After giving what I considered a fair trial in the field to all the methods now known, it was concluded to place the chief reliance on the transit of the moon. If, however, it happens to me to be again in charge of extensive operations of the kind, I shall make some effort to improve the instruments for the observation of lunar distances. I am satisfied it is in that direction itinerant observers must look for improved methods and facilities in obtaining longitude. When the reflecting instruments are made so as to be placed more firmly and quickly in any given plane, and the methods of computing lunar distances are improved and simplified, it will be in the power of the observer any clear night, when the moon is above the horizon, to multiply his observations so as to obtain close results. The instruments in present use have not sufficient power to observe near contacts of the moon and stars; and in the attempts which have been made to increase the power of the telescope, the instrument becomes insupportable by the hand for repeated or nice observations. In all cases where it was not necessary to declare the result on the spot, as at those stations at the extremities of azimuth lines, and at stations such as the 111th meridian of longitude, which formed turning-points in the boundary, the longitude was deduced from corresponding observations made at Greenwich. In some few cases we obtained corresponding observations at the American observatories; but the observations were not sufficiently continuous at any of these last-named observatories to enable us to rely upon them. And I have here to repeat (what I have heretofore expressed to the American Association for the Advancement of Science) my obligations to Astronomer Royal Airy for the trouble he has taken to furnish the corresponding observations in MSS. before they were published at Greenwich. In the personal account, mention is made of the agreement made with the Mexican commissioner to declare the 111th meridian, from computations based on the data afforded by the Greenwich Ephemeris,* before receiving the corresponding observations. This arrangement was a necessity arising from our isolated position near the centre of the continent, cut off from all intercourse except by expresses protected by armed escorts. To have awaited the reception of the corresponding observations would have detained us fully eighteen months, at great expense-a result not contemplated by either the United States or Mexican governments, and not contemplated by the treaty, which provided against any possible errors in the location of the line by declaring, "that line shall alone be established upon which the commissioners may fix; their consent in this particular being considered decisive and an integral part of this treaty, without necessity of ulterior ratification or approval, and without room for interpretation of any kind by either of the parties contracting." The observations at 1, 11, 13, 14, 15, 17, were made by myself in person; those at 2, by Lieutenant Whipple; at 4, by Señor Jimenez, first engineer Mexican boundary commission; at 5, 10, and 16, by Assistant John H. Clark; at 18, by Assistants Gardner and Clark; and at 12, by Lieutenant W. F. Smith. At most of the stations the observations were carried through at least three lunations; but, it will be seen, the result was not changed materially after the first lunation. The longitude of the point where the boundary leaves the Rio Bravo was transferred from Frontera by triangulation; and the longitude of El Paso and of No. 14 (the cañon) were respectively transferred from Frontera and San Elceario by flashes of gunpowder simultaneously When this agreement was made, no copy of the American Ephemeris had been received, nor was I aware it had been published. ASTRONOMY. observed. It was my desire to extend this beautiful and accurate mode of obtaining differences of longitude to many other stations; but in a country without settlements, and traversed by bands of savages who kill at sight, it was impossible to do so, as every party that went out had to be escorted by ten or fifteen armed men. Where neither of the above means could be resorted to, longitude was obtained by transmission of chronometers from some established point. This method, so successful at sea, where the motion is uniform and smooth, has objections on land, principally the impossibility of moving chronometers without deranging the rate. Every method of transporting them was tried-on carriages, on foot, and on horseback; and an ordinary spring-carriage was found to be the best. No test can be applied to check an error in determining longitude by the transmission of chronometers; for even with three chronometers it is possible for all to be affected in the same way, though of course not in the same degree-that is to say, all may run, travelling, too fast or too slow; and when you halt, may resume their former rates. The observations at the two stations 11 and 12-Frontera and San Elceario-being about the centre of the continent, and in a geographical point of view more important than any others, were combined to arrive at the results given. The longitude of Frontera from moon culminations, extending through four For the 1st lunation, December and January, 1851-'52...... 