Gust. Waldertragsregelung. Leipzig, 1893.
JupeEicu, F. Die Forsteinrichtung. Dresden, 1893.
Lorey, Tursko. Handbuch der Forstwissenschaft. 3d edition, Tiibingen, 1913.
Srérzpr, H. Die Forsteimrichtung. Frankfurt, 1898.
Weber, Rupoitr. Lehrbuch der Forsteinrichtung. Berlin, 1891.
Weise, W. Ertragsregelung. Berlin, 1904.
List of the most important works dealing with Forest Mensuration, in French.
From bibliography published in ‘*Studies of French Forestry,” by T.S. Woolsey, Jr.:
L’aménagement des foréts (2d Edit.). Puton. Paris, 1874.
Notice sur les dunes de la Coubre. Vasselot de Régné. Paris; 1878.
Aménagement des foréts-Estimation. Fallotte. Carcassonne, 1879.
La méthode du contréle de Gurnaud. Grandjean. Paris, 1885.
L’art forestier et le contréle. Gurnaud. Besancon, 1887.
L’aménagement des foréts (V. Edit.). assy. Paris, 1887.
Traité d’économie forestiére. Puton. Paris, 1888.
Cours d’aménagement professé 4 |’Ecole forestiére (1885-1886) 2 cahiers. Reuss.
Nancy, 1888.
Diagrammes et calculs d’accroissement. Bartet. Nancy, 1889.
Guide théorique et pratique de cubage des bois. Frochot. Paris, 1890.
La méthode du contréle 4 l’Exposition de 1889. Gurnaud. Paris, 1890.
Note sur une nouvelle méthode forestiére dite du contréle de Gurnaud. de Blonay.
Lausanne, 1890.
Traité d’économie forestiére. Aménagement. Puton. Paris, 1891.
Le traitement des bois en France. Broillard. Paris, 1894.
Estimations et exploitabilités forestiéres. Bizot de Jontenz. Gray, 1894.
Notes pour la vente et l’achat des foréts. Galmiche. Besancon, 1897.
Notes forestiéres—Cubage, estimation, ete. Devarenne. Chaumont, 1889.
Economie forestiére. Huffel. Paris, 1904—07.
Cubage des bois sur pied et abattus manuel pratique. Berger, Levrault et al. Paris,
1905.
Mathématiques et Nature. Broillard. Besancon, 1906.
Aide mémoire du forestier-Sylviculture, Demorlaine. Besancon, 1907.
INDEX
PAGE
BMSTE Ne CHIAG IIIS LEI Non iy eet EEN Ect ca) ohn ais Shrm, a6ascal suametis Sats wed onetote apabano aeit 239
Porras rama CLORSIGCCUIOWS a pews es 55's 4h 5 ais n's er ag NON sean ae es 17
plotssre ection ayieldytallesziiss.).-.4 5 1 < Seinen - eisteneneronnacien ke. 404
PAlipsOlUbe Orit aCbOns Seren emches clases asc aciacl 3 ote eon a ave euch) ancwoevemelot hous dte = 212
CULO LIST Ger ee era rae ren Fons is clanege oho ST ae RCo eee Papert 207
versus relative accuracy in mensuration.................-..-++----- 3
Accuracy in timber estimating, limits of............ APR ete as OOL
of results in timber estimating, mieice of eer fom Rated oie eae 4a |
of timber estimates, methods of improving......................... 288
OlavolumestalolesCHeCIM Gbps pniaesedvss sy1c vero, one st a ee eae 189
Oley ieldspredictionstra- isa eres aioe « acre in eco ERR nome 412
Acoumyeutonantnl by loyainillesia eas Bip a Glo eo trae ROO Ree mle erokae a c.e one 65
lo curulles seed et Olancrtes pears noe LS cries vice suche: Aare pede e eee ere 50
PNGTO MATCH MOLT TN a ene Se hh ni wnt ceyous, sis reead ge see Romance chs 6
Aciual density of stocking, determination Of... 0.2.6.5 <<... c08 vee ale ements 413
estimate or measurement of the dimensions of every tree of merchant-
ADIGESIZEL Mare Ta sot a mete ia ee a ESL PINE ees Ab inind wings RRR R EPS 2
AGINONGACKasStand anduon marke Gaemeee aes ac aie is ise eietene eicaens ucts 4 aie aj Seen 28
Adoption of a standard log length for volume tables........................- 182
JNGKYENANEERES) Oli HAE OE jolloyinioves @iClWiscoacoechoeseoeonneseuaoerndesescoa: 166
PAC russ UEC LOC MON aS ORCSSIOM fecal fy og cy ees) aa, eel < tnyhal(ar Wile idvsun, 94.0 Suess sh eodlene 341
average, definition and determination........................02e0+-0-> 337
GEO, Hao TOON, KEOHIPANIO Nos 5 oooeld woes Os en Oo ee oe ookaeee aco oudde 418
WHat Sate) GL Hiss of VEIT pees eres ooh etn 00S cy AL Rene RMI oc RUy Ae gate ONE SPT cca toe 397
CEO NO IDIG Cree arf actereroa Geis Sole G ae OH OMe Oe Tee te ets rela oo.oe oe 341
i EO VOOM Ap dev yal ESR peels MOY © Tete A ne I eee Re corel ee 337
(eanonuljoyst yayyAe) lo lina) 0} EIS oles Lk Warns bool oe eee ep ete oie I ine oes none 412
in even-aged versus many-aged stands, the factor of.................-++- 325
of average trees and of stand, determining..................0002-0000+- 339
CL Se a0 TAY ie Bk Me este one Re JAA ft ON A, SEER eee 336
Gis stand, CCE mmm i mc e Sete MRL ts css REE AES ASI cad os 335, 339
GuMtandsy relation tO: Vole... wR Nh loo lcs Ee At ery aliceistenn a 449
ot timber, effect on-methods of estimating... 2... 0. ssc ncc ce ws esp eutls 265
Giekees KGOELERIMINIG GE 6 ee 3. ok he ots ack ae och Hiss ceece arene orton Peer 335
SED ALA WOMEOTITRy el OS oe yy WAH eee eee ee ay a ete otek hs ko. 416
IVES ROS TILVITE ow eieEnms ha hesy eR A MMe pve fs ee OL Aa 36
ena increment of many-aged stands........ .<<s< cee seis sence ne eeeaeenee 390
whorls of branches as an indication of age..............0000.-00000- 337
Applicability of Hoejer’s formula in determining tree forms...............--- 210
523
524 ' INDEX
PAGE
Application of graphic method in constructing volume tables................. 169
of yield tables in predicting yields-/)2...). 2.2.22 3.0 22-2 eee 322
Appolonianiparaboloid’ 8 Seed 8 oe hc eee see ee leh WLS)
Appraisal, timber as distinguished from forest survey.....................--- 269
Arbitrary standards ‘in constructing log wulesia.f, {s0).-2 ao dst dn oe on toc ae 49
Area determination, importance in timber estimating.....................00. 267
forage groups'on basisof diameter groups... - 2. 2:94.28. leaner 422
for two age groups on basis of average age... ............02ceccseevees 419
of plots: yieldstalblestay) ccuse-es shapers visite 2's, < eae atets eek so a epee ue 397
Separationon da waeldsc st etter es, le 416
units, size, relation to per cent of area to be estimated.................. 262
Aréas determined from density factors 2770)... sade aes ce ee 416
ol-cincles= tablegizxoe@Villl seer ett ene ne nee 490
Ofvcrassisechions. 2.84 ..crtd.tacie terete aie © ak ds lope onaaanrone ere ae le
OLSCKOWIISEL (ae80o t OER ae aR err: nen 2) <n ee 423
of different ‘types; separation; method... . .. 3)... 02.2.0 - sade dee Oe 290
of immature timber, growiiron.. 5/2. 60.0 we oo. os ares 6 ee ee 451
separation of, effect on density................... 453
Arkansas sbatuce logurule x stpeercrins oho cre. coe ciait. ois tcoeaee Ro eR ee nee 68
Average age, basis for determining volume and area of two age groups........ 419
definition andideterminationy 44.1... .. ..ncecese co tec ee eee SBY/
Average board-ftoot volume stneeycombaimin gs scl). sb). laieerae eter lenis denen 311
diameter crowooeaetenminationnanss..49-— Janes oes wenn eee 346
heights: of timber andsite Glasses: ¢ o-c..(05 fess ade we See ee ee ee 291
heights\of trees pased'on-digmeter.’2 00.2) .0he ss ors wei» DAE 258
loginvethodtotestimating Worccis he obits we civeree ety fala oA eee 143
stand periacre from partial estimates...) .2.01.5(5). bide a's. oe o- cen ieee 260
trees jag enceterneimin oss ich Sah settbrind aie eene ce cithekivd. aie e250 oR 339
trees, volume and diameter, determination of.................+.+2.. 338
Averages employed in timber estimating, six classes of................-.2000- 258
Alou lop rage diy at. tens Sak a eases Fn Ne ates bone hs a eT aca ee 75
DaTbow: Crulgilig COMIPESS. |<. 6 27'4 nie yeas oe pte viva © ote ad tee eee 248
Barks aswaste products. oehres tsc sees males eotnhetale ues Sere die te ceeaeraee ee 13
astaiecting diameter: volume tabless..5.22 eee. he sens nent eee eee 150
maATks lop Ae hr ee ek Tarp EEN Ot eee eed GN ee cn A 99
MGASUPEMEMt GN COrGS iy.) tie a RAd ee bd oe AL AM cis a ee 134
PMU EEE Ae Pores Rtg si eae coe 6 RNC ce cin a one ac accey ites caste ee 163
width; measurement, for volumes to. ie Pet pcloc aiasle Pass t 2 ce ee 161
Basalrares definitions): ey y Si sin eee ee elt ond i ae of
areas talbole; LiXexXeVeLT Ie cue Fa A ne Bae Aaa PN ee 490
Wise.in predicting yacldshos.) Pow suie «0c on cciserte eeeee a eee 415
Base “Lin B 9-52) pees a AMM 2 EL 2 ca a Es 281
Basis fon/beard-taot/ volume tajoles).)\408 os. ncis ens cee oak oo anes Se ee 182
for comdwoodieonverting factors). t i2hsb ee. ok Sos. oe eee te lie 127
of determining dimensions’of the frustum..:.2.:)..'..0.:. 5620522500068 219
Banghmandopaulesssaie ces ok ees ei tee eR ie Oe ca Grater aan 12
Bangor log rule sh sc jasc oi a are ake see aoe ited oie a2 atete ke GLa es utetome & eives toga 85
Bauris;methodor constructing yielditables..- ees. a ee eee eae 396
Baxter log ruler .': scl cise eect kc Wo alg ee se A ea ea 67
INDEX
“eprnra arnt yearn ake i Ss RC RGR Ae kd ee Sh, er
TBM? Sparano hie (Cuil okey, jot ecard ae i le Aetna a aE a
IBVUUSHS, CLSTUATAONT ease ree Slane ended Stoee aoc ARORA oie Becicia Arcaaka id Sean A a ee
IMEA SUTEMEN Caer tewmeer tra. ene ne CRT Eng ecale Meat aed ec honk aN cee kt,
JOUROXGUUKOUS) 100VEVOLS AU KOLO Gao ner ch EM Caen Oss © B Olio Glo.n EMG T Sieh peace
Biltimorespachyrne terse eae reer nts... wl crs seo ee Rar rresan ast as clas es
SCLC KT eee Peon, oh: Ee Ae RE RET
ELLOLSMN USC Olmert Mec ie oat een aes, ene RON Ele ara we
Pa e MKS VTE hs ee eee tae eect Mest arn! ,
graduation......... SecA AEE betas tr be eacced A iki une Ries a aie
ANOS NENO NCIX. #30 44 Un em epi ey ae Aco tat a rN
PpiamKeareas: Separation ia eshimatiny. 2. o/s. ss. eels oe ce ae ee ues eas
[ETSI SRO Neat tile 0 at 0, 2 bf geo a At aad en
Or Newshlampshire lo parila pen ee i8 tu ee ee Neate OO
Board-feet, basis of application to standing timber..........................
ELROLSHNMUSE OMCUDIC Ul esOnere rater k eee eee een se
frustum form factors for merchantable contents in.
log rules expressed in, but based directly upon cubie eamian sesh
34
merchantable form factor ROL enriches AU RR crit erect ich cfovel hts cca aerate 225
VOLUIMENTADLESRLOL-Mayete ewer ret eo ache ene er ee hes 182
Board-foot contents, construction of log rules for..................0.-.000-. 58
muddlerdiamercm asi DasismtOLvae. 4 cae ce cies see ieee oe 46
Ole OSS RE ere Sn tar aN setae Akt ha RR a 40
RUlesko@thumbmpmemesny ce ace ae ete ee ae ee Paoloc:O otha 252
converting factors for various piece products, Table LXXVI....... 478
log rules, limitations to conversion of........ 83
MNCCESSILNAFORS A Set ee eee Ce a nites ee ene meee 40
rules, formula based on cubic contents’... 4.02002. .2. 5.60.5. ee 35
Wollwims WHOS, COMANUOWOM, Olecatadocddeo suite mooddopancbocunoo. 188
volume: tree contaming aVerage@ric.....0. 0025. y eect eee eee tees 311
MESNUTE NGeMMNONUe set ee osc oe see ere te oa ha nee mae 8
lOPESCHIMERTORSE Tete ree Tee ete eee eis ens area a 88
Bolewin=violumentablesiananaaa eer erie terete eee i al clare ata ener erttene vehement oie 158
TEXG) heSp se (= TUOILN(0) Nhe A atupaecrte ata net Sarees ahustiaes Auch Aart hic en Rn Re Red nr bene et aval 14
INEASUMEIMMEM Gaias cscs snc too ee enn eet epee aie Bes seat erate atees oie teaehe ears s 122
PLOCUC(S MMACCHEOMMN: praca erences ec se fs ce Set wate eS eel ine cea Stet ot 14
IBOTer gil CREIMEN Gens ae sae heen een Te renee eters ce fet Sie a aPeenaie re eteme Meret ca acl 358
Boundaries, determination in timber estimating.....................0.000.. 267
Boyton lOperUle ner ae ik eines ei eine een nia on en Pee eae Sree oO aes 85
Branch wood or lapwood im’ volume tablesie 026.0202 s occ. cea bas oe oe 177
Pate et Dn ON Rt re ester Riad, RUSE MINA RRMA Saenn ete fi 116
IBiREDSEavvealmy Mosaad, TEMG ss o 6 wiobic 10 6S DINGO BDH E BBibm ee ico Ne acl Ci coor Ngo 212
SPA DIO WANE ae ew en PERL e eng eee 497
jSARSy ene iin! S} HOLE eT TE yo A An tee ae eee dune tie ltr ct Scan ticle UPS ERE acc g EIR ac ir ad ree 22
Brrtisneeeumaialogimless,-/aeee whens sets oc vies ects Gees ei ss Free seats cle aly ve 64
PERNA CETL UTTER yee Chee tet eh MemetteNemey ctats ae tah "aNentgtaRatabatid Som a taner etoile teeta Ale 85
Brush setleekronswidbhion Strips ess =: 62 assis ese cee le tte ces a eeclelate © ole 6 2 eiere 275
Bulkgprodmcusmlonmsr Olsen erie ce hoster e rietale sk Ae aac ROE AERC DE Bl
EMISi CS MOPHETORE ere ir: ate e incite ay mien eieiccla c staiete state) ahs oie %s aims wi Balen ate eheite 2
JEXUABE TRON Heston ny yn upteh cath teu chy erouchics destrckn eye aun Co RCI ERO NCIO ONICICE LCDs ci IC RCIAICACe Oi ey SiC ea a ROR 110
526 INDEX
PAGE
Calcasieu log rule shh ou uit ere A Ree Ree Oracle ate oe 36
Calculationofatmiefrustum fornifiacton.. Wome 6+ are. hate ae 221
OfsvolumesiotirUsGUImists, se Aer eis oles creer oiaier tcc aia ae ea 221
Califonnia log aiile: sarin Qe eee Seo e ae ne OR eke oe a ae 75
Caliper scale pacify ae ord Se een LS opt eens 1 ae 97
CLE fT GIO TI Ae et ee, Sis ee Dae Scie ae Monee etree ee 23
Calipers deseription:and ‘methed:of uses: o2eeen.... . oka. 26 oats ne ee 227
Canada sDominionsiorestnya branch log amleeereenm ase coer ceric nae 73
Canadian dogawlésiiek Ano ey... ok i ee cee go ee sic ae oe a eee 76
@aney lop rmleaiy sch oe etek oie oie aicins i eI ea oN S05 joe Gp Oe, ee oe 66
Corinto: ena eens Ge hea mR a etreE aa ER St cia. o b aac RE Ceca cL SLM EMO CEES A G0. 115
Cedars westernimed: spolesse quien ne ec masnie ccd Gate biases re Reroc Gor anes 469
Wihnbes MOLES eRe icm us. sree edene ero U are AMT occ siecay tae Cun aicrese) Recta aR ae 467
ember sro tees Sea ee rola her OCR O RIE oae Os dt ac eo ee rere 108
Chain’ unit) ofimeasurement achnibioneseeeiese ccs os ee eee eee 6
Champ] aimiuooumulles fe. Setar toene aeete Gacv oc oda rele erste Ae enone haere donee 65
@handler: (Bir sAties 4) Ae varies ee a esa cton Sonal ee eee nik PO ee ee 220
Charon log: rulers. 4 past woes SCI MN Mees Ge Reha Ee Sen amenens hecendey Renee 85
Charactenandsutiiity of trustumylornmtactorss r-rel ee ele eee 219
oliicrowneiree tOrnvolumentalbolesHe cise ear erie eee 157
of, grow thiyper Cemtasc ae eaten he aeorer ties -yegstoncuryaita esa’ el aero Sees 318
Ghartroiterow,blhstu dies hb cieeeecre re eatstee ear cisec soe ee caer cro me eee 328
Gheck#éstinaatinig cel. cee aes el es oe ened atid Sse kee ee 308
@heckine the accuracyzofsvolumestalblestermers. > eyelets tonite ieee et eee 189
Ghrecle sealirce p a he pe ests ee Nie ed sc sha le pcr acd Sc ca euch ae eae 1K
heels, Hieairt Serer. 350: ee ee eee nh Sa ge ea 112
SULT COs gar ree eg en Oe e ned MEINE, © och Sta) Ieee eas Sint coy eae Ro 115
Chestnut oak, height growth, Milford, Pa., Table LVII...................... 371
volume growth, cubie, Table LiVUMb. a. 0.2... 2406 4. sione 2 ao
poles, minimum circumference, Table LXXII...................... 472
Choice of a board-foot log rule for a universal standard............. Sa eOe
system for timber estimating with relation fae accuracy of reali . 261
OfUnitsnetimbersestimatinen ee soso se Sele oeiel as ee eae 140
Christenyvhypsometerin A 2) schw. eo leee ss: Gi sey enolase SAV os ance unt on ceo ee 243
