results after n years being worked out and compared. Or, again, take the case of a wood having a crop or fall of timber F, that is m years of age, and whose present net monetary value, if now felled, is Fm, whereas, if allowed to grow on for another year, its net value will be Fm +1. Before any definite idea can be formed as to whether the increase during the year will be profitable or not, the other factors that must be considered are the value of the land, L, and the capital, G, covering general annual expenses G= (see pages 394 and 388). The current rate of interest or percentage of increase in monetary value during the year will therefore be found by dividing the difference between Fm+1 and Fm by the total of Fm +L+G, and multiplying by 100 as shown in the formula above

0.0 p

If, however, in place of reckoning thus from year to year, we wish to compare the present financial position of the crop with what it will be after n years, then we have two gross capital sums to deal with—namely (Fm +L+G) at present, and (Fm+n+L+G) at n years hence, when the crop of wood having the present net value, Fm, will not only give a larger, but also a more valuable, net yield, Fm+n. The problem to be solved therefore obviously is to try and determine the precentage or rate of interest at which (Fm+L+G) must increase annually in order to attain the value of (Fm+n+L+G) in n years. The equation will therefore be

(Fm +L+G) 10 p2 = (Fm+n+L+G).

Here the left-hand side represents the gross capital which would be available for investment during the next n years if the crop were felled at once and converted into money; while the right-hand side represents the gross capital similarly available on harvesting the crop n years hence. Reducing the above equation

Whatever value is thus shown for p is what Pressler, the pioneer of the purely financial principles of forestry in Germany about a generation ago, called the "indicating percentage," showing whether any particular crop has reached its full financial maturity or not. So long as the indicating precentage is higher than the normal rate of interest at which the woods are supposed to be worked, it will be profitable to let the crop grow on; if equal to this, it is financially immaterial whether the fall be made now or n years hence; while, if less than the accepted rate of interest, the wood has passed the profitable stage and should be felled as soon as convenient to make room for a new crop. If the indicating precentage be greater than the normal rate of interest when n=5 years, but less than that when n=10 years, this would show that the financial maturity or most profitable time of felling the crop has not yet arrived, but that 10 years hence it will already have been passed, so that the wood should be harvested between 5 and 10 years from now.

For general purposes of management n can most conveniently be taken at 10 years. If a thinning should be necessary during the 10 years thus included, the financial effect it produces on the equation must be calculated by capitalising its money yield from the time of the thinning till the end of the 10 years. In this case the F+n in the above equation would be the money value of the then remaining final crop, plus the previous thinning capitalised from the time it was made to the end of the period of 10 years at the rate of interest with which the woods are supposed to be worked, and in the same way as is done in Faustmann's formula (p. 239). The indicating precentage would then be

Here Fm+n must of course be a different quantity from what it would be if no thinning takes place, and the p used for capitalising the return from the thinning is the rate of interest at which the woods are supposed to be worked.

To simplify calculations of the indicating precentage, Graner (Forstbetriebseinricht ung, 1889, p. 123) has drawn up the following table, based on the formula for prolongation (10 p"):—

Example. Suppose an 80-year-old Larch crop has a present net value of £300 an acre (i.e., net monetary return, free from cost of felling, selling, and extracting), and average yield tables and local market rates justify the conclusion that at 90 years of age it would probably be worth £400 an acre net value. If the capital value of the land is assessed at £20 an acre, the annual general expenses g 0.0 p

(

=G) represent a further capital of £8

an acre, and the woods are worked under the impression that they should yield 3 per cent, whether will it be more profitable to clear the crop now or to let it grow to 90 years of age?

Here n=10 years, and

F90+L+G_400+20+8 428
= =1.30
F80+L+G300+20+8 328

=

From Graner's table this result corresponds with an indicating percentage of somewhat less than 3 per cent, therefore the proprietor will either have to fell the wood in question or else be contented with less than that rate of interest on the capital invested in continuing the growth of this crop.

