Principles of Economics

Marshall, Alfred
(1842-1924)
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1890
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London: Macmillan and Co., Ltd.
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1920
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8th edition
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APPENDIX G*64

THE INCIDENCE OF LOCAL RATES, WITH SOME SUGGESTIONS AS TO POLICY.

App.G.1

§ 1. We have seen*65 that the incidence of a new local tax on printing would differ from that of a national tax mainly by causing such parts of the local printing industry as could conveniently migrate beyond the boundaries of the local tax to do so. Those customers who needed their printing to be done in the locality would pay rather higher for it. Compositors would migrate till only enough remained to find employment locally at about the same wages as before; and some printing offices would be transferred to other industries. The incidence of general local rates on immovable property follows different lines in some respects. The power of migration beyond the boundaries of the rates is a very important factor here, as in the case of a local tax on printing. But of perhaps even greater importance is the fact that a large part of the local rates is spent in ways that conduce directly to the comfort of those very residents and workers in the locality, who might otherwise be driven away. Here two technical terms are needed. Onerous rates are those which yield no compensating benefit to the persons who pay them. An extreme case is that of rates devoted to paying interest on a loan incurred by a municipality for an enterprise which failed and has been abandoned. A more representative case is that of a poor-rate levied mainly from the well-to-do. Onerous rates tend of course to drive away those persons on whom they would fall.

App.G.2

On the other hand beneficial or remunerative rates are those spent on lighting, draining, and other purposes; so as to supply the people who pay the rates with certain necessaries, comforts and luxuries of life, which can be provided by the local authority more cheaply than in any other way. Such rates, ably and honestly administered, may confer a net benefit on those who pay them; and an increase in them may attract population and industry instead of repelling it. Of course a rate may be onerous to one class of the population and beneficial to another. A high rate spent on providing good primary and secondary schools may attract artisan residents, while repelling the well-to-do. "Services which are preponderantly National in character" are "generally onerous"; while "those which are preponderantly Local in character generally confer upon rate-payers a direct and peculiar benefit more or less commensurate with the burden*66."

App.G.3

But the term "rate-payer" needs to be interpreted differently in regard to different kinds of local expenditure. Rates spent on watering the streets are remunerative to the occupier: but of course those spent on permanent improvements yield only a part of their return to him: the greater part accrues in the long run to the landlord.

App.G.4

The occupier generally regards the rates which are collected from him as forming a single aggregate with his rent; but he makes his reckoning also for the amenities of life which are secured by remunerative local expenditure of rates: that is he tends, other things equal, to select districts in which the aggregate of rents and onerous rates is low. But there is great difficulty in estimating the extent to which migration is actually governed by this consideration. It is probably hindered less than is commonly supposed by ignorance and indifference. But it is much hindered by the special requirements of each individual. Low rates in Devonshire will not draw there people who prefer London life; and certain classes of manufacturers have practically little choice as to the place in which they settle. To say nothing of personal and business ties, the tenant is further hindered by the expense and trouble of moving: and, if that were the equivalent of two years' rent, he would lose by moving unless the advantage which he secured in rates amounted to two shillings in the pound for thirty years. When, however, a person is changing his abode for any reason, he is likely to allow their full weight to all considerations as to the present and prospective rates in different localities, which may be suitable for his purpose.

App.G.5

The mobility of the working classes is, in some respects, greater than that of the well-to-do; but, when rates are compounded, friction sometimes acts on the side of the tenant, and delays the transference to him of his share of new burdens. The manufacturer is often affected as much by the rates on his workmen's dwellings as by those on his own premises: and though high rates may be among the causes which have driven some manufacturers out of large towns, it is doubtful whether, when economically administered, they have had much net effect in this direction. For most new expenditure from the rates, when under able and upright management, materially increases local comforts or lessens local discomforts from the point of view of the workpeople, if not of the manufacturer himself. Further, although the balance of evidence goes to show that lessees consider carefully the present and probable immediate future of local rates, yet they cannot see far ahead, and they seldom even try to do so*67.