Circular plots “sizes; able Quin .4 ea hens oe. lent. o tee a he eon 286
Classification and averaging of tree volumes according to diameter and height
CLASSES Mes Wt oes atcise scr oy Papin eas na et a eee 163
of tree, measurements required in volume tables................ 156
ohatreesibyadinimeters iets casice bso siete een Saerieyole- ial ac eee 151
heights “yohime tables «s)6 5 tis sc lsssaiae oe Re Bese 151
C@lementistlom mules 1. Re eae lee hase ns srieiees iol. lesan ree 66
Chick's lapiniles is Sass Mees pan ras See a ei ates aa ee ee 66
Clmometer, Abney 0.46). 5). 6 a6 oe ses ho Se ad ee ee ieee 239
Codominantstreesd chinitioniAre eA cece See e ieee eee 158
Columbia River Log Scaling and Grading Bureau leg grades................. 460
Cambinationtlonmlesi a. it. Gees Aad Pies Reker ect ew tie. oe i eae eee eee 76
volume: tables for twolOr mMOre PrOGUCtS ae lee eee ele eee 193
Conimon: eradesof lumber? 34. 0). voce oa eee 2 ee eal 457
Comparison(of grawthfor diameter classes. 7. .... 2.5..).k cae 4k ee ieee 360
of log rules based on cubic contents, Table II................... 37
INDEX 527
PAGE
Comparison of log rules based on diameter at middle and at small end of log.. 26
oniformull setae aera wens ere hee eek nes 61
of scaled and cubic contents by different log rules................ 36
COTDDOGIS SE NOT leg noc iors Gee yee ene ee Ee AE Alc ee er 276
SRM Stel hy NREL: 2 see co CR Sa RS La ra aR GES UR Dac aoe 277
Composition of stands as to species, effect on yield.....................-.-.- 393
Computationior volume of theytree: 2a... ...c-wes ness cess ane mo ta on fae 161
(CIO: oe bstanta.c le bude etces a Sears Oo anes Aina e GS oon, niente ine ee 19
ConnecticutvRivertogmuleyeneciis. 6 cso cao. We aeeie sete Pamenemeie en sletera ne os 68
Wonstamiinedlogsrillemeee cee Mere ie ose cote ious eee en Tae eRe aA cathe, 3) cass 3 34
Construction and use.of, local volume:-tables..../<. 0%. onc) Oise eo ee ee 174
Olaboard-tootavolume: tables... ss ee ae anette cise a 188
of a log rule, standardization of variables in.................... 49
of logerules based’ony diagrams. «)'52).:4 5: 2eiaeioe Sea oes: 72
mathematical formulsey ees eee ee ae +: 59
formboaTd tootcontentssaq9e-s2nee eee eee 58
FORMA ESkE Prete cee co kecs ola nett Poe ee 78
of standard volume tables for total cubic contents.............. 154
of volume table from frustum form factors..:...:......-.--.-.- 224
of yield table with site classes based directly on yields per acre... 406
on height growth........... 401
based on crown space, for many-aged stands....... 422
tables Baumsmmebhodeae tess sas accdag deed cen eee 396
Contents of standing trees, rules of thumb for estimating.................... 251
Solid Motel ors fori some ees a bee ree ar. See atel aaa ot Sts NIE 20
Conversion of board-foot log rules, limitations to................:.:..-...-.- 83
of International rule }-inch saw kerf for other widths of kerf, Table
SNSTAIG oe) oe Gee ae ne CLEAN Se RN Wey Sake Stith, Meu 81
of log rules with 4-inch saw kerf to other widths of kerf, Table XIV.. 82
of values of a standard rule to apply to different widths of saw kerf
anaithickmessiotehimalyere pwn sis cue eitlens senescent aN ee 80
of volumeitablestoricubictoot, toicords...22.a094000¢-6 eee: 180
WONVE|T LST OES EL yeaa 5 Fey oe a ume ho eee A sip PERT ROO a SN or 473
Converting tactorsscord wood basis One ae eee ee ae eo eee 127
TOTKCOLGWOOd slab lePNeXtar.c as Aeros Nees a ee 129
10) eel Kayes DU ekSIG Reacnchn ty onto Sd eRe Re REE RICLeRe oe acs Shetek AC 20
foristicksyoL different; diameters-ss.)-1\eiec oe eee ele 129
lentes, Sirti Geek SORNE ak 128
pleceiprodiuctsstoboand-teeta.4. +e noses eee 478
stan dandscordwoodMeneeene aan Cente nie atihe beni see isc 128
stacked: cordsito, board-teet, factors'for....: Vaiss a2. 0avon ke. cee: 135
Cooks aomnile se wee eee eT eT AE Socata ee a chants cotanalor ca IS 35
Co6érdination of merchantable heights with top diameters..................-. 184
(OBIT N TOYS Fossler tc ee ee ee er 123
PIG OYEE 3 1 cy eee, ER BELG POR tid ticks Hage ts a ced ie Cay aL a 121
MCA SURG MEP Mew -g cass secede Meck eT netn tees ee vateners aie tata tN roeste She ote elas d's 121
(O GATUNIIHTO) Oe yan 5 ele ae oy Fe nae a or 7
discountingstormdefectshimeersacaeiae nite eet tee ee nine ste 133
Cords, conversion of volume tables from cubic feet to...................0-4- 180
(Congo GH aVoyelBs And sig-H ah dco Stags, Fh uacadeal oi hole cho. Bh VOR ORG eee aPC ae NC Re Renae ae 121
528 INDEX
Cord) standardy detinitions aio dew see nae Pee
versus short) cords,and: longicords43....2.2 sense oes ose eee
volume ‘tables iforsaiaiy-ib ieeere iso ie ieee Ate a ic
to board-feet,factorsidior. converting...) ¢ 5.2.0 2-4 « dee hae a cee eee
Cordwoodi converting factors, basis foros saw sc <b od ieee aielele oa ee
standards: Raises clin 7 nae Bet An ake
lo gyrrtalles 24 Varney eo Pia oeare alex cies AU a eA en ae
methodsolmeastinemen ha 2 sasewetves & cies 2s neces Koo gee eee
rule; ;HMumphrey. calipers i's is, s.cas ate av ssn ae A ee ee
weight asia, measure: Obes 2 28 Helens aioli =». s%~.5 cies ee
Correction factors for volume, ‘tse:of . {bee eis sok be Se ee ee
of'average stand per acre js qceee e210 a Oe ee Re eee
Cost ofestimating, timber-4 1 xc an ter ce eee Ae sk TL ee
Count and average tree In estimating, “sere a Gots > SRR oe ee
and: partial tally of dreesim estimatingwss. ...065.6006 coe oe oes eeeee
Cracks ftoste ee siattacc ee ee el SO IE TO ate reo ae, cio ee
Crookior sweep, deductions: for. Mable xcvallley ett) sine: «sets tei eeice eee
TD 5 CL ee re i ke ae, Seto Pik Foe ha 8 te PN ee
Waste fromumniemaseemelast: vane k eee ea eaeeay, Fas ee
GrookedsRiverdopirulemync Diiierate e Sao ee SeING Oe ee
Gross ‘sections'valbnonma lee rrt ae eet irene isos Seite. | esi eee ee
disinieters ahd areasry.way.nteieta lies ements ac bole es
ME EOSS TIES aes i oii! 52, SP dey te hoe a. ORR AUT ean dace
yvolume::tables: forgriage macaw erst aie wk La bee eee. CA
Crown class and suppression as affecting height growth.....................-
A SGC HOT 8s a,rsoy. bray gah ae RRO TON ages EEA
erection diameter growth nest aue delineation Sasa cee
COVER GENSIty yO Lait wee icehs Meee hse eave VaLllore R\ acre tase etieee ence
of trees character tion volume tableseen scm sie. . sents lee ents a ee
space, yield tables based on, for many-aged stands..................-.
spread: of loblollyspine, Alay, TablesLACl my scsek..s. eee Leek oa see
Grows) areasiol a4. xisicti Noh dale Bee ee ae SLR a Ee ee ea
widthvos, mmaensumemaeMbi se alc ace dec w x oiess So Oe wees ope od eyed
Cruisers’ method, Lake States estimating. 0. dc .w. 6. ot heehee be oye eee
methods, Southern estimating,.2 tees). Meee Wes Oe a 4 ee eee
Cuban: One With log wulesé: 22 .U Geers Re kai eek Ak i oe
Cube-Rule. BigtSandys 4 2.)23 5 sae ce ee Gee Ae eee
Cubic and board foot contents of logs compared, Table III..................
contents olicylinders salable: aXe Villar eer aaa ers ania eerie eee
scaled by various log rules, Table II.............
log rules based directly upon, but expressed in board-feet......
OD ys acess Git in AOA ie Sy Ae ee
of logs, mMleasubeuenihs 2/02 516 cide eee
scaled as board feet, by different log rules, comparison. .
OksquarcdstimbersslogmulestoOnssae eerie reece ae
olastacked wood isolidigysis science. oe cine Seneca SEE
mules ofvilocamalo me ysn dea Terns ROME hs coat: RMR Ree Greaves
total, construction of standard volume tables for..............
weightias:a) bAsistOL MMe aS UMN Seyi ere le eee ere eet ere ieie
foot, use,of; invlog sealing: ie = skaneins oe. SB SN iota deere deers lene gehen
INDEX 529
PAGE
MesRATCRIFIC RIF C}: CEM LIOR eR vey bystek. nsec sca anh HReve cP eee A CONS uae 8
INMOGHMEASTITEMENIGES 'ya)s,tncdeas adem ua RO LTS GS aes els 28
relation toxtrue! boatd-foot lop rulesies ....j0stoe ge tes ws cw a 39
Stacked id efimitiomy. 2k mieoe-cae see Net aR EPP Taco Bl ns eo5 7
MEASUTELAS a SUS LAGULE MORI ete ces one 121
MMC CELLO SMM CASTTEMIEIIG AR ais ot shea susheneeueaen neNca moe erIcl ae miata GIS 5 28
THUNK Mole ONAL AMeelh Gladovns) al Wino poe ob oabdGoboonsduccadabaser ee
Volumes GosrilesspASeCeOMas iia \s..s-6 oecsieme eee eMe ease kee etal eile «= - 28
merchantable, standard volume tables....................... 177
Cull factor, or deductions for defects in timber estimating................... 271
moe scaling, relation.to grades of timber..... ......... :laaSied, hd. bee oe. 458
HME OLUTMER bal lecrwpricy wh otecpetatsicys (cheese etcateoitcter delat oA aD nos, < 179
Cut o*eral EWayo dee hey gu Layee gD a at ee Re eB era at ae oe 35
CR OrRRE THETA TMLee Was teats Mele Meo Mectat iaou 9 Jodie oe oun qs © lene eve fe eyamy nano eee Sree: 315
growth, compared with yield tables and mean annual growth......... 445
loblollypine; diameter; Table LVL... «. cues MEN Gok 363
CTU CEM tie poeta Reap et iene ene sh URES OSs SEN Ha She races obs 429
permanent sample plots for measurement of................. 443
Spruce pAGironGacks, Wa mleCL LY x... ..:0..) ies ater SPA aes, wk 360
uselof yield tables:m: predicting): 6)... 0c. h cee heeds eo 436
hee intiero wit eens sky oe Meee Ie ee ss ie See, Be eR RM 371
periodic growth based on diameter classes..................000.000- 358
or periodic growth of stands, measurement.........0.2.....0..0004-- 436
Curves, harmonized, for volumes based on height........................... 170
for standard volume tables based on diameter..................... 169
fOrrtapen tables; onsedvon. Dy bu cbls, ratah £1-fe- Pies s cbt s aay nls a's 200
; onvtotaluheiehts of tneesaree see sees cae eee zO2
original based on height above stump............... 197
Cut-over areas, application of yield tables based on age to................... 441
BUTCH Vit AMOI lete eb cP pc dR SSI enn Shaheed SHOR AONE aya acts SVS Oe: & yan 438
(COPING (2) 2a a ee RE ne Pee PY DO eS Ee oR ee eS 19
ASiGherStancancduotesca lingers aay sq orate oak eis. heel eee ose aes sta: 90
d’Aboville method for determining form quotients.......................0.. 248
Data required from forest survey for growth................6.0c00eeeeeeees 447
which should accompany a volume table.:+:..) 0.4. J.5.4.5).2.2.5..... 188
eB. EH, correlation with stump grow tlt) 2 2 2% ek ae ag tea a 348
PSS aU EO} Tee ee, Se Mp pokes ass tO Oetina Gi a Ooh. 1 ee 150
MENCH Amita bles ann nt her tracy Meee eRe Ree ee alee eit ec step snoeebeie cealn ee 177
eeerdest metho Omeommuiapy te ee Mecrnnt tae, cules) sete ancien eyreavey ara Pela ae a ayo 343
Mecunale senbnerloprrulem chk ke act eae ae LE ah bisn be 74
HULLS MAS CHIDO MLEH ey Pore Sees aA AND eT Nt i ah UA ORAL Tae he live as a 73
values below 12 inches, Scribner log rule, Table XII................. 74
Weducting aapericent ol total Scale tac saeni Seen Pane se rwee AL ED 2 107
PMCE I CCOUSUD WSCC LOFB irr ores) (sia sheer pa ey ee NES ka tral petdeEs ees a wa 115
oSy GUA Si eae) ere oe) ee ie Or cea 114
fonicrooleor sweep sul ale) ou Villers ene has ce Sh a a eee eevee 116
fORGeLECiSsMN tim beries NAA GIN Gye veritas a aie serene ea cies 2a 271
ALOTONSCAl EMO UNSOUN CiGeree sma cmwsaien Mette e achat e)cl sicie lela rclacels 105
{TOMMESOUNG SCAle WVEISUs\OVELERUM wes seg co esieeincsse +n ees ec 90
530 INDEX
PAGE
Defect, effectupon, grades of logsiincs ce oeu sees oh ues Bee ae eee 460
Defective logs, merchantable’: 044/-2h ieee Se ee Le eee 99
Stalag ata = Ak Seki mee cee ee AR ey a ee 105
trees: «measurement for volume: tables).|. 4.4.0... se8ee ees ooo eeee 183
Defects, deductions for, im timber estimatme.:.....5...225..............0.55 271
O@XPOMION 3275.5 a sciid sean seed Pence BUS P etee ete cc RTPA ES, 113
in| cord measure, discounting for gay see aw. Ss Se ee on eee 133
F160 WLa0] Ofc eae Cre h cle Rr Se ch Mee Srackt cs pio a's os 6.0 < 456
F101 2) (0) Ree ee PET Oeste ners cars coh het REE Ee ee Sto taen cat eee ec 108
or, culljinsvolumettabless Ax ner ences. NPs Ee eee 179
sound/and unsound... if. 2530 See ole ae esd teks GAS oe pL
unsound deductions fromiscaletionser: «25 .2.se een eee 105
Degree of uniformity of stand as affecting methods employed in estimating. ... 265
MemdromMeters:.c eechicceks A Ee eens oan ee eee 247
Density factor, «determination, of aressiirom), +).{\ie05.6 4.20.) see ek a ee 416
factors, application in prediction of growth from yield tables......... 414
for mature stands, effect of separation of areas of immature
Gi DOT Te ae OR ee OO ees a eid ee 453
of crownares da.co 5 tee ies Se eta a cee 424
ofistandefiect on diametenerowt hikers eeerer ene sea rae een 352
of stocking as affecting growth and yields..............5...022...--: 392
of stocking ;empincak=c.ceerh ie. tenes sev beet eee eee eee 413
oljstocking,standardiiozrmormallaser et eee ion ere eee ee eee 397
Werby. log Wale: ox. 5 scat Aaya ac oe eS Io tial Se oe ach ra ence or 36
Derivation of local volume table from standard volume tables................ 175
Olustandanrd) breast-bigh Tormitactors= 4) eee eee eee 213
Descriptionzomplot.syielditablesse pence eer eine. eres cyaecin ec ci eee eee 399
Determination of what constitutes a merchantable log....................... 99
Determining, the ave: olistandssen. ceatin. at sleidc die Jee 335
OU AMEGS es couse seine ccna ead ee Oe ae 335
Diserams, construction of log miles based (on:.--.--2-40--2-- -- ses 6 oe eens
im. constructionjot log mulesi. ce. -r cee ete De eee 58
use of, for.deductions in Staling.*.. 250% ie-0.4 see 106
Diameter alone, versus diameter and height as basis of volume tables......... 152
and height classes, classification and averaging of tree volumes by.... 163
at mmddlevof log; scaling: practice based ons... 1... +. esac eee 97
at small end of log, scaling practice based on...................... 91
breast ligt: 5 aiicvtrsS Sate oa eee eee enero oe eee 150
IM, MeASUTImMoystancin cat rees eke eee ieee rere eae 226
GLASSES 5.5 cisco os agern tele dea Geeta yenceen Sieh ouaee 2arclin al shays, see ReRe Conk 2) one en 227
(Colsah oP natsOVNOVEAKOKVAUMIMOPposenvoconenocacudcaracconsasbeuc 360
current periodic, growth based on .@.:..2...,.. i.e ahe Sie os eee
clasification ofitreesybiyetr iis. gets Sete eer oh eee meee 151
STOUPS as, basis Ol are cTOMpSE.c..04 ona eee See ay eee eee 422
sTowth; basis for determining 205...) o . 55 Saiya)- eee eee 342
Computations ober idicc were euros Se Oe ee 346
Correctionmornseedlingvavel: (meer flan Eel ae eee 348
effect Of Species :Omy..a.19-es eee AT EG ee oe ee il
inveyen-ared stands. laws Oley. yn ae Sate et oea cree eee 354
in many-aged stands, daiwa of. seis tars Beene eee eae 357
INDEX 531
PAGE
Diameter growth of trees growing in stands, factors influencing.............. 351
on sections, measurement of................. oe aetlcce et % 342
PUB POSEOM SUL Chyeae tre «fis ET ee ene eR era ae cas dict 342
TENN. Ho) WOIlWNANS faOWWAIN. ooo soacenncornuicavocdneoaeeee BYE!
