Cornell University Library TANT HARVARD FOREST BULLETIN NO. 4 Ricuarp T. Fisuer, Director RED OAK AND WHITE ASH A STUDY OF GROWTH AND YIELD BY REUBEN T. PATTON Re : q i , HARVARD FOREST, PETERSHAM, MASS. 1922 HARVARD FOREST BULLETIN NO. 4 Ricuarp T. FisHer, Director RED OAK AND WHITE ASH A STUDY OF GROWTH AND YIELD BY REUBEN T. PATTON HARVARD FOREST, PETERSHAM, MASS. 1922 % @ SP ot Oise COPYRIGHT, 1922 HARVARD UNIVERSITY PRESS C 660/0 CONTENTS SuccESsIon oF TYPES ..........0.0. TREE Form IN THE FinaL STAND. .... A. B. Cc. D. E. DIAMETER GROWTH ........ INTERRELATION OF DIAMETER, BOLE, AND CROWN . RELATION OF WIDTH TO PRICE. . . AVERAGE WIDTHS AND VALUES OF YIELDS . Tue FiInaL OBJECTIVE. .... MIRgp “TABEES. 2 2 6.0. SS RB Re eR A. B. Prick INCREMENT .. 2. 16 ee ee ee ee EXPANSION OF CROWN... ... 2... 2-2 eee Yieip TABDES fos 2 44 wwe ee ae me es 11 11 12 17 19 22 24 24 34 RED OAK AND WHITE ASH A STUDY OF GROWTH AND YIELD SUCCESSION OF TYPES THESE studies were carried out on the Harvard Forest and surrounding woodlands. The country here is physiograph- ically simple and consists of wide open valleys running north and south. The bed rock is gneiss and this gives rise gen- erally to a sandy or light soil, but heavier soils also occur. The forest is not original, but is practically all second growth. Just prior to the Civil War, the farmers of central New England began to abandon their farms, partly on account of the opening up of the West, partly because of the growth of manufactures and later because of the Civil War. The ground was very stony and rough and the climate very bitter. No extensive cultivation was possible owing to the results of the glacial period. Boulders abound, particularly at the lower elevations, which normally are the most fertile. The higher elevations are the freest from stones, but they are also the most exposed. This had been a region of dense forests when first settled and the original homes bear witness of the magnificent trees which grew in those forests. As in every case of pioneer settlement, the rich stores of timber were swept away and this rock strewn, boulder-covered land was converted to farmland. This region is peculiar in that while the soil may be regarded as agricultural, the land as a whole, owing to the boulders, must be regarded as forest land. Once abandoned, the land was at once attacked by the forces of nature. The lightest seeded trees, white pine and gray birch, seeded up the greatest part. It would appear from many fields at present that the longer an area is left un- seeded the more difficult it becomes to establish tree growth 5 6 there. The soil appears to become more compacted and resistant to seed. Even gray birch, perhaps the most prolific seeder, makes slow headway on these old treeless fields. While white pine has been the most fruitful source of re- afforestation, a few fields were given back to oak, ash, and other hardwoods. Although white pine has reclothed these abandoned lands with dense stands yet to-day beneath these pines there is an abundant advance growth of all kinds of hardwoods, but particularly red oak, white ash, and red maple. These, in the seedling stage, are quite tolerant of shade and are growing freely, although the growth is much slower than in the open. The striking feature is the absence of pine in this advance growth. We have here a replacement going on, one step towards a reversion to the original highly mixed forest. This replace- ment or succession is due to four factors. In the first place, the site is as good a hardwood site as it is a white pine site. The original forest was mixed hardwood with scattering pine. Secondly, the pine has formed a suitable seed bed for hard- woods. It is probable that the absence of a seed bed, equally as much as the weight of the seed, prevented the hard- woods, such as oak, chestnut, and beech, from occupying the vacant lands. An examination of germinating acorns, scat- tered around under a parent tree, will show that those that have lain on the surface of the ground have, in the majority of cases, damaged or decayed radicles. Under the pines the seed, aided by the agency of small animals, becomes im- bedded in the litter of the forest floor and is here protected. Generally speaking, the smaller a seed, the better is its chance of forming a tree. Size of seed is as important as weight. How successfully the pine prepared the way for the hard- woods is shown by the following example. Along an old stone fence which runs north and south there stands a row of immense old trees whose diameters are given in the following table: 7 TABLE I D.B.H Species Inches Red Oak (2) ote sdce padi cc fears 30.4 43.5 Chestnwt-(2)) < cicsc iio sielhar a waces 26.0 29.8 PBN oc icedeeie CN AA a endinn ncunrasich cede 26.4 BaSSWO00 ics sci ana sien wacko ani hemes 26.4 Sugar Maples. 2 cc 3.< cute nyo ane se nase 23.1 Yellow Birch.....................00. 15.7 It is most probable that these trees were mature and bear- ing seed when the surrounding fields were abandoned. To the west of the fence and the row of old trees was formerly an abandoned field which grew up completely to pine. This stand was cut off a few years ago and to-day the field is com- pletely covered with hardwoods. There are no pines in the young stand, although there are mature pines in the sur- rounding areas. As the prevailing winds are northwest and southwest, the seeding up of the field by the row of old hard- woods was distinctly at a disadvantage both formerly and at the present. The following table gives some idea of the com- position of the young stand which is thirteen years old. The plot used for the estimation of the composition was one- twelfth of an acre and the number of trees per acre averaged 3800. TABLE II Percent of Species ixture AS issues Dragoon aod DR VRS ea ea aa Eee ents 57 Sugar Maplé..o ons sceswyien gry weenie wats Gee ee 20 Reed! Oakes ie es cde ace Bette ous Moat o lao wanudeee sree 8 Gray: Birchsdn so). beeen vee ted eae bes we 4 Red: Maples si: 03 ces ee bones ea ew ea ee Pe 3 BIB CRB InGhh issih 2 eras Gua ata uth war Rede acct ase Barts 2 Yellow Birohts x25 sac praieesicya- Geiss woapincs a ava tesa suave 2 Pine Ghetty cna eg cececp ney nteaahieln eitndie ha ate dba 2 Basswood. cccin gcncietnacs, Seared dabacw ave aude tend an 1 Miscellaneous: ¢ vsvsvaastitas natin ous Ok ale 1 The third factor influencing this succession is the intoler- ance of shade shown by the pine. It has been clearly shown on the Harvard Forest that by suitable fellings a reproduc- 8 tion of pine up to 40,000 trees per acre can be secured. But light is necessary. In the natural stand itself, whatever pine seedlings there may be, are very stunted. On the other hand, there is usually an