App.G.6

Any analysis that is offered of the incidence of rates, must be taken to refer to general tendencies, rather than actual facts. The causes which prevent these tendencies from being applied in prediction resemble those which prevent mathematical reasonings from being applied to the course of a ball on the deck of a ship that is rolling and pitching in cross seas. If the ship would but stay at one inclination, the movement of the ball could be calculated. But before any one tendency has had time to produce much result it will have ceased to exist, and its successor cannot be predicted. Just so, though economists settled once for all, nearly a century ago, the general tendencies of the shifting of taxation; yet the relative weight of onerous rates in different places often changes so rapidly that a tendency may make but little headway before it is stopped off, or even reversed, by changes which cannot be predicted.

App.G.7

§ 2. We have already seen that the ground rent which a builder is willing to pay for any site is governed by his estimate of the additional value which that site will give to the buildings erected on it. Before taking the lease his capital and that which he will borrow for the purpose is "free" and expressed in terms of money. The anticipated income from his investment is expressed also in money. He sets on the one side his outlay for building; and on the other side, the excess of the rental value of the building with its site over the ground rent to which he is about to commit himself. He works out—perhaps roughly and by instinct rather than definite arithmetical calculations—the present (discounted) value of this excess for the (say) 99 years of his lease. Finally he takes the lease if he sees his way to a good margin of profit; and no better opening for his enterprise is at hand*68.

App.G.8

He contrives to the best of his ability that the site and the house (or other building), which he puts upon it, shall be permanently appropriate the one to the other. In so far as he succeeds, the rent of the property at any future time is the sum of its annual site value and the annual value of the building: and this he expects to yield him full profits on his outlay, allowing for insurance against the risks of a rather hazardous industry. This second part of the rent is commonly, though perhaps not with strict propriety, called the (annual) building value, or the building rent of the house.

App.G.9

As time goes on, the purchasing power of money may change; the class of house for which that site is suitable is likely to change; and the technique of building is certain to be improved. Consequently the total annual value of the property at a later date consists of its annual site value, together with profits on the cost of building a house giving accommodation equally desirable at that date with the existing house. But all this is subject to the dominant condition that the general character of the house has remained appropriate to its site: if it has not, no precise statement as to the relation between total value, site value and building value can be made. If for instance a warehouse or a dwelling house of quite a different character is needed to develop the full resources of the site, the total value of the property as it stands may be less than its site value alone. For the site value cannot be developed without pulling down those buildings and erecting new. And the value of the old material in those buildings may be less than the cost of pulling them down, allowance being made for the obstruction and loss of time incident thereto.

App.G.10

§ 3. As between two buildings equally eligible in other respects, the occupier will pay for that which has the better situation an annual sum equivalent to its special advantages: but he does not care what part of this sum goes as rent and what as taxes. Therefore onerous taxes on site values tend to be deducted from the rental which the owner, or lessee receives: and they are accordingly deducted, in so far as they can be foreseen, from the ground rent which a builder, or anyone else, is willing to pay for a building lease. Such local rates as are remunerative, are in the long run paid by the occupier, but are no real burden to him. The condition "in the long run" is essential: for instance, rates levied on account of interest and sinking fund on a town improvement, which will for several years to come disturb the public thoroughfares, and yield none of its good fruit, will be onerous to the occupier, if he pays it. In strict justice it should be deducted from his rent; because when the improvement is in full working order and especially when the debt has been paid off, so that the rate in question lapses, the owner of the property will reap the benefit of the onerous rates levied on account of it from the first*69.

App.G.11

§ 4. Taxes on building values are on a different footing. If uniform all over the country, they do no alter the differential advantages of favoured sites; and therefore do not—directly at least—make the builder or anyone else less willing to pay a high ground rent for a good site. If they are so heavy as materially to narrow the area of ground built upon, they will indeed lower the value of all building ground: and special site values will fall with the rest. But their effect in this direction is so small, that no great error is made by saying that uniform taxes on building values do not fall on the ground owner. The builder, in so far as he anticipates such taxes, adjusts his plans to them: he aims at putting up buildings of only such expense as can be let to tenants at rents that will yield him normal profits; while the tenant pays the rates. He may of course miscalculate. But in the long run builders as a class, like all other able business men, are nearly right in their calculations. And in the long run, uniform taxes on building values fall upon the occupier; or at the last on his customers if he uses the building for trade purposes, and his competitors are subject to similar rates.

App.G.12

But the case is quite different in regard to special high onerous local rates on building values: and here comes in the chief difference between the incidence of national taxes on immovable property and local rates on it. Remunerative expenditure from the rates, which adds more to the conveniences of life than the equivalent of its cost, do not of course repel the occupier: that part of them which is assessed on building values is paid by him, but is no real burden on him; as we have seen in the case of remunerative rates on site values.