2d 66 3d 66 February and March, 7 06 11.38 13.34 14.73 12.48 while =7h 05m 55.3 7 06 12.98 Difference due to correction. The longitude of San Elceario deduced from observations on forty moon culminations, extending through three lunations, computed from the predicted place of the moon and moon culminating stars, given in the Greenwich Ephemeris for 1852 ...... The same, after applying the correction due for corresponding observations made at Greenwich, is For the 1st lunation, January and February, 1852....... 7 05 02.52 04.31 7 05 03.42 Mean.. By combining these observations with corresponding ones at Cambridge, Difference due to correction......... + 17.68 7h 04m 46.55 7 05 04.3 17.75 The coincidence between these differences is satisfactory. The computations were made by independent computers: the first, by Assistant J. H. Clark; the second, by Assistant J. O'Donoghue. The observations for the first were made by myself; those at San Elceario by Lieutenant W. F. Smith. To give greater effect to the results, and to establish beyond the probability of future change the longitude of Frontera-which is about the longitude of the middle of the continent, and is a primary station on the survey of the boundary-an attempt was made to connect the observatory of San Elceario with that of Frontera by flashes of gunpowder, and the following is the result. It should be observed that the Frontera here mentioned is not the Frontera of the old maps of North America. Frontera signifies a frontier town, but in this instance is the name given by its proprietor to a newly-constructed hut, built immediately on the ratification of the treaty of Guadalupe Hidalgo, at a point some eight miles above El Paso, where it was supposed the boundary under that treaty would leave the Rio Bravo. The difference of longitude between Frontera and San Elceario, observed by flashes on the nights of the 14th, 18th, 19th February, and 14th March, 1852, was found to be as follows: The difference of longitude by observations on the moon and moon culminating stars is 1m 08.58, which agrees with that determined by flashes within 1.3. Now, assuming the difference determined by flashes as correct, and giving equal weight to the observations at each station, the longitude of Frontera will be diminished by 0.65, and that of San Elceario will be increased by the same quantity; so that the final result will be: The longitude of the observatory at El Paso erected by the Mexican commission, two hundred feet south and five hundred feet west of the Cathedral tower, was determined by flashes observed simultaneously by Señor Salazar and myself on the nights stated in the preceding part of this article, to be 158.94 east of Frontera; hence the longitude of El Paso, 7h 05m 56.39. A discussion of the longitudes of the Presidio del Norte and of Eagle Pass, on the Rio Grande, shows a difference between the longitude obtained by using the Greenwich Ephemeris and that obtained by using the corresponding observations at Greenwich, to be in the first case +193, and in the second +17.1. Comparing these with the same quantities obtained at Frontera and San Elceario, made in the same year, it will be seen that there is a coincidence, showing that in this case the error in the predicted place of the moon is nearly uniform for the same year. The difference between the longitudes obtained in 1849, those computed from data in the ASTRONOMY. Greenwich Ephemeris, and those obtained by corresponding observations at Greenwich, was pretty generally + 12. This confirms the importance of a thorough revision of the lunar tables. The uniformity observable in these results shows, I hope, the probability of detecting the error, and eliminating or reducing it. I have deposited in the Department of the Interior two volumes containing, in tabulated form, all the individual observations and computations upon which the results obtained on the boundary for longitude are founded. I give a leaf from these volumes, to show the manner in which the observations were made and computed. It has been suggested to me to present them for publication; but as each would make a volume nearly the size of the Greenwich Observations, I have contented myself, in this publication, with presenting in tabulated form the separate results, and in two cases-at the initial point on the Pacific, and at the mouth of the Rio Bravo-I have extended the table so as to show in detail the manner in which all the observations and computations have been tabulated. It has been found convenient, also, to incorporate with these tables the computations by which the azimuth lines forming portions of the boundary were determined. III. LATITUDES. The latitudes of all the primary astronomical stations, except four, were determined either by myself or by Assistant J. H. Clark, with the zenith telescope. Two of the four excepted were determined by Lieutenant Whipple, the other two by Lieutenant Michler. I have placed in the Department of the Interior four volumes containing the individual observations and the computations for the latitude of the primary stations. In regard to the publication of these volumes, the same remarks that were made above