abundant advance growth of hardwood, as the following table will show. The plot used for the enumera- tion of the advance growth was .2 acre. The mature stand was pure pine, seventy years old, and averaged 300 trees per acre. TABLE III Percent of Species Mixture Red Maple icy «ccc atacens ihtetelin oe atels) 4 eel nels 36 Red Oak sa.2) Dec: dvoly xsl GRE Se Ra G dea Bee 12 White Oakes win trey Sav sncugta ramadan nee eae 12 Black Birchiy es scene uso kaise attain sane ee Gee’ 12 Chestniitic.:23.3..e pete cat bers teeters ees 10 Bleek: Cherry siiei none oy gee ok Seb we ee eo eee 9 White. ABRs oo2ns. 77h Secs due sdae aut bane Mev edietaes seeniens 6 Gray. Bnei dex ads Sh.cdtan nee Ravan Sk Gals name aud eae at 1 POPLAR ed sense act coe gam tA ced bead Made eet eoneeti Age. lawl 1 Miscellaneous...........0.0 0c e cece ee ene eae 7 1 The number of stems per acre of this advance growth averaged 2,600 and only stems over a foot in height were taken. In this particular area red maple is seeding in very freely. Plots ten feet square were used to count the number of red maples from one foot in height downwards. The greatest number recorded for one of these plots was 130, which is equivalent to 56,000 per acre. Gray birch, which so freely seeds up vacant areas, does not occur at all freely in this advance growth under pine. This is due to its demands for light. In this respect it stands away from the other hardwoods and closely approaches pine. Gray birch is practically a useless tree but a vigorous grower. Where the birch has occurred in quantity in cut-over land, this has been due to lack of density of the advance growth. The birch has seeded in after the cutting of the pine, and has gained a foothold in the vacant spaces. Adequately stocked land will not be attacked by gray birch. It may be here re- marked that no such thing as an average can be given for the 9 composition of this advance growth. There are over twenty species of hardwoods occurring here. Each pine stand has its own characteristic advance growth. The fourth factor influencing this reversion is the slow growth of pine in its early years. When the pine stand is logged all the hardwood advance growth is cut down. In the ' following spring the seedling and sapling stumps give forth vigorous shoots so that any pine seed which may have fallen the previous autumn germinates under a more or less dense shade. Red oak appears to have the least vigor in growth for the first year after the pine has been removed. The meas- urement of 330 oaks at the end of the first growing season after removing the pines gave the following results: TABLE IV Height — Inches Percentage ORIOS trels wae Relies. gaits PANGS eetiiede 54.9 WOH 20 ete tis earthed ete tonanctea aban Auta oe bates 31.5 QB O os taba cic sects aia face caacton Sachs Piatti oe So Oe ATA ES 11.2 BOHAO si acu aki nedlate hace atid a ope kale pues ree eat 2.1 4050 iss caus’ Redo dare ees Sin Wee aed eae ate es 0.0 5000 esate ss eae hes Gee ahead eee eek 0.3 100% Ash has a very vigorous growth in its early years, and in Table V is given a comparison in height growth of ash, oak, and pine for the first ten years. The areas from which the measurements were taken were close to one another and were originally covered with almost pure pine. TABLE V Age in Height in Feet Years As Oak Pine Tipe cape ose sn 1.5 7 1 ge SR Soe le ee ek MES 3.0 1.6 2 B iia gas Pauee Saaa toes 4.9 2.7 3 Becket heath aud wine Genes s 6.5 4.0 5 Gos LER ERGY CREE EY 8.1 5.4 1.0 Go escne sca nlncuer sated 9.9 6.7 2.0 Cri ihue Slain whe jes hasteneeaane 11.7 8.1 3.2 Save cedmc ee ae elle Les 13.7 10.4 4.6 Qos cccthe ace ie te fe ated dood amet ets 15.6 13.3 6.2 10h cermadde serdar pera es 17.9 16.1 7.8 10 Although the pine type is reverting to hardwood, the in- coming stands are not in themselves final. It would appear that mature hardwood stands do not provide such a good seed bed for their own seed as do the pine stands, and hence the advance growth under hardwoods is not so dense. This probably makes possible the reintroduction of the pine. The climax forest of the region is one of mixed pine and hard- woods with an understory of many species for the better sites. The question of the yield of unmanaged second growth hardwood stands has been fully considered and the results are given in Harvard Forest Bulletin No. 2, ‘‘Growth Study and Normal Yield Tables for Second Growth Hardwood Stands in Central New England,” by J. Nelson Spaeth. Since in these stands, arising from the cutting of both pine and hardwood, the most valuable trees are oak and ash and, also, since a great percentage of the young growth consists of these two trees, it is obvious that the forest of the next rota- tion will be largely an oak-ash stand. This type is now fully recognized by the silvicultural policy on the Harvard Forest, partly because of the great value of these two species and partly because of the prohibitive cost of reconstituting pine stands on the better soils. As these forests are situated in a region of wood-using industries where practically every load of lumber can be sold, as well as cordwood, they can be placed under intensive management. This has already been begun on the Harvard Forest, and the purpose of the present study was to obtain data for the purposes of future manage- ment. The specific questions for determination were, there- fore, rotation and density as related to growth, tree form, and value of yield. 11 TREE FORM IN THE FINAL STAND A. Diameter GRrowTH In studying the growth and development of oak and ash stump analyses of oak and ash were first made. These stumps were of trees which had produced the highest grade lumber in the district. They were of an age mainly between sixty and seventy years, with a few running up to seventy-five years. All the subsequent data were collected on sites similar to those on which the stumps occurred. The ages of the stands were similar to those of the stumps. No data were obtained for ages above seventy-five years. This was because the stands become merchantable at about seventy years and are felled at or about that age. So far, then, as local practice goes, seventy years may be regarded as the usual rotation. Stump taper curves were made from neighboring trees and from these curves the diameter at breast high of the various stumps determined. The amount of growth in diameter for each diameter class was also ascertained. Figure 1 gives the results of the examination of forty-two oak stumps and twenty-three ash stumps. The curves are for wood only and show some very characteristic features. In the early years, the growth of ash is much faster than that of oak. These forests have arisen mainly as sprouts from small advance growth, and hence