regard to the known laws of the diurnal irregularity, and of the ordinary tides.

Each determination gives a corresponding value of the maximum, or of the ordinate of high water, and in the case of the mean of the curves for January, February, and March, these maxima are 0.66 feet, 0.65, 0.60, 0.60, 0.58, 0.58. Mean 0.61 feet, differing .03 of a foot from the maximum found directly from the observations, and if the discrepancies are accidental, giving a mean probable error by the variations from the average of 0.02 feet (one-quarter of an inch) of any one of the determinations, and for the mean, 0.01 feet nearly.

9. By the kindness of Colonel Abert, of the topographical engineers, of Major Bache, of the same corps, and of Lieutenant Maury, superintendent of the National Observatory, I have been put in possession of tidal registers which have been kept during the progress of the local surveys made of harbors on the coast of the Gulf of Mexico. The tidal observations of Major Bache, United States topographical engineers, at Key West and the Tortugas, are the most complete of this series, and show, as a general phenomenon, the prevalence of the semi-diurnal wave at that point. I have not yet had the opportunity to examine fully these results, which are, however, under discussion.

APPENDIX No. S.

Method used in the Coast Survey of showing the results of current observations, by Professor A. D. Bache, Superintendent.

This method, while it is original. may not be new, though I am not aware that the system has been followed by others. It has some analogies with the representations of Berghaus, but is different essentially from them. The principle, and an application to the very elaborate current observations made in Boston harbor, under the immediate direction of Lieut. Charles H. Davis, by Lieut. J. N. Maffitt, are shown in the diagrams now presented to the Association.

Observations of the direction and velocity of the currents at and below the surface have been extensively introduced into the hdrography of the coast survey; their importance needs no remark. For most of the details of arrangement and suggestion in regard to the earlier observations, I am indebted to my brother, the late Lieut. Geo. M. Bache, U. S. N.; for much of the success of execution to Lieuts. Charles H. Davis and Carlisle P. Patterson, U. S. N., who have taken unwearied pains in the matter. For currents below the surface there is still wanted some sure and easy method of determining both direction and velocity, especially the latter elements.

Observations being multiplied at different periods of the current, from slack-water to slack-water, they are projected upon diagrams, showing at a glance the direction and velocity at any particular station. The average of the results is usually obtained by inspection. Dividing the intervals between slack-waters into quarters, we give the mean results for those periods in a table, and place usually upon the chart arrows

indicating the direction or set, and write at the extremity, numbers showing the velocity or rate in miles per hour. In case of the observations made in Boston harbor, the results are so unusally numerous that the lines of direction were confusing to the eye, and the connexion between the results was very difficult to seize, though from the pains taken, the motion of the water was traceable in nearly all its peculiarities, from the entrance through the tortuous passages among the islands, alternately narrowing and expanding to the city wharves.

In the current chart now brought before the Association, the direction and force of the currents are represented by lines, the distance between which is inversely as the rate in miles per hour. The scale was obtained by making the least velocity correspond to nearly half an inch, and the greatest to 0.06 of an inch. The reciprocals of the number of miles per hour are represented by tenths of inches in the diagram, currents of 0.2, 0.5, 1, 1.5, 2 miles per hour being represented by lines parallel to their directions, and distant 0.5, 0.2, 0.1, 0.67, 0.05 of an inch. The chart is on a scale of 200,000. The representation on one of the diagrams corresponds to the flood, and in the other to the ebb, referring to the motion of the current from slack-water to slack-water. If the current stations were very numerous, the straight lines tangent to the curves of motion of the water (set of the current) would become curves.

It is easy for the navigator to seize the relations of the currents he will meet, even by these tangent lines, to avail himself of the knowledge this imparts of the direct, lateral, and eddy currents, to avoid danger or secure advantage.

The cause of the change of directions and velocities is in most cases well marked, the generalization presented to the eye being connected with the form and position of the land above or below the water. In some cases the chart indicates that the observations should be repeated; and in others that, numerous as the stations are, they should still be increased in number. Its adoption will probably thus react, to improve the observations upon which it is founded.

