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where tenths of seconds of arc were the quantities under examination. The admirable agreement now found to exist uniformly between the work of different nights encouraged me to go back and remeasure, with greater care, the old work still remaining engraved on the plate. By using a mean of two or three measures the observations were brought to the most surprising coincidence. I did not attempt a remeasure of all the observations, but contented myself with a rigid examination of a single pair of N. A. stars, among whose observed differences of declination average discrepancies existed. I copy the final results, remarking simply that the observations were made between the 26th May and the 30th June inclusive.

The following are the decimals of a revolution of the inicrometer screw in the ten observations:

Seconds

of are. a Coronae to é Bootis.....6836 Diff. from mean... .0017 = 0.068 .6609

.0210 0.840 .6891

.0072 0.286 .6883

.0064 0.256 .6906

.0085 0.340

.0052 0.208 .6699

.0120

0.480 .6886

.0067 0.268 .6905

.0086 0.344 .6784

.0054 0.220

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0.05

.6819

0.340 Probable error, 0.250

Seconds. a Cor. to e Bootis, Greenwich Obs., 1840....

1.61
1.64
1.02
1.25
2.67
1.39
0.81
2.05
2.52

1.401 Prob. error, 1".3 I shall now present a few measures of the sun's diameter, in which it must be observed that only relative quantities are obtained. Taking the N. A. as accurate on any one day of those indicated in the observations, we found the power of the new apparatus to trace the apparent changes in the sun's diameter. This is not yet absolute work. Observations of the O diameter at the Cincinnati Observatory, Sept., 1850.

Obs.
Comp.

Diff. September 3 ............1906.68

1906.40

+ 0.28 ........1907.40

1906.80

+ 0.60

Obs.
Comp.

Diff. September 5

.1906.82
1907.40

- 0.58
.1907.62
1907.80

– 0.18 .1906.73 1908.40

- 1.67 .1910.74 1909.40

+ 1.34 .1911.58 1910.80

+0.78 .1910.17 1911.40

- 1.23 .1912.44 1913.00

- 0.56 .1912.65 1913.40

- 0.75 .1914.74 1914.60

+ 0.14 ..1916.00

1915.20

+ 0.80 ...1916.62

1915.60

+ 1.02 1851. May....15 ............1900.10

1900.02

+0.08 .......1897.80

1897.60

+ 0.20 24 ............1897.46

1896.80

- 0.66 26 ............1896.07

1896.20

– 0.13 The work in 1850 was measured with the defective micrometer, and I attribute the increased discrepancies to this cause, rather than to any inaccuracy in the observations or records.

On the application of the principle already explained, of intermingling the observations of two different nights, most of the large discrepancies which had for a long time annoyed me, and which I felt were due to imperfections in the micrometer (but which I had not hitherto been able to demonstrate,) all disappeared, and the results have since exhibited the most surprising harmony. I shall present only a few specimens of the work done, as a more full and elaborate report will be made hereafter. Observations of June 16 and 17, 1851.

16th. 17th. Diff. Sec'ds, Observer, M. & Bootis to B. A. C. 4969 L..6060 6064 0004 0.016

L. a Coronae....6508 6420 0088 0.352
M.4706.........3397 3288 0109 0.336
M. a Bootis.....8877 8687 0190 0.760
M. 4933........8882 8663 0199 0.796
L. 5120.........1430 1268 0162 0.648
L. a Serp........2245 2252 0007 0.029

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I present one more specimen of the same kind of work, with some slight additional security for accuracy, simply remarking that here again the stars were observed by L. and M. without any specific order:

Diff. Seconds. B. A. C. No. 6084, to 6323 5820 5896 0076 0.304

Bootis 1335 1319 0016 0.064 a Coronae 1407 1399 000S 0.032 6657 1662 1662

0000

0.000 6106 6430 6614 0234

0.936 6589 7340 7380 0040

0.160 a Bootis 1530 1670 0140 0.540

6110 1669 1699 0030 0.120 a Herculis 9980 0046 0066 0.264 a Serpentis 0540 0576 0036 0.140

10)2.560 2)0.256

0.1280 Here it will be seen there is no accumulation of error due to the increased distance between the stars observed. This will also become more evident by examining the observations of intervals between wide stars on the preceding nights already reported.

I am now satisfied that the errors which yet remain may be diminished one-half by the use of ten instead of five declination wires; and, finally, that all work for difference of declination between stars may be accomplished with an accuracy equal to the best micrometer work, when the stars are but a few seconds apart.

The best work done in the world, (so far as I know,) has been accomplished in the Imperial Russian Observatory at Pulkova, and is reported by M. Struve in his great work on that institution. By the greatest refinement of art and skill on a few stars, the accordance between the determinations of different nights has been brought to within a limit of probable error of two-tenths of one second of arc. It will be seen by examining the results reported, that the new method, in the very infancy of its application, with defective instruments, low optical power, and with every possible disadvantage to contend with, has already rivalled in accuracy the best work ever done. Indeed, the last work reported greatly surpasses the Pulkova work in accuracy, as the average error on ten differences of declination amounts to no more than twenty-five hundredths of one second of arc, while the average error in the Pulkova observations amounts (on differences of declination) to forty-hundredths of one second of arc.

