from which one may expect 7000 cb. ft. an acre as the normal mature fall, then the normal growing-stock would be 7000 x 40=280,000 cb. ft. Supposing, however, the actual stock is estimated as only 248,000 cb. ft., and the actual increment at 5400 ft., then the annual fall would be

But when fresh calculations of the actual growing-stock and increment have to be made every 10 or 20 years (and the shorter the period, the more nearly precise will the result be) this method becomes laborious, while at the same time the bases upon which it rests are insecure. It therefore never came into any extensive use. Heyer was himself aware of this defect, for he remarked of the method:

"These simple principles merely show arithmetically how the normal condition of the woods can be brought about and assured in general; but it does not follow that it is possible to carry out this method thoroughly in all cases. Indeed, one must not think that the annual fall can practically be fixed with advantage within the narrow limits of any mathematical formula. Again we repeat that the manifold differences in the condition of woods, the various necessities and desires of their owners, the many concrete circumstances affecting the yield, and other influences that cannot be determined in advance, may suggest or even necessitate deviations from a normal condition which may perhaps only have been attained after much trouble."

Heyer was therefore in this respect, and with regard to the fact that a rough working-plan was necessary for the proper application of his formula, in the main an adherent of the method of combining area and yield, much in the same way as is the case in Judeich's Saxon system.

Criticism of the Formular Methods.-These methods, of which there are several others besides those above described, all regard the attainment of a fully stocked condition of the woods, with a regular distribution of age-classes, as the ultimate object of management. The essentials for this normal condition are of course a definite normal growing-stock and normal increment, from which the actual growing-stock and the actual increment are usually found to deviate to a greater or less extent. Now, the formular methods aim at accomplishing these objects by means of reckoning the annual fall in such a manner as will gradually, or within some fixed period, adjust existing differences between the actual and the normal growing-stock, and the actual and the normal increment. And in doing this they, with one exception, overlook the necessity of having a regular workingplan taking into special consideration the areas that will be brought to the fall by means of the formula. They do not expressly say that such a detailed workingplan is unnecessary, but only one of them-Heyer's, a most complicated, ingenious, and mathematically correct, but rather unpractical system-distinctly stipulates for a plan in which the woods are arranged in age-classes, so that, after the fall has been fixed quantitatively in cubic feet by means of the formula, those crops may be selected for harvesting and reproduction in which the timber is mature or over-mature. Even here, however, the plan can only be made out as to yield for the short space of 10 years, during which the annual fall is fixed by the formula for each given sub-period of the total period of adjustment.

Unless there be a working-plan showing the mature crops, or, what amounts to the same, a definite understanding that the fellings are only to be made in mature woods, the formular methods would lead to results quite too ridiculous for practical work-e.g., when the normal growing-stock and the normal increment (as calculated for the formular methods) are present in the shape of crops having, say, the age of half the rotation, or otherwise consisting of immature woods. Here the annual fall would be equal to the full normal increment, and yet any attempt to fell would be merely a sacrifice of immature crops. All of the formular methods. are weak in respect of laying too much stress on the normal growing-stock and

not paying adequate attention to the actual distribution of very abnormal ageclasses.

Now, as a matter of fact, the annual fall-say, for the next 10 or 20 yearsis not fixed by the increment on the whole of the age-classes, but by the acreage of the crops now mature or approaching maturity. And these can only be properly noted for consideration when tabulated in some such system as obtains in the method of combining area and yield in fixing the annual fall.

Again, all deductions made exclusively from estimates regarding cubic contents of growing-stock and increment are fallacious, because these essential factors for correct calculations can only be approximately ascertained, and we can never be sure that they are absolutely correct in any given case. This is the rock upon which the formular methods all split.

Hence it is much safer to adopt the area, the only absolutely certain quantity the forester has to deal with in each working-circle, as the basis in fixing the annual fall. And this is a basis so secure that, even if the yield connected with it cannot be determined with mathematical precision, when area is duly considered in regulating the annual falls, greater security is attained than by the formular methods for the maintenance of a sustained yield and of the highest income from the woods.

10. The Method of Management recommended for British Woodlands. -There can be no doubt that for copsewoods and coppices the division of the total area into equal (or equally productive) annual falls is the best method of management in Britain; while as regards highwoods, and more especially conifer crops, the choice must practically lie between the Saxon system and the method of fixing the annual fall by combining area and yield.

The Saxon system has proved admirably satisfactory for the given circumstances in Saxony. There, forest management has been carried out on economic principles for considerably over a century; hence the distribution of the age-classes is by no means so abnormal as will usually be found to be the case throughout Britain. For this reason, and also because the majority of our land-agents, managers of woodlands and foresters, have had no special technical training in the business of forestry, the method of fixing the fall by combining the area and yield (in detail for the first two periods of 20 years, and in rough suggestion of area only during the subsequent periods) seems to be by far the preferable system of management for Britain. It has, as compared with the Saxon system, the advantage of readily conveying to those concerned with the general control of the estates and the carrying out of work in the woodlands a tolerably clear view of the objects of management and the methods of attaining them, and these advantages can be so easily obtained by a little time and thought that it would be a great pity to forego them. And, finally, for the circumstances of most British woodlands, the Saxon system, with its entirely new working-plan framed once every 10 years (which would probably have to be drawn up by a specialist in forestry), would, even from the financial considerations alone that form one of the guiding principles in fixing the fall, prove less suitable than the other method regulating the falls for the next two periods of 20 years each, and specially separating those of the I. period into two sub-periods of 10 years each.