APPENDIX No. 9.

Report of Professor O. M. Mitchel, Director of the Cincinnati Observatory, to the Superintendent of the Coast Survey, on a new method of recording differences of north polar distances, or declination, by electro-magnetism.

DEAR SIR: I have delayed thus far sending you any detailed account of the new methods of astronomical observation in use at the Cincinnati Observatory: partly because the subject was constantly developing by new experiments, and partly because at the New Haven meeting of the American Association for the Advancement of Science, this subject, at my request, was referred to a committee for examination. The report of this committee having now been made, and the whole subject having assumed (by another year's examination and experiment) a more definite and positive form, it is now proper to present some general features of this new method, some results already

reached, and the probable applications which remain to be made when suitable instruments shall have been provided for the purpose.

Observers are well aware of the difference between observations for right ascension and declination. In the first the principle of repetition has been extensively introduced, with the best results; while as to the other, reliance is mainly placed on the accuracy of a single bisection of the star observed on one declination wire. More than two years since a plan had been executed by myself, and applied to practice in the Cincinnati Observatory, by which, on the same night, during one and the same transit, a star or other heavenly body could be observed on ten declination wires, with all the precision due to a single observa tion by the old methods. More than a year has elapsed since I presented to the American Association some three thousand observations, taken in twelve nights by the new apparatus (a number exceeding the recorded observations of a whole year at one of the oldest European observatories.) Each of these observations presented an accuracy superior to those obtained by the old methods.

This astonishing rapidity and accuracy gave rise to a debate, and, finally, to the appointment of the committee above alluded to. A multitude of observations have been made during the past year, (and in accordance with the request of the chairman of this committee,) varied, with a view to test in every way the powers of the new machinery. The results, as will be seen by examining the report of the committee, were entirely satisfactory.

It is proper now to state, that by the new invention, the transit instrument is converted (at trifling expense) into a declinometer, or instrument for measuring N. P. D., or declination. The observer is released from the necessity of reading a divided circle, and the position of his instrument at the moment his star is bisected by the declination wire, is, by a single touch, engraved on metal, and stereotyped, to be read and examined when convenience may permit. On the swiftest moving stars, ten bisections are readily accomplished and engraved in the space of a single minute of time, and at a maximum hour angle of only thirty seconds of time. These records are now made on a circumference whose diameter is nearly twelve feet, and finally read up by a micrometer of as great perfection as can be applied to the measurement of any minute distances. The instrument used thus far is a transit by Dollond, the property of the United States Coast Survey, and furnished by the Superintendent of that work. It is of old construction, about five feet focus; and although the definition of its object-glass is satisfactory, yet the optical power is low, and a bisection by it is far inferior to one made with a powerful object-glass. The new machinery attached to this transit, to convert it into a declinometer, was made in the observatory by my assistant and myself, and is, of course, comparatively rough. The micrometer was made in this city, and although of workmanship highly creditable to the artist, yet, as it is the first ever constructed on this plan, it has been found comparatively defective, and quite incapable of detecting with certainty the minute quantities which have been presented for its examination. Perhaps no micrometer has ever been submitted to such severe tests.

Thus far in the application of the new methods, my examinations

have been confined to zones not exceeding twenty-five degrees in width. There is no difficulty, however, in extending these researches through the entire heavens, and comprehending on the same night the entire sweep of the meridian from north to south.

In case a known catalogue is under review, the amount of work done during the night will depend solely on the rapidity with which the finders of the telescope can be set. If we allow for each star three minutes, (which, with an assistant to set, has been found sufficient,) we have without difficulty two hundred observations on twenty different objects within the hour, and for a night's work of five hours, one thousand wires or observations recorded on one hundred stars or other objects. If, however, the work done is independent of any catalogue, and we are sweeping the heavens in zones, there is no difficulty in recording both right ascension and declination on single wires just as rapidly as the stars present themselves, even up to three hundred stars per hour of time. This has actually been done. For the purpose, therefore, of cataloguing the heavens, the new methods offer advantages of the highest importance.

