time to increase the area of the country trading on the improvement, a quantity equal to the whole of the shaded space in the figure, and to increase the revenue a quantity equal to whatever would be due to this additional trade and the charge upon it, determined in accordance with the principles here laid down.

16. It will be perceived that the increase of tonnage and revenue which, in the preceding article, is shown to have place, will be obtained without any increase of toll on any part whatever of the trade. We have only to take the present tariff of New York or Pennsylvania, or any other state or company, and obtain these results by a reduction of the charges.

For, at the point P, which is supposed to be two hundred miles from M, we have seen that a toll of one cent per ton per mile would entirely exclude the trade. But if, instead of a charge of one cent per ton per mile, at that point, or $2 for the entire toll from P to M, the article were taxed but seventy-five cents per ton, as is stated (in article 13) to be the proper toll under the circumstances, there would remain out of the $2, which is the limit of the charge for toll it would bear at that position, a balance of 81 25 to pay the expense of its transportation from p to P-a distance of twelve and a half miles on each side of the line. So that, by simply reducing the charge resulting from a tariff proportioned to the distance, we shall here obtain, instead of nothing, a revenue due to the tonnage that would be furnished by a district pp, twenty-five miles in breadth, at a charge of seventyfive cents per ton.

It is true that a much more important increase of revenue might be experienced by a modification of the uniform charge supposed to be levied from M to M', and a reduction from the new tariff beyond M'. For, even where we adopt the principle of fixing on a determinate toll per ton per mile for a certain distance, we should bear in mind that there is a certain uniform charge which will yield a higher result than any other. But, without any reference to this, or any of the other advantages which would be derived from a thorough and strict regard to the laws of trade in the establishment of the tariff, I have only sought to render clear the fact, that by simple reductions of the charges on a portion of the trade on all our public works, the revenue and tonnage may be simultaneously increased, and the tax on the public may be rendered more equitable.

17. The preceding conclusions are applicable only to the trade in heavy articles of small value. Equally salutary results might however be obtained by modifications of the charges on the other principal division of the commerce of the country-that which is rendered by its value an object for the competition of rival works. But the examination of the subject with reference to the latter division would, from its complication, be much less susceptible of receiving a popular form. This and other views of the subject, which have always to be considered in any attempt to establish a correct tariff, are examined in considerable detail in my "Essay on the Laws of Trade," where the methods to be adopted to obtain the greatest revenue which the work can possibly extract from the commerce of the country are fully exposed. It is not possible to repeat here, in the narrow space which can now be appropriated to the subject, even the most important of the principles to be regarded in the administration of our public works, which I have there attempted to develope. The glance which is here directed to the question is necessarily confined to a very few prominent points.

To establish a tariff of toll for all articles, on sound principles, requires a certain intimacy with the statistics of the line, and a proper acquaintance with the laws by which the tonnage and revenue are governed. This knowledge cannot be obtained intuitively; and a correct tariff cannot be devised, as those on all our improvements are, by the mere conjectures of the parties to whose discretion such subjects are usually referred.

§ 5. General Laws of Trade.

18. There are some facts of a general character relating to this subject which are susceptible of a most rigorous demonstration, that may be here profitably repeated. It has already been shown that a great loss of trade and revenue is sustained in the management of public works by the adoption of a uniform rate of assessment. In the examples adduced, this results from over-charges, which, under such regulations, invariably have place in some part of the line. It may be shown by a legitimate course of argument, that however we depart from the charge which will yield the greatest revenue, there will be an increase or diminution of tonnage, and, of course, always a decrease of revenue. If the departure be an overcharge, the tonnage will be reduced a quantity directly proportional to the value of the overcharge, and the revenue proportional to the square of that departure.

Nothing can prove more conclusively the danger of submitting so important a subject as the preparation of a tariff, to the uncertain guide of conjecture. For, if we err ten mills in the charge which we establish for any article, the loss will be one hundred times greater than if we err but one mill.

19. It is usual to assume that the charge for toll should be proportional to the distance the article is carried that it should be greater for a great distance than a short one. But we have already seen that, on the contrary, in most cases, the greater the distance the article is carried the less should be the aggregate toll upon it. (Art. 13.)

20. It is common to suppose either that the tariff of toll is independent of the cost of freight, or that the higher the expenses of carriage the greater should be the charge for toll. But, on the contrary, the fact is susceptible of general and easy proof, that the higher the charge for freight on the line, the lower must be the toll; and also that any increase of the cost of freight will at the same time diminish the toll or profit on the article, and increase the whole tax for its transportation.