This method of combining area and yield is all the more to be recom

mended as the system best suited for Britain, because most of our woodlands vary very considerably from the normal condition. Even in Germany, the home of forestry, it is the system mostly in use, and it is considered to have the advantage of giving more consideration than any other to the actual conditions found in forests, while it does as much as is possible to adjust the variations in the periodic falls, which would be unavoidable if any mere subdivision by area were adopted.

Under this, the clearance of over-mature or unsatisfactory crops, protective falls, &c., are provided for exactly as in the Saxon system, and the determination of the financial maturity or otherwise is just as feasible in that as in this, so that the advantages above noted remain to speak in its favour. But it must be distinctly borne in mind that the yield forecast for the II. period, and the areas likely to come to the fall in the later periods, are not to be regarded as anything more than mere probabilities and suggestions intended to be of assistance in the management meanwhile.

There is one other special advantage which the method of combining area and yield seems to have above any other method. Where woodlands exist to any great extent on large estates they will often be looked to, so far as the law of entail or other title to possession admits of this, as a fund to be drawn upon to meet succession duties. Such being the case, it is self-evident that the woods will be least damaged and crippled as producers of income (i.e., that the interests of the present and of the future owners will best be safeguarded) if they are being managed according to a well-considered scheme; and the method of management by combining area and yield in fixing the fall shows much clearer than any other system (1) exactly where the woods can best be made to furnish the money specially required; (2) how this will affect the falls for the next 20 or even 40 years, if the making good of the deficit be spread over so long a time; and (3) what this is in reality likely to cost the

owner.

If the conditions of the local timber market may permit of this, fellings to the extent of the whole of the falls of the first sub-period of 10 years could be made, and those intended for the second sub-period could be spread over the whole 20 years, so that the full income-producing capacity of the woods would be resumed from the commencement of the second period. This would, of course, be at variance with what is usually the main object of a working-plan-viz., the securing of a regularly sustained annual fall; but, after all, the raison d'être of a scheme of management is to indicate how the desires and intentions of the owner may best be attained or provided for.

Were woodlands good legal assets upon which money could be borrowed to pay the succession duties and the like, then it would always be preferable. and easier to borrow on the strength of a well-considered working-plan; and in place of making a very big fall of timber at once, the excess fellings could be spread over a number of years with advantage to the woods, unless the older woods were present to more than the normal extent. But various other measures might also be suggested. By restricting fellings slightly, a reserve of marketable wood might be built up for contingencies such as these, if the

present owner desired to do so. Yet this is not a procedure to recommend. Nor would the fixing of a somewhat higher rotation than is likely to prove most profitable-say, working with a rotation of 100 years when 80 or 90 would probably be more remunerative-be true economy, because each of these two procedures would, in reality, be failing to utilise the woodlands to their full extent as producers of income. They would increase the capital in growing-stock above what is really necessary for working the given area, as indicated by the most profitable rotation. A much better method would be simply to put aside a certain small percentage of the net income received each year from the woods and invest it on bank deposit or otherwise, so as to form a fund for this specific purpose.

In conclusion, the system for fixing the annual fall by combining area and yield seems to be so distinctly the method of management required generally for highwoods in Britain, that it will be the system to which the details regarding practical work in chap. iii. will be confined.

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THE MEASUREMENT OF TIMBER-CROPS.

1. Measurement of the Cubic Contents of―(1) Felled Trees or Timber in the Log; (2) Standing Trees; (3) Whole Crops of Wood.

2. Estimate of the Age of-(1) Felled Trees; (2) Standing Trees; (3) Whole Crops of Wood (Mean Age).

3. Measurement of the Increment or Rate of Growth—(1) Factors determining the Increment; (2) Measurement of Past Increment on Felled Trees and Logs; (3) Measurement of Past Increment and Estimate of Future Increment on Standing Trees; (4) Estimate of Past, Present, and Future Increment on whole Crops of Wood.

1. Measurement of the Cubic Contents is made by means of measuringtapes, compasses or callipers, and "hypsometers" or instruments for measuring heights. The measurements are made in lineal feet and inches, and the results obtained by multiplying these into each other, as below explained, are expressed in cubic feet.

(1) Measurement of Felled Trees or Timber in the Log.-The true cubic contents of any log of wood are found approximately enough for practical purposes by measuring its length and its girth or diameter midway between both ends, calculating the area of the section such girth or diameter represents, and multiplying this by the length. Expressed briefly, the formula is

Cubic contents = length x superficies of middle section.

Example.-A log is 18 ft. long and 24 in. in diameter midway between the two ends. Its actual cubic contents are therefore 18 ft. x 3'14 sq. ft. = 56 52 cb. ft. If sectional tables are not at hand, the calculation can easily be made approximately from the dia22 meter alone, found from the girth, if necessary, by dividing by =7

7. Thus, cubic con

length x (square of diameter

× 0.785). But as 0.785 is inconvenient to use, the product of length x square of diameter can be multiplied by 0·8, and the result reduced by 2 per cent. Thus, 18 × 4 = 72 ; 72×0.8=576; 57·6-18 (576)=56 45 cb. ft.

In Britain, however, timber in the log is not measured, bought, or sold by true cubic contents, but by a quaint system (which makes an allowance of 21 per cent for wastage in sawing) known as "square-of-quarter

VOL. II.

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