in reference to the longitudes apply here. I give a leaf from them also, to show the mode of tabulating and computing the observations: The tables attached hereto present a recapitulation of all the results for the latitudes of the primary stations, including the station determined by Lieutenant Michler, by circum-meridian altitudes of northern and southern stars observed with a sextant, and those determined by Lieutenant Whipple, by observing the transit of stars over the prime vertical. The method habitually used on the boundary for obtaining latitude that by the measurement of the difference of zenith distance of stars near the zenith, and nearly equidistant, north and south-is now so generally used and approved as to make no particular notice of it necessary. It was first adopted by Captain Talcott, in 1835, on the survey of the Ohio boundary. It was resumed by myself on the northeastern boundary; and some of my results coming under the eye of Professor Bache, he concluded to try it on the Coast Survey, and called on me for any suggestion I might have to make in reference to the form. I made the suggestions which resulted in the form in which the instrument is now made by Troughton & Simms, of London, and is that which I used on the present boundary survey. Attached to the table combining the results of the observations at each station is a table showing the correction applied to the places of stars, derived either from actual observations of stars at the Washington Observatory, and politely furnished for the use of the boundary survey, or from the Twelve-year Catalogue of the Greenwich Observatory. A comparison of the results obtained by the zenith telescope, with the errors developed in the declination of stars of the British Association catalogue, will show the rapid march field operations have made, in point of accuracy, upon the observations at the fixed observatories. While the results confirm the excellence of the zenith telescope for field operations, they indicate the necessity of a more extended and accurate catalogue of stars. IV. GEODETIC MEASUREMENT. The azimuth lines were ascertained by observations on the elongation of Polaris, and the measurement on the face of the earth was made with several different instruments. Those in California with a transit by Ertel & Son, Munich; with a horizontal limb of fifteen inches. diameter, graduated to read to 10". The instruments used in tracing the parallel of latitude were a ten-inch azimuth circle, by Gambey, of Paris; two by Bruner; and one by Draper, of Philadelphia. Some of the barometers used were by Bunten, of Paris; but they were chiefly made by James Green, of New York. They, together with the thermometers, were compared with the standard at the Smithsonian Institution, both before and after being used. In tracing the parallels of latitude 31° 47′ and 31° 20′, and also in prolonging the azimuth line across California, and from the Rio Colorado to the 111th meridian of longitude, it frequently happened that it was convenient to take the meridians determined by the transit instrument, but most usually they were taken from the measurements of the elongation of Polaris. V. TRACING THE PARALLELS. The parallels were determined by tracing a tangent to the prime vertical at any given point, and measuring the ordinates to the parallel. The use of the tangent instead of the chord was preferred, because the measurement of the ordinates, confided to a variety of assistants, presented always an increasing series, and was less liable to lead to confusion; a precaution very necessary in a country where water is scarce, and where parties operating have constantly to be on the alert against attacks of Indians. A general sketch of the stations established in latitude to trace these parallels is stated in the agreement with the Mexican commissioner, which will be found under the head of Personal Account, in Chapter II, and it is therefore unnecessary to repeat it here. Great as were the embarrassments in other respects, the absence of trees gave us great facility in tracing these lines, and enabled us easily to correct errors resulting from producing long lines. In the determinations of latitude along the same parallel, it will be seen we used the same instrument, and, as far as practicable, the same sets of stars; so we were quite certain of getting correct differences of latitude between two stations. In no case was it attempted to produce the same tangent in one direction more than thirty miles, and it was then always compared with the tangent from the new latitude station. The parallel of latitude thus deduced by separate and independent operations seldom differed more than a few feet; and in no case was the discrepancy sufficiently great to make it necessary to retrace our steps. The tangents, being few in number, were generally laid off by myself, and prolonged by the principal assistant surveyors, who were furnished with tables of ordinates and angles, which will be found in the appendix, that enabled us at once, and by simple measurements, to establish points in the parallels forming the boundary. VI. COMPUTATIONS. The computations were all made in the field originally, and subsequently revised in the office. |