Vol. 1. JANUARY, 1874. No. 1. INTRODUCTORY REMARKS THE PRESENT is eminently a period of activity, both physical and mental. Science is daily developing new truths, and thereby increasing the sum of human knowledge. Guided by analysis, the mechanic is daily improving and perfecting labor-saving machinery, thereby augmenting the amount of human hapiness; and the astronomer is re-examining his conclusions, and, with the help of new and improved instruments, correcting his data, thereby perfecting our knowledge of the extent and harmony of the material universe. As a knowledge of the laws of natural phenomena (and as a consequence the happiness and welfare of mankind) is promoted by community of mind, it is believed that by such an intercourse of thought as this journal is intended to induce, the sum of human happiness will be increased. The editor is fully aware that no effort on his part alone can make such a publication as this is intended to be generally interesting to its readers; he only hopes for success in that respect by enlisting as contributors a majority of its readers. He therefore invites all who may feel an interest in its success to contribute to its pages their best thoughts and most valuable conclusions, embodied in brief and concise notes or essays. As the scientific characte of the ANALYST has not been fully explained by circular, we embrace this opportunity to state that, as its title imports, it is intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure or applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy and engineering. We are fully aware of the difficulty of publishing such a periodical as we have above indicated, and of the apparent presumption of attempting it at this place, where we have no prominent institution of learning, nor the facilities for printing that might be obtained farther east. Nevertheless, as there seems to be an obvious want of a suitable medium of communication between a large class of investigators and students in science, comprising the various grades from the students in our high schools and colleges to the college professor; and moreover, as we have been encouraged by kind с words, and promises of assistance from various eminent teachers and professors, which, from the contributions received for this our first number, we have reason to believe will be fully realized, we have determined to venture the publication. We invite, and expect to obtain, the following two classes of persons as readers of our Journal, viz: 1st, Those who are able and willing to communicate valuable information through the Journal; and, 2nd, Those who desire to increase their stock of knowledge and shall find that desire partly supplied by the Journrl. All who feel an interest in the success of the Journal are respectfully solicited to co-operate with, and assist us in extending its circulation. We earnestly solicit contributions for publication from all who desire to promote the interest and usefulness of the Journal. In selecting matter for publication each month, we will present such as we may think most inteaesting or of greatest utility. We will publish from three to five mathematical questions in each number, and will endeaver to select such as are believed to be new, or as seem to possess special interest, and will try to grade them so as to suit the different degrees of advancement of our readers. The solutions to mathematical questions will, in general, be published in the second No. succeding the one in which the questions are published. ON THE RELATIVE POSITION OF THE ASTEROIDAL ORBITS. BY PROF. DANIEL KIRKWOOD. The Annuaire du Bureau des Longitudes pour l'an 1873 contains the elements of the orbits of 115 minor planets. The mean number of perihelia for every 15° of longitude is therefore 4.79. It is proposed to inquire whether any marked irregularity obtains in their distribution around the ecliptic. Of the 115 asteroids in the table only 27 have their perihelia between 150° and 300° of longitude. This is a mean of 2.7 for evry 15° of arc; while the average number for every 15° of the remaining 210° is 6.29. Again: a similar irregularity is found in the postion of the ascending nodes; the region of sparse distribution being less extensive than the former. but included within it. Thus; between 225° and 285° we find but 5 ascending nodes, or 1.25 for 15°; while the mean for the remaining 300° is 5.5 for each are of 15°. Is this striking disparity merely accidental? or has it resulted from the operation of a physical cause? The fact may perhaps be sufficiently explained by the remark of Prof Newcomb that "there is always a tendency in the perihelia of the asteroids to coincide in longitude with the perihelion of Jupiter and in their nodes to coincide in longitude with the nodes of Jupiter." THE RECURRENCE OF ECIPSES. BY PROF. DAVID TROWBRIDGE, WATERBURGH, N. Y. That eclipses recur in the same order in a cycle of about eighteen years was known to the ancient Chaldeans, who probably discovered the period from observations, by comparing together the records of maney eclipses. This period, which they called the saros, must have been of great advantage to the ancient astronomer in predicting eclipses; since a record of all the solar eclipses (on an average about 41), and of all the lunar eclipses (on an average about 29) in the order in which they occurred, during any one of the complete cycles, would enable him to predict approximately the eclepses of the next succeeding period or cycle. The coincidences required, however, are not sufficiently exact to give more than approximate results; and if there are several intervening cycles, the recurrence is not very reliable even as an approximation. I have never seen in any astronomical work any other periods referred to,(though it is quite possible that some work may contain such reference), though other and much more exact periods exist, and one of them only about three times the length of the saros, as I shall now show. According to Bessel the length of the sidereal year is 365.2563582 mean solar days. The mean sidereal revolution of the moon's nodes is equal to 6793.39108 mean solar days. The revolution of the moon's nodes being accomplished in a direction opposite to the apparent revolution of the sun, if they set out together at any time, they will again come togeiher in less than a year; or really in 346.619849 mean solar days. This is called the mean (as all these periods are mean periods) synodical revolution of the moon's nodes. The mean synodical revolution of the moon, or the period from one new moon to the next succeeding new moon, is 29.5305887 mean solar days. The several approximate ratios of these last two numbers will make known to us the time required for the sun, moon and nodes, all setting out from the same point in the heavens, to return, approximately, to the same relative mean position. If we reduce the ratio of these periods to a continued fraction, we shall have The several approximate ratios, or the sums of the partial fractions, are 11, 12, 35, 47, 223, 716, 3808, 179457, &c. 199 3249 The fifth ratio in this series is that known as the saros. The sixth and seventh, so far as I know, have not been given before, and the eighth one is too long to be useful. The errors of the periods are as follows: 297.5305887×223=6585.32128=18" (of 365 days) and 15.231. 294.5305887×716=21143.901509=57%. (of 365 days) and 338.901. 3464.619848 ×61 =21143a.810728. Difference, 6.090781=2".1787. 294.5305887X3803=1123044.828826=307"(Of 365 days) and 249.828 346.619848 ×324 =112304.830752. Although these numbers are the mean values, yet the true values will only change the character of the eclipse, and not prevent it from taking place. This is especially true in the periods of 57 and 307 years. Ten successive recurrences of the 307-year cycle will not be half an hour from exact coincidence. It seems, therefore, that this period will serve as a check in computing the time when ancient eclipses happened. A total eclipse of the sun is referred to by Herodotus, which has been the subject of much discussion. Baily placed it by his calculations on the 30th Eight times the 307-year cycle brings us to the of September, 610 B. C. 28th of July, 1851, the great total eclipse of that year. Prof. Airy's calculations fixed the time of the eclipse on the 28th of may, |