App.G.13

But that part of the rates on building values which is onerous, and in excess of corresponding charges in other localities, does not fall mainly on the occupiers. Any exceptional pressure will cause them to migrate beyond its reach in sufficient numbers to reduce the demand for houses and other buildings in the locality, till the burden of these exceptional rates falls upon the lessees or owners. Builders therefore, in so far as they can foresee the future, deduct the equivalent of these exceptional onerous rates on building values, together with all rates and taxes on site values from the ground rents which they are willing to pay.

App.G.14

But the cases, in which great deductions of this kind are made, are not numerous and important. For permanent inequalities of onerous rates, though considerable, are less than is commonly thought: and many of them are due to accidents which cannot easily be foreseen, such as mismanagement by a particular group of local administrators. There is indeed one broad and perhaps permanent cause, which throws its shadow before, namely the tendency of the well-to-do to move away from crowded districts to roomy and fashionable suburbs: thus leaving the working classes to bear an undue share of the national duties towards the very poor. But no sooner does this evil become conspicuous, than legislation is invoked to remedy it, by widening the areas of rating for some purposes, so as to include poor and rich districts under the same budget; and in other ways.

App.G.15

It is of greater importance to remember that exceptional onerous rates on building values, while tending to lower site rents, and to lower the ground rents on new leases in the districts to which they apply, are not as great a burden on the whole body of owners of land as seems at first sight. For much of the building enterprise, which is checked by such rates, is not destroyed but directed to other districts, and raises the competition for new building leases there.

App.G.16

§ 5. The incidence of a long-established rate is little affected by its being collected from the tenant, and not from the owners; though it is vitally affected by the proportions in which the rate is assessed on site and building values respectively. On the other hand, the incidence for the first few years of an increase in onerous rates is much affected by the mode of collection. The occupier bears more of the new burden than he would if part of the rates were collected from the owners, or he were allowed to deduct a part of them from his rent. This applies only to neighbourhoods that are making progress. Where the population is receding, and building has ceased, onerous rates tend to press upon owners. But in such places economic friction is generally strong.

App.G.17

It seems probable that the total pressure of onerous rates on the enterprise of building speculators and other interim owners is not very great; and that many rates, of which they have complained, have really enriched them. But vicissitudes of the rates increase slightly the great risks of the building trade, and inevitably the community pays for such risks more than their actuarial equivalent. All this points to the grievous evils which arise from great and sudden increases in the rates, especially in regard to premises the rateable value of which is high relatively to the net income of the occupier.

App.G.18

The trader, especially if a shopkeeper, is often able to throw some part of the burden of his rates on his customers, at all events if he deals in things which cannot be easily got from a distance. But the shopkeeper's rates are very large relatively to his income; and some of that expenditure from the rates, which is remunerative from the point of view of well-to-do residents, appears onerous to him. His work belongs to that group in which economic progress is raising supply relatively to demand. A little while ago his remuneration was artificially high, at the expense of society: but now it is falling to a lower and perhaps more equitable level, and he is slow to recognize the new conditions. His mind fastens on the real injustice which he suffers when rates are suddenly raised much; and he attributes to that some of the pressure on him which is really due to deeper causes. His sense of injustice is sharpened by the fact that he does not always bargain on quite even terms with his landlord; for, to say nothing of the cost of fixtures and the general expense of a change, he might lose a great part of his custom by moving to equally good premises even a little way off. It must however be remembered that the shopkeeper does migrate sometimes, that his mind is alert, and he takes full account of the rates; and thus, after a few years, he shifts the burden of onerous rates on to the owners and customers more fully than a man of almost any other class does. (The hotel and lodging-house keeper may rank here with the shopkeeper.)

App.G.19

§ 6. Land near to a growing town, which is still used for agriculture, may yield very little net rent: and yet be a valuable property. For its future ground rents are anticipated in its capital value; and further its ownership is likely to yield an income of satisfaction outside of the money rent received for it. In this case, it is apt to be under-assessed even when rated at its full rental value; and the question arises whether it should not be assessed at a percentage on its capital value instead of at a percentage on its rent.

