resting on original research. The first memoir presented, and found to be of the character prescribed by the resolution of the Board, was one on the remains of the ancient inhabitants of the North American continent. It contains the result of several years' labor in the survey and exploration of the mounds and earthworks of the Mississippi valley, and will furnish a highly interesting addition to the antiquities of our country, which could not have been given to the world, but for the timely aid extended to it by this institution. The memoir was referred to the American Ethnological Society, with a request that a committee of its members might be appointed to examine and report on its character, as to fitness for publication in the Smithsonian Contributions to Knowledge. On the favorable report of this committee, and on the responsibility of the Society, the memoir has been accepted for publication. *

The memoirs of Messrs. Squier and Davis will occupy the greater portion, if not the whole, of the first volume of the Contributions. The illustrations will consist of fifty-five quarto plates of the mounds, earthworks, and maps of the adjacent country; also, of about two hundred wood-cuts, principally delineations of the various articles found in the mounds. Those who consider no branch of knowledge of any value but such as relates to the immediate gratification of our physical wants, have objected to the acceptance of this memoir as one of the first publications of the institution; but it must be recollected that the will of Smithson makes no restriction in favor of any particular kind of knowledge, and that each branch is, therefore, entitled to a share of his bequest. The Ethnological memoir of Messrs. Squier and Davis was the first, of the proper character, presented for publication, and hence it was entitled to the first place in the series of Smithsonian Contributions. Besides this, it furnishes an addition to a branch of knowledge which is at this time occupying the attention of a large class of minds, and which cannot fail to be interesting to every intelligent person who would learn something of the changes to which man has been subjected.

One of the volumes of the Contributions will contain a sketch of the life of Smithson, by the Chancellor. The materials for this have been collected from the several volumes of the Transactions of the Royal Society, and the scientific journals of the beginning of the present, and the latter part of the last century. The first volume will be published as soon as the wood-cuts and plates, now in the course of preparation, are finished.

Besides the memoirs before mentioned, a number of others have been presented, some of which though apparently of interest, and the product of thought and labor, were not of the character required by the resolution of the Board, and these have

either been returned to the authors, or are in the possession of the Secretary. A number of others have also been provisionally adopted, or are in the course of preparation. Some of these are on the most abstruse parts of physical science, and all will do honor to the intellectual character of our country. Though the number of original memoirs which will be found worthy of a place in the Contributions will probably not be large, yet it will, perhaps, be best to set apart a definite portion of the income of the bequest-as, for example, at present three or four thousand dollars annually-to defray the expense of this part of the plan of increasing knowledge. A considerable portion, however, of the sum thus expended will be returned to the institution in the form of additions to its library. I may also suggest, in this place, the propriety of the adoption, by the board, of the resolution inviting all engaged in original research, to send the results of their labors for publication in the Smithsonian Contributions.

The Board also directed me to commence the collection of apparatus, and I accordingly sent orders to Europe, to the amount of twelve hundred dollars, for the purchase of such articles as could not be procured in the United States. Most of the instruments have been received, and will be found of importance, not only in the way of original research, but also in illustrating some of the most interesting and recent phenomena of physical science, as well as serving as samples for imitation to the artists of this country. It was thought that these articles would be admitted free of duty, and a petition to this effect was presented to the Secretary of the Treasury; but, though this officer is well known to be much interested in the prosperity of the institution, such is the nature of the law that the duty could not be remitted.

There is an article of apparatus which, within a few years past, has opened almost a new world of research in the phenomena of life and organization, the use of which is now indispensable in advancing our knowledge of physiology and its kindred branches of science. I allude to the achromatic microscope, to increase the power of which, the artists of Germany, France, and England have vied with each other. On account of the small number of persons who are capable of constructing the proper lenses, the best specimens of this instrument are very scarce in this country, and can be procured only at a great expense. Under these circumstances, it was a matter of much interest to learn, from a source which could be relied upon, that an individual in the interior of the state of New York had successfully devoted himself to the study of the microscope, and that he was able to produce instruments of this kind which would compete with the best of those constructed in Europe. In order to do justice to the talents and labors of this person, as well as to furnish the institution with a valuable instrument of research, I requested him

to construct a microscope, to be paid for out of the funds for the purchase of apparatus, provided that a commission, appointed by myself, should find it capable of producing certain effects. This proposition was accepted, and the result will probably be given to the Board at the next meeting.

