The author discusses anew the expressed values of the distances in question, in view of the fact that Kepler's third law is itself slightly modified by the consideration due to the masses of the revolving bodies. After an exhibition and discussion of the appropriate formula, the author arranges the results in the form of a table; in which the results thus shown are respectively consistent with two values of the solar parallax, viz, Professor Newcomb's value, 8".848, and that which others prefer, x = = 8".78.

=

Section II exhibits the laws of arrangement of the distances, both of planets and their satellites, from their respective centers of attraction, without the introduction in the same connection of any physical bypothesis on which those laws seem to be founded or of which they are the exponents.

From a comparison of the several distances of the planets, taking five. ninths of the distance of Neptune from the center of attraction and fiveninths of this product, &c., he finds among the several terms of the geometrical series thus formed, those which represent the relative dis tance of Saturn and Jupiter, also a position among the asteroids and those which represent the distance of Mars, and of Mercury in aphelion. There are, however, in the geometrical series just mentioned, terms which do not find their correspondences in the series of distances of the planets, but which the author very ingeniously supplies by attributing to certain of the planets the characteristic of half planets, the term pertaining to them being indicative of the distance between the two planets at which their masses would be united.

Section III exhibits an explanation of the phenomena founded on the nebular hypothesis of La Place, which seems to reconcile and account for the laws in question as well as a number of other phenomena.

Approximation to these laws have, from time to time, been exhibited by the author of this paper to the American Association for the Advancement of Science at several of its meetings, beginning with that at New Haven, in 1850; but it is only within the past few months that the entire form and consistency of the results have been quite fully made out. The principal part of the memoir was read before the National Academy of Sciences at its meeting in April, 1873, and some additional portions of the same at the meeting in April, 1874. In accordance with usage in such cases, the work was accepted for publication in the Smithsonian Contributions to Knowledge.

3. The Winds of the Globe, by the late Prof. J. H. Coffin, prepared at the expense of the Institution, relative to which further information will be given under the head of meteorology. Of this, 250 quarto pages have been stereotyped, and the whole work, which will form an entire volume of the Smithsonian Contributions to Knowledge, will be published during the year 1875.

4. The Temperature-Tables of the North American Continent, prepared

at the expense of the Institution, under the direction of Mr. C. A. Schott. Of this, 100 pages have been stereotyped.

Of the octavo publications there are in press:

1. The monograph on the American Vespida or wasps, by Professor de Saussure, of Geneva. Of this a full account was given in the last report. The rapidity of printing in this case is diminished by the neces sity of sending the proof-sheets to Switzerland. The work has been stereotyped as far as the 236th page, and we trust will be completed in the course of a few months.

The Botanical Index, of which a notice was given in the Report for 1870, has been commenced, and 72 pages printed. This work is a complete index to all the species of plants of North America, with their synonyms, and all descriptions and important references to them. It is intended to facilitate the labors of working botanists, especially in the study of our western plants, the search for what has been written in regard to them requiring in many cases nearly as much time and labor as all the rest of their work.

As a further contribution to the "Constants of Nature" mentioned in the last report, Prof. F. W. Clarke has furnished an additional series of tables of specific heat and of expansion by heat for solids and liquids. We have also received from our collaborator, Prof. John L. LeConte, of the University of California, a series of constants relative to the weight of air, pressure of the atmosphere, length of seconds, pendulum-velocity generated by gravity in a mean solar second of time at various places, velocity of sound, &c. It is the intention of the Institution to continue this work, and to endeavor to enlist other co-laborers in its prosecution.

RESEARCHES.

Meteorology. It was stated in the last report that the meteorological system of records by voluntary observers, which had been in operation under the direction of the Institution for about twenty-five years, had been transferred to the signal-office of the War Department, under General A. J. Myer. This transfer was made in accordance with the general policy of the Institution, namely, that of abandoning any field of enter prise as soon as the work could be done as well through other agencies, thus reserving the energy of the establishment for labors which required more aid in their accomplishment. We think this transfer has received the approbation of observers generally; who also, while they are now co-operating with the Signal-Service, still keep up their correspondence with the Institution on subjects of general scientific interest. The labors of the Institution in the line of meteorology are now confined to working up the material which it has collected during the last quarter of a century. The materials, however, are not limited to that period, but embrace everything that could be obtained on the subject from the records of previous observers.

The first work of this class which has been published is that of the the Rain-fall. It included all the material which had been collected down to 1866. It is now proposed to publish a new edition of this work, containing the additions since made, with improved maps, on a larger scale.

The next work of the same class is that on the Winds of the Globe, comprising the result of the discussion of not only the observations. made under the direction of the Smithsonian Institution in the United States, but of those of every other part of the world of which the records were attainable. This work, to which the labors of Prof. J. H. Coffin, of Lafayette College, were for many years devoted, was nearly completed at the time of his death, has been continued by his son, Prof. Selden J. Coffin, and is now in the press. Very little, however, was done by the elder Coffin in the way of stating, in general propositions, the results contained in the large number of tables which he had elaborated. To supply this deficiency the Institution has fortunately been enabled to avail itself of the assistance of Dr. A. Woeikof, member of the Geographical Society of Russia, and late secretary of its meteorological commission, who, visiting this country for the study of its climatology, cheerfully undertook the required task.