Spruce wy S015, js. say yew TRS 2 345
harmonized curves for volume based on................... 169
ial Glaeemuboenntorn Orr lhore farrKoso nocd odandacecco.csaanusnscomoeasae 459
MS LUMENCS COT MMeAS ULI Os ye\ ms vs eae arpa Onno anaes esa. 227
Ofgavenacesturees ad ebermimin pyar sey. Arian ts eenarininen Cen ees ee 338
of log, relation to per cent of utilization in sawed lumber........... 40
GAT Caceres estates Ma cas cle yarn cnet sis eae dota chao SAMS Mth dens dteed MeN ies 2s 229
AID) Terre T So VED IN TD A rere pn ee peg dais 210% he os Sipe ack ToD A SR Re ERE = 18
AM GRANeAS Ola CHESS TCC HONS Sec. .ne teas o8hd SMES ous em Me ee es 17
barkvasjaiecting im, volume:-tables. .. 6. scicwcsenite sos os eee 150
MEasuTEdHAtKeD GSiOLlelO eMac eco ks ols lv sy sSE Ee rade 22
AbMTTAT CLS TO Lal @ Deer ashe resis kia a7 OIE Ae SN ee 23
point of measurement, in volume tables......................... 148
(Soe VT OH rey ORS ky RSC ON ne eRe 92
Dimensions of frustum, basis, in form factors. . a) REE eta anne 2)
of stick, effect of, on solid contents ‘of stacked! wood igi Cea 126
of tree containing average board-foot volume.................... 311
Winanishin gum bers< lawOles oc. <A... Se aes oa eae Re POs ey 318
Directocular estimate of total volumeim stand.:.................-.-.-...... 256
Discounting for defects im cordwood measure.5.........-.4-...22.520.00.0.08 133
Distances between strips: in estimating. a. ...... . cewewesetk ves 00 ke 264
eee na CPM OPY TUG tia aie iattn oA ren oie Game Midi ak hk ake A ae Oe 77
ees Loe meters iste eter nA Pac eon oe stis ovals Stee Sos fava 3G Rater sld Sale ARM oes 68
rule, errors in, effect.upon scaling and over-run.........-..-............ 70
SCT CEMLO PIN Grey tah 8 OM t oe lances ayfiiac Maic ees ses ln Welhacroiate Al aia leon x See 76
oAINAMt aT GeMMILTOM sy Men eicteis <x: -charcbdids ee As MR ie Sl) Ss ed eS 158
ID Ivey 1G (ee Int SO A ates a a Se oe one es Rc ee 85
IDURD ONIN SURI Ge aA Aono male Ge ORL A One kt? MRTG tt. ee ere eres 466
Musen bertylopsnUles,., ge. 1. instr oe renee Wet: US Ns a We Nee aS 85
HOM OMICE eS Ol IETCCR sees ts SMEAR ee Saas eet y Lia raeia ns wh A RN SN A 341
PORTO Syme le NOTE peek eT shea AE hat aici “Vian wet detec nat eteaskel, See Re 50
Effect of dimensions of stick on solid contents of stacked wood............... 126
of errors in Doyle rule upon scaling and over-run...................... 70
of irregular piling on solid contents of stacked wood................... 124
of. lossesiversus;thinmingssuponsyields. 8's. Pe ee ee 324
of minimum dimensions.of merchantable boards upon deductions in scaling 107
of seasoning on-volume,of stacked woods... 0.234d¢0030.0oe.2- 015.00! 123
of variation in form of sticks on solid contents....................... 125
Hpi CA Oe RS y, Olt OGM Rey stage. 2h we SMe Sse ee AL re Se. 413
Plc La Deane mera emureeh yn ae RR me AEA 4 Hh Gulia sais MORE te gy 396
IUIS(2) (0) batons ice ete > Cac cl RAPE tak Pee ee 413
Fnghsh system of measunemenmtey . «ste. flea. eek Po De 6
Errors in Doyle rule, effect upon scaling and over-run....................0.. 70
IGUBE RO ie EN TLIT ORE SLEEK ties ances PIE Ata ITY, Set SE ee) a 232
532 INDEX
PAGE
Estimate; ocular, :of-total.wolumestuu. ghsee ange eet Make Rae ee 256
OPS VERS GEES YF tents 510 6:5 ce ic RPI Se eT icp ee 257
Histimates coverine.aiparborthentotalianea aces eerie eer eael rere ieee ae aenae 273
OXtONSIW eC socie sere teyh celta see be TE ret 5 1 SEN oc Ss eat 308
otal ors 1 00s per Centre Gad See eleereie cats Sebi en etree ol. crane 271
Estimating a part of the timber as an average of the whole.................. 257
byameans) ofielledisamplestreesmaemenics 2: aeetsetereeee eae ee 310
by plotearbitrarily, located: 0227 pean whoa 8) Pe eee ee 297
contents of standing trees, rules of thumb....................... 251
log asthe mits obeiey Beats Neyer ke tee 4 Se deere aye ee ee ee 141
Qualitviotstandmestimbetesece errr. elect tae eee eee 297
SUT SY SEMIS IM USE tee tes eave 2-5 3 niet chanel ove ee 282
timber, (choiceior units sae a ee eee be es ee ee 140
COS bios cis: 5 heiccecacssya teens NS NER calle GI, TON RSTO RE aie) Ee er 302
tTES AS (0 UNE am es 2s ek ee Se ete cot BCs, oie Sf ARR Py ie or 144
use Ob foreststypestneeeeec ce cise oe elo = aie ee ors eee 288
Estimation of standing timber, principles underlying the.................... 255
of tree dimensions ocullamscrmitctet wersre 1s Suche cis) 5 ents aaele rene Ciera 234
Kivansville-logyrulle set) jcc an cereseetcec citar iae ais ahd ueeiisie 42 Selaisien: Se ene 35
Even-aged stands, laws of diameter growth................... 00sec eee ee eee 354
normal iyaeldittablesWforms8-ceeesce asso Se ee aes 395
versusimany-sged form of stands,.........2..25) eee eee 388
Stands:cefinition! race siots-nietaie. ee ere a ee 337
HIGONSIVE" CS FUMIO LOS oi os css-ih> veut paces sees eeeRame A ce rete Rae, Ch Sat cee eee 308
Extension: Scribner logarullet Aaa cess sec scene eateieeae oer cane ee ee ee 74
Bhxterior elects ceca cs Borne eis Das eceaes veer ates 4 Vin aie ce 113
Baloian’s log miles. c.is ition oes tec cee eae state, BO oe ee 76
Baca sluamlperares sternite korres ts cle s.s © ola yan ao wai ce hcl Ney 456
Hactors atectine, the crow on stamdsia. oe c). sss oe 9 ea ieee ee 384
determining the methods used in timber estimating.................. 255
WACtHKON SUEIDSE es oto clerk clase ac odaint ets cc eae 274
for converting stacked cords to board-feet.............9. #6 ike oe eee 135
Haetory ior shop praded..sixcgsis seo ee ye tul. Ayers ile rds elaier aero ee 457
Raustmann hy psometer sis... ne ak oat eth, does is 2 eee 240
Ran orite: Log: muller tar. tt a palh ciety a eyaicionctions, eis Siete eels wcligg s\n A crc eR eee 85
Felled sample trees, methods of estimating: ......2...-.9:......-.-+.+52--90- 310
Hence stays sie cus Satter eee Seis tae eer fe Sere ey ee 473
TRUER gran op s\n. Sim ame Ween ne RR tee are Se Wee hl Se Sta Se A 25
Hinance forest, relation! to;mensurstion: = +). ba. stein cacti ieee ieee 3
Binch and. Apgar log wrule:4c0 0c sy seat! dea tenet den SA a ee 85
Himished dumber eradesk.s.2% ees eae ne ne a ot ed A el ea ee 456
Hinishing pradesicic. Pan Capi ae le ie PE Bos ee Soe 457
Kixed’orsvamiable limitston toprdiameters=. 1) aai selene erent ee cenit 183
Plorida; statute dog mule ss.) 5% 25s miaeeadls brads mah ha ot ges rls 3 ee 68
Horest: Cover <a. iphone Phe yee ta eee, Seo sicestnods de, § kava ates eee keke oie 268
finance. relawonxOoMMensUra gions cries: ees eee re et eet eee 3
growth determination for, codrdination of forest survey............... 447
management, relation to mensuration.................-. tisk Sey tek ee 3
Miensura tions Gel UOM |), wiapeikis oi. cuataveeeomeatateatatins pllal a slahebelieped tetonetcatel =, shevanete ie 1
INDEX 533
PAGE
eae RPO pert iG CiMitIGiMe ois cee. bc tee Bide Pe acaba aways 4c, Oe ate SH. auesleais 1
Senviceraypsometeniearcs. | wanes keel Aree tee Wei ara cine ie eirarsiiy sw k's: 241
Standardiyalitationisuinvey: ast ciieeie emcee oe nie eam. 46s. 6 282
survey as distinguished from timber estimating....................... 268
coordination with growth determination for forest.............. 447
datamrequired for crow ul ..) 2 75 eieierasiie hacia oie esetspew ate iatcley 202 447
GLE fiNaT ETO TM se spepen eee he yet ctap ons, 2) US el amen eeweealene eee ata eye sea ney ll et 2 aes 5
SnVeyane-wasia pany Olmme Tonest SUVey maa liericriiee yal ate eer « © <i 270
Kel AtlONarOMMENS UNA GLOM seas SNE Race ake aia oes OV 5
survey, timber appraisal distinguished from.........................- 269
total increment of, inclusive of immature stands...................... 443
ay DESH USE HINUES UMMA DINO Mpa scenes, his ele ee Aedes Ce A tah GS Petey Reb aeouen 288
valuation nelatonaonimben appraisals: acre riseralaeiaeielasiie cl sis © 269
Horestry, relation to growth measurements.-....-.:2.2-ees:-seseds--5---- 2
Forests composed of all age classes, growth per cent of..................000. 434
having a: group OMIM Ol APE: ClASSCSS, ba... x: br.y<70.- leysvaysrobsr = Ser etepe ee ee wie a 418
Horm asa third tactor atlecting VOlUMe weyers myo.) crates oee@lerogs « Releae oe we ee 196
class, determination from form point, Table XL........................ 250
Classestam Gafonmatactonseene-t ets si i iae ieyer so :c) aie F ais. in Sistine ner misoaiara tae 205
and universal volume tables as applied to conditions in America.. 215
basedionmormyquotientiracstis:veaancets nine cic tat ace anie tenets 206
fachorAphviniikxercrallosOlUlerera scare tieks ceteie ieicts o jee ces achat he wena: 212
PACTOTS erase Caen Tee Clty is Oe aes tad orgeh © seca, Se ctw ANS Seaeg p 211
SONGS Rae ttle ecw petten ye pagtas cao ds vaitey sy cas ySubiea Ey tba ich eqs tee MoE ie meee 212
lpreastolave liver ne erranat sue areks 2c < sack aa. sig ies Aang Eero 212
HORI OOALG Tee tere pene a eect ss resus Oats aiekerc/ a 6. RE oe 225
frIshumMenchanazebercanduutilitiyes apes are iers aie masts -.s ieee 219
ieaYe| Ce ove ots) 6) C= balateee Chaaeat nme wo WO aan ine One gine ewes 6) Aenea res 214
TRO TETTI ll erry wee Creede ey ene 2 nancy, no aes) token) AR aee eS ee en 212
fsioiioVo Fens Moyet 25 02) of a ale Sa ne OS BPM Se rn. se re 213
ere bere ween ea ee a ea enchant oat ont geese c Slee ay oa 215
Olio rsa therere we nae en eA ae chara nae are okatl Parana te tetensg cs omen eran AS caste 18
COTIAIR SLO |] OV IMS) mare te Be HEN neta ogee nine RRA g Ree Ea c Sn ces Oat Cae 210
OlpSU aI See Vaca ea et hey Re ee sty at 5 roi TaN ed eee Py aa ee pte a aes 388
olsticksettection soliducubie;combentss qari. ascent meters ee ere coast 125
Olubreestandeta penta Wles: arama ce win Rr etd chet Uae mien rare teas ok 196
EOE ES MOTINU gel OTe es wee piece eee et tars ays optus ee eens, Ss 209
Ovary Ouila(es | ODED w eb os ita RRS ct cer atte eae, aie Cnn ene Sala RIE ol SNe 210
point method of determining form classes, Jonson..................4-- 249
position of, to determine form class; Table XL................. 250
Guo tient raOSOlie yee eye yar eee ee aed s rete gto Vek a cert annreth ya eea ech eh ee gal east 207
as. thejbasisyotstotmuyclassesn crs cries fm etotuesveisis aici eee: cu sie =. cote 206
quotients, d’Aboville method for determining ........................ 248
Olgbrees ewilhd ypressune ses sxc. sacha < ceeaca sy amie, caeclattemre ele enaioet 4 aye 208
relation to volume and diameter growth................2-.+.sseeeees 374
Formula for board-foot rules based on cubic contents.............0..00000 08 35
THO) HIRES) Lito ad al BLOYENS) State cle Dict co ele o Gicta miolol G Mamie Ore ai oie cha Bee cieneen ts coro 209
FAD er Peres ayers ose eh ae ner bent ers tokelecpapatt Seek dnt ae Gh aveLS 20-21
LOSI Sree sce ar rere We 3) Soar Napieyeustateualtiis 4,4 decaaega aaa eo 65
log rules inaccurately construched, oo... 6 sna. actetajae loeitercs e+ « 67
534 INDEX
PAGE
Bormula; Newton?sicias i oiedeccn ia sa cueteeiat be yatilabingete ni tes ele er 21
PHISMOIGAl! Wp cu Gaile say eo Rea ie eee SST Rae ee 21
Schiffel’s, derivation «2222.70. eee ee ee ee a eee 206
use in computing volume’ of tres. ..2. 5.004.920. 0.5 See 163
Smal sr! SAA ee te, J SR Oi 20-21
Formuln;. general; forall log rulésice aOR, ee aes
In Constructionvof log mulestea swe sic aoe ee eee eee 58
Wasteciromiusaw (Kerignin.p meta mete tins ae oh eek ence Cee 53
Porties, UnitoF esta timed ria Ce eee Rene ee tee ccc eee 263
Borty, detinition ®.2% 292 2/424.o4 a ee.) Cot. Coe ee ee eee 6
Horty-five loprrule ssi ney eet ey etc estes chest otedins Peale Sey sete 85
Rirost iGraicks ise s.2 8) ee a tenn see aati rsac ewe gS bs coc 5 ea eR ae 112
Frustum, basis of determining dimensions of, in frustum form factors......... 219
form ‘factor, principle of Smee cree eee oe ee Oe eee 278
true:-calculationvoisthers.. 6.054. econ oe one te ee 221
factors, character and utility. 2 >.dor tk SA ee 219
construction of volume table from.................... 224
for merchantable contents in board-feet................ 218
RIGS TUNIS 296. ctor oe) A eos Pee ne Cc cleat a Oe I DR Pe er 20
volume; ealewlationy tyros. Se SRA ee ee ee 221
Full and scant thicknesses of boards as affecting over-run.................... 49
General formuls for: all log rullesi. chant os cc pa eas ae oe oles Oe Ti
Girth as a substitute for diameter in log measurements.....................- 24
Glens Halls stamdardis 7142p. ceboncesintet eal ts si Weher ed stn ec ioe Oe oe 28
Goblevlog mule ich, Men sae ieee ky ae eke ota 28 RL ad Ree ee Oe ie ee 33
Graded log males: j7.5 cestode We Dees be entek Aeie a Meies © ae aR eo 78
applied tothe log,.in estimating... <2... 22e eee. eee 299
ADIGE ae lascna: Rack toe netae-t he ca hctaved uk bab uakchaash acts loth ws = an ao ee 195
VOMUIMIG Tables A551 dom sc oh sti dosg ano tee Ce eke bee ee eee 193
appliedito treeinestimatine, 1.0.55...) oe eee 299
Grades, finishing’... 25 st)cte ci bhe tos tors [arose othe oto atetetel state lutadefotelch.ta A 457
Of Tamaer 24h ee A alta el ee 455
amid log pra des x... 6-26 Ss-usetclonsehvetori ts esi cat ole iahatalel od HO 103
in estimating, method based on sample plots and log tables. 300
in standing timber: 2: hs,cencr w+ eb ek coon eon eee ne 298
re‘ation to-culll.in log sealing: : .{0...). soe 2b os dene 458
0) eee eee ee en ee Cre ee een ER Eee i. 103
Grading rules, ‘Southern yellow pine s225 S25. 0S. ee eee 457
Graduation of Biltmore stick, Table XX XIX. oo .50. 0) 00005005. BR ace eke 233
Graphic method, application in constructing volume tables................... 169
of determining diameter growth 7... 6.0.60. oe ca eee 347