the growth is much greater than would be the case if the tree originated from seed. Ash grows better under shade than does oak, and hence forms a better root system for the subsequent sprouts. The size of the sprouts is directly governed by the root system of the ad- vance growth and the size of the latter is largely a question of age. The main feature of the graphs is, however, the course of the curves at the seventieth year. Oak is still growing vigor- ously and is producing wood at the rate of .2” a year, or for ten years two inches of diameter. Ash, on the other hand, is only producing wood at the rate of one inch for every ten. 12 years. Many ash trees have twenty-five rings to the last inch. This is very characteristic of ash and is due to its capacity to endure congestion or crowding of the crown. Oak, on the other hand, demands space. For these characteristics we require new terms. We might say that oak is space de- manding, while ash is crowd enduring. Since, however, increase of diameter is closely. associated with clear length of bole and crown development, these two latter factors must be studied before it can be ascertained how far this rapid increase of diameter of oak can be main- tained and how far the slow growth of ash may be avoided. The curves for diameter growth are in no way final in them- selves since they are in no way correlated with clear bole or radius of crown. All that they do show is the characteristic type of diameter growth of each. Oak shows a desirable diameter growth while ash shows in its latter years very undesirable growth. B. INTERRELATION OF DIAMETER, BOLE, AND CROWN An examination was next made of the dominant trees in the age class sixty to seventy years, and for each tree the height, length of clear bole, diameter breast high and radius of crown were taken. In measuring the crown four radii were taken and the mean calculated. The measurements were re- peated later on a number of the same trees, other radii being used, and it was found that the differences resulting were small and could be neglected. Trees having very irregular crowns were rejected. The term clear bole was taken to mean the length to any branch, dead or alive, beyond which there was not a clear log length. This gives correct results so far as the uncultivated forest is concerned, but it does not correctly indicate the length of clear bole obtainable under systematic control. However, it has been retained as introducing a conservative element into the conclusions. This will be referred to again. 14 In the following table are given the results for ash. The trees are grouped by one-inch diameter classes. The figures given are the actual averages obtained in the field. TABLE VI. ASH D.B.H. Height Bole Crown Radius _ Equivalent Inches in Feet in Feet in Feet Trees per Acre 7.0 72 47 6.5 459 8.1 74 46 6.0 385 9.0 79 47 6.6 318 10.1 79 45 7.1 275 10.9 82 48 7.7 234 12.0 80 44 8.7 183 13.1 80 44 10.0 139 Basis 109 trees. Age 60 — 70 years. It will be seen that though the spacing of the trees as given by the crowns amounts to a difference of nearly one hundred per cent yet the total height averages about the same for all classes, except the first two. This implies that up to a certain point, at all events, closeness or openness of the stand does not affect height growth. The average length of clear bole in all is comparable. This length averages around forty-five feet but in a managed forest it could be taken at fifty feet, or even at fifty-five feet. Ash trees felled on Harvard Forest, from 8” to 12” in diameter have given a clear length of sixty feet. That the average length of clear bole is practically the same for all the crown radii given is important since it indicates that the limit of thinning an adequately stocked young forest of ash has not yet been reached; or, in other words, a system of thinning which would produce these results is not severe enough to re- tard natural pruning. Each row of figures in the preceding table represents a possible end point at seventy years for any system of progressive thinning. Which is the best, however, must be settled by the objective of the forester. In general, this objective is the greatest money return. The financial yield is itself governed by the total yield and value of that yield. 15 In Table VII is given the board foot content per acre for an ideal stand of each diameter class. The bole has been taken at forty-five feet and all the trees have been assumed to have the same taper. TABLE VII. ASH Yield per Acre D.B.H. Board Feet Bi faceted ee ae eee eae 29,300 iO sais hic duke Ss See MAA Rew eedelt actin es Guan dl aden anelalincs 27,400 MON 53.0 nad babe ie sie ane eeseees ate 25,400 HEE Oe cation Aes Atine fenlacacmiea tnd ean oae eat a meeEa 24,700 TO at ev eae ene wae aneen Dand Me wan .aeas 24,400 DBO wrested reateeen ee tats Sek ue RoE ny Spon rsa ace gaa 23,200 The yield decreases with increasing diameter of stem. In the table we have not considered cordwood, which would increase the yields of the larger diameter classes. This, however, need not be considered as the volume of the wood involved is slight and the aim of the investigation was to as- certain the greatest financial return from saw timber. Before considering the ash further, the results for oak will be given. It has already been mentioned that ash differs materially from oak when grown in high forest. This is fully borne out by a consideration of Table VIII, which gives for oak the relations between diameter, height, clear bole, and crown radius. TABLE VIII. OAK Height Bole Crown Radius -_ Equivalent D.B.H. in Feet in Feet in Feet Trees per Acre 11.2 78 40 8.8 179 12.1 80 38 9.7 147 13.0 82 37 10.6 123 14.0 81 34 11.4 107 15.0 83 33 12.5 89 16.0 84 31 13.6 75 17.1 83 29 14.8 63 17.9 84 28 15.5 58 19.0 83 27 16.6 50 20.0 83 22 17.5 45 Basis 193 trees. Age 60-70 years. 