We now present some of the results tending to demonstrate the degree of precision already reached in the determination of the differences of declination. As the whole subject was entirely new, no advantage could be gained from the experience of other observatories, and hence the difficulties which have been met were encountered under the most unfavorable circumstances. Having, however, implicit confidence in the great principles involved in the new machinery, I never doubted for a moment that the discrepancies which arose would finally be traced to mechanical defects, or to accidental and unanticipated causes.

My attention has been exclusively directed to this single point: within what limits of error could the new apparatus repeat its own work on different nights on stars whose difference of declination varied from a second or two of are up to 25° or 30°?

To convert the records into degrees, minutes, and seconds, presents no serious difficulty, and has, therefore, not as yet occupied my attention further than to demonstrate with certainty its practicability.

In my very earliest observations with ten declination wires, more than two and a half years since, a simple inspection of the record in the shape of ten delicate wedge-shaped dots on metal, with a powerful microscope, demonstrated at once the perfection with which these records were made within the narrow space occupied by these ten dots. The wires were as nearly parallel and equidistant as we could place them. Yet the small inequalities of distance were always measured with a precision only limited by the power of bisection under the circumstances existing during the observation. When the weather was tranquil and the stars steady, the most admirably accordant results were reached: on the contrary, when the stars were dancing or ill-defined, discrepancies were recorded doubtless due to errors of bisection. It is quite unnecessary to present the evidence of accurate movement within the above narrow limits, inasmuch as the wider range of observation will include the more restricted.

When, on a comparison of the work of two different nights, the discrepancies were reduced to the fraction of a second of arc, it became

manifest that the micrometer was (as built) incapable of measuring with certainty such minute quantities. I had neither time nor means to build a new and more perfect instrument; and finding the micrometer reliable for half a dozen revolutions of the micrometer screw, a method of intercomparison of the work of two different nights occurred to me, which, with my defective micrometer, would test in the most absolute manner the powers of the new machinery. This was as follows, viz: The stars of the catalogue were observed during one night on the odd wires, 1, 3, 5, 7, and 9, leaving the spaces blank on the engraved record, which corresponded to the even wires, 2, 4, 6, 8, and 10. Everything remaining untouched, on the following clear night the same stars were observed on these even wires, and thus a decade of dots was recorded, of which five were engraved on one night, and five others on the following one.

These records thus intermingled and interlocked, were now easily read by the micrometer; and falling, as they did, within the limits of reliable performance of the micrometer, the capacity of the instrument to repeat itself on different nights was tested in the most absolute manner, no matter if the stars observed comprehended a zone of even 25° or 30°. It is proper to remark that in all these observations I was assisted by Mrs. Mitchel, the stars being taken by us alternately; the reading up was done principally by herself, while the duty of recording fell to me. In this way the results reached would be independent of any personal idiosyncracy, while the readings being made by one person and recorded by another, no bias could possibly be given to the person reading.

In our first experiment of interlocking observations, forty-eight hours elapsed before it became possible to remove the metal plate from the pier, during which interval of time there were constant changes in the atmosphere, with storms of rain and wind. It was therefore with no small anxiety that, on closing the observations, the microscope was turned upon the decade of dots, the work of two nights, at intervals of forty-eight hours. The examination was in the highest degree satisfactory. The dots were placed with a precision and beauty perfectly astonishing, and no eye, thus far, with the microscope itself, has been able to mark the difference between a decade of dots struck on two different nights, and one struck all on the same night. It did not require the micrometer screw to decide the question as to whether the instrument had repeated itself on the two different nights. This was obvious from a mere inspection of the dots by the microscope. In two instances on the extreme stars there was a slight deviation from the uniformity of the placing of the dots. I suspected this to be owing to the action of the wires attached to the arm and conducting the current from the battery through the electro-magnet. Ample length was given to the wire, but there yet remained in it a sufficient stiffness to affect the place of the arm in its extreme positions, by a minute amount. This was fully demonstrated by experiment on the following night. A star was brought to bisection on a wire, and while thus located the conducting wires were gently touched by the hand of the observer and the instrument was seen to yield to every touch. A source of error was thus detected, of a minute character indeed, but of vast importance