plotting of dati; -its-advantages ge... i. oo ee a 166
Graves,: H..S; Method of stem-analysis.....¢. 0... 0.0.0 000.4 cn ee ce debe ae 382
Ground mote. cin ake € is Aik enlcaceyd is ee eect ye Ne ete 110
Group form of age classes, separation of areas...............00..0eceee ee eee 418
Growth and yields, density of stocking as affecting.....................2.05- 392
by diameter classes, projectiony 9. \s0.-iihtee te kieiets ge lel ae kee 361
correlation‘ol/ stump with ele. meh eee ele ee eter 269
(yh ge) Leary SONU TC) [een ey eM OR PRE, Ree aA OR ORE Eh ae eR cea 315
INDEX 535
PAGE
Growth current periodic, based on diameter classes......................... 358
data, relative utility of different classes’ of... .. 5: 25s06....5...6...... 327
determination for forest, co-ordination of forest survey with.......... 447
CAME TER UN OSESOlISLU Cys + Mins stare Cane on eee Mee =e shore ct eee 342
CEC EROMMURE A UIMIEN OMS => ocr: eaten daca eer Re ast ey sions 391
forn@rametemClassess COMpPATISONOL. -- se eee seen aeons. . 360
mercased, method of determination... .< 2. ..5 ios moh ws eeieeilns lo od 363
loblolly pine, old field, diameter; Table LIII....................... 350
PALES TATAN SAT UI ei etyesets seeds nee a ns 5 cc. 5s 5 5vsches se cellos GSC SRSA heer IG Shea = 315
OlestandstahtericuttingssMcreased'. 04.5...) eee eee 438
PECUCEC Sih o2 2: seeile ps RAE eee MIRE tata 439
Current) or periodic. measurement. .04e oe eee eee a. 436
PACCOES BAMNCGULI ce ecol-s = Sous oo «sits ohana Gal eat he MS NE OE 384
prediction bysgrowbbyper cent....... 5. 1.25. 0ee eee eee 432
of trees as basis for method of predicting current growth of stands...... 436
NOW LENT ReI cute blero, CRERENG Stare LCE CE NCRREME O Ne ES Rarice oes boda atten 342
Tp M Gary ene ect easly aie Sac ls c -act « Sey. eke ae ee ee 365
TENE; © [UTI Cee ere eee Ran Ate nena pats bce wa se ale Me 374
Oneareastofeimmature:timbenjsacey cee aes ast. oe eee eee eae 450
on even-aged stands, in large age groups..........................-. 412
] OLE) CEI cto crakawce oer eee eet etic cob Ee ICO, ACs CREME ROE ELEN LEPC SIRS, 316
CHaraCherne Asus RNs ie eM is oe o sete tacit Meta cre a oa 318
Gennitioney remeron ecetr eh ae nol os sel ke Ue eee ae 429
CARS| Rey aa) TST NTO) Toe ecient a oC et ra 429
in forests composed of all age classes......................-. 434
InvqualihyAanGdevaliehe: Gene see rs Ss el rapier aes 435
to determine growth of stands by comparison with measured
DIGUSEN as Fewer Ta veces AAG. & Se ee 433
Use toypredich erowubvof stamdshs=...cb ieee ese oe ose 432
PECIOCIC MER OR rr Cer r iet te eter ele. ren Sou Sa 315
EN CTALUED De a8, beets espn sp 6 oro ae HNO er AC CoP ee as 315
prediction by projecting past growth of trees....................... 323
short leaf pine, diameter, La., Table LV..........0.......ce000+- petra 362
SLADIOIES A OVW ALG) Genser pA a ht ele OI a Re errs Re = OES el ae 328
PULPOse aiNG) Claracheiee sso. o.6 <2 \-ie<<yaconsconeysisvs oie ae 315
volume for single trees “computtatione..2 4+. see eee eo 289
SUbShtUMOnROMuaApersHOLMe acme lene ellen. asec aera 379
Gnd icompass,. Use in simp Surveys diver! i. 25). 5.0 See se a ewes ORI 276
freaeeteTPD LOE EUG Sarge neN ee R ee ieee eee, Oe eee ee so las 75
Harmonized curves for standard volume tables based on diameter............ 169
HOE WOLMOUAMEY, JORNSEC! IM. META MG. 5 oood hoes asnaeeconsoe Sno ns 170
PPS rt CeCe tao. Se ER Ba eck he ep ea ieee tab Eri 112
Heicht classes; tree volumes averaged by... 2.60. ee ee eee e ce vnie donee segs 163
classification of trees by, in volume tables,....:..................--- 151
Grow luvanwanis for sive qualities: sac... «och ow sieve. e« o tedeindoe Sees 386
basis for site classes in construction of yield table.............. 401
ehestnut oak; Milford, Pa, Table LViles: 2.200. 20. 55005 00008 371
(WIGAN i petal Boece eces8 21510 6-5 Di. U RIE CIS CICERO Eo ee 371
536 INDEX
PAGE
Height, crowth ofitrees: im’! .7...0./) eerste ae ere aac eee tive, epee ale ere ee ae 365
{TN GASULEMENIG . Jiceapeia POR One era Fue eRe nee oe nt eee 368
relations toidiameternerowlbarem mene acme ake te cet 367 .
substitution of curves of height on diameter................... 371
harmonized. curves for volume basedion=...4....eeetes as nae eee 170
of seedlings, western yellow pine, Table ei:i..00. 22: So ee 336
OP SHUM ee eo cisco ar A oan aS Cee ETT ook ete atte Seo 156
total measurements. .< fou kim ere eee e re eer ote Le 156
Heishts-~messurementt Of} yeatarie tie teu s cee eie © atte cite aerate oral ne ae een 235
measuring. techniques «2525 e eee ae ele ee ie cin en eee 245
OL timbervaverare valdsiterclasseseemer ne: eerie cisien aoe renee ree 291
total-versusimerchantablessyee emits ih ro re ein ee Ore ee 184
erring log mules: cs clr la eevee t yaeter Caer 1. oetae Ramee ate rea eee 85
FTG wa wGIES:, “cpens a.-to hibac ee Gens tons ee SPN TS ee ac Pc ee heer 474
Heyer’s method) xylometriciforicordwood! 2). 02s. 2 ee 132
Hoejer’sormuls.toritreevioniiy-. mers cb ce oe ct cac tae rae rene ae a 209
Holland logéruless ee ever eye cele cere ree trac RRR eS 76
Oppo les ae wut e he nO MeN Sle At Gea eee earn nee ee A 473
Hoppus; or, Quarter: Ginthogaillems acs.) = in seep eee ee 25
TUM eo hehe cccene 3 tate STO ee Re eee ee ae en ae 34
Horseshoe methodiofestimatines. -<4.. ach. 1+. cdecee ee coker eee eee 284
ossteldi stormy nee se cael roe cee Gere ie ale am Ae forks ee 22
Bh ber’s: figrrinall Sigs Sew ies Ge 6k Chie ae woe he 6 Ge a at eee 20
MMVMeaSUTINg OTaMCH WOO ree = ee noe ere ee eee ee ee 177
Wse im computing volume ontree:d...4.-.. ogee ol ee. nee 162
Humphrey Galiper.cordwoodirule: 25 5... .. se ae eee OR ee eee 132
Hy briddloganumles sy aaa wire ee 6 ESA RO en Ne Se ee a eee 76
biypsometen, @bristennnc. nrc ee Mk acd oe owe eee ce 4 ed cee tien ee Ocean 243
HIS LIMA eek cer ee te ne ea ee ee oe 240
Honest iSenviGesy. tus once eon mona ethos: heed nde eee eee 241
ICI SUISSIN GR fA crear ere ee corsa att Tatars sco node ee cars ta a 236
MUerritttnacccmcn se Se a roe iS rea oe OE te de ee 238
WIGS Site ad accor telat a Ie een cae ae alee orate Cen ne eee 240
Wilkens iic cc's «a vise ooeie te Cotas te dianeia eae aa eb dale alert eo eee 241
ERYIOSOMLELETS seo, ote ee Coie rev tere vee ety Ava ate are ee a tart ete coe ae 235
based’ on the pendulum’.or plumib-bob.222 2 2259.9 eee 239
Idaho statute yoo rules 7) 628 tits nas ele cie retest oe inst ane ane eee 73
Immature stands, increment of, as part of total increment of forest........... 443
Caen! SOTO W UA OL ts ciation ciel commision BW cited tals olf eicle ae eaten cen neon 450
Importance of area determination in timber estimating...................... 267
Increased) growth. of ‘stands ‘after cutting: 252 Aen). oe 2) Sree 2 oe eee 438
method of detenminatioweas-c.-- 4s. o ot es nore eee 363
Increment) WOKeR Sie.c7. Acree SOMME See wick eee ee Teed ae ee ev ee 358
UG RR en OS er ls Lee WRT AMAR ROMS nok OS Nee Au Ly oN 336
Index yield talolesists.< otis | 40a sale 55 sce eie tl eco ee RIOT Se Ue ORE oe et che een 396
Influence of log rule‘on deductions fordefects: 34-45 -esce eee Je eer 107
Influences attectine; heielitnenoywt a neeya eeel ene eet eee 365
over-run, methods ot manufacture... .-..dgeee + os else 47
the logrule ataelf;.. ho Tos ee eR ee: 47
INDEX 537
PAGE
PECAN SO UATO TOP NTULE a Baya nites doddicns cahenotaneeer ee reehe Boies Mahala, Susk atWehege) a Alon aeld 33
Inspection and measurement of piece products.............-0.02-0e sees eres 477
InstoumMentsHoraAneasuninerGiamMeter. . ..ss-p-ronaniciarereete ci larbeiie soci ciate aie 227
LUE STE 1S SI SG FSG Ae SYR) es 2 oe Se 108
littenmedialbewtnee n Ge mrt] OLE are 7, ro.sc 5) as os Seat eI ore SI Pete eat ero Tastee gl bs ve 158
International loganuletor=mch) kerf "able xXexXOxe, yes eee seed ee es 493
LETT C AGC E Tie |) OTUs wists \eteins bs te Voters POR TN PS cao nee ke eee are eis 63
PSITNC MM KO Tsbie LO BeeTGUE firs este rstashacs tere ce toore tl Natoviote tite ha eeake ne ea eA pe hee atch re = 64
imtiroduchontotatapermmitomog mules: c.. vo5. - ec nrona ce ot ee ieee ene sean = 44
My emro Taya OLUTION OCI airy § aysks Ae o Uae )h hao .fo tre ras eves ro stow geite ede es cobel umes ae epatere stele 268
Isosceles triangles as basis of height measure.................20-ee eee eeees 235
lackseine crowth Minnesotaslalble oxi Vile 2. vacua 8e eines eile ome ena = 318
Jonson form point method of determining form classes...................-.- 249
“I RCOY ee ecco OP PREECE, Di cy EEA ORR AC ede NRO Cte PIPED 5 io. bs CANE 207
IWanssnemhaypsometen:prinlcipleyOlwy sagem oe ac 4 aes ee ade cee ae Sensei 235
nots arOtMenLeninouhro may secricersisic et tks = oe accuse fase c Fas etic als eee heel 112
TLE yegeabayie 5 '5 °c, onceoho by cha im MONAIES Ge ONE el CRON Chet cc. OCC Caen eam aan ere gee Ace 474
ake’ states, cruisers: method of strip estimating... ...-...525....2.2-255-5-- 283
Hes W.OO CaaevOlUTMeEtallo lesan senis sy sre seeeora ee Soucts Gos) farm deeb lb ous ibd cee eevee malas 177
Large timber on the Pacific Coast, methods of estimating.................... 287
Law of diminishing numbers as affecting growth of trees and stands........... 318
Laws of diameter growth in even-aged stands, based on age..............-.-. 354
in many-aged stands, based on diameter............ 357
Meaninestreeswheight) measurement... os) east elas asikisele as a ylcas ove em olsen rare 245
eo es tabusvo trace lenin wacuecd ee rexstnctor vaca terend ons ooo ere auc iel ialeres srcoe Syd ae cee terns cane 119
te mr etael oom UL epee sts neers eee apcler eat sie syarine ett ys uate MITA Menaye Set ean a e, aliciiont 3D
Deepavali)” lkoyeas: ce MA Aare Or Ae ee rseieeent nN UNG Ce te re er Re er ar eee 16
SCalin Peer ei Leas IN eer yee C Eta ed maul s ARR Sparse 2. 2 Si, sais, Bhs 91
Mickineeiverd oar emery teeth ante eee eine Satitiars naa ele ahs a) duane 86
hima tionsrol ta perntalb lesan aaceys ste sera etter acta aie eleanor ate + ayo cugcousteuae 204
touconversion of board-toot lop rules). 3095. SU eb ee ie ee a ese 83
Tamits.of accuracy in timber estimating 3 624.252.0456 06 abot eels teens 301
Loblolly pine crown spread, Ala., Table LX............2........---. CeO 389
currenterowthoydiametenme lable WiVlians eso ere oe 363
oldittelds crowthim diameters Mable LEI s.- 2.25. sees. 350
ocal.volume table form), Walle xOxoxs 5 ss. Says a5 saci aoa Seale ete sees © 175
Cablesad chnition see elie oie ie atet ee stots Siatre 153
derivation trommscandard tables:ee- eee adsense oa 175
CONSCRUCHIOMPAMGRUSeHR mary aes sa erate ee ae eiera cerns: a,c) on 174
iogrvassthenunit/of estimating. sae oni acm ticle mists oroiseret eters cia sake sd ole, « 141
FV eURReI Seay ja, Seca a NS Ae SGA ETIa a eeee get Lee Anabaena Ze th sho is do 99
FaE BSl., es Reg gE RES Gea) ae MMOLE PMG EEO ec CA Ran SATE OEL e Uisrat 2toe o ete e 103
defechmeitectmipomisersn sas remanent ss ais iets aie ous fs eisices: saeetehe! setae ai-che 460
GhNerH ene Scena oi 6 hos o cid clog Keys Sar eond 0 Oi CRC CIC AeA a eee 459
CRAM OLES la CivyO OUSe perverts arn eR ENE itee tare alee Seas eae eat tee elmira 460
STOVE KOLOLO [Sta oA ole Ch red RRC PLT Cucncc cis ORCI REC ACER EBE Ena 460
WUE DOS Me Mera et Mo ere ron Te vetoes Nasietarcleetatede reiteisvate sue lo welinne's waueia 455
leng¢hystandarditonmvolumertablestmemsee cic ice ce cece ac iicia cas 6 o- 182
538 INDEX
PAGE
Teor lengths’. i) cisucte Sai cor eae Bech oo eee eI ena Oc 2 SIEVE co IR 16
merchantable what constitutes aac ae eer eis ooeieeict cain cee eee 99
Tule; Baxter ciao he ju estes J eersigcenh cg ee oe be on eee 67
British. Columbia: s.42. sce ore oe Oe Cr EOL oe ee 64
Blodsettior New, Hampshire see cer 9.00017 SEE ate el aeiniae eee 30
board-foot, choice of, for a universal standard..................... 84
Carey 53 5 oa epse ae ae ee ee en Cee CUM oe ae we. eo 0 66
Champlain... 3.) st oheaiene tates Oo oe ATT ee OE ee 65
Clements eases 4 tie teatlok fe tetatbere O2Aa Gh isl ene See 66
LC) 100 ree ee ein ae eeu sien oli ao A eA ison ric cin® wid oo 66
| io) 4 | ee i eee rE ase 2 CRETE ne Cito He among c.o.0.a6c °.0 c 68
Doyle-Scmbmer ica gaeycie en peyote: s arocn «th choc ter ote ia tae eee 76
for round edged lumber, Massachusetits.......0......0.0..0. 001.088. 79
influence onvdeductionsMomdelectsmmmtss-s eaneeie eaeeeiae ee 107
Internationalligainchy keris acces ose sel so ov oa ceetoly retold ae ae eee 63
EPENTAVEL ONCE) Gg Mee ne Sen ae EERE NS UME TREE re oo « 64
WY ASV ATi ann aici Solu orto AA net eCN co eee a ern Ma, cio 5 5 o 63
1G Wha ee SIRE cardiae ene tse Serta eine RM PE EE a oi 76
New bsrumswickcoss smrete oo < soney sate orate oie Gece Soest ie ee 76
New Hampshireor Blodrettie a ods-e sence noose ie. ire ee Gee 30
| Ries) URNA ERRD. POOR TO oe ERR NMI AG GENIN titl bo Sono 3/5 Dtro;6 aco 66
Quebe Gs 25), 3) dese eas See hae BEES Ogee) AO Lae 76
Scrilbmens cyt ic )5 oleae Ae eS tte Re ao ae ee ing en er 73
pceribnersDoylems cA sbepccuk node sites rcord Markie hae Oe ih
S pail inte: sate ing. Petes Swe acute oe. cestopeRtl <ietax chen Oxo eeee een 75
MGV ATVT ok ee he Gut soot a thas Ciaran tees, ors dae barn ta eae Saye cett> ae aie eee 67
Mifomas VaCCUrate x, cea syeis kon 5 ea ection) sary a gaeeye i ee SER 66
WWallSOMS Aaa aero recta tains etse ees clctacs cts sea 4) ole ean cy eS ee 66
based onicubic jcomtemts). 2.56 5,535 gas Se 4 dives oes cra ies nee 26
onidiacrams consirmictioniOtee. 42.4.6 ses ae eee 72
on diameter at middle and at small end of log, comparison.... 26
on, formule: comparison: of: .. ....-.... 5. emhset eee ee 61
on mathematical formula, construction of................... 59