16 With two exceptions, the figures are the actual averages obtained for each diameter class. This table shows that there is a much greater variation in the case of oak than is the case with ash. Yet both species occur together in the same stand. Oak demands space and struggles to obtain it. Its lower branches persist much longer than do those of ash, and this despite the fact that ash appears to be much more tol- erant of shade in the seedling stage. Oak will maintain a lower branch and thrust it out towards a source of light where ash would sacrifice the branch. Oak is similar to ash in that the height growth is not af- fected by the density of the stand. This is true, of course, only within certain limits; but so far as the tables given go those limits have not yet been reached. While total height is not affected by the degree of spacing, the length of clear bole is seriously decreased by the wider spacing. It will be seen that there is a gradual decrease in length of clear bole with increase of crown radius. When the crown canopy closes the lower branches are killed, and it comes about where the density was small in the early years that there is a big difference between length of clear bole and length to first living branch. In the larger diameter classes length of clear bole and length to first living branch usually coincide. This will be dealt with later when the trees will be grouped under bole classes of different lengths. In Table IX is given the yield per acre for an ideal stand of each diameter class given in the last table. The yields are taken from mill tally studies made on the Harvard Forest. The clear bole has been divided into the standard log lengths of the district eight, ten, and twelve feet and the board feet contents have been read from the log tables. 17 TABLE IX. OAK D.B.H. Board Feet Inches Per Acre 1 ee ne eee ene ee 23,000 ND oa lane pe wicca atan era: ache awa aes wose 19,100 WS ou creas Rec oe eee ee eae 17,700 DA evs Mike are alate at essai eit eabedivonteaay 16,400 WSs halo eels aa engens ee aivite aly 15,700 NGS 3 iso ieabiand RON ted de aadbOaee dai carsbcdeel taste 14,900 Messe eh ats ati ae dae outa PONS CLR TRISTE 13,400 18 13,100 TO sich coee deste ads ee ieee Ben eee ole 11,650 Qs awe hacen aaa wea seas Meera ae 10,750 As in the case of ash, the yield steadily decreases with in- creasing diameter of stem. But yield is not the only factor, for the lumber from the different diameter classes has dif- ferent values and before discussing the value of the yield, the variation in price according to the average width of board will be considered. C. RELATION oF WipTH TO PrRicE It is well enough known that the narrower the board used in any particular industry, the greater the percentage of waste. Hence, it is to be expected that the value will bear some relation to the percentage of useable lumber in a board. The percentage of waste rapidly decreases as the boards in- crease in width until, above a certain width, the difference in the amount of loss is negligible. Hence, with wide boards the value ought not to change. In local hardwood using industries, this was found to be the case and prices were obtained for oak from both chair manu- facturers and wholesale dealers. It was found impossible to get a series of values for ash, partly because it is not greatly used locally and partly because it is used in certain specific industries where only particular qualities or sizes are re- quired, such as tennis rackets, baseball bats, oars, motor cars, airplanes, etc. On account of its use for these special purposes higher prices are paid for ash than for oak. Oak, on 18 the other hand, is used locally in large quantities and in all sizes. In the chair industry where most of the red oak is con- sumed the logs are sawn into plank 2” to 4” thick, round edge. For first quality, the timber must be practically clear, free from defects and straight in grain. Width of ring, or, in other words, whether the timber be fast or slow grown, is of no im- portance and does not affect price. In an examination of lumber piles, the widest rings seen in oak were half an inch. The source of this lumber was not known, except that it was not obtained in New England. In the various operations in the factories, such as turning, bending or polishing, width of ring was of no importance. This is not the case with ash, for width of ring is an important factor in certain industries. These, however, were not investigated. The highest price paid for oak is for plank averaging about 10” and upwards in width. Wide planks are not favored owing to the greater difficulty of handling them. The smallest average width for which a price was quoted was six inches, and the price paid for this ranges from about fifty-three per cent to sixty-three per cent of the price of the 10” lumber. There is an abrupt rise to the price of 7”, and each succeeding rise is less as the limiting value is reached. If we consider the highest price paid as one hundred per cent, the prices of the various sizes would be as in the following table: Average Percentage of Approximate Width Highest Price Fraction Value 10 100 1 9 97-95 1 8 92-89 9/10 7 82-77 8/10 6.5 68-60 7/10-6/10 6.0 62-53 6/10-5/10 5.5 34-18 3/10-2/10 5.0 22-5 2/10-1/20 The percentage values of 5 and 5.5 inch lumber have been calculated from the prices obtained. It would appear from this that timber averaging five inches in width, if used in the same industry as the wider material, has very little value. 19 Timber averaging four inches would have no value in the same industry. It will be observed that prices rise for each inch class by gradually decreasing increments and proceed to a limiting value. The increases in value when the boards become wide are very small, and are neglected commercially. The law underlying the increases in value appears to be that the in- crement in value from one inch class to another is approxi- mately a definite fraction of the difference between the value of the lower class and the maximum or limiting value. This fraction appears to be about one-half. For example, if the maximum value of oak is $60 a thousand, and the price of six-inch be $40 then the value of the seven-inch would be $50 a thousand. D. AVERAGE WIDTHS AND VALUES OF YIELDS Since increase of the average width of the lumber is the important factor in value, it is of interest to know what average width of 23” plank each diameter class of tree will produce. In Table XI is given the average width of ash lumber sawn 23” with 12” sidings. Loeally, all good grade lumber is cut into planks with a thickness of 2” and over. The 22” is surveyed as 2” and the 12” sidings as 1”. For thickness 2” and over the price does not vary. TABLE XI. ASH D.B.H. Av. Width Board Feet Inches of 23” Per Acre 8 4.9 28,600 9 5.5 26,800 10 6.1 23,600 11 6.7 24,000 12 7.3 22,400 13 7.9 22,100 The board feet per acre include the sidings and the per- centage of sidings increases with decrease in the diameter of the log. As it was found impossible to obtain a series of 20 prices for ash for the various average widths of the lumber, the fractional values given for oak in Table X have been used. These have been multiplied by the board feet per acre to obtain what has been called the relative value per acre. The yield per acre is considered as consisting wholly of 2” plank. The results are given in Table XII. TABLE XII. ASH D.B.H. Fractional Board Feet Relative Value Inches Value Per Acre Per Acre 8 1/5 28,600 5,720 9 3/10 26,800 8,040 10 3/5 23,600 14,160 11 3/5 24,000 14,400 12 4/5 22,400 17,920 13 9/10 22,100 19,890 The