App.G.20

Such a plan would hasten on building, and thus tend to glut the market for buildings. Therefore rents would tend to fall, and builders would be unable to take building leases on high ground rents. The change would therefore transfer to the people at large some part of "the public value" of land which now goes to owners of land, that is built upon or is likely to be built upon. But unless accompanied by energetic action on the part of urban authorities in planning out the lines on which towns should grow, it would result in hasty and inappropriate building; a mistake for which coming generations would pay a high price in the loss of beauty and perhaps of health.

App.G.21

The principle which lies at the base of this scheme is capable of larger application: and something may be said as to one suggestion of an extreme character, which has recently attracted some attention, to the effect that in future rates should be assessed mainly or even wholly on site values, with little or no reference to the value of the buildings. Its immediate effect would be an addition to the value of some properties at the expense of others. In particular it would raise the value of high and expensive buildings in districts in which the rates were heavy, even more than those in which they were low; because it would afford relief from a greater burden. But it would lower the value of low obsolete buildings on large sites in heavily rated districts. After a time, the amount of building put upon a site would vary generally, subject to the bylaws, with its advantages of situation; instead of as now partly in proportion to these advantages, and partly inversely as the rates. This would increase concentration and tend to raise gross site values in advantageous districts: but it would also increase the aggregate expenditure from the rates; and, as this would fall on site values, the net site values might be very low. Whether on the whole the concentration of population would be increased, it is difficult to say: for the most active building would probably be in the suburbs, where vacant land no longer escaped heavy rating. Much would depend on the building bylaws: the concentration might be much lessened by a rigorous rule that there should be a large free space at the back as well as in front of all high buildings*70.

App.G.22

§ 7. Reference has already been made to the latent partnership between tenant and landlord in British agriculture generally*71. Competition is less effective in rural than in urban districts. But on the other hand the contributions which the landlord makes to the effective capital of the farm are elastic, and liable to variation according to the stress of circumstances. These adjustments obscure the incidence of agricultural rates, as the eddies of wind rushing past a house will often carry snow-flakes upwards, overbearing, but not destroying, the tendency of gravitation; and hence arises the common saying that the farmer will pay both his and the landlord's share of new rates, if the competition for farms is strong; while the landlord will pay all, if he has reason to fear that farms will be thrown on his hands.

App.G.23

However, rural populations probably bear less onerous rates than is commonly supposed. They have gained by improved police service and the abolition of turnpikes, and they have increasing access to advantages purchased by rates in the neighbouring towns, to which they do not contribute, and which are generally much higher than their own rates. In so far as the rates are remunerative in the immediate present, they are no net burden to the occupier, though he pays them. But rates are a considerable percentage on the farmer's net income; and the burden on him is apt to be heavy in those very rare cases in which onerous rural rates are increased greatly. As already indicated, an onerous rate confined to one district is likely to press more heavily on the local landlords and farmers than if general throughout the country*72.

App.G.24

§ 8. This volume is mainly occupied with scientific inquiries; but yet not without some glances at the practical issues, which supply a motive to economic studies*73. And here some consideration of policy seems desirable in regard to rates. For all economists are agreed that land in an old country resembles other forms of wealth in many respects, and that it differs in others: and in some recent controversial writings there has appeared a tendency to relegate the points of difference to a secondary place, and to give almost exclusive prominence to those of similarity. A moderate tendency in that direction might be judicious, if the points of similarity alone were of high importance in urgent practical issues. But the contrary is the fact. And therefore it may be well to consider some great issues of administrative finance, in which a leading part is played by those attributes of land which are not largely shared by other forms of wealth. But first a little must be said as to equity.

App.G.25

When a special tax is levied for a particular purpose and the case is not one for any interference by public authority with existing rights of ownership—as, for instance, when an arterial system of land drainage is created—the owners of the properties to be benefited may fitly be assessed on the "joint stock principle," according to which calls are made from shareholders in proportion to their stake in the common venture. The equity of every such charge must be judged separately. But on the other hand all onerous taxes and rates must be judged in equity as a whole. Almost every onerous tax taken by itself presses with undue weight on some class or other; but this is of no moment so long as the inequalities of each are compensated by those of others, and variations in the several parts synchronize. If that difficult condition is satisfied, the system may be equitable, though any one part of it regarded alone would be inequitable.