rules! Baughman 927 Wao gant are = cI eee ae a 72
board=foot, mecessity for cc obitoe ack cto GRA ie eee 40
Canadiaia cise. ache eae «Peon ho COE IG eae eae Sih ae
comparison of sealed cubic contents by different.................... 36
Ge fin GION oo Gis seen ays es ee eee Ree 8
expressed in board-feet but based directly upon cubic contents.... .. 34
for board-lootucontente consumuchonvoles-sne- seria. 2 eee
for cubicicontents oljsquareds timbers. ni nia Le ieeee 33
formiul sy, ACCUPAtC . a6 A Neuen, strc o nes Ae oe ORO ee ee 65
from mill tallies, construction....ge............-. iis ciaos eee 78
general tormiulse forall... 12528 uso cs oy aah ee ta
2716 (20 Cae eR a a RRR eR SE TIME Ae iirc ec gerietele 78
appliedetorlorsnnestmma tim peer qr eter eet nena eee 299
jd UISep LOMVSIerol Oval @HlONe NOME AB odeaco os socccconocvencussose 28
NGedsfOr MOTE ACCULALE = 5. hes oon 1-5, Saat SS sey oleae ee eee 50
obsolete sae eo csece ate es Aue AE oo tee ideas aval n ooe piel che eno 36, 85
INDEX 539
PAGE
Log rules, true board-foot, relation to cubic measure................2.00005: 39
TRUMAN, Oe GInigeveayexes Koyer 100 (EA OVO le so pekbre pa OO cloiiete bro E.oeicoss cH BU dicG Sobre ciumtone 143
SOT AD NV Siets Og oe Gas 8 c'd 6 Sew Ot PE EERE EIS ee eT aga itciiotecem ponent eis Gan 88
Scale cull srelationgionerades or lumber.) 415s acme eeieccemee see nerar: 458
for oand pe sUTC Kp es i15. 5.5: vic: eet ee aie OL eee Or tuactsls as 88
MSErOlgCUbICMaG UEinlenr ns ht 5/iraladas mee Thai eter aes Ooo ences, joonahe 31
SEDO OS aetna ce chet ede om. 6.0 vd sore RSI ae REE AP cora te ear ee 99
DLS SIerea eee b AS Bete co's 0. os Gy ce RENE ICE OR CLERC ERS OES IEG RSS ee 195
MEG SoM SACOMCITIONS Mersin Ree rae eran coe oReT ae cede opens ae Hee Oh ane ai 269
Meo MATd—LOOt/COMLEDUS: -ammetecckeceeoiy se csalolelecsernccdutl eel ele: ene. oa ae cere esses 40
Cefec tives Calin C4G 1 Pewee SEN su5-succ1c oyoreusicse aragcooero sae tos, icune 105
MA SULeIMenp OMmCubICICOMbeMtse ss ceca casecia ss sec eee cle laces 16
SOlliGl ormrernsOll, OMIA ES. 4. ord a eer einai Olsbieaieeamioks oi cueesin gio bicep Bic olor 20
Fechni GU ex Ol 1 CASUGIM OAM rete seuss ene csi susis «1s oe Meee teen alka eestelaeneietes 22
(WOVES THOTT OT RR MWe ea Cits Os ec Beco wiih ey soma eared 18
TLearaee Gorell, 5's Saleen cee DP Ore Eh GA ors S bmi eine eset hes ieee APO Ad ete Ae ie ae ee 122
Losses of trees, correction for, in growth prediction.....................e05- 437
VeErslsuMMMIngs eect pon yleldseeeeseeyca ce sie dee tl ce ee ice eee 324
oO ROVeAm IM GG CLMNTIOM errata ee a ate ae ceo crs celts d AR) BAmc ainda s 6
LET uuTal OE OEITECLES wo b evi cach sn ae el ns rene eae 456
PAG esrandsloctonaGdeseea a cee nie sweet ee RE eel te eis. co AeeA oie 455
OLE er MRE Seperate ss Aut L/ouees cup RIM AMT aa “Swans 103
liimabering srelationytontimben estimating ens. clk sis a aelioisse ae sataelan ein see 2
tin perm an: Sal avOniienlo pL ewes: ri a sly elie ay. ekoannt Segrels aierory lg i seas cusbeoshe 85
NORE Sere Me MR RA eee ahs tne Ace Sian sos: Gina & aula ateiecatens 35
Lumber, thicknesses of, conversion of values of a standard rule to apply to
ENCED Ey Pe RIN AP IT Ce Sea EES EIS Se n) Montes Aaraa Selle Oe 80
Li Kenrtianey hove THUS ss His LE cot ue eas Sytien REG ole MOIR CRRA aay TMT Crt acm ere ee 76
Manacements forest, relation toy mensurdtiom....2-...5. 42.5405 08.005+--04- 3
Mamutachunemunenactantotawasteslnnercrie-ei case tren: serie iciene rae eeetensiat oe 13
Lara NO ONREOL TORROVCHUKOUS) THAIN Oty nao po eawoda done som er oAeosbbob os oueeons 11
Mamyqar ecelormyoristamdssaat inert meee trees creeks ce ale, eden eC Reece ene 388
SMACK, EhoNbrAll MANO AMEM, Ole skoocnngocdensoedusanecncobavcadve 390
application of yield table based on crown space to......... 425
Gefimiitio ney srs threat wee uerary et tha seme eave yeas sat cee 337
fACLOIMOMACE Mea Apne ns Petter ats,, 8.8 Steeee clase aaah 325
lawsotciammeterserowuler cers y renee eee) are a: 357
yield tables based on crown space for.................... 422
Na eeLONEStRCOV CLE eit areal eit eer arte Th Ac coaae stir ene Navan bsites 268
SOT ots Se Ala Ate RO OR MER Ean Bn cy one CROLL mR ar ee or at a 268
Uva] OVE Lng aXe sts oars ars Lontale ic LAIR St BPA tcc ret OG can eae 268
PO}OUV ENF) OAT Oe ret Ba oan tors Statin cittict din. Shes etd meee A or 268
Miarketacuibiess tema arden, sney.vn weiss onic eter ty epee eer ARR, HAR cs dis 28
Massachusetts log rule for round-edged lumber..................0.0000 0000 79
Mathematical formule, construction of log rules based on.................... 59
Mathenatics, relation co mmensuratiom. rated cclitterisale tie «ici. oe ee eee 3
IMIG) ROT OWATES Motte TAILS... arsed nt cr) ho cwect hen cs Onto io StS EI ona. conic Cee CR eA ee 63
Ry leerbecrarn tab oorenpyrtah eee oe ree act ee nie Me ACA LOS Sate ahs BUG Manel wldla dc 315
540 INDEX
PAGE
Mean’ diameters, error im xise of Sic sie etic. oan ae eee ee eee 23
end formula, use in computing volume of tree.) .. 05.) 3. 320.22. Boek 161
sample: tree, method... <5. = ccc qe eM AGE eek wa ee hae se Ges eee 311
Measurement of barkain ‘cords... ...:. >. S94RReS paee on Ae eae ce 134
of cord wood methodsiofiieeseaenee nee eee ee 123
of current growth on permanent sample plots.................. 443
of defective trees for volume tables.................0..00e0ee8 183
ofvdiametercrowth on sechionssrra. ene ce ee eee 342
of height by a straight stick held in hand..................... 235
Prowl. 2.'5.00%, Sebel <= o b's Dsl ee 368
Gf Heigbig ia. SS bau) seve a eaette hes, ws = olan, Ee 235
of log lenigbhss)y+.caescrs alee Beh te OR ee Lae ee 16
of permanent sample ploisseul- W..... 2). ease See ee 312
Of-Plece PrOGuUCtss Ak sere ten eG kas. aes Se Aa eee 466
of solid.cantents/of Gtaeked cords... o.).i.2< i. cvs oie ia ee eee 132
of stacked wood cut for special purposes...................--- 122
of standing. trees:7. Retttiheiss citi, Gi. a. ee 226
of tree diameters cite... 2.50 cthesed NAL ee seen 227
oimipperdismeterss 5. 6ies 0 (wh apices 2S oe Re an el 247
OE WALES, ON eRe ices Sask Maal sits Wxsieees es Cae 179
oP width of crowns... 62.o<.3. Stace aus + sR Dee LAR ee 423
Systems) Usedunitonreshumensurabion, -se 4. se oars ieee 6
Measurements of the tree required for classification in volume tables.......... 156
required for tree analyses. 2. f...\...%. > 2k s seluk Sake ae 289
Onveach plot, anvyield-tables:.....2: d.cueaeck See cee 398
to obtain the volume of the tree. Systems used...... 158
Measuring and predicting the current or periodic growth of stands............ 486
diameter winstrumentstoneacy tos cae erie ioe See 227
Heights WecMMIGHe WIS cain c oe wor os 0 pu. Ld oe oc laotk « OL 245
logs, technique tof..92 4 os ert Se. a5 ae, oe 22
standing timber for volumie:........<....04.cRae Ms Sone eee 226
Stick-for Jog lengths os. - 22% oew kee ee oe eee. ee ee 16
Medwiedew's methods ucm.4se Be aus, Jere ok eo Re eee 387
Mensur tion; Forest: definition: < .......34...45 16 4aae. voor Jeeaa. eee oe 1
Merchantable boards, minimum dimensions, effect of, in making deductions in
SAULT A SeA6 RM eh nccetaed ag casks cepa eves Magers Sea te i eas NSA OR eis ra 107
Merchantable contents in board-feet, frustum form factors for................ 218
cubic volume, standard volume tables......................-- 177
form factors sen ee A Ee a et Br see 214
foriboard-feebe..6 oo5.020 2.b5.05 63 20s cs Se 225
heights'as 9, basis forriresiclasses (3/40. 4a 22-4 ue 184
coérdination with top diameters..................0005- 184
Limitin tops arid: ath eB cildite oars) stac)-sea a a,apste ewe nee eee re
log, \determinigtiomOl svi. oY ic< eevee cn se cine ee 99
versus used: lémgtihiysn yt Stee Oa ey ee ee ee 178
Merritt hypsometerse.. 2 < Piz dc oe Raed - en, sha Sak Ee Lee 238
for merchantable heights. ei saree Malle eee ee 246
Method of constructing taper tables. (av s+ occ. wsinisdu atta. aaclaeattnee Oe 197
of ‘counting: decades for growth... 2.5. 5.:7..a00 ys tee eee seen. 343
of deducting sawdust first, construction of log rules.................. 59
INDEX 541
PAGE
Method of deducting slabs first, construction of log rules...:................ 59
of determining form classes, Jonson form point...................... 249
of graded log rulestapplied to the log... 25. 6... obec hee ces ccsedescs 299
volume*taloles applied to’ trees. >: 5522 sect score. ee, 299
or mill-runtapplied iso stand): 22 sasosee tt eon eee ee. 299
GMTUNHING StLIpiSUGVeY Rass.) |S ok hee Pelee gee Pee et 276
of separating areas of different: types:../..3....6./0620behedstaaveen. 290
of volume crowthibysuse of tapers... ... 5.0552: 5-82 ne oee ke ode 379
Methods of estimating dependent on use of plots arbitrarily located........... 297
systematically spaced........ 285
PSIG UCHCO RSD stt hs s.2 ds ic8S RR 2b crak cole SE nee 284
plots, large timber on the Pacific coast................ 237
spnuceah: Northeast: s:$ ist 2) eke kee 287
SUM OESES DOG. 2)5s)2 2055 64 Nae Lees eee ee 284
Lake States timber cruisers..................... 288
Southerm timber eruisers.. 0... oo sce ee 283
ValtatiomsurveysiiNc..sc coke Tae nee ORD
Walesblorestiscnool 90). Sah shoe eee cer 284
which utilize types and site classes.................... 292
of height measurement based on similarity of isosceles triangles... .. . 235
of right triangles......... 238
of improving the accuracy of timber estimates..................... 288
opmaking deductions for defects: 03.065 sel e i gas oe asus s Vacaten es 105
Of MeASUTEMEN GOL COLAWOOG ....2..:5.5 66 <5, clings saw: orsiw wi cantare «peje hk 123
olscaling ya: log, election, Wable: Vi. 22 22 isc. 6 oe 5.4 + wisi Qebieis u's ae 45
Dug LUMEN CS UMA UMN erate 2b Nee hci ea So a she 3 cast ats i cle vote, cela ea, 267
of training required to produce efficient timber cruisers.............. 303
used in constructing log rules for board-feet........................ 58
in timber estimating, factors determining the.................. 255
Metric'system; conversion table, Table LXXTX a. .... 006 pon een e ok one ee ce 492
OE AMEACUMOMIOM Geen yee ie ete ALA ofthe a i ce Ba ce 6
Middle diameter as a basis for board-foot contents........0...............0. 46
Mill factor, substitution for log rules, in universal tables..................... 146
Prade Gn Milli sealer StVGled: ie MPa se Aa cea aRgh cele 3) aceite ls Sas Seed cole ioe 461
=r as basis of grades im standing timber... .).. <2: 2 lciis< dade dunaacle 299
Tero (EMS HUT U (Oconee RA tanegeicnse the Ae eV ge a Ree eed TRG Aa eS 461
methodsat conducting. 4.6) 284 eet eRe eee le 462
MO Gia CMEC OME Sea IN 4 ap agashinc ads ayossita yestread Ao oe ee 118
tallies, CONSCEUCHION Ollog- Tiled trom. - 5 ./2/iho skeet a ate ero ea ee ae 78
LALLY; Wl CONSEFUC HOM OF MOP TUE Be pps. Fos ot sicie fae) sh2i 2/0) athe ea es eee gee ad 58
Pau area ee REUMLG. © otey ceed tee ead stot dt PM ae A dacs, Na: Src SE a cet ga ga Let AY Lae ve 85
URN SMALE sack, « San cas PRR CRS yall oes Wer PRN Pega) shod sid ne, Sean siavk Lik es AS AT 2 474
ITEP EL CCST SAREE chs MME RCP e Na BA oe De PO oe oo ee 473
AR CI plepwmel ete tite chiara tn ee id cA ae ake Vees, Sepca eh rave MMe UN P24 1, 35
Minimum dimensions of merchantable boards, effect on deductions in scaling... . 107
ZCI MMOLE MAMA OLE MO PA Ayan en eerae wh fo tical ie ele elses atc agteic he oie 99
NMiNESO ba, Rebate) LOM MUS ada ae e tele Sieeree asc ln A ciale ate lialg dic. decw che wb ESTEE 73
ESISSID pI At uUbeplOR CUO se -.dussn sabia tas oS Mee ela ck vokeie oSivis ds dae’e chews 68
Mixed‘ species; yield tables foristamdsiof jai. 025. ac eles ees ee ce es 408
Stans: CHeCh OM VIEL. ca reins ceed anes UNG o.aal a acta A ae eet 393
542 INDEX
PAGE
Miodijiansky, A: J:; method of stem: analysis a0..1<0 6S eee 382
Moore-Beeman log rale inc Sate Wears Sere el ain IS AOA ne oe 68
National jforests; log-rulle see oc.ciccctouto eee lacie b)00e Sie Ree eine Se ae 73
Necessity for board-footdog mules c¢ & a2 eG aucd,-/ 4-0 hoes. tae ee 40
Need for form classes: im volume tables: ce emencv iodss o2:t cotati oy som ee oe ee 205
Netloid. « sciisa% OF oflnere eu as ase ee Ree cs chee 4 thoi oer eee 19
Nevada statute: loo rule:. mm acinar ees cae PRS EE re Fre sc 73
INew Brunswick#logamule s3¢ 25st shegeac. ace We eer isooctane mice a ee 76
New HampshirevorBlodgettlogmulesseaeeece see eas as omen oe ee eee 30
Newton's: formulae ceetcrss ion cssiaein ce RCE Ee ickaiors, soe eR Ee ieee cana 20-21
INoble and: CooleyMlorinulesys eis a areca eh a ose) seuss Oia Sk ne eee 35,
Normalidensitiys® ean cajwdh oie ee stains 5 renal one cs 2c eee ee 397
TOTTI LACTOTS ys Les eee ot ee Oa ea Echoes ade Seon ete aA an ie 212
yield ‘tables fer even-aged stand asc ee. eas. s+ = ace 2k dee re 395
USE yOL /DyaneGUGbiONye wees ioe wig sie ie ee ea oe ee 413
Northwestern log rule.......... AS AOR MEAS WRI E RS SPEER EA REN ts is 86
Numberand widthvotstripsarela tian: an mine aeeiinccrica: tice oie ene 274
ol trees! peracre,aniluencexonyieldsss secede oe ele eine 414
required: fora volume: tales. gc 05 <gore ace cr sess igyous eget ak eee 155
Oak: White and Red. log grades:.<. sis .5.<5,0 04 os ssa 68 swe ee 460
Obsoletetlow rales’ te iq:< hese eseroee ei eess che eye toes nce pe ee ee 36, 85
Ocular estate 6.55 cesses sae he MER ele ees hee ge ae eet ene 256
eshimartiontortreerdimensionsease sacroiliac cis oi ee ee eee 234
Old! Seribner lop ile se eee en cRecse css cos he bis ees le ee ee 73
Ontario; Doydimule jover-rinte:. 2) setae as oe cn 6s 2 oor eee ee 71
NG PEW ore. ae meets oe ecco re elo ed cent Re ac Servs One AG Oe en rR 68
