measure with its corresponding weight would enter, such omissions could of course not be permitted.

Reducing and comparing with each other, each of the eight arcs, he obtains twenty eight binary combinations, which he communicates in detail; but this can only be for the purpose of showing the impossibility of an agreement by the assumption hitherto made. For instance, the Russian arc compared with the English gives 277, the French compared with the English gives, and the deviations from the general mean are still greater in comparing the Prussian and Pennsylvanian arcs with all the others. It is thence inferred that the meridians of the earth are not equal to each other, and thence that the equator and the parallels are not circles, so that it is generally impossible to draw a great circle on the earth's surface anywhere.

Meridians different in form and length really indicate different polar compressions, a non-agreement of the results found, proving nothing against the accuracy of the measures.

Now since all meridians must converge at the poles they must all have in common one and the same diameter, viz., the smallest (the axis of rotation) which can be obtained from each of the large arcs referred to.

The three greatest measured arcs are

the Russo-Scandinavian.
"Indian

"French.

= 25° 20′ 08′′.5,

=21 21 16 6,

= 12 22 12 4,

whilst all the others, including those not used by the writer, are less than 5° in extent.

By dividing each of these three arcs into two equal parts and comparing one part with the other and also each part with the whole, the writer obtains the following mean values:

In the first two, the differences are unimportant, but the last shows a greater deviation. Schubert remarks that this latter deviation can be got rid of by changing the latitude of Carcassonne, the selected point of division of the French arc, by 1"-96, which may not exceed the limits of uncertainty. He considers it safer, however, to obtain the semi-minor axis from the first two arcs alone, the greater arc (the Russian) having twice the weight of that of India. In this manner he deduces the semiminor axis:

3261467.9 toises.

SECOND SERIES, VOL. XXX, No. 88.—JULY, 1860.

By means of this value the semi-major axis can be found for each measure of an arc. It results as follows:

For the meridian of Kaliana in Long. 95° 20′

3272581.3

(6 " Dorpat
“ Tarqui

66 44° 23' 10" 3272650-1 "298° 44′ 3272382.8

Three radii and their included angles suffice for the determination of the ellipse. The writer finds for the semi-major axis

of the equatorial ellipse

and its direction

3272671-5 toises

58° 44'

for the semi-minor axis of the equatorial ellipse 3272303-2

and its direction

Compression of the equator.,

Polar compression of the greatest meridian

and the separate arcs calculated with these values have the following deviations:

In reference to the arcs showing greater deviations the writer remarks that the Pennsylvanian arc was measured with imperfect means (by the chain only, and without triangulation) and that he has taken it merely for trial.* The other seven deviations are so small that no one exceeds the ten thousandth part of the measured length, and the great accnracy of the Peruvian measure, which had been already shown in former discussions, appears here in its true excellence. Honor is justly due to the memory of the men who, at so early a period, accomplished such a work under the untold difficulties of ten years' separation from all ciyilized countries.

It has frequently been shown that the geodetic measures, in particular the longitudes, do not harmonize with astronomical observations, but no one has yet succeeded in discovering the cause of this disagreement. The ellipticity of the earth's equator, as discovered by the writer, will call forth new investigations,

* Dr. Maskelyne in his description of Mason and Dixon's base (Phil. Trans., London, 1768) says they employed rods of fir frequently compared with a standard brass measure at a fixed temperature. This line was revised in 1849 and 1850 by Lt. Col. Graham, U. S. Top. Eng. See Message of the Gov. of Md., &c., in relation to the intersection of the boundary lines of the States of Maryland, Pennsyl vania and Delaware. Washington, 1850.

since it shows that each geodetic survey, and particularly the longitudinal differences, require correction. The writer shows from two examples how we must proceed and what we may expect.

Between Pulkowa and Dorpat the difference of longitude was found as follows:

The first error is thus completely got rid of and the second is reduced to nearly one half.

The writer concludes with the following remarks:

"This determination of the earth's figure is only an approximation, subject to many improvements, when we have more data, and when we use more rigorous methods of reduction. But it shows that we can obtain an agreement of the measures in which we have not heretofore succeeded. The determination of the general figure of the earth does not exclude local irregularities of its surface.

When this hypothesis of the earth's figure, after a scrutinizing investigation, finds general adoption, all geographical positions determined by geodetic means must have corrections applied, which will refer principally to the differences of longitude."

