any short period, this liability is so multiplied by time, and the chances of accident, as to deprive even those which are most carefully constructed of all claim to perfect confidence. In cases where their use is indispensable, as in detached and local surveys, in the cursory examination of distant and inhospitable regions, or in carrying a chain of longitudes around the globe, and generally where strict and careful measurement is for any reason forbidden, their imperfection is in some measure remedied by numbers. Acting as checks upon each other, the amount of error is reduced, and the observer is enabled to fix, with a degree of precision sufficient for the security of ordinary navigation, the simple position of certain points and headlands. This, however, is regarded only as the palliation of an evil; the evil itself is fundamental, and admits of no complete remedy.

In determining differences of time between meridians widely separated, chronometers have sometimes proved remarkably successful, and have exhibited results of surprising accuracy. The reverse of this proves to be the case in the adjustment of minor differences, where the essential defects of the instrument are particularly displayed. There is no space, however small, of perceptible magnitude, which may not be submitted to trigonometrical measurement; but it will be readily understood, that there are points, at minute distances asunder, between which no difference of local time can be estimated. If it be asserted, which we are by no means prepared to admit, that such distances are unimportant in a geographical view, it will appear that they are of the highest topographical value when we come to consider the character of our southern coast.

If chronometers, however, could be implicitly relied on, and the determination of longitudes by means of them admitted of greater exactness, still it is to be borne in mind that their use, in connexion with the sextant, goes so far only, as to decide a certain number of fixed points.

This cannot in any strictness of language be called a survey. It still remains to fill up the intermediate spaces by some sort of measurement, and the mode and result of this operation are questions of serious importance. We need not enter into any detail to show, that a survey of this kind must content itself with the bare outline of coast, harbours, islands, &c., neglecting all the valuable details belonging to

physical and statistical geography, differences of level, and the distribution, limits, and peculiarities of the country under inspection, all of which are included in the operations of a geodesical survey.

We are told, that despatch is one of the recommendations of the chronometric plan. Numerous parties will probably, therefore, be immediately employed, and it will remain afterwards to harmonize their labors by joining the distant points of observation. To do this will, we conceive, be no easy task; and, if such a plan be adopted, we shall not be astonished to learn hereafter, that the attempted meeting of these unconnected operations is likely to break up in the most admired disorder.

We do not mean, in any thing we have said, to underrate the value of chronometers in their legitimate sphere. They might, undoubtedly, be advantageously employed in the preliminary determination of important points on the coast, which are known to be erroneously laid down.

Their accuracy may be depended upon within a mile, and even this imperfect knowledge will be in some degree a relief to navigators, where errors of alarming and uncertain magnitude are known to exist in their charts. Mr. Hassler has, in his letter to Mr. Gallatin, given to this proposition all the consideration it merits.* If such occasional use should be made of them, and the present system of survey should be continued, subsequent comparisons will abundantly prove, that even the simple determination of geographical positions by chronometers (omitting all question of a connected survey), however skilfully and expensively conducted, is unavoidably defective.

In a matter that may be subjected to rigid mathematical investigation, results are anticipated, and conclusions distinctly enunciated. But perhaps it will enforce our argument to exhibit some facts, that have immediate relation to the present inquiry. We select such as are nearest at hand. An attempt was made to determine the place of the Capitol, by means of chronometers, by Mr. Paine of Massachusetts, a gentleman distinguished for his zeal and ability in these calculations. He carried three chronometers from Boston to Washington, through Philadelphia, and back, observing the difference of

*American Philosophical Transactions, New Series. Vol. II. pp. 238,

meridians of the three cities, both going and returning. The results of these are spoken of as important. The difference of his two longitudes of Washington, by Philadelphia and by Boston, is 14."25. The difference between the mean of his observations, and the adopted longitude of Washington is 12."9; whilst Mr. Paine's longitude of Washington differs from the mean of seven results of astronomical observations, solar eclipses, and occultations, by 41."4.*

In the trigonometrical survey of the State of Massachusetts, begun in 1831, and concluded about a year since, embracing a territory of 8230 square miles, we find an exemplification of our argument at once pertinent and conclusive.

A letter from Mr. Simeon Borden, the superintendent of this survey, to the American Philosophical Society, in addition to an account of the work, gives a "comparison of his own results with those obtained by Robert Treat Paine, Esquire, from observations with a Troughton's sextant and mercurial horizon, and chronometers transported to different stations."