largest diameter class has the greatest relative value, and the relative value increases from the smaller diameter classes upwards. From Table XII it is apparent that the most profitable diameter class to produce is the largest. The number of trees having a diameter of 13” at seventy years was very small and, therefore, it is at present doubtful if that diameter could be generally produced at that age. The 12” class is frequent and, therefore, we may at present consider this to be the ideal diameter to be produced in seventy years. In Table XIII is given the average width of lumber from the oak according to lengths of bole and diameters given in Table VIII. TABLE XIII. OAK Av. Width Yield Per Acre D.B.H. 23” Plank Board Feet 11 6.4 23,000 12 7.3 19,100 13 8.1 17,700 14 8.8 16,400 15 9.5 15,700 16 10.2 14,900 17 10.9 13,400 18 11.5 13,100 19 12.1 11,650 20 12.7 10,700 21 i¢ Since the maximum price is paid for ten-inch lumber and since all stands of diameter classes from sixteen inches on- wards have an average width of 10” and over and produce progressively less lumber per acre, there is no need to consider these further. The larger diameter trees could not be con- sidered in any controlled forest, since, in order to obtain a large diameter, length of bole would have to be sacrificed. In these larger trees, as has already been mentioned, the top of the bole ends at the first living branch. Therefore, the large diameter could not be secured with a longer bole in a rotation of seventy years. There is another consideration, and this is that these larger trees are seventy years of age or slightly over, while the smaller diameter classes are about sixty-five years. However, for the present all are being considered as of “the same age. In Table XIV is given the total value per acre of a stand of the various diameter classes. The amount of 12” sidings is taken from local mill practice. The prices given for the average width have been averaged from actual prices ob- tained. The limits are actual ruling prices. TABLE XIV. OAK Av. Width Price Price Total D.B.H. 24° Board Ft. Yield M. Ft. Value Yield M.Ft. Value Value Inches Plank Per Acre 2y 3 $ 1yVv $ 3 $ 11 6.4 23000 19,550 36 704 3450 25 86 790 12 7.3 19,100 16,235 46 747 = 2865 ¢ 72 819 13 8.1 17,700 15,050 51 768 2650 = 66 834 14 8.8 16,400 14,760 53.5 790 1640 30 49 839 15 9.5 15,700 14,130 55 777 ~—:1570 . 47 824 16 10.2 14,900 13,410 55 738 1490 “ 45 783 The average width of lumber from the 15” class was 9.54 and, therefore, the price given to this class was the maxi- mum. The highest return comes from the 14” class, followed closely by the 13”; but there is, on the whole, not much dif- ference between the total values. The length of bole of the 14” class was thirty-four feet, but it is to be expected that under systematic management the forest will be able to produce a much longer bole than this. 22 E. Tue Fina OBJeEctTIive From the previous discussion of ash, it was seen that the greatest diameter class gives the greatest return. However, since the 13” class in ash was not frequently found, it is as yet doubtful if this diameter can generally be produced in seventy years. The next class, the 12”, is abundant. The age of this class was between sixty-five and seventy years. Sample trees which were felled showed that a diameter of 11.6” was produced in sixty-five years. At the same rate of growth occurring during the previous five years, a diameter of 12.4” would be produced in seventy years. These sample trees had clear boles of fifty-five feet. In Table VI the 12” diameter was associated with a crown radius of 8.7. From a graph of crown radii against diameters of stem we find that a diameter of 12.4” would be associated with a crown radius of 9.1 feet. We may say then that the trees of the final harvest of ash at seventy years would average 12.4” diameter, 9.1 feet crown, fifty feet bole, and a height of eighty-two feet. In the case of oak where the bole gradually decreases with increasing diameter, the difference between clear length of bole and length of trunk to first living branch is very great, especially in the medium diameter classes. In ash this dif- ference is small. Hence in oak with each diameter class there is a great variation in length of bole, and this variation diminishes as diameter increases. That portion of the bole which bears dead branches could be greatly reduced if the forest were adequately stocked in ‘its early life. Boles fifty feet in length occur, and this is the desirable length. The largest clear bole found in oak was fifty-four feet, while the longest in ash was sixty-eight feet. It may be said in passing that if a clean bole of fifty feet can be obtained on a ten-inch tree it can be secured for the higher diameters and later years. If the trees in Table VIII be. grouped by length of clear bole we get the results given in Table XV. 23 TABLE XV. OAK Bole Diameter Crown Radius Feet Inches Feet 50 13.4 10.4 45 13.6 11.0 40 13.8 11.3 35 13.9 12.0 It will be observed that the 11” and 12” diameters have be- come merged into the 13” and 14” classes. It will be noticed also that while the difference between the diameters amount to 3.7 per cent, the difference in crown radii amounts to 15.4 per cent. Within narrow limits each diameter can be pro- duced by different sized crowns. Generally, however, the larger crown is associated, as in the table, with a shorter bole. The extra energy developed by the larger crown is used up in ‘forming branch wood. Sample trees with boles above forty-five feet which were felled as well as the stump analyses showed that a diameter of 13.4 to 14.9 was produced in sixty-five years. At the rate of growth occurring in the 13.4” tree during the decade prior to felling, a diameter of 15” would be produced in seventy years. It was found, by the method to be discussed in the next sec- tion, that a crown of 11.2 feet radius would be associated with a fifteen-inch diameter and fifty-foot bole. In the 15” diameter class the longest clean bole was forty-nine feet and was associated with a crown radius of only nine feet. The average for the class was 12.5 feet, so that the radius 11.2 feet is well within the lower limit of the range found in nature. It may be again stated that in each diameter class the longest boles are associated with the smallest crown radii. The final harvest of oak then will consist of trees averaging, at seventy years, 15” in diameter, fifty feet bole, 11.2 feet crown, and a height of eighty-five feet. A tree of these dimensions will produce an average width of 9.1’ for 2” plank. Having selected the type of tree that is to form the final harvest, the question arises as to how to treat these areas, which have reverted to hardwood, so