Ordnge*itver ioe nUle se cap arene Getic oe oe ance oem emt ioc ao pee 36
Greson statutelor TUlet fe. shee fe ech Meee we Sve wae nein ete co) eee 73
Overrun detmition dnd /basis Of, 2-05 55 . obese nn A nee oa oe eee 46
deductions tromisoundsscalenyensuSaac mmm se cee ee ce oe er ceneeneieaeae 90
effect: of-errors in Doyle rule Wpone —. 25: voscce ee ee ee 70
influences affecting. Methods of manufacture.................... 47
The loo mule*itselie.| Aetr- asec ene eee ee 47
=EGDped: tree, CeMOIhIONe v.05 sities nee Gare Eee 6 one coche eke eee 158
Pace; unit)‘of measurement, definition. (0.2.25 60) 206 Mei sek wy. . oo ee 6
Rachymeter, Biltmore). i. s.5 eee ee oe eR Ge Lets) aos oe ee 248
Pacifie Coast method of estimating ..5.5. : Ayaets aaa 4c eee 284
Pacing, use! in €stimating 6.8 Vee see. hc b fice whe wei Cle Sees ane eee 262
Raralboloidappoloniansdetnitioneps eee eer rae cer oeeiio: ei ene 19
Parson’s lop ques: <.\....02 See ke Se Be PO ele Se kn Me ria ES aaa coe eee ae 85
Partial arcaestimates:. "P.schek sacs aserMe cs fe. ors Game e even tee 273
ESUIINA LES Racy noel aR ienckernien Se teres Ay etene Sica dna sic be cust Okc neue ane ee 257
Partridge cordwoodwulle sy); Aisa ee es oe eee ea eee erie ee 133
1foys20 48) (ee nn eee ee ere eee ne NR MNO EL etchd 06° 5 Arce 6 OMENS. © 36
Peck 1) CYPFESS! scam cst ee he ere aaa Mh ate ceoatre ipa rises Tan Te ee toed EE iS
Peeled or solid-wood contents, volume tables for.................0 00sec eee 176
Pendulum, or plumb-bob, hypsometers based on the..................0-005- 239
Renobscotlog walle hseal) aaa ga wile 2 ie ee tie Beta ts anemic 85
INDEX 543
PAGE
Per cent of area to be estimated, relation to size of area............2.2-.005- 262
of total area required in estimating, Table XLIV................... 292
seals asa, Cochin mn eels ost cnc os eno bdonooomoodnadce 107
Oi wastesmearlommbOuale mit. 12 oettete cinate. os etecteens Ora tata eic areaene ue 55
enodio annus lignowthmeee eae. wi. 2 a. os noe ahh ees cre deo braid eects same 315
PaeS NATH Sl LS Regs g HAok 3. |, aol arte a Rae Sa Tae Sn ang acer 315
OLS URIS neers Ta 2k Ll meet Be ee Seeman Reo teh Mums fone cout 436
DEEICCIT LE SEP 8), ls sie okt eat A hae wo ole wena cec a genie 429
Permanent sample plots for measurement of current growth...............--- 443
TRVEASUEEMMEM Gis, pauses) ase onions, See aporareachel i aha var eraue wisi 312
Fase ete Gee IM Oe ae Cr RITE NS ics s-2lc) vtakes Sods isiAe wun oernareciereys we aighe st bealtcne 118
ihiippine Islands, logameasurement........5...00. 0550.26 Ue en eee eee ene
iecev asa Unit Of timber-estimating: .... 66.56. be ee eee eee nee een 140
THTTATSTWIRS (ITO 4's choc. OS DOI Oe OB mee ome. anis Ui tid o bots © 7
products, converting factors for board feet, Table LXXVI............ 478
Imspection-and measurement. ..65. 64.0.2 cc Ns ewe eet ee 477
IMEASUTEMEN Ith Olee EEN Iter ceria. ise ere 466
\HallbaaYs WMS) SSAA 9 4 coe a edo oo Aaa OOS cicnn combed cle 191
HEITOR eo Feo Pe Bohs er elt acd ttagte Sota Jog Vola a re “ade ob np erate of Bah Miele leat 470
CHMeN SONG eA GVO ony. Le ANA ee eee Aboot en east alee 473
irregular, effect on solid cubic contents of stacked wood................ 124
BT CURSE EIN SA eI eRe eat eS Rote cer eens etee his | hoferaade vee tale celehaw atau ameter 112
Plots, arbitrarily located, use of in estimating.................05.00s eee ees 297
permanent sample; measurement. ..........- 02... sees es cerns eee 312
systematically spaced, in estimating.................8 cress eee eee eee 285
WAG! Tin CSTE - 5 a> Shou cc osdadogaan dee obepa Co nveooeR seDooods.9.0 263
PEsleairP APE A DING e (ehh oh = eee echcee Moen ers Ae eghiad ta aectate lel sbals level Sheela eed See la tallied aes 166
Plumb=bob, hypsometers based om the. .0. 0... 6 2b se eee ee ee eee 239
Point of measurement of diameters in volume tables.................0-05055 148
TUG) EM byuccaiiny, 5 50 cep erp tg Nie RCW eG A Or oh at en 2 ei eee Re 474
CICS ee RRP iets See a ASE A Nes GH et Bre Smee, Sint te ap A SA Pensa AERIS SOEs ec ee 474
Rolessand saplings, ;stamG table forssee facto sets clas «eras a clolcelats aide sie ce «tar 454
CHESEMUT REM ECIICA LIONS ane re werkt ee a ee Ata teeta ne Mn eens sal end foe 469
SLOW LAVOE aE Ne St Ie EM ARe ete TO, SLA. CATE AO Reet cae cael earns Bait 452
yrds) | Pew ere, 2 Pigs A eee De ere CE ried Seer nara cet Rk a ean cane Orr Paes A471
SPEC MICATIONS ste deol rae area 287. ais ce ohne QE etierm meee ae aa 467
Evin] noe OI COyee 0 Ne ea oan de ai iS aoe SDL Ra i ALi ea aol 35
Rests; laree posts and.small poles; sie. (55 Sf ein De PAea Aees one 471
Predicting futine growth. methods-Oluane..0-'2a00. 0002 sana gat woome we hes 320
yields, application iol yieldttables im... <2. 559. Mase ess he Ieee 322
Prediction of current growth of stands, methods......................0--5 436
of growth by projecting past growth of trees into the future........ 323
from yield tables, by application of density factor........ 414
in even-aged stands, yield tables for..................-. 412
of stands) by growth pencenty...cc.0..:.4.0+-...:ocane £oe
Pressler’s formula for volume growth per cent.................-.-+-+ ese eees 429
JRives}royavedboses 110 De, 2 ack canter Mee rer ete oir eee ene PaO a a 66
Principle of the Christian hypsometer..................:c cece eee e tence 243
Gil WINS UAMONN WOATN NENCWOIED 6 sooonnn Goode ae ene ee cbeee oop aDcdom co 218
235
Olatne Idlatsster lnypsometensas.<2 55) a<n<) 2c noo ene de elecies ovine bige
5A4 INDEX
PAGE
Principles underlying the estimation of standing timber...................... 255
thestudysoljerowtheereeeee as her ee ieee eee 315
Prsmoidalformalay, > :.1 2/2. Meccan «cee epee Pan dandioe Sneeye eine ane eae 21
Products, forms of, into which the contents of trees are converted............ if!
made-from; bolts and ‘billetas, 32) tases. vs 02s oe Steere ee cee 14
volume tables for two or more, combination....................... 193
Projection of growth by diameter classes... > 5052. + ¥: Jaseeoee ees: eee 361
Purposerand chanacteriot prow burstl lesa: ci aerier scr) ae Alea cre nena 315
and derivation of tables for cubic volume of trees..................- 177
Rurposesyoustudyxotener chino wit leer else rien ne rs reccue i ware: eee eee 365
Qualitiestot site: separation niheldee-- ss aspeer re Le aa Ser nee ee eee 448
volume growth ja: basis fOr soe. gens ee Aue See se 385
Quahty: crowth percents 3. since See Coe re oS 2 ot es RO eee 435
Of site: b: 3 Pee se icad cee eee ee trate kocianwey Aine a eye Pea 384
asiattectinge heihtrenowlhaeeepenaere ceeter eee ree on oe 366
elfectronidiametenienowler -eees ene eee ree. ree 352
of ‘standing timber, cstiniaiMey...-os.c.5 6 < opaleReelee-lesn owes: > ee 297
@tartersointlis ce yetve ce, seks Me oases choy Cascrentiate cee Pete maT ane ee 25
or Hoppus log rien. i2. cM boc. eee OA Oen Re bee chao ee 34
Section, (definatiomiee Sef ioanton misevbetcioois mie aie dts Sie eA ee 6
Ouchecdog rule isis fet yak Gee pamees cule otk cencrnces DER Mow aoe are oe 76
Record/of dataroniplotsayieldktabless--eeeieenice eae eee ens Eee 400
oftinaber: asloy 5, eek Alaa eee Oe on Reinier s Bic Slo eRe een ee 276
RECOLOS SCH] Clues. opt eset aoe hmiet ice suv, aetna re cot ermne ints 6 ols = Re ee te Oe 98
nedweedionowtbvolustandsiattericuublne erect as tein eee ee ee ee 439
Reduction in diameter, in scaling defective logs....................-.-..+--- 105
iInvength inescalimp i detectiyevogssaqe sameeren 720 aie eee 105
Reisic methodmscvlometinics fonGOrdwooderc.-esn ae alee eo a ie ae 132
Relation between cubic measure and true board-foot log rules................ 39
currentjand meantanniallorow tobe ees eae eee 316
plots and area, covered, Table XLIIT.,........5..-.22+-25- 286
size of area units and per cent of area to be estimated....... 262
of cubic and board-foot contents of 16-foot logs, Table III........... 41
of diameter of log to per cent of utilization in sawed lumber......... 40
Relations of height growth and diameter growth.....................-+-+--- 367
Relative diameter, in determining growth per cent................-..-.0000- 430
utility of different classes of growth data................00.0ee0e0- 327
Re-manutactured lumber, srades....2 oi) pantie ieeinc ts ket ioe ere 2enc ere eee 456
Re=plotting*curves. strip meuhod..5..eie seer. sea kk see ee See eee 173
Resistance to wind pressure as the determining factor of tree form............ 208
Retracine*bounelamiest raya ts laa ath, Re ee Se Sf eae Bart-e) she. oc teas 267
Richt triangles memeasuninoshelenitertec serene ee eee teins ieee ee nee 238
Jeet Coeeieys ce einem Sica AEN os oo 5 363 o hoo duh goo Sion A ha dees ameery ole 109
Riniker’s: absolute tormfactor.. 1.64. shee see ene cee Aa ine 212
E50} a) SyAspa Coyeaa DU Ce teria en ik ale Ran Repent iene MMI Derm, . nie Aba tn aias my deo ccc 86
RSE iG ens A Ne OE i oa 110
Us) I 3) ne MEM AEC a Semin MG SPE L anom et ews iis oh p bes oe Ata ames e 108
entering ‘from knote 20 2.2). ce © are oe on eres SOOT ere oie 112
INDEX 545
PAGE
Rdlty QUT Gob Uo cGadbod ooo Co coUU.cbid. on obooinln cnn Gaul co bode clo dion Amibinicis 100
epee WUTC E UETACCa Pte a aie soe a is 40's ors oisisls) 4 apalera ekettiaia tb lola stonete ain ehs 456
ERATE GULUC TSH e) Hate ear Sonn WAS Ret ace cs, AREA eles ied cet AO
PEM SGC lu DEr ee eeeiae ts eo. alns,5.0 ai a(elale Gispsleis 6 me einloralalels ooMahers ete nly 14
Massachusetts log mule for: Acie ie hice sec ctelee ec 79
frulesiot thumb, for board-toot/contents....... 22.8. Se eeiee ee ee eee 252
HOTACILOICRCOMEGTIES Het i2 nee cheneieiene ter auee eR TENG eet Greeks 251
for estimating the contents of standing trees... ... heed pacha 251
funning strip surveys, method! Ob. 0.6... cee eee viele rei te aloes oie) eels 276
Reominiven lomarUle =a. e Scene tre sis bo. 6a sae e wine 210 odie, So Buellele heels: ey am sae 36
SMU ROM Op Elen: sae yee. ac 2 o4 ist ts SDR Mans ale ethetnatnis tata carNionae a omeantae 68
Se eoSAELAT El WwOOWMylopmuUlemm name ti. <M sae a a sfe elasts tated poldlne ea ielete aici e ne sets one 35
Sample plots, permanent, measurement................ 60.0 e ee ee eee eee eee 312
for measurement of current growth................. 443
(Hees Method stof-estimmaAbiMe. oyu. sl. oye. ene Seleraiale a b/s SMe eee te oneal 310
SED SELIM eC ee vee-to ance, a Aes a sal OAS Sots <vayslgiatelereiale, elvis Solas pcchabgtes oens Th aget ane 115
See POO GU MMNTNINUTETE 2980 cles Vo aif, ayeva vielen svete a cet teeta ees he's (welche glob sada deaacntebaaes 161
Saplinge eemowiUMtOroen Ge atisek es atstanlraektnted gig else nile lgla el bb. bier. Shi eh ieee 451
Saw lerf, and slabbing, deductions in certain log rules, Table IX............. 62
Are CHEN PUOMER-UMM, 45 aise ard as a sarg caesar 5 te ene tsnetel earn I eOS Eto ai mina = 48
conversion of values of a standard rule to apply to different widths of 80
Waste TRON Gear cae tthe eee ede RST PSN Ae Aah ta fae shoe svete dase 53
Sawrkenslotaiterentawidthsmcorechions Ol... 2 oc0 66s alles em meee ere 55
Sawaust, methodror deducting yi j2. .ges s6 souls caledaeneit od denier lee eens ae 60
Sawed lumber superiicial’ contents... 222.2522 6s.s 50.00 sels dee see seveaclneecns 13
Semlles Toyarol len cic aic Sic nettle SAenes olG EN AIC EReR ANS FOE SUE OVC O NRO ROE RRC NIEE nC aR Cn eRe acca 2 99
GEL C E28 ANA ere) rrr gt Ct ge Peek en ee cn a ee 97
ELITE OTRR ace EAT Oe rete enters ome eID hts inks lohan eines chee 88
LOC OLAS SPA SELLE Tey Ay Ses AAO ai cucn h nhctetiarin on shaialak abrarcahshoy sho a bc cy evel ete 98
TAD Lakh Ge CA Ni Ns A nein me ae ca a Ao ee heal ase 88
FSA (Ole sed neo nt ie Waa eeiG LG Da ib xe TET RNORDIE Cee OR Ee RO ee ORR ois Sica 88
Sealer, legaltstatuse estas jac sincidcioniolnnce catemits o ebosieininten: leer etaiete olensye Rhatcieteg 119
(Sera etietae ties chotercnaci arctic cudinncts.c cr Gist aai Race aisle antes bi ie ie sto acne eee 118
PSECEUILT) RMA levis ck elevates NERY eg fore atte GA Teta ehMac ra ote tel os ite cate ta ante nit 88
CLOVSY eet Mare ge PORT Sepak eon oe 2 OB Re iS ane, cab fed «corde ie tiny Ope perc EEL 117
eylinder/as the standardtof.. 20.0 00ee ots). a cise Selaels ee nail hele eleroe 90
OIPITIVSHD cls Prete 4 eee oro seoiIa Li oto.o DC CAE ee ERE ape poe Be idl or Caras cane Dic 92
TAROT VA MELT AUUICY Oe Me a MPI ay ert ie SOTA LARA tr PTO AL orm acca unites 118
length oflogs,;tapertas Uimibimg 2 5.0... ike SRE ee alas 43
ESTP UTITSL APE ho at cne Alesina set aus OE Re Rote Ao Er ca coh ea 91
MINGLE STEVE LOGS ates tics hn 593. ai aay hh Laid slo are ania ees RR Ine) sean Selden ede 105
practice, based on measurement of dinthetet at middle of log, or caliper
BCA LO Ree ar OR NP ete RE eaters PAHS EL Gh aps ee PNSTS Se He, aR eee 97
practice, based on measurement of diameter at small melo Moye, ooo oc 91
in different logging regions, ts ble PROVA Lilie pete eyesre we cies by Sin eh 94
UES OH CULO. NOS, pogcdsece couple ou nec obo ods Obe6 Odum DoS open acc 28
DSephicls’ sormulbaera rave tlOm rene ye sien nets oie cealare 5 |. Slee)! ale aualda > a hdl 206
use in\computine volume of tree. .....060. 004. aese iss 2 ee). 168
PTS melt ONO Satna 25,5 py a rcmale SIA © a Rinieleie ape Renee « 494
546 INDEX
PAGE
Schneider’s formula for growth per cent on standing trees.................... 481
senibner ‘devinaal logue a2 '5 ou: % pecetet 45 nn ae hacia sg sic ones atate okie oe ee 7135
C log sulle; Valle Wa XoXcXnValy os. a lo ee Sees eee ee 504
Senbmer log rules yot oh oe tech inns Chie ee ee yt is se ee a eee 73
decimal values) Mable sxe gcse hse erste ooo ee ais 74.