In the longitude of Pittsfield the chronometers exhibit a difference of 28."98,- nearly one half of a mile; yet thirtynine chronometers were used in thirteen journeys. The meridians of Cambridge and Dedham are 3.'30."43 apart by trigonometrical measurement; the chronometers give the dif ference of longitude 3.'11."10, making an error of 19."33. In the case of Cambridge, twenty chronometers were used in six journeys, and in that of Dedham twenty-three chronometers in seven journeys. Gloucester and Plymouth, both seaport towns, which ought therefore to be known correctly, coincide in longitude, within 2."10. The chronometers have increased that difference to 8."55. This instance illustrates what we have before said of the incapacity of chronometers to note minute differences of local time with the requisite accuracy.

Williamstown, where twenty-eight chronometers were employed in ten journeys, is placed 19."24 to the west of its true position. We have already remarked, that Pittsfield is 28."98 in error. The sum of these two variations is 48."22, or eight tenths of a mile, and one third nearly of the difference of longitude of the two places.

* Determination of the Longitude of several Stations, &c. reported by Sears C. Walker. See American Philosophical Transactions, Vol. VI. p. 265, note.

The longitudes of Williamstown and Dedham, as decided by the chronometric method, present a discrepancy of 29."32, or one half a mile nearly; fifty-one chronometers, in seventeen journeys, were used to fix the position of these two towns. Other instances might be added to this list, but the table of comparative latitudes demands a passing notice.

The determination of this element, as is well known, is much less liable to error. A combined difference of 9."86, or one sixth of a mile, appears in the latitudes of Boston and Squam Light; and here the industry of Mr. Paine accumulated no less than four hundred and eighty altitudes for the determination of these two places. Three hundred and ten altitudes place Amherst 8."70 south of Cambridge; but an error of 4."80, more than one half of the difference of latitude, is proved in these observations by Mr. Borden's

measurement.

The two greatest errors in this table are 7."30 and 7."81, the sum of which makes the possibility of error amount to 15.11, or one quarter of a mile.

We will add one more case. Mr. W. C. Bond, the distinguished astronomer of Harvard College, whose remarkable accuracy and skill in the use of instruments, place him by the side of the best European observers, says, in a paper now before us; "In June, 1839, I had observations with a transit circle, the illuminated end of the axis east and west, on the 16th, 17th, 20th, 21st, 23d, 24th, and 25th. These observations gave for the latitude of the instrument, 42°.19.16."9." Reduced by the measurement of Mr. Borden, they determine the latitude of the State House, in Boston, to be 420.21.30.3". Mr. Paine's observations with the sextant and artificial horizon give 420.21.22.7". Four hundred and forty-two altitudes were taken by Mr. Paine, yet these insufficient instruments, in the hands of one perfectly skilled in their use, and guarded as far as possible against error by multiplied observations, fall short of the truth 7.6. Mr. Borden's latitude of the State House differs three tenths of a second from that of Mr. Bond's. * The comparison of the precision of the two methods afforded by the Massachusetts survey is highly favorable to sextants and chronometers. would be too tedious and expensive to apply to a great ex

It

* Proceedings of the American Philosophical Society, May and June,

tent of territory, including a large and indented seacoast, the reiterated and laborious processes of Mr. Paine.

The survey of a portion of the earth's surface is a work which comes within the domain of the mathematics; it may safely be said, that any determination of a place, in which the mathematical theory is disregarded, must be fundamentally defective. A reference to this theory brings us to an argument which, we trust, no misapprehended views of science, and no preconceived notions of utility or expediency, will overlook.

The system of triangulation, conducted upon the principles in physics which direct this department of science, takes into consideration the spheroidal form of the earth, and enables the surveyor to construct such a map of that portion of the spheroid which is comprised in his labors, as will be an exact representation of its real figure. This mode of surveying, and this only, regards the earth as it actually is, in its irregularly elliptical form, delineates its surface correctly, and treats of the true measure and configuration of the planet on which we live. Topography, and many of the details of physical geography, come within its province; as the courses of rivers, the direction and elevation of mountain ridges, the nature of the land, &c. ; — knowledge, which is essential to the defence of the coast, to the construction of fortifications, and to all the duties of the military engineer. It furnishes the most accurate and convenient bases, from which a network of triangles may be thrown over any of the States through which it has passed. Some of them have already united their local operations with the general survey, to their great advantage. We may add, finally, in relation to this topic, that, when we are called upon hereafter to make our contributions to the common treasury of similar knowledge, this work will supply the requisite data for the measurement of degrees on the earth's surface, and for the "accurate determination of the elements of the terrestrial spheroid."

It promises, also, to be of especial value in giving future security to the intricate navigation of the southern shores, a part of the coast of the United States rendered particularly dangerous by numberless reefs, shoals, and sandspits. It is well known, that these are variable in their limits and condition, gradually forming in some places, and in others changing their extent and direction, under the influ