Preparations have also been made for instituting various lines of physical research. Among the subjects mentioned in the programme as an example for the application of the funds of the institution, is terrestrial magnetism. I need scarcely say that this is a subject not only of high interest in a theoretical point of view, but also in its direct reference to navigation and the various geodetical operations of civil and military life. A resolution of Congress, authorizing the exploration of the mineral lands adjacent to the great lakes, has given to us the means of advancing this branch of knowledge with but little expenditure of the funds of the institution. The Secretary of the Treasury readily agreed to the proposition that there should be added to the mineralogical and geological surveys of these regions, determinations of the dip, the variation, and the intensity of the magnetic forces, provided that the Smithsonian Institution would furnish one set of the instruments, and take charge of the direction of the observations, and of reducing and publishing them. In the survey of the mineral lands in the vicinity of lake Michigan under Dr. Jackson, Dr. Locke, of Cincinnati, has been employed with his own apparatus; and to supply the necessary instruments for the survey in Wisconsin, preliminary steps have been taken to procure other instruments from London.

It

Another subject of research mentioned in the programme, and which has been urged upon the immediate attention of the institution, is that of an extensive system of meteorological observations, particularly with reference to the phenomena of American storms. Of late years, in our country, more additions have been made to meteorology than to any other branch of physical science. Several important generalizations have been arrived at, and definite theories proposed, which now enable us to direct our attention, with scientific precision, to such points of observation as cannot fail to reward us with new and interesting results. is proposed to organize a system of observations which shall extend as far as possible over the North American continent; and in order to this, it will be necessary to engage the coöperation of the British government. I have accordingly addressed a letter on this subject to Lieutenant Colonel Sabine, Corresponding Secretary of the Royal Society, who assures me that, as soon as the plan is fully matured for this country, there will be no difficulty in establishing a system of corresponding observations in the British provinces. I have also addressed letters to several gentlemen distinguished for their attainments in meteorology, asking

for suggestions as to the plan of observation; and I beg leave to refer the Board to the report of Prof. Loomis, of New York University, and also to the communication of Prof. Espy, received in answer. The former contains an exposition of the advantages which may be derived from the study of meteorology, and what has been done in this branch of science in this country, and what encouragement there is for the further prosecution of the same subject, together with a general plan of operations. The present time appears to be peculiarly auspicious for commencing an enterprise of the proposed kind. The citizens of the United States are now scattered over every part of the southern and western portion of North America, and the extended lines of telegraph will furnish a ready means of warning the more northern and eastern observers to be on the watch for the first appearance of an advancing storm.

ART. XXIX.-On a New empirical Formula for ascertaining the Tension of Vapor of Water at any Temperature; by J. H. ALEXANDER, Esq.

(Concluded from page 223.)

In the last number of this Journal, I gave the formula itself, the principles from which it was deduced, and a comparison of results by it, with those by experiment at numerous identical temperatures. Want of room excluded then what remained to complete this Memoir, in shewing the probable errors of the formula as compared with the principal experiments, and with the probable errors affecting too those different series of experiments themselves. Such a discussion is the object of the present paper.

It was already said, in the preceding part, that the most proper mode of expressing these errors is by the linear scale of temperature; which both in theory is the most important, and in practice is the most accessible and usual. In this last aspect, it is on this scale too where errors of observation are the most easy to be made, and likely to occur. With this view, the formula need be repeated here only in its converse form, (i. e., for ascertaining temperatures from given pressures,) as under:

=

to Fahr. 180/p-105°.13; p being in inches of mercury: and

to Fahr. 317.13/p'-1050.13; p' being in atmospheres at 32°.

As this will have to be frequently applied for interpolation throughout the following discussion, it may be as well to remark

here, once for all, in justification of such application, that there need be no apprehension of its affecting the results; for it is easy to see, by inspecting a few instances taken at random from the table, that the rational deviation of the formula (i. e., the difference between calculated and observed pressures) is, for small differences of temperature, either null, or so remote a fraction as to be inappreciable in the calculation.

In applying this formula, I shall take up the principal series of experiments separately, beginning with the most recent; and shall then make assemblage of the mean results.

1. Experiments of Mr. Regnault.-To deduce the absolute mean error of the numerous quantities of this observer, it would be obviously requisite to take up each experiment;-a labor of which I am by no means ambitious, and which would be disproportionate at once to what is admissible in the other series presently to be noticed, and to the present aim. I shall, therefore, in all, only make use of short general methods which, without laying claim to the accuracy of geometrical refinements, will yet be recognized as having foundation in the theory of mathematical probabilities; and will, by their popular form, recommend themselves the more readily to the convictions of those who are chiefly conversant with steam in practice, and for whose benefit the whole of the present discussion is mainly intended.

It is obvious, then, in the first place, that the idea of freedom from error is associated with symmetry in the results. Such symmetry will always be observable in quantities that progress (as natural quantities may be assumed to do) according to some constant law; and as, in our ignorance of what the true law is in this case, all that we can deal with is relative symmetry, it is of no importance what law or formula we take as the other term of comparison, provided there be no material difference between the origin and termination of the two. I shall therefore compare a few of Mr. Regnault's observations at the lower temperatures with the results of the present formula; as under:

It is apparent then, that so far, these observations do not follow any uniform or symmetrical progression; and without pretending to criticize the experiments themselves, which doubtless have as