erroneously termed................. be kid. See 68
EXTENSIONS ot sho saa Be eee a tw oe ee eon ee ee 74
ScrbnerDoyle-log nuleiices io Bibi te eee make ies Sal: oe eee ae
Scribner's log.and lumber book..dn.i 5 sce a Oe eee ee 68
Deas Af hs ee Se ep EE ae LOUD: 3G a anit eee Tene ed 112
JONG Olephte A aera RAN AR me at ede Yn 8 140 eS ee A REI Ss 112
Seasoning, effect.on, volume of stacked woods... .....: 01... 0s:...-.keueee 123
Second growth hardwoods, yield table, Central New England, Table LXII..... 409
Section, definition. area unit. 21 joe ee tame ol se aoe eee 6
Sections, measurement of diameter growth on...............2000e cece eeeeee 342
Sectors; deduction by stor detects..4-. bs. 4.6. .sseeieeSiaic es eee ee 115
Seedling “age oltsc i. ety re an oo ete an Re A ee 336
Seedlings, height, western yellow pime, Table L..................0..000 00008 336
Selection of trees for measurement in constructing volume tables............. 154
Separation of factors.of volume, ape andgarea.. ....\s.acn ic odes eA o4 hci ee 416
ofsitetqualities; in heldWiia.4%.. cs pacts malachite SIG Re ee ee 448
Seventeen (inch ooy rule ys ties eye ee er pecs ke ae cec te tiles lon ee Sa ee 33
Bhade, effegs on diameter growthib.<oo6. 06. 2... 6 i st aigondd oan epee Oe 353
ShAKG 224. betes eA Oe eee aoa Soon ae aot Zoe 111
Shingle: bolte; definition: s-e.6 eek yen be ce wads 0 ans ke ge eae 15
INEASUPEMENG sayie:e, Sttyclescycseeeis = = vm whe Tea hers ot ee Nc eee 122
Shop: gradestee Ar sofas ty Fats rahe Ao OG uo Sak ed adeia eas Be 457
Short Condy + semi ae. ew eens shea teen ig Heese tes eo, Yk odes et os Se ee 121
Shortleaf pine, diameter growth, La. Table LV.................:0.avesebah ongOe
SHrinkA ge sa watts ees mises od ee aloes Pe tai Sind iin as Sov ee 54
Similar triangles as: basis: of heightmeasures «.).4/-.5. co Gus se- soos eee 235
Simomey S toranlay tea act ye ul noch ee heigl el heres, ocr, eee and yee tals 22
Site classes and average heightof timber: ..).. <6). p0s.s oe oes ae Ae 291
based on height growth for construction of yield table............. 401
on yields per acre, for yield tables................-.....-.- 406
Use unVes timate.) se aa pe eas sp ep eee case skeet ee 292
classifications, standards based on height of tree at 100 years, Table LX.. 387
factorswor quality: Of: Sites Ocecraci tossed Pick: Rosse dls, ola te ee 384
qualities: height) growth a basis for:..5/ 24s... «22 scemnsideoc eines 386
Separation! inwields. 525.4... <Leboatlne daa Soo eee 448
Volumes eTOW bia DaASISMOna acces eet cca tection erate 385
Site qualityaaverscing tonentire anes see see aero eee nee ieee 449
effection) diameter: prowthity. 2 emer orien ocic ioe Reece | ets reir 352
Six classes of averages employed in timber estimating.....................-- 258
Size of area units, relation to per cent of area to be estimated................ 262
Slabbing and sawdust deductions in 10 log rules, Table IX................... 62
MAH Cle malowmnty IY NAM scp. soccossGcgotacocce 56
Slabs and edgings, waste fromis.): : 2204 Gi casniec s\ cae meio nines ene eraae ome 50
as affecting: OVErTUM.,... notes o Gk dee ier Saxelsactids. to Jerse bit taco 48
deductions: by, ior defects ../5 5.2.0 Sei meres sea kaks eee neta ea 114
INDEX 547
PAGE
PRIME HOM OM GEQUCtIMP kes boats ai oe oe es +o ob eure Cae Ee es cbr ee 59
Shona ain Siatoy co EW ac a ato cathe bac gith eReuCec tone cure ces See Deere ms cooker ea Tre erage 20
useinicomputing, tree volumes! .....-¢44.2 555 senieee 161
Spam) [xO oo Nea) és crisperenerao iio CRE CREM a NE Oi er Soo a ee 471
Olea peer ntNt ore ease ess ec So ec a RE ED DIOR s eae aan 268
Solid contents, effect of dimensions of stick on......:..... 0605.5 00ceccecewes 126
OlsirrepularapilinstOMetcse sae. MAO Fok h eae ie aco os 124
of variation» formyof sticks ont).%.).. 242.24. 5+.005<'.4- 125
Giglo me Porimalssamryes sist. 29S Sela le pees sylh cates So yoke ee 20
aistacked" cords. measurement 42.00% cides boas tiow. vido ete we 13
SUOCIC Me: By tn RPP CRS Me de ean gnater duets Btls o's acca Re 124
171 0) (0. B, Cae ears Ln eva ccm et cid Se 127
=wood combents.. volume) tables for... . 2. .s deluge see orieto sme date be os 176
Sound scale; deductions from versus Over-Tun..............000seeeec ees ecus 90
Southern timber cruisers’ method of estimating.........................50-- 283
yellows pineseradin gules. 4-mrpecer wien we tiie ye see oe 457
poles, minimum dimensions, Table LXXI.............. 471
SSDTENG MIO 1 Sis TEIN ae a Hehe bid aba es Lc a 75
SAGES OS Miicrnayes lava teadane PaRon Ale aaoogboadons ed aMaseuannunpuedouoncasdob. 365
eiectyonadiameteripro wither sayen ae sie AS 8 age esl as Eke c Se 351
Eee cer DINe tS Gemini GG Mens ge 6 a has so o's G50 Fee TAR STEN Sl a he ae ye 15
spruce; Adirondacks, current growth, Table LIV... .. 2... 000068 beecas nese 360
growth on cut-over lands, Table LXVI................. 440
Giameterorowtasoigurcesselalole Ilene se eles a onal ainierreee 345
in Northeast, on large tracts, method of estimating.................. 287
Sauareion anree-rourths logue... i524. ots cb dklo wie tie web RG Mea wie des we bs 35
se WO=thindsilo par] mers yap teers ever etna eNe Sictial- Wate CENSUS IFaIoA os wae oe aN 35
Sauared. timbers, log rules'for cubic. contentsiof. «52055 5452 sses ¢ sare hres aes 33
Rctianhes SOCHIIbION ete ete On eee oa.3 Smee LIAR: lar ead Bisasie LC ode dd a Be 14
Stacked cords; measurement, of solid contents). ; ..4 aise niedhim. ea tons dees 132
Cubichmessune ma chnitionerere se oen eer cater iiine erence 7
measure asa substitute for cubic measures.sci ts. oie ess ae es 121
OTICOLOMMEASTITE | choi: Hata SOS co ele ne et ee beter gh eure yl | 121
WOOdssolidecubicrcontentslolemm aerial aetna tials oe 124
SEHACO INS a Meer eLL Te LOCA Re ea he ft coe E bit eB aOR SY Sted hs Ae my 277
“S(AEEED@TO LAS 0) praia mene atta ge Alco tr ce a ee ES ETL een Sa ey 115
SUIT OFS} Faye Aiko Roaches ered Seared oa oti acters clnfend ch her aeam en Roe Fy ca ey cued fo ea cat 99
BeNO Ce Commi pYa pe: Ol eas Soe ETRE ee tre eoslcies on DPS ae AL ee 339
peraere estima Ledupyyeye vasrericci- 9 si u aye sclde Sos tee a Re AE Se 260
table; application invsrowthjstidies (5% 2.5656 geass dee sae e e's: « 421
for POlES BG RA DLA Snes s,s Sire ain tla a thee ee anios eed 454
(oD) OTE SERS or Sieenet ed at bs chil a Re eR PE Re coe Pa 227
uniformity of, as affecting methods in estimating..................... 265
Slancander cerondackey peared bey were a ers Sarl esc ANAK valk eee ae 28
preasc-mighetonmpractorsee eee ree aor eae aioe lode e ake es 213
EDT ove, Be BS) te onli, Raho sche Se cS iO IS ENCRED RICHER RETR CAG 121
CoOLawooG convertingitActonsans a4 ee Ho dus eile howe ae wee we bh 128
for NommMAldensitiy, OF SLOCKINGseelrs se esters daniatadinse dubia ws eee hs 397
logilenctlsinevolumetablesstiyes soy. am seu. alesre wes . ante) om od loi stee 182
Ofjecalingweyimoe;nr agithe. mn <5 Ohana does se ky fe abn ee hee teh 90
548 INDEX
PAGE
Standard, Twenty-two Inch: 22). 925.0% Ss.cr Soke hoe an sea eies Be oe ee 29
universal, choice of a board-foot log rule for...................... 84
volume table. form; Wableexexexeas eine Hier ey eran ener 174
tables\construction, oyacunvess-r)- 5 ssicaieis aicicierte nee 174
Gehinitiont Aenea ete oe. ace ree ae ee 153
LON (COLGS se Min etter, ee Webi CaS at ae 177
for merchantable cubic volume and cords........... 177
for total cubic contents, construction of............. 154
harmonized curves for, based on diameter........... 169
Standardization, need of, in forest measurements................0.00e0e00ee 10
of variables in construction of a log rule.................... 49
Standards for yielditiablese yen see eee aes coc te ene ot a ee 395
mm constructinglog rules Assia ee Leet Ee ead ee 49
of site classification based on height of tree at 100 years, Table LX. 387
Standing timber, estimating, principles underlying.......................... 255
units of measurement for. ). cen ae ee eee 139
LEGS, -MEASUTEME Mba yr wee us cAcianetn Micke. eae Rekevcloe ie. oh Ree 226
rules of thumb for estimating the contents of................. 251
Stands formcoiey.< fr oe eens coe tik aa leein 6 Oks OER Cereb as pete 388
grown under management, yield tables for...................... 407, 427
prowth. ol, factors) atectin gs, .an)-1- ciao ledeiaici se alee eee 384
of mixed!species: yield: talblestiorsene: «iene shcre «cece ane 408
Slave Olt.) so FS eRe ede eee eee ce Renae tne ot SIS LLG EERE cee Warren 15
Staves) lem othhss . 1:5 cnsocnnewero ae ueeieiracec hance ae ni « ile Ae See Seen pee ee 122
Stem analysis, limitationswimsesay 62 fsck 5 cre cee Pa gee ee 326
Olver trees Dale IGEN 8 Fs .ch sets ovsro vase oILE eae Oe 378
purpose andtapplicatione sa. -muci) aa Seas ae ee eee 374
Stereometricamessurementonecordwooderrea-me mere. wee eee ee nee 132
StillywellismVadesMecumulog mulleteeyn eee a ore aes caters crete ice ee 36
Dirip estimating, systems in Uses:...:.... 2m ate a ees cee, 282
method. of estimating <7 csie aA coher tse: oie sew sete aaah = RRL 273
of. replotting curves? isaocs aS oS i gk ae 173
surveys; method of ruMMIN Gs Gp he sae ovis, i dos 3 se ee eee 276
Strips, relation of width and number, to area covered, Table XLI............. 274
tying in, @elhe ase dines.)\22 020 fo Jeger aokln es se 281
USEC in EStimatim a2 cle a ap shens cere: Soreiceuey alas ier sy eec ara ehaereieer cin Lin eon 263
Widthrofeactors(determintn earners eicietesterc ere sree icra | eee ae 274
cues ey. Be RRC We PUR ecn cpaterateh cectal Mba aa Radste Sisal OR CRN AL ek 473
Stump, height Of ss.) Sb Shes See a as oon oad da ae ee 156
heights 220.5 yi Fe 4 ae pcan crane nd See Cae tie oes, 2 es 178
POG cris ties Ui a 5 Oy wraed Mora careers, sat Dennen Mocbagalee side Rae ens Siewmeeteen ats fe tec 110
COUN 82 0 Mas a ARN ay, SEMEL Meter 78 vice sch hs tations eat Sl rel eee 118
tapers, Table LEDs eee sa A is a Fe acta. ae See ae 350
Stumpage value, definition. Relation to forest mensuration ................. 3
of products as affecting accuracy sought in timber esti-
TONSA GLEN D bce stig vate Brees Cider kc eter nes ioral ake ee ane ee eee 266
Substitution of mill factor for log rules in universal tables.................... 146
of taper-tables for tree vanally isis fi2h% 24 leeks Seite Sek ae 382
Superficial board-feet, correction in per cents for lumber sawed less than one
inch thick, Table XVI.......... ee ae sical eRe ee srSiaeay, istaaebegats bt aaie aI
INDEX 549
PAGE
Superficial contents of lumber, correction of log rule for..................... 83
Obese COmbnA DORE ry aster Rice Mart sid cu.loltpeleele: aud ieie'é.« Sa eiclert 13
CSUIMA LS Me Pee peer atte Eee ee pa rao oar ellen ss) aul. Scapa ahah 308
PRAM TeSS GeO reCOs emt OIMGas lo AA sma e/ac oar isle atone vieieoieveidisise/s de ee ves antes 158
Ua PENS SION ACTA TTC LEG MOY 1 asi ws, cs «Alsace c.obalalns svete oa ciays sie o e-eiae we eeu 341
ASectiMgahelpint OT Owl Me Meri Meuse ayalelcectean cls eles ch aot cate 366
SORES ELGG EG | eo 0 hgetg cis in eat one nen Ree CER ae ne ee 115
GUSTS GUSTS 5 oe alate oid gaee yi cutleate. chdncec to cue een ot heey A MRC Rae Ora nae ee 115
Survey, forest, as distinguished from timber estimating...................... 268
Cle faTANE TOMA oe peyer ee ere ites oe ck ors oun ATP Case coeraus a) PSG a ohi dsl 5
SBurveying, forest,.as’a part ofthe forest survey... 5.262... e602 0.00.00 ee05s 270
Fe lap OnMEtOpMensuratlon sass 27 ese meeitccien eccrete ase 5
SSACE [OBLTINS Coll ht ORS, A prea Arete SPF ey iso, aks icc oe uss ae eu ee ie or ie ohenaties ehaisa usevoe 116
SVVEUS LIC GLO TN epee Ors PMN A 25 Eka 28 ic prorat MMU A puna 8 Oop Ascent 51
SVStemMEroriiimmben EsuimeatinowCMOlCe OL 14. - ane: 6 a+ see eis eee cisoele eo seers 261
Systems of measurement used in forest mensuration..............-2+00e0005- 6
CHES EMIOFES ULI GIR MMSE S Kees ehh os Sx hs to: Se ea aoe 282
used in taking measurements of the tree for volume................. 158
BMA SECU MMM ROE es AeA eee evel ic txar (lode ie Tals. noises Seay aayosauetenie fa ayia cs Shouse» 277
MMiGOlemeasunement Geli iONe se sree rein teats cic iel: 6
DDS, CHAAR. os amteiod otc Gh bir OID Ib CIC ONES LEO NCE Re aT EIR RR aie ae a eae enn ot" 229
Taper as a factor in limiting the scaling length of logs for board-foot contents.. 43
GUESTDIIUETLONI c, lynch ee ea Cie cl eee LUNG OPERA oa ne Ie are ee In 18
MITLOCUCHIONMIMCOMOFenUl eSupir etree a oes «see os Gcckae es aur ata Stine CAA:
en Lol] ES ewe ie | 8s MU ER cs 2H ce oh GRNEeS curnious AitouaYs uses 1a, WSEAS Soy aN 196
GENT EONS ATG PURPOSE Mann ct eet e ts Sac ates. bless Sik Zaiajeeuee-oneies as 197
lab AI ODAO Lanse als 2 sso oars Saati te Se mtatiath okays es 204
AME UMOG OlCON SUG LING ies oe ie cyetec clare oe ees 8 sends ausiibinseGyea'e ee oe be 197
SUDStIbUtIOMOr i CerANANYSIS 2.2. )< piatis be she os ten suo ads d+ Abe 382
Dapers, stahdard,ias) basisiot yvolume-tables-. <2 2 < c.5 acs shiccisecie acess os ess 144
SMOSH Nove WOliUTe MaknHN. .5sonneee 4 boon bane cocoons oo vol odeame 379
RRS op Cover Ul Koei OE Ss a so Sol ca ENE RRR Oe ar Mi Se Mi leo cts ee > ate
mMechniquevolmeasunringvheights,. ene ckisesserr ices cialevae cre cider seucsieraie ayetene.: 245
sllennesscemhiver Lo garters rama cictacs, 4 <ssieia aula oie e210) lesoutie rele) ara Gi apetecelie Ueto 35
phexasw Doyle rile Movereanum ces le lem rcosterere a lclece revs iaietas ses, aoa choles stay nesjtus terme ca ehh 71
aires BR ait nel oman e ees ayecsy coee, ca eae tel oie occ a soos ree oe lea hres cathe escier ele scent 35
areas: “Aceurateslap rile: 2.0%. ¥ “cnr sere oi hos Cale wae ible We 8 sabes eye eushe DE! s.che 66
“IM noir oer ovens WV ee oot Oaks pittanlecie ond cic cole SRE TORE Dic ern OEIC OI ISIE 68
pemarinel Og erUl] Cee ee EIN Tey etme See Sc cosh euih, hm eee aenatcha ereneel a aa vons 67
ADA Cie UD.O. OG INNS ES eR Cine 500
COmMpanisonhwithwhuod cecum Wle nse Anse cies eae ie so 42
reduced to small end diameters, Table LXXXV............ 502
Timber appraisal as distinguished from forest survey................0-+- 269
CUS CUS HEGIAINNLIY awa a er vane kos ese IADR nn NTI adie Ah Dials kcal alleouailaves 303
estimates, accuracy, methods of improving..............-.-++-+++-0-: 288