App.G.26

Secondly, there is a general agreement that a system of taxation should be adjusted, in more or less steep graduation, to people's incomes: or better still to their expenditures. For that part of a man's income, which he saves, contributes again to the Exchequer until it is consumed by expenditure. Consequently, when considering the fact that our present system of taxation, general and local, bears heavily on houses, it should be remembered that large expenditure generally requires large house-room: and that while taxes, and especially graduated taxes on expenditure in general, present great technical difficulties to the tax collector; and further cost much more to the consumer directly and indirectly than they bring into the revenue; taxes on houses are technically simple, cheap in collection, not liable to evasion, and easy of graduation*74.

App.G.27

But, thirdly, this argument does not apply to buildings other than houses. And for that reason it may be equitable to tax shops, warehouses, factories, etc. on a lower scale than houses, at all events as far as new rates are concerned: the burden of old rates is already shifted from the occupiers of business premises partly on to their landlords and partly on to their customers. This process of shifting is constantly going on; and therefore no great hardship would be inflicted on the trading classes in urban districts if they were charged at once with a farthing for every penny of new rates; while a part, or the whole, of the remaining three farthings were left to be added to their burden gradually by small annual percentages. It may be that some such plan will be necessary, if the expenses of urban local government continue to increase fast.

App.G.28

These considerations lead us to repeat that, whether in an old or a new country, a far-seeing statesman will feel a greater responsibility to future generations when legislating as to land than as to other forms of wealth; and that, from the economic and from the ethical point of view, land must everywhere and always be classed as a thing by itself. If from the first the State had retained true rents in its own hands, the vigour of industry and accumulation need not have been impaired, though in a very few cases the settlement of new countries might have been delayed a little. Nothing at all like this can be said of the incomes derived from property made by man. But the very greatness of the public interests concerned makes it specially necessary to bear in mind, when discussing the equities of the public value of land, that a sudden appropriation by the State of any incomes from property, the private ownership of which had once been recognized by it, would destroy security and shake the foundations of society. Sudden and extreme measures would be inequitable; and partly, but not solely for that reason, they would be unbusiness-like and even foolish.

App.G.29

Caution is necessary. But the cause of high site values is that concentration of population, which is threatening a scarcity of fresh air and light and playroom so grievous as to lower the vigour and the joyousness of the rising generation. Thus rich private gains accrue, not merely through causes which are public rather than private in their character, but also at the expense of one of the chief forms of public wealth. Large expenditure is needed to secure air and light and playroom. And the most appropriate source from which that expense can be defrayed seems to be those extreme rights of private property in land, which have grown up almost imperceptibly from the time when the king, representing the State, was the sole landowner. Private persons were but landholders subject to the obligation to work for the public wellbeing: they have no equitable right to mar that wellbeing by congested building.

App.G.30

§ 9. Accordingly the following practical suggestions seem to emerge:—As regards old rates a sudden change in the person from whom they are collected seems unadvisable: but additional rates should, as far as may be convenient, be collected from the person on whom they are ultimately to fall; unless, like the income tax under Schedule A, they are collected from the tenant with the instruction that they are to be deducted from his rent.

App.G.31

The reasons for this are that nearly the whole of that part of old rates, which is assessed on public or site value of land, is already borne by owners (including lessees, so far as those rates go, which, though old, were not anticipated when their leases were taken); and nearly all the remainder of it is borne by tenants or their customers. This result would not be very greatly disturbed by allowing the tenant to deduct a half or even the whole of his rates from his rent: though such a law would run some risk of handing over some of the property of the owners to lessees, who had reckoned for paying those old rates when taking their leases. On the other hand, a provision for the division of new, that is additional, rates would have great advantages: the occupier whether of a farm, of business premises or a house would deduct one half of the new rates from his rent; his immediate landlord would deduct in proportion from his payments to the superior holder next to him; and so on. And in addition new local taxes on business premises of all kinds might be assessed, as has just been suggested, at less than full rates in the first instance; and gradually increased. By these provisions farmers, shopkeepers and other traders would be relieved from the occasional injustice, and the constant fear of injustice, which are now associated with sudden, disproportionate additions to the public burdens thrown upon particular classes.