as to produce the de- 24 sired crop. This is primarily a matter of the proper control of the density throughout the life of the stand. There was an abundance of material for study below twenty years and above sixty years, but there was rather a scarcity of material between these ages. It was, therefore, necessary to follow in part some other line of study in order that the deficiency might be overcome. It was decided to make a study of crown development both from living material and from existing yield tables. If the area of the ideal crown for any age be known, then the corresponding number of trees per acre could be found, and thus a criterion established for periodic thinnings. YIELD TABLES A. EXPANSION OF CROWN It has been noticed in Tables VI and VIII that stem diam- eter is a function of crown radius. In general, the larger the crown the larger the diameter of the stem. Growth of crown is essentially different from either height growth or diameter growth. We have already seen that within at least certain wide limits growth in height is not affected by the density of the stand. For the variations in density in ordinary forest practice, height growth may be said to be beyond the control of the forester. Diameter, however, being a function of the crown radius, may be varied by varying the crown radius, or, in other words, by varying the density of the stand. This latter is secured by various degrees of thinning. With open grown trees height growth, diameter growth and crown growth follow much the same curves of growth. If we consider an open grown oak or pine, the longest branches are very low down and may even rest on the ground. Pine branches are easy to study and these show that the ex- pansion of the crown is at first very slow, then very rapid for a few years, and then after this rapid growth there is a very gradual decline. This is precisely the same type of growth as for height and diameter. 25 In a forest, however, crown growth is entirely different from other forms of growth, and may be put into a class by itself. In the forest the crown is engaged in a struggle for existence; it is constantly surrounded by forces opposing its development, while both height and diameter are free. The crown has either to overcome or be overcome, to win or to be subdued. If we consider pine for the sake of simplicity, we find that the attack by the crown is carried on and main- tained in intensity by reinforcements in the form of new branches. In both height and diameter development, the new additions are always placed upon the old, but in the crown struggle new units are constantly being added and the old ones pass to their death. In the open grown specimen the position of the crown is fixed, but in the forest tree the crown moves up the stem. Since the growth of the crown then is constantly impeded and resisted, it is to be expected that its curve of growth will differ materially from that of diameter or height. Since all forests, no matter what their composition, are engaged in the same struggle, it is not unreasonable to expect that some common law holds for the development of the crown. Naturally, development of the crown means the constant elimination of trees and the lessening of the density. Although all engage in this struggle, it does not say that all trees engage in it with the same intensity: It has already been noted that oak is space demanding, while ash is crowd enduring. The feebleness of the struggle carried on by ash is reflected in the decrease of the rate of diameter growth as already mentioned. White pine seems to stand midway be- tween those two trees. From a study of the crowns of various species, it was assumed that the expansion of the crown was a linear function of time. To see how far this might be true an examination of a very large number of European yield tables was made and the crown radius determined for each decade. In the calculation the crown has been assumed to be circular. Figures 2, 3, 4 give the radii of the various crowns plotted against time. Figure 2 is taken from Grave’s Mensura- 26 tion. Figure 3 is taken from The Reports of the Swedish In- stitute of Experimental Forestry, 1916-17. Figure 4 is from the Allgemeine Forst und Jadg Zeitung, vol. 84, p. 266. Only one graph in those given is a distinct curve. Many crown graphs are distinct curves. Yet the majority show a straight line. In many the curve is so slight as to be approxi- mately a straight line. This is the case in each of the three site qualities given by Fleury in Frtragstafeln fiir die Fichte und Buche der Schweiz, Zurich, 1907, and also in the four site qualities given by Wimmenauer for oak in Allgemeine Forst und Jadg Zeitung, vol. 89, p. 261. Slight curves might also be drawn in Figures 2, 3, and 4. Since the expansion of the crown can be represented by a straight line, it follows that the crown growth is a linear function of time. Before applying this law to the data given for oak and ash it is as well to consider the equation for the the straight line. The statement that the expansion of the crown is a linear function of time refers only to the period of time covered by the average rotation. The general equa- tion for the straight line is: PS OME ace ee Oe ee (1) = radius of the crown in feet intercept on the axis of r tangent which the graph makes with the ¢ axis t = time in years where r b m Now b may be either positive or negative. If b be positive it implies either that there was already a crown existing when the forest commenced or else that the greatest period of growth was in its earliest years. In the latter case the curve of expansion would be convex upwards until the straight line was reached. Neither assumption is true; and, therefore, b cannot be positive. Such graphs arise through the stand being either insufficiently stocked in its early life or else through its being too congested later in life. In white pine stands, both factors are operating and from most stands a 30 graph would be obtained cutting the vertical axis above the origin. It may be here remarked that the congestion of the crown canopy at the later periods of the forest’s life may so restrict the crowns that any thinning experiments carried out on such a forest would yield negative results. As has been shown already, the smaller the crown for any given age, the smaller the diameter. The smaller the diameter for any given height the less the rigidity of the stem. The thin stemmed, small crowned trees sway in the wind and their crowns rub off all the lateral buds from their own and the neighboring crowns. This occurs particularly in ash and pine. Such trees cannot respond actively, if at all, if the stand be thinned. A tree does not differ from any other biological