SLATTED, 65 3 ccs cuaic.o.e/: cynic oils Mien, OL SISO RC CE ace acne ee 9
CHOTCEIOM SY SUCMAUlO UMM Mp eine eite, tele tre -< Glsiel al cret aureus oie) ors) ie 261
LRU SPIT P eee hehe Bie messes aie ea coe) ch ne) disuse ley ioks pace 140
PC TNUUN TICE ae age APSE A eae alias n) oS) als Sow sha sh alleiayele oi, Sipe Gas 2
550 INDEX
PAGE
Timber estimating, factors determining the methods used in................. 255
forestisurvey.as distinowished from +:.-4...5-..-40. seen 268
importance of area determination in..................... 267
limitsiofaccuracy am tees: ohod aces a ncaste Sele eee 301
methodat a ecitecies bok sie one anele ade ofr eae ence eae 267
six classes of averages employed in...................... 258
record: of}. 3 25 VAS) ATS She ee ede Feet AOR ID) Sr 276
GypPess maps 2.25 SOS oe TA erecta: Wines a eae ee no ts en oe 268
Top diameters, co-ordination of merchantable heights with................... 184
fixed ‘or variable tlimittignre.4ae0. ..) Sock acer oe ee 183
versus variable, influence on frustum form factors........ 221
MOPGereap MiG MAA Ee SA Aid sel ia 2 ees eee aks acscn socket ns Oh 268
Topography, effect on:methods’of estimating. ..............0.20. 000.00 meee 265
Topsamerchantalblevlimituntes ese Geert ee tk cle eee ere eee 177
Mor Jonson Akash wees ee eee eee ME eee a rods-cieac a nen a ore cee 207
Total prowth onid latge-aréas factors. Vin... lc os pl ee oe ee 447
height-ofstree smesstrementi\ 5 ciao tte an a hee hon ee ies 156
increment of a forest includes that of immature stands................. 443
or 100 percent estimatesi 5... ask tro aod de et eee. oe ak ce 271
percent ofswasteumya logis ae Ae ieee, dele aie eS ns 55
versus merchantableicontentsiof logss..... +. 2s sees ee ane cries 16
heights as a basis for tree classes.................. 184
ICME 50 oe Avr arsid sa alto, BPG oe Ot RIE ORR ie oe ee UA STIR het Re ne er ee 315
townships «definition... o ceca. cette eras oss os i be 40 See canoe tee ee 6
‘Training oftinbereniisers), Manta cc as ok eels oe es oe oe Ree eee eee 303
Treatment, @iectonrmrowtllen 2 heirs c a cas sp aee wale aes Sales be Oe eee 391
olgshand wefiechionsdiameternprowthee es. ome ee eee ae ee einen 353
iree analysis smitations(OLusess 2 se lose selec ele tw hee ee eee eee 326
measurements required 1OLs sees. sane eee es ee ee 289
puLposevandsapplicatione.... ane cele oes aoe ae eek Cee 374
SUDStiinition ob tapem tablestoresseee een: eiocc os eee ore 382
substitution ‘of volume tables fors.-+2..:-.ccee .--: +55 702 eee 375
Somapuinitin' es tims tina aek eae ee a sisi hoes Seles Oe eee eee 144
classes, total versus merchantable heights as a basis for................. 184
diameters @measurements ci lscs ccos.so MY secede boats eee cites Orne eee 227
Gimensions ,ocularvestimationiols- erento sie cesar tee eee 234
form EoOeler:Sormulavionaeieas ca. sas see ks coe STS a le a ee 209
resistance’ tov wild 'pressune.23,2..5 ..ftis oon eee e enc at a terre 208
record, in’ connection with volume tables.-5.-.)...2.+-+- 260. noe 155
Volume; computa tiomys. yey a ae ei sisisne eo Bec eae re 161
systems used in taking measurements of..................----- 158
Trees for measurement, selection for volume tables.........................- 154
Standing measurement’, .cc roe foe sc ee aol ena e brn sacar hs Reese ae 226
‘Erimimiin gall owWanceiy cient CIA ce teke eee ester tere ore mec a terraces ect eae 92
lengths, in measuring trees for volume....................--++-e= 161
“Prun Gated Cowes yy ye ees Oe resect 1s Aiea ee Paes Peake a eae ae 19
MeN Kay (0 See RE OME MA EE APP RA SEE Uoeke. Se See Whe ei. il bac 19
Parabolord see wc Hye Le ae ewe ts ta corer Se YA I I 19
‘Twenty-tworlhchstandardaune cote acae eon te ee a ee eee ee 29
wo-thitdsvom Tule as. 2. os 3e sees eee eect ya eae On aay 5 ee 34, 35
INDEX 551
PAGE
Peenesin the strips, ; Che baselines: < 5.5 og Re W.tetas betwee wer lew sate 281
Pes mores, MSG Mestalla gs. Acct Aci eine kA areycncvpaviocnsl sine oc o a keke 288
methodol separating areasiot differemt....2 oc. aees eens st ee ee eee 290
He MEMOS UMA GEM soe eb aye Pes ahCMye eter ais Acie, estas rai ialerave & 4.9. 5 5 Oe 292
Uniformity of stand as affecting methods in estimating...................... 265
Unitsiof measurement for standing timber......-..-....40.-acs2.n-es-s5- 139
Universal standard, choice of a board-foot log rule for....................... 84
tables, substitution of mill factor for log rules in................... 146
TAO) MULTAN WD OLR aA PaO Recht 6 fash ree eal ae ees cole Chere mecees Cretan ag 144
tablesramcdstormpclasses:.2 25.4.4 ute een Mises ites one © Nera 215
(Unsoumd defects, deductions from scale for......+....5.:2-:-see+-+++es+-e- 105
misedslo cantleswemrerrmsm eee: ssc /5.c aie tae ae CREATE tts, Seaiee eats 85
Wp persdiametenss AMeASuTeMenbeerrystis cs 04 oases otsso hee seialsl tip seisle ais ogg siebe 247
lWsevotacorrectionstactors on volume.) oa-2'- 4 4)-10-4-.ae aan Hosa es seme se sa: 293
GM CUIOKO THUULSS} ore lovonNel ES, GRO Mipgoe nooo oe oncobcosoouomhHoboomonS 42
Olmdiaorams tori deductionsmnyscalin ges seers oasis eee ee ere eae se 106
OLE HOMES CIN OES IN CSIC MUN ccs e Guo mlGrcionD olen id o memo Rela ac 8 Oe colon a een 288
lWsedelensthmmversis mercuanmballemeassmaecis nace eaeeicese reer nes os arts eee 178
RUIZ GOMPINGLOPSe eraser eas cctere ie eke a ols eget ckareriasser ebay aetNee eis mia see Boon UES
Waluationisunveymiorestisenvice standard... 44205 46 scciaae + see oss oe sacle 282
Reema STO Witt DELCO caer ene Ae eee Stod ase Stal His ea oa eeehevae oe oe Aad ane 435
Nisin @ Vall OORT Comune meer Meme oS Secs Lets, Se ec cin Cem ieadA Ne ole eee oe 68
Wemable standards. in constructingilog miles: oa. 4.442005 0noee ose see 50
WMermomtslogarulle wens) werner ree its ee shes iets apsest stn becunne care Sse eealeas yy sock cate eens 35
Wolume, age and ‘area, separation of} m yields: ... ci. 24.4.4 206 «.o63 cece ees 416
ANGE CLOMstANGS We AOMmErm Asa erate cat eee a Ae eicemcces she ee 449
and area for age groups based on diameter groups..................- 422
for two age groups on basis of average age..............:.. 419
and diameter of average trees, determining......................... 338
COAAAHO NANG KOS) Joye, Mn CSN | oH soca paebsoooaddoouobeaueoe 293
fOEMAs aeLMird faCLOr ailectiNng.:.6. 2: 4% 2. sca arhtin namely ees em ce a6 196
ANOKA OIE IO) SIE OURIEMES ols otic ob Goons bapodd on ocueo mer 385
ADA y SISA ULUTIG Ven eee ey OR Turis het a er Ieee te 332
forsinpleatrees ecompUtatiOnen see eer eee ae LOO
OEGRCCO CITI (nae en nth oe Rls he oi ERE Ae Ng ar oye 374
per cent, bressieris ormulastsco- sae. cteetareus olen miei ae 429
ree] Oil Se aay ol atte Cae RSE NE 5 colo ar MOTEL en a Re aE oe ER 163
of standing timber “measurement. ..2. .',!,2)4;ateonart metroid eo ckhs aoe 226
OLstreeHCOMPULAION pee eee- SU Pie eh See perce aie ner eR tle eins caer 161
system used in taking measurements................ 158
table based onemill factors. Mable XOX Vibes yon.) «aw eieto estas acieon LAM
data which should)accomipanynn steer Aerie kes aie cis esc ese se 188
from frustum form factors, construction of.................-. 224
tables;/bark-as.atecting diameteram, |. 5.0. oc -aecs->--+s sgiss sedate 150
based: onmactualivolumies Of trees. a2 | ale.c wt) bc) spares! erelevere one 147
OnistanGardstapers Pen LOR As Aas <iq dc aisle ce seo aes 144
anrGataot cons trCtlomen.s pio Goals con iit evnsaic cote, oe eae ueeleicpens + 188
StancdandsOmsOAasiSene tin: crsisan oc ous ave aise execeret er 182
552 INDEX
PAGE
Volume, tables, checking the-accuracy. of :--..,.cee 3.00 J... ve eee eee 189
classification. of trees: bysheight im)... 2a.) ten ae ieee eee 151
combination for two or more products................02.0005 193
construction, graphic method 2.0.0)... -. adeneeciss 2620 oe 169
conversion from cubic feet to cords......... ba fa sy eisi "ales oe 180
cords, standard Aspe We Me eho eae ees eee were
Gefiniti orgs shat tera es ene MEA ete) ald RAE ee 144
diameter alone versus diameter and height as basis of......... 152
for bosard=fectnkh. peh Bae een ales Sea aaa nee eee 182
for peeledior:solid-woodscomtents, a1. 2c eee one re eee 176
for piece ‘products.<.--. canes 5 x0) Se ate pies Sree. os ict ee 191
for railroad .6ross ‘ties: . -.eee eee ats 2} Re eee 191
2216 (0 Ea eee ay lh COR, AP Rn ag 193
applied! tovtree mmestimsating. s+... see eee 299
locgl; construchoniand Use 2... 80026 oie nde Se ee 174
definitions GAs e.21he See ea te Se 153
derivation from standard tables....................... 175
need ‘for-form: Glassen: «os As an ae eee. 205
point of measurement of diameters in....................... 148
standard detmnition 2)../9g je hs kv nna eee oe oat ee A 153
for total cubie contents, construction............... 154
for merchantable cubic volume and cords............ 177
substitution for tree-analysis. . 0. sco... abe hich eae 375
UUTALV CTSA] sx) as ihe REE ah Seanck oa loue: at Gvocetlacae io sec uchtofevesere'S yo MAR 144
Volumes, tree, classification by diameter and height......................... 163
Of Goustunes! caleulationl, Cs ccscs oc 0 6d a1 on oe + sc sheet see one ee 221
of trees, actual, volume tables based on...................2.+22.... 147
Wiarmeniiog alec as she cee tn: Soren eke a8 SPIRE ROE EE itl, SA 86
Waste, idetinition and measurement... feo. 2% 29826 ee et Jed. os ioe 179
from CLOOkKOr SWEEP: 1... Lesh aah eld oe CO Re ano Lee 51
PROM SAW WROTE | 85 32 oy) ose ahaha dome Re Shel eR eek: enemies OP ah Jee ne 53
from slabs. snd edgings. 22 32scicis Gers Bs tae ne Se ele Mk eae ao ae 50
analogs total per cent Ofc tacsa ck ie eae ee see ee ee 55
In wWanulacture, TaCtoriGh. Acceso ct ars Mae OR ee te eee 13
IN COPS: Anam Ss, \cveyasd sede eee Oe SA ae Ee ken ae 13
or cull; effectamiull-scale:studiess.4. 2.40) sccne ee eee a ee 463
slabbing and sawdust, distribution, Table VII....................... 56
‘Weight as.a, basis‘of measuring. cubie contents. .. 0.2.6 44... :.-< > os hee ee 33
asa measure: of cordwoodes. a: ts0 oe en ees coe Con ae ee 137
Weights per cord for various species, Table LXXXIII.....................05 498
Weise nypsometers...:4 5 Rey aie oriae. 1622 URS POEUN Re yn ore ete ae 240
Westernred«cedar poles™..05. 2.514 4A ues ers ere a 1 SE he ae 469
minimum dimensions, Table LXX................... 470
West ‘Virginia; statute log rales! Miia see ae Oe eee BS 5 ee 73
Wir eeler log mille ye ics, io gin on cdyeist cased en anes ae Berane. Ram Te ee 86
Wiite cedar Moles ps6 tosis. os 3,03 c0r3 8 tata Oe ol ARM ORE Stee 467
relation between circumference and diameter, Table LX VIII 467
POR TUG 3, oa Miah erste et oye ay ae Meliss AR AE AE SO es SEAT 75
pine; ‘vield'table; ‘Vable: 2c [lle cies 6G sets coves: Act volte ein ieee aaa 321
INDEX 553
PAGE
Maannot Strips, factors determining... . occu c 5a cea ec ete essere ech aeecenaes 274
SEFAVEI BSSTOY RL oy al (a0 Bate es eu eB ete a RO Na cg 161
TDR Bie DyaR TU Shel As Spel RS or ea tee er ee 86
\AViilisorm, Lkoyeg THOT es Aa ales Ol et Bay pCR REI ied DRG NESTON ERC Me eRe a 66
Mindepressure: Tesistance' Or, Im tree form. ....5. 020244050 ease dee ee ds cee ese 208
MERAMEACHRINVBOMACLER C18 2feysrt s,s '=°5 sis cae e]aisie ss atate deayeigie ois lB aiee Beata shallara geome Majoras 241
WUIACOMSIMMS CALUDENLO SITIO -gaejc. ceycheis & eleie oasis ie a/aeae alone, nin Pa eloiet aloe shana. e 73
i eIRRMMIRG CRM Reesor ait sere a lions, site hd cies ©) jana xjeaillern alate g AulNereva ayy wale Se bans 112
Yale Forest School method of estimating in southern pine................... 284
ReVemspine. outnerm, Sradimg Tiles... 2... 6... . oe cee rams oe cance ages does os 457
poplar, in Tennessee, yields of cordwood, Table LXV................ 426
Yield of second growth hardwoods in central New England, Table LXII....... 409
per acre, spruce, cutting to various diameter limits, Table XLIX........ 322
predictions, accuracy, OL tactors afiecting.---..2.4+.4..see6 2 eae 2 ... 412
table based on crown space, method of construction. .................- 424
construction with site classes based on height growth ............ 401
on yields per‘acre=..........-. 406
Vanibeypime allem x Vi 2h.< uence aie new eitis tite as fae sca vrees 321
red Eh Les e CRCIAISSC Sr re ee ANS es ca Bu aia: Give: aaa Ae eine w/a SSIS Hel eaves RS 397
applcstion inpredictingryieldss .. cca. os osu saw he weir © one caw 322
AIRE OVE TUCNIC Les, SP AND ge Or cs aed ee a Se ra 397
based on crown space for many-aged stands................... 422
on age, application to cut-over areaS...............~-...- 441
CONSE CG TIOM emp nee eer we es sthy oho oy eran py eI Bigs oast eatin (Woieuaeme edt 396
detinibrongandepunposerancsec: sc facie ce ale ge eo sete emia oa. seers 395
EMA ITI Cay MUSEEO teppeie esis serene cetaus) o aecete cians ta wis ale. e Bap toetenenel age 413
EXAMI) Le Meg MN e Mae APN cos ceria, Rush tnay seis GPin cd feselty te hoviss 3. sued Mere sslous 321
for stands grown under management..............--+---+-- 407, 427
OlemIKedEspeClesmy pyre ee ees ne Ca tees teats 408
measurements required on each plot.....:......-....-.-.--.-- 398
normal, for even-aged stands.......... J mA etarc SOMA ERC 395
record of data on plot............ Ee ROE EO Pera eae Ee Ree 400
rejechon omAbnormaliplotswasee. acieceecisen eee eis. 404
SEUCHTVO FS 0 (oya 0) eee a Lome eel de ete a ea ATO OR ERROR 395
use of, in prediction of current growth.....................+-: 436
GO Lele meagre ee ascot EN a pI Il eye Saud eras robbie ielace ayes ec chausl oie 315
Niclas; definition and purpose Of stlidyon-../o2...cic 2 cae se pa sn em erolne seals alees 320
densibygotsstockinoyastaitectimop amir. oii eys \o Se erse eres ei ie shen ol sie 392
effect of losses versus (hinnings UPON <0. 5 56s 2<)2 ocigs teste ee a ee cies Oe ks 324
of cordwood for yellow poplar in Tennessee, based on crown space, Table
TEA NGN fseem tet any aucun UU a cy WR RENO APES on | A ikeyas GMa enmaeA Ren Sg Seelam ster 426
Noun cloverloginulescy m.rrcneeeiccn cram rer tora ters: Sonicare cttthetereth ev eisial etmlele rahe leyesaus' «!' 86
PNGV OIMELETS pte eaten Race T EE o aro PA seis 9 os Sislbeemtansracths 132
NevLOMEe Me mMeASsUnenmien bt) OlaCOLUwWOOUerae ci setts silt ees cleislsinici|s «1 els./s)s 1-12 132
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