But the old methods have already been pushed to their ultimate limit of attainable precision. Of this, I think any one will be convinced who will read M. Struve's admirable history of the Pulkova Observatory and its instruments. On the contrary, in the new method, almost nothing has been done. Any one who has used telescopes of low power and those of great power, need not be reminded of the extraordinary advantage which high optical power and good definition gives in bisecting a star.

In the great refractor of the Cincinnati Observatory, & Bootis is divided into two beautiful stars, some two seconds of arc asunder, each round and sharp; while in the small instrument used in the foregoing observations, the same star appears as a single object, a large mass of light. In case it were possible to employ the optical power of the great refractor, the most astonishing increase of accuracy might be anticipated. If such an object-glass were mounted as a transit, the records would then be made very conveniently on the circumference of a circle thirty feet in diameter, and a second of arc would occupy a space nearly three-fold greater than that now in use by me, and four-fold greater than is elsewhere employed (so far as I know) in the world. Again, thus far, it must be remembered that the preceding results are the means of five wire observations. There is no difficulty in increasing the number of wires to ten or even fifteen, should it be desirable. In short, the new method is capable of almost indefinite expansion and increased accuracy-1. By increase of optical power. 2. By perfecting the mechanical arrangements. 3. By increasing the radius of the recording circle. 4. By increasing the number of observations, or the number of declination wires.

The new method also involves a principle of wonderful value in the delicate work to which it must be applied. I mean the power of stereotyping the positions of the instrument, so that the observations may be scrutinized at leisure, and be read and re-read until the error of reading up shall be reduced to an insensible quantity: this cannot be done in the old method.

What, then, may we not anticipate from the application of this new machinery, under favorable circumstances, to the examination of the heavens ? If Struve dared pronounce his instrument competent to the determination of parallax, proper motion, &c., with results discrepant to two-tenths of one second, then indeed has the new machinery converted a small inferior transit into an instrument competent to cope with these grand mechanical questions.

Apply it, then, to instruments of perfect construction, of high optical power, with equal advantages of high mechanical perfection, with a full ten-wire diaphragm, interlock the observations until the power of the micrometer is fully and positively determined, and then who will dare to anticipate the results which may be reached by such a combination of science and mechanical power ? Motions which have hitherto required centuries for their detection and measurement, variations in the proper motions of the fixed stars, which have only been suspected, parallax annual and systematic-even the position of the double stars themselves—may not all these, to say nothing of aberration, nutation, precession, fall fully within the range of rapid and positive research?

With the delicate and powerful machinery for determining R. A., on which no less than twenty-five wires are successfully employed, combined with this no less powerful means of measuring difference of declination, may we not hope that even in the lifetime of a single observer, some of the dark problems of the heavens which now defy our utmost efforts may be resolved and yield up their long and deeply concealed mysteries? My only regret is, that I do not possess the means to exe

cute an immediate application of these new methods to the resolution of these high and profound problems. Very respectfully, your obedient servant, - O. M. MITCHEL. Professor A. D. BACHE, Superintendent of the Coast Survey.

APPENDIX No. 10.

Ertracts from the report of Professor Agassiz to the Superintendent of the Coast Survey, on the examination of the Florida reefs, keys, and coast.

CAMBRIDGE, August, 1851. SIR: The following report of the examination made by me of the Florida reefs, keys, and coast, is prepared in compliance with your request: Topography of Florida.

To form a correct idea of the Florida reefs, it is of paramount importance to keep in mind the topographical features of the whole country. The peninsula of Florida projects between the Gulf of Mexico and the Atlantic, from the 30th degree of northern latitude, nearly to the 24th, as a broad, flat, low promontory, which has generally been considered a continuation of the low lands of the southern States. But, as we shall see hereafter, this is not the case, or, at least, not with respect to the southern extremity of the peninsula, which consists of the same formations as the reef itself. Again, in a physical point of view, Florida is not limited to those tracts of land, forming the peninsula, which rise above the level of the sea, for the extensive shoals along its southern extremity, between the main land and the keys and reefs, as well as those extending to the west as far as the Tortugas, whence they stretch along the western coast, in fact belong to it, and are intimately connected with it, by their physical character. There is a similar tract of flats along the eastern shore, but it is not so extensive as on the southern and western shores, nor does it partake as largely of the peculiar character of the peninsula, being chiefly formed of the alluvial sand, drifted ashore by the waters of the Atlantic.

We shall have occasion, however, to show hereafter that the narrow longitudinal islands, which extend close to the main land almost for the whole length of the eastern shore, are probably a direct continuation of the keys, covered with drifted sand." This is certainly the case with the range of keys extending from the main land to Cape Florida, which limits to the east the bay of Miami, their formation being of coral rock, but covered by silicious drift-sand.

As to the southernmost extremity of the main land proper, it is very difficult to determine its outlines, as it consists of innumerable islands,

*A direct investigation of this point, which did not come within the limits of my survey, would be of considerable practical importance, inasmuch as it may lead to the discovery of a basis of coral rock, affording a far more solid foundation for the construction of the lighthouses wanted along that coast than the loose shore detritus.

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