Pressler himself saw that it was desirable to do away with the necessity for using logarithms, so he endeavoured to simplify the calculation of the indicating percentage. The increase in value which takes place in the crop being the combined result of three separate factors—namely, a the percentage of increment in cubic contents, b the percentage of increment in quality or market value, and c the percentage of rise or fall in the local market value for timber of similar dimensions-this total increase in value within any given time will be

But it is evident that the difference between the net value of the crop now and n years hence must be compared, not only with the present net value of the crop, but also with the total capital employed in its production. Hence the following proportion is established ::

To simplify the calculation of a, the yield or cubic contents y, which becomes Y in n years, is reckoned (see also p. 322) as being expressed in percentage of the mean quantity

Y+Y

2

200 /Y

Y+ y 2

: Y-y=100: a ×n.. a= 2 (X = ~ )·

n

at the middle of the period n; hence The percentage of increment in quality, b, arising through the increase in the technical value of the crop as it increases in dimensions, and consequently in the market 200/Q

price per cubic foot, is also calculated in the same manner, hence b= n Q + 2

where 9 is the value per cubic foot of the present crop, and Q the value of the wood of a crop n years older. So, too, with regard to c, the percentage of rise or fall in 200/V - v the local market value of wood of the given kind and dimensions, for c= n V+ where represents its present value per cubic foot, and V its value n years hence.

The history of past and present prices shows that c will usually be a plus quantity; but, under certain circumstances, it can be a minus quantity by which a + b will have to be reduced in finding the indicating percentage. Anything that will increase the local demand for timber, or that will enable the wood from a particular estate to be put more cheaply on the market than formerly (e.g., opening out roads, railways, &c.), will tend to raise the percentage of value in timber; while any fall in the demand or abnormal increase in the supply (e.g., through extensive windfall, as in November 1893 in parts of the Scottish Highlands) will of course lower the percentage. If the existing balance of demand and supply be disturbed by the local markets being temporarily glutted, as after the storms of 1893, c may then be so much of a minus quantity as to outweigh both a + b in the reckoning; yet common-sense will indicate, more plainly than any indicating percentage reckoned out scientifically, that it would be folly to fell the crop in the meantime unless absolutely forced by other reasons to do so. And in any case a, the growth in mass or cubic contents, is what can be estimated with the closest approach to accuracy, hence it is the chief factor for practical purposes. If a crop approaching maturity shows a present annual rate of growth of 1.25 per cent of its cubic contents, then it is not likely that this rate will sink suddenly (except in case of accidents, like heavy windfall or snow-break, insects, &c.) during the next 5 to 10 years.

But Pressler's simplification of the formula for finding the indicating percentage may in turn be very much simplified and made far more suitable for practical use. Applying the same method as above used for determining a, b, and c, the whole crop or fall may at once be reckoned with, when

Fm+n
PFm
+ Fm

Fm

200 X n

m+n

Here a is the main factor taken into account; and as long as it does not extend to large differences, it affords a good practical means of determining, for short periods of 5 or 10 years, whether any particular crop is financially mature or not.

Applying this rough-and-ready practical method to the example given on the opposite page, we have

F90-F80 200 400-300 200 100 × 200 20,000
F90+ F80 10 400+300 10 700 × 10

7000

=2.85 per cent,

and this is just a little in excess of what the more intricate original formula gave as the indicating percentage.

The practical use of the indicating percentage may advantageously be confined to typical crops, so that at any rate the general tendency in the management of the forests should be in the financial direction indicated by it. And this method of reckoning can be applied not only to whole crops of highwoods, but also to individual age-classes, such

as old standard trees in copse or the older classes of trees in woods treated by selection fellings.

Again, its use can be applied either to determine the financial maturity of a single crop-i.e., the most profitable time for felling it, or else in comparing several crops with regard to the most profitable time for bringing them severally to the fall. In the former case the calculation is made for different periods, and the financial maturity of the crop will be when the indicating percentage is equal to the rate of interest at which the woods are supposed to be worked. But, in the latter case, the calculation is made for different crops, n being the same in each case (and usually 5 or 10 years), and those should first be harvested for which the indicating percentage is least.