unit and can only respond to a stimulus when kept in a condition to do so. For any graph b cannot be positive, but may be either zero or negative. If zero it assumes that crown expansion pro- ceeds regularly through the life of the stand. If b is negative, it implies that growth at the early period was slow and that a concave curve joins the straight line to the origin. In all four site qualities of oak as given by Wimmenauer 0 is negative. It will be seen that in the case of larch, Figure 3, the m values are not widely different. In some sets of graphs the m values are all the same. This would imply that the trees on all site qualities carried on the struggle for existence with the same intensity. This cannot be considered as correct, for since a lower site quality is indicated by a smaller height, a smaller diameter and a smaller volume, it follows that trees on a lower site quality carry on the struggle for existence with less in- tensity than those on a higher site quality. We may con- clude, therefore, that the higher the site quality the higher the value of m; and, hence, the graphs of crown expansion for the site qualities of any particular species will not be parallel. Now r is connected in the equation rrn=A When n = number of trees per acre and A = acre in square feet 31 Substituting for r in (1) we have A =b+mi eles aa which gives n(btmy?=A.... 2... (2) T If 6 be zero, then the equation simplifies into ni? = —— mar Since A and z are constants and mis also a constant for any one species on any one site we may replace the right hand member of the equation by the constant C. Hence we have Bib SNC e: Sob 1 3 Dredd PATE OG (3) This last equation says that the number of trees at any time multiplied by the square of the time gives a constant value. The simplified formula closely agrees with Wim- menauer’s now celebrated Scotch pine experiments. If the expansion of the crown be a linear function of time, then if any two points of the graph are known, the graph itself is known. From such a graph the number of trees per acre for any given year can readily be calculated by dividing the area of a single crown in square feet into the number of square feet in an acre. If, however, the graph passes through the origin then a good deal of calculation may be saved by merely cal- culating the trees per acre for any one year and then using formula (3) for the other years. For both oak and ash two points on the graph of the crown expansion were obtained. From young stands, presumably fully stocked, the following dimensions have been taken: TABLE XVI 7 D.B.H. Height Crown Radius Species Inches Feet Feet sk ee nis vanes cc 1.2 18 1.4 Ashis ohcipile ceaehans 1.2 16 1.2 82 It has already been mentioned that the final objectives for oak and ash at seventy years are as follows: TABLE XVII D.B.H. Height Bole Crown Radius Species Inches Feet Feet Feet Oa soi sn nation 15.0 85 50 11.2 ABs ices ng. 4 9 aie 12.4 82 50 9.1 From stumps whose diameters at breast high were within an inch of the expected or ideal final diameter, the curves of diameter growth for both oak and ash were obtained. From these curves the diameters and heights, falling between the limits given in the two preceding tables, were taken. From felled sample trees the curves of height growth were obtained similarly. The tabulated results were as follows: TABLE XVIII Ash Oak Agein D.B.H. Height D.B.H. Height Years Inches Feet Inches Feet LOS ean Gueaeiek 1.2 18 1.2 16 20vongiia eanenss 2.7 36 2.7 37 BOS ain ay eee £ 4.8 53 4.5 57 AD ha ie eee os Vain 7.0 68 6.8 68 DO ysea seore's Aicae ey ane 8.8 77 9.5 75 OO endian dace Aataleaet 10.6 81 12.2 81 ON cc euiesuets fheany 12,4 82 15.0 85 In the case of ash, if on the graph we join the point 9.1 feet, crown radius at seventy years, with the origin, it would give a crown radius of 1.3 at ten years. This agrees closely enough with the radius in Table XVI, which was 1.2 feet. Taking the value 1.3 feet for ten years, this would give a radius of 3.9 at thirty years. Two stands of this age were examined and the results are given in Table XIX. TABLE XIX. ASH D.B.H. Height Bole Crown Radius Inches Feet Feet ‘eet, 4.8 55 31 4.1 4.9 52 29 3.9 33 Both of these agree with the diameter and height of Table XVIII for thirty years. Hence, we may assume that the cal- culated crown radius of 3.9 is the correct one for thirty years. Measurements in a stand of from fifty to fifty-five years gave a crown radius 6.8. This latter would be correct for fifty-two years. The average height of seventy-three is fairly comparable with that given in Table XVIII. In the case of oak if we join the point 11.2 feet at seventy years to the origin we get a crown radius of 1.6 feet at ten years. There is not very much difference between this and the computed 1.4 feet. However, oak stands need to be kept dense in order to prevent as much as possible the large de- velopment of side branches. The graph connecting the points 11.2 feet at seventy years and 1.4 at ten years will put the r axis below the origin. A stand forty-three years of age with good boles and well formed crowns showed an average diameter of 7.1 inches and an average height of fifty-nine. The crown radius was 6.7 feet. While diameter and crown development agree gen- erally with the computed measurements for oak on the better sites, the height is considerably lower and, therefore, the site may be considered to be inferior to those from which the measurements in Table VIII were obtained. A stand whose age was from fifty to fifty-five years showed almost perfect agreement with the measurements in Table XVIII. Trees in this stand averaging 9.2 inches for the nine- inch diameter class had an average bole of forty feet, a height of seventy-six feet and a crown radius of 8.0 feet. In this same stand the ten-inch diameter class, averaging 10.1 inches, gave an average height of seventy-six feet, a bole of forty-two feet and a crown radius of 8.9 feet. While the stands available for the ages twenty to sixty years were not by any means abundant the results obtained from such stands are in agreement with the results derived from the assumption that the crown expansion is a linear function of time. 34 B. YreLp TABLES From the data given in the preceding pages the yield tables below have been constructed. As has already been remarked, pure stands do not occur and, therefore, a percentage com- position is given in Figure 5, so that the yield in any mixed stand may be ascertained by calculation. It is also true that pure ash-oak stands do not occur, but the percentage of other trees in the stand will depend greatly on the manage- ment. Where the percentage of such trees as red maple and gray birch is large at the commencement of the life of the