21. The charge for toll is also assumed, in the ordinary establishment of tariffs, to be independent of the mode by which the trade approaches the line; and, for many articles, this is true; but, for others, it is an ascertained fact, susceptible of easy demonstration, that if they are brought to the work by a common turnpike a higher toll should be charged for their passage on the improvement than if the same articles reach the work by a railroad, and, à fortiori, than if brought by a canal.

22. Where the object is to obtain the greatest possible revenue, it is a general law, susceptible of satisfactory proof, that the charge for toll should not exceed half that charge which would exclude the trade from the line. It may be shown, however, that, although a higher charge than this can never be advantageously adopted, it may frequently be reduced to three-eighths of the sum which would cause the exclusion of the trade, with a very beneficial effect on the tonnage, and without leading to any sacrifice on the score of

revenue.

23. Another fact, which may be derived immediately from the preceding, is, that where the most judicious charge is levied, the tonnage of the line will be one-half of the tonnage which would be obtained if no toll at all were exacted.

VOL. XXV.- No. 4.- APRIL 1840.

20

24. The charge for toll has already been shown to depend in part on the price of freight; and it is an established law that if the cost of freight be increased or diminished by any modifications of the work, or the system of transportation adopted on it, the toll must be increased just half as much as the freight is diminished, or diminished just half as much as the freight is increased. And it is further susceptible of demonstration, that the increase of revenue which will follow a general reduction of the charge for freight will at least be equal to the arithmetical mean between the values of the tonnage before and after the reduction multiplied by the amount that the freight is reduced. In other words, if the trade of the line be one hundred thousand tons, and the freight be from any cause reduced $1 per ton, and the tonnage thereby increased ten thousand tons, the revenue of the work will be increased more than $105,000; and this result will have place simultaneously with a reduction of the whole tax on the trade to the amount of $50,000, and the corresponding augmentation of the tonnage.

25. The fact is not usually recognised, that the toll, and tonnage, and revenue, are all more or less dependent on the length of the line of the improvement. It may, nevertheless, be easily proved by a general demonstration, that the tonnage, the charge which may be levied per ton per mile, and consequently the revenue, will all receive an increase by a reduction of the length of the line of transportation. So that if the toll be judiciously established on any given line, and any material change of location afterward be made, by which the distance, or cost of freight is diminished, there must be a certain increase of the charge for toll, from which an augmentation of revenue will necessarily result. The value of this increase of revenue is equal to the whole annual tonnage of the line, multiplied by the actual cost of freight through the distance saved-and, "considering only the value of the trade, it is therefore worth, to reduce the length of the line, the capital of which the interest is equal to that sum.

26. In the arrangement of the charges in a tariff, there is no subject of greater importance, for some articles, than the positive, and for others, than the relative, value of the mart. From the positive value of the article, is determined the tax which one division of the trade can sustain; and from the relative value is in part deduced the proper toll on all commodities for which other works are competitors.

A permanent change of the relative standing of the mart, ought, therefore, to superinduce a modification of the toll. And it may be easily shown that if the relative value of the market-by which is intended its value compared with that of the rival mart-be increased any given sum, we shall find the corresponding increase of toll per mile proper to be made, by dividing that increase by twice the length of the improvement in miles. If, for instance, the value of Philadelphia as a mart for tobacco, compared with the value of New Orleans in reference to the same article, be, from any cause, increased $4 per hogshead, and the distance from Philadelphia to Pittsburg be four hundred miles, then, I say, the toll on tobacco on the whole central line of the Pennsylvania improvement, should be increased a half-cent per ton per mile.

It is also easy to demonstrate that, at the same time, the revenue will be augmented by any increase of the relative value of the market, an amount obtained by multiplying the original tonnage added to half the increase of tonnage consequent on the improvement of the market, by the increased value of the tonnage at the market.

It is shown, in fact, that whatever circumstance occurs to increase the value of the property sent along an improvement, to the holder of the property, will cause a certain increase of tonnage, of which the measure can be obtained, and a simultaneous augmentation of revenue equal to the whole increase of its value; and that whatever unnecessary tax is levied on the trade, is at least so much deducted from the revenue of the improvement. If, for instance, the engineer in making the location permit his line to be one mile longer than is essential, he will thereby cause to the State or Company an annual tax, or equivalent loss of dividend, equal to the whole annual expense of transporting the whole trade of the country through that mile. He incurs, at the same time, the responsibility of reducing the tonnage of the work, and of injuring, to a certain extent, both the country that supplies the trade, and the emporium which receives it.