7. Subdivision of the Woodlands into Working-Circles and Compartments. Throughout Britain the woodlands are usually scattered about different parts of estates in groups or blocks of varying size, and generally bearing distinct local names. And when these blocks are of any considerable size, different parts of them have also their special names. For general purposes these blocks and local subdivisions are very useful, but the scheme of forest management can rarely be made to depend entirely on them, though they should of course be utilised so far as is practicable. Again, many large properties consist of two or more separate estates, for each of which separate estate accounts are kept; while a block system of working is applied to the management of the whole property, or of each of the different estates forming it. Hence the use of the term "block" with regard to British forestry might probably be rather confusing, if it were intended to convey any other idea than merely that implied in the common expression of such and such woods "forming a block," or of one of them being "in a block by itself."

There must, however, be some sort of definite unit recognised in order that any scheme of management may be properly framed, and subsequently carried out as intended; and this is found in the subdivison of the whole of the woodlands into compartments or units of area (though not necessarily of equal area) for purposes of management, supervision, and ordinary work in

the woods.

Working-Circles.-The scheme of management or working-plan may, and usually will, apply to all the woods owned by one proprietor that are situated in the same part of the country and are under one administration. It may therefore apply either to a whole property or merely to one or more of the separate estates forming a large property. But, on nearly all large properties, the woodlands in different portions will show such variations in kind of crop, rotation, method of treatment, and special objects of management, that they may have to be divided into working-circles, each of which will comprise within itself the whole of the regular series of annual (or periodic) falls of the woods, subject to the same details of treatment, and forming a complete self-contained series of crops. It stands to reason that such provisions of a working-plan as apply to highwoods cannot also be applied to copse or coppice; and it is equally clear that the details of management recommended for Beech-woods worked under a rotation of 120 years with natural regeneration must differ very materially from those suitable to

the proper treatment of pure or mixed conifer crops intended to be cleared completely and replanted every 60 to 70 or 80 years. Again, on the great majority of British estates there are almost sure to be parts of the wooded tracts which the owner desires to exclude from commercial treatment, as, for example, the woods near the mansion-house, those specially regarded as game-coverts, woods having special value for shelter, or woods on very steep rocky localities or exposed situations. Such areas, however, even though excluded from intensive economic treatment, can easily be included within the scheme of management so as to form a separate working-circle to be treated by casual or sporadic (selection) fellings in such manner as may best meet the object in view of the proprietor. The annual fall has to be calculated separately for each working-circle, and all the data requisite for this purpose must be collected and tabulated separately.

Compartments. As the compartments are the permanent framework upon which the scheme of management has to be built up now, and upon which it will continue to rest in the future, the subdivision of the woodlands into compartments of suitable size for convenient working is the first step which requires to be taken. Wherever it is apparent that different workingcircles will have to be formed, the endeavour should be made to accommodate the boundaries of the compartments to the boundaries of the workingcircles. It is therefore necessary, before dividing the whole area into compartments, to consider the various local circumstances first of all, and to make some sort of rough sketch of the general scheme of management; because on this the formation of working-circles will depend, and the boundaries of these often determine the position of the boundaries of compartments and the position of the main lines of transport, the broad green lanes, and the narrow rides necessary for general working and management, as well as for sport. It is, however, of far more importance to obtain good serviceable boundaries for compartments-the permanent subdivisions of the woodlands— than that these should be made to deviate from the best lines merely in order not to include within them portions of crops varying in one way or another from those growing within the rest of the compartment.

The objects and advantages of forming compartments are obvious. They enable all parts of the woods to be accurately described and shown on the map, while any particular locality can easily be found, both in the forest and on the map; and this is important, not only for the general management, but also for those having work or business of any sort in the woods-e.g., timber-merchants. They simplify the location, the measurement, and the revision of the annual or periodic falls, as the boundaries are formed by roads, green lanes, or rides. For the same reason they open up the woods and make the extraction of timber easier. Wherever roads or green lanes form the boundaries, the outer edge of the crop becomes firmly rooted and capable of resisting high winds if the crops to the windward of them have to be felled. The roads, green lanes, and drives forming the boundaries often of themselves prevent the spreading of ground fires, while they always form convenient bases from which measures can be taken to extinguish fire that has broken out inside the compartment. And lastly, they are very useful for sporting purposes, the green lanes and rides being necessary, indeed, for battue-shooting.