The printing of this work is very expensive. It will occupy an entire volume of the Smithsonian Contributions, and comprise upward of 600 quarto pages of tabular matter, besides the letter-press. It will, however, we are confident, form a contribution to knowledge which will be a lasting monument to the industry of Professor Coffin and to the policy of the Smithsonian Institution.

The next work of the same class is that on the Temperature of the United States. It has been in progress at the expense of the Institution for a number of years. It includes the result of the discussion of all the observations which have been made in this country from the earliest times down to the present. It is illustrated by three maps of isothermal spaces-one exhibiting the annual, another the summer, and the third the winter distribution of temperature-and a number of diagrams incorporated in the text. It has been from the first under the direction of Prof. Charles A. Schott, of the Coast Survey, assisted by a number of computors, at the expense of the Smithson fund. The maps have been drawn and are in the hands of the engraver, and the whole work will be printed and distributed during the present year. It will form the first trustworthy approximation to an exhibition of the temperature of the various portions of the United States which has ever been published. The preparation of it has been more expensive than any other work ever undertaken by the Institution.

Another work in progress is that relative to the geographical distribution in the United States of thunder-storms, the frequency of their occurrence in different seasons, and effects produced by discharges of lightning, as compiled from all the records of the Institution during

twenty-five years. The preliminary labor was the collection and arrangement of a full list of stations at which thunder-storms have been recorded, the number of observations at each place, the time of beginning and ending of each storm, and the whole number of thunder-storms occurring in each year, and during the whole time at each place. From these data the relative frequency of thunder-storms in different parts of the country can be determined; also their relative frequency in different seasons and years, as well as the extent of the area over which they occur on the same day. The attending casualties, collected from all the observations made by several hundred observers during a period of twenty-five years, when brought together and classified, will strikingly illustrate the operations of one of the most energetic agents of nature. For the preliminary arrangement of the materials preparatory to scientific deductions from them, the Institution has employed Mr. George H. Boehmer.

Another series of reductions relative to the meteorology of North America which will occupy the attention of the Institution is that of the discussion of the observations on the barometer in various parts of the United States. This will be commenced as soon as the other series of investigations are completed.

Comets.-The first research relative to these I have to mention is that relative to a comet of short period or one that returns after a few years. Of these, there are at present six known, namely, Encke's, which has a period of about 3 years; Winnecke's, of between 5 and 6 years; Biela's, of 63 years; Faye's, of 7 years; Tuttle's, of 137 years; and Halley's, of about 76 years.

All the other comets which have entered the solar system have never been known to return, their orbits having probably, in many cases, been changed by the perturbations of planets in whose vicinity they may have passed.

The motion of the periodical comets is an object of great interest to the astronomer, as well as to the general physicist, in its relation to the question of the existence of a retarding medium filling interplanetary spaces, and therefore it is considered an object of much importance, not only to observe their successive positions at their periodic returns, but also to calculate with great precision their orbits as affected by planetary perturbations. At a meeting of European astronomers in August, 1873, the work of discussing all the observations which have been made on four of these comets was parceled out among the continental astronomers, Halley's comet having previously received great attention from the English and other astronomers; and the fifth, that of Tuttle, discovered by an American astronomer, was left to be worked out in this country. This task has been undertaken at the expense of the Smithsonian Institution, under the direction of Prof. Ormond Stone, late of the National Observatory, and now professor of astronomy in the

University of Cincinnati. Professor Stone has chosen for this work a number of assistants, and will proceed with the reduction and discussion of the observations made on this comet at its several returns as rapidly as his other labors will permit.

The perturbations of the first order have been calculated, and the zerostars used in determining the place of the comet at the time of its last return in 1871 have been re-observed with the Washington meridian circle. An accurate determination of the orbit traversed by this comet in 1871, as based on the corrected position of these stars, has been in part completed.

In this connection it may be interesting to state that of the one hundred and forty asteroids discovered during this century, forty-two were first observed by American astronomers. It is not enough, however, that these bodies should be noted as planets, and their positions marked in the heavens for a given epoch; it is also necessary that their orbits should be accurately determined, and an ephemeris of each of them calculated by which its place can be ascertained at any future time. This work, however, is one, as it were, of approximation, and must be continued through a series of revolutions of each planet. In regard to the asteroids discovered in Europe, the investigation of them is under the charge of European astronomers; while for the investigation of those discovered in America, Congress has made an appropriation for the last three years, to be expended under the direction of Professor Coffin, director of the American Nautical Almanac.

Efficiency of steam-heaters.-Another investigation, at the partial expense of the Smithsonian Institution, has been undertaken under the direction of General W. B. Franklin, late of the United States Army, at the Colt's Fire-Arms Manufacturing Company, Hartford, Conn., by Mr. C. B. Richards, of which the following is an account:

The experiments which are proposed will be in continuation of two series already made, to ascertain the relative efficiency of the different kinds of steam-heaters used for warming buildings, and to determine also the laws of their operation. The first series related to what are known 23 "direct radiators," and in these the heaters were exposed in a large room whose temperature could be changed and regulated as desired. In the second series the heaters were of the kind called "indirect radiators," and were inclosed in a flue through which currents of air were passed. The initial and final temperatures, the barometric pressure, and the moisture of the air were noted, and the quantity passed through the flue was measured by a Casella meter.

In both series the pressure of the steam was measured by an accurate mercury column, and its temperature was noted, while the heating effect of the heater was calculated from data obtained by collecting, cooling, and weighing the water of condensation obtained from the steam which was passed through the heater.

*Since the above was written two additional asteroids have been discovered.