to, the same effect was produced; for most sediment would persist in settling on the dark side of the tube, that being least agitated by the action of light. To render the cause of this phenomenon a fact no longer to be doubted, a slip of black paper was procured, in width about half the circumference of the glass cylinder, and to one side of which it was applied in order to exclude the light from that side, while it had free access to the other; the result was as anticipated, for it caused a very much increased deposite on the sides shaded by the paper.

This variation, or inclined settling, progressively decreased as the lighter part of the tube, through which the particles had to fall, became shortened by its filling up with sediment.

The above fact is here noticed under the supposition that it may be something new, and that, by possibility, there may be connected with it, something which may be found beneficial to science; for it is, to say the least of it, a very strong evidence of the action of light upon delicate substances.

Having early perceived that this report would exhibit a series of results, varying very much from those obtained by Prof. Riddell, on the same subject, and reported to this Association in 1846, we have, on that account, been the more careful that accuracy should attend all our proceedings with respect to it. This has likewise enhanced our desire to possess the Association with as many of the details of the methods adopted to insure the proper results as should be the best calculated to show the confidence that was to be placed on the unquestionableness of their nature. By this report, the mean annual discharge of water, by the Mississippi, is 14,883,360,636,880 cubic feet; the Riddell report gives 11,108,275,200,000 cubic feet. This difference may be accounted for by the great uncertainty there must be in obtaining any correct mean where conditions and velocities are so changeable; at least there cannot certainly be the same dependence placed in quantities got by such a method, as there may be in that more mathematical one adopted for this report. But the difference in the two estimates, with respect to the solid matter held in suspension by the waters, may well seem the most extraordinary that can be conceived, in any two estimates for the same thing. This report gives to the solid matter, in bulk, in comparison with the bulk of water, as 1 is to 528, the Riddell report gives it as 1 to 3000. Why there should be any thing like this difference may seem difficult to determine, and is well calculated to abate the confidence to which either report may be entitled. Agreeably to the Riddell report, it

would require a column of water, 250 feet in height, to deposit 1 inch of sediment; were that so, it would have required that our tin tube should have been filled 1750 times, in order to have produced the quantity of sediment herewith submitted; in which case we would have contented ourselves with obtaining a much smaller quantity. According to this report, there is 1 inch of solid matter deposited from a column of water of 44 feet. Every one who has travelled on the Mississippi, and seen the turbid condition of its waters, will be able to decide between these two reported quantities. We will here remark, so as to account for the discrepancy, that if the waters of this river are not continually agitated by the force and turbulence of the current, the suspended sediment very soon subsides considerably below the surface; and at, or opposite the Mint, in New Orleans, is below almost all the wharves, and most of the shipping. Where the waters are very still, and where deposition takes place to a very great extent, so as to make much land, after the water has so parted with a portion of its sediment, it passes down past the Mint without being but very slightly agitated, the principal current being altogether on the other side of the river, and but very little on that side where Prof. Riddell procured the test-water for his experiments, according to his own statement.

Thus, when the true conditions are known, the discrepancies will cease to be so surprising; but it is certainly very unfortunate that they should have existed at all, or that the water opposite the Mint should have been collected as an example to establish the proportional quantities of solid matter held in suspension by the waters of the Mississippi.

One more remark and we will have done : It has been elicited by the circumstance of perceiving a very decided disposition in the procured sediment to continue settling down into a more compact condition by virtue of molecular affinity, or the arrangement of its constituent particles, and consists in accounting for the often noticed circumstance, that in a large excavation made for the Gas Works, at New Orleans, 18 feet deep, there were found embedded innumerable stumps of trees, buried at various levels, in an erect position, with their roots attached, implying the former existence there of fresh water swamps, covered with trees, over which the sediment of the Mississippi river had been spread during inundations. The site of the excavation is only about nine feet above the level of the sea; therefore the lowest of the embedded stumps must be nine feet below that level. Now this need not be at all surprising, when we reflect that

the first growth of trees, in this region, must have taken root on the surface of new-made ground, deposited from the Mississippi, and that ground, or deposite, of the depth of 1056 feet, with a continued tendency to settle into a more compact condition by incumbent pressure, molecular affinity, and arrangement of particles, as we found it to be the case with the settling of our sediment. Every year's sinking down, in this case, would be fully compensated by every year's deposite, for the lower it at any time sunk the longer it would be subject to inundation by the subsequent overflow, so that this sinking and compensatory process would go on together, and continue about equal, which well accounts for the circumstances of former forests being now found so far below the level of the sea. Should this subsidiary process be now, in any measure, incomplete in that region where the City of New Orleans now stands, and which we indeed very much question, in that case the compensatory equivalent being cut off by embankments, or the levying out of the waters, the time may, by possibility, yet come, when the ground on which the City of New Orleans now stands, may sink to a level with the ocean or even below it; at least, should there be any further settlement at all, it must, in the same ratio, approximate that level; for the final adjustment of particles in a deposite of 1056 feet deep, that will preclude any further settling, may be expected to take an immensity of time. ANDREW BROWN, M. W. DICKESON,

Committee.