stand, the removal of these will form the greater part of the early periodic thinnings. For the purposes of this yield table, basswood, beech, and chestnut may be considered as oak in regard to number per acre. Chestnut, however, may now be considered a thing of the past owing to the ravages of the disease Endothea para- sitica. Both basswood and beech are space demanding like oak. Neither of these trees occurs at all freely in the mature forest, but it is probable that they were present in the original forest in a greater percentage than to-day. Sugar maple, black cherry, red maple, black birch, and yellow birch may be regarded as ash as regards number per acre. All of these trees are crowd enduring and all form clear boles like ash. The difference in the height growth of oak and ash at any period is small and neither tree is in any danger of being over- topped by the other. There is a rather remarkable difference in their growth at about the sixteenth year and onwards. The annual height increment of ash, which is more regular than is the case with oak, suddenly becomes slower, so that the general increment at about the seventieth year is only one or two inches, while in oak it is about four inches. This sud- den decline in the rate of growth also occurs in white pine and apparently the height above ground or age at which it takes place varies according to the site. 36 The diameter given for oak at seventy years is considerably larger than that given for European oak at the same age, or indeed for any other hardwood. The shortening of the rota- tions at present employed in the older countries is at present one of the most urgent problems in forest research. Both the ash and oak as given in the yield tables can be considered as standards for quality I. No better growth is found in this locality. The quality I sites are mainly at the lower elevations. The lower slopes are moister. The same quality soil at a higher and drier elevation must be regarded as quality II. Only two site qualities occur for oak and ash. Where the soil becomes too dry or too wet other species re- place these two trees. From Table XVIII it will be seen that the difference in height growth between oak and ash is very small, the greatest difference, four feet, occuring at the thirtieth year. There is less variation in the average annual height increment of ash, from decade to decade, than is the case with oak. The greatest individual height increment in oak saplings was found to be four feet three inches, and this occurred at the eleventh year. A growth of four feet one inch was also found in the ninth year. Ash does not appear to make any such growth as this. The lower limit of quality I as indicated by height is shown by the figures given in the following table. Heights below this must be regarded as indicating quality II. TABLE XX Age in Height Years in Feet WO eaten ek eee cc seer tg eee tuk eas Bad ao GRbGa Cd drt ahdlarn aed 14 IDO cates Sid seksi ardsacabauls aun. abode Sa vatelceeca canis SMa ate pews 34 POO he csen t rie yao a tras tage re aera ans ote ntnn ores 50 AO) 2 cued lS acivnse tna riabea sdlreaeicvevte beeke lapoks enact 3 Wye tine aod 61 DU idiarave soreness wa aaa een eats hci heh he aya eo 69 OO rieie ua tgdaten aoa aus area each peaide meen oacaelale nts 74 37 The heights for the later years given for oak, quality I, in Table XVIII, are comparable with those given for oak, quality I, in European yield tables, as given by Wimmenauer in Forst und Jagdt Zeitung in 1913. What is a quality I hard- wood site is also a quality I pine site, but the reverse is not necessarily true. A study of plants associated with the oak and ash on the best sites showed that the following appeared to be the best site quality indicators: yellow violet, Viola rotundifolia, jack in the pulpit, Arisalura triphyllum, and Trillium erectum. These plants were not found on quality II sites. Assuming that a forest can be placed under intensive management, these tables may serve both as a guide for silvicultural treatment and as a statement of yield. ASH Age Trees Height : in per in D.B.H. Basal Area Cubic Ft. per Acre Total Yield Years Acre Feet Inches Sq. Feet Saw Logs Cordwood Cu.Ft. Bd. Ft. 10 8210 18 1.2 65 2a ae 20 2052 36 2.7 82 i 2131 1231 30 912 53 4.8 115 be 2650 2650 40 513 68 6.9 133 eli 4104 4104 50 328 77 8.8 139 en 4756 4756 60 228 81 10.6 140 4332 912 5244 25,000 70 168 82 12.4 141 4036 1344 5380 28,000 OAK Age Trees Height , in per in D.B.H. Basal Area | Cubic Ft. per Acre Total Yield Years Acre Feet Inches Sq. Feet Saw Logs Cordwood Cu. Ft. Bd. Ft. 10 7100 16 1.2 56 ae 93 any 20 1540 37 2.7 61 25 924 924 30 657 57 4.5 73 5 1840 1840 40 350 68 6.8 88 a 2660 2660 50 222 75 9.5 109 a 3760 3760 60 151 82 12.2 122 3694 906 4600 22,600 70 108 85 15.0 133 4108 972 5080 27,400 38 PRICE INCREMENT Although on the Harvard Forest the rotation for oak is seventy years, yet there remains the question whether a holding over of the crop would not be justified owing to the increment in price from year to year. In order to answer this question, annual prices were ob- tained from both lumber dealers and local furniture manu- facturers. There was a wide divergence in the amount of increase from the year 1900. In Figure 6 is given the price increase taken from the books of a large furniture manu- facturer. Complete records had been kept for many years. There was a steady increase from 1900 to 1917. In the latter year the first effects of the Great War began to be felt in the local wood using industries. Prices from 1917 onwards mounted rapidly until in 1920 the apex was reached. These inflated values have not been inserted. The price quoted for 1921 is a long way in advance of the 1917 price and this in spite of the fact that it is now some months since the great fall in prices. The price paid for oak to-day is also surprising since the output of the factories is small and they are working on short time. Even at the steady rate at which prices in- creased from 1900 to 1917, in a few years an almost prohibi- tive price would have been reached. This curve must surely bend over and a much slower rate of increase ensue. For the future, then, nothing can be learned from the study of the annual prices, except that the price increment cannot continue. TYPICAL ASH TREES right, 82 ft. 87 ft.; Height of trees: left anopied high forest. Grown in close ¢ TYPICAL ASH STAND D.B.H. central tree, 12’, Age 65 years. ‘SOIUBIG LOMOT SPL ASO] ATIpvar JOU SOP pu FuIpuvwop souds st YVQ “BuLNpus-pAoss aiv yJOR “asuap st puvyzs oy} Udy SOUT IOMOT ITOY} VSO] ATIPvat OWAOJ OY} YJOE “[VJWOZtoy oy} YOvorddy Aayy YVO Ut atyM ‘avpnsuv Ajoynov orv sayouvsq oy} ysy pur s[dvyy yyoq uy MVO GUT ATdVN Gay HSV GALIHM See =