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

measureinent.

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 42°.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. It would be too tedious and expensive to apply to a great ex

1841.

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

In order to ac

ence of violent winds and strong currents. quire a permanent and useful knowledge of their character, and to provide an accumulation of facts that will lead to an understanding of their probable formations, dispersions, and changes, a certain knowledge of their present state is indispensable beyond that which can be reached by sextants and chronometers. Rigorous observations upon these and similar subjects in Europe, by geologists and other men of science, have resulted in great benefits to navigation.

The increasing commerce at the south, the future establishment of naval stations there, and the close and hazardous sailing that must be pursued, both by merchant vessels and men-of-war, in the event of foreign aggression, make it desirable that the in-shore navigation of the southern coast should be well understood.

We have already shown what degree of reliance may be placed upon the chronometer under favorable circumstances and in skilful hands. We are justified, we believe, in saying, that longitudes by chronometers cannot generally be relied upon, as correct within less than one mile. But shoals of light and unstable sand, beaches widening and narrowing, and downs accumulating and dispersing, under the action of local and general causes, demand accurate measurements of feet and inches, by means of which the operations of nature may be carefully studied, future obstructions be prevented, present ones be removed, if possible, and an effectual security be given to the pilotage of the southern coast. A trigonometrical survey, made with all the fidelity that the improved state of the science insures, is the only method adapted to the attainment of all these desirable objects.

Some complaint has been made against the Superintendent of the Coast Survey, because its results have not been published from time to time as they have been determined. The power and duty to direct both the manner and the time of their publication rests with Congress, and to that body such a complaint may be appropriately referred. A full and sufficient reply to this charge is contained in the Report. We may add here, however, for general information, that engravers are now employed upon the first sheets, which will probably be issued in the course of the coming summer; and, if the work is continued, the publication will hereafter take place regularly, as the plates come from the hands of the enVOL. LIV. NO. 115.

58

gravers. When these charts, executed with precision and elegance, under the sanction of public authority, are produced, we shall, for the first time, be able to look upon similar works, contributed by the English and French governments to the safety of commerce and navigation, without envy and shame.

Much is said of the expense of the survey, as at present conducted. In this matter, we are not particularly careful to answer. An honest and prudent appropriation of the public money we are willing to leave in the hands of those to whom it is legally intrusted. In this case, at least, we may be contented to confide in their integrity. Economy, it is true, is a virtue; but mere saving is not always economy, it may be the most imprudent waste; and, being satisfied of the paramount importance of this work, both to the public interest and to the national honor, we might say, without further comment, that it should not be interrupted. It is in accordance, however, with our previous remarks to add, that this is one of those cases in which economy is not identical with retrenchment. If chronometers possess in themselves an insurmountable tendency to error, the survey undertaken by their means, and dependent on their results, is not likely to be ever completed. What is certain to-day may be doubtful to-morrow. Subsequent observations may bring discredit upon those which have gone before; and it is to be apprehended, that, however multiplied they may be, so far from ultimately removing the difficulty, they will only serve to strengthen doubt, and increase perplexity.

Besides this, experience will prove that the repeated transportation of numerous chronometers will be attended with but little less expense than a regular and scientific survey. As some ground for this opinion, we shall refer again to the high authority of Mr. Paine. In a letter to the Bureau des Longitudes at Paris, he gives the longitudes of several towns in Massachusetts, the results of his own observations, and adds;

"These longitudes have been generally determined by the transportation of time repeated several times with numerous chronometers. Thus, between Northampton and Boston, I have carried seventy-four chronometers in twenty-four journeys; between Amherst (the college) and Boston, or Northampton, twenty-seven chronometers in nine journeys; between Barnstable and Boston, fifty-nine chronometers in six

teen journeys; and between Gloucester and Boston, sixty chronometers in sixteen journeys." *

We have here an example of the manner in which chronometers are employed in the hands of a skilful observer. In estimating their use for a survey of the coast, the additional risk of transportation by sea is to be added to this ac

count.

The financial department of the Coast Survey does not however present any thing so startling as to render these statements necessary for its defence. They are in themselves valuable facts and considerations, tending immediately to elucidate the subject, and weighing heavily against the proposed change; but they are not, we imagine, essential to vindicate the present plan of operations from a suspicion of waste and extravagance.

Since the year 1832, six hundred and twenty thousand dollars have been appropriated to this service, one hundred and twenty thousand dollars of which remains on hand in the form of vessels, instruments, and other property, leaving a balance of five hundred thousand dollars to be charged to the survey. When we consider that this expenditure extends through a period of ten years, that it has been bestowed upon a great national work, of the highest importance to the commerce and defence of the country, that it is a contribution to knowledge, and that its investment in this way has gone further than any thing yet done, to establish the character of the country abroad for a liberal patronage of science, we are not disposed to regard it as an expense which the strictest economist may not approve.

As to the amount of money, and probable length of time required to complete the survey, we cannot do better than to say, that these questions are ably and properly treated in the document before us. "With the advancement of the mathematical and physical sciences, the means of acceleration of any work grounded upon them also increase. All that is needed is, that the whole work be carried on in the most economical manner." (p. 11.) We are satisfied, that its progress will compare favorably with that of any similar work

* Connaissance des Temps, 1843. Additions, p. 95. The Additions et Corrections sur les Tables des Positions Géographiques, by Mr. Daussy, will repay a critical examination.