As much as I may agree with this view and as certainly as the importance of the object requires the application of rigorous methods, it is yet clear that the trouble will be sufficiently rewarded when further reliable data, particularly from the western hemisphere, shall be available to the computer. It may be remarked here that the meridian in the western hemisphere corresponding to the small equatorial axes passes through Newfoundland, and, in the eastern, through the Amoor country and Eastern Siberia. For these countries we have at present not even approximate determinations. The Pennsylvania measure of 1764 is worthless for accurate investigation and the superior Peruvian measure is at too great a distance. Measurements of

arc in the meridian of Irkutsk and extending through Mantchooria southwards, through the Chinese empire, as well as the Atlantic States of the American Union* will give us the smallest meridian of the earth with the same accuracy, corresponding to the determination of the greatest, which passes through Eastern Europe (Kostromo, Stawropol, Erzerûm). Still, much requires to be done. The continuation of the Russian Survey through Turkey, and if possible to Eastern Africa, would be most important; and Struve has already (in 1857) advocated it in the Paris Academy. The opposite part of this greatest meridian passes over the icy deserts of North Western America and the group of islands known as the Marquesas, and hence afford no possibility of its completion on that side.

After this article was printed, the writer received the account of the New British Survey and notice of the correction of a small error of computation. This induced him to reprint some of the sheets on which the numerical results are given as above.

It will hardly be necessary to add anything in praise of the author. To bring up a question of such importance is sufficiently praiseworthy in itself, but the writer has done more; he has opened the way to a final determination and has given it, at least in its general aspect. We shall rejoice if this interesting subject calls other powers into the field to labor further in this direction. Corrections like those which the writer has made for Dorpat and Warsaw will be required for many other places, and each comparison of this kind furnishes its share to the final determination. MÄDLER.

ART. VII.-On the Transit Instrument as a substitute for the Zenith Telescope in determining Latitude, and on the Latitude of New Haven; by Prof. C. S. LYMAN.

THE method of determining latitude by measuring micrometrically the difference of meridional zenith distances of stars on opposite sides of the zenith, known commonly as Talcott's method, strongly commends itself to observers, both by its beautiful simplicity, and the very great accuracy of its results. It is the method of late years exclusively used in the operations of the United States Coast Survey, and may properly be regarded as one of the many excellent incidental fruits of that great National work. A special instrument, however, the zenith telescope, has been required for making the necessary observations, and sup

* It may be stated in connection with this subject that the geodetic surveys of two arcs, one in the New England States, the other on the Chesapeake Bay, are already completed and the astronomical part of the former is nearly so, promising an important result derived from the labors of the U. S. Coast Survey at no distant time.

posed to be indispensable for this purpose. It indeed admirably answers the end for which it was invented, and in respect to simplicity, convenience, and efficiency, leaves almost nothing to be desired. But being expensive, and of limited use, it is likely to be in the hands of but few observers. The suggestion, therefore, of additional instrumental facilities for using this method of latitude, so as to render it more widely available, may not be considered as without value.

At the recent meeting of the American Association, at Springfield, the writer, in a brief communication, pointed out the facility and efficiency with which a transit instrument may be used as a substitute for the zenith telescope, in such observations. The object of the present article is, in part, to exemplify further the same point, and at the same time to place on record the results of a more careful determination, astronomically, of the lat itude of New Haven, than, so far as appears, has heretofore been attempted.

The essential parts of the zenith telescope, as an instrument for determining latitude by Talcott's method, are its level and micrometer. And the superiority of the method itself rests mainly on the fact that its results depend on these simple and efficient instrumental means, instead of on graduation. It is obvious, that a transit instrument with a declination micrometer and a suitable level attached to its finding circle, is, at the same time, essentially a zenith telescope, and is capable of performing the whole work of that instrument as accurately, if of corresponding size and quality, and as conveniently, if furnished with a reversing apparatus. The advantages of such a use of the transit instrument, in a multitude of cases, scarcely need to be pointed out. Where both latitude and longitude are to be determined at the same station, as is usually the case, a single instrument will suffice for both, and thus half the ordinary equipment for the purpose may be dispensed with. The corresponding diminution of expense will be a consideration of weight where pecuniary means are limited, as will also the saving of transportation, in the case of boundary and other surveys in remote and uninhabited districts. The observer who has at command such an instrument, even of very moderate size, will have it in his power to fix his latitude with a degree of precision scarcely surpassed even in first class observatories.

The transit instrument with which the observations were made, the results of which are given in this article, has an object glass (by Fitz) of two and six-tenths inches aperture, and thirty-five and a half inches focal length; a filar-micrometer, so constructed as to be used with equal facility either in the plane of the meridian or perpendicular to it; and a twelve inch circle, (graduated on the new and excellent engine of Messrs. E. & G. W.