Table of Calculations made use of in the foregoing Report.

1. Quantity of water discharged by the Mississippi river, annually, 14,883,360,636,880 cubic feet.

2. Quantity of sediment discharged by the Mississippi river, annually, 28,188,083,892 cubic feet.

3. Area of the delta of the Mississippi, according to Mr. Lyell, 13,600 square miles.

4. Depth of the delta, according to Prof. Riddell, 1056 feet.

5. The delta, therefore, according to 3 and 4, contains 400,378,429, 440,000 cubic feet, or 2720 cubic miles.

6. According to 2, it would require, for the formation of one cubic mile of delta, 5 years 81 days.

7. For the formation of one square mile, of the depth of 1056 feet, 1 year 16 days.

8. For the formation of the delta, according to 2, 3, 4, 14,2034 years.

9. The Valley of the Mississippi, from Cape Girardeau to the delta, is estimated to contain 16,000 square miles, of 150 feet deep; it therefore contains 66,908,160,000,000 cubic feet, or 4541⁄2 cubic miles.

Prof. GERMAIN gave some views of his connected with this subject.

On motion of Prof. W. R. JOHNSON, it was recommended to the Association that thanks be presented to the Committee for the very able manner in which they have discharged their duty in this matter, and that the report be published in full as early as practicable. Dr. R. COATES moved that this Section adjourn to meet to-morrow at 10 A. M., which was agreed to.

R. W. GIBBES, Sec'ry.

September 22.

SECTION OF GENERAL PHYSICS, &c.

Second Meeting.

The Section met at 9 A. M. The following papers were read:

ON THE FUNDAMENTAL PRINCIPLES OF MATHEMATICS. BY PROF. STEPHEN ALEXANDER.

Prof. ALEXANDER remarked, the object of all scientific research was truth; a term too valuable to be misunderstood, and yet too general to admit of a ready definition. He proceeded, however, to characterize it, in some of its various aspects, observing that while each is applicable to its own object, that is true in mathematics, which, under the existing system of things, is supposable; that is true in physics, which, under the existing system of things, has been permitted to exist; that is true in matters of taste which is consistent with the laws of beauty, deduced from the observation of things actual; and that is true in morals (in the highest and best sense in which it is good) which is consistent with what is found in the GREAT SOURCE OF ALL GOOD.

He next proceeded to state that mathematics had not to do with things, but the relations of things, and it was sufficient that those relations should be supposable; and that the certainty of mathematical

reasoning rested upon the fact, that those relations could be more readily understood and completely defined, than the properties of the things themselves.

He stated moreover, that these were constituted relations, and not mere figments of the human mind; the things which we had to deal with, being made, in certain respects, not merely what they were but . as they were. Thus, that two bodies did not occupy the same space, and that it was true that one day of the week must follow another, were not true because his audience and himself might think so, but because the Creator had made them so.

He next commented upon the general term which was used to designate that to which mathematical reasoning was applicable; viz. quantity; and said, that in so far as mathematics had to do with it, it was that which admitted of the distinction of greater or less. Moreover, quantities were of the same species when each in itself exceeded its less in the self same respect in which the other in itself exceeded its less; whatever might be true of the boundaries or limits of either. Thus, a straight line and a curve were of the same species, since each exceeded its less in length; so, also, an hour and a minute were of the same species, since each exceeded its less in duration.

He remarked, that the only point of resemblance between quantities of different species was to be found in the fact, that the distinction of greater and less was admissible in the case of every species; and hence it was possible to compare the ratio of two quantities of one species, with that of two quantities of another species. He proceeded to the more special consideration of the two great relations of things, time, and space; remarking, that space might be described, as that wherein there was room for the separate existence of material substances; and duration, as that wherein there was room in another sense for the separate, and therefore successive, occurrence of events.

He next commented upon the nature of zero; showing that it implied the absence of the species of quantity which happened to be the subject of investigation, and not the absence of every other. That, thus, the surface which bounded a solid quantity, was not somewhat in the same sense in which the solid was somewhat, viz. in the property of occupying space, but only somewhere, viz. where the solid terminated, and space met it; the space without met it, though that surface was still somewhat in superficial extent. That the line which bordered the surface was not somewhat in this last respect, but only somewhere; though still somewhat in length.