If he embarrass the line by an unnecessary grade, or any other impediment which involves a similar increase of the charge for freight, he is responsible for the same result; and, before adopting such a measure, is bound to compare the value of the difficulties to be avoided, with that of these inevitable consequences to the future trade.

28. It is an error, and a very frequent one, to suppose that the toll is in any manner dependent on the cost of the work; or ought, under any circumstances, to be directly proportional to the value of the article. It is, however, not uncommon to assume, that it ought to bear some relation to the cost of construction; and there are tariffs of toll in the data for the calculation of which the value of the commodity is the principal, if not the only element. It is not a little singular that, after encountering an expense of hundreds of millions for our public works, the tariffs by which they are to be sustained should be entirely ruled by considerations which, however plausible in a superficial view, have no legitimate relation to the question.

For one division of the trade, it is not the positive value of the commodity, but the difference between the market value and the cost of production; and for the other, the difference between the value of the article at the mart of the improvement and at that of its rival, by which the toll is influenced. And this influence is only partial. The value of the article, taken in any sense, is only a part of the data by which the true charge must be determined.

29. It is by no means the intention here to attempt a general analysis of this most important subject. My object, as already announced, has been to show that, under certain circumstances, a marked increase of trade and revenue may be obtained on all our public works, by simply reducing the charges; and that such modifications of the tax levied on the community is rendered imperative by the first principles of equity. If I have succeeded in making this truth perfectly apparent, the design of these pages will be fully accomplished.

I scarce hope to have satisfied the reader in a discussion so brief and popular, that to enable a company to take the full advantage of its position, and obtain the highest degree of success of which their enterprise is susceptible, demands a careful and close investigation of the laws of trade in reference to every branch of the subject. To appreciate the importance of this course, requires that the mind should have investigated such questions sufficiently to estimate the consequences of its neglect. To know the value of establishing the most correct tariff, we need to know what we are likely to lose by the adoption of a conjectural or empirical one.

This subject, though usually taken under other auspices, is peculiarly a professional study. An intimate acquaintance with the principles which govern the trade of an improvement, is a department of knowledge which is essential to the engineer in the location of his line, and the establishment of many of the plans of his work. His first duties, when properly discharged, compel him to become the most intimately acquainted with the productions and statistics of the country, and the information acquired in the accomplishment of these labours, ought to be turned to account in directing the future administration of the line.

The preparation of the tariff is, or ought to be, the peculiar province of the engineer. For, though there may be many considerations of policy, which should have a certain weight with those whose final action is requisite to carry his recommendations into effect-and which may frequently render it advisable to modify the charges which an à priori investigation may indicate to be proper, where the questions of trade and revenue only are under consideration, still, it is not less important that the tariff should first be correct in itself, that some estimate may be inade of the effect that will be felt when such political modifications come to be admitted. And, withal, it is difficult to conceive what motives of policy should induce any material departure from those limits which the administration of justice, the promotion of the trade, and the augmentation of the revenue simultaneously recommend.

Philadelphia, November 6th, 1839.

Franklin Institute.

COMMITTEE ON SCIENCE AND THE ARTS.

Report on Mr. Edward Clark's process far making White Lead.

The Committee on Science and the Arts constituted by the Franklin Institute of the State of Pennsylvania, for the promotion of the Mechanic Arts, to whom was referred for examination the process for manufacturing White Lead, invented by Mr. Edward Clark, of New York; REPORT,

That it consists in the introduction of vapor of vinegar, carbonic acid and atmospheric air into chambers, which contain sheets of lead either rolled and placed on shelves, or open and hung on slats, the shelves or slats being supported by cleats attached to the posts forming the sides of the chambers, the vinegar is placed in a trough passing through the centre of the chambers and is heated by steam passing through its double bottom. The carbonic acid enters from the fire by which the steam is generated, and this gas, together with air, are forced into the chambers by bellows or from a gasometer. The main points of difference between the present and Richards' process, described in the Journal for 1839, lies in the introduction of steam by the latter into the chambers from above, and in the double walls of the chambers, which receiving steam maintain the inner chamber at a given temperature. Mr. Clarke's patent is dated Dec. 4th, 1828, reissued as amended in July 3d, 1832. Mr. Richards' was obtained a few years since. Between the present and the ordinary processes, the difference lies in the mode of elevating the temperature and generating the carbonic acid gas, which ordinarily are produced by the fermentation of vegetable matter (dung) which generates heat and carbonic acid, and vaporises the vinegar.

A process of a somewhat similar nature is pursued in the south of Germany, the lead sheets being hung on slats, which lie over troughs of about five feet in length, containing, on the bottom, vinegar mixed with wine-lees.