App.G.32

In regard to site values, it would seem well to rule that all land, whether technically urban or not, should be regarded as having a special site value if when cleared of buildings it could be sold at even a moderately high price, say £200 an acre. It might then be subjected to a general rate assessed on its capital value; and, in addition, to a "fresh air rate" to be spent by local authority under full central control for the purposes indicated above. This fresh air rate would not be a very heavy burden on owners, for a good deal of it would be returned to them in the form of higher values for those building sites which remained. As it is, the expenditure of such private societies as the Metropolitan Public Gardens Association, and much of the rates raised on building values for public improvements, is really a free gift of wealth to owners who are already fortunate.

App.G.33

For rural and urban districts alike, after reckoning for the initial rates on land, the remainder of the necessary funds would perhaps best be obtained by rates on immovable property, supplemented by some minor local taxes at the discretion of the local authorities. The Inhabited House Duty might be suppressed, unless it was needed for any great new expenditure such as old age pensions: and the main rates might be graduated as the present Inhabited House Duty is; but more gently for houses of moderate size, and more severely for very large houses. But no one should be exempted altogether: for so long as a person retains the right of voting on the levying and expenditure of rates, it is not safe that he should wholly escape their pressure. It may however be safe and reasonable to return to him or his children the equivalent of his payments in such benefits as will increase physical and mental health and vigour, and will not tend towards political corruption*75.


Notes for this chapter


64.
See pp. 453 and 659.
65.
Above V. IX. 1. This Appendix is largely based on the Memorandum there mentioned.
66.
Final Report of Royal Commission on Local Taxation, 1901, p. 12.
67.
A good deal of evidence on these points was taken by the Commission just named (p. 794, n. 3).
68.
See above, V. XI. 3 and 8. The builder generally looks to sell his lease before much of it has run out. But the price which he expects to get is the (discounted) excess of the rental value of the property over the ground rent for the remaining years: and therefore the substance of his calculations is nearly the same as it would be if he intended to keep the property in his own hands.
69.
This assumes that the land is assessed to the tax at the same amount, whatever the use to which it is put. The case of an extra tax for a special use can be treated as in V. X. 6. If agricultural land were exempt from the tax, then the tenant of a house or factory in the country would escape that part of the site tax which is assessed on the excess of the value of the land for building uses over its value for agriculture. This might slightly increase concentration in towns, and thus take a little from the burden on site owners in them: but it would not materially affect the values of sites in the centre of towns. See also below § 6.
70.
For instance suppose an area of a million square feet to be covered with rows of parallel buildings 40 feet high and 40 feet deep; a bylaw, that the sky must subtend half a right angle at the ground looking straight back as well as front, will cause the distance between each row and the next to be 40 feet: and the aggregate volume of building will be 40 feet multiplied into half the total area, i.e. 20,000,000 cubic feet. Now suppose the height of the buildings to be trebled. Under the same bylaw, the distances between the rows must be 120 feet: and, on the supposition that it is not convenient to increase the depth of the houses beyond 40 feet the aggregate volume of building will be 120 feet multiplied into a quarter of the total area, that is, 30,000,000 cubic feet. Thus the total accommodation will be increased by only one half; instead of being trebled, as would have been the case if the old distances of 40 feet between the rows had been maintained.
71.
See VI. X. 10.
72.
See above, p. 437.
73.
See I. IV. 2-4.
74.
In old times the windows of a house were taken as representative of the house, and were taxed heavily: but the tax did not strike, and was not intended to strike, persons as owners and users of windows only; it was intended to strike them, and did strike them, as owners and users of houses. And, just as the window is a more or less good representative of the house; so the house is a representative, perhaps a better representative, of a certain scale and style of household expenditure in general; and when houses are taxed, the tax is, and is intended to be, a tax upon the ownership and use of the means of living in certain general conditions of comfort and social position. If part of the tax assessed on houses were removed, and the deficit made up by taxes assessed on furniture and indoor servants, the true incidence of the taxes would be nearly the same as now.
75.
The recent Commission on Local Taxation was much occupied with the difficulty of assessing site values; and with the even greater difficulty of making ad interim arrangements by which an equitable share (whether more or less) of the rates, which were designed in the long run to be paid by the ultimate landowners, might be transferred from the occupiers to lessees. (See especially pp. 153-176 of the Final Report.) The difficulty of assessment, though undoubtedly very great, is of a kind to be diminished rapidly by experience: the first thousand such assessments might probably give more trouble, and yet be less accurately made than the next twenty thousand.

End of Notes


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